id sid tid token lemma pos cv43nv9583f 1 1 the the DET cv43nv9583f 1 2 mathematics mathematic NOUN cv43nv9583f 1 3 portion portion NOUN cv43nv9583f 1 4 of of ADP cv43nv9583f 1 5 this this DET cv43nv9583f 1 6 dissertation dissertation NOUN cv43nv9583f 1 7 is be AUX cv43nv9583f 1 8 a a DET cv43nv9583f 1 9 study study NOUN cv43nv9583f 1 10 of of ADP cv43nv9583f 1 11 the the DET cv43nv9583f 1 12 various various ADJ cv43nv9583f 1 13 interactions interaction NOUN cv43nv9583f 1 14 between between ADP cv43nv9583f 1 15 definitions definition NOUN cv43nv9583f 1 16 of of ADP cv43nv9583f 1 17 algorithmic algorithmic ADJ cv43nv9583f 1 18 randomness randomness NOUN cv43nv9583f 1 19 , , PUNCT cv43nv9583f 1 20 turing ture VERB cv43nv9583f 1 21 functionals functional NOUN cv43nv9583f 1 22 , , PUNCT cv43nv9583f 1 23 and and CCONJ cv43nv9583f 1 24 non non ADJ cv43nv9583f 1 25 - - ADJ cv43nv9583f 1 26 uniform uniform ADJ cv43nv9583f 1 27 probability probability NOUN cv43nv9583f 1 28 measures measure NOUN cv43nv9583f 1 29 on on ADP cv43nv9583f 1 30 cantor cantor NOUN cv43nv9583f 1 31 space space NOUN cv43nv9583f 1 32 . . PUNCT cv43nv9583f 2 1 in in ADP cv43nv9583f 2 2 chapter chapter NOUN cv43nv9583f 2 3 3 3 NUM cv43nv9583f 2 4 , , PUNCT cv43nv9583f 2 5 we we PRON cv43nv9583f 2 6 study study VERB cv43nv9583f 2 7 the the DET cv43nv9583f 2 8 connection connection NOUN cv43nv9583f 2 9 between between ADP cv43nv9583f 2 10 turing ture VERB cv43nv9583f 2 11 functionals functional NOUN cv43nv9583f 2 12 and and CCONJ cv43nv9583f 2 13 a a DET cv43nv9583f 2 14 number number NOUN cv43nv9583f 2 15 of of ADP cv43nv9583f 2 16 different different ADJ cv43nv9583f 2 17 definitions definition NOUN cv43nv9583f 2 18 of of ADP cv43nv9583f 2 19 randomness randomness NOUN cv43nv9583f 2 20 , , PUNCT cv43nv9583f 2 21 culminating culminate VERB cv43nv9583f 2 22 in in ADP cv43nv9583f 2 23 a a DET cv43nv9583f 2 24 number number NOUN cv43nv9583f 2 25 of of ADP cv43nv9583f 2 26 characterizations characterization NOUN cv43nv9583f 2 27 of of ADP cv43nv9583f 2 28 these these DET cv43nv9583f 2 29 definitions definition NOUN cv43nv9583f 2 30 of of ADP cv43nv9583f 2 31 randomness randomness NOUN cv43nv9583f 2 32 in in ADP cv43nv9583f 2 33 terms term NOUN cv43nv9583f 2 34 of of ADP cv43nv9583f 2 35 a a DET cv43nv9583f 2 36 priori priori ADJ cv43nv9583f 2 37 complexity complexity NOUN cv43nv9583f 2 38 , , PUNCT cv43nv9583f 2 39 a a DET cv43nv9583f 2 40 notion notion NOUN cv43nv9583f 2 41 of of ADP cv43nv9583f 2 42 initial initial ADJ cv43nv9583f 2 43 segment segment NOUN cv43nv9583f 2 44 complexity complexity NOUN cv43nv9583f 