id	sid	tid	token	lemma	pos
g445cc10r03	1	1	this	this	DET
g445cc10r03	1	2	dissertation	dissertation	NOUN
g445cc10r03	1	3	contains	contain	VERB
g445cc10r03	1	4	the	the	DET
g445cc10r03	1	5	results	result	NOUN
g445cc10r03	1	6	from	from	ADP
g445cc10r03	1	7	three	three	NUM
g445cc10r03	1	8	related	related	ADJ
g445cc10r03	1	9	projects	project	NOUN
g445cc10r03	1	10	,	,	PUNCT
g445cc10r03	1	11	each	each	PRON
g445cc10r03	1	12	within	within	ADP
g445cc10r03	1	13	the	the	DET
g445cc10r03	1	14	fields	field	NOUN
g445cc10r03	1	15	of	of	ADP
g445cc10r03	1	16	algorithmic	algorithmic	ADJ
g445cc10r03	1	17	randomness	randomness	NOUN
g445cc10r03	1	18	and	and	CCONJ
g445cc10r03	1	19	probability	probability	NOUN
g445cc10r03	1	20	theory	theory	NOUN
g445cc10r03	1	21	.	.	PUNCT
g445cc10r03	2	1	the	the	DET
g445cc10r03	2	2	first	first	ADJ
g445cc10r03	2	3	project	project	NOUN
g445cc10r03	2	4	we	we	PRON
g445cc10r03	2	5	undertake	undertake	VERB
g445cc10r03	2	6	,	,	PUNCT
g445cc10r03	2	7	which	which	PRON
g445cc10r03	2	8	can	can	AUX
g445cc10r03	2	9	be	be	AUX
g445cc10r03	2	10	found	find	VERB
g445cc10r03	2	11	in	in	ADP
g445cc10r03	2	12	chapter	chapter	NOUN
g445cc10r03	2	13	2	2	NUM
g445cc10r03	2	14	,	,	PUNCT
g445cc10r03	2	15	contains	contain	VERB
g445cc10r03	2	16	the	the	DET
g445cc10r03	2	17	definition	definition	NOUN
g445cc10r03	2	18	a	a	DET
g445cc10r03	2	19	natural	natural	ADJ
g445cc10r03	2	20	,	,	PUNCT
g445cc10r03	2	21	computable	computable	ADJ
g445cc10r03	2	22	borel	borel	PROPN
g445cc10r03	2	23	probability	probability	NOUN
g445cc10r03	2	24	measure	measure	NOUN
g445cc10r03	2	25	on	on	ADP
g445cc10r03	2	26	the	the	DET
g445cc10r03	2	27	space	space	NOUN
g445cc10r03	2	28	of	of	ADP
g445cc10r03	2	29	borel	borel	PROPN
g445cc10r03	2	30	probability	probability	NOUN
g445cc10r03	2	31	measures	measure	NOUN
g445cc10r03	2	32	over	over	ADP
g445cc10r03	2	33	2ω	2ω	NUM
g445cc10r03	2	34	that	that	PRON
g445cc10r03	2	35	allows	allow	VERB
g445cc10r03	2	36	us	we	PRON
g445cc10r03	2	37	to	to	PART
g445cc10r03	2	38	study	study	VERB
g445cc10r03	2	39	algorithmically	algorithmically	ADV
g445cc10r03	2	40	random	random	ADJ
g445cc10r03	2	41	measures	measure	NOUN
g445cc10r03	2	42	.	.	PUNCT
g445cc10r03	3	1	the	the	DET
g445cc10r03	3	2	main	main	ADJ
g445cc10r03	3	3	results	result	NOUN
g445cc10r03	3	4	here	here	ADV
g445cc10r03	3	5	are	be	AUX
g445cc10r03	3	6	as	as	ADP
g445cc10r03	3	7	follows	follow	NOUN
g445cc10r03	3	8	.	.	PUNCT
g445cc10r03	4	1	every	every	DET
