id	sid	tid	token	lemma	pos
ejpam-4115	1	1	european	european	PROPN
ejpam-4115	1	2	journal	journal	PROPN
ejpam-4115	1	3	of	of	ADP
ejpam-4115	1	4	pure	pure	ADJ
ejpam-4115	1	5	and	and	CCONJ
ejpam-4115	1	6	applied	apply	VERB
ejpam-4115	1	7	mathematics	mathematic	NOUN
ejpam-4115	1	8	vol	vol	NOUN
ejpam-4115	1	9	.	.	PUNCT
ejpam-4115	2	1	14	14	NUM
ejpam-4115	2	2	,	,	PUNCT
ejpam-4115	2	3	no	no	INTJ
ejpam-4115	2	4	.	.	NOUN
ejpam-4115	2	5	4	4	NUM
ejpam-4115	2	6	,	,	PUNCT
ejpam-4115	2	7	2021	2021	NUM
ejpam-4115	2	8	,	,	PUNCT
ejpam-4115	2	9	1169	1169	NUM
ejpam-4115	2	10	-	-	SYM
ejpam-4115	2	11	1183	1183	NUM
ejpam-4115	2	12	issn	issn	PROPN
ejpam-4115	2	13	1307	1307	NUM
ejpam-4115	2	14	-	-	SYM
ejpam-4115	2	15	5543	5543	NUM
ejpam-4115	2	16	–	–	PUNCT
ejpam-4115	2	17	ejpam.com	ejpam.com	X
ejpam-4115	2	18	published	publish	VERB
ejpam-4115	2	19	by	by	ADP
ejpam-4115	2	20	new	new	PROPN
ejpam-4115	2	21	york	york	PROPN
ejpam-4115	2	22	business	business	PROPN
ejpam-4115	2	23	global	global	ADJ
ejpam-4115	2	24	denjoy	denjoy	NOUN
ejpam-4115	2	25	-	-	PUNCT
ejpam-4115	2	26	type	type	NOUN
ejpam-4115	2	27	integrals	integral	NOUN
ejpam-4115	2	28	in	in	ADP
ejpam-4115	2	29	locally	locally	ADV
ejpam-4115	2	30	convex	convex	ADJ
ejpam-4115	2	31	topological	topological	ADJ
ejpam-4115	2	32	vector	vector	NOUN
ejpam-4115	2	33	space	space	NOUN
ejpam-4115	2	34	rodolfo	rodolfo	PROPN
ejpam-4115	2	35	e.	e.	PROPN
ejpam-4115	2	36	maza1,∗	maza1,∗	PROPN
ejpam-4115	2	37	,	,	PUNCT
ejpam-4115	2	38	sergio	sergio	PROPN
ejpam-4115	2	39	r.	r.	PROPN
ejpam-4115	2	40	canoy	canoy	PROPN
ejpam-4115	2	41	,	,	PUNCT
ejpam-4115	2	42	jr	jr	PROPN
ejpam-4115	2	43	.	.	PROPN
ejpam-4115	2	44	1	1	NUM
ejpam-4115	2	45	department	department	NOUN
ejpam-4115	2	46	of	of	ADP
ejpam-4115	2	47	mathematics	mathematic	NOUN
ejpam-4115	2	48	and	and	CCONJ
ejpam-4115	2	49	statistics	statistic	NOUN
ejpam-4115	2	50	,	,	PUNCT
ejpam-4115	2	51	college	college	NOUN
ejpam-4115	2	52	of	of	ADP
ejpam-4115	2	53	science	science	NOUN
ejpam-4115	2	54	and	and	CCONJ
ejpam-4115	2	55	mathematics	mathematic	NOUN
ejpam-4115	2	56	,	,	PUNCT
ejpam-4115	2	57	msu	msu	PROPN
ejpam-4115	2	58	-	-	PUNCT
ejpam-4115	2	59	iit	iit	PROPN
ejpam-4115	2	60	,	,	PUNCT
ejpam-4115	2	61	iligan	iligan	ADJ
ejpam-4115	2	62	city	city	PROPN
ejpam-4115	2	63	9200	9200	NUM
ejpam-4115	2	64	,	,	PUNCT
ejpam-4115	3	1	philippines	philippine	NOUN
ejpam-4115	3	2	abstract	abstract	ADJ
ejpam-4115	3	3	.	.	PUNCT
ejpam-4115	4	1	in	in	ADP
ejpam-4115	4	2	this	this	DET
ejpam-4115	4	3	paper	paper	NOUN
ejpam-4115	4	4	,	,	PUNCT
ejpam-4115	4	5	we	we	PRON
ejpam-4115	4	6	introduce	introduce	VERB
ejpam-4115	4	7	ac∗	ac∗	ADJ
ejpam-4115	4	8	and	and	CCONJ
ejpam-4115	4	9	acg∗-type	acg∗-type	PROPN
ejpam-4115	4	10	properties	property	NOUN
ejpam-4115	4	11	and	and	CCONJ
ejpam-4115	4	12	then	then	ADV
ejpam-4115	4	13	,	,	PUNCT
ejpam-4115	4	14	using	use	VERB
ejpam-4115	4	15	these	these	DET
ejpam-4115	4	16	conditions	condition	NOUN
ejpam-4115	4	17	along	along	ADP
ejpam-4115	4	18	with	with	ADP
ejpam-4115	4	19	other	other	ADJ
ejpam-4115	4	20	concepts	concept	NOUN
ejpam-4115	4	21	,	,	PUNCT
ejpam-4115	4	22	define	define	VERB
ejpam-4115	4	23	two	two	NUM
ejpam-4115	4	24	denjoy	denjoy	NOUN
ejpam-4115	4	25	-	-	PUNCT
ejpam-4115	4	26	type	type	NOUN
ejpam-4115	4	27	integrals	integral	NOUN
ejpam-4115	4	28	of	of	ADP
ejpam-4115	4	29	a	a	DET
ejpam-4115	4	30	function	function	NOUN
ejpam-4115	4	31	with	with	ADP
ejpam-4115	4	32	values	value	NOUN
ejpam-4115	4	33	in	in	ADP
ejpam-4115	4	34	a	a	DET
ejpam-4115	4	35	locally	locally	ADV
ejpam-4115	4	36	convex	convex	ADJ
ejpam-4115	4	37	topological	topological	ADJ
ejpam-4115	4	38	vector	vector	NOUN
ejpam-4115	4	39	space	space	NOUN
ejpam-4115	4	40	(	(	PUNCT
ejpam-4115	4	41	lctvs	lctvs	PROPN
ejpam-4115	4	42	)	)	PUNCT
ejpam-4115	4	43	.	.	PUNCT
ejpam-4115	5	1	we	we	PRON
ejpam-4115	5	2	show	show	VERB
ejpam-4115	5	3	,	,	PUNCT
ejpam-4115	5	4	among	among	ADP
ejpam-4115	5	5	others	other	NOUN
ejpam-4115	5	6	,	,	PUNCT
ejpam-4115	5	7	that	that	SCONJ
ejpam-4115	5	8	these	these	DET
ejpam-4115	5	9	newly	newly	ADV
ejpam-4115	5	10	defined	define	VERB
ejpam-4115	5	11	integrals	integral	NOUN
ejpam-4115	5	12	are	be	AUX
ejpam-4115	5	13	included	include	VERB
ejpam-4115	5	14	in	in	ADP
ejpam-4115	5	15	the	the	DET
ejpam-4115	5	16	sh	sh	PROPN
ejpam-4115	5	17	integral	integral	ADJ
ejpam-4115	5	18	,	,	PUNCT
ejpam-4115	5	19	a	a	DET
ejpam-4115	5	20	version	version	NOUN
ejpam-4115	5	21	of	of	ADP
ejpam-4115	5	22	the	the	DET
ejpam-4115	5	23	henstock	henstock	NOUN
ejpam-4115	5	24	integral	integral	ADJ
ejpam-4115	5	25	,	,	PUNCT
ejpam-4115	5	26	for	for	ADP
ejpam-4115	5	27	lctvsvalued	lctvsvalue	VERB
ejpam-4115	5	28	functions	function	NOUN
ejpam-4115	5	29	.	.	PUNCT
ejpam-4115	6	1	2020	2020	NUM
ejpam-4115	6	2	mathematics	mathematic	NOUN
ejpam-4115	6	3	subject	subject	NOUN
ejpam-4115	6	4	classifications	classification	NOUN
ejpam-4115	6	5	:	:	PUNCT
ejpam-4115	6	6	46g12	46g12	NUM
ejpam-4115	6	7	,	,	PUNCT
ejpam-4115	6	8	46g05	46g05	NUM
ejpam-4115	6	9	,	,	PUNCT
ejpam-4115	6	10	28b05	28b05	NUM
ejpam-4115	6	11	key	key	ADJ
ejpam-4115	6	12	words	word	NOUN
ejpam-4115	6	13	and	and	CCONJ
ejpam-4115	6	14	phrases	phrase	NOUN
ejpam-4115	6	15	:	:	PUNCT
ejpam-4115	6	16	ac∗	ac∗	ADJ
ejpam-4115	6	17	,	,	PUNCT
ejpam-4115	6	18	acg∗	acg∗	PROPN
ejpam-4115	6	19	,	,	PUNCT
ejpam-4115	6	20	denjoy	denjoy	NOUN
ejpam-4115	6	21	integral	integral	ADJ
ejpam-4115	6	22	,	,	PUNCT
ejpam-4115	6	23	weak	weak	ADJ
ejpam-4115	6	24	denjoy	denjoy	NOUN
ejpam-4115	6	25	integral	integral	ADJ
ejpam-4115	6	26	,	,	PUNCT
ejpam-4115	6	27	sh	sh	PROPN
ejpam-4115	6	28	integral	integral	ADJ
ejpam-4115	6	29	1	1	NUM
ejpam-4115	6	30	.	.	PUNCT
ejpam-4115	6	31	introduction	introduction	NOUN
ejpam-4115	6	32	the	the	DET
ejpam-4115	6	33	henstock	henstock	NOUN
ejpam-4115	6	34	-	-	PUNCT
ejpam-4115	6	35	kurzweil	kurzweil	PROPN
ejpam-4115	6	36	(	(	PUNCT
ejpam-4115	6	37	hk	hk	PROPN
ejpam-4115	6	38	)	)	PUNCT
ejpam-4115	6	39	integral	integral	ADJ
ejpam-4115	6	40	,	,	PUNCT
ejpam-4115	6	41	developed	develop	VERB
ejpam-4115	6	42	independently	independently	ADV
ejpam-4115	6	43	by	by	ADP
ejpam-4115	6	44	ralph	ralph	PROPN
ejpam-4115	6	45	henstock	henstock	PROPN
ejpam-4115	6	46	and	and	CCONJ
ejpam-4115	6	47	jaroslav	jaroslav	PROPN
ejpam-4115	6	48	kurzweil	kurzweil	PROPN
ejpam-4115	6	49	,	,	PUNCT
ejpam-4115	6	50	is	be	AUX
ejpam-4115	6	51	known	know	VERB
ejpam-4115	6	52	to	to	PART
ejpam-4115	6	53	generalize	generalize	VERB
ejpam-4115	6	54	the	the	DET
ejpam-4115	6	55	lebesgue	lebesgue	NOUN
ejpam-4115	6	56	integral	integral	ADJ
ejpam-4115	6	57	.	.	PUNCT
ejpam-4115	7	1	this	this	DET
ejpam-4115	7	2	integral	integral	ADJ
ejpam-4115	7	3	uses	use	VERB
ejpam-4115	7	4	partitions	partition	NOUN
ejpam-4115	7	5	called	call	VERB
ejpam-4115	7	6	δ	δ	PROPN
ejpam-4115	7	7	-	-	PUNCT
ejpam-4115	7	8	fine	fine	ADJ
ejpam-4115	7	9	partitions	partition	NOUN
ejpam-4115	7	10	in	in	ADP
ejpam-4115	7	11	its	its	PRON
ejpam-4115	7	12	definition	definition	NOUN
ejpam-4115	7	13	making	make	VERB
ejpam-4115	7	14	it	it	PRON
ejpam-4115	7	15	a	a	DET
ejpam-4115	7	16	riemann	riemann	ADJ
ejpam-4115	7	17	-	-	PUNCT
ejpam-4115	7	18	type	type	NOUN
ejpam-4115	7	19	integral	integral	ADJ
ejpam-4115	7	20	.	.	PUNCT
ejpam-4115	8	1	thus	thus	ADV
ejpam-4115	8	2	,	,	PUNCT
ejpam-4115	8	3	the	the	DET
ejpam-4115	8	4	hk	hk	PROPN
ejpam-4115	8	5	integral	integral	NOUN
ejpam-4115	8	6	is	be	AUX
ejpam-4115	8	7	much	much	ADV
ejpam-4115	8	8	simpler	simple	ADJ
ejpam-4115	8	9	to	to	PART
ejpam-4115	8	10	deal	deal	VERB
ejpam-4115	8	11	with	with	ADP
ejpam-4115	8	12	than	than	ADP
ejpam-4115	8	13	the	the	DET
ejpam-4115	8	14	lebesgue	lebesgue	NOUN
ejpam-4115	8	15	integral	integral	ADJ
ejpam-4115	8	16	which	which	PRON
ejpam-4115	8	17	requires	require	VERB
ejpam-4115	8	18	a	a	DET
ejpam-4115	8	19	considerable	considerable	ADJ
ejpam-4115	8	20	understanding	understanding	NOUN
ejpam-4115	8	21	of	of	ADP
ejpam-4115	8	22	measure	measure	NOUN
ejpam-4115	8	23	theory	theory	NOUN
ejpam-4115	8	24	to	to	PART
ejpam-4115	8	25	fully	fully	ADV
ejpam-4115	8	26	grasp	grasp	VERB
ejpam-4115	8	27	its	its	PRON
ejpam-4115	8	28	definition	definition	NOUN
ejpam-4115	8	29	.	.	PUNCT
ejpam-4115	9	1	in	in	ADP
ejpam-4115	9	2	the	the	DET
ejpam-4115	9	3	real	real	ADV
ejpam-4115	9	4	-	-	PUNCT
ejpam-4115	9	5	valued	value	VERB
ejpam-4115	9	6	case	case	NOUN
ejpam-4115	9	7	,	,	PUNCT
ejpam-4115	9	8	the	the	DET
ejpam-4115	9	9	hk	hk	PROPN
ejpam-4115	9	10	integral	integral	NOUN
ejpam-4115	9	11	is	be	AUX
ejpam-4115	9	12	known	know	VERB
ejpam-4115	9	13	to	to	PART
ejpam-4115	9	14	satisfy	satisfy	VERB
ejpam-4115	9	15	henstock	henstock	PROPN
ejpam-4115	9	16	’s	’s	PART
ejpam-4115	9	17	lemma	lemma	PROPN
ejpam-4115	10	1	[	[	X
ejpam-4115	10	2	15	15	NUM
ejpam-4115	10	3	]	]	PUNCT
ejpam-4115	10	4	.	.	PUNCT
ejpam-4115	11	1	however	however	ADV
ejpam-4115	11	2	,	,	PUNCT
ejpam-4115	11	3	this	this	DET
ejpam-4115	11	4	property	property	NOUN
ejpam-4115	11	5	does	do	AUX
ejpam-4115	11	6	not	not	PART
ejpam-4115	11	7	necessarily	necessarily	ADV
ejpam-4115	11	8	hold	hold	VERB
ejpam-4115	11	9	in	in	ADP
ejpam-4115	11	10	the	the	DET
ejpam-4115	11	11	banach	banach	ADV
ejpam-4115	11	12	-	-	PUNCT
ejpam-4115	11	13	valued	value	VERB
ejpam-4115	11	14	case	case	NOUN
ejpam-4115	11	15	(	(	PUNCT
ejpam-4115	11	16	see	see	VERB
ejpam-4115	11	17	[	[	X
ejpam-4115	11	18	2	2	NUM
ejpam-4115	11	19	]	]	NUM
ejpam-4115	11	20	)	)	PUNCT
ejpam-4115	11	21	.	.	PUNCT
ejpam-4115	12	1	thus	thus	ADV
ejpam-4115	12	2	,	,	PUNCT
ejpam-4115	12	3	for	for	ADP
ejpam-4115	12	4	non	non	ADJ
ejpam-4115	12	5	-	-	ADJ
ejpam-4115	12	6	real	real	ADJ
ejpam-4115	12	7	-	-	PUNCT
ejpam-4115	12	8	valued	value	VERB
ejpam-4115	12	9	functions	function	NOUN
ejpam-4115	12	10	,	,	PUNCT
ejpam-4115	12	11	some	some	DET
ejpam-4115	12	12	stronger	strong	ADJ
ejpam-4115	12	13	versions	version	NOUN
ejpam-4115	12	14	of	of	ADP
ejpam-4115	12	15	the	the	DET
ejpam-4115	12	16	hk	hk	PROPN
ejpam-4115	12	17	integral	integral	NOUN
ejpam-4115	12	18	had	have	AUX
ejpam-4115	12	19	been	be	AUX
ejpam-4115	12	20	introduced	introduce	VERB
ejpam-4115	12	21	.	.	PUNCT
ejpam-4115	13	1	in	in	ADP
ejpam-4115	13	2	[	[	X
ejpam-4115	13	3	2	2	NUM
ejpam-4115	13	4	]	]	PUNCT
ejpam-4115	13	5	,	,	PUNCT
ejpam-4115	13	6	cao	cao	PROPN
ejpam-4115	13	7	defined	define	VERB
ejpam-4115	13	8	the	the	DET
ejpam-4115	13	9	hl	hl	NOUN
ejpam-4115	13	10	integral	integral	ADJ
ejpam-4115	13	11	for	for	ADP
ejpam-4115	13	12	banach	banach	ADV
ejpam-4115	13	13	-	-	PUNCT
ejpam-4115	13	14	valued	value	VERB
ejpam-4115	13	15	functions	function	NOUN
ejpam-4115	13	16	.	.	PUNCT
ejpam-4115	14	1	paluga	paluga	NOUN
ejpam-4115	14	2	and	and	CCONJ
ejpam-4115	14	3	canoy	canoy	ADJ
ejpam-4115	14	4	[	[	X
ejpam-4115	14	5	9	9	NUM
ejpam-4115	14	6	]	]	PUNCT
ejpam-4115	14	7	introduced	introduce	VERB
ejpam-4115	14	8	the	the	DET
ejpam-4115	14	9	henstock	henstock	NOUN
ejpam-4115	14	10	-	-	PUNCT
ejpam-4115	14	11	kurzweil	kurzweil	NOUN
ejpam-4115	14	12	(	(	PUNCT
ejpam-4115	14	13	hk	hk	PROPN
ejpam-4115	14	14	)	)	PUNCT
ejpam-4115	14	15	and	and	CCONJ
ejpam-4115	14	16	the	the	DET
ejpam-4115	14	17	sh	sh	PROPN
ejpam-4115	14	18	integrals	integral	NOUN
ejpam-4115	14	19	for	for	ADP
ejpam-4115	14	20	functions	function	NOUN
ejpam-4115	14	21	taking	take	VERB
ejpam-4115	14	22	values	value	NOUN
ejpam-4115	14	23	in	in	ADP
ejpam-4115	14	24	a	a	DET
ejpam-4115	14	25	topological	topological	ADJ
ejpam-4115	14	26	vector	vector	NOUN
ejpam-4115	14	27	space	space	NOUN
ejpam-4115	14	28	.	.	PUNCT
ejpam-4115	15	1	from	from	ADP
ejpam-4115	15	2	their	their	PRON
ejpam-4115	15	3	respective	respective	ADJ
ejpam-4115	15	4	definitions	definition	NOUN
ejpam-4115	15	5	,	,	PUNCT
ejpam-4115	15	6	it	it	PRON
ejpam-4115	15	7	is	be	AUX
ejpam-4115	15	8	clear	clear	ADJ
ejpam-4115	15	9	that	that	SCONJ
ejpam-4115	15	10	for	for	ADP
ejpam-4115	15	11	functions	function	NOUN
ejpam-4115	15	12	taking	take	VERB
ejpam-4115	15	13	values	value	NOUN
ejpam-4115	15	14	in	in	ADP
ejpam-4115	15	15	a	a	DET
ejpam-4115	15	16	locally	locally	ADV
ejpam-4115	15	17	convex	convex	ADJ
ejpam-4115	15	18	topological	topological	ADJ
ejpam-4115	15	19	vector	vector	NOUN
ejpam-4115	15	20	spaces	space	NOUN
ejpam-4115	15	21	,	,	PUNCT
ejpam-4115	15	22	the	the	DET
ejpam-4115	15	23	family	family	NOUN
ejpam-4115	15	24	of	of	ADP
ejpam-4115	15	25	sh	sh	PROPN
ejpam-4115	15	26	integrable	integrable	ADJ
ejpam-4115	15	27	functions	function	NOUN
ejpam-4115	15	28	is	be	AUX
ejpam-4115	15	29	contained	contain	VERB
ejpam-4115	15	30	in	in	ADP
ejpam-4115	15	31	the	the	DET
ejpam-4115	15	32	family	family	NOUN
ejpam-4115	15	33	of	of	ADP
ejpam-4115	15	34	hk	hk	PROPN
ejpam-4115	15	35	integrable	integrable	ADJ
ejpam-4115	15	36	functions	function	NOUN
ejpam-4115	15	37	(	(	PUNCT
ejpam-4115	15	38	see	see	VERB
ejpam-4115	15	39	[	[	X
ejpam-4115	15	40	9	9	NUM
ejpam-4115	15	41	]	]	NUM
ejpam-4115	15	42	)	)	PUNCT
ejpam-4115	15	43	.	.	PUNCT
ejpam-4115	16	1	for	for	ADP
ejpam-4115	16	2	functions	function	NOUN
ejpam-4115	16	3	with	with	ADP
ejpam-4115	16	4	values	value	NOUN
ejpam-4115	16	5	in	in	ADP
ejpam-4115	16	6	a	a	DET
ejpam-4115	16	7	locally	locally	ADV
ejpam-4115	16	8	convex	convex	ADJ
ejpam-4115	16	9	topological	topological	ADJ
ejpam-4115	16	10	vector	vector	NOUN
ejpam-4115	16	11	space	space	NOUN
ejpam-4115	16	12	(	(	PUNCT
ejpam-4115	16	13	lctvs	lctvs	PROPN
ejpam-4115	16	14	)	)	PUNCT
ejpam-4115	16	15	,	,	PUNCT
ejpam-4115	16	16	maza	maza	PROPN
ejpam-4115	16	17	et	et	PROPN
ejpam-4115	16	18	al	al	PROPN
ejpam-4115	16	19	.	.	PUNCT
ejpam-4115	17	1	[	[	X
ejpam-4115	17	2	6	6	NUM
ejpam-4115	17	3	]	]	PUNCT
ejpam-4115	17	4	recently	recently	ADV
ejpam-4115	17	5	defined	define	VERB
ejpam-4115	17	6	an	an	DET
ejpam-4115	17	7	sl	sl	NOUN
ejpam-4115	17	8	-	-	PUNCT
ejpam-4115	17	9	type	type	NOUN
ejpam-4115	17	10	integral	integral	ADJ
ejpam-4115	17	11	(	(	PUNCT
ejpam-4115	17	12	an	an	DET
ejpam-4115	17	13	integral	integral	ADJ
ejpam-4115	17	14	which	which	PRON
ejpam-4115	17	15	uses	use	VERB
ejpam-4115	17	16	a	a	DET
ejpam-4115	17	17	strong	strong	ADJ
ejpam-4115	17	18	-	-	PUNCT
ejpam-4115	17	19	lusin	lusin	NOUN
ejpam-4115	17	20	-	-	PUNCT
ejpam-4115	17	21	type	type	NOUN
ejpam-4115	17	22	condition	condition	NOUN
ejpam-4115	17	23	)	)	PUNCT
ejpam-4115	17	24	and	and	CCONJ
ejpam-4115	17	25	showed	show	VERB
ejpam-4115	17	26	that	that	SCONJ
ejpam-4115	17	27	this	this	DET
ejpam-4115	17	28	integral	integral	NOUN
ejpam-4115	17	29	is	be	AUX
ejpam-4115	17	30	equivalent	equivalent	ADJ
ejpam-4115	17	31	to	to	ADP
ejpam-4115	17	32	the	the	DET
ejpam-4115	17	33	sh	sh	PROPN
ejpam-4115	17	34	integral	integral	ADJ
ejpam-4115	17	35	.	.	PUNCT
ejpam-4115	18	1	∗corresponding	∗corresponde	VERB
ejpam-4115	18	2	author	author	NOUN
ejpam-4115	18	3	.	.	PUNCT
ejpam-4115	19	1	doi	doi	PROPN
ejpam-4115	19	2	:	:	PUNCT
ejpam-4115	19	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4115	https://doi.org/10.29020/nybg.ejpam.v14i4.4115	PROPN
ejpam-4115	19	4	email	email	NOUN
ejpam-4115	19	5	addresses	address	NOUN
ejpam-4115	19	6	:	:	PUNCT
ejpam-4115	19	7	rodolfo.maza@g.msuiit.edu.ph	rodolfo.maza@g.msuiit.edu.ph	PROPN
ejpam-4115	19	8	(	(	PUNCT
ejpam-4115	19	9	r.	r.	PROPN
ejpam-4115	19	10	maza	maza	PROPN
ejpam-4115	19	11	)	)	PUNCT
ejpam-4115	19	12	,	,	PUNCT
ejpam-4115	19	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4115	19	14	(	(	PUNCT
ejpam-4115	19	15	s.	s.	PROPN
ejpam-4115	19	16	canoy	canoy	PROPN
ejpam-4115	19	17	)	)	PUNCT
ejpam-4115	19	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4115	20	1	1169	1169	NUM
ejpam-4115	21	1	©	©	PROPN
ejpam-4115	21	2	2021	2021	NUM
ejpam-4115	21	3	ejpam	ejpam	VERB
ejpam-4115	21	4	all	all	DET
ejpam-4115	21	5	rights	right	NOUN
ejpam-4115	21	6	reserved	reserve	VERB
ejpam-4115	21	7	.	.	PUNCT
ejpam-4115	22	1	r.	r.	PROPN
ejpam-4115	22	2	e.	e.	PROPN
ejpam-4115	22	3	maza	maza	PROPN
ejpam-4115	22	4	,	,	PUNCT
ejpam-4115	22	5	s.	s.	PROPN
ejpam-4115	22	6	r.	r.	PROPN
ejpam-4115	22	7	canoy	canoy	PROPN
ejpam-4115	22	8	,	,	PUNCT
ejpam-4115	22	9	jr	jr	PROPN
ejpam-4115	22	10	.	.	PROPN
ejpam-4115	22	11	/	/	SYM
ejpam-4115	22	12	eur	eur	PROPN
ejpam-4115	22	13	.	.	PUNCT
ejpam-4115	23	1	j.	j.	PROPN
ejpam-4115	23	2	pure	pure	PROPN
ejpam-4115	23	3	appl	appl	PROPN
ejpam-4115	23	4	.	.	PROPN
ejpam-4115	23	5	math	math	PROPN
ejpam-4115	23	6	,	,	PUNCT
ejpam-4115	23	7	14	14	NUM
ejpam-4115	23	8	(	(	PUNCT
ejpam-4115	23	9	4	4	NUM
ejpam-4115	23	10	)	)	PUNCT
ejpam-4115	23	11	(	(	PUNCT
ejpam-4115	23	12	2021	2021	NUM
ejpam-4115	23	13	)	)	PUNCT
ejpam-4115	23	14	,	,	PUNCT
ejpam-4115	23	15	1169	1169	NUM
ejpam-4115	23	16	-	-	SYM
ejpam-4115	23	17	1183	1183	NUM
ejpam-4115	23	18	1170	1170	NUM
ejpam-4115	23	19	other	other	ADJ
ejpam-4115	23	20	concepts	concept	NOUN
ejpam-4115	23	21	that	that	PRON
ejpam-4115	23	22	also	also	ADV
ejpam-4115	23	23	played	play	VERB
ejpam-4115	23	24	important	important	ADJ
ejpam-4115	23	25	roles	role	NOUN
ejpam-4115	23	26	in	in	ADP
ejpam-4115	23	27	integration	integration	NOUN
ejpam-4115	23	28	theory	theory	NOUN
ejpam-4115	23	29	are	be	AUX
ejpam-4115	23	30	the	the	DET
ejpam-4115	23	31	ac∗	ac∗	ADJ
ejpam-4115	23	32	and	and	CCONJ
ejpam-4115	23	33	acg∗	acg∗	NOUN
ejpam-4115	23	34	properties	property	NOUN
ejpam-4115	23	35	.	.	PUNCT
ejpam-4115	24	1	the	the	DET
ejpam-4115	24	2	notion	notion	NOUN
ejpam-4115	24	3	of	of	ADP
ejpam-4115	24	4	acg∗	acg∗	NOUN
ejpam-4115	24	5	dates	date	VERB
ejpam-4115	24	6	back	back	ADV
ejpam-4115	24	7	to	to	ADP
ejpam-4115	24	8	lusin	lusin	NOUN
ejpam-4115	24	9	and	and	CCONJ
ejpam-4115	24	10	khintchine	khintchine	VERB
ejpam-4115	24	11	(	(	PUNCT
ejpam-4115	24	12	[	[	X
ejpam-4115	24	13	5	5	NUM
ejpam-4115	24	14	]	]	PUNCT
ejpam-4115	24	15	,	,	PUNCT
ejpam-4115	24	16	[	[	X
ejpam-4115	24	17	4	4	NUM
ejpam-4115	24	18	]	]	NUM
ejpam-4115	24	19	)	)	PUNCT
ejpam-4115	24	20	.	.	PUNCT
ejpam-4115	25	1	alternative	alternative	ADJ
ejpam-4115	25	2	definitions	definition	NOUN
ejpam-4115	25	3	of	of	ADP
ejpam-4115	25	4	ac∗	ac∗	ADJ
ejpam-4115	25	5	and	and	CCONJ
ejpam-4115	25	6	acg∗	acg∗	NOUN
ejpam-4115	25	7	are	be	AUX
ejpam-4115	25	8	given	give	VERB
ejpam-4115	25	9	by	by	ADP
ejpam-4115	25	10	lee	lee	PROPN
ejpam-4115	25	11	and	and	CCONJ
ejpam-4115	25	12	vyborney	vyborney	VERB
ejpam-4115	25	13	in	in	ADP
ejpam-4115	25	14	[	[	X
ejpam-4115	25	15	16	16	NUM
ejpam-4115	25	16	]	]	PUNCT
ejpam-4115	25	17	and	and	CCONJ
ejpam-4115	25	18	[	[	X
ejpam-4115	25	19	14	14	NUM
ejpam-4115	25	20	]	]	PUNCT
ejpam-4115	25	21	,	,	PUNCT
ejpam-4115	25	22	where	where	SCONJ
ejpam-4115	25	23	they	they	PRON
ejpam-4115	25	24	used	use	VERB
ejpam-4115	25	25	this	this	DET
ejpam-4115	25	26	slightly	slightly	ADV
ejpam-4115	25	27	modified	modify	VERB
ejpam-4115	25	28	definition	definition	NOUN
ejpam-4115	25	29	of	of	ADP
ejpam-4115	25	30	acg∗	acg∗	NOUN
ejpam-4115	25	31	to	to	PART
ejpam-4115	25	32	characterize	characterize	VERB
ejpam-4115	25	33	the	the	DET
ejpam-4115	25	34	hkintegral	hkintegral	NOUN
ejpam-4115	25	35	.	.	PUNCT
ejpam-4115	26	1	more	more	ADV
ejpam-4115	26	2	specifically	specifically	ADV
ejpam-4115	26	3	,	,	PUNCT
ejpam-4115	26	4	they	they	PRON
ejpam-4115	26	5	showed	show	VERB
ejpam-4115	26	6	that	that	SCONJ
ejpam-4115	26	7	a	a	DET
ejpam-4115	26	8	function	function	NOUN
ejpam-4115	26	9	f	f	NOUN
ejpam-4115	26	10	:	:	PUNCT
ejpam-4115	27	1	[	[	X
ejpam-4115	27	2	a	a	X
ejpam-4115	27	3	,	,	PUNCT
ejpam-4115	27	4	b	b	NOUN
ejpam-4115	27	5	]	]	X
ejpam-4115	27	6	→	→	PUNCT
ejpam-4115	27	7	r	r	NOUN
ejpam-4115	27	8	is	be	AUX
ejpam-4115	27	9	hk	hk	NOUN
ejpam-4115	27	10	-	-	PUNCT
ejpam-4115	27	11	integrable	integrable	ADJ
ejpam-4115	27	12	on	on	ADP
ejpam-4115	27	13	[	[	X
ejpam-4115	27	14	a	a	X
ejpam-4115	27	15	,	,	PUNCT
ejpam-4115	27	16	b	b	NOUN
ejpam-4115	27	17	]	]	X
ejpam-4115	27	18	if	if	SCONJ
ejpam-4115	27	19	and	and	CCONJ
ejpam-4115	27	20	only	only	ADV
ejpam-4115	27	21	if	if	SCONJ
ejpam-4115	27	22	there	there	PRON
ejpam-4115	27	23	exists	exist	VERB
ejpam-4115	27	24	an	an	DET
ejpam-4115	27	25	acg∗-function	acg∗-function	PROPN
ejpam-4115	27	26	on	on	ADP
ejpam-4115	27	27	[	[	X
ejpam-4115	27	28	a	a	DET
ejpam-4115	27	29	,	,	PUNCT
ejpam-4115	27	30	b	b	NOUN
ejpam-4115	27	31	]	]	X
ejpam-4115	27	32	such	such	ADJ
ejpam-4115	27	33	that	that	SCONJ
ejpam-4115	27	34	f	f	PROPN
ejpam-4115	27	35	′(t	′(t	PROPN
ejpam-4115	27	36	)	)	PUNCT
ejpam-4115	27	37	=	=	SYM
ejpam-4115	27	38	f(t	f(t	NOUN
ejpam-4115	27	39	)	)	PUNCT
ejpam-4115	27	40	almost	almost	ADV
ejpam-4115	27	41	everywhere	everywhere	ADV
ejpam-4115	27	42	.	.	PUNCT
ejpam-4115	28	1	in	in	ADP
ejpam-4115	28	2	1995	1995	NUM
ejpam-4115	28	3	,	,	PUNCT
ejpam-4115	28	4	following	follow	VERB
ejpam-4115	28	5	lee	lee	PROPN
ejpam-4115	28	6	’s	’s	PART
ejpam-4115	28	7	alternative	alternative	ADJ
ejpam-4115	28	8	definitions	definition	NOUN
ejpam-4115	28	9	of	of	ADP
ejpam-4115	28	10	ac∗	ac∗	ADJ
ejpam-4115	28	11	and	and	CCONJ
ejpam-4115	28	12	acg∗	acg∗	NOUN
ejpam-4115	28	13	,	,	PUNCT
ejpam-4115	28	14	canoy	canoy	NOUN
ejpam-4115	28	15	and	and	CCONJ
ejpam-4115	28	16	navarro	navarro	ADJ
ejpam-4115	28	17	[	[	X
ejpam-4115	28	18	1	1	X
ejpam-4115	28	19	]	]	PUNCT
ejpam-4115	28	20	defined	define	VERB
ejpam-4115	28	21	a	a	DET
ejpam-4115	28	22	denjoy	denjoy	NOUN
ejpam-4115	28	23	-	-	PUNCT
ejpam-4115	28	24	type	type	NOUN
ejpam-4115	28	25	integral	integral	ADJ
ejpam-4115	28	26	for	for	ADP
ejpam-4115	28	27	banach	banach	ADV
ejpam-4115	28	28	-	-	PUNCT
ejpam-4115	28	29	valued	value	VERB
ejpam-4115	28	30	functions	function	NOUN
ejpam-4115	28	31	and	and	CCONJ
ejpam-4115	28	32	in	in	ADP
ejpam-4115	28	33	1998	1998	NUM
ejpam-4115	28	34	skvortsov	skvortsov	NOUN
ejpam-4115	28	35	and	and	CCONJ
ejpam-4115	28	36	solodov	solodov	NOUN
ejpam-4115	29	1	[	[	X
ejpam-4115	29	2	12	12	NUM
ejpam-4115	29	3	]	]	PUNCT
ejpam-4115	29	4	adopted	adopt	VERB
ejpam-4115	29	5	such	such	ADJ
ejpam-4115	29	6	definition	definition	NOUN
ejpam-4115	29	7	and	and	CCONJ
ejpam-4115	29	8	called	call	VERB
ejpam-4115	29	9	that	that	PRON
ejpam-4115	29	10	integral	integral	ADJ
ejpam-4115	29	11	the	the	DET
ejpam-4115	29	12	denjoy	denjoy	NOUN
ejpam-4115	29	13	-	-	PUNCT
ejpam-4115	29	14	bochner	bochner	NOUN
ejpam-4115	29	15	integral	integral	ADJ
ejpam-4115	29	16	.	.	PUNCT
ejpam-4115	30	1	in	in	ADP
ejpam-4115	30	2	this	this	DET
ejpam-4115	30	3	paper	paper	NOUN
ejpam-4115	30	4	,	,	PUNCT
ejpam-4115	30	5	following	follow	VERB
ejpam-4115	30	6	these	these	DET
ejpam-4115	30	7	earlier	early	ADJ
ejpam-4115	30	8	definitions	definition	NOUN
ejpam-4115	30	9	,	,	PUNCT
ejpam-4115	30	10	we	we	PRON
ejpam-4115	30	11	introduce	introduce	VERB
ejpam-4115	30	12	ac∗	ac∗	ADJ
ejpam-4115	30	13	and	and	CCONJ
ejpam-4115	30	14	acg∗-type	acg∗-type	PROPN
ejpam-4115	30	15	properties	property	NOUN
ejpam-4115	30	16	for	for	ADP
ejpam-4115	30	17	lctvs	lctv	NOUN
ejpam-4115	30	18	-	-	PUNCT
ejpam-4115	30	19	valued	value	VERB
ejpam-4115	30	20	functions	function	NOUN
ejpam-4115	30	21	and	and	CCONJ
ejpam-4115	30	22	,	,	PUNCT
ejpam-4115	30	23	subsequently	subsequently	ADV
ejpam-4115	30	24	,	,	PUNCT
ejpam-4115	30	25	define	define	VERB
ejpam-4115	30	26	two	two	NUM
ejpam-4115	30	27	denjoy	denjoy	NOUN
ejpam-4115	30	28	-	-	PUNCT
ejpam-4115	30	29	type	type	NOUN
ejpam-4115	30	30	integrals	integral	NOUN
ejpam-4115	30	31	.	.	PUNCT
ejpam-4115	31	1	further	far	ADV
ejpam-4115	31	2	,	,	PUNCT
ejpam-4115	31	3	we	we	PRON
ejpam-4115	31	4	show	show	VERB
ejpam-4115	31	5	among	among	ADP
ejpam-4115	31	6	others	other	NOUN
ejpam-4115	31	7	,	,	PUNCT
ejpam-4115	31	8	that	that	SCONJ
ejpam-4115	31	9	one	one	NUM
ejpam-4115	31	10	of	of	ADP
ejpam-4115	31	11	these	these	DET
ejpam-4115	31	12	integrals	integral	NOUN
ejpam-4115	31	13	is	be	AUX
ejpam-4115	31	14	included	include	VERB
ejpam-4115	31	15	in	in	ADP
ejpam-4115	31	16	the	the	DET
ejpam-4115	31	17	other	other	ADJ
ejpam-4115	31	18	and	and	CCONJ
ejpam-4115	31	19	that	that	SCONJ
ejpam-4115	31	20	both	both	PRON
ejpam-4115	31	21	are	be	AUX
ejpam-4115	31	22	included	include	VERB
ejpam-4115	31	23	in	in	ADP
ejpam-4115	31	24	the	the	DET
ejpam-4115	31	25	sh	sh	NOUN
ejpam-4115	31	26	-	-	PUNCT
ejpam-4115	31	27	integral	integral	ADJ
ejpam-4115	31	28	.	.	PUNCT
ejpam-4115	32	1	it	it	PRON
ejpam-4115	32	2	is	be	AUX
ejpam-4115	32	3	shown	show	VERB
ejpam-4115	32	4	that	that	SCONJ
ejpam-4115	32	5	for	for	ADP
ejpam-4115	32	6	functions	function	NOUN
ejpam-4115	32	7	taking	take	VERB
ejpam-4115	32	8	values	value	NOUN
ejpam-4115	32	9	in	in	ADP
ejpam-4115	32	10	a	a	DET
ejpam-4115	32	11	banach	banach	NOUN
ejpam-4115	32	12	space	space	NOUN
ejpam-4115	32	13	,	,	PUNCT
ejpam-4115	32	14	every	every	DET
ejpam-4115	32	15	denjoy	denjoy	NOUN
ejpam-4115	32	16	-	-	PUNCT
ejpam-4115	32	17	bochner	bochner	NOUN
ejpam-4115	32	18	integrable	integrable	ADJ
ejpam-4115	32	19	function	function	NOUN
ejpam-4115	32	20	is	be	AUX
ejpam-4115	32	21	denjoy	denjoy	VERB
ejpam-4115	32	22	integrable	integrable	ADJ
ejpam-4115	32	23	.	.	PUNCT
ejpam-4115	33	1	recall	recall	VERB
ejpam-4115	33	2	that	that	SCONJ
ejpam-4115	33	3	a	a	DET
ejpam-4115	33	4	topological	topological	ADJ
ejpam-4115	33	5	vector	vector	NOUN
ejpam-4115	33	6	space	space	NOUN
ejpam-4115	33	7	x	x	PUNCT
ejpam-4115	33	8	is	be	AUX
ejpam-4115	33	9	a	a	DET
ejpam-4115	33	10	real	real	ADJ
ejpam-4115	33	11	vector	vector	NOUN
ejpam-4115	33	12	space	space	NOUN
ejpam-4115	33	13	together	together	ADV
ejpam-4115	33	14	with	with	ADP
ejpam-4115	33	15	a	a	DET
ejpam-4115	33	16	hausdorff	hausdorff	NOUN
ejpam-4115	33	17	topology	topology	NOUN
ejpam-4115	33	18	τ	τ	PROPN
ejpam-4115	33	19	such	such	ADJ
ejpam-4115	33	20	that	that	SCONJ
ejpam-4115	33	21	the	the	DET
ejpam-4115	33	22	scalar	scalar	ADJ
ejpam-4115	33	23	multiplication	multiplication	NOUN
ejpam-4115	33	24	and	and	CCONJ
ejpam-4115	33	25	the	the	DET
ejpam-4115	33	26	vector	vector	NOUN
ejpam-4115	33	27	addition	addition	NOUN
ejpam-4115	33	28	associated	associate	VERB
ejpam-4115	33	29	with	with	ADP
ejpam-4115	33	30	x	x	PUNCT
ejpam-4115	33	31	are	be	AUX
ejpam-4115	33	32	continuous	continuous	ADJ
ejpam-4115	33	33	with	with	ADP
ejpam-4115	33	34	respect	respect	NOUN
ejpam-4115	33	35	to	to	ADP
ejpam-4115	33	36	τ	τ	PROPN
ejpam-4115	33	37	(	(	PUNCT
ejpam-4115	33	38	see	see	VERB
ejpam-4115	33	39	[	[	X
ejpam-4115	33	40	10	10	NUM
ejpam-4115	33	41	]	]	NUM
ejpam-4115	33	42	)	)	PUNCT
ejpam-4115	33	43	.	.	PUNCT
ejpam-4115	34	1	continuity	continuity	NOUN
ejpam-4115	34	2	of	of	ADP
ejpam-4115	34	3	the	the	DET
ejpam-4115	34	4	vector	vector	NOUN
ejpam-4115	34	5	addition	addition	NOUN
ejpam-4115	34	6	would	would	AUX
ejpam-4115	34	7	then	then	ADV
ejpam-4115	34	8	imply	imply	VERB
ejpam-4115	34	9	that	that	SCONJ
ejpam-4115	34	10	for	for	ADP
ejpam-4115	34	11	every	every	DET
ejpam-4115	34	12	open	open	ADJ
ejpam-4115	34	13	set	set	NOUN
ejpam-4115	34	14	u	u	NOUN
ejpam-4115	34	15	,	,	PUNCT
ejpam-4115	34	16	there	there	PRON
ejpam-4115	34	17	are	be	VERB
ejpam-4115	34	18	open	open	ADJ
ejpam-4115	34	19	sets	set	NOUN
ejpam-4115	34	20	v1	v1	VERB
ejpam-4115	34	21	and	and	CCONJ
ejpam-4115	34	22	v2	v2	VERB
ejpam-4115	34	23	such	such	ADJ
ejpam-4115	34	24	that	that	DET
ejpam-4115	34	25	v1	v1	NOUN
ejpam-4115	34	26	+	+	CCONJ
ejpam-4115	34	27	v2	v2	PROPN
ejpam-4115	34	28	⊆	⊆	NUM
ejpam-4115	34	29	u	u	NOUN
ejpam-4115	34	30	.	.	PUNCT
ejpam-4115	35	1	more	more	ADV
ejpam-4115	35	2	generally	generally	ADV
ejpam-4115	35	3	,	,	PUNCT
ejpam-4115	35	4	for	for	ADP
ejpam-4115	35	5	every	every	DET
ejpam-4115	35	6	θ	θ	PROPN
ejpam-4115	35	7	-	-	PUNCT
ejpam-4115	35	8	nbd	nbd	PROPN
ejpam-4115	35	9	u	u	PROPN
ejpam-4115	35	10	(	(	PUNCT
ejpam-4115	35	11	an	an	DET
ejpam-4115	35	12	open	open	ADJ
ejpam-4115	35	13	set	set	NOUN
ejpam-4115	35	14	containing	contain	VERB
ejpam-4115	35	15	the	the	DET
ejpam-4115	35	16	zero	zero	NUM
ejpam-4115	35	17	vector	vector	NOUN
ejpam-4115	35	18	θ	θ	PROPN
ejpam-4115	35	19	of	of	ADP
ejpam-4115	35	20	x	x	NOUN
ejpam-4115	35	21	)	)	PUNCT
ejpam-4115	35	22	and	and	CCONJ
ejpam-4115	35	23	n	n	PRON
ejpam-4115	35	24	∈	∈	PROPN
ejpam-4115	35	25	n	n	CCONJ
ejpam-4115	35	26	there	there	PRON
ejpam-4115	35	27	are	be	VERB
ejpam-4115	35	28	θ	θ	ADJ
ejpam-4115	35	29	-	-	PUNCT
ejpam-4115	35	30	nbds	nbds	NOUN
ejpam-4115	35	31	v1	v1	NOUN
ejpam-4115	35	32	,	,	PUNCT
ejpam-4115	35	33	v2	v2	NOUN
ejpam-4115	35	34	,	,	PUNCT
ejpam-4115	35	35	.	.	PUNCT
ejpam-4115	35	36	.	.	PUNCT
ejpam-4115	36	1	.	.	PUNCT
ejpam-4115	37	1	,	,	PUNCT
ejpam-4115	37	2	vn	vn	VERB
ejpam-4115	37	3	such	such	ADJ
ejpam-4115	37	4	that	that	DET
ejpam-4115	37	5	v1	v1	NOUN
ejpam-4115	37	6	+	+	X
ejpam-4115	37	7	v2	v2	X
ejpam-4115	37	8	+	+	X
ejpam-4115	37	9	·	·	PUNCT
ejpam-4115	37	10	·	·	PUNCT
ejpam-4115	37	11	·	·	PUNCT
ejpam-4115	38	1	+	+	NUM
ejpam-4115	38	2	vn	vn	VERB
ejpam-4115	38	3	⊆	⊆	NUM
ejpam-4115	38	4	u	u	NOUN
ejpam-4115	38	5	(	(	PUNCT
ejpam-4115	38	6	see	see	VERB
ejpam-4115	38	7	[	[	X
ejpam-4115	38	8	3	3	X
ejpam-4115	38	9	]	]	PUNCT
ejpam-4115	38	10	and	and	CCONJ
ejpam-4115	38	11	[	[	X
ejpam-4115	38	12	10	10	NUM
ejpam-4115	38	13	]	]	NUM
ejpam-4115	38	14	)	)	PUNCT
ejpam-4115	38	15	.	.	PUNCT
ejpam-4115	39	1	given	give	VERB
ejpam-4115	39	2	two	two	NUM
ejpam-4115	39	3	topological	topological	ADJ
ejpam-4115	39	4	spaces	space	NOUN
ejpam-4115	39	5	x	x	PUNCT
ejpam-4115	39	6	and	and	CCONJ
ejpam-4115	39	7	y	y	PROPN
ejpam-4115	39	8	,	,	PUNCT
ejpam-4115	39	9	a	a	DET
ejpam-4115	39	10	function	function	NOUN
ejpam-4115	39	11	f	f	NOUN
ejpam-4115	39	12	:	:	PUNCT
ejpam-4115	39	13	x	x	X
ejpam-4115	39	14	→	→	SYM
ejpam-4115	39	15	y	y	PROPN
ejpam-4115	39	16	is	be	AUX
ejpam-4115	39	17	continuous	continuous	ADJ
ejpam-4115	39	18	if	if	SCONJ
ejpam-4115	39	19	f−1(u	f−1(u	NOUN
ejpam-4115	39	20	)	)	PUNCT
ejpam-4115	39	21	is	be	AUX
ejpam-4115	39	22	open	open	ADJ
ejpam-4115	39	23	in	in	ADP
ejpam-4115	39	24	x	x	X
ejpam-4115	39	25	whenever	whenever	SCONJ
ejpam-4115	39	26	u	u	NOUN
ejpam-4115	39	27	is	be	AUX
ejpam-4115	39	28	open	open	ADJ
ejpam-4115	39	29	in	in	ADP
ejpam-4115	39	30	y	y	PROPN
ejpam-4115	40	1	[	[	X
ejpam-4115	40	2	3	3	NUM
ejpam-4115	40	3	]	]	PUNCT
ejpam-4115	40	4	.	.	PUNCT
ejpam-4115	41	1	a	a	DET
ejpam-4115	41	2	set	set	NOUN
ejpam-4115	41	3	a	a	DET
ejpam-4115	41	4	⊆	⊆	NUM
ejpam-4115	41	5	x	x	SYM
ejpam-4115	41	6	,	,	PUNCT
ejpam-4115	41	7	where	where	SCONJ
ejpam-4115	41	8	x	x	PRON
ejpam-4115	41	9	is	be	AUX
ejpam-4115	41	10	a	a	DET
ejpam-4115	41	11	topological	topological	ADJ
ejpam-4115	41	12	vector	vector	NOUN
ejpam-4115	41	13	space	space	NOUN
ejpam-4115	41	14	,	,	PUNCT
ejpam-4115	41	15	is	be	AUX
ejpam-4115	41	16	absorbing	absorb	VERB
ejpam-4115	41	17	if	if	SCONJ
ejpam-4115	41	18	for	for	ADP
ejpam-4115	41	19	every	every	DET
ejpam-4115	41	20	x	x	SYM
ejpam-4115	41	21	∈	∈	PROPN
ejpam-4115	41	22	x	x	NOUN
ejpam-4115	41	23	,	,	PUNCT
ejpam-4115	41	24	there	there	PRON
ejpam-4115	41	25	exists	exist	VERB
ejpam-4115	41	26	t	t	PROPN
ejpam-4115	41	27	>	>	X
ejpam-4115	41	28	0	0	NUM
ejpam-4115	42	1	such	such	ADJ
ejpam-4115	42	2	that	that	SCONJ
ejpam-4115	42	3	x	x	SYM
ejpam-4115	42	4	∈	∈	PROPN
ejpam-4115	42	5	ta	ta	PROPN
ejpam-4115	42	6	;	;	PUNCT
ejpam-4115	42	7	it	it	PRON
ejpam-4115	42	8	is	be	AUX
ejpam-4115	42	9	convex	convex	ADJ
ejpam-4115	42	10	if	if	SCONJ
ejpam-4115	42	11	for	for	ADP
ejpam-4115	42	12	every	every	DET
ejpam-4115	42	13	x	x	NOUN
ejpam-4115	42	14	,	,	PUNCT
ejpam-4115	42	15	y	y	PROPN
ejpam-4115	42	16	∈	∈	PROPN
ejpam-4115	42	17	a	a	PRON
ejpam-4115	42	18	and	and	CCONJ
ejpam-4115	42	19	0	0	NUM
ejpam-4115	42	20	≤	≤	NOUN
ejpam-4115	42	21	t	t	NOUN
ejpam-4115	42	22	≤	≤	NUM
ejpam-4115	42	23	1	1	NUM
ejpam-4115	42	24	,	,	PUNCT
ejpam-4115	42	25	tx+(1−	tx+(1−	PROPN
ejpam-4115	42	26	t)y	t)y	NOUN
ejpam-4115	42	27	∈	∈	PROPN
ejpam-4115	42	28	a	a	NOUN
ejpam-4115	42	29	;	;	PUNCT
ejpam-4115	42	30	it	it	PRON
ejpam-4115	42	31	is	be	AUX
ejpam-4115	42	32	balanced	balanced	ADJ
ejpam-4115	42	33	if	if	SCONJ
ejpam-4115	42	34	αa	αa	PROPN
ejpam-4115	42	35	⊆	⊆	NUM
ejpam-4115	42	36	a	a	PRON
ejpam-4115	42	37	for	for	ADP
ejpam-4115	42	38	every	every	DET
ejpam-4115	42	39	|α|	|α|	PROPN
ejpam-4115	42	40	≤	≤	NOUN
ejpam-4115	42	41	1	1	NUM
ejpam-4115	42	42	.	.	PUNCT
ejpam-4115	43	1	a	a	DET
ejpam-4115	43	2	sequence	sequence	NOUN
ejpam-4115	43	3	⟨ri⟩ni=1	⟨ri⟩ni=1	INTJ
ejpam-4115	43	4	of	of	ADP
ejpam-4115	43	5	positive	positive	ADJ
ejpam-4115	43	6	real	real	ADJ
ejpam-4115	43	7	numbers	number	NOUN
ejpam-4115	43	8	is	be	AUX
ejpam-4115	43	9	unitary	unitary	ADJ
ejpam-4115	43	10	if	if	SCONJ
ejpam-4115	43	11	∑n	∑n	PROPN
ejpam-4115	43	12	i=1	i=1	PROPN
ejpam-4115	43	13	ri	ri	PROPN
ejpam-4115	44	1	=	=	NOUN
ejpam-4115	44	2	1	1	X
ejpam-4115	44	3	.	.	PUNCT
ejpam-4115	45	1	a	a	DET
ejpam-4115	45	2	set	set	NOUN
ejpam-4115	45	3	a	a	PRON
ejpam-4115	45	4	is	be	AUX
ejpam-4115	45	5	convex	convex	ADJ
ejpam-4115	45	6	if	if	SCONJ
ejpam-4115	45	7	for	for	ADP
ejpam-4115	45	8	every	every	DET
ejpam-4115	45	9	unitary	unitary	ADJ
ejpam-4115	45	10	sequence	sequence	NOUN
ejpam-4115	45	11	⟨ri⟩ni=1	⟨ri⟩ni=1	PROPN
ejpam-4115	45	12	,	,	PUNCT
ejpam-4115	45	13	we	we	PRON
ejpam-4115	45	14	have	have	VERB
ejpam-4115	45	15	∑n	∑n	PROPN
ejpam-4115	45	16	i=1	i=1	PROPN
ejpam-4115	45	17	(	(	PUNCT
ejpam-4115	45	18	ria	ria	PROPN
ejpam-4115	45	19	)	)	PUNCT
ejpam-4115	45	20	⊆	⊆	NUM
ejpam-4115	45	21	a.	a.	NOUN
ejpam-4115	45	22	a	a	DET
ejpam-4115	45	23	topological	topological	ADJ
ejpam-4115	45	24	vector	vector	NOUN
ejpam-4115	45	25	space	space	NOUN
ejpam-4115	45	26	x	x	PRON
ejpam-4115	45	27	is	be	AUX
ejpam-4115	45	28	said	say	VERB
ejpam-4115	45	29	to	to	PART
ejpam-4115	45	30	be	be	AUX
ejpam-4115	45	31	locally	locally	ADV
ejpam-4115	45	32	convex	convex	ADJ
ejpam-4115	45	33	if	if	SCONJ
ejpam-4115	45	34	there	there	PRON
ejpam-4115	45	35	is	be	VERB
ejpam-4115	45	36	a	a	DET
ejpam-4115	45	37	local	local	ADJ
ejpam-4115	45	38	base	base	NOUN
ejpam-4115	45	39	consisting	consist	VERB
ejpam-4115	45	40	of	of	ADP
ejpam-4115	45	41	convex	convex	NOUN
ejpam-4115	45	42	sets	set	NOUN
ejpam-4115	45	43	in	in	ADP
ejpam-4115	45	44	x.	x.	NOUN
ejpam-4115	45	45	it	it	PRON
ejpam-4115	45	46	is	be	AUX
ejpam-4115	45	47	known	know	VERB
ejpam-4115	45	48	that	that	SCONJ
ejpam-4115	45	49	every	every	DET
ejpam-4115	45	50	locally	locally	ADV
ejpam-4115	45	51	convex	convex	ADJ
ejpam-4115	45	52	topological	topological	ADJ
ejpam-4115	45	53	vector	vector	NOUN
ejpam-4115	45	54	space	space	NOUN
ejpam-4115	45	55	has	have	VERB
ejpam-4115	45	56	a	a	DET
ejpam-4115	45	57	local	local	ADJ
ejpam-4115	45	58	base	base	NOUN
ejpam-4115	45	59	at	at	ADP
ejpam-4115	45	60	θ	θ	PROPN
ejpam-4115	45	61	consisting	consist	VERB
ejpam-4115	45	62	of	of	ADP
ejpam-4115	45	63	absorbing	absorbing	ADJ
ejpam-4115	45	64	,	,	PUNCT
ejpam-4115	45	65	balanced	balanced	ADJ
ejpam-4115	45	66	,	,	PUNCT
ejpam-4115	45	67	and	and	CCONJ
ejpam-4115	45	68	convex	convex	NOUN
ejpam-4115	45	69	sets	set	NOUN
ejpam-4115	45	70	.	.	PUNCT
ejpam-4115	46	1	a	a	DET
ejpam-4115	46	2	function	function	NOUN
ejpam-4115	46	3	ρ	ρ	NOUN
ejpam-4115	46	4	:	:	PUNCT
ejpam-4115	46	5	x	x	X
ejpam-4115	46	6	→	→	SYM
ejpam-4115	46	7	r	r	NOUN
ejpam-4115	46	8	is	be	AUX
ejpam-4115	46	9	a	a	DET
ejpam-4115	46	10	seminorm	seminorm	NOUN
ejpam-4115	46	11	if	if	SCONJ
ejpam-4115	46	12	for	for	ADP
ejpam-4115	46	13	all	all	DET
ejpam-4115	46	14	u	u	NOUN
ejpam-4115	46	15	,	,	PUNCT
ejpam-4115	46	16	v	v	NOUN
ejpam-4115	46	17	∈	∈	NOUN
ejpam-4115	46	18	x	x	X
ejpam-4115	46	19	and	and	CCONJ
ejpam-4115	46	20	k	k	PROPN
ejpam-4115	46	21	∈	∈	PROPN
ejpam-4115	46	22	r	r	NOUN
ejpam-4115	46	23	,	,	PUNCT
ejpam-4115	46	24	we	we	PRON
ejpam-4115	46	25	have	have	VERB
ejpam-4115	46	26	(	(	PUNCT
ejpam-4115	46	27	i	i	NOUN
ejpam-4115	46	28	)	)	PUNCT
ejpam-4115	46	29	(	(	PUNCT
ejpam-4115	46	30	sub	sub	NOUN
ejpam-4115	46	31	-	-	NOUN
ejpam-4115	46	32	additivity	additivity	ADJ
ejpam-4115	46	33	)	)	PUNCT
ejpam-4115	46	34	ρ(u+	ρ(u+	NOUN
ejpam-4115	46	35	v	v	NOUN
ejpam-4115	46	36	)	)	PUNCT
ejpam-4115	46	37	≤	≤	NOUN
ejpam-4115	46	38	ρ(u	ρ(u	NUM
ejpam-4115	46	39	)	)	PUNCT
ejpam-4115	47	1	+	+	CCONJ
ejpam-4115	47	2	ρ(v	ρ(v	PROPN
ejpam-4115	47	3	)	)	PUNCT
ejpam-4115	47	4	and	and	CCONJ
ejpam-4115	47	5	(	(	PUNCT
ejpam-4115	47	6	ii	ii	NOUN
ejpam-4115	47	7	)	)	PUNCT
ejpam-4115	47	8	(	(	PUNCT
ejpam-4115	47	9	absolute	absolute	ADJ
ejpam-4115	47	10	homogene.ity	homogene.ity	NOUN
ejpam-4115	47	11	)	)	PUNCT
ejpam-4115	47	12	ρ(ku	ρ(ku	PROPN
ejpam-4115	47	13	)	)	PUNCT
ejpam-4115	48	1	=	=	SYM
ejpam-4115	48	2	|k|ρ(u	|k|ρ(u	PROPN
ejpam-4115	48	3	)	)	PUNCT
ejpam-4115	48	4	.	.	PUNCT
ejpam-4115	49	1	a	a	DET
ejpam-4115	49	2	family	family	NOUN
ejpam-4115	49	3	of	of	ADP
ejpam-4115	49	4	seminorms	seminorm	NOUN
ejpam-4115	49	5	{	{	PUNCT
ejpam-4115	49	6	ρα}α	ρα}α	VERB
ejpam-4115	49	7	is	be	AUX
ejpam-4115	49	8	called	call	VERB
ejpam-4115	49	9	separated	separated	ADJ
ejpam-4115	49	10	(	(	PUNCT
ejpam-4115	49	11	or	or	CCONJ
ejpam-4115	49	12	separating	separate	VERB
ejpam-4115	49	13	)	)	PUNCT
ejpam-4115	49	14	if	if	SCONJ
ejpam-4115	49	15	whenever	whenever	SCONJ
ejpam-4115	49	16	ρα(x	ρα(x	NOUN
ejpam-4115	49	17	)	)	PUNCT
ejpam-4115	49	18	=	=	SYM
ejpam-4115	49	19	0	0	NUM
ejpam-4115	49	20	holds	hold	VERB
ejpam-4115	49	21	for	for	ADP
ejpam-4115	49	22	all	all	DET
ejpam-4115	49	23	α	α	NOUN
ejpam-4115	49	24	,	,	PUNCT
ejpam-4115	49	25	then	then	ADV
ejpam-4115	49	26	x	x	PUNCT
ejpam-4115	49	27	is	be	AUX
ejpam-4115	49	28	necessarily	necessarily	ADV
ejpam-4115	49	29	the	the	DET
ejpam-4115	49	30	zero	zero	NUM
ejpam-4115	49	31	vector	vector	NOUN
ejpam-4115	49	32	θ	θ	PROPN
ejpam-4115	49	33	.	.	PROPN
ejpam-4115	49	34	for	for	ADP
ejpam-4115	49	35	a	a	DET
ejpam-4115	49	36	given	give	VERB
ejpam-4115	49	37	absorbing	absorbing	NOUN
ejpam-4115	49	38	set	set	VERB
ejpam-4115	49	39	a	a	DET
ejpam-4115	49	40	⊆	⊆	NUM
ejpam-4115	49	41	x	x	NOUN
ejpam-4115	49	42	,	,	PUNCT
ejpam-4115	49	43	the	the	DET
ejpam-4115	49	44	minkowski	minkowski	ADJ
ejpam-4115	49	45	functional	functional	NOUN
ejpam-4115	49	46	of	of	ADP
ejpam-4115	49	47	a	a	DET
ejpam-4115	49	48	on	on	NOUN
ejpam-4115	49	49	x	x	VERB
ejpam-4115	49	50	is	be	AUX
ejpam-4115	49	51	defined	define	VERB
ejpam-4115	49	52	by	by	ADP
ejpam-4115	49	53	φa(x	φa(x	NOUN
ejpam-4115	49	54	)	)	PUNCT
ejpam-4115	49	55	=	=	SYM
ejpam-4115	49	56	inf{λ	inf{λ	X
ejpam-4115	49	57	>	>	X
ejpam-4115	49	58	0	0	NUM
ejpam-4115	50	1	:	:	PUNCT
ejpam-4115	50	2	x	x	X
ejpam-4115	50	3	∈	∈	PROPN
ejpam-4115	50	4	λa	λa	X
ejpam-4115	50	5	}	}	PUNCT
ejpam-4115	50	6	for	for	ADP
ejpam-4115	50	7	every	every	DET
ejpam-4115	50	8	x	x	SYM
ejpam-4115	50	9	∈	∈	PROPN
ejpam-4115	50	10	x.	x.	NOUN
ejpam-4115	51	1	if	if	SCONJ
ejpam-4115	51	2	u	u	PROPN
ejpam-4115	51	3	⊆	⊆	NUM
ejpam-4115	51	4	x	x	X
ejpam-4115	51	5	is	be	AUX
ejpam-4115	51	6	a	a	DET
ejpam-4115	51	7	balanced	balanced	ADJ
ejpam-4115	51	8	,	,	PUNCT
ejpam-4115	51	9	absorbing	absorb	VERB
ejpam-4115	51	10	and	and	CCONJ
ejpam-4115	51	11	convex	convex	NOUN
ejpam-4115	51	12	set	set	NOUN
ejpam-4115	51	13	,	,	PUNCT
ejpam-4115	51	14	then	then	ADV
ejpam-4115	51	15	u	u	X
ejpam-4115	51	16	=	=	PUNCT
ejpam-4115	51	17	{	{	PUNCT
ejpam-4115	51	18	x	x	SYM
ejpam-4115	51	19	∈	∈	PROPN
ejpam-4115	51	20	x	x	X
ejpam-4115	51	21	:	:	PUNCT
ejpam-4115	51	22	φu	φu	PROPN
ejpam-4115	51	23	(	(	PUNCT
ejpam-4115	51	24	x	x	X
ejpam-4115	51	25	)	)	PUNCT
ejpam-4115	51	26	<	<	X
ejpam-4115	51	27	1	1	X
ejpam-4115	51	28	}	}	PUNCT
ejpam-4115	51	29	and	and	CCONJ
ejpam-4115	51	30	φu	φu	NOUN
ejpam-4115	51	31	is	be	AUX
ejpam-4115	51	32	a	a	DET
ejpam-4115	51	33	semi	semi	ADJ
ejpam-4115	51	34	-	-	NOUN
ejpam-4115	51	35	norm	norm	ADJ
ejpam-4115	51	36	on	on	ADP
ejpam-4115	51	37	x.	x.	NOUN
ejpam-4115	51	38	also	also	ADV
ejpam-4115	51	39	,	,	PUNCT
ejpam-4115	51	40	for	for	ADP
ejpam-4115	51	41	any	any	DET
ejpam-4115	51	42	v	v	ADP
ejpam-4115	51	43	⊆	⊆	NUM
ejpam-4115	51	44	x	x	NOUN
ejpam-4115	51	45	,	,	PUNCT
ejpam-4115	51	46	φrv	φrv	X
ejpam-4115	51	47	(	(	PUNCT
ejpam-4115	51	48	x	x	NOUN
ejpam-4115	51	49	)	)	PUNCT
ejpam-4115	51	50	=	=	SYM
ejpam-4115	51	51	1	1	NUM
ejpam-4115	51	52	rφv	rφv	X
ejpam-4115	51	53	(	(	PUNCT
ejpam-4115	51	54	x	x	NOUN
ejpam-4115	51	55	)	)	PUNCT
ejpam-4115	51	56	for	for	ADP
ejpam-4115	51	57	all	all	DET
ejpam-4115	51	58	positive	positive	ADJ
ejpam-4115	51	59	real	real	ADJ
ejpam-4115	51	60	numbers	number	NOUN
ejpam-4115	51	61	r	r	NOUN
ejpam-4115	51	62	and	and	CCONJ
ejpam-4115	51	63	x	x	SYM
ejpam-4115	51	64	∈	∈	NOUN
ejpam-4115	51	65	x	x	PUNCT
ejpam-4115	51	66	(	(	PUNCT
ejpam-4115	51	67	see	see	VERB
ejpam-4115	51	68	[	[	X
ejpam-4115	51	69	11	11	NUM
ejpam-4115	51	70	]	]	NUM
ejpam-4115	51	71	)	)	PUNCT
ejpam-4115	51	72	.	.	PUNCT
ejpam-4115	52	1	for	for	ADP
ejpam-4115	52	2	any	any	DET
ejpam-4115	52	3	given	give	VERB
ejpam-4115	52	4	absorbing	absorbing	NOUN
ejpam-4115	52	5	sets	set	NOUN
ejpam-4115	52	6	a	a	PRON
ejpam-4115	52	7	and	and	CCONJ
ejpam-4115	52	8	b	b	NOUN
ejpam-4115	52	9	with	with	ADP
ejpam-4115	52	10	a	a	DET
ejpam-4115	52	11	⊆	⊆	NUM
ejpam-4115	52	12	b	b	NOUN
ejpam-4115	52	13	⊆	⊆	NUM
ejpam-4115	52	14	x	x	NOUN
ejpam-4115	52	15	,	,	PUNCT
ejpam-4115	52	16	φb(t	φb(t	NUM
ejpam-4115	52	17	)	)	PUNCT
ejpam-4115	52	18	≤	≤	NOUN
ejpam-4115	52	19	φa(t	φa(t	NOUN
ejpam-4115	52	20	)	)	PUNCT
ejpam-4115	52	21	for	for	ADP
ejpam-4115	52	22	all	all	PRON
ejpam-4115	52	23	t	t	NOUN
ejpam-4115	52	24	∈	∈	PROPN
ejpam-4115	52	25	x.	x.	NOUN
ejpam-4115	52	26	one	one	PRON
ejpam-4115	52	27	may	may	AUX
ejpam-4115	52	28	refer	refer	VERB
ejpam-4115	52	29	to	to	ADP
ejpam-4115	52	30	[	[	X
ejpam-4115	52	31	10	10	NUM
ejpam-4115	52	32	]	]	PUNCT
ejpam-4115	52	33	for	for	ADP
ejpam-4115	52	34	the	the	DET
ejpam-4115	52	35	definition	definition	NOUN
ejpam-4115	52	36	,	,	PUNCT
ejpam-4115	52	37	the	the	DET
ejpam-4115	52	38	earlier	early	ADV
ejpam-4115	52	39	mentioned	mention	VERB
ejpam-4115	52	40	results	result	NOUN
ejpam-4115	52	41	,	,	PUNCT
ejpam-4115	52	42	and	and	CCONJ
ejpam-4115	52	43	a	a	DET
ejpam-4115	52	44	detailed	detailed	ADJ
ejpam-4115	52	45	discussion	discussion	NOUN
ejpam-4115	52	46	of	of	ADP
ejpam-4115	52	47	the	the	DET
ejpam-4115	52	48	minkowski	minkowski	ADJ
ejpam-4115	52	49	functional	functional	ADJ
ejpam-4115	52	50	.	.	PUNCT
ejpam-4115	53	1	a	a	DET
ejpam-4115	53	2	function	function	NOUN
ejpam-4115	53	3	δ	δ	NOUN
ejpam-4115	53	4	:	:	PUNCT
ejpam-4115	54	1	[	[	X
ejpam-4115	54	2	a	a	X
ejpam-4115	54	3	,	,	PUNCT
ejpam-4115	54	4	b	b	NOUN
ejpam-4115	54	5	]	]	PUNCT
ejpam-4115	54	6	→	→	PUNCT
ejpam-4115	54	7	r+	r+	PRON
ejpam-4115	54	8	is	be	AUX