2 45 given give VERB cv43nv9583f 2 46 in in ADP cv43nv9583f 2 47 terms term NOUN cv43nv9583f 2 48 of of ADP cv43nv9583f 2 49 turing ture VERB cv43nv9583f 2 50 functionals functional NOUN cv43nv9583f 2 51 . . PUNCT cv43nv9583f 3 1 in in ADP cv43nv9583f 3 2 chapter chapter NOUN cv43nv9583f 3 3 4 4 NUM cv43nv9583f 3 4 , , PUNCT cv43nv9583f 3 5 we we PRON cv43nv9583f 3 6 investigate investigate VERB cv43nv9583f 3 7 possible possible ADJ cv43nv9583f 3 8 generalizations generalization NOUN cv43nv9583f 3 9 of of ADP cv43nv9583f 3 10 demuth demuth NOUN cv43nv9583f 3 11 's 's PART cv43nv9583f 3 12 theorem theorem NOUN cv43nv9583f 3 13 , , PUNCT cv43nv9583f 3 14 an an DET cv43nv9583f 3 15 important important ADJ cv43nv9583f 3 16 theorem theorem NOUN cv43nv9583f 3 17 in in ADP cv43nv9583f 3 18 algorithmic algorithmic ADJ cv43nv9583f 3 19 randomness randomness NOUN cv43nv9583f 3 20 concerning concern VERB cv43nv9583f 3 21 the the DET cv43nv9583f 3 22 behavior behavior NOUN cv43nv9583f 3 23 of of ADP cv43nv9583f 3 24 random random ADJ cv43nv9583f 3 25 sequences sequence NOUN cv43nv9583f 3 26 under under ADP cv43nv9583f 3 27 truth truth NOUN cv43nv9583f 3 28 - - PUNCT cv43nv9583f 3 29 table table NOUN cv43nv9583f 3 30 reducibility reducibility NOUN cv43nv9583f 3 31 . . PUNCT cv43nv9583f 4 1 one one NUM cv43nv9583f 4 2 technique technique NOUN cv43nv9583f 4 3 developed develop VERB cv43nv9583f 4 4 in in ADP cv43nv9583f 4 5 this this DET cv43nv9583f 4 6 chapter chapter NOUN cv43nv9583f 4 7 , , PUNCT cv43nv9583f 4 8 that that PRON cv43nv9583f 4 9 of of ADP cv43nv9583f 4 10 inducing induce VERB cv43nv9583f 4 11 a a DET cv43nv9583f 4 12 probability probability NOUN cv43nv9583f 4 13 measure measure NOUN cv43nv9583f 4 14 by by ADP cv43nv9583f 4 15 means mean NOUN cv43nv9583f 4 16 of of ADP cv43nv9583f 4 17 a a DET cv43nv9583f 4 18 special special ADJ cv43nv9583f 4 19 type type NOUN cv43nv9583f 4 20 of of ADP cv43nv9583f 4 21 truth truth NOUN cv43nv9583f 4 22 - - PUNCT cv43nv9583f 4 23 table table NOUN cv43nv9583f 4 24 functional functional NOUN cv43nv9583f 4 25 that that SCONJ cv43nv9583f 4 26 we we PRON cv43nv9583f 4 27 call call VERB cv43nv9583f 4 28 a a DET cv43nv9583f 4 29 tally tally NOUN cv43nv9583f 4 30 functional functional ADJ cv43nv9583f 4 31 , , PUNCT cv43nv9583f 4 32 proves prove VERB cv43nv9583f 4 33 to to PART cv43nv9583f 4 34 be be AUX cv43nv9583f 4 35 very very ADV cv43nv9583f 4 36 useful useful ADJ cv43nv9583f 4 37 . . PUNCT cv43nv9583f 5 1 we we PRON cv43nv9583f 5 2 use use VERB cv43nv9583f 5 3 this this DET cv43nv9583f 5 4 technique technique NOUN cv43nv9583f 5 5 