g445cc10r03	4	2	(	(	PUNCT
g445cc10r03	4	3	algorithmically	algorithmically	ADV
g445cc10r03	4	4	)	)	PUNCT
g445cc10r03	4	5	random	random	ADJ
g445cc10r03	4	6	measure	measure	NOUN
g445cc10r03	4	7	is	be	AUX
g445cc10r03	4	8	atomless	atomless	ADJ
g445cc10r03	4	9	yet	yet	CCONJ
g445cc10r03	4	10	mutually	mutually	ADV
g445cc10r03	4	11	singular	singular	ADJ
g445cc10r03	4	12	with	with	ADP
g445cc10r03	4	13	respect	respect	NOUN
g445cc10r03	4	14	to	to	ADP
g445cc10r03	4	15	the	the	DET
g445cc10r03	4	16	lebesgue	lebesgue	PROPN
g445cc10r03	4	17	measure	measure	NOUN
g445cc10r03	4	18	.	.	PUNCT
g445cc10r03	5	1	the	the	DET
g445cc10r03	5	2	random	random	ADJ
g445cc10r03	5	3	reals	real	NOUN
g445cc10r03	5	4	of	of	ADP
g445cc10r03	5	5	a	a	DET
g445cc10r03	5	6	random	random	ADJ
g445cc10r03	5	7	measure	measure	NOUN
g445cc10r03	5	8	are	be	AUX
g445cc10r03	5	9	random	random	ADJ
g445cc10r03	5	10	for	for	ADP
g445cc10r03	5	11	the	the	DET
g445cc10r03	5	12	lebesgue	lebesgue	PROPN
g445cc10r03	5	13	measure	measure	NOUN
g445cc10r03	5	14	,	,	PUNCT
g445cc10r03	5	15	and	and	CCONJ
g445cc10r03	5	16	every	every	DET
g445cc10r03	5	17	random	random	ADJ
g445cc10r03	5	18	real	real	NOUN
g445cc10r03	5	19	for	for	ADP
g445cc10r03	5	20	the	the	DET
g445cc10r03	5	21	lebesgue	lebesgue	PROPN
g445cc10r03	5	22	measure	measure	NOUN
g445cc10r03	5	23	is	be	AUX
g445cc10r03	5	24	random	random	ADJ
g445cc10r03	5	25	for	for	ADP
g445cc10r03	5	26	some	some	DET
g445cc10r03	5	27	random	random	ADJ
g445cc10r03	5	28	measure	measure	NOUN
g445cc10r03	5	29	.	.	PUNCT
g445cc10r03	6	1	however	however	ADV
g445cc10r03	6	2	,	,	PUNCT
g445cc10r03	6	3	for	for	ADP
g445cc10r03	6	4	a	a	DET
g445cc10r03	6	5	fixed	fix	VERB
g445cc10r03	6	6	lebesgue	lebesgue	PROPN
g445cc10r03	6	7	-	-	PUNCT
g445cc10r03	6	8	random	random	ADJ
g445cc10r03	6	9	real	real	NOUN
g445cc10r03	6	10	,	,	PUNCT
g445cc10r03	6	11	the	the	DET
g445cc10r03	6	12	set	set	NOUN
g445cc10r03	6	13	of	of	ADP
g445cc10r03	6	14	random	random	ADJ
g445cc10r03	6	15	measures	measure	NOUN
g445cc10r03	6	16	for	for	ADP
g445cc10r03	6	17	which	which	PRON
g445cc10r03	6	18	that	that	DET
g445cc10r03	6	19	real	real	ADJ
g445cc10r03	6	20	is	be	AUX
g445cc10r03	6	21	random	random	ADJ
g445cc10r03	6	22	is	be	AUX
g445cc10r03	6	23	small	small	ADJ
g445cc10r03	6	24	.	.	PUNCT
g445cc10r03	7	1	relatively	relatively	ADV
g445cc10r03	7	2	random	random	ADJ
g445cc10r03	7	3	measures	measure	NOUN
g445cc10r03	7	4	,	,	PUNCT
g445cc10r03	7	5	though	though	SCONJ
