id	sid	tid	token	lemma	pos
ejpam-5909	1	1	european	european	PROPN
ejpam-5909	1	2	journal	journal	PROPN
ejpam-5909	1	3	of	of	ADP
ejpam-5909	1	4	pure	pure	ADJ
ejpam-5909	1	5	and	and	CCONJ
ejpam-5909	1	6	applied	applied	ADJ
ejpam-5909	1	7	mathematics	mathematic	NOUN
ejpam-5909	1	8	2025	2025	NUM
ejpam-5909	1	9	,	,	PUNCT
ejpam-5909	1	10	vol	vol	NOUN
ejpam-5909	1	11	.	.	PROPN
ejpam-5909	1	12	18	18	NUM
ejpam-5909	1	13	,	,	PUNCT
ejpam-5909	1	14	issue	issue	NOUN
ejpam-5909	1	15	2	2	NUM
ejpam-5909	1	16	,	,	PUNCT
ejpam-5909	1	17	article	article	NOUN
ejpam-5909	1	18	number	number	NOUN
ejpam-5909	1	19	5909	5909	NUM
ejpam-5909	1	20	issn	issn	PROPN
ejpam-5909	1	21	1307	1307	NUM
ejpam-5909	1	22	-	-	SYM
ejpam-5909	1	23	5543	5543	NUM
ejpam-5909	1	24	–	–	PUNCT
ejpam-5909	1	25	ejpam.com	ejpam.com	X
ejpam-5909	1	26	published	publish	VERB
ejpam-5909	1	27	by	by	ADP
ejpam-5909	1	28	new	new	PROPN
ejpam-5909	1	29	york	york	PROPN
ejpam-5909	1	30	business	business	PROPN
ejpam-5909	1	31	global	global	ADJ
ejpam-5909	1	32	stieltjes	stieltjes	PROPN
ejpam-5909	1	33	limits	limit	NOUN
ejpam-5909	1	34	in	in	ADP
ejpam-5909	1	35	continuous	continuous	ADJ
ejpam-5909	1	36	function	function	NOUN
ejpam-5909	1	37	spaces	space	VERB
ejpam-5909	1	38	moch	moch	PROPN
ejpam-5909	1	39	.	.	PUNCT
ejpam-5909	2	1	alifuddin1	alifuddin1	PROPN
ejpam-5909	2	2	,	,	PUNCT
ejpam-5909	2	3	mahmud	mahmud	PROPN
ejpam-5909	2	4	yunus1,∗	yunus1,∗	PROPN
ejpam-5909	2	5	,	,	PUNCT
ejpam-5909	2	6	mohamad	mohamad	PROPN
ejpam-5909	2	7	ilham	ilham	PROPN
ejpam-5909	2	8	dwi	dwi	PROPN
ejpam-5909	2	9	firmansyah1	firmansyah1	PROPN
ejpam-5909	2	10	,	,	PUNCT
ejpam-5909	2	11	indra	indra	PROPN
ejpam-5909	2	12	cahya	cahya	PROPN
ejpam-5909	2	13	ramdani1	ramdani1	VERB
ejpam-5909	2	14	1	1	NUM
ejpam-5909	2	15	department	department	NOUN
ejpam-5909	2	16	of	of	ADP
ejpam-5909	2	17	mathematics	mathematic	NOUN
ejpam-5909	2	18	,	,	PUNCT
ejpam-5909	2	19	faculty	faculty	NOUN
ejpam-5909	2	20	of	of	ADP
ejpam-5909	2	21	sciences	science	NOUN
ejpam-5909	2	22	and	and	CCONJ
ejpam-5909	2	23	data	datum	NOUN
ejpam-5909	2	24	analytics	analytic	NOUN
ejpam-5909	2	25	,	,	PUNCT
ejpam-5909	2	26	institut	institut	PROPN
ejpam-5909	2	27	teknologi	teknologi	PROPN
ejpam-5909	2	28	sepuluh	sepuluh	PROPN
ejpam-5909	2	29	nopember	nopember	PROPN
ejpam-5909	2	30	,	,	PUNCT
ejpam-5909	2	31	surabaya	surabaya	PROPN
ejpam-5909	2	32	,	,	PUNCT
ejpam-5909	2	33	indonesia	indonesia	PROPN
ejpam-5909	2	34	abstract	abstract	NOUN
ejpam-5909	2	35	.	.	PUNCT
ejpam-5909	3	1	sir	sir	PROPN
ejpam-5909	3	2	isaac	isaac	PROPN
ejpam-5909	3	3	newton	newton	PROPN
ejpam-5909	3	4	and	and	CCONJ
ejpam-5909	3	5	gottfried	gottfried	PROPN
ejpam-5909	3	6	wilhelm	wilhelm	PROPN
ejpam-5909	3	7	leibniz	leibniz	PROPN
ejpam-5909	3	8	first	first	ADV
ejpam-5909	3	9	discovered	discover	VERB
ejpam-5909	3	10	the	the	DET
ejpam-5909	3	11	concept	concept	NOUN
ejpam-5909	3	12	of	of	ADP
ejpam-5909	3	13	limits	limit	NOUN
ejpam-5909	3	14	in	in	ADP
ejpam-5909	3	15	calculus	calculus	NOUN
ejpam-5909	3	16	in	in	ADP
ejpam-5909	3	17	the	the	DET
ejpam-5909	3	18	late	late	ADJ
ejpam-5909	3	19	17th	17th	ADJ
ejpam-5909	3	20	century	century	NOUN
ejpam-5909	3	21	.	.	PUNCT
ejpam-5909	4	1	both	both	DET
ejpam-5909	4	2	developed	develop	VERB
ejpam-5909	4	3	calculus	calculus	NOUN
ejpam-5909	4	4	with	with	ADP
ejpam-5909	4	5	different	different	ADJ
ejpam-5909	4	6	but	but	CCONJ
ejpam-5909	4	7	complementary	complementary	ADJ
ejpam-5909	4	8	approaches	approach	NOUN
ejpam-5909	4	9	and	and	CCONJ
ejpam-5909	4	10	notations	notation	NOUN
ejpam-5909	4	11	.	.	PUNCT
ejpam-5909	5	1	the	the	DET
ejpam-5909	5	2	stieltjes	stieltjes	PROPN
ejpam-5909	5	3	limit	limit	NOUN
ejpam-5909	5	4	is	be	AUX
ejpam-5909	5	5	a	a	DET
ejpam-5909	5	6	generalization	generalization	NOUN
ejpam-5909	5	7	of	of	ADP
ejpam-5909	5	8	the	the	DET
ejpam-5909	5	9	standard	standard	ADJ
ejpam-5909	5	10	limit	limit	NOUN
ejpam-5909	5	11	by	by	ADP
ejpam-5909	5	12	replacing	replace	VERB
ejpam-5909	5	13	x	x	PUNCT
ejpam-5909	5	14	approaching	approach	VERB
ejpam-5909	5	15	x0	x0	PROPN
ejpam-5909	5	16	with	with	ADP
ejpam-5909	5	17	f(x	f(x	PROPN
ejpam-5909	5	18	)	)	PUNCT
ejpam-5909	5	19	approaching	approach	VERB
ejpam-5909	5	20	f(x0	f(x0	NOUN
ejpam-5909	5	21	)	)	PUNCT
ejpam-5909	5	22	.	.	PUNCT
ejpam-5909	6	1	in	in	ADP
ejpam-5909	6	2	this	this	DET
ejpam-5909	6	3	paper	paper	NOUN
ejpam-5909	6	4	,	,	PUNCT
ejpam-5909	6	5	we	we	PRON
ejpam-5909	6	6	define	define	VERB
ejpam-5909	6	7	the	the	DET
ejpam-5909	6	8	limit	limit	NOUN
ejpam-5909	6	9	and	and	CCONJ
ejpam-5909	6	10	the	the	DET
ejpam-5909	6	11	stieltjes	stieltjes	NOUN
ejpam-5909	6	12	limit	limit	VERB
ejpam-5909	6	13	on	on	ADP
ejpam-5909	6	14	function	function	NOUN
ejpam-5909	6	15	-	-	PUNCT
ejpam-5909	6	16	valued	value	VERB
ejpam-5909	6	17	continuous	continuous	ADJ
ejpam-5909	6	18	operators	operator	NOUN
ejpam-5909	6	19	,	,	PUNCT
ejpam-5909	6	20	specifically	specifically	ADV
ejpam-5909	6	21	,	,	PUNCT
ejpam-5909	6	22	on	on	ADP
ejpam-5909	6	23	bounded	bounded	ADJ
ejpam-5909	6	24	operators	operator	NOUN
ejpam-5909	6	25	that	that	PRON
ejpam-5909	6	26	take	take	VERB
ejpam-5909	6	27	values	value	NOUN
ejpam-5909	6	28	in	in	ADP
ejpam-5909	6	29	continuous	continuous	ADJ
ejpam-5909	6	30	functions	function	NOUN
ejpam-5909	6	31	.	.	PUNCT
ejpam-5909	7	1	to	to	PART
ejpam-5909	7	2	support	support	VERB
ejpam-5909	7	3	this	this	DET
ejpam-5909	7	4	definition	definition	NOUN
ejpam-5909	7	5	,	,	PUNCT
ejpam-5909	7	6	we	we	PRON
ejpam-5909	7	7	first	first	ADV
ejpam-5909	7	8	introduce	introduce	VERB
ejpam-5909	7	9	the	the	DET
ejpam-5909	7	10	concepts	concept	NOUN
ejpam-5909	7	11	of	of	ADP
ejpam-5909	7	12	neighborhoods	neighborhood	NOUN
ejpam-5909	7	13	,	,	PUNCT
ejpam-5909	7	14	continuous	continuous	ADJ
ejpam-5909	7	15	function	function	NOUN
ejpam-5909	7	16	operators	operator	NOUN
ejpam-5909	7	17	,	,	PUNCT
ejpam-5909	7	18	increasing	increase	VERB
ejpam-5909	7	19	operators	operator	NOUN
ejpam-5909	7	20	,	,	PUNCT
ejpam-5909	7	21	strictly	strictly	ADV
ejpam-5909	7	22	increasing	increase	VERB
ejpam-5909	7	23	operators	operator	NOUN
ejpam-5909	7	24	,	,	PUNCT
ejpam-5909	7	25	decreasing	decrease	VERB
ejpam-5909	7	26	operators	operator	NOUN
ejpam-5909	7	27	,	,	PUNCT
ejpam-5909	7	28	strictly	strictly	ADV
ejpam-5909	7	29	decreasing	decrease	VERB
ejpam-5909	7	30	operators	operator	NOUN
ejpam-5909	7	31	,	,	PUNCT
ejpam-5909	7	32	and	and	CCONJ
ejpam-5909	7	33	their	their	PRON
ejpam-5909	7	34	respective	respective	ADJ
ejpam-5909	7	35	limits	limit	NOUN
ejpam-5909	7	36	in	in	ADP
ejpam-5909	7	37	function	function	NOUN
ejpam-5909	7	38	-	-	PUNCT
ejpam-5909	7	39	valued	value	VERB
ejpam-5909	7	40	operators	operator	NOUN
ejpam-5909	7	41	.	.	PUNCT
ejpam-5909	8	1	the	the	DET
ejpam-5909	8	2	results	result	NOUN
ejpam-5909	8	3	reveal	reveal	VERB
ejpam-5909	8	4	the	the	DET
ejpam-5909	8	5	necessary	necessary	ADJ
ejpam-5909	8	6	conditions	condition	NOUN
ejpam-5909	8	7	and	and	CCONJ
ejpam-5909	8	8	properties	property	NOUN
ejpam-5909	8	9	of	of	ADP
ejpam-5909	8	10	limits	limit	NOUN
ejpam-5909	8	11	and	and	CCONJ
ejpam-5909	8	12	stieltjes	stieltjes	NOUN
ejpam-5909	8	13	limits	limit	NOUN
ejpam-5909	8	14	on	on	ADP
ejpam-5909	8	15	function	function	NOUN
ejpam-5909	8	16	-	-	PUNCT
ejpam-5909	8	17	valued	value	VERB
ejpam-5909	8	18	operators	operator	NOUN
ejpam-5909	8	19	,	,	PUNCT
ejpam-5909	8	20	which	which	PRON
ejpam-5909	8	21	share	share	VERB
ejpam-5909	8	22	similarities	similarity	NOUN
ejpam-5909	8	23	with	with	ADP
ejpam-5909	8	24	limits	limit	NOUN
ejpam-5909	8	25	and	and	CCONJ
ejpam-5909	8	26	stieltjes	stieltjes	NOUN
ejpam-5909	8	27	limits	limit	NOUN
ejpam-5909	8	28	in	in	ADP
ejpam-5909	8	29	real	real	ADV
ejpam-5909	8	30	-	-	PUNCT
ejpam-5909	8	31	valued	value	VERB
ejpam-5909	8	32	functions	function	NOUN
ejpam-5909	8	33	.	.	PUNCT
ejpam-5909	9	1	these	these	DET
ejpam-5909	9	2	findings	finding	NOUN
ejpam-5909	9	3	broaden	broaden	VERB
ejpam-5909	9	4	our	our	PRON
ejpam-5909	9	5	understanding	understanding	NOUN
ejpam-5909	9	6	of	of	ADP
ejpam-5909	9	7	limit	limit	NOUN
ejpam-5909	9	8	concepts	concept	NOUN
ejpam-5909	9	9	in	in	ADP
ejpam-5909	9	10	a	a	DET
ejpam-5909	9	11	more	more	ADV
ejpam-5909	9	12	general	general	ADJ
ejpam-5909	9	13	context	context	NOUN
ejpam-5909	9	14	and	and	CCONJ
ejpam-5909	9	15	provide	provide	VERB
ejpam-5909	9	16	new	new	ADJ
ejpam-5909	9	17	insights	insight	NOUN
ejpam-5909	9	18	into	into	ADP
ejpam-5909	9	19	operator	operator	NOUN
ejpam-5909	9	20	analysis	analysis	NOUN
ejpam-5909	9	21	.	.	PUNCT
ejpam-5909	10	1	2020	2020	NUM
ejpam-5909	10	2	mathematics	mathematic	NOUN
ejpam-5909	10	3	subject	subject	NOUN
ejpam-5909	10	4	classifications	classification	NOUN
ejpam-5909	10	5	:	:	PUNCT
ejpam-5909	10	6	26a42	26a42	NUM
ejpam-5909	10	7	,	,	PUNCT
ejpam-5909	10	8	47g10	47g10	NUM
ejpam-5909	10	9	,	,	PUNCT
ejpam-5909	10	10	47b38	47b38	NUM
ejpam-5909	10	11	,	,	PUNCT
ejpam-5909	10	12	46e30	46e30	NUM
ejpam-5909	10	13	,	,	PUNCT
ejpam-5909	10	14	28a33	28a33	NUM
ejpam-5909	10	15	key	key	ADJ
ejpam-5909	10	16	words	word	NOUN
ejpam-5909	10	17	and	and	CCONJ
ejpam-5909	10	18	phrases	phrase	NOUN
ejpam-5909	10	19	:	:	PUNCT
ejpam-5909	10	20	stieltjes	stieltjes	PROPN
ejpam-5909	10	21	limit	limit	PROPN
ejpam-5909	10	22	,	,	PUNCT
ejpam-5909	10	23	function	function	NOUN
ejpam-5909	10	24	-	-	PUNCT
ejpam-5909	10	25	valued	value	VERB
ejpam-5909	10	26	continuous	continuous	ADJ
ejpam-5909	10	27	operator	operator	NOUN
ejpam-5909	10	28	,	,	PUNCT
ejpam-5909	10	29	stieltjes	stieltjes	PROPN
ejpam-5909	10	30	limit	limit	VERB
ejpam-5909	10	31	on	on	ADP
ejpam-5909	10	32	function	function	NOUN
ejpam-5909	10	33	-	-	PUNCT
ejpam-5909	10	34	valued	value	VERB
ejpam-5909	10	35	continuous	continuous	ADJ
ejpam-5909	10	36	operators	operator	NOUN
ejpam-5909	10	37	,	,	PUNCT
ejpam-5909	10	38	functional	functional	ADJ
ejpam-5909	10	39	analysis	analysis	NOUN
ejpam-5909	10	40	1	1	NUM
ejpam-5909	10	41	.	.	PUNCT
ejpam-5909	11	1	introduction	introduction	NOUN
ejpam-5909	11	2	mathematics	mathematic	NOUN
ejpam-5909	11	3	continuously	continuously	ADV
ejpam-5909	11	4	evolves	evolve	VERB
ejpam-5909	11	5	,	,	PUNCT
ejpam-5909	11	6	with	with	ADP
ejpam-5909	11	7	integral	integral	ADJ
ejpam-5909	11	8	theory	theory	NOUN
ejpam-5909	11	9	being	be	AUX
ejpam-5909	11	10	one	one	NUM
ejpam-5909	11	11	of	of	ADP
ejpam-5909	11	12	its	its	PRON
ejpam-5909	11	13	fundamental	fundamental	ADJ
ejpam-5909	11	14	branches	branch	NOUN
ejpam-5909	11	15	,	,	PUNCT
ejpam-5909	11	16	which	which	PRON
ejpam-5909	11	17	undergoes	undergo	VERB
ejpam-5909	11	18	ongoing	ongoing	ADJ
ejpam-5909	11	19	research	research	NOUN
ejpam-5909	11	20	and	and	CCONJ
ejpam-5909	11	21	development	development	NOUN
ejpam-5909	11	22	.	.	PUNCT
ejpam-5909	12	1	integral	integral	ADJ
ejpam-5909	12	2	theory	theory	NOUN
ejpam-5909	12	3	plays	play	VERB
ejpam-5909	12	4	a	a	DET
ejpam-5909	12	5	crucial	crucial	ADJ
ejpam-5909	12	6	role	role	NOUN
ejpam-5909	12	7	in	in	ADP
ejpam-5909	12	8	various	various	ADJ
ejpam-5909	12	9	mathematical	mathematical	ADJ
ejpam-5909	12	10	applications	application	NOUN
ejpam-5909	12	11	,	,	PUNCT
ejpam-5909	12	12	particularly	particularly	ADV
ejpam-5909	12	13	in	in	ADP
ejpam-5909	12	14	solving	solve	VERB
ejpam-5909	12	15	engineering	engineering	NOUN
ejpam-5909	12	16	problems	problem	NOUN
ejpam-5909	12	17	[	[	X
ejpam-5909	12	18	1	1	NUM
ejpam-5909	12	19	]	]	PUNCT
ejpam-5909	12	20	.	.	PUNCT
ejpam-5909	13	1	for	for	ADP
ejpam-5909	13	2	instance	instance	NOUN
ejpam-5909	13	3	,	,	PUNCT
ejpam-5909	13	4	in	in	ADP
ejpam-5909	13	5	financial	financial	ADJ
ejpam-5909	13	6	engineering	engineering	NOUN
ejpam-5909	13	7	,	,	PUNCT
ejpam-5909	13	8	integrals	integral	NOUN
ejpam-5909	13	9	are	be	AUX
ejpam-5909	13	10	utilized	utilize	VERB
ejpam-5909	13	11	in	in	ADP
ejpam-5909	13	12	investment	investment	NOUN
ejpam-5909	13	13	calculations	calculation	NOUN
ejpam-5909	14	1	[	[	X
ejpam-5909	14	2	2	2	NUM
ejpam-5909	14	3	]	]	PUNCT
ejpam-5909	14	4	;	;	PUNCT
ejpam-5909	14	5	in	in	ADP
ejpam-5909	14	6	mechanical	mechanical	ADJ
ejpam-5909	14	7	engineering	engineering	NOUN
ejpam-5909	14	8	,	,	PUNCT
ejpam-5909	14	9	integrals	integral	NOUN