to to PART cv43nv9583f 5 6 study study VERB cv43nv9583f 5 7 randomness randomness NOUN cv43nv9583f 5 8 with with ADP cv43nv9583f 5 9 respect respect NOUN cv43nv9583f 5 10 to to ADP cv43nv9583f 5 11 trivial trivial ADJ cv43nv9583f 5 12 computable computable ADJ cv43nv9583f 5 13 measures measure NOUN cv43nv9583f 5 14 in in ADP cv43nv9583f 5 15 both both DET cv43nv9583f 5 16 chapters chapter NOUN cv43nv9583f 5 17 5 5 NUM cv43nv9583f 5 18 and and CCONJ cv43nv9583f 5 19 6 6 NUM cv43nv9583f 5 20 . . PUNCT cv43nv9583f 6 1 in in ADP cv43nv9583f 6 2 the the DET cv43nv9583f 6 3 philosophy philosophy NOUN cv43nv9583f 6 4 portion portion NOUN cv43nv9583f 6 5 of of ADP cv43nv9583f 6 6 this this DET cv43nv9583f 6 7 dissertation dissertation NOUN cv43nv9583f 6 8 , , PUNCT cv43nv9583f 6 9 we we PRON cv43nv9583f 6 10 consider consider VERB cv43nv9583f 6 11 the the DET cv43nv9583f 6 12 problem problem NOUN cv43nv9583f 6 13 of of ADP cv43nv9583f 6 14 producing produce VERB cv43nv9583f 6 15 a a DET cv43nv9583f 6 16 correct correct ADJ cv43nv9583f 6 17 definition definition NOUN cv43nv9583f 6 18 of of ADP cv43nv9583f 6 19 randomness randomness NOUN cv43nv9583f 6 20 . . PUNCT cv43nv9583f 7 1 some some PRON cv43nv9583f 7 2 have have AUX cv43nv9583f 7 3 claim claim NOUN cv43nv9583f 7 4 that that SCONJ cv43nv9583f 7 5 one one NUM cv43nv9583f 7 6 definition definition NOUN cv43nv9583f 7 7 of of ADP cv43nv9583f 7 8 randomness randomness NOUN cv43nv9583f 7 9 in in ADP cv43nv9583f 7 10 particular particular ADJ cv43nv9583f 7 11 , , PUNCT cv43nv9583f 7 12 martin martin PROPN cv43nv9583f 7 13 - - PUNCT cv43nv9583f 7 14 l l PROPN cv43nv9583f 7 15 f f PROPN cv43nv9583f 7 16 randomness randomness PROPN cv43nv9583f 7 17 , , PUNCT cv43nv9583f 7 18 captures capture VERB cv43nv9583f 7 19 the the DET cv43nv9583f 7 20 so so ADV cv43nv9583f 7 21 - - PUNCT cv43nv9583f 7 22 called call VERB cv43nv9583f 7 23 intuitive intuitive ADJ cv43nv9583f 7 24 conception conception NOUN cv43nv9583f 7 25 of of ADP cv43nv9583f 7 26 randomness randomness NOUN cv43nv9583f 7 27 , , PUNCT cv43nv9583f 7 28 a a DET cv43nv9583f 7 29 claim claim NOUN cv43nv9583f 7 30 known know VERB cv43nv9583f 7 31 as as ADP cv43nv9583f 7 32 the the DET cv43nv9583f 7 33 martin martin PROPN cv43nv9583f 7 34 - - PUNCT cv43nv9583f 7 35 l l PROPN cv43nv9583f 7 36 f f PROPN cv43nv9583f 7 37 - - PUNCT cv43nv9583f 7 38 chaitin chaitin PROPN cv43nv9583f 7 39 thesis thesis PROPN cv43nv9583f 7 40 . . PUNCT cv43nv9583f 8 1 prior prior ADV cv43nv9583f 8 2 to to ADP cv43nv9583f 8 3 evaluating evaluate VERB cv43nv9583f 8 4 the the DET cv43nv9583f 8 5 martin