id	sid	tid	token	lemma	pos
ejpam-3626	1	1	european	european	PROPN
ejpam-3626	1	2	journal	journal	PROPN
ejpam-3626	1	3	of	of	ADP
ejpam-3626	1	4	pure	pure	ADJ
ejpam-3626	1	5	and	and	CCONJ
ejpam-3626	1	6	applied	apply	VERB
ejpam-3626	1	7	mathematics	mathematic	NOUN
ejpam-3626	1	8	vol	vol	NOUN
ejpam-3626	1	9	.	.	PROPN
ejpam-3626	2	1	13	13	NUM
ejpam-3626	2	2	,	,	PUNCT
ejpam-3626	2	3	no	no	INTJ
ejpam-3626	2	4	.	.	NOUN
ejpam-3626	2	5	1	1	NUM
ejpam-3626	2	6	,	,	PUNCT
ejpam-3626	2	7	2020	2020	NUM
ejpam-3626	2	8	,	,	PUNCT
ejpam-3626	2	9	130	130	NUM
ejpam-3626	2	10	-	-	SYM
ejpam-3626	2	11	143	143	NUM
ejpam-3626	2	12	issn	issn	PROPN
ejpam-3626	2	13	1307	1307	NUM
ejpam-3626	2	14	-	-	SYM
ejpam-3626	2	15	5543	5543	NUM
ejpam-3626	2	16	–	–	PUNCT
ejpam-3626	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3626	2	18	published	publish	VERB
ejpam-3626	2	19	by	by	ADP
ejpam-3626	2	20	new	new	PROPN
ejpam-3626	2	21	york	york	PROPN
ejpam-3626	2	22	business	business	PROPN
ejpam-3626	2	23	global	global	ADJ
ejpam-3626	2	24	simple	simple	ADJ
ejpam-3626	2	25	properties	property	NOUN
ejpam-3626	2	26	and	and	CCONJ
ejpam-3626	2	27	existence	existence	NOUN
ejpam-3626	2	28	theorem	theorem	VERB
ejpam-3626	2	29	for	for	ADP
ejpam-3626	2	30	the	the	DET
ejpam-3626	2	31	henstock	henstock	NOUN
ejpam-3626	2	32	–	–	PUNCT
ejpam-3626	2	33	kurzweil	kurzweil	PROPN
ejpam-3626	2	34	–	–	PUNCT
ejpam-3626	2	35	stieltjes	stieltjes	NOUN
ejpam-3626	2	36	integral	integral	ADJ
ejpam-3626	2	37	of	of	ADP
ejpam-3626	2	38	functions	function	NOUN
ejpam-3626	2	39	taking	take	VERB
ejpam-3626	2	40	values	value	NOUN
ejpam-3626	2	41	on	on	ADP
ejpam-3626	2	42	c[a	c[a	NUM
ejpam-3626	2	43	,	,	PUNCT
ejpam-3626	2	44	b	b	X
ejpam-3626	2	45	]	]	X
ejpam-3626	2	46	space	space	NOUN
ejpam-3626	2	47	-	-	PUNCT
ejpam-3626	2	48	valued	value	VERB
ejpam-3626	2	49	functions	function	NOUN
ejpam-3626	2	50	andrew	andrew	PROPN
ejpam-3626	2	51	felix	felix	PROPN
ejpam-3626	2	52	cunanan1,∗	cunanan1,∗	PROPN
ejpam-3626	2	53	,	,	PUNCT
ejpam-3626	2	54	julius	julius	PROPN
ejpam-3626	2	55	benitez2	benitez2	PROPN
ejpam-3626	2	56	1	1	NUM
ejpam-3626	2	57	department	department	NOUN
ejpam-3626	2	58	of	of	ADP
ejpam-3626	2	59	natural	natural	ADJ
ejpam-3626	2	60	sciences	science	NOUN
ejpam-3626	2	61	and	and	CCONJ
ejpam-3626	2	62	mathematics	mathematic	NOUN
ejpam-3626	2	63	,	,	PUNCT
ejpam-3626	2	64	college	college	NOUN
ejpam-3626	2	65	of	of	ADP
ejpam-3626	2	66	arts	art	NOUN
ejpam-3626	2	67	and	and	CCONJ
ejpam-3626	2	68	sciences	science	NOUN
ejpam-3626	2	69	,	,	PUNCT
ejpam-3626	2	70	surigao	surigao	NOUN
ejpam-3626	2	71	del	del	PROPN
ejpam-3626	2	72	sur	sur	PROPN
ejpam-3626	2	73	state	state	PROPN
ejpam-3626	2	74	university	university	PROPN
ejpam-3626	2	75	,	,	PUNCT
ejpam-3626	2	76	tandag	tandag	PROPN
ejpam-3626	2	77	city	city	PROPN
ejpam-3626	2	78	,	,	PUNCT
ejpam-3626	2	79	surigao	surigao	PROPN
ejpam-3626	2	80	del	del	PROPN
ejpam-3626	2	81	sur	sur	PROPN
ejpam-3626	2	82	,	,	PUNCT
ejpam-3626	2	83	philippines	philippines	PROPN
ejpam-3626	2	84	2	2	NUM
ejpam-3626	2	85	department	department	NOUN
ejpam-3626	2	86	of	of	ADP
ejpam-3626	2	87	mathematics	mathematic	NOUN
ejpam-3626	2	88	and	and	CCONJ
ejpam-3626	2	89	statistics	statistic	NOUN
ejpam-3626	2	90	,	,	PUNCT
ejpam-3626	2	91	college	college	NOUN
ejpam-3626	2	92	of	of	ADP
ejpam-3626	2	93	sciences	science	NOUN
ejpam-3626	2	94	and	and	CCONJ
ejpam-3626	2	95	mathematics	mathematic	NOUN
ejpam-3626	2	96	,	,	PUNCT
ejpam-3626	2	97	mindanao	mindanao	PROPN
ejpam-3626	2	98	state	state	PROPN
ejpam-3626	2	99	university	university	PROPN
ejpam-3626	2	100	-	-	PUNCT
ejpam-3626	2	101	iligan	iligan	PROPN
ejpam-3626	2	102	institute	institute	PROPN
ejpam-3626	2	103	of	of	ADP
ejpam-3626	2	104	technology	technology	PROPN
ejpam-3626	2	105	,	,	PUNCT
ejpam-3626	2	106	tibanga	tibanga	PROPN
ejpam-3626	2	107	,	,	PUNCT
ejpam-3626	2	108	iligan	iligan	ADJ
ejpam-3626	2	109	city	city	PROPN
ejpam-3626	2	110	,	,	PUNCT
ejpam-3626	2	111	philippines	philippine	NOUN
ejpam-3626	2	112	abstract	abstract	ADJ
ejpam-3626	2	113	.	.	PUNCT
ejpam-3626	3	1	henstock	henstock	PROPN
ejpam-3626	3	2	–	–	PUNCT
ejpam-3626	3	3	kurzweil	kurzweil	PROPN
ejpam-3626	3	4	integral	integral	PROPN
ejpam-3626	3	5	,	,	PUNCT
ejpam-3626	3	6	a	a	DET
ejpam-3626	3	7	nonabsolute	nonabsolute	ADJ
ejpam-3626	3	8	integral	integral	ADJ
ejpam-3626	3	9	,	,	PUNCT
ejpam-3626	3	10	is	be	AUX
ejpam-3626	3	11	a	a	DET
ejpam-3626	3	12	natural	natural	ADJ
ejpam-3626	3	13	extension	extension	NOUN
ejpam-3626	3	14	of	of	ADP
ejpam-3626	3	15	the	the	DET
ejpam-3626	3	16	riemann	riemann	PROPN
ejpam-3626	3	17	integral	integral	PROPN
ejpam-3626	3	18	that	that	PRON
ejpam-3626	3	19	was	be	AUX
ejpam-3626	3	20	studied	study	VERB
ejpam-3626	3	21	independently	independently	ADV
ejpam-3626	3	22	by	by	ADP
ejpam-3626	3	23	ralph	ralph	PROPN
ejpam-3626	3	24	henstock	henstock	PROPN
ejpam-3626	3	25	and	and	CCONJ
ejpam-3626	3	26	jaroslav	jaroslav	PROPN
ejpam-3626	3	27	kurzweil	kurzweil	PROPN
ejpam-3626	3	28	.	.	PUNCT
ejpam-3626	4	1	this	this	DET
ejpam-3626	4	2	paper	paper	NOUN
ejpam-3626	4	3	will	will	AUX
ejpam-3626	4	4	introduce	introduce	VERB
ejpam-3626	4	5	the	the	DET
ejpam-3626	4	6	henstock	henstock	NOUN
ejpam-3626	4	7	–	–	PUNCT
ejpam-3626	4	8	kurzweil	kurzweil	PROPN
ejpam-3626	4	9	–	–	PUNCT
ejpam-3626	4	10	stieltjes	stieltjes	NOUN
ejpam-3626	4	11	integral	integral	ADJ
ejpam-3626	4	12	of	of	ADP
ejpam-3626	4	13	c[a	c[a	NUM
ejpam-3626	4	14	,	,	PUNCT
ejpam-3626	4	15	b]-valued	b]-value	VERB
ejpam-3626	4	16	functions	function	NOUN
ejpam-3626	4	17	defined	define	VERB
ejpam-3626	4	18	on	on	ADP
ejpam-3626	4	19	a	a	DET
ejpam-3626	4	20	closed	closed	ADJ
ejpam-3626	4	21	interval	interval	NOUN
ejpam-3626	4	22	[	[	X
ejpam-3626	4	23	f	f	X
ejpam-3626	4	24	,	,	PUNCT
ejpam-3626	4	25	g	g	NOUN
ejpam-3626	4	26	]	]	X
ejpam-3626	4	27	⊆	⊆	NUM
ejpam-3626	4	28	c[a	c[a	NUM
ejpam-3626	4	29	,	,	PUNCT
ejpam-3626	4	30	b	b	NOUN
ejpam-3626	4	31	]	]	X
ejpam-3626	4	32	,	,	PUNCT
ejpam-3626	4	33	where	where	SCONJ
ejpam-3626	4	34	c[a	c[a	NOUN
ejpam-3626	4	35	,	,	PUNCT
ejpam-3626	4	36	b	b	AUX
ejpam-3626	4	37	]	]	X
ejpam-3626	4	38	is	be	AUX
ejpam-3626	4	39	the	the	DET
ejpam-3626	4	40	space	space	NOUN
ejpam-3626	4	41	of	of	ADP
ejpam-3626	4	42	all	all	DET
ejpam-3626	4	43	continuous	continuous	ADJ
ejpam-3626	4	44	real	real	ADV
ejpam-3626	4	45	-	-	PUNCT
ejpam-3626	4	46	valued	value	VERB
ejpam-3626	4	47	functions	function	NOUN
ejpam-3626	4	48	defined	define	VERB
ejpam-3626	4	49	on	on	ADP
ejpam-3626	4	50	[	[	X
ejpam-3626	4	51	a	a	PRON
ejpam-3626	4	52	,	,	PUNCT
ejpam-3626	4	53	b	b	NOUN
ejpam-3626	4	54	]	]	X
ejpam-3626	4	55	⊆	⊆	NUM
ejpam-3626	4	56	r.	r.	NOUN
ejpam-3626	4	57	some	some	DET
ejpam-3626	4	58	simple	simple	ADJ
ejpam-3626	4	59	properties	property	NOUN
ejpam-3626	4	60	of	of	ADP
ejpam-3626	4	61	this	this	DET
ejpam-3626	4	62	integral	integral	ADJ
ejpam-3626	4	63	will	will	AUX
ejpam-3626	4	64	be	be	AUX
ejpam-3626	4	65	formulated	formulate	VERB
ejpam-3626	4	66	including	include	VERB
ejpam-3626	4	67	the	the	DET
ejpam-3626	4	68	cauchy	cauchy	ADJ
ejpam-3626	4	69	criterion	criterion	NOUN
ejpam-3626	4	70	and	and	CCONJ
ejpam-3626	4	71	an	an	DET
ejpam-3626	4	72	existence	existence	NOUN
ejpam-3626	4	73	theorem	theorem	NOUN
ejpam-3626	4	74	will	will	AUX
ejpam-3626	4	75	be	be	AUX
ejpam-3626	4	76	provided	provide	VERB
ejpam-3626	4	77	.	.	PUNCT
ejpam-3626	5	1	2020	2020	NUM
ejpam-3626	5	2	mathematics	mathematic	NOUN
ejpam-3626	5	3	subject	subject	NOUN
ejpam-3626	5	4	classifications	classification	NOUN
ejpam-3626	5	5	:	:	PUNCT
ejpam-3626	5	6	58c06,51m20	58c06,51m20	NUM
ejpam-3626	5	7	,	,	PUNCT
ejpam-3626	5	8	26a42	26a42	NUM
ejpam-3626	5	9	,	,	PUNCT
ejpam-3626	5	10	26b05	26b05	NUM
ejpam-3626	5	11	,	,	PUNCT
ejpam-3626	5	12	26b30	26b30	DET
ejpam-3626	5	13	key	key	ADJ
ejpam-3626	5	14	words	word	NOUN
ejpam-3626	5	15	and	and	CCONJ
ejpam-3626	5	16	phrases	phrase	NOUN
ejpam-3626	5	17	:	:	PUNCT
ejpam-3626	5	18	c[a	c[a	NUM
ejpam-3626	5	19	,	,	PUNCT
ejpam-3626	5	20	b	b	X
ejpam-3626	5	21	]	]	X
ejpam-3626	5	22	space	space	NOUN
ejpam-3626	5	23	-	-	PUNCT
ejpam-3626	5	24	valued	value	VERB
ejpam-3626	5	25	function	function	NOUN
ejpam-3626	5	26	,	,	PUNCT
ejpam-3626	5	27	δ	δ	PROPN
ejpam-3626	5	28	-	-	PUNCT
ejpam-3626	5	29	fine	fine	ADJ
ejpam-3626	5	30	tagged	tag	VERB
ejpam-3626	5	31	division	division	NOUN
ejpam-3626	5	32	,	,	PUNCT
ejpam-3626	5	33	henstock	henstock	PROPN
ejpam-3626	5	34	–	–	PUNCT
ejpam-3626	5	35	kurzweil	kurzweil	PROPN
ejpam-3626	5	36	–	–	PUNCT
ejpam-3626	5	37	stieltjes	stieltjes	NOUN
ejpam-3626	5	38	integral	integral	ADJ
ejpam-3626	5	39	,	,	PUNCT
ejpam-3626	5	40	continuity	continuity	NOUN
ejpam-3626	5	41	,	,	PUNCT
ejpam-3626	5	42	bounded	bound	VERB
ejpam-3626	5	43	variation	variation	NOUN
ejpam-3626	5	44	.	.	PUNCT
ejpam-3626	6	1	1	1	X
ejpam-3626	6	2	.	.	X
ejpam-3626	6	3	introduction	introduction	NOUN
ejpam-3626	6	4	the	the	DET
ejpam-3626	6	5	henstock	henstock	NOUN
ejpam-3626	6	6	–	–	PUNCT
ejpam-3626	6	7	kurzweil	kurzweil	PROPN
ejpam-3626	6	8	–	–	PUNCT
ejpam-3626	6	9	stieltjes	stieltjes	NOUN
ejpam-3626	6	10	integral	integral	ADJ
ejpam-3626	6	11	is	be	AUX
ejpam-3626	6	12	a	a	DET
ejpam-3626	6	13	generalized	generalized	ADJ
ejpam-3626	6	14	riemann	riemann	PROPN
ejpam-3626	6	15	–	–	PUNCT
ejpam-3626	6	16	stieltjes	stieltjes	NOUN
ejpam-3626	6	17	integral	integral	ADJ
ejpam-3626	6	18	which	which	PRON
ejpam-3626	6	19	has	have	VERB
ejpam-3626	6	20	properties	property	NOUN
ejpam-3626	6	21	similar	similar	ADJ
ejpam-3626	6	22	to	to	ADP
ejpam-3626	6	23	it	it	PRON
ejpam-3626	6	24	.	.	PUNCT
ejpam-3626	7	1	in	in	ADP
ejpam-3626	7	2	the	the	DET
ejpam-3626	7	3	paper	paper	NOUN
ejpam-3626	7	4	[	[	X
ejpam-3626	7	5	9	9	NUM
ejpam-3626	7	6	]	]	PUNCT
ejpam-3626	7	7	,	,	PUNCT
ejpam-3626	7	8	ubaidillah	ubaidillah	PROPN
ejpam-3626	7	9	introduce	introduce	VERB
ejpam-3626	7	10	the	the	DET
ejpam-3626	7	11	henstock	henstock	NOUN
ejpam-3626	7	12	–	–	PUNCT
ejpam-3626	7	13	kurzweil	kurzweil	PROPN
ejpam-3626	7	14	integral	integral	ADJ
ejpam-3626	7	15	of	of	ADP
ejpam-3626	7	16	functions	function	NOUN
ejpam-3626	7	17	taking	take	VERB
ejpam-3626	7	18	values	value	NOUN
ejpam-3626	7	19	in	in	ADP
ejpam-3626	7	20	c[a	c[a	NUM
ejpam-3626	7	21	,	,	PUNCT
ejpam-3626	7	22	b	b	X
ejpam-3626	7	23	]	]	X
ejpam-3626	7	24	through	through	ADP
ejpam-3626	7	25	riemann	riemann	PROPN
ejpam-3626	7	26	sums	sums	ADP
ejpam-3626	7	27	s(f	s(f	PROPN
ejpam-3626	7	28	,	,	PUNCT
ejpam-3626	7	29	d	d	NOUN
ejpam-3626	7	30	)	)	PUNCT
ejpam-3626	7	31	=	=	PUNCT
ejpam-3626	8	1	∑	∑	PUNCT
ejpam-3626	8	2	d	d	PROPN
ejpam-3626	8	3	f	f	PROPN
ejpam-3626	8	4	(	(	PUNCT
ejpam-3626	8	5	ti)[hi−1	ti)[hi−1	PROPN
ejpam-3626	8	6	,	,	PUNCT
ejpam-3626	8	7	hi	hi	INTJ
ejpam-3626	8	8	]	]	X
ejpam-3626	8	9	where	where	SCONJ
ejpam-3626	8	10	d	d	NOUN
ejpam-3626	8	11	=	=	PRON
ejpam-3626	8	12	{	{	PUNCT
ejpam-3626	8	13	(	(	PUNCT
ejpam-3626	8	14	[	[	X
ejpam-3626	8	15	hi−1	hi−1	NOUN
ejpam-3626	8	16	,	,	PUNCT
ejpam-3626	8	17	hi	hi	ADJ
ejpam-3626	8	18	]	]	PUNCT
ejpam-3626	8	19	,	,	PUNCT
ejpam-3626	8	20	ti)}ni=1	ti)}ni=1	ADV
ejpam-3626	8	21	is	be	AUX
ejpam-3626	8	22	a	a	DET
ejpam-3626	8	23	tagged	tag	VERB
ejpam-3626	8	24	division	division	NOUN
ejpam-3626	8	25	of	of	ADP
ejpam-3626	8	26	[	[	X
ejpam-3626	8	27	f	f	X
ejpam-3626	8	28	,	,	PUNCT
ejpam-3626	8	29	g	g	NOUN
ejpam-3626	8	30	]	]	PUNCT
ejpam-3626	8	31	notion	notion	NOUN
ejpam-3626	8	32	of	of	ADP
ejpam-3626	8	33	integrals	integral	NOUN
ejpam-3626	8	34	for	for	ADP
ejpam-3626	8	35	banach	banach	NOUN
ejpam-3626	8	36	space	space	NOUN
ejpam-3626	8	37	-	-	PUNCT
ejpam-3626	8	38	valued	value	VERB
ejpam-3626	8	39	functions	function	NOUN
ejpam-3626	8	40	like	like	ADP
ejpam-3626	8	41	henstock	henstock	NOUN
ejpam-3626	8	42	integral	integral	ADJ
ejpam-3626	8	43	for	for	ADP
ejpam-3626	8	44	banach	banach	NOUN
ejpam-3626	8	45	space	space	NOUN
ejpam-3626	8	46	-	-	PUNCT
ejpam-3626	8	47	valued	value	VERB
ejpam-3626	8	48	functions	function	NOUN
ejpam-3626	8	49	,	,	PUNCT
ejpam-3626	8	50	henstock	henstock	PROPN
ejpam-3626	8	51	–	–	PUNCT
ejpam-3626	8	52	stieltjes	stieltjes	NOUN
ejpam-3626	8	53	integral	integral	ADJ
ejpam-3626	8	54	of	of	ADP
ejpam-3626	8	55	real	real	ADV
ejpam-3626	8	56	-	-	PUNCT
ejpam-3626	8	57	valued	value	VERB
ejpam-3626	8	58	functions	function	NOUN
ejpam-3626	8	59	with	with	ADP
ejpam-3626	8	60	respect	respect	NOUN
ejpam-3626	8	61	to	to	ADP
ejpam-3626	8	62	an	an	DET
ejpam-3626	8	63	increasing	increase	VERB
ejpam-3626	8	64	function	function	NOUN
ejpam-3626	8	65	and	and	CCONJ
ejpam-3626	8	66	henstock	henstock	NOUN
ejpam-3626	8	67	–	–	PUNCT
ejpam-3626	8	68	stieltjes	stieltjes	NOUN
ejpam-3626	8	69	integral	integral	ADJ
ejpam-3626	8	70	for	for	ADP
ejpam-3626	8	71	banach	banach	NOUN
ejpam-3626	8	72	spaces	space	NOUN
ejpam-3626	8	73	were	be	AUX
ejpam-3626	8	74	already	already	ADV
ejpam-3626	8	75	defined	define	VERB
ejpam-3626	8	76	by	by	ADP
ejpam-3626	8	77	cao	cao	PROPN
ejpam-3626	9	1	[	[	X
ejpam-3626	9	2	3	3	NUM
ejpam-3626	9	3	]	]	PUNCT
ejpam-3626	9	4	,	,	PUNCT
ejpam-3626	9	5	∗corresponding	∗corresponde	VERB
ejpam-3626	9	6	author	author	NOUN
ejpam-3626	9	7	.	.	PUNCT
ejpam-3626	10	1	doi	doi	NOUN
ejpam-3626	10	2	:	:	PUNCT
ejpam-3626	10	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3626	https://doi.org/10.29020/nybg.ejpam.v13i1.3626	PROPN
ejpam-3626	10	4	email	email	NOUN
ejpam-3626	10	5	addresses	address	VERB
ejpam-3626	10	6	:	:	PUNCT
ejpam-3626	11	1	deofscunananiv@yahoo.com	deofscunananiv@yahoo.com	X
ejpam-3626	11	2	(	(	PUNCT
ejpam-3626	11	3	a.	a.	NOUN
ejpam-3626	11	4	cunanan	cunanan	PROPN
ejpam-3626	11	5	)	)	PUNCT
ejpam-3626	11	6	,	,	PUNCT
ejpam-3626	11	7	julius.benitez@g.msuiit	julius.benitez@g.msuiit	PROPN
ejpam-3626	11	8	,	,	PUNCT
ejpam-3626	11	9	edu.ph	edu.ph	PROPN
ejpam-3626	11	10	(	(	PUNCT
ejpam-3626	11	11	j.	j.	PROPN
ejpam-3626	11	12	benitez	benitez	PROPN
ejpam-3626	11	13	)	)	PUNCT
ejpam-3626	11	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3626	12	1	130	130	NUM
ejpam-3626	12	2	c	c	NOUN
ejpam-3626	12	3	©	©	NOUN
ejpam-3626	12	4	2020	2020	NUM
ejpam-3626	12	5	ejpam	ejpam	VERB
ejpam-3626	12	6	all	all	DET
ejpam-3626	12	7	rights	right	NOUN
ejpam-3626	12	8	reserved	reserve	VERB
ejpam-3626	12	9	.	.	PUNCT
ejpam-3626	13	1	a.	a.	PROPN
ejpam-3626	13	2	cunanan	cunanan	PROPN
ejpam-3626	13	3	,	,	PUNCT
ejpam-3626	13	4	j.	j.	PROPN
ejpam-3626	13	5	benitez	benitez	PROPN
ejpam-3626	13	6	/	/	PUNCT
ejpam-3626	13	7	eur	eur	PROPN
ejpam-3626	13	8	.	.	PUNCT
ejpam-3626	14	1	j.	j.	PROPN
ejpam-3626	14	2	pure	pure	PROPN
ejpam-3626	14	3	appl	appl	PROPN
ejpam-3626	14	4	.	.	PROPN
ejpam-3626	14	5	math	math	PROPN
ejpam-3626	14	6	,	,	PUNCT
ejpam-3626	14	7	13	13	NUM
ejpam-3626	14	8	(	(	PUNCT
ejpam-3626	14	9	1	1	NUM
ejpam-3626	14	10	)	)	PUNCT
ejpam-3626	14	11	(	(	PUNCT
ejpam-3626	14	12	2020	2020	NUM
ejpam-3626	14	13	)	)	PUNCT
ejpam-3626	14	14	,	,	PUNCT
ejpam-3626	14	15	130	130	NUM
ejpam-3626	14	16	-	-	SYM
ejpam-3626	14	17	143	143	NUM
ejpam-3626	14	18	131	131	NUM
ejpam-3626	14	19	lim	lim	PROPN
ejpam-3626	15	1	[	[	X
ejpam-3626	15	2	7	7	X
ejpam-3626	15	3	]	]	PUNCT
ejpam-3626	15	4	and	and	CCONJ
ejpam-3626	15	5	tikare	tikare	VERB
ejpam-3626	16	1	[	[	X
ejpam-3626	16	2	8	8	NUM
ejpam-3626	16	3	]	]	PUNCT
ejpam-3626	16	4	,	,	PUNCT
ejpam-3626	16	5	respectively	respectively	ADV
ejpam-3626	16	6	.	.	PUNCT
ejpam-3626	17	1	in	in	ADP
ejpam-3626	17	2	this	this	DET
ejpam-3626	17	3	paper	paper	NOUN
ejpam-3626	17	4	we	we	PRON
ejpam-3626	17	5	change	change	VERB
ejpam-3626	17	6	the	the	DET
ejpam-3626	17	7	way	way	NOUN
ejpam-3626	17	8	to	to	PART
ejpam-3626	17	9	define	define	VERB
ejpam-3626	17	10	the	the	DET
ejpam-3626	17	11	domain	domain	NOUN
ejpam-3626	17	12	of	of	ADP
ejpam-3626	17	13	the	the	DET
ejpam-3626	17	14	function	function	NOUN
ejpam-3626	17	15	and	and	CCONJ
ejpam-3626	17	16	the	the	DET
ejpam-3626	17	17	integrator	integrator	NOUN
ejpam-3626	17	18	.	.	PUNCT
ejpam-3626	18	1	we	we	PRON
ejpam-3626	18	2	shall	shall	AUX
ejpam-3626	18	3	choose	choose	VERB
ejpam-3626	18	4	first	first	ADV
ejpam-3626	18	5	a	a	DET
ejpam-3626	18	6	closed	closed	ADJ
ejpam-3626	18	7	interval	interval	NOUN
ejpam-3626	18	8	[	[	X
ejpam-3626	18	9	f	f	X
ejpam-3626	18	10	,	,	PUNCT
ejpam-3626	18	11	g	g	NOUN
ejpam-3626	18	12	]	]	PUNCT
ejpam-3626	18	13	as	as	ADP
ejpam-3626	18	14	our	our	PRON
ejpam-3626	18	15	domain	domain	NOUN
ejpam-3626	18	16	and	and	CCONJ
ejpam-3626	18	17	a	a	DET
ejpam-3626	18	18	continuous	continuous	ADJ
ejpam-3626	18	19	real	real	ADV
ejpam-3626	18	20	-	-	PUNCT
ejpam-3626	18	21	valued	value	VERB
ejpam-3626	18	22	function	function	NOUN
ejpam-3626	18	23	h	h	NOUN
ejpam-3626	18	24	instead	instead	ADV
ejpam-3626	18	25	of	of	ADP
ejpam-3626	18	26	the	the	DET
ejpam-3626	18	27	identity	identity	NOUN
ejpam-3626	18	28	map	map	NOUN
ejpam-3626	18	29	as	as	ADP
ejpam-3626	18	30	our	our	PRON
ejpam-3626	18	31	integrator	integrator	NOUN
ejpam-3626	18	32	.	.	PUNCT
ejpam-3626	19	1	2	2	X
ejpam-3626	19	2	.	.	X
ejpam-3626	19	3	preliminaries	preliminary	NOUN
ejpam-3626	19	4	throughout	throughout	ADP
ejpam-3626	19	5	,	,	PUNCT
ejpam-3626	19	6	we	we	PRON
ejpam-3626	19	7	consider	consider	VERB
ejpam-3626	19	8	the	the	DET
ejpam-3626	19	9	space	space	NOUN
ejpam-3626	19	10	c[a	c[a	NOUN
ejpam-3626	19	11	,	,	PUNCT
ejpam-3626	19	12	b	b	X
ejpam-3626	19	13	]	]	PUNCT
ejpam-3626	19	14	of	of	ADP
ejpam-3626	19	15	all	all	DET
ejpam-3626	19	16	continuous	continuous	ADJ
ejpam-3626	19	17	real	real	ADV
ejpam-3626	19	18	-	-	PUNCT
ejpam-3626	19	19	valued	value	VERB
ejpam-3626	19	20	functions	function	NOUN
ejpam-3626	19	21	defined	define	VERB
ejpam-3626	19	22	on	on	ADP
ejpam-3626	19	23	[	[	X
ejpam-3626	19	24	a	a	X
ejpam-3626	19	25	,	,	PUNCT
ejpam-3626	19	26	b	b	NOUN
ejpam-3626	19	27	]	]	X
ejpam-3626	19	28	.	.	PUNCT
ejpam-3626	20	1	for	for	ADP
ejpam-3626	20	2	more	more	ADJ
ejpam-3626	20	3	details	detail	NOUN
ejpam-3626	20	4	of	of	ADP
ejpam-3626	20	5	the	the	DET
ejpam-3626	20	6	space	space	NOUN
ejpam-3626	20	7	c[a	c[a	NOUN
ejpam-3626	20	8	,	,	PUNCT
ejpam-3626	20	9	b	b	NOUN
ejpam-3626	20	10	]	]	X
ejpam-3626	20	11	,	,	PUNCT
ejpam-3626	20	12	see	see	VERB
ejpam-3626	20	13	[	[	X
ejpam-3626	20	14	2	2	NUM
ejpam-3626	20	15	]	]	PUNCT
ejpam-3626	20	16	,	,	PUNCT
ejpam-3626	20	17	[	[	X
ejpam-3626	20	18	5	5	NUM
ejpam-3626	20	19	]	]	PUNCT
ejpam-3626	20	20	or	or	CCONJ
ejpam-3626	20	21	[	[	X
ejpam-3626	20	22	9	9	NUM
ejpam-3626	20	23	]	]	PUNCT
ejpam-3626	20	24	.	.	PUNCT
ejpam-3626	21	1	let	let	VERB
ejpam-3626	21	2	[	[	X
ejpam-3626	21	3	f	f	X
ejpam-3626	21	4	,	,	PUNCT
ejpam-3626	21	5	g	g	NOUN
ejpam-3626	21	6	]	]	PUNCT
ejpam-3626	21	7	be	be	AUX
ejpam-3626	21	8	a	a	DET
ejpam-3626	21	9	closed	closed	ADJ
ejpam-3626	21	10	interval	interval	NOUN
ejpam-3626	21	11	of	of	ADP
ejpam-3626	21	12	c[a	c[a	NOUN
ejpam-3626	21	13	,	,	PUNCT
ejpam-3626	21	14	b	b	NOUN
ejpam-3626	21	15	]	]	X
ejpam-3626	21	16	.	.	PUNCT
ejpam-3626	22	1	a	a	DET
ejpam-3626	22	2	division	division	NOUN
ejpam-3626	22	3	of	of	ADP
ejpam-3626	22	4	[	[	X
ejpam-3626	22	5	f	f	X
ejpam-3626	22	6	,	,	PUNCT
ejpam-3626	22	7	g	g	NOUN
ejpam-3626	22	8	]	]	PUNCT
ejpam-3626	22	9	is	be	AUX
ejpam-3626	22	10	any	any	DET
ejpam-3626	22	11	finite	finite	NOUN
ejpam-3626	22	12	set	set	NOUN
ejpam-3626	22	13	{	{	PUNCT
ejpam-3626	22	14	h0	h0	PROPN
ejpam-3626	22	15	,	,	PUNCT
ejpam-3626	22	16	h1	h1	PROPN
ejpam-3626	22	17	,	,	PUNCT
ejpam-3626	22	18	.	.	PUNCT
ejpam-3626	22	19	.	.	PUNCT
ejpam-3626	23	1	.	.	PUNCT
ejpam-3626	24	1	,	,	PUNCT
ejpam-3626	24	2	hn	hn	PROPN
ejpam-3626	24	3	}	}	PUNCT
ejpam-3626	24	4	⊂	⊂	PROPN
ejpam-3626	25	1	[	[	X
ejpam-3626	25	2	f	f	X
ejpam-3626	25	3	,	,	PUNCT
ejpam-3626	25	4	g	g	NOUN
ejpam-3626	25	5	]	]	PUNCT
ejpam-3626	25	6	such	such	ADJ
ejpam-3626	25	7	that	that	DET
ejpam-3626	25	8	h0	h0	NOUN
ejpam-3626	25	9	=	=	PROPN
ejpam-3626	25	10	f	f	PROPN
ejpam-3626	25	11	,	,	PUNCT
ejpam-3626	25	12	hn	hn	PROPN
ejpam-3626	25	13	=	=	PUNCT
ejpam-3626	25	14	g	g	PROPN
ejpam-3626	25	15	and	and	CCONJ
ejpam-3626	25	16	hi−1	hi−1	PROPN
ejpam-3626	25	17	<	<	X
ejpam-3626	25	18	hi	hi	INTJ
ejpam-3626	25	19	for	for	ADP
ejpam-3626	25	20	all	all	DET
ejpam-3626	25	21	i	i	PRON
ejpam-3626	25	22	=	=	NOUN
ejpam-3626	25	23	1	1	NUM
ejpam-3626	25	24	,	,	PUNCT
ejpam-3626	25	25	2	2	NUM
ejpam-3626	25	26	,	,	PUNCT
ejpam-3626	25	27	.	.	PUNCT
ejpam-3626	25	28	.	.	PUNCT
ejpam-3626	26	1	.	.	PUNCT
ejpam-3626	27	1	,	,	PUNCT
ejpam-3626	27	2	n.	n.	PROPN
ejpam-3626	27	3	a	a	DET
ejpam-3626	27	4	tagged	tag	VERB
ejpam-3626	27	5	division	division	NOUN
ejpam-3626	27	6	of	of	ADP
ejpam-3626	27	7	[	[	X
ejpam-3626	27	8	f	f	X
ejpam-3626	27	9	,	,	PUNCT
ejpam-3626	27	10	g	g	NOUN
ejpam-3626	27	11	]	]	PUNCT
ejpam-3626	27	12	is	be	AUX
ejpam-3626	27	13	a	a	DET
ejpam-3626	27	14	finite	finite	ADJ
ejpam-3626	27	15	collection	collection	NOUN
ejpam-3626	27	16	{	{	PUNCT
ejpam-3626	27	17	(	(	PUNCT
ejpam-3626	27	18	[	[	X
ejpam-3626	27	19	hi−1	hi−1	PROPN
ejpam-3626	27	20	,	,	PUNCT
ejpam-3626	27	21	hi	hi	ADJ
ejpam-3626	27	22	]	]	PUNCT
ejpam-3626	27	23	,	,	PUNCT
ejpam-3626	27	24	ti	ti	NOUN
ejpam-3626	27	25	)	)	PUNCT
ejpam-3626	27	26	:	:	PUNCT
ejpam-3626	28	1	i	i	NOUN
ejpam-3626	28	2	=	=	NOUN
ejpam-3626	28	3	1	1	NUM
ejpam-3626	28	4	,	,	PUNCT
ejpam-3626	28	5	2	2	NUM
ejpam-3626	28	6	,	,	PUNCT
ejpam-3626	28	7	.	.	PUNCT
ejpam-3626	28	8	.	.	PUNCT
ejpam-3626	28	9	.	.	PUNCT
ejpam-3626	28	10	,	,	PUNCT
ejpam-3626	28	11	n	n	CCONJ
ejpam-3626	28	12	}	}	PUNCT
ejpam-3626	28	13	of	of	ADP
ejpam-3626	28	14	interval−point	interval−point	NOUN
ejpam-3626	28	15	pairs	pair	NOUN
ejpam-3626	28	16	such	such	ADJ
ejpam-3626	28	17	that	that	SCONJ
ejpam-3626	28	18	{	{	PUNCT
ejpam-3626	28	19	h0	h0	PROPN
ejpam-3626	28	20	,	,	PUNCT
ejpam-3626	28	21	h1	h1	PROPN
ejpam-3626	28	22	,	,	PUNCT
ejpam-3626	28	23	.	.	PUNCT
ejpam-3626	28	24	.	.	PUNCT
ejpam-3626	28	25	.	.	PUNCT
ejpam-3626	29	1	,	,	PUNCT
ejpam-3626	29	2	hn	hn	PROPN
ejpam-3626	29	3	}	}	PUNCT
ejpam-3626	29	4	is	be	AUX
ejpam-3626	29	5	a	a	DET
ejpam-3626	29	6	division	division	NOUN
ejpam-3626	29	7	of	of	ADP
ejpam-3626	29	8	[	[	X
ejpam-3626	29	9	f	f	X
ejpam-3626	29	10	,	,	PUNCT
ejpam-3626	29	11	g	g	NOUN
ejpam-3626	29	12	]	]	PUNCT
ejpam-3626	29	13	and	and	CCONJ
ejpam-3626	29	14	ti	ti	X
ejpam-3626	29	15	∈	∈	PROPN
ejpam-3626	29	16	[	[	X
ejpam-3626	29	17	hi−1	hi−1	PROPN
ejpam-3626	29	18	,	,	PUNCT
ejpam-3626	29	19	hi	hi	INTJ
ejpam-3626	29	20	]	]	X
ejpam-3626	29	21	for	for	ADP
ejpam-3626	29	22	every	every	DET
ejpam-3626	29	23	i	i	NOUN
ejpam-3626	29	24	=	=	NOUN
ejpam-3626	29	25	1	1	NUM
ejpam-3626	29	26	,	,	PUNCT
ejpam-3626	29	27	2	2	NUM
ejpam-3626	29	28	,	,	PUNCT
ejpam-3626	29	29	.	.	PUNCT
ejpam-3626	29	30	.	.	PUNCT
ejpam-3626	30	1	.	.	PUNCT
ejpam-3626	31	1	,	,	PUNCT
ejpam-3626	31	2	n.	n.	NOUN
ejpam-3626	31	3	each	each	DET
ejpam-3626	31	4	point	point	NOUN
ejpam-3626	31	5	ti	ti	NOUN
ejpam-3626	31	6	is	be	AUX
ejpam-3626	31	7	referred	refer	VERB
ejpam-3626	31	8	to	to	ADP
ejpam-3626	31	9	as	as	ADP
ejpam-3626	31	10	the	the	DET
ejpam-3626	31	11	tag	tag	NOUN
ejpam-3626	31	12	of	of	ADP
ejpam-3626	31	13	the	the	DET
ejpam-3626	31	14	corresponding	corresponding	ADJ
ejpam-3626	31	15	subinterval	subinterval	NOUN
ejpam-3626	31	16	[	[	X
ejpam-3626	31	17	hi−1	hi−1	PROPN
ejpam-3626	31	18	,	,	PUNCT
ejpam-3626	31	19	hi	hi	ADJ
ejpam-3626	31	20	]	]	PUNCT
ejpam-3626	31	21	.	.	PUNCT
ejpam-3626	32	1	let	let	VERB
ejpam-3626	32	2	θ	θ	NOUN
ejpam-3626	32	3	be	be	AUX
ejpam-3626	32	4	the	the	DET
ejpam-3626	32	5	null	null	ADJ
ejpam-3626	32	6	element	element	NOUN
ejpam-3626	32	7	in	in	ADP
ejpam-3626	32	8	c[a	c[a	PROPN
ejpam-3626	32	9	,	,	PUNCT
ejpam-3626	32	10	b	b	NOUN
ejpam-3626	32	11	]	]	X
ejpam-3626	32	12	,	,	PUNCT
ejpam-3626	32	13	that	that	ADV
ejpam-3626	32	14	is	is	ADV
ejpam-3626	32	15	,	,	PUNCT
ejpam-3626	32	16	θ(x	θ(x	PROPN
ejpam-3626	32	17	)	)	PUNCT
ejpam-3626	33	1	=	=	SYM
ejpam-3626	33	2	0	0	NUM
ejpam-3626	33	3	,	,	PUNCT
ejpam-3626	33	4	for	for	ADP
ejpam-3626	33	5	all	all	DET
ejpam-3626	33	6	x	x	SYM
ejpam-3626	33	7	∈	∈	PROPN
ejpam-3626	33	8	[	[	X
ejpam-3626	33	9	a	a	X
ejpam-3626	33	10	,	,	PUNCT
ejpam-3626	33	11	b	b	NOUN
ejpam-3626	33	12	]	]	X
ejpam-3626	33	13	.	.	PUNCT
ejpam-3626	34	1	a	a	DET
ejpam-3626	34	2	function	function	NOUN
ejpam-3626	34	3	δ	δ	NOUN
ejpam-3626	34	4	:	:	PUNCT
ejpam-3626	35	1	[	[	X
ejpam-3626	35	2	f	f	X
ejpam-3626	35	3	,	,	PUNCT
ejpam-3626	35	4	g	g	NOUN
ejpam-3626	35	5	]	]	X
ejpam-3626	35	6	→	→	SYM
ejpam-3626	35	7	c[a	c[a	NUM
ejpam-3626	35	8	,	,	PUNCT
ejpam-3626	35	9	b	b	AUX
ejpam-3626	35	10	]	]	PUNCT
ejpam-3626	35	11	is	be	AUX
ejpam-3626	35	12	said	say	VERB
ejpam-3626	35	13	to	to	PART
ejpam-3626	35	14	be	be	AUX
ejpam-3626	35	15	a	a	DET
ejpam-3626	35	16	gauge	gauge	NOUN
ejpam-3626	35	17	on	on	ADP
ejpam-3626	35	18	[	[	X
ejpam-3626	35	19	f	f	X
ejpam-3626	35	20	,	,	PUNCT
ejpam-3626	35	21	g	g	NOUN
ejpam-3626	35	22	]	]	X
ejpam-3626	35	23	if	if	SCONJ
ejpam-3626	35	24	θ	θ	PROPN
ejpam-3626	35	25	<	<	X
ejpam-3626	35	26	δ(h	δ(h	PROPN
ejpam-3626	35	27	)	)	PUNCT
ejpam-3626	35	28	for	for	ADP
ejpam-3626	35	29	every	every	DET
ejpam-3626	35	30	h	h	NOUN
ejpam-3626	35	31	∈	∈	PROPN
ejpam-3626	36	1	[	[	X
ejpam-3626	36	2	f	f	X
ejpam-3626	36	3	,	,	PUNCT
ejpam-3626	36	4	g	g	NOUN
ejpam-3626	36	5	]	]	PUNCT
ejpam-3626	36	6	.	.	PUNCT
ejpam-3626	37	1	definition	definition	NOUN
ejpam-3626	37	2	1	1	NUM
ejpam-3626	37	3	.	.	PUNCT
ejpam-3626	38	1	[	[	X
ejpam-3626	38	2	9	9	NUM
ejpam-3626	38	3	]	]	PUNCT
ejpam-3626	38	4	let	let	VERB
ejpam-3626	38	5	δ	δ	PRON
ejpam-3626	38	6	be	be	AUX
ejpam-3626	38	7	a	a	DET
ejpam-3626	38	8	gauge	gauge	NOUN
ejpam-3626	38	9	on	on	ADP
ejpam-3626	38	10	[	[	X
ejpam-3626	38	11	f	f	X
ejpam-3626	38	12	,	,	PUNCT
ejpam-3626	38	13	g	g	NOUN
ejpam-3626	38	14	]	]	X
ejpam-3626	38	15	.	.	PUNCT
ejpam-3626	39	1	a	a	DET
ejpam-3626	39	2	tagged	tag	VERB
ejpam-3626	39	3	division	division	NOUN
ejpam-3626	39	4	d	d	NOUN
ejpam-3626	39	5	=	=	PRON
ejpam-3626	39	6	{	{	PUNCT
ejpam-3626	39	7	(	(	PUNCT
ejpam-3626	39	8	[	[	X
ejpam-3626	39	9	hi−1	hi−1	NOUN
ejpam-3626	39	10	,	,	PUNCT
ejpam-3626	39	11	hi	hi	ADJ
ejpam-3626	39	12	]	]	PUNCT
ejpam-3626	39	13	,	,	PUNCT
ejpam-3626	39	14	ti	ti	NOUN
ejpam-3626	39	15	)	)	PUNCT