g445cc10r03	7	6	mutually	mutually	ADV
g445cc10r03	7	7	singular	singular	ADJ
g445cc10r03	7	8	,	,	PUNCT
g445cc10r03	7	9	always	always	ADV
g445cc10r03	7	10	share	share	VERB
g445cc10r03	7	11	a	a	DET
g445cc10r03	7	12	random	random	ADJ
g445cc10r03	7	13	real	real	NOUN
g445cc10r03	7	14	that	that	PRON
g445cc10r03	7	15	is	be	AUX
g445cc10r03	7	16	in	in	ADP
g445cc10r03	7	17	fact	fact	NOUN
g445cc10r03	7	18	computable	computable	NOUN
g445cc10r03	7	19	from	from	ADP
g445cc10r03	7	20	the	the	DET
g445cc10r03	7	21	join	join	NOUN
g445cc10r03	7	22	of	of	ADP
g445cc10r03	7	23	the	the	DET
g445cc10r03	7	24	measures	measure	NOUN
g445cc10r03	7	25	.	.	PUNCT
g445cc10r03	8	1	random	random	ADJ
g445cc10r03	8	2	measures	measure	NOUN
g445cc10r03	8	3	fail	fail	VERB
g445cc10r03	8	4	kolmogorov	kolmogorov	PROPN
g445cc10r03	8	5	's	's	PART
g445cc10r03	8	6	0	0	NUM
g445cc10r03	8	7	-	-	SYM
g445cc10r03	8	8	1	1	NUM
g445cc10r03	8	9	law	law	NOUN
g445cc10r03	8	10	.	.	PUNCT
g445cc10r03	9	1	the	the	DET
g445cc10r03	9	2	shift	shift	NOUN
g445cc10r03	9	3	of	of	ADP
g445cc10r03	9	4	a	a	DET
g445cc10r03	9	5	random	random	ADJ
g445cc10r03	9	6	real	real	NOUN
g445cc10r03	9	7	for	for	ADP
g445cc10r03	9	8	a	a	DET
g445cc10r03	9	9	random	random	ADJ
g445cc10r03	9	10	measure	measure	NOUN
g445cc10r03	9	11	is	be	AUX
g445cc10r03	9	12	no	no	PRON
g445cc10r03	9	13	longer	long	ADV
g445cc10r03	9	14	random	random	ADJ
g445cc10r03	9	15	for	for	ADP
g445cc10r03	9	16	that	that	DET
g445cc10r03	9	17	measure	measure	NOUN
g445cc10r03	9	18	.	.	PUNCT
g445cc10r03	10	1	in	in	ADP
g445cc10r03	10	2	our	our	PRON
g445cc10r03	10	3	second	second	ADJ
g445cc10r03	10	4	project	project	NOUN
g445cc10r03	10	5	,	,	PUNCT
g445cc10r03	10	6	which	which	PRON
g445cc10r03	10	7	makes	make	VERB
g445cc10r03	10	8	up	up	ADP
g445cc10r03	10	9	chapter	chapter	NOUN
g445cc10r03	10	10	3	3	NUM
g445cc10r03	10	11	,	,	PUNCT
g445cc10r03	10	12	we	we	PRON
g445cc10r03	10	13	study	study	VERB
g445cc10r03	10	14	algorithmically	algorithmically	ADV
g445cc10r03	10	15	random	random	ADJ
g445cc10r03	10	16	closed	close	VERB
g445cc10r03	10	17	subsets	subset	NOUN
g445cc10r03	10	18	of	of	ADP
g445cc10r03	10	19	2ω	2ω	NUM
g445cc10r03	10	20	,	,	PUNCT
g445cc10r03	10	21	algorithmically	algorithmically	ADV
g445cc10r03	10	22	random	random	ADJ
g445cc10r03	10	23	continuous	continuous	ADJ
g445cc10r03	10	24	functions	function	NOUN
g445cc10r03	10	25	from	from	ADP
g445cc10r03	10	26	2ω	2ω	NUM
g445cc10r03	10	27	to	to	ADP
g445cc10r03	10	28	2ω	2ω	NUM
