id	sid	tid	token	lemma	pos
ejpam-3342	1	1	backwards	backwards	ADV
ejpam-3342	1	2	itunhbox	itunhbox	PROPN
ejpam-3342	1	3	voidb@x	voidb@x	PROPN
ejpam-3342	1	4	�	�	PROPN
ejpam-3342	1	5	group	group	PROPN
ejpam-3342	1	6	let	let	VERB
ejpam-3342	1	7	unhbox	unhbox	PROPN
ejpam-3342	1	8	voidb@x	voidb@x	VERB
ejpam-3342	1	9	setbox	setbox	PROPN
ejpam-3342	1	10	@tempboxa	@tempboxa	PROPN
ejpam-3342	1	11	hbox	hbox	PROPN
ejpam-3342	1	12	{	{	PUNCT
ejpam-3342	1	13	oglobal	oglobal	ADJ
ejpam-3342	1	14	mathchardef	mathchardef	PROPN
ejpam-3342	1	15	accent@spacefactor	accent@spacefactor	PROPN
ejpam-3342	1	16	spacefactor	spacefactor	NOUN
ejpam-3342	1	17	}	}	PUNCT
ejpam-3342	1	18	accent	accent	VERB
ejpam-3342	1	19	94	94	NUM
ejpam-3342	1	20	oegroup	oegroup	NOUN
ejpam-3342	1	21	spacefactor	spacefactor	NOUN
ejpam-3342	1	22	accent@spacefactor	accent@spacefactor	NOUN
ejpam-3342	1	23	-henstock	-henstock	VERB
ejpam-3342	1	24	integral	integral	ADJ
ejpam-3342	1	25	for	for	ADP
ejpam-3342	1	26	the	the	DET
ejpam-3342	1	27	hilbert	hilbert	NOUN
ejpam-3342	1	28	-	-	PUNCT
ejpam-3342	1	29	schmidt	schmidt	VERB
ejpam-3342	1	30	-	-	PUNCT
ejpam-3342	1	31	valued	value	VERB
ejpam-3342	1	32	stochastic	stochastic	ADJ
ejpam-3342	1	33	process	process	NOUN
ejpam-3342	1	34	european	european	ADJ
ejpam-3342	1	35	journal	journal	PROPN
ejpam-3342	1	36	of	of	ADP
ejpam-3342	1	37	pure	pure	ADJ
ejpam-3342	1	38	and	and	CCONJ
ejpam-3342	1	39	applied	apply	VERB
ejpam-3342	1	40	mathematics	mathematic	NOUN
ejpam-3342	1	41	vol	vol	NOUN
ejpam-3342	1	42	.	.	PROPN
ejpam-3342	2	1	12	12	NUM
ejpam-3342	2	2	,	,	PUNCT
ejpam-3342	2	3	no	no	INTJ
ejpam-3342	2	4	.	.	NOUN
ejpam-3342	2	5	1	1	NUM
ejpam-3342	2	6	,	,	PUNCT
ejpam-3342	2	7	2019	2019	NUM
ejpam-3342	2	8	,	,	PUNCT
ejpam-3342	2	9	58	58	NUM
ejpam-3342	2	10	-	-	SYM
ejpam-3342	2	11	78	78	NUM
ejpam-3342	2	12	issn	issn	PROPN
ejpam-3342	2	13	1307	1307	NUM
ejpam-3342	2	14	-	-	SYM
ejpam-3342	2	15	5543	5543	NUM
ejpam-3342	2	16	–	–	PUNCT
ejpam-3342	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3342	3	2	published	publish	VERB
ejpam-3342	3	3	by	by	ADP
ejpam-3342	3	4	new	new	PROPN
ejpam-3342	3	5	york	york	PROPN
ejpam-3342	3	6	business	business	PROPN
ejpam-3342	3	7	global	global	PROPN
ejpam-3342	3	8	backwards	backwards	ADV
ejpam-3342	3	9	itô-henstock	itô-henstock	PROPN
ejpam-3342	3	10	integral	integral	ADJ
ejpam-3342	3	11	for	for	ADP
ejpam-3342	3	12	the	the	DET
ejpam-3342	3	13	hilbert	hilbert	NOUN
ejpam-3342	3	14	-	-	PUNCT
ejpam-3342	3	15	schmidt	schmidt	VERB
ejpam-3342	3	16	-	-	PUNCT
ejpam-3342	3	17	valued	value	VERB
ejpam-3342	3	18	stochastic	stochastic	ADJ
ejpam-3342	3	19	process	process	NOUN
ejpam-3342	3	20	ricky	ricky	PROPN
ejpam-3342	3	21	f.	f.	PROPN
ejpam-3342	3	22	rulete1	rulete1	PROPN
ejpam-3342	3	23	,	,	PUNCT
ejpam-3342	3	24	mhelmar	mhelmar	PROPN
ejpam-3342	3	25	a.	a.	PROPN
ejpam-3342	3	26	labendia2,∗	labendia2,∗	PROPN
ejpam-3342	3	27	1	1	NUM
ejpam-3342	3	28	department	department	NOUN
ejpam-3342	3	29	of	of	ADP
ejpam-3342	3	30	mathematics	mathematic	NOUN
ejpam-3342	3	31	and	and	CCONJ
ejpam-3342	3	32	statistics	statistic	NOUN
ejpam-3342	3	33	,	,	PUNCT
ejpam-3342	3	34	college	college	NOUN
ejpam-3342	3	35	of	of	ADP
ejpam-3342	3	36	arts	art	NOUN
ejpam-3342	3	37	and	and	CCONJ
ejpam-3342	3	38	sciences	science	NOUN
ejpam-3342	3	39	,	,	PUNCT
ejpam-3342	3	40	university	university	NOUN
ejpam-3342	3	41	of	of	ADP
ejpam-3342	3	42	southeastern	southeastern	ADJ
ejpam-3342	3	43	philippines	philippine	NOUN
ejpam-3342	3	44	,	,	PUNCT
ejpam-3342	3	45	bo	bo	PROPN
ejpam-3342	3	46	.	.	PROPN
ejpam-3342	3	47	obrero	obrero	PROPN
ejpam-3342	3	48	,	,	PUNCT
ejpam-3342	3	49	8000	8000	NUM
ejpam-3342	3	50	davao	davao	PROPN
ejpam-3342	3	51	city	city	NOUN
ejpam-3342	3	52	,	,	PUNCT
ejpam-3342	3	53	philippines	philippines	PROPN
ejpam-3342	3	54	2	2	NUM
ejpam-3342	3	55	department	department	NOUN
ejpam-3342	3	56	of	of	ADP
ejpam-3342	3	57	mathematics	mathematic	NOUN
ejpam-3342	3	58	and	and	CCONJ
ejpam-3342	3	59	statistics	statistic	NOUN
ejpam-3342	3	60	,	,	PUNCT
ejpam-3342	3	61	college	college	NOUN
ejpam-3342	3	62	of	of	ADP
ejpam-3342	3	63	science	science	NOUN
ejpam-3342	3	64	and	and	CCONJ
ejpam-3342	3	65	mathematics	mathematic	NOUN
ejpam-3342	3	66	,	,	PUNCT
ejpam-3342	3	67	mindanao	mindanao	PROPN
ejpam-3342	3	68	state	state	PROPN
ejpam-3342	3	69	university	university	PROPN
ejpam-3342	3	70	-	-	PUNCT
ejpam-3342	3	71	iligan	iligan	PROPN
ejpam-3342	3	72	institute	institute	PROPN
ejpam-3342	3	73	of	of	ADP
ejpam-3342	3	74	technology	technology	PROPN
ejpam-3342	3	75	,	,	PUNCT
ejpam-3342	3	76	9200	9200	NUM
ejpam-3342	3	77	iligan	iligan	ADJ
ejpam-3342	3	78	city	city	NOUN
ejpam-3342	3	79	,	,	PUNCT
ejpam-3342	3	80	philippines	philippine	NOUN
ejpam-3342	3	81	abstract	abstract	ADJ
ejpam-3342	3	82	.	.	PUNCT
ejpam-3342	4	1	in	in	ADP
ejpam-3342	4	2	this	this	DET
ejpam-3342	4	3	paper	paper	NOUN
ejpam-3342	4	4	,	,	PUNCT
ejpam-3342	4	5	a	a	DET
ejpam-3342	4	6	definition	definition	NOUN
ejpam-3342	4	7	of	of	ADP
ejpam-3342	4	8	backwards	backwards	ADV
ejpam-3342	4	9	itô-henstock	itô-henstock	NOUN
ejpam-3342	4	10	integral	integral	ADJ
ejpam-3342	4	11	for	for	SCONJ
ejpam-3342	4	12	the	the	DET
ejpam-3342	4	13	hilbert	hilbert	NOUN
ejpam-3342	4	14	-	-	PUNCT
ejpam-3342	4	15	schmidtvalued	schmidtvalue	VERB
ejpam-3342	4	16	stochastic	stochastic	ADJ
ejpam-3342	4	17	process	process	NOUN
ejpam-3342	4	18	is	be	AUX
ejpam-3342	4	19	introduced	introduce	VERB
ejpam-3342	4	20	.	.	PUNCT
ejpam-3342	5	1	we	we	PRON
ejpam-3342	5	2	formulate	formulate	VERB
ejpam-3342	5	3	the	the	DET
ejpam-3342	5	4	itô	itô	PROPN
ejpam-3342	5	5	isometry	isometry	NOUN
ejpam-3342	5	6	for	for	ADP
ejpam-3342	5	7	this	this	DET
ejpam-3342	5	8	integral	integral	ADJ
ejpam-3342	5	9	.	.	PUNCT
ejpam-3342	6	1	moreover	moreover	ADV
ejpam-3342	6	2	,	,	PUNCT
ejpam-3342	6	3	an	an	DET
ejpam-3342	6	4	equivalent	equivalent	ADJ
ejpam-3342	6	5	definition	definition	NOUN
ejpam-3342	6	6	for	for	ADP
ejpam-3342	6	7	this	this	DET
ejpam-3342	6	8	integral	integral	NOUN
ejpam-3342	6	9	is	be	AUX
ejpam-3342	6	10	given	give	VERB
ejpam-3342	6	11	using	use	VERB
ejpam-3342	6	12	the	the	DET
ejpam-3342	6	13	concept	concept	NOUN
ejpam-3342	6	14	of	of	ADP
ejpam-3342	6	15	ac2[0	ac2[0	ADJ
ejpam-3342	6	16	,	,	PUNCT
ejpam-3342	6	17	t	t	PROPN
ejpam-3342	6	18	]	]	PUNCT
ejpam-3342	6	19	-property	-property	PROPN
ejpam-3342	6	20	,	,	PUNCT
ejpam-3342	6	21	a	a	DET
ejpam-3342	6	22	version	version	NOUN
ejpam-3342	6	23	of	of	ADP
ejpam-3342	6	24	absolute	absolute	ADJ
ejpam-3342	6	25	continuity	continuity	NOUN
ejpam-3342	6	26	.	.	PUNCT
ejpam-3342	7	1	2010	2010	NUM
ejpam-3342	7	2	mathematics	mathematic	NOUN
ejpam-3342	7	3	subject	subject	NOUN
ejpam-3342	7	4	classifications	classification	NOUN
ejpam-3342	7	5	:	:	PUNCT
ejpam-3342	7	6	60h30	60h30	NUM
ejpam-3342	7	7	,	,	PUNCT
ejpam-3342	7	8	60h05	60h05	NUM
ejpam-3342	7	9	key	key	ADJ
ejpam-3342	7	10	words	word	NOUN
ejpam-3342	7	11	and	and	CCONJ
ejpam-3342	7	12	phrases	phrase	NOUN
ejpam-3342	7	13	:	:	PUNCT
ejpam-3342	7	14	backwards	backwards	ADV
ejpam-3342	7	15	itô-henstock	itô-henstock	PROPN
ejpam-3342	7	16	integral	integral	ADJ
ejpam-3342	7	17	,	,	PUNCT
ejpam-3342	7	18	itô	itô	PROPN
ejpam-3342	7	19	isometry	isometry	NOUN
ejpam-3342	7	20	,	,	PUNCT
ejpam-3342	7	21	ac2	ac2	PROPN
ejpam-3342	7	22	-	-	PUNCT
ejpam-3342	7	23	property	property	NOUN
ejpam-3342	7	24	1	1	NUM
ejpam-3342	7	25	.	.	PUNCT
ejpam-3342	8	1	introduction	introduction	NOUN
ejpam-3342	8	2	the	the	DET
ejpam-3342	8	3	most	most	ADV
ejpam-3342	8	4	well	well	ADV
ejpam-3342	8	5	-	-	PUNCT
ejpam-3342	8	6	known	know	VERB
ejpam-3342	8	7	integral	integral	NOUN
ejpam-3342	8	8	is	be	AUX
ejpam-3342	8	9	the	the	DET
ejpam-3342	8	10	riemann	riemann	PROPN
ejpam-3342	8	11	integral	integral	PROPN
ejpam-3342	8	12	.	.	PUNCT
ejpam-3342	9	1	it	it	PRON
ejpam-3342	9	2	was	be	AUX
ejpam-3342	9	3	formulated	formulate	VERB
ejpam-3342	9	4	by	by	ADP
ejpam-3342	9	5	bernhard	bernhard	PROPN
ejpam-3342	9	6	riemann	riemann	PROPN
ejpam-3342	9	7	in	in	ADP
ejpam-3342	9	8	1850	1850	NUM
ejpam-3342	9	9	.	.	PUNCT
ejpam-3342	10	1	this	this	PRON
ejpam-3342	10	2	is	be	AUX
ejpam-3342	10	3	the	the	DET
ejpam-3342	10	4	first	first	ADJ
ejpam-3342	10	5	integral	integral	ADJ
ejpam-3342	10	6	introduced	introduce	VERB
ejpam-3342	10	7	to	to	ADP
ejpam-3342	10	8	most	most	ADJ
ejpam-3342	10	9	students	student	NOUN
ejpam-3342	10	10	in	in	ADP
ejpam-3342	10	11	the	the	DET
ejpam-3342	10	12	study	study	NOUN
ejpam-3342	10	13	of	of	ADP
ejpam-3342	10	14	elementary	elementary	ADJ
ejpam-3342	10	15	calculus	calculus	NOUN
ejpam-3342	10	16	.	.	PUNCT
ejpam-3342	11	1	however	however	ADV
ejpam-3342	11	2	,	,	PUNCT
ejpam-3342	11	3	the	the	DET
ejpam-3342	11	4	class	class	NOUN
ejpam-3342	11	5	of	of	ADP
ejpam-3342	11	6	riemann	riemann	PROPN
ejpam-3342	11	7	-	-	PUNCT
ejpam-3342	11	8	integrable	integrable	ADJ
ejpam-3342	11	9	functions	function	NOUN
ejpam-3342	11	10	is	be	AUX
ejpam-3342	11	11	quite	quite	ADV
ejpam-3342	11	12	limited	limited	ADJ
ejpam-3342	11	13	.	.	PUNCT
ejpam-3342	12	1	henri	henri	PROPN
ejpam-3342	12	2	lebesgue	lebesgue	PROPN
ejpam-3342	12	3	attempts	attempt	VERB
ejpam-3342	12	4	to	to	PART
ejpam-3342	12	5	solve	solve	VERB
ejpam-3342	12	6	some	some	PRON
ejpam-3342	12	7	of	of	ADP
ejpam-3342	12	8	the	the	DET
ejpam-3342	12	9	shortcomings	shortcoming	NOUN
ejpam-3342	12	10	of	of	ADP
ejpam-3342	12	11	the	the	DET
ejpam-3342	12	12	riemann	riemann	PROPN
ejpam-3342	12	13	integral	integral	PROPN
ejpam-3342	12	14	.	.	PUNCT
ejpam-3342	13	1	however	however	ADV
ejpam-3342	13	2	,	,	PUNCT
ejpam-3342	13	3	for	for	ADP
ejpam-3342	13	4	non	non	NOUN
ejpam-3342	13	5	-	-	NOUN
ejpam-3342	13	6	mathematicians	mathematician	NOUN
ejpam-3342	13	7	the	the	DET
ejpam-3342	13	8	lebesgue	lebesgue	ADJ
ejpam-3342	13	9	integral	integral	ADJ
ejpam-3342	13	10	is	be	AUX
ejpam-3342	13	11	difficult	difficult	ADJ
ejpam-3342	13	12	to	to	PART
ejpam-3342	13	13	understand	understand	VERB
ejpam-3342	13	14	and	and	CCONJ
ejpam-3342	13	15	requires	require	VERB
ejpam-3342	13	16	enough	enough	ADJ
ejpam-3342	13	17	background	background	NOUN
ejpam-3342	13	18	of	of	ADP
ejpam-3342	13	19	measure	measure	NOUN
ejpam-3342	13	20	theory	theory	NOUN
ejpam-3342	13	21	.	.	PUNCT
ejpam-3342	14	1	in	in	ADP
ejpam-3342	14	2	1950s	1950s	NUM
ejpam-3342	14	3	,	,	PUNCT
ejpam-3342	14	4	a	a	DET
ejpam-3342	14	5	riemann	riemann	NOUN
ejpam-3342	14	6	-	-	PUNCT
ejpam-3342	14	7	type	type	NOUN
ejpam-3342	14	8	integral	integral	ADJ
ejpam-3342	14	9	was	be	AUX
ejpam-3342	14	10	discovered	discover	VERB
ejpam-3342	14	11	independently	independently	ADV
ejpam-3342	14	12	by	by	ADP
ejpam-3342	14	13	r.	r.	PROPN
ejpam-3342	14	14	henstock	henstock	PROPN
ejpam-3342	14	15	and	and	CCONJ
ejpam-3342	14	16	j.	j.	PROPN
ejpam-3342	14	17	kurzwiel	kurzwiel	PROPN
ejpam-3342	14	18	.	.	PUNCT
ejpam-3342	15	1	this	this	DET
ejpam-3342	15	2	integral	integral	ADJ
ejpam-3342	15	3	includes	include	VERB
ejpam-3342	15	4	riemann	riemann	PROPN
ejpam-3342	15	5	and	and	CCONJ
ejpam-3342	15	6	that	that	PRON
ejpam-3342	15	7	of	of	ADP
ejpam-3342	15	8	lebesgue	lebesgue	NOUN
ejpam-3342	15	9	.	.	PUNCT
ejpam-3342	16	1	this	this	DET
ejpam-3342	16	2	integral	integral	ADJ
ejpam-3342	16	3	is	be	AUX
ejpam-3342	16	4	now	now	ADV
ejpam-3342	16	5	known	know	VERB
ejpam-3342	16	6	as	as	ADP
ejpam-3342	16	7	henstock	henstock	NOUN
ejpam-3342	16	8	-	-	PUNCT
ejpam-3342	16	9	kurzwiel	kurzwiel	PROPN
ejpam-3342	16	10	or	or	CCONJ
ejpam-3342	16	11	hk	hk	PROPN
ejpam-3342	16	12	integral	integral	ADJ
ejpam-3342	16	13	.	.	PUNCT
ejpam-3342	17	1	in	in	ADP
ejpam-3342	17	2	this	this	DET
ejpam-3342	17	3	paper	paper	NOUN
ejpam-3342	17	4	,	,	PUNCT
ejpam-3342	17	5	however	however	ADV
ejpam-3342	17	6	,	,	PUNCT
ejpam-3342	17	7	we	we	PRON
ejpam-3342	17	8	will	will	AUX
ejpam-3342	17	9	call	call	VERB
ejpam-3342	17	10	this	this	DET
ejpam-3342	17	11	integral	integral	ADJ
ejpam-3342	17	12	simply	simply	ADV
ejpam-3342	17	13	as	as	SCONJ
ejpam-3342	17	14	henstock	henstock	NOUN
ejpam-3342	17	15	integral	integral	ADJ
ejpam-3342	17	16	.	.	PUNCT
ejpam-3342	18	1	the	the	DET
ejpam-3342	18	2	henstock	henstock	NOUN
ejpam-3342	18	3	integral	integral	ADJ
ejpam-3342	18	4	used	use	VERB
ejpam-3342	18	5	non	non	ADJ
ejpam-3342	18	6	-	-	ADJ
ejpam-3342	18	7	uniform	uniform	ADJ
ejpam-3342	18	8	meshes	mesh	NOUN
ejpam-3342	18	9	in	in	ADP
ejpam-3342	18	10	contrast	contrast	NOUN
ejpam-3342	18	11	to	to	ADP
ejpam-3342	18	12	riemann	riemann	PROPN
ejpam-3342	18	13	.	.	PUNCT
ejpam-3342	19	1	such	such	ADJ
ejpam-3342	19	2	technique	technique	NOUN
ejpam-3342	19	3	turns	turn	VERB
ejpam-3342	19	4	out	out	ADP
ejpam-3342	19	5	to	to	PART
ejpam-3342	19	6	encompass	encompass	VERB
ejpam-3342	19	7	the	the	DET
ejpam-3342	19	8	classical	classical	ADJ
ejpam-3342	19	9	stochastic	stochastic	ADJ
ejpam-3342	19	10	integral	integral	ADJ
ejpam-3342	19	11	,	,	PUNCT
ejpam-3342	19	12	see([7	see([7	NOUN
ejpam-3342	19	13	]	]	PUNCT
ejpam-3342	19	14	,	,	PUNCT
ejpam-3342	19	15	[	[	X
ejpam-3342	19	16	8	8	NUM
ejpam-3342	19	17	]	]	PUNCT
ejpam-3342	19	18	,	,	PUNCT
ejpam-3342	20	1	[	[	X
ejpam-3342	20	2	9	9	NUM
ejpam-3342	20	3	]	]	PUNCT
ejpam-3342	20	4	,	,	PUNCT
ejpam-3342	20	5	[	[	X
ejpam-3342	20	6	13	13	NUM
ejpam-3342	20	7	]	]	PUNCT
ejpam-3342	20	8	and	and	CCONJ
ejpam-3342	20	9	[	[	X
ejpam-3342	20	10	14	14	NUM
ejpam-3342	20	11	]	]	SYM
ejpam-3342	20	12	]	]	PUNCT
ejpam-3342	20	13	)	)	PUNCT
ejpam-3342	20	14	.	.	PUNCT
ejpam-3342	21	1	this	this	DET
ejpam-3342	21	2	technique	technique	NOUN
ejpam-3342	21	3	is	be	AUX
ejpam-3342	21	4	now	now	ADV
ejpam-3342	21	5	known	know	VERB
ejpam-3342	21	6	as	as	ADP
ejpam-3342	21	7	the	the	DET
ejpam-3342	21	8	henstock	henstock	NOUN
ejpam-3342	21	9	approach	approach	NOUN
ejpam-3342	21	10	.	.	PUNCT
ejpam-3342	22	1	in	in	ADP
ejpam-3342	22	2	stochastic	stochastic	ADJ
ejpam-3342	22	3	calculus	calculus	NOUN
ejpam-3342	22	4	,	,	PUNCT
ejpam-3342	22	5	the	the	DET
ejpam-3342	22	6	stochastic	stochastic	ADJ
ejpam-3342	22	7	integral	integral	NOUN
ejpam-3342	22	8	of	of	ADP
ejpam-3342	22	9	a	a	DET
ejpam-3342	22	10	real	real	ADV
ejpam-3342	22	11	-	-	PUNCT
ejpam-3342	22	12	valued	value	VERB
ejpam-3342	22	13	adapted	adapt	VERB
ejpam-3342	22	14	process	process	NOUN
ejpam-3342	22	15	is	be	AUX
ejpam-3342	22	16	obtained	obtain	VERB
ejpam-3342	22	17	from	from	ADP
ejpam-3342	22	18	the	the	DET
ejpam-3342	22	19	mean	mean	ADJ
ejpam-3342	22	20	square	square	ADJ
ejpam-3342	22	21	limit	limit	NOUN
ejpam-3342	22	22	of	of	ADP
ejpam-3342	22	23	stochastic	stochastic	ADJ
ejpam-3342	22	24	integrals	integral	NOUN
ejpam-3342	22	25	of	of	ADP
ejpam-3342	22	26	simple	simple	ADJ
ejpam-3342	22	27	processes	process	NOUN
ejpam-3342	22	28	,	,	PUNCT
ejpam-3342	22	29	see	see	VERB
ejpam-3342	22	30	[	[	X
ejpam-3342	22	31	16	16	NUM
ejpam-3342	22	32	]	]	PUNCT
ejpam-3342	22	33	.	.	PUNCT
ejpam-3342	23	1	∗corresponding	∗corresponde	VERB
ejpam-3342	23	2	author	author	NOUN
ejpam-3342	23	3	.	.	PUNCT
ejpam-3342	24	1	doi	doi	NOUN
ejpam-3342	24	2	:	:	PUNCT
ejpam-3342	24	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3342	https://doi.org/10.29020/nybg.ejpam.v12i1.3342	NUM
ejpam-3342	24	4	email	email	NOUN
ejpam-3342	24	5	addresses	address	NOUN
ejpam-3342	24	6	:	:	PUNCT
ejpam-3342	24	7	ricky	ricky	PROPN
ejpam-3342	24	8	rulete@yahoo.com.ph	rulete@yahoo.com.ph	PROPN
ejpam-3342	24	9	(	(	PUNCT
ejpam-3342	24	10	r.	r.	PROPN
ejpam-3342	24	11	rulete	rulete	PROPN
ejpam-3342	24	12	)	)	PUNCT
ejpam-3342	24	13	,	,	PUNCT
ejpam-3342	24	14	mhelmar.labendia@g.msuiit.edu.ph	mhelmar.labendia@g.msuiit.edu.ph	PROPN
ejpam-3342	24	15	(	(	PUNCT
ejpam-3342	24	16	m.	m.	NOUN
ejpam-3342	24	17	labendia	labendia	PROPN
ejpam-3342	24	18	)	)	PUNCT
ejpam-3342	24	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3342	25	1	58	58	NUM
ejpam-3342	25	2	c	c	X
ejpam-3342	25	3	©	©	PROPN
ejpam-3342	25	4	2019	2019	NUM
ejpam-3342	25	5	ejpam	ejpam	NOUN
ejpam-3342	25	6	all	all	DET
ejpam-3342	25	7	rights	right	NOUN
ejpam-3342	25	8	reserved	reserve	VERB
ejpam-3342	25	9	.	.	PUNCT
ejpam-3342	26	1	r.	r.	PROPN
ejpam-3342	26	2	rulete	rulete	PROPN
ejpam-3342	26	3	,	,	PUNCT
ejpam-3342	26	4	m.	m.	NOUN
ejpam-3342	26	5	labendia	labendia	PROPN
ejpam-3342	26	6	/	/	SYM
ejpam-3342	26	7	eur	eur	PROPN
ejpam-3342	26	8	.	.	PUNCT
ejpam-3342	27	1	j.	j.	PROPN
ejpam-3342	27	2	pure	pure	PROPN
ejpam-3342	27	3	appl	appl	PROPN
ejpam-3342	27	4	.	.	PROPN
ejpam-3342	27	5	math	math	PROPN
ejpam-3342	27	6	,	,	PUNCT
ejpam-3342	27	7	12	12	NUM
ejpam-3342	27	8	(	(	PUNCT
ejpam-3342	27	9	1	1	NUM
ejpam-3342	27	10	)	)	PUNCT
ejpam-3342	27	11	(	(	PUNCT
ejpam-3342	27	12	2019	2019	NUM
ejpam-3342	27	13	)	)	PUNCT
ejpam-3342	27	14	,	,	PUNCT
ejpam-3342	27	15	58	58	NUM
ejpam-3342	27	16	-	-	SYM
ejpam-3342	27	17	78	78	NUM
ejpam-3342	27	18	59	59	NUM
ejpam-3342	27	19	this	this	PRON
ejpam-3342	27	20	is	be	AUX
ejpam-3342	27	21	the	the	DET
ejpam-3342	27	22	classical	classical	ADJ
ejpam-3342	27	23	approach	approach	NOUN
ejpam-3342	27	24	to	to	ADP
ejpam-3342	27	25	stochastic	stochastic	ADJ
ejpam-3342	27	26	integration	integration	NOUN
ejpam-3342	27	27	which	which	PRON
ejpam-3342	27	28	is	be	AUX
ejpam-3342	27	29	almost	almost	ADV
ejpam-3342	27	30	similar	similar	ADJ
ejpam-3342	27	31	in	in	ADP
ejpam-3342	27	32	defining	define	VERB
ejpam-3342	27	33	the	the	DET
ejpam-3342	27	34	lebesgue	lebesgue	NOUN
ejpam-3342	27	35	integral	integral	ADJ
ejpam-3342	27	36	of	of	ADP
ejpam-3342	27	37	a	a	DET
ejpam-3342	27	38	measurable	measurable	ADJ
ejpam-3342	27	39	function	function	NOUN
ejpam-3342	27	40	.	.	PUNCT
ejpam-3342	28	1	hence	hence	ADV
ejpam-3342	28	2	,	,	PUNCT
ejpam-3342	28	3	henstock	henstock	NOUN
ejpam-3342	28	4	approach	approach	NOUN
ejpam-3342	28	5	to	to	ADP
ejpam-3342	28	6	stochastic	stochastic	ADJ
ejpam-3342	28	7	integration	integration	NOUN
ejpam-3342	28	8	have	have	AUX
ejpam-3342	28	9	been	be	AUX
ejpam-3342	28	10	studied	study	VERB
ejpam-3342	28	11	in	in	ADP
ejpam-3342	28	12	several	several	ADJ
ejpam-3342	28	13	papers	paper	NOUN
ejpam-3342	28	14	see([15	see([15	NOUN
ejpam-3342	28	15	]	]	X
ejpam-3342	28	16	,	,	PUNCT
ejpam-3342	28	17	[	[	X
ejpam-3342	28	18	17	17	NUM
ejpam-3342	28	19	]	]	PUNCT
ejpam-3342	28	20	,	,	PUNCT
ejpam-3342	28	21	[	[	X
ejpam-3342	28	22	21	21	NUM
ejpam-3342	28	23	]	]	PUNCT
ejpam-3342	28	24	,	,	PUNCT
ejpam-3342	29	1	[	[	X
ejpam-3342	29	2	22	22	NUM
ejpam-3342	29	3	]	]	PUNCT
ejpam-3342	29	4	and	and	CCONJ
ejpam-3342	29	5	[	[	X
ejpam-3342	29	6	23	23	NUM
ejpam-3342	29	7	]	]	PUNCT
ejpam-3342	29	8	)	)	PUNCT
ejpam-3342	29	9	since	since	SCONJ
ejpam-3342	29	10	it	it	PRON
ejpam-3342	29	11	gives	give	VERB
ejpam-3342	29	12	more	more	ADV
ejpam-3342	29	13	explicit	explicit	ADJ
ejpam-3342	29	14	definition	definition	NOUN
ejpam-3342	29	15	,	,	PUNCT
ejpam-3342	29	16	reduces	reduce	VERB
ejpam-3342	29	17	the	the	DET
ejpam-3342	29	18	technicalities	technicality	NOUN
ejpam-3342	29	19	in	in	ADP
ejpam-3342	29	20	the	the	DET
ejpam-3342	29	21	classical	classical	ADJ
ejpam-3342	29	22	way	way	NOUN
ejpam-3342	29	23	of	of	ADP
ejpam-3342	29	24	defining	define	VERB
ejpam-3342	29	25	the	the	DET
ejpam-3342	29	26	stochastic	stochastic	ADJ
ejpam-3342	29	27	integral	integral	ADJ
ejpam-3342	29	28	and	and	CCONJ
ejpam-3342	29	29	is	be	AUX
ejpam-3342	29	30	less	less	ADJ
ejpam-3342	29	31	measure	measure	NOUN
ejpam-3342	29	32	theoretic	theoretic	NOUN
ejpam-3342	29	33	.	.	PUNCT
ejpam-3342	30	1	in	in	ADP
ejpam-3342	30	2	[	[	X
ejpam-3342	30	3	6	6	NUM
ejpam-3342	30	4	]	]	PUNCT
ejpam-3342	30	5	,	,	PUNCT
ejpam-3342	30	6	[	[	X
ejpam-3342	30	7	19	19	NUM
ejpam-3342	30	8	]	]	PUNCT
ejpam-3342	30	9	,	,	PUNCT
ejpam-3342	30	10	and	and	CCONJ
ejpam-3342	30	11	[	[	X
ejpam-3342	30	12	18	18	NUM
ejpam-3342	30	13	]	]	PUNCT
ejpam-3342	30	14	,	,	PUNCT
ejpam-3342	30	15	the	the	DET
ejpam-3342	30	16	concept	concept	NOUN
ejpam-3342	30	17	of	of	ADP
ejpam-3342	30	18	stochastic	stochastic	ADJ
ejpam-3342	30	19	integral	integral	NOUN
ejpam-3342	30	20	has	have	AUX
ejpam-3342	30	21	been	be	AUX
ejpam-3342	30	22	extended	extend	VERB
ejpam-3342	30	23	to	to	ADP
ejpam-3342	30	24	infinitedimensional	infinitedimensional	ADJ
ejpam-3342	30	25	spaces	space	NOUN
ejpam-3342	30	26	,	,	PUNCT
ejpam-3342	30	27	namely	namely	ADV
ejpam-3342	30	28	hilbert	hilbert	NOUN
ejpam-3342	30	29	and	and	CCONJ
ejpam-3342	30	30	banach	banach	NOUN
ejpam-3342	30	31	spaces	space	VERB
ejpam-3342	30	32	.	.	PUNCT
ejpam-3342	31	1	in	in	ADP
ejpam-3342	31	2	a	a	DET
ejpam-3342	31	3	hilbert	hilbert	NOUN
ejpam-3342	31	4	space	space	NOUN
ejpam-3342	31	5	,	,	PUNCT
ejpam-3342	31	6	the	the	DET
ejpam-3342	31	7	stochastic	stochastic	ADJ
ejpam-3342	31	8	integral	integral	NOUN
ejpam-3342	31	9	is	be	AUX
ejpam-3342	31	10	presented	present	VERB
ejpam-3342	31	11	in	in	ADP
ejpam-3342	31	12	a	a	DET
ejpam-3342	31	13	manner	manner	NOUN
ejpam-3342	31	14	similar	similar	ADJ
ejpam-3342	31	15	to	to	ADP
ejpam-3342	31	16	the	the	DET
ejpam-3342	31	17	real	real	ADV
ejpam-3342	31	18	-	-	PUNCT
ejpam-3342	31	19	valued	value	VERB
ejpam-3342	31	20	case	case	NOUN
ejpam-3342	31	21	.	.	PUNCT
ejpam-3342	32	1	the	the	DET
ejpam-3342	32	2	integrator	integrator	NOUN
ejpam-3342	32	3	is	be	AUX
ejpam-3342	32	4	qwiener	qwiener	ADJ
ejpam-3342	32	5	process	process	NOUN
ejpam-3342	32	6	,	,	PUNCT
ejpam-3342	32	7	a	a	DET
ejpam-3342	32	8	hilbert	hilbert	NOUN
ejpam-3342	32	9	space	space	NOUN
ejpam-3342	32	10	-	-	PUNCT
ejpam-3342	32	11	valued	value	VERB
ejpam-3342	32	12	wiener	wiener	NOUN
ejpam-3342	32	13	process	process	NOUN
ejpam-3342	32	14	which	which	PRON
ejpam-3342	32	15	is	be	AUX
ejpam-3342	32	16	dependent	dependent	ADJ
ejpam-3342	32	17	on	on	ADP
ejpam-3342	32	18	a	a	DET
ejpam-3342	32	19	symmetric	symmetric	ADJ
ejpam-3342	32	20	nonnegative	nonnegative	ADJ
ejpam-3342	32	21	trace	trace	NOUN
ejpam-3342	32	22	-	-	PUNCT
ejpam-3342	32	23	class	class	NOUN
ejpam-3342	32	24	operator	operator	NOUN
ejpam-3342	32	25	q	q	NOUN
ejpam-3342	33	1	and	and	CCONJ
ejpam-3342	33	2	the	the	DET
ejpam-3342	33	3	integrand	integrand	NOUN
ejpam-3342	33	4	is	be	AUX
ejpam-3342	33	5	an	an	DET
ejpam-3342	33	6	operator	operator	NOUN
ejpam-3342	33	7	-	-	PUNCT
ejpam-3342	33	8	valued	value	VERB
ejpam-3342	33	9	stochastic	stochastic	ADJ
ejpam-3342	33	10	process	process	NOUN
ejpam-3342	33	11	.	.	PUNCT
ejpam-3342	34	1	in	in	ADP
ejpam-3342	34	2	a	a	DET
ejpam-3342	34	3	general	general	ADJ
ejpam-3342	34	4	banach	banach	NOUN
ejpam-3342	34	5	space	space	NOUN
ejpam-3342	34	6	,	,	PUNCT
ejpam-3342	34	7	however	however	ADV
ejpam-3342	34	8	,	,	PUNCT
ejpam-3342	34	9	there	there	PRON
ejpam-3342	34	10	seems	seem	VERB
ejpam-3342	34	11	to	to	PART
ejpam-3342	34	12	be	be	AUX
ejpam-3342	34	13	no	no	DET
ejpam-3342	34	14	unifying	unifying	ADJ
ejpam-3342	34	15	treatment	treatment	NOUN
ejpam-3342	34	16	of	of	ADP
ejpam-3342	34	17	stochastic	stochastic	ADJ
ejpam-3342	34	18	integration	integration	NOUN
ejpam-3342	34	19	.	.	PUNCT
ejpam-3342	35	1	in	in	ADP
ejpam-3342	35	2	2018	2018	NUM
ejpam-3342	35	3	,	,	PUNCT
ejpam-3342	35	4	labendia	labendia	PROPN
ejpam-3342	35	5	,	,	PUNCT
ejpam-3342	35	6	et.al	et.al	PROPN
ejpam-3342	35	7	.	.	PUNCT
ejpam-3342	36	1	[	[	X
ejpam-3342	36	2	11	11	NUM
ejpam-3342	36	3	]	]	PUNCT
ejpam-3342	36	4	,	,	PUNCT
ejpam-3342	36	5	introduced	introduce	VERB
ejpam-3342	36	6	the	the	DET
ejpam-3342	36	7	(	(	PUNCT
ejpam-3342	36	8	forward	forward	ADJ
ejpam-3342	36	9	)	)	PUNCT
ejpam-3342	36	10	itô-henstock	itô-henstock	NOUN
ejpam-3342	36	11	integral	integral	ADJ
ejpam-3342	36	12	of	of	ADP
ejpam-3342	36	13	an	an	DET
ejpam-3342	36	14	operator	operator	NOUN
ejpam-3342	36	15	-	-	PUNCT
ejpam-3342	36	16	valued	value	VERB
ejpam-3342	36	17	stochastic	stochastic	ADJ
ejpam-3342	36	18	process	process	NOUN
ejpam-3342	36	19	with	with	ADP
ejpam-3342	36	20	respect	respect	NOUN
ejpam-3342	36	21	to	to	ADP
ejpam-3342	36	22	a	a	DET
ejpam-3342	36	23	hilbert	hilbert	NOUN
ejpam-3342	36	24	space	space	NOUN
ejpam-3342	36	25	-	-	PUNCT
ejpam-3342	36	26	valued	value	VERB
ejpam-3342	36	27	q	q	ADJ
ejpam-3342	36	28	-	-	PUNCT
ejpam-3342	36	29	wiener	wiener	NOUN
ejpam-3342	36	30	process	process	NOUN
ejpam-3342	36	31	.	.	PUNCT
ejpam-3342	37	1	this	this	DET
ejpam-3342	37	2	integral	integral	ADJ
ejpam-3342	37	3	uses	use	NOUN
ejpam-3342	37	4	(	(	PUNCT
ejpam-3342	37	5	forward	forward	ADJ
ejpam-3342	37	6	)	)	PUNCT
ejpam-3342	37	7	filtration	filtration	NOUN
ejpam-3342	37	8	.	.	PUNCT
ejpam-3342	38	1	moreover	moreover	ADV
ejpam-3342	38	2	,	,	PUNCT
ejpam-3342	38	3	the	the	DET
ejpam-3342	38	4	δ	δ	PROPN
ejpam-3342	38	5	-	-	PUNCT
ejpam-3342	38	6	fine	fine	ADJ
ejpam-3342	38	7	partial	partial	ADJ
ejpam-3342	38	8	division	division	NOUN
ejpam-3342	38	9	is	be	AUX
ejpam-3342	38	10	belated	belate	VERB
ejpam-3342	38	11	in	in	ADP
ejpam-3342	38	12	the	the	DET
ejpam-3342	38	13	sense	sense	NOUN
ejpam-3342	38	14	that	that	SCONJ
ejpam-3342	38	15	the	the	DET
ejpam-3342	38	16	associated	associated	ADJ
ejpam-3342	38	17	points	point	NOUN
ejpam-3342	38	18	(	(	PUNCT
ejpam-3342	38	19	or	or	CCONJ
ejpam-3342	38	20	tags	tag	NOUN
ejpam-3342	38	21	)	)	PUNCT
ejpam-3342	38	22	are	be	AUX
ejpam-3342	38	23	always	always	ADV
ejpam-3342	38	24	on	on	ADP
ejpam-3342	38	25	the	the	DET
ejpam-3342	38	26	left	left	ADJ
ejpam-3342	38	27	endpoints	endpoint	NOUN
ejpam-3342	38	28	of	of	ADP
ejpam-3342	38	29	the	the	DET
ejpam-3342	38	30	subintervals	subinterval	NOUN
ejpam-3342	38	31	.	.	PUNCT
ejpam-3342	39	1	they	they	PRON
ejpam-3342	39	2	formulated	formulate	VERB
ejpam-3342	39	3	a	a	DET
ejpam-3342	39	4	version	version	NOUN
ejpam-3342	39	5	of	of	ADP
ejpam-3342	39	6	itô	itô	PROPN
ejpam-3342	39	7	’s	’s	PART
ejpam-3342	39	8	formula	formula	NOUN
ejpam-3342	39	9	and	and	CCONJ
ejpam-3342	39	10	gave	give	VERB
ejpam-3342	39	11	an	an	DET
ejpam-3342	39	12	alternative	alternative	ADJ
ejpam-3342	39	13	definition	definition	NOUN
ejpam-3342	39	14	of	of	ADP
ejpam-3342	39	15	the	the	DET
ejpam-3342	39	16	classical	classical	ADJ
ejpam-3342	39	17	itô	itô	PROPN
ejpam-3342	39	18	integral	integral	ADJ
ejpam-3342	39	19	of	of	ADP
ejpam-3342	39	20	an	an	DET
ejpam-3342	39	21	l(u	l(u	PROPN
ejpam-3342	39	22	,	,	PUNCT
ejpam-3342	39	23	v	v	NOUN
ejpam-3342	39	24	)	)	PUNCT
ejpam-3342	39	25	-valued	-value	VERB
ejpam-3342	39	26	stochastic	stochastic	ADJ
ejpam-3342	39	27	process	process	NOUN
ejpam-3342	39	28	using	use	VERB
ejpam-3342	39	29	henstock	henstock	NOUN
ejpam-3342	39	30	approach	approach	NOUN
ejpam-3342	39	31	,	,	PUNCT
ejpam-3342	39	32	where	where	SCONJ
ejpam-3342	39	33	u	u	NOUN
ejpam-3342	39	34	and	and	CCONJ
ejpam-3342	39	35	v	v	NOUN
ejpam-3342	39	36	are	be	AUX
ejpam-3342	39	37	separable	separable	ADJ
ejpam-3342	39	38	hilbert	hilbert	NOUN
ejpam-3342	39	39	spaces	space	NOUN
ejpam-3342	39	40	and	and	CCONJ
ejpam-3342	39	41	l(u	l(u	PROPN
ejpam-3342	39	42	,	,	PUNCT
ejpam-3342	39	43	v	v	NOUN
ejpam-3342	39	44	)	)	PUNCT
ejpam-3342	39	45	is	be	AUX
ejpam-3342	39	46	the	the	DET
ejpam-3342	39	47	space	space	NOUN
ejpam-3342	39	48	of	of	ADP
ejpam-3342	39	49	all	all	DET
ejpam-3342	39	50	bounded	bound	VERB
ejpam-3342	39	51	linear	linear	PROPN
ejpam-3342	39	52	operators	operator	NOUN
ejpam-3342	40	1	q	q	X
ejpam-3342	40	2	:	:	PUNCT
ejpam-3342	40	3	u	u	NOUN
ejpam-3342	40	4	→	→	SYM
ejpam-3342	40	5	v	v	NOUN
ejpam-3342	40	6	.	.	PUNCT
ejpam-3342	41	1	in	in	ADP
ejpam-3342	41	2	[	[	X
ejpam-3342	41	3	10	10	NUM
ejpam-3342	41	4	]	]	PUNCT
ejpam-3342	41	5	,	,	PUNCT
ejpam-3342	41	6	the	the	DET
ejpam-3342	41	7	(	(	PUNCT
ejpam-3342	41	8	forward	forward	ADJ
ejpam-3342	41	9	)	)	PUNCT
ejpam-3342	41	10	itô-henstock	itô-henstock	PROPN
ejpam-3342	41	11	integral	integral	ADJ
ejpam-3342	41	12	has	have	AUX
ejpam-3342	41	13	been	be	AUX
ejpam-3342	41	14	characterized	characterize	VERB
ejpam-3342	41	15	using	use	VERB
ejpam-3342	41	16	ac2[0	ac2[0	ADJ
ejpam-3342	41	17	,	,	PUNCT
ejpam-3342	41	18	t	t	PROPN
ejpam-3342	41	19	]	]	PUNCT
ejpam-3342	41	20	-property	-property	PROPN
ejpam-3342	41	21	,	,	PUNCT
ejpam-3342	41	22	a	a	DET
ejpam-3342	41	23	version	version	NOUN
ejpam-3342	41	24	of	of	ADP
ejpam-3342	41	25	absolute	absolute	ADJ
ejpam-3342	41	26	continuity	continuity	NOUN
ejpam-3342	41	27	.	.	PUNCT
ejpam-3342	42	1	the	the	DET
ejpam-3342	42	2	backwards	backwards	ADV
ejpam-3342	42	3	itô	itô	PROPN
ejpam-3342	42	4	integral	integral	ADJ
ejpam-3342	42	5	with	with	ADP
ejpam-3342	42	6	respect	respect	NOUN
ejpam-3342	42	7	to	to	ADP
ejpam-3342	42	8	a	a	DET
ejpam-3342	42	9	brownian	brownian	ADJ
ejpam-3342	42	10	motion	motion	NOUN
ejpam-3342	42	11	was	be	AUX
ejpam-3342	42	12	defined	define	VERB
ejpam-3342	42	13	by	by	ADP
ejpam-3342	42	14	arcede	arcede	NOUN
ejpam-3342	42	15	and	and	CCONJ
ejpam-3342	42	16	cabral	cabral	ADJ
ejpam-3342	42	17	in	in	ADP
ejpam-3342	42	18	2011	2011	NUM
ejpam-3342	42	19	,	,	PUNCT
ejpam-3342	42	20	see	see	VERB
ejpam-3342	42	21	[	[	X
ejpam-3342	42	22	3	3	NUM
ejpam-3342	42	23	]	]	PUNCT
ejpam-3342	42	24	.	.	PUNCT
ejpam-3342	43	1	in	in	ADP
ejpam-3342	43	2	this	this	DET
ejpam-3342	43	3	integral	integral	ADJ
ejpam-3342	43	4	,	,	PUNCT
ejpam-3342	43	5	all	all	DET
ejpam-3342	43	6	processes	process	NOUN
ejpam-3342	43	7	start	start	VERB
ejpam-3342	43	8	at	at	ADP
ejpam-3342	43	9	a	a	DET
ejpam-3342	43	10	fix	fix	NOUN
ejpam-3342	43	11	time	time	NOUN
ejpam-3342	43	12	t	t	PROPN
ejpam-3342	43	13	>	>	X
ejpam-3342	43	14	0	0	PUNCT
ejpam-3342	44	1	and	and	CCONJ
ejpam-3342	44	2	then	then	ADV
ejpam-3342	44	3	proceed	proceed	VERB
ejpam-3342	44	4	backwards	backwards	ADV
ejpam-3342	44	5	to	to	ADP
ejpam-3342	44	6	some	some	DET
ejpam-3342	44	7	earlier	early	ADJ
ejpam-3342	44	8	time	time	NOUN
ejpam-3342	44	9	s.	s.	PROPN
ejpam-3342	44	10	henstock	henstock	PROPN
ejpam-3342	44	11	approach	approach	NOUN
ejpam-3342	44	12	was	be	AUX
ejpam-3342	44	13	used	use	VERB
ejpam-3342	44	14	together	together	ADV
ejpam-3342	44	15	with	with	ADP
ejpam-3342	44	16	the	the	DET
ejpam-3342	44	17	notions	notion	NOUN
ejpam-3342	44	18	of	of	ADP
ejpam-3342	44	19	backwards	backwards	ADV
ejpam-3342	44	20	δ	δ	PROPN
ejpam-3342	44	21	-	-	PUNCT
ejpam-3342	44	22	fine	fine	ADJ
ejpam-3342	44	23	partial	partial	ADJ
ejpam-3342	44	24	division	division	NOUN
ejpam-3342	44	25	(	(	PUNCT
ejpam-3342	44	26	backwards	backwards	ADV
ejpam-3342	44	27	in	in	ADP
ejpam-3342	44	28	the	the	DET
ejpam-3342	44	29	sense	sense	NOUN
ejpam-3342	44	30	that	that	SCONJ
ejpam-3342	44	31	the	the	DET
ejpam-3342	44	32	tags	tag	NOUN
ejpam-3342	44	33	are	be	AUX
ejpam-3342	44	34	the	the	DET
ejpam-3342	44	35	right	right	ADJ
ejpam-3342	44	36	endpoints	endpoint	NOUN
ejpam-3342	44	37	of	of	ADP
ejpam-3342	44	38	the	the	DET
ejpam-3342	44	39	disjoint	disjoint	NOUN
ejpam-3342	44	40	left	left	ADJ
ejpam-3342	44	41	-	-	PUNCT
ejpam-3342	44	42	open	open	ADJ
ejpam-3342	44	43	subintervals	subinterval	NOUN
ejpam-3342	44	44	)	)	PUNCT
ejpam-3342	44	45	and	and	CCONJ
ejpam-3342	44	46	backwards	backwards	ADV
ejpam-3342	44	47	filtration	filtration	NOUN
ejpam-3342	44	48	.	.	PUNCT
ejpam-3342	45	1	one	one	NUM
ejpam-3342	45	2	of	of	ADP
ejpam-3342	45	3	their	their	PRON
ejpam-3342	45	4	results	result	NOUN
ejpam-3342	45	5	are	be	AUX
ejpam-3342	45	6	the	the	DET
ejpam-3342	45	7	fundamental	fundamental	ADJ
ejpam-3342	45	8	theorem	theorem	NOUN
ejpam-3342	45	9	of	of	ADP
ejpam-3342	45	10	calculus	calculus	NOUN
ejpam-3342	45	11	,	,	PUNCT
ejpam-3342	45	12	integration	integration	NOUN
ejpam-3342	45	13	-	-	PUNCT
ejpam-3342	45	14	by	by	ADP
ejpam-3342	45	15	-	-	PUNCT
ejpam-3342	45	16	parts	part	NOUN
ejpam-3342	45	17	and	and	CCONJ
ejpam-3342	45	18	the	the	DET
ejpam-3342	45	19	itô	itô	PROPN
ejpam-3342	45	20	formula	formula	NOUN
ejpam-3342	45	21	for	for	ADP
ejpam-3342	45	22	backwards	backwards	ADV
ejpam-3342	45	23	itô	itô	PROPN
ejpam-3342	45	24	integral	integral	ADJ
ejpam-3342	45	25	see([4	see([4	NOUN
ejpam-3342	45	26	]	]	PUNCT
ejpam-3342	45	27	,	,	PUNCT
ejpam-3342	45	28	[	[	X
ejpam-3342	45	29	5	5	NUM
ejpam-3342	45	30	]	]	PUNCT
ejpam-3342	45	31	)	)	PUNCT
ejpam-3342	45	32	.	.	PUNCT
ejpam-3342	46	1	in	in	ADP
ejpam-3342	46	2	this	this	DET
ejpam-3342	46	3	paper	paper	NOUN
ejpam-3342	46	4	,	,	PUNCT
ejpam-3342	46	5	we	we	PRON
ejpam-3342	46	6	define	define	VERB
ejpam-3342	46	7	the	the	DET
ejpam-3342	46	8	backwards	backwards	ADV
ejpam-3342	46	9	itô-henstock	itô-henstock	NOUN
ejpam-3342	46	10	integral	integral	ADJ
ejpam-3342	46	11	of	of	ADP
ejpam-3342	46	12	an	an	DET
ejpam-3342	46	13	operator	operator	NOUN
ejpam-3342	46	14	-	-	PUNCT
ejpam-3342	46	15	valued	value	VERB
ejpam-3342	46	16	stochastic	stochastic	ADJ
ejpam-3342	46	17	process	process	NOUN
ejpam-3342	46	18	with	with	ADP
ejpam-3342	46	19	respect	respect	NOUN
ejpam-3342	46	20	to	to	ADP
ejpam-3342	46	21	a	a	DET
ejpam-3342	46	22	hilbert	hilbert	NOUN
ejpam-3342	46	23	space	space	NOUN
ejpam-3342	46	24	-	-	PUNCT
ejpam-3342	46	25	valued	value	VERB
ejpam-3342	46	26	q	q	ADJ
ejpam-3342	46	27	-	-	PUNCT
ejpam-3342	46	28	wiener	wiener	NOUN
ejpam-3342	46	29	process	process	NOUN
ejpam-3342	46	30	which	which	PRON
ejpam-3342	46	31	is	be	AUX
ejpam-3342	46	32	actually	actually	ADV
ejpam-3342	46	33	an	an	DET
ejpam-3342	46	34	extension	extension	NOUN
ejpam-3342	46	35	of	of	ADP
ejpam-3342	46	36	the	the	DET
ejpam-3342	46	37	work	work	NOUN
ejpam-3342	46	38	of	of	ADP
ejpam-3342	46	39	arcede	arcede	NOUN
ejpam-3342	46	40	and	and	CCONJ
ejpam-3342	46	41	cabral	cabral	ADJ
ejpam-3342	46	42	in	in	ADP
ejpam-3342	46	43	[	[	X
ejpam-3342	46	44	3	3	NUM
ejpam-3342	46	45	]	]	PUNCT
ejpam-3342	46	46	.	.	PUNCT
ejpam-3342	47	1	here	here	ADV
ejpam-3342	47	2	,	,	PUNCT
ejpam-3342	47	3	we	we	PRON
ejpam-3342	47	4	formulate	formulate	VERB
ejpam-3342	47	5	the	the	DET
ejpam-3342	47	6	itô	itô	PROPN
ejpam-3342	47	7	isometry	isometry	NOUN
ejpam-3342	47	8	and	and	CCONJ
ejpam-3342	47	9	give	give	VERB
ejpam-3342	47	10	an	an	DET
ejpam-3342	47	11	equivalent	equivalent	ADJ
ejpam-3342	47	12	definition	definition	NOUN
ejpam-3342	47	13	using	use	VERB
ejpam-3342	47	14	the	the	DET
ejpam-3342	47	15	concept	concept	NOUN
ejpam-3342	47	16	of	of	ADP
ejpam-3342	47	17	ac2	ac2	PROPN
ejpam-3342	47	18	property	property	NOUN
ejpam-3342	47	19	,	,	PUNCT
ejpam-3342	47	20	a	a	DET
ejpam-3342	47	21	version	version	NOUN
ejpam-3342	47	22	of	of	ADP
ejpam-3342	47	23	absolute	absolute	ADJ
ejpam-3342	47	24	continuity	continuity	NOUN
ejpam-3342	47	25	.	.	PUNCT
ejpam-3342	48	1	2	2	X
ejpam-3342	48	2	.	.	X
ejpam-3342	48	3	preliminaries	preliminary	NOUN
ejpam-3342	48	4	throughout	throughout	ADP
ejpam-3342	48	5	this	this	DET
ejpam-3342	48	6	paper	paper	NOUN
ejpam-3342	48	7	,	,	PUNCT
ejpam-3342	48	8	r	r	NOUN
ejpam-3342	48	9	denotes	denote	VERB
ejpam-3342	48	10	the	the	DET
ejpam-3342	48	11	set	set	NOUN
ejpam-3342	48	12	of	of	ADP
ejpam-3342	48	13	real	real	ADJ
ejpam-3342	48	14	numbers	number	NOUN
ejpam-3342	48	15	,	,	PUNCT
ejpam-3342	48	16	r+	r+	X
ejpam-3342	48	17	0	0	NUM
ejpam-3342	48	18	denotes	denote	VERB
ejpam-3342	48	19	the	the	DET
ejpam-3342	48	20	set	set	NOUN
ejpam-3342	48	21	of	of	ADP
ejpam-3342	48	22	nonnegative	nonnegative	ADJ
ejpam-3342	48	23	real	real	ADJ
ejpam-3342	48	24	numbers	number	NOUN
ejpam-3342	48	25	,	,	PUNCT
ejpam-3342	48	26	n	n	CCONJ
ejpam-3342	48	27	the	the	DET
ejpam-3342	48	28	set	set	NOUN
ejpam-3342	48	29	of	of	ADP
ejpam-3342	48	30	positive	positive	ADJ
ejpam-3342	48	31	integers	integer	NOUN
ejpam-3342	48	32	and	and	CCONJ
ejpam-3342	48	33	{	{	PUNCT
ejpam-3342	48	34	ω	ω	NOUN
ejpam-3342	48	35	,	,	PUNCT
ejpam-3342	48	36	g	g	PROPN
ejpam-3342	48	37	,	,	PUNCT
ejpam-3342	48	38	p	p	NOUN
ejpam-3342	48	39	}	}	PUNCT
ejpam-3342	48	40	denotes	denote	VERB
ejpam-3342	48	41	a	a	DET
ejpam-3342	48	42	probability	probability	NOUN
ejpam-3342	48	43	space	space	NOUN
ejpam-3342	48	44	.	.	PUNCT
ejpam-3342	49	1	let	let	VERB
ejpam-3342	49	2	{	{	PUNCT
ejpam-3342	49	3	gt	gt	INTJ
ejpam-3342	49	4	:	:	PUNCT
ejpam-3342	49	5	0	0	NUM
ejpam-3342	49	6	≤	≤	NUM
ejpam-3342	49	7	t	t	PROPN
ejpam-3342	49	8	≤	≤	PROPN
ejpam-3342	49	9	t	t	PROPN
ejpam-3342	49	10	}	}	PUNCT
ejpam-3342	49	11	be	be	AUX
ejpam-3342	49	12	a	a	DET
ejpam-3342	49	13	family	family	NOUN
ejpam-3342	49	14	of	of	ADP
ejpam-3342	49	15	sub	sub	PROPN
ejpam-3342	49	16	σ	σ	PROPN
ejpam-3342	49	17	-	-	PUNCT
ejpam-3342	49	18	field	field	NOUN
ejpam-3342	49	19	of	of	ADP
ejpam-3342	49	20	g.	g.	PROPN
ejpam-3342	49	21	then	then	ADV
ejpam-3342	49	22	{	{	PUNCT
ejpam-3342	49	23	gt	gt	INTJ
ejpam-3342	49	24	:	:	PUNCT
ejpam-3342	49	25	0	0	NUM
ejpam-3342	49	26	≤	≤	NUM
ejpam-3342	49	27	t	t	PROPN
ejpam-3342	49	28	≤	≤	PROPN
ejpam-3342	49	29	t	t	PROPN
ejpam-3342	49	30	}	}	PUNCT
ejpam-3342	49	31	is	be	AUX
ejpam-3342	49	32	called	call	VERB
ejpam-3342	49	33	a	a	DET
ejpam-3342	49	34	backwards	backwards	ADJ
ejpam-3342	49	35	filtration	filtration	NOUN
ejpam-3342	49	36	if	if	SCONJ
ejpam-3342	49	37	gt	gt	PROPN
ejpam-3342	49	38	⊆	⊆	NUM
ejpam-3342	49	39	gs	gs	NOUN
ejpam-3342	49	40	for	for	ADP
ejpam-3342	49	41	all	all	DET
ejpam-3342	49	42	0	0	NUM
ejpam-3342	49	43	≤	≤	NUM
ejpam-3342	49	44	s	s	PART
ejpam-3342	49	45	≤	≤	NUM
ejpam-3342	49	46	t	t	NOUN
ejpam-3342	49	47	≤	≤	NOUN
ejpam-3342	49	48	t	t	PROPN
ejpam-3342	49	49	.	.	PUNCT
ejpam-3342	50	1	if	if	SCONJ
ejpam-3342	50	2	in	in	ADP
ejpam-3342	50	3	addition	addition	NOUN
ejpam-3342	50	4	,	,	PUNCT
ejpam-3342	50	5	{	{	PUNCT
ejpam-3342	50	6	gt	gt	INTJ
ejpam-3342	50	7	:	:	PUNCT
ejpam-3342	50	8	0	0	NUM
ejpam-3342	50	9	≤	≤	NUM
ejpam-3342	50	10	t	t	PROPN
ejpam-3342	50	11	≤	≤	PROPN
ejpam-3342	50	12	t	t	PROPN
ejpam-3342	50	13	}	}	PUNCT
ejpam-3342	50	14	satisfies	satisfy	VERB
ejpam-3342	50	15	the	the	DET
ejpam-3342	50	16	following	follow	VERB
ejpam-3342	50	17	condition	condition	NOUN
ejpam-3342	50	18	:	:	PUNCT
ejpam-3342	50	19	(	(	PUNCT
ejpam-3342	50	20	1	1	X
ejpam-3342	50	21	)	)	PUNCT
ejpam-3342	50	22	gt	gt	PROPN
ejpam-3342	50	23	contains	contain	VERB