martin PROPN cv43nv9583f 8 6 - - PUNCT cv43nv9583f 8 7 l l PROPN cv43nv9583f 8 8 f f PROPN cv43nv9583f 8 9 - - PUNCT cv43nv9583f 8 10 chaitin chaitin PROPN cv43nv9583f 8 11 thesis thesis NOUN cv43nv9583f 8 12 and and CCONJ cv43nv9583f 8 13 related related ADJ cv43nv9583f 8 14 randomness randomness ADJ cv43nv9583f 8 15 - - PUNCT cv43nv9583f 8 16 theoretic theoretic ADJ cv43nv9583f 8 17 theses theses NOUN cv43nv9583f 8 18 , , PUNCT cv43nv9583f 8 19 in in ADP cv43nv9583f 8 20 chapters chapter NOUN cv43nv9583f 8 21 8 8 NUM cv43nv9583f 8 22 and and CCONJ cv43nv9583f 8 23 9 9 NUM cv43nv9583f 8 24 we we PRON cv43nv9583f 8 25 discuss discuss VERB cv43nv9583f 8 26 two two NUM cv43nv9583f 8 27 roles role NOUN cv43nv9583f 8 28 of of ADP cv43nv9583f 8 29 definitions definition NOUN cv43nv9583f 8 30 of of ADP cv43nv9583f 8 31 randomness randomness NOUN cv43nv9583f 8 32 , , PUNCT cv43nv9583f 8 33 both both PRON cv43nv9583f 8 34 of of ADP cv43nv9583f 8 35 which which PRON cv43nv9583f 8 36 motivated motivate VERB cv43nv9583f 8 37 much much ADJ cv43nv9583f 8 38 early early ADJ cv43nv9583f 8 39 work work NOUN cv43nv9583f 8 40 in in ADP cv43nv9583f 8 41 the the DET cv43nv9583f 8 42 development development NOUN cv43nv9583f 8 43 of of ADP cv43nv9583f 8 44 algorithmic algorithmic PROPN cv43nv9583f 8 45 randomness randomness NOUN cv43nv9583f 8 46 : : PUNCT cv43nv9583f 8 47 the the DET cv43nv9583f 8 48 resolutory resolutory ADJ cv43nv9583f 8 49 role role NOUN cv43nv9583f 8 50 of of ADP cv43nv9583f 8 51 randomness randomness NOUN cv43nv9583f 8 52 , , PUNCT cv43nv9583f 8 53 which which PRON cv43nv9583f 8 54 is be AUX cv43nv9583f 8 55 successfully successfully ADV cv43nv9583f 8 56 filled fill VERB cv43nv9583f 8 57 by by ADP cv43nv9583f 8 58 a a DET cv43nv9583f 8 59 definition definition NOUN cv43nv9583f 8 60 of of ADP cv43nv9583f 8 61 randomness randomness NOUN cv43nv9583f 8 62 that that PRON cv43nv9583f 8 63 allows allow VERB cv43nv9583f 8 64 for for ADP cv43nv9583f 8 65 the the DET cv43nv9583f 8 66 solution solution NOUN cv43nv9583f 8 67 of of ADP cv43nv9583f 8 68 problems problem NOUN cv43nv9583f 8 69 in in ADP cv43nv9583f 8 70 a a DET cv43nv9583f 8 71 specific specific ADJ cv43nv9583f 8 72 theory theory NOUN cv43nv9583f 8 73 of of ADP cv43nv9583f 8 74 probability probability NOUN cv43nv9583f 8 75 , , PUNCT cv43nv9583f 8 76 and and CCONJ cv43nv9583f 8 77 the the DET cv43nv9583f 8 78 exemplary exemplary ADJ cv43nv9583f 8 79 role role NOUN cv43nv9583f 8 80 of of ADP cv43nv9583f 8 81 randomness randomness NOUN cv43nv9583f 8 82 , , PUNCT cv43nv9583f 8 83 which which PRON cv43nv9583f 8 84 is be