g445cc10r03	10	29	,	,	PUNCT
g445cc10r03	10	30	and	and	CCONJ
g445cc10r03	10	31	the	the	DET
g445cc10r03	10	32	algorithmically	algorithmically	ADV
g445cc10r03	10	33	random	random	ADJ
g445cc10r03	10	34	borel	borel	PROPN
g445cc10r03	10	35	probability	probability	NOUN
g445cc10r03	10	36	measures	measure	NOUN
g445cc10r03	10	37	on	on	ADP
g445cc10r03	10	38	2ω	2ω	NUM
g445cc10r03	10	39	from	from	ADP
g445cc10r03	10	40	chapter	chapter	NOUN
g445cc10r03	10	41	2	2	NUM
g445cc10r03	10	42	,	,	PUNCT
g445cc10r03	10	43	especially	especially	ADV
g445cc10r03	10	44	the	the	DET
g445cc10r03	10	45	interplay	interplay	NOUN
g445cc10r03	10	46	among	among	ADP
g445cc10r03	10	47	these	these	DET
g445cc10r03	10	48	three	three	NUM
g445cc10r03	10	49	classes	class	NOUN
g445cc10r03	10	50	of	of	ADP
g445cc10r03	10	51	objects	object	NOUN
g445cc10r03	10	52	.	.	PUNCT
g445cc10r03	11	1	our	our	PRON
g445cc10r03	11	2	main	main	ADJ
g445cc10r03	11	3	tools	tool	NOUN
g445cc10r03	11	4	are	be	AUX
g445cc10r03	11	5	preservation	preservation	NOUN
g445cc10r03	11	6	of	of	ADP
g445cc10r03	11	7	randomness	randomness	NOUN
g445cc10r03	11	8	and	and	CCONJ
g445cc10r03	11	9	its	its	PRON
g445cc10r03	11	10	converse	converse	NOUN
g445cc10r03	11	11	,	,	PUNCT
g445cc10r03	11	12	the	the	DET
g445cc10r03	11	13	"	"	PUNCT
g445cc10r03	11	14	no	no	DET
g445cc10r03	11	15	randomness	randomness	NOUN
g445cc10r03	11	16	ex	ex	NOUN
g445cc10r03	11	17	nihilo	nihilo	PROPN
g445cc10r03	11	18	principle	principle	NOUN
g445cc10r03	11	19	,	,	PUNCT
g445cc10r03	11	20	"	"	PUNCT
g445cc10r03	11	21	which	which	PRON
g445cc10r03	11	22	together	together	ADV
g445cc10r03	11	23	say	say	VERB
g445cc10r03	11	24	that	that	SCONJ
g445cc10r03	11	25	given	give	VERB
g445cc10r03	11	26	an	an	DET
g445cc10r03	11	27	almost	almost	ADV
g445cc10r03	11	28	-	-	PUNCT
g445cc10r03	11	29	everywhere	everywhere	ADV
g445cc10r03	11	30	defined	define	VERB
g445cc10r03	11	31	computable	computable	ADJ
g445cc10r03	11	32	map	map	NOUN
g445cc10r03	11	33	from	from	ADP
g445cc10r03	11	34	2ω	2ω	NUM
g445cc10r03	11	35	to	to	ADP
g445cc10r03	11	36	itself	itself	PRON
g445cc10r03	11	37	,	,	PUNCT
g445cc10r03	11	38	a	a	DET
g445cc10r03	11	39	real	real	NOUN
g445cc10r03	11	40	is	be	AUX
g445cc10r03	11	41	martin	martin	PROPN
g445cc10r03	11	42	lo¨f	lo¨f	PROPN
g445cc10r03	11	43	random	random	ADJ
g445cc10r03	11	44	for	for	ADP
g445cc10r03	11	45	the	the	DET
g445cc10r03	11	46	pushforward	pushforward	ADJ
g445cc10r03	11	47	measure	measure	NOUN