ejpam-4115	54	9	called	call	VERB
ejpam-4115	54	10	a	a	DET
ejpam-4115	54	11	gauge	gauge	NOUN
ejpam-4115	54	12	[	[	X
ejpam-4115	54	13	14	14	NUM
ejpam-4115	54	14	]	]	PUNCT
ejpam-4115	54	15	.	.	PUNCT
ejpam-4115	55	1	a	a	DET
ejpam-4115	55	2	finite	finite	ADJ
ejpam-4115	55	3	collection	collection	NOUN
ejpam-4115	55	4	d	d	NOUN
ejpam-4115	55	5	=	=	PRON
ejpam-4115	55	6	{	{	PUNCT
ejpam-4115	55	7	[	[	X
ejpam-4115	55	8	ui	ui	PROPN
ejpam-4115	55	9	,	,	PUNCT
ejpam-4115	55	10	vi	vi	PROPN
ejpam-4115	55	11	]	]	X
ejpam-4115	55	12	:	:	PUNCT
ejpam-4115	55	13	r.	r.	PROPN
ejpam-4115	55	14	e.	e.	PROPN
ejpam-4115	55	15	maza	maza	PROPN
ejpam-4115	55	16	,	,	PUNCT
ejpam-4115	55	17	s.	s.	PROPN
ejpam-4115	55	18	r.	r.	PROPN
ejpam-4115	55	19	canoy	canoy	PROPN
ejpam-4115	55	20	,	,	PUNCT
ejpam-4115	55	21	jr	jr	PROPN
ejpam-4115	55	22	.	.	PROPN
ejpam-4115	55	23	/	/	SYM
ejpam-4115	55	24	eur	eur	PROPN
ejpam-4115	55	25	.	.	PUNCT
ejpam-4115	56	1	j.	j.	PROPN
ejpam-4115	56	2	pure	pure	PROPN
ejpam-4115	56	3	appl	appl	PROPN
ejpam-4115	56	4	.	.	PROPN
ejpam-4115	56	5	math	math	PROPN
ejpam-4115	56	6	,	,	PUNCT
ejpam-4115	56	7	14	14	NUM
ejpam-4115	56	8	(	(	PUNCT
ejpam-4115	56	9	4	4	NUM
ejpam-4115	56	10	)	)	PUNCT
ejpam-4115	56	11	(	(	PUNCT
ejpam-4115	56	12	2021	2021	NUM
ejpam-4115	56	13	)	)	PUNCT
ejpam-4115	56	14	,	,	PUNCT
ejpam-4115	56	15	1169	1169	NUM
ejpam-4115	56	16	-	-	SYM
ejpam-4115	56	17	1183	1183	NUM
ejpam-4115	56	18	1171	1171	NUM
ejpam-4115	56	19	1	1	NUM
ejpam-4115	56	20	≤	≤	NUM
ejpam-4115	56	21	i	i	PRON
ejpam-4115	56	22	≤	≤	NOUN
ejpam-4115	56	23	n	n	CCONJ
ejpam-4115	56	24	}	}	PUNCT
ejpam-4115	56	25	of	of	ADP
ejpam-4115	56	26	non	non	ADJ
ejpam-4115	56	27	-	-	ADJ
ejpam-4115	56	28	overlapping	overlapping	ADJ
ejpam-4115	56	29	closed	closed	ADJ
ejpam-4115	56	30	sub	sub	NOUN
ejpam-4115	56	31	-	-	NOUN
ejpam-4115	56	32	intervals	interval	NOUN
ejpam-4115	56	33	of	of	ADP
ejpam-4115	56	34	[	[	X
ejpam-4115	56	35	a	a	X
ejpam-4115	56	36	,	,	PUNCT
ejpam-4115	56	37	b	b	NOUN
ejpam-4115	56	38	]	]	PUNCT
ejpam-4115	56	39	is	be	AUX
ejpam-4115	56	40	called	call	VERB
ejpam-4115	56	41	a	a	DET
ejpam-4115	56	42	partial	partial	ADJ
ejpam-4115	56	43	partition	partition	NOUN
ejpam-4115	56	44	of	of	ADP
ejpam-4115	56	45	[	[	X
ejpam-4115	56	46	a	a	X
ejpam-4115	56	47	,	,	PUNCT
ejpam-4115	56	48	b	b	NOUN
ejpam-4115	56	49	]	]	X
ejpam-4115	56	50	.	.	PUNCT
ejpam-4115	57	1	if	if	SCONJ
ejpam-4115	57	2	the	the	DET
ejpam-4115	57	3	union	union	NOUN
ejpam-4115	57	4	of	of	ADP
ejpam-4115	57	5	the	the	DET
ejpam-4115	57	6	intervals	interval	NOUN
ejpam-4115	57	7	in	in	ADP
ejpam-4115	57	8	d	d	PROPN
ejpam-4115	57	9	is	be	AUX
ejpam-4115	57	10	equal	equal	ADJ
ejpam-4115	57	11	to	to	ADP
ejpam-4115	57	12	[	[	X
ejpam-4115	57	13	a	a	X
ejpam-4115	57	14	,	,	PUNCT
ejpam-4115	57	15	b	b	NOUN
ejpam-4115	57	16	]	]	X
ejpam-4115	57	17	,	,	PUNCT
ejpam-4115	57	18	then	then	ADV
ejpam-4115	57	19	d	d	PROPN
ejpam-4115	57	20	is	be	AUX
ejpam-4115	57	21	called	call	VERB
ejpam-4115	57	22	partition	partition	NOUN
ejpam-4115	57	23	of	of	ADP
ejpam-4115	57	24	[	[	X
ejpam-4115	57	25	a	a	X
ejpam-4115	57	26	,	,	PUNCT
ejpam-4115	57	27	b	b	NOUN
ejpam-4115	57	28	]	]	X
ejpam-4115	57	29	.	.	PUNCT
ejpam-4115	58	1	a	a	DET
ejpam-4115	58	2	finite	finite	ADJ
ejpam-4115	58	3	collection	collection	NOUN
ejpam-4115	58	4	of	of	ADP
ejpam-4115	58	5	ordered	order	VERB
ejpam-4115	58	6	pairs	pair	NOUN
ejpam-4115	58	7	{	{	PUNCT
ejpam-4115	58	8	(	(	PUNCT
ejpam-4115	58	9	ii	ii	PROPN
ejpam-4115	58	10	,	,	PUNCT
ejpam-4115	58	11	ti	ti	NOUN
ejpam-4115	58	12	)	)	PUNCT
ejpam-4115	58	13	}	}	PUNCT
ejpam-4115	58	14	n	n	CCONJ
ejpam-4115	58	15	i=1	i=1	PROPN
ejpam-4115	58	16	of	of	ADP
ejpam-4115	58	17	non	non	ADJ
ejpam-4115	58	18	-	-	ADJ
ejpam-4115	58	19	overlapping	overlapping	ADJ
ejpam-4115	58	20	closed	closed	ADJ
ejpam-4115	58	21	sub	sub	NOUN
ejpam-4115	58	22	-	-	NOUN
ejpam-4115	58	23	intervals	interval	NOUN
ejpam-4115	58	24	of	of	ADP
ejpam-4115	58	25	[	[	X
ejpam-4115	58	26	a	a	X
ejpam-4115	58	27	,	,	PUNCT
ejpam-4115	58	28	b	b	NOUN
ejpam-4115	58	29	]	]	PUNCT
ejpam-4115	58	30	and	and	CCONJ
ejpam-4115	58	31	real	real	ADJ
ejpam-4115	58	32	numbers	number	NOUN
ejpam-4115	58	33	is	be	AUX
ejpam-4115	58	34	called	call	VERB
ejpam-4115	58	35	a	a	DET
ejpam-4115	58	36	δ	δ	NOUN
ejpam-4115	58	37	-	-	PUNCT
ejpam-4115	58	38	fine	fine	ADJ
ejpam-4115	58	39	partition	partition	NOUN
ejpam-4115	58	40	of	of	ADP
ejpam-4115	58	41	[	[	X
ejpam-4115	58	42	a	a	X
ejpam-4115	58	43	,	,	PUNCT
ejpam-4115	58	44	b	b	NOUN
ejpam-4115	58	45	]	]	X
ejpam-4115	58	46	if	if	SCONJ
ejpam-4115	58	47	{	{	PUNCT
ejpam-4115	58	48	ii}ni=1	ii}ni=1	ADV
ejpam-4115	58	49	is	be	AUX
ejpam-4115	58	50	a	a	DET
ejpam-4115	58	51	partition	partition	NOUN
ejpam-4115	58	52	of	of	ADP
ejpam-4115	58	53	[	[	X
ejpam-4115	58	54	a	a	X
ejpam-4115	58	55	,	,	PUNCT
ejpam-4115	58	56	b	b	NOUN
ejpam-4115	58	57	]	]	PUNCT
ejpam-4115	58	58	and	and	CCONJ
ejpam-4115	58	59	ti	ti	X
ejpam-4115	58	60	∈	∈	PROPN
ejpam-4115	58	61	ii	ii	PROPN
ejpam-4115	58	62	⊆	⊆	X
ejpam-4115	58	63	(	(	PUNCT
ejpam-4115	58	64	ti	ti	NOUN
ejpam-4115	58	65	−	−	PROPN
ejpam-4115	58	66	δ(ti	δ(ti	PROPN
ejpam-4115	58	67	)	)	PUNCT
ejpam-4115	58	68	,	,	PUNCT
ejpam-4115	58	69	ti	ti	X
ejpam-4115	58	70	+	+	CCONJ
ejpam-4115	58	71	δ(ti	δ(ti	NOUN
ejpam-4115	58	72	)	)	PUNCT
ejpam-4115	58	73	)	)	PUNCT
ejpam-4115	58	74	for	for	ADP
ejpam-4115	58	75	each	each	DET
ejpam-4115	58	76	i	i	PRON
ejpam-4115	58	77	∈	∈	PROPN
ejpam-4115	58	78	{	{	PUNCT
ejpam-4115	58	79	1	1	NUM
ejpam-4115	58	80	,	,	PUNCT
ejpam-4115	58	81	2	2	NUM
ejpam-4115	58	82	,	,	PUNCT
ejpam-4115	58	83	.	.	PUNCT
ejpam-4115	58	84	.	.	PUNCT
ejpam-4115	59	1	.	.	PUNCT
ejpam-4115	59	2	,	,	PUNCT
ejpam-4115	59	3	n	n	CCONJ
ejpam-4115	59	4	}	}	PUNCT
ejpam-4115	59	5	.	.	PUNCT
ejpam-4115	60	1	in	in	ADP
ejpam-4115	60	2	what	what	PRON
ejpam-4115	60	3	follows	follow	VERB
ejpam-4115	60	4	,	,	PUNCT
ejpam-4115	60	5	x	x	X
ejpam-4115	60	6	is	be	AUX
ejpam-4115	60	7	a	a	DET
ejpam-4115	60	8	locally	locally	ADV
ejpam-4115	60	9	convex	convex	ADJ
ejpam-4115	60	10	topological	topological	ADJ
ejpam-4115	60	11	vector	vector	NOUN
ejpam-4115	60	12	space	space	NOUN
ejpam-4115	60	13	.	.	PUNCT
ejpam-4115	61	1	definition	definition	NOUN
ejpam-4115	61	2	1	1	NUM
ejpam-4115	61	3	.	.	PUNCT
ejpam-4115	62	1	[	[	X
ejpam-4115	62	2	8	8	NUM
ejpam-4115	62	3	]	]	PUNCT
ejpam-4115	62	4	a	a	DET
ejpam-4115	62	5	function	function	NOUN
ejpam-4115	62	6	f	f	NOUN
ejpam-4115	62	7	:	:	PUNCT
ejpam-4115	63	1	[	[	X
ejpam-4115	63	2	a	a	X
ejpam-4115	63	3	,	,	PUNCT
ejpam-4115	63	4	b	b	NOUN
ejpam-4115	63	5	]	]	X
ejpam-4115	63	6	→	→	PUNCT
ejpam-4115	63	7	x	x	X
ejpam-4115	63	8	is	be	AUX
ejpam-4115	63	9	henstock	henstock	NOUN
ejpam-4115	63	10	integrable	integrable	ADJ
ejpam-4115	63	11	or	or	CCONJ
ejpam-4115	63	12	hk	hk	NOUN
ejpam-4115	63	13	-	-	PUNCT
ejpam-4115	63	14	integrable	integrable	ADJ
ejpam-4115	63	15	on	on	ADP
ejpam-4115	63	16	[	[	X
ejpam-4115	63	17	a	a	X
ejpam-4115	63	18	,	,	PUNCT
ejpam-4115	63	19	b	b	NOUN
ejpam-4115	63	20	]	]	X
ejpam-4115	63	21	,	,	PUNCT
ejpam-4115	63	22	if	if	SCONJ
ejpam-4115	63	23	there	there	PRON
ejpam-4115	63	24	is	be	VERB
ejpam-4115	63	25	an	an	DET
ejpam-4115	63	26	α	α	NOUN
ejpam-4115	63	27	∈	∈	NOUN
ejpam-4115	63	28	x	x	PUNCT
ejpam-4115	63	29	such	such	ADJ
ejpam-4115	63	30	that	that	PRON
ejpam-4115	63	31	for	for	ADP
ejpam-4115	63	32	any	any	DET
ejpam-4115	63	33	θ	θ	PROPN
ejpam-4115	63	34	-	-	PUNCT
ejpam-4115	63	35	nbd	nbd	PROPN
ejpam-4115	63	36	u	u	NOUN
ejpam-4115	63	37	there	there	PRON
ejpam-4115	63	38	is	be	VERB
ejpam-4115	63	39	a	a	DET
ejpam-4115	63	40	gauge	gauge	ADJ
ejpam-4115	63	41	δ	δ	NOUN
ejpam-4115	63	42	on	on	ADP
ejpam-4115	63	43	[	[	X
ejpam-4115	63	44	a	a	DET
ejpam-4115	63	45	,	,	PUNCT
ejpam-4115	63	46	b	b	NOUN
ejpam-4115	63	47	]	]	X
ejpam-4115	63	48	such	such	ADJ
ejpam-4115	63	49	that	that	PRON
ejpam-4115	63	50	for	for	ADP
ejpam-4115	63	51	any	any	DET
ejpam-4115	63	52	δ	δ	NOUN
ejpam-4115	63	53	-	-	PUNCT
ejpam-4115	63	54	fine	fine	ADJ
ejpam-4115	63	55	partition	partition	NOUN
ejpam-4115	63	56	p	p	NOUN
ejpam-4115	63	57	=	=	X
ejpam-4115	63	58	{	{	PUNCT
ejpam-4115	63	59	(	(	PUNCT
ejpam-4115	63	60	[	[	X
ejpam-4115	63	61	xi−1	xi−1	PROPN
ejpam-4115	63	62	,	,	PUNCT
ejpam-4115	63	63	xi	xi	ADP
ejpam-4115	63	64	]	]	PUNCT
ejpam-4115	63	65	,	,	PUNCT
ejpam-4115	63	66	ti	ti	NOUN
ejpam-4115	63	67	)	)	PUNCT
ejpam-4115	63	68	:	:	PUNCT
ejpam-4115	63	69	1	1	NUM
ejpam-4115	63	70	≤	≤	NUM
ejpam-4115	63	71	i	i	PRON
ejpam-4115	63	72	≤	≤	NOUN
ejpam-4115	63	73	n	n	CCONJ
ejpam-4115	63	74	}	}	PUNCT
ejpam-4115	63	75	of	of	ADP
ejpam-4115	63	76	[	[	X
ejpam-4115	63	77	a	a	X
ejpam-4115	63	78	,	,	PUNCT
ejpam-4115	63	79	b	b	NOUN
ejpam-4115	63	80	]	]	X
ejpam-4115	63	81	,	,	PUNCT
ejpam-4115	63	82	we	we	PRON
ejpam-4115	63	83	have	have	VERB
ejpam-4115	63	84	n∑	n∑	PROPN
ejpam-4115	63	85	i=1	i=1	PROPN
ejpam-4115	64	1	(	(	PUNCT
ejpam-4115	64	2	xi	xi	X
ejpam-4115	64	3	−	−	PROPN
ejpam-4115	65	1	xi−1)f(ti)−	xi−1)f(ti)−	PROPN
ejpam-4115	66	1	α	α	PROPN
ejpam-4115	66	2	∈	∈	PROPN
ejpam-4115	66	3	u.	u.	NOUN
ejpam-4115	66	4	in	in	ADP
ejpam-4115	66	5	this	this	DET
ejpam-4115	66	6	case	case	NOUN
ejpam-4115	66	7	,	,	PUNCT
ejpam-4115	66	8	we	we	PRON
ejpam-4115	66	9	write	write	VERB
ejpam-4115	66	10	f	f	PROPN
ejpam-4115	66	11	∈	∈	PROPN
ejpam-4115	67	1	h([a	h([a	PROPN
ejpam-4115	67	2	,	,	PUNCT
ejpam-4115	67	3	b	b	NOUN
ejpam-4115	67	4	]	]	X
ejpam-4115	67	5	,	,	PUNCT
ejpam-4115	67	6	x	x	X
ejpam-4115	67	7	)	)	PUNCT
ejpam-4115	67	8	and	and	CCONJ
ejpam-4115	67	9	(	(	PUNCT
ejpam-4115	67	10	h	h	PROPN
ejpam-4115	67	11	)	)	PUNCT
ejpam-4115	67	12	∫	∫	PROPN
ejpam-4115	68	1	b	b	PROPN
ejpam-4115	68	2	a	a	PRON
ejpam-4115	68	3	f	f	X
ejpam-4115	68	4	=	=	SYM
ejpam-4115	68	5	α	α	PROPN
ejpam-4115	68	6	.	.	PUNCT
ejpam-4115	69	1	definition	definition	NOUN
ejpam-4115	69	2	2	2	NUM
ejpam-4115	69	3	.	.	PUNCT
ejpam-4115	70	1	[	[	X
ejpam-4115	70	2	9	9	NUM
ejpam-4115	70	3	]	]	PUNCT
ejpam-4115	70	4	a	a	DET
ejpam-4115	70	5	function	function	NOUN
ejpam-4115	70	6	f	f	NOUN
ejpam-4115	70	7	:	:	PUNCT
ejpam-4115	71	1	[	[	X
ejpam-4115	71	2	a	a	X
ejpam-4115	71	3	,	,	PUNCT
ejpam-4115	71	4	b	b	NOUN
ejpam-4115	71	5	]	]	X
ejpam-4115	71	6	→	→	PUNCT
ejpam-4115	71	7	x	x	X
ejpam-4115	71	8	is	be	AUX
ejpam-4115	71	9	strongly	strongly	ADV
ejpam-4115	71	10	henstock	henstock	NOUN
ejpam-4115	71	11	integrable	integrable	ADJ
ejpam-4115	71	12	or	or	CCONJ
ejpam-4115	71	13	sh	sh	NOUN
ejpam-4115	71	14	-	-	PUNCT
ejpam-4115	71	15	integrable	integrable	ADJ
ejpam-4115	71	16	on	on	ADP
ejpam-4115	71	17	[	[	X
ejpam-4115	71	18	a	a	X
ejpam-4115	71	19	,	,	PUNCT
ejpam-4115	71	20	b	b	NOUN
ejpam-4115	71	21	]	]	X
ejpam-4115	71	22	if	if	SCONJ
ejpam-4115	71	23	there	there	PRON
ejpam-4115	71	24	is	be	VERB
ejpam-4115	71	25	a	a	DET
ejpam-4115	71	26	function	function	NOUN
ejpam-4115	71	27	f	f	NOUN
ejpam-4115	71	28	:	:	PUNCT
ejpam-4115	72	1	[	[	X
ejpam-4115	72	2	a	a	X
ejpam-4115	72	3	,	,	PUNCT
ejpam-4115	72	4	b	b	NOUN
ejpam-4115	72	5	]	]	X
ejpam-4115	72	6	→	→	SYM
ejpam-4115	72	7	x	x	X
ejpam-4115	72	8	,	,	PUNCT
ejpam-4115	72	9	called	call	VERB
ejpam-4115	72	10	the	the	DET
ejpam-4115	72	11	primitive	primitive	NOUN
ejpam-4115	72	12	of	of	ADP
ejpam-4115	72	13	f	f	PROPN
ejpam-4115	72	14	,	,	PUNCT
ejpam-4115	72	15	and	and	CCONJ
ejpam-4115	72	16	for	for	ADP
ejpam-4115	72	17	every	every	DET
ejpam-4115	72	18	θ	θ	PROPN
ejpam-4115	72	19	-	-	PUNCT
ejpam-4115	72	20	nbd	nbd	PROPN
ejpam-4115	72	21	u	u	PROPN
ejpam-4115	72	22	,	,	PUNCT
ejpam-4115	72	23	there	there	PRON
ejpam-4115	72	24	exists	exist	VERB
ejpam-4115	72	25	a	a	DET
ejpam-4115	72	26	gauge	gauge	NOUN
ejpam-4115	72	27	δ	δ	NOUN
ejpam-4115	72	28	such	such	ADJ
ejpam-4115	72	29	that	that	PRON
ejpam-4115	72	30	for	for	ADP
ejpam-4115	72	31	any	any	DET
ejpam-4115	72	32	δ	δ	NOUN
ejpam-4115	72	33	-	-	PUNCT
ejpam-4115	72	34	fine	fine	ADJ
ejpam-4115	72	35	partition	partition	NOUN
ejpam-4115	72	36	d	d	NOUN
ejpam-4115	72	37	=	=	PRON
ejpam-4115	72	38	{	{	PUNCT
ejpam-4115	72	39	(	(	PUNCT
ejpam-4115	72	40	[	[	X
ejpam-4115	72	41	ui	ui	NOUN
ejpam-4115	72	42	,	,	PUNCT
ejpam-4115	72	43	vi	vi	PROPN
ejpam-4115	72	44	]	]	PUNCT
ejpam-4115	72	45	,	,	PUNCT
ejpam-4115	72	46	ti	ti	NOUN
ejpam-4115	72	47	)	)	PUNCT
ejpam-4115	72	48	:	:	PUNCT
ejpam-4115	72	49	1	1	NUM
ejpam-4115	72	50	≤	≤	NUM
ejpam-4115	72	51	i	i	PRON
ejpam-4115	72	52	≤	≤	NOUN
ejpam-4115	72	53	n	n	CCONJ
ejpam-4115	72	54	}	}	PUNCT
ejpam-4115	72	55	,	,	PUNCT
ejpam-4115	72	56	there	there	PRON
ejpam-4115	72	57	exist	exist	VERB
ejpam-4115	72	58	θ	θ	PROPN
ejpam-4115	72	59	-	-	PUNCT
ejpam-4115	72	60	nbds	nbds	NOUN
ejpam-4115	72	61	u1	u1	NOUN
ejpam-4115	72	62	,	,	PUNCT
ejpam-4115	72	63	u2	u2	NOUN
ejpam-4115	72	64	,	,	PUNCT
ejpam-4115	72	65	.	.	PUNCT
ejpam-4115	72	66	.	.	PUNCT
ejpam-4115	73	1	.	.	PUNCT
ejpam-4115	74	1	,	,	PUNCT
ejpam-4115	74	2	un	un	PROPN
ejpam-4115	74	3	such	such	ADJ
ejpam-4115	74	4	that	that	SCONJ
ejpam-4115	74	5	∑n	∑n	PROPN
ejpam-4115	74	6	i=1	i=1	PROPN
ejpam-4115	74	7	ui	ui	PROPN
ejpam-4115	74	8	⊆	⊆	NUM
ejpam-4115	74	9	u	u	NOUN
ejpam-4115	74	10	and	and	CCONJ
ejpam-4115	74	11	f	f	PROPN
ejpam-4115	74	12	(	(	PUNCT
ejpam-4115	74	13	vi)−f	vi)−f	PROPN
ejpam-4115	74	14	(	(	PUNCT
ejpam-4115	74	15	ui)−f(ti)(vi−ui	ui)−f(ti)(vi−ui	NOUN
ejpam-4115	74	16	)	)	PUNCT
ejpam-4115	74	17	∈	∈	PROPN
ejpam-4115	74	18	ui	ui	NOUN
ejpam-4115	74	19	for	for	ADP
ejpam-4115	74	20	each	each	DET
ejpam-4115	74	21	i	i	PRON
ejpam-4115	74	22	∈	∈	PROPN
ejpam-4115	74	23	{	{	PUNCT
ejpam-4115	74	24	1	1	NUM
ejpam-4115	74	25	,	,	PUNCT
ejpam-4115	74	26	2	2	NUM
ejpam-4115	74	27	,	,	PUNCT
ejpam-4115	74	28	.	.	PUNCT
ejpam-4115	74	29	.	.	PUNCT
ejpam-4115	75	1	.	.	PUNCT
ejpam-4115	75	2	,	,	PUNCT
ejpam-4115	75	3	n	n	CCONJ
ejpam-4115	75	4	}	}	PUNCT
ejpam-4115	75	5	.	.	PUNCT
ejpam-4115	76	1	in	in	ADP
ejpam-4115	76	2	this	this	DET
ejpam-4115	76	3	case	case	NOUN
ejpam-4115	76	4	,	,	PUNCT
ejpam-4115	76	5	we	we	PRON
ejpam-4115	76	6	may	may	AUX
ejpam-4115	76	7	write	write	VERB
ejpam-4115	76	8	f	f	PROPN
ejpam-4115	76	9	∈	∈	PROPN
ejpam-4115	76	10	sh([a	sh([a	PROPN
ejpam-4115	76	11	,	,	PUNCT
ejpam-4115	76	12	b	b	NOUN
ejpam-4115	76	13	]	]	X
ejpam-4115	76	14	,	,	PUNCT
ejpam-4115	76	15	x	x	NOUN
ejpam-4115	76	16	)	)	PUNCT
ejpam-4115	76	17	.	.	PUNCT
ejpam-4115	77	1	the	the	DET
ejpam-4115	77	2	difference	difference	NOUN
ejpam-4115	77	3	f	f	PROPN
ejpam-4115	77	4	(	(	PUNCT
ejpam-4115	77	5	b)−	b)−	PROPN
ejpam-4115	77	6	f	f	X
ejpam-4115	77	7	(	(	PUNCT
ejpam-4115	77	8	a	a	NOUN
ejpam-4115	77	9	)	)	PUNCT
ejpam-4115	77	10	is	be	AUX
ejpam-4115	77	11	the	the	DET
ejpam-4115	77	12	sh	sh	NOUN
ejpam-4115	77	13	-	-	PUNCT
ejpam-4115	77	14	integral	integral	ADJ
ejpam-4115	77	15	of	of	ADP
ejpam-4115	77	16	f	f	PROPN
ejpam-4115	77	17	on	on	ADP
ejpam-4115	77	18	[	[	X
ejpam-4115	77	19	a	a	X
ejpam-4115	77	20	,	,	PUNCT
ejpam-4115	77	21	b	b	NOUN
ejpam-4115	77	22	]	]	X
ejpam-4115	77	23	.	.	PUNCT
ejpam-4115	78	1	in	in	ADP
ejpam-4115	78	2	symbols	symbol	NOUN
ejpam-4115	78	3	,	,	PUNCT
ejpam-4115	78	4	we	we	PRON
ejpam-4115	78	5	write	write	VERB
ejpam-4115	78	6	(	(	PUNCT
ejpam-4115	78	7	sh	sh	PROPN
ejpam-4115	78	8	)	)	PUNCT
ejpam-4115	78	9	∫	∫	PROPN
ejpam-4115	79	1	b	b	PROPN
ejpam-4115	79	2	a	a	DET
ejpam-4115	79	3	f	f	X
ejpam-4115	79	4	=	=	SYM
ejpam-4115	79	5	f	f	PROPN
ejpam-4115	79	6	(	(	PUNCT
ejpam-4115	79	7	b)−	b)−	PROPN
ejpam-4115	79	8	f	f	X
ejpam-4115	79	9	(	(	PUNCT
ejpam-4115	79	10	a	a	NOUN
ejpam-4115	79	11	)	)	PUNCT
ejpam-4115	79	12	.	.	PUNCT
ejpam-4115	80	1	from	from	ADP
ejpam-4115	80	2	the	the	DET
ejpam-4115	80	3	above	above	ADJ
ejpam-4115	80	4	definitions	definition	NOUN
ejpam-4115	80	5	,	,	PUNCT
ejpam-4115	80	6	it	it	PRON
ejpam-4115	80	7	is	be	AUX
ejpam-4115	80	8	easy	easy	ADJ
ejpam-4115	80	9	to	to	PART
ejpam-4115	80	10	show	show	VERB
ejpam-4115	80	11	that	that	SCONJ
ejpam-4115	80	12	every	every	DET
ejpam-4115	80	13	sh	sh	PROPN
ejpam-4115	80	14	integrable	integrable	ADJ
ejpam-4115	80	15	function	function	NOUN
ejpam-4115	80	16	is	be	AUX
ejpam-4115	80	17	hk	hk	PROPN
ejpam-4115	80	18	integrable	integrable	ADJ
ejpam-4115	80	19	.	.	PUNCT
ejpam-4115	81	1	definition	definition	NOUN
ejpam-4115	81	2	3	3	NUM
ejpam-4115	81	3	.	.	PUNCT
ejpam-4115	82	1	[	[	X
ejpam-4115	82	2	7	7	X
ejpam-4115	82	3	]	]	X
ejpam-4115	82	4	a	a	DET
ejpam-4115	82	5	function	function	NOUN
ejpam-4115	82	6	f	f	NOUN
ejpam-4115	82	7	:	:	PUNCT
ejpam-4115	83	1	[	[	X
ejpam-4115	83	2	a	a	X
ejpam-4115	83	3	,	,	PUNCT
ejpam-4115	83	4	b	b	NOUN
ejpam-4115	83	5	]	]	X
ejpam-4115	83	6	→	→	PUNCT
ejpam-4115	83	7	x	x	X
ejpam-4115	83	8	is	be	AUX
ejpam-4115	83	9	said	say	VERB
ejpam-4115	83	10	to	to	PART
ejpam-4115	83	11	be	be	AUX
ejpam-4115	83	12	absolutely	absolutely	ADV
ejpam-4115	83	13	continuous	continuous	ADJ
ejpam-4115	83	14	on	on	ADP
ejpam-4115	83	15	[	[	X
ejpam-4115	83	16	a	a	X
ejpam-4115	83	17	,	,	PUNCT
ejpam-4115	83	18	b	b	NOUN
ejpam-4115	83	19	]	]	X
ejpam-4115	83	20	(	(	PUNCT
ejpam-4115	83	21	or	or	CCONJ
ejpam-4115	83	22	f	f	PROPN
ejpam-4115	83	23	is	be	AUX
ejpam-4115	83	24	ac	ac	ADV
ejpam-4115	83	25	on	on	ADP
ejpam-4115	83	26	[	[	X
ejpam-4115	83	27	a	a	PRON
ejpam-4115	83	28	,	,	PUNCT
ejpam-4115	83	29	b	b	NOUN
ejpam-4115	83	30	]	]	X
ejpam-4115	83	31	)	)	PUNCT
ejpam-4115	83	32	if	if	SCONJ
ejpam-4115	83	33	for	for	ADP
ejpam-4115	83	34	every	every	DET
ejpam-4115	83	35	θ	θ	PROPN
ejpam-4115	83	36	-	-	PUNCT
ejpam-4115	83	37	nbd	nbd	PROPN
ejpam-4115	83	38	u	u	PROPN
ejpam-4115	83	39	,	,	PUNCT
ejpam-4115	83	40	there	there	PRON
ejpam-4115	83	41	exists	exist	VERB
ejpam-4115	83	42	an	an	DET
ejpam-4115	83	43	η	η	PROPN
ejpam-4115	83	44	>	>	X
ejpam-4115	83	45	0	0	NUM
ejpam-4115	83	46	such	such	ADJ
ejpam-4115	83	47	that	that	PRON
ejpam-4115	83	48	for	for	ADP
ejpam-4115	83	49	any	any	DET
ejpam-4115	83	50	partial	partial	ADJ
ejpam-4115	83	51	partition	partition	NOUN
ejpam-4115	83	52	d	d	NOUN
ejpam-4115	83	53	=	=	PRON
ejpam-4115	83	54	{	{	PUNCT
ejpam-4115	83	55	[	[	X
ejpam-4115	83	56	ui	ui	PROPN
ejpam-4115	83	57	,	,	PUNCT
ejpam-4115	83	58	vi	vi	PROPN
ejpam-4115	83	59	]	]	X
ejpam-4115	83	60	:	:	PUNCT
ejpam-4115	83	61	1	1	NUM
ejpam-4115	83	62	≤	≤	NUM
ejpam-4115	83	63	i	i	PRON
ejpam-4115	83	64	≤	≤	NOUN
ejpam-4115	83	65	n	n	CCONJ
ejpam-4115	83	66	}	}	PUNCT
ejpam-4115	83	67	of	of	ADP
ejpam-4115	83	68	[	[	X
ejpam-4115	83	69	a	a	X
ejpam-4115	83	70	,	,	PUNCT
ejpam-4115	83	71	b	b	NOUN
ejpam-4115	83	72	]	]	X
ejpam-4115	83	73	with	with	ADP
ejpam-4115	83	74	∑n	∑n	PROPN
ejpam-4115	83	75	i=1(vi	i=1(vi	NOUN
ejpam-4115	83	76	−	−	PROPN
ejpam-4115	83	77	ui	ui	PROPN
ejpam-4115	83	78	)	)	PUNCT
ejpam-4115	83	79	<	<	X
ejpam-4115	83	80	η	η	PROPN
ejpam-4115	83	81	,	,	PUNCT
ejpam-4115	83	82	there	there	PRON
ejpam-4115	83	83	exist	exist	VERB
ejpam-4115	83	84	θ	θ	PROPN
ejpam-4115	83	85	-	-	PUNCT
ejpam-4115	83	86	nbds	nbds	NOUN
ejpam-4115	83	87	u1	u1	NOUN
ejpam-4115	83	88	,	,	PUNCT
ejpam-4115	83	89	u2	u2	NOUN
ejpam-4115	83	90	,	,	PUNCT
ejpam-4115	83	91	.	.	PUNCT
ejpam-4115	83	92	.	.	PUNCT
ejpam-4115	83	93	.	.	PUNCT
ejpam-4115	84	1	,	,	PUNCT
ejpam-4115	84	2	un	un	PROPN
ejpam-4115	84	3	such	such	ADJ
ejpam-4115	84	4	that	that	SCONJ
ejpam-4115	84	5	∑n	∑n	PROPN
ejpam-4115	84	6	i=1	i=1	PROPN
ejpam-4115	84	7	ui	ui	PROPN
ejpam-4115	84	8	⊆	⊆	NUM
ejpam-4115	84	9	u	u	NOUN
ejpam-4115	84	10	and	and	CCONJ
ejpam-4115	84	11	f	f	PROPN
ejpam-4115	84	12	(	(	PUNCT
ejpam-4115	84	13	vi)−	vi)−	NOUN
ejpam-4115	84	14	f	f	PROPN
ejpam-4115	84	15	(	(	PUNCT
ejpam-4115	84	16	ui	ui	PROPN
ejpam-4115	84	17	)	)	PUNCT
ejpam-4115	84	18	∈	∈	PROPN
ejpam-4115	84	19	ui	ui	NOUN
ejpam-4115	84	20	for	for	ADP
ejpam-4115	84	21	each	each	DET
ejpam-4115	84	22	i	i	PRON
ejpam-4115	84	23	∈	∈	PROPN
ejpam-4115	84	24	{	{	PUNCT
ejpam-4115	84	25	1	1	NUM
ejpam-4115	84	26	,	,	PUNCT
ejpam-4115	84	27	2	2	NUM
ejpam-4115	84	28	,	,	PUNCT
ejpam-4115	84	29	.	.	PUNCT
ejpam-4115	84	30	.	.	PUNCT
ejpam-4115	85	1	.	.	PUNCT
ejpam-4115	85	2	,	,	PUNCT
ejpam-4115	86	1	n	n	CCONJ
ejpam-4115	86	2	}	}	PUNCT
ejpam-4115	86	3	.	.	PUNCT
ejpam-4115	87	1	definition	definition	NOUN
ejpam-4115	87	2	4	4	NUM
ejpam-4115	87	3	.	.	PUNCT
ejpam-4115	88	1	function	function	NOUN
ejpam-4115	88	2	f	f	NOUN
ejpam-4115	88	3	:	:	PUNCT
ejpam-4115	89	1	[	[	X
ejpam-4115	89	2	a	a	X
ejpam-4115	89	3	,	,	PUNCT
ejpam-4115	89	4	b	b	NOUN
ejpam-4115	89	5	]	]	X
ejpam-4115	89	6	→	→	PUNCT
ejpam-4115	89	7	x	x	X
ejpam-4115	89	8	is	be	AUX
ejpam-4115	89	9	said	say	VERB
ejpam-4115	89	10	to	to	PART
ejpam-4115	89	11	be	be	AUX
ejpam-4115	89	12	ac∗(e	ac∗(e	NUM
ejpam-4115	89	13	)	)	PUNCT
ejpam-4115	89	14	,	,	PUNCT
ejpam-4115	89	15	where	where	SCONJ
ejpam-4115	89	16	e	e	PROPN
ejpam-4115	89	17	⊆	⊆	NUM
ejpam-4115	89	18	[	[	X
ejpam-4115	89	19	a	a	X
ejpam-4115	89	20	,	,	PUNCT
ejpam-4115	89	21	b	b	NOUN
ejpam-4115	89	22	]	]	X
ejpam-4115	89	23	,	,	PUNCT
ejpam-4115	89	24	if	if	SCONJ
ejpam-4115	89	25	for	for	ADP
ejpam-4115	89	26	every	every	DET
ejpam-4115	89	27	θ	θ	PROPN
ejpam-4115	89	28	-	-	PUNCT
ejpam-4115	89	29	nbd	nbd	PROPN
ejpam-4115	89	30	u	u	PROPN
ejpam-4115	89	31	,	,	PUNCT
ejpam-4115	89	32	there	there	PRON
ejpam-4115	89	33	exists	exist	VERB
ejpam-4115	89	34	an	an	DET
ejpam-4115	89	35	η	η	PROPN
ejpam-4115	89	36	>	>	X
ejpam-4115	89	37	0	0	NUM
ejpam-4115	89	38	such	such	ADJ
ejpam-4115	89	39	that	that	PRON
ejpam-4115	89	40	for	for	ADP
ejpam-4115	89	41	any	any	DET
ejpam-4115	89	42	partial	partial	ADJ
ejpam-4115	89	43	partition	partition	NOUN
ejpam-4115	89	44	d	d	NOUN
ejpam-4115	89	45	=	=	PRON
ejpam-4115	89	46	{	{	PUNCT
ejpam-4115	89	47	[	[	X
ejpam-4115	89	48	ui	ui	PROPN
ejpam-4115	89	49	,	,	PUNCT
ejpam-4115	89	50	vi	vi	PROPN
ejpam-4115	89	51	]	]	X
ejpam-4115	89	52	:	:	PUNCT
ejpam-4115	89	53	1	1	NUM
ejpam-4115	89	54	≤	≤	NUM
ejpam-4115	89	55	i	i	PRON
ejpam-4115	89	56	≤	≤	NOUN
ejpam-4115	89	57	n	n	CCONJ
ejpam-4115	89	58	}	}	PUNCT
ejpam-4115	89	59	of	of	ADP
ejpam-4115	89	60	[	[	X
ejpam-4115	89	61	a	a	X
ejpam-4115	89	62	,	,	PUNCT
ejpam-4115	89	63	b	b	NOUN
ejpam-4115	89	64	]	]	X
ejpam-4115	89	65	with	with	ADP
ejpam-4115	89	66	ui	ui	NOUN
ejpam-4115	89	67	or	or	CCONJ
ejpam-4115	89	68	vi	vi	NOUN
ejpam-4115	89	69	∈	∈	PROPN
ejpam-4115	89	70	e	e	NOUN
ejpam-4115	89	71	and	and	CCONJ
ejpam-4115	89	72	∑n	∑n	PROPN
ejpam-4115	89	73	i=1(vi	i=1(vi	NOUN
ejpam-4115	89	74	−	−	PROPN
ejpam-4115	89	75	ui	ui	PROPN
ejpam-4115	89	76	)	)	PUNCT
ejpam-4115	89	77	<	<	X
ejpam-4115	89	78	η	η	PROPN
ejpam-4115	89	79	,	,	PUNCT
ejpam-4115	89	80	there	there	PRON
ejpam-4115	89	81	exist	exist	VERB
ejpam-4115	89	82	θ	θ	PROPN
ejpam-4115	89	83	-	-	PUNCT
ejpam-4115	89	84	nbds	nbds	NOUN
ejpam-4115	89	85	u1	u1	NOUN
ejpam-4115	89	86	,	,	PUNCT
ejpam-4115	89	87	u2	u2	NOUN
ejpam-4115	89	88	,	,	PUNCT
ejpam-4115	89	89	.	.	PUNCT
ejpam-4115	89	90	.	.	PUNCT
ejpam-4115	89	91	.	.	PUNCT
ejpam-4115	90	1	,	,	PUNCT
ejpam-4115	90	2	un	un	PROPN
ejpam-4115	90	3	such	such	ADJ
ejpam-4115	90	4	that	that	SCONJ
ejpam-4115	90	5	∑n	∑n	PROPN
ejpam-4115	90	6	i=1	i=1	PROPN
ejpam-4115	90	7	ui	ui	PROPN
ejpam-4115	90	8	⊆	⊆	NUM
ejpam-4115	90	9	u	u	NOUN
ejpam-4115	90	10	and	and	CCONJ
ejpam-4115	90	11	f	f	PROPN
ejpam-4115	90	12	(	(	PUNCT
ejpam-4115	90	13	vi)−	vi)−	NOUN
ejpam-4115	90	14	f	f	PROPN
ejpam-4115	90	15	(	(	PUNCT
ejpam-4115	90	16	ui	ui	PROPN
ejpam-4115	90	17	)	)	PUNCT
ejpam-4115	90	18	∈	∈	PROPN
ejpam-4115	90	19	ui	ui	NOUN
ejpam-4115	90	20	for	for	ADP
ejpam-4115	90	21	each	each	DET
ejpam-4115	90	22	i	i	PRON
ejpam-4115	90	23	∈	∈	PROPN
ejpam-4115	90	24	{	{	PUNCT
ejpam-4115	90	25	1	1	NUM
ejpam-4115	90	26	,	,	PUNCT
ejpam-4115	90	27	2	2	NUM
ejpam-4115	90	28	,	,	PUNCT
ejpam-4115	90	29	.	.	PUNCT
ejpam-4115	90	30	.	.	PUNCT
ejpam-4115	91	1	.	.	PUNCT
ejpam-4115	91	2	,	,	PUNCT
ejpam-4115	92	1	n	n	CCONJ
ejpam-4115	92	2	}	}	PUNCT
ejpam-4115	92	3	.	.	PUNCT
ejpam-4115	93	1	definition	definition	NOUN
ejpam-4115	93	2	5	5	NUM
ejpam-4115	93	3	.	.	PUNCT
ejpam-4115	94	1	a	a	DET
ejpam-4115	94	2	function	function	NOUN
ejpam-4115	94	3	f	f	NOUN
ejpam-4115	94	4	:	:	PUNCT
ejpam-4115	95	1	[	[	X
ejpam-4115	95	2	a	a	X
ejpam-4115	95	3	,	,	PUNCT
ejpam-4115	95	4	b	b	NOUN
ejpam-4115	95	5	]	]	X
ejpam-4115	95	6	→	→	PUNCT
ejpam-4115	95	7	x	x	X
ejpam-4115	95	8	is	be	AUX
ejpam-4115	95	9	said	say	VERB
ejpam-4115	95	10	to	to	PART
ejpam-4115	95	11	be	be	AUX
ejpam-4115	95	12	acg∗	acg∗	NOUN
ejpam-4115	95	13	on	on	ADP
ejpam-4115	95	14	[	[	X
ejpam-4115	95	15	a	a	X
ejpam-4115	95	16	,	,	PUNCT
ejpam-4115	95	17	b	b	NOUN
ejpam-4115	95	18	]	]	X
ejpam-4115	95	19	if	if	SCONJ
ejpam-4115	95	20	there	there	PRON
ejpam-4115	95	21	exists	exist	VERB
ejpam-4115	95	22	a	a	DET
ejpam-4115	95	23	collection	collection	NOUN
ejpam-4115	95	24	{	{	PUNCT
ejpam-4115	95	25	ei}∞i=1	ei}∞i=1	NOUN
ejpam-4115	95	26	of	of	ADP
ejpam-4115	95	27	subsets	subset	NOUN
ejpam-4115	95	28	of	of	ADP
ejpam-4115	95	29	[	[	X
ejpam-4115	95	30	a	a	X
ejpam-4115	95	31	,	,	PUNCT
ejpam-4115	95	32	b	b	NOUN
ejpam-4115	95	33	]	]	PUNCT
ejpam-4115	95	34	with	with	ADP
ejpam-4115	95	35	[	[	X
ejpam-4115	95	36	a	a	X
ejpam-4115	95	37	,	,	PUNCT
ejpam-4115	95	38	b	b	NOUN
ejpam-4115	95	39	]	]	X
ejpam-4115	95	40	=	=	PUNCT
ejpam-4115	95	41	⋃∞	⋃∞	X
ejpam-4115	95	42	i=1ei	i=1ei	ADV
ejpam-4115	95	43	such	such	ADJ
ejpam-4115	95	44	that	that	SCONJ
ejpam-4115	95	45	f	f	PROPN
ejpam-4115	95	46	is	be	AUX
ejpam-4115	95	47	ac∗(ei	ac∗(ei	PROPN
ejpam-4115	95	48	)	)	PUNCT
ejpam-4115	95	49	for	for	ADP
ejpam-4115	95	50	each	each	DET
ejpam-4115	95	51	i	i	PRON
ejpam-4115	95	52	∈	∈	PROPN
ejpam-4115	95	53	n.	n.	NOUN
ejpam-4115	95	54	definition	definition	NOUN
ejpam-4115	95	55	6	6	NUM
ejpam-4115	95	56	.	.	PUNCT
ejpam-4115	96	1	[	[	X
ejpam-4115	96	2	9	9	NUM
ejpam-4115	96	3	]	]	PUNCT
ejpam-4115	96	4	let	let	VERB
ejpam-4115	96	5	f	f	NOUN
ejpam-4115	96	6	:	:	PUNCT
ejpam-4115	97	1	[	[	X
ejpam-4115	97	2	a	a	X
ejpam-4115	97	3	,	,	PUNCT
ejpam-4115	97	4	b	b	NOUN
ejpam-4115	97	5	]	]	X
ejpam-4115	97	6	→	→	PUNCT
ejpam-4115	97	7	x	x	PART
ejpam-4115	97	8	be	be	AUX
ejpam-4115	97	9	a	a	DET
ejpam-4115	97	10	function	function	NOUN
ejpam-4115	97	11	and	and	CCONJ
ejpam-4115	97	12	let	let	VERB
ejpam-4115	97	13	t	t	X
ejpam-4115	97	14	∈	∈	PROPN
ejpam-4115	97	15	[	[	X
ejpam-4115	97	16	a	a	X
ejpam-4115	97	17	,	,	PUNCT
ejpam-4115	97	18	b	b	NOUN
ejpam-4115	97	19	]	]	X
ejpam-4115	97	20	.	.	PUNCT
ejpam-4115	98	1	then	then	ADV
ejpam-4115	98	2	f	f	PROPN
ejpam-4115	98	3	is	be	AUX
ejpam-4115	98	4	differentiable	differentiable	ADJ
ejpam-4115	98	5	at	at	ADP
ejpam-4115	98	6	t	t	PROPN
ejpam-4115	98	7	(	(	PUNCT
ejpam-4115	98	8	f	f	PROPN
ejpam-4115	98	9	′(t	′(t	PROPN
ejpam-4115	98	10	)	)	PUNCT
ejpam-4115	98	11	is	be	AUX
ejpam-4115	98	12	the	the	DET
ejpam-4115	98	13	derivative	derivative	NOUN
ejpam-4115	98	14	of	of	ADP
ejpam-4115	98	15	f	f	PROPN
ejpam-4115	98	16	at	at	ADP
ejpam-4115	98	17	t	t	PROPN
ejpam-4115	98	18	)	)	PUNCT
ejpam-4115	98	19	if	if	SCONJ
ejpam-4115	98	20	for	for	ADP
ejpam-4115	98	21	every	every	DET
ejpam-4115	98	22	θ	θ	PROPN
ejpam-4115	98	23	-	-	PUNCT
ejpam-4115	98	24	nbd	nbd	PROPN
ejpam-4115	98	25	u	u	PROPN
ejpam-4115	98	26	,	,	PUNCT
ejpam-4115	98	27	there	there	PRON
ejpam-4115	98	28	is	be	VERB
ejpam-4115	98	29	a	a	DET
ejpam-4115	98	30	δ	δ	PROPN
ejpam-4115	98	31	>	>	X
ejpam-4115	98	32	0	0	NUM
ejpam-4115	98	33	for	for	ADP
ejpam-4115	98	34	which	which	PRON
ejpam-4115	98	35	f	f	X
ejpam-4115	98	36	(	(	PUNCT
ejpam-4115	98	37	v)−	v)−	PROPN
ejpam-4115	98	38	f	f	X
ejpam-4115	98	39	(	(	PUNCT
ejpam-4115	98	40	u)−	u)−	PROPN
ejpam-4115	98	41	f	f	PROPN
ejpam-4115	99	1	′(t)(v	′(t)(v	PROPN
ejpam-4115	99	2	−	−	NUM
ejpam-4115	99	3	u	u	NOUN
ejpam-4115	99	4	)	)	PUNCT
ejpam-4115	99	5	∈	∈	PROPN
ejpam-4115	99	6	(	(	PUNCT
ejpam-4115	99	7	v	v	NOUN
ejpam-4115	99	8	−	−	NOUN
ejpam-4115	99	9	u)u	u)u	ADJ
ejpam-4115	99	10	whenever	whenever	SCONJ
ejpam-4115	99	11	t	t	PROPN
ejpam-4115	99	12	∈	∈	PROPN
ejpam-4115	100	1	[	[	X
ejpam-4115	100	2	u	u	NOUN
ejpam-4115	100	3	,	,	PUNCT
ejpam-4115	100	4	v	v	NOUN
ejpam-4115	100	5	]	]	PUNCT
ejpam-4115	100	6	⊆	⊆	NUM
ejpam-4115	100	7	[	[	X
ejpam-4115	100	8	a	a	X
ejpam-4115	100	9	,	,	PUNCT
ejpam-4115	100	10	b	b	NOUN
ejpam-4115	100	11	]	]	PUNCT
ejpam-4115	100	12	and	and	CCONJ
ejpam-4115	100	13	|v	|v	VERB
ejpam-4115	100	14	−	−	PROPN
ejpam-4115	101	1	u|	u|	PROPN
ejpam-4115	101	2	<	<	X
ejpam-4115	101	3	δ	δ	PROPN
ejpam-4115	101	4	.	.	PUNCT
ejpam-4115	101	5	r.	r.	PROPN
ejpam-4115	101	6	e.	e.	PROPN
ejpam-4115	101	7	maza	maza	PROPN
ejpam-4115	101	8	,	,	PUNCT
ejpam-4115	101	9	s.	s.	PROPN
ejpam-4115	101	10	r.	r.	PROPN
ejpam-4115	101	11	canoy	canoy	PROPN
ejpam-4115	101	12	,	,	PUNCT
ejpam-4115	101	13	jr	jr	PROPN
ejpam-4115	101	14	.	.	PROPN
ejpam-4115	101	15	/	/	SYM
ejpam-4115	101	16	eur	eur	PROPN
ejpam-4115	101	17	.	.	PUNCT
ejpam-4115	102	1	j.	j.	PROPN
ejpam-4115	102	2	pure	pure	PROPN
ejpam-4115	102	3	appl	appl	PROPN
ejpam-4115	102	4	.	.	PROPN
ejpam-4115	102	5	math	math	PROPN
ejpam-4115	102	6	,	,	PUNCT
ejpam-4115	102	7	14	14	NUM
ejpam-4115	102	8	(	(	PUNCT
ejpam-4115	102	9	4	4	NUM
ejpam-4115	102	10	)	)	PUNCT
ejpam-4115	102	11	(	(	PUNCT
ejpam-4115	102	12	2021	2021	NUM
ejpam-4115	102	13	)	)	PUNCT
ejpam-4115	102	14	,	,	PUNCT
ejpam-4115	102	15	1169	1169	NUM
ejpam-4115	102	16	-	-	SYM
ejpam-4115	102	17	1183	1183	NUM
ejpam-4115	102	18	1172	1172	NUM
ejpam-4115	102	19	definition	definition	NOUN
ejpam-4115	102	20	7	7	NUM
ejpam-4115	102	21	.	.	PUNCT
ejpam-4115	103	1	a	a	DET
ejpam-4115	103	2	function	function	NOUN
ejpam-4115	103	3	f	f	NOUN
ejpam-4115	103	4	:	:	PUNCT
ejpam-4115	104	1	[	[	X
ejpam-4115	104	2	a	a	X
ejpam-4115	104	3	,	,	PUNCT
ejpam-4115	104	4	b	b	NOUN
ejpam-4115	104	5	]	]	X
ejpam-4115	104	6	→	→	PUNCT
ejpam-4115	104	7	x	x	X
ejpam-4115	104	8	is	be	AUX
ejpam-4115	104	9	said	say	VERB
ejpam-4115	104	10	to	to	PART
ejpam-4115	104	11	be	be	AUX
ejpam-4115	104	12	denjoy	denjoy	VERB
ejpam-4115	104	13	integrable	integrable	ADJ
ejpam-4115	104	14	(	(	PUNCT
ejpam-4115	104	15	d∗-integrable	d∗-integrable	ADJ
ejpam-4115	104	16	)	)	PUNCT
ejpam-4115	104	17	on	on	ADP
ejpam-4115	104	18	[	[	X
ejpam-4115	104	19	a	a	X
ejpam-4115	104	20	,	,	PUNCT
ejpam-4115	104	21	b	b	NOUN
ejpam-4115	104	22	]	]	X
ejpam-4115	104	23	if	if	SCONJ
ejpam-4115	104	24	there	there	PRON
ejpam-4115	104	25	is	be	VERB
ejpam-4115	104	26	a	a	DET
ejpam-4115	104	27	function	function	NOUN
ejpam-4115	104	28	f	f	NOUN
ejpam-4115	104	29	:	:	PUNCT
ejpam-4115	105	1	[	[	X
ejpam-4115	105	2	a	a	X
ejpam-4115	105	3	,	,	PUNCT
ejpam-4115	105	4	b	b	NOUN
ejpam-4115	105	5	]	]	X
ejpam-4115	105	6	→	→	SYM
ejpam-4115	105	7	x	x	X
ejpam-4115	105	8	,	,	PUNCT
ejpam-4115	105	9	called	call	VERB
ejpam-4115	105	10	the	the	DET
ejpam-4115	105	11	denjoy	denjoy	NOUN
ejpam-4115	105	12	primitive	primitive	ADJ
ejpam-4115	105	13	of	of	ADP
ejpam-4115	105	14	f	f	PROPN
ejpam-4115	105	15	,	,	PUNCT
ejpam-4115	105	16	which	which	PRON
ejpam-4115	105	17	is	be	AUX
ejpam-4115	105	18	acg∗	acg∗	NOUN
ejpam-4115	105	19	on	on	ADP
ejpam-4115	105	20	[	[	X
ejpam-4115	105	21	a	a	X
ejpam-4115	105	22	,	,	PUNCT
ejpam-4115	105	23	b	b	NOUN
ejpam-4115	105	24	]	]	PUNCT
ejpam-4115	105	25	and	and	CCONJ
ejpam-4115	105	26	f	f	PROPN
ejpam-4115	105	27	′(t	′(t	PROPN
ejpam-4115	105	28	)	)	PUNCT
ejpam-4115	105	29	=	=	SYM
ejpam-4115	105	30	f(t	f(t	NOUN
ejpam-4115	105	31	)	)	PUNCT
ejpam-4115	105	32	almost	almost	ADV
ejpam-4115	105	33	everywhere	everywhere	ADV
ejpam-4115	105	34	on	on	ADP
ejpam-4115	105	35	[	[	X
ejpam-4115	105	36	a	a	X
ejpam-4115	105	37	,	,	PUNCT
ejpam-4115	105	38	b	b	NOUN
ejpam-4115	105	39	]	]	X
ejpam-4115	105	40	.	.	PUNCT
ejpam-4115	106	1	in	in	ADP
ejpam-4115	106	2	this	this	DET
ejpam-4115	106	3	case	case	NOUN
ejpam-4115	106	4	,	,	PUNCT
ejpam-4115	106	5	f	f	PROPN
ejpam-4115	106	6	(	(	PUNCT
ejpam-4115	106	7	b)−	b)−	PROPN
ejpam-4115	106	8	f	f	X
ejpam-4115	106	9	(	(	PUNCT
ejpam-4115	106	10	a	a	NOUN
ejpam-4115	106	11	)	)	PUNCT
ejpam-4115	106	12	is	be	AUX
ejpam-4115	106	13	the	the	DET
ejpam-4115	106	14	denjoy	denjoy	NOUN
ejpam-4115	106	15	integral	integral	ADJ
ejpam-4115	106	16	of	of	ADP
ejpam-4115	106	17	f	f	PROPN
ejpam-4115	106	18	on	on	ADP
ejpam-4115	106	19	[	[	X
ejpam-4115	106	20	a	a	X
ejpam-4115	106	21	,	,	PUNCT
ejpam-4115	106	22	b	b	NOUN
ejpam-4115	106	23	]	]	PUNCT
ejpam-4115	106	24	and	and	CCONJ
ejpam-4115	106	25	write	write	VERB
ejpam-4115	106	26	(	(	PUNCT
ejpam-4115	106	27	d∗	d∗	PROPN
ejpam-4115	106	28	)	)	PUNCT
ejpam-4115	106	29	∫	∫	PROPN
ejpam-4115	107	1	b	b	PROPN
ejpam-4115	107	2	a	a	DET
ejpam-4115	107	3	f	f	X
ejpam-4115	107	4	=	=	SYM
ejpam-4115	107	5	f	f	PROPN
ejpam-4115	107	6	(	(	PUNCT
ejpam-4115	107	7	b)−	b)−	PROPN
ejpam-4115	107	8	f	f	X
ejpam-4115	107	9	(	(	PUNCT
ejpam-4115	107	10	a	a	NOUN
ejpam-4115	107	11	)	)	PUNCT
ejpam-4115	107	12	.	.	PUNCT
ejpam-4115	108	1	definition	definition	NOUN
ejpam-4115	108	2	8	8	NUM
ejpam-4115	108	3	.	.	PUNCT
ejpam-4115	109	1	a	a	DET
ejpam-4115	109	2	function	function	NOUN
ejpam-4115	109	3	f	f	NOUN
ejpam-4115	109	4	:	:	PUNCT
ejpam-4115	110	1	[	[	X
ejpam-4115	110	2	a	a	X
ejpam-4115	110	3	,	,	PUNCT
ejpam-4115	110	4	b	b	NOUN
ejpam-4115	110	5	]	]	X
ejpam-4115	110	6	→	→	PUNCT
ejpam-4115	110	7	x	x	X
ejpam-4115	110	8	is	be	AUX
ejpam-4115	110	9	said	say	VERB
ejpam-4115	110	10	to	to	PART
ejpam-4115	110	11	be	be	AUX
ejpam-4115	110	12	weak	weak	ADJ
ejpam-4115	110	13	denjoy	denjoy	NOUN
ejpam-4115	110	14	integrable	integrable	ADJ
ejpam-4115	110	15	(	(	PUNCT
ejpam-4115	110	16	wd∗integrable	wd∗integrable	ADJ
ejpam-4115	110	17	)	)	PUNCT
ejpam-4115	110	18	on	on	ADP
ejpam-4115	110	19	[	[	X
ejpam-4115	110	20	a	a	X
ejpam-4115	110	21	,	,	PUNCT
ejpam-4115	110	22	b	b	NOUN
ejpam-4115	110	23	]	]	X
ejpam-4115	110	24	if	if	SCONJ
ejpam-4115	110	25	there	there	PRON
ejpam-4115	110	26	is	be	VERB
ejpam-4115	110	27	a	a	DET
ejpam-4115	110	28	function	function	NOUN
ejpam-4115	110	29	f	f	NOUN
ejpam-4115	110	30	:	:	PUNCT
ejpam-4115	111	1	[	[	X
ejpam-4115	111	2	a	a	X
ejpam-4115	111	3	,	,	PUNCT
ejpam-4115	111	4	b	b	NOUN
ejpam-4115	111	5	]	]	X
ejpam-4115	111	6	→	→	SYM
ejpam-4115	111	7	x	x	X
ejpam-4115	111	8	,	,	PUNCT
ejpam-4115	111	9	called	call	VERB
ejpam-4115	111	10	the	the	DET
ejpam-4115	111	11	weak	weak	ADJ
ejpam-4115	111	12	denjoy	denjoy	NOUN
ejpam-4115	111	13	primitive	primitive	ADJ
ejpam-4115	111	14	of	of	ADP
ejpam-4115	111	15	f	f	PROPN
ejpam-4115	111	16	,	,	PUNCT
ejpam-4115	111	17	which	which	PRON
ejpam-4115	111	18	is	be	AUX
ejpam-4115	111	19	acg∗	acg∗	NOUN
ejpam-4115	111	20	on	on	ADP
ejpam-4115	111	21	[	[	X
ejpam-4115	111	22	a	a	X
ejpam-4115	111	23	,	,	PUNCT
ejpam-4115	111	24	b	b	NOUN
ejpam-4115	111	25	]	]	X
ejpam-4115	111	26	and	and	CCONJ
ejpam-4115	111	27	∆(u	∆(u	ADJ
ejpam-4115	111	28	,	,	PUNCT
ejpam-4115	111	29	f	f	PROPN
ejpam-4115	111	30	,	,	PUNCT
ejpam-4115	111	31	f	f	X
ejpam-4115	111	32	)	)	PUNCT
ejpam-4115	111	33	has	have	VERB
ejpam-4115	111	34	measure	measure	NOUN
ejpam-4115	111	35	zero	zero	NUM
ejpam-4115	111	36	for	for	ADP
ejpam-4115	111	37	all	all	DET
ejpam-4115	111	38	θ	θ	PROPN
ejpam-4115	111	39	-	-	ADJ
ejpam-4115	111	40	nbds	nbds	NOUN
ejpam-4115	111	41	u	u	NOUN
ejpam-4115	111	42	,	,	PUNCT
ejpam-4115	111	43	where	where	SCONJ
ejpam-4115	111	44	∆(u	∆(u	NOUN
ejpam-4115	111	45	,	,	PUNCT
ejpam-4115	111	46	f	f	PROPN
ejpam-4115	111	47	,	,	PUNCT
ejpam-4115	111	48	f	f	X
ejpam-4115	111	49	)	)	PUNCT
ejpam-4115	111	50	=	=	PRON
ejpam-4115	111	51	{	{	PUNCT
ejpam-4115	111	52	t	t	NOUN
ejpam-4115	111	53	∈	∈	PROPN
ejpam-4115	112	1	[	[	X
ejpam-4115	112	2	a	a	X
ejpam-4115	112	3	,	,	PUNCT
ejpam-4115	112	4	b	b	NOUN
ejpam-4115	112	5	]	]	X
ejpam-4115	112	6	:	:	PUNCT
ejpam-4115	112	7	∀δ	∀δ	X
ejpam-4115	112	8	>	>	X
ejpam-4115	112	9	0	0	NUM
ejpam-4115	112	10	,	,	PUNCT
ejpam-4115	112	11	∃[u	∃[u	NOUN
ejpam-4115	112	12	,	,	PUNCT
ejpam-4115	112	13	v	v	NOUN
ejpam-4115	112	14	]	]	PUNCT
ejpam-4115	112	15	⊆	⊆	NUM
ejpam-4115	112	16	[	[	X
ejpam-4115	112	17	a	a	X
ejpam-4115	112	18	,	,	PUNCT
ejpam-4115	112	19	b	b	NOUN
ejpam-4115	112	20	]	]	X
ejpam-4115	112	21	with	with	ADP
ejpam-4115	112	22	t	t	PROPN
ejpam-4115	112	23	∈	∈	PROPN
ejpam-4115	113	1	[	[	X
ejpam-4115	113	2	u	u	NOUN
ejpam-4115	113	3	,	,	PUNCT
ejpam-4115	113	4	v	v	NOUN
ejpam-4115	113	5	]	]	PUNCT
ejpam-4115	113	6	and	and	CCONJ
ejpam-4115	113	7	|v	|v	VERB
ejpam-4115	113	8	−	−	PROPN
ejpam-4115	114	1	u|	u|	PROPN
ejpam-4115	114	2	<	<	X
ejpam-4115	114	3	δ	δ	PROPN
ejpam-4115	114	4	such	such	ADJ
ejpam-4115	114	5	that	that	SCONJ
ejpam-4115	114	6	f	f	PROPN
ejpam-4115	114	7	(	(	PUNCT
ejpam-4115	114	8	v)−	v)−	PROPN
ejpam-4115	114	9	f	f	X
ejpam-4115	114	10	(	(	PUNCT
ejpam-4115	114	11	u)−	u)−	PROPN
ejpam-4115	114	12	f(t)(v	f(t)(v	X
ejpam-4115	114	13	−	−	PROPN
ejpam-4115	114	14	u	u	NOUN
ejpam-4115	114	15	)	)	PUNCT
ejpam-4115	114	16	/∈	/∈	PUNCT
ejpam-4115	115	1	(	(	PUNCT
ejpam-4115	115	2	v	v	ADP
ejpam-4115	115	3	−	−	NOUN
ejpam-4115	115	4	u)u	u)u	ADJ
ejpam-4115	115	5	}	}	PUNCT
ejpam-4115	115	6	.	.	PUNCT
ejpam-4115	116	1	we	we	PRON
ejpam-4115	116	2	denote	denote	VERB
ejpam-4115	116	3	the	the	DET
ejpam-4115	116	4	weak	weak	ADJ
ejpam-4115	116	5	denjoy	denjoy	NOUN
ejpam-4115	116	6	integral	integral	ADJ
ejpam-4115	116	7	of	of	ADP
ejpam-4115	116	8	f	f	PROPN
ejpam-4115	116	9	on	on	ADP
ejpam-4115	116	10	[	[	X
ejpam-4115	116	11	a	a	X
ejpam-4115	116	12	,	,	PUNCT
ejpam-4115	116	13	b	b	NOUN
ejpam-4115	116	14	]	]	PUNCT
ejpam-4115	116	15	by	by	ADP
ejpam-4115	116	16	(	(	PUNCT
ejpam-4115	116	17	wd∗	wd∗	ADJ
ejpam-4115	116	18	)	)	PUNCT
ejpam-4115	116	19	∫	∫	PROPN
ejpam-4115	116	20	b	b	PROPN
ejpam-4115	116	21	a	a	DET
ejpam-4115	116	22	f	f	X
ejpam-4115	116	23	=	=	SYM
ejpam-4115	116	24	f	f	PROPN
ejpam-4115	116	25	(	(	PUNCT
ejpam-4115	116	26	b)−	b)−	PROPN
ejpam-4115	116	27	f	f	X
ejpam-4115	116	28	(	(	PUNCT
ejpam-4115	116	29	a	a	NOUN
ejpam-4115	116	30	)	)	PUNCT
ejpam-4115	116	31	.	.	PUNCT
ejpam-4115	117	1	for	for	ADP
ejpam-4115	117	2	a	a	DET
ejpam-4115	117	3	banach	banach	NOUN
ejpam-4115	117	4	space	space	NOUN
ejpam-4115	117	5	x	x	NOUN
ejpam-4115	117	6	,	,	PUNCT
ejpam-4115	117	7	the	the	DET
ejpam-4115	117	8	concepts	concept	NOUN
ejpam-4115	117	9	of	of	ADP
ejpam-4115	117	10	ac∗	ac∗	ADJ
ejpam-4115	117	11	and	and	CCONJ
ejpam-4115	117	12	acg∗	acg∗	NOUN
ejpam-4115	117	13	are	be	AUX
ejpam-4115	117	14	defined	define	VERB
ejpam-4115	117	15	in	in	ADP
ejpam-4115	117	16	the	the	DET
ejpam-4115	117	17	following	following	ADJ
ejpam-4115	117	18	way	way	NOUN
ejpam-4115	117	19	.	.	PUNCT
ejpam-4115	118	1	definition	definition	NOUN
ejpam-4115	118	2	9	9	NUM
ejpam-4115	118	3	.	.	PUNCT
ejpam-4115	119	1	[	[	X
ejpam-4115	119	2	1	1	NUM
ejpam-4115	119	3	,	,	PUNCT
ejpam-4115	119	4	12	12	NUM
ejpam-4115	119	5	]	]	PUNCT
ejpam-4115	119	6	a	a	DET
ejpam-4115	119	7	function	function	NOUN
ejpam-4115	119	8	f	f	NOUN
ejpam-4115	120	1	:	:	PUNCT
ejpam-4115	120	2	[	[	X
ejpam-4115	120	3	a	a	X
ejpam-4115	120	4	,	,	PUNCT
ejpam-4115	120	5	b	b	NOUN
ejpam-4115	120	6	]	]	X
ejpam-4115	120	7	→	→	PUNCT
ejpam-4115	120	8	x	x	X
ejpam-4115	120	9	is	be	AUX
ejpam-4115	120	10	said	say	VERB
ejpam-4115	120	11	to	to	PART
ejpam-4115	120	12	be	be	AUX
ejpam-4115	120	13	ac∗(e	ac∗(e	NUM
ejpam-4115	120	14	)	)	PUNCT
ejpam-4115	120	15	,	,	PUNCT
ejpam-4115	120	16	where	where	SCONJ
ejpam-4115	120	17	e	e	PROPN
ejpam-4115	120	18	⊂	⊂	PROPN
ejpam-4115	120	19	[	[	X
ejpam-4115	120	20	a	a	X
ejpam-4115	120	21	,	,	PUNCT
ejpam-4115	120	22	b	b	NOUN
ejpam-4115	120	23	]	]	X
ejpam-4115	120	24	,	,	PUNCT
ejpam-4115	120	25	if	if	SCONJ
ejpam-4115	120	26	for	for	ADP
ejpam-4115	120	27	every	every	DET
ejpam-4115	120	28	ϵ	ϵ	X
ejpam-4115	120	29	>	>	X
ejpam-4115	120	30	0	0	NUM
ejpam-4115	120	31	,	,	PUNCT
ejpam-4115	120	32	there	there	PRON
ejpam-4115	120	33	exists	exist	VERB
ejpam-4115	120	34	a	a	DET
ejpam-4115	120	35	δ	δ	PROPN
ejpam-4115	120	36	>	>	X
ejpam-4115	120	37	0	0	NUM
ejpam-4115	120	38	such	such	ADJ
ejpam-4115	120	39	that	that	PRON
ejpam-4115	120	40	for	for	ADP
ejpam-4115	120	41	any	any	DET
ejpam-4115	120	42	partial	partial	ADJ
ejpam-4115	120	43	partition	partition	NOUN
ejpam-4115	120	44	d	d	NOUN
ejpam-4115	120	45	=	=	PRON
ejpam-4115	120	46	{	{	PUNCT
ejpam-4115	120	47	[	[	X
ejpam-4115	120	48	ui	ui	PROPN
ejpam-4115	120	49	,	,	PUNCT
ejpam-4115	120	50	vi	vi	PROPN
ejpam-4115	120	51	]	]	X
ejpam-4115	120	52	:	:	PUNCT
ejpam-4115	120	53	1	1	NUM
ejpam-4115	120	54	≤	≤	NUM
ejpam-4115	120	55	i	i	PRON
ejpam-4115	120	56	≤	≤	NOUN
ejpam-4115	120	57	n	n	CCONJ
ejpam-4115	120	58	}	}	PUNCT
ejpam-4115	120	59	of	of	ADP
ejpam-4115	120	60	[	[	X
ejpam-4115	120	61	a	a	X
ejpam-4115	120	62	,	,	PUNCT
ejpam-4115	120	63	b	b	NOUN
ejpam-4115	120	64	]	]	X
ejpam-4115	120	65	with	with	ADP
ejpam-4115	120	66	ui	ui	NOUN
ejpam-4115	120	67	or	or	CCONJ
ejpam-4115	120	68	vi	vi	NOUN
ejpam-4115	120	69	∈	∈	PROPN
ejpam-4115	120	70	e	e	NOUN
ejpam-4115	120	71	and	and	CCONJ
ejpam-4115	120	72	∑n	∑n	PROPN
ejpam-4115	120	73	i=1(vi	i=1(vi	NOUN
ejpam-4115	120	74	−	−	PROPN
ejpam-4115	120	75	ui	ui	PROPN
ejpam-4115	120	76	)	)	PUNCT
ejpam-4115	120	77	<	<	X
ejpam-4115	120	78	δ	δ	PROPN
ejpam-4115	120	79	,	,	PUNCT
ejpam-4115	120	80	∑n	∑n	PROPN
ejpam-4115	120	81	i=1∥f	i=1∥f	PROPN
ejpam-4115	120	82	(	(	PUNCT
ejpam-4115	120	83	vi)−	vi)−	NOUN
ejpam-4115	120	84	f	f	NOUN
ejpam-4115	120	85	(	(	PUNCT
ejpam-4115	120	86	ui)∥	ui)∥	NOUN
ejpam-4115	120	87	<	<	X
ejpam-4115	120	88	ϵ.	ϵ.	NOUN
ejpam-4115	120	89	definition	definition	NOUN
ejpam-4115	120	90	10	10	NUM
ejpam-4115	120	91	.	.	PUNCT
ejpam-4115	121	1	[	[	X
ejpam-4115	121	2	1	1	NUM
ejpam-4115	121	3	,	,	PUNCT
ejpam-4115	121	4	12	12	NUM
ejpam-4115	121	5	]	]	PUNCT
ejpam-4115	121	6	a	a	DET
ejpam-4115	121	7	function	function	NOUN
ejpam-4115	121	8	f	f	NOUN
ejpam-4115	122	1	:	:	PUNCT
ejpam-4115	122	2	[	[	X
ejpam-4115	122	3	a	a	X
ejpam-4115	122	4	,	,	PUNCT
ejpam-4115	122	5	b	b	NOUN
ejpam-4115	122	6	]	]	X
ejpam-4115	122	7	→	→	PUNCT
ejpam-4115	122	8	x	x	X
ejpam-4115	122	9	is	be	AUX
ejpam-4115	122	10	said	say	VERB
ejpam-4115	122	11	to	to	PART
ejpam-4115	122	12	be	be	AUX
ejpam-4115	122	13	acg∗	acg∗	NOUN
ejpam-4115	122	14	on	on	ADP
ejpam-4115	122	15	[	[	X
ejpam-4115	122	16	a	a	X
ejpam-4115	122	17	,	,	PUNCT
ejpam-4115	122	18	b	b	NOUN
ejpam-4115	122	19	]	]	X
ejpam-4115	122	20	if	if	SCONJ
ejpam-4115	122	21	there	there	PRON
ejpam-4115	122	22	exists	exist	VERB
ejpam-4115	122	23	a	a	DET
ejpam-4115	122	24	collection	collection	NOUN
ejpam-4115	122	25	{	{	PUNCT
ejpam-4115	122	26	ei}∞i=1	ei}∞i=1	NOUN
ejpam-4115	122	27	of	of	ADP
ejpam-4115	122	28	subsets	subset	NOUN
ejpam-4115	122	29	of	of	ADP
ejpam-4115	122	30	[	[	X
ejpam-4115	122	31	a	a	X
ejpam-4115	122	32	,	,	PUNCT
ejpam-4115	122	33	b	b	NOUN