AUX cv43nv9583f 8 85 successfully successfully ADV cv43nv9583f 8 86 filled fill VERB cv43nv9583f 8 87 by by ADP cv43nv9583f 8 88 a a DET cv43nv9583f 8 89 definition definition NOUN cv43nv9583f 8 90 of of ADP cv43nv9583f 8 91 randomness randomness NOUN cv43nv9583f 8 92 that that PRON cv43nv9583f 8 93 counts count VERB cv43nv9583f 8 94 as as ADV cv43nv9583f 8 95 random random ADJ cv43nv9583f 8 96 certain certain ADJ cv43nv9583f 8 97 sequences sequence NOUN cv43nv9583f 8 98 that that PRON cv43nv9583f 8 99 exemplify exemplify VERB cv43nv9583f 8 100 the the DET cv43nv9583f 8 101 properties property NOUN cv43nv9583f 8 102 typically typically ADV cv43nv9583f 8 103 held hold VERB cv43nv9583f 8 104 by by ADP cv43nv9583f 8 105 sequences sequence NOUN cv43nv9583f 8 106 chosen choose VERB cv43nv9583f 8 107 at at ADP cv43nv9583f 8 108 random random ADJ cv43nv9583f 8 109 . . PUNCT cv43nv9583f 9 1 in in ADP cv43nv9583f 9 2 chapter chapter NOUN cv43nv9583f 9 3 10 10 NUM cv43nv9583f 9 4 , , PUNCT cv43nv9583f 9 5 we we PRON cv43nv9583f 9 6 lay lie VERB cv43nv9583f 9 7 out out ADP cv43nv9583f 9 8 the the DET cv43nv9583f 9 9 status status NOUN cv43nv9583f 9 10 of of ADP cv43nv9583f 9 11 the the DET cv43nv9583f 9 12 martin martin PROPN cv43nv9583f 9 13 - - PUNCT cv43nv9583f 9 14 l l PROPN cv43nv9583f 9 15 f f PROPN cv43nv9583f 9 16 - - PUNCT cv43nv9583f 9 17 chaitin chaitin PROPN cv43nv9583f 9 18 thesis thesis PROPN cv43nv9583f 9 19 , , PUNCT cv43nv9583f 9 20 discussing discuss VERB cv43nv9583f 9 21 the the DET cv43nv9583f 9 22 evidence evidence NOUN cv43nv9583f 9 23 that that PRON cv43nv9583f 9 24 has have AUX cv43nv9583f 9 25 been be AUX cv43nv9583f 9 26 offered offer VERB cv43nv9583f 9 27 in in ADP cv43nv9583f 9 28 support support NOUN cv43nv9583f 9 29 of of ADP cv43nv9583f 9 30 it it PRON cv43nv9583f 9 31 , , PUNCT cv43nv9583f 9 32 as as ADV cv43nv9583f 9 33 well well ADV cv43nv9583f 9 34 as as ADP cv43nv9583f 9 35 the the DET cv43nv9583f 9 36 arguments argument NOUN cv43nv9583f 9 37 that that PRON cv43nv9583f 9 38 have have AUX cv43nv9583f 9 39 been be AUX cv43nv9583f 9 40 raised raise VERB cv43nv9583f 9 41 against against ADP cv43nv9583f 9 42 it it PRON cv43nv9583f 9 43 . . PUNCT cv43nv9583f 10 1 in in ADP cv43nv9583f 10 2 chapter chapter NOUN cv43nv9583f 10 3 11 11 NUM cv43nv9583f 10 4 , , PUNCT cv43nv9583f 10 5 we we PRON cv43nv9583f 10 6 argue argue VERB cv43nv9583f 10 7 that that SCONJ cv43nv9583f 10 8 the the DET cv43nv9583f 10 9 advocate advocate NOUN cv43nv9583f 10 10 of of ADP cv43nv9583f 10 11 a a DET cv43nv9583f 10 12 claim claim NOUN cv43nv9583f 10 13 like like ADP