id	sid	tid	token	lemma	pos
ejpam-3200	1	1	european	european	PROPN
ejpam-3200	1	2	journal	journal	PROPN
ejpam-3200	1	3	of	of	ADP
ejpam-3200	1	4	pure	pure	ADJ
ejpam-3200	1	5	and	and	CCONJ
ejpam-3200	1	6	applied	apply	VERB
ejpam-3200	1	7	mathematics	mathematic	NOUN
ejpam-3200	1	8	vol	vol	NOUN
ejpam-3200	1	9	.	.	PUNCT
ejpam-3200	2	1	11	11	NUM
ejpam-3200	2	2	,	,	PUNCT
ejpam-3200	2	3	no	no	INTJ
ejpam-3200	2	4	.	.	NOUN
ejpam-3200	2	5	2	2	NUM
ejpam-3200	2	6	,	,	PUNCT
ejpam-3200	2	7	2018	2018	NUM
ejpam-3200	2	8	,	,	PUNCT
ejpam-3200	2	9	493	493	NUM
ejpam-3200	2	10	-	-	SYM
ejpam-3200	2	11	504	504	NUM
ejpam-3200	2	12	issn	issn	PROPN
ejpam-3200	2	13	1307	1307	NUM
ejpam-3200	2	14	-	-	SYM
ejpam-3200	2	15	5543	5543	NUM
ejpam-3200	2	16	–	–	PUNCT
ejpam-3200	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3200	2	18	published	publish	VERB
ejpam-3200	2	19	by	by	ADP
ejpam-3200	2	20	new	new	PROPN
ejpam-3200	2	21	york	york	PROPN
ejpam-3200	2	22	business	business	PROPN
ejpam-3200	2	23	global	global	PROPN
ejpam-3200	2	24	on	on	ADP
ejpam-3200	2	25	mcshane	mcshane	PROPN
ejpam-3200	2	26	-	-	PUNCT
ejpam-3200	2	27	stieltjes	stieltjes	PROPN
ejpam-3200	2	28	integrals	integral	NOUN
ejpam-3200	2	29	of	of	ADP
ejpam-3200	2	30	interval	interval	NOUN
ejpam-3200	2	31	-	-	PUNCT
ejpam-3200	2	32	valued	value	VERB
ejpam-3200	2	33	functions	function	NOUN
ejpam-3200	2	34	and	and	CCONJ
ejpam-3200	2	35	fuzzy	fuzzy	ADJ
ejpam-3200	2	36	-	-	PUNCT
ejpam-3200	2	37	number	number	NOUN
ejpam-3200	2	38	-	-	PUNCT
ejpam-3200	2	39	valued	value	VERB
ejpam-3200	2	40	functions	function	NOUN
ejpam-3200	2	41	on	on	ADP
ejpam-3200	2	42	time	time	NOUN
ejpam-3200	2	43	scales	scale	NOUN
ejpam-3200	2	44	muawya	muawya	NOUN
ejpam-3200	2	45	elsheikh	elsheikh	VERB
ejpam-3200	2	46	hamid1,2	hamid1,2	PROPN
ejpam-3200	2	47	1	1	NUM
ejpam-3200	2	48	school	school	NOUN
ejpam-3200	2	49	of	of	ADP
ejpam-3200	2	50	mathematical	mathematical	ADJ
ejpam-3200	2	51	science	science	NOUN
ejpam-3200	2	52	,	,	PUNCT
ejpam-3200	2	53	yangzhou	yangzhou	PROPN
ejpam-3200	2	54	university	university	PROPN
ejpam-3200	2	55	,	,	PUNCT
ejpam-3200	2	56	yangzhou	yangzhou	PROPN
ejpam-3200	2	57	225002	225002	NUM
ejpam-3200	2	58	,	,	PUNCT
ejpam-3200	2	59	china	china	PROPN
ejpam-3200	2	60	2	2	NUM
ejpam-3200	2	61	school	school	NOUN
ejpam-3200	2	62	of	of	ADP
ejpam-3200	2	63	management	management	NOUN
ejpam-3200	2	64	,	,	PUNCT
ejpam-3200	2	65	ahfad	ahfad	PROPN
ejpam-3200	2	66	university	university	PROPN
ejpam-3200	2	67	for	for	ADP
ejpam-3200	2	68	women	woman	NOUN
ejpam-3200	2	69	,	,	PUNCT
ejpam-3200	2	70	omdurman	omdurman	PROPN
ejpam-3200	2	71	,	,	PUNCT
ejpam-3200	2	72	sudan	sudan	PROPN
ejpam-3200	2	73	abstract	abstract	NOUN
ejpam-3200	2	74	.	.	PUNCT
ejpam-3200	3	1	in	in	ADP
ejpam-3200	3	2	this	this	DET
ejpam-3200	3	3	paper	paper	NOUN
ejpam-3200	3	4	,	,	PUNCT
ejpam-3200	3	5	we	we	PRON
ejpam-3200	3	6	introduce	introduce	VERB
ejpam-3200	3	7	the	the	DET
ejpam-3200	3	8	notion	notion	NOUN
ejpam-3200	3	9	of	of	ADP
ejpam-3200	3	10	the	the	DET
ejpam-3200	3	11	mcshane	mcshane	NOUN
ejpam-3200	3	12	-	-	PUNCT
ejpam-3200	3	13	stieltjes	stieltjes	PROPN
ejpam-3200	3	14	(	(	PUNCT
ejpam-3200	3	15	ms	ms	NOUN
ejpam-3200	3	16	)	)	PUNCT
ejpam-3200	3	17	integrals	integral	NOUN
ejpam-3200	3	18	of	of	ADP
ejpam-3200	3	19	interval	interval	NOUN
ejpam-3200	3	20	-	-	PUNCT
ejpam-3200	3	21	valued	value	VERB
ejpam-3200	3	22	functions	function	NOUN
ejpam-3200	3	23	and	and	CCONJ
ejpam-3200	3	24	fuzzy	fuzzy	ADJ
ejpam-3200	3	25	-	-	PUNCT
ejpam-3200	3	26	number	number	NOUN
ejpam-3200	3	27	-	-	PUNCT
ejpam-3200	3	28	valued	value	VERB
ejpam-3200	3	29	functions	function	NOUN
ejpam-3200	3	30	on	on	ADP
ejpam-3200	3	31	time	time	NOUN
ejpam-3200	3	32	scales	scale	NOUN
ejpam-3200	3	33	which	which	PRON
ejpam-3200	3	34	are	be	AUX
ejpam-3200	3	35	extensions	extension	NOUN
ejpam-3200	3	36	of	of	ADP
ejpam-3200	3	37	the	the	DET
ejpam-3200	3	38	mcshane	mcshane	NOUN
ejpam-3200	3	39	(	(	PUNCT
ejpam-3200	3	40	m	m	NOUN
ejpam-3200	3	41	)	)	PUNCT
ejpam-3200	3	42	integrals	integral	NOUN
ejpam-3200	3	43	of	of	ADP
ejpam-3200	3	44	interval	interval	NOUN
ejpam-3200	3	45	-	-	PUNCT
ejpam-3200	3	46	valued	value	VERB
ejpam-3200	3	47	functions	function	NOUN
ejpam-3200	3	48	and	and	CCONJ
ejpam-3200	3	49	fuzzy	fuzzy	ADJ
ejpam-3200	3	50	-	-	PUNCT
ejpam-3200	3	51	number	number	NOUN
ejpam-3200	3	52	-	-	PUNCT
ejpam-3200	3	53	valued	value	VERB
ejpam-3200	3	54	functions	function	NOUN
ejpam-3200	3	55	on	on	ADP
ejpam-3200	3	56	time	time	NOUN
ejpam-3200	3	57	scales	scale	NOUN
ejpam-3200	3	58	[	[	X
ejpam-3200	3	59	3	3	X
ejpam-3200	3	60	]	]	PUNCT
ejpam-3200	3	61	and	and	CCONJ
ejpam-3200	3	62	investigate	investigate	VERB
ejpam-3200	3	63	some	some	PRON
ejpam-3200	3	64	of	of	ADP
ejpam-3200	3	65	their	their	PRON
ejpam-3200	3	66	properties	property	NOUN
ejpam-3200	3	67	.	.	PUNCT
ejpam-3200	4	1	2010	2010	NUM
ejpam-3200	4	2	mathematics	mathematic	NOUN
ejpam-3200	4	3	subject	subject	NOUN
ejpam-3200	4	4	classifications	classification	NOUN
ejpam-3200	4	5	:	:	PUNCT
ejpam-3200	4	6	26a39	26a39	NUM
ejpam-3200	4	7	,	,	PUNCT
ejpam-3200	4	8	26e70	26e70	NUM
ejpam-3200	4	9	key	key	ADJ
ejpam-3200	4	10	words	word	NOUN
ejpam-3200	4	11	and	and	CCONJ
ejpam-3200	4	12	phrases	phrase	NOUN
ejpam-3200	4	13	:	:	PUNCT
ejpam-3200	4	14	fuzzy	fuzzy	ADJ
ejpam-3200	4	15	numbers	number	NOUN
ejpam-3200	4	16	;	;	PUNCT
ejpam-3200	4	17	(	(	PUNCT
ejpam-3200	4	18	ms	ms	PROPN
ejpam-3200	4	19	)	)	PUNCT
ejpam-3200	4	20	delta	delta	NOUN
ejpam-3200	4	21	integral	integral	ADJ
ejpam-3200	4	22	of	of	ADP
ejpam-3200	4	23	interval	interval	NOUN
ejpam-3200	4	24	-	-	PUNCT
ejpam-3200	4	25	valued	value	VERB
ejpam-3200	4	26	functions	function	NOUN
ejpam-3200	4	27	;	;	PUNCT
ejpam-3200	4	28	(	(	PUNCT
ejpam-3200	4	29	ms	ms	PROPN
ejpam-3200	4	30	)	)	PUNCT
ejpam-3200	4	31	delta	delta	NOUN
ejpam-3200	4	32	integral	integral	ADJ
ejpam-3200	4	33	of	of	ADP
ejpam-3200	4	34	fuzzy	fuzzy	ADJ
ejpam-3200	4	35	-	-	PUNCT
ejpam-3200	4	36	number	number	NOUN
ejpam-3200	4	37	-	-	PUNCT
ejpam-3200	4	38	valued	value	VERB
ejpam-3200	4	39	functions	function	NOUN
ejpam-3200	4	40	.	.	PUNCT
ejpam-3200	5	1	1	1	X
ejpam-3200	5	2	.	.	X
ejpam-3200	5	3	introduction	introduction	NOUN
ejpam-3200	5	4	the	the	DET
ejpam-3200	5	5	calculus	calculus	NOUN
ejpam-3200	5	6	on	on	ADP
ejpam-3200	5	7	time	time	NOUN
ejpam-3200	5	8	scales	scale	NOUN
ejpam-3200	5	9	was	be	AUX
ejpam-3200	5	10	introduced	introduce	VERB
ejpam-3200	5	11	for	for	ADP
ejpam-3200	5	12	the	the	DET
ejpam-3200	5	13	first	first	ADJ
ejpam-3200	5	14	time	time	NOUN
ejpam-3200	5	15	in	in	ADP
ejpam-3200	5	16	1988	1988	NUM
ejpam-3200	5	17	by	by	ADP
ejpam-3200	5	18	hilger	hilger	NOUN
ejpam-3200	5	19	[	[	X
ejpam-3200	5	20	2	2	NUM
ejpam-3200	5	21	]	]	PUNCT
ejpam-3200	5	22	to	to	PART
ejpam-3200	5	23	unify	unify	VERB
ejpam-3200	5	24	the	the	DET
ejpam-3200	5	25	theory	theory	NOUN
ejpam-3200	5	26	of	of	ADP
ejpam-3200	5	27	difference	difference	NOUN
ejpam-3200	5	28	equations	equation	NOUN
ejpam-3200	5	29	and	and	CCONJ
ejpam-3200	5	30	the	the	DET
ejpam-3200	5	31	theory	theory	NOUN
ejpam-3200	5	32	of	of	ADP
ejpam-3200	5	33	differential	differential	ADJ
ejpam-3200	5	34	equations	equation	NOUN
ejpam-3200	5	35	.	.	PUNCT
ejpam-3200	6	1	in	in	ADP
ejpam-3200	6	2	2016	2016	NUM
ejpam-3200	6	3	,	,	PUNCT
ejpam-3200	6	4	hamid	hamid	PROPN
ejpam-3200	6	5	and	and	CCONJ
ejpam-3200	6	6	elmuiz	elmuiz	NOUN
ejpam-3200	6	7	[	[	X
ejpam-3200	6	8	4	4	X
ejpam-3200	6	9	]	]	PUNCT
ejpam-3200	6	10	introduced	introduce	VERB
ejpam-3200	6	11	the	the	DET
ejpam-3200	6	12	concept	concept	NOUN
ejpam-3200	6	13	of	of	ADP
ejpam-3200	6	14	the	the	DET
ejpam-3200	6	15	henstock	henstock	NOUN
ejpam-3200	6	16	-	-	PUNCT
ejpam-3200	6	17	stieltjes	stieltjes	NOUN
ejpam-3200	6	18	(	(	PUNCT
ejpam-3200	6	19	hs	hs	NOUN
ejpam-3200	6	20	)	)	PUNCT
ejpam-3200	6	21	integrals	integral	NOUN
ejpam-3200	6	22	of	of	ADP
ejpam-3200	6	23	interval	interval	NOUN
ejpam-3200	6	24	-	-	PUNCT
ejpam-3200	6	25	valued	value	VERB
ejpam-3200	6	26	functions	function	NOUN
ejpam-3200	6	27	and	and	CCONJ
ejpam-3200	6	28	fuzzy	fuzzy	ADJ
ejpam-3200	6	29	-	-	PUNCT
ejpam-3200	6	30	number	number	NOUN
ejpam-3200	6	31	-	-	PUNCT
ejpam-3200	6	32	valued	value	VERB
ejpam-3200	6	33	functions	function	NOUN
ejpam-3200	6	34	and	and	CCONJ
ejpam-3200	6	35	discussed	discuss	VERB
ejpam-3200	6	36	a	a	DET
ejpam-3200	6	37	number	number	NOUN
ejpam-3200	6	38	of	of	ADP
ejpam-3200	6	39	their	their	PRON
ejpam-3200	6	40	properties	property	NOUN
ejpam-3200	6	41	.	.	PUNCT
ejpam-3200	7	1	very	very	ADV
ejpam-3200	7	2	recently	recently	ADV
ejpam-3200	7	3	,	,	PUNCT
ejpam-3200	7	4	hamid	hamid	PROPN
ejpam-3200	7	5	et	et	PROPN
ejpam-3200	7	6	al	al	PROPN
ejpam-3200	7	7	.	.	PUNCT
ejpam-3200	8	1	[	[	X
ejpam-3200	8	2	5	5	NUM
ejpam-3200	8	3	]	]	PUNCT
ejpam-3200	8	4	introduced	introduce	VERB
ejpam-3200	8	5	the	the	DET
ejpam-3200	8	6	thought	thought	NOUN
ejpam-3200	8	7	of	of	ADP
ejpam-3200	8	8	the	the	DET
ejpam-3200	8	9	aphenstock	aphenstock	ADJ
ejpam-3200	8	10	integrals	integral	NOUN
ejpam-3200	8	11	of	of	ADP
ejpam-3200	8	12	interval	interval	NOUN
ejpam-3200	8	13	-	-	PUNCT
ejpam-3200	8	14	valued	value	VERB
ejpam-3200	8	15	functions	function	NOUN
ejpam-3200	8	16	and	and	CCONJ
ejpam-3200	8	17	fuzzy	fuzzy	ADJ
ejpam-3200	8	18	-	-	PUNCT
ejpam-3200	8	19	number	number	NOUN
ejpam-3200	8	20	-	-	PUNCT
ejpam-3200	8	21	valued	value	VERB
ejpam-3200	8	22	functions	function	NOUN
ejpam-3200	8	23	and	and	CCONJ
ejpam-3200	8	24	obtained	obtain	VERB
ejpam-3200	8	25	some	some	PRON
ejpam-3200	8	26	of	of	ADP
ejpam-3200	8	27	their	their	PRON
ejpam-3200	8	28	properties	property	NOUN
ejpam-3200	8	29	.	.	PUNCT
ejpam-3200	9	1	in	in	ADP
ejpam-3200	9	2	this	this	DET
ejpam-3200	9	3	paper	paper	NOUN
ejpam-3200	9	4	,	,	PUNCT
ejpam-3200	9	5	we	we	PRON
ejpam-3200	9	6	introduce	introduce	VERB
ejpam-3200	9	7	the	the	DET
ejpam-3200	9	8	notion	notion	NOUN
ejpam-3200	9	9	of	of	ADP
ejpam-3200	9	10	the	the	DET
ejpam-3200	9	11	(	(	PUNCT
ejpam-3200	9	12	ms	ms	PROPN
ejpam-3200	9	13	)	)	PUNCT
ejpam-3200	9	14	delta	delta	NOUN
ejpam-3200	9	15	integrals	integral	NOUN
ejpam-3200	9	16	of	of	ADP
ejpam-3200	9	17	interval	interval	NOUN
ejpam-3200	9	18	-	-	PUNCT
ejpam-3200	9	19	valued	value	VERB
ejpam-3200	9	20	functions	function	NOUN
ejpam-3200	9	21	and	and	CCONJ
ejpam-3200	9	22	fuzzy	fuzzy	ADJ
ejpam-3200	9	23	-	-	PUNCT
ejpam-3200	9	24	number	number	NOUN
ejpam-3200	9	25	-	-	PUNCT
ejpam-3200	9	26	valued	value	VERB
ejpam-3200	9	27	functions	function	NOUN
ejpam-3200	9	28	on	on	ADP
ejpam-3200	9	29	time	time	NOUN
ejpam-3200	9	30	scales	scale	NOUN
ejpam-3200	9	31	and	and	CCONJ
ejpam-3200	9	32	investigate	investigate	VERB
ejpam-3200	9	33	some	some	PRON
ejpam-3200	9	34	of	of	ADP
ejpam-3200	9	35	their	their	PRON
ejpam-3200	9	36	properties	property	NOUN
ejpam-3200	9	37	.	.	PUNCT
ejpam-3200	10	1	the	the	DET
ejpam-3200	10	2	paper	paper	NOUN
ejpam-3200	10	3	is	be	AUX
ejpam-3200	10	4	organized	organize	VERB
ejpam-3200	10	5	as	as	SCONJ
ejpam-3200	10	6	follows	follow	VERB
ejpam-3200	10	7	,	,	PUNCT
ejpam-3200	10	8	in	in	ADP
ejpam-3200	10	9	section	section	NOUN
ejpam-3200	10	10	2	2	NUM
ejpam-3200	10	11	we	we	PRON
ejpam-3200	10	12	provide	provide	VERB
ejpam-3200	10	13	the	the	DET
ejpam-3200	10	14	preliminary	preliminary	ADJ
ejpam-3200	10	15	terminology	terminology	NOUN
ejpam-3200	10	16	used	use	VERB
ejpam-3200	10	17	in	in	ADP
ejpam-3200	10	18	this	this	DET
ejpam-3200	10	19	paper	paper	NOUN
ejpam-3200	10	20	.	.	PUNCT
ejpam-3200	11	1	section	section	NOUN
ejpam-3200	11	2	3	3	NUM
ejpam-3200	11	3	is	be	AUX
ejpam-3200	11	4	dedicated	dedicate	VERB
ejpam-3200	11	5	to	to	PART
ejpam-3200	11	6	discuss	discuss	VERB
ejpam-3200	11	7	the	the	DET
ejpam-3200	11	8	(	(	PUNCT
ejpam-3200	11	9	ms	ms	PROPN
ejpam-3200	11	10	)	)	PUNCT
ejpam-3200	11	11	delta	delta	NOUN
ejpam-3200	11	12	integral	integral	ADJ
ejpam-3200	11	13	of	of	ADP
ejpam-3200	11	14	intervalvalued	intervalvalue	VERB
ejpam-3200	11	15	functions	function	NOUN
ejpam-3200	11	16	on	on	ADP
ejpam-3200	11	17	time	time	NOUN
ejpam-3200	11	18	scales	scale	NOUN
ejpam-3200	11	19	.	.	PUNCT
ejpam-3200	12	1	in	in	ADP
ejpam-3200	12	2	section	section	NOUN
ejpam-3200	12	3	4	4	NUM
ejpam-3200	12	4	,	,	PUNCT
ejpam-3200	12	5	we	we	PRON
ejpam-3200	12	6	present	present	VERB
ejpam-3200	12	7	the	the	DET
ejpam-3200	12	8	(	(	PUNCT
ejpam-3200	12	9	ms	ms	PROPN
ejpam-3200	12	10	)	)	PUNCT
ejpam-3200	12	11	delta	delta	NOUN
ejpam-3200	12	12	integral	integral	ADJ
ejpam-3200	12	13	of	of	ADP
ejpam-3200	12	14	fuzzy	fuzzy	ADJ
ejpam-3200	12	15	-	-	PUNCT
ejpam-3200	12	16	number	number	NOUN
ejpam-3200	12	17	-	-	PUNCT
ejpam-3200	12	18	valued	value	VERB
ejpam-3200	12	19	functions	function	NOUN
ejpam-3200	12	20	on	on	ADP
ejpam-3200	12	21	time	time	NOUN
ejpam-3200	12	22	scales	scale	NOUN
ejpam-3200	12	23	.	.	PUNCT
ejpam-3200	13	1	the	the	DET
ejpam-3200	13	2	last	last	ADJ
ejpam-3200	13	3	section	section	NOUN
ejpam-3200	13	4	provides	provide	VERB
ejpam-3200	13	5	conclusions	conclusion	NOUN
ejpam-3200	13	6	.	.	PUNCT
ejpam-3200	14	1	email	email	NOUN
ejpam-3200	14	2	address	address	NOUN
ejpam-3200	14	3	:	:	PUNCT
ejpam-3200	14	4	mowia-84@hotmail.com	mowia-84@hotmail.com	PROPN
ejpam-3200	14	5	,	,	PUNCT
ejpam-3200	14	6	muawya.ebrahim@gmail.com	muawya.ebrahim@gmail.com	X
ejpam-3200	14	7	(	(	PUNCT
ejpam-3200	14	8	m.e	m.e	PROPN
ejpam-3200	14	9	.	.	PROPN
ejpam-3200	14	10	hamid	hamid	PROPN
ejpam-3200	14	11	)	)	PUNCT
ejpam-3200	14	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3200	15	1	493	493	NUM
ejpam-3200	15	2	c	c	X
ejpam-3200	15	3	©	©	PROPN
ejpam-3200	15	4	2018	2018	NUM
ejpam-3200	15	5	ejpam	ejpam	VERB
ejpam-3200	15	6	all	all	DET
ejpam-3200	15	7	rights	right	NOUN
ejpam-3200	15	8	reserved	reserve	VERB
ejpam-3200	15	9	.	.	PUNCT
ejpam-3200	16	1	m.	m.	NOUN
ejpam-3200	16	2	e.	e.	PROPN
ejpam-3200	16	3	hamid	hamid	PROPN
ejpam-3200	16	4	/	/	SYM
ejpam-3200	16	5	eur	eur	PROPN
ejpam-3200	16	6	.	.	PUNCT
ejpam-3200	17	1	j.	j.	PROPN
ejpam-3200	17	2	pure	pure	PROPN
ejpam-3200	17	3	appl	appl	PROPN
ejpam-3200	17	4	.	.	PROPN
ejpam-3200	17	5	math	math	PROPN
ejpam-3200	17	6	,	,	PUNCT
ejpam-3200	17	7	11	11	NUM
ejpam-3200	17	8	(	(	PUNCT
ejpam-3200	17	9	2	2	NUM
ejpam-3200	17	10	)	)	PUNCT
ejpam-3200	17	11	(	(	PUNCT
ejpam-3200	17	12	2018	2018	NUM
ejpam-3200	17	13	)	)	PUNCT
ejpam-3200	17	14	,	,	PUNCT
ejpam-3200	17	15	493	493	NUM
ejpam-3200	17	16	-	-	SYM
ejpam-3200	17	17	504	504	NUM
ejpam-3200	17	18	494	494	NUM
ejpam-3200	17	19	2	2	NUM
ejpam-3200	17	20	.	.	PUNCT
ejpam-3200	17	21	preliminaries	preliminary	NOUN
ejpam-3200	17	22	a	a	DET
ejpam-3200	17	23	time	time	NOUN
ejpam-3200	17	24	scale	scale	NOUN
ejpam-3200	17	25	t	t	PROPN
ejpam-3200	17	26	is	be	AUX
ejpam-3200	17	27	a	a	DET
ejpam-3200	17	28	nonempty	nonempty	ADV
ejpam-3200	17	29	closed	close	VERB
ejpam-3200	17	30	subset	subset	NOUN
ejpam-3200	17	31	of	of	ADP
ejpam-3200	17	32	real	real	ADJ
ejpam-3200	17	33	number	number	NOUN
ejpam-3200	17	34	r	r	NOUN
ejpam-3200	17	35	with	with	ADP
ejpam-3200	17	36	the	the	DET
ejpam-3200	17	37	subspace	subspace	NOUN
ejpam-3200	17	38	topology	topology	NOUN
ejpam-3200	17	39	inherited	inherit	VERB
ejpam-3200	17	40	from	from	ADP
ejpam-3200	17	41	the	the	DET
ejpam-3200	17	42	standard	standard	ADJ
ejpam-3200	17	43	topology	topology	NOUN
ejpam-3200	17	44	of	of	ADP
ejpam-3200	17	45	r.	r.	PROPN
ejpam-3200	17	46	for	for	ADP
ejpam-3200	17	47	t	t	PROPN
ejpam-3200	17	48	∈	∈	PROPN
ejpam-3200	17	49	t	t	NOUN
ejpam-3200	17	50	we	we	PRON
ejpam-3200	17	51	define	define	VERB
ejpam-3200	17	52	the	the	DET
ejpam-3200	17	53	forward	forward	ADJ
ejpam-3200	17	54	jump	jump	NOUN
ejpam-3200	17	55	operator	operator	NOUN
ejpam-3200	17	56	σ(t	σ(t	NOUN
ejpam-3200	17	57	)	)	PUNCT
ejpam-3200	18	1	=	=	PUNCT
ejpam-3200	18	2	inf{s	inf{s	PROPN
ejpam-3200	18	3	∈	∈	PROPN
ejpam-3200	18	4	t	t	NOUN
ejpam-3200	18	5	:	:	PUNCT
ejpam-3200	18	6	s	s	X
ejpam-3200	18	7	>	>	X
ejpam-3200	18	8	t	t	PROPN
ejpam-3200	18	9	}	}	PUNCT
ejpam-3200	18	10	where	where	SCONJ
ejpam-3200	18	11	inf	inf	PROPN
ejpam-3200	18	12	φ	φ	PROPN
ejpam-3200	18	13	=	=	SYM
ejpam-3200	18	14	sup{t	sup{t	PROPN
ejpam-3200	18	15	}	}	PUNCT
ejpam-3200	18	16	,	,	PUNCT
ejpam-3200	18	17	while	while	SCONJ
ejpam-3200	18	18	the	the	DET
ejpam-3200	18	19	backward	backward	ADJ
ejpam-3200	18	20	jump	jump	NOUN
ejpam-3200	18	21	operator	operator	NOUN
ejpam-3200	18	22	ρ(t	ρ(t	NUM
ejpam-3200	18	23	)	)	PUNCT
ejpam-3200	18	24	=	=	PUNCT
ejpam-3200	18	25	sup{s	sup{s	PROPN
ejpam-3200	18	26	∈	∈	PROPN
ejpam-3200	18	27	t	t	NOUN
ejpam-3200	18	28	:	:	PUNCT
ejpam-3200	18	29	s	s	X
ejpam-3200	18	30	<	<	X
ejpam-3200	18	31	t	t	PROPN
ejpam-3200	18	32	}	}	PUNCT
ejpam-3200	18	33	where	where	SCONJ
ejpam-3200	18	34	supφ	supφ	NOUN
ejpam-3200	18	35	=	=	SYM
ejpam-3200	18	36	inf{t	inf{t	NOUN
ejpam-3200	18	37	}	}	PUNCT
ejpam-3200	18	38	.	.	PUNCT
ejpam-3200	19	1	if	if	SCONJ
ejpam-3200	19	2	σ(t	σ(t	PROPN
ejpam-3200	19	3	)	)	PUNCT
ejpam-3200	19	4	>	>	X
ejpam-3200	20	1	t	t	PROPN
ejpam-3200	20	2	,	,	PUNCT
ejpam-3200	20	3	we	we	PRON
ejpam-3200	20	4	say	say	VERB
ejpam-3200	20	5	that	that	SCONJ
ejpam-3200	20	6	t	t	PROPN
ejpam-3200	20	7	is	be	AUX
ejpam-3200	20	8	right	right	ADV
ejpam-3200	20	9	-	-	PUNCT
ejpam-3200	20	10	scattered	scatter	VERB
ejpam-3200	20	11	,	,	PUNCT
ejpam-3200	20	12	while	while	SCONJ
ejpam-3200	20	13	if	if	SCONJ
ejpam-3200	20	14	ρ(t	ρ(t	NUM
ejpam-3200	20	15	)	)	PUNCT
ejpam-3200	20	16	<	<	X
ejpam-3200	20	17	t	t	PROPN
ejpam-3200	20	18	,	,	PUNCT
ejpam-3200	20	19	we	we	PRON
ejpam-3200	20	20	say	say	VERB
ejpam-3200	20	21	that	that	SCONJ
ejpam-3200	20	22	t	t	PROPN
ejpam-3200	20	23	is	be	AUX
ejpam-3200	20	24	left	leave	VERB
ejpam-3200	20	25	-	-	PUNCT
ejpam-3200	20	26	scattered	scatter	VERB
ejpam-3200	20	27	.	.	PUNCT
ejpam-3200	21	1	if	if	SCONJ
ejpam-3200	21	2	σ(t	σ(t	PROPN
ejpam-3200	21	3	)	)	PUNCT
ejpam-3200	21	4	=	=	SYM
ejpam-3200	21	5	t	t	PROPN
ejpam-3200	21	6	,	,	PUNCT
ejpam-3200	21	7	we	we	PRON
ejpam-3200	21	8	say	say	VERB
ejpam-3200	21	9	that	that	SCONJ
ejpam-3200	21	10	t	t	PROPN
ejpam-3200	21	11	is	be	AUX
ejpam-3200	21	12	right	right	ADJ
ejpam-3200	21	13	-	-	PUNCT
ejpam-3200	21	14	dense	dense	ADJ
ejpam-3200	21	15	,	,	PUNCT
ejpam-3200	21	16	while	while	SCONJ
ejpam-3200	21	17	if	if	SCONJ
ejpam-3200	21	18	ρ(t	ρ(t	NUM
ejpam-3200	21	19	)	)	PUNCT
ejpam-3200	22	1	=	=	SYM
ejpam-3200	22	2	t	t	PROPN
ejpam-3200	22	3	,	,	PUNCT
ejpam-3200	22	4	we	we	PRON
ejpam-3200	22	5	say	say	VERB
ejpam-3200	22	6	that	that	SCONJ
ejpam-3200	22	7	t	t	PROPN
ejpam-3200	22	8	is	be	AUX
ejpam-3200	22	9	left	leave	VERB
ejpam-3200	22	10	-	-	PUNCT
ejpam-3200	22	11	dense	dense	ADJ
ejpam-3200	22	12	.	.	PUNCT
ejpam-3200	23	1	the	the	DET
ejpam-3200	23	2	forward	forward	ADJ
ejpam-3200	23	3	graininess	graininess	NOUN
ejpam-3200	23	4	function	function	NOUN
ejpam-3200	23	5	µ(t	µ(t	ADJ
ejpam-3200	23	6	)	)	PUNCT
ejpam-3200	23	7	of	of	ADP
ejpam-3200	23	8	t	t	PROPN
ejpam-3200	23	9	∈	∈	PROPN
ejpam-3200	23	10	t	t	PROPN
ejpam-3200	23	11	is	be	AUX
ejpam-3200	23	12	defined	define	VERB
ejpam-3200	23	13	by	by	ADP
ejpam-3200	23	14	µ(t	µ(t	ADJ
ejpam-3200	23	15	)	)	PUNCT
ejpam-3200	23	16	=	=	SYM
ejpam-3200	23	17	σ(t)−	σ(t)−	PROPN
ejpam-3200	23	18	t	t	PROPN
ejpam-3200	23	19	,	,	PUNCT
ejpam-3200	23	20	whlie	whlie	NOUN
ejpam-3200	23	21	the	the	DET
ejpam-3200	23	22	backward	backward	ADJ
ejpam-3200	23	23	graininess	graininess	NOUN
ejpam-3200	23	24	function	function	NOUN
ejpam-3200	23	25	ν(t	ν(t	NOUN
ejpam-3200	23	26	)	)	PUNCT
ejpam-3200	23	27	of	of	ADP
ejpam-3200	23	28	t	t	PROPN
ejpam-3200	23	29	∈	∈	PROPN
ejpam-3200	23	30	t	t	PROPN
ejpam-3200	23	31	is	be	AUX
ejpam-3200	23	32	defined	define	VERB
ejpam-3200	23	33	by	by	ADP
ejpam-3200	23	34	ν(t	ν(t	NOUN
ejpam-3200	23	35	)	)	PUNCT
ejpam-3200	23	36	=	=	SYM
ejpam-3200	23	37	t	t	PROPN
ejpam-3200	23	38	−	−	PROPN
ejpam-3200	23	39	ρ(t	ρ(t	NUM
ejpam-3200	23	40	)	)	PUNCT
ejpam-3200	23	41	.	.	PUNCT
ejpam-3200	24	1	for	for	ADP
ejpam-3200	24	2	a	a	DET
ejpam-3200	24	3	,	,	PUNCT
ejpam-3200	24	4	b	b	PROPN
ejpam-3200	24	5	∈	∈	PROPN
ejpam-3200	24	6	t	t	NOUN
ejpam-3200	24	7	we	we	PRON
ejpam-3200	24	8	denote	denote	VERB
ejpam-3200	24	9	the	the	DET
ejpam-3200	24	10	closed	closed	ADJ
ejpam-3200	24	11	interval	interval	NOUN
ejpam-3200	24	12	[	[	X
ejpam-3200	24	13	a	a	DET
ejpam-3200	24	14	,	,	PUNCT
ejpam-3200	24	15	b]t	b]t	NOUN
ejpam-3200	24	16	=	=	SYM
ejpam-3200	24	17	{	{	PUNCT
ejpam-3200	24	18	t	t	PROPN
ejpam-3200	24	19	∈	∈	PROPN
ejpam-3200	24	20	t	t	PROPN
ejpam-3200	24	21	:	:	PUNCT
ejpam-3200	24	22	a	a	DET
ejpam-3200	24	23	≤	≤	NUM
ejpam-3200	24	24	t	t	X
ejpam-3200	24	25	≤	≤	NUM
ejpam-3200	24	26	b	b	NOUN
ejpam-3200	24	27	}	}	PUNCT
ejpam-3200	24	28	.	.	PUNCT
ejpam-3200	25	1	throughout	throughout	ADP
ejpam-3200	25	2	this	this	DET
ejpam-3200	25	3	paper	paper	NOUN
ejpam-3200	25	4	,	,	PUNCT
ejpam-3200	25	5	all	all	DET
ejpam-3200	25	6	considered	consider	VERB
ejpam-3200	25	7	intervals	interval	NOUN
ejpam-3200	25	8	will	will	AUX
ejpam-3200	25	9	be	be	AUX
ejpam-3200	25	10	intervals	interval	NOUN
ejpam-3200	25	11	in	in	ADP
ejpam-3200	25	12	t.	t.	PROPN
ejpam-3200	25	13	a	a	DET
ejpam-3200	25	14	division	division	NOUN
ejpam-3200	25	15	p	p	NOUN
ejpam-3200	25	16	of	of	ADP
ejpam-3200	25	17	[	[	X
ejpam-3200	25	18	a	a	PRON
ejpam-3200	25	19	,	,	PUNCT
ejpam-3200	25	20	b]t	b]t	NOUN
ejpam-3200	25	21	is	be	AUX
ejpam-3200	25	22	a	a	DET
ejpam-3200	25	23	finite	finite	ADJ
ejpam-3200	25	24	collection	collection	NOUN
ejpam-3200	25	25	of	of	ADP
ejpam-3200	25	26	interval	interval	NOUN
ejpam-3200	25	27	-	-	PUNCT
ejpam-3200	25	28	point	point	NOUN
ejpam-3200	25	29	pairs	pair	NOUN
ejpam-3200	25	30	{	{	PUNCT
ejpam-3200	25	31	(	(	PUNCT
ejpam-3200	25	32	[	[	X
ejpam-3200	25	33	ti−1	ti−1	NOUN
ejpam-3200	25	34	,	,	PUNCT
ejpam-3200	25	35	ti]t	ti]t	PROPN
ejpam-3200	25	36	;	;	PUNCT