g445cc10r03	11	48	if	if	SCONJ
g445cc10r03	11	49	and	and	CCONJ
g445cc10r03	11	50	only	only	ADV
g445cc10r03	11	51	if	if	SCONJ
g445cc10r03	11	52	its	its	PRON
g445cc10r03	11	53	preimage	preimage	NOUN
g445cc10r03	11	54	is	be	AUX
g445cc10r03	11	55	random	random	ADJ
g445cc10r03	11	56	with	with	ADP
g445cc10r03	11	57	respect	respect	NOUN
g445cc10r03	11	58	to	to	ADP
g445cc10r03	11	59	the	the	DET
g445cc10r03	11	60	measure	measure	NOUN
g445cc10r03	11	61	on	on	ADP
g445cc10r03	11	62	the	the	DET
g445cc10r03	11	63	domain	domain	NOUN
g445cc10r03	11	64	.	.	PUNCT
g445cc10r03	12	1	these	these	DET
g445cc10r03	12	2	tools	tool	NOUN
g445cc10r03	12	3	allow	allow	VERB
g445cc10r03	12	4	us	we	PRON
g445cc10r03	12	5	to	to	PART
g445cc10r03	12	6	prove	prove	VERB
g445cc10r03	12	7	new	new	ADJ
g445cc10r03	12	8	facts	fact	NOUN
g445cc10r03	12	9	,	,	PUNCT
g445cc10r03	12	10	some	some	PRON
g445cc10r03	12	11	of	of	ADP
g445cc10r03	12	12	which	which	PRON
g445cc10r03	12	13	answer	answer	VERB
g445cc10r03	12	14	previously	previously	ADV
g445cc10r03	12	15	open	open	ADJ
g445cc10r03	12	16	questions	question	NOUN
g445cc10r03	12	17	,	,	PUNCT
g445cc10r03	12	18	and	and	CCONJ
g445cc10r03	12	19	reprove	reprove	VERB
g445cc10r03	12	20	some	some	DET
g445cc10r03	12	21	known	know	VERB
g445cc10r03	12	22	results	result	NOUN
g445cc10r03	12	23	more	more	ADV
g445cc10r03	12	24	simply	simply	ADV
g445cc10r03	12	25	.	.	PUNCT
g445cc10r03	13	1	the	the	DET
g445cc10r03	13	2	main	main	ADJ
g445cc10r03	13	3	results	result	NOUN
g445cc10r03	13	4	of	of	ADP
g445cc10r03	13	5	chapter	chapter	NOUN
g445cc10r03	13	6	3	3	NUM
g445cc10r03	13	7	are	be	AUX
g445cc10r03	13	8	the	the	DET
g445cc10r03	13	9	following	following	NOUN
g445cc10r03	13	10	.	.	PUNCT
g445cc10r03	14	1	we	we	PRON
g445cc10r03	14	2	answer	answer	VERB
g445cc10r03	14	3	an	an	DET
g445cc10r03	14	4	open	open	ADJ
g445cc10r03	14	5	question	question	NOUN
g445cc10r03	14	6	in	in	ADP
g445cc10r03	14	7	[	[	X
g445cc10r03	14	8	3	3	NUM
g445cc10r03	14	9	]	]	PUNCT
g445cc10r03	14	10	by	by	ADP
g445cc10r03	14	11	showing	show	VERB
g445cc10r03	14	12	that	that	SCONJ
g445cc10r03	14	13	x	x	PROPN
g445cc10r03	14	14	⊆	⊆	PROPN
g445cc10r03	14	15	2ω	2ω	NUM
g445cc10r03	14	16	is	be	AUX
g445cc10r03	14	17	a	a	DET
g445cc10r03	14	18	random	random	ADJ
g445cc10r03	14	19	closed	closed	ADJ
g445cc10r03	14	20	set	set	NOUN
g445cc10r03	14	21	if	if	SCONJ
g445cc10r03	14	22	and	and	CCONJ
g445cc10r03	14	23	only	only	ADV
g445cc10r03	14	24	if	if	SCONJ