ejpam-4115	122	34	]	]	PUNCT
ejpam-4115	122	35	with	with	ADP
ejpam-4115	122	36	[	[	X
ejpam-4115	122	37	a	a	X
ejpam-4115	122	38	,	,	PUNCT
ejpam-4115	122	39	b	b	NOUN
ejpam-4115	122	40	]	]	X
ejpam-4115	122	41	=	=	PUNCT
ejpam-4115	122	42	⋃∞	⋃∞	X
ejpam-4115	122	43	i=1ei	i=1ei	ADV
ejpam-4115	122	44	such	such	ADJ
ejpam-4115	122	45	that	that	SCONJ
ejpam-4115	122	46	f	f	PROPN
ejpam-4115	122	47	is	be	AUX
ejpam-4115	122	48	ac∗(ei	ac∗(ei	PROPN
ejpam-4115	122	49	)	)	PUNCT
ejpam-4115	122	50	for	for	ADP
ejpam-4115	122	51	each	each	DET
ejpam-4115	122	52	i	i	PRON
ejpam-4115	122	53	∈	∈	PROPN
ejpam-4115	122	54	n.	n.	NOUN
ejpam-4115	122	55	definition	definition	NOUN
ejpam-4115	122	56	11	11	NUM
ejpam-4115	122	57	.	.	PUNCT
ejpam-4115	123	1	[	[	X
ejpam-4115	123	2	12	12	NUM
ejpam-4115	123	3	]	]	PUNCT
ejpam-4115	123	4	a	a	DET
ejpam-4115	123	5	function	function	NOUN
ejpam-4115	123	6	f	f	NOUN
ejpam-4115	123	7	:	:	PUNCT
ejpam-4115	124	1	[	[	X
ejpam-4115	124	2	a	a	X
ejpam-4115	124	3	,	,	PUNCT
ejpam-4115	124	4	b	b	NOUN
ejpam-4115	124	5	]	]	X
ejpam-4115	124	6	→	→	PUNCT
ejpam-4115	124	7	x	x	X
ejpam-4115	124	8	is	be	AUX
ejpam-4115	124	9	said	say	VERB
ejpam-4115	124	10	to	to	PART
ejpam-4115	124	11	be	be	AUX
ejpam-4115	124	12	denjoy	denjoy	NOUN
ejpam-4115	124	13	-	-	PUNCT
ejpam-4115	124	14	bochner	bochner	NOUN
ejpam-4115	124	15	integrable	integrable	ADJ
ejpam-4115	124	16	(	(	PUNCT
ejpam-4115	124	17	d∗b	d∗b	ADJ
ejpam-4115	124	18	-	-	ADJ
ejpam-4115	124	19	integrable	integrable	ADJ
ejpam-4115	124	20	)	)	PUNCT
ejpam-4115	124	21	on	on	ADP
ejpam-4115	124	22	[	[	X
ejpam-4115	124	23	a	a	X
ejpam-4115	124	24	,	,	PUNCT
ejpam-4115	124	25	b	b	NOUN
ejpam-4115	124	26	]	]	X
ejpam-4115	124	27	if	if	SCONJ
ejpam-4115	124	28	there	there	PRON
ejpam-4115	124	29	is	be	VERB
ejpam-4115	124	30	an	an	DET
ejpam-4115	124	31	acg∗-function	acg∗-function	PROPN
ejpam-4115	124	32	f	f	NOUN
ejpam-4115	124	33	:	:	PUNCT
ejpam-4115	125	1	[	[	X
ejpam-4115	125	2	a	a	X
ejpam-4115	125	3	,	,	PUNCT
ejpam-4115	125	4	b	b	NOUN
ejpam-4115	125	5	]	]	X
ejpam-4115	125	6	→	→	PUNCT
ejpam-4115	125	7	x	x	X
ejpam-4115	125	8	such	such	ADJ
ejpam-4115	125	9	that	that	SCONJ
ejpam-4115	125	10	f	f	PROPN
ejpam-4115	125	11	′(t	′(t	PROPN
ejpam-4115	125	12	)	)	PUNCT
ejpam-4115	125	13	=	=	SYM
ejpam-4115	125	14	f(t	f(t	NOUN
ejpam-4115	125	15	)	)	PUNCT
ejpam-4115	125	16	almost	almost	ADV
ejpam-4115	125	17	everywhere	everywhere	ADV
ejpam-4115	125	18	on	on	ADP
ejpam-4115	125	19	[	[	X
ejpam-4115	125	20	a	a	X
ejpam-4115	125	21	,	,	PUNCT
ejpam-4115	125	22	b	b	NOUN
ejpam-4115	125	23	]	]	X
ejpam-4115	125	24	.	.	PUNCT
ejpam-4115	126	1	2	2	X
ejpam-4115	126	2	.	.	X
ejpam-4115	126	3	results	result	NOUN
ejpam-4115	126	4	remark	remark	VERB
ejpam-4115	126	5	1	1	NUM
ejpam-4115	126	6	.	.	PUNCT
ejpam-4115	127	1	the	the	DET
ejpam-4115	127	2	conditions	condition	NOUN
ejpam-4115	127	3	ac	ac	VERB
ejpam-4115	127	4	and	and	CCONJ
ejpam-4115	127	5	ac∗	ac∗	PROPN
ejpam-4115	127	6	are	be	AUX
ejpam-4115	127	7	equivalent	equivalent	ADJ
ejpam-4115	127	8	when	when	SCONJ
ejpam-4115	127	9	e	e	X
ejpam-4115	127	10	=	=	PUNCT
ejpam-4115	128	1	[	[	X
ejpam-4115	128	2	a	a	X
ejpam-4115	128	3	,	,	PUNCT
ejpam-4115	128	4	b	b	NOUN
ejpam-4115	128	5	]	]	X
ejpam-4115	128	6	.	.	PUNCT
ejpam-4115	129	1	every	every	DET
ejpam-4115	129	2	absolutely	absolutely	ADV
ejpam-4115	129	3	continuous	continuous	ADJ
ejpam-4115	129	4	function	function	NOUN
ejpam-4115	129	5	on	on	ADP
ejpam-4115	129	6	[	[	X
ejpam-4115	129	7	a	a	X
ejpam-4115	129	8	,	,	PUNCT
ejpam-4115	129	9	b	b	NOUN
ejpam-4115	129	10	]	]	X
ejpam-4115	129	11	is	be	AUX
ejpam-4115	129	12	also	also	ADV
ejpam-4115	129	13	acg∗	acg∗	ADJ
ejpam-4115	129	14	on	on	ADP
ejpam-4115	129	15	[	[	X
ejpam-4115	129	16	a	a	X
ejpam-4115	129	17	,	,	PUNCT
ejpam-4115	129	18	b	b	NOUN
ejpam-4115	129	19	]	]	PUNCT
ejpam-4115	129	20	.	.	PUNCT
ejpam-4115	129	21	example	example	NOUN
ejpam-4115	130	1	1	1	NUM
ejpam-4115	130	2	.	.	PUNCT
ejpam-4115	131	1	any	any	DET
ejpam-4115	131	2	function	function	NOUN
ejpam-4115	131	3	of	of	ADP
ejpam-4115	131	4	the	the	DET
ejpam-4115	131	5	form	form	NOUN
ejpam-4115	131	6	l(t	l(t	X
ejpam-4115	131	7	)	)	PUNCT
ejpam-4115	132	1	=	=	PUNCT
ejpam-4115	132	2	tu+	tu+	X
ejpam-4115	132	3	v	v	NOUN
ejpam-4115	132	4	is	be	AUX
ejpam-4115	132	5	acg∗	acg∗	NOUN
ejpam-4115	132	6	on	on	ADP
ejpam-4115	132	7	[	[	X
ejpam-4115	132	8	a	a	X
ejpam-4115	132	9	,	,	PUNCT
ejpam-4115	132	10	b	b	NOUN
ejpam-4115	132	11	]	]	X
ejpam-4115	132	12	where	where	SCONJ
ejpam-4115	132	13	u	u	NOUN
ejpam-4115	132	14	,	,	PUNCT
ejpam-4115	132	15	v	v	PROPN
ejpam-4115	132	16	∈	∈	PROPN
ejpam-4115	132	17	x	x	PUNCT
ejpam-4115	132	18	is	be	AUX
ejpam-4115	132	19	absolutely	absolutely	ADV
ejpam-4115	132	20	continuous	continuous	ADJ
ejpam-4115	132	21	(	(	PUNCT
ejpam-4115	132	22	so	so	ADV
ejpam-4115	132	23	also	also	ADV
ejpam-4115	132	24	acg∗	acg∗	NOUN
ejpam-4115	132	25	on	on	ADP
ejpam-4115	132	26	[	[	X
ejpam-4115	132	27	a	a	PRON
ejpam-4115	132	28	,	,	PUNCT
ejpam-4115	132	29	b	b	NOUN
ejpam-4115	132	30	]	]	X
ejpam-4115	132	31	)	)	PUNCT
ejpam-4115	132	32	.	.	PUNCT
ejpam-4115	133	1	in	in	ADP
ejpam-4115	133	2	particular	particular	ADJ
ejpam-4115	133	3	,	,	PUNCT
ejpam-4115	133	4	every	every	DET
ejpam-4115	133	5	constant	constant	ADJ
ejpam-4115	133	6	function	function	NOUN
ejpam-4115	133	7	is	be	AUX
ejpam-4115	133	8	acg∗	acg∗	NOUN
ejpam-4115	133	9	on	on	ADP
ejpam-4115	133	10	[	[	X
ejpam-4115	133	11	a	a	X
ejpam-4115	133	12	,	,	PUNCT
ejpam-4115	133	13	b	b	NOUN
ejpam-4115	133	14	]	]	PUNCT
ejpam-4115	133	15	.	.	PUNCT
ejpam-4115	134	1	to	to	PART
ejpam-4115	134	2	see	see	VERB
ejpam-4115	134	3	this	this	PRON
ejpam-4115	134	4	,	,	PUNCT
ejpam-4115	134	5	let	let	VERB
ejpam-4115	134	6	v	v	PART
ejpam-4115	134	7	be	be	AUX
ejpam-4115	134	8	a	a	DET
ejpam-4115	134	9	given	give	VERB
ejpam-4115	134	10	θ	θ	PROPN
ejpam-4115	134	11	-	-	PUNCT
ejpam-4115	134	12	nbd	nbd	PROPN
ejpam-4115	134	13	.	.	PUNCT
ejpam-4115	135	1	let	let	VERB
ejpam-4115	135	2	u	u	PRON
ejpam-4115	135	3	⊆	⊆	NUM
ejpam-4115	135	4	v	v	NOUN
ejpam-4115	135	5	be	be	AUX
ejpam-4115	135	6	an	an	DET
ejpam-4115	135	7	absorbing	absorbing	ADJ
ejpam-4115	135	8	,	,	PUNCT
ejpam-4115	135	9	balanced	balanced	ADJ
ejpam-4115	135	10	and	and	CCONJ
ejpam-4115	135	11	convex	convex	ADJ
ejpam-4115	135	12	θ	θ	PROPN
ejpam-4115	135	13	-	-	PUNCT
ejpam-4115	135	14	nbd	nbd	PROPN
ejpam-4115	135	15	.	.	PUNCT
ejpam-4115	136	1	then	then	ADV
ejpam-4115	136	2	there	there	PRON
ejpam-4115	136	3	exists	exist	VERB
ejpam-4115	136	4	η	η	PROPN
ejpam-4115	136	5	>	>	X
ejpam-4115	136	6	0	0	NUM
ejpam-4115	136	7	such	such	ADJ
ejpam-4115	136	8	that	that	SCONJ
ejpam-4115	136	9	ru	ru	PROPN
ejpam-4115	136	10	∈	∈	PROPN
ejpam-4115	136	11	u	u	NOUN
ejpam-4115	136	12	for	for	ADP
ejpam-4115	136	13	all	all	DET
ejpam-4115	136	14	r	r	NOUN
ejpam-4115	136	15	∈	∈	NOUN
ejpam-4115	136	16	r	r	NOUN
ejpam-4115	136	17	with	with	ADP
ejpam-4115	136	18	|r|	|r|	PROPN
ejpam-4115	136	19	<	<	X
ejpam-4115	136	20	η	η	PROPN
ejpam-4115	136	21	.	.	PROPN
ejpam-4115	136	22	let	let	VERB
ejpam-4115	136	23	r.	r.	PROPN
ejpam-4115	136	24	e.	e.	PROPN
ejpam-4115	136	25	maza	maza	PROPN
ejpam-4115	136	26	,	,	PUNCT
ejpam-4115	136	27	s.	s.	PROPN
ejpam-4115	136	28	r.	r.	PROPN
ejpam-4115	136	29	canoy	canoy	PROPN
ejpam-4115	136	30	,	,	PUNCT
ejpam-4115	136	31	jr	jr	PROPN
ejpam-4115	136	32	.	.	PROPN
ejpam-4115	136	33	/	/	SYM
ejpam-4115	136	34	eur	eur	PROPN
ejpam-4115	136	35	.	.	PUNCT
ejpam-4115	137	1	j.	j.	PROPN
ejpam-4115	137	2	pure	pure	PROPN
ejpam-4115	137	3	appl	appl	PROPN
ejpam-4115	137	4	.	.	PROPN
ejpam-4115	137	5	math	math	PROPN
ejpam-4115	137	6	,	,	PUNCT
ejpam-4115	137	7	14	14	NUM
ejpam-4115	137	8	(	(	PUNCT
ejpam-4115	137	9	4	4	NUM
ejpam-4115	137	10	)	)	PUNCT
ejpam-4115	137	11	(	(	PUNCT
ejpam-4115	137	12	2021	2021	NUM
ejpam-4115	137	13	)	)	PUNCT
ejpam-4115	137	14	,	,	PUNCT
ejpam-4115	137	15	1169	1169	NUM
ejpam-4115	137	16	-	-	SYM
ejpam-4115	137	17	1183	1183	NUM
ejpam-4115	137	18	1173	1173	NUM
ejpam-4115	137	19	d	d	NOUN
ejpam-4115	137	20	=	=	PRON
ejpam-4115	137	21	{	{	PUNCT
ejpam-4115	137	22	[	[	X
ejpam-4115	137	23	xi	xi	X
ejpam-4115	137	24	,	,	PUNCT
ejpam-4115	137	25	yi	yi	NOUN
ejpam-4115	137	26	]	]	X
ejpam-4115	137	27	:	:	PUNCT
ejpam-4115	137	28	1	1	NUM
ejpam-4115	137	29	≤	≤	NUM
ejpam-4115	137	30	i	i	PRON
ejpam-4115	137	31	≤	≤	PROPN
ejpam-4115	137	32	n	n	CCONJ
ejpam-4115	137	33	}	}	PUNCT
ejpam-4115	137	34	be	be	AUX
ejpam-4115	137	35	a	a	DET
ejpam-4115	137	36	partial	partial	ADJ
ejpam-4115	137	37	partition	partition	NOUN
ejpam-4115	137	38	of	of	ADP
ejpam-4115	137	39	[	[	X
ejpam-4115	137	40	a	a	X
ejpam-4115	137	41	,	,	PUNCT
ejpam-4115	137	42	b	b	NOUN
ejpam-4115	137	43	]	]	X
ejpam-4115	137	44	with	with	ADP
ejpam-4115	137	45	∑n	∑n	PROPN
ejpam-4115	137	46	i=1(yi	i=1(yi	PRON
ejpam-4115	137	47	−	−	PROPN
ejpam-4115	137	48	xi	xi	NOUN
ejpam-4115	137	49	)	)	PUNCT
ejpam-4115	137	50	=	=	SYM
ejpam-4115	137	51	η∗	η∗	NOUN
ejpam-4115	137	52	<	<	X
ejpam-4115	137	53	η	η	PROPN
ejpam-4115	137	54	.	.	PROPN
ejpam-4115	138	1	then	then	ADV
ejpam-4115	138	2	u	u	PROPN
ejpam-4115	138	3	∈	∈	PROPN
ejpam-4115	138	4	1	1	NUM
ejpam-4115	138	5	η∗u	η∗u	NUM
ejpam-4115	138	6	and	and	CCONJ
ejpam-4115	138	7	(	(	PUNCT
ejpam-4115	138	8	yi	yi	NOUN
ejpam-4115	138	9	−	−	PROPN
ejpam-4115	138	10	xi)u	xi)u	PROPN
ejpam-4115	138	11	∈	∈	PROPN
ejpam-4115	138	12	ui	ui	NOUN
ejpam-4115	139	1	=	=	PUNCT
ejpam-4115	139	2	yi−xi	yi−xi	ADV
ejpam-4115	139	3	η∗	η∗	NOUN
ejpam-4115	139	4	u	u	PROPN
ejpam-4115	139	5	for	for	ADP
ejpam-4115	139	6	each	each	DET
ejpam-4115	139	7	i	i	PRON
ejpam-4115	139	8	∈	∈	PROPN
ejpam-4115	139	9	{	{	PUNCT
ejpam-4115	139	10	1	1	NUM
ejpam-4115	139	11	,	,	PUNCT
ejpam-4115	139	12	2	2	NUM
ejpam-4115	139	13	,	,	PUNCT
ejpam-4115	139	14	,	,	PUNCT
ejpam-4115	139	15	.	.	PUNCT
ejpam-4115	139	16	.	.	PUNCT
ejpam-4115	139	17	.	.	PUNCT
ejpam-4115	139	18	,	,	PUNCT
ejpam-4115	139	19	n	n	CCONJ
ejpam-4115	139	20	}	}	PUNCT
ejpam-4115	139	21	.	.	PUNCT
ejpam-4115	140	1	thus	thus	ADV
ejpam-4115	140	2	,	,	PUNCT
ejpam-4115	140	3	l(yi)−	l(yi)−	X
ejpam-4115	140	4	l(xi	l(xi	PROPN
ejpam-4115	140	5	)	)	PUNCT
ejpam-4115	140	6	=	=	SYM
ejpam-4115	141	1	yiu+	yiu+	NOUN
ejpam-4115	141	2	v−	v−	NOUN
ejpam-4115	141	3	(	(	PUNCT
ejpam-4115	141	4	xiu+	xiu+	PROPN
ejpam-4115	141	5	v	v	NOUN
ejpam-4115	141	6	)	)	PUNCT
ejpam-4115	141	7	=	=	SYM
ejpam-4115	141	8	(	(	PUNCT
ejpam-4115	141	9	yi	yi	NOUN
ejpam-4115	141	10	−	−	PROPN
ejpam-4115	141	11	xi)u	xi)u	PROPN
ejpam-4115	141	12	∈	∈	PROPN
ejpam-4115	141	13	yi	yi	NOUN
ejpam-4115	142	1	−	−	NOUN
ejpam-4115	142	2	xi	xi	ADP
ejpam-4115	142	3	η∗	η∗	PROPN
ejpam-4115	142	4	u	u	NOUN
ejpam-4115	142	5	=	=	PROPN
ejpam-4115	142	6	ui	ui	PROPN
ejpam-4115	142	7	for	for	ADP
ejpam-4115	142	8	all	all	PRON
ejpam-4115	142	9	i	i	PRON
ejpam-4115	142	10	∈	∈	PROPN
ejpam-4115	142	11	{	{	PUNCT
ejpam-4115	142	12	1	1	NUM
ejpam-4115	142	13	,	,	PUNCT
ejpam-4115	142	14	2	2	NUM
ejpam-4115	142	15	,	,	PUNCT
ejpam-4115	142	16	·	·	PUNCT
ejpam-4115	142	17	·	·	PUNCT
ejpam-4115	142	18	·	·	PUNCT
ejpam-4115	142	19	,	,	PUNCT
ejpam-4115	142	20	n	n	CCONJ
ejpam-4115	142	21	}	}	PUNCT
ejpam-4115	142	22	.	.	PUNCT
ejpam-4115	143	1	since	since	SCONJ
ejpam-4115	143	2	∑n	∑n	PROPN
ejpam-4115	143	3	i=1	i=1	PROPN
ejpam-4115	143	4	yi−xi	yi−xi	ADJ
ejpam-4115	143	5	η∗	η∗	NOUN
ejpam-4115	143	6	=	=	SYM
ejpam-4115	143	7	1	1	NUM
ejpam-4115	143	8	and	and	CCONJ
ejpam-4115	143	9	u	u	NOUN
ejpam-4115	143	10	is	be	AUX
ejpam-4115	143	11	convex	convex	ADJ
ejpam-4115	143	12	,	,	PUNCT
ejpam-4115	143	13	∑n	∑n	PROPN
ejpam-4115	143	14	i=1	i=1	PROPN
ejpam-4115	143	15	yi−xi	yi−xi	ADJ
ejpam-4115	143	16	η∗	η∗	NOUN
ejpam-4115	143	17	u	u	NOUN
ejpam-4115	144	1	=	=	PUNCT
ejpam-4115	144	2	∑n	∑n	PROPN
ejpam-4115	144	3	i=1	i=1	PROPN
ejpam-4115	144	4	ui	ui	PROPN
ejpam-4115	144	5	⊆	⊆	NUM
ejpam-4115	144	6	u	u	NOUN
ejpam-4115	144	7	.	.	PUNCT
ejpam-4115	145	1	therefore	therefore	ADV
ejpam-4115	145	2	,	,	PUNCT
ejpam-4115	145	3	l	l	NOUN
ejpam-4115	145	4	is	be	AUX
ejpam-4115	145	5	absolutely	absolutely	ADV
ejpam-4115	145	6	continuous	continuous	ADJ
ejpam-4115	145	7	on	on	ADP
ejpam-4115	145	8	[	[	X
ejpam-4115	145	9	a	a	X
ejpam-4115	145	10	,	,	PUNCT
ejpam-4115	145	11	b	b	NOUN
ejpam-4115	145	12	]	]	PUNCT
ejpam-4115	145	13	.	.	PUNCT
ejpam-4115	146	1	using	use	VERB
ejpam-4115	146	2	the	the	DET
ejpam-4115	146	3	above	above	ADJ
ejpam-4115	146	4	definition	definition	NOUN
ejpam-4115	146	5	,	,	PUNCT
ejpam-4115	146	6	the	the	DET
ejpam-4115	146	7	following	following	ADJ
ejpam-4115	146	8	result	result	NOUN
ejpam-4115	146	9	follows	follow	VERB
ejpam-4115	146	10	.	.	PUNCT
ejpam-4115	147	1	theorem	theorem	NOUN
ejpam-4115	147	2	1	1	X
ejpam-4115	147	3	.	.	PUNCT
ejpam-4115	148	1	let	let	VERB
ejpam-4115	148	2	a	a	DET
ejpam-4115	148	3	,	,	PUNCT
ejpam-4115	148	4	b	b	NOUN
ejpam-4115	148	5	⊆	⊆	NUM
ejpam-4115	148	6	[	[	X
ejpam-4115	148	7	a	a	X
ejpam-4115	148	8	,	,	PUNCT
ejpam-4115	148	9	b	b	NOUN
ejpam-4115	148	10	]	]	X
ejpam-4115	148	11	.	.	PUNCT
ejpam-4115	149	1	(	(	PUNCT
ejpam-4115	149	2	i	i	NOUN
ejpam-4115	149	3	)	)	PUNCT
ejpam-4115	149	4	if	if	SCONJ
ejpam-4115	149	5	a	a	DET
ejpam-4115	149	6	⊆	⊆	NUM
ejpam-4115	149	7	b	b	NOUN
ejpam-4115	149	8	and	and	CCONJ
ejpam-4115	149	9	f	f	NOUN
ejpam-4115	149	10	:	:	PUNCT
ejpam-4115	150	1	[	[	X
ejpam-4115	150	2	a	a	X
ejpam-4115	150	3	,	,	PUNCT
ejpam-4115	150	4	b	b	NOUN
ejpam-4115	150	5	]	]	X
ejpam-4115	150	6	→	→	PUNCT
ejpam-4115	150	7	x	x	X
ejpam-4115	150	8	is	be	AUX
ejpam-4115	150	9	ac∗(b	ac∗(b	NOUN
ejpam-4115	150	10	)	)	PUNCT
ejpam-4115	150	11	,	,	PUNCT
ejpam-4115	150	12	then	then	ADV
ejpam-4115	150	13	f	f	PROPN
ejpam-4115	150	14	is	be	AUX
ejpam-4115	150	15	ac∗(a	ac∗(a	ADJ
ejpam-4115	150	16	)	)	PUNCT
ejpam-4115	150	17	.	.	PUNCT
ejpam-4115	151	1	(	(	PUNCT
ejpam-4115	151	2	ii	ii	NOUN
ejpam-4115	151	3	)	)	PUNCT
ejpam-4115	151	4	if	if	SCONJ
ejpam-4115	151	5	f	f	X
ejpam-4115	151	6	:	:	PUNCT
ejpam-4115	152	1	[	[	X
ejpam-4115	152	2	a	a	X
ejpam-4115	152	3	,	,	PUNCT
ejpam-4115	152	4	b	b	NOUN
ejpam-4115	152	5	]	]	X
ejpam-4115	152	6	→	→	PUNCT
ejpam-4115	152	7	x	x	X
ejpam-4115	152	8	is	be	AUX
ejpam-4115	152	9	ac∗(a	ac∗(a	ADJ
ejpam-4115	152	10	)	)	PUNCT
ejpam-4115	152	11	and	and	CCONJ
ejpam-4115	152	12	c	c	NOUN
ejpam-4115	152	13	∈	∈	PROPN
ejpam-4115	152	14	r	r	NOUN
ejpam-4115	152	15	,	,	PUNCT
ejpam-4115	152	16	then	then	ADV
ejpam-4115	152	17	cf	cf	NOUN
ejpam-4115	152	18	is	be	AUX
ejpam-4115	152	19	ac∗(a	ac∗(a	ADJ
ejpam-4115	152	20	)	)	PUNCT
ejpam-4115	152	21	.	.	PUNCT
ejpam-4115	153	1	(	(	PUNCT
ejpam-4115	153	2	iii	iii	X
ejpam-4115	153	3	)	)	PUNCT
ejpam-4115	153	4	if	if	SCONJ
ejpam-4115	153	5	g	g	PROPN
ejpam-4115	153	6	,	,	PUNCT
ejpam-4115	153	7	h	h	NOUN
ejpam-4115	153	8	:	:	PUNCT
ejpam-4115	154	1	[	[	X
ejpam-4115	154	2	a	a	X
ejpam-4115	154	3	,	,	PUNCT
ejpam-4115	154	4	b	b	NOUN
ejpam-4115	154	5	]	]	X
ejpam-4115	154	6	→	→	PUNCT
ejpam-4115	154	7	x	x	X
ejpam-4115	154	8	are	be	AUX
ejpam-4115	154	9	ac∗(a	ac∗(a	ADJ
ejpam-4115	154	10	)	)	PUNCT
ejpam-4115	154	11	,	,	PUNCT
ejpam-4115	154	12	then	then	ADV
ejpam-4115	154	13	g+h	g+h	PROPN
ejpam-4115	154	14	is	be	AUX
ejpam-4115	154	15	ac∗(a	ac∗(a	ADJ
ejpam-4115	154	16	)	)	PUNCT
ejpam-4115	154	17	.	.	PUNCT
ejpam-4115	155	1	(	(	PUNCT
ejpam-4115	155	2	iv	iv	X
ejpam-4115	155	3	)	)	PUNCT
ejpam-4115	155	4	if	if	SCONJ
ejpam-4115	155	5	f	f	X
ejpam-4115	155	6	:	:	PUNCT
ejpam-4115	156	1	[	[	X
ejpam-4115	156	2	a	a	X
ejpam-4115	156	3	,	,	PUNCT
ejpam-4115	156	4	b	b	NOUN
ejpam-4115	156	5	]	]	X
ejpam-4115	156	6	→	→	PUNCT
ejpam-4115	156	7	x	x	X
ejpam-4115	156	8	is	be	AUX
ejpam-4115	156	9	both	both	CCONJ
ejpam-4115	156	10	ac∗(a	ac∗(a	ADJ
ejpam-4115	156	11	)	)	PUNCT
ejpam-4115	156	12	and	and	CCONJ
ejpam-4115	156	13	ac∗(b	ac∗(b	NOUN
ejpam-4115	156	14	)	)	PUNCT
ejpam-4115	156	15	,	,	PUNCT
ejpam-4115	156	16	then	then	ADV
ejpam-4115	156	17	f	f	PROPN
ejpam-4115	156	18	is	be	AUX
ejpam-4115	156	19	ac∗(a	ac∗(a	ADJ
ejpam-4115	156	20	∪b	∪b	NOUN
ejpam-4115	156	21	)	)	PUNCT
ejpam-4115	156	22	.	.	PUNCT
ejpam-4115	157	1	proof	proof	NOUN
ejpam-4115	157	2	.	.	PUNCT
ejpam-4115	158	1	(	(	PUNCT
ejpam-4115	158	2	i	i	NOUN
ejpam-4115	158	3	)	)	PUNCT
ejpam-4115	158	4	this	this	PRON
ejpam-4115	158	5	is	be	AUX
ejpam-4115	158	6	immediate	immediate	ADJ
ejpam-4115	158	7	from	from	ADP
ejpam-4115	158	8	definition	definition	NOUN
ejpam-4115	158	9	4	4	NUM
ejpam-4115	158	10	.	.	PUNCT
ejpam-4115	158	11	(	(	PUNCT
ejpam-4115	158	12	ii	ii	NOUN
ejpam-4115	158	13	)	)	PUNCT
ejpam-4115	158	14	the	the	DET
ejpam-4115	158	15	case	case	NOUN
ejpam-4115	158	16	c	c	NOUN
ejpam-4115	158	17	=	=	SYM
ejpam-4115	158	18	0	0	NUM
ejpam-4115	158	19	is	be	AUX
ejpam-4115	158	20	clear	clear	ADJ
ejpam-4115	158	21	.	.	PUNCT
ejpam-4115	159	1	suppose	suppose	VERB
ejpam-4115	159	2	c	c	PROPN
ejpam-4115	159	3	̸=	̸=	PROPN
ejpam-4115	159	4	0	0	NUM
ejpam-4115	159	5	.	.	PUNCT
ejpam-4115	160	1	for	for	ADP
ejpam-4115	160	2	any	any	DET
ejpam-4115	160	3	θ	θ	PROPN
ejpam-4115	160	4	-	-	PUNCT
ejpam-4115	160	5	nbd	nbd	PROPN
ejpam-4115	160	6	u	u	PROPN
ejpam-4115	160	7	,	,	PUNCT
ejpam-4115	160	8	there	there	PRON
ejpam-4115	160	9	exists	exist	VERB
ejpam-4115	160	10	η	η	PROPN
ejpam-4115	160	11	>	>	X
ejpam-4115	160	12	0	0	NUM
ejpam-4115	160	13	such	such	ADJ
ejpam-4115	160	14	that	that	PRON
ejpam-4115	160	15	for	for	ADP
ejpam-4115	160	16	any	any	DET
ejpam-4115	160	17	partial	partial	ADJ
ejpam-4115	160	18	partition	partition	NOUN
ejpam-4115	160	19	d	d	NOUN
ejpam-4115	160	20	=	=	PRON
ejpam-4115	160	21	{	{	PUNCT
ejpam-4115	160	22	[	[	X
ejpam-4115	160	23	ui	ui	PROPN
ejpam-4115	160	24	,	,	PUNCT
ejpam-4115	160	25	vi	vi	PROPN
ejpam-4115	160	26	]	]	X
ejpam-4115	160	27	:	:	PUNCT
ejpam-4115	160	28	1	1	NUM
ejpam-4115	160	29	≤	≤	NUM
ejpam-4115	160	30	i	i	PRON
ejpam-4115	160	31	≤	≤	NOUN
ejpam-4115	160	32	n	n	CCONJ
ejpam-4115	160	33	}	}	PUNCT
ejpam-4115	160	34	of	of	ADP
ejpam-4115	160	35	[	[	X
ejpam-4115	160	36	a	a	X
ejpam-4115	160	37	,	,	PUNCT
ejpam-4115	160	38	b	b	NOUN
ejpam-4115	160	39	]	]	X
ejpam-4115	160	40	with	with	ADP
ejpam-4115	160	41	ui	ui	PROPN
ejpam-4115	160	42	or	or	CCONJ
ejpam-4115	160	43	vi	vi	PROPN
ejpam-4115	160	44	in	in	ADP
ejpam-4115	160	45	a	a	PRON
ejpam-4115	160	46	and	and	CCONJ
ejpam-4115	160	47	(	(	PUNCT
ejpam-4115	160	48	d	d	X
ejpam-4115	160	49	)	)	PUNCT
ejpam-4115	160	50	∑n	∑n	PROPN
ejpam-4115	160	51	i=1(vi	i=1(vi	DET
ejpam-4115	160	52	−	−	PROPN
ejpam-4115	160	53	ui	ui	PROPN
ejpam-4115	160	54	)	)	PUNCT
ejpam-4115	160	55	<	<	X
ejpam-4115	160	56	η	η	PROPN
ejpam-4115	160	57	,	,	PUNCT
ejpam-4115	160	58	there	there	PRON
ejpam-4115	160	59	exist	exist	VERB
ejpam-4115	160	60	θ	θ	PROPN
ejpam-4115	160	61	-	-	PUNCT
ejpam-4115	160	62	nbds	nbds	NOUN
ejpam-4115	160	63	v1	v1	NOUN
ejpam-4115	160	64	,	,	PUNCT
ejpam-4115	160	65	v2	v2	NOUN
ejpam-4115	160	66	,	,	PUNCT
ejpam-4115	160	67	.	.	PUNCT
ejpam-4115	160	68	.	.	PUNCT
ejpam-4115	161	1	.	.	PUNCT
ejpam-4115	162	1	,	,	PUNCT
ejpam-4115	162	2	vn	vn	VERB
ejpam-4115	162	3	with	with	ADP
ejpam-4115	162	4	∑	∑	PART
ejpam-4115	162	5	vi	vi	PROPN
ejpam-4115	162	6	⊆	⊆	NUM
ejpam-4115	162	7	1	1	NUM
ejpam-4115	162	8	cu	cu	NOUN
ejpam-4115	162	9	for	for	ADP
ejpam-4115	162	10	which	which	PRON
ejpam-4115	162	11	f	f	PROPN
ejpam-4115	162	12	(	(	PUNCT
ejpam-4115	162	13	vi)−	vi)−	NOUN
ejpam-4115	162	14	f	f	PROPN
ejpam-4115	162	15	(	(	PUNCT
ejpam-4115	162	16	ui	ui	PROPN
ejpam-4115	162	17	)	)	PUNCT
ejpam-4115	162	18	∈	∈	PROPN
ejpam-4115	162	19	vi	vi	NOUN
ejpam-4115	162	20	for	for	ADP
ejpam-4115	162	21	1	1	NUM
ejpam-4115	162	22	≤	≤	NUM
ejpam-4115	162	23	i	i	PRON
ejpam-4115	162	24	≤	≤	NUM
ejpam-4115	162	25	n.	n.	NOUN
ejpam-4115	162	26	set	set	VERB
ejpam-4115	162	27	ui	ui	PROPN
ejpam-4115	163	1	=	=	PROPN
ejpam-4115	163	2	cvi	cvi	PROPN
ejpam-4115	163	3	for	for	ADP
ejpam-4115	163	4	each	each	DET
ejpam-4115	163	5	i	i	PRON
ejpam-4115	163	6	∈	∈	PROPN
ejpam-4115	163	7	{	{	PUNCT
ejpam-4115	163	8	1	1	NUM
ejpam-4115	163	9	,	,	PUNCT
ejpam-4115	163	10	2	2	NUM
ejpam-4115	163	11	,	,	PUNCT
ejpam-4115	163	12	·	·	PUNCT
ejpam-4115	163	13	·	·	PUNCT
ejpam-4115	163	14	·	·	PUNCT
ejpam-4115	163	15	,	,	PUNCT
ejpam-4115	163	16	n	n	CCONJ
ejpam-4115	163	17	}	}	PUNCT
ejpam-4115	163	18	.	.	PUNCT
ejpam-4115	164	1	then	then	ADV
ejpam-4115	164	2	ui	ui	PROPN
ejpam-4115	164	3	is	be	AUX
ejpam-4115	164	4	a	a	DET
ejpam-4115	164	5	θ	θ	PROPN
ejpam-4115	164	6	-	-	PUNCT
ejpam-4115	164	7	nbd	nbd	PROPN
ejpam-4115	164	8	for	for	ADP
ejpam-4115	164	9	1	1	NUM
ejpam-4115	164	10	≤	≤	NUM
ejpam-4115	164	11	i	i	PRON
ejpam-4115	164	12	≤	≤	ADJ
ejpam-4115	164	13	n	n	CCONJ
ejpam-4115	164	14	such	such	ADJ
ejpam-4115	164	15	that	that	SCONJ
ejpam-4115	164	16	∑n	∑n	PROPN
ejpam-4115	164	17	i=1	i=1	PROPN
ejpam-4115	164	18	ui	ui	PROPN
ejpam-4115	165	1	=	=	PUNCT
ejpam-4115	165	2	∑n	∑n	PROPN
ejpam-4115	165	3	i=1	i=1	PROPN
ejpam-4115	166	1	cvi	cvi	PROPN
ejpam-4115	166	2	⊆	⊆	NUM
ejpam-4115	166	3	u	u	NOUN
ejpam-4115	166	4	and	and	CCONJ
ejpam-4115	166	5	cf	cf	NOUN
ejpam-4115	166	6	(	(	PUNCT
ejpam-4115	166	7	vi)−	vi)−	NOUN
ejpam-4115	166	8	cf	cf	NOUN
ejpam-4115	166	9	(	(	PUNCT
ejpam-4115	166	10	ui	ui	NOUN
ejpam-4115	166	11	)	)	PUNCT
ejpam-4115	166	12	∈	∈	PROPN
ejpam-4115	166	13	ui	ui	NOUN
ejpam-4115	166	14	for	for	ADP
ejpam-4115	166	15	1	1	NUM
ejpam-4115	166	16	≤	≤	NUM
ejpam-4115	166	17	i	i	PRON
ejpam-4115	166	18	≤	≤	PROPN
ejpam-4115	166	19	n.	n.	NOUN
ejpam-4115	166	20	thus	thus	ADV
ejpam-4115	166	21	,	,	PUNCT
ejpam-4115	166	22	cf	cf	NOUN
ejpam-4115	166	23	is	be	AUX
ejpam-4115	166	24	ac∗(a	ac∗(a	ADJ
ejpam-4115	166	25	)	)	PUNCT
ejpam-4115	166	26	.	.	PUNCT
ejpam-4115	167	1	(	(	PUNCT
ejpam-4115	167	2	iii	iii	X
ejpam-4115	167	3	)	)	PUNCT
ejpam-4115	167	4	let	let	VERB
ejpam-4115	167	5	u	u	PRON
ejpam-4115	167	6	be	be	AUX
ejpam-4115	167	7	a	a	DET
ejpam-4115	167	8	θ	θ	PROPN
ejpam-4115	167	9	-	-	PUNCT
ejpam-4115	167	10	nbd	nbd	PROPN
ejpam-4115	167	11	u	u	PROPN
ejpam-4115	167	12	and	and	CCONJ
ejpam-4115	167	13	let	let	VERB
ejpam-4115	167	14	v	v	NOUN
ejpam-4115	167	15	and	and	CCONJ
ejpam-4115	167	16	w	w	AUX
ejpam-4115	167	17	be	be	AUX
ejpam-4115	167	18	θ	θ	NOUN
ejpam-4115	167	19	-	-	NOUN
ejpam-4115	167	20	nbds	nbds	NOUN
ejpam-4115	168	1	such	such	ADJ
ejpam-4115	168	2	that	that	PRON
ejpam-4115	168	3	v	v	NOUN
ejpam-4115	168	4	+	+	CCONJ
ejpam-4115	168	5	w	w	PROPN
ejpam-4115	168	6	⊆	⊆	NUM
ejpam-4115	168	7	u	u	NOUN
ejpam-4115	168	8	.	.	PUNCT
ejpam-4115	169	1	since	since	SCONJ
ejpam-4115	169	2	g	g	PROPN
ejpam-4115	169	3	is	be	AUX
ejpam-4115	169	4	ac∗(a	ac∗(a	ADJ
ejpam-4115	169	5	)	)	PUNCT
ejpam-4115	169	6	,	,	PUNCT
ejpam-4115	169	7	there	there	PRON
ejpam-4115	169	8	exists	exist	VERB
ejpam-4115	169	9	η1	η1	NOUN
ejpam-4115	169	10	>	>	X
ejpam-4115	169	11	0	0	NUM
ejpam-4115	169	12	such	such	ADJ
ejpam-4115	169	13	that	that	PRON
ejpam-4115	169	14	for	for	ADP
ejpam-4115	169	15	any	any	DET
ejpam-4115	169	16	given	give	VERB
ejpam-4115	169	17	a	a	DET
ejpam-4115	169	18	partial	partial	ADJ
ejpam-4115	169	19	partition	partition	NOUN
ejpam-4115	169	20	{	{	PUNCT
ejpam-4115	169	21	[	[	X
ejpam-4115	169	22	ui	ui	NOUN
ejpam-4115	169	23	,	,	PUNCT
ejpam-4115	169	24	vi	vi	PROPN
ejpam-4115	169	25	]	]	X
ejpam-4115	169	26	:	:	PUNCT
ejpam-4115	169	27	1	1	NUM
ejpam-4115	169	28	≤	≤	NUM
ejpam-4115	169	29	i	i	X
ejpam-4115	169	30	≤	≤	NOUN
ejpam-4115	169	31	m	m	VERB
ejpam-4115	169	32	}	}	PUNCT
ejpam-4115	169	33	of	of	ADP
ejpam-4115	169	34	[	[	X
ejpam-4115	169	35	a	a	X
ejpam-4115	169	36	,	,	PUNCT
ejpam-4115	169	37	b	b	NOUN
ejpam-4115	169	38	]	]	X
ejpam-4115	169	39	with	with	ADP
ejpam-4115	169	40	ui	ui	PROPN
ejpam-4115	169	41	or	or	CCONJ
ejpam-4115	169	42	vi	vi	PROPN
ejpam-4115	169	43	in	in	ADP
ejpam-4115	169	44	a	a	DET
ejpam-4115	169	45	and	and	CCONJ
ejpam-4115	169	46	∑m	∑m	ADJ
ejpam-4115	169	47	i=1(vi	i=1(vi	PRON
ejpam-4115	169	48	−	−	PROPN
ejpam-4115	169	49	ui	ui	PROPN
ejpam-4115	169	50	)	)	PUNCT
ejpam-4115	169	51	<	<	X
ejpam-4115	169	52	η1	η1	NOUN
ejpam-4115	169	53	,	,	PUNCT
ejpam-4115	169	54	there	there	PRON
ejpam-4115	169	55	exist	exist	VERB
ejpam-4115	169	56	θ	θ	PROPN
ejpam-4115	169	57	-	-	PUNCT
ejpam-4115	169	58	nbds	nbds	NOUN
ejpam-4115	169	59	v1	v1	NOUN
ejpam-4115	169	60	,	,	PUNCT
ejpam-4115	169	61	v2	v2	NOUN
ejpam-4115	169	62	,	,	PUNCT
ejpam-4115	169	63	.	.	PUNCT
ejpam-4115	169	64	.	.	PUNCT
ejpam-4115	170	1	.	.	PUNCT
ejpam-4115	171	1	,	,	PUNCT
ejpam-4115	171	2	vm	vm	X
ejpam-4115	171	3	such	such	ADJ
ejpam-4115	171	4	that	that	DET
ejpam-4115	171	5	∑m	∑m	PROPN
ejpam-4115	171	6	i=1	i=1	PROPN
ejpam-4115	171	7	vi	vi	PROPN
ejpam-4115	171	8	⊆	⊆	NUM
ejpam-4115	171	9	v	v	NOUN
ejpam-4115	171	10	and	and	CCONJ
ejpam-4115	171	11	g(vi)−g(ui	g(vi)−g(ui	NOUN
ejpam-4115	171	12	)	)	PUNCT
ejpam-4115	171	13	∈	∈	PROPN
ejpam-4115	171	14	vifor	vifor	VERB
ejpam-4115	171	15	1	1	NUM
ejpam-4115	171	16	≤	≤	NUM
ejpam-4115	171	17	i	i	PRON
ejpam-4115	171	18	≤	≤	ADJ
ejpam-4115	171	19	n.	n.	NOUN
ejpam-4115	171	20	similarly	similarly	ADV
ejpam-4115	171	21	,	,	PUNCT
ejpam-4115	171	22	there	there	PRON
ejpam-4115	171	23	exists	exist	VERB
ejpam-4115	171	24	η2	η2	ADJ
ejpam-4115	171	25	>	>	X
ejpam-4115	171	26	0	0	NUM
ejpam-4115	171	27	such	such	ADJ
ejpam-4115	171	28	that	that	PRON
ejpam-4115	171	29	for	for	ADP
ejpam-4115	171	30	any	any	DET
ejpam-4115	171	31	partial	partial	ADJ
ejpam-4115	171	32	partition	partition	NOUN
ejpam-4115	171	33	{	{	PUNCT
ejpam-4115	171	34	[	[	X
ejpam-4115	171	35	u′i	u′i	ADJ
ejpam-4115	171	36	,	,	PUNCT
ejpam-4115	171	37	v′i	v′i	NOUN
ejpam-4115	171	38	]	]	X
ejpam-4115	171	39	:	:	PUNCT
ejpam-4115	171	40	1	1	NUM
ejpam-4115	171	41	≤	≤	NUM
ejpam-4115	171	42	i	i	PRON
ejpam-4115	171	43	≤	≤	NOUN
ejpam-4115	171	44	n	n	CCONJ
ejpam-4115	171	45	}	}	PUNCT
ejpam-4115	171	46	of	of	ADP
ejpam-4115	171	47	[	[	X
ejpam-4115	171	48	a	a	X
ejpam-4115	171	49	,	,	PUNCT
ejpam-4115	171	50	b	b	X
ejpam-4115	171	51	]	]	X
ejpam-4115	171	52	with	with	ADP
ejpam-4115	171	53	u′i	u′i	ADJ
ejpam-4115	171	54	or	or	CCONJ
ejpam-4115	171	55	v	v	NOUN
ejpam-4115	171	56	′	′	NUM
ejpam-4115	172	1	i	i	PRON
ejpam-4115	172	2	in	in	ADP
ejpam-4115	172	3	a	a	PRON
ejpam-4115	172	4	and	and	CCONJ
ejpam-4115	172	5	∑n	∑n	NUM
ejpam-4115	172	6	i=1(v	i=1(v	NOUN
ejpam-4115	172	7	′	′	VERB
ejpam-4115	173	1	i	i	PRON
ejpam-4115	173	2	−	−	PROPN
ejpam-4115	174	1	u′i	u′i	ADJ
ejpam-4115	174	2	)	)	PUNCT
ejpam-4115	174	3	<	<	X
ejpam-4115	174	4	η2	η2	NOUN
ejpam-4115	174	5	,	,	PUNCT
ejpam-4115	174	6	there	there	PRON
ejpam-4115	174	7	exist	exist	VERB
ejpam-4115	174	8	θ	θ	PROPN
ejpam-4115	174	9	-	-	NOUN
ejpam-4115	174	10	nbds	nbds	NOUN
ejpam-4115	174	11	w1,w2	w1,w2	PROPN
ejpam-4115	174	12	,	,	PUNCT
ejpam-4115	174	13	.	.	PUNCT
ejpam-4115	174	14	.	.	PUNCT
ejpam-4115	175	1	.	.	PUNCT
ejpam-4115	176	1	,	,	PUNCT
ejpam-4115	176	2	wn	wn	PROPN
ejpam-4115	176	3	such	such	ADJ
ejpam-4115	176	4	that	that	DET
ejpam-4115	176	5	∑m	∑m	PROPN
ejpam-4115	176	6	i=1wi	i=1wi	NUM
ejpam-4115	176	7	⊆	⊆	NUM
ejpam-4115	176	8	w	w	PROPN
ejpam-4115	176	9	and	and	CCONJ
ejpam-4115	176	10	h(vi	h(vi	NOUN
ejpam-4115	176	11	)	)	PUNCT
ejpam-4115	177	1	−	−	ADP
ejpam-4115	177	2	h(ui	h(ui	NOUN
ejpam-4115	177	3	)	)	PUNCT
ejpam-4115	177	4	∈	∈	PROPN
ejpam-4115	177	5	wi	wi	PROPN
ejpam-4115	177	6	for	for	ADP
ejpam-4115	177	7	1	1	NUM
ejpam-4115	177	8	≤	≤	NUM
ejpam-4115	177	9	i	i	PRON
ejpam-4115	177	10	≤	≤	ADJ
ejpam-4115	177	11	n.	n.	NOUN
ejpam-4115	177	12	let	let	VERB
ejpam-4115	177	13	η	η	NOUN
ejpam-4115	177	14	=	=	NOUN
ejpam-4115	177	15	min{η1	min{η1	NOUN
ejpam-4115	177	16	,	,	PUNCT
ejpam-4115	177	17	η2	η2	PROPN
ejpam-4115	177	18	}	}	PUNCT
ejpam-4115	177	19	.	.	PUNCT
ejpam-4115	178	1	suppose	suppose	VERB
ejpam-4115	178	2	{	{	PUNCT
ejpam-4115	178	3	[	[	X
ejpam-4115	178	4	xi	xi	X
ejpam-4115	178	5	,	,	PUNCT
ejpam-4115	178	6	yi	yi	NOUN
ejpam-4115	178	7	]	]	X
ejpam-4115	178	8	:	:	PUNCT
ejpam-4115	178	9	1	1	NUM
ejpam-4115	178	10	≤	≤	NUM
ejpam-4115	178	11	i	i	NOUN
ejpam-4115	178	12	≤	≤	PUNCT
ejpam-4115	179	1	k	k	X
ejpam-4115	179	2	}	}	PUNCT
ejpam-4115	179	3	is	be	AUX
ejpam-4115	179	4	a	a	DET
ejpam-4115	179	5	partial	partial	ADJ
ejpam-4115	179	6	partition	partition	NOUN
ejpam-4115	179	7	of	of	ADP
ejpam-4115	179	8	[	[	X
ejpam-4115	179	9	a	a	X
ejpam-4115	179	10	,	,	PUNCT
ejpam-4115	179	11	b	b	NOUN
ejpam-4115	179	12	]	]	X
ejpam-4115	179	13	with	with	ADP
ejpam-4115	179	14	xi	xi	ADP
ejpam-4115	179	15	or	or	CCONJ
ejpam-4115	179	16	yi	yi	PROPN
ejpam-4115	179	17	in	in	ADP
ejpam-4115	179	18	a	a	DET
ejpam-4115	179	19	such	such	ADJ
ejpam-4115	179	20	that	that	SCONJ
ejpam-4115	179	21	∑k	∑k	PROPN
ejpam-4115	179	22	i=1(yi	i=1(yi	VERB
ejpam-4115	180	1	−	−	PROPN
ejpam-4115	180	2	xi	xi	PROPN
ejpam-4115	180	3	)	)	PUNCT
ejpam-4115	180	4	<	<	X
ejpam-4115	180	5	η	η	PROPN
ejpam-4115	180	6	.	.	PROPN
ejpam-4115	180	7	since	since	SCONJ
ejpam-4115	180	8	η	η	PROPN
ejpam-4115	180	9	≤	≤	X
ejpam-4115	180	10	η1	η1	NOUN
ejpam-4115	180	11	and	and	CCONJ
ejpam-4115	180	12	η	η	PROPN
ejpam-4115	180	13	≤	≤	NOUN
ejpam-4115	180	14	η2	η2	NOUN
ejpam-4115	180	15	,	,	PUNCT
ejpam-4115	180	16	there	there	PRON
ejpam-4115	180	17	exist	exist	VERB
ejpam-4115	180	18	collections	collection	NOUN
ejpam-4115	180	19	{	{	PUNCT
ejpam-4115	180	20	v	v	NOUN
ejpam-4115	180	21	′	′	NUM
ejpam-4115	181	1	i	i	PRON
ejpam-4115	181	2	}	}	PUNCT
ejpam-4115	181	3	ki=1	ki=1	INTJ
ejpam-4115	181	4	and	and	CCONJ
ejpam-4115	181	5	{	{	PUNCT
ejpam-4115	181	6	w	w	NOUN
ejpam-4115	181	7	′	′	NUM
ejpam-4115	181	8	i}ki=1	i}ki=1	PRON
ejpam-4115	181	9	of	of	ADP
ejpam-4115	181	10	θ	θ	PROPN
ejpam-4115	181	11	-	-	NOUN
ejpam-4115	181	12	nbds	nbds	NOUN
ejpam-4115	181	13	such	such	ADJ
ejpam-4115	181	14	that	that	SCONJ
ejpam-4115	181	15	∑k	∑k	PROPN
ejpam-4115	181	16	i=1	i=1	X
ejpam-4115	182	1	v	v	INTJ
ejpam-4115	182	2	′	′	NUM
ejpam-4115	183	1	i	i	PRON
ejpam-4115	183	2	⊆	⊆	NUM
ejpam-4115	183	3	v	v	NOUN
ejpam-4115	183	4	,	,	PUNCT
ejpam-4115	183	5	∑k	∑k	PROPN
ejpam-4115	183	6	i=1w	i=1w	VERB
ejpam-4115	183	7	′	′	NUM
ejpam-4115	183	8	i	i	NOUN
ejpam-4115	183	9	⊆	⊆	NUM
ejpam-4115	183	10	w	w	NOUN
ejpam-4115	183	11	and	and	CCONJ
ejpam-4115	183	12	g(yi)−g(xi	g(yi)−g(xi	ADJ
ejpam-4115	183	13	)	)	PUNCT
ejpam-4115	184	1	∈	∈	PROPN
ejpam-4115	185	1	v	v	ADP
ejpam-4115	185	2	′	′	NUM
ejpam-4115	186	1	i	i	PRON
ejpam-4115	186	2	,	,	PUNCT
ejpam-4115	186	3	h(yi)−h(xi	h(yi)−h(xi	ADJ
ejpam-4115	186	4	)	)	PUNCT
ejpam-4115	186	5	∈	∈	PROPN
ejpam-4115	187	1	w	w	NOUN
ejpam-4115	187	2	′	′	NUM
ejpam-4115	187	3	i	i	PRON
ejpam-4115	187	4	for	for	ADP
ejpam-4115	187	5	1	1	NUM
ejpam-4115	187	6	≤	≤	NUM
ejpam-4115	187	7	i	i	PRON
ejpam-4115	187	8	≤	≤	ADJ
ejpam-4115	188	1	n.	n.	NOUN
ejpam-4115	188	2	then	then	ADV
ejpam-4115	188	3	∑k	∑k	PROPN
ejpam-4115	188	4	i=1(vi	i=1(vi	X
ejpam-4115	189	1	+	+	ADJ
ejpam-4115	189	2	wi	wi	PROPN
ejpam-4115	189	3	)	)	PUNCT
ejpam-4115	190	1	⊆	⊆	NUM
ejpam-4115	190	2	v	v	ADP
ejpam-4115	190	3	+	+	PROPN
ejpam-4115	190	4	w	w	PROPN
ejpam-4115	190	5	⊆	⊆	NUM
ejpam-4115	190	6	u	u	NOUN
ejpam-4115	190	7	and	and	CCONJ
ejpam-4115	190	8	for	for	ADP
ejpam-4115	190	9	each	each	DET
ejpam-4115	190	10	i	i	PRON
ejpam-4115	190	11	∈	∈	PROPN
ejpam-4115	190	12	{	{	PUNCT
ejpam-4115	190	13	1	1	NUM
ejpam-4115	190	14	,	,	PUNCT
ejpam-4115	190	15	2	2	NUM
ejpam-4115	190	16	,	,	PUNCT
ejpam-4115	190	17	·	·	PUNCT
ejpam-4115	190	18	·	·	PUNCT
ejpam-4115	190	19	·	·	PUNCT
ejpam-4115	190	20	,	,	PUNCT
ejpam-4115	190	21	n	n	CCONJ
ejpam-4115	190	22	}	}	PUNCT
ejpam-4115	190	23	,	,	PUNCT
ejpam-4115	190	24	f	f	PROPN
ejpam-4115	190	25	(	(	PUNCT
ejpam-4115	190	26	vi	vi	NOUN
ejpam-4115	190	27	)	)	PUNCT
ejpam-4115	190	28	+	+	NOUN
ejpam-4115	190	29	g(vi)−	g(vi)−	NOUN
ejpam-4115	190	30	(	(	PUNCT
ejpam-4115	190	31	f	f	X
ejpam-4115	190	32	(	(	PUNCT
ejpam-4115	190	33	ui	ui	PROPN
ejpam-4115	190	34	)	)	PUNCT
ejpam-4115	190	35	+	+	PROPN
ejpam-4115	190	36	g(ui	g(ui	NOUN
ejpam-4115	190	37	)	)	PUNCT
ejpam-4115	190	38	)	)	PUNCT
ejpam-4115	191	1	=	=	SYM
ejpam-4115	191	2	f	f	PROPN
ejpam-4115	191	3	(	(	PUNCT
ejpam-4115	191	4	vi)−	vi)−	NOUN
ejpam-4115	191	5	f	f	PROPN
ejpam-4115	191	6	(	(	PUNCT
ejpam-4115	191	7	ui	ui	PROPN
ejpam-4115	191	8	)	)	PUNCT
ejpam-4115	191	9	+	+	NOUN
ejpam-4115	191	10	g(vi)−g(ui	g(vi)−g(ui	NOUN
ejpam-4115	191	11	)	)	PUNCT
ejpam-4115	191	12	∈	∈	PROPN
ejpam-4115	191	13	vi	vi	PROPN
ejpam-4115	191	14	+	+	PROPN
ejpam-4115	191	15	wi	wi	PROPN
ejpam-4115	191	16	.	.	PUNCT
ejpam-4115	192	1	therefore	therefore	ADV
ejpam-4115	192	2	,	,	PUNCT
ejpam-4115	192	3	f	f	PROPN
ejpam-4115	192	4	+	+	ADP
ejpam-4115	192	5	g	g	PROPN
ejpam-4115	192	6	is	be	AUX
ejpam-4115	192	7	ac∗(a	ac∗(a	ADJ
ejpam-4115	192	8	)	)	PUNCT
ejpam-4115	192	9	.	.	PUNCT
ejpam-4115	193	1	r.	r.	PROPN
ejpam-4115	193	2	e.	e.	PROPN
ejpam-4115	193	3	maza	maza	PROPN
ejpam-4115	193	4	,	,	PUNCT
ejpam-4115	193	5	s.	s.	PROPN
ejpam-4115	193	6	r.	r.	PROPN
ejpam-4115	193	7	canoy	canoy	PROPN
ejpam-4115	193	8	,	,	PUNCT
ejpam-4115	193	9	jr	jr	PROPN
ejpam-4115	193	10	.	.	PROPN
ejpam-4115	193	11	/	/	SYM
ejpam-4115	193	12	eur	eur	PROPN
ejpam-4115	193	13	.	.	PUNCT
ejpam-4115	194	1	j.	j.	PROPN
ejpam-4115	194	2	pure	pure	PROPN
ejpam-4115	194	3	appl	appl	PROPN
ejpam-4115	194	4	.	.	PROPN
ejpam-4115	194	5	math	math	PROPN
ejpam-4115	194	6	,	,	PUNCT
ejpam-4115	194	7	14	14	NUM
ejpam-4115	194	8	(	(	PUNCT
ejpam-4115	194	9	4	4	NUM
ejpam-4115	194	10	)	)	PUNCT
ejpam-4115	194	11	(	(	PUNCT
ejpam-4115	194	12	2021	2021	NUM
ejpam-4115	194	13	)	)	PUNCT
ejpam-4115	194	14	,	,	PUNCT
ejpam-4115	194	15	1169	1169	NUM
ejpam-4115	194	16	-	-	SYM
ejpam-4115	194	17	1183	1183	NUM
ejpam-4115	194	18	1174	1174	NUM
ejpam-4115	194	19	(	(	PUNCT
ejpam-4115	194	20	iv	iv	X
ejpam-4115	194	21	)	)	PUNCT
ejpam-4115	194	22	let	let	VERB
ejpam-4115	194	23	u	u	PRON
ejpam-4115	194	24	be	be	AUX
ejpam-4115	194	25	a	a	DET
ejpam-4115	194	26	θ	θ	PROPN
ejpam-4115	194	27	-	-	PUNCT
ejpam-4115	194	28	nbd	nbd	PROPN
ejpam-4115	194	29	and	and	CCONJ
ejpam-4115	194	30	let	let	VERB
ejpam-4115	194	31	v	v	NOUN
ejpam-4115	194	32	and	and	CCONJ
ejpam-4115	194	33	w	w	AUX
ejpam-4115	194	34	be	be	AUX
ejpam-4115	194	35	θ	θ	PROPN
ejpam-4115	194	36	-	-	NOUN
ejpam-4115	194	37	nbds	nbds	NOUN
ejpam-4115	194	38	with	with	ADP
ejpam-4115	194	39	v	v	NOUN
ejpam-4115	194	40	+	+	CCONJ
ejpam-4115	194	41	w	w	PROPN
ejpam-4115	194	42	⊆	⊆	NUM
ejpam-4115	194	43	u	u	NOUN
ejpam-4115	194	44	.	.	PUNCT
ejpam-4115	195	1	since	since	SCONJ
ejpam-4115	195	2	f	f	PROPN
ejpam-4115	195	3	is	be	AUX
ejpam-4115	195	4	ac∗(a	ac∗(a	ADJ
ejpam-4115	195	5	)	)	PUNCT
ejpam-4115	195	6	,	,	PUNCT
ejpam-4115	195	7	there	there	PRON
ejpam-4115	195	8	exists	exist	VERB
ejpam-4115	195	9	η1	η1	NOUN
ejpam-4115	195	10	>	>	X
ejpam-4115	195	11	0	0	NUM
ejpam-4115	195	12	such	such	ADJ
ejpam-4115	195	13	that	that	PRON
ejpam-4115	195	14	for	for	ADP
ejpam-4115	195	15	any	any	DET
ejpam-4115	195	16	partial	partial	ADJ
ejpam-4115	195	17	partition	partition	NOUN
ejpam-4115	195	18	{	{	PUNCT
ejpam-4115	195	19	[	[	X
ejpam-4115	195	20	ui	ui	NOUN
ejpam-4115	195	21	,	,	PUNCT
ejpam-4115	195	22	vi	vi	PROPN
ejpam-4115	195	23	]	]	X
ejpam-4115	195	24	:	:	PUNCT
ejpam-4115	195	25	1	1	NUM
ejpam-4115	195	26	≤	≤	NUM
ejpam-4115	195	27	i	i	X
ejpam-4115	195	28	≤	≤	NOUN
ejpam-4115	195	29	m	m	VERB
ejpam-4115	195	30	}	}	PUNCT
ejpam-4115	195	31	with	with	ADP
ejpam-4115	195	32	ui	ui	PROPN
ejpam-4115	195	33	or	or	CCONJ
ejpam-4115	195	34	vi	vi	PROPN
ejpam-4115	195	35	in	in	ADP
ejpam-4115	195	36	a	a	PRON
ejpam-4115	195	37	and	and	CCONJ
ejpam-4115	195	38	∑m	∑m	ADJ
ejpam-4115	195	39	i=1(vi	i=1(vi	PRON
ejpam-4115	195	40	−	−	PROPN
ejpam-4115	195	41	ui	ui	PROPN
ejpam-4115	195	42	)	)	PUNCT
ejpam-4115	195	43	<	<	X
ejpam-4115	195	44	η1	η1	NOUN
ejpam-4115	195	45	,	,	PUNCT
ejpam-4115	195	46	there	there	PRON
ejpam-4115	195	47	exist	exist	VERB
ejpam-4115	195	48	θ	θ	PROPN
ejpam-4115	195	49	-	-	PUNCT
ejpam-4115	195	50	nbds	nbds	NOUN
ejpam-4115	195	51	v1	v1	NOUN
ejpam-4115	195	52	,	,	PUNCT
ejpam-4115	195	53	v2	v2	NOUN
ejpam-4115	195	54	,	,	PUNCT
ejpam-4115	195	55	.	.	PUNCT
ejpam-4115	195	56	.	.	PUNCT
ejpam-4115	196	1	.	.	PUNCT
ejpam-4115	197	1	,	,	PUNCT
ejpam-4115	197	2	vm	vm	PROPN
ejpam-4115	197	3	with∑m	with∑m	PROPN
ejpam-4115	197	4	i=1	i=1	PROPN
ejpam-4115	197	5	vi	vi	PROPN
ejpam-4115	197	6	⊆	⊆	NUM
ejpam-4115	197	7	v	v	ADP
ejpam-4115	197	8	such	such	ADJ
ejpam-4115	197	9	that	that	SCONJ
ejpam-4115	197	10	f	f	PROPN
ejpam-4115	197	11	(	(	PUNCT
ejpam-4115	197	12	vi	vi	NOUN
ejpam-4115	197	13	)	)	PUNCT
ejpam-4115	198	1	−	−	PROPN
ejpam-4115	198	2	f	f	PROPN
ejpam-4115	198	3	(	(	PUNCT
ejpam-4115	198	4	ui	ui	PROPN
ejpam-4115	198	5	)	)	PUNCT
ejpam-4115	198	6	∈	∈	PROPN
ejpam-4115	198	7	vi	vi	NOUN
ejpam-4115	198	8	for	for	ADP
ejpam-4115	198	9	1	1	NUM
ejpam-4115	198	10	≤	≤	NUM
ejpam-4115	198	11	i	i	PRON
ejpam-4115	198	12	≤	≤	PROPN
ejpam-4115	198	13	n.	n.	NOUN
ejpam-4115	198	14	likewise	likewise	ADV
ejpam-4115	198	15	,	,	PUNCT
ejpam-4115	198	16	because	because	SCONJ
ejpam-4115	198	17	f	f	PROPN
ejpam-4115	198	18	is	be	AUX
ejpam-4115	198	19	ac∗(b	ac∗(b	NOUN
ejpam-4115	198	20	)	)	PUNCT
ejpam-4115	198	21	,	,	PUNCT
ejpam-4115	198	22	there	there	PRON
ejpam-4115	198	23	exists	exist	VERB
ejpam-4115	198	24	η2	η2	ADJ
ejpam-4115	198	25	>	>	X
ejpam-4115	198	26	0	0	NUM
ejpam-4115	199	1	such	such	ADJ
ejpam-4115	199	2	that	that	PRON
ejpam-4115	199	3	for	for	ADP
ejpam-4115	199	4	any	any	DET
ejpam-4115	199	5	partial	partial	ADJ
ejpam-4115	199	6	partition	partition	NOUN
ejpam-4115	199	7	{	{	PUNCT
ejpam-4115	199	8	[	[	X
ejpam-4115	199	9	u′i	u′i	ADJ
ejpam-4115	199	10	,	,	PUNCT
ejpam-4115	199	11	v′i	v′i	NOUN
ejpam-4115	199	12	]	]	X
ejpam-4115	199	13	:	:	PUNCT
ejpam-4115	199	14	1	1	NUM
ejpam-4115	199	15	≤	≤	NUM
ejpam-4115	199	16	i	i	PRON
ejpam-4115	199	17	≤	≤	NOUN
ejpam-4115	199	18	n	n	CCONJ
ejpam-4115	199	19	}	}	PUNCT
ejpam-4115	199	20	with	with	ADP
ejpam-4115	199	21	u′i	u′i	ADJ
ejpam-4115	199	22	or	or	CCONJ
ejpam-4115	199	23	v	v	NOUN
ejpam-4115	199	24	′	′	NUM
ejpam-4115	200	1	i	i	PRON
ejpam-4115	200	2	in	in	ADP
ejpam-4115	200	3	a	a	PRON
ejpam-4115	200	4	and	and	CCONJ
ejpam-4115	200	5	∑n	∑n	NUM
ejpam-4115	200	6	i=1(v	i=1(v	NOUN
ejpam-4115	200	7	′	′	VERB
ejpam-4115	201	1	i	i	PRON
ejpam-4115	201	2	−	−	PROPN
ejpam-4115	202	1	u′i	u′i	ADJ
ejpam-4115	202	2	)	)	PUNCT
ejpam-4115	202	3	<	<	X
ejpam-4115	202	4	η2	η2	NOUN
ejpam-4115	202	5	,	,	PUNCT
ejpam-4115	202	6	there	there	PRON
ejpam-4115	202	7	exist	exist	VERB
ejpam-4115	202	8	θ	θ	PROPN
ejpam-4115	202	9	-	-	NOUN
ejpam-4115	202	10	nbds	nbds	NOUN
ejpam-4115	202	11	w1,w2	w1,w2	PROPN
ejpam-4115	202	12	,	,	PUNCT
ejpam-4115	202	13	.	.	PUNCT
ejpam-4115	202	14	.	.	PUNCT
ejpam-4115	203	1	.	.	PUNCT
ejpam-4115	204	1	,	,	PUNCT
ejpam-4115	204	2	wn	wn	PROPN
ejpam-4115	204	3	with∑n	with∑n	PROPN
ejpam-4115	204	4	i=1wi	i=1wi	PROPN
ejpam-4115	204	5	⊆	⊆	NUM
ejpam-4115	205	1	w	w	ADP
ejpam-4115	205	2	such	such	ADJ
ejpam-4115	205	3	that	that	SCONJ
ejpam-4115	205	4	f	f	PROPN
ejpam-4115	205	5	(	(	PUNCT
ejpam-4115	205	6	yi	yi	PROPN
ejpam-4115	205	7	)	)	PUNCT
ejpam-4115	206	1	−	−	PROPN
ejpam-4115	207	1	f	f	PROPN
ejpam-4115	207	2	(	(	PUNCT
ejpam-4115	207	3	xi	xi	PROPN
ejpam-4115	207	4	)	)	PUNCT
ejpam-4115	207	5	∈	∈	PROPN
ejpam-4115	207	6	wi	wi	PROPN
ejpam-4115	207	7	for	for	ADP
ejpam-4115	207	8	1	1	NUM
ejpam-4115	207	9	≤	≤	NUM
ejpam-4115	207	10	i	i	PRON
ejpam-4115	207	11	≤	≤	ADJ
ejpam-4115	207	12	n.	n.	NOUN
ejpam-4115	207	13	let	let	VERB
ejpam-4115	207	14	η	η	NOUN
ejpam-4115	207	15	=	=	NOUN
ejpam-4115	207	16	min{η1	min{η1	NOUN
ejpam-4115	207	17	,	,	PUNCT
ejpam-4115	207	18	η2	η2	PROPN
ejpam-4115	207	19	}	}	PUNCT
ejpam-4115	207	20	.	.	PUNCT
ejpam-4115	208	1	suppose	suppose	VERB
ejpam-4115	208	2	d	d	X
ejpam-4115	208	3	=	=	PRON
ejpam-4115	208	4	{	{	PUNCT
ejpam-4115	208	5	[	[	X
ejpam-4115	208	6	xi	xi	X
ejpam-4115	208	7	,	,	PUNCT
ejpam-4115	208	8	yi	yi	NOUN
ejpam-4115	208	9	]	]	X
ejpam-4115	208	10	:	:	PUNCT
ejpam-4115	208	11	1	1	NUM
ejpam-4115	208	12	≤	≤	NUM
ejpam-4115	208	13	i	i	NOUN
ejpam-4115	208	14	≤	≤	PUNCT
ejpam-4115	209	1	k	k	X
ejpam-4115	209	2	}	}	PUNCT
ejpam-4115	209	3	is	be	AUX
ejpam-4115	209	4	a	a	DET
ejpam-4115	209	5	partial	partial	ADJ
ejpam-4115	209	6	partition	partition	NOUN
ejpam-4115	209	7	of	of	ADP
ejpam-4115	209	8	[	[	X
ejpam-4115	209	9	a	a	X
ejpam-4115	209	10	,	,	PUNCT
ejpam-4115	209	11	b	b	NOUN
ejpam-4115	209	12	]	]	X
ejpam-4115	209	13	with	with	ADP
ejpam-4115	209	14	xi	xi	ADP
ejpam-4115	209	15	or	or	CCONJ
ejpam-4115	209	16	yi	yi	PROPN
ejpam-4115	209	17	∈	∈	PROPN
ejpam-4115	209	18	a	a	DET
ejpam-4115	209	19	∪	∪	NOUN
ejpam-4115	209	20	b	b	NOUN
ejpam-4115	209	21	and	and	CCONJ
ejpam-4115	209	22	∑k	∑k	PROPN
ejpam-4115	209	23	i=1(vi	i=1(vi	VERB
ejpam-4115	209	24	−	−	PROPN
ejpam-4115	209	25	ui	ui	PROPN
ejpam-4115	209	26	)	)	PUNCT
ejpam-4115	209	27	<	<	X
ejpam-4115	209	28	η	η	PROPN
ejpam-4115	209	29	.	.	PROPN
ejpam-4115	209	30	let	let	VERB
ejpam-4115	209	31	d1	d1	PROPN
ejpam-4115	209	32	=	=	PUNCT
ejpam-4115	209	33	{	{	PUNCT
ejpam-4115	209	34	[	[	X
ejpam-4115	209	35	xi	xi	X
ejpam-4115	209	36	,	,	PUNCT
ejpam-4115	209	37	yi	yi	NOUN
ejpam-4115	209	38	]	]	X
ejpam-4115	209	39	∈	∈	PROPN
ejpam-4115	210	1	d	d	X
ejpam-4115	210	2	:	:	PUNCT
ejpam-4115	210	3	xi	xi	PROPN
ejpam-4115	210	4	or	or	CCONJ
ejpam-4115	210	5	yi	yi	PROPN
ejpam-4115	210	6	∈	∈	PROPN
ejpam-4115	210	7	a	a	PRON
ejpam-4115	210	8	}	}	PUNCT
ejpam-4115	210	9	and	and	CCONJ
ejpam-4115	210	10	d2	d2	PROPN
ejpam-4115	210	11	=	=	SYM
ejpam-4115	210	12	{	{	PUNCT
ejpam-4115	210	13	[	[	X
ejpam-4115	210	14	xi	xi	X
ejpam-4115	210	15	,	,	PUNCT
ejpam-4115	210	16	yi	yi	NOUN
ejpam-4115	210	17	]	]	X
ejpam-4115	210	18	∈	∈	PROPN
ejpam-4115	211	1	d	d	X
ejpam-4115	211	2	\d1	\d1	NOUN
ejpam-4115	211	3	:	:	PUNCT
ejpam-4115	211	4	xi	xi	NOUN
ejpam-4115	211	5	or	or	CCONJ
ejpam-4115	211	6	yi	yi	PROPN
ejpam-4115	211	7	∈	∈	PROPN
ejpam-4115	211	8	b	b	NOUN
ejpam-4115	211	9	}	}	PUNCT
ejpam-4115	211	10	.	.	PUNCT
ejpam-4115	212	1	if	if	SCONJ
ejpam-4115	212	2	d1	d1	NOUN
ejpam-4115	212	3	=	=	SYM
ejpam-4115	212	4	∅	∅	NOUN
ejpam-4115	212	5	or	or	CCONJ
ejpam-4115	212	6	d2	d2	NOUN
ejpam-4115	212	7	=	=	PUNCT
ejpam-4115	212	8	∅	∅	NOUN
ejpam-4115	212	9	,	,	PUNCT
ejpam-4115	212	10	then	then	ADV
ejpam-4115	212	11	we	we	PRON
ejpam-4115	212	12	are	be	AUX
ejpam-4115	212	13	done	do	VERB
ejpam-4115	212	14	.	.	PUNCT
ejpam-4115	213	1	so	so	ADV
ejpam-4115	213	2	suppose	suppose	VERB
ejpam-4115	213	3	that	that	SCONJ
ejpam-4115	213	4	d1	d1	PROPN
ejpam-4115	213	5	̸=	̸=	PROPN
ejpam-4115	213	6	∅	∅	NOUN
ejpam-4115	213	7	and	and	CCONJ
ejpam-4115	213	8	d2	d2	PROPN