ejpam-3200	25	37	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	25	38	,	,	PUNCT
ejpam-3200	25	39	where	where	SCONJ
ejpam-3200	25	40	{	{	PUNCT
ejpam-3200	25	41	a	a	PRON
ejpam-3200	25	42	=	=	X
ejpam-3200	25	43	t0	t0	PROPN
ejpam-3200	25	44	<	<	X
ejpam-3200	25	45	t1	t1	NOUN
ejpam-3200	25	46	<	<	X
ejpam-3200	25	47	·	·	PUNCT
ejpam-3200	25	48	·	·	PUNCT
ejpam-3200	25	49	·	·	PUNCT
ejpam-3200	26	1	<	<	X
ejpam-3200	26	2	tn−1	tn−1	PROPN
ejpam-3200	26	3	<	<	X
ejpam-3200	26	4	tn	tn	PROPN
ejpam-3200	26	5	=	=	SYM
ejpam-3200	26	6	b	b	NOUN
ejpam-3200	26	7	}	}	PUNCT
ejpam-3200	26	8	and	and	CCONJ
ejpam-3200	26	9	ξi	ξi	NUM
ejpam-3200	26	10	∈	∈	PROPN
ejpam-3200	27	1	[	[	X
ejpam-3200	27	2	a	a	DET
ejpam-3200	27	3	,	,	PUNCT
ejpam-3200	27	4	b]t	b]t	NOUN
ejpam-3200	27	5	for	for	ADP
ejpam-3200	27	6	i	i	PROPN
ejpam-3200	27	7	=	=	SYM
ejpam-3200	27	8	1	1	NUM
ejpam-3200	27	9	,	,	PUNCT
ejpam-3200	27	10	2	2	NUM
ejpam-3200	27	11	,	,	PUNCT
ejpam-3200	27	12	·	·	PUNCT
ejpam-3200	27	13	·	·	PUNCT
ejpam-3200	27	14	·	·	PUNCT
ejpam-3200	27	15	,	,	PUNCT
ejpam-3200	27	16	n.	n.	NOUN
ejpam-3200	27	17	by	by	ADP
ejpam-3200	27	18	∆ti	∆ti	NOUN
ejpam-3200	27	19	=	=	SYM
ejpam-3200	27	20	ti	ti	NOUN
ejpam-3200	27	21	−	−	NOUN
ejpam-3200	27	22	ti−1	ti−1	NOUN
ejpam-3200	27	23	we	we	PRON
ejpam-3200	27	24	denote	denote	VERB
ejpam-3200	27	25	the	the	DET
ejpam-3200	27	26	length	length	NOUN
ejpam-3200	27	27	of	of	ADP
ejpam-3200	27	28	ith	ith	PROPN
ejpam-3200	27	29	subinterval	subinterval	NOUN
ejpam-3200	27	30	in	in	ADP
ejpam-3200	27	31	the	the	DET
ejpam-3200	27	32	division	division	NOUN
ejpam-3200	27	33	p	p	NOUN
ejpam-3200	27	34	.	.	PUNCT
ejpam-3200	28	1	δ(ξ	δ(ξ	NOUN
ejpam-3200	28	2	)	)	PUNCT
ejpam-3200	28	3	=	=	SYM
ejpam-3200	28	4	(	(	PUNCT
ejpam-3200	28	5	δl(ξ	δl(ξ	NOUN
ejpam-3200	28	6	)	)	PUNCT
ejpam-3200	28	7	,	,	PUNCT
ejpam-3200	29	1	δr(ξ	δr(ξ	ADP
ejpam-3200	29	2	)	)	PUNCT
ejpam-3200	29	3	)	)	PUNCT
ejpam-3200	29	4	is	be	AUX
ejpam-3200	29	5	a	a	DET
ejpam-3200	29	6	∆gauge	∆gauge	NOUN
ejpam-3200	29	7	for	for	ADP
ejpam-3200	29	8	[	[	X
ejpam-3200	29	9	a	a	PRON
ejpam-3200	29	10	,	,	PUNCT
ejpam-3200	29	11	b]t	b]t	ADV
ejpam-3200	29	12	provided	provide	VERB
ejpam-3200	29	13	δl(ξ	δl(ξ	NOUN
ejpam-3200	29	14	)	)	PUNCT
ejpam-3200	29	15	>	>	X
ejpam-3200	29	16	0	0	PUNCT
ejpam-3200	30	1	on	on	ADP
ejpam-3200	30	2	(	(	PUNCT
ejpam-3200	30	3	a	a	DET
ejpam-3200	30	4	,	,	PUNCT
ejpam-3200	30	5	b]t	b]t	NOUN
ejpam-3200	30	6	,	,	PUNCT
ejpam-3200	30	7	δr(ξ	δr(ξ	ADP
ejpam-3200	30	8	)	)	PUNCT
ejpam-3200	30	9	>	>	X
ejpam-3200	30	10	0	0	PUNCT
ejpam-3200	31	1	on	on	ADP
ejpam-3200	31	2	[	[	X
ejpam-3200	31	3	a	a	PRON
ejpam-3200	31	4	,	,	PUNCT
ejpam-3200	31	5	b)t	b)t	NOUN
ejpam-3200	31	6	,	,	PUNCT
ejpam-3200	31	7	δl(a	δl(a	X
ejpam-3200	31	8	)	)	PUNCT
ejpam-3200	31	9	≥	≥	NOUN
ejpam-3200	31	10	0	0	NUM
ejpam-3200	31	11	,	,	PUNCT
ejpam-3200	31	12	δr(b	δr(b	NUM
ejpam-3200	31	13	)	)	PUNCT
ejpam-3200	31	14	≥	≥	NOUN
ejpam-3200	31	15	0	0	NUM
ejpam-3200	31	16	and	and	CCONJ
ejpam-3200	31	17	δr(b	δr(b	NUM
ejpam-3200	31	18	)	)	PUNCT
ejpam-3200	31	19	≥	≥	NOUN
ejpam-3200	31	20	µ(ξ	µ(ξ	NOUN
ejpam-3200	31	21	)	)	PUNCT
ejpam-3200	31	22	for	for	ADP
ejpam-3200	31	23	all	all	DET
ejpam-3200	31	24	ξ	ξ	X
ejpam-3200	31	25	∈	∈	PROPN
ejpam-3200	31	26	[	[	X
ejpam-3200	31	27	a	a	DET
ejpam-3200	31	28	,	,	PUNCT
ejpam-3200	31	29	b)t	b)t	NOUN
ejpam-3200	31	30	.	.	PUNCT
ejpam-3200	32	1	we	we	PRON
ejpam-3200	32	2	say	say	VERB
ejpam-3200	32	3	that	that	SCONJ
ejpam-3200	32	4	p	p	PROPN
ejpam-3200	32	5	=	=	X
ejpam-3200	32	6	{	{	PUNCT
ejpam-3200	32	7	(	(	PUNCT
ejpam-3200	32	8	[	[	X
ejpam-3200	32	9	ti−1	ti−1	NOUN
ejpam-3200	32	10	,	,	PUNCT
ejpam-3200	32	11	ti]t	ti]t	PROPN
ejpam-3200	32	12	;	;	PUNCT
ejpam-3200	32	13	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	32	14	is	be	AUX
ejpam-3200	32	15	a	a	DET
ejpam-3200	32	16	δ	δ	NOUN
ejpam-3200	32	17	-	-	PUNCT
ejpam-3200	32	18	fine	fine	ADJ
ejpam-3200	32	19	mcshane	mcshane	PROPN
ejpam-3200	32	20	division	division	NOUN
ejpam-3200	32	21	of	of	ADP
ejpam-3200	32	22	[	[	X
ejpam-3200	32	23	a	a	PRON
ejpam-3200	32	24	,	,	PUNCT
ejpam-3200	32	25	b]t	b]t	NOUN
ejpam-3200	32	26	if	if	SCONJ
ejpam-3200	32	27	[	[	X
ejpam-3200	32	28	ti−1	ti−1	NOUN
ejpam-3200	32	29	,	,	PUNCT
ejpam-3200	32	30	ti]t	ti]t	PROPN
ejpam-3200	32	31	⊂	⊂	PROPN
ejpam-3200	32	32	(	(	PUNCT
ejpam-3200	32	33	ξi	ξi	NOUN
ejpam-3200	32	34	−	−	PROPN
ejpam-3200	32	35	δl(ξi	δl(ξi	PROPN
ejpam-3200	32	36	)	)	PUNCT
ejpam-3200	32	37	,	,	PUNCT
ejpam-3200	32	38	ξi	ξi	NOUN
ejpam-3200	32	39	+	+	CCONJ
ejpam-3200	32	40	δr(ξi	δr(ξi	ADJ
ejpam-3200	32	41	)	)	PUNCT
ejpam-3200	32	42	)	)	PUNCT
ejpam-3200	33	1	t	t	NOUN
ejpam-3200	33	2	and	and	CCONJ
ejpam-3200	33	3	ξi	ξi	NUM
ejpam-3200	33	4	∈	∈	PROPN
ejpam-3200	34	1	[	[	X
ejpam-3200	34	2	a	a	DET
ejpam-3200	34	3	,	,	PUNCT
ejpam-3200	34	4	b]t	b]t	NOUN
ejpam-3200	34	5	for	for	ADP
ejpam-3200	34	6	all	all	PRON
ejpam-3200	34	7	i	i	PRON
ejpam-3200	34	8	=	=	NOUN
ejpam-3200	34	9	1	1	NUM
ejpam-3200	34	10	,	,	PUNCT
ejpam-3200	34	11	2	2	NUM
ejpam-3200	34	12	,	,	PUNCT
ejpam-3200	34	13	·	·	PUNCT
ejpam-3200	34	14	·	·	PUNCT
ejpam-3200	34	15	·	·	PUNCT
ejpam-3200	34	16	,	,	PUNCT
ejpam-3200	34	17	n.	n.	NOUN
ejpam-3200	34	18	definition	definition	NOUN
ejpam-3200	34	19	1	1	NUM
ejpam-3200	34	20	.	.	PUNCT
ejpam-3200	35	1	[	[	X
ejpam-3200	35	2	10	10	NUM
ejpam-3200	35	3	]	]	PUNCT
ejpam-3200	35	4	let	let	VERB
ejpam-3200	35	5	α	α	PRON
ejpam-3200	35	6	:	:	PUNCT
ejpam-3200	36	1	[	[	X
ejpam-3200	36	2	a	a	X
ejpam-3200	36	3	,	,	PUNCT
ejpam-3200	36	4	b	b	NOUN
ejpam-3200	36	5	]	]	X
ejpam-3200	36	6	→	→	PUNCT
ejpam-3200	36	7	r	r	NOUN
ejpam-3200	36	8	be	be	AUX
ejpam-3200	36	9	an	an	DET
ejpam-3200	36	10	increasing	increase	VERB
ejpam-3200	36	11	function	function	NOUN
ejpam-3200	36	12	.	.	PUNCT
ejpam-3200	37	1	a	a	DET
ejpam-3200	37	2	real	real	ADV
ejpam-3200	37	3	-	-	PUNCT
ejpam-3200	37	4	valued	value	VERB
ejpam-3200	37	5	function	function	NOUN
ejpam-3200	37	6	f	f	NOUN
ejpam-3200	37	7	:	:	PUNCT
ejpam-3200	37	8	[	[	X
ejpam-3200	37	9	a	a	X
ejpam-3200	37	10	,	,	PUNCT
ejpam-3200	37	11	b	b	NOUN
ejpam-3200	37	12	]	]	X
ejpam-3200	37	13	→	→	PUNCT
ejpam-3200	37	14	r	r	NOUN
ejpam-3200	37	15	is	be	AUX
ejpam-3200	37	16	said	say	VERB
ejpam-3200	37	17	to	to	PART
ejpam-3200	37	18	be	be	AUX
ejpam-3200	37	19	mcshane	mcshane	NOUN
ejpam-3200	37	20	-	-	PUNCT
ejpam-3200	37	21	stieltjes	stieltjes	PROPN
ejpam-3200	37	22	(	(	PUNCT
ejpam-3200	37	23	ms	ms	PROPN
ejpam-3200	37	24	)	)	PUNCT
ejpam-3200	37	25	integrable	integrable	ADJ
ejpam-3200	37	26	to	to	ADP
ejpam-3200	37	27	b	b	NOUN
ejpam-3200	37	28	with	with	ADP
ejpam-3200	37	29	respect	respect	NOUN
ejpam-3200	37	30	to	to	ADP
ejpam-3200	37	31	α	α	NOUN
ejpam-3200	37	32	on	on	ADP
ejpam-3200	37	33	[	[	X
ejpam-3200	37	34	a	a	X
ejpam-3200	37	35	,	,	PUNCT
ejpam-3200	37	36	b	b	NOUN
ejpam-3200	37	37	]	]	X
ejpam-3200	37	38	if	if	SCONJ
ejpam-3200	37	39	for	for	ADP
ejpam-3200	37	40	every	every	DET
ejpam-3200	37	41	ε	ε	PROPN
ejpam-3200	37	42	>	>	X
ejpam-3200	37	43	0	0	PROPN
ejpam-3200	37	44	,	,	PUNCT
ejpam-3200	37	45	there	there	PRON
ejpam-3200	37	46	is	be	VERB
ejpam-3200	37	47	a	a	DET
ejpam-3200	37	48	function	function	NOUN
ejpam-3200	37	49	δ(t	δ(t	NOUN
ejpam-3200	37	50	)	)	PUNCT
ejpam-3200	37	51	>	>	X
ejpam-3200	37	52	0	0	PUNCT
ejpam-3200	38	1	such	such	ADJ
ejpam-3200	38	2	that	that	PRON
ejpam-3200	38	3	for	for	ADP
ejpam-3200	38	4	any	any	DET
ejpam-3200	38	5	δ	δ	PROPN
ejpam-3200	38	6	-	-	PUNCT
ejpam-3200	38	7	fine	fine	ADJ
ejpam-3200	38	8	mcshane	mcshane	PROPN
ejpam-3200	38	9	division	division	NOUN
ejpam-3200	38	10	p	p	NOUN
ejpam-3200	38	11	=	=	PUNCT
ejpam-3200	38	12	{	{	PUNCT
ejpam-3200	38	13	[	[	X
ejpam-3200	38	14	ui	ui	PROPN
ejpam-3200	38	15	,	,	PUNCT
ejpam-3200	38	16	vi	vi	PROPN
ejpam-3200	38	17	]	]	PUNCT
ejpam-3200	38	18	;	;	PUNCT
ejpam-3200	38	19	ξi}ni=1	ξi}ni=1	PROPN
ejpam-3200	38	20	of	of	ADP
ejpam-3200	38	21	[	[	X
ejpam-3200	38	22	a	a	X
ejpam-3200	38	23	,	,	PUNCT
ejpam-3200	38	24	b	b	NOUN
ejpam-3200	38	25	]	]	X
ejpam-3200	38	26	,	,	PUNCT
ejpam-3200	38	27	we	we	PRON
ejpam-3200	38	28	have∣∣	have∣∣	VERB
ejpam-3200	38	29	n∑	n∑	PROPN
ejpam-3200	38	30	i=1	i=1	PROPN
ejpam-3200	38	31	f(ξi)[α(vi)−	f(ξi)[α(vi)−	PROPN
ejpam-3200	38	32	α(ui)]−b	α(ui)]−b	X
ejpam-3200	38	33	∣∣	∣∣	X
ejpam-3200	38	34	<	<	X
ejpam-3200	38	35	ε	ε	PROPN
ejpam-3200	38	36	,	,	PUNCT
ejpam-3200	38	37	(	(	PUNCT
ejpam-3200	38	38	2.1	2.1	NUM
ejpam-3200	38	39	)	)	PUNCT
ejpam-3200	38	40	we	we	PRON
ejpam-3200	38	41	write	write	VERB
ejpam-3200	38	42	(	(	PUNCT
ejpam-3200	38	43	ms	ms	PROPN
ejpam-3200	38	44	)	)	PUNCT
ejpam-3200	38	45	b∫	b∫	PROPN
ejpam-3200	38	46	a	a	DET
ejpam-3200	38	47	f(t)dα	f(t)dα	PROPN
ejpam-3200	38	48	=	=	SYM
ejpam-3200	38	49	b	b	PROPN
ejpam-3200	38	50	,	,	PUNCT
ejpam-3200	38	51	and	and	CCONJ
ejpam-3200	38	52	f	f	PROPN
ejpam-3200	38	53	∈msα[a	∈msα[a	PROPN
ejpam-3200	38	54	,	,	PUNCT
ejpam-3200	38	55	b	b	NOUN
ejpam-3200	38	56	]	]	PUNCT
ejpam-3200	38	57	.	.	PUNCT
ejpam-3200	39	1	definition	definition	NOUN
ejpam-3200	39	2	2	2	NUM
ejpam-3200	39	3	.	.	PUNCT
ejpam-3200	40	1	let	let	VERB
ejpam-3200	40	2	α	α	PRON
ejpam-3200	40	3	:	:	PUNCT
ejpam-3200	41	1	[	[	X
ejpam-3200	41	2	a	a	DET
ejpam-3200	41	3	,	,	PUNCT
ejpam-3200	41	4	b]t	b]t	NOUN
ejpam-3200	41	5	→	→	SYM
ejpam-3200	41	6	r	r	NOUN
ejpam-3200	41	7	be	be	AUX
ejpam-3200	41	8	an	an	DET
ejpam-3200	41	9	increasing	increase	VERB
ejpam-3200	41	10	function	function	NOUN
ejpam-3200	41	11	.	.	PUNCT
ejpam-3200	42	1	a	a	DET
ejpam-3200	42	2	function	function	NOUN
ejpam-3200	42	3	f	f	NOUN
ejpam-3200	42	4	:	:	PUNCT
ejpam-3200	43	1	[	[	X
ejpam-3200	43	2	a	a	PRON
ejpam-3200	43	3	,	,	PUNCT
ejpam-3200	43	4	b]t	b]t	NOUN
ejpam-3200	43	5	→	→	SYM
ejpam-3200	43	6	r	r	NOUN
ejpam-3200	43	7	is	be	AUX
ejpam-3200	43	8	mcshane	mcshane	NOUN
ejpam-3200	43	9	-	-	PUNCT
ejpam-3200	43	10	stieltjes	stieltjes	PROPN
ejpam-3200	43	11	delta	delta	PROPN
ejpam-3200	43	12	integrable	integrable	ADJ
ejpam-3200	43	13	(	(	PUNCT
ejpam-3200	43	14	ms	ms	NOUN
ejpam-3200	43	15	∆-integrable	∆-integrable	ADJ
ejpam-3200	43	16	)	)	PUNCT
ejpam-3200	43	17	with	with	ADP
ejpam-3200	43	18	respect	respect	NOUN
ejpam-3200	43	19	to	to	ADP
ejpam-3200	43	20	α	α	NOUN
ejpam-3200	43	21	on	on	ADP
ejpam-3200	43	22	[	[	X
ejpam-3200	43	23	a	a	DET
ejpam-3200	43	24	,	,	PUNCT
ejpam-3200	43	25	b]t	b]t	NOUN
ejpam-3200	43	26	if	if	SCONJ
ejpam-3200	43	27	there	there	PRON
ejpam-3200	43	28	exists	exist	VERB
ejpam-3200	43	29	a	a	DET
ejpam-3200	43	30	number	number	NOUN
ejpam-3200	43	31	a	a	DET
ejpam-3200	43	32	∈	∈	NOUN
ejpam-3200	43	33	r	r	NOUN
ejpam-3200	43	34	such	such	ADJ
ejpam-3200	43	35	that	that	PRON
ejpam-3200	43	36	for	for	ADP
ejpam-3200	43	37	each	each	DET
ejpam-3200	43	38	ε	ε	PROPN
ejpam-3200	43	39	>	>	X
ejpam-3200	43	40	0	0	PUNCT
ejpam-3200	44	1	there	there	PRON
ejpam-3200	44	2	is	be	VERB
ejpam-3200	44	3	a	a	DET
ejpam-3200	44	4	∆-gauge	∆-gauge	NOUN
ejpam-3200	44	5	,	,	PUNCT
ejpam-3200	44	6	δ	δ	PROPN
ejpam-3200	44	7	,	,	PUNCT
ejpam-3200	44	8	on	on	ADP
ejpam-3200	44	9	[	[	X
ejpam-3200	44	10	a	a	PRON
ejpam-3200	44	11	,	,	PUNCT
ejpam-3200	44	12	b]t	b]t	VERB
ejpam-3200	44	13	such	such	ADJ
ejpam-3200	44	14	that∣∣	that∣∣	PROPN
ejpam-3200	44	15	n∑	n∑	PROPN
ejpam-3200	44	16	i=1	i=1	PROPN
ejpam-3200	44	17	f(ξi)[α(ti)−	f(ξi)[α(ti)−	PROPN
ejpam-3200	44	18	α(ti−1)]−a	α(ti−1)]−a	NUM
ejpam-3200	44	19	∣∣	∣∣	X
ejpam-3200	44	20	<	<	X
ejpam-3200	44	21	ε	ε	PROPN
ejpam-3200	44	22	(	(	PUNCT
ejpam-3200	44	23	2.2	2.2	NUM
ejpam-3200	44	24	)	)	PUNCT
ejpam-3200	44	25	for	for	ADP
ejpam-3200	44	26	each	each	DET
ejpam-3200	44	27	δ	δ	PROPN
ejpam-3200	44	28	-	-	PUNCT
ejpam-3200	44	29	fine	fine	PROPN
ejpam-3200	44	30	mcshane	mcshane	PROPN
ejpam-3200	44	31	division	division	NOUN
ejpam-3200	44	32	p	p	NOUN
ejpam-3200	44	33	=	=	PUNCT
ejpam-3200	44	34	{	{	PUNCT
ejpam-3200	44	35	(	(	PUNCT
ejpam-3200	44	36	[	[	X
ejpam-3200	44	37	ti−1	ti−1	NOUN
ejpam-3200	44	38	,	,	PUNCT
ejpam-3200	44	39	ti]t	ti]t	PROPN
ejpam-3200	44	40	;	;	PUNCT
ejpam-3200	44	41	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	44	42	of	of	ADP
ejpam-3200	44	43	[	[	X
ejpam-3200	44	44	a	a	PRON
ejpam-3200	44	45	,	,	PUNCT
ejpam-3200	44	46	b]t	b]t	NOUN
ejpam-3200	44	47	.	.	PUNCT
ejpam-3200	45	1	a	a	PRON
ejpam-3200	45	2	is	be	AUX
ejpam-3200	45	3	called	call	VERB
ejpam-3200	45	4	(	(	PUNCT
ejpam-3200	45	5	ms	ms	PROPN
ejpam-3200	45	6	∆-integral	∆-integral	NOUN
ejpam-3200	45	7	)	)	PUNCT
ejpam-3200	45	8	of	of	ADP
ejpam-3200	45	9	f	f	PROPN
ejpam-3200	45	10	on	on	ADP
ejpam-3200	45	11	[	[	X
ejpam-3200	45	12	a	a	DET
ejpam-3200	45	13	,	,	PUNCT
ejpam-3200	45	14	b]t	b]t	NOUN
ejpam-3200	45	15	,	,	PUNCT
ejpam-3200	45	16	and	and	CCONJ
ejpam-3200	45	17	we	we	PRON
ejpam-3200	45	18	write	write	VERB
ejpam-3200	45	19	a	a	DET
ejpam-3200	45	20	=	=	X
ejpam-3200	45	21	(	(	PUNCT
ejpam-3200	45	22	ms∆	ms∆	PROPN
ejpam-3200	45	23	)	)	PUNCT
ejpam-3200	45	24	b∫	b∫	NOUN
ejpam-3200	45	25	a	a	DET
ejpam-3200	45	26	f(t)dα	f(t)dα	NOUN
ejpam-3200	45	27	.	.	PUNCT
ejpam-3200	46	1	theorem	theorem	NOUN
ejpam-3200	46	2	1	1	NUM
ejpam-3200	46	3	.	.	PUNCT
ejpam-3200	47	1	let	let	VERB
ejpam-3200	47	2	α	α	PRON
ejpam-3200	47	3	:	:	PUNCT
ejpam-3200	48	1	[	[	X
ejpam-3200	48	2	a	a	DET
ejpam-3200	48	3	,	,	PUNCT
ejpam-3200	48	4	b]t	b]t	NOUN
ejpam-3200	48	5	→	→	SYM
ejpam-3200	48	6	r	r	NOUN
ejpam-3200	48	7	be	be	AUX
ejpam-3200	48	8	an	an	DET
ejpam-3200	48	9	increasing	increase	VERB
ejpam-3200	48	10	function	function	NOUN
ejpam-3200	48	11	.	.	PUNCT
ejpam-3200	49	1	if	if	SCONJ
ejpam-3200	49	2	f(t	f(t	NOUN
ejpam-3200	49	3	)	)	PUNCT
ejpam-3200	49	4	and	and	CCONJ
ejpam-3200	49	5	g(t	g(t	PROPN
ejpam-3200	49	6	)	)	PUNCT
ejpam-3200	49	7	are	be	AUX
ejpam-3200	49	8	(	(	PUNCT
ejpam-3200	49	9	ms	ms	NOUN
ejpam-3200	49	10	)	)	PUNCT
ejpam-3200	49	11	∆-integrable	∆-integrable	ADJ
ejpam-3200	49	12	with	with	ADP
ejpam-3200	49	13	respect	respect	NOUN
ejpam-3200	49	14	to	to	ADP
ejpam-3200	49	15	α	α	NOUN
ejpam-3200	49	16	on	on	ADP
ejpam-3200	49	17	[	[	X
ejpam-3200	49	18	a	a	DET
ejpam-3200	49	19	,	,	PUNCT
ejpam-3200	49	20	b]t	b]t	NOUN
ejpam-3200	49	21	and	and	CCONJ
ejpam-3200	49	22	f(t	f(t	NOUN
ejpam-3200	49	23	)	)	PUNCT
ejpam-3200	49	24	≤	≤	NUM
ejpam-3200	49	25	g(t	g(t	PROPN
ejpam-3200	49	26	)	)	PUNCT
ejpam-3200	49	27	almost	almost	ADV
ejpam-3200	49	28	everywhere	everywhere	ADV
ejpam-3200	49	29	on	on	ADP
ejpam-3200	49	30	[	[	X
ejpam-3200	49	31	a	a	DET
ejpam-3200	49	32	,	,	PUNCT
ejpam-3200	49	33	b]t	b]t	NOUN
ejpam-3200	49	34	,	,	PUNCT
ejpam-3200	49	35	then	then	ADV
ejpam-3200	49	36	(	(	PUNCT
ejpam-3200	49	37	ms∆	ms∆	PROPN
ejpam-3200	49	38	)	)	PUNCT
ejpam-3200	49	39	b∫	b∫	NOUN
ejpam-3200	49	40	a	a	DET
ejpam-3200	49	41	f(t)dα	f(t)dα	ADJ
ejpam-3200	49	42	≤	≤	PROPN
ejpam-3200	49	43	(	(	PUNCT
ejpam-3200	49	44	ms∆	ms∆	PROPN
ejpam-3200	49	45	)	)	PUNCT
ejpam-3200	49	46	b∫	b∫	PROPN
ejpam-3200	49	47	a	a	DET
ejpam-3200	49	48	g(t)dα	g(t)dα	PROPN
ejpam-3200	49	49	.	.	PUNCT
ejpam-3200	50	1	(	(	PUNCT
ejpam-3200	50	2	2.3	2.3	NUM
ejpam-3200	50	3	)	)	PUNCT
ejpam-3200	50	4	m.	m.	NOUN
ejpam-3200	50	5	e.	e.	PROPN
ejpam-3200	50	6	hamid	hamid	PROPN
ejpam-3200	50	7	/	/	SYM
ejpam-3200	50	8	eur	eur	PROPN
ejpam-3200	50	9	.	.	PUNCT
ejpam-3200	51	1	j.	j.	PROPN
ejpam-3200	51	2	pure	pure	PROPN
ejpam-3200	51	3	appl	appl	PROPN
ejpam-3200	51	4	.	.	PROPN
ejpam-3200	51	5	math	math	PROPN
ejpam-3200	51	6	,	,	PUNCT
ejpam-3200	51	7	11	11	NUM
ejpam-3200	51	8	(	(	PUNCT
ejpam-3200	51	9	2	2	NUM
ejpam-3200	51	10	)	)	PUNCT
ejpam-3200	51	11	(	(	PUNCT
ejpam-3200	51	12	2018	2018	NUM
ejpam-3200	51	13	)	)	PUNCT
ejpam-3200	51	14	,	,	PUNCT
ejpam-3200	51	15	493	493	NUM
ejpam-3200	51	16	-	-	SYM
ejpam-3200	51	17	504	504	NUM
ejpam-3200	51	18	495	495	NUM
ejpam-3200	51	19	proof	proof	NOUN
ejpam-3200	51	20	.	.	PUNCT
ejpam-3200	52	1	the	the	DET
ejpam-3200	52	2	proof	proof	NOUN
ejpam-3200	52	3	is	be	AUX
ejpam-3200	52	4	similar	similar	ADJ
ejpam-3200	52	5	to	to	AUX
ejpam-3200	52	6	theorem	theorem	VERB
ejpam-3200	52	7	2.7	2.7	NUM
ejpam-3200	52	8	in	in	ADP
ejpam-3200	52	9	[	[	X
ejpam-3200	52	10	10	10	NUM
ejpam-3200	52	11	]	]	PUNCT
ejpam-3200	52	12	.	.	PUNCT
ejpam-3200	53	1	3	3	X
ejpam-3200	53	2	.	.	X
ejpam-3200	53	3	the	the	DET
ejpam-3200	53	4	ms∆	ms∆	PROPN
ejpam-3200	53	5	integral	integral	ADJ
ejpam-3200	53	6	of	of	ADP
ejpam-3200	53	7	interval	interval	NOUN
ejpam-3200	53	8	-	-	PUNCT
ejpam-3200	53	9	valued	value	VERB
ejpam-3200	53	10	functions	function	NOUN
ejpam-3200	53	11	on	on	ADP
ejpam-3200	53	12	time	time	NOUN
ejpam-3200	53	13	scales	scale	NOUN
ejpam-3200	53	14	this	this	DET
ejpam-3200	53	15	section	section	NOUN
ejpam-3200	53	16	introduces	introduce	VERB
ejpam-3200	53	17	the	the	DET
ejpam-3200	53	18	notion	notion	NOUN
ejpam-3200	53	19	of	of	ADP
ejpam-3200	53	20	the	the	DET
ejpam-3200	53	21	ms∆	ms∆	PROPN
ejpam-3200	53	22	integral	integral	ADJ
ejpam-3200	53	23	of	of	ADP
ejpam-3200	53	24	interval	interval	NOUN
ejpam-3200	53	25	-	-	PUNCT
ejpam-3200	53	26	valued	value	VERB
ejpam-3200	53	27	functions	function	NOUN
ejpam-3200	53	28	on	on	ADP
ejpam-3200	53	29	time	time	NOUN
ejpam-3200	53	30	scales	scale	NOUN
ejpam-3200	53	31	and	and	CCONJ
ejpam-3200	53	32	investigates	investigate	VERB
ejpam-3200	53	33	some	some	PRON
ejpam-3200	53	34	of	of	ADP
ejpam-3200	53	35	their	their	PRON
ejpam-3200	53	36	properties	property	NOUN
ejpam-3200	53	37	.	.	PUNCT
ejpam-3200	54	1	definition	definition	NOUN
ejpam-3200	54	2	3	3	NUM
ejpam-3200	54	3	.	.	PUNCT
ejpam-3200	55	1	[	[	X
ejpam-3200	55	2	7	7	X
ejpam-3200	55	3	]	]	PUNCT
ejpam-3200	55	4	let	let	VERB
ejpam-3200	55	5	ir	ir	X
ejpam-3200	55	6	=	=	PRON
ejpam-3200	55	7	{	{	PUNCT
ejpam-3200	55	8	i	i	NOUN
ejpam-3200	55	9	=	=	PUNCT
ejpam-3200	56	1	[	[	X
ejpam-3200	56	2	i−	i−	PROPN
ejpam-3200	56	3	,	,	PUNCT
ejpam-3200	56	4	i+	i+	NUM
ejpam-3200	56	5	]	]	PUNCT
ejpam-3200	56	6	:	:	PUNCT
ejpam-3200	57	1	i	i	PRON
ejpam-3200	57	2	is	be	AUX
ejpam-3200	57	3	the	the	DET
ejpam-3200	57	4	closed	closed	ADJ
ejpam-3200	57	5	bounded	bounded	ADJ
ejpam-3200	57	6	interval	interval	NOUN
ejpam-3200	57	7	on	on	ADP
ejpam-3200	57	8	the	the	DET
ejpam-3200	57	9	real	real	ADJ
ejpam-3200	57	10	line	line	NOUN
ejpam-3200	57	11	r	r	NOUN
ejpam-3200	57	12	}	}	PUNCT
ejpam-3200	57	13	.	.	PUNCT
ejpam-3200	58	1	for	for	ADP
ejpam-3200	58	2	a	a	DET
ejpam-3200	58	3	,	,	PUNCT
ejpam-3200	58	4	b	b	PROPN
ejpam-3200	58	5	∈	∈	PROPN
ejpam-3200	58	6	ir	ir	PROPN
ejpam-3200	58	7	,	,	PUNCT
ejpam-3200	58	8	we	we	PRON
ejpam-3200	58	9	define	define	VERB
ejpam-3200	58	10	a	a	DET
ejpam-3200	58	11	≤	≤	NUM
ejpam-3200	58	12	b	b	NOUN
ejpam-3200	58	13	iff	iff	ADJ
ejpam-3200	58	14	a−	a−	PROPN
ejpam-3200	58	15	≤	≤	NOUN
ejpam-3200	58	16	b−	b−	PROPN
ejpam-3200	58	17	and	and	CCONJ
ejpam-3200	58	18	a+	a+	PUNCT
ejpam-3200	58	19	≤	≤	X
ejpam-3200	58	20	b+	b+	NOUN
ejpam-3200	58	21	,	,	PUNCT
ejpam-3200	58	22	a	a	DET
ejpam-3200	58	23	+	+	X
ejpam-3200	58	24	b	b	NOUN
ejpam-3200	58	25	=	=	SYM
ejpam-3200	58	26	c	c	PROPN
ejpam-3200	58	27	iff	iff	PROPN
ejpam-3200	58	28	c−	c−	NOUN
ejpam-3200	58	29	=	=	SYM
ejpam-3200	58	30	a−	a−	PROPN
ejpam-3200	58	31	+	+	NOUN
ejpam-3200	58	32	b−	b−	PROPN
ejpam-3200	58	33	and	and	CCONJ
ejpam-3200	58	34	c+	c+	VERB
ejpam-3200	58	35	=	=	SYM
ejpam-3200	58	36	a+	a+	PUNCT
ejpam-3200	58	37	+	+	NOUN
ejpam-3200	58	38	b+	b+	NOUN
ejpam-3200	58	39	,	,	PUNCT
ejpam-3200	58	40	and	and	CCONJ
ejpam-3200	58	41	a	a	DET
ejpam-3200	58	42	·	·	SYM
ejpam-3200	58	43	b	b	X
ejpam-3200	58	44	=	=	PUNCT
ejpam-3200	58	45	{	{	PUNCT
ejpam-3200	58	46	a	a	DET
ejpam-3200	58	47	·	·	PUNCT
ejpam-3200	58	48	b	b	NOUN
ejpam-3200	58	49	:	:	PUNCT
ejpam-3200	58	50	a	a	DET
ejpam-3200	58	51	∈	∈	PROPN
ejpam-3200	58	52	a	a	PRON
ejpam-3200	58	53	,	,	PUNCT
ejpam-3200	58	54	b	b	PROPN
ejpam-3200	58	55	∈	∈	PROPN
ejpam-3200	58	56	b	b	NOUN
ejpam-3200	58	57	}	}	PUNCT
ejpam-3200	58	58	,	,	PUNCT
ejpam-3200	58	59	where	where	SCONJ
ejpam-3200	58	60	(	(	PUNCT
ejpam-3200	58	61	a	a	DET
ejpam-3200	58	62	·	·	PUNCT
ejpam-3200	58	63	b)−	b)−	PROPN
ejpam-3200	58	64	=	=	PUNCT
ejpam-3200	58	65	min{a−	min{a−	PROPN
ejpam-3200	58	66	·	·	SYM
ejpam-3200	58	67	b−	b−	PROPN
ejpam-3200	58	68	,	,	PUNCT
ejpam-3200	58	69	a−	a−	PROPN
ejpam-3200	58	70	·	·	PUNCT
ejpam-3200	58	71	b+	b+	X
ejpam-3200	58	72	,	,	PUNCT
ejpam-3200	58	73	a+	a+	PUNCT
ejpam-3200	58	74	·	·	PUNCT
ejpam-3200	58	75	b−	b−	NOUN
ejpam-3200	58	76	,	,	PUNCT
ejpam-3200	58	77	a+	a+	PUNCT
ejpam-3200	58	78	·	·	PUNCT
ejpam-3200	58	79	b+	b+	X
ejpam-3200	58	80	}	}	PUNCT
ejpam-3200	58	81	(	(	PUNCT
ejpam-3200	58	82	3.1	3.1	NUM
ejpam-3200	58	83	)	)	PUNCT
ejpam-3200	58	84	and	and	CCONJ
ejpam-3200	58	85	(	(	PUNCT
ejpam-3200	58	86	a	a	DET
ejpam-3200	58	87	·	·	SYM
ejpam-3200	58	88	b)+	b)+	NOUN
ejpam-3200	58	89	=	=	SYM
ejpam-3200	58	90	max{a−	max{a−	NOUN
ejpam-3200	58	91	·	·	PUNCT
ejpam-3200	58	92	b−	b−	PROPN
ejpam-3200	58	93	,	,	PUNCT
ejpam-3200	58	94	a−	a−	PROPN
ejpam-3200	58	95	·	·	PUNCT
ejpam-3200	58	96	b+	b+	X
ejpam-3200	58	97	,	,	PUNCT
ejpam-3200	58	98	a+	a+	PUNCT
ejpam-3200	58	99	·	·	PUNCT
ejpam-3200	58	100	b−	b−	NOUN
ejpam-3200	58	101	,	,	PUNCT
ejpam-3200	58	102	a+	a+	PUNCT
ejpam-3200	58	103	·	·	PUNCT
ejpam-3200	58	104	b+	b+	X
ejpam-3200	58	105	}	}	PUNCT
ejpam-3200	58	106	.	.	PUNCT
ejpam-3200	59	1	(	(	PUNCT
ejpam-3200	59	2	3.2	3.2	NUM
ejpam-3200	59	3	)	)	PUNCT
ejpam-3200	59	4	define	define	VERB
ejpam-3200	59	5	d(a	d(a	PROPN
ejpam-3200	59	6	,	,	PUNCT
ejpam-3200	59	7	b	b	NOUN
ejpam-3200	59	8	)	)	PUNCT
ejpam-3200	59	9	=	=	NOUN
ejpam-3200	59	10	max(|a−	max(|a−	NOUN
ejpam-3200	59	11	−b−|	−b−|	NOUN
ejpam-3200	59	12	,	,	PUNCT
ejpam-3200	59	13	|a+	|a+	PROPN
ejpam-3200	59	14	−b+|	−b+|	PROPN
ejpam-3200	59	15	)	)	PUNCT
ejpam-3200	59	16	as	as	ADP
ejpam-3200	59	17	the	the	DET
ejpam-3200	59	18	distance	distance	NOUN
ejpam-3200	59	19	between	between	ADP
ejpam-3200	59	20	intervals	interval	NOUN
ejpam-3200	59	21	a	a	DET
ejpam-3200	59	22	and	and	CCONJ