g445cc10r03	14	25	it	it	PRON
g445cc10r03	14	26	is	be	AUX
g445cc10r03	14	27	the	the	DET
g445cc10r03	14	28	set	set	NOUN
g445cc10r03	14	29	of	of	ADP
g445cc10r03	14	30	zeros	zero	NOUN
g445cc10r03	14	31	of	of	ADP
g445cc10r03	14	32	a	a	DET
g445cc10r03	14	33	random	random	ADJ
g445cc10r03	14	34	continuous	continuous	ADJ
g445cc10r03	14	35	function	function	NOUN
g445cc10r03	14	36	on	on	ADP
g445cc10r03	14	37	2ω	2ω	NUM
g445cc10r03	14	38	.	.	PUNCT
g445cc10r03	15	1	as	as	ADP
g445cc10r03	15	2	a	a	DET
g445cc10r03	15	3	corollary	corollary	NOUN
g445cc10r03	15	4	,	,	PUNCT
g445cc10r03	15	5	we	we	PRON
g445cc10r03	15	6	obtain	obtain	VERB
g445cc10r03	15	7	the	the	DET
g445cc10r03	15	8	result	result	NOUN
g445cc10r03	15	9	that	that	SCONJ
g445cc10r03	15	10	the	the	DET
g445cc10r03	15	11	collection	collection	NOUN
g445cc10r03	15	12	of	of	ADP
g445cc10r03	15	13	random	random	ADJ
g445cc10r03	15	14	continuous	continuous	ADJ
g445cc10r03	15	15	functions	function	NOUN
g445cc10r03	15	16	on	on	ADP
g445cc10r03	15	17	2ω	2ω	NUM
g445cc10r03	15	18	is	be	AUX
g445cc10r03	15	19	not	not	PART
g445cc10r03	15	20	closed	close	VERB
g445cc10r03	15	21	under	under	ADP
g445cc10r03	15	22	composition	composition	NOUN
g445cc10r03	15	23	.	.	PUNCT
g445cc10r03	16	1	we	we	PRON
g445cc10r03	16	2	construct	construct	VERB
g445cc10r03	16	3	a	a	DET
g445cc10r03	16	4	computable	computable	ADJ
g445cc10r03	16	5	measure	measure	NOUN
g445cc10r03	16	6	q	q	X
g445cc10r03	16	7	on	on	ADP
g445cc10r03	16	8	the	the	DET
g445cc10r03	16	9	space	space	NOUN
g445cc10r03	16	10	of	of	ADP
g445cc10r03	16	11	measures	measure	NOUN
g445cc10r03	16	12	on	on	ADP
g445cc10r03	16	13	2ω	2ω	NUM
g445cc10r03	16	14	such	such	ADJ
g445cc10r03	16	15	that	that	SCONJ
g445cc10r03	16	16	x	x	PROPN
g445cc10r03	16	17	⊆	⊆	PROPN
g445cc10r03	16	18	2ω	2ω	NUM
g445cc10r03	16	19	is	be	AUX
g445cc10r03	16	20	a	a	DET
g445cc10r03	16	21	random	random	ADJ
g445cc10r03	16	22	closed	closed	ADJ
g445cc10r03	16	23	set	set	NOUN
g445cc10r03	16	24	if	if	SCONJ
g445cc10r03	16	25	and	and	CCONJ
g445cc10r03	16	26	only	only	ADV
g445cc10r03	16	27	if	if	SCONJ
g445cc10r03	16	28	x	x	SYM
g445cc10r03	16	29	is	be	AUX
g445cc10r03	16	30	the	the	DET
g445cc10r03	16	31	support	support	NOUN
g445cc10r03	16	32	of	of	ADP
g445cc10r03	16	33	a	a	DET
g445cc10r03	16	34	q	q	ADJ
g445cc10r03	16	35	-	-	ADJ
g445cc10r03	16	36	random	random	ADJ
g445cc10r03	16	37	measure	measure	NOUN
g445cc10r03	16	38	.	.	PUNCT
g445cc10r03	17	1	we	we	PRON
g445cc10r03	17	2	also	also	ADV