ejpam-4115	213	9	̸=	̸=	PROPN
ejpam-4115	213	10	∅.	∅.	VERB
ejpam-4115	213	11	by	by	ADP
ejpam-4115	213	12	relabeling	relabele	VERB
ejpam-4115	213	13	the	the	DET
ejpam-4115	213	14	elements	element	NOUN
ejpam-4115	213	15	of	of	ADP
ejpam-4115	213	16	d1	d1	PROPN
ejpam-4115	213	17	and	and	CCONJ
ejpam-4115	213	18	d2	d2	PROPN
ejpam-4115	213	19	,	,	PUNCT
ejpam-4115	213	20	we	we	PRON
ejpam-4115	213	21	may	may	AUX
ejpam-4115	213	22	write	write	VERB
ejpam-4115	213	23	d1	d1	PROPN
ejpam-4115	213	24	=	=	PUNCT
ejpam-4115	213	25	{	{	PUNCT
ejpam-4115	214	1	[	[	X
ejpam-4115	214	2	ai	ai	NOUN
ejpam-4115	214	3	,	,	PUNCT
ejpam-4115	214	4	bi	bi	NOUN
ejpam-4115	214	5	]	]	X
ejpam-4115	214	6	:	:	PUNCT
ejpam-4115	214	7	1	1	NUM
ejpam-4115	214	8	≤	≤	NUM
ejpam-4115	214	9	i	i	PROPN
ejpam-4115	214	10	≤	≤	NUM
ejpam-4115	214	11	k1	k1	X
ejpam-4115	214	12	}	}	PUNCT
ejpam-4115	214	13	and	and	CCONJ
ejpam-4115	214	14	d2	d2	PROPN
ejpam-4115	214	15	=	=	SYM
ejpam-4115	214	16	{	{	PUNCT
ejpam-4115	214	17	[	[	X
ejpam-4115	214	18	a′j	a′j	X
ejpam-4115	214	19	,	,	PUNCT
ejpam-4115	214	20	b′j	b′j	VERB
ejpam-4115	214	21	]	]	X
ejpam-4115	214	22	:	:	PUNCT
ejpam-4115	214	23	1	1	NUM
ejpam-4115	214	24	≤	≤	NUM
ejpam-4115	214	25	j	j	PROPN
ejpam-4115	214	26	≤	≤	PROPN
ejpam-4115	214	27	k2	k2	PROPN
ejpam-4115	214	28	}	}	PUNCT
ejpam-4115	214	29	where	where	SCONJ
ejpam-4115	214	30	k	k	PROPN
ejpam-4115	214	31	=	=	SYM
ejpam-4115	214	32	k1	k1	PROPN
ejpam-4115	214	33	+	+	X
ejpam-4115	214	34	k2	k2	NOUN
ejpam-4115	214	35	.	.	PUNCT
ejpam-4115	215	1	then	then	ADV
ejpam-4115	215	2	by	by	ADP
ejpam-4115	215	3	assumption	assumption	NOUN
ejpam-4115	215	4	,	,	PUNCT
ejpam-4115	215	5	there	there	PRON
ejpam-4115	215	6	exist	exist	VERB
ejpam-4115	215	7	collections	collection	NOUN
ejpam-4115	215	8	{	{	PUNCT
ejpam-4115	215	9	vi}k1i=1	vi}k1i=1	NOUN
ejpam-4115	215	10	and	and	CCONJ
ejpam-4115	215	11	{	{	PUNCT
ejpam-4115	215	12	wi}k2i=1	wi}k2i=1	NOUN
ejpam-4115	215	13	of	of	ADP
ejpam-4115	215	14	θnbds	θnbds	NOUN
ejpam-4115	215	15	such	such	ADJ
ejpam-4115	215	16	that	that	SCONJ
ejpam-4115	215	17	∑k1	∑k1	PROPN
ejpam-4115	215	18	i=1	i=1	PROPN
ejpam-4115	215	19	vi	vi	PROPN
ejpam-4115	215	20	⊆	⊆	NUM
ejpam-4115	215	21	v	v	NOUN
ejpam-4115	215	22	and	and	CCONJ
ejpam-4115	215	23	∑k2	∑k2	ADJ
ejpam-4115	215	24	i=1wi	i=1wi	NOUN
ejpam-4115	216	1	⊆	⊆	NUM
ejpam-4115	216	2	w	w	NOUN
ejpam-4115	216	3	for	for	ADP
ejpam-4115	216	4	which	which	PRON
ejpam-4115	216	5	f	f	X
ejpam-4115	216	6	(	(	PUNCT
ejpam-4115	216	7	bi)−f	bi)−f	PROPN
ejpam-4115	216	8	(	(	PUNCT
ejpam-4115	216	9	ai	ai	NOUN
ejpam-4115	216	10	)	)	PUNCT
ejpam-4115	216	11	∈	∈	PROPN
ejpam-4115	216	12	vi	vi	PROPN
ejpam-4115	216	13	for	for	ADP
ejpam-4115	216	14	each	each	DET
ejpam-4115	216	15	i	i	PRON
ejpam-4115	216	16	∈	∈	PROPN
ejpam-4115	216	17	{	{	PUNCT
ejpam-4115	216	18	1	1	NUM
ejpam-4115	216	19	,	,	PUNCT
ejpam-4115	216	20	2	2	NUM
ejpam-4115	216	21	,	,	PUNCT
ejpam-4115	216	22	·	·	PUNCT
ejpam-4115	216	23	·	·	PUNCT
ejpam-4115	216	24	·	·	PUNCT
ejpam-4115	216	25	,	,	PUNCT
ejpam-4115	216	26	k1	k1	NOUN
ejpam-4115	216	27	}	}	PUNCT
ejpam-4115	216	28	and	and	CCONJ
ejpam-4115	216	29	f	f	PROPN
ejpam-4115	216	30	(	(	PUNCT
ejpam-4115	216	31	b′i)−f	b′i)−f	PROPN
ejpam-4115	216	32	(	(	PUNCT
ejpam-4115	216	33	a′i	a′i	PROPN
ejpam-4115	216	34	)	)	PUNCT
ejpam-4115	216	35	∈	∈	PROPN
ejpam-4115	216	36	wi	wi	PROPN
ejpam-4115	216	37	for	for	ADP
ejpam-4115	216	38	each	each	DET
ejpam-4115	216	39	i	i	PRON
ejpam-4115	216	40	∈	∈	PROPN
ejpam-4115	216	41	{	{	PUNCT
ejpam-4115	216	42	1	1	NUM
ejpam-4115	216	43	,	,	PUNCT
ejpam-4115	216	44	2	2	NUM
ejpam-4115	216	45	,	,	PUNCT
ejpam-4115	216	46	·	·	PUNCT
ejpam-4115	216	47	·	·	PUNCT
ejpam-4115	216	48	·	·	PUNCT
ejpam-4115	216	49	,	,	PUNCT
ejpam-4115	216	50	k2	k2	NOUN
ejpam-4115	216	51	}	}	PUNCT
ejpam-4115	216	52	.	.	PUNCT
ejpam-4115	217	1	let	let	VERB
ejpam-4115	217	2	vk1+j	vk1+j	NOUN
ejpam-4115	217	3	=	=	PUNCT
ejpam-4115	217	4	wj	wj	PROPN
ejpam-4115	217	5	for	for	ADP
ejpam-4115	217	6	each	each	DET
ejpam-4115	217	7	j	j	PROPN
ejpam-4115	217	8	∈	∈	PROPN
ejpam-4115	217	9	{	{	PUNCT
ejpam-4115	217	10	1	1	NUM
ejpam-4115	217	11	,	,	PUNCT
ejpam-4115	217	12	2	2	NUM
ejpam-4115	217	13	,	,	PUNCT
ejpam-4115	217	14	.	.	PUNCT
ejpam-4115	217	15	.	.	PUNCT
ejpam-4115	218	1	.	.	PUNCT
ejpam-4115	219	1	,	,	PUNCT
ejpam-4115	219	2	k2	k2	NOUN
ejpam-4115	219	3	}	}	PUNCT
ejpam-4115	219	4	.	.	PUNCT
ejpam-4115	220	1	then	then	ADV
ejpam-4115	220	2	v1	v1	VERB
ejpam-4115	220	3	,	,	PUNCT
ejpam-4115	220	4	v2	v2	PROPN
ejpam-4115	220	5	,	,	PUNCT
ejpam-4115	220	6	.	.	PUNCT
ejpam-4115	220	7	.	.	PUNCT
ejpam-4115	220	8	.	.	PUNCT
ejpam-4115	221	1	,	,	PUNCT
ejpam-4115	221	2	vk1	vk1	ADJ
ejpam-4115	221	3	,	,	PUNCT
ejpam-4115	221	4	vk1	vk1	ADJ
ejpam-4115	221	5	+	+	PROPN
ejpam-4115	221	6	1	1	NUM
ejpam-4115	221	7	,	,	PUNCT
ejpam-4115	221	8	.	.	PUNCT
ejpam-4115	221	9	.	.	PUNCT
ejpam-4115	221	10	.	.	PUNCT
ejpam-4115	222	1	,	,	PUNCT
ejpam-4115	222	2	vk1+k2−1	vk1+k2−1	NOUN
ejpam-4115	222	3	,	,	PUNCT
ejpam-4115	222	4	vk	vk	X
ejpam-4115	222	5	are	be	AUX
ejpam-4115	222	6	θ	θ	NOUN
ejpam-4115	222	7	-	-	NOUN
ejpam-4115	222	8	nbds	nbds	NOUN
ejpam-4115	223	1	and	and	CCONJ
ejpam-4115	223	2	∑k	∑k	PROPN
ejpam-4115	224	1	i=1	i=1	PROPN
ejpam-4115	224	2	vi	vi	PROPN
ejpam-4115	225	1	=	=	SYM
ejpam-4115	226	1	∑k1	∑k1	PROPN
ejpam-4115	227	1	i=1	i=1	PROPN
ejpam-4115	227	2	vi	vi	PROPN
ejpam-4115	228	1	+	+	CCONJ
ejpam-4115	228	2	∑k2	∑k2	ADJ
ejpam-4115	228	3	i=1wi	i=1wi	NOUN
ejpam-4115	229	1	⊆	⊆	NUM
ejpam-4115	229	2	v	v	ADP
ejpam-4115	229	3	+	+	PROPN
ejpam-4115	229	4	w	w	PROPN
ejpam-4115	229	5	⊆	⊆	NUM
ejpam-4115	229	6	u	u	NOUN
ejpam-4115	229	7	.	.	PUNCT
ejpam-4115	230	1	therefore	therefore	ADV
ejpam-4115	230	2	,	,	PUNCT
ejpam-4115	230	3	f	f	PROPN
ejpam-4115	230	4	is	be	AUX
ejpam-4115	230	5	ac∗(a	ac∗(a	ADJ
ejpam-4115	230	6	∪b	∪b	NOUN
ejpam-4115	230	7	)	)	PUNCT
ejpam-4115	230	8	.	.	PUNCT
ejpam-4115	231	1	remark	remark	NOUN
ejpam-4115	231	2	2	2	NUM
ejpam-4115	231	3	.	.	PUNCT
ejpam-4115	232	1	if	if	SCONJ
ejpam-4115	232	2	a	a	DET
ejpam-4115	232	3	function	function	NOUN
ejpam-4115	232	4	f	f	PROPN
ejpam-4115	232	5	is	be	AUX
ejpam-4115	232	6	acg∗	acg∗	NOUN
ejpam-4115	232	7	on	on	ADP
ejpam-4115	232	8	[	[	X
ejpam-4115	232	9	a	a	X
ejpam-4115	232	10	,	,	PUNCT
ejpam-4115	232	11	b	b	NOUN
ejpam-4115	232	12	]	]	X
ejpam-4115	232	13	,	,	PUNCT
ejpam-4115	232	14	then	then	ADV
ejpam-4115	232	15	[	[	X
ejpam-4115	232	16	a	a	X
ejpam-4115	232	17	,	,	PUNCT
ejpam-4115	232	18	b	b	X
ejpam-4115	232	19	]	]	X
ejpam-4115	232	20	is	be	AUX
ejpam-4115	232	21	the	the	DET
ejpam-4115	232	22	union	union	NOUN
ejpam-4115	232	23	of	of	ADP
ejpam-4115	232	24	sets	set	NOUN
ejpam-4115	232	25	in	in	ADP
ejpam-4115	232	26	some	some	DET
ejpam-4115	232	27	collection	collection	NOUN
ejpam-4115	232	28	{	{	PUNCT
ejpam-4115	232	29	yi}∞i=1	yi}∞i=1	NOUN
ejpam-4115	232	30	of	of	ADP
ejpam-4115	232	31	subsets	subset	NOUN
ejpam-4115	232	32	of	of	ADP
ejpam-4115	232	33	[	[	X
ejpam-4115	232	34	a	a	X
ejpam-4115	232	35	,	,	PUNCT
ejpam-4115	232	36	b	b	NOUN
ejpam-4115	232	37	]	]	X
ejpam-4115	232	38	for	for	ADP
ejpam-4115	232	39	which	which	PRON
ejpam-4115	232	40	f	f	PROPN
ejpam-4115	232	41	is	be	AUX
ejpam-4115	232	42	ac∗(yi	ac∗(yi	ADV
ejpam-4115	232	43	)	)	PUNCT
ejpam-4115	232	44	for	for	ADP
ejpam-4115	232	45	each	each	PRON
ejpam-4115	232	46	i	i	PRON
ejpam-4115	232	47	∈	∈	PROPN
ejpam-4115	233	1	n.	n.	NOUN
ejpam-4115	234	1	we	we	PRON
ejpam-4115	234	2	may	may	AUX
ejpam-4115	234	3	assume	assume	VERB
ejpam-4115	234	4	that	that	SCONJ
ejpam-4115	234	5	the	the	DET
ejpam-4115	234	6	sets	set	NOUN
ejpam-4115	234	7	are	be	AUX
ejpam-4115	234	8	disjoint	disjoint	ADJ
ejpam-4115	234	9	.	.	PUNCT
ejpam-4115	235	1	in	in	ADP
ejpam-4115	235	2	fact	fact	NOUN
ejpam-4115	235	3	,	,	PUNCT
ejpam-4115	235	4	the	the	DET
ejpam-4115	235	5	collection	collection	NOUN
ejpam-4115	235	6	{	{	PUNCT
ejpam-4115	235	7	zi}∞i=1	zi}∞i=1	X
ejpam-4115	235	8	is	be	AUX
ejpam-4115	235	9	mutually	mutually	ADV
ejpam-4115	235	10	disjoint	disjoint	ADJ
ejpam-4115	235	11	and	and	CCONJ
ejpam-4115	235	12	satisfies	satisfy	VERB
ejpam-4115	235	13	the	the	DET
ejpam-4115	235	14	condition	condition	NOUN
ejpam-4115	235	15	for	for	ADP
ejpam-4115	235	16	acg∗	acg∗	NOUN
ejpam-4115	235	17	where	where	SCONJ
ejpam-4115	235	18	zi	zi	NOUN
ejpam-4115	235	19	=	=	SYM
ejpam-4115	235	20	yi	yi	PROPN
ejpam-4115	235	21	\	\	PROPN
ejpam-4115	236	1	(	(	PUNCT
ejpam-4115	236	2	y1	y1	NOUN
ejpam-4115	236	3	∪	∪	ADJ
ejpam-4115	236	4	y2	y2	PROPN
ejpam-4115	236	5	∪	∪	X
ejpam-4115	236	6	·	·	PUNCT
ejpam-4115	236	7	·	·	PUNCT
ejpam-4115	236	8	·	·	PUNCT
ejpam-4115	236	9	∪	∪	ADP
ejpam-4115	236	10	yi−1	yi−1	PROPN
ejpam-4115	236	11	)	)	PUNCT
ejpam-4115	236	12	⊆	⊆	NUM
ejpam-4115	236	13	yi	yi	NOUN
ejpam-4115	236	14	.	.	PUNCT
ejpam-4115	237	1	the	the	DET
ejpam-4115	237	2	next	next	ADJ
ejpam-4115	237	3	result	result	NOUN
ejpam-4115	237	4	follows	follow	VERB
ejpam-4115	237	5	from	from	ADP
ejpam-4115	237	6	(	(	PUNCT
ejpam-4115	237	7	ii)and	ii)and	X
ejpam-4115	237	8	(	(	PUNCT
ejpam-4115	237	9	iii	iii	NOUN
ejpam-4115	237	10	)	)	PUNCT
ejpam-4115	237	11	of	of	ADP
ejpam-4115	237	12	theorem	theorem	ADJ
ejpam-4115	237	13	1	1	NUM
ejpam-4115	237	14	.	.	PUNCT
ejpam-4115	237	15	theorem	theorem	NOUN
ejpam-4115	237	16	2	2	NUM
ejpam-4115	237	17	.	.	PUNCT
ejpam-4115	238	1	let	let	VERB
ejpam-4115	238	2	f	f	X
ejpam-4115	238	3	,	,	PUNCT
ejpam-4115	238	4	g	g	NOUN
ejpam-4115	238	5	:	:	PUNCT
ejpam-4115	239	1	[	[	X
ejpam-4115	239	2	a	a	X
ejpam-4115	239	3	,	,	PUNCT
ejpam-4115	239	4	b	b	NOUN
ejpam-4115	239	5	]	]	X
ejpam-4115	239	6	→	→	PUNCT
ejpam-4115	239	7	x	x	PUNCT
ejpam-4115	239	8	be	be	AUX
ejpam-4115	239	9	acg∗	acg∗	ADJ
ejpam-4115	239	10	on	on	ADP
ejpam-4115	239	11	[	[	X
ejpam-4115	239	12	a	a	X
ejpam-4115	239	13	,	,	PUNCT
ejpam-4115	239	14	b	b	NOUN
ejpam-4115	239	15	]	]	PUNCT
ejpam-4115	239	16	and	and	CCONJ
ejpam-4115	239	17	let	let	VERB
ejpam-4115	239	18	c	c	PROPN
ejpam-4115	239	19	∈	∈	PROPN
ejpam-4115	239	20	r.	r.	PROPN
ejpam-4115	239	21	then	then	ADV
ejpam-4115	239	22	cf	cf	INTJ
ejpam-4115	239	23	and	and	CCONJ
ejpam-4115	239	24	f	f	PROPN
ejpam-4115	240	1	+	+	NOUN
ejpam-4115	240	2	g	g	PROPN
ejpam-4115	240	3	are	be	AUX
ejpam-4115	240	4	acg∗	acg∗	NOUN
ejpam-4115	240	5	on	on	ADP
ejpam-4115	240	6	[	[	X
ejpam-4115	240	7	a	a	X
ejpam-4115	240	8	,	,	PUNCT
ejpam-4115	240	9	b	b	NOUN
ejpam-4115	240	10	]	]	PUNCT
ejpam-4115	240	11	.	.	PUNCT
ejpam-4115	241	1	theorem	theorem	NOUN
ejpam-4115	241	2	3	3	X
ejpam-4115	241	3	.	.	PUNCT
ejpam-4115	242	1	if	if	SCONJ
ejpam-4115	242	2	f	f	PROPN
ejpam-4115	242	3	:	:	PUNCT
ejpam-4115	243	1	[	[	X
ejpam-4115	243	2	a	a	X
ejpam-4115	243	3	,	,	PUNCT
ejpam-4115	243	4	b	b	NOUN
ejpam-4115	243	5	]	]	X
ejpam-4115	243	6	→	→	PUNCT
ejpam-4115	243	7	x	x	X
ejpam-4115	243	8	is	be	AUX
ejpam-4115	243	9	an	an	DET
ejpam-4115	243	10	acg∗	acg∗	NOUN
ejpam-4115	243	11	function	function	NOUN
ejpam-4115	243	12	,	,	PUNCT
ejpam-4115	243	13	then	then	ADV
ejpam-4115	243	14	f	f	PROPN
ejpam-4115	243	15	is	be	AUX
ejpam-4115	243	16	continuous	continuous	ADJ
ejpam-4115	243	17	.	.	PUNCT
ejpam-4115	244	1	proof	proof	NOUN
ejpam-4115	244	2	.	.	PUNCT
ejpam-4115	245	1	let	let	VERB
ejpam-4115	245	2	u	u	PRON
ejpam-4115	245	3	be	be	AUX
ejpam-4115	245	4	an	an	DET
ejpam-4115	245	5	open	open	ADJ
ejpam-4115	245	6	set	set	NOUN
ejpam-4115	245	7	in	in	ADP
ejpam-4115	245	8	x.	x.	NOUN
ejpam-4115	245	9	let	let	VERB
ejpam-4115	245	10	c	c	PROPN
ejpam-4115	245	11	∈	∈	PROPN
ejpam-4115	245	12	f−1(u	f−1(u	PROPN
ejpam-4115	245	13	)	)	PUNCT
ejpam-4115	245	14	.	.	PUNCT
ejpam-4115	246	1	since	since	SCONJ
ejpam-4115	246	2	f	f	PROPN
ejpam-4115	246	3	is	be	AUX
ejpam-4115	246	4	acg∗	acg∗	ADJ
ejpam-4115	246	5	,	,	PUNCT
ejpam-4115	246	6	there	there	PRON
ejpam-4115	246	7	exists	exist	VERB
ejpam-4115	246	8	a	a	DET
ejpam-4115	246	9	countable	countable	ADJ
ejpam-4115	246	10	collection	collection	NOUN
ejpam-4115	246	11	{	{	PUNCT
ejpam-4115	246	12	ei}∞i=1	ei}∞i=1	NOUN
ejpam-4115	246	13	of	of	ADP
ejpam-4115	246	14	subsets	subset	NOUN
ejpam-4115	246	15	of	of	ADP
ejpam-4115	246	16	[	[	X
ejpam-4115	246	17	a	a	X
ejpam-4115	246	18	,	,	PUNCT
ejpam-4115	246	19	b	b	NOUN
ejpam-4115	246	20	]	]	X
ejpam-4115	246	21	whose	whose	DET
ejpam-4115	246	22	union	union	NOUN
ejpam-4115	246	23	is	be	AUX
ejpam-4115	246	24	[	[	X
ejpam-4115	246	25	a	a	DET
ejpam-4115	246	26	,	,	PUNCT
ejpam-4115	246	27	b	b	NOUN
ejpam-4115	246	28	]	]	X
ejpam-4115	246	29	such	such	ADJ
ejpam-4115	246	30	that	that	SCONJ
ejpam-4115	246	31	f	f	PROPN
ejpam-4115	246	32	is	be	AUX
ejpam-4115	246	33	ac∗(ei	ac∗(ei	PROPN
ejpam-4115	246	34	)	)	PUNCT
ejpam-4115	246	35	for	for	ADP
ejpam-4115	246	36	each	each	DET
ejpam-4115	246	37	i	i	PRON
ejpam-4115	246	38	∈	∈	PROPN
ejpam-4115	246	39	n.	n.	NOUN
ejpam-4115	246	40	let	let	VERB
ejpam-4115	246	41	c	c	PROPN
ejpam-4115	246	42	∈	∈	PROPN
ejpam-4115	246	43	ek	ek	VERB
ejpam-4115	246	44	for	for	ADP
ejpam-4115	246	45	some	some	DET
ejpam-4115	246	46	k	k	PROPN
ejpam-4115	246	47	∈	∈	PROPN
ejpam-4115	246	48	n.	n.	NOUN
ejpam-4115	246	49	clearly	clearly	ADV
ejpam-4115	246	50	,	,	PUNCT
ejpam-4115	246	51	u	u	NOUN
ejpam-4115	247	1	−	−	PROPN
ejpam-4115	247	2	f	f	X
ejpam-4115	247	3	(	(	PUNCT
ejpam-4115	247	4	c	c	NOUN
ejpam-4115	247	5	)	)	PUNCT
ejpam-4115	247	6	is	be	AUX
ejpam-4115	247	7	a	a	DET
ejpam-4115	247	8	θ	θ	PROPN
ejpam-4115	247	9	-	-	PUNCT
ejpam-4115	247	10	nbd	nbd	PROPN
ejpam-4115	247	11	.	.	PUNCT
ejpam-4115	248	1	let	let	VERB
ejpam-4115	248	2	w	w	NOUN
ejpam-4115	248	3	be	be	AUX
ejpam-4115	248	4	a	a	DET
ejpam-4115	248	5	balanced	balanced	ADJ
ejpam-4115	248	6	θ	θ	PROPN
ejpam-4115	248	7	-	-	PUNCT
ejpam-4115	248	8	nbd	nbd	PROPN
ejpam-4115	249	1	such	such	ADJ
ejpam-4115	249	2	that	that	SCONJ
ejpam-4115	249	3	w	w	PROPN
ejpam-4115	249	4	⊆	⊆	NUM
ejpam-4115	249	5	u	u	NOUN
ejpam-4115	249	6	−	−	PROPN
ejpam-4115	249	7	f	f	X
ejpam-4115	249	8	(	(	PUNCT
ejpam-4115	249	9	c	c	NOUN
ejpam-4115	249	10	)	)	PUNCT
ejpam-4115	249	11	and	and	CCONJ
ejpam-4115	249	12	let	let	VERB
ejpam-4115	249	13	η	η	PROPN
ejpam-4115	249	14	be	be	AUX
ejpam-4115	249	15	a	a	DET
ejpam-4115	249	16	positive	positive	ADJ
ejpam-4115	249	17	number	number	NOUN
ejpam-4115	249	18	associated	associate	VERB
ejpam-4115	249	19	with	with	ADP
ejpam-4115	249	20	f	f	PROPN
ejpam-4115	249	21	,	,	PUNCT
ejpam-4115	249	22	w	w	PROPN
ejpam-4115	249	23	,	,	PUNCT
ejpam-4115	249	24	ek	ek	PROPN
ejpam-4115	249	25	according	accord	VERB
ejpam-4115	249	26	to	to	ADP
ejpam-4115	249	27	the	the	DET
ejpam-4115	249	28	definition	definition	NOUN
ejpam-4115	249	29	of	of	ADP
ejpam-4115	249	30	ac∗.	ac∗.	PROPN
ejpam-4115	249	31	let	let	VERB
ejpam-4115	249	32	x	x	X
ejpam-4115	249	33	∈	∈	PROPN
ejpam-4115	249	34	[	[	X
ejpam-4115	249	35	a	a	X
ejpam-4115	249	36	,	,	PUNCT
ejpam-4115	249	37	b	b	AUX
ejpam-4115	249	38	]	]	PUNCT
ejpam-4115	249	39	be	be	AUX
ejpam-4115	249	40	such	such	ADJ
ejpam-4115	249	41	that	that	SCONJ
ejpam-4115	249	42	|x	|x	NOUN
ejpam-4115	249	43	−	−	PROPN
ejpam-4115	249	44	c|	c|	PROPN
ejpam-4115	249	45	<	<	X
ejpam-4115	249	46	η	η	PROPN
ejpam-4115	249	47	and	and	CCONJ
ejpam-4115	249	48	x	x	SYM
ejpam-4115	249	49	̸=	̸=	PROPN
ejpam-4115	249	50	c.	c.	NOUN
ejpam-4115	250	1	then	then	ADV
ejpam-4115	250	2	d	d	PROPN
ejpam-4115	250	3	=	=	PRON
ejpam-4115	250	4	{	{	PUNCT
ejpam-4115	250	5	[	[	X
ejpam-4115	250	6	x	x	X
ejpam-4115	250	7	,	,	PUNCT
ejpam-4115	250	8	c	c	NOUN
ejpam-4115	250	9	]	]	X
ejpam-4115	250	10	}	}	PUNCT
ejpam-4115	250	11	or	or	CCONJ
ejpam-4115	250	12	d	d	NOUN
ejpam-4115	250	13	=	=	SYM
ejpam-4115	250	14	{	{	PUNCT
ejpam-4115	250	15	[	[	X
ejpam-4115	250	16	c	c	X
ejpam-4115	250	17	,	,	PUNCT
ejpam-4115	250	18	x	x	NOUN
ejpam-4115	250	19	]	]	X
ejpam-4115	250	20	}	}	PUNCT
ejpam-4115	250	21	is	be	AUX
ejpam-4115	250	22	a	a	DET
ejpam-4115	250	23	partial	partial	ADJ
ejpam-4115	250	24	partition	partition	NOUN
ejpam-4115	250	25	of	of	ADP
ejpam-4115	250	26	[	[	X
ejpam-4115	250	27	a	a	X
ejpam-4115	250	28	,	,	PUNCT
ejpam-4115	250	29	b	b	NOUN
ejpam-4115	250	30	]	]	X
ejpam-4115	250	31	depending	depend	VERB
ejpam-4115	250	32	on	on	ADP
ejpam-4115	250	33	whether	whether	SCONJ
ejpam-4115	250	34	c	c	NOUN
ejpam-4115	250	35	>	>	X
ejpam-4115	250	36	x	x	X
ejpam-4115	250	37	or	or	CCONJ
ejpam-4115	250	38	c	c	X
ejpam-4115	250	39	<	<	X
ejpam-4115	250	40	x.	x.	NOUN
ejpam-4115	250	41	by	by	ADP
ejpam-4115	250	42	assumption	assumption	NOUN
ejpam-4115	250	43	,	,	PUNCT
ejpam-4115	250	44	there	there	PRON
ejpam-4115	250	45	exists	exist	VERB
ejpam-4115	250	46	a	a	DET
ejpam-4115	250	47	θ	θ	PROPN
ejpam-4115	250	48	-	-	PUNCT
ejpam-4115	250	49	nbd	nbd	PROPN
ejpam-4115	250	50	v	v	NOUN
ejpam-4115	250	51	with	with	ADP
ejpam-4115	250	52	v	v	NUM
ejpam-4115	250	53	⊆	⊆	NUM
ejpam-4115	250	54	w	w	NOUN
ejpam-4115	250	55	such	such	ADJ
ejpam-4115	250	56	that	that	SCONJ
ejpam-4115	250	57	f	f	PROPN
ejpam-4115	250	58	(	(	PUNCT
ejpam-4115	250	59	c)−f	c)−f	X
ejpam-4115	250	60	(	(	PUNCT
ejpam-4115	250	61	x	x	X
ejpam-4115	250	62	)	)	PUNCT
ejpam-4115	250	63	∈	∈	PROPN
ejpam-4115	250	64	v	v	NOUN
ejpam-4115	250	65	or	or	CCONJ
ejpam-4115	250	66	f	f	PROPN
ejpam-4115	250	67	(	(	PUNCT
ejpam-4115	250	68	x)−f	x)−f	PROPN
ejpam-4115	250	69	(	(	PUNCT
ejpam-4115	250	70	c	c	X
ejpam-4115	250	71	)	)	PUNCT
ejpam-4115	250	72	∈	∈	NOUN
ejpam-4115	250	73	v	v	NOUN
ejpam-4115	250	74	.	.	PUNCT
ejpam-4115	251	1	since	since	SCONJ
ejpam-4115	251	2	w	w	NOUN
ejpam-4115	251	3	is	be	AUX
ejpam-4115	251	4	balanced	balanced	ADJ
ejpam-4115	251	5	,	,	PUNCT
ejpam-4115	251	6	f	f	PROPN
ejpam-4115	251	7	(	(	PUNCT
ejpam-4115	251	8	x)−f	x)−f	PROPN
ejpam-4115	251	9	(	(	PUNCT
ejpam-4115	251	10	c	c	X
ejpam-4115	251	11	)	)	PUNCT
ejpam-4115	251	12	∈	∈	PROPN
ejpam-4115	251	13	w	w	ADP
ejpam-4115	251	14	⊆	⊆	NUM
ejpam-4115	251	15	u	u	NOUN
ejpam-4115	251	16	−f	−f	PROPN
ejpam-4115	251	17	(	(	PUNCT
ejpam-4115	251	18	c	c	NOUN
ejpam-4115	251	19	)	)	PUNCT
ejpam-4115	251	20	.	.	PUNCT
ejpam-4115	252	1	hence	hence	ADV
ejpam-4115	252	2	,	,	PUNCT
ejpam-4115	252	3	x	x	PROPN
ejpam-4115	252	4	∈	∈	PROPN
ejpam-4115	252	5	f−1(u	f−1(u	PROPN
ejpam-4115	252	6	)	)	PUNCT
ejpam-4115	252	7	,	,	PUNCT
ejpam-4115	252	8	implying	imply	VERB
ejpam-4115	252	9	that	that	SCONJ
ejpam-4115	252	10	(	(	PUNCT
ejpam-4115	252	11	c−	c−	X
ejpam-4115	252	12	η	η	PROPN
ejpam-4115	252	13	,	,	PUNCT
ejpam-4115	252	14	c+	c+	X
ejpam-4115	252	15	η	η	NOUN
ejpam-4115	252	16	)	)	PUNCT
ejpam-4115	252	17	⊆	⊆	NUM
ejpam-4115	252	18	f−1(u	f−1(u	NOUN
ejpam-4115	252	19	)	)	PUNCT
ejpam-4115	252	20	.	.	PUNCT
ejpam-4115	253	1	therefore	therefore	ADV
ejpam-4115	253	2	,	,	PUNCT
ejpam-4115	253	3	f	f	PROPN
ejpam-4115	253	4	is	be	AUX
ejpam-4115	253	5	continuous	continuous	ADJ
ejpam-4115	253	6	on	on	ADP
ejpam-4115	253	7	[	[	X
ejpam-4115	253	8	a	a	X
ejpam-4115	253	9	,	,	PUNCT
ejpam-4115	253	10	b	b	NOUN
ejpam-4115	253	11	]	]	X
ejpam-4115	253	12	.	.	PUNCT
ejpam-4115	254	1	the	the	DET
ejpam-4115	254	2	next	next	ADJ
ejpam-4115	254	3	two	two	NUM
ejpam-4115	254	4	results	result	NOUN
ejpam-4115	254	5	can	can	AUX
ejpam-4115	254	6	also	also	ADV
ejpam-4115	254	7	be	be	AUX
ejpam-4115	254	8	proved	prove	VERB
ejpam-4115	254	9	using	use	VERB
ejpam-4115	254	10	the	the	DET
ejpam-4115	254	11	definitions	definition	NOUN
ejpam-4115	254	12	.	.	PUNCT
ejpam-4115	255	1	r.	r.	PROPN
ejpam-4115	255	2	e.	e.	PROPN
ejpam-4115	255	3	maza	maza	PROPN
ejpam-4115	255	4	,	,	PUNCT
ejpam-4115	255	5	s.	s.	PROPN
ejpam-4115	255	6	r.	r.	PROPN
ejpam-4115	255	7	canoy	canoy	PROPN
ejpam-4115	255	8	,	,	PUNCT
ejpam-4115	255	9	jr	jr	PROPN
ejpam-4115	255	10	.	.	PROPN
ejpam-4115	255	11	/	/	SYM
ejpam-4115	255	12	eur	eur	PROPN
ejpam-4115	255	13	.	.	PUNCT
ejpam-4115	256	1	j.	j.	PROPN
ejpam-4115	256	2	pure	pure	PROPN
ejpam-4115	256	3	appl	appl	PROPN
ejpam-4115	256	4	.	.	PROPN
ejpam-4115	256	5	math	math	PROPN
ejpam-4115	256	6	,	,	PUNCT
ejpam-4115	256	7	14	14	NUM
ejpam-4115	256	8	(	(	PUNCT
ejpam-4115	256	9	4	4	NUM
ejpam-4115	256	10	)	)	PUNCT
ejpam-4115	256	11	(	(	PUNCT
ejpam-4115	256	12	2021	2021	NUM
ejpam-4115	256	13	)	)	PUNCT
ejpam-4115	256	14	,	,	PUNCT
ejpam-4115	256	15	1169	1169	NUM
ejpam-4115	256	16	-	-	SYM
ejpam-4115	256	17	1183	1183	NUM
ejpam-4115	256	18	1175	1175	NUM
ejpam-4115	256	19	theorem	theorem	VERB
ejpam-4115	256	20	4	4	NUM
ejpam-4115	256	21	.	.	PUNCT
ejpam-4115	257	1	let	let	VERB
ejpam-4115	257	2	a	a	DET
ejpam-4115	257	3	⊆	⊆	NUM
ejpam-4115	257	4	[	[	X
ejpam-4115	257	5	c	c	X
ejpam-4115	257	6	,	,	PUNCT
ejpam-4115	257	7	d	d	X
ejpam-4115	257	8	]	]	X
ejpam-4115	257	9	⊆	⊆	NUM
ejpam-4115	257	10	[	[	X
ejpam-4115	257	11	a	a	X
ejpam-4115	257	12	,	,	PUNCT
ejpam-4115	257	13	b	b	NOUN
ejpam-4115	257	14	]	]	PUNCT
ejpam-4115	257	15	and	and	CCONJ
ejpam-4115	257	16	f	f	NOUN
ejpam-4115	257	17	:	:	PUNCT
ejpam-4115	258	1	[	[	X
ejpam-4115	258	2	a	a	X
ejpam-4115	258	3	,	,	PUNCT
ejpam-4115	258	4	b	b	NOUN
ejpam-4115	258	5	]	]	X
ejpam-4115	258	6	→	→	PUNCT
ejpam-4115	258	7	x	x	PUNCT
ejpam-4115	258	8	be	be	AUX
ejpam-4115	258	9	ac∗(a	ac∗(a	ADJ
ejpam-4115	258	10	)	)	PUNCT
ejpam-4115	258	11	.	.	PUNCT
ejpam-4115	259	1	then	then	ADV
ejpam-4115	259	2	the	the	DET
ejpam-4115	259	3	restriction	restriction	NOUN
ejpam-4115	259	4	f	f	PROPN
ejpam-4115	259	5	|[c	|[c	PROPN
ejpam-4115	259	6	,	,	PUNCT
ejpam-4115	259	7	d	d	X
ejpam-4115	259	8	]	]	PUNCT
ejpam-4115	259	9	of	of	ADP
ejpam-4115	259	10	f	f	PROPN
ejpam-4115	259	11	to	to	ADP
ejpam-4115	259	12	[	[	X
ejpam-4115	259	13	c	c	X
ejpam-4115	259	14	,	,	PUNCT
ejpam-4115	259	15	d	d	X
ejpam-4115	259	16	]	]	X
ejpam-4115	259	17	is	be	AUX
ejpam-4115	259	18	ac∗(a	ac∗(a	ADJ
ejpam-4115	259	19	)	)	PUNCT
ejpam-4115	259	20	.	.	PUNCT
ejpam-4115	260	1	in	in	ADP
ejpam-4115	260	2	particular	particular	ADJ
ejpam-4115	260	3	,	,	PUNCT
ejpam-4115	260	4	if	if	SCONJ
ejpam-4115	260	5	f	f	PROPN
ejpam-4115	260	6	is	be	AUX
ejpam-4115	260	7	acg∗	acg∗	NOUN
ejpam-4115	260	8	on	on	ADP
ejpam-4115	260	9	[	[	X
ejpam-4115	260	10	a	a	X
ejpam-4115	260	11	,	,	PUNCT
ejpam-4115	260	12	b	b	NOUN
ejpam-4115	260	13	]	]	X
ejpam-4115	260	14	,	,	PUNCT
ejpam-4115	260	15	then	then	ADV
ejpam-4115	260	16	f	f	PROPN
ejpam-4115	260	17	|[c	|[c	PROPN
ejpam-4115	260	18	,	,	PUNCT
ejpam-4115	260	19	d	d	X
ejpam-4115	260	20	]	]	X
ejpam-4115	260	21	is	be	AUX
ejpam-4115	260	22	acg∗	acg∗	NOUN
ejpam-4115	260	23	on	on	ADP
ejpam-4115	260	24	[	[	X
ejpam-4115	260	25	c	c	X
ejpam-4115	260	26	,	,	PUNCT
ejpam-4115	260	27	d	d	NOUN
ejpam-4115	260	28	]	]	X
ejpam-4115	260	29	.	.	PUNCT
ejpam-4115	261	1	theorem	theorem	NOUN
ejpam-4115	261	2	5	5	NUM
ejpam-4115	261	3	.	.	PUNCT
ejpam-4115	262	1	let	let	VERB
ejpam-4115	262	2	f	f	X
ejpam-4115	262	3	,	,	PUNCT
ejpam-4115	262	4	g	g	PROPN
ejpam-4115	262	5	,	,	PUNCT
ejpam-4115	262	6	f	f	X
ejpam-4115	262	7	,	,	PUNCT
ejpam-4115	262	8	g	g	NOUN
ejpam-4115	262	9	:	:	PUNCT
ejpam-4115	263	1	[	[	X
ejpam-4115	263	2	a	a	X
ejpam-4115	263	3	,	,	PUNCT
ejpam-4115	263	4	b	b	NOUN
ejpam-4115	263	5	]	]	X
ejpam-4115	263	6	→	→	PUNCT
ejpam-4115	263	7	x	x	PART
ejpam-4115	263	8	be	be	AUX
ejpam-4115	263	9	functions	function	NOUN
ejpam-4115	263	10	.	.	PUNCT
ejpam-4115	264	1	then	then	ADV
ejpam-4115	264	2	each	each	PRON
ejpam-4115	264	3	of	of	ADP
ejpam-4115	264	4	following	follow	VERB
ejpam-4115	264	5	holds	hold	VERB
ejpam-4115	264	6	:	:	PUNCT
ejpam-4115	264	7	(	(	PUNCT
ejpam-4115	264	8	i	i	NOUN
ejpam-4115	264	9	)	)	PUNCT
ejpam-4115	264	10	{	{	PUNCT
ejpam-4115	264	11	t	t	NOUN
ejpam-4115	264	12	∈	∈	PROPN
ejpam-4115	265	1	[	[	X
ejpam-4115	265	2	a	a	X
ejpam-4115	265	3	,	,	PUNCT
ejpam-4115	265	4	b	b	NOUN
ejpam-4115	265	5	]	]	X
ejpam-4115	265	6	:	:	PUNCT
ejpam-4115	265	7	f	f	PROPN
ejpam-4115	265	8	′(t	′(t	PROPN
ejpam-4115	265	9	)	)	PUNCT
ejpam-4115	265	10	̸=	̸=	PROPN
ejpam-4115	265	11	f(t	f(t	PROPN
ejpam-4115	265	12	)	)	PUNCT
ejpam-4115	265	13	}	}	PUNCT
ejpam-4115	266	1	=	=	PUNCT
ejpam-4115	266	2	⋃	⋃	PROPN
ejpam-4115	266	3	θ	θ	PROPN
ejpam-4115	266	4	-	-	PUNCT
ejpam-4115	266	5	nbd	nbd	PROPN
ejpam-4115	266	6	u	u	PROPN
ejpam-4115	266	7	∆(u	∆(u	PROPN
ejpam-4115	266	8	,	,	PUNCT
ejpam-4115	266	9	f	f	PROPN
ejpam-4115	266	10	,	,	PUNCT
ejpam-4115	266	11	f	f	PROPN
ejpam-4115	266	12	)	)	PUNCT
ejpam-4115	266	13	.	.	PUNCT
ejpam-4115	267	1	(	(	PUNCT
ejpam-4115	267	2	ii	ii	NOUN
ejpam-4115	267	3	)	)	PUNCT
ejpam-4115	267	4	∆(u	∆(u	PROPN
ejpam-4115	267	5	,	,	PUNCT
ejpam-4115	267	6	cf	cf	NOUN
ejpam-4115	267	7	,	,	PUNCT
ejpam-4115	267	8	cf	cf	NOUN
ejpam-4115	267	9	)	)	PUNCT
ejpam-4115	267	10	=	=	SYM
ejpam-4115	267	11	∆(1cu	∆(1cu	PROPN
ejpam-4115	267	12	,	,	PUNCT
ejpam-4115	267	13	f	f	PROPN
ejpam-4115	267	14	,	,	PUNCT
ejpam-4115	267	15	f	f	X
ejpam-4115	267	16	)	)	PUNCT
ejpam-4115	267	17	for	for	ADP
ejpam-4115	267	18	each	each	DET
ejpam-4115	267	19	θ	θ	PROPN
ejpam-4115	267	20	-	-	PUNCT
ejpam-4115	267	21	nbd	nbd	PROPN
ejpam-4115	267	22	u	u	PROPN
ejpam-4115	267	23	and	and	CCONJ
ejpam-4115	267	24	0	0	NUM
ejpam-4115	267	25	̸=	̸=	PROPN
ejpam-4115	267	26	c	c	PROPN
ejpam-4115	267	27	∈	∈	PROPN
ejpam-4115	267	28	r.	r.	PROPN
ejpam-4115	267	29	(	(	PUNCT
ejpam-4115	267	30	iii	iii	NOUN
ejpam-4115	267	31	)	)	PUNCT
ejpam-4115	267	32	∆(u	∆(u	PROPN
ejpam-4115	267	33	,	,	PUNCT
ejpam-4115	267	34	f	f	PROPN
ejpam-4115	268	1	+	+	NOUN
ejpam-4115	268	2	g	g	PROPN
ejpam-4115	268	3	,	,	PUNCT
ejpam-4115	268	4	f	f	PROPN
ejpam-4115	269	1	+	+	CCONJ
ejpam-4115	269	2	g	g	NOUN
ejpam-4115	269	3	)	)	PUNCT
ejpam-4115	269	4	⊆	⊆	NUM
ejpam-4115	269	5	∆(12u	∆(12u	PROPN
ejpam-4115	269	6	,	,	PUNCT
ejpam-4115	269	7	f	f	PROPN
ejpam-4115	269	8	,	,	PUNCT
ejpam-4115	269	9	f	f	X
ejpam-4115	269	10	)	)	PUNCT
ejpam-4115	269	11	∪∆(12u	∪∆(12u	NOUN
ejpam-4115	269	12	,	,	PUNCT
ejpam-4115	269	13	g	g	NOUN
ejpam-4115	269	14	,	,	PUNCT
ejpam-4115	269	15	g	g	NOUN
ejpam-4115	269	16	)	)	PUNCT
ejpam-4115	269	17	for	for	ADP
ejpam-4115	269	18	each	each	DET
ejpam-4115	269	19	convex	convex	ADJ
ejpam-4115	269	20	θ	θ	PROPN
ejpam-4115	269	21	-	-	PUNCT
ejpam-4115	269	22	nbd	nbd	PROPN
ejpam-4115	269	23	u	u	PROPN
ejpam-4115	269	24	.	.	PUNCT
ejpam-4115	270	1	theorem	theorem	VERB
ejpam-4115	270	2	6	6	NUM
ejpam-4115	270	3	.	.	PUNCT
ejpam-4115	271	1	let	let	VERB
ejpam-4115	271	2	f	f	NOUN
ejpam-4115	271	3	:	:	PUNCT
ejpam-4115	272	1	[	[	X
ejpam-4115	272	2	a	a	X
ejpam-4115	272	3	,	,	PUNCT
ejpam-4115	272	4	b	b	NOUN
ejpam-4115	272	5	]	]	X
ejpam-4115	272	6	→	→	PUNCT
ejpam-4115	272	7	x	x	PUNCT
ejpam-4115	272	8	be	be	AUX
ejpam-4115	272	9	acg∗	acg∗	ADJ
ejpam-4115	272	10	on	on	ADP
ejpam-4115	272	11	[	[	X
ejpam-4115	272	12	a	a	X
ejpam-4115	272	13	,	,	PUNCT
ejpam-4115	272	14	b	b	NOUN
ejpam-4115	272	15	]	]	PUNCT
ejpam-4115	272	16	and	and	CCONJ
ejpam-4115	272	17	let	let	VERB
ejpam-4115	272	18	f	f	NOUN
ejpam-4115	272	19	:	:	PUNCT
ejpam-4115	273	1	[	[	X
ejpam-4115	273	2	a	a	X
ejpam-4115	273	3	,	,	PUNCT
ejpam-4115	273	4	b	b	NOUN
ejpam-4115	273	5	]	]	X
ejpam-4115	273	6	→	→	PUNCT
ejpam-4115	273	7	x	x	X
ejpam-4115	273	8	be	be	AUX
ejpam-4115	273	9	the	the	DET
ejpam-4115	273	10	zero	zero	NUM
ejpam-4115	273	11	function	function	NOUN
ejpam-4115	273	12	.	.	PUNCT
ejpam-4115	274	1	if	if	SCONJ
ejpam-4115	274	2	∆(u	∆(u	PROPN
ejpam-4115	274	3	,	,	PUNCT
ejpam-4115	274	4	f	f	PROPN
ejpam-4115	274	5	,	,	PUNCT
ejpam-4115	274	6	f	f	X
ejpam-4115	274	7	)	)	PUNCT
ejpam-4115	274	8	is	be	AUX
ejpam-4115	274	9	of	of	ADP
ejpam-4115	274	10	measure	measure	NOUN
ejpam-4115	274	11	zero	zero	NUM
ejpam-4115	274	12	for	for	ADP
ejpam-4115	274	13	all	all	DET
ejpam-4115	274	14	θ	θ	PROPN
ejpam-4115	274	15	-	-	ADJ
ejpam-4115	274	16	nbds	nbds	NOUN
ejpam-4115	274	17	u	u	NOUN
ejpam-4115	274	18	,	,	PUNCT
ejpam-4115	274	19	then	then	ADV
ejpam-4115	274	20	f	f	PROPN
ejpam-4115	274	21	is	be	AUX
ejpam-4115	274	22	a	a	DET
ejpam-4115	274	23	constant	constant	ADJ
ejpam-4115	274	24	function	function	NOUN
ejpam-4115	274	25	.	.	PUNCT
ejpam-4115	275	1	proof	proof	NOUN
ejpam-4115	275	2	.	.	PUNCT
ejpam-4115	276	1	let	let	VERB
ejpam-4115	276	2	a	a	DET
ejpam-4115	276	3	<	<	X
ejpam-4115	276	4	c	c	PROPN
ejpam-4115	276	5	≤	≤	PROPN
ejpam-4115	276	6	b.	b.	PROPN
ejpam-4115	276	7	since	since	SCONJ
ejpam-4115	276	8	f	f	PROPN
ejpam-4115	276	9	is	be	AUX
ejpam-4115	276	10	acg∗	acg∗	NOUN
ejpam-4115	276	11	on	on	ADP
ejpam-4115	276	12	[	[	X
ejpam-4115	276	13	a	a	X
ejpam-4115	276	14	,	,	PUNCT
ejpam-4115	276	15	b	b	NOUN
ejpam-4115	276	16	]	]	X
ejpam-4115	276	17	,	,	PUNCT
ejpam-4115	276	18	f	f	PROPN
ejpam-4115	276	19	|[a	|[a	NOUN
ejpam-4115	276	20	,	,	PUNCT
ejpam-4115	277	1	c	c	X
ejpam-4115	277	2	]	]	X
ejpam-4115	277	3	is	be	AUX
ejpam-4115	277	4	acg∗	acg∗	NOUN
ejpam-4115	277	5	on	on	ADP
ejpam-4115	277	6	[	[	X
ejpam-4115	277	7	a	a	X
ejpam-4115	277	8	,	,	PUNCT
ejpam-4115	277	9	c	c	NOUN
ejpam-4115	277	10	]	]	PUNCT
ejpam-4115	277	11	.	.	PUNCT
ejpam-4115	278	1	this	this	PRON
ejpam-4115	278	2	implies	imply	VERB
ejpam-4115	278	3	that	that	SCONJ
ejpam-4115	278	4	there	there	PRON
ejpam-4115	278	5	is	be	VERB
ejpam-4115	278	6	a	a	DET
ejpam-4115	278	7	disjoint	disjoint	ADJ
ejpam-4115	278	8	countable	countable	ADJ
ejpam-4115	278	9	collection	collection	NOUN
ejpam-4115	278	10	{	{	PUNCT
ejpam-4115	278	11	yi}∞i=1	yi}∞i=1	NOUN
ejpam-4115	278	12	of	of	ADP
ejpam-4115	278	13	subsets	subset	NOUN
ejpam-4115	278	14	of	of	ADP
ejpam-4115	278	15	[	[	X
ejpam-4115	278	16	a	a	X
ejpam-4115	278	17	,	,	PUNCT
ejpam-4115	278	18	c	c	NOUN
ejpam-4115	278	19	]	]	X
ejpam-4115	278	20	such	such	ADJ
ejpam-4115	278	21	that	that	SCONJ
ejpam-4115	278	22	[	[	X
ejpam-4115	278	23	a	a	X
ejpam-4115	278	24	,	,	PUNCT
ejpam-4115	278	25	c	c	NOUN
ejpam-4115	278	26	]	]	X
ejpam-4115	278	27	=	=	SYM
ejpam-4115	278	28	⋃∞	⋃∞	ADP
ejpam-4115	278	29	i=1	i=1	PROPN
ejpam-4115	278	30	yi	yi	PROPN
ejpam-4115	278	31	and	and	CCONJ
ejpam-4115	278	32	f	f	PROPN
ejpam-4115	278	33	is	be	AUX
ejpam-4115	278	34	ac∗(yi	ac∗(yi	PROPN
ejpam-4115	278	35	)	)	PUNCT
ejpam-4115	278	36	for	for	ADP
ejpam-4115	278	37	each	each	DET
ejpam-4115	278	38	i	i	PRON
ejpam-4115	278	39	∈	∈	PROPN
ejpam-4115	278	40	n.	n.	NOUN
ejpam-4115	278	41	let	let	VERB
ejpam-4115	278	42	u	u	PRON
ejpam-4115	278	43	be	be	AUX
ejpam-4115	278	44	a	a	DET
ejpam-4115	278	45	given	give	VERB
ejpam-4115	278	46	θ	θ	PROPN
ejpam-4115	278	47	-	-	PUNCT
ejpam-4115	278	48	nbd	nbd	PROPN
ejpam-4115	278	49	.	.	PUNCT
ejpam-4115	279	1	then	then	ADV
ejpam-4115	279	2	there	there	PRON
ejpam-4115	279	3	exist	exist	VERB
ejpam-4115	279	4	an	an	DET
ejpam-4115	279	5	absorbing	absorbing	ADJ
ejpam-4115	279	6	,	,	PUNCT
ejpam-4115	279	7	balanced	balanced	ADJ
ejpam-4115	279	8	and	and	CCONJ
ejpam-4115	279	9	convex	convex	ADJ
ejpam-4115	279	10	θ	θ	PROPN
ejpam-4115	279	11	-	-	PUNCT
ejpam-4115	279	12	nbd	nbd	PROPN
ejpam-4115	279	13	v	v	ADP
ejpam-4115	279	14	such	such	ADJ
ejpam-4115	279	15	that	that	PRON
ejpam-4115	279	16	(	(	PUNCT
ejpam-4115	279	17	c−a+1)v	c−a+1)v	PROPN
ejpam-4115	279	18	⊆	⊆	NUM
ejpam-4115	279	19	u	u	NOUN
ejpam-4115	279	20	.	.	PUNCT
ejpam-4115	280	1	note	note	VERB
ejpam-4115	280	2	that	that	SCONJ
ejpam-4115	280	3	if	if	SCONJ
ejpam-4115	280	4	t	t	PROPN
ejpam-4115	280	5	∈	∈	PROPN
ejpam-4115	280	6	[	[	X
ejpam-4115	280	7	a	a	X
ejpam-4115	280	8	,	,	PUNCT
ejpam-4115	280	9	c]\∆(v	c]\∆(v	PROPN
ejpam-4115	280	10	,	,	PUNCT
ejpam-4115	280	11	f	f	NOUN
ejpam-4115	280	12	|[a	|[a	NOUN
ejpam-4115	280	13	,	,	PUNCT
ejpam-4115	280	14	c	c	X
ejpam-4115	280	15	]	]	X
ejpam-4115	280	16	,	,	PUNCT
ejpam-4115	280	17	f	f	PROPN
ejpam-4115	280	18	|[a	|[a	NOUN
ejpam-4115	280	19	,	,	PUNCT
ejpam-4115	280	20	c	c	NOUN
ejpam-4115	280	21	]	]	X
ejpam-4115	280	22	)	)	PUNCT
ejpam-4115	280	23	,	,	PUNCT
ejpam-4115	280	24	then	then	ADV
ejpam-4115	280	25	there	there	PRON
ejpam-4115	280	26	exists	exist	VERB
ejpam-4115	280	27	δ0(t	δ0(t	NOUN
ejpam-4115	280	28	)	)	PUNCT
ejpam-4115	280	29	>	>	X
ejpam-4115	280	30	0	0	NUM
ejpam-4115	281	1	such	such	ADJ
ejpam-4115	281	2	that	that	SCONJ
ejpam-4115	281	3	f	f	PROPN
ejpam-4115	281	4	(	(	PUNCT
ejpam-4115	281	5	v)−f	v)−f	ADP
ejpam-4115	281	6	(	(	PUNCT
ejpam-4115	281	7	u	u	NOUN
ejpam-4115	281	8	)	)	PUNCT
ejpam-4115	281	9	∈	∈	PROPN
ejpam-4115	281	10	(	(	PUNCT
ejpam-4115	281	11	v−u)v	v−u)v	PROPN
ejpam-4115	281	12	whenever	whenever	SCONJ
ejpam-4115	281	13	t	t	PROPN
ejpam-4115	281	14	∈	∈	PROPN
ejpam-4115	281	15	[	[	X
ejpam-4115	281	16	u	u	NOUN
ejpam-4115	281	17	,	,	PUNCT
ejpam-4115	281	18	v	v	NOUN
ejpam-4115	281	19	]	]	PUNCT
ejpam-4115	281	20	⊆	⊆	NUM
ejpam-4115	281	21	[	[	X
ejpam-4115	281	22	a	a	X
ejpam-4115	281	23	,	,	PUNCT
ejpam-4115	281	24	c	c	NOUN
ejpam-4115	281	25	]	]	PUNCT
ejpam-4115	281	26	and	and	CCONJ
ejpam-4115	281	27	|v	|v	VERB
ejpam-4115	281	28	−	−	PROPN
ejpam-4115	282	1	u|	u|	PROPN
ejpam-4115	282	2	<	<	X
ejpam-4115	282	3	δ0(t	δ0(t	NOUN
ejpam-4115	282	4	)	)	PUNCT
ejpam-4115	282	5	.	.	PUNCT
ejpam-4115	283	1	let	let	VERB
ejpam-4115	283	2	ai	ai	VERB
ejpam-4115	283	3	=	=	SYM
ejpam-4115	283	4	∆(v	∆(v	PROPN
ejpam-4115	283	5	,	,	PUNCT
ejpam-4115	283	6	f	f	PROPN
ejpam-4115	283	7	|[a	|[a	NOUN
ejpam-4115	283	8	,	,	PUNCT
ejpam-4115	283	9	c	c	X
ejpam-4115	283	10	]	]	X
ejpam-4115	283	11	,	,	PUNCT
ejpam-4115	283	12	f	f	PROPN
ejpam-4115	283	13	|[a	|[a	NOUN
ejpam-4115	283	14	,	,	PUNCT
ejpam-4115	283	15	c	c	NOUN
ejpam-4115	283	16	]	]	X
ejpam-4115	283	17	)	)	PUNCT
ejpam-4115	283	18	∩	∩	PROPN
ejpam-4115	283	19	yi	yi	PROPN
ejpam-4115	283	20	for	for	ADP
ejpam-4115	283	21	each	each	DET
ejpam-4115	283	22	i	i	PRON
ejpam-4115	283	23	∈	∈	PROPN
ejpam-4115	284	1	n.	n.	NOUN
ejpam-4115	284	2	then	then	ADV
ejpam-4115	284	3	f	f	PROPN
ejpam-4115	284	4	|[a	|[a	NOUN
ejpam-4115	284	5	,	,	PUNCT
ejpam-4115	284	6	c	c	X
ejpam-4115	284	7	]	]	X
ejpam-4115	284	8	is	be	AUX
ejpam-4115	284	9	ac∗(ai	ac∗(ai	NOUN
ejpam-4115	284	10	)	)	PUNCT
ejpam-4115	284	11	for	for	ADP
ejpam-4115	284	12	each	each	DET
ejpam-4115	284	13	i	i	PROPN
ejpam-4115	284	14	∈	∈	PROPN
ejpam-4115	284	15	n.	n.	NOUN
ejpam-4115	284	16	thus	thus	ADV
ejpam-4115	284	17	,	,	PUNCT
ejpam-4115	284	18	for	for	ADP
ejpam-4115	284	19	each	each	DET
ejpam-4115	284	20	i	i	PROPN
ejpam-4115	284	21	∈	∈	PROPN
ejpam-4115	284	22	n	n	CCONJ
ejpam-4115	284	23	,	,	PUNCT
ejpam-4115	284	24	there	there	PRON
ejpam-4115	284	25	exist	exist	VERB
ejpam-4115	284	26	ηi	ηi	NOUN
ejpam-4115	284	27	>	>	X
ejpam-4115	284	28	0	0	NUM
ejpam-4115	284	29	such	such	ADJ
ejpam-4115	284	30	that	that	PRON
ejpam-4115	284	31	for	for	ADP
ejpam-4115	284	32	every	every	DET
ejpam-4115	284	33	partial	partial	ADJ
ejpam-4115	284	34	partition	partition	NOUN
ejpam-4115	284	35	d	d	NOUN
ejpam-4115	284	36	=	=	PRON
ejpam-4115	284	37	{	{	PUNCT
ejpam-4115	284	38	[	[	X
ejpam-4115	284	39	uj	uj	X
ejpam-4115	284	40	,	,	PUNCT
ejpam-4115	284	41	vj	vj	X
ejpam-4115	284	42	]	]	X
ejpam-4115	284	43	:	:	PUNCT
ejpam-4115	284	44	1	1	NUM
ejpam-4115	284	45	≤	≤	NUM
ejpam-4115	284	46	j	j	PROPN
ejpam-4115	284	47	≤	≤	PROPN
ejpam-4115	284	48	n	n	CCONJ
ejpam-4115	284	49	}	}	PUNCT
ejpam-4115	284	50	of	of	ADP
ejpam-4115	284	51	[	[	X
ejpam-4115	284	52	a	a	X
ejpam-4115	284	53	,	,	PUNCT
ejpam-4115	284	54	c	c	X
ejpam-4115	284	55	]	]	PUNCT
ejpam-4115	284	56	with	with	ADP
ejpam-4115	284	57	uj	uj	PROPN
ejpam-4115	284	58	or	or	CCONJ
ejpam-4115	284	59	vj	vj	INTJ
ejpam-4115	284	60	in	in	ADP
ejpam-4115	284	61	ai	ai	PROPN
ejpam-4115	284	62	and	and	CCONJ
ejpam-4115	284	63	∑n	∑n	PROPN
ejpam-4115	284	64	j=1(vj	j=1(vj	NOUN
ejpam-4115	284	65	−	−	PROPN
ejpam-4115	284	66	uj	uj	PROPN
ejpam-4115	284	67	)	)	PUNCT
ejpam-4115	284	68	<	<	X
ejpam-4115	284	69	ηi	ηi	PROPN
ejpam-4115	284	70	,	,	PUNCT
ejpam-4115	284	71	there	there	PRON
ejpam-4115	284	72	exist	exist	VERB
ejpam-4115	284	73	θ	θ	PROPN
ejpam-4115	284	74	-	-	PUNCT
ejpam-4115	284	75	nbds	nbds	NOUN
ejpam-4115	284	76	vi,1	vi,1	PROPN
ejpam-4115	284	77	,	,	PUNCT
ejpam-4115	284	78	vi,2	vi,2	PROPN
ejpam-4115	284	79	,	,	PUNCT
ejpam-4115	284	80	.	.	PUNCT
ejpam-4115	284	81	.	.	PUNCT
ejpam-4115	285	1	.	.	PUNCT
ejpam-4115	286	1	,	,	PUNCT
ejpam-4115	286	2	vi	vi	PROPN
ejpam-4115	286	3	,	,	PUNCT
ejpam-4115	286	4	ni	ni	NOUN
ejpam-4115	286	5	with	with	ADP
ejpam-4115	286	6	∑ni	∑ni	PUNCT
ejpam-4115	286	7	j=1	j=1	PROPN
ejpam-4115	286	8	vi	vi	PROPN
ejpam-4115	286	9	,	,	PUNCT
ejpam-4115	286	10	j	j	PROPN
ejpam-4115	286	11	⊆	⊆	NUM
ejpam-4115	286	12	1	1	NUM
ejpam-4115	286	13	2i	2i	NUM
ejpam-4115	286	14	v	v	NOUN
ejpam-4115	286	15	and	and	CCONJ
ejpam-4115	286	16	f	f	PROPN
ejpam-4115	286	17	(	(	PUNCT
ejpam-4115	286	18	vj	vj	PROPN
ejpam-4115	286	19	)	)	PUNCT
ejpam-4115	287	1	−	−	PROPN
ejpam-4115	287	2	f	f	PROPN
ejpam-4115	287	3	(	(	PUNCT
ejpam-4115	287	4	uj	uj	PROPN
ejpam-4115	287	5	)	)	PUNCT
ejpam-4115	287	6	∈	∈	PROPN
ejpam-4115	287	7	vi	vi	PROPN
ejpam-4115	287	8	,	,	PUNCT
ejpam-4115	287	9	j	j	PROPN
ejpam-4115	287	10	for	for	ADP
ejpam-4115	287	11	all	all	DET
ejpam-4115	287	12	1	1	NUM
ejpam-4115	287	13	≤	≤	NUM
ejpam-4115	287	14	j	j	PROPN
ejpam-4115	287	15	≤	≤	PROPN
ejpam-4115	287	16	ni	ni	PROPN
ejpam-4115	287	17	.	.	PUNCT
ejpam-4115	288	1	now	now	ADV
ejpam-4115	288	2	,	,	PUNCT
ejpam-4115	288	3	by	by	ADP
ejpam-4115	288	4	the	the	DET
ejpam-4115	288	5	definition	definition	NOUN
ejpam-4115	288	6	of	of	ADP
ejpam-4115	288	7	ai	ai	PROPN
ejpam-4115	288	8	,	,	PUNCT
ejpam-4115	288	9	m(ai	m(ai	ADJ
ejpam-4115	288	10	)	)	PUNCT
ejpam-4115	288	11	=	=	SYM
ejpam-4115	288	12	0	0	NUM
ejpam-4115	288	13	for	for	ADP
ejpam-4115	288	14	all	all	PRON
ejpam-4115	288	15	i	i	PRON
ejpam-4115	288	16	∈	∈	PROPN
ejpam-4115	288	17	n	n	INTJ
ejpam-4115	288	18	where	where	SCONJ
ejpam-4115	288	19	m	m	VERB
ejpam-4115	288	20	is	be	AUX
ejpam-4115	288	21	the	the	DET
ejpam-4115	288	22	lebesgue	lebesgue	ADJ
ejpam-4115	288	23	measure	measure	NOUN
ejpam-4115	288	24	.	.	PUNCT
ejpam-4115	289	1	hence	hence	ADV
ejpam-4115	289	2	,	,	PUNCT
ejpam-4115	289	3	there	there	PRON
ejpam-4115	289	4	exists	exist	VERB
ejpam-4115	289	5	a	a	DET
ejpam-4115	289	6	collection	collection	NOUN
ejpam-4115	289	7	{	{	PUNCT
ejpam-4115	289	8	gi}∞i=1	gi}∞i=1	X
ejpam-4115	289	9	of	of	ADP
ejpam-4115	289	10	open	open	ADJ
ejpam-4115	289	11	sets	set	NOUN
ejpam-4115	289	12	with	with	ADP
ejpam-4115	289	13	ai	ai	ADJ
ejpam-4115	289	14	⊆	⊆	NUM
ejpam-4115	289	15	gi	gi	NOUN
ejpam-4115	289	16	and	and	CCONJ
ejpam-4115	289	17	m(gi	m(gi	NOUN
ejpam-4115	289	18	)	)	PUNCT
ejpam-4115	289	19	<	<	X
ejpam-4115	289	20	ηi	ηi	PROPN
ejpam-4115	289	21	for	for	ADP
ejpam-4115	289	22	each	each	DET
ejpam-4115	289	23	i	i	PROPN
ejpam-4115	289	24	∈	∈	PROPN
ejpam-4115	289	25	n.	n.	NOUN
ejpam-4115	289	26	thus	thus	ADV
ejpam-4115	289	27	,	,	PUNCT
ejpam-4115	289	28	for	for	ADP
ejpam-4115	289	29	every	every	DET
ejpam-4115	289	30	t	t	NOUN
ejpam-4115	289	31	∈	∈	NOUN
ejpam-4115	289	32	ai	ai	VERB
ejpam-4115	289	33	there	there	PRON
ejpam-4115	289	34	is	be	VERB
ejpam-4115	289	35	a	a	DET
ejpam-4115	289	36	real	real	ADJ
ejpam-4115	289	37	number	number	NOUN
ejpam-4115	289	38	δi(t	δi(t	PUNCT
ejpam-4115	289	39	)	)	PUNCT
ejpam-4115	290	1	such	such	ADJ
ejpam-4115	290	2	that	that	SCONJ
ejpam-4115	290	3	(	(	PUNCT
ejpam-4115	290	4	t−	t−	NOUN
ejpam-4115	290	5	δi(t	δi(t	NUM
ejpam-4115	290	6	)	)	PUNCT
ejpam-4115	290	7	,	,	PUNCT
ejpam-4115	290	8	t+	t+	NOUN
ejpam-4115	290	9	δi(t	δi(t	NOUN
ejpam-4115	290	10	)	)	PUNCT
ejpam-4115	290	11	)	)	PUNCT
ejpam-4115	291	1	⊆	⊆	NUM
ejpam-4115	291	2	gi	gi	NOUN
ejpam-4115	291	3	.	.	PUNCT
ejpam-4115	291	4	define	define	VERB
ejpam-4115	291	5	δ(t	δ(t	PROPN
ejpam-4115	291	6	)	)	PUNCT
ejpam-4115	291	7	=	=	PUNCT
ejpam-4115	292	1	δ0(t	δ0(t	PROPN
ejpam-4115	292	2	)	)	PUNCT
ejpam-4115	292	3	if	if	SCONJ
ejpam-4115	292	4	t	t	PROPN
ejpam-4115	292	5	∈	∈	PROPN
ejpam-4115	293	1	[	[	X
ejpam-4115	293	2	a	a	X
ejpam-4115	293	3	,	,	PUNCT
ejpam-4115	293	4	c]\∆(v	c]\∆(v	PROPN
ejpam-4115	293	5	,	,	PUNCT
ejpam-4115	293	6	f	f	X
ejpam-4115	293	7	,	,	PUNCT
ejpam-4115	293	8	f	f	PROPN
ejpam-4115	293	9	)	)	PUNCT
ejpam-4115	293	10	and	and	CCONJ
ejpam-4115	293	11	δ(t	δ(t	PROPN
ejpam-4115	293	12	)	)	PUNCT
ejpam-4115	293	13	=	=	PUNCT
ejpam-4115	293	14	δi(t	δi(t	X
ejpam-4115	293	15	)	)	PUNCT
ejpam-4115	293	16	if	if	SCONJ
ejpam-4115	293	17	t	t	PROPN
ejpam-4115	293	18	∈	∈	NOUN
ejpam-4115	293	19	ai	ai	VERB
ejpam-4115	293	20	for	for	ADP
ejpam-4115	293	21	some	some	PRON
ejpam-4115	293	22	i	i	PRON
ejpam-4115	293	23	≥	≥	NOUN
ejpam-4115	293	24	1	1	NUM
ejpam-4115	293	25	.	.	PUNCT
ejpam-4115	294	1	let	let	VERB
ejpam-4115	294	2	d	d	NOUN
ejpam-4115	294	3	=	=	PRON
ejpam-4115	294	4	{	{	PUNCT
ejpam-4115	294	5	(	(	PUNCT
ejpam-4115	294	6	[	[	X
ejpam-4115	294	7	xj	xj	PROPN
ejpam-4115	294	8	,	,	PUNCT
ejpam-4115	294	9	yj	yj	PROPN
ejpam-4115	294	10	]	]	PUNCT
ejpam-4115	294	11	,	,	PUNCT
ejpam-4115	294	12	tj	tj	PROPN
ejpam-4115	294	13	)	)	PUNCT
ejpam-4115	294	14	:	:	PUNCT
ejpam-4115	294	15	1	1	NUM
ejpam-4115	294	16	≤	≤	NUM
ejpam-4115	294	17	j	j	PROPN
ejpam-4115	294	18	≤	≤	PROPN
ejpam-4115	294	19	k	k	PROPN
ejpam-4115	294	20	}	}	PUNCT
ejpam-4115	294	21	be	be	VERB
ejpam-4115	294	22	a	a	DET
ejpam-4115	294	23	δ	δ	NOUN
ejpam-4115	294	24	-	-	PUNCT
ejpam-4115	294	25	fine	fine	ADJ
ejpam-4115	294	26	partition	partition	NOUN
ejpam-4115	294	27	of	of	ADP
ejpam-4115	294	28	[	[	X
ejpam-4115	294	29	a	a	X
ejpam-4115	294	30	,	,	PUNCT
ejpam-4115	294	31	b	b	NOUN
ejpam-4115	294	32	]	]	X
ejpam-4115	294	33	.	.	PUNCT
ejpam-4115	295	1	then	then	ADV
ejpam-4115	295	2	the	the	DET
ejpam-4115	295	3	set	set	NOUN
ejpam-4115	295	4	of	of	ADP
ejpam-4115	295	5	intervals	interval	NOUN
ejpam-4115	295	6	in	in	ADP
ejpam-4115	295	7	d	d	PROPN
ejpam-4115	295	8	is	be	AUX
ejpam-4115	295	9	a	a	DET
ejpam-4115	295	10	disjoint	disjoint	ADJ
ejpam-4115	295	11	union	union	NOUN
ejpam-4115	295	12	of	of	ADP
ejpam-4115	295	13	d1	d1	PROPN
ejpam-4115	295	14	and	and	CCONJ
ejpam-4115	295	15	d2	d2	PROPN
ejpam-4115	295	16	where	where	SCONJ
ejpam-4115	295	17	d1	d1	PROPN
ejpam-4115	295	18	=	=	PUNCT
ejpam-4115	295	19	{	{	PUNCT
ejpam-4115	295	20	[	[	X
ejpam-4115	295	21	xj	xj	PROPN
ejpam-4115	295	22	,	,	PUNCT
ejpam-4115	295	23	yj	yj	PROPN
ejpam-4115	295	24	]	]	PUNCT
ejpam-4115	295	25	:	:	PUNCT
ejpam-4115	295	26	(	(	PUNCT
ejpam-4115	295	27	[	[	X
ejpam-4115	295	28	xj	xj	PROPN
ejpam-4115	295	29	,	,	PUNCT
ejpam-4115	295	30	yj	yj	PROPN
ejpam-4115	295	31	]	]	PUNCT
ejpam-4115	295	32	,	,	PUNCT
ejpam-4115	295	33	tj	tj	PROPN
ejpam-4115	295	34	)	)	PUNCT
ejpam-4115	295	35	∈	∈	PROPN
ejpam-4115	295	36	d	d	NOUN
ejpam-4115	295	37	and	and	CCONJ
ejpam-4115	295	38	tj	tj	NOUN
ejpam-4115	295	39	∈	∈	PROPN
ejpam-4115	296	1	[	[	X
ejpam-4115	296	2	a	a	X
ejpam-4115	296	3	,	,	PUNCT
ejpam-4115	296	4	c	c	NOUN
ejpam-4115	296	5	]	]	PUNCT
ejpam-4115	296	6	\	\	PROPN
ejpam-4115	296	7	∆(v	∆(v	PROPN