ejpam-3342	50	24	all	all	DET
ejpam-3342	50	25	sets	set	NOUN
ejpam-3342	50	26	of	of	ADP
ejpam-3342	50	27	p	p	NOUN
ejpam-3342	50	28	-	-	PUNCT
ejpam-3342	50	29	measure	measure	NOUN
ejpam-3342	50	30	zero	zero	NUM
ejpam-3342	50	31	in	in	ADP
ejpam-3342	50	32	g	g	NOUN
ejpam-3342	50	33	;	;	PUNCT
ejpam-3342	50	34	and	and	CCONJ
ejpam-3342	50	35	(	(	PUNCT
ejpam-3342	50	36	2	2	X
ejpam-3342	50	37	)	)	PUNCT
ejpam-3342	50	38	for	for	ADP
ejpam-3342	50	39	each	each	DET
ejpam-3342	50	40	t	t	NOUN
ejpam-3342	50	41	∈	∈	PROPN
ejpam-3342	51	1	[	[	X
ejpam-3342	51	2	0	0	NUM
ejpam-3342	51	3	,	,	PUNCT
ejpam-3342	51	4	t	t	X
ejpam-3342	51	5	]	]	PUNCT
ejpam-3342	51	6	,	,	PUNCT
ejpam-3342	51	7	gt	gt	PROPN
ejpam-3342	51	8	=	=	PUNCT
ejpam-3342	52	1	gt−	gt−	PUNCT
ejpam-3342	52	2	:	:	PUNCT
ejpam-3342	53	1	=	=	SYM
ejpam-3342	53	2	⋂	⋂	PROPN
ejpam-3342	53	3	s	s	X
ejpam-3342	53	4	<	<	X
ejpam-3342	53	5	t	t	PROPN
ejpam-3342	53	6	gs	gs	NOUN
ejpam-3342	53	7	.	.	PUNCT
ejpam-3342	54	1	then	then	ADV
ejpam-3342	54	2	{	{	PUNCT
ejpam-3342	54	3	gt	gt	INTJ
ejpam-3342	54	4	:	:	PUNCT
ejpam-3342	54	5	0	0	NUM
ejpam-3342	54	6	≤	≤	NUM
ejpam-3342	54	7	t	t	PROPN
ejpam-3342	54	8	≤	≤	PROPN
ejpam-3342	54	9	t	t	PROPN
ejpam-3342	54	10	}	}	PUNCT
ejpam-3342	54	11	is	be	AUX
ejpam-3342	54	12	called	call	VERB
ejpam-3342	54	13	a	a	DET
ejpam-3342	54	14	standard	standard	ADJ
ejpam-3342	54	15	r.	r.	PROPN
ejpam-3342	54	16	rulete	rulete	PROPN
ejpam-3342	54	17	,	,	PUNCT
ejpam-3342	54	18	m.	m.	NOUN
ejpam-3342	54	19	labendia	labendia	PROPN
ejpam-3342	54	20	/	/	SYM
ejpam-3342	54	21	eur	eur	PROPN
ejpam-3342	54	22	.	.	PUNCT
ejpam-3342	55	1	j.	j.	PROPN
ejpam-3342	55	2	pure	pure	PROPN
ejpam-3342	55	3	appl	appl	PROPN
ejpam-3342	55	4	.	.	PROPN
ejpam-3342	55	5	math	math	PROPN
ejpam-3342	55	6	,	,	PUNCT
ejpam-3342	55	7	12	12	NUM
ejpam-3342	55	8	(	(	PUNCT
ejpam-3342	55	9	1	1	NUM
ejpam-3342	55	10	)	)	PUNCT
ejpam-3342	55	11	(	(	PUNCT
ejpam-3342	55	12	2019	2019	NUM
ejpam-3342	55	13	)	)	PUNCT
ejpam-3342	55	14	,	,	PUNCT
ejpam-3342	55	15	58	58	NUM
ejpam-3342	55	16	-	-	SYM
ejpam-3342	55	17	78	78	NUM
ejpam-3342	55	18	60	60	NUM
ejpam-3342	55	19	backwards	backwards	ADV
ejpam-3342	55	20	filtration	filtration	NOUN
ejpam-3342	55	21	.	.	PUNCT
ejpam-3342	56	1	we	we	PRON
ejpam-3342	56	2	often	often	ADV
ejpam-3342	56	3	write	write	VERB
ejpam-3342	56	4	{	{	PUNCT
ejpam-3342	56	5	gt	gt	INTJ
ejpam-3342	56	6	}	}	PUNCT
ejpam-3342	56	7	instead	instead	ADV
ejpam-3342	56	8	of	of	ADP
ejpam-3342	56	9	{	{	PUNCT
ejpam-3342	56	10	gt	gt	INTJ
ejpam-3342	56	11	:	:	PUNCT
ejpam-3342	56	12	0	0	NUM
ejpam-3342	56	13	≤	≤	NUM
ejpam-3342	56	14	t	t	PROPN
ejpam-3342	56	15	≤	≤	NUM
ejpam-3342	56	16	t	t	PROPN
ejpam-3342	56	17	}	}	PUNCT
ejpam-3342	56	18	.	.	PUNCT
ejpam-3342	57	1	see	see	VERB
ejpam-3342	57	2	[	[	X
ejpam-3342	57	3	1	1	NUM
ejpam-3342	57	4	]	]	PUNCT
ejpam-3342	57	5	.	.	PUNCT
ejpam-3342	58	1	let	let	VERB
ejpam-3342	58	2	h	h	PRON
ejpam-3342	58	3	be	be	AUX
ejpam-3342	58	4	a	a	DET
ejpam-3342	58	5	separable	separable	ADJ
ejpam-3342	58	6	banach	banach	NOUN
ejpam-3342	58	7	space	space	NOUN
ejpam-3342	58	8	.	.	PUNCT
ejpam-3342	59	1	a	a	DET
ejpam-3342	59	2	stochastic	stochastic	ADJ
ejpam-3342	59	3	process	process	NOUN
ejpam-3342	59	4	f	f	NOUN
ejpam-3342	59	5	or	or	CCONJ
ejpam-3342	59	6	simply	simply	ADV
ejpam-3342	59	7	process	process	NOUN
ejpam-3342	59	8	is	be	AUX
ejpam-3342	59	9	a	a	DET
ejpam-3342	59	10	function	function	NOUN
ejpam-3342	59	11	f	f	NOUN
ejpam-3342	59	12	:	:	PUNCT
ejpam-3342	60	1	[	[	X
ejpam-3342	60	2	0	0	NUM
ejpam-3342	60	3	,	,	PUNCT
ejpam-3342	60	4	t	t	X
ejpam-3342	60	5	]	]	X
ejpam-3342	60	6	×	×	PROPN
ejpam-3342	60	7	ω→	ω→	PUNCT
ejpam-3342	60	8	h	h	NOUN
ejpam-3342	60	9	,	,	PUNCT
ejpam-3342	60	10	where	where	SCONJ
ejpam-3342	60	11	[	[	X
ejpam-3342	60	12	0	0	NUM
ejpam-3342	60	13	,	,	PUNCT
ejpam-3342	60	14	t	t	PROPN
ejpam-3342	60	15	]	]	PUNCT
ejpam-3342	60	16	is	be	AUX
ejpam-3342	60	17	an	an	DET
ejpam-3342	60	18	interval	interval	NOUN
ejpam-3342	60	19	in	in	ADP
ejpam-3342	60	20	r+	r+	NOUN
ejpam-3342	60	21	0	0	NUM
ejpam-3342	60	22	and	and	CCONJ
ejpam-3342	60	23	f	f	X
ejpam-3342	60	24	(	(	PUNCT
ejpam-3342	60	25	·	·	PUNCT
ejpam-3342	60	26	,	,	PUNCT
ejpam-3342	60	27	t	t	PROPN
ejpam-3342	60	28	)	)	PUNCT
ejpam-3342	60	29	is	be	AUX
ejpam-3342	60	30	gt	gt	NOUN
ejpam-3342	60	31	-	-	ADJ
ejpam-3342	60	32	measurable	measurable	NOUN
ejpam-3342	60	33	for	for	ADP
ejpam-3342	60	34	each	each	DET
ejpam-3342	60	35	t	t	NOUN
ejpam-3342	60	36	∈	∈	PROPN
ejpam-3342	61	1	[	[	X
ejpam-3342	61	2	0	0	NUM
ejpam-3342	61	3	,	,	PUNCT
ejpam-3342	61	4	t	t	X
ejpam-3342	61	5	]	]	PUNCT
ejpam-3342	61	6	.	.	PUNCT
ejpam-3342	62	1	a	a	DET
ejpam-3342	62	2	process	process	NOUN
ejpam-3342	62	3	f	f	NOUN
ejpam-3342	62	4	=	=	PRON
ejpam-3342	62	5	{	{	PUNCT
ejpam-3342	62	6	ft	ft	NOUN
ejpam-3342	62	7	:	:	PUNCT
ejpam-3342	62	8	t	t	PROPN
ejpam-3342	62	9	∈	∈	PROPN
ejpam-3342	63	1	[	[	X
ejpam-3342	63	2	0	0	NUM
ejpam-3342	63	3	,	,	PUNCT
ejpam-3342	63	4	t	t	X
ejpam-3342	63	5	]	]	PUNCT
ejpam-3342	63	6	}	}	PUNCT
ejpam-3342	63	7	is	be	AUX
ejpam-3342	63	8	said	say	VERB
ejpam-3342	63	9	to	to	PART
ejpam-3342	63	10	be	be	AUX
ejpam-3342	63	11	backwards	backwards	ADV
ejpam-3342	63	12	adapted	adapt	VERB
ejpam-3342	63	13	to	to	ADP
ejpam-3342	63	14	a	a	DET
ejpam-3342	63	15	standard	standard	ADJ
ejpam-3342	63	16	backwards	backwards	ADV
ejpam-3342	63	17	filtration	filtration	NOUN
ejpam-3342	63	18	{	{	PUNCT
ejpam-3342	63	19	gt	gt	INTJ
ejpam-3342	63	20	}	}	PUNCT
ejpam-3342	63	21	if	if	SCONJ
ejpam-3342	63	22	ft	ft	NOUN
ejpam-3342	63	23	is	be	AUX
ejpam-3342	63	24	gt	gt	NOUN
ejpam-3342	63	25	-	-	ADJ
ejpam-3342	63	26	measurable	measurable	NOUN
ejpam-3342	63	27	for	for	ADP
ejpam-3342	63	28	each	each	DET
ejpam-3342	63	29	t	t	NOUN
ejpam-3342	63	30	∈	∈	PROPN
ejpam-3342	64	1	[	[	X
ejpam-3342	64	2	0	0	NUM
ejpam-3342	64	3	,	,	PUNCT
ejpam-3342	64	4	t	t	X
ejpam-3342	64	5	]	]	PUNCT
ejpam-3342	64	6	.	.	PUNCT
ejpam-3342	65	1	let	let	VERB
ejpam-3342	65	2	u	u	PRON
ejpam-3342	65	3	and	and	CCONJ
ejpam-3342	65	4	v	v	NOUN
ejpam-3342	65	5	be	be	AUX
ejpam-3342	65	6	separable	separable	ADJ
ejpam-3342	65	7	hilbert	hilbert	PROPN
ejpam-3342	65	8	spaces	space	NOUN
ejpam-3342	65	9	.	.	PUNCT
ejpam-3342	66	1	denote	denote	VERB
ejpam-3342	66	2	l(u	l(u	PROPN
ejpam-3342	66	3	,	,	PUNCT
ejpam-3342	66	4	v	v	NOUN
ejpam-3342	66	5	)	)	PUNCT
ejpam-3342	66	6	the	the	DET
ejpam-3342	66	7	space	space	NOUN
ejpam-3342	66	8	of	of	ADP
ejpam-3342	66	9	all	all	DET
ejpam-3342	66	10	bounded	bound	VERB
ejpam-3342	66	11	linear	linear	PROPN
ejpam-3342	66	12	operators	operator	NOUN
ejpam-3342	66	13	from	from	ADP
ejpam-3342	66	14	u	u	PRON
ejpam-3342	66	15	to	to	ADP
ejpam-3342	66	16	v	v	NUM
ejpam-3342	66	17	,	,	PUNCT
ejpam-3342	66	18	l(u	l(u	PROPN
ejpam-3342	66	19	)	)	PUNCT
ejpam-3342	66	20	:	:	PUNCT
ejpam-3342	67	1	=	=	SYM
ejpam-3342	67	2	l(u	l(u	PROPN
ejpam-3342	67	3	,	,	PUNCT
ejpam-3342	67	4	u	u	NOUN
ejpam-3342	67	5	)	)	PUNCT
ejpam-3342	67	6	,	,	PUNCT
ejpam-3342	67	7	qu	qu	PROPN
ejpam-3342	67	8	:	:	PUNCT
ejpam-3342	67	9	=	=	SYM
ejpam-3342	67	10	q(u	q(u	X
ejpam-3342	67	11	)	)	PUNCT
ejpam-3342	67	12	if	if	SCONJ
ejpam-3342	67	13	q	q	PROPN
ejpam-3342	67	14	∈	∈	PROPN
ejpam-3342	67	15	l(u	l(u	PROPN
ejpam-3342	67	16	,	,	PUNCT
ejpam-3342	67	17	v	v	NOUN
ejpam-3342	67	18	)	)	PUNCT
ejpam-3342	67	19	,	,	PUNCT
ejpam-3342	67	20	and	and	CCONJ
ejpam-3342	67	21	l2(ω	l2(ω	PROPN
ejpam-3342	67	22	,	,	PUNCT
ejpam-3342	67	23	v	v	NOUN
ejpam-3342	67	24	)	)	PUNCT
ejpam-3342	67	25	the	the	DET
ejpam-3342	67	26	space	space	NOUN
ejpam-3342	67	27	of	of	ADP
ejpam-3342	67	28	all	all	DET
ejpam-3342	67	29	square	square	ADJ
ejpam-3342	67	30	-	-	PUNCT
ejpam-3342	67	31	integrable	integrable	ADJ
ejpam-3342	67	32	random	random	ADJ
ejpam-3342	67	33	variables	variable	NOUN
ejpam-3342	67	34	from	from	ADP
ejpam-3342	67	35	ω	ω	NUM
ejpam-3342	67	36	to	to	ADP
ejpam-3342	67	37	v	v	NOUN
ejpam-3342	67	38	.	.	PUNCT
ejpam-3342	68	1	an	an	DET
ejpam-3342	68	2	operator	operator	NOUN
ejpam-3342	68	3	q	q	PROPN
ejpam-3342	68	4	∈	∈	PROPN
ejpam-3342	68	5	l(u	l(u	PROPN
ejpam-3342	68	6	)	)	PUNCT
ejpam-3342	68	7	is	be	AUX
ejpam-3342	68	8	said	say	VERB
ejpam-3342	68	9	to	to	PART
ejpam-3342	68	10	be	be	AUX
ejpam-3342	68	11	self	self	NOUN
ejpam-3342	68	12	-	-	PUNCT
ejpam-3342	68	13	adjoint	adjoint	NOUN
ejpam-3342	68	14	or	or	CCONJ
ejpam-3342	68	15	symmetric	symmetric	ADJ
ejpam-3342	68	16	if	if	SCONJ
ejpam-3342	68	17	for	for	ADP
ejpam-3342	68	18	all	all	DET
ejpam-3342	68	19	u	u	NOUN
ejpam-3342	68	20	,	,	PUNCT
ejpam-3342	68	21	u′	u′	PROPN
ejpam-3342	68	22	∈	∈	PROPN
ejpam-3342	68	23	u	u	PROPN
ejpam-3342	68	24	,	,	PUNCT
ejpam-3342	68	25	〈	〈	PROPN
ejpam-3342	68	26	qu	qu	PROPN
ejpam-3342	68	27	,	,	PUNCT
ejpam-3342	68	28	u′〉u	u′〉u	PROPN
ejpam-3342	68	29	=	=	SYM
ejpam-3342	68	30	〈	〈	PROPN
ejpam-3342	68	31	u	u	NOUN
ejpam-3342	68	32	,	,	PUNCT
ejpam-3342	68	33	qu′〉u	qu′〉u	PROPN
ejpam-3342	68	34	and	and	CCONJ
ejpam-3342	68	35	is	be	AUX
ejpam-3342	68	36	said	say	VERB
ejpam-3342	68	37	to	to	PART
ejpam-3342	68	38	be	be	AUX
ejpam-3342	68	39	nonnegative	nonnegative	ADJ
ejpam-3342	68	40	definite	definite	ADJ
ejpam-3342	68	41	if	if	SCONJ
ejpam-3342	68	42	for	for	ADP
ejpam-3342	68	43	every	every	DET
ejpam-3342	68	44	u	u	PROPN
ejpam-3342	68	45	∈	∈	PROPN
ejpam-3342	68	46	u	u	NOUN
ejpam-3342	68	47	,	,	PUNCT
ejpam-3342	68	48	〈	〈	PROPN
ejpam-3342	68	49	qu	qu	PROPN
ejpam-3342	68	50	,	,	PUNCT
ejpam-3342	68	51	u〉u	u〉u	NOUN
ejpam-3342	68	52	≥	≥	NUM
ejpam-3342	68	53	0	0	NUM
ejpam-3342	68	54	.	.	PUNCT
ejpam-3342	69	1	let	let	VERB
ejpam-3342	69	2	{	{	PUNCT
ejpam-3342	69	3	ej}∞j=1	ej}∞j=1	X
ejpam-3342	69	4	,	,	PUNCT
ejpam-3342	69	5	or	or	CCONJ
ejpam-3342	69	6	simply	simply	ADV
ejpam-3342	69	7	{	{	PUNCT
ejpam-3342	69	8	ej	ej	NOUN
ejpam-3342	69	9	}	}	PUNCT
ejpam-3342	69	10	,	,	PUNCT
ejpam-3342	69	11	be	be	AUX
ejpam-3342	69	12	an	an	DET
ejpam-3342	69	13	orthonormal	orthonormal	ADJ
ejpam-3342	69	14	basis	basis	NOUN
ejpam-3342	69	15	(	(	PUNCT
ejpam-3342	69	16	abbrev	abbrev	NOUN
ejpam-3342	69	17	.	.	PUNCT
ejpam-3342	70	1	as	as	ADP
ejpam-3342	70	2	onb	onb	ADJ
ejpam-3342	70	3	)	)	PUNCT
ejpam-3342	70	4	in	in	ADP
ejpam-3342	70	5	u	u	NOUN
ejpam-3342	70	6	.	.	PUNCT
ejpam-3342	71	1	if	if	SCONJ
ejpam-3342	71	2	q	q	PROPN
ejpam-3342	71	3	∈	∈	PROPN
ejpam-3342	71	4	l(u	l(u	PROPN
ejpam-3342	71	5	)	)	PUNCT
ejpam-3342	71	6	is	be	AUX
ejpam-3342	71	7	nonnegative	nonnegative	ADJ
ejpam-3342	71	8	definite	definite	ADJ
ejpam-3342	71	9	,	,	PUNCT
ejpam-3342	71	10	then	then	ADV
ejpam-3342	71	11	the	the	DET
ejpam-3342	71	12	trace	trace	NOUN
ejpam-3342	71	13	ofq	ofq	NOUN
ejpam-3342	71	14	is	be	AUX
ejpam-3342	71	15	defined	define	VERB
ejpam-3342	71	16	by	by	ADP
ejpam-3342	71	17	trq	trq	NOUN
ejpam-3342	71	18	=	=	SYM
ejpam-3342	71	19	∑∞	∑∞	NOUN
ejpam-3342	71	20	j=1	j=1	PROPN
ejpam-3342	71	21	〈	〈	PROPN
ejpam-3342	71	22	qej	qej	NOUN
ejpam-3342	71	23	,	,	PUNCT
ejpam-3342	71	24	ej〉u	ej〉u	NOUN
ejpam-3342	71	25	.	.	PUNCT
ejpam-3342	72	1	it	it	PRON
ejpam-3342	72	2	is	be	AUX
ejpam-3342	72	3	shown	show	VERB
ejpam-3342	72	4	in	in	ADP
ejpam-3342	72	5	[	[	X
ejpam-3342	72	6	20	20	NUM
ejpam-3342	72	7	]	]	PUNCT
ejpam-3342	72	8	that	that	PRON
ejpam-3342	72	9	tr	tr	VERB
ejpam-3342	72	10	q	q	PROPN
ejpam-3342	72	11	is	be	AUX
ejpam-3342	72	12	well	well	ADV
ejpam-3342	72	13	-	-	PUNCT
ejpam-3342	72	14	defined	define	VERB
ejpam-3342	72	15	and	and	CCONJ
ejpam-3342	72	16	may	may	AUX
ejpam-3342	72	17	be	be	AUX
ejpam-3342	72	18	defined	define	VERB
ejpam-3342	72	19	in	in	ADP
ejpam-3342	72	20	terms	term	NOUN
ejpam-3342	72	21	of	of	ADP
ejpam-3342	72	22	an	an	DET
ejpam-3342	72	23	arbitrary	arbitrary	ADJ
ejpam-3342	72	24	onb	onb	ADJ
ejpam-3342	72	25	.	.	PUNCT
ejpam-3342	73	1	moreover	moreover	ADV
ejpam-3342	73	2	,	,	PUNCT
ejpam-3342	73	3	there	there	PRON
ejpam-3342	73	4	exists	exist	VERB
ejpam-3342	73	5	a	a	DET
ejpam-3342	73	6	unique	unique	ADJ
ejpam-3342	73	7	operator	operator	NOUN
ejpam-3342	73	8	q	q	NOUN
ejpam-3342	73	9	1	1	NUM
ejpam-3342	73	10	2	2	NUM
ejpam-3342	73	11	∈	∈	PROPN
ejpam-3342	73	12	l(u	l(u	PROPN
ejpam-3342	73	13	)	)	PUNCT
ejpam-3342	73	14	such	such	ADJ
ejpam-3342	73	15	that	that	PRON
ejpam-3342	73	16	q	q	NOUN
ejpam-3342	73	17	1	1	NUM
ejpam-3342	73	18	2	2	NUM
ejpam-3342	73	19	is	be	AUX
ejpam-3342	73	20	nonnegative	nonnegative	ADJ
ejpam-3342	73	21	definite	definite	ADJ
ejpam-3342	74	1	and	and	CCONJ
ejpam-3342	74	2	(	(	PUNCT
ejpam-3342	74	3	q	q	NOUN
ejpam-3342	74	4	1	1	NUM
ejpam-3342	74	5	2	2	NUM
ejpam-3342	74	6	)	)	PUNCT
ejpam-3342	74	7	2	2	NUM
ejpam-3342	74	8	=	=	SYM
ejpam-3342	74	9	q.	q.	NOUN
ejpam-3342	74	10	an	an	DET
ejpam-3342	74	11	operator	operator	NOUN
ejpam-3342	74	12	q	q	NOUN
ejpam-3342	74	13	:	:	PUNCT
ejpam-3342	74	14	u	u	PROPN
ejpam-3342	74	15	→	→	SYM
ejpam-3342	74	16	u	u	NOUN
ejpam-3342	74	17	is	be	AUX
ejpam-3342	74	18	said	say	VERB
ejpam-3342	74	19	to	to	PART
ejpam-3342	74	20	be	be	AUX
ejpam-3342	74	21	trace	trace	NOUN
ejpam-3342	74	22	-	-	PUNCT
ejpam-3342	74	23	class	class	NOUN
ejpam-3342	74	24	if	if	SCONJ
ejpam-3342	74	25	tr	tr	VERB
ejpam-3342	74	26	[	[	X
ejpam-3342	74	27	q	q	X
ejpam-3342	74	28	]	]	X
ejpam-3342	74	29	:	:	PUNCT
ejpam-3342	74	30	=	=	PUNCT
ejpam-3342	74	31	tr	tr	VERB
ejpam-3342	74	32	(	(	PUNCT
ejpam-3342	74	33	qq∗	qq∗	ADJ
ejpam-3342	74	34	)	)	PUNCT
ejpam-3342	74	35	1	1	NUM
ejpam-3342	74	36	2	2	NUM
ejpam-3342	74	37	<	<	X
ejpam-3342	74	38	∞.	∞.	PROPN
ejpam-3342	74	39	if	if	SCONJ
ejpam-3342	74	40	q	q	PROPN
ejpam-3342	74	41	∈	∈	PROPN
ejpam-3342	74	42	l(u	l(u	PROPN
ejpam-3342	74	43	)	)	PUNCT
ejpam-3342	74	44	is	be	AUX
ejpam-3342	74	45	a	a	DET
ejpam-3342	74	46	symmetric	symmetric	ADJ
ejpam-3342	74	47	nonnegative	nonnegative	ADJ
ejpam-3342	74	48	definite	definite	ADJ
ejpam-3342	74	49	trace	trace	NOUN
ejpam-3342	74	50	-	-	PUNCT
ejpam-3342	74	51	class	class	NOUN
ejpam-3342	74	52	operator	operator	NOUN
ejpam-3342	74	53	,	,	PUNCT
ejpam-3342	74	54	then	then	ADV
ejpam-3342	74	55	there	there	PRON
ejpam-3342	74	56	exists	exist	VERB
ejpam-3342	74	57	an	an	DET
ejpam-3342	74	58	onb	onb	ADJ
ejpam-3342	74	59	{	{	PUNCT
ejpam-3342	74	60	ej	ej	PROPN
ejpam-3342	74	61	}	}	PUNCT
ejpam-3342	74	62	⊂	⊂	PROPN
ejpam-3342	74	63	u	u	NOUN
ejpam-3342	74	64	and	and	CCONJ
ejpam-3342	74	65	a	a	DET
ejpam-3342	74	66	sequence	sequence	NOUN
ejpam-3342	74	67	of	of	ADP
ejpam-3342	74	68	nonnegative	nonnegative	ADJ
ejpam-3342	74	69	real	real	ADJ
ejpam-3342	74	70	numbers	number	NOUN
ejpam-3342	74	71	{	{	PUNCT
ejpam-3342	74	72	λj	λj	X
ejpam-3342	74	73	}	}	PUNCT
ejpam-3342	74	74	such	such	ADJ
ejpam-3342	74	75	that	that	DET
ejpam-3342	74	76	qej	qej	NOUN
ejpam-3342	74	77	=	=	PUNCT
ejpam-3342	74	78	λjej	λjej	NOUN
ejpam-3342	74	79	for	for	ADP
ejpam-3342	74	80	all	all	DET
ejpam-3342	74	81	j	j	PROPN
ejpam-3342	74	82	∈	∈	PROPN
ejpam-3342	74	83	n	n	CCONJ
ejpam-3342	74	84	,	,	PUNCT
ejpam-3342	74	85	and	and	CCONJ
ejpam-3342	74	86	λj	λj	PROPN
ejpam-3342	74	87	→	→	SYM
ejpam-3342	74	88	0	0	PUNCT
ejpam-3342	74	89	as	as	SCONJ
ejpam-3342	74	90	j	j	PROPN
ejpam-3342	74	91	→	→	SYM
ejpam-3342	74	92	∞	∞	PROPN
ejpam-3342	74	93	[	[	X
ejpam-3342	74	94	20	20	NUM
ejpam-3342	74	95	,	,	PUNCT
ejpam-3342	74	96	p.203	p.203	X
ejpam-3342	74	97	]	]	PUNCT
ejpam-3342	74	98	.	.	PUNCT
ejpam-3342	75	1	we	we	PRON
ejpam-3342	75	2	shall	shall	AUX
ejpam-3342	75	3	call	call	VERB
ejpam-3342	75	4	the	the	DET
ejpam-3342	75	5	sequence	sequence	NOUN
ejpam-3342	75	6	of	of	ADP
ejpam-3342	75	7	pairs	pair	NOUN
ejpam-3342	75	8	{	{	PUNCT
ejpam-3342	75	9	λj	λj	NOUN
ejpam-3342	75	10	,	,	PUNCT
ejpam-3342	75	11	ej	ej	PROPN
ejpam-3342	75	12	}	}	PUNCT
ejpam-3342	75	13	an	an	DET
ejpam-3342	75	14	eigensequence	eigensequence	NOUN
ejpam-3342	75	15	defined	define	VERB
ejpam-3342	75	16	by	by	ADP
ejpam-3342	75	17	q.	q.	PROPN
ejpam-3342	75	18	let	let	VERB
ejpam-3342	75	19	q	q	NOUN
ejpam-3342	75	20	:	:	PUNCT
ejpam-3342	75	21	u	u	X
ejpam-3342	75	22	→	→	SYM
ejpam-3342	75	23	u	u	X
ejpam-3342	75	24	be	be	VERB
ejpam-3342	75	25	a	a	DET
ejpam-3342	75	26	symmetric	symmetric	ADJ
ejpam-3342	75	27	nonnegative	nonnegative	ADJ
ejpam-3342	75	28	definite	definite	ADJ
ejpam-3342	75	29	trace	trace	NOUN
ejpam-3342	75	30	-	-	PUNCT
ejpam-3342	75	31	class	class	NOUN
ejpam-3342	75	32	operator	operator	NOUN
ejpam-3342	75	33	and	and	CCONJ
ejpam-3342	75	34	let	let	VERB
ejpam-3342	75	35	{	{	PUNCT
ejpam-3342	75	36	λj	λj	NOUN
ejpam-3342	75	37	,	,	PUNCT
ejpam-3342	75	38	ej	ej	AUX
ejpam-3342	75	39	}	}	PUNCT
ejpam-3342	75	40	be	be	AUX
ejpam-3342	75	41	an	an	DET
ejpam-3342	75	42	eigensequence	eigensequence	NOUN
ejpam-3342	75	43	defined	define	VERB
ejpam-3342	75	44	by	by	ADP
ejpam-3342	75	45	q.	q.	PROPN
ejpam-3342	75	46	then	then	ADV
ejpam-3342	75	47	the	the	DET
ejpam-3342	75	48	subspace	subspace	PROPN
ejpam-3342	75	49	uq	uq	NOUN
ejpam-3342	75	50	:	:	PUNCT
ejpam-3342	75	51	=	=	SYM
ejpam-3342	75	52	q	q	PROPN
ejpam-3342	75	53	1	1	NUM
ejpam-3342	75	54	2u	2u	NOUN
ejpam-3342	75	55	of	of	ADP
ejpam-3342	75	56	u	u	PRON
ejpam-3342	75	57	equipped	equip	VERB
ejpam-3342	75	58	with	with	ADP
ejpam-3342	75	59	the	the	DET
ejpam-3342	75	60	inner	inner	ADJ
ejpam-3342	75	61	product	product	NOUN
ejpam-3342	75	62	〈	〈	PROPN
ejpam-3342	75	63	u	u	NOUN
ejpam-3342	75	64	,	,	PUNCT
ejpam-3342	75	65	v〉uq	v〉uq	NOUN
ejpam-3342	75	66	=	=	SYM
ejpam-3342	75	67	〈	〈	PROPN
ejpam-3342	75	68	q−1/2u	q−1/2u	NOUN
ejpam-3342	75	69	,	,	PUNCT
ejpam-3342	75	70	q−1/2v	q−1/2v	NOUN
ejpam-3342	75	71	〉	〉	NOUN
ejpam-3342	75	72	u	u	NOUN
ejpam-3342	75	73	,	,	PUNCT
ejpam-3342	75	74	where	where	SCONJ
ejpam-3342	75	75	q1/2	q1/2	PROPN
ejpam-3342	75	76	is	be	AUX
ejpam-3342	75	77	being	be	AUX
ejpam-3342	75	78	restricted	restrict	VERB
ejpam-3342	75	79	to	to	ADP
ejpam-3342	75	80	[	[	X
ejpam-3342	75	81	kerq1/2]⊥	kerq1/2]⊥	PROPN
ejpam-3342	75	82	is	be	AUX
ejpam-3342	75	83	a	a	DET
ejpam-3342	75	84	separable	separable	ADJ
ejpam-3342	75	85	hilbert	hilbert	NOUN
ejpam-3342	75	86	space	space	NOUN
ejpam-3342	75	87	with	with	ADP
ejpam-3342	75	88	{	{	PUNCT
ejpam-3342	75	89	√	√	PROPN
ejpam-3342	75	90	λjej	λjej	NOUN
ejpam-3342	75	91	}	}	PUNCT
ejpam-3342	75	92	as	as	ADP
ejpam-3342	75	93	its	its	PRON
ejpam-3342	75	94	onb	onb	ADJ
ejpam-3342	75	95	,	,	PUNCT
ejpam-3342	75	96	see	see	VERB
ejpam-3342	75	97	[	[	X
ejpam-3342	75	98	18	18	NUM
ejpam-3342	75	99	,	,	PUNCT
ejpam-3342	75	100	p.90	p.90	PROPN
ejpam-3342	75	101	]	]	PUNCT
ejpam-3342	75	102	,	,	PUNCT
ejpam-3342	75	103	[	[	X
ejpam-3342	75	104	6	6	NUM
ejpam-3342	75	105	,	,	PUNCT
ejpam-3342	75	106	p.23	p.23	AUX
ejpam-3342	75	107	]	]	PUNCT
ejpam-3342	75	108	.	.	PUNCT
ejpam-3342	76	1	let	let	AUX
ejpam-3342	76	2	{	{	PUNCT
ejpam-3342	76	3	fj	fj	PART
ejpam-3342	76	4	}	}	PUNCT
ejpam-3342	76	5	be	be	AUX
ejpam-3342	76	6	an	an	DET
ejpam-3342	76	7	onb	onb	ADJ
ejpam-3342	76	8	in	in	ADP
ejpam-3342	76	9	uq	uq	NOUN
ejpam-3342	76	10	.	.	PUNCT
ejpam-3342	77	1	an	an	DET
ejpam-3342	77	2	operator	operator	NOUN
ejpam-3342	77	3	s	s	PART
ejpam-3342	77	4	∈	∈	PROPN
ejpam-3342	77	5	l(uq	l(uq	PROPN
ejpam-3342	77	6	,	,	PUNCT
ejpam-3342	77	7	v	v	NOUN
ejpam-3342	77	8	)	)	PUNCT
ejpam-3342	77	9	is	be	AUX
ejpam-3342	77	10	said	say	VERB
ejpam-3342	77	11	to	to	PART
ejpam-3342	77	12	be	be	AUX
ejpam-3342	77	13	hilbert	hilbert	NOUN
ejpam-3342	77	14	-	-	PUNCT
ejpam-3342	77	15	schmidt	schmidt	ADJ
ejpam-3342	77	16	if∑∞	if∑∞	NOUN
ejpam-3342	77	17	j=1	j=1	NOUN
ejpam-3342	77	18	‖sfj‖	‖sfj‖	PUNCT
ejpam-3342	77	19	2	2	NUM
ejpam-3342	77	20	v	v	NOUN
ejpam-3342	77	21	=	=	PUNCT
ejpam-3342	77	22	∑∞	∑∞	NOUN
ejpam-3342	77	23	j=1	j=1	PROPN
ejpam-3342	77	24	〈	〈	PROPN
ejpam-3342	77	25	sfj	sfj	NOUN
ejpam-3342	77	26	,	,	PUNCT
ejpam-3342	77	27	sfj〉v	sfj〉v	PROPN
ejpam-3342	77	28	<	<	X
ejpam-3342	77	29	∞.	∞.	PROPN
ejpam-3342	77	30	denote	denote	VERB
ejpam-3342	77	31	by	by	ADP
ejpam-3342	77	32	l2(uq	l2(uq	PROPN
ejpam-3342	77	33	,	,	PUNCT
ejpam-3342	77	34	v	v	NOUN
ejpam-3342	77	35	)	)	PUNCT
ejpam-3342	77	36	the	the	DET
ejpam-3342	77	37	space	space	NOUN
ejpam-3342	77	38	of	of	ADP
ejpam-3342	77	39	all	all	DET
ejpam-3342	77	40	hilbertschmidt	hilbertschmidt	ADJ
ejpam-3342	77	41	operators	operator	NOUN
ejpam-3342	77	42	from	from	ADP
ejpam-3342	77	43	uq	uq	NOUN
ejpam-3342	77	44	to	to	ADP
ejpam-3342	77	45	v	v	NOUN
ejpam-3342	77	46	,	,	PUNCT
ejpam-3342	77	47	which	which	PRON
ejpam-3342	77	48	is	be	AUX
ejpam-3342	77	49	known	know	VERB
ejpam-3342	77	50	[	[	X
ejpam-3342	77	51	19	19	NUM
ejpam-3342	77	52	,	,	PUNCT
ejpam-3342	77	53	p.112	p.112	NOUN
ejpam-3342	77	54	]	]	PUNCT
ejpam-3342	77	55	to	to	PART
ejpam-3342	77	56	be	be	AUX
ejpam-3342	77	57	a	a	DET
ejpam-3342	77	58	separable	separable	ADJ
ejpam-3342	77	59	hilbert	hilbert	NOUN
ejpam-3342	77	60	space	space	NOUN
ejpam-3342	77	61	with	with	ADP
ejpam-3342	77	62	norm	norm	NOUN
ejpam-3342	77	63	‖s‖l2(uq	‖s‖l2(uq	NOUN
ejpam-3342	77	64	,	,	PUNCT
ejpam-3342	77	65	v	v	NOUN
ejpam-3342	77	66	)	)	PUNCT
ejpam-3342	77	67	=	=	SYM
ejpam-3342	77	68	√∑∞	√∑∞	VERB
ejpam-3342	77	69	j=1	j=1	NOUN
ejpam-3342	77	70	‖sfj‖	‖sfj‖	PUNCT
ejpam-3342	77	71	2	2	NUM
ejpam-3342	77	72	v	v	NOUN
ejpam-3342	77	73	.	.	PUNCT
ejpam-3342	78	1	the	the	DET
ejpam-3342	78	2	hilbert	hilbert	PROPN
ejpam-3342	78	3	-	-	PUNCT
ejpam-3342	78	4	schmidt	schmidt	NOUN
ejpam-3342	78	5	operator	operator	NOUN
ejpam-3342	78	6	s	s	PART
ejpam-3342	78	7	∈	∈	PROPN
ejpam-3342	78	8	l2(uq	l2(uq	PROPN
ejpam-3342	78	9	,	,	PUNCT
ejpam-3342	78	10	v	v	NOUN
ejpam-3342	78	11	)	)	PUNCT
ejpam-3342	78	12	and	and	CCONJ
ejpam-3342	78	13	the	the	DET
ejpam-3342	78	14	norm	norm	NOUN
ejpam-3342	78	15	‖s‖l2(uq	‖s‖l2(uq	NOUN
ejpam-3342	78	16	,	,	PUNCT
ejpam-3342	78	17	v	v	NOUN
ejpam-3342	78	18	)	)	PUNCT
ejpam-3342	78	19	may	may	AUX
ejpam-3342	78	20	be	be	AUX
ejpam-3342	78	21	defined	define	VERB
ejpam-3342	78	22	in	in	ADP
ejpam-3342	78	23	terms	term	NOUN
ejpam-3342	78	24	of	of	ADP
ejpam-3342	78	25	an	an	DET
ejpam-3342	78	26	arbitrary	arbitrary	ADJ
ejpam-3342	78	27	onb	onb	ADJ
ejpam-3342	78	28	,	,	PUNCT
ejpam-3342	78	29	see	see	VERB
ejpam-3342	78	30	[	[	X
ejpam-3342	78	31	18	18	NUM
ejpam-3342	78	32	,	,	PUNCT
ejpam-3342	78	33	p.418	p.418	NOUN
ejpam-3342	78	34	]	]	X
ejpam-3342	78	35	,	,	PUNCT
ejpam-3342	78	36	[	[	X
ejpam-3342	78	37	19	19	NUM
ejpam-3342	78	38	,	,	PUNCT
ejpam-3342	78	39	p.111	p.111	ADJ
ejpam-3342	78	40	]	]	PUNCT
ejpam-3342	78	41	.	.	PUNCT
ejpam-3342	79	1	it	it	PRON
ejpam-3342	79	2	is	be	AUX
ejpam-3342	79	3	shown	show	VERB
ejpam-3342	79	4	in	in	ADP
ejpam-3342	79	5	[	[	X
ejpam-3342	79	6	6	6	NUM
ejpam-3342	79	7	,	,	PUNCT
ejpam-3342	79	8	p.25	p.25	NOUN
ejpam-3342	79	9	]	]	PUNCT
ejpam-3342	79	10	that	that	SCONJ
ejpam-3342	79	11	l(u	l(u	PROPN
ejpam-3342	79	12	,	,	PUNCT
ejpam-3342	79	13	v	v	NOUN
ejpam-3342	79	14	)	)	PUNCT
ejpam-3342	79	15	is	be	AUX
ejpam-3342	79	16	properly	properly	ADV
ejpam-3342	79	17	contained	contain	VERB
ejpam-3342	79	18	in	in	ADP
ejpam-3342	79	19	l2(uq	l2(uq	PROPN
ejpam-3342	79	20	,	,	PUNCT
ejpam-3342	79	21	v	v	NOUN
ejpam-3342	79	22	)	)	PUNCT
ejpam-3342	79	23	.	.	PUNCT
ejpam-3342	80	1	we	we	PRON
ejpam-3342	80	2	fix	fix	VERB
ejpam-3342	80	3	an	an	DET
ejpam-3342	80	4	element	element	NOUN
ejpam-3342	80	5	q	q	PROPN
ejpam-3342	80	6	∈	∈	PROPN
ejpam-3342	80	7	l(u	l(u	PROPN
ejpam-3342	80	8	)	)	PUNCT
ejpam-3342	80	9	,	,	PUNCT
ejpam-3342	80	10	symmetric	symmetric	ADJ
ejpam-3342	80	11	nonnegative	nonnegative	ADJ
ejpam-3342	80	12	definite	definite	ADJ
ejpam-3342	80	13	trace	trace	NOUN
ejpam-3342	80	14	-	-	PUNCT
ejpam-3342	80	15	class	class	NOUN
ejpam-3342	80	16	operator	operator	NOUN
ejpam-3342	80	17	.	.	PUNCT
ejpam-3342	81	1	a	a	DET
ejpam-3342	81	2	u	u	NOUN
ejpam-3342	81	3	-valued	-value	VERB
ejpam-3342	81	4	stochastic	stochastic	ADJ
ejpam-3342	81	5	process	process	NOUN
ejpam-3342	81	6	wt	wt	NOUN
ejpam-3342	81	7	,	,	PUNCT
ejpam-3342	81	8	t	t	PROPN
ejpam-3342	81	9	∈	∈	PROPN
ejpam-3342	82	1	[	[	X
ejpam-3342	82	2	0	0	NUM
ejpam-3342	82	3	,	,	PUNCT
ejpam-3342	82	4	t	t	X
ejpam-3342	82	5	]	]	PUNCT
ejpam-3342	82	6	,	,	PUNCT
ejpam-3342	82	7	on	on	ADP
ejpam-3342	82	8	a	a	DET
ejpam-3342	82	9	probability	probability	NOUN
ejpam-3342	82	10	space	space	NOUN
ejpam-3342	82	11	(	(	PUNCT
ejpam-3342	82	12	ω	ω	NOUN
ejpam-3342	82	13	,	,	PUNCT
ejpam-3342	82	14	g	g	PROPN
ejpam-3342	82	15	,	,	PUNCT
ejpam-3342	82	16	p	p	NOUN
ejpam-3342	82	17	)	)	PUNCT
ejpam-3342	82	18	is	be	AUX
ejpam-3342	82	19	called	call	VERB
ejpam-3342	82	20	a	a	DET
ejpam-3342	82	21	q	q	ADJ
ejpam-3342	82	22	-	-	PUNCT
ejpam-3342	82	23	wiener	wiener	NOUN
ejpam-3342	82	24	process	process	NOUN
ejpam-3342	82	25	in	in	ADP
ejpam-3342	82	26	u	u	PRON
ejpam-3342	82	27	if	if	SCONJ
ejpam-3342	82	28	:	:	PUNCT
ejpam-3342	82	29	(	(	PUNCT
ejpam-3342	82	30	i	i	NOUN
ejpam-3342	82	31	)	)	PUNCT
ejpam-3342	82	32	w	w	PROPN
ejpam-3342	82	33	(	(	PUNCT
ejpam-3342	82	34	0	0	NUM
ejpam-3342	82	35	,	,	PUNCT
ejpam-3342	82	36	ω	ω	NOUN
ejpam-3342	82	37	)	)	PUNCT
ejpam-3342	82	38	=	=	VERB
ejpam-3342	83	1	0u	0u	ADJ
ejpam-3342	83	2	for	for	ADP
ejpam-3342	83	3	each	each	DET
ejpam-3342	83	4	ω	ω	PROPN
ejpam-3342	83	5	∈	∈	PROPN
ejpam-3342	83	6	ω	ω	PROPN
ejpam-3342	83	7	,	,	PUNCT
ejpam-3342	83	8	(	(	PUNCT
ejpam-3342	83	9	ii	ii	NOUN
ejpam-3342	83	10	)	)	PUNCT
ejpam-3342	83	11	w	w	PROPN
ejpam-3342	83	12	has	have	VERB
ejpam-3342	83	13	p	p	NOUN
ejpam-3342	83	14	-	-	PUNCT
ejpam-3342	83	15	almost	almost	ADV
ejpam-3342	83	16	surely	surely	ADV
ejpam-3342	83	17	(	(	PUNCT
ejpam-3342	83	18	abbrev	abbrev	X
ejpam-3342	83	19	.	.	PUNCT
ejpam-3342	84	1	as	as	ADP
ejpam-3342	84	2	p	p	PROPN
ejpam-3342	84	3	-	-	PUNCT
ejpam-3342	84	4	a.s	a.s	PROPN
ejpam-3342	84	5	.	.	PROPN
ejpam-3342	84	6	)	)	PUNCT
ejpam-3342	84	7	continuous	continuous	ADJ
ejpam-3342	84	8	trajectories	trajectory	NOUN
ejpam-3342	84	9	,	,	PUNCT
ejpam-3342	84	10	i.e.	i.e.	X
ejpam-3342	84	11	,	,	PUNCT
ejpam-3342	84	12	w	w	PROPN
ejpam-3342	84	13	(	(	PUNCT
ejpam-3342	84	14	·	·	PUNCT
ejpam-3342	84	15	,	,	PUNCT
ejpam-3342	84	16	ω	ω	NUM
ejpam-3342	84	17	)	)	PUNCT
ejpam-3342	84	18	:	:	PUNCT
ejpam-3342	85	1	[	[	X
ejpam-3342	85	2	0	0	NUM
ejpam-3342	85	3	,	,	PUNCT
ejpam-3342	85	4	t	t	X
ejpam-3342	85	5	]	]	PUNCT
ejpam-3342	85	6	→	→	SYM
ejpam-3342	85	7	u	u	PROPN
ejpam-3342	85	8	is	be	AUX
ejpam-3342	85	9	p	p	PROPN
ejpam-3342	85	10	-	-	PUNCT
ejpam-3342	85	11	a.s	a.s	NOUN
ejpam-3342	85	12	.	.	PROPN
ejpam-3342	85	13	continuous	continuous	ADJ
ejpam-3342	85	14	(	(	PUNCT
ejpam-3342	85	15	iii	iii	NOUN
ejpam-3342	85	16	)	)	PUNCT
ejpam-3342	85	17	the	the	DET
ejpam-3342	85	18	increments	increment	NOUN
ejpam-3342	85	19	of	of	ADP
ejpam-3342	85	20	w	w	PROPN
ejpam-3342	85	21	are	be	AUX
ejpam-3342	85	22	independent	independent	ADJ
ejpam-3342	85	23	,	,	PUNCT
ejpam-3342	85	24	i.e.	i.e.	X
ejpam-3342	85	25	the	the	DET
ejpam-3342	85	26	random	random	ADJ
ejpam-3342	85	27	variables	variable	NOUN
ejpam-3342	85	28	wt1	wt1	VERB
ejpam-3342	85	29	,	,	PUNCT
ejpam-3342	85	30	wt2	wt2	VERB
ejpam-3342	85	31	−wt1	−wt1	PRON
ejpam-3342	85	32	,	,	PUNCT
ejpam-3342	85	33	wt3	wt3	NOUN
ejpam-3342	85	34	−wt2	−wt2	NOUN
ejpam-3342	85	35	,	,	PUNCT
ejpam-3342	85	36	.	.	PUNCT
ejpam-3342	85	37	.	.	PUNCT
ejpam-3342	85	38	.	.	PUNCT
ejpam-3342	86	1	,	,	PUNCT
ejpam-3342	86	2	wtn	wtn	NOUN
ejpam-3342	86	3	−wtn−1	−wtn−1	PROPN
ejpam-3342	86	4	are	be	AUX
ejpam-3342	86	5	independent	independent	ADJ
ejpam-3342	86	6	for	for	ADP
ejpam-3342	86	7	all	all	DET
ejpam-3342	86	8	0	0	NUM
ejpam-3342	86	9	≤	≤	NUM
ejpam-3342	86	10	t1	t1	NOUN
ejpam-3342	86	11	<	<	X
ejpam-3342	86	12	·	·	PUNCT
ejpam-3342	86	13	·	·	PUNCT
ejpam-3342	86	14	·	·	PUNCT
ejpam-3342	87	1	<	<	X
ejpam-3342	87	2	tn	tn	PROPN
ejpam-3342	87	3	≤	≤	PROPN
ejpam-3342	87	4	t	t	NOUN
ejpam-3342	87	5	,	,	PUNCT
ejpam-3342	87	6	n	n	PROPN
ejpam-3342	87	7	∈	∈	PROPN
ejpam-3342	87	8	n	n	PROPN
ejpam-3342	87	9	,	,	PUNCT
ejpam-3342	87	10	r.	r.	PROPN
ejpam-3342	87	11	rulete	rulete	PROPN
ejpam-3342	87	12	,	,	PUNCT
ejpam-3342	87	13	m.	m.	NOUN
ejpam-3342	87	14	labendia	labendia	PROPN
ejpam-3342	87	15	/	/	SYM
ejpam-3342	87	16	eur	eur	PROPN
ejpam-3342	87	17	.	.	PUNCT
ejpam-3342	88	1	j.	j.	PROPN
ejpam-3342	88	2	pure	pure	PROPN
ejpam-3342	88	3	appl	appl	PROPN
ejpam-3342	88	4	.	.	PROPN
ejpam-3342	88	5	math	math	PROPN
ejpam-3342	88	6	,	,	PUNCT
ejpam-3342	88	7	12	12	NUM
ejpam-3342	88	8	(	(	PUNCT
ejpam-3342	88	9	1	1	NUM
ejpam-3342	88	10	)	)	PUNCT
ejpam-3342	88	11	(	(	PUNCT
ejpam-3342	88	12	2019	2019	NUM
ejpam-3342	88	13	)	)	PUNCT
ejpam-3342	88	14	,	,	PUNCT
ejpam-3342	88	15	58	58	NUM
ejpam-3342	88	16	-	-	SYM
ejpam-3342	88	17	78	78	NUM
ejpam-3342	88	18	61	61	NUM
ejpam-3342	88	19	(	(	PUNCT
ejpam-3342	88	20	iv	iv	X
ejpam-3342	88	21	)	)	PUNCT
ejpam-3342	88	22	the	the	DET
ejpam-3342	88	23	increments	increment	NOUN
ejpam-3342	88	24	have	have	VERB
ejpam-3342	88	25	the	the	DET
ejpam-3342	88	26	following	follow	VERB
ejpam-3342	88	27	gaussian	gaussian	ADJ
ejpam-3342	88	28	laws	law	NOUN
ejpam-3342	88	29	:	:	PUNCT
ejpam-3342	88	30	p	p	X
ejpam-3342	88	31	◦	◦	NOUN
ejpam-3342	88	32	(	(	PUNCT
ejpam-3342	88	33	wt	wt	NOUN
ejpam-3342	88	34	−ws	−ws	NOUN
ejpam-3342	88	35	)	)	PUNCT
ejpam-3342	88	36	−1	−1	NOUN
ejpam-3342	88	37	=	=	SYM
ejpam-3342	88	38	n	n	CCONJ
ejpam-3342	88	39	(	(	PUNCT
ejpam-3342	88	40	0	0	NUM
ejpam-3342	88	41	,	,	PUNCT
ejpam-3342	88	42	(	(	PUNCT
ejpam-3342	88	43	t−	t−	NOUN
ejpam-3342	88	44	s)q	s)q	NOUN
ejpam-3342	88	45	)	)	PUNCT
ejpam-3342	88	46	for	for	ADP
ejpam-3342	88	47	all	all	PRON
ejpam-3342	88	48	0	0	NUM
ejpam-3342	88	49	≤	≤	NUM
ejpam-3342	88	50	s	s	PART
ejpam-3342	88	51	≤	≤	NUM
ejpam-3342	88	52	t	t	NOUN
ejpam-3342	88	53	≤	≤	PROPN
ejpam-3342	88	54	t	t	PROPN
ejpam-3342	88	55	.	.	PUNCT
ejpam-3342	89	1	by	by	ADP
ejpam-3342	89	2	proposition	proposition	NOUN
ejpam-3342	89	3	4.2	4.2	NUM
ejpam-3342	89	4	(	(	PUNCT
ejpam-3342	89	5	see	see	VERB
ejpam-3342	89	6	[	[	X
ejpam-3342	89	7	18	18	NUM
ejpam-3342	89	8	,	,	PUNCT
ejpam-3342	89	9	p.88	p.88	PROPN
ejpam-3342	89	10	]	]	X
ejpam-3342	89	11	)	)	PUNCT
ejpam-3342	89	12	,	,	PUNCT
ejpam-3342	89	13	such	such	DET
ejpam-3342	89	14	a	a	DET
ejpam-3342	89	15	q	q	ADJ
ejpam-3342	89	16	-	-	PUNCT
ejpam-3342	89	17	wiener	wiener	NOUN
ejpam-3342	89	18	process	process	NOUN
ejpam-3342	89	19	exists	exist	VERB
ejpam-3342	89	20	.	.	PUNCT
ejpam-3342	90	1	we	we	PRON
ejpam-3342	90	2	define	define	VERB
ejpam-3342	90	3	n	n	NOUN
ejpam-3342	90	4	:	:	PUNCT
ejpam-3342	90	5	=	=	SYM
ejpam-3342	90	6	{	{	PUNCT
ejpam-3342	90	7	a	a	DET
ejpam-3342	90	8	∈	∈	PROPN
ejpam-3342	90	9	g	g	PROPN
ejpam-3342	90	10	|	|	NOUN
ejpam-3342	90	11	p(a	p(a	PROPN
ejpam-3342	90	12	)	)	PUNCT
ejpam-3342	90	13	=	=	PUNCT
ejpam-3342	90	14	0	0	NUM
ejpam-3342	90	15	}	}	PUNCT
ejpam-3342	90	16	,	,	PUNCT
ejpam-3342	90	17	g̃t	g̃t	PROPN
ejpam-3342	90	18	:	:	PUNCT
ejpam-3342	90	19	=	=	PUNCT
ejpam-3342	90	20	σ(wt	σ(wt	NOUN
ejpam-3342	90	21	−ws	−ws	DET
ejpam-3342	90	22	|	|	NOUN
ejpam-3342	90	23	t	t	X
ejpam-3342	90	24	≤	≤	NUM
ejpam-3342	90	25	s	s	PART
ejpam-3342	90	26	≤	≤	PROPN
ejpam-3342	90	27	t	t	NOUN
ejpam-3342	90	28	)	)	PUNCT
ejpam-3342	90	29	,	,	PUNCT
ejpam-3342	90	30	g̃0	g̃0	PROPN
ejpam-3342	90	31	t	t	PROPN
ejpam-3342	90	32	:	:	PUNCT
ejpam-3342	90	33	=	=	SYM
ejpam-3342	90	34	σ(g̃t	σ(g̃t	ADJ
ejpam-3342	90	35	∪	∪	X
ejpam-3342	90	36	n	n	PROPN
ejpam-3342	90	37	)	)	PUNCT
ejpam-3342	90	38	and	and	CCONJ
ejpam-3342	90	39	gt	gt	INTJ
ejpam-3342	90	40	:	:	PUNCT
ejpam-3342	91	1	=	=	SYM
ejpam-3342	91	2	⋂	⋂	PROPN
ejpam-3342	91	3	s	s	X
ejpam-3342	91	4	<	<	X
ejpam-3342	91	5	t	t	X
ejpam-3342	91	6	g̃0	g̃0	PROPN
ejpam-3342	91	7	s	s	PROPN
ejpam-3342	91	8	,	,	PUNCT
ejpam-3342	91	9	t	t	PROPN
ejpam-3342	91	10	∈	∈	PROPN
ejpam-3342	92	1	[	[	X
ejpam-3342	92	2	0	0	NUM
ejpam-3342	92	3	,	,	PUNCT
ejpam-3342	92	4	t	t	X
ejpam-3342	92	5	]	]	PUNCT
ejpam-3342	92	6	.	.	PUNCT
ejpam-3342	93	1	(	(	PUNCT
ejpam-3342	93	2	1	1	X
ejpam-3342	93	3	)	)	PUNCT
ejpam-3342	93	4	since	since	SCONJ
ejpam-3342	93	5	n	n	ADV
ejpam-3342	93	6	⊆	⊆	NUM
ejpam-3342	93	7	g̃0	g̃0	PROPN
ejpam-3342	93	8	s	s	PROPN
ejpam-3342	93	9	for	for	ADP
ejpam-3342	93	10	all	all	DET
ejpam-3342	93	11	s	s	PART
ejpam-3342	93	12	∈	∈	NOUN
ejpam-3342	94	1	[	[	X
ejpam-3342	94	2	0	0	NUM
ejpam-3342	94	3	,	,	PUNCT
ejpam-3342	94	4	t	t	NOUN
ejpam-3342	94	5	]	]	PUNCT
ejpam-3342	94	6	and	and	CCONJ
ejpam-3342	94	7	{	{	PUNCT
ejpam-3342	94	8	gt}0≤t≤t	gt}0≤t≤t	NOUN
ejpam-3342	94	9	is	be	AUX
ejpam-3342	94	10	decreasing	decrease	VERB
ejpam-3342	94	11	,	,	PUNCT
ejpam-3342	94	12	we	we	PRON
ejpam-3342	94	13	have	have	VERB
ejpam-3342	94	14	the	the	DET
ejpam-3342	94	15	following	follow	VERB
ejpam-3342	94	16	result	result	NOUN
ejpam-3342	94	17	:	:	PUNCT
ejpam-3342	94	18	proposition	proposition	NOUN
ejpam-3342	94	19	1	1	X
ejpam-3342	94	20	.	.	PUNCT
ejpam-3342	95	1	let	let	VERB
ejpam-3342	95	2	t	t	PROPN
ejpam-3342	95	3	∈	∈	PROPN
ejpam-3342	96	1	[	[	X
ejpam-3342	96	2	0	0	NUM
ejpam-3342	96	3	,	,	PUNCT
ejpam-3342	96	4	t	t	X
ejpam-3342	96	5	]	]	PUNCT
ejpam-3342	96	6	.	.	PUNCT
ejpam-3342	97	1	then	then	ADV
ejpam-3342	97	2	the	the	DET
ejpam-3342	97	3	filtration	filtration	NOUN
ejpam-3342	97	4	gt	gt	PROPN
ejpam-3342	97	5	given	give	VERB
ejpam-3342	97	6	in	in	ADP
ejpam-3342	97	7	(	(	PUNCT
ejpam-3342	97	8	1	1	NUM
ejpam-3342	97	9	)	)	PUNCT
ejpam-3342	97	10	is	be	AUX
ejpam-3342	97	11	a	a	DET
ejpam-3342	97	12	standard	standard	ADJ
ejpam-3342	97	13	backwards	backwards	ADV
ejpam-3342	97	14	filtration	filtration	NOUN
ejpam-3342	97	15	.	.	PUNCT
ejpam-3342	98	1	we	we	PRON
ejpam-3342	98	2	note	note	VERB
ejpam-3342	98	3	that	that	SCONJ
ejpam-3342	98	4	the	the	DET
ejpam-3342	98	5	distance	distance	NOUN
ejpam-3342	98	6	from	from	ADP
ejpam-3342	98	7	an	an	DET
ejpam-3342	98	8	element	element	NOUN
ejpam-3342	98	9	u	u	NOUN
ejpam-3342	98	10	∈	∈	PROPN
ejpam-3342	98	11	u	u	NOUN
ejpam-3342	98	12	to	to	ADP
ejpam-3342	98	13	a	a	DET
ejpam-3342	98	14	nonempty	nonempty	NOUN
ejpam-3342	98	15	subset	subset	VERB
ejpam-3342	98	16	a	a	DET
ejpam-3342	98	17	⊂	⊂	PROPN
ejpam-3342	98	18	u	u	NOUN
ejpam-3342	98	19	,	,	PUNCT
ejpam-3342	98	20	denoted	denote	VERB
ejpam-3342	98	21	by	by	ADP
ejpam-3342	98	22	dist(u	dist(u	PROPN
ejpam-3342	98	23	,	,	PUNCT
ejpam-3342	98	24	a	a	PRON
ejpam-3342	98	25	)	)	PUNCT
ejpam-3342	98	26	is	be	AUX
ejpam-3342	98	27	defined	define	VERB
ejpam-3342	98	28	to	to	PART
ejpam-3342	98	29	be	be	AUX
ejpam-3342	98	30	dist(u	dist(u	PROPN
ejpam-3342	98	31	,	,	PUNCT
ejpam-3342	98	32	a	a	PRON
ejpam-3342	98	33	)	)	PUNCT
ejpam-3342	98	34	=	=	SYM
ejpam-3342	98	35	inf	inf	PROPN
ejpam-3342	98	36	a∈a	a∈a	ADJ
ejpam-3342	98	37	||u−	||u−	PROPN
ejpam-3342	98	38	a||u	a||u	PROPN
ejpam-3342	98	39	.	.	PUNCT
ejpam-3342	99	1	proposition	proposition	NOUN
ejpam-3342	99	2	2	2	NUM
ejpam-3342	99	3	.	.	PUNCT
ejpam-3342	100	1	let	let	VERB
ejpam-3342	100	2	wt	wt	VERB
ejpam-3342	100	3	,	,	PUNCT
ejpam-3342	100	4	t	t	PROPN
ejpam-3342	100	5	∈	∈	PROPN
ejpam-3342	101	1	[	[	X
ejpam-3342	101	2	0	0	NUM
ejpam-3342	101	3	,	,	PUNCT
ejpam-3342	101	4	t	t	X
ejpam-3342	101	5	]	]	PUNCT
ejpam-3342	101	6	,	,	PUNCT
ejpam-3342	101	7	be	be	AUX
ejpam-3342	101	8	an	an	DET
ejpam-3342	101	9	arbitrary	arbitrary	ADJ
ejpam-3342	101	10	u	u	NOUN
ejpam-3342	101	11	-valued	-valued	ADJ
ejpam-3342	101	12	q	q	ADJ
ejpam-3342	101	13	-	-	PUNCT
ejpam-3342	101	14	wiener	wiener	NOUN
ejpam-3342	101	15	process	process	NOUN
ejpam-3342	101	16	on	on	ADP
ejpam-3342	101	17	a	a	DET
ejpam-3342	101	18	probability	probability	NOUN
ejpam-3342	101	19	space	space	NOUN
ejpam-3342	101	20	(	(	PUNCT
ejpam-3342	101	21	ω	ω	NOUN
ejpam-3342	101	22	,	,	PUNCT
ejpam-3342	101	23	g	g	PROPN
ejpam-3342	101	24	,	,	PUNCT
ejpam-3342	101	25	p	p	NOUN
ejpam-3342	101	26	)	)	PUNCT
ejpam-3342	101	27	.	.	PUNCT
ejpam-3342	102	1	then	then	ADV
ejpam-3342	102	2	wt	wt	X
ejpam-3342	102	3	−ws	−ws	PROPN
ejpam-3342	102	4	is	be	AUX
ejpam-3342	102	5	independent	independent	ADJ
ejpam-3342	102	6	of	of	ADP
ejpam-3342	102	7	gt	gt	PROPN
ejpam-3342	102	8	for	for	ADP
ejpam-3342	102	9	all	all	DET
ejpam-3342	102	10	0	0	NUM
ejpam-3342	102	11	≤	≤	NUM
ejpam-3342	102	12	s	s	PART
ejpam-3342	102	13	≤	≤	NUM
ejpam-3342	102	14	t	t	PROPN
ejpam-3342	102	15	≤	≤	PROPN
ejpam-3342	102	16	t	t	NOUN
ejpam-3342	102	17	,	,	PUNCT
ejpam-3342	102	18	where	where	SCONJ
ejpam-3342	102	19	gt	gt	PROPN
ejpam-3342	102	20	is	be	AUX
ejpam-3342	102	21	given	give	VERB
ejpam-3342	102	22	in	in	ADP
ejpam-3342	102	23	(	(	PUNCT
ejpam-3342	102	24	1	1	NUM
ejpam-3342	102	25	)	)	PUNCT
ejpam-3342	102	26	.	.	PUNCT
ejpam-3342	103	1	proof	proof	NOUN
ejpam-3342	103	2	.	.	PUNCT
ejpam-3342	104	1	let	let	VERB
ejpam-3342	104	2	0	0	NUM
ejpam-3342	104	3	≤	≤	NUM
ejpam-3342	104	4	s	s	PART
ejpam-3342	104	5	≤	≤	NUM
ejpam-3342	104	6	t	t	NOUN
ejpam-3342	104	7	≤	≤	PROPN
ejpam-3342	104	8	t	t	PROPN
ejpam-3342	104	9	.	.	PUNCT
ejpam-3342	105	1	since	since	SCONJ
ejpam-3342	105	2	a	a	DET
ejpam-3342	105	3	u	u	NOUN
ejpam-3342	105	4	-valued	-valued	ADJ
ejpam-3342	105	5	q	q	ADJ
ejpam-3342	105	6	-	-	PUNCT
ejpam-3342	105	7	wiener	wiener	NOUN
ejpam-3342	105	8	process	process	NOUN
ejpam-3342	105	9	has	have	VERB
ejpam-3342	105	10	independent	independent	ADJ
ejpam-3342	105	11	increments	increment	NOUN
ejpam-3342	105	12	,	,	PUNCT
ejpam-3342	105	13	wt−ws	wt−ws	NOUN
ejpam-3342	105	14	and	and	CCONJ
ejpam-3342	105	15	wt	wt	PROPN
ejpam-3342	105	16	−wt	−wt	NOUN
ejpam-3342	105	17	are	be	AUX
ejpam-3342	105	18	independent	independent	ADJ
ejpam-3342	105	19	.	.	PUNCT
ejpam-3342	106	1	it	it	PRON
ejpam-3342	106	2	follows	follow	VERB
ejpam-3342	106	3	that	that	SCONJ
ejpam-3342	106	4	wt−ws	wt−ws	NOUN
ejpam-3342	107	1	and	and	CCONJ
ejpam-3342	107	2	wt	wt	SCONJ
ejpam-3342	107	3	−w	−w	ADV
ejpam-3342	107	4	′t	′t	PROPN
ejpam-3342	107	5	are	be	AUX
ejpam-3342	107	6	independent	independent	ADJ
ejpam-3342	107	7	for	for	ADP
ejpam-3342	107	8	all	all	DET
ejpam-3342	107	9	t	t	NOUN
ejpam-3342	107	10	≤	≤	NUM
ejpam-3342	107	11	t′	t′	NUM
ejpam-3342	107	12	≤	≤	NOUN