ejpam-3626	39	16	:	:	PUNCT
ejpam-3626	40	1	i	i	NOUN
ejpam-3626	40	2	=	=	NOUN
ejpam-3626	40	3	1	1	NUM
ejpam-3626	40	4	,	,	PUNCT
ejpam-3626	40	5	2	2	NUM
ejpam-3626	40	6	,	,	PUNCT
ejpam-3626	40	7	.	.	PUNCT
ejpam-3626	40	8	.	.	PUNCT
ejpam-3626	40	9	.	.	PUNCT
ejpam-3626	41	1	,	,	PUNCT
ejpam-3626	41	2	n	n	CCONJ
ejpam-3626	41	3	}	}	PUNCT
ejpam-3626	41	4	is	be	AUX
ejpam-3626	41	5	said	say	VERB
ejpam-3626	41	6	to	to	PART
ejpam-3626	41	7	be	be	AUX
ejpam-3626	41	8	δ	δ	NOUN
ejpam-3626	41	9	-	-	PUNCT
ejpam-3626	41	10	fine	fine	ADJ
ejpam-3626	41	11	if	if	SCONJ
ejpam-3626	41	12	ti	ti	PROPN
ejpam-3626	41	13	∈	∈	PROPN
ejpam-3626	41	14	[	[	X
ejpam-3626	41	15	hi−1	hi−1	PROPN
ejpam-3626	41	16	,	,	PUNCT
ejpam-3626	41	17	hi	hi	INTJ
ejpam-3626	41	18	]	]	X
ejpam-3626	41	19	⊂	⊂	X
ejpam-3626	41	20	(	(	PUNCT
ejpam-3626	41	21	ti	ti	X
ejpam-3626	41	22	−	−	PROPN
ejpam-3626	41	23	δ(ti	δ(ti	PROPN
ejpam-3626	41	24	)	)	PUNCT
ejpam-3626	41	25	,	,	PUNCT
ejpam-3626	41	26	ti	ti	X
ejpam-3626	41	27	+	+	CCONJ
ejpam-3626	41	28	δ(ti	δ(ti	NOUN
ejpam-3626	41	29	)	)	PUNCT
ejpam-3626	41	30	)	)	PUNCT
ejpam-3626	41	31	for	for	ADP
ejpam-3626	41	32	every	every	DET
ejpam-3626	41	33	i	i	NOUN
ejpam-3626	41	34	=	=	NOUN
ejpam-3626	41	35	1	1	NUM
ejpam-3626	41	36	,	,	PUNCT
ejpam-3626	41	37	2	2	NUM
ejpam-3626	41	38	,	,	PUNCT
ejpam-3626	41	39	.	.	PUNCT
ejpam-3626	41	40	.	.	PUNCT
ejpam-3626	42	1	.	.	PUNCT
ejpam-3626	43	1	,	,	PUNCT
ejpam-3626	43	2	n.	n.	PROPN
ejpam-3626	43	3	theorem	theorem	VERB
ejpam-3626	43	4	1	1	NUM
ejpam-3626	43	5	.	.	PUNCT
ejpam-3626	44	1	[	[	X
ejpam-3626	44	2	9	9	NUM
ejpam-3626	44	3	]	]	X
ejpam-3626	44	4	(	(	PUNCT
ejpam-3626	44	5	cousin	cousin	PROPN
ejpam-3626	44	6	’s	’s	PART
ejpam-3626	44	7	lemma	lemma	PROPN
ejpam-3626	44	8	)	)	PUNCT
ejpam-3626	44	9	if	if	SCONJ
ejpam-3626	44	10	δ	δ	PROPN
ejpam-3626	44	11	is	be	AUX
ejpam-3626	44	12	a	a	DET
ejpam-3626	44	13	gauge	gauge	NOUN
ejpam-3626	44	14	on	on	ADP
ejpam-3626	44	15	[	[	X
ejpam-3626	44	16	f	f	X
ejpam-3626	44	17	,	,	PUNCT
ejpam-3626	44	18	g	g	NOUN
ejpam-3626	44	19	]	]	X
ejpam-3626	44	20	⊂	⊂	PROPN
ejpam-3626	44	21	c[a	c[a	PROPN
ejpam-3626	44	22	,	,	PUNCT
ejpam-3626	44	23	b	b	NOUN
ejpam-3626	44	24	]	]	X
ejpam-3626	44	25	,	,	PUNCT
ejpam-3626	44	26	then	then	ADV
ejpam-3626	44	27	there	there	PRON
ejpam-3626	44	28	is	be	VERB
ejpam-3626	44	29	a	a	DET
ejpam-3626	44	30	δ	δ	NOUN
ejpam-3626	44	31	-	-	PUNCT
ejpam-3626	44	32	fine	fine	ADJ
ejpam-3626	44	33	tagged	tag	VERB
ejpam-3626	44	34	division	division	NOUN
ejpam-3626	44	35	of	of	ADP
ejpam-3626	44	36	[	[	X
ejpam-3626	44	37	f	f	X
ejpam-3626	44	38	,	,	PUNCT
ejpam-3626	44	39	g	g	NOUN
ejpam-3626	44	40	]	]	X
ejpam-3626	44	41	.	.	PUNCT
ejpam-3626	45	1	3	3	X
ejpam-3626	45	2	.	.	X
ejpam-3626	45	3	henstock	henstock	NOUN
ejpam-3626	45	4	-	-	PUNCT
ejpam-3626	45	5	kurzweil	kurzweil	NOUN
ejpam-3626	45	6	-	-	PUNCT
ejpam-3626	45	7	stieltjes	stieltjes	NOUN
ejpam-3626	45	8	integral	integral	ADJ
ejpam-3626	45	9	on	on	ADP
ejpam-3626	45	10	c[a	c[a	NUM
ejpam-3626	45	11	,	,	PUNCT
ejpam-3626	45	12	b	b	X
ejpam-3626	45	13	]	]	X
ejpam-3626	45	14	let	let	NOUN
ejpam-3626	45	15	d	d	X
ejpam-3626	45	16	=	=	PRON
ejpam-3626	45	17	{	{	PUNCT
ejpam-3626	45	18	(	(	PUNCT
ejpam-3626	45	19	[	[	X
ejpam-3626	45	20	hi−1	hi−1	NOUN
ejpam-3626	45	21	,	,	PUNCT
ejpam-3626	45	22	hi	hi	ADJ
ejpam-3626	45	23	]	]	PUNCT
ejpam-3626	45	24	,	,	PUNCT
ejpam-3626	45	25	ti	ti	NOUN
ejpam-3626	45	26	)	)	PUNCT
ejpam-3626	45	27	:	:	PUNCT
ejpam-3626	46	1	i	i	NOUN
ejpam-3626	46	2	=	=	NOUN
ejpam-3626	46	3	1	1	NUM
ejpam-3626	46	4	,	,	PUNCT
ejpam-3626	46	5	2	2	NUM
ejpam-3626	46	6	,	,	PUNCT
ejpam-3626	46	7	.	.	PUNCT
ejpam-3626	46	8	.	.	PUNCT
ejpam-3626	46	9	.	.	PUNCT
ejpam-3626	47	1	,	,	PUNCT
ejpam-3626	47	2	n	n	CCONJ
ejpam-3626	47	3	}	}	PUNCT
ejpam-3626	47	4	be	be	AUX
ejpam-3626	47	5	a	a	DET
ejpam-3626	47	6	tagged	tag	VERB
ejpam-3626	47	7	division	division	NOUN
ejpam-3626	47	8	of	of	ADP
ejpam-3626	47	9	[	[	X
ejpam-3626	47	10	f	f	X
ejpam-3626	47	11	,	,	PUNCT
ejpam-3626	47	12	g	g	NOUN
ejpam-3626	47	13	]	]	PUNCT
ejpam-3626	47	14	and	and	CCONJ
ejpam-3626	47	15	f	f	X
ejpam-3626	47	16	,	,	PUNCT
ejpam-3626	47	17	h	h	NOUN
ejpam-3626	47	18	:	:	PUNCT
ejpam-3626	48	1	[	[	X
ejpam-3626	48	2	f	f	X
ejpam-3626	48	3	,	,	PUNCT
ejpam-3626	48	4	g]→	g]→	NOUN
ejpam-3626	48	5	c[a	c[a	NOUN
ejpam-3626	48	6	,	,	PUNCT
ejpam-3626	48	7	b	b	AUX
ejpam-3626	48	8	]	]	PUNCT
ejpam-3626	48	9	be	be	AUX
ejpam-3626	48	10	functions	function	NOUN
ejpam-3626	48	11	.	.	PUNCT
ejpam-3626	49	1	we	we	PRON
ejpam-3626	49	2	write	write	VERB
ejpam-3626	49	3	s(f	s(f	PROPN
ejpam-3626	49	4	,	,	PUNCT
ejpam-3626	49	5	h;d	h;d	PUNCT
ejpam-3626	49	6	)	)	PUNCT
ejpam-3626	50	1	=	=	PUNCT
ejpam-3626	50	2	n∑	n∑	NOUN
ejpam-3626	50	3	i=1	i=1	PROPN
ejpam-3626	51	1	f	f	PROPN
ejpam-3626	51	2	(	(	PUNCT
ejpam-3626	51	3	ti)[h(hi)−h(hi−1	ti)[h(hi)−h(hi−1	PROPN
ejpam-3626	51	4	)	)	PUNCT
ejpam-3626	51	5	]	]	PUNCT
ejpam-3626	51	6	,	,	PUNCT
ejpam-3626	51	7	called	call	VERB
ejpam-3626	51	8	as	as	ADP
ejpam-3626	51	9	henstock−kurzweil−stieltjes	henstock−kurzweil−stieltjes	PROPN
ejpam-3626	51	10	sum	sum	NOUN
ejpam-3626	51	11	of	of	ADP
ejpam-3626	51	12	f	f	PROPN
ejpam-3626	51	13	with	with	ADP
ejpam-3626	51	14	respect	respect	NOUN
ejpam-3626	51	15	to	to	ADP
ejpam-3626	51	16	h	h	NOUN
ejpam-3626	51	17	on	on	ADP
ejpam-3626	51	18	[	[	X
ejpam-3626	51	19	f	f	X
ejpam-3626	51	20	,	,	PUNCT
ejpam-3626	51	21	g	g	NOUN
ejpam-3626	51	22	]	]	PUNCT
ejpam-3626	51	23	.	.	PUNCT
ejpam-3626	52	1	for	for	ADP
ejpam-3626	52	2	brevity	brevity	NOUN
ejpam-3626	52	3	,	,	PUNCT
ejpam-3626	52	4	we	we	PRON
ejpam-3626	52	5	write	write	VERB
ejpam-3626	52	6	d	d	PROPN
ejpam-3626	52	7	=	=	PRON
ejpam-3626	52	8	{	{	PUNCT
ejpam-3626	52	9	(	(	PUNCT
ejpam-3626	52	10	[	[	X
ejpam-3626	52	11	u	u	NOUN
ejpam-3626	52	12	,	,	PUNCT
ejpam-3626	52	13	v	v	ADP
ejpam-3626	52	14	]	]	X
ejpam-3626	52	15	,	,	PUNCT
ejpam-3626	52	16	t	t	PROPN
ejpam-3626	52	17	)	)	PUNCT
ejpam-3626	52	18	}	}	PUNCT
ejpam-3626	52	19	for	for	ADP
ejpam-3626	52	20	a	a	DET
ejpam-3626	52	21	tagged	tag	VERB
ejpam-3626	52	22	division	division	NOUN
ejpam-3626	52	23	of	of	ADP
ejpam-3626	52	24	[	[	X
ejpam-3626	52	25	f	f	X
ejpam-3626	52	26	,	,	PUNCT
ejpam-3626	52	27	g	g	NOUN
ejpam-3626	52	28	]	]	PUNCT
ejpam-3626	52	29	and	and	CCONJ
ejpam-3626	52	30	s(f	s(f	PROPN
ejpam-3626	52	31	,	,	PUNCT
ejpam-3626	52	32	h;d	h;d	PUNCT
ejpam-3626	52	33	)	)	PUNCT
ejpam-3626	53	1	=	=	PUNCT
ejpam-3626	54	1	∑	∑	PUNCT
ejpam-3626	54	2	d	d	X
ejpam-3626	54	3	f	f	X
ejpam-3626	54	4	(	(	PUNCT
ejpam-3626	54	5	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	54	6	)	)	PUNCT
ejpam-3626	54	7	]	]	PUNCT
ejpam-3626	54	8	.	.	PUNCT
ejpam-3626	55	1	a.	a.	PROPN
ejpam-3626	55	2	cunanan	cunanan	PROPN
ejpam-3626	55	3	,	,	PUNCT
ejpam-3626	55	4	j.	j.	PROPN
ejpam-3626	55	5	benitez	benitez	PROPN
ejpam-3626	55	6	/	/	PUNCT
ejpam-3626	55	7	eur	eur	PROPN
ejpam-3626	55	8	.	.	PUNCT
ejpam-3626	56	1	j.	j.	PROPN
ejpam-3626	56	2	pure	pure	PROPN
ejpam-3626	56	3	appl	appl	PROPN
ejpam-3626	56	4	.	.	PROPN
ejpam-3626	56	5	math	math	PROPN
ejpam-3626	56	6	,	,	PUNCT
ejpam-3626	56	7	13	13	NUM
ejpam-3626	56	8	(	(	PUNCT
ejpam-3626	56	9	1	1	NUM
ejpam-3626	56	10	)	)	PUNCT
ejpam-3626	56	11	(	(	PUNCT
ejpam-3626	56	12	2020	2020	NUM
ejpam-3626	56	13	)	)	PUNCT
ejpam-3626	56	14	,	,	PUNCT
ejpam-3626	56	15	130	130	NUM
ejpam-3626	56	16	-	-	SYM
ejpam-3626	56	17	143	143	NUM
ejpam-3626	56	18	132	132	NUM
ejpam-3626	56	19	definition	definition	NOUN
ejpam-3626	56	20	2	2	NUM
ejpam-3626	56	21	.	.	PUNCT
ejpam-3626	57	1	let	let	VERB
ejpam-3626	57	2	f	f	X
ejpam-3626	57	3	,	,	PUNCT
ejpam-3626	57	4	h	h	NOUN
ejpam-3626	57	5	:	:	PUNCT
ejpam-3626	58	1	[	[	X
ejpam-3626	58	2	f	f	X
ejpam-3626	58	3	,	,	PUNCT
ejpam-3626	58	4	g	g	NOUN
ejpam-3626	58	5	]	]	X
ejpam-3626	58	6	→	→	SYM
ejpam-3626	58	7	c[a	c[a	NUM
ejpam-3626	58	8	,	,	PUNCT
ejpam-3626	58	9	b	b	AUX
ejpam-3626	58	10	]	]	PUNCT
ejpam-3626	58	11	be	be	AUX
ejpam-3626	58	12	functions	function	NOUN
ejpam-3626	58	13	.	.	PUNCT
ejpam-3626	59	1	we	we	PRON
ejpam-3626	59	2	say	say	VERB
ejpam-3626	59	3	that	that	SCONJ
ejpam-3626	59	4	the	the	DET
ejpam-3626	59	5	function	function	NOUN
ejpam-3626	59	6	f	f	PROPN
ejpam-3626	59	7	is	be	AUX
ejpam-3626	59	8	henstock−kurzweil−stieltjes	henstock−kurzweil−stieltjes	PROPN
ejpam-3626	59	9	integrable	integrable	ADJ
ejpam-3626	59	10	with	with	ADP
ejpam-3626	59	11	respect	respect	NOUN
ejpam-3626	59	12	to	to	ADP
ejpam-3626	59	13	h	h	NOUN
ejpam-3626	59	14	on	on	ADP
ejpam-3626	59	15	[	[	X
ejpam-3626	59	16	f	f	X
ejpam-3626	59	17	,	,	PUNCT
ejpam-3626	59	18	g	g	NOUN
ejpam-3626	59	19	]	]	PUNCT
ejpam-3626	59	20	to	to	ADP
ejpam-3626	59	21	s	s	PROPN
ejpam-3626	59	22	∈	∈	PROPN
ejpam-3626	59	23	c[a	c[a	NOUN
ejpam-3626	59	24	,	,	PUNCT
ejpam-3626	59	25	b	b	NOUN
ejpam-3626	59	26	]	]	X
ejpam-3626	59	27	,	,	PUNCT
ejpam-3626	59	28	briefly	briefly	ADV
ejpam-3626	59	29	hks	hks	PROPN
ejpam-3626	59	30	-	-	PUNCT
ejpam-3626	59	31	integrable	integrable	ADJ
ejpam-3626	59	32	,	,	PUNCT
ejpam-3626	59	33	if	if	SCONJ
ejpam-3626	59	34	for	for	ADP
ejpam-3626	59	35	any	any	DET
ejpam-3626	59	36	ε	ε	PROPN
ejpam-3626	59	37	>	>	X
ejpam-3626	59	38	0	0	PROPN
ejpam-3626	59	39	,	,	PUNCT
ejpam-3626	59	40	there	there	PRON
ejpam-3626	59	41	exists	exist	VERB
ejpam-3626	59	42	a	a	DET
ejpam-3626	59	43	gauge	gauge	NOUN
ejpam-3626	59	44	δ	δ	NOUN
ejpam-3626	59	45	on	on	ADP
ejpam-3626	59	46	[	[	X
ejpam-3626	59	47	f	f	X
ejpam-3626	59	48	,	,	PUNCT
ejpam-3626	59	49	g	g	NOUN
ejpam-3626	59	50	]	]	PUNCT
ejpam-3626	59	51	such	such	ADJ
ejpam-3626	59	52	that	that	PRON
ejpam-3626	59	53	for	for	ADP
ejpam-3626	59	54	any	any	DET
ejpam-3626	59	55	δ	δ	NOUN
ejpam-3626	59	56	-	-	PUNCT
ejpam-3626	59	57	fine	fine	ADJ
ejpam-3626	59	58	tagged	tag	VERB
ejpam-3626	59	59	division	division	NOUN
ejpam-3626	59	60	d	d	NOUN
ejpam-3626	59	61	of	of	ADP
ejpam-3626	59	62	[	[	X
ejpam-3626	59	63	f	f	X
ejpam-3626	59	64	,	,	PUNCT
ejpam-3626	59	65	g	g	PROPN
ejpam-3626	59	66	]	]	X
ejpam-3626	59	67	,	,	PUNCT
ejpam-3626	59	68	we	we	PRON
ejpam-3626	59	69	have	have	VERB
ejpam-3626	59	70	|s(f	|s(f	PROPN
ejpam-3626	59	71	,	,	PUNCT
ejpam-3626	59	72	h;d)−	h;d)−	PROPN
ejpam-3626	59	73	s|	s|	VERB
ejpam-3626	59	74	<	<	X
ejpam-3626	59	75	ε	ε	X
ejpam-3626	59	76	·	·	PUNCT
ejpam-3626	59	77	e	e	X
ejpam-3626	59	78	,	,	PUNCT
ejpam-3626	59	79	where	where	SCONJ
ejpam-3626	59	80	e	e	NOUN
ejpam-3626	59	81	is	be	AUX
ejpam-3626	59	82	the	the	DET
ejpam-3626	59	83	multiplicative	multiplicative	ADJ
ejpam-3626	59	84	identity	identity	NOUN
ejpam-3626	59	85	in	in	ADP
ejpam-3626	59	86	c[a	c[a	NUM
ejpam-3626	59	87	,	,	PUNCT
ejpam-3626	59	88	b	b	NOUN
ejpam-3626	59	89	]	]	X
ejpam-3626	59	90	.	.	PUNCT
ejpam-3626	60	1	the	the	DET
ejpam-3626	60	2	element	element	NOUN
ejpam-3626	60	3	s	s	PROPN
ejpam-3626	60	4	∈	∈	PROPN
ejpam-3626	60	5	c[a	c[a	NOUN
ejpam-3626	60	6	,	,	PUNCT
ejpam-3626	60	7	b	b	AUX
ejpam-3626	60	8	]	]	PUNCT
ejpam-3626	60	9	is	be	AUX
ejpam-3626	60	10	called	call	VERB
ejpam-3626	60	11	henstock−kurweil−stieltjes	henstock−kurweil−stieltjes	PRON
ejpam-3626	60	12	integral	integral	ADJ
ejpam-3626	60	13	,	,	PUNCT
ejpam-3626	60	14	briefly	briefly	NOUN
ejpam-3626	60	15	hks	hks	PROPN
ejpam-3626	60	16	-	-	PUNCT
ejpam-3626	60	17	integral	integral	ADJ
ejpam-3626	60	18	,	,	PUNCT
ejpam-3626	60	19	of	of	ADP
ejpam-3626	60	20	f	f	PROPN
ejpam-3626	60	21	with	with	ADP
ejpam-3626	60	22	respect	respect	NOUN
ejpam-3626	60	23	to	to	ADP
ejpam-3626	60	24	h	h	NOUN
ejpam-3626	60	25	on	on	ADP
ejpam-3626	60	26	[	[	X
ejpam-3626	60	27	f	f	X
ejpam-3626	60	28	,	,	PUNCT
ejpam-3626	60	29	g	g	NOUN
ejpam-3626	60	30	]	]	PUNCT
ejpam-3626	60	31	and	and	CCONJ
ejpam-3626	60	32	is	be	AUX
ejpam-3626	60	33	written	write	VERB
ejpam-3626	60	34	by	by	ADP
ejpam-3626	60	35	s	s	NOUN
ejpam-3626	60	36	=	=	SYM
ejpam-3626	60	37	(	(	PUNCT
ejpam-3626	60	38	hks	hks	PROPN
ejpam-3626	60	39	)	)	PUNCT
ejpam-3626	60	40	∫	∫	PROPN
ejpam-3626	60	41	g	g	PROPN
ejpam-3626	60	42	f	f	PROPN
ejpam-3626	60	43	f	f	PROPN
ejpam-3626	60	44	dh	dh	PROPN
ejpam-3626	60	45	.	.	PUNCT
ejpam-3626	61	1	the	the	DET
ejpam-3626	61	2	collection	collection	NOUN
ejpam-3626	61	3	of	of	ADP
ejpam-3626	61	4	all	all	DET
ejpam-3626	61	5	functions	function	NOUN
ejpam-3626	61	6	which	which	PRON
ejpam-3626	61	7	are	be	AUX
ejpam-3626	61	8	hks	hks	PROPN
ejpam-3626	61	9	-	-	PUNCT
ejpam-3626	61	10	integrable	integrable	ADJ
ejpam-3626	61	11	with	with	ADP
ejpam-3626	61	12	respect	respect	NOUN
ejpam-3626	61	13	to	to	ADP
ejpam-3626	61	14	h	h	NOUN
ejpam-3626	61	15	on	on	ADP
ejpam-3626	61	16	[	[	X
ejpam-3626	61	17	f	f	X
ejpam-3626	61	18	,	,	PUNCT
ejpam-3626	61	19	g	g	NOUN
ejpam-3626	61	20	]	]	PUNCT
ejpam-3626	61	21	is	be	AUX
ejpam-3626	61	22	denoted	denote	VERB
ejpam-3626	61	23	by	by	ADP
ejpam-3626	61	24	hks([f	hks([f	NOUN
ejpam-3626	61	25	,	,	PUNCT
ejpam-3626	61	26	g	g	NOUN
ejpam-3626	61	27	]	]	X
ejpam-3626	61	28	,	,	PUNCT
ejpam-3626	61	29	h	h	NOUN
ejpam-3626	61	30	)	)	PUNCT
ejpam-3626	61	31	.	.	PUNCT
ejpam-3626	62	1	theorem	theorem	NOUN
ejpam-3626	62	2	2	2	NUM
ejpam-3626	62	3	.	.	PUNCT
ejpam-3626	62	4	(	(	PUNCT
ejpam-3626	62	5	uniqueness	uniqueness	NOUN
ejpam-3626	62	6	)	)	PUNCT
ejpam-3626	62	7	if	if	SCONJ
ejpam-3626	62	8	f	f	PROPN
ejpam-3626	62	9	is	be	AUX
ejpam-3626	62	10	hks	hks	PROPN
ejpam-3626	62	11	-	-	PUNCT
ejpam-3626	62	12	integrable	integrable	ADJ
ejpam-3626	62	13	with	with	ADP
ejpam-3626	62	14	respect	respect	NOUN
ejpam-3626	62	15	to	to	ADP
ejpam-3626	62	16	h	h	NOUN
ejpam-3626	62	17	on	on	ADP
ejpam-3626	62	18	[	[	X
ejpam-3626	62	19	f	f	X
ejpam-3626	62	20	,	,	PUNCT
ejpam-3626	62	21	g	g	PROPN
ejpam-3626	62	22	]	]	X
ejpam-3626	62	23	,	,	PUNCT
ejpam-3626	62	24	then	then	ADV
ejpam-3626	62	25	the	the	DET
ejpam-3626	62	26	hks	hks	PROPN
ejpam-3626	62	27	-	-	PUNCT
ejpam-3626	62	28	integral	integral	ADJ
ejpam-3626	62	29	of	of	ADP
ejpam-3626	62	30	f	f	PROPN
ejpam-3626	62	31	with	with	ADP
ejpam-3626	62	32	respect	respect	NOUN
ejpam-3626	62	33	to	to	ADP
ejpam-3626	62	34	h	h	NOUN
ejpam-3626	62	35	on	on	ADP
ejpam-3626	62	36	[	[	X
ejpam-3626	62	37	f	f	X
ejpam-3626	62	38	,	,	PUNCT
ejpam-3626	62	39	g	g	NOUN
ejpam-3626	62	40	]	]	PUNCT
ejpam-3626	62	41	is	be	AUX
ejpam-3626	62	42	unique	unique	ADJ
ejpam-3626	62	43	.	.	PUNCT
ejpam-3626	63	1	proof	proof	NOUN
ejpam-3626	63	2	.	.	PUNCT
ejpam-3626	64	1	suppose	suppose	VERB
ejpam-3626	64	2	that	that	SCONJ
ejpam-3626	64	3	f	f	PROPN
ejpam-3626	64	4	is	be	AUX
ejpam-3626	64	5	hks	hks	PROPN
ejpam-3626	64	6	-	-	PUNCT
ejpam-3626	64	7	integrable	integrable	ADJ
ejpam-3626	64	8	with	with	ADP
ejpam-3626	64	9	respect	respect	NOUN
ejpam-3626	64	10	to	to	ADP
ejpam-3626	64	11	h	h	NOUN
ejpam-3626	64	12	on	on	ADP
ejpam-3626	64	13	[	[	X
ejpam-3626	64	14	f	f	X
ejpam-3626	64	15	,	,	PUNCT
ejpam-3626	64	16	g	g	NOUN
ejpam-3626	64	17	]	]	PUNCT
ejpam-3626	64	18	to	to	ADP
ejpam-3626	64	19	s1	s1	PROPN
ejpam-3626	64	20	∈	∈	PROPN
ejpam-3626	64	21	c[a	c[a	NOUN
ejpam-3626	64	22	,	,	PUNCT
ejpam-3626	64	23	b	b	NOUN
ejpam-3626	64	24	]	]	PUNCT
ejpam-3626	64	25	and	and	CCONJ
ejpam-3626	64	26	s2	s2	PROPN
ejpam-3626	64	27	∈	∈	PROPN
ejpam-3626	64	28	c[a	c[a	NOUN
ejpam-3626	64	29	,	,	PUNCT
ejpam-3626	64	30	b	b	NOUN
ejpam-3626	64	31	]	]	PUNCT
ejpam-3626	64	32	.	.	PUNCT
ejpam-3626	65	1	let	let	VERB
ejpam-3626	65	2	ε	ε	PROPN
ejpam-3626	65	3	>	>	X
ejpam-3626	65	4	0	0	PROPN
ejpam-3626	65	5	.	.	PUNCT
ejpam-3626	66	1	then	then	ADV
ejpam-3626	66	2	there	there	PRON
ejpam-3626	66	3	exists	exist	VERB
ejpam-3626	66	4	a	a	DET
ejpam-3626	66	5	gauge	gauge	NOUN
ejpam-3626	66	6	δ1	δ1	NOUN
ejpam-3626	66	7	on	on	ADP
ejpam-3626	66	8	[	[	X
ejpam-3626	66	9	f	f	X
ejpam-3626	66	10	,	,	PUNCT
ejpam-3626	66	11	g	g	NOUN
ejpam-3626	66	12	]	]	PUNCT
ejpam-3626	66	13	such	such	ADJ
ejpam-3626	66	14	that	that	SCONJ
ejpam-3626	66	15	for	for	ADP
ejpam-3626	66	16	all	all	DET
ejpam-3626	66	17	δ1	δ1	NOUN
ejpam-3626	66	18	-	-	PUNCT
ejpam-3626	66	19	fine	fine	ADJ
ejpam-3626	66	20	tagged	tag	VERB
ejpam-3626	66	21	division	division	NOUN
ejpam-3626	66	22	d	d	NOUN
ejpam-3626	66	23	=	=	PRON
ejpam-3626	66	24	{	{	PUNCT
ejpam-3626	66	25	(	(	PUNCT
ejpam-3626	66	26	[	[	X
ejpam-3626	66	27	hi−1	hi−1	NOUN
ejpam-3626	66	28	,	,	PUNCT
ejpam-3626	66	29	hi	hi	ADJ
ejpam-3626	66	30	]	]	PUNCT
ejpam-3626	66	31	,	,	PUNCT
ejpam-3626	66	32	ti	ti	NOUN
ejpam-3626	66	33	)	)	PUNCT
ejpam-3626	66	34	:	:	PUNCT
ejpam-3626	67	1	i	i	NOUN
ejpam-3626	67	2	=	=	NOUN
ejpam-3626	67	3	1	1	NUM
ejpam-3626	67	4	,	,	PUNCT
ejpam-3626	67	5	2	2	NUM
ejpam-3626	67	6	,	,	PUNCT
ejpam-3626	67	7	.	.	PUNCT
ejpam-3626	67	8	.	.	PUNCT
ejpam-3626	67	9	.	.	PUNCT
ejpam-3626	67	10	,	,	PUNCT
ejpam-3626	67	11	n	n	CCONJ
ejpam-3626	67	12	}	}	PUNCT
ejpam-3626	67	13	of	of	ADP
ejpam-3626	67	14	[	[	X
ejpam-3626	67	15	f	f	X
ejpam-3626	67	16	,	,	PUNCT
ejpam-3626	67	17	g	g	PROPN
ejpam-3626	67	18	]	]	X
ejpam-3626	67	19	,	,	PUNCT
ejpam-3626	67	20	we	we	PRON
ejpam-3626	67	21	have	have	AUX
ejpam-3626	67	22	|s(f	|s(f	PROPN
ejpam-3626	67	23	,	,	PUNCT
ejpam-3626	67	24	h;d)−	h;d)−	PROPN
ejpam-3626	67	25	s1|	s1|	PROPN
ejpam-3626	67	26	<	<	X
ejpam-3626	67	27	ε	ε	PROPN
ejpam-3626	67	28	2	2	NUM
ejpam-3626	67	29	·	·	PUNCT
ejpam-3626	67	30	e.	e.	PROPN
ejpam-3626	67	31	(	(	PUNCT
ejpam-3626	67	32	1	1	NUM
ejpam-3626	67	33	)	)	PUNCT
ejpam-3626	67	34	similarly	similarly	ADV
ejpam-3626	67	35	,	,	PUNCT
ejpam-3626	67	36	there	there	PRON
ejpam-3626	67	37	exists	exist	VERB
ejpam-3626	67	38	a	a	DET
ejpam-3626	67	39	gauge	gauge	NOUN
ejpam-3626	67	40	δ2	δ2	VERB
ejpam-3626	67	41	on	on	ADP
ejpam-3626	67	42	[	[	X
ejpam-3626	67	43	f	f	X
ejpam-3626	67	44	,	,	PUNCT
ejpam-3626	67	45	g	g	NOUN
ejpam-3626	67	46	]	]	PUNCT
ejpam-3626	67	47	such	such	ADJ
ejpam-3626	67	48	that	that	SCONJ
ejpam-3626	67	49	for	for	ADP
ejpam-3626	67	50	all	all	DET
ejpam-3626	67	51	δ2	δ2	VERB
ejpam-3626	67	52	-	-	PUNCT
ejpam-3626	67	53	fine	fine	ADJ
ejpam-3626	67	54	tagged	tag	VERB
ejpam-3626	67	55	division	division	NOUN
ejpam-3626	67	56	q	q	NOUN
ejpam-3626	68	1	=	=	PUNCT
ejpam-3626	68	2	{	{	PUNCT
ejpam-3626	68	3	(	(	PUNCT
ejpam-3626	68	4	[	[	X
ejpam-3626	68	5	ki−1	ki−1	PROPN
ejpam-3626	68	6	,	,	PUNCT
ejpam-3626	68	7	ki	ki	PROPN
ejpam-3626	68	8	]	]	PUNCT
ejpam-3626	68	9	,	,	PUNCT
ejpam-3626	68	10	si	si	PROPN
ejpam-3626	68	11	)	)	PUNCT
ejpam-3626	68	12	:	:	PUNCT
ejpam-3626	69	1	i	i	NOUN
ejpam-3626	69	2	=	=	NOUN
ejpam-3626	69	3	1	1	NUM
ejpam-3626	69	4	,	,	PUNCT
ejpam-3626	69	5	2	2	NUM
ejpam-3626	69	6	,	,	PUNCT
ejpam-3626	69	7	.	.	PUNCT
ejpam-3626	69	8	.	.	PUNCT
ejpam-3626	69	9	.	.	PUNCT
ejpam-3626	70	1	,	,	PUNCT
ejpam-3626	70	2	m	m	VERB
ejpam-3626	70	3	}	}	PUNCT
ejpam-3626	70	4	of	of	ADP
ejpam-3626	70	5	[	[	X
ejpam-3626	70	6	f	f	X
ejpam-3626	70	7	,	,	PUNCT
ejpam-3626	70	8	g	g	PROPN
ejpam-3626	70	9	]	]	X
ejpam-3626	70	10	,	,	PUNCT
ejpam-3626	70	11	we	we	PRON
ejpam-3626	70	12	have	have	VERB
ejpam-3626	70	13	|s(f	|s(f	PROPN
ejpam-3626	70	14	,	,	PUNCT
ejpam-3626	70	15	h;q)−	h;q)−	PUNCT
ejpam-3626	70	16	s2|	s2|	AUX
ejpam-3626	70	17	<	<	X
ejpam-3626	70	18	ε	ε	PROPN
ejpam-3626	70	19	2	2	NUM
ejpam-3626	70	20	·	·	PUNCT
ejpam-3626	70	21	e.	e.	PROPN
ejpam-3626	70	22	(	(	PUNCT
ejpam-3626	70	23	2	2	X
ejpam-3626	70	24	)	)	PUNCT
ejpam-3626	70	25	define	define	VERB
ejpam-3626	70	26	a	a	DET
ejpam-3626	70	27	function	function	NOUN
ejpam-3626	70	28	δ	δ	NOUN
ejpam-3626	70	29	:	:	PUNCT
ejpam-3626	71	1	[	[	X
ejpam-3626	71	2	f	f	X
ejpam-3626	71	3	,	,	PUNCT
ejpam-3626	71	4	g]→	g]→	NOUN
ejpam-3626	71	5	c[a	c[a	NOUN
ejpam-3626	71	6	,	,	PUNCT
ejpam-3626	71	7	b	b	X
ejpam-3626	71	8	]	]	PUNCT
ejpam-3626	71	9	by	by	ADP
ejpam-3626	71	10	δ	δ	PROPN
ejpam-3626	71	11	=	=	PROPN
ejpam-3626	71	12	δ1	δ1	NOUN
ejpam-3626	71	13	∧	∧	PROPN
ejpam-3626	71	14	δ2	δ2	PROPN
ejpam-3626	71	15	.	.	PUNCT
ejpam-3626	72	1	hence	hence	ADV
ejpam-3626	72	2	,	,	PUNCT
ejpam-3626	72	3	by	by	ADP
ejpam-3626	72	4	(	(	PUNCT
ejpam-3626	72	5	1	1	NUM
ejpam-3626	72	6	)	)	PUNCT
ejpam-3626	72	7	and	and	CCONJ
ejpam-3626	72	8	(	(	PUNCT
ejpam-3626	72	9	2	2	NUM
ejpam-3626	72	10	)	)	PUNCT
ejpam-3626	72	11	|s1	|s1	NOUN
ejpam-3626	73	1	−	−	PROPN
ejpam-3626	73	2	s2|	s2|	VERB
ejpam-3626	73	3	<	<	X
ejpam-3626	73	4	ε	ε	PROPN
ejpam-3626	73	5	2	2	NUM
ejpam-3626	73	6	·	·	PUNCT
ejpam-3626	73	7	e+	e+	NUM
ejpam-3626	73	8	ε	ε	PROPN
ejpam-3626	73	9	2	2	NUM
ejpam-3626	73	10	·	·	PUNCT
ejpam-3626	73	11	e	e	X
ejpam-3626	73	12	=	=	SYM
ejpam-3626	73	13	ε	ε	PROPN
ejpam-3626	73	14	·	·	PUNCT
ejpam-3626	73	15	e.	e.	PROPN
ejpam-3626	73	16	this	this	PRON
ejpam-3626	73	17	shows	show	VERB
ejpam-3626	73	18	that	that	SCONJ
ejpam-3626	73	19	s1	s1	PROPN
ejpam-3626	73	20	=	=	SYM
ejpam-3626	73	21	s2	s2	PROPN
ejpam-3626	73	22	.	.	PUNCT
ejpam-3626	74	1	therefore	therefore	ADV
ejpam-3626	74	2	,	,	PUNCT
ejpam-3626	74	3	the	the	DET
ejpam-3626	74	4	hks	hks	PROPN
ejpam-3626	74	5	-	-	PUNCT
ejpam-3626	74	6	integral	integral	ADJ
ejpam-3626	74	7	of	of	ADP
ejpam-3626	74	8	f	f	PROPN
ejpam-3626	74	9	with	with	ADP
ejpam-3626	74	10	respect	respect	NOUN
ejpam-3626	74	11	to	to	ADP
ejpam-3626	74	12	h	h	NOUN
ejpam-3626	74	13	on	on	ADP
ejpam-3626	74	14	[	[	X
ejpam-3626	74	15	f	f	X
ejpam-3626	74	16	,	,	PUNCT
ejpam-3626	74	17	g	g	NOUN
ejpam-3626	74	18	]	]	PUNCT
ejpam-3626	74	19	is	be	AUX
ejpam-3626	74	20	unique	unique	ADJ
ejpam-3626	74	21	.	.	PUNCT
ejpam-3626	75	1	4	4	X
ejpam-3626	75	2	.	.	X
ejpam-3626	75	3	simple	simple	ADJ
ejpam-3626	75	4	properties	property	NOUN
ejpam-3626	75	5	theorem	theorem	VERB
ejpam-3626	75	6	3	3	X
ejpam-3626	75	7	.	.	PUNCT
ejpam-3626	76	1	if	if	SCONJ
ejpam-3626	76	2	f	f	PROPN
ejpam-3626	76	3	,	,	PUNCT
ejpam-3626	76	4	g	g	PROPN
ejpam-3626	76	5	∈	∈	PROPN
ejpam-3626	76	6	hks([f	hks([f	NOUN
ejpam-3626	76	7	,	,	PUNCT
ejpam-3626	76	8	g	g	NOUN
ejpam-3626	76	9	]	]	X
ejpam-3626	76	10	,	,	PUNCT
ejpam-3626	76	11	h	h	NOUN
ejpam-3626	76	12	)	)	PUNCT
ejpam-3626	76	13	and	and	CCONJ
ejpam-3626	76	14	α	α	PRON
ejpam-3626	76	15	∈	∈	PROPN
ejpam-3626	76	16	r	r	NOUN
ejpam-3626	76	17	,	,	PUNCT
ejpam-3626	76	18	then	then	ADV
ejpam-3626	76	19	(	(	PUNCT
ejpam-3626	76	20	i	i	NOUN
ejpam-3626	76	21	)	)	PUNCT
ejpam-3626	76	22	homogenity	homogenity	NOUN
ejpam-3626	76	23	:	:	PUNCT
ejpam-3626	76	24	α	α	X
ejpam-3626	76	25	·	·	PUNCT
ejpam-3626	76	26	f	f	X
ejpam-3626	76	27	∈	∈	PROPN
ejpam-3626	76	28	hks([f	hks([f	NOUN
ejpam-3626	76	29	,	,	PUNCT
ejpam-3626	76	30	g	g	NOUN
ejpam-3626	76	31	]	]	X
ejpam-3626	76	32	,	,	PUNCT
ejpam-3626	76	33	h	h	NOUN
ejpam-3626	76	34	)	)	PUNCT
ejpam-3626	76	35	and	and	CCONJ
ejpam-3626	76	36	(	(	PUNCT
ejpam-3626	76	37	hks	hks	PROPN
ejpam-3626	76	38	)	)	PUNCT
ejpam-3626	76	39	∫	∫	PROPN
ejpam-3626	77	1	g	g	PROPN
ejpam-3626	77	2	f	f	PROPN
ejpam-3626	77	3	(	(	PUNCT
ejpam-3626	77	4	α	α	NOUN
ejpam-3626	77	5	·	·	PUNCT
ejpam-3626	77	6	f	f	X
ejpam-3626	77	7	)	)	PUNCT
ejpam-3626	77	8	dh	dh	NOUN
ejpam-3626	77	9	=	=	PUNCT
ejpam-3626	77	10	α	α	PROPN
ejpam-3626	77	11	·	·	PUNCT
ejpam-3626	77	12	(	(	PUNCT
ejpam-3626	77	13	hks	hks	PROPN
ejpam-3626	77	14	)	)	PUNCT
ejpam-3626	77	15	∫	∫	PROPN
ejpam-3626	77	16	g	g	PROPN
ejpam-3626	77	17	f	f	PROPN
ejpam-3626	77	18	fdh	fdh	PROPN
ejpam-3626	77	19	.	.	PUNCT
ejpam-3626	77	20	a.	a.	PROPN
ejpam-3626	77	21	cunanan	cunanan	PROPN
ejpam-3626	77	22	,	,	PUNCT
ejpam-3626	77	23	j.	j.	PROPN
ejpam-3626	77	24	benitez	benitez	PROPN
ejpam-3626	77	25	/	/	PUNCT
ejpam-3626	77	26	eur	eur	PROPN
ejpam-3626	77	27	.	.	PUNCT
ejpam-3626	78	1	j.	j.	PROPN
ejpam-3626	78	2	pure	pure	PROPN
ejpam-3626	78	3	appl	appl	PROPN
ejpam-3626	78	4	.	.	PROPN
ejpam-3626	78	5	math	math	PROPN
ejpam-3626	78	6	,	,	PUNCT
ejpam-3626	78	7	13	13	NUM
ejpam-3626	78	8	(	(	PUNCT
ejpam-3626	78	9	1	1	NUM
ejpam-3626	78	10	)	)	PUNCT
ejpam-3626	78	11	(	(	PUNCT
ejpam-3626	78	12	2020	2020	NUM
ejpam-3626	78	13	)	)	PUNCT
ejpam-3626	78	14	,	,	PUNCT
ejpam-3626	78	15	130	130	NUM
ejpam-3626	78	16	-	-	SYM
ejpam-3626	78	17	143	143	NUM
ejpam-3626	78	18	133	133	NUM
ejpam-3626	78	19	(	(	PUNCT
ejpam-3626	78	20	ii	ii	NOUN
ejpam-3626	78	21	)	)	PUNCT
ejpam-3626	78	22	linearity	linearity	NOUN
ejpam-3626	78	23	:	:	PUNCT
ejpam-3626	78	24	f	f	PROPN
ejpam-3626	79	1	+	+	NOUN
ejpam-3626	79	2	g	g	PROPN
ejpam-3626	79	3	∈	∈	PROPN
ejpam-3626	79	4	hks([f	hks([f	NOUN
ejpam-3626	79	5	,	,	PUNCT
ejpam-3626	79	6	g	g	NOUN
ejpam-3626	79	7	]	]	X
ejpam-3626	79	8	,	,	PUNCT
ejpam-3626	79	9	h	h	NOUN
ejpam-3626	79	10	)	)	PUNCT
ejpam-3626	79	11	and	and	CCONJ
ejpam-3626	79	12	(	(	PUNCT
ejpam-3626	79	13	hks	hks	PROPN
ejpam-3626	79	14	)	)	PUNCT
ejpam-3626	79	15	∫	∫	PROPN
ejpam-3626	80	1	g	g	PROPN
ejpam-3626	80	2	f	f	PROPN
ejpam-3626	80	3	(	(	PUNCT
ejpam-3626	80	4	f	f	PROPN
ejpam-3626	80	5	+	+	PROPN
ejpam-3626	80	6	g)dh	g)dh	PROPN
ejpam-3626	80	7	=	=	SYM
ejpam-3626	80	8	(	(	PUNCT
ejpam-3626	80	9	hks	hks	PROPN
ejpam-3626	80	10	)	)	PUNCT
ejpam-3626	80	11	∫	∫	PROPN
ejpam-3626	81	1	g	g	PROPN
ejpam-3626	81	2	f	f	PROPN
ejpam-3626	81	3	fdh	fdh	PROPN
ejpam-3626	81	4	+	+	PROPN
ejpam-3626	81	5	(	(	PUNCT
ejpam-3626	81	6	hks	hks	PROPN
ejpam-3626	81	7	)	)	PUNCT
ejpam-3626	81	8	∫	∫	PROPN
ejpam-3626	81	9	g	g	PROPN
ejpam-3626	81	10	f	f	PROPN
ejpam-3626	81	11	gdh	gdh	PROPN
ejpam-3626	81	12	.	.	PUNCT
ejpam-3626	82	1	proof	proof	NOUN
ejpam-3626	82	2	.	.	PUNCT
ejpam-3626	83	1	(	(	PUNCT
ejpam-3626	83	2	i	i	NOUN
ejpam-3626	83	3	)	)	PUNCT
ejpam-3626	83	4	let	let	VERB
ejpam-3626	83	5	ε	ε	PROPN
ejpam-3626	83	6	>	>	X
ejpam-3626	83	7	0	0	PROPN
ejpam-3626	83	8	.	.	PUNCT
ejpam-3626	84	1	then	then	ADV
ejpam-3626	84	2	there	there	PRON
ejpam-3626	84	3	exists	exist	VERB
ejpam-3626	84	4	a	a	DET
ejpam-3626	84	5	gauge	gauge	NOUN
ejpam-3626	84	6	δ	δ	NOUN
ejpam-3626	84	7	on	on	ADP
ejpam-3626	84	8	[	[	X
ejpam-3626	84	9	f	f	X
ejpam-3626	84	10	,	,	PUNCT
ejpam-3626	84	11	g	g	NOUN
ejpam-3626	84	12	]	]	PUNCT
ejpam-3626	84	13	such	such	ADJ
ejpam-3626	84	14	that	that	PRON
ejpam-3626	84	15	for	for	ADP
ejpam-3626	84	16	any	any	DET
ejpam-3626	84	17	δ	δ	NOUN
ejpam-3626	84	18	-	-	PUNCT
ejpam-3626	84	19	fine	fine	ADJ
ejpam-3626	84	20	tagged	tag	VERB
ejpam-3626	84	21	division	division	NOUN
ejpam-3626	84	22	d	d	NOUN
ejpam-3626	84	23	=	=	PRON
ejpam-3626	84	24	{	{	PUNCT
ejpam-3626	84	25	(	(	PUNCT
ejpam-3626	84	26	[	[	X
ejpam-3626	84	27	hi−1	hi−1	NOUN
ejpam-3626	84	28	,	,	PUNCT
ejpam-3626	84	29	hi	hi	ADJ
