id sid tid token lemma pos work_fnploejenbc2raktl46esxm44i 1 1 PII PII NNP work_fnploejenbc2raktl46esxm44i 1 2 : : : work_fnploejenbc2raktl46esxm44i 1 3 0022 0022 CD work_fnploejenbc2raktl46esxm44i 1 4 - - SYM work_fnploejenbc2raktl46esxm44i 1 5 247X(91)90214-K 247x(91)90214-k CD work_fnploejenbc2raktl46esxm44i 1 6 JOURNAL JOURNAL NNP work_fnploejenbc2raktl46esxm44i 1 7 OF of IN work_fnploejenbc2raktl46esxm44i 1 8 MATHEMATICAL MATHEMATICAL NNP work_fnploejenbc2raktl46esxm44i 1 9 ANALYSIS analysi NNS work_fnploejenbc2raktl46esxm44i 1 10 AND and CC work_fnploejenbc2raktl46esxm44i 1 11 APPLICATIONS APPLICATIONS NNP work_fnploejenbc2raktl46esxm44i 1 12 159 159 CD work_fnploejenbc2raktl46esxm44i 1 13 , , , work_fnploejenbc2raktl46esxm44i 1 14 55&594 55&594 CD work_fnploejenbc2raktl46esxm44i 1 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 1 16 1991 1991 CD work_fnploejenbc2raktl46esxm44i 1 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 1 18 On on IN work_fnploejenbc2raktl46esxm44i 1 19 the the DT work_fnploejenbc2raktl46esxm44i 1 20 Scoring Scoring NNP work_fnploejenbc2raktl46esxm44i 1 21 Approach Approach NNP work_fnploejenbc2raktl46esxm44i 1 22 to to IN work_fnploejenbc2raktl46esxm44i 1 23 Admissibility Admissibility NNP work_fnploejenbc2raktl46esxm44i 1 24 of of IN work_fnploejenbc2raktl46esxm44i 1 25 Uncertainty Uncertainty NNP work_fnploejenbc2raktl46esxm44i 1 26 Measures Measures NNPS work_fnploejenbc2raktl46esxm44i 1 27 in in IN work_fnploejenbc2raktl46esxm44i 1 28 Expert Expert NNP work_fnploejenbc2raktl46esxm44i 1 29 Systems Systems NNP work_fnploejenbc2raktl46esxm44i 1 30 IRWIN IRWIN NNP work_fnploejenbc2raktl46esxm44i 1 31 R. R. NNP work_fnploejenbc2raktl46esxm44i 1 32 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 1 33 Naval Naval NNP work_fnploejenbc2raktl46esxm44i 1 34 Ocean Ocean NNP work_fnploejenbc2raktl46esxm44i 1 35 Systems Systems NNPS work_fnploejenbc2raktl46esxm44i 1 36 Center Center NNP work_fnploejenbc2raktl46esxm44i 1 37 , , , work_fnploejenbc2raktl46esxm44i 1 38 San San NNP work_fnploejenbc2raktl46esxm44i 1 39 Diego Diego NNP work_fnploejenbc2raktl46esxm44i 1 40 , , , work_fnploejenbc2raktl46esxm44i 1 41 California California NNP work_fnploejenbc2raktl46esxm44i 1 42 92152 92152 CD work_fnploejenbc2raktl46esxm44i 1 43 HUNG HUNG NNP work_fnploejenbc2raktl46esxm44i 1 44 T. T. NNP work_fnploejenbc2raktl46esxm44i 1 45 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 1 46 AND and CC work_fnploejenbc2raktl46esxm44i 1 47 GERALD GERALD NNP work_fnploejenbc2raktl46esxm44i 1 48 S. S. NNP work_fnploejenbc2raktl46esxm44i 1 49 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 1 50 Department Department NNP work_fnploejenbc2raktl46esxm44i 1 51 of of IN work_fnploejenbc2raktl46esxm44i 1 52 Mathematical Mathematical NNP work_fnploejenbc2raktl46esxm44i 1 53 Sciences Sciences NNPS work_fnploejenbc2raktl46esxm44i 1 54 , , , work_fnploejenbc2raktl46esxm44i 1 55 New New NNP work_fnploejenbc2raktl46esxm44i 1 56 Mexico Mexico NNP work_fnploejenbc2raktl46esxm44i 1 57 State State NNP work_fnploejenbc2raktl46esxm44i 1 58 University University NNP work_fnploejenbc2raktl46esxm44i 1 59 , , , work_fnploejenbc2raktl46esxm44i 1 60 Las Las NNP work_fnploejenbc2raktl46esxm44i 1 61 Cruces Cruces NNP work_fnploejenbc2raktl46esxm44i 1 62 , , , work_fnploejenbc2raktl46esxm44i 1 63 New New NNP work_fnploejenbc2raktl46esxm44i 1 64 Mexico Mexico NNP work_fnploejenbc2raktl46esxm44i 1 65 88003 88003 CD work_fnploejenbc2raktl46esxm44i 1 66 Submitted submit VBN work_fnploejenbc2raktl46esxm44i 1 67 by by IN work_fnploejenbc2raktl46esxm44i 1 68 L. L. NNP work_fnploejenbc2raktl46esxm44i 1 69 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 1 70 Received Received NNP work_fnploejenbc2raktl46esxm44i 1 71 March March NNP work_fnploejenbc2raktl46esxm44i 1 72 19 19 CD work_fnploejenbc2raktl46esxm44i 1 73 , , , work_fnploejenbc2raktl46esxm44i 1 74 1990 1990 CD work_fnploejenbc2raktl46esxm44i 1 75 This this DT work_fnploejenbc2raktl46esxm44i 1 76 paper paper NN work_fnploejenbc2raktl46esxm44i 1 77 arose arise VBD work_fnploejenbc2raktl46esxm44i 1 78 from from IN work_fnploejenbc2raktl46esxm44i 1 79 our -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 1 80 need need NN work_fnploejenbc2raktl46esxm44i 1 81 to to TO work_fnploejenbc2raktl46esxm44i 1 82 rigorize rigorize VB work_fnploejenbc2raktl46esxm44i 1 83 , , , work_fnploejenbc2raktl46esxm44i 1 84 clarify clarify NNP work_fnploejenbc2raktl46esxm44i 1 85 , , , work_fnploejenbc2raktl46esxm44i 1 86 and and CC work_fnploejenbc2raktl46esxm44i 1 87 address address NN work_fnploejenbc2raktl46esxm44i 1 88 fully fully RB work_fnploejenbc2raktl46esxm44i 1 89 the the DT work_fnploejenbc2raktl46esxm44i 1 90 results result NNS work_fnploejenbc2raktl46esxm44i 1 91 of of IN work_fnploejenbc2raktl46esxm44i 1 92 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 1 93 ’s ’s POS work_fnploejenbc2raktl46esxm44i 1 94 paper paper NN work_fnploejenbc2raktl46esxm44i 1 95 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 1 96 Scoring score VBG work_fnploejenbc2raktl46esxm44i 1 97 rules rule NNS work_fnploejenbc2raktl46esxm44i 1 98 and and CC work_fnploejenbc2raktl46esxm44i 1 99 the the DT work_fnploejenbc2raktl46esxm44i 1 100 inevitability inevitability NN work_fnploejenbc2raktl46esxm44i 1 101 of of IN work_fnploejenbc2raktl46esxm44i 1 102 probability probability NN work_fnploejenbc2raktl46esxm44i 1 103 , , , work_fnploejenbc2raktl46esxm44i 1 104 Znternat Znternat NNP work_fnploejenbc2raktl46esxm44i 1 105 . . . work_fnploejenbc2raktl46esxm44i 2 1 Statist statist JJ work_fnploejenbc2raktl46esxm44i 2 2 . . . work_fnploejenbc2raktl46esxm44i 3 1 Rev. Rev. NNP work_fnploejenbc2raktl46esxm44i 4 1 SO so RB work_fnploejenbc2raktl46esxm44i 4 2 , , , work_fnploejenbc2raktl46esxm44i 4 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 4 4 1982 1982 CD work_fnploejenbc2raktl46esxm44i 4 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 4 6 , , , work_fnploejenbc2raktl46esxm44i 4 7 l-26 l-26 NNP work_fnploejenbc2raktl46esxm44i 4 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 4 9 . . . work_fnploejenbc2raktl46esxm44i 5 1 Herein Herein NNP work_fnploejenbc2raktl46esxm44i 5 2 , , , work_fnploejenbc2raktl46esxm44i 5 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 5 4 develop develop VBP work_fnploejenbc2raktl46esxm44i 5 5 a a DT work_fnploejenbc2raktl46esxm44i 5 6 calculus calculus NN work_fnploejenbc2raktl46esxm44i 5 7 of of IN work_fnploejenbc2raktl46esxm44i 5 8 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 5 9 in in IN work_fnploejenbc2raktl46esxm44i 5 10 a a DT work_fnploejenbc2raktl46esxm44i 5 11 game game NN work_fnploejenbc2raktl46esxm44i 5 12 theoretic theoretic JJ work_fnploejenbc2raktl46esxm44i 5 13 setting setting NN work_fnploejenbc2raktl46esxm44i 5 14 . . . work_fnploejenbc2raktl46esxm44i 6 1 In in IN work_fnploejenbc2raktl46esxm44i 6 2 the the DT work_fnploejenbc2raktl46esxm44i 6 3 case case NN work_fnploejenbc2raktl46esxm44i 6 4 of of IN work_fnploejenbc2raktl46esxm44i 6 5 an an DT work_fnploejenbc2raktl46esxm44i 6 6 additive additive JJ work_fnploejenbc2raktl46esxm44i 6 7 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 6 8 function function NN work_fnploejenbc2raktl46esxm44i 6 9 , , , work_fnploejenbc2raktl46esxm44i 6 10 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 6 11 is be VBZ work_fnploejenbc2raktl46esxm44i 6 12 shown show VBN work_fnploejenbc2raktl46esxm44i 6 13 that that IN work_fnploejenbc2raktl46esxm44i 6 14 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 6 15 measures measure NNS work_fnploejenbc2raktl46esxm44i 6 16 , , , work_fnploejenbc2raktl46esxm44i 6 17 such such JJ work_fnploejenbc2raktl46esxm44i 6 18 as as IN work_fnploejenbc2raktl46esxm44i 6 19 those those DT work_fnploejenbc2raktl46esxm44i 6 20 used use VBN work_fnploejenbc2raktl46esxm44i 6 21 in in IN work_fnploejenbc2raktl46esxm44i 6 22 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 6 23 logics logic NNS work_fnploejenbc2raktl46esxm44i 6 24 , , , work_fnploejenbc2raktl46esxm44i 6 25 are be VBP work_fnploejenbc2raktl46esxm44i 6 26 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 6 27 . . . work_fnploejenbc2raktl46esxm44i 7 1 Also also RB work_fnploejenbc2raktl46esxm44i 7 2 , , , work_fnploejenbc2raktl46esxm44i 7 3 the the DT work_fnploejenbc2raktl46esxm44i 7 4 problem problem NN work_fnploejenbc2raktl46esxm44i 7 5 of of IN work_fnploejenbc2raktl46esxm44i 7 6 the the DT work_fnploejenbc2raktl46esxm44i 7 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 7 8 of of IN work_fnploejenbc2raktl46esxm44i 7 9 the the DT work_fnploejenbc2raktl46esxm44i 7 10 Dempster Dempster NNP work_fnploejenbc2raktl46esxm44i 7 11 - - HYPH work_fnploejenbc2raktl46esxm44i 7 12 Shafer Shafer NNP work_fnploejenbc2raktl46esxm44i 7 13 belief belief NN work_fnploejenbc2raktl46esxm44i 7 14 functions function NNS work_fnploejenbc2raktl46esxm44i 7 15 is be VBZ work_fnploejenbc2raktl46esxm44i 7 16 investigated investigate VBN work_fnploejenbc2raktl46esxm44i 7 17 via via IN work_fnploejenbc2raktl46esxm44i 7 18 the the DT work_fnploejenbc2raktl46esxm44i 7 19 concept concept NN work_fnploejenbc2raktl46esxm44i 7 20 of of IN work_fnploejenbc2raktl46esxm44i 7 21 random random JJ work_fnploejenbc2raktl46esxm44i 7 22 sets set NNS work_fnploejenbc2raktl46esxm44i 7 23 . . . work_fnploejenbc2raktl46esxm44i 8 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 8 2 is be VBZ work_fnploejenbc2raktl46esxm44i 8 3 shown show VBN work_fnploejenbc2raktl46esxm44i 8 4 that that IN work_fnploejenbc2raktl46esxm44i 8 5 the the DT work_fnploejenbc2raktl46esxm44i 8 6 class class NN work_fnploejenbc2raktl46esxm44i 8 7 of of IN work_fnploejenbc2raktl46esxm44i 8 8 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 8 9 measures measure NNS work_fnploejenbc2raktl46esxm44i 8 10 in in IN work_fnploejenbc2raktl46esxm44i 8 11 a a DT work_fnploejenbc2raktl46esxm44i 8 12 scoring score VBG work_fnploejenbc2raktl46esxm44i 8 13 framework framework NN work_fnploejenbc2raktl46esxm44i 8 14 depends depend VBZ work_fnploejenbc2raktl46esxm44i 8 15 on on IN work_fnploejenbc2raktl46esxm44i 8 16 the the DT work_fnploejenbc2raktl46esxm44i 8 17 assumptions assumption NNS work_fnploejenbc2raktl46esxm44i 8 18 concerning concern VBG work_fnploejenbc2raktl46esxm44i 8 19 the the DT work_fnploejenbc2raktl46esxm44i 8 20 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 8 21 function function NN work_fnploejenbc2raktl46esxm44i 8 22 in in IN work_fnploejenbc2raktl46esxm44i 8 23 use use NN work_fnploejenbc2raktl46esxm44i 8 24 . . . work_fnploejenbc2raktl46esxm44i 9 1 In in IN work_fnploejenbc2raktl46esxm44i 9 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 9 3 , , , work_fnploejenbc2raktl46esxm44i 9 4 for for IN work_fnploejenbc2raktl46esxm44i 9 5 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 9 6 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 9 7 functions function NNS work_fnploejenbc2raktl46esxm44i 9 8 , , , work_fnploejenbc2raktl46esxm44i 9 9 an an DT work_fnploejenbc2raktl46esxm44i 9 10 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 9 11 measure measure NN work_fnploejenbc2raktl46esxm44i 9 12 may may MD work_fnploejenbc2raktl46esxm44i 9 13 not not RB work_fnploejenbc2raktl46esxm44i 9 14 be be VB work_fnploejenbc2raktl46esxm44i 9 15 transformable transformable JJ work_fnploejenbc2raktl46esxm44i 9 16 to to IN work_fnploejenbc2raktl46esxm44i 9 17 a a DT work_fnploejenbc2raktl46esxm44i 9 18 finitely finitely RB work_fnploejenbc2raktl46esxm44i 9 19 additive additive JJ work_fnploejenbc2raktl46esxm44i 9 20 probability probability NN work_fnploejenbc2raktl46esxm44i 9 21 measure measure NN work_fnploejenbc2raktl46esxm44i 9 22 . . . work_fnploejenbc2raktl46esxm44i 10 1 0 0 NFP work_fnploejenbc2raktl46esxm44i 10 2 1991 1991 CD work_fnploejenbc2raktl46esxm44i 10 3 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 10 4 Press Press NNP work_fnploejenbc2raktl46esxm44i 10 5 , , , work_fnploejenbc2raktl46esxm44i 10 6 Inc. Inc. NNP work_fnploejenbc2raktl46esxm44i 10 7 1 1 CD work_fnploejenbc2raktl46esxm44i 10 8 . . . work_fnploejenbc2raktl46esxm44i 11 1 INTRODUCTION introduction NN work_fnploejenbc2raktl46esxm44i 11 2 With with IN work_fnploejenbc2raktl46esxm44i 11 3 the the DT work_fnploejenbc2raktl46esxm44i 11 4 advent advent NN work_fnploejenbc2raktl46esxm44i 11 5 of of IN work_fnploejenbc2raktl46esxm44i 11 6 Artificial Artificial NNP work_fnploejenbc2raktl46esxm44i 11 7 Intelligence Intelligence NNP work_fnploejenbc2raktl46esxm44i 11 8 and and CC work_fnploejenbc2raktl46esxm44i 11 9 the the DT work_fnploejenbc2raktl46esxm44i 11 10 development development NN work_fnploejenbc2raktl46esxm44i 11 11 of of IN work_fnploejenbc2raktl46esxm44i 11 12 expert expert NN work_fnploejenbc2raktl46esxm44i 11 13 systems system NNS work_fnploejenbc2raktl46esxm44i 11 14 , , , work_fnploejenbc2raktl46esxm44i 11 15 a a DT work_fnploejenbc2raktl46esxm44i 11 16 number number NN work_fnploejenbc2raktl46esxm44i 11 17 of of IN work_fnploejenbc2raktl46esxm44i 11 18 schools school NNS work_fnploejenbc2raktl46esxm44i 11 19 of of IN work_fnploejenbc2raktl46esxm44i 11 20 thought thought NN work_fnploejenbc2raktl46esxm44i 11 21 has have VBZ work_fnploejenbc2raktl46esxm44i 11 22 arisen arise VBN work_fnploejenbc2raktl46esxm44i 11 23 concerning concern VBG work_fnploejenbc2raktl46esxm44i 11 24 how how WRB work_fnploejenbc2raktl46esxm44i 11 25 uncer- uncer- JJ work_fnploejenbc2raktl46esxm44i 11 26 tainties taintie NNS work_fnploejenbc2raktl46esxm44i 11 27 in in IN work_fnploejenbc2raktl46esxm44i 11 28 complex complex JJ work_fnploejenbc2raktl46esxm44i 11 29 real real JJ work_fnploejenbc2raktl46esxm44i 11 30 - - HYPH work_fnploejenbc2raktl46esxm44i 11 31 world world NN work_fnploejenbc2raktl46esxm44i 11 32 situations situation NNS work_fnploejenbc2raktl46esxm44i 11 33 are be VBP work_fnploejenbc2raktl46esxm44i 11 34 to to TO work_fnploejenbc2raktl46esxm44i 11 35 be be VB work_fnploejenbc2raktl46esxm44i 11 36 modeled model VBN work_fnploejenbc2raktl46esxm44i 11 37 . . . work_fnploejenbc2raktl46esxm44i 12 1 In in IN work_fnploejenbc2raktl46esxm44i 12 2 addition addition NN work_fnploejenbc2raktl46esxm44i 12 3 to to IN work_fnploejenbc2raktl46esxm44i 12 4 probability probability NN work_fnploejenbc2raktl46esxm44i 12 5 in in IN work_fnploejenbc2raktl46esxm44i 12 6 all all DT work_fnploejenbc2raktl46esxm44i 12 7 of of IN work_fnploejenbc2raktl46esxm44i 12 8 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 12 9 variants variant NNS work_fnploejenbc2raktl46esxm44i 12 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 12 11 34 34 CD work_fnploejenbc2raktl46esxm44i 12 12 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 12 13 , , , work_fnploejenbc2raktl46esxm44i 12 14 approaches approach VBZ work_fnploejenbc2raktl46esxm44i 12 15 to to IN work_fnploejenbc2raktl46esxm44i 12 16 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 12 17 modeling model VBG work_fnploejenbc2raktl46esxm44i 12 18 now now RB work_fnploejenbc2raktl46esxm44i 12 19 include include VBP work_fnploejenbc2raktl46esxm44i 12 20 the the DT work_fnploejenbc2raktl46esxm44i 12 21 Dempster Dempster NNP work_fnploejenbc2raktl46esxm44i 12 22 - - HYPH work_fnploejenbc2raktl46esxm44i 12 23 Shafer Shafer NNP work_fnploejenbc2raktl46esxm44i 12 24 theory theory NN work_fnploejenbc2raktl46esxm44i 12 25 of of IN work_fnploejenbc2raktl46esxm44i 12 26 belief belief NN work_fnploejenbc2raktl46esxm44i 12 27 functions function NNS work_fnploejenbc2raktl46esxm44i 12 28 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 12 29 26 26 CD work_fnploejenbc2raktl46esxm44i 12 30 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 12 31 , , , work_fnploejenbc2raktl46esxm44i 12 32 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 12 33 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 12 34 logic logic NN work_fnploejenbc2raktl46esxm44i 12 35 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 12 36 32 32 CD work_fnploejenbc2raktl46esxm44i 12 37 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 12 38 , , , work_fnploejenbc2raktl46esxm44i 12 39 and and CC work_fnploejenbc2raktl46esxm44i 12 40 nonmonotonic nonmonotonic JJ work_fnploejenbc2raktl46esxm44i 12 41 logics logic NNS work_fnploejenbc2raktl46esxm44i 12 42 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 12 43 20 20 CD work_fnploejenbc2raktl46esxm44i 12 44 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 12 45 ; ; : work_fnploejenbc2raktl46esxm44i 12 46 a a DT work_fnploejenbc2raktl46esxm44i 12 47 survey survey NN work_fnploejenbc2raktl46esxm44i 12 48 of of IN work_fnploejenbc2raktl46esxm44i 12 49 these these DT work_fnploejenbc2raktl46esxm44i 12 50 approaches approach NNS work_fnploejenbc2raktl46esxm44i 12 51 is be VBZ work_fnploejenbc2raktl46esxm44i 12 52 in in IN work_fnploejenbc2raktl46esxm44i 12 53 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 12 54 28 28 CD work_fnploejenbc2raktl46esxm44i 12 55 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 12 56 . . . work_fnploejenbc2raktl46esxm44i 13 1 Roughly roughly RB work_fnploejenbc2raktl46esxm44i 13 2 speaking speak VBG work_fnploejenbc2raktl46esxm44i 13 3 , , , work_fnploejenbc2raktl46esxm44i 13 4 the the DT work_fnploejenbc2raktl46esxm44i 13 5 choice choice NN work_fnploejenbc2raktl46esxm44i 13 6 of of IN work_fnploejenbc2raktl46esxm44i 13 7 a a DT work_fnploejenbc2raktl46esxm44i 13 8 set set NN work_fnploejenbc2raktl46esxm44i 13 9 - - HYPH work_fnploejenbc2raktl46esxm44i 13 10 function function NN work_fnploejenbc2raktl46esxm44i 13 11 to to TO work_fnploejenbc2raktl46esxm44i 13 12 model model VB work_fnploejenbc2raktl46esxm44i 13 13 the the DT work_fnploejenbc2raktl46esxm44i 13 14 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 13 15 involved involve VBN work_fnploejenbc2raktl46esxm44i 13 16 in in IN work_fnploejenbc2raktl46esxm44i 13 17 a a DT work_fnploejenbc2raktl46esxm44i 13 18 problem problem NN work_fnploejenbc2raktl46esxm44i 13 19 at at IN work_fnploejenbc2raktl46esxm44i 13 20 hand hand NN work_fnploejenbc2raktl46esxm44i 13 21 is be VBZ work_fnploejenbc2raktl46esxm44i 13 22 related relate VBN work_fnploejenbc2raktl46esxm44i 13 23 to to IN work_fnploejenbc2raktl46esxm44i 13 24 the the DT work_fnploejenbc2raktl46esxm44i 13 25 pragmatic pragmatic JJ work_fnploejenbc2raktl46esxm44i 13 26 aspects aspect NNS work_fnploejenbc2raktl46esxm44i 13 27 or or CC work_fnploejenbc2raktl46esxm44i 13 28 , , , work_fnploejenbc2raktl46esxm44i 13 29 at at IN work_fnploejenbc2raktl46esxm44i 13 30 a a DT work_fnploejenbc2raktl46esxm44i 13 31 deeper deep JJR work_fnploejenbc2raktl46esxm44i 13 32 level level NN work_fnploejenbc2raktl46esxm44i 13 33 , , , work_fnploejenbc2raktl46esxm44i 13 34 to to IN work_fnploejenbc2raktl46esxm44i 13 35 the the DT work_fnploejenbc2raktl46esxm44i 13 36 semantic semantic JJ work_fnploejenbc2raktl46esxm44i 13 37 nature nature NN work_fnploejenbc2raktl46esxm44i 13 38 of of IN work_fnploejenbc2raktl46esxm44i 13 39 the the DT work_fnploejenbc2raktl46esxm44i 13 40 type type NN work_fnploejenbc2raktl46esxm44i 13 41 of of IN work_fnploejenbc2raktl46esxm44i 13 42 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 13 43 under under IN work_fnploejenbc2raktl46esxm44i 13 44 consideration consideration NN work_fnploejenbc2raktl46esxm44i 13 45 . . . work_fnploejenbc2raktl46esxm44i 14 1 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 14 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 14 3 16 16 CD work_fnploejenbc2raktl46esxm44i 14 4 , , , work_fnploejenbc2raktl46esxm44i 14 5 173 173 CD work_fnploejenbc2raktl46esxm44i 14 6 proposed propose VBD work_fnploejenbc2raktl46esxm44i 14 7 a a DT work_fnploejenbc2raktl46esxm44i 14 8 simple simple JJ work_fnploejenbc2raktl46esxm44i 14 9 but but CC work_fnploejenbc2raktl46esxm44i 14 10 novel novel JJ work_fnploejenbc2raktl46esxm44i 14 11 approach approach NN work_fnploejenbc2raktl46esxm44i 14 12 , , , work_fnploejenbc2raktl46esxm44i 14 13 extending extend VBG work_fnploejenbc2raktl46esxm44i 14 14 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 14 15 ’s ’s POS work_fnploejenbc2raktl46esxm44i 14 16 original original JJ work_fnploejenbc2raktl46esxm44i 14 17 considerations consideration NNS work_fnploejenbc2raktl46esxm44i 14 18 on on IN work_fnploejenbc2raktl46esxm44i 14 19 coherence coherence NN work_fnploejenbc2raktl46esxm44i 14 20 of of IN work_fnploejenbc2raktl46esxm44i 14 21 uncertainties uncertainty NNS work_fnploejenbc2raktl46esxm44i 14 22 to to IN work_fnploejenbc2raktl46esxm44i 14 23 a a DT work_fnploejenbc2raktl46esxm44i 14 24 more more JJR work_fnploejenbc2raktl46esxm44i 14 25 550 550 CD work_fnploejenbc2raktl46esxm44i 14 26 0022 0022 CD work_fnploejenbc2raktl46esxm44i 14 27 - - SYM work_fnploejenbc2raktl46esxm44i 14 28 247X/91 247x/91 CD work_fnploejenbc2raktl46esxm44i 14 29 $ $ $ work_fnploejenbc2raktl46esxm44i 14 30 3.00 3.00 CD work_fnploejenbc2raktl46esxm44i 14 31 Copyright copyright NN work_fnploejenbc2raktl46esxm44i 14 32 0 0 CD work_fnploejenbc2raktl46esxm44i 14 33 1991 1991 CD work_fnploejenbc2raktl46esxm44i 14 34 by by IN work_fnploejenbc2raktl46esxm44i 14 35 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 14 36 Press Press NNP work_fnploejenbc2raktl46esxm44i 14 37 , , , work_fnploejenbc2raktl46esxm44i 14 38 Inc. Inc. NNP work_fnploejenbc2raktl46esxm44i 14 39 All all DT work_fnploejenbc2raktl46esxm44i 14 40 rights right NNS work_fnploejenbc2raktl46esxm44i 14 41 of of IN work_fnploejenbc2raktl46esxm44i 14 42 reproduction reproduction NN work_fnploejenbc2raktl46esxm44i 14 43 in in IN work_fnploejenbc2raktl46esxm44i 14 44 any any DT work_fnploejenbc2raktl46esxm44i 14 45 form form NN work_fnploejenbc2raktl46esxm44i 14 46 reserved reserve VBN work_fnploejenbc2raktl46esxm44i 14 47 . . . work_fnploejenbc2raktl46esxm44i 15 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 15 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 15 3 TO to IN work_fnploejenbc2raktl46esxm44i 15 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 15 5 551 551 CD work_fnploejenbc2raktl46esxm44i 15 6 general general JJ work_fnploejenbc2raktl46esxm44i 15 7 setting setting NN work_fnploejenbc2raktl46esxm44i 15 8 , , , work_fnploejenbc2raktl46esxm44i 15 9 for for IN work_fnploejenbc2raktl46esxm44i 15 10 judging judge VBG work_fnploejenbc2raktl46esxm44i 15 11 the the DT work_fnploejenbc2raktl46esxm44i 15 12 usefulness usefulness NN work_fnploejenbc2raktl46esxm44i 15 13 of of IN work_fnploejenbc2raktl46esxm44i 15 14 different different JJ work_fnploejenbc2raktl46esxm44i 15 15 competing compete VBG work_fnploejenbc2raktl46esxm44i 15 16 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 15 17 measures measure NNS work_fnploejenbc2raktl46esxm44i 15 18 . . . work_fnploejenbc2raktl46esxm44i 16 1 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 16 2 ’s ’s POS work_fnploejenbc2raktl46esxm44i 16 3 original original JJ work_fnploejenbc2raktl46esxm44i 16 4 work work NN work_fnploejenbc2raktl46esxm44i 16 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 16 6 6 6 CD work_fnploejenbc2raktl46esxm44i 16 7 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 16 8 may may MD work_fnploejenbc2raktl46esxm44i 16 9 be be VB work_fnploejenbc2raktl46esxm44i 16 10 viewed view VBN work_fnploejenbc2raktl46esxm44i 16 11 as as IN work_fnploejenbc2raktl46esxm44i 16 12 a a DT work_fnploejenbc2raktl46esxm44i 16 13 two two CD work_fnploejenbc2raktl46esxm44i 16 14 - - HYPH work_fnploejenbc2raktl46esxm44i 16 15 person person NN work_fnploejenbc2raktl46esxm44i 16 16 zero zero CD work_fnploejenbc2raktl46esxm44i 16 17 - - HYPH work_fnploejenbc2raktl46esxm44i 16 18 sum sum NN work_fnploejenbc2raktl46esxm44i 16 19 game game NN work_fnploejenbc2raktl46esxm44i 16 20 , , , work_fnploejenbc2raktl46esxm44i 16 21 played play VBN work_fnploejenbc2raktl46esxm44i 16 22 between between IN work_fnploejenbc2raktl46esxm44i 16 23 player player NN work_fnploejenbc2raktl46esxm44i 16 24 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 16 25 , , , work_fnploejenbc2raktl46esxm44i 16 26 “ " `` work_fnploejenbc2raktl46esxm44i 16 27 nature nature NN work_fnploejenbc2raktl46esxm44i 16 28 ” " '' work_fnploejenbc2raktl46esxm44i 16 29 or or CC work_fnploejenbc2raktl46esxm44i 16 30 “ " `` work_fnploejenbc2raktl46esxm44i 16 31 the the DT work_fnploejenbc2raktl46esxm44i 16 32 master master NN work_fnploejenbc2raktl46esxm44i 16 33 of of IN work_fnploejenbc2raktl46esxm44i 16 34 ceremonies ceremony NNS work_fnploejenbc2raktl46esxm44i 16 35 , , , work_fnploejenbc2raktl46esxm44i 16 36 ” " '' work_fnploejenbc2raktl46esxm44i 16 37 and and CC work_fnploejenbc2raktl46esxm44i 16 38 player player NN work_fnploejenbc2raktl46esxm44i 16 39 II II NNP work_fnploejenbc2raktl46esxm44i 16 40 , , , work_fnploejenbc2raktl46esxm44i 16 41 “ " `` work_fnploejenbc2raktl46esxm44i 16 42 decision decision NN work_fnploejenbc2raktl46esxm44i 16 43 - - HYPH work_fnploejenbc2raktl46esxm44i 16 44 maker maker NN work_fnploejenbc2raktl46esxm44i 16 45 ” " '' work_fnploejenbc2raktl46esxm44i 16 46 or or CC work_fnploejenbc2raktl46esxm44i 16 47 “ " `` work_fnploejenbc2raktl46esxm44i 16 48 you -PRON- PRP work_fnploejenbc2raktl46esxm44i 16 49 ” " '' work_fnploejenbc2raktl46esxm44i 16 50 or or CC work_fnploejenbc2raktl46esxm44i 16 51 “ " `` work_fnploejenbc2raktl46esxm44i 16 52 bookie bookie NN work_fnploejenbc2raktl46esxm44i 16 53 ” " '' work_fnploejenbc2raktl46esxm44i 16 54 as as IN work_fnploejenbc2raktl46esxm44i 16 55 denoted denote VBN work_fnploejenbc2raktl46esxm44i 16 56 variously variously RB work_fnploejenbc2raktl46esxm44i 16 57 in in IN work_fnploejenbc2raktl46esxm44i 16 58 the the DT work_fnploejenbc2raktl46esxm44i 16 59 literature literature NN work_fnploejenbc2raktl46esxm44i 16 60 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 16 61 8 8 CD work_fnploejenbc2raktl46esxm44i 16 62 , , , work_fnploejenbc2raktl46esxm44i 16 63 13 13 CD work_fnploejenbc2raktl46esxm44i 16 64 , , , work_fnploejenbc2raktl46esxm44i 16 65 221 221 CD work_fnploejenbc2raktl46esxm44i 16 66 . . . work_fnploejenbc2raktl46esxm44i 17 1 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 17 2 ’s ’s POS work_fnploejenbc2raktl46esxm44i 17 3 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 17 4 game game NN work_fnploejenbc2raktl46esxm44i 17 5 has have VBZ work_fnploejenbc2raktl46esxm44i 17 6 great great JJ work_fnploejenbc2raktl46esxm44i 17 7 appeal appeal NN work_fnploejenbc2raktl46esxm44i 17 8 : : : work_fnploejenbc2raktl46esxm44i 17 9 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 17 10 is be VBZ work_fnploejenbc2raktl46esxm44i 17 11 determined determine VBN work_fnploejenbc2raktl46esxm44i 17 12 by by IN work_fnploejenbc2raktl46esxm44i 17 13 the the DT work_fnploejenbc2raktl46esxm44i 17 14 cumulative cumulative JJ work_fnploejenbc2raktl46esxm44i 17 15 amount amount NN work_fnploejenbc2raktl46esxm44i 17 16 of of IN work_fnploejenbc2raktl46esxm44i 17 17 the the DT work_fnploejenbc2raktl46esxm44i 17 18 bets bet NNS work_fnploejenbc2raktl46esxm44i 17 19 . . . work_fnploejenbc2raktl46esxm44i 18 1 The the DT work_fnploejenbc2raktl46esxm44i 18 2 concept concept NN work_fnploejenbc2raktl46esxm44i 18 3 of of IN work_fnploejenbc2raktl46esxm44i 18 4 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 18 5 in in IN work_fnploejenbc2raktl46esxm44i 18 6 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 18 7 ’s ’s POS work_fnploejenbc2raktl46esxm44i 18 8 game game NN work_fnploejenbc2raktl46esxm44i 18 9 is be VBZ work_fnploejenbc2raktl46esxm44i 18 10 in in IN work_fnploejenbc2raktl46esxm44i 18 11 fact fact NN work_fnploejenbc2raktl46esxm44i 18 12 a a DT work_fnploejenbc2raktl46esxm44i 18 13 type type NN work_fnploejenbc2raktl46esxm44i 18 14 of of IN work_fnploejenbc2raktl46esxm44i 18 15 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 18 16 local local JJ work_fnploejenbc2raktl46esxm44i 18 17 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 18 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 18 19 see see VB work_fnploejenbc2raktl46esxm44i 18 20 also also RB work_fnploejenbc2raktl46esxm44i 18 21 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 18 22 141 141 CD work_fnploejenbc2raktl46esxm44i 18 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 18 24 which which WDT work_fnploejenbc2raktl46esxm44i 18 25 is be VBZ work_fnploejenbc2raktl46esxm44i 18 26 commonly commonly RB work_fnploejenbc2raktl46esxm44i 18 27 expressed express VBN work_fnploejenbc2raktl46esxm44i 18 28 as as IN work_fnploejenbc2raktl46esxm44i 18 29 the the DT work_fnploejenbc2raktl46esxm44i 18 30 coherence coherence NN work_fnploejenbc2raktl46esxm44i 18 31 axiom axiom NN work_fnploejenbc2raktl46esxm44i 18 32 . . . work_fnploejenbc2raktl46esxm44i 19 1 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 19 2 ’s ’s POS work_fnploejenbc2raktl46esxm44i 19 3 chief chief JJ work_fnploejenbc2raktl46esxm44i 19 4 result result NN work_fnploejenbc2raktl46esxm44i 19 5 is be VBZ work_fnploejenbc2raktl46esxm44i 19 6 that that IN work_fnploejenbc2raktl46esxm44i 19 7 the the DT work_fnploejenbc2raktl46esxm44i 19 8 only only JJ work_fnploejenbc2raktl46esxm44i 19 9 coherent coherent JJ work_fnploejenbc2raktl46esxm44i 19 10 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 19 11 measures measure NNS work_fnploejenbc2raktl46esxm44i 19 12 are be VBP work_fnploejenbc2raktl46esxm44i 19 13 finitely finitely RB work_fnploejenbc2raktl46esxm44i 19 14 additive additive JJ work_fnploejenbc2raktl46esxm44i 19 15 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 19 16 probability probability NN work_fnploejenbc2raktl46esxm44i 19 17 measures measure NNS work_fnploejenbc2raktl46esxm44i 19 18 . . . work_fnploejenbc2raktl46esxm44i 20 1 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 20 2 ’s ’s POS work_fnploejenbc2raktl46esxm44i 20 3 main main JJ work_fnploejenbc2raktl46esxm44i 20 4 contribution contribution NN work_fnploejenbc2raktl46esxm44i 20 5 to to IN work_fnploejenbc2raktl46esxm44i 20 6 the the DT work_fnploejenbc2raktl46esxm44i 20 7 situation situation NN work_fnploejenbc2raktl46esxm44i 20 8 was be VBD work_fnploejenbc2raktl46esxm44i 20 9 to to TO work_fnploejenbc2raktl46esxm44i 20 10 investigate investigate VB work_fnploejenbc2raktl46esxm44i 20 11 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 20 12 ’s ’s POS work_fnploejenbc2raktl46esxm44i 20 13 game game NN work_fnploejenbc2raktl46esxm44i 20 14 by by IN work_fnploejenbc2raktl46esxm44i 20 15 replacing replace VBG work_fnploejenbc2raktl46esxm44i 20 16 the the DT work_fnploejenbc2raktl46esxm44i 20 17 squared square VBN work_fnploejenbc2raktl46esxm44i 20 18 loss loss NN work_fnploejenbc2raktl46esxm44i 20 19 functions function NNS work_fnploejenbc2raktl46esxm44i 20 20 by by IN work_fnploejenbc2raktl46esxm44i 20 21 a a DT work_fnploejenbc2raktl46esxm44i 20 22 more more RBR work_fnploejenbc2raktl46esxm44i 20 23 general general JJ work_fnploejenbc2raktl46esxm44i 20 24 score score NN work_fnploejenbc2raktl46esxm44i 20 25 function function NN work_fnploejenbc2raktl46esxm44i 20 26 . . . work_fnploejenbc2raktl46esxm44i 21 1 For for IN work_fnploejenbc2raktl46esxm44i 21 2 the the DT work_fnploejenbc2raktl46esxm44i 21 3 most most JJS work_fnploejenbc2raktl46esxm44i 21 4 part part NN work_fnploejenbc2raktl46esxm44i 21 5 , , , work_fnploejenbc2raktl46esxm44i 21 6 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 21 7 and and CC work_fnploejenbc2raktl46esxm44i 21 8 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 21 9 assumed assume VBD work_fnploejenbc2raktl46esxm44i 21 10 addition addition NN work_fnploejenbc2raktl46esxm44i 21 11 for for IN work_fnploejenbc2raktl46esxm44i 21 12 the the DT work_fnploejenbc2raktl46esxm44i 21 13 overall overall JJ work_fnploejenbc2raktl46esxm44i 21 14 loss loss NN work_fnploejenbc2raktl46esxm44i 21 15 function function NN work_fnploejenbc2raktl46esxm44i 21 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 21 17 or or CC work_fnploejenbc2raktl46esxm44i 21 18 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 21 19 function function NN work_fnploejenbc2raktl46esxm44i 21 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 21 21 . . . work_fnploejenbc2raktl46esxm44i 22 1 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 22 2 ’s ’s POS work_fnploejenbc2raktl46esxm44i 22 3 chief chief JJ work_fnploejenbc2raktl46esxm44i 22 4 results result NNS work_fnploejenbc2raktl46esxm44i 22 5 are be VBP work_fnploejenbc2raktl46esxm44i 22 6 as as IN work_fnploejenbc2raktl46esxm44i 22 7 follows follow VBZ work_fnploejenbc2raktl46esxm44i 22 8 : : : work_fnploejenbc2raktl46esxm44i 22 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 22 10 i i NN work_fnploejenbc2raktl46esxm44i 22 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 22 12 If if IN work_fnploejenbc2raktl46esxm44i 22 13 an an DT work_fnploejenbc2raktl46esxm44i 22 14 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 22 15 measure measure NN work_fnploejenbc2raktl46esxm44i 22 16 p p NN work_fnploejenbc2raktl46esxm44i 22 17 is be VBZ work_fnploejenbc2raktl46esxm44i 22 18 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 22 19 with with IN work_fnploejenbc2raktl46esxm44i 22 20 respect respect NN work_fnploejenbc2raktl46esxm44i 22 21 to to IN work_fnploejenbc2raktl46esxm44i 22 22 a a DT work_fnploejenbc2raktl46esxm44i 22 23 score score NN work_fnploejenbc2raktl46esxm44i 22 24 function function NN work_fnploejenbc2raktl46esxm44i 22 25 f f NNP work_fnploejenbc2raktl46esxm44i 22 26 , , , work_fnploejenbc2raktl46esxm44i 22 27 then then RB work_fnploejenbc2raktl46esxm44i 22 28 p p NN work_fnploejenbc2raktl46esxm44i 22 29 can can MD work_fnploejenbc2raktl46esxm44i 22 30 be be VB work_fnploejenbc2raktl46esxm44i 22 31 transformed transform VBN work_fnploejenbc2raktl46esxm44i 22 32 into into IN work_fnploejenbc2raktl46esxm44i 22 33 a a DT work_fnploejenbc2raktl46esxm44i 22 34 finitely finitely RB work_fnploejenbc2raktl46esxm44i 22 35 additive additive JJ work_fnploejenbc2raktl46esxm44i 22 36 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 22 37 probability probability NN work_fnploejenbc2raktl46esxm44i 22 38 measure measure NN work_fnploejenbc2raktl46esxm44i 22 39 via via IN work_fnploejenbc2raktl46esxm44i 22 40 a a DT work_fnploejenbc2raktl46esxm44i 22 41 known know VBN work_fnploejenbc2raktl46esxm44i 22 42 transform transform NN work_fnploejenbc2raktl46esxm44i 22 43 depending depend VBG work_fnploejenbc2raktl46esxm44i 22 44 on on IN work_fnploejenbc2raktl46esxm44i 22 45 f f NNP work_fnploejenbc2raktl46esxm44i 22 46 , , , work_fnploejenbc2raktl46esxm44i 22 47 say say VBP work_fnploejenbc2raktl46esxm44i 22 48 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 22 49 ; ; : work_fnploejenbc2raktl46esxm44i 22 50 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 22 51 ii ii LS work_fnploejenbc2raktl46esxm44i 22 52 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 22 53 Within within IN work_fnploejenbc2raktl46esxm44i 22 54 the the DT work_fnploejenbc2raktl46esxm44i 22 55 class class NN work_fnploejenbc2raktl46esxm44i 22 56 of of IN work_fnploejenbc2raktl46esxm44i 22 57 score score NN work_fnploejenbc2raktl46esxm44i 22 58 functions function NNS work_fnploejenbc2raktl46esxm44i 22 59 f f NNP work_fnploejenbc2raktl46esxm44i 22 60 such such JJ work_fnploejenbc2raktl46esxm44i 22 61 that that IN work_fnploejenbc2raktl46esxm44i 22 62 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 22 63 is be VBZ work_fnploejenbc2raktl46esxm44i 22 64 increasing increase VBG work_fnploejenbc2raktl46esxm44i 22 65 , , , work_fnploejenbc2raktl46esxm44i 22 66 the the DT work_fnploejenbc2raktl46esxm44i 22 67 necessary necessary JJ work_fnploejenbc2raktl46esxm44i 22 68 condition condition NN work_fnploejenbc2raktl46esxm44i 22 69 in in IN work_fnploejenbc2raktl46esxm44i 22 70 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 22 71 i i NN work_fnploejenbc2raktl46esxm44i 22 72 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 22 73 is be VBZ work_fnploejenbc2raktl46esxm44i 22 74 also also RB work_fnploejenbc2raktl46esxm44i 22 75 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 22 76 . . . work_fnploejenbc2raktl46esxm44i 23 1 Roughly roughly RB work_fnploejenbc2raktl46esxm44i 23 2 speaking speak VBG work_fnploejenbc2raktl46esxm44i 23 3 , , , work_fnploejenbc2raktl46esxm44i 23 4 an an DT work_fnploejenbc2raktl46esxm44i 23 5 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 23 6 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 23 7 measure measure NN work_fnploejenbc2raktl46esxm44i 23 8 has have VBZ work_fnploejenbc2raktl46esxm44i 23 9 to to TO work_fnploejenbc2raktl46esxm44i 23 10 be be VB work_fnploejenbc2raktl46esxm44i 23 11 a a DT work_fnploejenbc2raktl46esxm44i 23 12 func- func- JJ work_fnploejenbc2raktl46esxm44i 23 13 tion tion NN work_fnploejenbc2raktl46esxm44i 23 14 of of IN work_fnploejenbc2raktl46esxm44i 23 15 a a DT work_fnploejenbc2raktl46esxm44i 23 16 probability probability NN work_fnploejenbc2raktl46esxm44i 23 17 measure measure NN work_fnploejenbc2raktl46esxm44i 23 18 , , , work_fnploejenbc2raktl46esxm44i 23 19 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 23 20 , , , work_fnploejenbc2raktl46esxm44i 23 21 one one PRP work_fnploejenbc2raktl46esxm44i 23 22 can can MD work_fnploejenbc2raktl46esxm44i 23 23 not not RB work_fnploejenbc2raktl46esxm44i 23 24 avoid avoid VB work_fnploejenbc2raktl46esxm44i 23 25 probability probability NN work_fnploejenbc2raktl46esxm44i 23 26 ! ! . work_fnploejenbc2raktl46esxm44i 24 1 However however RB work_fnploejenbc2raktl46esxm44i 24 2 , , , work_fnploejenbc2raktl46esxm44i 24 3 note note VB work_fnploejenbc2raktl46esxm44i 24 4 that that IN work_fnploejenbc2raktl46esxm44i 24 5 such such PDT work_fnploejenbc2raktl46esxm44i 24 6 an an DT work_fnploejenbc2raktl46esxm44i 24 7 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 24 8 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 24 9 measure measure NN work_fnploejenbc2raktl46esxm44i 24 10 need nee MD work_fnploejenbc2raktl46esxm44i 24 11 not not RB work_fnploejenbc2raktl46esxm44i 24 12 be be VB work_fnploejenbc2raktl46esxm44i 24 13 a a DT work_fnploejenbc2raktl46esxm44i 24 14 probability probability NN work_fnploejenbc2raktl46esxm44i 24 15 measure measure NN work_fnploejenbc2raktl46esxm44i 24 16 ! ! . work_fnploejenbc2raktl46esxm44i 25 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 25 2 See see VB work_fnploejenbc2raktl46esxm44i 25 3 also also RB work_fnploejenbc2raktl46esxm44i 25 4 the the DT work_fnploejenbc2raktl46esxm44i 25 5 axiomatic axiomatic JJ work_fnploejenbc2raktl46esxm44i 25 6 work work NN work_fnploejenbc2raktl46esxm44i 25 7 of of IN work_fnploejenbc2raktl46esxm44i 25 8 Cox Cox NNP work_fnploejenbc2raktl46esxm44i 25 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 25 10 S S NNP work_fnploejenbc2raktl46esxm44i 25 11 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 25 12 . . . work_fnploejenbc2raktl46esxm44i 25 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 26 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 26 2 iii iii NNP work_fnploejenbc2raktl46esxm44i 26 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 26 4 As as IN work_fnploejenbc2raktl46esxm44i 26 5 implications implication NNS work_fnploejenbc2raktl46esxm44i 26 6 from from IN work_fnploejenbc2raktl46esxm44i 26 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 26 8 i i NN work_fnploejenbc2raktl46esxm44i 26 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 26 10 , , , work_fnploejenbc2raktl46esxm44i 26 11 the the DT work_fnploejenbc2raktl46esxm44i 26 12 Dempster Dempster NNP work_fnploejenbc2raktl46esxm44i 26 13 - - HYPH work_fnploejenbc2raktl46esxm44i 26 14 Shafer Shafer NNP work_fnploejenbc2raktl46esxm44i 26 15 belief belief NN work_fnploejenbc2raktl46esxm44i 26 16 function function NN work_fnploejenbc2raktl46esxm44i 26 17 , , , work_fnploejenbc2raktl46esxm44i 26 18 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 26 19 ’s ’s POS work_fnploejenbc2raktl46esxm44i 26 20 possibility possibility NN work_fnploejenbc2raktl46esxm44i 26 21 measure measure NN work_fnploejenbc2raktl46esxm44i 26 22 , , , work_fnploejenbc2raktl46esxm44i 26 23 confidence confidence NN work_fnploejenbc2raktl46esxm44i 26 24 values value NNS work_fnploejenbc2raktl46esxm44i 26 25 and and CC work_fnploejenbc2raktl46esxm44i 26 26 significant significant JJ work_fnploejenbc2raktl46esxm44i 26 27 statements statement NNS work_fnploejenbc2raktl46esxm44i 26 28 are be VBP work_fnploejenbc2raktl46esxm44i 26 29 all all RB work_fnploejenbc2raktl46esxm44i 26 30 inadmissible inadmissible JJ work_fnploejenbc2raktl46esxm44i 26 31 ! ! . work_fnploejenbc2raktl46esxm44i 27 1 The the DT work_fnploejenbc2raktl46esxm44i 27 2 purpose purpose NN work_fnploejenbc2raktl46esxm44i 27 3 of of IN work_fnploejenbc2raktl46esxm44i 27 4 our -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 27 5 work work NN work_fnploejenbc2raktl46esxm44i 27 6 is be VBZ work_fnploejenbc2raktl46esxm44i 27 7 threefold threefold JJ work_fnploejenbc2raktl46esxm44i 27 8 : : : work_fnploejenbc2raktl46esxm44i 27 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 27 10 a a LS work_fnploejenbc2raktl46esxm44i 27 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 27 12 To to TO work_fnploejenbc2raktl46esxm44i 27 13 analyze analyze VB work_fnploejenbc2raktl46esxm44i 27 14 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 27 15 ’s ’s POS work_fnploejenbc2raktl46esxm44i 27 16 results result NNS work_fnploejenbc2raktl46esxm44i 27 17 and and CC work_fnploejenbc2raktl46esxm44i 27 18 implications implication NNS work_fnploejenbc2raktl46esxm44i 27 19 , , , work_fnploejenbc2raktl46esxm44i 27 20 for for IN work_fnploejenbc2raktl46esxm44i 27 21 which which WDT work_fnploejenbc2raktl46esxm44i 27 22 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 27 23 recast recast VBP work_fnploejenbc2raktl46esxm44i 27 24 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 27 25 ’s ’s POS work_fnploejenbc2raktl46esxm44i 27 26 somewhat somewhat RB work_fnploejenbc2raktl46esxm44i 27 27 informal informal JJ work_fnploejenbc2raktl46esxm44i 27 28 arguments argument NNS work_fnploejenbc2raktl46esxm44i 27 29 and and CC work_fnploejenbc2raktl46esxm44i 27 30 concepts concept NNS work_fnploejenbc2raktl46esxm44i 27 31 totally totally RB work_fnploejenbc2raktl46esxm44i 27 32 within within IN work_fnploejenbc2raktl46esxm44i 27 33 a a DT work_fnploejenbc2raktl46esxm44i 27 34 game game NN work_fnploejenbc2raktl46esxm44i 27 35 theoretic theoretic JJ work_fnploejenbc2raktl46esxm44i 27 36 setting setting NN work_fnploejenbc2raktl46esxm44i 27 37 . . . work_fnploejenbc2raktl46esxm44i 28 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 28 2 is be VBZ work_fnploejenbc2raktl46esxm44i 28 3 pointed point VBN work_fnploejenbc2raktl46esxm44i 28 4 out out RP work_fnploejenbc2raktl46esxm44i 28 5 in in IN work_fnploejenbc2raktl46esxm44i 28 6 this this DT work_fnploejenbc2raktl46esxm44i 28 7 paper paper NN work_fnploejenbc2raktl46esxm44i 28 8 that that WDT work_fnploejenbc2raktl46esxm44i 28 9 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 28 10 in in IN work_fnploejenbc2raktl46esxm44i 28 11 his -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 28 12 earlier early JJR work_fnploejenbc2raktl46esxm44i 28 13 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 28 14 6 6 CD work_fnploejenbc2raktl46esxm44i 28 15 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 28 16 more more RBR work_fnploejenbc2raktl46esxm44i 28 17 restricted restricted JJ work_fnploejenbc2raktl46esxm44i 28 18 work work NN work_fnploejenbc2raktl46esxm44i 28 19 and and CC work_fnploejenbc2raktl46esxm44i 28 20 later later RBR work_fnploejenbc2raktl46esxm44i 28 21 , , , work_fnploejenbc2raktl46esxm44i 28 22 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 28 23 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 28 24 161 161 CD work_fnploejenbc2raktl46esxm44i 28 25 in in IN work_fnploejenbc2raktl46esxm44i 28 26 his -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 28 27 generalization generalization NN work_fnploejenbc2raktl46esxm44i 28 28 of of IN work_fnploejenbc2raktl46esxm44i 28 29 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 28 30 ’s ’s POS work_fnploejenbc2raktl46esxm44i 28 31 efforts effort NNS work_fnploejenbc2raktl46esxm44i 28 32 , , , work_fnploejenbc2raktl46esxm44i 28 33 both both DT work_fnploejenbc2raktl46esxm44i 28 34 tacitly tacitly RB work_fnploejenbc2raktl46esxm44i 28 35 assumed assume VBN work_fnploejenbc2raktl46esxm44i 28 36 : : : work_fnploejenbc2raktl46esxm44i 28 37 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 28 38 I i NN work_fnploejenbc2raktl46esxm44i 28 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 28 40 “ " `` work_fnploejenbc2raktl46esxm44i 28 41 measure measure NN work_fnploejenbc2raktl46esxm44i 28 42 - - HYPH work_fnploejenbc2raktl46esxm44i 28 43 free free JJ work_fnploejenbc2raktl46esxm44i 28 44 ” " '' work_fnploejenbc2raktl46esxm44i 28 45 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 28 46 events event NNS work_fnploejenbc2raktl46esxm44i 28 47 exist exist VBP work_fnploejenbc2raktl46esxm44i 28 48 independent independent JJ work_fnploejenbc2raktl46esxm44i 28 49 of of IN work_fnploejenbc2raktl46esxm44i 28 50 any any DT work_fnploejenbc2raktl46esxm44i 28 51 par- par- NN work_fnploejenbc2raktl46esxm44i 28 52 ticular ticular JJ work_fnploejenbc2raktl46esxm44i 28 53 choice choice NN work_fnploejenbc2raktl46esxm44i 28 54 of of IN work_fnploejenbc2raktl46esxm44i 28 55 probability probability NN work_fnploejenbc2raktl46esxm44i 28 56 measure measure NN work_fnploejenbc2raktl46esxm44i 28 57 , , , work_fnploejenbc2raktl46esxm44i 28 58 but but CC work_fnploejenbc2raktl46esxm44i 28 59 are be VBP work_fnploejenbc2raktl46esxm44i 28 60 compatible compatible JJ work_fnploejenbc2raktl46esxm44i 28 61 with with IN work_fnploejenbc2raktl46esxm44i 28 62 the the DT work_fnploejenbc2raktl46esxm44i 28 63 usual usual JJ work_fnploejenbc2raktl46esxm44i 28 64 evaluation evaluation NN work_fnploejenbc2raktl46esxm44i 28 65 of of IN work_fnploejenbc2raktl46esxm44i 28 66 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 28 67 probability probability NN work_fnploejenbc2raktl46esxm44i 28 68 . . . work_fnploejenbc2raktl46esxm44i 29 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 29 2 II II NNP work_fnploejenbc2raktl46esxm44i 29 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 29 4 The the DT work_fnploejenbc2raktl46esxm44i 29 5 usual usual JJ work_fnploejenbc2raktl46esxm44i 29 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 29 7 unconditional unconditional JJ work_fnploejenbc2raktl46esxm44i 29 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 29 9 event event NN work_fnploejenbc2raktl46esxm44i 29 10 indicator indicator NN work_fnploejenbc2raktl46esxm44i 29 11 function function NN work_fnploejenbc2raktl46esxm44i 29 12 can can MD work_fnploejenbc2raktl46esxm44i 29 13 be be VB work_fnploejenbc2raktl46esxm44i 29 14 extended extend VBN work_fnploejenbc2raktl46esxm44i 29 15 to to TO work_fnploejenbc2raktl46esxm44i 29 16 be be VB work_fnploejenbc2raktl46esxm44i 29 17 well well RB work_fnploejenbc2raktl46esxm44i 29 18 defined define VBN work_fnploejenbc2raktl46esxm44i 29 19 upon upon IN work_fnploejenbc2raktl46esxm44i 29 20 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 29 21 events event NNS work_fnploejenbc2raktl46esxm44i 29 22 . . . work_fnploejenbc2raktl46esxm44i 30 1 552 552 CD work_fnploejenbc2raktl46esxm44i 30 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 30 3 , , , work_fnploejenbc2raktl46esxm44i 30 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 30 5 , , , work_fnploejenbc2raktl46esxm44i 30 6 AND and CC work_fnploejenbc2raktl46esxm44i 30 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 30 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 30 9 III III NNP work_fnploejenbc2raktl46esxm44i 30 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 30 11 A a DT work_fnploejenbc2raktl46esxm44i 30 12 natural natural JJ work_fnploejenbc2raktl46esxm44i 30 13 conjunctive conjunctive JJ work_fnploejenbc2raktl46esxm44i 30 14 chaining chaining NN work_fnploejenbc2raktl46esxm44i 30 15 relation relation NN work_fnploejenbc2raktl46esxm44i 30 16 holds hold VBZ work_fnploejenbc2raktl46esxm44i 30 17 between between IN work_fnploejenbc2raktl46esxm44i 30 18 condi- condi- NNP work_fnploejenbc2raktl46esxm44i 30 19 tional tional JJ work_fnploejenbc2raktl46esxm44i 30 20 events event NNS work_fnploejenbc2raktl46esxm44i 30 21 . . . work_fnploejenbc2raktl46esxm44i 31 1 As as IN work_fnploejenbc2raktl46esxm44i 31 2 a a DT work_fnploejenbc2raktl46esxm44i 31 3 consequence consequence NN work_fnploejenbc2raktl46esxm44i 31 4 of of IN work_fnploejenbc2raktl46esxm44i 31 5 the the DT work_fnploejenbc2raktl46esxm44i 31 6 above above JJ work_fnploejenbc2raktl46esxm44i 31 7 assumptions assumption NNS work_fnploejenbc2raktl46esxm44i 31 8 , , , work_fnploejenbc2raktl46esxm44i 31 9 in in IN work_fnploejenbc2raktl46esxm44i 31 10 carrying carry VBG work_fnploejenbc2raktl46esxm44i 31 11 out out RP work_fnploejenbc2raktl46esxm44i 31 12 the the DT work_fnploejenbc2raktl46esxm44i 31 13 analysis analysis NN work_fnploejenbc2raktl46esxm44i 31 14 here here RB work_fnploejenbc2raktl46esxm44i 31 15 , , , work_fnploejenbc2raktl46esxm44i 31 16 basically basically RB work_fnploejenbc2raktl46esxm44i 31 17 two two CD work_fnploejenbc2raktl46esxm44i 31 18 cases case NNS work_fnploejenbc2raktl46esxm44i 31 19 are be VBP work_fnploejenbc2raktl46esxm44i 31 20 considered consider VBN work_fnploejenbc2raktl46esxm44i 31 21 apropos apropos ADD work_fnploejenbc2raktl46esxm44i 31 22 to to IN work_fnploejenbc2raktl46esxm44i 31 23 choosing choose VBG work_fnploejenbc2raktl46esxm44i 31 24 an an DT work_fnploejenbc2raktl46esxm44i 31 25 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 31 26 measure measure NN work_fnploejenbc2raktl46esxm44i 31 27 in in IN work_fnploejenbc2raktl46esxm44i 31 28 the the DT work_fnploejenbc2raktl46esxm44i 31 29 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 31 30 - - HYPH work_fnploejenbc2raktl46esxm44i 31 31 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 31 32 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 31 33 game game NN work_fnploejenbc2raktl46esxm44i 31 34 : : : work_fnploejenbc2raktl46esxm44i 31 35 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 31 36 1 1 LS work_fnploejenbc2raktl46esxm44i 31 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 31 38 all all DT work_fnploejenbc2raktl46esxm44i 31 39 finite finite JJ work_fnploejenbc2raktl46esxm44i 31 40 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 31 41 of of IN work_fnploejenbc2raktl46esxm44i 31 42 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 31 43 events event NNS work_fnploejenbc2raktl46esxm44i 31 44 , , , work_fnploejenbc2raktl46esxm44i 31 45 where where WRB work_fnploejenbc2raktl46esxm44i 31 46 each each DT work_fnploejenbc2raktl46esxm44i 31 47 such such JJ work_fnploejenbc2raktl46esxm44i 31 48 sequence sequence NN work_fnploejenbc2raktl46esxm44i 31 49 possesses possess VBZ work_fnploejenbc2raktl46esxm44i 31 50 a a DT work_fnploejenbc2raktl46esxm44i 31 51 common common JJ work_fnploejenbc2raktl46esxm44i 31 52 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 31 53 - - : work_fnploejenbc2raktl46esxm44i 31 54 this this DT work_fnploejenbc2raktl46esxm44i 31 55 includes include VBZ work_fnploejenbc2raktl46esxm44i 31 56 as as IN work_fnploejenbc2raktl46esxm44i 31 57 a a DT work_fnploejenbc2raktl46esxm44i 31 58 special special JJ work_fnploejenbc2raktl46esxm44i 31 59 case case NN work_fnploejenbc2raktl46esxm44i 31 60 all all DT work_fnploejenbc2raktl46esxm44i 31 61 finite finite JJ work_fnploejenbc2raktl46esxm44i 31 62 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 31 63 of of IN work_fnploejenbc2raktl46esxm44i 31 64 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 31 65 uncondi- uncondi- NN work_fnploejenbc2raktl46esxm44i 31 66 tional tional JJ work_fnploejenbc2raktl46esxm44i 31 67 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 31 68 events event NNS work_fnploejenbc2raktl46esxm44i 31 69 , , , work_fnploejenbc2raktl46esxm44i 31 70 by by IN work_fnploejenbc2raktl46esxm44i 31 71 identifying identify VBG work_fnploejenbc2raktl46esxm44i 31 72 unconditional unconditional JJ work_fnploejenbc2raktl46esxm44i 31 73 events event NNS work_fnploejenbc2raktl46esxm44i 31 74 as as IN work_fnploejenbc2raktl46esxm44i 31 75 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 31 76 ones one NNS work_fnploejenbc2raktl46esxm44i 31 77 having have VBG work_fnploejenbc2raktl46esxm44i 31 78 a a DT work_fnploejenbc2raktl46esxm44i 31 79 universal universal JJ work_fnploejenbc2raktl46esxm44i 31 80 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 31 81 - - : work_fnploejenbc2raktl46esxm44i 31 82 and and CC work_fnploejenbc2raktl46esxm44i 31 83 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 31 84 2 2 LS work_fnploejenbc2raktl46esxm44i 31 85 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 31 86 all all DT work_fnploejenbc2raktl46esxm44i 31 87 finite finite JJ work_fnploejenbc2raktl46esxm44i 31 88 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 31 89 of of IN work_fnploejenbc2raktl46esxm44i 31 90 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 31 91 events event NNS work_fnploejenbc2raktl46esxm44i 31 92 with with IN work_fnploejenbc2raktl46esxm44i 31 93 possibly possibly RB work_fnploejenbc2raktl46esxm44i 31 94 differing differ VBG work_fnploejenbc2raktl46esxm44i 31 95 antecedents antecedent NNS work_fnploejenbc2raktl46esxm44i 31 96 - - : work_fnploejenbc2raktl46esxm44i 31 97 this this DT work_fnploejenbc2raktl46esxm44i 31 98 case case NN work_fnploejenbc2raktl46esxm44i 31 99 obviously obviously RB work_fnploejenbc2raktl46esxm44i 31 100 includes include VBZ work_fnploejenbc2raktl46esxm44i 31 101 the the DT work_fnploejenbc2raktl46esxm44i 31 102 first first JJ work_fnploejenbc2raktl46esxm44i 31 103 as as IN work_fnploejenbc2raktl46esxm44i 31 104 a a DT work_fnploejenbc2raktl46esxm44i 31 105 special special JJ work_fnploejenbc2raktl46esxm44i 31 106 case case NN work_fnploejenbc2raktl46esxm44i 31 107 . . . work_fnploejenbc2raktl46esxm44i 32 1 The the DT work_fnploejenbc2raktl46esxm44i 32 2 structure structure NN work_fnploejenbc2raktl46esxm44i 32 3 of of IN work_fnploejenbc2raktl46esxm44i 32 4 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 32 5 games game NNS work_fnploejenbc2raktl46esxm44i 32 6 is be VBZ work_fnploejenbc2raktl46esxm44i 32 7 rigorously rigorously RB work_fnploejenbc2raktl46esxm44i 32 8 spelled spell VBN work_fnploejenbc2raktl46esxm44i 32 9 out out RP work_fnploejenbc2raktl46esxm44i 32 10 in in IN work_fnploejenbc2raktl46esxm44i 32 11 Section section NN work_fnploejenbc2raktl46esxm44i 32 12 2 2 CD work_fnploejenbc2raktl46esxm44i 32 13 . . . work_fnploejenbc2raktl46esxm44i 33 1 In in IN work_fnploejenbc2raktl46esxm44i 33 2 Section section NN work_fnploejenbc2raktl46esxm44i 33 3 3 3 CD work_fnploejenbc2raktl46esxm44i 33 4 , , , work_fnploejenbc2raktl46esxm44i 33 5 a a DT work_fnploejenbc2raktl46esxm44i 33 6 calculus calculus NN work_fnploejenbc2raktl46esxm44i 33 7 of of IN work_fnploejenbc2raktl46esxm44i 33 8 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 33 9 , , , work_fnploejenbc2raktl46esxm44i 33 10 from from IN work_fnploejenbc2raktl46esxm44i 33 11 an an DT work_fnploejenbc2raktl46esxm44i 33 12 analytic analytic JJ work_fnploejenbc2raktl46esxm44i 33 13 viewpoint viewpoint NN work_fnploejenbc2raktl46esxm44i 33 14 , , , work_fnploejenbc2raktl46esxm44i 33 15 is be VBZ work_fnploejenbc2raktl46esxm44i 33 16 developed develop VBN work_fnploejenbc2raktl46esxm44i 33 17 for for IN work_fnploejenbc2raktl46esxm44i 33 18 games game NNS work_fnploejenbc2raktl46esxm44i 33 19 with with IN work_fnploejenbc2raktl46esxm44i 33 20 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 33 21 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 33 22 functions function NNS work_fnploejenbc2raktl46esxm44i 33 23 . . . work_fnploejenbc2raktl46esxm44i 34 1 In in IN work_fnploejenbc2raktl46esxm44i 34 2 Section section NN work_fnploejenbc2raktl46esxm44i 34 3 4 4 CD work_fnploejenbc2raktl46esxm44i 34 4 , , , work_fnploejenbc2raktl46esxm44i 34 5 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 34 6 games game NNS work_fnploejenbc2raktl46esxm44i 34 7 with with IN work_fnploejenbc2raktl46esxm44i 34 8 an an DT work_fnploejenbc2raktl46esxm44i 34 9 additive additive JJ work_fnploejenbc2raktl46esxm44i 34 10 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 34 11 function function NN work_fnploejenbc2raktl46esxm44i 34 12 are be VBP work_fnploejenbc2raktl46esxm44i 34 13 considered consider VBN work_fnploejenbc2raktl46esxm44i 34 14 in in IN work_fnploejenbc2raktl46esxm44i 34 15 detail detail NN work_fnploejenbc2raktl46esxm44i 34 16 together together RB work_fnploejenbc2raktl46esxm44i 34 17 with with IN work_fnploejenbc2raktl46esxm44i 34 18 a a DT work_fnploejenbc2raktl46esxm44i 34 19 Bayesian bayesian JJ work_fnploejenbc2raktl46esxm44i 34 20 analysis analysis NN work_fnploejenbc2raktl46esxm44i 34 21 . . . work_fnploejenbc2raktl46esxm44i 35 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 35 2 b b LS work_fnploejenbc2raktl46esxm44i 35 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 35 4 To to TO work_fnploejenbc2raktl46esxm44i 35 5 show show VB work_fnploejenbc2raktl46esxm44i 35 6 , , , work_fnploejenbc2raktl46esxm44i 35 7 contrary contrary JJ work_fnploejenbc2raktl46esxm44i 35 8 to to IN work_fnploejenbc2raktl46esxm44i 35 9 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 35 10 ’s ’s POS work_fnploejenbc2raktl46esxm44i 35 11 conclusions conclusion NNS work_fnploejenbc2raktl46esxm44i 35 12 outlined outline VBN work_fnploejenbc2raktl46esxm44i 35 13 in in IN work_fnploejenbc2raktl46esxm44i 35 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 35 15 iii iii NN work_fnploejenbc2raktl46esxm44i 35 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 35 17 above above RB work_fnploejenbc2raktl46esxm44i 35 18 , , , work_fnploejenbc2raktl46esxm44i 35 19 that that IN work_fnploejenbc2raktl46esxm44i 35 20 there there EX work_fnploejenbc2raktl46esxm44i 35 21 are be VBP work_fnploejenbc2raktl46esxm44i 35 22 rather rather RB work_fnploejenbc2raktl46esxm44i 35 23 large large JJ work_fnploejenbc2raktl46esxm44i 35 24 classes class NNS work_fnploejenbc2raktl46esxm44i 35 25 of of IN work_fnploejenbc2raktl46esxm44i 35 26 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 35 27 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 35 28 measures measure NNS work_fnploejenbc2raktl46esxm44i 35 29 , , , work_fnploejenbc2raktl46esxm44i 35 30 such such JJ work_fnploejenbc2raktl46esxm44i 35 31 as as IN work_fnploejenbc2raktl46esxm44i 35 32 belief belief NN work_fnploejenbc2raktl46esxm44i 35 33 functions function NNS work_fnploejenbc2raktl46esxm44i 35 34 and and CC work_fnploejenbc2raktl46esxm44i 35 35 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 35 36 measures measure NNS work_fnploejenbc2raktl46esxm44i 35 37 in in IN work_fnploejenbc2raktl46esxm44i 35 38 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 35 39 logics logic NNS work_fnploejenbc2raktl46esxm44i 35 40 , , , work_fnploejenbc2raktl46esxm44i 35 41 which which WDT work_fnploejenbc2raktl46esxm44i 35 42 are be VBP work_fnploejenbc2raktl46esxm44i 35 43 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 35 44 . . . work_fnploejenbc2raktl46esxm44i 36 1 Also also RB work_fnploejenbc2raktl46esxm44i 36 2 , , , work_fnploejenbc2raktl46esxm44i 36 3 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 36 4 ’s ’s POS work_fnploejenbc2raktl46esxm44i 36 5 max max NN work_fnploejenbc2raktl46esxm44i 36 6 - - HYPH work_fnploejenbc2raktl46esxm44i 36 7 possibility possibility NN work_fnploejenbc2raktl46esxm44i 36 8 measures measure NNS work_fnploejenbc2raktl46esxm44i 36 9 are be VBP work_fnploejenbc2raktl46esxm44i 36 10 shown show VBN work_fnploejenbc2raktl46esxm44i 36 11 to to TO work_fnploejenbc2raktl46esxm44i 36 12 be be VB work_fnploejenbc2raktl46esxm44i 36 13 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 36 14 limits limit NNS work_fnploejenbc2raktl46esxm44i 36 15 of of IN work_fnploejenbc2raktl46esxm44i 36 16 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 36 17 measures measure NNS work_fnploejenbc2raktl46esxm44i 36 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 36 19 Sections section NNS work_fnploejenbc2raktl46esxm44i 36 20 5 5 CD work_fnploejenbc2raktl46esxm44i 36 21 and and CC work_fnploejenbc2raktl46esxm44i 36 22 6 6 CD work_fnploejenbc2raktl46esxm44i 36 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 36 24 . . . work_fnploejenbc2raktl46esxm44i 37 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 37 2 c c NN work_fnploejenbc2raktl46esxm44i 37 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 37 4 To to TO work_fnploejenbc2raktl46esxm44i 37 5 study study VB work_fnploejenbc2raktl46esxm44i 37 6 the the DT work_fnploejenbc2raktl46esxm44i 37 7 effects effect NNS work_fnploejenbc2raktl46esxm44i 37 8 of of IN work_fnploejenbc2raktl46esxm44i 37 9 the the DT work_fnploejenbc2raktl46esxm44i 37 10 assumption assumption NN work_fnploejenbc2raktl46esxm44i 37 11 of of IN work_fnploejenbc2raktl46esxm44i 37 12 additive additive JJ work_fnploejenbc2raktl46esxm44i 37 13 score score NN work_fnploejenbc2raktl46esxm44i 37 14 functions function NNS work_fnploejenbc2raktl46esxm44i 37 15 , , , work_fnploejenbc2raktl46esxm44i 37 16 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 37 17 present present VBP work_fnploejenbc2raktl46esxm44i 37 18 , , , work_fnploejenbc2raktl46esxm44i 37 19 in in IN work_fnploejenbc2raktl46esxm44i 37 20 Section section NN work_fnploejenbc2raktl46esxm44i 37 21 7 7 CD work_fnploejenbc2raktl46esxm44i 37 22 , , , work_fnploejenbc2raktl46esxm44i 37 23 various various JJ work_fnploejenbc2raktl46esxm44i 37 24 examples example NNS work_fnploejenbc2raktl46esxm44i 37 25 of of IN work_fnploejenbc2raktl46esxm44i 37 26 non non JJ work_fnploejenbc2raktl46esxm44i 37 27 - - JJ work_fnploejenbc2raktl46esxm44i 37 28 additive additive JJ work_fnploejenbc2raktl46esxm44i 37 29 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 37 30 functions function NNS work_fnploejenbc2raktl46esxm44i 37 31 . . . work_fnploejenbc2raktl46esxm44i 38 1 These these DT work_fnploejenbc2raktl46esxm44i 38 2 illustrate illustrate VBP work_fnploejenbc2raktl46esxm44i 38 3 the the DT work_fnploejenbc2raktl46esxm44i 38 4 fact fact NN work_fnploejenbc2raktl46esxm44i 38 5 that that IN work_fnploejenbc2raktl46esxm44i 38 6 the the DT work_fnploejenbc2raktl46esxm44i 38 7 class class NN work_fnploejenbc2raktl46esxm44i 38 8 of of IN work_fnploejenbc2raktl46esxm44i 38 9 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 38 10 measures measure NNS work_fnploejenbc2raktl46esxm44i 38 11 in in IN work_fnploejenbc2raktl46esxm44i 38 12 a a DT work_fnploejenbc2raktl46esxm44i 38 13 scoring score VBG work_fnploejenbc2raktl46esxm44i 38 14 framework framework NN work_fnploejenbc2raktl46esxm44i 38 15 depends depend VBZ work_fnploejenbc2raktl46esxm44i 38 16 heavily heavily RB work_fnploejenbc2raktl46esxm44i 38 17 on on IN work_fnploejenbc2raktl46esxm44i 38 18 the the DT work_fnploejenbc2raktl46esxm44i 38 19 nature nature NN work_fnploejenbc2raktl46esxm44i 38 20 of of IN work_fnploejenbc2raktl46esxm44i 38 21 the the DT work_fnploejenbc2raktl46esxm44i 38 22 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 38 23 functions function NNS work_fnploejenbc2raktl46esxm44i 38 24 . . . work_fnploejenbc2raktl46esxm44i 39 1 In in IN work_fnploejenbc2raktl46esxm44i 39 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 39 3 , , , work_fnploejenbc2raktl46esxm44i 39 4 there there EX work_fnploejenbc2raktl46esxm44i 39 5 exist exist VBP work_fnploejenbc2raktl46esxm44i 39 6 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 39 7 functions function NNS work_fnploejenbc2raktl46esxm44i 39 8 such such JJ work_fnploejenbc2raktl46esxm44i 39 9 that that IN work_fnploejenbc2raktl46esxm44i 39 10 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 39 11 measures measure NNS work_fnploejenbc2raktl46esxm44i 39 12 can can MD work_fnploejenbc2raktl46esxm44i 39 13 not not RB work_fnploejenbc2raktl46esxm44i 39 14 be be VB work_fnploejenbc2raktl46esxm44i 39 15 transformed transform VBN work_fnploejenbc2raktl46esxm44i 39 16 into into IN work_fnploejenbc2raktl46esxm44i 39 17 finitely finitely RB work_fnploejenbc2raktl46esxm44i 39 18 additive additive JJ work_fnploejenbc2raktl46esxm44i 39 19 probability probability NN work_fnploejenbc2raktl46esxm44i 39 20 measures measure NNS work_fnploejenbc2raktl46esxm44i 39 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 39 22 as as IN work_fnploejenbc2raktl46esxm44i 39 23 opposed oppose VBN work_fnploejenbc2raktl46esxm44i 39 24 to to IN work_fnploejenbc2raktl46esxm44i 39 25 the the DT work_fnploejenbc2raktl46esxm44i 39 26 case case NN work_fnploejenbc2raktl46esxm44i 39 27 of of IN work_fnploejenbc2raktl46esxm44i 39 28 the the DT work_fnploejenbc2raktl46esxm44i 39 29 additive additive JJ work_fnploejenbc2raktl46esxm44i 39 30 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 39 31 function function NN work_fnploejenbc2raktl46esxm44i 39 32 in in IN work_fnploejenbc2raktl46esxm44i 39 33 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 39 34 ’s ’s POS work_fnploejenbc2raktl46esxm44i 39 35 work work NN work_fnploejenbc2raktl46esxm44i 39 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 39 37 . . . work_fnploejenbc2raktl46esxm44i 40 1 In in IN work_fnploejenbc2raktl46esxm44i 40 2 summary summary NN work_fnploejenbc2raktl46esxm44i 40 3 , , , work_fnploejenbc2raktl46esxm44i 40 4 by by IN work_fnploejenbc2raktl46esxm44i 40 5 formalizing formalize VBG work_fnploejenbc2raktl46esxm44i 40 6 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 40 7 ’s ’s POS work_fnploejenbc2raktl46esxm44i 40 8 work work NN work_fnploejenbc2raktl46esxm44i 40 9 within within IN work_fnploejenbc2raktl46esxm44i 40 10 a a DT work_fnploejenbc2raktl46esxm44i 40 11 general general JJ work_fnploejenbc2raktl46esxm44i 40 12 and and CC work_fnploejenbc2raktl46esxm44i 40 13 rigorous rigorous JJ work_fnploejenbc2raktl46esxm44i 40 14 game game NN work_fnploejenbc2raktl46esxm44i 40 15 theory theory NN work_fnploejenbc2raktl46esxm44i 40 16 framework framework NN work_fnploejenbc2raktl46esxm44i 40 17 , , , work_fnploejenbc2raktl46esxm44i 40 18 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 40 19 develop develop VBP work_fnploejenbc2raktl46esxm44i 40 20 a a DT work_fnploejenbc2raktl46esxm44i 40 21 calculus calculus NN work_fnploejenbc2raktl46esxm44i 40 22 of of IN work_fnploejenbc2raktl46esxm44i 40 23 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 40 24 which which WDT work_fnploejenbc2raktl46esxm44i 40 25 can can MD work_fnploejenbc2raktl46esxm44i 40 26 be be VB work_fnploejenbc2raktl46esxm44i 40 27 used use VBN work_fnploejenbc2raktl46esxm44i 40 28 to to TO work_fnploejenbc2raktl46esxm44i 40 29 compare compare VB work_fnploejenbc2raktl46esxm44i 40 30 competing compete VBG work_fnploejenbc2raktl46esxm44i 40 31 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 40 32 measures measure NNS work_fnploejenbc2raktl46esxm44i 40 33 in in IN work_fnploejenbc2raktl46esxm44i 40 34 Artificial Artificial NNP work_fnploejenbc2raktl46esxm44i 40 35 Intelligence Intelligence NNP work_fnploejenbc2raktl46esxm44i 40 36 . . . work_fnploejenbc2raktl46esxm44i 41 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 41 2 shed shed VBD work_fnploejenbc2raktl46esxm44i 41 3 light light NN work_fnploejenbc2raktl46esxm44i 41 4 on on IN work_fnploejenbc2raktl46esxm44i 41 5 controversial controversial JJ work_fnploejenbc2raktl46esxm44i 41 6 conclusions conclusion NNS work_fnploejenbc2raktl46esxm44i 41 7 concerning concern VBG work_fnploejenbc2raktl46esxm44i 41 8 the the DT work_fnploejenbc2raktl46esxm44i 41 9 inadmissibility inadmissibility NN work_fnploejenbc2raktl46esxm44i 41 10 of of IN work_fnploejenbc2raktl46esxm44i 41 11 some some DT work_fnploejenbc2raktl46esxm44i 41 12 well well RB work_fnploejenbc2raktl46esxm44i 41 13 - - HYPH work_fnploejenbc2raktl46esxm44i 41 14 known know VBN work_fnploejenbc2raktl46esxm44i 41 15 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 41 16 measures measure NNS work_fnploejenbc2raktl46esxm44i 41 17 and and CC work_fnploejenbc2raktl46esxm44i 41 18 on on IN work_fnploejenbc2raktl46esxm44i 41 19 the the DT work_fnploejenbc2raktl46esxm44i 41 20 position position NN work_fnploejenbc2raktl46esxm44i 41 21 of of IN work_fnploejenbc2raktl46esxm44i 41 22 the the DT work_fnploejenbc2raktl46esxm44i 41 23 “ " `` work_fnploejenbc2raktl46esxm44i 41 24 inevitability inevitability NN work_fnploejenbc2raktl46esxm44i 41 25 of of IN work_fnploejenbc2raktl46esxm44i 41 26 probability probability NN work_fnploejenbc2raktl46esxm44i 41 27 . . . work_fnploejenbc2raktl46esxm44i 41 28 ” " '' work_fnploejenbc2raktl46esxm44i 41 29 2 2 CD work_fnploejenbc2raktl46esxm44i 41 30 . . . work_fnploejenbc2raktl46esxm44i 42 1 STRUCTURE STRUCTURE NNP work_fnploejenbc2raktl46esxm44i 42 2 OF of IN work_fnploejenbc2raktl46esxm44i 42 3 UNCERTAINTY UNCERTAINTY NNP work_fnploejenbc2raktl46esxm44i 42 4 GAMES GAMES NNP work_fnploejenbc2raktl46esxm44i 42 5 In in IN work_fnploejenbc2raktl46esxm44i 42 6 this this DT work_fnploejenbc2raktl46esxm44i 42 7 section section NN work_fnploejenbc2raktl46esxm44i 42 8 , , , work_fnploejenbc2raktl46esxm44i 42 9 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 42 10 will will MD work_fnploejenbc2raktl46esxm44i 42 11 formalize formalize VB work_fnploejenbc2raktl46esxm44i 42 12 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 42 13 ’s ’s POS work_fnploejenbc2raktl46esxm44i 42 14 scoring score VBG work_fnploejenbc2raktl46esxm44i 42 15 approach approach NN work_fnploejenbc2raktl46esxm44i 42 16 in in IN work_fnploejenbc2raktl46esxm44i 42 17 a a DT work_fnploejenbc2raktl46esxm44i 42 18 game game NN work_fnploejenbc2raktl46esxm44i 42 19 theory theory NN work_fnploejenbc2raktl46esxm44i 42 20 setting setting NN work_fnploejenbc2raktl46esxm44i 42 21 . . . work_fnploejenbc2raktl46esxm44i 43 1 Since since IN work_fnploejenbc2raktl46esxm44i 43 2 the the DT work_fnploejenbc2raktl46esxm44i 43 3 scoring score VBG work_fnploejenbc2raktl46esxm44i 43 4 approach approach NN work_fnploejenbc2raktl46esxm44i 43 5 involves involve VBZ work_fnploejenbc2raktl46esxm44i 43 6 concepts concept NNS work_fnploejenbc2raktl46esxm44i 43 7 such such JJ work_fnploejenbc2raktl46esxm44i 43 8 as as IN work_fnploejenbc2raktl46esxm44i 43 9 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 43 10 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 43 11 TO to IN work_fnploejenbc2raktl46esxm44i 43 12 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 43 13 553 553 CD work_fnploejenbc2raktl46esxm44i 43 14 “ " `` work_fnploejenbc2raktl46esxm44i 43 15 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 43 16 events event NNS work_fnploejenbc2raktl46esxm44i 43 17 , , , work_fnploejenbc2raktl46esxm44i 43 18 ” " '' work_fnploejenbc2raktl46esxm44i 43 19 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 43 20 measures measure NNS work_fnploejenbc2raktl46esxm44i 43 21 , , , work_fnploejenbc2raktl46esxm44i 43 22 score score NN work_fnploejenbc2raktl46esxm44i 43 23 functions function NNS work_fnploejenbc2raktl46esxm44i 43 24 , , , work_fnploejenbc2raktl46esxm44i 43 25 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 43 26 functions function NNS work_fnploejenbc2raktl46esxm44i 43 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 43 28 implicitly implicitly RB work_fnploejenbc2raktl46esxm44i 43 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 43 30 , , , work_fnploejenbc2raktl46esxm44i 43 31 and and CC work_fnploejenbc2raktl46esxm44i 43 32 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 43 33 , , , work_fnploejenbc2raktl46esxm44i 43 34 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 43 35 need need VBP work_fnploejenbc2raktl46esxm44i 43 36 to to TO work_fnploejenbc2raktl46esxm44i 43 37 define define VB work_fnploejenbc2raktl46esxm44i 43 38 these these DT work_fnploejenbc2raktl46esxm44i 43 39 terms term NNS work_fnploejenbc2raktl46esxm44i 43 40 rigorously rigorously RB work_fnploejenbc2raktl46esxm44i 43 41 . . . work_fnploejenbc2raktl46esxm44i 44 1 2.1 2.1 CD work_fnploejenbc2raktl46esxm44i 44 2 . . . work_fnploejenbc2raktl46esxm44i 45 1 Conditional conditional JJ work_fnploejenbc2raktl46esxm44i 45 2 Events event NNS work_fnploejenbc2raktl46esxm44i 45 3 Let let VBP work_fnploejenbc2raktl46esxm44i 45 4 Q Q NNP work_fnploejenbc2raktl46esxm44i 45 5 be be VB work_fnploejenbc2raktl46esxm44i 45 6 a a DT work_fnploejenbc2raktl46esxm44i 45 7 set set NN work_fnploejenbc2raktl46esxm44i 45 8 and and CC work_fnploejenbc2raktl46esxm44i 45 9 d d LS work_fnploejenbc2raktl46esxm44i 45 10 a a DT work_fnploejenbc2raktl46esxm44i 45 11 Boolean Boolean NNP work_fnploejenbc2raktl46esxm44i 45 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 45 13 or or CC work_fnploejenbc2raktl46esxm44i 45 14 0~ 0~ LS work_fnploejenbc2raktl46esxm44i 45 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 45 16 algebra algebra NN work_fnploejenbc2raktl46esxm44i 45 17 of of IN work_fnploejenbc2raktl46esxm44i 45 18 subsets subset NNS work_fnploejenbc2raktl46esxm44i 45 19 of of IN work_fnploejenbc2raktl46esxm44i 45 20 52 52 CD work_fnploejenbc2raktl46esxm44i 45 21 . . . work_fnploejenbc2raktl46esxm44i 46 1 Elements element NNS work_fnploejenbc2raktl46esxm44i 46 2 of of IN work_fnploejenbc2raktl46esxm44i 46 3 d d NN work_fnploejenbc2raktl46esxm44i 46 4 are be VBP work_fnploejenbc2raktl46esxm44i 46 5 called call VBN work_fnploejenbc2raktl46esxm44i 46 6 events event NNS work_fnploejenbc2raktl46esxm44i 46 7 . . . work_fnploejenbc2raktl46esxm44i 47 1 The the DT work_fnploejenbc2raktl46esxm44i 47 2 set set JJ work_fnploejenbc2raktl46esxm44i 47 3 complement complement NN work_fnploejenbc2raktl46esxm44i 47 4 of of IN work_fnploejenbc2raktl46esxm44i 47 5 A a NN work_fnploejenbc2raktl46esxm44i 47 6 in in IN work_fnploejenbc2raktl46esxm44i 47 7 52 52 CD work_fnploejenbc2raktl46esxm44i 47 8 is be VBZ work_fnploejenbc2raktl46esxm44i 47 9 denoted denote VBN work_fnploejenbc2raktl46esxm44i 47 10 by by IN work_fnploejenbc2raktl46esxm44i 47 11 A a NN work_fnploejenbc2raktl46esxm44i 47 12 ’ ' '' work_fnploejenbc2raktl46esxm44i 47 13 ; ; : work_fnploejenbc2raktl46esxm44i 47 14 the the DT work_fnploejenbc2raktl46esxm44i 47 15 intersection intersection NN work_fnploejenbc2raktl46esxm44i 47 16 of of IN work_fnploejenbc2raktl46esxm44i 47 17 A a NN work_fnploejenbc2raktl46esxm44i 47 18 , , , work_fnploejenbc2raktl46esxm44i 47 19 B b NN work_fnploejenbc2raktl46esxm44i 47 20 in in IN work_fnploejenbc2raktl46esxm44i 47 21 52 52 CD work_fnploejenbc2raktl46esxm44i 47 22 is be VBZ work_fnploejenbc2raktl46esxm44i 47 23 AB AB NNP work_fnploejenbc2raktl46esxm44i 47 24 ; ; : work_fnploejenbc2raktl46esxm44i 47 25 and and CC work_fnploejenbc2raktl46esxm44i 47 26 their -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 47 27 union union NN work_fnploejenbc2raktl46esxm44i 47 28 is be VBZ work_fnploejenbc2raktl46esxm44i 47 29 A a DT work_fnploejenbc2raktl46esxm44i 47 30 u u NNP work_fnploejenbc2raktl46esxm44i 47 31 B. B. NNP work_fnploejenbc2raktl46esxm44i 48 1 For for IN work_fnploejenbc2raktl46esxm44i 48 2 A a DT work_fnploejenbc2raktl46esxm44i 48 3 E e NN work_fnploejenbc2raktl46esxm44i 48 4 & & CC work_fnploejenbc2raktl46esxm44i 48 5 ‘ ' '' work_fnploejenbc2raktl46esxm44i 48 6 , , , work_fnploejenbc2raktl46esxm44i 48 7 the the DT work_fnploejenbc2raktl46esxm44i 48 8 indicator indicator NN work_fnploejenbc2raktl46esxm44i 48 9 function function NN work_fnploejenbc2raktl46esxm44i 48 10 has have VBZ work_fnploejenbc2raktl46esxm44i 48 11 values value NNS work_fnploejenbc2raktl46esxm44i 48 12 ifoEA ifoea ADD work_fnploejenbc2raktl46esxm44i 48 13 if if IN work_fnploejenbc2raktl46esxm44i 48 14 cuEA cuEA NNP work_fnploejenbc2raktl46esxm44i 48 15 ’ ' '' work_fnploejenbc2raktl46esxm44i 48 16 In in IN work_fnploejenbc2raktl46esxm44i 48 17 certain certain JJ work_fnploejenbc2raktl46esxm44i 48 18 forms form NNS work_fnploejenbc2raktl46esxm44i 48 19 , , , work_fnploejenbc2raktl46esxm44i 48 20 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 48 21 is be VBZ work_fnploejenbc2raktl46esxm44i 48 22 simpler simple JJR work_fnploejenbc2raktl46esxm44i 48 23 to to TO work_fnploejenbc2raktl46esxm44i 48 24 identify identify VB work_fnploejenbc2raktl46esxm44i 48 25 A a DT work_fnploejenbc2raktl46esxm44i 48 26 with with IN work_fnploejenbc2raktl46esxm44i 48 27 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 48 28 , , , work_fnploejenbc2raktl46esxm44i 48 29 so so IN work_fnploejenbc2raktl46esxm44i 48 30 that that IN work_fnploejenbc2raktl46esxm44i 48 31 A a NN work_fnploejenbc2raktl46esxm44i 48 32 = = SYM work_fnploejenbc2raktl46esxm44i 48 33 1 1 CD work_fnploejenbc2raktl46esxm44i 48 34 if if IN work_fnploejenbc2raktl46esxm44i 48 35 A a NN work_fnploejenbc2raktl46esxm44i 48 36 “ " `` work_fnploejenbc2raktl46esxm44i 48 37 occurs occur VBZ work_fnploejenbc2raktl46esxm44i 48 38 ” " '' work_fnploejenbc2raktl46esxm44i 48 39 and and CC work_fnploejenbc2raktl46esxm44i 48 40 A a NN work_fnploejenbc2raktl46esxm44i 48 41 = = SYM work_fnploejenbc2raktl46esxm44i 48 42 0 0 CD work_fnploejenbc2raktl46esxm44i 48 43 if if IN work_fnploejenbc2raktl46esxm44i 48 44 A a NN work_fnploejenbc2raktl46esxm44i 48 45 “ " `` work_fnploejenbc2raktl46esxm44i 48 46 does do VBZ work_fnploejenbc2raktl46esxm44i 48 47 not not RB work_fnploejenbc2raktl46esxm44i 48 48 occur occur VB work_fnploejenbc2raktl46esxm44i 48 49 . . . work_fnploejenbc2raktl46esxm44i 48 50 ” " '' work_fnploejenbc2raktl46esxm44i 48 51 For for IN work_fnploejenbc2raktl46esxm44i 48 52 A A NNP work_fnploejenbc2raktl46esxm44i 48 53 , , , work_fnploejenbc2raktl46esxm44i 48 54 BE BE NNP work_fnploejenbc2raktl46esxm44i 48 55 d d NN work_fnploejenbc2raktl46esxm44i 48 56 , , , work_fnploejenbc2raktl46esxm44i 48 57 the the DT work_fnploejenbc2raktl46esxm44i 48 58 “ " `` work_fnploejenbc2raktl46esxm44i 48 59 measure measure NN work_fnploejenbc2raktl46esxm44i 48 60 - - HYPH work_fnploejenbc2raktl46esxm44i 48 61 free free JJ work_fnploejenbc2raktl46esxm44i 48 62 ” " '' work_fnploejenbc2raktl46esxm44i 48 63 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 48 64 event event NN work_fnploejenbc2raktl46esxm44i 48 65 A a NN work_fnploejenbc2raktl46esxm44i 48 66 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 48 67 B b NN work_fnploejenbc2raktl46esxm44i 48 68 is be VBZ work_fnploejenbc2raktl46esxm44i 48 69 defined define VBN work_fnploejenbc2raktl46esxm44i 48 70 by by IN work_fnploejenbc2raktl46esxm44i 48 71 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 48 72 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 48 73 6 6 CD work_fnploejenbc2raktl46esxm44i 48 74 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 48 75 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 48 76 see see VB work_fnploejenbc2raktl46esxm44i 48 77 also also RB work_fnploejenbc2raktl46esxm44i 48 78 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 48 79 22 22 CD work_fnploejenbc2raktl46esxm44i 48 80 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 48 81 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 48 82 as as IN work_fnploejenbc2raktl46esxm44i 48 83 the the DT work_fnploejenbc2raktl46esxm44i 48 84 restriction restriction NN work_fnploejenbc2raktl46esxm44i 48 85 of of IN work_fnploejenbc2raktl46esxm44i 48 86 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 48 87 , , , work_fnploejenbc2raktl46esxm44i 48 88 to to IN work_fnploejenbc2raktl46esxm44i 48 89 B b NN work_fnploejenbc2raktl46esxm44i 48 90 , , , work_fnploejenbc2raktl46esxm44i 48 91 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 48 92 , , , work_fnploejenbc2raktl46esxm44i 48 93 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 48 94 AlB)(o)= AlB)(o)= NNS work_fnploejenbc2raktl46esxm44i 48 95 0 0 CD work_fnploejenbc2raktl46esxm44i 48 96 i i PRP work_fnploejenbc2raktl46esxm44i 48 97 1 1 CD work_fnploejenbc2raktl46esxm44i 48 98 if if IN work_fnploejenbc2raktl46esxm44i 48 99 weAB weAB NNP work_fnploejenbc2raktl46esxm44i 48 100 if if IN work_fnploejenbc2raktl46esxm44i 48 101 UEA’B UEA’B NNP work_fnploejenbc2raktl46esxm44i 48 102 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 48 103 undefined undefined JJ work_fnploejenbc2raktl46esxm44i 48 104 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 48 105 if if IN work_fnploejenbc2raktl46esxm44i 48 106 o o NN work_fnploejenbc2raktl46esxm44i 48 107 E e NN work_fnploejenbc2raktl46esxm44i 48 108 B b NN work_fnploejenbc2raktl46esxm44i 48 109 ” " '' work_fnploejenbc2raktl46esxm44i 48 110 . . . work_fnploejenbc2raktl46esxm44i 49 1 Except except IN work_fnploejenbc2raktl46esxm44i 49 2 when when WRB work_fnploejenbc2raktl46esxm44i 49 3 B b NN work_fnploejenbc2raktl46esxm44i 49 4 = = SYM work_fnploejenbc2raktl46esxm44i 49 5 Sz Sz NNP work_fnploejenbc2raktl46esxm44i 49 6 and and CC work_fnploejenbc2raktl46esxm44i 49 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 49 8 A a DT work_fnploejenbc2raktl46esxm44i 49 9 IQ iq NN work_fnploejenbc2raktl46esxm44i 49 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 49 11 is be VBZ work_fnploejenbc2raktl46esxm44i 49 12 identified identify VBN work_fnploejenbc2raktl46esxm44i 49 13 with with IN work_fnploejenbc2raktl46esxm44i 49 14 A a DT work_fnploejenbc2raktl46esxm44i 49 15 , , , work_fnploejenbc2raktl46esxm44i 49 16 these these DT work_fnploejenbc2raktl46esxm44i 49 17 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 49 18 events event NNS work_fnploejenbc2raktl46esxm44i 49 19 are be VBP work_fnploejenbc2raktl46esxm44i 49 20 not not RB work_fnploejenbc2raktl46esxm44i 49 21 elements element NNS work_fnploejenbc2raktl46esxm44i 49 22 of of IN work_fnploejenbc2raktl46esxm44i 49 23 d. d. NNP work_fnploejenbc2raktl46esxm44i 49 24 The the DT work_fnploejenbc2raktl46esxm44i 49 25 above above JJ work_fnploejenbc2raktl46esxm44i 49 26 definition definition NN work_fnploejenbc2raktl46esxm44i 49 27 implies imply VBZ work_fnploejenbc2raktl46esxm44i 49 28 the the DT work_fnploejenbc2raktl46esxm44i 49 29 invariant invariant JJ work_fnploejenbc2raktl46esxm44i 49 30 form form NN work_fnploejenbc2raktl46esxm44i 49 31 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 49 32 A a NN work_fnploejenbc2raktl46esxm44i 49 33 1 1 CD work_fnploejenbc2raktl46esxm44i 49 34 B b NN work_fnploejenbc2raktl46esxm44i 49 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 49 36 = = NFP work_fnploejenbc2raktl46esxm44i 49 37 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 49 38 ABI ABI NNP work_fnploejenbc2raktl46esxm44i 49 39 B B NNP work_fnploejenbc2raktl46esxm44i 49 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 49 41 . . . work_fnploejenbc2raktl46esxm44i 50 1 Assume Assume NNP work_fnploejenbc2raktl46esxm44i 50 2 , , , work_fnploejenbc2raktl46esxm44i 50 3 also also RB work_fnploejenbc2raktl46esxm44i 50 4 the the DT work_fnploejenbc2raktl46esxm44i 50 5 fundamental fundamental JJ work_fnploejenbc2raktl46esxm44i 50 6 homomorphic homomorphic JJ work_fnploejenbc2raktl46esxm44i 50 7 - - HYPH work_fnploejenbc2raktl46esxm44i 50 8 like like JJ work_fnploejenbc2raktl46esxm44i 50 9 forms form NNS work_fnploejenbc2raktl46esxm44i 50 10 compatible compatible JJ work_fnploejenbc2raktl46esxm44i 50 11 with with IN work_fnploejenbc2raktl46esxm44i 50 12 any any DT work_fnploejenbc2raktl46esxm44i 50 13 fixed fixed JJ work_fnploejenbc2raktl46esxm44i 50 14 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 50 15 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 50 16 probability probability NN work_fnploejenbc2raktl46esxm44i 50 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 50 18 A a DT work_fnploejenbc2raktl46esxm44i 50 19 I i NN work_fnploejenbc2raktl46esxm44i 50 20 B b NN work_fnploejenbc2raktl46esxm44i 50 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 50 22 ” " '' work_fnploejenbc2raktl46esxm44i 50 23 = = NFP work_fnploejenbc2raktl46esxm44i 50 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 50 25 A’1 A’1 NNP work_fnploejenbc2raktl46esxm44i 50 26 Bh Bh NNP work_fnploejenbc2raktl46esxm44i 50 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 50 28 AuC)lB)=(AlB)u(CIB auc)lb)=(alb)u(cib NN work_fnploejenbc2raktl46esxm44i 50 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 50 30 , , , work_fnploejenbc2raktl46esxm44i 50 31 MCI MCI NNP work_fnploejenbc2raktl46esxm44i 50 32 B B NNP work_fnploejenbc2raktl46esxm44i 50 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 50 34 = = NFP work_fnploejenbc2raktl46esxm44i 50 35 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 50 36 -4 -4 : work_fnploejenbc2raktl46esxm44i 50 37 I i NN work_fnploejenbc2raktl46esxm44i 50 38 @(Cl @(Cl . work_fnploejenbc2raktl46esxm44i 50 39 B b NN work_fnploejenbc2raktl46esxm44i 50 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 50 41 . . . work_fnploejenbc2raktl46esxm44i 51 1 Although although IN work_fnploejenbc2raktl46esxm44i 51 2 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 51 3 recognized recognize VBD work_fnploejenbc2raktl46esxm44i 51 4 the the DT work_fnploejenbc2raktl46esxm44i 51 5 potential potential JJ work_fnploejenbc2raktl46esxm44i 51 6 use use NN work_fnploejenbc2raktl46esxm44i 51 7 of of IN work_fnploejenbc2raktl46esxm44i 51 8 measure measure NN work_fnploejenbc2raktl46esxm44i 51 9 - - HYPH work_fnploejenbc2raktl46esxm44i 51 10 free free JJ work_fnploejenbc2raktl46esxm44i 51 11 condi- condi- IN work_fnploejenbc2raktl46esxm44i 51 12 tional tional JJ work_fnploejenbc2raktl46esxm44i 51 13 events event NNS work_fnploejenbc2raktl46esxm44i 51 14 , , , work_fnploejenbc2raktl46esxm44i 51 15 in in IN work_fnploejenbc2raktl46esxm44i 51 16 obtaining obtain VBG work_fnploejenbc2raktl46esxm44i 51 17 his -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 51 18 key key JJ work_fnploejenbc2raktl46esxm44i 51 19 results result NNS work_fnploejenbc2raktl46esxm44i 51 20 a a DT work_fnploejenbc2raktl46esxm44i 51 21 formal formal JJ work_fnploejenbc2raktl46esxm44i 51 22 calculus calculus NN work_fnploejenbc2raktl46esxm44i 51 23 of of IN work_fnploejenbc2raktl46esxm44i 51 24 relations relation NNS work_fnploejenbc2raktl46esxm44i 51 25 was be VBD work_fnploejenbc2raktl46esxm44i 51 26 not not RB work_fnploejenbc2raktl46esxm44i 51 27 developed develop VBN work_fnploejenbc2raktl46esxm44i 51 28 . . . work_fnploejenbc2raktl46esxm44i 52 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 52 2 Again again RB work_fnploejenbc2raktl46esxm44i 52 3 , , , work_fnploejenbc2raktl46esxm44i 52 4 see see VB work_fnploejenbc2raktl46esxm44i 52 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 52 6 6 6 CD work_fnploejenbc2raktl46esxm44i 52 7 , , , work_fnploejenbc2raktl46esxm44i 52 8 especially especially RB work_fnploejenbc2raktl46esxm44i 52 9 Vol Vol NNP work_fnploejenbc2raktl46esxm44i 52 10 . . . work_fnploejenbc2raktl46esxm44i 53 1 1 1 LS work_fnploejenbc2raktl46esxm44i 53 2 , , , work_fnploejenbc2raktl46esxm44i 53 3 Chap Chap NNP work_fnploejenbc2raktl46esxm44i 53 4 . . . work_fnploejenbc2raktl46esxm44i 54 1 4 4 LS work_fnploejenbc2raktl46esxm44i 54 2 , , , work_fnploejenbc2raktl46esxm44i 54 3 Vol Vol NNP work_fnploejenbc2raktl46esxm44i 54 4 . . . work_fnploejenbc2raktl46esxm44i 55 1 2 2 CD work_fnploejenbc2raktl46esxm44i 55 2 , , , work_fnploejenbc2raktl46esxm44i 55 3 pp pp NNP work_fnploejenbc2raktl46esxm44i 55 4 . . . work_fnploejenbc2raktl46esxm44i 56 1 266 266 CD work_fnploejenbc2raktl46esxm44i 56 2 et et NNP work_fnploejenbc2raktl46esxm44i 56 3 passim passim NN work_fnploejenbc2raktl46esxm44i 56 4 to to IN work_fnploejenbc2raktl46esxm44i 56 5 3333 3333 CD work_fnploejenbc2raktl46esxm44i 56 6 . . . work_fnploejenbc2raktl46esxm44i 56 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 57 1 However however RB work_fnploejenbc2raktl46esxm44i 57 2 , , , work_fnploejenbc2raktl46esxm44i 57 3 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 57 4 and and CC work_fnploejenbc2raktl46esxm44i 57 5 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 57 6 implicitly implicitly RB work_fnploejenbc2raktl46esxm44i 57 7 recognized recognize VBD work_fnploejenbc2raktl46esxm44i 57 8 the the DT work_fnploejenbc2raktl46esxm44i 57 9 natural natural JJ work_fnploejenbc2raktl46esxm44i 57 10 conjunctive conjunctive JJ work_fnploejenbc2raktl46esxm44i 57 11 chaining chaining NN work_fnploejenbc2raktl46esxm44i 57 12 relation relation NN work_fnploejenbc2raktl46esxm44i 57 13 among among IN work_fnploejenbc2raktl46esxm44i 57 14 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 57 15 events event NNS work_fnploejenbc2raktl46esxm44i 57 16 mentioned mention VBN work_fnploejenbc2raktl46esxm44i 57 17 earlier early RBR work_fnploejenbc2raktl46esxm44i 57 18 . . . work_fnploejenbc2raktl46esxm44i 58 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 58 2 Specifically specifically RB work_fnploejenbc2raktl46esxm44i 58 3 , , , work_fnploejenbc2raktl46esxm44i 58 4 see see VB work_fnploejenbc2raktl46esxm44i 58 5 the the DT work_fnploejenbc2raktl46esxm44i 58 6 remark remark NN work_fnploejenbc2raktl46esxm44i 58 7 at at IN work_fnploejenbc2raktl46esxm44i 58 8 the the DT work_fnploejenbc2raktl46esxm44i 58 9 end end NN work_fnploejenbc2raktl46esxm44i 58 10 of of IN work_fnploejenbc2raktl46esxm44i 58 11 Section section NN work_fnploejenbc2raktl46esxm44i 58 12 2.3 2.3 CD work_fnploejenbc2raktl46esxm44i 58 13 and and CC work_fnploejenbc2raktl46esxm44i 58 14 Theorems Theorems NNPS work_fnploejenbc2raktl46esxm44i 58 15 554 554 CD work_fnploejenbc2raktl46esxm44i 58 16 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 58 17 , , , work_fnploejenbc2raktl46esxm44i 58 18 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 58 19 , , , work_fnploejenbc2raktl46esxm44i 58 20 AND and CC work_fnploejenbc2raktl46esxm44i 58 21 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 58 22 3.23 3.23 CD work_fnploejenbc2raktl46esxm44i 58 23 and and CC work_fnploejenbc2raktl46esxm44i 58 24 4.21 4.21 CD work_fnploejenbc2raktl46esxm44i 58 25 ’ ' '' work_fnploejenbc2raktl46esxm44i 58 26 . . . work_fnploejenbc2raktl46esxm44i 58 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 59 1 For for IN work_fnploejenbc2raktl46esxm44i 59 2 a a DT work_fnploejenbc2raktl46esxm44i 59 3 general general JJ work_fnploejenbc2raktl46esxm44i 59 4 treatment treatment NN work_fnploejenbc2raktl46esxm44i 59 5 of of IN work_fnploejenbc2raktl46esxm44i 59 6 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 59 7 events event NNS work_fnploejenbc2raktl46esxm44i 59 8 , , , work_fnploejenbc2raktl46esxm44i 59 9 see see VB work_fnploejenbc2raktl46esxm44i 59 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 59 11 24 24 CD work_fnploejenbc2raktl46esxm44i 59 12 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 59 13 or or CC work_fnploejenbc2raktl46esxm44i 59 14 cw cw NNP work_fnploejenbc2raktl46esxm44i 59 15 Goodman Goodman NNP work_fnploejenbc2raktl46esxm44i 59 16 and and CC work_fnploejenbc2raktl46esxm44i 59 17 Nguyen Nguyen NNP work_fnploejenbc2raktl46esxm44i 59 18 have have VBP work_fnploejenbc2raktl46esxm44i 59 19 derived derive VBN work_fnploejenbc2raktl46esxm44i 59 20 a a DT work_fnploejenbc2raktl46esxm44i 59 21 full full JJ work_fnploejenbc2raktl46esxm44i 59 22 calculus calculus NN work_fnploejenbc2raktl46esxm44i 59 23 of of IN work_fnploejenbc2raktl46esxm44i 59 24 operators operator NNS work_fnploejenbc2raktl46esxm44i 59 25 and and CC work_fnploejenbc2raktl46esxm44i 59 26 relations relation NNS work_fnploejenbc2raktl46esxm44i 59 27 extending extend VBG work_fnploejenbc2raktl46esxm44i 59 28 the the DT work_fnploejenbc2raktl46esxm44i 59 29 unconditional unconditional JJ work_fnploejenbc2raktl46esxm44i 59 30 counterparts counterpart NNS work_fnploejenbc2raktl46esxm44i 59 31 for for IN work_fnploejenbc2raktl46esxm44i 59 32 boolean boolean NNP work_fnploejenbc2raktl46esxm44i 59 33 algebras algebras NNPS work_fnploejenbc2raktl46esxm44i 59 34 of of IN work_fnploejenbc2raktl46esxm44i 59 35 events event NNS work_fnploejenbc2raktl46esxm44i 59 36 to to IN work_fnploejenbc2raktl46esxm44i 59 37 the the DT work_fnploejenbc2raktl46esxm44i 59 38 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 59 39 case case NN work_fnploejenbc2raktl46esxm44i 59 40 . . . work_fnploejenbc2raktl46esxm44i 60 1 In in IN work_fnploejenbc2raktl46esxm44i 60 2 addition addition NN work_fnploejenbc2raktl46esxm44i 60 3 , , , work_fnploejenbc2raktl46esxm44i 60 4 a a DT work_fnploejenbc2raktl46esxm44i 60 5 wide wide JJ work_fnploejenbc2raktl46esxm44i 60 6 variety variety NN work_fnploejenbc2raktl46esxm44i 60 7 of of IN work_fnploejenbc2raktl46esxm44i 60 8 desirable desirable JJ work_fnploejenbc2raktl46esxm44i 60 9 mathematical mathematical JJ work_fnploejenbc2raktl46esxm44i 60 10 properties property NNS work_fnploejenbc2raktl46esxm44i 60 11 of of IN work_fnploejenbc2raktl46esxm44i 60 12 these these DT work_fnploejenbc2raktl46esxm44i 60 13 entities entity NNS work_fnploejenbc2raktl46esxm44i 60 14 have have VBP work_fnploejenbc2raktl46esxm44i 60 15 been be VBN work_fnploejenbc2raktl46esxm44i 60 16 proven prove VBN work_fnploejenbc2raktl46esxm44i 60 17 to to TO work_fnploejenbc2raktl46esxm44i 60 18 hold hold VB work_fnploejenbc2raktl46esxm44i 60 19 based base VBN work_fnploejenbc2raktl46esxm44i 60 20 upon upon IN work_fnploejenbc2raktl46esxm44i 60 21 a a DT work_fnploejenbc2raktl46esxm44i 60 22 minimal minimal JJ work_fnploejenbc2raktl46esxm44i 60 23 set set NN work_fnploejenbc2raktl46esxm44i 60 24 of of IN work_fnploejenbc2raktl46esxm44i 60 25 elementary elementary JJ work_fnploejenbc2raktl46esxm44i 60 26 assumptions assumption NNS work_fnploejenbc2raktl46esxm44i 60 27 , , , work_fnploejenbc2raktl46esxm44i 60 28 including include VBG work_fnploejenbc2raktl46esxm44i 60 29 the the DT work_fnploejenbc2raktl46esxm44i 60 30 tacitly tacitly RB work_fnploejenbc2raktl46esxm44i 60 31 assumed assume VBN work_fnploejenbc2raktl46esxm44i 60 32 conjunctive conjunctive JJ work_fnploejenbc2raktl46esxm44i 60 33 chaining chaining NN work_fnploejenbc2raktl46esxm44i 60 34 relation relation NN work_fnploejenbc2raktl46esxm44i 60 35 mentioned mention VBN work_fnploejenbc2raktl46esxm44i 60 36 above above RB work_fnploejenbc2raktl46esxm44i 60 37 . . . work_fnploejenbc2raktl46esxm44i 61 1 In in IN work_fnploejenbc2raktl46esxm44i 61 2 the the DT work_fnploejenbc2raktl46esxm44i 61 3 context context NN work_fnploejenbc2raktl46esxm44i 61 4 of of IN work_fnploejenbc2raktl46esxm44i 61 5 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 61 6 modeling modeling NN work_fnploejenbc2raktl46esxm44i 61 7 , , , work_fnploejenbc2raktl46esxm44i 61 8 the the DT work_fnploejenbc2raktl46esxm44i 61 9 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 61 10 of of IN work_fnploejenbc2raktl46esxm44i 61 11 an an DT work_fnploejenbc2raktl46esxm44i 61 12 event event NN work_fnploejenbc2raktl46esxm44i 61 13 A a NN work_fnploejenbc2raktl46esxm44i 61 14 is be VBZ work_fnploejenbc2raktl46esxm44i 61 15 , , , work_fnploejenbc2raktl46esxm44i 61 16 in in IN work_fnploejenbc2raktl46esxm44i 61 17 general general JJ work_fnploejenbc2raktl46esxm44i 61 18 , , , work_fnploejenbc2raktl46esxm44i 61 19 assigned assign VBN work_fnploejenbc2raktl46esxm44i 61 20 on on IN work_fnploejenbc2raktl46esxm44i 61 21 the the DT work_fnploejenbc2raktl46esxm44i 61 22 basis basis NN work_fnploejenbc2raktl46esxm44i 61 23 of of IN work_fnploejenbc2raktl46esxm44i 61 24 additional additional JJ work_fnploejenbc2raktl46esxm44i 61 25 information information NN work_fnploejenbc2raktl46esxm44i 61 26 , , , work_fnploejenbc2raktl46esxm44i 61 27 another another DT work_fnploejenbc2raktl46esxm44i 61 28 event event NN work_fnploejenbc2raktl46esxm44i 61 29 B. B. NNP work_fnploejenbc2raktl46esxm44i 62 1 But but CC work_fnploejenbc2raktl46esxm44i 62 2 , , , work_fnploejenbc2raktl46esxm44i 62 3 a a DT work_fnploejenbc2raktl46esxm44i 62 4 priori priori JJ work_fnploejenbc2raktl46esxm44i 62 5 , , , work_fnploejenbc2raktl46esxm44i 62 6 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 62 7 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 62 8 measure measure NN work_fnploejenbc2raktl46esxm44i 62 9 p p NNP work_fnploejenbc2raktl46esxm44i 62 10 need need NN work_fnploejenbc2raktl46esxm44i 62 11 not not RB work_fnploejenbc2raktl46esxm44i 62 12 be be VB work_fnploejenbc2raktl46esxm44i 62 13 a a DT work_fnploejenbc2raktl46esxm44i 62 14 probability probability NN work_fnploejenbc2raktl46esxm44i 62 15 so so IN work_fnploejenbc2raktl46esxm44i 62 16 that that IN work_fnploejenbc2raktl46esxm44i 62 17 an an DT work_fnploejenbc2raktl46esxm44i 62 18 algebra algebra NN work_fnploejenbc2raktl46esxm44i 62 19 of of IN work_fnploejenbc2raktl46esxm44i 62 20 measure measure NN work_fnploejenbc2raktl46esxm44i 62 21 - - HYPH work_fnploejenbc2raktl46esxm44i 62 22 free free JJ work_fnploejenbc2raktl46esxm44i 62 23 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 62 24 events event NNS work_fnploejenbc2raktl46esxm44i 62 25 has have VBZ work_fnploejenbc2raktl46esxm44i 62 26 to to TO work_fnploejenbc2raktl46esxm44i 62 27 be be VB work_fnploejenbc2raktl46esxm44i 62 28 investigated investigate VBN work_fnploejenbc2raktl46esxm44i 62 29 as as IN work_fnploejenbc2raktl46esxm44i 62 30 a a DT work_fnploejenbc2raktl46esxm44i 62 31 domain domain NN work_fnploejenbc2raktl46esxm44i 62 32 for for IN work_fnploejenbc2raktl46esxm44i 62 33 p. p. NN work_fnploejenbc2raktl46esxm44i 62 34 Now now RB work_fnploejenbc2raktl46esxm44i 62 35 let let VB work_fnploejenbc2raktl46esxm44i 62 36 d d MD work_fnploejenbc2raktl46esxm44i 62 37 be be VB work_fnploejenbc2raktl46esxm44i 62 38 the the DT work_fnploejenbc2raktl46esxm44i 62 39 class class NN work_fnploejenbc2raktl46esxm44i 62 40 of of IN work_fnploejenbc2raktl46esxm44i 62 41 all all DT work_fnploejenbc2raktl46esxm44i 62 42 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 62 43 events event NNS work_fnploejenbc2raktl46esxm44i 62 44 , , , work_fnploejenbc2raktl46esxm44i 62 45 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 62 46 , , , work_fnploejenbc2raktl46esxm44i 62 47 d= d= NNP work_fnploejenbc2raktl46esxm44i 62 48 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 62 49 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 62 50 A(B A(B NNS work_fnploejenbc2raktl46esxm44i 62 51 BE&~. BE&~. NNP work_fnploejenbc2raktl46esxm44i 63 1 By by IN work_fnploejenbc2raktl46esxm44i 63 2 the the DT work_fnploejenbc2raktl46esxm44i 63 3 identification identification NN work_fnploejenbc2raktl46esxm44i 63 4 of of IN work_fnploejenbc2raktl46esxm44i 63 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 63 6 A a DT work_fnploejenbc2raktl46esxm44i 63 7 10 10 CD work_fnploejenbc2raktl46esxm44i 63 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 63 9 with with IN work_fnploejenbc2raktl46esxm44i 63 10 A a NN work_fnploejenbc2raktl46esxm44i 63 11 , , , work_fnploejenbc2raktl46esxm44i 63 12 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 63 13 obtain obtain VBP work_fnploejenbc2raktl46esxm44i 63 14 d d NN work_fnploejenbc2raktl46esxm44i 63 15 c c NN work_fnploejenbc2raktl46esxm44i 63 16 2 2 CD work_fnploejenbc2raktl46esxm44i 63 17 . . . work_fnploejenbc2raktl46esxm44i 64 1 For for IN work_fnploejenbc2raktl46esxm44i 64 2 any any DT work_fnploejenbc2raktl46esxm44i 64 3 set set NN work_fnploejenbc2raktl46esxm44i 64 4 X x NN work_fnploejenbc2raktl46esxm44i 64 5 , , , work_fnploejenbc2raktl46esxm44i 64 6 and and CC work_fnploejenbc2raktl46esxm44i 64 7 n n CC work_fnploejenbc2raktl46esxm44i 64 8 2 2 CD work_fnploejenbc2raktl46esxm44i 64 9 1 1 CD work_fnploejenbc2raktl46esxm44i 64 10 , , , work_fnploejenbc2raktl46esxm44i 64 11 X X NNP work_fnploejenbc2raktl46esxm44i 64 12 ” " '' work_fnploejenbc2raktl46esxm44i 64 13 denotes denote VBZ work_fnploejenbc2raktl46esxm44i 64 14 the the DT work_fnploejenbc2raktl46esxm44i 64 15 product product NN work_fnploejenbc2raktl46esxm44i 64 16 space space NN work_fnploejenbc2raktl46esxm44i 64 17 Xx Xx NNP work_fnploejenbc2raktl46esxm44i 64 18 Xx Xx NNP work_fnploejenbc2raktl46esxm44i 64 19 . . . work_fnploejenbc2raktl46esxm44i 65 1 . . . work_fnploejenbc2raktl46esxm44i 66 1 . . . work_fnploejenbc2raktl46esxm44i 67 1 x x LS work_fnploejenbc2raktl46esxm44i 67 2 X X NNP work_fnploejenbc2raktl46esxm44i 67 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 67 4 n n CC work_fnploejenbc2raktl46esxm44i 67 5 times time NNS work_fnploejenbc2raktl46esxm44i 67 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 67 7 . . . work_fnploejenbc2raktl46esxm44i 68 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 68 2 will will MD work_fnploejenbc2raktl46esxm44i 68 3 use use VB work_fnploejenbc2raktl46esxm44i 68 4 the the DT work_fnploejenbc2raktl46esxm44i 68 5 notation notation NN work_fnploejenbc2raktl46esxm44i 68 6 A a NN work_fnploejenbc2raktl46esxm44i 68 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 68 8 , , , work_fnploejenbc2raktl46esxm44i 68 9 to to TO work_fnploejenbc2raktl46esxm44i 68 10 denote denote VB work_fnploejenbc2raktl46esxm44i 68 11 the the DT work_fnploejenbc2raktl46esxm44i 68 12 space space NN work_fnploejenbc2raktl46esxm44i 68 13 of of IN work_fnploejenbc2raktl46esxm44i 68 14 all all DT work_fnploejenbc2raktl46esxm44i 68 15 finite finite JJ work_fnploejenbc2raktl46esxm44i 68 16 n n NNP work_fnploejenbc2raktl46esxm44i 68 17 - - HYPH work_fnploejenbc2raktl46esxm44i 68 18 tuples tuple NNS work_fnploejenbc2raktl46esxm44i 68 19 { { -LRB- work_fnploejenbc2raktl46esxm44i 68 20 a a DT work_fnploejenbc2raktl46esxm44i 68 21 , , , work_fnploejenbc2raktl46esxm44i 68 22 : : : work_fnploejenbc2raktl46esxm44i 68 23 f f LS work_fnploejenbc2raktl46esxm44i 68 24 , , , work_fnploejenbc2raktl46esxm44i 68 25 = = NFP work_fnploejenbc2raktl46esxm44i 68 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 68 27 x x UH work_fnploejenbc2raktl46esxm44i 68 28 , , , work_fnploejenbc2raktl46esxm44i 68 29 , , , work_fnploejenbc2raktl46esxm44i 68 30 . . . work_fnploejenbc2raktl46esxm44i 69 1 . . . work_fnploejenbc2raktl46esxm44i 70 1 . . . work_fnploejenbc2raktl46esxm44i 71 1 . . . work_fnploejenbc2raktl46esxm44i 72 1 x x LS work_fnploejenbc2raktl46esxm44i 72 2 , , , work_fnploejenbc2raktl46esxm44i 72 3 , , , work_fnploejenbc2raktl46esxm44i 72 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 72 5 , , , work_fnploejenbc2raktl46esxm44i 72 6 xi xi NNP work_fnploejenbc2raktl46esxm44i 72 7 E E NNP work_fnploejenbc2raktl46esxm44i 72 8 A a NN work_fnploejenbc2raktl46esxm44i 72 9 ’ ' '' work_fnploejenbc2raktl46esxm44i 72 10 } } -RRB- work_fnploejenbc2raktl46esxm44i 72 11 . . . work_fnploejenbc2raktl46esxm44i 73 1 Unless unless IN work_fnploejenbc2raktl46esxm44i 73 2 otherwise otherwise RB work_fnploejenbc2raktl46esxm44i 73 3 indicated indicate VBN work_fnploejenbc2raktl46esxm44i 73 4 , , , work_fnploejenbc2raktl46esxm44i 73 5 “ " `` work_fnploejenbc2raktl46esxm44i 73 6 xi xi NNP work_fnploejenbc2raktl46esxm44i 73 7 E E NNP work_fnploejenbc2raktl46esxm44i 73 8 x x NN work_fnploejenbc2raktl46esxm44i 73 9 ” " '' work_fnploejenbc2raktl46esxm44i 73 10 and and CC work_fnploejenbc2raktl46esxm44i 73 11 the the DT work_fnploejenbc2raktl46esxm44i 73 12 like like JJ work_fnploejenbc2raktl46esxm44i 73 13 will will MD work_fnploejenbc2raktl46esxm44i 73 14 always always RB work_fnploejenbc2raktl46esxm44i 73 15 mean mean VB work_fnploejenbc2raktl46esxm44i 73 16 xi xi NNP work_fnploejenbc2raktl46esxm44i 73 17 , , , work_fnploejenbc2raktl46esxm44i 73 18 . . . work_fnploejenbc2raktl46esxm44i 74 1 . . . work_fnploejenbc2raktl46esxm44i 75 1 . . . work_fnploejenbc2raktl46esxm44i 76 1 . . . work_fnploejenbc2raktl46esxm44i 77 1 x x LS work_fnploejenbc2raktl46esxm44i 77 2 , , , work_fnploejenbc2raktl46esxm44i 77 3 for for IN work_fnploejenbc2raktl46esxm44i 77 4 a a DT work_fnploejenbc2raktl46esxm44i 77 5 generic generic JJ work_fnploejenbc2raktl46esxm44i 77 6 n. n. NN work_fnploejenbc2raktl46esxm44i 77 7 For for IN work_fnploejenbc2raktl46esxm44i 77 8 Al Al NNP work_fnploejenbc2raktl46esxm44i 77 9 , , , work_fnploejenbc2raktl46esxm44i 77 10 = = NFP work_fnploejenbc2raktl46esxm44i 77 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 77 12 A a DT work_fnploejenbc2raktl46esxm44i 77 13 1 1 CD work_fnploejenbc2raktl46esxm44i 77 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 77 15 . . . work_fnploejenbc2raktl46esxm44i 78 1 . . . work_fnploejenbc2raktl46esxm44i 79 1 . . . work_fnploejenbc2raktl46esxm44i 80 1 . . . work_fnploejenbc2raktl46esxm44i 81 1 A,,)EJP a,,)ejp ADD work_fnploejenbc2raktl46esxm44i 81 2 , , , work_fnploejenbc2raktl46esxm44i 81 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 81 4 identify identify VBP work_fnploejenbc2raktl46esxm44i 81 5 A a DT work_fnploejenbc2raktl46esxm44i 81 6 , , , work_fnploejenbc2raktl46esxm44i 81 7 with with IN work_fnploejenbc2raktl46esxm44i 81 8 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 81 9 indicator indicator NN work_fnploejenbc2raktl46esxm44i 81 10 function function NN work_fnploejenbc2raktl46esxm44i 81 11 A,(o A,(o NNP work_fnploejenbc2raktl46esxm44i 81 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 81 13 defined define VBN work_fnploejenbc2raktl46esxm44i 81 14 as as IN work_fnploejenbc2raktl46esxm44i 81 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 81 16 A,(o a,(o NN work_fnploejenbc2raktl46esxm44i 81 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 81 18 , , , work_fnploejenbc2raktl46esxm44i 81 19 . . . work_fnploejenbc2raktl46esxm44i 82 1 . . . work_fnploejenbc2raktl46esxm44i 83 1 . . . work_fnploejenbc2raktl46esxm44i 84 1 . . . work_fnploejenbc2raktl46esxm44i 85 1 A,(w))E A,(w))E NNP work_fnploejenbc2raktl46esxm44i 85 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 85 3 0 0 CD work_fnploejenbc2raktl46esxm44i 85 4 , , , work_fnploejenbc2raktl46esxm44i 85 5 l l NN work_fnploejenbc2raktl46esxm44i 85 6 } } -RRB- work_fnploejenbc2raktl46esxm44i 85 7 “ " '' work_fnploejenbc2raktl46esxm44i 85 8 . . . work_fnploejenbc2raktl46esxm44i 86 1 For for IN work_fnploejenbc2raktl46esxm44i 86 2 example example NN work_fnploejenbc2raktl46esxm44i 86 3 , , , work_fnploejenbc2raktl46esxm44i 86 4 as(o as(o NNP work_fnploejenbc2raktl46esxm44i 86 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 86 6 = = NFP work_fnploejenbc2raktl46esxm44i 86 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 86 8 1 1 CD work_fnploejenbc2raktl46esxm44i 86 9 , , , work_fnploejenbc2raktl46esxm44i 86 10 1 1 CD work_fnploejenbc2raktl46esxm44i 86 11 , , , work_fnploejenbc2raktl46esxm44i 86 12 0 0 CD work_fnploejenbc2raktl46esxm44i 86 13 , , , work_fnploejenbc2raktl46esxm44i 86 14 0 0 CD work_fnploejenbc2raktl46esxm44i 86 15 , , , work_fnploejenbc2raktl46esxm44i 86 16 0,O 0,o CD work_fnploejenbc2raktl46esxm44i 86 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 86 18 indicates indicate VBZ work_fnploejenbc2raktl46esxm44i 86 19 that that IN work_fnploejenbc2raktl46esxm44i 86 20 A A NNP work_fnploejenbc2raktl46esxm44i 86 21 , , , work_fnploejenbc2raktl46esxm44i 86 22 , , , work_fnploejenbc2raktl46esxm44i 86 23 A2 A2 NNP work_fnploejenbc2raktl46esxm44i 86 24 occurred occur VBD work_fnploejenbc2raktl46esxm44i 86 25 but but CC work_fnploejenbc2raktl46esxm44i 86 26 A3 a3 NN work_fnploejenbc2raktl46esxm44i 86 27 , , , work_fnploejenbc2raktl46esxm44i 86 28 Ah ah UH work_fnploejenbc2raktl46esxm44i 86 29 , , , work_fnploejenbc2raktl46esxm44i 86 30 A a NN work_fnploejenbc2raktl46esxm44i 86 31 , , , work_fnploejenbc2raktl46esxm44i 86 32 , , , work_fnploejenbc2raktl46esxm44i 86 33 A A NNP work_fnploejenbc2raktl46esxm44i 86 34 , , , work_fnploejenbc2raktl46esxm44i 86 35 did do VBD work_fnploejenbc2raktl46esxm44i 86 36 not not RB work_fnploejenbc2raktl46esxm44i 86 37 occur occur VB work_fnploejenbc2raktl46esxm44i 86 38 . . . work_fnploejenbc2raktl46esxm44i 87 1 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 87 2 , , , work_fnploejenbc2raktl46esxm44i 87 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 87 4 identify identify VBP work_fnploejenbc2raktl46esxm44i 87 5 with with IN work_fnploejenbc2raktl46esxm44i 87 6 the the DT work_fnploejenbc2raktl46esxm44i 87 7 function function NN work_fnploejenbc2raktl46esxm44i 87 8 a a DT work_fnploejenbc2raktl46esxm44i 87 9 , , , work_fnploejenbc2raktl46esxm44i 87 10 : : : work_fnploejenbc2raktl46esxm44i 87 11 B b NN work_fnploejenbc2raktl46esxm44i 87 12 + + CC work_fnploejenbc2raktl46esxm44i 87 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 87 14 0 0 CD work_fnploejenbc2raktl46esxm44i 87 15 , , , work_fnploejenbc2raktl46esxm44i 87 16 1 1 CD work_fnploejenbc2raktl46esxm44i 87 17 , , , work_fnploejenbc2raktl46esxm44i 87 18 u u NNP work_fnploejenbc2raktl46esxm44i 87 19 } } -RRB- work_fnploejenbc2raktl46esxm44i 87 20 ” " `` work_fnploejenbc2raktl46esxm44i 87 21 having have VBG work_fnploejenbc2raktl46esxm44i 87 22 values value NNS work_fnploejenbc2raktl46esxm44i 87 23 -&w -&w . work_fnploejenbc2raktl46esxm44i 87 24 = = FW work_fnploejenbc2raktl46esxm44i 87 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 87 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 87 27 4 4 CD work_fnploejenbc2raktl46esxm44i 87 28 I i NN work_fnploejenbc2raktl46esxm44i 87 29 F,)(o F,)(o NNP work_fnploejenbc2raktl46esxm44i 87 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 87 31 , , , work_fnploejenbc2raktl46esxm44i 87 32 . . . work_fnploejenbc2raktl46esxm44i 88 1 * * NFP work_fnploejenbc2raktl46esxm44i 88 2 a a LS work_fnploejenbc2raktl46esxm44i 88 3 , , , work_fnploejenbc2raktl46esxm44i 88 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 88 5 J% j% NN work_fnploejenbc2raktl46esxm44i 88 6 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 88 7 J J NNP work_fnploejenbc2raktl46esxm44i 88 8 - - HYPH work_fnploejenbc2raktl46esxm44i 88 9 n)(o n)(o NNP work_fnploejenbc2raktl46esxm44i 88 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 88 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 88 12 E e NN work_fnploejenbc2raktl46esxm44i 88 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 88 14 0 0 CD work_fnploejenbc2raktl46esxm44i 88 15 , , , work_fnploejenbc2raktl46esxm44i 88 16 1 1 CD work_fnploejenbc2raktl46esxm44i 88 17 , , , work_fnploejenbc2raktl46esxm44i 88 18 q. q. NNP work_fnploejenbc2raktl46esxm44i 89 1 2.2 2.2 CD work_fnploejenbc2raktl46esxm44i 89 2 . . . work_fnploejenbc2raktl46esxm44i 90 1 Uncertainty Uncertainty NNP work_fnploejenbc2raktl46esxm44i 90 2 Games Games NNPS work_fnploejenbc2raktl46esxm44i 90 3 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 90 4 proceed proceed VBP work_fnploejenbc2raktl46esxm44i 90 5 now now RB work_fnploejenbc2raktl46esxm44i 90 6 to to TO work_fnploejenbc2raktl46esxm44i 90 7 formalize formalize VB work_fnploejenbc2raktl46esxm44i 90 8 a a DT work_fnploejenbc2raktl46esxm44i 90 9 special special JJ work_fnploejenbc2raktl46esxm44i 90 10 class class NN work_fnploejenbc2raktl46esxm44i 90 11 of of IN work_fnploejenbc2raktl46esxm44i 90 12 games game NNS work_fnploejenbc2raktl46esxm44i 90 13 called call VBN work_fnploejenbc2raktl46esxm44i 90 14 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 90 15 games game NNS work_fnploejenbc2raktl46esxm44i 90 16 . . . work_fnploejenbc2raktl46esxm44i 91 1 Roughly roughly RB work_fnploejenbc2raktl46esxm44i 91 2 speaking speak VBG work_fnploejenbc2raktl46esxm44i 91 3 , , , work_fnploejenbc2raktl46esxm44i 91 4 these these DT work_fnploejenbc2raktl46esxm44i 91 5 are be VBP work_fnploejenbc2raktl46esxm44i 91 6 triples triple NNS work_fnploejenbc2raktl46esxm44i 91 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 91 8 A a NN work_fnploejenbc2raktl46esxm44i 91 9 , , , work_fnploejenbc2raktl46esxm44i 91 10 , , , work_fnploejenbc2raktl46esxm44i 91 11 A a NN work_fnploejenbc2raktl46esxm44i 91 12 , , , work_fnploejenbc2raktl46esxm44i 91 13 , , , work_fnploejenbc2raktl46esxm44i 91 14 L l NN work_fnploejenbc2raktl46esxm44i 91 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 91 16 in in IN work_fnploejenbc2raktl46esxm44i 91 17 which which WDT work_fnploejenbc2raktl46esxm44i 91 18 A A NNP work_fnploejenbc2raktl46esxm44i 91 19 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 91 20 is be VBZ work_fnploejenbc2raktl46esxm44i 91 21 a a DT work_fnploejenbc2raktl46esxm44i 91 22 set set NN work_fnploejenbc2raktl46esxm44i 91 23 of of IN work_fnploejenbc2raktl46esxm44i 91 24 configurations configuration NNS work_fnploejenbc2raktl46esxm44i 91 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 91 26 or or CC work_fnploejenbc2raktl46esxm44i 91 27 realizations realization NNS work_fnploejenbc2raktl46esxm44i 91 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 91 29 of of IN work_fnploejenbc2raktl46esxm44i 91 30 finite finite JJ work_fnploejenbc2raktl46esxm44i 91 31 collections collection NNS work_fnploejenbc2raktl46esxm44i 91 32 of of IN work_fnploejenbc2raktl46esxm44i 91 33 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 91 34 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 91 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 91 36 events event NNS work_fnploejenbc2raktl46esxm44i 91 37 , , , work_fnploejenbc2raktl46esxm44i 91 38 A a NN work_fnploejenbc2raktl46esxm44i 91 39 , , , work_fnploejenbc2raktl46esxm44i 91 40 is be VBZ work_fnploejenbc2raktl46esxm44i 91 41 a a DT work_fnploejenbc2raktl46esxm44i 91 42 collection collection NN work_fnploejenbc2raktl46esxm44i 91 43 of of IN work_fnploejenbc2raktl46esxm44i 91 44 “ " `` work_fnploejenbc2raktl46esxm44i 91 45 set’‘-functions set’‘-functions NN work_fnploejenbc2raktl46esxm44i 91 46 representing represent VBG work_fnploejenbc2raktl46esxm44i 91 47 “ " `` work_fnploejenbc2raktl46esxm44i 91 48 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 91 49 measures measure NNS work_fnploejenbc2raktl46esxm44i 91 50 , , , work_fnploejenbc2raktl46esxm44i 91 51 ” " '' work_fnploejenbc2raktl46esxm44i 91 52 and and CC work_fnploejenbc2raktl46esxm44i 91 53 L l NN work_fnploejenbc2raktl46esxm44i 91 54 is be VBZ work_fnploejenbc2raktl46esxm44i 91 55 a a DT work_fnploejenbc2raktl46esxm44i 91 56 real real RB work_fnploejenbc2raktl46esxm44i 91 57 - - HYPH work_fnploejenbc2raktl46esxm44i 91 58 valued value VBN work_fnploejenbc2raktl46esxm44i 91 59 loss loss NN work_fnploejenbc2raktl46esxm44i 91 60 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 91 61 or or CC work_fnploejenbc2raktl46esxm44i 91 62 penalty penalty NN work_fnploejenbc2raktl46esxm44i 91 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 91 64 function function NN work_fnploejenbc2raktl46esxm44i 91 65 . . . work_fnploejenbc2raktl46esxm44i 92 1 Specifically specifically RB work_fnploejenbc2raktl46esxm44i 92 2 , , , work_fnploejenbc2raktl46esxm44i 92 3 A a NN work_fnploejenbc2raktl46esxm44i 92 4 , , , work_fnploejenbc2raktl46esxm44i 92 5 = = NFP work_fnploejenbc2raktl46esxm44i 92 6 Jm Jm NNP work_fnploejenbc2raktl46esxm44i 92 7 x x NNP work_fnploejenbc2raktl46esxm44i 92 8 Q. Q. NNP work_fnploejenbc2raktl46esxm44i 93 1 This this DT work_fnploejenbc2raktl46esxm44i 93 2 set set VBD work_fnploejenbc2raktl46esxm44i 93 3 A a DT work_fnploejenbc2raktl46esxm44i 93 4 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 93 5 is be VBZ work_fnploejenbc2raktl46esxm44i 93 6 regarded regard VBN work_fnploejenbc2raktl46esxm44i 93 7 as as IN work_fnploejenbc2raktl46esxm44i 93 8 the the DT work_fnploejenbc2raktl46esxm44i 93 9 space space NN work_fnploejenbc2raktl46esxm44i 93 10 of of IN work_fnploejenbc2raktl46esxm44i 93 11 all all DT work_fnploejenbc2raktl46esxm44i 93 12 possible possible JJ work_fnploejenbc2raktl46esxm44i 93 13 “ " `` work_fnploejenbc2raktl46esxm44i 93 14 moves move NNS work_fnploejenbc2raktl46esxm44i 93 15 ” " '' work_fnploejenbc2raktl46esxm44i 93 16 or or CC work_fnploejenbc2raktl46esxm44i 93 17 “ " `` work_fnploejenbc2raktl46esxm44i 93 18 pure pure JJ work_fnploejenbc2raktl46esxm44i 93 19 strategies strategy NNS work_fnploejenbc2raktl46esxm44i 93 20 ” " '' work_fnploejenbc2raktl46esxm44i 93 21 of of IN work_fnploejenbc2raktl46esxm44i 93 22 player player NN work_fnploejenbc2raktl46esxm44i 93 23 I. I. NNP work_fnploejenbc2raktl46esxm44i 94 1 Next next RB work_fnploejenbc2raktl46esxm44i 94 2 , , , work_fnploejenbc2raktl46esxm44i 94 3 fix fix NN work_fnploejenbc2raktl46esxm44i 94 4 , , , work_fnploejenbc2raktl46esxm44i 94 5 once once RB work_fnploejenbc2raktl46esxm44i 94 6 for for IN work_fnploejenbc2raktl46esxm44i 94 7 all all DT work_fnploejenbc2raktl46esxm44i 94 8 , , , work_fnploejenbc2raktl46esxm44i 94 9 four four CD work_fnploejenbc2raktl46esxm44i 94 10 real real JJ work_fnploejenbc2raktl46esxm44i 94 11 numbers number NNS work_fnploejenbc2raktl46esxm44i 94 12 , , , work_fnploejenbc2raktl46esxm44i 94 13 a2 a2 NNP work_fnploejenbc2raktl46esxm44i 94 14 < < XX work_fnploejenbc2raktl46esxm44i 94 15 a a XX work_fnploejenbc2raktl46esxm44i 94 16 , , , work_fnploejenbc2raktl46esxm44i 94 17 < < XX work_fnploejenbc2raktl46esxm44i 94 18 a a XX work_fnploejenbc2raktl46esxm44i 94 19 , , , work_fnploejenbc2raktl46esxm44i 94 20 < < XX work_fnploejenbc2raktl46esxm44i 94 21 a a XX work_fnploejenbc2raktl46esxm44i 94 22 , , , work_fnploejenbc2raktl46esxm44i 94 23 ; ; : work_fnploejenbc2raktl46esxm44i 94 24 let let VB work_fnploejenbc2raktl46esxm44i 94 25 A,= A,= NNP work_fnploejenbc2raktl46esxm44i 94 26 { { -LRB- work_fnploejenbc2raktl46esxm44i 94 27 , , , work_fnploejenbc2raktl46esxm44i 94 28 u u LS work_fnploejenbc2raktl46esxm44i 94 29 : : : work_fnploejenbc2raktl46esxm44i 94 30 P