ejpam-3342	107	13	t	t	PROPN
ejpam-3342	107	14	.	.	PUNCT
ejpam-3342	108	1	hence	hence	ADV
ejpam-3342	108	2	,	,	PUNCT
ejpam-3342	108	3	wt−ws	wt−ws	X
ejpam-3342	108	4	is	be	AUX
ejpam-3342	108	5	independent	independent	ADJ
ejpam-3342	108	6	of	of	ADP
ejpam-3342	108	7	σ(wt	σ(wt	PROPN
ejpam-3342	108	8	−w	−w	ADV
ejpam-3342	108	9	′t	′t	NOUN
ejpam-3342	108	10	:	:	PUNCT
ejpam-3342	108	11	t	t	X
ejpam-3342	108	12	≤	≤	NUM
ejpam-3342	108	13	t′	t′	NUM
ejpam-3342	108	14	≤	≤	PROPN
ejpam-3342	108	15	t	t	PROPN
ejpam-3342	108	16	)	)	PUNCT
ejpam-3342	109	1	=	=	SYM
ejpam-3342	109	2	g̃t	g̃t	PROPN
ejpam-3342	109	3	.	.	PUNCT
ejpam-3342	110	1	also	also	ADV
ejpam-3342	110	2	,	,	PUNCT
ejpam-3342	110	3	wt−ws	wt−ws	X
ejpam-3342	110	4	is	be	AUX
ejpam-3342	110	5	independent	independent	ADJ
ejpam-3342	110	6	of	of	ADP
ejpam-3342	110	7	g̃0	g̃0	PROPN
ejpam-3342	110	8	t	t	PROPN
ejpam-3342	110	9	.	.	PUNCT
ejpam-3342	111	1	to	to	PART
ejpam-3342	111	2	prove	prove	VERB
ejpam-3342	111	3	now	now	ADV
ejpam-3342	111	4	that	that	SCONJ
ejpam-3342	111	5	wt−ws	wt−ws	NOUN
ejpam-3342	111	6	is	be	AUX
ejpam-3342	111	7	independent	independent	ADJ
ejpam-3342	111	8	of	of	ADP
ejpam-3342	111	9	gt	gt	PROPN
ejpam-3342	111	10	it	it	PRON
ejpam-3342	111	11	is	be	AUX
ejpam-3342	111	12	enough	enough	ADJ
ejpam-3342	111	13	to	to	PART
ejpam-3342	111	14	show	show	VERB
ejpam-3342	111	15	that	that	SCONJ
ejpam-3342	111	16	p	p	X
ejpam-3342	111	17	(	(	PUNCT
ejpam-3342	111	18	{	{	PUNCT
ejpam-3342	111	19	wt	wt	ADP
ejpam-3342	111	20	−ws	−ws	PROPN
ejpam-3342	111	21	∈	∈	NOUN
ejpam-3342	111	22	a	a	DET
ejpam-3342	111	23	}	}	PUNCT
ejpam-3342	111	24	∩b	∩b	NOUN
ejpam-3342	111	25	)	)	PUNCT
ejpam-3342	111	26	=	=	PUNCT
ejpam-3342	111	27	p({wt	p({wt	VERB
ejpam-3342	111	28	−ws	−ws	PRON
ejpam-3342	111	29	∈	∈	PROPN
ejpam-3342	111	30	a	a	PRON
ejpam-3342	111	31	}	}	PUNCT
ejpam-3342	111	32	)	)	PUNCT
ejpam-3342	111	33	·	·	PUNCT
ejpam-3342	112	1	p(b	p(b	NOUN
ejpam-3342	112	2	)	)	PUNCT
ejpam-3342	112	3	for	for	ADP
ejpam-3342	112	4	any	any	DET
ejpam-3342	112	5	b	b	PROPN
ejpam-3342	112	6	∈	∈	PROPN
ejpam-3342	112	7	gt	gt	PROPN
ejpam-3342	112	8	and	and	CCONJ
ejpam-3342	112	9	any	any	DET
ejpam-3342	112	10	closed	closed	NOUN
ejpam-3342	112	11	subset	subset	VERB
ejpam-3342	112	12	a	a	DET
ejpam-3342	112	13	∈	∈	PROPN
ejpam-3342	112	14	u	u	NOUN
ejpam-3342	112	15	as	as	ADP
ejpam-3342	112	16	{	{	PUNCT
ejpam-3342	112	17	a	a	DET
ejpam-3342	112	18	⊂	⊂	X
ejpam-3342	112	19	u	u	NOUN
ejpam-3342	112	20	|	|	ADV
ejpam-3342	112	21	a	a	DET
ejpam-3342	112	22	closed	closed	ADJ
ejpam-3342	112	23	}	}	PUNCT
ejpam-3342	112	24	generates	generate	VERB
ejpam-3342	112	25	b(u	b(u	NOUN
ejpam-3342	112	26	)	)	PUNCT
ejpam-3342	112	27	and	and	CCONJ
ejpam-3342	112	28	is	be	AUX
ejpam-3342	112	29	stable	stable	ADJ
ejpam-3342	112	30	under	under	ADP
ejpam-3342	112	31	finite	finite	ADJ
ejpam-3342	112	32	intersection	intersection	NOUN
ejpam-3342	112	33	.	.	PUNCT
ejpam-3342	113	1	but	but	CCONJ
ejpam-3342	113	2	we	we	PRON
ejpam-3342	113	3	have	have	VERB
ejpam-3342	113	4	p	p	NOUN
ejpam-3342	113	5	(	(	PUNCT
ejpam-3342	113	6	{	{	PUNCT
ejpam-3342	113	7	wt	wt	ADP
ejpam-3342	113	8	−ws	−ws	PROPN
ejpam-3342	113	9	∈	∈	NOUN
ejpam-3342	113	10	a	a	DET
ejpam-3342	113	11	}	}	PUNCT
ejpam-3342	113	12	∩b	∩b	NOUN
ejpam-3342	113	13	)	)	PUNCT
ejpam-3342	114	1	=	=	SYM
ejpam-3342	114	2	e	e	X
ejpam-3342	114	3	[	[	PUNCT
ejpam-3342	114	4	1{wt−ws∈a	1{wt−ws∈a	NUM
ejpam-3342	114	5	}	}	PUNCT
ejpam-3342	114	6	·	·	PUNCT
ejpam-3342	114	7	1b	1b	X
ejpam-3342	114	8	]	]	PUNCT
ejpam-3342	115	1	=	=	PUNCT
ejpam-3342	115	2	e	e	X
ejpam-3342	115	3	[	[	X
ejpam-3342	115	4	1a	1a	NUM
ejpam-3342	115	5	◦	◦	NOUN
ejpam-3342	115	6	(	(	PUNCT
ejpam-3342	115	7	wt	wt	NOUN
ejpam-3342	115	8	−ws	−ws	NOUN
ejpam-3342	115	9	)	)	PUNCT
ejpam-3342	115	10	·	·	PUNCT
ejpam-3342	115	11	1b	1b	NUM
ejpam-3342	115	12	]	]	PUNCT
ejpam-3342	115	13	.	.	PUNCT
ejpam-3342	116	1	let	let	VERB
ejpam-3342	116	2	f	f	X
ejpam-3342	116	3	:	:	PUNCT
ejpam-3342	116	4	ω→	ω→	PUNCT
ejpam-3342	116	5	{	{	PUNCT
ejpam-3342	116	6	0	0	NUM
ejpam-3342	116	7	,	,	PUNCT
ejpam-3342	116	8	1	1	NUM
ejpam-3342	116	9	}	}	PUNCT
ejpam-3342	116	10	be	be	AUX
ejpam-3342	116	11	defined	define	VERB
ejpam-3342	116	12	by	by	ADP
ejpam-3342	116	13	f	f	PROPN
ejpam-3342	116	14	(	(	PUNCT
ejpam-3342	116	15	ω	ω	NOUN
ejpam-3342	116	16	)	)	PUNCT
ejpam-3342	117	1	=	=	SYM
ejpam-3342	117	2	lim	lim	PROPN
ejpam-3342	117	3	n→∞	n→∞	X
ejpam-3342	118	1	(	(	PUNCT
ejpam-3342	118	2	1−	1−	NUM
ejpam-3342	118	3	ndist((wt	ndist((wt	PROPN
ejpam-3342	118	4	−ws)(ω	−ws)(ω	NOUN
ejpam-3342	118	5	)	)	PUNCT
ejpam-3342	118	6	,	,	PUNCT
ejpam-3342	118	7	a	a	X
ejpam-3342	118	8	)	)	PUNCT
ejpam-3342	118	9	)	)	PUNCT
ejpam-3342	118	10	∨	∨	ADP
ejpam-3342	118	11	0	0	NUM
ejpam-3342	118	12	,	,	PUNCT
ejpam-3342	118	13	ω	ω	PROPN
ejpam-3342	118	14	∈	∈	PROPN
ejpam-3342	118	15	ω	ω	NUM
ejpam-3342	118	16	where	where	SCONJ
ejpam-3342	118	17	∨	∨	NUM
ejpam-3342	118	18	denotes	denote	NOUN
ejpam-3342	118	19	“	"	PUNCT
ejpam-3342	118	20	maximum	maximum	ADJ
ejpam-3342	118	21	”	"	PUNCT
ejpam-3342	118	22	.	.	PUNCT
ejpam-3342	119	1	let	let	VERB
ejpam-3342	120	1	ω	ω	NUM
ejpam-3342	120	2	∈	∈	PROPN
ejpam-3342	120	3	ω	ω	NOUN
ejpam-3342	120	4	.	.	PUNCT
ejpam-3342	121	1	if	if	SCONJ
ejpam-3342	121	2	(	(	PUNCT
ejpam-3342	121	3	wt	wt	ADP
ejpam-3342	121	4	−	−	PROPN
ejpam-3342	121	5	ws)(ω	ws)(ω	NOUN
ejpam-3342	121	6	)	)	PUNCT
ejpam-3342	121	7	∈	∈	PROPN
ejpam-3342	122	1	a	a	DET
ejpam-3342	122	2	,	,	PUNCT
ejpam-3342	122	3	then	then	ADV
ejpam-3342	122	4	dist((wt	dist((wt	PROPN
ejpam-3342	122	5	−	−	PROPN
ejpam-3342	122	6	ws)(ω	ws)(ω	PROPN
ejpam-3342	122	7	)	)	PUNCT
ejpam-3342	122	8	,	,	PUNCT
ejpam-3342	122	9	a	a	X
ejpam-3342	122	10	)	)	PUNCT
ejpam-3342	122	11	=	=	SYM
ejpam-3342	122	12	0	0	NUM
ejpam-3342	122	13	and	and	CCONJ
ejpam-3342	122	14	f	f	PROPN
ejpam-3342	122	15	(	(	PUNCT
ejpam-3342	122	16	ω	ω	NOUN
ejpam-3342	122	17	)	)	PUNCT
ejpam-3342	122	18	=	=	SYM
ejpam-3342	122	19	1	1	NUM
ejpam-3342	122	20	=	=	SYM
ejpam-3342	122	21	(	(	PUNCT
ejpam-3342	122	22	1a	1a	X
ejpam-3342	122	23	◦	◦	NOUN
ejpam-3342	122	24	wt−ws)(ω	wt−ws)(ω	NUM
ejpam-3342	122	25	)	)	PUNCT
ejpam-3342	122	26	.	.	PUNCT
ejpam-3342	123	1	otherwise	otherwise	ADV
ejpam-3342	123	2	,	,	PUNCT
ejpam-3342	123	3	dist((wt−ws)(ω	dist((wt−ws)(ω	NOUN
ejpam-3342	123	4	)	)	PUNCT
ejpam-3342	123	5	,	,	PUNCT
ejpam-3342	123	6	a	a	X
ejpam-3342	123	7	)	)	PUNCT
ejpam-3342	123	8	>	>	SYM
ejpam-3342	123	9	0	0	PUNCT
ejpam-3342	124	1	and	and	CCONJ
ejpam-3342	124	2	f	f	PROPN
ejpam-3342	124	3	(	(	PUNCT
ejpam-3342	124	4	ω	ω	NOUN
ejpam-3342	124	5	)	)	PUNCT
ejpam-3342	124	6	=	=	SYM
ejpam-3342	124	7	0	0	PUNCT
ejpam-3342	125	1	=	=	SYM
ejpam-3342	125	2	(	(	PUNCT
ejpam-3342	125	3	1a	1a	X
ejpam-3342	125	4	◦	◦	NOUN
ejpam-3342	125	5	wt	wt	NOUN
ejpam-3342	125	6	−ws)(ω	−ws)(ω	NOUN
ejpam-3342	125	7	)	)	PUNCT
ejpam-3342	125	8	.	.	PUNCT
ejpam-3342	126	1	hence	hence	ADV
ejpam-3342	126	2	,	,	PUNCT
ejpam-3342	126	3	1a	1a	X
ejpam-3342	126	4	◦	◦	NOUN
ejpam-3342	126	5	(	(	PUNCT
ejpam-3342	126	6	wt	wt	NOUN
ejpam-3342	126	7	−ws	−ws	NOUN
ejpam-3342	126	8	)	)	PUNCT
ejpam-3342	126	9	=	=	SYM
ejpam-3342	126	10	f	f	PROPN
ejpam-3342	126	11	.	.	PUNCT
ejpam-3342	127	1	so	so	ADV
ejpam-3342	127	2	,	,	PUNCT
ejpam-3342	127	3	we	we	PRON
ejpam-3342	127	4	have	have	VERB
ejpam-3342	127	5	p	p	NOUN
ejpam-3342	127	6	(	(	PUNCT
ejpam-3342	127	7	{	{	PUNCT
ejpam-3342	127	8	wt	wt	ADP
ejpam-3342	127	9	−ws	−ws	PROPN
ejpam-3342	127	10	∈	∈	NOUN
ejpam-3342	127	11	a	a	DET
ejpam-3342	127	12	}	}	PUNCT
ejpam-3342	127	13	∩b	∩b	NOUN
ejpam-3342	127	14	)	)	PUNCT
ejpam-3342	127	15	=	=	SYM
ejpam-3342	128	1	e	e	X
ejpam-3342	129	1	[	[	X
ejpam-3342	129	2	(	(	PUNCT
ejpam-3342	129	3	lim	lim	PROPN
ejpam-3342	129	4	n→∞	n→∞	X
ejpam-3342	129	5	(	(	PUNCT
ejpam-3342	129	6	1−	1−	NUM
ejpam-3342	129	7	ndist(wt	ndist(wt	PROPN
ejpam-3342	129	8	−ws	−ws	PROPN
ejpam-3342	129	9	,	,	PUNCT
ejpam-3342	129	10	a	a	PRON
ejpam-3342	129	11	)	)	PUNCT
ejpam-3342	129	12	)	)	PUNCT
ejpam-3342	129	13	∨	∨	NOUN
ejpam-3342	129	14	0	0	NUM
ejpam-3342	129	15	)	)	PUNCT
ejpam-3342	129	16	·	·	PUNCT
ejpam-3342	129	17	1b	1b	X
ejpam-3342	129	18	]	]	PUNCT
ejpam-3342	129	19	r.	r.	PROPN
ejpam-3342	129	20	rulete	rulete	PROPN
ejpam-3342	129	21	,	,	PUNCT
ejpam-3342	129	22	m.	m.	NOUN
ejpam-3342	129	23	labendia	labendia	PROPN
ejpam-3342	129	24	/	/	SYM
ejpam-3342	129	25	eur	eur	PROPN
ejpam-3342	129	26	.	.	PUNCT
ejpam-3342	130	1	j.	j.	PROPN
ejpam-3342	130	2	pure	pure	PROPN
ejpam-3342	130	3	appl	appl	PROPN
ejpam-3342	130	4	.	.	PROPN
ejpam-3342	130	5	math	math	PROPN
ejpam-3342	130	6	,	,	PUNCT
ejpam-3342	130	7	12	12	NUM
ejpam-3342	130	8	(	(	PUNCT
ejpam-3342	130	9	1	1	NUM
ejpam-3342	130	10	)	)	PUNCT
ejpam-3342	130	11	(	(	PUNCT
ejpam-3342	130	12	2019	2019	NUM
ejpam-3342	130	13	)	)	PUNCT
ejpam-3342	130	14	,	,	PUNCT
ejpam-3342	130	15	58	58	NUM
ejpam-3342	130	16	-	-	SYM
ejpam-3342	130	17	78	78	NUM
ejpam-3342	130	18	62	62	NUM
ejpam-3342	130	19	=	=	SYM
ejpam-3342	130	20	e	e	X
ejpam-3342	130	21	[	[	PUNCT
ejpam-3342	130	22	lim	lim	PROPN
ejpam-3342	130	23	n→∞	n→∞	X
ejpam-3342	130	24	(	(	PUNCT
ejpam-3342	130	25	(	(	PUNCT
ejpam-3342	130	26	1−	1−	NUM
ejpam-3342	130	27	ndist(wt	ndist(wt	NOUN
ejpam-3342	130	28	−ws	−ws	PROPN
ejpam-3342	130	29	,	,	PUNCT
ejpam-3342	130	30	a	a	PRON
ejpam-3342	130	31	)	)	PUNCT
ejpam-3342	130	32	)	)	PUNCT
ejpam-3342	130	33	∨	∨	ADP
ejpam-3342	130	34	0	0	NUM
ejpam-3342	130	35	)	)	PUNCT
ejpam-3342	130	36	·	·	PUNCT
ejpam-3342	130	37	1b	1b	X
ejpam-3342	130	38	]	]	PUNCT
ejpam-3342	131	1	=	=	PUNCT
ejpam-3342	131	2	lim	lim	NOUN
ejpam-3342	131	3	n→∞	n→∞	NUM
ejpam-3342	131	4	e	e	X
ejpam-3342	131	5	[	[	X
ejpam-3342	131	6	(	(	PUNCT
ejpam-3342	131	7	(	(	PUNCT
ejpam-3342	131	8	1−	1−	NUM
ejpam-3342	131	9	ndist(wt	ndist(wt	NOUN
ejpam-3342	131	10	−ws	−ws	PROPN
ejpam-3342	131	11	,	,	PUNCT
ejpam-3342	131	12	a	a	PRON
ejpam-3342	131	13	)	)	PUNCT
ejpam-3342	131	14	)	)	PUNCT
ejpam-3342	131	15	∨	∨	ADP
ejpam-3342	131	16	0	0	NUM
ejpam-3342	131	17	)	)	PUNCT
ejpam-3342	131	18	·	·	PUNCT
ejpam-3342	131	19	1b	1b	NUM
ejpam-3342	131	20	]	]	PUNCT
ejpam-3342	131	21	.	.	PUNCT
ejpam-3342	132	1	moreover	moreover	ADV
ejpam-3342	132	2	,	,	PUNCT
ejpam-3342	132	3	for	for	ADP
ejpam-3342	132	4	each	each	DET
ejpam-3342	132	5	ω	ω	PROPN
ejpam-3342	132	6	∈	∈	PROPN
ejpam-3342	132	7	ω	ω	NOUN
ejpam-3342	132	8	,	,	PUNCT
ejpam-3342	132	9	we	we	PRON
ejpam-3342	132	10	have	have	VERB
ejpam-3342	132	11	dist((wt	dist((wt	NOUN
ejpam-3342	132	12	−ws)(ω	−ws)(ω	NOUN
ejpam-3342	132	13	)	)	PUNCT
ejpam-3342	132	14	,	,	PUNCT
ejpam-3342	132	15	a	a	X
ejpam-3342	132	16	)	)	PUNCT
ejpam-3342	132	17	=	=	SYM
ejpam-3342	132	18	inf	inf	PROPN
ejpam-3342	132	19	a∈a	a∈a	PROPN
ejpam-3342	132	20	||(wt	||(wt	PROPN
ejpam-3342	132	21	−ws)(ω)−	−ws)(ω)−	PROPN
ejpam-3342	132	22	a||u	a||u	PROPN
ejpam-3342	132	23	=	=	SYM
ejpam-3342	132	24	inf	inf	PROPN
ejpam-3342	132	25	a∈a	a∈a	ADJ
ejpam-3342	132	26	∥∥∥	∥∥∥	PROPN
ejpam-3342	132	27	lim	lim	PROPN
ejpam-3342	132	28	m→∞	m→∞	NUM
ejpam-3342	132	29	wt−	wt−	PROPN
ejpam-3342	132	30	1	1	NUM
ejpam-3342	132	31	m	m	NOUN
ejpam-3342	132	32	(	(	PUNCT
ejpam-3342	132	33	ω)−ws(ω)−	ω)−ws(ω)−	VERB
ejpam-3342	132	34	a	a	DET
ejpam-3342	132	35	∥∥∥	∥∥∥	PROPN
ejpam-3342	132	36	u	u	NOUN
ejpam-3342	132	37	=	=	PROPN
ejpam-3342	132	38	lim	lim	PROPN
ejpam-3342	132	39	m→∞	m→∞	NOUN
ejpam-3342	132	40	inf	inf	PROPN
ejpam-3342	132	41	a∈a	a∈a	PROPN
ejpam-3342	132	42	∥∥∥wt−	∥∥∥wt−	PROPN
ejpam-3342	132	43	1	1	NUM
ejpam-3342	132	44	m	m	PROPN
ejpam-3342	132	45	(	(	PUNCT
ejpam-3342	132	46	ω)−ws(ω)−	ω)−ws(ω)−	VERB
ejpam-3342	132	47	a	a	DET
ejpam-3342	132	48	∥∥∥	∥∥∥	PROPN
ejpam-3342	132	49	u	u	NOUN
ejpam-3342	132	50	=	=	PROPN
ejpam-3342	132	51	lim	lim	PROPN
ejpam-3342	132	52	m→∞	m→∞	NOUN
ejpam-3342	132	53	dist((wt−	dist((wt−	NOUN
ejpam-3342	132	54	1	1	NUM
ejpam-3342	132	55	m	m	NOUN
ejpam-3342	132	56	−ws)(ω	−ws)(ω	NOUN
ejpam-3342	132	57	)	)	PUNCT
ejpam-3342	132	58	,	,	PUNCT
ejpam-3342	132	59	a	a	PRON
ejpam-3342	132	60	)	)	PUNCT
ejpam-3342	132	61	.	.	PUNCT
ejpam-3342	133	1	this	this	PRON
ejpam-3342	133	2	implies	imply	VERB
ejpam-3342	133	3	that	that	SCONJ
ejpam-3342	133	4	p	p	X
ejpam-3342	133	5	(	(	PUNCT
ejpam-3342	133	6	{	{	PUNCT
ejpam-3342	133	7	wt	wt	ADP
ejpam-3342	133	8	−ws	−ws	PROPN
ejpam-3342	133	9	∈	∈	NOUN
ejpam-3342	133	10	a	a	DET
ejpam-3342	133	11	}	}	PUNCT
ejpam-3342	133	12	∩b	∩b	NOUN
ejpam-3342	133	13	)	)	PUNCT
ejpam-3342	133	14	=	=	VERB
ejpam-3342	133	15	lim	lim	NOUN
ejpam-3342	133	16	n→∞	n→∞	NUM
ejpam-3342	133	17	e	e	X
ejpam-3342	134	1	[	[	X
ejpam-3342	134	2	(	(	PUNCT
ejpam-3342	134	3	(	(	PUNCT
ejpam-3342	134	4	1−	1−	NUM
ejpam-3342	134	5	n	n	NUM
ejpam-3342	134	6	lim	lim	PROPN
ejpam-3342	134	7	m→∞	m→∞	NOUN
ejpam-3342	134	8	dist(wt−	dist(wt−	PROPN
ejpam-3342	134	9	1	1	NUM
ejpam-3342	134	10	m	m	NOUN
ejpam-3342	134	11	−ws	−ws	PRON
ejpam-3342	134	12	,	,	PUNCT
ejpam-3342	134	13	a	a	PRON
ejpam-3342	134	14	)	)	PUNCT
ejpam-3342	134	15	)	)	PUNCT
ejpam-3342	134	16	∨	∨	NOUN
ejpam-3342	134	17	0	0	NUM
ejpam-3342	134	18	)	)	PUNCT
ejpam-3342	134	19	·	·	PUNCT
ejpam-3342	134	20	1b	1b	X
ejpam-3342	134	21	]	]	PUNCT
ejpam-3342	135	1	=	=	PUNCT
ejpam-3342	135	2	lim	lim	NOUN
ejpam-3342	135	3	n→∞	n→∞	NUM
ejpam-3342	135	4	e	e	X
ejpam-3342	135	5	[	[	PUNCT
ejpam-3342	135	6	lim	lim	PROPN
ejpam-3342	135	7	m→∞	m→∞	NUM
ejpam-3342	135	8	(	(	PUNCT
ejpam-3342	135	9	(	(	PUNCT
ejpam-3342	135	10	1−	1−	NUM
ejpam-3342	135	11	ndist(wt−	ndist(wt−	NOUN
ejpam-3342	135	12	1	1	NUM
ejpam-3342	135	13	m	m	NOUN
ejpam-3342	135	14	−ws	−ws	PRON
ejpam-3342	135	15	,	,	PUNCT
ejpam-3342	135	16	a	a	PRON
ejpam-3342	135	17	)	)	PUNCT
ejpam-3342	135	18	)	)	PUNCT
ejpam-3342	135	19	∨	∨	NOUN
ejpam-3342	135	20	0	0	NUM
ejpam-3342	135	21	)	)	PUNCT
ejpam-3342	135	22	·	·	PUNCT
ejpam-3342	135	23	1b	1b	X
ejpam-3342	135	24	]	]	PUNCT
ejpam-3342	136	1	=	=	SYM
ejpam-3342	136	2	lim	lim	PROPN
ejpam-3342	136	3	n→∞	n→∞	NUM
ejpam-3342	136	4	lim	lim	PROPN
ejpam-3342	136	5	m→∞	m→∞	NOUN
ejpam-3342	136	6	e	e	NOUN
ejpam-3342	136	7	[	[	X
ejpam-3342	136	8	(	(	PUNCT
ejpam-3342	136	9	(	(	PUNCT
ejpam-3342	136	10	1−	1−	NUM
ejpam-3342	136	11	ndist(wt−	ndist(wt−	NOUN
ejpam-3342	136	12	1	1	NUM
ejpam-3342	136	13	m	m	NOUN
ejpam-3342	136	14	−ws	−ws	PRON
ejpam-3342	136	15	,	,	PUNCT
ejpam-3342	136	16	a	a	PRON
ejpam-3342	136	17	)	)	PUNCT
ejpam-3342	136	18	)	)	PUNCT
ejpam-3342	136	19	∨	∨	NOUN
ejpam-3342	136	20	0	0	NUM
ejpam-3342	136	21	)	)	PUNCT
ejpam-3342	136	22	·	·	PUNCT
ejpam-3342	136	23	1b	1b	NUM
ejpam-3342	136	24	]	]	PUNCT
ejpam-3342	136	25	.	.	PUNCT
ejpam-3342	137	1	since	since	SCONJ
ejpam-3342	137	2	wt−	wt−	PROPN
ejpam-3342	137	3	1	1	NUM
ejpam-3342	137	4	m	m	NOUN
ejpam-3342	137	5	−ws	−ws	PRON
ejpam-3342	137	6	is	be	AUX
ejpam-3342	137	7	independent	independent	ADJ
ejpam-3342	137	8	of	of	ADP
ejpam-3342	137	9	g̃0	g̃0	PROPN
ejpam-3342	137	10	t−	t−	PROPN
ejpam-3342	137	11	1	1	NUM
ejpam-3342	137	12	m	m	NOUN
ejpam-3342	137	13	⊇	⊇	NOUN
ejpam-3342	137	14	gt	gt	PROPN
ejpam-3342	137	15	if	if	SCONJ
ejpam-3342	137	16	m	m	NOUN
ejpam-3342	137	17	is	be	AUX
ejpam-3342	137	18	large	large	ADJ
ejpam-3342	137	19	,	,	PUNCT
ejpam-3342	137	20	we	we	PRON
ejpam-3342	137	21	have	have	VERB
ejpam-3342	137	22	p	p	NOUN
ejpam-3342	137	23	(	(	PUNCT
ejpam-3342	137	24	{	{	PUNCT
ejpam-3342	137	25	wt	wt	ADP
ejpam-3342	137	26	−ws	−ws	PROPN
ejpam-3342	137	27	∈	∈	NOUN
ejpam-3342	137	28	a	a	DET
ejpam-3342	137	29	}	}	PUNCT
ejpam-3342	137	30	∩b	∩b	NOUN
ejpam-3342	137	31	)	)	PUNCT
ejpam-3342	137	32	=	=	VERB
ejpam-3342	138	1	lim	lim	PROPN
ejpam-3342	138	2	n→∞	n→∞	NUM
ejpam-3342	138	3	lim	lim	PROPN
ejpam-3342	138	4	m→∞	m→∞	NUM
ejpam-3342	138	5	e	e	NOUN
ejpam-3342	138	6	[	[	PUNCT
ejpam-3342	138	7	(	(	PUNCT
ejpam-3342	138	8	1−	1−	NUM
ejpam-3342	138	9	ndist(wt−	ndist(wt−	NOUN
ejpam-3342	138	10	1	1	NUM
ejpam-3342	138	11	m	m	NOUN
ejpam-3342	138	12	−ws	−ws	PRON
ejpam-3342	138	13	,	,	PUNCT
ejpam-3342	138	14	a	a	PRON
ejpam-3342	138	15	)	)	PUNCT
ejpam-3342	138	16	)	)	PUNCT
ejpam-3342	138	17	∨	∨	ADP
ejpam-3342	138	18	0	0	NUM
ejpam-3342	138	19	]	]	PUNCT
ejpam-3342	138	20	·	·	PUNCT
ejpam-3342	138	21	e	e	X
ejpam-3342	138	22	[	[	X
ejpam-3342	138	23	1b	1b	X
ejpam-3342	138	24	]	]	X
ejpam-3342	138	25	=	=	SYM
ejpam-3342	138	26	p({wt	p({wt	VERB
ejpam-3342	138	27	−ws	−ws	PRON
ejpam-3342	138	28	∈	∈	PROPN
ejpam-3342	138	29	a	a	PRON
ejpam-3342	138	30	}	}	PUNCT
ejpam-3342	138	31	)	)	PUNCT
ejpam-3342	138	32	·	·	PUNCT
ejpam-3342	139	1	p(b	p(b	NUM
ejpam-3342	139	2	)	)	PUNCT
ejpam-3342	139	3	.	.	PUNCT
ejpam-3342	140	1	this	this	PRON
ejpam-3342	140	2	completes	complete	VERB
ejpam-3342	140	3	the	the	DET
ejpam-3342	140	4	proof	proof	NOUN
ejpam-3342	140	5	.	.	PUNCT
ejpam-3342	141	1	�	�	PROPN
ejpam-3342	141	2	from	from	ADP
ejpam-3342	141	3	now	now	ADV
ejpam-3342	141	4	onwards	onward	NOUN
ejpam-3342	141	5	,	,	PUNCT
ejpam-3342	141	6	the	the	DET
ejpam-3342	141	7	backwards	backwards	ADV
ejpam-3342	141	8	filtered	filter	VERB
ejpam-3342	141	9	probability	probability	NOUN
ejpam-3342	141	10	shall	shall	AUX
ejpam-3342	141	11	mean	mean	VERB
ejpam-3342	141	12	a	a	DET
ejpam-3342	141	13	filtered	filter	VERB
ejpam-3342	141	14	probability	probability	NOUN
ejpam-3342	141	15	space	space	NOUN
ejpam-3342	141	16	such	such	ADJ
ejpam-3342	141	17	that	that	SCONJ
ejpam-3342	141	18	wt	wt	PROPN
ejpam-3342	141	19	is	be	AUX
ejpam-3342	141	20	adapted	adapt	VERB
ejpam-3342	141	21	to	to	ADP
ejpam-3342	141	22	gt	gt	PROPN
ejpam-3342	141	23	and	and	CCONJ
ejpam-3342	141	24	wt−ws	wt−ws	X
ejpam-3342	141	25	is	be	AUX
ejpam-3342	141	26	independent	independent	ADJ
ejpam-3342	141	27	of	of	ADP
ejpam-3342	141	28	gt	gt	PROPN
ejpam-3342	141	29	for	for	ADP
ejpam-3342	141	30	all	all	DET
ejpam-3342	141	31	0	0	NUM
ejpam-3342	141	32	≤	≤	NUM
ejpam-3342	141	33	s	s	PART
ejpam-3342	141	34	≤	≤	NUM
ejpam-3342	141	35	t	t	NOUN
ejpam-3342	141	36	≤	≤	NOUN
ejpam-3342	141	37	t	t	PROPN
ejpam-3342	141	38	.	.	PUNCT
ejpam-3342	142	1	3	3	X
ejpam-3342	142	2	.	.	X
ejpam-3342	142	3	backwards	backwards	ADV
ejpam-3342	142	4	itô-henstock	itô-henstock	PROPN
ejpam-3342	142	5	integral	integral	ADJ
ejpam-3342	142	6	in	in	ADP
ejpam-3342	142	7	this	this	DET
ejpam-3342	142	8	section	section	NOUN
ejpam-3342	142	9	,	,	PUNCT
ejpam-3342	142	10	we	we	PRON
ejpam-3342	142	11	shall	shall	AUX
ejpam-3342	142	12	present	present	VERB
ejpam-3342	142	13	the	the	DET
ejpam-3342	142	14	backwards	backwards	ADV
ejpam-3342	142	15	itô-henstock	itô-henstock	NOUN
ejpam-3342	142	16	integral	integral	ADJ
ejpam-3342	142	17	and	and	CCONJ
ejpam-3342	142	18	some	some	DET
ejpam-3342	142	19	related	related	ADJ
ejpam-3342	142	20	results	result	NOUN
ejpam-3342	142	21	.	.	PUNCT
ejpam-3342	143	1	let	let	VERB
ejpam-3342	143	2	δ	δ	PRON
ejpam-3342	143	3	be	be	AUX
ejpam-3342	143	4	a	a	DET
ejpam-3342	143	5	positive	positive	ADJ
ejpam-3342	143	6	function	function	NOUN
ejpam-3342	143	7	on	on	ADP
ejpam-3342	143	8	(	(	PUNCT
ejpam-3342	143	9	0	0	NUM
ejpam-3342	143	10	,	,	PUNCT
ejpam-3342	143	11	t	t	X
ejpam-3342	143	12	]	]	PUNCT
ejpam-3342	143	13	.	.	PUNCT
ejpam-3342	144	1	a	a	DET
ejpam-3342	144	2	finite	finite	ADJ
ejpam-3342	144	3	collection	collection	NOUN
ejpam-3342	144	4	d	d	NOUN
ejpam-3342	144	5	=	=	PRON
ejpam-3342	144	6	{	{	PUNCT
ejpam-3342	144	7	(	(	PUNCT
ejpam-3342	144	8	(	(	PUNCT
ejpam-3342	144	9	ui	ui	NOUN
ejpam-3342	144	10	,	,	PUNCT
ejpam-3342	144	11	ξi	ξi	NOUN
ejpam-3342	144	12	]	]	X
ejpam-3342	144	13	,	,	PUNCT
ejpam-3342	144	14	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3342	144	15	of	of	ADP
ejpam-3342	144	16	interval	interval	NOUN
ejpam-3342	144	17	-	-	PUNCT
ejpam-3342	144	18	point	point	NOUN
ejpam-3342	144	19	pairs	pair	NOUN
ejpam-3342	144	20	is	be	AUX
ejpam-3342	144	21	said	say	VERB
ejpam-3342	144	22	to	to	PART
ejpam-3342	144	23	be	be	AUX
ejpam-3342	144	24	a	a	DET
ejpam-3342	144	25	backwards	backwards	ADV
ejpam-3342	144	26	partial	partial	ADJ
ejpam-3342	144	27	division	division	NOUN
ejpam-3342	144	28	of	of	ADP
ejpam-3342	144	29	[	[	X
ejpam-3342	144	30	0	0	NUM
ejpam-3342	144	31	,	,	PUNCT
ejpam-3342	144	32	t	t	X
ejpam-3342	144	33	]	]	PUNCT
ejpam-3342	144	34	if	if	SCONJ
ejpam-3342	144	35	{	{	PUNCT
ejpam-3342	144	36	(	(	PUNCT
ejpam-3342	144	37	ui	ui	NOUN
ejpam-3342	144	38	,	,	PUNCT
ejpam-3342	144	39	ξi]}ni=1	ξi]}ni=1	PROPN
ejpam-3342	144	40	is	be	AUX
ejpam-3342	144	41	a	a	DET
ejpam-3342	144	42	finite	finite	ADJ
ejpam-3342	144	43	collection	collection	NOUN
ejpam-3342	144	44	of	of	ADP
ejpam-3342	144	45	disjoint	disjoint	ADJ
ejpam-3342	144	46	subintervals	subinterval	NOUN
ejpam-3342	144	47	of	of	ADP
ejpam-3342	144	48	(	(	PUNCT
ejpam-3342	144	49	0	0	NUM
ejpam-3342	144	50	,	,	PUNCT
ejpam-3342	144	51	t	t	X
ejpam-3342	144	52	]	]	PUNCT
ejpam-3342	144	53	.	.	PUNCT
ejpam-3342	145	1	an	an	DET
ejpam-3342	145	2	interval	interval	NOUN
ejpam-3342	145	3	-	-	PUNCT
ejpam-3342	145	4	point	point	NOUN
ejpam-3342	145	5	pair	pair	NOUN
ejpam-3342	145	6	(	(	PUNCT
ejpam-3342	145	7	(	(	PUNCT
ejpam-3342	145	8	u	u	NOUN
ejpam-3342	145	9	,	,	PUNCT
ejpam-3342	145	10	ξ	ξ	PROPN
ejpam-3342	145	11	]	]	X
ejpam-3342	145	12	,	,	PUNCT
ejpam-3342	145	13	ξ	ξ	X
ejpam-3342	145	14	)	)	PUNCT
ejpam-3342	145	15	is	be	AUX
ejpam-3342	145	16	said	say	VERB
ejpam-3342	145	17	to	to	PART
ejpam-3342	145	18	be	be	AUX
ejpam-3342	145	19	backwards	backwards	ADV
ejpam-3342	145	20	δ	δ	NOUN
ejpam-3342	145	21	-	-	PUNCT
ejpam-3342	145	22	fine	fine	NOUN
ejpam-3342	145	23	if	if	SCONJ
ejpam-3342	145	24	(	(	PUNCT
ejpam-3342	145	25	u	u	NOUN
ejpam-3342	145	26	,	,	PUNCT
ejpam-3342	145	27	ξ	ξ	PROPN
ejpam-3342	145	28	]	]	X
ejpam-3342	145	29	⊆	⊆	NUM
ejpam-3342	145	30	(	(	PUNCT
ejpam-3342	145	31	ξ	ξ	X
ejpam-3342	145	32	−	−	NOUN
ejpam-3342	145	33	δ(ξ	δ(ξ	NOUN
ejpam-3342	145	34	)	)	PUNCT
ejpam-3342	145	35	,	,	PUNCT
ejpam-3342	145	36	ξ	ξ	PROPN
ejpam-3342	145	37	]	]	X
ejpam-3342	145	38	,	,	PUNCT
ejpam-3342	145	39	whenever	whenever	SCONJ
ejpam-3342	145	40	(	(	PUNCT
ejpam-3342	145	41	u	u	NOUN
ejpam-3342	145	42	,	,	PUNCT
ejpam-3342	145	43	ξ	ξ	PROPN
ejpam-3342	145	44	]	]	X
ejpam-3342	145	45	⊆	⊆	NUM
ejpam-3342	145	46	(	(	PUNCT
ejpam-3342	145	47	0	0	NUM
ejpam-3342	145	48	,	,	PUNCT
ejpam-3342	145	49	t	t	NOUN
ejpam-3342	145	50	]	]	PUNCT
ejpam-3342	145	51	and	and	CCONJ
ejpam-3342	145	52	ξ	ξ	X
ejpam-3342	145	53	∈	∈	PROPN
ejpam-3342	145	54	(	(	PUNCT
ejpam-3342	145	55	0	0	NUM
ejpam-3342	145	56	,	,	PUNCT
ejpam-3342	145	57	t	t	X
ejpam-3342	145	58	]	]	PUNCT
ejpam-3342	145	59	.	.	PUNCT
ejpam-3342	146	1	we	we	PRON
ejpam-3342	146	2	call	call	VERB
ejpam-3342	146	3	d	d	NOUN
ejpam-3342	146	4	=	=	PRON
ejpam-3342	146	5	{	{	PUNCT
ejpam-3342	146	6	(	(	PUNCT
ejpam-3342	146	7	(	(	PUNCT
ejpam-3342	146	8	ui	ui	NOUN
ejpam-3342	146	9	,	,	PUNCT
ejpam-3342	146	10	ξi	ξi	NOUN
ejpam-3342	146	11	]	]	PUNCT
ejpam-3342	146	12	,	,	PUNCT
ejpam-3342	146	13	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3342	146	14	a	a	DET
ejpam-3342	146	15	backwards	backwards	ADV
ejpam-3342	146	16	δ	δ	PROPN
ejpam-3342	146	17	-	-	PUNCT
ejpam-3342	146	18	fine	fine	ADJ
ejpam-3342	146	19	partial	partial	ADJ
ejpam-3342	146	20	division	division	NOUN
ejpam-3342	146	21	of	of	ADP
ejpam-3342	146	22	[	[	X
ejpam-3342	146	23	0	0	NUM
ejpam-3342	146	24	,	,	PUNCT
ejpam-3342	146	25	t	t	X
ejpam-3342	146	26	]	]	PUNCT
ejpam-3342	146	27	if	if	SCONJ
ejpam-3342	146	28	d	d	PROPN
ejpam-3342	146	29	is	be	AUX
ejpam-3342	146	30	a	a	DET
ejpam-3342	146	31	backwards	backwards	ADV
ejpam-3342	146	32	partial	partial	ADJ
ejpam-3342	146	33	division	division	NOUN
ejpam-3342	146	34	of	of	ADP
ejpam-3342	146	35	[	[	X
ejpam-3342	146	36	0	0	NUM
ejpam-3342	146	37	,	,	PUNCT
ejpam-3342	146	38	t	t	NOUN
ejpam-3342	146	39	]	]	PUNCT
ejpam-3342	146	40	and	and	CCONJ
ejpam-3342	146	41	for	for	ADP
ejpam-3342	146	42	each	each	DET
ejpam-3342	146	43	i	i	PRON
ejpam-3342	146	44	,	,	PUNCT
ejpam-3342	146	45	the	the	DET
ejpam-3342	146	46	interval	interval	NOUN
ejpam-3342	146	47	-	-	PUNCT
ejpam-3342	146	48	point	point	NOUN
ejpam-3342	146	49	pair	pair	NOUN
ejpam-3342	146	50	(	(	PUNCT
ejpam-3342	146	51	(	(	PUNCT
ejpam-3342	146	52	ui	ui	NOUN
ejpam-3342	146	53	,	,	PUNCT
ejpam-3342	146	54	ξi	ξi	NOUN
ejpam-3342	146	55	]	]	PUNCT
ejpam-3342	146	56	,	,	PUNCT
ejpam-3342	146	57	ξi	ξi	NOUN
ejpam-3342	146	58	)	)	PUNCT
ejpam-3342	146	59	is	be	AUX
ejpam-3342	146	60	backwards	backwards	ADV
ejpam-3342	146	61	δ	δ	NOUN
ejpam-3342	146	62	-	-	PUNCT
ejpam-3342	146	63	fine	fine	PROPN
ejpam-3342	146	64	.	.	PUNCT
ejpam-3342	147	1	r.	r.	PROPN
ejpam-3342	147	2	rulete	rulete	PROPN
ejpam-3342	147	3	,	,	PUNCT
ejpam-3342	147	4	m.	m.	NOUN
ejpam-3342	147	5	labendia	labendia	PROPN
ejpam-3342	147	6	/	/	SYM
ejpam-3342	147	7	eur	eur	PROPN
ejpam-3342	147	8	.	.	PUNCT
ejpam-3342	148	1	j.	j.	PROPN
ejpam-3342	148	2	pure	pure	PROPN
ejpam-3342	148	3	appl	appl	PROPN
ejpam-3342	148	4	.	.	PROPN
ejpam-3342	148	5	math	math	PROPN
ejpam-3342	148	6	,	,	PUNCT
ejpam-3342	148	7	12	12	NUM
ejpam-3342	148	8	(	(	PUNCT
ejpam-3342	148	9	1	1	NUM
ejpam-3342	148	10	)	)	PUNCT
ejpam-3342	148	11	(	(	PUNCT
ejpam-3342	148	12	2019	2019	NUM
ejpam-3342	148	13	)	)	PUNCT
ejpam-3342	148	14	,	,	PUNCT
ejpam-3342	148	15	58	58	NUM
ejpam-3342	148	16	-	-	SYM
ejpam-3342	148	17	78	78	NUM
ejpam-3342	148	18	63	63	NUM
ejpam-3342	148	19	we	we	PRON
ejpam-3342	148	20	note	note	VERB
ejpam-3342	148	21	that	that	SCONJ
ejpam-3342	148	22	given	give	VERB
ejpam-3342	148	23	any	any	DET
ejpam-3342	148	24	positive	positive	ADJ
ejpam-3342	148	25	function	function	NOUN
ejpam-3342	148	26	δ	δ	PROPN
ejpam-3342	148	27	,	,	PUNCT
ejpam-3342	148	28	one	one	PRON
ejpam-3342	148	29	may	may	AUX
ejpam-3342	148	30	not	not	PART
ejpam-3342	148	31	be	be	AUX
ejpam-3342	148	32	able	able	ADJ
ejpam-3342	148	33	to	to	PART
ejpam-3342	148	34	find	find	VERB
ejpam-3342	148	35	a	a	DET
ejpam-3342	148	36	full	full	ADJ
ejpam-3342	148	37	division	division	NOUN
ejpam-3342	148	38	that	that	PRON
ejpam-3342	148	39	covers	cover	VERB
ejpam-3342	148	40	the	the	DET
ejpam-3342	148	41	entire	entire	ADJ
ejpam-3342	148	42	interval	interval	NOUN
ejpam-3342	148	43	(	(	PUNCT
ejpam-3342	148	44	0	0	NUM
ejpam-3342	148	45	,	,	PUNCT
ejpam-3342	148	46	t	t	X
ejpam-3342	148	47	]	]	PUNCT
ejpam-3342	148	48	.	.	PUNCT
ejpam-3342	149	1	for	for	ADP
ejpam-3342	149	2	instance	instance	NOUN
ejpam-3342	149	3	,	,	PUNCT
ejpam-3342	149	4	let	let	VERB
ejpam-3342	149	5	δ(ξ	δ(ξ	PRON
ejpam-3342	149	6	)	)	PUNCT
ejpam-3342	149	7	=	=	PUNCT
ejpam-3342	149	8	ξ/2	ξ/2	NUM
ejpam-3342	149	9	.	.	PUNCT
ejpam-3342	150	1	then	then	ADV
ejpam-3342	150	2	the	the	DET
ejpam-3342	150	3	interval	interval	NOUN
ejpam-3342	150	4	(	(	PUNCT
ejpam-3342	150	5	0	0	NUM
ejpam-3342	150	6	,	,	PUNCT
ejpam-3342	150	7	t	t	X
ejpam-3342	150	8	]	]	PUNCT
ejpam-3342	150	9	can	can	AUX
ejpam-3342	150	10	not	not	PART
ejpam-3342	150	11	be	be	AUX
ejpam-3342	150	12	covered	cover	VERB
ejpam-3342	150	13	by	by	ADP
ejpam-3342	150	14	any	any	DET
ejpam-3342	150	15	finite	finite	ADJ
ejpam-3342	150	16	collection	collection	NOUN
ejpam-3342	150	17	of	of	ADP
ejpam-3342	150	18	backwards	backwards	ADV
ejpam-3342	150	19	δ	δ	PROPN
ejpam-3342	150	20	-	-	PUNCT
ejpam-3342	150	21	fine	fine	ADJ
ejpam-3342	150	22	intervals	interval	NOUN
ejpam-3342	150	23	.	.	PUNCT
ejpam-3342	151	1	given	give	VERB
ejpam-3342	151	2	η	η	PROPN
ejpam-3342	151	3	>	>	X
ejpam-3342	151	4	0	0	PROPN
ejpam-3342	151	5	,	,	PUNCT
ejpam-3342	151	6	a	a	DET
ejpam-3342	151	7	given	give	VERB
ejpam-3342	151	8	backwards	backwards	ADV
ejpam-3342	151	9	δ	δ	NOUN
ejpam-3342	151	10	-	-	PUNCT
ejpam-3342	151	11	fine	fine	ADJ
ejpam-3342	151	12	partial	partial	ADJ
ejpam-3342	151	13	division	division	NOUN
ejpam-3342	151	14	d	d	NOUN
ejpam-3342	151	15	=	=	PRON
ejpam-3342	151	16	{	{	PUNCT
ejpam-3342	151	17	(	(	PUNCT
ejpam-3342	151	18	(	(	PUNCT
ejpam-3342	151	19	ui	ui	NOUN
ejpam-3342	151	20	,	,	PUNCT
ejpam-3342	151	21	ξi	ξi	NOUN
ejpam-3342	151	22	]	]	PUNCT
ejpam-3342	151	23	,	,	PUNCT
ejpam-3342	151	24	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3342	151	25	is	be	AUX
ejpam-3342	151	26	said	say	VERB
ejpam-3342	151	27	to	to	PART
ejpam-3342	151	28	be	be	AUX
ejpam-3342	151	29	backwards	backwards	ADV
ejpam-3342	151	30	(	(	PUNCT
ejpam-3342	151	31	δ	δ	PROPN
ejpam-3342	151	32	,	,	PUNCT
ejpam-3342	151	33	η)-fine	η)-fine	X
ejpam-3342	151	34	partial	partial	ADJ
ejpam-3342	151	35	division	division	NOUN
ejpam-3342	151	36	of	of	ADP
ejpam-3342	151	37	[	[	X
ejpam-3342	151	38	0	0	NUM
ejpam-3342	151	39	,	,	PUNCT
ejpam-3342	151	40	t	t	X
ejpam-3342	151	41	]	]	PUNCT
ejpam-3342	151	42	if	if	SCONJ
ejpam-3342	151	43	it	it	PRON
ejpam-3342	151	44	fails	fail	VERB
ejpam-3342	151	45	to	to	PART
ejpam-3342	151	46	cover	cover	VERB
ejpam-3342	151	47	(	(	PUNCT
ejpam-3342	151	48	0	0	NUM
ejpam-3342	151	49	,	,	PUNCT
ejpam-3342	151	50	t	t	X
ejpam-3342	151	51	]	]	PUNCT
ejpam-3342	151	52	by	by	ADP
ejpam-3342	151	53	at	at	ADP
ejpam-3342	151	54	most	most	ADJ
ejpam-3342	151	55	length	length	NOUN
ejpam-3342	151	56	η	η	PROPN
ejpam-3342	151	57	,	,	PUNCT
ejpam-3342	151	58	that	that	ADV
ejpam-3342	151	59	is	is	ADV
ejpam-3342	151	60	,	,	PUNCT
ejpam-3342	151	61	∣∣∣∣∣t	∣∣∣∣∣t	NOUN
ejpam-3342	151	62	−	−	PROPN
ejpam-3342	152	1	(	(	PUNCT
ejpam-3342	152	2	d	d	NOUN
ejpam-3342	152	3	)	)	PUNCT
ejpam-3342	152	4	n∑	n∑	NOUN
ejpam-3342	152	5	i=1	i=1	PROPN
ejpam-3342	153	1	(	(	PUNCT
ejpam-3342	153	2	ξi	ξi	NOUN
ejpam-3342	153	3	−	−	PROPN
ejpam-3342	153	4	ui	ui	PROPN
ejpam-3342	153	5	)	)	PUNCT
ejpam-3342	154	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3342	154	2	≤	≤	PROPN
ejpam-3342	154	3	η	η	PROPN
ejpam-3342	154	4	.	.	PUNCT
ejpam-3342	155	1	we	we	PRON
ejpam-3342	155	2	are	be	AUX
ejpam-3342	155	3	now	now	ADV
ejpam-3342	155	4	ready	ready	ADJ
ejpam-3342	155	5	to	to	PART
ejpam-3342	155	6	define	define	VERB
ejpam-3342	155	7	the	the	DET
ejpam-3342	155	8	backwards	backwards	ADV
ejpam-3342	155	9	itô-henstock	itô-henstock	NOUN
ejpam-3342	155	10	integral	integral	PROPN
ejpam-3342	155	11	.	.	PUNCT
ejpam-3342	156	1	throughout	throughout	ADP
ejpam-3342	156	2	the	the	DET
ejpam-3342	156	3	following	follow	VERB
ejpam-3342	156	4	discussions	discussion	NOUN
ejpam-3342	156	5	,	,	PUNCT
ejpam-3342	156	6	assume	assume	VERB
ejpam-3342	156	7	that	that	SCONJ
ejpam-3342	156	8	u	u	PROPN
ejpam-3342	156	9	and	and	CCONJ
ejpam-3342	156	10	v	v	NOUN
ejpam-3342	156	11	are	be	AUX
ejpam-3342	156	12	separable	separable	ADJ
ejpam-3342	156	13	hilbert	hilbert	PROPN
ejpam-3342	156	14	spaces	space	NOUN
ejpam-3342	156	15	,	,	PUNCT
ejpam-3342	156	16	q	q	NOUN
ejpam-3342	156	17	:	:	PUNCT
ejpam-3342	156	18	u	u	X
ejpam-3342	156	19	→	→	SYM
ejpam-3342	156	20	u	u	PROPN
ejpam-3342	156	21	is	be	AUX
ejpam-3342	156	22	a	a	DET
ejpam-3342	156	23	symmetric	symmetric	ADJ
ejpam-3342	156	24	nonnegative	nonnegative	ADJ
ejpam-3342	156	25	definite	definite	ADJ
ejpam-3342	156	26	trace	trace	NOUN
ejpam-3342	156	27	-	-	PUNCT
ejpam-3342	156	28	class	class	NOUN
ejpam-3342	156	29	operator	operator	NOUN
ejpam-3342	156	30	,	,	PUNCT
ejpam-3342	156	31	{	{	PUNCT
ejpam-3342	156	32	λj	λj	PROPN
ejpam-3342	156	33	,	,	PUNCT
ejpam-3342	156	34	ej	ej	X
ejpam-3342	156	35	}	}	PUNCT
ejpam-3342	156	36	is	be	AUX
ejpam-3342	156	37	an	an	DET
ejpam-3342	156	38	eigensequence	eigensequence	NOUN
ejpam-3342	156	39	defined	define	VERB
ejpam-3342	156	40	by	by	ADP
ejpam-3342	156	41	q	q	PROPN
ejpam-3342	156	42	,	,	PUNCT
ejpam-3342	156	43	and	and	CCONJ
ejpam-3342	156	44	w	w	NOUN
ejpam-3342	156	45	is	be	AUX
ejpam-3342	156	46	a	a	DET
ejpam-3342	156	47	u	u	NOUN
ejpam-3342	156	48	-valued	-value	VERB
ejpam-3342	156	49	q	q	ADJ
ejpam-3342	156	50	-	-	PUNCT
ejpam-3342	156	51	weiner	weiner	NOUN
ejpam-3342	156	52	process	process	NOUN
ejpam-3342	156	53	.	.	PUNCT
ejpam-3342	157	1	definition	definition	NOUN
ejpam-3342	157	2	1	1	NUM
ejpam-3342	157	3	.	.	PUNCT
ejpam-3342	158	1	let	let	VERB
ejpam-3342	158	2	f	f	NOUN
ejpam-3342	158	3	:	:	PUNCT
ejpam-3342	159	1	[	[	X
ejpam-3342	159	2	0	0	NUM
ejpam-3342	159	3	,	,	PUNCT
ejpam-3342	159	4	t	t	X
ejpam-3342	159	5	]	]	PUNCT
ejpam-3342	159	6	×	×	PROPN
ejpam-3342	159	7	ω	ω	X
ejpam-3342	159	8	→	→	SYM
ejpam-3342	159	9	l2(uq	l2(uq	PROPN
ejpam-3342	159	10	,	,	PUNCT
ejpam-3342	159	11	v	v	NOUN
ejpam-3342	159	12	)	)	PUNCT
ejpam-3342	159	13	be	be	AUX
ejpam-3342	159	14	a	a	DET
ejpam-3342	159	15	backwards	backwards	ADV
ejpam-3342	159	16	adapted	adapt	VERB
ejpam-3342	159	17	process	process	NOUN
ejpam-3342	159	18	.	.	PUNCT
ejpam-3342	160	1	then	then	ADV
ejpam-3342	160	2	f	f	PROPN
ejpam-3342	160	3	is	be	AUX
ejpam-3342	160	4	said	say	VERB
ejpam-3342	160	5	to	to	PART
ejpam-3342	160	6	be	be	AUX
ejpam-3342	160	7	backwards	backwards	ADV
ejpam-3342	160	8	itô-henstock	itô-henstock	NOUN
ejpam-3342	160	9	integrable	integrable	ADJ
ejpam-3342	160	10	,	,	PUNCT
ejpam-3342	160	11	or	or	CCONJ
ejpam-3342	160	12	ihb	ihb	NOUN
ejpam-3342	160	13	-	-	ADJ
ejpam-3342	160	14	integrable	integrable	ADJ
ejpam-3342	160	15	,	,	PUNCT
ejpam-3342	160	16	on	on	ADP
ejpam-3342	160	17	[	[	X
ejpam-3342	160	18	0	0	NUM
ejpam-3342	160	19	,	,	PUNCT
ejpam-3342	160	20	t	t	X
ejpam-3342	160	21	]	]	PUNCT
ejpam-3342	160	22	with	with	ADP
ejpam-3342	160	23	respect	respect	NOUN
ejpam-3342	160	24	to	to	ADP
ejpam-3342	160	25	w	w	NOUN
ejpam-3342	160	26	if	if	SCONJ
ejpam-3342	160	27	there	there	PRON
ejpam-3342	160	28	exists	exist	VERB
ejpam-3342	160	29	a	a	DET
ejpam-3342	160	30	∈	∈	PROPN
ejpam-3342	160	31	l2(ω	l2(ω	PROPN
ejpam-3342	160	32	,	,	PUNCT
ejpam-3342	160	33	v	v	NOUN
ejpam-3342	160	34	)	)	PUNCT
ejpam-3342	160	35	such	such	ADJ
ejpam-3342	160	36	that	that	PRON
ejpam-3342	160	37	for	for	ADP
ejpam-3342	160	38	every	every	DET
ejpam-3342	160	39	ε	ε	PROPN
ejpam-3342	160	40	>	>	X
ejpam-3342	160	41	0	0	PROPN
ejpam-3342	160	42	,	,	PUNCT
ejpam-3342	160	43	there	there	PRON
ejpam-3342	160	44	is	be	VERB
ejpam-3342	160	45	a	a	DET
ejpam-3342	160	46	positive	positive	ADJ
ejpam-3342	160	47	function	function	NOUN
ejpam-3342	160	48	δ	δ	PROPN
ejpam-3342	160	49	on	on	ADP
ejpam-3342	160	50	(	(	PUNCT
ejpam-3342	160	51	0	0	NUM
ejpam-3342	160	52	,	,	PUNCT
ejpam-3342	160	53	t	t	NOUN
ejpam-3342	160	54	]	]	PUNCT
ejpam-3342	160	55	and	and	CCONJ
ejpam-3342	160	56	a	a	DET
ejpam-3342	160	57	positive	positive	ADJ
ejpam-3342	160	58	number	number	NOUN
ejpam-3342	160	59	η	η	NOUN
ejpam-3342	160	60	such	such	ADJ
ejpam-3342	160	61	that	that	PRON
ejpam-3342	160	62	for	for	ADP
ejpam-3342	160	63	any	any	DET
ejpam-3342	160	64	backwards	backwards	ADV
ejpam-3342	160	65	(	(	PUNCT
ejpam-3342	160	66	δ	δ	PROPN
ejpam-3342	160	67	,	,	PUNCT
ejpam-3342	160	68	η)-fine	η)-fine	X
ejpam-3342	160	69	partial	partial	ADJ
ejpam-3342	160	70	division	division	NOUN
ejpam-3342	160	71	d	d	NOUN
ejpam-3342	160	72	=	=	PRON
ejpam-3342	160	73	{	{	PUNCT
ejpam-3342	160	74	(	(	PUNCT
ejpam-3342	160	75	(	(	PUNCT
ejpam-3342	160	76	ui	ui	NOUN
ejpam-3342	160	77	,	,	PUNCT
ejpam-3342	160	78	ξi	ξi	NOUN
ejpam-3342	160	79	]	]	X
ejpam-3342	160	80	,	,	PUNCT
ejpam-3342	160	81	ξi)}ni=1	ξi)}ni=1	NOUN
ejpam-3342	160	82	of	of	ADP
ejpam-3342	160	83	[	[	X
ejpam-3342	160	84	0	0	NUM
ejpam-3342	160	85	,	,	PUNCT
ejpam-3342	160	86	t	t	X
ejpam-3342	160	87	]	]	PUNCT
ejpam-3342	160	88	,	,	PUNCT
ejpam-3342	160	89	we	we	PRON
ejpam-3342	160	90	have	have	VERB
ejpam-3342	160	91	e	e	X
ejpam-3342	160	92	[	[	PUNCT
ejpam-3342	160	93	‖s(f	‖s(f	ADJ
ejpam-3342	160	94	,	,	PUNCT
ejpam-3342	160	95	d	d	PROPN
ejpam-3342	160	96	,	,	PUNCT
ejpam-3342	160	97	δ	δ	PROPN
ejpam-3342	160	98	,	,	PUNCT
ejpam-3342	160	99	η)−a‖2v	η)−a‖2v	PROPN
ejpam-3342	160	100	]	]	PUNCT
ejpam-3342	160	101	<	<	X
ejpam-3342	160	102	ε	ε	PROPN
ejpam-3342	160	103	where	where	SCONJ
ejpam-3342	160	104	s(f	s(f	PROPN
ejpam-3342	160	105	,	,	PUNCT
ejpam-3342	160	106	d	d	PROPN
ejpam-3342	160	107	,	,	PUNCT
ejpam-3342	160	108	δ	δ	PROPN
ejpam-3342	160	109	,	,	PUNCT
ejpam-3342	160	110	η	η	PROPN
ejpam-3342	160	111	)	)	PUNCT
ejpam-3342	160	112	:	:	PUNCT
ejpam-3342	161	1	=	=	SYM
ejpam-3342	161	2	(	(	PUNCT
ejpam-3342	161	3	d	d	NOUN
ejpam-3342	161	4	)	)	PUNCT
ejpam-3342	161	5	∑	∑	PROPN
ejpam-3342	161	6	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	161	7	−wu	−wu	NOUN
ejpam-3342	161	8	)	)	PUNCT
ejpam-3342	161	9	:	:	PUNCT
ejpam-3342	162	1	=	=	SYM
ejpam-3342	162	2	n∑	n∑	PROPN
ejpam-3342	162	3	i=1	i=1	PROPN
ejpam-3342	162	4	fξi(wξi	fξi(wξi	PROPN
ejpam-3342	162	5	−wui	−wui	ADV
ejpam-3342	162	6	)	)	PUNCT
ejpam-3342	162	7	.	.	PUNCT
ejpam-3342	163	1	in	in	ADP
ejpam-3342	163	2	this	this	DET
ejpam-3342	163	3	case	case	NOUN
ejpam-3342	163	4	,	,	PUNCT
ejpam-3342	163	5	f	f	PROPN
ejpam-3342	163	6	is	be	AUX
ejpam-3342	163	7	ihb	ihb	NOUN
ejpam-3342	163	8	-	-	ADJ
ejpam-3342	163	9	integrable	integrable	ADJ
ejpam-3342	163	10	to	to	ADP
ejpam-3342	163	11	a	a	DET
ejpam-3342	163	12	on	on	ADP
ejpam-3342	163	13	[	[	X
ejpam-3342	163	14	0	0	NUM
ejpam-3342	163	15	,	,	PUNCT
ejpam-3342	163	16	t	t	NOUN
ejpam-3342	163	17	]	]	PUNCT
ejpam-3342	163	18	and	and	CCONJ
ejpam-3342	163	19	a	a	PRON
ejpam-3342	163	20	is	be	AUX
ejpam-3342	163	21	called	call	VERB
ejpam-3342	163	22	the	the	DET
ejpam-3342	163	23	ihb	ihb	NOUN
ejpam-3342	163	24	-	-	ADJ
ejpam-3342	163	25	integral	integral	ADJ
ejpam-3342	163	26	of	of	ADP
ejpam-3342	163	27	f	f	PRON
ejpam-3342	163	28	which	which	PRON
ejpam-3342	163	29	will	will	AUX
ejpam-3342	163	30	be	be	AUX
ejpam-3342	163	31	denoted	denote	VERB
ejpam-3342	163	32	by	by	ADP
ejpam-3342	163	33	(	(	PUNCT
ejpam-3342	163	34	ihb	ihb	NOUN
ejpam-3342	163	35	)	)	PUNCT
ejpam-3342	163	36	∫	∫	PROPN
ejpam-3342	163	37	t	t	PROPN
ejpam-3342	163	38	0	0	NUM
ejpam-3342	163	39	ft	ft	NOUN
ejpam-3342	163	40	dwt	dwt	PROPN
ejpam-3342	163	41	or	or	CCONJ
ejpam-3342	163	42	(	(	PUNCT
ejpam-3342	163	43	ihb	ihb	NOUN
ejpam-3342	163	44	)	)	PUNCT
ejpam-3342	163	45	∫	∫	PROPN
ejpam-3342	163	46	t	t	PROPN
ejpam-3342	163	47	0	0	NUM
ejpam-3342	163	48	f	f	PROPN