g445cc10r03	17	3	establish	establish	VERB
g445cc10r03	17	4	a	a	DET
g445cc10r03	17	5	correspondence	correspondence	NOUN
g445cc10r03	17	6	between	between	ADP
g445cc10r03	17	7	random	random	ADJ
g445cc10r03	17	8	closed	closed	ADJ
g445cc10r03	17	9	sets	set	NOUN
g445cc10r03	17	10	and	and	CCONJ
g445cc10r03	17	11	the	the	DET
g445cc10r03	17	12	random	random	ADJ
g445cc10r03	17	13	measures	measure	NOUN
g445cc10r03	17	14	studied	study	VERB
g445cc10r03	17	15	in	in	ADP
g445cc10r03	17	16	chapter	chapter	NOUN
g445cc10r03	17	17	2	2	NUM
g445cc10r03	17	18	.	.	PUNCT
g445cc10r03	18	1	lastly	lastly	ADV
g445cc10r03	18	2	,	,	PUNCT
g445cc10r03	18	3	we	we	PRON
g445cc10r03	18	4	study	study	VERB
g445cc10r03	18	5	the	the	DET
g445cc10r03	18	6	ranges	range	NOUN
g445cc10r03	18	7	of	of	ADP
g445cc10r03	18	8	random	random	ADJ
g445cc10r03	18	9	continuous	continuous	ADJ
g445cc10r03	18	10	functions	function	NOUN
g445cc10r03	18	11	,	,	PUNCT
g445cc10r03	18	12	showing	show	VERB
g445cc10r03	18	13	that	that	SCONJ
g445cc10r03	18	14	the	the	DET
g445cc10r03	18	15	lebesgue	lebesgue	PROPN
g445cc10r03	18	16	measure	measure	NOUN
g445cc10r03	18	17	of	of	ADP
g445cc10r03	18	18	the	the	DET
g445cc10r03	18	19	range	range	NOUN
g445cc10r03	18	20	of	of	ADP
g445cc10r03	18	21	a	a	DET
g445cc10r03	18	22	random	random	ADJ
g445cc10r03	18	23	continuous	continuous	ADJ
g445cc10r03	18	24	function	function	NOUN
g445cc10r03	18	25	is	be	AUX
g445cc10r03	18	26	always	always	ADV
g445cc10r03	18	27	strictly	strictly	ADV
g445cc10r03	18	28	between	between	ADP
g445cc10r03	18	29	0	0	NUM
g445cc10r03	18	30	and	and	CCONJ
g445cc10r03	18	31	1	1	NUM
g445cc10r03	18	32	.	.	PUNCT
g445cc10r03	19	1	in	in	ADP
g445cc10r03	19	2	chapter	chapter	NOUN
g445cc10r03	19	3	4	4	NUM
g445cc10r03	19	4	we	we	PRON
g445cc10r03	19	5	effectivize	effectivize	VERB
g445cc10r03	19	6	a	a	DET
g445cc10r03	19	7	theorem	theorem	NOUN
g445cc10r03	19	8	of	of	ADP
g445cc10r03	19	9	erd¨os	erd¨os	PROPN
g445cc10r03	19	10	and	and	CCONJ
g445cc10r03	19	11	r´enyi	r´enyi	PROPN
g445cc10r03	20	1	[	[	X
g445cc10r03	20	2	11	11	NUM
g445cc10r03	20	3	]	]	PUNCT
g445cc10r03	20	4	,	,	PUNCT
g445cc10r03	20	5	which	which	PRON
g445cc10r03	20	6	says	say	VERB
g445cc10r03	20	7	that	that	SCONJ
g445cc10r03	20	8	for	for	ADP
g445cc10r03	20	9	c	c	X
g445cc10r03	20	10	≥	≥	SYM
g445cc10r03	20	11	1	1	NUM
g445cc10r03	20	12	,	,	PUNCT
g445cc10r03	20	13	if	if	SCONJ
g445cc10r03	20	14	a	a	DET
g445cc10r03	20	15	fair	fair	ADJ