ejpam-3626	84	30	]	]	PUNCT
ejpam-3626	84	31	,	,	PUNCT
ejpam-3626	84	32	ti	ti	NOUN
ejpam-3626	84	33	)	)	PUNCT
ejpam-3626	84	34	:	:	PUNCT
ejpam-3626	85	1	i	i	NOUN
ejpam-3626	85	2	=	=	NOUN
ejpam-3626	85	3	1	1	NUM
ejpam-3626	85	4	,	,	PUNCT
ejpam-3626	85	5	2	2	NUM
ejpam-3626	85	6	,	,	PUNCT
ejpam-3626	85	7	.	.	PUNCT
ejpam-3626	85	8	.	.	PUNCT
ejpam-3626	85	9	.	.	PUNCT
ejpam-3626	85	10	,	,	PUNCT
ejpam-3626	85	11	n	n	CCONJ
ejpam-3626	85	12	}	}	PUNCT
ejpam-3626	85	13	of	of	ADP
ejpam-3626	85	14	[	[	X
ejpam-3626	85	15	f	f	X
ejpam-3626	85	16	,	,	PUNCT
ejpam-3626	85	17	g	g	PROPN
ejpam-3626	85	18	]	]	X
ejpam-3626	85	19	,	,	PUNCT
ejpam-3626	85	20	we	we	PRON
ejpam-3626	85	21	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	85	22	n∑	n∑	PROPN
ejpam-3626	85	23	i=1	i=1	PROPN
ejpam-3626	86	1	f	f	PROPN
ejpam-3626	86	2	(	(	PUNCT
ejpam-3626	86	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	86	4	(	(	PUNCT
ejpam-3626	86	5	hks	hks	PROPN
ejpam-3626	86	6	)	)	PUNCT
ejpam-3626	86	7	∫	∫	PROPN
ejpam-3626	86	8	g	g	PROPN
ejpam-3626	86	9	f	f	PROPN
ejpam-3626	86	10	fdh	fdh	PROPN
ejpam-3626	87	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	87	2	<	<	X
ejpam-3626	87	3	ε	ε	PROPN
ejpam-3626	87	4	|α|+	|α|+	PROPN
ejpam-3626	87	5	1	1	NUM
ejpam-3626	87	6	·	·	PUNCT
ejpam-3626	87	7	e.	e.	PROPN
ejpam-3626	87	8	thus	thus	ADV
ejpam-3626	87	9	,	,	PUNCT
ejpam-3626	87	10	for	for	ADP
ejpam-3626	87	11	any	any	DET
ejpam-3626	87	12	δ	δ	NOUN
ejpam-3626	87	13	-	-	PUNCT
ejpam-3626	87	14	fine	fine	ADJ
ejpam-3626	87	15	tagged	tag	VERB
ejpam-3626	87	16	division	division	NOUN
ejpam-3626	87	17	d	d	NOUN
ejpam-3626	87	18	=	=	PRON
ejpam-3626	87	19	{	{	PUNCT
ejpam-3626	87	20	(	(	PUNCT
ejpam-3626	87	21	[	[	X
ejpam-3626	87	22	hi−1	hi−1	NOUN
ejpam-3626	87	23	,	,	PUNCT
ejpam-3626	87	24	hi	hi	ADJ
ejpam-3626	87	25	]	]	PUNCT
ejpam-3626	87	26	,	,	PUNCT
ejpam-3626	87	27	ti	ti	NOUN
ejpam-3626	87	28	)	)	PUNCT
ejpam-3626	87	29	:	:	PUNCT
ejpam-3626	87	30	i	i	NOUN
ejpam-3626	87	31	=	=	NOUN
ejpam-3626	87	32	1	1	NUM
ejpam-3626	87	33	,	,	PUNCT
ejpam-3626	87	34	2	2	NUM
ejpam-3626	87	35	,	,	PUNCT
ejpam-3626	87	36	.	.	PUNCT
ejpam-3626	87	37	.	.	PUNCT
ejpam-3626	88	1	.	.	PUNCT
ejpam-3626	89	1	,	,	PUNCT
ejpam-3626	89	2	n	n	CCONJ
ejpam-3626	89	3	}	}	PUNCT
ejpam-3626	89	4	of	of	ADP
ejpam-3626	89	5	[	[	X
ejpam-3626	89	6	f	f	X
ejpam-3626	89	7	,	,	PUNCT
ejpam-3626	89	8	g]∣∣∣∣	g]∣∣∣∣	PROPN
ejpam-3626	89	9	n∑	n∑	PROPN
ejpam-3626	89	10	i=1	i=1	PROPN
ejpam-3626	89	11	(	(	PUNCT
ejpam-3626	89	12	α	α	X
ejpam-3626	89	13	·	·	PUNCT
ejpam-3626	89	14	f	f	X
ejpam-3626	89	15	)	)	PUNCT
ejpam-3626	89	16	(	(	PUNCT
ejpam-3626	89	17	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	PROPN
ejpam-3626	89	18	α	α	X
ejpam-3626	89	19	·	·	PUNCT
ejpam-3626	89	20	(	(	PUNCT
ejpam-3626	89	21	hks	hks	PROPN
ejpam-3626	89	22	)	)	PUNCT
ejpam-3626	89	23	∫	∫	PROPN
ejpam-3626	89	24	g	g	PROPN
ejpam-3626	89	25	f	f	PROPN
ejpam-3626	89	26	fdh	fdh	PROPN
ejpam-3626	89	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	89	28	=	=	PUNCT
ejpam-3626	89	29	∣∣∣∣α	∣∣∣∣α	NOUN
ejpam-3626	89	30	{	{	PUNCT
ejpam-3626	90	1	n∑	n∑	NOUN
ejpam-3626	90	2	i=1	i=1	PROPN
ejpam-3626	91	1	f	f	PROPN
ejpam-3626	91	2	(	(	PUNCT
ejpam-3626	91	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	91	4	(	(	PUNCT
ejpam-3626	91	5	hks	hks	PROPN
ejpam-3626	91	6	)	)	PUNCT
ejpam-3626	91	7	∫	∫	PROPN
ejpam-3626	92	1	g	g	PROPN
ejpam-3626	92	2	f	f	PROPN
ejpam-3626	92	3	fdh	fdh	PROPN
ejpam-3626	92	4	}	}	PUNCT
ejpam-3626	92	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	92	6	=	=	SYM
ejpam-3626	92	7	|α|	|α|	PROPN
ejpam-3626	92	8	·	·	PUNCT
ejpam-3626	92	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	92	10	n∑	n∑	PROPN
ejpam-3626	92	11	i=1	i=1	PROPN
ejpam-3626	93	1	f	f	PROPN
ejpam-3626	93	2	(	(	PUNCT
ejpam-3626	93	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	93	4	(	(	PUNCT
ejpam-3626	93	5	hks	hks	PROPN
ejpam-3626	93	6	)	)	PUNCT
ejpam-3626	93	7	∫	∫	PROPN
ejpam-3626	94	1	g	g	PROPN
ejpam-3626	94	2	f	f	PROPN
ejpam-3626	94	3	fdh	fdh	PROPN
ejpam-3626	94	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	94	5	<	<	X
ejpam-3626	94	6	|α|	|α|	PROPN
ejpam-3626	94	7	·	·	PUNCT
ejpam-3626	94	8	ε	ε	PROPN
ejpam-3626	94	9	|α|+	|α|+	PROPN
ejpam-3626	94	10	1	1	NUM
ejpam-3626	94	11	·	·	PUNCT
ejpam-3626	94	12	e	e	X
ejpam-3626	94	13	<	<	X
ejpam-3626	94	14	ε	ε	PROPN
ejpam-3626	94	15	·	·	PUNCT
ejpam-3626	94	16	e.	e.	PROPN
ejpam-3626	95	1	this	this	PRON
ejpam-3626	95	2	shows	show	VERB
ejpam-3626	95	3	that	that	SCONJ
ejpam-3626	95	4	α	α	PRON
ejpam-3626	95	5	·	·	PUNCT
ejpam-3626	95	6	f	f	PROPN
ejpam-3626	95	7	∈	∈	PROPN
ejpam-3626	95	8	hks([f	hks([f	NOUN
ejpam-3626	95	9	,	,	PUNCT
ejpam-3626	95	10	g	g	NOUN
ejpam-3626	95	11	]	]	X
ejpam-3626	95	12	,	,	PUNCT
ejpam-3626	95	13	h	h	NOUN
ejpam-3626	95	14	)	)	PUNCT
ejpam-3626	95	15	and	and	CCONJ
ejpam-3626	95	16	(	(	PUNCT
ejpam-3626	95	17	hks	hks	PROPN
ejpam-3626	95	18	)	)	PUNCT
ejpam-3626	95	19	∫	∫	PROPN
ejpam-3626	95	20	g	g	PROPN
ejpam-3626	95	21	f	f	PROPN
ejpam-3626	95	22	(	(	PUNCT
ejpam-3626	95	23	α	α	NOUN
ejpam-3626	95	24	·	·	PUNCT
ejpam-3626	95	25	f	f	X
ejpam-3626	95	26	)	)	PUNCT
ejpam-3626	95	27	dh	dh	NOUN
ejpam-3626	95	28	=	=	PUNCT
ejpam-3626	95	29	α	α	PROPN
ejpam-3626	95	30	·	·	PUNCT
ejpam-3626	95	31	(	(	PUNCT
ejpam-3626	95	32	hks	hks	PROPN
ejpam-3626	95	33	)	)	PUNCT
ejpam-3626	95	34	∫	∫	PROPN
ejpam-3626	95	35	g	g	PROPN
ejpam-3626	95	36	f	f	PROPN
ejpam-3626	95	37	fdh	fdh	PROPN
ejpam-3626	95	38	.	.	PUNCT
ejpam-3626	96	1	(	(	PUNCT
ejpam-3626	96	2	ii	ii	NOUN
ejpam-3626	96	3	)	)	PUNCT
ejpam-3626	96	4	let	let	VERB
ejpam-3626	96	5	ε	ε	PROPN
ejpam-3626	96	6	>	>	X
ejpam-3626	96	7	0	0	PROPN
ejpam-3626	96	8	.	.	PUNCT
ejpam-3626	97	1	then	then	ADV
ejpam-3626	97	2	there	there	PRON
ejpam-3626	97	3	exists	exist	VERB
ejpam-3626	97	4	gauge	gauge	NOUN
ejpam-3626	97	5	δf	δf	NOUN
ejpam-3626	97	6	on	on	ADP
ejpam-3626	97	7	[	[	X
ejpam-3626	97	8	f	f	X
ejpam-3626	97	9	,	,	PUNCT
ejpam-3626	97	10	g	g	NOUN
ejpam-3626	97	11	]	]	PUNCT
ejpam-3626	97	12	such	such	ADJ
ejpam-3626	97	13	that	that	SCONJ
ejpam-3626	97	14	for	for	ADP
ejpam-3626	97	15	any	any	DET
ejpam-3626	97	16	δf	δf	PART
ejpam-3626	97	17	-fine	-fine	ADJ
ejpam-3626	97	18	tagged	tag	VERB
ejpam-3626	97	19	division	division	NOUN
ejpam-3626	97	20	d	d	NOUN
ejpam-3626	97	21	=	=	PRON
ejpam-3626	97	22	{	{	PUNCT
ejpam-3626	97	23	(	(	PUNCT
ejpam-3626	97	24	[	[	X
ejpam-3626	97	25	hi−1	hi−1	NOUN
ejpam-3626	97	26	,	,	PUNCT
ejpam-3626	97	27	hi	hi	ADJ
ejpam-3626	97	28	]	]	PUNCT
ejpam-3626	97	29	,	,	PUNCT
ejpam-3626	97	30	ti	ti	NOUN
ejpam-3626	97	31	)	)	PUNCT
ejpam-3626	97	32	:	:	PUNCT
ejpam-3626	98	1	i	i	NOUN
ejpam-3626	98	2	=	=	NOUN
ejpam-3626	98	3	1	1	NUM
ejpam-3626	98	4	,	,	PUNCT
ejpam-3626	98	5	2	2	NUM
ejpam-3626	98	6	,	,	PUNCT
ejpam-3626	98	7	.	.	PUNCT
ejpam-3626	98	8	.	.	PUNCT
ejpam-3626	98	9	.	.	PUNCT
ejpam-3626	98	10	,	,	PUNCT
ejpam-3626	98	11	n	n	CCONJ
ejpam-3626	98	12	}	}	PUNCT
ejpam-3626	98	13	of	of	ADP
ejpam-3626	98	14	[	[	X
ejpam-3626	98	15	f	f	X
ejpam-3626	98	16	,	,	PUNCT
ejpam-3626	98	17	g	g	PROPN
ejpam-3626	98	18	]	]	X
ejpam-3626	98	19	,	,	PUNCT
ejpam-3626	98	20	we	we	PRON
ejpam-3626	98	21	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	98	22	n∑	n∑	PROPN
ejpam-3626	98	23	i=1	i=1	PROPN
ejpam-3626	99	1	f	f	PROPN
ejpam-3626	99	2	(	(	PUNCT
ejpam-3626	99	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	99	4	(	(	PUNCT
ejpam-3626	99	5	hks	hks	PROPN
ejpam-3626	99	6	)	)	PUNCT
ejpam-3626	99	7	∫	∫	PROPN
ejpam-3626	99	8	g	g	PROPN
ejpam-3626	99	9	f	f	PROPN
ejpam-3626	99	10	fdh	fdh	PROPN
ejpam-3626	99	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	99	12	<	<	X
ejpam-3626	99	13	ε	ε	PROPN
ejpam-3626	99	14	2	2	NUM
ejpam-3626	99	15	·	·	PUNCT
ejpam-3626	99	16	e.	e.	PROPN
ejpam-3626	99	17	(	(	PUNCT
ejpam-3626	99	18	3	3	NUM
ejpam-3626	99	19	)	)	PUNCT
ejpam-3626	99	20	similarly	similarly	ADV
ejpam-3626	99	21	,	,	PUNCT
ejpam-3626	99	22	there	there	PRON
ejpam-3626	99	23	exists	exist	VERB
ejpam-3626	99	24	gauge	gauge	NOUN
ejpam-3626	99	25	δg	δg	ADP
ejpam-3626	99	26	on	on	ADP
ejpam-3626	99	27	[	[	X
ejpam-3626	99	28	f	f	X
ejpam-3626	99	29	,	,	PUNCT
ejpam-3626	99	30	g	g	NOUN
ejpam-3626	99	31	]	]	PUNCT
ejpam-3626	99	32	such	such	ADJ
ejpam-3626	99	33	that	that	PRON
ejpam-3626	99	34	for	for	ADP
ejpam-3626	99	35	any	any	DET
ejpam-3626	99	36	δg	δg	ADJ
ejpam-3626	99	37	-	-	PUNCT
ejpam-3626	99	38	fine	fine	ADJ
ejpam-3626	99	39	tagged	tag	VERB
ejpam-3626	99	40	division	division	NOUN
ejpam-3626	99	41	q	q	NOUN
ejpam-3626	100	1	=	=	PUNCT
ejpam-3626	100	2	{	{	PUNCT
ejpam-3626	100	3	(	(	PUNCT
ejpam-3626	100	4	[	[	X
ejpam-3626	100	5	ki−1	ki−1	PROPN
ejpam-3626	100	6	,	,	PUNCT
ejpam-3626	100	7	ki	ki	PROPN
ejpam-3626	100	8	]	]	PUNCT
ejpam-3626	100	9	,	,	PUNCT
ejpam-3626	100	10	si	si	PROPN
ejpam-3626	100	11	)	)	PUNCT
ejpam-3626	100	12	:	:	PUNCT
ejpam-3626	101	1	i	i	NOUN
ejpam-3626	101	2	=	=	NOUN
ejpam-3626	101	3	1	1	NUM
ejpam-3626	101	4	,	,	PUNCT
ejpam-3626	101	5	2	2	NUM
ejpam-3626	101	6	,	,	PUNCT
ejpam-3626	101	7	.	.	PUNCT
ejpam-3626	101	8	.	.	PUNCT
ejpam-3626	101	9	.	.	PUNCT
ejpam-3626	102	1	,	,	PUNCT
ejpam-3626	102	2	m	m	VERB
ejpam-3626	102	3	}	}	PUNCT
ejpam-3626	102	4	of	of	ADP
ejpam-3626	102	5	[	[	X
ejpam-3626	102	6	f	f	X
ejpam-3626	102	7	,	,	PUNCT
ejpam-3626	102	8	g	g	PROPN
ejpam-3626	102	9	]	]	X
ejpam-3626	102	10	,	,	PUNCT
ejpam-3626	102	11	we	we	PRON
ejpam-3626	102	12	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	102	13	m∑	m∑	CCONJ
ejpam-3626	102	14	i=1	i=1	PROPN
ejpam-3626	102	15	g(si)[h(ki)−h(ki−1)]−	g(si)[h(ki)−h(ki−1)]−	PROPN
ejpam-3626	102	16	(	(	PUNCT
ejpam-3626	102	17	hks	hks	PROPN
ejpam-3626	102	18	)	)	PUNCT
ejpam-3626	102	19	∫	∫	PROPN
ejpam-3626	103	1	g	g	PROPN
ejpam-3626	103	2	f	f	PROPN
ejpam-3626	103	3	gdh	gdh	PROPN
ejpam-3626	104	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3626	104	2	<	<	X
ejpam-3626	104	3	ε	ε	PROPN
ejpam-3626	104	4	2	2	NUM
ejpam-3626	104	5	·	·	PUNCT
ejpam-3626	104	6	e.	e.	PROPN
ejpam-3626	104	7	(	(	PUNCT
ejpam-3626	104	8	4	4	NUM
ejpam-3626	104	9	)	)	PUNCT
ejpam-3626	104	10	a.	a.	NOUN
ejpam-3626	104	11	cunanan	cunanan	PROPN
ejpam-3626	104	12	,	,	PUNCT
ejpam-3626	104	13	j.	j.	PROPN
ejpam-3626	104	14	benitez	benitez	PROPN
ejpam-3626	104	15	/	/	PUNCT
ejpam-3626	104	16	eur	eur	PROPN
ejpam-3626	104	17	.	.	PUNCT
ejpam-3626	105	1	j.	j.	PROPN
ejpam-3626	105	2	pure	pure	PROPN
ejpam-3626	105	3	appl	appl	PROPN
ejpam-3626	105	4	.	.	PROPN
ejpam-3626	105	5	math	math	PROPN
ejpam-3626	105	6	,	,	PUNCT
ejpam-3626	105	7	13	13	NUM
ejpam-3626	105	8	(	(	PUNCT
ejpam-3626	105	9	1	1	NUM
ejpam-3626	105	10	)	)	PUNCT
ejpam-3626	105	11	(	(	PUNCT
ejpam-3626	105	12	2020	2020	NUM
ejpam-3626	105	13	)	)	PUNCT
ejpam-3626	105	14	,	,	PUNCT
ejpam-3626	105	15	130	130	NUM
ejpam-3626	105	16	-	-	SYM
ejpam-3626	105	17	143	143	NUM
ejpam-3626	105	18	134	134	NUM
ejpam-3626	105	19	define	define	VERB
ejpam-3626	105	20	δ	δ	PROPN
ejpam-3626	105	21	=	=	PUNCT
ejpam-3626	105	22	δf	δf	PROPN
ejpam-3626	105	23	∧	∧	NOUN
ejpam-3626	105	24	δg	δg	PROPN
ejpam-3626	105	25	.	.	PUNCT
ejpam-3626	106	1	then	then	ADV
ejpam-3626	106	2	δ	δ	PROPN
ejpam-3626	106	3	is	be	AUX
ejpam-3626	106	4	a	a	DET
ejpam-3626	106	5	gauge	gauge	NOUN
ejpam-3626	106	6	on	on	ADP
ejpam-3626	106	7	[	[	X
ejpam-3626	106	8	f	f	X
ejpam-3626	106	9	,	,	PUNCT
ejpam-3626	106	10	g	g	NOUN
ejpam-3626	106	11	]	]	PUNCT
ejpam-3626	106	12	.	.	PUNCT
ejpam-3626	107	1	let	let	VERB
ejpam-3626	108	1	d	d	NOUN
ejpam-3626	108	2	=	=	PRON
ejpam-3626	108	3	{	{	PUNCT
ejpam-3626	108	4	(	(	PUNCT
ejpam-3626	108	5	[	[	X
ejpam-3626	108	6	hi−1	hi−1	NOUN
ejpam-3626	108	7	,	,	PUNCT
ejpam-3626	108	8	hi	hi	ADJ
ejpam-3626	108	9	]	]	PUNCT
ejpam-3626	108	10	,	,	PUNCT
ejpam-3626	108	11	ti	ti	NOUN
ejpam-3626	108	12	)	)	PUNCT
ejpam-3626	108	13	:	:	PUNCT
ejpam-3626	108	14	i	i	NOUN
ejpam-3626	108	15	=	=	NOUN
ejpam-3626	108	16	1	1	NUM
ejpam-3626	108	17	,	,	PUNCT
ejpam-3626	108	18	2	2	NUM
ejpam-3626	108	19	,	,	PUNCT
ejpam-3626	108	20	.	.	PUNCT
ejpam-3626	108	21	.	.	PUNCT
ejpam-3626	108	22	.	.	PUNCT
ejpam-3626	108	23	,	,	PUNCT
ejpam-3626	108	24	n	n	CCONJ
ejpam-3626	108	25	}	}	PUNCT
ejpam-3626	108	26	be	be	AUX
ejpam-3626	108	27	a	a	DET
ejpam-3626	108	28	δ	δ	NOUN
ejpam-3626	108	29	-	-	PUNCT
ejpam-3626	108	30	fine	fine	ADJ
ejpam-3626	108	31	tagged	tag	VERB
ejpam-3626	108	32	division	division	NOUN
ejpam-3626	108	33	of	of	ADP
ejpam-3626	108	34	[	[	X
ejpam-3626	108	35	f	f	X
ejpam-3626	108	36	,	,	PUNCT
ejpam-3626	108	37	g	g	NOUN
ejpam-3626	108	38	]	]	PUNCT
ejpam-3626	108	39	.	.	PUNCT
ejpam-3626	109	1	then	then	ADV
ejpam-3626	109	2	d	d	PROPN
ejpam-3626	109	3	is	be	AUX
ejpam-3626	109	4	both	both	PRON
ejpam-3626	109	5	δf	δf	NOUN
ejpam-3626	109	6	and	and	CCONJ
ejpam-3626	109	7	δg	δg	NOUN
ejpam-3626	109	8	-	-	PUNCT
ejpam-3626	109	9	fine	fine	NOUN
ejpam-3626	109	10	.	.	PUNCT
ejpam-3626	110	1	by	by	ADP
ejpam-3626	110	2	(	(	PUNCT
ejpam-3626	110	3	3	3	NUM
ejpam-3626	110	4	)	)	PUNCT
ejpam-3626	110	5	and	and	CCONJ
ejpam-3626	110	6	(	(	PUNCT
ejpam-3626	110	7	4),∣∣∣∣	4),∣∣∣∣	NUM
ejpam-3626	110	8	n∑	n∑	NOUN
ejpam-3626	110	9	i=1	i=1	PROPN
ejpam-3626	111	1	(	(	PUNCT
ejpam-3626	111	2	f	f	PROPN
ejpam-3626	111	3	+	+	NOUN
ejpam-3626	111	4	g)(ti)[h(hi)−h(hi−1)]−	g)(ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	111	5	{	{	PUNCT
ejpam-3626	111	6	(	(	PUNCT
ejpam-3626	111	7	hks	hks	PROPN
ejpam-3626	111	8	)	)	PUNCT
ejpam-3626	111	9	∫	∫	PROPN
ejpam-3626	111	10	g	g	PROPN
ejpam-3626	111	11	f	f	PROPN
ejpam-3626	111	12	fdh	fdh	PROPN
ejpam-3626	111	13	+	+	PROPN
ejpam-3626	111	14	(	(	PUNCT
ejpam-3626	111	15	hks	hks	PROPN
ejpam-3626	111	16	)	)	PUNCT
ejpam-3626	111	17	∫	∫	PROPN
ejpam-3626	111	18	g	g	PROPN
ejpam-3626	111	19	f	f	PROPN
ejpam-3626	111	20	gdh	gdh	PROPN
ejpam-3626	111	21	}	}	PUNCT
ejpam-3626	111	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	111	23	≤	≤	NOUN
ejpam-3626	112	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	112	2	n∑	n∑	PROPN
ejpam-3626	112	3	i=1	i=1	PROPN
ejpam-3626	113	1	f	f	PROPN
ejpam-3626	113	2	(	(	PUNCT
ejpam-3626	113	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	113	4	(	(	PUNCT
ejpam-3626	113	5	hks	hks	PROPN
ejpam-3626	113	6	)	)	PUNCT
ejpam-3626	113	7	∫	∫	PROPN
ejpam-3626	113	8	g	g	PROPN
ejpam-3626	113	9	f	f	PROPN
ejpam-3626	113	10	fdh	fdh	PROPN
ejpam-3626	113	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	113	12	+	+	CCONJ
ejpam-3626	113	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	113	14	n∑	n∑	PROPN
ejpam-3626	113	15	i=1	i=1	PROPN
ejpam-3626	113	16	g(ti)[h(hi)−h(hi−1)]−	g(ti)[h(hi)−h(hi−1)]−	PROPN
ejpam-3626	113	17	(	(	PUNCT
ejpam-3626	113	18	hks	hks	PROPN
ejpam-3626	113	19	)	)	PUNCT
ejpam-3626	113	20	∫	∫	PROPN
ejpam-3626	114	1	g	g	PROPN
ejpam-3626	114	2	f	f	PROPN
ejpam-3626	114	3	gdh	gdh	X
ejpam-3626	114	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	114	5	<	<	X
ejpam-3626	114	6	ε	ε	PROPN
ejpam-3626	114	7	2	2	NUM
ejpam-3626	114	8	·	·	PUNCT
ejpam-3626	114	9	e+	e+	NUM
ejpam-3626	114	10	ε	ε	PROPN
ejpam-3626	114	11	2	2	NUM
ejpam-3626	114	12	·	·	PUNCT
ejpam-3626	114	13	e	e	X
ejpam-3626	114	14	=	=	SYM
ejpam-3626	114	15	ε	ε	PROPN
ejpam-3626	114	16	·	·	PUNCT
ejpam-3626	114	17	e.	e.	PROPN
ejpam-3626	114	18	therefore	therefore	ADV
ejpam-3626	114	19	,	,	PUNCT
ejpam-3626	114	20	f	f	PROPN
ejpam-3626	115	1	+	+	ADP
ejpam-3626	115	2	g	g	PROPN
ejpam-3626	115	3	∈	∈	PROPN
ejpam-3626	115	4	hks([f	hks([f	NOUN
ejpam-3626	115	5	,	,	PUNCT
ejpam-3626	115	6	g	g	NOUN
ejpam-3626	115	7	]	]	X
ejpam-3626	115	8	,	,	PUNCT
ejpam-3626	115	9	h	h	NOUN
ejpam-3626	115	10	)	)	PUNCT
ejpam-3626	115	11	and	and	CCONJ
ejpam-3626	115	12	(	(	PUNCT
ejpam-3626	115	13	hks	hks	PROPN
ejpam-3626	115	14	)	)	PUNCT
ejpam-3626	115	15	∫	∫	PROPN
ejpam-3626	116	1	g	g	PROPN
ejpam-3626	116	2	f	f	PROPN
ejpam-3626	116	3	(	(	PUNCT
ejpam-3626	116	4	f	f	PROPN
ejpam-3626	116	5	+	+	PROPN
ejpam-3626	116	6	g)dh	g)dh	PROPN
ejpam-3626	116	7	=	=	SYM
ejpam-3626	116	8	(	(	PUNCT
ejpam-3626	116	9	hks	hks	PROPN
ejpam-3626	116	10	)	)	PUNCT
ejpam-3626	116	11	∫	∫	PROPN
ejpam-3626	117	1	g	g	PROPN
ejpam-3626	117	2	f	f	PROPN
ejpam-3626	117	3	fdh	fdh	PROPN
ejpam-3626	117	4	+	+	PROPN
ejpam-3626	117	5	(	(	PUNCT
ejpam-3626	117	6	hks	hks	PROPN
ejpam-3626	117	7	)	)	PUNCT
ejpam-3626	117	8	∫	∫	PROPN
ejpam-3626	117	9	g	g	PROPN
ejpam-3626	117	10	f	f	PROPN
ejpam-3626	117	11	gdh	gdh	PROPN
ejpam-3626	117	12	.	.	PUNCT
ejpam-3626	118	1	theorem	theorem	ADJ
ejpam-3626	118	2	4	4	NUM
ejpam-3626	118	3	.	.	PUNCT
ejpam-3626	119	1	(	(	PUNCT
ejpam-3626	119	2	linearity	linearity	NOUN
ejpam-3626	119	3	of	of	ADP
ejpam-3626	119	4	integrator	integrator	NOUN
ejpam-3626	119	5	)	)	PUNCT
ejpam-3626	119	6	if	if	SCONJ
ejpam-3626	119	7	f	f	PROPN
ejpam-3626	119	8	∈	∈	PROPN
ejpam-3626	119	9	hks([f	hks([f	NOUN
ejpam-3626	119	10	,	,	PUNCT
ejpam-3626	119	11	g	g	NOUN
ejpam-3626	119	12	]	]	X
ejpam-3626	119	13	,	,	PUNCT
ejpam-3626	119	14	h1	h1	PROPN
ejpam-3626	119	15	)	)	PUNCT
ejpam-3626	119	16	∩	∩	ADJ
ejpam-3626	119	17	hks([f	hks([f	NOUN
ejpam-3626	119	18	,	,	PUNCT
ejpam-3626	119	19	g	g	NOUN
ejpam-3626	119	20	]	]	X
ejpam-3626	119	21	,	,	PUNCT
ejpam-3626	119	22	h2	h2	PROPN
ejpam-3626	119	23	)	)	PUNCT
ejpam-3626	119	24	,	,	PUNCT
ejpam-3626	119	25	then	then	ADV
ejpam-3626	119	26	f	f	PROPN
ejpam-3626	119	27	∈	∈	PROPN
ejpam-3626	119	28	hks([f	hks([f	NOUN
ejpam-3626	119	29	,	,	PUNCT
ejpam-3626	119	30	g	g	NOUN
ejpam-3626	119	31	]	]	PUNCT
ejpam-3626	119	32	,	,	PUNCT
ejpam-3626	119	33	h1	h1	PROPN
ejpam-3626	119	34	+	+	PROPN
ejpam-3626	119	35	h2	h2	NOUN
ejpam-3626	119	36	)	)	PUNCT
ejpam-3626	119	37	and	and	CCONJ
ejpam-3626	119	38	(	(	PUNCT
ejpam-3626	119	39	hks	hks	PROPN
ejpam-3626	119	40	)	)	PUNCT
ejpam-3626	119	41	∫	∫	PROPN
ejpam-3626	120	1	g	g	PROPN
ejpam-3626	120	2	f	f	PROPN
ejpam-3626	120	3	fd(h1	fd(h1	PROPN
ejpam-3626	120	4	+	+	NOUN
ejpam-3626	120	5	h2	h2	NOUN
ejpam-3626	120	6	)	)	PUNCT
ejpam-3626	121	1	=	=	PUNCT
ejpam-3626	121	2	(	(	PUNCT
ejpam-3626	121	3	hks	hks	PROPN
ejpam-3626	121	4	)	)	PUNCT
ejpam-3626	121	5	∫	∫	PROPN
ejpam-3626	121	6	g	g	PROPN
ejpam-3626	121	7	f	f	PROPN
ejpam-3626	121	8	fdh1	fdh1	PROPN
ejpam-3626	122	1	+	+	CCONJ
ejpam-3626	122	2	(	(	PUNCT
ejpam-3626	122	3	hks	hks	PROPN
ejpam-3626	122	4	)	)	PUNCT
ejpam-3626	122	5	∫	∫	PROPN
ejpam-3626	122	6	g	g	PROPN
ejpam-3626	122	7	f	f	PROPN
ejpam-3626	122	8	fdh2	fdh2	PROPN
ejpam-3626	122	9	.	.	PUNCT
ejpam-3626	123	1	proof	proof	NOUN
ejpam-3626	123	2	.	.	PUNCT
ejpam-3626	124	1	let	let	VERB
ejpam-3626	124	2	ε	ε	PROPN
ejpam-3626	124	3	>	>	X
ejpam-3626	124	4	0	0	PROPN
ejpam-3626	124	5	.	.	PUNCT
ejpam-3626	125	1	then	then	ADV
ejpam-3626	125	2	there	there	PRON
ejpam-3626	125	3	exists	exist	VERB
ejpam-3626	125	4	gauge	gauge	NOUN
ejpam-3626	125	5	δh1	δh1	VERB
ejpam-3626	125	6	on	on	ADP
ejpam-3626	125	7	[	[	X
ejpam-3626	125	8	f	f	X
ejpam-3626	125	9	,	,	PUNCT
ejpam-3626	125	10	g	g	NOUN
ejpam-3626	125	11	]	]	PUNCT
ejpam-3626	125	12	such	such	ADJ
ejpam-3626	125	13	that	that	PRON
ejpam-3626	125	14	for	for	ADP
ejpam-3626	125	15	any	any	DET
ejpam-3626	125	16	δh1	δh1	NOUN
ejpam-3626	125	17	-	-	PUNCT
ejpam-3626	125	18	fine	fine	ADJ
ejpam-3626	125	19	tagged	tag	VERB
ejpam-3626	125	20	division	division	NOUN
ejpam-3626	125	21	d	d	NOUN
ejpam-3626	125	22	=	=	PRON
ejpam-3626	125	23	{	{	PUNCT
ejpam-3626	125	24	(	(	PUNCT
ejpam-3626	125	25	[	[	X
ejpam-3626	125	26	hi−1	hi−1	NOUN
ejpam-3626	125	27	,	,	PUNCT
ejpam-3626	125	28	hi	hi	ADJ
ejpam-3626	125	29	]	]	PUNCT
ejpam-3626	125	30	,	,	PUNCT
ejpam-3626	125	31	ti	ti	NOUN
ejpam-3626	125	32	)	)	PUNCT
ejpam-3626	125	33	:	:	PUNCT
ejpam-3626	126	1	i	i	NOUN
ejpam-3626	126	2	=	=	NOUN
ejpam-3626	126	3	1	1	NUM
ejpam-3626	126	4	,	,	PUNCT
ejpam-3626	126	5	2	2	NUM
ejpam-3626	126	6	,	,	PUNCT
ejpam-3626	126	7	.	.	PUNCT
ejpam-3626	126	8	.	.	PUNCT
ejpam-3626	126	9	.	.	PUNCT
ejpam-3626	126	10	,	,	PUNCT
ejpam-3626	126	11	n	n	CCONJ
ejpam-3626	126	12	}	}	PUNCT
ejpam-3626	126	13	of	of	ADP
ejpam-3626	126	14	[	[	X
ejpam-3626	126	15	f	f	X
ejpam-3626	126	16	,	,	PUNCT
ejpam-3626	126	17	g	g	PROPN
ejpam-3626	126	18	]	]	X
ejpam-3626	126	19	,	,	PUNCT
ejpam-3626	126	20	we	we	PRON
ejpam-3626	126	21	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	126	22	n∑	n∑	PROPN
ejpam-3626	126	23	i=1	i=1	PROPN
ejpam-3626	127	1	f	f	PROPN
ejpam-3626	127	2	(	(	PUNCT
ejpam-3626	127	3	ti)[h1(hi)−h1(hi−1)]−	ti)[h1(hi)−h1(hi−1)]−	PROPN
ejpam-3626	127	4	(	(	PUNCT
ejpam-3626	127	5	hks	hks	PROPN
ejpam-3626	127	6	)	)	PUNCT
ejpam-3626	127	7	∫	∫	PROPN
ejpam-3626	127	8	g	g	PROPN
ejpam-3626	127	9	f	f	PROPN
ejpam-3626	127	10	fdh1	fdh1	PROPN
ejpam-3626	127	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	127	12	<	<	X
ejpam-3626	127	13	ε	ε	PROPN
ejpam-3626	127	14	2	2	NUM
ejpam-3626	127	15	·	·	PUNCT
ejpam-3626	127	16	e.	e.	PROPN
ejpam-3626	127	17	(	(	PUNCT
ejpam-3626	127	18	5	5	NUM
ejpam-3626	127	19	)	)	PUNCT
ejpam-3626	127	20	similarly	similarly	ADV
ejpam-3626	127	21	,	,	PUNCT
ejpam-3626	127	22	there	there	PRON
ejpam-3626	127	23	exists	exist	VERB
ejpam-3626	127	24	gauge	gauge	VERB
ejpam-3626	127	25	δh2	δh2	NOUN
ejpam-3626	127	26	on	on	ADP
ejpam-3626	127	27	[	[	X
ejpam-3626	127	28	f	f	X
ejpam-3626	127	29	,	,	PUNCT
ejpam-3626	127	30	g	g	NOUN
ejpam-3626	127	31	]	]	PUNCT
ejpam-3626	127	32	such	such	ADJ
ejpam-3626	127	33	that	that	PRON
ejpam-3626	127	34	for	for	ADP
ejpam-3626	127	35	any	any	DET
ejpam-3626	127	36	δh2	δh2	NOUN
ejpam-3626	127	37	-	-	PUNCT
ejpam-3626	127	38	fine	fine	NOUN
ejpam-3626	127	39	tagged	tag	VERB
ejpam-3626	127	40	division	division	NOUN
ejpam-3626	127	41	q	q	NOUN
ejpam-3626	128	1	=	=	PUNCT
ejpam-3626	128	2	{	{	PUNCT
ejpam-3626	128	3	(	(	PUNCT
ejpam-3626	128	4	[	[	X
ejpam-3626	128	5	ki−1	ki−1	PROPN
ejpam-3626	128	6	,	,	PUNCT
ejpam-3626	128	7	ki	ki	PROPN
ejpam-3626	128	8	]	]	PUNCT
ejpam-3626	128	9	,	,	PUNCT
ejpam-3626	128	10	si	si	PROPN
ejpam-3626	128	11	)	)	PUNCT
ejpam-3626	128	12	:	:	PUNCT
ejpam-3626	129	1	i	i	NOUN
ejpam-3626	129	2	=	=	NOUN
ejpam-3626	129	3	1	1	NUM
ejpam-3626	129	4	,	,	PUNCT
ejpam-3626	129	5	2	2	NUM
ejpam-3626	129	6	,	,	PUNCT
ejpam-3626	129	7	.	.	PUNCT
ejpam-3626	129	8	.	.	PUNCT
ejpam-3626	129	9	.	.	PUNCT
ejpam-3626	130	1	,	,	PUNCT
ejpam-3626	130	2	m	m	VERB
ejpam-3626	130	3	}	}	PUNCT
ejpam-3626	130	4	of	of	ADP
ejpam-3626	130	5	[	[	X
ejpam-3626	130	6	f	f	X
ejpam-3626	130	7	,	,	PUNCT
ejpam-3626	130	8	g	g	PROPN
ejpam-3626	130	9	]	]	X
ejpam-3626	130	10	,	,	PUNCT
ejpam-3626	130	11	we	we	PRON
ejpam-3626	130	12	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	130	13	m∑	m∑	VERB
ejpam-3626	131	1	i=1	i=1	PROPN
ejpam-3626	131	2	f	f	PROPN
ejpam-3626	131	3	(	(	PUNCT
ejpam-3626	131	4	si)[h2(ki)−h2(ki−1)]−	si)[h2(ki)−h2(ki−1)]−	PROPN
ejpam-3626	131	5	(	(	PUNCT
ejpam-3626	131	6	hks	hks	PROPN
ejpam-3626	131	7	)	)	PUNCT
ejpam-3626	131	8	∫	∫	PROPN
ejpam-3626	131	9	g	g	PROPN
ejpam-3626	131	10	f	f	PROPN
ejpam-3626	131	11	fdh2	fdh2	PROPN
ejpam-3626	131	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	131	13	<	<	X
ejpam-3626	131	14	ε	ε	PROPN
ejpam-3626	131	15	2	2	NUM
ejpam-3626	131	16	·	·	PUNCT
ejpam-3626	131	17	e.	e.	PROPN
ejpam-3626	131	18	(	(	PUNCT
ejpam-3626	131	19	6	6	NUM
ejpam-3626	131	20	)	)	PUNCT
ejpam-3626	131	21	define	define	VERB
ejpam-3626	131	22	δ	δ	PROPN
ejpam-3626	131	23	=	=	PUNCT
ejpam-3626	131	24	δh1	δh1	PROPN
ejpam-3626	131	25	∧	∧	PROPN
ejpam-3626	131	26	δh2	δh2	NOUN
ejpam-3626	131	27	.	.	PUNCT
ejpam-3626	132	1	then	then	ADV
ejpam-3626	132	2	δ	δ	PROPN
ejpam-3626	132	3	is	be	AUX
ejpam-3626	132	4	a	a	DET
ejpam-3626	132	5	gauge	gauge	NOUN
ejpam-3626	132	6	on	on	ADP
ejpam-3626	132	7	[	[	X
ejpam-3626	132	8	f	f	X
ejpam-3626	132	9	,	,	PUNCT
ejpam-3626	132	10	g	g	NOUN
ejpam-3626	132	11	]	]	PUNCT
ejpam-3626	132	12	.	.	PUNCT
ejpam-3626	133	1	let	let	VERB
ejpam-3626	134	1	d	d	NOUN
ejpam-3626	134	2	=	=	PRON
ejpam-3626	134	3	{	{	PUNCT
ejpam-3626	134	4	(	(	PUNCT
ejpam-3626	134	5	[	[	X
ejpam-3626	134	6	hi−1	hi−1	NOUN
ejpam-3626	134	7	,	,	PUNCT
ejpam-3626	134	8	hi	hi	ADJ
ejpam-3626	134	9	]	]	PUNCT
ejpam-3626	134	10	,	,	PUNCT
ejpam-3626	134	11	ti	ti	NOUN
ejpam-3626	134	12	)	)	PUNCT
ejpam-3626	134	13	:	:	PUNCT
ejpam-3626	134	14	i	i	NOUN
ejpam-3626	134	15	=	=	NOUN
ejpam-3626	134	16	1	1	NUM
ejpam-3626	134	17	,	,	PUNCT
ejpam-3626	134	18	2	2	NUM
ejpam-3626	134	19	,	,	PUNCT
ejpam-3626	134	20	.	.	PUNCT
ejpam-3626	134	21	.	.	PUNCT
ejpam-3626	134	22	.	.	PUNCT
ejpam-3626	134	23	,	,	PUNCT
ejpam-3626	134	24	n	n	CCONJ
ejpam-3626	134	25	}	}	PUNCT
ejpam-3626	134	26	be	be	AUX
ejpam-3626	134	27	a	a	DET
ejpam-3626	134	28	δ	δ	NOUN
ejpam-3626	134	29	-	-	PUNCT
ejpam-3626	134	30	fine	fine	ADJ
ejpam-3626	134	31	tagged	tag	VERB
ejpam-3626	134	32	division	division	NOUN
ejpam-3626	134	33	of	of	ADP
ejpam-3626	134	34	[	[	X
ejpam-3626	134	35	f	f	X
ejpam-3626	134	36	,	,	PUNCT
ejpam-3626	134	37	g	g	NOUN
ejpam-3626	134	38	]	]	PUNCT
ejpam-3626	134	39	.	.	PUNCT
ejpam-3626	135	1	then	then	ADV
ejpam-3626	135	2	d	d	PROPN
ejpam-3626	135	3	is	be	AUX
ejpam-3626	135	4	both	both	DET
ejpam-3626	135	5	δh1	δh1	NOUN
ejpam-3626	135	6	and	and	CCONJ
ejpam-3626	135	7	δh2	δh2	NOUN
ejpam-3626	135	8	-	-	PUNCT
ejpam-3626	135	9	fine	fine	NOUN
ejpam-3626	135	10	.	.	PUNCT
ejpam-3626	136	1	by	by	ADP
ejpam-3626	136	2	(	(	PUNCT
ejpam-3626	136	3	5	5	NUM
ejpam-3626	136	4	)	)	PUNCT
ejpam-3626	136	5	and	and	CCONJ
ejpam-3626	136	6	(	(	PUNCT
ejpam-3626	136	7	6),∣∣∣∣	6),∣∣∣∣	NUM
ejpam-3626	136	8	n∑	n∑	NOUN
ejpam-3626	136	9	i=1	i=1	PROPN
ejpam-3626	137	1	f	f	PROPN
ejpam-3626	138	1	(	(	PUNCT
ejpam-3626	138	2	ti)[(h1	ti)[(h1	NOUN
ejpam-3626	138	3	+	+	NOUN
ejpam-3626	138	4	h2)(hi)−	h2)(hi)−	NOUN
ejpam-3626	138	5	(	(	PUNCT
ejpam-3626	138	6	h1	h1	PROPN
ejpam-3626	138	7	+	+	NOUN
ejpam-3626	138	8	h2)(hi−1)]−	h2)(hi−1)]−	NOUN
ejpam-3626	138	9	{	{	PUNCT
ejpam-3626	138	10	(	(	PUNCT
ejpam-3626	138	11	hks	hks	PROPN
ejpam-3626	138	12	)	)	PUNCT
ejpam-3626	138	13	∫	∫	PROPN
ejpam-3626	138	14	g	g	PROPN
ejpam-3626	138	15	f	f	PROPN
ejpam-3626	138	16	fdh1	fdh1	PROPN
ejpam-3626	139	1	+	+	CCONJ
ejpam-3626	139	2	(	(	PUNCT
ejpam-3626	139	3	hks	hks	PROPN
ejpam-3626	139	4	)	)	PUNCT
ejpam-3626	139	5	∫	∫	PROPN
ejpam-3626	139	6	g	g	PROPN
ejpam-3626	139	7	f	f	PROPN