ejpam-5909	14	10	are	be	AUX
ejpam-5909	14	11	applied	apply	VERB
ejpam-5909	14	12	in	in	ADP
ejpam-5909	14	13	fluid	fluid	ADJ
ejpam-5909	14	14	mechanics	mechanic	NOUN
ejpam-5909	14	15	[	[	X
ejpam-5909	14	16	3	3	NUM
ejpam-5909	14	17	]	]	PUNCT
ejpam-5909	14	18	;	;	PUNCT
ejpam-5909	14	19	and	and	CCONJ
ejpam-5909	14	20	in	in	ADP
ejpam-5909	14	21	electrical	electrical	ADJ
ejpam-5909	14	22	engineering	engineering	NOUN
ejpam-5909	14	23	,	,	PUNCT
ejpam-5909	14	24	integral	integral	ADJ
ejpam-5909	14	25	analysis	analysis	NOUN
ejpam-5909	14	26	helps	help	VERB
ejpam-5909	14	27	determine	determine	VERB
ejpam-5909	14	28	the	the	DET
ejpam-5909	14	29	current	current	ADJ
ejpam-5909	14	30	,	,	PUNCT
ejpam-5909	14	31	voltage	voltage	NOUN
ejpam-5909	14	32	,	,	PUNCT
ejpam-5909	14	33	and	and	CCONJ
ejpam-5909	14	34	power	power	NOUN
ejpam-5909	14	35	in	in	ADP
ejpam-5909	14	36	electrical	electrical	ADJ
ejpam-5909	14	37	circuits	circuit	NOUN
ejpam-5909	14	38	[	[	X
ejpam-5909	14	39	4	4	NUM
ejpam-5909	14	40	]	]	PUNCT
ejpam-5909	14	41	.	.	PUNCT
ejpam-5909	15	1	isaac	isaac	PROPN
ejpam-5909	15	2	newton	newton	PROPN
ejpam-5909	15	3	(	(	PUNCT
ejpam-5909	15	4	1642–1727	1642–1727	NUM
ejpam-5909	15	5	)	)	PUNCT
ejpam-5909	15	6	and	and	CCONJ
ejpam-5909	15	7	gottfried	gottfried	PROPN
ejpam-5909	15	8	wilhelm	wilhelm	PROPN
ejpam-5909	15	9	leibniz	leibniz	PROPN
ejpam-5909	15	10	(	(	PUNCT
ejpam-5909	15	11	1646–1716	1646–1716	NUM
ejpam-5909	15	12	)	)	PUNCT
ejpam-5909	15	13	independently	independently	ADV
ejpam-5909	15	14	explored	explore	VERB
ejpam-5909	15	15	the	the	DET
ejpam-5909	15	16	fundamental	fundamental	ADJ
ejpam-5909	15	17	concept	concept	NOUN
ejpam-5909	15	18	of	of	ADP
ejpam-5909	15	19	integrals	integral	NOUN
ejpam-5909	15	20	.	.	PUNCT
ejpam-5909	16	1	their	their	PRON
ejpam-5909	16	2	work	work	NOUN
ejpam-5909	16	3	laid	lay	VERB
ejpam-5909	16	4	the	the	DET
ejpam-5909	16	5	foundation	foundation	NOUN
ejpam-5909	16	6	for	for	ADP
ejpam-5909	16	7	differentiation	differentiation	NOUN
ejpam-5909	16	8	and	and	CCONJ
ejpam-5909	16	9	integration	integration	NOUN
ejpam-5909	16	10	,	,	PUNCT
ejpam-5909	16	11	leading	lead	VERB
ejpam-5909	16	12	to	to	ADP
ejpam-5909	16	13	the	the	DET
ejpam-5909	16	14	continuous	continuous	ADJ
ejpam-5909	16	15	advancement	advancement	NOUN
ejpam-5909	16	16	of	of	ADP
ejpam-5909	16	17	integral	integral	ADJ
ejpam-5909	16	18	theory	theory	NOUN
ejpam-5909	16	19	,	,	PUNCT
ejpam-5909	16	20	∗corresponding	∗corresponde	VERB
ejpam-5909	16	21	author	author	NOUN
ejpam-5909	16	22	.	.	PUNCT
ejpam-5909	17	1	doi	doi	NOUN
ejpam-5909	17	2	:	:	PUNCT
ejpam-5909	17	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5909	https://doi.org/10.29020/nybg.ejpam.v18i2.5909	ADJ
ejpam-5909	17	4	email	email	NOUN
ejpam-5909	17	5	addresses	address	NOUN
ejpam-5909	17	6	:	:	PUNCT
ejpam-5909	17	7	yunusm@matematika.its.ac.id	yunusm@matematika.its.ac.id	PROPN
ejpam-5909	17	8	(	(	PUNCT
ejpam-5909	17	9	m.	m.	NOUN
ejpam-5909	17	10	yunus	yunus	PROPN
ejpam-5909	17	11	)	)	PUNCT
ejpam-5909	17	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5909	18	1	1	1	NUM
ejpam-5909	18	2	copyright	copyright	NOUN
ejpam-5909	18	3	:	:	PUNCT
ejpam-5909	18	4	©	©	PROPN
ejpam-5909	18	5	2025	2025	NUM
ejpam-5909	18	6	the	the	DET
ejpam-5909	18	7	author(s	author(s	NOUN
ejpam-5909	18	8	)	)	PUNCT
ejpam-5909	18	9	.	.	PUNCT
ejpam-5909	19	1	(	(	PUNCT
ejpam-5909	19	2	cc	cc	NOUN
ejpam-5909	19	3	by	by	ADP
ejpam-5909	19	4	-	-	PUNCT
ejpam-5909	19	5	nc	nc	PROPN
ejpam-5909	19	6	4.0	4.0	NUM
ejpam-5909	19	7	)	)	PUNCT
ejpam-5909	19	8	m.	m.	NOUN
ejpam-5909	19	9	alifuddin	alifuddin	VERB
ejpam-5909	19	10	et	et	PROPN
ejpam-5909	19	11	al	al	PROPN
ejpam-5909	19	12	.	.	PUNCT
ejpam-5909	19	13	/	/	SYM
ejpam-5909	19	14	eur	eur	PROPN
ejpam-5909	19	15	.	.	PUNCT
ejpam-5909	20	1	j.	j.	PROPN
ejpam-5909	20	2	pure	pure	PROPN
ejpam-5909	20	3	appl	appl	PROPN
ejpam-5909	20	4	.	.	PROPN
ejpam-5909	20	5	math	math	PROPN
ejpam-5909	20	6	,	,	PUNCT
ejpam-5909	20	7	18	18	NUM
ejpam-5909	20	8	(	(	PUNCT
ejpam-5909	20	9	2	2	NUM
ejpam-5909	20	10	)	)	PUNCT
ejpam-5909	20	11	(	(	PUNCT
ejpam-5909	20	12	2025	2025	NUM
ejpam-5909	20	13	)	)	PUNCT
ejpam-5909	20	14	,	,	PUNCT
ejpam-5909	20	15	5909	5909	NUM
ejpam-5909	20	16	2	2	NUM
ejpam-5909	20	17	of	of	ADP
ejpam-5909	20	18	17	17	NUM
ejpam-5909	20	19	including	include	VERB
ejpam-5909	20	20	its	its	PRON
ejpam-5909	20	21	modern	modern	ADJ
ejpam-5909	20	22	applications	application	NOUN
ejpam-5909	20	23	[	[	X
ejpam-5909	20	24	5	5	NUM
ejpam-5909	20	25	]	]	PUNCT
ejpam-5909	20	26	.	.	PUNCT
ejpam-5909	21	1	one	one	NUM
ejpam-5909	21	2	significant	significant	ADJ
ejpam-5909	21	3	development	development	NOUN
ejpam-5909	21	4	in	in	ADP
ejpam-5909	21	5	integral	integral	ADJ
ejpam-5909	21	6	theory	theory	NOUN
ejpam-5909	21	7	is	be	AUX
ejpam-5909	21	8	its	its	PRON
ejpam-5909	21	9	extension	extension	NOUN
ejpam-5909	21	10	to	to	ADP
ejpam-5909	21	11	function	function	NOUN
ejpam-5909	21	12	spaces	space	NOUN
ejpam-5909	21	13	,	,	PUNCT
ejpam-5909	21	14	particularly	particularly	ADV
ejpam-5909	21	15	for	for	ADP
ejpam-5909	21	16	continuous	continuous	ADJ
ejpam-5909	21	17	functions	function	NOUN
ejpam-5909	21	18	[	[	X
ejpam-5909	21	19	6	6	NUM
ejpam-5909	21	20	]	]	PUNCT
ejpam-5909	21	21	.	.	PUNCT
ejpam-5909	22	1	in	in	ADP
ejpam-5909	22	2	the	the	DET
ejpam-5909	22	3	19th	19th	ADJ
ejpam-5909	22	4	century	century	NOUN
ejpam-5909	22	5	,	,	PUNCT
ejpam-5909	22	6	german	german	ADJ
ejpam-5909	22	7	mathematician	mathematician	ADJ
ejpam-5909	22	8	georg	georg	PROPN
ejpam-5909	22	9	friedrich	friedrich	PROPN
ejpam-5909	22	10	bernhard	bernhard	PROPN
ejpam-5909	22	11	riemann	riemann	PROPN
ejpam-5909	22	12	(	(	PUNCT
ejpam-5909	22	13	1826	1826	NUM
ejpam-5909	22	14	–	–	SYM
ejpam-5909	22	15	1866	1866	NUM
ejpam-5909	22	16	)	)	PUNCT
ejpam-5909	22	17	formally	formally	ADV
ejpam-5909	22	18	defined	define	VERB
ejpam-5909	22	19	the	the	DET
ejpam-5909	22	20	concept	concept	NOUN
ejpam-5909	22	21	of	of	ADP
ejpam-5909	22	22	definite	definite	ADJ
ejpam-5909	22	23	integrals	integral	NOUN
ejpam-5909	22	24	,	,	PUNCT
ejpam-5909	22	25	even	even	ADV
ejpam-5909	22	26	though	though	SCONJ
ejpam-5909	22	27	newton	newton	PROPN
ejpam-5909	22	28	and	and	CCONJ
ejpam-5909	22	29	leibniz	leibniz	PROPN
ejpam-5909	22	30	had	have	AUX
ejpam-5909	22	31	already	already	ADV
ejpam-5909	22	32	established	establish	VERB
ejpam-5909	22	33	the	the	DET
ejpam-5909	22	34	fundamental	fundamental	ADJ
ejpam-5909	22	35	theorem	theorem	NOUN
ejpam-5909	22	36	of	of	ADP
ejpam-5909	22	37	calculus	calculus	NOUN
ejpam-5909	22	38	.	.	PUNCT
ejpam-5909	23	1	due	due	ADP
ejpam-5909	23	2	to	to	ADP
ejpam-5909	23	3	his	his	PRON
ejpam-5909	23	4	contributions	contribution	NOUN
ejpam-5909	23	5	to	to	ADP
ejpam-5909	23	6	integral	integral	ADJ
ejpam-5909	23	7	theory	theory	NOUN
ejpam-5909	23	8	,	,	PUNCT
ejpam-5909	23	9	the	the	DET
ejpam-5909	23	10	definite	definite	ADJ
ejpam-5909	23	11	integral	integral	NOUN
ejpam-5909	23	12	is	be	AUX
ejpam-5909	23	13	often	often	ADV
ejpam-5909	23	14	referred	refer	VERB
ejpam-5909	23	15	to	to	ADP
ejpam-5909	23	16	as	as	SCONJ
ejpam-5909	23	17	the	the	DET
ejpam-5909	23	18	riemann	riemann	PROPN
ejpam-5909	23	19	integral	integral	ADJ
ejpam-5909	24	1	[	[	X
ejpam-5909	24	2	7	7	NUM
ejpam-5909	24	3	]	]	PUNCT
ejpam-5909	24	4	.	.	PUNCT
ejpam-5909	25	1	this	this	DET
ejpam-5909	25	2	definition	definition	NOUN
ejpam-5909	25	3	serves	serve	VERB
ejpam-5909	25	4	as	as	ADP
ejpam-5909	25	5	the	the	DET
ejpam-5909	25	6	foundation	foundation	NOUN
ejpam-5909	25	7	for	for	ADP
ejpam-5909	25	8	solving	solve	VERB
ejpam-5909	25	9	various	various	ADJ
ejpam-5909	25	10	mathematical	mathematical	ADJ
ejpam-5909	25	11	problems	problem	NOUN
ejpam-5909	25	12	in	in	ADP
ejpam-5909	25	13	elementary	elementary	ADJ
ejpam-5909	25	14	calculus	calculus	NOUN
ejpam-5909	25	15	[	[	X
ejpam-5909	25	16	8	8	NUM
ejpam-5909	25	17	]	]	PUNCT
ejpam-5909	25	18	.	.	PUNCT
ejpam-5909	26	1	further	further	ADJ
ejpam-5909	26	2	advancements	advancement	NOUN
ejpam-5909	26	3	in	in	ADP
ejpam-5909	26	4	integral	integral	ADJ
ejpam-5909	26	5	theory	theory	NOUN
ejpam-5909	26	6	led	lead	VERB
ejpam-5909	26	7	to	to	ADP
ejpam-5909	26	8	the	the	DET
ejpam-5909	26	9	introduction	introduction	NOUN
ejpam-5909	26	10	of	of	ADP
ejpam-5909	26	11	a	a	DET
ejpam-5909	26	12	generalized	generalized	ADJ
ejpam-5909	26	13	form	form	NOUN
ejpam-5909	26	14	of	of	ADP
ejpam-5909	26	15	the	the	DET
ejpam-5909	26	16	riemann	riemann	PROPN
ejpam-5909	26	17	integral	integral	PROPN
ejpam-5909	26	18	,	,	PUNCT
ejpam-5909	26	19	known	know	VERB
ejpam-5909	26	20	as	as	ADP
ejpam-5909	26	21	the	the	DET
ejpam-5909	26	22	riemann	riemann	PROPN
ejpam-5909	26	23	-	-	PUNCT
ejpam-5909	26	24	stieltjes	stieltjes	PROPN
ejpam-5909	26	25	integral	integral	ADJ
ejpam-5909	26	26	,	,	PUNCT
ejpam-5909	26	27	which	which	PRON
ejpam-5909	26	28	addresses	address	VERB
ejpam-5909	26	29	functions	function	NOUN
ejpam-5909	26	30	that	that	PRON
ejpam-5909	26	31	are	be	AUX
ejpam-5909	26	32	not	not	PART
ejpam-5909	26	33	riemann	riemann	PROPN
ejpam-5909	26	34	-	-	PUNCT
ejpam-5909	26	35	integrable	integrable	ADJ
ejpam-5909	26	36	[	[	X
ejpam-5909	26	37	9	9	NUM
ejpam-5909	26	38	]	]	PUNCT
ejpam-5909	26	39	.	.	PUNCT
ejpam-5909	27	1	this	this	DET
ejpam-5909	27	2	integral	integral	ADJ
ejpam-5909	27	3	was	be	AUX
ejpam-5909	27	4	first	first	ADV
ejpam-5909	27	5	introduced	introduce	VERB
ejpam-5909	27	6	by	by	ADP
ejpam-5909	27	7	thomas	thomas	PROPN
ejpam-5909	27	8	joannes	joannes	PROPN
ejpam-5909	27	9	stieltjes	stieltjes	PROPN
ejpam-5909	27	10	in	in	ADP
ejpam-5909	27	11	1894	1894	NUM
ejpam-5909	27	12	[	[	X
ejpam-5909	27	13	10	10	NUM
ejpam-5909	27	14	]	]	PUNCT
ejpam-5909	27	15	.	.	PUNCT
ejpam-5909	28	1	the	the	DET
ejpam-5909	28	2	riemann	riemann	PROPN
ejpam-5909	28	3	-	-	PUNCT
ejpam-5909	28	4	stieltjes	stieltjes	PROPN
ejpam-5909	28	5	integral	integral	ADJ
ejpam-5909	28	6	extends	extend	VERB
ejpam-5909	28	7	the	the	DET
ejpam-5909	28	8	riemann	riemann	PROPN
ejpam-5909	28	9	integral	integral	ADJ
ejpam-5909	28	10	by	by	ADP
ejpam-5909	28	11	replacing	replace	VERB
ejpam-5909	28	12	the	the	DET
ejpam-5909	28	13	variable	variable	NOUN
ejpam-5909	28	14	of	of	ADP
ejpam-5909	28	15	integration	integration	NOUN
ejpam-5909	28	16	x	x	PUNCT
ejpam-5909	28	17	with	with	ADP
ejpam-5909	28	18	a	a	DET
ejpam-5909	28	19	function	function	NOUN
ejpam-5909	28	20	r(x	r(x	NOUN
ejpam-5909	28	21	)	)	PUNCT
ejpam-5909	28	22	,	,	PUNCT
ejpam-5909	28	23	thereby	thereby	ADV
ejpam-5909	28	24	generalizing	generalize	VERB
ejpam-5909	28	25	the	the	DET
ejpam-5909	28	26	concept	concept	NOUN
ejpam-5909	28	27	to	to	PART
ejpam-5909	28	28	accommodate	accommodate	VERB
ejpam-5909	28	29	a	a	DET
ejpam-5909	28	30	broader	broad	ADJ
ejpam-5909	28	31	class	class	NOUN
ejpam-5909	28	32	of	of	ADP
ejpam-5909	28	33	functions	function	NOUN
ejpam-5909	28	34	[	[	X
ejpam-5909	28	35	10	10	NUM
ejpam-5909	28	36	]	]	PUNCT
ejpam-5909	28	37	.	.	PUNCT
ejpam-5909	29	1	several	several	ADJ
ejpam-5909	29	2	studies	study	NOUN
ejpam-5909	29	3	have	have	AUX
ejpam-5909	29	4	investigated	investigate	VERB
ejpam-5909	29	5	the	the	DET
ejpam-5909	29	6	riemann	riemann	PROPN
ejpam-5909	29	7	-	-	PUNCT
ejpam-5909	29	8	stieltjes	stieltjes	NOUN
ejpam-5909	29	9	integral	integral	ADJ
ejpam-5909	29	10	with	with	ADP
ejpam-5909	29	11	real	real	ADJ
ejpam-5909	29	12	-	-	PUNCT
ejpam-5909	29	13	number	number	NOUN
ejpam-5909	29	14	boundaries	boundary	NOUN
ejpam-5909	29	15	,	,	PUNCT
ejpam-5909	29	16	including	include	VERB
ejpam-5909	29	17	works	work	NOUN
ejpam-5909	29	18	by	by	ADP
ejpam-5909	29	19	gregory	gregory	PROPN
ejpam-5909	29	20	convertito	convertito	PROPN
ejpam-5909	29	21	and	and	CCONJ
ejpam-5909	29	22	david	david	PROPN
ejpam-5909	29	23	cruz	cruz	PROPN
ejpam-5909	29	24	-	-	PUNCT
ejpam-5909	29	25	uribe	uribe	PROPN
ejpam-5909	30	1	[	[	X
ejpam-5909	30	2	11	11	NUM
ejpam-5909	30	3	]	]	PUNCT
ejpam-5909	30	4	,	,	PUNCT
ejpam-5909	30	5	as	as	ADV
ejpam-5909	30	6	well	well	ADV
ejpam-5909	30	7	as	as	ADP
ejpam-5909	30	8	joong	joong	PROPN
ejpam-5909	30	9	kwoen	kwoen	PROPN
ejpam-5909	30	10	lee	lee	PROPN
ejpam-5909	30	11	and	and	CCONJ