cv43nv9583f 10 14 the the DET cv43nv9583f 10 15 martin martin PROPN cv43nv9583f 10 16 - - PUNCT cv43nv9583f 10 17 l l PROPN cv43nv9583f 10 18 f f PROPN cv43nv9583f 10 19 - - PUNCT cv43nv9583f 10 20 chaitin chaitin PROPN cv43nv9583f 10 21 thesis thesis NOUN cv43nv9583f 10 22 faces face VERB cv43nv9583f 10 23 what what PRON cv43nv9583f 10 24 we we PRON cv43nv9583f 10 25 call call VERB cv43nv9583f 10 26 the the DET cv43nv9583f 10 27 justificatory justificatory ADJ cv43nv9583f 10 28 challenge challenge NOUN cv43nv9583f 10 29 : : PUNCT cv43nv9583f 10 30 she she PRON cv43nv9583f 10 31 must must AUX cv43nv9583f 10 32 present present VERB cv43nv9583f 10 33 a a DET cv43nv9583f 10 34 precise precise ADJ cv43nv9583f 10 35 account account NOUN cv43nv9583f 10 36 of of ADP cv43nv9583f 10 37 the the DET cv43nv9583f 10 38 so so ADV cv43nv9583f 10 39 - - PUNCT cv43nv9583f 10 40 called call VERB cv43nv9583f 10 41 intuitive intuitive ADJ cv43nv9583f 10 42 conception conception NOUN cv43nv9583f 10 43 of of ADP cv43nv9583f 10 44 randomness randomness NOUN cv43nv9583f 10 45 , , PUNCT cv43nv9583f 10 46 so so SCONJ cv43nv9583f 10 47 as as SCONJ cv43nv9583f 10 48 to to PART cv43nv9583f 10 49 justify justify VERB cv43nv9583f 10 50 the the DET cv43nv9583f 10 51 claim claim NOUN cv43nv9583f 10 52 that that SCONJ cv43nv9583f 10 53 her her PRON cv43nv9583f 10 54 preferred preferred ADJ cv43nv9583f 10 55 definition definition NOUN cv43nv9583f 10 56 of of ADP cv43nv9583f 10 57 randomness randomness NOUN cv43nv9583f 10 58 is be AUX cv43nv9583f 10 59 the the DET cv43nv9583f 10 60 correct correct ADJ cv43nv9583f 10 61 one one NUM cv43nv9583f 10 62 and and CCONJ cv43nv9583f 10 63 block block VERB cv43nv9583f 10 64 the the DET cv43nv9583f 10 65 claim claim NOUN cv43nv9583f 10 66 of of ADP cv43nv9583f 10 67 correctness correctness NOUN cv43nv9583f 10 68 made make VERB cv43nv9583f 10 69 on on ADP cv43nv9583f 10 70 behalf behalf NOUN cv43nv9583f 10 71 of of ADP cv43nv9583f 10 72 alternative alternative ADJ cv43nv9583f 10 73 definitions definition NOUN cv43nv9583f 10 74 of of ADP cv43nv9583f 10 75 randomness randomness NOUN cv43nv9583f 10 76 . . PUNCT cv43nv9583f 11 1 lastly lastly ADV cv43nv9583f 11 2 , , PUNCT cv43nv9583f 11 3 in in ADP cv43nv9583f 11 4 chapter chapter NOUN cv43nv9583f 11 5 12 12 NUM cv43nv9583f 11 6 , , PUNCT cv43nv9583f 11 7 we we PRON cv43nv9583f 11 8 present present VERB cv43nv9583f 11 9 two two NUM cv43nv9583f 11 10 further further ADJ cv43nv9583f 11 11 roles role NOUN cv43nv9583f 11 12 for for ADP cv43nv9583f 11 13 definitions definition NOUN cv43nv9583f 11 14 of of ADP cv43nv9583f 