ejpam-3626	139	8	fdh2	fdh2	PROPN
ejpam-3626	139	9	}	}	PUNCT
ejpam-3626	139	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	139	11	a.	a.	NOUN
ejpam-3626	139	12	cunanan	cunanan	PROPN
ejpam-3626	139	13	,	,	PUNCT
ejpam-3626	139	14	j.	j.	PROPN
ejpam-3626	139	15	benitez	benitez	PROPN
ejpam-3626	139	16	/	/	PUNCT
ejpam-3626	139	17	eur	eur	PROPN
ejpam-3626	139	18	.	.	PUNCT
ejpam-3626	140	1	j.	j.	PROPN
ejpam-3626	140	2	pure	pure	PROPN
ejpam-3626	140	3	appl	appl	PROPN
ejpam-3626	140	4	.	.	PROPN
ejpam-3626	140	5	math	math	PROPN
ejpam-3626	140	6	,	,	PUNCT
ejpam-3626	140	7	13	13	NUM
ejpam-3626	140	8	(	(	PUNCT
ejpam-3626	140	9	1	1	NUM
ejpam-3626	140	10	)	)	PUNCT
ejpam-3626	140	11	(	(	PUNCT
ejpam-3626	140	12	2020	2020	NUM
ejpam-3626	140	13	)	)	PUNCT
ejpam-3626	140	14	,	,	PUNCT
ejpam-3626	140	15	130	130	NUM
ejpam-3626	140	16	-	-	SYM
ejpam-3626	140	17	143	143	NUM
ejpam-3626	140	18	135	135	NUM
ejpam-3626	140	19	≤	≤	NOUN
ejpam-3626	140	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	140	21	n∑	n∑	PROPN
ejpam-3626	140	22	i=1	i=1	PROPN
ejpam-3626	141	1	f	f	PROPN
ejpam-3626	141	2	(	(	PUNCT
ejpam-3626	141	3	ti)[h1(hi)−h1(hi−1)]−	ti)[h1(hi)−h1(hi−1)]−	PROPN
ejpam-3626	141	4	(	(	PUNCT
ejpam-3626	141	5	hks	hks	PROPN
ejpam-3626	141	6	)	)	PUNCT
ejpam-3626	141	7	∫	∫	PROPN
ejpam-3626	141	8	g	g	PROPN
ejpam-3626	141	9	f	f	PROPN
ejpam-3626	141	10	fdh1	fdh1	PROPN
ejpam-3626	141	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	141	12	+	+	CCONJ
ejpam-3626	141	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	141	14	n∑	n∑	PROPN
ejpam-3626	141	15	i=1	i=1	PROPN
ejpam-3626	142	1	f	f	PROPN
ejpam-3626	142	2	(	(	PUNCT
ejpam-3626	142	3	ti)[h2(hi)−h2(hi−1)]−	ti)[h2(hi)−h2(hi−1)]−	PROPN
ejpam-3626	142	4	(	(	PUNCT
ejpam-3626	142	5	hks	hks	PROPN
ejpam-3626	142	6	)	)	PUNCT
ejpam-3626	142	7	∫	∫	PROPN
ejpam-3626	142	8	g	g	PROPN
ejpam-3626	142	9	f	f	PROPN
ejpam-3626	142	10	fdh2	fdh2	PROPN
ejpam-3626	142	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	142	12	<	<	X
ejpam-3626	142	13	ε	ε	PROPN
ejpam-3626	142	14	2	2	NUM
ejpam-3626	142	15	·	·	PUNCT
ejpam-3626	142	16	e+	e+	NUM
ejpam-3626	142	17	ε	ε	PROPN
ejpam-3626	142	18	2	2	NUM
ejpam-3626	142	19	·	·	PUNCT
ejpam-3626	142	20	e	e	X
ejpam-3626	142	21	=	=	SYM
ejpam-3626	142	22	ε	ε	PROPN
ejpam-3626	142	23	·	·	PUNCT
ejpam-3626	142	24	e.	e.	PROPN
ejpam-3626	142	25	therefore	therefore	ADV
ejpam-3626	142	26	,	,	PUNCT
ejpam-3626	142	27	f	f	PROPN
ejpam-3626	142	28	∈	∈	PROPN
ejpam-3626	142	29	hks([f	hks([f	NOUN
ejpam-3626	142	30	,	,	PUNCT
ejpam-3626	142	31	g	g	NOUN
ejpam-3626	142	32	]	]	PUNCT
ejpam-3626	142	33	,	,	PUNCT
ejpam-3626	142	34	h1	h1	PROPN
ejpam-3626	142	35	+	+	PROPN
ejpam-3626	142	36	h2	h2	NOUN
ejpam-3626	142	37	)	)	PUNCT
ejpam-3626	142	38	and	and	CCONJ
ejpam-3626	142	39	(	(	PUNCT
ejpam-3626	142	40	hks	hks	PROPN
ejpam-3626	142	41	)	)	PUNCT
ejpam-3626	142	42	∫	∫	PROPN
ejpam-3626	143	1	g	g	PROPN
ejpam-3626	143	2	f	f	PROPN
ejpam-3626	143	3	fd(h1	fd(h1	PROPN
ejpam-3626	143	4	+	+	NOUN
ejpam-3626	143	5	h2	h2	NOUN
ejpam-3626	143	6	)	)	PUNCT
ejpam-3626	144	1	=	=	PUNCT
ejpam-3626	144	2	(	(	PUNCT
ejpam-3626	144	3	hks	hks	PROPN
ejpam-3626	144	4	)	)	PUNCT
ejpam-3626	144	5	∫	∫	PROPN
ejpam-3626	144	6	g	g	PROPN
ejpam-3626	144	7	f	f	PROPN
ejpam-3626	144	8	fdh1	fdh1	PROPN
ejpam-3626	145	1	+	+	CCONJ
ejpam-3626	145	2	(	(	PUNCT
ejpam-3626	145	3	hks	hks	PROPN
ejpam-3626	145	4	)	)	PUNCT
ejpam-3626	145	5	∫	∫	PROPN
ejpam-3626	145	6	g	g	PROPN
ejpam-3626	145	7	f	f	PROPN
ejpam-3626	145	8	fdh2	fdh2	PROPN
ejpam-3626	145	9	.	.	PUNCT
ejpam-3626	146	1	theorem	theorem	ADJ
ejpam-3626	146	2	5	5	NUM
ejpam-3626	146	3	.	.	PUNCT
ejpam-3626	146	4	(	(	PUNCT
ejpam-3626	146	5	additivity	additivity	NOUN
ejpam-3626	146	6	)	)	PUNCT
ejpam-3626	146	7	let	let	VERB
ejpam-3626	146	8	f	f	PRON
ejpam-3626	146	9	≤	≤	NOUN
ejpam-3626	146	10	r	r	NOUN
ejpam-3626	146	11	≤	≤	NUM
ejpam-3626	146	12	g.	g.	NOUN
ejpam-3626	147	1	if	if	SCONJ
ejpam-3626	147	2	f	f	PROPN
ejpam-3626	147	3	∈	∈	PROPN
ejpam-3626	147	4	hks([f	hks([f	NOUN
ejpam-3626	147	5	,	,	PUNCT
ejpam-3626	147	6	r	r	NOUN
ejpam-3626	147	7	]	]	X
ejpam-3626	147	8	,	,	PUNCT
ejpam-3626	147	9	h	h	NOUN
ejpam-3626	147	10	)	)	PUNCT
ejpam-3626	147	11	and	and	CCONJ
ejpam-3626	147	12	f	f	PROPN
ejpam-3626	147	13	∈	∈	PROPN
ejpam-3626	147	14	hks([r	hks([r	PROPN
ejpam-3626	147	15	,	,	PUNCT
ejpam-3626	147	16	g	g	NOUN
ejpam-3626	147	17	]	]	X
ejpam-3626	147	18	,	,	PUNCT
ejpam-3626	147	19	h	h	NOUN
ejpam-3626	147	20	)	)	PUNCT
ejpam-3626	147	21	,	,	PUNCT
ejpam-3626	147	22	then	then	ADV
ejpam-3626	147	23	f	f	PROPN
ejpam-3626	147	24	∈	∈	PROPN
ejpam-3626	147	25	hks([f	hks([f	NOUN
ejpam-3626	147	26	,	,	PUNCT
ejpam-3626	147	27	g	g	NOUN
ejpam-3626	147	28	]	]	X
ejpam-3626	147	29	,	,	PUNCT
ejpam-3626	147	30	h	h	NOUN
ejpam-3626	147	31	)	)	PUNCT
ejpam-3626	147	32	and	and	CCONJ
ejpam-3626	147	33	(	(	PUNCT
ejpam-3626	147	34	hks	hks	PROPN
ejpam-3626	147	35	)	)	PUNCT
ejpam-3626	147	36	∫	∫	PROPN
ejpam-3626	148	1	g	g	PROPN
ejpam-3626	148	2	f	f	PROPN
ejpam-3626	148	3	fdh	fdh	PROPN
ejpam-3626	148	4	=	=	PROPN
ejpam-3626	148	5	(	(	PUNCT
ejpam-3626	148	6	hks	hks	PROPN
ejpam-3626	148	7	)	)	PUNCT
ejpam-3626	148	8	∫	∫	PROPN
ejpam-3626	149	1	r	r	PROPN
ejpam-3626	149	2	f	f	PROPN
ejpam-3626	149	3	fdh	fdh	PROPN
ejpam-3626	149	4	+	+	PROPN
ejpam-3626	149	5	(	(	PUNCT
ejpam-3626	149	6	hks	hks	PROPN
ejpam-3626	149	7	)	)	PUNCT
ejpam-3626	149	8	∫	∫	PROPN
ejpam-3626	149	9	g	g	PROPN
ejpam-3626	149	10	r	r	PROPN
ejpam-3626	149	11	fdh	fdh	PROPN
ejpam-3626	149	12	.	.	PUNCT
ejpam-3626	150	1	proof	proof	NOUN
ejpam-3626	150	2	.	.	PUNCT
ejpam-3626	151	1	let	let	VERB
ejpam-3626	151	2	ε	ε	PROPN
ejpam-3626	151	3	>	>	X
ejpam-3626	151	4	0	0	PROPN
ejpam-3626	151	5	.	.	PUNCT
ejpam-3626	152	1	then	then	ADV
ejpam-3626	152	2	there	there	PRON
ejpam-3626	152	3	exists	exist	VERB
ejpam-3626	152	4	gauge	gauge	ADJ
ejpam-3626	152	5	δ1	δ1	NOUN
ejpam-3626	152	6	on	on	ADP
ejpam-3626	152	7	[	[	X
ejpam-3626	152	8	f	f	X
ejpam-3626	152	9	,	,	PUNCT
ejpam-3626	152	10	r	r	X
ejpam-3626	152	11	]	]	PUNCT
ejpam-3626	152	12	such	such	ADJ
ejpam-3626	152	13	that	that	PRON
ejpam-3626	152	14	for	for	ADP
ejpam-3626	152	15	any	any	DET
ejpam-3626	152	16	δ1	δ1	NOUN
ejpam-3626	152	17	-	-	PUNCT
ejpam-3626	152	18	fine	fine	ADJ
ejpam-3626	152	19	tagged	tag	VERB
ejpam-3626	152	20	division	division	NOUN
ejpam-3626	152	21	d	d	NOUN
ejpam-3626	152	22	=	=	PRON
ejpam-3626	152	23	{	{	PUNCT
ejpam-3626	152	24	(	(	PUNCT
ejpam-3626	152	25	[	[	X
ejpam-3626	152	26	hi−1	hi−1	NOUN
ejpam-3626	152	27	,	,	PUNCT
ejpam-3626	152	28	hi	hi	ADJ
ejpam-3626	152	29	]	]	PUNCT
ejpam-3626	152	30	,	,	PUNCT
ejpam-3626	152	31	ti	ti	NOUN
ejpam-3626	152	32	)	)	PUNCT
ejpam-3626	152	33	:	:	PUNCT
ejpam-3626	153	1	i	i	NOUN
ejpam-3626	153	2	=	=	NOUN
ejpam-3626	153	3	1	1	NUM
ejpam-3626	153	4	,	,	PUNCT
ejpam-3626	153	5	2	2	NUM
ejpam-3626	153	6	,	,	PUNCT
ejpam-3626	153	7	.	.	PUNCT
ejpam-3626	153	8	.	.	PUNCT
ejpam-3626	153	9	.	.	PUNCT
ejpam-3626	153	10	,	,	PUNCT
ejpam-3626	153	11	n	n	CCONJ
ejpam-3626	153	12	}	}	PUNCT
ejpam-3626	153	13	of	of	ADP
ejpam-3626	153	14	[	[	X
ejpam-3626	153	15	f	f	X
ejpam-3626	153	16	,	,	PUNCT
ejpam-3626	153	17	r	r	NOUN
ejpam-3626	153	18	]	]	X
ejpam-3626	153	19	,	,	PUNCT
ejpam-3626	153	20	we	we	PRON
ejpam-3626	153	21	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	153	22	n∑	n∑	PROPN
ejpam-3626	153	23	i=1	i=1	PROPN
ejpam-3626	154	1	f	f	PROPN
ejpam-3626	154	2	(	(	PUNCT
ejpam-3626	154	3	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	154	4	(	(	PUNCT
ejpam-3626	154	5	hks	hks	PROPN
ejpam-3626	154	6	)	)	PUNCT
ejpam-3626	154	7	∫	∫	PROPN
ejpam-3626	154	8	r	r	PROPN
ejpam-3626	154	9	f	f	PROPN
ejpam-3626	154	10	fdh	fdh	PROPN
ejpam-3626	154	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	154	12	<	<	X
ejpam-3626	154	13	ε	ε	PROPN
ejpam-3626	154	14	2	2	NUM
ejpam-3626	154	15	·	·	PUNCT
ejpam-3626	154	16	e.	e.	PROPN
ejpam-3626	154	17	(	(	PUNCT
ejpam-3626	154	18	7	7	NUM
ejpam-3626	154	19	)	)	PUNCT
ejpam-3626	154	20	similarly	similarly	ADV
ejpam-3626	154	21	,	,	PUNCT
ejpam-3626	154	22	there	there	PRON
ejpam-3626	154	23	exists	exist	VERB
ejpam-3626	154	24	gauge	gauge	NOUN
ejpam-3626	154	25	δ2	δ2	ADJ
ejpam-3626	154	26	on	on	ADP
ejpam-3626	154	27	[	[	X
ejpam-3626	154	28	r	r	X
ejpam-3626	154	29	,	,	PUNCT
ejpam-3626	154	30	g	g	NOUN
ejpam-3626	154	31	]	]	PUNCT
ejpam-3626	154	32	such	such	ADJ
ejpam-3626	154	33	that	that	PRON
ejpam-3626	154	34	for	for	ADP
ejpam-3626	154	35	any	any	DET
ejpam-3626	154	36	δ2	δ2	VERB
ejpam-3626	154	37	-	-	PUNCT
ejpam-3626	154	38	fine	fine	ADJ
ejpam-3626	154	39	tagged	tag	VERB
ejpam-3626	154	40	division	division	NOUN
ejpam-3626	154	41	q	q	NOUN
ejpam-3626	155	1	=	=	PUNCT
ejpam-3626	155	2	{	{	PUNCT
ejpam-3626	155	3	(	(	PUNCT
ejpam-3626	155	4	[	[	X
ejpam-3626	155	5	ki−1	ki−1	PROPN
ejpam-3626	155	6	,	,	PUNCT
ejpam-3626	155	7	ki	ki	PROPN
ejpam-3626	155	8	]	]	PUNCT
ejpam-3626	155	9	,	,	PUNCT
ejpam-3626	155	10	si	si	PROPN
ejpam-3626	155	11	)	)	PUNCT
ejpam-3626	155	12	:	:	PUNCT
ejpam-3626	156	1	i	i	NOUN
ejpam-3626	156	2	=	=	NOUN
ejpam-3626	156	3	1	1	NUM
ejpam-3626	156	4	,	,	PUNCT
ejpam-3626	156	5	2	2	NUM
ejpam-3626	156	6	,	,	PUNCT
ejpam-3626	156	7	.	.	PUNCT
ejpam-3626	156	8	.	.	PUNCT
ejpam-3626	156	9	.	.	PUNCT
ejpam-3626	157	1	,	,	PUNCT
ejpam-3626	157	2	m	m	VERB
ejpam-3626	157	3	}	}	PUNCT
ejpam-3626	157	4	of	of	ADP
ejpam-3626	157	5	[	[	X
ejpam-3626	157	6	r	r	X
ejpam-3626	157	7	,	,	PUNCT
ejpam-3626	157	8	g	g	NOUN
ejpam-3626	157	9	]	]	X
ejpam-3626	157	10	,	,	PUNCT
ejpam-3626	157	11	we	we	PRON
ejpam-3626	157	12	have∣∣∣∣∣	have∣∣∣∣∣	PROPN
ejpam-3626	157	13	m∑	m∑	VERB
ejpam-3626	158	1	i=1	i=1	PROPN
ejpam-3626	158	2	f	f	PROPN
ejpam-3626	158	3	(	(	PUNCT
ejpam-3626	158	4	si)[h(ki)−h(ki−1)]−	si)[h(ki)−h(ki−1)]−	PROPN
ejpam-3626	158	5	(	(	PUNCT
ejpam-3626	158	6	hks	hks	PROPN
ejpam-3626	158	7	)	)	PUNCT
ejpam-3626	158	8	∫	∫	PROPN
ejpam-3626	158	9	g	g	PROPN
ejpam-3626	158	10	r	r	PROPN
ejpam-3626	158	11	fdh	fdh	PROPN
ejpam-3626	159	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3626	159	2	<	<	X
ejpam-3626	159	3	ε	ε	PROPN
ejpam-3626	159	4	2	2	NUM
ejpam-3626	159	5	·	·	PUNCT
ejpam-3626	159	6	e.	e.	PROPN
ejpam-3626	159	7	(	(	PUNCT
ejpam-3626	159	8	8)	8)	NUM
ejpam-3626	159	9	define	define	VERB
ejpam-3626	159	10	a	a	DET
ejpam-3626	159	11	function	function	NOUN
ejpam-3626	159	12	δ	δ	NOUN
ejpam-3626	159	13	:	:	PUNCT
ejpam-3626	160	1	[	[	X
ejpam-3626	160	2	f	f	X
ejpam-3626	160	3	,	,	PUNCT
ejpam-3626	160	4	g]→	g]→	NOUN
ejpam-3626	160	5	c[f	c[f	NOUN
ejpam-3626	160	6	,	,	PUNCT
ejpam-3626	160	7	g	g	NOUN
ejpam-3626	160	8	]	]	PUNCT
ejpam-3626	160	9	by	by	ADP
ejpam-3626	160	10	δ(h	δ(h	PROPN
ejpam-3626	160	11	)	)	PUNCT
ejpam-3626	160	12	=	=	PRON
ejpam-3626	160	13	{	{	PUNCT
ejpam-3626	160	14	δ1(h	δ1(h	NOUN
ejpam-3626	160	15	)	)	PUNCT
ejpam-3626	160	16	∧	∧	NOUN
ejpam-3626	160	17	(	(	PUNCT
ejpam-3626	160	18	r	r	NOUN
ejpam-3626	160	19	−	−	PROPN
ejpam-3626	160	20	h	h	NOUN
ejpam-3626	160	21	)	)	PUNCT
ejpam-3626	160	22	,	,	PUNCT
ejpam-3626	161	1	if	if	SCONJ
ejpam-3626	161	2	f	f	PROPN
ejpam-3626	161	3	≤	≤	NUM
ejpam-3626	161	4	h	h	NOUN
ejpam-3626	161	5	≤	≤	NUM
ejpam-3626	161	6	r	r	NOUN
ejpam-3626	161	7	δ1(h	δ1(h	X
ejpam-3626	161	8	∧	∧	PROPN
ejpam-3626	161	9	r	r	NOUN
ejpam-3626	161	10	)	)	PUNCT
ejpam-3626	161	11	∧	∧	NOUN
ejpam-3626	161	12	δ2(h	δ2(h	PROPN
ejpam-3626	161	13	∨	∨	NUM
ejpam-3626	161	14	r	r	NOUN
ejpam-3626	161	15	)	)	PUNCT
ejpam-3626	161	16	,	,	PUNCT
ejpam-3626	161	17	if	if	SCONJ
ejpam-3626	161	18	h	h	NOUN
ejpam-3626	161	19	=	=	SYM
ejpam-3626	161	20	r	r	NOUN
ejpam-3626	161	21	or	or	CCONJ
ejpam-3626	161	22	h	h	NOUN
ejpam-3626	161	23	is	be	AUX
ejpam-3626	161	24	incomparable	incomparable	ADJ
ejpam-3626	161	25	to	to	ADP
ejpam-3626	161	26	r	r	NOUN
ejpam-3626	161	27	δ2(h	δ2(h	PROPN
ejpam-3626	161	28	)	)	PUNCT
ejpam-3626	161	29	∧	∧	NOUN
ejpam-3626	161	30	(	(	PUNCT
ejpam-3626	161	31	h−	h−	NOUN
ejpam-3626	161	32	r	r	NOUN
ejpam-3626	161	33	)	)	PUNCT
ejpam-3626	161	34	,	,	PUNCT
ejpam-3626	161	35	if	if	SCONJ
ejpam-3626	161	36	r	r	NOUN
ejpam-3626	161	37	≤	≤	NUM
ejpam-3626	161	38	h	h	NOUN
ejpam-3626	161	39	≤	≤	NOUN
ejpam-3626	161	40	g.	g.	PROPN
ejpam-3626	161	41	then	then	ADV
ejpam-3626	161	42	δ	δ	PROPN
ejpam-3626	161	43	is	be	AUX
ejpam-3626	161	44	a	a	DET
ejpam-3626	161	45	gauge	gauge	NOUN
ejpam-3626	161	46	on	on	ADP
ejpam-3626	161	47	[	[	X
ejpam-3626	161	48	f	f	X
ejpam-3626	161	49	,	,	PUNCT
ejpam-3626	161	50	g	g	NOUN
ejpam-3626	161	51	]	]	PUNCT
ejpam-3626	161	52	.	.	PUNCT
ejpam-3626	162	1	let	let	VERB
ejpam-3626	163	1	d	d	NOUN
ejpam-3626	163	2	=	=	PRON
ejpam-3626	163	3	{	{	PUNCT
ejpam-3626	163	4	(	(	PUNCT
ejpam-3626	163	5	[	[	X
ejpam-3626	163	6	hi−1	hi−1	NOUN
ejpam-3626	163	7	,	,	PUNCT
ejpam-3626	163	8	hi	hi	ADJ
ejpam-3626	163	9	]	]	PUNCT
ejpam-3626	163	10	,	,	PUNCT
ejpam-3626	163	11	ti	ti	NOUN
ejpam-3626	163	12	)	)	PUNCT
ejpam-3626	163	13	:	:	PUNCT
ejpam-3626	163	14	i	i	NOUN
ejpam-3626	163	15	=	=	NOUN
ejpam-3626	163	16	1	1	NUM
ejpam-3626	163	17	,	,	PUNCT
ejpam-3626	163	18	2	2	NUM
ejpam-3626	163	19	,	,	PUNCT
ejpam-3626	163	20	.	.	PUNCT
ejpam-3626	163	21	.	.	PUNCT
ejpam-3626	163	22	.	.	PUNCT
ejpam-3626	163	23	,	,	PUNCT
ejpam-3626	163	24	n	n	CCONJ
ejpam-3626	163	25	}	}	PUNCT
ejpam-3626	163	26	be	be	AUX
ejpam-3626	163	27	a	a	DET
ejpam-3626	163	28	δ	δ	NOUN
ejpam-3626	163	29	-	-	PUNCT
ejpam-3626	163	30	fine	fine	ADJ
ejpam-3626	163	31	tagged	tag	VERB
ejpam-3626	163	32	division	division	NOUN
ejpam-3626	163	33	of	of	ADP
ejpam-3626	163	34	[	[	X
ejpam-3626	163	35	f	f	X
ejpam-3626	163	36	,	,	PUNCT
ejpam-3626	163	37	g	g	NOUN
ejpam-3626	163	38	]	]	PUNCT
ejpam-3626	163	39	.	.	PUNCT
ejpam-3626	164	1	by	by	ADP
ejpam-3626	164	2	definition	definition	NOUN
ejpam-3626	164	3	of	of	ADP
ejpam-3626	164	4	δ	δ	PROPN
ejpam-3626	164	5	,	,	PUNCT
ejpam-3626	164	6	we	we	PRON
ejpam-3626	164	7	have	have	VERB
ejpam-3626	164	8	r	r	NOUN
ejpam-3626	164	9	=	=	NOUN
ejpam-3626	164	10	hi0	hi0	NOUN
ejpam-3626	164	11	for	for	ADP
ejpam-3626	164	12	some	some	DET
ejpam-3626	164	13	i0	i0	PROPN
ejpam-3626	164	14	∈	∈	PROPN
ejpam-3626	164	15	{	{	PUNCT
ejpam-3626	164	16	1	1	NUM
ejpam-3626	164	17	,	,	PUNCT
ejpam-3626	164	18	2	2	NUM
ejpam-3626	164	19	,	,	PUNCT
ejpam-3626	164	20	.	.	PUNCT
ejpam-3626	164	21	.	.	PUNCT
ejpam-3626	165	1	.	.	PUNCT
ejpam-3626	165	2	,	,	PUNCT
ejpam-3626	165	3	n	n	CCONJ
ejpam-3626	165	4	}	}	PUNCT
ejpam-3626	165	5	.	.	PUNCT
ejpam-3626	166	1	hence	hence	ADV
ejpam-3626	166	2	,	,	PUNCT
ejpam-3626	166	3	d	d	PROPN
ejpam-3626	166	4	=	=	SYM
ejpam-3626	166	5	d1	d1	PROPN
ejpam-3626	166	6	∪d2	∪d2	NOUN
ejpam-3626	166	7	for	for	ADP
ejpam-3626	166	8	some	some	DET
ejpam-3626	166	9	δ1	δ1	NOUN
ejpam-3626	166	10	-	-	PUNCT
ejpam-3626	166	11	fine	fine	ADJ
ejpam-3626	166	12	tagged	tag	VERB
ejpam-3626	166	13	division	division	NOUN
ejpam-3626	166	14	d1	d1	NOUN
ejpam-3626	166	15	of	of	ADP
ejpam-3626	166	16	[	[	X
ejpam-3626	166	17	f	f	X
ejpam-3626	166	18	,	,	PUNCT
ejpam-3626	166	19	r	r	NOUN
ejpam-3626	166	20	]	]	PUNCT
ejpam-3626	166	21	and	and	CCONJ
ejpam-3626	166	22	δ2	δ2	VERB
ejpam-3626	166	23	-	-	PUNCT
ejpam-3626	166	24	fine	fine	ADJ
ejpam-3626	166	25	tagged	tag	VERB
ejpam-3626	166	26	division	division	NOUN
ejpam-3626	166	27	d2	d2	PROPN
ejpam-3626	166	28	of	of	ADP
ejpam-3626	166	29	[	[	X
ejpam-3626	166	30	r	r	X
ejpam-3626	166	31	,	,	PUNCT
ejpam-3626	166	32	g	g	NOUN
ejpam-3626	166	33	]	]	PUNCT
ejpam-3626	166	34	.	.	PUNCT
ejpam-3626	167	1	by	by	ADP
ejpam-3626	167	2	(	(	PUNCT
ejpam-3626	167	3	7	7	NUM
ejpam-3626	167	4	)	)	PUNCT
ejpam-3626	167	5	and	and	CCONJ
ejpam-3626	167	6	(	(	PUNCT
ejpam-3626	167	7	8),∣∣∣∣	8),∣∣∣∣	NUM
ejpam-3626	167	8	n∑	n∑	NOUN
ejpam-3626	167	9	i=1	i=1	PROPN
ejpam-3626	167	10	f	f	PROPN
ejpam-3626	167	11	(	(	PUNCT
ejpam-3626	167	12	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	167	13	{	{	PUNCT
ejpam-3626	167	14	(	(	PUNCT
ejpam-3626	167	15	hks	hks	PROPN
ejpam-3626	167	16	)	)	PUNCT
ejpam-3626	167	17	∫	∫	PROPN
ejpam-3626	167	18	r	r	PROPN
ejpam-3626	167	19	f	f	PROPN
ejpam-3626	167	20	fdh	fdh	PROPN
ejpam-3626	167	21	+	+	PROPN
ejpam-3626	167	22	(	(	PUNCT
ejpam-3626	167	23	hks	hks	PROPN
ejpam-3626	167	24	)	)	PUNCT
ejpam-3626	167	25	∫	∫	PROPN
ejpam-3626	167	26	g	g	PROPN
ejpam-3626	167	27	r	r	PROPN
ejpam-3626	167	28	fdh	fdh	PROPN
ejpam-3626	167	29	}	}	PUNCT
ejpam-3626	167	30	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	167	31	<	<	X
ejpam-3626	167	32	ε	ε	PROPN
ejpam-3626	167	33	·	·	PUNCT
ejpam-3626	167	34	e.	e.	PROPN
ejpam-3626	167	35	a.	a.	PROPN
ejpam-3626	167	36	cunanan	cunanan	PROPN
ejpam-3626	167	37	,	,	PUNCT
ejpam-3626	167	38	j.	j.	PROPN
ejpam-3626	167	39	benitez	benitez	PROPN
ejpam-3626	167	40	/	/	PUNCT
ejpam-3626	167	41	eur	eur	PROPN
ejpam-3626	167	42	.	.	PUNCT
ejpam-3626	168	1	j.	j.	PROPN
ejpam-3626	168	2	pure	pure	PROPN
ejpam-3626	168	3	appl	appl	PROPN
ejpam-3626	168	4	.	.	PROPN
ejpam-3626	168	5	math	math	PROPN
ejpam-3626	168	6	,	,	PUNCT
ejpam-3626	168	7	13	13	NUM
ejpam-3626	168	8	(	(	PUNCT
ejpam-3626	168	9	1	1	NUM
ejpam-3626	168	10	)	)	PUNCT
ejpam-3626	168	11	(	(	PUNCT
ejpam-3626	168	12	2020	2020	NUM
ejpam-3626	168	13	)	)	PUNCT
ejpam-3626	168	14	,	,	PUNCT
ejpam-3626	168	15	130	130	NUM
ejpam-3626	168	16	-	-	SYM
ejpam-3626	168	17	143	143	NUM
ejpam-3626	168	18	136	136	NUM
ejpam-3626	168	19	therefore	therefore	ADV
ejpam-3626	168	20	,	,	PUNCT
ejpam-3626	168	21	f	f	PROPN
ejpam-3626	168	22	∈	∈	PROPN
ejpam-3626	168	23	hks([f	hks([f	NOUN
ejpam-3626	168	24	,	,	PUNCT
ejpam-3626	168	25	g	g	NOUN
ejpam-3626	168	26	]	]	X
ejpam-3626	168	27	,	,	PUNCT
ejpam-3626	168	28	h	h	NOUN
ejpam-3626	168	29	)	)	PUNCT
ejpam-3626	168	30	and	and	CCONJ
ejpam-3626	168	31	(	(	PUNCT
ejpam-3626	168	32	hks	hks	PROPN
ejpam-3626	168	33	)	)	PUNCT
ejpam-3626	168	34	∫	∫	PROPN
ejpam-3626	168	35	g	g	PROPN
ejpam-3626	168	36	f	f	PROPN
ejpam-3626	168	37	fdh	fdh	PROPN
ejpam-3626	168	38	=	=	PROPN
ejpam-3626	168	39	(	(	PUNCT
ejpam-3626	168	40	hks	hks	PROPN
ejpam-3626	168	41	)	)	PUNCT
ejpam-3626	168	42	∫	∫	PROPN
ejpam-3626	169	1	r	r	PROPN
ejpam-3626	169	2	f	f	PROPN
ejpam-3626	169	3	fdh	fdh	PROPN
ejpam-3626	169	4	+	+	PROPN
ejpam-3626	169	5	(	(	PUNCT
ejpam-3626	169	6	hks	hks	PROPN
ejpam-3626	169	7	)	)	PUNCT
ejpam-3626	169	8	∫	∫	PROPN
ejpam-3626	169	9	g	g	PROPN
ejpam-3626	169	10	r	r	PROPN
ejpam-3626	169	11	fdh	fdh	PROPN
ejpam-3626	169	12	.	.	PUNCT
ejpam-3626	170	1	in	in	ADP
ejpam-3626	170	2	the	the	DET
ejpam-3626	170	3	next	next	ADJ
ejpam-3626	170	4	theorem	theorem	NOUN
ejpam-3626	170	5	,	,	PUNCT
ejpam-3626	170	6	we	we	PRON
ejpam-3626	170	7	give	give	VERB
ejpam-3626	170	8	an	an	DET
ejpam-3626	170	9	analogous	analogous	ADJ
ejpam-3626	170	10	form	form	NOUN
ejpam-3626	170	11	of	of	ADP
ejpam-3626	170	12	cauchy	cauchy	ADJ
ejpam-3626	170	13	criterion	criterion	NOUN
ejpam-3626	170	14	for	for	ADP
ejpam-3626	170	15	hks−integral	hks−integral	PROPN
ejpam-3626	170	16	.	.	PUNCT
ejpam-3626	170	17	theorem	theorem	VERB
ejpam-3626	170	18	6	6	NUM
ejpam-3626	170	19	.	.	PUNCT
ejpam-3626	171	1	(	(	PUNCT
ejpam-3626	171	2	cauchy	cauchy	NOUN
ejpam-3626	171	3	criterion	criterion	NOUN
ejpam-3626	171	4	)	)	PUNCT
ejpam-3626	171	5	f	f	PROPN
ejpam-3626	171	6	∈	∈	PROPN
ejpam-3626	171	7	hks([f	hks([f	NOUN
ejpam-3626	171	8	,	,	PUNCT
ejpam-3626	171	9	g	g	NOUN
ejpam-3626	171	10	]	]	X
ejpam-3626	171	11	,	,	PUNCT
ejpam-3626	171	12	h	h	NOUN
ejpam-3626	171	13	)	)	PUNCT
ejpam-3626	171	14	if	if	SCONJ
ejpam-3626	172	1	and	and	CCONJ
ejpam-3626	172	2	only	only	ADV
ejpam-3626	172	3	if	if	SCONJ
ejpam-3626	172	4	for	for	ADP
ejpam-3626	172	5	every	every	DET
ejpam-3626	172	6	ε	ε	PROPN
ejpam-3626	172	7	>	>	X
ejpam-3626	172	8	0	0	PUNCT
ejpam-3626	173	1	there	there	PRON
ejpam-3626	173	2	exists	exist	VERB
ejpam-3626	173	3	a	a	DET
ejpam-3626	173	4	gauge	gauge	NOUN
ejpam-3626	173	5	δ	δ	NOUN
ejpam-3626	173	6	on	on	ADP
ejpam-3626	173	7	[	[	X
ejpam-3626	173	8	f	f	X
ejpam-3626	173	9	,	,	PUNCT
ejpam-3626	173	10	g	g	NOUN
ejpam-3626	173	11	]	]	PUNCT
ejpam-3626	173	12	such	such	ADJ
ejpam-3626	173	13	that	that	PRON
ejpam-3626	173	14	for	for	ADP
ejpam-3626	173	15	any	any	DET
ejpam-3626	173	16	δ	δ	NOUN
ejpam-3626	173	17	-	-	PUNCT
ejpam-3626	173	18	fine	fine	ADJ
ejpam-3626	173	19	tagged	tag	VERB
ejpam-3626	173	20	divisions	division	NOUN
ejpam-3626	173	21	d	d	NOUN
ejpam-3626	173	22	=	=	PRON
ejpam-3626	173	23	{	{	PUNCT
ejpam-3626	173	24	(	(	PUNCT
ejpam-3626	173	25	[	[	X
ejpam-3626	173	26	u	u	NOUN
ejpam-3626	173	27	,	,	PUNCT
ejpam-3626	173	28	v	v	ADP
ejpam-3626	173	29	]	]	X
ejpam-3626	173	30	,	,	PUNCT
ejpam-3626	173	31	t	t	PROPN
ejpam-3626	173	32	)	)	PUNCT
ejpam-3626	173	33	}	}	PUNCT
ejpam-3626	173	34	and	and	CCONJ
ejpam-3626	173	35	q	q	NOUN
ejpam-3626	174	1	=	=	X
ejpam-3626	174	2	{	{	PUNCT
ejpam-3626	174	3	(	(	PUNCT
ejpam-3626	174	4	[	[	X
ejpam-3626	174	5	u′	u′	PROPN
ejpam-3626	174	6	,	,	PUNCT
ejpam-3626	174	7	v′	v′	PROPN
ejpam-3626	174	8	]	]	PUNCT
ejpam-3626	174	9	,	,	PUNCT
ejpam-3626	174	10	s	s	X
ejpam-3626	174	11	)	)	PUNCT
ejpam-3626	174	12	}	}	PUNCT
ejpam-3626	174	13	of	of	ADP
ejpam-3626	174	14	[	[	X
ejpam-3626	174	15	f	f	X
ejpam-3626	174	16	,	,	PUNCT
ejpam-3626	174	17	g	g	PROPN
ejpam-3626	174	18	]	]	X
ejpam-3626	174	19	,	,	PUNCT
ejpam-3626	174	20	we	we	PRON
ejpam-3626	174	21	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-3626	174	22	d	d	ADP
ejpam-3626	174	23	f	f	PROPN
ejpam-3626	174	24	(	(	PUNCT
ejpam-3626	174	25	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	174	26	∑	∑	ADP
ejpam-3626	174	27	q	q	PROPN
ejpam-3626	174	28	f	f	X
ejpam-3626	174	29	(	(	PUNCT
ejpam-3626	174	30	s)[h(v′)−h(u′	s)[h(v′)−h(u′	PROPN
ejpam-3626	174	31	)	)	PUNCT
ejpam-3626	174	32	]	]	PUNCT
ejpam-3626	174	33	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	174	34	<	<	X
ejpam-3626	174	35	ε	ε	PROPN
ejpam-3626	174	36	·	·	PUNCT
ejpam-3626	174	37	e.	e.	PROPN
ejpam-3626	174	38	proof	proof	PROPN
ejpam-3626	174	39	.	.	PUNCT
ejpam-3626	175	1	(	(	PUNCT
ejpam-3626	175	2	⇒	⇒	PROPN
ejpam-3626	175	3	)	)	PUNCT
ejpam-3626	175	4	let	let	VERB
ejpam-3626	175	5	ε	ε	PROPN
ejpam-3626	175	6	>	>	X
ejpam-3626	175	7	0	0	PROPN
ejpam-3626	175	8	.	.	PUNCT
ejpam-3626	176	1	then	then	ADV
ejpam-3626	176	2	there	there	PRON
ejpam-3626	176	3	exists	exist	VERB
ejpam-3626	176	4	a	a	DET
ejpam-3626	176	5	gauge	gauge	NOUN
ejpam-3626	176	6	δ	δ	NOUN
ejpam-3626	176	7	on	on	ADP
ejpam-3626	176	8	[	[	X
ejpam-3626	176	9	f	f	X
ejpam-3626	176	10	,	,	PUNCT
ejpam-3626	176	11	g	g	NOUN
ejpam-3626	176	12	]	]	PUNCT
ejpam-3626	176	13	such	such	ADJ
ejpam-3626	176	14	that	that	PRON
ejpam-3626	176	15	for	for	ADP
ejpam-3626	176	16	any	any	DET
ejpam-3626	176	17	δ	δ	NOUN
ejpam-3626	176	18	-	-	PUNCT
ejpam-3626	176	19	fine	fine	ADJ
ejpam-3626	176	20	tagged	tag	VERB
ejpam-3626	176	21	division	division	NOUN
ejpam-3626	177	1	d	d	NOUN
ejpam-3626	177	2	=	=	PRON
ejpam-3626	177	3	{	{	PUNCT
ejpam-3626	177	4	(	(	PUNCT
ejpam-3626	177	5	[	[	X
ejpam-3626	177	6	u	u	NOUN
ejpam-3626	177	7	,	,	PUNCT
ejpam-3626	177	8	v	v	ADP
ejpam-3626	177	9	]	]	X
ejpam-3626	177	10	,	,	PUNCT
ejpam-3626	177	11	t	t	PROPN
ejpam-3626	177	12	)	)	PUNCT
ejpam-3626	177	13	}	}	PUNCT
ejpam-3626	177	14	of	of	ADP
ejpam-3626	177	15	[	[	X
ejpam-3626	177	16	f	f	X
ejpam-3626	177	17	,	,	PUNCT
ejpam-3626	177	18	g	g	PROPN
ejpam-3626	177	19	]	]	X
ejpam-3626	177	20	,	,	PUNCT
ejpam-3626	177	21	we	we	PRON
ejpam-3626	177	22	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-3626	177	23	d	d	X
ejpam-3626	177	24	f	f	PROPN
ejpam-3626	177	25	(	(	PUNCT
ejpam-3626	177	26	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	PROPN
ejpam-3626	177	27	(	(	PUNCT
ejpam-3626	177	28	hks	hks	PROPN
ejpam-3626	177	29	)	)	PUNCT
ejpam-3626	177	30	∫	∫	PROPN
ejpam-3626	178	1	g	g	PROPN
ejpam-3626	178	2	f	f	PROPN
ejpam-3626	178	3	fdh	fdh	PROPN
ejpam-3626	178	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	178	5	<	<	X
ejpam-3626	178	6	ε	ε	PROPN
ejpam-3626	178	7	2	2	NUM
ejpam-3626	178	8	·	·	PUNCT
ejpam-3626	178	9	e.	e.	PROPN
ejpam-3626	178	10	(	(	PUNCT
ejpam-3626	178	11	9	9	X
ejpam-3626	178	12	)	)	PUNCT
ejpam-3626	178	13	let	let	VERB
ejpam-3626	178	14	d	d	NOUN
ejpam-3626	178	15	=	=	PRON
ejpam-3626	178	16	{	{	PUNCT
ejpam-3626	178	17	(	(	PUNCT
ejpam-3626	178	18	[	[	X
ejpam-3626	178	19	u	u	NOUN
ejpam-3626	178	20	,	,	PUNCT
ejpam-3626	178	21	v	v	ADP
ejpam-3626	178	22	]	]	X
ejpam-3626	178	23	,	,	PUNCT
ejpam-3626	178	24	t	t	PROPN
ejpam-3626	178	25	)	)	PUNCT
ejpam-3626	178	26	}	}	PUNCT
ejpam-3626	178	27	and	and	CCONJ
ejpam-3626	178	28	q	q	NOUN
ejpam-3626	179	1	=	=	X
ejpam-3626	179	2	{	{	PUNCT
ejpam-3626	179	3	(	(	PUNCT
ejpam-3626	179	4	[	[	X
ejpam-3626	179	5	u′	u′	PROPN
ejpam-3626	179	6	,	,	PUNCT
ejpam-3626	179	7	v′	v′	PROPN
ejpam-3626	179	8	]	]	PUNCT
ejpam-3626	179	9	,	,	PUNCT
ejpam-3626	179	10	s	s	X
ejpam-3626	179	11	)	)	PUNCT
ejpam-3626	179	12	}	}	PUNCT
ejpam-3626	179	13	be	be	AUX
ejpam-3626	179	14	any	any	DET
ejpam-3626	179	15	δ	δ	NOUN
ejpam-3626	179	16	-	-	PUNCT
ejpam-3626	179	17	fine	fine	ADJ
ejpam-3626	179	18	tagged	tag	VERB
ejpam-3626	179	19	divisions	division	NOUN
ejpam-3626	179	20	of	of	ADP
ejpam-3626	179	21	[	[	X
ejpam-3626	179	22	f	f	X
ejpam-3626	179	23	,	,	PUNCT
ejpam-3626	179	24	g	g	NOUN
ejpam-3626	179	25	]	]	PUNCT
ejpam-3626	179	26	.	.	PUNCT
ejpam-3626	180	1	by	by	ADP
ejpam-3626	180	2	(	(	PUNCT
ejpam-3626	180	3	9)∣∣∣∣∑	9)∣∣∣∣∑	PROPN
ejpam-3626	180	4	d	d	X
ejpam-3626	180	5	f	f	X
ejpam-3626	180	6	(	(	PUNCT
ejpam-3626	180	7	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	180	8	∑	∑	ADP
ejpam-3626	180	9	q	q	PROPN
ejpam-3626	180	10	f	f	X
ejpam-3626	180	11	(	(	PUNCT
ejpam-3626	180	12	s)[h(v′)−h(u′	s)[h(v′)−h(u′	PROPN
ejpam-3626	180	13	)	)	PUNCT
ejpam-3626	180	14	]	]	PUNCT
ejpam-3626	180	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	180	16	<	<	X
ejpam-3626	180	17	ε	ε	PROPN
ejpam-3626	180	18	·	·	PUNCT
ejpam-3626	180	19	e.	e.	PROPN
ejpam-3626	180	20	(	(	PUNCT
ejpam-3626	180	21	⇐	⇐	PROPN
ejpam-3626	180	22	)	)	PUNCT
ejpam-3626	180	23	by	by	ADP
ejpam-3626	180	24	assumption	assumption	NOUN
ejpam-3626	180	25	,	,	PUNCT
ejpam-3626	180	26	for	for	ADP
ejpam-3626	180	27	each	each	DET
ejpam-3626	180	28	n	n	PRON
ejpam-3626	180	29	∈	∈	PROPN
ejpam-3626	180	30	n	n	CCONJ