ejpam-3342	163	49	dw	dw	PROPN
ejpam-3342	163	50	.	.	PUNCT
ejpam-3342	164	1	refer	refer	VERB
ejpam-3342	164	2	to	to	ADP
ejpam-3342	164	3	[	[	X
ejpam-3342	164	4	11	11	NUM
ejpam-3342	164	5	,	,	PUNCT
ejpam-3342	164	6	lemma	lemma	PROPN
ejpam-3342	164	7	3.5	3.5	NUM
ejpam-3342	164	8	and	and	CCONJ
ejpam-3342	164	9	lemma	lemma	PROPN
ejpam-3342	164	10	3.6	3.6	NUM
ejpam-3342	164	11	]	]	PUNCT
ejpam-3342	164	12	for	for	ADP
ejpam-3342	164	13	the	the	DET
ejpam-3342	164	14	proofs	proof	NOUN
ejpam-3342	164	15	of	of	ADP
ejpam-3342	164	16	the	the	DET
ejpam-3342	164	17	following	follow	VERB
ejpam-3342	164	18	two	two	NUM
ejpam-3342	164	19	lemmas	lemma	NOUN
ejpam-3342	164	20	.	.	PUNCT
ejpam-3342	165	1	when	when	SCONJ
ejpam-3342	165	2	we	we	PRON
ejpam-3342	165	3	speak	speak	VERB
ejpam-3342	165	4	of	of	ADP
ejpam-3342	165	5	a	a	DET
ejpam-3342	165	6	subinterval	subinterval	NOUN
ejpam-3342	165	7	of	of	ADP
ejpam-3342	165	8	[	[	X
ejpam-3342	165	9	0	0	NUM
ejpam-3342	165	10	,	,	PUNCT
ejpam-3342	165	11	t	t	X
ejpam-3342	165	12	]	]	PUNCT
ejpam-3342	165	13	,	,	PUNCT
ejpam-3342	165	14	we	we	PRON
ejpam-3342	165	15	shall	shall	AUX
ejpam-3342	165	16	mean	mean	VERB
ejpam-3342	165	17	that	that	SCONJ
ejpam-3342	165	18	the	the	DET
ejpam-3342	165	19	subinterval	subinterval	NOUN
ejpam-3342	165	20	is	be	AUX
ejpam-3342	165	21	either	either	CCONJ
ejpam-3342	165	22	a	a	DET
ejpam-3342	165	23	closed	closed	ADJ
ejpam-3342	165	24	interval	interval	NOUN
ejpam-3342	166	1	[	[	X
ejpam-3342	166	2	v	v	NOUN
ejpam-3342	166	3	,	,	PUNCT
ejpam-3342	166	4	ξ	ξ	NOUN
ejpam-3342	166	5	]	]	PUNCT
ejpam-3342	166	6	or	or	CCONJ
ejpam-3342	166	7	half	half	ADJ
ejpam-3342	166	8	-	-	PUNCT
ejpam-3342	166	9	open	open	ADJ
ejpam-3342	166	10	interval	interval	NOUN
ejpam-3342	166	11	(	(	PUNCT
ejpam-3342	166	12	v	v	NOUN
ejpam-3342	166	13	,	,	PUNCT
ejpam-3342	166	14	ξ	ξ	PROPN
ejpam-3342	166	15	]	]	PUNCT
ejpam-3342	166	16	.	.	PUNCT
ejpam-3342	167	1	lemma	lemma	PROPN
ejpam-3342	167	2	1	1	X
ejpam-3342	167	3	.	.	PUNCT
ejpam-3342	168	1	let	let	VERB
ejpam-3342	168	2	f	f	NOUN
ejpam-3342	168	3	:	:	PUNCT
ejpam-3342	169	1	[	[	X
ejpam-3342	169	2	0	0	NUM
ejpam-3342	169	3	,	,	PUNCT
ejpam-3342	169	4	t	t	X
ejpam-3342	169	5	]	]	PUNCT
ejpam-3342	169	6	×ω→	×ω→	PROPN
ejpam-3342	169	7	l2(uq	l2(uq	PROPN
ejpam-3342	169	8	,	,	PUNCT
ejpam-3342	169	9	v	v	NOUN
ejpam-3342	169	10	)	)	PUNCT
ejpam-3342	169	11	be	be	AUX
ejpam-3342	169	12	a	a	DET
ejpam-3342	169	13	backwards	backwards	ADV
ejpam-3342	169	14	adapted	adapt	VERB
ejpam-3342	169	15	process	process	NOUN
ejpam-3342	169	16	and	and	CCONJ
ejpam-3342	169	17	{	{	PUNCT
ejpam-3342	169	18	[	[	X
ejpam-3342	169	19	vi	vi	ADP
ejpam-3342	169	20	,	,	PUNCT
ejpam-3342	169	21	ξi]}ni=1	ξi]}ni=1	PROPN
ejpam-3342	169	22	be	be	VERB
ejpam-3342	169	23	a	a	DET
ejpam-3342	169	24	finite	finite	ADJ
ejpam-3342	169	25	collection	collection	NOUN
ejpam-3342	169	26	of	of	ADP
ejpam-3342	169	27	disjoint	disjoint	ADJ
ejpam-3342	169	28	subintervals	subinterval	NOUN
ejpam-3342	169	29	of	of	ADP
ejpam-3342	169	30	[	[	X
ejpam-3342	169	31	0	0	NUM
ejpam-3342	169	32	,	,	PUNCT
ejpam-3342	169	33	t	t	X
ejpam-3342	169	34	]	]	PUNCT
ejpam-3342	169	35	.	.	PUNCT
ejpam-3342	170	1	then	then	ADV
ejpam-3342	170	2	e	e	X
ejpam-3342	170	3	∑	∑	NOUN
ejpam-3342	170	4	i	i	PRON
ejpam-3342	170	5	<	<	X
ejpam-3342	170	6	p	p	NOUN
ejpam-3342	170	7	〈	〈	PROPN
ejpam-3342	170	8	fξi(wξi	fξi(wξi	NOUN
ejpam-3342	170	9	−wvi	−wvi	NOUN
ejpam-3342	170	10	,	,	PUNCT
ejpam-3342	170	11	)	)	PUNCT
ejpam-3342	170	12	,	,	PUNCT
ejpam-3342	170	13	fξp(wξp	fξp(wξp	ADV
ejpam-3342	170	14	−wvp	−wvp	NOUN
ejpam-3342	170	15	)	)	PUNCT
ejpam-3342	170	16	〉	〉	NOUN
ejpam-3342	170	17	v	v	ADP
ejpam-3342	170	18			NOUN
ejpam-3342	170	19	=	=	SYM
ejpam-3342	170	20	0	0	X
ejpam-3342	170	21	.	.	PUNCT
ejpam-3342	171	1	lemma	lemma	PROPN
ejpam-3342	171	2	2	2	X
ejpam-3342	171	3	.	.	PUNCT
ejpam-3342	172	1	let	let	VERB
ejpam-3342	172	2	f	f	NOUN
ejpam-3342	172	3	:	:	PUNCT
ejpam-3342	173	1	[	[	X
ejpam-3342	173	2	0	0	NUM
ejpam-3342	173	3	,	,	PUNCT
ejpam-3342	173	4	t	t	X
ejpam-3342	173	5	]	]	PUNCT
ejpam-3342	173	6	×ω→	×ω→	PROPN
ejpam-3342	173	7	l2(uq	l2(uq	PROPN
ejpam-3342	173	8	,	,	PUNCT
ejpam-3342	173	9	v	v	NOUN
ejpam-3342	173	10	)	)	PUNCT
ejpam-3342	173	11	be	be	AUX
ejpam-3342	173	12	a	a	DET
ejpam-3342	173	13	backwards	backwards	ADV
ejpam-3342	173	14	adapted	adapt	VERB
ejpam-3342	173	15	process	process	NOUN
ejpam-3342	173	16	and	and	CCONJ
ejpam-3342	173	17	{	{	PUNCT
ejpam-3342	173	18	[	[	X
ejpam-3342	173	19	vi	vi	ADP
ejpam-3342	173	20	,	,	PUNCT
ejpam-3342	173	21	ξi]}ni=1	ξi]}ni=1	PROPN
ejpam-3342	173	22	be	be	VERB
ejpam-3342	173	23	a	a	DET
ejpam-3342	173	24	finite	finite	ADJ
ejpam-3342	173	25	collection	collection	NOUN
ejpam-3342	173	26	of	of	ADP
ejpam-3342	173	27	disjoint	disjoint	ADJ
ejpam-3342	173	28	subintervals	subinterval	NOUN
ejpam-3342	173	29	of	of	ADP
ejpam-3342	173	30	[	[	X
ejpam-3342	173	31	0	0	NUM
ejpam-3342	173	32	,	,	PUNCT
ejpam-3342	173	33	t	t	X
ejpam-3342	173	34	]	]	PUNCT
ejpam-3342	173	35	.	.	PUNCT
ejpam-3342	174	1	then	then	ADV
ejpam-3342	174	2	e	e	X
ejpam-3342	174	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3342	174	4	n∑	n∑	PROPN
ejpam-3342	174	5	i=1	i=1	PROPN
ejpam-3342	174	6	fξi(wξi	fξi(wξi	NOUN
ejpam-3342	174	7	−wvi	−wvi	ADV
ejpam-3342	174	8	)	)	PUNCT
ejpam-3342	174	9	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3342	174	10	2	2	NUM
ejpam-3342	174	11	v	v	NOUN
ejpam-3342	174	12			NOUN
ejpam-3342	174	13	=	=	PUNCT
ejpam-3342	175	1	n∑	n∑	NOUN
ejpam-3342	175	2	i=1	i=1	PROPN
ejpam-3342	176	1	e	e	X
ejpam-3342	176	2	[	[	PUNCT
ejpam-3342	176	3	‖fξi(wξi	‖fξi(wξi	PROPN
ejpam-3342	176	4	−wvi)‖	−wvi)‖	PROPN
ejpam-3342	176	5	2	2	NUM
ejpam-3342	176	6	v	v	NOUN
ejpam-3342	176	7	]	]	PUNCT
ejpam-3342	177	1	=	=	PUNCT
ejpam-3342	177	2	n∑	n∑	NOUN
ejpam-3342	177	3	i=1	i=1	PROPN
ejpam-3342	177	4	(	(	PUNCT
ejpam-3342	177	5	ξi−	ξi−	PROPN
ejpam-3342	177	6	vi)e	vi)e	PROPN
ejpam-3342	177	7	[	[	PUNCT
ejpam-3342	177	8	‖fξi‖	‖fξi‖	PROPN
ejpam-3342	177	9	2	2	NUM
ejpam-3342	177	10	l2(uq	l2(uq	PROPN
ejpam-3342	177	11	,	,	PUNCT
ejpam-3342	177	12	v	v	NOUN
ejpam-3342	177	13	)	)	PUNCT
ejpam-3342	177	14	]	]	PUNCT
ejpam-3342	177	15	.	.	PUNCT
ejpam-3342	178	1	r.	r.	PROPN
ejpam-3342	178	2	rulete	rulete	PROPN
ejpam-3342	178	3	,	,	PUNCT
ejpam-3342	178	4	m.	m.	NOUN
ejpam-3342	178	5	labendia	labendia	PROPN
ejpam-3342	178	6	/	/	SYM
ejpam-3342	178	7	eur	eur	PROPN
ejpam-3342	178	8	.	.	PUNCT
ejpam-3342	179	1	j.	j.	PROPN
ejpam-3342	179	2	pure	pure	PROPN
ejpam-3342	179	3	appl	appl	PROPN
ejpam-3342	179	4	.	.	PROPN
ejpam-3342	179	5	math	math	PROPN
ejpam-3342	179	6	,	,	PUNCT
ejpam-3342	179	7	12	12	NUM
ejpam-3342	179	8	(	(	PUNCT
ejpam-3342	179	9	1	1	NUM
ejpam-3342	179	10	)	)	PUNCT
ejpam-3342	179	11	(	(	PUNCT
ejpam-3342	179	12	2019	2019	NUM
ejpam-3342	179	13	)	)	PUNCT
ejpam-3342	179	14	,	,	PUNCT
ejpam-3342	179	15	58	58	NUM
ejpam-3342	179	16	-	-	SYM
ejpam-3342	179	17	78	78	NUM
ejpam-3342	179	18	64	64	NUM
ejpam-3342	179	19	theorem	theorem	NOUN
ejpam-3342	179	20	1	1	NUM
ejpam-3342	179	21	.	.	PUNCT
ejpam-3342	180	1	let	let	VERB
ejpam-3342	180	2	v	v	NOUN
ejpam-3342	180	3	,	,	PUNCT
ejpam-3342	180	4	ξ	ξ	PROPN
ejpam-3342	180	5	∈	∈	PROPN
ejpam-3342	181	1	[	[	X
ejpam-3342	181	2	0	0	NUM
ejpam-3342	181	3	,	,	PUNCT
ejpam-3342	181	4	t	t	X
ejpam-3342	181	5	]	]	PUNCT
ejpam-3342	181	6	with	with	ADP
ejpam-3342	181	7	v	v	ADP
ejpam-3342	181	8	<	<	X
ejpam-3342	181	9	ξ	ξ	PROPN
ejpam-3342	181	10	.	.	PUNCT
ejpam-3342	182	1	then	then	ADV
ejpam-3342	182	2	(	(	PUNCT
ejpam-3342	182	3	i	i	NOUN
ejpam-3342	182	4	)	)	PUNCT
ejpam-3342	182	5	e	e	X
ejpam-3342	182	6	[	[	PUNCT
ejpam-3342	182	7	||wξ	||wξ	NOUN
ejpam-3342	182	8	−wv||2u	−wv||2u	PROPN
ejpam-3342	182	9	]	]	X
ejpam-3342	182	10	=	=	PUNCT
ejpam-3342	182	11	(	(	PUNCT
ejpam-3342	182	12	ξ	ξ	X
ejpam-3342	182	13	−	−	NOUN
ejpam-3342	182	14	v)trq	v)trq	PROPN
ejpam-3342	182	15	;	;	PUNCT
ejpam-3342	182	16	(	(	PUNCT
ejpam-3342	182	17	ii	ii	NOUN
ejpam-3342	182	18	)	)	PUNCT
ejpam-3342	182	19	e	e	NOUN
ejpam-3342	182	20	[	[	PUNCT
ejpam-3342	182	21	||wξ	||wξ	NOUN
ejpam-3342	182	22	−wv||4u	−wv||4u	PROPN
ejpam-3342	182	23	]	]	X
ejpam-3342	182	24	=	=	PUNCT
ejpam-3342	182	25	(	(	PUNCT
ejpam-3342	182	26	ξ	ξ	X
ejpam-3342	182	27	−	−	PROPN
ejpam-3342	182	28	v)2	v)2	NOUN
ejpam-3342	182	29	2	2	ADP
ejpam-3342	182	30	∞∑	∞∑	NUM
ejpam-3342	182	31	j=1	j=1	ADJ
ejpam-3342	182	32	λ2	λ2	PROPN
ejpam-3342	182	33	j	j	PROPN
ejpam-3342	182	34	+	+	CCONJ
ejpam-3342	182	35	(	(	PUNCT
ejpam-3342	182	36	trq)2	trq)2	PROPN
ejpam-3342	182	37	.	.	PROPN
ejpam-3342	182	38	proof	proof	NOUN
ejpam-3342	182	39	.	.	PUNCT
ejpam-3342	183	1	let	let	VERB
ejpam-3342	183	2	v	v	NOUN
ejpam-3342	183	3	,	,	PUNCT
ejpam-3342	183	4	ξ	ξ	PROPN
ejpam-3342	183	5	∈	∈	PROPN
ejpam-3342	184	1	[	[	X
ejpam-3342	184	2	0	0	NUM
ejpam-3342	184	3	,	,	PUNCT
ejpam-3342	184	4	t	t	X
ejpam-3342	184	5	]	]	PUNCT
ejpam-3342	184	6	with	with	ADP
ejpam-3342	184	7	v	v	ADP
ejpam-3342	184	8	<	<	X
ejpam-3342	184	9	ξ	ξ	PROPN
ejpam-3342	184	10	.	.	PUNCT
ejpam-3342	185	1	then	then	ADV
ejpam-3342	185	2	(	(	PUNCT
ejpam-3342	185	3	i	i	NOUN
ejpam-3342	185	4	)	)	PUNCT
ejpam-3342	185	5	e	e	X
ejpam-3342	185	6	[	[	PUNCT
ejpam-3342	185	7	||wξ	||wξ	NOUN
ejpam-3342	185	8	−wv||2u	−wv||2u	PROPN
ejpam-3342	185	9	]	]	PUNCT
ejpam-3342	185	10	=	=	PUNCT
ejpam-3342	185	11	e	e	ADP
ejpam-3342	185	12			NOUN
ejpam-3342	185	13	∞∑	∞∑	NUM
ejpam-3342	185	14	j=1	j=1	ADJ
ejpam-3342	185	15	〈	〈	NOUN
ejpam-3342	185	16	wξ	wξ	NOUN
ejpam-3342	185	17	−wv	−wv	PROPN
ejpam-3342	185	18	,	,	PUNCT
ejpam-3342	185	19	ej〉2u	ej〉2u	X
ejpam-3342	185	20			NOUN
ejpam-3342	185	21	=	=	PUNCT
ejpam-3342	185	22	∞∑	∞∑	NUM
ejpam-3342	185	23	j=1	j=1	ADJ
ejpam-3342	185	24	e	e	X
ejpam-3342	185	25	[	[	PUNCT
ejpam-3342	185	26	〈	〈	PROPN
ejpam-3342	185	27	wξ	wξ	NOUN
ejpam-3342	185	28	−wv	−wv	PROPN
ejpam-3342	185	29	,	,	PUNCT
ejpam-3342	185	30	ej〉2u	ej〉2u	NOUN
ejpam-3342	185	31	]	]	PUNCT
ejpam-3342	185	32	.	.	PUNCT
ejpam-3342	186	1	since	since	SCONJ
ejpam-3342	186	2	〈	〈	PROPN
ejpam-3342	186	3	wt	wt	NUM
ejpam-3342	186	4	,	,	PUNCT
ejpam-3342	186	5	ej〉u√	ej〉u√	X
ejpam-3342	186	6	λj	λj	X
ejpam-3342	186	7	is	be	AUX
ejpam-3342	186	8	a	a	DET
ejpam-3342	186	9	brownian	brownian	ADJ
ejpam-3342	186	10	motion	motion	NOUN
ejpam-3342	186	11	,	,	PUNCT
ejpam-3342	186	12	e	e	X
ejpam-3342	186	13	(〈wξ	(〈wξ	ADJ
ejpam-3342	186	14	−wv	−wv	NOUN
ejpam-3342	186	15	,	,	PUNCT
ejpam-3342	186	16	ej〉u√	ej〉u√	ADJ
ejpam-3342	186	17	λj	λj	NOUN
ejpam-3342	186	18	)	)	PUNCT
ejpam-3342	186	19	2	2	NUM
ejpam-3342	186	20			NOUN
ejpam-3342	186	21	=	=	SYM
ejpam-3342	186	22	ξ	ξ	X
ejpam-3342	186	23	−	−	NOUN
ejpam-3342	186	24	v.	v.	ADP
ejpam-3342	186	25	hence	hence	ADV
ejpam-3342	186	26	,	,	PUNCT
ejpam-3342	186	27	e	e	X
ejpam-3342	186	28	[	[	PUNCT
ejpam-3342	186	29	||wξ	||wξ	NOUN
ejpam-3342	186	30	−wv||2u	−wv||2u	PROPN
ejpam-3342	186	31	]	]	PUNCT
ejpam-3342	187	1	=	=	PUNCT
ejpam-3342	187	2	∞∑	∞∑	NUM
ejpam-3342	187	3	j=1	j=1	NOUN
ejpam-3342	187	4	(	(	PUNCT
ejpam-3342	187	5	ξ	ξ	X
ejpam-3342	187	6	−	−	PROPN
ejpam-3342	187	7	v)λj	v)λj	PROPN
ejpam-3342	187	8	=	=	SYM
ejpam-3342	187	9	(	(	PUNCT
ejpam-3342	187	10	ξ	ξ	X
ejpam-3342	187	11	−	−	PROPN
ejpam-3342	187	12	v	v	NOUN
ejpam-3342	187	13	)	)	PUNCT
ejpam-3342	187	14	∞∑	∞∑	NUM
ejpam-3342	187	15	j=1	j=1	NOUN
ejpam-3342	187	16	λj	λj	X
ejpam-3342	187	17	=	=	SYM
ejpam-3342	187	18	(	(	PUNCT
ejpam-3342	187	19	ξ	ξ	X
ejpam-3342	187	20	−	−	NOUN
ejpam-3342	187	21	v)trq	v)trq	PROPN
ejpam-3342	187	22	.	.	PUNCT
ejpam-3342	187	23	(	(	PUNCT
ejpam-3342	187	24	ii	ii	NOUN
ejpam-3342	187	25	)	)	PUNCT
ejpam-3342	187	26	note	note	VERB
ejpam-3342	187	27	that	that	SCONJ
ejpam-3342	187	28	e	e	NOUN
ejpam-3342	187	29	[	[	PUNCT
ejpam-3342	187	30	||wξ	||wξ	NOUN
ejpam-3342	187	31	−wv||4u	−wv||4u	PROPN
ejpam-3342	187	32	]	]	PUNCT
ejpam-3342	187	33	=	=	PUNCT
ejpam-3342	187	34	e	e	PROPN
ejpam-3342	187	35			VERB
ejpam-3342	187	36	∞∑	∞∑	NUM
ejpam-3342	187	37	j=1	j=1	ADJ
ejpam-3342	187	38	〈	〈	NOUN
ejpam-3342	187	39	wξ	wξ	NOUN
ejpam-3342	187	40	−wv	−wv	PROPN
ejpam-3342	187	41	,	,	PUNCT
ejpam-3342	187	42	ej〉2u	ej〉2u	NOUN
ejpam-3342	187	43	2	2	X
ejpam-3342	187	44	=	=	PUNCT
ejpam-3342	187	45	e	e	ADP
ejpam-3342	187	46			NOUN
ejpam-3342	187	47	∞∑	∞∑	NUM
ejpam-3342	187	48	j=1	j=1	ADJ
ejpam-3342	187	49	〈	〈	NOUN
ejpam-3342	187	50	wξ	wξ	NOUN
ejpam-3342	187	51	−wv	−wv	PROPN
ejpam-3342	187	52	,	,	PUNCT
ejpam-3342	187	53	ej〉4u	ej〉4u	NOUN
ejpam-3342	188	1	+	+	CCONJ
ejpam-3342	188	2	∑	∑	PROPN
ejpam-3342	188	3	j	j	PROPN
ejpam-3342	188	4	6	6	NUM
ejpam-3342	188	5	=	=	NOUN
ejpam-3342	188	6	l	l	NOUN
ejpam-3342	188	7	〈	〈	NOUN
ejpam-3342	188	8	wξ	wξ	NOUN
ejpam-3342	188	9	−wv	−wv	PROPN
ejpam-3342	188	10	,	,	PUNCT
ejpam-3342	188	11	ej〉2u	ej〉2u	NOUN
ejpam-3342	188	12	〈	〈	PROPN
ejpam-3342	188	13	wξ	wξ	ADJ
ejpam-3342	188	14	−wv	−wv	PROPN
ejpam-3342	188	15	,	,	PUNCT
ejpam-3342	188	16	el〉2u	el〉2u	NOUN
ejpam-3342	188	17			NOUN
ejpam-3342	188	18	=	=	PUNCT
ejpam-3342	189	1	∞∑	∞∑	NUM
ejpam-3342	189	2	j=1	j=1	NOUN
ejpam-3342	189	3	e	e	X
ejpam-3342	189	4	〈	〈	NOUN
ejpam-3342	189	5	wξ	wξ	NOUN
ejpam-3342	189	6	−wv	−wv	PROPN
ejpam-3342	189	7	,	,	PUNCT
ejpam-3342	189	8	ej〉4u	ej〉4u	NOUN
ejpam-3342	189	9	+	+	CCONJ
ejpam-3342	189	10	∑	∑	PROPN
ejpam-3342	189	11	j	j	PROPN
ejpam-3342	189	12	6	6	NUM
ejpam-3342	189	13	=	=	NOUN
ejpam-3342	189	14	l	l	X
ejpam-3342	189	15	e	e	NOUN
ejpam-3342	189	16	[	[	PUNCT
ejpam-3342	189	17	〈	〈	PROPN
ejpam-3342	189	18	wξ	wξ	ADJ
ejpam-3342	189	19	−wv	−wv	PROPN
ejpam-3342	189	20	,	,	PUNCT
ejpam-3342	189	21	ej〉2u	ej〉2u	NOUN
ejpam-3342	189	22	]	]	X
ejpam-3342	189	23	e	e	X
ejpam-3342	189	24	[	[	PUNCT
ejpam-3342	189	25	〈	〈	PROPN
ejpam-3342	189	26	wξ	wξ	NOUN
ejpam-3342	189	27	−wv	−wv	PROPN
ejpam-3342	189	28	,	,	PUNCT
ejpam-3342	189	29	el〉2u	el〉2u	VERB
ejpam-3342	189	30	]	]	PUNCT
ejpam-3342	189	31	.	.	PUNCT
ejpam-3342	190	1	since	since	SCONJ
ejpam-3342	190	2	〈	〈	PROPN
ejpam-3342	190	3	wt	wt	NUM
ejpam-3342	190	4	,	,	PUNCT
ejpam-3342	190	5	ej〉u√	ej〉u√	X
ejpam-3342	190	6	λj	λj	X
ejpam-3342	190	7	is	be	AUX
ejpam-3342	190	8	a	a	DET
ejpam-3342	190	9	brownian	brownian	ADJ
ejpam-3342	190	10	motion	motion	NOUN
ejpam-3342	190	11	,	,	PUNCT
ejpam-3342	190	12	e	e	X
ejpam-3342	190	13	(〈wξ	(〈wξ	ADJ
ejpam-3342	190	14	−wv	−wv	NOUN
ejpam-3342	190	15	,	,	PUNCT
ejpam-3342	190	16	ej〉u√	ej〉u√	X
ejpam-3342	190	17	λj	λj	NOUN
ejpam-3342	190	18	)	)	PUNCT
ejpam-3342	190	19	4	4	NUM
ejpam-3342	190	20			NOUN
ejpam-3342	190	21	=	=	SYM
ejpam-3342	190	22	3(ξ	3(ξ	NUM
ejpam-3342	190	23	−	−	PRON
ejpam-3342	190	24	v)2	v)2	PROPN
ejpam-3342	190	25	and	and	CCONJ
ejpam-3342	190	26	e	e	PROPN
ejpam-3342	190	27	(〈wξ	(〈wξ	PROPN
ejpam-3342	190	28	−wv	−wv	NOUN
ejpam-3342	190	29	,	,	PUNCT
ejpam-3342	190	30	ej〉u√	ej〉u√	ADJ
ejpam-3342	190	31	λj	λj	NOUN
ejpam-3342	190	32	)	)	PUNCT
ejpam-3342	190	33	2	2	NUM
ejpam-3342	190	34			NOUN
ejpam-3342	190	35	=	=	SYM
ejpam-3342	190	36	ξ	ξ	X
ejpam-3342	190	37	−	−	PROPN
ejpam-3342	190	38	v.	v.	PROPN
ejpam-3342	190	39	r.	r.	PROPN
ejpam-3342	190	40	rulete	rulete	PROPN
ejpam-3342	190	41	,	,	PUNCT
ejpam-3342	190	42	m.	m.	NOUN
ejpam-3342	190	43	labendia	labendia	PROPN
ejpam-3342	190	44	/	/	SYM
ejpam-3342	190	45	eur	eur	PROPN
ejpam-3342	190	46	.	.	PUNCT
ejpam-3342	191	1	j.	j.	PROPN
ejpam-3342	191	2	pure	pure	PROPN
ejpam-3342	191	3	appl	appl	PROPN
ejpam-3342	191	4	.	.	PROPN
ejpam-3342	191	5	math	math	PROPN
ejpam-3342	191	6	,	,	PUNCT
ejpam-3342	191	7	12	12	NUM
ejpam-3342	191	8	(	(	PUNCT
ejpam-3342	191	9	1	1	NUM
ejpam-3342	191	10	)	)	PUNCT
ejpam-3342	191	11	(	(	PUNCT
ejpam-3342	191	12	2019	2019	NUM
ejpam-3342	191	13	)	)	PUNCT
ejpam-3342	191	14	,	,	PUNCT
ejpam-3342	191	15	58	58	NUM
ejpam-3342	191	16	-	-	SYM
ejpam-3342	191	17	78	78	NUM
ejpam-3342	191	18	65	65	NUM
ejpam-3342	191	19	thus	thus	ADV
ejpam-3342	191	20	,	,	PUNCT
ejpam-3342	191	21	e	e	X
ejpam-3342	191	22	[	[	PUNCT
ejpam-3342	191	23	||wξ	||wξ	NOUN
ejpam-3342	191	24	−wv||4u	−wv||4u	PROPN
ejpam-3342	191	25	]	]	PUNCT
ejpam-3342	191	26	=	=	PUNCT
ejpam-3342	192	1	∞∑	∞∑	NUM
ejpam-3342	192	2	j=1	j=1	NOUN
ejpam-3342	192	3	3λ2	3λ2	NUM
ejpam-3342	192	4	j	j	PROPN
ejpam-3342	192	5	(	(	PUNCT
ejpam-3342	192	6	ξ	ξ	PROPN
ejpam-3342	192	7	−	−	PROPN
ejpam-3342	192	8	v)2	v)2	NOUN
ejpam-3342	192	9	+	+	CCONJ
ejpam-3342	192	10	∑	∑	PROPN
ejpam-3342	192	11	j	j	PROPN
ejpam-3342	192	12	6	6	NUM
ejpam-3342	192	13	=	=	PROPN
ejpam-3342	192	14	l	l	NOUN
ejpam-3342	192	15	λjλl(ξ	λjλl(ξ	NOUN
ejpam-3342	192	16	−	−	X
ejpam-3342	192	17	v)2	v)2	NOUN
ejpam-3342	192	18	=	=	SYM
ejpam-3342	192	19	(	(	PUNCT
ejpam-3342	192	20	ξ	ξ	X
ejpam-3342	192	21	−	−	PROPN
ejpam-3342	192	22	v)2	v)2	ADJ
ejpam-3342	192	23	2	2	NOUN
ejpam-3342	192	24	∞∑	∞∑	NUM
ejpam-3342	192	25	j=1	j=1	ADJ
ejpam-3342	192	26	λ2	λ2	PROPN
ejpam-3342	192	27	j	j	PROPN
ejpam-3342	192	28	+	+	CCONJ
ejpam-3342	192	29			PROPN
ejpam-3342	192	30	∞∑	∞∑	NUM
ejpam-3342	192	31	j=1	j=1	ADJ
ejpam-3342	192	32	λ2	λ2	PROPN
ejpam-3342	192	33	j	j	PROPN
ejpam-3342	192	34	+	+	CCONJ
ejpam-3342	192	35	∑	∑	PROPN
ejpam-3342	192	36	j	j	PROPN
ejpam-3342	192	37	6	6	NUM
ejpam-3342	192	38	=	=	NOUN
ejpam-3342	192	39	l	l	NOUN
ejpam-3342	192	40	λjλl	λjλl	VERB
ejpam-3342	192	41			X
ejpam-3342	192	42	=	=	PUNCT
ejpam-3342	192	43	(	(	PUNCT
ejpam-3342	192	44	ξ	ξ	X
ejpam-3342	192	45	−	−	PROPN
ejpam-3342	192	46	v)2	v)2	ADJ
ejpam-3342	192	47	2	2	NOUN
ejpam-3342	192	48	∞∑	∞∑	NUM
ejpam-3342	192	49	j=1	j=1	ADJ
ejpam-3342	192	50	λ2	λ2	PROPN
ejpam-3342	192	51	j	j	PROPN
ejpam-3342	192	52	+	+	CCONJ
ejpam-3342	192	53			PROPN
ejpam-3342	192	54	∞∑	∞∑	PROPN
ejpam-3342	192	55	j=1	j=1	NOUN
ejpam-3342	192	56	λj	λj	X
ejpam-3342	192	57	2	2	PROPN
ejpam-3342	192	58	=	=	PUNCT
ejpam-3342	193	1	(	(	PUNCT
ejpam-3342	193	2	ξ	ξ	X
ejpam-3342	193	3	−	−	PROPN
ejpam-3342	193	4	v)2	v)2	ADJ
ejpam-3342	193	5	2	2	NOUN
ejpam-3342	193	6	∞∑	∞∑	NUM
ejpam-3342	193	7	j=1	j=1	ADJ
ejpam-3342	193	8	λ2	λ2	PROPN
ejpam-3342	193	9	j	j	PROPN
ejpam-3342	193	10	+	+	CCONJ
ejpam-3342	193	11	(	(	PUNCT
ejpam-3342	193	12	trq)2	trq)2	PROPN
ejpam-3342	193	13			NOUN
ejpam-3342	193	14	.	.	PUNCT
ejpam-3342	194	1	thereby	thereby	ADV
ejpam-3342	194	2	,	,	PUNCT
ejpam-3342	194	3	completing	complete	VERB
ejpam-3342	194	4	the	the	DET
ejpam-3342	194	5	proof	proof	NOUN
ejpam-3342	194	6	.	.	PUNCT
ejpam-3342	195	1	�	�	PROPN
ejpam-3342	195	2	example	example	NOUN
ejpam-3342	195	3	1	1	X
ejpam-3342	195	4	.	.	PUNCT
ejpam-3342	196	1	let	let	VERB
ejpam-3342	196	2	w	w	VERB
ejpam-3342	196	3	:	:	PUNCT
ejpam-3342	197	1	[	[	X
ejpam-3342	197	2	0	0	NUM
ejpam-3342	197	3	,	,	PUNCT
ejpam-3342	197	4	t	t	X
ejpam-3342	197	5	]	]	PUNCT
ejpam-3342	197	6	×	×	PROPN
ejpam-3342	197	7	ω	ω	PROPN
ejpam-3342	197	8	→	→	SYM
ejpam-3342	197	9	u	u	NOUN
ejpam-3342	197	10	be	be	VERB
ejpam-3342	197	11	a	a	DET
ejpam-3342	197	12	q	q	ADJ
ejpam-3342	197	13	-	-	PUNCT
ejpam-3342	197	14	weiner	weiner	NOUN
ejpam-3342	197	15	process	process	NOUN
ejpam-3342	197	16	.	.	PUNCT
ejpam-3342	198	1	then	then	ADV
ejpam-3342	198	2	〈	〈	PROPN
ejpam-3342	198	3	wt	wt	PROPN
ejpam-3342	198	4	,	,	PUNCT
ejpam-3342	198	5	·	·	PUNCT
ejpam-3342	198	6	〉	〉	NUM
ejpam-3342	198	7	u	u	NOUN
ejpam-3342	198	8	is	be	AUX
ejpam-3342	198	9	ihbintegrable	ihbintegrable	ADJ
ejpam-3342	198	10	on	on	ADP
ejpam-3342	198	11	[	[	X
ejpam-3342	198	12	0	0	NUM
ejpam-3342	198	13	,	,	PUNCT
ejpam-3342	198	14	t	t	NOUN
ejpam-3342	198	15	]	]	PUNCT
ejpam-3342	198	16	and	and	CCONJ
ejpam-3342	198	17	(	(	PUNCT
ejpam-3342	198	18	ihb	ihb	NOUN
ejpam-3342	198	19	)	)	PUNCT
ejpam-3342	198	20	∫	∫	PROPN
ejpam-3342	198	21	t	t	PROPN
ejpam-3342	198	22	0	0	NUM
ejpam-3342	198	23	〈	〈	PROPN
ejpam-3342	198	24	wt	wt	NUM
ejpam-3342	198	25	,	,	PUNCT
ejpam-3342	198	26	·	·	PUNCT
ejpam-3342	198	27	〉	〉	NUM
ejpam-3342	198	28	u	u	NOUN
ejpam-3342	198	29	dwt	dwt	NOUN
ejpam-3342	198	30	=	=	NOUN
ejpam-3342	198	31	1	1	NUM
ejpam-3342	198	32	2	2	NUM
ejpam-3342	198	33	(	(	PUNCT
ejpam-3342	198	34	||wt	||wt	ADJ
ejpam-3342	198	35	||2u	||2u	X
ejpam-3342	198	36	+	+	PROPN
ejpam-3342	198	37	t	t	PROPN
ejpam-3342	198	38	(	(	PUNCT
ejpam-3342	198	39	trq	trq	NOUN
ejpam-3342	198	40	)	)	PUNCT
ejpam-3342	198	41	)	)	PUNCT
ejpam-3342	198	42	.	.	PUNCT
ejpam-3342	199	1	proof	proof	NOUN
ejpam-3342	199	2	.	.	PUNCT
ejpam-3342	200	1	we	we	PRON
ejpam-3342	200	2	shall	shall	AUX
ejpam-3342	200	3	consider	consider	VERB
ejpam-3342	200	4	first	first	ADV
ejpam-3342	200	5	the	the	DET
ejpam-3342	200	6	following	follow	VERB
ejpam-3342	200	7	claims	claim	NOUN
ejpam-3342	200	8	.	.	PUNCT
ejpam-3342	201	1	claim	claim	NOUN
ejpam-3342	201	2	1	1	X
ejpam-3342	201	3	.	.	PUNCT
ejpam-3342	202	1	let	let	VERB
ejpam-3342	202	2	d	d	NOUN
ejpam-3342	202	3	=	=	PRON
ejpam-3342	202	4	{	{	PUNCT
ejpam-3342	202	5	[	[	X
ejpam-3342	202	6	vi	vi	ADP
ejpam-3342	202	7	,	,	PUNCT
ejpam-3342	202	8	ξi]}ni=1	ξi]}ni=1	PROPN
ejpam-3342	202	9	be	be	VERB
ejpam-3342	202	10	a	a	DET
ejpam-3342	202	11	finite	finite	ADJ
ejpam-3342	202	12	collection	collection	NOUN
ejpam-3342	202	13	of	of	ADP
ejpam-3342	202	14	disjoint	disjoint	ADJ
ejpam-3342	202	15	subintervals	subinterval	NOUN
ejpam-3342	202	16	of	of	ADP
ejpam-3342	202	17	[	[	X
ejpam-3342	202	18	0	0	NUM
ejpam-3342	202	19	,	,	PUNCT
ejpam-3342	202	20	t	t	X
ejpam-3342	202	21	]	]	PUNCT
ejpam-3342	202	22	.	.	PUNCT
ejpam-3342	203	1	then	then	ADV
ejpam-3342	203	2	e	e	PROPN
ejpam-3342	203	3	∣∣∣∣∣(d	∣∣∣∣∣(d	NOUN
ejpam-3342	203	4	)	)	PUNCT
ejpam-3342	204	1	n∑	n∑	PROPN
ejpam-3342	205	1	i=1	i=1	PROPN
ejpam-3342	205	2	{	{	PUNCT
ejpam-3342	205	3	||wξi	||wξi	PROPN
ejpam-3342	205	4	−wvi	−wvi	NOUN
ejpam-3342	205	5	||2u	||2u	PROPN
ejpam-3342	206	1	−	−	PROPN
ejpam-3342	207	1	(	(	PUNCT
ejpam-3342	207	2	ξi	ξi	NOUN
ejpam-3342	207	3	−	−	NOUN
ejpam-3342	207	4	vi)trq	vi)trq	NOUN
ejpam-3342	207	5	}	}	PUNCT
ejpam-3342	207	6	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3342	207	7	2	2	NUM
ejpam-3342	207	8			NOUN
ejpam-3342	207	9	=	=	PUNCT
ejpam-3342	207	10	2	2	NUM
ejpam-3342	207	11	m	m	NOUN
ejpam-3342	207	12	[	[	PUNCT
ejpam-3342	207	13	(	(	PUNCT
ejpam-3342	207	14	d	d	NOUN
ejpam-3342	207	15	)	)	PUNCT
ejpam-3342	208	1	n∑	n∑	NOUN
ejpam-3342	208	2	i=1	i=1	PROPN
ejpam-3342	209	1	(	(	PUNCT
ejpam-3342	209	2	ξi	ξi	NOUN
ejpam-3342	209	3	−	−	PROPN
ejpam-3342	210	1	vi)2	vi)2	PROPN
ejpam-3342	210	2	]	]	PUNCT
ejpam-3342	210	3	where	where	SCONJ
ejpam-3342	210	4	m	m	NOUN
ejpam-3342	210	5	=	=	PUNCT
ejpam-3342	210	6	∑∞	∑∞	NOUN
ejpam-3342	211	1	j=1	j=1	NOUN
ejpam-3342	211	2	λ	λ	PROPN
ejpam-3342	211	3	2	2	NUM
ejpam-3342	211	4	j	j	NOUN
ejpam-3342	211	5	<	<	X
ejpam-3342	211	6	∞.	∞.	PROPN
ejpam-3342	211	7	to	to	PART
ejpam-3342	211	8	verify	verify	VERB
ejpam-3342	211	9	the	the	DET
ejpam-3342	211	10	first	first	ADJ
ejpam-3342	211	11	claim	claim	NOUN
ejpam-3342	211	12	,	,	PUNCT
ejpam-3342	211	13	e	e	NOUN
ejpam-3342	211	14	∣∣∣∣∣(d	∣∣∣∣∣(d	NOUN
ejpam-3342	211	15	)	)	PUNCT
ejpam-3342	212	1	n∑	n∑	PROPN
ejpam-3342	213	1	i=1	i=1	PROPN
ejpam-3342	213	2	{	{	PUNCT
ejpam-3342	213	3	||wξi	||wξi	PROPN
ejpam-3342	213	4	−wvi	−wvi	NOUN
ejpam-3342	213	5	||2u	||2u	PROPN
ejpam-3342	214	1	−	−	PROPN
ejpam-3342	215	1	(	(	PUNCT
ejpam-3342	215	2	ξi	ξi	NOUN
ejpam-3342	215	3	−	−	NOUN
ejpam-3342	215	4	vi)trq	vi)trq	NOUN
ejpam-3342	215	5	}	}	PUNCT
ejpam-3342	215	6	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3342	215	7	2	2	NUM
ejpam-3342	215	8			NOUN
ejpam-3342	215	9	=	=	PUNCT
ejpam-3342	215	10	n∑	n∑	NOUN
ejpam-3342	215	11	i=1	i=1	X
ejpam-3342	216	1	e	e	X
ejpam-3342	217	1	[	[	X
ejpam-3342	217	2	(	(	PUNCT
ejpam-3342	217	3	||wξi	||wξi	PROPN
ejpam-3342	217	4	−wvi	−wvi	NOUN
ejpam-3342	217	5	||2u	||2u	PROPN
ejpam-3342	217	6	−	−	PROPN
ejpam-3342	217	7	(	(	PUNCT
ejpam-3342	217	8	ξi	ξi	NOUN
ejpam-3342	217	9	−	−	NOUN
ejpam-3342	217	10	vi)trq	vi)trq	NOUN
ejpam-3342	217	11	)	)	PUNCT
ejpam-3342	217	12	2	2	X
ejpam-3342	217	13	]	]	PUNCT
ejpam-3342	217	14	+	+	CCONJ
ejpam-3342	217	15	2	2	NUM
ejpam-3342	217	16	∑	∑	PUNCT
ejpam-3342	217	17	i	i	PRON
ejpam-3342	217	18	<	<	X
ejpam-3342	217	19	p	p	X
ejpam-3342	217	20	e	e	X
ejpam-3342	217	21	[	[	X
ejpam-3342	217	22	(	(	PUNCT
ejpam-3342	217	23	||wξi	||wξi	PROPN
ejpam-3342	217	24	−wvi	−wvi	NOUN
ejpam-3342	217	25	||2u	||2u	PROPN
ejpam-3342	217	26	−	−	PROPN
ejpam-3342	217	27	(	(	PUNCT
ejpam-3342	217	28	ξi	ξi	NOUN
ejpam-3342	217	29	−	−	PROPN
ejpam-3342	217	30	vi)trq	vi)trq	NOUN
ejpam-3342	217	31	)	)	PUNCT
ejpam-3342	217	32	(	(	PUNCT
ejpam-3342	217	33	||wξp	||wξp	PROPN
ejpam-3342	217	34	−wvp	−wvp	NOUN
ejpam-3342	217	35	||2u	||2u	X
ejpam-3342	217	36	−	−	PROPN
ejpam-3342	217	37	(	(	PUNCT
ejpam-3342	217	38	ξp	ξp	NUM
ejpam-3342	217	39	−	−	PROPN
ejpam-3342	217	40	vp)trq	vp)trq	NOUN
ejpam-3342	217	41	)	)	PUNCT
ejpam-3342	217	42	]	]	PUNCT
ejpam-3342	217	43	.	.	PUNCT
ejpam-3342	218	1	r.	r.	PROPN
ejpam-3342	218	2	rulete	rulete	PROPN
ejpam-3342	218	3	,	,	PUNCT
ejpam-3342	218	4	m.	m.	NOUN
ejpam-3342	218	5	labendia	labendia	PROPN
ejpam-3342	218	6	/	/	SYM
ejpam-3342	218	7	eur	eur	PROPN
ejpam-3342	218	8	.	.	PUNCT
ejpam-3342	219	1	j.	j.	PROPN
ejpam-3342	219	2	pure	pure	PROPN
ejpam-3342	219	3	appl	appl	PROPN
ejpam-3342	219	4	.	.	PROPN
ejpam-3342	219	5	math	math	PROPN
ejpam-3342	219	6	,	,	PUNCT
ejpam-3342	219	7	12	12	NUM
ejpam-3342	219	8	(	(	PUNCT
ejpam-3342	219	9	1	1	NUM
ejpam-3342	219	10	)	)	PUNCT
ejpam-3342	219	11	(	(	PUNCT
ejpam-3342	219	12	2019	2019	NUM
ejpam-3342	219	13	)	)	PUNCT
ejpam-3342	219	14	,	,	PUNCT
ejpam-3342	219	15	58	58	NUM
ejpam-3342	219	16	-	-	SYM
ejpam-3342	219	17	78	78	NUM
ejpam-3342	219	18	66	66	NUM
ejpam-3342	219	19	note	note	NOUN
ejpam-3342	219	20	that∑	that∑	VERB
ejpam-3342	220	1	i	i	PRON
ejpam-3342	220	2	<	<	X
ejpam-3342	220	3	p	p	X
ejpam-3342	220	4	e	e	X
ejpam-3342	220	5	[	[	X
ejpam-3342	220	6	(	(	PUNCT
ejpam-3342	220	7	||wξi	||wξi	PROPN
ejpam-3342	220	8	−wvi	−wvi	NOUN
ejpam-3342	220	9	||2u	||2u	PROPN
ejpam-3342	221	1	−	−	PROPN
ejpam-3342	221	2	(	(	PUNCT
ejpam-3342	221	3	ξi	ξi	NOUN
ejpam-3342	221	4	−	−	PROPN
ejpam-3342	221	5	vi)trq	vi)trq	NOUN
ejpam-3342	221	6	)	)	PUNCT
ejpam-3342	221	7	(	(	PUNCT
ejpam-3342	221	8	||wξp	||wξp	PROPN
ejpam-3342	221	9	−wvp	−wvp	NOUN
ejpam-3342	221	10	||2u	||2u	X
ejpam-3342	221	11	−	−	PROPN
ejpam-3342	221	12	(	(	PUNCT
ejpam-3342	221	13	ξp	ξp	NUM
ejpam-3342	221	14	−	−	PROPN
ejpam-3342	221	15	vp)trq	vp)trq	NOUN
ejpam-3342	221	16	)	)	PUNCT
ejpam-3342	221	17	]	]	PUNCT
ejpam-3342	222	1	=	=	PUNCT
ejpam-3342	222	2	∑	∑	PUNCT
ejpam-3342	222	3	i	i	X
ejpam-3342	222	4	<	<	X
ejpam-3342	222	5	p	p	X
ejpam-3342	222	6	e	e	X
ejpam-3342	222	7	[	[	PUNCT
ejpam-3342	222	8	e	e	X
ejpam-3342	222	9	[	[	X
ejpam-3342	222	10	(	(	PUNCT
ejpam-3342	222	11	||wξi	||wξi	PROPN
ejpam-3342	222	12	−wvi	−wvi	NOUN
ejpam-3342	222	13	||2u	||2u	PROPN
ejpam-3342	222	14	−	−	PROPN
ejpam-3342	222	15	(	(	PUNCT
ejpam-3342	222	16	ξi	ξi	NOUN
ejpam-3342	222	17	−	−	PROPN
ejpam-3342	222	18	vi)trq	vi)trq	NOUN
ejpam-3342	222	19	)	)	PUNCT
ejpam-3342	222	20	(	(	PUNCT
ejpam-3342	222	21	||wξp	||wξp	PROPN
ejpam-3342	222	22	−wvp	−wvp	NOUN
ejpam-3342	222	23	||2u	||2u	X
ejpam-3342	222	24	−	−	PROPN
ejpam-3342	222	25	(	(	PUNCT
ejpam-3342	222	26	ξp	ξp	NUM
ejpam-3342	222	27	−	−	PROPN
ejpam-3342	222	28	vp)trq	vp)trq	NOUN
ejpam-3342	222	29	)	)	PUNCT
ejpam-3342	223	1	∣∣∣∣gξi	∣∣∣∣gξi	NOUN
ejpam-3342	223	2	]	]	X
ejpam-3342	223	3	]	]	X
ejpam-3342	224	1	=	=	PUNCT
ejpam-3342	224	2	∑	∑	PUNCT
ejpam-3342	224	3	i	i	X
ejpam-3342	224	4	<	<	X
ejpam-3342	224	5	p	p	X
ejpam-3342	224	6	[	[	X
ejpam-3342	224	7	(	(	PUNCT
ejpam-3342	224	8	ξi	ξi	NOUN
ejpam-3342	224	9	−	−	PROPN
ejpam-3342	224	10	vi)(ξp	vi)(ξp	PUNCT
ejpam-3342	224	11	−	−	PROPN
ejpam-3342	224	12	vp)(trq)2	vp)(trq)2	NOUN
ejpam-3342	224	13	−	−	PROPN
ejpam-3342	224	14	(	(	PUNCT
ejpam-3342	224	15	ξi	ξi	NOUN
ejpam-3342	224	16	−	−	PROPN
ejpam-3342	225	1	vi)(ξp	vi)(ξp	PUNCT
ejpam-3342	225	2	−	−	PROPN
ejpam-3342	225	3	vp)(trq)2	vp)(trq)2	NOUN
ejpam-3342	226	1	−	−	PROPN
ejpam-3342	226	2	(	(	PUNCT
ejpam-3342	226	3	ξp	ξp	NUM
ejpam-3342	226	4	−	−	PROPN
ejpam-3342	226	5	vp)(ξi	vp)(ξi	ADP
ejpam-3342	226	6	−	−	PROPN
ejpam-3342	226	7	vi)(trq)2	vi)(trq)2	NOUN
ejpam-3342	226	8	+	+	CCONJ
ejpam-3342	226	9	(	(	PUNCT
ejpam-3342	226	10	ξi	ξi	NOUN
ejpam-3342	226	11	−	−	PROPN
ejpam-3342	226	12	vi)(ξp	vi)(ξp	PUNCT
ejpam-3342	226	13	−	−	NOUN
ejpam-3342	226	14	vp)(trq)2	vp)(trq)2	NOUN
ejpam-3342	226	15	]	]	X
ejpam-3342	226	16	=	=	SYM
ejpam-3342	226	17	0	0	X
ejpam-3342	226	18	.	.	PUNCT
ejpam-3342	227	1	it	it	PRON
ejpam-3342	227	2	follows	follow	VERB
ejpam-3342	227	3	that	that	SCONJ
ejpam-3342	227	4	e	e	PROPN
ejpam-3342	227	5	∣∣∣∣∣(d	∣∣∣∣∣(d	NOUN
ejpam-3342	227	6	)	)	PUNCT
ejpam-3342	228	1	n∑	n∑	PROPN
ejpam-3342	229	1	i=1	i=1	PROPN
ejpam-3342	229	2	{	{	PUNCT
ejpam-3342	229	3	||wξi	||wξi	PROPN
ejpam-3342	229	4	−wvi	−wvi	NOUN
ejpam-3342	229	5	||2u	||2u	PROPN
ejpam-3342	230	1	−	−	PROPN
ejpam-3342	231	1	(	(	PUNCT
ejpam-3342	231	2	ξi	ξi	NOUN
ejpam-3342	231	3	−	−	NOUN
ejpam-3342	231	4	vi)trq	vi)trq	NOUN
ejpam-3342	231	5	}	}	PUNCT
ejpam-3342	231	6	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3342	231	7	2	2	NUM
ejpam-3342	231	8			NOUN
ejpam-3342	231	9	=	=	PUNCT
ejpam-3342	231	10	n∑	n∑	NOUN
ejpam-3342	231	11	i=1	i=1	X
ejpam-3342	232	1	e	e	X
ejpam-3342	233	1	[	[	X
ejpam-3342	233	2	(	(	PUNCT
ejpam-3342	233	3	||wξi	||wξi	PROPN
ejpam-3342	233	4	−wvi	−wvi	NOUN
ejpam-3342	233	5	||2u	||2u	PROPN
ejpam-3342	233	6	−	−	PROPN
ejpam-3342	233	7	(	(	PUNCT
ejpam-3342	233	8	ξi	ξi	NOUN
ejpam-3342	233	9	−	−	NOUN
ejpam-3342	233	10	vi)trq	vi)trq	NOUN
ejpam-3342	233	11	)	)	PUNCT
ejpam-3342	233	12	2	2	NUM
ejpam-3342	233	13	]	]	PUNCT
ejpam-3342	233	14	.	.	PUNCT
ejpam-3342	234	1	by	by	ADP
ejpam-3342	234	2	theorem	theorem	NOUN
ejpam-3342	234	3	1	1	NUM
ejpam-3342	234	4	,	,	PUNCT
ejpam-3342	234	5	n∑	n∑	NOUN
ejpam-3342	234	6	i=1	i=1	PROPN
ejpam-3342	235	1	e	e	X
ejpam-3342	236	1	[	[	X
ejpam-3342	236	2	(	(	PUNCT
ejpam-3342	236	3	||wξi	||wξi	PROPN
ejpam-3342	236	4	−wvi	−wvi	NOUN
ejpam-3342	236	5	||2u	||2u	PROPN
ejpam-3342	236	6	−	−	PROPN
ejpam-3342	236	7	(	(	PUNCT
ejpam-3342	236	8	ξi	ξi	NOUN
ejpam-3342	236	9	−	−	NOUN
ejpam-3342	236	10	vi)trq	vi)trq	NOUN
ejpam-3342	236	11	)	)	PUNCT
ejpam-3342	236	12	2	2	X
ejpam-3342	236	13	]	]	PUNCT
ejpam-3342	236	14	=	=	PUNCT
ejpam-3342	236	15	n∑	n∑	NOUN
ejpam-3342	236	16	i=1	i=1	PROPN
ejpam-3342	237	1	e	e	X
ejpam-3342	237	2	[	[	PUNCT
ejpam-3342	237	3	||wξi	||wξi	NOUN
ejpam-3342	237	4	−wvi	−wvi	ADV
ejpam-3342	237	5	||4u	||4u	NOUN
ejpam-3342	237	6	−	−	PROPN
ejpam-3342	237	7	2(ξi	2(ξi	NUM
ejpam-3342	237	8	−	−	PROPN
ejpam-3342	237	9	vi)||wξi	vi)||wξi	NOUN
ejpam-3342	237	10	−wvi	−wvi	NOUN
ejpam-3342	237	11	||2u	||2u	PUNCT
ejpam-3342	238	1	trq+	trq+	PROPN
ejpam-3342	238	2	(	(	PUNCT
ejpam-3342	238	3	ξi	ξi	NOUN
ejpam-3342	238	4	−	−	PROPN
ejpam-3342	238	5	vi)2(trq)2	vi)2(trq)2	NOUN
ejpam-3342	238	6	]	]	X
ejpam-3342	239	1	=	=	PUNCT
ejpam-3342	239	2	n∑	n∑	NOUN
ejpam-3342	239	3	i=1	i=1	PROPN
ejpam-3342	240	1	(ξi	(ξi	VERB
ejpam-3342	240	2	−	−	PROPN
ejpam-3342	240	3	vi)2	vi)2	NOUN
ejpam-3342	240	4	2	2	PROPN
ejpam-3342	240	5	∞∑	∞∑	NUM
ejpam-3342	240	6	j=1	j=1	ADJ
ejpam-3342	240	7	λ2	λ2	PROPN
ejpam-3342	240	8	j	j	PROPN
ejpam-3342	241	1	+	+	CCONJ
ejpam-3342	241	2	(	(	PUNCT
ejpam-3342	241	3	trq)2	trq)2	PROPN
ejpam-3342	241	4	−	−	ADP
ejpam-3342	241	5	2(ξi	2(ξi	NUM
ejpam-3342	241	6	−	−	NOUN
ejpam-3342	241	7	vi)2(trq)2	vi)2(trq)2	NOUN
ejpam-3342	242	1	+	+	CCONJ
ejpam-3342	242	2	(	(	PUNCT
ejpam-3342	242	3	ξi	ξi	NOUN
ejpam-3342	242	4	−	−	PROPN
ejpam-3342	242	5	vi)2(trq)2	vi)2(trq)2	NOUN
ejpam-3342	242	6			PROPN
ejpam-3342	242	7	=	=	PUNCT
ejpam-3342	243	1	n∑	n∑	NOUN
ejpam-3342	243	2	i=1	i=1	PROPN
ejpam-3342	244	1	(ξi	(ξi	VERB
ejpam-3342	244	2	−	−	PROPN
ejpam-3342	244	3	vi)2	vi)2	NOUN
ejpam-3342	244	4	2	2	PROPN
ejpam-3342	244	5	∞∑	∞∑	NUM
ejpam-3342	244	6	j=1	j=1	ADJ
ejpam-3342	244	7	λ2	λ2	PROPN
ejpam-3342	244	8	j	j	PROPN
ejpam-3342	245	1	+	+	CCONJ
ejpam-3342	245	2	(	(	PUNCT
ejpam-3342	245	3	trq)2	trq)2	PROPN
ejpam-3342	245	4	−	−	ADV
ejpam-3342	245	5	(	(	PUNCT
ejpam-3342	245	6	ξi	ξi	NOUN
ejpam-3342	245	7	−	−	NOUN
ejpam-3342	245	8	vi)2(trq)2	vi)2(trq)2	NOUN
ejpam-3342	245	9			PROPN
ejpam-3342	245	10	=	=	PUNCT
ejpam-3342	246	1	n∑	n∑	NOUN
ejpam-3342	246	2	i=1	i=1	PROPN
ejpam-3342	247	1	(ξi	(ξi	VERB
ejpam-3342	247	2	−	−	PROPN
ejpam-3342	247	3	vi)2	vi)2	NOUN
ejpam-3342	247	4	2	2	PROPN
ejpam-3342	247	5	∞∑	∞∑	NUM
ejpam-3342	247	6	j=1	j=1	ADJ
ejpam-3342	247	7	λ2	λ2	PROPN
ejpam-3342	247	8	j	j	PROPN
ejpam-3342	248	1	+	+	CCONJ
ejpam-3342	249	1	(	(	PUNCT
ejpam-3342	249	2	trq)2	trq)2	PROPN
ejpam-3342	249	3	−	−	PROPN
ejpam-3342	249	4	(	(	PUNCT
ejpam-3342	249	5	trq)2	trq)2	PROPN
ejpam-3342	249	6			X
ejpam-3342	250	1	=	=	PUNCT
ejpam-3342	250	2	n∑	n∑	NOUN
ejpam-3342	250	3	i=1	i=1	PROPN
ejpam-3342	251	1	(ξi	(ξi	VERB
ejpam-3342	251	2	−	−	PROPN
ejpam-3342	251	3	vi)2	vi)2	NOUN
ejpam-3342	251	4	2	2	PROPN
ejpam-3342	251	5	∞∑	∞∑	NUM
ejpam-3342	251	6	j=1	j=1	ADJ
ejpam-3342	251	7	λ2	λ2	PROPN
ejpam-3342	251	8	j	j	PROPN
ejpam-3342	251	9			NOUN
ejpam-3342	252	1	=	=	PUNCT
ejpam-3342	252	2	2	2	ADP
ejpam-3342	252	3	∞∑	∞∑	NUM
ejpam-3342	252	4	j=1	j=1	ADJ
ejpam-3342	252	5	λ2	λ2	PROPN
ejpam-3342	252	6	j	j	PROPN
ejpam-3342	252	7			PROPN
ejpam-3342	252	8	(	(	PUNCT
ejpam-3342	252	9	n∑	n∑	NOUN
ejpam-3342	252	10	i=1	i=1	PROPN
ejpam-3342	253	1	(	(	PUNCT
ejpam-3342	253	2	ξi	ξi	NOUN
ejpam-3342	253	3	−	−	PROPN
ejpam-3342	253	4	vi)2	vi)2	PROPN
ejpam-3342	253	5	)	)	PUNCT
ejpam-3342	253	6	.	.	PUNCT
ejpam-3342	254	1	r.	r.	PROPN
ejpam-3342	254	2	rulete	rulete	PROPN
ejpam-3342	254	3	,	,	PUNCT
ejpam-3342	254	4	m.	m.	NOUN
ejpam-3342	254	5	labendia	labendia	PROPN
ejpam-3342	254	6	/	/	SYM
ejpam-3342	254	7	eur	eur	PROPN
ejpam-3342	254	8	.	.	PUNCT
ejpam-3342	255	1	j.	j.	PROPN
ejpam-3342	255	2	pure	pure	PROPN
ejpam-3342	255	3	appl	appl	PROPN
ejpam-3342	255	4	.	.	PROPN
ejpam-3342	255	5	math	math	PROPN
ejpam-3342	255	6	,	,	PUNCT
ejpam-3342	255	7	12	12	NUM
ejpam-3342	255	8	(	(	PUNCT
ejpam-3342	255	9	1	1	NUM
ejpam-3342	255	10	)	)	PUNCT
ejpam-3342	255	11	(	(	PUNCT
ejpam-3342	255	12	2019	2019	NUM
ejpam-3342	255	13	)	)	PUNCT
ejpam-3342	255	14	,	,	PUNCT
ejpam-3342	255	15	58	58	NUM
ejpam-3342	255	16	-	-	SYM
ejpam-3342	255	17	78	78	NUM
ejpam-3342	255	18	67	67	NUM
ejpam-3342	255	19	this	this	PRON
ejpam-3342	255	20	proves	prove	VERB
ejpam-3342	255	21	claim	claim	NOUN
ejpam-3342	255	22	1	1	NUM
ejpam-3342	255	23	.	.	X
ejpam-3342	255	24	claim	claim	NOUN
ejpam-3342	255	25	2	2	NUM
ejpam-3342	255	26	.	.	X
ejpam-3342	256	1	e	e	X
ejpam-3342	256	2	[	[	PUNCT
ejpam-3342	256	3	‖〈wt	‖〈wt	NUM
ejpam-3342	256	4	,	,	PUNCT
ejpam-3342	256	5	·	·	PUNCT
ejpam-3342	256	6	〉	〉	NUM
ejpam-3342	256	7	u‖	u‖	ADJ
ejpam-3342	256	8	2	2	NUM
ejpam-3342	256	9	l2(uq	l2(uq	PROPN
ejpam-3342	256	10	,	,	PUNCT
ejpam-3342	256	11	r	r	NOUN
ejpam-3342	256	12	)	)	PUNCT
ejpam-3342	256	13	]	]	PUNCT
ejpam-3342	257	1	=	=	PUNCT
ejpam-3342	257	2	tm	tm	NOUN
ejpam-3342	257	3	.	.	PUNCT
ejpam-3342	258	1	e	e	X
ejpam-3342	258	2	[	[	PUNCT
ejpam-3342	258	3	‖〈wt	‖〈wt	NUM
ejpam-3342	258	4	,	,	PUNCT
ejpam-3342	258	5	·	·	PUNCT
ejpam-3342	258	6	〉	〉	NUM
ejpam-3342	258	7	u‖	u‖	ADJ
ejpam-3342	258	8	2	2	NUM
ejpam-3342	258	9	l2(uq	l2(uq	PROPN
ejpam-3342	258	10	,	,	PUNCT
ejpam-3342	258	11	r	r	NOUN
ejpam-3342	258	12	)	)	PUNCT
ejpam-3342	258	13	]	]	PUNCT
ejpam-3342	259	1	=	=	PUNCT
ejpam-3342	259	2	e	e	X
ejpam-3342	259	3			NOUN
ejpam-3342	259	4	∞∑	∞∑	NUM
ejpam-3342	259	5	j=1	j=1	PROPN
ejpam-3342	259	6	∣∣∣〈wt	∣∣∣〈wt	PROPN
ejpam-3342	259	7	,	,	PUNCT
ejpam-3342	259	8	√	√	PUNCT
ejpam-3342	259	9	λjej	λjej	NOUN
ejpam-3342	259	10	〉	〉	NOUN
ejpam-3342	259	11	u	u	NOUN
ejpam-3342	259	12	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	259	13			NOUN
ejpam-3342	259	14	=	=	PUNCT
ejpam-3342	259	15	∞∑	∞∑	NUM
ejpam-3342	259	16	j=1	j=1	NOUN
ejpam-3342	259	17	λje	λje	NOUN
ejpam-3342	259	18	[	[	PUNCT
ejpam-3342	259	19	〈	〈	PROPN
ejpam-3342	259	20	wt	wt	PROPN
ejpam-3342	259	21	−w0	−w0	PROPN
ejpam-3342	259	22	,	,	PUNCT
ejpam-3342	259	23	ej〉2u	ej〉2u	NOUN
ejpam-3342	259	24	]	]	X
ejpam-3342	259	25	=	=	SYM
ejpam-3342	259	26	t	t	PROPN
ejpam-3342	260	1	∞∑	∞∑	PROPN
ejpam-3342	260	2	j=1	j=1	NOUN
ejpam-3342	260	3	λj	λj	X
ejpam-3342	260	4	〈	〈	PROPN
ejpam-3342	260	5	λjej	λjej	NOUN
ejpam-3342	260	6	,	,	PUNCT
ejpam-3342	260	7	ej〉2u	ej〉2u	X
ejpam-3342	260	8	=	=	SYM
ejpam-3342	260	9	t	t	PROPN
ejpam-3342	261	1	∞∑	∞∑	NUM
ejpam-3342	261	2	j=1	j=1	ADJ
ejpam-3342	261	3	λ2	λ2	PROPN
ejpam-3342	261	4	j	j	PROPN
ejpam-3342	261	5	=	=	SYM
ejpam-3342	261	6	tm	tm	PROPN
ejpam-3342	261	7	.	.	PROPN
ejpam-3342	262	1	this	this	PRON
ejpam-3342	262	2	proves	prove	VERB
ejpam-3342	262	3	claim	claim	NOUN
ejpam-3342	262	4	2	2	NUM
ejpam-3342	262	5	.	.	X
ejpam-3342	262	6	claim	claim	VERB
ejpam-3342	262	7	3	3	NUM
ejpam-3342	262	8	.	.	X
ejpam-3342	263	1	〈	〈	PROPN
ejpam-3342	263	2	wt	wt	NUM
ejpam-3342	263	3	,	,	PUNCT
ejpam-3342	263	4	·	·	PUNCT
ejpam-3342	263	5	〉	〉	NUM
ejpam-3342	263	6	u	u	NOUN
ejpam-3342	263	7	is	be	AUX
ejpam-3342	263	8	ihb	ihb	NOUN
ejpam-3342	263	9	-	-	ADJ
ejpam-3342	263	10	integrable	integrable	ADJ
ejpam-3342	263	11	to	to	ADP
ejpam-3342	263	12	1	1	NUM
ejpam-3342	263	13	2	2	NUM
ejpam-3342	263	14	(	(	PUNCT
ejpam-3342	263	15	||wt	||wt	ADJ
ejpam-3342	263	16	||2u	||2u	X
ejpam-3342	263	17	+	+	NUM
ejpam-3342	263	18	t	t	PROPN
ejpam-3342	263	19	trq	trq	NOUN
ejpam-3342	263	20	)	)	PUNCT
ejpam-3342	263	21	on	on	ADP
ejpam-3342	263	22	[	[	X
ejpam-3342	263	23	0	0	NUM
ejpam-3342	263	24	,	,	PUNCT
ejpam-3342	263	25	t	t	X
ejpam-3342	263	26	]	]	PUNCT
ejpam-3342	263	27	.	.	PUNCT
ejpam-3342	264	1	let	let	VERB
ejpam-3342	264	2	ε	ε	PROPN
ejpam-3342	264	3	>	>	X
ejpam-3342	264	4	0	0	PUNCT
ejpam-3342	264	5	be	be	AUX
ejpam-3342	264	6	given	give	VERB
ejpam-3342	264	7	.	.	PUNCT
ejpam-3342	265	1	let	let	VERB
ejpam-3342	265	2	m	m	NOUN