p NN work_fnploejenbc2raktl46esxm44i 94 31 : : : work_fnploejenbc2raktl46esxm44i 94 32 d+ d+ CD work_fnploejenbc2raktl46esxm44i 94 33 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 94 34 a a DT work_fnploejenbc2raktl46esxm44i 94 35 , , , work_fnploejenbc2raktl46esxm44i 94 36 , , , work_fnploejenbc2raktl46esxm44i 94 37 aJ aJ NNP work_fnploejenbc2raktl46esxm44i 94 38 } } -RRB- work_fnploejenbc2raktl46esxm44i 94 39 = = NFP work_fnploejenbc2raktl46esxm44i 94 40 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 94 41 a a DT work_fnploejenbc2raktl46esxm44i 94 42 * * NFP work_fnploejenbc2raktl46esxm44i 94 43 , , , work_fnploejenbc2raktl46esxm44i 94 44 a3]“l a3]“l ADD work_fnploejenbc2raktl46esxm44i 94 45 . . . work_fnploejenbc2raktl46esxm44i 95 1 Each each DT work_fnploejenbc2raktl46esxm44i 95 2 element element NN work_fnploejenbc2raktl46esxm44i 95 3 of of IN work_fnploejenbc2raktl46esxm44i 95 4 A a DT work_fnploejenbc2raktl46esxm44i 95 5 , , , work_fnploejenbc2raktl46esxm44i 95 6 is be VBZ work_fnploejenbc2raktl46esxm44i 95 7 a a DT work_fnploejenbc2raktl46esxm44i 95 8 map map NN work_fnploejenbc2raktl46esxm44i 95 9 , , , work_fnploejenbc2raktl46esxm44i 95 10 SCORING score VBG work_fnploejenbc2raktl46esxm44i 95 11 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 95 12 TO to IN work_fnploejenbc2raktl46esxm44i 95 13 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 95 14 555 555 CD work_fnploejenbc2raktl46esxm44i 95 15 which which WDT work_fnploejenbc2raktl46esxm44i 95 16 assigns assign VBZ work_fnploejenbc2raktl46esxm44i 95 17 a a DT work_fnploejenbc2raktl46esxm44i 95 18 number number NN work_fnploejenbc2raktl46esxm44i 95 19 , , , work_fnploejenbc2raktl46esxm44i 95 20 describing describe VBG work_fnploejenbc2raktl46esxm44i 95 21 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 95 22 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 95 23 , , , work_fnploejenbc2raktl46esxm44i 95 24 to to IN work_fnploejenbc2raktl46esxm44i 95 25 each each DT work_fnploejenbc2raktl46esxm44i 95 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 95 27 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 95 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 95 29 event event NN work_fnploejenbc2raktl46esxm44i 95 30 . . . work_fnploejenbc2raktl46esxm44i 96 1 A2 A2 NNP work_fnploejenbc2raktl46esxm44i 96 2 is be VBZ work_fnploejenbc2raktl46esxm44i 96 3 regarded regard VBN work_fnploejenbc2raktl46esxm44i 96 4 as as IN work_fnploejenbc2raktl46esxm44i 96 5 the the DT work_fnploejenbc2raktl46esxm44i 96 6 space space NN work_fnploejenbc2raktl46esxm44i 96 7 of of IN work_fnploejenbc2raktl46esxm44i 96 8 “ " `` work_fnploejenbc2raktl46esxm44i 96 9 moves move NNS work_fnploejenbc2raktl46esxm44i 96 10 ” " '' work_fnploejenbc2raktl46esxm44i 96 11 of of IN work_fnploejenbc2raktl46esxm44i 96 12 player player NN work_fnploejenbc2raktl46esxm44i 96 13 II II NNP work_fnploejenbc2raktl46esxm44i 96 14 . . . work_fnploejenbc2raktl46esxm44i 97 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 97 2 now now RB work_fnploejenbc2raktl46esxm44i 97 3 the the DT work_fnploejenbc2raktl46esxm44i 97 4 choice choice NN work_fnploejenbc2raktl46esxm44i 97 5 of of IN work_fnploejenbc2raktl46esxm44i 97 6 loss loss NN work_fnploejenbc2raktl46esxm44i 97 7 function function NN work_fnploejenbc2raktl46esxm44i 97 8 . . . work_fnploejenbc2raktl46esxm44i 98 1 This this DT work_fnploejenbc2raktl46esxm44i 98 2 is be VBZ work_fnploejenbc2raktl46esxm44i 98 3 carried carry VBN work_fnploejenbc2raktl46esxm44i 98 4 out out RP work_fnploejenbc2raktl46esxm44i 98 5 in in IN work_fnploejenbc2raktl46esxm44i 98 6 two two CD work_fnploejenbc2raktl46esxm44i 98 7 stages stage NNS work_fnploejenbc2raktl46esxm44i 98 8 as as IN work_fnploejenbc2raktl46esxm44i 98 9 the the DT work_fnploejenbc2raktl46esxm44i 98 10 composition composition NN work_fnploejenbc2raktl46esxm44i 98 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 98 12 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 98 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 98 14 of of IN work_fnploejenbc2raktl46esxm44i 98 15 other other JJ work_fnploejenbc2raktl46esxm44i 98 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 98 17 score score NN work_fnploejenbc2raktl46esxm44i 98 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 98 19 functions function NNS work_fnploejenbc2raktl46esxm44i 98 20 . . . work_fnploejenbc2raktl46esxm44i 99 1 As as IN work_fnploejenbc2raktl46esxm44i 99 2 in in IN work_fnploejenbc2raktl46esxm44i 99 3 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 99 4 ’s ’s POS work_fnploejenbc2raktl46esxm44i 99 5 paper paper NN work_fnploejenbc2raktl46esxm44i 99 6 , , , work_fnploejenbc2raktl46esxm44i 99 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 99 8 call call VBP work_fnploejenbc2raktl46esxm44i 99 9 any any DT work_fnploejenbc2raktl46esxm44i 99 10 function function NN work_fnploejenbc2raktl46esxm44i 99 11 f f XX work_fnploejenbc2raktl46esxm44i 99 12 : : : work_fnploejenbc2raktl46esxm44i 99 13 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 99 14 a a DT work_fnploejenbc2raktl46esxm44i 99 15 , , , work_fnploejenbc2raktl46esxm44i 99 16 , , , work_fnploejenbc2raktl46esxm44i 99 17 a3 a3 NNP work_fnploejenbc2raktl46esxm44i 99 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 99 19 x x NN work_fnploejenbc2raktl46esxm44i 99 20 { { -LRB- work_fnploejenbc2raktl46esxm44i 99 21 0 0 CD work_fnploejenbc2raktl46esxm44i 99 22 , , , work_fnploejenbc2raktl46esxm44i 99 23 1 1 CD work_fnploejenbc2raktl46esxm44i 99 24 , , , work_fnploejenbc2raktl46esxm44i 99 25 U u NN work_fnploejenbc2raktl46esxm44i 99 26 > > XX work_fnploejenbc2raktl46esxm44i 99 27 -+ -+ . work_fnploejenbc2raktl46esxm44i 99 28 R r NN work_fnploejenbc2raktl46esxm44i 99 29 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 30 the the DT work_fnploejenbc2raktl46esxm44i 99 31 real real JJ work_fnploejenbc2raktl46esxm44i 99 32 numbers number NNS work_fnploejenbc2raktl46esxm44i 99 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 34 , , , work_fnploejenbc2raktl46esxm44i 99 35 a a DT work_fnploejenbc2raktl46esxm44i 99 36 score score NN work_fnploejenbc2raktl46esxm44i 99 37 function function NN work_fnploejenbc2raktl46esxm44i 99 38 if if IN work_fnploejenbc2raktl46esxm44i 99 39 the the DT work_fnploejenbc2raktl46esxm44i 99 40 following follow VBG work_fnploejenbc2raktl46esxm44i 99 41 are be VBP work_fnploejenbc2raktl46esxm44i 99 42 satisfied satisfied JJ work_fnploejenbc2raktl46esxm44i 99 43 : : : work_fnploejenbc2raktl46esxm44i 99 44 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 45 i i NN work_fnploejenbc2raktl46esxm44i 99 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 47 For for IN work_fnploejenbc2raktl46esxm44i 99 48 each each DT work_fnploejenbc2raktl46esxm44i 99 49 Jo Jo NNP work_fnploejenbc2raktl46esxm44i 99 50 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 51 0 0 CD work_fnploejenbc2raktl46esxm44i 99 52 , , , work_fnploejenbc2raktl46esxm44i 99 53 l l NN work_fnploejenbc2raktl46esxm44i 99 54 } } -RRB- work_fnploejenbc2raktl46esxm44i 99 55 , , , work_fnploejenbc2raktl46esxm44i 99 56 f f NNP work_fnploejenbc2raktl46esxm44i 99 57 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 58 . . . work_fnploejenbc2raktl46esxm44i 99 59 , , , work_fnploejenbc2raktl46esxm44i 99 60 j j NNP work_fnploejenbc2raktl46esxm44i 99 61 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 62 : : : work_fnploejenbc2raktl46esxm44i 99 63 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 99 64 a a DT work_fnploejenbc2raktl46esxm44i 99 65 , , , work_fnploejenbc2raktl46esxm44i 99 66 , , , work_fnploejenbc2raktl46esxm44i 99 67 a31 a31 NN work_fnploejenbc2raktl46esxm44i 99 68 -+ -+ : work_fnploejenbc2raktl46esxm44i 99 69 If3 if3 NN work_fnploejenbc2raktl46esxm44i 99 70 satisfies satisfie NNS work_fnploejenbc2raktl46esxm44i 99 71 the the DT work_fnploejenbc2raktl46esxm44i 99 72 following follow VBG work_fnploejenbc2raktl46esxm44i 99 73 “ " `` work_fnploejenbc2raktl46esxm44i 99 74 regularity regularity NN work_fnploejenbc2raktl46esxm44i 99 75 ” " '' work_fnploejenbc2raktl46esxm44i 99 76 conditions condition NNS work_fnploejenbc2raktl46esxm44i 99 77 : : : work_fnploejenbc2raktl46esxm44i 99 78 f f NNP work_fnploejenbc2raktl46esxm44i 99 79 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 80 . . . work_fnploejenbc2raktl46esxm44i 99 81 , , , work_fnploejenbc2raktl46esxm44i 99 82 j j NNP work_fnploejenbc2raktl46esxm44i 99 83 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 84 is be VBZ work_fnploejenbc2raktl46esxm44i 99 85 continuously continuously RB work_fnploejenbc2raktl46esxm44i 99 86 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 99 87 , , , work_fnploejenbc2raktl46esxm44i 99 88 with with IN work_fnploejenbc2raktl46esxm44i 99 89 a a DT work_fnploejenbc2raktl46esxm44i 99 90 unique unique JJ work_fnploejenbc2raktl46esxm44i 99 91 global global JJ work_fnploejenbc2raktl46esxm44i 99 92 minimum minimum NN work_fnploejenbc2raktl46esxm44i 99 93 in in IN work_fnploejenbc2raktl46esxm44i 99 94 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 99 95 a a DT work_fnploejenbc2raktl46esxm44i 99 96 , , , work_fnploejenbc2raktl46esxm44i 99 97 , , , work_fnploejenbc2raktl46esxm44i 99 98 a a DT work_fnploejenbc2raktl46esxm44i 99 99 , , , work_fnploejenbc2raktl46esxm44i 99 100 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 99 101 at at IN work_fnploejenbc2raktl46esxm44i 99 102 aj aj NNP work_fnploejenbc2raktl46esxm44i 99 103 , , , work_fnploejenbc2raktl46esxm44i 99 104 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 105 decreasing decrease VBG work_fnploejenbc2raktl46esxm44i 99 106 over over IN work_fnploejenbc2raktl46esxm44i 99 107 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 99 108 a a DT work_fnploejenbc2raktl46esxm44i 99 109 , , , work_fnploejenbc2raktl46esxm44i 99 110 , , , work_fnploejenbc2raktl46esxm44i 99 111 ai ai VB work_fnploejenbc2raktl46esxm44i 99 112 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 99 113 and and CC work_fnploejenbc2raktl46esxm44i 99 114 increasing increase VBG work_fnploejenbc2raktl46esxm44i 99 115 over over IN work_fnploejenbc2raktl46esxm44i 99 116 Cq Cq NNP work_fnploejenbc2raktl46esxm44i 99 117 , , , work_fnploejenbc2raktl46esxm44i 99 118 ~~1 ~~1 NNP work_fnploejenbc2raktl46esxm44i 99 119 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 120 ; ; : work_fnploejenbc2raktl46esxm44i 99 121 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 99 122 ii ii NNP work_fnploejenbc2raktl46esxm44i 99 123 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 124 .f(x .f(x . work_fnploejenbc2raktl46esxm44i 99 125 , , , work_fnploejenbc2raktl46esxm44i 99 126 24 24 CD work_fnploejenbc2raktl46esxm44i 99 127 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 99 128 = = SYM work_fnploejenbc2raktl46esxm44i 99 129 0 0 NFP work_fnploejenbc2raktl46esxm44i 99 130 , , , work_fnploejenbc2raktl46esxm44i 99 131 Vx Vx NNP work_fnploejenbc2raktl46esxm44i 99 132 E E NNP work_fnploejenbc2raktl46esxm44i 99 133 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 99 134 a a DT work_fnploejenbc2raktl46esxm44i 99 135 , , , work_fnploejenbc2raktl46esxm44i 99 136 , , , work_fnploejenbc2raktl46esxm44i 99 137 ax ax NN work_fnploejenbc2raktl46esxm44i 99 138 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 99 139 . . . work_fnploejenbc2raktl46esxm44i 100 1 For for IN work_fnploejenbc2raktl46esxm44i 100 2 example example NN work_fnploejenbc2raktl46esxm44i 100 3 , , , work_fnploejenbc2raktl46esxm44i 100 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 100 5 may may MD work_fnploejenbc2raktl46esxm44i 100 6 interpret interpret VB work_fnploejenbc2raktl46esxm44i 100 7 the the DT work_fnploejenbc2raktl46esxm44i 100 8 score score NN work_fnploejenbc2raktl46esxm44i 100 9 function function NN work_fnploejenbc2raktl46esxm44i 100 10 as as IN work_fnploejenbc2raktl46esxm44i 100 11 follows follow VBZ work_fnploejenbc2raktl46esxm44i 100 12 : : : work_fnploejenbc2raktl46esxm44i 100 13 player player NN work_fnploejenbc2raktl46esxm44i 100 14 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 100 15 has have VBZ work_fnploejenbc2raktl46esxm44i 100 16 selected select VBN work_fnploejenbc2raktl46esxm44i 100 17 A a DT work_fnploejenbc2raktl46esxm44i 100 18 E e NN work_fnploejenbc2raktl46esxm44i 100 19 & & CC work_fnploejenbc2raktl46esxm44i 100 20 and and CC work_fnploejenbc2raktl46esxm44i 100 21 o o NN work_fnploejenbc2raktl46esxm44i 100 22 E E NNP work_fnploejenbc2raktl46esxm44i 100 23 Q q NN work_fnploejenbc2raktl46esxm44i 100 24 and and CC work_fnploejenbc2raktl46esxm44i 100 25 player player NN work_fnploejenbc2raktl46esxm44i 100 26 II II NNP work_fnploejenbc2raktl46esxm44i 100 27 has have VBZ work_fnploejenbc2raktl46esxm44i 100 28 selected select VBN work_fnploejenbc2raktl46esxm44i 100 29 p p NN work_fnploejenbc2raktl46esxm44i 100 30 E e NN work_fnploejenbc2raktl46esxm44i 100 31 AZ AZ NNP work_fnploejenbc2raktl46esxm44i 100 32 , , , work_fnploejenbc2raktl46esxm44i 100 33 then then RB work_fnploejenbc2raktl46esxm44i 100 34 the the DT work_fnploejenbc2raktl46esxm44i 100 35 score score NN work_fnploejenbc2raktl46esxm44i 100 36 for for IN work_fnploejenbc2raktl46esxm44i 100 37 player player NN work_fnploejenbc2raktl46esxm44i 100 38 II II NNP work_fnploejenbc2raktl46esxm44i 100 39 is be VBZ work_fnploejenbc2raktl46esxm44i 100 40 & & CC work_fnploejenbc2raktl46esxm44i 100 41 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 100 42 A a NN work_fnploejenbc2raktl46esxm44i 100 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 100 44 , , , work_fnploejenbc2raktl46esxm44i 100 45 1 1 LS work_fnploejenbc2raktl46esxm44i 100 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 100 47 if if IN work_fnploejenbc2raktl46esxm44i 100 48 A a DT work_fnploejenbc2raktl46esxm44i 100 49 happens happen VBZ work_fnploejenbc2raktl46esxm44i 100 50 to to TO work_fnploejenbc2raktl46esxm44i 100 51 occur occur VB work_fnploejenbc2raktl46esxm44i 100 52 , , , work_fnploejenbc2raktl46esxm44i 100 53 f(p(A f(p(A NNP work_fnploejenbc2raktl46esxm44i 100 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 100 55 , , , work_fnploejenbc2raktl46esxm44i 100 56 0 0 LS work_fnploejenbc2raktl46esxm44i 100 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 100 58 if if IN work_fnploejenbc2raktl46esxm44i 100 59 A a NN work_fnploejenbc2raktl46esxm44i 100 60 does do VBZ work_fnploejenbc2raktl46esxm44i 100 61 not not RB work_fnploejenbc2raktl46esxm44i 100 62 occur occur VB work_fnploejenbc2raktl46esxm44i 100 63 . . . work_fnploejenbc2raktl46esxm44i 101 1 Now now RB work_fnploejenbc2raktl46esxm44i 101 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 101 3 need need VBP work_fnploejenbc2raktl46esxm44i 101 4 to to TO work_fnploejenbc2raktl46esxm44i 101 5 extend extend VB work_fnploejenbc2raktl46esxm44i 101 6 f f XX work_fnploejenbc2raktl46esxm44i 101 7 as as IN work_fnploejenbc2raktl46esxm44i 101 8 a a DT work_fnploejenbc2raktl46esxm44i 101 9 map map NN work_fnploejenbc2raktl46esxm44i 101 10 from from IN work_fnploejenbc2raktl46esxm44i 101 11 the the DT work_fnploejenbc2raktl46esxm44i 101 12 space space NN work_fnploejenbc2raktl46esxm44i 101 13 { { -LRB- work_fnploejenbc2raktl46esxm44i 101 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 101 15 a a DT work_fnploejenbc2raktl46esxm44i 101 16 , , , work_fnploejenbc2raktl46esxm44i 101 17 , , , work_fnploejenbc2raktl46esxm44i 101 18 2 2 CD work_fnploejenbc2raktl46esxm44i 101 19 , , , work_fnploejenbc2raktl46esxm44i 101 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 101 21 : : : work_fnploejenbc2raktl46esxm44i 101 22 n n NNP work_fnploejenbc2raktl46esxm44i 101 23 B B NNP work_fnploejenbc2raktl46esxm44i 101 24 1 1 CD work_fnploejenbc2raktl46esxm44i 101 25 , , , work_fnploejenbc2raktl46esxm44i 101 26 jZ.,E jZ.,E NNP work_fnploejenbc2raktl46esxm44i 101 27 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 101 28 a a DT work_fnploejenbc2raktl46esxm44i 101 29 , , , work_fnploejenbc2raktl46esxm44i 101 30 , , , work_fnploejenbc2raktl46esxm44i 101 31 a31n a31n UH work_fnploejenbc2raktl46esxm44i 101 32 , , , work_fnploejenbc2raktl46esxm44i 101 33 i i PRP work_fnploejenbc2raktl46esxm44i 101 34 , , , work_fnploejenbc2raktl46esxm44i 101 35 E E NNP work_fnploejenbc2raktl46esxm44i 101 36 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 101 37 0 0 CD work_fnploejenbc2raktl46esxm44i 101 38 , , , work_fnploejenbc2raktl46esxm44i 101 39 1 1 CD work_fnploejenbc2raktl46esxm44i 101 40 , , , work_fnploejenbc2raktl46esxm44i 101 41 24 24 CD work_fnploejenbc2raktl46esxm44i 101 42 } } -RRB- work_fnploejenbc2raktl46esxm44i 101 43 “ " `` work_fnploejenbc2raktl46esxm44i 101 44 > > XX work_fnploejenbc2raktl46esxm44i 101 45 to to IN work_fnploejenbc2raktl46esxm44i 101 46 the the DT work_fnploejenbc2raktl46esxm44i 101 47 space space NN work_fnploejenbc2raktl46esxm44i 101 48 IR IR NNP work_fnploejenbc2raktl46esxm44i 101 49 , , , work_fnploejenbc2raktl46esxm44i 101 50 : : : work_fnploejenbc2raktl46esxm44i 101 51 for for IN work_fnploejenbc2raktl46esxm44i 101 52 each each DT work_fnploejenbc2raktl46esxm44i 101 53 n n CD work_fnploejenbc2raktl46esxm44i 101 54 2 2 CD work_fnploejenbc2raktl46esxm44i 101 55 1 1 CD work_fnploejenbc2raktl46esxm44i 101 56 , , , work_fnploejenbc2raktl46esxm44i 101 57 J J NNP work_fnploejenbc2raktl46esxm44i 101 58 ? ? . work_fnploejenbc2raktl46esxm44i 101 59 , , , work_fnploejenbc2raktl46esxm44i 101 60 , , , work_fnploejenbc2raktl46esxm44i 101 61 = = NFP work_fnploejenbc2raktl46esxm44i 101 62 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 101 63 x x UH work_fnploejenbc2raktl46esxm44i 101 64 , , , work_fnploejenbc2raktl46esxm44i 101 65 , , , work_fnploejenbc2raktl46esxm44i 101 66 . . . work_fnploejenbc2raktl46esxm44i 102 1 . . . work_fnploejenbc2raktl46esxm44i 103 1 . . . work_fnploejenbc2raktl46esxm44i 104 1 . . . work_fnploejenbc2raktl46esxm44i 105 1 x x LS work_fnploejenbc2raktl46esxm44i 105 2 , , , work_fnploejenbc2raktl46esxm44i 105 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 105 4 , , , work_fnploejenbc2raktl46esxm44i 105 5 i i PRP work_fnploejenbc2raktl46esxm44i 105 6 , , , work_fnploejenbc2raktl46esxm44i 105 7 = = NFP work_fnploejenbc2raktl46esxm44i 105 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 105 9 tl tl IN work_fnploejenbc2raktl46esxm44i 105 10 , , , work_fnploejenbc2raktl46esxm44i 105 11 . . . work_fnploejenbc2raktl46esxm44i 106 1 . . . work_fnploejenbc2raktl46esxm44i 107 1 . . . work_fnploejenbc2raktl46esxm44i 108 1 . . . work_fnploejenbc2raktl46esxm44i 109 1 t t NNP work_fnploejenbc2raktl46esxm44i 109 2 , , , work_fnploejenbc2raktl46esxm44i 109 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 109 4 , , , work_fnploejenbc2raktl46esxm44i 109 5 fcL~ fcL~ NNP work_fnploejenbc2raktl46esxm44i 109 6 , , , work_fnploejenbc2raktl46esxm44i 109 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 109 8 = = NFP work_fnploejenbc2raktl46esxm44i 109 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 109 10 f(XlY f(xly CD work_fnploejenbc2raktl46esxm44i 109 11 t t NN work_fnploejenbc2raktl46esxm44i 109 12 , , , work_fnploejenbc2raktl46esxm44i 109 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 109 14 , , , work_fnploejenbc2raktl46esxm44i 109 15 * * NFP work_fnploejenbc2raktl46esxm44i 109 16 .. .. NFP work_fnploejenbc2raktl46esxm44i 109 17 9 9 CD work_fnploejenbc2raktl46esxm44i 109 18 fkY fky CD work_fnploejenbc2raktl46esxm44i 109 19 , , , work_fnploejenbc2raktl46esxm44i 109 20 47 47 CD work_fnploejenbc2raktl46esxm44i 109 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 109 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 109 23 . . . work_fnploejenbc2raktl46esxm44i 110 1 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 110 2 , , , work_fnploejenbc2raktl46esxm44i 110 3 each each DT work_fnploejenbc2raktl46esxm44i 110 4 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 110 5 map map NN work_fnploejenbc2raktl46esxm44i 110 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 110 7 or or CC work_fnploejenbc2raktl46esxm44i 110 8 measure measure VB work_fnploejenbc2raktl46esxm44i 110 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 110 10 p p NN work_fnploejenbc2raktl46esxm44i 110 11 : : : work_fnploejenbc2raktl46esxm44i 110 12 d d LS work_fnploejenbc2raktl46esxm44i 110 13 -+ -+ : work_fnploejenbc2raktl46esxm44i 110 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 110 15 a a DT work_fnploejenbc2raktl46esxm44i 110 16 , , , work_fnploejenbc2raktl46esxm44i 110 17 , , , work_fnploejenbc2raktl46esxm44i 110 18 a a DT work_fnploejenbc2raktl46esxm44i 110 19 , , , work_fnploejenbc2raktl46esxm44i 110 20 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 110 21 is be VBZ work_fnploejenbc2raktl46esxm44i 110 22 extended extend VBN work_fnploejenbc2raktl46esxm44i 110 23 to to IN work_fnploejenbc2raktl46esxm44i 110 24 a a DT work_fnploejenbc2raktl46esxm44i 110 25 map map NN work_fnploejenbc2raktl46esxm44i 110 26 from from IN work_fnploejenbc2raktl46esxm44i 110 27 ZZ ZZ NNP work_fnploejenbc2raktl46esxm44i 110 28 & & CC work_fnploejenbc2raktl46esxm44i 110 29 to to IN work_fnploejenbc2raktl46esxm44i 110 30 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 110 31 al al NNP work_fnploejenbc2raktl46esxm44i 110 32 , , , work_fnploejenbc2raktl46esxm44i 110 33 a3100 a3100 NNP work_fnploejenbc2raktl46esxm44i 110 34 as as IN work_fnploejenbc2raktl46esxm44i 110 35 follows follow VBZ work_fnploejenbc2raktl46esxm44i 110 36 : : : work_fnploejenbc2raktl46esxm44i 110 37 for for IN work_fnploejenbc2raktl46esxm44i 110 38 each each DT work_fnploejenbc2raktl46esxm44i 110 39 n n CD work_fnploejenbc2raktl46esxm44i 110 40 2 2 CD work_fnploejenbc2raktl46esxm44i 110 41 1 1 CD work_fnploejenbc2raktl46esxm44i 110 42 , , , work_fnploejenbc2raktl46esxm44i 110 43 i,=(A i,=(A NNP work_fnploejenbc2raktl46esxm44i 110 44 1 1 CD work_fnploejenbc2raktl46esxm44i 110 45 , , , work_fnploejenbc2raktl46esxm44i 110 46 . . . work_fnploejenbc2raktl46esxm44i 111 1 . . . work_fnploejenbc2raktl46esxm44i 112 1 . . . work_fnploejenbc2raktl46esxm44i 113 1 . . . work_fnploejenbc2raktl46esxm44i 114 1 A a DT work_fnploejenbc2raktl46esxm44i 114 2 , , , work_fnploejenbc2raktl46esxm44i 114 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 114 4 Ed Ed NNP work_fnploejenbc2raktl46esxm44i 114 5 ” " '' work_fnploejenbc2raktl46esxm44i 114 6 , , , work_fnploejenbc2raktl46esxm44i 114 7 c((A^ c((A^ NNP work_fnploejenbc2raktl46esxm44i 114 8 , , , work_fnploejenbc2raktl46esxm44i 114 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 114 10 = = NFP work_fnploejenbc2raktl46esxm44i 114 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 114 12 AA AA NNP work_fnploejenbc2raktl46esxm44i 114 13 I I NNP work_fnploejenbc2raktl46esxm44i 114 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 114 15 , , , work_fnploejenbc2raktl46esxm44i 114 16 . . . work_fnploejenbc2raktl46esxm44i 115 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 115 2 t t NNP work_fnploejenbc2raktl46esxm44i 115 3 AA AA NNP work_fnploejenbc2raktl46esxm44i 115 4 , , , work_fnploejenbc2raktl46esxm44i 115 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 115 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 115 7 E e NN work_fnploejenbc2raktl46esxm44i 115 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 115 9 a a DT work_fnploejenbc2raktl46esxm44i 115 10 , , , work_fnploejenbc2raktl46esxm44i 115 11 , , , work_fnploejenbc2raktl46esxm44i 115 12 dn dn NNP work_fnploejenbc2raktl46esxm44i 115 13 . . . work_fnploejenbc2raktl46esxm44i 116 1 An an DT work_fnploejenbc2raktl46esxm44i 116 2 obvious obvious JJ work_fnploejenbc2raktl46esxm44i 116 3 way way NN work_fnploejenbc2raktl46esxm44i 116 4 of of IN work_fnploejenbc2raktl46esxm44i 116 5 combining combine VBG work_fnploejenbc2raktl46esxm44i 116 6 individual individual JJ work_fnploejenbc2raktl46esxm44i 116 7 scores score NNS work_fnploejenbc2raktl46esxm44i 116 8 & & CC work_fnploejenbc2raktl46esxm44i 116 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 116 10 A a DT work_fnploejenbc2raktl46esxm44i 116 11 ;) ;) NN work_fnploejenbc2raktl46esxm44i 116 12 , , , work_fnploejenbc2raktl46esxm44i 116 13 Ai Ai NNP work_fnploejenbc2raktl46esxm44i 116 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 116 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 116 16 i i PRP work_fnploejenbc2raktl46esxm44i 116 17 ’ ' '' work_fnploejenbc2raktl46esxm44i 116 18 1 1 CD work_fnploejenbc2raktl46esxm44i 116 19 , , , work_fnploejenbc2raktl46esxm44i 116 20 2 2 CD work_fnploejenbc2raktl46esxm44i 116 21 , , , work_fnploejenbc2raktl46esxm44i 116 22 . . . work_fnploejenbc2raktl46esxm44i 117 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 117 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 3 n n LS work_fnploejenbc2raktl46esxm44i 117 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 5 to to TO work_fnploejenbc2raktl46esxm44i 117 6 obtain obtain VB work_fnploejenbc2raktl46esxm44i 117 7 the the DT work_fnploejenbc2raktl46esxm44i 117 8 total total JJ work_fnploejenbc2raktl46esxm44i 117 9 score score NN work_fnploejenbc2raktl46esxm44i 117 10 is be VBZ work_fnploejenbc2raktl46esxm44i 117 11 using use VBG work_fnploejenbc2raktl46esxm44i 117 12 addition addition NN work_fnploejenbc2raktl46esxm44i 117 13 on on IN work_fnploejenbc2raktl46esxm44i 117 14 R R NNP work_fnploejenbc2raktl46esxm44i 117 15 , , , work_fnploejenbc2raktl46esxm44i 117 16 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 117 17 , , , work_fnploejenbc2raktl46esxm44i 117 18 take take VB work_fnploejenbc2raktl46esxm44i 117 19 Lf Lf NNP work_fnploejenbc2raktl46esxm44i 117 20 , , , work_fnploejenbc2raktl46esxm44i 117 21 + + CC work_fnploejenbc2raktl46esxm44i 117 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 117 23 a a DT work_fnploejenbc2raktl46esxm44i 117 24 , , , work_fnploejenbc2raktl46esxm44i 117 25 , , , work_fnploejenbc2raktl46esxm44i 117 26 w w NNP work_fnploejenbc2raktl46esxm44i 117 27 , , , work_fnploejenbc2raktl46esxm44i 117 28 p p NNP work_fnploejenbc2raktl46esxm44i 117 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 30 = = SYM work_fnploejenbc2raktl46esxm44i 117 31 Cr= Cr= NNP work_fnploejenbc2raktl46esxm44i 117 32 1 1 CD work_fnploejenbc2raktl46esxm44i 117 33 f(p(Ai f(p(ai NN work_fnploejenbc2raktl46esxm44i 117 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 35 , , , work_fnploejenbc2raktl46esxm44i 117 36 Ai(o Ai(o NNP work_fnploejenbc2raktl46esxm44i 117 37 Thus thus RB work_fnploejenbc2raktl46esxm44i 117 38 the the DT work_fnploejenbc2raktl46esxm44i 117 39 loss loss NN work_fnploejenbc2raktl46esxm44i 117 40 function function NN work_fnploejenbc2raktl46esxm44i 117 41 L L NNP work_fnploejenbc2raktl46esxm44i 117 42 , , , work_fnploejenbc2raktl46esxm44i 117 43 . . . work_fnploejenbc2raktl46esxm44i 117 44 , , , work_fnploejenbc2raktl46esxm44i 117 45 + + ADD work_fnploejenbc2raktl46esxm44i 117 46 depends depend VBZ work_fnploejenbc2raktl46esxm44i 117 47 on on IN work_fnploejenbc2raktl46esxm44i 117 48 two two CD work_fnploejenbc2raktl46esxm44i 117 49 functions function NNS work_fnploejenbc2raktl46esxm44i 117 50 : : : work_fnploejenbc2raktl46esxm44i 117 51 f f LS work_fnploejenbc2raktl46esxm44i 117 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 117 53 score score NN work_fnploejenbc2raktl46esxm44i 117 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 55 and and CC work_fnploejenbc2raktl46esxm44i 117 56 + + SYM work_fnploejenbc2raktl46esxm44i 117 57 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 117 58 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 117 59 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 117 60 , , , work_fnploejenbc2raktl46esxm44i 117 61 This this DT work_fnploejenbc2raktl46esxm44i 117 62 special special JJ work_fnploejenbc2raktl46esxm44i 117 63 case case NN work_fnploejenbc2raktl46esxm44i 117 64 will will MD work_fnploejenbc2raktl46esxm44i 117 65 be be VB work_fnploejenbc2raktl46esxm44i 117 66 referred refer VBN work_fnploejenbc2raktl46esxm44i 117 67 to to IN work_fnploejenbc2raktl46esxm44i 117 68 as as IN work_fnploejenbc2raktl46esxm44i 117 69 the the DT work_fnploejenbc2raktl46esxm44i 117 70 additive additive NNP work_fnploejenbc2raktl46esxm44i 117 71 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 117 72 case case NN work_fnploejenbc2raktl46esxm44i 117 73 . . . work_fnploejenbc2raktl46esxm44i 118 1 In in IN work_fnploejenbc2raktl46esxm44i 118 2 general general JJ work_fnploejenbc2raktl46esxm44i 118 3 , , , work_fnploejenbc2raktl46esxm44i 118 4 by by IN work_fnploejenbc2raktl46esxm44i 118 5 an an DT work_fnploejenbc2raktl46esxm44i 118 6 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 118 7 function function NN work_fnploejenbc2raktl46esxm44i 118 8 , , , work_fnploejenbc2raktl46esxm44i 118 9 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 118 10 mean mean VBP work_fnploejenbc2raktl46esxm44i 118 11 a a DT work_fnploejenbc2raktl46esxm44i 118 12 mapping mapping NN work_fnploejenbc2raktl46esxm44i 118 13 ~9 ~9 IN work_fnploejenbc2raktl46esxm44i 118 14 : : : work_fnploejenbc2raktl46esxm44i 118 15 IR IR NNP work_fnploejenbc2raktl46esxm44i 118 16 , , , work_fnploejenbc2raktl46esxm44i 118 17 --t --t . work_fnploejenbc2raktl46esxm44i 118 18 R r NN work_fnploejenbc2raktl46esxm44i 118 19 such such JJ work_fnploejenbc2raktl46esxm44i 118 20 that that IN work_fnploejenbc2raktl46esxm44i 118 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 118 22 a a LS work_fnploejenbc2raktl46esxm44i 118 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 118 24 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 118 25 is be VBZ work_fnploejenbc2raktl46esxm44i 118 26 continuously continuously RB work_fnploejenbc2raktl46esxm44i 118 27 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 118 28 in in IN work_fnploejenbc2raktl46esxm44i 118 29 all all DT work_fnploejenbc2raktl46esxm44i 118 30 of of IN work_fnploejenbc2raktl46esxm44i 118 31 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 118 32 arguments argument NNS work_fnploejenbc2raktl46esxm44i 118 33 ; ; , work_fnploejenbc2raktl46esxm44i 118 34 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 118 35 b b NN work_fnploejenbc2raktl46esxm44i 118 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 118 37 1 1 CD work_fnploejenbc2raktl46esxm44i 118 38 + + SYM work_fnploejenbc2raktl46esxm44i 118 39 9 9 CD work_fnploejenbc2raktl46esxm44i 118 40 is be VBZ work_fnploejenbc2raktl46esxm44i 118 41 increasing increase VBG work_fnploejenbc2raktl46esxm44i 118 42 in in IN work_fnploejenbc2raktl46esxm44i 118 43 each each DT work_fnploejenbc2raktl46esxm44i 118 44 of of IN work_fnploejenbc2raktl46esxm44i 118 45 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 118 46 arguments argument NNS work_fnploejenbc2raktl46esxm44i 118 47 . . . work_fnploejenbc2raktl46esxm44i 119 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 119 2 c c NN work_fnploejenbc2raktl46esxm44i 119 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 119 4 $ $ $ work_fnploejenbc2raktl46esxm44i 119 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 119 6 O o UH work_fnploejenbc2raktl46esxm44i 119 7 , , , work_fnploejenbc2raktl46esxm44i 119 8 , , , work_fnploejenbc2raktl46esxm44i 119 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 119 10 = = NFP work_fnploejenbc2raktl46esxm44i 119 11 0 0 NFP work_fnploejenbc2raktl46esxm44i 119 12 , , , work_fnploejenbc2raktl46esxm44i 119 13 Vn Vn NNP work_fnploejenbc2raktl46esxm44i 119 14 2 2 CD work_fnploejenbc2raktl46esxm44i 119 15 1 1 CD work_fnploejenbc2raktl46esxm44i 119 16 , , , work_fnploejenbc2raktl46esxm44i 119 17 where where WRB work_fnploejenbc2raktl46esxm44i 119 18 0 0 CD work_fnploejenbc2raktl46esxm44i 119 19 , , , work_fnploejenbc2raktl46esxm44i 119 20 is be VBZ work_fnploejenbc2raktl46esxm44i 119 21 the the DT work_fnploejenbc2raktl46esxm44i 119 22 zero zero CD work_fnploejenbc2raktl46esxm44i 119 23 vector vector NN work_fnploejenbc2raktl46esxm44i 119 24 in in IN work_fnploejenbc2raktl46esxm44i 119 25 R r NN work_fnploejenbc2raktl46esxm44i 119 26 ” " '' work_fnploejenbc2raktl46esxm44i 119 27 . . . work_fnploejenbc2raktl46esxm44i 120 1 Note note VB work_fnploejenbc2raktl46esxm44i 120 2 that that IN work_fnploejenbc2raktl46esxm44i 120 3 the the DT work_fnploejenbc2raktl46esxm44i 120 4 additive additive JJ work_fnploejenbc2raktl46esxm44i 120 5 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 120 6 function function NN work_fnploejenbc2raktl46esxm44i 120 7 is be VBZ work_fnploejenbc2raktl46esxm44i 120 8 generated generate VBN work_fnploejenbc2raktl46esxm44i 120 9 by by IN work_fnploejenbc2raktl46esxm44i 120 10 ordinary ordinary JJ work_fnploejenbc2raktl46esxm44i 120 11 addi- addi- JJ work_fnploejenbc2raktl46esxm44i 120 12 tion tion NN work_fnploejenbc2raktl46esxm44i 120 13 on on IN work_fnploejenbc2raktl46esxm44i 120 14 R r NN work_fnploejenbc2raktl46esxm44i 120 15 : : : work_fnploejenbc2raktl46esxm44i 120 16 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 120 17 = = SYM work_fnploejenbc2raktl46esxm44i 120 18 + + CC work_fnploejenbc2raktl46esxm44i 120 19 is be VBZ work_fnploejenbc2raktl46esxm44i 120 20 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 120 21 to to IN work_fnploejenbc2raktl46esxm44i 120 22 the the DT work_fnploejenbc2raktl46esxm44i 120 23 sequence sequence NN work_fnploejenbc2raktl46esxm44i 120 24 of of IN work_fnploejenbc2raktl46esxm44i 120 25 functions function NNS work_fnploejenbc2raktl46esxm44i 120 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 120 27 g g NNP work_fnploejenbc2raktl46esxm44i 120 28 , , , work_fnploejenbc2raktl46esxm44i 120 29 , , , work_fnploejenbc2raktl46esxm44i 120 30 n n CC work_fnploejenbc2raktl46esxm44i 120 31 2 2 CD work_fnploejenbc2raktl46esxm44i 120 32 l l NN work_fnploejenbc2raktl46esxm44i 120 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 120 34 , , , work_fnploejenbc2raktl46esxm44i 120 35 where where WRB work_fnploejenbc2raktl46esxm44i 120 36 g g NNP work_fnploejenbc2raktl46esxm44i 120 37 , , , work_fnploejenbc2raktl46esxm44i 120 38 : : : work_fnploejenbc2raktl46esxm44i 120 39 IR IR NNP work_fnploejenbc2raktl46esxm44i 120 40 ’ ' '' work_fnploejenbc2raktl46esxm44i 120 41 + + CC work_fnploejenbc2raktl46esxm44i 120 42 R r NN work_fnploejenbc2raktl46esxm44i 120 43 , , , work_fnploejenbc2raktl46esxm44i 120 44 g(x g(x NNP work_fnploejenbc2raktl46esxm44i 120 45 , , , work_fnploejenbc2raktl46esxm44i 120 46 , , , work_fnploejenbc2raktl46esxm44i 120 47 . . . work_fnploejenbc2raktl46esxm44i 121 1 . . . work_fnploejenbc2raktl46esxm44i 122 1 . . . work_fnploejenbc2raktl46esxm44i 123 1 . . . work_fnploejenbc2raktl46esxm44i 124 1 xn xn NNP work_fnploejenbc2raktl46esxm44i 124 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 124 3 = = NFP work_fnploejenbc2raktl46esxm44i 124 4 CF= CF= NNP work_fnploejenbc2raktl46esxm44i 124 5 1 1 CD work_fnploejenbc2raktl46esxm44i 124 6 xi xi NNS work_fnploejenbc2raktl46esxm44i 124 7 . . . work_fnploejenbc2raktl46esxm44i 125 1 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 125 2 , , , work_fnploejenbc2raktl46esxm44i 125 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 125 4 identify identify VBP work_fnploejenbc2raktl46esxm44i 125 5 an an DT work_fnploejenbc2raktl46esxm44i 125 6 aggrega- aggrega- NN work_fnploejenbc2raktl46esxm44i 125 7 tion tion NN work_fnploejenbc2raktl46esxm44i 125 8 function function NN work_fnploejenbc2raktl46esxm44i 125 9 $ $ $ work_fnploejenbc2raktl46esxm44i 125 10 with with IN work_fnploejenbc2raktl46esxm44i 125 11 the the DT work_fnploejenbc2raktl46esxm44i 125 12 sequence sequence NN work_fnploejenbc2raktl46esxm44i 125 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 125 14 + + SYM work_fnploejenbc2raktl46esxm44i 125 15 , , , work_fnploejenbc2raktl46esxm44i 125 16 , , , work_fnploejenbc2raktl46esxm44i 125 17 n n NN work_fnploejenbc2raktl46esxm44i 125 18 3 3 NNP work_fnploejenbc2raktl46esxm44i 125 19 l l NN work_fnploejenbc2raktl46esxm44i 125 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 125 21 , , , work_fnploejenbc2raktl46esxm44i 125 22 where where WRB work_fnploejenbc2raktl46esxm44i 125 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 125 24 I/ I/ NNP work_fnploejenbc2raktl46esxm44i 125 25 , , , work_fnploejenbc2raktl46esxm44i 125 26 is be VBZ work_fnploejenbc2raktl46esxm44i 125 27 the the DT work_fnploejenbc2raktl46esxm44i 125 28 restriction restriction NN work_fnploejenbc2raktl46esxm44i 125 29 of of IN work_fnploejenbc2raktl46esxm44i 125 30 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 125 31 to to IN work_fnploejenbc2raktl46esxm44i 125 32 R r NN work_fnploejenbc2raktl46esxm44i 125 33 ” " '' work_fnploejenbc2raktl46esxm44i 125 34 . . . work_fnploejenbc2raktl46esxm44i 126 1 Note note VB work_fnploejenbc2raktl46esxm44i 126 2 also also RB work_fnploejenbc2raktl46esxm44i 126 3 that that IN work_fnploejenbc2raktl46esxm44i 126 4 , , , work_fnploejenbc2raktl46esxm44i 126 5 while while IN work_fnploejenbc2raktl46esxm44i 126 6 the the DT work_fnploejenbc2raktl46esxm44i 126 7 additive additive NNP work_fnploejenbc2raktl46esxm44i 126 8 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 126 9 function function NN work_fnploejenbc2raktl46esxm44i 126 10 is be VBZ work_fnploejenbc2raktl46esxm44i 126 11 409’15912-IX 409’15912-ix CD work_fnploejenbc2raktl46esxm44i 126 12 556 556 CD work_fnploejenbc2raktl46esxm44i 126 13 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 126 14 , , , work_fnploejenbc2raktl46esxm44i 126 15 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 126 16 , , , work_fnploejenbc2raktl46esxm44i 126 17 AND and CC work_fnploejenbc2raktl46esxm44i 126 18 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 126 19 symmetric symmetric JJ work_fnploejenbc2raktl46esxm44i 126 20 , , , work_fnploejenbc2raktl46esxm44i 126 21 there there EX work_fnploejenbc2raktl46esxm44i 126 22 is be VBZ work_fnploejenbc2raktl46esxm44i 126 23 no no DT work_fnploejenbc2raktl46esxm44i 126 24 a a DT work_fnploejenbc2raktl46esxm44i 126 25 priori priori FW work_fnploejenbc2raktl46esxm44i 126 26 reason reason NN work_fnploejenbc2raktl46esxm44i 126 27 to to TO work_fnploejenbc2raktl46esxm44i 126 28 impose impose VB work_fnploejenbc2raktl46esxm44i 126 29 such such PDT work_fnploejenbc2raktl46esxm44i 126 30 a a DT work_fnploejenbc2raktl46esxm44i 126 31 condition condition NN work_fnploejenbc2raktl46esxm44i 126 32 on on IN work_fnploejenbc2raktl46esxm44i 126 33 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 126 34 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 126 35 functions function NNS work_fnploejenbc2raktl46esxm44i 126 36 . . . work_fnploejenbc2raktl46esxm44i 127 1 Now now RB work_fnploejenbc2raktl46esxm44i 127 2 , , , work_fnploejenbc2raktl46esxm44i 127 3 given give VBN work_fnploejenbc2raktl46esxm44i 127 4 a a DT work_fnploejenbc2raktl46esxm44i 127 5 score score NN work_fnploejenbc2raktl46esxm44i 127 6 functionf functionf NN work_fnploejenbc2raktl46esxm44i 127 7 and and CC work_fnploejenbc2raktl46esxm44i 127 8 an an DT work_fnploejenbc2raktl46esxm44i 127 9 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 127 10 function function NN work_fnploejenbc2raktl46esxm44i 127 11 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 127 12 , , , work_fnploejenbc2raktl46esxm44i 127 13 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 127 14 define define VBP work_fnploejenbc2raktl46esxm44i 127 15 the the DT work_fnploejenbc2raktl46esxm44i 127 16 loss loss NN work_fnploejenbc2raktl46esxm44i 127 17 function function NN work_fnploejenbc2raktl46esxm44i 127 18 Lf Lf NNP work_fnploejenbc2raktl46esxm44i 127 19 , , , work_fnploejenbc2raktl46esxm44i 127 20 , , , work_fnploejenbc2raktl46esxm44i 127 21 as as IN work_fnploejenbc2raktl46esxm44i 127 22 follows follow VBZ work_fnploejenbc2raktl46esxm44i 127 23 : : : work_fnploejenbc2raktl46esxm44i 127 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 127 25 Note note VB work_fnploejenbc2raktl46esxm44i 127 26 that that DT work_fnploejenbc2raktl46esxm44i 127 27 fand fand NN work_fnploejenbc2raktl46esxm44i 127 28 , , , work_fnploejenbc2raktl46esxm44i 127 29 u u NNP work_fnploejenbc2raktl46esxm44i 127 30 are be VBP work_fnploejenbc2raktl46esxm44i 127 31 used use VBN work_fnploejenbc2raktl46esxm44i 127 32 in in IN work_fnploejenbc2raktl46esxm44i 127 33 the the DT work_fnploejenbc2raktl46esxm44i 127 34 extended extended JJ work_fnploejenbc2raktl46esxm44i 127 35 sense sense NN work_fnploejenbc2raktl46esxm44i 127 36 . . . work_fnploejenbc2raktl46esxm44i 127 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 128 1 The the DT work_fnploejenbc2raktl46esxm44i 128 2 triple triple JJ work_fnploejenbc2raktl46esxm44i 128 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 128 4 A a NN work_fnploejenbc2raktl46esxm44i 128 5 1 1 CD work_fnploejenbc2raktl46esxm44i 128 6 , , , work_fnploejenbc2raktl46esxm44i 128 7 AZ AZ NNP work_fnploejenbc2raktl46esxm44i 128 8 , , , work_fnploejenbc2raktl46esxm44i 128 9 Lf,$ Lf,$ NNP work_fnploejenbc2raktl46esxm44i 128 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 128 11 is be VBZ work_fnploejenbc2raktl46esxm44i 128 12 called call VBN work_fnploejenbc2raktl46esxm44i 128 13 an an DT work_fnploejenbc2raktl46esxm44i 128 14 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 128 15 game game NN work_fnploejenbc2raktl46esxm44i 128 16 and and CC work_fnploejenbc2raktl46esxm44i 128 17 is be VBZ work_fnploejenbc2raktl46esxm44i 128 18 denoted denote VBN work_fnploejenbc2raktl46esxm44i 128 19 by by IN work_fnploejenbc2raktl46esxm44i 128 20 Gf Gf NNP work_fnploejenbc2raktl46esxm44i 128 21 , , , work_fnploejenbc2raktl46esxm44i 128 22 , , , work_fnploejenbc2raktl46esxm44i 128 23 . . . work_fnploejenbc2raktl46esxm44i 129 1 In in IN work_fnploejenbc2raktl46esxm44i 129 2 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 129 3 ’s ’s POS work_fnploejenbc2raktl46esxm44i 129 4 game game NN work_fnploejenbc2raktl46esxm44i 129 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 129 6 6 6 CD work_fnploejenbc2raktl46esxm44i 129 7 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 129 8 , , , work_fnploejenbc2raktl46esxm44i 129 9 a a NN work_fnploejenbc2raktl46esxm44i 129 10 , , , work_fnploejenbc2raktl46esxm44i 129 11 = = SYM work_fnploejenbc2raktl46esxm44i 129 12 a2 a2 NNP work_fnploejenbc2raktl46esxm44i 129 13 = = SYM work_fnploejenbc2raktl46esxm44i 129 14 0 0 CD work_fnploejenbc2raktl46esxm44i 129 15 , , , work_fnploejenbc2raktl46esxm44i 129 16 a a NN work_fnploejenbc2raktl46esxm44i 129 17 , , , work_fnploejenbc2raktl46esxm44i 129 18 = = NFP work_fnploejenbc2raktl46esxm44i 129 19 a3 a3 NNP work_fnploejenbc2raktl46esxm44i 129 20 = = SYM work_fnploejenbc2raktl46esxm44i 129 21 1 1 CD work_fnploejenbc2raktl46esxm44i 129 22 , , , work_fnploejenbc2raktl46esxm44i 129 23 and and CC work_fnploejenbc2raktl46esxm44i 129 24 fb fb NNP work_fnploejenbc2raktl46esxm44i 129 25 , , , work_fnploejenbc2raktl46esxm44i 129 26 A= A= NNP work_fnploejenbc2raktl46esxm44i 129 27 { { -LRB- work_fnploejenbc2raktl46esxm44i 129 28 b”-i b”-i NNP work_fnploejenbc2raktl46esxm44i 129 29 ” " '' work_fnploejenbc2raktl46esxm44i 129 30 ; ; : work_fnploejenbc2raktl46esxm44i 129 31 ; ; : work_fnploejenbc2raktl46esxm44i 129 32 I$ndefined i$ndefined LS work_fnploejenbc2raktl46esxm44i 129 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 129 34 ; ; : work_fnploejenbc2raktl46esxm44i 129 35 here here RB work_fnploejenbc2raktl46esxm44i 129 36 $ $ $ work_fnploejenbc2raktl46esxm44i 129 37 = = SYM work_fnploejenbc2raktl46esxm44i 129 38 + + XX work_fnploejenbc2raktl46esxm44i 129 39 . . . work_fnploejenbc2raktl46esxm44i 130 1 In in IN work_fnploejenbc2raktl46esxm44i 130 2 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 130 3 ’s ’s POS work_fnploejenbc2raktl46esxm44i 130 4 extension extension NN work_fnploejenbc2raktl46esxm44i 130 5 of of IN work_fnploejenbc2raktl46esxm44i 130 6 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 130 7 ’s ’s POS work_fnploejenbc2raktl46esxm44i 130 8 game game NN work_fnploejenbc2raktl46esxm44i 130 9 , , , work_fnploejenbc2raktl46esxm44i 130 10 uj uj NNP work_fnploejenbc2raktl46esxm44i 130 11 , , , work_fnploejenbc2raktl46esxm44i 130 12 j j NNP work_fnploejenbc2raktl46esxm44i 130 13 = = SYM work_fnploejenbc2raktl46esxm44i 130 14 0 0 CD work_fnploejenbc2raktl46esxm44i 130 15 , , , work_fnploejenbc2raktl46esxm44i 130 16 1,2 1,2 CD work_fnploejenbc2raktl46esxm44i 130 17 , , , work_fnploejenbc2raktl46esxm44i 130 18 3 3 CD work_fnploejenbc2raktl46esxm44i 130 19 , , , work_fnploejenbc2raktl46esxm44i 130 20 are be VBP work_fnploejenbc2raktl46esxm44i 130 21 not not RB work_fnploejenbc2raktl46esxm44i 130 22 restricted restrict VBN work_fnploejenbc2raktl46esxm44i 130 23 to to IN work_fnploejenbc2raktl46esxm44i 130 24 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 130 25 0 0 CD work_fnploejenbc2raktl46esxm44i 130 26 , , , work_fnploejenbc2raktl46esxm44i 130 27 11 11 CD work_fnploejenbc2raktl46esxm44i 130 28 , , , work_fnploejenbc2raktl46esxm44i 130 29 $ $ $ work_fnploejenbc2raktl46esxm44i 130 30 = = SYM work_fnploejenbc2raktl46esxm44i 130 31 + + CC work_fnploejenbc2raktl46esxm44i 130 32 , , , work_fnploejenbc2raktl46esxm44i 130 33 and and CC work_fnploejenbc2raktl46esxm44i 130 34 f f NNP work_fnploejenbc2raktl46esxm44i 130 35 is be VBZ work_fnploejenbc2raktl46esxm44i 130 36 an an DT work_fnploejenbc2raktl46esxm44i 130 37 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 130 38 score score NN work_fnploejenbc2raktl46esxm44i 130 39 function function NN work_fnploejenbc2raktl46esxm44i 130 40 . . . work_fnploejenbc2raktl46esxm44i 131 1 2.3 2.3 LS work_fnploejenbc2raktl46esxm44i 131 2 . . . work_fnploejenbc2raktl46esxm44i 132 1 Subgames subgame NNS work_fnploejenbc2raktl46esxm44i 132 2 To to TO work_fnploejenbc2raktl46esxm44i 132 3 formalize formalize VB work_fnploejenbc2raktl46esxm44i 132 4 various various JJ work_fnploejenbc2raktl46esxm44i 132 5 concepts concept NNS work_fnploejenbc2raktl46esxm44i 132 6 of of IN work_fnploejenbc2raktl46esxm44i 132 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 132 8 in in IN work_fnploejenbc2raktl46esxm44i 132 9 an an DT work_fnploejenbc2raktl46esxm44i 132 10 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 132 11 game game NN work_fnploejenbc2raktl46esxm44i 132 12 Gr,$ Gr,$ NNP work_fnploejenbc2raktl46esxm44i 132 13 , , , work_fnploejenbc2raktl46esxm44i 132 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 132 15 first first RB work_fnploejenbc2raktl46esxm44i 132 16 introduce introduce VBP work_fnploejenbc2raktl46esxm44i 132 17 the the DT work_fnploejenbc2raktl46esxm44i 132 18 concept concept NN work_fnploejenbc2raktl46esxm44i 132 19 of of IN work_fnploejenbc2raktl46esxm44i 132 20 subgame subgame NN work_fnploejenbc2raktl46esxm44i 132 21 . . . work_fnploejenbc2raktl46esxm44i 133 1 Suppose suppose VB work_fnploejenbc2raktl46esxm44i 133 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 133 3 are be VBP work_fnploejenbc2raktl46esxm44i 133 4 interested interested JJ work_fnploejenbc2raktl46esxm44i 133 5 only only RB work_fnploejenbc2raktl46esxm44i 133 6 in in IN work_fnploejenbc2raktl46esxm44i 133 7 some some DT work_fnploejenbc2raktl46esxm44i 133 8 given give VBN work_fnploejenbc2raktl46esxm44i 133 9 finite finite JJ work_fnploejenbc2raktl46esxm44i 133 10 collection collection NN work_fnploejenbc2raktl46esxm44i 133 11 of of IN work_fnploejenbc2raktl46esxm44i 133 12 condi- condi- NNP work_fnploejenbc2raktl46esxm44i 133 13 tional tional JJ work_fnploejenbc2raktl46esxm44i 133 14 events event NNS work_fnploejenbc2raktl46esxm44i 133 15 , , , work_fnploejenbc2raktl46esxm44i 133 16 say say VBP work_fnploejenbc2raktl46esxm44i 133 17 a a DT work_fnploejenbc2raktl46esxm44i 133 18 , , , work_fnploejenbc2raktl46esxm44i 133 19 then then RB work_fnploejenbc2raktl46esxm44i 133 20 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 133 21 need need VBP work_fnploejenbc2raktl46esxm44i 133 22 to to TO work_fnploejenbc2raktl46esxm44i 133 23 look look VB work_fnploejenbc2raktl46esxm44i 133 24 only only RB work_fnploejenbc2raktl46esxm44i 133 25 at at IN work_fnploejenbc2raktl46esxm44i 133 26 the the DT work_fnploejenbc2raktl46esxm44i 133 27 subgame subgame NN work_fnploejenbc2raktl46esxm44i 133 28 where where WRB work_fnploejenbc2raktl46esxm44i 133 29 and and CC work_fnploejenbc2raktl46esxm44i 133 30 For for IN work_fnploejenbc2raktl46esxm44i 133 31 example example NN work_fnploejenbc2raktl46esxm44i 133 32 , , , work_fnploejenbc2raktl46esxm44i 133 33 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 133 34 can can MD work_fnploejenbc2raktl46esxm44i 133 35 view view VB work_fnploejenbc2raktl46esxm44i 133 36 A a DT work_fnploejenbc2raktl46esxm44i 133 37 , , , work_fnploejenbc2raktl46esxm44i 133 38 E$ E$ NNP work_fnploejenbc2raktl46esxm44i 133 39 as as IN work_fnploejenbc2raktl46esxm44i 133 40 a a DT work_fnploejenbc2raktl46esxm44i 133 41 set set NN work_fnploejenbc2raktl46esxm44i 133 42 a,= a,= NN work_fnploejenbc2raktl46esxm44i 133 43 { { -LRB- work_fnploejenbc2raktl46esxm44i 133 44 A a NN work_fnploejenbc2raktl46esxm44i 133 45 , , , work_fnploejenbc2raktl46esxm44i 133 46 , , , work_fnploejenbc2raktl46esxm44i 133 47 . . . work_fnploejenbc2raktl46esxm44i 134 1 . . . work_fnploejenbc2raktl46esxm44i 135 1 . . . work_fnploejenbc2raktl46esxm44i 136 1 . . . work_fnploejenbc2raktl46esxm44i 137 1 A a DT work_fnploejenbc2raktl46esxm44i 137 2 , , , work_fnploejenbc2raktl46esxm44i 137 3 } } -RRB- work_fnploejenbc2raktl46esxm44i 137 4 se se FW work_fnploejenbc2raktl46esxm44i 137 5 . . . work_fnploejenbc2raktl46esxm44i 138 1 Then then RB work_fnploejenbc2raktl46esxm44i 138 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 138 3 a a DT work_fnploejenbc2raktl46esxm44i 138 4 * * NFP work_fnploejenbc2raktl46esxm44i 138 5 , , , work_fnploejenbc2raktl46esxm44i 138 6 a31An= a31an= IN work_fnploejenbc2raktl46esxm44i 138 7 { { -LRB- work_fnploejenbc2raktl46esxm44i 138 8 p p NN work_fnploejenbc2raktl46esxm44i 138 9 : : : work_fnploejenbc2raktl46esxm44i 138 10 { { -LRB- work_fnploejenbc2raktl46esxm44i 138 11 A a NN work_fnploejenbc2raktl46esxm44i 138 12 , , , work_fnploejenbc2raktl46esxm44i 138 13 , , , work_fnploejenbc2raktl46esxm44i 138 14 . . . work_fnploejenbc2raktl46esxm44i 139 1 . . . work_fnploejenbc2raktl46esxm44i 140 1 . . . work_fnploejenbc2raktl46esxm44i 141 1 . . . work_fnploejenbc2raktl46esxm44i 142 1 A a DT work_fnploejenbc2raktl46esxm44i 142 2 , , , work_fnploejenbc2raktl46esxm44i 142 3 } } -RRB- work_fnploejenbc2raktl46esxm44i 142 4 -- -- NFP work_fnploejenbc2raktl46esxm44i 142 5 * * NFP work_fnploejenbc2raktl46esxm44i 142 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 142 7 az az UH work_fnploejenbc2raktl46esxm44i 142 8 , , , work_fnploejenbc2raktl46esxm44i 142 9 a a DT work_fnploejenbc2raktl46esxm44i 142 10 , , , work_fnploejenbc2raktl46esxm44i 142 11 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 142 12 } } -RRB- work_fnploejenbc2raktl46esxm44i 142 13 so so IN work_fnploejenbc2raktl46esxm44i 142 14 that that IN work_fnploejenbc2raktl46esxm44i 142 15 each each DT work_fnploejenbc2raktl46esxm44i 142 16 p p NN work_fnploejenbc2raktl46esxm44i 142 17 in in IN work_fnploejenbc2raktl46esxm44i 142 18 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 142 19 a a DT work_fnploejenbc2raktl46esxm44i 142 20 , , , work_fnploejenbc2raktl46esxm44i 142 21 , , , work_fnploejenbc2raktl46esxm44i 142 22 ujlAn ujlan ADD work_fnploejenbc2raktl46esxm44i 142 23 is be VBZ work_fnploejenbc2raktl46esxm44i 142 24 the the DT work_fnploejenbc2raktl46esxm44i 142 25 restriction restriction NN work_fnploejenbc2raktl46esxm44i 142 26 of of IN work_fnploejenbc2raktl46esxm44i 142 27 a a DT work_fnploejenbc2raktl46esxm44i 142 28 p p NN work_fnploejenbc2raktl46esxm44i 142 29 in in IN work_fnploejenbc2raktl46esxm44i 142 30 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 142 31 a a DT work_fnploejenbc2raktl46esxm44i 142 32 , , , work_fnploejenbc2raktl46esxm44i 142 33 , , , work_fnploejenbc2raktl46esxm44i 142 34 a3 a3 NNP work_fnploejenbc2raktl46esxm44i 142 35 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 142 36 “ " `` work_fnploejenbc2raktl46esxm44i 142 37 . . . work_fnploejenbc2raktl46esxm44i 143 1 In in IN work_fnploejenbc2raktl46esxm44i 143 2 a a DT work_fnploejenbc2raktl46esxm44i 143 3 subgame subgame NN work_fnploejenbc2raktl46esxm44i 143 4 , , , work_fnploejenbc2raktl46esxm44i 143 5 the the DT work_fnploejenbc2raktl46esxm44i 143 6 finite finite JJ work_fnploejenbc2raktl46esxm44i 143 7 collection collection NN work_fnploejenbc2raktl46esxm44i 143 8 of of IN work_fnploejenbc2raktl46esxm44i 143 9 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 143 10 events event NNS work_fnploejenbc2raktl46esxm44i 143 11 in in IN work_fnploejenbc2raktl46esxm44i 143 12 a a DT work_fnploejenbc2raktl46esxm44i 143 13 is be VBZ work_fnploejenbc2raktl46esxm44i 143 14 specified specify VBN work_fnploejenbc2raktl46esxm44i 143 15 ; ; : work_fnploejenbc2raktl46esxm44i 143 16 if if IN work_fnploejenbc2raktl46esxm44i 143 17 player player NN work_fnploejenbc2raktl46esxm44i 143 18 II II NNP work_fnploejenbc2raktl46esxm44i 143 19 chooses choose VBZ work_fnploejenbc2raktl46esxm44i 143 20 p p NN work_fnploejenbc2raktl46esxm44i 143 21 to to TO work_fnploejenbc2raktl46esxm44i 143 22 express express VB work_fnploejenbc2raktl46esxm44i 143 23 an an DT work_fnploejenbc2raktl46esxm44i 143 24 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 143 25 about about IN work_fnploejenbc2raktl46esxm44i 143 26 these these DT work_fnploejenbc2raktl46esxm44i 143 27 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 143 28 events event NNS work_fnploejenbc2raktl46esxm44i 143 29 , , , work_fnploejenbc2raktl46esxm44i 143 30 then then RB work_fnploejenbc2raktl46esxm44i 143 31 the the DT work_fnploejenbc2raktl46esxm44i 143 32 overall overall JJ work_fnploejenbc2raktl46esxm44i 143 33 loss loss NN work_fnploejenbc2raktl46esxm44i 143 34 would would MD work_fnploejenbc2raktl46esxm44i 143 35 be be VB work_fnploejenbc2raktl46esxm44i 143 36 Lf Lf NNP work_fnploejenbc2raktl46esxm44i 143 37 , , , work_fnploejenbc2raktl46esxm44i 143 38 ti,,dw ti,,dw NNP work_fnploejenbc2raktl46esxm44i 143 39 ~1 ~1 CD work_fnploejenbc2raktl46esxm44i 143 40 . . . work_fnploejenbc2raktl46esxm44i 144 1 The the DT work_fnploejenbc2raktl46esxm44i 144 2 subgame subgame NN work_fnploejenbc2raktl46esxm44i 144 3 Gf,+.,i gf,+.,i NN work_fnploejenbc2raktl46esxm44i 144 4 is be VBZ work_fnploejenbc2raktl46esxm44i 144 5 regarded regard VBN work_fnploejenbc2raktl46esxm44i 144 6 as as IN work_fnploejenbc2raktl46esxm44i 144 7 a a DT work_fnploejenbc2raktl46esxm44i 144 8 game game NN work_fnploejenbc2raktl46esxm44i 144 9 with with IN work_fnploejenbc2raktl46esxm44i 144 10 partial partial JJ work_fnploejenbc2raktl46esxm44i 144 11 infor- infor- XX work_fnploejenbc2raktl46esxm44i 144 12 mation mation NN work_fnploejenbc2raktl46esxm44i 144 13 , , , work_fnploejenbc2raktl46esxm44i 144 14 namely namely RB work_fnploejenbc2raktl46esxm44i 144 15 player player NN work_fnploejenbc2raktl46esxm44i 144 16 II II NNP work_fnploejenbc2raktl46esxm44i 144 17 does do VBZ work_fnploejenbc2raktl46esxm44i 144 18 know know VB work_fnploejenbc2raktl46esxm44i 144 19 that that IN work_fnploejenbc2raktl46esxm44i 144 20 a a DT work_fnploejenbc2raktl46esxm44i 144 21 is be VBZ work_fnploejenbc2raktl46esxm44i 144 22 to to TO work_fnploejenbc2raktl46esxm44i 144 23 be be VB work_fnploejenbc2raktl46esxm44i 144 24 considered consider VBN work_fnploejenbc2raktl46esxm44i 144 25 . . . work_fnploejenbc2raktl46esxm44i 145 1 For for IN work_fnploejenbc2raktl46esxm44i 145 2 example example NN work_fnploejenbc2raktl46esxm44i 145 3 , , , work_fnploejenbc2raktl46esxm44i 145 4 if if IN work_fnploejenbc2raktl46esxm44i 145 5 a=((ElF a=((ElF NNS work_fnploejenbc2raktl46esxm44i 145 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 7 , , , work_fnploejenbc2raktl46esxm44i 145 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 9 E”(F e”(f NN work_fnploejenbc2raktl46esxm44i 145 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 12 and and CC work_fnploejenbc2raktl46esxm44i 145 13 $ $ $ work_fnploejenbc2raktl46esxm44i 145 14 = = SYM work_fnploejenbc2raktl46esxm44i 145 15 + + CC work_fnploejenbc2raktl46esxm44i 145 16 , , , work_fnploejenbc2raktl46esxm44i 145 17 ~(u)=((EIP)(~ ~(u)=((EIP)(~ NNP work_fnploejenbc2raktl46esxm44i 145 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 19 , , , work_fnploejenbc2raktl46esxm44i 145 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 21 EC1 EC1 NNP work_fnploejenbc2raktl46esxm44i 145 22 F)(o F)(o NNP work_fnploejenbc2raktl46esxm44i 145 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 25 , , , work_fnploejenbc2raktl46esxm44i 145 26 and and CC work_fnploejenbc2raktl46esxm44i 145 27 the the DT work_fnploejenbc2raktl46esxm44i 145 28 set set NN work_fnploejenbc2raktl46esxm44i 145 29 of of IN work_fnploejenbc2raktl46esxm44i 145 30 configurations configuration NNS work_fnploejenbc2raktl46esxm44i 145 31 of of IN work_fnploejenbc2raktl46esxm44i 145 32 a a DT work_fnploejenbc2raktl46esxm44i 145 33 giving give VBG work_fnploejenbc2raktl46esxm44i 145 34 rise rise NN work_fnploejenbc2raktl46esxm44i 145 35 to to IN work_fnploejenbc2raktl46esxm44i 145 36 non non JJ work_fnploejenbc2raktl46esxm44i 145 37 - - JJ work_fnploejenbc2raktl46esxm44i 145 38 zero zero JJ work_fnploejenbc2raktl46esxm44i 145 39 losses loss NNS work_fnploejenbc2raktl46esxm44i 145 40 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 41 f f NNP work_fnploejenbc2raktl46esxm44i 145 42 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 43 x x NNP work_fnploejenbc2raktl46esxm44i 145 44 , , , work_fnploejenbc2raktl46esxm44i 145 45 u u NNP work_fnploejenbc2raktl46esxm44i 145 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 47 z z NNP work_fnploejenbc2raktl46esxm44i 145 48 0 0 CD work_fnploejenbc2raktl46esxm44i 145 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 50 is be VBZ work_fnploejenbc2raktl46esxm44i 145 51 { { -LRB- work_fnploejenbc2raktl46esxm44i 145 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 53 EIF EIF NNP work_fnploejenbc2raktl46esxm44i 145 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 55 , , , work_fnploejenbc2raktl46esxm44i 145 56 11 11 CD work_fnploejenbc2raktl46esxm44i 145 57 , , , work_fnploejenbc2raktl46esxm44i 145 58 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 59 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 60 E”IF E”IF NNP work_fnploejenbc2raktl46esxm44i 145 61 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 62 , , , work_fnploejenbc2raktl46esxm44i 145 63 01 01 CD work_fnploejenbc2raktl46esxm44i 145 64 , , , work_fnploejenbc2raktl46esxm44i 145 65 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 66 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 67 EIF EIF NNP work_fnploejenbc2raktl46esxm44i 145 68 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 69 , , , work_fnploejenbc2raktl46esxm44i 145 70 O o UH work_fnploejenbc2raktl46esxm44i 145 71 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 72 , , , work_fnploejenbc2raktl46esxm44i 145 73 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 74 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 145 75 E”IF E”IF NNP work_fnploejenbc2raktl46esxm44i 145 76 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 145 77 , , , work_fnploejenbc2raktl46esxm44i 145 78 l l NN work_fnploejenbc2raktl46esxm44i 145 79 , , , work_fnploejenbc2raktl46esxm44i 145 80 } } -RRB- work_fnploejenbc2raktl46esxm44i 145 81 . . . work_fnploejenbc2raktl46esxm44i 146 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 146 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 146 3 TO to IN work_fnploejenbc2raktl46esxm44i 146 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 146 5 557 557 CD work_fnploejenbc2raktl46esxm44i 146 6 For for IN work_fnploejenbc2raktl46esxm44i 146 7 is be VBZ work_fnploejenbc2raktl46esxm44i 146 8 { { -LRB- work_fnploejenbc2raktl46esxm44i 146 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 146 10 AO AO NNP work_fnploejenbc2raktl46esxm44i 146 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 12 , , , work_fnploejenbc2raktl46esxm44i 146 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 146 14 0 0 NFP work_fnploejenbc2raktl46esxm44i 146 15 , , , work_fnploejenbc2raktl46esxm44i 146 16 l l NN work_fnploejenbc2raktl46esxm44i 146 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 18 } } -RRB- work_fnploejenbc2raktl46esxm44i 146 19 , , , work_fnploejenbc2raktl46esxm44i 146 20 2 2 CD work_fnploejenbc2raktl46esxm44i 146 21 = = SYM work_fnploejenbc2raktl46esxm44i 146 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 146 23 x1 x1 NNP work_fnploejenbc2raktl46esxm44i 146 24 , , , work_fnploejenbc2raktl46esxm44i 146 25 x x NNP work_fnploejenbc2raktl46esxm44i 146 26 , , , work_fnploejenbc2raktl46esxm44i 146 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 28 , , , work_fnploejenbc2raktl46esxm44i 146 29 where where WRB work_fnploejenbc2raktl46esxm44i 146 30 x1 x1 NNP work_fnploejenbc2raktl46esxm44i 146 31 = = SYM work_fnploejenbc2raktl46esxm44i 146 32 p(EI p(EI NNP work_fnploejenbc2raktl46esxm44i 146 33 F F NNP work_fnploejenbc2raktl46esxm44i 146 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 35 , , , work_fnploejenbc2raktl46esxm44i 146 36 .x2 .x2 . work_fnploejenbc2raktl46esxm44i 146 37 = = NFP work_fnploejenbc2raktl46esxm44i 146 38 p(E’I p(E’I NNP work_fnploejenbc2raktl46esxm44i 146 39 F F NNP work_fnploejenbc2raktl46esxm44i 146 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 41 , , , work_fnploejenbc2raktl46esxm44i 146 42 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 146 43 have have VBP work_fnploejenbc2raktl46esxm44i 146 44 two two CD work_fnploejenbc2raktl46esxm44i 146 45 overall overall JJ work_fnploejenbc2raktl46esxm44i 146 46 scores score NNS work_fnploejenbc2raktl46esxm44i 146 47 : : : work_fnploejenbc2raktl46esxm44i 146 48 f(xr f(xr CD work_fnploejenbc2raktl46esxm44i 146 49 , , , work_fnploejenbc2raktl46esxm44i 146 50 l)+f(Xz l)+f(xz NN work_fnploejenbc2raktl46esxm44i 146 51 , , , work_fnploejenbc2raktl46esxm44i 146 52 0 0 CD work_fnploejenbc2raktl46esxm44i 146 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 54 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 146 55 if if IN work_fnploejenbc2raktl46esxm44i 146 56 EIF EIF NNP work_fnploejenbc2raktl46esxm44i 146 57 occurs occur VBZ work_fnploejenbc2raktl46esxm44i 146 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 146 59 and and CC work_fnploejenbc2raktl46esxm44i 146 60 f(X f(x RBR work_fnploejenbc2raktl46esxm44i 146 61 , , , work_fnploejenbc2raktl46esxm44i 146 62 ? ? . work_fnploejenbc2raktl46esxm44i 147 1 0 0 LS work_fnploejenbc2raktl46esxm44i 147 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 147 3 + + CD work_fnploejenbc2raktl46esxm44i 147 4 f(x f(x CD work_fnploejenbc2raktl46esxm44i 147 5 * * NFP work_fnploejenbc2raktl46esxm44i 147 6 , , , work_fnploejenbc2raktl46esxm44i 147 7 1 1 CD work_fnploejenbc2raktl46esxm44i 147 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 147 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 147 10 if if IN work_fnploejenbc2raktl46esxm44i 147 11 E e NN work_fnploejenbc2raktl46esxm44i 147 12 ” " '' work_fnploejenbc2raktl46esxm44i 147 13 1 1 CD work_fnploejenbc2raktl46esxm44i 147 14 F f NN work_fnploejenbc2raktl46esxm44i 147 15 occurs occur VBZ work_fnploejenbc2raktl46esxm44i 147 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 147 17 . . . work_fnploejenbc2raktl46esxm44i 148 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 148 2 should should MD work_fnploejenbc2raktl46esxm44i 148 3 be be VB work_fnploejenbc2raktl46esxm44i 148 4 noted note VBN work_fnploejenbc2raktl46esxm44i 148 5 that that IN work_fnploejenbc2raktl46esxm44i 148 6 so so RB work_fnploejenbc2raktl46esxm44i 148 7 far far RB work_fnploejenbc2raktl46esxm44i 148 8 only only RB work_fnploejenbc2raktl46esxm44i 148 9 those those DT work_fnploejenbc2raktl46esxm44i 148 10 finite finite JJ work_fnploejenbc2raktl46esxm44i 148 11 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 148 12 of of IN work_fnploejenbc2raktl46esxm44i 148 13 events event NNS work_fnploejenbc2raktl46esxm44i 148 14 have have VBP work_fnploejenbc2raktl46esxm44i 148 15 been be VBN work_fnploejenbc2raktl46esxm44i 148 16 considered consider VBN work_fnploejenbc2raktl46esxm44i 148 17 which which WDT work_fnploejenbc2raktl46esxm44i 148 18 have have VBP work_fnploejenbc2raktl46esxm44i 148 19 a a DT work_fnploejenbc2raktl46esxm44i 148 20 common common JJ work_fnploejenbc2raktl46esxm44i 148 21 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 148 22 . . . work_fnploejenbc2raktl46esxm44i 149 1 Relevant relevant JJ work_fnploejenbc2raktl46esxm44i 149 2 to to IN work_fnploejenbc2raktl46esxm44i 149 3 this this DT work_fnploejenbc2raktl46esxm44i 149 4 , , , work_fnploejenbc2raktl46esxm44i 149 5 denote denote NN work_fnploejenbc2raktl46esxm44i 149 6 for for IN work_fnploejenbc2raktl46esxm44i 149 7 any any DT work_fnploejenbc2raktl46esxm44i 149 8 Fe Fe NNP work_fnploejenbc2raktl46esxm44i 149 9 ZZZ ZZZ NNP work_fnploejenbc2raktl46esxm44i 149 10 ’ ' '' work_fnploejenbc2raktl46esxm44i 149 11 , , , work_fnploejenbc2raktl46esxm44i 149 12 d d NN work_fnploejenbc2raktl46esxm44i 149 13 - - : work_fnploejenbc2raktl46esxm44i 149 14 fF= ff= FW work_fnploejenbc2raktl46esxm44i 149 15 { { -LRB- work_fnploejenbc2raktl46esxm44i 149 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 149 17 EIF EIF NNP work_fnploejenbc2raktl46esxm44i 149 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 149 19 : : : work_fnploejenbc2raktl46esxm44i 149 20 EEL EEL NNP work_fnploejenbc2raktl46esxm44i 149 21 } } -RRB- work_fnploejenbc2raktl46esxm44i 149 22 . . . work_fnploejenbc2raktl46esxm44i 150 1 The the DT work_fnploejenbc2raktl46esxm44i 150 2 reason reason NN work_fnploejenbc2raktl46esxm44i 150 3 for for IN work_fnploejenbc2raktl46esxm44i 150 4 this this DT work_fnploejenbc2raktl46esxm44i 150 5 is be VBZ work_fnploejenbc2raktl46esxm44i 150 6 that that IN work_fnploejenbc2raktl46esxm44i 150 7 if if IN work_fnploejenbc2raktl46esxm44i 150 8 one one CD work_fnploejenbc2raktl46esxm44i 150 9 wished wish VBD work_fnploejenbc2raktl46esxm44i 150 10 to to TO work_fnploejenbc2raktl46esxm44i 150 11 determine determine VB work_fnploejenbc2raktl46esxm44i 150 12 the the DT work_fnploejenbc2raktl46esxm44i 150 13 possible possible JJ work_fnploejenbc2raktl46esxm44i 150 14 indicator indicator NN work_fnploejenbc2raktl46esxm44i 150 15 evaluation evaluation NN work_fnploejenbc2raktl46esxm44i 150 16 combinations combination NNS work_fnploejenbc2raktl46esxm44i 150 17 among among IN work_fnploejenbc2raktl46esxm44i 150 18 any any DT work_fnploejenbc2raktl46esxm44i 150 19 sequence sequence NN work_fnploejenbc2raktl46esxm44i 150 20 such such JJ work_fnploejenbc2raktl46esxm44i 150 21 as as IN work_fnploejenbc2raktl46esxm44i 150 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 150 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 150 24 E e NN work_fnploejenbc2raktl46esxm44i 150 25 , , , work_fnploejenbc2raktl46esxm44i 150 26 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 150 27 F F NNP work_fnploejenbc2raktl46esxm44i 150 28 , , , work_fnploejenbc2raktl46esxm44i 150 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 150 30 , , , work_fnploejenbc2raktl46esxm44i 150 31 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 150 32 E e NN work_fnploejenbc2raktl46esxm44i 150 33 , , , work_fnploejenbc2raktl46esxm44i 150 34 / / SYM work_fnploejenbc2raktl46esxm44i 150 35 F2 f2 NN work_fnploejenbc2raktl46esxm44i 150 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 150 37 , , , work_fnploejenbc2raktl46esxm44i 150 38 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 150 39 E e UH work_fnploejenbc2raktl46esxm44i 150 40 , , , work_fnploejenbc2raktl46esxm44i 150 41 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 150 42 F3 f3 NN work_fnploejenbc2raktl46esxm44i 150 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 150 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 150 45 , , , work_fnploejenbc2raktl46esxm44i 150 46 until until IN work_fnploejenbc2raktl46esxm44i 150 47 recently recently RB work_fnploejenbc2raktl46esxm44i 150 48 , , , work_fnploejenbc2raktl46esxm44i 150 49 no no DT work_fnploejenbc2raktl46esxm44i 150 50 standard standard JJ work_fnploejenbc2raktl46esxm44i 150 51 technique technique NN work_fnploejenbc2raktl46esxm44i 150 52 existed exist VBD work_fnploejenbc2raktl46esxm44i 150 53 for for IN work_fnploejenbc2raktl46esxm44i 150 54 dealing deal VBG work_fnploejenbc2raktl46esxm44i 150 55 with with IN work_fnploejenbc2raktl46esxm44i 150 56 this this DT work_fnploejenbc2raktl46esxm44i 150 57 issue issue NN work_fnploejenbc2raktl46esxm44i 150 58 . . . work_fnploejenbc2raktl46esxm44i 151 1 However however RB work_fnploejenbc2raktl46esxm44i 151 2 , , , work_fnploejenbc2raktl46esxm44i 151 3 Goodman Goodman NNP work_fnploejenbc2raktl46esxm44i 151 4 , , , work_fnploejenbc2raktl46esxm44i 151 5 Nguyen Nguyen NNP work_fnploejenbc2raktl46esxm44i 151 6 , , , work_fnploejenbc2raktl46esxm44i 151 7 and and CC work_fnploejenbc2raktl46esxm44i 151 8 Walker Walker NNP work_fnploejenbc2raktl46esxm44i 151 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 151 10 121 121 CD work_fnploejenbc2raktl46esxm44i 151 11 and and CC work_fnploejenbc2raktl46esxm44i 151 12 Schay schay NN work_fnploejenbc2raktl46esxm44i 151 13 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 151 14 24 24 CD work_fnploejenbc2raktl46esxm44i 151 15 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 151 16 have have VBP work_fnploejenbc2raktl46esxm44i 151 17 proposed propose VBN work_fnploejenbc2raktl46esxm44i 151 18 independent independent JJ work_fnploejenbc2raktl46esxm44i 151 19 nonstandard nonstandard NN work_fnploejenbc2raktl46esxm44i 151 20 syntactic syntactic JJ work_fnploejenbc2raktl46esxm44i 151 21 approaches approach NNS work_fnploejenbc2raktl46esxm44i 151 22 for for IN work_fnploejenbc2raktl46esxm44i 151 23 treating treat VBG work_fnploejenbc2raktl46esxm44i 151 24 this this DT work_fnploejenbc2raktl46esxm44i 151 25 and and CC work_fnploejenbc2raktl46esxm44i 151 26 related related JJ work_fnploejenbc2raktl46esxm44i 151 27 problems problem NNS work_fnploejenbc2raktl46esxm44i 151 28 . . . work_fnploejenbc2raktl46esxm44i 152 1 Only only RB work_fnploejenbc2raktl46esxm44i 152 2 one one CD work_fnploejenbc2raktl46esxm44i 152 3 such such JJ work_fnploejenbc2raktl46esxm44i 152 4 situation situation NN work_fnploejenbc2raktl46esxm44i 152 5 will will MD work_fnploejenbc2raktl46esxm44i 152 6 be be VB work_fnploejenbc2raktl46esxm44i 152 7 considered consider VBN work_fnploejenbc2raktl46esxm44i 152 8 in in IN work_fnploejenbc2raktl46esxm44i 152 9 this this DT work_fnploejenbc2raktl46esxm44i 152 10 paper paper NN work_fnploejenbc2raktl46esxm44i 152 11 , , , work_fnploejenbc2raktl46esxm44i 152 12 namely namely RB work_fnploejenbc2raktl46esxm44i 152 13 the the DT work_fnploejenbc2raktl46esxm44i 152 14 fundamental fundamental JJ work_fnploejenbc2raktl46esxm44i 152 15 natural natural JJ work_fnploejenbc2raktl46esxm44i 152 16 conjunctive conjunctive JJ work_fnploejenbc2raktl46esxm44i 152 17 chaining chaining NN work_fnploejenbc2raktl46esxm44i 152 18 relation relation NN work_fnploejenbc2raktl46esxm44i 152 19 , , , work_fnploejenbc2raktl46esxm44i 152 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 152 21 El El NNP work_fnploejenbc2raktl46esxm44i 152 22 FG)(F fg)(f ADD work_fnploejenbc2raktl46esxm44i 152 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 152 24 G g NN work_fnploejenbc2raktl46esxm44i 152 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 152 26 = = NFP work_fnploejenbc2raktl46esxm44i 152 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 152 28 EFI EFI NNP work_fnploejenbc2raktl46esxm44i 152 29 G G NNP work_fnploejenbc2raktl46esxm44i 152 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 152 31 , , , work_fnploejenbc2raktl46esxm44i 152 32 which which WDT work_fnploejenbc2raktl46esxm44i 152 33 is be VBZ work_fnploejenbc2raktl46esxm44i 152 34 obviously obviously RB work_fnploejenbc2raktl46esxm44i 152 35 true true JJ work_fnploejenbc2raktl46esxm44i 152 36 for for IN work_fnploejenbc2raktl46esxm44i 152 37 all all DT work_fnploejenbc2raktl46esxm44i 152 38 corresponding correspond VBG work_fnploejenbc2raktl46esxm44i 152 39 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 152 40 probability probability NN work_fnploejenbc2raktl46esxm44i 152 41 evaluations evaluation NNS work_fnploejenbc2raktl46esxm44i 152 42 AEI AEI NNP work_fnploejenbc2raktl46esxm44i 152 43 = = FW work_fnploejenbc2raktl46esxm44i 152 44 I i NN work_fnploejenbc2raktl46esxm44i 152 45 .PV’I .PV’I . work_fnploejenbc2raktl46esxm44i 152 46 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 152 47 3 3 CD work_fnploejenbc2raktl46esxm44i 152 48 = = SYM work_fnploejenbc2raktl46esxm44i 152 49 PPI PPI NNP work_fnploejenbc2raktl46esxm44i 152 50 G G NNP work_fnploejenbc2raktl46esxm44i 152 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 152 52 for for IN work_fnploejenbc2raktl46esxm44i 152 53 p(G p(g LS work_fnploejenbc2raktl46esxm44i 152 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 152 55 > > XX work_fnploejenbc2raktl46esxm44i 152 56 0 0 NFP work_fnploejenbc2raktl46esxm44i 152 57 . . . work_fnploejenbc2raktl46esxm44i 153 1 More More JJR work_fnploejenbc2raktl46esxm44i 153 2 details detail NNS work_fnploejenbc2raktl46esxm44i 153 3 of of IN work_fnploejenbc2raktl46esxm44i 153 4 this this DT work_fnploejenbc2raktl46esxm44i 153 5 will will MD work_fnploejenbc2raktl46esxm44i 153 6 be be VB work_fnploejenbc2raktl46esxm44i 153 7 seen see VBN work_fnploejenbc2raktl46esxm44i 153 8 in in IN work_fnploejenbc2raktl46esxm44i 153 9 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 153 10 3.2.3 3.2.3 NNP work_fnploejenbc2raktl46esxm44i 153 11 et et NNP work_fnploejenbc2raktl46esxm44i 153 12 passim passim NN work_fnploejenbc2raktl46esxm44i 153 13 . . . work_fnploejenbc2raktl46esxm44i 154 1 2.4 2.4 CD work_fnploejenbc2raktl46esxm44i 154 2 . . . work_fnploejenbc2raktl46esxm44i 155 1 Equivalent Equivalent NNP work_fnploejenbc2raktl46esxm44i 155 2 Reduced Reduced NNP work_fnploejenbc2raktl46esxm44i 155 3 Forms Forms NNPS work_fnploejenbc2raktl46esxm44i 155 4 of of IN work_fnploejenbc2raktl46esxm44i 155 5 Games Games NNPS work_fnploejenbc2raktl46esxm44i 155 6 and and CC work_fnploejenbc2raktl46esxm44i 155 7 Subgames Subgames NNP work_fnploejenbc2raktl46esxm44i 155 8 The the DT work_fnploejenbc2raktl46esxm44i 155 9 space space NN work_fnploejenbc2raktl46esxm44i 155 10 /1 /1 . work_fnploejenbc2raktl46esxm44i 155 11 r r LS work_fnploejenbc2raktl46esxm44i 155 12 = = SYM work_fnploejenbc2raktl46esxm44i 155 13 J J NNP work_fnploejenbc2raktl46esxm44i 155 14 & & CC work_fnploejenbc2raktl46esxm44i 155 15 , , , work_fnploejenbc2raktl46esxm44i 155 16 x x SYM work_fnploejenbc2raktl46esxm44i 155 17 52 52 CD work_fnploejenbc2raktl46esxm44i 155 18 in in IN work_fnploejenbc2raktl46esxm44i 155 19 the the DT work_fnploejenbc2raktl46esxm44i 155 20 game game NN work_fnploejenbc2raktl46esxm44i 155 21 G/,@ G/,@ NNP work_fnploejenbc2raktl46esxm44i 155 22 is be VBZ work_fnploejenbc2raktl46esxm44i 155 23 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 155 24 , , , work_fnploejenbc2raktl46esxm44i 155 25 in in IN work_fnploejenbc2raktl46esxm44i 155 26 general general JJ work_fnploejenbc2raktl46esxm44i 155 27 , , , work_fnploejenbc2raktl46esxm44i 155 28 but but CC work_fnploejenbc2raktl46esxm44i 155 29 for for IN work_fnploejenbc2raktl46esxm44i 155 30 each each DT work_fnploejenbc2raktl46esxm44i 155 31 R r NN work_fnploejenbc2raktl46esxm44i 155 32 E E NNP work_fnploejenbc2raktl46esxm44i 155 33 Jm Jm NNP work_fnploejenbc2raktl46esxm44i 155 34 , , , work_fnploejenbc2raktl46esxm44i 155 35 the the DT work_fnploejenbc2raktl46esxm44i 155 36 space space NN work_fnploejenbc2raktl46esxm44i 155 37 of of IN work_fnploejenbc2raktl46esxm44i 155 38 configurations configuration NNS work_fnploejenbc2raktl46esxm44i 155 39 of of IN work_fnploejenbc2raktl46esxm44i 155 40 a a DT work_fnploejenbc2raktl46esxm44i 155 41 , , , work_fnploejenbc2raktl46esxm44i 155 42 namely namely RB work_fnploejenbc2raktl46esxm44i 155 43 a(Q a(Q , work_fnploejenbc2raktl46esxm44i 155 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 155 45 is be VBZ work_fnploejenbc2raktl46esxm44i 155 46 finite finite JJ work_fnploejenbc2raktl46esxm44i 155 47 , , , work_fnploejenbc2raktl46esxm44i 155 48 a a DT work_fnploejenbc2raktl46esxm44i 155 49 sub- sub- JJ work_fnploejenbc2raktl46esxm44i 155 50 set set NN work_fnploejenbc2raktl46esxm44i 155 51 of of IN work_fnploejenbc2raktl46esxm44i 155 52 10 10 CD work_fnploejenbc2raktl46esxm44i 155 53 , , , work_fnploejenbc2raktl46esxm44i 155 54 1 1 CD work_fnploejenbc2raktl46esxm44i 155 55 , , , work_fnploejenbc2raktl46esxm44i 155 56 u}lA^ u}lA^ NNP work_fnploejenbc2raktl46esxm44i 155 57 ‘ ' `` work_fnploejenbc2raktl46esxm44i 155 58 , , , work_fnploejenbc2raktl46esxm44i 155 59 where where WRB work_fnploejenbc2raktl46esxm44i 155 60 Ial Ial NNP work_fnploejenbc2raktl46esxm44i 155 61 denotes denote VBZ work_fnploejenbc2raktl46esxm44i 155 62 the the DT work_fnploejenbc2raktl46esxm44i 155 63 “ " `` work_fnploejenbc2raktl46esxm44i 155 64 dimension dimension NN work_fnploejenbc2raktl46esxm44i 155 65 ” " '' work_fnploejenbc2raktl46esxm44i 155 66 of of IN work_fnploejenbc2raktl46esxm44i 155 67 8 8 CD work_fnploejenbc2raktl46esxm44i 155 68 ; ; : work_fnploejenbc2raktl46esxm44i 155 69 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 155 70 , , , work_fnploejenbc2raktl46esxm44i 155 71 if if IN work_fnploejenbc2raktl46esxm44i 155 72 A a NN work_fnploejenbc2raktl46esxm44i 155 73 E e NN work_fnploejenbc2raktl46esxm44i 155 74 d d NN work_fnploejenbc2raktl46esxm44i 155 75 ” " '' work_fnploejenbc2raktl46esxm44i 155 76 , , , work_fnploejenbc2raktl46esxm44i 155 77 then then RB work_fnploejenbc2raktl46esxm44i 155 78 IAl IAl NNP work_fnploejenbc2raktl46esxm44i 155 79 = = SYM work_fnploejenbc2raktl46esxm44i 155 80 n. n. NN work_fnploejenbc2raktl46esxm44i 155 81 On on IN work_fnploejenbc2raktl46esxm44i 155 82 the the DT work_fnploejenbc2raktl46esxm44i 155 83 other other JJ work_fnploejenbc2raktl46esxm44i 155 84 hand hand NN work_fnploejenbc2raktl46esxm44i 155 85 , , , work_fnploejenbc2raktl46esxm44i 155 86 the the DT work_fnploejenbc2raktl46esxm44i 155 87 domain domain NN work_fnploejenbc2raktl46esxm44i 155 88 of of IN work_fnploejenbc2raktl46esxm44i 155 89 Lf,$ Lf,$ NNP work_fnploejenbc2raktl46esxm44i 155 90 involves involve VBZ work_fnploejenbc2raktl46esxm44i 155 91 a a DT work_fnploejenbc2raktl46esxm44i 155 92 , , , work_fnploejenbc2raktl46esxm44i 155 93 but but CC work_fnploejenbc2raktl46esxm44i 155 94 since since IN work_fnploejenbc2raktl46esxm44i 155 95 Lf Lf NNP work_fnploejenbc2raktl46esxm44i 155 96 , , , work_fnploejenbc2raktl46esxm44i 155 97 JA JA NNP work_fnploejenbc2raktl46esxm44i 155 98 , , , work_fnploejenbc2raktl46esxm44i 155 99 . . . work_fnploejenbc2raktl46esxm44i 155 100 , , , work_fnploejenbc2raktl46esxm44i 155 101 p p LS work_fnploejenbc2raktl46esxm44i 155 102 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 155 103 is be VBZ work_fnploejenbc2raktl46esxm44i 155 104 constant constant JJ work_fnploejenbc2raktl46esxm44i 155 105 on on IN work_fnploejenbc2raktl46esxm44i 155 106 each each DT work_fnploejenbc2raktl46esxm44i 155 107 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 155 108 A)- A)- NNP work_fnploejenbc2raktl46esxm44i 155 109 ’ ' '' work_fnploejenbc2raktl46esxm44i 155 110 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 155 111 t t NNP work_fnploejenbc2raktl46esxm44i 155 112 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 155 113 , , , work_fnploejenbc2raktl46esxm44i 155 114 t t NNP work_fnploejenbc2raktl46esxm44i 155 115 E E NNP work_fnploejenbc2raktl46esxm44i 155 116 A(Q A(Q NNP work_fnploejenbc2raktl46esxm44i 155 117 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 155 118 , , , work_fnploejenbc2raktl46esxm44i 155 119 8 8 CD work_fnploejenbc2raktl46esxm44i 155 120 can can MD work_fnploejenbc2raktl46esxm44i 155 121 be be VB work_fnploejenbc2raktl46esxm44i 155 122 replaced replace VBN work_fnploejenbc2raktl46esxm44i 155 123 by by IN work_fnploejenbc2raktl46esxm44i 155 124 the the DT work_fnploejenbc2raktl46esxm44i 155 125 finite finite NNP work_fnploejenbc2raktl46esxm44i 155 126 d d NN work_fnploejenbc2raktl46esxm44i 155 127 - - HYPH work_fnploejenbc2raktl46esxm44i 155 128 partition partition NN work_fnploejenbc2raktl46esxm44i 155 129 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 155 130 of of IN work_fnploejenbc2raktl46esxm44i 155 131 Q Q NNP work_fnploejenbc2raktl46esxm44i 155 132 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 155 133 generated generate VBN work_fnploejenbc2raktl46esxm44i 155 134 by by IN work_fnploejenbc2raktl46esxm44i 155 135 a. a. NN work_fnploejenbc2raktl46esxm44i 156 1 Specifically specifically RB work_fnploejenbc2raktl46esxm44i 156 2 , , , work_fnploejenbc2raktl46esxm44i 156 3 for for IN work_fnploejenbc2raktl46esxm44i 156 4 each each DT work_fnploejenbc2raktl46esxm44i 156 5 a a DT work_fnploejenbc2raktl46esxm44i 156 6 E E NNP work_fnploejenbc2raktl46esxm44i 156 7 Jm Jm NNP work_fnploejenbc2raktl46esxm44i 156 8 , , , work_fnploejenbc2raktl46esxm44i 156 9 say say VBP work_fnploejenbc2raktl46esxm44i 156 10 A a NN work_fnploejenbc2raktl46esxm44i 156 11 = = NFP work_fnploejenbc2raktl46esxm44i 156 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 156 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 156 14 E e NN work_fnploejenbc2raktl46esxm44i 156 15 , , , work_fnploejenbc2raktl46esxm44i 156 16 IF if IN work_fnploejenbc2raktl46esxm44i 156 17 , , , work_fnploejenbc2raktl46esxm44i 156 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 156 19 , , , work_fnploejenbc2raktl46esxm44i 156 20 . . . work_fnploejenbc2raktl46esxm44i 157 1 . . . work_fnploejenbc2raktl46esxm44i 158 1 . . . work_fnploejenbc2raktl46esxm44i 159 1 . . . work_fnploejenbc2raktl46esxm44i 160 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 160 2 E e NN work_fnploejenbc2raktl46esxm44i 160 3 , , , work_fnploejenbc2raktl46esxm44i 160 4 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 160 5 F F NNP work_fnploejenbc2raktl46esxm44i 160 6 , , , work_fnploejenbc2raktl46esxm44i 160 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 160 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 160 9 , , , work_fnploejenbc2raktl46esxm44i 160 10 consider consider VB work_fnploejenbc2raktl46esxm44i 160 11 the the DT work_fnploejenbc2raktl46esxm44i 160 12 finite finite JJ work_fnploejenbc2raktl46esxm44i 160 13 collection collection NN work_fnploejenbc2raktl46esxm44i 160 14 of of IN work_fnploejenbc2raktl46esxm44i 160 15 events event NNS work_fnploejenbc2raktl46esxm44i 160 16 % % NN work_fnploejenbc2raktl46esxm44i 160 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 160 18 A^)= A^)= NNP work_fnploejenbc2raktl46esxm44i 160 19 { { -LRB- work_fnploejenbc2raktl46esxm44i 160 20 E;F E;F NNP work_fnploejenbc2raktl46esxm44i 160 21 , , , work_fnploejenbc2raktl46esxm44i 160 22 , , , work_fnploejenbc2raktl46esxm44i 160 23 E;F E;F NNP work_fnploejenbc2raktl46esxm44i 160 24 ; ; : work_fnploejenbc2raktl46esxm44i 160 25 , , , work_fnploejenbc2raktl46esxm44i 160 26 F f NN work_fnploejenbc2raktl46esxm44i 160 27 ; ; : work_fnploejenbc2raktl46esxm44i 160 28 , , , work_fnploejenbc2raktl46esxm44i 160 29 i= i= NNP work_fnploejenbc2raktl46esxm44i 160 30 1 1 CD work_fnploejenbc2raktl46esxm44i 160 31 , , , work_fnploejenbc2raktl46esxm44i 160 32 . . . work_fnploejenbc2raktl46esxm44i 161 1 . . . work_fnploejenbc2raktl46esxm44i 162 1 . . . work_fnploejenbc2raktl46esxm44i 163 1 . . . work_fnploejenbc2raktl46esxm44i 164 1 n n LS work_fnploejenbc2raktl46esxm44i 164 2 } } -RRB- work_fnploejenbc2raktl46esxm44i 164 3 . . . work_fnploejenbc2raktl46esxm44i 165 1 Let let VB work_fnploejenbc2raktl46esxm44i 165 2 z(a z(a NNP work_fnploejenbc2raktl46esxm44i 165 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 165 4 denote denote VB work_fnploejenbc2raktl46esxm44i 165 5 the the DT work_fnploejenbc2raktl46esxm44i 165 6 canonical canonical JJ work_fnploejenbc2raktl46esxm44i 165 7 parti- parti- XX work_fnploejenbc2raktl46esxm44i 165 8 tion tion NN work_fnploejenbc2raktl46esxm44i 165 9 of of IN work_fnploejenbc2raktl46esxm44i 165 10 Q Q NNP work_fnploejenbc2raktl46esxm44i 165 11 generated generate VBN work_fnploejenbc2raktl46esxm44i 165 12 by by IN work_fnploejenbc2raktl46esxm44i 165 13 + + NNS work_fnploejenbc2raktl46esxm44i 165 14 ? ? . work_fnploejenbc2raktl46esxm44i 166 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 166 2 A a NN work_fnploejenbc2raktl46esxm44i 166 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 166 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 166 5 which which WDT work_fnploejenbc2raktl46esxm44i 166 6 reduces reduce VBZ work_fnploejenbc2raktl46esxm44i 166 7 to to IN work_fnploejenbc2raktl46esxm44i 166 8 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 166 9 = = NFP work_fnploejenbc2raktl46esxm44i 166 10 { { -LRB- work_fnploejenbc2raktl46esxm44i 166 11 Ei Ei NNP work_fnploejenbc2raktl46esxm44i 166 12 } } -RRB- work_fnploejenbc2raktl46esxm44i 166 13 when when WRB work_fnploejenbc2raktl46esxm44i 166 14 all all DT work_fnploejenbc2raktl46esxm44i 166 15 F f NN work_fnploejenbc2raktl46esxm44i 166 16 ; ; : work_fnploejenbc2raktl46esxm44i 166 17 = = NFP work_fnploejenbc2raktl46esxm44i 166 18 Q. Q. NNP work_fnploejenbc2raktl46esxm44i 167 1 Then then RB work_fnploejenbc2raktl46esxm44i 167 2 , , , work_fnploejenbc2raktl46esxm44i 167 3 rc(a)= rc(a)= FW work_fnploejenbc2raktl46esxm44i 167 4 { { -LRB- work_fnploejenbc2raktl46esxm44i 167 5 B,,j= b,,j= NN work_fnploejenbc2raktl46esxm44i 167 6 1 1 CD work_fnploejenbc2raktl46esxm44i 167 7 , , , work_fnploejenbc2raktl46esxm44i 167 8 2 2 CD work_fnploejenbc2raktl46esxm44i 167 9 , , , work_fnploejenbc2raktl46esxm44i 167 10 . . . work_fnploejenbc2raktl46esxm44i 168 1 . . . work_fnploejenbc2raktl46esxm44i 169 1 . . . work_fnploejenbc2raktl46esxm44i 170 1 . . . work_fnploejenbc2raktl46esxm44i 171 1 23n 23n NNS work_fnploejenbc2raktl46esxm44i 171 2 } } -RRB- work_fnploejenbc2raktl46esxm44i 171 3 , , , work_fnploejenbc2raktl46esxm44i 171 4 where where WRB work_fnploejenbc2raktl46esxm44i 171 5 each each DT work_fnploejenbc2raktl46esxm44i 171 6 B b NN work_fnploejenbc2raktl46esxm44i 171 7 , , , work_fnploejenbc2raktl46esxm44i 171 8 is be VBZ work_fnploejenbc2raktl46esxm44i 171 9 of of IN work_fnploejenbc2raktl46esxm44i 171 10 the the DT work_fnploejenbc2raktl46esxm44i 171 11 form form NN work_fnploejenbc2raktl46esxm44i 171 12 nr= nr= NNP work_fnploejenbc2raktl46esxm44i 171 13 , , , work_fnploejenbc2raktl46esxm44i 171 14 02 02 CD work_fnploejenbc2raktl46esxm44i 171 15 , , , work_fnploejenbc2raktl46esxm44i 171 16 Dk Dk NNP work_fnploejenbc2raktl46esxm44i 171 17 E E VBZ work_fnploejenbc2raktl46esxm44i 171 18 % % NN work_fnploejenbc2raktl46esxm44i 171 19 ‘ ' '' work_fnploejenbc2raktl46esxm44i 171 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 171 21 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 171 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 171 23 , , , work_fnploejenbc2raktl46esxm44i 171 24 sk sk NNP work_fnploejenbc2raktl46esxm44i 171 25 = = SYM work_fnploejenbc2raktl46esxm44i 171 26 1 1 CD work_fnploejenbc2raktl46esxm44i 171 27 or or CC work_fnploejenbc2raktl46esxm44i 171 28 c c NNP work_fnploejenbc2raktl46esxm44i 171 29 ; ; : work_fnploejenbc2raktl46esxm44i 171 30 0 0 CD work_fnploejenbc2raktl46esxm44i 171 31 : : : work_fnploejenbc2raktl46esxm44i 171 32 = = `` work_fnploejenbc2raktl46esxm44i 171 33 Dk Dk NNP work_fnploejenbc2raktl46esxm44i 171 34 , , , work_fnploejenbc2raktl46esxm44i 171 35 0 0 CD work_fnploejenbc2raktl46esxm44i 171 36 : : : work_fnploejenbc2raktl46esxm44i 171 37 is be VBZ work_fnploejenbc2raktl46esxm44i 171 38 the the DT work_fnploejenbc2raktl46esxm44i 171 39 set set JJ work_fnploejenbc2raktl46esxm44i 171 40 complement complement NN work_fnploejenbc2raktl46esxm44i 171 41 of of IN work_fnploejenbc2raktl46esxm44i 171 42 D d NN work_fnploejenbc2raktl46esxm44i 171 43 , , , work_fnploejenbc2raktl46esxm44i 171 44 . . . work_fnploejenbc2raktl46esxm44i 172 1 Also also RB work_fnploejenbc2raktl46esxm44i 172 2 , , , work_fnploejenbc2raktl46esxm44i 172 3 each each DT work_fnploejenbc2raktl46esxm44i 172 4 D d NN work_fnploejenbc2raktl46esxm44i 172 5 , , , work_fnploejenbc2raktl46esxm44i 172 6 is be VBZ work_fnploejenbc2raktl46esxm44i 172 7 a a DT work_fnploejenbc2raktl46esxm44i 172 8 union union NN work_fnploejenbc2raktl46esxm44i 172 9 of of IN work_fnploejenbc2raktl46esxm44i 172 10 the the DT work_fnploejenbc2raktl46esxm44i 172 11 Bis Bis NNP work_fnploejenbc2raktl46esxm44i 172 12 . . . work_fnploejenbc2raktl46esxm44i 173 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 173 2 See see VB work_fnploejenbc2raktl46esxm44i 173 3 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 173 4 23 23 CD work_fnploejenbc2raktl46esxm44i 173 5 , , , work_fnploejenbc2raktl46esxm44i 173 6 p. p. NN work_fnploejenbc2raktl46esxm44i 174 1 12 12 CD work_fnploejenbc2raktl46esxm44i 174 2 - - SYM work_fnploejenbc2raktl46esxm44i 174 3 153 153 CD work_fnploejenbc2raktl46esxm44i 174 4 . . . work_fnploejenbc2raktl46esxm44i 174 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 175 1 Note note VB work_fnploejenbc2raktl46esxm44i 175 2 that that IN work_fnploejenbc2raktl46esxm44i 175 3 because because IN work_fnploejenbc2raktl46esxm44i 175 4 the the DT work_fnploejenbc2raktl46esxm44i 175 5 E e NN work_fnploejenbc2raktl46esxm44i 175 6 ’s ’s NNP work_fnploejenbc2raktl46esxm44i 175 7 and and CC work_fnploejenbc2raktl46esxm44i 175 8 F F NNP work_fnploejenbc2raktl46esxm44i 175 9 ’s ’s '' work_fnploejenbc2raktl46esxm44i 175 10 are be VBP work_fnploejenbc2raktl46esxm44i 175 11 not not RB work_fnploejenbc2raktl46esxm44i 175 12 necessarily necessarily RB work_fnploejenbc2raktl46esxm44i 175 13 distinct distinct JJ work_fnploejenbc2raktl46esxm44i 175 14 , , , work_fnploejenbc2raktl46esxm44i 175 15 the the DT work_fnploejenbc2raktl46esxm44i 175 16 cardinality cardinality NN work_fnploejenbc2raktl46esxm44i 175 17 of of IN work_fnploejenbc2raktl46esxm44i 175 18 z(a z(a NNP work_fnploejenbc2raktl46esxm44i 175 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 175 20 , , , work_fnploejenbc2raktl46esxm44i 175 21 say say VBP work_fnploejenbc2raktl46esxm44i 175 22 m m NNP work_fnploejenbc2raktl46esxm44i 175 23 = = SYM work_fnploejenbc2raktl46esxm44i 175 24 ITCH ITCH NNP work_fnploejenbc2raktl46esxm44i 175 25 , , , work_fnploejenbc2raktl46esxm44i 175 26 is be VBZ work_fnploejenbc2raktl46esxm44i 175 27 most most RBS work_fnploejenbc2raktl46esxm44i 175 28 often often RB work_fnploejenbc2raktl46esxm44i 175 29 ~2~ ~2~ . work_fnploejenbc2raktl46esxm44i 175 30 “ " `` work_fnploejenbc2raktl46esxm44i 175 31 , , , work_fnploejenbc2raktl46esxm44i 175 32 but but CC work_fnploejenbc2raktl46esxm44i 175 33 at at IN work_fnploejenbc2raktl46esxm44i 175 34 least least JJS work_fnploejenbc2raktl46esxm44i 175 35 2 2 CD work_fnploejenbc2raktl46esxm44i 175 36 . . . work_fnploejenbc2raktl46esxm44i 176 1 The the DT work_fnploejenbc2raktl46esxm44i 176 2 cardinality cardinality NN work_fnploejenbc2raktl46esxm44i 176 3 of of IN work_fnploejenbc2raktl46esxm44i 176 4 rc(a rc(a NN work_fnploejenbc2raktl46esxm44i 176 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 176 6 may may MD work_fnploejenbc2raktl46esxm44i 176 7 be be VB work_fnploejenbc2raktl46esxm44i 176 8 less less JJR work_fnploejenbc2raktl46esxm44i 176 9 than than IN work_fnploejenbc2raktl46esxm44i 176 10 n n CC work_fnploejenbc2raktl46esxm44i 176 11 = = UH work_fnploejenbc2raktl46esxm44i 176 12 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 176 13 Al Al NNP work_fnploejenbc2raktl46esxm44i 176 14 as as IN work_fnploejenbc2raktl46esxm44i 176 15 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 176 16 now now RB work_fnploejenbc2raktl46esxm44i 176 17 demonstrate demonstrate VBP work_fnploejenbc2raktl46esxm44i 176 18 . . . work_fnploejenbc2raktl46esxm44i 177 1 558 558 CD work_fnploejenbc2raktl46esxm44i 177 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 177 3 , , , work_fnploejenbc2raktl46esxm44i 177 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 177 5 , , , work_fnploejenbc2raktl46esxm44i 177 6 AND and CC work_fnploejenbc2raktl46esxm44i 177 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 177 8 Let let VBP work_fnploejenbc2raktl46esxm44i 177 9 Then then RB work_fnploejenbc2raktl46esxm44i 177 10 a a DT work_fnploejenbc2raktl46esxm44i 177 11 = = NFP work_fnploejenbc2raktl46esxm44i 177 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 177 13 EF EF NNP work_fnploejenbc2raktl46esxm44i 177 14 , , , work_fnploejenbc2raktl46esxm44i 177 15 E”F e”f UH work_fnploejenbc2raktl46esxm44i 177 16 , , , work_fnploejenbc2raktl46esxm44i 177 17 F F NNP work_fnploejenbc2raktl46esxm44i 177 18 ” " '' work_fnploejenbc2raktl46esxm44i 177 19 , , , work_fnploejenbc2raktl46esxm44i 177 20 F F NNP work_fnploejenbc2raktl46esxm44i 177 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 177 22 . . . work_fnploejenbc2raktl46esxm44i 178 1 SF@ sf@ CD work_fnploejenbc2raktl46esxm44i 178 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 178 3 = = NFP work_fnploejenbc2raktl46esxm44i 178 4 { { -LRB- work_fnploejenbc2raktl46esxm44i 178 5 Dl Dl NNP work_fnploejenbc2raktl46esxm44i 178 6 = = SYM work_fnploejenbc2raktl46esxm44i 178 7 EF EF NNP work_fnploejenbc2raktl46esxm44i 178 8 , , , work_fnploejenbc2raktl46esxm44i 178 9 D d NN work_fnploejenbc2raktl46esxm44i 178 10 , , , work_fnploejenbc2raktl46esxm44i 178 11 = = NFP work_fnploejenbc2raktl46esxm44i 178 12 E”F e”f UH work_fnploejenbc2raktl46esxm44i 178 13 , , , work_fnploejenbc2raktl46esxm44i 178 14 D d NN work_fnploejenbc2raktl46esxm44i 178 15 , , , work_fnploejenbc2raktl46esxm44i 178 16 = = NFP work_fnploejenbc2raktl46esxm44i 178 17 F F NNP work_fnploejenbc2raktl46esxm44i 178 18 ” " '' work_fnploejenbc2raktl46esxm44i 178 19 , , , work_fnploejenbc2raktl46esxm44i 178 20 D d NN work_fnploejenbc2raktl46esxm44i 178 21 , , , work_fnploejenbc2raktl46esxm44i 178 22 = = NFP work_fnploejenbc2raktl46esxm44i 178 23 F F NNP work_fnploejenbc2raktl46esxm44i 178 24 } } -RRB- work_fnploejenbc2raktl46esxm44i 178 25 . . . work_fnploejenbc2raktl46esxm44i 179 1 Only only RB work_fnploejenbc2raktl46esxm44i 179 2 the the DT work_fnploejenbc2raktl46esxm44i 179 3 following follow VBG work_fnploejenbc2raktl46esxm44i 179 4 configurations configuration NNS work_fnploejenbc2raktl46esxm44i 179 5 of of IN work_fnploejenbc2raktl46esxm44i 179 6 “ " `` work_fnploejenbc2raktl46esxm44i 179 7 occurrences occurrence NNS work_fnploejenbc2raktl46esxm44i 179 8 ” " '' work_fnploejenbc2raktl46esxm44i 179 9 can can MD work_fnploejenbc2raktl46esxm44i 179 10 arise arise VB work_fnploejenbc2raktl46esxm44i 179 11 so so IN work_fnploejenbc2raktl46esxm44i 179 12 that that IN work_fnploejenbc2raktl46esxm44i 179 13 m m NN work_fnploejenbc2raktl46esxm44i 179 14 = = -RRB- work_fnploejenbc2raktl46esxm44i 179 15 l7c(A)l=3<4 l7c(A)l=3<4 NNP work_fnploejenbc2raktl46esxm44i 179 16 = = SYM work_fnploejenbc2raktl46esxm44i 179 17 lAj laj NN work_fnploejenbc2raktl46esxm44i 179 18 : : : work_fnploejenbc2raktl46esxm44i 179 19 1 1 CD work_fnploejenbc2raktl46esxm44i 179 20 0 0 CD work_fnploejenbc2raktl46esxm44i 179 21 0 0 CD work_fnploejenbc2raktl46esxm44i 179 22 1 1 CD work_fnploejenbc2raktl46esxm44i 179 23 for for IN work_fnploejenbc2raktl46esxm44i 179 24 B b NN work_fnploejenbc2raktl46esxm44i 179 25 , , , work_fnploejenbc2raktl46esxm44i 179 26 = = SYM work_fnploejenbc2raktl46esxm44i 179 27 EF EF NNP work_fnploejenbc2raktl46esxm44i 179 28 , , , work_fnploejenbc2raktl46esxm44i 179 29 0 0 CD work_fnploejenbc2raktl46esxm44i 179 30 1 1 CD work_fnploejenbc2raktl46esxm44i 179 31 0 0 CD work_fnploejenbc2raktl46esxm44i 179 32 1 1 CD work_fnploejenbc2raktl46esxm44i 179 33 for for IN work_fnploejenbc2raktl46esxm44i 179 34 B b NN work_fnploejenbc2raktl46esxm44i 179 35 , , , work_fnploejenbc2raktl46esxm44i 179 36 = = NFP work_fnploejenbc2raktl46esxm44i 179 37 E”F e”f UH work_fnploejenbc2raktl46esxm44i 179 38 , , , work_fnploejenbc2raktl46esxm44i 179 39 0 0 CD work_fnploejenbc2raktl46esxm44i 179 40 0 0 CD work_fnploejenbc2raktl46esxm44i 179 41 0 0 CD work_fnploejenbc2raktl46esxm44i 179 42 1 1 CD work_fnploejenbc2raktl46esxm44i 179 43 for for IN work_fnploejenbc2raktl46esxm44i 179 44 B,=F b,=f NN work_fnploejenbc2raktl46esxm44i 179 45 ” " '' work_fnploejenbc2raktl46esxm44i 179 46 . . . work_fnploejenbc2raktl46esxm44i 180 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 180 2 , , , work_fnploejenbc2raktl46esxm44i 180 3 B’BcBC b’bcbc ADD work_fnploejenbc2raktl46esxm44i 180 4 = = SYM work_fnploejenbc2raktl46esxm44i 180 5 EF EF NNP work_fnploejenbc2raktl46esxm44i 180 6 1 1 CD work_fnploejenbc2raktl46esxm44i 180 7 2 2 CD work_fnploejenbc2raktl46esxm44i 180 8 3 3 CD work_fnploejenbc2raktl46esxm44i 180 9 BCBIBC BCBIBC NNP work_fnploejenbc2raktl46esxm44i 180 10 = = SYM work_fnploejenbc2raktl46esxm44i 180 11 ECF ECF NNP work_fnploejenbc2raktl46esxm44i 180 12 1 1 CD work_fnploejenbc2raktl46esxm44i 180 13 2 2 CD work_fnploejenbc2raktl46esxm44i 180 14 3 3 CD work_fnploejenbc2raktl46esxm44i 180 15 B;B;B,=F B;B;B,=F NNS work_fnploejenbc2raktl46esxm44i 180 16 ” " '' work_fnploejenbc2raktl46esxm44i 180 17 B1B;B;uB;B2B;=F. b1b;b;ub;b2b;=f. NN work_fnploejenbc2raktl46esxm44i 181 1 Of of IN work_fnploejenbc2raktl46esxm44i 181 2 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 181 3 ourse ourse JJ work_fnploejenbc2raktl46esxm44i 181 4 , , , work_fnploejenbc2raktl46esxm44i 181 5 m=3>2when~=((ElF),(Ec m=3>2when~=((ElF),(Ec NNP work_fnploejenbc2raktl46esxm44i 181 6 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 181 7 F))for~(~)={EF F))for~(~)={EF NNS work_fnploejenbc2raktl46esxm44i 181 8 , , , work_fnploejenbc2raktl46esxm44i 181 9 EcF EcF NNP work_fnploejenbc2raktl46esxm44i 181 10 , , , work_fnploejenbc2raktl46esxm44i 181 11 FcJ= FcJ= NNP work_fnploejenbc2raktl46esxm44i 181 12 W W NNP work_fnploejenbc2raktl46esxm44i 181 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 181 14 . . . work_fnploejenbc2raktl46esxm44i 182 1 The the DT work_fnploejenbc2raktl46esxm44i 182 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 182 3 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 182 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 182 5 reduced reduce VBN work_fnploejenbc2raktl46esxm44i 182 6 form form NN work_fnploejenbc2raktl46esxm44i 182 7 of of IN work_fnploejenbc2raktl46esxm44i 182 8 GY,$ gy,$ PRP work_fnploejenbc2raktl46esxm44i 182 9 is be VBZ work_fnploejenbc2raktl46esxm44i 182 10 G g NN work_fnploejenbc2raktl46esxm44i 182 11 : : : work_fnploejenbc2raktl46esxm44i 182 12 , , , work_fnploejenbc2raktl46esxm44i 182 13 = = NFP work_fnploejenbc2raktl46esxm44i 182 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 182 15 A a NN work_fnploejenbc2raktl46esxm44i 182 16 : : : work_fnploejenbc2raktl46esxm44i 182 17 , , , work_fnploejenbc2raktl46esxm44i 182 18 AZ AZ NNP work_fnploejenbc2raktl46esxm44i 182 19 , , , work_fnploejenbc2raktl46esxm44i 182 20 L&l L&l NNP work_fnploejenbc2raktl46esxm44i 182 21 , , , work_fnploejenbc2raktl46esxm44i 182 22 where where WRB work_fnploejenbc2raktl46esxm44i 182 23 where where WRB work_fnploejenbc2raktl46esxm44i 182 24 n:={(a n:={(a JJR work_fnploejenbc2raktl46esxm44i 182 25 , , , work_fnploejenbc2raktl46esxm44i 182 26 B):a~~~,B~. B):a~~~,B~. NNP work_fnploejenbc2raktl46esxm44i 183 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 183 2 a a LS work_fnploejenbc2raktl46esxm44i 183 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 4 } } -RRB- work_fnploejenbc2raktl46esxm44i 183 5 , , , work_fnploejenbc2raktl46esxm44i 183 6 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 183 7 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 183 8 a a DT work_fnploejenbc2raktl46esxm44i 183 9 Lj!&k lj!&k NN work_fnploejenbc2raktl46esxm44i 183 10 4 4 CD work_fnploejenbc2raktl46esxm44i 183 11 ~0 ~0 CD work_fnploejenbc2raktl46esxm44i 183 12 = = SYM work_fnploejenbc2raktl46esxm44i 183 13 W(P(A W(P(A NNP work_fnploejenbc2raktl46esxm44i 183 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 15 , , , work_fnploejenbc2raktl46esxm44i 183 16 A(B A(B NNP work_fnploejenbc2raktl46esxm44i 183 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 20 , , , work_fnploejenbc2raktl46esxm44i 183 21 a(B a(b LS work_fnploejenbc2raktl46esxm44i 183 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 23 = = NFP work_fnploejenbc2raktl46esxm44i 183 24 t t NN work_fnploejenbc2raktl46esxm44i 183 25 E e NN work_fnploejenbc2raktl46esxm44i 183 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 183 27 0 0 CD work_fnploejenbc2raktl46esxm44i 183 28 , , , work_fnploejenbc2raktl46esxm44i 183 29 1 1 CD work_fnploejenbc2raktl46esxm44i 183 30 , , , work_fnploejenbc2raktl46esxm44i 183 31 u u NNP work_fnploejenbc2raktl46esxm44i 183 32 } } -RRB- work_fnploejenbc2raktl46esxm44i 183 33 ‘ ' `` work_fnploejenbc2raktl46esxm44i 183 34 “ " `` work_fnploejenbc2raktl46esxm44i 183 35 ’ ' '' work_fnploejenbc2raktl46esxm44i 183 36 -=-B={o:&)=t -=-b={o:&)=t RB work_fnploejenbc2raktl46esxm44i 183 37 } } -RRB- work_fnploejenbc2raktl46esxm44i 183 38 , , , work_fnploejenbc2raktl46esxm44i 183 39 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 183 40 , , , work_fnploejenbc2raktl46esxm44i 183 41 /i(B /i(B . work_fnploejenbc2raktl46esxm44i 183 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 43 = = NFP work_fnploejenbc2raktl46esxm44i 183 44 & & CC work_fnploejenbc2raktl46esxm44i 183 45 II II NNP work_fnploejenbc2raktl46esxm44i 183 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 183 47 for for IN work_fnploejenbc2raktl46esxm44i 183 48 any any DT work_fnploejenbc2raktl46esxm44i 183 49 choice choice NN work_fnploejenbc2raktl46esxm44i 183 50 of of IN work_fnploejenbc2raktl46esxm44i 183 51 w w NNP work_fnploejenbc2raktl46esxm44i 183 52 in in IN work_fnploejenbc2raktl46esxm44i 183 53 B. B. NNP work_fnploejenbc2raktl46esxm44i 184 1 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 184 2 , , , work_fnploejenbc2raktl46esxm44i 184 3 the the DT work_fnploejenbc2raktl46esxm44i 184 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 184 5 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 184 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 184 7 reduced reduce VBN work_fnploejenbc2raktl46esxm44i 184 8 form form NN work_fnploejenbc2raktl46esxm44i 184 9 G g NN work_fnploejenbc2raktl46esxm44i 184 10 , , , work_fnploejenbc2raktl46esxm44i 184 11 , , , work_fnploejenbc2raktl46esxm44i 184 12 , , , work_fnploejenbc2raktl46esxm44i 184 13 , , , work_fnploejenbc2raktl46esxm44i 184 14 A a DT work_fnploejenbc2raktl46esxm44i 184 15 is be VBZ work_fnploejenbc2raktl46esxm44i 184 16 G&A G&A NNP work_fnploejenbc2raktl46esxm44i 184 17 = = NFP work_fnploejenbc2raktl46esxm44i 184 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 184 19 Ata Ata NNP work_fnploejenbc2raktl46esxm44i 184 20 , , , work_fnploejenbc2raktl46esxm44i 184 21 Az Az NNP work_fnploejenbc2raktl46esxm44i 184 22 , , , work_fnploejenbc2raktl46esxm44i 184 23 a a DT work_fnploejenbc2raktl46esxm44i 184 24 , , , work_fnploejenbc2raktl46esxm44i 184 25 L&A L&A NNP work_fnploejenbc2raktl46esxm44i 184 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 184 27 , , , work_fnploejenbc2raktl46esxm44i 184 28 where where WRB work_fnploejenbc2raktl46esxm44i 184 29 ny,=?T(A ny,=?t(a NN work_fnploejenbc2raktl46esxm44i 184 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 184 31 SCORING score VBG work_fnploejenbc2raktl46esxm44i 184 32 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 184 33 TO to IN work_fnploejenbc2raktl46esxm44i 184 34 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 184 35 559 559 CD work_fnploejenbc2raktl46esxm44i 184 36 and and CC work_fnploejenbc2raktl46esxm44i 184 37 3 3 CD work_fnploejenbc2raktl46esxm44i 184 38 . . . work_fnploejenbc2raktl46esxm44i 185 1 ANALYTIC ANALYTIC NNP work_fnploejenbc2raktl46esxm44i 185 2 STUDY STUDY NNP work_fnploejenbc2raktl46esxm44i 185 3 OF of IN work_fnploejenbc2raktl46esxm44i 185 4 ADMISSIBILITY admissibility NN work_fnploejenbc2raktl46esxm44i 185 5 In in IN work_fnploejenbc2raktl46esxm44i 185 6 this this DT work_fnploejenbc2raktl46esxm44i 185 7 section section NN work_fnploejenbc2raktl46esxm44i 185 8 , , , work_fnploejenbc2raktl46esxm44i 185 9 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 185 10 will will MD work_fnploejenbc2raktl46esxm44i 185 11 introduce introduce VB work_fnploejenbc2raktl46esxm44i 185 12 various various JJ work_fnploejenbc2raktl46esxm44i 185 13 concepts concept NNS work_fnploejenbc2raktl46esxm44i 185 14 of of IN work_fnploejenbc2raktl46esxm44i 185 15 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 185 16 for for IN work_fnploejenbc2raktl46esxm44i 185 17 Gf,$ Gf,$ NNP work_fnploejenbc2raktl46esxm44i 185 18 and and CC work_fnploejenbc2raktl46esxm44i 185 19 then then RB work_fnploejenbc2raktl46esxm44i 185 20 develop develop VB work_fnploejenbc2raktl46esxm44i 185 21 analytic analytic JJ work_fnploejenbc2raktl46esxm44i 185 22 techniques technique NNS work_fnploejenbc2raktl46esxm44i 185 23 for for IN work_fnploejenbc2raktl46esxm44i 185 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 185 25 weak weak JJ work_fnploejenbc2raktl46esxm44i 185 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 185 27 local local JJ work_fnploejenbc2raktl46esxm44i 185 28 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 185 29 with with IN work_fnploejenbc2raktl46esxm44i 185 30 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 185 31 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 185 32 functions function NNS work_fnploejenbc2raktl46esxm44i 185 33 $ $ $ work_fnploejenbc2raktl46esxm44i 185 34 . . . work_fnploejenbc2raktl46esxm44i 186 1 This this DT work_fnploejenbc2raktl46esxm44i 186 2 also also RB work_fnploejenbc2raktl46esxm44i 186 3 extends extend VBZ work_fnploejenbc2raktl46esxm44i 186 4 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 186 5 ’s ’s POS work_fnploejenbc2raktl46esxm44i 186 6 results result NNS work_fnploejenbc2raktl46esxm44i 186 7 in in IN work_fnploejenbc2raktl46esxm44i 186 8 the the DT work_fnploejenbc2raktl46esxm44i 186 9 case case NN work_fnploejenbc2raktl46esxm44i 186 10 of of IN work_fnploejenbc2raktl46esxm44i 186 11 an an DT work_fnploejenbc2raktl46esxm44i 186 12 additive additive JJ work_fnploejenbc2raktl46esxm44i 186 13 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 186 14 function function NN work_fnploejenbc2raktl46esxm44i 186 15 , , , work_fnploejenbc2raktl46esxm44i 186 16 namely namely RB work_fnploejenbc2raktl46esxm44i 186 17 , , , work_fnploejenbc2raktl46esxm44i 186 18 giving give VBG work_fnploejenbc2raktl46esxm44i 186 19 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 186 20 conditions condition NNS work_fnploejenbc2raktl46esxm44i 186 21 for for IN work_fnploejenbc2raktl46esxm44i 186 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 186 23 weak weak JJ work_fnploejenbc2raktl46esxm44i 186 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 186 25 local local JJ work_fnploejenbc2raktl46esxm44i 186 26 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 186 27 . . . work_fnploejenbc2raktl46esxm44i 187 1 For for IN work_fnploejenbc2raktl46esxm44i 187 2 related related JJ work_fnploejenbc2raktl46esxm44i 187 3 works work NNS work_fnploejenbc2raktl46esxm44i 187 4 in in IN work_fnploejenbc2raktl46esxm44i 187 5 Statistics statistic NNS work_fnploejenbc2raktl46esxm44i 187 6 , , , work_fnploejenbc2raktl46esxm44i 187 7 see see VB work_fnploejenbc2raktl46esxm44i 187 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 187 9 4 4 CD work_fnploejenbc2raktl46esxm44i 187 10 , , , work_fnploejenbc2raktl46esxm44i 187 11 143 143 CD work_fnploejenbc2raktl46esxm44i 187 12 . . . work_fnploejenbc2raktl46esxm44i 188 1 For for IN work_fnploejenbc2raktl46esxm44i 188 2 the the DT work_fnploejenbc2raktl46esxm44i 188 3 concept concept NN work_fnploejenbc2raktl46esxm44i 188 4 of of IN work_fnploejenbc2raktl46esxm44i 188 5 Pareto Pareto NNP work_fnploejenbc2raktl46esxm44i 188 6 optimality optimality NN work_fnploejenbc2raktl46esxm44i 188 7 , , , work_fnploejenbc2raktl46esxm44i 188 8 see see VB work_fnploejenbc2raktl46esxm44i 188 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 188 10 2 2 CD work_fnploejenbc2raktl46esxm44i 188 11 , , , work_fnploejenbc2raktl46esxm44i 188 12 271 271 CD work_fnploejenbc2raktl46esxm44i 188 13 . . . work_fnploejenbc2raktl46esxm44i 189 1 3.1 3.1 CD work_fnploejenbc2raktl46esxm44i 189 2 . . . work_fnploejenbc2raktl46esxm44i 190 1 Concepts concept NNS work_fnploejenbc2raktl46esxm44i 190 2 of of IN work_fnploejenbc2raktl46esxm44i 190 3 Admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 190 4 In in IN work_fnploejenbc2raktl46esxm44i 190 5 this this DT work_fnploejenbc2raktl46esxm44i 190 6 subsection subsection NN work_fnploejenbc2raktl46esxm44i 190 7 , , , work_fnploejenbc2raktl46esxm44i 190 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 190 9 spell spell VBP work_fnploejenbc2raktl46esxm44i 190 10 out out RP work_fnploejenbc2raktl46esxm44i 190 11 relevant relevant JJ work_fnploejenbc2raktl46esxm44i 190 12 forms form NNS work_fnploejenbc2raktl46esxm44i 190 13 of of IN work_fnploejenbc2raktl46esxm44i 190 14 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 190 15 in in IN work_fnploejenbc2raktl46esxm44i 190 16 the the DT work_fnploejenbc2raktl46esxm44i 190 17 reduced reduce VBN work_fnploejenbc2raktl46esxm44i 190 18 form form NN work_fnploejenbc2raktl46esxm44i 190 19 of of IN work_fnploejenbc2raktl46esxm44i 190 20 the the DT work_fnploejenbc2raktl46esxm44i 190 21 game game NN work_fnploejenbc2raktl46esxm44i 190 22 First first RB work_fnploejenbc2raktl46esxm44i 190 23 , , , work_fnploejenbc2raktl46esxm44i 190 24 , , , work_fnploejenbc2raktl46esxm44i 190 25 LL LL NNP work_fnploejenbc2raktl46esxm44i 190 26 E E NNP work_fnploejenbc2raktl46esxm44i 190 27 A a NN work_fnploejenbc2raktl46esxm44i 190 28 , , , work_fnploejenbc2raktl46esxm44i 190 29 is be VBZ work_fnploejenbc2raktl46esxm44i 190 30 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 190 31 ordinary ordinary JJ work_fnploejenbc2raktl46esxm44i 190 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 190 33 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 190 34 with with IN work_fnploejenbc2raktl46esxm44i 190 35 respect respect NN work_fnploejenbc2raktl46esxm44i 190 36 to to IN work_fnploejenbc2raktl46esxm44i 190 37 GTIL GTIL NNP work_fnploejenbc2raktl46esxm44i 190 38 if if IN work_fnploejenbc2raktl46esxm44i 190 39 there there EX work_fnploejenbc2raktl46esxm44i 190 40 is be VBZ work_fnploejenbc2raktl46esxm44i 190 41 no no DT work_fnploejenbc2raktl46esxm44i 190 42 VIZ,~ VIZ,~ NNP work_fnploejenbc2raktl46esxm44i 190 43 , , , work_fnploejenbc2raktl46esxm44i 190 44 such such JJ work_fnploejenbc2raktl46esxm44i 190 45 that that IN work_fnploejenbc2raktl46esxm44i 190 46 Lz$(A lz$(a JJ work_fnploejenbc2raktl46esxm44i 190 47 , , , work_fnploejenbc2raktl46esxm44i 190 48 B b NN work_fnploejenbc2raktl46esxm44i 190 49 , , , work_fnploejenbc2raktl46esxm44i 190 50 v v LS work_fnploejenbc2raktl46esxm44i 190 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 190 52 < < XX work_fnploejenbc2raktl46esxm44i 190 53 , , , work_fnploejenbc2raktl46esxm44i 190 54 ! ! . work_fnploejenbc2raktl46esxm44i 190 55 , , , work_fnploejenbc2raktl46esxm44i 190 56 ; ; : work_fnploejenbc2raktl46esxm44i 190 57 + + ADD work_fnploejenbc2raktl46esxm44i 190 58 . . . work_fnploejenbc2raktl46esxm44i 191 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 191 2 A a NN work_fnploejenbc2raktl46esxm44i 191 3 , , , work_fnploejenbc2raktl46esxm44i 191 4 B b NN work_fnploejenbc2raktl46esxm44i 191 5 , , , work_fnploejenbc2raktl46esxm44i 191 6 p p NNP work_fnploejenbc2raktl46esxm44i 191 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 191 8 for for IN work_fnploejenbc2raktl46esxm44i 191 9 all all DT work_fnploejenbc2raktl46esxm44i 191 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 191 11 A a NN work_fnploejenbc2raktl46esxm44i 191 12 , , , work_fnploejenbc2raktl46esxm44i 191 13 B b NN work_fnploejenbc2raktl46esxm44i 191 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 191 15 E E NNP work_fnploejenbc2raktl46esxm44i 191 16 /1 /1 , work_fnploejenbc2raktl46esxm44i 191 17 : : : work_fnploejenbc2raktl46esxm44i 191 18 with with IN work_fnploejenbc2raktl46esxm44i 191 19 the the DT work_fnploejenbc2raktl46esxm44i 191 20 strict strict JJ work_fnploejenbc2raktl46esxm44i 191 21 inequality inequality NN work_fnploejenbc2raktl46esxm44i 191 22 for for IN work_fnploejenbc2raktl46esxm44i 191 23 at at RB work_fnploejenbc2raktl46esxm44i 191 24 least least RBS work_fnploejenbc2raktl46esxm44i 191 25 one one CD work_fnploejenbc2raktl46esxm44i 191 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 191 27 a a DT work_fnploejenbc2raktl46esxm44i 191 28 , , , work_fnploejenbc2raktl46esxm44i 191 29 B b NN work_fnploejenbc2raktl46esxm44i 191 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 191 31 . . . work_fnploejenbc2raktl46esxm44i 192 1 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 192 2 with with IN work_fnploejenbc2raktl46esxm44i 192 3 respect respect NN work_fnploejenbc2raktl46esxm44i 192 4 to to IN work_fnploejenbc2raktl46esxm44i 192 5 the the DT work_fnploejenbc2raktl46esxm44i 192 6 subgame subgame NN work_fnploejenbc2raktl46esxm44i 192 7 Gzti,~ gzti,~ NN work_fnploejenbc2raktl46esxm44i 192 8 , , , work_fnploejenbc2raktl46esxm44i 192 9 PE/~*,A PE/~*,A NNP work_fnploejenbc2raktl46esxm44i 192 10 = = NFP work_fnploejenbc2raktl46esxm44i 192 11 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 192 12 a a DT work_fnploejenbc2raktl46esxm44i 192 13 , , , work_fnploejenbc2raktl46esxm44i 192 14 , , , work_fnploejenbc2raktl46esxm44i 192 15 as as IN work_fnploejenbc2raktl46esxm44i 192 16 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 192 17 ” " `` work_fnploejenbc2raktl46esxm44i 192 18 is be VBZ work_fnploejenbc2raktl46esxm44i 192 19 a a DT work_fnploejenbc2raktl46esxm44i 192 20 - - HYPH work_fnploejenbc2raktl46esxm44i 192 21 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 192 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 192 23 A a NN work_fnploejenbc2raktl46esxm44i 192 24 - - HYPH work_fnploejenbc2raktl46esxm44i 192 25 AD ad NN work_fnploejenbc2raktl46esxm44i 192 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 192 27 if if IN work_fnploejenbc2raktl46esxm44i 192 28 there there EX work_fnploejenbc2raktl46esxm44i 192 29 is be VBZ work_fnploejenbc2raktl46esxm44i 192 30 no no DT work_fnploejenbc2raktl46esxm44i 192 31 v v NN work_fnploejenbc2raktl46esxm44i 192 32 E e NN work_fnploejenbc2raktl46esxm44i 192 33 AZ,2 az,2 NN work_fnploejenbc2raktl46esxm44i 192 34 such such JJ work_fnploejenbc2raktl46esxm44i 192 35 that that IN work_fnploejenbc2raktl46esxm44i 192 36 for for IN work_fnploejenbc2raktl46esxm44i 192 37 all all DT work_fnploejenbc2raktl46esxm44i 192 38 BE be NN work_fnploejenbc2raktl46esxm44i 192 39 ~(2 ~(2 . work_fnploejenbc2raktl46esxm44i 192 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 192 41 with with IN work_fnploejenbc2raktl46esxm44i 192 42 strict strict JJ work_fnploejenbc2raktl46esxm44i 192 43 inequality inequality NN work_fnploejenbc2raktl46esxm44i 192 44 for for IN work_fnploejenbc2raktl46esxm44i 192 45 at at RB work_fnploejenbc2raktl46esxm44i 192 46 least least RBS work_fnploejenbc2raktl46esxm44i 192 47 one one CD work_fnploejenbc2raktl46esxm44i 192 48 B. B. NNP work_fnploejenbc2raktl46esxm44i 193 1 More more RBR work_fnploejenbc2raktl46esxm44i 193 2 generally generally RB work_fnploejenbc2raktl46esxm44i 193 3 , , , work_fnploejenbc2raktl46esxm44i 193 4 let let VB work_fnploejenbc2raktl46esxm44i 193 5 8 8 CD work_fnploejenbc2raktl46esxm44i 193 6 belong belong VB work_fnploejenbc2raktl46esxm44i 193 7 to to IN work_fnploejenbc2raktl46esxm44i 193 8 the the DT work_fnploejenbc2raktl46esxm44i 193 9 power power NN work_fnploejenbc2raktl46esxm44i 193 10 set set VBN work_fnploejenbc2raktl46esxm44i 193 11 9(Jm 9(jm NN work_fnploejenbc2raktl46esxm44i 193 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 193 13 . . . work_fnploejenbc2raktl46esxm44i 194 1 Then then RB work_fnploejenbc2raktl46esxm44i 194 2 p p NN work_fnploejenbc2raktl46esxm44i 194 3 E e NN work_fnploejenbc2raktl46esxm44i 194 4 A2 a2 NN work_fnploejenbc2raktl46esxm44i 194 5 is be VBZ work_fnploejenbc2raktl46esxm44i 194 6 b b NN work_fnploejenbc2raktl46esxm44i 194 7 - - HYPH work_fnploejenbc2raktl46esxm44i 194 8 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 194 9 with with IN work_fnploejenbc2raktl46esxm44i 194 10 respect respect NN work_fnploejenbc2raktl46esxm44i 194 11 to to IN work_fnploejenbc2raktl46esxm44i 194 12 _ _ NNP work_fnploejenbc2raktl46esxm44i 194 13 Gf:+ Gf:+ NNP work_fnploejenbc2raktl46esxm44i 194 14 if if IN work_fnploejenbc2raktl46esxm44i 194 15 p p NN work_fnploejenbc2raktl46esxm44i 194 16 is be VBZ work_fnploejenbc2raktl46esxm44i 194 17 a a DT work_fnploejenbc2raktl46esxm44i 194 18 - - HYPH work_fnploejenbc2raktl46esxm44i 194 19 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 194 20 for for IN work_fnploejenbc2raktl46esxm44i 194 21 all all DT work_fnploejenbc2raktl46esxm44i 194 22 2 2 CD work_fnploejenbc2raktl46esxm44i 194 23 E e NN work_fnploejenbc2raktl46esxm44i 194 24 8 8 CD work_fnploejenbc2raktl46esxm44i 194 25 ’ ' '' work_fnploejenbc2raktl46esxm44i 194 26 . . . work_fnploejenbc2raktl46esxm44i 195 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 195 2 Note note VB work_fnploejenbc2raktl46esxm44i 195 3 that that IN work_fnploejenbc2raktl46esxm44i 195 4 A2,~ a2,~ DT work_fnploejenbc2raktl46esxm44i 195 5 E e NN work_fnploejenbc2raktl46esxm44i 195 6 A a NN work_fnploejenbc2raktl46esxm44i 195 7 , , , work_fnploejenbc2raktl46esxm44i 195 8 . . . work_fnploejenbc2raktl46esxm44i 195 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 196 1 When when WRB work_fnploejenbc2raktl46esxm44i 196 2 d d NNP work_fnploejenbc2raktl46esxm44i 196 3 = = SYM work_fnploejenbc2raktl46esxm44i 196 4 SZ!