ejpam-3626	180	31	,	,	PUNCT
ejpam-3626	180	32	there	there	PRON
ejpam-3626	180	33	exists	exist	VERB
ejpam-3626	180	34	a	a	DET
ejpam-3626	180	35	gauge	gauge	ADJ
ejpam-3626	180	36	δn	δn	NOUN
ejpam-3626	180	37	on	on	ADP
ejpam-3626	180	38	[	[	X
ejpam-3626	180	39	f	f	X
ejpam-3626	180	40	,	,	PUNCT
ejpam-3626	180	41	g	g	NOUN
ejpam-3626	180	42	]	]	PUNCT
ejpam-3626	180	43	such	such	ADJ
ejpam-3626	180	44	that	that	SCONJ
ejpam-3626	180	45	for	for	ADP
ejpam-3626	180	46	any	any	DET
ejpam-3626	180	47	δn	δn	ADJ
ejpam-3626	180	48	-	-	PUNCT
ejpam-3626	180	49	fine	fine	NOUN
ejpam-3626	180	50	division	division	NOUN
ejpam-3626	181	1	d	d	NOUN
ejpam-3626	181	2	=	=	PRON
ejpam-3626	181	3	{	{	PUNCT
ejpam-3626	181	4	(	(	PUNCT
ejpam-3626	181	5	[	[	X
ejpam-3626	181	6	u	u	NOUN
ejpam-3626	181	7	,	,	PUNCT
ejpam-3626	181	8	v	v	ADP
ejpam-3626	181	9	]	]	X
ejpam-3626	181	10	,	,	PUNCT
ejpam-3626	181	11	t	t	PROPN
ejpam-3626	181	12	)	)	PUNCT
ejpam-3626	181	13	}	}	PUNCT
ejpam-3626	181	14	and	and	CCONJ
ejpam-3626	181	15	q	q	NOUN
ejpam-3626	181	16	=	=	X
ejpam-3626	181	17	{	{	PUNCT
ejpam-3626	181	18	(	(	PUNCT
ejpam-3626	181	19	[	[	X
ejpam-3626	181	20	u′	u′	PROPN
ejpam-3626	181	21	,	,	PUNCT
ejpam-3626	181	22	v′	v′	PROPN
ejpam-3626	181	23	]	]	PUNCT
ejpam-3626	181	24	,	,	PUNCT
ejpam-3626	181	25	s	s	X
ejpam-3626	181	26	)	)	PUNCT
ejpam-3626	181	27	}	}	PUNCT
ejpam-3626	181	28	of	of	ADP
ejpam-3626	181	29	[	[	X
ejpam-3626	181	30	f	f	X
ejpam-3626	181	31	,	,	PUNCT
ejpam-3626	181	32	g	g	PROPN
ejpam-3626	181	33	]	]	X
ejpam-3626	181	34	,	,	PUNCT
ejpam-3626	181	35	we	we	PRON
ejpam-3626	181	36	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-3626	181	37	d	d	ADP
ejpam-3626	181	38	f	f	PROPN
ejpam-3626	181	39	(	(	PUNCT
ejpam-3626	181	40	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	181	41	∑	∑	ADP
ejpam-3626	181	42	q	q	PROPN
ejpam-3626	181	43	f	f	X
ejpam-3626	181	44	(	(	PUNCT
ejpam-3626	181	45	s)[h(v′)−h(u′	s)[h(v′)−h(u′	PROPN
ejpam-3626	181	46	)	)	PUNCT
ejpam-3626	181	47	]	]	PUNCT
ejpam-3626	181	48	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	181	49	<	<	X
ejpam-3626	181	50	1	1	NUM
ejpam-3626	181	51	n	n	PROPN
ejpam-3626	181	52	·	·	PUNCT
ejpam-3626	181	53	e.	e.	PROPN
ejpam-3626	181	54	(	(	PUNCT
ejpam-3626	181	55	10	10	NUM
ejpam-3626	181	56	)	)	PUNCT
ejpam-3626	181	57	we	we	PRON
ejpam-3626	181	58	may	may	AUX
ejpam-3626	181	59	assume	assume	VERB
ejpam-3626	181	60	that	that	SCONJ
ejpam-3626	181	61	{	{	PUNCT
ejpam-3626	181	62	δn	δn	NOUN
ejpam-3626	181	63	}	}	PUNCT
ejpam-3626	181	64	is	be	AUX
ejpam-3626	181	65	decreasing	decrease	VERB
ejpam-3626	181	66	;	;	PUNCT
ejpam-3626	181	67	that	that	PRON
ejpam-3626	181	68	is	is	ADV
ejpam-3626	181	69	,	,	PUNCT
ejpam-3626	181	70	δn	δn	X
ejpam-3626	181	71	≥	≥	NOUN
ejpam-3626	181	72	δn+1	δn+1	NOUN
ejpam-3626	181	73	for	for	ADP
ejpam-3626	181	74	all	all	DET
ejpam-3626	181	75	n.	n.	NOUN
ejpam-3626	181	76	now	now	ADV
ejpam-3626	181	77	,	,	PUNCT
ejpam-3626	181	78	for	for	ADP
ejpam-3626	181	79	each	each	DET
ejpam-3626	181	80	n	n	PRON
ejpam-3626	181	81	∈	∈	PROPN
ejpam-3626	181	82	n	n	CCONJ
ejpam-3626	181	83	,	,	PUNCT
ejpam-3626	181	84	fix	fix	VERB
ejpam-3626	181	85	a	a	DET
ejpam-3626	181	86	δn	δn	ADJ
ejpam-3626	181	87	-	-	PUNCT
ejpam-3626	181	88	fine	fine	ADJ
ejpam-3626	181	89	tagged	tag	VERB
ejpam-3626	181	90	division	division	NOUN
ejpam-3626	182	1	dn	dn	NOUN
ejpam-3626	182	2	=	=	PUNCT
ejpam-3626	182	3	{	{	PUNCT
ejpam-3626	182	4	(	(	PUNCT
ejpam-3626	182	5	[	[	X
ejpam-3626	182	6	u	u	NOUN
ejpam-3626	182	7	,	,	PUNCT
ejpam-3626	182	8	v	v	ADP
ejpam-3626	182	9	]	]	X
ejpam-3626	182	10	,	,	PUNCT
ejpam-3626	182	11	t	t	PROPN
ejpam-3626	182	12	)	)	PUNCT
ejpam-3626	182	13	}	}	PUNCT
ejpam-3626	182	14	of	of	ADP
ejpam-3626	182	15	[	[	X
ejpam-3626	182	16	f	f	X
ejpam-3626	182	17	,	,	PUNCT
ejpam-3626	182	18	g	g	NOUN
ejpam-3626	182	19	]	]	PUNCT
ejpam-3626	182	20	and	and	CCONJ
ejpam-3626	182	21	we	we	PRON
ejpam-3626	182	22	write	write	VERB
ejpam-3626	182	23	rn	rn	PROPN
ejpam-3626	182	24	=	=	PRON
ejpam-3626	182	25	∑	∑	PUNCT
ejpam-3626	182	26	dn	dn	PROPN
ejpam-3626	182	27	f	f	PROPN
ejpam-3626	182	28	(	(	PUNCT
ejpam-3626	182	29	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	182	30	)	)	PUNCT
ejpam-3626	182	31	]	]	PUNCT
ejpam-3626	182	32	.	.	PUNCT
ejpam-3626	183	1	note	note	VERB
ejpam-3626	183	2	that	that	SCONJ
ejpam-3626	183	3	if	if	SCONJ
ejpam-3626	183	4	m	m	PROPN
ejpam-3626	183	5	≥	≥	VERB
ejpam-3626	183	6	n	n	CCONJ
ejpam-3626	183	7	then	then	ADV
ejpam-3626	183	8	δn	δn	VERB
ejpam-3626	183	9	≥	≥	NOUN
ejpam-3626	183	10	δm	δm	ADV
ejpam-3626	183	11	;	;	PUNCT
ejpam-3626	183	12	implying	imply	VERB
ejpam-3626	183	13	that	that	SCONJ
ejpam-3626	183	14	every	every	DET
ejpam-3626	183	15	δm	δm	PROPN
ejpam-3626	183	16	-	-	PUNCT
ejpam-3626	183	17	fine	fine	ADJ
ejpam-3626	183	18	tagged	tag	VERB
ejpam-3626	183	19	division	division	NOUN
ejpam-3626	183	20	of	of	ADP
ejpam-3626	183	21	[	[	X
ejpam-3626	183	22	f	f	X
ejpam-3626	183	23	,	,	PUNCT
ejpam-3626	183	24	g	g	NOUN
ejpam-3626	183	25	]	]	PUNCT
ejpam-3626	183	26	is	be	AUX
ejpam-3626	183	27	also	also	ADV
ejpam-3626	183	28	a	a	DET
ejpam-3626	183	29	δn	δn	ADJ
ejpam-3626	183	30	-	-	PUNCT
ejpam-3626	183	31	fine	fine	ADJ
ejpam-3626	183	32	tagged	tag	VERB
ejpam-3626	183	33	division	division	NOUN
ejpam-3626	183	34	of	of	ADP
ejpam-3626	183	35	[	[	X
ejpam-3626	183	36	f	f	X
ejpam-3626	183	37	,	,	PUNCT
ejpam-3626	183	38	g	g	NOUN
ejpam-3626	183	39	]	]	PUNCT
ejpam-3626	183	40	.	.	PUNCT
ejpam-3626	184	1	thus	thus	ADV
ejpam-3626	184	2	,	,	PUNCT
ejpam-3626	184	3	for	for	ADP
ejpam-3626	184	4	all	all	DET
ejpam-3626	184	5	m	m	VERB
ejpam-3626	184	6	>	>	X
ejpam-3626	184	7	n	n	PROPN
ejpam-3626	184	8	|rn	|rn	NUM
ejpam-3626	184	9	−	−	PROPN
ejpam-3626	184	10	rm|	rm|	NOUN
ejpam-3626	184	11	=	=	SYM
ejpam-3626	184	12	∣∣∣∣∑	∣∣∣∣∑	PROPN
ejpam-3626	184	13	dn	dn	NOUN
ejpam-3626	184	14	f	f	PROPN
ejpam-3626	184	15	(	(	PUNCT
ejpam-3626	184	16	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	184	17	∑	∑	PROPN
ejpam-3626	184	18	dm	dm	PROPN
ejpam-3626	184	19	f	f	PROPN
ejpam-3626	184	20	(	(	PUNCT
ejpam-3626	184	21	s)[h(v′)−h(u′	s)[h(v′)−h(u′	PROPN
ejpam-3626	184	22	)	)	PUNCT
ejpam-3626	184	23	]	]	PUNCT
ejpam-3626	184	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	184	25	<	<	X
ejpam-3626	184	26	1	1	NUM
ejpam-3626	184	27	n	n	PROPN
ejpam-3626	184	28	·	·	PUNCT
ejpam-3626	184	29	e.	e.	PROPN
ejpam-3626	184	30	a.	a.	PROPN
ejpam-3626	184	31	cunanan	cunanan	PROPN
ejpam-3626	184	32	,	,	PUNCT
ejpam-3626	184	33	j.	j.	PROPN
ejpam-3626	184	34	benitez	benitez	PROPN
ejpam-3626	184	35	/	/	PUNCT
ejpam-3626	184	36	eur	eur	PROPN
ejpam-3626	184	37	.	.	PUNCT
ejpam-3626	185	1	j.	j.	PROPN
ejpam-3626	185	2	pure	pure	PROPN
ejpam-3626	185	3	appl	appl	PROPN
ejpam-3626	185	4	.	.	PROPN
ejpam-3626	185	5	math	math	PROPN
ejpam-3626	185	6	,	,	PUNCT
ejpam-3626	185	7	13	13	NUM
ejpam-3626	185	8	(	(	PUNCT
ejpam-3626	185	9	1	1	NUM
ejpam-3626	185	10	)	)	PUNCT
ejpam-3626	185	11	(	(	PUNCT
ejpam-3626	185	12	2020	2020	NUM
ejpam-3626	185	13	)	)	PUNCT
ejpam-3626	185	14	,	,	PUNCT
ejpam-3626	185	15	130	130	NUM
ejpam-3626	185	16	-	-	SYM
ejpam-3626	185	17	143	143	NUM
ejpam-3626	185	18	137	137	NUM
ejpam-3626	185	19	hence	hence	ADV
ejpam-3626	185	20	,	,	PUNCT
ejpam-3626	185	21	{	{	PUNCT
ejpam-3626	185	22	rn	rn	NOUN
ejpam-3626	185	23	}	}	PUNCT
ejpam-3626	185	24	is	be	AUX
ejpam-3626	185	25	a	a	DET
ejpam-3626	185	26	cauchy	cauchy	ADJ
ejpam-3626	185	27	sequence	sequence	NOUN
ejpam-3626	185	28	in	in	ADP
ejpam-3626	185	29	c[a	c[a	NUM
ejpam-3626	185	30	,	,	PUNCT
ejpam-3626	185	31	b	b	NOUN
ejpam-3626	185	32	]	]	X
ejpam-3626	185	33	.	.	PUNCT
ejpam-3626	186	1	since	since	SCONJ
ejpam-3626	186	2	c[a	c[a	NUM
ejpam-3626	186	3	,	,	PUNCT
ejpam-3626	186	4	b	b	AUX
ejpam-3626	186	5	]	]	PUNCT
ejpam-3626	186	6	is	be	AUX
ejpam-3626	186	7	complete	complete	ADJ
ejpam-3626	186	8	,	,	PUNCT
ejpam-3626	186	9	{	{	PUNCT
ejpam-3626	186	10	rn	rn	NOUN
ejpam-3626	186	11	}	}	PUNCT
ejpam-3626	186	12	converges	converge	VERB
ejpam-3626	186	13	to	to	ADP
ejpam-3626	186	14	some	some	DET
ejpam-3626	186	15	r	r	NOUN
ejpam-3626	186	16	∈	∈	PROPN
ejpam-3626	186	17	c[a	c[a	NOUN
ejpam-3626	186	18	,	,	PUNCT
ejpam-3626	186	19	b	b	NOUN
ejpam-3626	186	20	]	]	X
ejpam-3626	186	21	.	.	PUNCT
ejpam-3626	187	1	we	we	PRON
ejpam-3626	187	2	claim	claim	VERB
ejpam-3626	187	3	that	that	SCONJ
ejpam-3626	187	4	r	r	NOUN
ejpam-3626	187	5	=	=	SYM
ejpam-3626	187	6	(	(	PUNCT
ejpam-3626	187	7	hks	hks	PROPN
ejpam-3626	187	8	)	)	PUNCT
ejpam-3626	187	9	∫	∫	PROPN
ejpam-3626	187	10	g	g	PROPN
ejpam-3626	187	11	f	f	PROPN
ejpam-3626	187	12	fdh	fdh	PROPN
ejpam-3626	187	13	.	.	PUNCT
ejpam-3626	188	1	let	let	VERB
ejpam-3626	188	2	ε	ε	PROPN
ejpam-3626	188	3	>	>	X
ejpam-3626	188	4	0	0	PROPN
ejpam-3626	188	5	.	.	PUNCT
ejpam-3626	189	1	since	since	SCONJ
ejpam-3626	189	2	lim	lim	PROPN
ejpam-3626	189	3	n→∞	n→∞	PRON
ejpam-3626	189	4	rn	rn	PROPN
ejpam-3626	189	5	=	=	NOUN
ejpam-3626	189	6	r	r	NOUN
ejpam-3626	189	7	in	in	ADP
ejpam-3626	189	8	c[a	c[a	NUM
ejpam-3626	189	9	,	,	PUNCT
ejpam-3626	189	10	b	b	NOUN
ejpam-3626	189	11	]	]	X
ejpam-3626	189	12	,	,	PUNCT
ejpam-3626	189	13	there	there	PRON
ejpam-3626	189	14	exists	exist	VERB
ejpam-3626	189	15	n1	n1	PROPN
ejpam-3626	189	16	∈	∈	PROPN
ejpam-3626	189	17	n	n	PRON
ejpam-3626	189	18	such	such	ADJ
ejpam-3626	189	19	that	that	PRON
ejpam-3626	189	20	for	for	ADP
ejpam-3626	189	21	any	any	DET
ejpam-3626	189	22	n	n	PRON
ejpam-3626	189	23	≥	≥	NOUN
ejpam-3626	189	24	n1	n1	NOUN
ejpam-3626	189	25	,	,	PUNCT
ejpam-3626	189	26	∣∣rn	∣∣rn	ADJ
ejpam-3626	189	27	−	−	VERB
ejpam-3626	190	1	r∣∣	r∣∣	ADJ
ejpam-3626	190	2	<	<	X
ejpam-3626	190	3	e	e	X
ejpam-3626	190	4	·	·	PUNCT
ejpam-3626	190	5	ε	ε	PROPN
ejpam-3626	190	6	2	2	NUM
ejpam-3626	190	7	.	.	PUNCT
ejpam-3626	191	1	(	(	PUNCT
ejpam-3626	191	2	11	11	NUM
ejpam-3626	191	3	)	)	PUNCT
ejpam-3626	191	4	by	by	ADP
ejpam-3626	191	5	archimedean	archimedean	ADJ
ejpam-3626	191	6	principle	principle	NOUN
ejpam-3626	191	7	,	,	PUNCT
ejpam-3626	191	8	there	there	PRON
ejpam-3626	191	9	exists	exist	VERB
ejpam-3626	191	10	n2	n2	PROPN
ejpam-3626	191	11	∈	∈	PROPN
ejpam-3626	191	12	n	n	CCONJ
ejpam-3626	191	13	such	such	ADJ
ejpam-3626	191	14	that	that	SCONJ
ejpam-3626	191	15	1	1	NUM
ejpam-3626	191	16	n2	n2	NOUN
ejpam-3626	191	17	<	<	X
ejpam-3626	191	18	ε	ε	PROPN
ejpam-3626	191	19	2	2	NUM
ejpam-3626	191	20	.	.	PUNCT
ejpam-3626	192	1	take	take	VERB
ejpam-3626	192	2	n	n	NOUN
ejpam-3626	192	3	=	=	SYM
ejpam-3626	192	4	n1	n1	PROPN
ejpam-3626	192	5	∧	∧	PROPN
ejpam-3626	192	6	n2	n2	NOUN
ejpam-3626	192	7	.	.	PUNCT
ejpam-3626	193	1	define	define	VERB
ejpam-3626	193	2	a	a	DET
ejpam-3626	193	3	gauge	gauge	NOUN
ejpam-3626	193	4	δ	δ	NOUN
ejpam-3626	193	5	:	:	PUNCT
ejpam-3626	194	1	[	[	X
ejpam-3626	194	2	f	f	X
ejpam-3626	194	3	,	,	PUNCT
ejpam-3626	194	4	g	g	NOUN
ejpam-3626	194	5	]	]	X
ejpam-3626	194	6	→	→	SYM
ejpam-3626	194	7	c[a	c[a	NUM
ejpam-3626	194	8	,	,	PUNCT
ejpam-3626	194	9	b	b	NOUN
ejpam-3626	194	10	]	]	PUNCT
ejpam-3626	194	11	by	by	ADP
ejpam-3626	194	12	δ	δ	PROPN
ejpam-3626	194	13	=	=	SYM
ejpam-3626	194	14	δn	δn	PROPN
ejpam-3626	194	15	.	.	PUNCT
ejpam-3626	195	1	let	let	VERB
ejpam-3626	195	2	d	d	NOUN
ejpam-3626	195	3	=	=	PRON
ejpam-3626	195	4	{	{	PUNCT
ejpam-3626	195	5	(	(	PUNCT
ejpam-3626	195	6	[	[	X
ejpam-3626	195	7	u	u	NOUN
ejpam-3626	195	8	,	,	PUNCT
ejpam-3626	195	9	v	v	ADP
ejpam-3626	195	10	]	]	X
ejpam-3626	195	11	,	,	PUNCT
ejpam-3626	195	12	t	t	PROPN
ejpam-3626	195	13	)	)	PUNCT
ejpam-3626	195	14	}	}	PUNCT
ejpam-3626	195	15	be	be	AUX
ejpam-3626	195	16	any	any	DET
ejpam-3626	195	17	δ	δ	NOUN
ejpam-3626	195	18	-	-	PUNCT
ejpam-3626	195	19	fine	fine	ADJ
ejpam-3626	195	20	tagged	tag	VERB
ejpam-3626	195	21	division	division	NOUN
ejpam-3626	195	22	of	of	ADP
ejpam-3626	195	23	[	[	X
ejpam-3626	195	24	f	f	X
ejpam-3626	195	25	,	,	PUNCT
ejpam-3626	195	26	g	g	NOUN
ejpam-3626	195	27	]	]	PUNCT
ejpam-3626	195	28	.	.	PUNCT
ejpam-3626	196	1	note	note	VERB
ejpam-3626	196	2	that	that	SCONJ
ejpam-3626	196	3	d	d	NOUN
ejpam-3626	196	4	is	be	AUX
ejpam-3626	196	5	also	also	ADV
ejpam-3626	196	6	δn	δn	ADP
ejpam-3626	196	7	-fine	-fine	ADJ
ejpam-3626	196	8	tagged	tag	VERB
ejpam-3626	196	9	division	division	NOUN
ejpam-3626	196	10	of	of	ADP
ejpam-3626	196	11	[	[	X
ejpam-3626	196	12	f	f	X
ejpam-3626	196	13	,	,	PUNCT
ejpam-3626	196	14	g	g	PROPN
ejpam-3626	196	15	]	]	X
ejpam-3626	196	16	,	,	PUNCT
ejpam-3626	196	17	n	n	PRON
ejpam-3626	196	18	≥	≥	NOUN
ejpam-3626	196	19	n1	n1	PROPN
ejpam-3626	196	20	and	and	CCONJ
ejpam-3626	196	21	n	n	PRON
ejpam-3626	196	22	≥	≥	NOUN
ejpam-3626	196	23	n2	n2	NOUN
ejpam-3626	196	24	.	.	PUNCT
ejpam-3626	197	1	thus	thus	ADV
ejpam-3626	197	2	,	,	PUNCT
ejpam-3626	197	3	by	by	ADP
ejpam-3626	197	4	(	(	PUNCT
ejpam-3626	197	5	10	10	NUM
ejpam-3626	197	6	)	)	PUNCT
ejpam-3626	197	7	and	and	CCONJ
ejpam-3626	197	8	(	(	PUNCT
ejpam-3626	197	9	11	11	NUM
ejpam-3626	197	10	)	)	PUNCT
ejpam-3626	197	11	∣∣∣∣∑	∣∣∣∣∑	PUNCT
ejpam-3626	198	1	d	d	X
ejpam-3626	198	2	f	f	PROPN
ejpam-3626	198	3	(	(	PUNCT
ejpam-3626	198	4	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	198	5	r	r	NOUN
ejpam-3626	198	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	198	7	<	<	X
ejpam-3626	198	8	ε	ε	PROPN
ejpam-3626	198	9	·	·	PUNCT
ejpam-3626	198	10	e.	e.	PROPN
ejpam-3626	198	11	this	this	PRON
ejpam-3626	198	12	proves	prove	VERB
ejpam-3626	198	13	our	our	PRON
ejpam-3626	198	14	claim	claim	NOUN
ejpam-3626	198	15	.	.	PUNCT
ejpam-3626	199	1	theorem	theorem	ADJ
ejpam-3626	199	2	7	7	NUM
ejpam-3626	199	3	.	.	PUNCT
ejpam-3626	200	1	if	if	SCONJ
ejpam-3626	200	2	f	f	PROPN
ejpam-3626	200	3	∈	∈	PROPN
ejpam-3626	200	4	hks([f	hks([f	NOUN
ejpam-3626	200	5	,	,	PUNCT
ejpam-3626	200	6	g	g	NOUN
ejpam-3626	200	7	]	]	X
ejpam-3626	200	8	,	,	PUNCT
ejpam-3626	200	9	h	h	NOUN
ejpam-3626	200	10	)	)	PUNCT
ejpam-3626	200	11	and	and	CCONJ
ejpam-3626	200	12	[	[	X
ejpam-3626	200	13	r	r	X
ejpam-3626	200	14	,	,	PUNCT
ejpam-3626	200	15	s	s	PART
ejpam-3626	200	16	]	]	PUNCT
ejpam-3626	200	17	⊆	⊆	NUM
ejpam-3626	200	18	[	[	X
ejpam-3626	200	19	f	f	X
ejpam-3626	200	20	,	,	PUNCT
ejpam-3626	200	21	g	g	PROPN
ejpam-3626	200	22	]	]	X
ejpam-3626	200	23	,	,	PUNCT
ejpam-3626	200	24	then	then	ADV
ejpam-3626	200	25	f	f	PROPN
ejpam-3626	200	26	∈	∈	PROPN
ejpam-3626	200	27	hks([r	hks([r	PROPN
ejpam-3626	200	28	,	,	PUNCT
ejpam-3626	200	29	s	s	AUX
ejpam-3626	200	30	]	]	X
ejpam-3626	200	31	,	,	PUNCT
ejpam-3626	200	32	h	h	NOUN
ejpam-3626	200	33	)	)	PUNCT
ejpam-3626	200	34	.	.	PUNCT
ejpam-3626	201	1	proof	proof	NOUN
ejpam-3626	201	2	.	.	PUNCT
ejpam-3626	202	1	let	let	VERB
ejpam-3626	202	2	ε	ε	PROPN
ejpam-3626	202	3	>	>	X
ejpam-3626	202	4	0	0	PROPN
ejpam-3626	202	5	.	.	PUNCT
ejpam-3626	203	1	by	by	ADP
ejpam-3626	203	2	theorem	theorem	NOUN
ejpam-3626	203	3	6	6	NUM
ejpam-3626	203	4	,	,	PUNCT
ejpam-3626	203	5	there	there	PRON
ejpam-3626	203	6	exists	exist	VERB
ejpam-3626	203	7	a	a	DET
ejpam-3626	203	8	gauge	gauge	NOUN
ejpam-3626	203	9	δ	δ	NOUN
ejpam-3626	203	10	on	on	ADP
ejpam-3626	203	11	[	[	X
ejpam-3626	203	12	f	f	X
ejpam-3626	203	13	,	,	PUNCT
ejpam-3626	203	14	g	g	NOUN
ejpam-3626	203	15	]	]	PUNCT
ejpam-3626	203	16	such	such	ADJ
ejpam-3626	203	17	that	that	PRON
ejpam-3626	203	18	for	for	ADP
ejpam-3626	203	19	any	any	DET
ejpam-3626	203	20	δ	δ	NOUN
ejpam-3626	203	21	-	-	PUNCT
ejpam-3626	203	22	fine	fine	ADJ
ejpam-3626	203	23	tagged	tag	VERB
ejpam-3626	203	24	divisions	division	NOUN
ejpam-3626	203	25	d	d	NOUN
ejpam-3626	203	26	and	and	CCONJ
ejpam-3626	203	27	q	q	NOUN
ejpam-3626	203	28	of	of	ADP
ejpam-3626	203	29	[	[	X
ejpam-3626	203	30	f	f	X
ejpam-3626	203	31	,	,	PUNCT
ejpam-3626	203	32	g	g	PROPN
ejpam-3626	203	33	]	]	X
ejpam-3626	203	34	,	,	PUNCT
ejpam-3626	203	35	we	we	PRON
ejpam-3626	203	36	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-3626	203	37	d	d	ADP
ejpam-3626	203	38	f	f	PROPN
ejpam-3626	203	39	(	(	PUNCT
ejpam-3626	203	40	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	203	41	∑	∑	PROPN
ejpam-3626	203	42	q	q	PROPN
ejpam-3626	203	43	f	f	X
ejpam-3626	203	44	(	(	PUNCT
ejpam-3626	203	45	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	203	46	)	)	PUNCT
ejpam-3626	203	47	]	]	PUNCT
ejpam-3626	203	48	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	203	49	<	<	X
ejpam-3626	203	50	ε	ε	PROPN
ejpam-3626	203	51	·	·	PUNCT
ejpam-3626	203	52	e.	e.	PROPN
ejpam-3626	203	53	(	(	PUNCT
ejpam-3626	203	54	12	12	NUM
ejpam-3626	203	55	)	)	PUNCT
ejpam-3626	203	56	consider	consider	VERB
ejpam-3626	203	57	any	any	DET
ejpam-3626	203	58	δ	δ	NOUN
ejpam-3626	203	59	-	-	PUNCT
ejpam-3626	203	60	fine	fine	ADJ
ejpam-3626	203	61	tagged	tag	VERB
ejpam-3626	203	62	divisions	division	NOUN
ejpam-3626	203	63	p1	p1	NOUN
ejpam-3626	203	64	and	and	CCONJ
ejpam-3626	203	65	p2	p2	PROPN
ejpam-3626	203	66	of	of	ADP
ejpam-3626	203	67	[	[	X
ejpam-3626	203	68	r	r	X
ejpam-3626	203	69	,	,	PUNCT
ejpam-3626	203	70	s	s	PART
ejpam-3626	203	71	]	]	X
ejpam-3626	203	72	.	.	PUNCT
ejpam-3626	204	1	if	if	SCONJ
ejpam-3626	204	2	d1	d1	PROPN
ejpam-3626	204	3	is	be	AUX
ejpam-3626	204	4	any	any	DET
ejpam-3626	204	5	δ	δ	NOUN
ejpam-3626	204	6	-	-	PUNCT
ejpam-3626	204	7	fine	fine	ADJ
ejpam-3626	204	8	tagged	tag	VERB
ejpam-3626	204	9	division	division	NOUN
ejpam-3626	204	10	of	of	ADP
ejpam-3626	204	11	[	[	X
ejpam-3626	204	12	f	f	X
ejpam-3626	204	13	,	,	PUNCT
ejpam-3626	204	14	r	r	NOUN
ejpam-3626	204	15	]	]	PUNCT
ejpam-3626	204	16	and	and	CCONJ
ejpam-3626	204	17	d2	d2	PROPN
ejpam-3626	204	18	is	be	AUX
ejpam-3626	204	19	any	any	DET
ejpam-3626	204	20	δ	δ	NOUN
ejpam-3626	204	21	-	-	PUNCT
ejpam-3626	204	22	fine	fine	ADJ
ejpam-3626	204	23	tagged	tag	VERB
ejpam-3626	204	24	division	division	NOUN
ejpam-3626	204	25	of	of	ADP
ejpam-3626	204	26	[	[	X
ejpam-3626	204	27	s	s	X
ejpam-3626	204	28	,	,	PUNCT
ejpam-3626	204	29	g	g	NOUN
ejpam-3626	204	30	]	]	X
ejpam-3626	204	31	,	,	PUNCT
ejpam-3626	204	32	then	then	ADV
ejpam-3626	204	33	d	d	X
ejpam-3626	204	34	=	=	SYM
ejpam-3626	204	35	d1	d1	PROPN
ejpam-3626	204	36	∪	∪	VERB
ejpam-3626	204	37	p1	p1	PROPN
ejpam-3626	204	38	∪d2	∪d2	PROPN
ejpam-3626	204	39	and	and	CCONJ
ejpam-3626	204	40	q	q	NOUN
ejpam-3626	204	41	=	=	SYM
ejpam-3626	204	42	d1	d1	PROPN
ejpam-3626	204	43	∪	∪	ADJ
ejpam-3626	204	44	p2	p2	PROPN
ejpam-3626	204	45	∪d2	∪d2	ADJ
ejpam-3626	204	46	are	be	AUX
ejpam-3626	204	47	δ	δ	PROPN
ejpam-3626	204	48	-	-	PUNCT
ejpam-3626	204	49	fine	fine	ADJ
ejpam-3626	204	50	tagged	tag	VERB
ejpam-3626	204	51	divisions	division	NOUN
ejpam-3626	204	52	of	of	ADP
ejpam-3626	204	53	[	[	X
ejpam-3626	204	54	f	f	X
ejpam-3626	204	55	,	,	PUNCT
ejpam-3626	204	56	g	g	NOUN
ejpam-3626	204	57	]	]	PUNCT
ejpam-3626	204	58	and	and	CCONJ
ejpam-3626	204	59	by	by	ADP
ejpam-3626	204	60	(	(	PUNCT
ejpam-3626	204	61	12)∣∣∣∣∑	12)∣∣∣∣∑	PROPN
ejpam-3626	204	62	p1	p1	PROPN
ejpam-3626	204	63	f	f	PROPN
ejpam-3626	204	64	(	(	PUNCT
ejpam-3626	204	65	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	NOUN
ejpam-3626	204	66	∑	∑	INTJ
ejpam-3626	204	67	p2	p2	PROPN
ejpam-3626	204	68	f	f	PROPN
ejpam-3626	204	69	(	(	PUNCT
ejpam-3626	204	70	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	204	71	)	)	PUNCT
ejpam-3626	204	72	]	]	PUNCT
ejpam-3626	204	73	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	204	74	<	<	X
ejpam-3626	204	75	ε	ε	PROPN
ejpam-3626	204	76	·	·	PUNCT
ejpam-3626	204	77	e.	e.	PROPN
ejpam-3626	204	78	by	by	ADP
ejpam-3626	204	79	cauchy	cauchy	PROPN
ejpam-3626	204	80	criterion	criterion	NOUN
ejpam-3626	204	81	,	,	PUNCT
ejpam-3626	204	82	f	f	PROPN
ejpam-3626	204	83	∈	∈	PROPN
ejpam-3626	204	84	hks([r	hks([r	PROPN
ejpam-3626	204	85	,	,	PUNCT
ejpam-3626	204	86	s	s	AUX
ejpam-3626	204	87	]	]	X
ejpam-3626	204	88	,	,	PUNCT
ejpam-3626	204	89	h	h	NOUN
ejpam-3626	204	90	)	)	PUNCT
ejpam-3626	204	91	.	.	PUNCT
ejpam-3626	205	1	theorem	theorem	ADJ
ejpam-3626	205	2	8	8	NUM
ejpam-3626	205	3	.	.	PUNCT
ejpam-3626	206	1	let	let	VERB
ejpam-3626	206	2	h	h	NOUN
ejpam-3626	206	3	:	:	PUNCT
ejpam-3626	207	1	[	[	X
ejpam-3626	207	2	f	f	X
ejpam-3626	207	3	,	,	PUNCT
ejpam-3626	207	4	g	g	NOUN
ejpam-3626	207	5	]	]	X
ejpam-3626	207	6	→	→	SYM
ejpam-3626	207	7	c[a	c[a	NUM
ejpam-3626	207	8	,	,	PUNCT
ejpam-3626	207	9	b	b	AUX
ejpam-3626	207	10	]	]	PUNCT
ejpam-3626	207	11	be	be	AUX
ejpam-3626	207	12	increasing	increase	VERB
ejpam-3626	207	13	,	,	PUNCT
ejpam-3626	207	14	that	that	ADV
ejpam-3626	207	15	is	is	ADV
ejpam-3626	207	16	,	,	PUNCT
ejpam-3626	207	17	h(k	h(k	PROPN
ejpam-3626	207	18	)	)	PUNCT
ejpam-3626	207	19	≤	≤	NOUN
ejpam-3626	207	20	h(h	h(h	X
ejpam-3626	207	21	)	)	PUNCT
ejpam-3626	207	22	for	for	ADP
ejpam-3626	207	23	any	any	DET
ejpam-3626	207	24	k	k	PROPN
ejpam-3626	207	25	≤	≤	ADJ
ejpam-3626	207	26	h	h	NOUN
ejpam-3626	207	27	in	in	ADP
ejpam-3626	207	28	[	[	X
ejpam-3626	207	29	f	f	X
ejpam-3626	207	30	,	,	PUNCT
ejpam-3626	207	31	g	g	NOUN
ejpam-3626	207	32	]	]	X
ejpam-3626	207	33	.	.	PUNCT
ejpam-3626	208	1	if	if	SCONJ
ejpam-3626	208	2	f	f	PROPN
ejpam-3626	208	3	∈	∈	PROPN
ejpam-3626	208	4	hks([f	hks([f	NOUN
ejpam-3626	208	5	,	,	PUNCT
ejpam-3626	208	6	g	g	NOUN
ejpam-3626	208	7	]	]	X
ejpam-3626	208	8	,	,	PUNCT
ejpam-3626	208	9	h	h	NOUN
ejpam-3626	208	10	)	)	PUNCT
ejpam-3626	208	11	and	and	CCONJ
ejpam-3626	208	12	f	f	PROPN
ejpam-3626	208	13	(	(	PUNCT
ejpam-3626	208	14	h	h	NOUN
ejpam-3626	208	15	)	)	PUNCT
ejpam-3626	208	16	≥	≥	NOUN
ejpam-3626	208	17	θ	θ	NOUN
ejpam-3626	208	18	for	for	ADP
ejpam-3626	208	19	every	every	DET
ejpam-3626	208	20	h	h	NOUN
ejpam-3626	208	21	∈	∈	PROPN
ejpam-3626	209	1	[	[	X
ejpam-3626	209	2	f	f	X
ejpam-3626	209	3	,	,	PUNCT
ejpam-3626	209	4	g	g	PROPN
ejpam-3626	209	5	]	]	PUNCT
ejpam-3626	209	6	,	,	PUNCT
ejpam-3626	209	7	then	then	ADV
ejpam-3626	209	8	(	(	PUNCT
ejpam-3626	209	9	hks	hks	PROPN
ejpam-3626	209	10	)	)	PUNCT
ejpam-3626	209	11	∫	∫	PROPN
ejpam-3626	209	12	g	g	PROPN
ejpam-3626	209	13	f	f	PROPN
ejpam-3626	209	14	fdh	fdh	PROPN
ejpam-3626	209	15	≥	≥	PROPN
ejpam-3626	209	16	θ	θ	PROPN
ejpam-3626	209	17	.	.	PUNCT
ejpam-3626	209	18	a.	a.	PROPN
ejpam-3626	209	19	cunanan	cunanan	PROPN
ejpam-3626	209	20	,	,	PUNCT
ejpam-3626	209	21	j.	j.	PROPN
ejpam-3626	209	22	benitez	benitez	PROPN
ejpam-3626	209	23	/	/	PUNCT
ejpam-3626	209	24	eur	eur	PROPN
ejpam-3626	209	25	.	.	PUNCT
ejpam-3626	210	1	j.	j.	PROPN
ejpam-3626	210	2	pure	pure	PROPN
ejpam-3626	210	3	appl	appl	PROPN
ejpam-3626	210	4	.	.	PROPN
ejpam-3626	210	5	math	math	PROPN
ejpam-3626	210	6	,	,	PUNCT
ejpam-3626	210	7	13	13	NUM
ejpam-3626	210	8	(	(	PUNCT
ejpam-3626	210	9	1	1	NUM
ejpam-3626	210	10	)	)	PUNCT
ejpam-3626	210	11	(	(	PUNCT
ejpam-3626	210	12	2020	2020	NUM
ejpam-3626	210	13	)	)	PUNCT
ejpam-3626	210	14	,	,	PUNCT
ejpam-3626	210	15	130	130	NUM
ejpam-3626	210	16	-	-	SYM
ejpam-3626	210	17	143	143	NUM
ejpam-3626	210	18	138	138	NUM
ejpam-3626	210	19	proof	proof	NOUN
ejpam-3626	210	20	.	.	PUNCT
ejpam-3626	211	1	let	let	VERB
ejpam-3626	211	2	ε	ε	PROPN
ejpam-3626	211	3	>	>	X
ejpam-3626	211	4	0	0	PROPN
ejpam-3626	211	5	.	.	PUNCT
ejpam-3626	212	1	then	then	ADV
ejpam-3626	212	2	there	there	PRON
ejpam-3626	212	3	exists	exist	VERB
ejpam-3626	212	4	a	a	DET
ejpam-3626	212	5	gauge	gauge	NOUN
ejpam-3626	212	6	δ	δ	NOUN
ejpam-3626	212	7	on	on	ADP
ejpam-3626	212	8	[	[	X
ejpam-3626	212	9	f	f	X
ejpam-3626	212	10	,	,	PUNCT
ejpam-3626	212	11	g	g	NOUN
ejpam-3626	212	12	]	]	PUNCT
ejpam-3626	212	13	such	such	ADJ
ejpam-3626	212	14	that	that	PRON
ejpam-3626	212	15	for	for	ADP
ejpam-3626	212	16	any	any	DET
ejpam-3626	212	17	δ	δ	NOUN
ejpam-3626	212	18	-	-	PUNCT
ejpam-3626	212	19	fine	fine	ADJ
ejpam-3626	212	20	tagged	tag	VERB
ejpam-3626	212	21	division	division	NOUN
ejpam-3626	212	22	d	d	NOUN
ejpam-3626	212	23	of	of	ADP
ejpam-3626	212	24	[	[	X
ejpam-3626	212	25	f	f	X
ejpam-3626	212	26	,	,	PUNCT
ejpam-3626	212	27	g	g	PROPN
ejpam-3626	212	28	]	]	X
ejpam-3626	212	29	,	,	PUNCT
ejpam-3626	212	30	we	we	PRON
ejpam-3626	212	31	have∣∣∣∣∑	have∣∣∣∣∑	VERB
ejpam-3626	212	32	d	d	X
ejpam-3626	212	33	f	f	PROPN
ejpam-3626	212	34	(	(	PUNCT
ejpam-3626	212	35	t)[h(v)−h(u)]−	t)[h(v)−h(u)]−	PROPN
ejpam-3626	212	36	(	(	PUNCT
ejpam-3626	212	37	hks	hks	PROPN
ejpam-3626	212	38	)	)	PUNCT
ejpam-3626	212	39	∫	∫	PROPN
ejpam-3626	213	1	g	g	PROPN
ejpam-3626	213	2	f	f	PROPN
ejpam-3626	213	3	fdh	fdh	PROPN
ejpam-3626	213	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	213	5	<	<	X
ejpam-3626	213	6	ε	ε	PROPN
ejpam-3626	213	7	·	·	PUNCT
ejpam-3626	213	8	e.	e.	PROPN
ejpam-3626	213	9	(	(	PUNCT
ejpam-3626	213	10	13	13	NUM
ejpam-3626	213	11	)	)	PUNCT
ejpam-3626	213	12	since	since	SCONJ
ejpam-3626	213	13	f	f	PROPN
ejpam-3626	213	14	(	(	PUNCT
ejpam-3626	213	15	h	h	NOUN
ejpam-3626	213	16	)	)	PUNCT
ejpam-3626	213	17	≥	≥	NOUN
ejpam-3626	213	18	θ	θ	NOUN
ejpam-3626	213	19	for	for	ADP
ejpam-3626	213	20	all	all	DET
ejpam-3626	213	21	h	h	NOUN
ejpam-3626	213	22	∈	∈	PROPN
ejpam-3626	214	1	[	[	X
ejpam-3626	214	2	f	f	X
ejpam-3626	214	3	,	,	PUNCT
ejpam-3626	214	4	g	g	NOUN
ejpam-3626	214	5	]	]	PUNCT
ejpam-3626	214	6	and	and	CCONJ
ejpam-3626	214	7	h	h	NOUN
ejpam-3626	214	8	is	be	AUX
ejpam-3626	214	9	increasing,∑	increasing,∑	PROPN
ejpam-3626	214	10	d	d	PROPN
ejpam-3626	214	11	f	f	X
ejpam-3626	214	12	(	(	PUNCT
ejpam-3626	214	13	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	214	14	)	)	PUNCT
ejpam-3626	214	15	]	]	PUNCT
ejpam-3626	214	16	≥	≥	NUM
ejpam-3626	214	17	θ	θ	X
ejpam-3626	214	18	.	.	PUNCT
ejpam-3626	215	1	therefore	therefore	ADV
ejpam-3626	215	2	,	,	PUNCT
ejpam-3626	215	3	θ	θ	PROPN
ejpam-3626	215	4	≤	≤	VERB
ejpam-3626	215	5	∑	∑	PUNCT
ejpam-3626	216	1	d	d	PROPN
ejpam-3626	216	2	f	f	X
ejpam-3626	216	3	(	(	PUNCT
ejpam-3626	216	4	t)[h(v)−h(u	t)[h(v)−h(u	PROPN
ejpam-3626	216	5	)	)	PUNCT
ejpam-3626	216	6	]	]	PUNCT
ejpam-3626	216	7	<	<	X
ejpam-3626	216	8	(	(	PUNCT
ejpam-3626	216	9	hks	hks	PROPN
ejpam-3626	216	10	)	)	PUNCT
ejpam-3626	216	11	∫	∫	PROPN
ejpam-3626	216	12	g	g	PROPN
ejpam-3626	216	13	f	f	PROPN
ejpam-3626	216	14	fdh	fdh	PROPN
ejpam-3626	216	15	+	+	CCONJ
ejpam-3626	216	16	ε	ε	PROPN
ejpam-3626	216	17	·	·	PUNCT
ejpam-3626	216	18	e.	e.	PROPN
ejpam-3626	216	19	since	since	SCONJ
ejpam-3626	216	20	ε	ε	PROPN
ejpam-3626	216	21	>	>	X
ejpam-3626	216	22	0	0	NUM