ejpam-3342	265	3	=	=	PUNCT
ejpam-3342	266	1	∞∑	∞∑	NUM
ejpam-3342	266	2	j=1	j=1	NOUN
ejpam-3342	266	3	λ2	λ2	PROPN
ejpam-3342	266	4	j	j	PROPN
ejpam-3342	266	5	.	.	PUNCT
ejpam-3342	267	1	choose	choose	VERB
ejpam-3342	267	2	a	a	DET
ejpam-3342	267	3	constant	constant	ADJ
ejpam-3342	267	4	function	function	NOUN
ejpam-3342	267	5	δ	δ	PROPN
ejpam-3342	267	6	on	on	ADP
ejpam-3342	267	7	[	[	X
ejpam-3342	267	8	0	0	NUM
ejpam-3342	267	9	,	,	PUNCT
ejpam-3342	267	10	t	t	PROPN
ejpam-3342	267	11	]	]	PUNCT
ejpam-3342	267	12	defined	define	VERB
ejpam-3342	267	13	by	by	ADP
ejpam-3342	267	14	δ(t	δ(t	NOUN
ejpam-3342	267	15	)	)	PUNCT
ejpam-3342	267	16	=	=	SYM
ejpam-3342	267	17	ε	ε	PROPN
ejpam-3342	267	18	2mt	2mt	NOUN
ejpam-3342	267	19	and	and	CCONJ
ejpam-3342	267	20	a	a	DET
ejpam-3342	267	21	number	number	NOUN
ejpam-3342	267	22	η	η	NOUN
ejpam-3342	267	23	=	=	PROPN
ejpam-3342	267	24	ε	ε	PROPN
ejpam-3342	267	25	12mt	12mt	NOUN
ejpam-3342	267	26	.	.	PUNCT
ejpam-3342	268	1	let	let	VERB
ejpam-3342	268	2	d	d	NOUN
ejpam-3342	268	3	=	=	PRON
ejpam-3342	268	4	{	{	PUNCT
ejpam-3342	268	5	(	(	PUNCT
ejpam-3342	268	6	(	(	PUNCT
ejpam-3342	268	7	v	v	NOUN
ejpam-3342	268	8	,	,	PUNCT
ejpam-3342	268	9	ξ	ξ	PROPN
ejpam-3342	268	10	]	]	X
ejpam-3342	268	11	,	,	PUNCT
ejpam-3342	268	12	ξ	ξ	X
ejpam-3342	268	13	)	)	PUNCT
ejpam-3342	268	14	}	}	PUNCT
ejpam-3342	268	15	be	be	AUX
ejpam-3342	268	16	a	a	DET
ejpam-3342	268	17	backwards	backwards	ADV
ejpam-3342	268	18	(	(	PUNCT
ejpam-3342	268	19	δ	δ	PROPN
ejpam-3342	268	20	,	,	PUNCT
ejpam-3342	268	21	η)-fine	η)-fine	X
ejpam-3342	268	22	partial	partial	ADJ
ejpam-3342	268	23	division	division	NOUN
ejpam-3342	268	24	of	of	ADP
ejpam-3342	268	25	[	[	X
ejpam-3342	268	26	0	0	NUM
ejpam-3342	268	27	,	,	PUNCT
ejpam-3342	268	28	t	t	X
ejpam-3342	268	29	]	]	PUNCT
ejpam-3342	268	30	.	.	PUNCT
ejpam-3342	269	1	let	let	VERB
ejpam-3342	269	2	dc	dc	PROPN
ejpam-3342	269	3	be	be	AUX
ejpam-3342	269	4	the	the	DET
ejpam-3342	269	5	collection	collection	NOUN
ejpam-3342	269	6	of	of	ADP
ejpam-3342	269	7	all	all	DET
ejpam-3342	269	8	subintervals	subinterval	NOUN
ejpam-3342	269	9	of	of	ADP
ejpam-3342	269	10	[	[	X
ejpam-3342	269	11	0	0	NUM
ejpam-3342	269	12	,	,	PUNCT
ejpam-3342	269	13	t	t	PROPN
ejpam-3342	269	14	]	]	PUNCT
ejpam-3342	269	15	which	which	PRON
ejpam-3342	269	16	are	be	AUX
ejpam-3342	269	17	not	not	PART
ejpam-3342	269	18	included	include	VERB
ejpam-3342	269	19	in	in	ADP
ejpam-3342	269	20	d.	d.	PROPN
ejpam-3342	269	21	then	then	ADV
ejpam-3342	269	22	e	e	PROPN
ejpam-3342	270	1	[	[	X
ejpam-3342	270	2	∣∣∣∣(d	∣∣∣∣(d	X
ejpam-3342	270	3	)	)	PUNCT
ejpam-3342	270	4	∑	∑	PUNCT
ejpam-3342	270	5	〈	〈	PROPN
ejpam-3342	270	6	wξ	wξ	NOUN
ejpam-3342	270	7	,	,	PUNCT
ejpam-3342	270	8	·	·	PUNCT
ejpam-3342	270	9	〉	〉	NUM
ejpam-3342	270	10	u	u	NOUN
ejpam-3342	270	11	(	(	PUNCT
ejpam-3342	270	12	wξ	wξ	PROPN
ejpam-3342	270	13	−wv)−	−wv)−	PROPN
ejpam-3342	270	14	1	1	NUM
ejpam-3342	270	15	2	2	NUM
ejpam-3342	270	16	||wt	||wt	ADJ
ejpam-3342	270	17	||2u	||2u	X
ejpam-3342	270	18	−	−	PROPN
ejpam-3342	270	19	1	1	NUM
ejpam-3342	270	20	2	2	NUM
ejpam-3342	270	21	t	t	NOUN
ejpam-3342	270	22	(	(	PUNCT
ejpam-3342	270	23	trq	trq	NOUN
ejpam-3342	270	24	)	)	PUNCT
ejpam-3342	270	25	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	270	26	]	]	PUNCT
ejpam-3342	271	1	=	=	PUNCT
ejpam-3342	271	2	e	e	X
ejpam-3342	272	1	[	[	X
ejpam-3342	272	2	∣∣∣∣(d	∣∣∣∣(d	X
ejpam-3342	272	3	)	)	PUNCT
ejpam-3342	272	4	∑	∑	PUNCT
ejpam-3342	272	5	〈	〈	PROPN
ejpam-3342	272	6	wξ	wξ	NOUN
ejpam-3342	272	7	,	,	PUNCT
ejpam-3342	272	8	wξ	wξ	VERB
ejpam-3342	272	9	−wv〉u	−wv〉u	NOUN
ejpam-3342	272	10	−	−	PROPN
ejpam-3342	272	11	1	1	NUM
ejpam-3342	272	12	2	2	NUM
ejpam-3342	272	13	||wt	||wt	ADJ
ejpam-3342	272	14	||2u	||2u	X
ejpam-3342	272	15	−	−	PROPN
ejpam-3342	272	16	1	1	NUM
ejpam-3342	272	17	2	2	NUM
ejpam-3342	272	18	t	t	NOUN
ejpam-3342	272	19	(	(	PUNCT
ejpam-3342	272	20	trq	trq	NOUN
ejpam-3342	272	21	)	)	PUNCT
ejpam-3342	272	22	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	272	23	]	]	PUNCT
ejpam-3342	273	1	=	=	PUNCT
ejpam-3342	273	2	e	e	X
ejpam-3342	274	1	[	[	X
ejpam-3342	274	2	∣∣∣∣(d	∣∣∣∣(d	X
ejpam-3342	274	3	)	)	PUNCT
ejpam-3342	274	4	∑	∑	ADP
ejpam-3342	274	5	{	{	PUNCT
ejpam-3342	274	6	〈	〈	NOUN
ejpam-3342	274	7	wξ	wξ	NOUN
ejpam-3342	274	8	,	,	PUNCT
ejpam-3342	274	9	wξ	wξ	VERB
ejpam-3342	274	10	−wv〉u	−wv〉u	NOUN
ejpam-3342	274	11	−	−	PROPN
ejpam-3342	274	12	1	1	NUM
ejpam-3342	274	13	2	2	NUM
ejpam-3342	274	14	(	(	PUNCT
ejpam-3342	274	15	||wξ||2u	||wξ||2u	NUM
ejpam-3342	274	16	−	−	PROPN
ejpam-3342	274	17	||wv||2u	||wv||2u	NOUN
ejpam-3342	274	18	)	)	PUNCT
ejpam-3342	274	19	−	−	PROPN
ejpam-3342	274	20	1	1	NUM
ejpam-3342	274	21	2	2	NUM
ejpam-3342	274	22	(	(	PUNCT
ejpam-3342	274	23	ξ	ξ	X
ejpam-3342	274	24	−	−	NOUN
ejpam-3342	274	25	v)trq	v)trq	PROPN
ejpam-3342	274	26	}	}	PUNCT
ejpam-3342	274	27	+	+	PROPN
ejpam-3342	274	28	(	(	PUNCT
ejpam-3342	274	29	dc	dc	PROPN
ejpam-3342	274	30	)	)	PUNCT
ejpam-3342	274	31	∑	∑	PROPN
ejpam-3342	274	32	{	{	PUNCT
ejpam-3342	274	33	−1	−1	NOUN
ejpam-3342	274	34	2	2	NUM
ejpam-3342	274	35	(	(	PUNCT
ejpam-3342	274	36	||wξ||2u	||wξ||2u	X
ejpam-3342	274	37	−	−	PROPN
ejpam-3342	274	38	||wv||2u	||wv||2u	NOUN
ejpam-3342	274	39	)	)	PUNCT
ejpam-3342	274	40	−	−	PROPN
ejpam-3342	275	1	1	1	NUM
ejpam-3342	275	2	2	2	NUM
ejpam-3342	275	3	(	(	PUNCT
ejpam-3342	275	4	ξ	ξ	X
ejpam-3342	275	5	−	−	NOUN
ejpam-3342	275	6	v)trq	v)trq	PROPN
ejpam-3342	275	7	}	}	PUNCT
ejpam-3342	275	8	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	275	9	]	]	PUNCT
ejpam-3342	275	10	≤	≤	NUM
ejpam-3342	275	11	2e	2e	NOUN
ejpam-3342	276	1	[	[	X
ejpam-3342	276	2	∣∣∣∣(d	∣∣∣∣(d	X
ejpam-3342	276	3	)	)	PUNCT
ejpam-3342	276	4	∑	∑	ADP
ejpam-3342	276	5	{	{	PUNCT
ejpam-3342	276	6	〈	〈	NOUN
ejpam-3342	276	7	wξ	wξ	NOUN
ejpam-3342	276	8	,	,	PUNCT
ejpam-3342	276	9	wξ	wξ	VERB
ejpam-3342	276	10	−wv〉u	−wv〉u	NOUN
ejpam-3342	276	11	−	−	PROPN
ejpam-3342	276	12	1	1	NUM
ejpam-3342	276	13	2	2	NUM
ejpam-3342	276	14	(	(	PUNCT
ejpam-3342	276	15	||wξ||2u	||wξ||2u	NUM
ejpam-3342	276	16	−	−	PROPN
ejpam-3342	276	17	||wv||2u	||wv||2u	NOUN
ejpam-3342	276	18	)	)	PUNCT
ejpam-3342	276	19	−	−	PROPN
ejpam-3342	276	20	1	1	NUM
ejpam-3342	276	21	2	2	NUM
ejpam-3342	276	22	(	(	PUNCT
ejpam-3342	276	23	ξ	ξ	X
ejpam-3342	276	24	−	−	NOUN
ejpam-3342	276	25	v)trq	v)trq	PROPN
ejpam-3342	276	26	}	}	PUNCT
ejpam-3342	276	27	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	276	28	]	]	PUNCT
ejpam-3342	276	29	+	+	CCONJ
ejpam-3342	276	30	2e	2e	X
ejpam-3342	277	1	[	[	X
ejpam-3342	277	2	∣∣∣∣(dc	∣∣∣∣(dc	PROPN
ejpam-3342	277	3	)	)	PUNCT
ejpam-3342	277	4	∑	∑	PROPN
ejpam-3342	277	5	{	{	PUNCT
ejpam-3342	277	6	−1	−1	NOUN
ejpam-3342	277	7	2	2	NUM
ejpam-3342	277	8	(	(	PUNCT
ejpam-3342	277	9	||wξ||2u	||wξ||2u	X
ejpam-3342	277	10	−	−	PROPN
ejpam-3342	277	11	||wv||2u	||wv||2u	NOUN
ejpam-3342	277	12	)	)	PUNCT
ejpam-3342	277	13	−	−	PROPN
ejpam-3342	277	14	1	1	NUM
ejpam-3342	277	15	2	2	NUM
ejpam-3342	277	16	(	(	PUNCT
ejpam-3342	277	17	ξ	ξ	X
ejpam-3342	277	18	−	−	NOUN
ejpam-3342	277	19	v)trq	v)trq	PROPN
ejpam-3342	277	20	}	}	PUNCT
ejpam-3342	277	21	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	277	22	]	]	PUNCT
ejpam-3342	277	23	=	=	SYM
ejpam-3342	277	24	1	1	NUM
ejpam-3342	277	25	2	2	NUM
ejpam-3342	277	26	e	e	NOUN
ejpam-3342	277	27	[	[	X
ejpam-3342	277	28	∣∣∣(d	∣∣∣(d	X
ejpam-3342	277	29	)	)	PUNCT
ejpam-3342	277	30	∑	∑	PROPN
ejpam-3342	277	31	{	{	PUNCT
ejpam-3342	277	32	−2	−2	PROPN
ejpam-3342	277	33	〈	〈	PROPN
ejpam-3342	277	34	wξ	wξ	NOUN
ejpam-3342	277	35	,	,	PUNCT
ejpam-3342	277	36	wξ	wξ	VERB
ejpam-3342	277	37	−wv〉u	−wv〉u	NOUN
ejpam-3342	277	38	+	+	CCONJ
ejpam-3342	277	39	||wξ||2u	||wξ||2u	NUM
ejpam-3342	277	40	−	−	PROPN
ejpam-3342	277	41	||wv||2u	||wv||2u	X
ejpam-3342	277	42	+	+	CCONJ
ejpam-3342	277	43	(	(	PUNCT
ejpam-3342	277	44	ξ	ξ	X
ejpam-3342	277	45	−	−	NOUN
ejpam-3342	277	46	v)trq	v)trq	PROPN
ejpam-3342	277	47	}	}	PUNCT
ejpam-3342	277	48	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	277	49	]	]	PUNCT
ejpam-3342	277	50	r.	r.	PROPN
ejpam-3342	277	51	rulete	rulete	PROPN
ejpam-3342	277	52	,	,	PUNCT
ejpam-3342	277	53	m.	m.	NOUN
ejpam-3342	277	54	labendia	labendia	PROPN
ejpam-3342	277	55	/	/	SYM
ejpam-3342	277	56	eur	eur	PROPN
ejpam-3342	277	57	.	.	PUNCT
ejpam-3342	278	1	j.	j.	PROPN
ejpam-3342	278	2	pure	pure	PROPN
ejpam-3342	278	3	appl	appl	PROPN
ejpam-3342	278	4	.	.	PROPN
ejpam-3342	278	5	math	math	PROPN
ejpam-3342	278	6	,	,	PUNCT
ejpam-3342	278	7	12	12	NUM
ejpam-3342	278	8	(	(	PUNCT
ejpam-3342	278	9	1	1	NUM
ejpam-3342	278	10	)	)	PUNCT
ejpam-3342	278	11	(	(	PUNCT
ejpam-3342	278	12	2019	2019	NUM
ejpam-3342	278	13	)	)	PUNCT
ejpam-3342	278	14	,	,	PUNCT
ejpam-3342	278	15	58	58	NUM
ejpam-3342	278	16	-	-	SYM
ejpam-3342	278	17	78	78	NUM
ejpam-3342	278	18	68	68	NUM
ejpam-3342	278	19	+	+	CCONJ
ejpam-3342	278	20	1	1	NUM
ejpam-3342	278	21	2	2	NUM
ejpam-3342	278	22	e	e	NOUN
ejpam-3342	278	23	[	[	X
ejpam-3342	278	24	∣∣∣(dc	∣∣∣(dc	PROPN
ejpam-3342	278	25	)	)	PUNCT
ejpam-3342	278	26	∑	∑	PROPN
ejpam-3342	278	27	{	{	PUNCT
ejpam-3342	278	28	||wξ||2u	||wξ||2u	NUM
ejpam-3342	278	29	−	−	PROPN
ejpam-3342	278	30	||wv||2u	||wv||2u	X
ejpam-3342	278	31	+	+	CCONJ
ejpam-3342	278	32	(	(	PUNCT
ejpam-3342	278	33	ξ	ξ	X
ejpam-3342	278	34	−	−	NOUN
ejpam-3342	278	35	v)trq	v)trq	PROPN
ejpam-3342	278	36	}	}	PUNCT
ejpam-3342	278	37	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	278	38	]	]	X
ejpam-3342	278	39	=	=	SYM
ejpam-3342	278	40	1	1	NUM
ejpam-3342	278	41	2	2	NUM
ejpam-3342	278	42	e	e	NOUN
ejpam-3342	278	43	[	[	X
ejpam-3342	278	44	∣∣∣(d	∣∣∣(d	X
ejpam-3342	278	45	)	)	PUNCT
ejpam-3342	278	46	∑	∑	PROPN
ejpam-3342	278	47	{	{	PUNCT
ejpam-3342	278	48	−||wξ	−||wξ	PROPN
ejpam-3342	278	49	−wv||2u	−wv||2u	PROPN
ejpam-3342	278	50	+	+	PROPN
ejpam-3342	278	51	(	(	PUNCT
ejpam-3342	278	52	ξ	ξ	X
ejpam-3342	278	53	−	−	NOUN
ejpam-3342	278	54	v)trq	v)trq	PROPN
ejpam-3342	278	55	}	}	PUNCT
ejpam-3342	278	56	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	278	57	]	]	PUNCT
ejpam-3342	279	1	+	+	CCONJ
ejpam-3342	279	2	1	1	NUM
ejpam-3342	279	3	2	2	NUM
ejpam-3342	279	4	e	e	NOUN
ejpam-3342	279	5	[	[	X
ejpam-3342	279	6	∣∣∣(dc	∣∣∣(dc	PROPN
ejpam-3342	279	7	)	)	PUNCT
ejpam-3342	279	8	∑	∑	PROPN
ejpam-3342	279	9	{	{	PUNCT
ejpam-3342	279	10	||wξ||2u	||wξ||2u	NUM
ejpam-3342	279	11	−	−	PROPN
ejpam-3342	279	12	||wv||2u	||wv||2u	X
ejpam-3342	279	13	−	−	PROPN
ejpam-3342	279	14	2	2	NUM
ejpam-3342	279	15	〈	〈	NOUN
ejpam-3342	279	16	wξ	wξ	NOUN
ejpam-3342	279	17	,	,	PUNCT
ejpam-3342	279	18	wξ	wξ	VERB
ejpam-3342	279	19	−wv〉u	−wv〉u	NOUN
ejpam-3342	279	20	+2	+2	PROPN
ejpam-3342	279	21	〈	〈	PROPN
ejpam-3342	279	22	wξ	wξ	NOUN
ejpam-3342	279	23	,	,	PUNCT
ejpam-3342	279	24	wξ	wξ	VERB
ejpam-3342	279	25	−wv〉u	−wv〉u	NOUN
ejpam-3342	279	26	+	+	CCONJ
ejpam-3342	279	27	(	(	PUNCT
ejpam-3342	279	28	ξ	ξ	X
ejpam-3342	279	29	−	−	NOUN
ejpam-3342	279	30	v)trq	v)trq	PROPN
ejpam-3342	279	31	}	}	PUNCT
ejpam-3342	279	32	∣∣2	∣∣2	PROPN
ejpam-3342	279	33	]	]	PUNCT
ejpam-3342	279	34	≤	≤	NUM
ejpam-3342	279	35	1	1	NUM
ejpam-3342	279	36	2	2	NUM
ejpam-3342	279	37	e	e	NOUN
ejpam-3342	279	38	[	[	X
ejpam-3342	279	39	∣∣∣(d	∣∣∣(d	X
ejpam-3342	279	40	)	)	PUNCT
ejpam-3342	279	41	∑	∑	ADJ
ejpam-3342	279	42	{	{	PUNCT
ejpam-3342	279	43	||wξ	||wξ	PROPN
ejpam-3342	279	44	−wv||2u	−wv||2u	PROPN
ejpam-3342	279	45	−	−	PROPN
ejpam-3342	279	46	(	(	PUNCT
ejpam-3342	279	47	ξ	ξ	X
ejpam-3342	279	48	−	−	NOUN
ejpam-3342	279	49	v)trq	v)trq	PROPN
ejpam-3342	279	50	}	}	PUNCT
ejpam-3342	279	51	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	279	52	]	]	PUNCT
ejpam-3342	280	1	+	+	CCONJ
ejpam-3342	280	2	e	e	X
ejpam-3342	281	1	[	[	X
ejpam-3342	281	2	∣∣∣(dc	∣∣∣(dc	PROPN
ejpam-3342	281	3	)	)	PUNCT
ejpam-3342	281	4	∑	∑	PROPN
ejpam-3342	281	5	{	{	PUNCT
ejpam-3342	281	6	||wξ	||wξ	PROPN
ejpam-3342	281	7	−wv||2u	−wv||2u	PROPN
ejpam-3342	281	8	−	−	PROPN
ejpam-3342	281	9	(	(	PUNCT
ejpam-3342	281	10	ξ	ξ	X
ejpam-3342	281	11	−	−	NOUN
ejpam-3342	281	12	v)trq	v)trq	PROPN
ejpam-3342	281	13	}	}	PUNCT
ejpam-3342	281	14	∣∣∣2	∣∣∣2	NOUN
ejpam-3342	281	15	]	]	PUNCT
ejpam-3342	282	1	+	+	CCONJ
ejpam-3342	282	2	4e	4e	PROPN
ejpam-3342	282	3	[	[	X
ejpam-3342	282	4	∣∣∣(dc	∣∣∣(dc	PROPN
ejpam-3342	282	5	)	)	PUNCT
ejpam-3342	282	6	∑	∑	PUNCT
ejpam-3342	282	7	〈	〈	PROPN
ejpam-3342	282	8	wξ	wξ	NOUN
ejpam-3342	282	9	,	,	PUNCT
ejpam-3342	282	10	wξ	wξ	VERB
ejpam-3342	282	11	−wv〉u	−wv〉u	NOUN
ejpam-3342	282	12	∣∣∣2	∣∣∣2	PROPN
ejpam-3342	282	13	]	]	PUNCT
ejpam-3342	282	14	.	.	PUNCT
ejpam-3342	283	1	by	by	ADP
ejpam-3342	283	2	claim	claim	NOUN
ejpam-3342	283	3	1	1	NUM
ejpam-3342	283	4	,	,	PUNCT
ejpam-3342	283	5	claim	claim	NOUN
ejpam-3342	283	6	2	2	NUM
ejpam-3342	283	7	,	,	PUNCT
ejpam-3342	283	8	and	and	CCONJ
ejpam-3342	283	9	lemma	lemma	PROPN
ejpam-3342	283	10	2	2	NUM
ejpam-3342	283	11	,	,	PUNCT
ejpam-3342	283	12	we	we	PRON
ejpam-3342	283	13	have	have	VERB
ejpam-3342	283	14	e	e	NOUN
ejpam-3342	283	15	[	[	X
ejpam-3342	283	16	∣∣∣∣(d	∣∣∣∣(d	X
ejpam-3342	283	17	)	)	PUNCT
ejpam-3342	283	18	∑	∑	PUNCT
ejpam-3342	283	19	〈	〈	PROPN
ejpam-3342	283	20	wξ	wξ	NOUN
ejpam-3342	283	21	,	,	PUNCT
ejpam-3342	283	22	·	·	PUNCT
ejpam-3342	283	23	〉	〉	NUM
ejpam-3342	283	24	u	u	NOUN
ejpam-3342	283	25	(	(	PUNCT
ejpam-3342	283	26	wξ	wξ	PROPN
ejpam-3342	283	27	−wv)−	−wv)−	PROPN
ejpam-3342	283	28	1	1	NUM
ejpam-3342	283	29	2	2	NUM
ejpam-3342	283	30	||wt	||wt	ADJ
ejpam-3342	283	31	||2u	||2u	X
ejpam-3342	283	32	−	−	PROPN
ejpam-3342	283	33	1	1	NUM
ejpam-3342	283	34	2	2	NUM
ejpam-3342	283	35	t	t	NOUN
ejpam-3342	283	36	(	(	PUNCT
ejpam-3342	283	37	trq	trq	NOUN
ejpam-3342	283	38	)	)	PUNCT
ejpam-3342	283	39	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3342	283	40	]	]	PUNCT
ejpam-3342	283	41	≤m	≤m	NOUN
ejpam-3342	283	42	[	[	PUNCT
ejpam-3342	283	43	(	(	PUNCT
ejpam-3342	283	44	d	d	NOUN
ejpam-3342	283	45	)	)	PUNCT
ejpam-3342	283	46	∑	∑	PUNCT
ejpam-3342	283	47	(	(	PUNCT
ejpam-3342	283	48	ξ	ξ	X
ejpam-3342	283	49	−	−	PROPN
ejpam-3342	283	50	v)2	v)2	NOUN
ejpam-3342	283	51	]	]	PUNCT
ejpam-3342	284	1	+	+	PUNCT
ejpam-3342	284	2	2	2	NUM
ejpam-3342	284	3	m	m	NOUN
ejpam-3342	284	4	[	[	PUNCT
ejpam-3342	284	5	(	(	PUNCT
ejpam-3342	284	6	dc	dc	PROPN
ejpam-3342	284	7	)	)	PUNCT
ejpam-3342	284	8	∑	∑	PUNCT
ejpam-3342	284	9	(	(	PUNCT
ejpam-3342	284	10	ξ	ξ	X
ejpam-3342	284	11	−	−	PROPN
ejpam-3342	284	12	v)2	v)2	NOUN
ejpam-3342	284	13	]	]	PUNCT
ejpam-3342	285	1	+	+	CCONJ
ejpam-3342	285	2	4	4	NUM
ejpam-3342	285	3	·	·	PUNCT
ejpam-3342	285	4	(	(	PUNCT
ejpam-3342	285	5	dc	dc	PROPN
ejpam-3342	285	6	)	)	PUNCT
ejpam-3342	285	7	∑	∑	PUNCT
ejpam-3342	285	8	(	(	PUNCT
ejpam-3342	285	9	ξ	ξ	X
ejpam-3342	285	10	−	−	PROPN
ejpam-3342	285	11	v)ξm	v)ξm	PROPN
ejpam-3342	285	12	<	<	X
ejpam-3342	285	13	mtδ	mtδ	PROPN
ejpam-3342	285	14	+	+	CCONJ
ejpam-3342	285	15	2mtη	2mtη	NUM
ejpam-3342	286	1	+	+	CCONJ
ejpam-3342	286	2	4mtη	4mtη	PROPN
ejpam-3342	286	3	=	=	SYM
ejpam-3342	286	4	mt	mt	PROPN
ejpam-3342	286	5	(	(	PUNCT
ejpam-3342	286	6	ε	ε	PROPN
ejpam-3342	286	7	2mt	2mt	NOUN
ejpam-3342	286	8	)	)	PUNCT
ejpam-3342	287	1	+	+	CCONJ
ejpam-3342	288	1	6mt	6mt	ADJ
ejpam-3342	288	2	(	(	PUNCT
ejpam-3342	288	3	ε	ε	PROPN
ejpam-3342	288	4	12mt	12mt	NOUN
ejpam-3342	288	5	)	)	PUNCT
ejpam-3342	288	6	=	=	PUNCT
ejpam-3342	288	7	ε	ε	PROPN
ejpam-3342	288	8	.	.	PUNCT
ejpam-3342	288	9	thus	thus	ADV
ejpam-3342	288	10	,	,	PUNCT
ejpam-3342	288	11	〈	〈	PROPN
ejpam-3342	288	12	wt	wt	X
ejpam-3342	288	13	,	,	PUNCT
ejpam-3342	288	14	·	·	PUNCT
ejpam-3342	288	15	〉	〉	NUM
ejpam-3342	288	16	u	u	NOUN
ejpam-3342	288	17	is	be	AUX
ejpam-3342	288	18	ihb	ihb	NOUN
ejpam-3342	288	19	-	-	ADJ
ejpam-3342	288	20	integrable	integrable	ADJ
ejpam-3342	288	21	on	on	ADP
ejpam-3342	288	22	[	[	X
ejpam-3342	288	23	0	0	NUM
ejpam-3342	288	24	,	,	PUNCT
ejpam-3342	288	25	t	t	NOUN
ejpam-3342	288	26	]	]	PUNCT
ejpam-3342	288	27	and	and	CCONJ
ejpam-3342	288	28	(	(	PUNCT
ejpam-3342	288	29	ihb	ihb	NOUN
ejpam-3342	288	30	)	)	PUNCT
ejpam-3342	288	31	∫	∫	PROPN
ejpam-3342	288	32	t	t	PROPN
ejpam-3342	288	33	0	0	NUM
ejpam-3342	288	34	〈	〈	PROPN
ejpam-3342	288	35	wt	wt	NUM
ejpam-3342	288	36	,	,	PUNCT
ejpam-3342	288	37	·	·	PUNCT
ejpam-3342	288	38	〉	〉	NUM
ejpam-3342	288	39	u	u	NOUN
ejpam-3342	288	40	dwt	dwt	NOUN
ejpam-3342	288	41	=	=	NOUN
ejpam-3342	288	42	1	1	NUM
ejpam-3342	288	43	2	2	NUM
ejpam-3342	288	44	(	(	PUNCT
ejpam-3342	288	45	||wt	||wt	ADJ
ejpam-3342	288	46	||2u	||2u	X
ejpam-3342	288	47	+	+	NUM
ejpam-3342	288	48	t	t	PROPN
ejpam-3342	288	49	trq	trq	NOUN
ejpam-3342	288	50	)	)	PUNCT
ejpam-3342	288	51	.	.	PUNCT
ejpam-3342	289	1	�	�	PROPN
ejpam-3342	290	1	the	the	DET
ejpam-3342	290	2	following	follow	VERB
ejpam-3342	290	3	statements	statement	NOUN
ejpam-3342	290	4	show	show	VERB
ejpam-3342	290	5	that	that	SCONJ
ejpam-3342	290	6	the	the	DET
ejpam-3342	290	7	backwards	backwards	ADV
ejpam-3342	290	8	itô-henstock	itô-henstock	ADJ
ejpam-3342	290	9	integral	integral	ADJ
ejpam-3342	290	10	possesses	possesse	NOUN
ejpam-3342	290	11	the	the	DET
ejpam-3342	290	12	standard	standard	ADJ
ejpam-3342	290	13	properties	property	NOUN
ejpam-3342	290	14	of	of	ADP
ejpam-3342	290	15	an	an	DET
ejpam-3342	290	16	integral	integral	ADJ
ejpam-3342	290	17	.	.	PUNCT
ejpam-3342	291	1	refer	refer	VERB
ejpam-3342	291	2	to	to	ADP
ejpam-3342	291	3	[	[	X
ejpam-3342	291	4	12	12	NUM
ejpam-3342	291	5	]	]	PUNCT
ejpam-3342	291	6	for	for	ADP
ejpam-3342	291	7	analogous	analogous	ADJ
ejpam-3342	291	8	proofs	proof	NOUN
ejpam-3342	291	9	.	.	PUNCT
ejpam-3342	292	1	(	(	PUNCT
ejpam-3342	292	2	1	1	X
ejpam-3342	292	3	)	)	PUNCT
ejpam-3342	292	4	the	the	DET
ejpam-3342	292	5	backwards	backwards	ADV
ejpam-3342	292	6	itô-henstock	itô-henstock	PROPN
ejpam-3342	292	7	integral	integral	ADJ
ejpam-3342	292	8	is	be	AUX
ejpam-3342	292	9	uniquely	uniquely	ADV
ejpam-3342	292	10	determined	determine	VERB
ejpam-3342	292	11	,	,	PUNCT
ejpam-3342	292	12	in	in	ADP
ejpam-3342	292	13	the	the	DET
ejpam-3342	292	14	sense	sense	NOUN
ejpam-3342	292	15	that	that	SCONJ
ejpam-3342	292	16	if	if	SCONJ
ejpam-3342	292	17	a1	a1	NOUN
ejpam-3342	292	18	and	and	CCONJ
ejpam-3342	292	19	a2	a2	PROPN
ejpam-3342	292	20	are	be	AUX
ejpam-3342	292	21	two	two	NUM
ejpam-3342	292	22	backwards	backwards	ADV
ejpam-3342	292	23	itô-henstock	itô-henstock	ADJ
ejpam-3342	292	24	integrals	integral	NOUN
ejpam-3342	292	25	of	of	ADP
ejpam-3342	292	26	f	f	PROPN
ejpam-3342	292	27	in	in	ADP
ejpam-3342	292	28	definition	definition	NOUN
ejpam-3342	292	29	1	1	NUM
ejpam-3342	292	30	,	,	PUNCT
ejpam-3342	292	31	then	then	ADV
ejpam-3342	292	32	‖a1	‖a1	NOUN
ejpam-3342	292	33	−a2‖l2(ω	−a2‖l2(ω	PROPN
ejpam-3342	292	34	,	,	PUNCT
ejpam-3342	292	35	v	v	NOUN
ejpam-3342	292	36	)	)	PUNCT
ejpam-3342	292	37	=	=	SYM
ejpam-3342	293	1	0	0	X
ejpam-3342	293	2	.	.	PUNCT
ejpam-3342	294	1	(	(	PUNCT
ejpam-3342	294	2	2	2	X
ejpam-3342	294	3	)	)	PUNCT
ejpam-3342	294	4	let	let	VERB
ejpam-3342	294	5	α	α	PRON
ejpam-3342	294	6	∈	∈	PROPN
ejpam-3342	294	7	r.	r.	PROPN
ejpam-3342	294	8	if	if	SCONJ
ejpam-3342	294	9	f	f	PROPN
ejpam-3342	294	10	and	and	CCONJ
ejpam-3342	294	11	g	g	PROPN
ejpam-3342	294	12	are	be	AUX
ejpam-3342	294	13	ihb	ihb	NOUN
ejpam-3342	294	14	-	-	ADJ
ejpam-3342	294	15	integrable	integrable	ADJ
ejpam-3342	294	16	on	on	ADP
ejpam-3342	294	17	[	[	X
ejpam-3342	294	18	0	0	NUM
ejpam-3342	294	19	,	,	PUNCT
ejpam-3342	294	20	t	t	X
ejpam-3342	294	21	]	]	PUNCT
ejpam-3342	294	22	,	,	PUNCT
ejpam-3342	294	23	then	then	ADV
ejpam-3342	294	24	(	(	PUNCT
ejpam-3342	294	25	i	i	NOUN
ejpam-3342	294	26	)	)	PUNCT
ejpam-3342	294	27	f	f	PROPN
ejpam-3342	295	1	+	+	CCONJ
ejpam-3342	295	2	g	g	PROPN
ejpam-3342	295	3	is	be	AUX
ejpam-3342	295	4	ihb	ihb	NOUN
ejpam-3342	295	5	-	-	ADJ
ejpam-3342	295	6	integrable	integrable	ADJ
ejpam-3342	295	7	on	on	ADP
ejpam-3342	295	8	[	[	X
ejpam-3342	295	9	0	0	NUM
ejpam-3342	295	10	,	,	PUNCT
ejpam-3342	295	11	t	t	X
ejpam-3342	295	12	]	]	PUNCT
ejpam-3342	295	13	,	,	PUNCT
ejpam-3342	295	14	and	and	CCONJ
ejpam-3342	295	15	(	(	PUNCT
ejpam-3342	295	16	ihb	ihb	NOUN
ejpam-3342	295	17	)	)	PUNCT
ejpam-3342	295	18	∫	∫	PROPN
ejpam-3342	295	19	t	t	PROPN
ejpam-3342	295	20	0	0	NUM
ejpam-3342	296	1	(	(	PUNCT
ejpam-3342	296	2	f	f	PROPN
ejpam-3342	296	3	+	+	CCONJ
ejpam-3342	296	4	g	g	NOUN
ejpam-3342	296	5	)	)	PUNCT
ejpam-3342	296	6	dw	dw	NOUN
ejpam-3342	296	7	=	=	PUNCT
ejpam-3342	296	8	(	(	PUNCT
ejpam-3342	296	9	ihb	ihb	NOUN
ejpam-3342	296	10	)	)	PUNCT
ejpam-3342	296	11	∫	∫	PROPN
ejpam-3342	297	1	t	t	PROPN
ejpam-3342	297	2	0	0	NUM
ejpam-3342	297	3	f	f	PROPN
ejpam-3342	297	4	dw	dw	PROPN
ejpam-3342	297	5	+	+	CCONJ
ejpam-3342	297	6	(	(	PUNCT
ejpam-3342	297	7	ihb	ihb	NOUN
ejpam-3342	297	8	)	)	PUNCT
ejpam-3342	297	9	∫	∫	PROPN
ejpam-3342	298	1	t	t	PROPN
ejpam-3342	298	2	0	0	NUM
ejpam-3342	298	3	g	g	PROPN
ejpam-3342	298	4	dw	dw	PROPN
ejpam-3342	298	5	;	;	PUNCT
ejpam-3342	298	6	r.	r.	PROPN
ejpam-3342	298	7	rulete	rulete	PROPN
ejpam-3342	298	8	,	,	PUNCT
ejpam-3342	298	9	m.	m.	NOUN
ejpam-3342	298	10	labendia	labendia	PROPN
ejpam-3342	298	11	/	/	SYM
ejpam-3342	298	12	eur	eur	PROPN
ejpam-3342	298	13	.	.	PUNCT
ejpam-3342	299	1	j.	j.	PROPN
ejpam-3342	299	2	pure	pure	PROPN
ejpam-3342	299	3	appl	appl	PROPN
ejpam-3342	299	4	.	.	PROPN
ejpam-3342	299	5	math	math	PROPN
ejpam-3342	299	6	,	,	PUNCT
ejpam-3342	299	7	12	12	NUM
ejpam-3342	299	8	(	(	PUNCT
ejpam-3342	299	9	1	1	NUM
ejpam-3342	299	10	)	)	PUNCT
ejpam-3342	299	11	(	(	PUNCT
ejpam-3342	299	12	2019	2019	NUM
ejpam-3342	299	13	)	)	PUNCT
ejpam-3342	299	14	,	,	PUNCT
ejpam-3342	299	15	58	58	NUM
ejpam-3342	299	16	-	-	SYM
ejpam-3342	299	17	78	78	NUM
ejpam-3342	299	18	69	69	NUM
ejpam-3342	299	19	(	(	PUNCT
ejpam-3342	299	20	ii	ii	NOUN
ejpam-3342	299	21	)	)	PUNCT
ejpam-3342	299	22	αf	αf	VERB
ejpam-3342	299	23	is	be	AUX
ejpam-3342	299	24	ihb	ihb	NOUN
ejpam-3342	299	25	-	-	ADJ
ejpam-3342	299	26	integrable	integrable	ADJ
ejpam-3342	299	27	on	on	ADP
ejpam-3342	299	28	[	[	X
ejpam-3342	299	29	0	0	NUM
ejpam-3342	299	30	,	,	PUNCT
ejpam-3342	299	31	t	t	X
ejpam-3342	299	32	]	]	PUNCT
ejpam-3342	299	33	,	,	PUNCT
ejpam-3342	299	34	and	and	CCONJ
ejpam-3342	299	35	(	(	PUNCT
ejpam-3342	299	36	ihb	ihb	NOUN
ejpam-3342	299	37	)	)	PUNCT
ejpam-3342	299	38	∫	∫	PROPN
ejpam-3342	299	39	t	t	PROPN
ejpam-3342	299	40	0	0	NUM
ejpam-3342	299	41	(	(	PUNCT
ejpam-3342	299	42	αf	αf	NOUN
ejpam-3342	299	43	)	)	PUNCT
ejpam-3342	299	44	dw	dw	NOUN
ejpam-3342	299	45	=	=	SYM
ejpam-3342	299	46	α	α	PROPN
ejpam-3342	299	47	·	·	PUNCT
ejpam-3342	299	48	(	(	PUNCT
ejpam-3342	299	49	ihb	ihb	NOUN
ejpam-3342	299	50	)	)	PUNCT
ejpam-3342	299	51	∫	∫	PROPN
ejpam-3342	299	52	t	t	PROPN
ejpam-3342	299	53	0	0	NUM
ejpam-3342	299	54	f	f	PROPN
ejpam-3342	299	55	dw	dw	PROPN
ejpam-3342	299	56	.	.	PROPN
ejpam-3342	300	1	(	(	PUNCT
ejpam-3342	300	2	3	3	X
ejpam-3342	300	3	)	)	PUNCT
ejpam-3342	300	4	if	if	SCONJ
ejpam-3342	300	5	f	f	X
ejpam-3342	300	6	:	:	PUNCT
ejpam-3342	301	1	[	[	X
ejpam-3342	301	2	0	0	NUM
ejpam-3342	301	3	,	,	PUNCT
ejpam-3342	301	4	t	t	X
ejpam-3342	301	5	]	]	X
ejpam-3342	301	6	×	×	PROPN
ejpam-3342	301	7	ω→	ω→	PUNCT
ejpam-3342	301	8	l2(uq	l2(uq	PROPN
ejpam-3342	301	9	,	,	PUNCT
ejpam-3342	301	10	v	v	NOUN
ejpam-3342	301	11	)	)	PUNCT
ejpam-3342	301	12	is	be	AUX
ejpam-3342	301	13	ihb	ihb	NOUN
ejpam-3342	301	14	-	-	ADJ
ejpam-3342	301	15	integrable	integrable	ADJ
ejpam-3342	301	16	on	on	ADP
ejpam-3342	301	17	[	[	X
ejpam-3342	301	18	0	0	NUM
ejpam-3342	301	19	,	,	PUNCT
ejpam-3342	301	20	c	c	NOUN
ejpam-3342	301	21	]	]	PUNCT
ejpam-3342	301	22	and	and	CCONJ
ejpam-3342	301	23	[	[	X
ejpam-3342	301	24	c	c	X
ejpam-3342	301	25	,	,	PUNCT
ejpam-3342	301	26	t	t	NOUN
ejpam-3342	301	27	]	]	PUNCT
ejpam-3342	301	28	where	where	SCONJ
ejpam-3342	301	29	c	c	PROPN
ejpam-3342	301	30	∈	∈	PROPN
ejpam-3342	301	31	(	(	PUNCT
ejpam-3342	301	32	0	0	NUM
ejpam-3342	301	33	,	,	PUNCT
ejpam-3342	301	34	t	t	NOUN
ejpam-3342	301	35	)	)	PUNCT
ejpam-3342	301	36	,	,	PUNCT
ejpam-3342	301	37	then	then	ADV
ejpam-3342	301	38	f	f	PROPN
ejpam-3342	301	39	is	be	AUX
ejpam-3342	301	40	ihb	ihb	NOUN
ejpam-3342	301	41	-	-	ADJ
ejpam-3342	301	42	integrable	integrable	ADJ
ejpam-3342	301	43	on	on	ADP
ejpam-3342	301	44	[	[	X
ejpam-3342	301	45	0	0	NUM
ejpam-3342	301	46	,	,	PUNCT
ejpam-3342	301	47	t	t	NOUN
ejpam-3342	301	48	]	]	PUNCT
ejpam-3342	301	49	and	and	CCONJ
ejpam-3342	301	50	(	(	PUNCT
ejpam-3342	301	51	ihb	ihb	NOUN
ejpam-3342	301	52	)	)	PUNCT
ejpam-3342	302	1	∫	∫	PROPN
ejpam-3342	302	2	t	t	PROPN
ejpam-3342	302	3	0	0	NUM
ejpam-3342	303	1	f	f	PROPN
ejpam-3342	303	2	dw	dw	PROPN
ejpam-3342	303	3	=	=	SYM
ejpam-3342	303	4	(	(	PUNCT
ejpam-3342	303	5	ihb	ihb	NOUN
ejpam-3342	303	6	)	)	PUNCT
ejpam-3342	303	7	∫	∫	PROPN
ejpam-3342	304	1	c	c	NOUN
ejpam-3342	304	2	0	0	NUM
ejpam-3342	304	3	f	f	PROPN
ejpam-3342	304	4	dw	dw	PROPN
ejpam-3342	304	5	+	+	CCONJ
ejpam-3342	304	6	(	(	PUNCT
ejpam-3342	304	7	ihb	ihb	NOUN
ejpam-3342	304	8	)	)	PUNCT
ejpam-3342	304	9	∫	∫	PROPN
ejpam-3342	305	1	t	t	PROPN
ejpam-3342	305	2	c	c	PROPN
ejpam-3342	305	3	f	f	PROPN
ejpam-3342	305	4	dw	dw	PROPN
ejpam-3342	305	5	.	.	PROPN
ejpam-3342	306	1	(	(	PUNCT
ejpam-3342	306	2	4	4	X
ejpam-3342	306	3	)	)	PUNCT
ejpam-3342	306	4	if	if	SCONJ
ejpam-3342	306	5	f	f	X
ejpam-3342	306	6	:	:	PUNCT
ejpam-3342	307	1	[	[	X
ejpam-3342	307	2	0	0	NUM
ejpam-3342	307	3	,	,	PUNCT
ejpam-3342	307	4	t	t	X
ejpam-3342	307	5	]	]	PUNCT
ejpam-3342	307	6	×ω→	×ω→	PROPN
ejpam-3342	307	7	l2(uq	l2(uq	PROPN
ejpam-3342	307	8	,	,	PUNCT
ejpam-3342	307	9	v	v	NOUN
ejpam-3342	307	10	)	)	PUNCT
ejpam-3342	307	11	is	be	AUX
ejpam-3342	307	12	ihb	ihb	NOUN
ejpam-3342	307	13	-	-	ADJ
ejpam-3342	307	14	integrable	integrable	ADJ
ejpam-3342	307	15	on	on	ADP
ejpam-3342	307	16	[	[	X
ejpam-3342	307	17	0	0	NUM
ejpam-3342	307	18	,	,	PUNCT
ejpam-3342	307	19	t	t	X
ejpam-3342	307	20	]	]	PUNCT
ejpam-3342	307	21	,	,	PUNCT
ejpam-3342	307	22	then	then	ADV
ejpam-3342	307	23	f	f	PROPN
ejpam-3342	307	24	is	be	AUX
ejpam-3342	307	25	also	also	ADV
ejpam-3342	307	26	ihb	ihb	NOUN
ejpam-3342	307	27	-	-	ADJ
ejpam-3342	307	28	integrable	integrable	ADJ
ejpam-3342	307	29	on	on	ADP
ejpam-3342	307	30	every	every	DET
ejpam-3342	307	31	subinteval	subinteval	NOUN
ejpam-3342	308	1	[	[	X
ejpam-3342	308	2	c	c	X
ejpam-3342	308	3	,	,	PUNCT
ejpam-3342	308	4	d	d	X
ejpam-3342	308	5	]	]	X
ejpam-3342	308	6	of	of	ADP
ejpam-3342	308	7	[	[	X
ejpam-3342	308	8	0	0	NUM
ejpam-3342	308	9	,	,	PUNCT
ejpam-3342	308	10	t	t	X
ejpam-3342	308	11	]	]	PUNCT
ejpam-3342	308	12	.	.	PUNCT
ejpam-3342	309	1	(	(	PUNCT
ejpam-3342	309	2	5	5	X
ejpam-3342	309	3	)	)	PUNCT
ejpam-3342	309	4	a	a	DET
ejpam-3342	309	5	process	process	NOUN
ejpam-3342	309	6	f	f	NOUN
ejpam-3342	310	1	:	:	PUNCT
ejpam-3342	310	2	[	[	X
ejpam-3342	310	3	0	0	NUM
ejpam-3342	310	4	,	,	PUNCT
ejpam-3342	310	5	t	t	X
ejpam-3342	310	6	]	]	PUNCT
ejpam-3342	310	7	×	×	PROPN
ejpam-3342	310	8	ω	ω	X
ejpam-3342	310	9	→	→	SYM
ejpam-3342	310	10	l2(uq	l2(uq	PROPN
ejpam-3342	310	11	,	,	PUNCT
ejpam-3342	310	12	v	v	NOUN
ejpam-3342	310	13	)	)	PUNCT
ejpam-3342	310	14	is	be	AUX
ejpam-3342	310	15	ihb	ihb	NOUN
ejpam-3342	310	16	-	-	ADJ
ejpam-3342	310	17	integrable	integrable	ADJ
ejpam-3342	310	18	on	on	ADP
ejpam-3342	310	19	[	[	X
ejpam-3342	310	20	0	0	NUM
ejpam-3342	310	21	,	,	PUNCT
ejpam-3342	310	22	t	t	X
ejpam-3342	310	23	]	]	PUNCT
ejpam-3342	310	24	if	if	SCONJ
ejpam-3342	310	25	and	and	CCONJ
ejpam-3342	310	26	only	only	ADV
ejpam-3342	310	27	if	if	SCONJ
ejpam-3342	310	28	there	there	PRON
ejpam-3342	310	29	exist	exist	VERB
ejpam-3342	310	30	a	a	DET
ejpam-3342	310	31	∈	∈	PROPN
ejpam-3342	310	32	l2(ω	l2(ω	PROPN
ejpam-3342	310	33	,	,	PUNCT
ejpam-3342	310	34	v	v	NOUN
ejpam-3342	310	35	)	)	PUNCT
ejpam-3342	310	36	,	,	PUNCT
ejpam-3342	310	37	a	a	DET
ejpam-3342	310	38	decreasing	decrease	VERB
ejpam-3342	310	39	sequence	sequence	NOUN
ejpam-3342	310	40	{	{	PUNCT
ejpam-3342	310	41	δn	δn	NOUN
ejpam-3342	310	42	}	}	PUNCT
ejpam-3342	310	43	of	of	ADP
ejpam-3342	310	44	positive	positive	ADJ
ejpam-3342	310	45	functions	function	NOUN
ejpam-3342	310	46	defined	define	VERB
ejpam-3342	310	47	on	on	ADP
ejpam-3342	310	48	(	(	PUNCT
ejpam-3342	310	49	0	0	NUM
ejpam-3342	310	50	,	,	PUNCT
ejpam-3342	310	51	t	t	X
ejpam-3342	310	52	]	]	PUNCT
ejpam-3342	310	53	,	,	PUNCT
ejpam-3342	310	54	and	and	CCONJ
ejpam-3342	310	55	a	a	DET
ejpam-3342	310	56	decreasing	decrease	VERB
ejpam-3342	310	57	sequence	sequence	NOUN
ejpam-3342	310	58	of	of	ADP
ejpam-3342	310	59	positive	positive	ADJ
ejpam-3342	310	60	numbers	number	NOUN
ejpam-3342	310	61	{	{	PUNCT
ejpam-3342	310	62	ηn	ηn	ADJ
ejpam-3342	310	63	}	}	PUNCT
ejpam-3342	310	64	such	such	ADJ
ejpam-3342	310	65	that	that	PRON
ejpam-3342	310	66	for	for	ADP
ejpam-3342	310	67	any	any	DET
ejpam-3342	310	68	backwards	backwards	ADV
ejpam-3342	310	69	(	(	PUNCT
ejpam-3342	310	70	δn	δn	NOUN
ejpam-3342	310	71	,	,	PUNCT
ejpam-3342	310	72	ηn)-fine	ηn)-fine	ADJ
ejpam-3342	310	73	partial	partial	ADJ
ejpam-3342	310	74	division	division	NOUN
ejpam-3342	310	75	dn	dn	NOUN
ejpam-3342	310	76	of	of	ADP
ejpam-3342	310	77	[	[	X
ejpam-3342	310	78	0	0	NUM
ejpam-3342	310	79	,	,	PUNCT
ejpam-3342	310	80	t	t	X
ejpam-3342	310	81	]	]	PUNCT
ejpam-3342	310	82	,	,	PUNCT
ejpam-3342	310	83	we	we	PRON
ejpam-3342	310	84	have	have	VERB
ejpam-3342	310	85	lim	lim	PROPN
ejpam-3342	310	86	n→∞	n→∞	NUM
ejpam-3342	310	87	e	e	X
ejpam-3342	310	88	[	[	PUNCT
ejpam-3342	310	89	‖s(f	‖s(f	ADJ
ejpam-3342	310	90	,	,	PUNCT
ejpam-3342	310	91	dn	dn	NOUN
ejpam-3342	310	92	,	,	PUNCT
ejpam-3342	310	93	δn	δn	NOUN
ejpam-3342	310	94	,	,	PUNCT
ejpam-3342	310	95	ηn)−a‖2v	ηn)−a‖2v	PROPN
ejpam-3342	310	96	]	]	PUNCT
ejpam-3342	311	1	=	=	PUNCT
ejpam-3342	311	2	0	0	X
ejpam-3342	311	3	.	.	PUNCT
ejpam-3342	312	1	in	in	ADP
ejpam-3342	312	2	this	this	DET
ejpam-3342	312	3	case	case	NOUN
ejpam-3342	312	4	,	,	PUNCT
ejpam-3342	312	5	a	a	DET
ejpam-3342	312	6	=	=	X
ejpam-3342	312	7	(	(	PUNCT
ejpam-3342	312	8	ihb	ihb	NOUN
ejpam-3342	312	9	)	)	PUNCT
ejpam-3342	312	10	∫	∫	PROPN
ejpam-3342	312	11	t	t	PROPN
ejpam-3342	312	12	0	0	NUM
ejpam-3342	312	13	ft	ft	NOUN
ejpam-3342	312	14	dwt	dwt	PROPN
ejpam-3342	312	15	.	.	PUNCT
ejpam-3342	313	1	(	(	PUNCT
ejpam-3342	313	2	6	6	NUM
ejpam-3342	313	3	)	)	PUNCT
ejpam-3342	313	4	(	(	PUNCT
ejpam-3342	313	5	cauchy	cauchy	NOUN
ejpam-3342	313	6	criterion	criterion	NOUN
ejpam-3342	313	7	)	)	PUNCT
ejpam-3342	313	8	.	.	PUNCT
ejpam-3342	314	1	a	a	DET
ejpam-3342	314	2	process	process	NOUN
ejpam-3342	314	3	f	f	X
ejpam-3342	314	4	:	:	PUNCT
ejpam-3342	315	1	[	[	X
ejpam-3342	315	2	0	0	NUM
ejpam-3342	315	3	,	,	PUNCT
ejpam-3342	315	4	t	t	X
ejpam-3342	315	5	]	]	PUNCT
ejpam-3342	315	6	×	×	PROPN
ejpam-3342	315	7	ω	ω	X
ejpam-3342	315	8	→	→	SYM
ejpam-3342	315	9	l2(uq	l2(uq	PROPN
ejpam-3342	315	10	,	,	PUNCT
ejpam-3342	315	11	v	v	NOUN
ejpam-3342	315	12	)	)	PUNCT
ejpam-3342	315	13	is	be	AUX
ejpam-3342	315	14	ihb	ihb	NOUN
ejpam-3342	315	15	-	-	ADJ
ejpam-3342	315	16	integrable	integrable	ADJ
ejpam-3342	315	17	on	on	ADP
ejpam-3342	315	18	[	[	X
ejpam-3342	315	19	0	0	NUM
ejpam-3342	315	20	,	,	PUNCT
ejpam-3342	315	21	t	t	X
ejpam-3342	315	22	]	]	PUNCT
ejpam-3342	315	23	if	if	SCONJ
ejpam-3342	315	24	and	and	CCONJ
ejpam-3342	315	25	only	only	ADV
ejpam-3342	315	26	if	if	SCONJ
ejpam-3342	315	27	for	for	ADP
ejpam-3342	315	28	every	every	DET
ejpam-3342	315	29	ε	ε	PROPN
ejpam-3342	315	30	>	>	X
ejpam-3342	315	31	0	0	PROPN
ejpam-3342	315	32	,	,	PUNCT
ejpam-3342	315	33	there	there	PRON
ejpam-3342	315	34	exist	exist	VERB
ejpam-3342	315	35	a	a	DET
ejpam-3342	315	36	positive	positive	ADJ
ejpam-3342	315	37	function	function	NOUN
ejpam-3342	315	38	δ	δ	PROPN
ejpam-3342	315	39	on	on	ADP
ejpam-3342	315	40	(	(	PUNCT
ejpam-3342	315	41	0	0	NUM
ejpam-3342	315	42	,	,	PUNCT
ejpam-3342	315	43	t	t	NOUN
ejpam-3342	315	44	]	]	PUNCT
ejpam-3342	315	45	and	and	CCONJ
ejpam-3342	315	46	a	a	DET
ejpam-3342	315	47	positive	positive	ADJ
ejpam-3342	315	48	number	number	NOUN
ejpam-3342	315	49	η	η	NOUN
ejpam-3342	315	50	such	such	ADJ
ejpam-3342	315	51	that	that	PRON
ejpam-3342	315	52	for	for	ADP
ejpam-3342	315	53	any	any	DET
ejpam-3342	315	54	two	two	NUM
ejpam-3342	315	55	backwards	backwards	ADV
ejpam-3342	315	56	(	(	PUNCT
ejpam-3342	315	57	δ	δ	PROPN
ejpam-3342	315	58	,	,	PUNCT
ejpam-3342	315	59	η)-fine	η)-fine	X
ejpam-3342	315	60	partial	partial	ADJ
ejpam-3342	315	61	divisions	division	NOUN
ejpam-3342	315	62	d	d	NOUN
ejpam-3342	315	63	and	and	CCONJ
ejpam-3342	315	64	d′	d′	NUM
ejpam-3342	315	65	of	of	ADP
ejpam-3342	315	66	[	[	X
ejpam-3342	315	67	0	0	NUM
ejpam-3342	315	68	,	,	PUNCT
ejpam-3342	315	69	t	t	X
ejpam-3342	315	70	]	]	PUNCT
ejpam-3342	315	71	,	,	PUNCT
ejpam-3342	315	72	we	we	PRON
ejpam-3342	315	73	have	have	VERB
ejpam-3342	315	74	e	e	NOUN
ejpam-3342	315	75	[	[	X
ejpam-3342	315	76	∥∥s(f	∥∥s(f	X
ejpam-3342	315	77	,	,	PUNCT
ejpam-3342	315	78	d	d	NOUN
ejpam-3342	315	79	,	,	PUNCT
ejpam-3342	315	80	δ	δ	PROPN
ejpam-3342	315	81	,	,	PUNCT
ejpam-3342	315	82	η)−	η)−	PROPN
ejpam-3342	315	83	s(f	s(f	PROPN
ejpam-3342	315	84	,	,	PUNCT
ejpam-3342	315	85	d′	d′	X
ejpam-3342	315	86	,	,	PUNCT
ejpam-3342	315	87	δ	δ	PROPN
ejpam-3342	315	88	,	,	PUNCT
ejpam-3342	315	89	η	η	PROPN
ejpam-3342	315	90	)	)	PUNCT
ejpam-3342	315	91	∥∥2	∥∥2	PROPN
ejpam-3342	316	1	v	v	ADP
ejpam-3342	316	2	]	]	PUNCT
ejpam-3342	316	3	<	<	X
ejpam-3342	316	4	ε	ε	PROPN
ejpam-3342	316	5	.	.	PUNCT
ejpam-3342	316	6	(	(	PUNCT
ejpam-3342	316	7	7	7	NUM
ejpam-3342	316	8	)	)	PUNCT
ejpam-3342	316	9	(	(	PUNCT
ejpam-3342	316	10	weak	weak	ADJ
ejpam-3342	316	11	version	version	NOUN
ejpam-3342	316	12	of	of	ADP
ejpam-3342	316	13	saks	sak	NOUN
ejpam-3342	316	14	-	-	PUNCT
ejpam-3342	316	15	henstock	henstock	NOUN
ejpam-3342	316	16	lemma	lemma	PROPN
ejpam-3342	316	17	)	)	PUNCT
ejpam-3342	316	18	.	.	PUNCT
ejpam-3342	317	1	let	let	VERB
ejpam-3342	317	2	f	f	PRON
ejpam-3342	317	3	be	be	AUX
ejpam-3342	317	4	ihb	ihb	NOUN
ejpam-3342	317	5	-	-	ADJ
ejpam-3342	317	6	integrable	integrable	ADJ
ejpam-3342	317	7	on	on	ADP
ejpam-3342	317	8	[	[	X
ejpam-3342	317	9	0	0	NUM
ejpam-3342	317	10	,	,	PUNCT
ejpam-3342	317	11	t	t	NOUN
ejpam-3342	317	12	]	]	PUNCT
ejpam-3342	317	13	and	and	CCONJ
ejpam-3342	317	14	f	f	PROPN
ejpam-3342	317	15	(	(	PUNCT
ejpam-3342	317	16	u	u	NOUN
ejpam-3342	317	17	,	,	PUNCT
ejpam-3342	317	18	v	v	NOUN
ejpam-3342	317	19	)	)	PUNCT
ejpam-3342	317	20	:	:	PUNCT
ejpam-3342	318	1	=	=	SYM
ejpam-3342	318	2	(	(	PUNCT
ejpam-3342	318	3	ihb	ihb	NOUN
ejpam-3342	318	4	)	)	PUNCT
ejpam-3342	318	5	∫	∫	PROPN
ejpam-3342	318	6	v	v	NUM
ejpam-3342	318	7	u	u	PROPN
ejpam-3342	318	8	ft	ft	NOUN
ejpam-3342	318	9	dwt	dwt	NOUN
ejpam-3342	318	10	for	for	ADP
ejpam-3342	318	11	any	any	DET
ejpam-3342	318	12	(	(	PUNCT
ejpam-3342	318	13	u	u	NOUN
ejpam-3342	318	14	,	,	PUNCT
ejpam-3342	318	15	v	v	NOUN
ejpam-3342	318	16	]	]	PUNCT
ejpam-3342	318	17	⊆	⊆	NUM
ejpam-3342	318	18	[	[	X
ejpam-3342	318	19	0	0	NUM
ejpam-3342	318	20	,	,	PUNCT
ejpam-3342	318	21	t	t	X
ejpam-3342	318	22	]	]	PUNCT
ejpam-3342	318	23	.	.	PUNCT
ejpam-3342	319	1	then	then	ADV
ejpam-3342	319	2	for	for	ADP
ejpam-3342	319	3	every	every	DET
ejpam-3342	319	4	ε	ε	PROPN
ejpam-3342	319	5	>	>	X
ejpam-3342	319	6	0	0	PROPN
ejpam-3342	319	7	,	,	PUNCT
ejpam-3342	319	8	there	there	PRON
ejpam-3342	319	9	exist	exist	VERB
ejpam-3342	319	10	a	a	DET
ejpam-3342	319	11	positive	positive	ADJ
ejpam-3342	319	12	function	function	NOUN
ejpam-3342	319	13	δ	δ	PROPN
ejpam-3342	319	14	on	on	ADP
ejpam-3342	319	15	(	(	PUNCT
ejpam-3342	319	16	0	0	NUM
ejpam-3342	319	17	,	,	PUNCT
ejpam-3342	319	18	t	t	NOUN
ejpam-3342	319	19	]	]	PUNCT
ejpam-3342	319	20	and	and	CCONJ
ejpam-3342	319	21	a	a	DET
ejpam-3342	319	22	positive	positive	ADJ
ejpam-3342	319	23	number	number	NOUN
ejpam-3342	319	24	η	η	NOUN
ejpam-3342	319	25	such	such	ADJ
ejpam-3342	319	26	that	that	PRON
ejpam-3342	319	27	for	for	ADP
ejpam-3342	319	28	any	any	DET
ejpam-3342	319	29	backwards	backwards	ADV
ejpam-3342	319	30	(	(	PUNCT
ejpam-3342	319	31	δ	δ	PROPN
ejpam-3342	319	32	,	,	PUNCT
ejpam-3342	319	33	η)-fine	η)-fine	X
ejpam-3342	319	34	partial	partial	ADJ
ejpam-3342	319	35	division	division	NOUN
ejpam-3342	319	36	d	d	PROPN
ejpam-3342	319	37	of	of	ADP
ejpam-3342	319	38	[	[	X
ejpam-3342	319	39	0	0	NUM
ejpam-3342	319	40	,	,	PUNCT
ejpam-3342	319	41	t	t	X
ejpam-3342	319	42	]	]	PUNCT
ejpam-3342	319	43	,	,	PUNCT
ejpam-3342	319	44	we	we	PRON
ejpam-3342	319	45	have	have	VERB
ejpam-3342	319	46	e	e	NOUN
ejpam-3342	319	47	[	[	X
ejpam-3342	319	48	∥∥∥(d	∥∥∥(d	X
ejpam-3342	319	49	)	)	PUNCT
ejpam-3342	319	50	∑	∑	PRON
ejpam-3342	319	51	{	{	PUNCT
ejpam-3342	319	52	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	319	53	−wv)−	−wv)−	PROPN
ejpam-3342	319	54	f	f	X
ejpam-3342	319	55	(	(	PUNCT
ejpam-3342	319	56	v	v	NOUN
ejpam-3342	319	57	,	,	PUNCT
ejpam-3342	319	58	ξ	ξ	NOUN
ejpam-3342	319	59	)	)	PUNCT
ejpam-3342	319	60	}	}	PUNCT
ejpam-3342	319	61	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	319	62	v	v	ADP
ejpam-3342	319	63	]	]	PUNCT
ejpam-3342	319	64	<	<	X
ejpam-3342	319	65	ε	ε	PROPN
ejpam-3342	319	66	.	.	PUNCT
ejpam-3342	319	67	r.	r.	PROPN
ejpam-3342	319	68	rulete	rulete	PROPN
ejpam-3342	319	69	,	,	PUNCT
ejpam-3342	319	70	m.	m.	NOUN
ejpam-3342	319	71	labendia	labendia	PROPN
ejpam-3342	319	72	/	/	SYM
ejpam-3342	319	73	eur	eur	PROPN
ejpam-3342	319	74	.	.	PUNCT
ejpam-3342	320	1	j.	j.	PROPN
ejpam-3342	320	2	pure	pure	PROPN
ejpam-3342	320	3	appl	appl	PROPN
ejpam-3342	320	4	.	.	PROPN
ejpam-3342	320	5	math	math	PROPN
ejpam-3342	320	6	,	,	PUNCT
ejpam-3342	320	7	12	12	NUM
ejpam-3342	320	8	(	(	PUNCT
ejpam-3342	320	9	1	1	NUM
ejpam-3342	320	10	)	)	PUNCT
ejpam-3342	320	11	(	(	PUNCT
ejpam-3342	320	12	2019	2019	NUM
ejpam-3342	320	13	)	)	PUNCT
ejpam-3342	320	14	,	,	PUNCT
ejpam-3342	320	15	58	58	NUM
ejpam-3342	320	16	-	-	SYM
ejpam-3342	320	17	78	78	NUM