ejpam-5909	30	12	han	han	PROPN
ejpam-5909	30	13	ju	ju	PROPN
ejpam-5909	30	14	lee	lee	PROPN
ejpam-5909	31	1	[	[	X
ejpam-5909	31	2	12	12	NUM
ejpam-5909	31	3	]	]	PUNCT
ejpam-5909	31	4	.	.	PUNCT
ejpam-5909	32	1	however	however	ADV
ejpam-5909	32	2	,	,	PUNCT
ejpam-5909	32	3	this	this	DET
ejpam-5909	32	4	study	study	NOUN
ejpam-5909	32	5	defines	define	VERB
ejpam-5909	32	6	the	the	DET
ejpam-5909	32	7	riemann	riemann	PROPN
ejpam-5909	32	8	-	-	PUNCT
ejpam-5909	32	9	stieltjes	stieltjes	NOUN
ejpam-5909	32	10	integral	integral	ADJ
ejpam-5909	32	11	with	with	ADP
ejpam-5909	32	12	integration	integration	NOUN
ejpam-5909	32	13	limits	limit	NOUN
ejpam-5909	32	14	defined	define	VERB
ejpam-5909	32	15	by	by	ADP
ejpam-5909	32	16	continuous	continuous	ADJ
ejpam-5909	32	17	functions	function	NOUN
ejpam-5909	32	18	on	on	ADP
ejpam-5909	32	19	[	[	X
ejpam-5909	32	20	a	a	X
ejpam-5909	32	21	,	,	PUNCT
ejpam-5909	32	22	b	b	NOUN
ejpam-5909	32	23	]	]	PUNCT
ejpam-5909	32	24	.	.	PUNCT
ejpam-5909	33	1	using	use	VERB
ejpam-5909	33	2	the	the	DET
ejpam-5909	33	3	ordering	ordering	NOUN
ejpam-5909	33	4	relation	relation	NOUN
ejpam-5909	33	5	f	f	PROPN
ejpam-5909	33	6	⪯	⪯	PROPN
ejpam-5909	33	7	g	g	PROPN
ejpam-5909	33	8	,	,	PUNCT
ejpam-5909	33	9	which	which	PRON
ejpam-5909	33	10	implies	imply	VERB
ejpam-5909	33	11	f(x	f(x	PROPN
ejpam-5909	33	12	)	)	PUNCT
ejpam-5909	33	13	≤	≤	NOUN
ejpam-5909	33	14	g(x	g(x	NOUN
ejpam-5909	33	15	)	)	PUNCT
ejpam-5909	33	16	for	for	ADP
ejpam-5909	33	17	all	all	DET
ejpam-5909	33	18	x	x	NOUN
ejpam-5909	33	19	in	in	ADP
ejpam-5909	33	20	[	[	X
ejpam-5909	33	21	a	a	DET
ejpam-5909	33	22	,	,	PUNCT
ejpam-5909	33	23	b	b	NOUN
ejpam-5909	33	24	]	]	X
ejpam-5909	33	25	,	,	PUNCT
ejpam-5909	33	26	this	this	DET
ejpam-5909	33	27	research	research	NOUN
ejpam-5909	33	28	aims	aim	VERB
ejpam-5909	33	29	to	to	PART
ejpam-5909	33	30	establish	establish	VERB
ejpam-5909	33	31	the	the	DET
ejpam-5909	33	32	properties	property	NOUN
ejpam-5909	33	33	of	of	ADP
ejpam-5909	33	34	the	the	DET
ejpam-5909	33	35	riemann	riemann	PROPN
ejpam-5909	33	36	-	-	PUNCT
ejpam-5909	33	37	stieltjes	stieltjes	NOUN
ejpam-5909	33	38	integral	integral	ADJ
ejpam-5909	33	39	under	under	ADP
ejpam-5909	33	40	these	these	DET
ejpam-5909	33	41	integration	integration	NOUN
ejpam-5909	33	42	limits	limit	NOUN
ejpam-5909	33	43	.	.	PUNCT
ejpam-5909	34	1	by	by	ADP
ejpam-5909	34	2	extending	extend	VERB
ejpam-5909	34	3	the	the	DET
ejpam-5909	34	4	integral	integral	ADJ
ejpam-5909	34	5	boundaries	boundary	NOUN
ejpam-5909	34	6	to	to	ADP
ejpam-5909	34	7	continuous	continuous	ADJ
ejpam-5909	34	8	functions	function	NOUN
ejpam-5909	34	9	,	,	PUNCT
ejpam-5909	34	10	we	we	PRON
ejpam-5909	34	11	uncover	uncover	VERB
ejpam-5909	34	12	new	new	ADJ
ejpam-5909	34	13	properties	property	NOUN
ejpam-5909	34	14	and	and	CCONJ
ejpam-5909	34	15	insights	insight	NOUN
ejpam-5909	34	16	that	that	PRON
ejpam-5909	34	17	further	far	ADV
ejpam-5909	34	18	enrich	enrich	VERB
ejpam-5909	34	19	the	the	DET
ejpam-5909	34	20	integral	integral	ADJ
ejpam-5909	34	21	theory	theory	NOUN
ejpam-5909	34	22	landscape	landscape	NOUN
ejpam-5909	34	23	.	.	PUNCT
ejpam-5909	35	1	2	2	X
ejpam-5909	35	2	.	.	X
ejpam-5909	35	3	preliminaries	preliminary	NOUN
ejpam-5909	35	4	this	this	DET
ejpam-5909	35	5	study	study	NOUN
ejpam-5909	35	6	focuses	focus	VERB
ejpam-5909	35	7	on	on	ADP
ejpam-5909	35	8	the	the	DET
ejpam-5909	35	9	concept	concept	NOUN
ejpam-5909	35	10	of	of	ADP
ejpam-5909	35	11	the	the	DET
ejpam-5909	35	12	limit	limit	NOUN
ejpam-5909	35	13	of	of	ADP
ejpam-5909	35	14	operator	operator	NOUN
ejpam-5909	35	15	-	-	PUNCT
ejpam-5909	35	16	valued	value	VERB
ejpam-5909	35	17	continuous	continuous	ADJ
ejpam-5909	35	18	functions	function	NOUN
ejpam-5909	35	19	and	and	CCONJ
ejpam-5909	35	20	the	the	DET
ejpam-5909	35	21	stieltjes	stieltjes	NOUN
ejpam-5909	35	22	limit	limit	VERB
ejpam-5909	35	23	for	for	ADP
ejpam-5909	35	24	operator	operator	NOUN
ejpam-5909	35	25	-	-	PUNCT
ejpam-5909	35	26	valued	value	VERB
ejpam-5909	35	27	functions	function	NOUN
ejpam-5909	35	28	.	.	PUNCT
ejpam-5909	36	1	therefore	therefore	ADV
ejpam-5909	36	2	,	,	PUNCT
ejpam-5909	36	3	a	a	DET
ejpam-5909	36	4	deep	deep	ADJ
ejpam-5909	36	5	understanding	understanding	NOUN
ejpam-5909	36	6	of	of	ADP
ejpam-5909	36	7	the	the	DET
ejpam-5909	36	8	stieltjes	stieltjes	NOUN
ejpam-5909	36	9	limit	limit	NOUN
ejpam-5909	36	10	and	and	CCONJ
ejpam-5909	36	11	continuous	continuous	ADJ
ejpam-5909	36	12	functions	function	NOUN
ejpam-5909	36	13	in	in	ADP
ejpam-5909	36	14	the	the	DET
ejpam-5909	36	15	space	space	NOUN
ejpam-5909	36	16	c[a	c[a	NOUN
ejpam-5909	36	17	,	,	PUNCT
ejpam-5909	36	18	b	b	AUX
ejpam-5909	36	19	]	]	PUNCT
ejpam-5909	36	20	is	be	AUX
ejpam-5909	36	21	required	require	VERB
ejpam-5909	36	22	.	.	PUNCT
ejpam-5909	37	1	definition	definition	NOUN
ejpam-5909	37	2	1	1	NUM
ejpam-5909	37	3	.	.	PUNCT
ejpam-5909	38	1	[	[	X
ejpam-5909	38	2	13	13	NUM
ejpam-5909	38	3	]	]	PUNCT
ejpam-5909	38	4	the	the	DET
ejpam-5909	38	5	set	set	NOUN
ejpam-5909	38	6	c[a	c[a	NOUN
ejpam-5909	38	7	,	,	PUNCT
ejpam-5909	38	8	b	b	NOUN
ejpam-5909	38	9	]	]	PUNCT
ejpam-5909	38	10	consists	consist	VERB
ejpam-5909	38	11	of	of	ADP
ejpam-5909	38	12	all	all	DET
ejpam-5909	38	13	real	real	ADV
ejpam-5909	38	14	-	-	PUNCT
ejpam-5909	38	15	valued	value	VERB
ejpam-5909	38	16	continuous	continuous	ADJ
ejpam-5909	38	17	functions	function	NOUN
ejpam-5909	38	18	defined	define	VERB
ejpam-5909	38	19	on	on	ADP
ejpam-5909	38	20	[	[	X
ejpam-5909	38	21	a	a	X
ejpam-5909	38	22	,	,	PUNCT
ejpam-5909	38	23	b	b	NOUN
ejpam-5909	38	24	]	]	X
ejpam-5909	38	25	⊂	⊂	PROPN
ejpam-5909	38	26	r.	r.	PROPN
ejpam-5909	38	27	in	in	ADP
ejpam-5909	38	28	defining	define	VERB
ejpam-5909	38	29	and	and	CCONJ
ejpam-5909	38	30	proving	prove	VERB
ejpam-5909	38	31	theorems	theorem	NOUN
ejpam-5909	38	32	,	,	PUNCT
ejpam-5909	38	33	a	a	DET
ejpam-5909	38	34	unit	unit	NOUN
ejpam-5909	38	35	function	function	NOUN
ejpam-5909	38	36	in	in	ADP
ejpam-5909	38	37	c[a	c[a	NUM
ejpam-5909	38	38	,	,	PUNCT
ejpam-5909	38	39	b	b	AUX
ejpam-5909	38	40	]	]	X
ejpam-5909	38	41	is	be	AUX
ejpam-5909	38	42	required	require	VERB
ejpam-5909	38	43	to	to	PART
ejpam-5909	38	44	ensure	ensure	VERB
ejpam-5909	38	45	that	that	SCONJ
ejpam-5909	38	46	the	the	DET
ejpam-5909	38	47	results	result	NOUN
ejpam-5909	38	48	remain	remain	VERB
ejpam-5909	38	49	continuous	continuous	ADJ
ejpam-5909	38	50	functions	function	NOUN
ejpam-5909	38	51	.	.	PUNCT
ejpam-5909	39	1	the	the	DET
ejpam-5909	39	2	unit	unit	NOUN
ejpam-5909	39	3	function	function	NOUN
ejpam-5909	39	4	is	be	AUX
ejpam-5909	39	5	defined	define	VERB
ejpam-5909	39	6	as	as	SCONJ
ejpam-5909	39	7	follows	follow	VERB
ejpam-5909	39	8	:	:	PUNCT
ejpam-5909	39	9	definition	definition	NOUN
ejpam-5909	39	10	2	2	NUM
ejpam-5909	39	11	.	.	PUNCT
ejpam-5909	40	1	[	[	X
ejpam-5909	40	2	6	6	NUM
ejpam-5909	40	3	]	]	PUNCT
ejpam-5909	40	4	the	the	DET
ejpam-5909	40	5	function	function	NOUN
ejpam-5909	40	6	e	e	PROPN
ejpam-5909	40	7	is	be	AUX
ejpam-5909	40	8	the	the	DET
ejpam-5909	40	9	unit	unit	NOUN
ejpam-5909	40	10	element	element	NOUN
ejpam-5909	40	11	in	in	ADP
ejpam-5909	40	12	c[a	c[a	PROPN
ejpam-5909	40	13	,	,	PUNCT
ejpam-5909	40	14	b	b	NOUN
ejpam-5909	40	15	]	]	X
ejpam-5909	40	16	,	,	PUNCT
ejpam-5909	40	17	where	where	SCONJ
ejpam-5909	40	18	e(x	e(x	NUM
ejpam-5909	40	19	)	)	PUNCT
ejpam-5909	40	20	=	=	SYM
ejpam-5909	40	21	1	1	NUM
ejpam-5909	40	22	for	for	ADP
ejpam-5909	40	23	all	all	DET
ejpam-5909	40	24	x	x	NOUN
ejpam-5909	40	25	in	in	ADP
ejpam-5909	40	26	the	the	DET
ejpam-5909	40	27	interval	interval	NOUN
ejpam-5909	40	28	[	[	X
ejpam-5909	40	29	a	a	X
ejpam-5909	40	30	,	,	PUNCT
ejpam-5909	40	31	b	b	NOUN
ejpam-5909	40	32	]	]	X
ejpam-5909	40	33	.	.	PUNCT
ejpam-5909	41	1	the	the	DET
ejpam-5909	41	2	definition	definition	NOUN
ejpam-5909	41	3	of	of	ADP
ejpam-5909	41	4	the	the	DET
ejpam-5909	41	5	stieltjes	stieltjes	NOUN
ejpam-5909	41	6	limit	limit	NOUN
ejpam-5909	41	7	for	for	ADP
ejpam-5909	41	8	function	function	NOUN
ejpam-5909	41	9	-	-	PUNCT
ejpam-5909	41	10	valued	value	VERB
ejpam-5909	41	11	operators	operator	NOUN
ejpam-5909	41	12	involves	involve	VERB
ejpam-5909	41	13	operations	operation	NOUN
ejpam-5909	41	14	on	on	ADP
ejpam-5909	41	15	continuous	continuous	ADJ
ejpam-5909	41	16	functions	function	NOUN
ejpam-5909	41	17	.	.	PUNCT
ejpam-5909	42	1	therefore	therefore	ADV
ejpam-5909	42	2	,	,	PUNCT
ejpam-5909	42	3	we	we	PRON
ejpam-5909	42	4	present	present	VERB
ejpam-5909	42	5	some	some	DET
ejpam-5909	42	6	properties	property	NOUN
ejpam-5909	42	7	of	of	ADP
ejpam-5909	42	8	continuous	continuous	ADJ
ejpam-5909	42	9	functions	function	NOUN
ejpam-5909	42	10	in	in	ADP
ejpam-5909	42	11	c[a	c[a	NUM
ejpam-5909	42	12	,	,	PUNCT
ejpam-5909	42	13	b	b	AUX
ejpam-5909	42	14	]	]	PUNCT
ejpam-5909	42	15	as	as	SCONJ
ejpam-5909	42	16	follows	follow	VERB
ejpam-5909	42	17	:	:	PUNCT
ejpam-5909	42	18	theorem	theorem	NOUN
ejpam-5909	42	19	1	1	NUM
ejpam-5909	42	20	.	.	PUNCT
ejpam-5909	43	1	[	[	X
ejpam-5909	43	2	6	6	NUM
ejpam-5909	43	3	]	]	PUNCT
ejpam-5909	43	4	for	for	ADP
ejpam-5909	43	5	any	any	DET
ejpam-5909	43	6	f	f	NOUN
ejpam-5909	43	7	,	,	PUNCT
ejpam-5909	43	8	g	g	PROPN
ejpam-5909	43	9	∈	∈	PROPN
ejpam-5909	43	10	c[a	c[a	NOUN
ejpam-5909	43	11	,	,	PUNCT
ejpam-5909	43	12	b	b	NOUN
ejpam-5909	43	13	]	]	PUNCT
ejpam-5909	43	14	and	and	CCONJ
ejpam-5909	43	15	any	any	DET
ejpam-5909	43	16	α	α	NOUN
ejpam-5909	43	17	,	,	PUNCT
ejpam-5909	43	18	β	β	X
ejpam-5909	43	19	∈	∈	PROPN
ejpam-5909	43	20	r	r	NOUN
ejpam-5909	43	21	,	,	PUNCT
ejpam-5909	43	22	the	the	DET
ejpam-5909	43	23	following	follow	VERB
ejpam-5909	43	24	holds	hold	VERB
ejpam-5909	43	25	:	:	PUNCT
ejpam-5909	43	26	(	(	PUNCT
ejpam-5909	43	27	i	i	NOUN
ejpam-5909	43	28	)	)	PUNCT
ejpam-5909	43	29	αf	αf	VERB
ejpam-5909	44	1	+	+	X
ejpam-5909	44	2	βg	βg	NOUN
ejpam-5909	44	3	∈	∈	PROPN
ejpam-5909	44	4	c[a	c[a	NOUN
ejpam-5909	44	5	,	,	PUNCT
ejpam-5909	44	6	b	b	NOUN
ejpam-5909	44	7	]	]	X
ejpam-5909	44	8	m.	m.	NOUN
ejpam-5909	44	9	alifuddin	alifuddin	VERB
ejpam-5909	44	10	et	et	PROPN
ejpam-5909	44	11	al	al	PROPN
ejpam-5909	44	12	.	.	PUNCT
ejpam-5909	44	13	/	/	SYM
ejpam-5909	44	14	eur	eur	PROPN
ejpam-5909	44	15	.	.	PUNCT
ejpam-5909	45	1	j.	j.	PROPN
ejpam-5909	45	2	pure	pure	PROPN
ejpam-5909	45	3	appl	appl	PROPN
ejpam-5909	45	4	.	.	PROPN
ejpam-5909	45	5	math	math	PROPN
ejpam-5909	45	6	,	,	PUNCT
ejpam-5909	45	7	18	18	NUM
ejpam-5909	45	8	(	(	PUNCT
ejpam-5909	45	9	2	2	NUM
ejpam-5909	45	10	)	)	PUNCT
ejpam-5909	45	11	(	(	PUNCT
ejpam-5909	45	12	2025	2025	NUM
ejpam-5909	45	13	)	)	PUNCT
ejpam-5909	45	14	,	,	PUNCT
ejpam-5909	45	15	5909	5909	NUM
ejpam-5909	45	16	3	3	NUM
ejpam-5909	45	17	of	of	ADP
ejpam-5909	45	18	17	17	NUM
ejpam-5909	45	19	(	(	PUNCT
ejpam-5909	45	20	ii	ii	NOUN
ejpam-5909	45	21	)	)	PUNCT
ejpam-5909	45	22	fg	fg	PROPN
ejpam-5909	45	23	∈	∈	PROPN
ejpam-5909	45	24	c[a	c[a	NOUN
ejpam-5909	45	25	,	,	PUNCT
ejpam-5909	45	26	b	b	X
ejpam-5909	45	27	]	]	X
ejpam-5909	45	28	(	(	PUNCT
ejpam-5909	45	29	iii	iii	X
ejpam-5909	45	30	)	)	PUNCT
ejpam-5909	45	31	f	f	PROPN
ejpam-5909	45	32	g	g	PROPN
ejpam-5909	45	33	∈	∈	PROPN
ejpam-5909	45	34	c[a	c[a	NOUN
ejpam-5909	45	35	,	,	PUNCT
ejpam-5909	45	36	b	b	X
ejpam-5909	45	37	]	]	X
ejpam-5909	45	38	if	if	SCONJ
ejpam-5909	45	39	g(x	g(x	NOUN
ejpam-5909	45	40	)	)	PUNCT
ejpam-5909	45	41	̸=	̸=	NOUN
ejpam-5909	45	42	0	0	NUM
ejpam-5909	45	43	for	for	ADP
ejpam-5909	45	44	all	all	DET
ejpam-5909	45	45	x	x	SYM
ejpam-5909	45	46	∈	∈	PROPN
ejpam-5909	45	47	[	[	X
ejpam-5909	45	48	a	a	X
ejpam-5909	45	49	,	,	PUNCT
ejpam-5909	45	50	b	b	NOUN
ejpam-5909	45	51	]	]	X
ejpam-5909	45	52	in	in	ADP
ejpam-5909	45	53	addition	addition	NOUN
ejpam-5909	45	54	to	to	ADP
ejpam-5909	45	55	unit	unit	NOUN
ejpam-5909	45	56	function	function	NOUN
ejpam-5909	45	57	,	,	PUNCT
ejpam-5909	45	58	the	the	DET
ejpam-5909	45	59	ordering	ordering	NOUN
ejpam-5909	45	60	properties	property	NOUN
ejpam-5909	45	61	of	of	ADP
ejpam-5909	45	62	continuous	continuous	ADJ
ejpam-5909	45	63	functions	function	NOUN
ejpam-5909	45	64	in	in	ADP
ejpam-5909	45	65	c[a	c[a	NUM
ejpam-5909	45	66	,	,	PUNCT
ejpam-5909	45	67	b	b	AUX