ejpam-3626	216	23	is	be	AUX
ejpam-3626	216	24	arbitrary	arbitrary	ADJ
ejpam-3626	216	25	,	,	PUNCT
ejpam-3626	216	26	(	(	PUNCT
ejpam-3626	216	27	hks	hks	PROPN
ejpam-3626	216	28	)	)	PUNCT
ejpam-3626	216	29	∫	∫	PROPN
ejpam-3626	216	30	g	g	PROPN
ejpam-3626	216	31	f	f	PROPN
ejpam-3626	216	32	fdh	fdh	PROPN
ejpam-3626	216	33	≥	≥	PROPN
ejpam-3626	216	34	θ	θ	PROPN
ejpam-3626	216	35	.	.	PUNCT
ejpam-3626	216	36	theorem	theorem	NOUN
ejpam-3626	216	37	9	9	NUM
ejpam-3626	216	38	.	.	PUNCT
ejpam-3626	217	1	if	if	SCONJ
ejpam-3626	217	2	f	f	PROPN
ejpam-3626	217	3	,	,	PUNCT
ejpam-3626	217	4	g	g	PROPN
ejpam-3626	217	5	∈	∈	PROPN
ejpam-3626	217	6	hks([f	hks([f	NOUN
ejpam-3626	217	7	,	,	PUNCT
ejpam-3626	217	8	g	g	NOUN
ejpam-3626	217	9	]	]	X
ejpam-3626	217	10	,	,	PUNCT
ejpam-3626	217	11	h	h	NOUN
ejpam-3626	217	12	)	)	PUNCT
ejpam-3626	217	13	and	and	CCONJ
ejpam-3626	217	14	f	f	PROPN
ejpam-3626	217	15	(	(	PUNCT
ejpam-3626	217	16	h	h	NOUN
ejpam-3626	217	17	)	)	PUNCT
ejpam-3626	217	18	≤	≤	NOUN
ejpam-3626	217	19	g(h	g(h	NUM
ejpam-3626	217	20	)	)	PUNCT
ejpam-3626	217	21	,	,	PUNCT
ejpam-3626	217	22	for	for	ADP
ejpam-3626	217	23	all	all	DET
ejpam-3626	217	24	h	h	NOUN
ejpam-3626	217	25	∈	∈	PROPN
ejpam-3626	218	1	[	[	X
ejpam-3626	218	2	f	f	X
ejpam-3626	218	3	,	,	PUNCT
ejpam-3626	218	4	g	g	PROPN
ejpam-3626	218	5	]	]	PUNCT
ejpam-3626	218	6	,	,	PUNCT
ejpam-3626	218	7	then	then	ADV
ejpam-3626	218	8	(	(	PUNCT
ejpam-3626	218	9	hks	hks	PROPN
ejpam-3626	218	10	)	)	PUNCT
ejpam-3626	218	11	∫	∫	PROPN
ejpam-3626	218	12	g	g	PROPN
ejpam-3626	218	13	f	f	PROPN
ejpam-3626	218	14	fdh	fdh	PROPN
ejpam-3626	218	15	≤	≤	PROPN
ejpam-3626	218	16	(	(	PUNCT
ejpam-3626	218	17	hks	hks	PROPN
ejpam-3626	218	18	)	)	PUNCT
ejpam-3626	218	19	∫	∫	PROPN
ejpam-3626	219	1	g	g	PROPN
ejpam-3626	219	2	f	f	PROPN
ejpam-3626	219	3	gdh	gdh	PROPN
ejpam-3626	219	4	.	.	PUNCT
ejpam-3626	220	1	proof	proof	NOUN
ejpam-3626	220	2	.	.	PUNCT
ejpam-3626	221	1	define	define	VERB
ejpam-3626	221	2	a	a	DET
ejpam-3626	221	3	function	function	NOUN
ejpam-3626	221	4	e	e	NOUN
ejpam-3626	221	5	on	on	ADP
ejpam-3626	221	6	[	[	X
ejpam-3626	221	7	f	f	X
ejpam-3626	221	8	,	,	PUNCT
ejpam-3626	221	9	g	g	NOUN
ejpam-3626	221	10	]	]	PUNCT
ejpam-3626	221	11	by	by	ADP
ejpam-3626	221	12	setting	set	VERB
ejpam-3626	221	13	e(h	e(h	NOUN
ejpam-3626	221	14	)	)	PUNCT
ejpam-3626	221	15	=	=	NOUN
ejpam-3626	222	1	g(h)−	g(h)−	NOUN
ejpam-3626	222	2	f	f	PROPN
ejpam-3626	222	3	(	(	PUNCT
ejpam-3626	222	4	h	h	NOUN
ejpam-3626	222	5	)	)	PUNCT
ejpam-3626	222	6	,	,	PUNCT
ejpam-3626	222	7	for	for	ADP
ejpam-3626	222	8	all	all	DET
ejpam-3626	222	9	h	h	NOUN
ejpam-3626	222	10	∈	∈	PROPN
ejpam-3626	223	1	[	[	X
ejpam-3626	223	2	f	f	X
ejpam-3626	223	3	,	,	PUNCT
ejpam-3626	223	4	g	g	NOUN
ejpam-3626	223	5	]	]	PUNCT
ejpam-3626	223	6	.	.	PUNCT
ejpam-3626	224	1	then	then	ADV
ejpam-3626	224	2	e(h	e(h	PROPN
ejpam-3626	224	3	)	)	PUNCT
ejpam-3626	224	4	≥	≥	NUM
ejpam-3626	224	5	θ	θ	NOUN
ejpam-3626	224	6	,	,	PUNCT
ejpam-3626	224	7	for	for	ADP
ejpam-3626	224	8	all	all	DET
ejpam-3626	224	9	h	h	NOUN
ejpam-3626	224	10	∈	∈	PROPN
ejpam-3626	225	1	[	[	X
ejpam-3626	225	2	f	f	X
ejpam-3626	225	3	,	,	PUNCT
ejpam-3626	225	4	g	g	NOUN
ejpam-3626	225	5	]	]	PUNCT
ejpam-3626	225	6	.	.	PUNCT
ejpam-3626	226	1	since	since	SCONJ
ejpam-3626	226	2	f	f	PROPN
ejpam-3626	226	3	,	,	PUNCT
ejpam-3626	226	4	g	g	PROPN
ejpam-3626	226	5	∈	∈	PROPN
ejpam-3626	226	6	hks([f	hks([f	NOUN
ejpam-3626	226	7	,	,	PUNCT
ejpam-3626	226	8	g	g	NOUN
ejpam-3626	226	9	]	]	X
ejpam-3626	226	10	,	,	PUNCT
ejpam-3626	226	11	h	h	NOUN
ejpam-3626	226	12	)	)	PUNCT
ejpam-3626	226	13	,	,	PUNCT
ejpam-3626	226	14	e	e	PROPN
ejpam-3626	226	15	∈	∈	PROPN
ejpam-3626	226	16	hks([f	hks([f	NOUN
ejpam-3626	226	17	,	,	PUNCT
ejpam-3626	226	18	g	g	NOUN
ejpam-3626	226	19	]	]	X
ejpam-3626	226	20	,	,	PUNCT
ejpam-3626	226	21	h	h	NOUN
ejpam-3626	226	22	)	)	PUNCT
ejpam-3626	226	23	and	and	CCONJ
ejpam-3626	226	24	by	by	ADP
ejpam-3626	226	25	theorem	theorem	NOUN
ejpam-3626	226	26	8	8	NUM
ejpam-3626	226	27	(	(	PUNCT
ejpam-3626	226	28	hks	hks	PROPN
ejpam-3626	226	29	)	)	PUNCT
ejpam-3626	226	30	∫	∫	PROPN
ejpam-3626	226	31	g	g	PROPN
ejpam-3626	226	32	f	f	PROPN
ejpam-3626	226	33	edh	edh	PROPN
ejpam-3626	226	34	≥	≥	NUM
ejpam-3626	226	35	θ	θ	PROPN
ejpam-3626	226	36	.	.	PUNCT
ejpam-3626	226	37	hence	hence	ADV
ejpam-3626	226	38	,	,	PUNCT
ejpam-3626	226	39	θ	θ	PROPN
ejpam-3626	226	40	≤	≤	NUM
ejpam-3626	226	41	(	(	PUNCT
ejpam-3626	226	42	hks	hks	PROPN
ejpam-3626	226	43	)	)	PUNCT
ejpam-3626	226	44	∫	∫	PROPN
ejpam-3626	227	1	g	g	PROPN
ejpam-3626	227	2	f	f	PROPN
ejpam-3626	227	3	edh	edh	PROPN
ejpam-3626	227	4	=	=	PRON
ejpam-3626	227	5	(	(	PUNCT
ejpam-3626	227	6	hks	hks	PROPN
ejpam-3626	227	7	)	)	PUNCT
ejpam-3626	227	8	∫	∫	PROPN
ejpam-3626	228	1	g	g	PROPN
ejpam-3626	228	2	f	f	PROPN
ejpam-3626	228	3	(	(	PUNCT
ejpam-3626	228	4	g−	g−	PROPN
ejpam-3626	228	5	f	f	NOUN
ejpam-3626	228	6	)	)	PUNCT
ejpam-3626	228	7	dh	dh	NOUN
ejpam-3626	228	8	=	=	SYM
ejpam-3626	228	9	(	(	PUNCT
ejpam-3626	228	10	hks	hks	PROPN
ejpam-3626	228	11	)	)	PUNCT
ejpam-3626	228	12	∫	∫	PROPN
ejpam-3626	228	13	g	g	PROPN
ejpam-3626	228	14	f	f	PROPN
ejpam-3626	228	15	gdh	gdh	ADV
ejpam-3626	229	1	−	−	PROPN
ejpam-3626	229	2	(	(	PUNCT
ejpam-3626	229	3	hks	hks	PROPN
ejpam-3626	229	4	)	)	PUNCT
ejpam-3626	229	5	∫	∫	PROPN
ejpam-3626	229	6	g	g	PROPN
ejpam-3626	229	7	f	f	PROPN
ejpam-3626	229	8	fdh	fdh	PROPN
ejpam-3626	229	9	.	.	PUNCT
ejpam-3626	230	1	therefore	therefore	ADV
ejpam-3626	230	2	,	,	PUNCT
ejpam-3626	230	3	(	(	PUNCT
ejpam-3626	230	4	hks	hks	PROPN
ejpam-3626	230	5	)	)	PUNCT
ejpam-3626	230	6	∫	∫	PROPN
ejpam-3626	230	7	g	g	PROPN
ejpam-3626	230	8	f	f	PROPN
ejpam-3626	230	9	gdh	gdh	PROPN
ejpam-3626	230	10	≤	≤	NUM
ejpam-3626	230	11	(	(	PUNCT
ejpam-3626	230	12	hks	hks	PROPN
ejpam-3626	230	13	)	)	PUNCT
ejpam-3626	230	14	∫	∫	PROPN
ejpam-3626	230	15	g	g	PROPN
ejpam-3626	230	16	f	f	PROPN
ejpam-3626	230	17	fdh	fdh	PROPN
ejpam-3626	230	18	.	.	PROPN
ejpam-3626	230	19	5	5	NUM
ejpam-3626	230	20	.	.	X
ejpam-3626	230	21	an	an	DET
ejpam-3626	230	22	existence	existence	NOUN
ejpam-3626	230	23	theorem	theorem	VERB
ejpam-3626	230	24	a	a	DET
ejpam-3626	230	25	function	function	NOUN
ejpam-3626	230	26	f	f	NOUN
ejpam-3626	230	27	:	:	PUNCT
ejpam-3626	231	1	[	[	X
ejpam-3626	231	2	f	f	X
ejpam-3626	231	3	,	,	PUNCT
ejpam-3626	231	4	g]→	g]→	NOUN
ejpam-3626	231	5	c[a	c[a	NOUN
ejpam-3626	231	6	,	,	PUNCT
ejpam-3626	231	7	b	b	AUX
ejpam-3626	231	8	]	]	X
ejpam-3626	231	9	is	be	AUX
ejpam-3626	231	10	bounded	bound	VERB
ejpam-3626	231	11	on	on	ADP
ejpam-3626	231	12	[	[	X
ejpam-3626	231	13	f	f	X
ejpam-3626	231	14	,	,	PUNCT
ejpam-3626	231	15	g	g	NOUN
ejpam-3626	231	16	]	]	X
ejpam-3626	231	17	if	if	SCONJ
ejpam-3626	231	18	there	there	PRON
ejpam-3626	231	19	exists	exist	VERB
ejpam-3626	231	20	k	k	PROPN
ejpam-3626	231	21	≥	≥	NUM
ejpam-3626	231	22	θ	θ	NOUN
ejpam-3626	231	23	in	in	ADP
ejpam-3626	231	24	c[a	c[a	NUM
ejpam-3626	231	25	,	,	PUNCT
ejpam-3626	231	26	b	b	X
ejpam-3626	231	27	]	]	X
ejpam-3626	231	28	such	such	ADJ
ejpam-3626	231	29	that	that	SCONJ
ejpam-3626	231	30	|f	|f	PROPN
ejpam-3626	231	31	(	(	PUNCT
ejpam-3626	231	32	h)|	h)|	VERB
ejpam-3626	231	33	≤	≤	PROPN
ejpam-3626	231	34	k	k	PROPN
ejpam-3626	231	35	,	,	PUNCT
ejpam-3626	231	36	for	for	ADP
ejpam-3626	231	37	all	all	DET
ejpam-3626	231	38	h	h	NOUN
ejpam-3626	231	39	∈	∈	PROPN
ejpam-3626	232	1	[	[	X
ejpam-3626	232	2	f	f	X
ejpam-3626	232	3	,	,	PUNCT
ejpam-3626	232	4	g	g	NOUN
ejpam-3626	232	5	]	]	PUNCT
ejpam-3626	232	6	.	.	PUNCT
ejpam-3626	232	7	a.	a.	PROPN
ejpam-3626	232	8	cunanan	cunanan	PROPN
ejpam-3626	232	9	,	,	PUNCT
ejpam-3626	232	10	j.	j.	PROPN
ejpam-3626	232	11	benitez	benitez	PROPN
ejpam-3626	232	12	/	/	PUNCT
ejpam-3626	232	13	eur	eur	PROPN
ejpam-3626	232	14	.	.	PUNCT
ejpam-3626	233	1	j.	j.	PROPN
ejpam-3626	233	2	pure	pure	PROPN
ejpam-3626	233	3	appl	appl	PROPN
ejpam-3626	233	4	.	.	PROPN
ejpam-3626	233	5	math	math	PROPN
ejpam-3626	233	6	,	,	PUNCT
ejpam-3626	233	7	13	13	NUM
ejpam-3626	233	8	(	(	PUNCT
ejpam-3626	233	9	1	1	NUM
ejpam-3626	233	10	)	)	PUNCT
ejpam-3626	233	11	(	(	PUNCT
ejpam-3626	233	12	2020	2020	NUM
ejpam-3626	233	13	)	)	PUNCT
ejpam-3626	233	14	,	,	PUNCT
ejpam-3626	233	15	130	130	NUM
ejpam-3626	233	16	-	-	SYM
ejpam-3626	233	17	143	143	NUM
ejpam-3626	233	18	139	139	NUM
ejpam-3626	233	19	a	a	DET
ejpam-3626	233	20	function	function	NOUN
ejpam-3626	233	21	f	f	NOUN
ejpam-3626	234	1	:	:	PUNCT
ejpam-3626	235	1	[	[	X
ejpam-3626	235	2	f	f	X
ejpam-3626	235	3	,	,	PUNCT
ejpam-3626	235	4	g	g	NOUN
ejpam-3626	235	5	]	]	X
ejpam-3626	235	6	→	→	SYM
ejpam-3626	235	7	c[a	c[a	NUM
ejpam-3626	235	8	,	,	PUNCT
ejpam-3626	235	9	b	b	AUX
ejpam-3626	235	10	]	]	PUNCT
ejpam-3626	235	11	is	be	AUX
ejpam-3626	235	12	continuous	continuous	ADJ
ejpam-3626	235	13	at	at	ADP
ejpam-3626	235	14	h0	h0	PROPN
ejpam-3626	235	15	∈	∈	PROPN
ejpam-3626	236	1	[	[	X
ejpam-3626	236	2	f	f	X
ejpam-3626	236	3	,	,	PUNCT
ejpam-3626	236	4	g	g	PROPN
ejpam-3626	236	5	]	]	X
ejpam-3626	236	6	,	,	PUNCT
ejpam-3626	236	7	if	if	SCONJ
ejpam-3626	236	8	for	for	ADP
ejpam-3626	236	9	any	any	DET
ejpam-3626	236	10	ε	ε	PROPN
ejpam-3626	236	11	>	>	X
ejpam-3626	236	12	0	0	PUNCT
ejpam-3626	236	13	there	there	PRON
ejpam-3626	236	14	exists	exist	VERB
ejpam-3626	236	15	δ	δ	PROPN
ejpam-3626	236	16	=	=	PUNCT
ejpam-3626	236	17	δ(h0	δ(h0	PROPN
ejpam-3626	236	18	)	)	PUNCT
ejpam-3626	236	19	>	>	X
ejpam-3626	237	1	θ	θ	PROPN
ejpam-3626	237	2	such	such	ADJ
ejpam-3626	237	3	that	that	SCONJ
ejpam-3626	238	1	whenever	whenever	SCONJ
ejpam-3626	238	2	h	h	PRON
ejpam-3626	238	3	∈	∈	PROPN
ejpam-3626	239	1	[	[	X
ejpam-3626	239	2	f	f	X
ejpam-3626	239	3	,	,	PUNCT
ejpam-3626	239	4	g	g	NOUN
ejpam-3626	239	5	]	]	PUNCT
ejpam-3626	239	6	with	with	ADP
ejpam-3626	239	7	|h−	|h−	NOUN
ejpam-3626	239	8	h0|	h0|	X
ejpam-3626	239	9	<	<	X
ejpam-3626	239	10	δ	δ	PROPN
ejpam-3626	239	11	,	,	PUNCT
ejpam-3626	239	12	we	we	PRON
ejpam-3626	239	13	have∣∣f	have∣∣f	VERB
ejpam-3626	239	14	(	(	PUNCT
ejpam-3626	239	15	h)−	h)−	PROPN
ejpam-3626	239	16	f	f	PROPN
ejpam-3626	239	17	(	(	PUNCT
ejpam-3626	239	18	h0	h0	PROPN
ejpam-3626	239	19	)	)	PUNCT
ejpam-3626	239	20	∣∣	∣∣	X
ejpam-3626	240	1	<	<	X
ejpam-3626	240	2	ε	ε	PROPN
ejpam-3626	240	3	·	·	PUNCT
ejpam-3626	240	4	e.	e.	PROPN
ejpam-3626	240	5	f	f	PROPN
ejpam-3626	240	6	is	be	AUX
ejpam-3626	240	7	said	say	VERB
ejpam-3626	240	8	to	to	PART
ejpam-3626	240	9	be	be	AUX
ejpam-3626	240	10	uniformly	uniformly	ADV
ejpam-3626	240	11	continuous	continuous	ADJ
ejpam-3626	240	12	on	on	ADP
ejpam-3626	240	13	[	[	X
ejpam-3626	240	14	f	f	X
ejpam-3626	240	15	,	,	PUNCT
ejpam-3626	240	16	g	g	PROPN
ejpam-3626	240	17	]	]	X
ejpam-3626	240	18	,	,	PUNCT
ejpam-3626	240	19	if	if	SCONJ
ejpam-3626	240	20	for	for	ADP
ejpam-3626	240	21	any	any	DET
ejpam-3626	240	22	ε	ε	PROPN
ejpam-3626	240	23	>	>	X
ejpam-3626	240	24	0	0	PUNCT
ejpam-3626	240	25	there	there	PRON
ejpam-3626	240	26	exists	exist	VERB
ejpam-3626	240	27	δ	δ	PROPN
ejpam-3626	240	28	>	>	X
ejpam-3626	240	29	θ	θ	PROPN
ejpam-3626	240	30	such	such	ADJ
ejpam-3626	240	31	that	that	SCONJ
ejpam-3626	240	32	whenever	whenever	SCONJ
ejpam-3626	240	33	h	h	NOUN
ejpam-3626	240	34	,	,	PUNCT
ejpam-3626	240	35	h′	h′	PROPN
ejpam-3626	240	36	∈	∈	PROPN
ejpam-3626	241	1	[	[	X
ejpam-3626	241	2	f	f	X
ejpam-3626	241	3	,	,	PUNCT
ejpam-3626	241	4	g	g	NOUN
ejpam-3626	241	5	]	]	PUNCT
ejpam-3626	241	6	with	with	ADP
ejpam-3626	241	7	|h′	|h′	PROPN
ejpam-3626	241	8	−	−	PROPN
ejpam-3626	241	9	h|	h|	PROPN
ejpam-3626	241	10	<	<	X
ejpam-3626	241	11	δ	δ	PROPN
ejpam-3626	241	12	,	,	PUNCT
ejpam-3626	241	13	we	we	PRON
ejpam-3626	241	14	have∣∣f	have∣∣f	VERB
ejpam-3626	241	15	(	(	PUNCT
ejpam-3626	241	16	h′)−	h′)−	PROPN
ejpam-3626	241	17	f	f	PROPN
ejpam-3626	241	18	(	(	PUNCT
ejpam-3626	241	19	h	h	NOUN
ejpam-3626	241	20	)	)	PUNCT
ejpam-3626	241	21	∣∣	∣∣	X
ejpam-3626	241	22	<	<	X
ejpam-3626	241	23	ε	ε	PROPN
ejpam-3626	241	24	·	·	PUNCT
ejpam-3626	241	25	e.	e.	PROPN
ejpam-3626	242	1	if	if	SCONJ
ejpam-3626	242	2	f	f	X
ejpam-3626	242	3	:	:	PUNCT
ejpam-3626	243	1	[	[	X
ejpam-3626	243	2	f	f	X
ejpam-3626	243	3	,	,	PUNCT
ejpam-3626	243	4	g]→	g]→	NOUN
ejpam-3626	243	5	c[a	c[a	NOUN
ejpam-3626	243	6	,	,	PUNCT
ejpam-3626	243	7	b	b	AUX
ejpam-3626	243	8	]	]	PUNCT
ejpam-3626	243	9	is	be	AUX
ejpam-3626	243	10	uniformly	uniformly	ADV
ejpam-3626	243	11	continuous	continuous	ADJ
ejpam-3626	243	12	on	on	ADP
ejpam-3626	243	13	[	[	X
ejpam-3626	243	14	f	f	X
ejpam-3626	243	15	,	,	PUNCT
ejpam-3626	243	16	g	g	PROPN
ejpam-3626	243	17	]	]	X
ejpam-3626	243	18	,	,	PUNCT
ejpam-3626	243	19	then	then	ADV
ejpam-3626	243	20	it	it	PRON
ejpam-3626	243	21	is	be	AUX
ejpam-3626	243	22	continuous	continuous	ADJ
ejpam-3626	243	23	on	on	ADP
ejpam-3626	243	24	[	[	X
ejpam-3626	243	25	f	f	X
ejpam-3626	243	26	,	,	PUNCT
ejpam-3626	243	27	g	g	NOUN
ejpam-3626	243	28	]	]	PUNCT
ejpam-3626	243	29	.	.	PUNCT
ejpam-3626	244	1	definition	definition	NOUN
ejpam-3626	244	2	3	3	X
ejpam-3626	244	3	.	.	PUNCT
ejpam-3626	245	1	let	let	VERB
ejpam-3626	245	2	d1	d1	PROPN
ejpam-3626	245	3	and	and	CCONJ
ejpam-3626	245	4	d2	d2	PROPN
ejpam-3626	245	5	be	be	AUX
ejpam-3626	245	6	tagged	tag	VERB
ejpam-3626	245	7	divisions	division	NOUN
ejpam-3626	245	8	of	of	ADP
ejpam-3626	245	9	[	[	X
ejpam-3626	245	10	f	f	X
ejpam-3626	245	11	,	,	PUNCT
ejpam-3626	245	12	g	g	NOUN
ejpam-3626	245	13	]	]	X
ejpam-3626	245	14	.	.	PUNCT
ejpam-3626	246	1	we	we	PRON
ejpam-3626	246	2	say	say	VERB
ejpam-3626	246	3	that	that	SCONJ
ejpam-3626	246	4	d2	d2	PROPN
ejpam-3626	246	5	is	be	AUX
ejpam-3626	246	6	finer	fine	ADJ
ejpam-3626	246	7	than	than	ADP
ejpam-3626	246	8	d1	d1	PROPN
ejpam-3626	246	9	,	,	PUNCT
ejpam-3626	246	10	denoted	denote	VERB
ejpam-3626	246	11	by	by	ADP
ejpam-3626	246	12	d1	d1	PROPN
ejpam-3626	246	13	�	�	PROPN
ejpam-3626	246	14	d2	d2	PROPN
ejpam-3626	246	15	,	,	PUNCT
ejpam-3626	246	16	if	if	SCONJ
ejpam-3626	246	17	for	for	ADP
ejpam-3626	246	18	every	every	DET
ejpam-3626	246	19	(	(	PUNCT
ejpam-3626	246	20	[	[	X
ejpam-3626	246	21	u	u	NOUN
ejpam-3626	246	22	,	,	PUNCT
ejpam-3626	246	23	v	v	ADP
ejpam-3626	246	24	]	]	PUNCT
ejpam-3626	246	25	,	,	PUNCT
ejpam-3626	246	26	t	t	PROPN
ejpam-3626	246	27	)	)	PUNCT
ejpam-3626	246	28	∈	∈	PROPN
ejpam-3626	246	29	d2	d2	PROPN
ejpam-3626	246	30	there	there	ADV
ejpam-3626	246	31	exists	exist	VERB
ejpam-3626	246	32	(	(	PUNCT
ejpam-3626	246	33	[	[	X
ejpam-3626	246	34	u′	u′	PROPN
ejpam-3626	246	35	,	,	PUNCT
ejpam-3626	246	36	v′	v′	PROPN
ejpam-3626	246	37	]	]	PUNCT
ejpam-3626	246	38	,	,	PUNCT
ejpam-3626	246	39	t′	t′	NUM
ejpam-3626	246	40	)	)	PUNCT
ejpam-3626	246	41	∈	∈	NOUN
ejpam-3626	246	42	d1	d1	NOUN
ejpam-3626	246	43	such	such	ADJ
ejpam-3626	246	44	that	that	SCONJ
ejpam-3626	246	45	[	[	X
ejpam-3626	246	46	u	u	NOUN
ejpam-3626	246	47	,	,	PUNCT
ejpam-3626	246	48	v	v	NOUN
ejpam-3626	246	49	]	]	PUNCT
ejpam-3626	246	50	⊆	⊆	NUM
ejpam-3626	246	51	[	[	X
ejpam-3626	246	52	u′	u′	PROPN
ejpam-3626	246	53	,	,	PUNCT
ejpam-3626	246	54	v′	v′	PROPN
ejpam-3626	246	55	]	]	PUNCT
ejpam-3626	246	56	,	,	PUNCT
ejpam-3626	246	57	and	and	CCONJ
ejpam-3626	246	58	every	every	DET
ejpam-3626	246	59	tag	tag	NOUN
ejpam-3626	246	60	in	in	ADP
ejpam-3626	246	61	d1	d1	PROPN
ejpam-3626	246	62	is	be	AUX
ejpam-3626	246	63	a	a	DET
ejpam-3626	246	64	tag	tag	NOUN
ejpam-3626	246	65	in	in	ADP
ejpam-3626	246	66	d2	d2	PROPN
ejpam-3626	246	67	.	.	PUNCT
ejpam-3626	247	1	for	for	ADP
ejpam-3626	247	2	every	every	DET
ejpam-3626	247	3	(	(	PUNCT
ejpam-3626	247	4	[	[	X
ejpam-3626	247	5	u′	u′	PROPN
ejpam-3626	247	6	,	,	PUNCT
ejpam-3626	247	7	v′	v′	PROPN
ejpam-3626	247	8	]	]	PUNCT
ejpam-3626	247	9	,	,	PUNCT
ejpam-3626	247	10	t′	t′	NUM
ejpam-3626	247	11	)	)	PUNCT
ejpam-3626	247	12	∈	∈	NOUN
ejpam-3626	247	13	d1	d1	NOUN
ejpam-3626	247	14	,	,	PUNCT
ejpam-3626	247	15	the	the	DET
ejpam-3626	247	16	tagged	tag	VERB
ejpam-3626	247	17	division	division	NOUN
ejpam-3626	247	18	p	p	NOUN
ejpam-3626	247	19	=	=	PUNCT
ejpam-3626	247	20	{	{	PUNCT
ejpam-3626	247	21	(	(	PUNCT
ejpam-3626	247	22	[	[	X
ejpam-3626	247	23	zi−1	zi−1	PROPN
ejpam-3626	247	24	,	,	PUNCT
ejpam-3626	247	25	zi	zi	PROPN
ejpam-3626	247	26	]	]	PUNCT
ejpam-3626	247	27	,	,	PUNCT
ejpam-3626	247	28	ti	ti	NOUN
ejpam-3626	247	29	)	)	PUNCT
ejpam-3626	247	30	∈	∈	PROPN
ejpam-3626	247	31	d2	d2	NOUN
ejpam-3626	247	32	:	:	PUNCT
ejpam-3626	248	1	[	[	X
ejpam-3626	248	2	zi−1	zi−1	PROPN
ejpam-3626	248	3	,	,	PUNCT
ejpam-3626	248	4	zi	zi	PROPN
ejpam-3626	248	5	]	]	PUNCT
ejpam-3626	248	6	⊆	⊆	NUM
ejpam-3626	248	7	[	[	X
ejpam-3626	248	8	u′	u′	PROPN
ejpam-3626	248	9	,	,	PUNCT
ejpam-3626	248	10	v′	v′	PROPN
ejpam-3626	248	11	]	]	PUNCT
ejpam-3626	248	12	,	,	PUNCT
ejpam-3626	248	13	i	i	PRON
ejpam-3626	248	14	=	=	NOUN
ejpam-3626	248	15	1	1	NUM
ejpam-3626	248	16	,	,	PUNCT
ejpam-3626	248	17	2	2	NUM
ejpam-3626	248	18	,	,	PUNCT
ejpam-3626	248	19	.	.	PUNCT
ejpam-3626	248	20	.	.	PUNCT
ejpam-3626	248	21	.	.	PUNCT
ejpam-3626	248	22	,	,	PUNCT
ejpam-3626	248	23	n	n	CCONJ
ejpam-3626	248	24	}	}	PUNCT
ejpam-3626	248	25	is	be	AUX
ejpam-3626	248	26	the	the	DET
ejpam-3626	248	27	refinement	refinement	NOUN
ejpam-3626	248	28	of	of	ADP
ejpam-3626	248	29	(	(	PUNCT
ejpam-3626	248	30	[	[	X
ejpam-3626	248	31	u′	u′	PROPN
ejpam-3626	248	32	,	,	PUNCT
ejpam-3626	248	33	v′	v′	PROPN
ejpam-3626	248	34	]	]	PUNCT
ejpam-3626	248	35	,	,	PUNCT
ejpam-3626	248	36	t′	t′	NUM
ejpam-3626	248	37	)	)	PUNCT
ejpam-3626	248	38	in	in	ADP
ejpam-3626	248	39	d2	d2	PROPN
ejpam-3626	248	40	.	.	PUNCT
ejpam-3626	249	1	we	we	PRON
ejpam-3626	249	2	can	can	AUX
ejpam-3626	249	3	easily	easily	ADV
ejpam-3626	249	4	see	see	VERB
ejpam-3626	249	5	that	that	SCONJ
ejpam-3626	249	6	if	if	SCONJ
ejpam-3626	249	7	d1	d1	PROPN
ejpam-3626	249	8	and	and	CCONJ
ejpam-3626	249	9	d2	d2	PROPN
ejpam-3626	249	10	are	be	AUX
ejpam-3626	249	11	tagged	tag	VERB
ejpam-3626	249	12	divisions	division	NOUN
ejpam-3626	249	13	of	of	ADP
ejpam-3626	249	14	[	[	X
ejpam-3626	249	15	f	f	X
ejpam-3626	249	16	,	,	PUNCT
ejpam-3626	249	17	g	g	PROPN
ejpam-3626	249	18	]	]	PUNCT
ejpam-3626	249	19	,	,	PUNCT
ejpam-3626	249	20	then	then	ADV
ejpam-3626	249	21	there	there	PRON
ejpam-3626	249	22	exists	exist	VERB
ejpam-3626	249	23	a	a	DET
ejpam-3626	249	24	tagged	tag	VERB
ejpam-3626	249	25	division	division	NOUN
ejpam-3626	249	26	d0	d0	NOUN
ejpam-3626	249	27	of	of	ADP
ejpam-3626	249	28	[	[	X
ejpam-3626	249	29	f	f	X
ejpam-3626	249	30	,	,	PUNCT
ejpam-3626	249	31	g	g	NOUN
ejpam-3626	249	32	]	]	PUNCT
ejpam-3626	249	33	such	such	ADJ
ejpam-3626	249	34	that	that	SCONJ
ejpam-3626	249	35	d1	d1	PROPN
ejpam-3626	249	36	�	�	PROPN
ejpam-3626	249	37	d0	d0	PROPN
ejpam-3626	249	38	and	and	CCONJ
ejpam-3626	249	39	d2	d2	PROPN
ejpam-3626	249	40	�	�	PROPN
ejpam-3626	249	41	d0	d0	PROPN
ejpam-3626	249	42	.	.	PUNCT
ejpam-3626	250	1	let	let	AUX
ejpam-3626	250	2	d([f	d([f	VERB
ejpam-3626	250	3	,	,	PUNCT
ejpam-3626	250	4	g	g	NOUN
ejpam-3626	250	5	]	]	PUNCT
ejpam-3626	250	6	)	)	PUNCT
ejpam-3626	250	7	be	be	AUX
ejpam-3626	250	8	the	the	DET
ejpam-3626	250	9	collection	collection	NOUN
ejpam-3626	250	10	of	of	ADP
ejpam-3626	250	11	all	all	DET
ejpam-3626	250	12	divisions	division	NOUN
ejpam-3626	250	13	of	of	ADP
ejpam-3626	250	14	[	[	X
ejpam-3626	250	15	f	f	X
ejpam-3626	250	16	,	,	PUNCT
ejpam-3626	250	17	g	g	NOUN
ejpam-3626	250	18	]	]	PUNCT
ejpam-3626	250	19	.	.	PUNCT
ejpam-3626	251	1	for	for	ADP
ejpam-3626	251	2	f	f	PROPN
ejpam-3626	251	3	:	:	PUNCT
ejpam-3626	251	4	[	[	X
ejpam-3626	251	5	f	f	X
ejpam-3626	251	6	,	,	PUNCT
ejpam-3626	251	7	g	g	NOUN
ejpam-3626	251	8	]	]	X
ejpam-3626	251	9	→	→	SYM
ejpam-3626	251	10	c[a	c[a	NUM
ejpam-3626	251	11	,	,	PUNCT
ejpam-3626	251	12	b	b	NOUN
ejpam-3626	251	13	]	]	PUNCT
ejpam-3626	251	14	and	and	CCONJ
ejpam-3626	251	15	d	d	NOUN
ejpam-3626	251	16	=	=	SYM
ejpam-3626	251	17	{	{	PUNCT
ejpam-3626	251	18	[	[	X
ejpam-3626	251	19	u	u	NOUN
ejpam-3626	251	20	,	,	PUNCT
ejpam-3626	251	21	v	v	NOUN
ejpam-3626	251	22	]	]	PUNCT
ejpam-3626	251	23	}	}	PUNCT
ejpam-3626	251	24	∈	∈	PROPN
ejpam-3626	251	25	d([f	d([f	PROPN
ejpam-3626	251	26	,	,	PUNCT
ejpam-3626	251	27	g	g	NOUN
ejpam-3626	251	28	]	]	X
ejpam-3626	251	29	)	)	PUNCT
ejpam-3626	251	30	,	,	PUNCT
ejpam-3626	251	31	the	the	DET
ejpam-3626	251	32	variation	variation	NOUN
ejpam-3626	251	33	of	of	ADP
ejpam-3626	251	34	f	f	PROPN
ejpam-3626	251	35	over	over	ADP
ejpam-3626	251	36	d	d	PROPN
ejpam-3626	251	37	is	be	AUX
ejpam-3626	251	38	given	give	VERB
ejpam-3626	251	39	by	by	ADP
ejpam-3626	251	40	var(f	var(f	PROPN
ejpam-3626	251	41	,	,	PUNCT
ejpam-3626	251	42	d	d	NOUN
ejpam-3626	251	43	)	)	PUNCT
ejpam-3626	251	44	=	=	PUNCT
ejpam-3626	252	1	∑	∑	PUNCT
ejpam-3626	252	2	d	d	PROPN
ejpam-3626	252	3	∣∣f	∣∣f	PROPN
ejpam-3626	252	4	(	(	PUNCT
ejpam-3626	252	5	v)−	v)−	PROPN
ejpam-3626	252	6	f	f	X
ejpam-3626	252	7	(	(	PUNCT
ejpam-3626	252	8	u	u	NOUN
ejpam-3626	252	9	)	)	PUNCT
ejpam-3626	252	10	∣∣.	∣∣.	PROPN
ejpam-3626	252	11	note	note	VERB
ejpam-3626	252	12	that	that	SCONJ
ejpam-3626	252	13	for	for	ADP
ejpam-3626	252	14	any	any	DET
ejpam-3626	252	15	division	division	NOUN
ejpam-3626	252	16	d	d	NOUN
ejpam-3626	252	17	of	of	ADP
ejpam-3626	252	18	[	[	X
ejpam-3626	252	19	f	f	X
ejpam-3626	252	20	,	,	PUNCT
ejpam-3626	252	21	g	g	PROPN
ejpam-3626	252	22	]	]	X
ejpam-3626	252	23	,	,	PUNCT
ejpam-3626	252	24	var(f	var(f	PROPN
ejpam-3626	252	25	,	,	PUNCT
ejpam-3626	252	26	d	d	NOUN
ejpam-3626	252	27	)	)	PUNCT
ejpam-3626	252	28	is	be	AUX
ejpam-3626	252	29	a	a	DET
ejpam-3626	252	30	continuous	continuous	ADJ
ejpam-3626	252	31	function	function	NOUN
ejpam-3626	252	32	on	on	ADP
ejpam-3626	252	33	[	[	X
ejpam-3626	252	34	a	a	X
ejpam-3626	252	35	,	,	PUNCT
ejpam-3626	252	36	b	b	NOUN
ejpam-3626	252	37	]	]	X
ejpam-3626	252	38	;	;	PUNCT
ejpam-3626	252	39	that	that	PRON
ejpam-3626	252	40	is	is	ADV
ejpam-3626	252	41	,	,	PUNCT
ejpam-3626	252	42	var(f	var(f	PROPN
ejpam-3626	252	43	,	,	PUNCT
ejpam-3626	252	44	d	d	NOUN
ejpam-3626	252	45	)	)	PUNCT
ejpam-3626	252	46	∈	∈	PROPN
ejpam-3626	252	47	c[a	c[a	NOUN
ejpam-3626	252	48	,	,	PUNCT
ejpam-3626	252	49	b	b	NOUN
ejpam-3626	252	50	]	]	X
ejpam-3626	252	51	,	,	PUNCT
ejpam-3626	252	52	for	for	ADP
ejpam-3626	252	53	any	any	DET
ejpam-3626	252	54	d	d	PROPN
ejpam-3626	252	55	∈	∈	PROPN
ejpam-3626	252	56	d([f	d([f	PROPN
ejpam-3626	252	57	,	,	PUNCT
ejpam-3626	252	58	g	g	NOUN
ejpam-3626	252	59	]	]	X
ejpam-3626	252	60	)	)	PUNCT
ejpam-3626	252	61	.	.	PUNCT
ejpam-3626	253	1	definition	definition	NOUN
ejpam-3626	253	2	4	4	NUM
ejpam-3626	253	3	.	.	PUNCT
ejpam-3626	254	1	we	we	PRON
ejpam-3626	254	2	say	say	VERB
ejpam-3626	254	3	that	that	SCONJ
ejpam-3626	254	4	the	the	DET
ejpam-3626	254	5	function	function	NOUN
ejpam-3626	254	6	f	f	NOUN
ejpam-3626	254	7	:	:	PUNCT
ejpam-3626	255	1	[	[	X
ejpam-3626	255	2	f	f	X
ejpam-3626	255	3	,	,	PUNCT
ejpam-3626	255	4	g]→	g]→	NOUN
ejpam-3626	255	5	c[a	c[a	NOUN
ejpam-3626	255	6	,	,	PUNCT
ejpam-3626	255	7	b	b	AUX
ejpam-3626	255	8	]	]	X
ejpam-3626	255	9	is	be	AUX
ejpam-3626	255	10	of	of	ADP
ejpam-3626	255	11	bounded	bounded	ADJ
ejpam-3626	255	12	variation	variation	NOUN
ejpam-3626	255	13	on	on	ADP
ejpam-3626	255	14	[	[	X
ejpam-3626	255	15	f	f	X
ejpam-3626	255	16	,	,	PUNCT
ejpam-3626	255	17	g	g	NOUN
ejpam-3626	255	18	]	]	X
ejpam-3626	255	19	if	if	SCONJ
ejpam-3626	255	20	υf	υf	ADP
ejpam-3626	255	21	=	=	PROPN
ejpam-3626	255	22	υ(f	υ(f	PROPN
ejpam-3626	255	23	;	;	PUNCT
ejpam-3626	256	1	[	[	X
ejpam-3626	256	2	f	f	X
ejpam-3626	256	3	,	,	PUNCT
ejpam-3626	256	4	g	g	NOUN
ejpam-3626	256	5	]	]	X
ejpam-3626	256	6	)	)	PUNCT
ejpam-3626	256	7	=	=	SYM
ejpam-3626	256	8	sup	sup	PROPN
ejpam-3626	256	9	d∈d([f	d∈d([f	PROPN
ejpam-3626	256	10	,	,	PUNCT
ejpam-3626	256	11	g	g	NOUN
ejpam-3626	256	12	]	]	X
ejpam-3626	256	13	)	)	PUNCT
ejpam-3626	256	14	var(f	var(f	PROPN
ejpam-3626	256	15	,	,	PUNCT
ejpam-3626	256	16	d	d	NOUN
ejpam-3626	256	17	)	)	PUNCT
ejpam-3626	256	18	is	be	AUX
ejpam-3626	256	19	continuous	continuous	ADJ
ejpam-3626	256	20	on	on	ADP
ejpam-3626	256	21	[	[	X
ejpam-3626	256	22	a	a	X
ejpam-3626	256	23	,	,	PUNCT
ejpam-3626	256	24	b	b	NOUN
ejpam-3626	256	25	]	]	X
ejpam-3626	256	26	;	;	PUNCT
ejpam-3626	256	27	that	that	PRON
ejpam-3626	256	28	is	is	ADV
ejpam-3626	256	29	,	,	PUNCT
ejpam-3626	256	30	υf	υf	NOUN
ejpam-3626	256	31	∈	∈	PROPN
ejpam-3626	256	32	c[a	c[a	NUM
ejpam-3626	256	33	,	,	PUNCT
ejpam-3626	256	34	b	b	NOUN
ejpam-3626	256	35	]	]	PUNCT
ejpam-3626	256	36	.	.	PUNCT
ejpam-3626	257	1	note	note	VERB
ejpam-3626	257	2	that	that	SCONJ
ejpam-3626	257	3	for	for	ADP
ejpam-3626	257	4	any	any	DET
ejpam-3626	257	5	f	f	NOUN
ejpam-3626	257	6	:	:	PUNCT
ejpam-3626	258	1	[	[	X
ejpam-3626	258	2	f	f	X
ejpam-3626	258	3	,	,	PUNCT
ejpam-3626	258	4	g]→	g]→	NOUN
ejpam-3626	258	5	c[a	c[a	NOUN
ejpam-3626	258	6	,	,	PUNCT
ejpam-3626	258	7	b	b	NOUN
ejpam-3626	258	8	]	]	X
ejpam-3626	258	9	,	,	PUNCT
ejpam-3626	258	10	υf	υf	ADV
ejpam-3626	258	11	is	be	AUX
ejpam-3626	258	12	a	a	DET
ejpam-3626	258	13	mapping	mapping	NOUN
ejpam-3626	258	14	from	from	ADP
ejpam-3626	258	15	[	[	X
ejpam-3626	258	16	a	a	PRON
ejpam-3626	258	17	,	,	PUNCT
ejpam-3626	258	18	b	b	NOUN
ejpam-3626	258	19	]	]	PUNCT
ejpam-3626	258	20	to	to	ADP
ejpam-3626	258	21	[	[	X
ejpam-3626	258	22	0,+∞	0,+∞	NUM
ejpam-3626	258	23	]	]	X
ejpam-3626	258	24	;	;	PUNCT
ejpam-3626	258	25	that	that	PRON
ejpam-3626	258	26	is	be	AUX
ejpam-3626	258	27	,	,	PUNCT
ejpam-3626	258	28	0	0	NUM
ejpam-3626	258	29	≤	≤	NUM
ejpam-3626	258	30	υf	υf	NOUN
ejpam-3626	258	31	(	(	PUNCT
ejpam-3626	258	32	x	x	NOUN
ejpam-3626	258	33	)	)	PUNCT
ejpam-3626	258	34	≤	≤	NOUN
ejpam-3626	259	1	+	+	PUNCT
ejpam-3626	259	2	∞	∞	PROPN
ejpam-3626	259	3	,	,	PUNCT
ejpam-3626	259	4	for	for	ADP
ejpam-3626	259	5	all	all	DET
ejpam-3626	259	6	x	x	SYM
ejpam-3626	259	7	∈	∈	PROPN
ejpam-3626	259	8	[	[	X
ejpam-3626	259	9	a	a	X
ejpam-3626	259	10	,	,	PUNCT
ejpam-3626	259	11	b	b	NOUN
ejpam-3626	259	12	]	]	X
ejpam-3626	259	13	.	.	PUNCT
ejpam-3626	260	1	hence	hence	ADV
ejpam-3626	260	2	,	,	PUNCT
ejpam-3626	260	3	if	if	SCONJ
ejpam-3626	260	4	f	f	X
ejpam-3626	260	5	:	:	PUNCT
ejpam-3626	261	1	[	[	X
ejpam-3626	261	2	f	f	X
ejpam-3626	261	3	,	,	PUNCT
ejpam-3626	261	4	g]→	g]→	NOUN
ejpam-3626	261	5	c[a	c[a	NOUN