~ sz!~ NN work_fnploejenbc2raktl46esxm44i 196 5 , , , work_fnploejenbc2raktl46esxm44i 196 6 p p NNP work_fnploejenbc2raktl46esxm44i 196 7 is be VBZ work_fnploejenbc2raktl46esxm44i 196 8 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 196 9 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 196 10 . . . work_fnploejenbc2raktl46esxm44i 197 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 197 2 is be VBZ work_fnploejenbc2raktl46esxm44i 197 3 easy easy JJ work_fnploejenbc2raktl46esxm44i 197 4 to to TO work_fnploejenbc2raktl46esxm44i 197 5 see see VB work_fnploejenbc2raktl46esxm44i 197 6 that that DT work_fnploejenbc2raktl46esxm44i 197 7 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 197 8 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 197 9 implies imply VBZ work_fnploejenbc2raktl46esxm44i 197 10 ordinary ordinary JJ work_fnploejenbc2raktl46esxm44i 197 11 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 197 12 . . . work_fnploejenbc2raktl46esxm44i 198 1 Continuing continue VBG work_fnploejenbc2raktl46esxm44i 198 2 with with IN work_fnploejenbc2raktl46esxm44i 198 3 the the DT work_fnploejenbc2raktl46esxm44i 198 4 subgame subgame NN work_fnploejenbc2raktl46esxm44i 198 5 where where WRB work_fnploejenbc2raktl46esxm44i 198 6 2 2 CD work_fnploejenbc2raktl46esxm44i 198 7 is be VBZ work_fnploejenbc2raktl46esxm44i 198 8 fixed fix VBN work_fnploejenbc2raktl46esxm44i 198 9 , , , work_fnploejenbc2raktl46esxm44i 198 10 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 198 11 note note VBP work_fnploejenbc2raktl46esxm44i 198 12 that that IN work_fnploejenbc2raktl46esxm44i 198 13 p(A p(a JJ work_fnploejenbc2raktl46esxm44i 198 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 198 15 E e VB work_fnploejenbc2raktl46esxm44i 198 16 IR ir NN work_fnploejenbc2raktl46esxm44i 198 17 ” " '' work_fnploejenbc2raktl46esxm44i 198 18 for for IN work_fnploejenbc2raktl46esxm44i 198 19 which which WDT work_fnploejenbc2raktl46esxm44i 198 20 there there EX work_fnploejenbc2raktl46esxm44i 198 21 is be VBZ work_fnploejenbc2raktl46esxm44i 198 22 the the DT work_fnploejenbc2raktl46esxm44i 198 23 usual usual JJ work_fnploejenbc2raktl46esxm44i 198 24 topology topology NN work_fnploejenbc2raktl46esxm44i 198 25 based base VBN work_fnploejenbc2raktl46esxm44i 198 26 on on IN work_fnploejenbc2raktl46esxm44i 198 27 the the DT work_fnploejenbc2raktl46esxm44i 198 28 Euclidean euclidean JJ work_fnploejenbc2raktl46esxm44i 198 29 norm norm NN work_fnploejenbc2raktl46esxm44i 198 30 11 11 CD work_fnploejenbc2raktl46esxm44i 198 31 /I. /I. . work_fnploejenbc2raktl46esxm44i 199 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 199 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 199 3 may may MD work_fnploejenbc2raktl46esxm44i 199 4 have have VB work_fnploejenbc2raktl46esxm44i 199 5 a a DT work_fnploejenbc2raktl46esxm44i 199 6 neighborhood neighborhood NN work_fnploejenbc2raktl46esxm44i 199 7 of of IN work_fnploejenbc2raktl46esxm44i 199 8 p p NN work_fnploejenbc2raktl46esxm44i 199 9 WP,~)= wp,~)= NN work_fnploejenbc2raktl46esxm44i 199 10 { { -LRB- work_fnploejenbc2raktl46esxm44i 199 11 vEA~,A vEA~,A : work_fnploejenbc2raktl46esxm44i 199 12 : : : work_fnploejenbc2raktl46esxm44i 199 13 Ilv(~)--~(~)ll Ilv(~)--~(~)ll NNP work_fnploejenbc2raktl46esxm44i 199 14 < < XX work_fnploejenbc2raktl46esxm44i 199 15 r r NNP work_fnploejenbc2raktl46esxm44i 199 16 } } -RRB- work_fnploejenbc2raktl46esxm44i 199 17 . . . work_fnploejenbc2raktl46esxm44i 200 1 Then then RB work_fnploejenbc2raktl46esxm44i 200 2 p p NN work_fnploejenbc2raktl46esxm44i 200 3 E E NNP work_fnploejenbc2raktl46esxm44i 200 4 Ax,2 Ax,2 NNP work_fnploejenbc2raktl46esxm44i 200 5 is be VBZ work_fnploejenbc2raktl46esxm44i 200 6 A a NN work_fnploejenbc2raktl46esxm44i 200 7 - - HYPH work_fnploejenbc2raktl46esxm44i 200 8 focal focal JJ work_fnploejenbc2raktl46esxm44i 200 9 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 200 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 200 11 A A NNP work_fnploejenbc2raktl46esxm44i 200 12 - - HYPH work_fnploejenbc2raktl46esxm44i 200 13 LAD lad NN work_fnploejenbc2raktl46esxm44i 200 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 200 15 if if IN work_fnploejenbc2raktl46esxm44i 200 16 there there EX work_fnploejenbc2raktl46esxm44i 200 17 is be VBZ work_fnploejenbc2raktl46esxm44i 200 18 some some DT work_fnploejenbc2raktl46esxm44i 200 19 N(p N(p NNP work_fnploejenbc2raktl46esxm44i 200 20 , , , work_fnploejenbc2raktl46esxm44i 200 21 r r LS work_fnploejenbc2raktl46esxm44i 200 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 200 23 such such JJ work_fnploejenbc2raktl46esxm44i 200 24 that that IN work_fnploejenbc2raktl46esxm44i 200 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 200 26 1 1 LS work_fnploejenbc2raktl46esxm44i 200 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 200 28 does do VBZ work_fnploejenbc2raktl46esxm44i 200 29 not not RB work_fnploejenbc2raktl46esxm44i 200 30 hold hold VB work_fnploejenbc2raktl46esxm44i 200 31 for for IN work_fnploejenbc2raktl46esxm44i 200 32 all all DT work_fnploejenbc2raktl46esxm44i 200 33 VEN(~ VEN(~ NNP work_fnploejenbc2raktl46esxm44i 200 34 , , , work_fnploejenbc2raktl46esxm44i 200 35 r r NNP work_fnploejenbc2raktl46esxm44i 200 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 200 37 . . . work_fnploejenbc2raktl46esxm44i 201 1 For for IN work_fnploejenbc2raktl46esxm44i 201 2 the the DT work_fnploejenbc2raktl46esxm44i 201 3 last last JJ work_fnploejenbc2raktl46esxm44i 201 4 two two CD work_fnploejenbc2raktl46esxm44i 201 5 concepts concept NNS work_fnploejenbc2raktl46esxm44i 201 6 of of IN work_fnploejenbc2raktl46esxm44i 201 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 201 8 , , , work_fnploejenbc2raktl46esxm44i 201 9 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 201 10 will will MD work_fnploejenbc2raktl46esxm44i 201 11 be be VB work_fnploejenbc2raktl46esxm44i 201 12 convenient convenient JJ work_fnploejenbc2raktl46esxm44i 201 13 to to TO work_fnploejenbc2raktl46esxm44i 201 14 introduce introduce VB work_fnploejenbc2raktl46esxm44i 201 15 the the DT work_fnploejenbc2raktl46esxm44i 201 16 following follow VBG work_fnploejenbc2raktl46esxm44i 201 17 notation notation NN work_fnploejenbc2raktl46esxm44i 201 18 . . . work_fnploejenbc2raktl46esxm44i 202 1 560 560 CD work_fnploejenbc2raktl46esxm44i 202 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 202 3 , , , work_fnploejenbc2raktl46esxm44i 202 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 202 5 , , , work_fnploejenbc2raktl46esxm44i 202 6 AND and CC work_fnploejenbc2raktl46esxm44i 202 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 202 8 With with IN work_fnploejenbc2raktl46esxm44i 202 9 /i /i FW work_fnploejenbc2raktl46esxm44i 202 10 = = FW work_fnploejenbc2raktl46esxm44i 202 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 202 12 A a DT work_fnploejenbc2raktl46esxm44i 202 13 1 1 CD work_fnploejenbc2raktl46esxm44i 202 14 , , , work_fnploejenbc2raktl46esxm44i 202 15 . . . work_fnploejenbc2raktl46esxm44i 203 1 . . . work_fnploejenbc2raktl46esxm44i 204 1 . . . work_fnploejenbc2raktl46esxm44i 205 1 . . . work_fnploejenbc2raktl46esxm44i 206 1 4 4 LS work_fnploejenbc2raktl46esxm44i 206 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 206 3 , , , work_fnploejenbc2raktl46esxm44i 206 4 let let VB work_fnploejenbc2raktl46esxm44i 206 5 { { -LRB- work_fnploejenbc2raktl46esxm44i 206 6 B b NN work_fnploejenbc2raktl46esxm44i 206 7 , , , work_fnploejenbc2raktl46esxm44i 206 8 , , , work_fnploejenbc2raktl46esxm44i 206 9 . . . work_fnploejenbc2raktl46esxm44i 207 1 . . . work_fnploejenbc2raktl46esxm44i 208 1 . . . work_fnploejenbc2raktl46esxm44i 209 1 . . . work_fnploejenbc2raktl46esxm44i 210 1 B b UH work_fnploejenbc2raktl46esxm44i 210 2 , , , work_fnploejenbc2raktl46esxm44i 210 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 210 4 be be VB work_fnploejenbc2raktl46esxm44i 210 5 a a DT work_fnploejenbc2raktl46esxm44i 210 6 listing listing NN work_fnploejenbc2raktl46esxm44i 210 7 of of IN work_fnploejenbc2raktl46esxm44i 210 8 the the DT work_fnploejenbc2raktl46esxm44i 210 9 elements element NNS work_fnploejenbc2raktl46esxm44i 210 10 of of IN work_fnploejenbc2raktl46esxm44i 210 11 z(a z(a NNP work_fnploejenbc2raktl46esxm44i 210 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 210 13 . . . work_fnploejenbc2raktl46esxm44i 211 1 The the DT work_fnploejenbc2raktl46esxm44i 211 2 set set NN work_fnploejenbc2raktl46esxm44i 211 3 of of IN work_fnploejenbc2raktl46esxm44i 211 4 values value NNS work_fnploejenbc2raktl46esxm44i 211 5 Lj&i(B Lj&i(B NNP work_fnploejenbc2raktl46esxm44i 211 6 , , , work_fnploejenbc2raktl46esxm44i 211 7 , , , work_fnploejenbc2raktl46esxm44i 211 8 PL)= PL)= NNP work_fnploejenbc2raktl46esxm44i 211 9 W(P(~~ W(P(~~ NNP work_fnploejenbc2raktl46esxm44i 211 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 211 11 , , , work_fnploejenbc2raktl46esxm44i 211 12 A,(B A,(B NNP work_fnploejenbc2raktl46esxm44i 211 13 , , , work_fnploejenbc2raktl46esxm44i 211 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 211 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 211 16 , , , work_fnploejenbc2raktl46esxm44i 211 17 . . . work_fnploejenbc2raktl46esxm44i 212 1 . . . work_fnploejenbc2raktl46esxm44i 213 1 . . . work_fnploejenbc2raktl46esxm44i 214 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 214 2 fWL)~ fwl)~ JJ work_fnploejenbc2raktl46esxm44i 214 3 -MB -MB NNP work_fnploejenbc2raktl46esxm44i 214 4 , , , work_fnploejenbc2raktl46esxm44i 214 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 214 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 214 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 214 8 , , , work_fnploejenbc2raktl46esxm44i 214 9 . . . work_fnploejenbc2raktl46esxm44i 215 1 . . . work_fnploejenbc2raktl46esxm44i 216 1 . . . work_fnploejenbc2raktl46esxm44i 217 1 . . . work_fnploejenbc2raktl46esxm44i 218 1 L&-i(L L&-i(L NNP work_fnploejenbc2raktl46esxm44i 218 2 PL)= PL)= NNP work_fnploejenbc2raktl46esxm44i 218 3 Icl(f(A~~ Icl(f(A~~ NNP work_fnploejenbc2raktl46esxm44i 218 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 218 5 , , , work_fnploejenbc2raktl46esxm44i 218 6 A A NNP work_fnploejenbc2raktl46esxm44i 218 7 , , , work_fnploejenbc2raktl46esxm44i 218 8 Mn Mn NNP work_fnploejenbc2raktl46esxm44i 218 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 218 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 218 11 , , , work_fnploejenbc2raktl46esxm44i 218 12 . . . work_fnploejenbc2raktl46esxm44i 219 1 . . . work_fnploejenbc2raktl46esxm44i 220 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 220 2 f(~(An f(~(An NNP work_fnploejenbc2raktl46esxm44i 220 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 220 4 . . . work_fnploejenbc2raktl46esxm44i 221 1 4 4 LS work_fnploejenbc2raktl46esxm44i 221 2 , , , work_fnploejenbc2raktl46esxm44i 221 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 221 4 & & CC work_fnploejenbc2raktl46esxm44i 221 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 221 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 221 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 221 8 can can MD work_fnploejenbc2raktl46esxm44i 221 9 be be VB work_fnploejenbc2raktl46esxm44i 221 10 thought think VBN work_fnploejenbc2raktl46esxm44i 221 11 of of IN work_fnploejenbc2raktl46esxm44i 221 12 as as IN work_fnploejenbc2raktl46esxm44i 221 13 the the DT work_fnploejenbc2raktl46esxm44i 221 14 value value NN work_fnploejenbc2raktl46esxm44i 221 15 of of IN work_fnploejenbc2raktl46esxm44i 221 16 a a DT work_fnploejenbc2raktl46esxm44i 221 17 transformation transformation NN work_fnploejenbc2raktl46esxm44i 221 18 L;$,A L;$,A NNP work_fnploejenbc2raktl46esxm44i 221 19 : : : work_fnploejenbc2raktl46esxm44i 221 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 221 21 a a DT work_fnploejenbc2raktl46esxm44i 221 22 * * NFP work_fnploejenbc2raktl46esxm44i 221 23 , , , work_fnploejenbc2raktl46esxm44i 221 24 u31n u31n ADD work_fnploejenbc2raktl46esxm44i 221 25 + + CC work_fnploejenbc2raktl46esxm44i 221 26 Iw Iw NNP work_fnploejenbc2raktl46esxm44i 221 27 ” " '' work_fnploejenbc2raktl46esxm44i 221 28 at at IN work_fnploejenbc2raktl46esxm44i 221 29 the the DT work_fnploejenbc2raktl46esxm44i 221 30 point point NN work_fnploejenbc2raktl46esxm44i 221 31 , , , work_fnploejenbc2raktl46esxm44i 221 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 221 33 a a LS work_fnploejenbc2raktl46esxm44i 221 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 221 35 = = NFP work_fnploejenbc2raktl46esxm44i 221 36 @(A @(a FW work_fnploejenbc2raktl46esxm44i 221 37 , , , work_fnploejenbc2raktl46esxm44i 221 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 221 39 , , , work_fnploejenbc2raktl46esxm44i 221 40 . . . work_fnploejenbc2raktl46esxm44i 222 1 . . . work_fnploejenbc2raktl46esxm44i 223 1 . . . work_fnploejenbc2raktl46esxm44i 224 1 . . . work_fnploejenbc2raktl46esxm44i 225 1 , , , work_fnploejenbc2raktl46esxm44i 225 2 u(A u(A `` work_fnploejenbc2raktl46esxm44i 225 3 , , , work_fnploejenbc2raktl46esxm44i 225 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 225 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 225 6 . . . work_fnploejenbc2raktl46esxm44i 226 1 For for IN work_fnploejenbc2raktl46esxm44i 226 2 simplicity simplicity NN work_fnploejenbc2raktl46esxm44i 226 3 , , , work_fnploejenbc2raktl46esxm44i 226 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 226 5 drop drop VBP work_fnploejenbc2raktl46esxm44i 226 6 the the DT work_fnploejenbc2raktl46esxm44i 226 7 extra extra JJ work_fnploejenbc2raktl46esxm44i 226 8 symbols symbol NNS work_fnploejenbc2raktl46esxm44i 226 9 and and CC work_fnploejenbc2raktl46esxm44i 226 10 write write VB work_fnploejenbc2raktl46esxm44i 226 11 , , , work_fnploejenbc2raktl46esxm44i 226 12 in in IN work_fnploejenbc2raktl46esxm44i 226 13 general general JJ work_fnploejenbc2raktl46esxm44i 226 14 , , , work_fnploejenbc2raktl46esxm44i 226 15 L(a l(a ADD work_fnploejenbc2raktl46esxm44i 226 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 226 17 L(i)= L(i)= NNP work_fnploejenbc2raktl46esxm44i 226 18 ; ; : work_fnploejenbc2raktl46esxm44i 226 19 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 226 20 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 226 21 JLO jlo NN work_fnploejenbc2raktl46esxm44i 226 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 226 23 for for IN work_fnploejenbc2raktl46esxm44i 226 24 2 2 CD work_fnploejenbc2raktl46esxm44i 226 25 = = SYM work_fnploejenbc2raktl46esxm44i 226 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 226 27 x x NN work_fnploejenbc2raktl46esxm44i 226 28 , , , work_fnploejenbc2raktl46esxm44i 226 29 , , , work_fnploejenbc2raktl46esxm44i 226 30 . . . work_fnploejenbc2raktl46esxm44i 227 1 . . . work_fnploejenbc2raktl46esxm44i 228 1 . . . work_fnploejenbc2raktl46esxm44i 229 1 . . . work_fnploejenbc2raktl46esxm44i 230 1 X,)E X,)E NNP work_fnploejenbc2raktl46esxm44i 230 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 230 3 a a DT work_fnploejenbc2raktl46esxm44i 230 4 , , , work_fnploejenbc2raktl46esxm44i 230 5 , , , work_fnploejenbc2raktl46esxm44i 230 6 a,]“=D. a,]“=d. NN work_fnploejenbc2raktl46esxm44i 231 1 By by IN work_fnploejenbc2raktl46esxm44i 231 2 the the DT work_fnploejenbc2raktl46esxm44i 231 3 natures nature NNS work_fnploejenbc2raktl46esxm44i 231 4 of of IN work_fnploejenbc2raktl46esxm44i 231 5 $ $ $ work_fnploejenbc2raktl46esxm44i 231 6 andf andf NNS work_fnploejenbc2raktl46esxm44i 231 7 , , , work_fnploejenbc2raktl46esxm44i 231 8 L L NNP work_fnploejenbc2raktl46esxm44i 231 9 can can MD work_fnploejenbc2raktl46esxm44i 231 10 be be VB work_fnploejenbc2raktl46esxm44i 231 11 arranged arrange VBN work_fnploejenbc2raktl46esxm44i 231 12 in in IN work_fnploejenbc2raktl46esxm44i 231 13 the the DT work_fnploejenbc2raktl46esxm44i 231 14 partitioned partition VBN work_fnploejenbc2raktl46esxm44i 231 15 form form NN work_fnploejenbc2raktl46esxm44i 231 16 L(l L(l NNP work_fnploejenbc2raktl46esxm44i 231 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 231 18 il il NNP work_fnploejenbc2raktl46esxm44i 231 19 1 1 CD work_fnploejenbc2raktl46esxm44i 231 20 L(2 L(2 NNP work_fnploejenbc2raktl46esxm44i 231 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 231 22 ’ ' `` work_fnploejenbc2raktl46esxm44i 231 23 where where WRB work_fnploejenbc2raktl46esxm44i 231 24 L L NNP work_fnploejenbc2raktl46esxm44i 231 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 231 26 ‘ ' `` work_fnploejenbc2raktl46esxm44i 231 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 231 28 is be VBZ work_fnploejenbc2raktl46esxm44i 231 29 constant constant JJ work_fnploejenbc2raktl46esxm44i 231 30 on on IN work_fnploejenbc2raktl46esxm44i 231 31 D d NN work_fnploejenbc2raktl46esxm44i 231 32 but but CC work_fnploejenbc2raktl46esxm44i 231 33 L L NNP work_fnploejenbc2raktl46esxm44i 231 34 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 231 35 ‘ ' '' work_fnploejenbc2raktl46esxm44i 231 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 231 37 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 231 38 of of IN work_fnploejenbc2raktl46esxm44i 231 39 length length NN work_fnploejenbc2raktl46esxm44i 231 40 k k NN work_fnploejenbc2raktl46esxm44i 231 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 231 42 is be VBZ work_fnploejenbc2raktl46esxm44i 231 43 not not RB work_fnploejenbc2raktl46esxm44i 231 44 constant constant JJ work_fnploejenbc2raktl46esxm44i 231 45 in in IN work_fnploejenbc2raktl46esxm44i 231 46 any any DT work_fnploejenbc2raktl46esxm44i 231 47 neighborhood neighborhood NN work_fnploejenbc2raktl46esxm44i 231 48 in in IN work_fnploejenbc2raktl46esxm44i 231 49 D. D. NNP work_fnploejenbc2raktl46esxm44i 231 50 Of of RB work_fnploejenbc2raktl46esxm44i 231 51 course course RB work_fnploejenbc2raktl46esxm44i 231 52 , , , work_fnploejenbc2raktl46esxm44i 231 53 L l NN work_fnploejenbc2raktl46esxm44i 231 54 ” " '' work_fnploejenbc2raktl46esxm44i 231 55 ’ ' '' work_fnploejenbc2raktl46esxm44i 231 56 may may MD work_fnploejenbc2raktl46esxm44i 231 57 not not RB work_fnploejenbc2raktl46esxm44i 231 58 appear appear VB work_fnploejenbc2raktl46esxm44i 231 59 . . . work_fnploejenbc2raktl46esxm44i 232 1 Then then RB work_fnploejenbc2raktl46esxm44i 232 2 p p NN work_fnploejenbc2raktl46esxm44i 232 3 E e NN work_fnploejenbc2raktl46esxm44i 232 4 n2,~ n2,~ NN work_fnploejenbc2raktl46esxm44i 232 5 or or CC work_fnploejenbc2raktl46esxm44i 232 6 equivalently equivalently RB work_fnploejenbc2raktl46esxm44i 232 7 i i PRP work_fnploejenbc2raktl46esxm44i 232 8 E e NN work_fnploejenbc2raktl46esxm44i 232 9 D d NN work_fnploejenbc2raktl46esxm44i 232 10 , , , work_fnploejenbc2raktl46esxm44i 232 11 is be VBZ work_fnploejenbc2raktl46esxm44i 232 12 a a DT work_fnploejenbc2raktl46esxm44i 232 13 - - HYPH work_fnploejenbc2raktl46esxm44i 232 14 weak weak JJ work_fnploejenbc2raktl46esxm44i 232 15 / / SYM work_fnploejenbc2raktl46esxm44i 232 16 y y NN work_fnploejenbc2raktl46esxm44i 232 17 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 232 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 232 19 A A NNP work_fnploejenbc2raktl46esxm44i 232 20 - - HYPH work_fnploejenbc2raktl46esxm44i 232 21 WAD WAD NNP work_fnploejenbc2raktl46esxm44i 232 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 232 23 if if IN work_fnploejenbc2raktl46esxm44i 232 24 there there EX work_fnploejenbc2raktl46esxm44i 232 25 is be VBZ work_fnploejenbc2raktl46esxm44i 232 26 no no DT work_fnploejenbc2raktl46esxm44i 232 27 9 9 CD work_fnploejenbc2raktl46esxm44i 232 28 ED ed NN work_fnploejenbc2raktl46esxm44i 232 29 such such JJ work_fnploejenbc2raktl46esxm44i 232 30 that that IN work_fnploejenbc2raktl46esxm44i 232 31 L”‘(9 L”‘(9 NNP work_fnploejenbc2raktl46esxm44i 232 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 232 33 cs cs NNP work_fnploejenbc2raktl46esxm44i 232 34 L(‘)(Z L(‘)(Z NNP work_fnploejenbc2raktl46esxm44i 232 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 232 36 , , , work_fnploejenbc2raktl46esxm44i 232 37 where where WRB work_fnploejenbc2raktl46esxm44i 232 38 cs cs NNP work_fnploejenbc2raktl46esxm44i 232 39 is be VBZ work_fnploejenbc2raktl46esxm44i 232 40 the the DT work_fnploejenbc2raktl46esxm44i 232 41 strong strong JJ work_fnploejenbc2raktl46esxm44i 232 42 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 232 43 Pareto Pareto NNP work_fnploejenbc2raktl46esxm44i 232 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 232 45 order order NN work_fnploejenbc2raktl46esxm44i 232 46 in in IN work_fnploejenbc2raktl46esxm44i 232 47 real real JJ work_fnploejenbc2raktl46esxm44i 232 48 Euclidean euclidean JJ work_fnploejenbc2raktl46esxm44i 232 49 space space NN work_fnploejenbc2raktl46esxm44i 232 50 Rq rq NN work_fnploejenbc2raktl46esxm44i 232 51 : : : work_fnploejenbc2raktl46esxm44i 232 52 P p NN work_fnploejenbc2raktl46esxm44i 232 53 = = NFP work_fnploejenbc2raktl46esxm44i 232 54 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 232 55 PI pi NN work_fnploejenbc2raktl46esxm44i 232 56 9 9 CD work_fnploejenbc2raktl46esxm44i 232 57 * * NFP work_fnploejenbc2raktl46esxm44i 232 58 * * NFP work_fnploejenbc2raktl46esxm44i 232 59 . . . work_fnploejenbc2raktl46esxm44i 232 60 , , , work_fnploejenbc2raktl46esxm44i 232 61 P p NN work_fnploejenbc2raktl46esxm44i 232 62 , , , work_fnploejenbc2raktl46esxm44i 232 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 232 64 cs cs NNP work_fnploejenbc2raktl46esxm44i 232 65 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 232 66 v v NNP work_fnploejenbc2raktl46esxm44i 232 67 , , , work_fnploejenbc2raktl46esxm44i 232 68 3 3 CD work_fnploejenbc2raktl46esxm44i 232 69 . . . work_fnploejenbc2raktl46esxm44i 233 1 . . . work_fnploejenbc2raktl46esxm44i 234 1 . . . work_fnploejenbc2raktl46esxm44i 235 1 . . . work_fnploejenbc2raktl46esxm44i 236 1 vq vq NNP work_fnploejenbc2raktl46esxm44i 236 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 236 3 = = -RRB- work_fnploejenbc2raktl46esxm44i 236 4 v^ v^ NNS work_fnploejenbc2raktl46esxm44i 236 5 if if IN work_fnploejenbc2raktl46esxm44i 236 6 pj pj VBP work_fnploejenbc2raktl46esxm44i 236 7 < < XX work_fnploejenbc2raktl46esxm44i 236 8 vj vj NNP work_fnploejenbc2raktl46esxm44i 236 9 for for IN work_fnploejenbc2raktl46esxm44i 236 10 all all DT work_fnploejenbc2raktl46esxm44i 236 11 j j NN work_fnploejenbc2raktl46esxm44i 236 12 = = SYM work_fnploejenbc2raktl46esxm44i 236 13 1 1 CD work_fnploejenbc2raktl46esxm44i 236 14 , , , work_fnploejenbc2raktl46esxm44i 236 15 2 2 CD work_fnploejenbc2raktl46esxm44i 236 16 , , , work_fnploejenbc2raktl46esxm44i 236 17 . . . work_fnploejenbc2raktl46esxm44i 237 1 . . . work_fnploejenbc2raktl46esxm44i 238 1 . . . work_fnploejenbc2raktl46esxm44i 239 1 . . . work_fnploejenbc2raktl46esxm44i 240 1 q. q. NNP work_fnploejenbc2raktl46esxm44i 241 1 If if IN work_fnploejenbc2raktl46esxm44i 241 2 pj pj VB work_fnploejenbc2raktl46esxm44i 241 3 < < XX work_fnploejenbc2raktl46esxm44i 241 4 vi vi NNP work_fnploejenbc2raktl46esxm44i 241 5 for for IN work_fnploejenbc2raktl46esxm44i 241 6 all all DT work_fnploejenbc2raktl46esxm44i 241 7 j= j= NNP work_fnploejenbc2raktl46esxm44i 241 8 1 1 CD work_fnploejenbc2raktl46esxm44i 241 9 , , , work_fnploejenbc2raktl46esxm44i 241 10 2 2 CD work_fnploejenbc2raktl46esxm44i 241 11 , , , work_fnploejenbc2raktl46esxm44i 241 12 . . . work_fnploejenbc2raktl46esxm44i 242 1 . . . work_fnploejenbc2raktl46esxm44i 243 1 . . . work_fnploejenbc2raktl46esxm44i 244 1 . . . work_fnploejenbc2raktl46esxm44i 245 1 q q NNP work_fnploejenbc2raktl46esxm44i 245 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 245 3 write write VBP work_fnploejenbc2raktl46esxm44i 245 4 simply simply RB work_fnploejenbc2raktl46esxm44i 245 5 /i /i . work_fnploejenbc2raktl46esxm44i 245 6 Q q NN work_fnploejenbc2raktl46esxm44i 245 7 9 9 CD work_fnploejenbc2raktl46esxm44i 245 8 ; ; : work_fnploejenbc2raktl46esxm44i 245 9 when when WRB work_fnploejenbc2raktl46esxm44i 245 10 the the DT work_fnploejenbc2raktl46esxm44i 245 11 inequality inequality NN work_fnploejenbc2raktl46esxm44i 245 12 holds hold VBZ work_fnploejenbc2raktl46esxm44i 245 13 for for IN work_fnploejenbc2raktl46esxm44i 245 14 only only RB work_fnploejenbc2raktl46esxm44i 245 15 some some DT work_fnploejenbc2raktl46esxm44i 245 16 j j NN work_fnploejenbc2raktl46esxm44i 245 17 , , , work_fnploejenbc2raktl46esxm44i 245 18 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 245 19 write write VBP work_fnploejenbc2raktl46esxm44i 245 20 fi fi IN work_fnploejenbc2raktl46esxm44i 245 21 < < XX work_fnploejenbc2raktl46esxm44i 245 22 , , , work_fnploejenbc2raktl46esxm44i 245 23 , , , work_fnploejenbc2raktl46esxm44i 245 24 , , , work_fnploejenbc2raktl46esxm44i 245 25 t. t. NN work_fnploejenbc2raktl46esxm44i 245 26 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 245 27 is be VBZ work_fnploejenbc2raktl46esxm44i 245 28 easy easy JJ work_fnploejenbc2raktl46esxm44i 245 29 to to TO work_fnploejenbc2raktl46esxm44i 245 30 see see VB work_fnploejenbc2raktl46esxm44i 245 31 that that IN work_fnploejenbc2raktl46esxm44i 245 32 A a NN work_fnploejenbc2raktl46esxm44i 245 33 - - HYPH work_fnploejenbc2raktl46esxm44i 245 34 AD ad NN work_fnploejenbc2raktl46esxm44i 245 35 is be VBZ work_fnploejenbc2raktl46esxm44i 245 36 stronger strong JJR work_fnploejenbc2raktl46esxm44i 245 37 than than IN work_fnploejenbc2raktl46esxm44i 245 38 A A NNP work_fnploejenbc2raktl46esxm44i 245 39 - - HYPH work_fnploejenbc2raktl46esxm44i 245 40 WAD WAD NNP work_fnploejenbc2raktl46esxm44i 245 41 ; ; : work_fnploejenbc2raktl46esxm44i 245 42 for for IN work_fnploejenbc2raktl46esxm44i 245 43 , , , work_fnploejenbc2raktl46esxm44i 245 44 if if IN work_fnploejenbc2raktl46esxm44i 245 45 there there EX work_fnploejenbc2raktl46esxm44i 245 46 is be VBZ work_fnploejenbc2raktl46esxm44i 245 47 a a DT work_fnploejenbc2raktl46esxm44i 245 48 9 9 CD work_fnploejenbc2raktl46esxm44i 245 49 ED ed NN work_fnploejenbc2raktl46esxm44i 245 50 such such JJ work_fnploejenbc2raktl46esxm44i 245 51 that that IN work_fnploejenbc2raktl46esxm44i 245 52 L”)(p L”)(p NNP work_fnploejenbc2raktl46esxm44i 245 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 245 54 cs cs NNP work_fnploejenbc2raktl46esxm44i 245 55 L(‘)(a L(‘)(a NNP work_fnploejenbc2raktl46esxm44i 245 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 245 57 , , , work_fnploejenbc2raktl46esxm44i 245 58 then then RB work_fnploejenbc2raktl46esxm44i 245 59 since since IN work_fnploejenbc2raktl46esxm44i 245 60 , , , work_fnploejenbc2raktl46esxm44i 245 61 if if IN work_fnploejenbc2raktl46esxm44i 245 62 LC2 LC2 NNP work_fnploejenbc2raktl46esxm44i 245 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 245 64 appears appear VBZ work_fnploejenbc2raktl46esxm44i 245 65 , , , work_fnploejenbc2raktl46esxm44i 245 66 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 245 67 is be VBZ work_fnploejenbc2raktl46esxm44i 245 68 constant constant JJ work_fnploejenbc2raktl46esxm44i 245 69 on on IN work_fnploejenbc2raktl46esxm44i 245 70 D. D. NNP work_fnploejenbc2raktl46esxm44i 245 71 Moreover Moreover NNP work_fnploejenbc2raktl46esxm44i 245 72 , , , work_fnploejenbc2raktl46esxm44i 245 73 the the DT work_fnploejenbc2raktl46esxm44i 245 74 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 245 75 considered consider VBN work_fnploejenbc2raktl46esxm44i 245 76 informally informally RB work_fnploejenbc2raktl46esxm44i 245 77 by by IN work_fnploejenbc2raktl46esxm44i 245 78 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 245 79 turns turn VBZ work_fnploejenbc2raktl46esxm44i 245 80 out out RP work_fnploejenbc2raktl46esxm44i 245 81 to to TO work_fnploejenbc2raktl46esxm44i 245 82 be be VB work_fnploejenbc2raktl46esxm44i 245 83 “ " `` work_fnploejenbc2raktl46esxm44i 245 84 weak weak JJ work_fnploejenbc2raktl46esxm44i 245 85 - - HYPH work_fnploejenbc2raktl46esxm44i 245 86 local local JJ work_fnploejenbc2raktl46esxm44i 245 87 ” " '' work_fnploejenbc2raktl46esxm44i 245 88 and and CC work_fnploejenbc2raktl46esxm44i 245 89 will will MD work_fnploejenbc2raktl46esxm44i 245 90 be be VB work_fnploejenbc2raktl46esxm44i 245 91 considered consider VBN work_fnploejenbc2raktl46esxm44i 245 92 further further RB work_fnploejenbc2raktl46esxm44i 245 93 in in IN work_fnploejenbc2raktl46esxm44i 245 94 Section section NN work_fnploejenbc2raktl46esxm44i 245 95 4 4 CD work_fnploejenbc2raktl46esxm44i 245 96 . . . work_fnploejenbc2raktl46esxm44i 246 1 Finally finally RB work_fnploejenbc2raktl46esxm44i 246 2 , , , work_fnploejenbc2raktl46esxm44i 246 3 2 2 CD work_fnploejenbc2raktl46esxm44i 246 4 is be VBZ work_fnploejenbc2raktl46esxm44i 246 5 weak weak JJ work_fnploejenbc2raktl46esxm44i 246 6 - - HYPH work_fnploejenbc2raktl46esxm44i 246 7 local local JJ work_fnploejenbc2raktl46esxm44i 246 8 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 246 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 246 10 A a NN work_fnploejenbc2raktl46esxm44i 246 11 - - HYPH work_fnploejenbc2raktl46esxm44i 246 12 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 246 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 246 14 if if IN work_fnploejenbc2raktl46esxm44i 246 15 for for IN work_fnploejenbc2raktl46esxm44i 246 16 each each DT work_fnploejenbc2raktl46esxm44i 246 17 9 9 CD work_fnploejenbc2raktl46esxm44i 246 18 in in IN work_fnploejenbc2raktl46esxm44i 246 19 R r NN work_fnploejenbc2raktl46esxm44i 246 20 ” " '' work_fnploejenbc2raktl46esxm44i 246 21 with with IN work_fnploejenbc2raktl46esxm44i 246 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 246 23 lyJ/ lyJ/ NNP work_fnploejenbc2raktl46esxm44i 246 24 = = SYM work_fnploejenbc2raktl46esxm44i 246 25 1 1 CD work_fnploejenbc2raktl46esxm44i 246 26 , , , work_fnploejenbc2raktl46esxm44i 246 27 and and CC work_fnploejenbc2raktl46esxm44i 246 28 each each DT work_fnploejenbc2raktl46esxm44i 246 29 c c NN work_fnploejenbc2raktl46esxm44i 246 30 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 246 31 > > XX work_fnploejenbc2raktl46esxm44i 246 32 0 0 CD work_fnploejenbc2raktl46esxm44i 246 33 there there EX work_fnploejenbc2raktl46esxm44i 246 34 is be VBZ work_fnploejenbc2raktl46esxm44i 246 35 an an DT work_fnploejenbc2raktl46esxm44i 246 36 r r NN work_fnploejenbc2raktl46esxm44i 246 37 = = NN work_fnploejenbc2raktl46esxm44i 246 38 r(Z r(Z NNS work_fnploejenbc2raktl46esxm44i 246 39 , , , work_fnploejenbc2raktl46esxm44i 246 40 $ $ $ work_fnploejenbc2raktl46esxm44i 246 41 , , , work_fnploejenbc2raktl46esxm44i 246 42 a a DT work_fnploejenbc2raktl46esxm44i 246 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 246 44 > > XX work_fnploejenbc2raktl46esxm44i 246 45 0 0 CD work_fnploejenbc2raktl46esxm44i 246 46 such such JJ work_fnploejenbc2raktl46esxm44i 246 47 that that IN work_fnploejenbc2raktl46esxm44i 246 48 there there EX work_fnploejenbc2raktl46esxm44i 246 49 is be VBZ work_fnploejenbc2raktl46esxm44i 246 50 no no DT work_fnploejenbc2raktl46esxm44i 246 51 t t NN work_fnploejenbc2raktl46esxm44i 246 52 E e NN work_fnploejenbc2raktl46esxm44i 246 53 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 246 54 0 0 CD work_fnploejenbc2raktl46esxm44i 246 55 , , , work_fnploejenbc2raktl46esxm44i 246 56 r r LS work_fnploejenbc2raktl46esxm44i 246 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 246 58 for for IN work_fnploejenbc2raktl46esxm44i 246 59 which which WDT work_fnploejenbc2raktl46esxm44i 246 60 L”‘(?i++g)-L L”‘(?i++g)-L NNP work_fnploejenbc2raktl46esxm44i 246 61 ” " '' work_fnploejenbc2raktl46esxm44i 246 62 ‘ ' `` work_fnploejenbc2raktl46esxm44i 246 63 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 246 64 . . . work_fnploejenbc2raktl46esxm44i 246 65 ? ? . work_fnploejenbc2raktl46esxm44i 247 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 247 2 , , , work_fnploejenbc2raktl46esxm44i 247 3 < < XX work_fnploejenbc2raktl46esxm44i 247 4 -atl -atl : work_fnploejenbc2raktl46esxm44i 247 5 , , , work_fnploejenbc2raktl46esxm44i 247 6 . . . work_fnploejenbc2raktl46esxm44i 248 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 248 2 2 2 LS work_fnploejenbc2raktl46esxm44i 248 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 248 4 Here here RB work_fnploejenbc2raktl46esxm44i 248 5 1 1 CD work_fnploejenbc2raktl46esxm44i 248 6 , , , work_fnploejenbc2raktl46esxm44i 248 7 is be VBZ work_fnploejenbc2raktl46esxm44i 248 8 a a DT work_fnploejenbc2raktl46esxm44i 248 9 k k NN work_fnploejenbc2raktl46esxm44i 248 10 by by IN work_fnploejenbc2raktl46esxm44i 248 11 1 1 CD work_fnploejenbc2raktl46esxm44i 248 12 vector vector NN work_fnploejenbc2raktl46esxm44i 248 13 all all DT work_fnploejenbc2raktl46esxm44i 248 14 of of IN work_fnploejenbc2raktl46esxm44i 248 15 whose whose WP$ work_fnploejenbc2raktl46esxm44i 248 16 components component NNS work_fnploejenbc2raktl46esxm44i 248 17 are be VBP work_fnploejenbc2raktl46esxm44i 248 18 1 1 CD work_fnploejenbc2raktl46esxm44i 248 19 . . . work_fnploejenbc2raktl46esxm44i 249 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 249 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 249 3 TO to IN work_fnploejenbc2raktl46esxm44i 249 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 249 5 561 561 CD work_fnploejenbc2raktl46esxm44i 249 6 Note note NN work_fnploejenbc2raktl46esxm44i 249 7 that that IN work_fnploejenbc2raktl46esxm44i 249 8 -at -at : work_fnploejenbc2raktl46esxm44i 249 9 1 1 CD work_fnploejenbc2raktl46esxm44i 249 10 , , , work_fnploejenbc2raktl46esxm44i 249 11 cs cs NNP work_fnploejenbc2raktl46esxm44i 249 12 0 0 CD work_fnploejenbc2raktl46esxm44i 249 13 in in IN work_fnploejenbc2raktl46esxm44i 249 14 Rk Rk NNP work_fnploejenbc2raktl46esxm44i 249 15 . . . work_fnploejenbc2raktl46esxm44i 250 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 250 2 is be VBZ work_fnploejenbc2raktl46esxm44i 250 3 convenient convenient JJ work_fnploejenbc2raktl46esxm44i 250 4 to to TO work_fnploejenbc2raktl46esxm44i 250 5 refer refer VB work_fnploejenbc2raktl46esxm44i 250 6 to to IN work_fnploejenbc2raktl46esxm44i 250 7 such such JJ work_fnploejenbc2raktl46esxm44i 250 8 j j NNP work_fnploejenbc2raktl46esxm44i 250 9 as as IN work_fnploejenbc2raktl46esxm44i 250 10 a a DT work_fnploejenbc2raktl46esxm44i 250 11 direction direction NN work_fnploejenbc2raktl46esxm44i 250 12 . . . work_fnploejenbc2raktl46esxm44i 251 1 Then then RB work_fnploejenbc2raktl46esxm44i 251 2 , , , work_fnploejenbc2raktl46esxm44i 251 3 locally locally RB work_fnploejenbc2raktl46esxm44i 251 4 , , , work_fnploejenbc2raktl46esxm44i 251 5 z z XX work_fnploejenbc2raktl46esxm44i 251 6 ? ? . work_fnploejenbc2raktl46esxm44i 252 1 can can MD work_fnploejenbc2raktl46esxm44i 252 2 not not RB work_fnploejenbc2raktl46esxm44i 252 3 be be VB work_fnploejenbc2raktl46esxm44i 252 4 “ " `` work_fnploejenbc2raktl46esxm44i 252 5 beat beat VBN work_fnploejenbc2raktl46esxm44i 252 6 linearly linearly RB work_fnploejenbc2raktl46esxm44i 252 7 in in IN work_fnploejenbc2raktl46esxm44i 252 8 any any DT work_fnploejenbc2raktl46esxm44i 252 9 direction direction NN work_fnploejenbc2raktl46esxm44i 252 10 . . . work_fnploejenbc2raktl46esxm44i 252 11 ” " '' work_fnploejenbc2raktl46esxm44i 252 12 Of of RB work_fnploejenbc2raktl46esxm44i 252 13 course course RB work_fnploejenbc2raktl46esxm44i 252 14 , , , work_fnploejenbc2raktl46esxm44i 252 15 A A NNP work_fnploejenbc2raktl46esxm44i 252 16 - - HYPH work_fnploejenbc2raktl46esxm44i 252 17 WAD WAD NNP work_fnploejenbc2raktl46esxm44i 252 18 implies imply VBZ work_fnploejenbc2raktl46esxm44i 252 19 & & CC work_fnploejenbc2raktl46esxm44i 252 20 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 252 21 : : : work_fnploejenbc2raktl46esxm44i 252 22 if if IN work_fnploejenbc2raktl46esxm44i 252 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 252 24 2 2 CD work_fnploejenbc2raktl46esxm44i 252 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 252 26 holds hold VBZ work_fnploejenbc2raktl46esxm44i 252 27 for for IN work_fnploejenbc2raktl46esxm44i 252 28 some some DT work_fnploejenbc2raktl46esxm44i 252 29 j j NNP work_fnploejenbc2raktl46esxm44i 252 30 , , , work_fnploejenbc2raktl46esxm44i 252 31 a a NNP work_fnploejenbc2raktl46esxm44i 252 32 , , , work_fnploejenbc2raktl46esxm44i 252 33 t t NN work_fnploejenbc2raktl46esxm44i 252 34 , , , work_fnploejenbc2raktl46esxm44i 252 35 then then RB work_fnploejenbc2raktl46esxm44i 252 36 L”‘(i L”‘(i NNP work_fnploejenbc2raktl46esxm44i 252 37 + + SYM work_fnploejenbc2raktl46esxm44i 252 38 tf tf NNP work_fnploejenbc2raktl46esxm44i 252 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 252 40 < < XX work_fnploejenbc2raktl46esxm44i 252 41 s s NNP work_fnploejenbc2raktl46esxm44i 252 42 L”‘(3 L”‘(3 NNP work_fnploejenbc2raktl46esxm44i 252 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 252 44 . . . work_fnploejenbc2raktl46esxm44i 253 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 253 2 close close VBP work_fnploejenbc2raktl46esxm44i 253 3 this this DT work_fnploejenbc2raktl46esxm44i 253 4 section section NN work_fnploejenbc2raktl46esxm44i 253 5 with with IN work_fnploejenbc2raktl46esxm44i 253 6 a a DT work_fnploejenbc2raktl46esxm44i 253 7 theorem theorem NN work_fnploejenbc2raktl46esxm44i 253 8 which which WDT work_fnploejenbc2raktl46esxm44i 253 9 gives give VBZ work_fnploejenbc2raktl46esxm44i 253 10 global global JJ work_fnploejenbc2raktl46esxm44i 253 11 and and CC work_fnploejenbc2raktl46esxm44i 253 12 local local JJ work_fnploejenbc2raktl46esxm44i 253 13 equivalences equivalence NNS work_fnploejenbc2raktl46esxm44i 253 14 under under IN work_fnploejenbc2raktl46esxm44i 253 15 the the DT work_fnploejenbc2raktl46esxm44i 253 16 additional additional JJ work_fnploejenbc2raktl46esxm44i 253 17 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 253 18 that that WDT work_fnploejenbc2raktl46esxm44i 253 19 L L NNP work_fnploejenbc2raktl46esxm44i 253 20 is be VBZ work_fnploejenbc2raktl46esxm44i 253 21 convex convex NNP work_fnploejenbc2raktl46esxm44i 253 22 , , , work_fnploejenbc2raktl46esxm44i 253 23 that that RB work_fnploejenbc2raktl46esxm44i 253 24 is is RB work_fnploejenbc2raktl46esxm44i 253 25 , , , work_fnploejenbc2raktl46esxm44i 253 26 each each DT work_fnploejenbc2raktl46esxm44i 253 27 component component NN work_fnploejenbc2raktl46esxm44i 253 28 of of IN work_fnploejenbc2raktl46esxm44i 253 29 L L NNP work_fnploejenbc2raktl46esxm44i 253 30 is be VBZ work_fnploejenbc2raktl46esxm44i 253 31 convex convex NNP work_fnploejenbc2raktl46esxm44i 253 32 . . . work_fnploejenbc2raktl46esxm44i 254 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 254 2 3.1.1 3.1.1 CD work_fnploejenbc2raktl46esxm44i 254 3 . . . work_fnploejenbc2raktl46esxm44i 255 1 Let let VB work_fnploejenbc2raktl46esxm44i 255 2 L L NNP work_fnploejenbc2raktl46esxm44i 255 3 be be VB work_fnploejenbc2raktl46esxm44i 255 4 convex convex NNP work_fnploejenbc2raktl46esxm44i 255 5 . . . work_fnploejenbc2raktl46esxm44i 256 1 Then then RB work_fnploejenbc2raktl46esxm44i 256 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 256 3 i i NN work_fnploejenbc2raktl46esxm44i 256 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 256 5 a a DT work_fnploejenbc2raktl46esxm44i 256 6 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 256 7 is be VBZ work_fnploejenbc2raktl46esxm44i 256 8 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 256 9 to to IN work_fnploejenbc2raktl46esxm44i 256 10 A a DT work_fnploejenbc2raktl46esxm44i 256 11 local local JJ work_fnploejenbc2raktl46esxm44i 256 12 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 256 13 ; ; : work_fnploejenbc2raktl46esxm44i 256 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 256 15 ii ii LS work_fnploejenbc2raktl46esxm44i 256 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 256 17 A A NNP work_fnploejenbc2raktl46esxm44i 256 18 - - HYPH work_fnploejenbc2raktl46esxm44i 256 19 WAD WAD NNP work_fnploejenbc2raktl46esxm44i 256 20 is be VBZ work_fnploejenbc2raktl46esxm44i 256 21 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 256 22 to to IN work_fnploejenbc2raktl46esxm44i 256 23 A A NNP work_fnploejenbc2raktl46esxm44i 256 24 - - HYPH work_fnploejenbc2raktl46esxm44i 256 25 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 256 26 . . . work_fnploejenbc2raktl46esxm44i 257 1 Proof Proof NNP work_fnploejenbc2raktl46esxm44i 257 2 Since since IN work_fnploejenbc2raktl46esxm44i 257 3 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 257 4 is be VBZ work_fnploejenbc2raktl46esxm44i 257 5 obvious obvious JJ work_fnploejenbc2raktl46esxm44i 257 6 that that IN work_fnploejenbc2raktl46esxm44i 257 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 257 8 implies imply VBZ work_fnploejenbc2raktl46esxm44i 257 9 local local JJ work_fnploejenbc2raktl46esxm44i 257 10 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 257 11 , , , work_fnploejenbc2raktl46esxm44i 257 12 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 257 13 consider consider VBP work_fnploejenbc2raktl46esxm44i 257 14 only only RB work_fnploejenbc2raktl46esxm44i 257 15 the the DT work_fnploejenbc2raktl46esxm44i 257 16 converses converse NNS work_fnploejenbc2raktl46esxm44i 257 17 . . . work_fnploejenbc2raktl46esxm44i 258 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 258 2 i i NN work_fnploejenbc2raktl46esxm44i 258 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 258 4 In in IN work_fnploejenbc2raktl46esxm44i 258 5 terms term NNS work_fnploejenbc2raktl46esxm44i 258 6 of of IN work_fnploejenbc2raktl46esxm44i 258 7 L L NNP work_fnploejenbc2raktl46esxm44i 258 8 , , , work_fnploejenbc2raktl46esxm44i 258 9 . . . work_fnploejenbc2raktl46esxm44i 258 10 ? ? . work_fnploejenbc2raktl46esxm44i 259 1 is be VBZ work_fnploejenbc2raktl46esxm44i 259 2 not not RB work_fnploejenbc2raktl46esxm44i 259 3 A a NN work_fnploejenbc2raktl46esxm44i 259 4 - - HYPH work_fnploejenbc2raktl46esxm44i 259 5 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 259 6 if if IN work_fnploejenbc2raktl46esxm44i 259 7 there there EX work_fnploejenbc2raktl46esxm44i 259 8 is be VBZ work_fnploejenbc2raktl46esxm44i 259 9 a a DT work_fnploejenbc2raktl46esxm44i 259 10 i i NN work_fnploejenbc2raktl46esxm44i 259 11 , , , work_fnploejenbc2raktl46esxm44i 259 12 in in IN work_fnploejenbc2raktl46esxm44i 259 13 D d NN work_fnploejenbc2raktl46esxm44i 259 14 such such PDT work_fnploejenbc2raktl46esxm44i 259 15 that that DT work_fnploejenbc2raktl46esxm44i 259 16 L(9 L(9 NNP work_fnploejenbc2raktl46esxm44i 259 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 259 18 < < XX work_fnploejenbc2raktl46esxm44i 259 19 w w NNP work_fnploejenbc2raktl46esxm44i 259 20 L(Z L(Z NNP work_fnploejenbc2raktl46esxm44i 259 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 259 22 . . . work_fnploejenbc2raktl46esxm44i 260 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 260 2 3 3 LS work_fnploejenbc2raktl46esxm44i 260 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 260 4 Convexity Convexity NNP work_fnploejenbc2raktl46esxm44i 260 5 of of IN work_fnploejenbc2raktl46esxm44i 260 6 L L NNP work_fnploejenbc2raktl46esxm44i 260 7 means mean VBZ work_fnploejenbc2raktl46esxm44i 260 8 that that IN work_fnploejenbc2raktl46esxm44i 260 9 for for IN work_fnploejenbc2raktl46esxm44i 260 10 each each DT work_fnploejenbc2raktl46esxm44i 260 11 t t NN work_fnploejenbc2raktl46esxm44i 260 12 in in IN work_fnploejenbc2raktl46esxm44i 260 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 260 14 0 0 NFP work_fnploejenbc2raktl46esxm44i 260 15 , , , work_fnploejenbc2raktl46esxm44i 260 16 l l NN work_fnploejenbc2raktl46esxm44i 260 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 260 18 , , , work_fnploejenbc2raktl46esxm44i 260 19 L@+t(j L@+t(j NNP work_fnploejenbc2raktl46esxm44i 260 20 - - HYPH work_fnploejenbc2raktl46esxm44i 260 21 a))<(l a))<(l NN work_fnploejenbc2raktl46esxm44i 260 22 - - HYPH work_fnploejenbc2raktl46esxm44i 260 23 t)L(i)+tL(g t)l(i)+tl(g NN work_fnploejenbc2raktl46esxm44i 260 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 260 25 . . . work_fnploejenbc2raktl46esxm44i 261 1 Combining combine VBG work_fnploejenbc2raktl46esxm44i 261 2 this this DT work_fnploejenbc2raktl46esxm44i 261 3 with with IN work_fnploejenbc2raktl46esxm44i 261 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 261 5 3 3 CD work_fnploejenbc2raktl46esxm44i 261 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 261 7 , , , work_fnploejenbc2raktl46esxm44i 261 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 261 9 obtain obtain VBP work_fnploejenbc2raktl46esxm44i 261 10 L(Z+ L(Z+ NNP work_fnploejenbc2raktl46esxm44i 261 11 t(j t(j NNP work_fnploejenbc2raktl46esxm44i 261 12 - - : work_fnploejenbc2raktl46esxm44i 261 13 a a NN work_fnploejenbc2raktl46esxm44i 261 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 261 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 261 16 < < XX work_fnploejenbc2raktl46esxm44i 261 17 , , , work_fnploejenbc2raktl46esxm44i 261 18 L(i l(i ADD work_fnploejenbc2raktl46esxm44i 261 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 261 20 . . . work_fnploejenbc2raktl46esxm44i 262 1 For for IN work_fnploejenbc2raktl46esxm44i 262 2 any any DT work_fnploejenbc2raktl46esxm44i 262 3 r r NN work_fnploejenbc2raktl46esxm44i 262 4 > > NN work_fnploejenbc2raktl46esxm44i 262 5 0 0 CD work_fnploejenbc2raktl46esxm44i 262 6 , , , work_fnploejenbc2raktl46esxm44i 262 7 choosing choose VBG work_fnploejenbc2raktl46esxm44i 262 8 t t NN work_fnploejenbc2raktl46esxm44i 262 9 = = SYM work_fnploejenbc2raktl46esxm44i 262 10 r/(r r/(r NNP work_fnploejenbc2raktl46esxm44i 262 11 + + CC work_fnploejenbc2raktl46esxm44i 262 12 jl jl NNP work_fnploejenbc2raktl46esxm44i 262 13 j j NNP work_fnploejenbc2raktl46esxm44i 262 14 - - HYPH work_fnploejenbc2raktl46esxm44i 262 15 ill ill NNP work_fnploejenbc2raktl46esxm44i 262 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 262 17 makes make VBZ work_fnploejenbc2raktl46esxm44i 262 18 / / SYM work_fnploejenbc2raktl46esxm44i 262 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 262 20 t(j t(j NNP work_fnploejenbc2raktl46esxm44i 262 21 - - HYPH work_fnploejenbc2raktl46esxm44i 262 22 a)\\ a)\\ NNP work_fnploejenbc2raktl46esxm44i 262 23 < < XX work_fnploejenbc2raktl46esxm44i 262 24 r r NNP work_fnploejenbc2raktl46esxm44i 262 25 whence whence NN work_fnploejenbc2raktl46esxm44i 262 26 . . . work_fnploejenbc2raktl46esxm44i 262 27 ? ? . work_fnploejenbc2raktl46esxm44i 263 1 is be VBZ work_fnploejenbc2raktl46esxm44i 263 2 not not RB work_fnploejenbc2raktl46esxm44i 263 3 J J NNP work_fnploejenbc2raktl46esxm44i 263 4 - - HYPH work_fnploejenbc2raktl46esxm44i 263 5 LAD LAD NNP work_fnploejenbc2raktl46esxm44i 263 6 . . . work_fnploejenbc2raktl46esxm44i 264 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 264 2 ii ii LS work_fnploejenbc2raktl46esxm44i 264 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 264 4 If if IN work_fnploejenbc2raktl46esxm44i 264 5 i i PRP work_fnploejenbc2raktl46esxm44i 264 6 is be VBZ work_fnploejenbc2raktl46esxm44i 264 7 not not RB work_fnploejenbc2raktl46esxm44i 264 8 A A NNP work_fnploejenbc2raktl46esxm44i 264 9 - - HYPH work_fnploejenbc2raktl46esxm44i 264 10 WAD WAD NNP work_fnploejenbc2raktl46esxm44i 264 11 , , , work_fnploejenbc2raktl46esxm44i 264 12 there there EX work_fnploejenbc2raktl46esxm44i 264 13 is be VBZ work_fnploejenbc2raktl46esxm44i 264 14 a a DT work_fnploejenbc2raktl46esxm44i 264 15 j j NN work_fnploejenbc2raktl46esxm44i 264 16 such such JJ work_fnploejenbc2raktl46esxm44i 264 17 that that IN work_fnploejenbc2raktl46esxm44i 264 18 L(‘)(p L(‘)(p NNP work_fnploejenbc2raktl46esxm44i 264 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 264 20 cs cs NNP work_fnploejenbc2raktl46esxm44i 264 21 L(‘)(i L(‘)(i NNP work_fnploejenbc2raktl46esxm44i 264 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 264 23 . . . work_fnploejenbc2raktl46esxm44i 265 1 Then then RB work_fnploejenbc2raktl46esxm44i 265 2 a a DT work_fnploejenbc2raktl46esxm44i 265 3 = = SYM work_fnploejenbc2raktl46esxm44i 265 4 min(Lj”(f)-Lj’)(j),j= min(lj”(f)-lj’)(j),j= NN work_fnploejenbc2raktl46esxm44i 265 5 l(l)k l(l)k NN work_fnploejenbc2raktl46esxm44i 265 6 } } -RRB- work_fnploejenbc2raktl46esxm44i 265 7 > > XX work_fnploejenbc2raktl46esxm44i 265 8 O o NN work_fnploejenbc2raktl46esxm44i 265 9 and and CC work_fnploejenbc2raktl46esxm44i 265 10 L l NN work_fnploejenbc2raktl46esxm44i 265 11 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 265 12 l~(~) > XX work_fnploejenbc2raktl46esxm44i 285 19 0 0 NFP work_fnploejenbc2raktl46esxm44i 285 20 such such JJ work_fnploejenbc2raktl46esxm44i 285 21 that that IN work_fnploejenbc2raktl46esxm44i 285 22 for for IN work_fnploejenbc2raktl46esxm44i 285 23 all all DT work_fnploejenbc2raktl46esxm44i 285 24 r r NN work_fnploejenbc2raktl46esxm44i 285 25 so so RB work_fnploejenbc2raktl46esxm44i 285 26 there there EX work_fnploejenbc2raktl46esxm44i 285 27 is be VBZ work_fnploejenbc2raktl46esxm44i 285 28 a a DT work_fnploejenbc2raktl46esxm44i 285 29 t t NN work_fnploejenbc2raktl46esxm44i 285 30 , , , work_fnploejenbc2raktl46esxm44i 285 31 < < XX work_fnploejenbc2raktl46esxm44i 285 32 r r NNP work_fnploejenbc2raktl46esxm44i 285 33 for for IN work_fnploejenbc2raktl46esxm44i 285 34 which which WDT work_fnploejenbc2raktl46esxm44i 285 35 L(2 L(2 NNP work_fnploejenbc2raktl46esxm44i 285 36 + + CC work_fnploejenbc2raktl46esxm44i 285 37 t t NN work_fnploejenbc2raktl46esxm44i 285 38 , , , work_fnploejenbc2raktl46esxm44i 285 39 jq- jq- NNP work_fnploejenbc2raktl46esxm44i 285 40 L(i L(i NNP work_fnploejenbc2raktl46esxm44i 285 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 285 42 < < XX work_fnploejenbc2raktl46esxm44i 285 43 -E&l -E&l NNP work_fnploejenbc2raktl46esxm44i 285 44 , , , work_fnploejenbc2raktl46esxm44i 285 45 . . . work_fnploejenbc2raktl46esxm44i 286 1 Since since IN work_fnploejenbc2raktl46esxm44i 286 2 t,+O t,+O NNP work_fnploejenbc2raktl46esxm44i 286 3 as as IN work_fnploejenbc2raktl46esxm44i 286 4 r-+0 r-+0 NNP work_fnploejenbc2raktl46esxm44i 286 5 , , , work_fnploejenbc2raktl46esxm44i 286 6 J$<,O. j$<,o. NN work_fnploejenbc2raktl46esxm44i 287 1 1 1 CD work_fnploejenbc2raktl46esxm44i 287 2 Recall recall VB work_fnploejenbc2raktl46esxm44i 287 3 that that DT work_fnploejenbc2raktl46esxm44i 287 4 for for IN work_fnploejenbc2raktl46esxm44i 287 5 2 2 CD work_fnploejenbc2raktl46esxm44i 287 6 = = SYM work_fnploejenbc2raktl46esxm44i 287 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 287 8 A a NN work_fnploejenbc2raktl46esxm44i 287 9 , , , work_fnploejenbc2raktl46esxm44i 287 10 , , , work_fnploejenbc2raktl46esxm44i 287 11 . . . work_fnploejenbc2raktl46esxm44i 288 1 . . . work_fnploejenbc2raktl46esxm44i 289 1 . . . work_fnploejenbc2raktl46esxm44i 290 1 . . . work_fnploejenbc2raktl46esxm44i 291 1 A a DT work_fnploejenbc2raktl46esxm44i 291 2 , , , work_fnploejenbc2raktl46esxm44i 291 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 291 4 , , , work_fnploejenbc2raktl46esxm44i 291 5 PE PE NNP work_fnploejenbc2raktl46esxm44i 291 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 291 7 a a DT work_fnploejenbc2raktl46esxm44i 291 8 , , , work_fnploejenbc2raktl46esxm44i 291 9 , , , work_fnploejenbc2raktl46esxm44i 291 10 a31A a31a ADD work_fnploejenbc2raktl46esxm44i 291 11 is be VBZ work_fnploejenbc2raktl46esxm44i 291 12 identified identify VBN work_fnploejenbc2raktl46esxm44i 291 13 with with IN work_fnploejenbc2raktl46esxm44i 291 14 P p NN work_fnploejenbc2raktl46esxm44i 291 15 = = NFP work_fnploejenbc2raktl46esxm44i 291 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 291 17 X x NN work_fnploejenbc2raktl46esxm44i 291 18 , , , work_fnploejenbc2raktl46esxm44i 291 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 291 20 .. .. NFP work_fnploejenbc2raktl46esxm44i 291 21 * * NFP work_fnploejenbc2raktl46esxm44i 291 22 , , , work_fnploejenbc2raktl46esxm44i 291 23 x x SYM work_fnploejenbc2raktl46esxm44i 291 24 , , , work_fnploejenbc2raktl46esxm44i 291 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 291 26 E e NN work_fnploejenbc2raktl46esxm44i 291 27 D d NN work_fnploejenbc2raktl46esxm44i 291 28 = = NFP work_fnploejenbc2raktl46esxm44i 291 29 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 291 30 a a DT work_fnploejenbc2raktl46esxm44i 291 31 , , , work_fnploejenbc2raktl46esxm44i 291 32 , , , work_fnploejenbc2raktl46esxm44i 291 33 asIn asin XX work_fnploejenbc2raktl46esxm44i 291 34 . . . work_fnploejenbc2raktl46esxm44i 292 1 In in IN work_fnploejenbc2raktl46esxm44i 292 2 view view NN work_fnploejenbc2raktl46esxm44i 292 3 of of IN work_fnploejenbc2raktl46esxm44i 292 4 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 292 5 3.2.1 3.2.1 NNP work_fnploejenbc2raktl46esxm44i 292 6 , , , work_fnploejenbc2raktl46esxm44i 292 7 the the DT work_fnploejenbc2raktl46esxm44i 292 8 analytic analytic JJ work_fnploejenbc2raktl46esxm44i 292 9 study study NN work_fnploejenbc2raktl46esxm44i 292 10 of of IN work_fnploejenbc2raktl46esxm44i 292 11 weak weak JJ work_fnploejenbc2raktl46esxm44i 292 12 local local JJ work_fnploejenbc2raktl46esxm44i 292 13 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 292 14 of of IN work_fnploejenbc2raktl46esxm44i 292 15 p p NN work_fnploejenbc2raktl46esxm44i 292 16 or or CC work_fnploejenbc2raktl46esxm44i 292 17 2 2 CD work_fnploejenbc2raktl46esxm44i 292 18 is be VBZ work_fnploejenbc2raktl46esxm44i 292 19 reduced reduce VBN work_fnploejenbc2raktl46esxm44i 292 20 to to IN work_fnploejenbc2raktl46esxm44i 292 21 finding find VBG work_fnploejenbc2raktl46esxm44i 292 22 conditions condition NNS work_fnploejenbc2raktl46esxm44i 292 23 on on IN work_fnploejenbc2raktl46esxm44i 292 24 J(a J(a NNP work_fnploejenbc2raktl46esxm44i 292 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 292 26 so so IN work_fnploejenbc2raktl46esxm44i 292 27 that that IN work_fnploejenbc2raktl46esxm44i 292 28 there there EX work_fnploejenbc2raktl46esxm44i 292 29 is be VBZ work_fnploejenbc2raktl46esxm44i 292 30 no no DT work_fnploejenbc2raktl46esxm44i 292 31 9 9 CD work_fnploejenbc2raktl46esxm44i 292 32 E e NN work_fnploejenbc2raktl46esxm44i 292 33 Iw iw NN work_fnploejenbc2raktl46esxm44i 292 34 ” " '' work_fnploejenbc2raktl46esxm44i 292 35 for for IN work_fnploejenbc2raktl46esxm44i 292 36 which which WDT work_fnploejenbc2raktl46esxm44i 292 37 J(Z j(z NN work_fnploejenbc2raktl46esxm44i 292 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 292 39 . . . work_fnploejenbc2raktl46esxm44i 293 1 $ $ $ work_fnploejenbc2raktl46esxm44i 293 2 cs cs NNP work_fnploejenbc2raktl46esxm44i 293 3 0 0 CD work_fnploejenbc2raktl46esxm44i 293 4 . . . work_fnploejenbc2raktl46esxm44i 294 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 294 2 is be VBZ work_fnploejenbc2raktl46esxm44i 294 3 well well RB work_fnploejenbc2raktl46esxm44i 294 4 known know VBN work_fnploejenbc2raktl46esxm44i 294 5 that that IN work_fnploejenbc2raktl46esxm44i 294 6 the the DT work_fnploejenbc2raktl46esxm44i 294 7 solutions solution NNS work_fnploejenbc2raktl46esxm44i 294 8 of of IN work_fnploejenbc2raktl46esxm44i 294 9 a a DT work_fnploejenbc2raktl46esxm44i 294 10 system system NN work_fnploejenbc2raktl46esxm44i 294 11 like like IN work_fnploejenbc2raktl46esxm44i 294 12 Ji Ji NNP work_fnploejenbc2raktl46esxm44i 294 13 , , , work_fnploejenbc2raktl46esxm44i 294 14 = = NFP work_fnploejenbc2raktl46esxm44i 294 15 i i PRP work_fnploejenbc2raktl46esxm44i 294 16 depend depend VBP work_fnploejenbc2raktl46esxm44i 294 17 heavily heavily RB work_fnploejenbc2raktl46esxm44i 294 18 on on IN work_fnploejenbc2raktl46esxm44i 294 19 the the DT work_fnploejenbc2raktl46esxm44i 294 20 rank rank NN work_fnploejenbc2raktl46esxm44i 294 21 p p NN work_fnploejenbc2raktl46esxm44i 294 22 of of IN work_fnploejenbc2raktl46esxm44i 294 23 J. J. NNP work_fnploejenbc2raktl46esxm44i 295 1 Also also RB work_fnploejenbc2raktl46esxm44i 295 2 , , , work_fnploejenbc2raktl46esxm44i 295 3 the the DT work_fnploejenbc2raktl46esxm44i 295 4 columns column NNS work_fnploejenbc2raktl46esxm44i 295 5 of of IN work_fnploejenbc2raktl46esxm44i 295 6 J J NNP work_fnploejenbc2raktl46esxm44i 295 7 and and CC work_fnploejenbc2raktl46esxm44i 295 8 the the DT work_fnploejenbc2raktl46esxm44i 295 9 rows row NNS work_fnploejenbc2raktl46esxm44i 295 10 of of IN work_fnploejenbc2raktl46esxm44i 295 11 J J NNP work_fnploejenbc2raktl46esxm44i 295 12 , , , work_fnploejenbc2raktl46esxm44i 295 13 9 9 CD work_fnploejenbc2raktl46esxm44i 295 14 and and CC work_fnploejenbc2raktl46esxm44i 295 15 i i PRP work_fnploejenbc2raktl46esxm44i 295 16 can can MD work_fnploejenbc2raktl46esxm44i 295 17 be be VB work_fnploejenbc2raktl46esxm44i 295 18 permuted permute VBN work_fnploejenbc2raktl46esxm44i 295 19 without without IN work_fnploejenbc2raktl46esxm44i 295 20 changing change VBG work_fnploejenbc2raktl46esxm44i 295 21 the the DT work_fnploejenbc2raktl46esxm44i 295 22 rank rank NN work_fnploejenbc2raktl46esxm44i 295 23 or or CC work_fnploejenbc2raktl46esxm44i 295 24 character character NN work_fnploejenbc2raktl46esxm44i 295 25 of of IN work_fnploejenbc2raktl46esxm44i 295 26 the the DT work_fnploejenbc2raktl46esxm44i 295 27 solutions solution NNS work_fnploejenbc2raktl46esxm44i 295 28 ; ; : work_fnploejenbc2raktl46esxm44i 295 29 these these DT work_fnploejenbc2raktl46esxm44i 295 30 can can MD work_fnploejenbc2raktl46esxm44i 295 31 also also RB work_fnploejenbc2raktl46esxm44i 295 32 be be VB work_fnploejenbc2raktl46esxm44i 295 33 partitioned partition VBN work_fnploejenbc2raktl46esxm44i 295 34 . . . work_fnploejenbc2raktl46esxm44i 296 1 In in IN work_fnploejenbc2raktl46esxm44i 296 2 the the DT work_fnploejenbc2raktl46esxm44i 296 3 following following NN work_fnploejenbc2raktl46esxm44i 296 4 , , , work_fnploejenbc2raktl46esxm44i 296 5 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 296 6 assume assume VBP work_fnploejenbc2raktl46esxm44i 296 7 that that IN work_fnploejenbc2raktl46esxm44i 296 8 this this DT work_fnploejenbc2raktl46esxm44i 296 9 has have VBZ work_fnploejenbc2raktl46esxm44i 296 10 been be VBN work_fnploejenbc2raktl46esxm44i 296 11 done do VBN work_fnploejenbc2raktl46esxm44i 296 12 so so IN work_fnploejenbc2raktl46esxm44i 296 13 that that IN work_fnploejenbc2raktl46esxm44i 296 14 when when WRB work_fnploejenbc2raktl46esxm44i 296 15 the the DT work_fnploejenbc2raktl46esxm44i 296 16 rank rank NN work_fnploejenbc2raktl46esxm44i 296 17 is be VBZ work_fnploejenbc2raktl46esxm44i 296 18 p p NN work_fnploejenbc2raktl46esxm44i 296 19 , , , work_fnploejenbc2raktl46esxm44i 296 20 the the DT work_fnploejenbc2raktl46esxm44i 296 21 system system NN work_fnploejenbc2raktl46esxm44i 296 22 is be VBZ work_fnploejenbc2raktl46esxm44i 296 23 where where WRB work_fnploejenbc2raktl46esxm44i 296 24 J J NNP work_fnploejenbc2raktl46esxm44i 296 25 , , , work_fnploejenbc2raktl46esxm44i 296 26 is be VBZ work_fnploejenbc2raktl46esxm44i 296 27 p p NN work_fnploejenbc2raktl46esxm44i 296 28 by by IN work_fnploejenbc2raktl46esxm44i 296 29 p p NN work_fnploejenbc2raktl46esxm44i 296 30 and and CC work_fnploejenbc2raktl46esxm44i 296 31 nonsingular nonsingular JJ work_fnploejenbc2raktl46esxm44i 296 32 , , , work_fnploejenbc2raktl46esxm44i 296 33 C C NNP work_fnploejenbc2raktl46esxm44i 296 34 is be VBZ work_fnploejenbc2raktl46esxm44i 296 35 p p NN work_fnploejenbc2raktl46esxm44i 296 36 by by IN work_fnploejenbc2raktl46esxm44i 296 37 n n NN work_fnploejenbc2raktl46esxm44i 296 38 - - HYPH work_fnploejenbc2raktl46esxm44i 296 39 p p NN work_fnploejenbc2raktl46esxm44i 296 40 and and CC work_fnploejenbc2raktl46esxm44i 296 41 R r NN work_fnploejenbc2raktl46esxm44i 296 42 is be VBZ work_fnploejenbc2raktl46esxm44i 296 43 k k NN work_fnploejenbc2raktl46esxm44i 296 44 - - HYPH work_fnploejenbc2raktl46esxm44i 296 45 p p NN work_fnploejenbc2raktl46esxm44i 296 46 by by IN work_fnploejenbc2raktl46esxm44i 296 47 p. p. NN work_fnploejenbc2raktl46esxm44i 296 48 Of of RB work_fnploejenbc2raktl46esxm44i 296 49 course course RB work_fnploejenbc2raktl46esxm44i 296 50 , , , work_fnploejenbc2raktl46esxm44i 296 51 if if IN work_fnploejenbc2raktl46esxm44i 296 52 p p NN work_fnploejenbc2raktl46esxm44i 296 53 = = SYM work_fnploejenbc2raktl46esxm44i 296 54 n n XX work_fnploejenbc2raktl46esxm44i 296 55 , , , work_fnploejenbc2raktl46esxm44i 296 56 the the DT work_fnploejenbc2raktl46esxm44i 296 57 columns column NNS work_fnploejenbc2raktl46esxm44i 296 58 involving involve VBG work_fnploejenbc2raktl46esxm44i 296 59 C C NNP work_fnploejenbc2raktl46esxm44i 296 60 do do VBP work_fnploejenbc2raktl46esxm44i 296 61 not not RB work_fnploejenbc2raktl46esxm44i 296 62 appear appear VB work_fnploejenbc2raktl46esxm44i 296 63 and and CC work_fnploejenbc2raktl46esxm44i 296 64 if if IN work_fnploejenbc2raktl46esxm44i 296 65 p p NN work_fnploejenbc2raktl46esxm44i 296 66 = = SYM work_fnploejenbc2raktl46esxm44i 296 67 k k XX work_fnploejenbc2raktl46esxm44i 296 68 , , , work_fnploejenbc2raktl46esxm44i 296 69 the the DT work_fnploejenbc2raktl46esxm44i 296 70 rows row NNS work_fnploejenbc2raktl46esxm44i 296 71 involving involve VBG work_fnploejenbc2raktl46esxm44i 296 72 R R NNP work_fnploejenbc2raktl46esxm44i 296 73 do do VBP work_fnploejenbc2raktl46esxm44i 296 74 not not RB work_fnploejenbc2raktl46esxm44i 296 75 appear appear VB work_fnploejenbc2raktl46esxm44i 296 76 . . . work_fnploejenbc2raktl46esxm44i 297 1 The the DT work_fnploejenbc2raktl46esxm44i 297 2 following follow VBG work_fnploejenbc2raktl46esxm44i 297 3 theorem theorem NN work_fnploejenbc2raktl46esxm44i 297 4 contains contain VBZ work_fnploejenbc2raktl46esxm44i 297 5 several several JJ work_fnploejenbc2raktl46esxm44i 297 6 results result NNS work_fnploejenbc2raktl46esxm44i 297 7 relevant relevant JJ work_fnploejenbc2raktl46esxm44i 297 8 to to IN work_fnploejenbc2raktl46esxm44i 297 9 this this DT work_fnploejenbc2raktl46esxm44i 297 10 work work NN work_fnploejenbc2raktl46esxm44i 297 11 . . . work_fnploejenbc2raktl46esxm44i 298 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 298 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 298 3 TO to IN work_fnploejenbc2raktl46esxm44i 298 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 298 5 563 563 CD work_fnploejenbc2raktl46esxm44i 298 6 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 298 7 3.2.2 3.2.2 CD work_fnploejenbc2raktl46esxm44i 298 8 . . . work_fnploejenbc2raktl46esxm44i 299 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 299 2 a a LS work_fnploejenbc2raktl46esxm44i 299 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 299 4 Zf Zf NNP work_fnploejenbc2raktl46esxm44i 299 5 p p NN work_fnploejenbc2raktl46esxm44i 299 6 = = SYM work_fnploejenbc2raktl46esxm44i 299 7 n n NN work_fnploejenbc2raktl46esxm44i 299 8 = = SYM work_fnploejenbc2raktl46esxm44i 299 9 k k XX work_fnploejenbc2raktl46esxm44i 299 10 , , , work_fnploejenbc2raktl46esxm44i 299 11 then then RB work_fnploejenbc2raktl46esxm44i 299 12 i i PRP work_fnploejenbc2raktl46esxm44i 299 13 is be VBZ work_fnploejenbc2raktl46esxm44i 299 14 not not RB work_fnploejenbc2raktl46esxm44i 299 15 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 299 16 . . . work_fnploejenbc2raktl46esxm44i 300 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 300 2 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 300 3 , , , work_fnploejenbc2raktl46esxm44i 300 4 if if IN work_fnploejenbc2raktl46esxm44i 300 5 J J NNP work_fnploejenbc2raktl46esxm44i 300 6 is be VBZ work_fnploejenbc2raktl46esxm44i 300 7 non non JJ work_fnploejenbc2raktl46esxm44i 300 8 - - JJ work_fnploejenbc2raktl46esxm44i 300 9 singular singular JJ work_fnploejenbc2raktl46esxm44i 300 10 , , , work_fnploejenbc2raktl46esxm44i 300 11 then then RB work_fnploejenbc2raktl46esxm44i 300 12 the the DT work_fnploejenbc2raktl46esxm44i 300 13 system system NN work_fnploejenbc2raktl46esxm44i 300 14 Jy Jy NNP work_fnploejenbc2raktl46esxm44i 300 15 = = FW work_fnploejenbc2raktl46esxm44i 300 16 i i PRP work_fnploejenbc2raktl46esxm44i 300 17 has have VBZ work_fnploejenbc2raktl46esxm44i 300 18 a a DT work_fnploejenbc2raktl46esxm44i 300 19 solution solution NN work_fnploejenbc2raktl46esxm44i 300 20 j j NN work_fnploejenbc2raktl46esxm44i 300 21 for for IN work_fnploejenbc2raktl46esxm44i 300 22 every every DT work_fnploejenbc2raktl46esxm44i 300 23 i i NN work_fnploejenbc2raktl46esxm44i 300 24 , , , work_fnploejenbc2raktl46esxm44i 300 25 in in IN work_fnploejenbc2raktl46esxm44i 300 26 particular particular JJ work_fnploejenbc2raktl46esxm44i 300 27 2 2 CD work_fnploejenbc2raktl46esxm44i 300 28 < < XX work_fnploejenbc2raktl46esxm44i 300 29 , , , work_fnploejenbc2raktl46esxm44i 300 30 s s NNP work_fnploejenbc2raktl46esxm44i 300 31 0 0 CD work_fnploejenbc2raktl46esxm44i 300 32 . . . work_fnploejenbc2raktl46esxm44i 300 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 301 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 301 2 b b LS work_fnploejenbc2raktl46esxm44i 301 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 301 4 Zf Zf NNP work_fnploejenbc2raktl46esxm44i 301 5 n n CC work_fnploejenbc2raktl46esxm44i 301 6 = = SYM work_fnploejenbc2raktl46esxm44i 301 7 k k NN work_fnploejenbc2raktl46esxm44i 301 8 and and CC work_fnploejenbc2raktl46esxm44i 301 9 . . . work_fnploejenbc2raktl46esxm44i 301 10 ? ? . work_fnploejenbc2raktl46esxm44i 302 1 is be VBZ work_fnploejenbc2raktl46esxm44i 302 2 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 302 3 , , , work_fnploejenbc2raktl46esxm44i 302 4 then then RB work_fnploejenbc2raktl46esxm44i 302 5 det det NNP work_fnploejenbc2raktl46esxm44i 302 6 J= J= NNP work_fnploejenbc2raktl46esxm44i 302 7 0 0 NFP work_fnploejenbc2raktl46esxm44i 302 8 . . . work_fnploejenbc2raktl46esxm44i 303 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 303 2 cl cl UH work_fnploejenbc2raktl46esxm44i 303 3 , , , work_fnploejenbc2raktl46esxm44i 303 4 % % NN work_fnploejenbc2raktl46esxm44i 303 5 ? ? . work_fnploejenbc2raktl46esxm44i 304 1 is be VBZ work_fnploejenbc2raktl46esxm44i 304 2 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 304 3 zf zf NNS work_fnploejenbc2raktl46esxm44i 304 4 and and CC work_fnploejenbc2raktl46esxm44i 304 5 only only RB work_fnploejenbc2raktl46esxm44i 304 6 zf zf XX work_fnploejenbc2raktl46esxm44i 304 7 there there EX work_fnploejenbc2raktl46esxm44i 304 8 is be VBZ work_fnploejenbc2raktl46esxm44i 304 9 no no DT work_fnploejenbc2raktl46esxm44i 304 10 i i NN work_fnploejenbc2raktl46esxm44i 304 11 E E NNP work_fnploejenbc2raktl46esxm44i 304 12 IV IV NNP work_fnploejenbc2raktl46esxm44i 304 13 ’ ' '' work_fnploejenbc2raktl46esxm44i 304 14 such such JJ work_fnploejenbc2raktl46esxm44i 304 15 that that IN work_fnploejenbc2raktl46esxm44i 304 16 J J NNP work_fnploejenbc2raktl46esxm44i 304 17 , , , work_fnploejenbc2raktl46esxm44i 304 18 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 304 19 1 1 CD work_fnploejenbc2raktl46esxm44i 304 20 RJI rji NN work_fnploejenbc2raktl46esxm44i 304 21 i<,O. i<,O. NNP work_fnploejenbc2raktl46esxm44i 305 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 305 2 d d LS work_fnploejenbc2raktl46esxm44i 305 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 305 4 Zf Zf NNP work_fnploejenbc2raktl46esxm44i 305 5 p p NN work_fnploejenbc2raktl46esxm44i 305 6 = = SYM work_fnploejenbc2raktl46esxm44i 305 7 1 1 CD work_fnploejenbc2raktl46esxm44i 305 8 , , , work_fnploejenbc2raktl46esxm44i 305 9 then then RB work_fnploejenbc2raktl46esxm44i 305 10 2 2 CD work_fnploejenbc2raktl46esxm44i 305 11 is be VBZ work_fnploejenbc2raktl46esxm44i 305 12 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 305 13 if if IN work_fnploejenbc2raktl46esxm44i 305 14 and and CC work_fnploejenbc2raktl46esxm44i 305 15 only only RB work_fnploejenbc2raktl46esxm44i 305 16 if if IN work_fnploejenbc2raktl46esxm44i 305 17 the the DT work_fnploejenbc2raktl46esxm44i 305 18 vector vector NN work_fnploejenbc2raktl46esxm44i 305 19 has have VBZ work_fnploejenbc2raktl46esxm44i 305 20 both both CC work_fnploejenbc2raktl46esxm44i 305 21 positive positive JJ work_fnploejenbc2raktl46esxm44i 305 22 and and CC work_fnploejenbc2raktl46esxm44i 305 23 negative negative JJ work_fnploejenbc2raktl46esxm44i 305 24 components component NNS work_fnploejenbc2raktl46esxm44i 305 25 or or CC work_fnploejenbc2raktl46esxm44i 305 26 at at IN work_fnploejenbc2raktl46esxm44i 305 27 least least JJS work_fnploejenbc2raktl46esxm44i 305 28 a a DT work_fnploejenbc2raktl46esxm44i 305 29 zero zero CD work_fnploejenbc2raktl46esxm44i 305 30 component component NN work_fnploejenbc2raktl46esxm44i 305 31 . . . work_fnploejenbc2raktl46esxm44i 306 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 306 2 e e LS work_fnploejenbc2raktl46esxm44i 306 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 306 4 In in IN work_fnploejenbc2raktl46esxm44i 306 5 case case NN work_fnploejenbc2raktl46esxm44i 306 6 k k NN work_fnploejenbc2raktl46esxm44i 306 7 = = SYM work_fnploejenbc2raktl46esxm44i 306 8 n n NN work_fnploejenbc2raktl46esxm44i 306 9 = = SYM work_fnploejenbc2raktl46esxm44i 306 10 3 3 CD work_fnploejenbc2raktl46esxm44i 306 11 , , , work_fnploejenbc2raktl46esxm44i 306 12 j j NNP work_fnploejenbc2raktl46esxm44i 306 13 ? ? . work_fnploejenbc2raktl46esxm44i 307 1 is be VBZ work_fnploejenbc2raktl46esxm44i 307 2 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 307 3 if if IN work_fnploejenbc2raktl46esxm44i 307 4 and and CC work_fnploejenbc2raktl46esxm44i 307 5 only only RB work_fnploejenbc2raktl46esxm44i 307 6 if if IN work_fnploejenbc2raktl46esxm44i 307 7 det det NNP work_fnploejenbc2raktl46esxm44i 307 8 J J NNP work_fnploejenbc2raktl46esxm44i 307 9 = = SYM work_fnploejenbc2raktl46esxm44i 307 10 0 0 CD work_fnploejenbc2raktl46esxm44i 307 11 and and CC work_fnploejenbc2raktl46esxm44i 307 12 either either RB work_fnploejenbc2raktl46esxm44i 307 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 307 14 i i NN work_fnploejenbc2raktl46esxm44i 307 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 307 16 p p NN work_fnploejenbc2raktl46esxm44i 307 17 = = SYM work_fnploejenbc2raktl46esxm44i 307 18 1 1 CD work_fnploejenbc2raktl46esxm44i 307 19 and and CC work_fnploejenbc2raktl46esxm44i 307 20 J J NNP work_fnploejenbc2raktl46esxm44i 307 21 , , , work_fnploejenbc2raktl46esxm44i 307 22 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 307 23 1 1 CD work_fnploejenbc2raktl46esxm44i 307 24 RJ RJ NNP work_fnploejenbc2raktl46esxm44i 307 25 , , , work_fnploejenbc2raktl46esxm44i 307 26 has have VBZ work_fnploejenbc2raktl46esxm44i 307 27 a a DT work_fnploejenbc2raktl46esxm44i 307 28 zero zero CD work_fnploejenbc2raktl46esxm44i 307 29 component component NN work_fnploejenbc2raktl46esxm44i 307 30 or or CC work_fnploejenbc2raktl46esxm44i 307 31 contains contain VBZ work_fnploejenbc2raktl46esxm44i 307 32 both both CC work_fnploejenbc2raktl46esxm44i 307 33 positive positive JJ work_fnploejenbc2raktl46esxm44i 307 34 and and CC work_fnploejenbc2raktl46esxm44i 307 35 negative negative JJ work_fnploejenbc2raktl46esxm44i 307 36 components component NNS work_fnploejenbc2raktl46esxm44i 307 37 or or CC work_fnploejenbc2raktl46esxm44i 307 38 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 307 39 ii ii NNP work_fnploejenbc2raktl46esxm44i 307 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 307 41 p=2 p=2 VBN work_fnploejenbc2raktl46esxm44i 307 42 and and CC work_fnploejenbc2raktl46esxm44i 307 43 R R NNP work_fnploejenbc2raktl46esxm44i 307 44 < < XX work_fnploejenbc2raktl46esxm44i 307 45 O. o. NN work_fnploejenbc2raktl46esxm44i 308 1 Partial Partial NNP work_fnploejenbc2raktl46esxm44i 308 2 Proof Proof NNP work_fnploejenbc2raktl46esxm44i 308 3 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 308 4 , , , work_fnploejenbc2raktl46esxm44i 308 5 if if IN work_fnploejenbc2raktl46esxm44i 308 6 det det NNP work_fnploejenbc2raktl46esxm44i 308 7 J= J= NNP work_fnploejenbc2raktl46esxm44i 308 8 0 0 NFP work_fnploejenbc2raktl46esxm44i 308 9 , , , work_fnploejenbc2raktl46esxm44i 308 10 and and CC work_fnploejenbc2raktl46esxm44i 308 11 p p NN work_fnploejenbc2raktl46esxm44i 308 12 = = SYM work_fnploejenbc2raktl46esxm44i 308 13 1 1 CD work_fnploejenbc2raktl46esxm44i 308 14 with with IN work_fnploejenbc2raktl46esxm44i 308 15 the the DT work_fnploejenbc2raktl46esxm44i 308 16 above above JJ work_fnploejenbc2raktl46esxm44i 308 17 specified specify VBN work_fnploejenbc2raktl46esxm44i 308 18 structure structure NN work_fnploejenbc2raktl46esxm44i 308 19 of of IN work_fnploejenbc2raktl46esxm44i 308 20 J1 J1 NNP work_fnploejenbc2raktl46esxm44i 308 21 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 308 22 1 1 CD work_fnploejenbc2raktl46esxm44i 308 23 RJ RJ NNP work_fnploejenbc2raktl46esxm44i 308 24 , , , work_fnploejenbc2raktl46esxm44i 308 25 ’ ' '' work_fnploejenbc2raktl46esxm44i 308 26 then then RB work_fnploejenbc2raktl46esxm44i 308 27 i i PRP work_fnploejenbc2raktl46esxm44i 308 28 is be VBZ work_fnploejenbc2raktl46esxm44i 308 29 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 308 30 as as IN work_fnploejenbc2raktl46esxm44i 308 31 in in IN work_fnploejenbc2raktl46esxm44i 308 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 308 33 d d NN work_fnploejenbc2raktl46esxm44i 308 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 308 35 ; ; : work_fnploejenbc2raktl46esxm44i 308 36 if if IN work_fnploejenbc2raktl46esxm44i 308 37 det det NNP work_fnploejenbc2raktl46esxm44i 308 38 J= J= NNP work_fnploejenbc2raktl46esxm44i 308 39 0 0 NNP work_fnploejenbc2raktl46esxm44i 308 40 and and CC work_fnploejenbc2raktl46esxm44i 308 41 p p NN work_fnploejenbc2raktl46esxm44i 308 42 = = SYM work_fnploejenbc2raktl46esxm44i 308 43 2 2 CD work_fnploejenbc2raktl46esxm44i 308 44 , , , work_fnploejenbc2raktl46esxm44i 308 45 then then RB work_fnploejenbc2raktl46esxm44i 308 46 if if IN work_fnploejenbc2raktl46esxm44i 308 47 3 3 CD work_fnploejenbc2raktl46esxm44i 308 48 is be VBZ work_fnploejenbc2raktl46esxm44i 308 49 not not RB work_fnploejenbc2raktl46esxm44i 308 50 WLAD wlad NN work_fnploejenbc2raktl46esxm44i 308 51 , , , work_fnploejenbc2raktl46esxm44i 308 52 there there EX work_fnploejenbc2raktl46esxm44i 308 53 will will MD work_fnploejenbc2raktl46esxm44i 308 54 be be VB work_fnploejenbc2raktl46esxm44i 308 55 j j NNP work_fnploejenbc2raktl46esxm44i 308 56 E e NN work_fnploejenbc2raktl46esxm44i 308 57 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 308 58 w w NN work_fnploejenbc2raktl46esxm44i 308 59 * * NFP work_fnploejenbc2raktl46esxm44i 308 60 such such JJ work_fnploejenbc2raktl46esxm44i 308 61 that that IN work_fnploejenbc2raktl46esxm44i 308 62 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 308 63 , , , work_fnploejenbc2raktl46esxm44i 308 64 J J NNP work_fnploejenbc2raktl46esxm44i 308 65 , , , work_fnploejenbc2raktl46esxm44i 308 66 j j NNP work_fnploejenbc2raktl46esxm44i 308 67 = = SYM work_fnploejenbc2raktl46esxm44i 308 68 f f NN work_fnploejenbc2raktl46esxm44i 308 69 cS cs NN work_fnploejenbc2raktl46esxm44i 308 70 0 0 NFP work_fnploejenbc2raktl46esxm44i 308 71 and and CC work_fnploejenbc2raktl46esxm44i 308 72 Ri Ri NNP work_fnploejenbc2raktl46esxm44i 308 73 cS cS NNP work_fnploejenbc2raktl46esxm44i 308 74 0 0 NFP work_fnploejenbc2raktl46esxm44i 308 75 which which WDT work_fnploejenbc2raktl46esxm44i 308 76 is be VBZ work_fnploejenbc2raktl46esxm44i 308 77 only only RB work_fnploejenbc2raktl46esxm44i 308 78 possible possible JJ work_fnploejenbc2raktl46esxm44i 308 79 if if IN work_fnploejenbc2raktl46esxm44i 308 80 R r NN work_fnploejenbc2raktl46esxm44i 308 81 < < XX work_fnploejenbc2raktl46esxm44i 308 82 0 0 NFP work_fnploejenbc2raktl46esxm44i 308 83 . . . work_fnploejenbc2raktl46esxm44i 309 1 Conversely conversely RB work_fnploejenbc2raktl46esxm44i 309 2 , , , work_fnploejenbc2raktl46esxm44i 309 3 suppose suppose VB work_fnploejenbc2raktl46esxm44i 309 4 that that IN work_fnploejenbc2raktl46esxm44i 309 5 i i PRP work_fnploejenbc2raktl46esxm44i 309 6 is be VBZ work_fnploejenbc2raktl46esxm44i 309 7 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 309 8 . . . work_fnploejenbc2raktl46esxm44i 310 1 Then then RB work_fnploejenbc2raktl46esxm44i 310 2 first first RB work_fnploejenbc2raktl46esxm44i 310 3 , , , work_fnploejenbc2raktl46esxm44i 310 4 det det NNP work_fnploejenbc2raktl46esxm44i 310 5 J J NNP work_fnploejenbc2raktl46esxm44i 310 6 = = SYM work_fnploejenbc2raktl46esxm44i 310 7 0 0 NFP work_fnploejenbc2raktl46esxm44i 310 8 as as IN work_fnploejenbc2raktl46esxm44i 310 9 in in IN work_fnploejenbc2raktl46esxm44i 310 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 310 11 b b NN work_fnploejenbc2raktl46esxm44i 310 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 310 13 ; ; : work_fnploejenbc2raktl46esxm44i 310 14 thus thus RB work_fnploejenbc2raktl46esxm44i 310 15 p p NN work_fnploejenbc2raktl46esxm44i 310 16 = = SYM work_fnploejenbc2raktl46esxm44i 310 17 1 1 CD work_fnploejenbc2raktl46esxm44i 310 18 or or CC work_fnploejenbc2raktl46esxm44i 310 19 2 2 CD work_fnploejenbc2raktl46esxm44i 310 20 since since IN work_fnploejenbc2raktl46esxm44i 310 21 J J NNP work_fnploejenbc2raktl46esxm44i 310 22 z z NNP work_fnploejenbc2raktl46esxm44i 310 23 0 0 CD work_fnploejenbc2raktl46esxm44i 310 24 . . . work_fnploejenbc2raktl46esxm44i 311 1 If if IN work_fnploejenbc2raktl46esxm44i 311 2 p p NN work_fnploejenbc2raktl46esxm44i 311 3 = = SYM work_fnploejenbc2raktl46esxm44i 311 4 1 1 CD work_fnploejenbc2raktl46esxm44i 311 5 , , , work_fnploejenbc2raktl46esxm44i 311 6 and and CC work_fnploejenbc2raktl46esxm44i 311 7 i i PRP work_fnploejenbc2raktl46esxm44i 311 8 is be VBZ work_fnploejenbc2raktl46esxm44i 311 9 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 311 10 , , , work_fnploejenbc2raktl46esxm44i 311 11 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 311 12 have have VBP work_fnploejenbc2raktl46esxm44i 311 13 the the DT work_fnploejenbc2raktl46esxm44i 311 14 above above RB work_fnploejenbc2raktl46esxm44i 311 15 specified specify VBN work_fnploejenbc2raktl46esxm44i 311 16 structure structure NN work_fnploejenbc2raktl46esxm44i 311 17 of of IN work_fnploejenbc2raktl46esxm44i 311 18 564 564 CD work_fnploejenbc2raktl46esxm44i 311 19 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 311 20 , , , work_fnploejenbc2raktl46esxm44i 311 21 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 311 22 , , , work_fnploejenbc2raktl46esxm44i 311 23 AND and CC work_fnploejenbc2raktl46esxm44i 311 24 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 311 25 by by IN work_fnploejenbc2raktl46esxm44i 311 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 311 27 d d NN work_fnploejenbc2raktl46esxm44i 311 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 311 29 . . . work_fnploejenbc2raktl46esxm44i 312 1 If if IN work_fnploejenbc2raktl46esxm44i 312 2 p p NN work_fnploejenbc2raktl46esxm44i 312 3 = = SYM work_fnploejenbc2raktl46esxm44i 312 4 2 2 CD work_fnploejenbc2raktl46esxm44i 312 5 , , , work_fnploejenbc2raktl46esxm44i 312 6 and and CC work_fnploejenbc2raktl46esxm44i 312 7 2 2 CD work_fnploejenbc2raktl46esxm44i 312 8 is be VBZ work_fnploejenbc2raktl46esxm44i 312 9 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 312 10 , , , work_fnploejenbc2raktl46esxm44i 312 11 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 312 12 have have VBP work_fnploejenbc2raktl46esxm44i 312 13 by by IN work_fnploejenbc2raktl46esxm44i 312 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 312 15 c c NN work_fnploejenbc2raktl46esxm44i 312 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 312 17 : : : work_fnploejenbc2raktl46esxm44i 312 18 there there EX work_fnploejenbc2raktl46esxm44i 312 19 is be VBZ work_fnploejenbc2raktl46esxm44i 312 20 no no DT work_fnploejenbc2raktl46esxm44i 312 21 9 9 CD work_fnploejenbc2raktl46esxm44i 312 22 E e NN work_fnploejenbc2raktl46esxm44i 312 23 I@ I@ NNS work_fnploejenbc2raktl46esxm44i 312 24 such such JJ work_fnploejenbc2raktl46esxm44i 312 25 that that IN work_fnploejenbc2raktl46esxm44i 312 26 JI JI NNP work_fnploejenbc2raktl46esxm44i 312 27 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 312 28 1 1 CD work_fnploejenbc2raktl46esxm44i 312 29 RJ RJ NNP work_fnploejenbc2raktl46esxm44i 312 30 , , , work_fnploejenbc2raktl46esxm44i 312 31 f<,O f<,O NNP work_fnploejenbc2raktl46esxm44i 312 32 , , , work_fnploejenbc2raktl46esxm44i 312 33 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 312 34 , , , work_fnploejenbc2raktl46esxm44i 312 35 there there EX work_fnploejenbc2raktl46esxm44i 312 36 is be VBZ work_fnploejenbc2raktl46esxm44i 312 37 no no DT work_fnploejenbc2raktl46esxm44i 312 38 G g NN work_fnploejenbc2raktl46esxm44i 312 39 cS cs NN work_fnploejenbc2raktl46esxm44i 312 40 0 0 NFP work_fnploejenbc2raktl46esxm44i 312 41 such such JJ work_fnploejenbc2raktl46esxm44i 312 42 that that IN work_fnploejenbc2raktl46esxm44i 312 43 R6 R6 NNP work_fnploejenbc2raktl46esxm44i 312 44 -q -q NFP work_fnploejenbc2raktl46esxm44i 312 45 0 0 NFP work_fnploejenbc2raktl46esxm44i 312 46 , , , work_fnploejenbc2raktl46esxm44i 312 47 and and CC work_fnploejenbc2raktl46esxm44i 312 48 hence hence RB work_fnploejenbc2raktl46esxm44i 312 49 R r NN work_fnploejenbc2raktl46esxm44i 312 50 6 6 CD work_fnploejenbc2raktl46esxm44i 312 51 0 0 CD work_fnploejenbc2raktl46esxm44i 312 52 . . . work_fnploejenbc2raktl46esxm44i 313 1 1 1 CD work_fnploejenbc2raktl46esxm44i 313 2 COROLLARY COROLLARY NNP work_fnploejenbc2raktl46esxm44i 313 3 3.2.1 3.2.1 NN work_fnploejenbc2raktl46esxm44i 313 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 313 5 Corresponds correspond NNS work_fnploejenbc2raktl46esxm44i 313 6 to to IN work_fnploejenbc2raktl46esxm44i 313 7 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 313 8 16 16 CD work_fnploejenbc2raktl46esxm44i 313 9 , , , work_fnploejenbc2raktl46esxm44i 313 10 Lemma Lemma NNP work_fnploejenbc2raktl46esxm44i 313 11 11 11 CD work_fnploejenbc2raktl46esxm44i 313 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 313 13 . . . work_fnploejenbc2raktl46esxm44i 314 1 Let let VB work_fnploejenbc2raktl46esxm44i 314 2 a= a= NNP work_fnploejenbc2raktl46esxm44i 314 3 { { -LRB- work_fnploejenbc2raktl46esxm44i 314 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 314 5 EIF EIF NNP work_fnploejenbc2raktl46esxm44i 314 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 314 7 } } -RRB- work_fnploejenbc2raktl46esxm44i 314 8 . . . work_fnploejenbc2raktl46esxm44i 315 1 Then then RB work_fnploejenbc2raktl46esxm44i 315 2 p(EIF)=x p(EIF)=x NNP work_fnploejenbc2raktl46esxm44i 315 3 is be VBZ work_fnploejenbc2raktl46esxm44i 315 4 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 315 5 ifand ifand NNP work_fnploejenbc2raktl46esxm44i 315 6 only only RB work_fnploejenbc2raktl46esxm44i 315 7 ifxe ifxe NNP work_fnploejenbc2raktl46esxm44i 315 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 315 9 a a DT work_fnploejenbc2raktl46esxm44i 315 10 , , , work_fnploejenbc2raktl46esxm44i 315 11 , , , work_fnploejenbc2raktl46esxm44i 315 12 a a DT work_fnploejenbc2raktl46esxm44i 315 13 , , , work_fnploejenbc2raktl46esxm44i 315 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 315 15 . . . work_fnploejenbc2raktl46esxm44i 316 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 316 2 : : : work_fnploejenbc2raktl46esxm44i 316 3 Here here RB work_fnploejenbc2raktl46esxm44i 316 4 J= J= NNP work_fnploejenbc2raktl46esxm44i 316 5 Yw(4 Yw(4 NNP work_fnploejenbc2raktl46esxm44i 316 6 1 1 LS work_fnploejenbc2raktl46esxm44i 316 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 316 8 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 316 9 f’k f’k VBD work_fnploejenbc2raktl46esxm44i 316 10 1 1 CD work_fnploejenbc2raktl46esxm44i 316 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 316 12 1 1 CD work_fnploejenbc2raktl46esxm44i 316 13 IC/‘(f(X ic/‘(f(x RB work_fnploejenbc2raktl46esxm44i 316 14 ? ? . work_fnploejenbc2raktl46esxm44i 317 1 0 0 LS work_fnploejenbc2raktl46esxm44i 317 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 317 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 317 4 f’k f’k -LRB- work_fnploejenbc2raktl46esxm44i 317 5 0 0 CD work_fnploejenbc2raktl46esxm44i 317 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 317 7 * * NFP work_fnploejenbc2raktl46esxm44i 317 8 Obviously obviously RB work_fnploejenbc2raktl46esxm44i 317 9 , , , work_fnploejenbc2raktl46esxm44i 317 10 for for IN work_fnploejenbc2raktl46esxm44i 317 11 XE XE NNP work_fnploejenbc2raktl46esxm44i 317 12 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 317 13 az az UH work_fnploejenbc2raktl46esxm44i 317 14 , , , work_fnploejenbc2raktl46esxm44i 317 15 a31 a31 NN work_fnploejenbc2raktl46esxm44i 317 16 - - : work_fnploejenbc2raktl46esxm44i 317 17 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 317 18 a a DT work_fnploejenbc2raktl46esxm44i 317 19 , , , work_fnploejenbc2raktl46esxm44i 317 20 , , , work_fnploejenbc2raktl46esxm44i 317 21 a a DT work_fnploejenbc2raktl46esxm44i 317 22 , , , work_fnploejenbc2raktl46esxm44i 317 23 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 317 24 , , , work_fnploejenbc2raktl46esxm44i 317 25 the the DT work_fnploejenbc2raktl46esxm44i 317 26 components component NNS work_fnploejenbc2raktl46esxm44i 317 27 of of IN work_fnploejenbc2raktl46esxm44i 317 28 J J NNP work_fnploejenbc2raktl46esxm44i 317 29 are be VBP work_fnploejenbc2raktl46esxm44i 317 30 nonzero nonzero CD work_fnploejenbc2raktl46esxm44i 317 31 with with IN work_fnploejenbc2raktl46esxm44i 317 32 the the DT work_fnploejenbc2raktl46esxm44i 317 33 same same JJ work_fnploejenbc2raktl46esxm44i 317 34 sign sign NN work_fnploejenbc2raktl46esxm44i 317 35 , , , work_fnploejenbc2raktl46esxm44i 317 36 and and CC work_fnploejenbc2raktl46esxm44i 317 37 hence hence RB work_fnploejenbc2raktl46esxm44i 317 38 x x LS work_fnploejenbc2raktl46esxm44i 317 39 is be VBZ work_fnploejenbc2raktl46esxm44i 317 40 not not RB work_fnploejenbc2raktl46esxm44i 317 41 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 317 42 . . . work_fnploejenbc2raktl46esxm44i 318 1 For for IN work_fnploejenbc2raktl46esxm44i 318 2 XE XE NNP work_fnploejenbc2raktl46esxm44i 318 3 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 318 4 a a DT work_fnploejenbc2raktl46esxm44i 318 5 , , , work_fnploejenbc2raktl46esxm44i 318 6 , , , work_fnploejenbc2raktl46esxm44i 318 7 a a DT work_fnploejenbc2raktl46esxm44i 318 8 , , , work_fnploejenbc2raktl46esxm44i 318 9 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 318 10 , , , work_fnploejenbc2raktl46esxm44i 318 11 J J NNP work_fnploejenbc2raktl46esxm44i 318 12 has have VBZ work_fnploejenbc2raktl46esxm44i 318 13 at at IN work_fnploejenbc2raktl46esxm44i 318 14 least least JJS work_fnploejenbc2raktl46esxm44i 318 15 a a DT work_fnploejenbc2raktl46esxm44i 318 16 zero zero CD work_fnploejenbc2raktl46esxm44i 318 17 component component NN work_fnploejenbc2raktl46esxm44i 318 18 , , , work_fnploejenbc2raktl46esxm44i 318 19 or or CC work_fnploejenbc2raktl46esxm44i 318 20 two two CD work_fnploejenbc2raktl46esxm44i 318 21 nonzero nonzero NN work_fnploejenbc2raktl46esxm44i 318 22 components component NNS work_fnploejenbc2raktl46esxm44i 318 23 with with IN work_fnploejenbc2raktl46esxm44i 318 24 opposite opposite JJ work_fnploejenbc2raktl46esxm44i 318 25 signs sign NNS work_fnploejenbc2raktl46esxm44i 318 26 , , , work_fnploejenbc2raktl46esxm44i 318 27 and and CC work_fnploejenbc2raktl46esxm44i 318 28 thus thus RB work_fnploejenbc2raktl46esxm44i 318 29 x x LS work_fnploejenbc2raktl46esxm44i 318 30 is be VBZ work_fnploejenbc2raktl46esxm44i 318 31 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 318 32 . . . work_fnploejenbc2raktl46esxm44i 319 1 Remark Remark NNP work_fnploejenbc2raktl46esxm44i 319 2 . . . work_fnploejenbc2raktl46esxm44i 320 1 In in IN work_fnploejenbc2raktl46esxm44i 320 2 view view NN work_fnploejenbc2raktl46esxm44i 320 3 of of IN work_fnploejenbc2raktl46esxm44i 320 4 Corollary Corollary NNP work_fnploejenbc2raktl46esxm44i 320 5 3.2.1 3.2.1 NNP work_fnploejenbc2raktl46esxm44i 320 6 , , , work_fnploejenbc2raktl46esxm44i 320 7 from from IN work_fnploejenbc2raktl46esxm44i 320 8 now now RB work_fnploejenbc2raktl46esxm44i 320 9 on on RB work_fnploejenbc2raktl46esxm44i 320 10 , , , work_fnploejenbc2raktl46esxm44i 320 11 the the DT work_fnploejenbc2raktl46esxm44i 320 12 range range NN work_fnploejenbc2raktl46esxm44i 320 13 of of IN work_fnploejenbc2raktl46esxm44i 320 14 uncer- uncer- JJ work_fnploejenbc2raktl46esxm44i 320 15 tainty tainty NN work_fnploejenbc2raktl46esxm44i 320 16 measures measure NNS work_fnploejenbc2raktl46esxm44i 320 17 is be VBZ work_fnploejenbc2raktl46esxm44i 320 18 restricted restrict VBN work_fnploejenbc2raktl46esxm44i 320 19 to to IN work_fnploejenbc2raktl46esxm44i 320 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 320 21 a a DT work_fnploejenbc2raktl46esxm44i 320 22 , , , work_fnploejenbc2raktl46esxm44i 320 23 , , , work_fnploejenbc2raktl46esxm44i 320 24 al al NNP work_fnploejenbc2raktl46esxm44i 320 25 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 320 26 . . . work_fnploejenbc2raktl46esxm44i 321 1 COROLLARY COROLLARY NNP work_fnploejenbc2raktl46esxm44i 321 2 3.2.2 3.2.2 CD work_fnploejenbc2raktl46esxm44i 321 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 321 4 Corresponds correspond NNS work_fnploejenbc2raktl46esxm44i 321 5 to to IN work_fnploejenbc2raktl46esxm44i 321 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 321 7 16 16 CD work_fnploejenbc2raktl46esxm44i 321 8 , , , work_fnploejenbc2raktl46esxm44i 321 9 Lemma Lemma NNP work_fnploejenbc2raktl46esxm44i 321 10 23 23 CD work_fnploejenbc2raktl46esxm44i 321 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 321 12 . . . work_fnploejenbc2raktl46esxm44i 322 1 Let let VB work_fnploejenbc2raktl46esxm44i 322 2 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 322 3 = = NFP work_fnploejenbc2raktl46esxm44i 322 4 { { -LRB- work_fnploejenbc2raktl46esxm44i 322 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 322 6 El El NNP work_fnploejenbc2raktl46esxm44i 322 7 F F NNP work_fnploejenbc2raktl46esxm44i 322 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 322 9 , , , work_fnploejenbc2raktl46esxm44i 322 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 322 11 E’IF e’if XX work_fnploejenbc2raktl46esxm44i 322 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 322 13 } } -RRB- work_fnploejenbc2raktl46esxm44i 322 14 , , , work_fnploejenbc2raktl46esxm44i 322 15 then then RB work_fnploejenbc2raktl46esxm44i 322 16 Z= Z= NNP work_fnploejenbc2raktl46esxm44i 322 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 322 18 x x NNP work_fnploejenbc2raktl46esxm44i 322 19 , , , work_fnploejenbc2raktl46esxm44i 322 20 y y NNP work_fnploejenbc2raktl46esxm44i 322 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 322 22 , , , work_fnploejenbc2raktl46esxm44i 322 23 x=,u(E(F x=,u(E(F NNP work_fnploejenbc2raktl46esxm44i 322 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 322 25 , , , work_fnploejenbc2raktl46esxm44i 322 26 y y NNP work_fnploejenbc2raktl46esxm44i 322 27 = = SYM work_fnploejenbc2raktl46esxm44i 322 28 p(E’JF p(E’JF NNP work_fnploejenbc2raktl46esxm44i 322 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 322 30 , , , work_fnploejenbc2raktl46esxm44i 322 31 is be VBZ work_fnploejenbc2raktl46esxm44i 322 32 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 322 33 ifand ifand NN work_fnploejenbc2raktl46esxm44i 322 34 only only RB work_fnploejenbc2raktl46esxm44i 322 35 if if IN work_fnploejenbc2raktl46esxm44i 322 36 det det NNP work_fnploejenbc2raktl46esxm44i 322 37 J J NNP work_fnploejenbc2raktl46esxm44i 322 38 = = SYM work_fnploejenbc2raktl46esxm44i 322 39 O. O. NNP work_fnploejenbc2raktl46esxm44i 323 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 323 2 : : : work_fnploejenbc2raktl46esxm44i 323 3 Here here RB work_fnploejenbc2raktl46esxm44i 323 4 J= J= NNP work_fnploejenbc2raktl46esxm44i 323 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 323 6 u u NNP work_fnploejenbc2raktl46esxm44i 323 7 - - HYPH work_fnploejenbc2raktl46esxm44i 323 8 f(x f(x NNP work_fnploejenbc2raktl46esxm44i 323 9 , , , work_fnploejenbc2raktl46esxm44i 323 10 l l NN work_fnploejenbc2raktl46esxm44i 323 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 323 12 , , , work_fnploejenbc2raktl46esxm44i 323 13 f(Y f(y FW work_fnploejenbc2raktl46esxm44i 323 14 , , , work_fnploejenbc2raktl46esxm44i 323 15 011 011 CD work_fnploejenbc2raktl46esxm44i 323 16 .0x .0x . work_fnploejenbc2raktl46esxm44i 323 17 ? ? . work_fnploejenbc2raktl46esxm44i 324 1 1 1 LS work_fnploejenbc2raktl46esxm44i 324 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 324 3 cm cm NNP work_fnploejenbc2raktl46esxm44i 324 4 , , , work_fnploejenbc2raktl46esxm44i 324 5 11 11 CD work_fnploejenbc2raktl46esxm44i 324 6 , , , work_fnploejenbc2raktl46esxm44i 324 7 f(Y f(Y `` work_fnploejenbc2raktl46esxm44i 324 8 , , , work_fnploejenbc2raktl46esxm44i 324 9 011 011 CD work_fnploejenbc2raktl46esxm44i 324 10 S'(Y s'(y UH work_fnploejenbc2raktl46esxm44i 324 11 , , , work_fnploejenbc2raktl46esxm44i 324 12 0 0 LS work_fnploejenbc2raktl46esxm44i 324 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 324 14 ti’Cf(X~ ti’Cf(X~ NNP work_fnploejenbc2raktl46esxm44i 324 15 Oh oh UH work_fnploejenbc2raktl46esxm44i 324 16 f(Y f(Y NFP work_fnploejenbc2raktl46esxm44i 324 17 , , , work_fnploejenbc2raktl46esxm44i 324 18 1 1 LS work_fnploejenbc2raktl46esxm44i 324 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 324 20 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 324 21 f’CT f’ct VBP work_fnploejenbc2raktl46esxm44i 324 22 0 0 NFP work_fnploejenbc2raktl46esxm44i 324 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 324 24 Ic/‘Cf Ic/‘Cf NNP work_fnploejenbc2raktl46esxm44i 324 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 324 26 & & CC work_fnploejenbc2raktl46esxm44i 324 27 01 01 CD work_fnploejenbc2raktl46esxm44i 324 28 , , , work_fnploejenbc2raktl46esxm44i 324 29 f(Y f(y CD work_fnploejenbc2raktl46esxm44i 324 30 , , , work_fnploejenbc2raktl46esxm44i 324 31 111 111 CD work_fnploejenbc2raktl46esxm44i 324 32 S'(Y S'(Y JJS work_fnploejenbc2raktl46esxm44i 324 33 , , , work_fnploejenbc2raktl46esxm44i 324 34 1 1 CD work_fnploejenbc2raktl46esxm44i 324 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 324 36 1 1 CD work_fnploejenbc2raktl46esxm44i 324 37 . . . work_fnploejenbc2raktl46esxm44i 325 1 The the DT work_fnploejenbc2raktl46esxm44i 325 2 condition condition NN work_fnploejenbc2raktl46esxm44i 325 3 is be VBZ work_fnploejenbc2raktl46esxm44i 325 4 necessary necessary JJ work_fnploejenbc2raktl46esxm44i 325 5 by by IN work_fnploejenbc2raktl46esxm44i 325 6 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 325 7 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 325 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 325 9 b b NN work_fnploejenbc2raktl46esxm44i 325 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 325 11 . . . work_fnploejenbc2raktl46esxm44i 326 1 Suppose suppose VB work_fnploejenbc2raktl46esxm44i 326 2 det det NNP work_fnploejenbc2raktl46esxm44i 326 3 J J NNP work_fnploejenbc2raktl46esxm44i 326 4 = = NNP work_fnploejenbc2raktl46esxm44i 326 5 O o UH work_fnploejenbc2raktl46esxm44i 326 6 , , , work_fnploejenbc2raktl46esxm44i 326 7 then then RB work_fnploejenbc2raktl46esxm44i 326 8 p p NN work_fnploejenbc2raktl46esxm44i 326 9 = = SYM work_fnploejenbc2raktl46esxm44i 326 10 1 1 CD work_fnploejenbc2raktl46esxm44i 326 11 . . . work_fnploejenbc2raktl46esxm44i 327 1 The the DT work_fnploejenbc2raktl46esxm44i 327 2 sulkiency sulkiency NN work_fnploejenbc2raktl46esxm44i 327 3 follows follow VBZ work_fnploejenbc2raktl46esxm44i 327 4 by by IN work_fnploejenbc2raktl46esxm44i 327 5 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 327 6 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 327 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 327 8 d d NN work_fnploejenbc2raktl46esxm44i 327 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 327 10 . . . work_fnploejenbc2raktl46esxm44i 328 1 1 1 CD work_fnploejenbc2raktl46esxm44i 328 2 COROLLARY corollary NN work_fnploejenbc2raktl46esxm44i 328 3 3.2.3 3.2.3 CD work_fnploejenbc2raktl46esxm44i 328 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 328 5 New New NNP work_fnploejenbc2raktl46esxm44i 328 6 Result Result NNP work_fnploejenbc2raktl46esxm44i 328 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 328 8 . . . work_fnploejenbc2raktl46esxm44i 329 1 For for IN work_fnploejenbc2raktl46esxm44i 329 2 a a DT work_fnploejenbc2raktl46esxm44i 329 3 = = NN work_fnploejenbc2raktl46esxm44i 329 4 { { -LRB- work_fnploejenbc2raktl46esxm44i 329 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 329 6 E e NN work_fnploejenbc2raktl46esxm44i 329 7 , , , work_fnploejenbc2raktl46esxm44i 329 8 1 1 CD work_fnploejenbc2raktl46esxm44i 329 9 F f NN work_fnploejenbc2raktl46esxm44i 329 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 11 , , , work_fnploejenbc2raktl46esxm44i 329 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 329 13 E2 e2 NN work_fnploejenbc2raktl46esxm44i 329 14 IF if IN work_fnploejenbc2raktl46esxm44i 329 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 16 , , , work_fnploejenbc2raktl46esxm44i 329 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 329 18 E e NN work_fnploejenbc2raktl46esxm44i 329 19 , , , work_fnploejenbc2raktl46esxm44i 329 20 u u NN work_fnploejenbc2raktl46esxm44i 329 21 E e NN work_fnploejenbc2raktl46esxm44i 329 22 , , , work_fnploejenbc2raktl46esxm44i 329 23 IF if IN work_fnploejenbc2raktl46esxm44i 329 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 25 } } -RRB- work_fnploejenbc2raktl46esxm44i 329 26 with with IN work_fnploejenbc2raktl46esxm44i 329 27 E e NN work_fnploejenbc2raktl46esxm44i 329 28 , , , work_fnploejenbc2raktl46esxm44i 329 29 E e NN work_fnploejenbc2raktl46esxm44i 329 30 , , , work_fnploejenbc2raktl46esxm44i 329 31 = = SYM work_fnploejenbc2raktl46esxm44i 329 32 0 0 CD work_fnploejenbc2raktl46esxm44i 329 33 ; ; : work_fnploejenbc2raktl46esxm44i 329 34 set set VBN work_fnploejenbc2raktl46esxm44i 329 35 x x SYM work_fnploejenbc2raktl46esxm44i 329 36 = = SYM work_fnploejenbc2raktl46esxm44i 329 37 p(E p(e FW work_fnploejenbc2raktl46esxm44i 329 38 , , , work_fnploejenbc2raktl46esxm44i 329 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 40 F F NNP work_fnploejenbc2raktl46esxm44i 329 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 42 , , , work_fnploejenbc2raktl46esxm44i 329 43 y y NNP work_fnploejenbc2raktl46esxm44i 329 44 = = SYM work_fnploejenbc2raktl46esxm44i 329 45 p(E p(e UH work_fnploejenbc2raktl46esxm44i 329 46 , , , work_fnploejenbc2raktl46esxm44i 329 47 I I NNP work_fnploejenbc2raktl46esxm44i 329 48 F F NNP work_fnploejenbc2raktl46esxm44i 329 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 50 , , , work_fnploejenbc2raktl46esxm44i 329 51 z z NN work_fnploejenbc2raktl46esxm44i 329 52 = = SYM work_fnploejenbc2raktl46esxm44i 329 53 p(E p(e FW work_fnploejenbc2raktl46esxm44i 329 54 , , , work_fnploejenbc2raktl46esxm44i 329 55 u u NNP work_fnploejenbc2raktl46esxm44i 329 56 E E NNP work_fnploejenbc2raktl46esxm44i 329 57 , , , work_fnploejenbc2raktl46esxm44i 329 58 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 329 59 F F NNP work_fnploejenbc2raktl46esxm44i 329 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 61 with with IN work_fnploejenbc2raktl46esxm44i 329 62 x x NNP work_fnploejenbc2raktl46esxm44i 329 63 , , , work_fnploejenbc2raktl46esxm44i 329 64 y y NNP work_fnploejenbc2raktl46esxm44i 329 65 , , , work_fnploejenbc2raktl46esxm44i 329 66 z z NNP work_fnploejenbc2raktl46esxm44i 329 67 E e NN work_fnploejenbc2raktl46esxm44i 329 68 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 329 69 a a DT work_fnploejenbc2raktl46esxm44i 329 70 , , , work_fnploejenbc2raktl46esxm44i 329 71 , , , work_fnploejenbc2raktl46esxm44i 329 72 a a DT work_fnploejenbc2raktl46esxm44i 329 73 , , , work_fnploejenbc2raktl46esxm44i 329 74 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 329 75 , , , work_fnploejenbc2raktl46esxm44i 329 76 2 2 CD work_fnploejenbc2raktl46esxm44i 329 77 = = SYM work_fnploejenbc2raktl46esxm44i 329 78 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 329 79 x x NNP work_fnploejenbc2raktl46esxm44i 329 80 , , , work_fnploejenbc2raktl46esxm44i 329 81 y y NNP work_fnploejenbc2raktl46esxm44i 329 82 , , , work_fnploejenbc2raktl46esxm44i 329 83 z z NNP work_fnploejenbc2raktl46esxm44i 329 84 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 329 85 . . . work_fnploejenbc2raktl46esxm44i 330 1 Take take VB work_fnploejenbc2raktl46esxm44i 330 2 t t NN work_fnploejenbc2raktl46esxm44i 330 3 , , , work_fnploejenbc2raktl46esxm44i 330 4 b b NN work_fnploejenbc2raktl46esxm44i 330 5 = = SYM work_fnploejenbc2raktl46esxm44i 330 6 + + XX work_fnploejenbc2raktl46esxm44i 330 7 . . . work_fnploejenbc2raktl46esxm44i 331 1 Then then RB work_fnploejenbc2raktl46esxm44i 331 2 the the DT work_fnploejenbc2raktl46esxm44i 331 3 nonzero nonzero NN work_fnploejenbc2raktl46esxm44i 331 4 losses loss NNS work_fnploejenbc2raktl46esxm44i 331 5 are be VBP work_fnploejenbc2raktl46esxm44i 331 6 fk fk NNP work_fnploejenbc2raktl46esxm44i 331 7 l)+f(Y9o)+f(z l)+f(Y9o)+f(z NNP work_fnploejenbc2raktl46esxm44i 331 8 , , , work_fnploejenbc2raktl46esxm44i 331 9 11 11 CD work_fnploejenbc2raktl46esxm44i 331 10 , , , work_fnploejenbc2raktl46esxm44i 331 11 .mo)+f(Y .mo)+f(Y . work_fnploejenbc2raktl46esxm44i 331 12 , , , work_fnploejenbc2raktl46esxm44i 331 13 l)+f(z l)+f(z NNP work_fnploejenbc2raktl46esxm44i 331 14 , , , work_fnploejenbc2raktl46esxm44i 331 15 l l NN work_fnploejenbc2raktl46esxm44i 331 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 17 , , , work_fnploejenbc2raktl46esxm44i 331 18 f(x f(x NNP work_fnploejenbc2raktl46esxm44i 331 19 , , , work_fnploejenbc2raktl46esxm44i 331 20 O)+f(y O)+f(y NNP work_fnploejenbc2raktl46esxm44i 331 21 , , , work_fnploejenbc2raktl46esxm44i 331 22 O)+ O)+ NNP work_fnploejenbc2raktl46esxm44i 331 23 f(z f(z NNP work_fnploejenbc2raktl46esxm44i 331 24 , , , work_fnploejenbc2raktl46esxm44i 331 25 0 0 CD work_fnploejenbc2raktl46esxm44i 331 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 27 , , , work_fnploejenbc2raktl46esxm44i 331 28 and and CC work_fnploejenbc2raktl46esxm44i 331 29 hence hence RB work_fnploejenbc2raktl46esxm44i 331 30 f’(x f’(x JJ work_fnploejenbc2raktl46esxm44i 331 31 , , , work_fnploejenbc2raktl46esxm44i 331 32 1 1 CD work_fnploejenbc2raktl46esxm44i 331 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 34 f’(Y f’(Y NNP work_fnploejenbc2raktl46esxm44i 331 35 , , , work_fnploejenbc2raktl46esxm44i 331 36 0 0 CD work_fnploejenbc2raktl46esxm44i 331 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 38 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 331 39 1 1 CD work_fnploejenbc2raktl46esxm44i 331 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 41 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 331 42 0 0 CD work_fnploejenbc2raktl46esxm44i 331 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 44 f'(v f'(v IN work_fnploejenbc2raktl46esxm44i 331 45 , , , work_fnploejenbc2raktl46esxm44i 331 46 1 1 CD work_fnploejenbc2raktl46esxm44i 331 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 48 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 331 49 1 1 CD work_fnploejenbc2raktl46esxm44i 331 50 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 331 51 . . . work_fnploejenbc2raktl46esxm44i 332 1 S’(4 S’(4 NNP work_fnploejenbc2raktl46esxm44i 332 2 0 0 NFP work_fnploejenbc2raktl46esxm44i 332 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 332 4 f'(Y f'(Y NNP work_fnploejenbc2raktl46esxm44i 332 5 , , , work_fnploejenbc2raktl46esxm44i 332 6 0 0 CD work_fnploejenbc2raktl46esxm44i 332 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 332 8 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 332 9 0 0 CD work_fnploejenbc2raktl46esxm44i 332 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 332 11 1 1 CD work_fnploejenbc2raktl46esxm44i 332 12 SCORING score VBN work_fnploejenbc2raktl46esxm44i 332 13 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 332 14 TO to IN work_fnploejenbc2raktl46esxm44i 332 15 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 332 16 565 565 CD work_fnploejenbc2raktl46esxm44i 332 17 With with IN work_fnploejenbc2raktl46esxm44i 332 18 respect respect NN work_fnploejenbc2raktl46esxm44i 332 19 to to IN work_fnploejenbc2raktl46esxm44i 332 20 the the DT work_fnploejenbc2raktl46esxm44i 332 21 game game NN work_fnploejenbc2raktl46esxm44i 332 22 G g NN work_fnploejenbc2raktl46esxm44i 332 23 , , , work_fnploejenbc2raktl46esxm44i 332 24 + + CC work_fnploejenbc2raktl46esxm44i 332 25 , , , work_fnploejenbc2raktl46esxm44i 332 26 A a NN work_fnploejenbc2raktl46esxm44i 332 27 , , , work_fnploejenbc2raktl46esxm44i 332 28 the the DT work_fnploejenbc2raktl46esxm44i 332 29 following follow VBG work_fnploejenbc2raktl46esxm44i 332 30 are be VBP work_fnploejenbc2raktl46esxm44i 332 31 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 332 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 332 33 i i NN work_fnploejenbc2raktl46esxm44i 332 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 332 35 2 2 CD work_fnploejenbc2raktl46esxm44i 332 36 is be VBZ work_fnploejenbc2raktl46esxm44i 332 37 A a NN work_fnploejenbc2raktl46esxm44i 332 38 - - HYPH work_fnploejenbc2raktl46esxm44i 332 39 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 332 40 , , , work_fnploejenbc2raktl46esxm44i 332 41 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 332 42 ii ii NNP work_fnploejenbc2raktl46esxm44i 332 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 332 44 det det NNP work_fnploejenbc2raktl46esxm44i 332 45 J= J= NNP work_fnploejenbc2raktl46esxm44i 332 46 0 0 NFP work_fnploejenbc2raktl46esxm44i 332 47 . . . work_fnploejenbc2raktl46esxm44i 333 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 333 2 . . . work_fnploejenbc2raktl46esxm44i 334 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 334 2 i i NN work_fnploejenbc2raktl46esxm44i 334 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 334 4 j j NNP work_fnploejenbc2raktl46esxm44i 334 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 334 6 ii ii NNP work_fnploejenbc2raktl46esxm44i 334 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 334 8 by by IN work_fnploejenbc2raktl46esxm44i 334 9 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 334 10 3.2.1 3.2.1 CD work_fnploejenbc2raktl46esxm44i 334 11 . . . work_fnploejenbc2raktl46esxm44i 335 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 335 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 335 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 335 4 j j NNP work_fnploejenbc2raktl46esxm44i 335 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 335 6 i i NN work_fnploejenbc2raktl46esxm44i 335 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 335 8 . . . work_fnploejenbc2raktl46esxm44i 336 1 Since since IN work_fnploejenbc2raktl46esxm44i 336 2 det det NNP work_fnploejenbc2raktl46esxm44i 336 3 J J NNP work_fnploejenbc2raktl46esxm44i 336 4 = = NNP work_fnploejenbc2raktl46esxm44i 336 5 0 0 NFP work_fnploejenbc2raktl46esxm44i 336 6 , , , work_fnploejenbc2raktl46esxm44i 336 7 the the DT work_fnploejenbc2raktl46esxm44i 336 8 rank rank NN work_fnploejenbc2raktl46esxm44i 336 9 p p NN work_fnploejenbc2raktl46esxm44i 336 10 of of IN work_fnploejenbc2raktl46esxm44i 336 11 J J NNP work_fnploejenbc2raktl46esxm44i 336 12 is be VBZ work_fnploejenbc2raktl46esxm44i 336 13 either either CC work_fnploejenbc2raktl46esxm44i 336 14 1 1 CD work_fnploejenbc2raktl46esxm44i 336 15 or or CC work_fnploejenbc2raktl46esxm44i 336 16 2 2 CD work_fnploejenbc2raktl46esxm44i 336 17 . . . work_fnploejenbc2raktl46esxm44i 337 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 337 2 a a LS work_fnploejenbc2raktl46esxm44i 337 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 337 4 If if IN work_fnploejenbc2raktl46esxm44i 337 5 p p NN work_fnploejenbc2raktl46esxm44i 337 6 = = SYM work_fnploejenbc2raktl46esxm44i 337 7 1 1 CD work_fnploejenbc2raktl46esxm44i 337 8 , , , work_fnploejenbc2raktl46esxm44i 337 9 then then RB work_fnploejenbc2raktl46esxm44i 337 10 the the DT work_fnploejenbc2raktl46esxm44i 337 11 first first JJ work_fnploejenbc2raktl46esxm44i 337 12 column column NN work_fnploejenbc2raktl46esxm44i 337 13 of of IN work_fnploejenbc2raktl46esxm44i 337 14 J J NNP work_fnploejenbc2raktl46esxm44i 337 15 is be VBZ work_fnploejenbc2raktl46esxm44i 337 16 f f NNP work_fnploejenbc2raktl46esxm44i 337 17 ‘ ' `` work_fnploejenbc2raktl46esxm44i 337 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 337 19 a a DT work_fnploejenbc2raktl46esxm44i 337 20 , , , work_fnploejenbc2raktl46esxm44i 337 21 , , , work_fnploejenbc2raktl46esxm44i 337 22 1 1 CD work_fnploejenbc2raktl46esxm44i 337 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 337 24 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 337 25 1 1 CD work_fnploejenbc2raktl46esxm44i 337 26 0 0 CD work_fnploejenbc2raktl46esxm44i 337 27 with with IN work_fnploejenbc2raktl46esxm44i 337 28 f’(a f’(a NNP work_fnploejenbc2raktl46esxm44i 337 29 , , , work_fnploejenbc2raktl46esxm44i 337 30 , , , work_fnploejenbc2raktl46esxm44i 337 31 1 1 CD work_fnploejenbc2raktl46esxm44i 337 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 337 33 < < XX work_fnploejenbc2raktl46esxm44i 337 34 0 0 NFP work_fnploejenbc2raktl46esxm44i 337 35 when when WRB work_fnploejenbc2raktl46esxm44i 337 36 x x NNS work_fnploejenbc2raktl46esxm44i 337 37 = = SYM work_fnploejenbc2raktl46esxm44i 337 38 a a NN work_fnploejenbc2raktl46esxm44i 337 39 , , , work_fnploejenbc2raktl46esxm44i 337 40 0 0 CD work_fnploejenbc2raktl46esxm44i 337 41 and and CC work_fnploejenbc2raktl46esxm44i 337 42 is be VBZ work_fnploejenbc2raktl46esxm44i 337 43 with with IN work_fnploejenbc2raktl46esxm44i 337 44 f’(a f’(a NNP work_fnploejenbc2raktl46esxm44i 337 45 , , , work_fnploejenbc2raktl46esxm44i 337 46 , , , work_fnploejenbc2raktl46esxm44i 337 47 0 0 LS work_fnploejenbc2raktl46esxm44i 337 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 337 49 > > NFP work_fnploejenbc2raktl46esxm44i 337 50 0 0 NFP work_fnploejenbc2raktl46esxm44i 337 51 when when WRB work_fnploejenbc2raktl46esxm44i 337 52 x x NNS work_fnploejenbc2raktl46esxm44i 337 53 = = SYM work_fnploejenbc2raktl46esxm44i 337 54 a a XX work_fnploejenbc2raktl46esxm44i 337 55 , , , work_fnploejenbc2raktl46esxm44i 337 56 ; ; : work_fnploejenbc2raktl46esxm44i 337 57 for for IN work_fnploejenbc2raktl46esxm44i 337 58 XE XE NNP work_fnploejenbc2raktl46esxm44i 337 59 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 337 60 a a DT work_fnploejenbc2raktl46esxm44i 337 61 , , , work_fnploejenbc2raktl46esxm44i 337 62 , , , work_fnploejenbc2raktl46esxm44i 337 63 a a DT work_fnploejenbc2raktl46esxm44i 337 64 , , , work_fnploejenbc2raktl46esxm44i 337 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 337 66 , , , work_fnploejenbc2raktl46esxm44i 337 67 this this DT work_fnploejenbc2raktl46esxm44i 337 68 column column NN work_fnploejenbc2raktl46esxm44i 337 69 has have VBZ work_fnploejenbc2raktl46esxm44i 337 70 both both CC work_fnploejenbc2raktl46esxm44i 337 71 positive positive JJ work_fnploejenbc2raktl46esxm44i 337 72 and and CC work_fnploejenbc2raktl46esxm44i 337 73 negative negative JJ work_fnploejenbc2raktl46esxm44i 337 74 components component NNS work_fnploejenbc2raktl46esxm44i 337 75 . . . work_fnploejenbc2raktl46esxm44i 338 1 Hence hence RB work_fnploejenbc2raktl46esxm44i 338 2 1 1 CD work_fnploejenbc2raktl46esxm44i 338 3 is be VBZ work_fnploejenbc2raktl46esxm44i 338 4 & & CC work_fnploejenbc2raktl46esxm44i 338 5 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 338 6 . . . work_fnploejenbc2raktl46esxm44i 339 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 339 2 b b LS work_fnploejenbc2raktl46esxm44i 339 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 4 If if IN work_fnploejenbc2raktl46esxm44i 339 5 p p NN work_fnploejenbc2raktl46esxm44i 339 6 = = SYM work_fnploejenbc2raktl46esxm44i 339 7 2 2 CD work_fnploejenbc2raktl46esxm44i 339 8 , , , work_fnploejenbc2raktl46esxm44i 339 9 permute permute VB work_fnploejenbc2raktl46esxm44i 339 10 the the DT work_fnploejenbc2raktl46esxm44i 339 11 second second JJ work_fnploejenbc2raktl46esxm44i 339 12 and and CC work_fnploejenbc2raktl46esxm44i 339 13 third third JJ work_fnploejenbc2raktl46esxm44i 339 14 columns column NNS work_fnploejenbc2raktl46esxm44i 339 15 of of IN work_fnploejenbc2raktl46esxm44i 339 16 J J NNP work_fnploejenbc2raktl46esxm44i 339 17 to to TO work_fnploejenbc2raktl46esxm44i 339 18 obtain obtain VB work_fnploejenbc2raktl46esxm44i 339 19 the the DT work_fnploejenbc2raktl46esxm44i 339 20 partition partition NN work_fnploejenbc2raktl46esxm44i 339 21 where where WRB work_fnploejenbc2raktl46esxm44i 339 22 J J NNP work_fnploejenbc2raktl46esxm44i 339 23 = = SYM work_fnploejenbc2raktl46esxm44i 339 24 f’(x f’(x UH work_fnploejenbc2raktl46esxm44i 339 25 , , , work_fnploejenbc2raktl46esxm44i 339 26 1 1 CD work_fnploejenbc2raktl46esxm44i 339 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 28 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 339 29 1 1 CD work_fnploejenbc2raktl46esxm44i 339 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 31 l l NN work_fnploejenbc2raktl46esxm44i 339 32 C C NNP work_fnploejenbc2raktl46esxm44i 339 33 f’h f’h NN work_fnploejenbc2raktl46esxm44i 339 34 0 0 CD work_fnploejenbc2raktl46esxm44i 339 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 36 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 339 37 1 1 CD work_fnploejenbc2raktl46esxm44i 339 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 39 1 1 CD work_fnploejenbc2raktl46esxm44i 339 40 and and CC work_fnploejenbc2raktl46esxm44i 339 41 RJ RJ NNP work_fnploejenbc2raktl46esxm44i 339 42 , , , work_fnploejenbc2raktl46esxm44i 339 43 = = NFP work_fnploejenbc2raktl46esxm44i 339 44 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 339 45 f’(x f’(x UH work_fnploejenbc2raktl46esxm44i 339 46 , , , work_fnploejenbc2raktl46esxm44i 339 47 0 0 CD work_fnploejenbc2raktl46esxm44i 339 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 49 , , , work_fnploejenbc2raktl46esxm44i 339 50 f’(z f’(z NN work_fnploejenbc2raktl46esxm44i 339 51 , , , work_fnploejenbc2raktl46esxm44i 339 52 0 0 CD work_fnploejenbc2raktl46esxm44i 339 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 339 55 . . . work_fnploejenbc2raktl46esxm44i 340 1 Then then RB work_fnploejenbc2raktl46esxm44i 340 2 det det NNP work_fnploejenbc2raktl46esxm44i 340 3 J,=f’(x J,=f’(x NNP work_fnploejenbc2raktl46esxm44i 340 4 , , , work_fnploejenbc2raktl46esxm44i 340 5 l)f’(z l)f’(z NNP work_fnploejenbc2raktl46esxm44i 340 6 , , , work_fnploejenbc2raktl46esxm44i 340 7 l)-f’(x l)-f’(x NN work_fnploejenbc2raktl46esxm44i 340 8 , , , work_fnploejenbc2raktl46esxm44i 340 9 O)f’(z O)f’(z NNP work_fnploejenbc2raktl46esxm44i 340 10 , , , work_fnploejenbc2raktl46esxm44i 340 11 l)>O l)>O NNP work_fnploejenbc2raktl46esxm44i 340 12 when when WRB work_fnploejenbc2raktl46esxm44i 340 13 z z NNP work_fnploejenbc2raktl46esxm44i 340 14 # # $ work_fnploejenbc2raktl46esxm44i 340 15 a a NN work_fnploejenbc2raktl46esxm44i 340 16 , , , work_fnploejenbc2raktl46esxm44i 340 17 . . . work_fnploejenbc2raktl46esxm44i 341 1 In in IN work_fnploejenbc2raktl46esxm44i 341 2 this this DT work_fnploejenbc2raktl46esxm44i 341 3 case case NN work_fnploejenbc2raktl46esxm44i 341 4 , , , work_fnploejenbc2raktl46esxm44i 341 5 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 341 6 have have VBP work_fnploejenbc2raktl46esxm44i 341 7 R r NN work_fnploejenbc2raktl46esxm44i 341 8 = = SYM work_fnploejenbc2raktl46esxm44i 341 9 0 0 CD work_fnploejenbc2raktl46esxm44i 341 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 11 .I-‘(% .I-‘(% NFP work_fnploejenbc2raktl46esxm44i 341 12 1 1 LS work_fnploejenbc2raktl46esxm44i 341 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 14 -S’k -S’k NFP work_fnploejenbc2raktl46esxm44i 341 15 0 0 NFP work_fnploejenbc2raktl46esxm44i 341 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 17 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 341 18 0 0 CD work_fnploejenbc2raktl46esxm44i 341 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 20 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 341 21 1 1 CD work_fnploejenbc2raktl46esxm44i 341 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 23 f’k f’k NNP work_fnploejenbc2raktl46esxm44i 341 24 0 0 CD work_fnploejenbc2raktl46esxm44i 341 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 26 -S’(x -s’(x NN work_fnploejenbc2raktl46esxm44i 341 27 , , , work_fnploejenbc2raktl46esxm44i 341 28 0 0 LS work_fnploejenbc2raktl46esxm44i 341 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 30 f’(Z f’(z NN work_fnploejenbc2raktl46esxm44i 341 31 , , , work_fnploejenbc2raktl46esxm44i 341 32 1 1 CD work_fnploejenbc2raktl46esxm44i 341 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 34 det det NNP work_fnploejenbc2raktl46esxm44i 341 35 J J NNP work_fnploejenbc2raktl46esxm44i 341 36 , , , work_fnploejenbc2raktl46esxm44i 341 37 > > XX work_fnploejenbc2raktl46esxm44i 341 38 det det NNP work_fnploejenbc2raktl46esxm44i 341 