ejpam-3342	320	18	70	70	NUM
ejpam-3342	320	19	4	4	NUM
ejpam-3342	320	20	.	.	PUNCT
ejpam-3342	321	1	itô	itô	PROPN
ejpam-3342	321	2	isometry	isometry	NOUN
ejpam-3342	321	3	and	and	CCONJ
ejpam-3342	321	4	ac2[0	ac2[0	NOUN
ejpam-3342	321	5	,	,	PUNCT
ejpam-3342	321	6	t	t	X
ejpam-3342	321	7	]	]	PUNCT
ejpam-3342	321	8	-property	-property	NOUN
ejpam-3342	321	9	this	this	DET
ejpam-3342	321	10	section	section	NOUN
ejpam-3342	321	11	presents	present	VERB
ejpam-3342	321	12	the	the	DET
ejpam-3342	321	13	itô	itô	PROPN
ejpam-3342	321	14	isometry	isometry	NOUN
ejpam-3342	321	15	and	and	CCONJ
ejpam-3342	321	16	the	the	DET
ejpam-3342	321	17	equivalent	equivalent	ADJ
ejpam-3342	321	18	definition	definition	NOUN
ejpam-3342	321	19	of	of	ADP
ejpam-3342	321	20	backwards	backwards	ADV
ejpam-3342	321	21	itôhenstock	itôhenstock	NOUN
ejpam-3342	321	22	using	use	VERB
ejpam-3342	321	23	the	the	DET
ejpam-3342	321	24	notion	notion	NOUN
ejpam-3342	321	25	of	of	ADP
ejpam-3342	321	26	ac2[0	ac2[0	PROPN
ejpam-3342	321	27	,	,	PUNCT
ejpam-3342	321	28	t	t	PROPN
ejpam-3342	321	29	]	]	PUNCT
ejpam-3342	321	30	-property	-property	NOUN
ejpam-3342	321	31	.	.	PUNCT
ejpam-3342	322	1	before	before	SCONJ
ejpam-3342	322	2	we	we	PRON
ejpam-3342	322	3	proceed	proceed	VERB
ejpam-3342	322	4	with	with	ADP
ejpam-3342	322	5	the	the	DET
ejpam-3342	322	6	itô	itô	PROPN
ejpam-3342	322	7	isometry	isometry	NOUN
ejpam-3342	322	8	,	,	PUNCT
ejpam-3342	322	9	we	we	PRON
ejpam-3342	322	10	need	need	VERB
ejpam-3342	322	11	to	to	PART
ejpam-3342	322	12	define	define	VERB
ejpam-3342	322	13	the	the	DET
ejpam-3342	322	14	backwards	backwards	ADV
ejpam-3342	322	15	henstock	henstock	NOUN
ejpam-3342	322	16	integral	integral	ADJ
ejpam-3342	322	17	which	which	PRON
ejpam-3342	322	18	is	be	AUX
ejpam-3342	322	19	equivalent	equivalent	ADJ
ejpam-3342	322	20	to	to	ADP
ejpam-3342	322	21	the	the	DET
ejpam-3342	322	22	lebesgue	lebesgue	NOUN
ejpam-3342	322	23	integral	integral	ADJ
ejpam-3342	322	24	(	(	PUNCT
ejpam-3342	322	25	see	see	VERB
ejpam-3342	322	26	[	[	X
ejpam-3342	322	27	2	2	NUM
ejpam-3342	322	28	]	]	NUM
ejpam-3342	322	29	)	)	PUNCT
ejpam-3342	322	30	.	.	PUNCT
ejpam-3342	323	1	definition	definition	NOUN
ejpam-3342	323	2	2	2	NUM
ejpam-3342	323	3	.	.	PUNCT
ejpam-3342	324	1	a	a	DET
ejpam-3342	324	2	real	real	ADV
ejpam-3342	324	3	-	-	PUNCT
ejpam-3342	324	4	valued	value	VERB
ejpam-3342	324	5	function	function	NOUN
ejpam-3342	324	6	f	f	PROPN
ejpam-3342	324	7	defined	define	VERB
ejpam-3342	324	8	on	on	ADP
ejpam-3342	324	9	[	[	X
ejpam-3342	324	10	0	0	NUM
ejpam-3342	324	11	,	,	PUNCT
ejpam-3342	324	12	t	t	PROPN
ejpam-3342	324	13	]	]	PUNCT
ejpam-3342	324	14	is	be	AUX
ejpam-3342	324	15	said	say	VERB
ejpam-3342	324	16	to	to	PART
ejpam-3342	324	17	be	be	AUX
ejpam-3342	324	18	lebesgue	lebesgue	NOUN
ejpam-3342	324	19	integrable	integrable	ADJ
ejpam-3342	324	20	to	to	ADP
ejpam-3342	324	21	a	a	DET
ejpam-3342	324	22	∈	∈	NOUN
ejpam-3342	324	23	r	r	NOUN
ejpam-3342	324	24	if	if	SCONJ
ejpam-3342	324	25	given	give	VERB
ejpam-3342	324	26	ε	ε	PROPN
ejpam-3342	324	27	>	>	X
ejpam-3342	324	28	0	0	PROPN
ejpam-3342	324	29	,	,	PUNCT
ejpam-3342	324	30	there	there	PRON
ejpam-3342	324	31	exists	exist	VERB
ejpam-3342	324	32	a	a	DET
ejpam-3342	324	33	positive	positive	ADJ
ejpam-3342	324	34	function	function	NOUN
ejpam-3342	324	35	δ	δ	PROPN
ejpam-3342	324	36	on	on	ADP
ejpam-3342	324	37	(	(	PUNCT
ejpam-3342	324	38	0	0	NUM
ejpam-3342	324	39	,	,	PUNCT
ejpam-3342	324	40	t	t	NOUN
ejpam-3342	324	41	]	]	PUNCT
ejpam-3342	324	42	and	and	CCONJ
ejpam-3342	324	43	a	a	DET
ejpam-3342	324	44	real	real	ADJ
ejpam-3342	324	45	constant	constant	ADJ
ejpam-3342	324	46	η	η	PROPN
ejpam-3342	324	47	>	>	X
ejpam-3342	324	48	0	0	NUM
ejpam-3342	324	49	such	such	ADJ
ejpam-3342	324	50	that	that	SCONJ
ejpam-3342	324	51	∣∣∣(d	∣∣∣(d	AUX
ejpam-3342	324	52	)	)	PUNCT
ejpam-3342	324	53	∑	∑	DET
ejpam-3342	324	54	f(ξ)(ξ	f(ξ)(ξ	NOUN
ejpam-3342	324	55	−	−	X
ejpam-3342	324	56	v)−a	v)−a	ADV
ejpam-3342	324	57	∣∣∣	∣∣∣	NOUN
ejpam-3342	324	58	<	<	X
ejpam-3342	324	59	ε	ε	PROPN
ejpam-3342	324	60	whenever	whenever	SCONJ
ejpam-3342	324	61	d	d	PROPN
ejpam-3342	324	62	is	be	AUX
ejpam-3342	324	63	a	a	DET
ejpam-3342	324	64	backwards	backwards	ADV
ejpam-3342	324	65	δ	δ	NOUN
ejpam-3342	324	66	-	-	PUNCT
ejpam-3342	324	67	fine	fine	ADJ
ejpam-3342	324	68	partial	partial	ADJ
ejpam-3342	324	69	division	division	NOUN
ejpam-3342	324	70	of	of	ADP
ejpam-3342	324	71	[	[	X
ejpam-3342	324	72	0	0	NUM
ejpam-3342	324	73	,	,	PUNCT
ejpam-3342	324	74	t	t	X
ejpam-3342	324	75	]	]	PUNCT
ejpam-3342	324	76	with	with	ADP
ejpam-3342	324	77	(	(	PUNCT
ejpam-3342	324	78	d	d	NOUN
ejpam-3342	324	79	)	)	PUNCT
ejpam-3342	324	80	∑	∑	PUNCT
ejpam-3342	324	81	(	(	PUNCT
ejpam-3342	324	82	ξ	ξ	X
ejpam-3342	324	83	−	−	PROPN
ejpam-3342	324	84	v	v	NOUN
ejpam-3342	324	85	)	)	PUNCT
ejpam-3342	324	86	>	>	X
ejpam-3342	325	1	t	t	PROPN
ejpam-3342	325	2	−	−	PROPN
ejpam-3342	326	1	η	η	PROPN
ejpam-3342	326	2	.	.	PROPN
ejpam-3342	326	3	in	in	ADP
ejpam-3342	326	4	this	this	DET
ejpam-3342	326	5	case	case	NOUN
ejpam-3342	326	6	,	,	PUNCT
ejpam-3342	326	7	a	a	PRON
ejpam-3342	326	8	is	be	AUX
ejpam-3342	326	9	called	call	VERB
ejpam-3342	326	10	the	the	DET
ejpam-3342	326	11	lebesgue	lebesgue	NOUN
ejpam-3342	326	12	integral	integral	ADJ
ejpam-3342	326	13	of	of	ADP
ejpam-3342	326	14	f	f	PRON
ejpam-3342	326	15	which	which	PRON
ejpam-3342	326	16	will	will	AUX
ejpam-3342	326	17	be	be	AUX
ejpam-3342	326	18	denoted	denote	VERB
ejpam-3342	326	19	by	by	ADP
ejpam-3342	326	20	(	(	PUNCT
ejpam-3342	326	21	l	l	NOUN
ejpam-3342	326	22	)	)	PUNCT
ejpam-3342	326	23	∫	∫	PROPN
ejpam-3342	326	24	t	t	NOUN
ejpam-3342	326	25	0	0	NUM
ejpam-3342	326	26	f(t	f(t	NOUN
ejpam-3342	326	27	)	)	PUNCT
ejpam-3342	327	1	dt	dt	PROPN
ejpam-3342	327	2	.	.	PUNCT
ejpam-3342	328	1	note	note	VERB
ejpam-3342	328	2	that	that	SCONJ
ejpam-3342	328	3	the	the	DET
ejpam-3342	328	4	backwards	backwards	ADV
ejpam-3342	328	5	δ	δ	PROPN
ejpam-3342	328	6	-	-	PUNCT
ejpam-3342	328	7	fine	fine	ADJ
ejpam-3342	328	8	partial	partial	ADJ
ejpam-3342	328	9	division	division	NOUN
ejpam-3342	328	10	d	d	PROPN
ejpam-3342	328	11	of	of	ADP
ejpam-3342	328	12	[	[	X
ejpam-3342	328	13	0	0	NUM
ejpam-3342	328	14	,	,	PUNCT
ejpam-3342	328	15	t	t	X
ejpam-3342	328	16	]	]	PUNCT
ejpam-3342	328	17	in	in	ADP
ejpam-3342	328	18	definition	definition	NOUN
ejpam-3342	328	19	2	2	NUM
ejpam-3342	328	20	is	be	AUX
ejpam-3342	328	21	also	also	ADV
ejpam-3342	328	22	a	a	DET
ejpam-3342	328	23	backwards	backwards	ADV
ejpam-3342	328	24	(	(	PUNCT
ejpam-3342	328	25	δ	δ	PROPN
ejpam-3342	328	26	,	,	PUNCT
ejpam-3342	328	27	η)-fine	η)-fine	X
ejpam-3342	328	28	partial	partial	ADJ
ejpam-3342	328	29	division	division	NOUN
ejpam-3342	328	30	of	of	ADP
ejpam-3342	328	31	[	[	X
ejpam-3342	328	32	0	0	NUM
ejpam-3342	328	33	,	,	PUNCT
ejpam-3342	328	34	t	t	X
ejpam-3342	328	35	]	]	PUNCT
ejpam-3342	328	36	.	.	PUNCT
ejpam-3342	329	1	theorem	theorem	NOUN
ejpam-3342	329	2	2	2	NUM
ejpam-3342	329	3	.	.	PUNCT
ejpam-3342	330	1	the	the	DET
ejpam-3342	330	2	function	function	NOUN
ejpam-3342	330	3	f	f	NOUN
ejpam-3342	330	4	:	:	PUNCT
ejpam-3342	331	1	[	[	X
ejpam-3342	331	2	0	0	NUM
ejpam-3342	331	3	,	,	PUNCT
ejpam-3342	331	4	t	t	X
ejpam-3342	331	5	]	]	PUNCT
ejpam-3342	331	6	→	→	PUNCT
ejpam-3342	331	7	r	r	NOUN
ejpam-3342	331	8	is	be	AUX
ejpam-3342	331	9	lebesgue	lebesgue	NOUN
ejpam-3342	331	10	integrable	integrable	ADJ
ejpam-3342	331	11	to	to	ADP
ejpam-3342	331	12	a	a	DET
ejpam-3342	331	13	∈	∈	NOUN
ejpam-3342	331	14	r	r	NOUN
ejpam-3342	331	15	if	if	SCONJ
ejpam-3342	331	16	and	and	CCONJ
ejpam-3342	331	17	only	only	ADV
ejpam-3342	331	18	if	if	SCONJ
ejpam-3342	331	19	there	there	PRON
ejpam-3342	331	20	exists	exist	VERB
ejpam-3342	331	21	a	a	DET
ejpam-3342	331	22	decreasing	decrease	VERB
ejpam-3342	331	23	sequence	sequence	NOUN
ejpam-3342	331	24	of	of	ADP
ejpam-3342	331	25	positive	positive	ADJ
ejpam-3342	331	26	functions	function	NOUN
ejpam-3342	331	27	{	{	PUNCT
ejpam-3342	331	28	δn(ξ	δn(ξ	NOUN
ejpam-3342	331	29	)	)	PUNCT
ejpam-3342	331	30	}	}	PUNCT
ejpam-3342	331	31	on	on	ADP
ejpam-3342	331	32	(	(	PUNCT
ejpam-3342	331	33	0	0	NUM
ejpam-3342	331	34	,	,	PUNCT
ejpam-3342	331	35	t	t	NOUN
ejpam-3342	331	36	]	]	PUNCT
ejpam-3342	331	37	and	and	CCONJ
ejpam-3342	331	38	a	a	DET
ejpam-3342	331	39	decreasing	decrease	VERB
ejpam-3342	331	40	sequence	sequence	NOUN
ejpam-3342	331	41	of	of	ADP
ejpam-3342	331	42	positive	positive	ADJ
ejpam-3342	331	43	constants	constant	NOUN
ejpam-3342	331	44	{	{	PUNCT
ejpam-3342	331	45	ηn	ηn	ADV
ejpam-3342	331	46	}	}	PUNCT
ejpam-3342	332	1	such	such	ADJ
ejpam-3342	332	2	that	that	SCONJ
ejpam-3342	332	3	lim	lim	PROPN
ejpam-3342	332	4	n→∞	n→∞	NUM
ejpam-3342	332	5	∣∣∣(dn	∣∣∣(dn	PROPN
ejpam-3342	332	6	)	)	PUNCT
ejpam-3342	332	7	∑	∑	PUNCT
ejpam-3342	332	8	f(ξ(n))(ξ(n	f(ξ(n))(ξ(n	ADJ
ejpam-3342	332	9	)	)	PUNCT
ejpam-3342	332	10	−	−	PROPN
ejpam-3342	332	11	v(n))−a	v(n))−a	ADJ
ejpam-3342	332	12	∣∣∣	∣∣∣	NOUN
ejpam-3342	332	13	=	=	SYM
ejpam-3342	332	14	0	0	NUM
ejpam-3342	332	15	,	,	PUNCT
ejpam-3342	332	16	where	where	SCONJ
ejpam-3342	332	17	dn	dn	PROPN
ejpam-3342	332	18	is	be	AUX
ejpam-3342	332	19	any	any	DET
ejpam-3342	332	20	backwards	backwards	ADV
ejpam-3342	332	21	(	(	PUNCT
ejpam-3342	332	22	δn	δn	NOUN
ejpam-3342	332	23	,	,	PUNCT
ejpam-3342	332	24	ηn)-fine	ηn)-fine	ADJ
ejpam-3342	332	25	partial	partial	ADJ
ejpam-3342	332	26	division	division	NOUN
ejpam-3342	332	27	of	of	ADP
ejpam-3342	332	28	[	[	X
ejpam-3342	332	29	0	0	NUM
ejpam-3342	332	30	,	,	PUNCT
ejpam-3342	332	31	t	t	X
ejpam-3342	332	32	]	]	PUNCT
ejpam-3342	332	33	.	.	PUNCT
ejpam-3342	333	1	proof	proof	NOUN
ejpam-3342	333	2	.	.	PUNCT
ejpam-3342	334	1	suppose	suppose	VERB
ejpam-3342	334	2	that	that	SCONJ
ejpam-3342	334	3	f	f	X
ejpam-3342	334	4	:	:	PUNCT
ejpam-3342	335	1	[	[	X
ejpam-3342	335	2	0	0	NUM
ejpam-3342	335	3	,	,	PUNCT
ejpam-3342	335	4	t	t	X
ejpam-3342	335	5	]	]	PUNCT
ejpam-3342	335	6	→	→	PUNCT
ejpam-3342	335	7	r	r	NOUN
ejpam-3342	335	8	is	be	AUX
ejpam-3342	335	9	lebesgue	lebesgue	NOUN
ejpam-3342	335	10	integrable	integrable	ADJ
ejpam-3342	335	11	to	to	ADP
ejpam-3342	335	12	a	a	DET
ejpam-3342	335	13	∈	∈	PROPN
ejpam-3342	335	14	r.	r.	NOUN
ejpam-3342	335	15	then	then	ADV
ejpam-3342	335	16	,	,	PUNCT
ejpam-3342	335	17	by	by	ADP
ejpam-3342	335	18	definition	definition	NOUN
ejpam-3342	335	19	2	2	NUM
ejpam-3342	335	20	,	,	PUNCT
ejpam-3342	335	21	for	for	ADP
ejpam-3342	335	22	every	every	DET
ejpam-3342	335	23	ε	ε	PROPN
ejpam-3342	335	24	=	=	SYM
ejpam-3342	335	25	1	1	NUM
ejpam-3342	335	26	n	n	NOUN
ejpam-3342	335	27	,	,	PUNCT
ejpam-3342	335	28	n	n	NOUN
ejpam-3342	335	29	=	=	SYM
ejpam-3342	335	30	1	1	NUM
ejpam-3342	335	31	,	,	PUNCT
ejpam-3342	335	32	2	2	NUM
ejpam-3342	335	33	,	,	PUNCT
ejpam-3342	335	34	3	3	NUM
ejpam-3342	335	35	,	,	PUNCT
ejpam-3342	335	36	.	.	PUNCT
ejpam-3342	335	37	.	.	PUNCT
ejpam-3342	336	1	.	.	PUNCT
ejpam-3342	336	2	,	,	PUNCT
ejpam-3342	336	3	there	there	PRON
ejpam-3342	336	4	exists	exist	VERB
ejpam-3342	336	5	a	a	DET
ejpam-3342	336	6	positive	positive	ADJ
ejpam-3342	336	7	function	function	NOUN
ejpam-3342	336	8	δn	δn	NOUN
ejpam-3342	336	9	on	on	ADP
ejpam-3342	336	10	(	(	PUNCT
ejpam-3342	336	11	0	0	NUM
ejpam-3342	336	12	,	,	PUNCT
ejpam-3342	336	13	t	t	NOUN
ejpam-3342	336	14	]	]	PUNCT
ejpam-3342	336	15	and	and	CCONJ
ejpam-3342	336	16	a	a	DET
ejpam-3342	336	17	positive	positive	ADJ
ejpam-3342	336	18	number	number	NOUN
ejpam-3342	336	19	η	η	NOUN
ejpam-3342	336	20	such	such	ADJ
ejpam-3342	336	21	that	that	PRON
ejpam-3342	336	22	for	for	ADP
ejpam-3342	336	23	any	any	DET
ejpam-3342	336	24	backwards	backwards	ADJ
ejpam-3342	336	25	δn	δn	ADJ
ejpam-3342	336	26	-	-	PUNCT
ejpam-3342	336	27	fine	fine	ADJ
ejpam-3342	336	28	partial	partial	ADJ
ejpam-3342	336	29	division	division	NOUN
ejpam-3342	336	30	dn	dn	NOUN
ejpam-3342	336	31	=	=	PUNCT
ejpam-3342	336	32	{	{	PUNCT
ejpam-3342	336	33	(	(	PUNCT
ejpam-3342	336	34	(	(	PUNCT
ejpam-3342	336	35	v(n	v(n	NOUN
ejpam-3342	336	36	)	)	PUNCT
ejpam-3342	336	37	,	,	PUNCT
ejpam-3342	336	38	ξ(n	ξ(n	PROPN
ejpam-3342	336	39	)	)	PUNCT
ejpam-3342	336	40	]	]	X
ejpam-3342	336	41	,	,	PUNCT
ejpam-3342	336	42	ξ(n	ξ(n	PROPN
ejpam-3342	336	43	)	)	PUNCT
ejpam-3342	336	44	)	)	PUNCT
ejpam-3342	336	45	}	}	PUNCT
ejpam-3342	336	46	of	of	ADP
ejpam-3342	336	47	[	[	X
ejpam-3342	336	48	0	0	NUM
ejpam-3342	336	49	,	,	PUNCT
ejpam-3342	336	50	t	t	X
ejpam-3342	336	51	]	]	PUNCT
ejpam-3342	336	52	with	with	ADP
ejpam-3342	336	53	(	(	PUNCT
ejpam-3342	336	54	dn	dn	NOUN
ejpam-3342	336	55	)	)	PUNCT
ejpam-3342	336	56	∑	∑	PRON
ejpam-3342	336	57	(	(	PUNCT
ejpam-3342	336	58	ξ(n	ξ(n	NOUN
ejpam-3342	336	59	)	)	PUNCT
ejpam-3342	336	60	−	−	PROPN
ejpam-3342	336	61	v(n	v(n	NOUN
ejpam-3342	336	62	)	)	PUNCT
ejpam-3342	336	63	)	)	PUNCT
ejpam-3342	337	1	>	>	X
ejpam-3342	337	2	t	t	PROPN
ejpam-3342	338	1	−	−	PROPN
ejpam-3342	338	2	ηn	ηn	INTJ
ejpam-3342	338	3	we	we	PRON
ejpam-3342	338	4	have∣∣∣(dn	have∣∣∣(dn	NUM
ejpam-3342	338	5	)	)	PUNCT
ejpam-3342	338	6	∑	∑	PUNCT
ejpam-3342	338	7	f(ξ(n))(ξ(n	f(ξ(n))(ξ(n	ADJ
ejpam-3342	338	8	)	)	PUNCT
ejpam-3342	338	9	−	−	PROPN
ejpam-3342	339	1	v(n))−a	v(n))−a	ADJ
ejpam-3342	339	2	∣∣∣	∣∣∣	ADJ
ejpam-3342	339	3	≤	≤	NUM
ejpam-3342	339	4	1	1	NUM
ejpam-3342	339	5	n	n	NOUN
ejpam-3342	339	6	.	.	PUNCT
ejpam-3342	340	1	hence	hence	ADV
ejpam-3342	340	2	,	,	PUNCT
ejpam-3342	340	3	lim	lim	PROPN
ejpam-3342	340	4	n→∞	n→∞	NUM
ejpam-3342	340	5	∣∣∣(dn	∣∣∣(dn	PROPN
ejpam-3342	340	6	)	)	PUNCT
ejpam-3342	340	7	∑	∑	PUNCT
ejpam-3342	340	8	f(ξ(n))(ξ(n	f(ξ(n))(ξ(n	ADJ
ejpam-3342	340	9	)	)	PUNCT
ejpam-3342	340	10	−	−	PROPN
ejpam-3342	340	11	v(n))−a	v(n))−a	ADJ
ejpam-3342	340	12	∣∣∣	∣∣∣	NOUN
ejpam-3342	340	13	=	=	SYM
ejpam-3342	340	14	0	0	NUM
ejpam-3342	340	15	,	,	PUNCT
ejpam-3342	340	16	for	for	ADP
ejpam-3342	340	17	any	any	DET
ejpam-3342	340	18	backwards	backwards	ADV
ejpam-3342	340	19	(	(	PUNCT
ejpam-3342	340	20	δn	δn	NOUN
ejpam-3342	340	21	,	,	PUNCT
ejpam-3342	340	22	ηn)-fine	ηn)-fine	ADJ
ejpam-3342	340	23	partial	partial	ADJ
ejpam-3342	340	24	division	division	NOUN
ejpam-3342	340	25	dn	dn	NOUN
ejpam-3342	340	26	of	of	ADP
ejpam-3342	340	27	[	[	X
ejpam-3342	340	28	0	0	NUM
ejpam-3342	340	29	,	,	PUNCT
ejpam-3342	340	30	t	t	X
ejpam-3342	340	31	]	]	PUNCT
ejpam-3342	340	32	.	.	PUNCT
ejpam-3342	341	1	conversely	conversely	ADV
ejpam-3342	341	2	,	,	PUNCT
ejpam-3342	341	3	let	let	VERB
ejpam-3342	341	4	us	we	PRON
ejpam-3342	341	5	assume	assume	VERB
ejpam-3342	341	6	that	that	SCONJ
ejpam-3342	341	7	there	there	PRON
ejpam-3342	341	8	exists	exist	VERB
ejpam-3342	341	9	a	a	DET
ejpam-3342	341	10	∈	∈	NOUN
ejpam-3342	341	11	r	r	NOUN
ejpam-3342	341	12	and	and	CCONJ
ejpam-3342	341	13	a	a	DET
ejpam-3342	341	14	decreasing	decrease	VERB
ejpam-3342	341	15	sequence	sequence	NOUN
ejpam-3342	341	16	{	{	PUNCT
ejpam-3342	341	17	δn(ξ	δn(ξ	NOUN
ejpam-3342	341	18	)	)	PUNCT
ejpam-3342	341	19	}	}	PUNCT
ejpam-3342	341	20	of	of	ADP
ejpam-3342	341	21	positive	positive	ADJ
ejpam-3342	341	22	functions	function	NOUN
ejpam-3342	341	23	on	on	ADP
ejpam-3342	341	24	(	(	PUNCT
ejpam-3342	341	25	0	0	NUM
ejpam-3342	341	26	,	,	PUNCT
ejpam-3342	341	27	t	t	NOUN
ejpam-3342	341	28	]	]	PUNCT
ejpam-3342	341	29	and	and	CCONJ
ejpam-3342	341	30	a	a	DET
ejpam-3342	341	31	decreasing	decrease	VERB
ejpam-3342	341	32	sequence	sequence	NOUN
ejpam-3342	341	33	of	of	ADP
ejpam-3342	341	34	positive	positive	ADJ
ejpam-3342	341	35	numbers	number	NOUN
ejpam-3342	341	36	{	{	PUNCT
ejpam-3342	341	37	ηn	ηn	ADP
ejpam-3342	341	38	}	}	PUNCT
ejpam-3342	342	1	such	such	ADJ
ejpam-3342	342	2	that	that	SCONJ
ejpam-3342	342	3	lim	lim	PROPN
ejpam-3342	342	4	n→∞	n→∞	NUM
ejpam-3342	342	5	∣∣∣(dn	∣∣∣(dn	PROPN
ejpam-3342	342	6	)	)	PUNCT
ejpam-3342	342	7	∑	∑	PUNCT
ejpam-3342	342	8	f(ξ(n))(ξ(n	f(ξ(n))(ξ(n	ADJ
ejpam-3342	342	9	)	)	PUNCT
ejpam-3342	342	10	−	−	PROPN
ejpam-3342	342	11	v(n))−a	v(n))−a	ADJ
ejpam-3342	342	12	∣∣∣	∣∣∣	NOUN
ejpam-3342	342	13	=	=	SYM
ejpam-3342	342	14	0	0	NUM
ejpam-3342	342	15	suppose	suppose	VERB
ejpam-3342	342	16	that	that	SCONJ
ejpam-3342	342	17	f	f	PROPN
ejpam-3342	342	18	is	be	AUX
ejpam-3342	342	19	not	not	PART
ejpam-3342	342	20	lebesgue	lebesgue	NOUN
ejpam-3342	342	21	integrable	integrable	ADJ
ejpam-3342	342	22	to	to	ADP
ejpam-3342	342	23	a	a	PRON
ejpam-3342	342	24	on	on	ADP
ejpam-3342	342	25	[	[	X
ejpam-3342	342	26	0	0	NUM
ejpam-3342	342	27	,	,	PUNCT
ejpam-3342	342	28	t	t	X
ejpam-3342	342	29	]	]	PUNCT
ejpam-3342	342	30	.	.	PUNCT
ejpam-3342	343	1	then	then	ADV
ejpam-3342	343	2	there	there	PRON
ejpam-3342	343	3	exists	exist	VERB
ejpam-3342	343	4	ε	ε	PROPN
ejpam-3342	343	5	>	>	X
ejpam-3342	343	6	0	0	NUM
ejpam-3342	343	7	such	such	ADJ
ejpam-3342	343	8	that	that	PRON
ejpam-3342	343	9	for	for	ADP
ejpam-3342	343	10	every	every	DET
ejpam-3342	343	11	positive	positive	ADJ
ejpam-3342	343	12	function	function	NOUN
ejpam-3342	343	13	δ	δ	PROPN
ejpam-3342	343	14	on	on	ADP
ejpam-3342	343	15	(	(	PUNCT
ejpam-3342	343	16	0	0	NUM
ejpam-3342	343	17	,	,	PUNCT
ejpam-3342	343	18	t	t	NOUN
ejpam-3342	343	19	]	]	PUNCT
ejpam-3342	343	20	and	and	CCONJ
ejpam-3342	343	21	every	every	DET
ejpam-3342	343	22	positive	positive	ADJ
ejpam-3342	343	23	number	number	NOUN
ejpam-3342	343	24	η	η	PROPN
ejpam-3342	343	25	there	there	PRON
ejpam-3342	343	26	exists	exist	VERB
ejpam-3342	343	27	a	a	DET
ejpam-3342	343	28	r.	r.	PROPN
ejpam-3342	343	29	rulete	rulete	PROPN
ejpam-3342	343	30	,	,	PUNCT
ejpam-3342	343	31	m.	m.	NOUN
ejpam-3342	343	32	labendia	labendia	PROPN
ejpam-3342	343	33	/	/	SYM
ejpam-3342	343	34	eur	eur	PROPN
ejpam-3342	343	35	.	.	PUNCT
ejpam-3342	344	1	j.	j.	PROPN
ejpam-3342	344	2	pure	pure	PROPN
ejpam-3342	344	3	appl	appl	PROPN
ejpam-3342	344	4	.	.	PROPN
ejpam-3342	344	5	math	math	PROPN
ejpam-3342	344	6	,	,	PUNCT
ejpam-3342	344	7	12	12	NUM
ejpam-3342	344	8	(	(	PUNCT
ejpam-3342	344	9	1	1	NUM
ejpam-3342	344	10	)	)	PUNCT
ejpam-3342	344	11	(	(	PUNCT
ejpam-3342	344	12	2019	2019	NUM
ejpam-3342	344	13	)	)	PUNCT
ejpam-3342	344	14	,	,	PUNCT
ejpam-3342	344	15	58	58	NUM
ejpam-3342	344	16	-	-	SYM
ejpam-3342	344	17	78	78	NUM
ejpam-3342	344	18	71	71	NUM
ejpam-3342	344	19	backwards	backwards	ADV
ejpam-3342	344	20	δ	δ	PROPN
ejpam-3342	344	21	-	-	PUNCT
ejpam-3342	344	22	fine	fine	ADJ
ejpam-3342	344	23	partial	partial	ADJ
ejpam-3342	344	24	division	division	NOUN
ejpam-3342	344	25	d	d	NOUN
ejpam-3342	344	26	=	=	PRON
ejpam-3342	344	27	{	{	PUNCT
ejpam-3342	344	28	(	(	PUNCT
ejpam-3342	344	29	(	(	PUNCT
ejpam-3342	344	30	v	v	NOUN
ejpam-3342	344	31	,	,	PUNCT
ejpam-3342	344	32	ξ	ξ	PROPN
ejpam-3342	344	33	]	]	X
ejpam-3342	344	34	,	,	PUNCT
ejpam-3342	344	35	ξ	ξ	NOUN
ejpam-3342	344	36	)	)	PUNCT
ejpam-3342	344	37	}	}	PUNCT
ejpam-3342	344	38	of	of	ADP
ejpam-3342	344	39	[	[	X
ejpam-3342	344	40	0	0	NUM
ejpam-3342	344	41	,	,	PUNCT
ejpam-3342	344	42	t	t	X
ejpam-3342	344	43	]	]	PUNCT
ejpam-3342	344	44	with	with	ADP
ejpam-3342	344	45	(	(	PUNCT
ejpam-3342	344	46	d	d	NOUN
ejpam-3342	344	47	)	)	PUNCT
ejpam-3342	344	48	∑	∑	PROPN
ejpam-3342	344	49	(	(	PUNCT
ejpam-3342	344	50	ξ−v	ξ−v	PROPN
ejpam-3342	344	51	)	)	PUNCT
ejpam-3342	344	52	>	>	PUNCT
ejpam-3342	345	1	t	t	PROPN
ejpam-3342	346	1	−η	−η	NOUN
ejpam-3342	346	2	such	such	ADJ
ejpam-3342	346	3	that	that	SCONJ
ejpam-3342	346	4	∣∣∣(d	∣∣∣(d	AUX
ejpam-3342	346	5	)	)	PUNCT
ejpam-3342	346	6	∑	∑	DET
ejpam-3342	346	7	f(ξ)(ξ	f(ξ)(ξ	NOUN
ejpam-3342	346	8	−	−	X
ejpam-3342	346	9	v)−a	v)−a	ADV
ejpam-3342	346	10	∣∣∣	∣∣∣	ADJ
ejpam-3342	346	11	≥	≥	NUM
ejpam-3342	346	12	ε	ε	PROPN
ejpam-3342	346	13	.	.	PUNCT
ejpam-3342	346	14	hence	hence	ADV
ejpam-3342	346	15	,	,	PUNCT
ejpam-3342	346	16	for	for	ADP
ejpam-3342	346	17	each	each	DET
ejpam-3342	346	18	δn	δn	NOUN
ejpam-3342	346	19	and	and	CCONJ
ejpam-3342	346	20	ηn	ηn	ADJ
ejpam-3342	346	21	,	,	PUNCT
ejpam-3342	346	22	there	there	PRON
ejpam-3342	346	23	exists	exist	VERB
ejpam-3342	346	24	a	a	DET
ejpam-3342	346	25	δn	δn	ADJ
ejpam-3342	346	26	-	-	PUNCT
ejpam-3342	346	27	fine	fine	ADJ
ejpam-3342	346	28	partial	partial	ADJ
ejpam-3342	346	29	division	division	NOUN
ejpam-3342	346	30	dn	dn	NOUN
ejpam-3342	346	31	of	of	ADP
ejpam-3342	346	32	[	[	X
ejpam-3342	346	33	0	0	NUM
ejpam-3342	346	34	,	,	PUNCT
ejpam-3342	346	35	t	t	X
ejpam-3342	346	36	]	]	PUNCT
ejpam-3342	346	37	with	with	ADP
ejpam-3342	346	38	(	(	PUNCT
ejpam-3342	346	39	dn	dn	NOUN
ejpam-3342	346	40	)	)	PUNCT
ejpam-3342	346	41	∑	∑	PUNCT
ejpam-3342	346	42	(	(	PUNCT
ejpam-3342	346	43	ξ	ξ	X
ejpam-3342	346	44	−	−	PROPN
ejpam-3342	346	45	v	v	NOUN
ejpam-3342	346	46	)	)	PUNCT
ejpam-3342	346	47	>	>	X
ejpam-3342	347	1	t	t	PROPN
ejpam-3342	348	1	−	−	PROPN
ejpam-3342	348	2	ηn	ηn	INTJ
ejpam-3342	348	3	such	such	ADJ
ejpam-3342	348	4	that	that	DET
ejpam-3342	348	5	∣∣∣(dn	∣∣∣(dn	PROPN
ejpam-3342	348	6	)	)	PUNCT
ejpam-3342	348	7	∑	∑	DET
ejpam-3342	348	8	f(ξ)(ξ	f(ξ)(ξ	NOUN
ejpam-3342	349	1	−	−	X
ejpam-3342	349	2	v)−a	v)−a	ADV
ejpam-3342	349	3	∣∣∣	∣∣∣	ADJ
ejpam-3342	349	4	≥	≥	X
ejpam-3342	349	5	ε	ε	PROPN
ejpam-3342	349	6	,	,	PUNCT
ejpam-3342	349	7	leading	lead	VERB
ejpam-3342	349	8	to	to	ADP
ejpam-3342	349	9	a	a	DET
ejpam-3342	349	10	contradiction	contradiction	NOUN
ejpam-3342	349	11	.	.	PUNCT
ejpam-3342	350	1	�	�	PROPN
ejpam-3342	350	2	we	we	PRON
ejpam-3342	350	3	now	now	ADV
ejpam-3342	350	4	state	state	VERB
ejpam-3342	350	5	and	and	CCONJ
ejpam-3342	350	6	prove	prove	VERB
ejpam-3342	350	7	the	the	DET
ejpam-3342	350	8	itô	itô	PROPN
ejpam-3342	350	9	isometry	isometry	NOUN
ejpam-3342	350	10	.	.	PUNCT
ejpam-3342	351	1	theorem	theorem	NOUN
ejpam-3342	351	2	3	3	NUM
ejpam-3342	351	3	(	(	PUNCT
ejpam-3342	351	4	itô	itô	PROPN
ejpam-3342	351	5	isometry	isometry	PROPN
ejpam-3342	351	6	)	)	PUNCT
ejpam-3342	351	7	.	.	PUNCT
ejpam-3342	352	1	let	let	VERB
ejpam-3342	352	2	f	f	PRON
ejpam-3342	352	3	be	be	AUX
ejpam-3342	352	4	ihb	ihb	NOUN
ejpam-3342	352	5	-	-	ADJ
ejpam-3342	352	6	integrable	integrable	ADJ
ejpam-3342	352	7	on	on	ADP
ejpam-3342	352	8	[	[	X
ejpam-3342	352	9	0	0	NUM
ejpam-3342	352	10	,	,	PUNCT
ejpam-3342	352	11	t	t	X
ejpam-3342	352	12	]	]	PUNCT
ejpam-3342	352	13	.	.	PUNCT
ejpam-3342	353	1	then	then	ADV
ejpam-3342	353	2	e	e	X
ejpam-3342	353	3	[	[	PUNCT
ejpam-3342	353	4	‖ft‖2l2(uq	‖ft‖2l2(uq	NUM
ejpam-3342	353	5	,	,	PUNCT
ejpam-3342	353	6	v	v	NOUN
ejpam-3342	353	7	)	)	PUNCT
ejpam-3342	353	8	]	]	PUNCT
ejpam-3342	353	9	is	be	AUX
ejpam-3342	353	10	lebesgue	lebesgue	NOUN
ejpam-3342	353	11	integrable	integrable	ADJ
ejpam-3342	353	12	on	on	ADP
ejpam-3342	353	13	[	[	X
ejpam-3342	353	14	0	0	NUM
ejpam-3342	353	15	,	,	PUNCT
ejpam-3342	353	16	t	t	NOUN
ejpam-3342	353	17	]	]	PUNCT
ejpam-3342	353	18	and	and	CCONJ
ejpam-3342	353	19	e	e	X
ejpam-3342	353	20	[	[	SYM
ejpam-3342	353	21	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	353	22	)	)	PUNCT
ejpam-3342	353	23	∫	∫	PROPN
ejpam-3342	353	24	t	t	PROPN
ejpam-3342	353	25	0	0	NUM
ejpam-3342	353	26	ft	ft	NOUN
ejpam-3342	354	1	dwt	dwt	NOUN
ejpam-3342	354	2	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	354	3	v	v	ADP
ejpam-3342	354	4	]	]	X
ejpam-3342	354	5	=	=	SYM
ejpam-3342	354	6	(	(	PUNCT
ejpam-3342	354	7	l	l	NOUN
ejpam-3342	354	8	)	)	PUNCT
ejpam-3342	354	9	∫	∫	PROPN
ejpam-3342	355	1	t	t	NOUN
ejpam-3342	355	2	0	0	NUM
ejpam-3342	355	3	e	e	X
ejpam-3342	355	4	[	[	PUNCT
ejpam-3342	355	5	‖ft‖2l2(uq	‖ft‖2l2(uq	NUM
ejpam-3342	355	6	,	,	PUNCT
ejpam-3342	355	7	v	v	NOUN
ejpam-3342	355	8	)	)	PUNCT
ejpam-3342	355	9	]	]	PUNCT
ejpam-3342	355	10	dt	dt	X
ejpam-3342	356	1	<	<	X
ejpam-3342	356	2	∞.	∞.	PROPN
ejpam-3342	356	3	proof	proof	NOUN
ejpam-3342	356	4	.	.	PUNCT
ejpam-3342	357	1	from	from	ADP
ejpam-3342	357	2	property	property	NOUN
ejpam-3342	357	3	(	(	PUNCT
ejpam-3342	357	4	5	5	NUM
ejpam-3342	357	5	)	)	PUNCT
ejpam-3342	357	6	section	section	NOUN
ejpam-3342	357	7	3	3	NUM
ejpam-3342	357	8	,	,	PUNCT
ejpam-3342	357	9	there	there	PRON
ejpam-3342	357	10	exists	exist	VERB
ejpam-3342	357	11	a	a	DET
ejpam-3342	357	12	decreasing	decrease	VERB
ejpam-3342	357	13	sequence	sequence	NOUN
ejpam-3342	357	14	{	{	PUNCT
ejpam-3342	357	15	δn(ξ	δn(ξ	NOUN
ejpam-3342	357	16	)	)	PUNCT
ejpam-3342	357	17	}	}	PUNCT
ejpam-3342	357	18	of	of	ADP
ejpam-3342	357	19	positive	positive	ADJ
ejpam-3342	357	20	functions	function	NOUN
ejpam-3342	357	21	defined	define	VERB
ejpam-3342	357	22	on	on	ADP
ejpam-3342	357	23	(	(	PUNCT
ejpam-3342	357	24	0	0	NUM
ejpam-3342	357	25	,	,	PUNCT
ejpam-3342	357	26	t	t	X
ejpam-3342	357	27	]	]	PUNCT
ejpam-3342	357	28	,	,	PUNCT
ejpam-3342	357	29	and	and	CCONJ
ejpam-3342	357	30	a	a	DET
ejpam-3342	357	31	decreasing	decrease	VERB
ejpam-3342	357	32	sequence	sequence	NOUN
ejpam-3342	357	33	of	of	ADP
ejpam-3342	357	34	positive	positive	ADJ
ejpam-3342	357	35	numbers	number	NOUN
ejpam-3342	357	36	{	{	PUNCT
ejpam-3342	357	37	ηn	ηn	ADJ
ejpam-3342	357	38	}	}	PUNCT
ejpam-3342	357	39	such	such	ADJ
ejpam-3342	357	40	that	that	PRON
ejpam-3342	357	41	for	for	ADP
ejpam-3342	357	42	any	any	DET
ejpam-3342	357	43	backwards	backwards	ADV
ejpam-3342	357	44	(	(	PUNCT
ejpam-3342	357	45	δn	δn	NOUN
ejpam-3342	357	46	,	,	PUNCT
ejpam-3342	357	47	ηn)-fine	ηn)-fine	ADJ
ejpam-3342	357	48	partial	partial	ADJ
ejpam-3342	357	49	division	division	NOUN
ejpam-3342	357	50	dn	dn	NOUN
ejpam-3342	357	51	=	=	PUNCT
ejpam-3342	357	52	{	{	PUNCT
ejpam-3342	357	53	(	(	PUNCT
ejpam-3342	357	54	(	(	PUNCT
ejpam-3342	357	55	v(n	v(n	NOUN
ejpam-3342	357	56	)	)	PUNCT
ejpam-3342	358	1	i	i	PRON
ejpam-3342	358	2	,	,	PUNCT
ejpam-3342	358	3	ξ	ξ	PROPN
ejpam-3342	358	4	(	(	PUNCT
ejpam-3342	358	5	n	n	CCONJ
ejpam-3342	358	6	)	)	PUNCT
ejpam-3342	358	7	i	i	PRON
ejpam-3342	358	8	)	)	PUNCT
ejpam-3342	358	9	]	]	X
ejpam-3342	358	10	,	,	PUNCT
ejpam-3342	358	11	ξ	ξ	PROPN
ejpam-3342	358	12	(	(	PUNCT
ejpam-3342	358	13	n	n	CCONJ
ejpam-3342	358	14	)	)	PUNCT
ejpam-3342	358	15	i	i	PRON
ejpam-3342	358	16	)	)	PUNCT
ejpam-3342	358	17	}	}	PUNCT
ejpam-3342	358	18	p(n	p(n	PROPN
ejpam-3342	358	19	)	)	PUNCT
ejpam-3342	358	20	i=1	i=1	PRON
ejpam-3342	358	21	of	of	ADP
ejpam-3342	358	22	[	[	X
ejpam-3342	358	23	0	0	NUM
ejpam-3342	358	24	,	,	PUNCT
ejpam-3342	358	25	t	t	X
ejpam-3342	358	26	]	]	PUNCT
ejpam-3342	358	27	,	,	PUNCT
ejpam-3342	358	28	we	we	PRON
ejpam-3342	358	29	have	have	VERB
ejpam-3342	358	30	lim	lim	PROPN
ejpam-3342	358	31	n→∞	n→∞	NUM
ejpam-3342	358	32	e	e	PROPN
ejpam-3342	359	1	[	[	X
ejpam-3342	359	2	∥∥∥∥s(f	∥∥∥∥s(f	PROPN
ejpam-3342	359	3	,	,	PUNCT
ejpam-3342	359	4	dn	dn	NOUN
ejpam-3342	359	5	,	,	PUNCT
ejpam-3342	359	6	δn	δn	NOUN
ejpam-3342	359	7	,	,	PUNCT
ejpam-3342	359	8	ηn)−	ηn)−	NOUN
ejpam-3342	359	9	(	(	PUNCT
ejpam-3342	359	10	ihb	ihb	NOUN
ejpam-3342	359	11	)	)	PUNCT
ejpam-3342	359	12	∫	∫	PROPN
ejpam-3342	359	13	t	t	PROPN
ejpam-3342	359	14	0	0	NUM
ejpam-3342	359	15	ft	ft	NOUN
ejpam-3342	359	16	dwt	dwt	NOUN
ejpam-3342	359	17	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	359	18	v	v	ADP
ejpam-3342	359	19	]	]	PUNCT
ejpam-3342	359	20	=	=	PUNCT
ejpam-3342	359	21	0	0	X
ejpam-3342	359	22	.	.	PUNCT
ejpam-3342	360	1	this	this	PRON
ejpam-3342	360	2	means	mean	VERB
ejpam-3342	360	3	that	that	SCONJ
ejpam-3342	360	4	lim	lim	PROPN
ejpam-3342	360	5	n→∞	n→∞	PRON
ejpam-3342	360	6	s(f	s(f	PROPN
ejpam-3342	360	7	,	,	PUNCT
ejpam-3342	360	8	dn	dn	NOUN
ejpam-3342	360	9	,	,	PUNCT
ejpam-3342	360	10	δn	δn	NOUN
ejpam-3342	360	11	,	,	PUNCT
ejpam-3342	360	12	ηn	ηn	ADJ
ejpam-3342	360	13	)	)	PUNCT
ejpam-3342	360	14	=	=	SYM
ejpam-3342	360	15	(	(	PUNCT
ejpam-3342	360	16	ihb	ihb	NOUN
ejpam-3342	360	17	)	)	PUNCT
ejpam-3342	360	18	∫	∫	PROPN
ejpam-3342	361	1	t	t	PROPN
ejpam-3342	361	2	0	0	NUM
ejpam-3342	362	1	ft	ft	NOUN
ejpam-3342	362	2	dwt	dwt	NOUN
ejpam-3342	362	3	in	in	ADP
ejpam-3342	362	4	l2(ω	l2(ω	PROPN
ejpam-3342	362	5	,	,	PUNCT
ejpam-3342	362	6	v	v	NOUN
ejpam-3342	362	7	)	)	PUNCT
ejpam-3342	362	8	.	.	PUNCT
ejpam-3342	363	1	let	let	VERB
ejpam-3342	363	2	ε	ε	PROPN
ejpam-3342	363	3	>	>	X
ejpam-3342	363	4	0	0	PUNCT
ejpam-3342	363	5	be	be	AUX
ejpam-3342	363	6	given	give	VERB
ejpam-3342	363	7	.	.	PUNCT
ejpam-3342	364	1	then	then	ADV
ejpam-3342	364	2	there	there	PRON
ejpam-3342	364	3	exists	exist	VERB
ejpam-3342	364	4	n	n	PRON
ejpam-3342	364	5	∈	∈	PROPN
ejpam-3342	364	6	n	n	PRON
ejpam-3342	364	7	such	such	ADJ
ejpam-3342	364	8	that	that	PRON
ejpam-3342	364	9	for	for	ADP
ejpam-3342	364	10	all	all	DET
ejpam-3342	364	11	n	n	PRON
ejpam-3342	364	12	≥	≥	NUM
ejpam-3342	364	13	n	n	PROPN
ejpam-3342	364	14	,	,	PUNCT
ejpam-3342	364	15	∥∥∥∥s(f	∥∥∥∥s(f	PROPN
ejpam-3342	364	16	,	,	PUNCT
ejpam-3342	364	17	dn	dn	NOUN
ejpam-3342	364	18	,	,	PUNCT
ejpam-3342	364	19	δn	δn	NOUN
ejpam-3342	364	20	,	,	PUNCT
ejpam-3342	364	21	ηn)−	ηn)−	NOUN
ejpam-3342	364	22	(	(	PUNCT
ejpam-3342	364	23	ihb	ihb	NOUN
ejpam-3342	364	24	)	)	PUNCT
ejpam-3342	364	25	∫	∫	PROPN
ejpam-3342	365	1	t	t	PROPN
ejpam-3342	365	2	0	0	NUM
ejpam-3342	366	1	ft	ft	ADP
ejpam-3342	366	2	dwt	dwt	PROPN
ejpam-3342	366	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3342	367	1	l2(ω	l2(ω	PROPN
ejpam-3342	367	2	,	,	PUNCT
ejpam-3342	367	3	v	v	NOUN
ejpam-3342	367	4	)	)	PUNCT
ejpam-3342	367	5	<	<	X
ejpam-3342	367	6	ε	ε	PROPN
ejpam-3342	367	7	.	.	PUNCT
ejpam-3342	367	8	note	note	VERB
ejpam-3342	367	9	that	that	SCONJ
ejpam-3342	368	1	∣∣∣∣∣‖s(f	∣∣∣∣∣‖s(f	PROPN
ejpam-3342	368	2	,	,	PUNCT
ejpam-3342	368	3	dn	dn	NOUN
ejpam-3342	368	4	,	,	PUNCT
ejpam-3342	368	5	δn	δn	NOUN
ejpam-3342	368	6	,	,	PUNCT
ejpam-3342	368	7	ηn)‖l2(ω	ηn)‖l2(ω	NOUN
ejpam-3342	368	8	,	,	PUNCT
ejpam-3342	368	9	v	v	NOUN
ejpam-3342	368	10	)	)	PUNCT
ejpam-3342	368	11	−	−	PROPN
ejpam-3342	368	12	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	368	13	)	)	PUNCT
ejpam-3342	368	14	∫	∫	PROPN
ejpam-3342	369	1	t	t	PROPN
ejpam-3342	369	2	0	0	NUM
ejpam-3342	370	1	ft	ft	ADP
ejpam-3342	370	2	dwt	dwt	PROPN
ejpam-3342	370	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3342	371	1	l2(ω	l2(ω	PROPN
ejpam-3342	371	2	,	,	PUNCT
ejpam-3342	371	3	v	v	NOUN
ejpam-3342	371	4	)	)	PUNCT
ejpam-3342	372	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3342	372	2	≤	≤	PROPN
ejpam-3342	372	3	∥∥∥∥s(f	∥∥∥∥s(f	PROPN
ejpam-3342	372	4	,	,	PUNCT
ejpam-3342	372	5	dn	dn	NOUN
ejpam-3342	372	6	,	,	PUNCT
ejpam-3342	372	7	δn	δn	NOUN
ejpam-3342	372	8	,	,	PUNCT
ejpam-3342	372	9	ηn)−	ηn)−	NOUN
ejpam-3342	372	10	(	(	PUNCT
ejpam-3342	372	11	ihb	ihb	NOUN
ejpam-3342	372	12	)	)	PUNCT
ejpam-3342	372	13	∫	∫	PROPN
ejpam-3342	373	1	t	t	PROPN
ejpam-3342	373	2	0	0	NUM
ejpam-3342	374	1	ft	ft	ADP
ejpam-3342	374	2	dwt	dwt	PROPN
ejpam-3342	374	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3342	375	1	l2(ω	l2(ω	PROPN
ejpam-3342	375	2	,	,	PUNCT
ejpam-3342	375	3	v	v	NOUN
ejpam-3342	375	4	)	)	PUNCT
ejpam-3342	375	5	.	.	PUNCT
ejpam-3342	376	1	this	this	PRON
ejpam-3342	376	2	implies	imply	VERB
ejpam-3342	376	3	that	that	SCONJ
ejpam-3342	376	4	lim	lim	PROPN
ejpam-3342	376	5	n→∞	n→∞	NUM
ejpam-3342	376	6	‖s(f	‖s(f	PROPN
ejpam-3342	376	7	,	,	PUNCT
ejpam-3342	376	8	dn	dn	NOUN
ejpam-3342	376	9	,	,	PUNCT
ejpam-3342	376	10	δn	δn	NOUN
ejpam-3342	376	11	,	,	PUNCT
ejpam-3342	376	12	ηn)‖l2(ω	ηn)‖l2(ω	NOUN
ejpam-3342	376	13	,	,	PUNCT
ejpam-3342	376	14	v	v	NOUN
ejpam-3342	376	15	)	)	PUNCT
ejpam-3342	376	16	=	=	SYM
ejpam-3342	376	17	∥∥∥∥(ihb	∥∥∥∥(ihb	PROPN
ejpam-3342	376	18	)	)	PUNCT
ejpam-3342	376	19	∫	∫	PROPN
ejpam-3342	376	20	t	t	PROPN
ejpam-3342	376	21	0	0	NUM
ejpam-3342	376	22	ft	ft	ADP
ejpam-3342	376	23	dwt	dwt	PROPN
ejpam-3342	376	24	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3342	377	1	l2(ω	l2(ω	PROPN
ejpam-3342	377	2	,	,	PUNCT
ejpam-3342	377	3	v	v	NOUN
ejpam-3342	377	4	)	)	PUNCT
ejpam-3342	377	5	r.	r.	PROPN
ejpam-3342	377	6	rulete	rulete	PROPN
ejpam-3342	377	7	,	,	PUNCT
ejpam-3342	377	8	m.	m.	NOUN
ejpam-3342	377	9	labendia	labendia	PROPN
ejpam-3342	377	10	/	/	SYM
ejpam-3342	377	11	eur	eur	PROPN
ejpam-3342	377	12	.	.	PUNCT
ejpam-3342	378	1	j.	j.	PROPN
ejpam-3342	378	2	pure	pure	PROPN
ejpam-3342	378	3	appl	appl	PROPN
ejpam-3342	378	4	.	.	PROPN
ejpam-3342	378	5	math	math	PROPN
ejpam-3342	378	6	,	,	PUNCT
ejpam-3342	378	7	12	12	NUM
ejpam-3342	378	8	(	(	PUNCT
ejpam-3342	378	9	1	1	NUM
ejpam-3342	378	10	)	)	PUNCT
ejpam-3342	378	11	(	(	PUNCT
ejpam-3342	378	12	2019	2019	NUM
ejpam-3342	378	13	)	)	PUNCT
ejpam-3342	378	14	,	,	PUNCT
ejpam-3342	378	15	58	58	NUM
ejpam-3342	378	16	-	-	SYM
ejpam-3342	378	17	78	78	NUM
ejpam-3342	378	18	72	72	NUM
ejpam-3342	378	19	lim	lim	NOUN
ejpam-3342	378	20	n→∞	n→∞	NOUN
ejpam-3342	379	1	√	√	PROPN
ejpam-3342	379	2	e	e	X
ejpam-3342	379	3	[	[	PUNCT
ejpam-3342	379	4	‖s(f	‖s(f	ADJ
ejpam-3342	379	5	,	,	PUNCT
ejpam-3342	379	6	dn	dn	NOUN
ejpam-3342	379	7	,	,	PUNCT
ejpam-3342	379	8	δn	δn	NOUN
ejpam-3342	379	9	,	,	PUNCT
ejpam-3342	379	10	ηn)‖2v	ηn)‖2v	PROPN
ejpam-3342	379	11	]	]	PUNCT
ejpam-3342	379	12	=	=	PUNCT
ejpam-3342	379	13	√√√√e	√√√√e	PROPN
ejpam-3342	379	14	[	[	X
ejpam-3342	379	15	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	379	16	)	)	PUNCT
ejpam-3342	379	17	∫	∫	PROPN
ejpam-3342	379	18	t	t	PROPN
ejpam-3342	379	19	0	0	NUM
ejpam-3342	379	20	ft	ft	NOUN
ejpam-3342	379	21	dwt	dwt	NOUN
ejpam-3342	379	22	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	379	23	v	v	ADP
ejpam-3342	379	24	]	]	PUNCT
ejpam-3342	379	25	.	.	PUNCT
ejpam-3342	380	1	using	use	VERB
ejpam-3342	380	2	lemma	lemma	PROPN
ejpam-3342	380	3	2	2	NUM
ejpam-3342	380	4	,	,	PUNCT
ejpam-3342	380	5	we	we	PRON
ejpam-3342	380	6	have√√√√e	have√√√√e	VERB
ejpam-3342	380	7	[	[	X
ejpam-3342	380	8	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	380	9	)	)	PUNCT
ejpam-3342	380	10	∫	∫	PROPN
ejpam-3342	380	11	t	t	PROPN
ejpam-3342	380	12	0	0	NUM
ejpam-3342	381	1	ft	ft	NOUN
ejpam-3342	381	2	dwt	dwt	NOUN
ejpam-3342	381	3	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	381	4	v	v	ADP
ejpam-3342	381	5	]	]	PUNCT
ejpam-3342	381	6	=	=	SYM
ejpam-3342	381	7	lim	lim	PROPN
ejpam-3342	381	8	n→∞	n→∞	X
ejpam-3342	382	1	√	√	PROPN
ejpam-3342	382	2	e	e	X
ejpam-3342	382	3	[	[	PUNCT
ejpam-3342	382	4	‖s(f	‖s(f	ADJ
ejpam-3342	382	5	,	,	PUNCT
ejpam-3342	382	6	dn	dn	NOUN
ejpam-3342	382	7	,	,	PUNCT
ejpam-3342	382	8	δn	δn	NOUN
ejpam-3342	382	9	,	,	PUNCT
ejpam-3342	382	10	ηn)‖2v	ηn)‖2v	PROPN
ejpam-3342	382	11	]	]	PUNCT
ejpam-3342	383	1	=	=	PUNCT
ejpam-3342	383	2	lim	lim	PROPN
ejpam-3342	383	3	n→∞	n→∞	NUM
ejpam-3342	383	4	√√√√√e	√√√√√e	PROPN
ejpam-3342	383	5	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3342	383	6	p(n)∑	p(n)∑	NOUN
ejpam-3342	383	7	i=1	i=1	X
ejpam-3342	383	8	f	f	X
ejpam-3342	383	9	ξ	ξ	PROPN
ejpam-3342	383	10	(	(	PUNCT
ejpam-3342	383	11	n	n	CCONJ
ejpam-3342	383	12	)	)	PUNCT
ejpam-3342	383	13	i	i	PRON
ejpam-3342	383	14	(	(	PUNCT
ejpam-3342	383	15	w	w	PROPN
ejpam-3342	383	16	ξ	ξ	PROPN
ejpam-3342	383	17	(	(	PUNCT
ejpam-3342	383	18	n	n	CCONJ
ejpam-3342	383	19	)	)	PUNCT
ejpam-3342	383	20	i	i	PRON
ejpam-3342	383	21	−w	−w	ADV
ejpam-3342	383	22	v	v	X
ejpam-3342	383	23	(	(	PUNCT
ejpam-3342	383	24	n	n	CCONJ
ejpam-3342	383	25	)	)	PUNCT
ejpam-3342	383	26	i	i	PRON
ejpam-3342	383	27	)	)	PUNCT
ejpam-3342	383	28	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3342	383	29	2	2	NUM
ejpam-3342	383	30	v	v	NOUN
ejpam-3342	383	31			NOUN
ejpam-3342	383	32	=	=	SYM
ejpam-3342	383	33	lim	lim	PROPN
ejpam-3342	383	34	n→∞	n→∞	X
ejpam-3342	383	35	√√√√p(n)∑	√√√√p(n)∑	PROPN
ejpam-3342	383	36	i=1	i=1	PROPN
ejpam-3342	383	37	(	(	PUNCT
ejpam-3342	383	38	ξ	ξ	X
ejpam-3342	383	39	(	(	PUNCT
ejpam-3342	383	40	n	n	CCONJ
ejpam-3342	383	41	)	)	PUNCT
ejpam-3342	383	42	i	i	PRON
ejpam-3342	383	43	−	−	PROPN
ejpam-3342	383	44	v(n	v(n	NOUN
ejpam-3342	383	45	)	)	PUNCT
ejpam-3342	383	46	i	i	NOUN
ejpam-3342	383	47	)	)	PUNCT
ejpam-3342	383	48	e	e	X
ejpam-3342	384	1	[	[	X
ejpam-3342	384	2	∥∥∥f	∥∥∥f	NOUN
ejpam-3342	384	3	ξ	ξ	PROPN
ejpam-3342	384	4	(	(	PUNCT
ejpam-3342	384	5	n	n	CCONJ
ejpam-3342	384	6	)	)	PUNCT
ejpam-3342	384	7	i	i	PRON
ejpam-3342	384	8	∥∥∥2	∥∥∥2	VERB
ejpam-3342	384	9	l2(uq	l2(uq	PROPN
ejpam-3342	384	10	,	,	PUNCT
ejpam-3342	384	11	v	v	NOUN
ejpam-3342	384	12	)	)	PUNCT
ejpam-3342	384	13	]	]	PUNCT
ejpam-3342	384	14	.	.	PUNCT
ejpam-3342	385	1	this	this	PRON
ejpam-3342	385	2	implies	imply	VERB
ejpam-3342	385	3	that	that	SCONJ
ejpam-3342	385	4	lim	lim	PROPN
ejpam-3342	385	5	n→∞	n→∞	PRON
ejpam-3342	385	6	p(n)∑	p(n)∑	NOUN
ejpam-3342	385	7	i=1	i=1	X
ejpam-3342	385	8	(	(	PUNCT
ejpam-3342	385	9	ξ	ξ	X
ejpam-3342	385	10	(	(	PUNCT
ejpam-3342	385	11	n	n	CCONJ
ejpam-3342	385	12	)	)	PUNCT
ejpam-3342	386	1	i	i	PRON
ejpam-3342	386	2	−	−	PROPN
ejpam-3342	386	3	v(n	v(n	NOUN
ejpam-3342	386	4	)	)	PUNCT
ejpam-3342	386	5	i	i	NOUN
ejpam-3342	386	6	)	)	PUNCT
ejpam-3342	387	1	e	e	X
ejpam-3342	388	1	[	[	X
ejpam-3342	388	2	∥∥∥f	∥∥∥f	NOUN
ejpam-3342	388	3	ξ	ξ	PROPN
ejpam-3342	388	4	(	(	PUNCT
ejpam-3342	388	5	n	n	CCONJ
ejpam-3342	388	6	)	)	PUNCT
ejpam-3342	388	7	i	i	PRON
ejpam-3342	388	8	∥∥∥2	∥∥∥2	VERB
ejpam-3342	388	9	l2(uq	l2(uq	PROPN
ejpam-3342	388	10	,	,	PUNCT
ejpam-3342	388	11	v	v	NOUN
ejpam-3342	388	12	)	)	PUNCT
ejpam-3342	388	13	]	]	PUNCT
ejpam-3342	389	1	=	=	PUNCT
ejpam-3342	389	2	e	e	X
ejpam-3342	389	3	[	[	X
ejpam-3342	389	4	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	389	5	)	)	PUNCT
ejpam-3342	389	6	∫	∫	PROPN
ejpam-3342	389	7	t	t	PROPN
ejpam-3342	389	8	0	0	NUM
ejpam-3342	389	9	ft	ft	NOUN
ejpam-3342	389	10	dwt	dwt	NOUN
ejpam-3342	389	11	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	389	12	v	v	ADP
ejpam-3342	389	13	]	]	PUNCT
ejpam-3342	389	14	.	.	PUNCT
ejpam-3342	390	1	since	since	SCONJ
ejpam-3342	390	2	the	the	DET
ejpam-3342	390	3	above	above	ADJ
ejpam-3342	390	4	equality	equality	NOUN
ejpam-3342	390	5	holds	hold	VERB
ejpam-3342	390	6	for	for	ADP
ejpam-3342	390	7	any	any	DET
ejpam-3342	390	8	backwards	backwards	ADV
ejpam-3342	390	9	(	(	PUNCT
ejpam-3342	390	10	δn	δn	NOUN