ejpam-3626	261	6	,	,	PUNCT
ejpam-3626	261	7	b	b	AUX
ejpam-3626	261	8	]	]	X
ejpam-3626	261	9	is	be	AUX
ejpam-3626	261	10	of	of	ADP
ejpam-3626	261	11	bounded	bounded	ADJ
ejpam-3626	261	12	variation	variation	NOUN
ejpam-3626	261	13	,	,	PUNCT
ejpam-3626	261	14	then	then	ADV
ejpam-3626	261	15	0	0	NUM
ejpam-3626	261	16	≤	≤	NUM
ejpam-3626	262	1	υf	υf	NOUN
ejpam-3626	262	2	(	(	PUNCT
ejpam-3626	262	3	x	x	X
ejpam-3626	262	4	)	)	PUNCT
ejpam-3626	262	5	<	<	X
ejpam-3626	263	1	+	+	PROPN
ejpam-3626	263	2	∞	∞	PROPN
ejpam-3626	263	3	,	,	PUNCT
ejpam-3626	263	4	for	for	ADP
ejpam-3626	263	5	all	all	DET
ejpam-3626	263	6	x	x	SYM
ejpam-3626	263	7	∈	∈	PROPN
ejpam-3626	263	8	[	[	X
ejpam-3626	263	9	a	a	X
ejpam-3626	263	10	,	,	PUNCT
ejpam-3626	263	11	b	b	NOUN
ejpam-3626	263	12	]	]	PUNCT
ejpam-3626	263	13	.	.	PUNCT
ejpam-3626	264	1	theorem	theorem	ADJ
ejpam-3626	264	2	10	10	NUM
ejpam-3626	264	3	.	.	PUNCT
ejpam-3626	265	1	let	let	VERB
ejpam-3626	265	2	h	h	NOUN
ejpam-3626	265	3	:	:	PUNCT
ejpam-3626	266	1	[	[	X
ejpam-3626	266	2	f	f	X
ejpam-3626	266	3	,	,	PUNCT
ejpam-3626	266	4	g	g	NOUN
ejpam-3626	266	5	]	]	X
ejpam-3626	266	6	7→	7→	NUM
ejpam-3626	266	7	c[a	c[a	NOUN
ejpam-3626	266	8	,	,	PUNCT
ejpam-3626	266	9	b	b	AUX
ejpam-3626	266	10	]	]	X
ejpam-3626	266	11	be	be	AUX
ejpam-3626	266	12	of	of	ADP
ejpam-3626	266	13	bounded	bounded	ADJ
ejpam-3626	266	14	variation	variation	NOUN
ejpam-3626	266	15	.	.	PUNCT
ejpam-3626	267	1	then	then	ADV
ejpam-3626	267	2	the	the	DET
ejpam-3626	267	3	variation	variation	NOUN
ejpam-3626	267	4	of	of	ADP
ejpam-3626	267	5	h	h	NOUN
ejpam-3626	267	6	is	be	AUX
ejpam-3626	267	7	additive	additive	ADJ
ejpam-3626	267	8	;	;	PUNCT
ejpam-3626	267	9	that	that	ADV
ejpam-3626	267	10	is	is	ADV
ejpam-3626	267	11	,	,	PUNCT
ejpam-3626	267	12	if	if	SCONJ
ejpam-3626	267	13	f	f	PROPN
ejpam-3626	267	14	≤	≤	X
ejpam-3626	267	15	r	r	NOUN
ejpam-3626	267	16	≤	≤	NUM
ejpam-3626	267	17	g	g	NOUN
ejpam-3626	267	18	,	,	PUNCT
ejpam-3626	267	19	then	then	ADV
ejpam-3626	267	20	υ(h	υ(h	VERB
ejpam-3626	267	21	;	;	PUNCT
ejpam-3626	267	22	[	[	X
ejpam-3626	267	23	f	f	X
ejpam-3626	267	24	,	,	PUNCT
ejpam-3626	267	25	g	g	NOUN
ejpam-3626	267	26	]	]	X
ejpam-3626	267	27	)	)	PUNCT
ejpam-3626	267	28	=	=	SYM
ejpam-3626	267	29	υ(h	υ(h	NOUN
ejpam-3626	267	30	;	;	PUNCT
ejpam-3626	267	31	[	[	X
ejpam-3626	267	32	f	f	X
ejpam-3626	267	33	,	,	PUNCT
ejpam-3626	267	34	r	r	NOUN
ejpam-3626	267	35	]	]	PUNCT
ejpam-3626	267	36	)	)	PUNCT
ejpam-3626	268	1	+	+	CCONJ
ejpam-3626	268	2	υ(h	υ(h	NOUN
ejpam-3626	268	3	;	;	PUNCT
ejpam-3626	268	4	[	[	X
ejpam-3626	268	5	r	r	X
ejpam-3626	268	6	,	,	PUNCT
ejpam-3626	268	7	g	g	NOUN
ejpam-3626	268	8	]	]	X
ejpam-3626	268	9	)	)	PUNCT
ejpam-3626	268	10	.	.	PUNCT
ejpam-3626	269	1	a.	a.	PROPN
ejpam-3626	269	2	cunanan	cunanan	PROPN
ejpam-3626	269	3	,	,	PUNCT
ejpam-3626	269	4	j.	j.	PROPN
ejpam-3626	269	5	benitez	benitez	PROPN
ejpam-3626	269	6	/	/	PUNCT
ejpam-3626	269	7	eur	eur	PROPN
ejpam-3626	269	8	.	.	PUNCT
ejpam-3626	270	1	j.	j.	PROPN
ejpam-3626	270	2	pure	pure	PROPN
ejpam-3626	270	3	appl	appl	PROPN
ejpam-3626	270	4	.	.	PROPN
ejpam-3626	270	5	math	math	PROPN
ejpam-3626	270	6	,	,	PUNCT
ejpam-3626	270	7	13	13	NUM
ejpam-3626	270	8	(	(	PUNCT
ejpam-3626	270	9	1	1	NUM
ejpam-3626	270	10	)	)	PUNCT
ejpam-3626	270	11	(	(	PUNCT
ejpam-3626	270	12	2020	2020	NUM
ejpam-3626	270	13	)	)	PUNCT
ejpam-3626	270	14	,	,	PUNCT
ejpam-3626	270	15	130	130	NUM
ejpam-3626	270	16	-	-	SYM
ejpam-3626	270	17	143	143	NUM
ejpam-3626	270	18	140	140	NUM
ejpam-3626	270	19	proof	proof	NOUN
ejpam-3626	270	20	.	.	PUNCT
ejpam-3626	270	21	suppose	suppose	VERB
ejpam-3626	270	22	that	that	SCONJ
ejpam-3626	270	23	h	h	NOUN
ejpam-3626	270	24	:	:	PUNCT
ejpam-3626	271	1	[	[	X
ejpam-3626	271	2	f	f	X
ejpam-3626	271	3	,	,	PUNCT
ejpam-3626	271	4	g	g	NOUN
ejpam-3626	271	5	]	]	X
ejpam-3626	271	6	→	→	SYM
ejpam-3626	271	7	c[a	c[a	NUM
ejpam-3626	271	8	,	,	PUNCT
ejpam-3626	271	9	b	b	AUX
ejpam-3626	271	10	]	]	X
ejpam-3626	271	11	is	be	AUX
ejpam-3626	271	12	of	of	ADP
ejpam-3626	271	13	bounded	bounded	ADJ
ejpam-3626	271	14	variation	variation	NOUN
ejpam-3626	271	15	.	.	PUNCT
ejpam-3626	272	1	let	let	VERB
ejpam-3626	272	2	r	r	PRON
ejpam-3626	272	3	∈	∈	PROPN
ejpam-3626	273	1	[	[	X
ejpam-3626	273	2	f	f	X
ejpam-3626	273	3	,	,	PUNCT
ejpam-3626	273	4	g	g	NOUN
ejpam-3626	273	5	]	]	PUNCT
ejpam-3626	273	6	and	and	CCONJ
ejpam-3626	273	7	d	d	NOUN
ejpam-3626	273	8	=	=	SYM
ejpam-3626	273	9	{	{	PUNCT
ejpam-3626	273	10	h0	h0	PROPN
ejpam-3626	273	11	,	,	PUNCT
ejpam-3626	273	12	.	.	PUNCT
ejpam-3626	273	13	.	.	PUNCT
ejpam-3626	273	14	.	.	PUNCT
ejpam-3626	274	1	,	,	PUNCT
ejpam-3626	274	2	hn	hn	PROPN
ejpam-3626	274	3	}	}	PUNCT
ejpam-3626	274	4	be	be	AUX
ejpam-3626	274	5	a	a	DET
ejpam-3626	274	6	division	division	NOUN
ejpam-3626	274	7	of	of	ADP
ejpam-3626	274	8	[	[	X
ejpam-3626	274	9	f	f	X
ejpam-3626	274	10	,	,	PUNCT
ejpam-3626	274	11	g	g	NOUN
ejpam-3626	274	12	]	]	PUNCT
ejpam-3626	274	13	.	.	PUNCT
ejpam-3626	275	1	then	then	ADV
ejpam-3626	275	2	d′	d′	X
ejpam-3626	275	3	=	=	SYM
ejpam-3626	275	4	{	{	PUNCT
ejpam-3626	275	5	h0	h0	PROPN
ejpam-3626	275	6	,	,	PUNCT
ejpam-3626	275	7	.	.	PUNCT
ejpam-3626	275	8	.	.	PUNCT
ejpam-3626	276	1	.	.	PUNCT
ejpam-3626	277	1	,	,	PUNCT
ejpam-3626	277	2	hk−1	hk−1	NOUN
ejpam-3626	277	3	,	,	PUNCT
ejpam-3626	277	4	r	r	PROPN
ejpam-3626	277	5	,	,	PUNCT
ejpam-3626	277	6	hk	hk	PROPN
ejpam-3626	277	7	,	,	PUNCT
ejpam-3626	277	8	.	.	PUNCT
ejpam-3626	277	9	.	.	PUNCT
ejpam-3626	278	1	.	.	PUNCT
ejpam-3626	279	1	,	,	PUNCT
ejpam-3626	279	2	hn	hn	PROPN
ejpam-3626	279	3	}	}	PUNCT
ejpam-3626	279	4	is	be	AUX
ejpam-3626	279	5	a	a	DET
ejpam-3626	279	6	refinement	refinement	NOUN
ejpam-3626	279	7	of	of	ADP
ejpam-3626	279	8	d	d	PROPN
ejpam-3626	279	9	obtained	obtain	VERB
ejpam-3626	279	10	by	by	ADP
ejpam-3626	279	11	adjoining	adjoin	VERB
ejpam-3626	279	12	r	r	NOUN
ejpam-3626	279	13	to	to	ADP
ejpam-3626	279	14	d.	d.	PROPN
ejpam-3626	279	15	thus∑	thus∑	PROPN
ejpam-3626	280	1	d	d	NOUN
ejpam-3626	280	2	∣∣h(v)−h(u	∣∣h(v)−h(u	ADV
ejpam-3626	280	3	)	)	PUNCT
ejpam-3626	280	4	∣∣	∣∣	NUM
ejpam-3626	280	5	≤∑	≤∑	PROPN
ejpam-3626	280	6	d1	d1	PROPN
ejpam-3626	280	7	∣∣h(v)−h(u	∣∣h(v)−h(u	PROPN
ejpam-3626	280	8	)	)	PUNCT
ejpam-3626	280	9	∣∣+	∣∣+	PUNCT
ejpam-3626	280	10	∑	∑	PUNCT
ejpam-3626	280	11	d2	d2	PROPN
ejpam-3626	280	12	∣∣h(v)−h(u	∣∣h(v)−h(u	ADV
ejpam-3626	280	13	)	)	PUNCT
ejpam-3626	281	1	∣∣	∣∣	X
ejpam-3626	281	2	where	where	SCONJ
ejpam-3626	281	3	d1	d1	PROPN
ejpam-3626	281	4	=	=	PUNCT
ejpam-3626	281	5	{	{	PUNCT
ejpam-3626	281	6	f	f	PROPN
ejpam-3626	281	7	=	=	PROPN
ejpam-3626	281	8	h0	h0	PROPN
ejpam-3626	281	9	,	,	PUNCT
ejpam-3626	281	10	h1	h1	PROPN
ejpam-3626	281	11	,	,	PUNCT
ejpam-3626	281	12	.	.	PUNCT
ejpam-3626	281	13	.	.	PUNCT
ejpam-3626	282	1	.	.	PUNCT
ejpam-3626	283	1	,	,	PUNCT
ejpam-3626	283	2	hk−1	hk−1	NOUN
ejpam-3626	283	3	,	,	PUNCT
ejpam-3626	283	4	r	r	NOUN
ejpam-3626	283	5	}	}	PUNCT
ejpam-3626	283	6	and	and	CCONJ
ejpam-3626	283	7	d2	d2	PROPN
ejpam-3626	283	8	=	=	SYM
ejpam-3626	283	9	{	{	PUNCT
ejpam-3626	283	10	r	r	PROPN
ejpam-3626	283	11	,	,	PUNCT
ejpam-3626	283	12	hk	hk	PROPN
ejpam-3626	283	13	,	,	PUNCT
ejpam-3626	283	14	.	.	PUNCT
ejpam-3626	283	15	.	.	PUNCT
ejpam-3626	284	1	.	.	PUNCT
ejpam-3626	285	1	,	,	PUNCT
ejpam-3626	285	2	hn	hn	PROPN
ejpam-3626	285	3	=	=	PUNCT
ejpam-3626	285	4	g	g	NOUN
ejpam-3626	285	5	}	}	PUNCT
ejpam-3626	285	6	.	.	PUNCT
ejpam-3626	286	1	note	note	VERB
ejpam-3626	286	2	that	that	SCONJ
ejpam-3626	286	3	d′	d′	PRON
ejpam-3626	286	4	=	=	SYM
ejpam-3626	286	5	d1	d1	PROPN
ejpam-3626	286	6	∪d2	∪d2	PRON
ejpam-3626	286	7	and	and	CCONJ
ejpam-3626	286	8	that∑	that∑	VERB
ejpam-3626	286	9	d1	d1	NOUN
ejpam-3626	286	10	∣∣h(v)−h(u	∣∣h(v)−h(u	ADV
ejpam-3626	286	11	)	)	PUNCT
ejpam-3626	286	12	∣∣	∣∣	NUM
ejpam-3626	286	13	≤	≤	NUM
ejpam-3626	286	14	sup	sup	NOUN
ejpam-3626	286	15	d∈d([f	d∈d([f	PROPN
ejpam-3626	286	16	,	,	PUNCT
ejpam-3626	286	17	r	r	NOUN
ejpam-3626	286	18	]	]	PUNCT
ejpam-3626	286	19	)	)	PUNCT
ejpam-3626	286	20	(	(	PUNCT
ejpam-3626	286	21	∑	∑	PUNCT
ejpam-3626	286	22	d	d	NOUN
ejpam-3626	286	23	∣∣h(v)−h(u	∣∣h(v)−h(u	NOUN
ejpam-3626	286	24	)	)	PUNCT
ejpam-3626	287	1	∣∣	∣∣	X
ejpam-3626	287	2	)	)	PUNCT
ejpam-3626	287	3	=	=	SYM
ejpam-3626	287	4	υ(h	υ(h	NOUN
ejpam-3626	287	5	;	;	PUNCT
ejpam-3626	287	6	[	[	X
ejpam-3626	287	7	f	f	X
ejpam-3626	287	8	,	,	PUNCT
ejpam-3626	287	9	r	r	NOUN
ejpam-3626	287	10	]	]	PUNCT
ejpam-3626	287	11	)	)	PUNCT
ejpam-3626	287	12	and	and	CCONJ
ejpam-3626	287	13	∑	∑	ADV
ejpam-3626	287	14	d2	d2	PROPN
ejpam-3626	287	15	∣∣h(v)−h(u	∣∣h(v)−h(u	ADV
ejpam-3626	287	16	)	)	PUNCT
ejpam-3626	287	17	∣∣	∣∣	NUM
ejpam-3626	287	18	≤	≤	NUM
ejpam-3626	287	19	sup	sup	NOUN
ejpam-3626	287	20	d∈d([r	d∈d([r	PROPN
ejpam-3626	287	21	,	,	PUNCT
ejpam-3626	287	22	g	g	NOUN
ejpam-3626	287	23	]	]	X
ejpam-3626	287	24	)	)	PUNCT
ejpam-3626	287	25	(	(	PUNCT
ejpam-3626	287	26	∑	∑	PUNCT
ejpam-3626	287	27	d	d	NOUN
ejpam-3626	287	28	∣∣h(v)−h(u	∣∣h(v)−h(u	NOUN
ejpam-3626	287	29	)	)	PUNCT
ejpam-3626	287	30	∣∣	∣∣	X
ejpam-3626	287	31	)	)	PUNCT
ejpam-3626	287	32	=	=	SYM
ejpam-3626	287	33	υ(h	υ(h	NOUN
ejpam-3626	287	34	;	;	PUNCT
ejpam-3626	287	35	[	[	X
ejpam-3626	287	36	r	r	X
ejpam-3626	287	37	,	,	PUNCT
ejpam-3626	287	38	g	g	NOUN
ejpam-3626	287	39	]	]	X
ejpam-3626	287	40	)	)	PUNCT
ejpam-3626	287	41	.	.	PUNCT
ejpam-3626	288	1	hence	hence	ADV
ejpam-3626	288	2	,	,	PUNCT
ejpam-3626	288	3	υ(h	υ(h	X
ejpam-3626	288	4	;	;	PUNCT
ejpam-3626	288	5	[	[	X
ejpam-3626	288	6	f	f	X
ejpam-3626	288	7	,	,	PUNCT
ejpam-3626	288	8	g	g	NOUN
ejpam-3626	288	9	]	]	X
ejpam-3626	288	10	)	)	PUNCT
ejpam-3626	288	11	=	=	SYM
ejpam-3626	288	12	sup	sup	PROPN
ejpam-3626	288	13	d∈d([f	d∈d([f	PROPN
ejpam-3626	288	14	,	,	PUNCT
ejpam-3626	288	15	g	g	NOUN
ejpam-3626	288	16	]	]	X
ejpam-3626	288	17	)	)	PUNCT
ejpam-3626	288	18	(	(	PUNCT
ejpam-3626	288	19	∑	∑	PUNCT
ejpam-3626	288	20	d	d	NOUN
ejpam-3626	288	21	∣∣h(v)−h(u	∣∣h(v)−h(u	NOUN
ejpam-3626	288	22	)	)	PUNCT
ejpam-3626	288	23	∣∣	∣∣	NUM
ejpam-3626	288	24	)	)	PUNCT
ejpam-3626	288	25	≤	≤	NUM
ejpam-3626	288	26	υ(h	υ(h	NOUN
ejpam-3626	288	27	;	;	PUNCT
ejpam-3626	288	28	[	[	X
ejpam-3626	288	29	f	f	X
ejpam-3626	288	30	,	,	PUNCT
ejpam-3626	288	31	r	r	NOUN
ejpam-3626	288	32	]	]	PUNCT
ejpam-3626	288	33	)	)	PUNCT
ejpam-3626	289	1	+	+	CCONJ
ejpam-3626	289	2	υ(h	υ(h	NOUN
ejpam-3626	289	3	;	;	PUNCT
ejpam-3626	289	4	[	[	X
ejpam-3626	289	5	r	r	X
ejpam-3626	289	6	,	,	PUNCT
ejpam-3626	289	7	g	g	NOUN
ejpam-3626	289	8	]	]	X
ejpam-3626	289	9	)	)	PUNCT
ejpam-3626	289	10	.	.	PUNCT
ejpam-3626	290	1	on	on	ADP
ejpam-3626	290	2	the	the	DET
ejpam-3626	290	3	other	other	ADJ
ejpam-3626	290	4	hand	hand	NOUN
ejpam-3626	290	5	,	,	PUNCT
ejpam-3626	290	6	for	for	ADP
ejpam-3626	290	7	any	any	DET
ejpam-3626	290	8	d1	d1	PROPN
ejpam-3626	290	9	∈	∈	PROPN
ejpam-3626	290	10	d([f	d([f	PROPN
ejpam-3626	290	11	,	,	PUNCT
ejpam-3626	290	12	r	r	NOUN
ejpam-3626	290	13	]	]	PUNCT
ejpam-3626	290	14	)	)	PUNCT
ejpam-3626	290	15	and	and	CCONJ
ejpam-3626	290	16	d2	d2	PROPN
ejpam-3626	290	17	∈	∈	PROPN
ejpam-3626	290	18	d([r	d([r	PROPN
ejpam-3626	290	19	,	,	PUNCT
ejpam-3626	290	20	g	g	NOUN
ejpam-3626	290	21	]	]	X
ejpam-3626	290	22	)	)	PUNCT
ejpam-3626	290	23	,	,	PUNCT
ejpam-3626	290	24	their	their	PRON
ejpam-3626	290	25	union	union	NOUN
ejpam-3626	290	26	d′	d′	X
ejpam-3626	290	27	=	=	SYM
ejpam-3626	290	28	d1	d1	PROPN
ejpam-3626	290	29	∪	∪	VERB
ejpam-3626	290	30	d2	d2	PROPN
ejpam-3626	290	31	∈	∈	PROPN
ejpam-3626	290	32	dr([f	dr([f	PROPN
ejpam-3626	290	33	,	,	PUNCT
ejpam-3626	290	34	g	g	NOUN
ejpam-3626	290	35	]	]	X
ejpam-3626	290	36	)	)	PUNCT
ejpam-3626	290	37	,	,	PUNCT
ejpam-3626	290	38	where	where	SCONJ
ejpam-3626	290	39	dr([f	dr([f	PROPN
ejpam-3626	290	40	,	,	PUNCT
ejpam-3626	290	41	g	g	NOUN
ejpam-3626	290	42	]	]	PUNCT
ejpam-3626	290	43	)	)	PUNCT
ejpam-3626	290	44	is	be	AUX
ejpam-3626	290	45	the	the	DET
ejpam-3626	290	46	set	set	NOUN
ejpam-3626	290	47	of	of	ADP
ejpam-3626	290	48	all	all	DET
ejpam-3626	290	49	divisions	division	NOUN
ejpam-3626	290	50	of	of	ADP
ejpam-3626	290	51	[	[	X
ejpam-3626	290	52	f	f	X
ejpam-3626	290	53	,	,	PUNCT
ejpam-3626	290	54	g	g	NOUN
ejpam-3626	290	55	]	]	PUNCT
ejpam-3626	290	56	with	with	ADP
ejpam-3626	290	57	r	r	NOUN
ejpam-3626	290	58	as	as	ADP
ejpam-3626	290	59	one	one	NUM
ejpam-3626	290	60	of	of	ADP
ejpam-3626	290	61	the	the	DET
ejpam-3626	290	62	division	division	NOUN
ejpam-3626	290	63	points	point	NOUN
ejpam-3626	290	64	.	.	PUNCT
ejpam-3626	291	1	note	note	VERB
ejpam-3626	291	2	that	that	SCONJ
ejpam-3626	291	3	dr([f	dr([f	PROPN
ejpam-3626	291	4	,	,	PUNCT
ejpam-3626	291	5	g	g	NOUN
ejpam-3626	291	6	]	]	X
ejpam-3626	291	7	)	)	PUNCT
ejpam-3626	291	8	⊆	⊆	NUM
ejpam-3626	291	9	d([f	d([f	NOUN
ejpam-3626	291	10	,	,	PUNCT
ejpam-3626	291	11	g	g	NOUN
ejpam-3626	291	12	]	]	X
ejpam-3626	291	13	)	)	PUNCT
ejpam-3626	291	14	.	.	PUNCT
ejpam-3626	292	1	hence	hence	ADV
ejpam-3626	292	2	,	,	PUNCT
ejpam-3626	292	3	sup	sup	PROPN
ejpam-3626	292	4	d′∈dr([f	d′∈dr([f	PROPN
ejpam-3626	292	5	,	,	PUNCT
ejpam-3626	292	6	g	g	NOUN
ejpam-3626	292	7	]	]	X
ejpam-3626	292	8	)	)	PUNCT
ejpam-3626	292	9	(	(	PUNCT
ejpam-3626	292	10	∑	∑	PUNCT
ejpam-3626	292	11	d′	d′	ADJ
ejpam-3626	292	12	∣∣h(v)−h(u	∣∣h(v)−h(u	CCONJ
ejpam-3626	292	13	)	)	PUNCT
ejpam-3626	292	14	∣∣	∣∣	NUM
ejpam-3626	292	15	)	)	PUNCT
ejpam-3626	292	16	≤	≤	NUM
ejpam-3626	292	17	sup	sup	NOUN
ejpam-3626	292	18	d∈d([f	d∈d([f	PROPN
ejpam-3626	292	19	,	,	PUNCT
ejpam-3626	292	20	g	g	NOUN
ejpam-3626	292	21	]	]	X
ejpam-3626	292	22	)	)	PUNCT
ejpam-3626	292	23	(	(	PUNCT
ejpam-3626	292	24	∑	∑	PUNCT
ejpam-3626	292	25	d	d	NOUN
ejpam-3626	292	26	∣∣h(v)−h(u	∣∣h(v)−h(u	NOUN
ejpam-3626	292	27	)	)	PUNCT
ejpam-3626	292	28	∣∣	∣∣	X
ejpam-3626	292	29	)	)	PUNCT
ejpam-3626	292	30	=	=	SYM
ejpam-3626	292	31	υ(h	υ(h	NOUN
ejpam-3626	292	32	;	;	PUNCT
ejpam-3626	292	33	[	[	X
ejpam-3626	292	34	f	f	X
ejpam-3626	292	35	,	,	PUNCT
ejpam-3626	292	36	g	g	NOUN
ejpam-3626	292	37	]	]	X
ejpam-3626	292	38	)	)	PUNCT
ejpam-3626	292	39	thus	thus	ADV
ejpam-3626	292	40	,	,	PUNCT
ejpam-3626	292	41	υ(h	υ(h	X
ejpam-3626	292	42	;	;	PUNCT
ejpam-3626	292	43	[	[	X
ejpam-3626	292	44	f	f	X
ejpam-3626	292	45	,	,	PUNCT
ejpam-3626	292	46	r	r	NOUN
ejpam-3626	292	47	]	]	PUNCT
ejpam-3626	292	48	)	)	PUNCT
ejpam-3626	293	1	+	+	CCONJ
ejpam-3626	293	2	υ(h	υ(h	NOUN
ejpam-3626	293	3	;	;	PUNCT
ejpam-3626	293	4	[	[	X
ejpam-3626	293	5	r	r	X
ejpam-3626	293	6	,	,	PUNCT
ejpam-3626	293	7	g	g	NOUN
ejpam-3626	293	8	]	]	X
ejpam-3626	293	9	)	)	PUNCT
ejpam-3626	293	10	≤	≤	NUM
ejpam-3626	293	11	sup	sup	NOUN
ejpam-3626	293	12	d′∈dr([f	d′∈dr([f	PROPN
ejpam-3626	293	13	,	,	PUNCT
ejpam-3626	293	14	g	g	NOUN
ejpam-3626	293	15	]	]	X
ejpam-3626	293	16	)	)	PUNCT
ejpam-3626	293	17	(	(	PUNCT
ejpam-3626	293	18	∑	∑	PUNCT
ejpam-3626	293	19	d′	d′	ADJ
ejpam-3626	293	20	∣∣h(v)−h(u	∣∣h(v)−h(u	CCONJ
ejpam-3626	293	21	)	)	PUNCT
ejpam-3626	293	22	∣∣	∣∣	NUM
ejpam-3626	293	23	)	)	PUNCT
ejpam-3626	293	24	≤	≤	NUM
ejpam-3626	293	25	υ(h	υ(h	NOUN
ejpam-3626	293	26	;	;	PUNCT
ejpam-3626	293	27	[	[	X
ejpam-3626	293	28	f	f	X
ejpam-3626	293	29	,	,	PUNCT
ejpam-3626	293	30	g	g	NOUN
ejpam-3626	293	31	]	]	X
ejpam-3626	293	32	)	)	PUNCT
ejpam-3626	293	33	.	.	PUNCT
ejpam-3626	294	1	therefore	therefore	ADV
ejpam-3626	294	2	,	,	PUNCT
ejpam-3626	294	3	combining	combine	VERB
ejpam-3626	294	4	the	the	DET
ejpam-3626	294	5	two	two	NUM
ejpam-3626	294	6	inequalities	inequality	NOUN
ejpam-3626	294	7	υ(h	υ(h	NOUN
ejpam-3626	294	8	;	;	PUNCT
ejpam-3626	294	9	[	[	X
ejpam-3626	294	10	f	f	X
ejpam-3626	294	11	,	,	PUNCT
ejpam-3626	294	12	r	r	NOUN
ejpam-3626	294	13	]	]	PUNCT
ejpam-3626	294	14	)	)	PUNCT
ejpam-3626	295	1	+	+	CCONJ
ejpam-3626	295	2	υ(h	υ(h	NOUN
ejpam-3626	295	3	;	;	PUNCT
ejpam-3626	295	4	[	[	X
ejpam-3626	295	5	r	r	X
ejpam-3626	295	6	,	,	PUNCT
ejpam-3626	295	7	g	g	NOUN
ejpam-3626	295	8	]	]	X
ejpam-3626	295	9	)	)	PUNCT
ejpam-3626	295	10	=	=	SYM
ejpam-3626	295	11	υ(h	υ(h	NOUN
ejpam-3626	295	12	;	;	PUNCT
ejpam-3626	295	13	[	[	X
ejpam-3626	295	14	f	f	X
ejpam-3626	295	15	,	,	PUNCT
ejpam-3626	295	16	g	g	NOUN
ejpam-3626	295	17	]	]	X
ejpam-3626	295	18	)	)	PUNCT
ejpam-3626	295	19	.	.	PUNCT
ejpam-3626	296	1	theorem	theorem	VERB
ejpam-3626	296	2	11	11	NUM
ejpam-3626	296	3	.	.	PUNCT
ejpam-3626	297	1	(	(	PUNCT
ejpam-3626	297	2	existence	existence	NOUN
ejpam-3626	297	3	theorem	theorem	VERB
ejpam-3626	297	4	)	)	PUNCT
ejpam-3626	297	5	if	if	SCONJ
ejpam-3626	297	6	f	f	X
ejpam-3626	297	7	:	:	PUNCT
ejpam-3626	298	1	[	[	X
ejpam-3626	298	2	f	f	X
ejpam-3626	298	3	,	,	PUNCT
ejpam-3626	298	4	g	g	NOUN
ejpam-3626	298	5	]	]	X
ejpam-3626	298	6	→	→	SYM
ejpam-3626	298	7	c[a	c[a	NUM
ejpam-3626	298	8	,	,	PUNCT
ejpam-3626	298	9	b	b	AUX
ejpam-3626	298	10	]	]	PUNCT
ejpam-3626	298	11	is	be	AUX
ejpam-3626	298	12	continuous	continuous	ADJ
ejpam-3626	298	13	and	and	CCONJ
ejpam-3626	298	14	h	h	NOUN
ejpam-3626	298	15	:	:	PUNCT
ejpam-3626	299	1	[	[	X
ejpam-3626	299	2	f	f	X
ejpam-3626	299	3	,	,	PUNCT
ejpam-3626	299	4	g	g	NOUN
ejpam-3626	299	5	]	]	X
ejpam-3626	299	6	→	→	SYM
ejpam-3626	299	7	c[a	c[a	NUM
ejpam-3626	299	8	,	,	PUNCT
ejpam-3626	299	9	b	b	AUX
ejpam-3626	299	10	]	]	X
ejpam-3626	299	11	is	be	AUX
ejpam-3626	299	12	of	of	ADP
ejpam-3626	299	13	bounded	bounded	ADJ
ejpam-3626	299	14	variation	variation	NOUN
ejpam-3626	299	15	on	on	ADP
ejpam-3626	299	16	[	[	X
ejpam-3626	299	17	f	f	X
ejpam-3626	299	18	,	,	PUNCT
ejpam-3626	299	19	g	g	PROPN
ejpam-3626	299	20	]	]	X
ejpam-3626	299	21	,	,	PUNCT
ejpam-3626	299	22	then	then	ADV
ejpam-3626	299	23	f	f	PROPN
ejpam-3626	299	24	∈	∈	PROPN
ejpam-3626	299	25	hks([f	hks([f	NOUN
ejpam-3626	299	26	,	,	PUNCT
ejpam-3626	299	27	g	g	NOUN
ejpam-3626	299	28	]	]	X
ejpam-3626	299	29	,	,	PUNCT
ejpam-3626	299	30	h	h	NOUN
ejpam-3626	299	31	)	)	PUNCT
ejpam-3626	299	32	.	.	PUNCT
ejpam-3626	300	1	proof	proof	NOUN
ejpam-3626	300	2	.	.	PUNCT
ejpam-3626	301	1	let	let	VERB
ejpam-3626	301	2	ε	ε	PROPN
ejpam-3626	301	3	>	>	X
ejpam-3626	301	4	0	0	PROPN
ejpam-3626	301	5	.	.	PUNCT
ejpam-3626	302	1	since	since	SCONJ
ejpam-3626	302	2	h	h	NOUN
ejpam-3626	302	3	is	be	AUX
ejpam-3626	302	4	of	of	ADP
ejpam-3626	302	5	bounded	bounded	ADJ
ejpam-3626	302	6	variation	variation	NOUN
ejpam-3626	302	7	,	,	PUNCT
ejpam-3626	302	8	υh	υh	NOUN
ejpam-3626	302	9	∈	∈	PROPN
ejpam-3626	302	10	c[a	c[a	NOUN
ejpam-3626	302	11	,	,	PUNCT
ejpam-3626	302	12	b	b	NOUN
ejpam-3626	302	13	]	]	X
ejpam-3626	302	14	.	.	PUNCT
ejpam-3626	303	1	this	this	PRON
ejpam-3626	303	2	means	mean	VERB
ejpam-3626	303	3	that	that	SCONJ
ejpam-3626	303	4	there	there	PRON
ejpam-3626	303	5	exists	exist	VERB
ejpam-3626	303	6	k	k	PROPN
ejpam-3626	303	7	>	>	X
ejpam-3626	303	8	0	0	NUM
ejpam-3626	303	9	such	such	ADJ
ejpam-3626	303	10	that	that	PRON
ejpam-3626	303	11	υh(x	υh(x	PUNCT
ejpam-3626	303	12	)	)	PUNCT
ejpam-3626	303	13	≤	≤	NUM
ejpam-3626	304	1	k	k	NOUN
ejpam-3626	304	2	for	for	ADP
ejpam-3626	304	3	all	all	DET
ejpam-3626	304	4	x	x	SYM
ejpam-3626	304	5	∈	∈	PROPN
ejpam-3626	304	6	[	[	X
ejpam-3626	304	7	a	a	X
ejpam-3626	304	8	,	,	PUNCT
ejpam-3626	304	9	b	b	NOUN
ejpam-3626	304	10	]	]	PUNCT
ejpam-3626	304	11	.	.	PUNCT
ejpam-3626	305	1	since	since	SCONJ
ejpam-3626	305	2	f	f	PROPN
ejpam-3626	305	3	is	be	AUX
ejpam-3626	305	4	continuous	continuous	ADJ
ejpam-3626	305	5	on	on	ADP
ejpam-3626	305	6	[	[	X
ejpam-3626	305	7	f	f	X
ejpam-3626	305	8	,	,	PUNCT
ejpam-3626	305	9	g	g	PROPN
ejpam-3626	305	10	]	]	X
ejpam-3626	305	11	,	,	PUNCT
ejpam-3626	305	12	for	for	ADP
ejpam-3626	305	13	all	all	DET
ejpam-3626	305	14	h0	h0	NOUN
ejpam-3626	305	15	∈	∈	PROPN
ejpam-3626	305	16	[	[	X
ejpam-3626	305	17	f	f	X
ejpam-3626	305	18	,	,	PUNCT
ejpam-3626	305	19	g	g	NOUN
ejpam-3626	305	20	]	]	PUNCT
ejpam-3626	305	21	there	there	PRON
ejpam-3626	305	22	exists	exist	VERB
ejpam-3626	305	23	δ0(h0	δ0(h0	NOUN
ejpam-3626	305	24	)	)	PUNCT
ejpam-3626	305	25	>	>	X
ejpam-3626	305	26	θ	θ	PROPN
ejpam-3626	305	27	in	in	ADP
ejpam-3626	305	28	c[a	c[a	NUM
ejpam-3626	305	29	,	,	PUNCT
ejpam-3626	305	30	b	b	X
ejpam-3626	305	31	]	]	PUNCT
ejpam-3626	306	1	such	such	ADJ
ejpam-3626	306	2	that	that	SCONJ
ejpam-3626	306	3	whenever	whenever	SCONJ
ejpam-3626	306	4	h	h	PRON
ejpam-3626	306	5	∈	∈	PROPN
ejpam-3626	307	1	[	[	X
ejpam-3626	307	2	f	f	X
ejpam-3626	307	3	,	,	PUNCT
ejpam-3626	307	4	g	g	NOUN
ejpam-3626	307	5	]	]	PUNCT
ejpam-3626	307	6	with	with	ADP
ejpam-3626	307	7	|h−	|h−	NOUN
ejpam-3626	307	8	h0|	h0|	X
ejpam-3626	307	9	<	<	X
ejpam-3626	307	10	δ0(h0	δ0(h0	NUM
ejpam-3626	307	11	)	)	PUNCT
ejpam-3626	307	12	,	,	PUNCT
ejpam-3626	307	13	we	we	PRON
ejpam-3626	307	14	have	have	VERB
ejpam-3626	307	15	|f	|f	PROPN
ejpam-3626	308	1	(	(	PUNCT
ejpam-3626	308	2	h)−	h)−	PROPN
ejpam-3626	308	3	f	f	X
ejpam-3626	308	4	(	(	PUNCT
ejpam-3626	308	5	h0)|	h0)|	PROPN
ejpam-3626	308	6	<	<	X
ejpam-3626	308	7	ε	ε	PROPN
ejpam-3626	308	8	·	·	PUNCT
ejpam-3626	308	9	e.	e.	PROPN
ejpam-3626	308	10	a.	a.	PROPN
ejpam-3626	308	11	cunanan	cunanan	PROPN
ejpam-3626	308	12	,	,	PUNCT
ejpam-3626	308	13	j.	j.	PROPN
ejpam-3626	308	14	benitez	benitez	PROPN
ejpam-3626	308	15	/	/	PUNCT
ejpam-3626	308	16	eur	eur	PROPN
ejpam-3626	308	17	.	.	PUNCT
ejpam-3626	309	1	j.	j.	PROPN
ejpam-3626	309	2	pure	pure	PROPN
ejpam-3626	309	3	appl	appl	PROPN
ejpam-3626	309	4	.	.	PROPN
ejpam-3626	309	5	math	math	PROPN
ejpam-3626	309	6	,	,	PUNCT
ejpam-3626	309	7	13	13	NUM
ejpam-3626	309	8	(	(	PUNCT
ejpam-3626	309	9	1	1	NUM
ejpam-3626	309	10	)	)	PUNCT
ejpam-3626	309	11	(	(	PUNCT
ejpam-3626	309	12	2020	2020	NUM
ejpam-3626	309	13	)	)	PUNCT
ejpam-3626	309	14	,	,	PUNCT
ejpam-3626	309	15	130	130	NUM
ejpam-3626	309	16	-	-	SYM
ejpam-3626	309	17	143	143	NUM
ejpam-3626	309	18	141	141	NUM
ejpam-3626	309	19	define	define	VERB
ejpam-3626	309	20	a	a	DET
ejpam-3626	309	21	gauge	gauge	NOUN
ejpam-3626	309	22	δ	δ	NOUN
ejpam-3626	309	23	on	on	ADP
ejpam-3626	309	24	[	[	X
ejpam-3626	309	25	f	f	X
ejpam-3626	309	26	,	,	PUNCT
ejpam-3626	309	27	g	g	NOUN
ejpam-3626	309	28	]	]	PUNCT
ejpam-3626	309	29	by	by	ADP
ejpam-3626	309	30	δ(h	δ(h	PROPN
ejpam-3626	309	31	)	)	PUNCT
ejpam-3626	309	32	=	=	SYM
ejpam-3626	310	1	δ0(h	δ0(h	PROPN
ejpam-3626	310	2	)	)	PUNCT
ejpam-3626	310	3	2	2	NUM
ejpam-3626	310	4	,	,	PUNCT
ejpam-3626	310	5	for	for	ADP
ejpam-3626	310	6	all	all	DET
ejpam-3626	310	7	h	h	NOUN
ejpam-3626	310	8	∈	∈	PROPN
ejpam-3626	311	1	[	[	X
ejpam-3626	311	2	f	f	X
ejpam-3626	311	3	,	,	PUNCT
ejpam-3626	311	4	g	g	NOUN
ejpam-3626	311	5	]	]	PUNCT
ejpam-3626	311	6	.	.	PUNCT
ejpam-3626	312	1	let	let	VERB
ejpam-3626	312	2	d	d	NOUN
ejpam-3626	312	3	=	=	PRON
ejpam-3626	312	4	{	{	PUNCT
ejpam-3626	312	5	(	(	PUNCT
ejpam-3626	312	6	[	[	X
ejpam-3626	312	7	f	f	X
ejpam-3626	312	8	,	,	PUNCT
ejpam-3626	312	9	h1	h1	PROPN
ejpam-3626	312	10	]	]	PUNCT
ejpam-3626	312	11	,	,	PUNCT
ejpam-3626	312	12	t1	t1	NOUN
ejpam-3626	312	13	)	)	PUNCT
ejpam-3626	312	14	,	,	PUNCT
ejpam-3626	312	15	(	(	PUNCT
ejpam-3626	312	16	[	[	X
ejpam-3626	312	17	h1	h1	NOUN
ejpam-3626	312	18	,	,	PUNCT
ejpam-3626	312	19	h2	h2	PROPN
ejpam-3626	312	20	]	]	PUNCT
ejpam-3626	312	21	,	,	PUNCT
ejpam-3626	312	22	t2	t2	NOUN
ejpam-3626	312	23	)	)	PUNCT
ejpam-3626	312	24	,	,	PUNCT
ejpam-3626	312	25	.	.	PUNCT
ejpam-3626	312	26	.	.	PUNCT
ejpam-3626	313	1	.	.	PUNCT
ejpam-3626	314	1	,	,	PUNCT
ejpam-3626	314	2	(	(	PUNCT
ejpam-3626	314	3	[	[	X
ejpam-3626	314	4	hm−1	hm−1	NOUN
ejpam-3626	314	5	,	,	PUNCT
ejpam-3626	314	6	g	g	NOUN
ejpam-3626	314	7	]	]	X
ejpam-3626	314	8	,	,	PUNCT
ejpam-3626	314	9	tm	tm	NOUN
ejpam-3626	314	10	)	)	PUNCT
ejpam-3626	314	11	}	}	PUNCT
ejpam-3626	314	12	and	and	CCONJ
ejpam-3626	314	13	q	q	NOUN
ejpam-3626	314	14	=	=	X
ejpam-3626	314	15	{	{	PUNCT
ejpam-3626	314	16	(	(	PUNCT
ejpam-3626	314	17	[	[	X
ejpam-3626	314	18	f	f	X
ejpam-3626	314	19	,	,	PUNCT
ejpam-3626	314	20	k1	k1	PROPN
ejpam-3626	314	21	]	]	PUNCT
ejpam-3626	314	22	,	,	PUNCT
ejpam-3626	314	23	r1	r1	PROPN
ejpam-3626	314	24	)	)	PUNCT
ejpam-3626	314	25	,	,	PUNCT
ejpam-3626	314	26	(	(	PUNCT
ejpam-3626	314	27	[	[	X
ejpam-3626	314	28	k1	k1	X
ejpam-3626	314	29	,	,	PUNCT
ejpam-3626	314	30	k2	k2	NOUN
ejpam-3626	314	31	]	]	PUNCT
ejpam-3626	314	32	,	,	PUNCT
ejpam-3626	314	33	r2	r2	PROPN
ejpam-3626	314	34	)	)	PUNCT
ejpam-3626	314	35	,	,	PUNCT
ejpam-3626	314	36	.	.	PUNCT
ejpam-3626	314	37	.	.	PUNCT
ejpam-3626	314	38	.	.	PUNCT
ejpam-3626	315	1	,	,	PUNCT
ejpam-3626	315	2	(	(	PUNCT
ejpam-3626	315	3	[	[	X
ejpam-3626	315	4	kq−1	kq−1	X
ejpam-3626	315	5	,	,	PUNCT
ejpam-3626	315	6	g	g	PROPN
ejpam-3626	315	7	]	]	PUNCT
ejpam-3626	315	8	,	,	PUNCT
ejpam-3626	315	9	rq	rq	INTJ
ejpam-3626	315	10	)	)	PUNCT
ejpam-3626	315	11	}	}	PUNCT
ejpam-3626	315	12	be	be	VERB
ejpam-3626	315	13	δ	δ	PROPN
ejpam-3626	315	14	-	-	PUNCT
ejpam-3626	315	15	fine	fine	ADJ
ejpam-3626	315	16	tagged	tag	VERB
ejpam-3626	315	17	divisions	division	NOUN
ejpam-3626	315	18	of	of	ADP
ejpam-3626	315	19	[	[	X
ejpam-3626	315	20	f	f	X
ejpam-3626	315	21	,	,	PUNCT
ejpam-3626	315	22	g	g	NOUN
ejpam-3626	315	23	]	]	PUNCT
ejpam-3626	315	24	.	.	PUNCT
ejpam-3626	316	1	then	then	ADV
ejpam-3626	316	2	there	there	PRON
ejpam-3626	316	3	exists	exist	VERB
ejpam-3626	316	4	a	a	DET
ejpam-3626	316	5	tagged	tag	VERB
ejpam-3626	316	6	division	division	NOUN
ejpam-3626	316	7	d0	d0	NOUN
ejpam-3626	316	8	such	such	ADJ
ejpam-3626	316	9	that	that	SCONJ
ejpam-3626	316	10	d	d	PROPN
ejpam-3626	316	11	�	�	PROPN
ejpam-3626	316	12	d0	d0	PROPN
ejpam-3626	316	13	and	and	CCONJ
ejpam-3626	316	14	q	q	NOUN
ejpam-3626	316	15	�	�	PROPN
ejpam-3626	316	16	d0	d0	NOUN
ejpam-3626	316	17	.	.	PUNCT
ejpam-3626	317	1	now	now	ADV
ejpam-3626	317	2	,	,	PUNCT
ejpam-3626	317	3	for	for	SCONJ
ejpam-3626	317	4	every	every	DET
ejpam-3626	317	5	(	(	PUNCT
ejpam-3626	317	6	[	[	X
ejpam-3626	317	7	hi−1	hi−1	PROPN
ejpam-3626	317	8	,	,	PUNCT
ejpam-3626	317	9	hi	hi	ADJ
ejpam-3626	317	10	]	]	PUNCT
ejpam-3626	317	11	,	,	PUNCT
ejpam-3626	317	12	ti	ti	NOUN
ejpam-3626	317	13	)	)	PUNCT
ejpam-3626	317	14	∈	∈	PROPN
ejpam-3626	317	15	d	d	PROPN
ejpam-3626	317	16	,	,	PUNCT
ejpam-3626	317	17	f	f	PROPN
ejpam-3626	317	18	=	=	PROPN
ejpam-3626	317	19	h0	h0	PROPN
ejpam-3626	317	20	,	,	PUNCT
ejpam-3626	317	21	hm	hm	INTJ
ejpam-3626	317	22	=	=	SYM
ejpam-3626	317	23	g	g	NOUN