39 J J NNP work_fnploejenbc2raktl46esxm44i 341 40 , , , work_fnploejenbc2raktl46esxm44i 341 41 1 1 CD work_fnploejenbc2raktl46esxm44i 341 42 with with IN work_fnploejenbc2raktl46esxm44i 341 43 f’(x f’(x NNP work_fnploejenbc2raktl46esxm44i 341 44 , , , work_fnploejenbc2raktl46esxm44i 341 45 O)[f'(z O)[f'(z NNP work_fnploejenbc2raktl46esxm44i 341 46 , , , work_fnploejenbc2raktl46esxm44i 341 47 1 1 CD work_fnploejenbc2raktl46esxm44i 341 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 49 - - . work_fnploejenbc2raktl46esxm44i 341 50 f’(z f’(z NN work_fnploejenbc2raktl46esxm44i 341 51 , , , work_fnploejenbc2raktl46esxm44i 341 52 0 0 CD work_fnploejenbc2raktl46esxm44i 341 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 341 54 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 341 55 6 6 CD work_fnploejenbc2raktl46esxm44i 341 56 0 0 CD work_fnploejenbc2raktl46esxm44i 341 57 . . . work_fnploejenbc2raktl46esxm44i 342 1 Look look VB work_fnploejenbc2raktl46esxm44i 342 2 at at IN work_fnploejenbc2raktl46esxm44i 342 3 f’(x f’(x JJ work_fnploejenbc2raktl46esxm44i 342 4 , , , work_fnploejenbc2raktl46esxm44i 342 5 1 1 LS work_fnploejenbc2raktl46esxm44i 342 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 342 7 f’(z f’(z NN work_fnploejenbc2raktl46esxm44i 342 8 , , , work_fnploejenbc2raktl46esxm44i 342 9 0 0 LS work_fnploejenbc2raktl46esxm44i 342 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 342 11 -f’(x -f’(x NN work_fnploejenbc2raktl46esxm44i 342 12 , , , work_fnploejenbc2raktl46esxm44i 342 13 0 0 LS work_fnploejenbc2raktl46esxm44i 342 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 342 15 f’(z f’(z NN work_fnploejenbc2raktl46esxm44i 342 16 , , , work_fnploejenbc2raktl46esxm44i 342 17 1 1 CD work_fnploejenbc2raktl46esxm44i 342 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 342 19 . . . work_fnploejenbc2raktl46esxm44i 343 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 343 2 * * NFP work_fnploejenbc2raktl46esxm44i 343 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 4 566 566 CD work_fnploejenbc2raktl46esxm44i 343 5 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 343 6 , , , work_fnploejenbc2raktl46esxm44i 343 7 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 343 8 , , , work_fnploejenbc2raktl46esxm44i 343 9 AND and CC work_fnploejenbc2raktl46esxm44i 343 10 ROGERS roger NNS work_fnploejenbc2raktl46esxm44i 343 11 By by IN work_fnploejenbc2raktl46esxm44i 343 12 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 343 13 , , , work_fnploejenbc2raktl46esxm44i 343 14 det det NNP work_fnploejenbc2raktl46esxm44i 343 15 J= J= NNP work_fnploejenbc2raktl46esxm44i 343 16 0 0 NFP work_fnploejenbc2raktl46esxm44i 343 17 and and CC work_fnploejenbc2raktl46esxm44i 343 18 this this DT work_fnploejenbc2raktl46esxm44i 343 19 is be VBZ work_fnploejenbc2raktl46esxm44i 343 20 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 343 21 to to IN work_fnploejenbc2raktl46esxm44i 343 22 P,(z P,(z NNP work_fnploejenbc2raktl46esxm44i 343 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 24 = = NFP work_fnploejenbc2raktl46esxm44i 343 25 P,-(x p,-(x FW work_fnploejenbc2raktl46esxm44i 343 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 27 + + SYM work_fnploejenbc2raktl46esxm44i 343 28 P/(y P/(y NNP work_fnploejenbc2raktl46esxm44i 343 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 30 , , , work_fnploejenbc2raktl46esxm44i 343 31 where where WRB work_fnploejenbc2raktl46esxm44i 343 32 P,- P,- NNS work_fnploejenbc2raktl46esxm44i 343 33 : : : work_fnploejenbc2raktl46esxm44i 343 34 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 343 35 ao ao NNP work_fnploejenbc2raktl46esxm44i 343 36 , , , work_fnploejenbc2raktl46esxm44i 343 37 a a DT work_fnploejenbc2raktl46esxm44i 343 38 , , , work_fnploejenbc2raktl46esxm44i 343 39 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 343 40 -+ -+ . work_fnploejenbc2raktl46esxm44i 343 41 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 343 42 0 0 CD work_fnploejenbc2raktl46esxm44i 343 43 , , , work_fnploejenbc2raktl46esxm44i 343 44 l l NN work_fnploejenbc2raktl46esxm44i 343 45 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 343 46 is be VBZ work_fnploejenbc2raktl46esxm44i 343 47 given give VBN work_fnploejenbc2raktl46esxm44i 343 48 by by IN work_fnploejenbc2raktl46esxm44i 343 49 f f NNP work_fnploejenbc2raktl46esxm44i 343 50 ‘ ' '' work_fnploejenbc2raktl46esxm44i 343 51 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 343 52 x9 x9 NNP work_fnploejenbc2raktl46esxm44i 343 53 0 0 NFP work_fnploejenbc2raktl46esxm44i 343 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 55 pf(x pf(x NNP work_fnploejenbc2raktl46esxm44i 343 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 57 = = NFP work_fnploejenbc2raktl46esxm44i 343 58 f’(x f’(x UH work_fnploejenbc2raktl46esxm44i 343 59 , , , work_fnploejenbc2raktl46esxm44i 343 60 0 0 LS work_fnploejenbc2raktl46esxm44i 343 61 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 62 -f’(x -f’(x NNP work_fnploejenbc2raktl46esxm44i 343 63 , , , work_fnploejenbc2raktl46esxm44i 343 64 1 1 CD work_fnploejenbc2raktl46esxm44i 343 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 66 ’ ' '' work_fnploejenbc2raktl46esxm44i 343 67 Thus thus RB work_fnploejenbc2raktl46esxm44i 343 68 Pf(x Pf(x NNP work_fnploejenbc2raktl46esxm44i 343 69 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 70 < < XX work_fnploejenbc2raktl46esxm44i 343 71 P,(z P,(z NNP work_fnploejenbc2raktl46esxm44i 343 72 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 73 which which WDT work_fnploejenbc2raktl46esxm44i 343 74 in in IN work_fnploejenbc2raktl46esxm44i 343 75 turn turn NN work_fnploejenbc2raktl46esxm44i 343 76 implies imply VBZ work_fnploejenbc2raktl46esxm44i 343 77 that that IN work_fnploejenbc2raktl46esxm44i 343 78 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 343 79 * * NFP work_fnploejenbc2raktl46esxm44i 343 80 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 343 81 < < XX work_fnploejenbc2raktl46esxm44i 343 82 0 0 NFP work_fnploejenbc2raktl46esxm44i 343 83 . . . work_fnploejenbc2raktl46esxm44i 344 1 When when WRB work_fnploejenbc2raktl46esxm44i 344 2 z z NN work_fnploejenbc2raktl46esxm44i 344 3 = = SYM work_fnploejenbc2raktl46esxm44i 344 4 a a NN work_fnploejenbc2raktl46esxm44i 344 5 , , , work_fnploejenbc2raktl46esxm44i 344 6 , , , work_fnploejenbc2raktl46esxm44i 344 7 the the DT work_fnploejenbc2raktl46esxm44i 344 8 first first JJ work_fnploejenbc2raktl46esxm44i 344 9 and and CC work_fnploejenbc2raktl46esxm44i 344 10 third third JJ work_fnploejenbc2raktl46esxm44i 344 11 columns column NNS work_fnploejenbc2raktl46esxm44i 344 12 of of IN work_fnploejenbc2raktl46esxm44i 344 13 J J NNP work_fnploejenbc2raktl46esxm44i 344 14 become become VB work_fnploejenbc2raktl46esxm44i 344 15 Consider Consider NNP work_fnploejenbc2raktl46esxm44i 344 16 J J NNP work_fnploejenbc2raktl46esxm44i 344 17 , , , work_fnploejenbc2raktl46esxm44i 344 18 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 344 19 1 1 CD work_fnploejenbc2raktl46esxm44i 344 20 RJI rji NN work_fnploejenbc2raktl46esxm44i 344 21 ’ ' '' work_fnploejenbc2raktl46esxm44i 344 22 where where WRB work_fnploejenbc2raktl46esxm44i 344 23 0 0 CD work_fnploejenbc2raktl46esxm44i 344 24 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 344 25 d d NN work_fnploejenbc2raktl46esxm44i 344 26 1 1 CD work_fnploejenbc2raktl46esxm44i 344 27 0 0 CD work_fnploejenbc2raktl46esxm44i 344 28 . . . work_fnploejenbc2raktl46esxm44i 345 1 f'(Z130 f'(Z130 NNP work_fnploejenbc2raktl46esxm44i 345 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 3 J= J= NNP work_fnploejenbc2raktl46esxm44i 345 4 f’(%l f’(%l NNP work_fnploejenbc2raktl46esxm44i 345 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 6 0 0 CD work_fnploejenbc2raktl46esxm44i 345 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 345 8 1 1 CD work_fnploejenbc2raktl46esxm44i 345 9 f’(40 f’(40 NN work_fnploejenbc2raktl46esxm44i 345 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 11 f’(&,O f’(&,o NN work_fnploejenbc2raktl46esxm44i 345 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 13 1 1 CD work_fnploejenbc2raktl46esxm44i 345 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 345 15 * * NFP work_fnploejenbc2raktl46esxm44i 345 16 * * NFP work_fnploejenbc2raktl46esxm44i 345 17 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 345 18 and and CC work_fnploejenbc2raktl46esxm44i 345 19 RJ1 RJ1 NNP work_fnploejenbc2raktl46esxm44i 345 20 = = NFP work_fnploejenbc2raktl46esxm44i 345 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 345 22 f'(x f'(x UH work_fnploejenbc2raktl46esxm44i 345 23 , , , work_fnploejenbc2raktl46esxm44i 345 24 0 0 CD work_fnploejenbc2raktl46esxm44i 345 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 26 , , , work_fnploejenbc2raktl46esxm44i 345 27 0 0 CD work_fnploejenbc2raktl46esxm44i 345 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 345 29 . . . work_fnploejenbc2raktl46esxm44i 346 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 346 2 have have VBP work_fnploejenbc2raktl46esxm44i 346 3 det det NNP work_fnploejenbc2raktl46esxm44i 346 4 J1 J1 NNP work_fnploejenbc2raktl46esxm44i 346 5 = = SYM work_fnploejenbc2raktl46esxm44i 346 6 fl(x fl(x NNP work_fnploejenbc2raktl46esxm44i 346 7 , , , work_fnploejenbc2raktl46esxm44i 346 8 1 1 CD work_fnploejenbc2raktl46esxm44i 346 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 346 10 f'(a f'(a NN work_fnploejenbc2raktl46esxm44i 346 11 , , , work_fnploejenbc2raktl46esxm44i 346 12 , , , work_fnploejenbc2raktl46esxm44i 346 13 O) > XX work_fnploejenbc2raktl46esxm44i 349 18 0 0 NFP work_fnploejenbc2raktl46esxm44i 349 19 , , , work_fnploejenbc2raktl46esxm44i 349 20 and and CC work_fnploejenbc2raktl46esxm44i 349 21 R r NN work_fnploejenbc2raktl46esxm44i 349 22 = = NFP work_fnploejenbc2raktl46esxm44i 349 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 349 24 0,O 0,o NN work_fnploejenbc2raktl46esxm44i 349 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 349 26 . . . work_fnploejenbc2raktl46esxm44i 350 1 1 1 CD work_fnploejenbc2raktl46esxm44i 350 2 The the DT work_fnploejenbc2raktl46esxm44i 350 3 following follow VBG work_fnploejenbc2raktl46esxm44i 350 4 result result NN work_fnploejenbc2raktl46esxm44i 350 5 is be VBZ work_fnploejenbc2raktl46esxm44i 350 6 actually actually RB work_fnploejenbc2raktl46esxm44i 350 7 an an DT work_fnploejenbc2raktl46esxm44i 350 8 application application NN work_fnploejenbc2raktl46esxm44i 350 9 of of IN work_fnploejenbc2raktl46esxm44i 350 10 Corollary Corollary NNP work_fnploejenbc2raktl46esxm44i 350 11 3.2.3 3.2.3 CD work_fnploejenbc2raktl46esxm44i 350 12 . . . work_fnploejenbc2raktl46esxm44i 351 1 However however RB work_fnploejenbc2raktl46esxm44i 351 2 , , , work_fnploejenbc2raktl46esxm44i 351 3 as as IN work_fnploejenbc2raktl46esxm44i 351 4 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 351 5 is be VBZ work_fnploejenbc2raktl46esxm44i 351 6 basic basic JJ work_fnploejenbc2raktl46esxm44i 351 7 for for IN work_fnploejenbc2raktl46esxm44i 351 8 most most JJS work_fnploejenbc2raktl46esxm44i 351 9 of of IN work_fnploejenbc2raktl46esxm44i 351 10 the the DT work_fnploejenbc2raktl46esxm44i 351 11 rest rest NN work_fnploejenbc2raktl46esxm44i 351 12 of of IN work_fnploejenbc2raktl46esxm44i 351 13 our -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 351 14 work work NN work_fnploejenbc2raktl46esxm44i 351 15 , , , work_fnploejenbc2raktl46esxm44i 351 16 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 351 17 state state VBP work_fnploejenbc2raktl46esxm44i 351 18 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 351 19 as as IN work_fnploejenbc2raktl46esxm44i 351 20 a a DT work_fnploejenbc2raktl46esxm44i 351 21 theorem theorem NN work_fnploejenbc2raktl46esxm44i 351 22 . . . work_fnploejenbc2raktl46esxm44i 352 1 From from IN work_fnploejenbc2raktl46esxm44i 352 2 now now RB work_fnploejenbc2raktl46esxm44i 352 3 on on RB work_fnploejenbc2raktl46esxm44i 352 4 , , , work_fnploejenbc2raktl46esxm44i 352 5 PE PE NNP work_fnploejenbc2raktl46esxm44i 352 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 352 7 a a DT work_fnploejenbc2raktl46esxm44i 352 8 , , , work_fnploejenbc2raktl46esxm44i 352 9 , , , work_fnploejenbc2raktl46esxm44i 352 10 u,]~. u,]~. NNP work_fnploejenbc2raktl46esxm44i 353 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 353 2 say say VBP work_fnploejenbc2raktl46esxm44i 353 3 that that DT work_fnploejenbc2raktl46esxm44i 353 4 : : : work_fnploejenbc2raktl46esxm44i 353 5 p p LS work_fnploejenbc2raktl46esxm44i 353 6 is be VBZ work_fnploejenbc2raktl46esxm44i 353 7 g2-WLAD g2-WLAD NNP work_fnploejenbc2raktl46esxm44i 353 8 if if IN work_fnploejenbc2raktl46esxm44i 353 9 p p NN work_fnploejenbc2raktl46esxm44i 353 10 is be VBZ work_fnploejenbc2raktl46esxm44i 353 11 a a DT work_fnploejenbc2raktl46esxm44i 353 12 - - : work_fnploejenbc2raktl46esxm44i 353 13 WLAD wlad NN work_fnploejenbc2raktl46esxm44i 353 14 for for IN work_fnploejenbc2raktl46esxm44i 353 15 2 2 CD work_fnploejenbc2raktl46esxm44i 353 16 of of IN work_fnploejenbc2raktl46esxm44i 353 17 the the DT work_fnploejenbc2raktl46esxm44i 353 18 form form NN work_fnploejenbc2raktl46esxm44i 353 19 { { -LRB- work_fnploejenbc2raktl46esxm44i 353 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 21 E e NN work_fnploejenbc2raktl46esxm44i 353 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 23 F f NN work_fnploejenbc2raktl46esxm44i 353 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 25 , , , work_fnploejenbc2raktl46esxm44i 353 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 27 EC EC NNP work_fnploejenbc2raktl46esxm44i 353 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 29 8 8 CD work_fnploejenbc2raktl46esxm44i 353 30 ’ ' '' work_fnploejenbc2raktl46esxm44i 353 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 33 ; ; : work_fnploejenbc2raktl46esxm44i 353 34 SCORING score VBN work_fnploejenbc2raktl46esxm44i 353 35 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 353 36 TO to IN work_fnploejenbc2raktl46esxm44i 353 37 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 353 38 567 567 CD work_fnploejenbc2raktl46esxm44i 353 39 .H .H : work_fnploejenbc2raktl46esxm44i 353 40 is be VBZ work_fnploejenbc2raktl46esxm44i 353 41 & & CC work_fnploejenbc2raktl46esxm44i 353 42 & & CC work_fnploejenbc2raktl46esxm44i 353 43 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 353 44 if if IN work_fnploejenbc2raktl46esxm44i 353 45 p p NN work_fnploejenbc2raktl46esxm44i 353 46 is be VBZ work_fnploejenbc2raktl46esxm44i 353 47 A a NN work_fnploejenbc2raktl46esxm44i 353 48 - - HYPH work_fnploejenbc2raktl46esxm44i 353 49 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 353 50 for for IN work_fnploejenbc2raktl46esxm44i 353 51 a a DT work_fnploejenbc2raktl46esxm44i 353 52 of of IN work_fnploejenbc2raktl46esxm44i 353 53 the the DT work_fnploejenbc2raktl46esxm44i 353 54 form form NN work_fnploejenbc2raktl46esxm44i 353 55 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 56 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 57 E e NN work_fnploejenbc2raktl46esxm44i 353 58 , , , work_fnploejenbc2raktl46esxm44i 353 59 I I NNP work_fnploejenbc2raktl46esxm44i 353 60 F F NNP work_fnploejenbc2raktl46esxm44i 353 61 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 62 , , , work_fnploejenbc2raktl46esxm44i 353 63 L% L% NNP work_fnploejenbc2raktl46esxm44i 353 64 I I NNP work_fnploejenbc2raktl46esxm44i 353 65 F F NNP work_fnploejenbc2raktl46esxm44i 353 66 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 67 , , , work_fnploejenbc2raktl46esxm44i 353 68 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 353 69 El El NNP work_fnploejenbc2raktl46esxm44i 353 70 u u NNP work_fnploejenbc2raktl46esxm44i 353 71 J% j% NN work_fnploejenbc2raktl46esxm44i 353 72 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 353 73 F f NN work_fnploejenbc2raktl46esxm44i 353 74 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 353 75 } } -RRB- work_fnploejenbc2raktl46esxm44i 353 76 with with IN work_fnploejenbc2raktl46esxm44i 353 77 El El NNP work_fnploejenbc2raktl46esxm44i 353 78 4 4 CD work_fnploejenbc2raktl46esxm44i 353 79 = = SYM work_fnploejenbc2raktl46esxm44i 353 80 fzr fzr NN work_fnploejenbc2raktl46esxm44i 353 81 . . . work_fnploejenbc2raktl46esxm44i 354 1 Also also RB work_fnploejenbc2raktl46esxm44i 354 2 , , , work_fnploejenbc2raktl46esxm44i 354 3 P,-(x p,-(x FW work_fnploejenbc2raktl46esxm44i 354 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 354 5 is be VBZ work_fnploejenbc2raktl46esxm44i 354 6 always always RB work_fnploejenbc2raktl46esxm44i 354 7 given give VBN work_fnploejenbc2raktl46esxm44i 354 8 by by IN work_fnploejenbc2raktl46esxm44i 354 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 354 10 * * NFP work_fnploejenbc2raktl46esxm44i 354 11 * * NFP work_fnploejenbc2raktl46esxm44i 354 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 354 13 above above RB work_fnploejenbc2raktl46esxm44i 354 14 . . . work_fnploejenbc2raktl46esxm44i 355 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 355 2 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 355 3 ’ ' '' work_fnploejenbc2raktl46esxm44i 355 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 355 5 Equal Equal NNP work_fnploejenbc2raktl46esxm44i 355 6 Antecedent Antecedent NNP work_fnploejenbc2raktl46esxm44i 355 7 Counterpart Counterpart NNP work_fnploejenbc2raktl46esxm44i 355 8 of of IN work_fnploejenbc2raktl46esxm44i 355 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 355 10 16 16 CD work_fnploejenbc2raktl46esxm44i 355 11 , , , work_fnploejenbc2raktl46esxm44i 355 12 Lemma Lemma NNP work_fnploejenbc2raktl46esxm44i 355 13 51 51 CD work_fnploejenbc2raktl46esxm44i 355 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 355 15 . . . work_fnploejenbc2raktl46esxm44i 356 1 Suppose suppose VB work_fnploejenbc2raktl46esxm44i 356 2 $ $ $ work_fnploejenbc2raktl46esxm44i 356 3 = = SYM work_fnploejenbc2raktl46esxm44i 356 4 + + XX work_fnploejenbc2raktl46esxm44i 356 5 . . . work_fnploejenbc2raktl46esxm44i 357 1 Then then RB work_fnploejenbc2raktl46esxm44i 357 2 the the DT work_fnploejenbc2raktl46esxm44i 357 3 following follow VBG work_fnploejenbc2raktl46esxm44i 357 4 are be VBP work_fnploejenbc2raktl46esxm44i 357 5 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 357 6 . . . work_fnploejenbc2raktl46esxm44i 358 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 358 2 i i NN work_fnploejenbc2raktl46esxm44i 358 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 358 4 p p NNP work_fnploejenbc2raktl46esxm44i 358 5 is be VBZ work_fnploejenbc2raktl46esxm44i 358 6 & & CC work_fnploejenbc2raktl46esxm44i 358 7 ‘ ' `` work_fnploejenbc2raktl46esxm44i 358 8 * * NFP work_fnploejenbc2raktl46esxm44i 358 9 and and CC work_fnploejenbc2raktl46esxm44i 358 10 & & CC work_fnploejenbc2raktl46esxm44i 358 11 - - HYPH work_fnploejenbc2raktl46esxm44i 358 12 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 358 13 , , , work_fnploejenbc2raktl46esxm44i 358 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 358 15 ii ii NNP work_fnploejenbc2raktl46esxm44i 358 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 358 17 . . . work_fnploejenbc2raktl46esxm44i 359 1 Prop Prop NNP work_fnploejenbc2raktl46esxm44i 359 2 : : : work_fnploejenbc2raktl46esxm44i 359 3 ~4~4 ~4~4 . work_fnploejenbc2raktl46esxm44i 359 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 359 5 0 0 CD work_fnploejenbc2raktl46esxm44i 359 6 , , , work_fnploejenbc2raktl46esxm44i 359 7 l l NN work_fnploejenbc2raktl46esxm44i 359 8 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 359 9 is be VBZ work_fnploejenbc2raktl46esxm44i 359 10 afinitely afinitely RB work_fnploejenbc2raktl46esxm44i 359 11 add add VB work_fnploejenbc2raktl46esxm44i 359 12 ‘ ' `` work_fnploejenbc2raktl46esxm44i 359 13 ltive ltive JJ work_fnploejenbc2raktl46esxm44i 359 14 probability probability NN work_fnploejenbc2raktl46esxm44i 359 15 measure measure NN work_fnploejenbc2raktl46esxm44i 359 16 , , , work_fnploejenbc2raktl46esxm44i 359 17 for for IN work_fnploejenbc2raktl46esxm44i 359 18 all all DT work_fnploejenbc2raktl46esxm44i 359 19 FE FE NNP work_fnploejenbc2raktl46esxm44i 359 20 & & CC work_fnploejenbc2raktl46esxm44i 359 21 , , , work_fnploejenbc2raktl46esxm44i 359 22 where where WRB work_fnploejenbc2raktl46esxm44i 359 23 , , , work_fnploejenbc2raktl46esxm44i 359 24 Q1’F Q1’F NNP work_fnploejenbc2raktl46esxm44i 359 25 = = SYM work_fnploejenbc2raktl46esxm44i 359 26 d d XX work_fnploejenbc2raktl46esxm44i 359 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 359 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 359 29 E(F E(F NNP work_fnploejenbc2raktl46esxm44i 359 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 359 31 : : : work_fnploejenbc2raktl46esxm44i 359 32 EEL EEL NNP work_fnploejenbc2raktl46esxm44i 359 33 } } -RRB- work_fnploejenbc2raktl46esxm44i 359 34 . . . work_fnploejenbc2raktl46esxm44i 360 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 360 2 . . . work_fnploejenbc2raktl46esxm44i 361 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 361 2 i)= i)= NNP work_fnploejenbc2raktl46esxm44i 361 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 361 4 ii ii NNP work_fnploejenbc2raktl46esxm44i 361 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 361 6 . . . work_fnploejenbc2raktl46esxm44i 362 1 Since since IN work_fnploejenbc2raktl46esxm44i 362 2 p p NN work_fnploejenbc2raktl46esxm44i 362 3 is be VBZ work_fnploejenbc2raktl46esxm44i 362 4 gZ gZ NNP work_fnploejenbc2raktl46esxm44i 362 5 - - HYPH work_fnploejenbc2raktl46esxm44i 362 6 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 362 7 , , , work_fnploejenbc2raktl46esxm44i 362 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 362 9 have have VBP work_fnploejenbc2raktl46esxm44i 362 10 , , , work_fnploejenbc2raktl46esxm44i 362 11 for for IN work_fnploejenbc2raktl46esxm44i 362 12 any any DT work_fnploejenbc2raktl46esxm44i 362 13 E E NNP work_fnploejenbc2raktl46esxm44i 362 14 , , , work_fnploejenbc2raktl46esxm44i 362 15 FE FE NNP work_fnploejenbc2raktl46esxm44i 362 16 & & CC work_fnploejenbc2raktl46esxm44i 362 17 ‘ ' `` work_fnploejenbc2raktl46esxm44i 362 18 , , , work_fnploejenbc2raktl46esxm44i 362 19 p(EI p(EI NNP work_fnploejenbc2raktl46esxm44i 362 20 F F NNP work_fnploejenbc2raktl46esxm44i 362 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 22 = = SYM work_fnploejenbc2raktl46esxm44i 362 23 x x UH work_fnploejenbc2raktl46esxm44i 362 24 , , , work_fnploejenbc2raktl46esxm44i 362 25 , , , work_fnploejenbc2raktl46esxm44i 362 26 u(EC u(EC NNP work_fnploejenbc2raktl46esxm44i 362 27 1 1 CD work_fnploejenbc2raktl46esxm44i 362 28 F F NNP work_fnploejenbc2raktl46esxm44i 362 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 30 = = NFP work_fnploejenbc2raktl46esxm44i 362 31 y y NNP work_fnploejenbc2raktl46esxm44i 362 32 , , , work_fnploejenbc2raktl46esxm44i 362 33 det det NNP work_fnploejenbc2raktl46esxm44i 362 34 J= J= NNP work_fnploejenbc2raktl46esxm44i 362 35 0 0 NNP work_fnploejenbc2raktl46esxm44i 362 36 , , , work_fnploejenbc2raktl46esxm44i 362 37 where where WRB work_fnploejenbc2raktl46esxm44i 362 38 J= J= NNP work_fnploejenbc2raktl46esxm44i 362 39 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 362 40 f'h f'h RB work_fnploejenbc2raktl46esxm44i 362 41 1 1 CD work_fnploejenbc2raktl46esxm44i 362 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 43 f'(Y f'(y JJ work_fnploejenbc2raktl46esxm44i 362 44 , , , work_fnploejenbc2raktl46esxm44i 362 45 O o UH work_fnploejenbc2raktl46esxm44i 362 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 47 f'(-%O f'(-%O NNP work_fnploejenbc2raktl46esxm44i 362 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 49 f'(Y f'(y JJ work_fnploejenbc2raktl46esxm44i 362 50 , , , work_fnploejenbc2raktl46esxm44i 362 51 1 1 CD work_fnploejenbc2raktl46esxm44i 362 52 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 53 1 1 CD work_fnploejenbc2raktl46esxm44i 362 54 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 362 55 1 1 CD work_fnploejenbc2raktl46esxm44i 362 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 57 then then RB work_fnploejenbc2raktl46esxm44i 362 58 , , , work_fnploejenbc2raktl46esxm44i 362 59 P,(x P,(x NNP work_fnploejenbc2raktl46esxm44i 362 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 61 + + SYM work_fnploejenbc2raktl46esxm44i 362 62 P,-(y P,-(y NNP work_fnploejenbc2raktl46esxm44i 362 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 362 64 = = NFP work_fnploejenbc2raktl46esxm44i 362 65 1 1 CD work_fnploejenbc2raktl46esxm44i 362 66 . . . work_fnploejenbc2raktl46esxm44i 363 1 In in IN work_fnploejenbc2raktl46esxm44i 363 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 363 3 , , , work_fnploejenbc2raktl46esxm44i 363 4 for for IN work_fnploejenbc2raktl46esxm44i 363 5 F= F= NNP work_fnploejenbc2raktl46esxm44i 363 6 Q Q NNP work_fnploejenbc2raktl46esxm44i 363 7 , , , work_fnploejenbc2raktl46esxm44i 363 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 363 9 have have VBP work_fnploejenbc2raktl46esxm44i 363 10 Pfop(E Pfop(E NNP work_fnploejenbc2raktl46esxm44i 363 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 363 12 + + CD work_fnploejenbc2raktl46esxm44i 363 13 P,+(EC P,+(EC NNP work_fnploejenbc2raktl46esxm44i 363 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 363 15 = = SYM work_fnploejenbc2raktl46esxm44i 363 16 1 1 CD work_fnploejenbc2raktl46esxm44i 363 17 . . . work_fnploejenbc2raktl46esxm44i 364 1 Next next RB work_fnploejenbc2raktl46esxm44i 364 2 , , , work_fnploejenbc2raktl46esxm44i 364 3 since since IN work_fnploejenbc2raktl46esxm44i 364 4 p p NNP work_fnploejenbc2raktl46esxm44i 364 5 is be VBZ work_fnploejenbc2raktl46esxm44i 364 6 & & CC work_fnploejenbc2raktl46esxm44i 364 7 s s NNP work_fnploejenbc2raktl46esxm44i 364 8 - - HYPH work_fnploejenbc2raktl46esxm44i 364 9 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 364 10 , , , work_fnploejenbc2raktl46esxm44i 364 11 for for IN work_fnploejenbc2raktl46esxm44i 364 12 any any DT work_fnploejenbc2raktl46esxm44i 364 13 E e NN work_fnploejenbc2raktl46esxm44i 364 14 , , , work_fnploejenbc2raktl46esxm44i 364 15 , , , work_fnploejenbc2raktl46esxm44i 364 16 E e NN work_fnploejenbc2raktl46esxm44i 364 17 , , , work_fnploejenbc2raktl46esxm44i 364 18 , , , work_fnploejenbc2raktl46esxm44i 364 19 FE FE NNP work_fnploejenbc2raktl46esxm44i 364 20 d d NN work_fnploejenbc2raktl46esxm44i 364 21 with with IN work_fnploejenbc2raktl46esxm44i 364 22 E e NN work_fnploejenbc2raktl46esxm44i 364 23 , , , work_fnploejenbc2raktl46esxm44i 364 24 E e NN work_fnploejenbc2raktl46esxm44i 364 25 , , , work_fnploejenbc2raktl46esxm44i 364 26 = = NFP work_fnploejenbc2raktl46esxm44i 364 27 a a LS work_fnploejenbc2raktl46esxm44i 364 28 , , , work_fnploejenbc2raktl46esxm44i 364 29 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 364 30 have have VBP work_fnploejenbc2raktl46esxm44i 364 31 , , , work_fnploejenbc2raktl46esxm44i 364 32 det det NNP work_fnploejenbc2raktl46esxm44i 364 33 J J NNP work_fnploejenbc2raktl46esxm44i 364 34 = = SYM work_fnploejenbc2raktl46esxm44i 364 35 0 0 NFP work_fnploejenbc2raktl46esxm44i 364 36 , , , work_fnploejenbc2raktl46esxm44i 364 37 where where WRB work_fnploejenbc2raktl46esxm44i 364 38 , , , work_fnploejenbc2raktl46esxm44i 364 39 x x SYM work_fnploejenbc2raktl46esxm44i 364 40 = = SYM work_fnploejenbc2raktl46esxm44i 364 41 p(E p(e FW work_fnploejenbc2raktl46esxm44i 364 42 , , , work_fnploejenbc2raktl46esxm44i 364 43 1 1 CD work_fnploejenbc2raktl46esxm44i 364 44 F F NNP work_fnploejenbc2raktl46esxm44i 364 45 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 46 , , , work_fnploejenbc2raktl46esxm44i 364 47 y y NNP work_fnploejenbc2raktl46esxm44i 364 48 = = SYM work_fnploejenbc2raktl46esxm44i 364 49 p(E p(e UH work_fnploejenbc2raktl46esxm44i 364 50 , , , work_fnploejenbc2raktl46esxm44i 364 51 I I NNP work_fnploejenbc2raktl46esxm44i 364 52 F F NNP work_fnploejenbc2raktl46esxm44i 364 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 54 , , , work_fnploejenbc2raktl46esxm44i 364 55 z z NN work_fnploejenbc2raktl46esxm44i 364 56 = = SYM work_fnploejenbc2raktl46esxm44i 364 57 p(E p(e FW work_fnploejenbc2raktl46esxm44i 364 58 , , , work_fnploejenbc2raktl46esxm44i 364 59 u u NNP work_fnploejenbc2raktl46esxm44i 364 60 E E NNP work_fnploejenbc2raktl46esxm44i 364 61 , , , work_fnploejenbc2raktl46esxm44i 364 62 1 1 CD work_fnploejenbc2raktl46esxm44i 364 63 F f NN work_fnploejenbc2raktl46esxm44i 364 64 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 65 and and CC work_fnploejenbc2raktl46esxm44i 364 66 so so IN work_fnploejenbc2raktl46esxm44i 364 67 that that IN work_fnploejenbc2raktl46esxm44i 364 68 Pr(z Pr(z NNP work_fnploejenbc2raktl46esxm44i 364 69 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 70 = = NFP work_fnploejenbc2raktl46esxm44i 364 71 Pf(x Pf(x NNP work_fnploejenbc2raktl46esxm44i 364 72 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 73 + + NFP work_fnploejenbc2raktl46esxm44i 364 74 Pr Pr NNP work_fnploejenbc2raktl46esxm44i 364 75 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 364 76 y y NNP work_fnploejenbc2raktl46esxm44i 364 77 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 364 78 , , , work_fnploejenbc2raktl46esxm44i 364 79 by by IN work_fnploejenbc2raktl46esxm44i 364 80 computation computation NN work_fnploejenbc2raktl46esxm44i 364 81 . . . work_fnploejenbc2raktl46esxm44i 365 1 In in IN work_fnploejenbc2raktl46esxm44i 365 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 365 3 , , , work_fnploejenbc2raktl46esxm44i 365 4 for for IN work_fnploejenbc2raktl46esxm44i 365 5 F F NNP work_fnploejenbc2raktl46esxm44i 365 6 = = SYM work_fnploejenbc2raktl46esxm44i 365 7 Q Q NNP work_fnploejenbc2raktl46esxm44i 365 8 , , , work_fnploejenbc2raktl46esxm44i 365 9 PpdE PpdE NNP work_fnploejenbc2raktl46esxm44i 365 10 , , , work_fnploejenbc2raktl46esxm44i 365 11 u u NNP work_fnploejenbc2raktl46esxm44i 365 12 Ed Ed NNP work_fnploejenbc2raktl46esxm44i 365 13 = = SYM work_fnploejenbc2raktl46esxm44i 365 14 Pp/. pp/. CD work_fnploejenbc2raktl46esxm44i 366 1 @ @ NFP work_fnploejenbc2raktl46esxm44i 366 2 , , , work_fnploejenbc2raktl46esxm44i 366 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 366 4 + + CC work_fnploejenbc2raktl46esxm44i 366 5 P p NN work_fnploejenbc2raktl46esxm44i 366 6 , , , work_fnploejenbc2raktl46esxm44i 366 7 oP oP NNP work_fnploejenbc2raktl46esxm44i 366 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 366 9 & & CC work_fnploejenbc2raktl46esxm44i 366 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 366 11 . . . work_fnploejenbc2raktl46esxm44i 367 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 367 2 Q Q NNP work_fnploejenbc2raktl46esxm44i 367 3 = = , work_fnploejenbc2raktl46esxm44i 367 4 P p NN work_fnploejenbc2raktl46esxm44i 367 5 , , , work_fnploejenbc2raktl46esxm44i 367 6 o o NNP work_fnploejenbc2raktl46esxm44i 367 7 p p NN work_fnploejenbc2raktl46esxm44i 367 8 : : : work_fnploejenbc2raktl46esxm44i 367 9 & & CC work_fnploejenbc2raktl46esxm44i 367 10 - - HYPH work_fnploejenbc2raktl46esxm44i 367 11 + + NNP work_fnploejenbc2raktl46esxm44i 367 12 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 367 13 0 0 CD work_fnploejenbc2raktl46esxm44i 367 14 , , , work_fnploejenbc2raktl46esxm44i 367 15 l l NN work_fnploejenbc2raktl46esxm44i 367 16 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 367 17 is be VBZ work_fnploejenbc2raktl46esxm44i 367 18 a a DT work_fnploejenbc2raktl46esxm44i 367 19 finitely finitely RB work_fnploejenbc2raktl46esxm44i 367 20 additive additive JJ work_fnploejenbc2raktl46esxm44i 367 21 probability probability NN work_fnploejenbc2raktl46esxm44i 367 22 measure measure NN work_fnploejenbc2raktl46esxm44i 367 23 , , , work_fnploejenbc2raktl46esxm44i 367 24 for for IN work_fnploejenbc2raktl46esxm44i 367 25 all all DT work_fnploejenbc2raktl46esxm44i 367 26 FE FE NNP work_fnploejenbc2raktl46esxm44i 367 27 & & CC work_fnploejenbc2raktl46esxm44i 367 28 . . . work_fnploejenbc2raktl46esxm44i 368 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 368 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 368 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 368 4 = = NFP work_fnploejenbc2raktl46esxm44i 368 5 z- z- XX work_fnploejenbc2raktl46esxm44i 368 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 368 7 i i NN work_fnploejenbc2raktl46esxm44i 368 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 368 9 . . . work_fnploejenbc2raktl46esxm44i 369 1 First first RB work_fnploejenbc2raktl46esxm44i 369 2 note note VB work_fnploejenbc2raktl46esxm44i 369 3 that that IN work_fnploejenbc2raktl46esxm44i 369 4 p p NN work_fnploejenbc2raktl46esxm44i 369 5 : : : work_fnploejenbc2raktl46esxm44i 369 6 & & CC work_fnploejenbc2raktl46esxm44i 369 7 + + CC work_fnploejenbc2raktl46esxm44i 369 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 369 9 0 0 CD work_fnploejenbc2raktl46esxm44i 369 10 , , , work_fnploejenbc2raktl46esxm44i 369 11 11 11 CD work_fnploejenbc2raktl46esxm44i 369 12 , , , work_fnploejenbc2raktl46esxm44i 369 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 369 14 ii ii NNP work_fnploejenbc2raktl46esxm44i 369 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 369 16 means mean VBZ work_fnploejenbc2raktl46esxm44i 369 17 that that IN work_fnploejenbc2raktl46esxm44i 369 18 the the DT work_fnploejenbc2raktl46esxm44i 369 19 restric- restric- JJ work_fnploejenbc2raktl46esxm44i 369 20 tion tion NN work_fnploejenbc2raktl46esxm44i 369 21 of of IN work_fnploejenbc2raktl46esxm44i 369 22 p p NNP work_fnploejenbc2raktl46esxm44i 369 23 to to NN work_fnploejenbc2raktl46esxm44i 369 24 & & CC work_fnploejenbc2raktl46esxm44i 369 25 F F NNP work_fnploejenbc2raktl46esxm44i 369 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 369 27 still still RB work_fnploejenbc2raktl46esxm44i 369 28 denoted denote VBN work_fnploejenbc2raktl46esxm44i 369 29 by by IN work_fnploejenbc2raktl46esxm44i 369 30 p p NN work_fnploejenbc2raktl46esxm44i 369 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 369 32 is be VBZ work_fnploejenbc2raktl46esxm44i 369 33 such such JJ work_fnploejenbc2raktl46esxm44i 369 34 that that IN work_fnploejenbc2raktl46esxm44i 369 35 Pfop Pfop NNP work_fnploejenbc2raktl46esxm44i 369 36 is be VBZ work_fnploejenbc2raktl46esxm44i 369 37 a a DT work_fnploejenbc2raktl46esxm44i 369 38 finitely finitely RB work_fnploejenbc2raktl46esxm44i 369 39 additive additive JJ work_fnploejenbc2raktl46esxm44i 369 40 probability probability NN work_fnploejenbc2raktl46esxm44i 369 41 on on IN work_fnploejenbc2raktl46esxm44i 369 42 JZ?~ JZ?~ NNS work_fnploejenbc2raktl46esxm44i 369 43 , , , work_fnploejenbc2raktl46esxm44i 369 44 say say VBP work_fnploejenbc2raktl46esxm44i 369 45 QF QF NNP work_fnploejenbc2raktl46esxm44i 369 46 = = SYM work_fnploejenbc2raktl46esxm44i 369 47 P p NN work_fnploejenbc2raktl46esxm44i 369 48 , , , work_fnploejenbc2raktl46esxm44i 369 49 o o NN work_fnploejenbc2raktl46esxm44i 369 50 p p NN work_fnploejenbc2raktl46esxm44i 369 51 , , , work_fnploejenbc2raktl46esxm44i 369 52 for for IN work_fnploejenbc2raktl46esxm44i 369 53 all all DT work_fnploejenbc2raktl46esxm44i 369 54 FE FE NNP work_fnploejenbc2raktl46esxm44i 369 55 .r4 .r4 NFP work_fnploejenbc2raktl46esxm44i 369 56 . . . work_fnploejenbc2raktl46esxm44i 370 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 370 2 which which WDT work_fnploejenbc2raktl46esxm44i 370 3 means mean VBZ work_fnploejenbc2raktl46esxm44i 370 4 det det NNP work_fnploejenbc2raktl46esxm44i 370 5 J J NNP work_fnploejenbc2raktl46esxm44i 370 6 = = SYM work_fnploejenbc2raktl46esxm44i 370 7 0 0 NFP work_fnploejenbc2raktl46esxm44i 370 8 , , , work_fnploejenbc2raktl46esxm44i 370 9 where where WRB work_fnploejenbc2raktl46esxm44i 370 10 J J NNP work_fnploejenbc2raktl46esxm44i 370 11 is be VBZ work_fnploejenbc2raktl46esxm44i 370 12 as as IN work_fnploejenbc2raktl46esxm44i 370 13 in in IN work_fnploejenbc2raktl46esxm44i 370 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 370 15 1 1 CD work_fnploejenbc2raktl46esxm44i 370 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 370 17 . . . work_fnploejenbc2raktl46esxm44i 371 1 The the DT work_fnploejenbc2raktl46esxm44i 371 2 rank rank NN work_fnploejenbc2raktl46esxm44i 371 3 p p NN work_fnploejenbc2raktl46esxm44i 371 4 of of IN work_fnploejenbc2raktl46esxm44i 371 5 J J NNP work_fnploejenbc2raktl46esxm44i 371 6 is be VBZ work_fnploejenbc2raktl46esxm44i 371 7 therefore therefore RB work_fnploejenbc2raktl46esxm44i 371 8 1 1 CD work_fnploejenbc2raktl46esxm44i 371 9 . . . work_fnploejenbc2raktl46esxm44i 372 1 Since since IN work_fnploejenbc2raktl46esxm44i 372 2 x x SYM work_fnploejenbc2raktl46esxm44i 372 3 E e NN work_fnploejenbc2raktl46esxm44i 372 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 372 5 a a DT work_fnploejenbc2raktl46esxm44i 372 6 , , , work_fnploejenbc2raktl46esxm44i 372 7 , , , work_fnploejenbc2raktl46esxm44i 372 8 a a DT work_fnploejenbc2raktl46esxm44i 372 9 , , , work_fnploejenbc2raktl46esxm44i 372 10 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 372 11 , , , work_fnploejenbc2raktl46esxm44i 372 12 each each DT work_fnploejenbc2raktl46esxm44i 372 13 column column NN work_fnploejenbc2raktl46esxm44i 372 14 of of IN work_fnploejenbc2raktl46esxm44i 372 15 J J NNP work_fnploejenbc2raktl46esxm44i 372 16 contains contain VBZ work_fnploejenbc2raktl46esxm44i 372 17 a a DT work_fnploejenbc2raktl46esxm44i 372 18 zero zero CD work_fnploejenbc2raktl46esxm44i 372 19 component component NN work_fnploejenbc2raktl46esxm44i 372 20 or or CC work_fnploejenbc2raktl46esxm44i 372 21 has have VBZ work_fnploejenbc2raktl46esxm44i 372 22 568 568 CD work_fnploejenbc2raktl46esxm44i 372 23 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 372 24 , , , work_fnploejenbc2raktl46esxm44i 372 25 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 372 26 , , , work_fnploejenbc2raktl46esxm44i 372 27 ANDROGERS ANDROGERS NNP work_fnploejenbc2raktl46esxm44i 372 28 both both CC work_fnploejenbc2raktl46esxm44i 372 29 positive positive JJ work_fnploejenbc2raktl46esxm44i 372 30 and and CC work_fnploejenbc2raktl46esxm44i 372 31 negative negative JJ work_fnploejenbc2raktl46esxm44i 372 32 components component NNS work_fnploejenbc2raktl46esxm44i 372 33 , , , work_fnploejenbc2raktl46esxm44i 372 34 and and CC work_fnploejenbc2raktl46esxm44i 372 35 hence hence RB work_fnploejenbc2raktl46esxm44i 372 36 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 372 37 x x NNP work_fnploejenbc2raktl46esxm44i 372 38 , , , work_fnploejenbc2raktl46esxm44i 372 39 y y NNP work_fnploejenbc2raktl46esxm44i 372 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 372 41 is be VBZ work_fnploejenbc2raktl46esxm44i 372 42 a a DT work_fnploejenbc2raktl46esxm44i 372 43 - - : work_fnploejenbc2raktl46esxm44i 372 44 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 372 45 , , , work_fnploejenbc2raktl46esxm44i 372 46 VA VA NNP work_fnploejenbc2raktl46esxm44i 372 47 = = NFP work_fnploejenbc2raktl46esxm44i 372 48 { { -LRB- work_fnploejenbc2raktl46esxm44i 372 49 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 372 50 EJF EJF NNP work_fnploejenbc2raktl46esxm44i 372 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 372 52 , , , work_fnploejenbc2raktl46esxm44i 372 53 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 372 54 E’)F E’)F NNP work_fnploejenbc2raktl46esxm44i 372 55 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 372 56 } } -RRB- work_fnploejenbc2raktl46esxm44i 372 57 , , , work_fnploejenbc2raktl46esxm44i 372 58 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 372 59 , , , work_fnploejenbc2raktl46esxm44i 372 60 p p NNP work_fnploejenbc2raktl46esxm44i 372 61 is be VBZ work_fnploejenbc2raktl46esxm44i 372 62 $ $ $ work_fnploejenbc2raktl46esxm44i 372 63 -WLAD -wlad NN work_fnploejenbc2raktl46esxm44i 372 64 . . . work_fnploejenbc2raktl46esxm44i 373 1 The the DT work_fnploejenbc2raktl46esxm44i 373 2 fact fact NN work_fnploejenbc2raktl46esxm44i 373 3 that that IN work_fnploejenbc2raktl46esxm44i 373 4 p p NN work_fnploejenbc2raktl46esxm44i 373 5 is be VBZ work_fnploejenbc2raktl46esxm44i 373 6 & & CC work_fnploejenbc2raktl46esxm44i 373 7 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 373 8 follows follow VBZ work_fnploejenbc2raktl46esxm44i 373 9 from from IN work_fnploejenbc2raktl46esxm44i 373 10 Corollary Corollary NNP work_fnploejenbc2raktl46esxm44i 373 11 3.2.3 3.2.3 NNP work_fnploejenbc2raktl46esxm44i 373 12 , , , work_fnploejenbc2raktl46esxm44i 373 13 since since IN work_fnploejenbc2raktl46esxm44i 373 14 for for IN work_fnploejenbc2raktl46esxm44i 373 15 any any DT work_fnploejenbc2raktl46esxm44i 373 16 E e NN work_fnploejenbc2raktl46esxm44i 373 17 , , , work_fnploejenbc2raktl46esxm44i 373 18 , , , work_fnploejenbc2raktl46esxm44i 373 19 E e NN work_fnploejenbc2raktl46esxm44i 373 20 , , , work_fnploejenbc2raktl46esxm44i 373 21 , , , work_fnploejenbc2raktl46esxm44i 373 22 FE FE NNP work_fnploejenbc2raktl46esxm44i 373 23 -01 -01 NNP work_fnploejenbc2raktl46esxm44i 373 24 , , , work_fnploejenbc2raktl46esxm44i 373 25 with with IN work_fnploejenbc2raktl46esxm44i 373 26 E e NN work_fnploejenbc2raktl46esxm44i 373 27 , , , work_fnploejenbc2raktl46esxm44i 373 28 E2 E2 NNP work_fnploejenbc2raktl46esxm44i 373 29 = = SYM work_fnploejenbc2raktl46esxm44i 373 30 a a NN work_fnploejenbc2raktl46esxm44i 373 31 , , , work_fnploejenbc2raktl46esxm44i 373 32 the the DT work_fnploejenbc2raktl46esxm44i 373 33 condition condition NN work_fnploejenbc2raktl46esxm44i 373 34 < < XX work_fnploejenbc2raktl46esxm44i 373 35 /o /o NNP work_fnploejenbc2raktl46esxm44i 373 36 / / SYM work_fnploejenbc2raktl46esxm44i 373 37 W W NNP work_fnploejenbc2raktl46esxm44i 373 38 , , , work_fnploejenbc2raktl46esxm44i 373 39 u u NNP work_fnploejenbc2raktl46esxm44i 373 40 E e NN work_fnploejenbc2raktl46esxm44i 373 41 , , , work_fnploejenbc2raktl46esxm44i 373 42 I I NNP work_fnploejenbc2raktl46esxm44i 373 43 F F NNP work_fnploejenbc2raktl46esxm44i 373 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 373 45 = = NFP work_fnploejenbc2raktl46esxm44i 373 46 f f XX work_fnploejenbc2raktl46esxm44i 373 47 ’ ' '' work_fnploejenbc2raktl46esxm44i 373 48 , , , work_fnploejenbc2raktl46esxm44i 373 49 ” " '' work_fnploejenbc2raktl46esxm44i 373 50 ~(4 ~(4 NFP work_fnploejenbc2raktl46esxm44i 373 51 IF if IN work_fnploejenbc2raktl46esxm44i 373 52 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 373 53 + + SYM work_fnploejenbc2raktl46esxm44i 373 54 + + SYM work_fnploejenbc2raktl46esxm44i 373 55 P(E p(e NN work_fnploejenbc2raktl46esxm44i 373 56 , , , work_fnploejenbc2raktl46esxm44i 373 57 IF if IN work_fnploejenbc2raktl46esxm44i 373 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 373 59 is be VBZ work_fnploejenbc2raktl46esxm44i 373 60 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 373 61 to to IN work_fnploejenbc2raktl46esxm44i 373 62 det det NNP work_fnploejenbc2raktl46esxm44i 373 63 J= J= NNP work_fnploejenbc2raktl46esxm44i 373 64 0 0 NFP work_fnploejenbc2raktl46esxm44i 373 65 , , , work_fnploejenbc2raktl46esxm44i 373 66 where where WRB work_fnploejenbc2raktl46esxm44i 373 67 J J NNP work_fnploejenbc2raktl46esxm44i 373 68 is be VBZ work_fnploejenbc2raktl46esxm44i 373 69 as as IN work_fnploejenbc2raktl46esxm44i 373 70 in in IN work_fnploejenbc2raktl46esxm44i 373 71 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 373 72 2 2 CD work_fnploejenbc2raktl46esxm44i 373 73 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 373 74 . . . work_fnploejenbc2raktl46esxm44i 374 1 1 1 LS work_fnploejenbc2raktl46esxm44i 374 2 In in IN work_fnploejenbc2raktl46esxm44i 374 3 the the DT work_fnploejenbc2raktl46esxm44i 374 4 proof proof NN work_fnploejenbc2raktl46esxm44i 374 5 of of IN work_fnploejenbc2raktl46esxm44i 374 6 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 374 7 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 374 8 ’ ' '' work_fnploejenbc2raktl46esxm44i 374 9 , , , work_fnploejenbc2raktl46esxm44i 374 10 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 374 11 might may MD work_fnploejenbc2raktl46esxm44i 374 12 be be VB work_fnploejenbc2raktl46esxm44i 374 13 tempting tempting JJ work_fnploejenbc2raktl46esxm44i 374 14 to to TO work_fnploejenbc2raktl46esxm44i 374 15 conclude conclude VB work_fnploejenbc2raktl46esxm44i 374 16 that that IN work_fnploejenbc2raktl46esxm44i 374 17 the the DT work_fnploejenbc2raktl46esxm44i 374 18 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 374 19 probability probability NN work_fnploejenbc2raktl46esxm44i 374 20 is be VBZ work_fnploejenbc2raktl46esxm44i 374 21 uniquely uniquely RB work_fnploejenbc2raktl46esxm44i 374 22 compatible compatible JJ work_fnploejenbc2raktl46esxm44i 374 23 with with IN work_fnploejenbc2raktl46esxm44i 374 24 each each DT work_fnploejenbc2raktl46esxm44i 374 25 QF qf NN work_fnploejenbc2raktl46esxm44i 374 26 . . . work_fnploejenbc2raktl46esxm44i 375 1 But but CC work_fnploejenbc2raktl46esxm44i 375 2 this this DT work_fnploejenbc2raktl46esxm44i 375 3 is be VBZ work_fnploejenbc2raktl46esxm44i 375 4 not not RB work_fnploejenbc2raktl46esxm44i 375 5 necessarily necessarily RB work_fnploejenbc2raktl46esxm44i 375 6 so so RB work_fnploejenbc2raktl46esxm44i 375 7 . . . work_fnploejenbc2raktl46esxm44i 376 1 In in IN work_fnploejenbc2raktl46esxm44i 376 2 fact fact NN work_fnploejenbc2raktl46esxm44i 376 3 Aczel Aczel NNP work_fnploejenbc2raktl46esxm44i 376 4 Cl Cl NNP work_fnploejenbc2raktl46esxm44i 376 5 , , , work_fnploejenbc2raktl46esxm44i 376 6 pp pp NNP work_fnploejenbc2raktl46esxm44i 376 7 . . . work_fnploejenbc2raktl46esxm44i 377 1 321 321 CD work_fnploejenbc2raktl46esxm44i 377 2 - - SYM work_fnploejenbc2raktl46esxm44i 377 3 3241 3241 CD work_fnploejenbc2raktl46esxm44i 377 4 required require VBD work_fnploejenbc2raktl46esxm44i 377 5 additional additional JJ work_fnploejenbc2raktl46esxm44i 377 6 properties property NNS work_fnploejenbc2raktl46esxm44i 377 7 before before IN work_fnploejenbc2raktl46esxm44i 377 8 proving prove VBG work_fnploejenbc2raktl46esxm44i 377 9 such such JJ work_fnploejenbc2raktl46esxm44i 377 10 as as IN work_fnploejenbc2raktl46esxm44i 377 11 relation relation NN work_fnploejenbc2raktl46esxm44i 377 12 . . . work_fnploejenbc2raktl46esxm44i 378 1 These these DT work_fnploejenbc2raktl46esxm44i 378 2 properties property NNS work_fnploejenbc2raktl46esxm44i 378 3 include include VBP work_fnploejenbc2raktl46esxm44i 378 4 continuity continuity NN work_fnploejenbc2raktl46esxm44i 378 5 and and CC work_fnploejenbc2raktl46esxm44i 378 6 monotonicity monotonicity NN work_fnploejenbc2raktl46esxm44i 378 7 of of IN work_fnploejenbc2raktl46esxm44i 378 8 functional functional JJ work_fnploejenbc2raktl46esxm44i 378 9 forms form NNS work_fnploejenbc2raktl46esxm44i 378 10 in in IN work_fnploejenbc2raktl46esxm44i 378 11 both both DT work_fnploejenbc2raktl46esxm44i 378 12 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 378 13 and and CC work_fnploejenbc2raktl46esxm44i 378 14 consequent consequent JJ work_fnploejenbc2raktl46esxm44i 378 15 probabilities probability NNS work_fnploejenbc2raktl46esxm44i 378 16 . . . work_fnploejenbc2raktl46esxm44i 379 1 The the DT work_fnploejenbc2raktl46esxm44i 379 2 appropriate appropriate JJ work_fnploejenbc2raktl46esxm44i 379 3 strengthening strengthening NN work_fnploejenbc2raktl46esxm44i 379 4 of of IN work_fnploejenbc2raktl46esxm44i 379 5 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 379 6 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 379 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 379 8 to to TO work_fnploejenbc2raktl46esxm44i 379 9 account account VB work_fnploejenbc2raktl46esxm44i 379 10 for for IN work_fnploejenbc2raktl46esxm44i 379 11 possibly possibly RB work_fnploejenbc2raktl46esxm44i 379 12 varying vary VBG work_fnploejenbc2raktl46esxm44i 379 13 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 379 14 event event NN work_fnploejenbc2raktl46esxm44i 379 15 antecedents antecedent NNS work_fnploejenbc2raktl46esxm44i 379 16 utilizes utilize VBZ work_fnploejenbc2raktl46esxm44i 379 17 the the DT work_fnploejenbc2raktl46esxm44i 379 18 following follow VBG work_fnploejenbc2raktl46esxm44i 379 19 property property NN work_fnploejenbc2raktl46esxm44i 379 20 : : : work_fnploejenbc2raktl46esxm44i 379 21 For for IN work_fnploejenbc2raktl46esxm44i 379 22 any any DT work_fnploejenbc2raktl46esxm44i 379 23 P p NN work_fnploejenbc2raktl46esxm44i 379 24 E e NN work_fnploejenbc2raktl46esxm44i 379 25 La La NNP work_fnploejenbc2raktl46esxm44i 379 26 , , , work_fnploejenbc2raktl46esxm44i 379 27 , , , work_fnploejenbc2raktl46esxm44i 379 28 a a DT work_fnploejenbc2raktl46esxm44i 379 29 , , , work_fnploejenbc2raktl46esxm44i 379 30 19 19 CD work_fnploejenbc2raktl46esxm44i 379 31 ” " '' work_fnploejenbc2raktl46esxm44i 379 32 , , , work_fnploejenbc2raktl46esxm44i 379 33 call call VBP work_fnploejenbc2raktl46esxm44i 379 34 p p NNP work_fnploejenbc2raktl46esxm44i 379 35 & & CC work_fnploejenbc2raktl46esxm44i 379 36 -WLAD -WLAD NNP work_fnploejenbc2raktl46esxm44i 379 37 , , , work_fnploejenbc2raktl46esxm44i 379 38 if if IN work_fnploejenbc2raktl46esxm44i 379 39 p p NN work_fnploejenbc2raktl46esxm44i 379 40 is be VBZ work_fnploejenbc2raktl46esxm44i 379 41 A a NN work_fnploejenbc2raktl46esxm44i 379 42 - - HYPH work_fnploejenbc2raktl46esxm44i 379 43 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 379 44 for for IN work_fnploejenbc2raktl46esxm44i 379 45 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 379 46 of of IN work_fnploejenbc2raktl46esxm44i 379 47 the the DT work_fnploejenbc2raktl46esxm44i 379 48 form form NN work_fnploejenbc2raktl46esxm44i 379 49 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 50 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 51 El El NNP work_fnploejenbc2raktl46esxm44i 379 52 FG FG NNP work_fnploejenbc2raktl46esxm44i 379 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 54 , , , work_fnploejenbc2raktl46esxm44i 379 55 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 56 FI FI NNP work_fnploejenbc2raktl46esxm44i 379 57 G g NN work_fnploejenbc2raktl46esxm44i 379 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 59 , , , work_fnploejenbc2raktl46esxm44i 379 60 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 61 EF EF NNP work_fnploejenbc2raktl46esxm44i 379 62 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 63 G G NNP work_fnploejenbc2raktl46esxm44i 379 64 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 66 , , , work_fnploejenbc2raktl46esxm44i 379 67 assuming assume VBG work_fnploejenbc2raktl46esxm44i 379 68 the the DT work_fnploejenbc2raktl46esxm44i 379 69 natural natural JJ work_fnploejenbc2raktl46esxm44i 379 70 conjunctive conjunctive JJ work_fnploejenbc2raktl46esxm44i 379 71 chaining chaining NN work_fnploejenbc2raktl46esxm44i 379 72 relation relation NN work_fnploejenbc2raktl46esxm44i 379 73 that that IN work_fnploejenbc2raktl46esxm44i 379 74 both both DT work_fnploejenbc2raktl46esxm44i 379 75 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 379 76 and and CC work_fnploejenbc2raktl46esxm44i 379 77 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 379 78 implicitly implicitly RB work_fnploejenbc2raktl46esxm44i 379 79 assumed assume VBD work_fnploejenbc2raktl46esxm44i 379 80 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 81 see see VB work_fnploejenbc2raktl46esxm44i 379 82 earlier early JJR work_fnploejenbc2raktl46esxm44i 379 83 discussions discussion NNS work_fnploejenbc2raktl46esxm44i 379 84 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 85 , , , work_fnploejenbc2raktl46esxm44i 379 86 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 87 El El NNP work_fnploejenbc2raktl46esxm44i 379 88 FGWI FGWI NNP work_fnploejenbc2raktl46esxm44i 379 89 G G NNP work_fnploejenbc2raktl46esxm44i 379 90 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 91 = = NFP work_fnploejenbc2raktl46esxm44i 379 92 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 379 93 4 4 CD work_fnploejenbc2raktl46esxm44i 379 94 G g NN work_fnploejenbc2raktl46esxm44i 379 95 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 379 96 ; ; : work_fnploejenbc2raktl46esxm44i 379 97 all all DT work_fnploejenbc2raktl46esxm44i 379 98 E e NN work_fnploejenbc2raktl46esxm44i 379 99 , , , work_fnploejenbc2raktl46esxm44i 379 100 F f NN work_fnploejenbc2raktl46esxm44i 379 101 , , , work_fnploejenbc2raktl46esxm44i 379 102 G G NNP work_fnploejenbc2raktl46esxm44i 379 103 E E NNP work_fnploejenbc2raktl46esxm44i 379 104 RI RI NNP work_fnploejenbc2raktl46esxm44i 379 105 , , , work_fnploejenbc2raktl46esxm44i 379 106 and and CC work_fnploejenbc2raktl46esxm44i 379 107 interpreted interpret VBN work_fnploejenbc2raktl46esxm44i 379 108 via via IN work_fnploejenbc2raktl46esxm44i 379 109 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 379 110 ’s ’s POS work_fnploejenbc2raktl46esxm44i 379 111 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 379 112 event event NN work_fnploejenbc2raktl46esxm44i 379 113 indicator indicator NN work_fnploejenbc2raktl46esxm44i 379 114 function function NN work_fnploejenbc2raktl46esxm44i 379 115 . . . work_fnploejenbc2raktl46esxm44i 380 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 380 2 3.2.3 3.2.3 CD work_fnploejenbc2raktl46esxm44i 380 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 380 4 Corresponds correspond NNS work_fnploejenbc2raktl46esxm44i 380 5 to to IN work_fnploejenbc2raktl46esxm44i 380 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 380 7 16 16 CD work_fnploejenbc2raktl46esxm44i 380 8 , , , work_fnploejenbc2raktl46esxm44i 380 9 Lemma Lemma NNP work_fnploejenbc2raktl46esxm44i 380 10 51 51 CD work_fnploejenbc2raktl46esxm44i 380 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 380 12 . . . work_fnploejenbc2raktl46esxm44i 381 1 The the DT work_fnploejenbc2raktl46esxm44i 381 2 following follow VBG work_fnploejenbc2raktl46esxm44i 381 3 statements statement NNS work_fnploejenbc2raktl46esxm44i 381 4 are be VBP work_fnploejenbc2raktl46esxm44i 381 5 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 381 6 under under IN work_fnploejenbc2raktl46esxm44i 381 7 the the DT work_fnploejenbc2raktl46esxm44i 381 8 above above JJ work_fnploejenbc2raktl46esxm44i 381 9 assumption assumption NN work_fnploejenbc2raktl46esxm44i 381 10 and and CC work_fnploejenbc2raktl46esxm44i 381 11 for for IN work_fnploejenbc2raktl46esxm44i 381 12 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 381 13 = = SYM work_fnploejenbc2raktl46esxm44i 381 14 + + SYM work_fnploejenbc2raktl46esxm44i 381 15 : : : work_fnploejenbc2raktl46esxm44i 381 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 381 17 i i NN work_fnploejenbc2raktl46esxm44i 381 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 381 19 p p NN work_fnploejenbc2raktl46esxm44i 381 20 is be VBZ work_fnploejenbc2raktl46esxm44i 381 21 g2 g2 NNP work_fnploejenbc2raktl46esxm44i 381 22 ; ; : work_fnploejenbc2raktl46esxm44i 381 23 , , , work_fnploejenbc2raktl46esxm44i 381 24 6 6 CD work_fnploejenbc2raktl46esxm44i 381 25 ” " '' work_fnploejenbc2raktl46esxm44i 381 26 , , , work_fnploejenbc2raktl46esxm44i 381 27 & & CC work_fnploejenbc2raktl46esxm44i 381 28 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 381 29 . . . work_fnploejenbc2raktl46esxm44i 382 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 382 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 382 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 4 Pro pro RB work_fnploejenbc2raktl46esxm44i 382 5 , , , work_fnploejenbc2raktl46esxm44i 382 6 u u XX work_fnploejenbc2raktl46esxm44i 382 7 : : : work_fnploejenbc2raktl46esxm44i 382 8 SCI~ SCI~ . work_fnploejenbc2raktl46esxm44i 382 9 + + SYM work_fnploejenbc2raktl46esxm44i 382 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 382 11 O o UH work_fnploejenbc2raktl46esxm44i 382 12 , , , work_fnploejenbc2raktl46esxm44i 382 13 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 382 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 382 15 is be VBZ work_fnploejenbc2raktl46esxm44i 382 16 finitely finitely RB work_fnploejenbc2raktl46esxm44i 382 17 additive additive JJ work_fnploejenbc2raktl46esxm44i 382 18 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 382 19 probability probability NN work_fnploejenbc2raktl46esxm44i 382 20 measure measure NN work_fnploejenbc2raktl46esxm44i 382 21 for for IN work_fnploejenbc2raktl46esxm44i 382 22 each each DT work_fnploejenbc2raktl46esxm44i 382 23 FE FE NNP work_fnploejenbc2raktl46esxm44i 382 24 & & CC work_fnploejenbc2raktl46esxm44i 382 25 , , , work_fnploejenbc2raktl46esxm44i 382 26 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 382 27 , , , work_fnploejenbc2raktl46esxm44i 382 28 assuming assume VBG work_fnploejenbc2raktl46esxm44i 382 29 p(F p(f NN work_fnploejenbc2raktl46esxm44i 382 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 31 > > XX work_fnploejenbc2raktl46esxm44i 382 32 0 0 NFP work_fnploejenbc2raktl46esxm44i 382 33 , , , work_fnploejenbc2raktl46esxm44i 382 34 for for IN work_fnploejenbc2raktl46esxm44i 382 35 all all DT work_fnploejenbc2raktl46esxm44i 382 36 E e NN work_fnploejenbc2raktl46esxm44i 382 37 E e NN work_fnploejenbc2raktl46esxm44i 382 38 ~4 ~4 NNS work_fnploejenbc2raktl46esxm44i 382 39 , , , work_fnploejenbc2raktl46esxm44i 382 40 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 382 41 + + CC work_fnploejenbc2raktl46esxm44i 382 42 PMEI PMEI NNP work_fnploejenbc2raktl46esxm44i 382 43 F F NNP work_fnploejenbc2raktl46esxm44i 382 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 45 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 46 = = NFP work_fnploejenbc2raktl46esxm44i 382 47 U’p U’p NNP work_fnploejenbc2raktl46esxm44i 382 48 / / SYM work_fnploejenbc2raktl46esxm44i 382 49 WlF WlF NNP work_fnploejenbc2raktl46esxm44i 382 50 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 51 = = NFP work_fnploejenbc2raktl46esxm44i 382 52 f’,MWYPfMF f’,MWYPfMF NNP work_fnploejenbc2raktl46esxm44i 382 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 382 55 . . . work_fnploejenbc2raktl46esxm44i 383 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 383 2 : : : work_fnploejenbc2raktl46esxm44i 383 3 Follows follow VBZ work_fnploejenbc2raktl46esxm44i 383 4 a a DT work_fnploejenbc2raktl46esxm44i 383 5 similar similar JJ work_fnploejenbc2raktl46esxm44i 383 6 format format NN work_fnploejenbc2raktl46esxm44i 383 7 as as IN work_fnploejenbc2raktl46esxm44i 383 8 for for IN work_fnploejenbc2raktl46esxm44i 383 9 the the DT work_fnploejenbc2raktl46esxm44i 383 10 proof proof NN work_fnploejenbc2raktl46esxm44i 383 11 of of IN work_fnploejenbc2raktl46esxm44i 383 12 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 383 13 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 383 14 ’ ' '' work_fnploejenbc2raktl46esxm44i 383 15 , , , work_fnploejenbc2raktl46esxm44i 383 16 where where WRB work_fnploejenbc2raktl46esxm44i 383 17 now now RB work_fnploejenbc2raktl46esxm44i 383 18 , , , work_fnploejenbc2raktl46esxm44i 383 19 in in IN work_fnploejenbc2raktl46esxm44i 383 20 addition addition NN work_fnploejenbc2raktl46esxm44i 383 21 to to IN work_fnploejenbc2raktl46esxm44i 383 22 Eqs Eqs NNP work_fnploejenbc2raktl46esxm44i 383 23 . . . work_fnploejenbc2raktl46esxm44i 384 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 384 2 1 1 CD work_fnploejenbc2raktl46esxm44i 384 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 4 and and CC work_fnploejenbc2raktl46esxm44i 384 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 384 6 2 2 LS work_fnploejenbc2raktl46esxm44i 384 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 8 holding hold VBG work_fnploejenbc2raktl46esxm44i 384 9 when when WRB work_fnploejenbc2raktl46esxm44i 384 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 384 11 i i NN work_fnploejenbc2raktl46esxm44i 384 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 13 is be VBZ work_fnploejenbc2raktl46esxm44i 384 14 assumed assume VBN work_fnploejenbc2raktl46esxm44i 384 15 , , , work_fnploejenbc2raktl46esxm44i 384 16 one one PRP work_fnploejenbc2raktl46esxm44i 384 17 has have VBZ work_fnploejenbc2raktl46esxm44i 384 18 due due JJ work_fnploejenbc2raktl46esxm44i 384 19 to to IN work_fnploejenbc2raktl46esxm44i 384 20 p p NN work_fnploejenbc2raktl46esxm44i 384 21 being be VBG work_fnploejenbc2raktl46esxm44i 384 22 G$‘,-WLAD G$‘,-WLAD NNP work_fnploejenbc2raktl46esxm44i 384 23 , , , work_fnploejenbc2raktl46esxm44i 384 24 1 1 CD work_fnploejenbc2raktl46esxm44i 384 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 26 f’(h f’(h NNP work_fnploejenbc2raktl46esxm44i 384 27 1 1 CD work_fnploejenbc2raktl46esxm44i 384 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 29 f’(w f’(w ADD work_fnploejenbc2raktl46esxm44i 384 30 1 1 LS work_fnploejenbc2raktl46esxm44i 384 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 32 J= J= NNP work_fnploejenbc2raktl46esxm44i 384 33 0 0 NFP work_fnploejenbc2raktl46esxm44i 384 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 35 f’(o f’(o NNP work_fnploejenbc2raktl46esxm44i 384 36 , , , work_fnploejenbc2raktl46esxm44i 384 37 1 1 CD work_fnploejenbc2raktl46esxm44i 384 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 39 f’(w f’(w ADD work_fnploejenbc2raktl46esxm44i 384 40 , , , work_fnploejenbc2raktl46esxm44i 384 41 0 0 CD work_fnploejenbc2raktl46esxm44i 384 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 43 1 1 CD work_fnploejenbc2raktl46esxm44i 384 44 , , , work_fnploejenbc2raktl46esxm44i 384 45 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 384 46 3 3 LS work_fnploejenbc2raktl46esxm44i 384 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 48 f’(u f’(u ADD work_fnploejenbc2raktl46esxm44i 384 49 , , , work_fnploejenbc2raktl46esxm44i 384 50 0 0 LS work_fnploejenbc2raktl46esxm44i 384 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 52 S’(w S’(w NNP work_fnploejenbc2raktl46esxm44i 384 53 , , , work_fnploejenbc2raktl46esxm44i 384 54 0 0 CD work_fnploejenbc2raktl46esxm44i 384 55 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 56 where where WRB work_fnploejenbc2raktl46esxm44i 384 57 u u NNP work_fnploejenbc2raktl46esxm44i 384 58 = = SYM work_fnploejenbc2raktl46esxm44i 384 59 p(EJFG p(EJFG NNP work_fnploejenbc2raktl46esxm44i 384 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 61 , , , work_fnploejenbc2raktl46esxm44i 384 62 v v NN work_fnploejenbc2raktl46esxm44i 384 63 = = SYM work_fnploejenbc2raktl46esxm44i 384 64 p(FIG p(FIG NNP work_fnploejenbc2raktl46esxm44i 384 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 66 , , , work_fnploejenbc2raktl46esxm44i 384 67 w w NNP work_fnploejenbc2raktl46esxm44i 384 68 = = SYM work_fnploejenbc2raktl46esxm44i 384 69 p(EF(G p(EF(G NNP work_fnploejenbc2raktl46esxm44i 384 70 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 384 71 . . . work_fnploejenbc2raktl46esxm44i 385 1 1 1 LS work_fnploejenbc2raktl46esxm44i 385 2 SCORING score VBG work_fnploejenbc2raktl46esxm44i 385 3 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 385 4 TO to IN work_fnploejenbc2raktl46esxm44i 385 5 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 385 6 569 569 CD work_fnploejenbc2raktl46esxm44i 385 7 4 4 CD work_fnploejenbc2raktl46esxm44i 385 8 . . . work_fnploejenbc2raktl46esxm44i 386 1 GAMES game NNS work_fnploejenbc2raktl46esxm44i 386 2 WITH with IN work_fnploejenbc2raktl46esxm44i 386 3 AN an DT work_fnploejenbc2raktl46esxm44i 386 4 ADDITIVE ADDITIVE NNP work_fnploejenbc2raktl46esxm44i 386 5 AGGREGATION aggregation NN work_fnploejenbc2raktl46esxm44i 386 6 FUNCTION function NN work_fnploejenbc2raktl46esxm44i 386 7 AND and CC work_fnploejenbc2raktl46esxm44i 386 8 BAYESIAN bayesian VB work_fnploejenbc2raktl46esxm44i 386 9 ANALYSIS ANALYSIS NNP work_fnploejenbc2raktl46esxm44i 386 10 This this DT work_fnploejenbc2raktl46esxm44i 386 11 section section NN work_fnploejenbc2raktl46esxm44i 386 12 is be VBZ work_fnploejenbc2raktl46esxm44i 386 13 devoted devoted JJ work_fnploejenbc2raktl46esxm44i 386 14 to to IN work_fnploejenbc2raktl46esxm44i 386 15 a a DT work_fnploejenbc2raktl46esxm44i 386 16 detailed detailed JJ work_fnploejenbc2raktl46esxm44i 386 17 investigation investigation NN work_fnploejenbc2raktl46esxm44i 386 18 of of IN work_fnploejenbc2raktl46esxm44i 386 19 games game NNS work_fnploejenbc2raktl46esxm44i 386 20 with with IN work_fnploejenbc2raktl46esxm44i 386 21 an an DT work_fnploejenbc2raktl46esxm44i 386 22 additive additive JJ work_fnploejenbc2raktl46esxm44i 386 23 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 386 24 function function NN work_fnploejenbc2raktl46esxm44i 386 25 ; ; : work_fnploejenbc2raktl46esxm44i 386 26 to to TO work_fnploejenbc2raktl46esxm44i 386 27 be be VB work_fnploejenbc2raktl46esxm44i 386 28 complete complete JJ work_fnploejenbc2raktl46esxm44i 386 29 , , , work_fnploejenbc2raktl46esxm44i 386 30 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 386 31 consider consider VBP work_fnploejenbc2raktl46esxm44i 386 32 also also RB work_fnploejenbc2raktl46esxm44i 386 33 their -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 386 34 mixed mixed JJ work_fnploejenbc2raktl46esxm44i 386 35 extensions extension NNS work_fnploejenbc2raktl46esxm44i 386 36 . . . work_fnploejenbc2raktl46esxm44i 387 1 Under under IN work_fnploejenbc2raktl46esxm44i 387 2 an an DT work_fnploejenbc2raktl46esxm44i 387 3 additional additional JJ work_fnploejenbc2raktl46esxm44i 387 4 assumption assumption NN work_fnploejenbc2raktl46esxm44i 387 5 on on IN work_fnploejenbc2raktl46esxm44i 387 6 the the DT work_fnploejenbc2raktl46esxm44i 387 7 score score NN work_fnploejenbc2raktl46esxm44i 387 8 functions function NNS work_fnploejenbc2raktl46esxm44i 387 9 , , , work_fnploejenbc2raktl46esxm44i 387 10 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 387 11 establish establish VBP work_fnploejenbc2raktl46esxm44i 387 12 the the DT work_fnploejenbc2raktl46esxm44i 387 13 equivalences equivalence NNS work_fnploejenbc2raktl46esxm44i 387 14 among among IN work_fnploejenbc2raktl46esxm44i 387 15 different different JJ work_fnploejenbc2raktl46esxm44i 387 16 concepts concept NNS work_fnploejenbc2raktl46esxm44i 387 17 of of IN work_fnploejenbc2raktl46esxm44i 387 18 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 387 19 , , , work_fnploejenbc2raktl46esxm44i 387 20 including include VBG work_fnploejenbc2raktl46esxm44i 387 21 Bayesian bayesian JJ work_fnploejenbc2raktl46esxm44i 387 22 decision decision NN work_fnploejenbc2raktl46esxm44i 387 23 functions function NNS work_fnploejenbc2raktl46esxm44i 387 24 and and CC work_fnploejenbc2raktl46esxm44i 387 25 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 387 26 ’s ’s POS work_fnploejenbc2raktl46esxm44i 387 27 coherence coherence NN work_fnploejenbc2raktl46esxm44i 387 28 measures measure NNS work_fnploejenbc2raktl46esxm44i 387 29 . . . work_fnploejenbc2raktl46esxm44i 388 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 388 2 also also RB work_fnploejenbc2raktl46esxm44i 388 3 show show VBP work_fnploejenbc2raktl46esxm44i 388 4 that that IN work_fnploejenbc2raktl46esxm44i 388 5 nonatomic nonatomic JJ work_fnploejenbc2raktl46esxm44i 388 6 probability probability NN work_fnploejenbc2raktl46esxm44i 388 7 measures measure NNS work_fnploejenbc2raktl46esxm44i 388 8 are be VBP work_fnploejenbc2raktl46esxm44i 388 9 not not RB work_fnploejenbc2raktl46esxm44i 388 10 “ " `` work_fnploejenbc2raktl46esxm44i 388 11 coherent coherent JJ work_fnploejenbc2raktl46esxm44i 388 12 ” " '' work_fnploejenbc2raktl46esxm44i 388 13 in in IN work_fnploejenbc2raktl46esxm44i 388 14 games game NNS work_fnploejenbc2raktl46esxm44i 388 15 with with IN work_fnploejenbc2raktl46esxm44i 388 16 improper improper JJ work_fnploejenbc2raktl46esxm44i 388 17 score score NN work_fnploejenbc2raktl46esxm44i 388 18 functions function NNS work_fnploejenbc2raktl46esxm44i 388 19 . . . work_fnploejenbc2raktl46esxm44i 389 1 4.1 4.1 CD work_fnploejenbc2raktl46esxm44i 389 2 . . . work_fnploejenbc2raktl46esxm44i 390 1 Mixed mixed JJ work_fnploejenbc2raktl46esxm44i 390 2 Extensions extension NNS work_fnploejenbc2raktl46esxm44i 390 3 of of IN work_fnploejenbc2raktl46esxm44i 390 4 Uncertainty Uncertainty NNP work_fnploejenbc2raktl46esxm44i 390 5 Games Games NNPS work_fnploejenbc2raktl46esxm44i 390 6 Consider consider VB work_fnploejenbc2raktl46esxm44i 390 7 the the DT work_fnploejenbc2raktl46esxm44i 390 8 game game NN work_fnploejenbc2raktl46esxm44i 390 9 G,+ g,+ NN work_fnploejenbc2raktl46esxm44i 390 10 in in IN work_fnploejenbc2raktl46esxm44i 390 11 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 390 12 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 390 13 reduced reduce VBN work_fnploejenbc2raktl46esxm44i 390 14 form form NN work_fnploejenbc2raktl46esxm44i 390 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 390 16 A a NN work_fnploejenbc2raktl46esxm44i 390 17 : : : work_fnploejenbc2raktl46esxm44i 390 18 , , , work_fnploejenbc2raktl46esxm44i 390 19 A a DT work_fnploejenbc2raktl46esxm44i 390 20 2 2 CD work_fnploejenbc2raktl46esxm44i 390 21 , , , work_fnploejenbc2raktl46esxm44i 390 22 Lf+ Lf+ NNP work_fnploejenbc2raktl46esxm44i 390 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 390 24 with with IN work_fnploejenbc2raktl46esxm44i 390 25 Because because IN work_fnploejenbc2raktl46esxm44i 390 26 of of IN work_fnploejenbc2raktl46esxm44i 390 27 the the DT work_fnploejenbc2raktl46esxm44i 390 28 nature nature NN work_fnploejenbc2raktl46esxm44i 390 29 of of IN work_fnploejenbc2raktl46esxm44i 390 30 /i /i NN work_fnploejenbc2raktl46esxm44i 390 31 : : : work_fnploejenbc2raktl46esxm44i 390 32 , , , work_fnploejenbc2raktl46esxm44i 390 33 mixed mixed JJ work_fnploejenbc2raktl46esxm44i 390 34 strategies strategy NNS work_fnploejenbc2raktl46esxm44i 390 35 or or CC work_fnploejenbc2raktl46esxm44i 390 36 prior prior JJ work_fnploejenbc2raktl46esxm44i 390 37 probability probability NN work_fnploejenbc2raktl46esxm44i 390 38 measures measure NNS work_fnploejenbc2raktl46esxm44i 390 39 on on IN work_fnploejenbc2raktl46esxm44i 390 40 A a NN work_fnploejenbc2raktl46esxm44i 390 41 : : : work_fnploejenbc2raktl46esxm44i 390 42 will will MD work_fnploejenbc2raktl46esxm44i 390 43 be be VB work_fnploejenbc2raktl46esxm44i 390 44 defined define VBN work_fnploejenbc2raktl46esxm44i 390 45 as as IN work_fnploejenbc2raktl46esxm44i 390 46 follows follow VBZ work_fnploejenbc2raktl46esxm44i 390 47 . . . work_fnploejenbc2raktl46esxm44i 391 1 Player player NN work_fnploejenbc2raktl46esxm44i 391 2 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 391 3 will will MD work_fnploejenbc2raktl46esxm44i 391 4 first first RB work_fnploejenbc2raktl46esxm44i 391 5 pick pick VB work_fnploejenbc2raktl46esxm44i 391 6 an an DT work_fnploejenbc2raktl46esxm44i 391 7 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 391 8 E E NNP work_fnploejenbc2raktl46esxm44i 391 9 J J NNP work_fnploejenbc2raktl46esxm44i 391 10 & & CC work_fnploejenbc2raktl46esxm44i 391 11 according accord VBG work_fnploejenbc2raktl46esxm44i 391 12 to to IN work_fnploejenbc2raktl46esxm44i 391 13 some some DT work_fnploejenbc2raktl46esxm44i 391 14 probability probability NN work_fnploejenbc2raktl46esxm44i 391 15 measure measure NN work_fnploejenbc2raktl46esxm44i 391 16 4 4 CD work_fnploejenbc2raktl46esxm44i 391 17 on on IN work_fnploejenbc2raktl46esxm44i 391 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 391 19 s s NNP work_fnploejenbc2raktl46esxm44i 391 20 & & CC work_fnploejenbc2raktl46esxm44i 391 21 , , , work_fnploejenbc2raktl46esxm44i 391 22 , , , work_fnploejenbc2raktl46esxm44i 391 23 SJ SJ NNP work_fnploejenbc2raktl46esxm44i 391 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 25 , , , work_fnploejenbc2raktl46esxm44i 391 26 where where WRB work_fnploejenbc2raktl46esxm44i 391 27 3 3 CD work_fnploejenbc2raktl46esxm44i 391 28 is be VBZ work_fnploejenbc2raktl46esxm44i 391 29 some some DT work_fnploejenbc2raktl46esxm44i 391 30 a a NN work_fnploejenbc2raktl46esxm44i 391 31 - - HYPH work_fnploejenbc2raktl46esxm44i 391 32 algebra algebra NN work_fnploejenbc2raktl46esxm44i 391 33 of of IN work_fnploejenbc2raktl46esxm44i 391 34 subsets subset NNS work_fnploejenbc2raktl46esxm44i 391 35 of of IN work_fnploejenbc2raktl46esxm44i 391 36 s s NNP work_fnploejenbc2raktl46esxm44i 391 37 & & CC work_fnploejenbc2raktl46esxm44i 391 38 , , , work_fnploejenbc2raktl46esxm44i 391 39 and and CC work_fnploejenbc2raktl46esxm44i 391 40 then then RB work_fnploejenbc2raktl46esxm44i 391 41 depending depend VBG work_fnploejenbc2raktl46esxm44i 391 42 upon upon IN work_fnploejenbc2raktl46esxm44i 391 43 a a DT work_fnploejenbc2raktl46esxm44i 391 44 , , , work_fnploejenbc2raktl46esxm44i 391 45 pick pick VB work_fnploejenbc2raktl46esxm44i 391 46 a a DT work_fnploejenbc2raktl46esxm44i 391 47 configuration configuration NN work_fnploejenbc2raktl46esxm44i 391 48 of of IN work_fnploejenbc2raktl46esxm44i 391 49 occurrences occurrence NNS work_fnploejenbc2raktl46esxm44i 391 50 of of IN work_fnploejenbc2raktl46esxm44i 391 51 A^ A^ NNP work_fnploejenbc2raktl46esxm44i 391 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 391 53 as as IN work_fnploejenbc2raktl46esxm44i 391 54 a a DT work_fnploejenbc2raktl46esxm44i 391 55 finite finite JJ work_fnploejenbc2raktl46esxm44i 391 56 collection collection NN work_fnploejenbc2raktl46esxm44i 391 57 of of IN work_fnploejenbc2raktl46esxm44i 391 58 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 391 59 events event NNS work_fnploejenbc2raktl46esxm44i 391 60 , , , work_fnploejenbc2raktl46esxm44i 391 61 equivalently equivalently RB work_fnploejenbc2raktl46esxm44i 391 62 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 63 an an DT work_fnploejenbc2raktl46esxm44i 391 64 element element NN work_fnploejenbc2raktl46esxm44i 391 65 of of IN work_fnploejenbc2raktl46esxm44i 391 66 the the DT work_fnploejenbc2raktl46esxm44i 391 67 partition partition NN work_fnploejenbc2raktl46esxm44i 391 68 n(A n(a NN work_fnploejenbc2raktl46esxm44i 391 69 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 70 , , , work_fnploejenbc2raktl46esxm44i 391 71 according accord VBG work_fnploejenbc2raktl46esxm44i 391 72 to to IN work_fnploejenbc2raktl46esxm44i 391 73 some some DT work_fnploejenbc2raktl46esxm44i 391 74 probability probability NN work_fnploejenbc2raktl46esxm44i 391 75 measure measure VB work_fnploejenbc2raktl46esxm44i 391 76 rA rA NNP work_fnploejenbc2raktl46esxm44i 391 77 on on IN work_fnploejenbc2raktl46esxm44i 391 78 the the DT work_fnploejenbc2raktl46esxm44i 391 79 power power NN work_fnploejenbc2raktl46esxm44i 391 80 class class NN work_fnploejenbc2raktl46esxm44i 391 81 9y7c(A 9y7c(a CD work_fnploejenbc2raktl46esxm44i 391 82 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 83 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 84 of of IN work_fnploejenbc2raktl46esxm44i 391 85 7c(A 7c(a CD work_fnploejenbc2raktl46esxm44i 391 86 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 391 87 . . . work_fnploejenbc2raktl46esxm44i 392 1 Now now RB work_fnploejenbc2raktl46esxm44i 392 2 , , , work_fnploejenbc2raktl46esxm44i 392 3 since since IN work_fnploejenbc2raktl46esxm44i 392 4 ~(a ~(a NNP work_fnploejenbc2raktl46esxm44i 392 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 392 6 is be VBZ work_fnploejenbc2raktl46esxm44i 392 7 finite finite JJ work_fnploejenbc2raktl46esxm44i 392 8 , , , work_fnploejenbc2raktl46esxm44i 392 9 each each DT work_fnploejenbc2raktl46esxm44i 392 10 probability probability NN work_fnploejenbc2raktl46esxm44i 392 11 measure measure NN work_fnploejenbc2raktl46esxm44i 392 12 on on IN work_fnploejenbc2raktl46esxm44i 392 13 9(x(a 9(x(a NNP work_fnploejenbc2raktl46esxm44i 392 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 392 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 392 16 is be VBZ work_fnploejenbc2raktl46esxm44i 392 17 identified identify VBN work_fnploejenbc2raktl46esxm44i 392 18 by by IN work_fnploejenbc2raktl46esxm44i 392 19 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 392 20 probability probability NN work_fnploejenbc2raktl46esxm44i 392 21 density density NN work_fnploejenbc2raktl46esxm44i 392 22 function function NN work_fnploejenbc2raktl46esxm44i 392 23 on on IN work_fnploejenbc2raktl46esxm44i 392 24 X(A X(A NNP work_fnploejenbc2raktl46esxm44i 392 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 392 26 , , , work_fnploejenbc2raktl46esxm44i 392 27 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 392 28 , , , work_fnploejenbc2raktl46esxm44i 392 29 6 6 CD work_fnploejenbc2raktl46esxm44i 392 30 : : : work_fnploejenbc2raktl46esxm44i 392 31 { { -LRB- work_fnploejenbc2raktl46esxm44i 392 32 B,,j= b,,j= NN work_fnploejenbc2raktl46esxm44i 392 33 1 1 CD work_fnploejenbc2raktl46esxm44i 392 34 , , , work_fnploejenbc2raktl46esxm44i 392 35 . . . work_fnploejenbc2raktl46esxm44i 393 1 . . . work_fnploejenbc2raktl46esxm44i 394 1 . . . work_fnploejenbc2raktl46esxm44i 395 1 . . . work_fnploejenbc2raktl46esxm44i 396 1 m m LS work_fnploejenbc2raktl46esxm44i 396 2 } } -RRB- work_fnploejenbc2raktl46esxm44i 396 3 -+ -+ . work_fnploejenbc2raktl46esxm44i 396 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 396 5 0 0 CD work_fnploejenbc2raktl46esxm44i 396 6 , , , work_fnploejenbc2raktl46esxm44i 396 7 11 11 CD work_fnploejenbc2raktl46esxm44i 396 8 , , , work_fnploejenbc2raktl46esxm44i 396 9 f f NNP work_fnploejenbc2raktl46esxm44i 396 10 QB,)= QB,)= NNP work_fnploejenbc2raktl46esxm44i 396 11 1 1 CD work_fnploejenbc2raktl46esxm44i 396 12 , , , work_fnploejenbc2raktl46esxm44i 396 13 j= j= NNP work_fnploejenbc2raktl46esxm44i 396 14 1 1 CD work_fnploejenbc2raktl46esxm44i 396 15 where where WRB work_fnploejenbc2raktl46esxm44i 396 16 Bis Bis NNP work_fnploejenbc2raktl46esxm44i 396 17 are be VBP work_fnploejenbc2raktl46esxm44i 396 18 some some DT work_fnploejenbc2raktl46esxm44i 396 19 listing listing NN work_fnploejenbc2raktl46esxm44i 396 20 of of IN work_fnploejenbc2raktl46esxm44i 396 21 the the DT work_fnploejenbc2raktl46esxm44i 396 22 elements element NNS work_fnploejenbc2raktl46esxm44i 396 23 of of IN work_fnploejenbc2raktl46esxm44i 396 24 n(a n(a NNP work_fnploejenbc2raktl46esxm44i 396 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 396 26 , , , work_fnploejenbc2raktl46esxm44i 396 27 and and CC work_fnploejenbc2raktl46esxm44i 396 28 m m NN work_fnploejenbc2raktl46esxm44i 396 29 = = SYM work_fnploejenbc2raktl46esxm44i 396 30 In(a In(a NNP work_fnploejenbc2raktl46esxm44i 396 31 Next Next NNP work_fnploejenbc2raktl46esxm44i 396 32 , , , work_fnploejenbc2raktl46esxm44i 396 33 each each DT work_fnploejenbc2raktl46esxm44i 396 34 such such JJ work_fnploejenbc2raktl46esxm44i 396 35 8 8 CD work_fnploejenbc2raktl46esxm44i 396 36 generates generate VBZ work_fnploejenbc2raktl46esxm44i 396 37 a a DT work_fnploejenbc2raktl46esxm44i 396 38 probability probability NN work_fnploejenbc2raktl46esxm44i 396 39 measure measure NN work_fnploejenbc2raktl46esxm44i 396 40 P p NN work_fnploejenbc2raktl46esxm44i 396 41 , , , work_fnploejenbc2raktl46esxm44i 396 42 on on IN work_fnploejenbc2raktl46esxm44i 396 43 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 396 44 Sz Sz NNP work_fnploejenbc2raktl46esxm44i 396 45 , , , work_fnploejenbc2raktl46esxm44i 396 46 & & CC work_fnploejenbc2raktl46esxm44i 396 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 396 48 such such JJ work_fnploejenbc2raktl46esxm44i 396 49 that that IN work_fnploejenbc2raktl46esxm44i 396 50 PdBj PdBj NNP work_fnploejenbc2raktl46esxm44i 396 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 396 52 = = NFP work_fnploejenbc2raktl46esxm44i 396 53 e(Bj e(bj NN work_fnploejenbc2raktl46esxm44i 396 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 396 55 , , , work_fnploejenbc2raktl46esxm44i 396 56 Vj Vj NNP work_fnploejenbc2raktl46esxm44i 396 57 = = SYM work_fnploejenbc2raktl46esxm44i 396 58 1 1 CD work_fnploejenbc2raktl46esxm44i 396 59 , , , work_fnploejenbc2raktl46esxm44i 396 60 . . . work_fnploejenbc2raktl46esxm44i 397 1 . . . work_fnploejenbc2raktl46esxm44i 398 1 . . . work_fnploejenbc2raktl46esxm44i 399 1 . . . work_fnploejenbc2raktl46esxm44i 400 1 m. m. NNP work_fnploejenbc2raktl46esxm44i 400 2 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 400 3 , , , work_fnploejenbc2raktl46esxm44i 400 4 for for IN work_fnploejenbc2raktl46esxm44i 400 5 each each DT work_fnploejenbc2raktl46esxm44i 400 6 j j NN work_fnploejenbc2raktl46esxm44i 400 7 = = SYM work_fnploejenbc2raktl46esxm44i 400 8 1 1 CD work_fnploejenbc2raktl46esxm44i 400 9 , , , work_fnploejenbc2raktl46esxm44i 400 10 2 2 CD work_fnploejenbc2raktl46esxm44i 400 11 , , , work_fnploejenbc2raktl46esxm44i 400 12 . . . work_fnploejenbc2raktl46esxm44i 401 1 . . . work_fnploejenbc2raktl46esxm44i 402 1 . . . work_fnploejenbc2raktl46esxm44i 403 1 . . . work_fnploejenbc2raktl46esxm44i 404 1 m m LS work_fnploejenbc2raktl46esxm44i 404 2 , , , work_fnploejenbc2raktl46esxm44i 404 3 let let VB work_fnploejenbc2raktl46esxm44i 404 4 Pj Pj NNP work_fnploejenbc2raktl46esxm44i 404 5 be be VB work_fnploejenbc2raktl46esxm44i 404 6 a a DT work_fnploejenbc2raktl46esxm44i 404 7 probability probability NN work_fnploejenbc2raktl46esxm44i 404 8 measure measure NN work_fnploejenbc2raktl46esxm44i 404 9 on on IN work_fnploejenbc2raktl46esxm44i 404 10 B B NNP work_fnploejenbc2raktl46esxm44i 404 11 , , , work_fnploejenbc2raktl46esxm44i 404 12 , , , work_fnploejenbc2raktl46esxm44i 404 13 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 404 14 , , , work_fnploejenbc2raktl46esxm44i 404 15 on on IN work_fnploejenbc2raktl46esxm44i 404 16 the the DT work_fnploejenbc2raktl46esxm44i 404 17 a a DT work_fnploejenbc2raktl46esxm44i 404 18 - - HYPH work_fnploejenbc2raktl46esxm44i 404 19 algebra algebra NN work_fnploejenbc2raktl46esxm44i 404 20 trace trace NN work_fnploejenbc2raktl46esxm44i 404 21 { { -LRB- work_fnploejenbc2raktl46esxm44i 404 22 A a DT work_fnploejenbc2raktl46esxm44i 404 23 Bj Bj NNP work_fnploejenbc2raktl46esxm44i 404 24 : : : work_fnploejenbc2raktl46esxm44i 404 25 A a DT work_fnploejenbc2raktl46esxm44i 404 26 E e NN work_fnploejenbc2raktl46esxm44i 404 27 & & CC work_fnploejenbc2raktl46esxm44i 404 28 } } -RRB- work_fnploejenbc2raktl46esxm44i 404 29 with with IN work_fnploejenbc2raktl46esxm44i 404 30 Pj Pj NNP work_fnploejenbc2raktl46esxm44i 404 31 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 404 32 Bj Bj NNP work_fnploejenbc2raktl46esxm44i 404 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 404 34 = = SYM work_fnploejenbc2raktl46esxm44i 404 35 1 1 CD work_fnploejenbc2raktl46esxm44i 404 36 . . . work_fnploejenbc2raktl46esxm44i 405 1 Define define UH work_fnploejenbc2raktl46esxm44i 405 2 , , , work_fnploejenbc2raktl46esxm44i 405 3 for for IN work_fnploejenbc2raktl46esxm44i 405 4 A a DT work_fnploejenbc2raktl46esxm44i 405 5 E e NN work_fnploejenbc2raktl46esxm44i 405 6 A a NN work_fnploejenbc2raktl46esxm44i 405 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 405 8 , , , work_fnploejenbc2raktl46esxm44i 405 9 P,(A P,(A NNP work_fnploejenbc2raktl46esxm44i 405 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 405 11 = = NFP work_fnploejenbc2raktl46esxm44i 405 12 CJ’= cj’= FW work_fnploejenbc2raktl46esxm44i 405 13 , , , work_fnploejenbc2raktl46esxm44i 405 14 O o UH work_fnploejenbc2raktl46esxm44i 405 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 405 16 Bj Bj NNP work_fnploejenbc2raktl46esxm44i 405 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 405 18 Pj(ABj Pj(ABj NNP work_fnploejenbc2raktl46esxm44i 405 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 405 20 . . . work_fnploejenbc2raktl46esxm44i 406 1 Note note VB work_fnploejenbc2raktl46esxm44i 406 2 that that IN work_fnploejenbc2raktl46esxm44i 406 3 PO(A PO(A NNS work_fnploejenbc2raktl46esxm44i 406 4 _ _ NNP work_fnploejenbc2raktl46esxm44i 406 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 406 6 is be VBZ work_fnploejenbc2raktl46esxm44i 406 7 completely completely RB work_fnploejenbc2raktl46esxm44i 406 8 determined determine VBN work_fnploejenbc2raktl46esxm44i 406 9 by by IN work_fnploejenbc2raktl46esxm44i 406 10 8 8 CD work_fnploejenbc2raktl46esxm44i 406 11 , , , work_fnploejenbc2raktl46esxm44i 406 12 Vi Vi NNP work_fnploejenbc2raktl46esxm44i 406 13 = = SYM work_fnploejenbc2raktl46esxm44i 406 14 1 1 CD work_fnploejenbc2raktl46esxm44i 406 15 , , , work_fnploejenbc2raktl46esxm44i 406 16 . . . work_fnploejenbc2raktl46esxm44i 407 1 . . . work_fnploejenbc2raktl46esxm44i 408 1 . . . work_fnploejenbc2raktl46esxm44i 409 1 . . . work_fnploejenbc2raktl46esxm44i 410 1 n n LS work_fnploejenbc2raktl46esxm44i 410 2 , , , work_fnploejenbc2raktl46esxm44i 410 3 where where WRB work_fnploejenbc2raktl46esxm44i 410 4 a a DT work_fnploejenbc2raktl46esxm44i 410 5 = = FW work_fnploejenbc2raktl46esxm44i 410 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 410 7 A a NN work_fnploejenbc2raktl46esxm44i 410 8 r r NN work_fnploejenbc2raktl46esxm44i 410 9 , , , work_fnploejenbc2raktl46esxm44i 410 10 . . . work_fnploejenbc2raktl46esxm44i 411 1 . . . work_fnploejenbc2raktl46esxm44i 412 1 . . . work_fnploejenbc2raktl46esxm44i 413 1 . . . work_fnploejenbc2raktl46esxm44i 414 1 A a DT work_fnploejenbc2raktl46esxm44i 414 2 , , , work_fnploejenbc2raktl46esxm44i 414 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 414 4 , , , work_fnploejenbc2raktl46esxm44i 414 5 n= n= NNP work_fnploejenbc2raktl46esxm44i 414 6 IAJ IAJ NNP work_fnploejenbc2raktl46esxm44i 414 7 . . . work_fnploejenbc2raktl46esxm44i 415 1 Then then RB work_fnploejenbc2raktl46esxm44i 415 2 , , , work_fnploejenbc2raktl46esxm44i 415 3 since since IN work_fnploejenbc2raktl46esxm44i 415 4 each each DT work_fnploejenbc2raktl46esxm44i 415 5 Aims aim VBZ work_fnploejenbc2raktl46esxm44i 415 6 ? ? . work_fnploejenbc2raktl46esxm44i 416 1 in in IN work_fnploejenbc2raktl46esxm44i 416 2 general general JJ work_fnploejenbc2raktl46esxm44i 416 3 , , , work_fnploejenbc2raktl46esxm44i 416 4 the the DT work_fnploejenbc2raktl46esxm44i 416 5 probability probability NN work_fnploejenbc2raktl46esxm44i 416 6 measure measure NN work_fnploejenbc2raktl46esxm44i 416 7 P p NN work_fnploejenbc2raktl46esxm44i 416 8 , , , work_fnploejenbc2raktl46esxm44i 416 9 on on IN work_fnploejenbc2raktl46esxm44i 416 10 d d NNP work_fnploejenbc2raktl46esxm44i 416 11 is be VBZ work_fnploejenbc2raktl46esxm44i 416 12 extended extend VBN work_fnploejenbc2raktl46esxm44i 416 13 to to IN work_fnploejenbc2raktl46esxm44i 416 14 d d NN work_fnploejenbc2raktl46esxm44i 416 15 via via IN work_fnploejenbc2raktl46esxm44i 416 16 the the DT work_fnploejenbc2raktl46esxm44i 416 17 condi- condi- NNP work_fnploejenbc2raktl46esxm44i 416 18 tional tional JJ work_fnploejenbc2raktl46esxm44i 416 19 probability probability NN work_fnploejenbc2raktl46esxm44i 416 20 operation operation NN work_fnploejenbc2raktl46esxm44i 416 21 . . . work_fnploejenbc2raktl46esxm44i 417 1 For for IN work_fnploejenbc2raktl46esxm44i 417 2 a a DT work_fnploejenbc2raktl46esxm44i 417 3 rigorous rigorous JJ work_fnploejenbc2raktl46esxm44i 417 4 treatment treatment NN work_fnploejenbc2raktl46esxm44i 417 5 of of IN work_fnploejenbc2raktl46esxm44i 417 6 this this DT work_fnploejenbc2raktl46esxm44i 417 7 extension extension NN work_fnploejenbc2raktl46esxm44i 417 8 , , , work_fnploejenbc2raktl46esxm44i 417 9 see see VB work_fnploejenbc2raktl46esxm44i 417 10 c121 c121 NNP work_fnploejenbc2raktl46esxm44i 417 11 . . . work_fnploejenbc2raktl46esxm44i 418 1 570 570 CD work_fnploejenbc2raktl46esxm44i 418 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 418 3 , , , work_fnploejenbc2raktl46esxm44i 418 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 418 5 , , , work_fnploejenbc2raktl46esxm44i 418 6 AND and CC work_fnploejenbc2raktl46esxm44i 418 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 418 8 If if IN work_fnploejenbc2raktl46esxm44i 418 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 418 10 X X NNP work_fnploejenbc2raktl46esxm44i 418 11 , , , work_fnploejenbc2raktl46esxm44i 418 12 9 9 CD work_fnploejenbc2raktl46esxm44i 418 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 418 14 is be VBZ work_fnploejenbc2raktl46esxm44i 418 15 a a DT work_fnploejenbc2raktl46esxm44i 418 16 measurable measurable JJ work_fnploejenbc2raktl46esxm44i 418 17 space space NN work_fnploejenbc2raktl46esxm44i 418 18 , , , work_fnploejenbc2raktl46esxm44i 418 19 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 418 20 will will MD work_fnploejenbc2raktl46esxm44i 418 21 denote denote VB work_fnploejenbc2raktl46esxm44i 418 22 by by IN work_fnploejenbc2raktl46esxm44i 418 23 P(X P(X NNP work_fnploejenbc2raktl46esxm44i 418 24 , , , work_fnploejenbc2raktl46esxm44i 418 25 X X NNP work_fnploejenbc2raktl46esxm44i 418 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 418 27 the the DT work_fnploejenbc2raktl46esxm44i 418 28 collection collection NN work_fnploejenbc2raktl46esxm44i 418 29 of of IN work_fnploejenbc2raktl46esxm44i 418 30 all all DT work_fnploejenbc2raktl46esxm44i 418 31 probability probability NN work_fnploejenbc2raktl46esxm44i 418 32 measures measure NNS work_fnploejenbc2raktl46esxm44i 418 33 on on IN work_fnploejenbc2raktl46esxm44i 418 34 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 418 35 . . . work_fnploejenbc2raktl46esxm44i 419 1 The the DT work_fnploejenbc2raktl46esxm44i 419 2 collection collection NN work_fnploejenbc2raktl46esxm44i 419 3 of of IN work_fnploejenbc2raktl46esxm44i 419 4 probability probability NN work_fnploejenbc2raktl46esxm44i 419 5 density density NN work_fnploejenbc2raktl46esxm44i 419 6 func- func- JJ work_fnploejenbc2raktl46esxm44i 419 7 tions tion NNS work_fnploejenbc2raktl46esxm44i 419 8 on on IN work_fnploejenbc2raktl46esxm44i 419 9 z(a z(a NNP work_fnploejenbc2raktl46esxm44i 419 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 419 11 is be VBZ work_fnploejenbc2raktl46esxm44i 419 12 denoted denote VBN work_fnploejenbc2raktl46esxm44i 419 13 by by IN work_fnploejenbc2raktl46esxm44i 419 14 P(rc(a P(rc(a NNP work_fnploejenbc2raktl46esxm44i 419 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 419 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 419 17 . . . work_fnploejenbc2raktl46esxm44i 420 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 420 2 , , , work_fnploejenbc2raktl46esxm44i 420 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 420 4 have have VBP work_fnploejenbc2raktl46esxm44i 420 5 , , , work_fnploejenbc2raktl46esxm44i 420 6 by by IN work_fnploejenbc2raktl46esxm44i 420 7 identification identification NN work_fnploejenbc2raktl46esxm44i 420 8 , , , work_fnploejenbc2raktl46esxm44i 420 9 P(7Q P(7Q NNP work_fnploejenbc2raktl46esxm44i 420 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 420 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 420 12 c c NN work_fnploejenbc2raktl46esxm44i 420 13 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 420 14 , , , work_fnploejenbc2raktl46esxm44i 420 15 a a DT work_fnploejenbc2raktl46esxm44i 420 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 420 17 . . . work_fnploejenbc2raktl46esxm44i 421 1 The the DT work_fnploejenbc2raktl46esxm44i 421 2 space space NN work_fnploejenbc2raktl46esxm44i 421 3 of of IN work_fnploejenbc2raktl46esxm44i 421 4 prior prior JJ work_fnploejenbc2raktl46esxm44i 421 5 probability probability NN work_fnploejenbc2raktl46esxm44i 421 6 measures measure NNS work_fnploejenbc2raktl46esxm44i 421 7 on on IN work_fnploejenbc2raktl46esxm44i 421 8 Ai+ ai+ NN work_fnploejenbc2raktl46esxm44i 421 9 is be VBZ work_fnploejenbc2raktl46esxm44i 421 10 The the DT work_fnploejenbc2raktl46esxm44i 421 11 expected expected JJ work_fnploejenbc2raktl46esxm44i 421 12 loss loss NN work_fnploejenbc2raktl46esxm44i 421 13 of of IN work_fnploejenbc2raktl46esxm44i 421 14 p p NN work_fnploejenbc2raktl46esxm44i 421 15 E e NN work_fnploejenbc2raktl46esxm44i 421 16 AZ AZ NNP work_fnploejenbc2raktl46esxm44i 421 17 , , , work_fnploejenbc2raktl46esxm44i 421 18 with with IN work_fnploejenbc2raktl46esxm44i 421 19 respect respect NN work_fnploejenbc2raktl46esxm44i 421 20 to to IN work_fnploejenbc2raktl46esxm44i 421 21 a a DT work_fnploejenbc2raktl46esxm44i 421 22 prior prior JJ work_fnploejenbc2raktl46esxm44i 421 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 421 24 q q NNP work_fnploejenbc2raktl46esxm44i 421 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 421 26 . . . work_fnploejenbc2raktl46esxm44i 422 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 422 2 , , , work_fnploejenbc2raktl46esxm44i 422 3 z. z. NNP work_fnploejenbc2raktl46esxm44i 423 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 423 2 . . . work_fnploejenbc2raktl46esxm44i 423 3 , , , work_fnploejenbc2raktl46esxm44i 423 4 + + SYM work_fnploejenbc2raktl46esxm44i 423 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 423 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 423 7 is be VBZ work_fnploejenbc2raktl46esxm44i 423 8 so so IN work_fnploejenbc2raktl46esxm44i 423 9 that that IN work_fnploejenbc2raktl46esxm44i 423 10 the the DT work_fnploejenbc2raktl46esxm44i 423 11 mixed mixed JJ work_fnploejenbc2raktl46esxm44i 423 12 extension extension NN work_fnploejenbc2raktl46esxm44i 423 13 of of IN work_fnploejenbc2raktl46esxm44i 423 14 G g NN work_fnploejenbc2raktl46esxm44i 423 15 ; ; : work_fnploejenbc2raktl46esxm44i 423 16 , , , work_fnploejenbc2raktl46esxm44i 423 17 is be VBZ work_fnploejenbc2raktl46esxm44i 423 18 Similarly similarly RB work_fnploejenbc2raktl46esxm44i 423 19 , , , work_fnploejenbc2raktl46esxm44i 423 20 the the DT work_fnploejenbc2raktl46esxm44i 423 21 mixed mixed JJ work_fnploejenbc2raktl46esxm44i 423 22 extension extension NN work_fnploejenbc2raktl46esxm44i 423 23 of of IN work_fnploejenbc2raktl46esxm44i 423 24 the the DT work_fnploejenbc2raktl46esxm44i 423 25 subgame subgame NN work_fnploejenbc2raktl46esxm44i 423 26 CT CT NNP work_fnploejenbc2raktl46esxm44i 423 27 , , , work_fnploejenbc2raktl46esxm44i 423 28 , , , work_fnploejenbc2raktl46esxm44i 423 29 , , , work_fnploejenbc2raktl46esxm44i 423 30 is be VBZ work_fnploejenbc2raktl46esxm44i 423 31 where where WRB work_fnploejenbc2raktl46esxm44i 423 32 ~~,+,a ~~,+,a NNP work_fnploejenbc2raktl46esxm44i 423 33 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 423 34 & & CC work_fnploejenbc2raktl46esxm44i 423 35 PL PL NNP work_fnploejenbc2raktl46esxm44i 423 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 423 37 = = NFP work_fnploejenbc2raktl46esxm44i 423 38 Cj$ cj$ XX work_fnploejenbc2raktl46esxm44i 423 39 ’ ' '' work_fnploejenbc2raktl46esxm44i 423 40 Lf lf VB work_fnploejenbc2raktl46esxm44i 423 41 , , , work_fnploejenbc2raktl46esxm44i 423 42 S S NNP work_fnploejenbc2raktl46esxm44i 423 43 , , , work_fnploejenbc2raktl46esxm44i 423 44 A(Bj A(Bj NNP work_fnploejenbc2raktl46esxm44i 423 45 , , , work_fnploejenbc2raktl46esxm44i 423 46 P P NNP work_fnploejenbc2raktl46esxm44i 423 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 423 48 NBj nbj NN work_fnploejenbc2raktl46esxm44i 423 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 423 50 . . . work_fnploejenbc2raktl46esxm44i 424 1 Now now RB work_fnploejenbc2raktl46esxm44i 424 2 , , , work_fnploejenbc2raktl46esxm44i 424 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 424 4 view view VBP work_fnploejenbc2raktl46esxm44i 424 5 the the DT work_fnploejenbc2raktl46esxm44i 424 6 subgame subgame NN work_fnploejenbc2raktl46esxm44i 424 7 GTti,~=(n(A gtti,~=(n(a CD work_fnploejenbc2raktl46esxm44i 424 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 9 , , , work_fnploejenbc2raktl46esxm44i 424 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 424 11 a a DT work_fnploejenbc2raktl46esxm44i 424 12 , , , work_fnploejenbc2raktl46esxm44i 424 13 , , , work_fnploejenbc2raktl46esxm44i 424 14 uSI uSI NNP work_fnploejenbc2raktl46esxm44i 424 15 ’ ' '' work_fnploejenbc2raktl46esxm44i 424 16 , , , work_fnploejenbc2raktl46esxm44i 424 17 L!$,J L!$,J NNP work_fnploejenbc2raktl46esxm44i 424 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 19 as as IN work_fnploejenbc2raktl46esxm44i 424 20 a a DT work_fnploejenbc2raktl46esxm44i 424 21 statistical statistical JJ work_fnploejenbc2raktl46esxm44i 424 22 game game NN work_fnploejenbc2raktl46esxm44i 424 23 coupled couple VBN work_fnploejenbc2raktl46esxm44i 424 24 with with IN work_fnploejenbc2raktl46esxm44i 424 25 the the DT work_fnploejenbc2raktl46esxm44i 424 26 random random JJ work_fnploejenbc2raktl46esxm44i 424 27 variable variable JJ work_fnploejenbc2raktl46esxm44i 424 28 X x NN work_fnploejenbc2raktl46esxm44i 424 29 whose whose WP$ work_fnploejenbc2raktl46esxm44i 424 30 distribution distribution NN work_fnploejenbc2raktl46esxm44i 424 31 P p NN work_fnploejenbc2raktl46esxm44i 424 32 , , , work_fnploejenbc2raktl46esxm44i 424 33 depends depend VBZ work_fnploejenbc2raktl46esxm44i 424 34 on on IN work_fnploejenbc2raktl46esxm44i 424 35 BE BE NNP work_fnploejenbc2raktl46esxm44i 424 36 n(a n(a NNP work_fnploejenbc2raktl46esxm44i 424 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 38 ; ; : work_fnploejenbc2raktl46esxm44i 424 39 when when WRB work_fnploejenbc2raktl46esxm44i 424 40 X X NNP work_fnploejenbc2raktl46esxm44i 424 41 is be VBZ work_fnploejenbc2raktl46esxm44i 424 42 constant constant JJ work_fnploejenbc2raktl46esxm44i 424 43 , , , work_fnploejenbc2raktl46esxm44i 424 44 on on IN work_fnploejenbc2raktl46esxm44i 424 45 each each DT work_fnploejenbc2raktl46esxm44i 424 46 BE BE NNP work_fnploejenbc2raktl46esxm44i 424 47 n(a n(a NNP work_fnploejenbc2raktl46esxm44i 424 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 49 , , , work_fnploejenbc2raktl46esxm44i 424 50 the the DT work_fnploejenbc2raktl46esxm44i 424 51 risk risk NN work_fnploejenbc2raktl46esxm44i 424 52 is be VBZ work_fnploejenbc2raktl46esxm44i 424 53 L(B l(b JJ work_fnploejenbc2raktl46esxm44i 424 54 , , , work_fnploejenbc2raktl46esxm44i 424 55 p)+ p)+ NNP work_fnploejenbc2raktl46esxm44i 424 56 On on IN work_fnploejenbc2raktl46esxm44i 424 57 the the DT work_fnploejenbc2raktl46esxm44i 424 58 other other JJ work_fnploejenbc2raktl46esxm44i 424 59 hand hand NN work_fnploejenbc2raktl46esxm44i 424 60 , , , work_fnploejenbc2raktl46esxm44i 424 61 since since IN work_fnploejenbc2raktl46esxm44i 424 62 ~(2 ~(2 XX work_fnploejenbc2raktl46esxm44i 424 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 64 is be VBZ work_fnploejenbc2raktl46esxm44i 424 65 finite finite JJ work_fnploejenbc2raktl46esxm44i 424 66 , , , work_fnploejenbc2raktl46esxm44i 424 67 standard standard JJ work_fnploejenbc2raktl46esxm44i 424 68 results result NNS work_fnploejenbc2raktl46esxm44i 424 69 from from IN work_fnploejenbc2raktl46esxm44i 424 70 decision decision NN work_fnploejenbc2raktl46esxm44i 424 71 theory theory NN work_fnploejenbc2raktl46esxm44i 424 72 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 424 73 for for IN work_fnploejenbc2raktl46esxm44i 424 74 finite finite NNP work_fnploejenbc2raktl46esxm44i 424 75 games game NNS work_fnploejenbc2raktl46esxm44i 424 76 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 77 hold hold VBP work_fnploejenbc2raktl46esxm44i 424 78 for for IN work_fnploejenbc2raktl46esxm44i 424 79 Gzti Gzti NNP work_fnploejenbc2raktl46esxm44i 424 80 , , , work_fnploejenbc2raktl46esxm44i 424 81 A a DT work_fnploejenbc2raktl46esxm44i 424 82 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 424 83 see see UH work_fnploejenbc2raktl46esxm44i 424 84 , , , work_fnploejenbc2raktl46esxm44i 424 85 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 424 86 , , , work_fnploejenbc2raktl46esxm44i 424 87 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 424 88 7 7 CD work_fnploejenbc2raktl46esxm44i 424 89 , , , work_fnploejenbc2raktl46esxm44i 424 90 31 31 CD work_fnploejenbc2raktl46esxm44i 424 91 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 424 92 . . . work_fnploejenbc2raktl46esxm44i 425 1 Then then RB work_fnploejenbc2raktl46esxm44i 425 2 the the DT work_fnploejenbc2raktl46esxm44i 425 3 risk risk NN work_fnploejenbc2raktl46esxm44i 425 4 set set VBD work_fnploejenbc2raktl46esxm44i 425 5 L(D L(D NNP work_fnploejenbc2raktl46esxm44i 425 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 425 7 is be VBZ work_fnploejenbc2raktl46esxm44i 425 8 closed close VBN work_fnploejenbc2raktl46esxm44i 425 9 and and CC work_fnploejenbc2raktl46esxm44i 425 10 bounded bound VBN work_fnploejenbc2raktl46esxm44i 425 11 since since IN work_fnploejenbc2raktl46esxm44i 425 12 D d NN work_fnploejenbc2raktl46esxm44i 425 13 is be VBZ work_fnploejenbc2raktl46esxm44i 425 14 compact compact JJ work_fnploejenbc2raktl46esxm44i 425 15 in in IN work_fnploejenbc2raktl46esxm44i 425 16 R r NN work_fnploejenbc2raktl46esxm44i 425 17 ” " '' work_fnploejenbc2raktl46esxm44i 425 18 and and CC work_fnploejenbc2raktl46esxm44i 425 19 L l NN work_fnploejenbc2raktl46esxm44i 425 20 is be VBZ work_fnploejenbc2raktl46esxm44i 425 21 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 425 22 . . . work_fnploejenbc2raktl46esxm44i 426 1 For for IN work_fnploejenbc2raktl46esxm44i 426 2 convenience convenience NN work_fnploejenbc2raktl46esxm44i 426 3 , , , work_fnploejenbc2raktl46esxm44i 426 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 426 5 state state VBP work_fnploejenbc2raktl46esxm44i 426 6 below below IN work_fnploejenbc2raktl46esxm44i 426 7 some some DT work_fnploejenbc2raktl46esxm44i 426 8 definitions definition NNS work_fnploejenbc2raktl46esxm44i 426 9 and and CC work_fnploejenbc2raktl46esxm44i 426 10 basic basic JJ work_fnploejenbc2raktl46esxm44i 426 11 results result NNS work_fnploejenbc2raktl46esxm44i 426 12 . . . work_fnploejenbc2raktl46esxm44i 427 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 427 2 i i NN work_fnploejenbc2raktl46esxm44i 427 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 427 4 , , , work_fnploejenbc2raktl46esxm44i 427 5 U u NN work_fnploejenbc2raktl46esxm44i 427 6 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 427 7 E e NN work_fnploejenbc2raktl46esxm44i 427 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 427 9 a a DT work_fnploejenbc2raktl46esxm44i 427 10 , , , work_fnploejenbc2raktl46esxm44i 427 11 , , , work_fnploejenbc2raktl46esxm44i 427 12 al al NNP work_fnploejenbc2raktl46esxm44i 427 13 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 427 14 A A NNP work_fnploejenbc2raktl46esxm44i 427 15 is be VBZ work_fnploejenbc2raktl46esxm44i 427 16 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 427 17 with with IN work_fnploejenbc2raktl46esxm44i 427 18 respect respect NN work_fnploejenbc2raktl46esxm44i 427 19 to to IN work_fnploejenbc2raktl46esxm44i 427 20 a a DT work_fnploejenbc2raktl46esxm44i 427 21 prior prior JJ work_fnploejenbc2raktl46esxm44i 427 22 distribution distribution NN work_fnploejenbc2raktl46esxm44i 427 23 r r NN work_fnploejenbc2raktl46esxm44i 427 24 on on IN work_fnploejenbc2raktl46esxm44i 427 25 . . . work_fnploejenbc2raktl46esxm44i 428 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 428 2 A a NN work_fnploejenbc2raktl46esxm44i 428 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 428 4 if if IN work_fnploejenbc2raktl46esxm44i 428 5 which which WDT work_fnploejenbc2raktl46esxm44i 428 6 is be VBZ work_fnploejenbc2raktl46esxm44i 428 7 the the DT work_fnploejenbc2raktl46esxm44i 428 8 minimum minimum JJ work_fnploejenbc2raktl46esxm44i 428 9 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 428 10 risk risk NN work_fnploejenbc2raktl46esxm44i 428 11 ; ; : work_fnploejenbc2raktl46esxm44i 428 12 E E NNS work_fnploejenbc2raktl46esxm44i 428 13 , , , work_fnploejenbc2raktl46esxm44i 428 14 denotes denote VBZ work_fnploejenbc2raktl46esxm44i 428 15 the the DT work_fnploejenbc2raktl46esxm44i 428 16 expectation expectation NN work_fnploejenbc2raktl46esxm44i 428 17 with with IN work_fnploejenbc2raktl46esxm44i 428 18 respect respect NN work_fnploejenbc2raktl46esxm44i 428 19 to to IN work_fnploejenbc2raktl46esxm44i 428 20 t. t. NN work_fnploejenbc2raktl46esxm44i 428 21 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 428 22 write write VBP work_fnploejenbc2raktl46esxm44i 428 23 , , , work_fnploejenbc2raktl46esxm44i 428 24 nL nL NNP work_fnploejenbc2raktl46esxm44i 428 25 , , , work_fnploejenbc2raktl46esxm44i 428 26 for for IN work_fnploejenbc2raktl46esxm44i 428 27 the the DT work_fnploejenbc2raktl46esxm44i 428 28 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 428 29 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 428 30 measure measure NN work_fnploejenbc2raktl46esxm44i 428 31 with with IN work_fnploejenbc2raktl46esxm44i 428 32 respect respect NN work_fnploejenbc2raktl46esxm44i 428 33 to to IN work_fnploejenbc2raktl46esxm44i 428 34 r. r. NNP work_fnploejenbc2raktl46esxm44i 428 35 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 428 36 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 428 37 TO to IN work_fnploejenbc2raktl46esxm44i 428 38 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 428 39 571 571 CD work_fnploejenbc2raktl46esxm44i 428 40 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 428 41 ii ii NN work_fnploejenbc2raktl46esxm44i 428 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 428 43 r0 r0 NNP work_fnploejenbc2raktl46esxm44i 428 44 is be VBZ work_fnploejenbc2raktl46esxm44i 428 45 a a DT work_fnploejenbc2raktl46esxm44i 428 46 least least RBS work_fnploejenbc2raktl46esxm44i 428 47 favorable favorable JJ work_fnploejenbc2raktl46esxm44i 428 48 prior prior RB work_fnploejenbc2raktl46esxm44i 428 49 if if IN work_fnploejenbc2raktl46esxm44i 428 50 infE,,L(.,~)=supinfE infe,,l(.,~)=supinfe UH work_fnploejenbc2raktl46esxm44i 428 51 , , , work_fnploejenbc2raktl46esxm44i 428 52 L(.,~ L(.,~ NNP work_fnploejenbc2raktl46esxm44i 428 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 428 54 P p NN work_fnploejenbc2raktl46esxm44i 428 55 7 7 CD work_fnploejenbc2raktl46esxm44i 428 56 p p NN work_fnploejenbc2raktl46esxm44i 428 57 which which WDT work_fnploejenbc2raktl46esxm44i 428 58 is be VBZ work_fnploejenbc2raktl46esxm44i 428 59 the the DT work_fnploejenbc2raktl46esxm44i 428 60 lower low JJR work_fnploejenbc2raktl46esxm44i 428 61 value value NN work_fnploejenbc2raktl46esxm44i 428 62 of of IN work_fnploejenbc2raktl46esxm44i 428 63 the the DT work_fnploejenbc2raktl46esxm44i 428 64 game game NN work_fnploejenbc2raktl46esxm44i 428 65 . . . work_fnploejenbc2raktl46esxm44i 429 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 429 2 iii iii NN work_fnploejenbc2raktl46esxm44i 429 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 429 4 % % NN work_fnploejenbc2raktl46esxm44i 429 5 ? ? . work_fnploejenbc2raktl46esxm44i 429 6 L l NN work_fnploejenbc2raktl46esxm44i 429 7 ~cz ~cz NNP work_fnploejenbc2raktl46esxm44i 429 8 , , , work_fnploejenbc2raktl46esxm44i 429 9 , , , work_fnploejenbc2raktl46esxm44i 429 10 a a DT work_fnploejenbc2raktl46esxm44i 429 11 , , , work_fnploejenbc2raktl46esxm44i 429 12 ld ld NNP work_fnploejenbc2raktl46esxm44i 429 13 is be VBZ work_fnploejenbc2raktl46esxm44i 429 14 complete complete JJ work_fnploejenbc2raktl46esxm44i 429 15 if if IN work_fnploejenbc2raktl46esxm44i 429 16 for for IN work_fnploejenbc2raktl46esxm44i 429 17 each each DT work_fnploejenbc2raktl46esxm44i 429 18 ALE ALE NNP work_fnploejenbc2raktl46esxm44i 429 19 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 429 20 a a DT work_fnploejenbc2raktl46esxm44i 429 21 , , , work_fnploejenbc2raktl46esxm44i 429 22 , , , work_fnploejenbc2raktl46esxm44i 429 23 a,]“--% a,]“--% NNP work_fnploejenbc2raktl46esxm44i 429 24 ‘ ' `` work_fnploejenbc2raktl46esxm44i 429 25 , , , work_fnploejenbc2raktl46esxm44i 429 26 there there EX work_fnploejenbc2raktl46esxm44i 429 27 is be VBZ work_fnploejenbc2raktl46esxm44i 429 28 v v NN work_fnploejenbc2raktl46esxm44i 429 29 E e NN work_fnploejenbc2raktl46esxm44i 429 30 % % NN work_fnploejenbc2raktl46esxm44i 429 31 ? ? . work_fnploejenbc2raktl46esxm44i 430 1 which which WDT work_fnploejenbc2raktl46esxm44i 430 2 is be VBZ work_fnploejenbc2raktl46esxm44i 430 3 “ " `` work_fnploejenbc2raktl46esxm44i 430 4 better well JJR work_fnploejenbc2raktl46esxm44i 430 5 ” " '' work_fnploejenbc2raktl46esxm44i 430 6 than than IN work_fnploejenbc2raktl46esxm44i 430 7 p p NN work_fnploejenbc2raktl46esxm44i 430 8 , , , work_fnploejenbc2raktl46esxm44i 430 9 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 430 10 , , , work_fnploejenbc2raktl46esxm44i 430 11 L L NNP work_fnploejenbc2raktl46esxm44i 430 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 430 13 . . . work_fnploejenbc2raktl46esxm44i 430 14 , , , work_fnploejenbc2raktl46esxm44i 430 15 VI VI NNP work_fnploejenbc2raktl46esxm44i 430 16 cw cw NNP work_fnploejenbc2raktl46esxm44i 430 17 L L NNP work_fnploejenbc2raktl46esxm44i 430 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 430 19 . . . work_fnploejenbc2raktl46esxm44i 430 20 , , , work_fnploejenbc2raktl46esxm44i 430 21 P p NN work_fnploejenbc2raktl46esxm44i 430 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 430 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 430 24 A a NN work_fnploejenbc2raktl46esxm44i 430 25 - - HYPH work_fnploejenbc2raktl46esxm44i 430 26 AD ad NN work_fnploejenbc2raktl46esxm44i 430 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 430 28 . . . work_fnploejenbc2raktl46esxm44i 431 1 V V NNP work_fnploejenbc2raktl46esxm44i 431 2 is be VBZ work_fnploejenbc2raktl46esxm44i 431 3 minimal minimal JJ work_fnploejenbc2raktl46esxm44i 431 4 complete complete JJ work_fnploejenbc2raktl46esxm44i 431 5 if if IN work_fnploejenbc2raktl46esxm44i 431 6 % % NN work_fnploejenbc2raktl46esxm44i 431 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 431 8 is be VBZ work_fnploejenbc2raktl46esxm44i 431 9 complete complete JJ work_fnploejenbc2raktl46esxm44i 431 10 but but CC work_fnploejenbc2raktl46esxm44i 431 11 no no DT work_fnploejenbc2raktl46esxm44i 431 12 proper proper JJ work_fnploejenbc2raktl46esxm44i 431 13 subclass subclass NN work_fnploejenbc2raktl46esxm44i 431 14 of of IN work_fnploejenbc2raktl46esxm44i 431 15 5 5 CD work_fnploejenbc2raktl46esxm44i 431 16 % % NN work_fnploejenbc2raktl46esxm44i 431 17 ’ ' '' work_fnploejenbc2raktl46esxm44i 431 18 is be VBZ work_fnploejenbc2raktl46esxm44i 431 19 complete complete JJ work_fnploejenbc2raktl46esxm44i 431 20 . . . work_fnploejenbc2raktl46esxm44i 432 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 2 iv iv LS work_fnploejenbc2raktl46esxm44i 432 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 4 For for IN work_fnploejenbc2raktl46esxm44i 432 5 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 432 6 of of IN work_fnploejenbc2raktl46esxm44i 432 7 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 432 8 rules rule NNS work_fnploejenbc2raktl46esxm44i 432 9 in in IN work_fnploejenbc2raktl46esxm44i 432 10 G~, g~, NN work_fnploejenbc2raktl46esxm44i 432 11 . . . work_fnploejenbc2raktl46esxm44i 432 12 A a DT work_fnploejenbc2raktl46esxm44i 432 13 , , , work_fnploejenbc2raktl46esxm44i 432 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 432 15 have have VBP work_fnploejenbc2raktl46esxm44i 432 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 17 a a LS work_fnploejenbc2raktl46esxm44i 432 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 19 If if IN work_fnploejenbc2raktl46esxm44i 432 20 pL pL NNP work_fnploejenbc2raktl46esxm44i 432 21 , , , work_fnploejenbc2raktl46esxm44i 432 22 exists exist VBZ work_fnploejenbc2raktl46esxm44i 432 23 uniquely uniquely RB work_fnploejenbc2raktl46esxm44i 432 24 up up IN work_fnploejenbc2raktl46esxm44i 432 25 to to TO work_fnploejenbc2raktl46esxm44i 432 26 equivalence equivalence NN work_fnploejenbc2raktl46esxm44i 432 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 28 p p NN work_fnploejenbc2raktl46esxm44i 432 29 - - HYPH work_fnploejenbc2raktl46esxm44i 432 30 v v NN work_fnploejenbc2raktl46esxm44i 432 31 if if IN work_fnploejenbc2raktl46esxm44i 432 32 and and CC work_fnploejenbc2raktl46esxm44i 432 33 only only RB work_fnploejenbc2raktl46esxm44i 432 34 if if IN work_fnploejenbc2raktl46esxm44i 432 35 L L NNP work_fnploejenbc2raktl46esxm44i 432 36 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 37 . . . work_fnploejenbc2raktl46esxm44i 432 38 , , , work_fnploejenbc2raktl46esxm44i 432 39 p p LS work_fnploejenbc2raktl46esxm44i 432 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 41 = = NFP work_fnploejenbc2raktl46esxm44i 432 42 L L NNP work_fnploejenbc2raktl46esxm44i 432 43 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 44 . . . work_fnploejenbc2raktl46esxm44i 432 45 , , , work_fnploejenbc2raktl46esxm44i 432 46 v v LS work_fnploejenbc2raktl46esxm44i 432 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 49 , , , work_fnploejenbc2raktl46esxm44i 432 50 then then RB work_fnploejenbc2raktl46esxm44i 432 51 pL pL NNP work_fnploejenbc2raktl46esxm44i 432 52 , , , work_fnploejenbc2raktl46esxm44i 432 53 is be VBZ work_fnploejenbc2raktl46esxm44i 432 54 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 432 55 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 432 56 A a NN work_fnploejenbc2raktl46esxm44i 432 57 - - HYPH work_fnploejenbc2raktl46esxm44i 432 58 AD ad NN work_fnploejenbc2raktl46esxm44i 432 59 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 432 60 . . . work_fnploejenbc2raktl46esxm44i 433 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 433 2 b b LS work_fnploejenbc2raktl46esxm44i 433 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 433 4 If if IN work_fnploejenbc2raktl46esxm44i 433 5 the the DT work_fnploejenbc2raktl46esxm44i 433 6 prior prior JJ work_fnploejenbc2raktl46esxm44i 433 7 r r NN work_fnploejenbc2raktl46esxm44i 433 8 is be VBZ work_fnploejenbc2raktl46esxm44i 433 9 strictly strictly RB work_fnploejenbc2raktl46esxm44i 433 10 positive positive JJ work_fnploejenbc2raktl46esxm44i 433 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 433 12 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 433 13 , , , work_fnploejenbc2raktl46esxm44i 433 14 r(B r(B `` work_fnploejenbc2raktl46esxm44i 433 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 433 16 > > XX work_fnploejenbc2raktl46esxm44i 433 17 0 0 NFP work_fnploejenbc2raktl46esxm44i 433 18 , , , work_fnploejenbc2raktl46esxm44i 433 19 VBE VBE NNP work_fnploejenbc2raktl46esxm44i 433 20 n(a n(a NNP work_fnploejenbc2raktl46esxm44i 433 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 433 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 433 23 , , , work_fnploejenbc2raktl46esxm44i 433 24 then then RB work_fnploejenbc2raktl46esxm44i 433 25 pz pz NNP work_fnploejenbc2raktl46esxm44i 433 26 exists exist VBZ work_fnploejenbc2raktl46esxm44i 433 27 , , , work_fnploejenbc2raktl46esxm44i 433 28 and and CC work_fnploejenbc2raktl46esxm44i 433 29 is be VBZ work_fnploejenbc2raktl46esxm44i 433 30 A a NN work_fnploejenbc2raktl46esxm44i 433 31 - - HYPH work_fnploejenbc2raktl46esxm44i 433 32 AD ad NN work_fnploejenbc2raktl46esxm44i 433 33 . . . work_fnploejenbc2raktl46esxm44i 434 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 434 2 v v LS work_fnploejenbc2raktl46esxm44i 434 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 434 4 If if IN work_fnploejenbc2raktl46esxm44i 434 5 p p NN work_fnploejenbc2raktl46esxm44i 434 6 is be VBZ work_fnploejenbc2raktl46esxm44i 434 7 A a NN work_fnploejenbc2raktl46esxm44i 434 8 - - HYPH work_fnploejenbc2raktl46esxm44i 434 9 AD ad NN work_fnploejenbc2raktl46esxm44i 434 10 , , , work_fnploejenbc2raktl46esxm44i 434 11 then then RB work_fnploejenbc2raktl46esxm44i 434 12 p p NN work_fnploejenbc2raktl46esxm44i 434 13 = = SYM work_fnploejenbc2raktl46esxm44i 434 14 pr pr XX work_fnploejenbc2raktl46esxm44i 434 15 for for IN work_fnploejenbc2raktl46esxm44i 434 16 some some DT work_fnploejenbc2raktl46esxm44i 434 17 r. r. NNP work_fnploejenbc2raktl46esxm44i 434 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 434 19 vi vi NNP work_fnploejenbc2raktl46esxm44i 434 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 434 21 The the DT work_fnploejenbc2raktl46esxm44i 434 22 class class NN work_fnploejenbc2raktl46esxm44i 434 23 of of IN work_fnploejenbc2raktl46esxm44i 434 24 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 434 25 rules rule NNS work_fnploejenbc2raktl46esxm44i 434 26 is be VBZ work_fnploejenbc2raktl46esxm44i 434 27 complete complete JJ work_fnploejenbc2raktl46esxm44i 434 28 , , , work_fnploejenbc2raktl46esxm44i 434 29 and and CC work_fnploejenbc2raktl46esxm44i 434 30 the the DT work_fnploejenbc2raktl46esxm44i 434 31 class class NN work_fnploejenbc2raktl46esxm44i 434 32 of of IN work_fnploejenbc2raktl46esxm44i 434 33 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 434 34 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 434 35 rules rule NNS work_fnploejenbc2raktl46esxm44i 434 36 is be VBZ work_fnploejenbc2raktl46esxm44i 434 37 minimal minimal JJ work_fnploejenbc2raktl46esxm44i 434 38 complete complete JJ work_fnploejenbc2raktl46esxm44i 434 39 . . . work_fnploejenbc2raktl46esxm44i 435 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 435 2 vii vii NN work_fnploejenbc2raktl46esxm44i 435 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 435 4 Let let VB work_fnploejenbc2raktl46esxm44i 435 5 6r~ 6r~ NNP work_fnploejenbc2raktl46esxm44i 435 6 & & CC work_fnploejenbc2raktl46esxm44i 435 7 ; ; : work_fnploejenbc2raktl46esxm44i 435 8 then then RB work_fnploejenbc2raktl46esxm44i 435 9 p p NNP work_fnploejenbc2raktl46esxm44i 435 10 is be VBZ work_fnploejenbc2raktl46esxm44i 435 11 said say VBN work_fnploejenbc2raktl46esxm44i 435 12 to to TO work_fnploejenbc2raktl46esxm44i 435 13 be be VB work_fnploejenbc2raktl46esxm44i 435 14 b b NNP work_fnploejenbc2raktl46esxm44i 435 15 - - HYPH work_fnploejenbc2raktl46esxm44i 435 16 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 435 17 if if IN work_fnploejenbc2raktl46esxm44i 435 18 p p NN work_fnploejenbc2raktl46esxm44i 435 19 is