ejpam-5909	45	68	]	]	X
ejpam-5909	45	69	are	be	AUX
ejpam-5909	45	70	also	also	ADV
ejpam-5909	45	71	necessary	necessary	ADJ
ejpam-5909	45	72	for	for	ADP
ejpam-5909	45	73	defining	define	VERB
ejpam-5909	45	74	the	the	DET
ejpam-5909	45	75	stieltjes	stieltjes	PROPN
ejpam-5909	45	76	limit	limit	NOUN
ejpam-5909	45	77	.	.	PUNCT
ejpam-5909	46	1	the	the	DET
ejpam-5909	46	2	ordering	ordering	NOUN
ejpam-5909	46	3	properties	property	NOUN
ejpam-5909	46	4	of	of	ADP
ejpam-5909	46	5	continuous	continuous	ADJ
ejpam-5909	46	6	functions	function	NOUN
ejpam-5909	46	7	in	in	ADP
ejpam-5909	46	8	c[a	c[a	NUM
ejpam-5909	46	9	,	,	PUNCT
ejpam-5909	46	10	b	b	AUX
ejpam-5909	46	11	]	]	X
ejpam-5909	46	12	is	be	AUX
ejpam-5909	46	13	as	as	SCONJ
ejpam-5909	46	14	follows	follow	VERB
ejpam-5909	46	15	:	:	PUNCT
ejpam-5909	46	16	definition	definition	NOUN
ejpam-5909	46	17	3	3	NUM
ejpam-5909	46	18	.	.	PUNCT
ejpam-5909	47	1	[	[	X
ejpam-5909	47	2	6	6	NUM
ejpam-5909	47	3	]	]	PUNCT
ejpam-5909	47	4	for	for	ADP
ejpam-5909	47	5	any	any	DET
ejpam-5909	47	6	f	f	PROPN
ejpam-5909	47	7	and	and	CCONJ
ejpam-5909	47	8	g	g	NOUN
ejpam-5909	47	9	in	in	ADP
ejpam-5909	47	10	c[a	c[a	NUM
ejpam-5909	47	11	,	,	PUNCT
ejpam-5909	47	12	b	b	NOUN
ejpam-5909	47	13	]	]	X
ejpam-5909	47	14	,	,	PUNCT
ejpam-5909	47	15	we	we	PRON
ejpam-5909	47	16	define	define	VERB
ejpam-5909	47	17	:	:	PUNCT
ejpam-5909	47	18	(	(	PUNCT
ejpam-5909	47	19	i	i	NOUN
ejpam-5909	47	20	)	)	PUNCT
ejpam-5909	47	21	f	f	PROPN
ejpam-5909	48	1	=	=	SYM
ejpam-5909	48	2	g	g	PROPN
ejpam-5909	48	3	⇔	⇔	PROPN
ejpam-5909	48	4	f(x	f(x	PROPN
ejpam-5909	48	5	)	)	PUNCT
ejpam-5909	48	6	=	=	SYM
ejpam-5909	49	1	g(x	g(x	NOUN
ejpam-5909	49	2	)	)	PUNCT
ejpam-5909	49	3	for	for	ADP
ejpam-5909	49	4	every	every	DET
ejpam-5909	49	5	x	x	SYM
ejpam-5909	49	6	∈	∈	PROPN
ejpam-5909	49	7	[	[	X
ejpam-5909	49	8	a	a	X
ejpam-5909	49	9	,	,	PUNCT
ejpam-5909	49	10	b	b	NOUN
ejpam-5909	49	11	]	]	X
ejpam-5909	49	12	.	.	PUNCT
ejpam-5909	50	1	(	(	PUNCT
ejpam-5909	50	2	ii	ii	X
ejpam-5909	50	3	)	)	PUNCT
ejpam-5909	50	4	f	f	PROPN
ejpam-5909	50	5	⪯	⪯	NOUN
ejpam-5909	50	6	g	g	PROPN
ejpam-5909	50	7	⇔	⇔	PROPN
ejpam-5909	50	8	f(x	f(x	PROPN
ejpam-5909	50	9	)	)	PUNCT
ejpam-5909	50	10	≤	≤	PUNCT
ejpam-5909	51	1	g(x	g(x	NOUN
ejpam-5909	51	2	)	)	PUNCT
ejpam-5909	51	3	for	for	ADP
ejpam-5909	51	4	every	every	DET
ejpam-5909	51	5	x	x	SYM
ejpam-5909	51	6	∈	∈	PROPN
ejpam-5909	51	7	[	[	X
ejpam-5909	51	8	a	a	X
ejpam-5909	51	9	,	,	PUNCT
ejpam-5909	51	10	b	b	NOUN
ejpam-5909	51	11	]	]	X
ejpam-5909	51	12	.	.	PUNCT
ejpam-5909	52	1	(	(	PUNCT
ejpam-5909	52	2	iii	iii	X
ejpam-5909	52	3	)	)	PUNCT
ejpam-5909	52	4	f	f	PROPN
ejpam-5909	52	5	≺	≺	NOUN
ejpam-5909	52	6	g	g	PROPN
ejpam-5909	52	7	⇔	⇔	PROPN
ejpam-5909	52	8	f(x	f(x	PROPN
ejpam-5909	52	9	)	)	PUNCT
ejpam-5909	52	10	<	<	X
ejpam-5909	52	11	g(x	g(x	NOUN
ejpam-5909	52	12	)	)	PUNCT
ejpam-5909	52	13	for	for	ADP
ejpam-5909	52	14	every	every	DET
ejpam-5909	52	15	x	x	SYM
ejpam-5909	52	16	∈	∈	PROPN
ejpam-5909	52	17	[	[	X
ejpam-5909	52	18	a	a	X
ejpam-5909	52	19	,	,	PUNCT
ejpam-5909	52	20	b	b	NOUN
ejpam-5909	52	21	]	]	X
ejpam-5909	52	22	.	.	PUNCT
ejpam-5909	53	1	(	(	PUNCT
ejpam-5909	53	2	iv	iv	X
ejpam-5909	53	3	)	)	PUNCT
ejpam-5909	53	4	f	f	PROPN
ejpam-5909	53	5	⪰	⪰	NOUN
ejpam-5909	53	6	g	g	PROPN
ejpam-5909	53	7	⇔	⇔	PROPN
ejpam-5909	53	8	f(x	f(x	PROPN
ejpam-5909	53	9	)	)	PUNCT
ejpam-5909	53	10	≥	≥	NOUN
ejpam-5909	53	11	g(x	g(x	NOUN
ejpam-5909	53	12	)	)	PUNCT
ejpam-5909	53	13	for	for	ADP
ejpam-5909	53	14	every	every	DET
ejpam-5909	53	15	x	x	SYM
ejpam-5909	53	16	∈	∈	PROPN
ejpam-5909	53	17	[	[	X
ejpam-5909	53	18	a	a	X
ejpam-5909	53	19	,	,	PUNCT
ejpam-5909	53	20	b	b	NOUN
ejpam-5909	53	21	]	]	X
ejpam-5909	53	22	.	.	PUNCT
ejpam-5909	54	1	(	(	PUNCT
ejpam-5909	54	2	v	v	X
ejpam-5909	54	3	)	)	PUNCT
ejpam-5909	54	4	f	f	PROPN
ejpam-5909	54	5	≻	≻	PROPN
ejpam-5909	54	6	g	g	PROPN
ejpam-5909	54	7	⇔	⇔	PROPN
ejpam-5909	54	8	f(x	f(x	PROPN
ejpam-5909	54	9	)	)	PUNCT
ejpam-5909	54	10	>	>	X
ejpam-5909	55	1	g(x	g(x	NOUN
ejpam-5909	55	2	)	)	PUNCT
ejpam-5909	55	3	for	for	ADP
ejpam-5909	55	4	every	every	DET
ejpam-5909	55	5	x	x	SYM
ejpam-5909	55	6	∈	∈	PROPN
ejpam-5909	55	7	[	[	X
ejpam-5909	55	8	a	a	X
ejpam-5909	55	9	,	,	PUNCT
ejpam-5909	55	10	b	b	NOUN
ejpam-5909	55	11	]	]	PUNCT
ejpam-5909	55	12	.	.	PUNCT
ejpam-5909	56	1	theorem	theorem	NOUN
ejpam-5909	56	2	2	2	NUM
ejpam-5909	56	3	.	.	PUNCT
ejpam-5909	57	1	[	[	X
ejpam-5909	57	2	14	14	NUM
ejpam-5909	57	3	]	]	PUNCT
ejpam-5909	57	4	for	for	ADP
ejpam-5909	57	5	any	any	DET
ejpam-5909	57	6	f	f	PROPN
ejpam-5909	57	7	,	,	PUNCT
ejpam-5909	57	8	g	g	PROPN
ejpam-5909	57	9	,	,	PUNCT
ejpam-5909	57	10	and	and	CCONJ
ejpam-5909	57	11	h	h	NOUN
ejpam-5909	57	12	in	in	ADP
ejpam-5909	57	13	c[a	c[a	NUM
ejpam-5909	57	14	,	,	PUNCT
ejpam-5909	57	15	b	b	NOUN
ejpam-5909	57	16	]	]	X
ejpam-5909	57	17	,	,	PUNCT
ejpam-5909	57	18	the	the	DET
ejpam-5909	57	19	following	follow	VERB
ejpam-5909	57	20	holds	hold	VERB
ejpam-5909	57	21	:	:	PUNCT
ejpam-5909	57	22	(	(	PUNCT
ejpam-5909	57	23	i	i	NOUN
ejpam-5909	57	24	)	)	PUNCT
ejpam-5909	57	25	f	f	PROPN
ejpam-5909	57	26	≺	≺	VERB
ejpam-5909	57	27	g	g	PROPN
ejpam-5909	57	28	⇒	⇒	NOUN
ejpam-5909	57	29	(	(	PUNCT
ejpam-5909	57	30	f	f	X
ejpam-5909	57	31	+	+	NUM
ejpam-5909	57	32	h	h	NOUN
ejpam-5909	57	33	≺	≺	NOUN
ejpam-5909	57	34	g	g	PROPN
ejpam-5909	57	35	+	+	CCONJ
ejpam-5909	57	36	h	h	NOUN
ejpam-5909	57	37	)	)	PUNCT
ejpam-5909	57	38	for	for	ADP
ejpam-5909	57	39	every	every	DET
ejpam-5909	57	40	h	h	NOUN
ejpam-5909	57	41	∈	∈	PROPN
ejpam-5909	57	42	c[a	c[a	NOUN
ejpam-5909	57	43	,	,	PUNCT
ejpam-5909	57	44	b	b	NOUN
ejpam-5909	57	45	]	]	PUNCT
ejpam-5909	57	46	.	.	PUNCT
ejpam-5909	58	1	(	(	PUNCT
ejpam-5909	58	2	ii	ii	X
ejpam-5909	58	3	)	)	PUNCT
ejpam-5909	58	4	f	f	PROPN
ejpam-5909	58	5	≺	≺	VERB
ejpam-5909	58	6	g	g	PROPN
ejpam-5909	58	7	⇒	⇒	NOUN
ejpam-5909	58	8	(	(	PUNCT
ejpam-5909	58	9	αf	αf	NOUN
ejpam-5909	58	10	≺	≺	NOUN
ejpam-5909	58	11	αg	αg	NOUN
ejpam-5909	58	12	)	)	PUNCT
ejpam-5909	58	13	for	for	ADP
ejpam-5909	58	14	every	every	DET
ejpam-5909	58	15	α	α	NOUN
ejpam-5909	58	16	preceded	precede	VERB
ejpam-5909	58	17	by	by	ADP
ejpam-5909	58	18	0	0	NUM
ejpam-5909	58	19	.	.	PUNCT
ejpam-5909	59	1	to	to	PART
ejpam-5909	59	2	compute	compute	VERB
ejpam-5909	59	3	the	the	DET
ejpam-5909	59	4	stieltjes	stieltjes	NOUN
ejpam-5909	59	5	limit	limit	VERB
ejpam-5909	59	6	for	for	ADP
ejpam-5909	59	7	function	function	NOUN
ejpam-5909	59	8	-	-	PUNCT
ejpam-5909	59	9	valued	value	VERB
ejpam-5909	59	10	operators	operator	NOUN
ejpam-5909	59	11	,	,	PUNCT
ejpam-5909	59	12	we	we	PRON
ejpam-5909	59	13	define	define	VERB
ejpam-5909	59	14	open	open	ADJ
ejpam-5909	59	15	and	and	CCONJ
ejpam-5909	59	16	closed	closed	ADJ
ejpam-5909	59	17	intervals	interval	NOUN
ejpam-5909	59	18	,	,	PUNCT
ejpam-5909	59	19	which	which	PRON
ejpam-5909	59	20	serve	serve	VERB
ejpam-5909	59	21	as	as	ADP
ejpam-5909	59	22	the	the	DET
ejpam-5909	59	23	domain	domain	NOUN
ejpam-5909	59	24	for	for	ADP
ejpam-5909	59	25	the	the	DET
ejpam-5909	59	26	limit	limit	NOUN
ejpam-5909	59	27	process	process	NOUN
ejpam-5909	59	28	,	,	PUNCT
ejpam-5909	59	29	as	as	SCONJ
ejpam-5909	59	30	follows	follow	VERB
ejpam-5909	59	31	:	:	PUNCT
ejpam-5909	59	32	definition	definition	NOUN
ejpam-5909	59	33	4	4	NUM
ejpam-5909	59	34	.	.	PUNCT
ejpam-5909	60	1	[	[	X
ejpam-5909	60	2	13	13	NUM
ejpam-5909	60	3	]	]	PUNCT
ejpam-5909	60	4	for	for	ADP
ejpam-5909	60	5	any	any	DET
ejpam-5909	60	6	f	f	PROPN
ejpam-5909	60	7	and	and	CCONJ
ejpam-5909	60	8	g	g	NOUN
ejpam-5909	60	9	in	in	ADP
ejpam-5909	60	10	c[a	c[a	NUM
ejpam-5909	60	11	,	,	PUNCT
ejpam-5909	60	12	b	b	X
ejpam-5909	60	13	]	]	PUNCT
ejpam-5909	60	14	such	such	ADJ
ejpam-5909	60	15	that	that	SCONJ
ejpam-5909	60	16	f	f	PROPN
ejpam-5909	60	17	≺	≺	VERB
ejpam-5909	60	18	g	g	NOUN
ejpam-5909	60	19	,	,	PUNCT
ejpam-5909	60	20	we	we	PRON
ejpam-5909	60	21	define	define	VERB
ejpam-5909	60	22	:	:	PUNCT
ejpam-5909	60	23	(	(	PUNCT
ejpam-5909	60	24	i	i	NOUN
ejpam-5909	60	25	)	)	PUNCT
ejpam-5909	60	26	(	(	PUNCT
ejpam-5909	60	27	f	f	X
ejpam-5909	60	28	,	,	PUNCT
ejpam-5909	60	29	g	g	NOUN
ejpam-5909	60	30	)	)	PUNCT
ejpam-5909	60	31	=	=	PRON
ejpam-5909	61	1	{	{	PUNCT
ejpam-5909	61	2	h	h	NOUN
ejpam-5909	61	3	∈	∈	PROPN
ejpam-5909	61	4	c[a	c[a	PROPN
ejpam-5909	61	5	,	,	PUNCT
ejpam-5909	61	6	b	b	X
ejpam-5909	61	7	]	]	X
ejpam-5909	61	8	:	:	PUNCT
ejpam-5909	61	9	f	f	PROPN
ejpam-5909	61	10	≺	≺	NOUN
ejpam-5909	61	11	h	h	NOUN
ejpam-5909	61	12	≺	≺	NOUN
ejpam-5909	61	13	g	g	NOUN
ejpam-5909	61	14	}	}	PUNCT
ejpam-5909	61	15	as	as	ADP
ejpam-5909	61	16	the	the	DET
ejpam-5909	61	17	open	open	ADJ
ejpam-5909	61	18	interval	interval	NOUN
ejpam-5909	61	19	in	in	ADP
ejpam-5909	61	20	c[a	c[a	NUM
ejpam-5909	61	21	,	,	PUNCT
ejpam-5909	61	22	b	b	NOUN
ejpam-5909	61	23	]	]	PUNCT
ejpam-5909	61	24	.	.	PUNCT
ejpam-5909	62	1	(	(	PUNCT
ejpam-5909	62	2	ii	ii	NOUN
ejpam-5909	62	3	)	)	PUNCT
ejpam-5909	63	1	[	[	X
ejpam-5909	63	2	f	f	X
ejpam-5909	63	3	,	,	PUNCT
ejpam-5909	63	4	g	g	NOUN
ejpam-5909	63	5	]	]	X
ejpam-5909	63	6	=	=	SYM
ejpam-5909	63	7	{	{	PUNCT
ejpam-5909	63	8	h	h	NOUN
ejpam-5909	63	9	∈	∈	PROPN
ejpam-5909	63	10	c[a	c[a	PROPN
ejpam-5909	63	11	,	,	PUNCT
ejpam-5909	63	12	b	b	X
ejpam-5909	63	13	]	]	X
ejpam-5909	63	14	:	:	PUNCT
ejpam-5909	63	15	f	f	PROPN
ejpam-5909	63	16	⪯	⪯	PROPN
ejpam-5909	63	17	h	h	PROPN
ejpam-5909	63	18	⪯	⪯	VERB
ejpam-5909	63	19	g	g	NOUN
ejpam-5909	63	20	}	}	PUNCT
ejpam-5909	63	21	as	as	ADP
ejpam-5909	63	22	the	the	DET
ejpam-5909	63	23	closed	closed	ADJ
ejpam-5909	63	24	interval	interval	NOUN
ejpam-5909	63	25	in	in	ADP
ejpam-5909	63	26	c[a	c[a	NUM
ejpam-5909	63	27	,	,	PUNCT
ejpam-5909	63	28	b	b	NOUN
ejpam-5909	63	29	]	]	PUNCT
ejpam-5909	63	30	.	.	PUNCT
ejpam-5909	64	1	definition	definition	NOUN
ejpam-5909	64	2	5	5	NUM
ejpam-5909	64	3	.	.	PUNCT
ejpam-5909	65	1	[	[	X
ejpam-5909	65	2	15	15	NUM
ejpam-5909	65	3	]	]	PUNCT
ejpam-5909	65	4	let	let	VERB
ejpam-5909	65	5	a	a	DET
ejpam-5909	65	6	⊆	⊆	NUM
ejpam-5909	65	7	c[a	c[a	NOUN
ejpam-5909	65	8	,	,	PUNCT
ejpam-5909	65	9	b	b	AUX
ejpam-5909	65	10	]	]	X
ejpam-5909	65	11	be	be	AUX
ejpam-5909	65	12	a	a	DET
ejpam-5909	65	13	non	non	ADJ
ejpam-5909	65	14	-	-	ADJ
ejpam-5909	65	15	empty	empty	ADJ
ejpam-5909	65	16	set	set	NOUN
ejpam-5909	65	17	.	.	PUNCT
ejpam-5909	66	1	(	(	PUNCT
ejpam-5909	66	2	i	i	NOUN
ejpam-5909	66	3	)	)	PUNCT
ejpam-5909	66	4	the	the	DET
ejpam-5909	66	5	set	set	NOUN
ejpam-5909	66	6	a	a	PRON
ejpam-5909	66	7	is	be	AUX
ejpam-5909	66	8	said	say	VERB
ejpam-5909	66	9	to	to	PART
ejpam-5909	66	10	be	be	AUX
ejpam-5909	66	11	bounded	bound	VERB
ejpam-5909	66	12	above	above	ADV
ejpam-5909	66	13	if	if	SCONJ
ejpam-5909	66	14	there	there	PRON
ejpam-5909	66	15	exists	exist	VERB
ejpam-5909	66	16	m	m	VERB
ejpam-5909	66	17	∈	∈	ADJ
ejpam-5909	66	18	c[a	c[a	NOUN
ejpam-5909	66	19	,	,	PUNCT
ejpam-5909	66	20	b	b	X
ejpam-5909	66	21	]	]	PUNCT
ejpam-5909	67	1	such	such	ADJ
ejpam-5909	67	2	that	that	SCONJ
ejpam-5909	67	3	m	m	VERB
ejpam-5909	67	4	⪰	⪰	PROPN
ejpam-5909	67	5	f	f	PROPN
ejpam-5909	67	6	for	for	ADP
ejpam-5909	67	7	every	every	DET
ejpam-5909	67	8	f	f	PROPN
ejpam-5909	67	9	∈	∈	PROPN
ejpam-5909	67	10	a.	a.	NOUN
ejpam-5909	67	11	in	in	ADP
ejpam-5909	67	12	this	this	DET
ejpam-5909	67	13	case	case	NOUN
ejpam-5909	67	14	,	,	PUNCT
ejpam-5909	67	15	m	m	VERB
ejpam-5909	67	16	is	be	AUX
ejpam-5909	67	17	called	call	VERB
ejpam-5909	67	18	an	an	DET
ejpam-5909	67	19	upper	upper	ADJ
ejpam-5909	67	20	bound	bind	VERB
ejpam-5909	67	21	of	of	ADP
ejpam-5909	67	22	a.	a.	PROPN
ejpam-5909	67	23	(	(	PUNCT
ejpam-5909	67	24	ii	ii	PROPN
ejpam-5909	67	25	)	)	PUNCT
ejpam-5909	67	26	the	the	DET
ejpam-5909	67	27	set	set	NOUN
ejpam-5909	67	28	a	a	PRON
ejpam-5909	67	29	is	be	AUX
ejpam-5909	67	30	said	say	VERB
ejpam-5909	67	31	to	to	PART
ejpam-5909	67	32	be	be	AUX
ejpam-5909	67	33	bounded	bound	VERB
ejpam-5909	67	34	below	below	ADV
ejpam-5909	67	35	if	if	SCONJ
ejpam-5909	67	36	there	there	PRON
ejpam-5909	67	37	exists	exist	VERB
ejpam-5909	67	38	n	n	PRON
ejpam-5909	67	39	∈	∈	PROPN
ejpam-5909	67	40	c[a	c[a	NOUN
ejpam-5909	67	41	,	,	PUNCT
ejpam-5909	67	42	b	b	X
ejpam-5909	67	43	]	]	X
ejpam-5909	67	44	such	such	ADJ