ejpam-4115	296	8	,	,	PUNCT
ejpam-4115	296	9	f	f	PROPN
ejpam-4115	296	10	|[a	|[a	NOUN
ejpam-4115	296	11	,	,	PUNCT
ejpam-4115	296	12	c	c	X
ejpam-4115	296	13	]	]	X
ejpam-4115	296	14	,	,	PUNCT
ejpam-4115	296	15	f	f	PROPN
ejpam-4115	296	16	|[a	|[a	NOUN
ejpam-4115	296	17	,	,	PUNCT
ejpam-4115	296	18	c	c	NOUN
ejpam-4115	296	19	]	]	X
ejpam-4115	296	20	)	)	PUNCT
ejpam-4115	296	21	}	}	PUNCT
ejpam-4115	296	22	and	and	CCONJ
ejpam-4115	296	23	d2	d2	PROPN
ejpam-4115	296	24	=	=	SYM
ejpam-4115	296	25	{	{	PUNCT
ejpam-4115	296	26	[	[	X
ejpam-4115	296	27	xj	xj	PROPN
ejpam-4115	296	28	,	,	PUNCT
ejpam-4115	296	29	yj	yj	PROPN
ejpam-4115	296	30	]	]	PUNCT
ejpam-4115	296	31	:	:	PUNCT
ejpam-4115	296	32	(	(	PUNCT
ejpam-4115	296	33	[	[	X
ejpam-4115	296	34	xj	xj	PROPN
ejpam-4115	296	35	,	,	PUNCT
ejpam-4115	296	36	yj	yj	PROPN
ejpam-4115	296	37	]	]	PUNCT
ejpam-4115	296	38	,	,	PUNCT
ejpam-4115	296	39	tj	tj	PROPN
ejpam-4115	296	40	)	)	PUNCT
ejpam-4115	296	41	∈	∈	PROPN
ejpam-4115	296	42	d	d	NOUN
ejpam-4115	296	43	and	and	CCONJ
ejpam-4115	296	44	tj	tj	PROPN
ejpam-4115	296	45	∈	∈	PROPN
ejpam-4115	296	46	∆(v	∆(v	PROPN
ejpam-4115	296	47	,	,	PUNCT
ejpam-4115	296	48	f	f	PROPN
ejpam-4115	296	49	|[a	|[a	NOUN
ejpam-4115	296	50	,	,	PUNCT
ejpam-4115	296	51	c	c	X
ejpam-4115	296	52	]	]	X
ejpam-4115	296	53	,	,	PUNCT
ejpam-4115	296	54	f	f	PROPN
ejpam-4115	296	55	|[a	|[a	NOUN
ejpam-4115	296	56	,	,	PUNCT
ejpam-4115	296	57	c	c	NOUN
ejpam-4115	296	58	]	]	X
ejpam-4115	296	59	)	)	PUNCT
ejpam-4115	296	60	}	}	PUNCT
ejpam-4115	296	61	.	.	PUNCT
ejpam-4115	297	1	if	if	SCONJ
ejpam-4115	297	2	[	[	X
ejpam-4115	297	3	xi	xi	X
ejpam-4115	297	4	,	,	PUNCT
ejpam-4115	297	5	yi	yi	NOUN
ejpam-4115	297	6	]	]	PUNCT
ejpam-4115	297	7	∈	∈	NOUN
ejpam-4115	297	8	d1	d1	PROPN
ejpam-4115	297	9	,	,	PUNCT
ejpam-4115	297	10	then	then	ADV
ejpam-4115	297	11	[	[	X
ejpam-4115	297	12	xi	xi	X
ejpam-4115	297	13	,	,	PUNCT
ejpam-4115	297	14	yi	yi	PROPN
ejpam-4115	297	15	]	]	X
ejpam-4115	297	16	⊆	⊆	NUM
ejpam-4115	297	17	(	(	PUNCT
ejpam-4115	297	18	ti	ti	NOUN
ejpam-4115	297	19	−	−	PROPN
ejpam-4115	297	20	δ(ti	δ(ti	PROPN
ejpam-4115	297	21	)	)	PUNCT
ejpam-4115	297	22	,	,	PUNCT
ejpam-4115	297	23	ti	ti	X
ejpam-4115	297	24	+	+	CCONJ
ejpam-4115	297	25	δ(ti	δ(ti	NOUN
ejpam-4115	297	26	)	)	PUNCT
ejpam-4115	297	27	)	)	PUNCT
ejpam-4115	297	28	because	because	SCONJ
ejpam-4115	297	29	d	d	PROPN
ejpam-4115	297	30	is	be	AUX
ejpam-4115	297	31	δ	δ	NOUN
ejpam-4115	297	32	-	-	PUNCT
ejpam-4115	297	33	fine	fine	ADJ
ejpam-4115	297	34	.	.	PUNCT
ejpam-4115	298	1	since	since	SCONJ
ejpam-4115	298	2	ti	ti	PROPN
ejpam-4115	298	3	∈	∈	PROPN
ejpam-4115	298	4	[	[	X
ejpam-4115	298	5	a	a	X
ejpam-4115	298	6	,	,	PUNCT
ejpam-4115	298	7	c	c	NOUN
ejpam-4115	298	8	]	]	PUNCT
ejpam-4115	298	9	\	\	PROPN
ejpam-4115	298	10	∆(v	∆(v	PROPN
ejpam-4115	298	11	,	,	PUNCT
ejpam-4115	298	12	f	f	PROPN
ejpam-4115	298	13	|[a	|[a	NOUN
ejpam-4115	298	14	,	,	PUNCT
ejpam-4115	298	15	c	c	X
ejpam-4115	298	16	]	]	X
ejpam-4115	298	17	,	,	PUNCT
ejpam-4115	298	18	f	f	PROPN
ejpam-4115	298	19	|[a	|[a	NOUN
ejpam-4115	298	20	,	,	PUNCT
ejpam-4115	298	21	c	c	NOUN
ejpam-4115	298	22	]	]	X
ejpam-4115	298	23	)	)	PUNCT
ejpam-4115	298	24	,	,	PUNCT
ejpam-4115	298	25	f	f	PROPN
ejpam-4115	298	26	(	(	PUNCT
ejpam-4115	298	27	yi	yi	PROPN
ejpam-4115	298	28	)	)	PUNCT
ejpam-4115	299	1	−	−	PROPN
ejpam-4115	299	2	f	f	PROPN
ejpam-4115	299	3	(	(	PUNCT
ejpam-4115	299	4	xi	xi	NOUN
ejpam-4115	299	5	)	)	PUNCT
ejpam-4115	299	6	∈	∈	PROPN
ejpam-4115	299	7	(	(	PUNCT
ejpam-4115	299	8	yi	yi	NOUN
ejpam-4115	299	9	−	−	PROPN
ejpam-4115	299	10	xi)v	xi)v	PROPN
ejpam-4115	299	11	.	.	PUNCT
ejpam-4115	300	1	if	if	SCONJ
ejpam-4115	300	2	[	[	X
ejpam-4115	300	3	xi	xi	X
ejpam-4115	300	4	,	,	PUNCT
ejpam-4115	300	5	yi	yi	NOUN
ejpam-4115	300	6	]	]	X
ejpam-4115	300	7	∈	∈	PROPN
ejpam-4115	300	8	d2	d2	PROPN
ejpam-4115	300	9	,	,	PUNCT
ejpam-4115	300	10	then	then	ADV
ejpam-4115	300	11	ti	ti	PROPN
ejpam-4115	300	12	∈	∈	PROPN
ejpam-4115	300	13	aj	aj	PROPN
ejpam-4115	300	14	for	for	ADP
ejpam-4115	300	15	exactly	exactly	ADV
ejpam-4115	300	16	one	one	NUM
ejpam-4115	300	17	j	j	PROPN
ejpam-4115	300	18	≥	≥	NOUN
ejpam-4115	300	19	1	1	NUM
ejpam-4115	300	20	with	with	ADP
ejpam-4115	300	21	[	[	X
ejpam-4115	300	22	xi	xi	PROPN
ejpam-4115	300	23	,	,	PUNCT
ejpam-4115	300	24	yi	yi	PROPN
ejpam-4115	300	25	]	]	X
ejpam-4115	300	26	⊆	⊆	NUM
ejpam-4115	300	27	(	(	PUNCT
ejpam-4115	300	28	ti	ti	NOUN
ejpam-4115	300	29	−	−	PROPN
ejpam-4115	300	30	δ(ti	δ(ti	PROPN
ejpam-4115	300	31	)	)	PUNCT
ejpam-4115	300	32	,	,	PUNCT
ejpam-4115	300	33	ti	ti	X
ejpam-4115	300	34	+	+	CCONJ
ejpam-4115	300	35	δ(ti	δ(ti	NOUN
ejpam-4115	300	36	)	)	PUNCT
ejpam-4115	300	37	)	)	PUNCT
ejpam-4115	301	1	=	=	SYM
ejpam-4115	301	2	(	(	PUNCT
ejpam-4115	301	3	ti	ti	NOUN
ejpam-4115	301	4	−	−	PROPN
ejpam-4115	301	5	δj(ti	δj(ti	PROPN
ejpam-4115	301	6	)	)	PUNCT
ejpam-4115	301	7	,	,	PUNCT
ejpam-4115	301	8	ti	ti	X
ejpam-4115	301	9	+	+	CCONJ
ejpam-4115	301	10	δj(ti	δj(ti	NOUN
ejpam-4115	301	11	)	)	PUNCT
ejpam-4115	301	12	)	)	PUNCT
ejpam-4115	302	1	⊆	⊆	NUM
ejpam-4115	302	2	gj	gj	NOUN
ejpam-4115	302	3	.	.	PUNCT
ejpam-4115	303	1	here	here	ADV
ejpam-4115	303	2	,	,	PUNCT
ejpam-4115	303	3	we	we	PRON
ejpam-4115	303	4	may	may	AUX
ejpam-4115	303	5	assume	assume	VERB
ejpam-4115	303	6	that	that	SCONJ
ejpam-4115	303	7	xi	xi	PROPN
ejpam-4115	303	8	∈	∈	PROPN
ejpam-4115	303	9	aj	aj	PROPN
ejpam-4115	303	10	or	or	CCONJ
ejpam-4115	303	11	yi	yi	PROPN
ejpam-4115	303	12	∈	∈	PROPN
ejpam-4115	303	13	aj	aj	PROPN
ejpam-4115	303	14	(	(	PUNCT
ejpam-4115	303	15	otherwise	otherwise	ADV
ejpam-4115	303	16	,	,	PUNCT
ejpam-4115	303	17	we	we	PRON
ejpam-4115	303	18	replace	replace	VERB
ejpam-4115	303	19	[	[	X
ejpam-4115	303	20	xi	xi	PROPN
ejpam-4115	303	21	,	,	PUNCT
ejpam-4115	303	22	yi	yi	NOUN
ejpam-4115	303	23	]	]	PUNCT
ejpam-4115	303	24	with	with	ADP
ejpam-4115	303	25	the	the	DET
ejpam-4115	303	26	intervals	interval	NOUN
ejpam-4115	303	27	[	[	X
ejpam-4115	303	28	xi	xi	X
ejpam-4115	303	29	,	,	PUNCT
ejpam-4115	303	30	ti	ti	NOUN
ejpam-4115	303	31	]	]	PUNCT
ejpam-4115	303	32	and	and	CCONJ
ejpam-4115	303	33	[	[	X
ejpam-4115	303	34	ti	ti	X
ejpam-4115	303	35	,	,	PUNCT
ejpam-4115	303	36	yi	yi	NOUN
ejpam-4115	303	37	]	]	NOUN
ejpam-4115	303	38	)	)	PUNCT
ejpam-4115	303	39	.	.	PUNCT
ejpam-4115	304	1	hence	hence	ADV
ejpam-4115	304	2	,	,	PUNCT
ejpam-4115	304	3	the	the	DET
ejpam-4115	304	4	union	union	NOUN
ejpam-4115	304	5	of	of	ADP
ejpam-4115	304	6	the	the	DET
ejpam-4115	304	7	non	non	ADJ
ejpam-4115	304	8	-	-	ADJ
ejpam-4115	304	9	overlapping	overlapping	ADJ
ejpam-4115	304	10	intervals	interval	NOUN
ejpam-4115	304	11	[	[	X
ejpam-4115	304	12	xi	xi	X
ejpam-4115	304	13	,	,	PUNCT
ejpam-4115	304	14	yi	yi	NOUN
ejpam-4115	304	15	]	]	PUNCT
ejpam-4115	304	16	with	with	ADP
ejpam-4115	304	17	ti	ti	PROPN
ejpam-4115	304	18	∈	∈	PROPN
ejpam-4115	304	19	aj	aj	PROPN
ejpam-4115	304	20	is	be	AUX
ejpam-4115	304	21	contained	contain	VERB
ejpam-4115	304	22	in	in	ADP
ejpam-4115	304	23	gj	gj	NOUN
ejpam-4115	304	24	.	.	PUNCT
ejpam-4115	305	1	this	this	PRON
ejpam-4115	305	2	implies	imply	VERB
ejpam-4115	305	3	that	that	SCONJ
ejpam-4115	305	4	∑	∑	ADP
ejpam-4115	305	5	ti∈aj	ti∈aj	X
ejpam-4115	305	6	(	(	PUNCT
ejpam-4115	305	7	yi	yi	NOUN
ejpam-4115	305	8	−	−	PROPN
ejpam-4115	305	9	xi	xi	PROPN
ejpam-4115	305	10	)	)	PUNCT
ejpam-4115	305	11	≤	≤	NOUN
ejpam-4115	305	12	m∗(gj	m∗(gj	PROPN
ejpam-4115	305	13	)	)	PUNCT
ejpam-4115	305	14	<	<	X
ejpam-4115	305	15	ηj	ηj	NOUN
ejpam-4115	305	16	.	.	PUNCT
ejpam-4115	306	1	thus	thus	ADV
ejpam-4115	306	2	,	,	PUNCT
ejpam-4115	306	3	there	there	PRON
ejpam-4115	306	4	exist	exist	VERB
ejpam-4115	306	5	θ	θ	PROPN
ejpam-4115	306	6	-	-	PUNCT
ejpam-4115	306	7	nbds	nbds	NOUN
ejpam-4115	306	8	vj,1	vj,1	NOUN
ejpam-4115	306	9	,	,	PUNCT
ejpam-4115	306	10	vj,2	vj,2	PROPN
ejpam-4115	306	11	,	,	PUNCT
ejpam-4115	306	12	.	.	PUNCT
ejpam-4115	306	13	.	.	PUNCT
ejpam-4115	307	1	.	.	PUNCT
ejpam-4115	308	1	,	,	PUNCT
ejpam-4115	308	2	vj	vj	PROPN
ejpam-4115	308	3	,	,	PUNCT
ejpam-4115	308	4	nj	nj	PROPN
ejpam-4115	308	5	with	with	ADP
ejpam-4115	308	6	∑nj	∑nj	ADP
ejpam-4115	308	7	i=1	i=1	PROPN
ejpam-4115	308	8	vj	vj	PROPN
ejpam-4115	308	9	,	,	PUNCT
ejpam-4115	308	10	i	i	PRON
ejpam-4115	308	11	⊆	⊆	NUM
ejpam-4115	308	12	1	1	NUM
ejpam-4115	308	13	2j	2j	NUM
ejpam-4115	308	14	v	v	NOUN
ejpam-4115	308	15	and	and	CCONJ
ejpam-4115	308	16	f	f	PROPN
ejpam-4115	308	17	(	(	PUNCT
ejpam-4115	308	18	yi)−f	yi)−f	PROPN
ejpam-4115	308	19	(	(	PUNCT
ejpam-4115	308	20	xi	xi	PROPN
ejpam-4115	308	21	)	)	PUNCT
ejpam-4115	308	22	∈	∈	PROPN
ejpam-4115	308	23	vj	vj	PROPN
ejpam-4115	308	24	,	,	PUNCT
ejpam-4115	308	25	i	i	PRON
ejpam-4115	308	26	for	for	ADP
ejpam-4115	308	27	each	each	DET
ejpam-4115	308	28	i	i	PRON
ejpam-4115	308	29	∈	∈	PROPN
ejpam-4115	308	30	{	{	PUNCT
ejpam-4115	308	31	1	1	NUM
ejpam-4115	308	32	,	,	PUNCT
ejpam-4115	308	33	2	2	NUM
ejpam-4115	308	34	,	,	PUNCT
ejpam-4115	308	35	.	.	PUNCT
ejpam-4115	308	36	.	.	PUNCT
ejpam-4115	308	37	.	.	PUNCT
ejpam-4115	309	1	,	,	PUNCT
ejpam-4115	309	2	nj	nj	PROPN
ejpam-4115	309	3	}	}	PUNCT
ejpam-4115	309	4	.	.	PUNCT
ejpam-4115	310	1	let	let	VERB
ejpam-4115	310	2	k	k	NOUN
ejpam-4115	311	1	=	=	PRON
ejpam-4115	311	2	{	{	PUNCT
ejpam-4115	311	3	i	i	NOUN
ejpam-4115	311	4	∈	∈	PROPN
ejpam-4115	311	5	{	{	PUNCT
ejpam-4115	311	6	1	1	NUM
ejpam-4115	311	7	,	,	PUNCT
ejpam-4115	311	8	2	2	NUM
ejpam-4115	311	9	,	,	PUNCT
ejpam-4115	311	10	.	.	PUNCT
ejpam-4115	311	11	.	.	PUNCT
ejpam-4115	311	12	.	.	PUNCT
ejpam-4115	312	1	,	,	PUNCT
ejpam-4115	312	2	k	k	X
ejpam-4115	312	3	}	}	PUNCT
ejpam-4115	312	4	:	:	PUNCT
ejpam-4115	312	5	ti	ti	X
ejpam-4115	312	6	∈	∈	PROPN
ejpam-4115	312	7	[	[	X
ejpam-4115	312	8	a	a	X
ejpam-4115	312	9	,	,	PUNCT
ejpam-4115	312	10	c	c	NOUN
ejpam-4115	312	11	]	]	PUNCT
ejpam-4115	312	12	\	\	PROPN
ejpam-4115	312	13	∆(v	∆(v	PROPN
ejpam-4115	312	14	,	,	PUNCT
ejpam-4115	312	15	f	f	PROPN
ejpam-4115	312	16	|[a	|[a	NOUN
ejpam-4115	312	17	,	,	PUNCT
ejpam-4115	312	18	c	c	X
ejpam-4115	312	19	]	]	X
ejpam-4115	312	20	,	,	PUNCT
ejpam-4115	312	21	f	f	PROPN
ejpam-4115	312	22	|[a	|[a	NOUN
ejpam-4115	312	23	,	,	PUNCT
ejpam-4115	312	24	c	c	NOUN
ejpam-4115	312	25	]	]	X
ejpam-4115	312	26	)	)	PUNCT
ejpam-4115	312	27	}	}	PUNCT
ejpam-4115	312	28	and	and	CCONJ
ejpam-4115	312	29	s	s	VERB
ejpam-4115	312	30	=	=	PUNCT
ejpam-4115	312	31	{	{	PUNCT
ejpam-4115	312	32	j	j	PROPN
ejpam-4115	312	33	∈	∈	PROPN
ejpam-4115	313	1	n	n	CCONJ
ejpam-4115	313	2	:	:	PUNCT
ejpam-4115	313	3	ti	ti	PROPN
ejpam-4115	313	4	∈	∈	PROPN
ejpam-4115	313	5	aj	aj	PROPN
ejpam-4115	313	6	for	for	ADP
ejpam-4115	313	7	some	some	DET
ejpam-4115	313	8	i	i	PRON
ejpam-4115	313	9	∈	∈	PROPN
ejpam-4115	313	10	{	{	PUNCT
ejpam-4115	313	11	1	1	NUM
ejpam-4115	313	12	,	,	PUNCT
ejpam-4115	313	13	2	2	NUM
ejpam-4115	313	14	,	,	PUNCT
ejpam-4115	313	15	.	.	PUNCT
ejpam-4115	313	16	.	.	PUNCT
ejpam-4115	313	17	.	.	PUNCT
ejpam-4115	314	1	,	,	PUNCT
ejpam-4115	314	2	k	k	X
ejpam-4115	314	3	}	}	PUNCT
ejpam-4115	314	4	}	}	PUNCT
ejpam-4115	314	5	.	.	PUNCT
ejpam-4115	315	1	consequently	consequently	ADV
ejpam-4115	315	2	,	,	PUNCT
ejpam-4115	315	3	by	by	ADP
ejpam-4115	315	4	convexity	convexity	NOUN
ejpam-4115	315	5	of	of	ADP
ejpam-4115	315	6	v	v	NOUN
ejpam-4115	315	7	,	,	PUNCT
ejpam-4115	315	8	f	f	PROPN
ejpam-4115	315	9	(	(	PUNCT
ejpam-4115	315	10	c)−	c)−	PROPN
ejpam-4115	315	11	f	f	PROPN
ejpam-4115	315	12	(	(	PUNCT
ejpam-4115	315	13	a	a	X
ejpam-4115	315	14	)	)	PUNCT
ejpam-4115	315	15	=	=	PUNCT
ejpam-4115	316	1	∑	∑	PUNCT
ejpam-4115	317	1	[	[	X
ejpam-4115	317	2	xi	xi	X
ejpam-4115	317	3	,	,	PUNCT
ejpam-4115	317	4	yi]∈d1	yi]∈d1	PROPN
ejpam-4115	317	5	(	(	PUNCT
ejpam-4115	317	6	f	f	PROPN
ejpam-4115	317	7	(	(	PUNCT
ejpam-4115	317	8	yi)−	yi)−	NOUN
ejpam-4115	317	9	f	f	PROPN
ejpam-4115	317	10	(	(	PUNCT
ejpam-4115	317	11	xi	xi	PROPN
ejpam-4115	317	12	)	)	PUNCT
ejpam-4115	317	13	)	)	PUNCT
ejpam-4115	318	1	+	+	CCONJ
ejpam-4115	318	2	∑	∑	PUNCT
ejpam-4115	318	3	[	[	X
ejpam-4115	318	4	xi	xi	ADP
ejpam-4115	318	5	,	,	PUNCT
ejpam-4115	318	6	yi]∈d2	yi]∈d2	PROPN
ejpam-4115	318	7	(	(	PUNCT
ejpam-4115	318	8	f	f	PROPN
ejpam-4115	318	9	(	(	PUNCT
ejpam-4115	318	10	yi)−	yi)−	NOUN
ejpam-4115	318	11	f	f	PROPN
ejpam-4115	318	12	(	(	PUNCT
ejpam-4115	318	13	xi	xi	PROPN
ejpam-4115	318	14	)	)	PUNCT
ejpam-4115	318	15	)	)	PUNCT
ejpam-4115	319	1	∈	∈	PROPN
ejpam-4115	319	2	∑	∑	PUNCT
ejpam-4115	319	3	i∈k	i∈k	NOUN
ejpam-4115	319	4	(	(	PUNCT
ejpam-4115	319	5	yi	yi	NOUN
ejpam-4115	319	6	−	−	PROPN
ejpam-4115	319	7	xi)v	xi)v	PROPN
ejpam-4115	320	1	+	+	CCONJ
ejpam-4115	320	2	∑	∑	ADJ
ejpam-4115	320	3	j∈s	j∈	NOUN
ejpam-4115	320	4	1	1	NUM
ejpam-4115	320	5	2j	2j	NUM
ejpam-4115	320	6	v	v	ADP
ejpam-4115	320	7	r.	r.	PROPN
ejpam-4115	320	8	e.	e.	PROPN
ejpam-4115	320	9	maza	maza	PROPN
ejpam-4115	320	10	,	,	PUNCT
ejpam-4115	320	11	s.	s.	PROPN
ejpam-4115	320	12	r.	r.	PROPN
ejpam-4115	320	13	canoy	canoy	PROPN
ejpam-4115	320	14	,	,	PUNCT
ejpam-4115	320	15	jr	jr	PROPN
ejpam-4115	320	16	.	.	PROPN
ejpam-4115	320	17	/	/	SYM
ejpam-4115	320	18	eur	eur	PROPN
ejpam-4115	320	19	.	.	PUNCT
ejpam-4115	321	1	j.	j.	PROPN
ejpam-4115	321	2	pure	pure	PROPN
ejpam-4115	321	3	appl	appl	PROPN
ejpam-4115	321	4	.	.	PROPN
ejpam-4115	321	5	math	math	PROPN
ejpam-4115	321	6	,	,	PUNCT
ejpam-4115	321	7	14	14	NUM
ejpam-4115	321	8	(	(	PUNCT
ejpam-4115	321	9	4	4	NUM
ejpam-4115	321	10	)	)	PUNCT
ejpam-4115	321	11	(	(	PUNCT
ejpam-4115	321	12	2021	2021	NUM
ejpam-4115	321	13	)	)	PUNCT
ejpam-4115	321	14	,	,	PUNCT
ejpam-4115	321	15	1169	1169	NUM
ejpam-4115	321	16	-	-	SYM
ejpam-4115	321	17	1183	1183	NUM
ejpam-4115	321	18	1176	1176	NUM
ejpam-4115	321	19	⊆	⊆	NUM
ejpam-4115	321	20	(	(	PUNCT
ejpam-4115	321	21	c−	c−	NOUN
ejpam-4115	321	22	a)v	a)v	X
ejpam-4115	322	1	+	+	CCONJ
ejpam-4115	322	2	v	v	ADP
ejpam-4115	322	3	⊆	⊆	NUM
ejpam-4115	322	4	(	(	PUNCT
ejpam-4115	322	5	c−	c−	NOUN
ejpam-4115	322	6	a+	a+	PUNCT
ejpam-4115	322	7	1)v	1)v	NUM
ejpam-4115	322	8	⊆	⊆	NUM
ejpam-4115	322	9	u	u	NOUN
ejpam-4115	322	10	since	since	SCONJ
ejpam-4115	322	11	u	u	PRON
ejpam-4115	322	12	was	be	AUX
ejpam-4115	322	13	arbitrarily	arbitrarily	ADV
ejpam-4115	322	14	chosen	choose	VERB
ejpam-4115	322	15	,	,	PUNCT
ejpam-4115	322	16	f	f	PROPN
ejpam-4115	322	17	(	(	PUNCT
ejpam-4115	322	18	a	a	X
ejpam-4115	322	19	)	)	PUNCT
ejpam-4115	322	20	=	=	SYM
ejpam-4115	322	21	f	f	X
ejpam-4115	322	22	(	(	PUNCT
ejpam-4115	322	23	c	c	NOUN
ejpam-4115	322	24	)	)	PUNCT
ejpam-4115	322	25	.	.	PUNCT
ejpam-4115	323	1	therefore	therefore	ADV
ejpam-4115	323	2	,	,	PUNCT
ejpam-4115	323	3	f	f	PROPN
ejpam-4115	323	4	is	be	AUX
ejpam-4115	323	5	a	a	DET
ejpam-4115	323	6	constant	constant	ADJ
ejpam-4115	323	7	function	function	NOUN
ejpam-4115	323	8	.	.	PUNCT
ejpam-4115	324	1	3	3	X
ejpam-4115	324	2	.	.	X
ejpam-4115	324	3	the	the	DET
ejpam-4115	324	4	denjoy	denjoy	NOUN
ejpam-4115	324	5	and	and	CCONJ
ejpam-4115	324	6	weak	weak	ADJ
ejpam-4115	324	7	denjoy	denjoy	NOUN
ejpam-4115	324	8	integrals	integral	NOUN
ejpam-4115	324	9	theorem	theorem	VERB
ejpam-4115	324	10	7	7	NUM
ejpam-4115	324	11	.	.	PUNCT
ejpam-4115	325	1	let	let	VERB
ejpam-4115	325	2	f	f	NOUN
ejpam-4115	325	3	:	:	PUNCT
ejpam-4115	326	1	[	[	X
ejpam-4115	326	2	a	a	X
ejpam-4115	326	3	,	,	PUNCT
ejpam-4115	326	4	b	b	NOUN
ejpam-4115	326	5	]	]	X
ejpam-4115	326	6	→	→	PUNCT
ejpam-4115	326	7	x	x	PUNCT
ejpam-4115	326	8	be	be	AUX
ejpam-4115	326	9	weak	weak	ADJ
ejpam-4115	326	10	denjoy	denjoy	NOUN
ejpam-4115	326	11	integrable	integrable	ADJ
ejpam-4115	326	12	on	on	ADP
ejpam-4115	326	13	[	[	X
ejpam-4115	326	14	a	a	X
ejpam-4115	326	15	,	,	PUNCT
ejpam-4115	326	16	b	b	NOUN
ejpam-4115	326	17	]	]	X
ejpam-4115	326	18	.	.	PUNCT
ejpam-4115	327	1	then	then	ADV
ejpam-4115	327	2	the	the	DET
ejpam-4115	327	3	weak	weak	ADJ
ejpam-4115	327	4	denjoy	denjoy	NOUN
ejpam-4115	327	5	integral	integral	ADJ
ejpam-4115	327	6	of	of	ADP
ejpam-4115	327	7	f	f	PROPN
ejpam-4115	327	8	is	be	AUX
ejpam-4115	327	9	unique	unique	ADJ
ejpam-4115	327	10	.	.	PUNCT
ejpam-4115	328	1	proof	proof	NOUN
ejpam-4115	328	2	.	.	PUNCT
ejpam-4115	329	1	let	let	VERB
ejpam-4115	329	2	f1	f1	PROPN
ejpam-4115	329	3	and	and	CCONJ
ejpam-4115	329	4	f2	f2	PROPN
ejpam-4115	329	5	be	be	AUX
ejpam-4115	329	6	weak	weak	ADJ
ejpam-4115	329	7	denjoy	denjoy	NOUN
ejpam-4115	329	8	primitives	primitive	NOUN
ejpam-4115	329	9	of	of	ADP
ejpam-4115	329	10	f	f	PROPN
ejpam-4115	329	11	.	.	PUNCT
ejpam-4115	330	1	since	since	SCONJ
ejpam-4115	330	2	f1	f1	NOUN
ejpam-4115	330	3	and	and	CCONJ
ejpam-4115	330	4	f2	f2	PROPN
ejpam-4115	330	5	are	be	AUX
ejpam-4115	330	6	acg∗	acg∗	NOUN
ejpam-4115	330	7	on	on	ADP
ejpam-4115	330	8	[	[	X
ejpam-4115	330	9	a	a	X
ejpam-4115	330	10	,	,	PUNCT
ejpam-4115	330	11	b	b	NOUN
ejpam-4115	330	12	]	]	X
ejpam-4115	330	13	,	,	PUNCT
ejpam-4115	330	14	f1−f2	f1−f2	PROPN
ejpam-4115	330	15	is	be	AUX
ejpam-4115	330	16	acg∗	acg∗	NOUN
ejpam-4115	330	17	on	on	ADP
ejpam-4115	330	18	[	[	X
ejpam-4115	330	19	a	a	X
ejpam-4115	330	20	,	,	PUNCT
ejpam-4115	330	21	b	b	NOUN
ejpam-4115	330	22	]	]	PUNCT
ejpam-4115	330	23	by	by	ADP
ejpam-4115	330	24	theorem	theorem	NOUN
ejpam-4115	330	25	2	2	NUM
ejpam-4115	330	26	.	.	PUNCT
ejpam-4115	331	1	let	let	VERB
ejpam-4115	331	2	u	u	PRON
ejpam-4115	331	3	be	be	AUX
ejpam-4115	331	4	a	a	DET
ejpam-4115	331	5	θ	θ	PROPN
ejpam-4115	331	6	-	-	PUNCT
ejpam-4115	331	7	nbd	nbd	PROPN
ejpam-4115	331	8	and	and	CCONJ
ejpam-4115	331	9	let	let	VERB
ejpam-4115	331	10	v	v	PART
ejpam-4115	331	11	be	be	AUX
ejpam-4115	331	12	a	a	DET
ejpam-4115	331	13	balancedθnbds	balancedθnbds	NOUN
ejpam-4115	331	14	with	with	ADP
ejpam-4115	331	15	v	v	NOUN
ejpam-4115	331	16	+	+	NOUN
ejpam-4115	331	17	v	v	NUM
ejpam-4115	331	18	⊆	⊆	NUM
ejpam-4115	331	19	u	u	NOUN
ejpam-4115	331	20	.	.	PUNCT
ejpam-4115	332	1	then	then	ADV
ejpam-4115	332	2	both	both	DET
ejpam-4115	332	3	∆(v	∆(v	PROPN
ejpam-4115	332	4	,	,	PUNCT
ejpam-4115	332	5	f1	f1	NOUN
ejpam-4115	332	6	,	,	PUNCT
ejpam-4115	332	7	f	f	PROPN
ejpam-4115	332	8	)	)	PUNCT
ejpam-4115	332	9	and	and	CCONJ
ejpam-4115	332	10	∆(v	∆(v	PROPN
ejpam-4115	332	11	,	,	PUNCT
ejpam-4115	332	12	f2	f2	PROPN
ejpam-4115	332	13	,	,	PUNCT
ejpam-4115	332	14	f	f	X
ejpam-4115	332	15	)	)	PUNCT
ejpam-4115	332	16	have	have	VERB
ejpam-4115	332	17	measure	measure	NOUN
ejpam-4115	332	18	zero	zero	NUM
ejpam-4115	332	19	.	.	PUNCT
ejpam-4115	333	1	let	let	VERB
ejpam-4115	333	2	t	t	PROPN
ejpam-4115	333	3	∈	∈	PROPN
ejpam-4115	333	4	∆(u	∆(u	PROPN
ejpam-4115	333	5	,	,	PUNCT
ejpam-4115	333	6	f1	f1	NOUN
ejpam-4115	333	7	−	−	PROPN
ejpam-4115	333	8	f2	f2	PROPN
ejpam-4115	333	9	,	,	PUNCT
ejpam-4115	333	10	0	0	NUM
ejpam-4115	333	11	)	)	PUNCT
ejpam-4115	333	12	where	where	SCONJ
ejpam-4115	333	13	0	0	NUM
ejpam-4115	333	14	is	be	AUX
ejpam-4115	333	15	the	the	DET
ejpam-4115	333	16	zero	zero	NUM
ejpam-4115	333	17	function	function	NOUN
ejpam-4115	333	18	on	on	ADP
ejpam-4115	333	19	[	[	X
ejpam-4115	333	20	a	a	X
ejpam-4115	333	21	,	,	PUNCT
ejpam-4115	333	22	b	b	NOUN
ejpam-4115	333	23	]	]	PUNCT
ejpam-4115	333	24	.	.	PUNCT
ejpam-4115	334	1	suppose	suppose	VERB
ejpam-4115	334	2	t	t	PROPN
ejpam-4115	334	3	/∈	/∈	PUNCT
ejpam-4115	334	4	∆(v	∆(v	PROPN
ejpam-4115	334	5	,	,	PUNCT
ejpam-4115	334	6	f1	f1	NOUN
ejpam-4115	334	7	,	,	PUNCT
ejpam-4115	334	8	f	f	X
ejpam-4115	334	9	)	)	PUNCT
ejpam-4115	334	10	∪	∪	PROPN
ejpam-4115	334	11	∆(v	∆(v	PROPN
ejpam-4115	334	12	,	,	PUNCT
ejpam-4115	334	13	f2	f2	PROPN
ejpam-4115	334	14	,	,	PUNCT
ejpam-4115	334	15	f	f	PROPN
ejpam-4115	334	16	)	)	PUNCT
ejpam-4115	334	17	.	.	PUNCT
ejpam-4115	335	1	then	then	ADV
ejpam-4115	335	2	there	there	PRON
ejpam-4115	335	3	exists	exist	VERB
ejpam-4115	335	4	δ	δ	PROPN
ejpam-4115	335	5	>	>	X
ejpam-4115	335	6	0	0	NUM
ejpam-4115	336	1	such	such	ADJ
ejpam-4115	336	2	that	that	DET
ejpam-4115	336	3	f1(v	f1(v	PROPN
ejpam-4115	336	4	)	)	PUNCT
ejpam-4115	336	5	−	−	PROPN
ejpam-4115	336	6	f1(u	f1(u	X
ejpam-4115	336	7	)	)	PUNCT
ejpam-4115	336	8	−	−	NOUN
ejpam-4115	336	9	f(t)(v	f(t)(v	NUM
ejpam-4115	336	10	−	−	PROPN
ejpam-4115	336	11	u	u	NOUN
ejpam-4115	336	12	)	)	PUNCT
ejpam-4115	336	13	∈	∈	PROPN
ejpam-4115	336	14	(	(	PUNCT
ejpam-4115	336	15	v	v	NOUN
ejpam-4115	336	16	−	−	PROPN
ejpam-4115	336	17	u)v	u)v	PUNCT
ejpam-4115	336	18	and	and	CCONJ
ejpam-4115	336	19	f2(v)−	f2(v)−	PROPN
ejpam-4115	336	20	f2(u)−	f2(u)−	ADP
ejpam-4115	336	21	f(t)(v	f(t)(v	NUM
ejpam-4115	336	22	−	−	PROPN
ejpam-4115	336	23	u	u	NOUN
ejpam-4115	336	24	)	)	PUNCT
ejpam-4115	336	25	∈	∈	PROPN
ejpam-4115	336	26	(	(	PUNCT
ejpam-4115	336	27	v	v	NOUN
ejpam-4115	336	28	−	−	NOUN
ejpam-4115	336	29	u)v	u)v	PUNCT
ejpam-4115	336	30	=	=	SYM
ejpam-4115	336	31	−(v	−(v	NOUN
ejpam-4115	336	32	−	−	PROPN
ejpam-4115	336	33	u)v	u)v	PUNCT
ejpam-4115	336	34	(	(	PUNCT
ejpam-4115	336	35	since	since	SCONJ
ejpam-4115	336	36	v	v	NOUN
ejpam-4115	336	37	is	be	AUX
ejpam-4115	336	38	balanced	balanced	ADJ
ejpam-4115	336	39	)	)	PUNCT
ejpam-4115	336	40	whenever	whenever	SCONJ
ejpam-4115	336	41	t	t	X
ejpam-4115	336	42	∈	∈	PROPN
ejpam-4115	336	43	[	[	X
ejpam-4115	336	44	u	u	NOUN
ejpam-4115	336	45	,	,	PUNCT
ejpam-4115	336	46	v	v	NOUN
ejpam-4115	336	47	]	]	PUNCT
ejpam-4115	336	48	⊆	⊆	NUM
ejpam-4115	336	49	[	[	X
ejpam-4115	336	50	a	a	X
ejpam-4115	336	51	,	,	PUNCT
ejpam-4115	336	52	b	b	NOUN
ejpam-4115	336	53	]	]	PUNCT
ejpam-4115	336	54	and	and	CCONJ
ejpam-4115	336	55	|v	|v	VERB
ejpam-4115	336	56	−	−	PROPN
ejpam-4115	337	1	u|	u|	PROPN
ejpam-4115	337	2	<	<	X
ejpam-4115	337	3	δ	δ	PROPN
ejpam-4115	337	4	.	.	PUNCT
ejpam-4115	338	1	it	it	PRON
ejpam-4115	338	2	follows	follow	VERB
ejpam-4115	338	3	that	that	SCONJ
ejpam-4115	338	4	f1(v)−	f1(v)−	PROPN
ejpam-4115	338	5	f1(u)−	f1(u)−	PRON
ejpam-4115	338	6	(	(	PUNCT
ejpam-4115	338	7	f2(v)−	f2(v)−	PROPN
ejpam-4115	338	8	f2(u	f2(u	NOUN
ejpam-4115	338	9	)	)	PUNCT
ejpam-4115	338	10	)	)	PUNCT
ejpam-4115	339	1	=	=	SYM
ejpam-4115	340	1	f1(v)−	f1(v)−	PROPN
ejpam-4115	340	2	f1(u)−	f1(u)−	PRON
ejpam-4115	340	3	f(t)(v	f(t)(v	NUM
ejpam-4115	340	4	−	−	PART
ejpam-4115	340	5	u	u	NOUN
ejpam-4115	340	6	)	)	PUNCT
ejpam-4115	340	7	−	−	PROPN
ejpam-4115	340	8	(	(	PUNCT
ejpam-4115	340	9	f2(v)−	f2(v)−	PROPN
ejpam-4115	340	10	f2(u)−	f2(u)−	ADP
ejpam-4115	340	11	f(t)(v	f(t)(v	X
ejpam-4115	340	12	−	−	PROPN
ejpam-4115	340	13	u	u	NOUN
ejpam-4115	340	14	)	)	PUNCT
ejpam-4115	340	15	)	)	PUNCT
ejpam-4115	341	1	∈	∈	PROPN
ejpam-4115	341	2	(	(	PUNCT
ejpam-4115	341	3	v	v	NOUN
ejpam-4115	341	4	−	−	PROPN
ejpam-4115	341	5	u)v	u)v	PUNCT
ejpam-4115	341	6	+	+	CCONJ
ejpam-4115	341	7	(	(	PUNCT
ejpam-4115	341	8	v	v	NUM
ejpam-4115	341	9	−	−	PROPN
ejpam-4115	341	10	u)v	u)v	ADJ
ejpam-4115	341	11	⊆	⊆	NUM
ejpam-4115	341	12	(	(	PUNCT
ejpam-4115	341	13	v	v	NOUN
ejpam-4115	341	14	−	−	NOUN
ejpam-4115	341	15	u)u	u)u	ADJ
ejpam-4115	341	16	.	.	PUNCT
ejpam-4115	342	1	this	this	PRON
ejpam-4115	342	2	implies	imply	VERB
ejpam-4115	342	3	that	that	SCONJ
ejpam-4115	342	4	t	t	PROPN
ejpam-4115	342	5	/∈	/∈	PUNCT
ejpam-4115	343	1	∆(u	∆(u	ADJ
ejpam-4115	343	2	,	,	PUNCT
ejpam-4115	343	3	f1	f1	NOUN
ejpam-4115	343	4	−	−	PROPN
ejpam-4115	343	5	f2	f2	PROPN
ejpam-4115	343	6	,	,	PUNCT
ejpam-4115	343	7	0	0	NUM
ejpam-4115	343	8	)	)	PUNCT
ejpam-4115	343	9	,	,	PUNCT
ejpam-4115	343	10	contrary	contrary	ADV
ejpam-4115	343	11	to	to	ADP
ejpam-4115	343	12	our	our	PRON
ejpam-4115	343	13	assumption	assumption	NOUN
ejpam-4115	343	14	.	.	PUNCT
ejpam-4115	344	1	hence	hence	ADV
ejpam-4115	344	2	,	,	PUNCT
ejpam-4115	344	3	∆(u	∆(u	ADJ
ejpam-4115	344	4	,	,	PUNCT
ejpam-4115	344	5	f1	f1	NOUN
ejpam-4115	344	6	−	−	PROPN
ejpam-4115	344	7	f2	f2	PROPN
ejpam-4115	344	8	,	,	PUNCT
ejpam-4115	344	9	0	0	NUM
ejpam-4115	344	10	)	)	PUNCT
ejpam-4115	344	11	⊆	⊆	NUM
ejpam-4115	344	12	∆(v	∆(v	PROPN
ejpam-4115	344	13	,	,	PUNCT
ejpam-4115	344	14	f1	f1	NOUN
ejpam-4115	344	15	,	,	PUNCT
ejpam-4115	344	16	f	f	X
ejpam-4115	344	17	)	)	PUNCT
ejpam-4115	344	18	∪	∪	PROPN
ejpam-4115	344	19	∆(v	∆(v	PROPN
ejpam-4115	344	20	,	,	PUNCT
ejpam-4115	344	21	f2	f2	PROPN
ejpam-4115	344	22	,	,	PUNCT
ejpam-4115	344	23	f	f	PROPN
ejpam-4115	344	24	)	)	PUNCT
ejpam-4115	344	25	.	.	PUNCT
ejpam-4115	345	1	consequently	consequently	ADV
ejpam-4115	345	2	,	,	PUNCT
ejpam-4115	345	3	∆(u	∆(u	ADJ
ejpam-4115	345	4	,	,	PUNCT
ejpam-4115	345	5	f1	f1	NOUN
ejpam-4115	345	6	−	−	PROPN
ejpam-4115	345	7	f2	f2	PROPN
ejpam-4115	345	8	,	,	PUNCT
ejpam-4115	345	9	0	0	NUM
ejpam-4115	345	10	)	)	PUNCT
ejpam-4115	345	11	has	have	VERB
ejpam-4115	345	12	measure	measure	NOUN
ejpam-4115	345	13	zero	zero	NUM
ejpam-4115	345	14	for	for	ADP
ejpam-4115	345	15	allθ	allθ	NOUN
ejpam-4115	345	16	-	-	PUNCT
ejpam-4115	345	17	nbdss	nbdss	NOUN
ejpam-4115	345	18	u	u	NOUN
ejpam-4115	345	19	.	.	PUNCT
ejpam-4115	346	1	by	by	ADP
ejpam-4115	346	2	theorem	theorem	NOUN
ejpam-4115	346	3	6	6	NUM
ejpam-4115	346	4	,	,	PUNCT
ejpam-4115	346	5	there	there	PRON
ejpam-4115	346	6	is	be	VERB
ejpam-4115	346	7	α	α	PRON
ejpam-4115	346	8	∈	∈	PROPN
ejpam-4115	346	9	x	x	PUNCT
ejpam-4115	346	10	such	such	ADJ
ejpam-4115	346	11	that	that	DET
ejpam-4115	346	12	f1	f1	NOUN
ejpam-4115	346	13	−	−	PROPN
ejpam-4115	346	14	f2	f2	PROPN
ejpam-4115	346	15	=	=	NOUN
ejpam-4115	346	16	α	α	NOUN
ejpam-4115	346	17	on	on	ADP
ejpam-4115	346	18	[	[	X
ejpam-4115	346	19	a	a	X
ejpam-4115	346	20	,	,	PUNCT
ejpam-4115	346	21	b	b	NOUN
ejpam-4115	346	22	]	]	X
ejpam-4115	346	23	,	,	PUNCT
ejpam-4115	346	24	that	that	ADV
ejpam-4115	346	25	is	is	ADV
ejpam-4115	346	26	,	,	PUNCT
ejpam-4115	346	27	f1(b)−	f1(b)−	NOUN
ejpam-4115	346	28	f1(a	f1(a	PROPN
ejpam-4115	346	29	)	)	PUNCT
ejpam-4115	346	30	=	=	PUNCT
ejpam-4115	346	31	f2(b	f2(b	X
ejpam-4115	346	32	)	)	PUNCT
ejpam-4115	347	1	+	+	CCONJ
ejpam-4115	347	2	α−	α−	X
ejpam-4115	347	3	(	(	PUNCT
ejpam-4115	347	4	f2(a	f2(a	NOUN
ejpam-4115	347	5	)	)	PUNCT
ejpam-4115	347	6	+	+	CCONJ
ejpam-4115	347	7	α	α	X
ejpam-4115	347	8	)	)	PUNCT
ejpam-4115	347	9	=	=	SYM
ejpam-4115	347	10	f2(b)−	f2(b)−	PROPN
ejpam-4115	347	11	f2(a	f2(a	NOUN
ejpam-4115	347	12	)	)	PUNCT
ejpam-4115	347	13	.	.	PUNCT
ejpam-4115	348	1	this	this	PRON
ejpam-4115	348	2	proves	prove	VERB
ejpam-4115	348	3	the	the	DET
ejpam-4115	348	4	assertion	assertion	NOUN
ejpam-4115	348	5	.	.	PUNCT
ejpam-4115	349	1	similarly	similarly	ADV
ejpam-4115	349	2	,	,	PUNCT
ejpam-4115	349	3	the	the	DET
ejpam-4115	349	4	denjoy	denjoy	NOUN
ejpam-4115	349	5	integral	integral	ADJ
ejpam-4115	349	6	of	of	ADP
ejpam-4115	349	7	a	a	DET
ejpam-4115	349	8	function	function	NOUN
ejpam-4115	349	9	,	,	PUNCT
ejpam-4115	349	10	if	if	SCONJ
ejpam-4115	349	11	it	it	PRON
ejpam-4115	349	12	exists	exist	VERB
ejpam-4115	349	13	,	,	PUNCT
ejpam-4115	349	14	is	be	AUX
ejpam-4115	349	15	also	also	ADV
ejpam-4115	349	16	unique	unique	ADJ
ejpam-4115	349	17	.	.	PUNCT
ejpam-4115	350	1	further	far	ADV
ejpam-4115	350	2	,	,	PUNCT
ejpam-4115	350	3	it	it	PRON
ejpam-4115	350	4	can	can	AUX
ejpam-4115	350	5	easily	easily	ADV
ejpam-4115	350	6	be	be	AUX
ejpam-4115	350	7	proved	prove	VERB
ejpam-4115	350	8	that	that	SCONJ
ejpam-4115	350	9	denjoy	denjoy	NOUN
ejpam-4115	350	10	integrability	integrability	NOUN
ejpam-4115	350	11	implies	imply	VERB
ejpam-4115	350	12	weak	weak	ADJ
ejpam-4115	350	13	denjoy	denjoy	NOUN
ejpam-4115	350	14	integrability	integrability	NOUN
ejpam-4115	350	15	.	.	PUNCT
ejpam-4115	350	16	theorem	theorem	NOUN
ejpam-4115	350	17	8	8	NUM
ejpam-4115	350	18	.	.	PUNCT
ejpam-4115	351	1	if	if	SCONJ
ejpam-4115	351	2	f	f	PROPN
ejpam-4115	351	3	:	:	PUNCT
ejpam-4115	352	1	[	[	X
ejpam-4115	352	2	a	a	X
ejpam-4115	352	3	,	,	PUNCT
ejpam-4115	352	4	b	b	NOUN
ejpam-4115	352	5	]	]	X
ejpam-4115	352	6	→	→	PUNCT
ejpam-4115	352	7	x	x	X
ejpam-4115	352	8	is	be	AUX
ejpam-4115	352	9	denjoy	denjoy	VERB
ejpam-4115	352	10	integrable	integrable	ADJ
ejpam-4115	352	11	on	on	ADP
ejpam-4115	352	12	[	[	X
ejpam-4115	352	13	a	a	X
ejpam-4115	352	14	,	,	PUNCT
ejpam-4115	352	15	b	b	NOUN
ejpam-4115	352	16	]	]	X
ejpam-4115	352	17	,	,	PUNCT
ejpam-4115	352	18	then	then	ADV
ejpam-4115	352	19	its	its	PRON
ejpam-4115	352	20	denjoy	denjoy	NOUN
ejpam-4115	352	21	integral	integral	ADJ
ejpam-4115	352	22	is	be	AUX
ejpam-4115	352	23	unique	unique	ADJ
ejpam-4115	352	24	.	.	PUNCT
ejpam-4115	353	1	theorem	theorem	NOUN
ejpam-4115	353	2	9	9	NUM
ejpam-4115	353	3	.	.	PUNCT
ejpam-4115	354	1	if	if	SCONJ
ejpam-4115	354	2	f	f	PROPN
ejpam-4115	354	3	:	:	PUNCT
ejpam-4115	355	1	[	[	X
ejpam-4115	355	2	a	a	X
ejpam-4115	355	3	,	,	PUNCT
ejpam-4115	355	4	b	b	NOUN
ejpam-4115	355	5	]	]	X
ejpam-4115	355	6	→	→	PUNCT
ejpam-4115	355	7	x	x	X
ejpam-4115	355	8	is	be	AUX
ejpam-4115	355	9	denjoy	denjoy	VERB
ejpam-4115	355	10	integrable	integrable	ADJ
ejpam-4115	355	11	on	on	ADP
ejpam-4115	355	12	[	[	X
ejpam-4115	355	13	a	a	X
ejpam-4115	355	14	,	,	PUNCT
ejpam-4115	355	15	b	b	NOUN
ejpam-4115	355	16	]	]	X
ejpam-4115	355	17	,	,	PUNCT
ejpam-4115	355	18	then	then	ADV
ejpam-4115	355	19	it	it	PRON
ejpam-4115	355	20	is	be	AUX
ejpam-4115	355	21	weak	weak	ADJ
ejpam-4115	355	22	denjoy	denjoy	NOUN
ejpam-4115	355	23	integrable	integrable	ADJ
ejpam-4115	355	24	on	on	ADP
ejpam-4115	355	25	[	[	X
ejpam-4115	355	26	a	a	X
ejpam-4115	355	27	,	,	PUNCT
ejpam-4115	355	28	b	b	NOUN
ejpam-4115	355	29	]	]	X
ejpam-4115	355	30	.	.	PUNCT
ejpam-4115	356	1	moreover	moreover	ADV
ejpam-4115	356	2	,	,	PUNCT
ejpam-4115	356	3	their	their	PRON
ejpam-4115	356	4	primitives	primitive	NOUN
ejpam-4115	356	5	and	and	CCONJ
ejpam-4115	356	6	integrals	integral	NOUN
ejpam-4115	356	7	coincide	coincide	VERB
ejpam-4115	356	8	.	.	PUNCT
ejpam-4115	357	1	example	example	NOUN
ejpam-4115	358	1	2	2	NUM
ejpam-4115	358	2	.	.	PUNCT
ejpam-4115	358	3	the	the	DET
ejpam-4115	358	4	constant	constant	ADJ
ejpam-4115	358	5	function	function	NOUN
ejpam-4115	358	6	f(t	f(t	NOUN
ejpam-4115	358	7	)	)	PUNCT
ejpam-4115	358	8	=	=	SYM
ejpam-4115	358	9	α	α	PROPN
ejpam-4115	358	10	for	for	ADP
ejpam-4115	358	11	all	all	DET
ejpam-4115	358	12	t	t	NOUN
ejpam-4115	358	13	∈	∈	PROPN
ejpam-4115	359	1	[	[	X
ejpam-4115	359	2	a	a	X
ejpam-4115	359	3	,	,	PUNCT
ejpam-4115	359	4	b	b	NOUN
ejpam-4115	359	5	]	]	X
ejpam-4115	359	6	,	,	PUNCT
ejpam-4115	359	7	where	where	SCONJ
ejpam-4115	359	8	α	α	PROPN
ejpam-4115	359	9	∈	∈	PROPN
ejpam-4115	359	10	x	x	X
ejpam-4115	359	11	,	,	PUNCT
ejpam-4115	359	12	is	be	AUX
ejpam-4115	359	13	denjoy	denjoy	VERB
ejpam-4115	359	14	integrable	integrable	ADJ
ejpam-4115	359	15	on	on	ADP
ejpam-4115	359	16	[	[	X
ejpam-4115	359	17	a	a	X
ejpam-4115	359	18	,	,	PUNCT
ejpam-4115	359	19	b	b	NOUN
ejpam-4115	359	20	]	]	PUNCT
ejpam-4115	359	21	and	and	CCONJ
ejpam-4115	359	22	(	(	PUNCT
ejpam-4115	359	23	d∗	d∗	PROPN
ejpam-4115	359	24	)	)	PUNCT
ejpam-4115	359	25	∫	∫	PROPN
ejpam-4115	360	1	b	b	PROPN
ejpam-4115	360	2	a	a	DET
ejpam-4115	360	3	f	f	X
ejpam-4115	360	4	=	=	SYM
ejpam-4115	360	5	(	(	PUNCT
ejpam-4115	360	6	b−	b−	PROPN
ejpam-4115	360	7	a)α	a)α	PUNCT
ejpam-4115	360	8	.	.	PUNCT
ejpam-4115	361	1	indeed	indeed	ADV
ejpam-4115	361	2	,	,	PUNCT
ejpam-4115	361	3	f	f	PROPN
ejpam-4115	361	4	(	(	PUNCT
ejpam-4115	361	5	t	t	PROPN
ejpam-4115	361	6	)	)	PUNCT
ejpam-4115	361	7	=	=	SYM
ejpam-4115	361	8	t	t	PROPN
ejpam-4115	361	9	·	·	PUNCT
ejpam-4115	361	10	α	α	PROPN
ejpam-4115	361	11	for	for	ADP
ejpam-4115	361	12	all	all	DET
ejpam-4115	361	13	t	t	NOUN
ejpam-4115	361	14	∈	∈	PROPN
ejpam-4115	362	1	[	[	X
ejpam-4115	362	2	a	a	X
ejpam-4115	362	3	,	,	PUNCT
ejpam-4115	362	4	b	b	X
ejpam-4115	362	5	]	]	X
ejpam-4115	362	6	is	be	AUX
ejpam-4115	362	7	absolutely	absolutely	ADV
ejpam-4115	362	8	continuous	continuous	ADJ
ejpam-4115	362	9	and	and	CCONJ
ejpam-4115	362	10	f	f	PROPN
ejpam-4115	362	11	′(t	′(t	PROPN
ejpam-4115	362	12	)	)	PUNCT
ejpam-4115	362	13	=	=	PUNCT
ejpam-4115	362	14	α	α	NOUN
ejpam-4115	362	15	=	=	PUNCT
ejpam-4115	362	16	f(t	f(t	NOUN
ejpam-4115	362	17	)	)	PUNCT
ejpam-4115	362	18	on	on	ADP
ejpam-4115	362	19	[	[	X
ejpam-4115	362	20	a	a	X
ejpam-4115	362	21	,	,	PUNCT
ejpam-4115	362	22	b	b	NOUN
ejpam-4115	362	23	]	]	X
ejpam-4115	362	24	.	.	PUNCT
ejpam-4115	363	1	hence	hence	ADV
ejpam-4115	363	2	,	,	PUNCT
ejpam-4115	363	3	by	by	ADP
ejpam-4115	363	4	remark	remark	NOUN
ejpam-4115	363	5	1	1	NUM
ejpam-4115	363	6	,	,	PUNCT
ejpam-4115	363	7	f	f	PROPN
ejpam-4115	363	8	is	be	AUX
ejpam-4115	363	9	a	a	DET
ejpam-4115	363	10	primitive	primitive	NOUN
ejpam-4115	363	11	of	of	ADP
ejpam-4115	363	12	f	f	PROPN
ejpam-4115	363	13	and	and	CCONJ
ejpam-4115	363	14	(	(	PUNCT
ejpam-4115	363	15	d∗	d∗	PROPN
ejpam-4115	363	16	)	)	PUNCT
ejpam-4115	363	17	∫	∫	PROPN
ejpam-4115	364	1	b	b	PROPN
ejpam-4115	364	2	a	a	DET
ejpam-4115	364	3	f	f	X
ejpam-4115	364	4	=	=	SYM
ejpam-4115	364	5	f	f	PROPN
ejpam-4115	364	6	(	(	PUNCT
ejpam-4115	364	7	b)−	b)−	PROPN
ejpam-4115	364	8	f	f	X
ejpam-4115	364	9	(	(	PUNCT
ejpam-4115	364	10	a	a	X
ejpam-4115	364	11	)	)	PUNCT
ejpam-4115	364	12	=	=	SYM
ejpam-4115	364	13	b	b	X
ejpam-4115	364	14	·	·	PUNCT
ejpam-4115	364	15	α−	α−	ADP
ejpam-4115	364	16	a	a	DET
ejpam-4115	364	17	·	·	PUNCT
ejpam-4115	364	18	α	α	NOUN
ejpam-4115	364	19	=	=	SYM
ejpam-4115	364	20	(	(	PUNCT
ejpam-4115	364	21	b−	b−	PROPN
ejpam-4115	364	22	a)α	a)α	PUNCT
ejpam-4115	364	23	.	.	PUNCT
ejpam-4115	365	1	r.	r.	PROPN
ejpam-4115	365	2	e.	e.	PROPN
ejpam-4115	365	3	maza	maza	PROPN
ejpam-4115	365	4	,	,	PUNCT
ejpam-4115	365	5	s.	s.	PROPN
ejpam-4115	365	6	r.	r.	PROPN
ejpam-4115	365	7	canoy	canoy	PROPN
ejpam-4115	365	8	,	,	PUNCT
ejpam-4115	365	9	jr	jr	PROPN
ejpam-4115	365	10	.	.	PROPN
ejpam-4115	365	11	/	/	SYM
ejpam-4115	365	12	eur	eur	PROPN
ejpam-4115	365	13	.	.	PUNCT
ejpam-4115	366	1	j.	j.	PROPN
ejpam-4115	366	2	pure	pure	PROPN
ejpam-4115	366	3	appl	appl	PROPN
ejpam-4115	366	4	.	.	PROPN
ejpam-4115	366	5	math	math	PROPN
ejpam-4115	366	6	,	,	PUNCT
ejpam-4115	366	7	14	14	NUM
ejpam-4115	366	8	(	(	PUNCT
ejpam-4115	366	9	4	4	NUM
ejpam-4115	366	10	)	)	PUNCT
ejpam-4115	366	11	(	(	PUNCT
ejpam-4115	366	12	2021	2021	NUM
ejpam-4115	366	13	)	)	PUNCT
ejpam-4115	366	14	,	,	PUNCT
ejpam-4115	366	15	1169	1169	NUM
ejpam-4115	366	16	-	-	SYM
ejpam-4115	366	17	1183	1183	NUM
ejpam-4115	366	18	1177	1177	NUM
ejpam-4115	366	19	theorem	theorem	VERB
ejpam-4115	366	20	10	10	NUM
ejpam-4115	366	21	.	.	PUNCT
ejpam-4115	367	1	let	let	VERB
ejpam-4115	367	2	f	f	X
ejpam-4115	367	3	,	,	PUNCT
ejpam-4115	367	4	g	g	NOUN
ejpam-4115	367	5	:	:	PUNCT
ejpam-4115	368	1	[	[	X
ejpam-4115	368	2	a	a	X
ejpam-4115	368	3	,	,	PUNCT
ejpam-4115	368	4	b	b	NOUN
ejpam-4115	368	5	]	]	X
ejpam-4115	368	6	→	→	PUNCT
ejpam-4115	368	7	x	x	PUNCT
ejpam-4115	368	8	be	be	AUX
ejpam-4115	368	9	weak	weak	ADJ
ejpam-4115	368	10	denjoy	denjoy	NOUN
ejpam-4115	368	11	integrable	integrable	ADJ
ejpam-4115	368	12	functions	function	NOUN
ejpam-4115	368	13	and	and	CCONJ
ejpam-4115	368	14	c	c	PROPN
ejpam-4115	368	15	∈	∈	PROPN
ejpam-4115	368	16	r.	r.	PROPN
ejpam-4115	368	17	then	then	ADV
ejpam-4115	368	18	each	each	PRON
ejpam-4115	368	19	of	of	ADP
ejpam-4115	368	20	the	the	DET
ejpam-4115	368	21	following	following	ADJ
ejpam-4115	368	22	statements	statement	NOUN
ejpam-4115	368	23	holds	hold	VERB
ejpam-4115	368	24	.	.	PUNCT
ejpam-4115	369	1	(	(	PUNCT
ejpam-4115	369	2	i	i	NOUN
ejpam-4115	369	3	)	)	PUNCT
ejpam-4115	369	4	cf	cf	NOUN
ejpam-4115	369	5	is	be	AUX
ejpam-4115	369	6	weak	weak	ADJ
ejpam-4115	369	7	denjoy	denjoy	NOUN
ejpam-4115	369	8	integrable	integrable	ADJ
ejpam-4115	369	9	and	and	CCONJ
ejpam-4115	369	10	(	(	PUNCT
ejpam-4115	369	11	wd∗	wd∗	ADJ
ejpam-4115	369	12	)	)	PUNCT
ejpam-4115	369	13	∫	∫	PROPN
ejpam-4115	370	1	b	b	PROPN
ejpam-4115	370	2	a	a	DET
ejpam-4115	370	3	(	(	PUNCT
ejpam-4115	370	4	cf	cf	NOUN
ejpam-4115	370	5	)	)	PUNCT
ejpam-4115	370	6	=	=	SYM
ejpam-4115	371	1	c	c	NOUN
ejpam-4115	371	2	·	·	PUNCT
ejpam-4115	371	3	(	(	PUNCT
ejpam-4115	371	4	wd∗	wd∗	X
ejpam-4115	371	5	)	)	PUNCT
ejpam-4115	371	6	∫	∫	PROPN
ejpam-4115	372	1	b	b	PROPN
ejpam-4115	372	2	a	a	DET
ejpam-4115	372	3	f.	f.	PROPN
ejpam-4115	372	4	(	(	PUNCT
ejpam-4115	372	5	ii	ii	PROPN
ejpam-4115	372	6	)	)	PUNCT
ejpam-4115	372	7	f	f	PROPN
ejpam-4115	373	1	+	+	CCONJ
ejpam-4115	373	2	g	g	PROPN
ejpam-4115	373	3	is	be	AUX
ejpam-4115	373	4	weak	weak	ADJ
ejpam-4115	373	5	denjoy	denjoy	NOUN
ejpam-4115	373	6	integrable	integrable	ADJ
ejpam-4115	373	7	and	and	CCONJ
ejpam-4115	373	8	(	(	PUNCT
ejpam-4115	373	9	wd∗	wd∗	ADJ
ejpam-4115	373	10	)	)	PUNCT
ejpam-4115	373	11	∫	∫	PROPN
ejpam-4115	374	1	b	b	PROPN
ejpam-4115	374	2	a	a	PRON
ejpam-4115	374	3	(	(	PUNCT
ejpam-4115	374	4	f	f	PROPN
ejpam-4115	374	5	+	+	CCONJ
ejpam-4115	374	6	g	g	NOUN
ejpam-4115	374	7	)	)	PUNCT
ejpam-4115	374	8	=	=	SYM
ejpam-4115	374	9	(	(	PUNCT
ejpam-4115	374	10	wd∗	wd∗	ADJ
ejpam-4115	374	11	)	)	PUNCT
ejpam-4115	374	12	∫	∫	PROPN
ejpam-4115	375	1	b	b	PROPN
ejpam-4115	375	2	a	a	DET
ejpam-4115	375	3	f	f	X
ejpam-4115	375	4	+	+	CCONJ
ejpam-4115	375	5	(	(	PUNCT
ejpam-4115	375	6	wd∗	wd∗	ADJ
ejpam-4115	375	7	)	)	PUNCT
ejpam-4115	375	8	∫	∫	PROPN
ejpam-4115	376	1	b	b	PROPN
ejpam-4115	376	2	a	a	DET
ejpam-4115	376	3	g.	g.	NOUN
ejpam-4115	376	4	proof	proof	NOUN
ejpam-4115	376	5	.	.	PUNCT
ejpam-4115	377	1	let	let	VERB
ejpam-4115	377	2	f	f	PROPN
ejpam-4115	377	3	and	and	CCONJ
ejpam-4115	377	4	g	g	PROPN
ejpam-4115	377	5	be	be	AUX
ejpam-4115	377	6	weak	weak	ADJ
ejpam-4115	377	7	denjoy	denjoy	NOUN
ejpam-4115	377	8	primitives	primitive	NOUN
ejpam-4115	377	9	of	of	ADP
ejpam-4115	377	10	f	f	PROPN
ejpam-4115	377	11	and	and	CCONJ
ejpam-4115	377	12	g	g	NOUN
ejpam-4115	377	13	,	,	PUNCT
ejpam-4115	377	14	respectively	respectively	ADV
ejpam-4115	377	15	.	.	PUNCT
ejpam-4115	378	1	(	(	PUNCT
ejpam-4115	378	2	i	i	NOUN
ejpam-4115	378	3	)	)	PUNCT
ejpam-4115	378	4	by	by	ADP
ejpam-4115	378	5	theorem	theorem	NOUN
ejpam-4115	378	6	2	2	NUM
ejpam-4115	378	7	,	,	PUNCT
ejpam-4115	378	8	cf	cf	X
ejpam-4115	378	9	is	be	AUX
ejpam-4115	378	10	acg∗	acg∗	NOUN
ejpam-4115	378	11	on	on	ADP
ejpam-4115	378	12	[	[	X
ejpam-4115	378	13	a	a	X
ejpam-4115	378	14	,	,	PUNCT
ejpam-4115	378	15	b	b	NOUN
ejpam-4115	378	16	]	]	X
ejpam-4115	378	17	.	.	PUNCT
ejpam-4115	379	1	the	the	DET
ejpam-4115	379	2	result	result	NOUN
ejpam-4115	379	3	is	be	AUX
ejpam-4115	379	4	clear	clear	ADJ
ejpam-4115	379	5	if	if	SCONJ
ejpam-4115	379	6	c	c	NOUN
ejpam-4115	379	7	=	=	NOUN
ejpam-4115	379	8	0	0	X
ejpam-4115	379	9	.	.	PUNCT
ejpam-4115	380	1	so	so	ADV
ejpam-4115	380	2	suppose	suppose	VERB
ejpam-4115	380	3	c	c	PROPN
ejpam-4115	380	4	̸=	̸=	PROPN
ejpam-4115	380	5	0	0	NUM
ejpam-4115	380	6	.	.	PUNCT
ejpam-4115	381	1	then	then	ADV
ejpam-4115	381	2	∆(u	∆(u	NOUN
ejpam-4115	381	3	,	,	PUNCT
ejpam-4115	381	4	cf	cf	NOUN
ejpam-4115	381	5	,	,	PUNCT
ejpam-4115	381	6	cf	cf	NOUN
ejpam-4115	381	7	)	)	PUNCT
ejpam-4115	381	8	=	=	SYM
ejpam-4115	381	9	∆(1cu	∆(1cu	PROPN
ejpam-4115	381	10	,	,	PUNCT
ejpam-4115	381	11	f	f	PROPN
ejpam-4115	381	12	,	,	PUNCT
ejpam-4115	381	13	f	f	PROPN
ejpam-4115	381	14	)	)	PUNCT
ejpam-4115	381	15	by	by	ADP
ejpam-4115	381	16	theorem	theorem	NOUN
ejpam-4115	381	17	5(ii	5(ii	NUM
ejpam-4115	381	18	)	)	PUNCT
ejpam-4115	381	19	.	.	PUNCT
ejpam-4115	382	1	since	since	SCONJ
ejpam-4115	382	2	∆(1cu	∆(1cu	PROPN
ejpam-4115	382	3	,	,	PUNCT
ejpam-4115	382	4	f	f	PROPN
ejpam-4115	382	5	,	,	PUNCT
ejpam-4115	382	6	f	f	X
ejpam-4115	382	7	)	)	PUNCT
ejpam-4115	382	8	has	have	VERB
ejpam-4115	382	9	measure	measure	NOUN
ejpam-4115	382	10	zero	zero	NUM
ejpam-4115	382	11	for	for	ADP
ejpam-4115	382	12	all	all	DET
ejpam-4115	382	13	θ	θ	PROPN
ejpam-4115	382	14	-	-	ADJ
ejpam-4115	382	15	nbds	nbds	NOUN
ejpam-4115	382	16	u	u	NOUN
ejpam-4115	382	17	,	,	PUNCT
ejpam-4115	382	18	∆(u	∆(u	PROPN
ejpam-4115	382	19	,	,	PUNCT
ejpam-4115	382	20	cf	cf	NOUN
ejpam-4115	382	21	,	,	PUNCT
ejpam-4115	382	22	cf	cf	NOUN
ejpam-4115	382	23	)	)	PUNCT
ejpam-4115	382	24	has	have	VERB
ejpam-4115	382	25	measure	measure	NOUN
ejpam-4115	382	26	zero	zero	NUM
ejpam-4115	382	27	for	for	ADP
ejpam-4115	382	28	all	all	DET
ejpam-4115	382	29	θ	θ	PROPN
ejpam-4115	382	30	-	-	ADJ
ejpam-4115	382	31	nbds	nbds	NOUN
ejpam-4115	382	32	u	u	NOUN
ejpam-4115	382	33	.	.	PUNCT
ejpam-4115	383	1	hence	hence	ADV
ejpam-4115	383	2	,	,	PUNCT
ejpam-4115	383	3	cf	cf	X
ejpam-4115	383	4	is	be	AUX
ejpam-4115	383	5	weak	weak	ADJ
ejpam-4115	383	6	denjoy	denjoy	NOUN
ejpam-4115	383	7	integrable	integrable	ADJ
ejpam-4115	383	8	with	with	ADP
ejpam-4115	383	9	primitive	primitive	ADJ
ejpam-4115	383	10	cf	cf	NOUN
ejpam-4115	383	11	on	on	ADP
ejpam-4115	383	12	[	[	X
ejpam-4115	383	13	a	a	X
ejpam-4115	383	14	,	,	PUNCT
ejpam-4115	383	15	b	b	NOUN
ejpam-4115	383	16	]	]	X
ejpam-4115	383	17	.	.	PUNCT
ejpam-4115	384	1	furthermore	furthermore	ADV
ejpam-4115	384	2	,	,	PUNCT
ejpam-4115	384	3	(	(	PUNCT
ejpam-4115	384	4	wd∗	wd∗	X
ejpam-4115	384	5	)	)	PUNCT
ejpam-4115	384	6	∫	∫	PROPN
ejpam-4115	385	1	b	b	PROPN
ejpam-4115	385	2	a	a	DET
ejpam-4115	385	3	(	(	PUNCT
ejpam-4115	385	4	cf	cf	NOUN
ejpam-4115	385	5	)	)	PUNCT
ejpam-4115	385	6	=	=	SYM
ejpam-4115	386	1	cf	cf	NOUN
ejpam-4115	386	2	(	(	PUNCT
ejpam-4115	386	3	b)−	b)−	PROPN
ejpam-4115	386	4	cf	cf	X
ejpam-4115	386	5	(	(	PUNCT
ejpam-4115	386	6	a	a	X
ejpam-4115	386	7	)	)	PUNCT
ejpam-4115	386	8	=	=	SYM
ejpam-4115	386	9	c	c	NOUN
ejpam-4115	386	10	·	·	PUNCT
ejpam-4115	386	11	(	(	PUNCT
ejpam-4115	386	12	wd∗	wd∗	X
ejpam-4115	386	13	)	)	PUNCT
ejpam-4115	386	14	∫	∫	PROPN
ejpam-4115	386	15	b	b	PROPN
ejpam-4115	386	16	a	a	DET
ejpam-4115	386	17	f.	f.	PROPN
ejpam-4115	386	18	(	(	PUNCT
ejpam-4115	386	19	ii	ii	PROPN
ejpam-4115	386	20	)	)	PUNCT
ejpam-4115	386	21	the	the	DET
ejpam-4115	386	22	function	function	NOUN
ejpam-4115	386	23	f	f	PROPN
ejpam-4115	387	1	+	+	NOUN
ejpam-4115	387	2	g	g	PROPN
ejpam-4115	387	3	is	be	AUX
ejpam-4115	387	4	acg∗	acg∗	NOUN
ejpam-4115	387	5	on	on	ADP
ejpam-4115	387	6	[	[	X
ejpam-4115	387	7	a	a	X
ejpam-4115	387	8	,	,	PUNCT
ejpam-4115	387	9	b	b	NOUN
ejpam-4115	387	10	]	]	PUNCT
ejpam-4115	387	11	by	by	ADP
ejpam-4115	387	12	theorem	theorem	NOUN
ejpam-4115	387	13	2	2	NUM
ejpam-4115	387	14	.	.	PUNCT
ejpam-4115	388	1	let	let	VERB
ejpam-4115	388	2	u	u	PRON
ejpam-4115	388	3	be	be	AUX
ejpam-4115	388	4	a	a	DET
ejpam-4115	388	5	given	give	VERB
ejpam-4115	388	6	θ	θ	PROPN
ejpam-4115	388	7	-	-	PUNCT
ejpam-4115	388	8	nbd	nbd	PROPN
ejpam-4115	388	9	and	and	CCONJ
ejpam-4115	388	10	let	let	VERB
ejpam-4115	388	11	v	v	PRON
ejpam-4115	388	12	⊆	⊆	NUM
ejpam-4115	388	13	u	u	NOUN
ejpam-4115	388	14	be	be	AUX
ejpam-4115	388	15	a	a	DET
ejpam-4115	388	16	convex	convex	ADJ
ejpam-4115	388	17	θ	θ	PROPN
ejpam-4115	388	18	-	-	PUNCT
ejpam-4115	388	19	nbd	nbd	PROPN
ejpam-4115	388	20	.	.	PUNCT
ejpam-4115	389	1	then	then	ADV