ejpam-3200	59	23	b.	b.	PROPN
ejpam-3200	59	24	definition	definition	NOUN
ejpam-3200	59	25	4	4	NUM
ejpam-3200	59	26	.	.	PUNCT
ejpam-3200	60	1	[	[	X
ejpam-3200	60	2	3	3	X
ejpam-3200	60	3	]	]	PUNCT
ejpam-3200	60	4	an	an	DET
ejpam-3200	60	5	interval	interval	NOUN
ejpam-3200	60	6	-	-	PUNCT
ejpam-3200	60	7	valued	value	VERB
ejpam-3200	60	8	function	function	NOUN
ejpam-3200	60	9	f	f	NOUN
ejpam-3200	60	10	:	:	PUNCT
ejpam-3200	61	1	[	[	X
ejpam-3200	61	2	a	a	PRON
ejpam-3200	61	3	,	,	PUNCT
ejpam-3200	61	4	b]t	b]t	NOUN
ejpam-3200	61	5	→	→	SYM
ejpam-3200	61	6	ir	ir	PROPN
ejpam-3200	61	7	is	be	AUX
ejpam-3200	61	8	mcshane	mcshane	PROPN
ejpam-3200	61	9	delta	delta	PROPN
ejpam-3200	61	10	(	(	PUNCT
ejpam-3200	61	11	m∆	m∆	X
ejpam-3200	61	12	)	)	PUNCT
ejpam-3200	61	13	integrable	integrable	ADJ
ejpam-3200	61	14	to	to	ADP
ejpam-3200	61	15	i0	i0	PROPN
ejpam-3200	61	16	∈	∈	PROPN
ejpam-3200	61	17	ir	ir	X
ejpam-3200	61	18	on	on	ADP
ejpam-3200	61	19	[	[	X
ejpam-3200	61	20	a	a	DET
ejpam-3200	61	21	,	,	PUNCT
ejpam-3200	61	22	b]t	b]t	NOUN
ejpam-3200	61	23	if	if	SCONJ
ejpam-3200	61	24	for	for	ADP
ejpam-3200	61	25	every	every	DET
ejpam-3200	61	26	ε	ε	PROPN
ejpam-3200	61	27	>	>	X
ejpam-3200	61	28	0	0	PUNCT
ejpam-3200	62	1	there	there	PRON
ejpam-3200	62	2	exists	exist	VERB
ejpam-3200	62	3	a	a	DET
ejpam-3200	62	4	∆-gauge	∆-gauge	NOUN
ejpam-3200	62	5	,	,	PUNCT
ejpam-3200	62	6	δ	δ	PROPN
ejpam-3200	62	7	,	,	PUNCT
ejpam-3200	62	8	on	on	ADP
ejpam-3200	62	9	[	[	X
ejpam-3200	62	10	a	a	PRON
ejpam-3200	62	11	,	,	PUNCT
ejpam-3200	62	12	b]t	b]t	NOUN
ejpam-3200	62	13	such	such	ADJ
ejpam-3200	62	14	that	that	SCONJ
ejpam-3200	62	15	d	d	NOUN
ejpam-3200	62	16	(	(	PUNCT
ejpam-3200	62	17	n∑	n∑	NOUN
ejpam-3200	62	18	i=1	i=1	PROPN
ejpam-3200	63	1	f	f	X
ejpam-3200	63	2	(	(	PUNCT
ejpam-3200	63	3	ξi)(ti	ξi)(ti	PROPN
ejpam-3200	63	4	−	−	PROPN
ejpam-3200	63	5	ti−1	ti−1	PROPN
ejpam-3200	63	6	)	)	PUNCT
ejpam-3200	63	7	,	,	PUNCT
ejpam-3200	63	8	i0	i0	PROPN
ejpam-3200	63	9	)	)	PUNCT
ejpam-3200	63	10	<	<	X
ejpam-3200	63	11	ε	ε	PROPN
ejpam-3200	63	12	,	,	PUNCT
ejpam-3200	63	13	(	(	PUNCT
ejpam-3200	63	14	3.3	3.3	NUM
ejpam-3200	63	15	)	)	PUNCT
ejpam-3200	63	16	whenever	whenever	SCONJ
ejpam-3200	63	17	p	p	NOUN
ejpam-3200	63	18	=	=	X
ejpam-3200	63	19	{	{	PUNCT
ejpam-3200	63	20	(	(	PUNCT
ejpam-3200	63	21	[	[	X
ejpam-3200	63	22	ti−1	ti−1	NOUN
ejpam-3200	63	23	,	,	PUNCT
ejpam-3200	63	24	ti]t	ti]t	PROPN
ejpam-3200	63	25	;	;	PUNCT
ejpam-3200	63	26	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	63	27	is	be	AUX
ejpam-3200	63	28	a	a	DET
ejpam-3200	63	29	δ	δ	NOUN
ejpam-3200	63	30	-	-	PUNCT
ejpam-3200	63	31	fine	fine	ADJ
ejpam-3200	63	32	mcshane	mcshane	PROPN
ejpam-3200	63	33	division	division	NOUN
ejpam-3200	63	34	of	of	ADP
ejpam-3200	63	35	[	[	X
ejpam-3200	63	36	a	a	PRON
ejpam-3200	63	37	,	,	PUNCT
ejpam-3200	63	38	b]t	b]t	NOUN
ejpam-3200	63	39	.	.	PUNCT
ejpam-3200	64	1	we	we	PRON
ejpam-3200	64	2	write	write	VERB
ejpam-3200	64	3	(	(	PUNCT
ejpam-3200	64	4	im∆	im∆	PROPN
ejpam-3200	64	5	)	)	PUNCT
ejpam-3200	64	6	b∫	b∫	NOUN
ejpam-3200	64	7	a	a	DET
ejpam-3200	64	8	f	f	X
ejpam-3200	64	9	(	(	PUNCT
ejpam-3200	64	10	t)∆t	t)∆t	PROPN
ejpam-3200	64	11	=	=	SYM
ejpam-3200	64	12	i0	i0	PROPN
ejpam-3200	64	13	and	and	CCONJ
ejpam-3200	64	14	f	f	PROPN
ejpam-3200	64	15	∈	∈	PROPN
ejpam-3200	64	16	im∆[a	im∆[a	PROPN
ejpam-3200	64	17	,	,	PUNCT
ejpam-3200	64	18	b]t	b]t	NOUN
ejpam-3200	64	19	.	.	PUNCT
ejpam-3200	65	1	definition	definition	NOUN
ejpam-3200	65	2	5	5	NUM
ejpam-3200	65	3	.	.	PUNCT
ejpam-3200	66	1	let	let	VERB
ejpam-3200	66	2	α	α	PRON
ejpam-3200	66	3	:	:	PUNCT
ejpam-3200	67	1	[	[	X
ejpam-3200	67	2	a	a	DET
ejpam-3200	67	3	,	,	PUNCT
ejpam-3200	67	4	b]t	b]t	NOUN
ejpam-3200	67	5	→	→	SYM
ejpam-3200	67	6	r	r	NOUN
ejpam-3200	67	7	be	be	AUX
ejpam-3200	67	8	an	an	DET
ejpam-3200	67	9	increasing	increase	VERB
ejpam-3200	67	10	function	function	NOUN
ejpam-3200	67	11	.	.	PUNCT
ejpam-3200	68	1	an	an	DET
ejpam-3200	68	2	interval	interval	NOUN
ejpam-3200	68	3	-	-	PUNCT
ejpam-3200	68	4	valued	value	VERB
ejpam-3200	68	5	function	function	NOUN
ejpam-3200	68	6	f	f	NOUN
ejpam-3200	68	7	:	:	PUNCT
ejpam-3200	69	1	[	[	X
ejpam-3200	69	2	a	a	DET
ejpam-3200	69	3	,	,	PUNCT
ejpam-3200	69	4	b]t	b]t	NOUN
ejpam-3200	69	5	→	→	SYM
ejpam-3200	69	6	ir	ir	X
ejpam-3200	69	7	is	be	AUX
ejpam-3200	69	8	(	(	PUNCT
ejpam-3200	69	9	ms∆	ms∆	PROPN
ejpam-3200	69	10	)	)	PUNCT
ejpam-3200	69	11	integrable	integrable	ADJ
ejpam-3200	69	12	to	to	ADP
ejpam-3200	69	13	i0	i0	PROPN
ejpam-3200	69	14	∈	∈	PROPN
ejpam-3200	69	15	ir	ir	PROPN
ejpam-3200	69	16	with	with	ADP
ejpam-3200	69	17	respect	respect	NOUN
ejpam-3200	69	18	to	to	ADP
ejpam-3200	69	19	α	α	NOUN
ejpam-3200	69	20	on	on	ADP
ejpam-3200	69	21	[	[	X
ejpam-3200	69	22	a	a	DET
ejpam-3200	69	23	,	,	PUNCT
ejpam-3200	69	24	b]t	b]t	NOUN
ejpam-3200	69	25	if	if	SCONJ
ejpam-3200	69	26	for	for	ADP
ejpam-3200	69	27	every	every	DET
ejpam-3200	69	28	ε	ε	PROPN
ejpam-3200	69	29	>	>	X
ejpam-3200	69	30	0	0	PUNCT
ejpam-3200	70	1	there	there	PRON
ejpam-3200	70	2	exists	exist	VERB
ejpam-3200	70	3	a	a	DET
ejpam-3200	70	4	∆-gauge	∆-gauge	NOUN
ejpam-3200	70	5	,	,	PUNCT
ejpam-3200	70	6	δ	δ	PROPN
ejpam-3200	70	7	,	,	PUNCT
ejpam-3200	70	8	on	on	ADP
ejpam-3200	70	9	[	[	X
ejpam-3200	70	10	a	a	PRON
ejpam-3200	70	11	,	,	PUNCT
ejpam-3200	70	12	b]t	b]t	NOUN
ejpam-3200	70	13	such	such	ADJ
ejpam-3200	70	14	that	that	SCONJ
ejpam-3200	70	15	d	d	NOUN
ejpam-3200	70	16	(	(	PUNCT
ejpam-3200	70	17	n∑	n∑	NOUN
ejpam-3200	70	18	i=1	i=1	PROPN
ejpam-3200	70	19	f	f	PROPN
ejpam-3200	70	20	(	(	PUNCT
ejpam-3200	70	21	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	70	22	α(ti−1	α(ti−1	NUM
ejpam-3200	70	23	)	)	PUNCT
ejpam-3200	70	24	]	]	PUNCT
ejpam-3200	70	25	,	,	PUNCT
ejpam-3200	70	26	i0	i0	PROPN
ejpam-3200	70	27	)	)	PUNCT
ejpam-3200	70	28	<	<	X
ejpam-3200	70	29	ε	ε	PROPN
ejpam-3200	70	30	,	,	PUNCT
ejpam-3200	70	31	(	(	PUNCT
ejpam-3200	70	32	3.4	3.4	NUM
ejpam-3200	70	33	)	)	PUNCT
ejpam-3200	70	34	whenever	whenever	SCONJ
ejpam-3200	70	35	p	p	NOUN
ejpam-3200	70	36	=	=	X
ejpam-3200	70	37	{	{	PUNCT
ejpam-3200	70	38	(	(	PUNCT
ejpam-3200	70	39	[	[	X
ejpam-3200	70	40	ti−1	ti−1	NOUN
ejpam-3200	70	41	,	,	PUNCT
ejpam-3200	70	42	ti]t	ti]t	PROPN
ejpam-3200	70	43	;	;	PUNCT
ejpam-3200	70	44	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	70	45	is	be	AUX
ejpam-3200	70	46	a	a	DET
ejpam-3200	70	47	δ	δ	NOUN
ejpam-3200	70	48	-	-	PUNCT
ejpam-3200	70	49	fine	fine	ADJ
ejpam-3200	70	50	mcshane	mcshane	PROPN
ejpam-3200	70	51	division	division	NOUN
ejpam-3200	70	52	of	of	ADP
ejpam-3200	70	53	[	[	X
ejpam-3200	70	54	a	a	PRON
ejpam-3200	70	55	,	,	PUNCT
ejpam-3200	70	56	b]t	b]t	NOUN
ejpam-3200	70	57	.	.	PUNCT
ejpam-3200	71	1	we	we	PRON
ejpam-3200	71	2	write	write	VERB
ejpam-3200	71	3	(	(	PUNCT
ejpam-3200	71	4	ims∆	ims∆	NOUN
ejpam-3200	71	5	)	)	PUNCT
ejpam-3200	71	6	b∫	b∫	NOUN
ejpam-3200	71	7	a	a	PRON
ejpam-3200	71	8	f	f	X
ejpam-3200	71	9	(	(	PUNCT
ejpam-3200	71	10	t)dα	t)dα	PROPN
ejpam-3200	71	11	=	=	SYM
ejpam-3200	71	12	i0	i0	PROPN
ejpam-3200	71	13	and	and	CCONJ
ejpam-3200	71	14	f	f	PROPN
ejpam-3200	71	15	∈	∈	PROPN
ejpam-3200	71	16	imsα∆[a	imsα∆[a	ADP
ejpam-3200	71	17	,	,	PUNCT
ejpam-3200	71	18	b]t	b]t	NOUN
ejpam-3200	71	19	.	.	PUNCT
ejpam-3200	71	20	remark	remark	PROPN
ejpam-3200	71	21	1	1	NUM
ejpam-3200	71	22	.	.	PUNCT
ejpam-3200	72	1	let	let	VERB
ejpam-3200	72	2	α	α	PRON
ejpam-3200	72	3	:	:	PUNCT
ejpam-3200	73	1	[	[	X
ejpam-3200	73	2	a	a	DET
ejpam-3200	73	3	,	,	PUNCT
ejpam-3200	73	4	b]t	b]t	NOUN
ejpam-3200	73	5	→	→	SYM
ejpam-3200	73	6	r	r	NOUN
ejpam-3200	73	7	be	be	AUX
ejpam-3200	73	8	an	an	DET
ejpam-3200	73	9	increasing	increase	VERB
ejpam-3200	73	10	function	function	NOUN
ejpam-3200	73	11	.	.	PUNCT
ejpam-3200	74	1	if	if	SCONJ
ejpam-3200	74	2	f	f	PROPN
ejpam-3200	74	3	(	(	PUNCT
ejpam-3200	74	4	t	t	PROPN
ejpam-3200	74	5	)	)	PUNCT
ejpam-3200	74	6	∈	∈	PROPN
ejpam-3200	74	7	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	74	8	,	,	PUNCT
ejpam-3200	74	9	b]t	b]t	NOUN
ejpam-3200	74	10	,	,	PUNCT
ejpam-3200	74	11	then	then	ADV
ejpam-3200	74	12	the	the	DET
ejpam-3200	74	13	integral	integral	ADJ
ejpam-3200	74	14	value	value	NOUN
ejpam-3200	74	15	is	be	AUX
ejpam-3200	74	16	unique	unique	ADJ
ejpam-3200	74	17	.	.	PUNCT
ejpam-3200	75	1	theorem	theorem	NOUN
ejpam-3200	75	2	2	2	NUM
ejpam-3200	75	3	.	.	PUNCT
ejpam-3200	76	1	let	let	VERB
ejpam-3200	76	2	α	α	PRON
ejpam-3200	76	3	:	:	PUNCT
ejpam-3200	77	1	[	[	X
ejpam-3200	77	2	a	a	DET
ejpam-3200	77	3	,	,	PUNCT
ejpam-3200	77	4	b]t	b]t	NOUN
ejpam-3200	77	5	→	→	SYM
ejpam-3200	77	6	r	r	NOUN
ejpam-3200	77	7	be	be	AUX
ejpam-3200	77	8	an	an	DET
ejpam-3200	77	9	increasing	increase	VERB
ejpam-3200	77	10	function	function	NOUN
ejpam-3200	77	11	.	.	PUNCT
ejpam-3200	78	1	an	an	DET
ejpam-3200	78	2	interval	interval	NOUN
ejpam-3200	78	3	-	-	PUNCT
ejpam-3200	78	4	valued	value	VERB
ejpam-3200	78	5	function	function	NOUN
ejpam-3200	78	6	f	f	NOUN
ejpam-3200	78	7	:	:	PUNCT
ejpam-3200	79	1	[	[	X
ejpam-3200	79	2	a	a	DET
ejpam-3200	79	3	,	,	PUNCT
ejpam-3200	79	4	b]t	b]t	NOUN
ejpam-3200	79	5	→	→	SYM
ejpam-3200	79	6	ir	ir	X
ejpam-3200	79	7	is	be	AUX
ejpam-3200	79	8	(	(	PUNCT
ejpam-3200	79	9	ms∆	ms∆	PROPN
ejpam-3200	79	10	)	)	PUNCT
ejpam-3200	79	11	integrable	integrable	ADJ
ejpam-3200	79	12	with	with	ADP
ejpam-3200	79	13	respect	respect	NOUN
ejpam-3200	79	14	to	to	ADP
ejpam-3200	79	15	α	α	NOUN
ejpam-3200	79	16	on	on	ADP
ejpam-3200	79	17	[	[	X
ejpam-3200	79	18	a	a	DET
ejpam-3200	79	19	,	,	PUNCT
ejpam-3200	79	20	b]t	b]t	NOUN
ejpam-3200	79	21	if	if	SCONJ
ejpam-3200	79	22	and	and	CCONJ
ejpam-3200	79	23	only	only	ADV
ejpam-3200	79	24	if	if	SCONJ
ejpam-3200	79	25	f−	f−	PROPN
ejpam-3200	79	26	,	,	PUNCT
ejpam-3200	79	27	f+	f+	NOUN
ejpam-3200	79	28	∈	∈	PROPN
ejpam-3200	79	29	msα∆[a	msα∆[a	PROPN
ejpam-3200	79	30	,	,	PUNCT
ejpam-3200	79	31	b]t	b]t	NOUN
ejpam-3200	79	32	and	and	CCONJ
ejpam-3200	79	33	(	(	PUNCT
ejpam-3200	79	34	ims∆	ims∆	NOUN
ejpam-3200	79	35	)	)	PUNCT
ejpam-3200	79	36	b∫	b∫	NOUN
ejpam-3200	79	37	a	a	PRON
ejpam-3200	79	38	f	f	X
ejpam-3200	79	39	(	(	PUNCT
ejpam-3200	79	40	t)dα	t)dα	PROPN
ejpam-3200	79	41	=	=	PRON
ejpam-3200	79	42	[	[	PUNCT
ejpam-3200	79	43	(	(	PUNCT
ejpam-3200	79	44	ms∆	ms∆	PROPN
ejpam-3200	79	45	)	)	PUNCT
ejpam-3200	79	46	b∫	b∫	NOUN
ejpam-3200	79	47	a	a	DET
ejpam-3200	79	48	f−(t)dα	f−(t)dα	PROPN
ejpam-3200	79	49	,	,	PUNCT
ejpam-3200	79	50	(	(	PUNCT
ejpam-3200	79	51	ms∆	ms∆	PROPN
ejpam-3200	79	52	)	)	PUNCT
ejpam-3200	79	53	b∫	b∫	PROPN
ejpam-3200	79	54	a	a	DET
ejpam-3200	79	55	f+(t)dα	f+(t)dα	PROPN
ejpam-3200	79	56	]	]	PUNCT
ejpam-3200	79	57	.	.	PUNCT
ejpam-3200	80	1	(	(	PUNCT
ejpam-3200	80	2	3.5	3.5	NUM
ejpam-3200	80	3	)	)	PUNCT
ejpam-3200	80	4	m.	m.	NOUN
ejpam-3200	80	5	e.	e.	PROPN
ejpam-3200	80	6	hamid	hamid	PROPN
ejpam-3200	80	7	/	/	SYM
ejpam-3200	80	8	eur	eur	PROPN
ejpam-3200	80	9	.	.	PUNCT
ejpam-3200	81	1	j.	j.	PROPN
ejpam-3200	81	2	pure	pure	PROPN
ejpam-3200	81	3	appl	appl	PROPN
ejpam-3200	81	4	.	.	PROPN
ejpam-3200	81	5	math	math	PROPN
ejpam-3200	81	6	,	,	PUNCT
ejpam-3200	81	7	11	11	NUM
ejpam-3200	81	8	(	(	PUNCT
ejpam-3200	81	9	2	2	NUM
ejpam-3200	81	10	)	)	PUNCT
ejpam-3200	81	11	(	(	PUNCT
ejpam-3200	81	12	2018	2018	NUM
ejpam-3200	81	13	)	)	PUNCT
ejpam-3200	81	14	,	,	PUNCT
ejpam-3200	81	15	493	493	NUM
ejpam-3200	81	16	-	-	SYM
ejpam-3200	81	17	504	504	NUM
ejpam-3200	81	18	496	496	NUM
ejpam-3200	81	19	proof	proof	NOUN
ejpam-3200	81	20	.	.	PUNCT
ejpam-3200	82	1	let	let	VERB
ejpam-3200	82	2	f	f	PROPN
ejpam-3200	82	3	∈	∈	PROPN
ejpam-3200	82	4	imsα∆[a	imsα∆[a	X
ejpam-3200	82	5	,	,	PUNCT
ejpam-3200	82	6	b]t	b]t	NOUN
ejpam-3200	82	7	,	,	PUNCT
ejpam-3200	82	8	then	then	ADV
ejpam-3200	82	9	there	there	PRON
ejpam-3200	82	10	exists	exist	VERB
ejpam-3200	82	11	an	an	DET
ejpam-3200	82	12	interval	interval	NOUN
ejpam-3200	82	13	i0	i0	PROPN
ejpam-3200	82	14	=	=	PUNCT
ejpam-3200	83	1	[	[	X
ejpam-3200	83	2	i−0	i−0	PROPN
ejpam-3200	83	3	,	,	PUNCT
ejpam-3200	83	4	i	i	PRON
ejpam-3200	83	5	+	+	X
ejpam-3200	83	6	0	0	NUM
ejpam-3200	83	7	]	]	PUNCT
ejpam-3200	83	8	with	with	ADP
ejpam-3200	83	9	the	the	DET
ejpam-3200	83	10	property	property	NOUN
ejpam-3200	84	1	that	that	PRON
ejpam-3200	84	2	for	for	ADP
ejpam-3200	84	3	any	any	DET
ejpam-3200	84	4	ε	ε	PROPN
ejpam-3200	84	5	>	>	X
ejpam-3200	84	6	0	0	PUNCT
ejpam-3200	84	7	there	there	PRON
ejpam-3200	84	8	exists	exist	VERB
ejpam-3200	84	9	a	a	DET
ejpam-3200	84	10	∆-gauge	∆-gauge	NOUN
ejpam-3200	84	11	,	,	PUNCT
ejpam-3200	84	12	δ	δ	NOUN
ejpam-3200	84	13	with	with	ADP
ejpam-3200	84	14	respect	respect	NOUN
ejpam-3200	84	15	to	to	ADP
ejpam-3200	84	16	α	α	NOUN
ejpam-3200	84	17	on	on	ADP
ejpam-3200	84	18	[	[	X
ejpam-3200	84	19	a	a	PRON
ejpam-3200	84	20	,	,	PUNCT
ejpam-3200	84	21	b]t	b]t	NOUN
ejpam-3200	84	22	such	such	ADJ
ejpam-3200	84	23	that	that	SCONJ
ejpam-3200	84	24	d	d	NOUN
ejpam-3200	84	25	(	(	PUNCT
ejpam-3200	84	26	n∑	n∑	NOUN
ejpam-3200	84	27	i=1	i=1	PROPN
ejpam-3200	84	28	f	f	PROPN
ejpam-3200	84	29	(	(	PUNCT
ejpam-3200	84	30	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	84	31	α(ti−1	α(ti−1	NUM
ejpam-3200	84	32	)	)	PUNCT
ejpam-3200	84	33	]	]	PUNCT
ejpam-3200	84	34	,	,	PUNCT
ejpam-3200	84	35	i0	i0	PROPN
ejpam-3200	84	36	)	)	PUNCT
ejpam-3200	84	37	<	<	X
ejpam-3200	84	38	ε	ε	PROPN
ejpam-3200	84	39	,	,	PUNCT
ejpam-3200	84	40	(	(	PUNCT
ejpam-3200	84	41	3.6	3.6	NUM
ejpam-3200	84	42	)	)	PUNCT
ejpam-3200	84	43	whenever	whenever	SCONJ
ejpam-3200	84	44	p	p	NOUN
ejpam-3200	84	45	=	=	X
ejpam-3200	84	46	{	{	PUNCT
ejpam-3200	84	47	(	(	PUNCT
ejpam-3200	84	48	[	[	X
ejpam-3200	84	49	ti−1	ti−1	NOUN
ejpam-3200	84	50	,	,	PUNCT
ejpam-3200	84	51	ti]t	ti]t	PROPN
ejpam-3200	84	52	;	;	PUNCT
ejpam-3200	84	53	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	84	54	is	be	AUX
ejpam-3200	84	55	a	a	DET
ejpam-3200	84	56	δ	δ	NOUN
ejpam-3200	84	57	-	-	PUNCT
ejpam-3200	84	58	fine	fine	ADJ
ejpam-3200	84	59	mcshane	mcshane	PROPN
ejpam-3200	84	60	division	division	NOUN
ejpam-3200	84	61	of	of	ADP
ejpam-3200	84	62	[	[	X
ejpam-3200	84	63	a	a	PRON
ejpam-3200	84	64	,	,	PUNCT
ejpam-3200	84	65	b]t	b]t	NOUN
ejpam-3200	84	66	.	.	PUNCT
ejpam-3200	85	1	since	since	SCONJ
ejpam-3200	85	2	α(ti)−	α(ti)−	NOUN
ejpam-3200	85	3	α(ti−1	α(ti−1	NUM
ejpam-3200	85	4	)	)	PUNCT
ejpam-3200	85	5	≥	≥	NOUN
ejpam-3200	85	6	0	0	NUM
ejpam-3200	85	7	for	for	ADP
ejpam-3200	85	8	1	1	NUM
ejpam-3200	85	9	≤	≤	NUM
ejpam-3200	85	10	i	i	PRON
ejpam-3200	85	11	≤	≤	PROPN
ejpam-3200	85	12	n	n	CCONJ
ejpam-3200	85	13	,	,	PUNCT
ejpam-3200	85	14	we	we	PRON
ejpam-3200	85	15	have	have	VERB
ejpam-3200	85	16	d	d	NOUN
ejpam-3200	85	17	(	(	PUNCT
ejpam-3200	86	1	n∑	n∑	NOUN
ejpam-3200	86	2	i=1	i=1	PROPN
ejpam-3200	87	1	f	f	PROPN
ejpam-3200	87	2	(	(	PUNCT
ejpam-3200	87	3	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	87	4	α(ti−1	α(ti−1	NUM
ejpam-3200	87	5	)	)	PUNCT
ejpam-3200	87	6	]	]	PUNCT
ejpam-3200	87	7	,	,	PUNCT
ejpam-3200	87	8	i0	i0	PROPN
ejpam-3200	87	9	)	)	PUNCT
ejpam-3200	88	1	=	=	SYM
ejpam-3200	88	2	max	max	PROPN
ejpam-3200	88	3	(	(	PUNCT
ejpam-3200	88	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	88	5	[	[	PUNCT
ejpam-3200	88	6	n∑	n∑	NOUN
ejpam-3200	88	7	i=1	i=1	PROPN
ejpam-3200	88	8	f	f	PROPN
ejpam-3200	88	9	(	(	PUNCT
ejpam-3200	88	10	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	88	11	α(ti−1	α(ti−1	NUM
ejpam-3200	88	12	)	)	PUNCT
ejpam-3200	88	13	]	]	PUNCT
ejpam-3200	89	1	]	]	X
ejpam-3200	89	2	−	−	X
ejpam-3200	89	3	−	−	PROPN
ejpam-3200	89	4	i−0	i−0	PROPN
ejpam-3200	89	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	89	6	,	,	PUNCT
ejpam-3200	89	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	89	8	[	[	PUNCT
ejpam-3200	89	9	n∑	n∑	NOUN
ejpam-3200	89	10	i=1	i=1	PROPN
ejpam-3200	89	11	f	f	PROPN
ejpam-3200	89	12	(	(	PUNCT
ejpam-3200	89	13	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	89	14	α(ti−1	α(ti−1	NUM
ejpam-3200	89	15	)	)	PUNCT
ejpam-3200	89	16	]	]	PUNCT
ejpam-3200	90	1	]	]	X
ejpam-3200	90	2	+	+	CCONJ
ejpam-3200	90	3	−	−	X
ejpam-3200	90	4	i+	i+	PUNCT
ejpam-3200	90	5	0	0	NUM
ejpam-3200	90	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	90	7	)	)	PUNCT
ejpam-3200	90	8	<	<	X
ejpam-3200	90	9	ε	ε	PROPN
ejpam-3200	90	10	.	.	PUNCT
ejpam-3200	90	11	=	=	SYM
ejpam-3200	90	12	max	max	PROPN
ejpam-3200	90	13	(	(	PUNCT
ejpam-3200	90	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	90	15	n∑	n∑	PROPN
ejpam-3200	90	16	i=1	i=1	PROPN
ejpam-3200	90	17	f−(ξi)[α(ti)−	f−(ξi)[α(ti)−	PROPN
ejpam-3200	90	18	α(ti−1)]−	α(ti−1)]−	PROPN
ejpam-3200	90	19	i−0	i−0	PROPN
ejpam-3200	90	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	90	21	,	,	PUNCT
ejpam-3200	90	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	90	23	n∑	n∑	PROPN
ejpam-3200	90	24	i=1	i=1	PROPN
ejpam-3200	90	25	f+(ξi)[α(ti)−	f+(ξi)[α(ti)−	NOUN
ejpam-3200	90	26	α(ti−1)]−	α(ti−1)]−	PROPN
ejpam-3200	90	27	i+	i+	PROPN
ejpam-3200	90	28	0	0	NUM
ejpam-3200	90	29	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	90	30	)	)	PUNCT
ejpam-3200	90	31	<	<	X
ejpam-3200	90	32	ε	ε	PROPN
ejpam-3200	90	33	.	.	PUNCT
ejpam-3200	90	34	(	(	PUNCT
ejpam-3200	90	35	3.7	3.7	NUM
ejpam-3200	90	36	)	)	PUNCT
ejpam-3200	90	37	hence	hence	ADV
ejpam-3200	90	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	90	39	n∑	n∑	PROPN
ejpam-3200	90	40	i=1	i=1	PROPN
ejpam-3200	90	41	f−(ξi)[α(ti)−α(ti−1)]−i−0	f−(ξi)[α(ti)−α(ti−1)]−i−0	PROPN
ejpam-3200	90	42	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	90	43	<	<	X
ejpam-3200	90	44	ε	ε	PROPN
ejpam-3200	90	45	,	,	PUNCT
ejpam-3200	90	46	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	90	47	n∑	n∑	PROPN
ejpam-3200	90	48	i=1	i=1	PROPN
ejpam-3200	90	49	f+(ξi)[α(ti)−α(ti−1)]−i+	f+(ξi)[α(ti)−α(ti−1)]−i+	ADJ
ejpam-3200	90	50	0	0	NUM
ejpam-3200	90	51	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	90	52	<	<	X
ejpam-3200	90	53	ε	ε	PROPN
ejpam-3200	90	54	whenever	whenever	SCONJ
ejpam-3200	90	55	p	p	NOUN
ejpam-3200	90	56	=	=	X
ejpam-3200	90	57	{	{	PUNCT
ejpam-3200	90	58	(	(	PUNCT
ejpam-3200	90	59	[	[	X
ejpam-3200	90	60	ti−1	ti−1	NOUN
ejpam-3200	90	61	,	,	PUNCT
ejpam-3200	90	62	ti]t	ti]t	PROPN
ejpam-3200	90	63	;	;	PUNCT
ejpam-3200	90	64	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	90	65	is	be	AUX
ejpam-3200	90	66	a	a	DET
ejpam-3200	90	67	δ	δ	NOUN
ejpam-3200	90	68	-	-	PUNCT
ejpam-3200	90	69	fine	fine	ADJ
ejpam-3200	90	70	mcshane	mcshane	PROPN
ejpam-3200	90	71	division	division	NOUN
ejpam-3200	90	72	of	of	ADP
ejpam-3200	90	73	[	[	X
ejpam-3200	90	74	a	a	PRON
ejpam-3200	90	75	,	,	PUNCT
ejpam-3200	90	76	b]t	b]t	NOUN
ejpam-3200	90	77	.	.	PUNCT
ejpam-3200	91	1	thus	thus	ADV
ejpam-3200	91	2	f−	f−	PROPN
ejpam-3200	91	3	,	,	PUNCT
ejpam-3200	91	4	f+	f+	NUM
ejpam-3200	91	5	∈msα∆[a	∈msα∆[a	NOUN
ejpam-3200	91	6	,	,	PUNCT
ejpam-3200	91	7	b]t	b]t	NOUN
ejpam-3200	91	8	and	and	CCONJ
ejpam-3200	91	9	(	(	PUNCT
ejpam-3200	91	10	ims∆	ims∆	NOUN
ejpam-3200	91	11	)	)	PUNCT
ejpam-3200	91	12	b∫	b∫	NOUN
ejpam-3200	91	13	a	a	PRON
ejpam-3200	91	14	f	f	X
ejpam-3200	91	15	(	(	PUNCT
ejpam-3200	91	16	t)dα	t)dα	PROPN
ejpam-3200	91	17	=	=	PRON
ejpam-3200	91	18	[	[	PUNCT
ejpam-3200	91	19	(	(	PUNCT
ejpam-3200	91	20	ms∆	ms∆	PROPN
ejpam-3200	91	21	)	)	PUNCT
ejpam-3200	91	22	b∫	b∫	NOUN
ejpam-3200	91	23	a	a	DET
ejpam-3200	91	24	f−(t)dα	f−(t)dα	PROPN
ejpam-3200	91	25	,	,	PUNCT
ejpam-3200	91	26	(	(	PUNCT
ejpam-3200	91	27	ms∆	ms∆	PROPN
ejpam-3200	91	28	)	)	PUNCT
ejpam-3200	91	29	b∫	b∫	PROPN
ejpam-3200	91	30	a	a	DET
ejpam-3200	91	31	f+(t)dα	f+(t)dα	PROPN
ejpam-3200	91	32	]	]	PUNCT
ejpam-3200	91	33	.	.	PUNCT
ejpam-3200	92	1	(	(	PUNCT
ejpam-3200	92	2	3.8	3.8	NUM
ejpam-3200	92	3	)	)	PUNCT
ejpam-3200	92	4	conversely	conversely	ADV
ejpam-3200	92	5	,	,	PUNCT
ejpam-3200	92	6	let	let	VERB
ejpam-3200	92	7	f−	f−	PROPN
ejpam-3200	92	8	,	,	PUNCT
ejpam-3200	92	9	f+	f+	NUM
ejpam-3200	92	10	∈msα∆[a	∈msα∆[a	NOUN
ejpam-3200	92	11	,	,	PUNCT
ejpam-3200	92	12	b]t	b]t	NOUN
ejpam-3200	92	13	.	.	PUNCT
ejpam-3200	93	1	then	then	ADV
ejpam-3200	93	2	there	there	PRON
ejpam-3200	93	3	exists	exist	VERB
ejpam-3200	93	4	m1,m2	m1,m2	PROPN
ejpam-3200	93	5	∈	∈	PROPN
ejpam-3200	93	6	r	r	NOUN
ejpam-3200	93	7	with	with	ADP
ejpam-3200	93	8	the	the	DET
ejpam-3200	93	9	property	property	NOUN
ejpam-3200	93	10	that	that	PRON
ejpam-3200	93	11	given	give	VERB
ejpam-3200	93	12	ε	ε	PROPN
ejpam-3200	93	13	>	>	X
ejpam-3200	93	14	0	0	PUNCT
ejpam-3200	94	1	there	there	PRON
ejpam-3200	94	2	exists	exist	VERB
ejpam-3200	94	3	a	a	DET
ejpam-3200	94	4	∆-gauge	∆-gauge	NOUN
ejpam-3200	94	5	,	,	PUNCT
ejpam-3200	94	6	δ	δ	NOUN
ejpam-3200	94	7	with	with	ADP
ejpam-3200	94	8	respect	respect	NOUN
ejpam-3200	94	9	to	to	ADP
ejpam-3200	94	10	α	α	NOUN
ejpam-3200	94	11	on	on	ADP
ejpam-3200	94	12	[	[	X
ejpam-3200	94	13	a	a	DET
ejpam-3200	94	14	,	,	PUNCT
ejpam-3200	94	15	b]t	b]t	NOUN
ejpam-3200	94	16	such	such	ADJ
ejpam-3200	94	17	that∣∣∣∣	that∣∣∣∣	PROPN
ejpam-3200	94	18	n∑	n∑	PROPN
ejpam-3200	94	19	i=1	i=1	PROPN
ejpam-3200	94	20	f−(ξi)[α(ti)−	f−(ξi)[α(ti)−	ADJ
ejpam-3200	94	21	α(ti−1)]−m1	α(ti−1)]−m1	PROPN
ejpam-3200	94	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	94	23	<	<	X
ejpam-3200	94	24	ε	ε	PROPN
ejpam-3200	94	25	,	,	PUNCT
ejpam-3200	94	26	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	94	27	n∑	n∑	PROPN
ejpam-3200	94	28	i=1	i=1	PROPN
ejpam-3200	94	29	f+(ξi)[α(ti)−	f+(ξi)[α(ti)−	NOUN
ejpam-3200	94	30	α(ti−1)]−m2	α(ti−1)]−m2	NOUN
ejpam-3200	94	31	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	94	32	<	<	X
ejpam-3200	94	33	ε	ε	PROPN
ejpam-3200	94	34	whenever	whenever	SCONJ
ejpam-3200	94	35	p	p	NOUN
ejpam-3200	94	36	=	=	X
ejpam-3200	94	37	{	{	PUNCT
ejpam-3200	94	38	(	(	PUNCT
ejpam-3200	94	39	[	[	X
ejpam-3200	94	40	ti−1	ti−1	NOUN
ejpam-3200	94	41	,	,	PUNCT
ejpam-3200	94	42	ti]t	ti]t	PROPN
ejpam-3200	94	43	;	;	PUNCT