ejpam-5909	67	45	that	that	SCONJ
ejpam-5909	67	46	n	n	PRON
ejpam-5909	67	47	⪯	⪯	X
ejpam-5909	67	48	f	f	PROPN
ejpam-5909	67	49	for	for	ADP
ejpam-5909	67	50	every	every	DET
ejpam-5909	67	51	f	f	PROPN
ejpam-5909	67	52	∈	∈	PROPN
ejpam-5909	67	53	a.	a.	NOUN
ejpam-5909	67	54	in	in	ADP
ejpam-5909	67	55	this	this	DET
ejpam-5909	67	56	case	case	NOUN
ejpam-5909	67	57	,	,	PUNCT
ejpam-5909	67	58	n	n	PRON
ejpam-5909	67	59	is	be	AUX
ejpam-5909	67	60	called	call	VERB
ejpam-5909	67	61	a	a	DET
ejpam-5909	67	62	lower	low	ADJ
ejpam-5909	67	63	bound	bind	VERB
ejpam-5909	67	64	of	of	ADP
ejpam-5909	67	65	a.	a.	NOUN
ejpam-5909	67	66	(	(	PUNCT
ejpam-5909	67	67	iii	iii	NOUN
ejpam-5909	67	68	)	)	PUNCT
ejpam-5909	67	69	the	the	DET
ejpam-5909	67	70	set	set	NOUN
ejpam-5909	67	71	a	a	PRON
ejpam-5909	67	72	is	be	AUX
ejpam-5909	67	73	said	say	VERB
ejpam-5909	67	74	to	to	PART
ejpam-5909	67	75	be	be	AUX
ejpam-5909	67	76	bounded	bound	VERB
ejpam-5909	67	77	if	if	SCONJ
ejpam-5909	67	78	it	it	PRON
ejpam-5909	67	79	is	be	AUX
ejpam-5909	67	80	both	both	PRON
ejpam-5909	67	81	bounded	bound	VERB
ejpam-5909	67	82	above	above	ADP
ejpam-5909	67	83	and	and	CCONJ
ejpam-5909	67	84	below	below	ADV
ejpam-5909	67	85	.	.	PUNCT
ejpam-5909	68	1	(	(	PUNCT
ejpam-5909	68	2	iv	iv	X
ejpam-5909	68	3	)	)	PUNCT
ejpam-5909	68	4	if	if	SCONJ
ejpam-5909	68	5	a	a	PRON
ejpam-5909	68	6	is	be	AUX
ejpam-5909	68	7	bounded	bound	VERB
ejpam-5909	68	8	above	above	ADV
ejpam-5909	68	9	,	,	PUNCT
ejpam-5909	68	10	a	a	DET
ejpam-5909	68	11	function	function	NOUN
ejpam-5909	68	12	u	u	NOUN
ejpam-5909	68	13	∈	∈	PROPN
ejpam-5909	68	14	c[a	c[a	NOUN
ejpam-5909	68	15	,	,	PUNCT
ejpam-5909	68	16	b	b	AUX
ejpam-5909	68	17	]	]	PUNCT
ejpam-5909	68	18	is	be	AUX
ejpam-5909	68	19	called	call	VERB
ejpam-5909	68	20	the	the	DET
ejpam-5909	68	21	least	least	ADV
ejpam-5909	68	22	upper	upper	ADJ
ejpam-5909	68	23	bound	bind	VERB
ejpam-5909	68	24	or	or	CCONJ
ejpam-5909	68	25	supremum	supremum	NOUN
ejpam-5909	68	26	of	of	ADP
ejpam-5909	68	27	a	a	PRON
ejpam-5909	68	28	if	if	SCONJ
ejpam-5909	68	29	u	u	NOUN
ejpam-5909	68	30	is	be	AUX
ejpam-5909	68	31	an	an	DET
ejpam-5909	68	32	upper	upper	ADJ
ejpam-5909	68	33	bound	bound	NOUN
ejpam-5909	68	34	of	of	ADP
ejpam-5909	68	35	a	a	PRON
ejpam-5909	68	36	and	and	CCONJ
ejpam-5909	68	37	for	for	ADP
ejpam-5909	68	38	every	every	DET
ejpam-5909	68	39	upper	upper	ADJ
ejpam-5909	68	40	bound	bind	VERB
ejpam-5909	68	41	m	m	NOUN
ejpam-5909	68	42	of	of	ADP
ejpam-5909	68	43	a	a	PRON
ejpam-5909	68	44	,	,	PUNCT
ejpam-5909	68	45	we	we	PRON
ejpam-5909	68	46	have	have	VERB
ejpam-5909	68	47	u	u	PRON
ejpam-5909	68	48	⪯	⪯	NOUN
ejpam-5909	68	49	m	m	PRON
ejpam-5909	68	50	,	,	PUNCT
ejpam-5909	68	51	denoted	denote	VERB
ejpam-5909	68	52	as	as	ADP
ejpam-5909	68	53	:	:	PUNCT
ejpam-5909	68	54	u	u	NOUN
ejpam-5909	68	55	=	=	PROPN
ejpam-5909	68	56	sup(a	sup(a	PROPN
ejpam-5909	68	57	)	)	PUNCT
ejpam-5909	68	58	.	.	PUNCT
ejpam-5909	69	1	(	(	PUNCT
ejpam-5909	69	2	v	v	NOUN
ejpam-5909	69	3	)	)	PUNCT
ejpam-5909	69	4	if	if	SCONJ
ejpam-5909	69	5	a	a	PRON
ejpam-5909	69	6	is	be	AUX
ejpam-5909	69	7	bounded	bound	VERB
ejpam-5909	69	8	below	below	ADV
ejpam-5909	69	9	,	,	PUNCT
ejpam-5909	69	10	a	a	DET
ejpam-5909	69	11	function	function	NOUN
ejpam-5909	69	12	l	l	PROPN
ejpam-5909	69	13	∈	∈	PROPN
ejpam-5909	69	14	c[a	c[a	NOUN
ejpam-5909	69	15	,	,	PUNCT
ejpam-5909	69	16	b	b	AUX
ejpam-5909	69	17	]	]	PUNCT
ejpam-5909	69	18	is	be	AUX
ejpam-5909	69	19	called	call	VERB
ejpam-5909	69	20	the	the	DET
ejpam-5909	69	21	greatest	greatest	ADV
ejpam-5909	69	22	lower	lower	ADV
ejpam-5909	69	23	bound	bind	VERB
ejpam-5909	69	24	or	or	CCONJ
ejpam-5909	69	25	infimum	infimum	NOUN
ejpam-5909	69	26	of	of	ADP
ejpam-5909	69	27	a	a	PRON
ejpam-5909	69	28	if	if	SCONJ
ejpam-5909	69	29	l	l	NOUN
ejpam-5909	69	30	is	be	AUX
ejpam-5909	69	31	a	a	DET
ejpam-5909	69	32	lower	low	ADJ
ejpam-5909	69	33	bound	bind	VERB
ejpam-5909	69	34	of	of	ADP
ejpam-5909	69	35	a	a	PRON
ejpam-5909	69	36	and	and	CCONJ
ejpam-5909	69	37	for	for	ADP
ejpam-5909	69	38	every	every	DET
ejpam-5909	69	39	lower	lower	ADV
ejpam-5909	69	40	bound	bind	VERB
ejpam-5909	69	41	n	n	NOUN
ejpam-5909	69	42	of	of	ADP
ejpam-5909	69	43	a	a	PRON
ejpam-5909	69	44	,	,	PUNCT
ejpam-5909	69	45	we	we	PRON
ejpam-5909	69	46	have	have	VERB
ejpam-5909	69	47	l	l	NOUN
ejpam-5909	69	48	⪰	⪰	NOUN
ejpam-5909	69	49	n	n	ADP
ejpam-5909	69	50	,	,	PUNCT
ejpam-5909	69	51	denoted	denote	VERB
ejpam-5909	69	52	as	as	ADP
ejpam-5909	69	53	:	:	PUNCT
ejpam-5909	69	54	l	l	NOUN
ejpam-5909	69	55	=	=	SYM
ejpam-5909	69	56	inf(a	inf(a	PROPN
ejpam-5909	69	57	)	)	PUNCT
ejpam-5909	69	58	.	.	PUNCT
ejpam-5909	70	1	m.	m.	NOUN
ejpam-5909	70	2	alifuddin	alifuddin	VERB
ejpam-5909	70	3	et	et	PROPN
ejpam-5909	70	4	al	al	PROPN
ejpam-5909	70	5	.	.	PUNCT
ejpam-5909	70	6	/	/	SYM
ejpam-5909	70	7	eur	eur	PROPN
ejpam-5909	70	8	.	.	PUNCT
ejpam-5909	71	1	j.	j.	PROPN
ejpam-5909	71	2	pure	pure	PROPN
ejpam-5909	71	3	appl	appl	PROPN
ejpam-5909	71	4	.	.	PROPN
ejpam-5909	71	5	math	math	PROPN
ejpam-5909	71	6	,	,	PUNCT
ejpam-5909	71	7	18	18	NUM
ejpam-5909	71	8	(	(	PUNCT
ejpam-5909	71	9	2	2	NUM
ejpam-5909	71	10	)	)	PUNCT
ejpam-5909	71	11	(	(	PUNCT
ejpam-5909	71	12	2025	2025	NUM
ejpam-5909	71	13	)	)	PUNCT
ejpam-5909	71	14	,	,	PUNCT
ejpam-5909	71	15	5909	5909	NUM
ejpam-5909	71	16	4	4	NUM
ejpam-5909	71	17	of	of	ADP
ejpam-5909	71	18	17	17	NUM
ejpam-5909	71	19	3	3	NUM
ejpam-5909	71	20	.	.	PUNCT
ejpam-5909	71	21	main	main	ADJ
ejpam-5909	71	22	theorem	theorem	NOUN
ejpam-5909	71	23	this	this	DET
ejpam-5909	71	24	section	section	NOUN
ejpam-5909	71	25	addresses	address	VERB
ejpam-5909	71	26	the	the	DET
ejpam-5909	71	27	limit	limit	NOUN
ejpam-5909	71	28	of	of	ADP
ejpam-5909	71	29	operators	operator	NOUN
ejpam-5909	71	30	on	on	ADP
ejpam-5909	71	31	c[a	c[a	NUM
ejpam-5909	71	32	,	,	PUNCT
ejpam-5909	71	33	b	b	X
ejpam-5909	71	34	]	]	PUNCT
ejpam-5909	71	35	and	and	CCONJ
ejpam-5909	71	36	the	the	DET
ejpam-5909	71	37	stieltjes	stieltjes	NOUN
ejpam-5909	71	38	limit	limit	NOUN
ejpam-5909	71	39	on	on	ADP
ejpam-5909	71	40	c[a	c[a	NUM
ejpam-5909	71	41	,	,	PUNCT
ejpam-5909	71	42	b	b	NOUN
ejpam-5909	71	43	]	]	X
ejpam-5909	71	44	.	.	PUNCT
ejpam-5909	72	1	the	the	DET
ejpam-5909	72	2	proof	proof	NOUN
ejpam-5909	72	3	of	of	ADP
ejpam-5909	72	4	the	the	DET
ejpam-5909	72	5	main	main	ADJ
ejpam-5909	72	6	theorem	theorem	NOUN
ejpam-5909	72	7	is	be	AUX
ejpam-5909	72	8	established	establish	VERB
ejpam-5909	72	9	through	through	ADP
ejpam-5909	72	10	a	a	DET
ejpam-5909	72	11	rigorous	rigorous	ADJ
ejpam-5909	72	12	analysis	analysis	NOUN
ejpam-5909	72	13	,	,	PUNCT
ejpam-5909	72	14	following	follow	VERB
ejpam-5909	72	15	a	a	DET
ejpam-5909	72	16	structured	structured	ADJ
ejpam-5909	72	17	approach	approach	NOUN
ejpam-5909	72	18	that	that	PRON
ejpam-5909	72	19	builds	build	VERB
ejpam-5909	72	20	upon	upon	SCONJ
ejpam-5909	72	21	the	the	DET
ejpam-5909	72	22	results	result	NOUN
ejpam-5909	72	23	and	and	CCONJ
ejpam-5909	72	24	concepts	concept	NOUN
ejpam-5909	72	25	developed	develop	VERB
ejpam-5909	72	26	in	in	ADP
ejpam-5909	72	27	the	the	DET
ejpam-5909	72	28	preceding	precede	VERB
ejpam-5909	72	29	subsections	subsection	NOUN
ejpam-5909	72	30	,	,	PUNCT
ejpam-5909	72	31	which	which	PRON
ejpam-5909	72	32	serve	serve	VERB
ejpam-5909	72	33	as	as	ADP
ejpam-5909	72	34	the	the	DET
ejpam-5909	72	35	theoretical	theoretical	ADJ
ejpam-5909	72	36	foundation	foundation	NOUN
ejpam-5909	72	37	for	for	ADP
ejpam-5909	72	38	the	the	DET
ejpam-5909	72	39	argument	argument	NOUN
ejpam-5909	72	40	.	.	PUNCT
ejpam-5909	73	1	3.1	3.1	NUM
ejpam-5909	73	2	.	.	PUNCT
ejpam-5909	73	3	limit	limit	NOUN
ejpam-5909	73	4	of	of	ADP
ejpam-5909	73	5	operators	operator	NOUN
ejpam-5909	73	6	on	on	ADP
ejpam-5909	73	7	c[a	c[a	NUM
ejpam-5909	73	8	,	,	PUNCT
ejpam-5909	73	9	b	b	X
ejpam-5909	73	10	]	]	X
ejpam-5909	73	11	in	in	ADP
ejpam-5909	73	12	this	this	DET
ejpam-5909	73	13	subsection	subsection	NOUN
ejpam-5909	73	14	,	,	PUNCT
ejpam-5909	73	15	we	we	PRON
ejpam-5909	73	16	define	define	VERB
ejpam-5909	73	17	the	the	DET
ejpam-5909	73	18	concept	concept	NOUN
ejpam-5909	73	19	of	of	ADP
ejpam-5909	73	20	the	the	DET
ejpam-5909	73	21	limit	limit	NOUN
ejpam-5909	73	22	point	point	NOUN
ejpam-5909	73	23	of	of	ADP
ejpam-5909	73	24	a	a	DET
ejpam-5909	73	25	set	set	NOUN
ejpam-5909	73	26	of	of	ADP
ejpam-5909	73	27	continuous	continuous	ADJ
ejpam-5909	73	28	functions	function	NOUN
ejpam-5909	73	29	and	and	CCONJ
ejpam-5909	73	30	the	the	DET
ejpam-5909	73	31	limit	limit	NOUN
ejpam-5909	73	32	of	of	ADP
ejpam-5909	73	33	an	an	DET
ejpam-5909	73	34	operator	operator	NOUN
ejpam-5909	73	35	whose	whose	DET
ejpam-5909	73	36	values	value	NOUN
ejpam-5909	73	37	are	be	AUX
ejpam-5909	73	38	continuous	continuous	ADJ
ejpam-5909	73	39	functions	function	NOUN
ejpam-5909	73	40	.	.	PUNCT
ejpam-5909	74	1	this	this	DET
ejpam-5909	74	2	definition	definition	NOUN
ejpam-5909	74	3	serves	serve	VERB
ejpam-5909	74	4	as	as	ADP
ejpam-5909	74	5	the	the	DET
ejpam-5909	74	6	foundation	foundation	NOUN
ejpam-5909	74	7	for	for	ADP
ejpam-5909	74	8	defining	define	VERB
ejpam-5909	74	9	the	the	DET
ejpam-5909	74	10	stieltjes	stieltjes	NOUN
ejpam-5909	74	11	limit	limit	VERB
ejpam-5909	74	12	on	on	ADP
ejpam-5909	74	13	operators	operator	NOUN
ejpam-5909	74	14	that	that	PRON
ejpam-5909	74	15	take	take	VERB
ejpam-5909	74	16	continuous	continuous	ADJ
ejpam-5909	74	17	function	function	NOUN
ejpam-5909	74	18	values	value	NOUN
ejpam-5909	74	19	.	.	PUNCT
ejpam-5909	75	1	definition	definition	NOUN
ejpam-5909	75	2	6	6	NUM
ejpam-5909	75	3	.	.	PUNCT
ejpam-5909	76	1	given	give	VERB
ejpam-5909	76	2	f	f	PROPN
ejpam-5909	76	3	∈	∈	PROPN
ejpam-5909	76	4	c[a	c[a	PROPN
ejpam-5909	76	5	,	,	PUNCT
ejpam-5909	76	6	b	b	X
ejpam-5909	76	7	]	]	PUNCT
ejpam-5909	76	8	and	and	CCONJ
ejpam-5909	76	9	a	a	DET
ejpam-5909	76	10	positive	positive	ADJ
ejpam-5909	76	11	real	real	ADJ
ejpam-5909	76	12	number	number	NOUN
ejpam-5909	76	13	ε	ε	PROPN
ejpam-5909	76	14	,	,	PUNCT
ejpam-5909	76	15	the	the	DET
ejpam-5909	76	16	ε	ε	PROPN
ejpam-5909	76	17	-	-	PUNCT
ejpam-5909	76	18	neighborhood	neighborhood	NOUN
ejpam-5909	76	19	of	of	ADP
ejpam-5909	76	20	the	the	DET
ejpam-5909	76	21	function	function	NOUN
ejpam-5909	76	22	f	f	PROPN
ejpam-5909	76	23	is	be	AUX
ejpam-5909	76	24	defined	define	VERB
ejpam-5909	76	25	as	as	ADP
ejpam-5909	76	26	the	the	DET
ejpam-5909	76	27	set	set	NOUN
ejpam-5909	76	28	:	:	PUNCT
ejpam-5909	76	29	vε(f	vε(f	X
ejpam-5909	76	30	)	)	PUNCT
ejpam-5909	76	31	=	=	PRON
ejpam-5909	76	32	{	{	PUNCT
ejpam-5909	76	33	g	g	PROPN
ejpam-5909	76	34	∈	∈	PROPN
ejpam-5909	76	35	c[a	c[a	NOUN
ejpam-5909	76	36	,	,	PUNCT
ejpam-5909	77	1	b	b	X
ejpam-5909	77	2	]	]	X
ejpam-5909	77	3	:	:	PUNCT
ejpam-5909	77	4	|g	|g	VERB
ejpam-5909	77	5	−	−	PROPN
ejpam-5909	77	6	f	f	PROPN
ejpam-5909	77	7	|	|	ADV
ejpam-5909	77	8	≺	≺	VERB
ejpam-5909	77	9	εe	εe	VERB
ejpam-5909	77	10	}	}	PUNCT
ejpam-5909	77	11	.	.	PUNCT
ejpam-5909	78	1	for	for	ADP
ejpam-5909	78	2	example	example	NOUN
ejpam-5909	78	3	,	,	PUNCT
ejpam-5909	78	4	if	if	SCONJ
ejpam-5909	78	5	we	we	PRON
ejpam-5909	78	6	consider	consider	VERB
ejpam-5909	78	7	0	0	NUM
ejpam-5909	78	8	∈	∈	PROPN
ejpam-5909	78	9	c[0	c[0	PROPN
ejpam-5909	78	10	,	,	PUNCT
ejpam-5909	78	11	1	1	NUM
ejpam-5909	78	12	]	]	PUNCT
ejpam-5909	78	13	,	,	PUNCT
ejpam-5909	78	14	the	the	DET
ejpam-5909	78	15	3	3	NUM
ejpam-5909	78	16	-	-	PUNCT
ejpam-5909	78	17	neighborhood	neighborhood	NOUN
ejpam-5909	78	18	of	of	ADP
ejpam-5909	78	19	0	0	NUM
ejpam-5909	78	20	is	be	AUX
ejpam-5909	78	21	given	give	VERB
ejpam-5909	78	22	by	by	ADP
ejpam-5909	78	23	v3(0	v3(0	PROPN
ejpam-5909	78	24	)	)	PUNCT
ejpam-5909	78	25	=	=	PRON
ejpam-5909	78	26	{	{	PUNCT
ejpam-5909	78	27	g	g	PROPN
ejpam-5909	78	28	∈	∈	PROPN
ejpam-5909	78	29	c[0	c[0	PROPN
ejpam-5909	78	30	,	,	PUNCT
ejpam-5909	78	31	1	1	NUM
ejpam-5909	78	32	]	]	PUNCT
ejpam-5909	78	33	:	:	PUNCT
ejpam-5909	78	34	|g	|g	VERB
ejpam-5909	78	35	−	−	NOUN
ejpam-5909	79	1	0|	0|	NUM
ejpam-5909	79	2	≺	≺	NOUN
ejpam-5909	79	3	3e	3e	X
ejpam-5909	79	4	}	}	PUNCT
ejpam-5909	79	5	=	=	SYM
ejpam-5909	79	6	{	{	PUNCT
ejpam-5909	79	7	g	g	PROPN
ejpam-5909	79	8	∈	∈	PROPN
ejpam-5909	79	9	c[0	c[0	PROPN