be VBZ work_fnploejenbc2raktl46esxm44i 435 20 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 435 21 with with IN work_fnploejenbc2raktl46esxm44i 435 22 respect respect NN work_fnploejenbc2raktl46esxm44i 435 23 to to IN work_fnploejenbc2raktl46esxm44i 435 24 Gzi,~ Gzi,~ NNP work_fnploejenbc2raktl46esxm44i 435 25 for for IN work_fnploejenbc2raktl46esxm44i 435 26 all all PDT work_fnploejenbc2raktl46esxm44i 435 27 a a DT work_fnploejenbc2raktl46esxm44i 435 28 E e NN work_fnploejenbc2raktl46esxm44i 435 29 8 8 CD work_fnploejenbc2raktl46esxm44i 435 30 ’ ' '' work_fnploejenbc2raktl46esxm44i 435 31 . . . work_fnploejenbc2raktl46esxm44i 436 1 In in IN work_fnploejenbc2raktl46esxm44i 436 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 436 3 , , , work_fnploejenbc2raktl46esxm44i 436 4 p p NNP work_fnploejenbc2raktl46esxm44i 436 5 is be VBZ work_fnploejenbc2raktl46esxm44i 436 6 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 436 7 Buyes Buyes NNP work_fnploejenbc2raktl46esxm44i 436 8 if if IN work_fnploejenbc2raktl46esxm44i 436 9 d d NNP work_fnploejenbc2raktl46esxm44i 436 10 = = SYM work_fnploejenbc2raktl46esxm44i 436 11 s s NNP work_fnploejenbc2raktl46esxm44i 436 12 & & CC work_fnploejenbc2raktl46esxm44i 436 13 . . . work_fnploejenbc2raktl46esxm44i 437 1 Note note VB work_fnploejenbc2raktl46esxm44i 437 2 that that IN work_fnploejenbc2raktl46esxm44i 437 3 p p NN work_fnploejenbc2raktl46esxm44i 437 4 is be VBZ work_fnploejenbc2raktl46esxm44i 437 5 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 437 6 with with IN work_fnploejenbc2raktl46esxm44i 437 7 respect respect NN work_fnploejenbc2raktl46esxm44i 437 8 to to IN work_fnploejenbc2raktl46esxm44i 437 9 G G NNP work_fnploejenbc2raktl46esxm44i 437 10 , , , work_fnploejenbc2raktl46esxm44i 437 11 ! ! . work_fnploejenbc2raktl46esxm44i 437 12 , , , work_fnploejenbc2raktl46esxm44i 437 13 when when WRB work_fnploejenbc2raktl46esxm44i 437 14 the the DT work_fnploejenbc2raktl46esxm44i 437 15 prior prior NN work_fnploejenbc2raktl46esxm44i 437 16 is be VBZ work_fnploejenbc2raktl46esxm44i 437 17 in in IN work_fnploejenbc2raktl46esxm44i 437 18 P(/l P(/l NNP work_fnploejenbc2raktl46esxm44i 437 19 , , , work_fnploejenbc2raktl46esxm44i 437 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 437 21 , , , work_fnploejenbc2raktl46esxm44i 437 22 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 437 23 , , , work_fnploejenbc2raktl46esxm44i 437 24 of of IN work_fnploejenbc2raktl46esxm44i 437 25 the the DT work_fnploejenbc2raktl46esxm44i 437 26 form form NN work_fnploejenbc2raktl46esxm44i 437 27 r r NNP work_fnploejenbc2raktl46esxm44i 437 28 = = SYM work_fnploejenbc2raktl46esxm44i 437 29 q q NNP work_fnploejenbc2raktl46esxm44i 437 30 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 437 31 . . . work_fnploejenbc2raktl46esxm44i 438 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 438 2 , , , work_fnploejenbc2raktl46esxm44i 438 3 r. r. NNP work_fnploejenbc2raktl46esxm44i 438 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 438 5 . . . work_fnploejenbc2raktl46esxm44i 438 6 , , , work_fnploejenbc2raktl46esxm44i 438 7 . . . work_fnploejenbc2raktl46esxm44i 438 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 438 9 . . . work_fnploejenbc2raktl46esxm44i 439 1 4.2 4.2 CD work_fnploejenbc2raktl46esxm44i 439 2 . . . work_fnploejenbc2raktl46esxm44i 440 1 Equivalences equivalence NNS work_fnploejenbc2raktl46esxm44i 440 2 of of IN work_fnploejenbc2raktl46esxm44i 440 3 Various various JJ work_fnploejenbc2raktl46esxm44i 440 4 Concepts concept NNS work_fnploejenbc2raktl46esxm44i 440 5 of of IN work_fnploejenbc2raktl46esxm44i 440 6 Admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 440 7 In in IN work_fnploejenbc2raktl46esxm44i 440 8 the the DT work_fnploejenbc2raktl46esxm44i 440 9 rest rest NN work_fnploejenbc2raktl46esxm44i 440 10 of of IN work_fnploejenbc2raktl46esxm44i 440 11 this this DT work_fnploejenbc2raktl46esxm44i 440 12 section section NN work_fnploejenbc2raktl46esxm44i 440 13 , , , work_fnploejenbc2raktl46esxm44i 440 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 440 15 consider consider VBP work_fnploejenbc2raktl46esxm44i 440 16 $ $ $ work_fnploejenbc2raktl46esxm44i 440 17 = = SYM work_fnploejenbc2raktl46esxm44i 440 18 + + XX work_fnploejenbc2raktl46esxm44i 440 19 . . . work_fnploejenbc2raktl46esxm44i 441 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 441 2 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 441 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 441 4 Equal Equal NNP work_fnploejenbc2raktl46esxm44i 441 5 Antecedent Antecedent NNP work_fnploejenbc2raktl46esxm44i 441 6 Form form NN work_fnploejenbc2raktl46esxm44i 441 7 of of IN work_fnploejenbc2raktl46esxm44i 441 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 441 9 16 16 CD work_fnploejenbc2raktl46esxm44i 441 10 , , , work_fnploejenbc2raktl46esxm44i 441 11 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 441 12 21 21 CD work_fnploejenbc2raktl46esxm44i 441 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 441 14 . . . work_fnploejenbc2raktl46esxm44i 442 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 442 2 the the DT work_fnploejenbc2raktl46esxm44i 442 3 game game NN work_fnploejenbc2raktl46esxm44i 442 4 Gl Gl NNP work_fnploejenbc2raktl46esxm44i 442 5 + + NNP work_fnploejenbc2raktl46esxm44i 442 6 with with IN work_fnploejenbc2raktl46esxm44i 442 7 f f NNP work_fnploejenbc2raktl46esxm44i 442 8 such such JJ work_fnploejenbc2raktl46esxm44i 442 9 that that IN work_fnploejenbc2raktl46esxm44i 442 10 PY PY NNP work_fnploejenbc2raktl46esxm44i 442 11 is be VBZ work_fnploejenbc2raktl46esxm44i 442 12 increasing increase VBG work_fnploejenbc2raktl46esxm44i 442 13 . . . work_fnploejenbc2raktl46esxm44i 443 1 Let let VB work_fnploejenbc2raktl46esxm44i 443 2 p p NN work_fnploejenbc2raktl46esxm44i 443 3 E e VB work_fnploejenbc2raktl46esxm44i 443 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 443 5 a a DT work_fnploejenbc2raktl46esxm44i 443 6 , , , work_fnploejenbc2raktl46esxm44i 443 7 , , , work_fnploejenbc2raktl46esxm44i 443 8 alId alid UH work_fnploejenbc2raktl46esxm44i 443 9 . . . work_fnploejenbc2raktl46esxm44i 444 1 The the DT work_fnploejenbc2raktl46esxm44i 444 2 following follow VBG work_fnploejenbc2raktl46esxm44i 444 3 are be VBP work_fnploejenbc2raktl46esxm44i 444 4 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 444 5 . . . work_fnploejenbc2raktl46esxm44i 445 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 445 2 i i NN work_fnploejenbc2raktl46esxm44i 445 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 445 4 u u NNP work_fnploejenbc2raktl46esxm44i 445 5 is be VBZ work_fnploejenbc2raktl46esxm44i 445 6 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 445 7 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 445 8 , , , work_fnploejenbc2raktl46esxm44i 445 9 w.r.t w.r.t JJ work_fnploejenbc2raktl46esxm44i 445 10 . . . work_fnploejenbc2raktl46esxm44i 446 1 all all DT work_fnploejenbc2raktl46esxm44i 446 2 finite finite NNP work_fnploejenbc2raktl46esxm44i 446 3 equal equal JJ work_fnploejenbc2raktl46esxm44i 446 4 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 446 5 condi- condi- NNP work_fnploejenbc2raktl46esxm44i 446 6 tional tional JJ work_fnploejenbc2raktl46esxm44i 446 7 event event NN work_fnploejenbc2raktl46esxm44i 446 8 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 446 9 . . . work_fnploejenbc2raktl46esxm44i 447 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 447 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 447 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 447 4 p p NNP work_fnploejenbc2raktl46esxm44i 447 5 is be VBZ work_fnploejenbc2raktl46esxm44i 447 6 & & CC work_fnploejenbc2raktl46esxm44i 447 7 and and CC work_fnploejenbc2raktl46esxm44i 447 8 & & CC work_fnploejenbc2raktl46esxm44i 447 9 -weak -weak VB work_fnploejenbc2raktl46esxm44i 447 10 local local JJ work_fnploejenbc2raktl46esxm44i 447 11 admissible admissible NN work_fnploejenbc2raktl46esxm44i 447 12 . . . work_fnploejenbc2raktl46esxm44i 448 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 448 2 iii iii NNP work_fnploejenbc2raktl46esxm44i 448 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 448 4 u u NNP work_fnploejenbc2raktl46esxm44i 448 5 is be VBZ work_fnploejenbc2raktl46esxm44i 448 6 untform untform JJ work_fnploejenbc2raktl46esxm44i 448 7 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 448 8 , , , work_fnploejenbc2raktl46esxm44i 448 9 w.r.t w.r.t NNP work_fnploejenbc2raktl46esxm44i 448 10 . . . work_fnploejenbc2raktl46esxm44i 449 1 all all DT work_fnploejenbc2raktl46esxm44i 449 2 finite finite NNP work_fnploejenbc2raktl46esxm44i 449 3 equal equal JJ work_fnploejenbc2raktl46esxm44i 449 4 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 449 5 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 449 6 event event NN work_fnploejenbc2raktl46esxm44i 449 7 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 449 8 . . . work_fnploejenbc2raktl46esxm44i 450 1 tttve tttve NNP work_fnploejenbc2raktl46esxm44i 450 2 probability probability NN work_fnploejenbc2raktl46esxm44i 450 3 measure measure NN work_fnploejenbc2raktl46esxm44i 450 4 , , , work_fnploejenbc2raktl46esxm44i 450 5 for for IN work_fnploejenbc2raktl46esxm44i 450 6 all all DT work_fnploejenbc2raktl46esxm44i 450 7 PEvL pevl JJ work_fnploejenbc2raktl46esxm44i 450 8 Prop Prop NNP work_fnploejenbc2raktl46esxm44i 450 9 : : : work_fnploejenbc2raktl46esxm44i 450 10 ~4~ ~4~ ADD work_fnploejenbc2raktl46esxm44i 450 11 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 450 12 0 0 CD work_fnploejenbc2raktl46esxm44i 450 13 , , , work_fnploejenbc2raktl46esxm44i 450 14 l l NN work_fnploejenbc2raktl46esxm44i 450 15 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 450 16 is be VBZ work_fnploejenbc2raktl46esxm44i 450 17 a a DT work_fnploejenbc2raktl46esxm44i 450 18 finitely finitely RB work_fnploejenbc2raktl46esxm44i 450 19 add add VB work_fnploejenbc2raktl46esxm44i 450 20 ’ ' '' work_fnploejenbc2raktl46esxm44i 450 21 Proof Proof NNP work_fnploejenbc2raktl46esxm44i 450 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 450 23 i i NN work_fnploejenbc2raktl46esxm44i 450 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 450 25 = = NFP work_fnploejenbc2raktl46esxm44i 450 26 S S NNP work_fnploejenbc2raktl46esxm44i 450 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 450 28 ii ii NNP work_fnploejenbc2raktl46esxm44i 450 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 450 30 . . . work_fnploejenbc2raktl46esxm44i 451 1 Obvious obvious JJ work_fnploejenbc2raktl46esxm44i 451 2 by by IN work_fnploejenbc2raktl46esxm44i 451 3 definition definition NN work_fnploejenbc2raktl46esxm44i 451 4 . . . work_fnploejenbc2raktl46esxm44i 452 1 W w NN work_fnploejenbc2raktl46esxm44i 452 2 / / SYM work_fnploejenbc2raktl46esxm44i 452 3 l l NN work_fnploejenbc2raktl46esxm44i 452 4 5912 5912 CD work_fnploejenbc2raktl46esxm44i 452 5 . . . work_fnploejenbc2raktl46esxm44i 453 1 I9 I9 NNP work_fnploejenbc2raktl46esxm44i 453 2 572 572 CD work_fnploejenbc2raktl46esxm44i 453 3 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 453 4 , , , work_fnploejenbc2raktl46esxm44i 453 5 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 453 6 , , , work_fnploejenbc2raktl46esxm44i 453 7 ANDROGERS ANDROGERS NNP work_fnploejenbc2raktl46esxm44i 453 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 453 9 i i NN work_fnploejenbc2raktl46esxm44i 453 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 453 11 = = NFP work_fnploejenbc2raktl46esxm44i 453 12 z. z. NNP work_fnploejenbc2raktl46esxm44i 454 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 454 2 iii iii NNP work_fnploejenbc2raktl46esxm44i 454 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 454 4 . . . work_fnploejenbc2raktl46esxm44i 455 1 Follows follow VBZ work_fnploejenbc2raktl46esxm44i 455 2 by by IN work_fnploejenbc2raktl46esxm44i 455 3 standard standard JJ work_fnploejenbc2raktl46esxm44i 455 4 results result NNS work_fnploejenbc2raktl46esxm44i 455 5 of of IN work_fnploejenbc2raktl46esxm44i 455 6 the the DT work_fnploejenbc2raktl46esxm44i 455 7 game game NN work_fnploejenbc2raktl46esxm44i 455 8 GT GT NNP work_fnploejenbc2raktl46esxm44i 455 9 + + CD work_fnploejenbc2raktl46esxm44i 455 10 , , , work_fnploejenbc2raktl46esxm44i 455 11 2 2 CD work_fnploejenbc2raktl46esxm44i 455 12 , , , work_fnploejenbc2raktl46esxm44i 455 13 namely namely RB work_fnploejenbc2raktl46esxm44i 455 14 if if IN work_fnploejenbc2raktl46esxm44i 455 15 p p NN work_fnploejenbc2raktl46esxm44i 455 16 is be VBZ work_fnploejenbc2raktl46esxm44i 455 17 A a NN work_fnploejenbc2raktl46esxm44i 455 18 - - HYPH work_fnploejenbc2raktl46esxm44i 455 19 AD ad NN work_fnploejenbc2raktl46esxm44i 455 20 , , , work_fnploejenbc2raktl46esxm44i 455 21 then then RB work_fnploejenbc2raktl46esxm44i 455 22 , , , work_fnploejenbc2raktl46esxm44i 455 23 u u NNP work_fnploejenbc2raktl46esxm44i 455 24 is be VBZ work_fnploejenbc2raktl46esxm44i 455 25 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 455 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 455 27 with with IN work_fnploejenbc2raktl46esxm44i 455 28 respect respect NN work_fnploejenbc2raktl46esxm44i 455 29 to to IN work_fnploejenbc2raktl46esxm44i 455 30 some some DT work_fnploejenbc2raktl46esxm44i 455 31 prior prior JJ work_fnploejenbc2raktl46esxm44i 455 32 z z NN work_fnploejenbc2raktl46esxm44i 455 33 on on IN work_fnploejenbc2raktl46esxm44i 455 34 . . . work_fnploejenbc2raktl46esxm44i 456 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 456 2 a a LS work_fnploejenbc2raktl46esxm44i 456 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 456 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 456 5 , , , work_fnploejenbc2raktl46esxm44i 456 6 and and CC work_fnploejenbc2raktl46esxm44i 456 7 conversely conversely RB work_fnploejenbc2raktl46esxm44i 456 8 , , , work_fnploejenbc2raktl46esxm44i 456 9 if if IN work_fnploejenbc2raktl46esxm44i 456 10 p p NN work_fnploejenbc2raktl46esxm44i 456 11 is be VBZ work_fnploejenbc2raktl46esxm44i 456 12 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 456 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 456 14 p p NNP work_fnploejenbc2raktl46esxm44i 456 15 = = NNPS work_fnploejenbc2raktl46esxm44i 456 16 , , , work_fnploejenbc2raktl46esxm44i 456 17 u~ u~ NNP work_fnploejenbc2raktl46esxm44i 456 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 456 19 , , , work_fnploejenbc2raktl46esxm44i 456 20 then then RB work_fnploejenbc2raktl46esxm44i 456 21 since since IN work_fnploejenbc2raktl46esxm44i 456 22 , , , work_fnploejenbc2raktl46esxm44i 456 23 u~ u~ NNP work_fnploejenbc2raktl46esxm44i 456 24 is be VBZ work_fnploejenbc2raktl46esxm44i 456 25 unique unique JJ work_fnploejenbc2raktl46esxm44i 456 26 , , , work_fnploejenbc2raktl46esxm44i 456 27 pL pL NNP work_fnploejenbc2raktl46esxm44i 456 28 , , , work_fnploejenbc2raktl46esxm44i 456 29 is be VBZ work_fnploejenbc2raktl46esxm44i 456 30 R r NN work_fnploejenbc2raktl46esxm44i 456 31 - - HYPH work_fnploejenbc2raktl46esxm44i 456 32 AD ad NN work_fnploejenbc2raktl46esxm44i 456 33 . . . work_fnploejenbc2raktl46esxm44i 457 1 The the DT work_fnploejenbc2raktl46esxm44i 457 2 uniqueness uniqueness NN work_fnploejenbc2raktl46esxm44i 457 3 of of IN work_fnploejenbc2raktl46esxm44i 457 4 e e NN work_fnploejenbc2raktl46esxm44i 457 5 , , , work_fnploejenbc2raktl46esxm44i 457 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 457 7 up up IN work_fnploejenbc2raktl46esxm44i 457 8 to to IN work_fnploejenbc2raktl46esxm44i 457 9 equivalence equivalence NN work_fnploejenbc2raktl46esxm44i 457 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 457 11 can can MD work_fnploejenbc2raktl46esxm44i 457 12 be be VB work_fnploejenbc2raktl46esxm44i 457 13 seen see VBN work_fnploejenbc2raktl46esxm44i 457 14 as as IN work_fnploejenbc2raktl46esxm44i 457 15 follows follow VBZ work_fnploejenbc2raktl46esxm44i 457 16 . . . work_fnploejenbc2raktl46esxm44i 458 1 Let let VB work_fnploejenbc2raktl46esxm44i 458 2 ZE ZE NNP work_fnploejenbc2raktl46esxm44i 458 3 P’(a(A P’(a(A NNP work_fnploejenbc2raktl46esxm44i 458 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 458 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 458 6 , , , work_fnploejenbc2raktl46esxm44i 458 7 a a FW work_fnploejenbc2raktl46esxm44i 458 8 = = NFP work_fnploejenbc2raktl46esxm44i 458 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 458 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 458 11 EiJFi EiJFi NNP work_fnploejenbc2raktl46esxm44i 458 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 458 13 , , , work_fnploejenbc2raktl46esxm44i 458 14 i= i= NNP work_fnploejenbc2raktl46esxm44i 458 15 1 1 CD work_fnploejenbc2raktl46esxm44i 458 16 , , , work_fnploejenbc2raktl46esxm44i 458 17 . . . work_fnploejenbc2raktl46esxm44i 459 1 . . . work_fnploejenbc2raktl46esxm44i 460 1 . . . work_fnploejenbc2raktl46esxm44i 461 1 . . . work_fnploejenbc2raktl46esxm44i 462 1 n n LS work_fnploejenbc2raktl46esxm44i 462 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 3 ; ; : work_fnploejenbc2raktl46esxm44i 462 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 462 5 have have VBP work_fnploejenbc2raktl46esxm44i 462 6 E7L(a e7l(a CD work_fnploejenbc2raktl46esxm44i 462 7 , , , work_fnploejenbc2raktl46esxm44i 462 8 PI= pi= XX work_fnploejenbc2raktl46esxm44i 462 9 i i PRP work_fnploejenbc2raktl46esxm44i 462 10 C C NNP work_fnploejenbc2raktl46esxm44i 462 11 fCP(Ai)3 fCP(Ai)3 NNP work_fnploejenbc2raktl46esxm44i 462 12 Ai(B)I Ai(B)I NNP work_fnploejenbc2raktl46esxm44i 462 13 T(B T(B NNP work_fnploejenbc2raktl46esxm44i 462 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 15 i i NN work_fnploejenbc2raktl46esxm44i 462 16 = = NFP work_fnploejenbc2raktl46esxm44i 462 17 l l NN work_fnploejenbc2raktl46esxm44i 462 18 Ben(A ben(a XX work_fnploejenbc2raktl46esxm44i 462 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 20 = = NFP work_fnploejenbc2raktl46esxm44i 462 21 , , , work_fnploejenbc2raktl46esxm44i 462 22 $ $ $ work_fnploejenbc2raktl46esxm44i 462 23 , , , work_fnploejenbc2raktl46esxm44i 462 24 { { -LRB- work_fnploejenbc2raktl46esxm44i 462 25 fCP(ai)9 fCP(ai)9 NNP work_fnploejenbc2raktl46esxm44i 462 26 ll will NNP work_fnploejenbc2raktl46esxm44i 462 27 C C NNP work_fnploejenbc2raktl46esxm44i 462 28 r(B r(b NN work_fnploejenbc2raktl46esxm44i 462 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 30 + + NFP work_fnploejenbc2raktl46esxm44i 462 31 fCPCAih fCPCAih NNP work_fnploejenbc2raktl46esxm44i 462 32 Ol old NN work_fnploejenbc2raktl46esxm44i 462 33 C c NN work_fnploejenbc2raktl46esxm44i 462 34 BE be NN work_fnploejenbc2raktl46esxm44i 462 35 QlW qlw NN work_fnploejenbc2raktl46esxm44i 462 36 BE be VB work_fnploejenbc2raktl46esxm44i 462 37 Q2(G q2(g CD work_fnploejenbc2raktl46esxm44i 462 38 Q,(i)= Q,(i)= NNP work_fnploejenbc2raktl46esxm44i 462 39 { { -LRB- work_fnploejenbc2raktl46esxm44i 462 40 BE7C(A BE7C(A NNP work_fnploejenbc2raktl46esxm44i 462 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 42 : : : work_fnploejenbc2raktl46esxm44i 462 43 BGEiFi BGEiFi NNP work_fnploejenbc2raktl46esxm44i 462 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 45 Then then RB work_fnploejenbc2raktl46esxm44i 462 46 Qz(i Qz(i NNP work_fnploejenbc2raktl46esxm44i 462 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 48 = = NFP work_fnploejenbc2raktl46esxm44i 462 49 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 462 50 BE be VB work_fnploejenbc2raktl46esxm44i 462 51 X(A X(A NNP work_fnploejenbc2raktl46esxm44i 462 52 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 462 53 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 462 54 BEiF,= BEiF,= NNP work_fnploejenbc2raktl46esxm44i 462 55 a a NN work_fnploejenbc2raktl46esxm44i 462 56 } } -RRB- work_fnploejenbc2raktl46esxm44i 462 57 . . . work_fnploejenbc2raktl46esxm44i 463 1 since since IN work_fnploejenbc2raktl46esxm44i 463 2 2 2 CD work_fnploejenbc2raktl46esxm44i 463 3 r(B)=l- r(b)=l- CD work_fnploejenbc2raktl46esxm44i 463 4 c c NN work_fnploejenbc2raktl46esxm44i 463 5 t(B t(b NN work_fnploejenbc2raktl46esxm44i 463 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 463 7 . . . work_fnploejenbc2raktl46esxm44i 464 1 BE be VB work_fnploejenbc2raktl46esxm44i 464 2 PAi PAi NNS work_fnploejenbc2raktl46esxm44i 464 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 4 BE BE NNP work_fnploejenbc2raktl46esxm44i 464 5 Ql(i Ql(i NNP work_fnploejenbc2raktl46esxm44i 464 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 7 Therefore therefore RB work_fnploejenbc2raktl46esxm44i 464 8 , , , work_fnploejenbc2raktl46esxm44i 464 9 p(Ai p(Ai NNP work_fnploejenbc2raktl46esxm44i 464 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 11 = = SYM work_fnploejenbc2raktl46esxm44i 464 12 P;l[&EQ P;l[&EQ NNP work_fnploejenbc2raktl46esxm44i 464 13 , , , work_fnploejenbc2raktl46esxm44i 464 14 cil cil NNP work_fnploejenbc2raktl46esxm44i 464 15 r(B r(b NN work_fnploejenbc2raktl46esxm44i 464 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 17 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 464 18 is be VBZ work_fnploejenbc2raktl46esxm44i 464 19 uniquely uniquely RB work_fnploejenbc2raktl46esxm44i 464 20 determined determine VBN work_fnploejenbc2raktl46esxm44i 464 21 by by IN work_fnploejenbc2raktl46esxm44i 464 22 r. r. NNP work_fnploejenbc2raktl46esxm44i 464 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 464 24 ii ii NNP work_fnploejenbc2raktl46esxm44i 464 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 26 * * NFP work_fnploejenbc2raktl46esxm44i 464 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 464 28 iv iv NN work_fnploejenbc2raktl46esxm44i 464 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 464 30 . . . work_fnploejenbc2raktl46esxm44i 465 1 By by IN work_fnploejenbc2raktl46esxm44i 465 2 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 465 3 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 465 4 ’ ' '' work_fnploejenbc2raktl46esxm44i 465 5 . . . work_fnploejenbc2raktl46esxm44i 466 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 466 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 466 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 466 4 * * NFP work_fnploejenbc2raktl46esxm44i 466 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 466 6 iii iii NNP work_fnploejenbc2raktl46esxm44i 466 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 466 8 . . . work_fnploejenbc2raktl46esxm44i 467 1 Assume Assume NNP work_fnploejenbc2raktl46esxm44i 467 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 467 3 ii ii NNP work_fnploejenbc2raktl46esxm44i 467 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 467 5 . . . work_fnploejenbc2raktl46esxm44i 468 1 Then then RB work_fnploejenbc2raktl46esxm44i 468 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 468 3 iv iv NN work_fnploejenbc2raktl46esxm44i 468 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 468 5 holds hold VBZ work_fnploejenbc2raktl46esxm44i 468 6 . . . work_fnploejenbc2raktl46esxm44i 469 1 Since since IN work_fnploejenbc2raktl46esxm44i 469 2 Cecnc~ cecnc~ NN work_fnploejenbc2raktl46esxm44i 469 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 469 4 r(B)= r(B)= NNP work_fnploejenbc2raktl46esxm44i 469 5 1 1 CD work_fnploejenbc2raktl46esxm44i 469 6 , , , work_fnploejenbc2raktl46esxm44i 469 7 r r NNP work_fnploejenbc2raktl46esxm44i 469 8 = = SYM work_fnploejenbc2raktl46esxm44i 469 9 Prop Prop NNP work_fnploejenbc2raktl46esxm44i 469 10 can can MD work_fnploejenbc2raktl46esxm44i 469 11 be be VB work_fnploejenbc2raktl46esxm44i 469 12 taken take VBN work_fnploejenbc2raktl46esxm44i 469 13 as as IN work_fnploejenbc2raktl46esxm44i 469 14 a a DT work_fnploejenbc2raktl46esxm44i 469 15 prior prior NN work_fnploejenbc2raktl46esxm44i 469 16 for for IN work_fnploejenbc2raktl46esxm44i 469 17 x(a x(a NNP work_fnploejenbc2raktl46esxm44i 469 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 469 19 . . . work_fnploejenbc2raktl46esxm44i 470 1 Then then RB work_fnploejenbc2raktl46esxm44i 470 2 p p NNP work_fnploejenbc2raktl46esxm44i 470 3 = = SYM work_fnploejenbc2raktl46esxm44i 470 4 ~1~ ~1~ NFP work_fnploejenbc2raktl46esxm44i 470 5 and and CC work_fnploejenbc2raktl46esxm44i 470 6 hence hence RB work_fnploejenbc2raktl46esxm44i 470 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 470 8 iii iii NN work_fnploejenbc2raktl46esxm44i 470 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 470 10 holds hold VBZ work_fnploejenbc2raktl46esxm44i 470 11 . . . work_fnploejenbc2raktl46esxm44i 471 1 Conversely conversely RB work_fnploejenbc2raktl46esxm44i 471 2 , , , work_fnploejenbc2raktl46esxm44i 471 3 when when WRB work_fnploejenbc2raktl46esxm44i 471 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 471 5 iii iii NN work_fnploejenbc2raktl46esxm44i 471 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 471 7 holds hold VBZ work_fnploejenbc2raktl46esxm44i 471 8 , , , work_fnploejenbc2raktl46esxm44i 471 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 471 10 i i NN work_fnploejenbc2raktl46esxm44i 471 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 471 12 also also RB work_fnploejenbc2raktl46esxm44i 471 13 holds hold VBZ work_fnploejenbc2raktl46esxm44i 471 14 , , , work_fnploejenbc2raktl46esxm44i 471 15 and and CC work_fnploejenbc2raktl46esxm44i 471 16 , , , work_fnploejenbc2raktl46esxm44i 471 17 a a DT work_fnploejenbc2raktl46esxm44i 471 18 fortiori fortiori NN work_fnploejenbc2raktl46esxm44i 471 19 , , , work_fnploejenbc2raktl46esxm44i 471 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 471 21 ii ii NNP work_fnploejenbc2raktl46esxm44i 471 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 471 23 . . . work_fnploejenbc2raktl46esxm44i 472 1 1 1 CD work_fnploejenbc2raktl46esxm44i 472 2 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 472 3 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 472 4 ’ ' '' work_fnploejenbc2raktl46esxm44i 472 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 472 6 Corresponds correspond NNS work_fnploejenbc2raktl46esxm44i 472 7 to to IN work_fnploejenbc2raktl46esxm44i 472 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 472 9 16 16 CD work_fnploejenbc2raktl46esxm44i 472 10 , , , work_fnploejenbc2raktl46esxm44i 472 11 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 472 12 21 21 CD work_fnploejenbc2raktl46esxm44i 472 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 472 14 . . . work_fnploejenbc2raktl46esxm44i 473 1 Make make VB work_fnploejenbc2raktl46esxm44i 473 2 the the DT work_fnploejenbc2raktl46esxm44i 473 3 same same JJ work_fnploejenbc2raktl46esxm44i 473 4 assumptions assumption NNS work_fnploejenbc2raktl46esxm44i 473 5 as as IN work_fnploejenbc2raktl46esxm44i 473 6 in in IN work_fnploejenbc2raktl46esxm44i 473 7 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 473 8 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 473 9 . . . work_fnploejenbc2raktl46esxm44i 474 1 Then then RB work_fnploejenbc2raktl46esxm44i 474 2 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 474 3 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 474 4 holds hold VBZ work_fnploejenbc2raktl46esxm44i 474 5 with with IN work_fnploejenbc2raktl46esxm44i 474 6 the the DT work_fnploejenbc2raktl46esxm44i 474 7 folIowing foliowing NN work_fnploejenbc2raktl46esxm44i 474 8 strengthening strengthening NN work_fnploejenbc2raktl46esxm44i 474 9 . . . work_fnploejenbc2raktl46esxm44i 475 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 475 2 1 1 LS work_fnploejenbc2raktl46esxm44i 475 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 475 4 Omit omit VB work_fnploejenbc2raktl46esxm44i 475 5 the the DT work_fnploejenbc2raktl46esxm44i 475 6 constraint constraint NN work_fnploejenbc2raktl46esxm44i 475 7 “ " `` work_fnploejenbc2raktl46esxm44i 475 8 w.r.t w.r.t NN work_fnploejenbc2raktl46esxm44i 475 9 . . . work_fnploejenbc2raktl46esxm44i 476 1 all all DT work_fnploejenbc2raktl46esxm44i 476 2 finite finite NNP work_fnploejenbc2raktl46esxm44i 476 3 equal equal JJ work_fnploejenbc2raktl46esxm44i 476 4 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 476 5 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 476 6 event event NN work_fnploejenbc2raktl46esxm44i 476 7 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 476 8 ” " '' work_fnploejenbc2raktl46esxm44i 476 9 in in IN work_fnploejenbc2raktl46esxm44i 476 10 both both DT work_fnploejenbc2raktl46esxm44i 476 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 476 12 i i NN work_fnploejenbc2raktl46esxm44i 476 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 476 14 and and CC work_fnploejenbc2raktl46esxm44i 476 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 476 16 iii iii NNP work_fnploejenbc2raktl46esxm44i 476 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 476 18 . . . work_fnploejenbc2raktl46esxm44i 477 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 477 2 2 2 LS work_fnploejenbc2raktl46esxm44i 477 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 477 4 Add add VB work_fnploejenbc2raktl46esxm44i 477 5 the the DT work_fnploejenbc2raktl46esxm44i 477 6 property property NN work_fnploejenbc2raktl46esxm44i 477 7 that that WDT work_fnploejenbc2raktl46esxm44i 477 8 p p NN work_fnploejenbc2raktl46esxm44i 477 9 is be VBZ work_fnploejenbc2raktl46esxm44i 477 10 gh gh NNP work_fnploejenbc2raktl46esxm44i 477 11 - - HYPH work_fnploejenbc2raktl46esxm44i 477 12 weak weak JJ work_fnploejenbc2raktl46esxm44i 477 13 local local JJ work_fnploejenbc2raktl46esxm44i 477 14 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 477 15 to to IN work_fnploejenbc2raktl46esxm44i 477 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 477 17 ii ii NNP work_fnploejenbc2raktl46esxm44i 477 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 477 19 . . . work_fnploejenbc2raktl46esxm44i 478 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 478 2 3 3 LS work_fnploejenbc2raktl46esxm44i 478 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 478 4 Replace Replace NNP work_fnploejenbc2raktl46esxm44i 478 5 s s NNP work_fnploejenbc2raktl46esxm44i 478 6 & & CC work_fnploejenbc2raktl46esxm44i 478 7 . . NNP work_fnploejenbc2raktl46esxm44i 478 8 , , , work_fnploejenbc2raktl46esxm44i 478 9 for for IN work_fnploejenbc2raktl46esxm44i 478 10 each each DT work_fnploejenbc2raktl46esxm44i 478 11 FE FE NNP work_fnploejenbc2raktl46esxm44i 478 12 d d NN work_fnploejenbc2raktl46esxm44i 478 13 by by IN work_fnploejenbc2raktl46esxm44i 478 14 simply simply RB work_fnploejenbc2raktl46esxm44i 478 15 d d NN work_fnploejenbc2raktl46esxm44i 478 16 in in IN work_fnploejenbc2raktl46esxm44i 478 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 478 18 iv iv NN work_fnploejenbc2raktl46esxm44i 478 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 478 20 . . . work_fnploejenbc2raktl46esxm44i 479 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 479 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 479 3 TO to IN work_fnploejenbc2raktl46esxm44i 479 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 479 5 573 573 CD work_fnploejenbc2raktl46esxm44i 479 6 Proof proof NN work_fnploejenbc2raktl46esxm44i 479 7 : : : work_fnploejenbc2raktl46esxm44i 479 8 Obvious obvious JJ work_fnploejenbc2raktl46esxm44i 479 9 by by IN work_fnploejenbc2raktl46esxm44i 479 10 inspection inspection NN work_fnploejenbc2raktl46esxm44i 479 11 of of IN work_fnploejenbc2raktl46esxm44i 479 12 the the DT work_fnploejenbc2raktl46esxm44i 479 13 proof proof NN work_fnploejenbc2raktl46esxm44i 479 14 of of IN work_fnploejenbc2raktl46esxm44i 479 15 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 479 16 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 479 17 and and CC work_fnploejenbc2raktl46esxm44i 479 18 the the DT work_fnploejenbc2raktl46esxm44i 479 19 role role NN work_fnploejenbc2raktl46esxm44i 479 20 that that WDT work_fnploejenbc2raktl46esxm44i 479 21 & & CC work_fnploejenbc2raktl46esxm44i 479 22 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 479 23 plays play VBZ work_fnploejenbc2raktl46esxm44i 479 24 in in IN work_fnploejenbc2raktl46esxm44i 479 25 making make VBG work_fnploejenbc2raktl46esxm44i 479 26 stronger strong JJR work_fnploejenbc2raktl46esxm44i 479 27 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 479 28 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 479 29 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 479 30 iv iv NN work_fnploejenbc2raktl46esxm44i 479 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 479 32 . . . work_fnploejenbc2raktl46esxm44i 480 1 1 1 CD work_fnploejenbc2raktl46esxm44i 480 2 Remark Remark NNP work_fnploejenbc2raktl46esxm44i 480 3 . . . work_fnploejenbc2raktl46esxm44i 481 1 For for IN work_fnploejenbc2raktl46esxm44i 481 2 any any DT work_fnploejenbc2raktl46esxm44i 481 3 a a DT work_fnploejenbc2raktl46esxm44i 481 4 E E NNP work_fnploejenbc2raktl46esxm44i 481 5 J J NNP work_fnploejenbc2raktl46esxm44i 481 6 & & CC work_fnploejenbc2raktl46esxm44i 481 7 , , , work_fnploejenbc2raktl46esxm44i 481 8 relative relative JJ work_fnploejenbc2raktl46esxm44i 481 9 to to IN work_fnploejenbc2raktl46esxm44i 481 10 CT CT NNP work_fnploejenbc2raktl46esxm44i 481 11 + + SYM work_fnploejenbc2raktl46esxm44i 481 12 , , , work_fnploejenbc2raktl46esxm44i 481 13 A a NN work_fnploejenbc2raktl46esxm44i 481 14 , , , work_fnploejenbc2raktl46esxm44i 481 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 481 16 i i NN work_fnploejenbc2raktl46esxm44i 481 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 18 A a DT work_fnploejenbc2raktl46esxm44i 481 19 least least RBS work_fnploejenbc2raktl46esxm44i 481 20 favorable favorable JJ work_fnploejenbc2raktl46esxm44i 481 21 prior prior JJ work_fnploejenbc2raktl46esxm44i 481 22 rOg rOg NNS work_fnploejenbc2raktl46esxm44i 481 23 p(rr(A p(rr(A NNP work_fnploejenbc2raktl46esxm44i 481 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 26 can can MD work_fnploejenbc2raktl46esxm44i 481 27 be be VB work_fnploejenbc2raktl46esxm44i 481 28 obtained obtain VBN work_fnploejenbc2raktl46esxm44i 481 29 by by IN work_fnploejenbc2raktl46esxm44i 481 30 minimizing minimize VBG work_fnploejenbc2raktl46esxm44i 481 31 the the DT work_fnploejenbc2raktl46esxm44i 481 32 objective objective JJ work_fnploejenbc2raktl46esxm44i 481 33 function function NN work_fnploejenbc2raktl46esxm44i 481 34 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 481 35 , , , work_fnploejenbc2raktl46esxm44i 481 36 + + SYM work_fnploejenbc2raktl46esxm44i 481 37 , , , work_fnploejenbc2raktl46esxm44i 481 38 , , , work_fnploejenbc2raktl46esxm44i 481 39 it59 it59 NNP work_fnploejenbc2raktl46esxm44i 481 40 Pu Pu NNP work_fnploejenbc2raktl46esxm44i 481 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 42 ’ ' '' work_fnploejenbc2raktl46esxm44i 481 43 1 1 CD work_fnploejenbc2raktl46esxm44i 481 44 C c NN work_fnploejenbc2raktl46esxm44i 481 45 fCPtA fCPtA NNS work_fnploejenbc2raktl46esxm44i 481 46 , , , work_fnploejenbc2raktl46esxm44i 481 47 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 48 , , , work_fnploejenbc2raktl46esxm44i 481 49 Ai(B)I Ai(B)I NNP work_fnploejenbc2raktl46esxm44i 481 50 t(B t(B '' work_fnploejenbc2raktl46esxm44i 481 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 52 i i NN work_fnploejenbc2raktl46esxm44i 481 53 = = NFP work_fnploejenbc2raktl46esxm44i 481 54 l l NN work_fnploejenbc2raktl46esxm44i 481 55 Bcsn(A Bcsn(A NNP work_fnploejenbc2raktl46esxm44i 481 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 57 subject subject JJ work_fnploejenbc2raktl46esxm44i 481 58 to to IN work_fnploejenbc2raktl46esxm44i 481 59 the the DT work_fnploejenbc2raktl46esxm44i 481 60 constraint constraint NN work_fnploejenbc2raktl46esxm44i 481 61 CBEkCAI CBEkCAI NNP work_fnploejenbc2raktl46esxm44i 481 62 z(B z(B NNP work_fnploejenbc2raktl46esxm44i 481 63 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 481 64 = = SYM work_fnploejenbc2raktl46esxm44i 481 65 1 1 CD work_fnploejenbc2raktl46esxm44i 481 66 . . . work_fnploejenbc2raktl46esxm44i 482 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 482 2 ii ii LS work_fnploejenbc2raktl46esxm44i 482 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 482 4 Using use VBG work_fnploejenbc2raktl46esxm44i 482 5 the the DT work_fnploejenbc2raktl46esxm44i 482 6 proof proof NN work_fnploejenbc2raktl46esxm44i 482 7 of of IN work_fnploejenbc2raktl46esxm44i 482 8 the the DT work_fnploejenbc2raktl46esxm44i 482 9 uniqueness uniqueness NN work_fnploejenbc2raktl46esxm44i 482 10 of of IN work_fnploejenbc2raktl46esxm44i 482 11 pr pr NN work_fnploejenbc2raktl46esxm44i 482 12 in in IN work_fnploejenbc2raktl46esxm44i 482 13 the the DT work_fnploejenbc2raktl46esxm44i 482 14 above above JJ work_fnploejenbc2raktl46esxm44i 482 15 theorem theorem NN work_fnploejenbc2raktl46esxm44i 482 16 , , , work_fnploejenbc2raktl46esxm44i 482 17 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 482 18 can can MD work_fnploejenbc2raktl46esxm44i 482 19 obtain obtain VB work_fnploejenbc2raktl46esxm44i 482 20 a a DT work_fnploejenbc2raktl46esxm44i 482 21 minimax minimax NNP work_fnploejenbc2raktl46esxm44i 482 22 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 482 23 measure measure NN work_fnploejenbc2raktl46esxm44i 482 24 p0 p0 NN work_fnploejenbc2raktl46esxm44i 482 25 E e NN work_fnploejenbc2raktl46esxm44i 482 26 n n CC work_fnploejenbc2raktl46esxm44i 482 27 2,A 2,a CD work_fnploejenbc2raktl46esxm44i 482 28 , , , work_fnploejenbc2raktl46esxm44i 482 29 where where WRB work_fnploejenbc2raktl46esxm44i 482 30 inf inf NN work_fnploejenbc2raktl46esxm44i 482 31 sup sup NNP work_fnploejenbc2raktl46esxm44i 482 32 P.f P.f NNP work_fnploejenbc2raktl46esxm44i 482 33 , , , work_fnploejenbc2raktl46esxm44i 482 34 + + CC work_fnploejenbc2raktl46esxm44i 482 35 , , , work_fnploejenbc2raktl46esxm44i 482 36 A a NN work_fnploejenbc2raktl46esxm44i 482 37 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 482 38 ? ? . work_fnploejenbc2raktl46esxm44i 483 1 PL pl NN work_fnploejenbc2raktl46esxm44i 483 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 483 3 = = NFP work_fnploejenbc2raktl46esxm44i 483 4 sup sup VBP work_fnploejenbc2raktl46esxm44i 483 5 PEA2.A PEA2.A NNP work_fnploejenbc2raktl46esxm44i 483 6 ’ ' '' work_fnploejenbc2raktl46esxm44i 483 7 rEP(Tc(a rEP(Tc(a NNP work_fnploejenbc2raktl46esxm44i 483 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 483 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 483 10 rtP(n(A rtp(n(a UH work_fnploejenbc2raktl46esxm44i 483 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 483 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 483 13 Pr pr NN work_fnploejenbc2raktl46esxm44i 483 14 , , , work_fnploejenbc2raktl46esxm44i 483 15 + + CC work_fnploejenbc2raktl46esxm44i 483 16 , , , work_fnploejenbc2raktl46esxm44i 483 17 A a NN work_fnploejenbc2raktl46esxm44i 483 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 483 19 ? ? . work_fnploejenbc2raktl46esxm44i 484 1 PO po NN work_fnploejenbc2raktl46esxm44i 484 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 484 3 . . . work_fnploejenbc2raktl46esxm44i 485 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 485 2 iii iii NNP work_fnploejenbc2raktl46esxm44i 485 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 485 4 G g NN work_fnploejenbc2raktl46esxm44i 485 5 T t NN work_fnploejenbc2raktl46esxm44i 485 6 + + SYM work_fnploejenbc2raktl46esxm44i 485 7 , , , work_fnploejenbc2raktl46esxm44i 485 8 A a DT work_fnploejenbc2raktl46esxm44i 485 9 has have VBZ work_fnploejenbc2raktl46esxm44i 485 10 the the DT work_fnploejenbc2raktl46esxm44i 485 11 value value NN work_fnploejenbc2raktl46esxm44i 485 12 V,(f V,(f NNP work_fnploejenbc2raktl46esxm44i 485 13 , , , work_fnploejenbc2raktl46esxm44i 485 14 a a DT work_fnploejenbc2raktl46esxm44i 485 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 485 16 , , , work_fnploejenbc2raktl46esxm44i 485 17 where where WRB work_fnploejenbc2raktl46esxm44i 485 18 Vo(f9 Vo(f9 NNP work_fnploejenbc2raktl46esxm44i 485 19 4 4 CD work_fnploejenbc2raktl46esxm44i 485 20 = = SYM work_fnploejenbc2raktl46esxm44i 485 21 sup sup NNP work_fnploejenbc2raktl46esxm44i 485 22 reP(n(A reP(n(A NNP work_fnploejenbc2raktl46esxm44i 485 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 485 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 485 25 Pr pr NN work_fnploejenbc2raktl46esxm44i 485 26 . . . work_fnploejenbc2raktl46esxm44i 486 1 + + RB work_fnploejenbc2raktl46esxm44i 486 2 , , , work_fnploejenbc2raktl46esxm44i 486 3 , , , work_fnploejenbc2raktl46esxm44i 486 4 .&r .&r XX work_fnploejenbc2raktl46esxm44i 486 5 , , , work_fnploejenbc2raktl46esxm44i 486 6 /%I /%I NFP work_fnploejenbc2raktl46esxm44i 486 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 486 8 = = NFP work_fnploejenbc2raktl46esxm44i 486 9 P/ P/ NNP work_fnploejenbc2raktl46esxm44i 486 10 , , , work_fnploejenbc2raktl46esxm44i 486 11 + + CC work_fnploejenbc2raktl46esxm44i 486 12 , , , work_fnploejenbc2raktl46esxm44i 486 13 A(%3 A(%3 NNP work_fnploejenbc2raktl46esxm44i 486 14 I%J. I%J. NNP work_fnploejenbc2raktl46esxm44i 487 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 487 2 4.2.2 4.2.2 CD work_fnploejenbc2raktl46esxm44i 487 3 . . . work_fnploejenbc2raktl46esxm44i 488 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 488 2 the the DT work_fnploejenbc2raktl46esxm44i 488 3 game game NN work_fnploejenbc2raktl46esxm44i 488 4 GT gt NN work_fnploejenbc2raktl46esxm44i 488 5 + + CC work_fnploejenbc2raktl46esxm44i 488 6 with with IN work_fnploejenbc2raktl46esxm44i 488 7 PJ PJ NNP work_fnploejenbc2raktl46esxm44i 488 8 increasing increase VBG work_fnploejenbc2raktl46esxm44i 488 9 . . . work_fnploejenbc2raktl46esxm44i 489 1 Suppose suppose VB work_fnploejenbc2raktl46esxm44i 489 2 that that IN work_fnploejenbc2raktl46esxm44i 489 3 f f NNP work_fnploejenbc2raktl46esxm44i 489 4 is be VBZ work_fnploejenbc2raktl46esxm44i 489 5 not not RB work_fnploejenbc2raktl46esxm44i 489 6 a a DT work_fnploejenbc2raktl46esxm44i 489 7 proper proper JJ work_fnploejenbc2raktl46esxm44i 489 8 score score NN work_fnploejenbc2raktl46esxm44i 489 9 function function NN work_fnploejenbc2raktl46esxm44i 489 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 489 11 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 489 12 , , , work_fnploejenbc2raktl46esxm44i 489 13 P,(x P,(x NNP work_fnploejenbc2raktl46esxm44i 489 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 489 15 E E NNP work_fnploejenbc2raktl46esxm44i 489 16 x x LS work_fnploejenbc2raktl46esxm44i 489 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 489 18 andf andf NNP work_fnploejenbc2raktl46esxm44i 489 19 is be VBZ work_fnploejenbc2raktl46esxm44i 489 20 twice twice RB work_fnploejenbc2raktl46esxm44i 489 21 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 489 22 . . . work_fnploejenbc2raktl46esxm44i 490 1 Then then RB work_fnploejenbc2raktl46esxm44i 490 2 no no DT work_fnploejenbc2raktl46esxm44i 490 3 nonatomic nonatomic JJ work_fnploejenbc2raktl46esxm44i 490 4 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 490 5 probability probability NN work_fnploejenbc2raktl46esxm44i 490 6 measure measure NN work_fnploejenbc2raktl46esxm44i 490 7 p p NN work_fnploejenbc2raktl46esxm44i 490 8 on on IN work_fnploejenbc2raktl46esxm44i 490 9 d d NN work_fnploejenbc2raktl46esxm44i 490 10 can can MD work_fnploejenbc2raktl46esxm44i 490 11 be be VB work_fnploejenbc2raktl46esxm44i 490 12 Gf Gf NNP work_fnploejenbc2raktl46esxm44i 490 13 + + SYM work_fnploejenbc2raktl46esxm44i 490 14 - - HYPH work_fnploejenbc2raktl46esxm44i 490 15 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 490 16 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 490 17 . . . work_fnploejenbc2raktl46esxm44i 491 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 491 2 . . . work_fnploejenbc2raktl46esxm44i 492 1 Assume assume VB work_fnploejenbc2raktl46esxm44i 492 2 the the DT work_fnploejenbc2raktl46esxm44i 492 3 contrary contrary NN work_fnploejenbc2raktl46esxm44i 492 4 , , , work_fnploejenbc2raktl46esxm44i 492 5 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 492 6 , , , work_fnploejenbc2raktl46esxm44i 492 7 the the DT work_fnploejenbc2raktl46esxm44i 492 8 nonatomic nonatomic JJ work_fnploejenbc2raktl46esxm44i 492 9 probability probability NNP work_fnploejenbc2raktl46esxm44i 492 10 p p NNP work_fnploejenbc2raktl46esxm44i 492 11 on on IN work_fnploejenbc2raktl46esxm44i 492 12 d d NN work_fnploejenbc2raktl46esxm44i 492 13 is be VBZ work_fnploejenbc2raktl46esxm44i 492 14 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 492 15 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 492 16 with with IN work_fnploejenbc2raktl46esxm44i 492 17 respect respect NN work_fnploejenbc2raktl46esxm44i 492 18 to to IN work_fnploejenbc2raktl46esxm44i 492 19 GT GT NNP work_fnploejenbc2raktl46esxm44i 492 20 + + SYM work_fnploejenbc2raktl46esxm44i 492 21 . . . work_fnploejenbc2raktl46esxm44i 493 1 By by IN work_fnploejenbc2raktl46esxm44i 493 2 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 493 3 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 493 4 , , , work_fnploejenbc2raktl46esxm44i 493 5 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 493 6 should should MD work_fnploejenbc2raktl46esxm44i 493 7 have have VB work_fnploejenbc2raktl46esxm44i 493 8 , , , work_fnploejenbc2raktl46esxm44i 493 9 by by IN work_fnploejenbc2raktl46esxm44i 493 10 the the DT work_fnploejenbc2raktl46esxm44i 493 11 nonatomicity nonatomicity NN work_fnploejenbc2raktl46esxm44i 493 12 of of IN work_fnploejenbc2raktl46esxm44i 493 13 p p NN work_fnploejenbc2raktl46esxm44i 493 14 , , , work_fnploejenbc2raktl46esxm44i 493 15 < < XX work_fnploejenbc2raktl46esxm44i 493 16 r(t r(t NNP work_fnploejenbc2raktl46esxm44i 493 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 493 18 + + NNP work_fnploejenbc2raktl46esxm44i 493 19 P p NN work_fnploejenbc2raktl46esxm44i 493 20 , , , work_fnploejenbc2raktl46esxm44i 493 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 493 22 1 1 CD work_fnploejenbc2raktl46esxm44i 493 23 - - HYPH work_fnploejenbc2raktl46esxm44i 493 24 t t NN work_fnploejenbc2raktl46esxm44i 493 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 493 26 = = SYM work_fnploejenbc2raktl46esxm44i 493 27 1 1 CD work_fnploejenbc2raktl46esxm44i 493 28 , , , work_fnploejenbc2raktl46esxm44i 493 29 VtE vte NN work_fnploejenbc2raktl46esxm44i 493 30 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 493 31 O o UH work_fnploejenbc2raktl46esxm44i 493 32 , , , work_fnploejenbc2raktl46esxm44i 493 33 11 11 CD work_fnploejenbc2raktl46esxm44i 493 34 . . . work_fnploejenbc2raktl46esxm44i 494 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 494 2 1 1 LS work_fnploejenbc2raktl46esxm44i 494 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 494 4 By by IN work_fnploejenbc2raktl46esxm44i 494 5 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 494 6 here here RB work_fnploejenbc2raktl46esxm44i 494 7 , , , work_fnploejenbc2raktl46esxm44i 494 8 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 494 9 can can MD work_fnploejenbc2raktl46esxm44i 494 10 be be VB work_fnploejenbc2raktl46esxm44i 494 11 shown show VBN work_fnploejenbc2raktl46esxm44i 494 12 Pf(XY pf(xy NN work_fnploejenbc2raktl46esxm44i 494 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 494 14 = = NFP work_fnploejenbc2raktl46esxm44i 494 15 P,(x P,(x NNP work_fnploejenbc2raktl46esxm44i 494 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 494 17 Pf(Yh Pf(Yh NNP work_fnploejenbc2raktl46esxm44i 494 18 vx vx NNP work_fnploejenbc2raktl46esxm44i 494 19 , , , work_fnploejenbc2raktl46esxm44i 494 20 y y NNP work_fnploejenbc2raktl46esxm44i 494 21 E E NNP work_fnploejenbc2raktl46esxm44i 494 22 I3 I3 NNP work_fnploejenbc2raktl46esxm44i 494 23 11 11 CD work_fnploejenbc2raktl46esxm44i 494 24 . . . work_fnploejenbc2raktl46esxm44i 495 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 2 2 2 LS work_fnploejenbc2raktl46esxm44i 495 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 4 Differentiate Differentiate NNP work_fnploejenbc2raktl46esxm44i 495 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 6 2 2 CD work_fnploejenbc2raktl46esxm44i 495 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 8 with with IN work_fnploejenbc2raktl46esxm44i 495 9 respect respect NN work_fnploejenbc2raktl46esxm44i 495 10 to to IN work_fnploejenbc2raktl46esxm44i 495 11 x x NNS work_fnploejenbc2raktl46esxm44i 495 12 and and CC work_fnploejenbc2raktl46esxm44i 495 13 then then RB work_fnploejenbc2raktl46esxm44i 495 14 separately separately RB work_fnploejenbc2raktl46esxm44i 495 15 with with IN work_fnploejenbc2raktl46esxm44i 495 16 respect respect NN work_fnploejenbc2raktl46esxm44i 495 17 to to IN work_fnploejenbc2raktl46esxm44i 495 18 y y NNP work_fnploejenbc2raktl46esxm44i 495 19 , , , work_fnploejenbc2raktl46esxm44i 495 20 to to TO work_fnploejenbc2raktl46esxm44i 495 21 obtain obtain VB work_fnploejenbc2raktl46esxm44i 495 22 YV YV NNP work_fnploejenbc2raktl46esxm44i 495 23 , , , work_fnploejenbc2raktl46esxm44i 495 24 , , , work_fnploejenbc2raktl46esxm44i 495 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 26 XY XY NNP work_fnploejenbc2raktl46esxm44i 495 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 28 = = NFP work_fnploejenbc2raktl46esxm44i 495 29 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 30 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 495 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 32 ’ ' '' work_fnploejenbc2raktl46esxm44i 495 33 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 34 x x LS work_fnploejenbc2raktl46esxm44i 495 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 36 pf(YL pf(yl NN work_fnploejenbc2raktl46esxm44i 495 37 X(Pf X(Pf NNP work_fnploejenbc2raktl46esxm44i 495 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 39 ’ ' '' work_fnploejenbc2raktl46esxm44i 495 40 bYI bYI NNP work_fnploejenbc2raktl46esxm44i 495 41 = = NFP work_fnploejenbc2raktl46esxm44i 495 42 PfbNPJ pfbnpj NN work_fnploejenbc2raktl46esxm44i 495 43 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 495 44 Y Y NNP work_fnploejenbc2raktl46esxm44i 495 45 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 495 46 . . . work_fnploejenbc2raktl46esxm44i 496 1 Simple simple JJ work_fnploejenbc2raktl46esxm44i 496 2 division division NN work_fnploejenbc2raktl46esxm44i 496 3 yields yield NNS work_fnploejenbc2raktl46esxm44i 496 4 x[log x[log NNP work_fnploejenbc2raktl46esxm44i 496 5 PJx PJx NNS work_fnploejenbc2raktl46esxm44i 496 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 496 7 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 496 8 ’ ' '' work_fnploejenbc2raktl46esxm44i 496 9 = = NFP work_fnploejenbc2raktl46esxm44i 496 10 y[log y[log NNP work_fnploejenbc2raktl46esxm44i 496 11 P,(y p,(y NN work_fnploejenbc2raktl46esxm44i 496 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 496 13 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 496 14 ‘ ' `` work_fnploejenbc2raktl46esxm44i 496 15 , , , work_fnploejenbc2raktl46esxm44i 496 16 so so IN work_fnploejenbc2raktl46esxm44i 496 17 that that IN work_fnploejenbc2raktl46esxm44i 496 18 x[log x[log NNP work_fnploejenbc2raktl46esxm44i 496 19 PJX PJX NNP work_fnploejenbc2raktl46esxm44i 496 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 496 21 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 496 22 = = NFP work_fnploejenbc2raktl46esxm44i 496 23 c c NN work_fnploejenbc2raktl46esxm44i 496 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 496 25 a a DT work_fnploejenbc2raktl46esxm44i 496 26 constant constant NN work_fnploejenbc2raktl46esxm44i 496 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 496 28 , , , work_fnploejenbc2raktl46esxm44i 496 29 and and CC work_fnploejenbc2raktl46esxm44i 496 30 hence hence RB work_fnploejenbc2raktl46esxm44i 496 31 I’,(x I’,(x NNP work_fnploejenbc2raktl46esxm44i 496 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 496 33 = = SYM work_fnploejenbc2raktl46esxm44i 496 34 xc xc NNP work_fnploejenbc2raktl46esxm44i 496 35 . . . work_fnploejenbc2raktl46esxm44i 497 1 Then then RB work_fnploejenbc2raktl46esxm44i 497 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 497 3 1 1 LS work_fnploejenbc2raktl46esxm44i 497 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 497 5 forces force VBZ work_fnploejenbc2raktl46esxm44i 497 6 c c NNP work_fnploejenbc2raktl46esxm44i 497 7 to to TO work_fnploejenbc2raktl46esxm44i 497 8 be be VB work_fnploejenbc2raktl46esxm44i 497 9 1 1 CD work_fnploejenbc2raktl46esxm44i 497 10 . . . work_fnploejenbc2raktl46esxm44i 498 1 1 1 CD work_fnploejenbc2raktl46esxm44i 498 2 574 574 CD work_fnploejenbc2raktl46esxm44i 498 3 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 498 4 , , , work_fnploejenbc2raktl46esxm44i 498 5 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 498 6 , , , work_fnploejenbc2raktl46esxm44i 498 7 AND and CC work_fnploejenbc2raktl46esxm44i 498 8 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 498 9 Remarks Remarks NNPS work_fnploejenbc2raktl46esxm44i 498 10 . . . work_fnploejenbc2raktl46esxm44i 499 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 499 2 i i NN work_fnploejenbc2raktl46esxm44i 499 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 499 4 To to TO work_fnploejenbc2raktl46esxm44i 499 5 accomodate accomodate VB work_fnploejenbc2raktl46esxm44i 499 6 this this DT work_fnploejenbc2raktl46esxm44i 499 7 situation situation NN work_fnploejenbc2raktl46esxm44i 499 8 , , , work_fnploejenbc2raktl46esxm44i 499 9 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 499 10 will will MD work_fnploejenbc2raktl46esxm44i 499 11 consider consider VB work_fnploejenbc2raktl46esxm44i 499 12 a a DT work_fnploejenbc2raktl46esxm44i 499 13 concept concept NN work_fnploejenbc2raktl46esxm44i 499 14 of of IN work_fnploejenbc2raktl46esxm44i 499 15 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 499 16 in in IN work_fnploejenbc2raktl46esxm44i 499 17 the the DT work_fnploejenbc2raktl46esxm44i 499 18 wide wide JJ work_fnploejenbc2raktl46esxm44i 499 19 sense sense NN work_fnploejenbc2raktl46esxm44i 499 20 of of IN work_fnploejenbc2raktl46esxm44i 499 21 Section section NN work_fnploejenbc2raktl46esxm44i 499 22 5 5 CD work_fnploejenbc2raktl46esxm44i 499 23 . . . work_fnploejenbc2raktl46esxm44i 500 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 500 2 ii ii LS work_fnploejenbc2raktl46esxm44i 500 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 500 4 The the DT work_fnploejenbc2raktl46esxm44i 500 5 condition condition NN work_fnploejenbc2raktl46esxm44i 500 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 500 7 iv iv NN work_fnploejenbc2raktl46esxm44i 500 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 500 9 in in IN work_fnploejenbc2raktl46esxm44i 500 10 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 500 11 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 500 12 is be VBZ work_fnploejenbc2raktl46esxm44i 500 13 the the DT work_fnploejenbc2raktl46esxm44i 500 14 coherence coherence NN work_fnploejenbc2raktl46esxm44i 500 15 principle principle NN work_fnploejenbc2raktl46esxm44i 500 16 of of IN work_fnploejenbc2raktl46esxm44i 500 17 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 500 18 . . . work_fnploejenbc2raktl46esxm44i 501 1 The the DT work_fnploejenbc2raktl46esxm44i 501 2 equivalences equivalence NNS work_fnploejenbc2raktl46esxm44i 501 3 in in IN work_fnploejenbc2raktl46esxm44i 501 4 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 501 5 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 501 6 explain explain VBP work_fnploejenbc2raktl46esxm44i 501 7 the the DT work_fnploejenbc2raktl46esxm44i 501 8 concept concept NN work_fnploejenbc2raktl46esxm44i 501 9 of of IN work_fnploejenbc2raktl46esxm44i 501 10 “ " `` work_fnploejenbc2raktl46esxm44i 501 11 reasonable reasonable JJ work_fnploejenbc2raktl46esxm44i 501 12 ” " '' work_fnploejenbc2raktl46esxm44i 501 13 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 501 14 measures measure NNS work_fnploejenbc2raktl46esxm44i 501 15 , , , work_fnploejenbc2raktl46esxm44i 501 16 from from IN work_fnploejenbc2raktl46esxm44i 501 17 a a DT work_fnploejenbc2raktl46esxm44i 501 18 decision decision NN work_fnploejenbc2raktl46esxm44i 501 19 viewpoint viewpoint NN work_fnploejenbc2raktl46esxm44i 501 20 , , , work_fnploejenbc2raktl46esxm44i 501 21 and and CC work_fnploejenbc2raktl46esxm44i 501 22 lead lead VB work_fnploejenbc2raktl46esxm44i 501 23 to to IN work_fnploejenbc2raktl46esxm44i 501 24 the the DT work_fnploejenbc2raktl46esxm44i 501 25 discoveries discovery NNS work_fnploejenbc2raktl46esxm44i 501 26 of of IN work_fnploejenbc2raktl46esxm44i 501 27 other other JJ work_fnploejenbc2raktl46esxm44i 501 28 “ " `` work_fnploejenbc2raktl46esxm44i 501 29 reasonable reasonable JJ work_fnploejenbc2raktl46esxm44i 501 30 ” " '' work_fnploejenbc2raktl46esxm44i 501 31 measures measure NNS work_fnploejenbc2raktl46esxm44i 501 32 which which WDT work_fnploejenbc2raktl46esxm44i 501 33 need need VBP work_fnploejenbc2raktl46esxm44i 501 34 not not RB work_fnploejenbc2raktl46esxm44i 501 35 be be VB work_fnploejenbc2raktl46esxm44i 501 36 probability probability NN work_fnploejenbc2raktl46esxm44i 501 37 measures measure NNS work_fnploejenbc2raktl46esxm44i 501 38 . . . work_fnploejenbc2raktl46esxm44i 502 1 In in IN work_fnploejenbc2raktl46esxm44i 502 2 view view NN work_fnploejenbc2raktl46esxm44i 502 3 of of IN work_fnploejenbc2raktl46esxm44i 502 4 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 502 5 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 502 6 , , , work_fnploejenbc2raktl46esxm44i 502 7 the the DT work_fnploejenbc2raktl46esxm44i 502 8 coherence coherence NN work_fnploejenbc2raktl46esxm44i 502 9 principle principle NN work_fnploejenbc2raktl46esxm44i 502 10 can can MD work_fnploejenbc2raktl46esxm44i 502 11 be be VB work_fnploejenbc2raktl46esxm44i 502 12 used use VBN work_fnploejenbc2raktl46esxm44i 502 13 as as IN work_fnploejenbc2raktl46esxm44i 502 14 a a DT work_fnploejenbc2raktl46esxm44i 502 15 definition definition NN work_fnploejenbc2raktl46esxm44i 502 16 of of IN work_fnploejenbc2raktl46esxm44i 502 17 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 502 18 . . . work_fnploejenbc2raktl46esxm44i 503 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 503 2 iii iii NNP work_fnploejenbc2raktl46esxm44i 503 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 503 4 Relative relative JJ work_fnploejenbc2raktl46esxm44i 503 5 to to IN work_fnploejenbc2raktl46esxm44i 503 6 the the DT work_fnploejenbc2raktl46esxm44i 503 7 invariance invariance NN work_fnploejenbc2raktl46esxm44i 503 8 property property NN work_fnploejenbc2raktl46esxm44i 503 9 of of IN work_fnploejenbc2raktl46esxm44i 503 10 the the DT work_fnploejenbc2raktl46esxm44i 503 11 probability probability NN work_fnploejenbc2raktl46esxm44i 503 12 transform transform NN work_fnploejenbc2raktl46esxm44i 503 13 Ps Ps NNP work_fnploejenbc2raktl46esxm44i 503 14 , , , work_fnploejenbc2raktl46esxm44i 503 15 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 503 16 present present VBP work_fnploejenbc2raktl46esxm44i 503 17 the the DT work_fnploejenbc2raktl46esxm44i 503 18 following following NN work_fnploejenbc2raktl46esxm44i 503 19 . . . work_fnploejenbc2raktl46esxm44i 504 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 504 2 two two CD work_fnploejenbc2raktl46esxm44i 504 3 games game NNS work_fnploejenbc2raktl46esxm44i 504 4 G g NN work_fnploejenbc2raktl46esxm44i 504 5 , , , work_fnploejenbc2raktl46esxm44i 504 6 , , , work_fnploejenbc2raktl46esxm44i 504 7 + + RB work_fnploejenbc2raktl46esxm44i 504 8 , , , work_fnploejenbc2raktl46esxm44i 504 9 G g NN work_fnploejenbc2raktl46esxm44i 504 10 , , , work_fnploejenbc2raktl46esxm44i 504 11 + + CC work_fnploejenbc2raktl46esxm44i 504 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 504 13 say say VB work_fnploejenbc2raktl46esxm44i 504 14 , , , work_fnploejenbc2raktl46esxm44i 504 15 with with IN work_fnploejenbc2raktl46esxm44i 504 16 the the DT work_fnploejenbc2raktl46esxm44i 504 17 same same JJ work_fnploejenbc2raktl46esxm44i 504 18 aj aj NNP work_fnploejenbc2raktl46esxm44i 504 19 , , , work_fnploejenbc2raktl46esxm44i 504 20 j j NNP work_fnploejenbc2raktl46esxm44i 504 21 = = SYM work_fnploejenbc2raktl46esxm44i 504 22 0 0 CD work_fnploejenbc2raktl46esxm44i 504 23 , , , work_fnploejenbc2raktl46esxm44i 504 24 1,2 1,2 CD work_fnploejenbc2raktl46esxm44i 504 25 , , , work_fnploejenbc2raktl46esxm44i 504 26 3 3 CD work_fnploejenbc2raktl46esxm44i 504 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 504 28 , , , work_fnploejenbc2raktl46esxm44i 504 29 with with IN work_fnploejenbc2raktl46esxm44i 504 30 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 504 31 , , , work_fnploejenbc2raktl46esxm44i 504 32 P p NN work_fnploejenbc2raktl46esxm44i 504 33 , , , work_fnploejenbc2raktl46esxm44i 504 34 increasing increase VBG work_fnploejenbc2raktl46esxm44i 504 35 . . . work_fnploejenbc2raktl46esxm44i 505 1 Let let VB work_fnploejenbc2raktl46esxm44i 505 2 p p PRP work_fnploejenbc2raktl46esxm44i 505 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 505 4 resp resp NN work_fnploejenbc2raktl46esxm44i 505 5 . . . work_fnploejenbc2raktl46esxm44i 506 1 v v LS work_fnploejenbc2raktl46esxm44i 506 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 506 3 be be VB work_fnploejenbc2raktl46esxm44i 506 4 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 506 5 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 506 6 with with IN work_fnploejenbc2raktl46esxm44i 506 7 respect respect NN work_fnploejenbc2raktl46esxm44i 506 8 to to IN work_fnploejenbc2raktl46esxm44i 506 9 G g NN work_fnploejenbc2raktl46esxm44i 506 10 , , , work_fnploejenbc2raktl46esxm44i 506 11 , , , work_fnploejenbc2raktl46esxm44i 506 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 506 13 resp resp NN work_fnploejenbc2raktl46esxm44i 506 14 . . . work_fnploejenbc2raktl46esxm44i 507 1 G G NNP work_fnploejenbc2raktl46esxm44i 507 2 , , , work_fnploejenbc2raktl46esxm44i 507 3 + + SYM work_fnploejenbc2raktl46esxm44i 507 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 507 5 . . . work_fnploejenbc2raktl46esxm44i 508 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 508 2 is be VBZ work_fnploejenbc2raktl46esxm44i 508 3 not not RB work_fnploejenbc2raktl46esxm44i 508 4 true true JJ work_fnploejenbc2raktl46esxm44i 508 5 in in IN work_fnploejenbc2raktl46esxm44i 508 6 general general JJ work_fnploejenbc2raktl46esxm44i 508 7 Pfo Pfo NNP work_fnploejenbc2raktl46esxm44i 508 8 , , , work_fnploejenbc2raktl46esxm44i 508 9 urPgoV. urpgov. RB work_fnploejenbc2raktl46esxm44i 509 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 509 2 * * NFP work_fnploejenbc2raktl46esxm44i 509 3 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 509 4 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 509 5 , , , work_fnploejenbc2raktl46esxm44i 509 6 let let VBD work_fnploejenbc2raktl46esxm44i 509 7 Q Q NNP work_fnploejenbc2raktl46esxm44i 509 8 , , , work_fnploejenbc2raktl46esxm44i 509 9 , , , work_fnploejenbc2raktl46esxm44i 509 10 Q Q NNP work_fnploejenbc2raktl46esxm44i 509 11 , , , work_fnploejenbc2raktl46esxm44i 509 12 be be VB work_fnploejenbc2raktl46esxm44i 509 13 two two CD work_fnploejenbc2raktl46esxm44i 509 14 probability probability NN work_fnploejenbc2raktl46esxm44i 509 15 measures measure NNS work_fnploejenbc2raktl46esxm44i 509 16 on on IN work_fnploejenbc2raktl46esxm44i 509 17 & & CC work_fnploejenbc2raktl46esxm44i 509 18 , , , work_fnploejenbc2raktl46esxm44i 509 19 with with IN work_fnploejenbc2raktl46esxm44i 509 20 Q Q NNP work_fnploejenbc2raktl46esxm44i 509 21 , , , work_fnploejenbc2raktl46esxm44i 509 22 # # NNP work_fnploejenbc2raktl46esxm44i 509 23 Q2 q2 NN work_fnploejenbc2raktl46esxm44i 509 24 , , , work_fnploejenbc2raktl46esxm44i 509 25 take take VB work_fnploejenbc2raktl46esxm44i 509 26 , , , work_fnploejenbc2raktl46esxm44i 509 27 u u LS work_fnploejenbc2raktl46esxm44i 509 28 = = SYM work_fnploejenbc2raktl46esxm44i 509 29 P+Q P+Q NNP work_fnploejenbc2raktl46esxm44i 509 30 , , , work_fnploejenbc2raktl46esxm44i 509 31 and and CC work_fnploejenbc2raktl46esxm44i 509 32 v v LS work_fnploejenbc2raktl46esxm44i 509 33 = = SYM work_fnploejenbc2raktl46esxm44i 509 34 Pi pi NN work_fnploejenbc2raktl46esxm44i 509 35 ’ ' '' work_fnploejenbc2raktl46esxm44i 509 36 0 0 CD work_fnploejenbc2raktl46esxm44i 509 37 Q q NN work_fnploejenbc2raktl46esxm44i 509 38 , , , work_fnploejenbc2raktl46esxm44i 509 39 . . . work_fnploejenbc2raktl46esxm44i 510 1 For for IN work_fnploejenbc2raktl46esxm44i 510 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 3 * * NFP work_fnploejenbc2raktl46esxm44i 510 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 5 to to TO work_fnploejenbc2raktl46esxm44i 510 6 hold hold VB work_fnploejenbc2raktl46esxm44i 510 7 , , , work_fnploejenbc2raktl46esxm44i 510 8 one one PRP work_fnploejenbc2raktl46esxm44i 510 9 needs need VBZ work_fnploejenbc2raktl46esxm44i 510 10 to to TO work_fnploejenbc2raktl46esxm44i 510 11 consider consider VB work_fnploejenbc2raktl46esxm44i 510 12 the the DT work_fnploejenbc2raktl46esxm44i 510 13 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 510 14 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 510 15 of of IN work_fnploejenbc2raktl46esxm44i 510 16 the the DT work_fnploejenbc2raktl46esxm44i 510 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 18 vector vector NN work_fnploejenbc2raktl46esxm44i 510 19 - - HYPH work_fnploejenbc2raktl46esxm44i 510 20 valued value VBN work_fnploejenbc2raktl46esxm44i 510 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 22 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 510 23 measure measure NN work_fnploejenbc2raktl46esxm44i 510 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 25 , , , work_fnploejenbc2raktl46esxm44i 510 26 u u NNP work_fnploejenbc2raktl46esxm44i 510 27 , , , work_fnploejenbc2raktl46esxm44i 510 28 v v LS work_fnploejenbc2raktl46esxm44i 510 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 30 with with IN work_fnploejenbc2raktl46esxm44i 510 31 respect respect NN work_fnploejenbc2raktl46esxm44i 510 32 to to IN work_fnploejenbc2raktl46esxm44i 510 33 the the DT work_fnploejenbc2raktl46esxm44i 510 34 joint joint JJ work_fnploejenbc2raktl46esxm44i 510 35 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 510 36 game game NN work_fnploejenbc2raktl46esxm44i 510 37 GcJ GcJ NNP work_fnploejenbc2raktl46esxm44i 510 38 , , , work_fnploejenbc2raktl46esxm44i 510 39 , , , work_fnploejenbc2raktl46esxm44i 510 40 , , , work_fnploejenbc2raktl46esxm44i 510 41 , , , work_fnploejenbc2raktl46esxm44i 510 42 + + SYM work_fnploejenbc2raktl46esxm44i 510 43 = = NFP work_fnploejenbc2raktl46esxm44i 510 44 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 45 /ii /ii NFP work_fnploejenbc2raktl46esxm44i 510 46 , , , work_fnploejenbc2raktl46esxm44i 510 47 , , , work_fnploejenbc2raktl46esxm44i 510 48 4 4 CD work_fnploejenbc2raktl46esxm44i 510 49 : : : work_fnploejenbc2raktl46esxm44i 510 50 , , , work_fnploejenbc2raktl46esxm44i 510 51 Lcf Lcf NNP work_fnploejenbc2raktl46esxm44i 510 52 , , , work_fnploejenbc2raktl46esxm44i 510 53 , , , work_fnploejenbc2raktl46esxm44i 510 54 , , , work_fnploejenbc2raktl46esxm44i 510 55 , , , work_fnploejenbc2raktl46esxm44i 510 56 + + SYM work_fnploejenbc2raktl46esxm44i 510 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 58 , , , work_fnploejenbc2raktl46esxm44i 510 59 where where WRB work_fnploejenbc2raktl46esxm44i 510 60 L L NNP work_fnploejenbc2raktl46esxm44i 510 61 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 62 / / SYM work_fnploejenbc2raktl46esxm44i 510 63 , , , work_fnploejenbc2raktl46esxm44i 510 64 g g NN work_fnploejenbc2raktl46esxm44i 510 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 66 , , , work_fnploejenbc2raktl46esxm44i 510 67 + + CC work_fnploejenbc2raktl46esxm44i 510 68 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 69 A a NN work_fnploejenbc2raktl46esxm44i 510 70 03 03 CD work_fnploejenbc2raktl46esxm44i 510 71 PL PL NNP work_fnploejenbc2raktl46esxm44i 510 72 , , , work_fnploejenbc2raktl46esxm44i 510 73 VI VI NNP work_fnploejenbc2raktl46esxm44i 510 74 = = SYM work_fnploejenbc2raktl46esxm44i 510 75 Lf Lf NNP work_fnploejenbc2raktl46esxm44i 510 76 , , , work_fnploejenbc2raktl46esxm44i 510 77 + + NFP work_fnploejenbc2raktl46esxm44i 510 78 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 79 A a DT work_fnploejenbc2raktl46esxm44i 510 80 a a NN work_fnploejenbc2raktl46esxm44i 510 81 , , , work_fnploejenbc2raktl46esxm44i 510 82 P p NN work_fnploejenbc2raktl46esxm44i 510 83 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 510 84 + + NNP work_fnploejenbc2raktl46esxm44i 510 85 L l NN work_fnploejenbc2raktl46esxm44i 510 86 , , , work_fnploejenbc2raktl46esxm44i 510 87 , , , work_fnploejenbc2raktl46esxm44i 510 88 + + NFP work_fnploejenbc2raktl46esxm44i 510 89 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 510 90 4 4 CD work_fnploejenbc2raktl46esxm44i 510 91 0 0 CD work_fnploejenbc2raktl46esxm44i 510 92 , , , work_fnploejenbc2raktl46esxm44i 510 93 VI VI NNP work_fnploejenbc2raktl46esxm44i 510 94 . . . work_fnploejenbc2raktl46esxm44i 511 1 5 5 CD work_fnploejenbc2raktl46esxm44i 511 2 . . . work_fnploejenbc2raktl46esxm44i 512 1 ADMISSIBILITY admissibility JJ work_fnploejenbc2raktl46esxm44i 512 2 OF of IN work_fnploejenbc2raktl46esxm44i 512 3 POSSIBILITY POSSIBILITY NNP work_fnploejenbc2raktl46esxm44i 512 4 MEASURES MEASURES NNP work_fnploejenbc2raktl46esxm44i 512 5 This this DT work_fnploejenbc2raktl46esxm44i 512 6 section section NN work_fnploejenbc2raktl46esxm44i 512 7 is be VBZ work_fnploejenbc2raktl46esxm44i 512 8 devoted devoted JJ work_fnploejenbc2raktl46esxm44i 512 9 to to IN work_fnploejenbc2raktl46esxm44i 512 10 the the DT work_fnploejenbc2raktl46esxm44i 512 11 study study NN work_fnploejenbc2raktl46esxm44i 512 12 of of IN work_fnploejenbc2raktl46esxm44i 512 13 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 512 14 of of IN work_fnploejenbc2raktl46esxm44i 512 15 a a DT work_fnploejenbc2raktl46esxm44i 512 16 class class NN work_fnploejenbc2raktl46esxm44i 512 17 of of IN work_fnploejenbc2raktl46esxm44i 512 18 uncer- uncer- JJ work_fnploejenbc2raktl46esxm44i 512 19 tainty tainty NN work_fnploejenbc2raktl46esxm44i 512 20 measures measure NNS work_fnploejenbc2raktl46esxm44i 512 21 called call VBN work_fnploejenbc2raktl46esxm44i 512 22 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 512 23 measures measure NNS work_fnploejenbc2raktl46esxm44i 512 24 and and CC work_fnploejenbc2raktl46esxm44i 512 25 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 512 26 implications implication NNS work_fnploejenbc2raktl46esxm44i 512 27 for for IN work_fnploejenbc2raktl46esxm44i 512 28 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 512 29 logics logic NNS work_fnploejenbc2raktl46esxm44i 512 30 . . . work_fnploejenbc2raktl46esxm44i 513 1 5.1 5.1 CD work_fnploejenbc2raktl46esxm44i 513 2 . . . work_fnploejenbc2raktl46esxm44i 514 1 Decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 514 2 Measures measure NNS work_fnploejenbc2raktl46esxm44i 514 3 and and CC work_fnploejenbc2raktl46esxm44i 514 4 Fuzzy Fuzzy NNP work_fnploejenbc2raktl46esxm44i 514 5 Logics Logics NNPS work_fnploejenbc2raktl46esxm44i 514 6 Since since IN work_fnploejenbc2raktl46esxm44i 514 7 the the DT work_fnploejenbc2raktl46esxm44i 514 8 concept concept NN work_fnploejenbc2raktl46esxm44i 514 9 of of IN work_fnploejenbc2raktl46esxm44i 514 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 514 11 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 514 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 514 13 possibility possibility NN work_fnploejenbc2raktl46esxm44i 514 14 measures measure NNS work_fnploejenbc2raktl46esxm44i 514 15 and and CC work_fnploejenbc2raktl46esxm44i 514 16 the the DT work_fnploejenbc2raktl46esxm44i 514 17 techniques technique NNS work_fnploejenbc2raktl46esxm44i 514 18 in in IN work_fnploejenbc2raktl46esxm44i 514 19 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 514 20 logics logic NNS work_fnploejenbc2raktl46esxm44i 514 21 might may MD work_fnploejenbc2raktl46esxm44i 514 22 not not RB work_fnploejenbc2raktl46esxm44i 514 23 be be VB work_fnploejenbc2raktl46esxm44i 514 24 familiar familiar JJ work_fnploejenbc2raktl46esxm44i 514 25 to to IN work_fnploejenbc2raktl46esxm44i 514 26 all all DT work_fnploejenbc2raktl46esxm44i 514 27 , , , work_fnploejenbc2raktl46esxm44i 514 28 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 514 29 first first RB work_fnploejenbc2raktl46esxm44i 514 30 present present VBP work_fnploejenbc2raktl46esxm44i 514 31 some some DT work_fnploejenbc2raktl46esxm44i 514 32 background background NN work_fnploejenbc2raktl46esxm44i 514 33 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 514 34 see see VB work_fnploejenbc2raktl46esxm44i 514 35 , , , work_fnploejenbc2raktl46esxm44i 514 36 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 514 37 , , , work_fnploejenbc2raktl46esxm44i 514 38 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 514 39 33 33 CD work_fnploejenbc2raktl46esxm44i 514 40 , , , work_fnploejenbc2raktl46esxm44i 514 41 32 32 CD work_fnploejenbc2raktl46esxm44i 514 42 , , , work_fnploejenbc2raktl46esxm44i 514 43 111 111 CD work_fnploejenbc2raktl46esxm44i 514 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 514 45 . . . work_fnploejenbc2raktl46esxm44i 515 1 Roughly roughly RB work_fnploejenbc2raktl46esxm44i 515 2 speaking speak VBG work_fnploejenbc2raktl46esxm44i 515 3 , , , work_fnploejenbc2raktl46esxm44i 515 4 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 515 5 logics logic NNS work_fnploejenbc2raktl46esxm44i 515 6 differ differ VBP work_fnploejenbc2raktl46esxm44i 515 7 from from IN work_fnploejenbc2raktl46esxm44i 515 8 ordinary ordinary JJ work_fnploejenbc2raktl46esxm44i 515 9 two two CD work_fnploejenbc2raktl46esxm44i 515 10 - - HYPH work_fnploejenbc2raktl46esxm44i 515 11 valued value VBN work_fnploejenbc2raktl46esxm44i 515 12 logic logic NN work_fnploejenbc2raktl46esxm44i 515 13 by by IN work_fnploejenbc2raktl46esxm44i 515 14 their -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 515 15 semantic semantic JJ work_fnploejenbc2raktl46esxm44i 515 16 evaluations evaluation NNS work_fnploejenbc2raktl46esxm44i 515 17 of of IN work_fnploejenbc2raktl46esxm44i 515 18 logical logical JJ work_fnploejenbc2raktl46esxm44i 515 19 connectives connective NNS work_fnploejenbc2raktl46esxm44i 515 20 . . . work_fnploejenbc2raktl46esxm44i 516 1 For for IN work_fnploejenbc2raktl46esxm44i 516 2 our -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 516 3 purpose purpose NN work_fnploejenbc2raktl46esxm44i 516 4 here here RB work_fnploejenbc2raktl46esxm44i 516 5 , , , work_fnploejenbc2raktl46esxm44i 516 6 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 516 7 will will MD work_fnploejenbc2raktl46esxm44i 516 8 focus focus VB work_fnploejenbc2raktl46esxm44i 516 9 on on IN work_fnploejenbc2raktl46esxm44i 516 10 the the DT work_fnploejenbc2raktl46esxm44i 516 11 evaluations evaluation NNS work_fnploejenbc2raktl46esxm44i 516 12 of of IN work_fnploejenbc2raktl46esxm44i 516 13 the the DT work_fnploejenbc2raktl46esxm44i 516 14 connective connective JJ work_fnploejenbc2raktl46esxm44i 516 15 “ " `` work_fnploejenbc2raktl46esxm44i 516 16 or or CC work_fnploejenbc2raktl46esxm44i 516 17 ” " '' work_fnploejenbc2raktl46esxm44i 516 18 which which WDT work_fnploejenbc2raktl46esxm44i 516 19 corresponds correspond VBZ work_fnploejenbc2raktl46esxm44i 516 20 to to IN work_fnploejenbc2raktl46esxm44i 516 21 the the DT work_fnploejenbc2raktl46esxm44i 516 22 main main JJ work_fnploejenbc2raktl46esxm44i 516 23 properties property NNS work_fnploejenbc2raktl46esxm44i 516 24 of of IN work_fnploejenbc2raktl46esxm44i 516 25 associated associate VBN work_fnploejenbc2raktl46esxm44i 516 26 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 516 27 measures measure NNS work_fnploejenbc2raktl46esxm44i 516 28 . . . work_fnploejenbc2raktl46esxm44i 517 1 A a DT work_fnploejenbc2raktl46esxm44i 517 2 function function NN work_fnploejenbc2raktl46esxm44i 517 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 517 4 operator operator NN work_fnploejenbc2raktl46esxm44i 517 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 517 6 T t NN work_fnploejenbc2raktl46esxm44i 517 7 : : : work_fnploejenbc2raktl46esxm44i 517 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 517 9 O o UH work_fnploejenbc2raktl46esxm44i 517 10 , , , work_fnploejenbc2raktl46esxm44i 517 11 l l NN work_fnploejenbc2raktl46esxm44i 517 12 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 517 13 x x NNP work_fnploejenbc2raktl46esxm44i 517 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 517 15 0 0 CD work_fnploejenbc2raktl46esxm44i 517 16 , , , work_fnploejenbc2raktl46esxm44i 517 17 l l NN work_fnploejenbc2raktl46esxm44i 517 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 517 19 + + CC work_fnploejenbc2raktl46esxm44i 517 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 517 21 0 0 CD work_fnploejenbc2raktl46esxm44i 517 22 , , , work_fnploejenbc2raktl46esxm44i 517 23 l l NN work_fnploejenbc2raktl46esxm44i 517 24 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 517 25 is be VBZ work_fnploejenbc2raktl46esxm44i 517 26 called call VBN work_fnploejenbc2raktl46esxm44i 517 27 a a DT work_fnploejenbc2raktl46esxm44i 517 28 t t NN work_fnploejenbc2raktl46esxm44i 517 29 - - HYPH work_fnploejenbc2raktl46esxm44i 517 30 conorm conorm NN work_fnploejenbc2raktl46esxm44i 517 31 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 517 32 see see VB work_fnploejenbc2raktl46esxm44i 517 33 , , , work_fnploejenbc2raktl46esxm44i 517 34 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 517 35 , , , work_fnploejenbc2raktl46esxm44i 517 36 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 517 37 25 25 CD work_fnploejenbc2raktl46esxm44i 517 38 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 517 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 517 40 if if IN work_fnploejenbc2raktl46esxm44i 517 41 T t NN work_fnploejenbc2raktl46esxm44i 517 42 is be VBZ work_fnploejenbc2raktl46esxm44i 517 43 associative associative JJ work_fnploejenbc2raktl46esxm44i 517 44 , , , work_fnploejenbc2raktl46esxm44i 517 45 commutative commutative JJ work_fnploejenbc2raktl46esxm44i 517 46 , , , work_fnploejenbc2raktl46esxm44i 517 47 and and CC work_fnploejenbc2raktl46esxm44i 517 48 nondecreasing nondecrease VBG work_fnploejenbc2raktl46esxm44i 517 49 in in IN work_fnploejenbc2raktl46esxm44i 517 50 each each DT work_fnploejenbc2raktl46esxm44i 517 51 argument argument NN work_fnploejenbc2raktl46esxm44i 517 52 ; ; : work_fnploejenbc2raktl46esxm44i 517 53 also also RB work_fnploejenbc2raktl46esxm44i 517 54 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 517 55 , , , work_fnploejenbc2raktl46esxm44i 517 56 0 0 CD work_fnploejenbc2raktl46esxm44i 517 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 517 58 = = NFP work_fnploejenbc2raktl46esxm44i 517 59 x x NN work_fnploejenbc2raktl46esxm44i 517 60 and and CC work_fnploejenbc2raktl46esxm44i 517 61 T(l t(l NN work_fnploejenbc2raktl46esxm44i 517 62 , , , work_fnploejenbc2raktl46esxm44i 517 63 X x NN work_fnploejenbc2raktl46esxm44i 517 64 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 517 65 = = SYM work_fnploejenbc2raktl46esxm44i 517 66 1 1 CD work_fnploejenbc2raktl46esxm44i 517 67 , , , work_fnploejenbc2raktl46esxm44i 517 68 VXE VXE NNP work_fnploejenbc2raktl46esxm44i 517 69 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 517 70 0 0 CD work_fnploejenbc2raktl46esxm44i 517 71 , , , work_fnploejenbc2raktl46esxm44i 517 72 11 11 CD work_fnploejenbc2raktl46esxm44i 517 73 . . . work_fnploejenbc2raktl46esxm44i 518 1 A a DT work_fnploejenbc2raktl46esxm44i 518 2 t t NN work_fnploejenbc2raktl46esxm44i 518 3 - - HYPH work_fnploejenbc2raktl46esxm44i 518 4 conorm conorm NN work_fnploejenbc2raktl46esxm44i 518 5 T T NNP work_fnploejenbc2raktl46esxm44i 518 6 is be VBZ work_fnploejenbc2raktl46esxm44i 518 7 said say VBN work_fnploejenbc2raktl46esxm44i 518 8 to to TO work_fnploejenbc2raktl46esxm44i 518 9 be be VB work_fnploejenbc2raktl46esxm44i 518 10 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 518 11 if if IN work_fnploejenbc2raktl46esxm44i 518 12 T T NNP work_fnploejenbc2raktl46esxm44i 518 13 is be VBZ work_fnploejenbc2raktl46esxm44i 518 14 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 518 15 and and CC work_fnploejenbc2raktl46esxm44i 518 16 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 518 17 , , , work_fnploejenbc2raktl46esxm44i 518 18 x x LS work_fnploejenbc2raktl46esxm44i 518 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 518 20 > > XX work_fnploejenbc2raktl46esxm44i 518 21 x x LS work_fnploejenbc2raktl46esxm44i 518 22 , , , work_fnploejenbc2raktl46esxm44i 518 23 Vx Vx NNP work_fnploejenbc2raktl46esxm44i 518 24 E E NNP work_fnploejenbc2raktl46esxm44i 518 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 518 26 0 0 CD work_fnploejenbc2raktl46esxm44i 518 27 , , , work_fnploejenbc2raktl46esxm44i 518 28 1 1 CD work_fnploejenbc2raktl46esxm44i 518 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 518 30 . . . work_fnploejenbc2raktl46esxm44i 519 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 519 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 519 3 TO to IN work_fnploejenbc2raktl46esxm44i 519 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 519 5 575 575 CD work_fnploejenbc2raktl46esxm44i 519 6 Some some DT work_fnploejenbc2raktl46esxm44i 519 7 examples example NNS work_fnploejenbc2raktl46esxm44i 519 8 of of IN work_fnploejenbc2raktl46esxm44i 519 9 t t NN work_fnploejenbc2raktl46esxm44i 519 10 - - HYPH work_fnploejenbc2raktl46esxm44i 519 11 conorms conorm NNS work_fnploejenbc2raktl46esxm44i 519 12 are be VBP work_fnploejenbc2raktl46esxm44i 519 13 x x NNS work_fnploejenbc2raktl46esxm44i 519 14 if if IN work_fnploejenbc2raktl46esxm44i 519 15 y y NN work_fnploejenbc2raktl46esxm44i 519 16 = = SYM work_fnploejenbc2raktl46esxm44i 519 17 O o UH work_fnploejenbc2raktl46esxm44i 519 18 T(x t(x NN work_fnploejenbc2raktl46esxm44i 519 19 , , , work_fnploejenbc2raktl46esxm44i 519 20 Y Y NNP work_fnploejenbc2raktl46esxm44i 519 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 22 ’ ' '' work_fnploejenbc2raktl46esxm44i 519 23 Y y UH work_fnploejenbc2raktl46esxm44i 519 24 if if IN work_fnploejenbc2raktl46esxm44i 519 25 x=0 x=0 NN work_fnploejenbc2raktl46esxm44i 519 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 519 27 not not RB work_fnploejenbc2raktl46esxm44i 519 28 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 519 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 30 1 1 CD work_fnploejenbc2raktl46esxm44i 519 31 otherwise otherwise RB work_fnploejenbc2raktl46esxm44i 519 32 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 519 33 , , , work_fnploejenbc2raktl46esxm44i 519 34 Y Y NNP work_fnploejenbc2raktl46esxm44i 519 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 36 = = SYM work_fnploejenbc2raktl46esxm44i 519 37 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 519 38 , , , work_fnploejenbc2raktl46esxm44i 519 39 Y Y NNP work_fnploejenbc2raktl46esxm44i 519 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 41 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 519 42 not not RB work_fnploejenbc2raktl46esxm44i 519 43 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 519 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 45 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 519 46 , , , work_fnploejenbc2raktl46esxm44i 519 47 y y NNP work_fnploejenbc2raktl46esxm44i 519 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 49 = = SYM work_fnploejenbc2raktl46esxm44i 519 50 Min(x min(x CD work_fnploejenbc2raktl46esxm44i 519 51 + + SYM work_fnploejenbc2raktl46esxm44i 519 52 y y NN work_fnploejenbc2raktl46esxm44i 519 53 , , , work_fnploejenbc2raktl46esxm44i 519 54 1 1 CD work_fnploejenbc2raktl46esxm44i 519 55 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 56 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 519 57 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 519 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 519 59 . . . work_fnploejenbc2raktl46esxm44i 520 1 For for IN work_fnploejenbc2raktl46esxm44i 520 2 the the DT work_fnploejenbc2raktl46esxm44i 520 3 related related JJ work_fnploejenbc2raktl46esxm44i 520 4 concept concept NN work_fnploejenbc2raktl46esxm44i 520 5 of of IN work_fnploejenbc2raktl46esxm44i 520 6 copulas copulas NN work_fnploejenbc2raktl46esxm44i 520 7 in in IN work_fnploejenbc2raktl46esxm44i 520 8 Statistics Statistics NNP work_fnploejenbc2raktl46esxm44i 520 9 , , , work_fnploejenbc2raktl46esxm44i 520 10 see see VB work_fnploejenbc2raktl46esxm44i 520 11 , , , work_fnploejenbc2raktl46esxm44i 520 12 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 520 13 , , , work_fnploejenbc2raktl46esxm44i 520 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 520 15 9 9 CD work_fnploejenbc2raktl46esxm44i 520 16 , , , work_fnploejenbc2raktl46esxm44i 520 17 10 10 CD work_fnploejenbc2raktl46esxm44i 520 18 , , , work_fnploejenbc2raktl46esxm44i 520 19 191 191 CD work_fnploejenbc2raktl46esxm44i 520 20 . . . work_fnploejenbc2raktl46esxm44i 521 1 An an DT work_fnploejenbc2raktl46esxm44i 521 2 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 521 3 t t NN work_fnploejenbc2raktl46esxm44i 521 4 - - HYPH work_fnploejenbc2raktl46esxm44i 521 5 conorm conorm NN work_fnploejenbc2raktl46esxm44i 521 6 T T NNP work_fnploejenbc2raktl46esxm44i 521 7 has have VBZ work_fnploejenbc2raktl46esxm44i 521 8 the the DT work_fnploejenbc2raktl46esxm44i 521 9 following follow VBG work_fnploejenbc2raktl46esxm44i 521 10 representation representation NN work_fnploejenbc2raktl46esxm44i 521 11 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 521 12 181 181 CD work_fnploejenbc2raktl46esxm44i 521 13 : : : work_fnploejenbc2raktl46esxm44i 521 14 T T NNP work_fnploejenbc2raktl46esxm44i 521 15 is be VBZ work_fnploejenbc2raktl46esxm44i 521 16 an an DT work_fnploejenbc2raktl46esxm44i 521 17 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 521 18 l l NN work_fnploejenbc2raktl46esxm44i 521 19 - - HYPH work_fnploejenbc2raktl46esxm44i 521 20 conorm conorm NN work_fnploejenbc2raktl46esxm44i 521 21 if if IN work_fnploejenbc2raktl46esxm44i 521 22 and and CC work_fnploejenbc2raktl46esxm44i 521 23 only only RB work_fnploejenbc2raktl46esxm44i 521 24 if if IN work_fnploejenbc2raktl46esxm44i 521 25 there there EX work_fnploejenbc2raktl46esxm44i 521 26 exists exist VBZ work_fnploejenbc2raktl46esxm44i 521 27 an an DT work_fnploejenbc2raktl46esxm44i 521 28 increasing increase VBG work_fnploejenbc2raktl46esxm44i 521 29 , , , work_fnploejenbc2raktl46esxm44i 521 30 con- con- NN work_fnploejenbc2raktl46esxm44i 521 31 tinuous tinuous JJ work_fnploejenbc2raktl46esxm44i 521 32 function function NN work_fnploejenbc2raktl46esxm44i 521 33 g g NNP work_fnploejenbc2raktl46esxm44i 521 34 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 521 35 called call VBN work_fnploejenbc2raktl46esxm44i 521 36 the the DT work_fnploejenbc2raktl46esxm44i 521 37 additive additive JJ work_fnploejenbc2raktl46esxm44i 521 38 generator generator NN work_fnploejenbc2raktl46esxm44i 521 39 or or CC work_fnploejenbc2raktl46esxm44i 521 40 generator generator NN work_fnploejenbc2raktl46esxm44i 521 41 of of IN work_fnploejenbc2raktl46esxm44i 521 42 T T NNP work_fnploejenbc2raktl46esxm44i 521 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 44 which which WDT work_fnploejenbc2raktl46esxm44i 521 45 maps map VBZ work_fnploejenbc2raktl46esxm44i 521 46 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 521 47 0 0 CD work_fnploejenbc2raktl46esxm44i 521 48 , , , work_fnploejenbc2raktl46esxm44i 521 49 l l NN work_fnploejenbc2raktl46esxm44i 521 50 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 521 51 -+ -+ . work_fnploejenbc2raktl46esxm44i 521 52 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 521 53 0 0 CD work_fnploejenbc2raktl46esxm44i 521 54 , , , work_fnploejenbc2raktl46esxm44i 521 55 + + CC work_fnploejenbc2raktl46esxm44i 521 56 co co NN work_fnploejenbc2raktl46esxm44i 521 57 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 521 58 with with IN work_fnploejenbc2raktl46esxm44i 521 59 g(0 g(0 NNP work_fnploejenbc2raktl46esxm44i 521 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 61 = = NFP work_fnploejenbc2raktl46esxm44i 521 62 0 0 NFP work_fnploejenbc2raktl46esxm44i 521 63 , , , work_fnploejenbc2raktl46esxm44i 521 64 and and CC work_fnploejenbc2raktl46esxm44i 521 65 such such JJ work_fnploejenbc2raktl46esxm44i 521 66 that that IN work_fnploejenbc2raktl46esxm44i 521 67 vx vx NNP work_fnploejenbc2raktl46esxm44i 521 68 , , , work_fnploejenbc2raktl46esxm44i 521 69 YE YE NNP work_fnploejenbc2raktl46esxm44i 521 70 lx lx NNP work_fnploejenbc2raktl46esxm44i 521 71 , , , work_fnploejenbc2raktl46esxm44i 521 72 11 11 CD work_fnploejenbc2raktl46esxm44i 521 73 , , , work_fnploejenbc2raktl46esxm44i 521 74 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 521 75 > > XX work_fnploejenbc2raktl46esxm44i 521 76 Y Y NNP work_fnploejenbc2raktl46esxm44i 521 77 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 78 = = NFP work_fnploejenbc2raktl46esxm44i 521 79 g*Mx g*Mx NNP work_fnploejenbc2raktl46esxm44i 521 80 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 81 + + SYM work_fnploejenbc2raktl46esxm44i 521 82 gb)L gb)L NNP work_fnploejenbc2raktl46esxm44i 521 83 where where WRB work_fnploejenbc2raktl46esxm44i 521 84 the the DT work_fnploejenbc2raktl46esxm44i 521 85 pseudo pseudo NN work_fnploejenbc2raktl46esxm44i 521 86 - - NN work_fnploejenbc2raktl46esxm44i 521 87 inuerse inuerse NN work_fnploejenbc2raktl46esxm44i 521 88 g g NN work_fnploejenbc2raktl46esxm44i 521 89 * * NFP work_fnploejenbc2raktl46esxm44i 521 90 : : : work_fnploejenbc2raktl46esxm44i 521 91 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 521 92 0 0 CD work_fnploejenbc2raktl46esxm44i 521 93 , , , work_fnploejenbc2raktl46esxm44i 521 94 + + CC work_fnploejenbc2raktl46esxm44i 521 95 co co NN work_fnploejenbc2raktl46esxm44i 521 96 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 521 97 + + CC work_fnploejenbc2raktl46esxm44i 521 98 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 521 99 0 0 CD work_fnploejenbc2raktl46esxm44i 521 100 , , , work_fnploejenbc2raktl46esxm44i 521 101 l l NN work_fnploejenbc2raktl46esxm44i 521 102 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 521 103 is be VBZ work_fnploejenbc2raktl46esxm44i 521 104 detined detine VBN work_fnploejenbc2raktl46esxm44i 521 105 by by IN work_fnploejenbc2raktl46esxm44i 521 106 g*(x)= g*(x)= NNP work_fnploejenbc2raktl46esxm44i 521 107 1 1 CD work_fnploejenbc2raktl46esxm44i 521 108 i i PRP work_fnploejenbc2raktl46esxm44i 521 109 g-‘(x g-‘(x NNP work_fnploejenbc2raktl46esxm44i 521 110 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 111 if if IN work_fnploejenbc2raktl46esxm44i 521 112 XE XE NNP work_fnploejenbc2raktl46esxm44i 521 113 CO CO NNP work_fnploejenbc2raktl46esxm44i 521 114 , , , work_fnploejenbc2raktl46esxm44i 521 115 g(l)1 g(l)1 NN work_fnploejenbc2raktl46esxm44i 521 116 if if IN work_fnploejenbc2raktl46esxm44i 521 117 x x NNP work_fnploejenbc2raktl46esxm44i 521 118 > > XX work_fnploejenbc2raktl46esxm44i 521 119 g(l g(l ADD work_fnploejenbc2raktl46esxm44i 521 120 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 521 121 . . . work_fnploejenbc2raktl46esxm44i 522 1 For for IN work_fnploejenbc2raktl46esxm44i 522 2 example example NN work_fnploejenbc2raktl46esxm44i 522 3 , , , work_fnploejenbc2raktl46esxm44i 522 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 522 5 i i NN work_fnploejenbc2raktl46esxm44i 522 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 7 For for IN work_fnploejenbc2raktl46esxm44i 522 8 p p NN work_fnploejenbc2raktl46esxm44i 522 9 > > XX work_fnploejenbc2raktl46esxm44i 522 10 O o UH work_fnploejenbc2raktl46esxm44i 522 11 , , , work_fnploejenbc2raktl46esxm44i 522 12 Tp(x Tp(x NNP work_fnploejenbc2raktl46esxm44i 522 13 , , , work_fnploejenbc2raktl46esxm44i 522 14 Y Y NNP work_fnploejenbc2raktl46esxm44i 522 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 16 = = NFP work_fnploejenbc2raktl46esxm44i 522 17 W w NN work_fnploejenbc2raktl46esxm44i 522 18 ’ ' '' work_fnploejenbc2raktl46esxm44i 522 19 + + CC work_fnploejenbc2raktl46esxm44i 522 20 Y Y NNP work_fnploejenbc2raktl46esxm44i 522 21 ’ ' '' work_fnploejenbc2raktl46esxm44i 522 22 - - HYPH work_fnploejenbc2raktl46esxm44i 522 23 x x NNS work_fnploejenbc2raktl46esxm44i 522 24 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 522 25 Y~)“~ Y~)“~ NNS work_fnploejenbc2raktl46esxm44i 522 26 = = SYM work_fnploejenbc2raktl46esxm44i 522 27 g;(g,(x g;(g,(x JJ work_fnploejenbc2raktl46esxm44i 522 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 29 + + NFP work_fnploejenbc2raktl46esxm44i 522 30 g,(y g,(y NNP work_fnploejenbc2raktl46esxm44i 522 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 33 , , , work_fnploejenbc2raktl46esxm44i 522 34 where where WRB work_fnploejenbc2raktl46esxm44i 522 35 g,(x g,(x NNP work_fnploejenbc2raktl46esxm44i 522 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 37 = = NFP work_fnploejenbc2raktl46esxm44i 522 38 - - : work_fnploejenbc2raktl46esxm44i 522 39 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 522 40 l l NN work_fnploejenbc2raktl46esxm44i 522 41 / / SYM work_fnploejenbc2raktl46esxm44i 522 42 p p NNP work_fnploejenbc2raktl46esxm44i 522 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 44 log log NN work_fnploejenbc2raktl46esxm44i 522 45 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 522 46 1 1 CD work_fnploejenbc2raktl46esxm44i 522 47 - - HYPH work_fnploejenbc2raktl46esxm44i 522 48 xp xp NNP work_fnploejenbc2raktl46esxm44i 522 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 50 , , , work_fnploejenbc2raktl46esxm44i 522 51 g;‘(x g;‘(x NNP work_fnploejenbc2raktl46esxm44i 522 52 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 53 = = NFP work_fnploejenbc2raktl46esxm44i 522 54 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 522 55 1 1 CD work_fnploejenbc2raktl46esxm44i 522 56 - - HYPH work_fnploejenbc2raktl46esxm44i 522 57 eppx)“P eppx)“P NNP work_fnploejenbc2raktl46esxm44i 522 58 = = SYM work_fnploejenbc2raktl46esxm44i 522 59 g,*(x g,*(x CD work_fnploejenbc2raktl46esxm44i 522 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 61 ; ; : work_fnploejenbc2raktl46esxm44i 522 62 note note VB work_fnploejenbc2raktl46esxm44i 522 63 that that IN work_fnploejenbc2raktl46esxm44i 522 64 g g NN work_fnploejenbc2raktl46esxm44i 522 65 , , , work_fnploejenbc2raktl46esxm44i 522 66 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 522 67 1 1 LS work_fnploejenbc2raktl46esxm44i 522 68 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 522 69 = = NFP work_fnploejenbc2raktl46esxm44i 522 70 + + CC work_fnploejenbc2raktl46esxm44i 522 71 co co NN work_fnploejenbc2raktl46esxm44i 522 72 here here RB work_fnploejenbc2raktl46esxm44i 522 73 . . . work_fnploejenbc2raktl46esxm44i 523 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 523 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 523 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 523 4 For for IN work_fnploejenbc2raktl46esxm44i 523 5 p p NN work_fnploejenbc2raktl46esxm44i 523 6 B b NN work_fnploejenbc2raktl46esxm44i 523 7 1 1 CD work_fnploejenbc2raktl46esxm44i 523 8 , , , work_fnploejenbc2raktl46esxm44i 523 9 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 523 10 , , , work_fnploejenbc2raktl46esxm44i 523 11 JJ JJ NNP work_fnploejenbc2raktl46esxm44i 523 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 523 13 = = NFP work_fnploejenbc2raktl46esxm44i 523 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 523 15 Min(xP Min(xP NNP work_fnploejenbc2raktl46esxm44i 523 16 -I- -I- : work_fnploejenbc2raktl46esxm44i 523 17 yp yp NNP work_fnploejenbc2raktl46esxm44i 523 18 , , , work_fnploejenbc2raktl46esxm44i 523 19 l l NNP work_fnploejenbc2raktl46esxm44i 523 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 523 21 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 523 22 “ " `` work_fnploejenbc2raktl46esxm44i 523 23 ” " '' work_fnploejenbc2raktl46esxm44i 523 24 has have VBZ work_fnploejenbc2raktl46esxm44i 523 25 generator generator NN work_fnploejenbc2raktl46esxm44i 523 26 g,(x g,(x NNP work_fnploejenbc2raktl46esxm44i 523 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 523 28 = = NFP work_fnploejenbc2raktl46esxm44i 523 29 xp xp NNP work_fnploejenbc2raktl46esxm44i 523 30 , , , work_fnploejenbc2raktl46esxm44i 523 31 1 1 CD work_fnploejenbc2raktl46esxm44i 523 32 x’IP x’IP NNP work_fnploejenbc2raktl46esxm44i 523 33 g*(x)= g*(x)= NNP work_fnploejenbc2raktl46esxm44i 523 34 1 1 CD work_fnploejenbc2raktl46esxm44i 523 35 if if IN work_fnploejenbc2raktl46esxm44i 523 36 xE[O xE[O NNP work_fnploejenbc2raktl46esxm44i 523 37 , , , work_fnploejenbc2raktl46esxm44i 523 38 l l NN work_fnploejenbc2raktl46esxm44i 523 39 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 523 40 if if IN work_fnploejenbc2raktl46esxm44i 523 41 x x NNP work_fnploejenbc2raktl46esxm44i 523 42 > > XX work_fnploejenbc2raktl46esxm44i 523 43 l l NN work_fnploejenbc2raktl46esxm44i 523 44 with with IN work_fnploejenbc2raktl46esxm44i 523 45 g g NN work_fnploejenbc2raktl46esxm44i 523 46 , , , work_fnploejenbc2raktl46esxm44i 523 47 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 523 48 1 1 LS work_fnploejenbc2raktl46esxm44i 523 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 523 50 = = SYM work_fnploejenbc2raktl46esxm44i 523 51 1 1 CD work_fnploejenbc2raktl46esxm44i 523 52 here here RB work_fnploejenbc2raktl46esxm44i 523 53 . . . work_fnploejenbc2raktl46esxm44i 524 1 Since since IN work_fnploejenbc2raktl46esxm44i 524 2 a a DT work_fnploejenbc2raktl46esxm44i 524 3 t t NN work_fnploejenbc2raktl46esxm44i 524 4 - - HYPH work_fnploejenbc2raktl46esxm44i 524 5 conorm conorm NN work_fnploejenbc2raktl46esxm44i 524 6 T t NN work_fnploejenbc2raktl46esxm44i 524 7 is be VBZ work_fnploejenbc2raktl46esxm44i 524 8 associative associative JJ work_fnploejenbc2raktl46esxm44i 524 9 and and CC work_fnploejenbc2raktl46esxm44i 524 10 commutative commutative JJ work_fnploejenbc2raktl46esxm44i 524 11 , , , work_fnploejenbc2raktl46esxm44i 524 12 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 524 13 can can MD work_fnploejenbc2raktl46esxm44i 524 14 extend extend VB work_fnploejenbc2raktl46esxm44i 524 15 T t NN work_fnploejenbc2raktl46esxm44i 524 16 to to IN work_fnploejenbc2raktl46esxm44i 524 17 T t NN work_fnploejenbc2raktl46esxm44i 524 18 : : : work_fnploejenbc2raktl46esxm44i 524 19 co co NN work_fnploejenbc2raktl46esxm44i 524 20 , , , work_fnploejenbc2raktl46esxm44i 524 21 11 11 CD work_fnploejenbc2raktl46esxm44i 524 22 , , , work_fnploejenbc2raktl46esxm44i 524 23 + + CC work_fnploejenbc2raktl46esxm44i 524 24 co co NN work_fnploejenbc2raktl46esxm44i 524 25 , , , work_fnploejenbc2raktl46esxm44i 524 26 11 11 CD work_fnploejenbc2raktl46esxm44i 524 27 , , , work_fnploejenbc2raktl46esxm44i 524 28 where where WRB work_fnploejenbc2raktl46esxm44i 524 29 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 524 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 524 31 = = SYM work_fnploejenbc2raktl46esxm44i 524 32 x x LS work_fnploejenbc2raktl46esxm44i 524 33 , , , work_fnploejenbc2raktl46esxm44i 524 34 by by IN work_fnploejenbc2raktl46esxm44i 524 35 convention convention NN work_fnploejenbc2raktl46esxm44i 524 36 , , , work_fnploejenbc2raktl46esxm44i 524 37 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 524 38 I I NNP work_fnploejenbc2raktl46esxm44i 524 39 , , , work_fnploejenbc2raktl46esxm44i 524 40 -*- -*- NFP work_fnploejenbc2raktl46esxm44i 524 41 , , , work_fnploejenbc2raktl46esxm44i 524 42 xx xx NNP work_fnploejenbc2raktl46esxm44i 524 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 524 44 = = NFP work_fnploejenbc2raktl46esxm44i 524 45 Tb Tb NNP work_fnploejenbc2raktl46esxm44i 524 46 , , , work_fnploejenbc2raktl46esxm44i 524 47 , , , work_fnploejenbc2raktl46esxm44i 524 48 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 524 49 , , , work_fnploejenbc2raktl46esxm44i 524 50 , , , work_fnploejenbc2raktl46esxm44i 524 51 . . . work_fnploejenbc2raktl46esxm44i 525 1 . . . work_fnploejenbc2raktl46esxm44i 526 1 . . . work_fnploejenbc2raktl46esxm44i 527 1 . . . work_fnploejenbc2raktl46esxm44i 528 1 x,)1 x,)1 NNP work_fnploejenbc2raktl46esxm44i 528 2 , , , work_fnploejenbc2raktl46esxm44i 528 3 n n CC work_fnploejenbc2raktl46esxm44i 528 4 2 2 CD work_fnploejenbc2raktl46esxm44i 528 5 2 2 CD work_fnploejenbc2raktl46esxm44i 528 6 . . . work_fnploejenbc2raktl46esxm44i 529 1 The the DT work_fnploejenbc2raktl46esxm44i 529 2 representation representation NN work_fnploejenbc2raktl46esxm44i 529 3 of of IN work_fnploejenbc2raktl46esxm44i 529 4 an an DT work_fnploejenbc2raktl46esxm44i 529 5 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 529 6 t t NN work_fnploejenbc2raktl46esxm44i 529 7 - - HYPH work_fnploejenbc2raktl46esxm44i 529 8 conorm conorm NN work_fnploejenbc2raktl46esxm44i 529 9 T t NN work_fnploejenbc2raktl46esxm44i 529 10 becomes become VBZ work_fnploejenbc2raktl46esxm44i 529 11 W W NNP work_fnploejenbc2raktl46esxm44i 529 12 , , , work_fnploejenbc2raktl46esxm44i 529 13 , , , work_fnploejenbc2raktl46esxm44i 529 14 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 529 15 , , , work_fnploejenbc2raktl46esxm44i 529 16 . . . work_fnploejenbc2raktl46esxm44i 530 1 . . . work_fnploejenbc2raktl46esxm44i 531 1 . . . work_fnploejenbc2raktl46esxm44i 532 1 . . . work_fnploejenbc2raktl46esxm44i 533 1 x x LS work_fnploejenbc2raktl46esxm44i 533 2 , , , work_fnploejenbc2raktl46esxm44i 533 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 533 4 = = NFP work_fnploejenbc2raktl46esxm44i 533 5 g g NN work_fnploejenbc2raktl46esxm44i 533 6 * * NFP work_fnploejenbc2raktl46esxm44i 533 7 0 0 CD work_fnploejenbc2raktl46esxm44i 533 8 1 1 CD work_fnploejenbc2raktl46esxm44i 533 9 . . . work_fnploejenbc2raktl46esxm44i 534 1 576 576 CD work_fnploejenbc2raktl46esxm44i 534 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 534 3 , , , work_fnploejenbc2raktl46esxm44i 534 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 534 5 , , , work_fnploejenbc2raktl46esxm44i 534 6 AND and CC work_fnploejenbc2raktl46esxm44i 534 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 534 8 Now now RB work_fnploejenbc2raktl46esxm44i 534 9 , , , work_fnploejenbc2raktl46esxm44i 534 10 let let VB work_fnploejenbc2raktl46esxm44i 534 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 534 12 52 52 CD work_fnploejenbc2raktl46esxm44i 534 13 , , , work_fnploejenbc2raktl46esxm44i 534 14 J J NNP work_fnploejenbc2raktl46esxm44i 534 15 & & CC work_fnploejenbc2raktl46esxm44i 534 16 ‘ ' `` work_fnploejenbc2raktl46esxm44i 534 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 534 18 be be VB work_fnploejenbc2raktl46esxm44i 534 19 a a DT work_fnploejenbc2raktl46esxm44i 534 20 measurable measurable JJ work_fnploejenbc2raktl46esxm44i 534 21 space space NN work_fnploejenbc2raktl46esxm44i 534 22 . . . work_fnploejenbc2raktl46esxm44i 535 1 A a DT work_fnploejenbc2raktl46esxm44i 535 2 mapping mapping NN work_fnploejenbc2raktl46esxm44i 535 3 p p NN work_fnploejenbc2raktl46esxm44i 535 4 from from IN work_fnploejenbc2raktl46esxm44i 535 5 & & CC work_fnploejenbc2raktl46esxm44i 535 6 to to IN work_fnploejenbc2raktl46esxm44i 535 7 some some DT work_fnploejenbc2raktl46esxm44i 535 8 interval interval NN work_fnploejenbc2raktl46esxm44i 535 9 of of IN work_fnploejenbc2raktl46esxm44i 535 10 R r NN work_fnploejenbc2raktl46esxm44i 535 11 , , , work_fnploejenbc2raktl46esxm44i 535 12 say say VB work_fnploejenbc2raktl46esxm44i 535 13 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 535 14 a a DT work_fnploejenbc2raktl46esxm44i 535 15 , , , work_fnploejenbc2raktl46esxm44i 535 16 , , , work_fnploejenbc2raktl46esxm44i 535 17 a a DT work_fnploejenbc2raktl46esxm44i 535 18 , , , work_fnploejenbc2raktl46esxm44i 535 19 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 535 20 , , , work_fnploejenbc2raktl46esxm44i 535 21 is be VBZ work_fnploejenbc2raktl46esxm44i 535 22 called call VBN work_fnploejenbc2raktl46esxm44i 535 23 a a DT work_fnploejenbc2raktl46esxm44i 535 24 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 535 25 measure measure NN work_fnploejenbc2raktl46esxm44i 535 26 if if IN work_fnploejenbc2raktl46esxm44i 535 27 there there EX work_fnploejenbc2raktl46esxm44i 535 28 exists exist VBZ work_fnploejenbc2raktl46esxm44i 535 29 T t NN work_fnploejenbc2raktl46esxm44i 535 30 : : : work_fnploejenbc2raktl46esxm44i 535 31 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 535 32 a a DT work_fnploejenbc2raktl46esxm44i 535 33 , , , work_fnploejenbc2raktl46esxm44i 535 34 , , , work_fnploejenbc2raktl46esxm44i 535 35 a31 a31 NN work_fnploejenbc2raktl46esxm44i 535 36 x x SYM work_fnploejenbc2raktl46esxm44i 535 37 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 535 38 a a DT work_fnploejenbc2raktl46esxm44i 535 39 , , , work_fnploejenbc2raktl46esxm44i 535 40 , , , work_fnploejenbc2raktl46esxm44i 535 41 a31 a31 NN work_fnploejenbc2raktl46esxm44i 535 42 + + CC work_fnploejenbc2raktl46esxm44i 535 43 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 535 44 a a DT work_fnploejenbc2raktl46esxm44i 535 45 , , , work_fnploejenbc2raktl46esxm44i 535 46 , , , work_fnploejenbc2raktl46esxm44i 535 47 a a DT work_fnploejenbc2raktl46esxm44i 535 48 , , , work_fnploejenbc2raktl46esxm44i 535 49 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 535 50 such such JJ work_fnploejenbc2raktl46esxm44i 535 51 that that IN work_fnploejenbc2raktl46esxm44i 535 52 , , , work_fnploejenbc2raktl46esxm44i 535 53 for for IN work_fnploejenbc2raktl46esxm44i 535 54 A a DT work_fnploejenbc2raktl46esxm44i 535 55 , , , work_fnploejenbc2raktl46esxm44i 535 56 BE BE NNP work_fnploejenbc2raktl46esxm44i 535 57 d d VBN work_fnploejenbc2raktl46esxm44i 535 58 with with IN work_fnploejenbc2raktl46esxm44i 535 59 AB= ab= ADD work_fnploejenbc2raktl46esxm44i 535 60 a a DT work_fnploejenbc2raktl46esxm44i 535 61 , , , work_fnploejenbc2raktl46esxm44i 535 62 p(A p(a IN work_fnploejenbc2raktl46esxm44i 535 63 u u NNP work_fnploejenbc2raktl46esxm44i 535 64 B b NN work_fnploejenbc2raktl46esxm44i 535 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 535 66 = = NFP work_fnploejenbc2raktl46esxm44i 535 67 T(p(A t(p(a ADD work_fnploejenbc2raktl46esxm44i 535 68 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 535 69 , , , work_fnploejenbc2raktl46esxm44i 535 70 p(B p(b LS work_fnploejenbc2raktl46esxm44i 535 71 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 535 72 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 535 73 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 535 74 see see VB work_fnploejenbc2raktl46esxm44i 535 75 , , , work_fnploejenbc2raktl46esxm44i 535 76 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 535 77 , , , work_fnploejenbc2raktl46esxm44i 535 78 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 535 79 31 31 CD work_fnploejenbc2raktl46esxm44i 535 80 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 535 81 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 535 82 . . . work_fnploejenbc2raktl46esxm44i 536 1 When when WRB work_fnploejenbc2raktl46esxm44i 536 2 such such PDT work_fnploejenbc2raktl46esxm44i 536 3 a a DT work_fnploejenbc2raktl46esxm44i 536 4 Texists texist NNS work_fnploejenbc2raktl46esxm44i 536 5 , , , work_fnploejenbc2raktl46esxm44i 536 6 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 536 7 is be VBZ work_fnploejenbc2raktl46esxm44i 536 8 called call VBN work_fnploejenbc2raktl46esxm44i 536 9 the the DT work_fnploejenbc2raktl46esxm44i 536 10 composition composition NN work_fnploejenbc2raktl46esxm44i 536 11 law law NN work_fnploejenbc2raktl46esxm44i 536 12 of of IN work_fnploejenbc2raktl46esxm44i 536 13 p. p. NN work_fnploejenbc2raktl46esxm44i 536 14 As as IN work_fnploejenbc2raktl46esxm44i 536 15 a a DT work_fnploejenbc2raktl46esxm44i 536 16 generic generic JJ work_fnploejenbc2raktl46esxm44i 536 17 example example NN work_fnploejenbc2raktl46esxm44i 536 18 of of IN work_fnploejenbc2raktl46esxm44i 536 19 a a DT work_fnploejenbc2raktl46esxm44i 536 20 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 536 21 measure measure NN work_fnploejenbc2raktl46esxm44i 536 22 , , , work_fnploejenbc2raktl46esxm44i 536 23 begin begin VB work_fnploejenbc2raktl46esxm44i 536 24 with with IN work_fnploejenbc2raktl46esxm44i 536 25 any any DT work_fnploejenbc2raktl46esxm44i 536 26 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 536 27 set set VBN work_fnploejenbc2raktl46esxm44i 536 28 membership membership NN work_fnploejenbc2raktl46esxm44i 536 29 function function NN work_fnploejenbc2raktl46esxm44i 536 30 01 01 CD work_fnploejenbc2raktl46esxm44i 536 31 : : : work_fnploejenbc2raktl46esxm44i 536 32 D d NN work_fnploejenbc2raktl46esxm44i 536 33 -- -- : work_fnploejenbc2raktl46esxm44i 536 34 , , , work_fnploejenbc2raktl46esxm44i 536 35 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 536 36 0 0 CD work_fnploejenbc2raktl46esxm44i 536 37 , , , work_fnploejenbc2raktl46esxm44i 536 38 l l NN work_fnploejenbc2raktl46esxm44i 536 39 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 536 40 and and CC work_fnploejenbc2raktl46esxm44i 536 41 any any DT work_fnploejenbc2raktl46esxm44i 536 42 t t NN work_fnploejenbc2raktl46esxm44i 536 43 - - HYPH work_fnploejenbc2raktl46esxm44i 536 44 conorm conorm NN work_fnploejenbc2raktl46esxm44i 536 45 T. T. NNP work_fnploejenbc2raktl46esxm44i 536 46 Then then RB work_fnploejenbc2raktl46esxm44i 536 47 , , , work_fnploejenbc2raktl46esxm44i 536 48 if if IN work_fnploejenbc2raktl46esxm44i 536 49 0 0 CD work_fnploejenbc2raktl46esxm44i 536 50 is be VBZ work_fnploejenbc2raktl46esxm44i 536 51 finite finite JJ work_fnploejenbc2raktl46esxm44i 536 52 , , , work_fnploejenbc2raktl46esxm44i 536 53 one one PRP work_fnploejenbc2raktl46esxm44i 536 54 can can MD work_fnploejenbc2raktl46esxm44i 536 55 make make VB work_fnploejenbc2raktl46esxm44i 536 56 the the DT work_fnploejenbc2raktl46esxm44i 536 57 extension extension NN work_fnploejenbc2raktl46esxm44i 536 58 of of IN work_fnploejenbc2raktl46esxm44i 536 59 a a DT work_fnploejenbc2raktl46esxm44i 536 60 as as IN work_fnploejenbc2raktl46esxm44i 536 61 , , , work_fnploejenbc2raktl46esxm44i 536 62 u,,~ u,,~ NNP work_fnploejenbc2raktl46esxm44i 536 63 : : : work_fnploejenbc2raktl46esxm44i 536 64 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 536 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 536 66 + + CC work_fnploejenbc2raktl46esxm44i 536 67 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 536 68 0 0 CD work_fnploejenbc2raktl46esxm44i 536 69 , , , work_fnploejenbc2raktl46esxm44i 536 70 11 11 CD work_fnploejenbc2raktl46esxm44i 536 71 , , , work_fnploejenbc2raktl46esxm44i 536 72 where where WRB work_fnploejenbc2raktl46esxm44i 536 73 for for IN work_fnploejenbc2raktl46esxm44i 536 74 any any DT work_fnploejenbc2raktl46esxm44i 536 75 AcSZ AcSZ NNP work_fnploejenbc2raktl46esxm44i 536 76 , , , work_fnploejenbc2raktl46esxm44i 536 77 , , , work_fnploejenbc2raktl46esxm44i 536 78 ua ua NNP work_fnploejenbc2raktl46esxm44i 536 79 , , , work_fnploejenbc2raktl46esxm44i 536 80 T(A t(a NN work_fnploejenbc2raktl46esxm44i 536 81 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 536 82 = = NFP work_fnploejenbc2raktl46esxm44i 536 83 T(a(o t(a(o NN work_fnploejenbc2raktl46esxm44i 536 84 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 536 85 : : : work_fnploejenbc2raktl46esxm44i 536 86 w w NNP work_fnploejenbc2raktl46esxm44i 536 87 E E NNP work_fnploejenbc2raktl46esxm44i 536 88 A a NN work_fnploejenbc2raktl46esxm44i 536 89 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 536 90 . . . work_fnploejenbc2raktl46esxm44i 537 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 537 2 + + NFP work_fnploejenbc2raktl46esxm44i 537 3 I i NN work_fnploejenbc2raktl46esxm44i 537 4 P p NN work_fnploejenbc2raktl46esxm44i 537 5 is be VBZ work_fnploejenbc2raktl46esxm44i 537 6 clearly clearly RB work_fnploejenbc2raktl46esxm44i 537 7 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 537 8 . . . work_fnploejenbc2raktl46esxm44i 538 1 Conversely conversely RB work_fnploejenbc2raktl46esxm44i 538 2 , , , work_fnploejenbc2raktl46esxm44i 538 3 given give VBN work_fnploejenbc2raktl46esxm44i 538 4 any any DT work_fnploejenbc2raktl46esxm44i 538 5 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 538 6 measure measure NN work_fnploejenbc2raktl46esxm44i 538 7 pa’G.r.t pa’G.r.t NNP work_fnploejenbc2raktl46esxm44i 538 8 . . . work_fnploejenbc2raktl46esxm44i 539 1 some some DT work_fnploejenbc2raktl46esxm44i 539 2 t t NN work_fnploejenbc2raktl46esxm44i 539 3 - - HYPH work_fnploejenbc2raktl46esxm44i 539 4 conorm conorm NN work_fnploejenbc2raktl46esxm44i 539 5 T T NNP work_fnploejenbc2raktl46esxm44i 539 6 , , , work_fnploejenbc2raktl46esxm44i 539 7 for for IN work_fnploejenbc2raktl46esxm44i 539 8 any any DT work_fnploejenbc2raktl46esxm44i 539 9 finite finite JJ work_fnploejenbc2raktl46esxm44i 539 10 A A NNP work_fnploejenbc2raktl46esxm44i 539 11 as as IN work_fnploejenbc2raktl46esxm44i 539 12 above above RB work_fnploejenbc2raktl46esxm44i 539 13 , , , work_fnploejenbc2raktl46esxm44i 539 14 Eq Eq NNP work_fnploejenbc2raktl46esxm44i 539 15 . . . work_fnploejenbc2raktl46esxm44i 540 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 540 2 + + NFP work_fnploejenbc2raktl46esxm44i 540 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 540 4 holds hold VBZ work_fnploejenbc2raktl46esxm44i 540 5 with with IN work_fnploejenbc2raktl46esxm44i 540 6 h h NN work_fnploejenbc2raktl46esxm44i 540 7 , , , work_fnploejenbc2raktl46esxm44i 540 8 T t NN work_fnploejenbc2raktl46esxm44i 540 9 = = SYM work_fnploejenbc2raktl46esxm44i 540 10 k k NN work_fnploejenbc2raktl46esxm44i 540 11 In in IN work_fnploejenbc2raktl46esxm44i 540 12 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 540 13 logics logic NNS work_fnploejenbc2raktl46esxm44i 540 14 , , , work_fnploejenbc2raktl46esxm44i 540 15 composition composition NN work_fnploejenbc2raktl46esxm44i 540 16 laws law NNS work_fnploejenbc2raktl46esxm44i 540 17 are be VBP work_fnploejenbc2raktl46esxm44i 540 18 t t NN work_fnploejenbc2raktl46esxm44i 540 19 - - HYPH work_fnploejenbc2raktl46esxm44i 540 20 conorms conorm NNS work_fnploejenbc2raktl46esxm44i 540 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 540 22 with with IN work_fnploejenbc2raktl46esxm44i 540 23 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 540 24 a a DT work_fnploejenbc2raktl46esxm44i 540 25 , , , work_fnploejenbc2raktl46esxm44i 540 26 , , , work_fnploejenbc2raktl46esxm44i 540 27 a3 a3 NNP work_fnploejenbc2raktl46esxm44i 540 28 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 540 29 = = FW work_fnploejenbc2raktl46esxm44i 540 30 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 540 31 0 0 CD work_fnploejenbc2raktl46esxm44i 540 32 , , , work_fnploejenbc2raktl46esxm44i 540 33 11 11 CD work_fnploejenbc2raktl46esxm44i 540 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 540 35 . . . work_fnploejenbc2raktl46esxm44i 541 1 Note note VB work_fnploejenbc2raktl46esxm44i 541 2 that that IN work_fnploejenbc2raktl46esxm44i 541 3 probability probability NN work_fnploejenbc2raktl46esxm44i 541 4 measures measure NNS work_fnploejenbc2raktl46esxm44i 541 5 are be VBP work_fnploejenbc2raktl46esxm44i 541 6 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 541 7 measures measure NNS work_fnploejenbc2raktl46esxm44i 541 8 with with IN work_fnploejenbc2raktl46esxm44i 541 9 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 541 10 , , , work_fnploejenbc2raktl46esxm44i 541 11 y y NNP work_fnploejenbc2raktl46esxm44i 541 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 541 13 = = SYM work_fnploejenbc2raktl46esxm44i 541 14 Min(x min(x CD work_fnploejenbc2raktl46esxm44i 541 15 + + SYM work_fnploejenbc2raktl46esxm44i 541 16 y y NN work_fnploejenbc2raktl46esxm44i 541 17 , , , work_fnploejenbc2raktl46esxm44i 541 18 1 1 CD work_fnploejenbc2raktl46esxm44i 541 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 541 20 ; ; : work_fnploejenbc2raktl46esxm44i 541 21 this this DT work_fnploejenbc2raktl46esxm44i 541 22 is be VBZ work_fnploejenbc2raktl46esxm44i 541 23 an an DT work_fnploejenbc2raktl46esxm44i 541 24 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 541 25 t t NN work_fnploejenbc2raktl46esxm44i 541 26 - - HYPH work_fnploejenbc2raktl46esxm44i 541 27 conorm conorm NN work_fnploejenbc2raktl46esxm44i 541 28 with with IN work_fnploejenbc2raktl46esxm44i 541 29 generator generator NN work_fnploejenbc2raktl46esxm44i 541 30 g(x)= g(x)= NNP work_fnploejenbc2raktl46esxm44i 541 31 -log(l -log(l : work_fnploejenbc2raktl46esxm44i 541 32 - - HYPH work_fnploejenbc2raktl46esxm44i 541 33 x x NNPS work_fnploejenbc2raktl46esxm44i 541 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 541 35 and and CC work_fnploejenbc2raktl46esxm44i 541 36 g*(x)=g-‘(x)=1-e- g*(x)=g-‘(x)=1-e- NNP work_fnploejenbc2raktl46esxm44i 541 37 “ " '' work_fnploejenbc2raktl46esxm44i 541 38 , , , work_fnploejenbc2raktl46esxm44i 541 39 since since IN work_fnploejenbc2raktl46esxm44i 541 40 g(l)= g(l)= CD work_fnploejenbc2raktl46esxm44i 541 41 + + CC work_fnploejenbc2raktl46esxm44i 541 42 oo oo NN work_fnploejenbc2raktl46esxm44i 541 43 . . . work_fnploejenbc2raktl46esxm44i 542 1 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 542 2 , , , work_fnploejenbc2raktl46esxm44i 