ejpam-3200	94	44	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	94	45	is	be	AUX
ejpam-3200	94	46	a	a	DET
ejpam-3200	94	47	δ	δ	NOUN
ejpam-3200	94	48	-	-	PUNCT
ejpam-3200	94	49	fine	fine	ADJ
ejpam-3200	94	50	mcshane	mcshane	PROPN
ejpam-3200	94	51	division	division	NOUN
ejpam-3200	94	52	of	of	ADP
ejpam-3200	94	53	[	[	X
ejpam-3200	94	54	a	a	PRON
ejpam-3200	94	55	,	,	PUNCT
ejpam-3200	94	56	b]t	b]t	NOUN
ejpam-3200	94	57	.	.	PUNCT
ejpam-3200	95	1	we	we	PRON
ejpam-3200	95	2	define	define	VERB
ejpam-3200	95	3	i0	i0	PROPN
ejpam-3200	95	4	=	=	PUNCT
ejpam-3200	96	1	[	[	X
ejpam-3200	96	2	m1,m2	m1,m2	PROPN
ejpam-3200	96	3	]	]	PUNCT
ejpam-3200	96	4	,	,	PUNCT
ejpam-3200	96	5	then	then	ADV
ejpam-3200	96	6	if	if	SCONJ
ejpam-3200	96	7	p	p	NOUN
ejpam-3200	96	8	=	=	X
ejpam-3200	96	9	{	{	PUNCT
ejpam-3200	96	10	(	(	PUNCT
ejpam-3200	96	11	[	[	X
ejpam-3200	96	12	ti−1	ti−1	NOUN
ejpam-3200	96	13	,	,	PUNCT
ejpam-3200	96	14	ti]t	ti]t	PROPN
ejpam-3200	96	15	;	;	PUNCT
ejpam-3200	96	16	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3200	96	17	is	be	AUX
ejpam-3200	96	18	a	a	DET
ejpam-3200	96	19	δ	δ	NOUN
ejpam-3200	96	20	-	-	PUNCT
ejpam-3200	96	21	fine	fine	ADJ
ejpam-3200	96	22	mcshane	mcshane	PROPN
ejpam-3200	96	23	division	division	NOUN
ejpam-3200	96	24	of	of	ADP
ejpam-3200	96	25	[	[	X
ejpam-3200	96	26	a	a	DET
ejpam-3200	96	27	,	,	PUNCT
ejpam-3200	96	28	b]t	b]t	NOUN
ejpam-3200	96	29	,	,	PUNCT
ejpam-3200	96	30	we	we	PRON
ejpam-3200	96	31	have	have	VERB
ejpam-3200	96	32	d	d	NOUN
ejpam-3200	96	33	(	(	PUNCT
ejpam-3200	97	1	n∑	n∑	NOUN
ejpam-3200	97	2	i=1	i=1	PROPN
ejpam-3200	98	1	f	f	PROPN
ejpam-3200	98	2	(	(	PUNCT
ejpam-3200	98	3	ξi)[α(ti)−	ξi)[α(ti)−	PROPN
ejpam-3200	98	4	α(ti−1	α(ti−1	NUM
ejpam-3200	98	5	)	)	PUNCT
ejpam-3200	98	6	]	]	PUNCT
ejpam-3200	98	7	,	,	PUNCT
ejpam-3200	98	8	i0	i0	PROPN
ejpam-3200	98	9	)	)	PUNCT
ejpam-3200	98	10	<	<	X
ejpam-3200	98	11	ε	ε	PROPN
ejpam-3200	98	12	.	.	PUNCT
ejpam-3200	99	1	(	(	PUNCT
ejpam-3200	99	2	3.9	3.9	NUM
ejpam-3200	99	3	)	)	PUNCT
ejpam-3200	99	4	hence	hence	ADV
ejpam-3200	99	5	f	f	NOUN
ejpam-3200	100	1	:	:	PUNCT
ejpam-3200	100	2	[	[	X
ejpam-3200	100	3	a	a	DET
ejpam-3200	100	4	,	,	PUNCT
ejpam-3200	100	5	b]t	b]t	NOUN
ejpam-3200	100	6	→	→	SYM
ejpam-3200	100	7	ir	ir	X
ejpam-3200	100	8	is	be	AUX
ejpam-3200	100	9	(	(	PUNCT
ejpam-3200	100	10	ms∆	ms∆	PROPN
ejpam-3200	100	11	)	)	PUNCT
ejpam-3200	100	12	integrable	integrable	ADJ
ejpam-3200	100	13	with	with	ADP
ejpam-3200	100	14	respect	respect	NOUN
ejpam-3200	100	15	to	to	ADP
ejpam-3200	100	16	α	α	NOUN
ejpam-3200	100	17	on	on	ADP
ejpam-3200	100	18	[	[	X
ejpam-3200	100	19	a	a	DET
ejpam-3200	100	20	,	,	PUNCT
ejpam-3200	100	21	b]t	b]t	NOUN
ejpam-3200	100	22	.	.	PUNCT
ejpam-3200	101	1	theorem	theorem	NOUN
ejpam-3200	101	2	3	3	X
ejpam-3200	101	3	.	.	PUNCT
ejpam-3200	102	1	let	let	VERB
ejpam-3200	102	2	α	α	PRON
ejpam-3200	102	3	:	:	PUNCT
ejpam-3200	103	1	[	[	X
ejpam-3200	103	2	a	a	DET
ejpam-3200	103	3	,	,	PUNCT
ejpam-3200	103	4	b]t	b]t	NOUN
ejpam-3200	103	5	→	→	SYM
ejpam-3200	103	6	r	r	NOUN
ejpam-3200	103	7	be	be	AUX
ejpam-3200	103	8	an	an	DET
ejpam-3200	103	9	increasing	increase	VERB
ejpam-3200	103	10	function	function	NOUN
ejpam-3200	103	11	.	.	PUNCT
ejpam-3200	104	1	if	if	SCONJ
ejpam-3200	104	2	f	f	PROPN
ejpam-3200	104	3	(	(	PUNCT
ejpam-3200	104	4	t	t	PROPN
ejpam-3200	104	5	)	)	PUNCT
ejpam-3200	104	6	,	,	PUNCT
ejpam-3200	104	7	g(t	g(t	PROPN
ejpam-3200	104	8	)	)	PUNCT
ejpam-3200	104	9	∈	∈	PROPN
ejpam-3200	104	10	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	104	11	,	,	PUNCT
ejpam-3200	104	12	b]t	b]t	NOUN
ejpam-3200	104	13	and	and	CCONJ
ejpam-3200	104	14	β	β	X
ejpam-3200	104	15	,	,	PUNCT
ejpam-3200	104	16	γ	γ	PROPN
ejpam-3200	104	17	∈	∈	PROPN
ejpam-3200	104	18	r.	r.	NOUN
ejpam-3200	104	19	then	then	ADV
ejpam-3200	104	20	[	[	PUNCT
ejpam-3200	104	21	βf	βf	INTJ
ejpam-3200	104	22	(	(	PUNCT
ejpam-3200	104	23	t	t	NOUN
ejpam-3200	104	24	)	)	PUNCT
ejpam-3200	104	25	+	+	NUM
ejpam-3200	104	26	γg(t	γg(t	NUM
ejpam-3200	104	27	)	)	PUNCT
ejpam-3200	104	28	]	]	PUNCT
ejpam-3200	105	1	∈	∈	PROPN
ejpam-3200	105	2	imsα∆[a	imsα∆[a	ADP
ejpam-3200	105	3	,	,	PUNCT
ejpam-3200	105	4	b]t	b]t	NOUN
ejpam-3200	105	5	and	and	CCONJ
ejpam-3200	105	6	(	(	PUNCT
ejpam-3200	105	7	ims∆	ims∆	NOUN
ejpam-3200	105	8	)	)	PUNCT
ejpam-3200	105	9	b∫	b∫	NOUN
ejpam-3200	105	10	a	a	X
ejpam-3200	105	11	(	(	PUNCT
ejpam-3200	105	12	βf	βf	INTJ
ejpam-3200	105	13	(	(	PUNCT
ejpam-3200	105	14	t	t	NOUN
ejpam-3200	105	15	)	)	PUNCT
ejpam-3200	105	16	+	+	CCONJ
ejpam-3200	105	17	γg(t))dα	γg(t))dα	NOUN
ejpam-3200	105	18	=	=	SYM
ejpam-3200	105	19	β(ims∆	β(ims∆	NUM
ejpam-3200	105	20	)	)	PUNCT
ejpam-3200	105	21	b∫	b∫	NOUN
ejpam-3200	105	22	a	a	DET
ejpam-3200	105	23	f	f	X
ejpam-3200	105	24	(	(	PUNCT
ejpam-3200	105	25	t)dα+	t)dα+	NUM
ejpam-3200	105	26	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	105	27	)	)	PUNCT
ejpam-3200	105	28	b∫	b∫	NOUN
ejpam-3200	105	29	a	a	DET
ejpam-3200	105	30	g(t)dα	g(t)dα	PROPN
ejpam-3200	105	31	.	.	PUNCT
ejpam-3200	106	1	(	(	PUNCT
ejpam-3200	106	2	3.10	3.10	NUM
ejpam-3200	106	3	)	)	PUNCT
ejpam-3200	106	4	m.	m.	NOUN
ejpam-3200	106	5	e.	e.	PROPN
ejpam-3200	106	6	hamid	hamid	PROPN
ejpam-3200	106	7	/	/	SYM
ejpam-3200	106	8	eur	eur	PROPN
ejpam-3200	106	9	.	.	PUNCT
ejpam-3200	107	1	j.	j.	PROPN
ejpam-3200	107	2	pure	pure	PROPN
ejpam-3200	107	3	appl	appl	PROPN
ejpam-3200	107	4	.	.	PROPN
ejpam-3200	107	5	math	math	PROPN
ejpam-3200	107	6	,	,	PUNCT
ejpam-3200	107	7	11	11	NUM
ejpam-3200	107	8	(	(	PUNCT
ejpam-3200	107	9	2	2	NUM
ejpam-3200	107	10	)	)	PUNCT
ejpam-3200	107	11	(	(	PUNCT
ejpam-3200	107	12	2018	2018	NUM
ejpam-3200	107	13	)	)	PUNCT
ejpam-3200	107	14	,	,	PUNCT
ejpam-3200	107	15	493	493	NUM
ejpam-3200	107	16	-	-	SYM
ejpam-3200	107	17	504	504	NUM
ejpam-3200	107	18	497	497	NUM
ejpam-3200	107	19	proof	proof	NOUN
ejpam-3200	107	20	.	.	PUNCT
ejpam-3200	108	1	if	if	SCONJ
ejpam-3200	108	2	f	f	PROPN
ejpam-3200	108	3	(	(	PUNCT
ejpam-3200	108	4	t	t	PROPN
ejpam-3200	108	5	)	)	PUNCT
ejpam-3200	108	6	,	,	PUNCT
ejpam-3200	108	7	g(t	g(t	PROPN
ejpam-3200	108	8	)	)	PUNCT
ejpam-3200	108	9	∈	∈	PROPN
ejpam-3200	108	10	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	108	11	,	,	PUNCT
ejpam-3200	108	12	b]t	b]t	NOUN
ejpam-3200	108	13	,	,	PUNCT
ejpam-3200	108	14	then	then	ADV
ejpam-3200	108	15	f−(t	f−(t	PROPN
ejpam-3200	108	16	)	)	PUNCT
ejpam-3200	108	17	,	,	PUNCT
ejpam-3200	108	18	f+(t	f+(t	PROPN
ejpam-3200	108	19	)	)	PUNCT
ejpam-3200	108	20	,	,	PUNCT
ejpam-3200	108	21	g−(t	g−(t	PROPN
ejpam-3200	108	22	)	)	PUNCT
ejpam-3200	108	23	,	,	PUNCT
ejpam-3200	108	24	g+(t	g+(t	NOUN
ejpam-3200	108	25	)	)	PUNCT
ejpam-3200	108	26	∈	∈	PROPN
ejpam-3200	108	27	msα∆[a	msα∆[a	PROPN
ejpam-3200	108	28	,	,	PUNCT
ejpam-3200	108	29	b]t	b]t	VERB
ejpam-3200	108	30	by	by	ADP
ejpam-3200	108	31	theorem	theorem	NOUN
ejpam-3200	108	32	2	2	NUM
ejpam-3200	108	33	.	.	PUNCT
ejpam-3200	108	34	hence	hence	ADV
ejpam-3200	108	35	βf−(t)+γg−(t	βf−(t)+γg−(t	NUM
ejpam-3200	108	36	)	)	PUNCT
ejpam-3200	108	37	,	,	PUNCT
ejpam-3200	108	38	βf−(t)+γg+(t	βf−(t)+γg+(t	NOUN
ejpam-3200	108	39	)	)	PUNCT
ejpam-3200	108	40	,	,	PUNCT
ejpam-3200	108	41	βf+(t)+γg−(t	βf+(t)+γg−(t	PROPN
ejpam-3200	108	42	)	)	PUNCT
ejpam-3200	108	43	,	,	PUNCT
ejpam-3200	108	44	βf+(t)+γg+(t	βf+(t)+γg+(t	PROPN
ejpam-3200	108	45	)	)	PUNCT
ejpam-3200	108	46	∈	∈	PROPN
ejpam-3200	108	47	msα∆[a	msα∆[a	PROPN
ejpam-3200	108	48	,	,	PUNCT
ejpam-3200	108	49	b]t	b]t	NOUN
ejpam-3200	108	50	.	.	PUNCT
ejpam-3200	109	1	(	(	PUNCT
ejpam-3200	109	2	1	1	X
ejpam-3200	109	3	)	)	PUNCT
ejpam-3200	109	4	if	if	SCONJ
ejpam-3200	109	5	β	β	X
ejpam-3200	109	6	>	>	X
ejpam-3200	109	7	0	0	NUM
ejpam-3200	109	8	and	and	CCONJ
ejpam-3200	109	9	γ	γ	X
ejpam-3200	109	10	>	>	X
ejpam-3200	109	11	0	0	NUM
ejpam-3200	109	12	,	,	PUNCT
ejpam-3200	109	13	then	then	ADV
ejpam-3200	109	14	(	(	PUNCT
ejpam-3200	109	15	ms∆	ms∆	PROPN
ejpam-3200	109	16	)	)	PUNCT
ejpam-3200	109	17	b∫	b∫	PROPN
ejpam-3200	109	18	a	a	X
ejpam-3200	109	19	(	(	PUNCT
ejpam-3200	109	20	βf	βf	INTJ
ejpam-3200	109	21	(	(	PUNCT
ejpam-3200	109	22	t	t	NOUN
ejpam-3200	109	23	)	)	PUNCT
ejpam-3200	109	24	+	+	PUNCT
ejpam-3200	109	25	γg(t))−dα	γg(t))−dα	NOUN
ejpam-3200	109	26	=	=	SYM
ejpam-3200	109	27	(	(	PUNCT
ejpam-3200	109	28	ms∆	ms∆	PROPN
ejpam-3200	109	29	)	)	PUNCT
ejpam-3200	109	30	b∫	b∫	PROPN
ejpam-3200	109	31	a	a	DET
ejpam-3200	109	32	(	(	PUNCT
ejpam-3200	109	33	βf−(t	βf−(t	PROPN
ejpam-3200	109	34	)	)	PUNCT
ejpam-3200	110	1	+	+	CCONJ
ejpam-3200	110	2	γg−(t))dα	γg−(t))dα	ADJ
ejpam-3200	110	3	=	=	SYM
ejpam-3200	110	4	β(ms∆	β(ms∆	NOUN
ejpam-3200	110	5	)	)	PUNCT
ejpam-3200	110	6	b∫	b∫	NOUN
ejpam-3200	110	7	a	a	DET
ejpam-3200	110	8	f−(t)dα+	f−(t)dα+	NUM
ejpam-3200	110	9	γ(ms∆	γ(ms∆	NOUN
ejpam-3200	110	10	)	)	PUNCT
ejpam-3200	110	11	b∫	b∫	PROPN
ejpam-3200	110	12	a	a	DET
ejpam-3200	110	13	g−(t)dα	g−(t)dα	PROPN
ejpam-3200	110	14	=	=	PUNCT
ejpam-3200	110	15	β	β	X
ejpam-3200	110	16	(	(	PUNCT
ejpam-3200	110	17	(	(	PUNCT
ejpam-3200	110	18	ims∆	ims∆	NOUN
ejpam-3200	110	19	)	)	PUNCT
ejpam-3200	110	20	b∫	b∫	NOUN
ejpam-3200	111	1	a	a	PRON
ejpam-3200	111	2	f	f	X
ejpam-3200	111	3	(	(	PUNCT
ejpam-3200	111	4	t)dα	t)dα	PROPN
ejpam-3200	111	5	)	)	PUNCT
ejpam-3200	111	6	−	−	PROPN
ejpam-3200	112	1	+	+	CCONJ
ejpam-3200	112	2	γ	γ	X
ejpam-3200	112	3	(	(	PUNCT
ejpam-3200	112	4	(	(	PUNCT
ejpam-3200	112	5	ims∆	ims∆	NOUN
ejpam-3200	112	6	)	)	PUNCT
ejpam-3200	112	7	b∫	b∫	NOUN
ejpam-3200	112	8	a	a	DET
ejpam-3200	112	9	g(t)dα	g(t)dα	NOUN
ejpam-3200	112	10	)	)	PUNCT
ejpam-3200	112	11	−	−	PROPN
ejpam-3200	112	12	=	=	PUNCT
ejpam-3200	112	13	(	(	PUNCT
ejpam-3200	112	14	β(ims∆	β(ims∆	NUM
ejpam-3200	112	15	)	)	PUNCT
ejpam-3200	112	16	b∫	b∫	NOUN
ejpam-3200	112	17	a	a	DET
ejpam-3200	112	18	f	f	X
ejpam-3200	112	19	(	(	PUNCT
ejpam-3200	112	20	t)dα+	t)dα+	NUM
ejpam-3200	112	21	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	112	22	)	)	PUNCT
ejpam-3200	112	23	b∫	b∫	NOUN
ejpam-3200	112	24	a	a	DET
ejpam-3200	112	25	g(t)dα	g(t)dα	NOUN
ejpam-3200	112	26	)	)	PUNCT
ejpam-3200	112	27	−	−	PROPN
ejpam-3200	112	28	.	.	PUNCT
ejpam-3200	113	1	(	(	PUNCT
ejpam-3200	113	2	2	2	X
ejpam-3200	113	3	)	)	PUNCT
ejpam-3200	113	4	if	if	SCONJ
ejpam-3200	113	5	β	β	X
ejpam-3200	113	6	<	<	X
ejpam-3200	113	7	0	0	NUM
ejpam-3200	113	8	and	and	CCONJ
ejpam-3200	113	9	γ	γ	X
ejpam-3200	113	10	<	<	X
ejpam-3200	113	11	0	0	NUM
ejpam-3200	113	12	,	,	PUNCT
ejpam-3200	113	13	then	then	ADV
ejpam-3200	113	14	(	(	PUNCT
ejpam-3200	113	15	ms∆	ms∆	PROPN
ejpam-3200	113	16	)	)	PUNCT
ejpam-3200	113	17	b∫	b∫	PROPN
ejpam-3200	113	18	a	a	X
ejpam-3200	113	19	(	(	PUNCT
ejpam-3200	113	20	βf	βf	INTJ
ejpam-3200	113	21	(	(	PUNCT
ejpam-3200	113	22	t	t	NOUN
ejpam-3200	113	23	)	)	PUNCT
ejpam-3200	113	24	+	+	PUNCT
ejpam-3200	113	25	γg(t))−dα	γg(t))−dα	NOUN
ejpam-3200	113	26	=	=	SYM
ejpam-3200	113	27	(	(	PUNCT
ejpam-3200	113	28	ms∆	ms∆	PROPN
ejpam-3200	113	29	)	)	PUNCT
ejpam-3200	113	30	b∫	b∫	PROPN
ejpam-3200	113	31	a	a	DET
ejpam-3200	113	32	(	(	PUNCT
ejpam-3200	113	33	βf+(t	βf+(t	NOUN
ejpam-3200	113	34	)	)	PUNCT
ejpam-3200	114	1	+	+	NUM
ejpam-3200	114	2	γg+(t))dα	γg+(t))dα	NOUN
ejpam-3200	114	3	=	=	SYM
ejpam-3200	114	4	β(ms∆	β(ms∆	X
ejpam-3200	114	5	)	)	PUNCT
ejpam-3200	114	6	b∫	b∫	NOUN
ejpam-3200	114	7	a	a	DET
ejpam-3200	114	8	f+(t)dα+	f+(t)dα+	NOUN
ejpam-3200	114	9	γ(ms∆	γ(ms∆	NOUN
ejpam-3200	114	10	)	)	PUNCT
ejpam-3200	114	11	b∫	b∫	NOUN
ejpam-3200	114	12	a	a	DET
ejpam-3200	114	13	g+(t)dα	g+(t)dα	NOUN
ejpam-3200	114	14	=	=	SYM
ejpam-3200	114	15	β	β	X
ejpam-3200	114	16	(	(	PUNCT
ejpam-3200	114	17	(	(	PUNCT
ejpam-3200	114	18	ims∆	ims∆	NOUN
ejpam-3200	114	19	)	)	PUNCT
ejpam-3200	114	20	b∫	b∫	NOUN
ejpam-3200	115	1	a	a	PRON
ejpam-3200	115	2	f	f	X
ejpam-3200	115	3	(	(	PUNCT
ejpam-3200	115	4	t)dα	t)dα	PROPN
ejpam-3200	115	5	)	)	PUNCT
ejpam-3200	115	6	+	+	PROPN
ejpam-3200	115	7	+	+	CCONJ
ejpam-3200	115	8	γ	γ	X
ejpam-3200	115	9	(	(	PUNCT
ejpam-3200	115	10	(	(	PUNCT
ejpam-3200	115	11	ims∆	ims∆	NOUN
ejpam-3200	115	12	)	)	PUNCT
ejpam-3200	115	13	b∫	b∫	NOUN
ejpam-3200	115	14	a	a	DET
ejpam-3200	115	15	g(t)dα	g(t)dα	NOUN
ejpam-3200	115	16	)	)	PUNCT
ejpam-3200	115	17	+	+	PUNCT
ejpam-3200	115	18	=	=	SYM
ejpam-3200	115	19	(	(	PUNCT
ejpam-3200	115	20	β(ims∆	β(ims∆	NUM
ejpam-3200	115	21	)	)	PUNCT
ejpam-3200	115	22	b∫	b∫	NOUN
ejpam-3200	115	23	a	a	DET
ejpam-3200	115	24	f	f	X
ejpam-3200	115	25	(	(	PUNCT
ejpam-3200	115	26	t)dα+	t)dα+	NUM
ejpam-3200	115	27	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	115	28	)	)	PUNCT
ejpam-3200	115	29	b∫	b∫	NOUN
ejpam-3200	115	30	a	a	DET
ejpam-3200	115	31	g(t)dα	g(t)dα	NOUN
ejpam-3200	115	32	)	)	PUNCT
ejpam-3200	115	33	−	−	PROPN
ejpam-3200	115	34	.	.	PUNCT
ejpam-3200	116	1	(	(	PUNCT
ejpam-3200	116	2	3	3	X
ejpam-3200	116	3	)	)	PUNCT
ejpam-3200	116	4	if	if	SCONJ
ejpam-3200	116	5	β	β	X
ejpam-3200	116	6	>	>	X
ejpam-3200	116	7	0	0	NUM
ejpam-3200	116	8	and	and	CCONJ
ejpam-3200	116	9	γ	γ	X
ejpam-3200	116	10	<	<	X
ejpam-3200	116	11	0	0	NUM
ejpam-3200	116	12	,	,	PUNCT
ejpam-3200	116	13	(	(	PUNCT
ejpam-3200	116	14	or	or	CCONJ
ejpam-3200	116	15	β	β	X
ejpam-3200	116	16	<	<	X
ejpam-3200	116	17	0	0	PROPN
ejpam-3200	116	18	and	and	CCONJ
ejpam-3200	116	19	γ	γ	X
ejpam-3200	116	20	>	>	X
ejpam-3200	116	21	0	0	NUM
ejpam-3200	116	22	)	)	PUNCT
ejpam-3200	116	23	,	,	PUNCT
ejpam-3200	116	24	then	then	ADV
ejpam-3200	116	25	(	(	PUNCT
ejpam-3200	116	26	ms∆	ms∆	PROPN
ejpam-3200	116	27	)	)	PUNCT
ejpam-3200	116	28	b∫	b∫	PROPN
ejpam-3200	116	29	a	a	X
ejpam-3200	116	30	(	(	PUNCT
ejpam-3200	116	31	βf	βf	INTJ
ejpam-3200	116	32	(	(	PUNCT
ejpam-3200	116	33	t	t	NOUN
ejpam-3200	116	34	)	)	PUNCT
ejpam-3200	116	35	+	+	PUNCT
ejpam-3200	116	36	γg(t))−dα	γg(t))−dα	NOUN
ejpam-3200	116	37	=	=	SYM
ejpam-3200	116	38	(	(	PUNCT
ejpam-3200	116	39	ms∆	ms∆	PROPN
ejpam-3200	116	40	)	)	PUNCT
ejpam-3200	116	41	b∫	b∫	PROPN
ejpam-3200	116	42	a	a	DET
ejpam-3200	116	43	(	(	PUNCT
ejpam-3200	116	44	βf−(t	βf−(t	PROPN
ejpam-3200	116	45	)	)	PUNCT
ejpam-3200	117	1	+	+	NUM
ejpam-3200	117	2	γg+(t))dα	γg+(t))dα	NOUN
ejpam-3200	117	3	=	=	SYM
ejpam-3200	117	4	β(ms∆	β(ms∆	X
ejpam-3200	117	5	)	)	PUNCT
ejpam-3200	117	6	b∫	b∫	NOUN
ejpam-3200	117	7	a	a	DET
ejpam-3200	117	8	f−(t)dα+	f−(t)dα+	NUM
ejpam-3200	117	9	γ(ms∆	γ(ms∆	NOUN
ejpam-3200	117	10	)	)	PUNCT
ejpam-3200	117	11	b∫	b∫	NOUN
ejpam-3200	117	12	a	a	DET
ejpam-3200	117	13	g+(t)dα	g+(t)dα	NOUN
ejpam-3200	117	14	=	=	SYM
ejpam-3200	117	15	β	β	X
ejpam-3200	117	16	(	(	PUNCT
ejpam-3200	117	17	(	(	PUNCT
ejpam-3200	117	18	ims∆	ims∆	NOUN
ejpam-3200	117	19	)	)	PUNCT
ejpam-3200	117	20	b∫	b∫	NOUN
ejpam-3200	117	21	a	a	PRON
ejpam-3200	117	22	f	f	X
ejpam-3200	117	23	(	(	PUNCT
ejpam-3200	117	24	t)dα	t)dα	PROPN
ejpam-3200	117	25	)	)	PUNCT
ejpam-3200	117	26	−	−	PROPN
ejpam-3200	118	1	+	+	CCONJ
ejpam-3200	118	2	γ	γ	X
ejpam-3200	118	3	(	(	PUNCT
ejpam-3200	118	4	(	(	PUNCT
ejpam-3200	118	5	ims∆	ims∆	NOUN
ejpam-3200	118	6	)	)	PUNCT
ejpam-3200	118	7	b∫	b∫	NOUN
ejpam-3200	118	8	a	a	DET
ejpam-3200	118	9	g(t)dα	g(t)dα	NOUN
ejpam-3200	118	10	)	)	PUNCT
ejpam-3200	118	11	+	+	CCONJ
ejpam-3200	118	12	m.	m.	NOUN
ejpam-3200	118	13	e.	e.	PROPN
ejpam-3200	118	14	hamid	hamid	PROPN
ejpam-3200	118	15	/	/	SYM
ejpam-3200	118	16	eur	eur	PROPN
ejpam-3200	118	17	.	.	PUNCT
ejpam-3200	119	1	j.	j.	PROPN
ejpam-3200	119	2	pure	pure	PROPN
ejpam-3200	119	3	appl	appl	PROPN
ejpam-3200	119	4	.	.	PROPN
ejpam-3200	119	5	math	math	PROPN
ejpam-3200	119	6	,	,	PUNCT
ejpam-3200	119	7	11	11	NUM
ejpam-3200	119	8	(	(	PUNCT
ejpam-3200	119	9	2	2	NUM
ejpam-3200	119	10	)	)	PUNCT
ejpam-3200	119	11	(	(	PUNCT
ejpam-3200	119	12	2018	2018	NUM
ejpam-3200	119	13	)	)	PUNCT
ejpam-3200	119	14	,	,	PUNCT
ejpam-3200	119	15	493	493	NUM
ejpam-3200	119	16	-	-	SYM
ejpam-3200	119	17	504	504	NUM
ejpam-3200	119	18	498	498	NUM
ejpam-3200	119	19	=	=	SYM
ejpam-3200	119	20	(	(	PUNCT
ejpam-3200	119	21	β(ims∆	β(ims∆	NUM
ejpam-3200	119	22	)	)	PUNCT
ejpam-3200	119	23	b∫	b∫	NOUN
ejpam-3200	119	24	a	a	DET
ejpam-3200	119	25	f	f	X
ejpam-3200	119	26	(	(	PUNCT
ejpam-3200	119	27	t)dα+	t)dα+	NUM
ejpam-3200	119	28	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	119	29	)	)	PUNCT
ejpam-3200	119	30	b∫	b∫	NOUN
ejpam-3200	119	31	a	a	DET
ejpam-3200	119	32	g(t)dα	g(t)dα	NOUN
ejpam-3200	119	33	)	)	PUNCT
ejpam-3200	119	34	−	−	PROPN
ejpam-3200	119	35	.	.	PUNCT
ejpam-3200	120	1	similarly	similarly	ADV
ejpam-3200	120	2	,	,	PUNCT
ejpam-3200	120	3	for	for	ADP
ejpam-3200	120	4	four	four	NUM
ejpam-3200	120	5	cases	case	NOUN
ejpam-3200	120	6	above	above	ADP
ejpam-3200	120	7	we	we	PRON
ejpam-3200	120	8	have	have	VERB
ejpam-3200	120	9	(	(	PUNCT
ejpam-3200	120	10	ms∆	ms∆	PROPN
ejpam-3200	120	11	)	)	PUNCT
ejpam-3200	120	12	b∫	b∫	PROPN
ejpam-3200	120	13	a	a	X
ejpam-3200	120	14	(	(	PUNCT
ejpam-3200	120	15	βf	βf	INTJ
ejpam-3200	120	16	(	(	PUNCT
ejpam-3200	120	17	t	t	NOUN
ejpam-3200	120	18	)	)	PUNCT
ejpam-3200	120	19	+	+	PUNCT
ejpam-3200	120	20	γg(t))+dα	γg(t))+dα	NOUN
ejpam-3200	120	21	=	=	SYM
ejpam-3200	120	22	(	(	PUNCT
ejpam-3200	120	23	β(ims∆	β(ims∆	NUM
ejpam-3200	120	24	)	)	PUNCT
ejpam-3200	120	25	b∫	b∫	NOUN
ejpam-3200	120	26	a	a	DET
ejpam-3200	120	27	f	f	X
ejpam-3200	120	28	(	(	PUNCT
ejpam-3200	120	29	t)dα+	t)dα+	NUM
ejpam-3200	120	30	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	120	31	)	)	PUNCT
ejpam-3200	120	32	b∫	b∫	NOUN
ejpam-3200	120	33	a	a	DET
ejpam-3200	120	34	g(t)dα	g(t)dα	NOUN
ejpam-3200	120	35	)	)	PUNCT
ejpam-3200	121	1	+	+	CCONJ
ejpam-3200	121	2	.	.	PUNCT
ejpam-3200	122	1	(	(	PUNCT
ejpam-3200	122	2	3.11	3.11	NUM
ejpam-3200	122	3	)	)	PUNCT
ejpam-3200	122	4	hence	hence	ADV
ejpam-3200	122	5	by	by	ADP
ejpam-3200	122	6	theorem	theorem	NOUN
ejpam-3200	122	7	2	2	NUM
ejpam-3200	122	8	βf	βf	SYM
ejpam-3200	122	9	(	(	PUNCT
ejpam-3200	122	10	t	t	PROPN
ejpam-3200	122	11	)	)	PUNCT
ejpam-3200	122	12	+	+	NUM
ejpam-3200	122	13	γg(t	γg(t	X
ejpam-3200	122	14	)	)	PUNCT
ejpam-3200	122	15	∈	∈	PROPN
ejpam-3200	122	16	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	122	17	,	,	PUNCT
ejpam-3200	122	18	b]t	b]t	NOUN
ejpam-3200	122	19	and	and	CCONJ
ejpam-3200	122	20	(	(	PUNCT
ejpam-3200	122	21	ims∆	ims∆	NOUN
ejpam-3200	122	22	)	)	PUNCT
ejpam-3200	122	23	b∫	b∫	NOUN
ejpam-3200	122	24	a	a	X
ejpam-3200	122	25	(	(	PUNCT
ejpam-3200	122	26	βf	βf	INTJ
ejpam-3200	122	27	(	(	PUNCT
ejpam-3200	122	28	t	t	NOUN
ejpam-3200	122	29	)	)	PUNCT
ejpam-3200	122	30	+	+	CCONJ
ejpam-3200	122	31	γg(t))dα	γg(t))dα	NOUN
ejpam-3200	122	32	=	=	SYM
ejpam-3200	122	33	β(ims∆	β(ims∆	NUM
ejpam-3200	122	34	)	)	PUNCT
ejpam-3200	122	35	b∫	b∫	NOUN
ejpam-3200	122	36	a	a	DET
ejpam-3200	122	37	f	f	X
ejpam-3200	122	38	(	(	PUNCT
ejpam-3200	122	39	t)dα+	t)dα+	NUM
ejpam-3200	122	40	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	122	41	)	)	PUNCT
ejpam-3200	122	42	b∫	b∫	NOUN
ejpam-3200	122	43	a	a	DET
ejpam-3200	122	44	g(t)dα	g(t)dα	PROPN
ejpam-3200	122	45	.	.	PUNCT
ejpam-3200	123	1	(	(	PUNCT
ejpam-3200	123	2	3.12	3.12	NUM
ejpam-3200	123	3	)	)	PUNCT
ejpam-3200	123	4	theorem	theorem	NOUN
ejpam-3200	123	5	4	4	NUM
ejpam-3200	123	6	.	.	PUNCT
ejpam-3200	124	1	let	let	VERB
ejpam-3200	124	2	α	α	PRON
ejpam-3200	124	3	:	:	PUNCT
ejpam-3200	125	1	[	[	X
ejpam-3200	125	2	a	a	DET
ejpam-3200	125	3	,	,	PUNCT
ejpam-3200	125	4	b]t	b]t	NOUN
ejpam-3200	125	5	→	→	SYM
ejpam-3200	125	6	r	r	NOUN
ejpam-3200	125	7	be	be	AUX
ejpam-3200	125	8	an	an	DET
ejpam-3200	125	9	increasing	increase	VERB
ejpam-3200	125	10	function	function	NOUN
ejpam-3200	125	11	.	.	PUNCT
ejpam-3200	126	1	if	if	SCONJ
ejpam-3200	126	2	f	f	PROPN
ejpam-3200	126	3	(	(	PUNCT
ejpam-3200	126	4	t	t	PROPN
ejpam-3200	126	5	)	)	PUNCT
ejpam-3200	126	6	∈	∈	PROPN
ejpam-3200	126	7	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	126	8	,	,	PUNCT
ejpam-3200	126	9	c]t	c]t	NOUN
ejpam-3200	126	10	and	and	CCONJ
ejpam-3200	126	11	f	f	PROPN
ejpam-3200	126	12	(	(	PUNCT
ejpam-3200	126	13	t	t	PROPN
ejpam-3200	126	14	)	)	PUNCT
ejpam-3200	126	15	∈	∈	PROPN
ejpam-3200	126	16	imsα∆[c	imsα∆[c	NOUN
ejpam-3200	126	17	,	,	PUNCT
ejpam-3200	126	18	b]t	b]t	NOUN
ejpam-3200	126	19	,	,	PUNCT
ejpam-3200	126	20	then	then	ADV
ejpam-3200	126	21	f	f	PROPN
ejpam-3200	126	22	(	(	PUNCT
ejpam-3200	126	23	t	t	PROPN
ejpam-3200	126	24	)	)	PUNCT
ejpam-3200	126	25	∈	∈	PROPN
ejpam-3200	126	26	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	126	27	,	,	PUNCT
ejpam-3200	126	28	b]t	b]t	NOUN
ejpam-3200	126	29	and	and	CCONJ
ejpam-3200	126	30	(	(	PUNCT
ejpam-3200	126	31	ims∆	ims∆	NOUN
ejpam-3200	126	32	)	)	PUNCT
ejpam-3200	126	33	b∫	b∫	NOUN
ejpam-3200	126	34	a	a	PRON
ejpam-3200	126	35	f	f	X
ejpam-3200	126	36	(	(	PUNCT
ejpam-3200	126	37	t)dα	t)dα	PROPN
ejpam-3200	126	38	=	=	SYM
ejpam-3200	126	39	(	(	PUNCT
ejpam-3200	126	40	ims∆	ims∆	NOUN
ejpam-3200	126	41	)	)	PUNCT
ejpam-3200	126	42	c∫	c∫	NOUN
ejpam-3200	126	43	a	a	DET
ejpam-3200	126	44	f	f	X
ejpam-3200	126	45	(	(	PUNCT
ejpam-3200	126	46	t)dα+	t)dα+	X
ejpam-3200	126	47	(	(	PUNCT
ejpam-3200	126	48	ims∆	ims∆	NOUN
ejpam-3200	126	49	)	)	PUNCT
ejpam-3200	126	50	b∫	b∫	NOUN
ejpam-3200	126	51	c	c	PROPN
ejpam-3200	126	52	f	f	PROPN
ejpam-3200	126	53	(	(	PUNCT
ejpam-3200	126	54	t)dα	t)dα	PROPN
ejpam-3200	126	55	.	.	PUNCT
ejpam-3200	127	1	(	(	PUNCT
ejpam-3200	127	2	3.13	3.13	NUM
ejpam-3200	127	3	)	)	PUNCT
ejpam-3200	127	4	proof	proof	NOUN
ejpam-3200	127	5	.	.	PUNCT
ejpam-3200	128	1	if	if	SCONJ
ejpam-3200	128	2	f	f	PROPN
ejpam-3200	128	3	(	(	PUNCT
ejpam-3200	128	4	t	t	PROPN
ejpam-3200	128	5	)	)	PUNCT
ejpam-3200	128	6	∈	∈	PROPN
ejpam-3200	128	7	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	128	8	,	,	PUNCT
ejpam-3200	128	9	c]t	c]t	NOUN
ejpam-3200	128	10	and	and	CCONJ
ejpam-3200	128	11	f	f	PROPN
ejpam-3200	128	12	(	(	PUNCT
ejpam-3200	128	13	t	t	PROPN
ejpam-3200	128	14	)	)	PUNCT
ejpam-3200	128	15	∈	∈	PROPN
ejpam-3200	128	16	imsα∆[c	imsα∆[c	NOUN
ejpam-3200	128	17	,	,	PUNCT