ejpam-3342	390	11	,	,	PUNCT
ejpam-3342	390	12	ηn)-fine	ηn)-fine	ADJ
ejpam-3342	390	13	partial	partial	ADJ
ejpam-3342	390	14	division	division	NOUN
ejpam-3342	390	15	of	of	ADP
ejpam-3342	390	16	[	[	X
ejpam-3342	390	17	0	0	NUM
ejpam-3342	390	18	,	,	PUNCT
ejpam-3342	390	19	t	t	X
ejpam-3342	390	20	]	]	PUNCT
ejpam-3342	390	21	,	,	PUNCT
ejpam-3342	390	22	by	by	ADP
ejpam-3342	390	23	theorem	theorem	NOUN
ejpam-3342	390	24	2	2	NUM
ejpam-3342	390	25	,	,	PUNCT
ejpam-3342	390	26	e	e	X
ejpam-3342	391	1	[	[	X
ejpam-3342	391	2	∥∥∥f	∥∥∥f	NOUN
ejpam-3342	391	3	ξ	ξ	PROPN
ejpam-3342	391	4	(	(	PUNCT
ejpam-3342	391	5	n	n	CCONJ
ejpam-3342	391	6	)	)	PUNCT
ejpam-3342	391	7	i	i	PRON
ejpam-3342	391	8	∥∥∥2	∥∥∥2	VERB
ejpam-3342	391	9	l2(uq	l2(uq	PROPN
ejpam-3342	391	10	,	,	PUNCT
ejpam-3342	391	11	v	v	NOUN
ejpam-3342	391	12	)	)	PUNCT
ejpam-3342	391	13	]	]	PUNCT
ejpam-3342	391	14	is	be	AUX
ejpam-3342	391	15	lebesgue	lebesgue	NOUN
ejpam-3342	391	16	integrable	integrable	ADJ
ejpam-3342	391	17	on	on	ADP
ejpam-3342	391	18	[	[	X
ejpam-3342	391	19	0	0	NUM
ejpam-3342	391	20	,	,	PUNCT
ejpam-3342	391	21	t	t	NOUN
ejpam-3342	391	22	]	]	PUNCT
ejpam-3342	391	23	and	and	CCONJ
ejpam-3342	391	24	e	e	X
ejpam-3342	391	25	[	[	SYM
ejpam-3342	391	26	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	391	27	)	)	PUNCT
ejpam-3342	391	28	∫	∫	PROPN
ejpam-3342	391	29	t	t	PROPN
ejpam-3342	391	30	0	0	NUM
ejpam-3342	391	31	ft	ft	NOUN
ejpam-3342	392	1	dwt	dwt	NOUN
ejpam-3342	392	2	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	392	3	v	v	ADP
ejpam-3342	392	4	]	]	X
ejpam-3342	392	5	=	=	SYM
ejpam-3342	392	6	(	(	PUNCT
ejpam-3342	392	7	l	l	NOUN
ejpam-3342	392	8	)	)	PUNCT
ejpam-3342	392	9	∫	∫	PROPN
ejpam-3342	393	1	t	t	NOUN
ejpam-3342	393	2	0	0	NUM
ejpam-3342	393	3	e	e	X
ejpam-3342	393	4	[	[	PUNCT
ejpam-3342	393	5	‖ft‖2l2(uq	‖ft‖2l2(uq	NUM
ejpam-3342	393	6	,	,	PUNCT
ejpam-3342	393	7	v	v	NOUN
ejpam-3342	393	8	)	)	PUNCT
ejpam-3342	393	9	]	]	PUNCT
ejpam-3342	393	10	dt	dt	X
ejpam-3342	394	1	<	<	X
ejpam-3342	394	2	∞.	∞.	PROPN
ejpam-3342	394	3	�	�	PROPN
ejpam-3342	394	4	throughout	throughout	ADP
ejpam-3342	394	5	the	the	DET
ejpam-3342	394	6	following	following	NOUN
ejpam-3342	394	7	,	,	PUNCT
ejpam-3342	394	8	denote	denote	VERB
ejpam-3342	394	9	by	by	ADP
ejpam-3342	394	10	j	j	PROPN
ejpam-3342	394	11	the	the	DET
ejpam-3342	394	12	family	family	NOUN
ejpam-3342	394	13	of	of	ADP
ejpam-3342	394	14	all	all	DET
ejpam-3342	394	15	left	left	ADJ
ejpam-3342	394	16	-	-	PUNCT
ejpam-3342	394	17	open	open	ADJ
ejpam-3342	394	18	subintervals	subinterval	NOUN
ejpam-3342	394	19	(	(	PUNCT
ejpam-3342	394	20	v	v	NOUN
ejpam-3342	394	21	,	,	PUNCT
ejpam-3342	394	22	ξ	ξ	NOUN
ejpam-3342	394	23	]	]	PUNCT
ejpam-3342	394	24	of	of	ADP
ejpam-3342	394	25	[	[	X
ejpam-3342	394	26	0	0	NUM
ejpam-3342	394	27	,	,	PUNCT
ejpam-3342	394	28	t	t	X
ejpam-3342	394	29	]	]	PUNCT
ejpam-3342	394	30	.	.	PUNCT
ejpam-3342	395	1	in	in	ADP
ejpam-3342	395	2	the	the	DET
ejpam-3342	395	3	following	following	NOUN
ejpam-3342	395	4	,	,	PUNCT
ejpam-3342	395	5	when	when	SCONJ
ejpam-3342	395	6	no	no	DET
ejpam-3342	395	7	confusion	confusion	NOUN
ejpam-3342	395	8	arises	arise	VERB
ejpam-3342	395	9	,	,	PUNCT
ejpam-3342	395	10	we	we	PRON
ejpam-3342	395	11	may	may	AUX
ejpam-3342	395	12	refer	refer	VERB
ejpam-3342	395	13	to	to	ADP
ejpam-3342	395	14	f	f	PROPN
ejpam-3342	395	15	(	(	PUNCT
ejpam-3342	395	16	(	(	PUNCT
ejpam-3342	395	17	u	u	NOUN
ejpam-3342	395	18	,	,	PUNCT
ejpam-3342	395	19	v	v	ADP
ejpam-3342	395	20	]	]	X
ejpam-3342	395	21	,	,	PUNCT
ejpam-3342	395	22	·	·	PUNCT
ejpam-3342	395	23	)	)	PUNCT
ejpam-3342	395	24	or	or	CCONJ
ejpam-3342	395	25	f	f	X
ejpam-3342	395	26	(	(	PUNCT
ejpam-3342	395	27	(	(	PUNCT
ejpam-3342	395	28	u	u	NOUN
ejpam-3342	395	29	,	,	PUNCT
ejpam-3342	395	30	v	v	ADP
ejpam-3342	395	31	]	]	X
ejpam-3342	395	32	,	,	PUNCT
ejpam-3342	395	33	ω	ω	NOUN
ejpam-3342	395	34	)	)	PUNCT
ejpam-3342	395	35	as	as	ADP
ejpam-3342	395	36	simply	simply	ADV
ejpam-3342	395	37	f	f	PROPN
ejpam-3342	395	38	(	(	PUNCT
ejpam-3342	395	39	u	u	NOUN
ejpam-3342	395	40	,	,	PUNCT
ejpam-3342	395	41	v	v	NOUN
ejpam-3342	395	42	)	)	PUNCT
ejpam-3342	395	43	.	.	PUNCT
ejpam-3342	396	1	definition	definition	NOUN
ejpam-3342	396	2	3	3	NUM
ejpam-3342	396	3	.	.	PUNCT
ejpam-3342	397	1	a	a	DET
ejpam-3342	397	2	function	function	NOUN
ejpam-3342	397	3	f	f	NOUN
ejpam-3342	397	4	:	:	PUNCT
ejpam-3342	397	5	j	j	PROPN
ejpam-3342	397	6	×	×	PROPN
ejpam-3342	397	7	ω	ω	PROPN
ejpam-3342	397	8	→	→	SYM
ejpam-3342	397	9	v	v	PROPN
ejpam-3342	397	10	is	be	AUX
ejpam-3342	397	11	said	say	VERB
ejpam-3342	397	12	to	to	PART
ejpam-3342	397	13	be	be	AUX
ejpam-3342	397	14	ac2[0	ac2[0	ADJ
ejpam-3342	397	15	,	,	PUNCT
ejpam-3342	397	16	t	t	X
ejpam-3342	397	17	]	]	PUNCT
ejpam-3342	397	18	if	if	SCONJ
ejpam-3342	397	19	for	for	ADP
ejpam-3342	397	20	every	every	DET
ejpam-3342	397	21	ε	ε	PROPN
ejpam-3342	397	22	>	>	X
ejpam-3342	397	23	0	0	PROPN
ejpam-3342	397	24	,	,	PUNCT
ejpam-3342	397	25	there	there	PRON
ejpam-3342	397	26	exists	exist	VERB
ejpam-3342	397	27	η	η	PROPN
ejpam-3342	397	28	>	>	X
ejpam-3342	397	29	0	0	NUM
ejpam-3342	397	30	such	such	ADJ
ejpam-3342	397	31	that	that	PRON
ejpam-3342	397	32	for	for	ADP
ejpam-3342	397	33	any	any	DET
ejpam-3342	397	34	finite	finite	ADJ
ejpam-3342	397	35	collection	collection	NOUN
ejpam-3342	397	36	d	d	NOUN
ejpam-3342	397	37	=	=	SYM
ejpam-3342	397	38	{	{	PUNCT
ejpam-3342	397	39	(	(	PUNCT
ejpam-3342	397	40	v	v	NOUN
ejpam-3342	397	41	,	,	PUNCT
ejpam-3342	397	42	ξ	ξ	NOUN
ejpam-3342	397	43	]	]	PUNCT
ejpam-3342	397	44	}	}	PUNCT
ejpam-3342	397	45	of	of	ADP
ejpam-3342	397	46	disjoint	disjoint	NOUN
ejpam-3342	397	47	subintervals	subinterval	NOUN
ejpam-3342	397	48	(	(	PUNCT
ejpam-3342	397	49	v	v	NOUN
ejpam-3342	397	50	,	,	PUNCT
ejpam-3342	397	51	ξ	ξ	X
ejpam-3342	397	52	]	]	X
ejpam-3342	397	53	∈	∈	PROPN
ejpam-3342	397	54	j	j	PROPN
ejpam-3342	397	55	with	with	ADP
ejpam-3342	397	56	(	(	PUNCT
ejpam-3342	397	57	d	d	NOUN
ejpam-3342	397	58	)	)	PUNCT
ejpam-3342	397	59	∑	∑	PUNCT
ejpam-3342	397	60	(	(	PUNCT
ejpam-3342	397	61	ξ	ξ	X
ejpam-3342	397	62	−	−	PROPN
ejpam-3342	397	63	v	v	NOUN
ejpam-3342	397	64	)	)	PUNCT
ejpam-3342	398	1	<	<	X
ejpam-3342	398	2	η	η	PROPN
ejpam-3342	398	3	,	,	PUNCT
ejpam-3342	398	4	we	we	PRON
ejpam-3342	398	5	have	have	VERB
ejpam-3342	398	6	∫	∫	PROPN
ejpam-3342	398	7	ω	ω	PROPN
ejpam-3342	398	8	∥∥∥(d	∥∥∥(d	PROPN
ejpam-3342	398	9	)	)	PUNCT
ejpam-3342	398	10	∑	∑	PROPN
ejpam-3342	398	11	f	f	PROPN
ejpam-3342	398	12	(	(	PUNCT
ejpam-3342	398	13	(	(	PUNCT
ejpam-3342	398	14	v	v	NOUN
ejpam-3342	398	15	,	,	PUNCT
ejpam-3342	398	16	ξ	ξ	NOUN
ejpam-3342	398	17	)	)	PUNCT
ejpam-3342	398	18	,	,	PUNCT
ejpam-3342	398	19	ω	ω	X
ejpam-3342	398	20	)	)	PUNCT
ejpam-3342	398	21	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	398	22	v	v	ADP
ejpam-3342	398	23	dp(ω	dp(ω	PROPN
ejpam-3342	398	24	)	)	PUNCT
ejpam-3342	398	25	:	:	PUNCT
ejpam-3342	399	1	=	=	PUNCT
ejpam-3342	399	2	e	e	X
ejpam-3342	399	3	[	[	X
ejpam-3342	399	4	∥∥∥(d	∥∥∥(d	X
ejpam-3342	399	5	)	)	PUNCT
ejpam-3342	399	6	∑	∑	PROPN
ejpam-3342	399	7	f	f	PROPN
ejpam-3342	399	8	(	(	PUNCT
ejpam-3342	399	9	v	v	NOUN
ejpam-3342	399	10	,	,	PUNCT
ejpam-3342	399	11	ξ	ξ	NOUN
ejpam-3342	399	12	)	)	PUNCT
ejpam-3342	399	13	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	399	14	v	v	ADP
ejpam-3342	399	15	]	]	PUNCT
ejpam-3342	399	16	<	<	X
ejpam-3342	399	17	ε	ε	PROPN
ejpam-3342	399	18	.	.	PUNCT
ejpam-3342	399	19	r.	r.	PROPN
ejpam-3342	399	20	rulete	rulete	PROPN
ejpam-3342	399	21	,	,	PUNCT
ejpam-3342	399	22	m.	m.	NOUN
ejpam-3342	399	23	labendia	labendia	PROPN
ejpam-3342	399	24	/	/	SYM
ejpam-3342	399	25	eur	eur	PROPN
ejpam-3342	399	26	.	.	PUNCT
ejpam-3342	400	1	j.	j.	PROPN
ejpam-3342	400	2	pure	pure	PROPN
ejpam-3342	400	3	appl	appl	PROPN
ejpam-3342	400	4	.	.	PROPN
ejpam-3342	400	5	math	math	PROPN
ejpam-3342	400	6	,	,	PUNCT
ejpam-3342	400	7	12	12	NUM
ejpam-3342	400	8	(	(	PUNCT
ejpam-3342	400	9	1	1	NUM
ejpam-3342	400	10	)	)	PUNCT
ejpam-3342	400	11	(	(	PUNCT
ejpam-3342	400	12	2019	2019	NUM
ejpam-3342	400	13	)	)	PUNCT
ejpam-3342	400	14	,	,	PUNCT
ejpam-3342	400	15	58	58	NUM
ejpam-3342	400	16	-	-	SYM
ejpam-3342	400	17	78	78	NUM
ejpam-3342	400	18	73	73	NUM
ejpam-3342	400	19	lemma	lemma	PROPN
ejpam-3342	400	20	3	3	X
ejpam-3342	400	21	.	.	PUNCT
ejpam-3342	401	1	let	let	VERB
ejpam-3342	401	2	f	f	PRON
ejpam-3342	401	3	be	be	AUX
ejpam-3342	401	4	ihb	ihb	NOUN
ejpam-3342	401	5	-	-	ADJ
ejpam-3342	401	6	integrable	integrable	ADJ
ejpam-3342	401	7	on	on	ADP
ejpam-3342	401	8	[	[	X
ejpam-3342	401	9	0	0	NUM
ejpam-3342	401	10	,	,	PUNCT
ejpam-3342	401	11	t	t	X
ejpam-3342	401	12	]	]	PUNCT
ejpam-3342	401	13	.	.	PUNCT
ejpam-3342	402	1	then	then	ADV
ejpam-3342	402	2	for	for	ADP
ejpam-3342	402	3	every	every	DET
ejpam-3342	402	4	ε	ε	PROPN
ejpam-3342	402	5	>	>	X
ejpam-3342	402	6	0	0	PROPN
ejpam-3342	402	7	,	,	PUNCT
ejpam-3342	402	8	there	there	PRON
ejpam-3342	402	9	exist	exist	VERB
ejpam-3342	402	10	a	a	DET
ejpam-3342	402	11	positive	positive	ADJ
ejpam-3342	402	12	function	function	NOUN
ejpam-3342	402	13	δ	δ	PROPN
ejpam-3342	402	14	on	on	ADP
ejpam-3342	402	15	(	(	PUNCT
ejpam-3342	402	16	0	0	NUM
ejpam-3342	402	17	,	,	PUNCT
ejpam-3342	402	18	t	t	NOUN
ejpam-3342	402	19	]	]	PUNCT
ejpam-3342	402	20	and	and	CCONJ
ejpam-3342	402	21	a	a	DET
ejpam-3342	402	22	positive	positive	ADJ
ejpam-3342	402	23	number	number	NOUN
ejpam-3342	402	24	η	η	NOUN
ejpam-3342	402	25	such	such	ADJ
ejpam-3342	402	26	that	that	SCONJ
ejpam-3342	402	27	e	e	X
ejpam-3342	402	28	[	[	X
ejpam-3342	402	29	∥∥∥(d	∥∥∥(d	X
ejpam-3342	402	30	)	)	PUNCT
ejpam-3342	402	31	∑	∑	PUNCT
ejpam-3342	402	32	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	402	33	−wv	−wv	NOUN
ejpam-3342	402	34	)	)	PUNCT
ejpam-3342	402	35	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	402	36	v	v	ADP
ejpam-3342	402	37	]	]	PUNCT
ejpam-3342	402	38	<	<	X
ejpam-3342	402	39	ε	ε	PROPN
ejpam-3342	402	40	for	for	ADP
ejpam-3342	402	41	any	any	DET
ejpam-3342	402	42	backwards	backwards	ADV
ejpam-3342	402	43	δ	δ	NOUN
ejpam-3342	402	44	-	-	PUNCT
ejpam-3342	402	45	fine	fine	ADJ
ejpam-3342	402	46	partial	partial	ADJ
ejpam-3342	402	47	division	division	NOUN
ejpam-3342	403	1	d	d	NOUN
ejpam-3342	403	2	=	=	PRON
ejpam-3342	403	3	{	{	PUNCT
ejpam-3342	403	4	(	(	PUNCT
ejpam-3342	403	5	(	(	PUNCT
ejpam-3342	403	6	v	v	NOUN
ejpam-3342	403	7	,	,	PUNCT
ejpam-3342	403	8	ξ	ξ	PROPN
ejpam-3342	403	9	]	]	X
ejpam-3342	403	10	,	,	PUNCT
ejpam-3342	403	11	ξ	ξ	NOUN
ejpam-3342	403	12	)	)	PUNCT
ejpam-3342	403	13	}	}	PUNCT
ejpam-3342	403	14	of	of	ADP
ejpam-3342	403	15	[	[	X
ejpam-3342	403	16	0	0	NUM
ejpam-3342	403	17	,	,	PUNCT
ejpam-3342	403	18	t	t	X
ejpam-3342	403	19	]	]	PUNCT
ejpam-3342	403	20	with	with	ADP
ejpam-3342	403	21	(	(	PUNCT
ejpam-3342	403	22	d	d	NOUN
ejpam-3342	403	23	)	)	PUNCT
ejpam-3342	403	24	∑	∑	PUNCT
ejpam-3342	403	25	|ξ	|ξ	VERB
ejpam-3342	403	26	−	−	PROPN
ejpam-3342	403	27	v|	v|	PROPN
ejpam-3342	403	28	≤	≤	NUM
ejpam-3342	403	29	η	η	PROPN
ejpam-3342	403	30	.	.	PROPN
ejpam-3342	403	31	proof	proof	NOUN
ejpam-3342	403	32	.	.	PUNCT
ejpam-3342	404	1	let	let	VERB
ejpam-3342	404	2	ε	ε	PROPN
ejpam-3342	404	3	>	>	X
ejpam-3342	404	4	0	0	PUNCT
ejpam-3342	404	5	be	be	AUX
ejpam-3342	404	6	given	give	VERB
ejpam-3342	404	7	.	.	PUNCT
ejpam-3342	405	1	then	then	ADV
ejpam-3342	405	2	there	there	PRON
ejpam-3342	405	3	exist	exist	VERB
ejpam-3342	405	4	a	a	DET
ejpam-3342	405	5	positive	positive	ADJ
ejpam-3342	405	6	function	function	NOUN
ejpam-3342	405	7	δ	δ	PROPN
ejpam-3342	405	8	on	on	ADP
ejpam-3342	405	9	(	(	PUNCT
ejpam-3342	405	10	0	0	NUM
ejpam-3342	405	11	,	,	PUNCT
ejpam-3342	405	12	t	t	NOUN
ejpam-3342	405	13	]	]	PUNCT
ejpam-3342	405	14	and	and	CCONJ
ejpam-3342	405	15	a	a	DET
ejpam-3342	405	16	positive	positive	ADJ
ejpam-3342	405	17	number	number	NOUN
ejpam-3342	405	18	η	η	NOUN
ejpam-3342	405	19	such	such	ADJ
ejpam-3342	405	20	that	that	PRON
ejpam-3342	405	21	for	for	ADP
ejpam-3342	405	22	any	any	DET
ejpam-3342	405	23	backwards	backwards	ADV
ejpam-3342	405	24	(	(	PUNCT
ejpam-3342	405	25	δ	δ	PROPN
ejpam-3342	405	26	,	,	PUNCT
ejpam-3342	405	27	η)-fine	η)-fine	X
ejpam-3342	405	28	partial	partial	ADJ
ejpam-3342	405	29	division	division	NOUN
ejpam-3342	405	30	p	p	NOUN
ejpam-3342	405	31	of	of	ADP
ejpam-3342	405	32	[	[	X
ejpam-3342	405	33	0	0	NUM
ejpam-3342	405	34	,	,	PUNCT
ejpam-3342	405	35	t	t	X
ejpam-3342	405	36	]	]	PUNCT
ejpam-3342	405	37	,	,	PUNCT
ejpam-3342	405	38	we	we	PRON
ejpam-3342	405	39	have	have	VERB
ejpam-3342	405	40	e	e	NOUN
ejpam-3342	405	41	[	[	X
ejpam-3342	405	42	∥∥∥∥s(f	∥∥∥∥s(f	NOUN
ejpam-3342	405	43	,	,	PUNCT
ejpam-3342	405	44	p	p	X
ejpam-3342	405	45	,	,	PUNCT
ejpam-3342	405	46	δ	δ	PROPN
ejpam-3342	405	47	,	,	PUNCT
ejpam-3342	405	48	η)−	η)−	PROPN
ejpam-3342	405	49	(	(	PUNCT
ejpam-3342	405	50	ihb	ihb	NOUN
ejpam-3342	405	51	)	)	PUNCT
ejpam-3342	405	52	∫	∫	PROPN
ejpam-3342	406	1	t	t	PROPN
ejpam-3342	406	2	0	0	NUM
ejpam-3342	406	3	ft	ft	NOUN
ejpam-3342	406	4	dwt	dwt	NOUN
ejpam-3342	406	5	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	406	6	v	v	ADP
ejpam-3342	406	7	]	]	PUNCT
ejpam-3342	406	8	<	<	X
ejpam-3342	406	9	ε	ε	PROPN
ejpam-3342	406	10	4	4	NUM
ejpam-3342	406	11	.	.	PUNCT
ejpam-3342	407	1	let	let	VERB
ejpam-3342	407	2	d	d	NOUN
ejpam-3342	407	3	=	=	PRON
ejpam-3342	407	4	{	{	PUNCT
ejpam-3342	407	5	(	(	PUNCT
ejpam-3342	407	6	(	(	PUNCT
ejpam-3342	407	7	v	v	NOUN
ejpam-3342	407	8	,	,	PUNCT
ejpam-3342	407	9	ξ	ξ	PROPN
ejpam-3342	407	10	]	]	X
ejpam-3342	407	11	,	,	PUNCT
ejpam-3342	407	12	ξ	ξ	X
ejpam-3342	407	13	)	)	PUNCT
ejpam-3342	407	14	be	be	VERB
ejpam-3342	407	15	a	a	DET
ejpam-3342	407	16	backwards	backwards	ADV
ejpam-3342	407	17	δ	δ	NOUN
ejpam-3342	407	18	-	-	PUNCT
ejpam-3342	407	19	fine	fine	ADJ
ejpam-3342	407	20	partial	partial	ADJ
ejpam-3342	407	21	division	division	NOUN
ejpam-3342	407	22	of	of	ADP
ejpam-3342	407	23	[	[	X
ejpam-3342	407	24	0	0	NUM
ejpam-3342	407	25	,	,	PUNCT
ejpam-3342	407	26	t	t	X
ejpam-3342	407	27	]	]	PUNCT
ejpam-3342	407	28	with	with	ADP
ejpam-3342	407	29	(	(	PUNCT
ejpam-3342	407	30	d	d	NOUN
ejpam-3342	407	31	)	)	PUNCT
ejpam-3342	407	32	∑	∑	PUNCT
ejpam-3342	407	33	|ξ	|ξ	VERB
ejpam-3342	407	34	−	−	PROPN
ejpam-3342	407	35	v|	v|	PROPN
ejpam-3342	407	36	≤	≤	PROPN
ejpam-3342	407	37	η	η	PROPN
ejpam-3342	407	38	.	.	PROPN
ejpam-3342	407	39	construct	construct	VERB
ejpam-3342	407	40	a	a	DET
ejpam-3342	407	41	backwards	backwards	ADV
ejpam-3342	407	42	(	(	PUNCT
ejpam-3342	407	43	δ	δ	PROPN
ejpam-3342	407	44	,	,	PUNCT
ejpam-3342	407	45	η)-fine	η)-fine	X
ejpam-3342	407	46	partial	partial	ADJ
ejpam-3342	407	47	division	division	NOUN
ejpam-3342	407	48	d1	d1	NOUN
ejpam-3342	407	49	of	of	ADP
ejpam-3342	407	50	[	[	X
ejpam-3342	407	51	0	0	NUM
ejpam-3342	407	52	,	,	PUNCT
ejpam-3342	407	53	t	t	X
ejpam-3342	407	54	]	]	PUNCT
ejpam-3342	407	55	such	such	ADJ
ejpam-3342	407	56	that	that	SCONJ
ejpam-3342	407	57	d	d	NOUN
ejpam-3342	407	58	and	and	CCONJ
ejpam-3342	407	59	d1	d1	PROPN
ejpam-3342	407	60	are	be	AUX
ejpam-3342	407	61	disjoint	disjoint	ADJ
ejpam-3342	407	62	and	and	CCONJ
ejpam-3342	407	63	d	d	DET
ejpam-3342	407	64	∪d1	∪d1	PROPN
ejpam-3342	407	65	is	be	AUX
ejpam-3342	407	66	a	a	DET
ejpam-3342	407	67	backwards	backwards	ADV
ejpam-3342	407	68	(	(	PUNCT
ejpam-3342	407	69	δ	δ	PROPN
ejpam-3342	407	70	,	,	PUNCT
ejpam-3342	407	71	η)-fine	η)-fine	X
ejpam-3342	407	72	partial	partial	ADJ
ejpam-3342	407	73	division	division	NOUN
ejpam-3342	407	74	of	of	ADP
ejpam-3342	407	75	[	[	X
ejpam-3342	407	76	0	0	NUM
ejpam-3342	407	77	,	,	PUNCT
ejpam-3342	407	78	t	t	X
ejpam-3342	407	79	]	]	PUNCT
ejpam-3342	407	80	.	.	PUNCT
ejpam-3342	408	1	by	by	ADP
ejpam-3342	408	2	assumption	assumption	NOUN
ejpam-3342	408	3	,	,	PUNCT
ejpam-3342	408	4	e	e	X
ejpam-3342	408	5	[	[	X
ejpam-3342	408	6	∥∥∥∥(d	∥∥∥∥(d	PROPN
ejpam-3342	408	7	∪d1	∪d1	PROPN
ejpam-3342	408	8	)	)	PUNCT
ejpam-3342	408	9	∑	∑	PUNCT
ejpam-3342	408	10	fξ(wξ	fξ(wξ	PROPN
ejpam-3342	408	11	−wv)−	−wv)−	PROPN
ejpam-3342	408	12	(	(	PUNCT
ejpam-3342	408	13	ihb	ihb	NOUN
ejpam-3342	408	14	)	)	PUNCT
ejpam-3342	408	15	∫	∫	PROPN
ejpam-3342	409	1	t	t	PROPN
ejpam-3342	409	2	0	0	NUM
ejpam-3342	409	3	ft	ft	NOUN
ejpam-3342	409	4	dwt	dwt	NOUN
ejpam-3342	409	5	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	409	6	v	v	ADP
ejpam-3342	409	7	]	]	PUNCT
ejpam-3342	409	8	<	<	X
ejpam-3342	409	9	ε	ε	PROPN
ejpam-3342	409	10	4	4	NUM
ejpam-3342	409	11	.	.	PUNCT
ejpam-3342	410	1	hence	hence	ADV
ejpam-3342	410	2	,	,	PUNCT
ejpam-3342	410	3	e	e	X
ejpam-3342	410	4	[	[	X
ejpam-3342	410	5	∥∥∥(d	∥∥∥(d	X
ejpam-3342	410	6	)	)	PUNCT
ejpam-3342	410	7	∑	∑	PUNCT
ejpam-3342	410	8	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	410	9	−wv	−wv	NOUN
ejpam-3342	410	10	)	)	PUNCT
ejpam-3342	410	11	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	410	12	v	v	ADP
ejpam-3342	410	13	]	]	PUNCT
ejpam-3342	411	1	=	=	PUNCT
ejpam-3342	411	2	e	e	X
ejpam-3342	411	3	[	[	X
ejpam-3342	411	4	∥∥∥∥(d	∥∥∥∥(d	PROPN
ejpam-3342	411	5	∪d1	∪d1	PROPN
ejpam-3342	411	6	)	)	PUNCT
ejpam-3342	411	7	∑	∑	PUNCT
ejpam-3342	411	8	fξ(wξ	fξ(wξ	PROPN
ejpam-3342	411	9	−wv)−	−wv)−	PROPN
ejpam-3342	411	10	(	(	PUNCT
ejpam-3342	411	11	ihb	ihb	NOUN
ejpam-3342	411	12	)	)	PUNCT
ejpam-3342	411	13	∫	∫	PROPN
ejpam-3342	411	14	t	t	PROPN
ejpam-3342	411	15	0	0	NUM
ejpam-3342	412	1	ft	ft	NOUN
ejpam-3342	412	2	dwt	dwt	NOUN
ejpam-3342	412	3	+	+	PROPN
ejpam-3342	412	4	(	(	PUNCT
ejpam-3342	412	5	ihb	ihb	NOUN
ejpam-3342	412	6	)	)	PUNCT
ejpam-3342	412	7	∫	∫	PROPN
ejpam-3342	412	8	t	t	PROPN
ejpam-3342	412	9	0	0	NUM
ejpam-3342	413	1	ft	ft	NOUN
ejpam-3342	413	2	dwt	dwt	NOUN
ejpam-3342	413	3	−	−	PROPN
ejpam-3342	413	4	(	(	PUNCT
ejpam-3342	413	5	d1	d1	PROPN
ejpam-3342	413	6	)	)	PUNCT
ejpam-3342	413	7	∑	∑	PUNCT
ejpam-3342	413	8	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	413	9	−wv	−wv	NOUN
ejpam-3342	413	10	)	)	PUNCT
ejpam-3342	414	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	414	2	v	v	ADP
ejpam-3342	414	3	]	]	PUNCT
ejpam-3342	414	4	≤	≤	NUM
ejpam-3342	414	5	2e	2e	NOUN
ejpam-3342	415	1	[	[	X
ejpam-3342	415	2	∥∥∥∥(d	∥∥∥∥(d	PROPN
ejpam-3342	415	3	∪d1	∪d1	PROPN
ejpam-3342	415	4	)	)	PUNCT
ejpam-3342	415	5	∑	∑	PUNCT
ejpam-3342	415	6	fξ(wξ	fξ(wξ	PROPN
ejpam-3342	415	7	−wv)−	−wv)−	PROPN
ejpam-3342	415	8	(	(	PUNCT
ejpam-3342	415	9	ihb	ihb	NOUN
ejpam-3342	415	10	)	)	PUNCT
ejpam-3342	415	11	∫	∫	PROPN
ejpam-3342	415	12	t	t	PROPN
ejpam-3342	415	13	0	0	NUM
ejpam-3342	415	14	ft	ft	NOUN
ejpam-3342	415	15	dwt	dwt	NOUN
ejpam-3342	415	16	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	415	17	v	v	ADP
ejpam-3342	415	18	]	]	PUNCT
ejpam-3342	415	19	+	+	CCONJ
ejpam-3342	415	20	2e	2e	PROPN
ejpam-3342	415	21	[	[	X
ejpam-3342	415	22	∥∥∥∥(ihb	∥∥∥∥(ihb	NOUN
ejpam-3342	415	23	)	)	PUNCT
ejpam-3342	415	24	∫	∫	PROPN
ejpam-3342	415	25	t	t	PROPN
ejpam-3342	415	26	0	0	NUM
ejpam-3342	416	1	ft	ft	NOUN
ejpam-3342	416	2	dwt	dwt	NOUN
ejpam-3342	416	3	−	−	PROPN
ejpam-3342	416	4	(	(	PUNCT
ejpam-3342	416	5	d1	d1	PROPN
ejpam-3342	416	6	)	)	PUNCT
ejpam-3342	416	7	∑	∑	PUNCT
ejpam-3342	416	8	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	416	9	−wv	−wv	NOUN
ejpam-3342	416	10	)	)	PUNCT
ejpam-3342	417	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3342	417	2	v	v	ADP
ejpam-3342	417	3	]	]	PUNCT
ejpam-3342	417	4	<	<	X
ejpam-3342	417	5	2	2	NUM
ejpam-3342	417	6	(	(	PUNCT
ejpam-3342	417	7	ε	ε	PROPN
ejpam-3342	417	8	4	4	NUM
ejpam-3342	417	9	)	)	PUNCT
ejpam-3342	418	1	+	+	CCONJ
ejpam-3342	418	2	2	2	NUM
ejpam-3342	418	3	(	(	PUNCT
ejpam-3342	418	4	ε	ε	PROPN
ejpam-3342	418	5	4	4	NUM
ejpam-3342	418	6	)	)	PUNCT
ejpam-3342	419	1	=	=	SYM
ejpam-3342	419	2	ε	ε	PROPN
ejpam-3342	419	3	.	.	PUNCT
ejpam-3342	420	1	this	this	PRON
ejpam-3342	420	2	proves	prove	VERB
ejpam-3342	420	3	the	the	DET
ejpam-3342	420	4	lemma	lemma	PROPN
ejpam-3342	420	5	.	.	PUNCT
ejpam-3342	421	1	�	�	PROPN
ejpam-3342	421	2	r.	r.	PROPN
ejpam-3342	421	3	rulete	rulete	PROPN
ejpam-3342	421	4	,	,	PUNCT
ejpam-3342	421	5	m.	m.	NOUN
ejpam-3342	421	6	labendia	labendia	PROPN
ejpam-3342	421	7	/	/	SYM
ejpam-3342	421	8	eur	eur	PROPN
ejpam-3342	421	9	.	.	PUNCT
ejpam-3342	422	1	j.	j.	PROPN
ejpam-3342	422	2	pure	pure	PROPN
ejpam-3342	422	3	appl	appl	PROPN
ejpam-3342	422	4	.	.	PROPN
ejpam-3342	422	5	math	math	PROPN
ejpam-3342	422	6	,	,	PUNCT
ejpam-3342	422	7	12	12	NUM
ejpam-3342	422	8	(	(	PUNCT
ejpam-3342	422	9	1	1	NUM
ejpam-3342	422	10	)	)	PUNCT
ejpam-3342	422	11	(	(	PUNCT
ejpam-3342	422	12	2019	2019	NUM
ejpam-3342	422	13	)	)	PUNCT
ejpam-3342	422	14	,	,	PUNCT
ejpam-3342	422	15	58	58	NUM
ejpam-3342	422	16	-	-	SYM
ejpam-3342	422	17	78	78	NUM
ejpam-3342	422	18	74	74	NUM
ejpam-3342	422	19	theorem	theorem	NOUN
ejpam-3342	422	20	4	4	NUM
ejpam-3342	422	21	.	.	PUNCT
ejpam-3342	423	1	let	let	VERB
ejpam-3342	423	2	f	f	PRON
ejpam-3342	423	3	be	be	AUX
ejpam-3342	423	4	ihb	ihb	NOUN
ejpam-3342	423	5	-	-	ADJ
ejpam-3342	423	6	integrable	integrable	ADJ
ejpam-3342	423	7	on	on	ADP
ejpam-3342	423	8	[	[	X
ejpam-3342	423	9	0	0	NUM
ejpam-3342	423	10	,	,	PUNCT
ejpam-3342	423	11	t	t	NOUN
ejpam-3342	423	12	]	]	PUNCT
ejpam-3342	423	13	and	and	CCONJ
ejpam-3342	423	14	define	define	VERB
ejpam-3342	423	15	f	f	PROPN
ejpam-3342	423	16	(	(	PUNCT
ejpam-3342	423	17	v	v	NOUN
ejpam-3342	423	18	,	,	PUNCT
ejpam-3342	423	19	ξ	ξ	NOUN
ejpam-3342	423	20	)	)	PUNCT
ejpam-3342	423	21	:	:	PUNCT
ejpam-3342	424	1	=	=	SYM
ejpam-3342	424	2	(	(	PUNCT
ejpam-3342	424	3	ihb	ihb	NOUN
ejpam-3342	424	4	)	)	PUNCT
ejpam-3342	424	5	∫	∫	PROPN
ejpam-3342	425	1	ξ	ξ	PROPN
ejpam-3342	425	2	v	v	NOUN
ejpam-3342	425	3	ft	ft	NOUN
ejpam-3342	425	4	dwt	dwt	NOUN
ejpam-3342	425	5	for	for	ADP
ejpam-3342	425	6	all	all	DET
ejpam-3342	425	7	(	(	PUNCT
ejpam-3342	425	8	v	v	NOUN
ejpam-3342	425	9	,	,	PUNCT
ejpam-3342	425	10	ξ	ξ	X
ejpam-3342	425	11	]	]	X
ejpam-3342	425	12	∈	∈	PROPN
ejpam-3342	425	13	j	j	PROPN
ejpam-3342	425	14	.	.	PUNCT
ejpam-3342	426	1	then	then	ADV
ejpam-3342	426	2	f	f	PROPN
ejpam-3342	426	3	is	be	AUX
ejpam-3342	426	4	ac2[0	ac2[0	ADJ
ejpam-3342	426	5	,	,	PUNCT
ejpam-3342	426	6	t	t	X
ejpam-3342	426	7	]	]	PUNCT
ejpam-3342	426	8	.	.	PUNCT
ejpam-3342	427	1	proof	proof	NOUN
ejpam-3342	427	2	.	.	PUNCT
ejpam-3342	428	1	let	let	VERB
ejpam-3342	428	2	ε	ε	PROPN
ejpam-3342	428	3	>	>	X
ejpam-3342	428	4	0	0	PUNCT
ejpam-3342	428	5	be	be	AUX
ejpam-3342	428	6	given	give	VERB
ejpam-3342	428	7	.	.	PUNCT
ejpam-3342	429	1	by	by	ADP
ejpam-3342	429	2	lemma	lemma	PROPN
ejpam-3342	429	3	3	3	NUM
ejpam-3342	429	4	,	,	PUNCT
ejpam-3342	429	5	there	there	PRON
ejpam-3342	429	6	exist	exist	VERB
ejpam-3342	429	7	a	a	DET
ejpam-3342	429	8	positive	positive	ADJ
ejpam-3342	429	9	function	function	NOUN
ejpam-3342	429	10	δ	δ	PROPN
ejpam-3342	429	11	on	on	ADP
ejpam-3342	429	12	(	(	PUNCT
ejpam-3342	429	13	0	0	NUM
ejpam-3342	429	14	,	,	PUNCT
ejpam-3342	429	15	t	t	NOUN
ejpam-3342	429	16	]	]	PUNCT
ejpam-3342	429	17	and	and	CCONJ
ejpam-3342	429	18	a	a	DET
ejpam-3342	429	19	positive	positive	ADJ
ejpam-3342	429	20	number	number	NOUN
ejpam-3342	429	21	η	η	NOUN
ejpam-3342	429	22	such	such	ADJ
ejpam-3342	429	23	that	that	SCONJ
ejpam-3342	429	24	e	e	X
ejpam-3342	429	25	[	[	X
ejpam-3342	429	26	∥∥∥(d	∥∥∥(d	X
ejpam-3342	429	27	)	)	PUNCT
ejpam-3342	429	28	∑	∑	PUNCT
ejpam-3342	429	29	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	429	30	−wv	−wv	NOUN
ejpam-3342	429	31	)	)	PUNCT
ejpam-3342	429	32	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	429	33	v	v	ADP
ejpam-3342	429	34	]	]	PUNCT
ejpam-3342	429	35	<	<	X
ejpam-3342	429	36	ε	ε	PROPN
ejpam-3342	429	37	4	4	NUM
ejpam-3342	429	38	for	for	ADP
ejpam-3342	429	39	any	any	DET
ejpam-3342	429	40	backwards	backwards	ADV
ejpam-3342	429	41	δ	δ	NOUN
ejpam-3342	429	42	-	-	PUNCT
ejpam-3342	429	43	fine	fine	ADJ
ejpam-3342	429	44	partial	partial	ADJ
ejpam-3342	429	45	division	division	NOUN
ejpam-3342	430	1	d	d	NOUN
ejpam-3342	430	2	=	=	PRON
ejpam-3342	430	3	{	{	PUNCT
ejpam-3342	430	4	(	(	PUNCT
ejpam-3342	430	5	(	(	PUNCT
ejpam-3342	430	6	v	v	NOUN
ejpam-3342	430	7	,	,	PUNCT
ejpam-3342	430	8	ξ	ξ	PROPN
ejpam-3342	430	9	]	]	X
ejpam-3342	430	10	,	,	PUNCT
ejpam-3342	430	11	ξ	ξ	NOUN
ejpam-3342	430	12	)	)	PUNCT
ejpam-3342	430	13	}	}	PUNCT
ejpam-3342	430	14	of	of	ADP
ejpam-3342	430	15	[	[	X
ejpam-3342	430	16	0	0	NUM
ejpam-3342	430	17	,	,	PUNCT
ejpam-3342	430	18	t	t	X
ejpam-3342	430	19	]	]	PUNCT
ejpam-3342	430	20	with	with	ADP
ejpam-3342	430	21	(	(	PUNCT
ejpam-3342	430	22	d	d	NOUN
ejpam-3342	430	23	)	)	PUNCT
ejpam-3342	430	24	∑	∑	PUNCT
ejpam-3342	430	25	|ξ	|ξ	VERB
ejpam-3342	430	26	−	−	PROPN
ejpam-3342	430	27	v|	v|	PROPN
ejpam-3342	430	28	≤	≤	NUM
ejpam-3342	430	29	η	η	PROPN
ejpam-3342	430	30	.	.	PROPN
ejpam-3342	431	1	let	let	AUX
ejpam-3342	431	2	{	{	PUNCT
ejpam-3342	431	3	(	(	PUNCT
ejpam-3342	431	4	aj	aj	PROPN
ejpam-3342	431	5	,	,	PUNCT
ejpam-3342	431	6	bj	bj	ADP
ejpam-3342	431	7	]	]	PUNCT
ejpam-3342	431	8	}	}	PUNCT
ejpam-3342	431	9	mj=1	mj=1	NOUN
ejpam-3342	431	10	be	be	VERB
ejpam-3342	431	11	a	a	DET
ejpam-3342	431	12	finite	finite	ADJ
ejpam-3342	431	13	collection	collection	NOUN
ejpam-3342	431	14	of	of	ADP
ejpam-3342	431	15	disjoint	disjoint	NOUN
ejpam-3342	431	16	subintervals	subinterval	NOUN
ejpam-3342	431	17	(	(	PUNCT
ejpam-3342	431	18	aj	aj	PROPN
ejpam-3342	431	19	,	,	PUNCT
ejpam-3342	431	20	bj	bj	VERB
ejpam-3342	431	21	]	]	PUNCT
ejpam-3342	431	22	∈	∈	PROPN
ejpam-3342	431	23	j	j	PROPN
ejpam-3342	431	24	with	with	ADP
ejpam-3342	431	25	∑m	∑m	PROPN
ejpam-3342	431	26	j=1	j=1	PROPN
ejpam-3342	432	1	|bj	|bj	PROPN
ejpam-3342	432	2	−	−	PROPN
ejpam-3342	432	3	aj	aj	VERB
ejpam-3342	432	4	|	|	ADV
ejpam-3342	432	5	≤	≤	PROPN
ejpam-3342	432	6	η	η	PROPN
ejpam-3342	432	7	.	.	PROPN
ejpam-3342	432	8	by	by	ADP
ejpam-3342	432	9	property	property	NOUN
ejpam-3342	432	10	(	(	PUNCT
ejpam-3342	432	11	4	4	NUM
ejpam-3342	432	12	)	)	PUNCT
ejpam-3342	432	13	section	section	NOUN
ejpam-3342	432	14	3	3	NUM
ejpam-3342	432	15	,	,	PUNCT
ejpam-3342	432	16	f	f	PROPN
ejpam-3342	432	17	is	be	AUX
ejpam-3342	432	18	also	also	ADV
ejpam-3342	432	19	ihb	ihb	NOUN
ejpam-3342	432	20	-	-	ADJ
ejpam-3342	432	21	integrable	integrable	ADJ
ejpam-3342	432	22	on	on	ADP
ejpam-3342	432	23	[	[	X
ejpam-3342	432	24	aj	aj	PROPN
ejpam-3342	432	25	,	,	PUNCT
ejpam-3342	432	26	bj	bj	VERB
ejpam-3342	432	27	]	]	PUNCT
ejpam-3342	432	28	for	for	ADP
ejpam-3342	432	29	all	all	DET
ejpam-3342	432	30	j.	j.	PROPN
ejpam-3342	432	31	this	this	PRON
ejpam-3342	432	32	means	mean	VERB
ejpam-3342	432	33	that	that	SCONJ
ejpam-3342	432	34	for	for	ADP
ejpam-3342	432	35	all	all	DET
ejpam-3342	432	36	j	j	NOUN
ejpam-3342	432	37	,	,	PUNCT
ejpam-3342	432	38	there	there	PRON
ejpam-3342	432	39	exist	exist	VERB
ejpam-3342	432	40	positive	positive	ADJ
ejpam-3342	432	41	function	function	NOUN
ejpam-3342	432	42	δj	δj	ADP
ejpam-3342	432	43	on	on	ADP
ejpam-3342	432	44	(	(	PUNCT
ejpam-3342	432	45	aj	aj	PROPN
ejpam-3342	432	46	,	,	PUNCT
ejpam-3342	432	47	bj	bj	VERB
ejpam-3342	432	48	]	]	PUNCT
ejpam-3342	432	49	and	and	CCONJ
ejpam-3342	432	50	a	a	DET
ejpam-3342	432	51	positive	positive	ADJ
ejpam-3342	432	52	number	number	NOUN
ejpam-3342	432	53	ηj	ηj	ADP
ejpam-3342	432	54	such	such	DET
ejpam-3342	432	55	that	that	PRON
ejpam-3342	432	56	for	for	ADP
ejpam-3342	432	57	any	any	DET
ejpam-3342	432	58	backwards	backwards	ADV
ejpam-3342	432	59	(	(	PUNCT
ejpam-3342	432	60	δj	δj	NOUN
ejpam-3342	432	61	,	,	PUNCT
ejpam-3342	432	62	ηj)-fine	ηj)-fine	ADV
ejpam-3342	432	63	partial	partial	ADJ
ejpam-3342	432	64	division	division	NOUN
ejpam-3342	432	65	dj	dj	NOUN
ejpam-3342	432	66	of	of	ADP
ejpam-3342	432	67	[	[	X
ejpam-3342	432	68	aj	aj	PROPN
ejpam-3342	432	69	,	,	PUNCT
ejpam-3342	432	70	bj	bj	ADP
ejpam-3342	432	71	]	]	PUNCT
ejpam-3342	432	72	,	,	PUNCT
ejpam-3342	432	73	we	we	PRON
ejpam-3342	432	74	have	have	VERB
ejpam-3342	432	75	e	e	X
ejpam-3342	432	76	[	[	PUNCT
ejpam-3342	432	77	||s(f	||s(f	ADJ
ejpam-3342	432	78	,	,	PUNCT
ejpam-3342	432	79	dj	dj	NOUN
ejpam-3342	432	80	,	,	PUNCT
ejpam-3342	432	81	δj	δj	INTJ
ejpam-3342	432	82	,	,	PUNCT
ejpam-3342	432	83	ηj)−	ηj)−	NOUN
ejpam-3342	432	84	f	f	PROPN
ejpam-3342	432	85	(	(	PUNCT
ejpam-3342	432	86	aj	aj	PROPN
ejpam-3342	432	87	,	,	PUNCT
ejpam-3342	432	88	bj)||2v	bj)||2v	PROPN
ejpam-3342	432	89	]	]	PUNCT
ejpam-3342	432	90	<	<	X
ejpam-3342	432	91	ε	ε	PROPN
ejpam-3342	432	92	4	4	NUM
ejpam-3342	432	93	·	·	SYM
ejpam-3342	432	94	22j	22j	NOUN
ejpam-3342	432	95	.	.	PUNCT
ejpam-3342	433	1	we	we	PRON
ejpam-3342	433	2	can	can	AUX
ejpam-3342	433	3	choose	choose	VERB
ejpam-3342	433	4	{	{	PUNCT
ejpam-3342	433	5	δj}mj=1	δj}mj=1	PROPN
ejpam-3342	433	6	and	and	CCONJ
ejpam-3342	433	7	{	{	PUNCT
ejpam-3342	433	8	ηj}mj=1	ηj}mj=1	X
ejpam-3342	433	9	such	such	ADJ
ejpam-3342	433	10	that	that	DET
ejpam-3342	433	11	δj(ξ	δj(ξ	NOUN
ejpam-3342	433	12	)	)	PUNCT
ejpam-3342	433	13	≤	≤	NOUN
ejpam-3342	433	14	δ(ξ	δ(ξ	NOUN
ejpam-3342	433	15	)	)	PUNCT
ejpam-3342	433	16	for	for	ADP
ejpam-3342	433	17	all	all	DET
ejpam-3342	433	18	j	j	PROPN
ejpam-3342	433	19	and	and	CCONJ
ejpam-3342	433	20	m∑	m∑	ADV
ejpam-3342	433	21	j=1	j=1	NOUN
ejpam-3342	433	22	ηj	ηj	ADP
ejpam-3342	433	23	≤	≤	PROPN
ejpam-3342	433	24	η	η	PROPN
ejpam-3342	433	25	.	.	PROPN
ejpam-3342	433	26	let	let	VERB
ejpam-3342	433	27	p	p	NOUN
ejpam-3342	433	28	=	=	PUNCT
ejpam-3342	433	29	d1	d1	PROPN
ejpam-3342	433	30	∪d2	∪d2	ADJ
ejpam-3342	433	31	∪	∪	ADP
ejpam-3342	433	32	·	·	PUNCT
ejpam-3342	433	33	·	·	PUNCT
ejpam-3342	433	34	·	·	PUNCT
ejpam-3342	434	1	∪dm	∪dm	NOUN
ejpam-3342	434	2	,	,	PUNCT
ejpam-3342	434	3	which	which	PRON
ejpam-3342	434	4	is	be	AUX
ejpam-3342	434	5	a	a	DET
ejpam-3342	434	6	backwards	backwards	ADV
ejpam-3342	434	7	δ	δ	NOUN
ejpam-3342	434	8	-	-	PUNCT
ejpam-3342	434	9	fine	fine	ADJ
ejpam-3342	434	10	partial	partial	ADJ
ejpam-3342	434	11	division	division	NOUN
ejpam-3342	434	12	of	of	ADP
ejpam-3342	434	13	[	[	X
ejpam-3342	434	14	0	0	NUM
ejpam-3342	434	15	,	,	PUNCT
ejpam-3342	434	16	t	t	X
ejpam-3342	434	17	]	]	PUNCT
ejpam-3342	434	18	with	with	ADP
ejpam-3342	434	19	(	(	PUNCT
ejpam-3342	434	20	p	p	NOUN
ejpam-3342	434	21	)	)	PUNCT
ejpam-3342	434	22	∑	∑	PUNCT
ejpam-3342	434	23	|ξ	|ξ	VERB
ejpam-3342	434	24	−	−	PROPN
ejpam-3342	434	25	v|	v|	ADV
ejpam-3342	434	26	≤	≤	NUM
ejpam-3342	434	27	m∑	m∑	VERB
ejpam-3342	435	1	j=1	j=1	PROPN
ejpam-3342	435	2	|bj	|bj	PROPN
ejpam-3342	436	1	−	−	PROPN
ejpam-3342	436	2	aj	aj	VERB
ejpam-3342	436	3	|	|	ADV
ejpam-3342	436	4	≤	≤	PROPN
ejpam-3342	436	5	η	η	PROPN
ejpam-3342	436	6	.	.	PROPN
ejpam-3342	437	1	this	this	PRON
ejpam-3342	437	2	implies	imply	VERB
ejpam-3342	437	3	that	that	SCONJ
ejpam-3342	437	4	e	e	PROPN
ejpam-3342	437	5	[	[	X
ejpam-3342	437	6	∥∥∥(p	∥∥∥(p	PUNCT
ejpam-3342	437	7	)	)	PUNCT
ejpam-3342	437	8	∑	∑	PUNCT
ejpam-3342	437	9	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	437	10	−wv	−wv	NOUN
ejpam-3342	437	11	)	)	PUNCT
ejpam-3342	437	12	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	437	13	v	v	ADP
ejpam-3342	437	14	]	]	PUNCT
ejpam-3342	437	15	<	<	X
ejpam-3342	437	16	ε	ε	PROPN
ejpam-3342	437	17	4	4	NUM
ejpam-3342	437	18	.	.	PUNCT
ejpam-3342	438	1	hence	hence	ADV
ejpam-3342	438	2	,	,	PUNCT
ejpam-3342	438	3	e	e	PROPN
ejpam-3342	438	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3342	438	5	m∑	m∑	ADV
ejpam-3342	438	6	j=1	j=1	PROPN
ejpam-3342	438	7	f	f	PROPN
ejpam-3342	438	8	(	(	PUNCT
ejpam-3342	438	9	aj	aj	PROPN
ejpam-3342	438	10	,	,	PUNCT
ejpam-3342	438	11	bj	bj	VERB
ejpam-3342	438	12	)	)	PUNCT
ejpam-3342	438	13	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3342	439	1	2	2	NUM
ejpam-3342	439	2	v	v	NOUN
ejpam-3342	439	3			NOUN
ejpam-3342	439	4	≤	≤	NOUN
ejpam-3342	439	5	2e	2e	NOUN
ejpam-3342	439	6	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3342	440	1	m∑	m∑	ADV
ejpam-3342	440	2	j=1	j=1	PROPN
ejpam-3342	440	3	{	{	PUNCT
ejpam-3342	440	4	f	f	PROPN
ejpam-3342	440	5	(	(	PUNCT
ejpam-3342	440	6	aj	aj	PROPN
ejpam-3342	440	7	,	,	PUNCT
ejpam-3342	440	8	bj)−	bj)−	ADP
ejpam-3342	441	1	s(f	s(f	PROPN
ejpam-3342	441	2	,	,	PUNCT
ejpam-3342	441	3	dj	dj	NOUN
ejpam-3342	441	4	,	,	PUNCT
ejpam-3342	441	5	δj	δj	INTJ
ejpam-3342	441	6	,	,	PUNCT
ejpam-3342	441	7	ηj	ηj	NOUN
ejpam-3342	441	8	)	)	PUNCT
ejpam-3342	441	9	}	}	PUNCT
ejpam-3342	441	10	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3342	441	11	2	2	NUM
ejpam-3342	441	12	v	v	NOUN
ejpam-3342	441	13			NOUN
ejpam-3342	441	14	+	+	CCONJ
ejpam-3342	441	15	2e	2e	NOUN
ejpam-3342	441	16	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3342	441	17	m∑	m∑	ADV
ejpam-3342	441	18	j=1	j=1	PROPN
ejpam-3342	441	19	s(f	s(f	PROPN
ejpam-3342	441	20	,	,	PUNCT
ejpam-3342	441	21	dj	dj	NOUN
ejpam-3342	441	22	,	,	PUNCT
ejpam-3342	441	23	δj	δj	INTJ
ejpam-3342	441	24	,	,	PUNCT
ejpam-3342	441	25	ηj	ηj	NOUN
ejpam-3342	441	26	)	)	PUNCT
ejpam-3342	441	27	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3342	441	28	2	2	NUM
ejpam-3342	441	29	v	v	NOUN
ejpam-3342	441	30			NOUN
ejpam-3342	441	31	r.	r.	PROPN
ejpam-3342	441	32	rulete	rulete	ADJ
ejpam-3342	441	33	,	,	PUNCT
ejpam-3342	441	34	m.	m.	NOUN
ejpam-3342	441	35	labendia	labendia	PROPN
ejpam-3342	441	36	/	/	SYM
ejpam-3342	441	37	eur	eur	PROPN
ejpam-3342	441	38	.	.	PUNCT
ejpam-3342	442	1	j.	j.	PROPN
ejpam-3342	442	2	pure	pure	PROPN
ejpam-3342	442	3	appl	appl	PROPN
ejpam-3342	442	4	.	.	PROPN
ejpam-3342	442	5	math	math	PROPN
ejpam-3342	442	6	,	,	PUNCT
ejpam-3342	442	7	12	12	NUM
ejpam-3342	442	8	(	(	PUNCT
ejpam-3342	442	9	1	1	NUM
ejpam-3342	442	10	)	)	PUNCT
ejpam-3342	442	11	(	(	PUNCT
ejpam-3342	442	12	2019	2019	NUM
ejpam-3342	442	13	)	)	PUNCT
ejpam-3342	442	14	,	,	PUNCT
ejpam-3342	442	15	58	58	NUM
ejpam-3342	442	16	-	-	SYM
ejpam-3342	442	17	78	78	NUM
ejpam-3342	442	18	75	75	NUM
ejpam-3342	442	19	=	=	SYM
ejpam-3342	442	20	2	2	NUM
ejpam-3342	442	21	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-3342	443	1	m∑	m∑	VERB
ejpam-3342	443	2	j=1	j=1	PROPN
ejpam-3342	443	3	{	{	PUNCT
ejpam-3342	443	4	f	f	PROPN
ejpam-3342	443	5	(	(	PUNCT
ejpam-3342	443	6	aj	aj	PROPN
ejpam-3342	443	7	,	,	PUNCT
ejpam-3342	443	8	bj)−	bj)−	ADP
ejpam-3342	443	9	s(f	s(f	PROPN
ejpam-3342	443	10	,	,	PUNCT
ejpam-3342	443	11	dj	dj	NOUN
ejpam-3342	443	12	,	,	PUNCT
ejpam-3342	443	13	δj	δj	INTJ
ejpam-3342	443	14	,	,	PUNCT
ejpam-3342	443	15	ηj	ηj	NOUN
ejpam-3342	443	16	)	)	PUNCT
ejpam-3342	443	17	}	}	PUNCT
ejpam-3342	443	18	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3342	443	19	2	2	NUM
ejpam-3342	443	20	l2(ω	l2(ω	NOUN
ejpam-3342	443	21	,	,	PUNCT
ejpam-3342	443	22	v	v	NOUN
ejpam-3342	443	23	)	)	PUNCT
ejpam-3342	444	1	+	+	NUM
ejpam-3342	444	2	2e	2e	NUM
ejpam-3342	445	1	[	[	X
ejpam-3342	445	2	∥∥∥(p	∥∥∥(p	PUNCT
ejpam-3342	445	3	)	)	PUNCT
ejpam-3342	445	4	∑	∑	PUNCT
ejpam-3342	445	5	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	445	6	−wv	−wv	NOUN
ejpam-3342	445	7	)	)	PUNCT
ejpam-3342	445	8	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	445	9	v	v	ADP
ejpam-3342	445	10	]	]	X
ejpam-3342	446	1	=	=	SYM
ejpam-3342	446	2	2	2	X
ejpam-3342	446	3			PROPN
ejpam-3342	446	4	m∑	m∑	ADV
ejpam-3342	446	5	j=1	j=1	ADJ
ejpam-3342	446	6	√	√	NUM
ejpam-3342	446	7	e	e	X
ejpam-3342	446	8	[	[	PUNCT
ejpam-3342	446	9	‖f	‖f	ADJ
ejpam-3342	446	10	(	(	PUNCT
ejpam-3342	446	11	aj	aj	PROPN
ejpam-3342	446	12	,	,	PUNCT
ejpam-3342	446	13	bj)−	bj)−	ADP
ejpam-3342	446	14	s(f	s(f	PROPN
ejpam-3342	446	15	,	,	PUNCT
ejpam-3342	446	16	dj	dj	NOUN
ejpam-3342	446	17	,	,	PUNCT
ejpam-3342	446	18	δj	δj	INTJ
ejpam-3342	446	19	,	,	PUNCT
ejpam-3342	446	20	ηj)‖2v	ηj)‖2v	PROPN
ejpam-3342	446	21	]	]	PUNCT
ejpam-3342	446	22	2	2	X
ejpam-3342	446	23	+	+	X
ejpam-3342	446	24	2e	2e	NUM
ejpam-3342	446	25	[	[	X
ejpam-3342	446	26	∥∥∥(p	∥∥∥(p	PUNCT
ejpam-3342	446	27	)	)	PUNCT
ejpam-3342	446	28	∑	∑	PUNCT
ejpam-3342	446	29	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	446	30	−wv	−wv	NOUN
ejpam-3342	446	31	)	)	PUNCT
ejpam-3342	446	32	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	446	33	v	v	ADP
ejpam-3342	446	34	]	]	PUNCT
ejpam-3342	446	35	<	<	X
ejpam-3342	446	36	2	2	NUM
ejpam-3342	446	37			PROPN
ejpam-3342	446	38	m∑	m∑	ADV
ejpam-3342	446	39	j=1	j=1	PROPN
ejpam-3342	446	40	√	√	PROPN
ejpam-3342	446	41	ε	ε	PROPN
ejpam-3342	446	42	2	2	NUM
ejpam-3342	446	43	·	·	PUNCT
ejpam-3342	446	44	2j	2j	X
ejpam-3342	446	45	2	2	X
ejpam-3342	447	1	+	+	CCONJ
ejpam-3342	447	2	2	2	NUM
ejpam-3342	447	3	(	(	PUNCT
ejpam-3342	447	4	ε	ε	PROPN
ejpam-3342	447	5	4	4	NUM
ejpam-3342	447	6	)	)	PUNCT
ejpam-3342	447	7	<	<	X
ejpam-3342	447	8	ε	ε	PROPN
ejpam-3342	447	9	.	.	PUNCT
ejpam-3342	448	1	thus	thus	ADV
ejpam-3342	448	2	,	,	PUNCT
ejpam-3342	448	3	f	f	PROPN
ejpam-3342	448	4	is	be	AUX
ejpam-3342	448	5	ac2[0	ac2[0	ADJ
ejpam-3342	448	6	,	,	PUNCT
ejpam-3342	448	7	t	t	X
ejpam-3342	448	8	]	]	PUNCT
ejpam-3342	448	9	.	.	PUNCT
ejpam-3342	449	1	�	�	PROPN
ejpam-3342	449	2	the	the	DET
ejpam-3342	449	3	following	following	ADJ
ejpam-3342	449	4	result	result	NOUN
ejpam-3342	449	5	provides	provide	VERB
ejpam-3342	449	6	an	an	DET
ejpam-3342	449	7	equivalent	equivalent	ADJ
ejpam-3342	449	8	definition	definition	NOUN
ejpam-3342	449	9	of	of	ADP
ejpam-3342	449	10	an	an	DET
ejpam-3342	449	11	ihb	ihb	ADV
ejpam-3342	449	12	-	-	ADJ
ejpam-3342	449	13	integrable	integrable	ADJ
ejpam-3342	449	14	process	process	NOUN
ejpam-3342	449	15	using	use	VERB
ejpam-3342	449	16	ac2	ac2	PROPN
ejpam-3342	449	17	property	property	NOUN
ejpam-3342	449	18	.	.	PUNCT
ejpam-3342	450	1	theorem	theorem	NOUN
ejpam-3342	450	2	5	5	NUM
ejpam-3342	450	3	.	.	PUNCT
ejpam-3342	451	1	let	let	VERB
ejpam-3342	451	2	f	f	NOUN
ejpam-3342	451	3	:	:	PUNCT
ejpam-3342	452	1	[	[	X
ejpam-3342	452	2	0	0	NUM
ejpam-3342	452	3	,	,	PUNCT
ejpam-3342	452	4	t	t	X
ejpam-3342	452	5	]	]	PUNCT