542 3 let let VB work_fnploejenbc2raktl46esxm44i 542 4 P p NN work_fnploejenbc2raktl46esxm44i 542 5 be be VB work_fnploejenbc2raktl46esxm44i 542 6 a a DT work_fnploejenbc2raktl46esxm44i 542 7 probability probability NN work_fnploejenbc2raktl46esxm44i 542 8 measure measure NN work_fnploejenbc2raktl46esxm44i 542 9 on on IN work_fnploejenbc2raktl46esxm44i 542 10 d d NN work_fnploejenbc2raktl46esxm44i 542 11 , , , work_fnploejenbc2raktl46esxm44i 542 12 and and CC work_fnploejenbc2raktl46esxm44i 542 13 A A NNP work_fnploejenbc2raktl46esxm44i 542 14 , , , work_fnploejenbc2raktl46esxm44i 542 15 BE be VB work_fnploejenbc2raktl46esxm44i 542 16 d d NN work_fnploejenbc2raktl46esxm44i 542 17 with with IN work_fnploejenbc2raktl46esxm44i 542 18 AB AB NNP work_fnploejenbc2raktl46esxm44i 542 19 = = SYM work_fnploejenbc2raktl46esxm44i 542 20 0 0 NFP work_fnploejenbc2raktl46esxm44i 542 21 . . . work_fnploejenbc2raktl46esxm44i 543 1 Since since IN work_fnploejenbc2raktl46esxm44i 543 2 P(A P(A NNS work_fnploejenbc2raktl46esxm44i 543 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 4 + + SYM work_fnploejenbc2raktl46esxm44i 543 5 P(B p(b NN work_fnploejenbc2raktl46esxm44i 543 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 7 = = NFP work_fnploejenbc2raktl46esxm44i 543 8 P(A P(A NNS work_fnploejenbc2raktl46esxm44i 543 9 u u NNP work_fnploejenbc2raktl46esxm44i 543 10 B B NNP work_fnploejenbc2raktl46esxm44i 543 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 12 < < XX work_fnploejenbc2raktl46esxm44i 543 13 1 1 CD work_fnploejenbc2raktl46esxm44i 543 14 , , , work_fnploejenbc2raktl46esxm44i 543 15 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 543 16 have have VBP work_fnploejenbc2raktl46esxm44i 543 17 P(A P(A NNS work_fnploejenbc2raktl46esxm44i 543 18 u u NNP work_fnploejenbc2raktl46esxm44i 543 19 B b NN work_fnploejenbc2raktl46esxm44i 543 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 21 = = SYM work_fnploejenbc2raktl46esxm44i 543 22 P(A P(A NNS work_fnploejenbc2raktl46esxm44i 543 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 24 + + SYM work_fnploejenbc2raktl46esxm44i 543 25 P(B p(b NN work_fnploejenbc2raktl46esxm44i 543 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 27 = = NFP work_fnploejenbc2raktl46esxm44i 543 28 Min(P(A min(p(a CD work_fnploejenbc2raktl46esxm44i 543 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 30 + + NFP work_fnploejenbc2raktl46esxm44i 543 31 P(B p(b NN work_fnploejenbc2raktl46esxm44i 543 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 33 , , , work_fnploejenbc2raktl46esxm44i 543 34 1 1 CD work_fnploejenbc2raktl46esxm44i 543 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 543 36 . . . work_fnploejenbc2raktl46esxm44i 544 1 Furthermore furthermore RB work_fnploejenbc2raktl46esxm44i 544 2 , , , work_fnploejenbc2raktl46esxm44i 544 3 in in IN work_fnploejenbc2raktl46esxm44i 544 4 the the DT work_fnploejenbc2raktl46esxm44i 544 5 case case NN work_fnploejenbc2raktl46esxm44i 544 6 of of IN work_fnploejenbc2raktl46esxm44i 544 7 probability probability NN work_fnploejenbc2raktl46esxm44i 544 8 measures measure NNS work_fnploejenbc2raktl46esxm44i 544 9 , , , work_fnploejenbc2raktl46esxm44i 544 10 the the DT work_fnploejenbc2raktl46esxm44i 544 11 generator generator NN work_fnploejenbc2raktl46esxm44i 544 12 g g NN work_fnploejenbc2raktl46esxm44i 544 13 is be VBZ work_fnploejenbc2raktl46esxm44i 544 14 such such JJ work_fnploejenbc2raktl46esxm44i 544 15 that that IN work_fnploejenbc2raktl46esxm44i 544 16 g g NN work_fnploejenbc2raktl46esxm44i 544 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 544 18 1 1 CD work_fnploejenbc2raktl46esxm44i 544 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 544 20 = = NFP work_fnploejenbc2raktl46esxm44i 544 21 + + CC work_fnploejenbc2raktl46esxm44i 544 22 co co NN work_fnploejenbc2raktl46esxm44i 544 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 544 24 and and CC work_fnploejenbc2raktl46esxm44i 544 25 hence hence RB work_fnploejenbc2raktl46esxm44i 544 26 g g NN work_fnploejenbc2raktl46esxm44i 544 27 * * NFP work_fnploejenbc2raktl46esxm44i 544 28 = = SYM work_fnploejenbc2raktl46esxm44i 544 29 g g NNP work_fnploejenbc2raktl46esxm44i 544 30 - - HYPH work_fnploejenbc2raktl46esxm44i 544 31 r r NNP work_fnploejenbc2raktl46esxm44i 544 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 544 33 ; ; : work_fnploejenbc2raktl46esxm44i 544 34 the the DT work_fnploejenbc2raktl46esxm44i 544 35 corresponding corresponding JJ work_fnploejenbc2raktl46esxm44i 544 36 t t NN work_fnploejenbc2raktl46esxm44i 544 37 - - HYPH work_fnploejenbc2raktl46esxm44i 544 38 conorm conorm NN work_fnploejenbc2raktl46esxm44i 544 39 T T NNP work_fnploejenbc2raktl46esxm44i 544 40 is be VBZ work_fnploejenbc2raktl46esxm44i 544 41 called call VBN work_fnploejenbc2raktl46esxm44i 544 42 a a DT work_fnploejenbc2raktl46esxm44i 544 43 strict strict JJ work_fnploejenbc2raktl46esxm44i 544 44 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 544 45 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 544 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 544 47 t t NN work_fnploejenbc2raktl46esxm44i 544 48 - - HYPH work_fnploejenbc2raktl46esxm44i 544 49 conorm conorm NN work_fnploejenbc2raktl46esxm44i 544 50 . . . work_fnploejenbc2raktl46esxm44i 545 1 For for IN work_fnploejenbc2raktl46esxm44i 545 2 a a DT work_fnploejenbc2raktl46esxm44i 545 3 t t NN work_fnploejenbc2raktl46esxm44i 545 4 - - HYPH work_fnploejenbc2raktl46esxm44i 545 5 conorm conorm NN work_fnploejenbc2raktl46esxm44i 545 6 T T NNP work_fnploejenbc2raktl46esxm44i 545 7 , , , work_fnploejenbc2raktl46esxm44i 545 8 a a DT work_fnploejenbc2raktl46esxm44i 545 9 T t NN work_fnploejenbc2raktl46esxm44i 545 10 - - HYPH work_fnploejenbc2raktl46esxm44i 545 11 possibility possibility NN work_fnploejenbc2raktl46esxm44i 545 12 measure measure NN work_fnploejenbc2raktl46esxm44i 545 13 is be VBZ work_fnploejenbc2raktl46esxm44i 545 14 defined define VBN work_fnploejenbc2raktl46esxm44i 545 15 to to TO work_fnploejenbc2raktl46esxm44i 545 16 be be VB work_fnploejenbc2raktl46esxm44i 545 17 a a DT work_fnploejenbc2raktl46esxm44i 545 18 map map NN work_fnploejenbc2raktl46esxm44i 545 19 from from IN work_fnploejenbc2raktl46esxm44i 545 20 d d NN work_fnploejenbc2raktl46esxm44i 545 21 to to IN work_fnploejenbc2raktl46esxm44i 545 22 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 545 23 0 0 CD work_fnploejenbc2raktl46esxm44i 545 24 , , , work_fnploejenbc2raktl46esxm44i 545 25 1 1 CD work_fnploejenbc2raktl46esxm44i 545 26 J j NN work_fnploejenbc2raktl46esxm44i 545 27 with with IN work_fnploejenbc2raktl46esxm44i 545 28 T T NNP work_fnploejenbc2raktl46esxm44i 545 29 as as IN work_fnploejenbc2raktl46esxm44i 545 30 composition composition NN work_fnploejenbc2raktl46esxm44i 545 31 law law NN work_fnploejenbc2raktl46esxm44i 545 32 . . . work_fnploejenbc2raktl46esxm44i 546 1 For for IN work_fnploejenbc2raktl46esxm44i 546 2 example example NN work_fnploejenbc2raktl46esxm44i 546 3 , , , work_fnploejenbc2raktl46esxm44i 546 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 546 5 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 546 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 546 7 max- max- NN work_fnploejenbc2raktl46esxm44i 546 8 possibility possibility NN work_fnploejenbc2raktl46esxm44i 546 9 measure measure NN work_fnploejenbc2raktl46esxm44i 546 10 is be VBZ work_fnploejenbc2raktl46esxm44i 546 11 a a DT work_fnploejenbc2raktl46esxm44i 546 12 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 546 13 measure measure NN work_fnploejenbc2raktl46esxm44i 546 14 with with IN work_fnploejenbc2raktl46esxm44i 546 15 T(x T(x NNP work_fnploejenbc2raktl46esxm44i 546 16 , , , work_fnploejenbc2raktl46esxm44i 546 17 y y NNP work_fnploejenbc2raktl46esxm44i 546 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 546 19 = = SYM work_fnploejenbc2raktl46esxm44i 546 20 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 546 21 , , , work_fnploejenbc2raktl46esxm44i 546 22 y y NNP work_fnploejenbc2raktl46esxm44i 546 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 546 24 . . . work_fnploejenbc2raktl46esxm44i 547 1 Let let VB work_fnploejenbc2raktl46esxm44i 547 2 B B NNP work_fnploejenbc2raktl46esxm44i 547 3 be be VB work_fnploejenbc2raktl46esxm44i 547 4 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 547 5 and and CC work_fnploejenbc2raktl46esxm44i 547 6 a a DT work_fnploejenbc2raktl46esxm44i 547 7 : : : work_fnploejenbc2raktl46esxm44i 547 8 Q q NN work_fnploejenbc2raktl46esxm44i 547 9 + + CC work_fnploejenbc2raktl46esxm44i 547 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 547 11 0 0 CD work_fnploejenbc2raktl46esxm44i 547 12 , , , work_fnploejenbc2raktl46esxm44i 547 13 11 11 CD work_fnploejenbc2raktl46esxm44i 547 14 . . . work_fnploejenbc2raktl46esxm44i 548 1 Let let VB work_fnploejenbc2raktl46esxm44i 548 2 T t PRP work_fnploejenbc2raktl46esxm44i 548 3 be be VB work_fnploejenbc2raktl46esxm44i 548 4 an an DT work_fnploejenbc2raktl46esxm44i 548 5 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 548 6 t t NN work_fnploejenbc2raktl46esxm44i 548 7 - - HYPH work_fnploejenbc2raktl46esxm44i 548 8 conorm conorm NN work_fnploejenbc2raktl46esxm44i 548 9 with with IN work_fnploejenbc2raktl46esxm44i 548 10 generator generator NN work_fnploejenbc2raktl46esxm44i 548 11 g. g. . work_fnploejenbc2raktl46esxm44i 548 12 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 548 13 denote denote VBP work_fnploejenbc2raktl46esxm44i 548 14 by by IN work_fnploejenbc2raktl46esxm44i 548 15 , , , work_fnploejenbc2raktl46esxm44i 548 16 u~,~ u~,~ VBZ work_fnploejenbc2raktl46esxm44i 548 17 the the DT work_fnploejenbc2raktl46esxm44i 548 18 T t NN work_fnploejenbc2raktl46esxm44i 548 19 - - HYPH work_fnploejenbc2raktl46esxm44i 548 20 possibility possibility NN work_fnploejenbc2raktl46esxm44i 548 21 measure measure NN work_fnploejenbc2raktl46esxm44i 548 22 defined define VBN work_fnploejenbc2raktl46esxm44i 548 23 as as IN work_fnploejenbc2raktl46esxm44i 548 24 follows follow VBZ work_fnploejenbc2raktl46esxm44i 548 25 . . . work_fnploejenbc2raktl46esxm44i 549 1 For for IN work_fnploejenbc2raktl46esxm44i 549 2 A a DT work_fnploejenbc2raktl46esxm44i 549 3 E e NN work_fnploejenbc2raktl46esxm44i 549 4 Q q NN work_fnploejenbc2raktl46esxm44i 549 5 , , , work_fnploejenbc2raktl46esxm44i 549 6 finite finite NN work_fnploejenbc2raktl46esxm44i 549 7 , , , work_fnploejenbc2raktl46esxm44i 549 8 p,,T(A)= p,,T(A)= NNP work_fnploejenbc2raktl46esxm44i 549 9 T(a(o T(a(o NNP work_fnploejenbc2raktl46esxm44i 549 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 549 11 , , , work_fnploejenbc2raktl46esxm44i 549 12 wEA)=g wea)=g NN work_fnploejenbc2raktl46esxm44i 549 13 * * NFP work_fnploejenbc2raktl46esxm44i 549 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 549 15 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 549 16 & & CC work_fnploejenbc2raktl46esxm44i 549 17 44 44 CD work_fnploejenbc2raktl46esxm44i 549 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 549 19 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 549 20 . . . work_fnploejenbc2raktl46esxm44i 550 1 A a DT work_fnploejenbc2raktl46esxm44i 550 2 For for IN work_fnploejenbc2raktl46esxm44i 550 3 A a DT work_fnploejenbc2raktl46esxm44i 550 4 countably countably RB work_fnploejenbc2raktl46esxm44i 550 5 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 550 6 , , , work_fnploejenbc2raktl46esxm44i 550 7 PL,,r(A)=g pl,,r(a)=g JJ work_fnploejenbc2raktl46esxm44i 550 8 * * NFP work_fnploejenbc2raktl46esxm44i 550 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 550 10 z z NNP work_fnploejenbc2raktl46esxm44i 550 11 da(w da(w NNP work_fnploejenbc2raktl46esxm44i 550 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 550 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 550 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 550 15 . . . work_fnploejenbc2raktl46esxm44i 551 1 A a DT work_fnploejenbc2raktl46esxm44i 551 2 Note note NN work_fnploejenbc2raktl46esxm44i 551 3 that that IN work_fnploejenbc2raktl46esxm44i 551 4 CA CA NNP work_fnploejenbc2raktl46esxm44i 551 5 g(a(w g(a(w NN work_fnploejenbc2raktl46esxm44i 551 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 551 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 551 8 < < XX work_fnploejenbc2raktl46esxm44i 551 9 + + NNP work_fnploejenbc2raktl46esxm44i 551 10 CCL CCL NNP work_fnploejenbc2raktl46esxm44i 551 11 5.2 5.2 CD work_fnploejenbc2raktl46esxm44i 551 12 . . . work_fnploejenbc2raktl46esxm44i 552 1 General General NNP work_fnploejenbc2raktl46esxm44i 552 2 Admissibility Admissibility NNP work_fnploejenbc2raktl46esxm44i 552 3 under under IN work_fnploejenbc2raktl46esxm44i 552 4 Additive Additive NNP work_fnploejenbc2raktl46esxm44i 552 5 Aggregation Aggregation NNP work_fnploejenbc2raktl46esxm44i 552 6 In in IN work_fnploejenbc2raktl46esxm44i 552 7 order order NN work_fnploejenbc2raktl46esxm44i 552 8 to to TO work_fnploejenbc2raktl46esxm44i 552 9 discuss discuss VB work_fnploejenbc2raktl46esxm44i 552 10 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 552 11 ’s ’s POS work_fnploejenbc2raktl46esxm44i 552 12 conclusions conclusion NNS work_fnploejenbc2raktl46esxm44i 552 13 about about IN work_fnploejenbc2raktl46esxm44i 552 14 the the DT work_fnploejenbc2raktl46esxm44i 552 15 inadmissibility inadmissibility NN work_fnploejenbc2raktl46esxm44i 552 16 of of IN work_fnploejenbc2raktl46esxm44i 552 17 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 552 18 measures measure NNS work_fnploejenbc2raktl46esxm44i 552 19 , , , work_fnploejenbc2raktl46esxm44i 552 20 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 552 21 consider consider VBP work_fnploejenbc2raktl46esxm44i 552 22 G G NNP work_fnploejenbc2raktl46esxm44i 552 23 , , , work_fnploejenbc2raktl46esxm44i 552 24 + + ADD work_fnploejenbc2raktl46esxm44i 552 25 . . . work_fnploejenbc2raktl46esxm44i 553 1 In in IN work_fnploejenbc2raktl46esxm44i 553 2 view view NN work_fnploejenbc2raktl46esxm44i 553 3 of of IN work_fnploejenbc2raktl46esxm44i 553 4 the the DT work_fnploejenbc2raktl46esxm44i 553 5 results result NNS work_fnploejenbc2raktl46esxm44i 553 6 of of IN work_fnploejenbc2raktl46esxm44i 553 7 Sections section NNS work_fnploejenbc2raktl46esxm44i 553 8 SCORING score VBN work_fnploejenbc2raktl46esxm44i 553 9 APPROACH APPROACH NNS work_fnploejenbc2raktl46esxm44i 553 10 TO to IN work_fnploejenbc2raktl46esxm44i 553 11 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 553 12 577 577 CD work_fnploejenbc2raktl46esxm44i 553 13 3 3 CD work_fnploejenbc2raktl46esxm44i 553 14 and and CC work_fnploejenbc2raktl46esxm44i 553 15 4 4 CD work_fnploejenbc2raktl46esxm44i 553 16 , , , work_fnploejenbc2raktl46esxm44i 553 17 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 553 18 have have VBP work_fnploejenbc2raktl46esxm44i 553 19 to to TO work_fnploejenbc2raktl46esxm44i 553 20 consider consider VB work_fnploejenbc2raktl46esxm44i 553 21 the the DT work_fnploejenbc2raktl46esxm44i 553 22 concept concept NN work_fnploejenbc2raktl46esxm44i 553 23 of of IN work_fnploejenbc2raktl46esxm44i 553 24 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 553 25 of of IN work_fnploejenbc2raktl46esxm44i 553 26 a a DT work_fnploejenbc2raktl46esxm44i 553 27 given give VBN work_fnploejenbc2raktl46esxm44i 553 28 uncer- uncer- NN work_fnploejenbc2raktl46esxm44i 553 29 tainty tainty NN work_fnploejenbc2raktl46esxm44i 553 30 measure measure NN work_fnploejenbc2raktl46esxm44i 553 31 in in IN work_fnploejenbc2raktl46esxm44i 553 32 a a DT work_fnploejenbc2raktl46esxm44i 553 33 wide wide JJ work_fnploejenbc2raktl46esxm44i 553 34 sense sense NN work_fnploejenbc2raktl46esxm44i 553 35 . . . work_fnploejenbc2raktl46esxm44i 554 1 Specifically specifically RB work_fnploejenbc2raktl46esxm44i 554 2 , , , work_fnploejenbc2raktl46esxm44i 554 3 an an DT work_fnploejenbc2raktl46esxm44i 554 4 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 554 5 measure measure NN work_fnploejenbc2raktl46esxm44i 554 6 I I NNP work_fnploejenbc2raktl46esxm44i 554 7 - - HYPH work_fnploejenbc2raktl46esxm44i 554 8 L l NN work_fnploejenbc2raktl46esxm44i 554 9 E e NN work_fnploejenbc2raktl46esxm44i 554 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 554 11 a a DT work_fnploejenbc2raktl46esxm44i 554 12 , , , work_fnploejenbc2raktl46esxm44i 554 13 , , , work_fnploejenbc2raktl46esxm44i 554 14 aIlJ aIlJ NNP work_fnploejenbc2raktl46esxm44i 554 15 is be VBZ work_fnploejenbc2raktl46esxm44i 554 16 said say VBN work_fnploejenbc2raktl46esxm44i 554 17 to to TO work_fnploejenbc2raktl46esxm44i 554 18 be be VB work_fnploejenbc2raktl46esxm44i 554 19 general general JJ work_fnploejenbc2raktl46esxm44i 554 20 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 554 21 if if IN work_fnploejenbc2raktl46esxm44i 554 22 there there EX work_fnploejenbc2raktl46esxm44i 554 23 is be VBZ work_fnploejenbc2raktl46esxm44i 554 24 a a DT work_fnploejenbc2raktl46esxm44i 554 25 game game NN work_fnploejenbc2raktl46esxm44i 554 26 Gf Gf NNP work_fnploejenbc2raktl46esxm44i 554 27 , , , work_fnploejenbc2raktl46esxm44i 554 28 + + CC work_fnploejenbc2raktl46esxm44i 554 29 such such JJ work_fnploejenbc2raktl46esxm44i 554 30 that that IN work_fnploejenbc2raktl46esxm44i 554 31 p p NN work_fnploejenbc2raktl46esxm44i 554 32 is be VBZ work_fnploejenbc2raktl46esxm44i 554 33 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 554 34 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 554 35 with with IN work_fnploejenbc2raktl46esxm44i 554 36 respect respect NN work_fnploejenbc2raktl46esxm44i 554 37 to to IN work_fnploejenbc2raktl46esxm44i 554 38 that that DT work_fnploejenbc2raktl46esxm44i 554 39 game game NN work_fnploejenbc2raktl46esxm44i 554 40 . . . work_fnploejenbc2raktl46esxm44i 555 1 In in IN work_fnploejenbc2raktl46esxm44i 555 2 this this DT work_fnploejenbc2raktl46esxm44i 555 3 sense sense NN work_fnploejenbc2raktl46esxm44i 555 4 , , , work_fnploejenbc2raktl46esxm44i 555 5 any any DT work_fnploejenbc2raktl46esxm44i 555 6 probability probability NN work_fnploejenbc2raktl46esxm44i 555 7 measure measure NN work_fnploejenbc2raktl46esxm44i 555 8 is be VBZ work_fnploejenbc2raktl46esxm44i 555 9 general general JJ work_fnploejenbc2raktl46esxm44i 555 10 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 555 11 by by IN work_fnploejenbc2raktl46esxm44i 555 12 taking take VBG work_fnploejenbc2raktl46esxm44i 555 13 the the DT work_fnploejenbc2raktl46esxm44i 555 14 score score NN work_fnploejenbc2raktl46esxm44i 555 15 functionf functionf NN work_fnploejenbc2raktl46esxm44i 555 16 to to TO work_fnploejenbc2raktl46esxm44i 555 17 be be VB work_fnploejenbc2raktl46esxm44i 555 18 a a DT work_fnploejenbc2raktl46esxm44i 555 19 proper proper JJ work_fnploejenbc2raktl46esxm44i 555 20 score score NN work_fnploejenbc2raktl46esxm44i 555 21 function function NN work_fnploejenbc2raktl46esxm44i 555 22 ! ! . work_fnploejenbc2raktl46esxm44i 556 1 But but CC work_fnploejenbc2raktl46esxm44i 556 2 for for IN work_fnploejenbc2raktl46esxm44i 556 3 a a DT work_fnploejenbc2raktl46esxm44i 556 4 proper proper JJ work_fnploejenbc2raktl46esxm44i 556 5 score score NN work_fnploejenbc2raktl46esxm44i 556 6 function function NN work_fnploejenbc2raktl46esxm44i 556 7 f f NNP work_fnploejenbc2raktl46esxm44i 556 8 , , , work_fnploejenbc2raktl46esxm44i 556 9 the the DT work_fnploejenbc2raktl46esxm44i 556 10 associated associate VBN work_fnploejenbc2raktl46esxm44i 556 11 probability probability NN work_fnploejenbc2raktl46esxm44i 556 12 transform transform NN work_fnploejenbc2raktl46esxm44i 556 13 P,-(x p,-(x FW work_fnploejenbc2raktl46esxm44i 556 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 556 15 = = NFP work_fnploejenbc2raktl46esxm44i 556 16 x x LS work_fnploejenbc2raktl46esxm44i 556 17 , , , work_fnploejenbc2raktl46esxm44i 556 18 Vx Vx NNP work_fnploejenbc2raktl46esxm44i 556 19 E E NNP work_fnploejenbc2raktl46esxm44i 556 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 556 21 0 0 CD work_fnploejenbc2raktl46esxm44i 556 22 , , , work_fnploejenbc2raktl46esxm44i 556 23 11 11 CD work_fnploejenbc2raktl46esxm44i 556 24 , , , work_fnploejenbc2raktl46esxm44i 556 25 is be VBZ work_fnploejenbc2raktl46esxm44i 556 26 increasing increase VBG work_fnploejenbc2raktl46esxm44i 556 27 , , , work_fnploejenbc2raktl46esxm44i 556 28 and and CC work_fnploejenbc2raktl46esxm44i 556 29 hence hence RB work_fnploejenbc2raktl46esxm44i 556 30 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 556 31 ’ ' '' work_fnploejenbc2raktl46esxm44i 556 32 ; ; : work_fnploejenbc2raktl46esxm44i 556 33 ’ ' '' work_fnploejenbc2raktl46esxm44i 556 34 exists exist VBZ work_fnploejenbc2raktl46esxm44i 556 35 . . . work_fnploejenbc2raktl46esxm44i 557 1 So so RB work_fnploejenbc2raktl46esxm44i 557 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 557 3 require require VBP work_fnploejenbc2raktl46esxm44i 557 4 , , , work_fnploejenbc2raktl46esxm44i 557 5 in in IN work_fnploejenbc2raktl46esxm44i 557 6 general general JJ work_fnploejenbc2raktl46esxm44i 557 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 557 8 , , , work_fnploejenbc2raktl46esxm44i 557 9 the the DT work_fnploejenbc2raktl46esxm44i 557 10 existence existence NN work_fnploejenbc2raktl46esxm44i 557 11 of of IN work_fnploejenbc2raktl46esxm44i 557 12 a a DT work_fnploejenbc2raktl46esxm44i 557 13 score score NN work_fnploejenbc2raktl46esxm44i 557 14 function function NN work_fnploejenbc2raktl46esxm44i 557 15 f f NNP work_fnploejenbc2raktl46esxm44i 557 16 such such JJ work_fnploejenbc2raktl46esxm44i 557 17 that that IN work_fnploejenbc2raktl46esxm44i 557 18 Py Py NNP work_fnploejenbc2raktl46esxm44i 557 19 ’ ' '' work_fnploejenbc2raktl46esxm44i 557 20 exists exist VBZ work_fnploejenbc2raktl46esxm44i 557 21 . . . work_fnploejenbc2raktl46esxm44i 558 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 558 2 is be VBZ work_fnploejenbc2raktl46esxm44i 558 3 seen see VBN work_fnploejenbc2raktl46esxm44i 558 4 that that IN work_fnploejenbc2raktl46esxm44i 558 5 with with IN work_fnploejenbc2raktl46esxm44i 558 6 respect respect NN work_fnploejenbc2raktl46esxm44i 558 7 to to IN work_fnploejenbc2raktl46esxm44i 558 8 a a DT work_fnploejenbc2raktl46esxm44i 558 9 game game NN work_fnploejenbc2raktl46esxm44i 558 10 G’,.+ g’,.+ NN work_fnploejenbc2raktl46esxm44i 558 11 with with IN work_fnploejenbc2raktl46esxm44i 558 12 Pf Pf NNP work_fnploejenbc2raktl46esxm44i 558 13 increasing increase VBG work_fnploejenbc2raktl46esxm44i 558 14 , , , work_fnploejenbc2raktl46esxm44i 558 15 p p NNP work_fnploejenbc2raktl46esxm44i 558 16 is be VBZ work_fnploejenbc2raktl46esxm44i 558 17 general general JJ work_fnploejenbc2raktl46esxm44i 558 18 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 558 19 if if IN work_fnploejenbc2raktl46esxm44i 558 20 and and CC work_fnploejenbc2raktl46esxm44i 558 21 only only RB work_fnploejenbc2raktl46esxm44i 558 22 if if IN work_fnploejenbc2raktl46esxm44i 558 23 P p NN work_fnploejenbc2raktl46esxm44i 558 24 , , , work_fnploejenbc2raktl46esxm44i 558 25 o o NN work_fnploejenbc2raktl46esxm44i 558 26 p p NN work_fnploejenbc2raktl46esxm44i 558 27 is be VBZ work_fnploejenbc2raktl46esxm44i 558 28 a a DT work_fnploejenbc2raktl46esxm44i 558 29 limtely limtely JJ work_fnploejenbc2raktl46esxm44i 558 30 additive additive JJ work_fnploejenbc2raktl46esxm44i 558 31 probability probability NN work_fnploejenbc2raktl46esxm44i 558 32 . . . work_fnploejenbc2raktl46esxm44i 559 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 559 2 is be VBZ work_fnploejenbc2raktl46esxm44i 559 3 this this DT work_fnploejenbc2raktl46esxm44i 559 4 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 559 5 property property NN work_fnploejenbc2raktl46esxm44i 559 6 that that WDT work_fnploejenbc2raktl46esxm44i 559 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 559 8 will will MD work_fnploejenbc2raktl46esxm44i 559 9 use use VB work_fnploejenbc2raktl46esxm44i 559 10 as as IN work_fnploejenbc2raktl46esxm44i 559 11 a a DT work_fnploejenbc2raktl46esxm44i 559 12 definition definition NN work_fnploejenbc2raktl46esxm44i 559 13 for for IN work_fnploejenbc2raktl46esxm44i 559 14 general general JJ work_fnploejenbc2raktl46esxm44i 559 15 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 559 16 . . . work_fnploejenbc2raktl46esxm44i 560 1 In in IN work_fnploejenbc2raktl46esxm44i 560 2 discussing discuss VBG work_fnploejenbc2raktl46esxm44i 560 3 possibility possibility NN work_fnploejenbc2raktl46esxm44i 560 4 measures measure NNS work_fnploejenbc2raktl46esxm44i 560 5 on on IN work_fnploejenbc2raktl46esxm44i 560 6 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 560 7 spaces space NNS work_fnploejenbc2raktl46esxm44i 560 8 , , , work_fnploejenbc2raktl46esxm44i 560 9 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 560 10 can can MD work_fnploejenbc2raktl46esxm44i 560 11 even even RB work_fnploejenbc2raktl46esxm44i 560 12 consider consider VB work_fnploejenbc2raktl46esxm44i 560 13 a a DT work_fnploejenbc2raktl46esxm44i 560 14 stronger strong JJR work_fnploejenbc2raktl46esxm44i 560 15 concept concept NN work_fnploejenbc2raktl46esxm44i 560 16 of of IN work_fnploejenbc2raktl46esxm44i 560 17 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 560 18 , , , work_fnploejenbc2raktl46esxm44i 560 19 namely namely RB work_fnploejenbc2raktl46esxm44i 560 20 general general JJ work_fnploejenbc2raktl46esxm44i 560 21 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 560 22 in in IN work_fnploejenbc2raktl46esxm44i 560 23 the the DT work_fnploejenbc2raktl46esxm44i 560 24 a a DT work_fnploejenbc2raktl46esxm44i 560 25 - - HYPH work_fnploejenbc2raktl46esxm44i 560 26 additive additive JJ work_fnploejenbc2raktl46esxm44i 560 27 sense sense NN work_fnploejenbc2raktl46esxm44i 560 28 , , , work_fnploejenbc2raktl46esxm44i 560 29 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 560 30 , , , work_fnploejenbc2raktl46esxm44i 560 31 Prop Prop NNP work_fnploejenbc2raktl46esxm44i 560 32 is be VBZ work_fnploejenbc2raktl46esxm44i 560 33 a a DT work_fnploejenbc2raktl46esxm44i 560 34 a a DT work_fnploejenbc2raktl46esxm44i 560 35 - - HYPH work_fnploejenbc2raktl46esxm44i 560 36 additive additive JJ work_fnploejenbc2raktl46esxm44i 560 37 probability probability NN work_fnploejenbc2raktl46esxm44i 560 38 measure measure NN work_fnploejenbc2raktl46esxm44i 560 39 . . . work_fnploejenbc2raktl46esxm44i 561 1 It -PRON- PRP work_fnploejenbc2raktl46esxm44i 561 2 will will MD work_fnploejenbc2raktl46esxm44i 561 3 be be VB work_fnploejenbc2raktl46esxm44i 561 4 shown show VBN work_fnploejenbc2raktl46esxm44i 561 5 in in IN work_fnploejenbc2raktl46esxm44i 561 6 this this DT work_fnploejenbc2raktl46esxm44i 561 7 subsection subsection NN work_fnploejenbc2raktl46esxm44i 561 8 that that IN work_fnploejenbc2raktl46esxm44i 561 9 operations operation NNS work_fnploejenbc2raktl46esxm44i 561 10 in in IN work_fnploejenbc2raktl46esxm44i 561 11 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 561 12 logics logic NNS work_fnploejenbc2raktl46esxm44i 561 13 are be VBP work_fnploejenbc2raktl46esxm44i 561 14 , , , work_fnploejenbc2raktl46esxm44i 561 15 in in IN work_fnploejenbc2raktl46esxm44i 561 16 general general JJ work_fnploejenbc2raktl46esxm44i 561 17 , , , work_fnploejenbc2raktl46esxm44i 561 18 “ " `` work_fnploejenbc2raktl46esxm44i 561 19 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 561 20 , , , work_fnploejenbc2raktl46esxm44i 561 21 ” " '' work_fnploejenbc2raktl46esxm44i 561 22 and and CC work_fnploejenbc2raktl46esxm44i 561 23 even even RB work_fnploejenbc2raktl46esxm44i 561 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 561 25 Zadeh)-max Zadeh)-max NNP work_fnploejenbc2raktl46esxm44i 561 26 possibility possibility NN work_fnploejenbc2raktl46esxm44i 561 27 measures measure NNS work_fnploejenbc2raktl46esxm44i 561 28 are be VBP work_fnploejenbc2raktl46esxm44i 561 29 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 561 30 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 561 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 561 32 limits limit NNS work_fnploejenbc2raktl46esxm44i 561 33 of of IN work_fnploejenbc2raktl46esxm44i 561 34 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 561 35 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 561 36 measures measure NNS work_fnploejenbc2raktl46esxm44i 561 37 . . . work_fnploejenbc2raktl46esxm44i 562 1 For for IN work_fnploejenbc2raktl46esxm44i 562 2 related related JJ work_fnploejenbc2raktl46esxm44i 562 3 works work NNS work_fnploejenbc2raktl46esxm44i 562 4 in in IN work_fnploejenbc2raktl46esxm44i 562 5 Statistics statistic NNS work_fnploejenbc2raktl46esxm44i 562 6 see see VBP work_fnploejenbc2raktl46esxm44i 562 7 , , , work_fnploejenbc2raktl46esxm44i 562 8 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 562 9 , , , work_fnploejenbc2raktl46esxm44i 562 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 562 11 lS lS NNP work_fnploejenbc2raktl46esxm44i 562 12 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 562 13 . . . work_fnploejenbc2raktl46esxm44i 563 1 Throughout throughout IN work_fnploejenbc2raktl46esxm44i 563 2 this this DT work_fnploejenbc2raktl46esxm44i 563 3 subsection subsection NN work_fnploejenbc2raktl46esxm44i 563 4 , , , work_fnploejenbc2raktl46esxm44i 563 5 Q Q NNP work_fnploejenbc2raktl46esxm44i 563 6 is be VBZ work_fnploejenbc2raktl46esxm44i 563 7 a a DT work_fnploejenbc2raktl46esxm44i 563 8 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 563 9 space space NN work_fnploejenbc2raktl46esxm44i 563 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 563 11 finite finite VB work_fnploejenbc2raktl46esxm44i 563 12 or or CC work_fnploejenbc2raktl46esxm44i 563 13 countably countably RB work_fnploejenbc2raktl46esxm44i 563 14 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 563 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 16 , , , work_fnploejenbc2raktl46esxm44i 563 17 d d LS work_fnploejenbc2raktl46esxm44i 563 18 = = SYM work_fnploejenbc2raktl46esxm44i 563 19 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 563 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 21 and and CC work_fnploejenbc2raktl46esxm44i 563 22 restrict restrict VB work_fnploejenbc2raktl46esxm44i 563 23 d d NN work_fnploejenbc2raktl46esxm44i 563 24 to to IN work_fnploejenbc2raktl46esxm44i 563 25 all all DT work_fnploejenbc2raktl46esxm44i 563 26 & & CC work_fnploejenbc2raktl46esxm44i 563 27 , , , work_fnploejenbc2raktl46esxm44i 563 28 , , , work_fnploejenbc2raktl46esxm44i 563 29 , , , work_fnploejenbc2raktl46esxm44i 563 30 FE FE NNP work_fnploejenbc2raktl46esxm44i 563 31 d. d. NN work_fnploejenbc2raktl46esxm44i 563 32 For for IN work_fnploejenbc2raktl46esxm44i 563 33 CL CL NNP work_fnploejenbc2raktl46esxm44i 563 34 : : : work_fnploejenbc2raktl46esxm44i 563 35 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 563 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 37 + + CC work_fnploejenbc2raktl46esxm44i 563 38 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 563 39 0 0 CD work_fnploejenbc2raktl46esxm44i 563 40 , , , work_fnploejenbc2raktl46esxm44i 563 41 11 11 CD work_fnploejenbc2raktl46esxm44i 563 42 , , , work_fnploejenbc2raktl46esxm44i 563 43 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 563 44 write write VBP work_fnploejenbc2raktl46esxm44i 563 45 p p NN work_fnploejenbc2raktl46esxm44i 563 46 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 563 47 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 563 48 0 0 NFP work_fnploejenbc2raktl46esxm44i 563 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 50 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 51 = = NFP work_fnploejenbc2raktl46esxm44i 563 52 p(w p(w NNP work_fnploejenbc2raktl46esxm44i 563 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 563 54 , , , work_fnploejenbc2raktl46esxm44i 563 55 so so IN work_fnploejenbc2raktl46esxm44i 563 56 that that IN work_fnploejenbc2raktl46esxm44i 563 57 the the DT work_fnploejenbc2raktl46esxm44i 563 58 restriction restriction NN work_fnploejenbc2raktl46esxm44i 563 59 of of IN work_fnploejenbc2raktl46esxm44i 563 60 p p NN work_fnploejenbc2raktl46esxm44i 563 61 to to IN work_fnploejenbc2raktl46esxm44i 563 62 singletons singleton NNS work_fnploejenbc2raktl46esxm44i 563 63 is be VBZ work_fnploejenbc2raktl46esxm44i 563 64 regarded regard VBN work_fnploejenbc2raktl46esxm44i 563 65 as as IN work_fnploejenbc2raktl46esxm44i 563 66 a a DT work_fnploejenbc2raktl46esxm44i 563 67 function function NN work_fnploejenbc2raktl46esxm44i 563 68 , , , work_fnploejenbc2raktl46esxm44i 563 69 still still RB work_fnploejenbc2raktl46esxm44i 563 70 denoted denote VBN work_fnploejenbc2raktl46esxm44i 563 71 as as IN work_fnploejenbc2raktl46esxm44i 563 72 p p NNP work_fnploejenbc2raktl46esxm44i 563 73 , , , work_fnploejenbc2raktl46esxm44i 563 74 from from IN work_fnploejenbc2raktl46esxm44i 563 75 Q q NN work_fnploejenbc2raktl46esxm44i 563 76 to to IN work_fnploejenbc2raktl46esxm44i 563 77 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 563 78 0 0 CD work_fnploejenbc2raktl46esxm44i 563 79 , , , work_fnploejenbc2raktl46esxm44i 563 80 11 11 CD work_fnploejenbc2raktl46esxm44i 563 81 . . . work_fnploejenbc2raktl46esxm44i 564 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 564 2 also also RB work_fnploejenbc2raktl46esxm44i 564 3 omit omit VBP work_fnploejenbc2raktl46esxm44i 564 4 , , , work_fnploejenbc2raktl46esxm44i 564 5 from from IN work_fnploejenbc2raktl46esxm44i 564 6 now now RB work_fnploejenbc2raktl46esxm44i 564 7 on on RB work_fnploejenbc2raktl46esxm44i 564 8 , , , work_fnploejenbc2raktl46esxm44i 564 9 the the DT work_fnploejenbc2raktl46esxm44i 564 10 qualification qualification NN work_fnploejenbc2raktl46esxm44i 564 11 “ " `` work_fnploejenbc2raktl46esxm44i 564 12 w.r.t w.r.t NNP work_fnploejenbc2raktl46esxm44i 564 13 . . . work_fnploejenbc2raktl46esxm44i 565 1 all all DT work_fnploejenbc2raktl46esxm44i 565 2 finite finite NNP work_fnploejenbc2raktl46esxm44i 565 3 equal equal JJ work_fnploejenbc2raktl46esxm44i 565 4 antecedent antecedent NN work_fnploejenbc2raktl46esxm44i 565 5 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 565 6 event event NN work_fnploejenbc2raktl46esxm44i 565 7 sequences sequence NNS work_fnploejenbc2raktl46esxm44i 565 8 . . . work_fnploejenbc2raktl46esxm44i 565 9 ” " '' work_fnploejenbc2raktl46esxm44i 565 10 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 565 11 5.2.1 5.2.1 CD work_fnploejenbc2raktl46esxm44i 565 12 . . . work_fnploejenbc2raktl46esxm44i 566 1 Let let VB work_fnploejenbc2raktl46esxm44i 566 2 p p PRP work_fnploejenbc2raktl46esxm44i 566 3 ’ ' '' work_fnploejenbc2raktl46esxm44i 566 4 : : : work_fnploejenbc2raktl46esxm44i 566 5 8(Q 8(Q NNP work_fnploejenbc2raktl46esxm44i 566 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 566 7 + + CC work_fnploejenbc2raktl46esxm44i 566 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 566 9 0 0 CD work_fnploejenbc2raktl46esxm44i 566 10 , , , work_fnploejenbc2raktl46esxm44i 566 11 11 11 CD work_fnploejenbc2raktl46esxm44i 566 12 . . . work_fnploejenbc2raktl46esxm44i 567 1 Then then RB work_fnploejenbc2raktl46esxm44i 567 2 the the DT work_fnploejenbc2raktl46esxm44i 567 3 following follow VBG work_fnploejenbc2raktl46esxm44i 567 4 are be VBP work_fnploejenbc2raktl46esxm44i 567 5 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 567 6 : : : work_fnploejenbc2raktl46esxm44i 567 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 567 8 i i NN work_fnploejenbc2raktl46esxm44i 567 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 567 10 p p NN work_fnploejenbc2raktl46esxm44i 567 11 is be VBZ work_fnploejenbc2raktl46esxm44i 567 12 general general JJ work_fnploejenbc2raktl46esxm44i 567 13 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 567 14 in in IN work_fnploejenbc2raktl46esxm44i 567 15 the the DT work_fnploejenbc2raktl46esxm44i 567 16 a a DT work_fnploejenbc2raktl46esxm44i 567 17 - - HYPH work_fnploejenbc2raktl46esxm44i 567 18 additive additive JJ work_fnploejenbc2raktl46esxm44i 567 19 sense sense NN work_fnploejenbc2raktl46esxm44i 567 20 . . . work_fnploejenbc2raktl46esxm44i 568 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 568 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 568 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 568 4 p p NN work_fnploejenbc2raktl46esxm44i 568 5 is be VBZ work_fnploejenbc2raktl46esxm44i 568 6 a a DT work_fnploejenbc2raktl46esxm44i 568 7 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 568 8 measure measure NN work_fnploejenbc2raktl46esxm44i 568 9 with with IN work_fnploejenbc2raktl46esxm44i 568 10 composition composition NN work_fnploejenbc2raktl46esxm44i 568 11 law law NN work_fnploejenbc2raktl46esxm44i 568 12 T t NN work_fnploejenbc2raktl46esxm44i 568 13 being be VBG work_fnploejenbc2raktl46esxm44i 568 14 an an DT work_fnploejenbc2raktl46esxm44i 568 15 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 568 16 t t NN work_fnploejenbc2raktl46esxm44i 568 17 - - HYPH work_fnploejenbc2raktl46esxm44i 568 18 conorm conorm NN work_fnploejenbc2raktl46esxm44i 568 19 with with IN work_fnploejenbc2raktl46esxm44i 568 20 generator generator NN work_fnploejenbc2raktl46esxm44i 568 21 g g NN work_fnploejenbc2raktl46esxm44i 568 22 such such JJ work_fnploejenbc2raktl46esxm44i 568 23 that that IN work_fnploejenbc2raktl46esxm44i 568 24 g g NN work_fnploejenbc2raktl46esxm44i 568 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 568 26 1 1 CD work_fnploejenbc2raktl46esxm44i 568 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 568 28 = = SYM work_fnploejenbc2raktl46esxm44i 568 29 1 1 CD work_fnploejenbc2raktl46esxm44i 568 30 , , , work_fnploejenbc2raktl46esxm44i 568 31 and and CC work_fnploejenbc2raktl46esxm44i 568 32 ; ; : work_fnploejenbc2raktl46esxm44i 568 33 gtAw gtaw LS work_fnploejenbc2raktl46esxm44i 568 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 568 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 568 36 = = NFP work_fnploejenbc2raktl46esxm44i 568 37 1 1 CD work_fnploejenbc2raktl46esxm44i 568 38 . . . work_fnploejenbc2raktl46esxm44i 569 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 569 2 * * NFP work_fnploejenbc2raktl46esxm44i 569 3 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 569 4 ProojI ProojI NNS work_fnploejenbc2raktl46esxm44i 569 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 569 6 i i NN work_fnploejenbc2raktl46esxm44i 569 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 569 8 * * NFP work_fnploejenbc2raktl46esxm44i 569 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 569 10 ii ii NNP work_fnploejenbc2raktl46esxm44i 569 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 569 12 . . . work_fnploejenbc2raktl46esxm44i 570 1 Let let VB work_fnploejenbc2raktl46esxm44i 570 2 f f PRP work_fnploejenbc2raktl46esxm44i 570 3 be be VB work_fnploejenbc2raktl46esxm44i 570 4 a a DT work_fnploejenbc2raktl46esxm44i 570 5 score score NN work_fnploejenbc2raktl46esxm44i 570 6 function function NN work_fnploejenbc2raktl46esxm44i 570 7 such such JJ work_fnploejenbc2raktl46esxm44i 570 8 that that IN work_fnploejenbc2raktl46esxm44i 570 9 tr tr NNP work_fnploejenbc2raktl46esxm44i 570 10 is be VBZ work_fnploejenbc2raktl46esxm44i 570 11 increasing increase VBG work_fnploejenbc2raktl46esxm44i 570 12 and and CC work_fnploejenbc2raktl46esxm44i 570 13 such such JJ work_fnploejenbc2raktl46esxm44i 570 14 that that IN work_fnploejenbc2raktl46esxm44i 570 15 P,.op p,.op NN work_fnploejenbc2raktl46esxm44i 570 16 is be VBZ work_fnploejenbc2raktl46esxm44i 570 17 a a DT work_fnploejenbc2raktl46esxm44i 570 18 o o NN work_fnploejenbc2raktl46esxm44i 570 19 - - HYPH work_fnploejenbc2raktl46esxm44i 570 20 additive additive JJ work_fnploejenbc2raktl46esxm44i 570 21 probability probability NN work_fnploejenbc2raktl46esxm44i 570 22 measure measure NN work_fnploejenbc2raktl46esxm44i 570 23 . . . work_fnploejenbc2raktl46esxm44i 571 1 For for IN work_fnploejenbc2raktl46esxm44i 571 2 A a DT work_fnploejenbc2raktl46esxm44i 571 3 E e NN work_fnploejenbc2raktl46esxm44i 571 4 9(Q 9(q NN work_fnploejenbc2raktl46esxm44i 571 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 6 , , , work_fnploejenbc2raktl46esxm44i 571 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 571 8 have have VBP work_fnploejenbc2raktl46esxm44i 571 9 P p NN work_fnploejenbc2raktl46esxm44i 571 10 , , , work_fnploejenbc2raktl46esxm44i 571 11 WW WW NNP work_fnploejenbc2raktl46esxm44i 571 12 = = SYM work_fnploejenbc2raktl46esxm44i 571 13 2 2 CD work_fnploejenbc2raktl46esxm44i 571 14 P P NNP work_fnploejenbc2raktl46esxm44i 571 15 / / SYM work_fnploejenbc2raktl46esxm44i 571 16 tA~ tA~ NNP work_fnploejenbc2raktl46esxm44i 571 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 19 , , , work_fnploejenbc2raktl46esxm44i 571 20 A a NN work_fnploejenbc2raktl46esxm44i 571 21 and and CC work_fnploejenbc2raktl46esxm44i 571 22 hence hence RB work_fnploejenbc2raktl46esxm44i 571 23 p(A p(a JJ work_fnploejenbc2raktl46esxm44i 571 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 25 = = NFP work_fnploejenbc2raktl46esxm44i 571 26 PF PF NNP work_fnploejenbc2raktl46esxm44i 571 27 ‘ ' `` work_fnploejenbc2raktl46esxm44i 571 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 571 29 CA CA NNP work_fnploejenbc2raktl46esxm44i 571 30 P&(o p&(o NN work_fnploejenbc2raktl46esxm44i 571 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 571 33 . . . work_fnploejenbc2raktl46esxm44i 572 1 By by IN work_fnploejenbc2raktl46esxm44i 572 2 taking take VBG work_fnploejenbc2raktl46esxm44i 572 3 g g NN work_fnploejenbc2raktl46esxm44i 572 4 = = NFP work_fnploejenbc2raktl46esxm44i 572 5 Pr pr UH work_fnploejenbc2raktl46esxm44i 572 6 , , , work_fnploejenbc2raktl46esxm44i 572 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 572 8 have have VBP work_fnploejenbc2raktl46esxm44i 572 9 g g NN work_fnploejenbc2raktl46esxm44i 572 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 572 11 1 1 CD work_fnploejenbc2raktl46esxm44i 572 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 572 13 = = SYM work_fnploejenbc2raktl46esxm44i 572 14 1 1 CD work_fnploejenbc2raktl46esxm44i 572 15 , , , work_fnploejenbc2raktl46esxm44i 572 16 and and CC work_fnploejenbc2raktl46esxm44i 572 17 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 572 18 see see VBP work_fnploejenbc2raktl46esxm44i 572 19 that that IN work_fnploejenbc2raktl46esxm44i 572 20 p p NN work_fnploejenbc2raktl46esxm44i 572 21 is be VBZ work_fnploejenbc2raktl46esxm44i 572 22 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 572 23 with with IN work_fnploejenbc2raktl46esxm44i 572 24 Ttx Ttx NNP work_fnploejenbc2raktl46esxm44i 572 25 , , , work_fnploejenbc2raktl46esxm44i 572 26 Y Y NNP work_fnploejenbc2raktl46esxm44i 572 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 572 28 = = SYM work_fnploejenbc2raktl46esxm44i 572 29 P?tP P?tP NNP work_fnploejenbc2raktl46esxm44i 572 30 , , , work_fnploejenbc2raktl46esxm44i 572 31 tx tx NNP work_fnploejenbc2raktl46esxm44i 572 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 572 33 + + NNP work_fnploejenbc2raktl46esxm44i 572 34 Prty Prty NNP work_fnploejenbc2raktl46esxm44i 572 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 572 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 572 37 . . . work_fnploejenbc2raktl46esxm44i 573 1 578 578 CD work_fnploejenbc2raktl46esxm44i 573 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 573 3 , , , work_fnploejenbc2raktl46esxm44i 573 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 573 5 , , , work_fnploejenbc2raktl46esxm44i 573 6 ANDRoGERS androgers CD work_fnploejenbc2raktl46esxm44i 573 7 Of of RB work_fnploejenbc2raktl46esxm44i 573 8 course course RB work_fnploejenbc2raktl46esxm44i 573 9 , , , work_fnploejenbc2raktl46esxm44i 573 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 573 11 ii)*(i ii)*(i NNP work_fnploejenbc2raktl46esxm44i 573 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 573 13 . . . work_fnploejenbc2raktl46esxm44i 574 1 Since since IN work_fnploejenbc2raktl46esxm44i 574 2 p p NN work_fnploejenbc2raktl46esxm44i 574 3 is be VBZ work_fnploejenbc2raktl46esxm44i 574 4 T t NN work_fnploejenbc2raktl46esxm44i 574 5 - - HYPH work_fnploejenbc2raktl46esxm44i 574 6 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 574 7 on on IN work_fnploejenbc2raktl46esxm44i 574 8 a a DT work_fnploejenbc2raktl46esxm44i 574 9 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 574 10 space space NN work_fnploejenbc2raktl46esxm44i 574 11 , , , work_fnploejenbc2raktl46esxm44i 574 12 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 574 13 have have VBP work_fnploejenbc2raktl46esxm44i 574 14 VA VA NNP work_fnploejenbc2raktl46esxm44i 574 15 E E NNP work_fnploejenbc2raktl46esxm44i 574 16 LqQ lqq NN work_fnploejenbc2raktl46esxm44i 574 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 574 18 , , , work_fnploejenbc2raktl46esxm44i 574 19 p(A)= p(A)= NNP work_fnploejenbc2raktl46esxm44i 574 20 T(P(~ T(P(~ NNP work_fnploejenbc2raktl46esxm44i 574 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 574 22 , , , work_fnploejenbc2raktl46esxm44i 574 23 WEA WEA NNP work_fnploejenbc2raktl46esxm44i 574 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 574 25 . . . work_fnploejenbc2raktl46esxm44i 575 1 Take take VB work_fnploejenbc2raktl46esxm44i 575 2 P,-= P,-= NNP work_fnploejenbc2raktl46esxm44i 575 3 g g NN work_fnploejenbc2raktl46esxm44i 575 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 575 5 noting note VBG work_fnploejenbc2raktl46esxm44i 575 6 that that IN work_fnploejenbc2raktl46esxm44i 575 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 575 8 can can MD work_fnploejenbc2raktl46esxm44i 575 9 solve solve VB work_fnploejenbc2raktl46esxm44i 575 10 for for IN work_fnploejenbc2raktl46esxm44i 575 11 f f NNP work_fnploejenbc2raktl46esxm44i 575 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 575 13 , , , work_fnploejenbc2raktl46esxm44i 575 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 575 15 have have VBP work_fnploejenbc2raktl46esxm44i 575 16 PpPc(~)=dm4~ PpPc(~)=dm4~ NNP work_fnploejenbc2raktl46esxm44i 575 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 575 18 ? ? . work_fnploejenbc2raktl46esxm44i 576 1 meA meA NNP work_fnploejenbc2raktl46esxm44i 576 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 3 = = NFP work_fnploejenbc2raktl46esxm44i 576 4 g g NN work_fnploejenbc2raktl46esxm44i 576 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 576 6 g g NN work_fnploejenbc2raktl46esxm44i 576 7 * * NFP work_fnploejenbc2raktl46esxm44i 576 8 (; (; NN work_fnploejenbc2raktl46esxm44i 576 9 g(cw g(cw NNP work_fnploejenbc2raktl46esxm44i 576 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 11 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 576 12 = = NFP work_fnploejenbc2raktl46esxm44i 576 13 ; ; : work_fnploejenbc2raktl46esxm44i 576 14 dP(W dp(w NN work_fnploejenbc2raktl46esxm44i 576 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 17 since since IN work_fnploejenbc2raktl46esxm44i 576 18 , , , work_fnploejenbc2raktl46esxm44i 576 19 by by IN work_fnploejenbc2raktl46esxm44i 576 20 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 576 21 CA CA NNP work_fnploejenbc2raktl46esxm44i 576 22 g(p(o g(p(o NN work_fnploejenbc2raktl46esxm44i 576 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 25 < < XX work_fnploejenbc2raktl46esxm44i 576 26 C C NNP work_fnploejenbc2raktl46esxm44i 576 27 , , , work_fnploejenbc2raktl46esxm44i 576 28 g@(w g@(w CD work_fnploejenbc2raktl46esxm44i 576 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 31 = = NFP work_fnploejenbc2raktl46esxm44i 576 32 1 1 CD work_fnploejenbc2raktl46esxm44i 576 33 = = SYM work_fnploejenbc2raktl46esxm44i 576 34 g g NN work_fnploejenbc2raktl46esxm44i 576 35 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 576 36 1 1 CD work_fnploejenbc2raktl46esxm44i 576 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 576 38 . . . work_fnploejenbc2raktl46esxm44i 577 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 577 2 Pro Pro NNP work_fnploejenbc2raktl46esxm44i 577 3 , , , work_fnploejenbc2raktl46esxm44i 577 4 u u NNP work_fnploejenbc2raktl46esxm44i 577 5 is be VBZ work_fnploejenbc2raktl46esxm44i 577 6 a a DT work_fnploejenbc2raktl46esxm44i 577 7 a a DT work_fnploejenbc2raktl46esxm44i 577 8 - - HYPH work_fnploejenbc2raktl46esxm44i 577 9 additive additive JJ work_fnploejenbc2raktl46esxm44i 577 10 probability probability NN work_fnploejenbc2raktl46esxm44i 577 11 measure measure NN work_fnploejenbc2raktl46esxm44i 577 12 . . . work_fnploejenbc2raktl46esxm44i 578 1 1 1 CD work_fnploejenbc2raktl46esxm44i 578 2 Remark Remark NNP work_fnploejenbc2raktl46esxm44i 578 3 . . . work_fnploejenbc2raktl46esxm44i 579 1 In in IN work_fnploejenbc2raktl46esxm44i 579 2 view view NN work_fnploejenbc2raktl46esxm44i 579 3 of of IN work_fnploejenbc2raktl46esxm44i 579 4 the the DT work_fnploejenbc2raktl46esxm44i 579 5 above above JJ work_fnploejenbc2raktl46esxm44i 579 6 theorem theorem NN work_fnploejenbc2raktl46esxm44i 579 7 , , , work_fnploejenbc2raktl46esxm44i 579 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 579 9 see see VBP work_fnploejenbc2raktl46esxm44i 579 10 that that IN work_fnploejenbc2raktl46esxm44i 579 11 if if IN work_fnploejenbc2raktl46esxm44i 579 12 p p NN work_fnploejenbc2raktl46esxm44i 579 13 is be VBZ work_fnploejenbc2raktl46esxm44i 579 14 T t NN work_fnploejenbc2raktl46esxm44i 579 15 - - HYPH work_fnploejenbc2raktl46esxm44i 579 16 composable composable JJ work_fnploejenbc2raktl46esxm44i 579 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 579 18 or or CC work_fnploejenbc2raktl46esxm44i 579 19 equivalently equivalently RB work_fnploejenbc2raktl46esxm44i 579 20 , , , work_fnploejenbc2raktl46esxm44i 579 21 if if IN work_fnploejenbc2raktl46esxm44i 579 22 p p NN work_fnploejenbc2raktl46esxm44i 579 23 is be VBZ work_fnploejenbc2raktl46esxm44i 579 24 generated generate VBN work_fnploejenbc2raktl46esxm44i 579 25 by by IN work_fnploejenbc2raktl46esxm44i 579 26 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 579 27 restriction restriction NN work_fnploejenbc2raktl46esxm44i 579 28 to to IN work_fnploejenbc2raktl46esxm44i 579 29 singletons singleton NNS work_fnploejenbc2raktl46esxm44i 579 30 and and CC work_fnploejenbc2raktl46esxm44i 579 31 T t NN work_fnploejenbc2raktl46esxm44i 579 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 579 33 and and CC work_fnploejenbc2raktl46esxm44i 579 34 if if IN work_fnploejenbc2raktl46esxm44i 579 35 p p NN work_fnploejenbc2raktl46esxm44i 579 36 is be VBZ work_fnploejenbc2raktl46esxm44i 579 37 general general JJ work_fnploejenbc2raktl46esxm44i 579 38 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 579 39 in in IN work_fnploejenbc2raktl46esxm44i 579 40 the the DT work_fnploejenbc2raktl46esxm44i 579 41 o o NN work_fnploejenbc2raktl46esxm44i 579 42 - - HYPH work_fnploejenbc2raktl46esxm44i 579 43 additive additive JJ work_fnploejenbc2raktl46esxm44i 579 44 sense sense NN work_fnploejenbc2raktl46esxm44i 579 45 , , , work_fnploejenbc2raktl46esxm44i 579 46 then then RB work_fnploejenbc2raktl46esxm44i 579 47 p p NN work_fnploejenbc2raktl46esxm44i 579 48 = = SYM work_fnploejenbc2raktl46esxm44i 579 49 6 6 CD work_fnploejenbc2raktl46esxm44i 579 50 , , , work_fnploejenbc2raktl46esxm44i 579 51 , , , work_fnploejenbc2raktl46esxm44i 579 52 , , , work_fnploejenbc2raktl46esxm44i 579 53 the the DT work_fnploejenbc2raktl46esxm44i 579 54 Dirac Dirac NNP work_fnploejenbc2raktl46esxm44i 579 55 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 579 56 probability probability NN work_fnploejenbc2raktl46esxm44i 579 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 579 58 measure measure NN work_fnploejenbc2raktl46esxm44i 579 59 at at IN work_fnploejenbc2raktl46esxm44i 579 60 o0 o0 JJ work_fnploejenbc2raktl46esxm44i 579 61 E e NN work_fnploejenbc2raktl46esxm44i 579 62 R r NN work_fnploejenbc2raktl46esxm44i 579 63 when when WRB work_fnploejenbc2raktl46esxm44i 579 64 v(wO v(wo NN work_fnploejenbc2raktl46esxm44i 579 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 579 66 = = NFP work_fnploejenbc2raktl46esxm44i 579 67 1 1 CD work_fnploejenbc2raktl46esxm44i 579 68 . . . work_fnploejenbc2raktl46esxm44i 580 1 The the DT work_fnploejenbc2raktl46esxm44i 580 2 following follow VBG work_fnploejenbc2raktl46esxm44i 580 3 result result NN work_fnploejenbc2raktl46esxm44i 580 4 provides provide VBZ work_fnploejenbc2raktl46esxm44i 580 5 a a DT work_fnploejenbc2raktl46esxm44i 580 6 necessary necessary JJ work_fnploejenbc2raktl46esxm44i 580 7 and and CC work_fnploejenbc2raktl46esxm44i 580 8 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 580 9 condition condition NN work_fnploejenbc2raktl46esxm44i 580 10 for for IN work_fnploejenbc2raktl46esxm44i 580 11 p p NN work_fnploejenbc2raktl46esxm44i 580 12 to to TO work_fnploejenbc2raktl46esxm44i 580 13 be be VB work_fnploejenbc2raktl46esxm44i 580 14 general general JJ work_fnploejenbc2raktl46esxm44i 580 15 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 580 16 in in IN work_fnploejenbc2raktl46esxm44i 580 17 the the DT work_fnploejenbc2raktl46esxm44i 580 18 o o NN work_fnploejenbc2raktl46esxm44i 580 19 - - HYPH work_fnploejenbc2raktl46esxm44i 580 20 additive additive JJ work_fnploejenbc2raktl46esxm44i 580 21 sense sense NN work_fnploejenbc2raktl46esxm44i 580 22 when when WRB work_fnploejenbc2raktl46esxm44i 580 23 sup sup NNP work_fnploejenbc2raktl46esxm44i 580 24 , , , work_fnploejenbc2raktl46esxm44i 580 25 p(o p(o NNP work_fnploejenbc2raktl46esxm44i 580 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 580 27 < < XX work_fnploejenbc2raktl46esxm44i 580 28 1 1 CD work_fnploejenbc2raktl46esxm44i 580 29 . . . work_fnploejenbc2raktl46esxm44i 581 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 581 2 5.2.2 5.2.2 CD work_fnploejenbc2raktl46esxm44i 581 3 . . . work_fnploejenbc2raktl46esxm44i 582 1 Let let VB work_fnploejenbc2raktl46esxm44i 582 2 CC cc NN work_fnploejenbc2raktl46esxm44i 582 3 52 52 CD work_fnploejenbc2raktl46esxm44i 582 4 -+ -+ . work_fnploejenbc2raktl46esxm44i 582 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 582 6 0 0 CD work_fnploejenbc2raktl46esxm44i 582 7 , , , work_fnploejenbc2raktl46esxm44i 582 8 l l NN work_fnploejenbc2raktl46esxm44i 582 9 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 582 10 with with IN work_fnploejenbc2raktl46esxm44i 582 11 Q Q NNP work_fnploejenbc2raktl46esxm44i 582 12 countably countably RB work_fnploejenbc2raktl46esxm44i 582 13 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 582 14 , , , work_fnploejenbc2raktl46esxm44i 582 15 such such JJ work_fnploejenbc2raktl46esxm44i 582 16 that that IN work_fnploejenbc2raktl46esxm44i 582 17 sup sup NN work_fnploejenbc2raktl46esxm44i 582 18 , , , work_fnploejenbc2raktl46esxm44i 582 19 U(O U(O NNP work_fnploejenbc2raktl46esxm44i 582 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 582 21 < < XX work_fnploejenbc2raktl46esxm44i 582 22 1 1 CD work_fnploejenbc2raktl46esxm44i 582 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 582 24 a a DT work_fnploejenbc2raktl46esxm44i 582 25 f f NN work_fnploejenbc2raktl46esxm44i 582 26 0 0 CD work_fnploejenbc2raktl46esxm44i 582 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 582 28 . . . work_fnploejenbc2raktl46esxm44i 583 1 Then then RB work_fnploejenbc2raktl46esxm44i 583 2 a a DT work_fnploejenbc2raktl46esxm44i 583 3 necessary necessary JJ work_fnploejenbc2raktl46esxm44i 583 4 and and CC work_fnploejenbc2raktl46esxm44i 583 5 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 583 6 condition condition NN work_fnploejenbc2raktl46esxm44i 583 7 for for IN work_fnploejenbc2raktl46esxm44i 583 8 the the DT work_fnploejenbc2raktl46esxm44i 583 9 existence existence NN work_fnploejenbc2raktl46esxm44i 583 10 of of IN work_fnploejenbc2raktl46esxm44i 583 11 a a DT work_fnploejenbc2raktl46esxm44i 583 12 T t NN work_fnploejenbc2raktl46esxm44i 583 13 - - HYPH work_fnploejenbc2raktl46esxm44i 583 14 possibility possibility NN work_fnploejenbc2raktl46esxm44i 583 15 measure measure NN work_fnploejenbc2raktl46esxm44i 583 16 , , , work_fnploejenbc2raktl46esxm44i 583 17 u u NNP work_fnploejenbc2raktl46esxm44i 583 18 , , , work_fnploejenbc2raktl46esxm44i 583 19 generated generate VBN work_fnploejenbc2raktl46esxm44i 583 20 by by IN work_fnploejenbc2raktl46esxm44i 583 21 c1 c1 NN work_fnploejenbc2raktl46esxm44i 583 22 and and CC work_fnploejenbc2raktl46esxm44i 583 23 some some DT work_fnploejenbc2raktl46esxm44i 583 24 T t NN work_fnploejenbc2raktl46esxm44i 583 25 , , , work_fnploejenbc2raktl46esxm44i 583 26 which which WDT work_fnploejenbc2raktl46esxm44i 583 27 is be VBZ work_fnploejenbc2raktl46esxm44i 583 28 general general JJ work_fnploejenbc2raktl46esxm44i 583 29 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 583 30 in in IN work_fnploejenbc2raktl46esxm44i 583 31 the the DT work_fnploejenbc2raktl46esxm44i 583 32 o o NN work_fnploejenbc2raktl46esxm44i 583 33 - - HYPH work_fnploejenbc2raktl46esxm44i 583 34 additive additive JJ work_fnploejenbc2raktl46esxm44i 583 35 sense sense NN work_fnploejenbc2raktl46esxm44i 583 36 , , , work_fnploejenbc2raktl46esxm44i 583 37 is be VBZ work_fnploejenbc2raktl46esxm44i 583 38 that that IN work_fnploejenbc2raktl46esxm44i 583 39 VXE(O VXE(O NNP work_fnploejenbc2raktl46esxm44i 583 40 , , , work_fnploejenbc2raktl46esxm44i 583 41 11 11 CD work_fnploejenbc2raktl46esxm44i 583 42 , , , work_fnploejenbc2raktl46esxm44i 583 43 a-‘[x a-‘[x CD work_fnploejenbc2raktl46esxm44i 583 44 , , , work_fnploejenbc2raktl46esxm44i 583 45 1]={o 1]={o CD work_fnploejenbc2raktl46esxm44i 583 46 : : : work_fnploejenbc2raktl46esxm44i 583 47 x x LS work_fnploejenbc2raktl46esxm44i 583 48 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 583 49 fx(o)~1 fx(o)~1 NN work_fnploejenbc2raktl46esxm44i 583 50 } } -RRB- work_fnploejenbc2raktl46esxm44i 583 51 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 583 52 * * NFP work_fnploejenbc2raktl46esxm44i 583 53 * * NFP work_fnploejenbc2raktl46esxm44i 583 54 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 583 55 is be VBZ work_fnploejenbc2raktl46esxm44i 583 56 finite finite JJ work_fnploejenbc2raktl46esxm44i 583 57 . . . work_fnploejenbc2raktl46esxm44i 584 1 In in IN work_fnploejenbc2raktl46esxm44i 584 2 particular particular JJ work_fnploejenbc2raktl46esxm44i 584 3 , , , work_fnploejenbc2raktl46esxm44i 584 4 if if IN work_fnploejenbc2raktl46esxm44i 584 5 S S NNP work_fnploejenbc2raktl46esxm44i 584 6 is be VBZ work_fnploejenbc2raktl46esxm44i 584 7 finite finite JJ work_fnploejenbc2raktl46esxm44i 584 8 and and CC work_fnploejenbc2raktl46esxm44i 584 9 sup sup JJ work_fnploejenbc2raktl46esxm44i 584 10 , , , work_fnploejenbc2raktl46esxm44i 584 11 M(W m(w NN work_fnploejenbc2raktl46esxm44i 584 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 584 13 < < XX work_fnploejenbc2raktl46esxm44i 584 14 1 1 CD work_fnploejenbc2raktl46esxm44i 584 15 , , , work_fnploejenbc2raktl46esxm44i 584 16 then then RB work_fnploejenbc2raktl46esxm44i 584 17 there there EX work_fnploejenbc2raktl46esxm44i 584 18 exists exist VBZ work_fnploejenbc2raktl46esxm44i 584 19 T t NN work_fnploejenbc2raktl46esxm44i 584 20 such such JJ work_fnploejenbc2raktl46esxm44i 584 21 that that IN work_fnploejenbc2raktl46esxm44i 584 22 pa,= pa,= NNP work_fnploejenbc2raktl46esxm44i 584 23 is be VBZ work_fnploejenbc2raktl46esxm44i 584 24 general general JJ work_fnploejenbc2raktl46esxm44i 584 25 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 584 26 in in IN work_fnploejenbc2raktl46esxm44i 584 27 the the DT work_fnploejenbc2raktl46esxm44i 584 28 o o NN work_fnploejenbc2raktl46esxm44i 584 29 - - HYPH work_fnploejenbc2raktl46esxm44i 584 30 additive additive JJ work_fnploejenbc2raktl46esxm44i 584 31 sense sense NN work_fnploejenbc2raktl46esxm44i 584 32 . . . work_fnploejenbc2raktl46esxm44i 585 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 585 2 : : : work_fnploejenbc2raktl46esxm44i 585 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 585 4 a a LS work_fnploejenbc2raktl46esxm44i 585 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 585 6 Necessity necessity NN work_fnploejenbc2raktl46esxm44i 585 7 . . . work_fnploejenbc2raktl46esxm44i 586 1 If if IN work_fnploejenbc2raktl46esxm44i 586 2 there there EX work_fnploejenbc2raktl46esxm44i 586 3 is be VBZ work_fnploejenbc2raktl46esxm44i 586 4 X,,E x,,e JJ work_fnploejenbc2raktl46esxm44i 586 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 586 6 O o UH work_fnploejenbc2raktl46esxm44i 586 7 , , , work_fnploejenbc2raktl46esxm44i 586 8 l l NN work_fnploejenbc2raktl46esxm44i 586 9 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 586 10 such such JJ work_fnploejenbc2raktl46esxm44i 586 11 that that IN work_fnploejenbc2raktl46esxm44i 586 12 cr-‘C.-C cr-‘C.-C NNP work_fnploejenbc2raktl46esxm44i 586 13 , , , work_fnploejenbc2raktl46esxm44i 586 14 , , , work_fnploejenbc2raktl46esxm44i 586 15 l l NN work_fnploejenbc2raktl46esxm44i 586 16 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 586 17 is be VBZ work_fnploejenbc2raktl46esxm44i 586 18 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 586 19 , , , work_fnploejenbc2raktl46esxm44i 586 20 then then RB work_fnploejenbc2raktl46esxm44i 586 21 lim lim NNP work_fnploejenbc2raktl46esxm44i 586 22 1 1 CD work_fnploejenbc2raktl46esxm44i 586 23 g(Ao))= g(Ao))= NNS work_fnploejenbc2raktl46esxm44i 586 24 + + SYM work_fnploejenbc2raktl46esxm44i 586 25 ~0 ~0 CD work_fnploejenbc2raktl46esxm44i 586 26 , , , work_fnploejenbc2raktl46esxm44i 586 27 n n NNP work_fnploejenbc2raktl46esxm44i 586 28 - - HYPH work_fnploejenbc2raktl46esxm44i 586 29 t t NN work_fnploejenbc2raktl46esxm44i 586 30 + + CC work_fnploejenbc2raktl46esxm44i 586 31 m m NN work_fnploejenbc2raktl46esxm44i 586 32 4 4 CD work_fnploejenbc2raktl46esxm44i 586 33 where where WRB work_fnploejenbc2raktl46esxm44i 586 34 A a NN work_fnploejenbc2raktl46esxm44i 586 35 , , , work_fnploejenbc2raktl46esxm44i 586 36 cc~[x cc~[x NNP work_fnploejenbc2raktl46esxm44i 586 37 , , , work_fnploejenbc2raktl46esxm44i 586 38 , , , work_fnploejenbc2raktl46esxm44i 586 39 , , , work_fnploejenbc2raktl46esxm44i 586 40 11 11 CD work_fnploejenbc2raktl46esxm44i 586 41 . . . work_fnploejenbc2raktl46esxm44i 587 1 For for IN work_fnploejenbc2raktl46esxm44i 587 2 , , , work_fnploejenbc2raktl46esxm44i 587 3 although although IN work_fnploejenbc2raktl46esxm44i 587 4 A A NNP work_fnploejenbc2raktl46esxm44i 587 5 , , , work_fnploejenbc2raktl46esxm44i 587 6 is be VBZ work_fnploejenbc2raktl46esxm44i 587 7 finite finite JJ work_fnploejenbc2raktl46esxm44i 587 8 , , , work_fnploejenbc2raktl46esxm44i 587 9 and and CC work_fnploejenbc2raktl46esxm44i 587 10 A,~c~[x A,~c~[x NNP work_fnploejenbc2raktl46esxm44i 587 11 , , , work_fnploejenbc2raktl46esxm44i 587 12 , , , work_fnploejenbc2raktl46esxm44i 587 13 l l NN work_fnploejenbc2raktl46esxm44i 587 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 587 15 for for IN work_fnploejenbc2raktl46esxm44i 587 16 each each DT work_fnploejenbc2raktl46esxm44i 587 17 n n CD work_fnploejenbc2raktl46esxm44i 587 18 > > NN work_fnploejenbc2raktl46esxm44i 587 19 1 1 CD work_fnploejenbc2raktl46esxm44i 587 20 , , , work_fnploejenbc2raktl46esxm44i 587 21 & & CC work_fnploejenbc2raktl46esxm44i 587 22 g(p(o))>g(x g(p(o))>g(x NNPS work_fnploejenbc2raktl46esxm44i 587 23 , , , work_fnploejenbc2raktl46esxm44i 587 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 587 25 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 587 26 A a NN work_fnploejenbc2raktl46esxm44i 587 27 , , , work_fnploejenbc2raktl46esxm44i 587 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 587 29 . . . work_fnploejenbc2raktl46esxm44i 588 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 588 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 588 3 * * NFP work_fnploejenbc2raktl46esxm44i 588 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 588 5 of of IN work_fnploejenbc2raktl46esxm44i 588 6 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 588 7 5.2.1 5.2.1 NNP work_fnploejenbc2raktl46esxm44i 588 8 will will MD work_fnploejenbc2raktl46esxm44i 588 9 not not RB work_fnploejenbc2raktl46esxm44i 588 10 hold hold VB work_fnploejenbc2raktl46esxm44i 588 11 . . . work_fnploejenbc2raktl46esxm44i 589 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 589 2 b b LS work_fnploejenbc2raktl46esxm44i 589 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 589 4 Sufficiency Sufficiency NNP work_fnploejenbc2raktl46esxm44i 589 5 . . . work_fnploejenbc2raktl46esxm44i 590 1 In in IN work_fnploejenbc2raktl46esxm44i 590 2 view view NN work_fnploejenbc2raktl46esxm44i 590 3 of of IN work_fnploejenbc2raktl46esxm44i 590 4 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 590 5 5.2.1 5.2.1 CD work_fnploejenbc2raktl46esxm44i 590 6 , , , work_fnploejenbc2raktl46esxm44i 590 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 590 8 need need VBP work_fnploejenbc2raktl46esxm44i 590 9 to to TO work_fnploejenbc2raktl46esxm44i 590 10 show show VB work_fnploejenbc2raktl46esxm44i 590 11 only only RB work_fnploejenbc2raktl46esxm44i 590 12 the the DT work_fnploejenbc2raktl46esxm44i 590 13 existence existence NN work_fnploejenbc2raktl46esxm44i 590 14 of of IN work_fnploejenbc2raktl46esxm44i 590 15 a a DT work_fnploejenbc2raktl46esxm44i 590 16 generator generator NN work_fnploejenbc2raktl46esxm44i 590 17 g g NN work_fnploejenbc2raktl46esxm44i 590 18 such such JJ work_fnploejenbc2raktl46esxm44i 590 19 that that IN work_fnploejenbc2raktl46esxm44i 590 20 g g NN work_fnploejenbc2raktl46esxm44i 590 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 590 22 1 1 CD work_fnploejenbc2raktl46esxm44i 590 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 590 24 = = SYM work_fnploejenbc2raktl46esxm44i 590 25 1 1 CD work_fnploejenbc2raktl46esxm44i 590 26 and and CC work_fnploejenbc2raktl46esxm44i 590 27 Cn Cn NNP work_fnploejenbc2raktl46esxm44i 590 28 g(a(w g(a(w NN work_fnploejenbc2raktl46esxm44i 590 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 590 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 590 31 = = NFP work_fnploejenbc2raktl46esxm44i 590 32 1 1 CD work_fnploejenbc2raktl46esxm44i 590 33 . . . work_fnploejenbc2raktl46esxm44i 591 1 Then then RB work_fnploejenbc2raktl46esxm44i 591 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 591 3 SCORING score VBD work_fnploejenbc2raktl46esxm44i 591 4 APPROACH APPROACH NNS work_fnploejenbc2raktl46esxm44i 591 5 TO to IN work_fnploejenbc2raktl46esxm44i 591 6 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 591 7 579 579 CD work_fnploejenbc2raktl46esxm44i 591 8 can can MD work_fnploejenbc2raktl46esxm44i 591 9 take take VB work_fnploejenbc2raktl46esxm44i 591 10 pd pd NN work_fnploejenbc2raktl46esxm44i 591 11 , , , work_fnploejenbc2raktl46esxm44i 591 12 r(A r(a VB work_fnploejenbc2raktl46esxm44i 591 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 591 14 = = NFP work_fnploejenbc2raktl46esxm44i 591 15 g g NN work_fnploejenbc2raktl46esxm44i 591 16 * * NFP work_fnploejenbc2raktl46esxm44i 591 17 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 591 18 CA CA NNP work_fnploejenbc2raktl46esxm44i 591 19 g(cl(w g(cl(w NNP work_fnploejenbc2raktl46esxm44i 591 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 591 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 591 22 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 591 23 , , , work_fnploejenbc2raktl46esxm44i 591 24 where where WRB work_fnploejenbc2raktl46esxm44i 591 25 T T NNP work_fnploejenbc2raktl46esxm44i 591 26 is be VBZ work_fnploejenbc2raktl46esxm44i 591 27 the the DT work_fnploejenbc2raktl46esxm44i 591 28 Archimedean Archimedean NNP work_fnploejenbc2raktl46esxm44i 591 29 t t NN work_fnploejenbc2raktl46esxm44i 591 30 - - HYPH work_fnploejenbc2raktl46esxm44i 591 31 conorm conorm NN work_fnploejenbc2raktl46esxm44i 591 32 with with IN work_fnploejenbc2raktl46esxm44i 591 33 generator generator NN work_fnploejenbc2raktl46esxm44i 591 34 g. g. . work_fnploejenbc2raktl46esxm44i 591 35 Let let VB work_fnploejenbc2raktl46esxm44i 591 36 O o UH work_fnploejenbc2raktl46esxm44i 591 37 < < XX work_fnploejenbc2raktl46esxm44i 591 38 x,=sup x,=sup NNP work_fnploejenbc2raktl46esxm44i 591 39 , , , work_fnploejenbc2raktl46esxm44i 591 40 a(w)0)={~:01(~)>O}=U~~~K 01>0)={~:01(~)>o}=u~~~k NN work_fnploejenbc2raktl46esxm44i 592 4 , , , work_fnploejenbc2raktl46esxm44i 592 5 , , , work_fnploejenbc2raktl46esxm44i 592 6 where where WRB work_fnploejenbc2raktl46esxm44i 592 7 K K NNP work_fnploejenbc2raktl46esxm44i 592 8 , , , work_fnploejenbc2raktl46esxm44i 592 9 = = NFP work_fnploejenbc2raktl46esxm44i 592 10 { { -LRB- work_fnploejenbc2raktl46esxm44i 592 11 o o NN work_fnploejenbc2raktl46esxm44i 592 12 : : : work_fnploejenbc2raktl46esxm44i 592 13 l l NN work_fnploejenbc2raktl46esxm44i 592 14 / / SYM work_fnploejenbc2raktl46esxm44i 592 15 n n NNP work_fnploejenbc2raktl46esxm44i 592 16 < < XX work_fnploejenbc2raktl46esxm44i 592 17 a(o a(o NNP work_fnploejenbc2raktl46esxm44i 592 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 592 19 d d NNP work_fnploejenbc2raktl46esxm44i 592 20 l/(n l/(n NNP work_fnploejenbc2raktl46esxm44i 592 21 - - HYPH work_fnploejenbc2raktl46esxm44i 592 22 l l NN work_fnploejenbc2raktl46esxm44i 592 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 592 24 } } -RRB- work_fnploejenbc2raktl46esxm44i 592 25 , , , work_fnploejenbc2raktl46esxm44i 592 26 n n NN work_fnploejenbc2raktl46esxm44i 592 27 > > NN work_fnploejenbc2raktl46esxm44i 592 28 2 2 CD work_fnploejenbc2raktl46esxm44i 592 29 . . . work_fnploejenbc2raktl46esxm44i 593 1 Let let VB work_fnploejenbc2raktl46esxm44i 593 2 n n NNP work_fnploejenbc2raktl46esxm44i 593 3 , , , work_fnploejenbc2raktl46esxm44i 593 4 k k NNP work_fnploejenbc2raktl46esxm44i 593 5 2 2 CD work_fnploejenbc2raktl46esxm44i 593 6 such such JJ work_fnploejenbc2raktl46esxm44i 593 7 that that IN work_fnploejenbc2raktl46esxm44i 593 8 l l NN work_fnploejenbc2raktl46esxm44i 593 9 / / SYM work_fnploejenbc2raktl46esxm44i 593 10 n n NNP work_fnploejenbc2raktl46esxm44i 593 11 , , , work_fnploejenbc2raktl46esxm44i 593 12 < < XX work_fnploejenbc2raktl46esxm44i 593 13 x0 x0 NNP work_fnploejenbc2raktl46esxm44i 593 14 < < XX work_fnploejenbc2raktl46esxm44i 593 15 l/(n,-- l/(n,-- NNP work_fnploejenbc2raktl46esxm44i 593 16 1 1 CD work_fnploejenbc2raktl46esxm44i 593 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 593 18 . . . work_fnploejenbc2raktl46esxm44i 594 1 By by IN work_fnploejenbc2raktl46esxm44i 594 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 594 3 * * NFP work_fnploejenbc2raktl46esxm44i 594 4 * * NFP work_fnploejenbc2raktl46esxm44i 594 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 594 6 , , , work_fnploejenbc2raktl46esxm44i 594 7 cr-‘[l cr-‘[l . work_fnploejenbc2raktl46esxm44i 594 8 / / SYM work_fnploejenbc2raktl46esxm44i 594 9 n n NNP work_fnploejenbc2raktl46esxm44i 594 10 , , , work_fnploejenbc2raktl46esxm44i 594 11 , , , work_fnploejenbc2raktl46esxm44i 594 12 , , , work_fnploejenbc2raktl46esxm44i 594 13 1 1 CD work_fnploejenbc2raktl46esxm44i 594 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 594 15 is be VBZ work_fnploejenbc2raktl46esxm44i 594 16 finite finite JJ work_fnploejenbc2raktl46esxm44i 594 17 ; ; : work_fnploejenbc2raktl46esxm44i 594 18 thus thus RB work_fnploejenbc2raktl46esxm44i 594 19 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 594 20 a(u a(u NNP work_fnploejenbc2raktl46esxm44i 594 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 594 22 : : : work_fnploejenbc2raktl46esxm44i 594 23 coEKno coekno NN work_fnploejenbc2raktl46esxm44i 594 24 } } -RRB- work_fnploejenbc2raktl46esxm44i 594 25 = = SYM work_fnploejenbc2raktl46esxm44i 594 26 1 1 CD work_fnploejenbc2raktl46esxm44i 594 27 Xl xl NN work_fnploejenbc2raktl46esxm44i 594 28 9 9 CD work_fnploejenbc2raktl46esxm44i 594 29 x2 x2 NN work_fnploejenbc2raktl46esxm44i 594 30 , , , work_fnploejenbc2raktl46esxm44i 594 31 . . . work_fnploejenbc2raktl46esxm44i 595 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 595 2 1 1 LS work_fnploejenbc2raktl46esxm44i 595 3 x,~ x,~ ADD work_fnploejenbc2raktl46esxm44i 595 4 } } -RRB- work_fnploejenbc2raktl46esxm44i 595 5 for for IN work_fnploejenbc2raktl46esxm44i 595 6 some some DT work_fnploejenbc2raktl46esxm44i 595 7 n n JJ work_fnploejenbc2raktl46esxm44i 595 8 , , , work_fnploejenbc2raktl46esxm44i 595 9 . . . work_fnploejenbc2raktl46esxm44i 596 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 596 2 can can MD work_fnploejenbc2raktl46esxm44i 596 3 assume assume VB work_fnploejenbc2raktl46esxm44i 596 4 1 1 CD work_fnploejenbc2raktl46esxm44i 596 5 1 1 CD work_fnploejenbc2raktl46esxm44i 596 6 - > XX work_fnploejenbc2raktl46esxm44i 597 9 a(d a(d NNP work_fnploejenbc2raktl46esxm44i 597 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 597 11 = = SYM work_fnploejenbc2raktl46esxm44i 597 12 x x UH work_fnploejenbc2raktl46esxm44i 597 13 , , , work_fnploejenbc2raktl46esxm44i 597 14 , , , work_fnploejenbc2raktl46esxm44i 597 15 , , , work_fnploejenbc2raktl46esxm44i 597 16 then then RB work_fnploejenbc2raktl46esxm44i 597 17 0 0 NFP work_fnploejenbc2raktl46esxm44i 597 18 ” " `` work_fnploejenbc2raktl46esxm44i 597 19 E E NNP work_fnploejenbc2raktl46esxm44i 597 20 K k NN work_fnploejenbc2raktl46esxm44i 597 21 , , , work_fnploejenbc2raktl46esxm44i 597 22 , , , work_fnploejenbc2raktl46esxm44i 597 23 . . . work_fnploejenbc2raktl46esxm44i 598 1 and and CC work_fnploejenbc2raktl46esxm44i 598 2 hence hence RB work_fnploejenbc2raktl46esxm44i 598 3 contradicts contradict VBZ work_fnploejenbc2raktl46esxm44i 598 4 the the DT work_fnploejenbc2raktl46esxm44i 598 5 definition definition NN work_fnploejenbc2raktl46esxm44i 598 6 x x NN work_fnploejenbc2raktl46esxm44i 598 7 , , , work_fnploejenbc2raktl46esxm44i 598 8 , , , work_fnploejenbc2raktl46esxm44i 598 9 = = SYM work_fnploejenbc2raktl46esxm44i 598 10 M$x M$x NNP work_fnploejenbc2raktl46esxm44i 598 11 a(w a(w NNP work_fnploejenbc2raktl46esxm44i 598 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 598 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 598 14 . . . work_fnploejenbc2raktl46esxm44i 599 1 Since since IN work_fnploejenbc2raktl46esxm44i 599 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 599 3 0 0 CD work_fnploejenbc2raktl46esxm44i 599 4 , , , work_fnploejenbc2raktl46esxm44i 599 5 1 1 CD work_fnploejenbc2raktl46esxm44i 599 6 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 599 7 = = SYM work_fnploejenbc2raktl46esxm44i 599 8 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 599 9 0 0 CD work_fnploejenbc2raktl46esxm44i 599 10 , , , work_fnploejenbc2raktl46esxm44i 599 11 l l NN work_fnploejenbc2raktl46esxm44i 599 12 / / SYM work_fnploejenbc2raktl46esxm44i 599 13 no no NN work_fnploejenbc2raktl46esxm44i 599 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 599 15 u u NNP work_fnploejenbc2raktl46esxm44i 599 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 599 17 l l NN work_fnploejenbc2raktl46esxm44i 599 18 / / SYM work_fnploejenbc2raktl46esxm44i 599 19 n n NNP work_fnploejenbc2raktl46esxm44i 599 20 , , , work_fnploejenbc2raktl46esxm44i 599 21 , , , work_fnploejenbc2raktl46esxm44i 599 22 11 11 CD work_fnploejenbc2raktl46esxm44i 599 23 , , , work_fnploejenbc2raktl46esxm44i 599 24 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 599 25 first first RB work_fnploejenbc2raktl46esxm44i 599 26 construct construct VBP work_fnploejenbc2raktl46esxm44i 599 27 g g NN work_fnploejenbc2raktl46esxm44i 599 28 on on IN work_fnploejenbc2raktl46esxm44i 599 29 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 599 30 0 0 CD work_fnploejenbc2raktl46esxm44i 599 31 , , , work_fnploejenbc2raktl46esxm44i 599 32 l l NN work_fnploejenbc2raktl46esxm44i 599 33 / / SYM work_fnploejenbc2raktl46esxm44i 599 34 n n NNP work_fnploejenbc2raktl46esxm44i 599 35 , , , work_fnploejenbc2raktl46esxm44i 599 36 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 599 37 . . . work_fnploejenbc2raktl46esxm44i 600 1 For for IN work_fnploejenbc2raktl46esxm44i 600 2 n n CC work_fnploejenbc2raktl46esxm44i 600 3 an an DT work_fnploejenbc2raktl46esxm44i 600 4 , , , work_fnploejenbc2raktl46esxm44i 600 5 and and CC work_fnploejenbc2raktl46esxm44i 600 6 r r NN work_fnploejenbc2raktl46esxm44i 600 7 > > XX work_fnploejenbc2raktl46esxm44i 600 8 O o UH work_fnploejenbc2raktl46esxm44i 600 9 , , , work_fnploejenbc2raktl46esxm44i 600 10 define define VB work_fnploejenbc2raktl46esxm44i 600 11 g,(O g,(o NN work_fnploejenbc2raktl46esxm44i 600 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 600 13 = = NFP work_fnploejenbc2raktl46esxm44i 600 14 0 0 NFP work_fnploejenbc2raktl46esxm44i 600 15 and and CC work_fnploejenbc2raktl46esxm44i 600 16 Then then RB work_fnploejenbc2raktl46esxm44i 600 17 l l NN work_fnploejenbc2raktl46esxm44i 600 18 / / SYM work_fnploejenbc2raktl46esxm44i 600 19 m m NNP work_fnploejenbc2raktl46esxm44i 600 20 < < XX work_fnploejenbc2raktl46esxm44i 600 21 l l NNP work_fnploejenbc2raktl46esxm44i 600 22 / / SYM work_fnploejenbc2raktl46esxm44i 600 23 n n NN work_fnploejenbc2raktl46esxm44i 600 24 = = SYM work_fnploejenbc2raktl46esxm44i 600 25 z. z. NNP work_fnploejenbc2raktl46esxm44i 601 1 g g NNP work_fnploejenbc2raktl46esxm44i 601 2 , , , work_fnploejenbc2raktl46esxm44i 601 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 601 4 l l NN work_fnploejenbc2raktl46esxm44i 601 5 / / SYM work_fnploejenbc2raktl46esxm44i 601 6 m m NNP work_fnploejenbc2raktl46esxm44i 601 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 601 8 < < XX work_fnploejenbc2raktl46esxm44i 601 9 g g NNP work_fnploejenbc2raktl46esxm44i 601 10 , , , work_fnploejenbc2raktl46esxm44i 601 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 601 12 l l NN work_fnploejenbc2raktl46esxm44i 601 13 / / SYM work_fnploejenbc2raktl46esxm44i 601 14 n n NNP work_fnploejenbc2raktl46esxm44i 601 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 601 16 and and CC work_fnploejenbc2raktl46esxm44i 601 17 lim lim NNP work_fnploejenbc2raktl46esxm44i 601 18 , , , work_fnploejenbc2raktl46esxm44i 601 19 _ _ NNP work_fnploejenbc2raktl46esxm44i 601 20 o. o. NNP work_fnploejenbc2raktl46esxm44i 601 21 g g NNP work_fnploejenbc2raktl46esxm44i 601 22 , , , work_fnploejenbc2raktl46esxm44i 601 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 601 24 l l NN work_fnploejenbc2raktl46esxm44i 601 25 / / SYM work_fnploejenbc2raktl46esxm44i 601 26 n n NNP work_fnploejenbc2raktl46esxm44i 601 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 601 28 = = SYM work_fnploejenbc2raktl46esxm44i 601 29 0 0 NFP work_fnploejenbc2raktl46esxm44i 601 30 . . . work_fnploejenbc2raktl46esxm44i 602 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 602 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 602 3 construct construct VBP work_fnploejenbc2raktl46esxm44i 602 4 a a DT work_fnploejenbc2raktl46esxm44i 602 5 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 602 6 , , , work_fnploejenbc2raktl46esxm44i 602 7 increasing increase VBG work_fnploejenbc2raktl46esxm44i 602 8 function function NN work_fnploejenbc2raktl46esxm44i 602 9 on on IN work_fnploejenbc2raktl46esxm44i 602 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 602 11 0 0 CD work_fnploejenbc2raktl46esxm44i 602 12 , , , work_fnploejenbc2raktl46esxm44i 602 13 l l NN work_fnploejenbc2raktl46esxm44i 602 14 / / SYM work_fnploejenbc2raktl46esxm44i 602 15 n n NNP work_fnploejenbc2raktl46esxm44i 602 16 , , , work_fnploejenbc2raktl46esxm44i 602 17 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 602 18 by by IN work_fnploejenbc2raktl46esxm44i 602 19 extending extend VBG work_fnploejenbc2raktl46esxm44i 602 20 g g NN work_fnploejenbc2raktl46esxm44i 602 21 , , , work_fnploejenbc2raktl46esxm44i 602 22 continuously continuously RB work_fnploejenbc2raktl46esxm44i 602 23 on on IN work_fnploejenbc2raktl46esxm44i 602 24 each each DT work_fnploejenbc2raktl46esxm44i 602 25 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 602 26 l l NN work_fnploejenbc2raktl46esxm44i 602 27 / / SYM work_fnploejenbc2raktl46esxm44i 602 28 n n CC work_fnploejenbc2raktl46esxm44i 602 29 , , , work_fnploejenbc2raktl46esxm44i 602 30 l/(n l/(n NNP work_fnploejenbc2raktl46esxm44i 602 31 - - HYPH work_fnploejenbc2raktl46esxm44i 602 32 l l NN work_fnploejenbc2raktl46esxm44i 602 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 602 34 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 602 35 , , , work_fnploejenbc2raktl46esxm44i 602 36 for for IN work_fnploejenbc2raktl46esxm44i 602 37 n n NN work_fnploejenbc2raktl46esxm44i 602 38 > > NN work_fnploejenbc2raktl46esxm44i 602 39 no no UH work_fnploejenbc2raktl46esxm44i 602 40 , , , work_fnploejenbc2raktl46esxm44i 602 41 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 602 42 say say VB work_fnploejenbc2raktl46esxm44i 602 43 by by IN work_fnploejenbc2raktl46esxm44i 602 44 joining join VBG work_fnploejenbc2raktl46esxm44i 602 45 g,(l g,(l NNP work_fnploejenbc2raktl46esxm44i 602 46 / / SYM work_fnploejenbc2raktl46esxm44i 602 47 n n NNP work_fnploejenbc2raktl46esxm44i 602 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 602 49 and and CC work_fnploejenbc2raktl46esxm44i 602 50 g g NN work_fnploejenbc2raktl46esxm44i 602 51 , , , work_fnploejenbc2raktl46esxm44i 602 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 602 53 l/(n l/(n NNP work_fnploejenbc2raktl46esxm44i 602 54 - - HYPH work_fnploejenbc2raktl46esxm44i 602 55 1 1 CD work_fnploejenbc2raktl46esxm44i 602 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 602 57 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 602 58 by by IN work_fnploejenbc2raktl46esxm44i 602 59 a a DT work_fnploejenbc2raktl46esxm44i 602 60 straight straight JJ work_fnploejenbc2raktl46esxm44i 602 61 line line NN work_fnploejenbc2raktl46esxm44i 602 62 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 602 63 . . . work_fnploejenbc2raktl46esxm44i 603 1 On on IN work_fnploejenbc2raktl46esxm44i 603 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 603 3 l l NN work_fnploejenbc2raktl46esxm44i 603 4 / / SYM work_fnploejenbc2raktl46esxm44i 603 5 n n NNP work_fnploejenbc2raktl46esxm44i 603 6 , , , work_fnploejenbc2raktl46esxm44i 603 7 , , , work_fnploejenbc2raktl46esxm44i 603 8 11 11 CD work_fnploejenbc2raktl46esxm44i 603 9 , , , work_fnploejenbc2raktl46esxm44i 603 10 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 603 11 proceed proceed VBP work_fnploejenbc2raktl46esxm44i 603 12 as as IN work_fnploejenbc2raktl46esxm44i 603 13 follows follow VBZ work_fnploejenbc2raktl46esxm44i 603 14 . . . work_fnploejenbc2raktl46esxm44i 604 1 Let let VB work_fnploejenbc2raktl46esxm44i 604 2 a(r a(r NNP work_fnploejenbc2raktl46esxm44i 604 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 604 4 = = NFP work_fnploejenbc2raktl46esxm44i 604 5 1 1 CD work_fnploejenbc2raktl46esxm44i 604 6 s,(a(o s,(a(o NNP work_fnploejenbc2raktl46esxm44i 604 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 604 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 604 9 . . . work_fnploejenbc2raktl46esxm44i 605 1 G G NNP work_fnploejenbc2raktl46esxm44i 605 2 Since since IN work_fnploejenbc2raktl46esxm44i 605 3 x0 x0 NNP work_fnploejenbc2raktl46esxm44i 605 4 E E NNP work_fnploejenbc2raktl46esxm44i 605 5 K K NNP work_fnploejenbc2raktl46esxm44i 605 6 , , , work_fnploejenbc2raktl46esxm44i 605 7 , , , work_fnploejenbc2raktl46esxm44i 605 8 K&= K&= NNP work_fnploejenbc2raktl46esxm44i 605 9 { { -LRB- work_fnploejenbc2raktl46esxm44i 605 10 o o NN work_fnploejenbc2raktl46esxm44i 605 11 : : : work_fnploejenbc2raktl46esxm44i 605 12 a(w a(w NNP work_fnploejenbc2raktl46esxm44i 605 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 605 14 < < XX work_fnploejenbc2raktl46esxm44i 605 15 l l NN work_fnploejenbc2raktl46esxm44i 605 16 / / SYM work_fnploejenbc2raktl46esxm44i 605 17 n n NN work_fnploejenbc2raktl46esxm44i 605 18 , , , work_fnploejenbc2raktl46esxm44i 605 19 } } -RRB- work_fnploejenbc2raktl46esxm44i 605 20 ; ; : work_fnploejenbc2raktl46esxm44i 605 21 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 605 22 , , , work_fnploejenbc2raktl46esxm44i 605 23 for for IN work_fnploejenbc2raktl46esxm44i 605 24 OE OE NNP work_fnploejenbc2raktl46esxm44i 605 25 K’n K’n NNP work_fnploejenbc2raktl46esxm44i 605 26 , , , work_fnploejenbc2raktl46esxm44i 605 27 , , , work_fnploejenbc2raktl46esxm44i 605 28 a(o a(o NNP work_fnploejenbc2raktl46esxm44i 605 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 605 30 e e NNP work_fnploejenbc2raktl46esxm44i 605 31 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 605 32 0 0 CD work_fnploejenbc2raktl46esxm44i 605 33 , , , work_fnploejenbc2raktl46esxm44i 605 34 l l NN work_fnploejenbc2raktl46esxm44i 605 35 / / SYM work_fnploejenbc2raktl46esxm44i 605 36 n n NNP work_fnploejenbc2raktl46esxm44i 605 37 , , , work_fnploejenbc2raktl46esxm44i 605 38 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 605 39 , , , work_fnploejenbc2raktl46esxm44i 605 40 which which WDT work_fnploejenbc2raktl46esxm44i 605 41 is be VBZ work_fnploejenbc2raktl46esxm44i 605 42 the the DT work_fnploejenbc2raktl46esxm44i 605 43 domain domain NN work_fnploejenbc2raktl46esxm44i 605 44 of of IN work_fnploejenbc2raktl46esxm44i 605 45 g g NN work_fnploejenbc2raktl46esxm44i 605 46 , , , work_fnploejenbc2raktl46esxm44i 605 47 defined define VBN work_fnploejenbc2raktl46esxm44i 605 48 above above RB work_fnploejenbc2raktl46esxm44i 605 49 . . . work_fnploejenbc2raktl46esxm44i 606 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 606 2 have have VBP work_fnploejenbc2raktl46esxm44i 606 3 OGa(r)= OGa(r)= NNS work_fnploejenbc2raktl46esxm44i 606 4 + + SYM work_fnploejenbc2raktl46esxm44i 606 5 c c NN work_fnploejenbc2raktl46esxm44i 606 6 ” " '' work_fnploejenbc2raktl46esxm44i 606 7 1 1 CD work_fnploejenbc2raktl46esxm44i 606 8 g,(a(o g,(a(o NNP work_fnploejenbc2raktl46esxm44i 606 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 606 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 606 11 n n LS work_fnploejenbc2raktl46esxm44i 606 12 = = SYM work_fnploejenbc2raktl46esxm44i 606 13 n,,+l n,,+l NNP work_fnploejenbc2raktl46esxm44i 606 14 K. K. NNP work_fnploejenbc2raktl46esxm44i 606 15 < < XX work_fnploejenbc2raktl46esxm44i 606 16 y y NNP work_fnploejenbc2raktl46esxm44i 606 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 606 18 lK lK NNP work_fnploejenbc2raktl46esxm44i 606 19 , , , work_fnploejenbc2raktl46esxm44i 606 20 l)g l)g NNP work_fnploejenbc2raktl46esxm44i 606 21 , , , work_fnploejenbc2raktl46esxm44i 606 22 < < XX work_fnploejenbc2raktl46esxm44i 606 23 + + CC work_fnploejenbc2raktl46esxm44i 606 24 f f NN work_fnploejenbc2raktl46esxm44i 606 25 1 1 CD work_fnploejenbc2raktl46esxm44i 606 26 n n NN work_fnploejenbc2raktl46esxm44i 606 27 = = SYM work_fnploejenbc2raktl46esxm44i 606 28 ng+ ng+ NNP work_fnploejenbc2raktl46esxm44i 606 29 1 1 CD work_fnploejenbc2raktl46esxm44i 606 30 n n NN work_fnploejenbc2raktl46esxm44i 606 31 = = SYM work_fnploejenbc2raktl46esxm44i 606 32 no+l no+l NNP work_fnploejenbc2raktl46esxm44i 606 33 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 606 34 n- n- XX work_fnploejenbc2raktl46esxm44i 606 35 1 1 CD work_fnploejenbc2raktl46esxm44i 606 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 606 37 ’ ' '' work_fnploejenbc2raktl46esxm44i 606 38 Thus thus RB work_fnploejenbc2raktl46esxm44i 606 39 lim lim NNP work_fnploejenbc2raktl46esxm44i 606 40 , , , work_fnploejenbc2raktl46esxm44i 606 41 _ _ NNP work_fnploejenbc2raktl46esxm44i 606 42 o1 o1 NN work_fnploejenbc2raktl46esxm44i 606 43 u(r u(r NNP work_fnploejenbc2raktl46esxm44i 606 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 606 45 = = NFP work_fnploejenbc2raktl46esxm44i 606 46 0 0 NFP work_fnploejenbc2raktl46esxm44i 606 47 . . . work_fnploejenbc2raktl46esxm44i 607 1 580 580 CD work_fnploejenbc2raktl46esxm44i 607 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 607 3 , , , work_fnploejenbc2raktl46esxm44i 607 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 607 5 , , , work_fnploejenbc2raktl46esxm44i 607 6 AND and CC work_fnploejenbc2raktl46esxm44i 607 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 607 8 Let let VBP work_fnploejenbc2raktl46esxm44i 607 9 r r NN work_fnploejenbc2raktl46esxm44i 607 10 be be VB work_fnploejenbc2raktl46esxm44i 607 11 large large JJ work_fnploejenbc2raktl46esxm44i 607 12 enough enough RB work_fnploejenbc2raktl46esxm44i 607 13 so so IN work_fnploejenbc2raktl46esxm44i 607 14 that that IN work_fnploejenbc2raktl46esxm44i 607 15 where where WRB work_fnploejenbc2raktl46esxm44i 607 16 C,=a-‘(xi)cK C,=a-‘(xi)cK NNP work_fnploejenbc2raktl46esxm44i 607 17 , , , work_fnploejenbc2raktl46esxm44i 607 18 , , , work_fnploejenbc2raktl46esxm44i 607 19 , , , work_fnploejenbc2raktl46esxm44i 607 20 , , , work_fnploejenbc2raktl46esxm44i 607 21 Vj= Vj= NNP work_fnploejenbc2raktl46esxm44i 607 22 1 1 CD work_fnploejenbc2raktl46esxm44i 607 23 , , , work_fnploejenbc2raktl46esxm44i 607 24 . . . work_fnploejenbc2raktl46esxm44i 608 1 . . . work_fnploejenbc2raktl46esxm44i 609 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 609 2 n n XX work_fnploejenbc2raktl46esxm44i 609 3 .. .. . work_fnploejenbc2raktl46esxm44i 610 1 There there EX work_fnploejenbc2raktl46esxm44i 610 2 exist exist VBP work_fnploejenbc2raktl46esxm44i 610 3 real real JJ work_fnploejenbc2raktl46esxm44i 610 4 numbers number NNS work_fnploejenbc2raktl46esxm44i 610 5 yj yj NNP work_fnploejenbc2raktl46esxm44i 610 6 , , , work_fnploejenbc2raktl46esxm44i 610 7 j j NNP work_fnploejenbc2raktl46esxm44i 610 8 = = SYM work_fnploejenbc2raktl46esxm44i 610 9 1 1 CD work_fnploejenbc2raktl46esxm44i 610 10 , , , work_fnploejenbc2raktl46esxm44i 610 11 . . . work_fnploejenbc2raktl46esxm44i 611 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 611 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 611 3 n n IN work_fnploejenbc2raktl46esxm44i 611 4 such such PDT work_fnploejenbc2raktl46esxm44i 611 5 that that DT work_fnploejenbc2raktl46esxm44i 611 6 max(,(,),g,(~))o nj]p’>o NNP work_fnploejenbc2raktl46esxm44i 634 18 , , , work_fnploejenbc2raktl46esxm44i 634 19 j j NNP work_fnploejenbc2raktl46esxm44i 634 20 = = SYM work_fnploejenbc2raktl46esxm44i 634 21 l l NN work_fnploejenbc2raktl46esxm44i 634 22 j= j= NNP work_fnploejenbc2raktl46esxm44i 634 23 1 1 CD work_fnploejenbc2raktl46esxm44i 634 24 Thus thus RB work_fnploejenbc2raktl46esxm44i 634 25 qo qo NNP work_fnploejenbc2raktl46esxm44i 634 26 < < XX work_fnploejenbc2raktl46esxm44i 634 27 y, > NN work_fnploejenbc2raktl46esxm44i 642 5 1 1 CD work_fnploejenbc2raktl46esxm44i 642 6 , , , work_fnploejenbc2raktl46esxm44i 642 7 T T NNP work_fnploejenbc2raktl46esxm44i 642 8 , , , work_fnploejenbc2raktl46esxm44i 642 9 is be VBZ work_fnploejenbc2raktl46esxm44i 642 10 an an DT work_fnploejenbc2raktl46esxm44i 642 11 Archimedean archimedean JJ work_fnploejenbc2raktl46esxm44i 642 12 t t NN work_fnploejenbc2raktl46esxm44i 642 13 - - HYPH work_fnploejenbc2raktl46esxm44i 642 14 conorm conorm NN work_fnploejenbc2raktl46esxm44i 642 15 with with IN work_fnploejenbc2raktl46esxm44i 642 16 generator generator NN work_fnploejenbc2raktl46esxm44i 642 17 g,(x g,(x NNP work_fnploejenbc2raktl46esxm44i 642 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 642 19 = = NFP work_fnploejenbc2raktl46esxm44i 642 20 xp xp NNP work_fnploejenbc2raktl46esxm44i 642 21 , , , work_fnploejenbc2raktl46esxm44i 642 22 g g NNP work_fnploejenbc2raktl46esxm44i 642 23 , , , work_fnploejenbc2raktl46esxm44i 642 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 642 25 1 1 LS work_fnploejenbc2raktl46esxm44i 642 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 642 27 = = SYM work_fnploejenbc2raktl46esxm44i 642 28 1 1 CD work_fnploejenbc2raktl46esxm44i 642 29 . . . work_fnploejenbc2raktl46esxm44i 643 1 As as IN work_fnploejenbc2raktl46esxm44i 643 2 usual usual JJ work_fnploejenbc2raktl46esxm44i 643 3 , , , work_fnploejenbc2raktl46esxm44i 643 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 643 5 extend extend VBP work_fnploejenbc2raktl46esxm44i 643 6 T t NN work_fnploejenbc2raktl46esxm44i 643 7 , , , work_fnploejenbc2raktl46esxm44i 643 8 to to IN work_fnploejenbc2raktl46esxm44i 643 9 n n CD work_fnploejenbc2raktl46esxm44i 643 10 arguments argument NNS work_fnploejenbc2raktl46esxm44i 643 11 , , , work_fnploejenbc2raktl46esxm44i 643 12 as as IN work_fnploejenbc2raktl46esxm44i 643 13 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 643 14 , , , work_fnploejenbc2raktl46esxm44i 643 15 , , , work_fnploejenbc2raktl46esxm44i 643 16 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 643 17 , , , work_fnploejenbc2raktl46esxm44i 643 18 . . . work_fnploejenbc2raktl46esxm44i 644 1 . . . work_fnploejenbc2raktl46esxm44i 645 1 . . . work_fnploejenbc2raktl46esxm44i 646 1 . . . work_fnploejenbc2raktl46esxm44i 647 1 x x LS work_fnploejenbc2raktl46esxm44i 647 2 , , , work_fnploejenbc2raktl46esxm44i 647 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 647 4 = = NFP work_fnploejenbc2raktl46esxm44i 647 5 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 647 6 , , , work_fnploejenbc2raktl46esxm44i 647 7 , , , work_fnploejenbc2raktl46esxm44i 647 8 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 647 9 , , , work_fnploejenbc2raktl46esxm44i 647 10 , , , work_fnploejenbc2raktl46esxm44i 647 11 . . . work_fnploejenbc2raktl46esxm44i 648 1 . . . work_fnploejenbc2raktl46esxm44i 649 1 . . . work_fnploejenbc2raktl46esxm44i 650 1 . . . work_fnploejenbc2raktl46esxm44i 651 1 -4 -4 NFP work_fnploejenbc2raktl46esxm44i 651 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 651 3 . . . work_fnploejenbc2raktl46esxm44i 652 1 Then then RB work_fnploejenbc2raktl46esxm44i 652 2 for for IN work_fnploejenbc2raktl46esxm44i 652 3 each each DT work_fnploejenbc2raktl46esxm44i 652 4 fixed fix VBN work_fnploejenbc2raktl46esxm44i 652 5 n n JJ work_fnploejenbc2raktl46esxm44i 652 6 , , , work_fnploejenbc2raktl46esxm44i 652 7 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 652 8 , , , work_fnploejenbc2raktl46esxm44i 652 9 , , , work_fnploejenbc2raktl46esxm44i 652 10 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 652 11 , , , work_fnploejenbc2raktl46esxm44i 652 12 . . . work_fnploejenbc2raktl46esxm44i 653 1 . . . work_fnploejenbc2raktl46esxm44i 654 1 . . . work_fnploejenbc2raktl46esxm44i 655 1 . . . work_fnploejenbc2raktl46esxm44i 656 1 x x LS work_fnploejenbc2raktl46esxm44i 656 2 , , , work_fnploejenbc2raktl46esxm44i 656 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 656 4 + + CC work_fnploejenbc2raktl46esxm44i 656 5 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 656 6 , , , work_fnploejenbc2raktl46esxm44i 656 7 , , , work_fnploejenbc2raktl46esxm44i 656 8 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 656 9 , , , work_fnploejenbc2raktl46esxm44i 656 10 . . . work_fnploejenbc2raktl46esxm44i 657 1 . . . work_fnploejenbc2raktl46esxm44i 658 1 . . . work_fnploejenbc2raktl46esxm44i 659 1 . . . work_fnploejenbc2raktl46esxm44i 660 1 x x LS work_fnploejenbc2raktl46esxm44i 660 2 , , , work_fnploejenbc2raktl46esxm44i 660 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 660 4 as as IN work_fnploejenbc2raktl46esxm44i 660 5 p p NN work_fnploejenbc2raktl46esxm44i 660 6 + + SYM work_fnploejenbc2raktl46esxm44i 660 7 + + CC work_fnploejenbc2raktl46esxm44i 660 8 cc cc NN work_fnploejenbc2raktl46esxm44i 660 9 , , , work_fnploejenbc2raktl46esxm44i 660 10 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 660 11 in in IN work_fnploejenbc2raktl46esxm44i 660 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 660 13 x x NN work_fnploejenbc2raktl46esxm44i 660 14 , , , work_fnploejenbc2raktl46esxm44i 660 15 , , , work_fnploejenbc2raktl46esxm44i 660 16 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 660 17 , , , work_fnploejenbc2raktl46esxm44i 660 18 . . . work_fnploejenbc2raktl46esxm44i 661 1 . . . work_fnploejenbc2raktl46esxm44i 662 1 . . . work_fnploejenbc2raktl46esxm44i 663 1 . . . work_fnploejenbc2raktl46esxm44i 664 1 x x LS work_fnploejenbc2raktl46esxm44i 664 2 , , , work_fnploejenbc2raktl46esxm44i 664 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 664 4 . . . work_fnploejenbc2raktl46esxm44i 665 1 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 665 2 , , , work_fnploejenbc2raktl46esxm44i 665 3 since since IN work_fnploejenbc2raktl46esxm44i 665 4 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 665 5 have have VBP work_fnploejenbc2raktl46esxm44i 665 6 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 665 7 , , , work_fnploejenbc2raktl46esxm44i 665 8 , , , work_fnploejenbc2raktl46esxm44i 665 9 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 665 10 , , , work_fnploejenbc2raktl46esxm44i 665 11 . . . work_fnploejenbc2raktl46esxm44i 666 1 . . . work_fnploejenbc2raktl46esxm44i 667 1 . . . work_fnploejenbc2raktl46esxm44i 668 1 . . . work_fnploejenbc2raktl46esxm44i 669 1 x,1 x,1 NNP work_fnploejenbc2raktl46esxm44i 669 2 d d NNP work_fnploejenbc2raktl46esxm44i 669 3 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 669 4 , , , work_fnploejenbc2raktl46esxm44i 669 5 , , , work_fnploejenbc2raktl46esxm44i 669 6 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 669 7 , , , work_fnploejenbc2raktl46esxm44i 669 8 . . . work_fnploejenbc2raktl46esxm44i 670 1 . . . work_fnploejenbc2raktl46esxm44i 671 1 . . . work_fnploejenbc2raktl46esxm44i 672 1 . . . work_fnploejenbc2raktl46esxm44i 673 1 x x LS work_fnploejenbc2raktl46esxm44i 673 2 , , , work_fnploejenbc2raktl46esxm44i 673 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 673 4 < < XX work_fnploejenbc2raktl46esxm44i 673 5 Min[Max(x min[max(x JJ work_fnploejenbc2raktl46esxm44i 673 6 , , , work_fnploejenbc2raktl46esxm44i 673 7 , , , work_fnploejenbc2raktl46esxm44i 673 8 . . . work_fnploejenbc2raktl46esxm44i 674 1 . . . work_fnploejenbc2raktl46esxm44i 675 1 . . . work_fnploejenbc2raktl46esxm44i 676 1 . . . work_fnploejenbc2raktl46esxm44i 677 1 xn)n’Ip xn)n’Ip NNP work_fnploejenbc2raktl46esxm44i 677 2 , , , work_fnploejenbc2raktl46esxm44i 677 3 11 11 CD work_fnploejenbc2raktl46esxm44i 677 4 0~ 0~ CD work_fnploejenbc2raktl46esxm44i 677 5 T,(x T,(x NNP work_fnploejenbc2raktl46esxm44i 677 6 , , , work_fnploejenbc2raktl46esxm44i 677 7 , , , work_fnploejenbc2raktl46esxm44i 677 8 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 677 9 , , , work_fnploejenbc2raktl46esxm44i 677 10 . . . work_fnploejenbc2raktl46esxm44i 678 1 . . . work_fnploejenbc2raktl46esxm44i 679 1 . . . work_fnploejenbc2raktl46esxm44i 680 1 . . . work_fnploejenbc2raktl46esxm44i 681 1 x x LS work_fnploejenbc2raktl46esxm44i 681 2 , , , work_fnploejenbc2raktl46esxm44i 681 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 681 4 = = SYM work_fnploejenbc2raktl46esxm44i 681 5 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 681 6 , , , work_fnploejenbc2raktl46esxm44i 681 7 , , , work_fnploejenbc2raktl46esxm44i 681 8 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 681 9 , , , work_fnploejenbc2raktl46esxm44i 681 10 . . . work_fnploejenbc2raktl46esxm44i 682 1 . . . work_fnploejenbc2raktl46esxm44i 683 1 . . . work_fnploejenbc2raktl46esxm44i 684 1 . . . work_fnploejenbc2raktl46esxm44i 685 1 x x LS work_fnploejenbc2raktl46esxm44i 685 2 , , , work_fnploejenbc2raktl46esxm44i 685 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 685 4 d d NNP work_fnploejenbc2raktl46esxm44i 685 5 nlip nlip NNP work_fnploejenbc2raktl46esxm44i 685 6 - - HYPH work_fnploejenbc2raktl46esxm44i 685 7 1 1 NNP work_fnploejenbc2raktl46esxm44i 685 8 . . . work_fnploejenbc2raktl46esxm44i 686 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 686 2 , , , work_fnploejenbc2raktl46esxm44i 686 3 if if IN work_fnploejenbc2raktl46esxm44i 686 4 Q q NN work_fnploejenbc2raktl46esxm44i 686 5 is be VBZ work_fnploejenbc2raktl46esxm44i 686 6 finite finite JJ work_fnploejenbc2raktl46esxm44i 686 7 , , , work_fnploejenbc2raktl46esxm44i 686 8 and and CC work_fnploejenbc2raktl46esxm44i 686 9 CL CL NNP work_fnploejenbc2raktl46esxm44i 686 10 : : : work_fnploejenbc2raktl46esxm44i 686 11 Y(Q Y(Q NNP work_fnploejenbc2raktl46esxm44i 686 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 686 13 + + CC work_fnploejenbc2raktl46esxm44i 686 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 686 15 0 0 CD work_fnploejenbc2raktl46esxm44i 686 16 , , , work_fnploejenbc2raktl46esxm44i 686 17 l l NN work_fnploejenbc2raktl46esxm44i 686 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 686 19 has have VBZ work_fnploejenbc2raktl46esxm44i 686 20 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 686 21 , , , work_fnploejenbc2raktl46esxm44i 686 22 y y NNP work_fnploejenbc2raktl46esxm44i 686 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 686 24 as as IN work_fnploejenbc2raktl46esxm44i 686 25 composition composition NN work_fnploejenbc2raktl46esxm44i 686 26 law law NN work_fnploejenbc2raktl46esxm44i 686 27 , , , work_fnploejenbc2raktl46esxm44i 686 28 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 686 29 , , , work_fnploejenbc2raktl46esxm44i 686 30 VA VA NNP work_fnploejenbc2raktl46esxm44i 686 31 C C NNP work_fnploejenbc2raktl46esxm44i 686 32 Q Q NNP work_fnploejenbc2raktl46esxm44i 686 33 , , , work_fnploejenbc2raktl46esxm44i 686 34 p(A p(a JJ work_fnploejenbc2raktl46esxm44i 686 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 686 36 = = NFP work_fnploejenbc2raktl46esxm44i 686 37 My -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 686 38 P(W p(w NN work_fnploejenbc2raktl46esxm44i 686 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 686 40 , , , work_fnploejenbc2raktl46esxm44i 686 41 582 582 CD work_fnploejenbc2raktl46esxm44i 686 42 then then RB work_fnploejenbc2raktl46esxm44i 686 43 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 686 44 , , , work_fnploejenbc2raktl46esxm44i 686 45 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 686 46 , , , work_fnploejenbc2raktl46esxm44i 686 47 AND and CC work_fnploejenbc2raktl46esxm44i 686 48 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 686 49 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 686 50 in in IN work_fnploejenbc2raktl46esxm44i 686 51 A. a. NN work_fnploejenbc2raktl46esxm44i 687 1 Now now RB work_fnploejenbc2raktl46esxm44i 687 2 , , , work_fnploejenbc2raktl46esxm44i 687 3 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 687 4 is be VBZ work_fnploejenbc2raktl46esxm44i 687 5 easy easy JJ work_fnploejenbc2raktl46esxm44i 687 6 to to TO work_fnploejenbc2raktl46esxm44i 687 7 see see VB work_fnploejenbc2raktl46esxm44i 687 8 that that DT work_fnploejenbc2raktl46esxm44i 687 9 , , , work_fnploejenbc2raktl46esxm44i 687 10 in in IN work_fnploejenbc2raktl46esxm44i 687 11 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 687 12 52.1 52.1 CD work_fnploejenbc2raktl46esxm44i 687 13 , , , work_fnploejenbc2raktl46esxm44i 687 14 if if IN work_fnploejenbc2raktl46esxm44i 687 15 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 687 16 require require VBP work_fnploejenbc2raktl46esxm44i 687 17 only only RB work_fnploejenbc2raktl46esxm44i 687 18 general general JJ work_fnploejenbc2raktl46esxm44i 687 19 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 687 20 in in IN work_fnploejenbc2raktl46esxm44i 687 21 the the DT work_fnploejenbc2raktl46esxm44i 687 22 additive additive JJ work_fnploejenbc2raktl46esxm44i 687 23 sense sense NN work_fnploejenbc2raktl46esxm44i 687 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 687 25 which which WDT work_fnploejenbc2raktl46esxm44i 687 26 is be VBZ work_fnploejenbc2raktl46esxm44i 687 27 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 687 28 to to TO work_fnploejenbc2raktl46esxm44i 687 29 uniform uniform VB work_fnploejenbc2raktl46esxm44i 687 30 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 687 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 32 the the DT work_fnploejenbc2raktl46esxm44i 687 33 condition condition NN work_fnploejenbc2raktl46esxm44i 687 34 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 687 35 * * NFP work_fnploejenbc2raktl46esxm44i 687 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 37 can can MD work_fnploejenbc2raktl46esxm44i 687 38 be be VB work_fnploejenbc2raktl46esxm44i 687 39 weakened weaken VBN work_fnploejenbc2raktl46esxm44i 687 40 to to IN work_fnploejenbc2raktl46esxm44i 687 41 Thus thus RB work_fnploejenbc2raktl46esxm44i 687 42 , , , work_fnploejenbc2raktl46esxm44i 687 43 assuming assume VBG work_fnploejenbc2raktl46esxm44i 687 44 in in IN work_fnploejenbc2raktl46esxm44i 687 45 addition addition NN work_fnploejenbc2raktl46esxm44i 687 46 that that IN work_fnploejenbc2raktl46esxm44i 687 47 En En NNP work_fnploejenbc2raktl46esxm44i 687 48 p(w p(w NNP work_fnploejenbc2raktl46esxm44i 687 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 50 < < XX work_fnploejenbc2raktl46esxm44i 687 51 1 1 CD work_fnploejenbc2raktl46esxm44i 687 52 , , , work_fnploejenbc2raktl46esxm44i 687 53 for for IN work_fnploejenbc2raktl46esxm44i 687 54 all all DT work_fnploejenbc2raktl46esxm44i 687 55 Vpa Vpa NNP work_fnploejenbc2raktl46esxm44i 687 56 1 1 CD work_fnploejenbc2raktl46esxm44i 687 57 , , , work_fnploejenbc2raktl46esxm44i 687 58 v,(A v,(A NNP work_fnploejenbc2raktl46esxm44i 687 59 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 60 = = NFP work_fnploejenbc2raktl46esxm44i 687 61 T,(p(o t,(p(o NN work_fnploejenbc2raktl46esxm44i 687 62 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 63 , , , work_fnploejenbc2raktl46esxm44i 687 64 o o UH work_fnploejenbc2raktl46esxm44i 687 65 E e NN work_fnploejenbc2raktl46esxm44i 687 66 A a NN work_fnploejenbc2raktl46esxm44i 687 67 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 687 68 is be VBZ work_fnploejenbc2raktl46esxm44i 687 69 general general JJ work_fnploejenbc2raktl46esxm44i 687 70 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 687 71 in in IN work_fnploejenbc2raktl46esxm44i 687 72 the the DT work_fnploejenbc2raktl46esxm44i 687 73 additive additive JJ work_fnploejenbc2raktl46esxm44i 687 74 sense sense NN work_fnploejenbc2raktl46esxm44i 687 75 , , , work_fnploejenbc2raktl46esxm44i 687 76 since since IN work_fnploejenbc2raktl46esxm44i 687 77 Therefore therefore RB work_fnploejenbc2raktl46esxm44i 687 78 , , , work_fnploejenbc2raktl46esxm44i 687 79 in in IN work_fnploejenbc2raktl46esxm44i 687 80 this this DT work_fnploejenbc2raktl46esxm44i 687 81 case case NN work_fnploejenbc2raktl46esxm44i 687 82 , , , work_fnploejenbc2raktl46esxm44i 687 83 Max Max NNP work_fnploejenbc2raktl46esxm44i 687 84 - - HYPH work_fnploejenbc2raktl46esxm44i 687 85 possibility possibility NN work_fnploejenbc2raktl46esxm44i 687 86 measures measure NNS work_fnploejenbc2raktl46esxm44i 687 87 are be VBP work_fnploejenbc2raktl46esxm44i 687 88 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 687 89 limits limit NNS work_fnploejenbc2raktl46esxm44i 687 90 of of IN work_fnploejenbc2raktl46esxm44i 687 91 general general JJ work_fnploejenbc2raktl46esxm44i 687 92 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 687 93 T,-possibility t,-possibility NN work_fnploejenbc2raktl46esxm44i 687 94 measures measure NNS work_fnploejenbc2raktl46esxm44i 687 95 . . . work_fnploejenbc2raktl46esxm44i 688 1 More more RBR work_fnploejenbc2raktl46esxm44i 688 2 generally generally RB work_fnploejenbc2raktl46esxm44i 688 3 , , , work_fnploejenbc2raktl46esxm44i 688 4 for for IN work_fnploejenbc2raktl46esxm44i 688 5 Sz Sz NNP work_fnploejenbc2raktl46esxm44i 688 6 countably countably RB work_fnploejenbc2raktl46esxm44i 688 7 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 688 8 , , , work_fnploejenbc2raktl46esxm44i 688 9 and and CC work_fnploejenbc2raktl46esxm44i 688 10 a a DT work_fnploejenbc2raktl46esxm44i 688 11 : : : work_fnploejenbc2raktl46esxm44i 688 12 D d NN work_fnploejenbc2raktl46esxm44i 688 13 + + CC work_fnploejenbc2raktl46esxm44i 688 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 688 15 0 0 CD work_fnploejenbc2raktl46esxm44i 688 16 , , , work_fnploejenbc2raktl46esxm44i 688 17 l l NN work_fnploejenbc2raktl46esxm44i 688 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 688 19 such such JJ work_fnploejenbc2raktl46esxm44i 688 20 that that IN work_fnploejenbc2raktl46esxm44i 688 21 sup sup NN work_fnploejenbc2raktl46esxm44i 688 22 , , , work_fnploejenbc2raktl46esxm44i 688 23 a(o a(o NNP work_fnploejenbc2raktl46esxm44i 688 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 688 25 < < XX work_fnploejenbc2raktl46esxm44i 688 26 1 1 CD work_fnploejenbc2raktl46esxm44i 688 27 , , , work_fnploejenbc2raktl46esxm44i 688 28 the the DT work_fnploejenbc2raktl46esxm44i 688 29 max max NNP work_fnploejenbc2raktl46esxm44i 688 30 - - HYPH work_fnploejenbc2raktl46esxm44i 688 31 possibility possibility NN work_fnploejenbc2raktl46esxm44i 688 32 measure measure NN work_fnploejenbc2raktl46esxm44i 688 33 generated generate VBN work_fnploejenbc2raktl46esxm44i 688 34 by by IN work_fnploejenbc2raktl46esxm44i 688 35 tl tl NN work_fnploejenbc2raktl46esxm44i 688 36 is be VBZ work_fnploejenbc2raktl46esxm44i 688 37 Pa(A Pa(A NNP work_fnploejenbc2raktl46esxm44i 688 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 688 39 = = NFP work_fnploejenbc2raktl46esxm44i 688 40 sup sup NNP work_fnploejenbc2raktl46esxm44i 688 41 a(o a(o NNP work_fnploejenbc2raktl46esxm44i 688 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 688 43 A a NN work_fnploejenbc2raktl46esxm44i 688 44 and and CC work_fnploejenbc2raktl46esxm44i 688 45 this this DT work_fnploejenbc2raktl46esxm44i 688 46 can can MD work_fnploejenbc2raktl46esxm44i 688 47 be be VB work_fnploejenbc2raktl46esxm44i 688 48 approximated approximate VBN work_fnploejenbc2raktl46esxm44i 688 49 by by IN work_fnploejenbc2raktl46esxm44i 688 50 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 688 51 measures measure NNS work_fnploejenbc2raktl46esxm44i 688 52 , , , work_fnploejenbc2raktl46esxm44i 688 53 Specifically specifically RB work_fnploejenbc2raktl46esxm44i 688 54 , , , work_fnploejenbc2raktl46esxm44i 688 55 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 688 56 5.2.3 5.2.3 CD work_fnploejenbc2raktl46esxm44i 688 57 . . . work_fnploejenbc2raktl46esxm44i 689 1 Let let VB work_fnploejenbc2raktl46esxm44i 689 2 l2 l2 NN work_fnploejenbc2raktl46esxm44i 689 3 be be VB work_fnploejenbc2raktl46esxm44i 689 4 countably countably RB work_fnploejenbc2raktl46esxm44i 689 5 infinite infinite JJ work_fnploejenbc2raktl46esxm44i 689 6 and and CC work_fnploejenbc2raktl46esxm44i 689 7 a a DT work_fnploejenbc2raktl46esxm44i 689 8 : : : work_fnploejenbc2raktl46esxm44i 689 9 Sz sz NN work_fnploejenbc2raktl46esxm44i 689 10 + + NFP work_fnploejenbc2raktl46esxm44i 689 11 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 689 12 O o NN work_fnploejenbc2raktl46esxm44i 689 13 , , , work_fnploejenbc2raktl46esxm44i 689 14 l l NN work_fnploejenbc2raktl46esxm44i 689 15 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 689 16 such such JJ work_fnploejenbc2raktl46esxm44i 689 17 that that IN work_fnploejenbc2raktl46esxm44i 689 18 sup sup NN work_fnploejenbc2raktl46esxm44i 689 19 , , , work_fnploejenbc2raktl46esxm44i 689 20 a(o a(o NNP work_fnploejenbc2raktl46esxm44i 689 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 689 22 -C -C NFP work_fnploejenbc2raktl46esxm44i 689 23 1 1 CD work_fnploejenbc2raktl46esxm44i 689 24 . . . work_fnploejenbc2raktl46esxm44i 690 1 Suppose suppose VB work_fnploejenbc2raktl46esxm44i 690 2 that that IN work_fnploejenbc2raktl46esxm44i 690 3 there there EX work_fnploejenbc2raktl46esxm44i 690 4 are be VBP work_fnploejenbc2raktl46esxm44i 690 5 non non JJ work_fnploejenbc2raktl46esxm44i 690 6 - - JJ work_fnploejenbc2raktl46esxm44i 690 7 negative negative JJ work_fnploejenbc2raktl46esxm44i 690 8 reals real NNS work_fnploejenbc2raktl46esxm44i 690 9 a a RB work_fnploejenbc2raktl46esxm44i 690 10 , , , work_fnploejenbc2raktl46esxm44i 690 11 b b NN work_fnploejenbc2raktl46esxm44i 690 12 such such JJ work_fnploejenbc2raktl46esxm44i 690 13 that that IN work_fnploejenbc2raktl46esxm44i 690 14 Then then RB work_fnploejenbc2raktl46esxm44i 690 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 690 16 i i NN work_fnploejenbc2raktl46esxm44i 690 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 690 18 For for IN work_fnploejenbc2raktl46esxm44i 690 19 A a DT work_fnploejenbc2raktl46esxm44i 690 20 EP(Q ep(q NN work_fnploejenbc2raktl46esxm44i 690 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 690 22 , , , work_fnploejenbc2raktl46esxm44i 690 23 such such JJ work_fnploejenbc2raktl46esxm44i 690 24 that that IN work_fnploejenbc2raktl46esxm44i 690 25 Aa-‘(t Aa-‘(t NNP work_fnploejenbc2raktl46esxm44i 690 26 , , , work_fnploejenbc2raktl46esxm44i 690 27 p=(A)=lim p=(A)=lim NNP work_fnploejenbc2raktl46esxm44i 690 28 , , , work_fnploejenbc2raktl46esxm44i 690 29 , , , work_fnploejenbc2raktl46esxm44i 690 30 , , , work_fnploejenbc2raktl46esxm44i 690 31 + + CC work_fnploejenbc2raktl46esxm44i 690 32 m m NNP work_fnploejenbc2raktl46esxm44i 690 33 p,,=,(A p,,=,(A NNP work_fnploejenbc2raktl46esxm44i 690 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 690 35 , , , work_fnploejenbc2raktl46esxm44i 690 36 the the DT work_fnploejenbc2raktl46esxm44i 690 37 limit limit NN work_fnploejenbc2raktl46esxm44i 690 38 being be VBG work_fnploejenbc2raktl46esxm44i 690 39 uniform uniform NN work_fnploejenbc2raktl46esxm44i 690 40 in in IN work_fnploejenbc2raktl46esxm44i 690 41 all all DT work_fnploejenbc2raktl46esxm44i 690 42 such such JJ work_fnploejenbc2raktl46esxm44i 690 43 A a NN work_fnploejenbc2raktl46esxm44i 690 44 with with IN work_fnploejenbc2raktl46esxm44i 690 45 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 690 46 Al Al NNP work_fnploejenbc2raktl46esxm44i 690 47 in in IN work_fnploejenbc2raktl46esxm44i 690 48 , , , work_fnploejenbc2raktl46esxm44i 690 49 , , , work_fnploejenbc2raktl46esxm44i 690 50 for for IN work_fnploejenbc2raktl46esxm44i 690 51 any any DT work_fnploejenbc2raktl46esxm44i 690 52 fixed fix VBN work_fnploejenbc2raktl46esxm44i 690 53 positive positive JJ work_fnploejenbc2raktl46esxm44i 690 54 integer integer NN work_fnploejenbc2raktl46esxm44i 690 55 n n NN work_fnploejenbc2raktl46esxm44i 690 56 , , , work_fnploejenbc2raktl46esxm44i 690 57 ; ; : work_fnploejenbc2raktl46esxm44i 690 58 also also RB work_fnploejenbc2raktl46esxm44i 690 59 t t NN work_fnploejenbc2raktl46esxm44i 690 60 , , , work_fnploejenbc2raktl46esxm44i 690 61 = = SYM work_fnploejenbc2raktl46esxm44i 690 62 sup sup UH work_fnploejenbc2raktl46esxm44i 690 63 , , , work_fnploejenbc2raktl46esxm44i 690 64 u.(o u.