ejpam-3200	128	18	b]t	b]t	NOUN
ejpam-3200	128	19	,	,	PUNCT
ejpam-3200	128	20	then	then	ADV
ejpam-3200	128	21	by	by	ADP
ejpam-3200	128	22	theorem	theorem	ADJ
ejpam-3200	128	23	2	2	NUM
ejpam-3200	128	24	f−(t	f−(t	NOUN
ejpam-3200	128	25	)	)	PUNCT
ejpam-3200	128	26	,	,	PUNCT
ejpam-3200	128	27	f+(t	f+(t	X
ejpam-3200	128	28	)	)	PUNCT
ejpam-3200	128	29	∈	∈	PROPN
ejpam-3200	128	30	msα∆[a	msα∆[a	PROPN
ejpam-3200	128	31	,	,	PUNCT
ejpam-3200	128	32	c]t	c]t	NOUN
ejpam-3200	128	33	and	and	CCONJ
ejpam-3200	128	34	f−(t	f−(t	PROPN
ejpam-3200	128	35	)	)	PUNCT
ejpam-3200	128	36	,	,	PUNCT
ejpam-3200	128	37	f+(t	f+(t	NOUN
ejpam-3200	128	38	)	)	PUNCT
ejpam-3200	128	39	∈msα∆[c	∈msα∆[c	NOUN
ejpam-3200	128	40	,	,	PUNCT
ejpam-3200	128	41	b]t	b]t	NOUN
ejpam-3200	128	42	.	.	PUNCT
ejpam-3200	128	43	hence	hence	ADV
ejpam-3200	128	44	f−(t	f−(t	PROPN
ejpam-3200	128	45	)	)	PUNCT
ejpam-3200	128	46	,	,	PUNCT
ejpam-3200	128	47	f+(t	f+(t	PROPN
ejpam-3200	128	48	)	)	PUNCT
ejpam-3200	128	49	∈msα∆[a	∈msα∆[a	NOUN
ejpam-3200	128	50	,	,	PUNCT
ejpam-3200	128	51	b]t	b]t	NOUN
ejpam-3200	128	52	and	and	CCONJ
ejpam-3200	128	53	(	(	PUNCT
ejpam-3200	128	54	ms∆	ms∆	PROPN
ejpam-3200	128	55	)	)	PUNCT
ejpam-3200	128	56	b∫	b∫	NOUN
ejpam-3200	128	57	a	a	DET
ejpam-3200	128	58	f−(t)dα	f−(t)dα	NOUN
ejpam-3200	128	59	=	=	SYM
ejpam-3200	128	60	(	(	PUNCT
ejpam-3200	128	61	ms∆	ms∆	PROPN
ejpam-3200	128	62	)	)	PUNCT
ejpam-3200	128	63	c∫	c∫	NOUN
ejpam-3200	128	64	a	a	DET
ejpam-3200	128	65	f−(t)dα+	f−(t)dα+	PROPN
ejpam-3200	128	66	(	(	PUNCT
ejpam-3200	128	67	ms∆	ms∆	PROPN
ejpam-3200	128	68	)	)	PUNCT
ejpam-3200	128	69	b∫	b∫	PROPN
ejpam-3200	128	70	c	c	NOUN
ejpam-3200	128	71	f−(t)dα	f−(t)dα	PROPN
ejpam-3200	128	72	=	=	SYM
ejpam-3200	128	73	(	(	PUNCT
ejpam-3200	128	74	(	(	PUNCT
ejpam-3200	128	75	ims∆	ims∆	NOUN
ejpam-3200	128	76	)	)	PUNCT
ejpam-3200	128	77	c∫	c∫	NOUN
ejpam-3200	128	78	a	a	DET
ejpam-3200	128	79	f	f	X
ejpam-3200	128	80	(	(	PUNCT
ejpam-3200	128	81	t)dα+	t)dα+	X
ejpam-3200	128	82	(	(	PUNCT
ejpam-3200	128	83	ims∆	ims∆	NOUN
ejpam-3200	128	84	)	)	PUNCT
ejpam-3200	128	85	b∫	b∫	NOUN
ejpam-3200	128	86	c	c	PROPN
ejpam-3200	128	87	f	f	PROPN
ejpam-3200	128	88	(	(	PUNCT
ejpam-3200	128	89	t)dα	t)dα	PROPN
ejpam-3200	128	90	)	)	PUNCT
ejpam-3200	128	91	−	−	PROPN
ejpam-3200	128	92	.	.	PUNCT
ejpam-3200	129	1	similarly	similarly	ADV
ejpam-3200	129	2	,	,	PUNCT
ejpam-3200	129	3	(	(	PUNCT
ejpam-3200	129	4	ms∆	ms∆	PROPN
ejpam-3200	129	5	)	)	PUNCT
ejpam-3200	129	6	b∫	b∫	PROPN
ejpam-3200	129	7	a	a	DET
ejpam-3200	129	8	f+(t)dα	f+(t)dα	PROPN
ejpam-3200	129	9	=	=	PUNCT
ejpam-3200	129	10	(	(	PUNCT
ejpam-3200	129	11	(	(	PUNCT
ejpam-3200	129	12	ims∆	ims∆	NOUN
ejpam-3200	129	13	)	)	PUNCT
ejpam-3200	129	14	c∫	c∫	NOUN
ejpam-3200	129	15	a	a	DET
ejpam-3200	129	16	f	f	X
ejpam-3200	129	17	(	(	PUNCT
ejpam-3200	129	18	t)dα	t)dα	PROPN
ejpam-3200	129	19	+	+	CCONJ
ejpam-3200	129	20	(	(	PUNCT
ejpam-3200	129	21	ims∆	ims∆	NOUN
ejpam-3200	129	22	)	)	PUNCT
ejpam-3200	129	23	b∫	b∫	NOUN
ejpam-3200	129	24	c	c	PROPN
ejpam-3200	129	25	f	f	PROPN
ejpam-3200	129	26	(	(	PUNCT
ejpam-3200	129	27	t)dα	t)dα	PROPN
ejpam-3200	129	28	)	)	PUNCT
ejpam-3200	129	29	+	+	CCONJ
ejpam-3200	129	30	.	.	PUNCT
ejpam-3200	130	1	hence	hence	ADV
ejpam-3200	130	2	by	by	ADP
ejpam-3200	130	3	theorem	theorem	ADJ
ejpam-3200	130	4	2	2	NUM
ejpam-3200	130	5	f	f	PROPN
ejpam-3200	130	6	(	(	PUNCT
ejpam-3200	130	7	t	t	PROPN
ejpam-3200	130	8	)	)	PUNCT
ejpam-3200	130	9	∈	∈	PROPN
ejpam-3200	130	10	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	130	11	,	,	PUNCT
ejpam-3200	130	12	b]t	b]t	NOUN
ejpam-3200	130	13	and	and	CCONJ
ejpam-3200	130	14	(	(	PUNCT
ejpam-3200	130	15	ims∆	ims∆	NOUN
ejpam-3200	130	16	)	)	PUNCT
ejpam-3200	130	17	b∫	b∫	NOUN
ejpam-3200	130	18	a	a	PRON
ejpam-3200	130	19	f	f	X
ejpam-3200	130	20	(	(	PUNCT
ejpam-3200	131	1	t)dα	t)dα	PROPN
ejpam-3200	131	2	=	=	SYM
ejpam-3200	131	3	(	(	PUNCT
ejpam-3200	131	4	ims∆	ims∆	NOUN
ejpam-3200	131	5	)	)	PUNCT
ejpam-3200	131	6	c∫	c∫	NOUN
ejpam-3200	131	7	a	a	DET
ejpam-3200	131	8	f	f	X
ejpam-3200	131	9	(	(	PUNCT
ejpam-3200	131	10	t)dα+	t)dα+	X
ejpam-3200	131	11	(	(	PUNCT
ejpam-3200	131	12	ims∆	ims∆	NOUN
ejpam-3200	131	13	)	)	PUNCT
ejpam-3200	131	14	b∫	b∫	NOUN
ejpam-3200	131	15	c	c	PROPN
ejpam-3200	131	16	f	f	PROPN
ejpam-3200	131	17	(	(	PUNCT
ejpam-3200	131	18	t)dα	t)dα	PROPN
ejpam-3200	131	19	.	.	PUNCT
ejpam-3200	132	1	(	(	PUNCT
ejpam-3200	132	2	3.14	3.14	NUM
ejpam-3200	132	3	)	)	PUNCT
ejpam-3200	132	4	theorem	theorem	NOUN
ejpam-3200	132	5	5	5	NUM
ejpam-3200	132	6	.	.	PUNCT
ejpam-3200	133	1	let	let	VERB
ejpam-3200	133	2	α	α	PRON
ejpam-3200	133	3	:	:	PUNCT
ejpam-3200	134	1	[	[	X
ejpam-3200	134	2	a	a	DET
ejpam-3200	134	3	,	,	PUNCT
ejpam-3200	134	4	b]t	b]t	NOUN
ejpam-3200	134	5	→	→	SYM
ejpam-3200	134	6	r	r	NOUN
ejpam-3200	134	7	be	be	AUX
ejpam-3200	134	8	an	an	DET
ejpam-3200	134	9	increasing	increase	VERB
ejpam-3200	134	10	function	function	NOUN
ejpam-3200	134	11	.	.	PUNCT
ejpam-3200	135	1	if	if	SCONJ
ejpam-3200	135	2	f	f	PROPN
ejpam-3200	135	3	(	(	PUNCT
ejpam-3200	135	4	t	t	PROPN
ejpam-3200	135	5	)	)	PUNCT
ejpam-3200	135	6	≤	≤	NUM
ejpam-3200	135	7	g(t	g(t	PROPN
ejpam-3200	135	8	)	)	PUNCT
ejpam-3200	135	9	almost	almost	ADV
ejpam-3200	135	10	everywhere	everywhere	ADV
ejpam-3200	135	11	with	with	ADP
ejpam-3200	135	12	respect	respect	NOUN
ejpam-3200	135	13	to	to	ADP
ejpam-3200	135	14	α	α	NOUN
ejpam-3200	135	15	on	on	ADP
ejpam-3200	135	16	[	[	X
ejpam-3200	135	17	a	a	DET
ejpam-3200	135	18	,	,	PUNCT
ejpam-3200	135	19	b]t	b]t	NOUN
ejpam-3200	135	20	and	and	CCONJ
ejpam-3200	135	21	f	f	PROPN
ejpam-3200	135	22	(	(	PUNCT
ejpam-3200	135	23	t	t	PROPN
ejpam-3200	135	24	)	)	PUNCT
ejpam-3200	135	25	,	,	PUNCT
ejpam-3200	135	26	g(t	g(t	PROPN
ejpam-3200	135	27	)	)	PUNCT
ejpam-3200	135	28	∈	∈	PROPN
ejpam-3200	135	29	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	135	30	,	,	PUNCT
ejpam-3200	135	31	b]t	b]t	NOUN
ejpam-3200	135	32	,	,	PUNCT
ejpam-3200	135	33	then	then	ADV
ejpam-3200	135	34	(	(	PUNCT
ejpam-3200	135	35	ims∆	ims∆	NOUN
ejpam-3200	135	36	)	)	PUNCT
ejpam-3200	135	37	b∫	b∫	NOUN
ejpam-3200	135	38	a	a	DET
ejpam-3200	135	39	f	f	X
ejpam-3200	135	40	(	(	PUNCT
ejpam-3200	135	41	t)dα	t)dα	PROPN
ejpam-3200	135	42	≤	≤	PROPN
ejpam-3200	135	43	(	(	PUNCT
ejpam-3200	135	44	ims∆	ims∆	NUM
ejpam-3200	135	45	)	)	PUNCT
ejpam-3200	135	46	b∫	b∫	NOUN
ejpam-3200	135	47	a	a	DET
ejpam-3200	135	48	g(t)dα	g(t)dα	PROPN
ejpam-3200	135	49	.	.	PUNCT
ejpam-3200	136	1	(	(	PUNCT
ejpam-3200	136	2	3.15	3.15	NUM
ejpam-3200	136	3	)	)	PUNCT
ejpam-3200	136	4	m.	m.	NOUN
ejpam-3200	136	5	e.	e.	PROPN
ejpam-3200	136	6	hamid	hamid	PROPN
ejpam-3200	136	7	/	/	SYM
ejpam-3200	136	8	eur	eur	PROPN
ejpam-3200	136	9	.	.	PUNCT
ejpam-3200	137	1	j.	j.	PROPN
ejpam-3200	137	2	pure	pure	PROPN
ejpam-3200	137	3	appl	appl	PROPN
ejpam-3200	137	4	.	.	PROPN
ejpam-3200	137	5	math	math	PROPN
ejpam-3200	137	6	,	,	PUNCT
ejpam-3200	137	7	11	11	NUM
ejpam-3200	137	8	(	(	PUNCT
ejpam-3200	137	9	2	2	NUM
ejpam-3200	137	10	)	)	PUNCT
ejpam-3200	137	11	(	(	PUNCT
ejpam-3200	137	12	2018	2018	NUM
ejpam-3200	137	13	)	)	PUNCT
ejpam-3200	137	14	,	,	PUNCT
ejpam-3200	137	15	493	493	NUM
ejpam-3200	137	16	-	-	SYM
ejpam-3200	137	17	504	504	NUM
ejpam-3200	137	18	499	499	NUM
ejpam-3200	137	19	proof	proof	NOUN
ejpam-3200	137	20	.	.	PUNCT
ejpam-3200	138	1	let	let	VERB
ejpam-3200	138	2	f	f	PROPN
ejpam-3200	138	3	(	(	PUNCT
ejpam-3200	138	4	t	t	PROPN
ejpam-3200	138	5	)	)	PUNCT
ejpam-3200	138	6	≤	≤	NUM
ejpam-3200	138	7	g(t	g(t	PROPN
ejpam-3200	138	8	)	)	PUNCT
ejpam-3200	138	9	almost	almost	ADV
ejpam-3200	138	10	everywhere	everywhere	ADV
ejpam-3200	138	11	with	with	ADP
ejpam-3200	138	12	respect	respect	NOUN
ejpam-3200	138	13	to	to	ADP
ejpam-3200	138	14	α	α	NOUN
ejpam-3200	138	15	on	on	ADP
ejpam-3200	138	16	[	[	X
ejpam-3200	138	17	a	a	DET
ejpam-3200	138	18	,	,	PUNCT
ejpam-3200	138	19	b]t	b]t	NOUN
ejpam-3200	138	20	and	and	CCONJ
ejpam-3200	138	21	f	f	PROPN
ejpam-3200	138	22	(	(	PUNCT
ejpam-3200	138	23	t	t	PROPN
ejpam-3200	138	24	)	)	PUNCT
ejpam-3200	138	25	,	,	PUNCT
ejpam-3200	138	26	g(t	g(t	PROPN
ejpam-3200	138	27	)	)	PUNCT
ejpam-3200	138	28	∈	∈	PROPN
ejpam-3200	138	29	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	138	30	,	,	PUNCT
ejpam-3200	138	31	b]t	b]t	NOUN
ejpam-3200	138	32	.	.	PUNCT
ejpam-3200	139	1	then	then	ADV
ejpam-3200	139	2	f−(t	f−(t	PROPN
ejpam-3200	139	3	)	)	PUNCT
ejpam-3200	139	4	,	,	PUNCT
ejpam-3200	139	5	f+(t	f+(t	PROPN
ejpam-3200	139	6	)	)	PUNCT
ejpam-3200	139	7	,	,	PUNCT
ejpam-3200	139	8	g−(t	g−(t	PROPN
ejpam-3200	139	9	)	)	PUNCT
ejpam-3200	139	10	,	,	PUNCT
ejpam-3200	139	11	g+(t	g+(t	NOUN
ejpam-3200	139	12	)	)	PUNCT
ejpam-3200	139	13	∈msα∆[a	∈msα∆[a	NOUN
ejpam-3200	139	14	,	,	PUNCT
ejpam-3200	139	15	b]t	b]t	NOUN
ejpam-3200	139	16	and	and	CCONJ
ejpam-3200	139	17	f−(t	f−(t	NOUN
ejpam-3200	139	18	)	)	PUNCT
ejpam-3200	139	19	≤	≤	NUM
ejpam-3200	139	20	g−(t	g−(t	PROPN
ejpam-3200	139	21	)	)	PUNCT
ejpam-3200	139	22	,	,	PUNCT
ejpam-3200	139	23	f+(t	f+(t	PROPN
ejpam-3200	139	24	)	)	PUNCT
ejpam-3200	139	25	≤	≤	NUM
ejpam-3200	139	26	g+(t	g+(t	NOUN
ejpam-3200	139	27	)	)	PUNCT
ejpam-3200	139	28	nearly	nearly	ADV
ejpam-3200	139	29	everywhere	everywhere	ADV
ejpam-3200	139	30	with	with	ADP
ejpam-3200	139	31	respect	respect	NOUN
ejpam-3200	139	32	to	to	ADP
ejpam-3200	139	33	α	α	NOUN
ejpam-3200	139	34	on	on	ADP
ejpam-3200	139	35	[	[	X
ejpam-3200	139	36	a	a	DET
ejpam-3200	139	37	,	,	PUNCT
ejpam-3200	139	38	b]t	b]t	NOUN
ejpam-3200	139	39	.	.	PUNCT
ejpam-3200	140	1	by	by	ADP
ejpam-3200	140	2	theorem	theorem	NOUN
ejpam-3200	140	3	1	1	NUM
ejpam-3200	140	4	(	(	PUNCT
ejpam-3200	140	5	ms∆	ms∆	PROPN
ejpam-3200	140	6	)	)	PUNCT
ejpam-3200	140	7	b∫	b∫	NOUN
ejpam-3200	140	8	a	a	DET
ejpam-3200	140	9	f−(t)dα	f−(t)dα	NOUN
ejpam-3200	140	10	≤	≤	NOUN
ejpam-3200	140	11	(	(	PUNCT
ejpam-3200	140	12	ms∆	ms∆	PROPN
ejpam-3200	140	13	)	)	PUNCT
ejpam-3200	140	14	b∫	b∫	PROPN
ejpam-3200	140	15	a	a	DET
ejpam-3200	140	16	g−(t)dα	g−(t)dα	PROPN
ejpam-3200	140	17	and	and	CCONJ
ejpam-3200	140	18	(	(	PUNCT
ejpam-3200	140	19	ms∆	ms∆	PROPN
ejpam-3200	140	20	)	)	PUNCT
ejpam-3200	140	21	b∫	b∫	PROPN
ejpam-3200	140	22	a	a	DET
ejpam-3200	140	23	f+(t)dα	f+(t)dα	PROPN
ejpam-3200	140	24	≤	≤	NOUN
ejpam-3200	140	25	(	(	PUNCT
ejpam-3200	140	26	ms∆	ms∆	PROPN
ejpam-3200	140	27	)	)	PUNCT
ejpam-3200	140	28	b∫	b∫	NOUN
ejpam-3200	140	29	a	a	DET
ejpam-3200	140	30	g+(t)dα	g+(t)dα	NOUN
ejpam-3200	140	31	.	.	PUNCT
ejpam-3200	141	1	hence	hence	ADV
ejpam-3200	141	2	(	(	PUNCT
ejpam-3200	141	3	ims∆	ims∆	NOUN
ejpam-3200	141	4	)	)	PUNCT
ejpam-3200	141	5	b∫	b∫	NOUN
ejpam-3200	141	6	a	a	DET
ejpam-3200	141	7	f	f	X
ejpam-3200	141	8	(	(	PUNCT
ejpam-3200	141	9	t)dα	t)dα	PROPN
ejpam-3200	141	10	≤	≤	PROPN
ejpam-3200	141	11	(	(	PUNCT
ejpam-3200	141	12	ims∆	ims∆	NUM
ejpam-3200	141	13	)	)	PUNCT
ejpam-3200	141	14	b∫	b∫	PROPN
ejpam-3200	141	15	a	a	DET
ejpam-3200	141	16	g(t)dα	g(t)dα	PROPN
ejpam-3200	141	17	,	,	PUNCT
ejpam-3200	141	18	(	(	PUNCT
ejpam-3200	141	19	3.16	3.16	NUM
ejpam-3200	141	20	)	)	PUNCT
ejpam-3200	141	21	by	by	ADP
ejpam-3200	141	22	theorem	theorem	NOUN
ejpam-3200	141	23	2	2	NUM
ejpam-3200	141	24	.	.	PUNCT
ejpam-3200	141	25	theorem	theorem	NOUN
ejpam-3200	141	26	6	6	NUM
ejpam-3200	141	27	.	.	PUNCT
ejpam-3200	142	1	let	let	VERB
ejpam-3200	142	2	α	α	PRON
ejpam-3200	142	3	:	:	PUNCT
ejpam-3200	143	1	[	[	X
ejpam-3200	143	2	a	a	DET
ejpam-3200	143	3	,	,	PUNCT
ejpam-3200	143	4	b]t	b]t	NOUN
ejpam-3200	143	5	→	→	SYM
ejpam-3200	143	6	r	r	NOUN
ejpam-3200	143	7	be	be	AUX
ejpam-3200	143	8	an	an	DET
ejpam-3200	143	9	increasing	increase	VERB
ejpam-3200	143	10	function	function	NOUN
ejpam-3200	143	11	.	.	PUNCT
ejpam-3200	144	1	let	let	VERB
ejpam-3200	144	2	f	f	PROPN
ejpam-3200	144	3	(	(	PUNCT
ejpam-3200	144	4	t	t	PROPN
ejpam-3200	144	5	)	)	PUNCT
ejpam-3200	144	6	,	,	PUNCT
ejpam-3200	144	7	g(t	g(t	PROPN
ejpam-3200	144	8	)	)	PUNCT
ejpam-3200	144	9	∈	∈	PROPN
ejpam-3200	144	10	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	144	11	,	,	PUNCT
ejpam-3200	144	12	b]t	b]t	NOUN
ejpam-3200	144	13	and	and	CCONJ
ejpam-3200	144	14	d(f	d(f	NOUN
ejpam-3200	144	15	(	(	PUNCT
ejpam-3200	144	16	t	t	NOUN
ejpam-3200	144	17	)	)	PUNCT
ejpam-3200	144	18	,	,	PUNCT
ejpam-3200	144	19	g(t	g(t	PROPN
ejpam-3200	144	20	)	)	PUNCT
ejpam-3200	144	21	)	)	PUNCT
ejpam-3200	144	22	is	be	AUX
ejpam-3200	144	23	(	(	PUNCT
ejpam-3200	144	24	ms∆	ms∆	PROPN
ejpam-3200	144	25	)	)	PUNCT
ejpam-3200	144	26	integrable	integrable	ADJ
ejpam-3200	144	27	with	with	ADP
ejpam-3200	144	28	respect	respect	NOUN
ejpam-3200	144	29	to	to	ADP
ejpam-3200	144	30	α	α	NOUN
ejpam-3200	144	31	on	on	ADP
ejpam-3200	144	32	[	[	X
ejpam-3200	144	33	a	a	DET
ejpam-3200	144	34	,	,	PUNCT
ejpam-3200	144	35	b]t	b]t	NOUN
ejpam-3200	144	36	.	.	PUNCT
ejpam-3200	145	1	then	then	ADV
ejpam-3200	145	2	d	d	X
ejpam-3200	145	3	(	(	PUNCT
ejpam-3200	145	4	(	(	PUNCT
ejpam-3200	145	5	ims∆	ims∆	NOUN
ejpam-3200	145	6	)	)	PUNCT
ejpam-3200	145	7	b∫	b∫	NOUN
ejpam-3200	145	8	a	a	DET
ejpam-3200	145	9	f	f	X
ejpam-3200	145	10	(	(	PUNCT
ejpam-3200	145	11	t)dα	t)dα	PROPN
ejpam-3200	145	12	,	,	PUNCT
ejpam-3200	145	13	(	(	PUNCT
ejpam-3200	145	14	ims∆	ims∆	NOUN
ejpam-3200	145	15	)	)	PUNCT
ejpam-3200	145	16	b∫	b∫	NOUN
ejpam-3200	145	17	a	a	DET
ejpam-3200	145	18	g(t)dα	g(t)dα	NOUN
ejpam-3200	145	19	)	)	PUNCT
ejpam-3200	145	20	≤	≤	NOUN
ejpam-3200	145	21	(	(	PUNCT
ejpam-3200	145	22	ms∆	ms∆	PROPN
ejpam-3200	145	23	)	)	PUNCT
ejpam-3200	145	24	b∫	b∫	PROPN
ejpam-3200	145	25	a	a	PROPN
ejpam-3200	145	26	d	d	X
ejpam-3200	145	27	(	(	PUNCT
ejpam-3200	145	28	f	f	PROPN
ejpam-3200	145	29	(	(	PUNCT
ejpam-3200	145	30	t	t	PROPN
ejpam-3200	145	31	)	)	PUNCT
ejpam-3200	145	32	,	,	PUNCT
ejpam-3200	145	33	g(t	g(t	PROPN
ejpam-3200	145	34	)	)	PUNCT
ejpam-3200	145	35	)	)	PUNCT
ejpam-3200	146	1	dα	dα	PROPN
ejpam-3200	146	2	.	.	PUNCT
ejpam-3200	147	1	(	(	PUNCT
ejpam-3200	147	2	3.17	3.17	NUM
ejpam-3200	147	3	)	)	PUNCT
ejpam-3200	147	4	proof	proof	NOUN
ejpam-3200	147	5	.	.	PUNCT
ejpam-3200	148	1	by	by	ADP
ejpam-3200	148	2	definition	definition	NOUN
ejpam-3200	148	3	of	of	ADP
ejpam-3200	148	4	distance	distance	NOUN
ejpam-3200	148	5	,	,	PUNCT
ejpam-3200	148	6	d	d	X
ejpam-3200	148	7	(	(	PUNCT
ejpam-3200	148	8	(	(	PUNCT
ejpam-3200	148	9	ims∆	ims∆	NOUN
ejpam-3200	148	10	)	)	PUNCT
ejpam-3200	148	11	b∫	b∫	NOUN
ejpam-3200	148	12	a	a	DET
ejpam-3200	148	13	f	f	X
ejpam-3200	148	14	(	(	PUNCT
ejpam-3200	148	15	t)dα	t)dα	PROPN
ejpam-3200	148	16	,	,	PUNCT
ejpam-3200	148	17	(	(	PUNCT
ejpam-3200	148	18	ims∆	ims∆	NOUN
ejpam-3200	148	19	)	)	PUNCT
ejpam-3200	148	20	b∫	b∫	NOUN
ejpam-3200	148	21	a	a	DET
ejpam-3200	148	22	g(t)dα	g(t)dα	NOUN
ejpam-3200	148	23	)	)	PUNCT
ejpam-3200	149	1	=	=	SYM
ejpam-3200	149	2	max	max	PROPN
ejpam-3200	149	3	(	(	PUNCT
ejpam-3200	149	4	∣∣∣∣((ims∆	∣∣∣∣((ims∆	PROPN
ejpam-3200	149	5	)	)	PUNCT
ejpam-3200	149	6	b∫	b∫	NOUN
ejpam-3200	150	1	a	a	PRON
ejpam-3200	150	2	f	f	X
ejpam-3200	150	3	(	(	PUNCT
ejpam-3200	150	4	t)dα	t)dα	PROPN
ejpam-3200	150	5	)	)	PUNCT
ejpam-3200	150	6	−	−	PROPN
ejpam-3200	151	1	−	−	PROPN
ejpam-3200	151	2	(	(	PUNCT
ejpam-3200	151	3	(	(	PUNCT
ejpam-3200	151	4	ims∆	ims∆	NOUN
ejpam-3200	151	5	)	)	PUNCT
ejpam-3200	151	6	b∫	b∫	NOUN
ejpam-3200	151	7	a	a	DET
ejpam-3200	151	8	g(t)dα	g(t)dα	PROPN
ejpam-3200	151	9	)	)	PUNCT
ejpam-3200	151	10	−∣∣∣∣	−∣∣∣∣	PROPN
ejpam-3200	151	11	,	,	PUNCT
ejpam-3200	151	12	∣∣∣∣((ims∆	∣∣∣∣((ims∆	PROPN
ejpam-3200	151	13	)	)	PUNCT
ejpam-3200	151	14	b∫	b∫	NOUN
ejpam-3200	152	1	a	a	PRON
ejpam-3200	152	2	f	f	X
ejpam-3200	152	3	(	(	PUNCT
ejpam-3200	152	4	t)dα	t)dα	PROPN
ejpam-3200	152	5	)	)	PUNCT
ejpam-3200	152	6	+	+	NUM
ejpam-3200	152	7	−	−	PROPN
ejpam-3200	152	8	(	(	PUNCT
ejpam-3200	152	9	(	(	PUNCT
ejpam-3200	152	10	ims∆	ims∆	NOUN
ejpam-3200	152	11	)	)	PUNCT
ejpam-3200	152	12	b∫	b∫	NOUN
ejpam-3200	152	13	a	a	DET
ejpam-3200	152	14	g(t)dα	g(t)dα	NOUN
ejpam-3200	152	15	)	)	PUNCT
ejpam-3200	153	1	+	+	NOUN
ejpam-3200	153	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3200	153	3	)	)	PUNCT
ejpam-3200	153	4	=	=	SYM
ejpam-3200	153	5	max	max	PROPN
ejpam-3200	153	6	(	(	PUNCT
ejpam-3200	153	7	∣∣∣∣(ms∆	∣∣∣∣(ms∆	PROPN
ejpam-3200	153	8	)	)	PUNCT
ejpam-3200	153	9	b∫	b∫	PROPN
ejpam-3200	153	10	a	a	PRON
ejpam-3200	153	11	(	(	PUNCT
ejpam-3200	153	12	f−(t)−g−(t	f−(t)−g−(t	PROPN
ejpam-3200	153	13	)	)	PUNCT
ejpam-3200	153	14	)	)	PUNCT
ejpam-3200	154	1	dα	dα	ADP
ejpam-3200	154	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	154	3	,	,	PUNCT
ejpam-3200	154	4	∣∣∣∣(ms∆	∣∣∣∣(ms∆	PROPN
ejpam-3200	154	5	)	)	PUNCT
ejpam-3200	154	6	b∫	b∫	PROPN
ejpam-3200	154	7	a	a	DET
ejpam-3200	154	8	(	(	PUNCT
ejpam-3200	154	9	f+(t)−g+(t	f+(t)−g+(t	NOUN
ejpam-3200	154	10	)	)	PUNCT
ejpam-3200	154	11	)	)	PUNCT
ejpam-3200	155	1	dα	dα	DET
ejpam-3200	155	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3200	155	3	)	)	PUNCT
ejpam-3200	155	4	≤	≤	NUM
ejpam-3200	155	5	max	max	NOUN
ejpam-3200	155	6	(	(	PUNCT
ejpam-3200	155	7	(	(	PUNCT
ejpam-3200	155	8	ms∆	ms∆	PROPN
ejpam-3200	155	9	)	)	PUNCT
ejpam-3200	155	10	b∫	b∫	PROPN
ejpam-3200	155	11	a	a	DET
ejpam-3200	155	12	∣∣∣∣f−(t)−g−(t	∣∣∣∣f−(t)−g−(t	NOUN
ejpam-3200	155	13	)	)	PUNCT
ejpam-3200	155	14	∣∣∣∣dα	∣∣∣∣dα	NOUN
ejpam-3200	155	15	,	,	PUNCT
ejpam-3200	155	16	(	(	PUNCT
ejpam-3200	155	17	ms∆	ms∆	PROPN
ejpam-3200	155	18	)	)	PUNCT
ejpam-3200	155	19	b∫	b∫	PROPN
ejpam-3200	155	20	a	a	DET
ejpam-3200	155	21	∣∣∣∣f+(t)−g+(t	∣∣∣∣f+(t)−g+(t	PROPN
ejpam-3200	155	22	)	)	PUNCT
ejpam-3200	155	23	∣∣∣∣dα	∣∣∣∣dα	NOUN
ejpam-3200	155	24	)	)	PUNCT
ejpam-3200	155	25	≤	≤	NOUN
ejpam-3200	155	26	(	(	PUNCT
ejpam-3200	155	27	ms∆	ms∆	PROPN
ejpam-3200	155	28	)	)	PUNCT
ejpam-3200	155	29	b∫	b∫	PROPN
ejpam-3200	155	30	a	a	DET
ejpam-3200	155	31	max	max	PROPN
ejpam-3200	155	32	(	(	PUNCT
ejpam-3200	155	33	∣∣∣∣f−(t)−g−(t	∣∣∣∣f−(t)−g−(t	NOUN
ejpam-3200	155	34	)	)	PUNCT
ejpam-3200	155	35	∣∣∣∣dα	∣∣∣∣dα	NOUN
ejpam-3200	155	36	,	,	PUNCT
ejpam-3200	155	37	∣∣∣∣f+(t)−g+(t	∣∣∣∣f+(t)−g+(t	NOUN
ejpam-3200	155	38	)	)	PUNCT
ejpam-3200	155	39	∣∣∣∣dα	∣∣∣∣dα	NOUN
ejpam-3200	155	40	)	)	PUNCT
ejpam-3200	155	41	=	=	PUNCT
ejpam-3200	155	42	(	(	PUNCT
ejpam-3200	155	43	ms∆	ms∆	PROPN
ejpam-3200	155	44	)	)	PUNCT
ejpam-3200	155	45	b∫	b∫	PROPN
ejpam-3200	155	46	a	a	PROPN
ejpam-3200	155	47	d	d	X
ejpam-3200	155	48	(	(	PUNCT
ejpam-3200	155	49	f	f	PROPN
ejpam-3200	155	50	(	(	PUNCT
ejpam-3200	155	51	t	t	PROPN
ejpam-3200	155	52	)	)	PUNCT
ejpam-3200	155	53	,	,	PUNCT
ejpam-3200	155	54	g(t	g(t	PROPN
ejpam-3200	155	55	)	)	PUNCT
ejpam-3200	155	56	)	)	PUNCT
ejpam-3200	156	1	dα	dα	PROPN
ejpam-3200	156	2	.	.	PUNCT
ejpam-3200	157	1	(	(	PUNCT
ejpam-3200	157	2	3.18	3.18	NUM
ejpam-3200	157	3	)	)	PUNCT
ejpam-3200	157	4	m.	m.	NOUN
ejpam-3200	157	5	e.	e.	PROPN
ejpam-3200	157	6	hamid	hamid	PROPN
ejpam-3200	157	7	/	/	SYM
ejpam-3200	157	8	eur	eur	PROPN
ejpam-3200	157	9	.	.	PUNCT
ejpam-3200	158	1	j.	j.	PROPN
ejpam-3200	158	2	pure	pure	PROPN
ejpam-3200	158	3	appl	appl	PROPN
ejpam-3200	158	4	.	.	PROPN
ejpam-3200	158	5	math	math	PROPN
ejpam-3200	158	6	,	,	PUNCT
ejpam-3200	158	7	11	11	NUM
ejpam-3200	158	8	(	(	PUNCT
ejpam-3200	158	9	2	2	NUM
ejpam-3200	158	10	)	)	PUNCT
ejpam-3200	158	11	(	(	PUNCT
ejpam-3200	158	12	2018	2018	NUM
ejpam-3200	158	13	)	)	PUNCT
ejpam-3200	158	14	,	,	PUNCT
ejpam-3200	158	15	493	493	NUM
ejpam-3200	158	16	-	-	SYM
ejpam-3200	158	17	504	504	NUM
ejpam-3200	158	18	500	500	NUM
ejpam-3200	158	19	4	4	NUM
ejpam-3200	158	20	.	.	PUNCT
ejpam-3200	159	1	the	the	DET
ejpam-3200	159	2	ms∆	ms∆	PROPN
ejpam-3200	159	3	integral	integral	ADJ
ejpam-3200	159	4	of	of	ADP
ejpam-3200	159	5	fuzzy	fuzzy	ADJ
ejpam-3200	159	6	-	-	PUNCT
ejpam-3200	159	7	number	number	NOUN
ejpam-3200	159	8	-	-	PUNCT
ejpam-3200	159	9	valued	value	VERB
ejpam-3200	159	10	functions	function	NOUN
ejpam-3200	159	11	on	on	ADP
ejpam-3200	159	12	time	time	NOUN
ejpam-3200	159	13	scales	scale	NOUN
ejpam-3200	159	14	in	in	ADP
ejpam-3200	159	15	this	this	DET
ejpam-3200	159	16	section	section	NOUN
ejpam-3200	159	17	,	,	PUNCT
ejpam-3200	159	18	we	we	PRON
ejpam-3200	159	19	introduce	introduce	VERB
ejpam-3200	159	20	the	the	DET
ejpam-3200	159	21	notion	notion	NOUN
ejpam-3200	159	22	of	of	ADP
ejpam-3200	159	23	the	the	DET
ejpam-3200	159	24	(	(	PUNCT
ejpam-3200	159	25	ms∆	ms∆	PROPN
ejpam-3200	159	26	)	)	PUNCT
ejpam-3200	159	27	integral	integral	ADJ
ejpam-3200	159	28	of	of	ADP
ejpam-3200	159	29	fuzzy	fuzzy	ADJ
ejpam-3200	159	30	-	-	PUNCT
ejpam-3200	159	31	number	number	NOUN
ejpam-3200	159	32	-	-	PUNCT
ejpam-3200	159	33	valued	value	VERB
ejpam-3200	159	34	functions	function	NOUN
ejpam-3200	159	35	on	on	ADP
ejpam-3200	159	36	time	time	NOUN
ejpam-3200	159	37	scales	scale	NOUN
ejpam-3200	159	38	and	and	CCONJ
ejpam-3200	159	39	discusses	discuss	VERB
ejpam-3200	159	40	some	some	PRON
ejpam-3200	159	41	of	of	ADP
ejpam-3200	159	42	their	their	PRON
ejpam-3200	159	43	properties	property	NOUN
ejpam-3200	159	44	.	.	PUNCT
ejpam-3200	160	1	definition	definition	NOUN
ejpam-3200	160	2	6	6	NUM
ejpam-3200	160	3	.	.	PUNCT
ejpam-3200	161	1	[	[	X
ejpam-3200	161	2	6	6	NUM
ejpam-3200	161	3	,	,	PUNCT
ejpam-3200	161	4	8	8	NUM
ejpam-3200	161	5	,	,	PUNCT
ejpam-3200	161	6	9	9	NUM
ejpam-3200	161	7	]	]	PUNCT
ejpam-3200	161	8	let	let	VERB
ejpam-3200	161	9	ã	ã	PROPN
ejpam-3200	161	10	∈	∈	PROPN
ejpam-3200	161	11	f	f	X
ejpam-3200	161	12	(	(	PUNCT
ejpam-3200	161	13	r	r	NOUN
ejpam-3200	161	14	)	)	PUNCT
ejpam-3200	161	15	be	be	AUX
ejpam-3200	161	16	a	a	DET
ejpam-3200	161	17	fuzzy	fuzzy	ADJ
ejpam-3200	161	18	subset	subset	NOUN
ejpam-3200	161	19	on	on	ADP
ejpam-3200	161	20	r.	r.	PROPN
ejpam-3200	161	21	if	if	SCONJ
ejpam-3200	161	22	for	for	ADP
ejpam-3200	161	23	any	any	DET
ejpam-3200	161	24	λ	λ	PROPN
ejpam-3200	161	25	∈	∈	PROPN
ejpam-3200	162	1	[	[	X
ejpam-3200	162	2	0	0	NUM
ejpam-3200	162	3	,	,	PUNCT
ejpam-3200	162	4	1	1	NUM
ejpam-3200	162	5	]	]	PUNCT