ejpam-4115	389	2	∆(v	∆(v	PROPN
ejpam-4115	389	3	,	,	PUNCT
ejpam-4115	389	4	f+g	f+g	PROPN
ejpam-4115	389	5	,	,	PUNCT
ejpam-4115	389	6	f+g	f+g	X
ejpam-4115	389	7	)	)	PUNCT
ejpam-4115	390	1	⊆	⊆	NUM
ejpam-4115	390	2	∆(12v	∆(12v	ADJ
ejpam-4115	390	3	,	,	PUNCT
ejpam-4115	390	4	f	f	X
ejpam-4115	390	5	,	,	PUNCT
ejpam-4115	390	6	f)∪∆(12v	f)∪∆(12v	PROPN
ejpam-4115	390	7	,	,	PUNCT
ejpam-4115	390	8	g	g	NOUN
ejpam-4115	390	9	,	,	PUNCT
ejpam-4115	390	10	g	g	NOUN
ejpam-4115	390	11	)	)	PUNCT
ejpam-4115	390	12	by	by	ADP
ejpam-4115	390	13	theorem	theorem	ADJ
ejpam-4115	390	14	5(iii	5(iii	NUM
ejpam-4115	390	15	)	)	PUNCT
ejpam-4115	390	16	.	.	PUNCT
ejpam-4115	391	1	since	since	SCONJ
ejpam-4115	391	2	both	both	PRON
ejpam-4115	391	3	∆(12v	∆(12v	ADJ
ejpam-4115	391	4	,	,	PUNCT
ejpam-4115	391	5	f	f	PROPN
ejpam-4115	391	6	,	,	PUNCT
ejpam-4115	391	7	f	f	NOUN
ejpam-4115	391	8	)	)	PUNCT
ejpam-4115	391	9	and	and	CCONJ
ejpam-4115	391	10	∆(12v	∆(12v	ADJ
ejpam-4115	391	11	,	,	PUNCT
ejpam-4115	391	12	g	g	NOUN
ejpam-4115	391	13	,	,	PUNCT
ejpam-4115	391	14	g	g	NOUN
ejpam-4115	391	15	)	)	PUNCT
ejpam-4115	391	16	have	have	VERB
ejpam-4115	391	17	measure	measure	NOUN
ejpam-4115	391	18	zero	zero	NUM
ejpam-4115	391	19	,	,	PUNCT
ejpam-4115	391	20	∆(v	∆(v	PROPN
ejpam-4115	391	21	,	,	PUNCT
ejpam-4115	391	22	f	f	PROPN
ejpam-4115	392	1	+	+	CCONJ
ejpam-4115	392	2	g	g	PROPN
ejpam-4115	392	3	,	,	PUNCT
ejpam-4115	392	4	f	f	PROPN
ejpam-4115	393	1	+	+	CCONJ
ejpam-4115	393	2	g	g	NOUN
ejpam-4115	393	3	)	)	PUNCT
ejpam-4115	393	4	is	be	AUX
ejpam-4115	393	5	of	of	ADP
ejpam-4115	393	6	measure	measure	NOUN
ejpam-4115	393	7	zero	zero	NUM
ejpam-4115	393	8	.	.	PUNCT
ejpam-4115	394	1	thus	thus	ADV
ejpam-4115	394	2	,	,	PUNCT
ejpam-4115	394	3	∆(u	∆(u	PROPN
ejpam-4115	394	4	,	,	PUNCT
ejpam-4115	394	5	f	f	PROPN
ejpam-4115	395	1	+	+	NOUN
ejpam-4115	395	2	g	g	PROPN
ejpam-4115	395	3	,	,	PUNCT
ejpam-4115	395	4	f	f	PROPN
ejpam-4115	396	1	+	+	CCONJ
ejpam-4115	396	2	g	g	NOUN
ejpam-4115	396	3	)	)	PUNCT
ejpam-4115	396	4	has	have	VERB
ejpam-4115	396	5	measure	measure	NOUN
ejpam-4115	396	6	zero	zero	NUM
ejpam-4115	396	7	,	,	PUNCT
ejpam-4115	396	8	implying	imply	VERB
ejpam-4115	396	9	that	that	SCONJ
ejpam-4115	396	10	f	f	PROPN
ejpam-4115	397	1	+	+	CCONJ
ejpam-4115	397	2	g	g	PROPN
ejpam-4115	397	3	is	be	AUX
ejpam-4115	397	4	weak	weak	ADJ
ejpam-4115	397	5	denjoy	denjoy	NOUN
ejpam-4115	397	6	integrable	integrable	ADJ
ejpam-4115	397	7	with	with	ADP
ejpam-4115	397	8	primitive	primitive	ADJ
ejpam-4115	397	9	f	f	NOUN
ejpam-4115	398	1	+	+	NOUN
ejpam-4115	398	2	g	g	NOUN
ejpam-4115	398	3	on	on	ADP
ejpam-4115	398	4	[	[	X
ejpam-4115	398	5	a	a	X
ejpam-4115	398	6	,	,	PUNCT
ejpam-4115	398	7	b	b	NOUN
ejpam-4115	398	8	]	]	PUNCT
ejpam-4115	398	9	and	and	CCONJ
ejpam-4115	398	10	(	(	PUNCT
ejpam-4115	398	11	wd∗	wd∗	ADJ
ejpam-4115	398	12	)	)	PUNCT
ejpam-4115	398	13	∫	∫	PROPN
ejpam-4115	399	1	b	b	PROPN
ejpam-4115	399	2	a	a	PRON
ejpam-4115	399	3	(	(	PUNCT
ejpam-4115	399	4	f	f	PROPN
ejpam-4115	399	5	+	+	CCONJ
ejpam-4115	399	6	g	g	NOUN
ejpam-4115	399	7	)	)	PUNCT
ejpam-4115	399	8	=	=	PUNCT
ejpam-4115	400	1	(	(	PUNCT
ejpam-4115	400	2	f	f	PROPN
ejpam-4115	400	3	+	+	NOUN
ejpam-4115	400	4	g)(b)−	g)(b)−	PROPN
ejpam-4115	400	5	(	(	PUNCT
ejpam-4115	400	6	f	f	NOUN
ejpam-4115	400	7	+	+	NOUN
ejpam-4115	400	8	g)(a	g)(a	PROPN
ejpam-4115	400	9	)	)	PUNCT
ejpam-4115	400	10	=	=	SYM
ejpam-4115	400	11	(	(	PUNCT
ejpam-4115	400	12	wd∗	wd∗	ADJ
ejpam-4115	400	13	)	)	PUNCT
ejpam-4115	400	14	∫	∫	PROPN
ejpam-4115	400	15	b	b	PROPN
ejpam-4115	400	16	a	a	DET
ejpam-4115	400	17	f	f	X
ejpam-4115	400	18	+	+	CCONJ
ejpam-4115	400	19	(	(	PUNCT
ejpam-4115	400	20	wd∗	wd∗	ADJ
ejpam-4115	400	21	)	)	PUNCT
ejpam-4115	400	22	∫	∫	PROPN
ejpam-4115	401	1	b	b	PROPN
ejpam-4115	401	2	a	a	DET
ejpam-4115	401	3	f.	f.	PROPN
ejpam-4115	401	4	remark	remark	NOUN
ejpam-4115	401	5	3	3	X
ejpam-4115	401	6	.	.	PUNCT
ejpam-4115	402	1	an	an	DET
ejpam-4115	402	2	analog	analog	NOUN
ejpam-4115	402	3	of	of	ADP
ejpam-4115	402	4	theorem	theorem	ADJ
ejpam-4115	402	5	10	10	NUM
ejpam-4115	402	6	holds	hold	NOUN
ejpam-4115	402	7	for	for	SCONJ
ejpam-4115	402	8	the	the	DET
ejpam-4115	402	9	denjoy	denjoy	NOUN
ejpam-4115	402	10	integral	integral	ADJ
ejpam-4115	402	11	and	and	CCONJ
ejpam-4115	402	12	the	the	DET
ejpam-4115	402	13	proof	proof	NOUN
ejpam-4115	402	14	is	be	AUX
ejpam-4115	402	15	easy	easy	ADJ
ejpam-4115	402	16	.	.	PUNCT
ejpam-4115	403	1	for	for	ADP
ejpam-4115	403	2	the	the	DET
ejpam-4115	403	3	next	next	ADJ
ejpam-4115	403	4	result	result	NOUN
ejpam-4115	403	5	,	,	PUNCT
ejpam-4115	403	6	one	one	PRON
ejpam-4115	403	7	may	may	AUX
ejpam-4115	403	8	also	also	ADV
ejpam-4115	403	9	refer	refer	VERB
ejpam-4115	403	10	to	to	ADP
ejpam-4115	403	11	[	[	X
ejpam-4115	403	12	6	6	NUM
ejpam-4115	403	13	]	]	PUNCT
ejpam-4115	403	14	.	.	PUNCT
ejpam-4115	404	1	theorem	theorem	NOUN
ejpam-4115	404	2	11	11	NUM
ejpam-4115	404	3	.	.	PUNCT
ejpam-4115	405	1	let	let	VERB
ejpam-4115	405	2	f	f	NOUN
ejpam-4115	405	3	:	:	PUNCT
ejpam-4115	406	1	[	[	X
ejpam-4115	406	2	a	a	X
ejpam-4115	406	3	,	,	PUNCT
ejpam-4115	406	4	b	b	NOUN
ejpam-4115	406	5	]	]	X
ejpam-4115	406	6	→	→	SYM
ejpam-4115	406	7	x.	x.	NOUN
ejpam-4115	406	8	if	if	SCONJ
ejpam-4115	406	9	f	f	PROPN
ejpam-4115	406	10	=	=	SYM
ejpam-4115	406	11	θ	θ	PROPN
ejpam-4115	406	12	almost	almost	ADV
ejpam-4115	406	13	everywhere	everywhere	ADV
ejpam-4115	406	14	,	,	PUNCT
ejpam-4115	406	15	then	then	ADV
ejpam-4115	406	16	f	f	PROPN
ejpam-4115	406	17	is	be	AUX
ejpam-4115	406	18	sh	sh	PROPN
ejpam-4115	406	19	-	-	PUNCT
ejpam-4115	406	20	integrable	integrable	ADJ
ejpam-4115	406	21	and	and	CCONJ
ejpam-4115	407	1	(	(	PUNCT
ejpam-4115	407	2	sh	sh	INTJ
ejpam-4115	407	3	)	)	PUNCT
ejpam-4115	407	4	∫	∫	PROPN
ejpam-4115	408	1	b	b	PROPN
ejpam-4115	408	2	a	a	DET
ejpam-4115	408	3	f	f	PROPN
ejpam-4115	408	4	=	=	SYM
ejpam-4115	408	5	θ	θ	PROPN
ejpam-4115	408	6	.	.	PUNCT
ejpam-4115	408	7	proof	proof	NOUN
ejpam-4115	408	8	.	.	PUNCT
ejpam-4115	409	1	we	we	PRON
ejpam-4115	409	2	show	show	VERB
ejpam-4115	409	3	that	that	SCONJ
ejpam-4115	409	4	f	f	X
ejpam-4115	409	5	:	:	PUNCT
ejpam-4115	410	1	[	[	X
ejpam-4115	410	2	a	a	X
ejpam-4115	410	3	,	,	PUNCT
ejpam-4115	410	4	b	b	NOUN
ejpam-4115	410	5	]	]	X
ejpam-4115	410	6	→	→	PUNCT
ejpam-4115	410	7	x	x	SYM
ejpam-4115	410	8	defined	define	VERB
ejpam-4115	410	9	by	by	ADP
ejpam-4115	410	10	f	f	PROPN
ejpam-4115	410	11	(	(	PUNCT
ejpam-4115	410	12	t	t	PROPN
ejpam-4115	410	13	)	)	PUNCT
ejpam-4115	411	1	=	=	SYM
ejpam-4115	411	2	θ	θ	PROPN
ejpam-4115	411	3	is	be	AUX
ejpam-4115	411	4	an	an	DET
ejpam-4115	411	5	sh	sh	NOUN
ejpam-4115	411	6	primitive	primitive	ADJ
ejpam-4115	411	7	of	of	ADP
ejpam-4115	411	8	f	f	PROPN
ejpam-4115	411	9	.	.	PUNCT
ejpam-4115	412	1	let	let	VERB
ejpam-4115	412	2	v	v	PART
ejpam-4115	412	3	be	be	AUX
ejpam-4115	412	4	a	a	DET
ejpam-4115	412	5	θ	θ	PROPN
ejpam-4115	412	6	-	-	PUNCT
ejpam-4115	412	7	nbd	nbd	PROPN
ejpam-4115	412	8	.	.	PUNCT
ejpam-4115	413	1	let	let	VERB
ejpam-4115	413	2	u	u	PRON
ejpam-4115	413	3	be	be	AUX
ejpam-4115	413	4	an	an	DET
ejpam-4115	413	5	absorbing	absorbing	ADJ
ejpam-4115	413	6	,	,	PUNCT
ejpam-4115	413	7	balanced	balanced	ADJ
ejpam-4115	413	8	,	,	PUNCT
ejpam-4115	413	9	and	and	CCONJ
ejpam-4115	413	10	convex	convex	ADJ
ejpam-4115	413	11	θ	θ	PROPN
ejpam-4115	413	12	-	-	PUNCT
ejpam-4115	413	13	nbd	nbd	PROPN
ejpam-4115	413	14	with	with	ADP
ejpam-4115	413	15	u	u	PROPN
ejpam-4115	413	16	⊆	⊆	NUM
ejpam-4115	413	17	v	v	NOUN
ejpam-4115	413	18	.	.	PUNCT
ejpam-4115	414	1	let	let	VERB
ejpam-4115	414	2	s	s	PRON
ejpam-4115	414	3	=	=	PUNCT
ejpam-4115	414	4	{	{	PUNCT
ejpam-4115	414	5	t	t	NOUN
ejpam-4115	414	6	∈	∈	PROPN
ejpam-4115	415	1	[	[	X
ejpam-4115	415	2	a	a	X
ejpam-4115	415	3	,	,	PUNCT
ejpam-4115	415	4	b	b	NOUN
ejpam-4115	415	5	]	]	X
ejpam-4115	415	6	:	:	PUNCT
ejpam-4115	415	7	f(t	f(t	NOUN
ejpam-4115	415	8	)	)	PUNCT
ejpam-4115	415	9	̸=	̸=	PROPN
ejpam-4115	415	10	θ	θ	PROPN
ejpam-4115	415	11	}	}	PUNCT
ejpam-4115	415	12	and	and	CCONJ
ejpam-4115	415	13	ek	ek	NOUN
ejpam-4115	415	14	=	=	PUNCT
ejpam-4115	415	15	{	{	PUNCT
ejpam-4115	415	16	t	t	PROPN
ejpam-4115	415	17	∈	∈	PROPN
ejpam-4115	415	18	s	s	PART
ejpam-4115	415	19	:	:	PUNCT
ejpam-4115	415	20	f(t	f(t	NOUN
ejpam-4115	415	21	)	)	PUNCT
ejpam-4115	415	22	∈	∈	PROPN
ejpam-4115	415	23	ku	ku	NOUN
ejpam-4115	415	24	\	\	PROPN
ejpam-4115	416	1	(	(	PUNCT
ejpam-4115	416	2	k	k	PROPN
ejpam-4115	416	3	−	−	PROPN
ejpam-4115	416	4	1)u	1)u	NOUN
ejpam-4115	416	5	}	}	PUNCT
ejpam-4115	416	6	for	for	ADP
ejpam-4115	416	7	each	each	DET
ejpam-4115	416	8	positive	positive	ADJ
ejpam-4115	416	9	integer	integer	NOUN
ejpam-4115	416	10	k.	k.	PROPN
ejpam-4115	417	1	then	then	ADV
ejpam-4115	417	2	the	the	DET
ejpam-4115	417	3	collection	collection	NOUN
ejpam-4115	417	4	{	{	PUNCT
ejpam-4115	417	5	ei}∞i=1	ei}∞i=1	X
ejpam-4115	417	6	is	be	AUX
ejpam-4115	417	7	pairwise	pairwise	PROPN
ejpam-4115	417	8	disjoint	disjoint	NOUN
ejpam-4115	417	9	.	.	PUNCT
ejpam-4115	418	1	let	let	VERB
ejpam-4115	418	2	t	t	PROPN
ejpam-4115	418	3	∈	∈	PROPN
ejpam-4115	418	4	s.	s.	PROPN
ejpam-4115	418	5	then	then	ADV
ejpam-4115	418	6	f(t	f(t	PROPN
ejpam-4115	418	7	)	)	PUNCT
ejpam-4115	418	8	̸=	̸=	PROPN
ejpam-4115	418	9	θ	θ	PROPN
ejpam-4115	418	10	.	.	PUNCT
ejpam-4115	419	1	since	since	SCONJ
ejpam-4115	419	2	u	u	NOUN
ejpam-4115	419	3	is	be	AUX
ejpam-4115	419	4	absorbing	absorbing	ADJ
ejpam-4115	419	5	,	,	PUNCT
ejpam-4115	419	6	there	there	PRON
ejpam-4115	419	7	is	be	VERB
ejpam-4115	419	8	a	a	DET
ejpam-4115	419	9	positive	positive	ADJ
ejpam-4115	419	10	integer	integer	NOUN
ejpam-4115	419	11	r	r	NOUN
ejpam-4115	419	12	such	such	ADJ
ejpam-4115	419	13	that	that	SCONJ
ejpam-4115	419	14	f(t	f(t	NOUN
ejpam-4115	419	15	)	)	PUNCT
ejpam-4115	419	16	∈	∈	PROPN
ejpam-4115	419	17	ru	ru	NOUN
ejpam-4115	419	18	.	.	PUNCT
ejpam-4115	420	1	we	we	PRON
ejpam-4115	420	2	may	may	AUX
ejpam-4115	420	3	choose	choose	VERB
ejpam-4115	420	4	r	r	NOUN
ejpam-4115	420	5	to	to	PART
ejpam-4115	420	6	be	be	AUX
ejpam-4115	420	7	the	the	DET
ejpam-4115	420	8	smallest	small	ADJ
ejpam-4115	420	9	positive	positive	ADJ
ejpam-4115	420	10	integer	integer	NOUN
ejpam-4115	420	11	with	with	ADP
ejpam-4115	420	12	this	this	DET
ejpam-4115	420	13	property	property	NOUN
ejpam-4115	420	14	.	.	PUNCT
ejpam-4115	421	1	thus	thus	ADV
ejpam-4115	421	2	,	,	PUNCT
ejpam-4115	421	3	f(t	f(t	PROPN
ejpam-4115	421	4	)	)	PUNCT
ejpam-4115	421	5	∈	∈	PROPN
ejpam-4115	421	6	er	er	INTJ
ejpam-4115	421	7	,	,	PUNCT
ejpam-4115	421	8	showing	show	VERB
ejpam-4115	421	9	that	that	SCONJ
ejpam-4115	421	10	s	s	VERB
ejpam-4115	421	11	⊆	⊆	NUM
ejpam-4115	421	12	⋃∞	⋃∞	X
ejpam-4115	421	13	i=1ei	i=1ei	X
ejpam-4115	421	14	.	.	PUNCT
ejpam-4115	422	1	since	since	SCONJ
ejpam-4115	422	2	⋃∞	⋃∞	PUNCT
ejpam-4115	422	3	i=1ei	i=1ei	ADV
ejpam-4115	422	4	⊆	⊆	NUM
ejpam-4115	422	5	s	s	NOUN
ejpam-4115	422	6	,	,	PUNCT
ejpam-4115	422	7	s	s	PART
ejpam-4115	422	8	=	=	NOUN
ejpam-4115	422	9	⋃∞	⋃∞	X
ejpam-4115	422	10	i=1ei	i=1ei	X
ejpam-4115	422	11	.	.	PUNCT
ejpam-4115	423	1	also	also	ADV
ejpam-4115	423	2	,	,	PUNCT
ejpam-4115	423	3	m(s	m(s	PROPN
ejpam-4115	423	4	)	)	PUNCT
ejpam-4115	423	5	=	=	SYM
ejpam-4115	423	6	0	0	NUM
ejpam-4115	423	7	implies	imply	VERB
ejpam-4115	423	8	that	that	SCONJ
ejpam-4115	423	9	m(ek	m(ek	X
ejpam-4115	423	10	)	)	PUNCT
ejpam-4115	423	11	=	=	SYM
ejpam-4115	423	12	0	0	PROPN
ejpam-4115	423	13	r.	r.	PROPN
ejpam-4115	423	14	e.	e.	PROPN
ejpam-4115	423	15	maza	maza	PROPN
ejpam-4115	423	16	,	,	PUNCT
ejpam-4115	423	17	s.	s.	PROPN
ejpam-4115	423	18	r.	r.	PROPN
ejpam-4115	423	19	canoy	canoy	PROPN
ejpam-4115	423	20	,	,	PUNCT
ejpam-4115	423	21	jr	jr	PROPN
ejpam-4115	423	22	.	.	PROPN
ejpam-4115	423	23	/	/	SYM
ejpam-4115	423	24	eur	eur	PROPN
ejpam-4115	423	25	.	.	PUNCT
ejpam-4115	424	1	j.	j.	PROPN
ejpam-4115	424	2	pure	pure	PROPN
ejpam-4115	424	3	appl	appl	PROPN
ejpam-4115	424	4	.	.	PROPN
ejpam-4115	424	5	math	math	PROPN
ejpam-4115	424	6	,	,	PUNCT
ejpam-4115	424	7	14	14	NUM
ejpam-4115	424	8	(	(	PUNCT
ejpam-4115	424	9	4	4	NUM
ejpam-4115	424	10	)	)	PUNCT
ejpam-4115	424	11	(	(	PUNCT
ejpam-4115	424	12	2021	2021	NUM
ejpam-4115	424	13	)	)	PUNCT
ejpam-4115	424	14	,	,	PUNCT
ejpam-4115	424	15	1169	1169	NUM
ejpam-4115	424	16	-	-	SYM
ejpam-4115	424	17	1183	1183	NUM
ejpam-4115	424	18	1178	1178	NUM
ejpam-4115	424	19	for	for	ADP
ejpam-4115	424	20	each	each	DET
ejpam-4115	424	21	positive	positive	ADJ
ejpam-4115	424	22	integer	integer	NOUN
ejpam-4115	424	23	k.	k.	PROPN
ejpam-4115	425	1	thus	thus	ADV
ejpam-4115	425	2	,	,	PUNCT
ejpam-4115	425	3	for	for	ADP
ejpam-4115	425	4	each	each	DET
ejpam-4115	425	5	positive	positive	ADJ
ejpam-4115	425	6	integer	integer	NOUN
ejpam-4115	425	7	k	k	NOUN
ejpam-4115	425	8	,	,	PUNCT
ejpam-4115	425	9	there	there	PRON
ejpam-4115	425	10	exists	exist	VERB
ejpam-4115	425	11	an	an	DET
ejpam-4115	425	12	open	open	ADJ
ejpam-4115	425	13	set	set	NOUN
ejpam-4115	425	14	gk	gk	PROPN
ejpam-4115	425	15	such	such	ADJ
ejpam-4115	425	16	that	that	SCONJ
ejpam-4115	425	17	ek	ek	PROPN
ejpam-4115	425	18	⊆	⊆	NUM
ejpam-4115	425	19	gk	gk	NOUN
ejpam-4115	425	20	and	and	CCONJ
ejpam-4115	425	21	m(gk	m(gk	NOUN
ejpam-4115	425	22	)	)	PUNCT
ejpam-4115	425	23	<	<	X
ejpam-4115	425	24	1	1	NUM
ejpam-4115	425	25	k2k	k2k	X
ejpam-4115	425	26	.	.	PUNCT
ejpam-4115	426	1	set	set	VERB
ejpam-4115	426	2	δ(t	δ(t	PROPN
ejpam-4115	426	3	)	)	PUNCT
ejpam-4115	426	4	=	=	SYM
ejpam-4115	426	5	1	1	NUM
ejpam-4115	426	6	if	if	SCONJ
ejpam-4115	426	7	t	t	PROPN
ejpam-4115	426	8	∈	∈	PROPN
ejpam-4115	427	1	[	[	X
ejpam-4115	427	2	a	a	X
ejpam-4115	427	3	,	,	PUNCT
ejpam-4115	427	4	b]\s	b]\s	PROPN
ejpam-4115	428	1	and	and	CCONJ
ejpam-4115	428	2	let	let	VERB
ejpam-4115	428	3	δ(t	δ(t	NOUN
ejpam-4115	428	4	)	)	PUNCT
ejpam-4115	428	5	>	>	X
ejpam-4115	428	6	0	0	PUNCT
ejpam-4115	428	7	be	be	AUX
ejpam-4115	428	8	a	a	DET
ejpam-4115	428	9	real	real	ADJ
ejpam-4115	428	10	number	number	NOUN
ejpam-4115	428	11	such	such	ADJ
ejpam-4115	428	12	that	that	SCONJ
ejpam-4115	428	13	(	(	PUNCT
ejpam-4115	428	14	t	t	PROPN
ejpam-4115	428	15	−	−	PROPN
ejpam-4115	428	16	δ(t	δ(t	PROPN
ejpam-4115	428	17	)	)	PUNCT
ejpam-4115	428	18	,	,	PUNCT
ejpam-4115	428	19	t	t	PROPN
ejpam-4115	428	20	+	+	NUM
ejpam-4115	428	21	δ(t	δ(t	PROPN
ejpam-4115	428	22	)	)	PUNCT
ejpam-4115	428	23	)	)	PUNCT
ejpam-4115	429	1	⊆	⊆	NUM
ejpam-4115	429	2	gk	gk	NOUN
ejpam-4115	429	3	,	,	PUNCT
ejpam-4115	429	4	if	if	SCONJ
ejpam-4115	429	5	t	t	PROPN
ejpam-4115	429	6	∈	∈	PROPN
ejpam-4115	429	7	ek	ek	PROPN
ejpam-4115	429	8	.	.	PUNCT
ejpam-4115	429	9	let	let	VERB
ejpam-4115	429	10	d	d	NOUN
ejpam-4115	429	11	=	=	PRON
ejpam-4115	429	12	{	{	PUNCT
ejpam-4115	429	13	(	(	PUNCT
ejpam-4115	429	14	[	[	X
ejpam-4115	429	15	ui	ui	NOUN
ejpam-4115	429	16	,	,	PUNCT
ejpam-4115	429	17	vi	vi	PROPN
ejpam-4115	429	18	]	]	PUNCT
ejpam-4115	429	19	,	,	PUNCT
ejpam-4115	429	20	ti	ti	NOUN
ejpam-4115	429	21	)	)	PUNCT
ejpam-4115	429	22	:	:	PUNCT
ejpam-4115	429	23	1	1	NUM
ejpam-4115	429	24	≤	≤	NUM
ejpam-4115	429	25	i	i	PRON
ejpam-4115	429	26	≤	≤	PROPN
ejpam-4115	429	27	n	n	CCONJ
ejpam-4115	429	28	}	}	PUNCT
ejpam-4115	429	29	be	be	AUX
ejpam-4115	429	30	a	a	DET
ejpam-4115	429	31	δ	δ	NOUN
ejpam-4115	429	32	-	-	PUNCT
ejpam-4115	429	33	fine	fine	ADJ
ejpam-4115	429	34	partition	partition	NOUN
ejpam-4115	429	35	of	of	ADP
ejpam-4115	429	36	[	[	X
ejpam-4115	429	37	a	a	X
ejpam-4115	429	38	,	,	PUNCT
ejpam-4115	429	39	b	b	NOUN
ejpam-4115	429	40	]	]	PUNCT
ejpam-4115	429	41	.	.	PUNCT
ejpam-4115	430	1	let	let	VERB
ejpam-4115	430	2	d0	d0	NOUN
ejpam-4115	430	3	be	be	AUX
ejpam-4115	430	4	the	the	DET
ejpam-4115	430	5	elements	element	NOUN
ejpam-4115	430	6	in	in	ADP
ejpam-4115	430	7	d	d	PROPN
ejpam-4115	430	8	for	for	ADP
ejpam-4115	430	9	which	which	PRON
ejpam-4115	430	10	the	the	DET
ejpam-4115	430	11	tags	tag	NOUN
ejpam-4115	430	12	are	be	AUX
ejpam-4115	430	13	not	not	PART
ejpam-4115	430	14	in	in	ADP
ejpam-4115	430	15	s	s	PRON
ejpam-4115	430	16	and	and	CCONJ
ejpam-4115	430	17	let	let	VERB
ejpam-4115	430	18	dk	dk	NOUN
ejpam-4115	430	19	=	=	PRON
ejpam-4115	430	20	{	{	PUNCT
ejpam-4115	430	21	(	(	PUNCT
ejpam-4115	430	22	[	[	X
ejpam-4115	430	23	ui	ui	NOUN
ejpam-4115	430	24	,	,	PUNCT
ejpam-4115	430	25	vi	vi	PROPN
ejpam-4115	430	26	]	]	PUNCT
ejpam-4115	430	27	,	,	PUNCT
ejpam-4115	430	28	ti	ti	NOUN
ejpam-4115	430	29	)	)	PUNCT
ejpam-4115	430	30	∈	∈	PROPN
ejpam-4115	431	1	d	d	NOUN
ejpam-4115	431	2	:	:	PUNCT
ejpam-4115	431	3	ti	ti	PROPN
ejpam-4115	431	4	∈	∈	PROPN
ejpam-4115	431	5	ek	ek	PROPN
ejpam-4115	431	6	}	}	PUNCT
ejpam-4115	431	7	for	for	ADP
ejpam-4115	431	8	each	each	DET
ejpam-4115	431	9	positive	positive	ADJ
ejpam-4115	431	10	integer	integer	NOUN
ejpam-4115	431	11	k.	k.	PROPN
ejpam-4115	432	1	then	then	ADV
ejpam-4115	432	2	φu	φu	X
ejpam-4115	432	3	(	(	PUNCT
ejpam-4115	432	4	f(t	f(t	PROPN
ejpam-4115	432	5	)	)	PUNCT
ejpam-4115	432	6	)	)	PUNCT
ejpam-4115	433	1	≤	≤	NUM
ejpam-4115	433	2	j	j	PROPN
ejpam-4115	433	3	and	and	CCONJ
ejpam-4115	433	4	[	[	X
ejpam-4115	433	5	ui	ui	PROPN
ejpam-4115	433	6	,	,	PUNCT
ejpam-4115	433	7	vi	vi	PROPN
ejpam-4115	433	8	]	]	X
ejpam-4115	433	9	⊆	⊆	NUM
ejpam-4115	433	10	(	(	PUNCT
ejpam-4115	433	11	ti−	ti−	NOUN
ejpam-4115	433	12	δ(ti	δ(ti	NOUN
ejpam-4115	433	13	)	)	PUNCT
ejpam-4115	433	14	,	,	PUNCT
ejpam-4115	433	15	ti+	ti+	PRON
ejpam-4115	433	16	δ(ti	δ(ti	NOUN
ejpam-4115	433	17	)	)	PUNCT
ejpam-4115	433	18	)	)	PUNCT
ejpam-4115	434	1	⊆	⊆	NUM
ejpam-4115	434	2	gj	gj	NOUN
ejpam-4115	434	3	for	for	ADP
ejpam-4115	434	4	each	each	DET
ejpam-4115	434	5	t	t	NOUN
ejpam-4115	434	6	∈	∈	PROPN
ejpam-4115	434	7	ej	ej	PROPN
ejpam-4115	434	8	.	.	PUNCT
ejpam-4115	435	1	hence	hence	ADV
ejpam-4115	435	2	,	,	PUNCT
ejpam-4115	435	3	⋃	⋃	PROPN
ejpam-4115	435	4	{	{	PUNCT
ejpam-4115	435	5	[	[	X
ejpam-4115	435	6	ui	ui	NOUN
ejpam-4115	435	7	,	,	PUNCT
ejpam-4115	435	8	vi	vi	PROPN
ejpam-4115	435	9	]	]	PUNCT
ejpam-4115	435	10	:	:	PUNCT
ejpam-4115	435	11	ti	ti	X
ejpam-4115	435	12	∈	∈	PROPN
ejpam-4115	435	13	ej	ej	PROPN
ejpam-4115	435	14	}	}	PUNCT
ejpam-4115	435	15	⊆	⊆	NUM
ejpam-4115	435	16	gj	gj	NOUN
ejpam-4115	435	17	.	.	PUNCT
ejpam-4115	436	1	so	so	ADV
ejpam-4115	436	2	,	,	PUNCT
ejpam-4115	436	3	∑	∑	ADP
ejpam-4115	436	4	ti∈ej	ti∈ej	NOUN
ejpam-4115	436	5	(	(	PUNCT
ejpam-4115	436	6	vi	vi	NOUN
ejpam-4115	436	7	−	−	PROPN
ejpam-4115	436	8	ui	ui	PROPN
ejpam-4115	436	9	)	)	PUNCT
ejpam-4115	436	10	≤	≤	NOUN
ejpam-4115	436	11	m(gj	m(gj	X
ejpam-4115	436	12	)	)	PUNCT
ejpam-4115	436	13	<	<	X
ejpam-4115	436	14	1	1	NUM
ejpam-4115	436	15	j2j	j2j	PROPN
ejpam-4115	436	16	.	.	PUNCT
ejpam-4115	437	1	consequently	consequently	ADV
ejpam-4115	437	2	,	,	PUNCT
ejpam-4115	437	3	(	(	PUNCT
ejpam-4115	437	4	d	d	X
ejpam-4115	437	5	)	)	PUNCT
ejpam-4115	437	6	∑	∑	PUNCT
ejpam-4115	437	7	φv	φv	ADP
ejpam-4115	437	8	(	(	PUNCT
ejpam-4115	437	9	−	−	PROPN
ejpam-4115	437	10	f(t)(v	f(t)(v	NUM
ejpam-4115	437	11	−	−	PROPN
ejpam-4115	437	12	u	u	NOUN
ejpam-4115	437	13	)	)	PUNCT
ejpam-4115	437	14	)	)	PUNCT
ejpam-4115	437	15	≤	≤	NOUN
ejpam-4115	437	16	(	(	PUNCT
ejpam-4115	437	17	d	d	X
ejpam-4115	437	18	)	)	PUNCT
ejpam-4115	437	19	∑	∑	ADV
ejpam-4115	437	20	φu	φu	INTJ
ejpam-4115	437	21	(	(	PUNCT
ejpam-4115	437	22	−	−	PROPN
ejpam-4115	437	23	f(t)(v	f(t)(v	NUM
ejpam-4115	437	24	−	−	PROPN
ejpam-4115	437	25	u	u	NOUN
ejpam-4115	437	26	)	)	PUNCT
ejpam-4115	437	27	)	)	PUNCT
ejpam-4115	438	1	=	=	PUNCT
ejpam-4115	438	2	(	(	PUNCT
ejpam-4115	438	3	d	d	X
ejpam-4115	438	4	)	)	PUNCT
ejpam-4115	438	5	∑	∑	ADV
ejpam-4115	438	6	φu	φu	INTJ
ejpam-4115	438	7	(	(	PUNCT
ejpam-4115	438	8	−	−	PROPN
ejpam-4115	438	9	f(t)(v	f(t)(v	NUM
ejpam-4115	438	10	−	−	PROPN
ejpam-4115	438	11	u	u	NOUN
ejpam-4115	438	12	)	)	PUNCT
ejpam-4115	438	13	)	)	PUNCT
ejpam-4115	439	1	+	+	CCONJ
ejpam-4115	439	2	(	(	PUNCT
ejpam-4115	439	3	d	d	X
ejpam-4115	439	4	\d0	\d0	PROPN
ejpam-4115	439	5	)	)	PUNCT
ejpam-4115	439	6	∑	∑	PROPN
ejpam-4115	439	7	φu	φu	PROPN
ejpam-4115	439	8	(	(	PUNCT
ejpam-4115	439	9	−	−	PROPN
ejpam-4115	439	10	f(ti)(vi	f(ti)(vi	PROPN
ejpam-4115	439	11	−	−	PROPN
ejpam-4115	439	12	ui	ui	PROPN
ejpam-4115	439	13	)	)	PUNCT
ejpam-4115	439	14	)	)	PUNCT
ejpam-4115	440	1	=	=	PUNCT
ejpam-4115	440	2	(	(	PUNCT
ejpam-4115	440	3	d	d	NOUN
ejpam-4115	440	4	\d0	\d0	PROPN
ejpam-4115	440	5	)	)	PUNCT
ejpam-4115	440	6	∑	∑	PROPN
ejpam-4115	440	7	φu	φu	PROPN
ejpam-4115	440	8	(	(	PUNCT
ejpam-4115	440	9	−	−	PROPN
ejpam-4115	440	10	f(t)(v	f(t)(v	NUM
ejpam-4115	440	11	−	−	PROPN
ejpam-4115	440	12	u	u	NOUN
ejpam-4115	440	13	)	)	PUNCT
ejpam-4115	440	14	)	)	PUNCT
ejpam-4115	440	15	≤	≤	NOUN
ejpam-4115	441	1	∞∑	∞∑	NUM
ejpam-4115	441	2	j=1	j=1	NOUN
ejpam-4115	441	3	∑	∑	PUNCT
ejpam-4115	441	4	ti∈ej	ti∈ej	PROPN
ejpam-4115	441	5	(	(	PUNCT
ejpam-4115	441	6	vi	vi	NOUN
ejpam-4115	441	7	−	−	NOUN
ejpam-4115	441	8	ui)φu	ui)φu	PROPN
ejpam-4115	441	9	(	(	PUNCT
ejpam-4115	441	10	−f(ti	−f(ti	NOUN
ejpam-4115	441	11	)	)	PUNCT
ejpam-4115	441	12	)	)	PUNCT
ejpam-4115	442	1	≤	≤	NOUN
ejpam-4115	443	1	∞∑	∞∑	NUM
ejpam-4115	443	2	j=1	j=1	NOUN
ejpam-4115	443	3	∑	∑	PUNCT
ejpam-4115	443	4	ti∈ej	ti∈ej	PROPN
ejpam-4115	443	5	(	(	PUNCT
ejpam-4115	443	6	vi	vi	NOUN
ejpam-4115	443	7	−	−	NOUN
ejpam-4115	443	8	ui)j	ui)j	NOUN
ejpam-4115	443	9	<	<	X
ejpam-4115	443	10	∞∑	∞∑	NUM
ejpam-4115	443	11	j=1	j=1	NOUN
ejpam-4115	443	12	1	1	NUM
ejpam-4115	443	13	j2j	j2j	PROPN
ejpam-4115	443	14	j	j	PROPN
ejpam-4115	443	15	=	=	SYM
ejpam-4115	443	16	1	1	NUM
ejpam-4115	443	17	let	let	VERB
ejpam-4115	443	18	ϵ	ϵ	X
ejpam-4115	443	19	=	=	PUNCT
ejpam-4115	443	20	1−(d	1−(d	NUM
ejpam-4115	443	21	)	)	PUNCT
ejpam-4115	443	22	∑	∑	ADV
ejpam-4115	443	23	φu	φu	X
ejpam-4115	443	24	(	(	PUNCT
ejpam-4115	443	25	−f(t)(v−u	−f(t)(v−u	X
ejpam-4115	443	26	)	)	PUNCT
ejpam-4115	443	27	)	)	PUNCT
ejpam-4115	443	28	>	>	X
ejpam-4115	444	1	0	0	X
ejpam-4115	444	2	.	.	PUNCT
ejpam-4115	445	1	for	for	ADP
ejpam-4115	445	2	each	each	DET
ejpam-4115	445	3	i	i	PRON
ejpam-4115	445	4	∈	∈	PROPN
ejpam-4115	445	5	{	{	PUNCT
ejpam-4115	445	6	1	1	NUM
ejpam-4115	445	7	,	,	PUNCT
ejpam-4115	445	8	2	2	NUM
ejpam-4115	445	9	,	,	PUNCT
ejpam-4115	445	10	.	.	PUNCT
ejpam-4115	445	11	.	.	PUNCT
ejpam-4115	445	12	.	.	PUNCT
ejpam-4115	446	1	,	,	PUNCT
ejpam-4115	446	2	n	n	CCONJ
ejpam-4115	446	3	}	}	PUNCT
ejpam-4115	446	4	,	,	PUNCT
ejpam-4115	446	5	let	let	VERB
ejpam-4115	446	6	ri	ri	PRON
ejpam-4115	446	7	=	=	NOUN
ejpam-4115	446	8	φu	φu	PROPN
ejpam-4115	446	9	(	(	PUNCT
ejpam-4115	446	10	−f(ti)(vi−	−f(ti)(vi−	NOUN
ejpam-4115	446	11	ui	ui	PROPN
ejpam-4115	446	12	)	)	PUNCT
ejpam-4115	446	13	)	)	PUNCT
ejpam-4115	447	1	+	+	CCONJ
ejpam-4115	447	2	ϵ	ϵ	X
ejpam-4115	447	3	n	n	NOUN
ejpam-4115	447	4	.	.	PUNCT
ejpam-4115	448	1	because	because	SCONJ
ejpam-4115	448	2	u	u	PRON
ejpam-4115	448	3	is	be	AUX
ejpam-4115	448	4	balanced	balanced	ADJ
ejpam-4115	448	5	,	,	PUNCT
ejpam-4115	448	6	f	f	PROPN
ejpam-4115	448	7	(	(	PUNCT
ejpam-4115	448	8	vi)−	vi)−	NOUN
ejpam-4115	448	9	f	f	X
ejpam-4115	448	10	(	(	PUNCT
ejpam-4115	448	11	ui)−	ui)−	X
ejpam-4115	448	12	f(ti)(vi	f(ti)(vi	PROPN
ejpam-4115	448	13	−	−	PROPN
ejpam-4115	448	14	ui	ui	NOUN
ejpam-4115	448	15	)	)	PUNCT
ejpam-4115	448	16	=	=	PUNCT
ejpam-4115	449	1	θ	θ	NOUN
ejpam-4115	449	2	−	−	NOUN
ejpam-4115	449	3	θ	θ	SYM
ejpam-4115	449	4	−	−	PROPN
ejpam-4115	449	5	f(ti)(vi	f(ti)(vi	PROPN
ejpam-4115	449	6	−	−	PROPN
ejpam-4115	449	7	ui	ui	NOUN
ejpam-4115	449	8	)	)	PUNCT
ejpam-4115	449	9	=	=	PUNCT
ejpam-4115	449	10	−f(ti)(vi	−f(ti)(vi	PROPN
ejpam-4115	449	11	−	−	PROPN
ejpam-4115	449	12	ui	ui	PROPN
ejpam-4115	449	13	)	)	PUNCT
ejpam-4115	449	14	∈	∈	PROPN
ejpam-4115	449	15	riu	riu	PROPN
ejpam-4115	449	16	.	.	PUNCT
ejpam-4115	450	1	note	note	VERB
ejpam-4115	450	2	that	that	SCONJ
ejpam-4115	450	3	∑n	∑n	PROPN
ejpam-4115	450	4	i=1	i=1	PROPN
ejpam-4115	450	5	ri	ri	PROPN
ejpam-4115	451	1	=	=	PUNCT
ejpam-4115	451	2	∑n	∑n	PROPN
ejpam-4115	451	3	i=1	i=1	PROPN
ejpam-4115	452	1	(	(	PUNCT
ejpam-4115	452	2	φu	φu	INTJ
ejpam-4115	452	3	(	(	PUNCT
ejpam-4115	452	4	−f(ti)(vi−ui))+	−f(ti)(vi−ui))+	NOUN
ejpam-4115	452	5	ϵ	ϵ	PROPN
ejpam-4115	452	6	n	n	PROPN
ejpam-4115	452	7	)	)	PUNCT
ejpam-4115	452	8	=	=	SYM
ejpam-4115	453	1	1	1	X
ejpam-4115	453	2	.	.	PUNCT
ejpam-4115	453	3	since	since	SCONJ
ejpam-4115	453	4	u	u	NOUN
ejpam-4115	453	5	is	be	AUX
ejpam-4115	453	6	convex	convex	ADJ
ejpam-4115	453	7	,	,	PUNCT
ejpam-4115	453	8	∑n	∑n	PROPN
ejpam-4115	453	9	i=1	i=1	PROPN
ejpam-4115	453	10	(	(	PUNCT
ejpam-4115	453	11	riu	riu	PROPN
ejpam-4115	453	12	)	)	PUNCT
ejpam-4115	453	13	⊆	⊆	NUM
ejpam-4115	453	14	u	u	NOUN
ejpam-4115	453	15	.	.	PUNCT
ejpam-4115	454	1	thus	thus	ADV
ejpam-4115	454	2	,	,	PUNCT
ejpam-4115	454	3	f	f	PROPN
ejpam-4115	454	4	is	be	AUX
ejpam-4115	454	5	sh	sh	PROPN
ejpam-4115	454	6	-	-	PUNCT
ejpam-4115	454	7	integrable	integrable	ADJ
ejpam-4115	454	8	and	and	CCONJ
ejpam-4115	454	9	(	(	PUNCT
ejpam-4115	454	10	sh	sh	INTJ
ejpam-4115	454	11	)	)	PUNCT
ejpam-4115	454	12	∫	∫	PROPN
ejpam-4115	455	1	b	b	PROPN
ejpam-4115	455	2	a	a	DET
ejpam-4115	455	3	f	f	X
ejpam-4115	455	4	=	=	SYM
ejpam-4115	455	5	f	f	PROPN
ejpam-4115	455	6	(	(	PUNCT
ejpam-4115	455	7	b)−	b)−	PROPN
ejpam-4115	455	8	f	f	X
ejpam-4115	455	9	(	(	PUNCT
ejpam-4115	455	10	a	a	NOUN
ejpam-4115	455	11	)	)	PUNCT
ejpam-4115	455	12	=	=	SYM
ejpam-4115	456	1	θ	θ	NOUN
ejpam-4115	456	2	−	−	PUNCT
ejpam-4115	456	3	θ	θ	NOUN
ejpam-4115	456	4	=	=	SYM
ejpam-4115	456	5	θ	θ	PROPN
ejpam-4115	456	6	.	.	PUNCT
ejpam-4115	456	7	theorem	theorem	NOUN
ejpam-4115	456	8	12	12	NUM
ejpam-4115	456	9	.	.	PUNCT
ejpam-4115	457	1	if	if	SCONJ
ejpam-4115	457	2	f	f	PROPN
ejpam-4115	457	3	:	:	PUNCT
ejpam-4115	458	1	[	[	X
ejpam-4115	458	2	a	a	X
ejpam-4115	458	3	,	,	PUNCT
ejpam-4115	458	4	b	b	NOUN
ejpam-4115	458	5	]	]	X
ejpam-4115	458	6	→	→	PUNCT
ejpam-4115	458	7	x	x	X
ejpam-4115	458	8	is	be	AUX
ejpam-4115	458	9	weak	weak	ADJ
ejpam-4115	458	10	denjoy	denjoy	NOUN
ejpam-4115	458	11	integrable	integrable	ADJ
ejpam-4115	458	12	on	on	ADP
ejpam-4115	458	13	[	[	X
ejpam-4115	458	14	a	a	X
ejpam-4115	458	15	,	,	PUNCT
ejpam-4115	458	16	b	b	NOUN
ejpam-4115	458	17	]	]	X
ejpam-4115	458	18	,	,	PUNCT
ejpam-4115	458	19	then	then	ADV
ejpam-4115	458	20	it	it	PRON
ejpam-4115	458	21	is	be	AUX
ejpam-4115	458	22	sh	sh	PRON
ejpam-4115	458	23	integrable	integrable	ADJ
ejpam-4115	458	24	on	on	ADP
ejpam-4115	458	25	[	[	X
ejpam-4115	458	26	a	a	X
ejpam-4115	458	27	,	,	PUNCT
ejpam-4115	458	28	b	b	NOUN
ejpam-4115	458	29	]	]	PUNCT
ejpam-4115	458	30	.	.	PUNCT
ejpam-4115	459	1	proof	proof	NOUN
ejpam-4115	459	2	.	.	PUNCT
ejpam-4115	460	1	let	let	VERB
ejpam-4115	460	2	f	f	NOUN
ejpam-4115	460	3	:	:	PUNCT
ejpam-4115	461	1	[	[	X
ejpam-4115	461	2	a	a	X
ejpam-4115	461	3	,	,	PUNCT
ejpam-4115	461	4	b	b	NOUN
ejpam-4115	461	5	]	]	X
ejpam-4115	461	6	→	→	PUNCT
ejpam-4115	461	7	x	x	PART
ejpam-4115	461	8	be	be	AUX
ejpam-4115	461	9	a	a	DET
ejpam-4115	461	10	weak	weak	ADJ
ejpam-4115	461	11	denjoy	denjoy	NOUN
ejpam-4115	461	12	primitive	primitive	ADJ
ejpam-4115	461	13	of	of	ADP
ejpam-4115	461	14	f	f	PROPN
ejpam-4115	461	15	.	.	PUNCT
ejpam-4115	462	1	let	let	VERB
ejpam-4115	462	2	u	u	PRON
ejpam-4115	462	3	be	be	AUX
ejpam-4115	462	4	a	a	DET
ejpam-4115	462	5	θ	θ	PROPN
ejpam-4115	462	6	-	-	PUNCT
ejpam-4115	462	7	nbd	nbd	PROPN
ejpam-4115	462	8	and	and	CCONJ
ejpam-4115	462	9	let	let	VERB
ejpam-4115	462	10	v	v	PART
ejpam-4115	462	11	be	be	AUX
ejpam-4115	462	12	an	an	DET
ejpam-4115	462	13	absorbing	absorbing	ADJ
ejpam-4115	462	14	,	,	PUNCT
ejpam-4115	462	15	balanced	balanced	ADJ
ejpam-4115	462	16	and	and	CCONJ
ejpam-4115	462	17	convex	convex	ADJ
ejpam-4115	462	18	θ	θ	PROPN
ejpam-4115	462	19	-	-	PUNCT
ejpam-4115	462	20	nbd	nbd	PROPN
ejpam-4115	462	21	such	such	ADJ
ejpam-4115	462	22	that	that	SCONJ
ejpam-4115	462	23	(	(	PUNCT
ejpam-4115	462	24	2	2	NUM
ejpam-4115	462	25	+	+	SYM
ejpam-4115	462	26	b	b	NOUN
ejpam-4115	462	27	−	−	NOUN
ejpam-4115	462	28	a)v	a)v	NOUN
ejpam-4115	462	29	⊆	⊆	NUM
ejpam-4115	462	30	u	u	NOUN
ejpam-4115	462	31	.	.	PUNCT
ejpam-4115	463	1	let	let	VERB
ejpam-4115	463	2	f0	f0	PROPN
ejpam-4115	463	3	=	=	SYM
ejpam-4115	463	4	f	f	PROPN
ejpam-4115	463	5	·	·	PUNCT
ejpam-4115	463	6	1∆(v	1∆(v	NUM
ejpam-4115	463	7	,	,	PUNCT
ejpam-4115	463	8	f	f	PROPN
ejpam-4115	463	9	,	,	PUNCT
ejpam-4115	463	10	f	f	PROPN
ejpam-4115	463	11	)	)	PUNCT
ejpam-4115	463	12	.	.	PUNCT
ejpam-4115	464	1	since	since	SCONJ
ejpam-4115	464	2	f	f	PROPN
ejpam-4115	464	3	weak	weak	ADJ
ejpam-4115	464	4	denjoy	denjoy	NOUN
ejpam-4115	464	5	integrable	integrable	ADJ
ejpam-4115	464	6	on	on	ADP
ejpam-4115	464	7	[	[	X
ejpam-4115	464	8	a	a	X
ejpam-4115	464	9	,	,	PUNCT
ejpam-4115	464	10	b	b	NOUN
ejpam-4115	464	11	]	]	X
ejpam-4115	464	12	,	,	PUNCT
ejpam-4115	464	13	∆(v	∆(v	PROPN
ejpam-4115	464	14	,	,	PUNCT
ejpam-4115	464	15	f	f	PROPN
ejpam-4115	464	16	,	,	PUNCT
ejpam-4115	464	17	f	f	X
ejpam-4115	464	18	)	)	PUNCT
ejpam-4115	464	19	is	be	AUX
ejpam-4115	464	20	of	of	ADP
ejpam-4115	464	21	measure	measure	NOUN
ejpam-4115	464	22	zero	zero	NUM
ejpam-4115	464	23	.	.	PUNCT
ejpam-4115	465	1	hence	hence	ADV
ejpam-4115	465	2	,	,	PUNCT
ejpam-4115	465	3	f0(t	f0(t	PROPN
ejpam-4115	465	4	)	)	PUNCT
ejpam-4115	465	5	=	=	SYM
ejpam-4115	465	6	θ	θ	NOUN
ejpam-4115	465	7	almost	almost	ADV
ejpam-4115	465	8	everywhere	everywhere	ADV
ejpam-4115	465	9	on	on	ADP
ejpam-4115	465	10	[	[	X
ejpam-4115	465	11	a	a	X
ejpam-4115	465	12	,	,	PUNCT
ejpam-4115	465	13	b	b	NOUN
ejpam-4115	465	14	]	]	PUNCT
ejpam-4115	465	15	.	.	PUNCT
ejpam-4115	466	1	by	by	ADP
ejpam-4115	466	2	theorem	theorem	NOUN
ejpam-4115	466	3	11	11	NUM
ejpam-4115	466	4	,	,	PUNCT
ejpam-4115	466	5	there	there	PRON
ejpam-4115	466	6	is	be	VERB
ejpam-4115	466	7	a	a	DET
ejpam-4115	466	8	gauge	gauge	NOUN
ejpam-4115	466	9	δ0	δ0	NOUN
ejpam-4115	466	10	such	such	ADJ
ejpam-4115	466	11	that	that	PRON
ejpam-4115	466	12	for	for	ADP
ejpam-4115	466	13	every	every	DET
ejpam-4115	466	14	δ0	δ0	NOUN
ejpam-4115	466	15	-	-	PUNCT
ejpam-4115	466	16	fine	fine	ADJ
ejpam-4115	466	17	partition	partition	NOUN
ejpam-4115	466	18	d	d	NOUN
ejpam-4115	466	19	=	=	PRON
ejpam-4115	466	20	{	{	PUNCT
ejpam-4115	466	21	(	(	PUNCT
ejpam-4115	466	22	[	[	X
ejpam-4115	466	23	ui	ui	NOUN
ejpam-4115	466	24	,	,	PUNCT
ejpam-4115	466	25	vi	vi	PROPN
ejpam-4115	466	26	]	]	PUNCT
ejpam-4115	466	27	,	,	PUNCT
ejpam-4115	466	28	ti	ti	NOUN
ejpam-4115	466	29	)	)	PUNCT
ejpam-4115	466	30	:	:	PUNCT
ejpam-4115	466	31	1	1	NUM
ejpam-4115	466	32	≤	≤	NUM
ejpam-4115	466	33	i	i	PRON
ejpam-4115	466	34	≤	≤	NOUN
ejpam-4115	466	35	n	n	CCONJ
ejpam-4115	466	36	}	}	PUNCT
ejpam-4115	466	37	of	of	ADP
ejpam-4115	466	38	[	[	X
ejpam-4115	466	39	a	a	X
ejpam-4115	466	40	,	,	PUNCT
ejpam-4115	466	41	b	b	NOUN
ejpam-4115	466	42	]	]	X
ejpam-4115	466	43	,	,	PUNCT
ejpam-4115	466	44	there	there	PRON
ejpam-4115	466	45	exist	exist	VERB
ejpam-4115	466	46	θ	θ	PROPN
ejpam-4115	466	47	-	-	PUNCT
ejpam-4115	466	48	nbds	nbds	NOUN
ejpam-4115	466	49	u1	u1	NOUN
ejpam-4115	466	50	,	,	PUNCT
ejpam-4115	466	51	u2	u2	NOUN
ejpam-4115	466	52	,	,	PUNCT
ejpam-4115	466	53	.	.	PUNCT
ejpam-4115	466	54	.	.	PUNCT
ejpam-4115	467	1	.	.	PUNCT
ejpam-4115	468	1	,	,	PUNCT
ejpam-4115	468	2	un	un	PROPN
ejpam-4115	468	3	with	with	ADP
ejpam-4115	468	4	∑n	∑n	PROPN
ejpam-4115	468	5	i=1	i=1	PROPN
ejpam-4115	468	6	ui	ui	PROPN
ejpam-4115	469	1	⊆	⊆	NUM
ejpam-4115	469	2	v	v	NOUN
ejpam-4115	469	3	and	and	CCONJ
ejpam-4115	469	4	−f0(ti)(vi	−f0(ti)(vi	NUM
ejpam-4115	469	5	−	−	PROPN
ejpam-4115	469	6	ui	ui	PROPN
ejpam-4115	469	7	)	)	PUNCT
ejpam-4115	469	8	∈	∈	PROPN
ejpam-4115	469	9	ui	ui	PROPN
ejpam-4115	469	10	.	.	PUNCT
ejpam-4115	470	1	now	now	ADV
ejpam-4115	470	2	,	,	PUNCT
ejpam-4115	470	3	since	since	SCONJ
ejpam-4115	470	4	f	f	PROPN
ejpam-4115	470	5	is	be	AUX
ejpam-4115	470	6	acg∗	acg∗	NOUN
ejpam-4115	470	7	on	on	ADP
ejpam-4115	470	8	[	[	X
ejpam-4115	470	9	a	a	X
ejpam-4115	470	10	,	,	PUNCT
ejpam-4115	470	11	b	b	NOUN
ejpam-4115	470	12	]	]	X
ejpam-4115	470	13	,	,	PUNCT
ejpam-4115	470	14	there	there	PRON
ejpam-4115	470	15	is	be	VERB
ejpam-4115	470	16	a	a	DET
ejpam-4115	470	17	disjoint	disjoint	ADJ
ejpam-4115	470	18	collection	collection	NOUN
ejpam-4115	470	19	{	{	PUNCT
ejpam-4115	470	20	yi}∞i=1	yi}∞i=1	NUM
ejpam-4115	470	21	of	of	ADP
ejpam-4115	470	22	subsets	subset	NOUN
ejpam-4115	470	23	of	of	ADP
ejpam-4115	470	24	[	[	X
ejpam-4115	470	25	a	a	X
ejpam-4115	470	26	,	,	PUNCT
ejpam-4115	470	27	b	b	NOUN
ejpam-4115	470	28	]	]	PUNCT
ejpam-4115	470	29	with	with	ADP
ejpam-4115	470	30	[	[	X
ejpam-4115	470	31	a	a	X
ejpam-4115	470	32	,	,	PUNCT
ejpam-4115	470	33	b	b	NOUN
ejpam-4115	470	34	]	]	X
ejpam-4115	470	35	=	=	SYM
ejpam-4115	470	36	⋃∞	⋃∞	ADP
ejpam-4115	470	37	i=1	i=1	PROPN
ejpam-4115	470	38	yi	yi	PROPN
ejpam-4115	470	39	such	such	ADJ
ejpam-4115	470	40	that	that	SCONJ
ejpam-4115	470	41	f	f	PROPN
ejpam-4115	470	42	is	be	AUX
ejpam-4115	470	43	ac∗(yi	ac∗(yi	ADV
ejpam-4115	470	44	)	)	PUNCT
ejpam-4115	470	45	for	for	ADP
ejpam-4115	470	46	all	all	DET
ejpam-4115	470	47	i	i	PRON
ejpam-4115	470	48	∈	∈	PROPN
ejpam-4115	470	49	n.	n.	NOUN
ejpam-4115	470	50	for	for	ADP
ejpam-4115	470	51	each	each	DET
ejpam-4115	470	52	i	i	PROPN
ejpam-4115	470	53	∈	∈	PROPN
ejpam-4115	470	54	n	n	CCONJ
ejpam-4115	470	55	,	,	PUNCT
ejpam-4115	470	56	let	let	VERB
ejpam-4115	470	57	ei	ei	INTJ
ejpam-4115	470	58	=	=	PUNCT
ejpam-4115	470	59	∆(u	∆(u	PROPN
ejpam-4115	470	60	,	,	PUNCT
ejpam-4115	470	61	f	f	PROPN
ejpam-4115	470	62	,	,	PUNCT
ejpam-4115	470	63	f	f	X
ejpam-4115	470	64	)	)	PUNCT
ejpam-4115	470	65	∩	∩	ADJ
ejpam-4115	470	66	yi	yi	PROPN
ejpam-4115	470	67	.	.	PUNCT
ejpam-4115	471	1	then	then	ADV
ejpam-4115	471	2	f	f	PROPN
ejpam-4115	471	3	is	be	AUX
ejpam-4115	471	4	r.	r.	PROPN
ejpam-4115	471	5	e.	e.	PROPN
ejpam-4115	471	6	maza	maza	PROPN
ejpam-4115	471	7	,	,	PUNCT
ejpam-4115	471	8	s.	s.	PROPN
ejpam-4115	471	9	r.	r.	PROPN
ejpam-4115	471	10	canoy	canoy	PROPN
ejpam-4115	471	11	,	,	PUNCT
ejpam-4115	471	12	jr	jr	PROPN
ejpam-4115	471	13	.	.	PROPN
ejpam-4115	471	14	/	/	SYM
ejpam-4115	471	15	eur	eur	PROPN
ejpam-4115	471	16	.	.	PUNCT
ejpam-4115	472	1	j.	j.	PROPN
ejpam-4115	472	2	pure	pure	PROPN
ejpam-4115	472	3	appl	appl	PROPN
ejpam-4115	472	4	.	.	PROPN
ejpam-4115	472	5	math	math	PROPN
ejpam-4115	472	6	,	,	PUNCT
ejpam-4115	472	7	14	14	NUM
ejpam-4115	472	8	(	(	PUNCT
ejpam-4115	472	9	4	4	NUM
ejpam-4115	472	10	)	)	PUNCT
ejpam-4115	472	11	(	(	PUNCT
ejpam-4115	472	12	2021	2021	NUM
ejpam-4115	472	13	)	)	PUNCT
ejpam-4115	472	14	,	,	PUNCT
ejpam-4115	472	15	1169	1169	NUM
ejpam-4115	472	16	-	-	SYM
ejpam-4115	472	17	1183	1183	NUM
ejpam-4115	472	18	1179	1179	NUM
ejpam-4115	472	19	ac∗(ei	ac∗(ei	PROPN
ejpam-4115	472	20	)	)	PUNCT
ejpam-4115	472	21	and	and	CCONJ
ejpam-4115	472	22	ei	ei	NOUN
ejpam-4115	472	23	is	be	AUX
ejpam-4115	472	24	of	of	ADP
ejpam-4115	472	25	measure	measure	NOUN
ejpam-4115	472	26	zero	zero	NUM
ejpam-4115	472	27	for	for	ADP
ejpam-4115	472	28	all	all	PRON
ejpam-4115	472	29	i	i	PRON
ejpam-4115	472	30	∈	∈	PROPN
ejpam-4115	472	31	n.	n.	NOUN
ejpam-4115	472	32	by	by	ADP
ejpam-4115	472	33	definition	definition	NOUN
ejpam-4115	472	34	,	,	PUNCT
ejpam-4115	472	35	for	for	ADP
ejpam-4115	472	36	each	each	DET
ejpam-4115	472	37	i	i	PROPN
ejpam-4115	472	38	∈	∈	PROPN
ejpam-4115	472	39	n	n	CCONJ
ejpam-4115	472	40	,	,	PUNCT
ejpam-4115	472	41	there	there	PRON
ejpam-4115	472	42	is	be	VERB
ejpam-4115	472	43	an	an	DET
ejpam-4115	472	44	ηi	ηi	NOUN
ejpam-4115	472	45	>	>	PUNCT
ejpam-4115	472	46	0	0	NUM
ejpam-4115	472	47	such	such	ADJ
ejpam-4115	472	48	that	that	PRON
ejpam-4115	472	49	for	for	ADP
ejpam-4115	472	50	every	every	DET
ejpam-4115	472	51	partial	partial	ADJ
ejpam-4115	472	52	partition	partition	NOUN
ejpam-4115	472	53	d	d	NOUN
ejpam-4115	472	54	=	=	PRON
ejpam-4115	472	55	{	{	PUNCT
ejpam-4115	472	56	[	[	X
ejpam-4115	472	57	uj	uj	X
ejpam-4115	472	58	,	,	PUNCT
ejpam-4115	472	59	vj	vj	X
ejpam-4115	472	60	]	]	X
ejpam-4115	472	61	:	:	PUNCT
ejpam-4115	472	62	1	1	NUM
ejpam-4115	472	63	≤	≤	NUM
ejpam-4115	472	64	j	j	PROPN
ejpam-4115	472	65	≤	≤	PROPN
ejpam-4115	472	66	n	n	CCONJ
ejpam-4115	472	67	}	}	PUNCT
ejpam-4115	472	68	of	of	ADP
ejpam-4115	472	69	[	[	X
ejpam-4115	472	70	a	a	X
ejpam-4115	472	71	,	,	PUNCT
ejpam-4115	472	72	b	b	NOUN
ejpam-4115	472	73	]	]	PUNCT
ejpam-4115	472	74	with	with	ADP
ejpam-4115	472	75	uj	uj	PROPN
ejpam-4115	472	76	or	or	CCONJ
ejpam-4115	472	77	vj	vj	INTJ
ejpam-4115	472	78	∈	∈	PROPN
ejpam-4115	472	79	ei	ei	NOUN
ejpam-4115	472	80	and	and	CCONJ
ejpam-4115	472	81	∑n	∑n	PROPN
ejpam-4115	472	82	j=1(vj	j=1(vj	NOUN
ejpam-4115	472	83	−	−	PROPN
ejpam-4115	472	84	uj	uj	PROPN
ejpam-4115	472	85	)	)	PUNCT
ejpam-4115	472	86	<	<	X
ejpam-4115	472	87	ηi	ηi	PROPN
ejpam-4115	472	88	,	,	PUNCT
ejpam-4115	472	89	there	there	PRON
ejpam-4115	472	90	exist	exist	VERB
ejpam-4115	472	91	θ	θ	PROPN
ejpam-4115	472	92	-	-	PUNCT
ejpam-4115	472	93	nbds	nbds	NOUN
ejpam-4115	472	94	u1	u1	NOUN
ejpam-4115	472	95	,	,	PUNCT
ejpam-4115	472	96	u2	u2	NOUN
ejpam-4115	472	97	,	,	PUNCT
ejpam-4115	472	98	.	.	PUNCT
ejpam-4115	472	99	.	.	PUNCT
ejpam-4115	472	100	.	.	PUNCT
ejpam-4115	473	1	,	,	PUNCT
ejpam-4115	473	2	un	un	PROPN
ejpam-4115	473	3	such	such	ADJ
ejpam-4115	473	4	that∑n	that∑n	NOUN
ejpam-4115	473	5	j=1	j=1	PROPN
ejpam-4115	473	6	uj	uj	PROPN
ejpam-4115	473	7	⊆	⊆	NUM
ejpam-4115	473	8	1	1	NUM
ejpam-4115	473	9	2i	2i	NUM
ejpam-4115	473	10	v	v	NOUN
ejpam-4115	473	11	and	and	CCONJ
ejpam-4115	473	12	f	f	PROPN
ejpam-4115	473	13	(	(	PUNCT
ejpam-4115	473	14	vj)−f	vj)−f	PROPN
ejpam-4115	473	15	(	(	PUNCT
ejpam-4115	473	16	uj	uj	PROPN
ejpam-4115	473	17	)	)	PUNCT
ejpam-4115	473	18	∈	∈	PROPN
ejpam-4115	473	19	uj	uj	PROPN
ejpam-4115	473	20	for	for	ADP
ejpam-4115	473	21	1	1	NUM
ejpam-4115	473	22	≤	≤	NUM
ejpam-4115	473	23	j	j	PROPN
ejpam-4115	473	24	≤	≤	PROPN
ejpam-4115	473	25	n.	n.	NOUN
ejpam-4115	473	26	also	also	ADV
ejpam-4115	473	27	,	,	PUNCT
ejpam-4115	473	28	since	since	SCONJ
ejpam-4115	473	29	m(ei	m(ei	PROPN
ejpam-4115	473	30	)	)	PUNCT
ejpam-4115	473	31	=	=	SYM
ejpam-4115	473	32	0	0	NUM
ejpam-4115	473	33	for	for	ADP
ejpam-4115	473	34	all	all	PRON
ejpam-4115	473	35	i	i	PRON
ejpam-4115	473	36	∈	∈	PROPN
ejpam-4115	473	37	n	n	CCONJ
ejpam-4115	473	38	,	,	PUNCT
ejpam-4115	473	39	there	there	PRON
ejpam-4115	473	40	is	be	VERB
ejpam-4115	473	41	a	a	DET
ejpam-4115	473	42	collection	collection	NOUN
ejpam-4115	473	43	{	{	PUNCT
ejpam-4115	473	44	gi}∞i=1	gi}∞i=1	X
ejpam-4115	473	45	of	of	ADP
ejpam-4115	473	46	open	open	ADJ
ejpam-4115	473	47	sets	set	NOUN
ejpam-4115	473	48	such	such	ADJ
ejpam-4115	473	49	that	that	DET
ejpam-4115	473	50	ei	ei	NOUN
ejpam-4115	473	51	⊆	⊆	NUM
ejpam-4115	473	52	gi	gi	NOUN
ejpam-4115	473	53	and	and	CCONJ
ejpam-4115	473	54	m(gi	m(gi	NOUN
ejpam-4115	473	55	)	)	PUNCT
ejpam-4115	473	56	<	<	X
ejpam-4115	473	57	ηi	ηi	PROPN
ejpam-4115	473	58	for	for	ADP
ejpam-4115	473	59	all	all	DET
ejpam-4115	473	60	i	i	PRON
ejpam-4115	473	61	∈	∈	PROPN
ejpam-4115	473	62	n.	n.	NOUN
ejpam-4115	473	63	if	if	SCONJ
ejpam-4115	473	64	t	t	PROPN
ejpam-4115	473	65	∈	∈	PROPN
ejpam-4115	473	66	∆(v	∆(v	PROPN
ejpam-4115	473	67	,	,	PUNCT
ejpam-4115	473	68	f	f	PROPN
ejpam-4115	473	69	,	,	PUNCT
ejpam-4115	473	70	f	f	PROPN
ejpam-4115	473	71	)	)	PUNCT
ejpam-4115	473	72	,	,	PUNCT
ejpam-4115	473	73	then	then	ADV
ejpam-4115	473	74	t	t	PROPN
ejpam-4115	473	75	∈	∈	PROPN
ejpam-4115	473	76	ej	ej	PROPN
ejpam-4115	473	77	⊂	⊂	PROPN
ejpam-4115	473	78	gj	gj	PROPN
ejpam-4115	473	79	for	for	ADP
ejpam-4115	473	80	some	some	DET
ejpam-4115	473	81	j	j	PROPN
ejpam-4115	473	82	∈	∈	PROPN
ejpam-4115	473	83	n.	n.	NOUN
ejpam-4115	473	84	in	in	ADP
ejpam-4115	473	85	this	this	DET
ejpam-4115	473	86	case	case	NOUN
ejpam-4115	473	87	,	,	PUNCT
ejpam-4115	473	88	we	we	PRON
ejpam-4115	473	89	choose	choose	VERB
ejpam-4115	473	90	δ1(t	δ1(t	ADV
ejpam-4115	473	91	)	)	PUNCT
ejpam-4115	473	92	>	>	X
ejpam-4115	473	93	0	0	PUNCT
ejpam-4115	473	94	be	be	AUX
ejpam-4115	473	95	such	such	ADJ
ejpam-4115	473	96	that	that	SCONJ
ejpam-4115	473	97	(	(	PUNCT
ejpam-4115	473	98	t−	t−	PROPN
ejpam-4115	473	99	δ1(t	δ1(t	PROPN
ejpam-4115	473	100	)	)	PUNCT
ejpam-4115	473	101	,	,	PUNCT
ejpam-4115	473	102	t+	t+	X
ejpam-4115	473	103	δ1(t	δ1(t	ADV
ejpam-4115	473	104	)	)	PUNCT
ejpam-4115	473	105	)	)	PUNCT
ejpam-4115	474	1	⊆	⊆	NUM
ejpam-4115	474	2	gj	gj	NOUN
ejpam-4115	474	3	.	.	PUNCT
ejpam-4115	475	1	if	if	SCONJ
ejpam-4115	475	2	t	t	PROPN
ejpam-4115	475	3	∈	∈	PROPN
ejpam-4115	475	4	[	[	X
ejpam-4115	475	5	a	a	X
ejpam-4115	475	6	,	,	PUNCT
ejpam-4115	475	7	b	b	NOUN
ejpam-4115	475	8	]	]	X
ejpam-4115	475	9	\∆(v	\∆(v	NOUN
ejpam-4115	475	10	,	,	PUNCT
ejpam-4115	475	11	f	f	PROPN
ejpam-4115	475	12	,	,	PUNCT
ejpam-4115	475	13	f	f	PROPN
ejpam-4115	475	14	)	)	PUNCT
ejpam-4115	475	15	,	,	PUNCT
ejpam-4115	475	16	then	then	ADV
ejpam-4115	475	17	let	let	VERB
ejpam-4115	475	18	δ2(t	δ2(t	PRON
ejpam-4115	475	19	)	)	PUNCT
ejpam-4115	475	20	>	>	X
ejpam-4115	475	21	0	0	NUM
ejpam-4115	475	22	such	such	ADJ
ejpam-4115	475	23	that	that	SCONJ
ejpam-4115	475	24	f	f	PROPN
ejpam-4115	475	25	(	(	PUNCT
ejpam-4115	475	26	v)−	v)−	PROPN
ejpam-4115	475	27	f	f	X
ejpam-4115	475	28	(	(	PUNCT
ejpam-4115	475	29	u)−	u)−	PROPN
ejpam-4115	475	30	f(t)(v	f(t)(v	X
ejpam-4115	475	31	−	−	NOUN
ejpam-4115	475	32	u	u	NOUN
ejpam-4115	475	33	)	)	PUNCT
ejpam-4115	475	34	∈	∈	PROPN
ejpam-4115	475	35	(	(	PUNCT
ejpam-4115	475	36	v	v	NOUN
ejpam-4115	475	37	−	−	NOUN
ejpam-4115	475	38	u)v	u)v	PUNCT
ejpam-4115	475	39	whenever	whenever	SCONJ
ejpam-4115	475	40	t	t	PROPN
ejpam-4115	475	41	∈	∈	PROPN
ejpam-4115	475	42	[	[	X
ejpam-4115	475	43	u	u	NOUN
ejpam-4115	475	44	,	,	PUNCT
ejpam-4115	475	45	v	v	NOUN
ejpam-4115	475	46	]	]	X
ejpam-4115	475	47	⊆	⊆	NUM
ejpam-4115	475	48	(	(	PUNCT
ejpam-4115	475	49	t−	t−	PROPN
ejpam-4115	475	50	δ2(t	δ2(t	PROPN
ejpam-4115	475	51	)	)	PUNCT
ejpam-4115	475	52	,	,	PUNCT
ejpam-4115	475	53	t+	t+	X
ejpam-4115	475	54	δ2(t	δ2(t	NOUN
ejpam-4115	475	55	)	)	PUNCT
ejpam-4115	475	56	)	)	PUNCT
ejpam-4115	475	57	.	.	PUNCT
ejpam-4115	476	1	define	define	VERB
ejpam-4115	476	2	δ	δ	PROPN
ejpam-4115	476	3	as	as	SCONJ
ejpam-4115	476	4	follows	follow	VERB
ejpam-4115	476	5	:	:	PUNCT
ejpam-4115	476	6	δ(t	δ(t	X
ejpam-4115	476	7	)	)	PUNCT
ejpam-4115	477	1	=	=	PRON
ejpam-4115	477	2	{	{	PUNCT
ejpam-4115	477	3	min{δ0(t	min{δ0(t	PROPN
ejpam-4115	477	4	)	)	PUNCT
ejpam-4115	477	5	,	,	PUNCT
ejpam-4115	477	6	δ1(t	δ1(t	X
ejpam-4115	477	7	)	)	PUNCT
ejpam-4115	477	8	}	}	PUNCT
ejpam-4115	477	9	if	if	SCONJ
ejpam-4115	477	10	t	t	PROPN