(o NNP work_fnploejenbc2raktl46esxm44i 690 65 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 690 66 . . . work_fnploejenbc2raktl46esxm44i 691 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 691 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 691 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 691 4 For for IN work_fnploejenbc2raktl46esxm44i 691 5 Aa-‘(t Aa-‘(t NNP work_fnploejenbc2raktl46esxm44i 691 6 , , , work_fnploejenbc2raktl46esxm44i 691 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 691 8 # # $ work_fnploejenbc2raktl46esxm44i 691 9 0 0 CD work_fnploejenbc2raktl46esxm44i 691 10 , , , work_fnploejenbc2raktl46esxm44i 691 11 SCORING score VBG work_fnploejenbc2raktl46esxm44i 691 12 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 691 13 TO to IN work_fnploejenbc2raktl46esxm44i 691 14 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 691 15 583 583 CD work_fnploejenbc2raktl46esxm44i 691 16 Proof Proof NNP work_fnploejenbc2raktl46esxm44i 691 17 . . . work_fnploejenbc2raktl46esxm44i 692 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 692 2 i i NN work_fnploejenbc2raktl46esxm44i 692 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 692 4 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 692 5 are be VBP work_fnploejenbc2raktl46esxm44i 692 6 now now RB work_fnploejenbc2raktl46esxm44i 692 7 going go VBG work_fnploejenbc2raktl46esxm44i 692 8 to to TO work_fnploejenbc2raktl46esxm44i 692 9 construct construct VB work_fnploejenbc2raktl46esxm44i 692 10 generators generator NNS work_fnploejenbc2raktl46esxm44i 692 11 g g NN work_fnploejenbc2raktl46esxm44i 692 12 , , , work_fnploejenbc2raktl46esxm44i 692 13 , , , work_fnploejenbc2raktl46esxm44i 692 14 for for IN work_fnploejenbc2raktl46esxm44i 692 15 suf- suf- DT work_fnploejenbc2raktl46esxm44i 692 16 ficiently ficiently RB work_fnploejenbc2raktl46esxm44i 692 17 large large JJ work_fnploejenbc2raktl46esxm44i 692 18 p p NN work_fnploejenbc2raktl46esxm44i 692 19 , , , work_fnploejenbc2raktl46esxm44i 692 20 such such JJ work_fnploejenbc2raktl46esxm44i 692 21 that that IN work_fnploejenbc2raktl46esxm44i 692 22 kp(A)=gpl kp(A)=gpl NNP work_fnploejenbc2raktl46esxm44i 692 23 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 692 24 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 692 25 g,(a(w g,(a(w VBD work_fnploejenbc2raktl46esxm44i 692 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 692 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 692 28 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 692 29 A a DT work_fnploejenbc2raktl46esxm44i 692 30 are be VBP work_fnploejenbc2raktl46esxm44i 692 31 general general JJ work_fnploejenbc2raktl46esxm44i 692 32 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 692 33 in in IN work_fnploejenbc2raktl46esxm44i 692 34 the the DT work_fnploejenbc2raktl46esxm44i 692 35 o o NN work_fnploejenbc2raktl46esxm44i 692 36 - - HYPH work_fnploejenbc2raktl46esxm44i 692 37 additive additive JJ work_fnploejenbc2raktl46esxm44i 692 38 sense sense NN work_fnploejenbc2raktl46esxm44i 692 39 . . . work_fnploejenbc2raktl46esxm44i 693 1 More more RBR work_fnploejenbc2raktl46esxm44i 693 2 specifically specifically RB work_fnploejenbc2raktl46esxm44i 693 3 , , , work_fnploejenbc2raktl46esxm44i 693 4 not not RB work_fnploejenbc2raktl46esxm44i 693 5 only only RB work_fnploejenbc2raktl46esxm44i 693 6 is be VBZ work_fnploejenbc2raktl46esxm44i 693 7 g g NN work_fnploejenbc2raktl46esxm44i 693 8 , , , work_fnploejenbc2raktl46esxm44i 693 9 such such JJ work_fnploejenbc2raktl46esxm44i 693 10 that that IN work_fnploejenbc2raktl46esxm44i 693 11 g g NN work_fnploejenbc2raktl46esxm44i 693 12 , , , work_fnploejenbc2raktl46esxm44i 693 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 693 14 1 1 LS work_fnploejenbc2raktl46esxm44i 693 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 16 = = SYM work_fnploejenbc2raktl46esxm44i 693 17 1 1 CD work_fnploejenbc2raktl46esxm44i 693 18 and and CC work_fnploejenbc2raktl46esxm44i 693 19 C C NNP work_fnploejenbc2raktl46esxm44i 693 20 , , , work_fnploejenbc2raktl46esxm44i 693 21 g,(a(o g,(a(o NNP work_fnploejenbc2raktl46esxm44i 693 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 24 = = NFP work_fnploejenbc2raktl46esxm44i 693 25 1 1 CD work_fnploejenbc2raktl46esxm44i 693 26 , , , work_fnploejenbc2raktl46esxm44i 693 27 but but CC work_fnploejenbc2raktl46esxm44i 693 28 precisely precisely RB work_fnploejenbc2raktl46esxm44i 693 29 g,(x g,(x NNP work_fnploejenbc2raktl46esxm44i 693 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 31 = = NFP work_fnploejenbc2raktl46esxm44i 693 32 xp xp VB work_fnploejenbc2raktl46esxm44i 693 33 on on IN work_fnploejenbc2raktl46esxm44i 693 34 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 693 35 0 0 CD work_fnploejenbc2raktl46esxm44i 693 36 , , , work_fnploejenbc2raktl46esxm44i 693 37 t t NN work_fnploejenbc2raktl46esxm44i 693 38 , , , work_fnploejenbc2raktl46esxm44i 693 39 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 693 40 , , , work_fnploejenbc2raktl46esxm44i 693 41 where where WRB work_fnploejenbc2raktl46esxm44i 693 42 t t NN work_fnploejenbc2raktl46esxm44i 693 43 , , , work_fnploejenbc2raktl46esxm44i 693 44 > > XX work_fnploejenbc2raktl46esxm44i 693 45 t t NNP work_fnploejenbc2raktl46esxm44i 693 46 , , , work_fnploejenbc2raktl46esxm44i 693 47 , , , work_fnploejenbc2raktl46esxm44i 693 48 t t NN work_fnploejenbc2raktl46esxm44i 693 49 , , , work_fnploejenbc2raktl46esxm44i 693 50 = = SYM work_fnploejenbc2raktl46esxm44i 693 51 sup sup NNP work_fnploejenbc2raktl46esxm44i 693 52 a(0 a(0 NNP work_fnploejenbc2raktl46esxm44i 693 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 54 CT CT NNP work_fnploejenbc2raktl46esxm44i 693 55 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 693 56 > > XX work_fnploejenbc2raktl46esxm44i 693 57 O o NN work_fnploejenbc2raktl46esxm44i 693 58 by by IN work_fnploejenbc2raktl46esxm44i 693 59 assumption assumption NN work_fnploejenbc2raktl46esxm44i 693 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 61 and and CC work_fnploejenbc2raktl46esxm44i 693 62 C C NNP work_fnploejenbc2raktl46esxm44i 693 63 , , , work_fnploejenbc2raktl46esxm44i 693 64 = = -RRB- work_fnploejenbc2raktl46esxm44i 693 65 a-‘(t a-‘(t NNP work_fnploejenbc2raktl46esxm44i 693 66 , , , work_fnploejenbc2raktl46esxm44i 693 67 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 693 68 . . . work_fnploejenbc2raktl46esxm44i 694 1 First first RB work_fnploejenbc2raktl46esxm44i 694 2 Vp Vp NNP work_fnploejenbc2raktl46esxm44i 694 3 > > XX work_fnploejenbc2raktl46esxm44i 694 4 0 0 NFP work_fnploejenbc2raktl46esxm44i 694 5 , , , work_fnploejenbc2raktl46esxm44i 694 6 define define NNP work_fnploejenbc2raktl46esxm44i 694 7 g,(x g,(x NNP work_fnploejenbc2raktl46esxm44i 694 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 694 9 = = NFP work_fnploejenbc2raktl46esxm44i 694 10 xp xp VB work_fnploejenbc2raktl46esxm44i 694 11 on on IN work_fnploejenbc2raktl46esxm44i 694 12 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 694 13 O o NN work_fnploejenbc2raktl46esxm44i 694 14 , , , work_fnploejenbc2raktl46esxm44i 694 15 t t NN work_fnploejenbc2raktl46esxm44i 694 16 , , , work_fnploejenbc2raktl46esxm44i 694 17 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 694 18 . . . work_fnploejenbc2raktl46esxm44i 695 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 695 2 will will MD work_fnploejenbc2raktl46esxm44i 695 3 extend extend VB work_fnploejenbc2raktl46esxm44i 695 4 gP gP NNP work_fnploejenbc2raktl46esxm44i 695 5 to to IN work_fnploejenbc2raktl46esxm44i 695 6 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 695 7 0 0 CD work_fnploejenbc2raktl46esxm44i 695 8 , , , work_fnploejenbc2raktl46esxm44i 695 9 l l NN work_fnploejenbc2raktl46esxm44i 695 10 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 695 11 by by IN work_fnploejenbc2raktl46esxm44i 695 12 defining define VBG work_fnploejenbc2raktl46esxm44i 695 13 a a DT work_fnploejenbc2raktl46esxm44i 695 14 value value NN work_fnploejenbc2raktl46esxm44i 695 15 for for IN work_fnploejenbc2raktl46esxm44i 695 16 g,(tl g,(tl NNP work_fnploejenbc2raktl46esxm44i 695 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 695 18 such such JJ work_fnploejenbc2raktl46esxm44i 695 19 that that IN work_fnploejenbc2raktl46esxm44i 695 20 tz tz NNP work_fnploejenbc2raktl46esxm44i 695 21 < < XX work_fnploejenbc2raktl46esxm44i 695 22 gp(t gp(t NNP work_fnploejenbc2raktl46esxm44i 695 23 , , , work_fnploejenbc2raktl46esxm44i 695 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 695 25 < < XX work_fnploejenbc2raktl46esxm44i 695 26 1 1 CD work_fnploejenbc2raktl46esxm44i 695 27 , , , work_fnploejenbc2raktl46esxm44i 695 28 set set VBN work_fnploejenbc2raktl46esxm44i 695 29 g(l)= g(l)= NNP work_fnploejenbc2raktl46esxm44i 695 30 1 1 CD work_fnploejenbc2raktl46esxm44i 695 31 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 695 32 with with IN work_fnploejenbc2raktl46esxm44i 695 33 extension extension NN work_fnploejenbc2raktl46esxm44i 695 34 by by IN work_fnploejenbc2raktl46esxm44i 695 35 continuity continuity NN work_fnploejenbc2raktl46esxm44i 695 36 as as IN work_fnploejenbc2raktl46esxm44i 695 37 usual usual JJ work_fnploejenbc2raktl46esxm44i 695 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 695 39 and and CC work_fnploejenbc2raktl46esxm44i 695 40 obtain obtain VB work_fnploejenbc2raktl46esxm44i 695 41 C C NNP work_fnploejenbc2raktl46esxm44i 695 42 g,(a(w g,(a(w NN work_fnploejenbc2raktl46esxm44i 695 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 695 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 695 45 = = NFP work_fnploejenbc2raktl46esxm44i 695 46 1 1 CD work_fnploejenbc2raktl46esxm44i 695 47 R r NN work_fnploejenbc2raktl46esxm44i 695 48 Let let VB work_fnploejenbc2raktl46esxm44i 695 49 a(Q)= a(q)= VB work_fnploejenbc2raktl46esxm44i 695 50 { { -LRB- work_fnploejenbc2raktl46esxm44i 695 51 ti ti NNP work_fnploejenbc2raktl46esxm44i 695 52 , , , work_fnploejenbc2raktl46esxm44i 695 53 j= j= NNP work_fnploejenbc2raktl46esxm44i 695 54 1 1 CD work_fnploejenbc2raktl46esxm44i 695 55 , , , work_fnploejenbc2raktl46esxm44i 695 56 2 2 CD work_fnploejenbc2raktl46esxm44i 695 57 , , , work_fnploejenbc2raktl46esxm44i 695 58 . . . work_fnploejenbc2raktl46esxm44i 696 1 .. .. NFP work_fnploejenbc2raktl46esxm44i 696 2 } } -RRB- work_fnploejenbc2raktl46esxm44i 696 3 and and CC work_fnploejenbc2raktl46esxm44i 696 4 Cj Cj NNP work_fnploejenbc2raktl46esxm44i 696 5 = = SYM work_fnploejenbc2raktl46esxm44i 696 6 aP1(tj aP1(tj NNP work_fnploejenbc2raktl46esxm44i 696 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 696 8 . . . work_fnploejenbc2raktl46esxm44i 697 1 where where WRB work_fnploejenbc2raktl46esxm44i 697 2 @p,3= @p,3= . work_fnploejenbc2raktl46esxm44i 697 3 C C NNP work_fnploejenbc2raktl46esxm44i 697 4 ap(w)=+f ap(w)=+f NNP work_fnploejenbc2raktl46esxm44i 697 5 lC$/lT=+f lC$/lT=+f NNP work_fnploejenbc2raktl46esxm44i 697 6 C C NNP work_fnploejenbc2raktl46esxm44i 697 7 IC IC NNP work_fnploejenbc2raktl46esxm44i 697 8 , , , work_fnploejenbc2raktl46esxm44i 697 9 l l NNP work_fnploejenbc2raktl46esxm44i 697 10 t t NN work_fnploejenbc2raktl46esxm44i 697 11 ; ; : work_fnploejenbc2raktl46esxm44i 697 12 c;c c;c NNP work_fnploejenbc2raktl46esxm44i 697 13 ; ; : work_fnploejenbc2raktl46esxm44i 697 14 j=3 j=3 NNP work_fnploejenbc2raktl46esxm44i 697 15 n=2 n=2 NNP work_fnploejenbc2raktl46esxm44i 697 16 l l NN work_fnploejenbc2raktl46esxm44i 697 17 / / SYM work_fnploejenbc2raktl46esxm44i 697 18 n n NNP work_fnploejenbc2raktl46esxm44i 697 19 < < XX work_fnploejenbc2raktl46esxm44i 697 20 r, > XX work_fnploejenbc2raktl46esxm44i 699 63 -==a(3/2)b -==a(3/2)b : work_fnploejenbc2raktl46esxm44i 699 64 + + CC work_fnploejenbc2raktl46esxm44i 699 65 f f NNP work_fnploejenbc2raktl46esxm44i 699 66 n-(~-b n-(~-b NN work_fnploejenbc2raktl46esxm44i 699 67 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 699 68 . . . work_fnploejenbc2raktl46esxm44i 700 1 n=2 n=2 NNP work_fnploejenbc2raktl46esxm44i 700 2 2 2 CD work_fnploejenbc2raktl46esxm44i 700 3 np np NNP work_fnploejenbc2raktl46esxm44i 700 4 n=2 n=2 NNS work_fnploejenbc2raktl46esxm44i 700 5 Thus thus RB work_fnploejenbc2raktl46esxm44i 700 6 lim lim NNP work_fnploejenbc2raktl46esxm44i 700 7 , , , work_fnploejenbc2raktl46esxm44i 700 8 _ _ NNP work_fnploejenbc2raktl46esxm44i 700 9 + + SYM work_fnploejenbc2raktl46esxm44i 700 10 o. o. NN work_fnploejenbc2raktl46esxm44i 701 1 @P,3 @P,3 NFP work_fnploejenbc2raktl46esxm44i 701 2 = = NFP work_fnploejenbc2raktl46esxm44i 701 3 0 0 NFP work_fnploejenbc2raktl46esxm44i 701 4 . . . work_fnploejenbc2raktl46esxm44i 702 1 Let let VB work_fnploejenbc2raktl46esxm44i 702 2 p p PRP work_fnploejenbc2raktl46esxm44i 702 3 be be VB work_fnploejenbc2raktl46esxm44i 702 4 large large JJ work_fnploejenbc2raktl46esxm44i 702 5 enough enough RB work_fnploejenbc2raktl46esxm44i 702 6 so so IN work_fnploejenbc2raktl46esxm44i 702 7 that that DT work_fnploejenbc2raktl46esxm44i 702 8 @P,3 @P,3 . work_fnploejenbc2raktl46esxm44i 702 9 < < XX work_fnploejenbc2raktl46esxm44i 702 10 $ $ $ work_fnploejenbc2raktl46esxm44i 702 11 and and CC work_fnploejenbc2raktl46esxm44i 702 12 f f LS work_fnploejenbc2raktl46esxm44i 702 13 ; ; : work_fnploejenbc2raktl46esxm44i 702 14 < < XX work_fnploejenbc2raktl46esxm44i 702 15 l/2 l/2 NNP work_fnploejenbc2raktl46esxm44i 702 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 702 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 702 18 C1 c1 NN work_fnploejenbc2raktl46esxm44i 702 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 702 20 + + NFP work_fnploejenbc2raktl46esxm44i 702 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 702 22 CJ CJ NNP work_fnploejenbc2raktl46esxm44i 702 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 702 24 . . . work_fnploejenbc2raktl46esxm44i 703 1 Define Define NNP work_fnploejenbc2raktl46esxm44i 703 2 g,(t,)=(l--~,,)/IC g,(t,)=(l--~,,)/IC NNP work_fnploejenbc2raktl46esxm44i 703 3 , , , work_fnploejenbc2raktl46esxm44i 703 4 I. I. NNP work_fnploejenbc2raktl46esxm44i 704 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 704 2 have have VBP work_fnploejenbc2raktl46esxm44i 704 3 t$‘ > NN work_fnploejenbc2raktl46esxm44i 704 36 0 0 CD work_fnploejenbc2raktl46esxm44i 704 37 since since IN work_fnploejenbc2raktl46esxm44i 704 38 f2 f2 NNP work_fnploejenbc2raktl46esxm44i 704 39 > > XX work_fnploejenbc2raktl46esxm44i 704 40 0 0 CD work_fnploejenbc2raktl46esxm44i 704 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 704 42 . . . work_fnploejenbc2raktl46esxm44i 705 1 Also also RB work_fnploejenbc2raktl46esxm44i 705 2 , , , work_fnploejenbc2raktl46esxm44i 705 3 by by IN work_fnploejenbc2raktl46esxm44i 705 4 construction construction NN work_fnploejenbc2raktl46esxm44i 705 5 , , , work_fnploejenbc2raktl46esxm44i 705 6 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 705 7 have have VBP work_fnploejenbc2raktl46esxm44i 705 8 1 1 CD work_fnploejenbc2raktl46esxm44i 705 9 = = SYM work_fnploejenbc2raktl46esxm44i 705 10 Qp,2 Qp,2 NNP work_fnploejenbc2raktl46esxm44i 705 11 + + SYM work_fnploejenbc2raktl46esxm44i 705 12 ICll ICll NNP work_fnploejenbc2raktl46esxm44i 705 13 & & CC work_fnploejenbc2raktl46esxm44i 705 14 # # $ work_fnploejenbc2raktl46esxm44i 705 15 l l NN work_fnploejenbc2raktl46esxm44i 705 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 705 17 = = NFP work_fnploejenbc2raktl46esxm44i 705 18 c c NN work_fnploejenbc2raktl46esxm44i 705 19 gpke4 gpke4 NN work_fnploejenbc2raktl46esxm44i 705 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 705 21 . . . work_fnploejenbc2raktl46esxm44i 706 1 52 52 CD work_fnploejenbc2raktl46esxm44i 706 2 Thus thus RB work_fnploejenbc2raktl46esxm44i 706 3 , , , work_fnploejenbc2raktl46esxm44i 706 4 if if IN work_fnploejenbc2raktl46esxm44i 706 5 Aa- Aa- NNP work_fnploejenbc2raktl46esxm44i 706 6 ‘ ' `` work_fnploejenbc2raktl46esxm44i 706 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 706 8 $ $ $ work_fnploejenbc2raktl46esxm44i 706 9 3 3 CD work_fnploejenbc2raktl46esxm44i 706 10 , , , work_fnploejenbc2raktl46esxm44i 706 11 = = SYM work_fnploejenbc2raktl46esxm44i 706 12 T,(a(w T,(a(w NNP work_fnploejenbc2raktl46esxm44i 706 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 706 14 , , , work_fnploejenbc2raktl46esxm44i 706 15 w w NNP work_fnploejenbc2raktl46esxm44i 706 16 E E NNP work_fnploejenbc2raktl46esxm44i 706 17 A A NNP work_fnploejenbc2raktl46esxm44i 706 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 706 19 with with IN work_fnploejenbc2raktl46esxm44i 706 20 7’,(x 7’,(x NN work_fnploejenbc2raktl46esxm44i 706 21 , , , work_fnploejenbc2raktl46esxm44i 706 22 y y NNP work_fnploejenbc2raktl46esxm44i 706 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 706 24 = = NFP work_fnploejenbc2raktl46esxm44i 706 25 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 706 26 Min(xP min(xp CD work_fnploejenbc2raktl46esxm44i 706 27 + + CC work_fnploejenbc2raktl46esxm44i 706 28 yP yP NNP work_fnploejenbc2raktl46esxm44i 706 29 , , , work_fnploejenbc2raktl46esxm44i 706 30 l l NNP work_fnploejenbc2raktl46esxm44i 706 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 706 32 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 706 33 “ " `` work_fnploejenbc2raktl46esxm44i 706 34 “ " `` work_fnploejenbc2raktl46esxm44i 706 35 . . . work_fnploejenbc2raktl46esxm44i 707 1 Hence hence RB work_fnploejenbc2raktl46esxm44i 707 2 lim lim NN work_fnploejenbc2raktl46esxm44i 707 3 , , , work_fnploejenbc2raktl46esxm44i 707 4 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 707 5 + + SYM work_fnploejenbc2raktl46esxm44i 707 6 o. o. NN work_fnploejenbc2raktl46esxm44i 708 1 ~~,~$A)=Max(a(o ~~,~$A)=Max(a(o NNP work_fnploejenbc2raktl46esxm44i 708 2 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 708 3 , , , work_fnploejenbc2raktl46esxm44i 708 4 weA wea LS work_fnploejenbc2raktl46esxm44i 708 5 } } -RRB- work_fnploejenbc2raktl46esxm44i 708 6 for for IN work_fnploejenbc2raktl46esxm44i 708 7 any any DT work_fnploejenbc2raktl46esxm44i 708 8 finite finite NN work_fnploejenbc2raktl46esxm44i 708 9 A. a. NN work_fnploejenbc2raktl46esxm44i 709 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 709 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 709 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 709 4 For for IN work_fnploejenbc2raktl46esxm44i 709 5 Aa-‘(t,)#@ aa-‘(t,)#@ UH work_fnploejenbc2raktl46esxm44i 709 6 , , , work_fnploejenbc2raktl46esxm44i 709 7 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 709 8 have have VBP work_fnploejenbc2raktl46esxm44i 709 9 t t NN work_fnploejenbc2raktl46esxm44i 709 10 , , , work_fnploejenbc2raktl46esxm44i 709 11 = = SYM work_fnploejenbc2raktl46esxm44i 709 12 Max{a(o Max{a(o NNP work_fnploejenbc2raktl46esxm44i 709 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 709 14 , , , work_fnploejenbc2raktl46esxm44i 709 15 ok ok UH work_fnploejenbc2raktl46esxm44i 709 16 A a NN work_fnploejenbc2raktl46esxm44i 709 17 } } -RRB- work_fnploejenbc2raktl46esxm44i 709 18 < < XX work_fnploejenbc2raktl46esxm44i 709 19 T,(cr(w T,(cr(w NNP work_fnploejenbc2raktl46esxm44i 709 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 709 21 , , , work_fnploejenbc2raktl46esxm44i 709 22 o~,4 o~,4 NN work_fnploejenbc2raktl46esxm44i 709 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 709 24 < < XX work_fnploejenbc2raktl46esxm44i 709 25 1 1 CD work_fnploejenbc2raktl46esxm44i 709 26 and and CC work_fnploejenbc2raktl46esxm44i 709 27 hence hence RB work_fnploejenbc2raktl46esxm44i 709 28 I/4z i/4z JJ work_fnploejenbc2raktl46esxm44i 709 29 , , , work_fnploejenbc2raktl46esxm44i 709 30 Tp(4-P12(~)l Tp(4-P12(~)l NNP work_fnploejenbc2raktl46esxm44i 709 31 G G NNP work_fnploejenbc2raktl46esxm44i 709 32 1 1 CD work_fnploejenbc2raktl46esxm44i 709 33 -t -t : work_fnploejenbc2raktl46esxm44i 709 34 , , , work_fnploejenbc2raktl46esxm44i 709 35 . . . work_fnploejenbc2raktl46esxm44i 710 1 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 710 2 Remarks remark VBZ work_fnploejenbc2raktl46esxm44i 710 3 . . . work_fnploejenbc2raktl46esxm44i 711 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 711 2 i i NN work_fnploejenbc2raktl46esxm44i 711 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 711 4 Let let VB work_fnploejenbc2raktl46esxm44i 711 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 711 6 Sz sz VB work_fnploejenbc2raktl46esxm44i 711 7 , , , work_fnploejenbc2raktl46esxm44i 711 8 ~44 ~44 NFP work_fnploejenbc2raktl46esxm44i 711 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 711 10 be be VB work_fnploejenbc2raktl46esxm44i 711 11 an an DT work_fnploejenbc2raktl46esxm44i 711 12 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 711 13 measurable measurable JJ work_fnploejenbc2raktl46esxm44i 711 14 space space NN work_fnploejenbc2raktl46esxm44i 711 15 , , , work_fnploejenbc2raktl46esxm44i 711 16 and and CC work_fnploejenbc2raktl46esxm44i 711 17 , , , work_fnploejenbc2raktl46esxm44i 711 18 u u NN work_fnploejenbc2raktl46esxm44i 711 19 : : : work_fnploejenbc2raktl46esxm44i 711 20 d d NNP work_fnploejenbc2raktl46esxm44i 711 21 + + SYM work_fnploejenbc2raktl46esxm44i 711 22 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 711 23 a a DT work_fnploejenbc2raktl46esxm44i 711 24 , , , work_fnploejenbc2raktl46esxm44i 711 25 , , , work_fnploejenbc2raktl46esxm44i 711 26 a a DT work_fnploejenbc2raktl46esxm44i 711 27 , , , work_fnploejenbc2raktl46esxm44i 711 28 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 711 29 be be VB work_fnploejenbc2raktl46esxm44i 711 30 general general JJ work_fnploejenbc2raktl46esxm44i 711 31 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 711 32 in in IN work_fnploejenbc2raktl46esxm44i 711 33 the the DT work_fnploejenbc2raktl46esxm44i 711 34 a a DT work_fnploejenbc2raktl46esxm44i 711 35 - - HYPH work_fnploejenbc2raktl46esxm44i 711 36 additive additive JJ work_fnploejenbc2raktl46esxm44i 711 37 sense sense NN work_fnploejenbc2raktl46esxm44i 711 38 with with IN work_fnploejenbc2raktl46esxm44i 711 39 Prop Prop NNP work_fnploejenbc2raktl46esxm44i 711 40 = = SYM work_fnploejenbc2raktl46esxm44i 711 41 Q Q NNP work_fnploejenbc2raktl46esxm44i 711 42 , , , work_fnploejenbc2raktl46esxm44i 711 43 where where WRB work_fnploejenbc2raktl46esxm44i 711 44 Q Q NNP work_fnploejenbc2raktl46esxm44i 711 45 is be VBZ work_fnploejenbc2raktl46esxm44i 711 46 a a DT work_fnploejenbc2raktl46esxm44i 711 47 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 711 48 probability probability NN work_fnploejenbc2raktl46esxm44i 711 49 measure measure NN work_fnploejenbc2raktl46esxm44i 711 50 on on IN work_fnploejenbc2raktl46esxm44i 711 51 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 711 52 0 0 CD work_fnploejenbc2raktl46esxm44i 711 53 , , , work_fnploejenbc2raktl46esxm44i 711 54 , , , work_fnploejenbc2raktl46esxm44i 711 55 pP pP NNP work_fnploejenbc2raktl46esxm44i 711 56 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 711 57 . . . work_fnploejenbc2raktl46esxm44i 712 1 Then then RB work_fnploejenbc2raktl46esxm44i 712 2 p p NNP work_fnploejenbc2raktl46esxm44i 712 3 has have VBZ work_fnploejenbc2raktl46esxm44i 712 4 the the DT work_fnploejenbc2raktl46esxm44i 712 5 same same JJ work_fnploejenbc2raktl46esxm44i 712 6 representation representation NN work_fnploejenbc2raktl46esxm44i 712 7 as as IN work_fnploejenbc2raktl46esxm44i 712 8 in in IN work_fnploejenbc2raktl46esxm44i 712 9 the the DT work_fnploejenbc2raktl46esxm44i 712 10 discrete discrete JJ work_fnploejenbc2raktl46esxm44i 712 11 case case NN work_fnploejenbc2raktl46esxm44i 712 12 . . . work_fnploejenbc2raktl46esxm44i 713 1 Indeed indeed RB work_fnploejenbc2raktl46esxm44i 713 2 , , , work_fnploejenbc2raktl46esxm44i 713 3 let let VB work_fnploejenbc2raktl46esxm44i 713 4 B0 B0 NNP work_fnploejenbc2raktl46esxm44i 713 5 CO CO NNP work_fnploejenbc2raktl46esxm44i 713 6 , , , work_fnploejenbc2raktl46esxm44i 713 7 countable countable JJ work_fnploejenbc2raktl46esxm44i 713 8 such such JJ work_fnploejenbc2raktl46esxm44i 713 9 that that IN work_fnploejenbc2raktl46esxm44i 713 10 Q(sZ Q(sZ NNP work_fnploejenbc2raktl46esxm44i 713 11 , , , work_fnploejenbc2raktl46esxm44i 713 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 713 13 = = NFP work_fnploejenbc2raktl46esxm44i 713 14 1 1 CD work_fnploejenbc2raktl46esxm44i 713 15 . . . work_fnploejenbc2raktl46esxm44i 714 1 Then then RB work_fnploejenbc2raktl46esxm44i 714 2 VA VA NNP work_fnploejenbc2raktl46esxm44i 714 3 E E NNP work_fnploejenbc2raktl46esxm44i 714 4 & & CC work_fnploejenbc2raktl46esxm44i 714 5 , , , work_fnploejenbc2raktl46esxm44i 714 6 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 714 7 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 714 8 TO to IN work_fnploejenbc2raktl46esxm44i 714 9 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 714 10 585 585 CD work_fnploejenbc2raktl46esxm44i 714 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 714 12 ii ii NN work_fnploejenbc2raktl46esxm44i 714 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 714 14 A a DT work_fnploejenbc2raktl46esxm44i 714 15 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 714 16 analog analog NN work_fnploejenbc2raktl46esxm44i 714 17 is be VBZ work_fnploejenbc2raktl46esxm44i 714 18 as as IN work_fnploejenbc2raktl46esxm44i 714 19 follows follow VBZ work_fnploejenbc2raktl46esxm44i 714 20 . . . work_fnploejenbc2raktl46esxm44i 715 1 Let let VB work_fnploejenbc2raktl46esxm44i 715 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 3 ~2 ~2 NFP work_fnploejenbc2raktl46esxm44i 715 4 , , , work_fnploejenbc2raktl46esxm44i 715 5 ~4 ~4 NFP work_fnploejenbc2raktl46esxm44i 715 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 7 = = NFP work_fnploejenbc2raktl46esxm44i 715 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 9 R r NN work_fnploejenbc2raktl46esxm44i 715 10 , , , work_fnploejenbc2raktl46esxm44i 715 11 B b NN work_fnploejenbc2raktl46esxm44i 715 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 13 , , , work_fnploejenbc2raktl46esxm44i 715 14 ho ho XX work_fnploejenbc2raktl46esxm44i 715 15 : : : work_fnploejenbc2raktl46esxm44i 715 16 R r NN work_fnploejenbc2raktl46esxm44i 715 17 + + CC work_fnploejenbc2raktl46esxm44i 715 18 CO co NN work_fnploejenbc2raktl46esxm44i 715 19 , , , work_fnploejenbc2raktl46esxm44i 715 20 11 11 CD work_fnploejenbc2raktl46esxm44i 715 21 , , , work_fnploejenbc2raktl46esxm44i 715 22 Fe(x Fe(x NNP work_fnploejenbc2raktl46esxm44i 715 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 24 = = NFP work_fnploejenbc2raktl46esxm44i 715 25 Q q NN work_fnploejenbc2raktl46esxm44i 715 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 28 - - HYPH work_fnploejenbc2raktl46esxm44i 715 29 co co NN work_fnploejenbc2raktl46esxm44i 715 30 , , , work_fnploejenbc2raktl46esxm44i 715 31 xl xl NNP work_fnploejenbc2raktl46esxm44i 715 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 33 and and CC work_fnploejenbc2raktl46esxm44i 715 34 F F NNP work_fnploejenbc2raktl46esxm44i 715 35 , , , work_fnploejenbc2raktl46esxm44i 715 36 : : : work_fnploejenbc2raktl46esxm44i 715 37 R r NN work_fnploejenbc2raktl46esxm44i 715 38 -- -- : work_fnploejenbc2raktl46esxm44i 715 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 40 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 715 41 a a DT work_fnploejenbc2raktl46esxm44i 715 42 , , , work_fnploejenbc2raktl46esxm44i 715 43 , , , work_fnploejenbc2raktl46esxm44i 715 44 a a DT work_fnploejenbc2raktl46esxm44i 715 45 , , , work_fnploejenbc2raktl46esxm44i 715 46 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 715 47 , , , work_fnploejenbc2raktl46esxm44i 715 48 F,,(x F,,(x NNP work_fnploejenbc2raktl46esxm44i 715 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 50 = = NFP work_fnploejenbc2raktl46esxm44i 715 51 p p FW work_fnploejenbc2raktl46esxm44i 715 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 53 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 715 54 - - HYPH work_fnploejenbc2raktl46esxm44i 715 55 00 00 NNP work_fnploejenbc2raktl46esxm44i 715 56 , , , work_fnploejenbc2raktl46esxm44i 715 57 xl xl NNP work_fnploejenbc2raktl46esxm44i 715 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 715 59 . . . work_fnploejenbc2raktl46esxm44i 716 1 Since since IN work_fnploejenbc2raktl46esxm44i 716 2 p p NN work_fnploejenbc2raktl46esxm44i 716 3 = = SYM work_fnploejenbc2raktl46esxm44i 716 4 P p NN work_fnploejenbc2raktl46esxm44i 716 5 ; ; : work_fnploejenbc2raktl46esxm44i 716 6 ’ ' '' work_fnploejenbc2raktl46esxm44i 716 7 0 0 NFP work_fnploejenbc2raktl46esxm44i 716 8 Q q NN work_fnploejenbc2raktl46esxm44i 716 9 , , , work_fnploejenbc2raktl46esxm44i 716 10 and and CC work_fnploejenbc2raktl46esxm44i 716 11 P p NN work_fnploejenbc2raktl46esxm44i 716 12 ; ; : work_fnploejenbc2raktl46esxm44i 716 13 ’ ' '' work_fnploejenbc2raktl46esxm44i 716 14 is be VBZ work_fnploejenbc2raktl46esxm44i 716 15 increasing increase VBG work_fnploejenbc2raktl46esxm44i 716 16 , , , work_fnploejenbc2raktl46esxm44i 716 17 /J /J NNP work_fnploejenbc2raktl46esxm44i 716 18 is be VBZ work_fnploejenbc2raktl46esxm44i 716 19 a a DT work_fnploejenbc2raktl46esxm44i 716 20 nondecreasing nondecrease VBG work_fnploejenbc2raktl46esxm44i 716 21 set set NN work_fnploejenbc2raktl46esxm44i 716 22 - - HYPH work_fnploejenbc2raktl46esxm44i 716 23 function function NN work_fnploejenbc2raktl46esxm44i 716 24 ; ; : work_fnploejenbc2raktl46esxm44i 716 25 hence hence RB work_fnploejenbc2raktl46esxm44i 716 26 F F NNP work_fnploejenbc2raktl46esxm44i 716 27 , , , work_fnploejenbc2raktl46esxm44i 716 28 is be VBZ work_fnploejenbc2raktl46esxm44i 716 29 nondecreasing nondecrease VBG work_fnploejenbc2raktl46esxm44i 716 30 , , , work_fnploejenbc2raktl46esxm44i 716 31 and and CC work_fnploejenbc2raktl46esxm44i 716 32 A a DT work_fnploejenbc2raktl46esxm44i 716 33 E e NN work_fnploejenbc2raktl46esxm44i 716 34 93 93 CD work_fnploejenbc2raktl46esxm44i 716 35 , , , work_fnploejenbc2raktl46esxm44i 716 36 p(A p(a JJ work_fnploejenbc2raktl46esxm44i 716 37 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 716 38 = = NFP work_fnploejenbc2raktl46esxm44i 716 39 9 9 CD work_fnploejenbc2raktl46esxm44i 716 40 ; ; : work_fnploejenbc2raktl46esxm44i 716 41 ’ ' '' work_fnploejenbc2raktl46esxm44i 716 42 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 716 43 j j NNP work_fnploejenbc2raktl46esxm44i 716 44 , , , work_fnploejenbc2raktl46esxm44i 716 45 , , , work_fnploejenbc2raktl46esxm44i 716 46 d(P d(P NNP work_fnploejenbc2raktl46esxm44i 716 47 , , , work_fnploejenbc2raktl46esxm44i 716 48 o o XX work_fnploejenbc2raktl46esxm44i 716 49 F,(x F,(x NNP work_fnploejenbc2raktl46esxm44i 716 50 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 716 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 716 52 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 716 53 . . . work_fnploejenbc2raktl46esxm44i 717 1 If if IN work_fnploejenbc2raktl46esxm44i 717 2 , , , work_fnploejenbc2raktl46esxm44i 717 3 in in IN work_fnploejenbc2raktl46esxm44i 717 4 addition addition NN work_fnploejenbc2raktl46esxm44i 717 5 , , , work_fnploejenbc2raktl46esxm44i 717 6 P,- P,- NNP work_fnploejenbc2raktl46esxm44i 717 7 is be VBZ work_fnploejenbc2raktl46esxm44i 717 8 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 717 9 , , , work_fnploejenbc2raktl46esxm44i 717 10 then then RB work_fnploejenbc2raktl46esxm44i 717 11 P(A P(A NNS work_fnploejenbc2raktl46esxm44i 717 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 717 13 = = NFP work_fnploejenbc2raktl46esxm44i 717 14 PF1 PF1 NNP work_fnploejenbc2raktl46esxm44i 717 15 j j NNP work_fnploejenbc2raktl46esxm44i 717 16 P;-(F,(x p;-(f,(x NN work_fnploejenbc2raktl46esxm44i 717 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 717 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 717 19 dl;,(x dl;,(x NN work_fnploejenbc2raktl46esxm44i 717 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 717 21 . . . work_fnploejenbc2raktl46esxm44i 718 1 A a DT work_fnploejenbc2raktl46esxm44i 718 2 1 1 CD work_fnploejenbc2raktl46esxm44i 718 3 6 6 CD work_fnploejenbc2raktl46esxm44i 718 4 . . . work_fnploejenbc2raktl46esxm44i 719 1 ADMISSIBILITY admissibility JJ work_fnploejenbc2raktl46esxm44i 719 2 OF of IN work_fnploejenbc2raktl46esxm44i 719 3 DEMPSTER DEMPSTER NNP work_fnploejenbc2raktl46esxm44i 719 4 - - HYPH work_fnploejenbc2raktl46esxm44i 719 5 SHAFER SHAFER NNP work_fnploejenbc2raktl46esxm44i 719 6 BELIEF BELIEF NNP work_fnploejenbc2raktl46esxm44i 719 7 FUNCTIONS FUNCTIONS NNP work_fnploejenbc2raktl46esxm44i 719 8 Dempster Dempster NNP work_fnploejenbc2raktl46esxm44i 719 9 - - HYPH work_fnploejenbc2raktl46esxm44i 719 10 Shafer Shafer NNP work_fnploejenbc2raktl46esxm44i 719 11 belief belief NN work_fnploejenbc2raktl46esxm44i 719 12 functions function NNS work_fnploejenbc2raktl46esxm44i 719 13 have have VBP work_fnploejenbc2raktl46esxm44i 719 14 become become VBN work_fnploejenbc2raktl46esxm44i 719 15 very very RB work_fnploejenbc2raktl46esxm44i 719 16 popular popular JJ work_fnploejenbc2raktl46esxm44i 719 17 in in IN work_fnploejenbc2raktl46esxm44i 719 18 recent recent JJ work_fnploejenbc2raktl46esxm44i 719 19 years year NNS work_fnploejenbc2raktl46esxm44i 719 20 for for IN work_fnploejenbc2raktl46esxm44i 719 21 modeling model VBG work_fnploejenbc2raktl46esxm44i 719 22 aspects aspect NNS work_fnploejenbc2raktl46esxm44i 719 23 of of IN work_fnploejenbc2raktl46esxm44i 719 24 expert expert NN work_fnploejenbc2raktl46esxm44i 719 25 systems system NNS work_fnploejenbc2raktl46esxm44i 719 26 and and CC work_fnploejenbc2raktl46esxm44i 719 27 combination combination NN work_fnploejenbc2raktl46esxm44i 719 28 of of IN work_fnploejenbc2raktl46esxm44i 719 29 evidence evidence NN work_fnploejenbc2raktl46esxm44i 719 30 problems problem NNS work_fnploejenbc2raktl46esxm44i 719 31 in in IN work_fnploejenbc2raktl46esxm44i 719 32 AI AI NNP work_fnploejenbc2raktl46esxm44i 719 33 . . . work_fnploejenbc2raktl46esxm44i 720 1 The the DT work_fnploejenbc2raktl46esxm44i 720 2 purpose purpose NN work_fnploejenbc2raktl46esxm44i 720 3 of of IN work_fnploejenbc2raktl46esxm44i 720 4 this this DT work_fnploejenbc2raktl46esxm44i 720 5 section section NN work_fnploejenbc2raktl46esxm44i 720 6 is be VBZ work_fnploejenbc2raktl46esxm44i 720 7 to to TO work_fnploejenbc2raktl46esxm44i 720 8 respond respond VB work_fnploejenbc2raktl46esxm44i 720 9 to to IN work_fnploejenbc2raktl46esxm44i 720 10 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 720 11 ’s ’s POS work_fnploejenbc2raktl46esxm44i 720 12 comments comment NNS work_fnploejenbc2raktl46esxm44i 720 13 about about IN work_fnploejenbc2raktl46esxm44i 720 14 the the DT work_fnploejenbc2raktl46esxm44i 720 15 inadmissibility inadmissibility NN work_fnploejenbc2raktl46esxm44i 720 16 of of IN work_fnploejenbc2raktl46esxm44i 720 17 belief belief NN work_fnploejenbc2raktl46esxm44i 720 18 functions function NNS work_fnploejenbc2raktl46esxm44i 720 19 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 720 20 16 16 CD work_fnploejenbc2raktl46esxm44i 720 21 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 720 22 . . . work_fnploejenbc2raktl46esxm44i 721 1 For for IN work_fnploejenbc2raktl46esxm44i 721 2 simplicity simplicity NN work_fnploejenbc2raktl46esxm44i 721 3 let let VB work_fnploejenbc2raktl46esxm44i 721 4 C2 c2 NN work_fnploejenbc2raktl46esxm44i 721 5 be be VB work_fnploejenbc2raktl46esxm44i 721 6 a a DT work_fnploejenbc2raktl46esxm44i 721 7 finite finite JJ work_fnploejenbc2raktl46esxm44i 721 8 set set NN work_fnploejenbc2raktl46esxm44i 721 9 . . . work_fnploejenbc2raktl46esxm44i 722 1 A a DT work_fnploejenbc2raktl46esxm44i 722 2 belief belief NN work_fnploejenbc2raktl46esxm44i 722 3 function function NN work_fnploejenbc2raktl46esxm44i 722 4 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 722 5 on on IN work_fnploejenbc2raktl46esxm44i 722 6 P(a P(a NNP work_fnploejenbc2raktl46esxm44i 722 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 722 8 , , , work_fnploejenbc2raktl46esxm44i 722 9 the the DT work_fnploejenbc2raktl46esxm44i 722 10 power power NN work_fnploejenbc2raktl46esxm44i 722 11 class class NN work_fnploejenbc2raktl46esxm44i 722 12 of of IN work_fnploejenbc2raktl46esxm44i 722 13 G g NN work_fnploejenbc2raktl46esxm44i 722 14 , , , work_fnploejenbc2raktl46esxm44i 722 15 can can MD work_fnploejenbc2raktl46esxm44i 722 16 be be VB work_fnploejenbc2raktl46esxm44i 722 17 defined define VBN work_fnploejenbc2raktl46esxm44i 722 18 as as IN work_fnploejenbc2raktl46esxm44i 722 19 follows follow VBZ work_fnploejenbc2raktl46esxm44i 722 20 . . . work_fnploejenbc2raktl46esxm44i 723 1 Let let VB work_fnploejenbc2raktl46esxm44i 723 2 m m NN work_fnploejenbc2raktl46esxm44i 723 3 : : : work_fnploejenbc2raktl46esxm44i 723 4 Y’(n Y’(n NNP work_fnploejenbc2raktl46esxm44i 723 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 723 6 -+ -+ NFP work_fnploejenbc2raktl46esxm44i 723 7 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 723 8 0 0 CD work_fnploejenbc2raktl46esxm44i 723 9 , , , work_fnploejenbc2raktl46esxm44i 723 10 l l NN work_fnploejenbc2raktl46esxm44i 723 11 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 723 12 such such JJ work_fnploejenbc2raktl46esxm44i 723 13 that that IN work_fnploejenbc2raktl46esxm44i 723 14 m(0 m(0 NNP work_fnploejenbc2raktl46esxm44i 723 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 723 16 = = SYM work_fnploejenbc2raktl46esxm44i 723 17 0 0 NFP work_fnploejenbc2raktl46esxm44i 723 18 , , , work_fnploejenbc2raktl46esxm44i 723 19 Cscn Cscn NNP work_fnploejenbc2raktl46esxm44i 723 20 , , , work_fnploejenbc2raktl46esxm44i 723 21 m(A m(a NN work_fnploejenbc2raktl46esxm44i 723 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 723 23 = = NFP work_fnploejenbc2raktl46esxm44i 723 24 1 1 CD work_fnploejenbc2raktl46esxm44i 723 25 . . . work_fnploejenbc2raktl46esxm44i 724 1 Then then RB work_fnploejenbc2raktl46esxm44i 724 2 , , , work_fnploejenbc2raktl46esxm44i 724 3 Bel(B)= Bel(B)= NNP work_fnploejenbc2raktl46esxm44i 724 4 1 1 CD work_fnploejenbc2raktl46esxm44i 724 5 m(A m(a NN work_fnploejenbc2raktl46esxm44i 724 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 724 7 . . . work_fnploejenbc2raktl46esxm44i 725 1 AGE age NN work_fnploejenbc2raktl46esxm44i 725 2 m m NNP work_fnploejenbc2raktl46esxm44i 725 3 is be VBZ work_fnploejenbc2raktl46esxm44i 725 4 the the DT work_fnploejenbc2raktl46esxm44i 725 5 probability probability NN work_fnploejenbc2raktl46esxm44i 725 6 allocation allocation NN work_fnploejenbc2raktl46esxm44i 725 7 for for IN work_fnploejenbc2raktl46esxm44i 725 8 Bel Bel NNP work_fnploejenbc2raktl46esxm44i 725 9 . . . work_fnploejenbc2raktl46esxm44i 726 1 By by IN work_fnploejenbc2raktl46esxm44i 726 2 the the DT work_fnploejenbc2raktl46esxm44i 726 3 Mobius Mobius NNP work_fnploejenbc2raktl46esxm44i 726 4 inversion inversion NN work_fnploejenbc2raktl46esxm44i 726 5 formula formula NN work_fnploejenbc2raktl46esxm44i 726 6 , , , work_fnploejenbc2raktl46esxm44i 726 7 m m NNP work_fnploejenbc2raktl46esxm44i 726 8 can can MD work_fnploejenbc2raktl46esxm44i 726 9 be be VB work_fnploejenbc2raktl46esxm44i 726 10 recovered recover VBN work_fnploejenbc2raktl46esxm44i 726 11 from from IN work_fnploejenbc2raktl46esxm44i 726 12 Bel Bel NNP work_fnploejenbc2raktl46esxm44i 726 13 , , , work_fnploejenbc2raktl46esxm44i 726 14 m(A)= m(A)= NNP work_fnploejenbc2raktl46esxm44i 726 15 c c NNP work_fnploejenbc2raktl46esxm44i 726 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 726 17 -l)'"-"I -l)'"-"I VBN work_fnploejenbc2raktl46esxm44i 726 18 Bel(B Bel(B NNP work_fnploejenbc2raktl46esxm44i 726 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 726 20 , , , work_fnploejenbc2raktl46esxm44i 726 21 BCA BCA NNP work_fnploejenbc2raktl46esxm44i 726 22 where where WRB work_fnploejenbc2raktl46esxm44i 726 23 JA JA NNP work_fnploejenbc2raktl46esxm44i 726 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 726 25 denotes denote VBZ work_fnploejenbc2raktl46esxm44i 726 26 the the DT work_fnploejenbc2raktl46esxm44i 726 27 cardinality cardinality NN work_fnploejenbc2raktl46esxm44i 726 28 of of IN work_fnploejenbc2raktl46esxm44i 726 29 A. a. NN work_fnploejenbc2raktl46esxm44i 727 1 Note note VB work_fnploejenbc2raktl46esxm44i 727 2 that that IN work_fnploejenbc2raktl46esxm44i 727 3 if if IN work_fnploejenbc2raktl46esxm44i 727 4 p p NN work_fnploejenbc2raktl46esxm44i 727 5 : : : work_fnploejenbc2raktl46esxm44i 727 6 B(G b(g NN work_fnploejenbc2raktl46esxm44i 727 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 727 8 -+ -+ NFP work_fnploejenbc2raktl46esxm44i 727 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 727 10 0 0 CD work_fnploejenbc2raktl46esxm44i 727 11 , , , work_fnploejenbc2raktl46esxm44i 727 12 l l NN work_fnploejenbc2raktl46esxm44i 727 13 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 727 14 is be VBZ work_fnploejenbc2raktl46esxm44i 727 15 such such JJ work_fnploejenbc2raktl46esxm44i 727 16 that that IN work_fnploejenbc2raktl46esxm44i 727 17 p(sZ p(sZ NNP work_fnploejenbc2raktl46esxm44i 727 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 727 19 = = NFP work_fnploejenbc2raktl46esxm44i 727 20 1 1 CD work_fnploejenbc2raktl46esxm44i 727 21 and and CC work_fnploejenbc2raktl46esxm44i 727 22 VAGQ VAGQ NNP work_fnploejenbc2raktl46esxm44i 727 23 , , , work_fnploejenbc2raktl46esxm44i 727 24 2 2 CD work_fnploejenbc2raktl46esxm44i 727 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 727 26 -l)‘“-B’/@)>O -l)‘“-B’/@)>O NFP work_fnploejenbc2raktl46esxm44i 727 27 Bc_A Bc_A NNP work_fnploejenbc2raktl46esxm44i 727 28 then then RB work_fnploejenbc2raktl46esxm44i 727 29 p p NNP work_fnploejenbc2raktl46esxm44i 727 30 is be VBZ work_fnploejenbc2raktl46esxm44i 727 31 a a DT work_fnploejenbc2raktl46esxm44i 727 32 belief belief NN work_fnploejenbc2raktl46esxm44i 727 33 function function NN work_fnploejenbc2raktl46esxm44i 727 34 . . . work_fnploejenbc2raktl46esxm44i 728 1 If if IN work_fnploejenbc2raktl46esxm44i 728 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 728 3 think think VBP work_fnploejenbc2raktl46esxm44i 728 4 of of IN work_fnploejenbc2raktl46esxm44i 728 5 “ " `` work_fnploejenbc2raktl46esxm44i 728 6 sets set NNS work_fnploejenbc2raktl46esxm44i 728 7 ” " '' work_fnploejenbc2raktl46esxm44i 728 8 as as IN work_fnploejenbc2raktl46esxm44i 728 9 “ " `` work_fnploejenbc2raktl46esxm44i 728 10 points point NNS work_fnploejenbc2raktl46esxm44i 728 11 , , , work_fnploejenbc2raktl46esxm44i 728 12 ” " '' work_fnploejenbc2raktl46esxm44i 728 13 then then RB work_fnploejenbc2raktl46esxm44i 728 14 m m NNP work_fnploejenbc2raktl46esxm44i 728 15 plays play VBZ work_fnploejenbc2raktl46esxm44i 728 16 the the DT work_fnploejenbc2raktl46esxm44i 728 17 role role NN work_fnploejenbc2raktl46esxm44i 728 18 of of IN work_fnploejenbc2raktl46esxm44i 728 19 a a DT work_fnploejenbc2raktl46esxm44i 728 20 probability probability NN work_fnploejenbc2raktl46esxm44i 728 21 mass mass NN work_fnploejenbc2raktl46esxm44i 728 22 function function NN work_fnploejenbc2raktl46esxm44i 728 23 , , , work_fnploejenbc2raktl46esxm44i 728 24 and and CC work_fnploejenbc2raktl46esxm44i 728 25 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 728 26 is be VBZ work_fnploejenbc2raktl46esxm44i 728 27 a a DT work_fnploejenbc2raktl46esxm44i 728 28 “ " `` work_fnploejenbc2raktl46esxm44i 728 29 cumulative cumulative JJ work_fnploejenbc2raktl46esxm44i 728 30 distribution distribution NN work_fnploejenbc2raktl46esxm44i 728 31 function function NN work_fnploejenbc2raktl46esxm44i 728 32 . . . work_fnploejenbc2raktl46esxm44i 728 33 ” " '' work_fnploejenbc2raktl46esxm44i 728 34 Since since IN work_fnploejenbc2raktl46esxm44i 728 35 Sz Sz NNP work_fnploejenbc2raktl46esxm44i 728 36 is be VBZ work_fnploejenbc2raktl46esxm44i 728 37 finite finite JJ work_fnploejenbc2raktl46esxm44i 728 38 , , , work_fnploejenbc2raktl46esxm44i 728 39 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 728 40 have have VBP work_fnploejenbc2raktl46esxm44i 728 41 Bel(A)= bel(a)= CD work_fnploejenbc2raktl46esxm44i 728 42 P(Xe.tT(A p(xe.tt(a NN work_fnploejenbc2raktl46esxm44i 728 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 728 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 728 45 , , , work_fnploejenbc2raktl46esxm44i 728 46 VAEQ VAEQ NNP work_fnploejenbc2raktl46esxm44i 728 47 , , , work_fnploejenbc2raktl46esxm44i 728 48 where where WRB work_fnploejenbc2raktl46esxm44i 728 49 X X NNP work_fnploejenbc2raktl46esxm44i 728 50 is be VBZ work_fnploejenbc2raktl46esxm44i 728 51 a a DT work_fnploejenbc2raktl46esxm44i 728 52 random random JJ work_fnploejenbc2raktl46esxm44i 728 53 set set NN work_fnploejenbc2raktl46esxm44i 728 54 , , , work_fnploejenbc2raktl46esxm44i 728 55 defined define VBN work_fnploejenbc2raktl46esxm44i 728 56 on on IN work_fnploejenbc2raktl46esxm44i 728 57 some some DT work_fnploejenbc2raktl46esxm44i 728 58 probability probability NN work_fnploejenbc2raktl46esxm44i 728 59 space space NN work_fnploejenbc2raktl46esxm44i 728 60 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 728 61 a a DT work_fnploejenbc2raktl46esxm44i 728 62 , , , work_fnploejenbc2raktl46esxm44i 728 63 9 9 CD work_fnploejenbc2raktl46esxm44i 728 64 , , , work_fnploejenbc2raktl46esxm44i 728 65 P p NN work_fnploejenbc2raktl46esxm44i 728 66 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 728 67 , , , work_fnploejenbc2raktl46esxm44i 728 68 and and CC work_fnploejenbc2raktl46esxm44i 728 69 taking take VBG work_fnploejenbc2raktl46esxm44i 728 70 values value NNS work_fnploejenbc2raktl46esxm44i 728 71 in in IN work_fnploejenbc2raktl46esxm44i 728 72 P(s2 P(s2 NNP work_fnploejenbc2raktl46esxm44i 728 73 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 728 74 with with IN work_fnploejenbc2raktl46esxm44i 728 75 “ " `` work_fnploejenbc2raktl46esxm44i 728 76 density density NN work_fnploejenbc2raktl46esxm44i 728 77 ” " '' work_fnploejenbc2raktl46esxm44i 728 78 m m NN work_fnploejenbc2raktl46esxm44i 728 79 , , , work_fnploejenbc2raktl46esxm44i 728 80 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 728 81 , , , work_fnploejenbc2raktl46esxm44i 728 82 P(B P(B NNP work_fnploejenbc2raktl46esxm44i 728 83 : : : work_fnploejenbc2raktl46esxm44i 728 84 X(O)=A)=m(A x(o)=a)=m(a VB work_fnploejenbc2raktl46esxm44i 728 85 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 728 86 . . . work_fnploejenbc2raktl46esxm44i 729 1 586 586 CD work_fnploejenbc2raktl46esxm44i 729 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 729 3 , , , work_fnploejenbc2raktl46esxm44i 729 4 NGIJYEN NGIJYEN NNP work_fnploejenbc2raktl46esxm44i 729 5 , , , work_fnploejenbc2raktl46esxm44i 729 6 ANDROGERS ANDROGERS NNPS work_fnploejenbc2raktl46esxm44i 729 7 Note note VBP work_fnploejenbc2raktl46esxm44i 729 8 that that IN work_fnploejenbc2raktl46esxm44i 729 9 Bel(A Bel(A NNP work_fnploejenbc2raktl46esxm44i 729 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 729 11 + + SYM work_fnploejenbc2raktl46esxm44i 729 12 Bel(A bel(a ADD work_fnploejenbc2raktl46esxm44i 729 13 ” " '' work_fnploejenbc2raktl46esxm44i 729 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 729 15 < < XX work_fnploejenbc2raktl46esxm44i 729 16 1 1 CD work_fnploejenbc2raktl46esxm44i 729 17 . . . work_fnploejenbc2raktl46esxm44i 730 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 730 2 extend extend VBP work_fnploejenbc2raktl46esxm44i 730 3 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 730 4 to to IN work_fnploejenbc2raktl46esxm44i 730 5 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 730 6 events event NNS work_fnploejenbc2raktl46esxm44i 730 7 s’(Q s’(q VB work_fnploejenbc2raktl46esxm44i 730 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 730 9 as as IN work_fnploejenbc2raktl46esxm44i 730 10 follows follow VBZ work_fnploejenbc2raktl46esxm44i 730 11 . . . work_fnploejenbc2raktl46esxm44i 731 1 For for IN work_fnploejenbc2raktl46esxm44i 731 2 E e NN work_fnploejenbc2raktl46esxm44i 731 3 , , , work_fnploejenbc2raktl46esxm44i 731 4 FEY(G FEY(G NNP work_fnploejenbc2raktl46esxm44i 731 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 731 6 , , , work_fnploejenbc2raktl46esxm44i 731 7 define define VB work_fnploejenbc2raktl46esxm44i 731 8 Bel(E)F)=P(XcEjXGF Bel(E)F)=P(XcEjXGF , work_fnploejenbc2raktl46esxm44i 731 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 731 10 when when WRB work_fnploejenbc2raktl46esxm44i 731 11 P(Xs P(Xs NNP work_fnploejenbc2raktl46esxm44i 731 12 F F NNP work_fnploejenbc2raktl46esxm44i 731 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 731 14 > > XX work_fnploejenbc2raktl46esxm44i 731 15 0 0 NFP work_fnploejenbc2raktl46esxm44i 731 16 . . . work_fnploejenbc2raktl46esxm44i 732 1 For for IN work_fnploejenbc2raktl46esxm44i 732 2 more more JJR work_fnploejenbc2raktl46esxm44i 732 3 information information NN work_fnploejenbc2raktl46esxm44i 732 4 on on IN work_fnploejenbc2raktl46esxm44i 732 5 belief belief NN work_fnploejenbc2raktl46esxm44i 732 6 functions function NNS work_fnploejenbc2raktl46esxm44i 732 7 , , , work_fnploejenbc2raktl46esxm44i 732 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 732 9 refer refer VBP work_fnploejenbc2raktl46esxm44i 732 10 the the DT work_fnploejenbc2raktl46esxm44i 732 11 reader reader NN work_fnploejenbc2raktl46esxm44i 732 12 to to IN work_fnploejenbc2raktl46esxm44i 732 13 126 126 CD work_fnploejenbc2raktl46esxm44i 732 14 , , , work_fnploejenbc2raktl46esxm44i 732 15 21 21 CD work_fnploejenbc2raktl46esxm44i 732 16 , , , work_fnploejenbc2raktl46esxm44i 732 17 11 11 CD work_fnploejenbc2raktl46esxm44i 732 18 , , , work_fnploejenbc2raktl46esxm44i 732 19 303 303 CD work_fnploejenbc2raktl46esxm44i 732 20 . . . work_fnploejenbc2raktl46esxm44i 733 1 As as IN work_fnploejenbc2raktl46esxm44i 733 2 in in IN work_fnploejenbc2raktl46esxm44i 733 3 Section section NN work_fnploejenbc2raktl46esxm44i 733 4 5 5 CD work_fnploejenbc2raktl46esxm44i 733 5 , , , work_fnploejenbc2raktl46esxm44i 733 6 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 733 7 consider consider VBP work_fnploejenbc2raktl46esxm44i 733 8 Gf Gf NNP work_fnploejenbc2raktl46esxm44i 733 9 , , , work_fnploejenbc2raktl46esxm44i 733 10 , , , work_fnploejenbc2raktl46esxm44i 733 11 with with IN work_fnploejenbc2raktl46esxm44i 733 12 Pr Pr NNP work_fnploejenbc2raktl46esxm44i 733 13 increasing increase VBG work_fnploejenbc2raktl46esxm44i 733 14 . . . work_fnploejenbc2raktl46esxm44i 734 1 By by IN work_fnploejenbc2raktl46esxm44i 734 2 the the DT work_fnploejenbc2raktl46esxm44i 734 3 nature nature NN work_fnploejenbc2raktl46esxm44i 734 4 of of IN work_fnploejenbc2raktl46esxm44i 734 5 belief belief NN work_fnploejenbc2raktl46esxm44i 734 6 functions function NNS work_fnploejenbc2raktl46esxm44i 734 7 , , , work_fnploejenbc2raktl46esxm44i 734 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 734 9 consider consider VBP work_fnploejenbc2raktl46esxm44i 734 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 734 11 a a DT work_fnploejenbc2raktl46esxm44i 734 12 , , , work_fnploejenbc2raktl46esxm44i 734 13 , , , work_fnploejenbc2raktl46esxm44i 734 14 a a DT work_fnploejenbc2raktl46esxm44i 734 15 , , , work_fnploejenbc2raktl46esxm44i 734 16 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 734 17 = = NFP work_fnploejenbc2raktl46esxm44i 734 18 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 734 19 O o UH work_fnploejenbc2raktl46esxm44i 734 20 , , , work_fnploejenbc2raktl46esxm44i 734 21 11 11 CD work_fnploejenbc2raktl46esxm44i 734 22 . . . work_fnploejenbc2raktl46esxm44i 735 1 Note note VB work_fnploejenbc2raktl46esxm44i 735 2 also also RB work_fnploejenbc2raktl46esxm44i 735 3 that that IN work_fnploejenbc2raktl46esxm44i 735 4 the the DT work_fnploejenbc2raktl46esxm44i 735 5 existence existence NN work_fnploejenbc2raktl46esxm44i 735 6 of of IN work_fnploejenbc2raktl46esxm44i 735 7 f f NNP work_fnploejenbc2raktl46esxm44i 735 8 such such JJ work_fnploejenbc2raktl46esxm44i 735 9 that that IN work_fnploejenbc2raktl46esxm44i 735 10 Pr Pr NNP work_fnploejenbc2raktl46esxm44i 735 11 is be VBZ work_fnploejenbc2raktl46esxm44i 735 12 increasing increase VBG work_fnploejenbc2raktl46esxm44i 735 13 is be VBZ work_fnploejenbc2raktl46esxm44i 735 14 equivalent equivalent JJ work_fnploejenbc2raktl46esxm44i 735 15 to to IN work_fnploejenbc2raktl46esxm44i 735 16 that that DT work_fnploejenbc2raktl46esxm44i 735 17 of of IN work_fnploejenbc2raktl46esxm44i 735 18 a a DT work_fnploejenbc2raktl46esxm44i 735 19 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 735 20 surjective surjective JJ work_fnploejenbc2raktl46esxm44i 735 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 735 22 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 735 23 , , , work_fnploejenbc2raktl46esxm44i 735 24 increasing increase VBG work_fnploejenbc2raktl46esxm44i 735 25 function function NN work_fnploejenbc2raktl46esxm44i 735 26 h h NN work_fnploejenbc2raktl46esxm44i 735 27 : : : work_fnploejenbc2raktl46esxm44i 735 28 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 735 29 O o UH work_fnploejenbc2raktl46esxm44i 735 30 , , , work_fnploejenbc2raktl46esxm44i 735 31 1 1 CD work_fnploejenbc2raktl46esxm44i 735 32 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 735 33 + + CC work_fnploejenbc2raktl46esxm44i 735 34 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 735 35 O o UH work_fnploejenbc2raktl46esxm44i 735 36 , , , work_fnploejenbc2raktl46esxm44i 735 37 11 11 CD work_fnploejenbc2raktl46esxm44i 735 38 . . . work_fnploejenbc2raktl46esxm44i 736 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 736 2 , , , work_fnploejenbc2raktl46esxm44i 736 3 in in IN work_fnploejenbc2raktl46esxm44i 736 4 view view NN work_fnploejenbc2raktl46esxm44i 736 5 of of IN work_fnploejenbc2raktl46esxm44i 736 6 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 736 7 4.2.1 4.2.1 CD work_fnploejenbc2raktl46esxm44i 736 8 , , , work_fnploejenbc2raktl46esxm44i 736 9 p p NN work_fnploejenbc2raktl46esxm44i 736 10 E e NN work_fnploejenbc2raktl46esxm44i 736 11 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 736 12 0 0 CD work_fnploejenbc2raktl46esxm44i 736 13 , , , work_fnploejenbc2raktl46esxm44i 736 14 1 1 CD work_fnploejenbc2raktl46esxm44i 736 15 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 736 16 d d NN work_fnploejenbc2raktl46esxm44i 736 17 is be VBZ work_fnploejenbc2raktl46esxm44i 736 18 general general JJ work_fnploejenbc2raktl46esxm44i 736 19 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 736 20 if if IN work_fnploejenbc2raktl46esxm44i 736 21 and and CC work_fnploejenbc2raktl46esxm44i 736 22 only only RB work_fnploejenbc2raktl46esxm44i 736 23 if if IN work_fnploejenbc2raktl46esxm44i 736 24 there there EX work_fnploejenbc2raktl46esxm44i 736 25 is be VBZ work_fnploejenbc2raktl46esxm44i 736 26 such such PDT work_fnploejenbc2raktl46esxm44i 736 27 an an DT work_fnploejenbc2raktl46esxm44i 736 28 h h NN work_fnploejenbc2raktl46esxm44i 736 29 for for IN work_fnploejenbc2raktl46esxm44i 736 30 which which WDT work_fnploejenbc2raktl46esxm44i 736 31 h h NN work_fnploejenbc2raktl46esxm44i 736 32 0 0 CD work_fnploejenbc2raktl46esxm44i 736 33 p p NN work_fnploejenbc2raktl46esxm44i 736 34 is be VBZ work_fnploejenbc2raktl46esxm44i 736 35 a a DT work_fnploejenbc2raktl46esxm44i 736 36 finitely finitely RB work_fnploejenbc2raktl46esxm44i 736 37 additive additive JJ work_fnploejenbc2raktl46esxm44i 736 38 probability probability NN work_fnploejenbc2raktl46esxm44i 736 39 measure measure NN work_fnploejenbc2raktl46esxm44i 736 40 . . . work_fnploejenbc2raktl46esxm44i 737 1 In in IN work_fnploejenbc2raktl46esxm44i 737 2 discussing discuss VBG work_fnploejenbc2raktl46esxm44i 737 3 the the DT work_fnploejenbc2raktl46esxm44i 737 4 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 737 5 of of IN work_fnploejenbc2raktl46esxm44i 737 6 belief belief NN work_fnploejenbc2raktl46esxm44i 737 7 functions function NNS work_fnploejenbc2raktl46esxm44i 737 8 on on IN work_fnploejenbc2raktl46esxm44i 737 9 Sz Sz NNP work_fnploejenbc2raktl46esxm44i 737 10 finite finite NN work_fnploejenbc2raktl46esxm44i 737 11 , , , work_fnploejenbc2raktl46esxm44i 737 12 & & CC work_fnploejenbc2raktl46esxm44i 737 13 = = SYM work_fnploejenbc2raktl46esxm44i 737 14 P(Q P(Q NNP work_fnploejenbc2raktl46esxm44i 737 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 737 16 , , , work_fnploejenbc2raktl46esxm44i 737 17 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 737 18 should should MD work_fnploejenbc2raktl46esxm44i 737 19 be be VB work_fnploejenbc2raktl46esxm44i 737 20 noted note VBN work_fnploejenbc2raktl46esxm44i 737 21 that that IN work_fnploejenbc2raktl46esxm44i 737 22 the the DT work_fnploejenbc2raktl46esxm44i 737 23 range range NN work_fnploejenbc2raktl46esxm44i 737 24 of of IN work_fnploejenbc2raktl46esxm44i 737 25 a a DT work_fnploejenbc2raktl46esxm44i 737 26 belief belief NN work_fnploejenbc2raktl46esxm44i 737 27 function function NN work_fnploejenbc2raktl46esxm44i 737 28 is be VBZ work_fnploejenbc2raktl46esxm44i 737 29 not not RB work_fnploejenbc2raktl46esxm44i 737 30 the the DT work_fnploejenbc2raktl46esxm44i 737 31 whole whole JJ work_fnploejenbc2raktl46esxm44i 737 32 inter- inter- NN work_fnploejenbc2raktl46esxm44i 737 33 val val NN work_fnploejenbc2raktl46esxm44i 737 34 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 737 35 O o NN work_fnploejenbc2raktl46esxm44i 737 36 , , , work_fnploejenbc2raktl46esxm44i 737 37 1 1 CD work_fnploejenbc2raktl46esxm44i 737 38 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 737 39 ! ! . work_fnploejenbc2raktl46esxm44i 738 1 As as IN work_fnploejenbc2raktl46esxm44i 738 2 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 738 3 will will MD work_fnploejenbc2raktl46esxm44i 738 4 see see VB work_fnploejenbc2raktl46esxm44i 738 5 , , , work_fnploejenbc2raktl46esxm44i 738 6 as as IN work_fnploejenbc2raktl46esxm44i 738 7 in in IN work_fnploejenbc2raktl46esxm44i 738 8 the the DT work_fnploejenbc2raktl46esxm44i 738 9 case case NN work_fnploejenbc2raktl46esxm44i 738 10 of of IN work_fnploejenbc2raktl46esxm44i 738 11 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 738 12 logics logic NNS work_fnploejenbc2raktl46esxm44i 738 13 , , , work_fnploejenbc2raktl46esxm44i 738 14 some some DT work_fnploejenbc2raktl46esxm44i 738 15 classes class NNS work_fnploejenbc2raktl46esxm44i 738 16 of of IN work_fnploejenbc2raktl46esxm44i 738 17 belief belief NN work_fnploejenbc2raktl46esxm44i 738 18 functions function NNS work_fnploejenbc2raktl46esxm44i 738 19 are be VBP work_fnploejenbc2raktl46esxm44i 738 20 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 738 21 while while IN work_fnploejenbc2raktl46esxm44i 738 22 others other NNS work_fnploejenbc2raktl46esxm44i 738 23 are be VBP work_fnploejenbc2raktl46esxm44i 738 24 not not RB work_fnploejenbc2raktl46esxm44i 738 25 . . . work_fnploejenbc2raktl46esxm44i 739 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 739 2 , , , work_fnploejenbc2raktl46esxm44i 739 3 if if IN work_fnploejenbc2raktl46esxm44i 739 4 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 739 5 ’s ’s POS work_fnploejenbc2raktl46esxm44i 739 6 coherence coherence NN work_fnploejenbc2raktl46esxm44i 739 7 principle principle NN work_fnploejenbc2raktl46esxm44i 739 8 is be VBZ work_fnploejenbc2raktl46esxm44i 739 9 viewed view VBN work_fnploejenbc2raktl46esxm44i 739 10 as as IN work_fnploejenbc2raktl46esxm44i 739 11 a a DT work_fnploejenbc2raktl46esxm44i 739 12 rational rational JJ work_fnploejenbc2raktl46esxm44i 739 13 way way NN work_fnploejenbc2raktl46esxm44i 739 14 of of IN work_fnploejenbc2raktl46esxm44i 739 15 choosing choose VBG work_fnploejenbc2raktl46esxm44i 739 16 “ " `` work_fnploejenbc2raktl46esxm44i 739 17 reasonable reasonable JJ work_fnploejenbc2raktl46esxm44i 739 18 ” " '' work_fnploejenbc2raktl46esxm44i 739 19 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 739 20 measures measure NNS work_fnploejenbc2raktl46esxm44i 739 21 , , , work_fnploejenbc2raktl46esxm44i 739 22 the the DT work_fnploejenbc2raktl46esxm44i 739 23 following follow VBG work_fnploejenbc2raktl46esxm44i 739 24 analysis analysis NN work_fnploejenbc2raktl46esxm44i 739 25 will will MD work_fnploejenbc2raktl46esxm44i 739 26 provide provide VB work_fnploejenbc2raktl46esxm44i 739 27 criteria criterion NNS work_fnploejenbc2raktl46esxm44i 739 28 for for IN work_fnploejenbc2raktl46esxm44i 739 29 selecting select VBG work_fnploejenbc2raktl46esxm44i 739 30 “ " `` work_fnploejenbc2raktl46esxm44i 739 31 good good JJ work_fnploejenbc2raktl46esxm44i 739 32 ” " '' work_fnploejenbc2raktl46esxm44i 739 33 belief belief NN work_fnploejenbc2raktl46esxm44i 739 34 functions function NNS work_fnploejenbc2raktl46esxm44i 739 35 . . . work_fnploejenbc2raktl46esxm44i 740 1 First first RB work_fnploejenbc2raktl46esxm44i 740 2 , , , work_fnploejenbc2raktl46esxm44i 740 3 a a DT work_fnploejenbc2raktl46esxm44i 740 4 simple simple JJ work_fnploejenbc2raktl46esxm44i 740 5 condition condition NN work_fnploejenbc2raktl46esxm44i 740 6 of of IN work_fnploejenbc2raktl46esxm44i 740 7 inadmissibility inadmissibility NN work_fnploejenbc2raktl46esxm44i 740 8 . . . work_fnploejenbc2raktl46esxm44i 741 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 741 2 6.1 6.1 CD work_fnploejenbc2raktl46esxm44i 741 3 . . . work_fnploejenbc2raktl46esxm44i 742 1 Let let VB work_fnploejenbc2raktl46esxm44i 742 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 742 3 0 0 CD work_fnploejenbc2raktl46esxm44i 742 4 , , , work_fnploejenbc2raktl46esxm44i 742 5 d d LS work_fnploejenbc2raktl46esxm44i 742 6 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 742 7 be be VB work_fnploejenbc2raktl46esxm44i 742 8 a a DT work_fnploejenbc2raktl46esxm44i 742 9 measurable measurable JJ work_fnploejenbc2raktl46esxm44i 742 10 space space NN work_fnploejenbc2raktl46esxm44i 742 11 and and CC work_fnploejenbc2raktl46esxm44i 742 12 p p NN work_fnploejenbc2raktl46esxm44i 742 13 E e NN work_fnploejenbc2raktl46esxm44i 742 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 742 15 0 0 CD work_fnploejenbc2raktl46esxm44i 742 16 , , , work_fnploejenbc2raktl46esxm44i 742 17 1 1 CD work_fnploejenbc2raktl46esxm44i 742 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 742 19 d. d. NNP work_fnploejenbc2raktl46esxm44i 742 20 Zf Zf NNP work_fnploejenbc2raktl46esxm44i 742 21 there there EX work_fnploejenbc2raktl46esxm44i 742 22 is be VBZ work_fnploejenbc2raktl46esxm44i 742 23 E e NN work_fnploejenbc2raktl46esxm44i 742 24 , , , work_fnploejenbc2raktl46esxm44i 742 25 FE FE NNP work_fnploejenbc2raktl46esxm44i 742 26 d d NN work_fnploejenbc2raktl46esxm44i 742 27 such such JJ work_fnploejenbc2raktl46esxm44i 742 28 that that WDT work_fnploejenbc2raktl46esxm44i 742 29 I@ I@ NNS work_fnploejenbc2raktl46esxm44i 742 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 742 31 = = NFP work_fnploejenbc2raktl46esxm44i 742 32 P(F p(f NN work_fnploejenbc2raktl46esxm44i 742 33 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 742 34 and and CC work_fnploejenbc2raktl46esxm44i 742 35 AEC AEC NNP work_fnploejenbc2raktl46esxm44i 742 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 742 37 Z Z NNP work_fnploejenbc2raktl46esxm44i 742 38 , , , work_fnploejenbc2raktl46esxm44i 742 39 W w NN work_fnploejenbc2raktl46esxm44i 742 40 ” " '' work_fnploejenbc2raktl46esxm44i 742 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 742 42 > > XX work_fnploejenbc2raktl46esxm44i 742 43 then then RB work_fnploejenbc2raktl46esxm44i 742 44 p p NNP work_fnploejenbc2raktl46esxm44i 742 45 is be VBZ work_fnploejenbc2raktl46esxm44i 742 46 not not RB work_fnploejenbc2raktl46esxm44i 742 47 general general JJ work_fnploejenbc2raktl46esxm44i 742 48 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 742 49 . . . work_fnploejenbc2raktl46esxm44i 743 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 743 2 . . . work_fnploejenbc2raktl46esxm44i 744 1 If if IN work_fnploejenbc2raktl46esxm44i 744 2 /J /J NNP work_fnploejenbc2raktl46esxm44i 744 3 were be VBD work_fnploejenbc2raktl46esxm44i 744 4 general general JJ work_fnploejenbc2raktl46esxm44i 744 5 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 744 6 , , , work_fnploejenbc2raktl46esxm44i 744 7 then then RB work_fnploejenbc2raktl46esxm44i 744 8 there there EX work_fnploejenbc2raktl46esxm44i 744 9 would would MD work_fnploejenbc2raktl46esxm44i 744 10 be be VB work_fnploejenbc2raktl46esxm44i 744 11 an an DT work_fnploejenbc2raktl46esxm44i 744 12 h h NN work_fnploejenbc2raktl46esxm44i 744 13 : : : work_fnploejenbc2raktl46esxm44i 744 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 744 15 0 0 CD work_fnploejenbc2raktl46esxm44i 744 16 , , , work_fnploejenbc2raktl46esxm44i 744 17 l l NN work_fnploejenbc2raktl46esxm44i 744 18 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 744 19 + + CC work_fnploejenbc2raktl46esxm44i 744 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 744 21 O o UH work_fnploejenbc2raktl46esxm44i 744 22 , , , work_fnploejenbc2raktl46esxm44i 744 23 11 11 CD work_fnploejenbc2raktl46esxm44i 744 24 , , , work_fnploejenbc2raktl46esxm44i 744 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 744 26 surjective surjective JJ work_fnploejenbc2raktl46esxm44i 744 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 744 28 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 744 29 , , , work_fnploejenbc2raktl46esxm44i 744 30 increasing increase VBG work_fnploejenbc2raktl46esxm44i 744 31 , , , work_fnploejenbc2raktl46esxm44i 744 32 such such JJ work_fnploejenbc2raktl46esxm44i 744 33 that that IN work_fnploejenbc2raktl46esxm44i 744 34 h h NN work_fnploejenbc2raktl46esxm44i 744 35 0 0 CD work_fnploejenbc2raktl46esxm44i 744 36 , , , work_fnploejenbc2raktl46esxm44i 744 37 u u NNP work_fnploejenbc2raktl46esxm44i 744 38 is be VBZ work_fnploejenbc2raktl46esxm44i 744 39 a a DT work_fnploejenbc2raktl46esxm44i 744 40 finitely finitely RB work_fnploejenbc2raktl46esxm44i 744 41 additive additive JJ work_fnploejenbc2raktl46esxm44i 744 42 probability probability NN work_fnploejenbc2raktl46esxm44i 744 43 measure measure NN work_fnploejenbc2raktl46esxm44i 744 44 . . . work_fnploejenbc2raktl46esxm44i 745 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 745 2 and and CC work_fnploejenbc2raktl46esxm44i 745 3 hence hence RB work_fnploejenbc2raktl46esxm44i 745 4 h h NN work_fnploejenbc2raktl46esxm44i 745 5 0 0 CD work_fnploejenbc2raktl46esxm44i 745 6 , , , work_fnploejenbc2raktl46esxm44i 745 7 u(E u(E '' work_fnploejenbc2raktl46esxm44i 745 8 ” " '' work_fnploejenbc2raktl46esxm44i 745 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 745 10 = = NFP work_fnploejenbc2raktl46esxm44i 745 11 h h NNP work_fnploejenbc2raktl46esxm44i 745 12 0 0 NFP work_fnploejenbc2raktl46esxm44i 745 13 p(FC p(FC NNP work_fnploejenbc2raktl46esxm44i 745 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 745 15 which which WDT work_fnploejenbc2raktl46esxm44i 745 16 contradicts contradict VBZ work_fnploejenbc2raktl46esxm44i 745 17 the the DT work_fnploejenbc2raktl46esxm44i 745 18 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 745 19 , , , work_fnploejenbc2raktl46esxm44i 745 20 since since IN work_fnploejenbc2raktl46esxm44i 745 21 h- h- XX work_fnploejenbc2raktl46esxm44i 745 22 ’ ' '' work_fnploejenbc2raktl46esxm44i 745 23 exists exist VBZ work_fnploejenbc2raktl46esxm44i 745 24 . . . work_fnploejenbc2raktl46esxm44i 746 1 1 1 LS work_fnploejenbc2raktl46esxm44i 746 2 SCORING score VBG work_fnploejenbc2raktl46esxm44i 746 3 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 746 4 TO to IN work_fnploejenbc2raktl46esxm44i 746 5 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 746 6 587 587 CD work_fnploejenbc2raktl46esxm44i 746 7 EXAMPLES example NNS work_fnploejenbc2raktl46esxm44i 746 8 . . . work_fnploejenbc2raktl46esxm44i 747 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 747 2 a a DT work_fnploejenbc2raktl46esxm44i 747 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 747 4 0 0 NFP work_fnploejenbc2raktl46esxm44i 747 5 = = NFP work_fnploejenbc2raktl46esxm44i 747 6 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 747 7 ml ml NNP work_fnploejenbc2raktl46esxm44i 747 8 , , , work_fnploejenbc2raktl46esxm44i 747 9 02 02 CD work_fnploejenbc2raktl46esxm44i 747 10 , , , work_fnploejenbc2raktl46esxm44i 747 11 w3 w3 NNP work_fnploejenbc2raktl46esxm44i 747 12 , , , work_fnploejenbc2raktl46esxm44i 747 13 m4 m4 NNP work_fnploejenbc2raktl46esxm44i 747 14 , , , work_fnploejenbc2raktl46esxm44i 747 15 w5 w5 NNP work_fnploejenbc2raktl46esxm44i 747 16 , , , work_fnploejenbc2raktl46esxm44i 747 17 w6 w6 NNP work_fnploejenbc2raktl46esxm44i 747 18 } } -RRB- work_fnploejenbc2raktl46esxm44i 747 19 . . . work_fnploejenbc2raktl46esxm44i 748 1 Let let VB work_fnploejenbc2raktl46esxm44i 748 2 E e NN work_fnploejenbc2raktl46esxm44i 748 3 = = NFP work_fnploejenbc2raktl46esxm44i 748 4 { { -LRB- work_fnploejenbc2raktl46esxm44i 748 5 wl wl UH work_fnploejenbc2raktl46esxm44i 748 6 , , , work_fnploejenbc2raktl46esxm44i 748 7 w2 w2 JJ work_fnploejenbc2raktl46esxm44i 748 8 } } -RRB- work_fnploejenbc2raktl46esxm44i 748 9 , , , work_fnploejenbc2raktl46esxm44i 748 10 F= F= NNP work_fnploejenbc2raktl46esxm44i 748 11 { { -LRB- work_fnploejenbc2raktl46esxm44i 748 12 03 03 CD work_fnploejenbc2raktl46esxm44i 748 13 , , , work_fnploejenbc2raktl46esxm44i 748 14 w4 w4 NNP work_fnploejenbc2raktl46esxm44i 748 15 } } -RRB- work_fnploejenbc2raktl46esxm44i 748 16 . . . work_fnploejenbc2raktl46esxm44i 749 1 Let let VB work_fnploejenbc2raktl46esxm44i 749 2 m m NN work_fnploejenbc2raktl46esxm44i 749 3 : : : work_fnploejenbc2raktl46esxm44i 749 4 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 749 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 749 6 + + CC work_fnploejenbc2raktl46esxm44i 749 7 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 749 8 0 0 CD work_fnploejenbc2raktl46esxm44i 749 9 , , , work_fnploejenbc2raktl46esxm44i 749 10 l l NN work_fnploejenbc2raktl46esxm44i 749 11 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 749 12 with with IN work_fnploejenbc2raktl46esxm44i 749 13 m(w1 m(w1 NNP work_fnploejenbc2raktl46esxm44i 749 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 749 15 = = NFP work_fnploejenbc2raktl46esxm44i 749 16 m(w3 m(w3 NNP work_fnploejenbc2raktl46esxm44i 749 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 749 18 = = NFP work_fnploejenbc2raktl46esxm44i 749 19 p p NN work_fnploejenbc2raktl46esxm44i 749 20 , , , work_fnploejenbc2raktl46esxm44i 749 21 > > XX work_fnploejenbc2raktl46esxm44i 749 22 0 0 NFP work_fnploejenbc2raktl46esxm44i 749 23 m(w2 m(w2 NNP work_fnploejenbc2raktl46esxm44i 749 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 749 25 = = NFP work_fnploejenbc2raktl46esxm44i 749 26 m(w4 m(w4 NNP work_fnploejenbc2raktl46esxm44i 749 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 749 28 = = NFP work_fnploejenbc2raktl46esxm44i 749 29 p2 p2 NN work_fnploejenbc2raktl46esxm44i 749 30 > > XX work_fnploejenbc2raktl46esxm44i 749 31 0 0 NFP work_fnploejenbc2raktl46esxm44i 749 32 m({w,,w,})=m({w,,o,))=p,>O m({w,,w,})=m({w,,o,))=p,>O NNPS work_fnploejenbc2raktl46esxm44i 749 33 ~({w,~w,~%))=P4~O ~({w,~w,~%))=p4~o NN work_fnploejenbc2raktl46esxm44i 749 34 m({w m({w NNP work_fnploejenbc2raktl46esxm44i 749 35 , , , work_fnploejenbc2raktl46esxm44i 749 36 Y%))=P,>O y%))=p,>o NN work_fnploejenbc2raktl46esxm44i 749 37 ~({%~4))=P,~O ~({%~4))=p,~o NN work_fnploejenbc2raktl46esxm44i 749 38 m(A)=0 m(a)=0 CD work_fnploejenbc2raktl46esxm44i 749 39 for for IN work_fnploejenbc2raktl46esxm44i 749 40 all all DT work_fnploejenbc2raktl46esxm44i 749 41 other other JJ work_fnploejenbc2raktl46esxm44i 749 42 subsets subset NNS work_fnploejenbc2raktl46esxm44i 749 43 and and CC work_fnploejenbc2raktl46esxm44i 749 44 Pl+Pz+P3+P4+P5+!76 Pl+Pz+P3+P4+P5+!76 NNP work_fnploejenbc2raktl46esxm44i 749 45 = = SYM work_fnploejenbc2raktl46esxm44i 749 46 f f XX work_fnploejenbc2raktl46esxm44i 749 47 . . . work_fnploejenbc2raktl46esxm44i 750 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 750 2 have have VBP work_fnploejenbc2raktl46esxm44i 750 3 Bel(E)=Bel(F)=p,+p,+p Bel(E)=Bel(F)=p,+p,+p NNP work_fnploejenbc2raktl46esxm44i 750 4 , , , work_fnploejenbc2raktl46esxm44i 750 5 . . . work_fnploejenbc2raktl46esxm44i 751 1 Bel(Ec)=p,+p,+p,+p4+p Bel(Ec)=p,+p,+p,+p4+p NNP work_fnploejenbc2raktl46esxm44i 751 2 , , , work_fnploejenbc2raktl46esxm44i 751 3 , , , work_fnploejenbc2raktl46esxm44i 751 4 but but CC work_fnploejenbc2raktl46esxm44i 751 5 Bel(F Bel(F NNP work_fnploejenbc2raktl46esxm44i 751 6 ” " '' work_fnploejenbc2raktl46esxm44i 751 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 751 8 = = NFP work_fnploejenbc2raktl46esxm44i 751 9 pl pl NNP work_fnploejenbc2raktl46esxm44i 751 10 + + CC work_fnploejenbc2raktl46esxm44i 751 11 pZ pZ NNP work_fnploejenbc2raktl46esxm44i 751 12 + + SYM work_fnploejenbc2raktl46esxm44i 751 13 p3 p3 NN work_fnploejenbc2raktl46esxm44i 751 14 # # $ work_fnploejenbc2raktl46esxm44i 751 15 Bel(E Bel(E NNP work_fnploejenbc2raktl46esxm44i 751 16 ” " '' work_fnploejenbc2raktl46esxm44i 751 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 751 18 . . . work_fnploejenbc2raktl46esxm44i 752 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 752 2 b b LS work_fnploejenbc2raktl46esxm44i 752 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 752 4 Consider consider VB work_fnploejenbc2raktl46esxm44i 752 5 the the DT work_fnploejenbc2raktl46esxm44i 752 6 degenerate degenerate NN work_fnploejenbc2raktl46esxm44i 752 7 belief belief NN work_fnploejenbc2raktl46esxm44i 752 8 function function NN work_fnploejenbc2raktl46esxm44i 752 9 focused focus VBD work_fnploejenbc2raktl46esxm44i 752 10 on on IN work_fnploejenbc2raktl46esxm44i 752 11 A A NNP work_fnploejenbc2raktl46esxm44i 752 12 , , , work_fnploejenbc2raktl46esxm44i 752 13 Bel,(B Bel,(B NNP work_fnploejenbc2raktl46esxm44i 752 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 752 15 = = NFP work_fnploejenbc2raktl46esxm44i 752 16 1 1 CD work_fnploejenbc2raktl46esxm44i 752 17 if if IN work_fnploejenbc2raktl46esxm44i 752 18 AcB acb NN work_fnploejenbc2raktl46esxm44i 752 19 and and CC work_fnploejenbc2raktl46esxm44i 752 20 zero zero CD work_fnploejenbc2raktl46esxm44i 752 21 otherwise otherwise RB work_fnploejenbc2raktl46esxm44i 752 22 . . . work_fnploejenbc2raktl46esxm44i 753 1 Let let VB work_fnploejenbc2raktl46esxm44i 753 2 B B NNP work_fnploejenbc2raktl46esxm44i 753 3 , , , work_fnploejenbc2raktl46esxm44i 753 4 A a DT work_fnploejenbc2raktl46esxm44i 753 5 # # NN work_fnploejenbc2raktl46esxm44i 753 6 @ @ NN work_fnploejenbc2raktl46esxm44i 753 7 and and CC work_fnploejenbc2raktl46esxm44i 753 8 B b NN work_fnploejenbc2raktl46esxm44i 753 9 , , , work_fnploejenbc2raktl46esxm44i 753 10 A a NN work_fnploejenbc2raktl46esxm44i 753 11 = = SYM work_fnploejenbc2raktl46esxm44i 753 12 @. @. XX work_fnploejenbc2raktl46esxm44i 754 1 Then then RB work_fnploejenbc2raktl46esxm44i 754 2 Bel,(B Bel,(B NNP work_fnploejenbc2raktl46esxm44i 754 3 , , , work_fnploejenbc2raktl46esxm44i 754 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 754 5 = = NFP work_fnploejenbc2raktl46esxm44i 754 6 Bel,(B bel,(b XX work_fnploejenbc2raktl46esxm44i 754 7 , , , work_fnploejenbc2raktl46esxm44i 754 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 754 9 = = NFP work_fnploejenbc2raktl46esxm44i 754 10 0 0 NFP work_fnploejenbc2raktl46esxm44i 754 11 , , , work_fnploejenbc2raktl46esxm44i 754 12 but but CC work_fnploejenbc2raktl46esxm44i 754 13 Bel,(B;)=O bel,(b;)=o NN work_fnploejenbc2raktl46esxm44i 754 14 # # $ work_fnploejenbc2raktl46esxm44i 754 15 1 1 CD work_fnploejenbc2raktl46esxm44i 754 16 = = SYM work_fnploejenbc2raktl46esxm44i 754 17 Bel,(B bel,(b NN work_fnploejenbc2raktl46esxm44i 754 18 ” " '' work_fnploejenbc2raktl46esxm44i 754 19 , , , work_fnploejenbc2raktl46esxm44i 754 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 754 21 . . . work_fnploejenbc2raktl46esxm44i 755 1 The the DT work_fnploejenbc2raktl46esxm44i 755 2 hypothesis hypothesis NN work_fnploejenbc2raktl46esxm44i 755 3 of of IN work_fnploejenbc2raktl46esxm44i 755 4 Theorem theorem NN work_fnploejenbc2raktl46esxm44i 755 5 6.1 6.1 CD work_fnploejenbc2raktl46esxm44i 755 6 expresses express VBZ work_fnploejenbc2raktl46esxm44i 755 7 the the DT work_fnploejenbc2raktl46esxm44i 755 8 fact fact NN work_fnploejenbc2raktl46esxm44i 755 9 that that IN work_fnploejenbc2raktl46esxm44i 755 10 p(E p(E NFP work_fnploejenbc2raktl46esxm44i 755 11 ” " '' work_fnploejenbc2raktl46esxm44i 755 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 755 13 is be VBZ work_fnploejenbc2raktl46esxm44i 755 14 not not RB work_fnploejenbc2raktl46esxm44i 755 15 a a DT work_fnploejenbc2raktl46esxm44i 755 16 function function NN work_fnploejenbc2raktl46esxm44i 755 17 of of IN work_fnploejenbc2raktl46esxm44i 755 18 p(E p(e NN work_fnploejenbc2raktl46esxm44i 755 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 755 20 . . . work_fnploejenbc2raktl46esxm44i 756 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 756 2 , , , work_fnploejenbc2raktl46esxm44i 756 3 an an DT work_fnploejenbc2raktl46esxm44i 756 4 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 756 5 measure measure NN work_fnploejenbc2raktl46esxm44i 756 6 p p NN work_fnploejenbc2raktl46esxm44i 756 7 is be VBZ work_fnploejenbc2raktl46esxm44i 756 8 not not RB work_fnploejenbc2raktl46esxm44i 756 9 general general JJ work_fnploejenbc2raktl46esxm44i 756 10 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 756 11 if if IN work_fnploejenbc2raktl46esxm44i 756 12 there there EX work_fnploejenbc2raktl46esxm44i 756 13 is be VBZ work_fnploejenbc2raktl46esxm44i 756 14 no no DT work_fnploejenbc2raktl46esxm44i 756 15 rp rp NN work_fnploejenbc2raktl46esxm44i 756 16 : : : work_fnploejenbc2raktl46esxm44i 756 17 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 756 18 0 0 CD work_fnploejenbc2raktl46esxm44i 756 19 , , , work_fnploejenbc2raktl46esxm44i 756 20 l l NN work_fnploejenbc2raktl46esxm44i 756 21 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 756 22 + + CC work_fnploejenbc2raktl46esxm44i 756 23 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 756 24 0 0 CD work_fnploejenbc2raktl46esxm44i 756 25 , , , work_fnploejenbc2raktl46esxm44i 756 26 l l NN work_fnploejenbc2raktl46esxm44i 756 27 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 756 28 such such JJ work_fnploejenbc2raktl46esxm44i 756 29 that that IN work_fnploejenbc2raktl46esxm44i 756 30 YE YE NNP work_fnploejenbc2raktl46esxm44i 756 31 , , , work_fnploejenbc2raktl46esxm44i 756 32 FE FE NNP work_fnploejenbc2raktl46esxm44i 756 33 d d NNP work_fnploejenbc2raktl46esxm44i 756 34 , , , work_fnploejenbc2raktl46esxm44i 756 35 AE AE NNP work_fnploejenbc2raktl46esxm44i 756 36 ” " '' work_fnploejenbc2raktl46esxm44i 756 37 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 756 38 -F -F , work_fnploejenbc2raktl46esxm44i 756 39 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 756 40 = = NFP work_fnploejenbc2raktl46esxm44i 756 41 cpbWl cpbWl NFP work_fnploejenbc2raktl46esxm44i 756 42 F F NNP work_fnploejenbc2raktl46esxm44i 756 43 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 756 44 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 756 45 . . . work_fnploejenbc2raktl46esxm44i 757 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 757 2 * * NFP work_fnploejenbc2raktl46esxm44i 757 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 757 4 A a DT work_fnploejenbc2raktl46esxm44i 757 5 typical typical JJ work_fnploejenbc2raktl46esxm44i 757 6 example example NN work_fnploejenbc2raktl46esxm44i 757 7 is be VBZ work_fnploejenbc2raktl46esxm44i 757 8 the the DT work_fnploejenbc2raktl46esxm44i 757 9 Max Max NNP work_fnploejenbc2raktl46esxm44i 757 10 - - HYPH work_fnploejenbc2raktl46esxm44i 757 11 possibility possibility NN work_fnploejenbc2raktl46esxm44i 757 12 measure measure NN work_fnploejenbc2raktl46esxm44i 757 13 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 757 14 which which WDT work_fnploejenbc2raktl46esxm44i 757 15 explains explain VBZ work_fnploejenbc2raktl46esxm44i 757 16 its -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 757 17 inadmissibility inadmissibility NN work_fnploejenbc2raktl46esxm44i 757 18 mentioned mention VBN work_fnploejenbc2raktl46esxm44i 757 19 in in IN work_fnploejenbc2raktl46esxm44i 757 20 Section section NN work_fnploejenbc2raktl46esxm44i 757 21 5 5 CD work_fnploejenbc2raktl46esxm44i 757 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 757 23 . . . work_fnploejenbc2raktl46esxm44i 758 1 The the DT work_fnploejenbc2raktl46esxm44i 758 2 relation relation NN work_fnploejenbc2raktl46esxm44i 758 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 758 4 * * NFP work_fnploejenbc2raktl46esxm44i 758 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 758 6 always always RB work_fnploejenbc2raktl46esxm44i 758 7 holds hold VBZ work_fnploejenbc2raktl46esxm44i 758 8 for for IN work_fnploejenbc2raktl46esxm44i 758 9 probability probability NN work_fnploejenbc2raktl46esxm44i 758 10 measures measure NNS work_fnploejenbc2raktl46esxm44i 758 11 , , , work_fnploejenbc2raktl46esxm44i 758 12 but but CC work_fnploejenbc2raktl46esxm44i 758 13 as as IN work_fnploejenbc2raktl46esxm44i 758 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 758 15 have have VBP work_fnploejenbc2raktl46esxm44i 758 16 just just RB work_fnploejenbc2raktl46esxm44i 758 17 seen see VBN work_fnploejenbc2raktl46esxm44i 758 18 , , , work_fnploejenbc2raktl46esxm44i 758 19 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 758 20 * * NFP work_fnploejenbc2raktl46esxm44i 758 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 758 22 might may MD work_fnploejenbc2raktl46esxm44i 758 23 fail fail VB work_fnploejenbc2raktl46esxm44i 758 24 in in IN work_fnploejenbc2raktl46esxm44i 758 25 the the DT work_fnploejenbc2raktl46esxm44i 758 26 case case NN work_fnploejenbc2raktl46esxm44i 758 27 of of IN work_fnploejenbc2raktl46esxm44i 758 28 belief belief NN work_fnploejenbc2raktl46esxm44i 758 29 functions function NNS work_fnploejenbc2raktl46esxm44i 758 30 . . . work_fnploejenbc2raktl46esxm44i 759 1 The the DT work_fnploejenbc2raktl46esxm44i 759 2 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 759 3 6.1 6.1 CD work_fnploejenbc2raktl46esxm44i 759 4 provides provide VBZ work_fnploejenbc2raktl46esxm44i 759 5 a a DT work_fnploejenbc2raktl46esxm44i 759 6 necessary necessary JJ work_fnploejenbc2raktl46esxm44i 759 7 condition condition NN work_fnploejenbc2raktl46esxm44i 759 8 for for IN work_fnploejenbc2raktl46esxm44i 759 9 general general JJ work_fnploejenbc2raktl46esxm44i 759 10 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 759 11 : : : work_fnploejenbc2raktl46esxm44i 759 12 If if IN work_fnploejenbc2raktl46esxm44i 759 13 p p NN work_fnploejenbc2raktl46esxm44i 759 14 is be VBZ work_fnploejenbc2raktl46esxm44i 759 15 general general JJ work_fnploejenbc2raktl46esxm44i 759 16 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 759 17 , , , work_fnploejenbc2raktl46esxm44i 759 18 then then RB work_fnploejenbc2raktl46esxm44i 759 19 necessarily necessarily RB work_fnploejenbc2raktl46esxm44i 759 20 , , , work_fnploejenbc2raktl46esxm44i 759 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 759 22 * * NFP work_fnploejenbc2raktl46esxm44i 759 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 759 24 must must MD work_fnploejenbc2raktl46esxm44i 759 25 hold hold VB work_fnploejenbc2raktl46esxm44i 759 26 . . . work_fnploejenbc2raktl46esxm44i 760 1 The the DT work_fnploejenbc2raktl46esxm44i 760 2 following follow VBG work_fnploejenbc2raktl46esxm44i 760 3 result result NN work_fnploejenbc2raktl46esxm44i 760 4 provides provide VBZ work_fnploejenbc2raktl46esxm44i 760 5 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 760 6 conditions condition NNS work_fnploejenbc2raktl46esxm44i 760 7 for for IN work_fnploejenbc2raktl46esxm44i 760 8 general general JJ work_fnploejenbc2raktl46esxm44i 760 9 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 760 10 of of IN work_fnploejenbc2raktl46esxm44i 760 11 belief belief NN work_fnploejenbc2raktl46esxm44i 760 12 functions function NNS work_fnploejenbc2raktl46esxm44i 760 13 . . . work_fnploejenbc2raktl46esxm44i 761 1 THEOREM theorem NN work_fnploejenbc2raktl46esxm44i 761 2 6.2 6.2 CD work_fnploejenbc2raktl46esxm44i 761 3 . . . work_fnploejenbc2raktl46esxm44i 762 1 Let let VB work_fnploejenbc2raktl46esxm44i 762 2 l2 l2 NN work_fnploejenbc2raktl46esxm44i 762 3 be be VB work_fnploejenbc2raktl46esxm44i 762 4 finite finite JJ work_fnploejenbc2raktl46esxm44i 762 5 and and CC work_fnploejenbc2raktl46esxm44i 762 6 d d JJ work_fnploejenbc2raktl46esxm44i 762 7 = = SYM work_fnploejenbc2raktl46esxm44i 762 8 P(Q p(q NN work_fnploejenbc2raktl46esxm44i 762 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 762 10 . . . work_fnploejenbc2raktl46esxm44i 763 1 409/159/2 409/159/2 LS work_fnploejenbc2raktl46esxm44i 763 2 - - SYM work_fnploejenbc2raktl46esxm44i 763 3 20 20 CD work_fnploejenbc2raktl46esxm44i 763 4 588 588 CD work_fnploejenbc2raktl46esxm44i 763 5 GOODMAN GOODMAN NNS work_fnploejenbc2raktl46esxm44i 763 6 , , , work_fnploejenbc2raktl46esxm44i 763 7 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 763 8 , , , work_fnploejenbc2raktl46esxm44i 763 9 AND and CC work_fnploejenbc2raktl46esxm44i 763 10 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 763 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 763 12 i i NN work_fnploejenbc2raktl46esxm44i 763 13 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 763 14 Zf Zf NNP work_fnploejenbc2raktl46esxm44i 763 15 Bel Bel NNP work_fnploejenbc2raktl46esxm44i 763 16 : : : work_fnploejenbc2raktl46esxm44i 763 17 J J NNP work_fnploejenbc2raktl46esxm44i 763 18 ? ? . work_fnploejenbc2raktl46esxm44i 764 1 + + NFP work_fnploejenbc2raktl46esxm44i 764 2 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 764 3 O o UH work_fnploejenbc2raktl46esxm44i 764 4 , , , work_fnploejenbc2raktl46esxm44i 764 5 l l NN work_fnploejenbc2raktl46esxm44i 764 6 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 764 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 764 8 extended extend VBN work_fnploejenbc2raktl46esxm44i 764 9 to to IN work_fnploejenbc2raktl46esxm44i 764 10 d d XX work_fnploejenbc2raktl46esxm44i 764 11 as as IN work_fnploejenbc2raktl46esxm44i 764 12 mentioned mention VBN work_fnploejenbc2raktl46esxm44i 764 13 previously previously RB work_fnploejenbc2raktl46esxm44i 764 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 764 15 is be VBZ work_fnploejenbc2raktl46esxm44i 764 16 such such JJ work_fnploejenbc2raktl46esxm44i 764 17 that that IN work_fnploejenbc2raktl46esxm44i 764 18 VE VE NNP work_fnploejenbc2raktl46esxm44i 764 19 , , , work_fnploejenbc2raktl46esxm44i 764 20 FE FE NNP work_fnploejenbc2raktl46esxm44i 764 21 s s POS work_fnploejenbc2raktl46esxm44i 764 22 # # NNP work_fnploejenbc2raktl46esxm44i 764 23 ‘ ' '' work_fnploejenbc2raktl46esxm44i 764 24 , , , work_fnploejenbc2raktl46esxm44i 764 25 with with IN work_fnploejenbc2raktl46esxm44i 764 26 Bel(F Bel(F NNP work_fnploejenbc2raktl46esxm44i 764 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 764 28 > > XX work_fnploejenbc2raktl46esxm44i 764 29 0 0 NFP work_fnploejenbc2raktl46esxm44i 764 30 , , , work_fnploejenbc2raktl46esxm44i 764 31 Bel(E’IF)=q[Bel(ElF Bel(E’IF)=q[Bel(ElF NNP work_fnploejenbc2raktl46esxm44i 764 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 764 33 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 764 34 , , , work_fnploejenbc2raktl46esxm44i 764 35 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 764 36 * * NFP work_fnploejenbc2raktl46esxm44i 764 37 * * NFP work_fnploejenbc2raktl46esxm44i 764 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 764 39 where where WRB work_fnploejenbc2raktl46esxm44i 764 40 cp cp NNP work_fnploejenbc2raktl46esxm44i 764 41 : : : work_fnploejenbc2raktl46esxm44i 764 42 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 764 43 0 0 CD work_fnploejenbc2raktl46esxm44i 764 44 , , , work_fnploejenbc2raktl46esxm44i 764 45 11 11 CD work_fnploejenbc2raktl46esxm44i 764 46 + + SYM work_fnploejenbc2raktl46esxm44i 764 47 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 764 48 O o NN work_fnploejenbc2raktl46esxm44i 764 49 , , , work_fnploejenbc2raktl46esxm44i 764 50 1 1 CD work_fnploejenbc2raktl46esxm44i 764 51 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 764 52 is be VBZ work_fnploejenbc2raktl46esxm44i 764 53 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 764 54 , , , work_fnploejenbc2raktl46esxm44i 764 55 then then RB work_fnploejenbc2raktl46esxm44i 764 56 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 764 57 is be VBZ work_fnploejenbc2raktl46esxm44i 764 58 general general JJ work_fnploejenbc2raktl46esxm44i 764 59 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 764 60 . . . work_fnploejenbc2raktl46esxm44i 765 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 765 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 765 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 765 4 For for IN work_fnploejenbc2raktl46esxm44i 765 5 each each DT work_fnploejenbc2raktl46esxm44i 765 6 , , , work_fnploejenbc2raktl46esxm44i 765 7 r r NNP work_fnploejenbc2raktl46esxm44i 765 8 B b NN work_fnploejenbc2raktl46esxm44i 765 9 1 1 CD work_fnploejenbc2raktl46esxm44i 765 10 and and CC work_fnploejenbc2raktl46esxm44i 765 11 Q Q NNP work_fnploejenbc2raktl46esxm44i 765 12 : : : work_fnploejenbc2raktl46esxm44i 765 13 STJ STJ NNP work_fnploejenbc2raktl46esxm44i 765 14 ’ ' '' work_fnploejenbc2raktl46esxm44i 765 15 + + CC work_fnploejenbc2raktl46esxm44i 765 16 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 765 17 0 0 CD work_fnploejenbc2raktl46esxm44i 765 18 , , , work_fnploejenbc2raktl46esxm44i 765 19 1 1 LS work_fnploejenbc2raktl46esxm44i 765 20 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 765 21 a a DT work_fnploejenbc2raktl46esxm44i 765 22 finitely finitely RB work_fnploejenbc2raktl46esxm44i 765 23 additive additive JJ work_fnploejenbc2raktl46esxm44i 765 24 probability probability NN work_fnploejenbc2raktl46esxm44i 765 25 measure measure NN work_fnploejenbc2raktl46esxm44i 765 26 , , , work_fnploejenbc2raktl46esxm44i 765 27 Qr Qr NNP work_fnploejenbc2raktl46esxm44i 765 28 is be VBZ work_fnploejenbc2raktl46esxm44i 765 29 a a DT work_fnploejenbc2raktl46esxm44i 765 30 belief belief NN work_fnploejenbc2raktl46esxm44i 765 31 function function NN work_fnploejenbc2raktl46esxm44i 765 32 on on IN work_fnploejenbc2raktl46esxm44i 765 33 zl zl NNP work_fnploejenbc2raktl46esxm44i 765 34 which which WDT work_fnploejenbc2raktl46esxm44i 765 35 is be VBZ work_fnploejenbc2raktl46esxm44i 765 36 general general JJ work_fnploejenbc2raktl46esxm44i 765 37 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 765 38 . . . work_fnploejenbc2raktl46esxm44i 766 1 Proof proof NN work_fnploejenbc2raktl46esxm44i 766 2 : : : work_fnploejenbc2raktl46esxm44i 766 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 766 4 i i NN work_fnploejenbc2raktl46esxm44i 766 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 766 6 The the DT work_fnploejenbc2raktl46esxm44i 766 7 proof proof NN work_fnploejenbc2raktl46esxm44i 766 8 of of IN work_fnploejenbc2raktl46esxm44i 766 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 766 10 i i NN work_fnploejenbc2raktl46esxm44i 766 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 766 12 follows follow VBZ work_fnploejenbc2raktl46esxm44i 766 13 from from IN work_fnploejenbc2raktl46esxm44i 766 14 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 766 15 S S NNP work_fnploejenbc2raktl46esxm44i 766 16 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 766 17 : : : work_fnploejenbc2raktl46esxm44i 766 18 let let VB work_fnploejenbc2raktl46esxm44i 766 19 E e NN work_fnploejenbc2raktl46esxm44i 766 20 , , , work_fnploejenbc2raktl46esxm44i 766 21 , , , work_fnploejenbc2raktl46esxm44i 766 22 E e NN work_fnploejenbc2raktl46esxm44i 766 23 , , , work_fnploejenbc2raktl46esxm44i 766 24 , , , work_fnploejenbc2raktl46esxm44i 766 25 FE FE NNP work_fnploejenbc2raktl46esxm44i 766 26 & & CC work_fnploejenbc2raktl46esxm44i 766 27 with with IN work_fnploejenbc2raktl46esxm44i 766 28 Bel(F Bel(F NNP work_fnploejenbc2raktl46esxm44i 766 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 766 30 > > XX work_fnploejenbc2raktl46esxm44i 766 31 0 0 NFP work_fnploejenbc2raktl46esxm44i 766 32 . . . work_fnploejenbc2raktl46esxm44i 767 1 Using use VBG work_fnploejenbc2raktl46esxm44i 767 2 the the DT work_fnploejenbc2raktl46esxm44i 767 3 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 767 4 extension extension NN work_fnploejenbc2raktl46esxm44i 767 5 of of IN work_fnploejenbc2raktl46esxm44i 767 6 Bel Bel NNP work_fnploejenbc2raktl46esxm44i 767 7 , , , work_fnploejenbc2raktl46esxm44i 767 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 767 9 have have VBP work_fnploejenbc2raktl46esxm44i 767 10 where where WRB work_fnploejenbc2raktl46esxm44i 767 11 A a NN work_fnploejenbc2raktl46esxm44i 767 12 : : : work_fnploejenbc2raktl46esxm44i 767 13 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 767 14 0 0 CD work_fnploejenbc2raktl46esxm44i 767 15 , , , work_fnploejenbc2raktl46esxm44i 767 16 l l NN work_fnploejenbc2raktl46esxm44i 767 17 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 767 18 * * NFP work_fnploejenbc2raktl46esxm44i 767 19 + + CC work_fnploejenbc2raktl46esxm44i 767 20 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 767 21 0 0 CD work_fnploejenbc2raktl46esxm44i 767 22 , , , work_fnploejenbc2raktl46esxm44i 767 23 11 11 CD work_fnploejenbc2raktl46esxm44i 767 24 , , , work_fnploejenbc2raktl46esxm44i 767 25 A(x a(x NN work_fnploejenbc2raktl46esxm44i 767 26 , , , work_fnploejenbc2raktl46esxm44i 767 27 y y NNP work_fnploejenbc2raktl46esxm44i 767 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 767 29 = = VBZ work_fnploejenbc2raktl46esxm44i 767 30 xy xy NNP work_fnploejenbc2raktl46esxm44i 767 31 . . . work_fnploejenbc2raktl46esxm44i 768 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 768 2 also also RB work_fnploejenbc2raktl46esxm44i 768 3 have have VBP work_fnploejenbc2raktl46esxm44i 768 4 Bel(F Bel(F NNP work_fnploejenbc2raktl46esxm44i 768 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 768 6 F f NN work_fnploejenbc2raktl46esxm44i 768 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 768 8 = = SYM work_fnploejenbc2raktl46esxm44i 768 9 1 1 CD work_fnploejenbc2raktl46esxm44i 768 10 . . . work_fnploejenbc2raktl46esxm44i 769 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 769 2 , , , work_fnploejenbc2raktl46esxm44i 769 3 together together RB work_fnploejenbc2raktl46esxm44i 769 4 with with IN work_fnploejenbc2raktl46esxm44i 769 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 769 6 * * NFP work_fnploejenbc2raktl46esxm44i 769 7 * * NFP work_fnploejenbc2raktl46esxm44i 769 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 769 9 , , , work_fnploejenbc2raktl46esxm44i 769 10 Bel Bel NNP work_fnploejenbc2raktl46esxm44i 769 11 ’ ' '' work_fnploejenbc2raktl46esxm44i 769 12 is be VBZ work_fnploejenbc2raktl46esxm44i 769 13 a a DT work_fnploejenbc2raktl46esxm44i 769 14 finitely finitely RB work_fnploejenbc2raktl46esxm44i 769 15 additive additive JJ work_fnploejenbc2raktl46esxm44i 769 16 probability probability NN work_fnploejenbc2raktl46esxm44i 769 17 measure measure NN work_fnploejenbc2raktl46esxm44i 769 18 on on IN work_fnploejenbc2raktl46esxm44i 769 19 d d NN work_fnploejenbc2raktl46esxm44i 769 20 for for IN work_fnploejenbc2raktl46esxm44i 769 21 some some DT work_fnploejenbc2raktl46esxm44i 769 22 positive positive JJ work_fnploejenbc2raktl46esxm44i 769 23 real real JJ work_fnploejenbc2raktl46esxm44i 769 24 r. r. NN work_fnploejenbc2raktl46esxm44i 769 25 Since Since NNP work_fnploejenbc2raktl46esxm44i 769 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 769 27 . . . work_fnploejenbc2raktl46esxm44i 770 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 770 2 ‘ ' `` work_fnploejenbc2raktl46esxm44i 770 3 : : : work_fnploejenbc2raktl46esxm44i 770 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 770 5 0 0 CD work_fnploejenbc2raktl46esxm44i 770 6 , , , work_fnploejenbc2raktl46esxm44i 770 7 l l NN work_fnploejenbc2raktl46esxm44i 770 8 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 770 9 -+ -+ . work_fnploejenbc2raktl46esxm44i 770 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 770 11 0 0 CD work_fnploejenbc2raktl46esxm44i 770 12 , , , work_fnploejenbc2raktl46esxm44i 770 13 l l NN work_fnploejenbc2raktl46esxm44i 770 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 770 15 is be VBZ work_fnploejenbc2raktl46esxm44i 770 16 surjective surjective JJ work_fnploejenbc2raktl46esxm44i 770 17 , , , work_fnploejenbc2raktl46esxm44i 770 18 continuous continuous JJ work_fnploejenbc2raktl46esxm44i 770 19 and and CC work_fnploejenbc2raktl46esxm44i 770 20 increasing increasing JJ work_fnploejenbc2raktl46esxm44i 770 21 , , , work_fnploejenbc2raktl46esxm44i 770 22 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 770 23 is be VBZ work_fnploejenbc2raktl46esxm44i 770 24 general general JJ work_fnploejenbc2raktl46esxm44i 770 25 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 770 26 . . . work_fnploejenbc2raktl46esxm44i 771 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 771 2 ii ii NNP work_fnploejenbc2raktl46esxm44i 771 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 771 4 For for IN work_fnploejenbc2raktl46esxm44i 771 5 r r NN work_fnploejenbc2raktl46esxm44i 771 6 > > NN work_fnploejenbc2raktl46esxm44i 771 7 1 1 CD work_fnploejenbc2raktl46esxm44i 771 8 and and CC work_fnploejenbc2raktl46esxm44i 771 9 Q Q NNP work_fnploejenbc2raktl46esxm44i 771 10 a a DT work_fnploejenbc2raktl46esxm44i 771 11 finitely finitely RB work_fnploejenbc2raktl46esxm44i 771 12 additive additive JJ work_fnploejenbc2raktl46esxm44i 771 13 probability probability NN work_fnploejenbc2raktl46esxm44i 771 14 measure measure NN work_fnploejenbc2raktl46esxm44i 771 15 in in IN work_fnploejenbc2raktl46esxm44i 771 16 52 52 CD work_fnploejenbc2raktl46esxm44i 771 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 771 18 finite finite NNP work_fnploejenbc2raktl46esxm44i 771 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 771 20 , , , work_fnploejenbc2raktl46esxm44i 771 21 Q Q NNP work_fnploejenbc2raktl46esxm44i 771 22 ’ ' '' work_fnploejenbc2raktl46esxm44i 771 23 is be VBZ work_fnploejenbc2raktl46esxm44i 771 24 a a DT work_fnploejenbc2raktl46esxm44i 771 25 belief belief NN work_fnploejenbc2raktl46esxm44i 771 26 function function NN work_fnploejenbc2raktl46esxm44i 771 27 if if IN work_fnploejenbc2raktl46esxm44i 771 28 VAGQ VAGQ NNP work_fnploejenbc2raktl46esxm44i 771 29 , , , work_fnploejenbc2raktl46esxm44i 771 30 m,(A)= m,(A)= NFP work_fnploejenbc2raktl46esxm44i 771 31 c c NN work_fnploejenbc2raktl46esxm44i 771 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 771 33 -l)lA -l)la NN work_fnploejenbc2raktl46esxm44i 771 34 - - HYPH work_fnploejenbc2raktl46esxm44i 771 35 BI BI NNP work_fnploejenbc2raktl46esxm44i 771 36 Q’(B)>O. Q’(B)>O. NNP work_fnploejenbc2raktl46esxm44i 772 1 BEA BEA NNP work_fnploejenbc2raktl46esxm44i 772 2 For for IN work_fnploejenbc2raktl46esxm44i 772 3 JAI JAI NNP work_fnploejenbc2raktl46esxm44i 772 4 = = SYM work_fnploejenbc2raktl46esxm44i 772 5 0 0 NFP work_fnploejenbc2raktl46esxm44i 772 6 , , , work_fnploejenbc2raktl46esxm44i 772 7 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 772 8 , , , work_fnploejenbc2raktl46esxm44i 772 9 A=@ a=@ UH work_fnploejenbc2raktl46esxm44i 772 10 , , , work_fnploejenbc2raktl46esxm44i 772 11 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 772 12 have have VBP work_fnploejenbc2raktl46esxm44i 772 13 m,(@)=O. m,(@)=O. VBN work_fnploejenbc2raktl46esxm44i 773 1 For for IN work_fnploejenbc2raktl46esxm44i 773 2 IAl IAl NNS work_fnploejenbc2raktl46esxm44i 773 3 = = SYM work_fnploejenbc2raktl46esxm44i 773 4 1 1 CD work_fnploejenbc2raktl46esxm44i 773 5 , , , work_fnploejenbc2raktl46esxm44i 773 6 say say VB work_fnploejenbc2raktl46esxm44i 773 7 , , , work_fnploejenbc2raktl46esxm44i 773 8 A a NN work_fnploejenbc2raktl46esxm44i 773 9 = = NFP work_fnploejenbc2raktl46esxm44i 773 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 773 11 or or CC work_fnploejenbc2raktl46esxm44i 773 12 > > XX work_fnploejenbc2raktl46esxm44i 773 13 , , , work_fnploejenbc2raktl46esxm44i 773 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 773 15 have have VBP work_fnploejenbc2raktl46esxm44i 773 16 m,(~~l~)=Q’(~~l~)~O. m,(~~l~)=Q’(~~l~)~O. NNP work_fnploejenbc2raktl46esxm44i 774 1 For for IN work_fnploejenbc2raktl46esxm44i 774 2 IAJ iaj NN work_fnploejenbc2raktl46esxm44i 774 3 = = SYM work_fnploejenbc2raktl46esxm44i 774 4 2 2 CD work_fnploejenbc2raktl46esxm44i 774 5 , , , work_fnploejenbc2raktl46esxm44i 774 6 say say VBP work_fnploejenbc2raktl46esxm44i 774 7 A= A= NNP work_fnploejenbc2raktl46esxm44i 774 8 { { -LRB- work_fnploejenbc2raktl46esxm44i 774 9 CD CD NNP work_fnploejenbc2raktl46esxm44i 774 10 , , , work_fnploejenbc2raktl46esxm44i 774 11 , , , work_fnploejenbc2raktl46esxm44i 774 12 co co NN work_fnploejenbc2raktl46esxm44i 774 13 , , , work_fnploejenbc2raktl46esxm44i 774 14 } } -RRB- work_fnploejenbc2raktl46esxm44i 774 15 , , , work_fnploejenbc2raktl46esxm44i 774 16 mr({~~~~2~)=Q mr({~~~~2~)=Q NNP work_fnploejenbc2raktl46esxm44i 774 17 ' ' '' work_fnploejenbc2raktl46esxm44i 774 18 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 774 19 { { -LRB- work_fnploejenbc2raktl46esxm44i 774 20 o,,w,>,-Q'((ol>,-Q'((~2 o,,w,>,-Q'((ol>,-Q'((~2 : work_fnploejenbc2raktl46esxm44i 774 21 } } -RRB- work_fnploejenbc2raktl46esxm44i 774 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 774 23 = = SYM work_fnploejenbc2raktl46esxm44i 774 24 CQ({o,>,+Q({o,>,lr CQ({o,>,+Q({o,>,lr NNP work_fnploejenbc2raktl46esxm44i 774 25 - - HYPH work_fnploejenbc2raktl46esxm44i 774 26 Q'({o Q'({o NNP work_fnploejenbc2raktl46esxm44i 774 27 , , , work_fnploejenbc2raktl46esxm44i 774 28 > > XX work_fnploejenbc2raktl46esxm44i 774 29 > > XX work_fnploejenbc2raktl46esxm44i 774 30 -QW4)N. -QW4)N. : work_fnploejenbc2raktl46esxm44i 774 31 Since since IN work_fnploejenbc2raktl46esxm44i 774 32 the the DT work_fnploejenbc2raktl46esxm44i 774 33 function function NN work_fnploejenbc2raktl46esxm44i 774 34 u(tl u(tl PRP work_fnploejenbc2raktl46esxm44i 774 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 774 36 = = NFP work_fnploejenbc2raktl46esxm44i 774 37 CZ CZ NNP work_fnploejenbc2raktl46esxm44i 774 38 ” " '' work_fnploejenbc2raktl46esxm44i 774 39 + + CC work_fnploejenbc2raktl46esxm44i 774 40 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 774 41 1 1 CD work_fnploejenbc2raktl46esxm44i 774 42 - - HYPH work_fnploejenbc2raktl46esxm44i 774 43 a)l a)l NNP work_fnploejenbc2raktl46esxm44i 774 44 is be VBZ work_fnploejenbc2raktl46esxm44i 774 45 such such JJ work_fnploejenbc2raktl46esxm44i 774 46 that that IN work_fnploejenbc2raktl46esxm44i 774 47 u(O u(o LS work_fnploejenbc2raktl46esxm44i 774 48 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 774 49 = = NFP work_fnploejenbc2raktl46esxm44i 774 50 u u NNP work_fnploejenbc2raktl46esxm44i 774 51 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 774 52 1 1 CD work_fnploejenbc2raktl46esxm44i 774 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 774 54 = = SYM work_fnploejenbc2raktl46esxm44i 774 55 1 1 CD work_fnploejenbc2raktl46esxm44i 774 56 and and CC work_fnploejenbc2raktl46esxm44i 774 57 u u NNP work_fnploejenbc2raktl46esxm44i 774 58 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 774 59 . . . work_fnploejenbc2raktl46esxm44i 774 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 775 1 is be VBZ work_fnploejenbc2raktl46esxm44i 775 2 convex convex NNP work_fnploejenbc2raktl46esxm44i 775 3 with with IN work_fnploejenbc2raktl46esxm44i 775 4 minimum minimum NN work_fnploejenbc2raktl46esxm44i 775 5 at at IN work_fnploejenbc2raktl46esxm44i 775 6 LI LI NNP work_fnploejenbc2raktl46esxm44i 775 7 = = SYM work_fnploejenbc2raktl46esxm44i 775 8 i i NN work_fnploejenbc2raktl46esxm44i 775 9 , , , work_fnploejenbc2raktl46esxm44i 775 10 u(f u(f NNP work_fnploejenbc2raktl46esxm44i 775 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 775 12 < < XX work_fnploejenbc2raktl46esxm44i 775 13 1 1 CD work_fnploejenbc2raktl46esxm44i 775 14 , , , work_fnploejenbc2raktl46esxm44i 775 15 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 775 16 have have VBP work_fnploejenbc2raktl46esxm44i 775 17 SCORING score VBN work_fnploejenbc2raktl46esxm44i 775 18 APPROACH APPROACH NNS work_fnploejenbc2raktl46esxm44i 775 19 TO to IN work_fnploejenbc2raktl46esxm44i 775 20 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 775 21 589 589 CD work_fnploejenbc2raktl46esxm44i 775 22 For for IN work_fnploejenbc2raktl46esxm44i 775 23 IAl=3 IAl=3 NNP work_fnploejenbc2raktl46esxm44i 775 24 , , , work_fnploejenbc2raktl46esxm44i 775 25 say say VBP work_fnploejenbc2raktl46esxm44i 775 26 A={w,~~,w~ A={w,~~,w~ NNP work_fnploejenbc2raktl46esxm44i 775 27 } } -RRB- work_fnploejenbc2raktl46esxm44i 775 28 , , , work_fnploejenbc2raktl46esxm44i 775 29 let let VB work_fnploejenbc2raktl46esxm44i 775 30 a a DT work_fnploejenbc2raktl46esxm44i 775 31 = = NFP work_fnploejenbc2raktl46esxm44i 775 32 Q{w q{w ADD work_fnploejenbc2raktl46esxm44i 775 33 , , , work_fnploejenbc2raktl46esxm44i 775 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 775 35 , , , work_fnploejenbc2raktl46esxm44i 775 36 b b NN work_fnploejenbc2raktl46esxm44i 775 37 = = SYM work_fnploejenbc2raktl46esxm44i 775 38 Q({w2 Q({w2 NNP work_fnploejenbc2raktl46esxm44i 775 39 } } -RRB- work_fnploejenbc2raktl46esxm44i 775 40 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 775 41 , , , work_fnploejenbc2raktl46esxm44i 775 42 c c NN work_fnploejenbc2raktl46esxm44i 775 43 = = NFP work_fnploejenbc2raktl46esxm44i 775 44 Q((c+ q((c+ NN work_fnploejenbc2raktl46esxm44i 775 45 } } -RRB- work_fnploejenbc2raktl46esxm44i 775 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 775 47 . . . work_fnploejenbc2raktl46esxm44i 776 1 Then then RB work_fnploejenbc2raktl46esxm44i 776 2 m,(A)=(a+b+c)‘-(a+h)‘-(a+~)‘-(b+c)’+ m,(A)=(a+b+c)‘-(a+h)‘-(a+~)‘-(b+c)’+ NNP work_fnploejenbc2raktl46esxm44i 776 3 u u NNP work_fnploejenbc2raktl46esxm44i 776 4 ’ ' '' work_fnploejenbc2raktl46esxm44i 776 5 + + CC work_fnploejenbc2raktl46esxm44i 776 6 b b NN work_fnploejenbc2raktl46esxm44i 776 7 ’ ' '' work_fnploejenbc2raktl46esxm44i 776 8 + + CC work_fnploejenbc2raktl46esxm44i 776 9 c c NN work_fnploejenbc2raktl46esxm44i 776 10 ’ ' '' work_fnploejenbc2raktl46esxm44i 776 11 . . . work_fnploejenbc2raktl46esxm44i 777 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 777 2 m’(A m’(A NNS work_fnploejenbc2raktl46esxm44i 777 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 777 4 3 3 CD work_fnploejenbc2raktl46esxm44i 777 5 0 0 CD work_fnploejenbc2raktl46esxm44i 777 6 if if IN work_fnploejenbc2raktl46esxm44i 777 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 777 8 a+b+c)‘>(u+b)‘-a’+(u+c)‘-c’+(b+c)’-b a+b+c)‘>(u+b)‘-a’+(u+c)‘-c’+(b+c)’-b CD work_fnploejenbc2raktl46esxm44i 777 9 ’ ' '' work_fnploejenbc2raktl46esxm44i 777 10 . . . work_fnploejenbc2raktl46esxm44i 778 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 778 2 * * NFP work_fnploejenbc2raktl46esxm44i 778 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 778 4 Now now RB work_fnploejenbc2raktl46esxm44i 778 5 , , , work_fnploejenbc2raktl46esxm44i 778 6 if if IN work_fnploejenbc2raktl46esxm44i 778 7 r r NN work_fnploejenbc2raktl46esxm44i 778 8 = = SYM work_fnploejenbc2raktl46esxm44i 778 9 n n NN work_fnploejenbc2raktl46esxm44i 778 10 > > XX work_fnploejenbc2raktl46esxm44i 778 11 , , , work_fnploejenbc2raktl46esxm44i 778 12 1 1 CD work_fnploejenbc2raktl46esxm44i 778 13 is be VBZ work_fnploejenbc2raktl46esxm44i 778 14 integral integral JJ work_fnploejenbc2raktl46esxm44i 778 15 , , , work_fnploejenbc2raktl46esxm44i 778 16 then then RB work_fnploejenbc2raktl46esxm44i 778 17 the the DT work_fnploejenbc2raktl46esxm44i 778 18 right right JJ work_fnploejenbc2raktl46esxm44i 778 19 hand hand NN work_fnploejenbc2raktl46esxm44i 778 20 side side NN work_fnploejenbc2raktl46esxm44i 778 21 of of IN work_fnploejenbc2raktl46esxm44i 778 22 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 778 23 * * NFP work_fnploejenbc2raktl46esxm44i 778 24 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 778 25 is be VBZ work_fnploejenbc2raktl46esxm44i 778 26 uibJck uibjck JJ work_fnploejenbc2raktl46esxm44i 778 27 , , , work_fnploejenbc2raktl46esxm44i 778 28 where where WRB work_fnploejenbc2raktl46esxm44i 778 29 S s NN work_fnploejenbc2raktl46esxm44i 778 30 = = NFP work_fnploejenbc2raktl46esxm44i 778 31 { { -LRB- work_fnploejenbc2raktl46esxm44i 778 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 778 33 i i PRP work_fnploejenbc2raktl46esxm44i 778 34 , , , work_fnploejenbc2raktl46esxm44i 778 35 j j NNP work_fnploejenbc2raktl46esxm44i 778 36 , , , work_fnploejenbc2raktl46esxm44i 778 37 k k NNP work_fnploejenbc2raktl46esxm44i 778 38 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 778 39 : : : work_fnploejenbc2raktl46esxm44i 778 40 i+ i+ NNP work_fnploejenbc2raktl46esxm44i 778 41 j j NNP work_fnploejenbc2raktl46esxm44i 778 42 + + NNP work_fnploejenbc2raktl46esxm44i 778 43 k k NN work_fnploejenbc2raktl46esxm44i 778 44 = = SYM work_fnploejenbc2raktl46esxm44i 778 45 n n NN work_fnploejenbc2raktl46esxm44i 778 46 and and CC work_fnploejenbc2raktl46esxm44i 778 47 not not RB work_fnploejenbc2raktl46esxm44i 778 48 all all PDT work_fnploejenbc2raktl46esxm44i 778 49 the the DT work_fnploejenbc2raktl46esxm44i 778 50 i i NNP work_fnploejenbc2raktl46esxm44i 778 51 , , , work_fnploejenbc2raktl46esxm44i 778 52 j j NNP work_fnploejenbc2raktl46esxm44i 778 53 , , , work_fnploejenbc2raktl46esxm44i 778 54 k k NNP work_fnploejenbc2raktl46esxm44i 778 55 are be VBP work_fnploejenbc2raktl46esxm44i 778 56 positive positive JJ work_fnploejenbc2raktl46esxm44i 778 57 } } -RRB- work_fnploejenbc2raktl46esxm44i 778 58 . . . work_fnploejenbc2raktl46esxm44i 779 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 779 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 779 3 * * NFP work_fnploejenbc2raktl46esxm44i 779 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 779 5 holds hold VBZ work_fnploejenbc2raktl46esxm44i 779 6 since since IN work_fnploejenbc2raktl46esxm44i 779 7 a a DT work_fnploejenbc2raktl46esxm44i 779 8 , , , work_fnploejenbc2raktl46esxm44i 779 9 b b NN work_fnploejenbc2raktl46esxm44i 779 10 , , , work_fnploejenbc2raktl46esxm44i 779 11 c c NN work_fnploejenbc2raktl46esxm44i 779 12 3 3 CD work_fnploejenbc2raktl46esxm44i 779 13 0 0 CD work_fnploejenbc2raktl46esxm44i 779 14 and and CC work_fnploejenbc2raktl46esxm44i 779 15 Sc{(i Sc{(i NNP work_fnploejenbc2raktl46esxm44i 779 16 , , , work_fnploejenbc2raktl46esxm44i 779 17 j j NNP work_fnploejenbc2raktl46esxm44i 779 18 , , , work_fnploejenbc2raktl46esxm44i 779 19 k):i+j+k k):i+j+k NNP work_fnploejenbc2raktl46esxm44i 779 20 = = SYM work_fnploejenbc2raktl46esxm44i 779 21 n n IN work_fnploejenbc2raktl46esxm44i 779 22 } } -RRB- work_fnploejenbc2raktl46esxm44i 779 23 . . . work_fnploejenbc2raktl46esxm44i 780 1 For for IN work_fnploejenbc2raktl46esxm44i 780 2 r r NN work_fnploejenbc2raktl46esxm44i 780 3 > > NN work_fnploejenbc2raktl46esxm44i 780 4 1 1 CD work_fnploejenbc2raktl46esxm44i 780 5 , , , work_fnploejenbc2raktl46esxm44i 780 6 real real JJ work_fnploejenbc2raktl46esxm44i 780 7 , , , work_fnploejenbc2raktl46esxm44i 780 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 780 9 rewrite rewrite VBP work_fnploejenbc2raktl46esxm44i 780 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 780 11 * * NFP work_fnploejenbc2raktl46esxm44i 780 12 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 780 13 as as IN work_fnploejenbc2raktl46esxm44i 780 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 780 15 u+b+c)‘+a’+b’+c’~(u+b)‘+(u+c)‘+(b+c u+b+c)‘+a’+b’+c’~(u+b)‘+(u+c)‘+(b+c NNP work_fnploejenbc2raktl46esxm44i 780 16 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 780 17 ’ ' '' work_fnploejenbc2raktl46esxm44i 780 18 . . . work_fnploejenbc2raktl46esxm44i 781 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 781 2 * * NFP work_fnploejenbc2raktl46esxm44i 781 3 * * NFP work_fnploejenbc2raktl46esxm44i 781 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 781 5 Let let VB work_fnploejenbc2raktl46esxm44i 781 6 u(r u(r NNP work_fnploejenbc2raktl46esxm44i 781 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 781 8 , , , work_fnploejenbc2raktl46esxm44i 781 9 w(r w(r NNP work_fnploejenbc2raktl46esxm44i 781 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 781 11 be be VB work_fnploejenbc2raktl46esxm44i 781 12 the the DT work_fnploejenbc2raktl46esxm44i 781 13 left left JJ work_fnploejenbc2raktl46esxm44i 781 14 and and CC work_fnploejenbc2raktl46esxm44i 781 15 right right JJ work_fnploejenbc2raktl46esxm44i 781 16 hand hand NN work_fnploejenbc2raktl46esxm44i 781 17 sides side NNS work_fnploejenbc2raktl46esxm44i 781 18 of of IN work_fnploejenbc2raktl46esxm44i 781 19 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 781 20 * * NFP work_fnploejenbc2raktl46esxm44i 781 21 * * NFP work_fnploejenbc2raktl46esxm44i 781 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 781 23 , , , work_fnploejenbc2raktl46esxm44i 781 24 respectively respectively RB work_fnploejenbc2raktl46esxm44i 781 25 . . . work_fnploejenbc2raktl46esxm44i 782 1 Observe observe VB work_fnploejenbc2raktl46esxm44i 782 2 that that IN work_fnploejenbc2raktl46esxm44i 782 3 u(r u(r NN work_fnploejenbc2raktl46esxm44i 782 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 782 5 and and CC work_fnploejenbc2raktl46esxm44i 782 6 w(r w(r NN work_fnploejenbc2raktl46esxm44i 782 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 782 8 are be VBP work_fnploejenbc2raktl46esxm44i 782 9 convex convex NNP work_fnploejenbc2raktl46esxm44i 782 10 functions function NNS work_fnploejenbc2raktl46esxm44i 782 11 on on IN work_fnploejenbc2raktl46esxm44i 782 12 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 782 13 1 1 CD work_fnploejenbc2raktl46esxm44i 782 14 , , , work_fnploejenbc2raktl46esxm44i 782 15 + + CC work_fnploejenbc2raktl46esxm44i 782 16 cc cc NNP work_fnploejenbc2raktl46esxm44i 782 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 782 18 , , , work_fnploejenbc2raktl46esxm44i 782 19 since since IN work_fnploejenbc2raktl46esxm44i 782 20 Ofu+b+c ofu+b+c CD work_fnploejenbc2raktl46esxm44i 782 21 < < XX work_fnploejenbc2raktl46esxm44i 782 22 l l NN work_fnploejenbc2raktl46esxm44i 782 23 . . . work_fnploejenbc2raktl46esxm44i 783 1 Also also RB work_fnploejenbc2raktl46esxm44i 783 2 u(l)=w(1)=2(u+b+c u(l)=w(1)=2(u+b+c NNP work_fnploejenbc2raktl46esxm44i 783 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 783 4 and and CC work_fnploejenbc2raktl46esxm44i 783 5 lim lim NNP work_fnploejenbc2raktl46esxm44i 783 6 u(r)= u(r)= NNP work_fnploejenbc2raktl46esxm44i 783 7 lim lim NNP work_fnploejenbc2raktl46esxm44i 783 8 w(r)=O. w(r)=O. NNP work_fnploejenbc2raktl46esxm44i 784 1 r- r- XX work_fnploejenbc2raktl46esxm44i 784 2 + + NNP work_fnploejenbc2raktl46esxm44i 784 3 cr cr NN work_fnploejenbc2raktl46esxm44i 784 4 ” " '' work_fnploejenbc2raktl46esxm44i 784 5 + + CC work_fnploejenbc2raktl46esxm44i 784 6 r r NN work_fnploejenbc2raktl46esxm44i 784 7 Thus thus RB work_fnploejenbc2raktl46esxm44i 784 8 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 784 9 * * NFP work_fnploejenbc2raktl46esxm44i 784 10 * * NFP work_fnploejenbc2raktl46esxm44i 784 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 784 12 holds hold VBZ work_fnploejenbc2raktl46esxm44i 784 13 since since IN work_fnploejenbc2raktl46esxm44i 784 14 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 784 15 * * NFP work_fnploejenbc2raktl46esxm44i 784 16 * * NFP work_fnploejenbc2raktl46esxm44i 784 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 784 18 holds hold VBZ work_fnploejenbc2raktl46esxm44i 784 19 for for IN work_fnploejenbc2raktl46esxm44i 784 20 any any DT work_fnploejenbc2raktl46esxm44i 784 21 integer integer NN work_fnploejenbc2raktl46esxm44i 784 22 r r NN work_fnploejenbc2raktl46esxm44i 784 23 > > NN work_fnploejenbc2raktl46esxm44i 784 24 1 1 CD work_fnploejenbc2raktl46esxm44i 784 25 . . . work_fnploejenbc2raktl46esxm44i 785 1 The the DT work_fnploejenbc2raktl46esxm44i 785 2 above above JJ work_fnploejenbc2raktl46esxm44i 785 3 argument argument NN work_fnploejenbc2raktl46esxm44i 785 4 applies apply VBZ work_fnploejenbc2raktl46esxm44i 785 5 to to IN work_fnploejenbc2raktl46esxm44i 785 6 the the DT work_fnploejenbc2raktl46esxm44i 785 7 case case NN work_fnploejenbc2raktl46esxm44i 785 8 IAl IAl NNP work_fnploejenbc2raktl46esxm44i 785 9 > > XX work_fnploejenbc2raktl46esxm44i 785 10 4 4 CD work_fnploejenbc2raktl46esxm44i 785 11 as as RB work_fnploejenbc2raktl46esxm44i 785 12 well well RB work_fnploejenbc2raktl46esxm44i 785 13 . . . work_fnploejenbc2raktl46esxm44i 786 1 1 1 CD work_fnploejenbc2raktl46esxm44i 786 2 Remarks remark NNS work_fnploejenbc2raktl46esxm44i 786 3 . . . work_fnploejenbc2raktl46esxm44i 787 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 787 2 i i NN work_fnploejenbc2raktl46esxm44i 787 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 787 4 Of of RB work_fnploejenbc2raktl46esxm44i 787 5 course course RB work_fnploejenbc2raktl46esxm44i 787 6 if if IN work_fnploejenbc2raktl46esxm44i 787 7 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 787 8 = = NN work_fnploejenbc2raktl46esxm44i 787 9 Q q NN work_fnploejenbc2raktl46esxm44i 787 10 ’ ' '' work_fnploejenbc2raktl46esxm44i 787 11 where where WRB work_fnploejenbc2raktl46esxm44i 787 12 Q Q NNP work_fnploejenbc2raktl46esxm44i 787 13 is be VBZ work_fnploejenbc2raktl46esxm44i 787 14 a a DT work_fnploejenbc2raktl46esxm44i 787 15 finitely finitely RB work_fnploejenbc2raktl46esxm44i 787 16 additive additive JJ work_fnploejenbc2raktl46esxm44i 787 17 probability probability NN work_fnploejenbc2raktl46esxm44i 787 18 measure measure NN work_fnploejenbc2raktl46esxm44i 787 19 and and CC work_fnploejenbc2raktl46esxm44i 787 20 r r NN work_fnploejenbc2raktl46esxm44i 787 21 > > XX work_fnploejenbc2raktl46esxm44i 787 22 1 1 CD work_fnploejenbc2raktl46esxm44i 787 23 , , , work_fnploejenbc2raktl46esxm44i 787 24 then then RB work_fnploejenbc2raktl46esxm44i 787 25 Be1 be1 NN work_fnploejenbc2raktl46esxm44i 787 26 is be VBZ work_fnploejenbc2raktl46esxm44i 787 27 general general JJ work_fnploejenbc2raktl46esxm44i 787 28 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 787 29 by by IN work_fnploejenbc2raktl46esxm44i 787 30 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 787 31 6.2 6.2 CD work_fnploejenbc2raktl46esxm44i 787 32 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 787 33 i i NN work_fnploejenbc2raktl46esxm44i 787 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 787 35 : : : work_fnploejenbc2raktl46esxm44i 787 36 VE VE NNP work_fnploejenbc2raktl46esxm44i 787 37 , , , work_fnploejenbc2raktl46esxm44i 787 38 FE FE NNP work_fnploejenbc2raktl46esxm44i 787 39 .ra2 .ra2 NNP work_fnploejenbc2raktl46esxm44i 787 40 , , , work_fnploejenbc2raktl46esxm44i 787 41 Bel(E Bel(E NNP work_fnploejenbc2raktl46esxm44i 787 42 ’ ' '' work_fnploejenbc2raktl46esxm44i 787 43 1 1 CD work_fnploejenbc2raktl46esxm44i 787 44 F F NNP work_fnploejenbc2raktl46esxm44i 787 45 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 787 46 is be VBZ work_fnploejenbc2raktl46esxm44i 787 47 a a DT work_fnploejenbc2raktl46esxm44i 787 48 function function NN work_fnploejenbc2raktl46esxm44i 787 49 of of IN work_fnploejenbc2raktl46esxm44i 787 50 Bel(E Bel(E NNP work_fnploejenbc2raktl46esxm44i 787 51 1 1 CD work_fnploejenbc2raktl46esxm44i 787 52 F F NNP work_fnploejenbc2raktl46esxm44i 787 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 787 54 , , , work_fnploejenbc2raktl46esxm44i 787 55 namely namely RB work_fnploejenbc2raktl46esxm44i 787 56 cp(x)=(l cp(x)=(l NNPS work_fnploejenbc2raktl46esxm44i 787 57 -x -x : work_fnploejenbc2raktl46esxm44i 787 58 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 787 59 ‘ ' '' work_fnploejenbc2raktl46esxm44i 787 60 . . . work_fnploejenbc2raktl46esxm44i 788 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 788 2 ii ii LS work_fnploejenbc2raktl46esxm44i 788 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 788 4 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 788 5 have have VBP work_fnploejenbc2raktl46esxm44i 788 6 seen see VBN work_fnploejenbc2raktl46esxm44i 788 7 that that IN work_fnploejenbc2raktl46esxm44i 788 8 , , , work_fnploejenbc2raktl46esxm44i 788 9 in in IN work_fnploejenbc2raktl46esxm44i 788 10 the the DT work_fnploejenbc2raktl46esxm44i 788 11 scoring score VBG work_fnploejenbc2raktl46esxm44i 788 12 approach approach NN work_fnploejenbc2raktl46esxm44i 788 13 to to IN work_fnploejenbc2raktl46esxm44i 788 14 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 788 15 of of IN work_fnploejenbc2raktl46esxm44i 788 16 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 788 17 measures