ejpam-3200	162	6	,	,	PUNCT
ejpam-3200	162	7	aλ	aλ	ADP
ejpam-3200	162	8	=	=	PUNCT
ejpam-3200	163	1	[	[	X
ejpam-3200	163	2	a−λ	a−λ	X
ejpam-3200	163	3	,	,	PUNCT
ejpam-3200	163	4	a	a	DET
ejpam-3200	163	5	+	+	X
ejpam-3200	163	6	λ	λ	X
ejpam-3200	163	7	]	]	PUNCT
ejpam-3200	163	8	and	and	CCONJ
ejpam-3200	163	9	a1	a1	PROPN
ejpam-3200	163	10	6=	6=	PROPN
ejpam-3200	163	11	φ	φ	PROPN
ejpam-3200	163	12	,	,	PUNCT
ejpam-3200	163	13	where	where	SCONJ
ejpam-3200	163	14	aλ	aλ	ADP
ejpam-3200	163	15	=	=	SYM
ejpam-3200	163	16	{	{	PUNCT
ejpam-3200	163	17	t	t	X
ejpam-3200	163	18	:	:	PUNCT
ejpam-3200	163	19	ã(t	ã(t	PROPN
ejpam-3200	163	20	)	)	PUNCT
ejpam-3200	163	21	≥	≥	X
ejpam-3200	163	22	λ	λ	NOUN
ejpam-3200	163	23	}	}	PUNCT
ejpam-3200	163	24	,	,	PUNCT
ejpam-3200	163	25	then	then	ADV
ejpam-3200	163	26	ã	ã	PROPN
ejpam-3200	163	27	is	be	AUX
ejpam-3200	163	28	called	call	VERB
ejpam-3200	163	29	a	a	DET
ejpam-3200	163	30	fuzzy	fuzzy	ADJ
ejpam-3200	163	31	number	number	NOUN
ejpam-3200	163	32	.	.	PUNCT
ejpam-3200	164	1	if	if	SCONJ
ejpam-3200	164	2	ã	ã	PROPN
ejpam-3200	164	3	is	be	AUX
ejpam-3200	164	4	(	(	PUNCT
ejpam-3200	164	5	1	1	NUM
ejpam-3200	164	6	)	)	PUNCT
ejpam-3200	164	7	convex	convex	NOUN
ejpam-3200	164	8	,	,	PUNCT
ejpam-3200	164	9	(	(	PUNCT
ejpam-3200	164	10	2	2	X
ejpam-3200	164	11	)	)	PUNCT
ejpam-3200	164	12	normal	normal	ADJ
ejpam-3200	164	13	,	,	PUNCT
ejpam-3200	164	14	(	(	PUNCT
ejpam-3200	164	15	3	3	X
ejpam-3200	164	16	)	)	PUNCT
ejpam-3200	164	17	upper	upper	ADJ
ejpam-3200	164	18	semi	semi	ADJ
ejpam-3200	164	19	-	-	ADJ
ejpam-3200	164	20	continuous	continuous	ADJ
ejpam-3200	164	21	,	,	PUNCT
ejpam-3200	164	22	(	(	PUNCT
ejpam-3200	164	23	4	4	X
ejpam-3200	164	24	)	)	PUNCT
ejpam-3200	164	25	has	have	VERB
ejpam-3200	164	26	the	the	DET
ejpam-3200	164	27	compact	compact	ADJ
ejpam-3200	164	28	support	support	NOUN
ejpam-3200	164	29	,	,	PUNCT
ejpam-3200	164	30	we	we	PRON
ejpam-3200	164	31	say	say	VERB
ejpam-3200	164	32	that	that	SCONJ
ejpam-3200	164	33	ã	ã	PROPN
ejpam-3200	164	34	is	be	AUX
ejpam-3200	164	35	a	a	DET
ejpam-3200	164	36	compact	compact	ADJ
ejpam-3200	164	37	fuzzy	fuzzy	ADJ
ejpam-3200	164	38	number	number	NOUN
ejpam-3200	164	39	.	.	PUNCT
ejpam-3200	165	1	let	let	VERB
ejpam-3200	165	2	r̃	r̃	NOUN
ejpam-3200	165	3	denote	denote	VERB
ejpam-3200	165	4	the	the	DET
ejpam-3200	165	5	set	set	NOUN
ejpam-3200	165	6	of	of	ADP
ejpam-3200	165	7	all	all	DET
ejpam-3200	165	8	compact	compact	ADJ
ejpam-3200	165	9	.	.	PUNCT
ejpam-3200	166	1	definition	definition	NOUN
ejpam-3200	166	2	7	7	NUM
ejpam-3200	166	3	.	.	PUNCT
ejpam-3200	167	1	[	[	X
ejpam-3200	167	2	6	6	NUM
ejpam-3200	167	3	]	]	PUNCT
ejpam-3200	167	4	let	let	VERB
ejpam-3200	167	5	ã	ã	PROPN
ejpam-3200	167	6	,	,	PUNCT
ejpam-3200	167	7	b̃	b̃	PROPN
ejpam-3200	167	8	∈	∈	PROPN
ejpam-3200	167	9	r̃	r̃	PROPN
ejpam-3200	167	10	,	,	PUNCT
ejpam-3200	167	11	we	we	PRON
ejpam-3200	167	12	define	define	VERB
ejpam-3200	167	13	(	(	PUNCT
ejpam-3200	167	14	1	1	X
ejpam-3200	167	15	)	)	PUNCT
ejpam-3200	167	16	ã	ã	PROPN
ejpam-3200	167	17	≤	≤	ADJ
ejpam-3200	167	18	b̃	b̃	PROPN
ejpam-3200	167	19	iff	iff	NOUN
ejpam-3200	167	20	aλ	aλ	NOUN
ejpam-3200	167	21	≤	≤	NOUN
ejpam-3200	167	22	bλ	bλ	NOUN
ejpam-3200	167	23	for	for	ADP
ejpam-3200	167	24	all	all	DET
ejpam-3200	167	25	λ	λ	X
ejpam-3200	167	26	∈	∈	PROPN
ejpam-3200	167	27	(	(	PUNCT
ejpam-3200	167	28	0	0	NUM
ejpam-3200	167	29	,	,	PUNCT
ejpam-3200	167	30	1	1	NUM
ejpam-3200	167	31	]	]	PUNCT
ejpam-3200	167	32	,	,	PUNCT
ejpam-3200	167	33	(	(	PUNCT
ejpam-3200	167	34	2	2	X
ejpam-3200	167	35	)	)	PUNCT
ejpam-3200	167	36	ã	ã	PROPN
ejpam-3200	168	1	+	+	CCONJ
ejpam-3200	168	2	b̃	b̃	PROPN
ejpam-3200	168	3	=	=	PROPN
ejpam-3200	168	4	c̃	c̃	PROPN
ejpam-3200	168	5	iff	iff	NOUN
ejpam-3200	168	6	aλ	aλ	ADP
ejpam-3200	168	7	+	+	NOUN
ejpam-3200	168	8	bλ	bλ	NOUN
ejpam-3200	168	9	=	=	SYM
ejpam-3200	168	10	cλ	cλ	PROPN
ejpam-3200	168	11	for	for	ADP
ejpam-3200	168	12	any	any	DET
ejpam-3200	168	13	λ	λ	PROPN
ejpam-3200	168	14	∈	∈	PROPN
ejpam-3200	168	15	(	(	PUNCT
ejpam-3200	168	16	0	0	NUM
ejpam-3200	168	17	,	,	PUNCT
ejpam-3200	168	18	1	1	NUM
ejpam-3200	168	19	]	]	PUNCT
ejpam-3200	168	20	,	,	PUNCT
ejpam-3200	168	21	(	(	PUNCT
ejpam-3200	168	22	3	3	X
ejpam-3200	168	23	)	)	PUNCT
ejpam-3200	169	1	ã	ã	PROPN
ejpam-3200	169	2	·	·	PUNCT
ejpam-3200	169	3	b̃	b̃	PROPN
ejpam-3200	169	4	=	=	PUNCT
ejpam-3200	170	1	d̃	d̃	PROPN
ejpam-3200	170	2	iff	iff	PROPN
ejpam-3200	170	3	aλ	aλ	ADP
ejpam-3200	170	4	·	·	PUNCT
ejpam-3200	170	5	bλ	bλ	PROPN
ejpam-3200	170	6	=	=	SYM
ejpam-3200	170	7	dλ	dλ	NOUN
ejpam-3200	170	8	for	for	ADP
ejpam-3200	170	9	any	any	DET
ejpam-3200	170	10	λ	λ	PROPN
ejpam-3200	170	11	∈	∈	PROPN
ejpam-3200	170	12	(	(	PUNCT
ejpam-3200	170	13	0	0	NUM
ejpam-3200	170	14	,	,	PUNCT
ejpam-3200	170	15	1	1	NUM
ejpam-3200	170	16	]	]	PUNCT
ejpam-3200	170	17	.	.	PUNCT
ejpam-3200	171	1	for	for	ADP
ejpam-3200	171	2	ã	ã	PROPN
ejpam-3200	171	3	,	,	PUNCT
ejpam-3200	171	4	b̃	b̃	PROPN
ejpam-3200	171	5	∈	∈	PROPN
ejpam-3200	171	6	r̃c	r̃c	NOUN
ejpam-3200	171	7	,	,	PUNCT
ejpam-3200	171	8	then	then	ADV
ejpam-3200	171	9	d(ã	d(ã	PROPN
ejpam-3200	171	10	,	,	PUNCT
ejpam-3200	171	11	b̃	b̃	PROPN
ejpam-3200	171	12	)	)	PUNCT
ejpam-3200	172	1	=	=	PUNCT
ejpam-3200	172	2	sup	sup	NOUN
ejpam-3200	172	3	λ∈[0,1	λ∈[0,1	PROPN
ejpam-3200	172	4	]	]	PUNCT
ejpam-3200	173	1	d(aλ	d(aλ	NOUN
ejpam-3200	173	2	,	,	PUNCT
ejpam-3200	173	3	bλ	bλ	NOUN
ejpam-3200	173	4	)	)	PUNCT
ejpam-3200	173	5	,	,	PUNCT
ejpam-3200	173	6	(	(	PUNCT
ejpam-3200	173	7	4.1	4.1	NUM
ejpam-3200	173	8	)	)	PUNCT
ejpam-3200	173	9	is	be	AUX
ejpam-3200	173	10	called	call	VERB
ejpam-3200	173	11	the	the	DET
ejpam-3200	173	12	distance	distance	NOUN
ejpam-3200	173	13	between	between	ADP
ejpam-3200	173	14	ã	ã	PROPN
ejpam-3200	173	15	and	and	CCONJ
ejpam-3200	173	16	b̃.	b̃.	PROPN
ejpam-3200	173	17	lemma	lemma	PROPN
ejpam-3200	173	18	1	1	NUM
ejpam-3200	173	19	.	.	PUNCT
ejpam-3200	174	1	[	[	X
ejpam-3200	174	2	1	1	X
ejpam-3200	174	3	]	]	X
ejpam-3200	174	4	if	if	SCONJ
ejpam-3200	174	5	a	a	DET
ejpam-3200	174	6	mapping	mapping	NOUN
ejpam-3200	174	7	h	h	NOUN
ejpam-3200	174	8	:	:	PUNCT
ejpam-3200	175	1	[	[	X
ejpam-3200	175	2	0	0	NUM
ejpam-3200	175	3	,	,	PUNCT
ejpam-3200	175	4	1]→	1]→	PROPN
ejpam-3200	175	5	ir	ir	PROPN
ejpam-3200	175	6	,	,	PUNCT
ejpam-3200	175	7	λ→	λ→	PUNCT
ejpam-3200	175	8	h(λ	h(λ	NOUN
ejpam-3200	175	9	)	)	PUNCT
ejpam-3200	175	10	=	=	PUNCT
ejpam-3200	176	1	[	[	X
ejpam-3200	176	2	mλ	mλ	INTJ
ejpam-3200	176	3	,	,	PUNCT
ejpam-3200	176	4	nλ	nλ	NOUN
ejpam-3200	176	5	]	]	PUNCT
ejpam-3200	176	6	,	,	PUNCT
ejpam-3200	176	7	satisfies	satisfy	VERB
ejpam-3200	176	8	[	[	X
ejpam-3200	176	9	mλ1	mλ1	NOUN
ejpam-3200	176	10	,	,	PUNCT
ejpam-3200	176	11	nλ1	nλ1	PROPN
ejpam-3200	176	12	]	]	PUNCT
ejpam-3200	176	13	⊃	⊃	X
ejpam-3200	177	1	[	[	X
ejpam-3200	177	2	mλ2	mλ2	NOUN
ejpam-3200	177	3	,	,	PUNCT
ejpam-3200	177	4	nλ2	nλ2	PROPN
ejpam-3200	177	5	]	]	PUNCT
ejpam-3200	177	6	when	when	SCONJ
ejpam-3200	177	7	λ1	λ1	ADJ
ejpam-3200	177	8	<	<	X
ejpam-3200	177	9	λ2	λ2	PROPN
ejpam-3200	177	10	,	,	PUNCT
ejpam-3200	177	11	then	then	ADV
ejpam-3200	177	12	ã	ã	PROPN
ejpam-3200	177	13	:	:	PUNCT
ejpam-3200	177	14	=	=	SYM
ejpam-3200	177	15	⋃	⋃	NOUN
ejpam-3200	177	16	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	177	17	]	]	PUNCT
ejpam-3200	177	18	λh(λ	λh(λ	X
ejpam-3200	177	19	)	)	PUNCT
ejpam-3200	177	20	∈	∈	PROPN
ejpam-3200	177	21	r̃	r̃	NOUN
ejpam-3200	177	22	(	(	PUNCT
ejpam-3200	177	23	4.2	4.2	NUM
ejpam-3200	177	24	)	)	PUNCT
ejpam-3200	177	25	and	and	CCONJ
ejpam-3200	177	26	aλ	aλ	ADP
ejpam-3200	177	27	=	=	SYM
ejpam-3200	177	28	∞⋂	∞⋂	PROPN
ejpam-3200	177	29	n=1	n=1	PROPN
ejpam-3200	177	30	h(λn	h(λn	PROPN
ejpam-3200	177	31	)	)	PUNCT
ejpam-3200	177	32	,	,	PUNCT
ejpam-3200	177	33	(	(	PUNCT
ejpam-3200	177	34	4.3	4.3	NUM
ejpam-3200	177	35	)	)	PUNCT
ejpam-3200	177	36	where	where	SCONJ
ejpam-3200	177	37	λn	λn	NOUN
ejpam-3200	177	38	=	=	PUNCT
ejpam-3200	178	1	[	[	X
ejpam-3200	178	2	1−	1−	NUM
ejpam-3200	178	3	1	1	NUM
ejpam-3200	178	4	(	(	PUNCT
ejpam-3200	178	5	n+1	n+1	PROPN
ejpam-3200	178	6	)	)	PUNCT
ejpam-3200	178	7	]	]	X
ejpam-3200	178	8	λ	λ	X
ejpam-3200	178	9	.	.	PUNCT
ejpam-3200	178	10	definition	definition	NOUN
ejpam-3200	178	11	8	8	NUM
ejpam-3200	178	12	.	.	PUNCT
ejpam-3200	179	1	let	let	VERB
ejpam-3200	179	2	α	α	PRON
ejpam-3200	179	3	:	:	PUNCT
ejpam-3200	180	1	[	[	X
ejpam-3200	180	2	a	a	DET
ejpam-3200	180	3	,	,	PUNCT
ejpam-3200	180	4	b]t	b]t	NOUN
ejpam-3200	180	5	→	→	SYM
ejpam-3200	180	6	r	r	NOUN
ejpam-3200	180	7	be	be	AUX
ejpam-3200	180	8	an	an	DET
ejpam-3200	180	9	increasing	increase	VERB
ejpam-3200	180	10	function	function	NOUN
ejpam-3200	180	11	and	and	CCONJ
ejpam-3200	180	12	let	let	VERB
ejpam-3200	180	13	f̃	f̃	PROPN
ejpam-3200	180	14	:	:	PUNCT
ejpam-3200	180	15	[	[	X
ejpam-3200	180	16	a	a	PRON
ejpam-3200	180	17	,	,	PUNCT
ejpam-3200	180	18	b]t	b]t	NOUN
ejpam-3200	180	19	→	→	SYM
ejpam-3200	180	20	r̃.	r̃.	NOUN
ejpam-3200	180	21	if	if	SCONJ
ejpam-3200	180	22	the	the	DET
ejpam-3200	180	23	interval	interval	NOUN
ejpam-3200	180	24	-	-	PUNCT
ejpam-3200	180	25	valued	value	VERB
ejpam-3200	180	26	function	function	NOUN
ejpam-3200	180	27	fλ(t	fλ(t	PUNCT
ejpam-3200	180	28	)	)	PUNCT
ejpam-3200	180	29	=	=	PUNCT
ejpam-3200	181	1	[	[	X
ejpam-3200	181	2	f−λ	f−λ	X
ejpam-3200	181	3	(	(	PUNCT
ejpam-3200	181	4	t	t	NOUN
ejpam-3200	181	5	)	)	PUNCT
ejpam-3200	181	6	,	,	PUNCT
ejpam-3200	181	7	f+	f+	PROPN
ejpam-3200	181	8	λ	λ	PROPN
ejpam-3200	181	9	(	(	PUNCT
ejpam-3200	181	10	t	t	PROPN
ejpam-3200	181	11	)	)	PUNCT
ejpam-3200	181	12	]	]	PUNCT
ejpam-3200	181	13	is	be	AUX
ejpam-3200	181	14	(	(	PUNCT
ejpam-3200	181	15	ms∆	ms∆	PROPN
ejpam-3200	181	16	)	)	PUNCT
ejpam-3200	181	17	integrable	integrable	ADJ
ejpam-3200	181	18	with	with	ADP
ejpam-3200	181	19	respect	respect	NOUN
ejpam-3200	181	20	to	to	ADP
ejpam-3200	181	21	α	α	NOUN
ejpam-3200	181	22	on	on	ADP
ejpam-3200	181	23	[	[	X
ejpam-3200	181	24	a	a	DET
ejpam-3200	181	25	,	,	PUNCT
ejpam-3200	181	26	b]t	b]t	NOUN
ejpam-3200	181	27	for	for	ADP
ejpam-3200	181	28	any	any	DET
ejpam-3200	181	29	λ	λ	PROPN
ejpam-3200	181	30	∈	∈	PROPN
ejpam-3200	181	31	(	(	PUNCT
ejpam-3200	181	32	0	0	NUM
ejpam-3200	181	33	,	,	PUNCT
ejpam-3200	181	34	1	1	NUM
ejpam-3200	181	35	]	]	PUNCT
ejpam-3200	181	36	,	,	PUNCT
ejpam-3200	181	37	then	then	ADV
ejpam-3200	181	38	f̃	f̃	PROPN
ejpam-3200	181	39	(	(	PUNCT
ejpam-3200	181	40	t	t	PROPN
ejpam-3200	181	41	)	)	PUNCT
ejpam-3200	181	42	is	be	AUX
ejpam-3200	181	43	called	call	VERB
ejpam-3200	181	44	(	(	PUNCT
ejpam-3200	181	45	ms∆	ms∆	PROPN
ejpam-3200	181	46	)	)	PUNCT
ejpam-3200	181	47	integrable	integrable	ADJ
ejpam-3200	181	48	with	with	ADP
ejpam-3200	181	49	respect	respect	NOUN
ejpam-3200	181	50	to	to	ADP
ejpam-3200	181	51	α	α	NOUN
ejpam-3200	181	52	on	on	ADP
ejpam-3200	181	53	[	[	X
ejpam-3200	181	54	a	a	DET
ejpam-3200	181	55	,	,	PUNCT
ejpam-3200	181	56	b]t	b]t	NOUN
ejpam-3200	181	57	and	and	CCONJ
ejpam-3200	181	58	the	the	DET
ejpam-3200	181	59	integral	integral	ADJ
ejpam-3200	181	60	is	be	AUX
ejpam-3200	181	61	defined	define	VERB
ejpam-3200	181	62	by	by	ADP
ejpam-3200	181	63	(	(	PUNCT
ejpam-3200	181	64	ms∆	ms∆	PROPN
ejpam-3200	181	65	)	)	PUNCT
ejpam-3200	181	66	integral	integral	ADJ
ejpam-3200	181	67	as	as	ADP
ejpam-3200	181	68	follow	follow	NOUN
ejpam-3200	181	69	:	:	PUNCT
ejpam-3200	181	70	(	(	PUNCT
ejpam-3200	181	71	fms∆	fms∆	NOUN
ejpam-3200	181	72	)	)	PUNCT
ejpam-3200	181	73	b∫	b∫	NOUN
ejpam-3200	181	74	a	a	DET
ejpam-3200	181	75	f̃	f̃	PROPN
ejpam-3200	181	76	(	(	PUNCT
ejpam-3200	181	77	t)dα	t)dα	PROPN
ejpam-3200	181	78	:	:	PUNCT
ejpam-3200	181	79	=	=	SYM
ejpam-3200	181	80	⋃	⋃	NOUN
ejpam-3200	181	81	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	181	82	]	]	X
ejpam-3200	181	83	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	181	84	)	)	PUNCT
ejpam-3200	181	85	b∫	b∫	NOUN
ejpam-3200	181	86	a	a	DET
ejpam-3200	181	87	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	181	88	=	=	SYM
ejpam-3200	181	89	⋃	⋃	NOUN
ejpam-3200	181	90	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	181	91	]	]	X
ejpam-3200	181	92	λ	λ	X
ejpam-3200	181	93	[	[	PUNCT
ejpam-3200	181	94	(	(	PUNCT
ejpam-3200	181	95	ms∆	ms∆	PROPN
ejpam-3200	181	96	)	)	PUNCT
ejpam-3200	181	97	b∫	b∫	PROPN
ejpam-3200	181	98	a	a	DET
ejpam-3200	181	99	f−λ	f−λ	NOUN
ejpam-3200	181	100	(	(	PUNCT
ejpam-3200	181	101	t)dα	t)dα	PROPN
ejpam-3200	181	102	,	,	PUNCT
ejpam-3200	181	103	(	(	PUNCT
ejpam-3200	181	104	ms∆	ms∆	PROPN
ejpam-3200	181	105	)	)	PUNCT
ejpam-3200	181	106	b∫	b∫	PROPN
ejpam-3200	181	107	a	a	DET
ejpam-3200	181	108	f+	f+	ADJ
ejpam-3200	181	109	λ	λ	X
ejpam-3200	181	110	(	(	PUNCT
ejpam-3200	181	111	t)dα	t)dα	PROPN
ejpam-3200	181	112	]	]	PUNCT
ejpam-3200	181	113	.	.	PUNCT
ejpam-3200	182	1	we	we	PRON
ejpam-3200	182	2	write	write	VERB
ejpam-3200	182	3	f̃	f̃	PROPN
ejpam-3200	182	4	(	(	PUNCT
ejpam-3200	182	5	t	t	PROPN
ejpam-3200	182	6	)	)	PUNCT
ejpam-3200	182	7	∈	∈	PROPN
ejpam-3200	182	8	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	182	9	,	,	PUNCT
ejpam-3200	182	10	b]t	b]t	NOUN
ejpam-3200	182	11	.	.	PUNCT
ejpam-3200	183	1	m.	m.	PROPN
ejpam-3200	183	2	e.	e.	PROPN
ejpam-3200	183	3	hamid	hamid	PROPN
ejpam-3200	183	4	/	/	SYM
ejpam-3200	183	5	eur	eur	PROPN
ejpam-3200	183	6	.	.	PUNCT
ejpam-3200	184	1	j.	j.	PROPN
ejpam-3200	184	2	pure	pure	PROPN
ejpam-3200	184	3	appl	appl	PROPN
ejpam-3200	184	4	.	.	PROPN
ejpam-3200	184	5	math	math	PROPN
ejpam-3200	184	6	,	,	PUNCT
ejpam-3200	184	7	11	11	NUM
ejpam-3200	184	8	(	(	PUNCT
ejpam-3200	184	9	2	2	NUM
ejpam-3200	184	10	)	)	PUNCT
ejpam-3200	184	11	(	(	PUNCT
ejpam-3200	184	12	2018	2018	NUM
ejpam-3200	184	13	)	)	PUNCT
ejpam-3200	184	14	,	,	PUNCT
ejpam-3200	184	15	493	493	NUM
ejpam-3200	184	16	-	-	SYM
ejpam-3200	184	17	504	504	NUM
ejpam-3200	184	18	501	501	NUM
ejpam-3200	184	19	theorem	theorem	NOUN
ejpam-3200	184	20	7	7	NUM
ejpam-3200	184	21	.	.	PUNCT
ejpam-3200	185	1	if	if	SCONJ
ejpam-3200	185	2	f̃	f̃	PROPN
ejpam-3200	185	3	(	(	PUNCT
ejpam-3200	185	4	t	t	PROPN
ejpam-3200	185	5	)	)	PUNCT
ejpam-3200	185	6	∈	∈	PROPN
ejpam-3200	185	7	fmsα∆[a	fmsα∆[a	PROPN
ejpam-3200	185	8	,	,	PUNCT
ejpam-3200	185	9	b]t	b]t	NOUN
ejpam-3200	185	10	,	,	PUNCT
ejpam-3200	185	11	then	then	ADV
ejpam-3200	185	12	(	(	PUNCT
ejpam-3200	185	13	fms∆	fms∆	NOUN
ejpam-3200	185	14	)	)	PUNCT
ejpam-3200	185	15	b∫	b∫	NOUN
ejpam-3200	185	16	a	a	DET
ejpam-3200	185	17	f̃	f̃	PROPN
ejpam-3200	185	18	(	(	PUNCT
ejpam-3200	185	19	t)dα	t)dα	PROPN
ejpam-3200	185	20	∈	∈	PROPN
ejpam-3200	185	21	r̃	r̃	NOUN
ejpam-3200	185	22	and	and	CCONJ
ejpam-3200	185	23	[	[	PUNCT
ejpam-3200	185	24	(	(	PUNCT
ejpam-3200	185	25	fms∆	fms∆	NOUN
ejpam-3200	185	26	)	)	PUNCT
ejpam-3200	185	27	b∫	b∫	NOUN
ejpam-3200	185	28	a	a	DET
ejpam-3200	185	29	f̃	f̃	PROPN
ejpam-3200	185	30	(	(	PUNCT
ejpam-3200	185	31	t)dα	t)dα	PROPN
ejpam-3200	185	32	]	]	PUNCT
ejpam-3200	185	33	λ	λ	X
ejpam-3200	185	34	=	=	SYM
ejpam-3200	185	35	∞⋂	∞⋂	PROPN
ejpam-3200	185	36	n=1	n=1	PROPN
ejpam-3200	185	37	(	(	PUNCT
ejpam-3200	185	38	ims∆	ims∆	NOUN
ejpam-3200	185	39	)	)	PUNCT
ejpam-3200	185	40	b∫	b∫	NOUN
ejpam-3200	185	41	a	a	DET
ejpam-3200	185	42	fλn(t)dα	fλn(t)dα	PROPN
ejpam-3200	185	43	,	,	PUNCT
ejpam-3200	185	44	(	(	PUNCT
ejpam-3200	185	45	4.4	4.4	NUM
ejpam-3200	185	46	)	)	PUNCT
ejpam-3200	185	47	where	where	SCONJ
ejpam-3200	185	48	λn	λn	NOUN
ejpam-3200	185	49	=	=	PUNCT
ejpam-3200	186	1	[	[	X
ejpam-3200	186	2	1−	1−	NUM
ejpam-3200	186	3	1	1	NUM
ejpam-3200	186	4	(	(	PUNCT
ejpam-3200	186	5	n+1	n+1	PROPN
ejpam-3200	186	6	)	)	PUNCT
ejpam-3200	186	7	]	]	X
ejpam-3200	186	8	λ	λ	X
ejpam-3200	186	9	.	.	PUNCT
ejpam-3200	186	10	proof	proof	NOUN
ejpam-3200	186	11	.	.	PUNCT
ejpam-3200	187	1	leth	leth	PROPN
ejpam-3200	187	2	:	:	PUNCT
ejpam-3200	187	3	(	(	PUNCT
ejpam-3200	187	4	0	0	NUM
ejpam-3200	187	5	,	,	PUNCT
ejpam-3200	187	6	1]→	1]→	PROPN
ejpam-3200	187	7	ir	ir	PROPN
ejpam-3200	187	8	,	,	PUNCT
ejpam-3200	187	9	be	be	AUX
ejpam-3200	187	10	defined	define	VERB
ejpam-3200	187	11	byh(λ	byh(λ	PROPN
ejpam-3200	187	12	)	)	PUNCT
ejpam-3200	187	13	=	=	PUNCT
ejpam-3200	188	1	[	[	PUNCT
ejpam-3200	188	2	(	(	PUNCT
ejpam-3200	188	3	ms∆	ms∆	PROPN
ejpam-3200	188	4	)	)	PUNCT
ejpam-3200	188	5	b∫	b∫	PROPN
ejpam-3200	188	6	a	a	DET
ejpam-3200	188	7	f−λ	f−λ	NOUN
ejpam-3200	188	8	(	(	PUNCT
ejpam-3200	188	9	t)dα	t)dα	PROPN
ejpam-3200	188	10	,	,	PUNCT
ejpam-3200	188	11	(	(	PUNCT
ejpam-3200	188	12	ms∆	ms∆	PROPN
ejpam-3200	188	13	)	)	PUNCT
ejpam-3200	188	14	b∫	b∫	PROPN
ejpam-3200	188	15	a	a	DET
ejpam-3200	188	16	f+	f+	ADJ
ejpam-3200	188	17	λ	λ	X
ejpam-3200	188	18	(	(	PUNCT
ejpam-3200	188	19	t)dα	t)dα	PROPN
ejpam-3200	188	20	]	]	PUNCT
ejpam-3200	188	21	.	.	PUNCT
ejpam-3200	189	1	since	since	SCONJ
ejpam-3200	189	2	f−λ	f−λ	NOUN
ejpam-3200	189	3	(	(	PUNCT
ejpam-3200	189	4	t	t	NOUN
ejpam-3200	189	5	)	)	PUNCT
ejpam-3200	189	6	and	and	CCONJ
ejpam-3200	189	7	f+	f+	PROPN
ejpam-3200	189	8	λ	λ	PROPN
ejpam-3200	189	9	(	(	PUNCT
ejpam-3200	189	10	t	t	PROPN
ejpam-3200	189	11	)	)	PUNCT
ejpam-3200	189	12	are	be	AUX
ejpam-3200	189	13	increasing	increase	VERB
ejpam-3200	189	14	and	and	CCONJ
ejpam-3200	189	15	decreasing	decrease	VERB
ejpam-3200	189	16	on	on	ADP
ejpam-3200	189	17	λ	λ	PROPN
ejpam-3200	189	18	respectively	respectively	ADV
ejpam-3200	189	19	,	,	PUNCT
ejpam-3200	189	20	therefore	therefore	ADV
ejpam-3200	189	21	,	,	PUNCT
ejpam-3200	189	22	when	when	SCONJ
ejpam-3200	189	23	0	0	NUM
ejpam-3200	189	24	<	<	X
ejpam-3200	189	25	λ1	λ1	ADJ
ejpam-3200	189	26	≤	≤	NUM
ejpam-3200	189	27	λ2	λ2	NOUN
ejpam-3200	189	28	≤	≤	NUM
ejpam-3200	189	29	1	1	NUM
ejpam-3200	189	30	,	,	PUNCT
ejpam-3200	189	31	we	we	PRON
ejpam-3200	189	32	have	have	VERB
ejpam-3200	189	33	f−λ1(t	f−λ1(t	NOUN
ejpam-3200	189	34	)	)	PUNCT
ejpam-3200	189	35	≤	≤	NUM
ejpam-3200	189	36	f−λ2(t	f−λ2(t	NOUN
ejpam-3200	189	37	)	)	PUNCT
ejpam-3200	189	38	,	,	PUNCT
ejpam-3200	189	39	f+	f+	PROPN
ejpam-3200	189	40	λ1	λ1	PROPN
ejpam-3200	189	41	(	(	PUNCT
ejpam-3200	189	42	t	t	PROPN
ejpam-3200	189	43	)	)	PUNCT
ejpam-3200	189	44	≥	≥	NOUN
ejpam-3200	189	45	f+	f+	PROPN
ejpam-3200	189	46	λ2	λ2	PROPN
ejpam-3200	189	47	(	(	PUNCT
ejpam-3200	189	48	t	t	PROPN
ejpam-3200	189	49	)	)	PUNCT
ejpam-3200	189	50	,	,	PUNCT
ejpam-3200	189	51	on	on	ADP
ejpam-3200	189	52	[	[	X
ejpam-3200	189	53	a	a	DET
ejpam-3200	189	54	,	,	PUNCT
ejpam-3200	189	55	b]t	b]t	NOUN
ejpam-3200	189	56	.	.	PUNCT
ejpam-3200	190	1	from	from	ADP
ejpam-3200	190	2	theorem	theorem	NOUN
ejpam-3200	190	3	5	5	NUM
ejpam-3200	190	4	we	we	PRON
ejpam-3200	190	5	have	have	VERB
ejpam-3200	190	6	[	[	PUNCT
ejpam-3200	190	7	(	(	PUNCT
ejpam-3200	190	8	ms∆	ms∆	PROPN
ejpam-3200	190	9	)	)	PUNCT
ejpam-3200	190	10	b∫	b∫	PROPN
ejpam-3200	190	11	a	a	DET
ejpam-3200	190	12	f−λ1(t)dα	f−λ1(t)dα	PROPN
ejpam-3200	190	13	,	,	PUNCT
ejpam-3200	190	14	(	(	PUNCT
ejpam-3200	190	15	ms∆	ms∆	PROPN
ejpam-3200	190	16	)	)	PUNCT
ejpam-3200	190	17	b∫	b∫	PROPN
ejpam-3200	191	1	a	a	DET
ejpam-3200	191	2	f+	f+	NUM
ejpam-3200	191	3	λ1	λ1	PROPN
ejpam-3200	191	4	(	(	PUNCT
ejpam-3200	191	5	t)dα	t)dα	PROPN
ejpam-3200	191	6	]	]	PUNCT
ejpam-3200	191	7	⊃	⊃	X
ejpam-3200	191	8	[	[	PUNCT
ejpam-3200	191	9	(	(	PUNCT
ejpam-3200	191	10	ms∆	ms∆	PROPN
ejpam-3200	191	11	)	)	PUNCT
ejpam-3200	191	12	b∫	b∫	PROPN
ejpam-3200	191	13	a	a	DET
ejpam-3200	191	14	f−λ2(t)dα	f−λ2(t)dα	PROPN
ejpam-3200	191	15	,	,	PUNCT
ejpam-3200	191	16	(	(	PUNCT
ejpam-3200	191	17	ms∆	ms∆	PROPN
ejpam-3200	191	18	)	)	PUNCT
ejpam-3200	191	19	b∫	b∫	PROPN
ejpam-3200	191	20	a	a	DET
ejpam-3200	191	21	f+	f+	NUM
ejpam-3200	191	22	λ2	λ2	NOUN
ejpam-3200	191	23	(	(	PUNCT
ejpam-3200	191	24	t)dα	t)dα	PROPN
ejpam-3200	191	25	]	]	PUNCT
ejpam-3200	191	26	.	.	PUNCT
ejpam-3200	192	1	(	(	PUNCT
ejpam-3200	192	2	4.5	4.5	NUM
ejpam-3200	192	3	)	)	PUNCT
ejpam-3200	192	4	using	use	VERB
ejpam-3200	192	5	theorem	theorem	ADJ
ejpam-3200	192	6	2	2	NUM
ejpam-3200	192	7	and	and	CCONJ
ejpam-3200	192	8	lemma	lemma	PROPN
ejpam-3200	192	9	1	1	NUM
ejpam-3200	192	10	we	we	PRON
ejpam-3200	192	11	obtain	obtain	VERB
ejpam-3200	192	12	(	(	PUNCT
ejpam-3200	192	13	fms∆	fms∆	NOUN
ejpam-3200	192	14	)	)	PUNCT
ejpam-3200	192	15	b∫	b∫	NOUN
ejpam-3200	192	16	a	a	DET
ejpam-3200	192	17	f̃	f̃	PROPN
ejpam-3200	192	18	(	(	PUNCT
ejpam-3200	192	19	t)dα	t)dα	PROPN
ejpam-3200	192	20	:	:	PUNCT
ejpam-3200	192	21	=	=	SYM
ejpam-3200	193	1	⋃	⋃	NOUN
ejpam-3200	193	2	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	193	3	]	]	X
ejpam-3200	193	4	λ	λ	X
ejpam-3200	193	5	[	[	PUNCT
ejpam-3200	193	6	(	(	PUNCT
ejpam-3200	193	7	ms∆	ms∆	PROPN
ejpam-3200	193	8	)	)	PUNCT
ejpam-3200	193	9	b∫	b∫	PROPN
ejpam-3200	193	10	a	a	DET
ejpam-3200	193	11	f−λ	f−λ	NOUN
ejpam-3200	193	12	(	(	PUNCT
ejpam-3200	193	13	t)dα	t)dα	PROPN
ejpam-3200	193	14	,	,	PUNCT
ejpam-3200	193	15	(	(	PUNCT
ejpam-3200	193	16	ms∆	ms∆	PROPN
ejpam-3200	193	17	)	)	PUNCT
ejpam-3200	193	18	b∫	b∫	PROPN
ejpam-3200	193	19	a	a	DET
ejpam-3200	193	20	f+	f+	ADJ
ejpam-3200	193	21	λ	λ	PROPN
ejpam-3200	193	22	(	(	PUNCT
ejpam-3200	193	23	t)dα	t)dα	PROPN
ejpam-3200	193	24	]	]	PUNCT
ejpam-3200	193	25	∈	∈	PROPN
ejpam-3200	193	26	r̃	r̃	NOUN
ejpam-3200	193	27	(	(	PUNCT
ejpam-3200	193	28	4.6	4.6	NUM
ejpam-3200	193	29	)	)	PUNCT
ejpam-3200	193	30	and	and	CCONJ
ejpam-3200	193	31	for	for	ADP
ejpam-3200	193	32	all	all	DET
ejpam-3200	193	33	λ	λ	X
ejpam-3200	193	34	∈	∈	PROPN
ejpam-3200	193	35	(	(	PUNCT
ejpam-3200	193	36	0	0	NUM
ejpam-3200	193	37	,	,	PUNCT
ejpam-3200	193	38	1	1	NUM
ejpam-3200	193	39	]	]	PUNCT
ejpam-3200	193	40	,	,	PUNCT
ejpam-3200	193	41	[	[	PUNCT
ejpam-3200	193	42	(	(	PUNCT
ejpam-3200	193	43	fms∆	fms∆	NOUN
ejpam-3200	193	44	)	)	PUNCT
ejpam-3200	193	45	b∫	b∫	NOUN
ejpam-3200	193	46	a	a	DET
ejpam-3200	193	47	f̃	f̃	PROPN
ejpam-3200	193	48	(	(	PUNCT
ejpam-3200	193	49	t)dα	t)dα	PROPN
ejpam-3200	193	50	]	]	PUNCT
ejpam-3200	193	51	λ	λ	X