ejpam-3626	317	24	,	,	PUNCT
ejpam-3626	317	25	1	1	NUM
ejpam-3626	317	26	≤	≤	NUM
ejpam-3626	317	27	i	i	X
ejpam-3626	317	28	≤	≤	NOUN
ejpam-3626	317	29	m	m	VERB
ejpam-3626	317	30	,	,	PUNCT
ejpam-3626	317	31	consider	consider	VERB
ejpam-3626	317	32	the	the	DET
ejpam-3626	317	33	difference	difference	NOUN
ejpam-3626	317	34	∆(hi−1	∆(hi−1	PROPN
ejpam-3626	317	35	,	,	PUNCT
ejpam-3626	317	36	hi	hi	INTJ
ejpam-3626	317	37	)	)	PUNCT
ejpam-3626	317	38	=	=	SYM
ejpam-3626	317	39	f	f	PROPN
ejpam-3626	317	40	(	(	PUNCT
ejpam-3626	317	41	ti	ti	NOUN
ejpam-3626	317	42	)	)	PUNCT
ejpam-3626	317	43	[	[	PUNCT
ejpam-3626	317	44	h(hi)−h(hi−1	h(hi)−h(hi−1	PROPN
ejpam-3626	317	45	)	)	PUNCT
ejpam-3626	317	46	]	]	PUNCT
ejpam-3626	318	1	−	−	PROPN
ejpam-3626	318	2	s(f	s(f	PROPN
ejpam-3626	318	3	,	,	PUNCT
ejpam-3626	318	4	h;pi	h;pi	NOUN
ejpam-3626	318	5	)	)	PUNCT
ejpam-3626	318	6	where	where	SCONJ
ejpam-3626	318	7	pi	pi	NOUN
ejpam-3626	318	8	=	=	PUNCT
ejpam-3626	318	9	{	{	PUNCT
ejpam-3626	318	10	(	(	PUNCT
ejpam-3626	318	11	[	[	PUNCT
ejpam-3626	318	12	z	z	X
ejpam-3626	318	13	(	(	PUNCT
ejpam-3626	318	14	i	i	NOUN
ejpam-3626	318	15	)	)	PUNCT
ejpam-3626	318	16	j−1	j−1	PROPN
ejpam-3626	318	17	,	,	PUNCT
ejpam-3626	318	18	z	z	PROPN
ejpam-3626	318	19	(	(	PUNCT
ejpam-3626	318	20	i	i	NOUN
ejpam-3626	318	21	)	)	PUNCT
ejpam-3626	318	22	j	j	PROPN
ejpam-3626	318	23	]	]	PUNCT
ejpam-3626	318	24	,	,	PUNCT
ejpam-3626	318	25	s	s	X
ejpam-3626	318	26	(	(	PUNCT
ejpam-3626	318	27	i	i	NOUN
ejpam-3626	318	28	)	)	PUNCT
ejpam-3626	318	29	j	j	PROPN
ejpam-3626	318	30	)	)	PUNCT
ejpam-3626	318	31	}	}	PUNCT
ejpam-3626	318	32	ni	ni	PROPN
ejpam-3626	318	33	j−1	j−1	PROPN
ejpam-3626	318	34	,	,	PUNCT
ejpam-3626	318	35	z	z	PROPN
ejpam-3626	318	36	(	(	PUNCT
ejpam-3626	318	37	i	i	NOUN
ejpam-3626	318	38	)	)	PUNCT
ejpam-3626	318	39	0	0	PUNCT
ejpam-3626	319	1	=	=	SYM
ejpam-3626	319	2	hi−1	hi−1	PROPN
ejpam-3626	319	3	,	,	PUNCT
ejpam-3626	319	4	z	z	PROPN
ejpam-3626	319	5	(	(	PUNCT
ejpam-3626	319	6	i	i	NOUN
ejpam-3626	319	7	)	)	PUNCT
ejpam-3626	319	8	ni	ni	PROPN
ejpam-3626	320	1	=	=	PRON
ejpam-3626	320	2	hi	hi	PROPN
ejpam-3626	320	3	is	be	AUX
ejpam-3626	320	4	the	the	DET
ejpam-3626	320	5	refinement	refinement	NOUN
ejpam-3626	320	6	of	of	ADP
ejpam-3626	320	7	(	(	PUNCT
ejpam-3626	320	8	[	[	X
ejpam-3626	320	9	hi−1	hi−1	PROPN
ejpam-3626	320	10	,	,	PUNCT
ejpam-3626	320	11	hi	hi	ADJ
ejpam-3626	320	12	]	]	PUNCT
ejpam-3626	320	13	,	,	PUNCT
ejpam-3626	320	14	ti	ti	NOUN
ejpam-3626	320	15	)	)	PUNCT
ejpam-3626	320	16	in	in	ADP
ejpam-3626	320	17	d0	d0	NOUN
ejpam-3626	320	18	.	.	PUNCT
ejpam-3626	321	1	then	then	ADV
ejpam-3626	321	2	∆(hi−1	∆(hi−1	PROPN
ejpam-3626	321	3	,	,	PUNCT
ejpam-3626	321	4	hi	hi	INTJ
ejpam-3626	321	5	)	)	PUNCT
ejpam-3626	321	6	=	=	PUNCT
ejpam-3626	322	1	ni∑	ni∑	NOUN
ejpam-3626	322	2	j=1	j=1	NOUN
ejpam-3626	322	3	[	[	PUNCT
ejpam-3626	322	4	f	f	X
ejpam-3626	322	5	(	(	PUNCT
ejpam-3626	322	6	ti)−	ti)−	NOUN
ejpam-3626	322	7	f	f	X
ejpam-3626	322	8	(	(	PUNCT
ejpam-3626	322	9	s	s	X
ejpam-3626	322	10	(	(	PUNCT
ejpam-3626	322	11	i	i	NOUN
ejpam-3626	322	12	)	)	PUNCT
ejpam-3626	322	13	j	j	PROPN
ejpam-3626	322	14	)	)	PUNCT
ejpam-3626	322	15	]	]	PUNCT
ejpam-3626	322	16	[	[	PUNCT
ejpam-3626	322	17	h(z	h(z	NOUN
ejpam-3626	322	18	(	(	PUNCT
ejpam-3626	322	19	i	i	PROPN
ejpam-3626	322	20	)	)	PUNCT
ejpam-3626	322	21	j	j	PROPN
ejpam-3626	322	22	)	)	PUNCT
ejpam-3626	322	23	−h(z	−h(z	PROPN
ejpam-3626	322	24	(	(	PUNCT
ejpam-3626	322	25	i	i	NOUN
ejpam-3626	322	26	)	)	PUNCT
ejpam-3626	322	27	j−1	j−1	PROPN
ejpam-3626	322	28	)	)	PUNCT
ejpam-3626	322	29	]	]	PUNCT
ejpam-3626	322	30	.	.	PUNCT
ejpam-3626	323	1	now	now	ADV
ejpam-3626	323	2	,	,	PUNCT
ejpam-3626	323	3	s	s	X
ejpam-3626	323	4	(	(	PUNCT
ejpam-3626	323	5	i	i	NOUN
ejpam-3626	323	6	)	)	PUNCT
ejpam-3626	323	7	j	j	PROPN
ejpam-3626	323	8	,	,	PUNCT
ejpam-3626	323	9	ti	ti	NOUN
ejpam-3626	323	10	∈	∈	PROPN
ejpam-3626	323	11	[	[	X
ejpam-3626	323	12	hi−1	hi−1	PROPN
ejpam-3626	323	13	,	,	PUNCT
ejpam-3626	323	14	hi	hi	INTJ
ejpam-3626	323	15	]	]	X
ejpam-3626	323	16	⊆	⊆	NUM
ejpam-3626	323	17	(	(	PUNCT
ejpam-3626	323	18	ti	ti	NOUN
ejpam-3626	323	19	−	−	PROPN
ejpam-3626	323	20	δ(ti	δ(ti	PROPN
ejpam-3626	323	21	)	)	PUNCT
ejpam-3626	323	22	,	,	PUNCT
ejpam-3626	323	23	ti	ti	X
ejpam-3626	323	24	+	+	CCONJ
ejpam-3626	323	25	δ(ti	δ(ti	NOUN
ejpam-3626	323	26	)	)	PUNCT
ejpam-3626	323	27	)	)	PUNCT
ejpam-3626	323	28	which	which	PRON
ejpam-3626	323	29	implies	imply	VERB
ejpam-3626	323	30	that∣∣∣∣ti	that∣∣∣∣ti	PROPN
ejpam-3626	323	31	−	−	PROPN
ejpam-3626	323	32	s(i)j	s(i)j	PROPN
ejpam-3626	323	33	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	323	34	≤	≤	PUNCT
ejpam-3626	323	35	∣∣hi	∣∣hi	VERB
ejpam-3626	323	36	−	−	PROPN
ejpam-3626	323	37	hi−1∣∣	hi−1∣∣	PROPN
ejpam-3626	323	38	<	<	X
ejpam-3626	323	39	δ(ti	δ(ti	NOUN
ejpam-3626	323	40	)	)	PUNCT
ejpam-3626	323	41	.	.	PUNCT
ejpam-3626	324	1	by	by	ADP
ejpam-3626	324	2	continuity	continuity	NOUN
ejpam-3626	324	3	of	of	ADP
ejpam-3626	324	4	f	f	PROPN
ejpam-3626	324	5	at	at	ADP
ejpam-3626	324	6	ti,∣∣∣∣s(i)j	ti,∣∣∣∣s(i)j	PROPN
ejpam-3626	324	7	−	−	PROPN
ejpam-3626	324	8	ti∣∣∣∣	ti∣∣∣∣	NOUN
ejpam-3626	324	9	<	<	X
ejpam-3626	324	10	δ(ti	δ(ti	NOUN
ejpam-3626	324	11	)	)	PUNCT
ejpam-3626	324	12	=	=	PUNCT
ejpam-3626	324	13	δ0(ti	δ0(ti	NOUN
ejpam-3626	324	14	)	)	PUNCT
ejpam-3626	324	15	2	2	NUM
ejpam-3626	324	16	<	<	X
ejpam-3626	324	17	δ0(ti)⇒	δ0(ti)⇒	PROPN
ejpam-3626	324	18	∣∣f	∣∣f	NOUN
ejpam-3626	324	19	(	(	PUNCT
ejpam-3626	324	20	s	s	X
ejpam-3626	324	21	(	(	PUNCT
ejpam-3626	324	22	i	i	NOUN
ejpam-3626	324	23	)	)	PUNCT
ejpam-3626	324	24	j	j	PROPN
ejpam-3626	324	25	)	)	PUNCT
ejpam-3626	325	1	−	−	PROPN
ejpam-3626	325	2	f	f	PROPN
ejpam-3626	325	3	(	(	PUNCT
ejpam-3626	325	4	ti	ti	NOUN
ejpam-3626	325	5	)	)	PUNCT
ejpam-3626	325	6	∣∣	∣∣	X
ejpam-3626	325	7	<	<	X
ejpam-3626	325	8	ε	ε	PROPN
ejpam-3626	325	9	·	·	PUNCT
ejpam-3626	325	10	e.	e.	PROPN
ejpam-3626	326	1	so	so	ADV
ejpam-3626	326	2	,	,	PUNCT
ejpam-3626	326	3	|∆(hi−1	|∆(hi−1	PROPN
ejpam-3626	326	4	,	,	PUNCT
ejpam-3626	326	5	hi)|	hi)|	PROPN
ejpam-3626	326	6	=	=	SYM
ejpam-3626	326	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	326	8	ni∑	ni∑	NOUN
ejpam-3626	326	9	j=1	j=1	NOUN
ejpam-3626	326	10	[	[	PUNCT
ejpam-3626	326	11	f	f	X
ejpam-3626	326	12	(	(	PUNCT
ejpam-3626	326	13	ti)−	ti)−	NOUN
ejpam-3626	326	14	f	f	X
ejpam-3626	326	15	(	(	PUNCT
ejpam-3626	326	16	s	s	X
ejpam-3626	326	17	(	(	PUNCT
ejpam-3626	326	18	i	i	NOUN
ejpam-3626	326	19	)	)	PUNCT
ejpam-3626	326	20	j	j	PROPN
ejpam-3626	326	21	)	)	PUNCT
ejpam-3626	326	22	]	]	PUNCT
ejpam-3626	327	1	[	[	PUNCT
ejpam-3626	327	2	h(z	h(z	NOUN
ejpam-3626	327	3	(	(	PUNCT
ejpam-3626	327	4	i	i	PROPN
ejpam-3626	327	5	)	)	PUNCT
ejpam-3626	327	6	j	j	PROPN
ejpam-3626	327	7	)	)	PUNCT
ejpam-3626	327	8	−h(z	−h(z	PROPN
ejpam-3626	327	9	(	(	PUNCT
ejpam-3626	327	10	i	i	NOUN
ejpam-3626	327	11	)	)	PUNCT
ejpam-3626	327	12	j−1	j−1	PROPN
ejpam-3626	327	13	)	)	PUNCT
ejpam-3626	327	14	]	]	PUNCT
ejpam-3626	327	15	∣∣∣∣.	∣∣∣∣.	PRON
ejpam-3626	327	16	hence	hence	ADV
ejpam-3626	327	17	,	,	PUNCT
ejpam-3626	327	18	by	by	ADP
ejpam-3626	327	19	theorem	theorem	NOUN
ejpam-3626	327	20	10	10	NUM
ejpam-3626	327	21	,	,	PUNCT
ejpam-3626	327	22	we	we	PRON
ejpam-3626	327	23	have∣∣∣s(f	have∣∣∣s(f	PROPN
ejpam-3626	327	24	,	,	PUNCT
ejpam-3626	327	25	h;d)−	h;d)−	PROPN
ejpam-3626	327	26	s(f	s(f	PROPN
ejpam-3626	327	27	,	,	PUNCT
ejpam-3626	327	28	h;d0	h;d0	NOUN
ejpam-3626	327	29	)	)	PUNCT
ejpam-3626	327	30	∣∣∣	∣∣∣	NOUN
ejpam-3626	327	31	=	=	PUNCT
ejpam-3626	327	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	327	33	m∑	m∑	NOUN
ejpam-3626	327	34	i=1	i=1	PROPN
ejpam-3626	327	35	f	f	PROPN
ejpam-3626	327	36	(	(	PUNCT
ejpam-3626	327	37	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	NUM
ejpam-3626	327	38	m∑	m∑	CCONJ
ejpam-3626	327	39	i=1	i=1	PROPN
ejpam-3626	328	1	s(f	s(f	PROPN
ejpam-3626	328	2	,	,	PUNCT
ejpam-3626	328	3	h	h	NOUN
ejpam-3626	328	4	,	,	PUNCT
ejpam-3626	328	5	pi	pi	NOUN
ejpam-3626	328	6	)	)	PUNCT
ejpam-3626	328	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	328	8	=	=	SYM
ejpam-3626	328	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	328	10	m∑	m∑	VERB
ejpam-3626	328	11	i=1	i=1	PROPN
ejpam-3626	328	12	{	{	PUNCT
ejpam-3626	328	13	f	f	X
ejpam-3626	328	14	(	(	PUNCT
ejpam-3626	328	15	ti)[h(hi)−h(hi−1)]−	ti)[h(hi)−h(hi−1)]−	X
ejpam-3626	328	16	s(f	s(f	PROPN
ejpam-3626	328	17	,	,	PUNCT
ejpam-3626	328	18	h	h	NOUN
ejpam-3626	328	19	,	,	PUNCT
ejpam-3626	328	20	pi	pi	NOUN
ejpam-3626	328	21	)	)	PUNCT
ejpam-3626	328	22	}	}	PUNCT
ejpam-3626	329	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	329	2	=	=	SYM
ejpam-3626	329	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	329	4	m∑	m∑	PROPN
ejpam-3626	329	5	i=1	i=1	PROPN
ejpam-3626	329	6	∆(hi−1	∆(hi−1	PROPN
ejpam-3626	329	7	,	,	PUNCT
ejpam-3626	329	8	hi	hi	INTJ
ejpam-3626	329	9	)	)	PUNCT
ejpam-3626	329	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	329	11	≤	≤	NOUN
ejpam-3626	329	12	m∑	m∑	CCONJ
ejpam-3626	329	13	i=1	i=1	PROPN
ejpam-3626	329	14	∣∣∣∆(hi−1	∣∣∣∆(hi−1	PROPN
ejpam-3626	329	15	,	,	PUNCT
ejpam-3626	329	16	hi	hi	ADJ
ejpam-3626	329	17	)	)	PUNCT
ejpam-3626	329	18	∣∣∣	∣∣∣	NOUN
ejpam-3626	329	19	references	reference	NOUN
ejpam-3626	329	20	142	142	NUM
ejpam-3626	329	21	=	=	SYM
ejpam-3626	329	22	m∑	m∑	CCONJ
ejpam-3626	329	23	i=1	i=1	PROPN
ejpam-3626	329	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	329	25	ni∑	ni∑	PROPN
ejpam-3626	329	26	j=1	j=1	NOUN
ejpam-3626	329	27	[	[	PUNCT
ejpam-3626	329	28	f	f	X
ejpam-3626	329	29	(	(	PUNCT
ejpam-3626	329	30	ti)−	ti)−	NOUN
ejpam-3626	329	31	f	f	X
ejpam-3626	329	32	(	(	PUNCT
ejpam-3626	329	33	s	s	X
ejpam-3626	329	34	(	(	PUNCT
ejpam-3626	329	35	i	i	NOUN
ejpam-3626	329	36	)	)	PUNCT
ejpam-3626	329	37	j	j	PROPN
ejpam-3626	329	38	)	)	PUNCT
ejpam-3626	330	1	]	]	PUNCT
ejpam-3626	330	2	[	[	PUNCT
ejpam-3626	330	3	h(z	h(z	NOUN
ejpam-3626	330	4	(	(	PUNCT
ejpam-3626	330	5	i	i	PROPN
ejpam-3626	330	6	)	)	PUNCT
ejpam-3626	330	7	j	j	PROPN
ejpam-3626	330	8	)	)	PUNCT
ejpam-3626	330	9	−h(z	−h(z	PROPN
ejpam-3626	330	10	(	(	PUNCT
ejpam-3626	330	11	i	i	NOUN
ejpam-3626	330	12	)	)	PUNCT
ejpam-3626	330	13	j−1	j−1	PROPN
ejpam-3626	330	14	)	)	PUNCT
ejpam-3626	330	15	]	]	PUNCT
ejpam-3626	330	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	330	17	≤	≤	NUM
ejpam-3626	330	18	m∑	m∑	VERB
ejpam-3626	330	19	i=1	i=1	PROPN
ejpam-3626	330	20	(	(	PUNCT
ejpam-3626	330	21	ni∑	ni∑	PROPN
ejpam-3626	330	22	j=1	j=1	PROPN
ejpam-3626	330	23	∣∣f	∣∣f	NOUN
ejpam-3626	330	24	(	(	PUNCT
ejpam-3626	330	25	ti)−	ti)−	NOUN
ejpam-3626	330	26	f	f	X
ejpam-3626	330	27	(	(	PUNCT
ejpam-3626	330	28	s	s	X
ejpam-3626	330	29	(	(	PUNCT
ejpam-3626	330	30	i	i	NOUN
ejpam-3626	330	31	)	)	PUNCT
ejpam-3626	330	32	j	j	PROPN
ejpam-3626	330	33	)	)	PUNCT
ejpam-3626	331	1	∣∣∣∣h(z	∣∣∣∣h(z	PROPN
ejpam-3626	331	2	(	(	PUNCT
ejpam-3626	331	3	i	i	NOUN
ejpam-3626	331	4	)	)	PUNCT
ejpam-3626	331	5	j	j	PROPN
ejpam-3626	331	6	)	)	PUNCT
ejpam-3626	331	7	−h(z	−h(z	PROPN
ejpam-3626	331	8	(	(	PUNCT
ejpam-3626	331	9	i	i	NOUN
ejpam-3626	331	10	)	)	PUNCT
ejpam-3626	331	11	j−1	j−1	PROPN
ejpam-3626	331	12	)	)	PUNCT
ejpam-3626	331	13	∣∣	∣∣	X
ejpam-3626	331	14	)	)	PUNCT
ejpam-3626	331	15	≤	≤	NOUN
ejpam-3626	331	16	m∑	m∑	CCONJ
ejpam-3626	331	17	i=1	i=1	PROPN
ejpam-3626	331	18	(	(	PUNCT
ejpam-3626	331	19	ni∑	ni∑	PROPN
ejpam-3626	331	20	j=1	j=1	PROPN
ejpam-3626	331	21	ε	ε	PROPN
ejpam-3626	331	22	k	k	PROPN
ejpam-3626	331	23	·	·	PUNCT
ejpam-3626	331	24	e	e	X
ejpam-3626	331	25	·	·	PUNCT
ejpam-3626	331	26	∣∣h(z	∣∣h(z	PROPN
ejpam-3626	331	27	(	(	PUNCT
ejpam-3626	331	28	i	i	NOUN
ejpam-3626	331	29	)	)	PUNCT
ejpam-3626	331	30	j	j	PROPN
ejpam-3626	331	31	)	)	PUNCT
ejpam-3626	331	32	−h(z	−h(z	PROPN
ejpam-3626	331	33	(	(	PUNCT
ejpam-3626	331	34	i	i	NOUN
ejpam-3626	331	35	)	)	PUNCT
ejpam-3626	331	36	j−1	j−1	PROPN
ejpam-3626	331	37	)	)	PUNCT
ejpam-3626	331	38	∣∣	∣∣	X
ejpam-3626	331	39	)	)	PUNCT
ejpam-3626	331	40	≤	≤	PUNCT
ejpam-3626	331	41	ε	ε	PROPN
ejpam-3626	331	42	k	k	X
ejpam-3626	331	43	·	·	PUNCT
ejpam-3626	331	44	e	e	X
ejpam-3626	331	45	·	·	PUNCT
ejpam-3626	331	46	m∑	m∑	INTJ
ejpam-3626	331	47	i=1	i=1	PROPN
ejpam-3626	331	48	(	(	PUNCT
ejpam-3626	331	49	ni∑	ni∑	ADJ
ejpam-3626	331	50	j=1	j=1	NOUN
ejpam-3626	331	51	∣∣h(z	∣∣h(z	PROPN
ejpam-3626	331	52	(	(	PUNCT
ejpam-3626	331	53	i	i	NOUN
ejpam-3626	331	54	)	)	PUNCT
ejpam-3626	331	55	j	j	PROPN
ejpam-3626	331	56	)	)	PUNCT
ejpam-3626	331	57	−h(z	−h(z	PROPN
ejpam-3626	331	58	(	(	PUNCT
ejpam-3626	331	59	i	i	NOUN
ejpam-3626	331	60	)	)	PUNCT
ejpam-3626	331	61	j−1	j−1	PROPN
ejpam-3626	331	62	)	)	PUNCT
ejpam-3626	331	63	∣∣	∣∣	X
ejpam-3626	331	64	)	)	PUNCT
ejpam-3626	331	65	≤	≤	PUNCT
ejpam-3626	331	66	ε	ε	PROPN
ejpam-3626	331	67	k	k	X
ejpam-3626	331	68	·	·	PUNCT
ejpam-3626	331	69	e	e	X
ejpam-3626	331	70	·	·	PUNCT
ejpam-3626	331	71	m∑	m∑	CCONJ
ejpam-3626	331	72	i=1	i=1	PROPN
ejpam-3626	331	73	υ(h	υ(h	PROPN
ejpam-3626	331	74	;	;	PUNCT
ejpam-3626	331	75	[	[	X
ejpam-3626	331	76	hi−1	hi−1	PROPN
ejpam-3626	331	77	,	,	PUNCT
ejpam-3626	331	78	hi	hi	ADJ
ejpam-3626	331	79	]	]	X
ejpam-3626	331	80	)	)	PUNCT
ejpam-3626	331	81	=	=	SYM
ejpam-3626	331	82	ε	ε	PROPN
ejpam-3626	331	83	k	k	X
ejpam-3626	331	84	·	·	PUNCT
ejpam-3626	331	85	e	e	X
ejpam-3626	331	86	·	·	PUNCT
ejpam-3626	331	87	υh	υh	X
ejpam-3626	331	88	<	<	X
ejpam-3626	331	89	ε	ε	PROPN
ejpam-3626	331	90	k	k	X
ejpam-3626	331	91	·	·	PUNCT
ejpam-3626	331	92	e	e	X
ejpam-3626	331	93	·	·	PUNCT
ejpam-3626	331	94	k	k	X
ejpam-3626	331	95	<	<	X
ejpam-3626	331	96	ε	ε	PROPN
ejpam-3626	331	97	·	·	PUNCT
ejpam-3626	331	98	e.	e.	PROPN
ejpam-3626	331	99	by	by	ADP
ejpam-3626	331	100	similar	similar	ADJ
ejpam-3626	331	101	argument	argument	NOUN
ejpam-3626	331	102	,	,	PUNCT
ejpam-3626	331	103	∣∣s(f	∣∣s(f	PROPN
ejpam-3626	331	104	,	,	PUNCT
ejpam-3626	331	105	h;q)−	h;q)−	PROPN
ejpam-3626	331	106	s(f	s(f	PROPN
ejpam-3626	331	107	,	,	PUNCT
ejpam-3626	331	108	h;d0	h;d0	ADV
ejpam-3626	331	109	)	)	PUNCT
ejpam-3626	331	110	∣∣	∣∣	X
ejpam-3626	331	111	<	<	X
ejpam-3626	331	112	ε	ε	PROPN
ejpam-3626	331	113	·	·	PUNCT
ejpam-3626	331	114	e.	e.	PROPN
ejpam-3626	331	115	thus,∣∣s(f	thus,∣∣s(f	PROPN
ejpam-3626	331	116	,	,	PUNCT
ejpam-3626	331	117	h;d)−	h;d)−	PROPN
ejpam-3626	331	118	s(f	s(f	PROPN
ejpam-3626	331	119	,	,	PUNCT
ejpam-3626	331	120	h;q	h;q	PROPN
ejpam-3626	331	121	)	)	PUNCT
ejpam-3626	331	122	∣∣	∣∣	NUM
ejpam-3626	331	123	=	=	SYM
ejpam-3626	331	124	∣∣∣∣s(f	∣∣∣∣s(f	PROPN
ejpam-3626	331	125	,	,	PUNCT
ejpam-3626	331	126	h;d)−	h;d)−	PROPN
ejpam-3626	331	127	s(f	s(f	PROPN
ejpam-3626	331	128	,	,	PUNCT
ejpam-3626	331	129	h;d0	h;d0	ADV
ejpam-3626	331	130	)	)	PUNCT
ejpam-3626	331	131	+	+	CCONJ
ejpam-3626	331	132	s(f	s(f	PROPN
ejpam-3626	331	133	,	,	PUNCT
ejpam-3626	331	134	h;d0)−	h;d0)−	PROPN
ejpam-3626	331	135	s(f	s(f	PROPN
ejpam-3626	331	136	,	,	PUNCT
ejpam-3626	331	137	h;q	h;q	PROPN
ejpam-3626	331	138	)	)	PUNCT
ejpam-3626	331	139	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3626	331	140	≤	≤	PUNCT
ejpam-3626	331	141	∣∣∣∣s(f	∣∣∣∣s(f	PROPN
ejpam-3626	331	142	,	,	PUNCT
ejpam-3626	331	143	h;d)−	h;d)−	PROPN
ejpam-3626	331	144	s(f	s(f	PROPN
ejpam-3626	331	145	,	,	PUNCT
ejpam-3626	331	146	h;d0	h;d0	PROPN
ejpam-3626	331	147	)	)	PUNCT
ejpam-3626	331	148	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3626	331	149	∣∣∣∣s(f	∣∣∣∣s(f	PROPN
ejpam-3626	331	150	,	,	PUNCT
ejpam-3626	331	151	h;q)−	h;q)−	PROPN
ejpam-3626	331	152	s(f	s(f	PROPN
ejpam-3626	331	153	,	,	PUNCT
ejpam-3626	331	154	h;d0	h;d0	NOUN
ejpam-3626	331	155	)	)	PUNCT
ejpam-3626	331	156	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3626	331	157	<	<	X
ejpam-3626	331	158	ε	ε	PROPN
ejpam-3626	331	159	·	·	PUNCT
ejpam-3626	331	160	e+	e+	NUM
ejpam-3626	331	161	ε	ε	PROPN
ejpam-3626	331	162	·	·	PUNCT
ejpam-3626	331	163	e	e	X
ejpam-3626	331	164	=	=	PUNCT
ejpam-3626	331	165	2ε	2ε	PROPN
ejpam-3626	331	166	·	·	PUNCT
ejpam-3626	331	167	e.	e.	PROPN
ejpam-3626	331	168	by	by	ADP
ejpam-3626	331	169	cauchy	cauchy	PROPN
ejpam-3626	331	170	criterion	criterion	NOUN
ejpam-3626	331	171	,	,	PUNCT
ejpam-3626	331	172	f	f	PROPN
ejpam-3626	331	173	∈	∈	PROPN
ejpam-3626	331	174	hks([f	hks([f	NOUN
ejpam-3626	331	175	,	,	PUNCT
ejpam-3626	331	176	g	g	NOUN
ejpam-3626	331	177	]	]	X
ejpam-3626	331	178	,	,	PUNCT
ejpam-3626	331	179	h	h	NOUN
ejpam-3626	331	180	)	)	PUNCT
ejpam-3626	331	181	.	.	PUNCT
ejpam-3626	332	1	acknowledgements	acknowledgement	NOUN
ejpam-3626	332	2	this	this	DET
ejpam-3626	332	3	article	article	NOUN
ejpam-3626	332	4	is	be	AUX
ejpam-3626	332	5	funded	fund	VERB
ejpam-3626	332	6	by	by	ADP
ejpam-3626	332	7	ched	che	VERB
ejpam-3626	332	8	-	-	PUNCT
ejpam-3626	332	9	k12	k12	NOUN
ejpam-3626	332	10	transition	transition	NOUN
ejpam-3626	332	11	program	program	NOUN
ejpam-3626	332	12	.	.	PUNCT
ejpam-3626	333	1	references	reference	NOUN
ejpam-3626	333	2	[	[	X
ejpam-3626	333	3	1	1	NUM
ejpam-3626	333	4	]	]	PUNCT
ejpam-3626	333	5	t.	t.	PROPN
ejpam-3626	333	6	m.	m.	NOUN
ejpam-3626	333	7	apostol	apostol	PROPN
ejpam-3626	333	8	,	,	PUNCT
ejpam-3626	333	9	mathematical	mathematical	ADJ
ejpam-3626	333	10	analysis	analysis	NOUN
ejpam-3626	333	11	,	,	PUNCT
ejpam-3626	333	12	2nd	2nd	ADJ
ejpam-3626	333	13	edition	edition	NOUN
ejpam-3626	333	14	,	,	PUNCT
ejpam-3626	333	15	narosa	narosa	PROPN
ejpam-3626	333	16	publishing	publishing	PROPN
ejpam-3626	333	17	house	house	PROPN
ejpam-3626	333	18	,	,	PUNCT
ejpam-3626	333	19	new	new	PROPN
ejpam-3626	333	20	delhi	delhi	PROPN
ejpam-3626	333	21	,	,	PUNCT
ejpam-3626	333	22	2002	2002	NUM
ejpam-3626	333	23	.	.	PUNCT
ejpam-3626	334	1	[	[	X
ejpam-3626	334	2	2	2	NUM
ejpam-3626	334	3	]	]	PUNCT
ejpam-3626	334	4	r.	r.	PROPN
ejpam-3626	334	5	g.	g.	PROPN
ejpam-3626	334	6	bartle	bartle	PROPN
ejpam-3626	334	7	and	and	CCONJ
ejpam-3626	334	8	d.	d.	PROPN
ejpam-3626	334	9	r.	r.	PROPN
ejpam-3626	334	10	sherbert	sherbert	PROPN
ejpam-3626	334	11	,	,	PUNCT
ejpam-3626	334	12	introduction	introduction	NOUN
ejpam-3626	334	13	to	to	ADP
ejpam-3626	334	14	real	real	ADJ
ejpam-3626	334	15	analysis	analysis	NOUN
ejpam-3626	334	16	,	,	PUNCT
ejpam-3626	334	17	4th	4th	ADJ
ejpam-3626	334	18	edition	edition	NOUN
ejpam-3626	334	19	,	,	PUNCT
ejpam-3626	334	20	john	john	PROPN
ejpam-3626	334	21	wiley	wiley	PROPN
ejpam-3626	334	22	,	,	PUNCT
ejpam-3626	334	23	new	new	PROPN
ejpam-3626	334	24	york	york	PROPN
ejpam-3626	334	25	,	,	PUNCT
ejpam-3626	334	26	2011	2011	NUM
ejpam-3626	334	27	.	.	PUNCT
ejpam-3626	335	1	[	[	X
ejpam-3626	335	2	3	3	X
ejpam-3626	335	3	]	]	PUNCT
ejpam-3626	335	4	s.	s.	PROPN
ejpam-3626	335	5	s.	s.	PROPN
ejpam-3626	335	6	cao	cao	PROPN
ejpam-3626	335	7	,	,	PUNCT
ejpam-3626	335	8	the	the	DET
ejpam-3626	335	9	henstock	henstock	NOUN
ejpam-3626	335	10	integral	integral	ADJ
ejpam-3626	335	11	for	for	ADP
ejpam-3626	335	12	banach	banach	ADV
ejpam-3626	335	13	-	-	PUNCT
ejpam-3626	335	14	valued	value	VERB
ejpam-3626	335	15	functions	function	NOUN
ejpam-3626	335	16	,	,	PUNCT
ejpam-3626	335	17	southeast	southeast	ADJ
ejpam-3626	335	18	asian	asian	ADJ
ejpam-3626	335	19	bull	bull	NOUN
ejpam-3626	335	20	.	.	PUNCT
ejpam-3626	336	1	math	math	NOUN
ejpam-3626	336	2	.	.	PUNCT
ejpam-3626	337	1	16	16	NUM
ejpam-3626	337	2	,	,	PUNCT
ejpam-3626	337	3	n0	n0	PROPN
ejpam-3626	337	4	.	.	PROPN
ejpam-3626	337	5	1	1	NUM
ejpam-3626	337	6	,	,	PUNCT
ejpam-3626	337	7	(	(	PUNCT
ejpam-3626	337	8	1992	1992	NUM
ejpam-3626	337	9	)	)	PUNCT
ejpam-3626	337	10	,	,	PUNCT
ejpam-3626	337	11	35	35	NUM
ejpam-3626	337	12	-	-	SYM
ejpam-3626	337	13	40	40	NUM
ejpam-3626	337	14	.	.	PUNCT
ejpam-3626	338	1	references	reference	NOUN
ejpam-3626	338	2	143	143	NUM
ejpam-3626	339	1	[	[	X
ejpam-3626	339	2	4	4	X
ejpam-3626	339	3	]	]	X
ejpam-3626	339	4	d.	d.	PROPN
ejpam-3626	339	5	h.	h.	PROPN
ejpam-3626	339	6	fremlin	fremlin	PROPN
ejpam-3626	339	7	,	,	PUNCT
ejpam-3626	339	8	topological	topological	ADJ
ejpam-3626	339	9	riesz	riesz	NOUN
ejpam-3626	339	10	spaces	space	NOUN
ejpam-3626	339	11	and	and	CCONJ
ejpam-3626	339	12	measure	measure	NOUN
ejpam-3626	339	13	theory	theory	NOUN
ejpam-3626	339	14	,	,	PUNCT
ejpam-3626	339	15	(	(	PUNCT
ejpam-3626	339	16	cambridge	cambridge	PROPN
ejpam-3626	339	17	university	university	PROPN
ejpam-3626	339	18	press	press	PROPN
ejpam-3626	339	19	)	)	PUNCT
ejpam-3626	339	20	.	.	PUNCT
ejpam-3626	340	1	978	978	NUM
ejpam-3626	340	2	-	-	SYM
ejpam-3626	340	3	0	0	NUM
ejpam-3626	340	4	-	-	PUNCT
ejpam-3626	340	5	0521	0521	NUM
ejpam-3626	340	6	-	-	PUNCT
ejpam-3626	340	7	09031	09031	NUM
ejpam-3626	340	8	-	-	SYM
ejpam-3626	340	9	5	5	NUM
ejpam-3626	340	10	.	.	PUNCT
ejpam-3626	341	1	[	[	X
ejpam-3626	341	2	5	5	X
ejpam-3626	341	3	]	]	PUNCT
ejpam-3626	341	4	e.	e.	PROPN
ejpam-3626	341	5	kreyszig	kreyszig	PROPN
ejpam-3626	341	6	,	,	PUNCT
ejpam-3626	341	7	introductory	introductory	ADJ
ejpam-3626	341	8	functional	functional	ADJ
ejpam-3626	341	9	analysis	analysis	NOUN
ejpam-3626	341	10	with	with	ADP
ejpam-3626	341	11	application	application	NOUN
ejpam-3626	341	12	,	,	PUNCT
ejpam-3626	341	13	john	john	PROPN
ejpam-3626	341	14	wiley	wiley	PROPN
ejpam-3626	341	15	and	and	CCONJ
ejpam-3626	341	16	sons	son	NOUN
ejpam-3626	341	17	.	.	PUNCT
ejpam-3626	342	1	inc	inc	PROPN
ejpam-3626	342	2	.	.	PROPN
ejpam-3626	342	3	,	,	PUNCT
ejpam-3626	342	4	new	new	PROPN
ejpam-3626	342	5	york	york	PROPN
ejpam-3626	342	6	,	,	PUNCT
ejpam-3626	342	7	1978	1978	NUM
ejpam-3626	342	8	.	.	PUNCT
ejpam-3626	343	1	[	[	X
ejpam-3626	343	2	6	6	NUM
ejpam-3626	343	3	]	]	PUNCT
ejpam-3626	343	4	j.	j.	PROPN
ejpam-3626	343	5	kurzweil	kurzweil	PROPN
ejpam-3626	343	6	,	,	PUNCT
ejpam-3626	343	7	generalized	generalize	VERB
ejpam-3626	343	8	ordinary	ordinary	ADJ
ejpam-3626	343	9	differential	differential	ADJ
ejpam-3626	343	10	equation	equation	NOUN
ejpam-3626	343	11	and	and	CCONJ
ejpam-3626	343	12	continuous	continuous	ADJ
ejpam-3626	343	13	dependence	dependence	NOUN
ejpam-3626	343	14	on	on	ADP
ejpam-3626	343	15	a	a	DET
ejpam-3626	343	16	parameter	parameter	NOUN
ejpam-3626	343	17	,	,	PUNCT
ejpam-3626	343	18	cmj	cmj	NOUN
ejpam-3626	343	19	,	,	PUNCT
ejpam-3626	343	20	7(82	7(82	NUM
ejpam-3626	343	21	)	)	PUNCT
ejpam-3626	343	22	(	(	PUNCT
ejpam-3626	343	23	1957	1957	NUM
ejpam-3626	343	24	)	)	PUNCT
ejpam-3626	343	25	,	,	PUNCT
ejpam-3626	343	26	418	418	NUM
ejpam-3626	343	27	-	-	SYM
ejpam-3626	343	28	449	449	NUM
ejpam-3626	343	29	.	.	PUNCT
ejpam-3626	344	1	[	[	X
ejpam-3626	344	2	7	7	X
ejpam-3626	344	3	]	]	PUNCT
ejpam-3626	344	4	j.	j.	PROPN
ejpam-3626	344	5	s.	s.	PROPN
ejpam-3626	344	6	lim	lim	PROPN
ejpam-3626	344	7	,	,	PUNCT
ejpam-3626	344	8	j.	j.	PROPN
ejpam-3626	344	9	h.	h.	PROPN
ejpam-3626	344	10	yoon	yoon	PROPN
ejpam-3626	344	11	,	,	PUNCT
ejpam-3626	344	12	and	and	CCONJ
ejpam-3626	344	13	g.	g.	PROPN
ejpam-3626	344	14	s.	s.	PROPN
ejpam-3626	344	15	eun	eun	PROPN
ejpam-3626	344	16	,	,	PUNCT
ejpam-3626	344	17	on	on	ADP
ejpam-3626	344	18	henstock	henstock	NOUN
ejpam-3626	344	19	-	-	PUNCT
ejpam-3626	344	20	stieltjes	stieltjes	NOUN
ejpam-3626	344	21	integral	integral	ADJ
ejpam-3626	344	22	,	,	PUNCT
ejpam-3626	344	23	kangweonkyungki	kangweonkyungki	NOUN
ejpam-3626	344	24	math	math	NOUN
ejpam-3626	344	25	.	.	PUNCT
ejpam-3626	345	1	j.6	j.6	VERB
ejpam-3626	345	2	,	,	PUNCT
ejpam-3626	345	3	no.1	no.1	NUM
ejpam-3626	345	4	,	,	PUNCT
ejpam-3626	345	5	(	(	PUNCT
ejpam-3626	345	6	1998	1998	NUM
ejpam-3626	345	7	)	)	PUNCT
ejpam-3626	345	8	,	,	PUNCT
ejpam-3626	345	9	87	87	NUM
ejpam-3626	345	10	-	-	SYM
ejpam-3626	345	11	96	96	NUM
ejpam-3626	345	12	.	.	PUNCT
ejpam-3626	346	1	[	[	X
ejpam-3626	346	2	8	8	X
ejpam-3626	346	3	]	]	PUNCT
ejpam-3626	346	4	s.	s.	PROPN
ejpam-3626	346	5	a.	a.	PROPN
ejpam-3626	346	6	tikare	tikare	PROPN
ejpam-3626	346	7	and	and	CCONJ
ejpam-3626	346	8	m.	m.	NOUN
ejpam-3626	346	9	s.	s.	PROPN
ejpam-3626	346	10	chaudhary	chaudhary	PROPN
ejpam-3626	346	11	,	,	PUNCT
ejpam-3626	346	12	the	the	DET
ejpam-3626	346	13	henstock−stieltjes	henstock−stieltjes	NOUN
ejpam-3626	346	14	integral	integral	ADJ
ejpam-3626	346	15	for	for	ADP
ejpam-3626	346	16	banach	banach	NOUN
ejpam-3626	346	17	space	space	NOUN
ejpam-3626	346	18	-	-	PUNCT
ejpam-3626	346	19	valued	value	VERB
ejpam-3626	346	20	functions	function	NOUN
ejpam-3626	346	21	,	,	PUNCT
ejpam-3626	346	22	bull	bull	NOUN
ejpam-3626	346	23	.	.	PUNCT
ejpam-3626	347	1	kerala	kerala	PROPN
ejpam-3626	347	2	math	math	PROPN
ejpam-3626	347	3	.	.	PUNCT
ejpam-3626	348	1	assoc	assoc	PROPN
ejpam-3626	348	2	.	.	PUNCT
ejpam-3626	349	1	vol	vol	NOUN
ejpam-3626	349	2	.	.	PROPN
ejpam-3626	350	1	6	6	NUM
ejpam-3626	350	2	,	,	PUNCT
ejpam-3626	350	3	n0	n0	NUM
ejpam-3626	350	4	.	.	NOUN
ejpam-3626	350	5	2	2	NUM
ejpam-3626	350	6	,	,	PUNCT
ejpam-3626	350	7	(	(	PUNCT
ejpam-3626	350	8	2010	2010	NUM
ejpam-3626	350	9	)	)	PUNCT
ejpam-3626	350	10	,	,	PUNCT
ejpam-3626	350	11	83	83	NUM
ejpam-3626	350	12	-	-	SYM
ejpam-3626	350	13	92	92	NUM
ejpam-3626	350	14	.	.	PUNCT
ejpam-3626	351	1	[	[	X
ejpam-3626	351	2	9	9	NUM
ejpam-3626	351	3	]	]	X
ejpam-3626	351	4	f.	f.	NOUN
ejpam-3626	351	5	ubaidillah	ubaidillah	PROPN
ejpam-3626	351	6	,	,	PUNCT
ejpam-3626	351	7	s.	s.	PROPN
ejpam-3626	351	8	darmawijaya	darmawijaya	PROPN
ejpam-3626	351	9	,	,	PUNCT
ejpam-3626	351	10	and	and	CCONJ
ejpam-3626	351	11	ch	ch	PROPN
ejpam-3626	351	12	.	.	PROPN
ejpam-3626	351	13	r.	r.	PROPN
ejpam-3626	351	14	indrati	indrati	PROPN
ejpam-3626	351	15	on	on	ADP
ejpam-3626	351	16	the	the	DET
ejpam-3626	351	17	henstock	henstock	NOUN
ejpam-3626	351	18	-	-	PUNCT
ejpam-3626	351	19	kurzweil	kurzweil	NOUN
ejpam-3626	351	20	integral	integral	ADJ
ejpam-3626	351	21	of	of	ADP
ejpam-3626	351	22	c[a	c[a	NUM
ejpam-3626	351	23	,	,	PUNCT
ejpam-3626	351	24	b	b	NOUN
ejpam-3626	351	25	]	]	X
ejpam-3626	351	26	space	space	NOUN
ejpam-3626	351	27	-	-	PUNCT
ejpam-3626	351	28	valued	value	VERB
ejpam-3626	351	29	functions	function	NOUN
ejpam-3626	351	30	,	,	PUNCT
ejpam-3626	351	31	ijma	ijma	NOUN
ejpam-3626	351	32	,	,	PUNCT
ejpam-3626	351	33	37(9)(2015	37(9)(2015	NUM
ejpam-3626	351	34	)	)	PUNCT
ejpam-3626	351	35	,	,	PUNCT
ejpam-3626	351	36	1831	1831	NUM
ejpam-3626	351	37	-	-	SYM
ejpam-3626	351	38	1846	1846	NUM
ejpam-3626	351	39	.	.	PUNCT