11 15 randomness randomness NOUN cv43nv9583f 11 16 to to PART cv43nv9583f 11 17 play play VERB cv43nv9583f 11 18 , , PUNCT cv43nv9583f 11 19 which which PRON cv43nv9583f 11 20 we we PRON cv43nv9583f 11 21 call call VERB cv43nv9583f 11 22 the the DET cv43nv9583f 11 23 calibrative calibrative ADJ cv43nv9583f 11 24 role role NOUN cv43nv9583f 11 25 of of ADP cv43nv9583f 11 26 randomness randomness NOUN cv43nv9583f 11 27 and and CCONJ cv43nv9583f 11 28 the the DET cv43nv9583f 11 29 limitative limitative ADJ cv43nv9583f 11 30 role role NOUN cv43nv9583f 11 31 of of ADP cv43nv9583f 11 32 randomness randomness NOUN cv43nv9583f 11 33 , , PUNCT cv43nv9583f 11 34 which which PRON cv43nv9583f 11 35 can can AUX cv43nv9583f 11 36 be be AUX cv43nv9583f 11 37 successfully successfully ADV cv43nv9583f 11 38 filled fill VERB cv43nv9583f 11 39 by by ADP cv43nv9583f 11 40 multiple multiple ADJ cv43nv9583f 11 41 definitions definition NOUN cv43nv9583f 11 42 of of ADP cv43nv9583f 11 43 randomness randomness NOUN cv43nv9583f 11 44 . . PUNCT cv43nv9583f 12 1 definitions definition NOUN cv43nv9583f 12 2 filling fill VERB cv43nv9583f 12 3 the the DET cv43nv9583f 12 4 calibrative calibrative ADJ cv43nv9583f 12 5 role role NOUN cv43nv9583f 12 6 allow allow VERB cv43nv9583f 12 7 us we PRON cv43nv9583f 12 8 to to PART cv43nv9583f 12 9 calibrate calibrate VERB cv43nv9583f 12 10 the the DET cv43nv9583f 12 11 level level NOUN cv43nv9583f 12 12 of of ADP cv43nv9583f 12 13 randomness randomness NOUN cv43nv9583f 12 14 necessary necessary ADJ cv43nv9583f 12 15 and and CCONJ cv43nv9583f 12 16 sufficient sufficient ADJ cv43nv9583f 12 17 for for SCONJ cv43nv9583f 12 18 certain certain ADJ cv43nv9583f 12 19 " " PUNCT cv43nv9583f 12 20 almost almost ADV cv43nv9583f 12 21 - - PUNCT cv43nv9583f 12 22 everywhere everywhere ADV cv43nv9583f 12 23 " " PUNCT cv43nv9583f 12 24 results result NOUN cv43nv9583f 12 25 in in ADP cv43nv9583f 12 26 classical classical ADJ cv43nv9583f 12 27 mathematics mathematic NOUN cv43nv9583f 12 28 to to PART cv43nv9583f 12 29 hold hold VERB cv43nv9583f 12 30 , , PUNCT cv43nv9583f 12 31 while while SCONJ cv43nv9583f 12 32 definitions definition NOUN cv43nv9583f 12 33 filling fill VERB cv43nv9583f 12 34 the the DET cv43nv9583f 12 35 limitative limitative ADJ cv43nv9583f 12 36 role role NOUN cv43nv9583f 12 37 illuminate illuminate VERB cv43nv9583f 12 38 a a DET cv43nv9583f 12 39 phenomenon phenomenon NOUN cv43nv9583f 12 40 known know VERB cv43nv9583f 12 41 as as ADP cv43nv9583f 12 42 the the DET cv43nv9583f 12 43 indefinite indefinite ADJ cv43nv9583f 12 44 contractibility contractibility