ejpam-4115	477	11	∈	∈	PROPN
ejpam-4115	477	12	∆(v	∆(v	PROPN
ejpam-4115	477	13	,	,	PUNCT
ejpam-4115	477	14	f	f	PROPN
ejpam-4115	477	15	,	,	PUNCT
ejpam-4115	477	16	f	f	X
ejpam-4115	477	17	)	)	PUNCT
ejpam-4115	477	18	δ2(t	δ2(t	NOUN
ejpam-4115	477	19	)	)	PUNCT
ejpam-4115	477	20	otherwise	otherwise	ADV
ejpam-4115	477	21	.	.	PUNCT
ejpam-4115	477	22	.	.	PUNCT
ejpam-4115	478	1	let	let	VERB
ejpam-4115	478	2	d	d	NOUN
ejpam-4115	478	3	=	=	PRON
ejpam-4115	478	4	{	{	PUNCT
ejpam-4115	478	5	(	(	PUNCT
ejpam-4115	478	6	[	[	X
ejpam-4115	478	7	uj	uj	X
ejpam-4115	478	8	,	,	PUNCT
ejpam-4115	478	9	vj	vj	X
ejpam-4115	478	10	]	]	X
ejpam-4115	478	11	,	,	PUNCT
ejpam-4115	478	12	tj	tj	PROPN
ejpam-4115	478	13	)	)	PUNCT
ejpam-4115	478	14	:	:	PUNCT
ejpam-4115	478	15	1	1	NUM
ejpam-4115	478	16	≤	≤	NUM
ejpam-4115	478	17	j	j	PROPN
ejpam-4115	478	18	≤	≤	PROPN
ejpam-4115	478	19	n	n	CCONJ
ejpam-4115	478	20	}	}	PUNCT
ejpam-4115	478	21	be	be	AUX
ejpam-4115	478	22	a	a	DET
ejpam-4115	478	23	δ	δ	NOUN
ejpam-4115	478	24	-	-	PUNCT
ejpam-4115	478	25	fine	fine	ADJ
ejpam-4115	478	26	partition	partition	NOUN
ejpam-4115	478	27	of	of	ADP
ejpam-4115	478	28	[	[	X
ejpam-4115	478	29	a	a	X
ejpam-4115	478	30	,	,	PUNCT
ejpam-4115	478	31	b	b	NOUN
ejpam-4115	478	32	]	]	X
ejpam-4115	478	33	.	.	PUNCT
ejpam-4115	479	1	then	then	ADV
ejpam-4115	479	2	d	d	X
ejpam-4115	479	3	=	=	PUNCT
ejpam-4115	479	4	d1∪d2	d1∪d2	PRON
ejpam-4115	479	5	where	where	SCONJ
ejpam-4115	479	6	d1	d1	PROPN
ejpam-4115	479	7	=	=	PUNCT
ejpam-4115	479	8	{	{	PUNCT
ejpam-4115	479	9	(	(	PUNCT
ejpam-4115	479	10	[	[	X
ejpam-4115	479	11	uj	uj	X
ejpam-4115	479	12	,	,	PUNCT
ejpam-4115	479	13	vj	vj	X
ejpam-4115	479	14	]	]	X
ejpam-4115	479	15	,	,	PUNCT
ejpam-4115	479	16	tj	tj	PROPN
ejpam-4115	479	17	)	)	PUNCT
ejpam-4115	479	18	:	:	PUNCT
ejpam-4115	479	19	tj	tj	PROPN
ejpam-4115	479	20	∈	∈	PROPN
ejpam-4115	479	21	∆(v	∆(v	PROPN
ejpam-4115	479	22	,	,	PUNCT
ejpam-4115	479	23	f	f	PROPN
ejpam-4115	479	24	,	,	PUNCT
ejpam-4115	479	25	f	f	NOUN
ejpam-4115	479	26	)	)	PUNCT
ejpam-4115	479	27	}	}	PUNCT
ejpam-4115	479	28	and	and	CCONJ
ejpam-4115	479	29	d2	d2	PROPN
ejpam-4115	479	30	=	=	SYM
ejpam-4115	479	31	{	{	PUNCT
ejpam-4115	479	32	(	(	PUNCT
ejpam-4115	479	33	[	[	X
ejpam-4115	479	34	uj	uj	X
ejpam-4115	479	35	,	,	PUNCT
ejpam-4115	479	36	vj	vj	X
ejpam-4115	479	37	]	]	X
ejpam-4115	479	38	,	,	PUNCT
ejpam-4115	479	39	tj	tj	PROPN
ejpam-4115	479	40	)	)	PUNCT
ejpam-4115	479	41	:	:	PUNCT
ejpam-4115	479	42	tj	tj	PROPN
ejpam-4115	479	43	∈	∈	PROPN
ejpam-4115	479	44	[	[	X
ejpam-4115	479	45	a	a	X
ejpam-4115	479	46	,	,	PUNCT
ejpam-4115	479	47	b	b	NOUN
ejpam-4115	479	48	]	]	X
ejpam-4115	479	49	\∆(v	\∆(v	NOUN
ejpam-4115	479	50	,	,	PUNCT
ejpam-4115	479	51	f	f	PROPN
ejpam-4115	479	52	,	,	PUNCT
ejpam-4115	479	53	f	f	PROPN
ejpam-4115	479	54	)	)	PUNCT
ejpam-4115	479	55	}	}	PUNCT
ejpam-4115	479	56	.	.	PUNCT
ejpam-4115	480	1	let	let	VERB
ejpam-4115	480	2	s	s	PRON
ejpam-4115	480	3	=	=	PUNCT
ejpam-4115	480	4	{	{	PUNCT
ejpam-4115	480	5	i	i	NOUN
ejpam-4115	480	6	∈	∈	PROPN
ejpam-4115	480	7	n	n	CCONJ
ejpam-4115	480	8	:	:	PUNCT
ejpam-4115	480	9	tj	tj	PROPN
ejpam-4115	480	10	∈	∈	PROPN
ejpam-4115	480	11	ei	ei	NOUN
ejpam-4115	480	12	for	for	ADP
ejpam-4115	480	13	some	some	DET
ejpam-4115	480	14	1	1	NUM
ejpam-4115	480	15	≤	≤	NUM
ejpam-4115	480	16	j	j	PROPN
ejpam-4115	480	17	≤	≤	PROPN
ejpam-4115	480	18	n	n	CCONJ
ejpam-4115	480	19	}	}	PUNCT
ejpam-4115	480	20	.	.	PUNCT
ejpam-4115	481	1	for	for	ADP
ejpam-4115	481	2	each	each	DET
ejpam-4115	481	3	i	i	PRON
ejpam-4115	481	4	∈	∈	PROPN
ejpam-4115	481	5	s	s	VERB
ejpam-4115	481	6	,	,	PUNCT
ejpam-4115	481	7	let	let	VERB
ejpam-4115	481	8	d1,i	d1,i	PROPN
ejpam-4115	481	9	=	=	PRON
ejpam-4115	481	10	{	{	PUNCT
ejpam-4115	481	11	(	(	PUNCT
ejpam-4115	481	12	[	[	X
ejpam-4115	481	13	uj	uj	X
ejpam-4115	481	14	,	,	PUNCT
ejpam-4115	481	15	vj	vj	X
ejpam-4115	481	16	]	]	X
ejpam-4115	481	17	,	,	PUNCT
ejpam-4115	481	18	tj	tj	PROPN
ejpam-4115	481	19	)	)	PUNCT
ejpam-4115	481	20	∈	∈	NOUN
ejpam-4115	481	21	d1	d1	NOUN
ejpam-4115	481	22	:	:	PUNCT
ejpam-4115	481	23	tj	tj	PROPN
ejpam-4115	481	24	∈	∈	PROPN
ejpam-4115	481	25	ei	ei	X
ejpam-4115	481	26	}	}	PUNCT
ejpam-4115	481	27	.	.	PUNCT
ejpam-4115	482	1	then	then	ADV
ejpam-4115	482	2	d1	d1	PROPN
ejpam-4115	482	3	=	=	PUNCT
ejpam-4115	482	4	⋃	⋃	ADP
ejpam-4115	482	5	i∈s	i∈s	ADJ
ejpam-4115	482	6	d1,i	d1,i	PROPN
ejpam-4115	482	7	.	.	PUNCT
ejpam-4115	483	1	since	since	SCONJ
ejpam-4115	483	2	d1	d1	PROPN
ejpam-4115	483	3	is	be	AUX
ejpam-4115	483	4	a	a	DET
ejpam-4115	483	5	δ0	δ0	NOUN
ejpam-4115	483	6	-	-	PUNCT
ejpam-4115	483	7	fine	fine	ADJ
ejpam-4115	483	8	partial	partial	ADJ
ejpam-4115	483	9	partition	partition	NOUN
ejpam-4115	483	10	of	of	ADP
ejpam-4115	483	11	[	[	X
ejpam-4115	483	12	a	a	X
ejpam-4115	483	13	,	,	PUNCT
ejpam-4115	483	14	b	b	NOUN
ejpam-4115	483	15	]	]	X
ejpam-4115	483	16	,	,	PUNCT
ejpam-4115	483	17	there	there	PRON
ejpam-4115	483	18	exist	exist	VERB
ejpam-4115	483	19	θ	θ	PROPN
ejpam-4115	483	20	-	-	PUNCT
ejpam-4115	483	21	nbds	nbds	NOUN
ejpam-4115	483	22	vi	vi	PROPN
ejpam-4115	483	23	,	,	PUNCT
ejpam-4115	483	24	j	j	PROPN
ejpam-4115	483	25	such	such	ADJ
ejpam-4115	483	26	that	that	SCONJ
ejpam-4115	483	27	∑	∑	PUNCT
ejpam-4115	483	28	i∈s(d	i∈s(d	PROPN
ejpam-4115	483	29	)	)	PUNCT
ejpam-4115	483	30	∑	∑	PUNCT
ejpam-4115	483	31	vi	vi	PROPN
ejpam-4115	483	32	,	,	PUNCT
ejpam-4115	483	33	j	j	PROPN
ejpam-4115	483	34	⊆	⊆	NUM
ejpam-4115	483	35	v	v	NOUN
ejpam-4115	483	36	and	and	CCONJ
ejpam-4115	483	37	−f(tj)(vj	−f(tj)(vj	VERB
ejpam-4115	483	38	−	−	PROPN
ejpam-4115	483	39	uj	uj	PROPN
ejpam-4115	483	40	)	)	PUNCT
ejpam-4115	483	41	∈	∈	PROPN
ejpam-4115	483	42	vi	vi	PROPN
ejpam-4115	483	43	,	,	PUNCT
ejpam-4115	483	44	j	j	NOUN
ejpam-4115	483	45	for	for	ADP
ejpam-4115	483	46	(	(	PUNCT
ejpam-4115	483	47	[	[	X
ejpam-4115	483	48	uj	uj	X
ejpam-4115	483	49	,	,	PUNCT
ejpam-4115	483	50	vj	vj	X
ejpam-4115	483	51	]	]	X
ejpam-4115	483	52	,	,	PUNCT
ejpam-4115	483	53	tj	tj	PROPN
ejpam-4115	483	54	)	)	PUNCT
ejpam-4115	483	55	∈	∈	PROPN
ejpam-4115	483	56	d1,i	d1,i	PROPN
ejpam-4115	483	57	.	.	PUNCT
ejpam-4115	484	1	also	also	ADV
ejpam-4115	484	2	,	,	PUNCT
ejpam-4115	484	3	for	for	SCONJ
ejpam-4115	484	4	each	each	DET
ejpam-4115	484	5	i	i	PRON
ejpam-4115	484	6	∈	∈	PROPN
ejpam-4115	484	7	s	s	PART
ejpam-4115	484	8	,	,	PUNCT
ejpam-4115	484	9	we	we	PRON
ejpam-4115	484	10	have	have	VERB
ejpam-4115	484	11	⋃	⋃	PROPN
ejpam-4115	484	12	tj∈ei	tj∈ei	PUNCT
ejpam-4115	484	13	(	(	PUNCT
ejpam-4115	484	14	uj	uj	PROPN
ejpam-4115	484	15	,	,	PUNCT
ejpam-4115	484	16	vj	vj	PROPN
ejpam-4115	484	17	)	)	PUNCT
ejpam-4115	484	18	⊆	⊆	NUM
ejpam-4115	484	19	gi	gi	NOUN
ejpam-4115	484	20	implying	imply	VERB
ejpam-4115	484	21	that	that	SCONJ
ejpam-4115	484	22	(	(	PUNCT
ejpam-4115	484	23	d1,i	d1,i	PROPN
ejpam-4115	484	24	)	)	PUNCT
ejpam-4115	484	25	∑	∑	PROPN
ejpam-4115	484	26	(	(	PUNCT
ejpam-4115	484	27	vj	vj	INTJ
ejpam-4115	484	28	−	−	PROPN
ejpam-4115	484	29	uj	uj	PROPN
ejpam-4115	484	30	)	)	PUNCT
ejpam-4115	484	31	<	<	X
ejpam-4115	484	32	ηi	ηi	PROPN
ejpam-4115	484	33	.	.	PUNCT
ejpam-4115	485	1	hence	hence	ADV
ejpam-4115	485	2	,	,	PUNCT
ejpam-4115	485	3	there	there	PRON
ejpam-4115	485	4	are	be	VERB
ejpam-4115	485	5	θ	θ	PROPN
ejpam-4115	485	6	-	-	PUNCT
ejpam-4115	485	7	nbds	nbds	PROPN
ejpam-4115	485	8	ui	ui	PROPN
ejpam-4115	485	9	,	,	PUNCT
ejpam-4115	485	10	j	j	PROPN
ejpam-4115	485	11	such	such	ADJ
ejpam-4115	485	12	that	that	SCONJ
ejpam-4115	485	13	(	(	PUNCT
ejpam-4115	485	14	d1,i	d1,i	PROPN
ejpam-4115	485	15	)	)	PUNCT
ejpam-4115	485	16	∑	∑	PROPN
ejpam-4115	485	17	ui	ui	PROPN
ejpam-4115	485	18	,	,	PUNCT
ejpam-4115	485	19	j	j	PROPN
ejpam-4115	485	20	⊆	⊆	NUM
ejpam-4115	485	21	1	1	NUM
ejpam-4115	485	22	2i	2i	NUM
ejpam-4115	485	23	v	v	NOUN
ejpam-4115	485	24	and	and	CCONJ
ejpam-4115	485	25	f	f	PROPN
ejpam-4115	485	26	(	(	PUNCT
ejpam-4115	485	27	vj)−f	vj)−f	PROPN
ejpam-4115	485	28	(	(	PUNCT
ejpam-4115	485	29	uj	uj	PROPN
ejpam-4115	485	30	)	)	PUNCT
ejpam-4115	485	31	∈	∈	PROPN
ejpam-4115	485	32	ui	ui	PROPN
ejpam-4115	485	33	,	,	PUNCT
ejpam-4115	485	34	j	j	PROPN
ejpam-4115	485	35	for	for	ADP
ejpam-4115	485	36	(	(	PUNCT
ejpam-4115	485	37	[	[	X
ejpam-4115	485	38	uj	uj	X
ejpam-4115	485	39	,	,	PUNCT
ejpam-4115	485	40	vj	vj	X
ejpam-4115	485	41	]	]	X
ejpam-4115	485	42	,	,	PUNCT
ejpam-4115	485	43	tj	tj	PROPN
ejpam-4115	485	44	)	)	PUNCT
ejpam-4115	485	45	∈	∈	PROPN
ejpam-4115	485	46	d1,i	d1,i	PROPN
ejpam-4115	485	47	.	.	PUNCT
ejpam-4115	486	1	consequently	consequently	ADV
ejpam-4115	486	2	,	,	PUNCT
ejpam-4115	486	3	f	f	PROPN
ejpam-4115	486	4	(	(	PUNCT
ejpam-4115	486	5	vj)−f	vj)−f	PROPN
ejpam-4115	486	6	(	(	PUNCT
ejpam-4115	486	7	uj)−f(ti)(vj−uj	uj)−f(ti)(vj−uj	NOUN
ejpam-4115	486	8	)	)	PUNCT
ejpam-4115	486	9	∈	∈	PROPN
ejpam-4115	486	10	ui	ui	PROPN
ejpam-4115	486	11	,	,	PUNCT
ejpam-4115	486	12	j+vi	j+vi	PROPN
ejpam-4115	486	13	,	,	PUNCT
ejpam-4115	486	14	j	j	PROPN
ejpam-4115	486	15	for	for	ADP
ejpam-4115	486	16	(	(	PUNCT
ejpam-4115	486	17	[	[	X
ejpam-4115	486	18	uj	uj	X
ejpam-4115	486	19	,	,	PUNCT
ejpam-4115	486	20	vj	vj	X
ejpam-4115	486	21	]	]	X
ejpam-4115	486	22	,	,	PUNCT
ejpam-4115	486	23	tj	tj	PROPN
ejpam-4115	486	24	)	)	PUNCT
ejpam-4115	486	25	∈	∈	PROPN
ejpam-4115	486	26	d1,i	d1,i	PROPN
ejpam-4115	486	27	.	.	PUNCT
ejpam-4115	487	1	let	let	VERB
ejpam-4115	487	2	k	k	PROPN
ejpam-4115	487	3	=	=	PRON
ejpam-4115	487	4	{	{	PUNCT
ejpam-4115	487	5	j	j	PROPN
ejpam-4115	487	6	∈	∈	PROPN
ejpam-4115	487	7	{	{	PUNCT
ejpam-4115	487	8	1	1	NUM
ejpam-4115	487	9	,	,	PUNCT
ejpam-4115	487	10	2	2	NUM
ejpam-4115	487	11	,	,	PUNCT
ejpam-4115	487	12	.	.	PUNCT
ejpam-4115	487	13	.	.	PUNCT
ejpam-4115	488	1	.	.	PUNCT
ejpam-4115	489	1	,	,	PUNCT
ejpam-4115	489	2	n	n	CCONJ
ejpam-4115	489	3	}	}	PUNCT
ejpam-4115	489	4	:	:	PUNCT
ejpam-4115	489	5	tj	tj	PART
ejpam-4115	489	6	∈	∈	PROPN
ejpam-4115	490	1	[	[	X
ejpam-4115	490	2	a	a	X
ejpam-4115	490	3	,	,	PUNCT
ejpam-4115	490	4	b]\∆(v	b]\∆(v	PROPN
ejpam-4115	490	5	,	,	PUNCT
ejpam-4115	490	6	f	f	X
ejpam-4115	490	7	,	,	PUNCT
ejpam-4115	490	8	f	f	PROPN
ejpam-4115	490	9	)	)	PUNCT
ejpam-4115	490	10	}	}	PUNCT
ejpam-4115	490	11	.	.	PUNCT
ejpam-4115	491	1	then	then	ADV
ejpam-4115	491	2	f	f	PROPN
ejpam-4115	491	3	(	(	PUNCT
ejpam-4115	491	4	vj)−f	vj)−f	PROPN
ejpam-4115	491	5	(	(	PUNCT
ejpam-4115	491	6	uj)−f(tj)(vj−uj	uj)−f(tj)(vj−uj	ADJ
ejpam-4115	491	7	)	)	PUNCT
ejpam-4115	491	8	∈	∈	NOUN
ejpam-4115	491	9	(	(	PUNCT
ejpam-4115	491	10	vj−uj)v	vj−uj)v	VERB
ejpam-4115	491	11	for	for	ADP
ejpam-4115	491	12	each	each	DET
ejpam-4115	491	13	j	j	PROPN
ejpam-4115	491	14	∈	∈	PROPN
ejpam-4115	491	15	k	k	PROPN
ejpam-4115	491	16	and	and	CCONJ
ejpam-4115	491	17	∑	∑	PROPN
ejpam-4115	491	18	j∈k(vj−uj)v	j∈k(vj−uj)v	ADJ
ejpam-4115	491	19	⊆	⊆	NUM
ejpam-4115	491	20	(	(	PUNCT
ejpam-4115	491	21	b−a)v	b−a)v	PROPN
ejpam-4115	491	22	.	.	PUNCT
ejpam-4115	492	1	let	let	VERB
ejpam-4115	492	2	wi	wi	PROPN
ejpam-4115	492	3	,	,	PUNCT
ejpam-4115	492	4	j	j	PROPN
ejpam-4115	492	5	=	=	SYM
ejpam-4115	492	6	ui	ui	PROPN
ejpam-4115	492	7	,	,	PUNCT
ejpam-4115	492	8	j	j	PROPN
ejpam-4115	492	9	+	+	PROPN
ejpam-4115	492	10	vi	vi	PROPN
ejpam-4115	492	11	,	,	PUNCT
ejpam-4115	492	12	j	j	NOUN
ejpam-4115	492	13	for	for	ADP
ejpam-4115	492	14	(	(	PUNCT
ejpam-4115	492	15	[	[	X
ejpam-4115	492	16	uj	uj	X
ejpam-4115	492	17	,	,	PUNCT
ejpam-4115	492	18	vj	vj	X
ejpam-4115	492	19	]	]	X
ejpam-4115	492	20	,	,	PUNCT
ejpam-4115	492	21	tj	tj	PROPN
ejpam-4115	492	22	)	)	PUNCT
ejpam-4115	492	23	∈	∈	PROPN
ejpam-4115	492	24	d1,i	d1,i	PROPN
ejpam-4115	492	25	and	and	CCONJ
ejpam-4115	492	26	i	i	PRON
ejpam-4115	492	27	∈	∈	PROPN
ejpam-4115	492	28	si	si	X
ejpam-4115	492	29	and	and	CCONJ
ejpam-4115	492	30	wj	wj	PROPN
ejpam-4115	492	31	=	=	PUNCT
ejpam-4115	492	32	(	(	PUNCT
ejpam-4115	492	33	vj	vj	INTJ
ejpam-4115	492	34	−	−	PROPN
ejpam-4115	492	35	uj)v	uj)v	PROPN
ejpam-4115	492	36	for	for	ADP
ejpam-4115	492	37	j	j	PROPN
ejpam-4115	492	38	∈	∈	PROPN
ejpam-4115	492	39	k.	k.	PROPN
ejpam-4115	493	1	then	then	ADV
ejpam-4115	493	2	f	f	PROPN
ejpam-4115	493	3	(	(	PUNCT
ejpam-4115	493	4	vj)−	vj)−	NOUN
ejpam-4115	493	5	f	f	PROPN
ejpam-4115	493	6	(	(	PUNCT
ejpam-4115	493	7	uj)−	uj)−	NOUN
ejpam-4115	493	8	f(tj)(vj	f(tj)(vj	PROPN
ejpam-4115	493	9	−	−	PROPN
ejpam-4115	493	10	uj	uj	PROPN
ejpam-4115	493	11	)	)	PUNCT
ejpam-4115	493	12	∈	∈	PROPN
ejpam-4115	493	13	wj	wj	PROPN
ejpam-4115	493	14	for	for	ADP
ejpam-4115	493	15	each	each	DET
ejpam-4115	493	16	1	1	NUM
ejpam-4115	493	17	≤	≤	NUM
ejpam-4115	493	18	j	j	PROPN
ejpam-4115	493	19	≤	≤	PROPN
ejpam-4115	493	20	n	n	CCONJ
ejpam-4115	493	21	and∑	and∑	PRON
ejpam-4115	493	22	i∈s	i∈	NOUN
ejpam-4115	493	23	(	(	PUNCT
ejpam-4115	493	24	d1,i	d1,i	PROPN
ejpam-4115	493	25	)	)	PUNCT
ejpam-4115	493	26	∑	∑	PROPN
ejpam-4115	493	27	wi	wi	PROPN
ejpam-4115	493	28	,	,	PUNCT
ejpam-4115	493	29	j	j	PROPN
ejpam-4115	494	1	+	+	CCONJ
ejpam-4115	494	2	∑	∑	PROPN
ejpam-4115	494	3	j∈k	j∈k	PROPN
ejpam-4115	494	4	wj	wj	NOUN
ejpam-4115	494	5	=	=	PUNCT
ejpam-4115	494	6	∑	∑	NUM
ejpam-4115	494	7	i∈s	i∈	NOUN
ejpam-4115	494	8	(	(	PUNCT
ejpam-4115	494	9	d1,i	d1,i	PROPN
ejpam-4115	494	10	)	)	PUNCT
ejpam-4115	494	11	∑	∑	PROPN
ejpam-4115	494	12	(	(	PUNCT
ejpam-4115	494	13	ui	ui	PROPN
ejpam-4115	494	14	,	,	PUNCT
ejpam-4115	494	15	j	j	PROPN
ejpam-4115	494	16	+	+	PROPN
ejpam-4115	494	17	vi	vi	PROPN
ejpam-4115	494	18	,	,	PUNCT
ejpam-4115	494	19	j	j	NOUN
ejpam-4115	494	20	)	)	PUNCT
ejpam-4115	495	1	+	+	CCONJ
ejpam-4115	495	2	∑	∑	PROPN
ejpam-4115	495	3	j∈k	j∈k	PROPN
ejpam-4115	495	4	(	(	PUNCT
ejpam-4115	495	5	vj	vj	INTJ
ejpam-4115	495	6	−	−	PROPN
ejpam-4115	495	7	uj)v	uj)v	PROPN
ejpam-4115	495	8	⊆	⊆	NUM
ejpam-4115	495	9	∑	∑	ADP
ejpam-4115	495	10	i∈s	i∈	NOUN
ejpam-4115	495	11	1	1	NUM
ejpam-4115	495	12	2i	2i	NUM
ejpam-4115	495	13	v	v	ADP
ejpam-4115	495	14	+	+	NOUN
ejpam-4115	495	15	∑	∑	ADV
ejpam-4115	495	16	i∈s	i∈	NOUN
ejpam-4115	495	17	(	(	PUNCT
ejpam-4115	495	18	d1,i	d1,i	PROPN
ejpam-4115	495	19	)	)	PUNCT
ejpam-4115	495	20	∑	∑	PROPN
ejpam-4115	495	21	vi	vi	PROPN
ejpam-4115	495	22	,	,	PUNCT
ejpam-4115	495	23	j	j	PROPN
ejpam-4115	495	24	+	+	CCONJ
ejpam-4115	495	25	(	(	PUNCT
ejpam-4115	495	26	b−	b−	NOUN
ejpam-4115	495	27	a)v	a)v	PUNCT
ejpam-4115	496	1	⊆	⊆	NUM
ejpam-4115	496	2	v	v	NOUN
ejpam-4115	496	3	+	+	X
ejpam-4115	496	4	v	v	NOUN
ejpam-4115	496	5	+	+	CCONJ
ejpam-4115	496	6	(	(	PUNCT
ejpam-4115	496	7	b−	b−	NOUN
ejpam-4115	496	8	a)v	a)v	NOUN
ejpam-4115	497	1	⊆	⊆	NUM
ejpam-4115	497	2	(	(	PUNCT
ejpam-4115	497	3	2	2	NUM
ejpam-4115	497	4	+	+	NUM
ejpam-4115	497	5	b−	b−	NOUN
ejpam-4115	497	6	a)v	a)v	NOUN
ejpam-4115	498	1	⊆	⊆	NUM
ejpam-4115	498	2	u.	u.	NOUN
ejpam-4115	498	3	therefore	therefore	ADV
ejpam-4115	498	4	,	,	PUNCT
ejpam-4115	498	5	f	f	PROPN
ejpam-4115	498	6	is	be	AUX
ejpam-4115	498	7	sh	sh	PRON
ejpam-4115	498	8	integrable	integrable	ADJ
ejpam-4115	498	9	on	on	ADP
ejpam-4115	498	10	[	[	X
ejpam-4115	498	11	a	a	X
ejpam-4115	498	12	,	,	PUNCT
ejpam-4115	498	13	b	b	NOUN
ejpam-4115	498	14	]	]	X
ejpam-4115	498	15	.	.	PUNCT
ejpam-4115	499	1	one	one	NUM
ejpam-4115	499	2	difficulty	difficulty	NOUN
ejpam-4115	499	3	that	that	PRON
ejpam-4115	499	4	one	one	PRON
ejpam-4115	499	5	may	may	AUX
ejpam-4115	499	6	encounter	encounter	VERB
ejpam-4115	499	7	in	in	ADP
ejpam-4115	499	8	showing	show	VERB
ejpam-4115	499	9	the	the	DET
ejpam-4115	499	10	converse	converse	NOUN
ejpam-4115	499	11	(	(	PUNCT
ejpam-4115	499	12	if	if	SCONJ
ejpam-4115	499	13	it	it	PRON
ejpam-4115	499	14	were	be	AUX
ejpam-4115	499	15	true	true	ADJ
ejpam-4115	499	16	)	)	PUNCT
ejpam-4115	499	17	of	of	ADP
ejpam-4115	499	18	theorem	theorem	NOUN
ejpam-4115	499	19	12	12	NUM
ejpam-4115	499	20	is	be	AUX
ejpam-4115	499	21	in	in	ADP
ejpam-4115	499	22	dealing	deal	VERB
ejpam-4115	499	23	with	with	ADP
ejpam-4115	499	24	the	the	DET
ejpam-4115	499	25	“	"	PUNCT
ejpam-4115	499	26	differentiabilty	differentiabilty	NOUN
ejpam-4115	499	27	”	"	PUNCT
ejpam-4115	499	28	aspect	aspect	NOUN
ejpam-4115	499	29	.	.	PUNCT
ejpam-4115	500	1	in	in	ADP
ejpam-4115	500	2	the	the	DET
ejpam-4115	500	3	banach	banach	ADV
ejpam-4115	500	4	-	-	PUNCT
ejpam-4115	500	5	valued	value	VERB
ejpam-4115	500	6	case	case	NOUN
ejpam-4115	500	7	,	,	PUNCT
ejpam-4115	500	8	the	the	DET
ejpam-4115	500	9	proof	proof	NOUN
ejpam-4115	500	10	in	in	ADP
ejpam-4115	500	11	moving	move	VERB
ejpam-4115	500	12	from	from	ADP
ejpam-4115	500	13	the	the	DET
ejpam-4115	500	14	strong	strong	ADJ
ejpam-4115	500	15	henstock	henstock	NOUN
ejpam-4115	500	16	integral	integral	ADJ
ejpam-4115	500	17	to	to	PART
ejpam-4115	500	18	d∗b	d∗b	VERB
ejpam-4115	500	19	uses	use	VERB
ejpam-4115	500	20	the	the	DET
ejpam-4115	500	21	condition	condition	NOUN
ejpam-4115	500	22	of	of	ADP
ejpam-4115	500	23	the	the	DET
ejpam-4115	500	24	henstock	henstock	NOUN
ejpam-4115	500	25	lemma	lemma	PROPN
ejpam-4115	500	26	(	(	PUNCT
ejpam-4115	500	27	which	which	PRON
ejpam-4115	500	28	the	the	DET
ejpam-4115	500	29	strong	strong	ADJ
ejpam-4115	500	30	henstock	henstock	NOUN
ejpam-4115	500	31	integral	integral	ADJ
ejpam-4115	500	32	possesses	possesse	NOUN
ejpam-4115	500	33	)	)	PUNCT
ejpam-4115	500	34	to	to	PART
ejpam-4115	500	35	prove	prove	VERB
ejpam-4115	500	36	differentiability	differentiability	NOUN
ejpam-4115	500	37	.	.	PUNCT
ejpam-4115	501	1	however	however	ADV
ejpam-4115	501	2	,	,	PUNCT
ejpam-4115	501	3	the	the	DET
ejpam-4115	501	4	sh	sh	PROPN
ejpam-4115	501	5	-	-	ADJ
ejpam-4115	501	6	integral	integral	ADJ
ejpam-4115	501	7	defined	define	VERB
ejpam-4115	501	8	in	in	ADP
ejpam-4115	501	9	this	this	DET
ejpam-4115	501	10	paper	paper	NOUN
ejpam-4115	501	11	does	do	AUX
ejpam-4115	501	12	not	not	PART
ejpam-4115	501	13	possess	possess	VERB
ejpam-4115	501	14	a	a	DET
ejpam-4115	501	15	similar	similar	ADJ
ejpam-4115	501	16	property	property	NOUN
ejpam-4115	501	17	.	.	PUNCT
ejpam-4115	502	1	we	we	PRON
ejpam-4115	502	2	now	now	ADV
ejpam-4115	502	3	show	show	VERB
ejpam-4115	502	4	that	that	SCONJ
ejpam-4115	502	5	for	for	ADP
ejpam-4115	502	6	functions	function	NOUN
ejpam-4115	502	7	taking	take	VERB
ejpam-4115	502	8	values	value	NOUN
ejpam-4115	502	9	in	in	ADP
ejpam-4115	502	10	a	a	DET
ejpam-4115	502	11	banach	banach	NOUN
ejpam-4115	502	12	spacex	spacex	NOUN
ejpam-4115	502	13	,	,	PUNCT
ejpam-4115	502	14	the	the	DET
ejpam-4115	502	15	denjoy	denjoy	NOUN
ejpam-4115	502	16	-	-	PUNCT
ejpam-4115	502	17	bochner	bochner	NOUN
ejpam-4115	502	18	integral	integral	ADJ
ejpam-4115	502	19	defined	define	VERB
ejpam-4115	502	20	by	by	ADP
ejpam-4115	502	21	solodov	solodov	PROPN
ejpam-4115	502	22	in	in	ADP
ejpam-4115	502	23	[	[	X
ejpam-4115	502	24	12	12	NUM
ejpam-4115	502	25	]	]	PUNCT
ejpam-4115	502	26	is	be	AUX
ejpam-4115	502	27	stronger	strong	ADJ
ejpam-4115	502	28	than	than	ADP
ejpam-4115	502	29	the	the	DET
ejpam-4115	502	30	denjoy	denjoy	NOUN
ejpam-4115	502	31	integral	integral	ADJ
ejpam-4115	502	32	.	.	PUNCT
ejpam-4115	503	1	theorem	theorem	NOUN
ejpam-4115	503	2	13	13	NUM
ejpam-4115	503	3	.	.	PUNCT
ejpam-4115	504	1	let	let	VERB
ejpam-4115	504	2	x	x	PRON
ejpam-4115	504	3	be	be	AUX
ejpam-4115	504	4	a	a	DET
ejpam-4115	504	5	banach	banach	NOUN
ejpam-4115	504	6	space	space	NOUN
ejpam-4115	504	7	.	.	PUNCT
ejpam-4115	505	1	if	if	SCONJ
ejpam-4115	505	2	f	f	X
ejpam-4115	505	3	:	:	PUNCT
ejpam-4115	506	1	[	[	X
ejpam-4115	506	2	a	a	X
ejpam-4115	506	3	,	,	PUNCT
ejpam-4115	506	4	b	b	NOUN
ejpam-4115	506	5	]	]	X
ejpam-4115	506	6	→	→	PUNCT
ejpam-4115	506	7	x	x	X
ejpam-4115	506	8	is	be	AUX
ejpam-4115	506	9	d∗b	d∗b	NOUN
ejpam-4115	506	10	-	-	ADJ
ejpam-4115	506	11	integrable	integrable	ADJ
ejpam-4115	506	12	,	,	PUNCT
ejpam-4115	506	13	then	then	ADV
ejpam-4115	506	14	it	it	PRON
ejpam-4115	506	15	is	be	AUX
ejpam-4115	506	16	d∗-integrable	d∗-integrable	PROPN
ejpam-4115	506	17	.	.	PUNCT
ejpam-4115	507	1	r.	r.	PROPN
ejpam-4115	507	2	e.	e.	PROPN
ejpam-4115	507	3	maza	maza	PROPN
ejpam-4115	507	4	,	,	PUNCT
ejpam-4115	507	5	s.	s.	PROPN
ejpam-4115	507	6	r.	r.	PROPN
ejpam-4115	507	7	canoy	canoy	PROPN
ejpam-4115	507	8	,	,	PUNCT
ejpam-4115	507	9	jr	jr	PROPN
ejpam-4115	507	10	.	.	PROPN
ejpam-4115	507	11	/	/	SYM
ejpam-4115	507	12	eur	eur	PROPN
ejpam-4115	507	13	.	.	PUNCT
ejpam-4115	508	1	j.	j.	PROPN
ejpam-4115	508	2	pure	pure	PROPN
ejpam-4115	508	3	appl	appl	PROPN
ejpam-4115	508	4	.	.	PROPN
ejpam-4115	508	5	math	math	PROPN
ejpam-4115	508	6	,	,	PUNCT
ejpam-4115	508	7	14	14	NUM
ejpam-4115	508	8	(	(	PUNCT
ejpam-4115	508	9	4	4	NUM
ejpam-4115	508	10	)	)	PUNCT
ejpam-4115	508	11	(	(	PUNCT
ejpam-4115	508	12	2021	2021	NUM
ejpam-4115	508	13	)	)	PUNCT
ejpam-4115	508	14	,	,	PUNCT
ejpam-4115	508	15	1169	1169	NUM
ejpam-4115	508	16	-	-	SYM
ejpam-4115	508	17	1183	1183	NUM
ejpam-4115	508	18	1180	1180	NUM
ejpam-4115	508	19	proof	proof	NOUN
ejpam-4115	508	20	.	.	PUNCT
ejpam-4115	508	21	suppose	suppose	VERB
ejpam-4115	508	22	that	that	SCONJ
ejpam-4115	508	23	f	f	PROPN
ejpam-4115	508	24	is	be	AUX
ejpam-4115	508	25	d∗b	d∗b	NOUN
ejpam-4115	508	26	-	-	NOUN
ejpam-4115	508	27	integrable	integrable	ADJ
ejpam-4115	508	28	on	on	ADP
ejpam-4115	508	29	[	[	X
ejpam-4115	508	30	a	a	X
ejpam-4115	508	31	,	,	PUNCT
ejpam-4115	508	32	b	b	NOUN
ejpam-4115	508	33	]	]	PUNCT
ejpam-4115	508	34	.	.	PUNCT
ejpam-4115	509	1	let	let	VERB
ejpam-4115	509	2	f	f	PRON
ejpam-4115	509	3	be	be	AUX
ejpam-4115	509	4	an	an	DET
ejpam-4115	509	5	acg∗-function	acg∗-function	PROPN
ejpam-4115	509	6	such	such	ADJ
ejpam-4115	509	7	that	that	SCONJ
ejpam-4115	509	8	f	f	PROPN
ejpam-4115	509	9	′(t	′(t	PROPN
ejpam-4115	509	10	)	)	PUNCT
ejpam-4115	509	11	=	=	SYM
ejpam-4115	510	1	f(t	f(t	NOUN
ejpam-4115	510	2	)	)	PUNCT
ejpam-4115	510	3	a.e	a.e	PROPN
ejpam-4115	510	4	.	.	PROPN
ejpam-4115	511	1	on	on	ADP
ejpam-4115	511	2	[	[	X
ejpam-4115	511	3	a	a	X
ejpam-4115	511	4	,	,	PUNCT
ejpam-4115	511	5	b	b	NOUN
ejpam-4115	511	6	]	]	PUNCT
ejpam-4115	511	7	.	.	PUNCT
ejpam-4115	512	1	let	let	AUX
ejpam-4115	512	2	{	{	PUNCT
ejpam-4115	512	3	ei}∞i=1	ei}∞i=1	ADV
ejpam-4115	512	4	be	be	AUX
ejpam-4115	512	5	a	a	DET
ejpam-4115	512	6	collection	collection	NOUN
ejpam-4115	512	7	of	of	ADP
ejpam-4115	512	8	subsets	subset	NOUN
ejpam-4115	512	9	of	of	ADP
ejpam-4115	512	10	[	[	X
ejpam-4115	512	11	a	a	X
ejpam-4115	512	12	,	,	PUNCT
ejpam-4115	512	13	b	b	NOUN
ejpam-4115	512	14	]	]	PUNCT
ejpam-4115	512	15	with	with	ADP
ejpam-4115	512	16	[	[	X
ejpam-4115	512	17	a	a	X
ejpam-4115	512	18	,	,	PUNCT
ejpam-4115	512	19	b	b	NOUN
ejpam-4115	512	20	]	]	X
ejpam-4115	512	21	=	=	PUNCT
ejpam-4115	512	22	⋃∞	⋃∞	X
ejpam-4115	512	23	i=1ei	i=1ei	ADV
ejpam-4115	512	24	such	such	ADJ
ejpam-4115	512	25	that	that	SCONJ
ejpam-4115	512	26	f	f	PROPN
ejpam-4115	512	27	is	be	AUX
ejpam-4115	512	28	ac∗(ei	ac∗(ei	PROPN
ejpam-4115	512	29	)	)	PUNCT
ejpam-4115	512	30	for	for	ADP
ejpam-4115	512	31	each	each	DET
ejpam-4115	512	32	i	i	PRON
ejpam-4115	512	33	∈	∈	PROPN
ejpam-4115	512	34	n.	n.	NOUN
ejpam-4115	512	35	let	let	VERB
ejpam-4115	512	36	u	u	PRON
ejpam-4115	512	37	be	be	AUX
ejpam-4115	512	38	a	a	DET
ejpam-4115	512	39	θ	θ	NOUN
ejpam-4115	512	40	-	-	PUNCT
ejpam-4115	512	41	neighborhood	neighborhood	NOUN
ejpam-4115	512	42	.	.	PUNCT
ejpam-4115	513	1	then	then	ADV
ejpam-4115	513	2	there	there	PRON
ejpam-4115	513	3	exists	exist	VERB
ejpam-4115	513	4	ϵ	ϵ	X
ejpam-4115	513	5	>	>	X
ejpam-4115	513	6	0	0	NUM
ejpam-4115	513	7	such	such	ADJ
ejpam-4115	513	8	that	that	SCONJ
ejpam-4115	513	9	bϵ	bϵ	PROPN
ejpam-4115	513	10	⊆	⊆	NUM
ejpam-4115	513	11	u	u	NOUN
ejpam-4115	513	12	.	.	PUNCT
ejpam-4115	514	1	let	let	VERB
ejpam-4115	514	2	k	k	PROPN
ejpam-4115	514	3	∈	∈	PROPN
ejpam-4115	514	4	n.	n.	NOUN
ejpam-4115	514	5	since	since	SCONJ
ejpam-4115	514	6	f	f	PROPN
ejpam-4115	514	7	is	be	AUX
ejpam-4115	514	8	ac∗(ek	ac∗(ek	PROPN
ejpam-4115	514	9	)	)	PUNCT
ejpam-4115	514	10	,	,	PUNCT
ejpam-4115	514	11	there	there	PRON
ejpam-4115	514	12	exists	exist	VERB
ejpam-4115	514	13	a	a	DET
ejpam-4115	514	14	δ	δ	PROPN
ejpam-4115	514	15	>	>	X
ejpam-4115	514	16	0	0	NUM
ejpam-4115	515	1	such	such	ADJ
ejpam-4115	515	2	that	that	PRON
ejpam-4115	515	3	for	for	ADP
ejpam-4115	515	4	any	any	DET
ejpam-4115	515	5	partial	partial	ADJ
ejpam-4115	515	6	partition	partition	NOUN
ejpam-4115	515	7	d	d	NOUN
ejpam-4115	515	8	=	=	PRON
ejpam-4115	515	9	{	{	PUNCT
ejpam-4115	515	10	(	(	PUNCT
ejpam-4115	515	11	[	[	X
ejpam-4115	515	12	ui	ui	NOUN
ejpam-4115	515	13	,	,	PUNCT
ejpam-4115	515	14	vi	vi	PROPN
ejpam-4115	515	15	]	]	PUNCT
ejpam-4115	515	16	,	,	PUNCT
ejpam-4115	515	17	ti	ti	NOUN
ejpam-4115	515	18	)	)	PUNCT
ejpam-4115	515	19	:	:	PUNCT
ejpam-4115	515	20	1	1	NUM
ejpam-4115	515	21	≤	≤	NUM
ejpam-4115	515	22	i	i	PRON
ejpam-4115	515	23	≤	≤	NOUN
ejpam-4115	515	24	n	n	CCONJ
ejpam-4115	515	25	}	}	PUNCT
ejpam-4115	515	26	of	of	ADP
ejpam-4115	515	27	[	[	X
ejpam-4115	515	28	a	a	X
ejpam-4115	515	29	,	,	PUNCT
ejpam-4115	515	30	b	b	NOUN
ejpam-4115	515	31	]	]	X
ejpam-4115	515	32	with	with	ADP
ejpam-4115	515	33	ui	ui	PROPN
ejpam-4115	515	34	∈	∈	PROPN
ejpam-4115	515	35	ek	ek	PROPN
ejpam-4115	515	36	or	or	CCONJ
ejpam-4115	515	37	vi	vi	PROPN
ejpam-4115	515	38	∈	∈	PROPN
ejpam-4115	515	39	ek	ek	NOUN
ejpam-4115	515	40	and	and	CCONJ
ejpam-4115	515	41	∑n	∑n	PROPN
ejpam-4115	515	42	i=1(vi	i=1(vi	X
ejpam-4115	515	43	−	−	PROPN
ejpam-4115	515	44	ui	ui	PROPN
ejpam-4115	515	45	)	)	PUNCT
ejpam-4115	515	46	<	<	X
ejpam-4115	516	1	δ	δ	PROPN
ejpam-4115	516	2	,	,	PUNCT
ejpam-4115	516	3	we	we	PRON
ejpam-4115	516	4	have	have	VERB
ejpam-4115	516	5	∑n	∑n	PROPN
ejpam-4115	516	6	i=1∥f	i=1∥f	PROPN
ejpam-4115	516	7	(	(	PUNCT
ejpam-4115	516	8	vi	vi	NOUN
ejpam-4115	516	9	)	)	PUNCT
ejpam-4115	516	10	−	−	PROPN
ejpam-4115	516	11	f	f	PROPN
ejpam-4115	516	12	(	(	PUNCT
ejpam-4115	516	13	ui)∥	ui)∥	ADP
ejpam-4115	516	14	<	<	X
ejpam-4115	516	15	ϵ.	ϵ.	NOUN
ejpam-4115	516	16	choose	choose	VERB
ejpam-4115	516	17	positive	positive	ADJ
ejpam-4115	516	18	numbers	number	NOUN
ejpam-4115	516	19	ϵ1	ϵ1	VERB
ejpam-4115	516	20	,	,	PUNCT
ejpam-4115	516	21	ϵ2	ϵ2	ADJ
ejpam-4115	516	22	,	,	PUNCT
ejpam-4115	516	23	.	.	PUNCT
ejpam-4115	516	24	.	.	PUNCT
ejpam-4115	516	25	.	.	PUNCT
ejpam-4115	517	1	,	,	PUNCT
ejpam-4115	517	2	ϵn	ϵn	INTJ
ejpam-4115	517	3	such	such	ADJ
ejpam-4115	517	4	that	that	SCONJ
ejpam-4115	517	5	∥f	∥f	PROPN
ejpam-4115	517	6	(	(	PUNCT
ejpam-4115	517	7	vi	vi	NOUN
ejpam-4115	517	8	)	)	PUNCT
ejpam-4115	517	9	−	−	PROPN
ejpam-4115	518	1	f	f	PROPN
ejpam-4115	518	2	(	(	PUNCT
ejpam-4115	518	3	ui)∥	ui)∥	NOUN
ejpam-4115	518	4	<	<	X
ejpam-4115	518	5	ϵi	ϵi	PROPN
ejpam-4115	518	6	for	for	ADP
ejpam-4115	518	7	each	each	DET
ejpam-4115	518	8	i	i	PRON
ejpam-4115	518	9	∈	∈	PROPN
ejpam-4115	518	10	{	{	PUNCT
ejpam-4115	518	11	1	1	NUM
ejpam-4115	518	12	,	,	PUNCT
ejpam-4115	518	13	2	2	NUM
ejpam-4115	518	14	,	,	PUNCT
ejpam-4115	518	15	.	.	PUNCT
ejpam-4115	518	16	.	.	PUNCT
ejpam-4115	518	17	.	.	PUNCT
ejpam-4115	518	18	,	,	PUNCT
ejpam-4115	518	19	n	n	CCONJ
ejpam-4115	518	20	}	}	PUNCT
ejpam-4115	518	21	and	and	CCONJ
ejpam-4115	518	22	ϵ1	ϵ1	VERB
ejpam-4115	518	23	+	+	CCONJ
ejpam-4115	518	24	ϵ2	ϵ2	ADJ
ejpam-4115	518	25	+	+	X
ejpam-4115	518	26	.	.	PUNCT
ejpam-4115	518	27	.	.	PUNCT
ejpam-4115	518	28	.	.	PUNCT
ejpam-4115	519	1	+	+	CCONJ
ejpam-4115	519	2	ϵn	ϵn	PROPN
ejpam-4115	519	3	≤	≤	NUM
ejpam-4115	519	4	ϵ.	ϵ.	NOUN
ejpam-4115	519	5	let	let	VERB
ejpam-4115	519	6	ui	ui	NOUN
ejpam-4115	520	1	=	=	PUNCT
ejpam-4115	520	2	bϵi	bϵi	PROPN
ejpam-4115	520	3	=	=	SYM
ejpam-4115	520	4	{	{	PUNCT
ejpam-4115	520	5	x	x	SYM
ejpam-4115	520	6	∈	∈	NOUN
ejpam-4115	520	7	x	x	X
ejpam-4115	520	8	:	:	PUNCT
ejpam-4115	520	9	∥x∥	∥x∥	NOUN
ejpam-4115	520	10	<	<	X
ejpam-4115	520	11	ϵi	ϵi	X
ejpam-4115	520	12	}	}	PUNCT
ejpam-4115	520	13	for	for	ADP
ejpam-4115	520	14	each	each	DET
ejpam-4115	520	15	i	i	PRON
ejpam-4115	520	16	∈	∈	PROPN
ejpam-4115	520	17	{	{	PUNCT
ejpam-4115	520	18	1	1	NUM
ejpam-4115	520	19	,	,	PUNCT
ejpam-4115	520	20	2	2	NUM
ejpam-4115	520	21	,	,	PUNCT
ejpam-4115	520	22	.	.	PUNCT
ejpam-4115	520	23	.	.	PUNCT
ejpam-4115	521	1	.	.	PUNCT
ejpam-4115	521	2	,	,	PUNCT
ejpam-4115	521	3	n	n	CCONJ
ejpam-4115	521	4	}	}	PUNCT
ejpam-4115	521	5	.	.	PUNCT
ejpam-4115	522	1	then	then	ADV
ejpam-4115	522	2	∑n	∑n	PROPN
ejpam-4115	522	3	i=1	i=1	PROPN
ejpam-4115	522	4	ui	ui	PROPN
ejpam-4115	522	5	⊆	⊆	NUM
ejpam-4115	522	6	bϵ	bϵ	NOUN
ejpam-4115	522	7	⊆	⊆	NUM
ejpam-4115	522	8	u	u	NOUN
ejpam-4115	522	9	and	and	CCONJ
ejpam-4115	522	10	f	f	PROPN
ejpam-4115	522	11	(	(	PUNCT
ejpam-4115	522	12	vi	vi	NOUN
ejpam-4115	522	13	)	)	PUNCT
ejpam-4115	522	14	−	−	PROPN
ejpam-4115	522	15	f	f	PROPN
ejpam-4115	522	16	(	(	PUNCT
ejpam-4115	522	17	ui	ui	PROPN
ejpam-4115	522	18	)	)	PUNCT
ejpam-4115	522	19	∈	∈	PROPN
ejpam-4115	522	20	ui	ui	NOUN
ejpam-4115	522	21	for	for	ADP
ejpam-4115	522	22	each	each	DET
ejpam-4115	522	23	i	i	PRON
ejpam-4115	522	24	∈	∈	PROPN
ejpam-4115	522	25	{	{	PUNCT
ejpam-4115	522	26	1	1	NUM
ejpam-4115	522	27	,	,	PUNCT
ejpam-4115	522	28	2	2	NUM
ejpam-4115	522	29	,	,	PUNCT
ejpam-4115	522	30	.	.	PUNCT
ejpam-4115	522	31	.	.	PUNCT
ejpam-4115	522	32	.	.	PUNCT
ejpam-4115	522	33	,	,	PUNCT
ejpam-4115	522	34	n	n	CCONJ
ejpam-4115	522	35	}	}	PUNCT
ejpam-4115	522	36	.	.	PUNCT
ejpam-4115	523	1	hence	hence	ADV
ejpam-4115	523	2	,	,	PUNCT
ejpam-4115	523	3	f	f	PROPN
ejpam-4115	523	4	is	be	AUX
ejpam-4115	523	5	ac∗(ek	ac∗(ek	PRON
ejpam-4115	523	6	)	)	PUNCT
ejpam-4115	523	7	in	in	ADP
ejpam-4115	523	8	the	the	DET
ejpam-4115	523	9	sense	sense	NOUN
ejpam-4115	523	10	of	of	ADP
ejpam-4115	523	11	definition	definition	NOUN
ejpam-4115	523	12	4	4	NUM
ejpam-4115	523	13	.	.	PUNCT
ejpam-4115	524	1	therefore	therefore	ADV
ejpam-4115	524	2	,	,	PUNCT
ejpam-4115	524	3	f	f	PROPN
ejpam-4115	524	4	is	be	AUX
ejpam-4115	524	5	an	an	DET
ejpam-4115	524	6	acg∗-function	acg∗-function	PROPN
ejpam-4115	524	7	in	in	ADP
ejpam-4115	524	8	the	the	DET
ejpam-4115	524	9	sense	sense	NOUN
ejpam-4115	524	10	of	of	ADP
ejpam-4115	524	11	definition	definition	NOUN
ejpam-4115	524	12	5	5	NUM
ejpam-4115	524	13	.	.	PUNCT
ejpam-4115	525	1	next	next	ADV
ejpam-4115	525	2	,	,	PUNCT
ejpam-4115	525	3	let	let	VERB
ejpam-4115	525	4	e	e	NOUN
ejpam-4115	525	5	=	=	PRON
ejpam-4115	525	6	{	{	PUNCT
ejpam-4115	525	7	t′	t′	NUM
ejpam-4115	525	8	∈	∈	PROPN
ejpam-4115	526	1	[	[	X
ejpam-4115	526	2	a	a	X
ejpam-4115	526	3	,	,	PUNCT
ejpam-4115	526	4	b	b	NOUN
ejpam-4115	526	5	]	]	X
ejpam-4115	526	6	:	:	PUNCT
ejpam-4115	526	7	f	f	PROPN
ejpam-4115	526	8	′(t	′(t	PROPN
ejpam-4115	526	9	)	)	PUNCT
ejpam-4115	526	10	=	=	SYM
ejpam-4115	527	1	f(t	f(t	NOUN
ejpam-4115	527	2	)	)	PUNCT
ejpam-4115	527	3	}	}	PUNCT
ejpam-4115	527	4	.	.	PUNCT
ejpam-4115	528	1	let	let	VERB
ejpam-4115	528	2	v	v	PART
ejpam-4115	528	3	be	be	AUX
ejpam-4115	528	4	a	a	DET
ejpam-4115	528	5	θ	θ	NOUN
ejpam-4115	528	6	-	-	PUNCT
ejpam-4115	528	7	neighborhood	neighborhood	NOUN
ejpam-4115	528	8	and	and	CCONJ
ejpam-4115	528	9	let	let	VERB
ejpam-4115	528	10	ϵ	ϵ	PRON
ejpam-4115	528	11	>	>	X
ejpam-4115	528	12	0	0	NUM
ejpam-4115	529	1	such	such	ADJ
ejpam-4115	529	2	that	that	SCONJ
ejpam-4115	529	3	bϵ	bϵ	NOUN
ejpam-4115	529	4	⊆	⊆	NUM
ejpam-4115	529	5	v	v	NOUN
ejpam-4115	529	6	.	.	PUNCT
ejpam-4115	530	1	by	by	ADP
ejpam-4115	530	2	assumption	assumption	NOUN
ejpam-4115	530	3	,	,	PUNCT
ejpam-4115	530	4	there	there	PRON
ejpam-4115	530	5	exists	exist	VERB
ejpam-4115	530	6	δ	δ	PROPN
ejpam-4115	530	7	>	>	X
ejpam-4115	530	8	0	0	NUM
ejpam-4115	531	1	such	such	ADJ
ejpam-4115	531	2	that	that	SCONJ
ejpam-4115	531	3	that	that	SCONJ
ejpam-4115	531	4	∥	∥	PROPN
ejpam-4115	531	5	1	1	NUM
ejpam-4115	531	6	v−u	v−u	NOUN
ejpam-4115	531	7	[	[	X
ejpam-4115	531	8	f	f	X
ejpam-4115	531	9	(	(	PUNCT
ejpam-4115	531	10	v)−f	v)−f	ADP
ejpam-4115	531	11	(	(	PUNCT
ejpam-4115	531	12	u)−f	u)−f	NOUN
ejpam-4115	531	13	′(t)(v−	′(t)(v−	PUNCT
ejpam-4115	532	1	u)]∥	u)]∥	ADV
ejpam-4115	532	2	<	<	X
ejpam-4115	533	1	ϵ	ϵ	X
ejpam-4115	533	2	whenever	whenever	SCONJ
ejpam-4115	533	3	t	t	PROPN
ejpam-4115	533	4	∈	∈	PROPN
ejpam-4115	533	5	[	[	X
ejpam-4115	533	6	u	u	NOUN
ejpam-4115	533	7	,	,	PUNCT
ejpam-4115	533	8	v]∩e	v]∩e	NUM
ejpam-4115	533	9	⊆	⊆	NUM
ejpam-4115	533	10	[	[	X
ejpam-4115	533	11	a	a	X
ejpam-4115	533	12	,	,	PUNCT
ejpam-4115	533	13	b]∩e	b]∩e	NOUN
ejpam-4115	533	14	and	and	CCONJ
ejpam-4115	533	15	|v−	|v−	NOUN
ejpam-4115	533	16	u|	u|	PROPN
ejpam-4115	533	17	<	<	X
ejpam-4115	533	18	δ	δ	PROPN
ejpam-4115	533	19	.	.	PUNCT
ejpam-4115	534	1	this	this	PRON
ejpam-4115	534	2	implies	imply	VERB
ejpam-4115	534	3	that	that	SCONJ
ejpam-4115	534	4	1	1	NUM
ejpam-4115	534	5	v−u	v−u	NOUN
ejpam-4115	535	1	[	[	X
ejpam-4115	535	2	f	f	X
ejpam-4115	535	3	(	(	PUNCT
ejpam-4115	535	4	v)−f	v)−f	ADP
ejpam-4115	535	5	(	(	PUNCT
ejpam-4115	535	6	u)−f	u)−f	NOUN
ejpam-4115	535	7	′(t)(v−u	′(t)(v−u	NOUN
ejpam-4115	535	8	)	)	PUNCT
ejpam-4115	535	9	]	]	PUNCT
ejpam-4115	535	10	∈	∈	PROPN
ejpam-4115	535	11	bϵ	bϵ	ADP
ejpam-4115	535	12	⊆	⊆	NUM
ejpam-4115	535	13	v	v	NOUN
ejpam-4115	535	14	or	or	CCONJ
ejpam-4115	535	15	f	f	X
ejpam-4115	535	16	(	(	PUNCT
ejpam-4115	535	17	v)−f	v)−f	ADP
ejpam-4115	535	18	(	(	PUNCT
ejpam-4115	535	19	u)−f	u)−f	NOUN
ejpam-4115	535	20	′(t)(v−u	′(t)(v−u	NOUN
ejpam-4115	535	21	)	)	PUNCT
ejpam-4115	535	22	∈	∈	PROPN
ejpam-4115	535	23	(	(	PUNCT
ejpam-4115	535	24	v	v	NOUN
ejpam-4115	535	25	−	−	NOUN
ejpam-4115	535	26	u)v	u)v	PUNCT
ejpam-4115	535	27	whenever	whenever	SCONJ
ejpam-4115	535	28	t	t	PROPN
ejpam-4115	535	29	∈	∈	PROPN
ejpam-4115	536	1	[	[	X
ejpam-4115	536	2	u	u	NOUN
ejpam-4115	536	3	,	,	PUNCT
ejpam-4115	536	4	v	v	NOUN
ejpam-4115	536	5	]	]	PUNCT
ejpam-4115	536	6	∩	∩	NOUN
ejpam-4115	536	7	e	e	PROPN
ejpam-4115	536	8	⊆	⊆	NUM
ejpam-4115	536	9	[	[	X
ejpam-4115	536	10	a	a	X
ejpam-4115	536	11	,	,	PUNCT
ejpam-4115	536	12	b	b	NOUN
ejpam-4115	536	13	]	]	X
ejpam-4115	536	14	∩	∩	ADJ
ejpam-4115	536	15	e	e	NOUN
ejpam-4115	536	16	and	and	CCONJ
ejpam-4115	536	17	|v	|v	VERB
ejpam-4115	536	18	−	−	PROPN
ejpam-4115	537	1	u|	u|	PROPN
ejpam-4115	537	2	<	<	X
ejpam-4115	537	3	δ	δ	PROPN
ejpam-4115	537	4	.	.	PUNCT
ejpam-4115	538	1	this	this	PRON
ejpam-4115	538	2	shows	show	VERB
ejpam-4115	538	3	that	that	SCONJ
ejpam-4115	538	4	f	f	PROPN
ejpam-4115	538	5	is	be	AUX
ejpam-4115	538	6	d∗integrable	d∗integrable	ADJ
ejpam-4115	538	7	.	.	PUNCT
ejpam-4115	539	1	we	we	PRON
ejpam-4115	539	2	point	point	VERB
ejpam-4115	539	3	out	out	ADP
ejpam-4115	539	4	that	that	SCONJ
ejpam-4115	539	5	the	the	DET
ejpam-4115	539	6	difficulty	difficulty	NOUN
ejpam-4115	539	7	in	in	ADP
ejpam-4115	539	8	showing	show	VERB
ejpam-4115	539	9	the	the	DET
ejpam-4115	539	10	converse	converse	NOUN
ejpam-4115	539	11	of	of	ADP
ejpam-4115	539	12	theorem	theorem	NOUN
ejpam-4115	539	13	13	13	NUM
ejpam-4115	539	14	,	,	PUNCT
ejpam-4115	539	15	if	if	SCONJ
ejpam-4115	539	16	it	it	PRON
ejpam-4115	539	17	were	be	AUX
ejpam-4115	539	18	true	true	ADJ
ejpam-4115	539	19	,	,	PUNCT
ejpam-4115	539	20	lies	lie	VERB
ejpam-4115	539	21	in	in	ADP
ejpam-4115	539	22	showing	show	VERB
ejpam-4115	539	23	that	that	SCONJ
ejpam-4115	539	24	ac∗	ac∗	ADJ
ejpam-4115	539	25	in	in	ADP
ejpam-4115	539	26	the	the	DET
ejpam-4115	539	27	sense	sense	NOUN
ejpam-4115	539	28	of	of	ADP
ejpam-4115	539	29	definition	definition	NOUN
ejpam-4115	539	30	4	4	NUM
ejpam-4115	539	31	implies	imply	VERB
ejpam-4115	539	32	ac∗	ac∗	ADJ
ejpam-4115	539	33	in	in	ADP
ejpam-4115	539	34	the	the	DET
ejpam-4115	539	35	sense	sense	NOUN
ejpam-4115	539	36	of	of	ADP
ejpam-4115	539	37	definition	definition	NOUN
ejpam-4115	539	38	9	9	NUM
ejpam-4115	539	39	.	.	PUNCT
ejpam-4115	540	1	indeed	indeed	ADV
ejpam-4115	540	2	,	,	PUNCT
ejpam-4115	540	3	if	if	SCONJ
ejpam-4115	540	4	the	the	DET
ejpam-4115	540	5	norm	norm	NOUN
ejpam-4115	540	6	of	of	ADP
ejpam-4115	540	7	the	the	DET
ejpam-4115	540	8	sum	sum	NOUN
ejpam-4115	540	9	of	of	ADP
ejpam-4115	540	10	vectors	vector	NOUN
ejpam-4115	540	11	is	be	AUX
ejpam-4115	540	12	strictly	strictly	ADV
ejpam-4115	540	13	smaller	small	ADJ
ejpam-4115	540	14	than	than	ADP
ejpam-4115	540	15	some	some	DET
ejpam-4115	540	16	positive	positive	ADJ
ejpam-4115	540	17	number	number	NOUN
ejpam-4115	540	18	,	,	PUNCT
ejpam-4115	540	19	the	the	DET
ejpam-4115	540	20	sum	sum	NOUN
ejpam-4115	540	21	of	of	ADP
ejpam-4115	540	22	the	the	DET
ejpam-4115	540	23	norms	norm	NOUN
ejpam-4115	540	24	of	of	ADP
ejpam-4115	540	25	the	the	DET
ejpam-4115	540	26	vectors	vector	NOUN
ejpam-4115	540	27	can	can	AUX
ejpam-4115	540	28	not	not	PART
ejpam-4115	540	29	be	be	AUX
ejpam-4115	540	30	forced	force	VERB
ejpam-4115	540	31	to	to	PART
ejpam-4115	540	32	be	be	AUX
ejpam-4115	540	33	strictly	strictly	ADV
ejpam-4115	540	34	smaller	small	ADJ
ejpam-4115	540	35	than	than	ADP
ejpam-4115	540	36	the	the	DET
ejpam-4115	540	37	same	same	ADJ
ejpam-4115	540	38	positive	positive	ADJ
ejpam-4115	540	39	number	number	NOUN
ejpam-4115	540	40	.	.	PUNCT
ejpam-4115	541	1	it	it	PRON
ejpam-4115	541	2	seems	seem	VERB
ejpam-4115	541	3	that	that	SCONJ
ejpam-4115	541	4	a	a	DET
ejpam-4115	541	5	weaker	weak	ADJ
ejpam-4115	541	6	version	version	NOUN
ejpam-4115	541	7	of	of	ADP
ejpam-4115	541	8	the	the	DET
ejpam-4115	541	9	d∗b	d∗b	ADV
ejpam-4115	541	10	-	-	NOUN
ejpam-4115	541	11	integral	integral	ADJ
ejpam-4115	541	12	for	for	ADP
ejpam-4115	541	13	banachvalued	banachvalued	ADJ
ejpam-4115	541	14	functions	function	NOUN
ejpam-4115	541	15	(	(	PUNCT
ejpam-4115	541	16	possibly	possibly	ADV
ejpam-4115	541	17	not	not	PART
ejpam-4115	541	18	yet	yet	ADV
ejpam-4115	541	19	defined	define	VERB
ejpam-4115	541	20	)	)	PUNCT
ejpam-4115	541	21	may	may	AUX
ejpam-4115	541	22	be	be	AUX
ejpam-4115	541	23	equivalent	equivalent	ADJ
ejpam-4115	541	24	to	to	ADP
ejpam-4115	541	25	the	the	DET
ejpam-4115	541	26	d∗-integral	d∗-integral	PROPN
ejpam-4115	541	27	.	.	PUNCT
ejpam-4115	542	1	this	this	PRON
ejpam-4115	542	2	still	still	ADV
ejpam-4115	542	3	remains	remain	VERB
ejpam-4115	542	4	to	to	PART
ejpam-4115	542	5	be	be	AUX
ejpam-4115	542	6	investigated	investigate	VERB
ejpam-4115	542	7	and	and	CCONJ
ejpam-4115	542	8	seen	see	VERB
ejpam-4115	542	9	.	.	PUNCT
ejpam-4115	543	1	solodov	solodov	PROPN
ejpam-4115	543	2	in	in	ADP
ejpam-4115	543	3	[	[	X
ejpam-4115	543	4	13	13	NUM
ejpam-4115	543	5	]	]	PUNCT
ejpam-4115	543	6	gave	give	VERB
ejpam-4115	543	7	a	a	DET
ejpam-4115	543	8	characterization	characterization	NOUN
ejpam-4115	543	9	of	of	ADP
ejpam-4115	543	10	the	the	DET
ejpam-4115	543	11	strong	strong	ADJ
ejpam-4115	543	12	henstock	henstock	NOUN
ejpam-4115	543	13	integral	integral	ADJ
ejpam-4115	543	14	using	use	VERB
ejpam-4115	543	15	acg∗functions	acg∗function	NOUN
ejpam-4115	543	16	(	(	PUNCT
ejpam-4115	543	17	the	the	DET
ejpam-4115	543	18	denjoy	denjoy	NOUN
ejpam-4115	543	19	-	-	PUNCT
ejpam-4115	543	20	bochner	bochner	NOUN
ejpam-4115	543	21	integral	integral	ADJ
ejpam-4115	543	22	)	)	PUNCT
ejpam-4115	543	23	.	.	PUNCT
ejpam-4115	544	1	the	the	DET
ejpam-4115	544	2	next	next	ADJ
ejpam-4115	544	3	result	result	NOUN
ejpam-4115	544	4	is	be	AUX
ejpam-4115	544	5	somehow	somehow	ADV
ejpam-4115	544	6	related	relate	VERB
ejpam-4115	544	7	to	to	ADP
ejpam-4115	544	8	that	that	DET
ejpam-4115	544	9	work	work	NOUN
ejpam-4115	544	10	of	of	ADP
ejpam-4115	544	11	solodov	solodov	PROPN
ejpam-4115	544	12	.	.	PUNCT
ejpam-4115	545	1	however	however	ADV
ejpam-4115	545	2	,	,	PUNCT
ejpam-4115	545	3	as	as	SCONJ
ejpam-4115	545	4	our	our	PRON
ejpam-4115	545	5	example	example	NOUN
ejpam-4115	545	6	will	will	AUX
ejpam-4115	545	7	show	show	VERB
ejpam-4115	545	8	,	,	PUNCT
ejpam-4115	545	9	the	the	DET
ejpam-4115	545	10	converse	converse	NOUN
ejpam-4115	545	11	of	of	ADP
ejpam-4115	545	12	this	this	DET
ejpam-4115	545	13	result	result	NOUN
ejpam-4115	545	14	is	be	AUX
ejpam-4115	545	15	not	not	PART
ejpam-4115	545	16	true	true	ADJ
ejpam-4115	545	17	.	.	PUNCT
ejpam-4115	546	1	further	far	ADV
ejpam-4115	546	2	,	,	PUNCT
ejpam-4115	546	3	note	note	VERB
ejpam-4115	546	4	that	that	SCONJ
ejpam-4115	546	5	this	this	DET
ejpam-4115	546	6	result	result	NOUN
ejpam-4115	546	7	is	be	AUX
ejpam-4115	546	8	immediate	immediate	ADJ
ejpam-4115	546	9	from	from	ADP
ejpam-4115	546	10	theorem	theorem	ADJ
ejpam-4115	546	11	9	9	NUM
ejpam-4115	546	12	and	and	CCONJ
ejpam-4115	546	13	theorem	theorem	VERB
ejpam-4115	546	14	12	12	NUM
ejpam-4115	546	15	.	.	PUNCT
ejpam-4115	547	1	theorem	theorem	VERB
ejpam-4115	547	2	14	14	NUM
ejpam-4115	547	3	.	.	PUNCT
ejpam-4115	548	1	if	if	SCONJ
ejpam-4115	548	2	f	f	PROPN
ejpam-4115	548	3	:	:	PUNCT
ejpam-4115	549	1	[	[	X
ejpam-4115	549	2	a	a	X
ejpam-4115	549	3	,	,	PUNCT
ejpam-4115	549	4	b	b	NOUN
ejpam-4115	549	5	]	]	X
ejpam-4115	549	6	→	→	PUNCT
ejpam-4115	549	7	x	x	X
ejpam-4115	549	8	is	be	AUX
ejpam-4115	549	9	denjoy	denjoy	VERB
ejpam-4115	549	10	integrable	integrable	ADJ
ejpam-4115	549	11	on	on	ADP
ejpam-4115	549	12	[	[	X
ejpam-4115	549	13	a	a	X
ejpam-4115	549	14	,	,	PUNCT
ejpam-4115	549	15	b	b	NOUN
ejpam-4115	549	16	]	]	X
ejpam-4115	549	17	,	,	PUNCT
ejpam-4115	549	18	then	then	ADV
ejpam-4115	549	19	it	it	PRON
ejpam-4115	549	20	is	be	AUX
ejpam-4115	549	21	sh	sh	PRON
ejpam-4115	549	22	integrable	integrable	ADJ
ejpam-4115	549	23	on	on	ADP
ejpam-4115	549	24	[	[	X
ejpam-4115	549	25	a	a	X
ejpam-4115	549	26	,	,	PUNCT
ejpam-4115	549	27	b	b	NOUN
ejpam-4115	549	28	]	]	PUNCT
ejpam-4115	549	29	.	.	PUNCT
ejpam-4115	549	30	example	example	NOUN
ejpam-4115	550	1	3	3	NUM
ejpam-4115	550	2	.	.	PUNCT
ejpam-4115	550	3	to	to	PART
ejpam-4115	550	4	see	see	VERB
ejpam-4115	550	5	that	that	SCONJ
ejpam-4115	550	6	the	the	DET
ejpam-4115	550	7	converse	converse	NOUN
ejpam-4115	550	8	of	of	ADP
ejpam-4115	550	9	theorem	theorem	ADJ
ejpam-4115	550	10	9	9	NUM
ejpam-4115	550	11	and	and	CCONJ
ejpam-4115	550	12	theorem	theorem	VERB
ejpam-4115	550	13	14	14	NUM
ejpam-4115	550	14	are	be	AUX
ejpam-4115	550	15	not	not	PART
ejpam-4115	550	16	true	true	ADJ
ejpam-4115	550	17	,	,	PUNCT
ejpam-4115	550	18	consider	consider	VERB
ejpam-4115	550	19	the	the	DET
ejpam-4115	550	20	space	space	NOUN
ejpam-4115	550	21	f	f	NOUN
ejpam-4115	551	1	[	[	X
ejpam-4115	551	2	0	0	NUM
ejpam-4115	551	3	,	,	PUNCT
ejpam-4115	551	4	1	1	NUM
ejpam-4115	551	5	]	]	PUNCT
ejpam-4115	551	6	of	of	ADP
ejpam-4115	551	7	all	all	DET
ejpam-4115	551	8	real	real	ADV
ejpam-4115	551	9	-	-	PUNCT
ejpam-4115	551	10	valued	value	VERB
ejpam-4115	551	11	functions	function	NOUN
ejpam-4115	551	12	on	on	ADP
ejpam-4115	551	13	[	[	X
ejpam-4115	551	14	0	0	NUM
ejpam-4115	551	15	,	,	PUNCT
ejpam-4115	551	16	1	1	NUM
ejpam-4115	551	17	]	]	PUNCT
ejpam-4115	551	18	.	.	PUNCT