measure NNS work_fnploejenbc2raktl46esxm44i 788 18 , , , work_fnploejenbc2raktl46esxm44i 788 19 if if IN work_fnploejenbc2raktl46esxm44i 788 20 the the DT work_fnploejenbc2raktl46esxm44i 788 21 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 788 22 function function NN work_fnploejenbc2raktl46esxm44i 788 23 is be VBZ work_fnploejenbc2raktl46esxm44i 788 24 taken take VBN work_fnploejenbc2raktl46esxm44i 788 25 to to TO work_fnploejenbc2raktl46esxm44i 788 26 be be VB work_fnploejenbc2raktl46esxm44i 788 27 addition addition NN work_fnploejenbc2raktl46esxm44i 788 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 788 29 as as IN work_fnploejenbc2raktl46esxm44i 788 30 in in IN work_fnploejenbc2raktl46esxm44i 788 31 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 788 32 ’s ’s POS work_fnploejenbc2raktl46esxm44i 788 33 work work NN work_fnploejenbc2raktl46esxm44i 788 34 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 788 35 , , , work_fnploejenbc2raktl46esxm44i 788 36 then then RB work_fnploejenbc2raktl46esxm44i 788 37 well well RB work_fnploejenbc2raktl46esxm44i 788 38 - - HYPH work_fnploejenbc2raktl46esxm44i 788 39 known know VBN work_fnploejenbc2raktl46esxm44i 788 40 measures measure NNS work_fnploejenbc2raktl46esxm44i 788 41 such such JJ work_fnploejenbc2raktl46esxm44i 788 42 as as IN work_fnploejenbc2raktl46esxm44i 788 43 Max Max NNP work_fnploejenbc2raktl46esxm44i 788 44 - - HYPH work_fnploejenbc2raktl46esxm44i 788 45 possibility possibility NN work_fnploejenbc2raktl46esxm44i 788 46 measures measure NNS work_fnploejenbc2raktl46esxm44i 788 47 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 788 48 which which WDT work_fnploejenbc2raktl46esxm44i 788 49 are be VBP work_fnploejenbc2raktl46esxm44i 788 50 consonant consonant JJ work_fnploejenbc2raktl46esxm44i 788 51 plausibility plausibility NN work_fnploejenbc2raktl46esxm44i 788 52 functions function NNS work_fnploejenbc2raktl46esxm44i 788 53 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 788 54 and and CC work_fnploejenbc2raktl46esxm44i 788 55 degenerate degenerate VB work_fnploejenbc2raktl46esxm44i 788 56 belief belief NN work_fnploejenbc2raktl46esxm44i 788 57 functions function NNS work_fnploejenbc2raktl46esxm44i 788 58 are be VBP work_fnploejenbc2raktl46esxm44i 788 59 not not RB work_fnploejenbc2raktl46esxm44i 788 60 general general JJ work_fnploejenbc2raktl46esxm44i 788 61 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 788 62 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 788 63 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 788 64 , , , work_fnploejenbc2raktl46esxm44i 788 65 they -PRON- PRP work_fnploejenbc2raktl46esxm44i 788 66 are be VBP work_fnploejenbc2raktl46esxm44i 788 67 incoherent incoherent JJ work_fnploejenbc2raktl46esxm44i 788 68 in in IN work_fnploejenbc2raktl46esxm44i 788 69 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 788 70 ’s ’s POS work_fnploejenbc2raktl46esxm44i 788 71 sense sense NN work_fnploejenbc2raktl46esxm44i 788 72 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 788 73 . . . work_fnploejenbc2raktl46esxm44i 789 1 Although although IN work_fnploejenbc2raktl46esxm44i 789 2 , , , work_fnploejenbc2raktl46esxm44i 789 3 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 789 4 have have VBP work_fnploejenbc2raktl46esxm44i 789 5 shown show VBN work_fnploejenbc2raktl46esxm44i 789 6 that that IN work_fnploejenbc2raktl46esxm44i 789 7 , , , work_fnploejenbc2raktl46esxm44i 789 8 in in IN work_fnploejenbc2raktl46esxm44i 789 9 this this DT work_fnploejenbc2raktl46esxm44i 789 10 case case NN work_fnploejenbc2raktl46esxm44i 789 11 , , , work_fnploejenbc2raktl46esxm44i 789 12 there there EX work_fnploejenbc2raktl46esxm44i 789 13 exist exist VBP work_fnploejenbc2raktl46esxm44i 789 14 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 789 15 T t NN work_fnploejenbc2raktl46esxm44i 789 16 - - HYPH work_fnploejenbc2raktl46esxm44i 789 17 possibility possibility NN work_fnploejenbc2raktl46esxm44i 789 18 measures measure NNS work_fnploejenbc2raktl46esxm44i 789 19 and and CC work_fnploejenbc2raktl46esxm44i 789 20 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 789 21 belief belief NN work_fnploejenbc2raktl46esxm44i 789 22 functions function NNS work_fnploejenbc2raktl46esxm44i 789 23 , , , work_fnploejenbc2raktl46esxm44i 789 24 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 789 25 is be VBZ work_fnploejenbc2raktl46esxm44i 789 26 useful useful JJ work_fnploejenbc2raktl46esxm44i 789 27 to to TO work_fnploejenbc2raktl46esxm44i 789 28 consider consider VB work_fnploejenbc2raktl46esxm44i 789 29 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 789 30 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 789 31 functions function NNS work_fnploejenbc2raktl46esxm44i 789 32 in in IN work_fnploejenbc2raktl46esxm44i 789 33 order order NN work_fnploejenbc2raktl46esxm44i 789 34 to to TO work_fnploejenbc2raktl46esxm44i 789 35 set set VB work_fnploejenbc2raktl46esxm44i 789 36 up up RP work_fnploejenbc2raktl46esxm44i 789 37 a a DT work_fnploejenbc2raktl46esxm44i 789 38 general general JJ work_fnploejenbc2raktl46esxm44i 789 39 framework framework NN work_fnploejenbc2raktl46esxm44i 789 40 for for IN work_fnploejenbc2raktl46esxm44i 789 41 studying study VBG work_fnploejenbc2raktl46esxm44i 789 42 the the DT work_fnploejenbc2raktl46esxm44i 789 43 question question NN work_fnploejenbc2raktl46esxm44i 789 44 of of IN work_fnploejenbc2raktl46esxm44i 789 45 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 789 46 , , , work_fnploejenbc2raktl46esxm44i 789 47 i.e. i.e. FW work_fnploejenbc2raktl46esxm44i 789 48 , , , work_fnploejenbc2raktl46esxm44i 789 49 a a DT work_fnploejenbc2raktl46esxm44i 789 50 general general JJ work_fnploejenbc2raktl46esxm44i 789 51 concept concept NN work_fnploejenbc2raktl46esxm44i 789 52 590 590 CD work_fnploejenbc2raktl46esxm44i 789 53 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 789 54 , , , work_fnploejenbc2raktl46esxm44i 789 55 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 789 56 , , , work_fnploejenbc2raktl46esxm44i 789 57 AND and CC work_fnploejenbc2raktl46esxm44i 789 58 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 789 59 of of IN work_fnploejenbc2raktl46esxm44i 789 60 coherence coherence NN work_fnploejenbc2raktl46esxm44i 789 61 . . . work_fnploejenbc2raktl46esxm44i 790 1 From from IN work_fnploejenbc2raktl46esxm44i 790 2 a a DT work_fnploejenbc2raktl46esxm44i 790 3 logical logical JJ work_fnploejenbc2raktl46esxm44i 790 4 viewpoint viewpoint NN work_fnploejenbc2raktl46esxm44i 790 5 , , , work_fnploejenbc2raktl46esxm44i 790 6 this this DT work_fnploejenbc2raktl46esxm44i 790 7 is be VBZ work_fnploejenbc2raktl46esxm44i 790 8 precisely precisely RB work_fnploejenbc2raktl46esxm44i 790 9 the the DT work_fnploejenbc2raktl46esxm44i 790 10 concern concern NN work_fnploejenbc2raktl46esxm44i 790 11 of of IN work_fnploejenbc2raktl46esxm44i 790 12 AZ AZ NNP work_fnploejenbc2raktl46esxm44i 790 13 researchers researcher NNS work_fnploejenbc2raktl46esxm44i 790 14 as as RB work_fnploejenbc2raktl46esxm44i 790 15 well well RB work_fnploejenbc2raktl46esxm44i 790 16 as as IN work_fnploejenbc2raktl46esxm44i 790 17 statisticians statistician NNS work_fnploejenbc2raktl46esxm44i 790 18 dealing deal VBG work_fnploejenbc2raktl46esxm44i 790 19 with with IN work_fnploejenbc2raktl46esxm44i 790 20 applications application NNS work_fnploejenbc2raktl46esxm44i 790 21 of of IN work_fnploejenbc2raktl46esxm44i 790 22 belief belief NN work_fnploejenbc2raktl46esxm44i 790 23 functions function NNS work_fnploejenbc2raktl46esxm44i 790 24 to to IN work_fnploejenbc2raktl46esxm44i 790 25 statistical statistical JJ work_fnploejenbc2raktl46esxm44i 790 26 inference inference NN work_fnploejenbc2raktl46esxm44i 790 27 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 790 28 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 790 29 , , , work_fnploejenbc2raktl46esxm44i 790 30 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 790 31 30 30 CD work_fnploejenbc2raktl46esxm44i 790 32 , , , work_fnploejenbc2raktl46esxm44i 790 33 p. p. NN work_fnploejenbc2raktl46esxm44i 790 34 1061071 1061071 CD work_fnploejenbc2raktl46esxm44i 790 35 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 790 36 . . . work_fnploejenbc2raktl46esxm44i 791 1 Section section NN work_fnploejenbc2raktl46esxm44i 791 2 7 7 CD work_fnploejenbc2raktl46esxm44i 791 3 will will MD work_fnploejenbc2raktl46esxm44i 791 4 give give VB work_fnploejenbc2raktl46esxm44i 791 5 some some DT work_fnploejenbc2raktl46esxm44i 791 6 insights insight NNS work_fnploejenbc2raktl46esxm44i 791 7 in in IN work_fnploejenbc2raktl46esxm44i 791 8 this this DT work_fnploejenbc2raktl46esxm44i 791 9 direction direction NN work_fnploejenbc2raktl46esxm44i 791 10 . . . work_fnploejenbc2raktl46esxm44i 792 1 7 7 LS work_fnploejenbc2raktl46esxm44i 792 2 . . . work_fnploejenbc2raktl46esxm44i 793 1 UNCERTAINTY UNCERTAINTY NNP work_fnploejenbc2raktl46esxm44i 793 2 GAMES GAMES NNP work_fnploejenbc2raktl46esxm44i 793 3 WITH with IN work_fnploejenbc2raktl46esxm44i 793 4 NONADDITIVE NONADDITIVE NNP work_fnploejenbc2raktl46esxm44i 793 5 AGGREGATION aggregation NN work_fnploejenbc2raktl46esxm44i 793 6 FUNCTIONS functions NN work_fnploejenbc2raktl46esxm44i 793 7 In in IN work_fnploejenbc2raktl46esxm44i 793 8 this this DT work_fnploejenbc2raktl46esxm44i 793 9 section section NN work_fnploejenbc2raktl46esxm44i 793 10 , , , work_fnploejenbc2raktl46esxm44i 793 11 some some DT work_fnploejenbc2raktl46esxm44i 793 12 specific specific JJ work_fnploejenbc2raktl46esxm44i 793 13 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 793 14 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 793 15 functions function NNS work_fnploejenbc2raktl46esxm44i 793 16 are be VBP work_fnploejenbc2raktl46esxm44i 793 17 considered consider VBN work_fnploejenbc2raktl46esxm44i 793 18 . . . work_fnploejenbc2raktl46esxm44i 794 1 In in IN work_fnploejenbc2raktl46esxm44i 794 2 Example example NN work_fnploejenbc2raktl46esxm44i 794 3 1 1 CD work_fnploejenbc2raktl46esxm44i 794 4 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 794 5 is be VBZ work_fnploejenbc2raktl46esxm44i 794 6 shown show VBN work_fnploejenbc2raktl46esxm44i 794 7 that that IN work_fnploejenbc2raktl46esxm44i 794 8 a a DT work_fnploejenbc2raktl46esxm44i 794 9 simple simple JJ work_fnploejenbc2raktl46esxm44i 794 10 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 794 11 form form NN work_fnploejenbc2raktl46esxm44i 794 12 of of IN work_fnploejenbc2raktl46esxm44i 794 13 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 794 14 leads lead VBZ work_fnploejenbc2raktl46esxm44i 794 15 to to IN work_fnploejenbc2raktl46esxm44i 794 16 a a DT work_fnploejenbc2raktl46esxm44i 794 17 corresponding corresponding JJ work_fnploejenbc2raktl46esxm44i 794 18 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 794 19 game game NN work_fnploejenbc2raktl46esxm44i 794 20 for for IN work_fnploejenbc2raktl46esxm44i 794 21 which which WDT work_fnploejenbc2raktl46esxm44i 794 22 uniformly uniformly JJ work_fnploejenbc2raktl46esxm44i 794 23 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 794 24 measures measure NNS work_fnploejenbc2raktl46esxm44i 794 25 are be VBP work_fnploejenbc2raktl46esxm44i 794 26 not not RB work_fnploejenbc2raktl46esxm44i 794 27 transformable transformable JJ work_fnploejenbc2raktl46esxm44i 794 28 to to IN work_fnploejenbc2raktl46esxm44i 794 29 probabilities probability NNS work_fnploejenbc2raktl46esxm44i 794 30 ; ; : work_fnploejenbc2raktl46esxm44i 794 31 this this DT work_fnploejenbc2raktl46esxm44i 794 32 is be VBZ work_fnploejenbc2raktl46esxm44i 794 33 in in IN work_fnploejenbc2raktl46esxm44i 794 34 opposition opposition NN work_fnploejenbc2raktl46esxm44i 794 35 to to IN work_fnploejenbc2raktl46esxm44i 794 36 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 794 37 ’s ’s POS work_fnploejenbc2raktl46esxm44i 794 38 games game NNS work_fnploejenbc2raktl46esxm44i 794 39 with with IN work_fnploejenbc2raktl46esxm44i 794 40 an an DT work_fnploejenbc2raktl46esxm44i 794 41 additive additive JJ work_fnploejenbc2raktl46esxm44i 794 42 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 794 43 function function NN work_fnploejenbc2raktl46esxm44i 794 44 . . . work_fnploejenbc2raktl46esxm44i 795 1 Example example NN work_fnploejenbc2raktl46esxm44i 795 2 2 2 CD work_fnploejenbc2raktl46esxm44i 795 3 presents present VBZ work_fnploejenbc2raktl46esxm44i 795 4 a a DT work_fnploejenbc2raktl46esxm44i 795 5 situation situation NN work_fnploejenbc2raktl46esxm44i 795 6 in in IN work_fnploejenbc2raktl46esxm44i 795 7 which which WDT work_fnploejenbc2raktl46esxm44i 795 8 a a DT work_fnploejenbc2raktl46esxm44i 795 9 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 795 10 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 795 11 function function NN work_fnploejenbc2raktl46esxm44i 795 12 has have VBZ work_fnploejenbc2raktl46esxm44i 795 13 a a DT work_fnploejenbc2raktl46esxm44i 795 14 general general JJ work_fnploejenbc2raktl46esxm44i 795 15 additive additive JJ work_fnploejenbc2raktl46esxm44i 795 16 form form NN work_fnploejenbc2raktl46esxm44i 795 17 . . . work_fnploejenbc2raktl46esxm44i 796 1 In in IN work_fnploejenbc2raktl46esxm44i 796 2 this this DT work_fnploejenbc2raktl46esxm44i 796 3 case case NN work_fnploejenbc2raktl46esxm44i 796 4 , , , work_fnploejenbc2raktl46esxm44i 796 5 uniformly uniformly JJ work_fnploejenbc2raktl46esxm44i 796 6 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 796 7 measures measure NNS work_fnploejenbc2raktl46esxm44i 796 8 have have VBP work_fnploejenbc2raktl46esxm44i 796 9 probability probability NN work_fnploejenbc2raktl46esxm44i 796 10 - - HYPH work_fnploejenbc2raktl46esxm44i 796 11 like like JJ work_fnploejenbc2raktl46esxm44i 796 12 characterizations characterization NNS work_fnploejenbc2raktl46esxm44i 796 13 . . . work_fnploejenbc2raktl46esxm44i 797 1 In in IN work_fnploejenbc2raktl46esxm44i 797 2 Example example NN work_fnploejenbc2raktl46esxm44i 797 3 3 3 CD work_fnploejenbc2raktl46esxm44i 797 4 , , , work_fnploejenbc2raktl46esxm44i 797 5 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 797 6 present present VBP work_fnploejenbc2raktl46esxm44i 797 7 some some DT work_fnploejenbc2raktl46esxm44i 797 8 specialized specialized JJ work_fnploejenbc2raktl46esxm44i 797 9 cases case NNS work_fnploejenbc2raktl46esxm44i 797 10 of of IN work_fnploejenbc2raktl46esxm44i 797 11 Example Example NNP work_fnploejenbc2raktl46esxm44i 797 12 2 2 CD work_fnploejenbc2raktl46esxm44i 797 13 . . . work_fnploejenbc2raktl46esxm44i 798 1 EXAMPLE example NN work_fnploejenbc2raktl46esxm44i 798 2 1 1 CD work_fnploejenbc2raktl46esxm44i 798 3 . . . work_fnploejenbc2raktl46esxm44i 799 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 799 2 a a DT work_fnploejenbc2raktl46esxm44i 799 3 = = NN work_fnploejenbc2raktl46esxm44i 799 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 799 5 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 799 6 E e NN work_fnploejenbc2raktl46esxm44i 799 7 , , , work_fnploejenbc2raktl46esxm44i 799 8 1 1 CD work_fnploejenbc2raktl46esxm44i 799 9 F f NN work_fnploejenbc2raktl46esxm44i 799 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 799 11 , , , work_fnploejenbc2raktl46esxm44i 799 12 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 799 13 E e NN work_fnploejenbc2raktl46esxm44i 799 14 , , , work_fnploejenbc2raktl46esxm44i 799 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 799 16 F f NN work_fnploejenbc2raktl46esxm44i 799 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 799 18 , , , work_fnploejenbc2raktl46esxm44i 799 19 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 799 20 E e NN work_fnploejenbc2raktl46esxm44i 799 21 , , , work_fnploejenbc2raktl46esxm44i 799 22 u u NNP work_fnploejenbc2raktl46esxm44i 799 23 Ez Ez NNP work_fnploejenbc2raktl46esxm44i 799 24 1 1 CD work_fnploejenbc2raktl46esxm44i 799 25 t t NNP work_fnploejenbc2raktl46esxm44i 799 26 ; ; : work_fnploejenbc2raktl46esxm44i 799 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 799 28 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 799 29 , , , work_fnploejenbc2raktl46esxm44i 799 30 with with IN work_fnploejenbc2raktl46esxm44i 799 31 E e NN work_fnploejenbc2raktl46esxm44i 799 32 , , , work_fnploejenbc2raktl46esxm44i 799 33 E,=@. E,=@. NNP work_fnploejenbc2raktl46esxm44i 800 1 Let let VB work_fnploejenbc2raktl46esxm44i 800 2 x x DT work_fnploejenbc2raktl46esxm44i 800 3 = = NFP work_fnploejenbc2raktl46esxm44i 800 4 WI WI NNP work_fnploejenbc2raktl46esxm44i 800 5 If if IN work_fnploejenbc2raktl46esxm44i 800 6 ’ ' '' work_fnploejenbc2raktl46esxm44i 800 7 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 800 8 , , , work_fnploejenbc2raktl46esxm44i 800 9 Y Y NNP work_fnploejenbc2raktl46esxm44i 800 10 = = SYM work_fnploejenbc2raktl46esxm44i 800 11 AE2 AE2 NNP work_fnploejenbc2raktl46esxm44i 800 12 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 800 13 J J NNP work_fnploejenbc2raktl46esxm44i 800 14 ’ ' '' work_fnploejenbc2raktl46esxm44i 800 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 800 16 , , , work_fnploejenbc2raktl46esxm44i 800 17 z z XX work_fnploejenbc2raktl46esxm44i 800 18 = = SYM work_fnploejenbc2raktl46esxm44i 800 19 WI WI NNP work_fnploejenbc2raktl46esxm44i 800 20 u u NN work_fnploejenbc2raktl46esxm44i 800 21 E2 E2 NNP work_fnploejenbc2raktl46esxm44i 800 22 IF if RB work_fnploejenbc2raktl46esxm44i 800 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 800 24 . . . work_fnploejenbc2raktl46esxm44i 801 1 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 801 2 will will MD work_fnploejenbc2raktl46esxm44i 801 3 discuss discuss VB work_fnploejenbc2raktl46esxm44i 801 4 the the DT work_fnploejenbc2raktl46esxm44i 801 5 weak weak JJ work_fnploejenbc2raktl46esxm44i 801 6 local local JJ work_fnploejenbc2raktl46esxm44i 801 7 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 801 8 of of IN work_fnploejenbc2raktl46esxm44i 801 9 2 2 CD work_fnploejenbc2raktl46esxm44i 801 10 = = SYM work_fnploejenbc2raktl46esxm44i 801 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 801 12 x x NNP work_fnploejenbc2raktl46esxm44i 801 13 , , , work_fnploejenbc2raktl46esxm44i 801 14 y y NNP work_fnploejenbc2raktl46esxm44i 801 15 , , , work_fnploejenbc2raktl46esxm44i 801 16 z z NNP work_fnploejenbc2raktl46esxm44i 801 17 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 801 18 with with IN work_fnploejenbc2raktl46esxm44i 801 19 respect respect NN work_fnploejenbc2raktl46esxm44i 801 20 to to IN work_fnploejenbc2raktl46esxm44i 801 21 the the DT work_fnploejenbc2raktl46esxm44i 801 22 game game NN work_fnploejenbc2raktl46esxm44i 801 23 GJti,~ GJti,~ NNP work_fnploejenbc2raktl46esxm44i 801 24 , , , work_fnploejenbc2raktl46esxm44i 801 25 where where WRB work_fnploejenbc2raktl46esxm44i 801 26 the the DT work_fnploejenbc2raktl46esxm44i 801 27 game game NN work_fnploejenbc2raktl46esxm44i 801 28 is be VBZ work_fnploejenbc2raktl46esxm44i 801 29 specified specify VBN work_fnploejenbc2raktl46esxm44i 801 30 as as IN work_fnploejenbc2raktl46esxm44i 801 31 follows follow VBZ work_fnploejenbc2raktl46esxm44i 801 32 . . . work_fnploejenbc2raktl46esxm44i 802 1 Recall recall VB work_fnploejenbc2raktl46esxm44i 802 2 that that IN work_fnploejenbc2raktl46esxm44i 802 3 $ $ $ work_fnploejenbc2raktl46esxm44i 802 4 : : : work_fnploejenbc2raktl46esxm44i 802 5 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 802 6 w w NN work_fnploejenbc2raktl46esxm44i 802 7 , , , work_fnploejenbc2raktl46esxm44i 802 8 + + CC work_fnploejenbc2raktl46esxm44i 802 9 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 802 10 w w NNP work_fnploejenbc2raktl46esxm44i 802 11 is be VBZ work_fnploejenbc2raktl46esxm44i 802 12 specified specify VBN work_fnploejenbc2raktl46esxm44i 802 13 by by IN work_fnploejenbc2raktl46esxm44i 802 14 the the DT work_fnploejenbc2raktl46esxm44i 802 15 sequence sequence NN work_fnploejenbc2raktl46esxm44i 802 16 Ic/ Ic/ NNP work_fnploejenbc2raktl46esxm44i 802 17 , , , work_fnploejenbc2raktl46esxm44i 802 18 : : : work_fnploejenbc2raktl46esxm44i 802 19 BY BY NNP work_fnploejenbc2raktl46esxm44i 802 20 --t --t : work_fnploejenbc2raktl46esxm44i 802 21 58 58 CD work_fnploejenbc2raktl46esxm44i 802 22 , , , work_fnploejenbc2raktl46esxm44i 802 23 n n NN work_fnploejenbc2raktl46esxm44i 802 24 > > NN work_fnploejenbc2raktl46esxm44i 802 25 1 1 CD work_fnploejenbc2raktl46esxm44i 802 26 . . . work_fnploejenbc2raktl46esxm44i 803 1 For for IN work_fnploejenbc2raktl46esxm44i 803 2 our -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 803 3 purpose purpose NN work_fnploejenbc2raktl46esxm44i 803 4 here here RB work_fnploejenbc2raktl46esxm44i 803 5 , , , work_fnploejenbc2raktl46esxm44i 803 6 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 803 7 suffices suffice VBZ work_fnploejenbc2raktl46esxm44i 803 8 to to TO work_fnploejenbc2raktl46esxm44i 803 9 consider consider VB work_fnploejenbc2raktl46esxm44i 803 10 ti3 ti3 NN work_fnploejenbc2raktl46esxm44i 803 11 : : : work_fnploejenbc2raktl46esxm44i 803 12 R3 r3 NN work_fnploejenbc2raktl46esxm44i 803 13 + + CC work_fnploejenbc2raktl46esxm44i 803 14 R. R. NNP work_fnploejenbc2raktl46esxm44i 803 15 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 803 16 take take VBP work_fnploejenbc2raktl46esxm44i 803 17 $ $ $ work_fnploejenbc2raktl46esxm44i 803 18 Ju ju NN work_fnploejenbc2raktl46esxm44i 803 19 , , , work_fnploejenbc2raktl46esxm44i 803 20 u u NNP work_fnploejenbc2raktl46esxm44i 803 21 , , , work_fnploejenbc2raktl46esxm44i 803 22 w w NNP work_fnploejenbc2raktl46esxm44i 803 23 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 24 = = NFP work_fnploejenbc2raktl46esxm44i 803 25 uu uu NNP work_fnploejenbc2raktl46esxm44i 803 26 + + NNP work_fnploejenbc2raktl46esxm44i 803 27 w. w. NN work_fnploejenbc2raktl46esxm44i 803 28 For for IN work_fnploejenbc2raktl46esxm44i 803 29 the the DT work_fnploejenbc2raktl46esxm44i 803 30 score score NN work_fnploejenbc2raktl46esxm44i 803 31 function function NN work_fnploejenbc2raktl46esxm44i 803 32 f f NNP work_fnploejenbc2raktl46esxm44i 803 33 , , , work_fnploejenbc2raktl46esxm44i 803 34 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 803 35 take take VBP work_fnploejenbc2raktl46esxm44i 803 36 a a DT work_fnploejenbc2raktl46esxm44i 803 37 , , , work_fnploejenbc2raktl46esxm44i 803 38 = = SYM work_fnploejenbc2raktl46esxm44i 803 39 0 0 CD work_fnploejenbc2raktl46esxm44i 803 40 , , , work_fnploejenbc2raktl46esxm44i 803 41 a a NN work_fnploejenbc2raktl46esxm44i 803 42 , , , work_fnploejenbc2raktl46esxm44i 803 43 = = SYM work_fnploejenbc2raktl46esxm44i 803 44 1 1 CD work_fnploejenbc2raktl46esxm44i 803 45 and and CC work_fnploejenbc2raktl46esxm44i 803 46 f(x f(x CD work_fnploejenbc2raktl46esxm44i 803 47 , , , work_fnploejenbc2raktl46esxm44i 803 48 0 0 LS work_fnploejenbc2raktl46esxm44i 803 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 50 = = NFP work_fnploejenbc2raktl46esxm44i 803 51 x2 x2 NN work_fnploejenbc2raktl46esxm44i 803 52 , , , work_fnploejenbc2raktl46esxm44i 803 53 f(x f(x NNP work_fnploejenbc2raktl46esxm44i 803 54 , , , work_fnploejenbc2raktl46esxm44i 803 55 1)=(x-1)2 1)=(x-1)2 CD work_fnploejenbc2raktl46esxm44i 803 56 on on IN work_fnploejenbc2raktl46esxm44i 803 57 CO CO NNP work_fnploejenbc2raktl46esxm44i 803 58 , , , work_fnploejenbc2raktl46esxm44i 803 59 11 11 CD work_fnploejenbc2raktl46esxm44i 803 60 , , , work_fnploejenbc2raktl46esxm44i 803 61 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 803 62 are be VBP work_fnploejenbc2raktl46esxm44i 803 63 going go VBG work_fnploejenbc2raktl46esxm44i 803 64 to to TO work_fnploejenbc2raktl46esxm44i 803 65 show show VB work_fnploejenbc2raktl46esxm44i 803 66 that that IN work_fnploejenbc2raktl46esxm44i 803 67 there there EX work_fnploejenbc2raktl46esxm44i 803 68 is be VBZ work_fnploejenbc2raktl46esxm44i 803 69 no no DT work_fnploejenbc2raktl46esxm44i 803 70 transform transform NN work_fnploejenbc2raktl46esxm44i 803 71 h h NN work_fnploejenbc2raktl46esxm44i 803 72 : : : work_fnploejenbc2raktl46esxm44i 803 73 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 803 74 0 0 CD work_fnploejenbc2raktl46esxm44i 803 75 , , , work_fnploejenbc2raktl46esxm44i 803 76 l l NN work_fnploejenbc2raktl46esxm44i 803 77 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 803 78 -+ -+ . work_fnploejenbc2raktl46esxm44i 803 79 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 803 80 0 0 CD work_fnploejenbc2raktl46esxm44i 803 81 , , , work_fnploejenbc2raktl46esxm44i 803 82 l l NN work_fnploejenbc2raktl46esxm44i 803 83 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 803 84 such such JJ work_fnploejenbc2raktl46esxm44i 803 85 that that IN work_fnploejenbc2raktl46esxm44i 803 86 h(z h(z NNP work_fnploejenbc2raktl46esxm44i 803 87 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 88 = = NFP work_fnploejenbc2raktl46esxm44i 803 89 h(x h(x NNP work_fnploejenbc2raktl46esxm44i 803 90 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 91 + + SYM work_fnploejenbc2raktl46esxm44i 803 92 h(Y h(y LS work_fnploejenbc2raktl46esxm44i 803 93 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 94 when when WRB work_fnploejenbc2raktl46esxm44i 803 95 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 803 96 x x NNP work_fnploejenbc2raktl46esxm44i 803 97 , , , work_fnploejenbc2raktl46esxm44i 803 98 y y NNP work_fnploejenbc2raktl46esxm44i 803 99 , , , work_fnploejenbc2raktl46esxm44i 803 100 z z NNP work_fnploejenbc2raktl46esxm44i 803 101 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 803 102 is be VBZ work_fnploejenbc2raktl46esxm44i 803 103 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 803 104 . . . work_fnploejenbc2raktl46esxm44i 804 1 As as IN work_fnploejenbc2raktl46esxm44i 804 2 a a DT work_fnploejenbc2raktl46esxm44i 804 3 consequence consequence NN work_fnploejenbc2raktl46esxm44i 804 4 , , , work_fnploejenbc2raktl46esxm44i 804 5 if if IN work_fnploejenbc2raktl46esxm44i 804 6 p p NN work_fnploejenbc2raktl46esxm44i 804 7 is be VBZ work_fnploejenbc2raktl46esxm44i 804 8 uniformly uniformly RB work_fnploejenbc2raktl46esxm44i 804 9 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 804 10 , , , work_fnploejenbc2raktl46esxm44i 804 11 p p LS work_fnploejenbc2raktl46esxm44i 804 12 need nee MD work_fnploejenbc2raktl46esxm44i 804 13 not not RB work_fnploejenbc2raktl46esxm44i 804 14 be be VB work_fnploejenbc2raktl46esxm44i 804 15 transformable transformable JJ work_fnploejenbc2raktl46esxm44i 804 16 to to IN work_fnploejenbc2raktl46esxm44i 804 17 a a DT work_fnploejenbc2raktl46esxm44i 804 18 finitely finitely RB work_fnploejenbc2raktl46esxm44i 804 19 additive additive JJ work_fnploejenbc2raktl46esxm44i 804 20 probability probability NN work_fnploejenbc2raktl46esxm44i 804 21 measure measure NN work_fnploejenbc2raktl46esxm44i 804 22 . . . work_fnploejenbc2raktl46esxm44i 805 1 With with IN work_fnploejenbc2raktl46esxm44i 805 2 the the DT work_fnploejenbc2raktl46esxm44i 805 3 notation notation NN work_fnploejenbc2raktl46esxm44i 805 4 of of IN work_fnploejenbc2raktl46esxm44i 805 5 Section section NN work_fnploejenbc2raktl46esxm44i 805 6 3 3 CD work_fnploejenbc2raktl46esxm44i 805 7 , , , work_fnploejenbc2raktl46esxm44i 805 8 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 805 9 have have VBP work_fnploejenbc2raktl46esxm44i 805 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 805 11 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 805 12 x x NN work_fnploejenbc2raktl46esxm44i 805 13 - - NN work_fnploejenbc2raktl46esxm44i 805 14 l)y2 l)y2 NNP work_fnploejenbc2raktl46esxm44i 805 15 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 805 16 x-1)2y x-1)2y NNP work_fnploejenbc2raktl46esxm44i 805 17 z z NNP work_fnploejenbc2raktl46esxm44i 805 18 - - HYPH work_fnploejenbc2raktl46esxm44i 805 19 l l NNP work_fnploejenbc2raktl46esxm44i 805 20 J=2 J=2 NNP work_fnploejenbc2raktl46esxm44i 805 21 x(y-1)2 x(y-1)2 NNP work_fnploejenbc2raktl46esxm44i 805 22 x2 x2 NN work_fnploejenbc2raktl46esxm44i 805 23 + + CC work_fnploejenbc2raktl46esxm44i 805 24 1 1 CD work_fnploejenbc2raktl46esxm44i 805 25 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 805 26 z z NNP work_fnploejenbc2raktl46esxm44i 805 27 - - HYPH work_fnploejenbc2raktl46esxm44i 805 28 l l NN work_fnploejenbc2raktl46esxm44i 805 29 . . . work_fnploejenbc2raktl46esxm44i 806 1 XY2 XY2 NNP work_fnploejenbc2raktl46esxm44i 806 2 X’Y X’Y NNP work_fnploejenbc2raktl46esxm44i 806 3 Z z NN work_fnploejenbc2raktl46esxm44i 806 4 1 1 CD work_fnploejenbc2raktl46esxm44i 806 5 To to TO work_fnploejenbc2raktl46esxm44i 806 6 find find VB work_fnploejenbc2raktl46esxm44i 806 7 2 2 CD work_fnploejenbc2raktl46esxm44i 806 8 = = SYM work_fnploejenbc2raktl46esxm44i 806 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 806 10 x x NNP work_fnploejenbc2raktl46esxm44i 806 11 , , , work_fnploejenbc2raktl46esxm44i 806 12 y y NNP work_fnploejenbc2raktl46esxm44i 806 13 , , , work_fnploejenbc2raktl46esxm44i 806 14 z z NNP work_fnploejenbc2raktl46esxm44i 806 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 806 16 - - . work_fnploejenbc2raktl46esxm44i 806 17 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 806 18 , , , work_fnploejenbc2raktl46esxm44i 806 19 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 806 20 use use VBP work_fnploejenbc2raktl46esxm44i 806 21 the the DT work_fnploejenbc2raktl46esxm44i 806 22 sufficient sufficient JJ work_fnploejenbc2raktl46esxm44i 806 23 condition condition NN work_fnploejenbc2raktl46esxm44i 806 24 given give VBN work_fnploejenbc2raktl46esxm44i 806 25 in in IN work_fnploejenbc2raktl46esxm44i 806 26 Theorem Theorem NNP work_fnploejenbc2raktl46esxm44i 806 27 3.2.2 3.2.2 NNP work_fnploejenbc2raktl46esxm44i 806 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 806 29 e e NN work_fnploejenbc2raktl46esxm44i 806 30 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 806 31 . . . work_fnploejenbc2raktl46esxm44i 807 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 807 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 807 3 TO to IN work_fnploejenbc2raktl46esxm44i 807 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 807 5 591 591 CD work_fnploejenbc2raktl46esxm44i 807 6 First first RB work_fnploejenbc2raktl46esxm44i 807 7 , , , work_fnploejenbc2raktl46esxm44i 807 8 det det NNP work_fnploejenbc2raktl46esxm44i 807 9 J J NNP work_fnploejenbc2raktl46esxm44i 807 10 = = SYM work_fnploejenbc2raktl46esxm44i 807 11 0 0 NFP work_fnploejenbc2raktl46esxm44i 807 12 gives give VBZ work_fnploejenbc2raktl46esxm44i 807 13 x*+-y*-xy(x+y x*+-y*-xy(x+y NNP work_fnploejenbc2raktl46esxm44i 807 14 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 807 15 ‘ ' `` work_fnploejenbc2raktl46esxm44i 807 16 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 807 17 ” " '' work_fnploejenbc2raktl46esxm44i 807 18 ‘ ' `` work_fnploejenbc2raktl46esxm44i 807 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 807 20 = = NFP work_fnploejenbc2raktl46esxm44i 807 21 2(x+y)-3xy- 2(x+y)-3xy- CD work_fnploejenbc2raktl46esxm44i 807 22 1 1 CD work_fnploejenbc2raktl46esxm44i 807 23 for for IN work_fnploejenbc2raktl46esxm44i 807 24 xy#O xy#O NNP work_fnploejenbc2raktl46esxm44i 807 25 , , , work_fnploejenbc2raktl46esxm44i 807 26 1 1 CD work_fnploejenbc2raktl46esxm44i 807 27 . . . work_fnploejenbc2raktl46esxm44i 808 1 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 808 2 * * NFP work_fnploejenbc2raktl46esxm44i 808 3 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 808 4 ForO foro NN work_fnploejenbc2raktl46esxm44i 808 5 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 808 6 x x SYM work_fnploejenbc2raktl46esxm44i 808 7 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 808 8 l l NNP work_fnploejenbc2raktl46esxm44i 808 9 , , , work_fnploejenbc2raktl46esxm44i 808 10 y y NNP work_fnploejenbc2raktl46esxm44i 808 11 = = SYM work_fnploejenbc2raktl46esxm44i 808 12 l l NN work_fnploejenbc2raktl46esxm44i 808 13 , , , work_fnploejenbc2raktl46esxm44i 808 14 wehavez=1.For~=(x,1,l)withO wehavez=1.For~=(x,1,l)withO NNP work_fnploejenbc2raktl46esxm44i 808 15 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 808 16 x x SYM work_fnploejenbc2raktl46esxm44i 808 17 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 808 18 l l NN work_fnploejenbc2raktl46esxm44i 808 19 , , , work_fnploejenbc2raktl46esxm44i 808 20 Jhas Jhas NNP work_fnploejenbc2raktl46esxm44i 808 21 rank rank NNP work_fnploejenbc2raktl46esxm44i 808 22 p p NN work_fnploejenbc2raktl46esxm44i 808 23 = = SYM work_fnploejenbc2raktl46esxm44i 808 24 2 2 CD work_fnploejenbc2raktl46esxm44i 808 25 with with IN work_fnploejenbc2raktl46esxm44i 808 26 R r NN work_fnploejenbc2raktl46esxm44i 808 27 = = SYM work_fnploejenbc2raktl46esxm44i 808 28 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 808 29 0 0 NFP work_fnploejenbc2raktl46esxm44i 808 30 , , , work_fnploejenbc2raktl46esxm44i 808 31 0 0 CD work_fnploejenbc2raktl46esxm44i 808 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 808 33 , , , work_fnploejenbc2raktl46esxm44i 808 34 and and CC work_fnploejenbc2raktl46esxm44i 808 35 so so RB work_fnploejenbc2raktl46esxm44i 808 36 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 808 37 x x NNS work_fnploejenbc2raktl46esxm44i 808 38 , , , work_fnploejenbc2raktl46esxm44i 808 39 1 1 CD work_fnploejenbc2raktl46esxm44i 808 40 , , , work_fnploejenbc2raktl46esxm44i 808 41 1 1 CD work_fnploejenbc2raktl46esxm44i 808 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 808 43 is be VBZ work_fnploejenbc2raktl46esxm44i 808 44 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 808 45 . . . work_fnploejenbc2raktl46esxm44i 809 1 If if IN work_fnploejenbc2raktl46esxm44i 809 2 h h NN work_fnploejenbc2raktl46esxm44i 809 3 : : : work_fnploejenbc2raktl46esxm44i 809 4 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 809 5 0 0 CD work_fnploejenbc2raktl46esxm44i 809 6 , , , work_fnploejenbc2raktl46esxm44i 809 7 l l NN work_fnploejenbc2raktl46esxm44i 809 8 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 809 9 -+ -+ . work_fnploejenbc2raktl46esxm44i 809 10 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 809 11 0 0 NFP work_fnploejenbc2raktl46esxm44i 809 12 , , , work_fnploejenbc2raktl46esxm44i 809 13 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 809 14 ] ] -RRB- work_fnploejenbc2raktl46esxm44i 809 15 is be VBZ work_fnploejenbc2raktl46esxm44i 809 16 such such JJ work_fnploejenbc2raktl46esxm44i 809 17 that that IN work_fnploejenbc2raktl46esxm44i 809 18 h(z h(z NNP work_fnploejenbc2raktl46esxm44i 809 19 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 20 = = NFP work_fnploejenbc2raktl46esxm44i 809 21 h(x)-th(y h(x)-th(y NNP work_fnploejenbc2raktl46esxm44i 809 22 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 23 for for IN work_fnploejenbc2raktl46esxm44i 809 24 any any DT work_fnploejenbc2raktl46esxm44i 809 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 809 26 x x NN work_fnploejenbc2raktl46esxm44i 809 27 , , , work_fnploejenbc2raktl46esxm44i 809 28 y y NNP work_fnploejenbc2raktl46esxm44i 809 29 , , , work_fnploejenbc2raktl46esxm44i 809 30 z z NNP work_fnploejenbc2raktl46esxm44i 809 31 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 32 - - . work_fnploejenbc2raktl46esxm44i 809 33 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 809 34 , , , work_fnploejenbc2raktl46esxm44i 809 35 then then RB work_fnploejenbc2raktl46esxm44i 809 36 , , , work_fnploejenbc2raktl46esxm44i 809 37 in in IN work_fnploejenbc2raktl46esxm44i 809 38 particular particular JJ work_fnploejenbc2raktl46esxm44i 809 39 , , , work_fnploejenbc2raktl46esxm44i 809 40 h(l)=h(x)+h(l h(l)=h(x)+h(l NNP work_fnploejenbc2raktl46esxm44i 809 41 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 42 , , , work_fnploejenbc2raktl46esxm44i 809 43 VXE(O VXE(O NNP work_fnploejenbc2raktl46esxm44i 809 44 , , , work_fnploejenbc2raktl46esxm44i 809 45 l l NN work_fnploejenbc2raktl46esxm44i 809 46 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 47 , , , work_fnploejenbc2raktl46esxm44i 809 48 implying imply VBG work_fnploejenbc2raktl46esxm44i 809 49 that that IN work_fnploejenbc2raktl46esxm44i 809 50 h(x h(x NNP work_fnploejenbc2raktl46esxm44i 809 51 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 52 = = NFP work_fnploejenbc2raktl46esxm44i 809 53 0 0 NFP work_fnploejenbc2raktl46esxm44i 809 54 , , , work_fnploejenbc2raktl46esxm44i 809 55 Vx Vx NNP work_fnploejenbc2raktl46esxm44i 809 56 E E NNP work_fnploejenbc2raktl46esxm44i 809 57 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 809 58 0 0 CD work_fnploejenbc2raktl46esxm44i 809 59 , , , work_fnploejenbc2raktl46esxm44i 809 60 1 1 CD work_fnploejenbc2raktl46esxm44i 809 61 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 809 62 . . . work_fnploejenbc2raktl46esxm44i 810 1 From from IN work_fnploejenbc2raktl46esxm44i 810 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 810 3 * * NFP work_fnploejenbc2raktl46esxm44i 810 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 810 5 , , , work_fnploejenbc2raktl46esxm44i 810 6 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 810 7 see see VBP work_fnploejenbc2raktl46esxm44i 810 8 that that IN work_fnploejenbc2raktl46esxm44i 810 9 when when WRB work_fnploejenbc2raktl46esxm44i 810 10 x= x= NNP work_fnploejenbc2raktl46esxm44i 810 11 y= y= NNP work_fnploejenbc2raktl46esxm44i 810 12 i i PRP work_fnploejenbc2raktl46esxm44i 810 13 , , , work_fnploejenbc2raktl46esxm44i 810 14 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 810 15 have have VBP work_fnploejenbc2raktl46esxm44i 810 16 z= z= NNP work_fnploejenbc2raktl46esxm44i 810 17 1 1 CD work_fnploejenbc2raktl46esxm44i 810 18 . . . work_fnploejenbc2raktl46esxm44i 811 1 For for IN work_fnploejenbc2raktl46esxm44i 811 2 x= x= NNP work_fnploejenbc2raktl46esxm44i 811 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 811 4 $ $ $ work_fnploejenbc2raktl46esxm44i 811 5 , , , work_fnploejenbc2raktl46esxm44i 811 6 i i PRP work_fnploejenbc2raktl46esxm44i 811 7 , , , work_fnploejenbc2raktl46esxm44i 811 8 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 811 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 811 10 , , , work_fnploejenbc2raktl46esxm44i 811 11 and and CC work_fnploejenbc2raktl46esxm44i 811 12 p p NN work_fnploejenbc2raktl46esxm44i 811 13 = = SYM work_fnploejenbc2raktl46esxm44i 811 14 2 2 CD work_fnploejenbc2raktl46esxm44i 811 15 . . . work_fnploejenbc2raktl46esxm44i 812 1 For for IN work_fnploejenbc2raktl46esxm44i 812 2 with with IN work_fnploejenbc2raktl46esxm44i 812 3 and and CC work_fnploejenbc2raktl46esxm44i 812 4 RJ RJ NNP work_fnploejenbc2raktl46esxm44i 812 5 , , , work_fnploejenbc2raktl46esxm44i 812 6 = = NFP work_fnploejenbc2raktl46esxm44i 812 7 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 812 8 $ $ $ work_fnploejenbc2raktl46esxm44i 812 9 , , , work_fnploejenbc2raktl46esxm44i 812 10 -a -a NFP work_fnploejenbc2raktl46esxm44i 812 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 812 12 , , , work_fnploejenbc2raktl46esxm44i 812 13 we -PRON- PRP work_fnploejenbc2raktl46esxm44i 812 14 have have VBP work_fnploejenbc2raktl46esxm44i 812 15 R r NN work_fnploejenbc2raktl46esxm44i 812 16 = = NFP work_fnploejenbc2raktl46esxm44i 812 17 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 812 18 - - HYPH work_fnploejenbc2raktl46esxm44i 812 19 LO LO NNP work_fnploejenbc2raktl46esxm44i 812 20 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 812 21 , , , work_fnploejenbc2raktl46esxm44i 812 22 so so IN work_fnploejenbc2raktl46esxm44i 812 23 that that IN work_fnploejenbc2raktl46esxm44i 812 24 f f NN work_fnploejenbc2raktl46esxm44i 812 25 = = NN work_fnploejenbc2raktl46esxm44i 812 26 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 812 27 4 4 CD work_fnploejenbc2raktl46esxm44i 812 28 , , , work_fnploejenbc2raktl46esxm44i 812 29 4 4 CD work_fnploejenbc2raktl46esxm44i 812 30 , , , work_fnploejenbc2raktl46esxm44i 812 31 1 1 CD work_fnploejenbc2raktl46esxm44i 812 32 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 812 33 is be VBZ work_fnploejenbc2raktl46esxm44i 812 34 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 812 35 , , , work_fnploejenbc2raktl46esxm44i 812 36 and and CC work_fnploejenbc2raktl46esxm44i 812 37 hence hence RB work_fnploejenbc2raktl46esxm44i 812 38 Now now RB work_fnploejenbc2raktl46esxm44i 812 39 it -PRON- PRP work_fnploejenbc2raktl46esxm44i 812 40 can can MD work_fnploejenbc2raktl46esxm44i 812 41 be be VB work_fnploejenbc2raktl46esxm44i 812 42 seen see VBN work_fnploejenbc2raktl46esxm44i 812 43 that that IN work_fnploejenbc2raktl46esxm44i 812 44 i i PRP work_fnploejenbc2raktl46esxm44i 812 45 = = NFP work_fnploejenbc2raktl46esxm44i 812 46 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 812 47 0 0 NFP work_fnploejenbc2raktl46esxm44i 812 48 , , , work_fnploejenbc2raktl46esxm44i 812 49 0,O 0,o CD work_fnploejenbc2raktl46esxm44i 812 50 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 812 51 is be VBZ work_fnploejenbc2raktl46esxm44i 812 52 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 812 53 , , , work_fnploejenbc2raktl46esxm44i 812 54 since since IN work_fnploejenbc2raktl46esxm44i 812 55 P’L P’L NNS work_fnploejenbc2raktl46esxm44i 812 56 and and CC work_fnploejenbc2raktl46esxm44i 812 57 contains contain VBZ work_fnploejenbc2raktl46esxm44i 812 58 one one CD work_fnploejenbc2raktl46esxm44i 812 59 zero zero CD work_fnploejenbc2raktl46esxm44i 812 60 component component NN work_fnploejenbc2raktl46esxm44i 812 61 . . . work_fnploejenbc2raktl46esxm44i 813 1 Thus thus RB work_fnploejenbc2raktl46esxm44i 813 2 h(O)= h(O)= NNP work_fnploejenbc2raktl46esxm44i 813 3 h(O)+ h(O)+ NNS work_fnploejenbc2raktl46esxm44i 813 4 h(O h(O NNP work_fnploejenbc2raktl46esxm44i 813 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 813 6 , , , work_fnploejenbc2raktl46esxm44i 813 7 implying imply VBG work_fnploejenbc2raktl46esxm44i 813 8 that that IN work_fnploejenbc2raktl46esxm44i 813 9 h(O h(o NN work_fnploejenbc2raktl46esxm44i 813 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 813 11 = = NFP work_fnploejenbc2raktl46esxm44i 813 12 0 0 NFP work_fnploejenbc2raktl46esxm44i 813 13 . . . work_fnploejenbc2raktl46esxm44i 814 1 Therefore therefore RB work_fnploejenbc2raktl46esxm44i 814 2 , , , work_fnploejenbc2raktl46esxm44i 814 3 h h NN work_fnploejenbc2raktl46esxm44i 814 4 c c NN work_fnploejenbc2raktl46esxm44i 814 5 0 0 CD work_fnploejenbc2raktl46esxm44i 814 6 on on IN work_fnploejenbc2raktl46esxm44i 814 7 [ [ -LRB- work_fnploejenbc2raktl46esxm44i 814 8 0 0 CD work_fnploejenbc2raktl46esxm44i 814 9 , , , work_fnploejenbc2raktl46esxm44i 814 10 11 11 CD work_fnploejenbc2raktl46esxm44i 814 11 . . . work_fnploejenbc2raktl46esxm44i 815 1 592 592 CD work_fnploejenbc2raktl46esxm44i 815 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 815 3 , , , work_fnploejenbc2raktl46esxm44i 815 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 815 5 , , , work_fnploejenbc2raktl46esxm44i 815 6 AND and CC work_fnploejenbc2raktl46esxm44i 815 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 815 8 EXAMPLE EXAMPLE NNP work_fnploejenbc2raktl46esxm44i 815 9 2 2 CD work_fnploejenbc2raktl46esxm44i 815 10 . . . work_fnploejenbc2raktl46esxm44i 816 1 Consider consider VB work_fnploejenbc2raktl46esxm44i 816 2 a a DT work_fnploejenbc2raktl46esxm44i 816 3 as as IN work_fnploejenbc2raktl46esxm44i 816 4 in in IN work_fnploejenbc2raktl46esxm44i 816 5 Example Example NNP work_fnploejenbc2raktl46esxm44i 816 6 1 1 CD work_fnploejenbc2raktl46esxm44i 816 7 . . . work_fnploejenbc2raktl46esxm44i 817 1 Let let VB work_fnploejenbc2raktl46esxm44i 817 2 f f PRP work_fnploejenbc2raktl46esxm44i 817 3 be be VB work_fnploejenbc2raktl46esxm44i 817 4 an an DT work_fnploejenbc2raktl46esxm44i 817 5 arbitrary arbitrary JJ work_fnploejenbc2raktl46esxm44i 817 6 score score NN work_fnploejenbc2raktl46esxm44i 817 7 function function NN work_fnploejenbc2raktl46esxm44i 817 8 and and CC work_fnploejenbc2raktl46esxm44i 817 9 ti3 ti3 NNP work_fnploejenbc2raktl46esxm44i 817 10 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 817 11 & & CC work_fnploejenbc2raktl46esxm44i 817 12 u u NNP work_fnploejenbc2raktl46esxm44i 817 13 , , , work_fnploejenbc2raktl46esxm44i 817 14 w w NNP work_fnploejenbc2raktl46esxm44i 817 15 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 817 16 = = SYM work_fnploejenbc2raktl46esxm44i 817 17 4%(401(~ 4%(401(~ CD work_fnploejenbc2raktl46esxm44i 817 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 817 19 + + CC work_fnploejenbc2raktl46esxm44i 817 20 e(u e(u NN work_fnploejenbc2raktl46esxm44i 817 21 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 817 22 + + CC work_fnploejenbc2raktl46esxm44i 817 23 % % NN work_fnploejenbc2raktl46esxm44i 817 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 817 25 W w NN work_fnploejenbc2raktl46esxm44i 817 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 817 27 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 817 28 > > XX work_fnploejenbc2raktl46esxm44i 817 29 where where WRB work_fnploejenbc2raktl46esxm44i 817 30 ‘ ' `` work_fnploejenbc2raktl46esxm44i 817 31 pi pi NN work_fnploejenbc2raktl46esxm44i 817 32 : : : work_fnploejenbc2raktl46esxm44i 817 33 R r NN work_fnploejenbc2raktl46esxm44i 817 34 + + CC work_fnploejenbc2raktl46esxm44i 817 35 R r NN work_fnploejenbc2raktl46esxm44i 817 36 , , , work_fnploejenbc2raktl46esxm44i 817 37 j j NNP work_fnploejenbc2raktl46esxm44i 817 38 = = SYM work_fnploejenbc2raktl46esxm44i 817 39 0 0 CD work_fnploejenbc2raktl46esxm44i 817 40 , , , work_fnploejenbc2raktl46esxm44i 817 41 1,2 1,2 CD work_fnploejenbc2raktl46esxm44i 817 42 , , , work_fnploejenbc2raktl46esxm44i 817 43 3 3 CD work_fnploejenbc2raktl46esxm44i 817 44 are be VBP work_fnploejenbc2raktl46esxm44i 817 45 four four CD work_fnploejenbc2raktl46esxm44i 817 46 surjective surjective JJ work_fnploejenbc2raktl46esxm44i 817 47 , , , work_fnploejenbc2raktl46esxm44i 817 48 increasing increase VBG work_fnploejenbc2raktl46esxm44i 817 49 , , , work_fnploejenbc2raktl46esxm44i 817 50 continuously continuously RB work_fnploejenbc2raktl46esxm44i 817 51 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 817 52 functions function NNS work_fnploejenbc2raktl46esxm44i 817 53 . . . work_fnploejenbc2raktl46esxm44i 818 1 This this DT work_fnploejenbc2raktl46esxm44i 818 2 is be VBZ work_fnploejenbc2raktl46esxm44i 818 3 a a DT work_fnploejenbc2raktl46esxm44i 818 4 generalized generalize VBN work_fnploejenbc2raktl46esxm44i 818 5 form form NN work_fnploejenbc2raktl46esxm44i 818 6 of of IN work_fnploejenbc2raktl46esxm44i 818 7 the the DT work_fnploejenbc2raktl46esxm44i 818 8 additive additive JJ work_fnploejenbc2raktl46esxm44i 818 9 aggrega- aggrega- NN work_fnploejenbc2raktl46esxm44i 818 10 tion tion NN work_fnploejenbc2raktl46esxm44i 818 11 function function NN work_fnploejenbc2raktl46esxm44i 818 12 . . . work_fnploejenbc2raktl46esxm44i 819 1 Note note VB work_fnploejenbc2raktl46esxm44i 819 2 that that IN work_fnploejenbc2raktl46esxm44i 819 3 11/3(~ 11/3(~ CD work_fnploejenbc2raktl46esxm44i 819 4 , , , work_fnploejenbc2raktl46esxm44i 819 5 v v NNP work_fnploejenbc2raktl46esxm44i 819 6 , , , work_fnploejenbc2raktl46esxm44i 819 7 w w NNP work_fnploejenbc2raktl46esxm44i 819 8 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 819 9 = = NFP work_fnploejenbc2raktl46esxm44i 819 10 UD UD NNP work_fnploejenbc2raktl46esxm44i 819 11 + + SYM work_fnploejenbc2raktl46esxm44i 819 12 w w NN work_fnploejenbc2raktl46esxm44i 819 13 in in IN work_fnploejenbc2raktl46esxm44i 819 14 Example Example NNP work_fnploejenbc2raktl46esxm44i 819 15 1 1 CD work_fnploejenbc2raktl46esxm44i 819 16 is be VBZ work_fnploejenbc2raktl46esxm44i 819 17 not not RB work_fnploejenbc2raktl46esxm44i 819 18 of of IN work_fnploejenbc2raktl46esxm44i 819 19 this this DT work_fnploejenbc2raktl46esxm44i 819 20 form form NN work_fnploejenbc2raktl46esxm44i 819 21 . . . work_fnploejenbc2raktl46esxm44i 820 1 Large large JJ work_fnploejenbc2raktl46esxm44i 820 2 classes class NNS work_fnploejenbc2raktl46esxm44i 820 3 of of IN work_fnploejenbc2raktl46esxm44i 820 4 functions function NNS work_fnploejenbc2raktl46esxm44i 820 5 of of IN work_fnploejenbc2raktl46esxm44i 820 6 several several JJ work_fnploejenbc2raktl46esxm44i 820 7 variables variable NNS work_fnploejenbc2raktl46esxm44i 820 8 can can MD work_fnploejenbc2raktl46esxm44i 820 9 be be VB work_fnploejenbc2raktl46esxm44i 820 10 represented represent VBN work_fnploejenbc2raktl46esxm44i 820 11 , , , work_fnploejenbc2raktl46esxm44i 820 12 or or CC work_fnploejenbc2raktl46esxm44i 820 13 approximated approximate VBN work_fnploejenbc2raktl46esxm44i 820 14 , , , work_fnploejenbc2raktl46esxm44i 820 15 by by IN work_fnploejenbc2raktl46esxm44i 820 16 general general JJ work_fnploejenbc2raktl46esxm44i 820 17 forms form NNS work_fnploejenbc2raktl46esxm44i 820 18 of of IN work_fnploejenbc2raktl46esxm44i 820 19 addition addition NN work_fnploejenbc2raktl46esxm44i 820 20 of of IN work_fnploejenbc2raktl46esxm44i 820 21 simple simple JJ work_fnploejenbc2raktl46esxm44i 820 22 argument argument NN work_fnploejenbc2raktl46esxm44i 820 23 functions function NNS work_fnploejenbc2raktl46esxm44i 820 24 as as IN work_fnploejenbc2raktl46esxm44i 820 25 above above RB work_fnploejenbc2raktl46esxm44i 820 26 ; ; : work_fnploejenbc2raktl46esxm44i 820 27 see see VB work_fnploejenbc2raktl46esxm44i 820 28 , , , work_fnploejenbc2raktl46esxm44i 820 29 e.g. e.g. RB work_fnploejenbc2raktl46esxm44i 820 30 , , , work_fnploejenbc2raktl46esxm44i 820 31 the the DT work_fnploejenbc2raktl46esxm44i 820 32 survey survey NN work_fnploejenbc2raktl46esxm44i 820 33 paper paper NN work_fnploejenbc2raktl46esxm44i 820 34 of of IN work_fnploejenbc2raktl46esxm44i 820 35 Sprecher Sprecher NNP work_fnploejenbc2raktl46esxm44i 820 36 1291 1291 CD work_fnploejenbc2raktl46esxm44i 820 37 on on IN work_fnploejenbc2raktl46esxm44i 820 38 the the DT work_fnploejenbc2raktl46esxm44i 820 39 work work NN work_fnploejenbc2raktl46esxm44i 820 40 of of IN work_fnploejenbc2raktl46esxm44i 820 41 Kolmogorov Kolmogorov NNP work_fnploejenbc2raktl46esxm44i 820 42 and and CC work_fnploejenbc2raktl46esxm44i 820 43 others other NNS work_fnploejenbc2raktl46esxm44i 820 44 in in IN work_fnploejenbc2raktl46esxm44i 820 45 considering consider VBG work_fnploejenbc2raktl46esxm44i 820 46 the the DT work_fnploejenbc2raktl46esxm44i 820 47 related related JJ work_fnploejenbc2raktl46esxm44i 820 48 13th 13th NN work_fnploejenbc2raktl46esxm44i 820 49 - - HYPH work_fnploejenbc2raktl46esxm44i 820 50 problem problem NN work_fnploejenbc2raktl46esxm44i 820 51 of of IN work_fnploejenbc2raktl46esxm44i 820 52 Hilbert Hilbert NNP work_fnploejenbc2raktl46esxm44i 820 53 . . . work_fnploejenbc2raktl46esxm44i 821 1 If if IN work_fnploejenbc2raktl46esxm44i 821 2 $ $ $ work_fnploejenbc2raktl46esxm44i 821 3 = = SYM work_fnploejenbc2raktl46esxm44i 821 4 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 821 5 x x NN work_fnploejenbc2raktl46esxm44i 821 6 , , , work_fnploejenbc2raktl46esxm44i 821 7 y y NNP work_fnploejenbc2raktl46esxm44i 821 8 , , , work_fnploejenbc2raktl46esxm44i 821 9 z z NNP work_fnploejenbc2raktl46esxm44i 821 10 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 11 is be VBZ work_fnploejenbc2raktl46esxm44i 821 12 WLAD WLAD NNP work_fnploejenbc2raktl46esxm44i 821 13 then then RB work_fnploejenbc2raktl46esxm44i 821 14 det det NNP work_fnploejenbc2raktl46esxm44i 821 15 J= J= NNP work_fnploejenbc2raktl46esxm44i 821 16 0 0 NFP work_fnploejenbc2raktl46esxm44i 821 17 , , , work_fnploejenbc2raktl46esxm44i 821 18 implying imply VBG work_fnploejenbc2raktl46esxm44i 821 19 that that IN work_fnploejenbc2raktl46esxm44i 821 20 p p NN work_fnploejenbc2raktl46esxm44i 821 21 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 821 22 p p NN work_fnploejenbc2raktl46esxm44i 821 23 , , , work_fnploejenbc2raktl46esxm44i 821 24 of(4 of(4 RB work_fnploejenbc2raktl46esxm44i 821 25 = = NFP work_fnploejenbc2raktl46esxm44i 821 26 Pqp Pqp NNP work_fnploejenbc2raktl46esxm44i 821 27 , , , work_fnploejenbc2raktl46esxm44i 821 28 & & CC work_fnploejenbc2raktl46esxm44i 821 29 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 30 + + SYM work_fnploejenbc2raktl46esxm44i 821 31 p,,of(Y)7 p,,of(Y)7 NNP work_fnploejenbc2raktl46esxm44i 821 32 where where WRB work_fnploejenbc2raktl46esxm44i 821 33 Pa Pa NNP work_fnploejenbc2raktl46esxm44i 821 34 , , , work_fnploejenbc2raktl46esxm44i 821 35 & & CC work_fnploejenbc2raktl46esxm44i 821 36 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 37 = = SYM work_fnploejenbc2raktl46esxm44i 821 38 dCf(c dCf(c NNP work_fnploejenbc2raktl46esxm44i 821 39 011 011 CD work_fnploejenbc2raktl46esxm44i 821 40 f’(c f’(c JJ work_fnploejenbc2raktl46esxm44i 821 41 0 0 NFP work_fnploejenbc2raktl46esxm44i 821 42 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 43 cp cp NNP work_fnploejenbc2raktl46esxm44i 821 44 : : : work_fnploejenbc2raktl46esxm44i 821 45 Cf(k Cf(k NNP work_fnploejenbc2raktl46esxm44i 821 46 O)l O)l NNP work_fnploejenbc2raktl46esxm44i 821 47 f’(c f’(c NN work_fnploejenbc2raktl46esxm44i 821 48 0 0 CD work_fnploejenbc2raktl46esxm44i 821 49 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 50 - - HYPH work_fnploejenbc2raktl46esxm44i 821 51 dCf dCf NNP work_fnploejenbc2raktl46esxm44i 821 52 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 821 53 & & CC work_fnploejenbc2raktl46esxm44i 821 54 1 1 LS work_fnploejenbc2raktl46esxm44i 821 55 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 56 I i NN work_fnploejenbc2raktl46esxm44i 821 57 f’(t f’(t . work_fnploejenbc2raktl46esxm44i 821 58 , , , work_fnploejenbc2raktl46esxm44i 821 59 1 1 CD work_fnploejenbc2raktl46esxm44i 821 60 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 821 61 ’ ' '' work_fnploejenbc2raktl46esxm44i 821 62 EXAMPLE example NN work_fnploejenbc2raktl46esxm44i 821 63 3 3 CD work_fnploejenbc2raktl46esxm44i 821 64 . . . work_fnploejenbc2raktl46esxm44i 822 1 As as IN work_fnploejenbc2raktl46esxm44i 822 2 a a DT work_fnploejenbc2raktl46esxm44i 822 3 special special JJ work_fnploejenbc2raktl46esxm44i 822 4 case case NN work_fnploejenbc2raktl46esxm44i 822 5 of of IN work_fnploejenbc2raktl46esxm44i 822 6 Example Example NNP work_fnploejenbc2raktl46esxm44i 822 7 2 2 CD work_fnploejenbc2raktl46esxm44i 822 8 , , , work_fnploejenbc2raktl46esxm44i 822 9 one one PRP work_fnploejenbc2raktl46esxm44i 822 10 can can MD work_fnploejenbc2raktl46esxm44i 822 11 consider consider VB work_fnploejenbc2raktl46esxm44i 822 12 uncer- uncer- JJ work_fnploejenbc2raktl46esxm44i 822 13 tainty tainty NN work_fnploejenbc2raktl46esxm44i 822 14 games game NNS work_fnploejenbc2raktl46esxm44i 822 15 with with IN work_fnploejenbc2raktl46esxm44i 822 16 symmetric symmetric JJ work_fnploejenbc2raktl46esxm44i 822 17 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 822 18 functions function NNS work_fnploejenbc2raktl46esxm44i 822 19 as as IN work_fnploejenbc2raktl46esxm44i 822 20 follows follow VBZ work_fnploejenbc2raktl46esxm44i 822 21 . . . work_fnploejenbc2raktl46esxm44i 823 1 Let let VB work_fnploejenbc2raktl46esxm44i 823 2 g g NN work_fnploejenbc2raktl46esxm44i 823 3 : : : work_fnploejenbc2raktl46esxm44i 823 4 R r NN work_fnploejenbc2raktl46esxm44i 823 5 + + CC work_fnploejenbc2raktl46esxm44i 823 6 R r NN work_fnploejenbc2raktl46esxm44i 823 7 be be VB work_fnploejenbc2raktl46esxm44i 823 8 a a DT work_fnploejenbc2raktl46esxm44i 823 9 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 823 10 surjective surjective JJ work_fnploejenbc2raktl46esxm44i 823 11 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 823 12 , , , work_fnploejenbc2raktl46esxm44i 823 13 increasing increase VBG work_fnploejenbc2raktl46esxm44i 823 14 , , , work_fnploejenbc2raktl46esxm44i 823 15 continuously continuously RB work_fnploejenbc2raktl46esxm44i 823 16 differentiable differentiable JJ work_fnploejenbc2raktl46esxm44i 823 17 function function NN work_fnploejenbc2raktl46esxm44i 823 18 . . . work_fnploejenbc2raktl46esxm44i 824 1 For for IN work_fnploejenbc2raktl46esxm44i 824 2 n n IN work_fnploejenbc2raktl46esxm44i 824 3 2 2 CD work_fnploejenbc2raktl46esxm44i 824 4 1 1 CD work_fnploejenbc2raktl46esxm44i 824 5 , , , work_fnploejenbc2raktl46esxm44i 824 6 define define VB work_fnploejenbc2raktl46esxm44i 824 7 as as IN work_fnploejenbc2raktl46esxm44i 824 8 IClg IClg NNP work_fnploejenbc2raktl46esxm44i 824 9 , , , work_fnploejenbc2raktl46esxm44i 824 10 ntXIY ntxiy IN work_fnploejenbc2raktl46esxm44i 824 11 ae.9 ae.9 NNP work_fnploejenbc2raktl46esxm44i 824 12 xn)=g xn)=g NNP work_fnploejenbc2raktl46esxm44i 824 13 - - : work_fnploejenbc2raktl46esxm44i 824 14 l l NNP work_fnploejenbc2raktl46esxm44i 824 15 , , , work_fnploejenbc2raktl46esxm44i 824 16 i i PRP work_fnploejenbc2raktl46esxm44i 824 17 gtxi gtxi VBP work_fnploejenbc2raktl46esxm44i 824 18 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 824 19 L l NN work_fnploejenbc2raktl46esxm44i 824 20 > > XX work_fnploejenbc2raktl46esxm44i 824 21 The the DT work_fnploejenbc2raktl46esxm44i 824 22 game game NN work_fnploejenbc2raktl46esxm44i 824 23 Gs Gs NNP work_fnploejenbc2raktl46esxm44i 824 24 , , , work_fnploejenbc2raktl46esxm44i 824 25 * * NFP work_fnploejenbc2raktl46esxm44i 824 26 , , , work_fnploejenbc2raktl46esxm44i 824 27 can can MD work_fnploejenbc2raktl46esxm44i 824 28 be be VB work_fnploejenbc2raktl46esxm44i 824 29 identified identify VBN work_fnploejenbc2raktl46esxm44i 824 30 with with IN work_fnploejenbc2raktl46esxm44i 824 31 G g NN work_fnploejenbc2raktl46esxm44i 824 32 , , , work_fnploejenbc2raktl46esxm44i 824 33 , , , work_fnploejenbc2raktl46esxm44i 824 34 , , , work_fnploejenbc2raktl46esxm44i 824 35 + + CC work_fnploejenbc2raktl46esxm44i 824 36 , , , work_fnploejenbc2raktl46esxm44i 824 37 where where WRB work_fnploejenbc2raktl46esxm44i 824 38 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 824 39 , , , work_fnploejenbc2raktl46esxm44i 824 40 is be VBZ work_fnploejenbc2raktl46esxm44i 824 41 specified specify VBN work_fnploejenbc2raktl46esxm44i 824 42 by by IN work_fnploejenbc2raktl46esxm44i 824 43 $ $ $ work_fnploejenbc2raktl46esxm44i 824 44 g g NN work_fnploejenbc2raktl46esxm44i 824 45 , , , work_fnploejenbc2raktl46esxm44i 824 46 n n NN work_fnploejenbc2raktl46esxm44i 824 47 , , , work_fnploejenbc2raktl46esxm44i 824 48 n n NN work_fnploejenbc2raktl46esxm44i 824 49 > > NN work_fnploejenbc2raktl46esxm44i 824 50 1 1 CD work_fnploejenbc2raktl46esxm44i 824 51 . . . work_fnploejenbc2raktl46esxm44i 825 1 For for IN work_fnploejenbc2raktl46esxm44i 825 2 example example NN work_fnploejenbc2raktl46esxm44i 825 3 , , , work_fnploejenbc2raktl46esxm44i 825 4 for for IN work_fnploejenbc2raktl46esxm44i 825 5 a a DT work_fnploejenbc2raktl46esxm44i 825 6 fixed fix VBN work_fnploejenbc2raktl46esxm44i 825 7 p p NN work_fnploejenbc2raktl46esxm44i 825 8 > > XX work_fnploejenbc2raktl46esxm44i 825 9 1 1 CD work_fnploejenbc2raktl46esxm44i 825 10 , , , work_fnploejenbc2raktl46esxm44i 825 11 take take VB work_fnploejenbc2raktl46esxm44i 825 12 gpw gpw NNP work_fnploejenbc2raktl46esxm44i 825 13 = = NNPS work_fnploejenbc2raktl46esxm44i 825 14 tP tP NNP work_fnploejenbc2raktl46esxm44i 825 15 for for IN work_fnploejenbc2raktl46esxm44i 825 16 t t NNP work_fnploejenbc2raktl46esxm44i 825 17 > > XX work_fnploejenbc2raktl46esxm44i 825 18 O. o. NN work_fnploejenbc2raktl46esxm44i 826 1 Note note VB work_fnploejenbc2raktl46esxm44i 826 2 that that IN work_fnploejenbc2raktl46esxm44i 826 3 Max(x max(x CD work_fnploejenbc2raktl46esxm44i 826 4 , , , work_fnploejenbc2raktl46esxm44i 826 5 , , , work_fnploejenbc2raktl46esxm44i 826 6 x2 x2 NNP work_fnploejenbc2raktl46esxm44i 826 7 , , , work_fnploejenbc2raktl46esxm44i 826 8 . . . work_fnploejenbc2raktl46esxm44i 827 1 . . . work_fnploejenbc2raktl46esxm44i 828 1 . . . work_fnploejenbc2raktl46esxm44i 829 1 . . . work_fnploejenbc2raktl46esxm44i 830 1 However however RB work_fnploejenbc2raktl46esxm44i 830 2 , , , work_fnploejenbc2raktl46esxm44i 830 3 II/ ii/ NN work_fnploejenbc2raktl46esxm44i 830 4 = = NFP work_fnploejenbc2raktl46esxm44i 830 5 Max Max NNP work_fnploejenbc2raktl46esxm44i 830 6 yields yield NNS work_fnploejenbc2raktl46esxm44i 830 7 x x RB work_fnploejenbc2raktl46esxm44i 830 8 , , , work_fnploejenbc2raktl46esxm44i 830 9 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 830 10 is be VBZ work_fnploejenbc2raktl46esxm44i 830 11 a a DT work_fnploejenbc2raktl46esxm44i 830 12 limiting limiting JJ work_fnploejenbc2raktl46esxm44i 830 13 case case NN work_fnploejenbc2raktl46esxm44i 830 14 of of IN work_fnploejenbc2raktl46esxm44i 830 15 tigptn tigptn NN work_fnploejenbc2raktl46esxm44i 830 16 when when WRB work_fnploejenbc2raktl46esxm44i 830 17 p p NN work_fnploejenbc2raktl46esxm44i 830 18 + + CC work_fnploejenbc2raktl46esxm44i 830 19 + + CC work_fnploejenbc2raktl46esxm44i 830 20 co. co. NN work_fnploejenbc2raktl46esxm44i 830 21 essentially essentially RB work_fnploejenbc2raktl46esxm44i 830 22 only only RB work_fnploejenbc2raktl46esxm44i 830 23 trivial trivial JJ work_fnploejenbc2raktl46esxm44i 830 24 admissible admissible JJ work_fnploejenbc2raktl46esxm44i 830 25 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 830 26 measures measure NNS work_fnploejenbc2raktl46esxm44i 830 27 and and CC work_fnploejenbc2raktl46esxm44i 830 28 hence hence RB work_fnploejenbc2raktl46esxm44i 830 29 is be VBZ work_fnploejenbc2raktl46esxm44i 830 30 not not RB work_fnploejenbc2raktl46esxm44i 830 31 a a DT work_fnploejenbc2raktl46esxm44i 830 32 good good JJ work_fnploejenbc2raktl46esxm44i 830 33 candidate candidate NN work_fnploejenbc2raktl46esxm44i 830 34 for for IN work_fnploejenbc2raktl46esxm44i 830 35 being be VBG work_fnploejenbc2raktl46esxm44i 830 36 a a DT work_fnploejenbc2raktl46esxm44i 830 37 viable viable JJ work_fnploejenbc2raktl46esxm44i 830 38 nonadditive nonadditive JJ work_fnploejenbc2raktl46esxm44i 830 39 aggregation aggregation NN work_fnploejenbc2raktl46esxm44i 830 40 function function NN work_fnploejenbc2raktl46esxm44i 830 41 . . . work_fnploejenbc2raktl46esxm44i 831 1 SCORING SCORING NNP work_fnploejenbc2raktl46esxm44i 831 2 APPROACH APPROACH NNP work_fnploejenbc2raktl46esxm44i 831 3 TO to IN work_fnploejenbc2raktl46esxm44i 831 4 ADMISSIBILITY ADMISSIBILITY NNP work_fnploejenbc2raktl46esxm44i 831 5 593 593 CD work_fnploejenbc2raktl46esxm44i 831 6 ACKNOWLEDGMENTS acknowledgment NNS work_fnploejenbc2raktl46esxm44i 831 7 We -PRON- PRP work_fnploejenbc2raktl46esxm44i 831 8 thank thank VBP work_fnploejenbc2raktl46esxm44i 831 9 D. D. NNP work_fnploejenbc2raktl46esxm44i 831 10 V. V. NNP work_fnploejenbc2raktl46esxm44i 831 11 Lindley Lindley NNP work_fnploejenbc2raktl46esxm44i 831 12 and and CC work_fnploejenbc2raktl46esxm44i 831 13 L. L. NNP work_fnploejenbc2raktl46esxm44i 831 14 A. A. NNP work_fnploejenbc2raktl46esxm44i 831 15 Zadeh Zadeh NNP work_fnploejenbc2raktl46esxm44i 831 16 for for IN work_fnploejenbc2raktl46esxm44i 831 17 their -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 831 18 kind kind NN work_fnploejenbc2raktl46esxm44i 831 19 discussion discussion NN work_fnploejenbc2raktl46esxm44i 831 20 on on IN work_fnploejenbc2raktl46esxm44i 831 21 an an DT work_fnploejenbc2raktl46esxm44i 831 22 earlier early JJR work_fnploejenbc2raktl46esxm44i 831 23 draft draft NN work_fnploejenbc2raktl46esxm44i 831 24 of of IN work_fnploejenbc2raktl46esxm44i 831 25 this this DT work_fnploejenbc2raktl46esxm44i 831 26 work work NN work_fnploejenbc2raktl46esxm44i 831 27 . . . work_fnploejenbc2raktl46esxm44i 832 1 REFERENCES reference NNS work_fnploejenbc2raktl46esxm44i 832 2 1 1 CD work_fnploejenbc2raktl46esxm44i 832 3 . . . work_fnploejenbc2raktl46esxm44i 833 1 J. J. NNP work_fnploejenbc2raktl46esxm44i 833 2 ACZEL ACZEL NNP work_fnploejenbc2raktl46esxm44i 833 3 , , , work_fnploejenbc2raktl46esxm44i 833 4 “ " `` work_fnploejenbc2raktl46esxm44i 833 5 Lectures lecture NNS work_fnploejenbc2raktl46esxm44i 833 6 on on IN work_fnploejenbc2raktl46esxm44i 833 7 Functional Functional NNP work_fnploejenbc2raktl46esxm44i 833 8 Equations Equations NNPS work_fnploejenbc2raktl46esxm44i 833 9 and and CC work_fnploejenbc2raktl46esxm44i 833 10 Their -PRON- PRP$ work_fnploejenbc2raktl46esxm44i 833 11 Applications application NNS work_fnploejenbc2raktl46esxm44i 833 12 , , , work_fnploejenbc2raktl46esxm44i 833 13 ” " '' work_fnploejenbc2raktl46esxm44i 833 14 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 833 15 Press Press NNP work_fnploejenbc2raktl46esxm44i 833 16 , , , work_fnploejenbc2raktl46esxm44i 833 17 New New NNP work_fnploejenbc2raktl46esxm44i 833 18 York York NNP work_fnploejenbc2raktl46esxm44i 833 19 , , , work_fnploejenbc2raktl46esxm44i 833 20 1966 1966 CD work_fnploejenbc2raktl46esxm44i 833 21 . . . work_fnploejenbc2raktl46esxm44i 834 1 2 2 LS work_fnploejenbc2raktl46esxm44i 834 2 . . . work_fnploejenbc2raktl46esxm44i 835 1 J. J. NNP work_fnploejenbc2raktl46esxm44i 835 2 P. P. NNP work_fnploejenbc2raktl46esxm44i 835 3 AUL AUL NNP work_fnploejenbc2raktl46esxm44i 835 4 ~ ~ NFP work_fnploejenbc2raktl46esxm44i 835 5 N n NN work_fnploejenbc2raktl46esxm44i 835 6 , , , work_fnploejenbc2raktl46esxm44i 835 7 A a DT work_fnploejenbc2raktl46esxm44i 835 8 Pareto Pareto NNP work_fnploejenbc2raktl46esxm44i 835 9 minimum minimum NN work_fnploejenbc2raktl46esxm44i 835 10 principle principle NN work_fnploejenbc2raktl46esxm44i 835 11 , , , work_fnploejenbc2raktl46esxm44i 835 12 in in IN work_fnploejenbc2raktl46esxm44i 835 13 “ " `` work_fnploejenbc2raktl46esxm44i 835 14 Differential Differential NNP work_fnploejenbc2raktl46esxm44i 835 15 Games Games NNPS work_fnploejenbc2raktl46esxm44i 835 16 and and CC work_fnploejenbc2raktl46esxm44i 835 17 Related Related NNP work_fnploejenbc2raktl46esxm44i 835 18 Topics Topics NNPS work_fnploejenbc2raktl46esxm44i 835 19 ” " '' work_fnploejenbc2raktl46esxm44i 835 20 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 835 21 H. H. NNP work_fnploejenbc2raktl46esxm44i 835 22 W. W. NNP work_fnploejenbc2raktl46esxm44i 835 23 Kuhn Kuhn NNP work_fnploejenbc2raktl46esxm44i 835 24 and and CC work_fnploejenbc2raktl46esxm44i 835 25 G. G. NNP work_fnploejenbc2raktl46esxm44i 835 26 P. P. NNP work_fnploejenbc2raktl46esxm44i 835 27 Szego Szego NNP work_fnploejenbc2raktl46esxm44i 835 28 , , , work_fnploejenbc2raktl46esxm44i 835 29 Eds Eds NNP work_fnploejenbc2raktl46esxm44i 835 30 . . . work_fnploejenbc2raktl46esxm44i 836 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 836 2 , , , work_fnploejenbc2raktl46esxm44i 836 3 pp pp NNP work_fnploejenbc2raktl46esxm44i 836 4 . . . work_fnploejenbc2raktl46esxm44i 837 1 147 147 CD work_fnploejenbc2raktl46esxm44i 837 2 - - SYM work_fnploejenbc2raktl46esxm44i 837 3 175 175 CD work_fnploejenbc2raktl46esxm44i 837 4 , , , work_fnploejenbc2raktl46esxm44i 837 5 North North NNP work_fnploejenbc2raktl46esxm44i 837 6 - - HYPH work_fnploejenbc2raktl46esxm44i 837 7 Holland Holland NNP work_fnploejenbc2raktl46esxm44i 837 8 , , , work_fnploejenbc2raktl46esxm44i 837 9 Amsterdam Amsterdam NNP work_fnploejenbc2raktl46esxm44i 837 10 , , , work_fnploejenbc2raktl46esxm44i 837 11 1971 1971 CD work_fnploejenbc2raktl46esxm44i 837 12 . . . work_fnploejenbc2raktl46esxm44i 838 1 3 3 LS work_fnploejenbc2raktl46esxm44i 838 2 . . . work_fnploejenbc2raktl46esxm44i 839 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 839 2 BLACKWELL BLACKWELL NNP work_fnploejenbc2raktl46esxm44i 839 3 AND and CC work_fnploejenbc2raktl46esxm44i 839 4 M. M. NNP work_fnploejenbc2raktl46esxm44i 839 5 A. A. NNP work_fnploejenbc2raktl46esxm44i 839 6 GIRSHICK GIRSHICK NNP work_fnploejenbc2raktl46esxm44i 839 7 , , , work_fnploejenbc2raktl46esxm44i 839 8 “ " `` work_fnploejenbc2raktl46esxm44i 839 9 Theory theory NN work_fnploejenbc2raktl46esxm44i 839 10 of of IN work_fnploejenbc2raktl46esxm44i 839 11 Games Games NNPS work_fnploejenbc2raktl46esxm44i 839 12 and and CC work_fnploejenbc2raktl46esxm44i 839 13 Statistical Statistical NNP work_fnploejenbc2raktl46esxm44i 839 14 Decisions Decisions NNPS work_fnploejenbc2raktl46esxm44i 839 15 , , , work_fnploejenbc2raktl46esxm44i 839 16 ” " '' work_fnploejenbc2raktl46esxm44i 839 17 Dover Dover NNP work_fnploejenbc2raktl46esxm44i 839 18 , , , work_fnploejenbc2raktl46esxm44i 839 19 New New NNP work_fnploejenbc2raktl46esxm44i 839 20 York York NNP work_fnploejenbc2raktl46esxm44i 839 21 , , , work_fnploejenbc2raktl46esxm44i 839 22 1979 1979 CD work_fnploejenbc2raktl46esxm44i 839 23 . . . work_fnploejenbc2raktl46esxm44i 840 1 4 4 LS work_fnploejenbc2raktl46esxm44i 840 2 . . . work_fnploejenbc2raktl46esxm44i 841 1 L. L. NNP work_fnploejenbc2raktl46esxm44i 841 2 D. D. NNP work_fnploejenbc2raktl46esxm44i 841 3 BROWN BROWN NNP work_fnploejenbc2raktl46esxm44i 841 4 , , , work_fnploejenbc2raktl46esxm44i 841 5 A a DT work_fnploejenbc2raktl46esxm44i 841 6 heuristic heuristic JJ work_fnploejenbc2raktl46esxm44i 841 7 method method NN work_fnploejenbc2raktl46esxm44i 841 8 for for IN work_fnploejenbc2raktl46esxm44i 841 9 determining determine VBG work_fnploejenbc2raktl46esxm44i 841 10 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 841 11 of of IN work_fnploejenbc2raktl46esxm44i 841 12 estimators estimator NNS work_fnploejenbc2raktl46esxm44i 841 13 - - : work_fnploejenbc2raktl46esxm44i 841 14 with with IN work_fnploejenbc2raktl46esxm44i 841 15 applications application NNS work_fnploejenbc2raktl46esxm44i 841 16 , , , work_fnploejenbc2raktl46esxm44i 841 17 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 841 18 . . . work_fnploejenbc2raktl46esxm44i 842 1 Sfatisi Sfatisi NNP work_fnploejenbc2raktl46esxm44i 842 2 . . . work_fnploejenbc2raktl46esxm44i 843 1 7 7 LS work_fnploejenbc2raktl46esxm44i 843 2 , , , work_fnploejenbc2raktl46esxm44i 843 3 No no UH work_fnploejenbc2raktl46esxm44i 843 4 . . . work_fnploejenbc2raktl46esxm44i 844 1 5 5 CD work_fnploejenbc2raktl46esxm44i 844 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 844 3 1979 1979 CD work_fnploejenbc2raktl46esxm44i 844 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 844 5 , , , work_fnploejenbc2raktl46esxm44i 844 6 96&994 96&994 CD work_fnploejenbc2raktl46esxm44i 844 7 . . . work_fnploejenbc2raktl46esxm44i 845 1 5 5 CD work_fnploejenbc2raktl46esxm44i 845 2 . . . work_fnploejenbc2raktl46esxm44i 846 1 R. R. NNP work_fnploejenbc2raktl46esxm44i 846 2 T. T. NNP work_fnploejenbc2raktl46esxm44i 846 3 Cox Cox NNP work_fnploejenbc2raktl46esxm44i 846 4 , , , work_fnploejenbc2raktl46esxm44i 846 5 “ " `` work_fnploejenbc2raktl46esxm44i 846 6 The the DT work_fnploejenbc2raktl46esxm44i 846 7 Algebra Algebra NNP work_fnploejenbc2raktl46esxm44i 846 8 of of IN work_fnploejenbc2raktl46esxm44i 846 9 Probable probable JJ work_fnploejenbc2raktl46esxm44i 846 10 Inference inference NN work_fnploejenbc2raktl46esxm44i 846 11 , , , work_fnploejenbc2raktl46esxm44i 846 12 ” " '' work_fnploejenbc2raktl46esxm44i 846 13 The the DT work_fnploejenbc2raktl46esxm44i 846 14 Johns Johns NNP work_fnploejenbc2raktl46esxm44i 846 15 Hopkins Hopkins NNP work_fnploejenbc2raktl46esxm44i 846 16 Press Press NNP work_fnploejenbc2raktl46esxm44i 846 17 , , , work_fnploejenbc2raktl46esxm44i 846 18 Baltimore Baltimore NNP work_fnploejenbc2raktl46esxm44i 846 19 . . . work_fnploejenbc2raktl46esxm44i 847 1 1961 1961 CD work_fnploejenbc2raktl46esxm44i 847 2 . . . work_fnploejenbc2raktl46esxm44i 848 1 6 6 CD work_fnploejenbc2raktl46esxm44i 848 2 . . . work_fnploejenbc2raktl46esxm44i 849 1 B. B. NNP work_fnploejenbc2raktl46esxm44i 849 2 DEFINETTI DEFINETTI NNP work_fnploejenbc2raktl46esxm44i 849 3 , , , work_fnploejenbc2raktl46esxm44i 849 4 “ " `` work_fnploejenbc2raktl46esxm44i 849 5 Theory theory NN work_fnploejenbc2raktl46esxm44i 849 6 of of IN work_fnploejenbc2raktl46esxm44i 849 7 Probability Probability NNP work_fnploejenbc2raktl46esxm44i 849 8 , , , work_fnploejenbc2raktl46esxm44i 849 9 ” " '' work_fnploejenbc2raktl46esxm44i 849 10 Vols vol NNS work_fnploejenbc2raktl46esxm44i 849 11 . . . work_fnploejenbc2raktl46esxm44i 850 1 1 1 CD work_fnploejenbc2raktl46esxm44i 850 2 and and CC work_fnploejenbc2raktl46esxm44i 850 3 2 2 CD work_fnploejenbc2raktl46esxm44i 850 4 , , , work_fnploejenbc2raktl46esxm44i 850 5 Wiley Wiley NNP work_fnploejenbc2raktl46esxm44i 850 6 , , , work_fnploejenbc2raktl46esxm44i 850 7 New New NNP work_fnploejenbc2raktl46esxm44i 850 8 York York NNP work_fnploejenbc2raktl46esxm44i 850 9 , , , work_fnploejenbc2raktl46esxm44i 850 10 1974 1974 CD work_fnploejenbc2raktl46esxm44i 850 11 . . . work_fnploejenbc2raktl46esxm44i 851 1 7 7 LS work_fnploejenbc2raktl46esxm44i 851 2 . . . work_fnploejenbc2raktl46esxm44i 852 1 T. T. NNP work_fnploejenbc2raktl46esxm44i 852 2 S. S. NNP work_fnploejenbc2raktl46esxm44i 852 3 FERGUSON FERGUSON NNP work_fnploejenbc2raktl46esxm44i 852 4 , , , work_fnploejenbc2raktl46esxm44i 852 5 “ " `` work_fnploejenbc2raktl46esxm44i 852 6 Mathematical Mathematical NNP work_fnploejenbc2raktl46esxm44i 852 7 Statistics Statistics NNPS work_fnploejenbc2raktl46esxm44i 852 8 , , , work_fnploejenbc2raktl46esxm44i 852 9 ” " '' work_fnploejenbc2raktl46esxm44i 852 10 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 852 11 Press Press NNP work_fnploejenbc2raktl46esxm44i 852 12 , , , work_fnploejenbc2raktl46esxm44i 852 13 New New NNP work_fnploejenbc2raktl46esxm44i 852 14 York York NNP work_fnploejenbc2raktl46esxm44i 852 15 , , , work_fnploejenbc2raktl46esxm44i 852 16 1967 1967 CD work_fnploejenbc2raktl46esxm44i 852 17 . . . work_fnploejenbc2raktl46esxm44i 853 1 8 8 LS work_fnploejenbc2raktl46esxm44i 853 2 . . . work_fnploejenbc2raktl46esxm44i 854 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 854 2 A. A. NNP work_fnploejenbc2raktl46esxm44i 854 3 FREEDMAN FREEDMAN NNP work_fnploejenbc2raktl46esxm44i 854 4 AND and CC work_fnploejenbc2raktl46esxm44i 854 5 R. R. NNP work_fnploejenbc2raktl46esxm44i 854 6 A. A. NNP work_fnploejenbc2raktl46esxm44i 854 7 F?JRVES F?JRVES NNP work_fnploejenbc2raktl46esxm44i 854 8 , , , work_fnploejenbc2raktl46esxm44i 854 9 Bayes Bayes NNP work_fnploejenbc2raktl46esxm44i 854 10 ’ ’ POS work_fnploejenbc2raktl46esxm44i 854 11 method method NN work_fnploejenbc2raktl46esxm44i 854 12 for for IN work_fnploejenbc2raktl46esxm44i 854 13 bookies bookie NNS work_fnploejenbc2raktl46esxm44i 854 14 , , , work_fnploejenbc2raktl46esxm44i 854 15 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 854 16 , , , work_fnploejenbc2raktl46esxm44i 854 17 Math Math NNP work_fnploejenbc2raktl46esxm44i 854 18 . . . work_fnploejenbc2raktl46esxm44i 855 1 Statist statist JJ work_fnploejenbc2raktl46esxm44i 855 2 . . . work_fnploejenbc2raktl46esxm44i 856 1 40 40 CD work_fnploejenbc2raktl46esxm44i 856 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 856 3 1969 1969 CD work_fnploejenbc2raktl46esxm44i 856 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 856 5 , , , work_fnploejenbc2raktl46esxm44i 856 6 1177 1177 CD work_fnploejenbc2raktl46esxm44i 856 7 - - SYM work_fnploejenbc2raktl46esxm44i 856 8 1186 1186 CD work_fnploejenbc2raktl46esxm44i 856 9 . . . work_fnploejenbc2raktl46esxm44i 857 1 9 9 CD work_fnploejenbc2raktl46esxm44i 857 2 . . . work_fnploejenbc2raktl46esxm44i 858 1 C. C. NNP work_fnploejenbc2raktl46esxm44i 858 2 GENES GENES NNP work_fnploejenbc2raktl46esxm44i 858 3 AND and CC work_fnploejenbc2raktl46esxm44i 858 4 R. R. NNP work_fnploejenbc2raktl46esxm44i 858 5 J. J. NNP work_fnploejenbc2raktl46esxm44i 858 6 MACKAY MACKAY NNP work_fnploejenbc2raktl46esxm44i 858 7 , , , work_fnploejenbc2raktl46esxm44i 858 8 Copules Copules NNP work_fnploejenbc2raktl46esxm44i 858 9 ArchimCdiennes ArchimCdiennes NNP work_fnploejenbc2raktl46esxm44i 858 10 et et NNP work_fnploejenbc2raktl46esxm44i 858 11 families family NNS work_fnploejenbc2raktl46esxm44i 858 12 de de NNP work_fnploejenbc2raktl46esxm44i 858 13 lois lois NNP work_fnploejenbc2raktl46esxm44i 858 14 bidimension- bidimension- NNP work_fnploejenbc2raktl46esxm44i 858 15 nelles nelle NNS work_fnploejenbc2raktl46esxm44i 858 16 do do VBP work_fnploejenbc2raktl46esxm44i 858 17 nt not RB work_fnploejenbc2raktl46esxm44i 858 18 les les VB work_fnploejenbc2raktl46esxm44i 858 19 marges marge NNS work_fnploejenbc2raktl46esxm44i 858 20 sent send VBD work_fnploejenbc2raktl46esxm44i 858 21 donnkes donnke NNS work_fnploejenbc2raktl46esxm44i 858 22 , , , work_fnploejenbc2raktl46esxm44i 858 23 Canad Canad NNP work_fnploejenbc2raktl46esxm44i 858 24 . . . work_fnploejenbc2raktl46esxm44i 859 1 J. J. NNP work_fnploejenbc2raktl46esxm44i 859 2 Statist Statist NNP work_fnploejenbc2raktl46esxm44i 859 3 . . . work_fnploejenbc2raktl46esxm44i 860 1 14 14 CD work_fnploejenbc2raktl46esxm44i 860 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 860 3 1986 1986 CD work_fnploejenbc2raktl46esxm44i 860 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 860 5 , , , work_fnploejenbc2raktl46esxm44i 860 6 145 145 CD work_fnploejenbc2raktl46esxm44i 860 7 - - SYM work_fnploejenbc2raktl46esxm44i 860 8 159 159 CD work_fnploejenbc2raktl46esxm44i 860 9 . . . work_fnploejenbc2raktl46esxm44i 861 1 10 10 CD work_fnploejenbc2raktl46esxm44i 861 2 . . . work_fnploejenbc2raktl46esxm44i 862 1 C. C. NNP work_fnploejenbc2raktl46esxm44i 862 2 GENEST GENEST NNP work_fnploejenbc2raktl46esxm44i 862 3 AND and CC work_fnploejenbc2raktl46esxm44i 862 4 R. R. NNP work_fnploejenbc2raktl46esxm44i 862 5 J. J. NNP work_fnploejenbc2raktl46esxm44i 862 6 MACKAY MACKAY NNP work_fnploejenbc2raktl46esxm44i 862 7 , , , work_fnploejenbc2raktl46esxm44i 862 8 The the DT work_fnploejenbc2raktl46esxm44i 862 9 joy joy NN work_fnploejenbc2raktl46esxm44i 862 10 of of IN work_fnploejenbc2raktl46esxm44i 862 11 copulas copulas NN work_fnploejenbc2raktl46esxm44i 862 12 : : : work_fnploejenbc2raktl46esxm44i 862 13 bivariate bivariate JJ work_fnploejenbc2raktl46esxm44i 862 14 distributions distribution NNS work_fnploejenbc2raktl46esxm44i 862 15 with with IN work_fnploejenbc2raktl46esxm44i 862 16 uniform uniform JJ work_fnploejenbc2raktl46esxm44i 862 17 marginals marginal NNS work_fnploejenbc2raktl46esxm44i 862 18 , , , work_fnploejenbc2raktl46esxm44i 862 19 Amer Amer NNP work_fnploejenbc2raktl46esxm44i 862 20 . . . work_fnploejenbc2raktl46esxm44i 863 1 Statist statist JJ work_fnploejenbc2raktl46esxm44i 863 2 . . . work_fnploejenbc2raktl46esxm44i 864 1 40 40 CD work_fnploejenbc2raktl46esxm44i 864 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 864 3 1986 1986 CD work_fnploejenbc2raktl46esxm44i 864 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 864 5 , , , work_fnploejenbc2raktl46esxm44i 864 6 28&283 28&283 CD work_fnploejenbc2raktl46esxm44i 864 7 . . . work_fnploejenbc2raktl46esxm44i 865 1 11 11 CD work_fnploejenbc2raktl46esxm44i 865 2 . . . work_fnploejenbc2raktl46esxm44i 866 1 I. I. NNP work_fnploejenbc2raktl46esxm44i 866 2 R. R. NNP work_fnploejenbc2raktl46esxm44i 866 3 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 866 4 AND and CC work_fnploejenbc2raktl46esxm44i 866 5 H. H. NNP work_fnploejenbc2raktl46esxm44i 866 6 T. T. NNP work_fnploejenbc2raktl46esxm44i 866 7 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 866 8 , , , work_fnploejenbc2raktl46esxm44i 866 9 “ " `` work_fnploejenbc2raktl46esxm44i 866 10 Uncertainty Uncertainty NNP work_fnploejenbc2raktl46esxm44i 866 11 Models Models NNPS work_fnploejenbc2raktl46esxm44i 866 12 for for IN work_fnploejenbc2raktl46esxm44i 866 13 Knowledge Knowledge NNP work_fnploejenbc2raktl46esxm44i 866 14 - - HYPH work_fnploejenbc2raktl46esxm44i 866 15 Based base VBN work_fnploejenbc2raktl46esxm44i 866 16 Systems Systems NNPS work_fnploejenbc2raktl46esxm44i 866 17 , , , work_fnploejenbc2raktl46esxm44i 866 18 ” " '' work_fnploejenbc2raktl46esxm44i 866 19 North North NNP work_fnploejenbc2raktl46esxm44i 866 20 - - HYPH work_fnploejenbc2raktl46esxm44i 866 21 Holland Holland NNP work_fnploejenbc2raktl46esxm44i 866 22 , , , work_fnploejenbc2raktl46esxm44i 866 23 Amsterdam Amsterdam NNP work_fnploejenbc2raktl46esxm44i 866 24 , , , work_fnploejenbc2raktl46esxm44i 866 25 1985 1985 CD work_fnploejenbc2raktl46esxm44i 866 26 . . . work_fnploejenbc2raktl46esxm44i 867 1 12 12 CD work_fnploejenbc2raktl46esxm44i 867 2 . . . work_fnploejenbc2raktl46esxm44i 868 1 I. I. NNP work_fnploejenbc2raktl46esxm44i 868 2 R. R. NNP work_fnploejenbc2raktl46esxm44i 868 3 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 868 4 , , , work_fnploejenbc2raktl46esxm44i 868 5 H. H. NNP work_fnploejenbc2raktl46esxm44i 868 6 T. T. NNP work_fnploejenbc2raktl46esxm44i 868 7 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 868 8 , , , work_fnploejenbc2raktl46esxm44i 868 9 AND and CC work_fnploejenbc2raktl46esxm44i 868 10 E. E. NNP work_fnploejenbc2raktl46esxm44i 868 11 A. A. NNP work_fnploejenbc2raktl46esxm44i 868 12 WALKER WALKER NNP work_fnploejenbc2raktl46esxm44i 868 13 , , , work_fnploejenbc2raktl46esxm44i 868 14 ‘ ' '' work_fnploejenbc2raktl46esxm44i 868 15 * * NFP work_fnploejenbc2raktl46esxm44i 868 16 Conditional Conditional NNP work_fnploejenbc2raktl46esxm44i 868 17 Inference Inference NNP work_fnploejenbc2raktl46esxm44i 868 18 and and CC work_fnploejenbc2raktl46esxm44i 868 19 Logic Logic NNP work_fnploejenbc2raktl46esxm44i 868 20 for for IN work_fnploejenbc2raktl46esxm44i 868 21 Intelligent Intelligent NNP work_fnploejenbc2raktl46esxm44i 868 22 Systems Systems NNPS work_fnploejenbc2raktl46esxm44i 868 23 : : : work_fnploejenbc2raktl46esxm44i 868 24 A a DT work_fnploejenbc2raktl46esxm44i 868 25 Theory Theory NNP work_fnploejenbc2raktl46esxm44i 868 26 of of IN work_fnploejenbc2raktl46esxm44i 868 27 Measure measure NN work_fnploejenbc2raktl46esxm44i 868 28 - - HYPH work_fnploejenbc2raktl46esxm44i 868 29 Free Free NNP work_fnploejenbc2raktl46esxm44i 868 30 Conditioning Conditioning NNP work_fnploejenbc2raktl46esxm44i 868 31 , , , work_fnploejenbc2raktl46esxm44i 868 32 ” " '' work_fnploejenbc2raktl46esxm44i 868 33 North North NNP work_fnploejenbc2raktl46esxm44i 868 34 - - HYPH work_fnploejenbc2raktl46esxm44i 868 35 Holland Holland NNP work_fnploejenbc2raktl46esxm44i 868 36 , , , work_fnploejenbc2raktl46esxm44i 868 37 Amsterdam Amsterdam NNP work_fnploejenbc2raktl46esxm44i 868 38 , , , work_fnploejenbc2raktl46esxm44i 868 39 1991 1991 CD work_fnploejenbc2raktl46esxm44i 868 40 . . . work_fnploejenbc2raktl46esxm44i 869 1 13 13 CD work_fnploejenbc2raktl46esxm44i 869 2 . . . work_fnploejenbc2raktl46esxm44i 870 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 870 2 HEATH HEATH NNP work_fnploejenbc2raktl46esxm44i 870 3 AND and CC work_fnploejenbc2raktl46esxm44i 870 4 W. W. NNP work_fnploejenbc2raktl46esxm44i 870 5 SUDDERTH SUDDERTH NNP work_fnploejenbc2raktl46esxm44i 870 6 , , , work_fnploejenbc2raktl46esxm44i 870 7 On on IN work_fnploejenbc2raktl46esxm44i 870 8 finitely finitely RB work_fnploejenbc2raktl46esxm44i 870 9 additive additive JJ work_fnploejenbc2raktl46esxm44i 870 10 priors prior NNS work_fnploejenbc2raktl46esxm44i 870 11 , , , work_fnploejenbc2raktl46esxm44i 870 12 coherence coherence NN work_fnploejenbc2raktl46esxm44i 870 13 , , , work_fnploejenbc2raktl46esxm44i 870 14 and and CC work_fnploejenbc2raktl46esxm44i 870 15 extended extended JJ work_fnploejenbc2raktl46esxm44i 870 16 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 870 17 , , , work_fnploejenbc2raktl46esxm44i 870 18 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 870 19 . . . work_fnploejenbc2raktl46esxm44i 871 1 Sfafisr Sfafisr NNP work_fnploejenbc2raktl46esxm44i 871 2 . . . work_fnploejenbc2raktl46esxm44i 872 1 6 6 CD work_fnploejenbc2raktl46esxm44i 872 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 872 3 1978 1978 CD work_fnploejenbc2raktl46esxm44i 872 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 872 5 , , , work_fnploejenbc2raktl46esxm44i 872 6 333 333 CD work_fnploejenbc2raktl46esxm44i 872 7 - - SYM work_fnploejenbc2raktl46esxm44i 872 8 345 345 CD work_fnploejenbc2raktl46esxm44i 872 9 . . . work_fnploejenbc2raktl46esxm44i 873 1 14 14 CD work_fnploejenbc2raktl46esxm44i 873 2 . . . work_fnploejenbc2raktl46esxm44i 874 1 A. a. JJ work_fnploejenbc2raktl46esxm44i 874 2 KOZEK KOZEK NNP work_fnploejenbc2raktl46esxm44i 874 3 , , , work_fnploejenbc2raktl46esxm44i 874 4 Towards towards IN work_fnploejenbc2raktl46esxm44i 874 5 a a DT work_fnploejenbc2raktl46esxm44i 874 6 calculus calculus NN work_fnploejenbc2raktl46esxm44i 874 7 for for IN work_fnploejenbc2raktl46esxm44i 874 8 admissibility admissibility NN work_fnploejenbc2raktl46esxm44i 874 9 , , , work_fnploejenbc2raktl46esxm44i 874 10 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 874 11 . . . work_fnploejenbc2raktl46esxm44i 875 1 Statist statist JJ work_fnploejenbc2raktl46esxm44i 875 2 . . . work_fnploejenbc2raktl46esxm44i 876 1 10 10 CD work_fnploejenbc2raktl46esxm44i 876 2 , , , work_fnploejenbc2raktl46esxm44i 876 3 No no UH work_fnploejenbc2raktl46esxm44i 876 4 . . . work_fnploejenbc2raktl46esxm44i 877 1 3 3 CD work_fnploejenbc2raktl46esxm44i 877 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 877 3 1982 1982 CD work_fnploejenbc2raktl46esxm44i 877 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 877 5 , , , work_fnploejenbc2raktl46esxm44i 877 6 825 825 CD work_fnploejenbc2raktl46esxm44i 877 7 - - SYM work_fnploejenbc2raktl46esxm44i 877 8 837 837 CD work_fnploejenbc2raktl46esxm44i 877 9 . . . work_fnploejenbc2raktl46esxm44i 878 1 15 15 CD work_fnploejenbc2raktl46esxm44i 878 2 . . . work_fnploejenbc2raktl46esxm44i 879 1 R. R. NNP work_fnploejenbc2raktl46esxm44i 879 2 B. B. NNP work_fnploejenbc2raktl46esxm44i 879 3 LATTA LATTA NNP work_fnploejenbc2raktl46esxm44i 879 4 , , , work_fnploejenbc2raktl46esxm44i 879 5 Composition composition NN work_fnploejenbc2raktl46esxm44i 879 6 rules rule NNS work_fnploejenbc2raktl46esxm44i 879 7 for for IN work_fnploejenbc2raktl46esxm44i 879 8 probabilities probability NNS work_fnploejenbc2raktl46esxm44i 879 9 from from IN work_fnploejenbc2raktl46esxm44i 879 10 paired pair VBN work_fnploejenbc2raktl46esxm44i 879 11 comparisons comparison NNS work_fnploejenbc2raktl46esxm44i 879 12 , , , work_fnploejenbc2raktl46esxm44i 879 13 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 879 14 . . . work_fnploejenbc2raktl46esxm44i 880 1 Sfafisf sfafisf RB work_fnploejenbc2raktl46esxm44i 880 2 . . . work_fnploejenbc2raktl46esxm44i 881 1 7 7 LS work_fnploejenbc2raktl46esxm44i 881 2 , , , work_fnploejenbc2raktl46esxm44i 881 3 No no UH work_fnploejenbc2raktl46esxm44i 881 4 . . . work_fnploejenbc2raktl46esxm44i 882 1 2 2 CD work_fnploejenbc2raktl46esxm44i 882 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 882 3 1979 1979 CD work_fnploejenbc2raktl46esxm44i 882 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 882 5 , , , work_fnploejenbc2raktl46esxm44i 882 6 349 349 CD work_fnploejenbc2raktl46esxm44i 882 7 - - SYM work_fnploejenbc2raktl46esxm44i 882 8 371 371 CD work_fnploejenbc2raktl46esxm44i 882 9 . . . work_fnploejenbc2raktl46esxm44i 883 1 16 16 CD work_fnploejenbc2raktl46esxm44i 883 2 . . . work_fnploejenbc2raktl46esxm44i 884 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 884 2 V. V. NNP work_fnploejenbc2raktl46esxm44i 884 3 LINDLEY LINDLEY NNP work_fnploejenbc2raktl46esxm44i 884 4 , , , work_fnploejenbc2raktl46esxm44i 884 5 Scoring Scoring NNP work_fnploejenbc2raktl46esxm44i 884 6 rules rule NNS work_fnploejenbc2raktl46esxm44i 884 7 and and CC work_fnploejenbc2raktl46esxm44i 884 8 the the DT work_fnploejenbc2raktl46esxm44i 884 9 inevitability inevitability NN work_fnploejenbc2raktl46esxm44i 884 10 of of IN work_fnploejenbc2raktl46esxm44i 884 11 probability probability NN work_fnploejenbc2raktl46esxm44i 884 12 , , , work_fnploejenbc2raktl46esxm44i 884 13 Intern Intern NNP work_fnploejenbc2raktl46esxm44i 884 14 . . . work_fnploejenbc2raktl46esxm44i 885 1 Statist statist JJ work_fnploejenbc2raktl46esxm44i 885 2 . . . work_fnploejenbc2raktl46esxm44i 886 1 Reo Reo NNP work_fnploejenbc2raktl46esxm44i 886 2 . . . work_fnploejenbc2raktl46esxm44i 887 1 50 50 CD work_fnploejenbc2raktl46esxm44i 887 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 887 3 1982 1982 CD work_fnploejenbc2raktl46esxm44i 887 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 887 5 , , , work_fnploejenbc2raktl46esxm44i 887 6 l-26 l-26 NNP work_fnploejenbc2raktl46esxm44i 887 7 . . . work_fnploejenbc2raktl46esxm44i 888 1 17 17 CD work_fnploejenbc2raktl46esxm44i 888 2 . . . work_fnploejenbc2raktl46esxm44i 889 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 889 2 V. V. NNP work_fnploejenbc2raktl46esxm44i 889 3 LINDLEY LINDLEY NNP work_fnploejenbc2raktl46esxm44i 889 4 , , , work_fnploejenbc2raktl46esxm44i 889 5 The the DT work_fnploejenbc2raktl46esxm44i 889 6 probability probability NN work_fnploejenbc2raktl46esxm44i 889 7 approach approach NN work_fnploejenbc2raktl46esxm44i 889 8 to to IN work_fnploejenbc2raktl46esxm44i 889 9 the the DT work_fnploejenbc2raktl46esxm44i 889 10 treatment treatment NN work_fnploejenbc2raktl46esxm44i 889 11 of of IN work_fnploejenbc2raktl46esxm44i 889 12 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 889 13 in in IN work_fnploejenbc2raktl46esxm44i 889 14 Artilicial Artilicial NNP work_fnploejenbc2raktl46esxm44i 889 15 Intelligence Intelligence NNP work_fnploejenbc2raktl46esxm44i 889 16 and and CC work_fnploejenbc2raktl46esxm44i 889 17 expert expert NN work_fnploejenbc2raktl46esxm44i 889 18 systems system NNS work_fnploejenbc2raktl46esxm44i 889 19 , , , work_fnploejenbc2raktl46esxm44i 889 20 Statist statist JJ work_fnploejenbc2raktl46esxm44i 889 21 . . . work_fnploejenbc2raktl46esxm44i 890 1 Sci Sci NNP work_fnploejenbc2raktl46esxm44i 890 2 . . . work_fnploejenbc2raktl46esxm44i 891 1 2 2 LS work_fnploejenbc2raktl46esxm44i 891 2 , , , work_fnploejenbc2raktl46esxm44i 891 3 No no UH work_fnploejenbc2raktl46esxm44i 891 4 . . . work_fnploejenbc2raktl46esxm44i 892 1 1 1 CD work_fnploejenbc2raktl46esxm44i 892 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 892 3 1987 1987 CD work_fnploejenbc2raktl46esxm44i 892 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 892 5 , , , work_fnploejenbc2raktl46esxm44i 892 6 17 17 CD work_fnploejenbc2raktl46esxm44i 892 7 - - SYM work_fnploejenbc2raktl46esxm44i 892 8 24 24 CD work_fnploejenbc2raktl46esxm44i 892 9 . . . work_fnploejenbc2raktl46esxm44i 893 1 18 18 CD work_fnploejenbc2raktl46esxm44i 893 2 . . . work_fnploejenbc2raktl46esxm44i 894 1 C. C. NNP work_fnploejenbc2raktl46esxm44i 894 2 H. H. NNP work_fnploejenbc2raktl46esxm44i 894 3 LING LING NNP work_fnploejenbc2raktl46esxm44i 894 4 , , , work_fnploejenbc2raktl46esxm44i 894 5 Representation Representation NNP work_fnploejenbc2raktl46esxm44i 894 6 of of IN work_fnploejenbc2raktl46esxm44i 894 7 associative associative JJ work_fnploejenbc2raktl46esxm44i 894 8 functions function NNS work_fnploejenbc2raktl46esxm44i 894 9 , , , work_fnploejenbc2raktl46esxm44i 894 10 Puhl Puhl NNP work_fnploejenbc2raktl46esxm44i 894 11 . . . work_fnploejenbc2raktl46esxm44i 895 1 Math math NN work_fnploejenbc2raktl46esxm44i 895 2 . . . work_fnploejenbc2raktl46esxm44i 896 1 Debrecen Debrecen NNP work_fnploejenbc2raktl46esxm44i 896 2 12 12 CD work_fnploejenbc2raktl46esxm44i 896 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 896 4 1965 1965 CD work_fnploejenbc2raktl46esxm44i 896 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 896 6 , , , work_fnploejenbc2raktl46esxm44i 896 7 189 189 CD work_fnploejenbc2raktl46esxm44i 896 8 - - SYM work_fnploejenbc2raktl46esxm44i 896 9 2 2 CD work_fnploejenbc2raktl46esxm44i 896 10 12 12 CD work_fnploejenbc2raktl46esxm44i 896 11 . . . work_fnploejenbc2raktl46esxm44i 897 1 19 19 CD work_fnploejenbc2raktl46esxm44i 897 2 . . . work_fnploejenbc2raktl46esxm44i 898 1 A. A. NNP work_fnploejenbc2raktl46esxm44i 898 2 W. W. NNP work_fnploejenbc2raktl46esxm44i 898 3 MARSHALL MARSHALL NNP work_fnploejenbc2raktl46esxm44i 898 4 AND and CC work_fnploejenbc2raktl46esxm44i 898 5 I. I. NNP work_fnploejenbc2raktl46esxm44i 898 6 OLKIN OLKIN NNP work_fnploejenbc2raktl46esxm44i 898 7 , , , work_fnploejenbc2raktl46esxm44i 898 8 Families Families NNPS work_fnploejenbc2raktl46esxm44i 898 9 of of IN work_fnploejenbc2raktl46esxm44i 898 10 multivariate multivariate NN work_fnploejenbc2raktl46esxm44i 898 11 distributions distribution NNS work_fnploejenbc2raktl46esxm44i 898 12 , , , work_fnploejenbc2raktl46esxm44i 898 13 J. J. NNP work_fnploejenbc2raktl46esxm44i 898 14 Amer Amer NNP work_fnploejenbc2raktl46esxm44i 898 15 . . . work_fnploejenbc2raktl46esxm44i 899 1 Stofisf Stofisf NNP work_fnploejenbc2raktl46esxm44i 899 2 . . . work_fnploejenbc2raktl46esxm44i 900 1 Assoc Assoc NNP work_fnploejenbc2raktl46esxm44i 900 2 . . . work_fnploejenbc2raktl46esxm44i 901 1 83 83 CD work_fnploejenbc2raktl46esxm44i 901 2 , , , work_fnploejenbc2raktl46esxm44i 901 3 No no UH work_fnploejenbc2raktl46esxm44i 901 4 . . . work_fnploejenbc2raktl46esxm44i 902 1 403 403 CD work_fnploejenbc2raktl46esxm44i 902 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 902 3 1988 1988 CD work_fnploejenbc2raktl46esxm44i 902 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 902 5 , , , work_fnploejenbc2raktl46esxm44i 902 6 834 834 CD work_fnploejenbc2raktl46esxm44i 902 7 - - SYM work_fnploejenbc2raktl46esxm44i 902 8 841 841 CD work_fnploejenbc2raktl46esxm44i 902 9 . . . work_fnploejenbc2raktl46esxm44i 903 1 20 20 CD work_fnploejenbc2raktl46esxm44i 903 2 . . . work_fnploejenbc2raktl46esxm44i 904 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 904 2 MCDERMOTT MCDERMOTT NNP work_fnploejenbc2raktl46esxm44i 904 3 AND and CC work_fnploejenbc2raktl46esxm44i 904 4 J. J. NNP work_fnploejenbc2raktl46esxm44i 904 5 DOYLE DOYLE NNP work_fnploejenbc2raktl46esxm44i 904 6 , , , work_fnploejenbc2raktl46esxm44i 904 7 Non non JJ work_fnploejenbc2raktl46esxm44i 904 8 - - JJ work_fnploejenbc2raktl46esxm44i 904 9 monotonic monotonic JJ work_fnploejenbc2raktl46esxm44i 904 10 logic logic NN work_fnploejenbc2raktl46esxm44i 904 11 , , , work_fnploejenbc2raktl46esxm44i 904 12 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 904 13 , , , work_fnploejenbc2raktl46esxm44i 904 14 Artificial Artificial NNP work_fnploejenbc2raktl46esxm44i 904 15 Intelligence Intelligence NNP work_fnploejenbc2raktl46esxm44i 904 16 13 13 CD work_fnploejenbc2raktl46esxm44i 904 17 , , , work_fnploejenbc2raktl46esxm44i 904 18 No no UH work_fnploejenbc2raktl46esxm44i 904 19 . . . work_fnploejenbc2raktl46esxm44i 905 1 1 1 CD work_fnploejenbc2raktl46esxm44i 905 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 905 3 1980 1980 CD work_fnploejenbc2raktl46esxm44i 905 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 905 5 , , , work_fnploejenbc2raktl46esxm44i 905 6 41 41 CD work_fnploejenbc2raktl46esxm44i 905 7 - - SYM work_fnploejenbc2raktl46esxm44i 905 8 72 72 CD work_fnploejenbc2raktl46esxm44i 905 9 . . . work_fnploejenbc2raktl46esxm44i 906 1 21 21 CD work_fnploejenbc2raktl46esxm44i 906 2 . . . work_fnploejenbc2raktl46esxm44i 907 1 H. H. NNP work_fnploejenbc2raktl46esxm44i 907 2 T. T. NNP work_fnploejenbc2raktl46esxm44i 907 3 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 907 4 , , , work_fnploejenbc2raktl46esxm44i 907 5 On on IN work_fnploejenbc2raktl46esxm44i 907 6 random random JJ work_fnploejenbc2raktl46esxm44i 907 7 sets set NNS work_fnploejenbc2raktl46esxm44i 907 8 and and CC work_fnploejenbc2raktl46esxm44i 907 9 belief belief NN work_fnploejenbc2raktl46esxm44i 907 10 functions function NNS work_fnploejenbc2raktl46esxm44i 907 11 , , , work_fnploejenbc2raktl46esxm44i 907 12 J. J. NNP work_fnploejenbc2raktl46esxm44i 908 1 Math math NN work_fnploejenbc2raktl46esxm44i 908 2 . . . work_fnploejenbc2raktl46esxm44i 909 1 Anal anal JJ work_fnploejenbc2raktl46esxm44i 909 2 . . . work_fnploejenbc2raktl46esxm44i 910 1 Appl Appl NNP work_fnploejenbc2raktl46esxm44i 910 2 . . . work_fnploejenbc2raktl46esxm44i 911 1 65 65 CD work_fnploejenbc2raktl46esxm44i 911 2 , , , work_fnploejenbc2raktl46esxm44i 911 3 No no UH work_fnploejenbc2raktl46esxm44i 911 4 . . . work_fnploejenbc2raktl46esxm44i 912 1 3 3 CD work_fnploejenbc2raktl46esxm44i 912 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 912 3 1978 1978 CD work_fnploejenbc2raktl46esxm44i 912 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 912 5 , , , work_fnploejenbc2raktl46esxm44i 912 6 531 531 CD work_fnploejenbc2raktl46esxm44i 912 7 - - SYM work_fnploejenbc2raktl46esxm44i 912 8 542 542 CD work_fnploejenbc2raktl46esxm44i 912 9 . . . work_fnploejenbc2raktl46esxm44i 913 1 22 22 CD work_fnploejenbc2raktl46esxm44i 913 2 . . . work_fnploejenbc2raktl46esxm44i 914 1 E. E. NNP work_fnploejenbc2raktl46esxm44i 914 2 REGAZZINI REGAZZINI NNP work_fnploejenbc2raktl46esxm44i 914 3 , , , work_fnploejenbc2raktl46esxm44i 914 4 DeFinetti DeFinetti NNP work_fnploejenbc2raktl46esxm44i 914 5 ’s ’s POS work_fnploejenbc2raktl46esxm44i 914 6 coherence coherence NN work_fnploejenbc2raktl46esxm44i 914 7 and and CC work_fnploejenbc2raktl46esxm44i 914 8 statistical statistical JJ work_fnploejenbc2raktl46esxm44i 914 9 inference inference NN work_fnploejenbc2raktl46esxm44i 914 10 , , , work_fnploejenbc2raktl46esxm44i 914 11 Ann Ann NNP work_fnploejenbc2raktl46esxm44i 914 12 . . . work_fnploejenbc2raktl46esxm44i 915 1 Sratisf sratisf RB work_fnploejenbc2raktl46esxm44i 915 2 . . . work_fnploejenbc2raktl46esxm44i 916 1 15 15 CD work_fnploejenbc2raktl46esxm44i 916 2 , , , work_fnploejenbc2raktl46esxm44i 916 3 No no UH work_fnploejenbc2raktl46esxm44i 916 4 . . . work_fnploejenbc2raktl46esxm44i 917 1 2 2 CD work_fnploejenbc2raktl46esxm44i 917 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 917 3 1987 1987 CD work_fnploejenbc2raktl46esxm44i 917 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 917 5 . . . work_fnploejenbc2raktl46esxm44i 918 1 845 845 CD work_fnploejenbc2raktl46esxm44i 918 2 - - SYM work_fnploejenbc2raktl46esxm44i 918 3 864 864 CD work_fnploejenbc2raktl46esxm44i 918 4 . . . work_fnploejenbc2raktl46esxm44i 919 1 594 594 CD work_fnploejenbc2raktl46esxm44i 919 2 GOODMAN GOODMAN NNP work_fnploejenbc2raktl46esxm44i 919 3 , , , work_fnploejenbc2raktl46esxm44i 919 4 NGUYEN NGUYEN NNP work_fnploejenbc2raktl46esxm44i 919 5 , , , work_fnploejenbc2raktl46esxm44i 919 6 AND and CC work_fnploejenbc2raktl46esxm44i 919 7 ROGERS ROGERS NNP work_fnploejenbc2raktl46esxm44i 919 8 23 23 CD work_fnploejenbc2raktl46esxm44i 919 9 . . . work_fnploejenbc2raktl46esxm44i 920 1 A. A. NNP work_fnploejenbc2raktl46esxm44i 920 2 RENYI RENYI NNP work_fnploejenbc2raktl46esxm44i 920 3 , , , work_fnploejenbc2raktl46esxm44i 920 4 “ " `` work_fnploejenbc2raktl46esxm44i 920 5 Foundations foundation NNS work_fnploejenbc2raktl46esxm44i 920 6 of of IN work_fnploejenbc2raktl46esxm44i 920 7 Probability Probability NNP work_fnploejenbc2raktl46esxm44i 920 8 , , , work_fnploejenbc2raktl46esxm44i 920 9 ” " '' work_fnploejenbc2raktl46esxm44i 920 10 Holden Holden NNP work_fnploejenbc2raktl46esxm44i 920 11 - - HYPH work_fnploejenbc2raktl46esxm44i 920 12 Day Day NNP work_fnploejenbc2raktl46esxm44i 920 13 , , , work_fnploejenbc2raktl46esxm44i 920 14 San San NNP work_fnploejenbc2raktl46esxm44i 920 15 Francisco Francisco NNP work_fnploejenbc2raktl46esxm44i 920 16 , , , work_fnploejenbc2raktl46esxm44i 920 17 1970 1970 CD work_fnploejenbc2raktl46esxm44i 920 18 . . . work_fnploejenbc2raktl46esxm44i 921 1 24 24 CD work_fnploejenbc2raktl46esxm44i 921 2 . . . work_fnploejenbc2raktl46esxm44i 922 1 G. G. NNP work_fnploejenbc2raktl46esxm44i 922 2 SWAY SWAY NNP work_fnploejenbc2raktl46esxm44i 922 3 , , , work_fnploejenbc2raktl46esxm44i 922 4 An an DT work_fnploejenbc2raktl46esxm44i 922 5 algebra algebra NN work_fnploejenbc2raktl46esxm44i 922 6 of of IN work_fnploejenbc2raktl46esxm44i 922 7 conditional conditional JJ work_fnploejenbc2raktl46esxm44i 922 8 events event NNS work_fnploejenbc2raktl46esxm44i 922 9 , , , work_fnploejenbc2raktl46esxm44i 922 10 J. J. NNP work_fnploejenbc2raktl46esxm44i 923 1 Math math NN work_fnploejenbc2raktl46esxm44i 923 2 . . . work_fnploejenbc2raktl46esxm44i 924 1 Anal anal JJ work_fnploejenbc2raktl46esxm44i 924 2 . . . work_fnploejenbc2raktl46esxm44i 925 1 Appl Appl NNP work_fnploejenbc2raktl46esxm44i 925 2 . . . work_fnploejenbc2raktl46esxm44i 926 1 24 24 CD work_fnploejenbc2raktl46esxm44i 926 2 , , , work_fnploejenbc2raktl46esxm44i 926 3 No no UH work_fnploejenbc2raktl46esxm44i 926 4 . . . work_fnploejenbc2raktl46esxm44i 927 1 2 2 CD work_fnploejenbc2raktl46esxm44i 927 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 927 3 1968 1968 CD work_fnploejenbc2raktl46esxm44i 927 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 927 5 , , , work_fnploejenbc2raktl46esxm44i 927 6 334344 334344 CD work_fnploejenbc2raktl46esxm44i 927 7 . . . work_fnploejenbc2raktl46esxm44i 928 1 25 25 CD work_fnploejenbc2raktl46esxm44i 928 2 . . . work_fnploejenbc2raktl46esxm44i 929 1 B. B. NNP work_fnploejenbc2raktl46esxm44i 929 2 SCHWEIZER SCHWEIZER NNP work_fnploejenbc2raktl46esxm44i 929 3 AND and CC work_fnploejenbc2raktl46esxm44i 929 4 A. a. NN work_fnploejenbc2raktl46esxm44i 929 5 SKLAR SKLAR NNP work_fnploejenbc2raktl46esxm44i 929 6 , , , work_fnploejenbc2raktl46esxm44i 929 7 “ " `` work_fnploejenbc2raktl46esxm44i 929 8 Probabilistic Probabilistic NNP work_fnploejenbc2raktl46esxm44i 929 9 Metric Metric NNP work_fnploejenbc2raktl46esxm44i 929 10 Spaces Spaces NNPS work_fnploejenbc2raktl46esxm44i 929 11 , , , work_fnploejenbc2raktl46esxm44i 929 12 ” " '' work_fnploejenbc2raktl46esxm44i 929 13 North North NNP work_fnploejenbc2raktl46esxm44i 929 14 - - HYPH work_fnploejenbc2raktl46esxm44i 929 15 Holland Holland NNP work_fnploejenbc2raktl46esxm44i 929 16 , , , work_fnploejenbc2raktl46esxm44i 929 17 Amsterdam Amsterdam NNP work_fnploejenbc2raktl46esxm44i 929 18 , , , work_fnploejenbc2raktl46esxm44i 929 19 1983 1983 CD work_fnploejenbc2raktl46esxm44i 929 20 . . . work_fnploejenbc2raktl46esxm44i 930 1 26 26 CD work_fnploejenbc2raktl46esxm44i 930 2 . . . work_fnploejenbc2raktl46esxm44i 931 1 G. G. NNP work_fnploejenbc2raktl46esxm44i 931 2 SHAFER SHAFER NNP work_fnploejenbc2raktl46esxm44i 931 3 , , , work_fnploejenbc2raktl46esxm44i 931 4 “ " `` work_fnploejenbc2raktl46esxm44i 931 5 A a DT work_fnploejenbc2raktl46esxm44i 931 6 Mathematical mathematical JJ work_fnploejenbc2raktl46esxm44i 931 7 Theory Theory NNP work_fnploejenbc2raktl46esxm44i 931 8 of of IN work_fnploejenbc2raktl46esxm44i 931 9 Evidence evidence NN work_fnploejenbc2raktl46esxm44i 931 10 , , , work_fnploejenbc2raktl46esxm44i 931 11 ” " '' work_fnploejenbc2raktl46esxm44i 931 12 Princeton Princeton NNP work_fnploejenbc2raktl46esxm44i 931 13 Univ Univ NNP work_fnploejenbc2raktl46esxm44i 931 14 . . . work_fnploejenbc2raktl46esxm44i 932 1 Press Press NNP work_fnploejenbc2raktl46esxm44i 932 2 , , , work_fnploejenbc2raktl46esxm44i 932 3 Princeton Princeton NNP work_fnploejenbc2raktl46esxm44i 932 4 , , , work_fnploejenbc2raktl46esxm44i 932 5 NJ NJ NNP work_fnploejenbc2raktl46esxm44i 932 6 , , , work_fnploejenbc2raktl46esxm44i 932 7 1976 1976 CD work_fnploejenbc2raktl46esxm44i 932 8 . . . work_fnploejenbc2raktl46esxm44i 933 1 27 27 CD work_fnploejenbc2raktl46esxm44i 933 2 . . . work_fnploejenbc2raktl46esxm44i 934 1 S. S. NNP work_fnploejenbc2raktl46esxm44i 934 2 SMALE SMALE NNP work_fnploejenbc2raktl46esxm44i 934 3 , , , work_fnploejenbc2raktl46esxm44i 934 4 Global global JJ work_fnploejenbc2raktl46esxm44i 934 5 analysis analysis NN work_fnploejenbc2raktl46esxm44i 934 6 and and CC work_fnploejenbc2raktl46esxm44i 934 7 economics economics NN work_fnploejenbc2raktl46esxm44i 934 8 , , , work_fnploejenbc2raktl46esxm44i 934 9 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 934 10 , , , work_fnploejenbc2raktl46esxm44i 934 11 Pareto Pareto NNP work_fnploejenbc2raktl46esxm44i 934 12 optimum optimum NN work_fnploejenbc2raktl46esxm44i 934 13 and and CC work_fnploejenbc2raktl46esxm44i 934 14 a a DT work_fnploejenbc2raktl46esxm44i 934 15 generalization generalization NN work_fnploejenbc2raktl46esxm44i 934 16 of of IN work_fnploejenbc2raktl46esxm44i 934 17 Morse Morse NNP work_fnploejenbc2raktl46esxm44i 934 18 theory theory NN work_fnploejenbc2raktl46esxm44i 934 19 , , , work_fnploejenbc2raktl46esxm44i 934 20 in in IN work_fnploejenbc2raktl46esxm44i 934 21 “ " `` work_fnploejenbc2raktl46esxm44i 934 22 Dynamical Dynamical NNP work_fnploejenbc2raktl46esxm44i 934 23 Systems Systems NNPS work_fnploejenbc2raktl46esxm44i 934 24 ” " '' work_fnploejenbc2raktl46esxm44i 934 25 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 934 26 M. M. NNP work_fnploejenbc2raktl46esxm44i 934 27 M. M. NNP work_fnploejenbc2raktl46esxm44i 934 28 Peixoto Peixoto NNP work_fnploejenbc2raktl46esxm44i 934 29 , , , work_fnploejenbc2raktl46esxm44i 934 30 Ed Ed NNP work_fnploejenbc2raktl46esxm44i 934 31 . . . work_fnploejenbc2raktl46esxm44i 935 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 935 2 , , , work_fnploejenbc2raktl46esxm44i 935 3 pp pp NNP work_fnploejenbc2raktl46esxm44i 935 4 . . . work_fnploejenbc2raktl46esxm44i 936 1 531 531 CD work_fnploejenbc2raktl46esxm44i 936 2 - - SYM work_fnploejenbc2raktl46esxm44i 936 3 544 544 CD work_fnploejenbc2raktl46esxm44i 936 4 , , , work_fnploejenbc2raktl46esxm44i 936 5 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 936 6 Press Press NNP work_fnploejenbc2raktl46esxm44i 936 7 , , , work_fnploejenbc2raktl46esxm44i 936 8 New New NNP work_fnploejenbc2raktl46esxm44i 936 9 York York NNP work_fnploejenbc2raktl46esxm44i 936 10 , , , work_fnploejenbc2raktl46esxm44i 936 11 1973 1973 CD work_fnploejenbc2raktl46esxm44i 936 12 . . . work_fnploejenbc2raktl46esxm44i 937 1 28 28 CD work_fnploejenbc2raktl46esxm44i 937 2 . . . work_fnploejenbc2raktl46esxm44i 938 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 938 2 J. J. NNP work_fnploejenbc2raktl46esxm44i 938 3 SPIEGELHALTER SPIEGELHALTER NNP work_fnploejenbc2raktl46esxm44i 938 4 , , , work_fnploejenbc2raktl46esxm44i 938 5 A a DT work_fnploejenbc2raktl46esxm44i 938 6 statistical statistical JJ work_fnploejenbc2raktl46esxm44i 938 7 view view NN work_fnploejenbc2raktl46esxm44i 938 8 of of IN work_fnploejenbc2raktl46esxm44i 938 9 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 938 10 in in IN work_fnploejenbc2raktl46esxm44i 938 11 expert expert NN work_fnploejenbc2raktl46esxm44i 938 12 systems system NNS work_fnploejenbc2raktl46esxm44i 938 13 , , , work_fnploejenbc2raktl46esxm44i 938 14 in in IN work_fnploejenbc2raktl46esxm44i 938 15 “ " `` work_fnploejenbc2raktl46esxm44i 938 16 Artificial Artificial NNP work_fnploejenbc2raktl46esxm44i 938 17 Intelligence Intelligence NNP work_fnploejenbc2raktl46esxm44i 938 18 and and CC work_fnploejenbc2raktl46esxm44i 938 19 Statistics Statistics NNPS work_fnploejenbc2raktl46esxm44i 938 20 ” " '' work_fnploejenbc2raktl46esxm44i 938 21 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 938 22 W. W. NNP work_fnploejenbc2raktl46esxm44i 938 23 A. A. NNP work_fnploejenbc2raktl46esxm44i 938 24 Gale Gale NNP work_fnploejenbc2raktl46esxm44i 938 25 , , , work_fnploejenbc2raktl46esxm44i 938 26 Ed Ed NNP work_fnploejenbc2raktl46esxm44i 938 27 . . . work_fnploejenbc2raktl46esxm44i 939 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 939 2 , , , work_fnploejenbc2raktl46esxm44i 939 3 pp pp NNP work_fnploejenbc2raktl46esxm44i 939 4 . . . work_fnploejenbc2raktl46esxm44i 940 1 17 17 CD work_fnploejenbc2raktl46esxm44i 940 2 - - SYM work_fnploejenbc2raktl46esxm44i 940 3 56 56 CD work_fnploejenbc2raktl46esxm44i 940 4 , , , work_fnploejenbc2raktl46esxm44i 940 5 Addison Addison NNP work_fnploejenbc2raktl46esxm44i 940 6 - - HYPH work_fnploejenbc2raktl46esxm44i 940 7 Wesley Wesley NNP work_fnploejenbc2raktl46esxm44i 940 8 , , , work_fnploejenbc2raktl46esxm44i 940 9 Reading Reading NNP work_fnploejenbc2raktl46esxm44i 940 10 , , , work_fnploejenbc2raktl46esxm44i 940 11 MA MA NNP work_fnploejenbc2raktl46esxm44i 940 12 , , , work_fnploejenbc2raktl46esxm44i 940 13 1986 1986 CD work_fnploejenbc2raktl46esxm44i 940 14 . . . work_fnploejenbc2raktl46esxm44i 941 1 29 29 CD work_fnploejenbc2raktl46esxm44i 941 2 . . . work_fnploejenbc2raktl46esxm44i 942 1 D. D. NNP work_fnploejenbc2raktl46esxm44i 942 2 A. A. NNP work_fnploejenbc2raktl46esxm44i 942 3 SPRECHER SPRECHER NNP work_fnploejenbc2raktl46esxm44i 942 4 , , , work_fnploejenbc2raktl46esxm44i 942 5 A a DT work_fnploejenbc2raktl46esxm44i 942 6 survey survey NN work_fnploejenbc2raktl46esxm44i 942 7 of of IN work_fnploejenbc2raktl46esxm44i 942 8 solved solve VBN work_fnploejenbc2raktl46esxm44i 942 9 and and CC work_fnploejenbc2raktl46esxm44i 942 10 unsolved unsolved JJ work_fnploejenbc2raktl46esxm44i 942 11 problems problem NNS work_fnploejenbc2raktl46esxm44i 942 12 on on IN work_fnploejenbc2raktl46esxm44i 942 13 super super JJ work_fnploejenbc2raktl46esxm44i 942 14 - - NNS work_fnploejenbc2raktl46esxm44i 942 15 positions position NNS work_fnploejenbc2raktl46esxm44i 942 16 of of IN work_fnploejenbc2raktl46esxm44i 942 17 functions function NNS work_fnploejenbc2raktl46esxm44i 942 18 , , , work_fnploejenbc2raktl46esxm44i 942 19 J. J. NNP work_fnploejenbc2raktl46esxm44i 942 20 Approx Approx NNP work_fnploejenbc2raktl46esxm44i 942 21 . . . work_fnploejenbc2raktl46esxm44i 943 1 Theory theory NN work_fnploejenbc2raktl46esxm44i 943 2 6 6 CD work_fnploejenbc2raktl46esxm44i 943 3 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 943 4 1972 1972 CD work_fnploejenbc2raktl46esxm44i 943 5 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 943 6 , , , work_fnploejenbc2raktl46esxm44i 943 7 123 123 CD work_fnploejenbc2raktl46esxm44i 943 8 - - SYM work_fnploejenbc2raktl46esxm44i 943 9 134 134 CD work_fnploejenbc2raktl46esxm44i 943 10 . . . work_fnploejenbc2raktl46esxm44i 944 1 30 30 CD work_fnploejenbc2raktl46esxm44i 944 2 . . . work_fnploejenbc2raktl46esxm44i 945 1 L. L. NNP work_fnploejenbc2raktl46esxm44i 945 2 A. A. NNP work_fnploejenbc2raktl46esxm44i 945 3 WASSERMAN WASSERMAN NNP work_fnploejenbc2raktl46esxm44i 945 4 , , , work_fnploejenbc2raktl46esxm44i 945 5 “ " `` work_fnploejenbc2raktl46esxm44i 945 6 Some some DT work_fnploejenbc2raktl46esxm44i 945 7 Applications Applications NNPS work_fnploejenbc2raktl46esxm44i 945 8 of of IN work_fnploejenbc2raktl46esxm44i 945 9 Belief Belief NNP work_fnploejenbc2raktl46esxm44i 945 10 Functions Functions NNPS work_fnploejenbc2raktl46esxm44i 945 11 to to IN work_fnploejenbc2raktl46esxm44i 945 12 Statistical Statistical NNP work_fnploejenbc2raktl46esxm44i 945 13 Inference Inference NNP work_fnploejenbc2raktl46esxm44i 945 14 , , , work_fnploejenbc2raktl46esxm44i 945 15 ” " '' work_fnploejenbc2raktl46esxm44i 945 16 Ph.D. ph.d. NN work_fnploejenbc2raktl46esxm44i 945 17 thesis thesis NN work_fnploejenbc2raktl46esxm44i 945 18 , , , work_fnploejenbc2raktl46esxm44i 945 19 Univ Univ NNP work_fnploejenbc2raktl46esxm44i 945 20 . . . work_fnploejenbc2raktl46esxm44i 946 1 of of IN work_fnploejenbc2raktl46esxm44i 946 2 Toronto Toronto NNP work_fnploejenbc2raktl46esxm44i 946 3 , , , work_fnploejenbc2raktl46esxm44i 946 4 Ontario Ontario NNP work_fnploejenbc2raktl46esxm44i 946 5 , , , work_fnploejenbc2raktl46esxm44i 946 6 1987 1987 CD work_fnploejenbc2raktl46esxm44i 946 7 . . . work_fnploejenbc2raktl46esxm44i 947 1 31 31 CD work_fnploejenbc2raktl46esxm44i 947 2 . . . work_fnploejenbc2raktl46esxm44i 948 1 S. S. NNP work_fnploejenbc2raktl46esxm44i 948 2 WEBER WEBER NNP work_fnploejenbc2raktl46esxm44i 948 3 , , , work_fnploejenbc2raktl46esxm44i 948 4 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 948 5 - - HYPH work_fnploejenbc2raktl46esxm44i 948 6 decomposable decomposable JJ work_fnploejenbc2raktl46esxm44i 948 7 measures measure NNS work_fnploejenbc2raktl46esxm44i 948 8 and and CC work_fnploejenbc2raktl46esxm44i 948 9 integrals integral NNS work_fnploejenbc2raktl46esxm44i 948 10 for for IN work_fnploejenbc2raktl46esxm44i 948 11 archimedean archimedean NNP work_fnploejenbc2raktl46esxm44i 948 12 f f NNP work_fnploejenbc2raktl46esxm44i 948 13 - - HYPH work_fnploejenbc2raktl46esxm44i 948 14 conorms conorm NNS work_fnploejenbc2raktl46esxm44i 948 15 I -PRON- PRP work_fnploejenbc2raktl46esxm44i 948 16 , , , work_fnploejenbc2raktl46esxm44i 948 17 J. J. NNP work_fnploejenbc2raktl46esxm44i 949 1 Math math NN work_fnploejenbc2raktl46esxm44i 949 2 . . . work_fnploejenbc2raktl46esxm44i 950 1 Anal anal JJ work_fnploejenbc2raktl46esxm44i 950 2 . . . work_fnploejenbc2raktl46esxm44i 951 1 Appl Appl NNP work_fnploejenbc2raktl46esxm44i 951 2 . . . work_fnploejenbc2raktl46esxm44i 952 1 101 101 CD work_fnploejenbc2raktl46esxm44i 952 2 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 952 3 1984 1984 CD work_fnploejenbc2raktl46esxm44i 952 4 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 952 5 , , , work_fnploejenbc2raktl46esxm44i 952 6 114 114 CD work_fnploejenbc2raktl46esxm44i 952 7 - - SYM work_fnploejenbc2raktl46esxm44i 952 8 138 138 CD work_fnploejenbc2raktl46esxm44i 952 9 . . . work_fnploejenbc2raktl46esxm44i 953 1 32 32 CD work_fnploejenbc2raktl46esxm44i 953 2 . . . work_fnploejenbc2raktl46esxm44i 954 1 L. L. NNP work_fnploejenbc2raktl46esxm44i 954 2 A. A. NNP work_fnploejenbc2raktl46esxm44i 954 3 ZADEH ZADEH NNP work_fnploejenbc2raktl46esxm44i 954 4 , , , work_fnploejenbc2raktl46esxm44i 954 5 The the DT work_fnploejenbc2raktl46esxm44i 954 6 role role NN work_fnploejenbc2raktl46esxm44i 954 7 of of IN work_fnploejenbc2raktl46esxm44i 954 8 fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 954 9 logic logic NN work_fnploejenbc2raktl46esxm44i 954 10 in in IN work_fnploejenbc2raktl46esxm44i 954 11 the the DT work_fnploejenbc2raktl46esxm44i 954 12 management management NN work_fnploejenbc2raktl46esxm44i 954 13 of of IN work_fnploejenbc2raktl46esxm44i 954 14 uncertainty uncertainty NN work_fnploejenbc2raktl46esxm44i 954 15 in in IN work_fnploejenbc2raktl46esxm44i 954 16 expert expert NN work_fnploejenbc2raktl46esxm44i 954 17 systems system NNS work_fnploejenbc2raktl46esxm44i 954 18 , , , work_fnploejenbc2raktl46esxm44i 954 19 Fuzzy fuzzy JJ work_fnploejenbc2raktl46esxm44i 954 20 Sets Sets NNPS work_fnploejenbc2raktl46esxm44i 954 21 and and CC work_fnploejenbc2raktl46esxm44i 954 22 Systems system NNS work_fnploejenbc2raktl46esxm44i 954 23 11 11 CD work_fnploejenbc2raktl46esxm44i 954 24 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 954 25 1983 1983 CD work_fnploejenbc2raktl46esxm44i 954 26 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 954 27 , , , work_fnploejenbc2raktl46esxm44i 954 28 199 199 CD work_fnploejenbc2raktl46esxm44i 954 29 - - SYM work_fnploejenbc2raktl46esxm44i 954 30 227 227 CD work_fnploejenbc2raktl46esxm44i 954 31 . . . work_fnploejenbc2raktl46esxm44i 955 1 33 33 CD work_fnploejenbc2raktl46esxm44i 955 2 . . . work_fnploejenbc2raktl46esxm44i 956 1 L. L. NNP work_fnploejenbc2raktl46esxm44i 956 2 A. A. NNP work_fnploejenbc2raktl46esxm44i 956 3 ZADEH ZADEH NNP work_fnploejenbc2raktl46esxm44i 956 4 , , , work_fnploejenbc2raktl46esxm44i 956 5 Possibility possibility NN work_fnploejenbc2raktl46esxm44i 956 6 theory theory NN work_fnploejenbc2raktl46esxm44i 956 7 and and CC work_fnploejenbc2raktl46esxm44i 956 8 soft soft JJ work_fnploejenbc2raktl46esxm44i 956 9 data datum NNS work_fnploejenbc2raktl46esxm44i 956 10 analysis analysis NN work_fnploejenbc2raktl46esxm44i 956 11 , , , work_fnploejenbc2raktl46esxm44i 956 12 in in IN work_fnploejenbc2raktl46esxm44i 956 13 “ " `` work_fnploejenbc2raktl46esxm44i 956 14 Mathematical Mathematical NNP work_fnploejenbc2raktl46esxm44i 956 15 Frontier Frontier NNP work_fnploejenbc2raktl46esxm44i 956 16 of of IN work_fnploejenbc2raktl46esxm44i 956 17 the the DT work_fnploejenbc2raktl46esxm44i 956 18 Social Social NNP work_fnploejenbc2raktl46esxm44i 956 19 and and CC work_fnploejenbc2raktl46esxm44i 956 20 Policy Policy NNP work_fnploejenbc2raktl46esxm44i 956 21 Sciences Sciences NNPS work_fnploejenbc2raktl46esxm44i 956 22 ” " '' work_fnploejenbc2raktl46esxm44i 956 23 ( ( -LRB- work_fnploejenbc2raktl46esxm44i 956 24 L. L. NNP work_fnploejenbc2raktl46esxm44i 956 25 Cobb Cobb NNP work_fnploejenbc2raktl46esxm44i 956 26 and and CC work_fnploejenbc2raktl46esxm44i 956 27 R. R. NNP work_fnploejenbc2raktl46esxm44i 956 28 M. M. NNP work_fnploejenbc2raktl46esxm44i 956 29 Thrall Thrall NNP work_fnploejenbc2raktl46esxm44i 956 30 , , , work_fnploejenbc2raktl46esxm44i 956 31 Eds Eds NNP work_fnploejenbc2raktl46esxm44i 956 32 . . . work_fnploejenbc2raktl46esxm44i 957 1 ) ) -RRB- work_fnploejenbc2raktl46esxm44i 957 2 , , , work_fnploejenbc2raktl46esxm44i 957 3 pp pp NNP work_fnploejenbc2raktl46esxm44i 957 4 . . . work_fnploejenbc2raktl46esxm44i 958 1 69 69 CD work_fnploejenbc2raktl46esxm44i 958 2 - - SYM work_fnploejenbc2raktl46esxm44i 958 3 129 129 CD work_fnploejenbc2raktl46esxm44i 958 4 , , , work_fnploejenbc2raktl46esxm44i 958 5 Westview Westview NNP work_fnploejenbc2raktl46esxm44i 958 6 , , , work_fnploejenbc2raktl46esxm44i 958 7 Boulder Boulder NNP work_fnploejenbc2raktl46esxm44i 958 8 , , , work_fnploejenbc2raktl46esxm44i 958 9 CO CO NNP work_fnploejenbc2raktl46esxm44i 958 10 , , , work_fnploejenbc2raktl46esxm44i 958 11 1981 1981 CD work_fnploejenbc2raktl46esxm44i 958 12 . . . work_fnploejenbc2raktl46esxm44i 959 1 34 34 CD work_fnploejenbc2raktl46esxm44i 959 2 . . . work_fnploejenbc2raktl46esxm44i 960 1 T. T. NNP work_fnploejenbc2raktl46esxm44i 960 2 L. L. NNP work_fnploejenbc2raktl46esxm44i 960 3 FINE FINE NNP work_fnploejenbc2raktl46esxm44i 960 4 , , , work_fnploejenbc2raktl46esxm44i 960 5 “ " `` work_fnploejenbc2raktl46esxm44i 960 6 Theories theory NNS work_fnploejenbc2raktl46esxm44i 960 7 of of IN work_fnploejenbc2raktl46esxm44i 960 8 Probability Probability NNP work_fnploejenbc2raktl46esxm44i 960 9 , , , work_fnploejenbc2raktl46esxm44i 960 10 ” " '' work_fnploejenbc2raktl46esxm44i 960 11 Academic Academic NNP work_fnploejenbc2raktl46esxm44i 960 12 Press Press NNP work_fnploejenbc2raktl46esxm44i 960 13 , , , work_fnploejenbc2raktl46esxm44i 960 14 New New NNP work_fnploejenbc2raktl46esxm44i 960 15 York York NNP work_fnploejenbc2raktl46esxm44i 960 16 , , , work_fnploejenbc2raktl46esxm44i 960 17 1973 1973 CD work_fnploejenbc2raktl46esxm44i 960 18 . . .