g445cc10r03	20	16	coin	coin	NOUN
g445cc10r03	20	17	is	be	AUX
g445cc10r03	20	18	used	use	VERB
g445cc10r03	20	19	to	to	PART
g445cc10r03	20	20	generate	generate	VERB
g445cc10r03	20	21	a	a	DET
g445cc10r03	20	22	length	length	ADJ
g445cc10r03	20	23	-	-	PUNCT
g445cc10r03	20	24	n	n	NOUN
g445cc10r03	20	25	string	string	NOUN
g445cc10r03	20	26	of	of	ADP
g445cc10r03	20	27	1	1	NUM
g445cc10r03	20	28	's	's	PART
g445cc10r03	20	29	and	and	CCONJ
g445cc10r03	20	30	−1	−1	SPACE
g445cc10r03	20	31	's	's	NUM
g445cc10r03	20	32	,	,	PUNCT
g445cc10r03	20	33	which	which	PRON
g445cc10r03	20	34	are	be	AUX
g445cc10r03	20	35	interpreted	interpret	VERB
g445cc10r03	20	36	as	as	ADP
g445cc10r03	20	37	gain	gain	NOUN
g445cc10r03	20	38	and	and	CCONJ
g445cc10r03	20	39	loss	loss	NOUN
g445cc10r03	20	40	,	,	PUNCT
g445cc10r03	20	41	then	then	ADV
g445cc10r03	20	42	the	the	DET
g445cc10r03	20	43	maximal	maximal	ADJ
g445cc10r03	20	44	average	average	ADJ
g445cc10r03	20	45	gain	gain	NOUN
g445cc10r03	20	46	over	over	ADP
g445cc10r03	20	47	lc	lc	PROPN
g445cc10r03	20	48	log	log	PROPN
g445cc10r03	20	49	nj	nj	PROPN
g445cc10r03	20	50	-	-	PUNCT
g445cc10r03	20	51	length	length	NOUN
g445cc10r03	20	52	substrings	substring	NOUN
g445cc10r03	20	53	converges	converge	NOUN
g445cc10r03	20	54	almost	almost	ADV
g445cc10r03	20	55	surely	surely	ADV
g445cc10r03	20	56	(	(	PUNCT
g445cc10r03	20	57	in	in	ADP
g445cc10r03	20	58	n	n	NOUN
g445cc10r03	20	59	)	)	PUNCT
g445cc10r03	20	60	to	to	ADP
g445cc10r03	20	61	the	the	DET
g445cc10r03	20	62	same	same	ADJ
g445cc10r03	20	63	limit	limit	NOUN
g445cc10r03	20	64	α(c	α(c	NUM
g445cc10r03	20	65	)	)	PUNCT
g445cc10r03	20	66	.	.	PUNCT
g445cc10r03	21	1	we	we	PRON
g445cc10r03	21	2	show	show	VERB
g445cc10r03	21	3	that	that	SCONJ
g445cc10r03	21	4	if	if	SCONJ
g445cc10r03	21	5	the	the	DET
g445cc10r03	21	6	1	1	PROPN
g445cc10r03	21	7	's	be	AUX
g445cc10r03	21	8	and	and	CCONJ
g445cc10r03	21	9	−1	−1	NOUN
g445cc10r03	21	10	's	's	PART
g445cc10r03	21	11	are	be	AUX
g445cc10r03	21	12	determined	determine	VERB
g445cc10r03	21	13	by	by	ADP
g445cc10r03	21	14	the	the	DET
g445cc10r03	21	15	bits	bit	NOUN
g445cc10r03	21	16	of	of	ADP
g445cc10r03	21	17	a	a	DET
g445cc10r03	21	18	martin	martin	PROPN
g445cc10r03	21	19	lo¨f	lo¨f	PROPN
g445cc10r03	21	20	random	random	PROPN
g445cc10r03	21	21	,	,	PUNCT
g445cc10r03	21	22	then	then	ADV
g445cc10r03	21	23	the	the	DET
g445cc10r03	21	24	convergence	convergence	NOUN
g445cc10r03	21	25	holds	hold	VERB
g445cc10r03	21	26	.	.	PUNCT