ejpam-3200	193	52	=	=	SYM
ejpam-3200	193	53	∞⋂	∞⋂	PROPN
ejpam-3200	193	54	n=1	n=1	PROPN
ejpam-3200	193	55	(	(	PUNCT
ejpam-3200	193	56	ims∆	ims∆	NOUN
ejpam-3200	193	57	)	)	PUNCT
ejpam-3200	193	58	b∫	b∫	NOUN
ejpam-3200	193	59	a	a	DET
ejpam-3200	193	60	fλn(t)dα	fλn(t)dα	PROPN
ejpam-3200	193	61	,	,	PUNCT
ejpam-3200	193	62	(	(	PUNCT
ejpam-3200	193	63	4.7	4.7	NUM
ejpam-3200	193	64	)	)	PUNCT
ejpam-3200	193	65	where	where	SCONJ
ejpam-3200	193	66	λn	λn	NOUN
ejpam-3200	193	67	=	=	PUNCT
ejpam-3200	194	1	[	[	X
ejpam-3200	194	2	1−	1−	NUM
ejpam-3200	194	3	1	1	NUM
ejpam-3200	194	4	(	(	PUNCT
ejpam-3200	194	5	n+1	n+1	PROPN
ejpam-3200	194	6	)	)	PUNCT
ejpam-3200	194	7	]	]	X
ejpam-3200	194	8	λ	λ	X
ejpam-3200	194	9	.	.	PROPN
ejpam-3200	194	10	theorem	theorem	VERB
ejpam-3200	194	11	8	8	NUM
ejpam-3200	194	12	.	.	PUNCT
ejpam-3200	195	1	let	let	VERB
ejpam-3200	195	2	α	α	PRON
ejpam-3200	195	3	:	:	PUNCT
ejpam-3200	196	1	[	[	X
ejpam-3200	196	2	a	a	DET
ejpam-3200	196	3	,	,	PUNCT
ejpam-3200	196	4	b]t	b]t	NOUN
ejpam-3200	196	5	→	→	SYM
ejpam-3200	196	6	r	r	NOUN
ejpam-3200	196	7	be	be	AUX
ejpam-3200	196	8	an	an	DET
ejpam-3200	196	9	increasing	increase	VERB
ejpam-3200	196	10	function	function	NOUN
ejpam-3200	196	11	.	.	PUNCT
ejpam-3200	197	1	if	if	SCONJ
ejpam-3200	197	2	f̃	f̃	PROPN
ejpam-3200	197	3	(	(	PUNCT
ejpam-3200	197	4	t	t	PROPN
ejpam-3200	197	5	)	)	PUNCT
ejpam-3200	197	6	,	,	PUNCT
ejpam-3200	197	7	g̃(t	g̃(t	PROPN
ejpam-3200	197	8	)	)	PUNCT
ejpam-3200	197	9	∈	∈	PROPN
ejpam-3200	197	10	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	197	11	,	,	PUNCT
ejpam-3200	197	12	b]t	b]t	NOUN
ejpam-3200	197	13	and	and	CCONJ
ejpam-3200	197	14	β	β	X
ejpam-3200	197	15	,	,	PUNCT
ejpam-3200	197	16	γ	γ	PROPN
ejpam-3200	197	17	∈	∈	PROPN
ejpam-3200	197	18	r.	r.	PROPN
ejpam-3200	197	19	then	then	ADV
ejpam-3200	197	20	βf̃	βf̃	PUNCT
ejpam-3200	197	21	(	(	PUNCT
ejpam-3200	197	22	t	t	NOUN
ejpam-3200	197	23	)	)	PUNCT
ejpam-3200	197	24	+	+	NUM
ejpam-3200	197	25	γg̃(t	γg̃(t	SYM
ejpam-3200	197	26	)	)	PUNCT
ejpam-3200	197	27	∈	∈	PROPN
ejpam-3200	197	28	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	197	29	,	,	PUNCT
ejpam-3200	197	30	b]t	b]t	NOUN
ejpam-3200	197	31	and	and	CCONJ
ejpam-3200	197	32	(	(	PUNCT
ejpam-3200	197	33	fms∆	fms∆	NOUN
ejpam-3200	197	34	)	)	PUNCT
ejpam-3200	197	35	b∫	b∫	NOUN
ejpam-3200	197	36	a	a	X
ejpam-3200	197	37	(	(	PUNCT
ejpam-3200	197	38	βf̃	βf̃	X
ejpam-3200	197	39	(	(	PUNCT
ejpam-3200	197	40	t	t	NOUN
ejpam-3200	197	41	)	)	PUNCT
ejpam-3200	197	42	+	+	NUM
ejpam-3200	197	43	γg̃(t	γg̃(t	NOUN
ejpam-3200	197	44	)	)	PUNCT
ejpam-3200	197	45	)	)	PUNCT
ejpam-3200	198	1	dα	dα	VERB
ejpam-3200	198	2	=	=	PUNCT
ejpam-3200	199	1	β(fms∆	β(fms∆	X
ejpam-3200	199	2	)	)	PUNCT
ejpam-3200	199	3	b∫	b∫	NOUN
ejpam-3200	199	4	a	a	DET
ejpam-3200	199	5	f̃	f̃	PROPN
ejpam-3200	199	6	(	(	PUNCT
ejpam-3200	199	7	t)dα+	t)dα+	NOUN
ejpam-3200	199	8	γ(fms∆	γ(fms∆	NOUN
ejpam-3200	199	9	)	)	PUNCT
ejpam-3200	199	10	b∫	b∫	NOUN
ejpam-3200	199	11	a	a	DET
ejpam-3200	199	12	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	199	13	.	.	PUNCT
ejpam-3200	200	1	(	(	PUNCT
ejpam-3200	200	2	4.8	4.8	NUM
ejpam-3200	200	3	)	)	PUNCT
ejpam-3200	200	4	proof	proof	NOUN
ejpam-3200	200	5	.	.	PUNCT
ejpam-3200	201	1	if	if	SCONJ
ejpam-3200	201	2	f̃	f̃	PROPN
ejpam-3200	201	3	(	(	PUNCT
ejpam-3200	201	4	t	t	PROPN
ejpam-3200	201	5	)	)	PUNCT
ejpam-3200	201	6	,	,	PUNCT
ejpam-3200	201	7	g̃(t	g̃(t	PROPN
ejpam-3200	201	8	)	)	PUNCT
ejpam-3200	201	9	∈	∈	PROPN
ejpam-3200	201	10	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	201	11	,	,	PUNCT
ejpam-3200	201	12	b]t	b]t	NOUN
ejpam-3200	201	13	,	,	PUNCT
ejpam-3200	201	14	then	then	ADV
ejpam-3200	201	15	the	the	DET
ejpam-3200	201	16	interval	interval	NOUN
ejpam-3200	201	17	-	-	PUNCT
ejpam-3200	201	18	valued	value	VERB
ejpam-3200	201	19	function	function	NOUN
ejpam-3200	201	20	fλ(t	fλ(t	PUNCT
ejpam-3200	201	21	)	)	PUNCT
ejpam-3200	201	22	=	=	PUNCT
ejpam-3200	202	1	[	[	X
ejpam-3200	202	2	f−λ	f−λ	X
ejpam-3200	202	3	(	(	PUNCT
ejpam-3200	202	4	t	t	NOUN
ejpam-3200	202	5	)	)	PUNCT
ejpam-3200	202	6	,	,	PUNCT
ejpam-3200	202	7	f+	f+	PROPN
ejpam-3200	202	8	λ	λ	PROPN
ejpam-3200	202	9	(	(	PUNCT
ejpam-3200	202	10	t	t	PROPN
ejpam-3200	202	11	)	)	PUNCT
ejpam-3200	202	12	]	]	PUNCT
ejpam-3200	202	13	and	and	CCONJ
ejpam-3200	202	14	gλ(t	gλ(t	NOUN
ejpam-3200	202	15	)	)	PUNCT
ejpam-3200	203	1	=	=	PUNCT
ejpam-3200	204	1	[	[	X
ejpam-3200	204	2	g−λ	g−λ	PROPN
ejpam-3200	204	3	(	(	PUNCT
ejpam-3200	204	4	t	t	PROPN
ejpam-3200	204	5	)	)	PUNCT
ejpam-3200	204	6	,	,	PUNCT
ejpam-3200	204	7	g+	g+	ADP
ejpam-3200	204	8	λ	λ	X
ejpam-3200	204	9	(	(	PUNCT
ejpam-3200	204	10	t	t	PROPN
ejpam-3200	204	11	)	)	PUNCT
ejpam-3200	204	12	]	]	PUNCT
ejpam-3200	204	13	are	be	AUX
ejpam-3200	204	14	(	(	PUNCT
ejpam-3200	204	15	ms∆	ms∆	PROPN
ejpam-3200	204	16	)	)	PUNCT
ejpam-3200	204	17	integrable	integrable	ADJ
ejpam-3200	204	18	with	with	ADP
ejpam-3200	204	19	respect	respect	NOUN
ejpam-3200	204	20	to	to	ADP
ejpam-3200	204	21	α	α	NOUN
ejpam-3200	204	22	on	on	ADP
ejpam-3200	204	23	[	[	X
ejpam-3200	204	24	a	a	DET
ejpam-3200	204	25	,	,	PUNCT
ejpam-3200	204	26	b]t	b]t	NOUN
ejpam-3200	204	27	for	for	ADP
ejpam-3200	204	28	any	any	DET
ejpam-3200	204	29	λ	λ	PROPN
ejpam-3200	204	30	∈	∈	PROPN
ejpam-3200	204	31	(	(	PUNCT
ejpam-3200	204	32	0	0	NUM
ejpam-3200	204	33	,	,	PUNCT
ejpam-3200	204	34	1	1	NUM
ejpam-3200	204	35	]	]	PUNCT
ejpam-3200	204	36	and	and	CCONJ
ejpam-3200	204	37	(	(	PUNCT
ejpam-3200	204	38	fms∆	fms∆	NOUN
ejpam-3200	204	39	)	)	PUNCT
ejpam-3200	204	40	b∫	b∫	NOUN
ejpam-3200	204	41	a	a	DET
ejpam-3200	204	42	f̃	f̃	PROPN
ejpam-3200	204	43	(	(	PUNCT
ejpam-3200	204	44	t)dα	t)dα	PROPN
ejpam-3200	204	45	=	=	SYM
ejpam-3200	204	46	⋃	⋃	NOUN
ejpam-3200	204	47	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	204	48	]	]	X
ejpam-3200	204	49	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	204	50	)	)	PUNCT
ejpam-3200	204	51	b∫	b∫	NOUN
ejpam-3200	204	52	a	a	DET
ejpam-3200	204	53	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	204	54	and	and	CCONJ
ejpam-3200	204	55	(	(	PUNCT
ejpam-3200	204	56	fms∆	fms∆	NOUN
ejpam-3200	204	57	)	)	PUNCT
ejpam-3200	204	58	b∫	b∫	NOUN
ejpam-3200	204	59	a	a	DET
ejpam-3200	204	60	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	204	61	=	=	SYM
ejpam-3200	204	62	m.	m.	NOUN
ejpam-3200	204	63	e.	e.	PROPN
ejpam-3200	204	64	hamid	hamid	PROPN
ejpam-3200	204	65	/	/	SYM
ejpam-3200	204	66	eur	eur	PROPN
ejpam-3200	204	67	.	.	PUNCT
ejpam-3200	205	1	j.	j.	PROPN
ejpam-3200	205	2	pure	pure	PROPN
ejpam-3200	205	3	appl	appl	PROPN
ejpam-3200	205	4	.	.	PROPN
ejpam-3200	205	5	math	math	PROPN
ejpam-3200	205	6	,	,	PUNCT
ejpam-3200	205	7	11	11	NUM
ejpam-3200	205	8	(	(	PUNCT
ejpam-3200	205	9	2	2	NUM
ejpam-3200	205	10	)	)	PUNCT
ejpam-3200	205	11	(	(	PUNCT
ejpam-3200	205	12	2018	2018	NUM
ejpam-3200	205	13	)	)	PUNCT
ejpam-3200	205	14	,	,	PUNCT
ejpam-3200	205	15	493	493	NUM
ejpam-3200	205	16	-	-	SYM
ejpam-3200	205	17	504	504	NUM
ejpam-3200	205	18	502	502	NUM
ejpam-3200	205	19	⋃	⋃	NOUN
ejpam-3200	205	20	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	205	21	]	]	X
ejpam-3200	205	22	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	205	23	)	)	PUNCT
ejpam-3200	205	24	b∫	b∫	NOUN
ejpam-3200	205	25	a	a	DET
ejpam-3200	205	26	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	205	27	.	.	PUNCT
ejpam-3200	206	1	from	from	ADP
ejpam-3200	206	2	theorem	theorem	NOUN
ejpam-3200	206	3	3	3	NUM
ejpam-3200	206	4	we	we	PRON
ejpam-3200	206	5	have	have	VERB
ejpam-3200	206	6	βfλ(t	βfλ(t	NOUN
ejpam-3200	206	7	)	)	PUNCT
ejpam-3200	207	1	+	+	NUM
ejpam-3200	207	2	γgλ(t	γgλ(t	X
ejpam-3200	207	3	)	)	PUNCT
ejpam-3200	207	4	∈	∈	NOUN
ejpam-3200	207	5	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	207	6	,	,	PUNCT
ejpam-3200	207	7	b]t	b]t	NOUN
ejpam-3200	207	8	and	and	CCONJ
ejpam-3200	207	9	(	(	PUNCT
ejpam-3200	207	10	ims∆	ims∆	NOUN
ejpam-3200	207	11	)	)	PUNCT
ejpam-3200	207	12	b∫	b∫	NOUN
ejpam-3200	207	13	a	a	DET
ejpam-3200	207	14	(	(	PUNCT
ejpam-3200	207	15	βfλ(t)+γgλ(t	βfλ(t)+γgλ(t	NOUN
ejpam-3200	207	16	)	)	PUNCT
ejpam-3200	207	17	)	)	PUNCT
ejpam-3200	208	1	dα	dα	VERB
ejpam-3200	208	2	=	=	PUNCT
ejpam-3200	208	3	β(ims∆	β(ims∆	NUM
ejpam-3200	208	4	)	)	PUNCT
ejpam-3200	208	5	b∫	b∫	NOUN
ejpam-3200	208	6	a	a	DET
ejpam-3200	208	7	fλ(t)dα+γ(ims∆	fλ(t)dα+γ(ims∆	NOUN
ejpam-3200	208	8	)	)	PUNCT
ejpam-3200	208	9	b∫	b∫	NOUN
ejpam-3200	208	10	a	a	DET
ejpam-3200	208	11	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	208	12	for	for	ADP
ejpam-3200	208	13	any	any	DET
ejpam-3200	208	14	λ	λ	PROPN
ejpam-3200	208	15	∈	∈	PROPN
ejpam-3200	208	16	(	(	PUNCT
ejpam-3200	208	17	0	0	NUM
ejpam-3200	208	18	,	,	PUNCT
ejpam-3200	208	19	1	1	NUM
ejpam-3200	208	20	]	]	PUNCT
ejpam-3200	208	21	.	.	PUNCT
ejpam-3200	209	1	hence	hence	ADV
ejpam-3200	209	2	βf̃	βf̃	PUNCT
ejpam-3200	209	3	(	(	PUNCT
ejpam-3200	209	4	t	t	NOUN
ejpam-3200	209	5	)	)	PUNCT
ejpam-3200	209	6	+	+	NUM
ejpam-3200	209	7	γg̃(t	γg̃(t	SYM
ejpam-3200	209	8	)	)	PUNCT
ejpam-3200	209	9	∈	∈	PROPN
ejpam-3200	209	10	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	209	11	,	,	PUNCT
ejpam-3200	209	12	b]t	b]t	NOUN
ejpam-3200	209	13	and	and	CCONJ
ejpam-3200	209	14	(	(	PUNCT
ejpam-3200	209	15	fms∆	fms∆	NOUN
ejpam-3200	209	16	)	)	PUNCT
ejpam-3200	209	17	b∫	b∫	NOUN
ejpam-3200	209	18	a	a	X
ejpam-3200	209	19	(	(	PUNCT
ejpam-3200	209	20	βf̃	βf̃	X
ejpam-3200	209	21	(	(	PUNCT
ejpam-3200	209	22	t	t	NOUN
ejpam-3200	209	23	)	)	PUNCT
ejpam-3200	209	24	+	+	NUM
ejpam-3200	209	25	γg̃(t	γg̃(t	NOUN
ejpam-3200	209	26	)	)	PUNCT
ejpam-3200	209	27	)	)	PUNCT
ejpam-3200	210	1	dα	dα	VERB
ejpam-3200	211	1	=	=	PUNCT
ejpam-3200	211	2	⋃	⋃	NOUN
ejpam-3200	211	3	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	211	4	]	]	X
ejpam-3200	211	5	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	211	6	)	)	PUNCT
ejpam-3200	211	7	b∫	b∫	NOUN
ejpam-3200	211	8	a	a	X
ejpam-3200	211	9	(	(	PUNCT
ejpam-3200	211	10	βfλ(t	βfλ(t	PROPN
ejpam-3200	211	11	)	)	PUNCT
ejpam-3200	211	12	+	+	NUM
ejpam-3200	211	13	γgλ(t	γgλ(t	NOUN
ejpam-3200	211	14	)	)	PUNCT
ejpam-3200	211	15	)	)	PUNCT
ejpam-3200	212	1	dα	dα	VERB
ejpam-3200	213	1	=	=	PUNCT
ejpam-3200	213	2	⋃	⋃	NOUN
ejpam-3200	213	3	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	213	4	]	]	X
ejpam-3200	213	5	λ	λ	X
ejpam-3200	213	6	(	(	PUNCT
ejpam-3200	213	7	β(ims∆	β(ims∆	NUM
ejpam-3200	213	8	)	)	PUNCT
ejpam-3200	213	9	b∫	b∫	NOUN
ejpam-3200	213	10	a	a	DET
ejpam-3200	213	11	fλ(t)dα+	fλ(t)dα+	NOUN
ejpam-3200	213	12	γ(ims∆	γ(ims∆	NOUN
ejpam-3200	213	13	)	)	PUNCT
ejpam-3200	213	14	b∫	b∫	NOUN
ejpam-3200	213	15	a	a	DET
ejpam-3200	213	16	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	213	17	)	)	PUNCT
ejpam-3200	214	1	=	=	PUNCT
ejpam-3200	214	2	β	β	X
ejpam-3200	214	3	⋃	⋃	NOUN
ejpam-3200	214	4	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	214	5	]	]	X
ejpam-3200	214	6	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	214	7	)	)	PUNCT
ejpam-3200	214	8	b∫	b∫	NOUN
ejpam-3200	214	9	a	a	DET
ejpam-3200	214	10	fλ(t)dα+	fλ(t)dα+	NOUN
ejpam-3200	214	11	γ	γ	NOUN
ejpam-3200	214	12	⋃	⋃	PROPN
ejpam-3200	214	13	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	214	14	]	]	X
ejpam-3200	214	15	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	214	16	)	)	PUNCT
ejpam-3200	214	17	b∫	b∫	NOUN
ejpam-3200	214	18	a	a	DET
ejpam-3200	214	19	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	214	20	=	=	SYM
ejpam-3200	214	21	β(fms∆	β(fms∆	X
ejpam-3200	214	22	)	)	PUNCT
ejpam-3200	214	23	b∫	b∫	NOUN
ejpam-3200	214	24	a	a	DET
ejpam-3200	214	25	f̃	f̃	PROPN
ejpam-3200	214	26	(	(	PUNCT
ejpam-3200	214	27	t)dα+	t)dα+	NOUN
ejpam-3200	214	28	γ(fms∆	γ(fms∆	NOUN
ejpam-3200	214	29	)	)	PUNCT
ejpam-3200	214	30	b∫	b∫	NOUN
ejpam-3200	214	31	a	a	DET
ejpam-3200	214	32	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	214	33	.	.	PUNCT
ejpam-3200	215	1	theorem	theorem	NOUN
ejpam-3200	215	2	9	9	NUM
ejpam-3200	215	3	.	.	PUNCT
ejpam-3200	216	1	let	let	VERB
ejpam-3200	216	2	α	α	PRON
ejpam-3200	216	3	:	:	PUNCT
ejpam-3200	217	1	[	[	X
ejpam-3200	217	2	a	a	DET
ejpam-3200	217	3	,	,	PUNCT
ejpam-3200	217	4	b]t	b]t	NOUN
ejpam-3200	217	5	→	→	SYM
ejpam-3200	217	6	r	r	NOUN
ejpam-3200	217	7	be	be	AUX
ejpam-3200	217	8	an	an	DET
ejpam-3200	217	9	increasing	increase	VERB
ejpam-3200	217	10	function	function	NOUN
ejpam-3200	217	11	.	.	PUNCT
ejpam-3200	218	1	if	if	SCONJ
ejpam-3200	218	2	f̃	f̃	PROPN
ejpam-3200	218	3	(	(	PUNCT
ejpam-3200	218	4	t	t	PROPN
ejpam-3200	218	5	)	)	PUNCT
ejpam-3200	218	6	∈	∈	PROPN
ejpam-3200	218	7	fmsα∆[a	fmsα∆[a	PROPN
ejpam-3200	218	8	,	,	PUNCT
ejpam-3200	218	9	c]t	c]t	NOUN
ejpam-3200	218	10	and	and	CCONJ
ejpam-3200	218	11	f̃	f̃	PROPN
ejpam-3200	218	12	(	(	PUNCT
ejpam-3200	218	13	t	t	PROPN
ejpam-3200	218	14	)	)	PUNCT
ejpam-3200	218	15	∈	∈	PROPN
ejpam-3200	218	16	fmsα∆[c	fmsα∆[c	NOUN
ejpam-3200	218	17	,	,	PUNCT
ejpam-3200	218	18	b]t	b]t	NOUN
ejpam-3200	218	19	,	,	PUNCT
ejpam-3200	218	20	then	then	ADV
ejpam-3200	218	21	f̃	f̃	PROPN
ejpam-3200	218	22	(	(	PUNCT
ejpam-3200	218	23	t	t	PROPN
ejpam-3200	218	24	)	)	PUNCT
ejpam-3200	218	25	∈	∈	PROPN
ejpam-3200	218	26	fmsα∆[a	fmsα∆[a	ADV
ejpam-3200	218	27	,	,	PUNCT
ejpam-3200	218	28	b]t	b]t	NOUN
ejpam-3200	218	29	and	and	CCONJ
ejpam-3200	218	30	(	(	PUNCT
ejpam-3200	218	31	fms∆	fms∆	NOUN
ejpam-3200	218	32	)	)	PUNCT
ejpam-3200	218	33	b∫	b∫	NOUN
ejpam-3200	218	34	a	a	DET
ejpam-3200	218	35	f̃	f̃	PROPN
ejpam-3200	218	36	(	(	PUNCT
ejpam-3200	218	37	t)dα	t)dα	PROPN
ejpam-3200	218	38	=	=	SYM
ejpam-3200	218	39	(	(	PUNCT
ejpam-3200	218	40	fms∆	fms∆	NOUN
ejpam-3200	218	41	)	)	PUNCT
ejpam-3200	218	42	c∫	c∫	NOUN
ejpam-3200	218	43	a	a	DET
ejpam-3200	218	44	f̃	f̃	PROPN
ejpam-3200	218	45	(	(	PUNCT
ejpam-3200	218	46	t)dα+	t)dα+	X
ejpam-3200	218	47	(	(	PUNCT
ejpam-3200	218	48	fms∆	fms∆	NOUN
ejpam-3200	218	49	)	)	PUNCT
ejpam-3200	218	50	b∫	b∫	PROPN
ejpam-3200	218	51	c	c	PROPN
ejpam-3200	218	52	f̃	f̃	PROPN
ejpam-3200	218	53	(	(	PUNCT
ejpam-3200	218	54	t)dα	t)dα	PROPN
ejpam-3200	218	55	.	.	PROPN
ejpam-3200	219	1	(	(	PUNCT
ejpam-3200	219	2	4.9	4.9	NUM
ejpam-3200	219	3	)	)	PUNCT
ejpam-3200	219	4	proof	proof	NOUN
ejpam-3200	219	5	.	.	PUNCT
ejpam-3200	220	1	if	if	SCONJ
ejpam-3200	220	2	f̃	f̃	PROPN
ejpam-3200	220	3	(	(	PUNCT
ejpam-3200	220	4	t	t	PROPN
ejpam-3200	220	5	)	)	PUNCT
ejpam-3200	220	6	∈	∈	PROPN
ejpam-3200	220	7	fmsα∆[a	fmsα∆[a	PROPN
ejpam-3200	220	8	,	,	PUNCT
ejpam-3200	220	9	c]t	c]t	NOUN
ejpam-3200	220	10	and	and	CCONJ
ejpam-3200	220	11	f̃	f̃	PROPN
ejpam-3200	220	12	(	(	PUNCT
ejpam-3200	220	13	t	t	PROPN
ejpam-3200	220	14	)	)	PUNCT
ejpam-3200	220	15	∈	∈	PROPN
ejpam-3200	220	16	fmsα∆[c	fmsα∆[c	NOUN
ejpam-3200	220	17	,	,	PUNCT
ejpam-3200	220	18	b]t	b]t	NOUN
ejpam-3200	220	19	,	,	PUNCT
ejpam-3200	220	20	then	then	ADV
ejpam-3200	220	21	the	the	DET
ejpam-3200	220	22	interval	interval	NOUN
ejpam-3200	220	23	-	-	PUNCT
ejpam-3200	220	24	valued	value	VERB
ejpam-3200	220	25	function	function	NOUN
ejpam-3200	220	26	fλ(t	fλ(t	PUNCT
ejpam-3200	220	27	)	)	PUNCT
ejpam-3200	220	28	=	=	PUNCT
ejpam-3200	221	1	[	[	X
ejpam-3200	221	2	f−λ	f−λ	X
ejpam-3200	221	3	(	(	PUNCT
ejpam-3200	221	4	t	t	NOUN
ejpam-3200	221	5	)	)	PUNCT
ejpam-3200	221	6	,	,	PUNCT
ejpam-3200	221	7	f+	f+	PROPN
ejpam-3200	221	8	λ	λ	PROPN
ejpam-3200	221	9	(	(	PUNCT
ejpam-3200	221	10	t	t	PROPN
ejpam-3200	221	11	)	)	PUNCT
ejpam-3200	221	12	]	]	PUNCT
ejpam-3200	221	13	is	be	AUX
ejpam-3200	221	14	(	(	PUNCT
ejpam-3200	221	15	ms∆	ms∆	PROPN
ejpam-3200	221	16	)	)	PUNCT
ejpam-3200	221	17	integrable	integrable	ADJ
ejpam-3200	221	18	with	with	ADP
ejpam-3200	221	19	respect	respect	NOUN
ejpam-3200	221	20	to	to	ADP
ejpam-3200	221	21	α	α	NOUN
ejpam-3200	221	22	on	on	ADP
ejpam-3200	221	23	[	[	X
ejpam-3200	221	24	a	a	DET
ejpam-3200	221	25	,	,	PUNCT
ejpam-3200	221	26	c]t	c]t	NOUN
ejpam-3200	221	27	and	and	CCONJ
ejpam-3200	221	28	[	[	X
ejpam-3200	221	29	c	c	NOUN
ejpam-3200	221	30	,	,	PUNCT
ejpam-3200	221	31	b]t	b]t	VERB
ejpam-3200	221	32	for	for	ADP
ejpam-3200	221	33	any	any	DET
ejpam-3200	221	34	λ	λ	PROPN
ejpam-3200	221	35	∈	∈	PROPN
ejpam-3200	221	36	(	(	PUNCT
ejpam-3200	221	37	0	0	NUM
ejpam-3200	221	38	,	,	PUNCT
ejpam-3200	221	39	1	1	NUM
ejpam-3200	221	40	]	]	PUNCT
ejpam-3200	221	41	and	and	CCONJ
ejpam-3200	221	42	(	(	PUNCT
ejpam-3200	221	43	fms∆	fms∆	NOUN
ejpam-3200	221	44	)	)	PUNCT
ejpam-3200	221	45	c∫	c∫	NOUN
ejpam-3200	221	46	a	a	DET
ejpam-3200	221	47	f̃	f̃	PROPN
ejpam-3200	221	48	(	(	PUNCT
ejpam-3200	221	49	t)dα	t)dα	PROPN
ejpam-3200	221	50	=	=	SYM
ejpam-3200	221	51	⋃	⋃	NOUN
ejpam-3200	221	52	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	221	53	]	]	X
ejpam-3200	221	54	λ(ims∆	λ(ims∆	X
ejpam-3200	221	55	)	)	PUNCT
ejpam-3200	221	56	c∫	c∫	NOUN
ejpam-3200	221	57	a	a	DET
ejpam-3200	221	58	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	221	59	and	and	CCONJ
ejpam-3200	221	60	(	(	PUNCT
ejpam-3200	221	61	fms∆	fms∆	NOUN
ejpam-3200	221	62	)	)	PUNCT
ejpam-3200	221	63	b∫	b∫	PROPN
ejpam-3200	221	64	c	c	PROPN
ejpam-3200	221	65	f̃	f̃	PROPN
ejpam-3200	221	66	(	(	PUNCT
ejpam-3200	221	67	t)dα	t)dα	PROPN
ejpam-3200	221	68	=	=	SYM
ejpam-3200	221	69	⋃	⋃	NOUN
ejpam-3200	221	70	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	221	71	]	]	X
ejpam-3200	221	72	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	221	73	)	)	PUNCT
ejpam-3200	221	74	b∫	b∫	NOUN
ejpam-3200	221	75	c	c	NOUN
ejpam-3200	221	76	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	221	77	.	.	PUNCT
ejpam-3200	222	1	from	from	ADP
ejpam-3200	222	2	theorem	theorem	NOUN
ejpam-3200	222	3	4	4	NUM
ejpam-3200	222	4	we	we	PRON
ejpam-3200	222	5	have	have	VERB
ejpam-3200	222	6	fλ(t	fλ(t	NOUN
ejpam-3200	222	7	)	)	PUNCT
ejpam-3200	222	8	∈	∈	NOUN
ejpam-3200	222	9	imsα∆[a	imsα∆[a	NOUN
ejpam-3200	222	10	,	,	PUNCT
ejpam-3200	222	11	b]t	b]t	NOUN
ejpam-3200	222	12	and	and	CCONJ
ejpam-3200	222	13	(	(	PUNCT
ejpam-3200	222	14	ims∆	ims∆	NOUN
ejpam-3200	222	15	)	)	PUNCT
ejpam-3200	222	16	b∫	b∫	NOUN
ejpam-3200	222	17	a	a	DET
ejpam-3200	222	18	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	222	19	=	=	SYM
ejpam-3200	222	20	(	(	PUNCT
ejpam-3200	222	21	ims∆	ims∆	NOUN
ejpam-3200	222	22	)	)	PUNCT
ejpam-3200	222	23	c∫	c∫	NOUN
ejpam-3200	222	24	a	a	DET
ejpam-3200	222	25	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	222	26	+	+	CCONJ
ejpam-3200	222	27	(	(	PUNCT
ejpam-3200	222	28	ims∆	ims∆	NOUN
ejpam-3200	222	29	)	)	PUNCT
ejpam-3200	222	30	b∫	b∫	NOUN
ejpam-3200	222	31	c	c	NOUN
ejpam-3200	222	32	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	222	33	for	for	ADP
ejpam-3200	222	34	any	any	DET
ejpam-3200	222	35	λ	λ	PROPN
ejpam-3200	222	36	∈	∈	PROPN
ejpam-3200	222	37	(	(	PUNCT
ejpam-3200	222	38	0	0	NUM
ejpam-3200	222	39	,	,	PUNCT
ejpam-3200	222	40	1	1	NUM
ejpam-3200	222	41	]	]	PUNCT
ejpam-3200	222	42	.	.	PUNCT
ejpam-3200	223	1	hence	hence	ADV
ejpam-3200	223	2	f̃	f̃	PROPN
ejpam-3200	223	3	(	(	PUNCT
ejpam-3200	223	4	t	t	PROPN
ejpam-3200	223	5	)	)	PUNCT
ejpam-3200	223	6	∈	∈	PROPN
ejpam-3200	223	7	fmsα∆[a	fmsα∆[a	ADV
ejpam-3200	223	8	,	,	PUNCT
ejpam-3200	223	9	b]t	b]t	NOUN
ejpam-3200	223	10	and	and	CCONJ
ejpam-3200	223	11	(	(	PUNCT
ejpam-3200	223	12	fms∆	fms∆	NOUN
ejpam-3200	223	13	)	)	PUNCT
ejpam-3200	223	14	b∫	b∫	NOUN
ejpam-3200	223	15	a	a	DET
ejpam-3200	223	16	f̃	f̃	PROPN
ejpam-3200	223	17	(	(	PUNCT
ejpam-3200	223	18	t)dα	t)dα	PROPN
ejpam-3200	223	19	=	=	SYM
ejpam-3200	223	20	⋃	⋃	NOUN
ejpam-3200	223	21	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	223	22	]	]	X
ejpam-3200	223	23	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	223	24	)	)	PUNCT
ejpam-3200	223	25	b∫	b∫	NOUN
ejpam-3200	223	26	a	a	DET
ejpam-3200	223	27	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	223	28	=	=	SYM
ejpam-3200	223	29	⋃	⋃	NOUN
ejpam-3200	223	30	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	223	31	]	]	X
ejpam-3200	223	32	λ	λ	X
ejpam-3200	223	33	(	(	PUNCT
ejpam-3200	223	34	(	(	PUNCT
ejpam-3200	223	35	ims∆	ims∆	NOUN
ejpam-3200	223	36	)	)	PUNCT
ejpam-3200	223	37	c∫	c∫	NOUN
ejpam-3200	223	38	a	a	DET
ejpam-3200	223	39	fλ(t)dα+	fλ(t)dα+	NOUN
ejpam-3200	223	40	(	(	PUNCT
ejpam-3200	223	41	ims∆	ims∆	NOUN
ejpam-3200	223	42	)	)	PUNCT
ejpam-3200	223	43	b∫	b∫	NOUN
ejpam-3200	223	44	c	c	NOUN
ejpam-3200	223	45	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	223	46	)	)	PUNCT
ejpam-3200	223	47	m.	m.	NOUN
ejpam-3200	223	48	e.	e.	PROPN
ejpam-3200	223	49	hamid	hamid	PROPN
ejpam-3200	223	50	/	/	SYM
ejpam-3200	223	51	eur	eur	PROPN
ejpam-3200	223	52	.	.	PUNCT
ejpam-3200	224	1	j.	j.	PROPN
ejpam-3200	224	2	pure	pure	PROPN
ejpam-3200	224	3	appl	appl	PROPN
ejpam-3200	224	4	.	.	PROPN
ejpam-3200	224	5	math	math	PROPN
ejpam-3200	224	6	,	,	PUNCT
ejpam-3200	224	7	11	11	NUM
ejpam-3200	224	8	(	(	PUNCT
ejpam-3200	224	9	2	2	NUM
ejpam-3200	224	10	)	)	PUNCT
ejpam-3200	224	11	(	(	PUNCT
ejpam-3200	224	12	2018	2018	NUM
ejpam-3200	224	13	)	)	PUNCT
ejpam-3200	224	14	,	,	PUNCT
ejpam-3200	224	15	493	493	NUM
ejpam-3200	224	16	-	-	SYM
ejpam-3200	224	17	504	504	NUM
ejpam-3200	224	18	503	503	NUM
ejpam-3200	224	19	=	=	NOUN
ejpam-3200	224	20	⋃	⋃	NOUN
ejpam-3200	224	21	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	224	22	]	]	X
ejpam-3200	224	23	λ(ims∆	λ(ims∆	X
ejpam-3200	224	24	)	)	PUNCT
ejpam-3200	224	25	c∫	c∫	NOUN
ejpam-3200	224	26	a	a	DET
ejpam-3200	224	27	fλ(t)dα+	fλ(t)dα+	NOUN
ejpam-3200	224	28	⋃	⋃	NOUN
ejpam-3200	224	29	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	224	30	]	]	X
ejpam-3200	224	31	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	224	32	)	)	PUNCT
ejpam-3200	224	33	b∫	b∫	NOUN
ejpam-3200	224	34	c	c	NOUN
ejpam-3200	224	35	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	224	36	=	=	SYM
ejpam-3200	224	37	(	(	PUNCT
ejpam-3200	224	38	fms∆	fms∆	NOUN
ejpam-3200	224	39	)	)	PUNCT
ejpam-3200	224	40	c∫	c∫	NOUN