ejpam-5909	79	10	,	,	PUNCT
ejpam-5909	79	11	1	1	NUM
ejpam-5909	79	12	]	]	PUNCT
ejpam-5909	79	13	:	:	PUNCT
ejpam-5909	79	14	|g|	|g|	ADJ
ejpam-5909	79	15	≺	≺	NOUN
ejpam-5909	79	16	3e	3e	NOUN
ejpam-5909	79	17	}	}	PUNCT
ejpam-5909	79	18	.	.	PUNCT
ejpam-5909	80	1	definition	definition	NOUN
ejpam-5909	80	2	7	7	NUM
ejpam-5909	80	3	.	.	PUNCT
ejpam-5909	80	4	given	give	VERB
ejpam-5909	80	5	a	a	DET
ejpam-5909	80	6	⊂	⊂	PROPN
ejpam-5909	80	7	c[a	c[a	NOUN
ejpam-5909	80	8	,	,	PUNCT
ejpam-5909	80	9	b	b	NOUN
ejpam-5909	80	10	]	]	X
ejpam-5909	80	11	,	,	PUNCT
ejpam-5909	80	12	a	a	DET
ejpam-5909	80	13	function	function	NOUN
ejpam-5909	80	14	f0	f0	PROPN
ejpam-5909	80	15	∈	∈	PROPN
ejpam-5909	80	16	c[a	c[a	NOUN
ejpam-5909	80	17	,	,	PUNCT
ejpam-5909	80	18	b	b	AUX
ejpam-5909	80	19	]	]	PUNCT
ejpam-5909	80	20	is	be	AUX
ejpam-5909	80	21	called	call	VERB
ejpam-5909	80	22	a	a	DET
ejpam-5909	80	23	limit	limit	NOUN
ejpam-5909	80	24	point	point	NOUN
ejpam-5909	80	25	of	of	ADP
ejpam-5909	80	26	the	the	DET
ejpam-5909	80	27	set	set	NOUN
ejpam-5909	80	28	a	a	DET
ejpam-5909	80	29	if	if	NOUN
ejpam-5909	80	30	,	,	PUNCT
ejpam-5909	80	31	for	for	ADP
ejpam-5909	80	32	any	any	DET
ejpam-5909	80	33	real	real	ADJ
ejpam-5909	80	34	number	number	NOUN
ejpam-5909	80	35	ε	ε	PROPN
ejpam-5909	80	36	>	>	X
ejpam-5909	80	37	0	0	PROPN
ejpam-5909	80	38	,	,	PUNCT
ejpam-5909	80	39	the	the	DET
ejpam-5909	80	40	following	follow	VERB
ejpam-5909	80	41	condition	condition	NOUN
ejpam-5909	80	42	holds	hold	VERB
ejpam-5909	80	43	:	:	PUNCT
ejpam-5909	80	44	(	(	PUNCT
ejpam-5909	80	45	vε(f0	vε(f0	NOUN
ejpam-5909	80	46	)	)	PUNCT
ejpam-5909	80	47	∩a	∩a	PROPN
ejpam-5909	80	48	)	)	PUNCT
ejpam-5909	80	49	\	\	PROPN
ejpam-5909	80	50	{	{	PUNCT
ejpam-5909	80	51	f0	f0	PROPN
ejpam-5909	80	52	}	}	PUNCT
ejpam-5909	80	53	=	=	NOUN
ejpam-5909	80	54	̸	̸	ADV
ejpam-5909	80	55	∅.	∅.	ADP
ejpam-5909	80	56	the	the	DET
ejpam-5909	80	57	function	function	NOUN
ejpam-5909	80	58	f0	f0	NOUN
ejpam-5909	80	59	may	may	AUX
ejpam-5909	80	60	or	or	CCONJ
ejpam-5909	80	61	may	may	AUX
ejpam-5909	80	62	not	not	PART
ejpam-5909	80	63	be	be	AUX
ejpam-5909	80	64	contained	contain	VERB
ejpam-5909	80	65	in	in	ADP
ejpam-5909	80	66	a.	a.	NOUN
ejpam-5909	80	67	explicitly	explicitly	ADV
ejpam-5909	80	68	,	,	PUNCT
ejpam-5909	80	69	there	there	PRON
ejpam-5909	80	70	must	must	AUX
ejpam-5909	80	71	exist	exist	VERB
ejpam-5909	80	72	a	a	DET
ejpam-5909	80	73	function	function	NOUN
ejpam-5909	80	74	in	in	ADP
ejpam-5909	80	75	(	(	PUNCT
ejpam-5909	80	76	vε(f0	vε(f0	ADJ
ejpam-5909	80	77	)	)	PUNCT
ejpam-5909	80	78	∩	∩	NOUN
ejpam-5909	80	79	a	a	X
ejpam-5909	80	80	)	)	PUNCT
ejpam-5909	80	81	that	that	PRON
ejpam-5909	80	82	is	be	AUX
ejpam-5909	80	83	different	different	ADJ
ejpam-5909	80	84	from	from	ADP
ejpam-5909	80	85	f0	f0	PROPN
ejpam-5909	80	86	for	for	SCONJ
ejpam-5909	80	87	f0	f0	PROPN
ejpam-5909	80	88	to	to	PART
ejpam-5909	80	89	be	be	AUX
ejpam-5909	80	90	a	a	DET
ejpam-5909	80	91	limit	limit	NOUN
ejpam-5909	80	92	point	point	NOUN
ejpam-5909	80	93	of	of	ADP
ejpam-5909	80	94	the	the	DET
ejpam-5909	80	95	set	set	NOUN
ejpam-5909	80	96	a.	a.	NOUN
ejpam-5909	80	97	as	as	ADP
ejpam-5909	80	98	an	an	DET
ejpam-5909	80	99	illustration	illustration	NOUN
ejpam-5909	80	100	,	,	PUNCT
ejpam-5909	80	101	consider	consider	VERB
ejpam-5909	80	102	the	the	DET
ejpam-5909	80	103	following	follow	VERB
ejpam-5909	80	104	example	example	NOUN
ejpam-5909	80	105	.	.	PUNCT
ejpam-5909	81	1	example	example	NOUN
ejpam-5909	82	1	1	1	NUM
ejpam-5909	82	2	.	.	PUNCT
ejpam-5909	82	3	given	give	VERB
ejpam-5909	82	4	a	a	DET
ejpam-5909	82	5	=	=	X
ejpam-5909	82	6	(	(	PUNCT
ejpam-5909	82	7	g1	g1	PROPN
ejpam-5909	82	8	,	,	PUNCT
ejpam-5909	82	9	g2	g2	PROPN
ejpam-5909	82	10	)	)	PUNCT
ejpam-5909	82	11	∪	∪	ADP
ejpam-5909	82	12	{	{	PUNCT
ejpam-5909	82	13	g3	g3	PROPN
ejpam-5909	82	14	}	}	PUNCT
ejpam-5909	82	15	⊂	⊂	PROPN
ejpam-5909	82	16	c[1	c[1	PROPN
ejpam-5909	82	17	,	,	PUNCT
ejpam-5909	82	18	2	2	NUM
ejpam-5909	82	19	]	]	PUNCT
ejpam-5909	82	20	with	with	ADP
ejpam-5909	82	21	g1(x	g1(x	NOUN
ejpam-5909	82	22	)	)	PUNCT
ejpam-5909	82	23	=	=	SYM
ejpam-5909	82	24	x	x	NOUN
ejpam-5909	82	25	,	,	PUNCT
ejpam-5909	82	26	g2(x	g2(x	X
ejpam-5909	82	27	)	)	PUNCT
ejpam-5909	82	28	=	=	SYM
ejpam-5909	82	29	3x	3x	NUM
ejpam-5909	82	30	,	,	PUNCT
ejpam-5909	82	31	and	and	CCONJ
ejpam-5909	82	32	g3(x	g3(x	PROPN
ejpam-5909	82	33	)	)	PUNCT
ejpam-5909	82	34	=	=	PUNCT
ejpam-5909	82	35	5x	5x	NOUN
ejpam-5909	82	36	,	,	PUNCT
ejpam-5909	82	37	each	each	PRON
ejpam-5909	82	38	defined	define	VERB
ejpam-5909	82	39	on	on	ADP
ejpam-5909	82	40	the	the	DET
ejpam-5909	82	41	interval	interval	NOUN
ejpam-5909	82	42	[	[	X
ejpam-5909	82	43	1	1	NUM
ejpam-5909	82	44	,	,	PUNCT
ejpam-5909	82	45	2	2	NUM
ejpam-5909	82	46	]	]	PUNCT
ejpam-5909	82	47	,	,	PUNCT
ejpam-5909	82	48	we	we	PRON
ejpam-5909	82	49	will	will	AUX
ejpam-5909	82	50	show	show	VERB
ejpam-5909	82	51	that	that	SCONJ
ejpam-5909	82	52	the	the	DET
ejpam-5909	82	53	function	function	NOUN
ejpam-5909	82	54	h	h	NOUN
ejpam-5909	82	55	∈	∈	PROPN
ejpam-5909	82	56	a	a	PRON
ejpam-5909	82	57	with	with	ADP
ejpam-5909	82	58	h(x	h(x	PROPN
ejpam-5909	82	59	)	)	PUNCT
ejpam-5909	82	60	=	=	PUNCT
ejpam-5909	82	61	2x	2x	NOUN
ejpam-5909	82	62	and	and	CCONJ
ejpam-5909	82	63	g1	g1	NOUN
ejpam-5909	82	64	/∈	/∈	PUNCT
ejpam-5909	83	1	a	a	PRON
ejpam-5909	83	2	is	be	AUX
ejpam-5909	83	3	a	a	DET
ejpam-5909	83	4	limit	limit	NOUN
ejpam-5909	83	5	point	point	NOUN
ejpam-5909	83	6	of	of	ADP
ejpam-5909	83	7	a	a	PRON
ejpam-5909	83	8	,	,	PUNCT
ejpam-5909	83	9	while	while	SCONJ
ejpam-5909	83	10	g3	g3	PROPN
ejpam-5909	83	11	∈	∈	PROPN
ejpam-5909	83	12	a	a	PRON
ejpam-5909	83	13	is	be	AUX
ejpam-5909	83	14	not	not	PART
ejpam-5909	83	15	a	a	DET
ejpam-5909	83	16	limit	limit	NOUN
ejpam-5909	83	17	point	point	NOUN
ejpam-5909	83	18	of	of	ADP
ejpam-5909	83	19	a.	a.	NOUN
ejpam-5909	83	20	the	the	DET
ejpam-5909	83	21	function	function	NOUN
ejpam-5909	83	22	h(t	h(t	PROPN
ejpam-5909	83	23	)	)	PUNCT
ejpam-5909	83	24	is	be	AUX
ejpam-5909	83	25	a	a	DET
ejpam-5909	83	26	limit	limit	NOUN
ejpam-5909	83	27	point	point	NOUN
ejpam-5909	83	28	of	of	ADP
ejpam-5909	83	29	the	the	DET
ejpam-5909	83	30	set	set	NOUN
ejpam-5909	83	31	a	a	PRON
ejpam-5909	83	32	because	because	SCONJ
ejpam-5909	83	33	for	for	ADP
ejpam-5909	83	34	any	any	DET
ejpam-5909	83	35	real	real	ADJ
ejpam-5909	83	36	number	number	NOUN
ejpam-5909	83	37	ε	ε	PROPN
ejpam-5909	83	38	>	>	X
ejpam-5909	83	39	0	0	PROPN
ejpam-5909	83	40	,	,	PUNCT
ejpam-5909	83	41	there	there	PRON
ejpam-5909	83	42	exists	exist	VERB
ejpam-5909	83	43	:	:	PUNCT
ejpam-5909	83	44	f(x	f(x	PROPN
ejpam-5909	83	45	)	)	PUNCT
ejpam-5909	84	1	=	=	PRON
ejpam-5909	84	2	{	{	PUNCT
ejpam-5909	84	3	h+	h+	PROPN
ejpam-5909	84	4	1	1	NUM
ejpam-5909	84	5	2εe	2εe	NOUN
ejpam-5909	84	6	,	,	PUNCT
ejpam-5909	84	7	if	if	SCONJ
ejpam-5909	84	8	ε	ε	PROPN
ejpam-5909	84	9	<	<	X
ejpam-5909	84	10	1	1	NUM
ejpam-5909	84	11	,	,	PUNCT
ejpam-5909	84	12	3	3	NUM
ejpam-5909	84	13	2h	2h	NUM
ejpam-5909	84	14	,	,	PUNCT
ejpam-5909	84	15	if	if	SCONJ
ejpam-5909	84	16	ε	ε	PROPN
ejpam-5909	84	17	>	>	X
ejpam-5909	84	18	1	1	NUM
ejpam-5909	84	19	,	,	PUNCT
ejpam-5909	84	20	such	such	ADJ
ejpam-5909	84	21	that	that	SCONJ
ejpam-5909	84	22	f	f	PROPN
ejpam-5909	84	23	∈	∈	PROPN
ejpam-5909	84	24	(	(	PUNCT
ejpam-5909	84	25	vε(h	vε(h	ADJ
ejpam-5909	84	26	)	)	PUNCT
ejpam-5909	84	27	∩a	∩a	PROPN
ejpam-5909	84	28	)	)	PUNCT
ejpam-5909	84	29	and	and	CCONJ
ejpam-5909	84	30	f	f	PROPN
ejpam-5909	84	31	̸=	̸=	PROPN
ejpam-5909	84	32	h	h	NOUN
ejpam-5909	84	33	,	,	PUNCT
ejpam-5909	84	34	or	or	CCONJ
ejpam-5909	84	35	equivalently	equivalently	ADV
ejpam-5909	84	36	,	,	PUNCT
ejpam-5909	84	37	(	(	PUNCT
ejpam-5909	84	38	vε(h	vε(h	ADV
ejpam-5909	84	39	)	)	PUNCT
ejpam-5909	84	40	∩a	∩a	PROPN
ejpam-5909	84	41	)	)	PUNCT
ejpam-5909	84	42	\	\	NOUN
ejpam-5909	84	43	{	{	PUNCT
ejpam-5909	84	44	h	h	NOUN
ejpam-5909	84	45	}	}	PUNCT
ejpam-5909	84	46	=	=	NOUN
ejpam-5909	84	47	̸	̸	X
ejpam-5909	84	48	∅.	∅.	VERB
ejpam-5909	84	49	similarly	similarly	ADV
ejpam-5909	84	50	,	,	PUNCT
ejpam-5909	84	51	the	the	DET
ejpam-5909	84	52	function	function	NOUN
ejpam-5909	84	53	g1	g1	PROPN
ejpam-5909	84	54	/∈	/∈	PUNCT
ejpam-5909	85	1	a	a	PRON
ejpam-5909	85	2	is	be	AUX
ejpam-5909	85	3	a	a	DET
ejpam-5909	85	4	limit	limit	NOUN
ejpam-5909	85	5	point	point	NOUN
ejpam-5909	85	6	of	of	ADP
ejpam-5909	85	7	the	the	DET
ejpam-5909	85	8	set	set	NOUN
ejpam-5909	85	9	a	a	PRON
ejpam-5909	85	10	because	because	SCONJ
ejpam-5909	85	11	for	for	ADP
ejpam-5909	85	12	any	any	DET
ejpam-5909	85	13	real	real	ADJ
ejpam-5909	85	14	number	number	NOUN
ejpam-5909	85	15	ε	ε	PROPN
ejpam-5909	85	16	>	>	X
ejpam-5909	85	17	0	0	PROPN
ejpam-5909	85	18	,	,	PUNCT
ejpam-5909	85	19	there	there	PRON
ejpam-5909	85	20	exists	exist	VERB
ejpam-5909	85	21	:	:	PUNCT
ejpam-5909	85	22	f(x	f(x	PROPN
ejpam-5909	85	23	)	)	PUNCT
ejpam-5909	86	1	=	=	PRON
ejpam-5909	86	2	{	{	PUNCT
ejpam-5909	86	3	g	g	PROPN
ejpam-5909	86	4	+	+	CCONJ
ejpam-5909	86	5	1	1	NUM
ejpam-5909	86	6	2εe	2εe	NOUN
ejpam-5909	86	7	,	,	PUNCT
ejpam-5909	86	8	if	if	SCONJ
ejpam-5909	86	9	ε	ε	PROPN
ejpam-5909	86	10	<	<	X
ejpam-5909	86	11	2	2	NUM
ejpam-5909	86	12	,	,	PUNCT
ejpam-5909	86	13	2g1	2g1	NUM
ejpam-5909	86	14	,	,	PUNCT
ejpam-5909	86	15	if	if	SCONJ
ejpam-5909	86	16	ε	ε	PROPN
ejpam-5909	86	17	>	>	X
ejpam-5909	86	18	2	2	NUM
ejpam-5909	86	19	,	,	PUNCT
ejpam-5909	86	20	such	such	ADJ
ejpam-5909	86	21	that	that	SCONJ
ejpam-5909	86	22	f	f	PROPN
ejpam-5909	86	23	∈	∈	PROPN
ejpam-5909	86	24	(	(	PUNCT
ejpam-5909	86	25	vε(g1	vε(g1	NOUN
ejpam-5909	86	26	)	)	PUNCT
ejpam-5909	86	27	∩a	∩a	PROPN
ejpam-5909	86	28	)	)	PUNCT
ejpam-5909	86	29	and	and	CCONJ
ejpam-5909	86	30	f	f	PROPN
ejpam-5909	86	31	̸=	̸=	PROPN
ejpam-5909	86	32	g1	g1	PROPN
ejpam-5909	86	33	,	,	PUNCT
ejpam-5909	86	34	or	or	CCONJ
ejpam-5909	86	35	equivalently	equivalently	ADV
ejpam-5909	86	36	,	,	PUNCT
ejpam-5909	86	37	(	(	PUNCT
ejpam-5909	86	38	vε(g1	vε(g1	NOUN
ejpam-5909	86	39	)	)	PUNCT
ejpam-5909	86	40	∩a	∩a	PROPN
ejpam-5909	86	41	)	)	PUNCT
ejpam-5909	86	42	\	\	NOUN
ejpam-5909	86	43	{	{	PUNCT
ejpam-5909	86	44	g1	g1	PROPN
ejpam-5909	86	45	}	}	PUNCT
ejpam-5909	86	46	=	=	SYM
ejpam-5909	86	47	̸	̸	ADV
ejpam-5909	86	48	∅.	∅.	PRON
ejpam-5909	86	49	m.	m.	NOUN
ejpam-5909	86	50	alifuddin	alifuddin	VERB
ejpam-5909	86	51	et	et	PROPN
ejpam-5909	86	52	al	al	PROPN
ejpam-5909	86	53	.	.	PUNCT
ejpam-5909	86	54	/	/	SYM
ejpam-5909	86	55	eur	eur	PROPN
ejpam-5909	86	56	.	.	PUNCT
ejpam-5909	87	1	j.	j.	PROPN
ejpam-5909	87	2	pure	pure	PROPN
ejpam-5909	87	3	appl	appl	PROPN
ejpam-5909	87	4	.	.	PROPN
ejpam-5909	87	5	math	math	PROPN
ejpam-5909	87	6	,	,	PUNCT
ejpam-5909	87	7	18	18	NUM
ejpam-5909	87	8	(	(	PUNCT
ejpam-5909	87	9	2	2	NUM
ejpam-5909	87	10	)	)	PUNCT
ejpam-5909	87	11	(	(	PUNCT
ejpam-5909	87	12	2025	2025	NUM
ejpam-5909	87	13	)	)	PUNCT
ejpam-5909	87	14	,	,	PUNCT
ejpam-5909	87	15	5909	5909	NUM
ejpam-5909	87	16	5	5	NUM
ejpam-5909	87	17	of	of	ADP
ejpam-5909	87	18	17	17	NUM
ejpam-5909	87	19	next	next	ADV
ejpam-5909	88	1	,	,	PUNCT
ejpam-5909	88	2	we	we	PRON
ejpam-5909	88	3	show	show	VERB
ejpam-5909	88	4	that	that	SCONJ
ejpam-5909	88	5	g3	g3	PROPN
ejpam-5909	88	6	∈	∈	PROPN
ejpam-5909	88	7	a	a	PRON
ejpam-5909	88	8	is	be	AUX
ejpam-5909	88	9	not	not	PART
ejpam-5909	88	10	a	a	DET
ejpam-5909	88	11	limit	limit	NOUN
ejpam-5909	88	12	point	point	NOUN
ejpam-5909	88	13	of	of	ADP
ejpam-5909	88	14	the	the	DET
ejpam-5909	88	15	set	set	NOUN
ejpam-5909	88	16	a.	a.	NOUN
ejpam-5909	88	17	the	the	DET
ejpam-5909	88	18	function	function	NOUN
ejpam-5909	88	19	g3	g3	PROPN
ejpam-5909	88	20	∈	∈	PROPN
ejpam-5909	88	21	a	a	PRON
ejpam-5909	88	22	is	be	AUX
ejpam-5909	88	23	not	not	PART
ejpam-5909	88	24	a	a	DET
ejpam-5909	88	25	limit	limit	NOUN
ejpam-5909	88	26	point	point	NOUN
ejpam-5909	88	27	of	of	ADP
ejpam-5909	88	28	a	a	PRON
ejpam-5909	88	29	because	because	SCONJ
ejpam-5909	88	30	there	there	PRON
ejpam-5909	88	31	exists	exist	VERB
ejpam-5909	88	32	a	a	DET
ejpam-5909	88	33	real	real	ADJ
ejpam-5909	88	34	number	number	NOUN
ejpam-5909	88	35	ε	ε	NOUN
ejpam-5909	88	36	=	=	NOUN
ejpam-5909	88	37	1	1	NUM