ejpam-3342	452	6	×	×	PROPN
ejpam-3342	452	7	ω	ω	X
ejpam-3342	452	8	→	→	SYM
ejpam-3342	452	9	l2(uq	l2(uq	PROPN
ejpam-3342	452	10	,	,	PUNCT
ejpam-3342	452	11	v	v	NOUN
ejpam-3342	452	12	)	)	PUNCT
ejpam-3342	452	13	be	be	AUX
ejpam-3342	452	14	a	a	DET
ejpam-3342	452	15	backwards	backwards	ADJ
ejpam-3342	452	16	process	process	NOUN
ejpam-3342	452	17	.	.	PUNCT
ejpam-3342	453	1	then	then	ADV
ejpam-3342	453	2	f	f	PROPN
ejpam-3342	453	3	is	be	AUX
ejpam-3342	453	4	ihbintegrable	ihbintegrable	ADJ
ejpam-3342	453	5	on	on	ADP
ejpam-3342	453	6	[	[	X
ejpam-3342	453	7	0	0	NUM
ejpam-3342	453	8	,	,	PUNCT
ejpam-3342	453	9	t	t	X
ejpam-3342	453	10	]	]	PUNCT
ejpam-3342	453	11	if	if	SCONJ
ejpam-3342	453	12	and	and	CCONJ
ejpam-3342	453	13	only	only	ADV
ejpam-3342	453	14	if	if	SCONJ
ejpam-3342	453	15	there	there	PRON
ejpam-3342	453	16	exists	exist	VERB
ejpam-3342	453	17	an	an	DET
ejpam-3342	453	18	ac2[0	ac2[0	NOUN
ejpam-3342	453	19	,	,	PUNCT
ejpam-3342	453	20	t	t	PROPN
ejpam-3342	453	21	]	]	PUNCT
ejpam-3342	453	22	function	function	NOUN
ejpam-3342	453	23	f	f	PROPN
ejpam-3342	453	24	such	such	ADJ
ejpam-3342	453	25	that	that	PRON
ejpam-3342	453	26	for	for	ADP
ejpam-3342	453	27	every	every	DET
ejpam-3342	453	28	ε	ε	PROPN
ejpam-3342	453	29	>	>	X
ejpam-3342	453	30	0	0	PROPN
ejpam-3342	453	31	,	,	PUNCT
ejpam-3342	453	32	there	there	PRON
ejpam-3342	453	33	exist	exist	VERB
ejpam-3342	453	34	a	a	DET
ejpam-3342	453	35	positive	positive	ADJ
ejpam-3342	453	36	function	function	NOUN
ejpam-3342	453	37	δ	δ	PROPN
ejpam-3342	453	38	on	on	ADP
ejpam-3342	453	39	(	(	PUNCT
ejpam-3342	453	40	0	0	NUM
ejpam-3342	453	41	,	,	PUNCT
ejpam-3342	453	42	t	t	X
ejpam-3342	453	43	]	]	PUNCT
ejpam-3342	453	44	such	such	ADJ
ejpam-3342	453	45	that	that	SCONJ
ejpam-3342	453	46	whenever	whenever	SCONJ
ejpam-3342	453	47	d	d	NOUN
ejpam-3342	453	48	=	=	PRON
ejpam-3342	453	49	{	{	PUNCT
ejpam-3342	453	50	(	(	PUNCT
ejpam-3342	453	51	(	(	PUNCT
ejpam-3342	453	52	v	v	NOUN
ejpam-3342	453	53	,	,	PUNCT
ejpam-3342	453	54	ξ	ξ	PROPN
ejpam-3342	453	55	]	]	X
ejpam-3342	453	56	,	,	PUNCT
ejpam-3342	453	57	ξ	ξ	X
ejpam-3342	453	58	)	)	PUNCT
ejpam-3342	453	59	}	}	PUNCT
ejpam-3342	453	60	is	be	AUX
ejpam-3342	453	61	a	a	DET
ejpam-3342	453	62	backwards	backwards	ADV
ejpam-3342	453	63	δ	δ	NOUN
ejpam-3342	453	64	-	-	PUNCT
ejpam-3342	453	65	fine	fine	ADJ
ejpam-3342	453	66	partial	partial	ADJ
ejpam-3342	453	67	division	division	NOUN
ejpam-3342	453	68	of	of	ADP
ejpam-3342	453	69	[	[	X
ejpam-3342	453	70	0	0	NUM
ejpam-3342	453	71	,	,	PUNCT
ejpam-3342	453	72	t	t	X
ejpam-3342	453	73	]	]	PUNCT
ejpam-3342	453	74	,	,	PUNCT
ejpam-3342	453	75	we	we	PRON
ejpam-3342	453	76	have	have	VERB
ejpam-3342	453	77	e	e	NOUN
ejpam-3342	453	78	[	[	X
ejpam-3342	453	79	∥∥∥(d	∥∥∥(d	X
ejpam-3342	453	80	)	)	PUNCT
ejpam-3342	453	81	∑	∑	PRON
ejpam-3342	453	82	{	{	PUNCT
ejpam-3342	453	83	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	453	84	−wv)−	−wv)−	PROPN
ejpam-3342	453	85	f	f	X
ejpam-3342	453	86	(	(	PUNCT
ejpam-3342	453	87	v	v	NOUN
ejpam-3342	453	88	,	,	PUNCT
ejpam-3342	453	89	ξ	ξ	NOUN
ejpam-3342	453	90	)	)	PUNCT
ejpam-3342	453	91	}	}	PUNCT
ejpam-3342	453	92	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	453	93	v	v	ADP
ejpam-3342	453	94	]	]	PUNCT
ejpam-3342	453	95	<	<	X
ejpam-3342	453	96	ε	ε	PROPN
ejpam-3342	453	97	.	.	PUNCT
ejpam-3342	453	98	proof	proof	NOUN
ejpam-3342	453	99	.	.	PUNCT
ejpam-3342	454	1	suppose	suppose	VERB
ejpam-3342	454	2	that	that	SCONJ
ejpam-3342	454	3	f	f	PROPN
ejpam-3342	454	4	is	be	AUX
ejpam-3342	454	5	ihb	ihb	NOUN
ejpam-3342	454	6	-	-	ADJ
ejpam-3342	454	7	integrable	integrable	ADJ
ejpam-3342	454	8	on	on	ADP
ejpam-3342	454	9	[	[	X
ejpam-3342	454	10	0	0	NUM
ejpam-3342	454	11	,	,	PUNCT
ejpam-3342	454	12	t	t	X
ejpam-3342	454	13	]	]	PUNCT
ejpam-3342	454	14	.	.	PUNCT
ejpam-3342	455	1	by	by	ADP
ejpam-3342	455	2	theorem	theorem	NOUN
ejpam-3342	455	3	4	4	NUM
ejpam-3342	455	4	and	and	CCONJ
ejpam-3342	455	5	property	property	NOUN
ejpam-3342	455	6	(	(	PUNCT
ejpam-3342	455	7	7	7	NUM
ejpam-3342	455	8	)	)	PUNCT
ejpam-3342	455	9	section	section	NOUN
ejpam-3342	455	10	3	3	NUM
ejpam-3342	455	11	,	,	PUNCT
ejpam-3342	455	12	the	the	DET
ejpam-3342	455	13	result	result	NOUN
ejpam-3342	455	14	follows	follow	VERB
ejpam-3342	455	15	.	.	PUNCT
ejpam-3342	456	1	for	for	ADP
ejpam-3342	456	2	the	the	DET
ejpam-3342	456	3	converse	converse	NOUN
ejpam-3342	456	4	,	,	PUNCT
ejpam-3342	456	5	let	let	VERB
ejpam-3342	456	6	ε	ε	PROPN
ejpam-3342	456	7	>	>	X
ejpam-3342	456	8	0	0	PUNCT
ejpam-3342	456	9	be	be	AUX
ejpam-3342	456	10	given	give	VERB
ejpam-3342	456	11	.	.	PUNCT
ejpam-3342	457	1	since	since	SCONJ
ejpam-3342	457	2	f	f	PROPN
ejpam-3342	457	3	is	be	AUX
ejpam-3342	457	4	ac2[0	ac2[0	ADJ
ejpam-3342	457	5	,	,	PUNCT
ejpam-3342	457	6	t	t	X
ejpam-3342	457	7	]	]	PUNCT
ejpam-3342	457	8	,	,	PUNCT
ejpam-3342	457	9	choose	choose	VERB
ejpam-3342	457	10	η	η	X
ejpam-3342	457	11	>	>	X
ejpam-3342	457	12	0	0	NUM
ejpam-3342	457	13	such	such	ADJ
ejpam-3342	457	14	that	that	SCONJ
ejpam-3342	457	15	whenever	whenever	SCONJ
ejpam-3342	457	16	{	{	PUNCT
ejpam-3342	457	17	(	(	PUNCT
ejpam-3342	457	18	vj	vj	INTJ
ejpam-3342	457	19	,	,	PUNCT
ejpam-3342	457	20	ξj	ξj	NOUN
ejpam-3342	457	21	]	]	PUNCT
ejpam-3342	457	22	}	}	PUNCT
ejpam-3342	457	23	mj=1	mj=1	PRON
ejpam-3342	457	24	is	be	AUX
ejpam-3342	457	25	a	a	DET
ejpam-3342	457	26	finite	finite	ADJ
ejpam-3342	457	27	collection	collection	NOUN
ejpam-3342	457	28	of	of	ADP
ejpam-3342	457	29	subintervals	subinterval	NOUN
ejpam-3342	457	30	(	(	PUNCT
ejpam-3342	457	31	vj	vj	INTJ
ejpam-3342	457	32	,	,	PUNCT
ejpam-3342	457	33	ξj	ξj	NOUN
ejpam-3342	457	34	]	]	PUNCT
ejpam-3342	457	35	∈	∈	PROPN
ejpam-3342	457	36	j	j	PROPN
ejpam-3342	457	37	with	with	ADP
ejpam-3342	457	38	m∑	m∑	ADV
ejpam-3342	457	39	j=1	j=1	PROPN
ejpam-3342	457	40	|ξj	|ξj	PRON
ejpam-3342	457	41	−	−	NOUN
ejpam-3342	458	1	vj	vj	INTJ
ejpam-3342	458	2	|	|	ADV
ejpam-3342	458	3	≤	≤	NUM
ejpam-3342	458	4	η	η	PROPN
ejpam-3342	458	5	we	we	PRON
ejpam-3342	458	6	have	have	VERB
ejpam-3342	458	7	e	e	X
ejpam-3342	458	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3342	458	9	m∑	m∑	ADV
ejpam-3342	459	1	j=1	j=1	PROPN
ejpam-3342	459	2	f	f	PROPN
ejpam-3342	459	3	(	(	PUNCT
ejpam-3342	459	4	vj	vj	INTJ
ejpam-3342	459	5	,	,	PUNCT
ejpam-3342	459	6	ξj	ξj	NOUN
ejpam-3342	459	7	)	)	PUNCT
ejpam-3342	459	8	∥∥∥∥∥∥	∥∥∥∥∥∥	NOUN
ejpam-3342	459	9	2	2	NUM
ejpam-3342	459	10	v	v	NOUN
ejpam-3342	459	11			NOUN
ejpam-3342	459	12	<	<	X
ejpam-3342	459	13	ε	ε	PROPN
ejpam-3342	459	14	4	4	NUM
ejpam-3342	459	15	.	.	PUNCT
ejpam-3342	460	1	let	let	VERB
ejpam-3342	460	2	d	d	NOUN
ejpam-3342	460	3	=	=	PRON
ejpam-3342	460	4	{	{	PUNCT
ejpam-3342	460	5	(	(	PUNCT
ejpam-3342	460	6	(	(	PUNCT
ejpam-3342	460	7	v	v	NOUN
ejpam-3342	460	8	,	,	PUNCT
ejpam-3342	460	9	ξ	ξ	PROPN
ejpam-3342	460	10	]	]	X
ejpam-3342	460	11	,	,	PUNCT
ejpam-3342	460	12	ξ	ξ	X
ejpam-3342	460	13	)	)	PUNCT
ejpam-3342	460	14	}	}	PUNCT
ejpam-3342	460	15	be	be	AUX
ejpam-3342	460	16	a	a	DET
ejpam-3342	460	17	backwards	backwards	ADV
ejpam-3342	460	18	(	(	PUNCT
ejpam-3342	460	19	δ	δ	PROPN
ejpam-3342	460	20	,	,	PUNCT
ejpam-3342	460	21	η)-fine	η)-fine	X
ejpam-3342	460	22	partial	partial	ADJ
ejpam-3342	460	23	division	division	NOUN
ejpam-3342	460	24	of	of	ADP
ejpam-3342	460	25	[	[	X
ejpam-3342	460	26	0	0	NUM
ejpam-3342	460	27	,	,	PUNCT
ejpam-3342	460	28	t	t	NOUN
ejpam-3342	460	29	]	]	PUNCT
ejpam-3342	460	30	and	and	CCONJ
ejpam-3342	460	31	let	let	VERB
ejpam-3342	460	32	dc	dc	PROPN
ejpam-3342	460	33	be	be	AUX
ejpam-3342	460	34	the	the	DET
ejpam-3342	460	35	collection	collection	NOUN
ejpam-3342	460	36	of	of	ADP
ejpam-3342	460	37	all	all	DET
ejpam-3342	460	38	subintervals	subinterval	NOUN
ejpam-3342	460	39	of	of	ADP
ejpam-3342	460	40	[	[	X
ejpam-3342	460	41	0	0	NUM
ejpam-3342	460	42	,	,	PUNCT
ejpam-3342	460	43	t	t	PROPN
ejpam-3342	460	44	]	]	PUNCT
ejpam-3342	460	45	which	which	PRON
ejpam-3342	460	46	are	be	AUX
ejpam-3342	460	47	not	not	PART
ejpam-3342	460	48	included	include	VERB
ejpam-3342	460	49	in	in	ADP
ejpam-3342	460	50	the	the	DET
ejpam-3342	460	51	set	set	NOUN
ejpam-3342	460	52	d.	d.	PROPN
ejpam-3342	460	53	since	since	SCONJ
ejpam-3342	460	54	f	f	PROPN
ejpam-3342	460	55	is	be	AUX
ejpam-3342	460	56	ac2[0	ac2[0	ADJ
ejpam-3342	460	57	,	,	PUNCT
ejpam-3342	460	58	t	t	X
ejpam-3342	460	59	]	]	PUNCT
ejpam-3342	460	60	,	,	PUNCT
ejpam-3342	460	61	e	e	PROPN
ejpam-3342	461	1	[	[	X
ejpam-3342	461	2	∥∥∥(dc	∥∥∥(dc	PROPN
ejpam-3342	461	3	)	)	PUNCT
ejpam-3342	461	4	∑	∑	PROPN
ejpam-3342	461	5	f	f	PROPN
ejpam-3342	461	6	(	(	PUNCT
ejpam-3342	461	7	v	v	NOUN
ejpam-3342	461	8	,	,	PUNCT
ejpam-3342	461	9	ξ	ξ	NOUN
ejpam-3342	461	10	)	)	PUNCT
ejpam-3342	461	11	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	461	12	v	v	ADP
ejpam-3342	461	13	]	]	PUNCT
ejpam-3342	461	14	<	<	X
ejpam-3342	461	15	ε	ε	PROPN
ejpam-3342	461	16	4	4	NUM
ejpam-3342	461	17	.	.	PUNCT
ejpam-3342	462	1	references	reference	NOUN
ejpam-3342	462	2	76	76	NUM
ejpam-3342	462	3	hence	hence	ADV
ejpam-3342	462	4	,	,	PUNCT
ejpam-3342	462	5	e	e	X
ejpam-3342	462	6	[	[	X
ejpam-3342	462	7	∥∥∥(d	∥∥∥(d	X
ejpam-3342	462	8	)	)	PUNCT
ejpam-3342	462	9	∑	∑	PUNCT
ejpam-3342	462	10	fξ(wξ	fξ(wξ	PROPN
ejpam-3342	462	11	−wv)−	−wv)−	PROPN
ejpam-3342	462	12	f	f	X
ejpam-3342	462	13	(	(	PUNCT
ejpam-3342	462	14	0	0	NUM
ejpam-3342	462	15	,	,	PUNCT
ejpam-3342	462	16	t	t	NOUN
ejpam-3342	462	17	)	)	PUNCT
ejpam-3342	462	18	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	463	1	v	v	ADP
ejpam-3342	463	2	]	]	PUNCT
ejpam-3342	463	3	=	=	PUNCT
ejpam-3342	463	4	e	e	X
ejpam-3342	463	5	[	[	X
ejpam-3342	463	6	∥∥∥(d	∥∥∥(d	X
ejpam-3342	463	7	)	)	PUNCT
ejpam-3342	463	8	∑	∑	PRON
ejpam-3342	463	9	{	{	PUNCT
ejpam-3342	463	10	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	463	11	−wv)−	−wv)−	PROPN
ejpam-3342	463	12	f	f	X
ejpam-3342	463	13	(	(	PUNCT
ejpam-3342	463	14	v	v	NOUN
ejpam-3342	463	15	,	,	PUNCT
ejpam-3342	463	16	ξ	ξ	NOUN
ejpam-3342	463	17	)	)	PUNCT
ejpam-3342	463	18	}	}	PUNCT
ejpam-3342	463	19	−	−	PROPN
ejpam-3342	463	20	(	(	PUNCT
ejpam-3342	463	21	dc	dc	PROPN
ejpam-3342	463	22	)	)	PUNCT
ejpam-3342	463	23	∑	∑	PROPN
ejpam-3342	463	24	f	f	PROPN
ejpam-3342	463	25	(	(	PUNCT
ejpam-3342	463	26	v	v	NOUN
ejpam-3342	463	27	,	,	PUNCT
ejpam-3342	463	28	ξ	ξ	NOUN
ejpam-3342	463	29	)	)	PUNCT
ejpam-3342	463	30	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	463	31	v	v	ADP
ejpam-3342	463	32	]	]	PUNCT
ejpam-3342	463	33	≤	≤	NUM
ejpam-3342	463	34	2e	2e	NOUN
ejpam-3342	464	1	[	[	X
ejpam-3342	464	2	∥∥∥(d	∥∥∥(d	X
ejpam-3342	464	3	)	)	PUNCT
ejpam-3342	464	4	∑	∑	PRON
ejpam-3342	464	5	{	{	PUNCT
ejpam-3342	464	6	fξ(wξ	fξ(wξ	NOUN
ejpam-3342	464	7	−wv)−	−wv)−	PROPN
ejpam-3342	464	8	f	f	X
ejpam-3342	464	9	(	(	PUNCT
ejpam-3342	464	10	v	v	NOUN
ejpam-3342	464	11	,	,	PUNCT
ejpam-3342	464	12	ξ	ξ	NOUN
ejpam-3342	464	13	)	)	PUNCT
ejpam-3342	464	14	}	}	PUNCT
ejpam-3342	464	15	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	464	16	v	v	NOUN
ejpam-3342	464	17	]	]	PUNCT
ejpam-3342	465	1	+	+	CCONJ
ejpam-3342	465	2	2e	2e	NUM
ejpam-3342	465	3	[	[	X
ejpam-3342	465	4	∥∥∥(dc	∥∥∥(dc	PROPN
ejpam-3342	465	5	)	)	PUNCT
ejpam-3342	465	6	∑	∑	PROPN
ejpam-3342	465	7	f	f	PROPN
ejpam-3342	465	8	(	(	PUNCT
ejpam-3342	465	9	v	v	NOUN
ejpam-3342	465	10	,	,	PUNCT
ejpam-3342	465	11	ξ	ξ	NOUN
ejpam-3342	465	12	)	)	PUNCT
ejpam-3342	465	13	∥∥∥2	∥∥∥2	NOUN
ejpam-3342	465	14	v	v	ADP
ejpam-3342	465	15	]	]	PUNCT
ejpam-3342	465	16	<	<	X
ejpam-3342	465	17	2	2	NUM
ejpam-3342	465	18	(	(	PUNCT
ejpam-3342	465	19	ε	ε	PROPN
ejpam-3342	465	20	4	4	NUM
ejpam-3342	465	21	)	)	PUNCT
ejpam-3342	465	22	+	+	CCONJ
ejpam-3342	465	23	2	2	NUM
ejpam-3342	465	24	(	(	PUNCT
ejpam-3342	465	25	ε	ε	PROPN
ejpam-3342	465	26	4	4	NUM
ejpam-3342	465	27	)	)	PUNCT
ejpam-3342	465	28	=	=	SYM
ejpam-3342	465	29	ε	ε	PROPN
ejpam-3342	465	30	.	.	PUNCT
ejpam-3342	466	1	thus	thus	ADV
ejpam-3342	466	2	,	,	PUNCT
ejpam-3342	466	3	f	f	PROPN
ejpam-3342	466	4	is	be	AUX
ejpam-3342	466	5	ihb	ihb	NOUN
ejpam-3342	466	6	-	-	ADJ
ejpam-3342	466	7	integrable	integrable	ADJ
ejpam-3342	466	8	on	on	ADP
ejpam-3342	466	9	[	[	X
ejpam-3342	466	10	0	0	NUM
ejpam-3342	466	11	,	,	PUNCT
ejpam-3342	466	12	t	t	X
ejpam-3342	466	13	]	]	PUNCT
ejpam-3342	466	14	.	.	PUNCT
ejpam-3342	467	1	�	�	PROPN
ejpam-3342	467	2	5	5	NUM
ejpam-3342	467	3	.	.	PUNCT
ejpam-3342	467	4	conclusion	conclusion	NOUN
ejpam-3342	467	5	and	and	CCONJ
ejpam-3342	467	6	recommendation	recommendation	NOUN
ejpam-3342	467	7	in	in	ADP
ejpam-3342	467	8	this	this	DET
ejpam-3342	467	9	paper	paper	NOUN
ejpam-3342	467	10	,	,	PUNCT
ejpam-3342	467	11	we	we	PRON
ejpam-3342	467	12	formulate	formulate	VERB
ejpam-3342	467	13	the	the	DET
ejpam-3342	467	14	itô	itô	PROPN
ejpam-3342	467	15	isometry	isometry	NOUN
ejpam-3342	467	16	for	for	ADP
ejpam-3342	467	17	the	the	DET
ejpam-3342	467	18	backwards	backwards	ADV
ejpam-3342	467	19	itô-henstock	itô-henstock	NOUN
ejpam-3342	467	20	integral	integral	NOUN
ejpam-3342	467	21	of	of	ADP
ejpam-3342	467	22	an	an	DET
ejpam-3342	467	23	operator	operator	NOUN
ejpam-3342	467	24	-	-	PUNCT
ejpam-3342	467	25	valued	value	VERB
ejpam-3342	467	26	stochastic	stochastic	ADJ
ejpam-3342	467	27	process	process	NOUN
ejpam-3342	467	28	with	with	ADP
ejpam-3342	467	29	respect	respect	NOUN
ejpam-3342	467	30	to	to	ADP
ejpam-3342	467	31	a	a	DET
ejpam-3342	467	32	hilbert	hilbert	NOUN
ejpam-3342	467	33	space	space	NOUN
ejpam-3342	467	34	-	-	PUNCT
ejpam-3342	467	35	valued	value	VERB
ejpam-3342	467	36	q	q	ADJ
ejpam-3342	467	37	-	-	PUNCT
ejpam-3342	467	38	wiener	wiener	NOUN
ejpam-3342	467	39	process	process	NOUN
ejpam-3342	467	40	and	and	CCONJ
ejpam-3342	467	41	provide	provide	VERB
ejpam-3342	467	42	an	an	DET
ejpam-3342	467	43	equivalent	equivalent	ADJ
ejpam-3342	467	44	definition	definition	NOUN
ejpam-3342	467	45	for	for	ADP
ejpam-3342	467	46	this	this	DET
ejpam-3342	467	47	integral	integral	ADJ
ejpam-3342	467	48	using	use	VERB
ejpam-3342	467	49	the	the	DET
ejpam-3342	467	50	concept	concept	NOUN
ejpam-3342	467	51	ac2[0	ac2[0	ADJ
ejpam-3342	467	52	,	,	PUNCT
ejpam-3342	467	53	t	t	NOUN
ejpam-3342	467	54	]	]	PUNCT
ejpam-3342	467	55	property	property	NOUN
ejpam-3342	467	56	,	,	PUNCT
ejpam-3342	467	57	a	a	DET
ejpam-3342	467	58	version	version	NOUN
ejpam-3342	467	59	of	of	ADP
ejpam-3342	467	60	absolute	absolute	ADJ
ejpam-3342	467	61	continuity	continuity	NOUN
ejpam-3342	467	62	.	.	PUNCT
ejpam-3342	468	1	a	a	DET
ejpam-3342	468	2	worthwhile	worthwhile	ADJ
ejpam-3342	468	3	direction	direction	NOUN
ejpam-3342	468	4	for	for	ADP
ejpam-3342	468	5	further	further	ADJ
ejpam-3342	468	6	investigation	investigation	NOUN
ejpam-3342	468	7	is	be	AUX
ejpam-3342	468	8	to	to	PART
ejpam-3342	468	9	formulate	formulate	VERB
ejpam-3342	468	10	a	a	DET
ejpam-3342	468	11	version	version	NOUN
ejpam-3342	468	12	of	of	ADP
ejpam-3342	468	13	itô	itô	PROPN
ejpam-3342	468	14	’s	’s	PART
ejpam-3342	468	15	formula	formula	NOUN
ejpam-3342	468	16	for	for	ADP
ejpam-3342	468	17	this	this	DET
ejpam-3342	468	18	type	type	NOUN
ejpam-3342	468	19	of	of	ADP
ejpam-3342	468	20	integral	integral	ADJ
ejpam-3342	468	21	.	.	PUNCT
ejpam-3342	469	1	acknowledgement	acknowledgement	NOUN
ejpam-3342	469	2	the	the	DET
ejpam-3342	469	3	authors	author	NOUN
ejpam-3342	469	4	would	would	AUX
ejpam-3342	469	5	like	like	VERB
ejpam-3342	469	6	to	to	PART
ejpam-3342	469	7	acknowledge	acknowledge	VERB
ejpam-3342	469	8	the	the	DET
ejpam-3342	469	9	financial	financial	ADJ
ejpam-3342	469	10	support	support	NOUN
ejpam-3342	469	11	from	from	ADP
ejpam-3342	469	12	the	the	DET
ejpam-3342	469	13	department	department	NOUN
ejpam-3342	469	14	of	of	ADP
ejpam-3342	469	15	science	science	NOUN
ejpam-3342	469	16	and	and	CCONJ
ejpam-3342	469	17	technology	technology	NOUN
ejpam-3342	469	18	-	-	PUNCT
ejpam-3342	469	19	accelerated	accelerate	VERB
ejpam-3342	469	20	science	science	NOUN
ejpam-3342	469	21	and	and	CCONJ
ejpam-3342	469	22	technology	technology	NOUN
ejpam-3342	469	23	human	human	ADJ
ejpam-3342	469	24	resource	resource	NOUN
ejpam-3342	469	25	development	development	NOUN
ejpam-3342	469	26	program	program	NOUN
ejpam-3342	469	27	(	(	PUNCT
ejpam-3342	469	28	dost	dost	NOUN
ejpam-3342	469	29	-	-	PUNCT
ejpam-3342	469	30	asthrdp	asthrdp	NOUN
ejpam-3342	469	31	)	)	PUNCT
ejpam-3342	469	32	and	and	CCONJ
ejpam-3342	469	33	to	to	PART
ejpam-3342	469	34	thank	thank	VERB
ejpam-3342	469	35	the	the	DET
ejpam-3342	469	36	unknown	unknown	ADJ
ejpam-3342	469	37	referee	referee	NOUN
ejpam-3342	469	38	for	for	ADP
ejpam-3342	469	39	the	the	DET
ejpam-3342	469	40	helpful	helpful	ADJ
ejpam-3342	469	41	comments	comment	NOUN
ejpam-3342	469	42	for	for	ADP
ejpam-3342	469	43	the	the	DET
ejpam-3342	469	44	improvement	improvement	NOUN
ejpam-3342	469	45	of	of	ADP
ejpam-3342	469	46	this	this	DET
ejpam-3342	469	47	paper	paper	NOUN
ejpam-3342	469	48	.	.	PUNCT
ejpam-3342	470	1	references	reference	NOUN
ejpam-3342	470	2	[	[	X
ejpam-3342	470	3	1	1	NUM
ejpam-3342	470	4	]	]	X
ejpam-3342	470	5	d.	d.	PROPN
ejpam-3342	470	6	applebaum	applebaum	PROPN
ejpam-3342	470	7	.	.	PUNCT
ejpam-3342	471	1	lévy	lévy	X
ejpam-3342	471	2	processes	process	NOUN
ejpam-3342	471	3	and	and	CCONJ
ejpam-3342	471	4	stochastic	stochastic	ADJ
ejpam-3342	471	5	calculus	calculus	NOUN
ejpam-3342	471	6	.	.	PUNCT
ejpam-3342	472	1	cambridge	cambridge	PROPN
ejpam-3342	472	2	university	university	PROPN
ejpam-3342	472	3	press	press	PROPN
ejpam-3342	472	4	,	,	PUNCT
ejpam-3342	472	5	new	new	PROPN
ejpam-3342	472	6	york	york	PROPN
ejpam-3342	472	7	,	,	PUNCT
ejpam-3342	472	8	2004	2004	NUM
ejpam-3342	472	9	.	.	PUNCT
ejpam-3342	473	1	[	[	X
ejpam-3342	473	2	2	2	X
ejpam-3342	473	3	]	]	PUNCT
ejpam-3342	473	4	j.	j.	PROPN
ejpam-3342	473	5	arcede	arcede	PROPN
ejpam-3342	473	6	and	and	CCONJ
ejpam-3342	473	7	e.	e.	PROPN
ejpam-3342	473	8	cabral	cabral	PROPN
ejpam-3342	473	9	.	.	PUNCT
ejpam-3342	474	1	backwards	backwards	ADV
ejpam-3342	474	2	henstock	henstock	PROPN
ejpam-3342	474	3	integral	integral	ADJ
ejpam-3342	474	4	.	.	PUNCT
ejpam-3342	475	1	matimyás	matimyás	NOUN
ejpam-3342	475	2	matematika	matematika	NOUN
ejpam-3342	475	3	,	,	PUNCT
ejpam-3342	475	4	journal	journal	NOUN
ejpam-3342	475	5	of	of	ADP
ejpam-3342	475	6	the	the	DET
ejpam-3342	475	7	mathematical	mathematical	ADJ
ejpam-3342	475	8	society	society	NOUN
ejpam-3342	475	9	of	of	ADP
ejpam-3342	475	10	the	the	DET
ejpam-3342	475	11	philippines	philippine	NOUN
ejpam-3342	475	12	,	,	PUNCT
ejpam-3342	475	13	32:1–12	32:1–12	NUM
ejpam-3342	475	14	,	,	PUNCT
ejpam-3342	475	15	2009	2009	NUM
ejpam-3342	475	16	.	.	PUNCT
ejpam-3342	476	1	[	[	X
ejpam-3342	476	2	3	3	X
ejpam-3342	476	3	]	]	X
ejpam-3342	476	4	j.	j.	PROPN
ejpam-3342	476	5	arcede	arcede	PROPN
ejpam-3342	476	6	and	and	CCONJ
ejpam-3342	476	7	e.	e.	PROPN
ejpam-3342	476	8	cabral	cabral	PROPN
ejpam-3342	476	9	.	.	PUNCT
ejpam-3342	477	1	an	an	DET
ejpam-3342	477	2	equivalent	equivalent	ADJ
ejpam-3342	477	3	definition	definition	NOUN
ejpam-3342	477	4	for	for	ADP
ejpam-3342	477	5	the	the	DET
ejpam-3342	477	6	backwards	backwards	ADV
ejpam-3342	477	7	itô	itô	PROPN
ejpam-3342	477	8	integral	integral	ADJ
ejpam-3342	477	9	.	.	PUNCT
ejpam-3342	478	1	thai	thai	PROPN
ejpam-3342	478	2	journal	journal	PROPN
ejpam-3342	478	3	of	of	ADP
ejpam-3342	478	4	mathematics	mathematic	NOUN
ejpam-3342	478	5	,	,	PUNCT
ejpam-3342	478	6	9:619–630	9:619–630	NOUN
ejpam-3342	478	7	,	,	PUNCT
ejpam-3342	478	8	2011	2011	NUM
ejpam-3342	478	9	.	.	PUNCT
ejpam-3342	479	1	references	reference	NOUN
ejpam-3342	479	2	77	77	NUM
ejpam-3342	480	1	[	[	X
ejpam-3342	480	2	4	4	NUM
ejpam-3342	480	3	]	]	X
ejpam-3342	480	4	j.	j.	PROPN
ejpam-3342	480	5	arcede	arcede	PROPN
ejpam-3342	480	6	and	and	CCONJ
ejpam-3342	480	7	e.	e.	PROPN
ejpam-3342	480	8	cabral	cabral	PROPN
ejpam-3342	480	9	.	.	PUNCT
ejpam-3342	481	1	fundamental	fundamental	ADJ
ejpam-3342	481	2	theorem	theorem	NOUN
ejpam-3342	481	3	of	of	ADP
ejpam-3342	481	4	calculus	calculus	NOUN
ejpam-3342	481	5	for	for	ADP
ejpam-3342	481	6	the	the	DET
ejpam-3342	481	7	backwards	backwards	ADV
ejpam-3342	481	8	itô	itô	PROPN
ejpam-3342	481	9	integral	integral	ADJ
ejpam-3342	481	10	.	.	PUNCT
ejpam-3342	482	1	matimyás	matimyás	NOUN
ejpam-3342	482	2	matematika	matematika	NOUN
ejpam-3342	482	3	,	,	PUNCT
ejpam-3342	482	4	journal	journal	NOUN
ejpam-3342	482	5	of	of	ADP
ejpam-3342	482	6	the	the	DET
ejpam-3342	482	7	mathematical	mathematical	ADJ
ejpam-3342	482	8	society	society	NOUN
ejpam-3342	482	9	of	of	ADP
ejpam-3342	482	10	the	the	DET
ejpam-3342	482	11	philippines	philippine	NOUN
ejpam-3342	482	12	,	,	PUNCT
ejpam-3342	482	13	34:1–9	34:1–9	NOUN
ejpam-3342	482	14	,	,	PUNCT
ejpam-3342	482	15	2011	2011	NUM
ejpam-3342	482	16	.	.	PUNCT
ejpam-3342	483	1	[	[	X
ejpam-3342	483	2	5	5	X
ejpam-3342	483	3	]	]	PUNCT
ejpam-3342	483	4	j.	j.	PROPN
ejpam-3342	483	5	arcede	arcede	PROPN
ejpam-3342	483	6	and	and	CCONJ
ejpam-3342	483	7	e.	e.	PROPN
ejpam-3342	483	8	cabral	cabral	PROPN
ejpam-3342	483	9	.	.	PUNCT
ejpam-3342	484	1	on	on	ADP
ejpam-3342	484	2	integration	integration	NOUN
ejpam-3342	484	3	-	-	PUNCT
ejpam-3342	484	4	by	by	ADP
ejpam-3342	484	5	-	-	PUNCT
ejpam-3342	484	6	parts	part	NOUN
ejpam-3342	484	7	and	and	CCONJ
ejpam-3342	484	8	itô	itô	PROPN
ejpam-3342	484	9	formula	formula	NOUN
ejpam-3342	484	10	for	for	ADP
ejpam-3342	484	11	backwards	backwards	ADV
ejpam-3342	484	12	itô	itô	PROPN
ejpam-3342	484	13	integral	integral	ADJ
ejpam-3342	484	14	.	.	PUNCT
ejpam-3342	485	1	the	the	DET
ejpam-3342	485	2	mindanawan	mindanawan	PROPN
ejpam-3342	485	3	journal	journal	PROPN
ejpam-3342	485	4	of	of	ADP
ejpam-3342	485	5	mathematics	mathematic	NOUN
ejpam-3342	485	6	,	,	PUNCT
ejpam-3342	485	7	3:112–132	3:112–132	NUM
ejpam-3342	485	8	,	,	PUNCT
ejpam-3342	485	9	2012	2012	NUM
ejpam-3342	485	10	.	.	PUNCT
ejpam-3342	486	1	[	[	X
ejpam-3342	486	2	6	6	NUM
ejpam-3342	486	3	]	]	PUNCT
ejpam-3342	486	4	l.	l.	PROPN
ejpam-3342	486	5	gawarecki	gawarecki	PROPN
ejpam-3342	486	6	and	and	CCONJ
ejpam-3342	486	7	v.	v.	ADP
ejpam-3342	486	8	mandrekar	mandrekar	PROPN
ejpam-3342	486	9	.	.	PUNCT
ejpam-3342	487	1	stochastic	stochastic	ADJ
ejpam-3342	487	2	differential	differential	ADJ
ejpam-3342	487	3	equations	equation	NOUN
ejpam-3342	487	4	in	in	ADP
ejpam-3342	487	5	infinite	infinite	ADJ
ejpam-3342	487	6	dimensions	dimension	NOUN
ejpam-3342	487	7	with	with	ADP
ejpam-3342	487	8	applications	application	NOUN
ejpam-3342	487	9	to	to	PART
ejpam-3342	487	10	stochastic	stochastic	VERB
ejpam-3342	487	11	partial	partial	ADJ
ejpam-3342	487	12	differential	differential	NOUN
ejpam-3342	487	13	equations	equation	NOUN
ejpam-3342	487	14	.	.	PUNCT
ejpam-3342	488	1	springer	springer	NOUN
ejpam-3342	488	2	,	,	PUNCT
ejpam-3342	488	3	berlin	berlin	PROPN
ejpam-3342	488	4	,	,	PUNCT
ejpam-3342	488	5	2011	2011	NUM
ejpam-3342	488	6	.	.	PUNCT
ejpam-3342	489	1	[	[	X
ejpam-3342	489	2	7	7	X
ejpam-3342	489	3	]	]	X
ejpam-3342	489	4	r.	r.	PROPN
ejpam-3342	489	5	a.	a.	PROPN
ejpam-3342	489	6	gordon	gordon	PROPN
ejpam-3342	489	7	.	.	PUNCT
ejpam-3342	490	1	the	the	DET
ejpam-3342	490	2	integrals	integral	NOUN
ejpam-3342	490	3	of	of	ADP
ejpam-3342	490	4	lebesgue	lebesgue	NOUN
ejpam-3342	490	5	,	,	PUNCT
ejpam-3342	490	6	denjoy	denjoy	PROPN
ejpam-3342	490	7	,	,	PUNCT
ejpam-3342	490	8	perron	perron	PROPN
ejpam-3342	490	9	and	and	CCONJ
ejpam-3342	490	10	henstock	henstock	PROPN
ejpam-3342	490	11	.	.	PUNCT
ejpam-3342	491	1	american	american	PROPN
ejpam-3342	491	2	mathematical	mathematical	PROPN
ejpam-3342	491	3	society	society	NOUN
ejpam-3342	491	4	,	,	PUNCT
ejpam-3342	491	5	1994	1994	NUM
ejpam-3342	491	6	.	.	PUNCT
ejpam-3342	492	1	[	[	X
ejpam-3342	492	2	8	8	NUM
ejpam-3342	492	3	]	]	X
ejpam-3342	492	4	r.	r.	PROPN
ejpam-3342	492	5	henstock	henstock	PROPN
ejpam-3342	492	6	.	.	PUNCT
ejpam-3342	493	1	lectures	lecture	NOUN
ejpam-3342	493	2	on	on	ADP
ejpam-3342	493	3	the	the	DET
ejpam-3342	493	4	theory	theory	NOUN
ejpam-3342	493	5	of	of	ADP
ejpam-3342	493	6	integration	integration	NOUN
ejpam-3342	493	7	.	.	PUNCT
ejpam-3342	494	1	world	world	NOUN
ejpam-3342	494	2	scientific	scientific	PROPN
ejpam-3342	494	3	,	,	PUNCT
ejpam-3342	494	4	singapore	singapore	PROPN
ejpam-3342	494	5	,	,	PUNCT
ejpam-3342	494	6	1988	1988	NUM
ejpam-3342	494	7	.	.	PUNCT
ejpam-3342	495	1	[	[	X
ejpam-3342	495	2	9	9	X
ejpam-3342	495	3	]	]	PUNCT
ejpam-3342	495	4	j.	j.	PROPN
ejpam-3342	495	5	kurzweil	kurzweil	PROPN
ejpam-3342	495	6	.	.	PUNCT
ejpam-3342	495	7	henstock	henstock	PROPN
ejpam-3342	495	8	-	-	PUNCT
ejpam-3342	495	9	kurzweil	kurzweil	NOUN
ejpam-3342	495	10	integration	integration	NOUN
ejpam-3342	495	11	:	:	PUNCT
ejpam-3342	495	12	its	its	PRON
ejpam-3342	495	13	relation	relation	NOUN
ejpam-3342	495	14	to	to	ADP
ejpam-3342	495	15	topological	topological	ADJ
ejpam-3342	495	16	vector	vector	NOUN
ejpam-3342	495	17	spaces	space	NOUN
ejpam-3342	495	18	.	.	PUNCT
ejpam-3342	496	1	world	world	NOUN
ejpam-3342	496	2	scientific	scientific	PROPN
ejpam-3342	496	3	,	,	PUNCT
ejpam-3342	496	4	singapore	singapore	PROPN
ejpam-3342	496	5	,	,	PUNCT
ejpam-3342	496	6	2000	2000	NUM
ejpam-3342	496	7	.	.	PUNCT
ejpam-3342	497	1	[	[	X
ejpam-3342	497	2	10	10	NUM
ejpam-3342	497	3	]	]	PUNCT
ejpam-3342	497	4	m.	m.	NOUN
ejpam-3342	497	5	labendia	labendia	PROPN
ejpam-3342	497	6	and	and	CCONJ
ejpam-3342	497	7	j.	j.	PROPN
ejpam-3342	497	8	benitez	benitez	PROPN
ejpam-3342	497	9	.	.	PUNCT
ejpam-3342	498	1	convergence	convergence	NOUN
ejpam-3342	498	2	theorems	theorem	VERB
ejpam-3342	498	3	for	for	ADP
ejpam-3342	498	4	the	the	DET
ejpam-3342	498	5	itô-henstock	itô-henstock	PROPN
ejpam-3342	498	6	integrable	integrable	ADJ
ejpam-3342	498	7	operator	operator	NOUN
ejpam-3342	498	8	-	-	PUNCT
ejpam-3342	498	9	valued	value	VERB
ejpam-3342	498	10	stochastic	stochastic	ADJ
ejpam-3342	498	11	process	process	NOUN
ejpam-3342	498	12	.	.	PUNCT
ejpam-3342	499	1	malaysian	malaysian	ADJ
ejpam-3342	499	2	journal	journal	PROPN
ejpam-3342	499	3	of	of	ADP
ejpam-3342	499	4	mathematical	mathematical	ADJ
ejpam-3342	499	5	sciences	science	NOUN
ejpam-3342	499	6	,	,	PUNCT
ejpam-3342	499	7	to	to	PART
ejpam-3342	499	8	appear	appear	VERB
ejpam-3342	499	9	.	.	PUNCT
ejpam-3342	500	1	[	[	X
ejpam-3342	500	2	11	11	NUM
ejpam-3342	500	3	]	]	PUNCT
ejpam-3342	500	4	m.	m.	NOUN
ejpam-3342	500	5	labendia	labendia	PROPN
ejpam-3342	500	6	e.	e.	PROPN
ejpam-3342	500	7	de	de	PROPN
ejpam-3342	500	8	lara	lara	PROPN
ejpam-3342	500	9	-	-	PUNCT
ejpam-3342	500	10	tuprio	tuprio	PROPN
ejpam-3342	500	11	and	and	CCONJ
ejpam-3342	500	12	t.	t.	PROPN
ejpam-3342	500	13	r.	r.	PROPN
ejpam-3342	500	14	teng	teng	PROPN
ejpam-3342	500	15	.	.	PUNCT
ejpam-3342	501	1	itô-henstock	itô-henstock	PROPN
ejpam-3342	501	2	integral	integral	ADJ
ejpam-3342	501	3	and	and	CCONJ
ejpam-3342	501	4	itô	itô	PROPN
ejpam-3342	501	5	’s	’s	PART
ejpam-3342	501	6	formula	formula	NOUN
ejpam-3342	501	7	for	for	ADP
ejpam-3342	501	8	the	the	DET
ejpam-3342	501	9	operator	operator	NOUN
ejpam-3342	501	10	-	-	PUNCT
ejpam-3342	501	11	valued	value	VERB
ejpam-3342	501	12	stochastic	stochastic	ADJ
ejpam-3342	501	13	process	process	NOUN
ejpam-3342	501	14	.	.	PUNCT
ejpam-3342	502	1	mathematica	mathematica	PROPN
ejpam-3342	502	2	bohemica	bohemica	PROPN
ejpam-3342	502	3	,	,	PUNCT
ejpam-3342	502	4	143:135	143:135	NUM
ejpam-3342	502	5	–	–	PUNCT
ejpam-3342	502	6	160	160	NUM
ejpam-3342	502	7	,	,	PUNCT
ejpam-3342	502	8	2018	2018	NUM
ejpam-3342	502	9	.	.	PUNCT
ejpam-3342	503	1	[	[	X
ejpam-3342	503	2	12	12	NUM
ejpam-3342	503	3	]	]	PUNCT
ejpam-3342	503	4	p.	p.	PROPN
ejpam-3342	503	5	y.	y.	PROPN
ejpam-3342	503	6	lee	lee	PROPN
ejpam-3342	503	7	.	.	PUNCT
ejpam-3342	504	1	lanzhou	lanzhou	PROPN
ejpam-3342	504	2	lectures	lecture	VERB
ejpam-3342	504	3	on	on	ADP
ejpam-3342	504	4	henstock	henstock	NOUN
ejpam-3342	504	5	integration	integration	NOUN
ejpam-3342	504	6	.	.	PUNCT
ejpam-3342	505	1	world	world	NOUN
ejpam-3342	505	2	scientific	scientific	PROPN
ejpam-3342	505	3	,	,	PUNCT
ejpam-3342	505	4	singapore	singapore	PROPN
ejpam-3342	505	5	,	,	PUNCT
ejpam-3342	505	6	1989	1989	NUM
ejpam-3342	505	7	.	.	PUNCT
ejpam-3342	506	1	[	[	X
ejpam-3342	506	2	13	13	NUM
ejpam-3342	506	3	]	]	PUNCT
ejpam-3342	506	4	p.	p.	PROPN
ejpam-3342	506	5	y.	y.	PROPN
ejpam-3342	506	6	lee	lee	PROPN
ejpam-3342	506	7	and	and	CCONJ
ejpam-3342	506	8	r.	r.	PROPN
ejpam-3342	506	9	výborný.	výborný.	VERB
ejpam-3342	506	10	the	the	DET
ejpam-3342	506	11	integral	integral	ADJ
ejpam-3342	506	12	:	:	PUNCT
ejpam-3342	506	13	an	an	DET
ejpam-3342	506	14	easy	easy	ADJ
ejpam-3342	506	15	approach	approach	NOUN
ejpam-3342	506	16	after	after	ADP
ejpam-3342	506	17	kurzweil	kurzweil	PROPN
ejpam-3342	506	18	and	and	CCONJ
ejpam-3342	506	19	henstock	henstock	PROPN
ejpam-3342	506	20	.	.	PUNCT
ejpam-3342	507	1	cambridge	cambridge	PROPN
ejpam-3342	507	2	university	university	PROPN
ejpam-3342	507	3	press	press	PROPN
ejpam-3342	507	4	,	,	PUNCT
ejpam-3342	507	5	cambridge	cambridge	PROPN
ejpam-3342	507	6	,	,	PUNCT
ejpam-3342	507	7	2000	2000	NUM
ejpam-3342	507	8	.	.	PUNCT
ejpam-3342	508	1	[	[	X
ejpam-3342	508	2	14	14	NUM
ejpam-3342	508	3	]	]	PUNCT
ejpam-3342	508	4	t.	t.	PROPN
ejpam-3342	508	5	y.	y.	PROPN
ejpam-3342	508	6	lee	lee	PROPN
ejpam-3342	508	7	.	.	PUNCT
ejpam-3342	509	1	henstock	henstock	PROPN
ejpam-3342	509	2	-	-	PUNCT
ejpam-3342	509	3	kurzweil	kurzweil	NOUN
ejpam-3342	509	4	integration	integration	NOUN
ejpam-3342	509	5	on	on	ADP
ejpam-3342	509	6	euclidean	euclidean	ADJ
ejpam-3342	509	7	spaces	space	NOUN
ejpam-3342	509	8	.	.	PUNCT
ejpam-3342	510	1	world	world	NOUN
ejpam-3342	510	2	scientific	scientific	PROPN
ejpam-3342	510	3	,	,	PUNCT
ejpam-3342	510	4	singapore	singapore	PROPN
ejpam-3342	510	5	,	,	PUNCT
ejpam-3342	510	6	2011	2011	NUM
ejpam-3342	510	7	.	.	PUNCT
ejpam-3342	511	1	[	[	X
ejpam-3342	511	2	15	15	NUM
ejpam-3342	511	3	]	]	X
ejpam-3342	511	4	e.	e.	PROPN
ejpam-3342	511	5	j.	j.	PROPN
ejpam-3342	511	6	mcshane	mcshane	PROPN
ejpam-3342	511	7	.	.	PUNCT
ejpam-3342	512	1	stochastic	stochastic	ADJ
ejpam-3342	512	2	integrals	integral	NOUN
ejpam-3342	512	3	and	and	CCONJ
ejpam-3342	512	4	stochastic	stochastic	ADJ
ejpam-3342	512	5	functional	functional	ADJ
ejpam-3342	512	6	equations	equation	NOUN
ejpam-3342	512	7	.	.	PUNCT
ejpam-3342	513	1	siam	siam	PROPN
ejpam-3342	513	2	j.	j.	PROPN
ejpam-3342	513	3	appl	appl	PROPN
ejpam-3342	513	4	.	.	PROPN
ejpam-3342	513	5	math	math	PROPN
ejpam-3342	513	6	.	.	PUNCT
ejpam-3342	513	7	,	,	PUNCT
ejpam-3342	514	1	17:287–306	17:287–306	NUM
ejpam-3342	514	2	,	,	PUNCT
ejpam-3342	514	3	1969	1969	NUM
ejpam-3342	514	4	.	.	PUNCT
ejpam-3342	515	1	[	[	X
ejpam-3342	515	2	16	16	NUM
ejpam-3342	515	3	]	]	PUNCT
ejpam-3342	515	4	b.	b.	PROPN
ejpam-3342	515	5	øksendal	øksendal	NOUN
ejpam-3342	515	6	.	.	PUNCT
ejpam-3342	516	1	stochastic	stochastic	ADJ
ejpam-3342	516	2	differential	differential	ADJ
ejpam-3342	516	3	equations	equation	NOUN
ejpam-3342	516	4	(	(	PUNCT
ejpam-3342	516	5	5th	5th	ADJ
ejpam-3342	516	6	edition	edition	NOUN
ejpam-3342	516	7	)	)	PUNCT
ejpam-3342	516	8	.	.	PUNCT
ejpam-3342	517	1	springer	springer	NOUN
ejpam-3342	517	2	-	-	PUNCT
ejpam-3342	517	3	verlag	verlag	PROPN
ejpam-3342	517	4	,	,	PUNCT
ejpam-3342	517	5	new	new	PROPN
ejpam-3342	517	6	york	york	PROPN
ejpam-3342	517	7	,	,	PUNCT
ejpam-3342	517	8	1998	1998	NUM
ejpam-3342	517	9	.	.	PUNCT
ejpam-3342	518	1	[	[	X
ejpam-3342	518	2	17	17	NUM
ejpam-3342	518	3	]	]	PUNCT
ejpam-3342	518	4	z.	z.	PROPN
ejpam-3342	518	5	r.	r.	PROPN
ejpam-3342	518	6	pop	pop	PROPN
ejpam-3342	518	7	-	-	PUNCT
ejpam-3342	518	8	stojanovic	stojanovic	ADJ
ejpam-3342	518	9	.	.	PUNCT
ejpam-3342	519	1	on	on	ADP
ejpam-3342	519	2	mcshane	mcshane	PROPN
ejpam-3342	519	3	’s	’s	PART
ejpam-3342	519	4	belated	belate	VERB
ejpam-3342	519	5	stochastic	stochastic	ADJ
ejpam-3342	519	6	integral	integral	ADJ
ejpam-3342	519	7	.	.	PUNCT
ejpam-3342	520	1	siam	siam	PROPN
ejpam-3342	520	2	j.	j.	PROPN
ejpam-3342	520	3	appl	appl	PROPN
ejpam-3342	520	4	.	.	PROPN
ejpam-3342	520	5	math	math	PROPN
ejpam-3342	520	6	.	.	PUNCT
ejpam-3342	520	7	,	,	PUNCT
ejpam-3342	520	8	22:87–92	22:87–92	PROPN
ejpam-3342	520	9	,	,	PUNCT
ejpam-3342	520	10	1972	1972	NUM
ejpam-3342	520	11	.	.	PUNCT
ejpam-3342	521	1	[	[	X
ejpam-3342	521	2	18	18	NUM
ejpam-3342	521	3	]	]	X
ejpam-3342	521	4	g.	g.	PROPN
ejpam-3342	521	5	da	da	PROPN
ejpam-3342	521	6	prato	prato	PROPN
ejpam-3342	521	7	and	and	CCONJ
ejpam-3342	521	8	j.	j.	PROPN
ejpam-3342	521	9	zabczyk	zabczyk	PROPN
ejpam-3342	521	10	.	.	PUNCT
ejpam-3342	522	1	stochastic	stochastic	ADJ
ejpam-3342	522	2	equations	equation	NOUN
ejpam-3342	522	3	in	in	ADP
ejpam-3342	522	4	infinite	infinite	ADJ
ejpam-3342	522	5	dimensions	dimension	NOUN
ejpam-3342	522	6	.	.	PUNCT
ejpam-3342	523	1	cambridge	cambridge	PROPN
ejpam-3342	523	2	university	university	PROPN
ejpam-3342	523	3	press	press	PROPN
ejpam-3342	523	4	,	,	PUNCT
ejpam-3342	523	5	cambridge	cambridge	PROPN
ejpam-3342	523	6	,	,	PUNCT
ejpam-3342	523	7	1992	1992	NUM
ejpam-3342	523	8	.	.	PUNCT
ejpam-3342	524	1	references	reference	NOUN
ejpam-3342	524	2	78	78	NUM
ejpam-3342	524	3	[	[	SYM
ejpam-3342	524	4	19	19	NUM
ejpam-3342	524	5	]	]	X
ejpam-3342	524	6	c.	c.	NOUN
ejpam-3342	524	7	prévôt	prévôt	NOUN
ejpam-3342	524	8	and	and	CCONJ
ejpam-3342	524	9	m.	m.	NOUN
ejpam-3342	524	10	röckner	röckner	NOUN
ejpam-3342	524	11	.	.	PUNCT
ejpam-3342	525	1	a	a	DET
ejpam-3342	525	2	concise	concise	ADJ
ejpam-3342	525	3	course	course	NOUN
ejpam-3342	525	4	on	on	ADP
ejpam-3342	525	5	stochastic	stochastic	ADJ
ejpam-3342	525	6	partial	partial	ADJ
ejpam-3342	525	7	differential	differential	NOUN
ejpam-3342	525	8	equations	equation	NOUN
ejpam-3342	525	9	.	.	PUNCT
ejpam-3342	526	1	2007	2007	NUM
ejpam-3342	526	2	.	.	PUNCT
ejpam-3342	527	1	[	[	X
ejpam-3342	527	2	20	20	NUM
ejpam-3342	527	3	]	]	PUNCT
ejpam-3342	527	4	m.	m.	NOUN
ejpam-3342	527	5	reed	reed	PROPN
ejpam-3342	527	6	and	and	CCONJ
ejpam-3342	527	7	b.	b.	PROPN
ejpam-3342	527	8	simon	simon	PROPN
ejpam-3342	527	9	.	.	PUNCT
ejpam-3342	528	1	methods	method	NOUN
ejpam-3342	528	2	of	of	ADP
ejpam-3342	528	3	modern	modern	ADJ
ejpam-3342	528	4	mathematical	mathematical	ADJ
ejpam-3342	528	5	physics	physics	NOUN
ejpam-3342	528	6	i	i	PRON
ejpam-3342	528	7	:	:	PUNCT
ejpam-3342	528	8	functional	functional	ADJ
ejpam-3342	528	9	analysis	analysis	NOUN
ejpam-3342	528	10	.	.	PUNCT
ejpam-3342	528	11	1980	1980	NUM
ejpam-3342	528	12	.	.	PUNCT
ejpam-3342	529	1	[	[	X
ejpam-3342	529	2	21	21	NUM
ejpam-3342	529	3	]	]	PUNCT
ejpam-3342	529	4	t.	t.	PROPN
ejpam-3342	529	5	l.	l.	PROPN
ejpam-3342	529	6	toh	toh	PROPN
ejpam-3342	529	7	and	and	CCONJ
ejpam-3342	529	8	t.	t.	PROPN
ejpam-3342	529	9	s.	s.	PROPN
ejpam-3342	529	10	chew	chew	VERB
ejpam-3342	529	11	.	.	PUNCT
ejpam-3342	530	1	the	the	DET
ejpam-3342	530	2	riemann	riemann	PROPN
ejpam-3342	530	3	approach	approach	NOUN
ejpam-3342	530	4	to	to	ADP
ejpam-3342	530	5	stochastic	stochastic	ADJ
ejpam-3342	530	6	integration	integration	NOUN
ejpam-3342	530	7	using	use	VERB
ejpam-3342	530	8	non	non	ADJ
ejpam-3342	530	9	-	-	ADJ
ejpam-3342	530	10	uniform	uniform	ADJ
ejpam-3342	530	11	meshes	mesh	NOUN
ejpam-3342	530	12	.	.	PUNCT
ejpam-3342	531	1	j.	j.	PROPN
ejpam-3342	531	2	math	math	PROPN
ejpam-3342	531	3	.	.	PUNCT
ejpam-3342	532	1	anal	anal	PROPN
ejpam-3342	532	2	.	.	PUNCT
ejpam-3342	533	1	appl	appl	PROPN
ejpam-3342	533	2	.	.	PROPN
ejpam-3342	533	3	,	,	PUNCT
ejpam-3342	533	4	280:133–147	280:133–147	NUM
ejpam-3342	533	5	,	,	PUNCT
ejpam-3342	533	6	2003	2003	NUM
ejpam-3342	533	7	.	.	PUNCT
ejpam-3342	534	1	[	[	X
ejpam-3342	534	2	22	22	NUM
ejpam-3342	534	3	]	]	PUNCT
ejpam-3342	534	4	t.	t.	PROPN
ejpam-3342	534	5	l.	l.	PROPN
ejpam-3342	534	6	toh	toh	PROPN
ejpam-3342	534	7	and	and	CCONJ
ejpam-3342	534	8	t.	t.	PROPN
ejpam-3342	534	9	s.	s.	PROPN
ejpam-3342	534	10	chew	chew	VERB
ejpam-3342	534	11	.	.	PUNCT
ejpam-3342	535	1	on	on	ADP
ejpam-3342	535	2	the	the	DET
ejpam-3342	535	3	henstock	henstock	NOUN
ejpam-3342	535	4	-	-	PUNCT
ejpam-3342	535	5	fubini	fubini	NOUN
ejpam-3342	535	6	theorem	theorem	NOUN
ejpam-3342	535	7	for	for	ADP
ejpam-3342	535	8	multiple	multiple	ADJ
ejpam-3342	535	9	stochastic	stochastic	ADJ
ejpam-3342	535	10	integrals	integral	NOUN
ejpam-3342	535	11	.	.	PUNCT
ejpam-3342	536	1	real	real	ADJ
ejpam-3342	536	2	anal	anal	PROPN
ejpam-3342	536	3	.	.	PUNCT
ejpam-3342	537	1	exchange	exchange	NOUN
ejpam-3342	537	2	,	,	PUNCT
ejpam-3342	537	3	30:295–310	30:295–310	NUM
ejpam-3342	537	4	,	,	PUNCT
ejpam-3342	537	5	2004	2004	NUM
ejpam-3342	537	6	-	-	SYM
ejpam-3342	537	7	2005	2005	NUM
ejpam-3342	537	8	.	.	PUNCT
ejpam-3342	538	1	[	[	X
ejpam-3342	538	2	23	23	NUM
ejpam-3342	538	3	]	]	PUNCT
ejpam-3342	538	4	t.	t.	PROPN
ejpam-3342	538	5	s.	s.	PROPN
ejpam-3342	538	6	chew	chew	VERB
ejpam-3342	538	7	t.	t.	PROPN
ejpam-3342	538	8	l.	l.	PROPN
ejpam-3342	538	9	toh	toh	PROPN
ejpam-3342	538	10	and	and	CCONJ
ejpam-3342	538	11	j.	j.	PROPN
ejpam-3342	538	12	y.	y.	PROPN
ejpam-3342	538	13	tay	tay	PROPN
ejpam-3342	538	14	.	.	PUNCT
ejpam-3342	539	1	the	the	DET
ejpam-3342	539	2	non	non	ADJ
ejpam-3342	539	3	-	-	ADJ
ejpam-3342	539	4	uniform	uniform	ADJ
ejpam-3342	539	5	riemann	riemann	PROPN
ejpam-3342	539	6	approach	approach	NOUN
ejpam-3342	539	7	to	to	ADP
ejpam-3342	539	8	itô	itô	PROPN
ejpam-3342	539	9	’s	’s	PART
ejpam-3342	539	10	integral	integral	ADJ
ejpam-3342	539	11	.	.	PUNCT
ejpam-3342	540	1	real	real	ADJ
ejpam-3342	540	2	anal	anal	PROPN
ejpam-3342	540	3	.	.	PUNCT
ejpam-3342	541	1	exchange	exchange	NOUN
ejpam-3342	541	2	,	,	PUNCT
ejpam-3342	541	3	27:495–514	27:495–514	NUM
ejpam-3342	541	4	,	,	PUNCT
ejpam-3342	541	5	2002	2002	NUM
ejpam-3342	541	6	-	-	SYM
ejpam-3342	541	7	2003	2003	NUM
ejpam-3342	541	8	.	.	PUNCT