ejpam-3200	224	41	a	a	DET
ejpam-3200	224	42	f̃	f̃	PROPN
ejpam-3200	224	43	(	(	PUNCT
ejpam-3200	224	44	t)dα+	t)dα+	X
ejpam-3200	224	45	(	(	PUNCT
ejpam-3200	224	46	fms∆	fms∆	NOUN
ejpam-3200	224	47	)	)	PUNCT
ejpam-3200	224	48	b∫	b∫	PROPN
ejpam-3200	224	49	c	c	PROPN
ejpam-3200	224	50	f̃	f̃	PROPN
ejpam-3200	224	51	(	(	PUNCT
ejpam-3200	224	52	t)dα	t)dα	PROPN
ejpam-3200	224	53	.	.	PUNCT
ejpam-3200	224	54	theorem	theorem	VERB
ejpam-3200	224	55	10	10	NUM
ejpam-3200	224	56	.	.	PUNCT
ejpam-3200	225	1	let	let	VERB
ejpam-3200	225	2	α	α	PRON
ejpam-3200	225	3	:	:	PUNCT
ejpam-3200	226	1	[	[	X
ejpam-3200	226	2	a	a	DET
ejpam-3200	226	3	,	,	PUNCT
ejpam-3200	226	4	b]t	b]t	NOUN
ejpam-3200	226	5	→	→	SYM
ejpam-3200	226	6	r	r	NOUN
ejpam-3200	226	7	be	be	AUX
ejpam-3200	226	8	an	an	DET
ejpam-3200	226	9	increasing	increase	VERB
ejpam-3200	226	10	function	function	NOUN
ejpam-3200	226	11	.	.	PUNCT
ejpam-3200	227	1	if	if	SCONJ
ejpam-3200	227	2	f̃	f̃	PROPN
ejpam-3200	227	3	(	(	PUNCT
ejpam-3200	227	4	t	t	PROPN
ejpam-3200	227	5	)	)	PUNCT
ejpam-3200	227	6	≤	≤	NUM
ejpam-3200	227	7	g̃(t	g̃(t	PROPN
ejpam-3200	227	8	)	)	PUNCT
ejpam-3200	227	9	almost	almost	ADV
ejpam-3200	227	10	everywhere	everywhere	ADV
ejpam-3200	227	11	with	with	ADP
ejpam-3200	227	12	respect	respect	NOUN
ejpam-3200	227	13	to	to	ADP
ejpam-3200	227	14	α	α	NOUN
ejpam-3200	227	15	on	on	ADP
ejpam-3200	227	16	[	[	X
ejpam-3200	227	17	a	a	DET
ejpam-3200	227	18	,	,	PUNCT
ejpam-3200	227	19	b]t	b]t	NOUN
ejpam-3200	227	20	and	and	CCONJ
ejpam-3200	227	21	f̃	f̃	PROPN
ejpam-3200	227	22	(	(	PUNCT
ejpam-3200	227	23	t	t	PROPN
ejpam-3200	227	24	)	)	PUNCT
ejpam-3200	227	25	,	,	PUNCT
ejpam-3200	227	26	g̃(t	g̃(t	PROPN
ejpam-3200	227	27	)	)	PUNCT
ejpam-3200	227	28	∈	∈	PROPN
ejpam-3200	227	29	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	227	30	,	,	PUNCT
ejpam-3200	227	31	b]t	b]t	NOUN
ejpam-3200	227	32	,	,	PUNCT
ejpam-3200	227	33	then	then	ADV
ejpam-3200	227	34	(	(	PUNCT
ejpam-3200	227	35	fms∆	fms∆	NOUN
ejpam-3200	227	36	)	)	PUNCT
ejpam-3200	227	37	b∫	b∫	NOUN
ejpam-3200	227	38	a	a	DET
ejpam-3200	227	39	f̃	f̃	PROPN
ejpam-3200	227	40	(	(	PUNCT
ejpam-3200	227	41	t)dα	t)dα	PROPN
ejpam-3200	227	42	≤	≤	PROPN
ejpam-3200	227	43	(	(	PUNCT
ejpam-3200	227	44	fms∆	fms∆	NOUN
ejpam-3200	227	45	)	)	PUNCT
ejpam-3200	227	46	b∫	b∫	NOUN
ejpam-3200	227	47	a	a	DET
ejpam-3200	227	48	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	227	49	.	.	PUNCT
ejpam-3200	228	1	(	(	PUNCT
ejpam-3200	228	2	4.10	4.10	NUM
ejpam-3200	228	3	)	)	PUNCT
ejpam-3200	228	4	proof	proof	NOUN
ejpam-3200	228	5	.	.	PUNCT
ejpam-3200	229	1	if	if	SCONJ
ejpam-3200	229	2	f̃	f̃	PROPN
ejpam-3200	229	3	(	(	PUNCT
ejpam-3200	229	4	t	t	PROPN
ejpam-3200	229	5	)	)	PUNCT
ejpam-3200	229	6	≤	≤	NUM
ejpam-3200	229	7	g̃(t	g̃(t	PROPN
ejpam-3200	229	8	)	)	PUNCT
ejpam-3200	229	9	almost	almost	ADV
ejpam-3200	229	10	everywhere	everywhere	ADV
ejpam-3200	229	11	with	with	ADP
ejpam-3200	229	12	respect	respect	NOUN
ejpam-3200	229	13	to	to	ADP
ejpam-3200	229	14	α	α	NOUN
ejpam-3200	229	15	on	on	ADP
ejpam-3200	229	16	[	[	X
ejpam-3200	229	17	a	a	DET
ejpam-3200	229	18	,	,	PUNCT
ejpam-3200	229	19	b]t	b]t	NOUN
ejpam-3200	229	20	and	and	CCONJ
ejpam-3200	229	21	f̃	f̃	PROPN
ejpam-3200	229	22	(	(	PUNCT
ejpam-3200	229	23	t	t	PROPN
ejpam-3200	229	24	)	)	PUNCT
ejpam-3200	229	25	,	,	PUNCT
ejpam-3200	229	26	g̃(t	g̃(t	PROPN
ejpam-3200	229	27	)	)	PUNCT
ejpam-3200	229	28	∈	∈	PROPN
ejpam-3200	229	29	fmsα∆[a	fmsα∆[a	VERB
ejpam-3200	229	30	,	,	PUNCT
ejpam-3200	229	31	b]t	b]t	NOUN
ejpam-3200	229	32	,	,	PUNCT
ejpam-3200	229	33	then	then	ADV
ejpam-3200	229	34	fλ(t	fλ(t	NOUN
ejpam-3200	229	35	)	)	PUNCT
ejpam-3200	229	36	≤	≤	NOUN
ejpam-3200	229	37	gλ(t	gλ(t	NOUN
ejpam-3200	229	38	)	)	PUNCT
ejpam-3200	229	39	nearly	nearly	ADV
ejpam-3200	229	40	everywhere	everywhere	ADV
ejpam-3200	229	41	with	with	ADP
ejpam-3200	229	42	respect	respect	NOUN
ejpam-3200	229	43	to	to	ADP
ejpam-3200	229	44	α	α	NOUN
ejpam-3200	229	45	on	on	ADP
ejpam-3200	229	46	[	[	X
ejpam-3200	229	47	a	a	DET
ejpam-3200	229	48	,	,	PUNCT
ejpam-3200	229	49	b]t	b]t	NOUN
ejpam-3200	229	50	for	for	ADP
ejpam-3200	229	51	any	any	DET
ejpam-3200	229	52	λ	λ	PROPN
ejpam-3200	229	53	∈	∈	PROPN
ejpam-3200	229	54	(	(	PUNCT
ejpam-3200	229	55	0	0	NUM
ejpam-3200	229	56	,	,	PUNCT
ejpam-3200	229	57	1	1	NUM
ejpam-3200	229	58	]	]	PUNCT
ejpam-3200	229	59	and	and	CCONJ
ejpam-3200	229	60	fλ(t	fλ(t	NOUN
ejpam-3200	229	61	)	)	PUNCT
ejpam-3200	229	62	and	and	CCONJ
ejpam-3200	229	63	gλ(t	gλ(t	NOUN
ejpam-3200	229	64	)	)	PUNCT
ejpam-3200	229	65	are	be	AUX
ejpam-3200	229	66	(	(	PUNCT
ejpam-3200	229	67	ms∆	ms∆	PROPN
ejpam-3200	229	68	)	)	PUNCT
ejpam-3200	229	69	integrable	integrable	ADJ
ejpam-3200	229	70	with	with	ADP
ejpam-3200	229	71	respect	respect	NOUN
ejpam-3200	229	72	to	to	ADP
ejpam-3200	229	73	α	α	NOUN
ejpam-3200	229	74	on	on	ADP
ejpam-3200	229	75	[	[	X
ejpam-3200	229	76	a	a	DET
ejpam-3200	229	77	,	,	PUNCT
ejpam-3200	229	78	b]t	b]t	NOUN
ejpam-3200	229	79	for	for	ADP
ejpam-3200	229	80	any	any	DET
ejpam-3200	229	81	λ	λ	PROPN
ejpam-3200	229	82	∈	∈	PROPN
ejpam-3200	229	83	(	(	PUNCT
ejpam-3200	229	84	0	0	NUM
ejpam-3200	229	85	,	,	PUNCT
ejpam-3200	229	86	1	1	NUM
ejpam-3200	229	87	]	]	PUNCT
ejpam-3200	229	88	and	and	CCONJ
ejpam-3200	229	89	(	(	PUNCT
ejpam-3200	229	90	fms∆	fms∆	NOUN
ejpam-3200	229	91	)	)	PUNCT
ejpam-3200	229	92	b∫	b∫	NOUN
ejpam-3200	229	93	a	a	DET
ejpam-3200	229	94	f̃	f̃	PROPN
ejpam-3200	229	95	(	(	PUNCT
ejpam-3200	229	96	t)dα	t)dα	PROPN
ejpam-3200	229	97	=	=	SYM
ejpam-3200	229	98	⋃	⋃	NOUN
ejpam-3200	229	99	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	229	100	]	]	X
ejpam-3200	229	101	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	229	102	)	)	PUNCT
ejpam-3200	229	103	b∫	b∫	NOUN
ejpam-3200	229	104	a	a	DET
ejpam-3200	229	105	fλ(t)dα	fλ(t)dα	NOUN
ejpam-3200	229	106	and	and	CCONJ
ejpam-3200	229	107	(	(	PUNCT
ejpam-3200	229	108	fms∆	fms∆	NOUN
ejpam-3200	229	109	)	)	PUNCT
ejpam-3200	229	110	b∫	b∫	NOUN
ejpam-3200	229	111	a	a	DET
ejpam-3200	229	112	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	229	113	=	=	SYM
ejpam-3200	229	114	⋃	⋃	NOUN
ejpam-3200	229	115	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	229	116	]	]	X
ejpam-3200	229	117	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	229	118	)	)	PUNCT
ejpam-3200	229	119	b∫	b∫	NOUN
ejpam-3200	229	120	a	a	DET
ejpam-3200	229	121	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	229	122	.	.	PUNCT
ejpam-3200	230	1	from	from	ADP
ejpam-3200	230	2	theorem	theorem	NOUN
ejpam-3200	230	3	5	5	NUM
ejpam-3200	230	4	we	we	PRON
ejpam-3200	230	5	have	have	AUX
ejpam-3200	230	6	(	(	PUNCT
ejpam-3200	230	7	ims∆	ims∆	NOUN
ejpam-3200	230	8	)	)	PUNCT
ejpam-3200	230	9	b∫	b∫	NOUN
ejpam-3200	230	10	a	a	DET
ejpam-3200	230	11	fλ(t)dα	fλ(t)dα	ADJ
ejpam-3200	230	12	≤	≤	NUM
ejpam-3200	230	13	(	(	PUNCT
ejpam-3200	230	14	ims∆	ims∆	NUM
ejpam-3200	230	15	)	)	PUNCT
ejpam-3200	230	16	b∫	b∫	NOUN
ejpam-3200	230	17	a	a	DET
ejpam-3200	230	18	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	230	19	for	for	ADP
ejpam-3200	230	20	any	any	DET
ejpam-3200	230	21	λ	λ	PROPN
ejpam-3200	230	22	∈	∈	PROPN
ejpam-3200	230	23	(	(	PUNCT
ejpam-3200	230	24	0	0	NUM
ejpam-3200	230	25	,	,	PUNCT
ejpam-3200	230	26	1	1	NUM
ejpam-3200	230	27	]	]	PUNCT
ejpam-3200	230	28	.	.	PUNCT
ejpam-3200	231	1	hence	hence	ADV
ejpam-3200	231	2	(	(	PUNCT
ejpam-3200	231	3	fms∆	fms∆	NOUN
ejpam-3200	231	4	)	)	PUNCT
ejpam-3200	231	5	b∫	b∫	NOUN
ejpam-3200	231	6	a	a	DET
ejpam-3200	231	7	f̃	f̃	PROPN
ejpam-3200	231	8	(	(	PUNCT
ejpam-3200	231	9	t)dα	t)dα	PROPN
ejpam-3200	231	10	=	=	SYM
ejpam-3200	231	11	⋃	⋃	NOUN
ejpam-3200	231	12	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	231	13	]	]	X
ejpam-3200	231	14	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	231	15	)	)	PUNCT
ejpam-3200	231	16	b∫	b∫	NOUN
ejpam-3200	231	17	a	a	DET
ejpam-3200	231	18	fλ(t)dα	fλ(t)dα	ADJ
ejpam-3200	231	19	≤	≤	NOUN
ejpam-3200	231	20	⋃	⋃	PUNCT
ejpam-3200	231	21	λ∈(0,1	λ∈(0,1	NOUN
ejpam-3200	231	22	]	]	X
ejpam-3200	231	23	λ(ims∆	λ(ims∆	NOUN
ejpam-3200	231	24	)	)	PUNCT
ejpam-3200	231	25	b∫	b∫	NOUN
ejpam-3200	231	26	a	a	DET
ejpam-3200	231	27	gλ(t)dα	gλ(t)dα	NOUN
ejpam-3200	231	28	=	=	SYM
ejpam-3200	231	29	(	(	PUNCT
ejpam-3200	231	30	fms∆	fms∆	NOUN
ejpam-3200	231	31	)	)	PUNCT
ejpam-3200	231	32	b∫	b∫	NOUN
ejpam-3200	231	33	a	a	DET
ejpam-3200	231	34	g̃(t)dα	g̃(t)dα	NOUN
ejpam-3200	231	35	.	.	PUNCT
ejpam-3200	232	1	5	5	NUM
ejpam-3200	232	2	.	.	X
ejpam-3200	232	3	conclusions	conclusion	NOUN
ejpam-3200	232	4	in	in	ADP
ejpam-3200	232	5	this	this	DET
ejpam-3200	232	6	paper	paper	NOUN
ejpam-3200	232	7	,	,	PUNCT
ejpam-3200	232	8	we	we	PRON
ejpam-3200	232	9	introduced	introduce	VERB
ejpam-3200	232	10	the	the	DET
ejpam-3200	232	11	concept	concept	NOUN
ejpam-3200	232	12	of	of	ADP
ejpam-3200	232	13	the	the	DET
ejpam-3200	232	14	(	(	PUNCT
ejpam-3200	232	15	ms∆	ms∆	PROPN
ejpam-3200	232	16	)	)	PUNCT
ejpam-3200	232	17	integrals	integral	NOUN
ejpam-3200	232	18	of	of	ADP
ejpam-3200	232	19	interval	interval	NOUN
ejpam-3200	232	20	-	-	PUNCT
ejpam-3200	232	21	valued	value	VERB
ejpam-3200	232	22	functions	function	NOUN
ejpam-3200	232	23	and	and	CCONJ
ejpam-3200	232	24	fuzzy	fuzzy	ADJ
ejpam-3200	232	25	numbervalued	numbervalue	VERB
ejpam-3200	232	26	functions	function	NOUN
ejpam-3200	232	27	on	on	ADP
ejpam-3200	232	28	time	time	NOUN
ejpam-3200	232	29	scales	scale	NOUN
ejpam-3200	232	30	and	and	CCONJ
ejpam-3200	232	31	investigated	investigate	VERB
ejpam-3200	232	32	some	some	DET
ejpam-3200	232	33	properties	property	NOUN
ejpam-3200	232	34	of	of	ADP
ejpam-3200	232	35	those	those	DET
ejpam-3200	232	36	integrals	integral	NOUN
ejpam-3200	232	37	.	.	PUNCT
ejpam-3200	233	1	references	reference	NOUN
ejpam-3200	233	2	504	504	NUM
ejpam-3200	233	3	references	reference	NOUN
ejpam-3200	233	4	[	[	X
ejpam-3200	233	5	1	1	NUM
ejpam-3200	233	6	]	]	X
ejpam-3200	233	7	z.l	z.l	PROPN
ejpam-3200	233	8	.	.	PROPN
ejpam-3200	233	9	cheng	cheng	PROPN
ejpam-3200	233	10	and	and	CCONJ
ejpam-3200	233	11	w.	w.	PROPN
ejpam-3200	233	12	demou	demou	PROPN
ejpam-3200	233	13	.	.	PUNCT
ejpam-3200	234	1	extension	extension	NOUN
ejpam-3200	234	2	of	of	ADP
ejpam-3200	234	3	the	the	DET
ejpam-3200	234	4	integral	integral	ADJ
ejpam-3200	234	5	of	of	ADP
ejpam-3200	234	6	interval	interval	NOUN
ejpam-3200	234	7	-	-	PUNCT
ejpam-3200	234	8	valued	value	VERB
ejpam-3200	234	9	function	function	NOUN
ejpam-3200	234	10	and	and	CCONJ
ejpam-3200	234	11	the	the	DET
ejpam-3200	234	12	integral	integral	ADJ
ejpam-3200	234	13	of	of	ADP
ejpam-3200	234	14	fuzzy	fuzzy	ADV
ejpam-3200	234	15	-	-	PUNCT
ejpam-3200	234	16	valued	value	VERB
ejpam-3200	234	17	function	function	NOUN
ejpam-3200	234	18	.	.	PUNCT
ejpam-3200	235	1	fuzzy	fuzzy	ADJ
ejpam-3200	235	2	math	math	NOUN
ejpam-3200	235	3	,	,	PUNCT
ejpam-3200	235	4	3	3	NUM
ejpam-3200	235	5	,	,	PUNCT
ejpam-3200	235	6	45	45	NUM
ejpam-3200	235	7	-	-	SYM
ejpam-3200	235	8	52	52	NUM
ejpam-3200	235	9	,	,	PUNCT
ejpam-3200	235	10	(	(	PUNCT
ejpam-3200	235	11	1983	1983	NUM
ejpam-3200	235	12	)	)	PUNCT
ejpam-3200	235	13	.	.	PUNCT
ejpam-3200	236	1	[	[	X
ejpam-3200	236	2	2	2	X
ejpam-3200	236	3	]	]	PUNCT
ejpam-3200	236	4	s.	s.	PROPN
ejpam-3200	236	5	hilger	hilger	PROPN
ejpam-3200	236	6	.	.	PUNCT
ejpam-3200	237	1	ein	ein	PROPN
ejpam-3200	237	2	makettenkalkl	makettenkalkl	PROPN
ejpam-3200	237	3	mit	mit	PROPN
ejpam-3200	237	4	anwendung	anwendung	PROPN
ejpam-3200	237	5	auf	auf	PROPN
ejpam-3200	237	6	zentrumsmannigfaltigkeiten	zentrumsmannigfaltigkeiten	PROPN
ejpam-3200	237	7	,	,	PUNCT
ejpam-3200	237	8	ph	ph	PROPN
ejpam-3200	237	9	.	.	PROPN
ejpam-3200	237	10	d.	d.	PROPN
ejpam-3200	237	11	thesis	thesis	PROPN
ejpam-3200	237	12	.	.	PUNCT
ejpam-3200	238	1	universtat	universtat	PROPN
ejpam-3200	238	2	wurzburg	wurzburg	PROPN
ejpam-3200	238	3	,	,	PUNCT
ejpam-3200	238	4	(	(	PUNCT
ejpam-3200	238	5	1988	1988	NUM
ejpam-3200	238	6	)	)	PUNCT
ejpam-3200	238	7	.	.	PUNCT
ejpam-3200	239	1	[	[	X
ejpam-3200	239	2	3	3	X
ejpam-3200	239	3	]	]	X
ejpam-3200	239	4	m.e	m.e	PROPN
ejpam-3200	239	5	.	.	PROPN
ejpam-3200	239	6	hamid	hamid	PROPN
ejpam-3200	239	7	,	,	PUNCT
ejpam-3200	239	8	l.s	l.s	PROPN
ejpam-3200	239	9	.	.	PROPN
ejpam-3200	239	10	xu	xu	PROPN
ejpam-3200	239	11	and	and	CCONJ
ejpam-3200	239	12	a.h	a.h	PROPN
ejpam-3200	239	13	.	.	PROPN
ejpam-3200	239	14	elmuiz	elmuiz	PROPN
ejpam-3200	239	15	.	.	PUNCT
ejpam-3200	240	1	on	on	ADP
ejpam-3200	240	2	mcshane	mcshane	PROPN
ejpam-3200	240	3	integrals	integral	NOUN
ejpam-3200	240	4	of	of	ADP
ejpam-3200	240	5	interval	interval	NOUN
ejpam-3200	240	6	-	-	PUNCT
ejpam-3200	240	7	valued	value	VERB
ejpam-3200	240	8	functions	function	NOUN
ejpam-3200	240	9	and	and	CCONJ
ejpam-3200	240	10	fuzzy	fuzzy	ADJ
ejpam-3200	240	11	-	-	PUNCT
ejpam-3200	240	12	number	number	NOUN
ejpam-3200	240	13	-	-	PUNCT
ejpam-3200	240	14	valued	value	VERB
ejpam-3200	240	15	functions	function	NOUN
ejpam-3200	240	16	on	on	ADP
ejpam-3200	240	17	time	time	NOUN
ejpam-3200	240	18	scales	scale	NOUN
ejpam-3200	240	19	.	.	PUNCT
ejpam-3200	241	1	journal	journal	NOUN
ejpam-3200	241	2	of	of	ADP
ejpam-3200	241	3	progressive	progressive	ADJ
ejpam-3200	241	4	research	research	NOUN
ejpam-3200	241	5	in	in	ADP
ejpam-3200	241	6	mathematics	mathematic	NOUN
ejpam-3200	241	7	,	,	PUNCT
ejpam-3200	241	8	12(1	12(1	NUM
ejpam-3200	241	9	)	)	PUNCT
ejpam-3200	241	10	,	,	PUNCT
ejpam-3200	241	11	1780	1780	NUM
ejpam-3200	241	12	-	-	SYM
ejpam-3200	241	13	1788	1788	NUM
ejpam-3200	241	14	,	,	PUNCT
ejpam-3200	241	15	(	(	PUNCT
ejpam-3200	241	16	2017	2017	NUM
ejpam-3200	241	17	)	)	PUNCT
ejpam-3200	241	18	.	.	PUNCT
ejpam-3200	242	1	[	[	X
ejpam-3200	242	2	4	4	NUM
ejpam-3200	242	3	]	]	X
ejpam-3200	242	4	m.e	m.e	PROPN
ejpam-3200	242	5	.	.	PROPN
ejpam-3200	242	6	hamid	hamid	PROPN
ejpam-3200	242	7	and	and	CCONJ
ejpam-3200	242	8	a.h	a.h	PROPN
ejpam-3200	242	9	.	.	PROPN
ejpam-3200	242	10	elmuiz	elmuiz	PROPN
ejpam-3200	242	11	.	.	PUNCT
ejpam-3200	243	1	on	on	ADP
ejpam-3200	243	2	henstock	henstock	NOUN
ejpam-3200	243	3	-	-	PUNCT
ejpam-3200	243	4	stieljes	stieljes	NOUN
ejpam-3200	243	5	integrals	integral	NOUN
ejpam-3200	243	6	of	of	ADP
ejpam-3200	243	7	interval	interval	NOUN
ejpam-3200	243	8	-	-	PUNCT
ejpam-3200	243	9	valued	value	VERB
ejpam-3200	243	10	functions	function	NOUN
ejpam-3200	243	11	and	and	CCONJ
ejpam-3200	243	12	fuzzy	fuzzy	ADJ
ejpam-3200	243	13	-	-	PUNCT
ejpam-3200	243	14	number	number	NOUN
ejpam-3200	243	15	-	-	PUNCT
ejpam-3200	243	16	valued	value	VERB
ejpam-3200	243	17	functions	function	NOUN
ejpam-3200	243	18	.	.	PUNCT
ejpam-3200	244	1	journal	journal	NOUN
ejpam-3200	244	2	of	of	ADP
ejpam-3200	244	3	applied	apply	VERB
ejpam-3200	244	4	mathematics	mathematic	NOUN
ejpam-3200	244	5	and	and	CCONJ
ejpam-3200	244	6	physics	physics	NOUN
ejpam-3200	244	7	,	,	PUNCT
ejpam-3200	244	8	4	4	NUM
ejpam-3200	244	9	,	,	PUNCT
ejpam-3200	244	10	779	779	NUM
ejpam-3200	244	11	-	-	SYM
ejpam-3200	244	12	786	786	NUM
ejpam-3200	244	13	,	,	PUNCT
ejpam-3200	244	14	(	(	PUNCT
ejpam-3200	244	15	2016	2016	NUM
ejpam-3200	244	16	)	)	PUNCT
ejpam-3200	244	17	.	.	PUNCT
ejpam-3200	245	1	[	[	X
ejpam-3200	245	2	5	5	NUM
ejpam-3200	245	3	]	]	X
ejpam-3200	245	4	m.e	m.e	PROPN
ejpam-3200	245	5	.	.	PROPN
ejpam-3200	245	6	hamid	hamid	PROPN
ejpam-3200	245	7	,	,	PUNCT
ejpam-3200	245	8	a.h	a.h	PROPN
ejpam-3200	245	9	.	.	PROPN
ejpam-3200	245	10	elmuiz	elmuiz	PROPN
ejpam-3200	245	11	and	and	CCONJ
ejpam-3200	245	12	m.e	m.e	PROPN
ejpam-3200	245	13	.	.	PROPN
ejpam-3200	245	14	sheima	sheima	PROPN
ejpam-3200	245	15	.	.	PUNCT
ejpam-3200	246	1	on	on	ADP
ejpam-3200	246	2	ap	ap	PROPN
ejpam-3200	246	3	-	-	PUNCT
ejpam-3200	246	4	henstock	henstock	NOUN
ejpam-3200	246	5	integrals	integral	NOUN
ejpam-3200	246	6	of	of	ADP
ejpam-3200	246	7	intervalvalued	intervalvalue	VERB
ejpam-3200	246	8	functions	function	NOUN
ejpam-3200	246	9	and	and	CCONJ
ejpam-3200	246	10	fuzzy	fuzzy	ADJ
ejpam-3200	246	11	-	-	PUNCT
ejpam-3200	246	12	number	number	NOUN
ejpam-3200	246	13	-	-	PUNCT
ejpam-3200	246	14	valued	value	VERB
ejpam-3200	246	15	functions	function	NOUN
ejpam-3200	246	16	.	.	PUNCT
ejpam-3200	247	1	applied	apply	VERB
ejpam-3200	247	2	mathematics	mathematic	NOUN
ejpam-3200	247	3	,	,	PUNCT
ejpam-3200	247	4	7	7	NUM
ejpam-3200	247	5	,	,	PUNCT
ejpam-3200	247	6	22852295	22852295	NUM
ejpam-3200	247	7	,	,	PUNCT
ejpam-3200	247	8	(	(	PUNCT
ejpam-3200	247	9	2016	2016	NUM
ejpam-3200	247	10	)	)	PUNCT
ejpam-3200	247	11	.	.	PUNCT
ejpam-3200	248	1	[	[	X
ejpam-3200	248	2	6	6	NUM
ejpam-3200	248	3	]	]	PUNCT
ejpam-3200	248	4	s.	s.	PROPN
ejpam-3200	248	5	nanda	nanda	PROPN
ejpam-3200	248	6	.	.	PUNCT
ejpam-3200	249	1	on	on	ADP
ejpam-3200	249	2	integration	integration	NOUN
ejpam-3200	249	3	of	of	ADP
ejpam-3200	249	4	fuzzy	fuzzy	ADJ
ejpam-3200	249	5	mappings	mapping	NOUN
ejpam-3200	249	6	.	.	PUNCT
ejpam-3200	250	1	fuzzy	fuzzy	ADJ
ejpam-3200	250	2	sets	set	NOUN
ejpam-3200	250	3	and	and	CCONJ
ejpam-3200	250	4	systems	system	NOUN
ejpam-3200	250	5	,	,	PUNCT
ejpam-3200	250	6	32	32	NUM
ejpam-3200	250	7	,	,	PUNCT
ejpam-3200	250	8	95	95	NUM
ejpam-3200	250	9	-	-	SYM
ejpam-3200	250	10	101	101	NUM
ejpam-3200	250	11	,	,	PUNCT
ejpam-3200	250	12	(	(	PUNCT
ejpam-3200	250	13	1989	1989	NUM
ejpam-3200	250	14	)	)	PUNCT
ejpam-3200	250	15	.	.	PUNCT
ejpam-3200	251	1	[	[	X
ejpam-3200	251	2	7	7	X
ejpam-3200	251	3	]	]	X
ejpam-3200	251	4	c.x	c.x	PROPN
ejpam-3200	251	5	.	.	PROPN
ejpam-3200	251	6	wu	wu	PROPN
ejpam-3200	251	7	and	and	CCONJ
ejpam-3200	251	8	z.t	z.t	PROPN
ejpam-3200	251	9	.	.	PROPN
ejpam-3200	251	10	gong	gong	PROPN
ejpam-3200	251	11	.	.	PUNCT
ejpam-3200	252	1	on	on	ADP
ejpam-3200	252	2	henstock	henstock	NOUN
ejpam-3200	252	3	integrals	integral	NOUN
ejpam-3200	252	4	of	of	ADP
ejpam-3200	252	5	interval	interval	NOUN
ejpam-3200	252	6	-	-	PUNCT
ejpam-3200	252	7	valued	value	VERB
ejpam-3200	252	8	functions	function	NOUN
ejpam-3200	252	9	and	and	CCONJ
ejpam-3200	252	10	fuzzy	fuzzy	ADV
ejpam-3200	252	11	-	-	PUNCT
ejpam-3200	252	12	valued	value	VERB
ejpam-3200	252	13	functions	function	NOUN
ejpam-3200	252	14	.	.	PUNCT
ejpam-3200	253	1	fuzzy	fuzzy	ADJ
ejpam-3200	253	2	sets	set	NOUN
ejpam-3200	253	3	and	and	CCONJ
ejpam-3200	253	4	systems	system	NOUN
ejpam-3200	253	5	,	,	PUNCT
ejpam-3200	253	6	115	115	NUM
ejpam-3200	253	7	,	,	PUNCT
ejpam-3200	253	8	377	377	NUM
ejpam-3200	253	9	-	-	SYM
ejpam-3200	253	10	391	391	NUM
ejpam-3200	253	11	,	,	PUNCT
ejpam-3200	253	12	(	(	PUNCT
ejpam-3200	253	13	2000	2000	NUM
ejpam-3200	253	14	)	)	PUNCT
ejpam-3200	253	15	.	.	PUNCT
ejpam-3200	254	1	[	[	X
ejpam-3200	254	2	8	8	NUM
ejpam-3200	254	3	]	]	X
ejpam-3200	254	4	c.x	c.x	PROPN
ejpam-3200	254	5	.	.	PROPN
ejpam-3200	254	6	wu	wu	PROPN
ejpam-3200	254	7	and	and	CCONJ
ejpam-3200	254	8	m.	m.	PROPN
ejpam-3200	254	9	ma	ma	PROPN
ejpam-3200	254	10	.	.	PUNCT
ejpam-3200	254	11	embedding	embed	VERB
ejpam-3200	254	12	problem	problem	NOUN
ejpam-3200	254	13	of	of	ADP
ejpam-3200	254	14	fuzzy	fuzzy	ADJ
ejpam-3200	254	15	number	number	NOUN
ejpam-3200	254	16	spaces	space	NOUN
ejpam-3200	254	17	:	:	PUNCT
ejpam-3200	254	18	part	part	NOUN
ejpam-3200	254	19	i.	i.	PROPN
ejpam-3200	254	20	fuzzy	fuzzy	PROPN
ejpam-3200	254	21	sets	set	NOUN
ejpam-3200	254	22	and	and	CCONJ
ejpam-3200	254	23	systems	system	NOUN
ejpam-3200	254	24	,	,	PUNCT
ejpam-3200	254	25	44	44	NUM
ejpam-3200	254	26	,	,	PUNCT
ejpam-3200	254	27	33	33	NUM
ejpam-3200	254	28	-	-	SYM
ejpam-3200	254	29	38	38	NUM
ejpam-3200	254	30	,	,	PUNCT
ejpam-3200	254	31	(	(	PUNCT
ejpam-3200	254	32	1991	1991	NUM
ejpam-3200	254	33	)	)	PUNCT
ejpam-3200	254	34	.	.	PUNCT
ejpam-3200	255	1	[	[	X
ejpam-3200	255	2	9	9	NUM
ejpam-3200	255	3	]	]	X
ejpam-3200	255	4	c.x	c.x	PROPN
ejpam-3200	255	5	.	.	PROPN
ejpam-3200	255	6	wu	wu	PROPN
ejpam-3200	255	7	and	and	CCONJ
ejpam-3200	255	8	m.	m.	PROPN
ejpam-3200	255	9	ma	ma	PROPN
ejpam-3200	255	10	.	.	PUNCT
ejpam-3200	255	11	embedding	embed	VERB
ejpam-3200	255	12	problem	problem	NOUN
ejpam-3200	255	13	of	of	ADP
ejpam-3200	255	14	fuzzy	fuzzy	ADJ
ejpam-3200	255	15	number	number	NOUN
ejpam-3200	255	16	spaces	space	NOUN
ejpam-3200	255	17	:	:	PUNCT
ejpam-3200	255	18	part	part	PROPN
ejpam-3200	255	19	ii	ii	PROPN
ejpam-3200	255	20	.	.	PROPN
ejpam-3200	255	21	fuzzy	fuzzy	ADJ
ejpam-3200	255	22	sets	set	NOUN
ejpam-3200	255	23	and	and	CCONJ
ejpam-3200	255	24	systems	system	NOUN
ejpam-3200	255	25	,	,	PUNCT
ejpam-3200	255	26	45	45	NUM
ejpam-3200	255	27	,	,	PUNCT
ejpam-3200	255	28	189	189	NUM
ejpam-3200	255	29	-	-	SYM
ejpam-3200	255	30	202	202	NUM
ejpam-3200	255	31	,	,	PUNCT
ejpam-3200	255	32	(	(	PUNCT
ejpam-3200	255	33	1992	1992	NUM
ejpam-3200	255	34	)	)	PUNCT
ejpam-3200	255	35	.	.	PUNCT
ejpam-3200	256	1	[	[	X
ejpam-3200	256	2	10	10	NUM
ejpam-3200	256	3	]	]	PUNCT
ejpam-3200	256	4	j.	j.	PROPN
ejpam-3200	256	5	h.	h.	PROPN
ejpam-3200	256	6	yoon	yoon	PROPN
ejpam-3200	256	7	,	,	PUNCT
ejpam-3200	256	8	g.	g.	PROPN
ejpam-3200	256	9	s.	s.	PROPN
ejpam-3200	256	10	eun	eun	PROPN
ejpam-3200	256	11	and	and	CCONJ
ejpam-3200	256	12	y.	y.	PROPN
ejpam-3200	256	13	c.	c.	PROPN
ejpam-3200	256	14	lee	lee	PROPN
ejpam-3200	256	15	.	.	PUNCT
ejpam-3200	257	1	on	on	ADP
ejpam-3200	257	2	mcshane	mcshane	PROPN
ejpam-3200	257	3	-	-	PUNCT
ejpam-3200	257	4	stieltjes	stieltjes	PROPN
ejpam-3200	257	5	integral	integral	ADJ
ejpam-3200	257	6	.	.	PUNCT
ejpam-3200	258	1	kangweon	kangweon	PROPN
ejpam-3200	258	2	kyungki	kyungki	PROPN
ejpam-3200	258	3	math	math	PROPN
ejpam-3200	258	4	.	.	PUNCT
ejpam-3200	259	1	journal	journal	PROPN
ejpam-3200	259	2	,	,	PUNCT
ejpam-3200	259	3	52	52	NUM
ejpam-3200	259	4	,	,	PUNCT
ejpam-3200	259	5	217	217	NUM
ejpam-3200	259	6	-	-	SYM
ejpam-3200	259	7	225	225	NUM
ejpam-3200	259	8	,	,	PUNCT
ejpam-3200	259	9	(	(	PUNCT
ejpam-3200	259	10	1997	1997	NUM
ejpam-3200	259	11	)	)	PUNCT
ejpam-3200	259	12	.	.	PUNCT