ejpam-5909	88	38	such	such	ADJ
ejpam-5909	88	39	that	that	SCONJ
ejpam-5909	88	40	(	(	PUNCT
ejpam-5909	88	41	vε(g3	vε(g3	NOUN
ejpam-5909	88	42	)	)	PUNCT
ejpam-5909	88	43	∩a	∩a	NOUN
ejpam-5909	88	44	)	)	PUNCT
ejpam-5909	88	45	\	\	PROPN
ejpam-5909	88	46	{	{	PUNCT
ejpam-5909	88	47	g3	g3	PROPN
ejpam-5909	88	48	}	}	PUNCT
ejpam-5909	88	49	=	=	SYM
ejpam-5909	88	50	{	{	PUNCT
ejpam-5909	88	51	g3	g3	NOUN
ejpam-5909	88	52	}	}	PUNCT
ejpam-5909	88	53	,	,	PUNCT
ejpam-5909	88	54	which	which	PRON
ejpam-5909	88	55	simplifies	simplify	VERB
ejpam-5909	88	56	to	to	ADP
ejpam-5909	88	57	(	(	PUNCT
ejpam-5909	88	58	vε(g3	vε(g3	NOUN
ejpam-5909	88	59	)	)	PUNCT
ejpam-5909	88	60	∩a	∩a	NOUN
ejpam-5909	88	61	)	)	PUNCT
ejpam-5909	88	62	\	\	PROPN
ejpam-5909	88	63	{	{	PUNCT
ejpam-5909	88	64	g3	g3	NOUN
ejpam-5909	88	65	}	}	PUNCT
ejpam-5909	88	66	=	=	PUNCT
ejpam-5909	88	67	∅.	∅.	PRON
ejpam-5909	88	68	definition	definition	NOUN
ejpam-5909	88	69	8	8	NUM
ejpam-5909	88	70	.	.	PUNCT
ejpam-5909	89	1	given	give	VERB
ejpam-5909	89	2	a	a	DET
ejpam-5909	89	3	⊆	⊆	NUM
ejpam-5909	89	4	c[a	c[a	NUM
ejpam-5909	89	5	,	,	PUNCT
ejpam-5909	89	6	b	b	NOUN
ejpam-5909	89	7	]	]	PUNCT
ejpam-5909	89	8	and	and	CCONJ
ejpam-5909	89	9	a	a	DET
ejpam-5909	89	10	function	function	NOUN
ejpam-5909	89	11	f0	f0	NOUN
ejpam-5909	89	12	as	as	ADP
ejpam-5909	89	13	a	a	DET
ejpam-5909	89	14	limit	limit	NOUN
ejpam-5909	89	15	point	point	NOUN
ejpam-5909	89	16	of	of	ADP
ejpam-5909	89	17	the	the	DET
ejpam-5909	89	18	set	set	NOUN
ejpam-5909	89	19	a	a	NOUN
ejpam-5909	89	20	,	,	PUNCT
ejpam-5909	89	21	an	an	DET
ejpam-5909	89	22	operator	operator	NOUN
ejpam-5909	89	23	f	f	NOUN
ejpam-5909	89	24	:	:	PUNCT
ejpam-5909	89	25	a	a	PRON
ejpam-5909	89	26	→	→	SYM
ejpam-5909	89	27	c[a	c[a	NUM
ejpam-5909	89	28	,	,	PUNCT
ejpam-5909	89	29	b	b	AUX
ejpam-5909	89	30	]	]	X
ejpam-5909	89	31	has	have	VERB
ejpam-5909	89	32	a	a	DET
ejpam-5909	89	33	limit	limit	NOUN
ejpam-5909	89	34	operator	operator	NOUN
ejpam-5909	89	35	l	l	NOUN
ejpam-5909	89	36	at	at	ADP
ejpam-5909	89	37	f0	f0	PROPN
ejpam-5909	89	38	if	if	SCONJ
ejpam-5909	89	39	for	for	ADP
ejpam-5909	89	40	every	every	DET
ejpam-5909	89	41	real	real	ADJ
ejpam-5909	89	42	number	number	NOUN
ejpam-5909	89	43	ε	ε	PROPN
ejpam-5909	89	44	>	>	X
ejpam-5909	89	45	0	0	PROPN
ejpam-5909	89	46	,	,	PUNCT
ejpam-5909	89	47	there	there	PRON
ejpam-5909	89	48	exists	exist	VERB
ejpam-5909	89	49	a	a	DET
ejpam-5909	89	50	real	real	ADJ
ejpam-5909	89	51	number	number	NOUN
ejpam-5909	89	52	δ	δ	NOUN
ejpam-5909	89	53	>	>	X
ejpam-5909	89	54	0	0	NUM
ejpam-5909	89	55	such	such	ADJ
ejpam-5909	89	56	that	that	PRON
ejpam-5909	89	57	for	for	ADP
ejpam-5909	89	58	every	every	DET
ejpam-5909	89	59	f	f	PROPN
ejpam-5909	89	60	∈	∈	PROPN
ejpam-5909	89	61	a	a	DET
ejpam-5909	89	62	satisfying	satisfy	VERB
ejpam-5909	89	63	0	0	NUM
ejpam-5909	89	64	≺	≺	NOUN
ejpam-5909	89	65	|f	|f	ADP
ejpam-5909	89	66	−	−	PROPN
ejpam-5909	89	67	f0|	f0|	PROPN
ejpam-5909	89	68	≺	≺	NOUN
ejpam-5909	89	69	δe	δe	NOUN
ejpam-5909	89	70	,	,	PUNCT
ejpam-5909	89	71	the	the	DET
ejpam-5909	89	72	following	follow	VERB
ejpam-5909	89	73	holds	hold	VERB
ejpam-5909	89	74	:	:	PUNCT
ejpam-5909	89	75	|f	|f	PROPN
ejpam-5909	90	1	(	(	PUNCT
ejpam-5909	90	2	f)−	f)−	PROPN
ejpam-5909	90	3	l|	l|	ADJ
ejpam-5909	90	4	≺	≺	NOUN
ejpam-5909	90	5	εe	εe	NOUN
ejpam-5909	90	6	.	.	PUNCT
ejpam-5909	91	1	the	the	DET
ejpam-5909	91	2	inequality	inequality	NOUN
ejpam-5909	91	3	0	0	NUM
ejpam-5909	91	4	≺	≺	NOUN
ejpam-5909	91	5	|f	|f	PRON
ejpam-5909	91	6	−	−	PROPN
ejpam-5909	92	1	f0|	f0|	PROPN
ejpam-5909	92	2	is	be	AUX
ejpam-5909	92	3	equivalent	equivalent	ADJ
ejpam-5909	92	4	to	to	ADP
ejpam-5909	92	5	the	the	DET
ejpam-5909	92	6	statement	statement	NOUN
ejpam-5909	92	7	f	f	PROPN
ejpam-5909	92	8	̸=	̸=	PROPN
ejpam-5909	92	9	f0	f0	PROPN
ejpam-5909	92	10	.	.	PUNCT
ejpam-5909	93	1	if	if	SCONJ
ejpam-5909	93	2	l	l	NOUN
ejpam-5909	93	3	is	be	AUX
ejpam-5909	93	4	the	the	DET
ejpam-5909	93	5	limit	limit	NOUN
ejpam-5909	93	6	operator	operator	NOUN
ejpam-5909	93	7	of	of	ADP
ejpam-5909	93	8	f	f	PROPN
ejpam-5909	93	9	at	at	ADP
ejpam-5909	93	10	f0	f0	PROPN
ejpam-5909	93	11	,	,	PUNCT
ejpam-5909	93	12	then	then	ADV
ejpam-5909	93	13	it	it	PRON
ejpam-5909	93	14	can	can	AUX
ejpam-5909	93	15	be	be	AUX
ejpam-5909	93	16	written	write	VERB
ejpam-5909	93	17	as	as	ADP
ejpam-5909	93	18	:	:	PUNCT
ejpam-5909	93	19	l	l	NOUN
ejpam-5909	93	20	=	=	PROPN
ejpam-5909	94	1	lim	lim	PROPN
ejpam-5909	94	2	f→f0	f→f0	PROPN
ejpam-5909	95	1	f	f	X
ejpam-5909	95	2	(	(	PUNCT
ejpam-5909	95	3	f	f	PROPN
ejpam-5909	95	4	)	)	PUNCT
ejpam-5909	95	5	.	.	PUNCT
ejpam-5909	96	1	example	example	NOUN
ejpam-5909	97	1	2	2	NUM
ejpam-5909	97	2	.	.	X
ejpam-5909	97	3	it	it	PRON
ejpam-5909	97	4	will	will	AUX
ejpam-5909	97	5	be	be	AUX
ejpam-5909	97	6	shown	show	VERB
ejpam-5909	97	7	that	that	SCONJ
ejpam-5909	97	8	:	:	PUNCT
ejpam-5909	97	9	lim	lim	PROPN
ejpam-5909	97	10	f→2e	f→2e	NOUN
ejpam-5909	97	11	(	(	PUNCT
ejpam-5909	97	12	2f	2f	NOUN
ejpam-5909	97	13	+	+	CCONJ
ejpam-5909	97	14	e	e	X
ejpam-5909	97	15	)	)	PUNCT
ejpam-5909	97	16	=	=	SYM
ejpam-5909	97	17	5e	5e	NOUN
ejpam-5909	97	18	.	.	PUNCT
ejpam-5909	98	1	for	for	ADP
ejpam-5909	98	2	any	any	DET
ejpam-5909	98	3	positive	positive	ADJ
ejpam-5909	98	4	real	real	ADJ
ejpam-5909	98	5	number	number	NOUN
ejpam-5909	98	6	ε	ε	PROPN
ejpam-5909	98	7	,	,	PUNCT
ejpam-5909	98	8	we	we	PRON
ejpam-5909	98	9	choose	choose	VERB
ejpam-5909	98	10	a	a	DET
ejpam-5909	98	11	positive	positive	ADJ
ejpam-5909	98	12	real	real	ADJ
ejpam-5909	98	13	number	number	NOUN
ejpam-5909	98	14	δ	δ	NOUN
ejpam-5909	98	15	=	=	SYM
ejpam-5909	98	16	ε	ε	PROPN
ejpam-5909	98	17	2	2	NUM
ejpam-5909	98	18	such	such	ADJ
ejpam-5909	98	19	that	that	PRON
ejpam-5909	98	20	for	for	ADP
ejpam-5909	98	21	every	every	DET
ejpam-5909	98	22	f	f	PROPN
ejpam-5909	98	23	∈	∈	PROPN
ejpam-5909	98	24	a	a	DET
ejpam-5909	98	25	satisfying	satisfy	VERB
ejpam-5909	98	26	0	0	NUM
ejpam-5909	98	27	≺	≺	NOUN
ejpam-5909	98	28	|f	|f	PUNCT
ejpam-5909	98	29	−	−	PROPN
ejpam-5909	98	30	2e|	2e|	NUM
ejpam-5909	98	31	≺	≺	NOUN
ejpam-5909	98	32	δe	δe	ADP
ejpam-5909	98	33	,	,	PUNCT
ejpam-5909	98	34	we	we	PRON
ejpam-5909	98	35	obtain	obtain	VERB
ejpam-5909	98	36	:	:	PUNCT
ejpam-5909	98	37	|(2f	|(2f	X
ejpam-5909	98	38	+	+	X
ejpam-5909	98	39	e)−	e)−	PROPN
ejpam-5909	98	40	(	(	PUNCT
ejpam-5909	98	41	5e)|	5e)|	NOUN
ejpam-5909	98	42	≺	≺	NOUN
ejpam-5909	98	43	|2f	|2f	X
ejpam-5909	98	44	−	−	NOUN
ejpam-5909	98	45	4e|	4e|	NUM
ejpam-5909	99	1	=	=	PRON
ejpam-5909	99	2	|2(f	|2(f	ADP
ejpam-5909	99	3	−	−	PROPN
ejpam-5909	99	4	2e)|	2e)|	NUM
ejpam-5909	99	5	.	.	PUNCT
ejpam-5909	100	1	|	|	ADV
ejpam-5909	100	2	2(f	2(f	NUM
ejpam-5909	100	3	−	−	NUM
ejpam-5909	101	1	2e)|	2e)|	NUM
ejpam-5909	101	2	=	=	SYM
ejpam-5909	101	3	|2|	|2|	PROPN
ejpam-5909	101	4	|f	|f	PROPN
ejpam-5909	101	5	−	−	PROPN
ejpam-5909	101	6	2e|	2e|	NUM
ejpam-5909	102	1	=	=	SYM
ejpam-5909	102	2	2|f	2|f	NUM
ejpam-5909	103	1	−	−	ADP
ejpam-5909	103	2	2e|	2e|	NUM
ejpam-5909	103	3	≺	≺	VERB
ejpam-5909	103	4	2δe	2δe	NOUN
ejpam-5909	103	5	=	=	SYM
ejpam-5909	103	6	2δe	2δe	NOUN
ejpam-5909	103	7	.	.	PUNCT
ejpam-5909	104	1	by	by	ADP
ejpam-5909	104	2	substituting	substitute	VERB
ejpam-5909	104	3	δ	δ	PROPN
ejpam-5909	104	4	=	=	SYM
ejpam-5909	104	5	ε	ε	PROPN
ejpam-5909	104	6	2	2	NUM
ejpam-5909	104	7	,	,	PUNCT
ejpam-5909	104	8	we	we	PRON
ejpam-5909	104	9	obtain	obtain	VERB
ejpam-5909	104	10	:	:	PUNCT
ejpam-5909	104	11	2δe	2δe	NOUN
ejpam-5909	104	12	=	=	SYM
ejpam-5909	104	13	2	2	NUM
ejpam-5909	104	14	(	(	PUNCT
ejpam-5909	104	15	ε	ε	PROPN
ejpam-5909	104	16	2	2	NUM
ejpam-5909	104	17	)	)	PUNCT
ejpam-5909	104	18	e	e	NOUN
ejpam-5909	104	19	=	=	SYM
ejpam-5909	104	20	εe	εe	PROPN
ejpam-5909	104	21	.	.	PUNCT
ejpam-5909	105	1	thus	thus	ADV
ejpam-5909	105	2	:	:	PUNCT
ejpam-5909	105	3	lim	lim	PROPN
ejpam-5909	105	4	f→2e	f→2e	NOUN
ejpam-5909	105	5	(	(	PUNCT
ejpam-5909	105	6	2f	2f	NOUN
ejpam-5909	105	7	+	+	CCONJ
ejpam-5909	105	8	e	e	X
ejpam-5909	105	9	)	)	PUNCT
ejpam-5909	105	10	=	=	SYM
ejpam-5909	105	11	5e	5e	NOUN
ejpam-5909	105	12	.	.	PUNCT
ejpam-5909	106	1	example	example	NOUN
ejpam-5909	107	1	3	3	X
ejpam-5909	107	2	.	.	X
ejpam-5909	107	3	consider	consider	VERB
ejpam-5909	107	4	f	f	NOUN
ejpam-5909	107	5	:	:	PUNCT
ejpam-5909	107	6	c[a	c[a	NUM
ejpam-5909	107	7	,	,	PUNCT
ejpam-5909	107	8	b	b	X
ejpam-5909	107	9	]	]	X
ejpam-5909	107	10	→	→	SYM
ejpam-5909	107	11	c[a	c[a	NUM
ejpam-5909	107	12	,	,	PUNCT
ejpam-5909	107	13	b	b	NOUN
ejpam-5909	107	14	]	]	X
ejpam-5909	107	15	defined	define	VERB
ejpam-5909	107	16	as	as	ADP
ejpam-5909	107	17	:	:	PUNCT
ejpam-5909	107	18	f	f	PROPN
ejpam-5909	107	19	(	(	PUNCT
ejpam-5909	107	20	f	f	X
ejpam-5909	107	21	)	)	PUNCT
ejpam-5909	107	22	=	=	PRON
ejpam-5909	107	23	{	{	PUNCT
ejpam-5909	107	24	e	e	X
ejpam-5909	107	25	,	,	PUNCT
ejpam-5909	107	26	if	if	SCONJ
ejpam-5909	107	27	f	f	PROPN
ejpam-5909	107	28	⪯	⪯	PROPN
ejpam-5909	107	29	0	0	NUM
ejpam-5909	107	30	,	,	PUNCT
ejpam-5909	107	31	2e	2e	NUM
ejpam-5909	107	32	,	,	PUNCT
ejpam-5909	107	33	if	if	SCONJ
ejpam-5909	107	34	f	f	PROPN
ejpam-5909	107	35	≻	≻	PROPN
ejpam-5909	107	36	0	0	PROPN
ejpam-5909	107	37	.	.	PUNCT
ejpam-5909	107	38	m.	m.	NOUN
ejpam-5909	107	39	alifuddin	alifuddin	VERB
ejpam-5909	107	40	et	et	PROPN
ejpam-5909	107	41	al	al	PROPN
ejpam-5909	107	42	.	.	PUNCT
ejpam-5909	107	43	/	/	SYM
ejpam-5909	107	44	eur	eur	PROPN
ejpam-5909	107	45	.	.	PUNCT
ejpam-5909	108	1	j.	j.	PROPN
ejpam-5909	108	2	pure	pure	PROPN
ejpam-5909	108	3	appl	appl	PROPN
ejpam-5909	108	4	.	.	PROPN
ejpam-5909	108	5	math	math	PROPN
ejpam-5909	108	6	,	,	PUNCT
ejpam-5909	108	7	18	18	NUM
ejpam-5909	108	8	(	(	PUNCT
ejpam-5909	108	9	2	2	NUM
ejpam-5909	108	10	)	)	PUNCT
ejpam-5909	108	11	(	(	PUNCT
ejpam-5909	108	12	2025	2025	NUM
ejpam-5909	108	13	)	)	PUNCT
ejpam-5909	108	14	,	,	PUNCT
ejpam-5909	108	15	5909	5909	NUM
ejpam-5909	108	16	6	6	NUM
ejpam-5909	108	17	of	of	ADP
ejpam-5909	108	18	17	17	NUM
ejpam-5909	108	19	it	it	PRON
ejpam-5909	108	20	will	will	AUX
ejpam-5909	108	21	be	be	AUX
ejpam-5909	108	22	shown	show	VERB
ejpam-5909	108	23	that	that	SCONJ
ejpam-5909	108	24	f	f	PROPN
ejpam-5909	108	25	(	(	PUNCT
ejpam-5909	108	26	0	0	NUM
ejpam-5909	108	27	)	)	PUNCT
ejpam-5909	108	28	=	=	SYM
ejpam-5909	109	1	e	e	NOUN
ejpam-5909	109	2	is	be	AUX
ejpam-5909	109	3	not	not	PART
ejpam-5909	109	4	a	a	DET
ejpam-5909	109	5	limit	limit	NOUN
ejpam-5909	109	6	operator	operator	NOUN
ejpam-5909	109	7	of	of	ADP
ejpam-5909	109	8	f	f	PROPN
ejpam-5909	109	9	at	at	ADP
ejpam-5909	109	10	0	0	NUM
ejpam-5909	109	11	.	.	PUNCT
ejpam-5909	110	1	the	the	DET
ejpam-5909	110	2	continuous	continuous	ADJ
ejpam-5909	110	3	function	function	NOUN
ejpam-5909	110	4	f	f	PROPN
ejpam-5909	110	5	(	(	PUNCT
ejpam-5909	110	6	0	0	NUM
ejpam-5909	110	7	)	)	PUNCT
ejpam-5909	110	8	=	=	SYM
ejpam-5909	111	1	e	e	NOUN
ejpam-5909	111	2	is	be	AUX
ejpam-5909	111	3	not	not	PART
ejpam-5909	111	4	a	a	DET
ejpam-5909	111	5	limit	limit	NOUN
ejpam-5909	111	6	operator	operator	NOUN
ejpam-5909	111	7	of	of	ADP
ejpam-5909	111	8	f	f	PROPN
ejpam-5909	111	9	at	at	ADP
ejpam-5909	111	10	0	0	NUM
ejpam-5909	111	11	because	because	SCONJ
ejpam-5909	111	12	there	there	PRON
ejpam-5909	111	13	exists	exist	VERB
ejpam-5909	111	14	a	a	DET
ejpam-5909	111	15	positive	positive	ADJ
ejpam-5909	111	16	real	real	ADJ
ejpam-5909	111	17	number	number	NOUN
ejpam-5909	111	18	ε	ε	NOUN
ejpam-5909	111	19	=	=	SYM
ejpam-5909	111	20	1	1	NUM
ejpam-5909	111	21	2	2	NUM
ejpam-5909	111	22	and	and	CCONJ
ejpam-5909	111	23	any	any	DET
ejpam-5909	111	24	real	real	ADJ
ejpam-5909	111	25	number	number	NOUN
ejpam-5909	111	26	δ	δ	PROPN
ejpam-5909	111	27	>	>	X
ejpam-5909	111	28	0	0	NUM
ejpam-5909	111	29	such	such	ADJ
ejpam-5909	111	30	that	that	SCONJ
ejpam-5909	111	31	there	there	PRON
ejpam-5909	111	32	exists	exist	VERB
ejpam-5909	111	33	f0	f0	PROPN
ejpam-5909	111	34	=	=	PUNCT
ejpam-5909	111	35	(	(	PUNCT
ejpam-5909	111	36	0	0	NUM
ejpam-5909	111	37	+	+	NUM
ejpam-5909	111	38	1	1	NUM
ejpam-5909	111	39	2δe	2δe	NOUN
ejpam-5909	111	40	)	)	PUNCT
ejpam-5909	111	41	∈	∈	PROPN
ejpam-5909	111	42	a	a	DET
ejpam-5909	111	43	satisfying	satisfying	NOUN
ejpam-5909	111	44	:	:	PUNCT
ejpam-5909	111	45	0	0	NUM