NOUN cv43nv9583f 12 45 of of ADP cv43nv9583f 12 46 the the DET cv43nv9583f 12 47 notion notion NOUN cv43nv9583f 12 48 of of ADP cv43nv9583f 12 49 randomness randomness NOUN cv43nv9583f 12 50 . . PUNCT cv43nv9583f 13 1 moreover moreover ADV cv43nv9583f 13 2 , , PUNCT cv43nv9583f 13 3 we we PRON cv43nv9583f 13 4 argue argue VERB cv43nv9583f 13 5 that that SCONJ cv43nv9583f 13 6 in in ADP cv43nv9583f 13 7 light light NOUN cv43nv9583f 13 8 of of ADP cv43nv9583f 13 9 the the DET cv43nv9583f 13 10 fact fact NOUN cv43nv9583f 13 11 that that SCONJ cv43nv9583f 13 12 many many ADJ cv43nv9583f 13 13 definitions definition NOUN cv43nv9583f 13 14 can can AUX cv43nv9583f 13 15 successfully successfully ADV cv43nv9583f 13 16 fill fill VERB cv43nv9583f 13 17 these these DET cv43nv9583f 13 18 two two NUM cv43nv9583f 13 19 roles role NOUN cv43nv9583f 13 20 , , PUNCT cv43nv9583f 13 21 we we PRON cv43nv9583f 13 22 should should AUX cv43nv9583f 13 23 accept accept VERB cv43nv9583f 13 24 what what PRON cv43nv9583f 13 25 we we PRON cv43nv9583f 13 26 call call VERB cv43nv9583f 13 27 the the DET cv43nv9583f 13 28 no no DET cv43nv9583f 13 29 - - PUNCT cv43nv9583f 13 30 thesis thesis NOUN cv43nv9583f 13 31 thesis thesis NOUN cv43nv9583f 13 32 : : PUNCT cv43nv9583f 13 33 there there PRON cv43nv9583f 13 34 is be VERB cv43nv9583f 13 35 no no DET cv43nv9583f 13 36 definition definition NOUN cv43nv9583f 13 37 of of ADP cv43nv9583f 13 38 randomness randomness NOUN cv43nv9583f 13 39 that that SCONJ cv43nv9583f 13 40 ( ( PUNCT cv43nv9583f 13 41 i i NOUN cv43nv9583f 13 42 ) ) PUNCT cv43nv9583f 13 43 yields yield VERB cv43nv9583f 13 44 a a DET cv43nv9583f 13 45 well well ADV cv43nv9583f 13 46 - - PUNCT cv43nv9583f 13 47 defined define VERB cv43nv9583f 13 48 , , PUNCT cv43nv9583f 13 49 definite definite ADJ cv43nv9583f 13 50 collection collection NOUN cv43nv9583f 13 51 of of ADP cv43nv9583f 13 52 random random ADJ cv43nv9583f 13 53 sequences sequence NOUN cv43nv9583f 13 54 and and CCONJ cv43nv9583f 13 55 ( ( PUNCT cv43nv9583f 13 56 ii ii PROPN cv43nv9583f 13 57 ) ) PUNCT cv43nv9583f 13 58 captures capture VERB cv43nv9583f 13 59 everything everything PRON cv43nv9583f 13 60 that that PRON cv43nv9583f 13 61 mathematicians mathematician NOUN cv43nv9583f 13 62 have have AUX cv43nv9583f 13 63 taken take VERB cv43nv9583f 13 64 to to PART cv43nv9583f 13 65 be be AUX cv43nv9583f 13 66 significant significant ADJ cv43nv9583f 13 67 about about ADP cv43nv9583f 13 68 the the DET cv43nv9583f 13 69 concept concept NOUN cv43nv9583f 13 70 of of ADP cv43nv9583f 13 71 randomness randomness NOUN cv43nv9583f 13 72 . . PUNCT