ejpam-4115	552	1	we	we	PRON
ejpam-4115	552	2	will	will	AUX
ejpam-4115	552	3	construct	construct	VERB
ejpam-4115	552	4	a	a	DET
ejpam-4115	552	5	separated	separated	ADJ
ejpam-4115	552	6	family	family	NOUN
ejpam-4115	552	7	of	of	ADP
ejpam-4115	552	8	semi	semi	NOUN
ejpam-4115	552	9	-	-	NOUN
ejpam-4115	552	10	norms	norm	NOUN
ejpam-4115	552	11	on	on	ADP
ejpam-4115	552	12	f	f	PROPN
ejpam-4115	553	1	[	[	X
ejpam-4115	553	2	0	0	NUM
ejpam-4115	553	3	,	,	PUNCT
ejpam-4115	553	4	1	1	NUM
ejpam-4115	553	5	]	]	PUNCT
ejpam-4115	553	6	from	from	ADP
ejpam-4115	553	7	which	which	PRON
ejpam-4115	553	8	a	a	DET
ejpam-4115	553	9	locally	locally	ADV
ejpam-4115	553	10	convex	convex	ADJ
ejpam-4115	553	11	topology	topology	NOUN
ejpam-4115	553	12	on	on	ADP
ejpam-4115	553	13	f	f	PROPN
ejpam-4115	553	14	[	[	X
ejpam-4115	553	15	0	0	NUM
ejpam-4115	553	16	,	,	PUNCT
ejpam-4115	553	17	1	1	NUM
ejpam-4115	553	18	]	]	PUNCT
ejpam-4115	553	19	exists	exist	VERB
ejpam-4115	553	20	(	(	PUNCT
ejpam-4115	553	21	see	see	VERB
ejpam-4115	553	22	[	[	X
ejpam-4115	553	23	10	10	NUM
ejpam-4115	553	24	]	]	NUM
ejpam-4115	553	25	)	)	PUNCT
ejpam-4115	553	26	.	.	PUNCT
ejpam-4115	554	1	for	for	ADP
ejpam-4115	554	2	each	each	DET
ejpam-4115	554	3	α	α	NOUN
ejpam-4115	554	4	∈	∈	PROPN
ejpam-4115	555	1	[	[	X
ejpam-4115	555	2	0	0	NUM
ejpam-4115	555	3	,	,	PUNCT
ejpam-4115	555	4	1	1	NUM
ejpam-4115	555	5	]	]	PUNCT
ejpam-4115	555	6	,	,	PUNCT
ejpam-4115	555	7	let	let	VERB
ejpam-4115	555	8	ρα(f	ρα(f	PUNCT
ejpam-4115	555	9	)	)	PUNCT
ejpam-4115	555	10	=	=	PUNCT
ejpam-4115	556	1	|f(α)|	|f(α)|	ADJ
ejpam-4115	556	2	for	for	ADP
ejpam-4115	556	3	all	all	DET
ejpam-4115	556	4	f	f	PROPN
ejpam-4115	556	5	∈	∈	PROPN
ejpam-4115	556	6	f	f	X
ejpam-4115	557	1	[	[	X
ejpam-4115	557	2	0	0	NUM
ejpam-4115	557	3	,	,	PUNCT
ejpam-4115	557	4	1	1	NUM
ejpam-4115	557	5	]	]	PUNCT
ejpam-4115	557	6	and	and	CCONJ
ejpam-4115	557	7	let	let	VERB
ejpam-4115	557	8	p	p	NOUN
ejpam-4115	557	9	=	=	PUNCT
ejpam-4115	557	10	{	{	PUNCT
ejpam-4115	557	11	ρα	ρα	X
ejpam-4115	557	12	:	:	PUNCT
ejpam-4115	557	13	α	α	PROPN
ejpam-4115	557	14	∈	∈	PROPN
ejpam-4115	558	1	[	[	X
ejpam-4115	558	2	0	0	NUM
ejpam-4115	558	3	,	,	PUNCT
ejpam-4115	558	4	1	1	NUM
ejpam-4115	558	5	]	]	PUNCT
ejpam-4115	558	6	}	}	PUNCT
ejpam-4115	558	7	.	.	PUNCT
ejpam-4115	559	1	for	for	ADP
ejpam-4115	559	2	f	f	PROPN
ejpam-4115	559	3	,	,	PUNCT
ejpam-4115	559	4	g	g	PROPN
ejpam-4115	559	5	∈	∈	PROPN
ejpam-4115	559	6	f	f	X
ejpam-4115	560	1	[	[	X
ejpam-4115	560	2	0	0	NUM
ejpam-4115	560	3	,	,	PUNCT
ejpam-4115	560	4	1	1	NUM
ejpam-4115	560	5	]	]	PUNCT
ejpam-4115	560	6	and	and	CCONJ
ejpam-4115	560	7	c	c	NOUN
ejpam-4115	560	8	∈	∈	PROPN
ejpam-4115	560	9	r	r	NOUN
ejpam-4115	560	10	,	,	PUNCT
ejpam-4115	560	11	ρα(f	ρα(f	X
ejpam-4115	560	12	+	+	CCONJ
ejpam-4115	560	13	g	g	NOUN
ejpam-4115	560	14	)	)	PUNCT
ejpam-4115	560	15	=	=	SYM
ejpam-4115	560	16	|f(α	|f(α	NOUN
ejpam-4115	560	17	)	)	PUNCT
ejpam-4115	561	1	+	+	CCONJ
ejpam-4115	561	2	g(α)|	g(α)|	VERB
ejpam-4115	561	3	≤	≤	NUM
ejpam-4115	561	4	|f(α)|+	|f(α)|+	NOUN
ejpam-4115	561	5	|g(α)|	|g(α)|	NOUN
ejpam-4115	561	6	=	=	SYM
ejpam-4115	561	7	ρα(f	ρα(f	ADJ
ejpam-4115	561	8	)	)	PUNCT
ejpam-4115	561	9	+	+	NUM
ejpam-4115	561	10	ρα(g	ρα(g	NUM
ejpam-4115	561	11	)	)	PUNCT
ejpam-4115	561	12	and	and	CCONJ
ejpam-4115	561	13	ρα(cf	ρα(cf	VERB
ejpam-4115	561	14	)	)	PUNCT
ejpam-4115	561	15	=	=	SYM
ejpam-4115	561	16	|cf(α)|	|cf(α)|	X
ejpam-4115	561	17	=	=	SYM
ejpam-4115	561	18	|c|ρα(f	|c|ρα(f	PROPN
ejpam-4115	561	19	)	)	PUNCT
ejpam-4115	561	20	.	.	PUNCT
ejpam-4115	562	1	if	if	SCONJ
ejpam-4115	562	2	ρα(f	ρα(f	NOUN
ejpam-4115	562	3	)	)	PUNCT
ejpam-4115	562	4	=	=	SYM
ejpam-4115	562	5	0	0	NUM
ejpam-4115	562	6	for	for	ADP
ejpam-4115	562	7	all	all	DET
ejpam-4115	562	8	α	α	PRON
ejpam-4115	562	9	∈	∈	PROPN
ejpam-4115	563	1	[	[	X
ejpam-4115	563	2	0	0	NUM
ejpam-4115	563	3	,	,	PUNCT
ejpam-4115	563	4	1	1	NUM
ejpam-4115	563	5	]	]	PUNCT
ejpam-4115	563	6	,	,	PUNCT
ejpam-4115	563	7	then	then	ADV
ejpam-4115	563	8	f	f	PROPN
ejpam-4115	563	9	is	be	AUX
ejpam-4115	563	10	the	the	DET
ejpam-4115	563	11	zero	zero	NUM
ejpam-4115	563	12	function	function	NOUN
ejpam-4115	563	13	.	.	PUNCT
ejpam-4115	564	1	hence	hence	ADV
ejpam-4115	564	2	,	,	PUNCT
ejpam-4115	564	3	p	p	PROPN
ejpam-4115	564	4	is	be	AUX
ejpam-4115	564	5	a	a	DET
ejpam-4115	564	6	separating	separate	VERB
ejpam-4115	564	7	family	family	NOUN
ejpam-4115	564	8	of	of	ADP
ejpam-4115	564	9	semi	semi	NOUN
ejpam-4115	564	10	-	-	NOUN
ejpam-4115	564	11	norms	norm	NOUN
ejpam-4115	564	12	.	.	PUNCT
ejpam-4115	565	1	in	in	ADP
ejpam-4115	565	2	this	this	DET
ejpam-4115	565	3	space	space	NOUN
ejpam-4115	565	4	,	,	PUNCT
ejpam-4115	565	5	the	the	DET
ejpam-4115	565	6	set	set	NOUN
ejpam-4115	565	7	vα	vα	PROPN
ejpam-4115	565	8	,	,	PUNCT
ejpam-4115	565	9	n	n	NOUN
ejpam-4115	565	10	=	=	PRON
ejpam-4115	565	11	{	{	PUNCT
ejpam-4115	565	12	x	x	SYM
ejpam-4115	565	13	∈	∈	NOUN
ejpam-4115	565	14	f	f	X
ejpam-4115	566	1	[	[	X
ejpam-4115	566	2	0	0	NUM
ejpam-4115	566	3	,	,	PUNCT
ejpam-4115	566	4	1	1	NUM
ejpam-4115	566	5	]	]	PUNCT
ejpam-4115	566	6	:	:	PUNCT
ejpam-4115	566	7	ρα(x	ρα(x	NUM
ejpam-4115	566	8	)	)	PUNCT
ejpam-4115	566	9	<	<	X
ejpam-4115	566	10	1	1	NUM
ejpam-4115	566	11	n	n	CCONJ
ejpam-4115	566	12	}	}	PUNCT
ejpam-4115	566	13	is	be	AUX
ejpam-4115	566	14	an	an	DET
ejpam-4115	566	15	absorbing	absorbing	ADJ
ejpam-4115	566	16	,	,	PUNCT
ejpam-4115	566	17	balanced	balanced	ADJ
ejpam-4115	566	18	and	and	CCONJ
ejpam-4115	566	19	convex	convex	ADJ
ejpam-4115	566	20	θ	θ	PROPN
ejpam-4115	566	21	-	-	PUNCT
ejpam-4115	566	22	nbd	nbd	PROPN
ejpam-4115	566	23	for	for	ADP
ejpam-4115	566	24	α	α	PROPN
ejpam-4115	566	25	∈	∈	PROPN
ejpam-4115	567	1	[	[	X
ejpam-4115	567	2	0	0	NUM
ejpam-4115	567	3	,	,	PUNCT
ejpam-4115	567	4	1	1	NUM
ejpam-4115	567	5	]	]	PUNCT
ejpam-4115	567	6	and	and	CCONJ
ejpam-4115	567	7	n	n	DET
ejpam-4115	567	8	∈	∈	PROPN
ejpam-4115	567	9	n.	n.	NOUN
ejpam-4115	567	10	the	the	DET
ejpam-4115	567	11	finite	finite	ADJ
ejpam-4115	567	12	intersections	intersection	NOUN
ejpam-4115	567	13	of	of	ADP
ejpam-4115	567	14	sets	set	NOUN
ejpam-4115	567	15	of	of	ADP
ejpam-4115	567	16	this	this	DET
ejpam-4115	567	17	form	form	NOUN
ejpam-4115	567	18	is	be	AUX
ejpam-4115	567	19	a	a	DET
ejpam-4115	567	20	local	local	ADJ
ejpam-4115	567	21	base	base	NOUN
ejpam-4115	567	22	at	at	ADP
ejpam-4115	567	23	θ	θ	PROPN
ejpam-4115	567	24	for	for	ADP
ejpam-4115	567	25	the	the	DET
ejpam-4115	567	26	topology	topology	NOUN
ejpam-4115	567	27	on	on	ADP
ejpam-4115	567	28	f	f	PROPN
ejpam-4115	568	1	[	[	X
ejpam-4115	568	2	0	0	NUM
ejpam-4115	568	3	,	,	PUNCT
ejpam-4115	568	4	1	1	NUM
ejpam-4115	568	5	]	]	PUNCT
ejpam-4115	568	6	(	(	PUNCT
ejpam-4115	568	7	see	see	VERB
ejpam-4115	568	8	[	[	X
ejpam-4115	568	9	10	10	NUM
ejpam-4115	568	10	]	]	NUM
ejpam-4115	568	11	)	)	PUNCT
ejpam-4115	568	12	)	)	PUNCT
ejpam-4115	568	13	.	.	PUNCT
ejpam-4115	569	1	r.	r.	PROPN
ejpam-4115	569	2	e.	e.	PROPN
ejpam-4115	569	3	maza	maza	PROPN
ejpam-4115	569	4	,	,	PUNCT
ejpam-4115	569	5	s.	s.	PROPN
ejpam-4115	569	6	r.	r.	PROPN
ejpam-4115	569	7	canoy	canoy	PROPN
ejpam-4115	569	8	,	,	PUNCT
ejpam-4115	569	9	jr	jr	PROPN
ejpam-4115	569	10	.	.	PROPN
ejpam-4115	569	11	/	/	SYM
ejpam-4115	569	12	eur	eur	PROPN
ejpam-4115	569	13	.	.	PUNCT
ejpam-4115	570	1	j.	j.	PROPN
ejpam-4115	570	2	pure	pure	PROPN
ejpam-4115	570	3	appl	appl	PROPN
ejpam-4115	570	4	.	.	PROPN
ejpam-4115	570	5	math	math	PROPN
ejpam-4115	570	6	,	,	PUNCT
ejpam-4115	570	7	14	14	NUM
ejpam-4115	570	8	(	(	PUNCT
ejpam-4115	570	9	4	4	NUM
ejpam-4115	570	10	)	)	PUNCT
ejpam-4115	570	11	(	(	PUNCT
ejpam-4115	570	12	2021	2021	NUM
ejpam-4115	570	13	)	)	PUNCT
ejpam-4115	570	14	,	,	PUNCT
ejpam-4115	570	15	1169	1169	NUM
ejpam-4115	570	16	-	-	SYM
ejpam-4115	570	17	1183	1183	NUM
ejpam-4115	570	18	1181	1181	NUM
ejpam-4115	570	19	next	next	ADV
ejpam-4115	570	20	,	,	PUNCT
ejpam-4115	570	21	define	define	VERB
ejpam-4115	570	22	h	h	NOUN
ejpam-4115	570	23	:	:	PUNCT
ejpam-4115	571	1	[	[	X
ejpam-4115	571	2	0	0	NUM
ejpam-4115	571	3	,	,	PUNCT
ejpam-4115	571	4	1	1	NUM
ejpam-4115	571	5	]	]	PUNCT
ejpam-4115	571	6	→	→	SYM
ejpam-4115	571	7	f	f	X
ejpam-4115	572	1	[	[	X
ejpam-4115	572	2	0	0	NUM
ejpam-4115	572	3	,	,	PUNCT
ejpam-4115	572	4	1	1	NUM
ejpam-4115	572	5	]	]	PUNCT
ejpam-4115	572	6	by	by	ADP
ejpam-4115	572	7	h(t	h(t	PROPN
ejpam-4115	572	8	)	)	PUNCT
ejpam-4115	572	9	=	=	SYM
ejpam-4115	572	10	et	et	NOUN
ejpam-4115	572	11	where	where	SCONJ
ejpam-4115	572	12	et	et	PROPN
ejpam-4115	572	13	is	be	AUX
ejpam-4115	572	14	a	a	DET
ejpam-4115	572	15	function	function	NOUN
ejpam-4115	572	16	on	on	ADP
ejpam-4115	572	17	[	[	X
ejpam-4115	572	18	0	0	NUM
ejpam-4115	572	19	,	,	PUNCT
ejpam-4115	572	20	1	1	NUM
ejpam-4115	572	21	]	]	PUNCT
ejpam-4115	572	22	given	give	VERB
ejpam-4115	572	23	by	by	ADP
ejpam-4115	572	24	et(x	et(x	NOUN
ejpam-4115	572	25	)	)	PUNCT
ejpam-4115	572	26	=	=	PRON
ejpam-4115	572	27	{	{	PUNCT
ejpam-4115	572	28	1	1	NUM
ejpam-4115	572	29	,	,	PUNCT
ejpam-4115	572	30	for	for	ADP
ejpam-4115	572	31	x	x	X
ejpam-4115	572	32	=	=	SYM
ejpam-4115	572	33	t	t	PROPN
ejpam-4115	572	34	0	0	NUM
ejpam-4115	572	35	,	,	PUNCT
ejpam-4115	572	36	for	for	SCONJ
ejpam-4115	572	37	x	x	SYM
ejpam-4115	572	38	̸=	̸=	PROPN
ejpam-4115	572	39	t.	t.	NOUN
ejpam-4115	572	40	consider	consider	VERB
ejpam-4115	572	41	the	the	DET
ejpam-4115	572	42	function	function	NOUN
ejpam-4115	572	43	θ	θ	NOUN
ejpam-4115	572	44	:	:	PUNCT
ejpam-4115	573	1	[	[	X
ejpam-4115	573	2	0	0	NUM
ejpam-4115	573	3	,	,	PUNCT
ejpam-4115	573	4	1	1	NUM
ejpam-4115	573	5	]	]	PUNCT
ejpam-4115	573	6	→	→	SYM
ejpam-4115	573	7	f	f	X
ejpam-4115	574	1	[	[	X
ejpam-4115	574	2	0	0	NUM
ejpam-4115	574	3	,	,	PUNCT
ejpam-4115	574	4	1	1	NUM
ejpam-4115	574	5	]	]	PUNCT
ejpam-4115	574	6	that	that	PRON
ejpam-4115	574	7	maps	map	VERB
ejpam-4115	574	8	each	each	DET
ejpam-4115	574	9	number	number	NOUN
ejpam-4115	574	10	in	in	ADP
ejpam-4115	574	11	[	[	X
ejpam-4115	574	12	0	0	NUM
ejpam-4115	574	13	,	,	PUNCT
ejpam-4115	574	14	1	1	NUM
ejpam-4115	574	15	]	]	PUNCT
ejpam-4115	574	16	to	to	ADP
ejpam-4115	574	17	the	the	DET
ejpam-4115	574	18	zero	zero	NUM
ejpam-4115	574	19	function	function	NOUN
ejpam-4115	574	20	on	on	ADP
ejpam-4115	574	21	[	[	X
ejpam-4115	574	22	0	0	NUM
ejpam-4115	574	23	,	,	PUNCT
ejpam-4115	574	24	1	1	NUM
ejpam-4115	574	25	]	]	PUNCT
ejpam-4115	574	26	.	.	PUNCT
ejpam-4115	575	1	clearly	clearly	ADV
ejpam-4115	575	2	,	,	PUNCT
ejpam-4115	575	3	θ	θ	PROPN
ejpam-4115	575	4	is	be	AUX
ejpam-4115	575	5	an	an	DET
ejpam-4115	575	6	acg∗	acg∗	NOUN
ejpam-4115	575	7	function	function	NOUN
ejpam-4115	575	8	.	.	PUNCT
ejpam-4115	576	1	since	since	SCONJ
ejpam-4115	576	2	∆(v	∆(v	PROPN
ejpam-4115	576	3	,	,	PUNCT
ejpam-4115	576	4	θ	θ	PROPN
ejpam-4115	576	5	,	,	PUNCT
ejpam-4115	576	6	h	h	NOUN
ejpam-4115	576	7	)	)	PUNCT
ejpam-4115	576	8	⊆	⊆	NUM
ejpam-4115	576	9	∆(u	∆(u	PROPN
ejpam-4115	576	10	,	,	PUNCT
ejpam-4115	576	11	θ	θ	PROPN
ejpam-4115	576	12	,	,	PUNCT
ejpam-4115	576	13	h	h	NOUN
ejpam-4115	576	14	)	)	PUNCT
ejpam-4115	576	15	whenever	whenever	SCONJ
ejpam-4115	576	16	u	u	PROPN
ejpam-4115	576	17	⊆	⊆	NUM
ejpam-4115	576	18	v	v	NOUN
ejpam-4115	576	19	,	,	PUNCT
ejpam-4115	576	20	it	it	PRON
ejpam-4115	576	21	is	be	AUX
ejpam-4115	576	22	enough	enough	ADJ
ejpam-4115	576	23	to	to	PART
ejpam-4115	576	24	prove	prove	VERB
ejpam-4115	576	25	that	that	SCONJ
ejpam-4115	576	26	∆(u	∆(u	PROPN
ejpam-4115	576	27	,	,	PUNCT
ejpam-4115	576	28	θ	θ	PROPN
ejpam-4115	576	29	,	,	PUNCT
ejpam-4115	576	30	h	h	NOUN
ejpam-4115	576	31	)	)	PUNCT
ejpam-4115	576	32	has	have	VERB
ejpam-4115	576	33	measure	measure	NOUN
ejpam-4115	576	34	zero	zero	NUM
ejpam-4115	576	35	for	for	ADP
ejpam-4115	576	36	any	any	DET
ejpam-4115	576	37	local	local	ADJ
ejpam-4115	576	38	base	base	NOUN
ejpam-4115	576	39	u	u	NOUN
ejpam-4115	576	40	at	at	ADP
ejpam-4115	576	41	θ	θ	PROPN
ejpam-4115	576	42	to	to	PART
ejpam-4115	576	43	show	show	VERB
ejpam-4115	576	44	that	that	SCONJ
ejpam-4115	576	45	h	h	NOUN
ejpam-4115	576	46	is	be	AUX
ejpam-4115	576	47	weak	weak	ADJ
ejpam-4115	576	48	denjoy	denjoy	NOUN
ejpam-4115	576	49	integrable	integrable	ADJ
ejpam-4115	576	50	(	(	PUNCT
ejpam-4115	576	51	hence	hence	ADV
ejpam-4115	576	52	,	,	PUNCT
ejpam-4115	576	53	also	also	ADV
ejpam-4115	576	54	sh	sh	PROPN
ejpam-4115	576	55	-	-	PUNCT
ejpam-4115	576	56	integrable	integrable	ADJ
ejpam-4115	576	57	by	by	ADP
ejpam-4115	576	58	theorem	theorem	NOUN
ejpam-4115	576	59	12	12	NUM
ejpam-4115	576	60	)	)	PUNCT
ejpam-4115	576	61	.	.	PUNCT
ejpam-4115	577	1	now	now	ADV
ejpam-4115	577	2	,	,	PUNCT
ejpam-4115	577	3	given	give	VERB
ejpam-4115	577	4	a	a	DET
ejpam-4115	577	5	local	local	ADJ
ejpam-4115	577	6	base	base	NOUN
ejpam-4115	577	7	u	u	NOUN
ejpam-4115	577	8	at	at	ADP
ejpam-4115	577	9	θ	θ	PROPN
ejpam-4115	577	10	,	,	PUNCT
ejpam-4115	577	11	u	u	NOUN
ejpam-4115	577	12	is	be	AUX
ejpam-4115	577	13	a	a	DET
ejpam-4115	577	14	finite	finite	ADJ
ejpam-4115	577	15	intersection	intersection	NOUN
ejpam-4115	577	16	of	of	ADP
ejpam-4115	577	17	some	some	DET
ejpam-4115	577	18	sets	set	NOUN
ejpam-4115	577	19	of	of	ADP
ejpam-4115	577	20	the	the	DET
ejpam-4115	577	21	form	form	NOUN
ejpam-4115	577	22	vαi	vαi	ADJ
ejpam-4115	577	23	,	,	PUNCT
ejpam-4115	577	24	ni	ni	NOUN
ejpam-4115	577	25	for	for	ADP
ejpam-4115	577	26	1	1	NUM
ejpam-4115	577	27	≤	≤	NUM
ejpam-4115	577	28	i	i	PRON
ejpam-4115	577	29	≤	≤	PROPN
ejpam-4115	577	30	k.	k.	PROPN
ejpam-4115	578	1	let	let	VERB
ejpam-4115	578	2	β	β	X
ejpam-4115	578	3	∈	∈	PROPN
ejpam-4115	579	1	[	[	X
ejpam-4115	579	2	0	0	NUM
ejpam-4115	579	3	,	,	PUNCT
ejpam-4115	579	4	1	1	NUM
ejpam-4115	579	5	]	]	PUNCT
ejpam-4115	579	6	.	.	PUNCT
ejpam-4115	580	1	if	if	SCONJ
ejpam-4115	580	2	β	β	X
ejpam-4115	580	3	is	be	AUX
ejpam-4115	580	4	distinct	distinct	ADJ
ejpam-4115	580	5	from	from	ADP
ejpam-4115	580	6	αi	αi	PRON
ejpam-4115	580	7	for	for	ADP
ejpam-4115	580	8	each	each	DET
ejpam-4115	580	9	1	1	NUM
ejpam-4115	580	10	≤	≤	NUM
ejpam-4115	580	11	i	i	NOUN
ejpam-4115	580	12	≤	≤	PUNCT
ejpam-4115	581	1	k	k	X
ejpam-4115	581	2	,	,	PUNCT
ejpam-4115	581	3	then	then	ADV
ejpam-4115	581	4	we	we	PRON
ejpam-4115	581	5	may	may	AUX
ejpam-4115	581	6	choose	choose	VERB
ejpam-4115	581	7	δ	δ	PROPN
ejpam-4115	581	8	>	>	X
ejpam-4115	581	9	0	0	PUNCT
ejpam-4115	581	10	to	to	PART
ejpam-4115	581	11	be	be	AUX
ejpam-4115	581	12	sufficiently	sufficiently	ADV
ejpam-4115	581	13	small	small	ADJ
ejpam-4115	581	14	so	so	SCONJ
ejpam-4115	581	15	that	that	SCONJ
ejpam-4115	581	16	αi	αi	VERB
ejpam-4115	581	17	/∈	/∈	PUNCT
ejpam-4115	582	1	(	(	PUNCT
ejpam-4115	582	2	β	β	X
ejpam-4115	582	3	−	−	PROPN
ejpam-4115	582	4	δ	δ	PROPN
ejpam-4115	582	5	,	,	PUNCT
ejpam-4115	582	6	β	β	X
ejpam-4115	582	7	+	+	CCONJ
ejpam-4115	582	8	δ	δ	PROPN
ejpam-4115	582	9	)	)	PUNCT
ejpam-4115	582	10	for	for	ADP
ejpam-4115	582	11	each	each	DET
ejpam-4115	582	12	1	1	NUM
ejpam-4115	582	13	≤	≤	NUM
ejpam-4115	582	14	i	i	PRON
ejpam-4115	582	15	≤	≤	PROPN
ejpam-4115	583	1	k.	k.	NOUN
ejpam-4115	584	1	then	then	ADV
ejpam-4115	584	2	ραi	ραi	X
ejpam-4115	584	3	(	(	PUNCT
ejpam-4115	584	4	θ(v)−θ(u)−	θ(v)−θ(u)−	NOUN
ejpam-4115	584	5	h(β)(v	h(β)(v	X
ejpam-4115	584	6	−	−	PROPN
ejpam-4115	584	7	u	u	NOUN
ejpam-4115	584	8	)	)	PUNCT
ejpam-4115	584	9	)	)	PUNCT
ejpam-4115	585	1	=	=	PUNCT
ejpam-4115	585	2	0	0	PUNCT
ejpam-4115	586	1	whenever	whenever	SCONJ
ejpam-4115	586	2	0	0	NUM
ejpam-4115	586	3	≤	≤	NUM
ejpam-4115	586	4	u	u	NOUN
ejpam-4115	586	5	≤	≤	X
ejpam-4115	586	6	β	β	X
ejpam-4115	586	7	≤	≤	NUM
ejpam-4115	586	8	v	v	NUM
ejpam-4115	586	9	≤	≤	NUM
ejpam-4115	586	10	1	1	NUM
ejpam-4115	586	11	with	with	ADP
ejpam-4115	586	12	v	v	NUM
ejpam-4115	586	13	−	−	PROPN
ejpam-4115	586	14	u	u	NOUN
ejpam-4115	586	15	<	<	X
ejpam-4115	586	16	δ	δ	PROPN
ejpam-4115	586	17	and	and	CCONJ
ejpam-4115	586	18	1	1	NUM
ejpam-4115	586	19	≤	≤	NUM
ejpam-4115	586	20	i	i	PRON
ejpam-4115	586	21	≤	≤	PROPN
ejpam-4115	586	22	k.	k.	INTJ
ejpam-4115	587	1	this	this	PRON
ejpam-4115	587	2	certainly	certainly	ADV
ejpam-4115	587	3	implies	imply	VERB
ejpam-4115	587	4	that	that	SCONJ
ejpam-4115	587	5	β	β	PROPN
ejpam-4115	587	6	/∈	/∈	PUNCT
ejpam-4115	588	1	∆(u	∆(u	ADJ
ejpam-4115	588	2	,	,	PUNCT
ejpam-4115	588	3	θ	θ	PROPN
ejpam-4115	588	4	,	,	PUNCT
ejpam-4115	588	5	h	h	NOUN
ejpam-4115	588	6	)	)	PUNCT
ejpam-4115	588	7	.	.	PUNCT
ejpam-4115	589	1	so	so	ADV
ejpam-4115	589	2	,	,	PUNCT
ejpam-4115	589	3	∆(u	∆(u	ADJ
ejpam-4115	589	4	,	,	PUNCT
ejpam-4115	589	5	θ	θ	PROPN
ejpam-4115	589	6	,	,	PUNCT
ejpam-4115	589	7	h	h	NOUN
ejpam-4115	589	8	)	)	PUNCT
ejpam-4115	589	9	⊆	⊆	NUM
ejpam-4115	589	10	{	{	PUNCT
ejpam-4115	589	11	αi	αi	X
ejpam-4115	589	12	:	:	PUNCT
ejpam-4115	589	13	1	1	NUM
ejpam-4115	589	14	≤	≤	NUM
ejpam-4115	589	15	i	i	X
ejpam-4115	589	16	≤	≤	PUNCT
ejpam-4115	590	1	k	k	X
ejpam-4115	590	2	}	}	PUNCT
ejpam-4115	590	3	and	and	CCONJ
ejpam-4115	590	4	∆(u	∆(u	ADJ
ejpam-4115	590	5	,	,	PUNCT
ejpam-4115	590	6	θ	θ	PROPN
ejpam-4115	590	7	,	,	PUNCT
ejpam-4115	590	8	h	h	NOUN
ejpam-4115	590	9	)	)	PUNCT
ejpam-4115	590	10	has	have	VERB
ejpam-4115	590	11	a	a	DET
ejpam-4115	590	12	measure	measure	NOUN
ejpam-4115	590	13	zero	zero	NUM
ejpam-4115	590	14	.	.	PUNCT
ejpam-4115	591	1	therefore	therefore	ADV
ejpam-4115	591	2	,	,	PUNCT
ejpam-4115	591	3	h	h	NOUN
ejpam-4115	591	4	is	be	AUX
ejpam-4115	591	5	weak	weak	ADJ
ejpam-4115	591	6	denjoy	denjoy	NOUN
ejpam-4115	591	7	integrable	integrable	ADJ
ejpam-4115	591	8	with	with	ADP
ejpam-4115	591	9	weak	weak	ADJ
ejpam-4115	591	10	denjoy	denjoy	NOUN
ejpam-4115	591	11	primitive	primitive	ADJ
ejpam-4115	591	12	θ	θ	PROPN
ejpam-4115	591	13	.	.	PUNCT
ejpam-4115	591	14	by	by	ADP
ejpam-4115	591	15	theorem	theorem	NOUN
ejpam-4115	591	16	5	5	NUM
ejpam-4115	591	17	,	,	PUNCT
ejpam-4115	591	18	observe	observe	VERB
ejpam-4115	591	19	that	that	SCONJ
ejpam-4115	591	20	[	[	X
ejpam-4115	591	21	0	0	NUM
ejpam-4115	591	22	,	,	PUNCT
ejpam-4115	591	23	1	1	NUM
ejpam-4115	591	24	]	]	PUNCT
ejpam-4115	591	25	=	=	SYM
ejpam-4115	591	26	⋃	⋃	PROPN
ejpam-4115	591	27	α∈[0,1],n∈n	α∈[0,1],n∈n	PROPN
ejpam-4115	591	28	∆(vα	∆(vα	NOUN
ejpam-4115	591	29	,	,	PUNCT
ejpam-4115	591	30	n	n	CCONJ
ejpam-4115	591	31	,	,	PUNCT
ejpam-4115	591	32	θ	θ	PROPN
ejpam-4115	591	33	,	,	PUNCT
ejpam-4115	591	34	h	h	NOUN
ejpam-4115	591	35	)	)	PUNCT
ejpam-4115	591	36	⊆	⊆	NUM
ejpam-4115	591	37	⋃	⋃	PROPN
ejpam-4115	591	38	θ	θ	PROPN
ejpam-4115	591	39	-	-	PUNCT
ejpam-4115	591	40	nbd	nbd	PROPN
ejpam-4115	591	41	u	u	PROPN
ejpam-4115	591	42	∆(u	∆(u	PROPN
ejpam-4115	591	43	,	,	PUNCT
ejpam-4115	591	44	θ	θ	PROPN
ejpam-4115	591	45	,	,	PUNCT
ejpam-4115	591	46	h	h	NOUN
ejpam-4115	591	47	)	)	PUNCT
ejpam-4115	591	48	⊆	⊆	NUM
ejpam-4115	592	1	[	[	X
ejpam-4115	592	2	0	0	NUM
ejpam-4115	592	3	,	,	PUNCT
ejpam-4115	592	4	1	1	NUM
ejpam-4115	592	5	]	]	PUNCT
ejpam-4115	592	6	is	be	AUX
ejpam-4115	592	7	the	the	DET
ejpam-4115	592	8	set	set	NOUN
ejpam-4115	592	9	at	at	ADP
ejpam-4115	592	10	which	which	PRON
ejpam-4115	592	11	the	the	DET
ejpam-4115	592	12	derivative	derivative	NOUN
ejpam-4115	592	13	of	of	ADP
ejpam-4115	592	14	θ	θ	PROPN
ejpam-4115	592	15	does	do	AUX
ejpam-4115	592	16	not	not	PART
ejpam-4115	592	17	exist	exist	VERB
ejpam-4115	592	18	.	.	PUNCT
ejpam-4115	593	1	thus	thus	ADV
ejpam-4115	593	2	,	,	PUNCT
ejpam-4115	593	3	h	h	NOUN
ejpam-4115	593	4	is	be	AUX
ejpam-4115	593	5	not	not	PART
ejpam-4115	593	6	denjoy	denjoy	VERB
ejpam-4115	593	7	integrable	integrable	ADJ
ejpam-4115	593	8	.	.	PUNCT
ejpam-4115	594	1	4	4	X
ejpam-4115	594	2	.	.	X
ejpam-4115	594	3	conclusion	conclusion	NOUN
ejpam-4115	594	4	although	although	SCONJ
ejpam-4115	594	5	it	it	PRON
ejpam-4115	594	6	is	be	AUX
ejpam-4115	594	7	likely	likely	ADJ
ejpam-4115	594	8	that	that	SCONJ
ejpam-4115	594	9	the	the	DET
ejpam-4115	594	10	hk	hk	PROPN
ejpam-4115	594	11	and	and	CCONJ
ejpam-4115	594	12	the	the	DET
ejpam-4115	594	13	sh	sh	PROPN
ejpam-4115	594	14	integrals	integral	NOUN
ejpam-4115	594	15	coincide	coincide	VERB
ejpam-4115	594	16	,	,	PUNCT
ejpam-4115	594	17	showing	show	VERB
ejpam-4115	594	18	the	the	DET
ejpam-4115	594	19	possible	possible	ADJ
ejpam-4115	594	20	equivalence	equivalence	NOUN
ejpam-4115	594	21	is	be	AUX
ejpam-4115	594	22	not	not	PART
ejpam-4115	594	23	the	the	DET
ejpam-4115	594	24	focus	focus	NOUN
ejpam-4115	594	25	of	of	ADP
ejpam-4115	594	26	this	this	DET
ejpam-4115	594	27	present	present	ADJ
ejpam-4115	594	28	paper	paper	NOUN
ejpam-4115	594	29	.	.	PUNCT
ejpam-4115	595	1	we	we	PRON
ejpam-4115	595	2	thus	thus	ADV
ejpam-4115	595	3	leave	leave	VERB
ejpam-4115	595	4	to	to	ADP
ejpam-4115	595	5	the	the	DET
ejpam-4115	595	6	interested	interested	ADJ
ejpam-4115	595	7	readers	reader	NOUN
ejpam-4115	595	8	the	the	DET
ejpam-4115	595	9	task	task	NOUN
ejpam-4115	595	10	of	of	ADP
ejpam-4115	595	11	showing	show	VERB
ejpam-4115	595	12	whether	whether	SCONJ
ejpam-4115	595	13	or	or	CCONJ
ejpam-4115	595	14	not	not	PART
ejpam-4115	595	15	these	these	DET
ejpam-4115	595	16	integrals	integral	NOUN
ejpam-4115	595	17	are	be	AUX
ejpam-4115	595	18	equivalent	equivalent	ADJ
ejpam-4115	595	19	.	.	PUNCT
ejpam-4115	596	1	in	in	ADP
ejpam-4115	596	2	this	this	DET
ejpam-4115	596	3	paper	paper	NOUN
ejpam-4115	596	4	,	,	PUNCT
ejpam-4115	596	5	ac∗	ac∗	ADJ
ejpam-4115	596	6	and	and	CCONJ
ejpam-4115	596	7	acg∗	acg∗	NOUN
ejpam-4115	596	8	properties	property	NOUN
ejpam-4115	596	9	have	have	AUX
ejpam-4115	596	10	been	be	AUX
ejpam-4115	596	11	introduced	introduce	VERB
ejpam-4115	596	12	for	for	ADP
ejpam-4115	596	13	lctvs	lctv	NOUN
ejpam-4115	596	14	-	-	PUNCT
ejpam-4115	596	15	valued	value	VERB
ejpam-4115	596	16	functions	function	NOUN
ejpam-4115	596	17	.	.	PUNCT
ejpam-4115	597	1	the	the	DET
ejpam-4115	597	2	acg∗	acg∗	PROPN
ejpam-4115	597	3	property	property	NOUN
ejpam-4115	597	4	together	together	ADV
ejpam-4115	597	5	with	with	ADP
ejpam-4115	597	6	the	the	DET
ejpam-4115	597	7	concepts	concept	NOUN
ejpam-4115	597	8	of	of	ADP
ejpam-4115	597	9	differentiability	differentiability	NOUN
ejpam-4115	597	10	and	and	CCONJ
ejpam-4115	597	11	∆(u	∆(u	ADJ
ejpam-4115	597	12	,	,	PUNCT
ejpam-4115	597	13	f	f	PROPN
ejpam-4115	597	14	,	,	PUNCT
ejpam-4115	597	15	f	f	PROPN
ejpam-4115	597	16	)	)	PUNCT
ejpam-4115	597	17	,	,	PUNCT
ejpam-4115	597	18	where	where	SCONJ
ejpam-4115	597	19	u	u	NOUN
ejpam-4115	597	20	is	be	AUX
ejpam-4115	597	21	a	a	DET
ejpam-4115	597	22	θ	θ	PROPN
ejpam-4115	597	23	-	-	PUNCT
ejpam-4115	597	24	nbd	nbd	PROPN
ejpam-4115	597	25	and	and	CCONJ
ejpam-4115	597	26	f	f	PROPN
ejpam-4115	597	27	and	and	CCONJ
ejpam-4115	597	28	f	f	PROPN
ejpam-4115	597	29	are	be	AUX
ejpam-4115	597	30	lctvs	lctvs	NOUN
ejpam-4115	597	31	-	-	PUNCT
ejpam-4115	597	32	valued	value	VERB
ejpam-4115	597	33	functions	function	NOUN
ejpam-4115	597	34	,	,	PUNCT
ejpam-4115	597	35	have	have	AUX
ejpam-4115	597	36	been	be	AUX
ejpam-4115	597	37	used	use	VERB
ejpam-4115	597	38	to	to	PART
ejpam-4115	597	39	define	define	VERB
ejpam-4115	597	40	two	two	NUM
ejpam-4115	597	41	denjoy	denjoy	NOUN
ejpam-4115	597	42	-	-	PUNCT
ejpam-4115	597	43	type	type	NOUN
ejpam-4115	597	44	integrals	integral	NOUN
ejpam-4115	597	45	.	.	PUNCT
ejpam-4115	598	1	when	when	SCONJ
ejpam-4115	598	2	x	x	PRON
ejpam-4115	598	3	is	be	AUX
ejpam-4115	598	4	a	a	DET
ejpam-4115	598	5	banach	banach	NOUN
ejpam-4115	598	6	space	space	NOUN
ejpam-4115	598	7	,	,	PUNCT
ejpam-4115	598	8	the	the	DET
ejpam-4115	598	9	denjoy	denjoy	NOUN
ejpam-4115	598	10	-	-	PUNCT
ejpam-4115	598	11	bochner	bochner	NOUN
ejpam-4115	598	12	integral	integral	ADJ
ejpam-4115	598	13	defined	define	VERB
ejpam-4115	598	14	by	by	ADP
ejpam-4115	598	15	solodov	solodov	PROPN
ejpam-4115	598	16	is	be	AUX
ejpam-4115	598	17	included	include	VERB
ejpam-4115	598	18	in	in	ADP
ejpam-4115	598	19	the	the	DET
ejpam-4115	598	20	denjoy	denjoy	NOUN
ejpam-4115	598	21	integral	integral	ADJ
ejpam-4115	598	22	.	.	PUNCT
ejpam-4115	599	1	it	it	PRON
ejpam-4115	599	2	shown	show	VERB
ejpam-4115	599	3	that	that	SCONJ
ejpam-4115	599	4	these	these	DET
ejpam-4115	599	5	denjoy	denjoy	NOUN
ejpam-4115	599	6	-	-	PUNCT
ejpam-4115	599	7	type	type	NOUN
ejpam-4115	599	8	integrals	integral	NOUN
ejpam-4115	599	9	are	be	AUX
ejpam-4115	599	10	included	include	VERB
ejpam-4115	599	11	in	in	ADP
ejpam-4115	599	12	the	the	DET
ejpam-4115	599	13	sh	sh	PROPN
ejpam-4115	599	14	-	-	PUNCT
ejpam-4115	599	15	integral	integral	ADJ
ejpam-4115	599	16	.	.	PUNCT
ejpam-4115	600	1	however	however	ADV
ejpam-4115	600	2	,	,	PUNCT
ejpam-4115	600	3	as	as	SCONJ
ejpam-4115	600	4	shown	show	VERB
ejpam-4115	600	5	in	in	ADP
ejpam-4115	600	6	the	the	DET
ejpam-4115	600	7	paper	paper	NOUN
ejpam-4115	600	8	,	,	PUNCT
ejpam-4115	600	9	there	there	PRON
ejpam-4115	600	10	exists	exist	VERB
ejpam-4115	600	11	a	a	DET
ejpam-4115	600	12	weak	weak	ADJ
ejpam-4115	600	13	denjoy	denjoy	NOUN
ejpam-4115	600	14	integrable	integrable	ADJ
ejpam-4115	600	15	(	(	PUNCT
ejpam-4115	600	16	also	also	ADV
ejpam-4115	600	17	an	an	DET
ejpam-4115	600	18	sh	sh	PROPN
ejpam-4115	600	19	-	-	PUNCT
ejpam-4115	600	20	integrable	integrable	ADJ
ejpam-4115	600	21	)	)	PUNCT
ejpam-4115	600	22	function	function	NOUN
ejpam-4115	600	23	which	which	PRON
ejpam-4115	600	24	is	be	AUX
ejpam-4115	600	25	not	not	PART
ejpam-4115	600	26	denjoy	denjoy	VERB
ejpam-4115	600	27	integrable	integrable	ADJ
ejpam-4115	600	28	.	.	PUNCT
ejpam-4115	601	1	it	it	PRON
ejpam-4115	601	2	may	may	AUX
ejpam-4115	601	3	be	be	AUX
ejpam-4115	601	4	worthwhile	worthwhile	ADJ
ejpam-4115	601	5	to	to	PART
ejpam-4115	601	6	investigate	investigate	VERB
ejpam-4115	601	7	whether	whether	SCONJ
ejpam-4115	601	8	or	or	CCONJ
ejpam-4115	601	9	not	not	PART
ejpam-4115	601	10	the	the	DET
ejpam-4115	601	11	converse	converse	NOUN
ejpam-4115	601	12	of	of	ADP
ejpam-4115	601	13	theorem	theorem	NOUN
ejpam-4115	601	14	12	12	NUM
ejpam-4115	601	15	is	be	AUX
ejpam-4115	601	16	true	true	ADJ
ejpam-4115	601	17	.	.	PUNCT
ejpam-4115	602	1	the	the	DET
ejpam-4115	602	2	authors	author	NOUN
ejpam-4115	602	3	conjecture	conjecture	VERB
ejpam-4115	602	4	that	that	SCONJ
ejpam-4115	602	5	the	the	DET
ejpam-4115	602	6	converse	converse	NOUN
ejpam-4115	602	7	of	of	ADP
ejpam-4115	602	8	that	that	DET
ejpam-4115	602	9	result	result	NOUN
ejpam-4115	602	10	is	be	AUX
ejpam-4115	602	11	not	not	PART
ejpam-4115	602	12	true	true	ADJ
ejpam-4115	602	13	.	.	PUNCT
ejpam-4115	603	1	references	reference	NOUN
ejpam-4115	603	2	1182	1182	NUM
ejpam-4115	603	3	acknowledgements	acknowledgement	NOUN
ejpam-4115	603	4	we	we	PRON
ejpam-4115	603	5	would	would	AUX
ejpam-4115	603	6	like	like	VERB
ejpam-4115	603	7	to	to	PART
ejpam-4115	603	8	extend	extend	VERB
ejpam-4115	603	9	our	our	PRON
ejpam-4115	603	10	heartfelt	heartfelt	ADJ
ejpam-4115	603	11	thankfulness	thankfulness	NOUN
ejpam-4115	603	12	to	to	ADP
ejpam-4115	603	13	the	the	DET
ejpam-4115	603	14	referee	referee	NOUN
ejpam-4115	603	15	for	for	ADP
ejpam-4115	603	16	taking	take	VERB
ejpam-4115	603	17	the	the	DET
ejpam-4115	603	18	time	time	NOUN
ejpam-4115	603	19	to	to	PART
ejpam-4115	603	20	read	read	VERB
ejpam-4115	603	21	the	the	DET
ejpam-4115	603	22	initial	initial	ADJ
ejpam-4115	603	23	manuscript	manuscript	NOUN
ejpam-4115	603	24	and	and	CCONJ
ejpam-4115	603	25	for	for	ADP
ejpam-4115	603	26	the	the	DET
ejpam-4115	603	27	comments	comment	NOUN
ejpam-4115	603	28	and	and	CCONJ
ejpam-4115	603	29	suggestions	suggestion	NOUN
ejpam-4115	603	30	that	that	PRON
ejpam-4115	603	31	led	lead	VERB
ejpam-4115	603	32	us	we	PRON
ejpam-4115	603	33	to	to	ADP
ejpam-4115	603	34	this	this	DET
ejpam-4115	603	35	improved	improve	VERB
ejpam-4115	603	36	version	version	NOUN
ejpam-4115	603	37	of	of	ADP
ejpam-4115	603	38	the	the	DET
ejpam-4115	603	39	paper	paper	NOUN
ejpam-4115	603	40	.	.	PUNCT
ejpam-4115	604	1	further	far	ADV
ejpam-4115	604	2	,	,	PUNCT
ejpam-4115	604	3	we	we	PRON
ejpam-4115	604	4	would	would	AUX
ejpam-4115	604	5	like	like	VERB
ejpam-4115	604	6	to	to	PART
ejpam-4115	604	7	thank	thank	VERB
ejpam-4115	604	8	the	the	DET
ejpam-4115	604	9	department	department	NOUN
ejpam-4115	604	10	of	of	ADP
ejpam-4115	604	11	science	science	NOUN
ejpam-4115	604	12	and	and	CCONJ
ejpam-4115	604	13	technology	technology	NOUN
ejpam-4115	604	14	(	(	PUNCT
ejpam-4115	604	15	dost	dost	NOUN
ejpam-4115	604	16	)	)	PUNCT
ejpam-4115	604	17	,	,	PUNCT
ejpam-4115	604	18	phillipines	phillipine	NOUN
ejpam-4115	604	19	,	,	PUNCT
ejpam-4115	604	20	and	and	CCONJ
ejpam-4115	604	21	msu	msu	PROPN
ejpam-4115	604	22	-	-	PUNCT
ejpam-4115	604	23	iligan	iligan	PROPN
ejpam-4115	604	24	institute	institute	PROPN
ejpam-4115	604	25	of	of	ADP
ejpam-4115	604	26	technology	technology	NOUN
ejpam-4115	604	27	for	for	ADP
ejpam-4115	604	28	funding	fund	VERB
ejpam-4115	604	29	this	this	DET
ejpam-4115	604	30	research	research	NOUN
ejpam-4115	604	31	.	.	PUNCT
ejpam-4115	605	1	references	reference	NOUN
ejpam-4115	605	2	[	[	X
ejpam-4115	605	3	1	1	X
ejpam-4115	605	4	]	]	PUNCT
ejpam-4115	605	5	s.	s.	PROPN
ejpam-4115	605	6	canoy	canoy	PROPN
ejpam-4115	605	7	jr	jr	PROPN
ejpam-4115	605	8	.	.	PROPN
ejpam-4115	605	9	and	and	CCONJ
ejpam-4115	605	10	m.	m.	PROPN
ejpam-4115	605	11	navarro	navarro	PROPN
ejpam-4115	605	12	.	.	PUNCT
ejpam-4115	606	1	a	a	DET
ejpam-4115	606	2	denjoy	denjoy	NOUN
ejpam-4115	606	3	-	-	PUNCT
ejpam-4115	606	4	type	type	NOUN
ejpam-4115	606	5	integral	integral	ADJ
ejpam-4115	606	6	for	for	ADP
ejpam-4115	606	7	banach	banach	ADV
ejpam-4115	606	8	-	-	PUNCT
ejpam-4115	606	9	valued	value	VERB
ejpam-4115	606	10	functions	function	NOUN
ejpam-4115	606	11	.	.	PUNCT
ejpam-4115	607	1	rend	rend	VERB
ejpam-4115	607	2	.	.	PUNCT
ejpam-4115	608	1	circ	circ	PROPN
ejpam-4115	608	2	.	.	PUNCT
ejpam-4115	609	1	mat	mat	NOUN
ejpam-4115	609	2	.	.	PUNCT
ejpam-4115	609	3	palermo	palermo	PROPN
ejpam-4115	609	4	,	,	PUNCT
ejpam-4115	609	5	44(2):330–336	44(2):330–336	PROPN
ejpam-4115	609	6	,	,	PUNCT
ejpam-4115	609	7	1995	1995	NUM
ejpam-4115	609	8	.	.	PUNCT
ejpam-4115	610	1	[	[	X
ejpam-4115	610	2	2	2	X
ejpam-4115	610	3	]	]	PUNCT
ejpam-4115	610	4	s.	s.	PROPN
ejpam-4115	610	5	cao	cao	PROPN
ejpam-4115	610	6	.	.	PUNCT
ejpam-4115	611	1	the	the	DET
ejpam-4115	611	2	henstock	henstock	NOUN
ejpam-4115	611	3	integral	integral	ADJ
ejpam-4115	611	4	for	for	ADP
ejpam-4115	611	5	banach	banach	ADV
ejpam-4115	611	6	-	-	PUNCT
ejpam-4115	611	7	valued	value	VERB
ejpam-4115	611	8	functions	function	NOUN
ejpam-4115	611	9	.	.	PUNCT
ejpam-4115	612	1	southeast	southeast	ADJ
ejpam-4115	612	2	asian	asian	ADJ
ejpam-4115	612	3	bull	bull	PROPN
ejpam-4115	612	4	.	.	PUNCT
ejpam-4115	613	1	math	math	NOUN
ejpam-4115	613	2	.	.	PUNCT
ejpam-4115	613	3	,	,	PUNCT
ejpam-4115	613	4	16(1):35–40	16(1):35–40	NUM
ejpam-4115	613	5	,	,	PUNCT
ejpam-4115	613	6	1992	1992	NUM
ejpam-4115	613	7	.	.	PUNCT
ejpam-4115	614	1	[	[	X
ejpam-4115	614	2	3	3	X
ejpam-4115	614	3	]	]	X
ejpam-4115	614	4	j.	j.	PROPN
ejpam-4115	614	5	dugundji	dugundji	PROPN
ejpam-4115	614	6	.	.	PUNCT
ejpam-4115	614	7	topology	topology	PROPN
ejpam-4115	614	8	.	.	PUNCT
ejpam-4115	615	1	allyn	allyn	PROPN
ejpam-4115	615	2	and	and	CCONJ
ejpam-4115	615	3	bacon	bacon	PROPN
ejpam-4115	615	4	,	,	PUNCT
ejpam-4115	615	5	inc	inc	PROPN
ejpam-4115	615	6	.	.	PROPN
ejpam-4115	615	7	,	,	PUNCT
ejpam-4115	615	8	470	470	NUM
ejpam-4115	615	9	atlantic	atlantic	PROPN
ejpam-4115	615	10	avenue	avenue	PROPN
ejpam-4115	615	11	,	,	PUNCT
ejpam-4115	615	12	boston	boston	PROPN
ejpam-4115	615	13	,	,	PUNCT
ejpam-4115	615	14	usa	usa	PROPN
ejpam-4115	615	15	,	,	PUNCT
ejpam-4115	615	16	1966	1966	NUM
ejpam-4115	615	17	.	.	PUNCT
ejpam-4115	616	1	[	[	X
ejpam-4115	616	2	4	4	NUM
ejpam-4115	616	3	]	]	PUNCT
ejpam-4115	616	4	a.	a.	NOUN
ejpam-4115	616	5	khintchine	khintchine	PROPN
ejpam-4115	616	6	.	.	PUNCT
ejpam-4115	617	1	sur	sur	PROPN
ejpam-4115	617	2	le	le	AUX
ejpam-4115	617	3	procede	procede	PROPN
ejpam-4115	617	4	d’integration	d’integration	NOUN
ejpam-4115	617	5	de	de	X
ejpam-4115	617	6	m.	m.	NOUN
ejpam-4115	617	7	denjoy	denjoy	PROPN
ejpam-4115	617	8	.	.	PUNCT
ejpam-4115	618	1	mat	mat	PROPN
ejpam-4115	618	2	.	.	PUNCT
ejpam-4115	618	3	sbornik	sbornik	PROPN
ejpam-4115	618	4	,	,	PUNCT
ejpam-4115	618	5	30:548–557	30:548–557	PROPN
ejpam-4115	618	6	,	,	PUNCT
ejpam-4115	618	7	1916	1916	NUM
ejpam-4115	618	8	.	.	PUNCT
ejpam-4115	619	1	[	[	X
ejpam-4115	619	2	5	5	NUM
ejpam-4115	619	3	]	]	X
ejpam-4115	619	4	n.	n.	NOUN
ejpam-4115	619	5	lusin	lusin	NOUN
ejpam-4115	619	6	.	.	PUNCT
ejpam-4115	620	1	sur	sur	PROPN
ejpam-4115	620	2	les	les	PROPN
ejpam-4115	620	3	proprietes	proprietes	PROPN
ejpam-4115	620	4	de	de	X
ejpam-4115	620	5	l’integrale	l’integrale	X
ejpam-4115	620	6	de	de	PROPN
ejpam-4115	620	7	m.	m.	NOUN
ejpam-4115	620	8	denjoy	denjoy	PROPN
ejpam-4115	620	9	.	.	PUNCT
ejpam-4115	621	1	comptes	compte	VERB
ejpam-4115	621	2	rendus	rendus	PROPN
ejpam-4115	621	3	de	de	PROPN
ejpam-4115	621	4	l’academie	l’academie	VERB
ejpam-4115	621	5	des	des	PROPN
ejpam-4115	621	6	sciences	sciences	PROPN
ejpam-4115	621	7	,	,	PUNCT
ejpam-4115	621	8	155:1475–1478	155:1475–1478	NUM
ejpam-4115	621	9	,	,	PUNCT
ejpam-4115	621	10	1912	1912	NUM
ejpam-4115	621	11	.	.	PUNCT
ejpam-4115	622	1	[	[	X
ejpam-4115	622	2	6	6	NUM
ejpam-4115	622	3	]	]	PUNCT
ejpam-4115	622	4	r.	r.	PROPN
ejpam-4115	622	5	maza	maza	PROPN
ejpam-4115	622	6	and	and	CCONJ
ejpam-4115	622	7	s.	s.	PROPN
ejpam-4115	622	8	canoy	canoy	PROPN
ejpam-4115	622	9	jr	jr	PROPN
ejpam-4115	622	10	.	.	PROPN
ejpam-4115	622	11	on	on	ADP
ejpam-4115	622	12	sl	sl	NOUN
ejpam-4115	622	13	-	-	PUNCT
ejpam-4115	622	14	integral	integral	ADJ
ejpam-4115	622	15	of	of	ADP
ejpam-4115	622	16	lctvs	lctvs	NOUN
ejpam-4115	622	17	-	-	PUNCT
ejpam-4115	622	18	valued	value	VERB
ejpam-4115	622	19	functions	function	NOUN
ejpam-4115	622	20	.	.	PUNCT
ejpam-4115	623	1	real	real	ADJ
ejpam-4115	623	2	analysis	analysis	NOUN
ejpam-4115	623	3	exchange	exchange	NOUN
ejpam-4115	623	4	,	,	PUNCT
ejpam-4115	623	5	46(2):505–522	46(2):505–522	PROPN
ejpam-4115	623	6	,	,	PUNCT
ejpam-4115	623	7	2021	2021	NUM
ejpam-4115	623	8	.	.	PUNCT
ejpam-4115	624	1	[	[	X
ejpam-4115	624	2	7	7	X
ejpam-4115	624	3	]	]	X
ejpam-4115	624	4	r.	r.	NOUN
ejpam-4115	624	5	paluga	paluga	PROPN
ejpam-4115	624	6	.	.	PUNCT
ejpam-4115	625	1	absolute	absolute	ADJ
ejpam-4115	625	2	continuity	continuity	NOUN
ejpam-4115	625	3	in	in	ADP
ejpam-4115	625	4	topological	topological	ADJ
ejpam-4115	625	5	vector	vector	NOUN
ejpam-4115	625	6	spaces	space	NOUN
ejpam-4115	625	7	.	.	PUNCT
ejpam-4115	626	1	matimyas	matimyas	PROPN
ejpam-4115	626	2	matematika	matematika	PROPN
ejpam-4115	626	3	,	,	PUNCT
ejpam-4115	626	4	27(3):42–46	27(3):42–46	NUM
ejpam-4115	626	5	,	,	PUNCT
ejpam-4115	626	6	2004	2004	NUM
ejpam-4115	626	7	.	.	PUNCT
ejpam-4115	627	1	[	[	X
ejpam-4115	627	2	8	8	NUM
ejpam-4115	627	3	]	]	X
ejpam-4115	627	4	r.	r.	PROPN
ejpam-4115	627	5	paluga	paluga	PROPN
ejpam-4115	627	6	and	and	CCONJ
ejpam-4115	627	7	s.	s.	PROPN
ejpam-4115	627	8	canoy	canoy	PROPN
ejpam-4115	627	9	jr	jr	PROPN
ejpam-4115	627	10	.	.	PUNCT
ejpam-4115	628	1	the	the	DET
ejpam-4115	628	2	henstock	henstock	NOUN
ejpam-4115	628	3	integral	integral	ADJ
ejpam-4115	628	4	in	in	ADP
ejpam-4115	628	5	topological	topological	ADJ
ejpam-4115	628	6	vector	vector	NOUN
ejpam-4115	628	7	spaces	space	NOUN
ejpam-4115	628	8	.	.	PUNCT
ejpam-4115	629	1	matimyas	matimyas	PROPN
ejpam-4115	629	2	matematika	matematika	PROPN
ejpam-4115	629	3	,	,	PUNCT
ejpam-4115	629	4	24(3):34–47	24(3):34–47	NUM
ejpam-4115	629	5	,	,	PUNCT
ejpam-4115	629	6	2001	2001	NUM
ejpam-4115	629	7	.	.	PUNCT
ejpam-4115	630	1	[	[	X
ejpam-4115	630	2	9	9	NUM
ejpam-4115	630	3	]	]	X
ejpam-4115	630	4	r.	r.	NOUN
ejpam-4115	630	5	paluga	paluga	PROPN
ejpam-4115	630	6	and	and	CCONJ
ejpam-4115	630	7	s.	s.	PROPN
ejpam-4115	630	8	canoy	canoy	PROPN
ejpam-4115	630	9	jr	jr	PROPN
ejpam-4115	630	10	.	.	PROPN
ejpam-4115	631	1	on	on	ADP
ejpam-4115	631	2	the	the	DET
ejpam-4115	631	3	strongly	strongly	ADV
ejpam-4115	631	4	henstock	henstock	NOUN
ejpam-4115	631	5	integral	integral	ADJ
ejpam-4115	631	6	in	in	ADP
ejpam-4115	631	7	topological	topological	ADJ
ejpam-4115	631	8	vector	vector	NOUN
ejpam-4115	631	9	spaces	space	NOUN
ejpam-4115	631	10	.	.	PUNCT
ejpam-4115	632	1	journal	journal	NOUN
ejpam-4115	632	2	of	of	ADP
ejpam-4115	632	3	research	research	NOUN
ejpam-4115	632	4	in	in	ADP
ejpam-4115	632	5	science	science	NOUN
ejpam-4115	632	6	and	and	CCONJ
ejpam-4115	632	7	engineering	engineering	NOUN
ejpam-4115	632	8	,	,	PUNCT
ejpam-4115	632	9	1(3):46–50	1(3):46–50	NUM
ejpam-4115	632	10	,	,	PUNCT
ejpam-4115	632	11	2004	2004	NUM
ejpam-4115	632	12	.	.	PUNCT
ejpam-4115	633	1	[	[	X
ejpam-4115	633	2	10	10	NUM
ejpam-4115	633	3	]	]	X
ejpam-4115	633	4	w.	w.	PROPN
ejpam-4115	633	5	rudin	rudin	PROPN
ejpam-4115	633	6	.	.	PUNCT
ejpam-4115	634	1	functional	functional	ADJ
ejpam-4115	634	2	analysis	analysis	NOUN
ejpam-4115	634	3	.	.	PUNCT
ejpam-4115	635	1	mcgraw	mcgraw	PROPN
ejpam-4115	635	2	-	-	PUNCT
ejpam-4115	635	3	hill	hill	PROPN
ejpam-4115	635	4	,	,	PUNCT
ejpam-4115	635	5	inc	inc	PROPN
ejpam-4115	635	6	.	.	PROPN
ejpam-4115	635	7	,	,	PUNCT
ejpam-4115	635	8	singapore	singapore	PROPN
ejpam-4115	635	9	,	,	PUNCT
ejpam-4115	635	10	second	second	ADJ
ejpam-4115	635	11	edition	edition	NOUN
ejpam-4115	635	12	edition	edition	NOUN
ejpam-4115	635	13	,	,	PUNCT
ejpam-4115	635	14	1991	1991	NUM
ejpam-4115	635	15	.	.	PUNCT
ejpam-4115	636	1	[	[	X
ejpam-4115	636	2	11	11	NUM
ejpam-4115	636	3	]	]	X
ejpam-4115	636	4	h.	h.	PROPN
ejpam-4115	636	5	schaefer	schaefer	PROPN
ejpam-4115	636	6	.	.	PUNCT
ejpam-4115	637	1	topological	topological	ADJ
ejpam-4115	637	2	vector	vector	NOUN
ejpam-4115	637	3	spaces	space	NOUN
ejpam-4115	637	4	.	.	PUNCT
ejpam-4115	638	1	springer	springer	NOUN
ejpam-4115	638	2	-	-	PUNCT
ejpam-4115	638	3	verlag	verlag	PROPN
ejpam-4115	638	4	,	,	PUNCT
ejpam-4115	638	5	new	new	PROPN
ejpam-4115	638	6	york	york	PROPN
ejpam-4115	638	7	heidelberg	heidelberg	PROPN
ejpam-4115	638	8	berlin	berlin	PROPN
ejpam-4115	638	9	,	,	PUNCT
ejpam-4115	638	10	1971	1971	NUM
ejpam-4115	638	11	.	.	PUNCT
ejpam-4115	639	1	[	[	X
ejpam-4115	639	2	12	12	NUM
ejpam-4115	639	3	]	]	X
ejpam-4115	639	4	v.	v.	ADP
ejpam-4115	639	5	skvortsov	skvortsov	NOUN
ejpam-4115	639	6	and	and	CCONJ
ejpam-4115	639	7	a.	a.	NOUN
ejpam-4115	639	8	solodov	solodov	PROPN
ejpam-4115	639	9	.	.	PUNCT
ejpam-4115	640	1	a	a	DET
ejpam-4115	640	2	variational	variational	ADJ
ejpam-4115	640	3	integral	integral	NOUN
ejpam-4115	640	4	for	for	ADP
ejpam-4115	640	5	banach	banach	ADV
ejpam-4115	640	6	-	-	PUNCT
ejpam-4115	640	7	valued	value	VERB
ejpam-4115	640	8	functions	function	NOUN
ejpam-4115	640	9	.	.	PUNCT
ejpam-4115	641	1	real	real	ADJ
ejpam-4115	641	2	analysis	analysis	NOUN
ejpam-4115	641	3	exchange	exchange	NOUN
ejpam-4115	641	4	,	,	PUNCT
ejpam-4115	641	5	24(2):799–805	24(2):799–805	PROPN
ejpam-4115	641	6	,	,	PUNCT
ejpam-4115	641	7	1998	1998	NUM
ejpam-4115	641	8	-	-	SYM
ejpam-4115	641	9	1989	1989	NUM
ejpam-4115	641	10	.	.	PUNCT
ejpam-4115	642	1	[	[	X
ejpam-4115	642	2	13	13	NUM
ejpam-4115	642	3	]	]	PUNCT
ejpam-4115	642	4	a.	a.	NOUN
ejpam-4115	642	5	solodov	solodov	PROPN
ejpam-4115	642	6	.	.	PUNCT
ejpam-4115	643	1	a	a	DET
ejpam-4115	643	2	riemann	riemann	NOUN
ejpam-4115	643	3	-	-	PUNCT
ejpam-4115	643	4	type	type	NOUN
ejpam-4115	643	5	definition	definition	NOUN
ejpam-4115	643	6	for	for	ADP
ejpam-4115	643	7	the	the	DET
ejpam-4115	643	8	restricted	restrict	VERB
ejpam-4115	643	9	denjoy	denjoy	NOUN
ejpam-4115	643	10	-	-	PUNCT
ejpam-4115	643	11	bochner	bochner	NOUN
ejpam-4115	643	12	integral	integral	ADJ
ejpam-4115	643	13	.	.	PUNCT
ejpam-4115	644	1	fundam	fundam	PROPN
ejpam-4115	644	2	.	.	PUNCT
ejpam-4115	645	1	prikl	prikl	PROPN
ejpam-4115	645	2	.	.	PUNCT
ejpam-4115	645	3	mat	mat	PROPN
ejpam-4115	645	4	.	.	PROPN
ejpam-4115	645	5	,	,	PUNCT
ejpam-4115	645	6	7(3):887–895	7(3):887–895	NUM
ejpam-4115	645	7	,	,	PUNCT
ejpam-4115	645	8	2001	2001	NUM
ejpam-4115	645	9	.	.	PUNCT
ejpam-4115	646	1	references	reference	NOUN
ejpam-4115	646	2	1183	1183	NUM
ejpam-4115	647	1	[	[	X
ejpam-4115	647	2	14	14	NUM
ejpam-4115	647	3	]	]	PUNCT
ejpam-4115	647	4	l.	l.	PROPN
ejpam-4115	647	5	yee	yee	PROPN
ejpam-4115	647	6	and	and	CCONJ
ejpam-4115	647	7	r.	r.	PROPN
ejpam-4115	647	8	výborný.	výborný.	PROPN
ejpam-4115	647	9	integral	integral	ADJ
ejpam-4115	647	10	:	:	PUNCT
ejpam-4115	647	11	an	an	DET
ejpam-4115	647	12	easy	easy	ADJ
ejpam-4115	647	13	approach	approach	NOUN
ejpam-4115	647	14	after	after	ADP
ejpam-4115	647	15	kurzweil	kurzweil	PROPN
ejpam-4115	647	16	and	and	CCONJ
ejpam-4115	647	17	henstock	henstock	PROPN
ejpam-4115	647	18	.	.	PUNCT
ejpam-4115	648	1	cambridge	cambridge	PROPN
ejpam-4115	648	2	university	university	PROPN
ejpam-4115	648	3	press	press	PROPN
ejpam-4115	648	4	,	,	PUNCT
ejpam-4115	648	5	new	new	PROPN
ejpam-4115	648	6	york	york	PROPN
ejpam-4115	648	7	,	,	PUNCT
ejpam-4115	648	8	2000	2000	NUM
ejpam-4115	648	9	.	.	PUNCT
ejpam-4115	649	1	[	[	X
ejpam-4115	649	2	15	15	NUM
ejpam-4115	649	3	]	]	X
ejpam-4115	649	4	l.p	l.p	PROPN
ejpam-4115	649	5	.	.	PROPN
ejpam-4115	649	6	yee	yee	PROPN
ejpam-4115	649	7	.	.	PUNCT
ejpam-4115	650	1	lanzhou	lanzhou	PROPN
ejpam-4115	650	2	lectures	lecture	VERB
ejpam-4115	650	3	on	on	ADP
ejpam-4115	650	4	henstock	henstock	NOUN
ejpam-4115	650	5	integration	integration	NOUN
ejpam-4115	650	6	,	,	PUNCT
ejpam-4115	650	7	volume	volume	NOUN
ejpam-4115	650	8	2	2	NUM
ejpam-4115	650	9	of	of	ADP
ejpam-4115	650	10	series	series	NOUN
ejpam-4115	650	11	in	in	ADP
ejpam-4115	650	12	real	real	ADJ
ejpam-4115	650	13	analysis	analysis	NOUN
ejpam-4115	650	14	.	.	PUNCT
ejpam-4115	651	1	world	world	NOUN
ejpam-4115	651	2	scientific	scientific	PROPN
ejpam-4115	651	3	,	,	PUNCT
ejpam-4115	651	4	nus	nus	PROPN
ejpam-4115	651	5	,	,	PUNCT
ejpam-4115	651	6	singapore	singapore	PROPN
ejpam-4115	651	7	,	,	PUNCT
ejpam-4115	651	8	1989	1989	NUM
ejpam-4115	651	9	.	.	PUNCT
ejpam-4115	652	1	[	[	X
ejpam-4115	652	2	16	16	NUM
ejpam-4115	652	3	]	]	X
ejpam-4115	652	4	l.p	l.p	PROPN
ejpam-4115	652	5	.	.	PROPN
ejpam-4115	652	6	yee	yee	PROPN
ejpam-4115	652	7	.	.	PUNCT
ejpam-4115	653	1	on	on	ADP
ejpam-4115	653	2	acg∗	acg∗	NOUN
ejpam-4115	653	3	functions	function	NOUN
ejpam-4115	653	4	.	.	PUNCT
ejpam-4115	654	1	real	real	ADJ
ejpam-4115	654	2	analysis	analysis	NOUN
ejpam-4115	654	3	exchange	exchange	NOUN
ejpam-4115	654	4	,	,	PUNCT
ejpam-4115	654	5	15(2):754–759	15(2):754–759	PROPN
ejpam-4115	654	6	,	,	PUNCT
ejpam-4115	654	7	2001	2001	NUM
ejpam-4115	654	8	.	.	PUNCT