ejpam-5909	111	46	≺	≺	NOUN
ejpam-5909	112	1	|f0	|f0	X
ejpam-5909	112	2	−	−	NOUN
ejpam-5909	112	3	0|	0|	NOUN
ejpam-5909	112	4	≺	≺	NOUN
ejpam-5909	112	5	δe	δe	NOUN
ejpam-5909	112	6	,	,	PUNCT
ejpam-5909	112	7	but	but	CCONJ
ejpam-5909	112	8	:	:	PUNCT
ejpam-5909	112	9	|f	|f	PROPN
ejpam-5909	112	10	(	(	PUNCT
ejpam-5909	112	11	f0)−	f0)−	PROPN
ejpam-5909	112	12	f	f	X
ejpam-5909	112	13	(	(	PUNCT
ejpam-5909	112	14	0)|	0)|	NUM
ejpam-5909	112	15	=	=	SYM
ejpam-5909	112	16	|2e−	|2e−	PROPN
ejpam-5909	112	17	e|	e|	PROPN
ejpam-5909	112	18	=	=	PUNCT
ejpam-5909	112	19	|e|	|e|	PROPN
ejpam-5909	112	20	=	=	SYM
ejpam-5909	112	21	e	e	NOUN
ejpam-5909	112	22	≻	≻	NOUN
ejpam-5909	112	23	1	1	NUM
ejpam-5909	112	24	2	2	NUM
ejpam-5909	112	25	e	e	NOUN
ejpam-5909	112	26	=	=	PUNCT
ejpam-5909	112	27	εe	εe	PROPN
ejpam-5909	112	28	.	.	PUNCT
ejpam-5909	113	1	thus	thus	ADV
ejpam-5909	113	2	,	,	PUNCT
ejpam-5909	113	3	f	f	PROPN
ejpam-5909	113	4	(	(	PUNCT
ejpam-5909	113	5	0	0	NUM
ejpam-5909	113	6	)	)	PUNCT
ejpam-5909	114	1	=	=	SYM
ejpam-5909	115	1	e	e	NOUN
ejpam-5909	115	2	is	be	AUX
ejpam-5909	115	3	not	not	PART
ejpam-5909	115	4	a	a	DET
ejpam-5909	115	5	limit	limit	NOUN
ejpam-5909	115	6	operator	operator	NOUN
ejpam-5909	115	7	of	of	ADP
ejpam-5909	115	8	f	f	PROPN
ejpam-5909	115	9	at	at	ADP
ejpam-5909	115	10	0	0	NUM
ejpam-5909	115	11	.	.	PUNCT
ejpam-5909	116	1	before	before	ADP
ejpam-5909	116	2	discussing	discuss	VERB
ejpam-5909	116	3	the	the	DET
ejpam-5909	116	4	properties	property	NOUN
ejpam-5909	116	5	of	of	ADP
ejpam-5909	116	6	limit	limit	NOUN
ejpam-5909	116	7	operators	operator	NOUN
ejpam-5909	116	8	on	on	ADP
ejpam-5909	116	9	c[a	c[a	NUM
ejpam-5909	116	10	,	,	PUNCT
ejpam-5909	116	11	b	b	NOUN
ejpam-5909	116	12	]	]	X
ejpam-5909	116	13	,	,	PUNCT
ejpam-5909	116	14	we	we	PRON
ejpam-5909	116	15	define	define	VERB
ejpam-5909	116	16	the	the	DET
ejpam-5909	116	17	addition	addition	NOUN
ejpam-5909	116	18	,	,	PUNCT
ejpam-5909	116	19	subtraction	subtraction	NOUN
ejpam-5909	116	20	,	,	PUNCT
ejpam-5909	116	21	multiplication	multiplication	NOUN
ejpam-5909	116	22	,	,	PUNCT
ejpam-5909	116	23	and	and	CCONJ
ejpam-5909	116	24	division	division	NOUN
ejpam-5909	116	25	of	of	ADP
ejpam-5909	116	26	operators	operator	NOUN
ejpam-5909	116	27	on	on	ADP
ejpam-5909	116	28	c[a	c[a	NUM
ejpam-5909	116	29	,	,	PUNCT
ejpam-5909	116	30	b	b	NOUN
ejpam-5909	116	31	]	]	X
ejpam-5909	116	32	.	.	PUNCT
ejpam-5909	117	1	this	this	DET
ejpam-5909	117	2	definition	definition	NOUN
ejpam-5909	117	3	is	be	AUX
ejpam-5909	117	4	crucial	crucial	ADJ
ejpam-5909	117	5	for	for	ADP
ejpam-5909	117	6	the	the	DET
ejpam-5909	117	7	subsequent	subsequent	ADJ
ejpam-5909	117	8	discussion	discussion	NOUN
ejpam-5909	117	9	.	.	PUNCT
ejpam-5909	118	1	definition	definition	NOUN
ejpam-5909	118	2	9	9	NUM
ejpam-5909	118	3	.	.	PUNCT
ejpam-5909	119	1	given	give	VERB
ejpam-5909	119	2	a	a	DET
ejpam-5909	119	3	⊆	⊆	NUM
ejpam-5909	119	4	c[a	c[a	NUM
ejpam-5909	119	5	,	,	PUNCT
ejpam-5909	119	6	b	b	NOUN
ejpam-5909	119	7	]	]	PUNCT
ejpam-5909	119	8	and	and	CCONJ
ejpam-5909	119	9	operators	operator	NOUN
ejpam-5909	119	10	f	f	PROPN
ejpam-5909	119	11	and	and	CCONJ
ejpam-5909	119	12	g	g	PROPN
ejpam-5909	119	13	,	,	PUNCT
ejpam-5909	119	14	each	each	DET
ejpam-5909	119	15	mapping	mapping	NOUN
ejpam-5909	119	16	a	a	PRON
ejpam-5909	119	17	to	to	ADP
ejpam-5909	119	18	c[a	c[a	NUM
ejpam-5909	119	19	,	,	PUNCT
ejpam-5909	119	20	b	b	NOUN
ejpam-5909	119	21	]	]	X
ejpam-5909	119	22	,	,	PUNCT
ejpam-5909	119	23	the	the	DET
ejpam-5909	119	24	definitions	definition	NOUN
ejpam-5909	119	25	of	of	ADP
ejpam-5909	119	26	addition	addition	NOUN
ejpam-5909	119	27	f	f	X
ejpam-5909	120	1	+	+	NOUN
ejpam-5909	120	2	g	g	NOUN
ejpam-5909	120	3	,	,	PUNCT
ejpam-5909	120	4	subtraction	subtraction	NOUN
ejpam-5909	120	5	f	f	PROPN
ejpam-5909	120	6	−g	−g	NOUN
ejpam-5909	120	7	,	,	PUNCT
ejpam-5909	120	8	and	and	CCONJ
ejpam-5909	120	9	multiplication	multiplication	NOUN
ejpam-5909	120	10	fg	fg	ADP
ejpam-5909	120	11	,	,	PUNCT
ejpam-5909	120	12	each	each	PRON
ejpam-5909	120	13	from	from	ADP
ejpam-5909	120	14	a	a	PRON
ejpam-5909	120	15	to	to	ADP
ejpam-5909	120	16	c[a	c[a	NUM
ejpam-5909	120	17	,	,	PUNCT
ejpam-5909	120	18	b	b	NOUN
ejpam-5909	120	19	]	]	X
ejpam-5909	120	20	,	,	PUNCT
ejpam-5909	120	21	are	be	AUX
ejpam-5909	120	22	as	as	SCONJ
ejpam-5909	120	23	follows	follow	VERB
ejpam-5909	120	24	:	:	PUNCT
ejpam-5909	120	25	(	(	PUNCT
ejpam-5909	120	26	f	f	X
ejpam-5909	120	27	+	+	ADV
ejpam-5909	120	28	g)(f	g)(f	ADV
ejpam-5909	120	29	)	)	PUNCT
ejpam-5909	121	1	=	=	SYM
ejpam-5909	121	2	f	f	X
ejpam-5909	121	3	(	(	PUNCT
ejpam-5909	121	4	f	f	X
ejpam-5909	121	5	)	)	PUNCT
ejpam-5909	121	6	+	+	NOUN
ejpam-5909	121	7	g(f	g(f	NOUN
ejpam-5909	121	8	)	)	PUNCT
ejpam-5909	121	9	,	,	PUNCT
ejpam-5909	121	10	(	(	PUNCT
ejpam-5909	121	11	f	f	PROPN
ejpam-5909	121	12	−g)(f	−g)(f	PROPN
ejpam-5909	121	13	)	)	PUNCT
ejpam-5909	122	1	=	=	SYM
ejpam-5909	122	2	f	f	PROPN
ejpam-5909	122	3	(	(	PUNCT
ejpam-5909	122	4	f)−g(f	f)−g(f	X
ejpam-5909	122	5	)	)	PUNCT
ejpam-5909	122	6	,	,	PUNCT
ejpam-5909	122	7	(	(	PUNCT
ejpam-5909	122	8	fg)(f	fg)(f	NOUN
ejpam-5909	122	9	)	)	PUNCT
ejpam-5909	123	1	=	=	SYM
ejpam-5909	123	2	f	f	PROPN
ejpam-5909	123	3	(	(	PUNCT
ejpam-5909	123	4	f)g(f	f)g(f	PROPN
ejpam-5909	123	5	)	)	PUNCT
ejpam-5909	123	6	,	,	PUNCT
ejpam-5909	123	7	for	for	ADP
ejpam-5909	123	8	every	every	DET
ejpam-5909	123	9	f	f	PROPN
ejpam-5909	123	10	∈	∈	PROPN
ejpam-5909	123	11	a.	a.	NOUN
ejpam-5909	123	12	in	in	ADP
ejpam-5909	123	13	addtition	addtition	NOUN
ejpam-5909	123	14	,	,	PUNCT
ejpam-5909	123	15	if	if	SCONJ
ejpam-5909	123	16	γ	γ	X
ejpam-5909	123	17	∈	∈	PROPN
ejpam-5909	123	18	c[a	c[a	NOUN
ejpam-5909	123	19	,	,	PUNCT
ejpam-5909	123	20	b	b	NOUN
ejpam-5909	123	21	]	]	X
ejpam-5909	123	22	,	,	PUNCT
ejpam-5909	123	23	we	we	PRON
ejpam-5909	123	24	define	define	VERB
ejpam-5909	123	25	γf	γf	PROPN
ejpam-5909	123	26	as	as	SCONJ
ejpam-5909	123	27	follows	follow	VERB
ejpam-5909	123	28	:	:	PUNCT
ejpam-5909	123	29	(	(	PUNCT
ejpam-5909	123	30	γf	γf	ADJ
ejpam-5909	123	31	)	)	PUNCT
ejpam-5909	123	32	(	(	PUNCT
ejpam-5909	123	33	f	f	X
ejpam-5909	123	34	)	)	PUNCT
ejpam-5909	123	35	=	=	SYM
ejpam-5909	123	36	γf	γf	INTJ
ejpam-5909	123	37	(	(	PUNCT
ejpam-5909	123	38	f	f	NOUN
ejpam-5909	123	39	)	)	PUNCT
ejpam-5909	123	40	,	,	PUNCT
ejpam-5909	123	41	for	for	ADP
ejpam-5909	123	42	every	every	DET
ejpam-5909	123	43	f	f	PROPN
ejpam-5909	123	44	∈	∈	PROPN
ejpam-5909	123	45	a.	a.	NOUN
ejpam-5909	123	46	finally	finally	ADV
ejpam-5909	123	47	,	,	PUNCT
ejpam-5909	123	48	if	if	SCONJ
ejpam-5909	123	49	g(f)(x	g(f)(x	PRON
ejpam-5909	123	50	)	)	PUNCT
ejpam-5909	123	51	̸=	̸=	PROPN
ejpam-5909	123	52	0	0	NUM
ejpam-5909	123	53	for	for	ADP
ejpam-5909	123	54	all	all	DET
ejpam-5909	123	55	x	x	SYM
ejpam-5909	123	56	∈	∈	PROPN
ejpam-5909	123	57	[	[	X
ejpam-5909	123	58	a	a	X
ejpam-5909	123	59	,	,	PUNCT
ejpam-5909	123	60	b	b	NOUN
ejpam-5909	123	61	]	]	X
ejpam-5909	123	62	,	,	PUNCT
ejpam-5909	123	63	we	we	PRON
ejpam-5909	123	64	define	define	VERB
ejpam-5909	123	65	f	f	PROPN
ejpam-5909	123	66	g	g	PROPN
ejpam-5909	123	67	as	as	SCONJ
ejpam-5909	123	68	follows	follow	VERB
ejpam-5909	123	69	:(	:(	PUNCT
ejpam-5909	123	70	f	f	PROPN
ejpam-5909	123	71	g	g	PROPN
ejpam-5909	123	72	)	)	PUNCT
ejpam-5909	123	73	(	(	PUNCT
ejpam-5909	123	74	f	f	X
ejpam-5909	123	75	)	)	PUNCT
ejpam-5909	123	76	=	=	SYM
ejpam-5909	123	77	f	f	X
ejpam-5909	123	78	(	(	PUNCT
ejpam-5909	123	79	f	f	X
ejpam-5909	123	80	)	)	PUNCT
ejpam-5909	123	81	g(f	g(f	PROPN
ejpam-5909	123	82	)	)	PUNCT
ejpam-5909	123	83	,	,	PUNCT
ejpam-5909	123	84	for	for	ADP
ejpam-5909	123	85	every	every	DET
ejpam-5909	123	86	f	f	PROPN
ejpam-5909	123	87	∈	∈	PROPN
ejpam-5909	123	88	a.	a.	NOUN
ejpam-5909	123	89	theorem	theorem	NOUN
ejpam-5909	123	90	3	3	X
ejpam-5909	123	91	.	.	PUNCT
ejpam-5909	124	1	if	if	SCONJ
ejpam-5909	124	2	f0	f0	PROPN
ejpam-5909	124	3	∈	∈	PROPN
ejpam-5909	124	4	c[a	c[a	NOUN
ejpam-5909	124	5	,	,	PUNCT
ejpam-5909	124	6	b	b	X
ejpam-5909	124	7	]	]	X
ejpam-5909	124	8	such	such	ADJ
ejpam-5909	124	9	that	that	SCONJ
ejpam-5909	124	10	0	0	NUM
ejpam-5909	124	11	⪯	⪯	NOUN
ejpam-5909	124	12	f0	f0	PROPN
ejpam-5909	124	13	≺	≺	NOUN
ejpam-5909	124	14	εe	εe	VERB
ejpam-5909	124	15	for	for	ADP
ejpam-5909	124	16	every	every	DET
ejpam-5909	124	17	ε	ε	PROPN
ejpam-5909	124	18	>	>	X
ejpam-5909	124	19	0	0	PROPN
ejpam-5909	124	20	,	,	PUNCT
ejpam-5909	124	21	then	then	ADV
ejpam-5909	124	22	f0	f0	PROPN
ejpam-5909	124	23	=	=	SYM
ejpam-5909	124	24	0	0	X
ejpam-5909	124	25	.	.	PUNCT
ejpam-5909	125	1	proof	proof	NOUN
ejpam-5909	125	2	.	.	PUNCT
ejpam-5909	126	1	suppose	suppose	VERB
ejpam-5909	127	1	f0	f0	PROPN
ejpam-5909	127	2	≻	≻	PROPN
ejpam-5909	127	3	0	0	NUM
ejpam-5909	127	4	.	.	PUNCT
ejpam-5909	128	1	choosing	choose	VERB
ejpam-5909	128	2	a	a	DET
ejpam-5909	128	3	positive	positive	ADJ
ejpam-5909	128	4	real	real	ADJ
ejpam-5909	128	5	number	number	NOUN
ejpam-5909	128	6	ε0	ε0	NOUN
ejpam-5909	128	7	<	<	X
ejpam-5909	128	8	min{1	min{1	PROPN
ejpam-5909	128	9	2f0(x)|x	2f0(x)|x	NUM
ejpam-5909	128	10	∈	∈	PROPN
ejpam-5909	128	11	[	[	X
ejpam-5909	128	12	a	a	X
ejpam-5909	128	13	,	,	PUNCT
ejpam-5909	128	14	b	b	NOUN
ejpam-5909	128	15	]	]	X
ejpam-5909	128	16	}	}	PUNCT
ejpam-5909	128	17	,	,	PUNCT
ejpam-5909	128	18	we	we	PRON
ejpam-5909	128	19	obtain	obtain	VERB
ejpam-5909	128	20	:	:	PUNCT
ejpam-5909	128	21	0	0	NUM
ejpam-5909	128	22	≺	≺	NOUN
ejpam-5909	128	23	ε0e	ε0e	PUNCT
ejpam-5909	128	24	⪯	⪯	NOUN
ejpam-5909	128	25	1	1	NUM
ejpam-5909	128	26	2	2	NUM
ejpam-5909	128	27	f0	f0	PROPN
ejpam-5909	128	28	≺	≺	NOUN
ejpam-5909	128	29	f0	f0	PROPN
ejpam-5909	128	30	or	or	CCONJ
ejpam-5909	128	31	equivalently	equivalently	ADV
ejpam-5909	128	32	,	,	PUNCT
ejpam-5909	128	33	ε0e	ε0e	PUNCT
ejpam-5909	128	34	≺	≺	NOUN
ejpam-5909	128	35	f0	f0	PROPN
ejpam-5909	128	36	.	.	PUNCT
ejpam-5909	129	1	this	this	PRON
ejpam-5909	129	2	contradicts	contradict	VERB
ejpam-5909	129	3	f0	f0	ADJ
ejpam-5909	129	4	≺	≺	NOUN
ejpam-5909	129	5	εe	εe	VERB
ejpam-5909	129	6	for	for	ADP
ejpam-5909	129	7	every	every	DET
ejpam-5909	129	8	positive	positive	ADJ
ejpam-5909	129	9	real	real	ADJ
ejpam-5909	129	10	number	number	NOUN
ejpam-5909	129	11	ε	ε	PROPN
ejpam-5909	129	12	.	.	PUNCT
ejpam-5909	130	1	thus	thus	ADV
ejpam-5909	130	2	,	,	PUNCT
ejpam-5909	130	3	it	it	PRON
ejpam-5909	130	4	must	must	AUX
ejpam-5909	130	5	be	be	AUX
ejpam-5909	130	6	that	that	PRON
ejpam-5909	130	7	f0	f0	PROPN
ejpam-5909	130	8	=	=	SYM
ejpam-5909	130	9	0	0	PROPN
ejpam-5909	130	10	.	.	PUNCT
ejpam-5909	131	1	from	from	ADP
ejpam-5909	131	2	definition	definition	NOUN
ejpam-5909	131	3	4.1.7	4.1.7	NUM
ejpam-5909	131	4	and	and	CCONJ
ejpam-5909	131	5	theorem	theorem	VERB
ejpam-5909	131	6	4.1.4	4.1.4	NUM
ejpam-5909	131	7	,	,	PUNCT
ejpam-5909	131	8	several	several	ADJ
ejpam-5909	131	9	properties	property	NOUN
ejpam-5909	131	10	of	of	ADP
ejpam-5909	131	11	the	the	DET
ejpam-5909	131	12	limit	limit	NOUN
ejpam-5909	131	13	operator	operator	NOUN
ejpam-5909	131	14	on	on	ADP
ejpam-5909	131	15	c[a	c[a	NUM
ejpam-5909	131	16	,	,	PUNCT
ejpam-5909	131	17	b	b	AUX
ejpam-5909	131	18	]	]	PUNCT
ejpam-5909	131	19	can	can	AUX
ejpam-5909	131	20	be	be	AUX
ejpam-5909	131	21	established	establish	VERB
ejpam-5909	131	22	as	as	SCONJ
ejpam-5909	131	23	follows	follow	VERB
ejpam-5909	131	24	:	:	PUNCT
ejpam-5909	131	25	m.	m.	NOUN
ejpam-5909	131	26	alifuddin	alifuddin	VERB
ejpam-5909	131	27	et	et	PROPN
ejpam-5909	131	28	al	al	PROPN
ejpam-5909	131	29	.	.	PUNCT
ejpam-5909	131	30	/	/	SYM
ejpam-5909	131	31	eur	eur	PROPN
ejpam-5909	131	32	.	.	PUNCT
ejpam-5909	132	1	j.	j.	PROPN
ejpam-5909	132	2	pure	pure	PROPN
ejpam-5909	132	3	appl	appl	PROPN
ejpam-5909	132	4	.	.	PROPN
ejpam-5909	132	5	math	math	PROPN
ejpam-5909	132	6	,	,	PUNCT
ejpam-5909	132	7	18	18	NUM
ejpam-5909	132	8	(	(	PUNCT
ejpam-5909	132	9	2	2	NUM
ejpam-5909	132	10	)	)	PUNCT
ejpam-5909	132	11	(	(	PUNCT
ejpam-5909	132	12	2025	2025	NUM
ejpam-5909	132	13	)	)	PUNCT
ejpam-5909	132	14	,	,	PUNCT
ejpam-5909	132	15	5909	5909	NUM
ejpam-5909	132	16	7	7	NUM
ejpam-5909	132	17	of	of	ADP
ejpam-5909	132	18	17	17	NUM
ejpam-5909	132	19	theorem	theorem	NOUN
ejpam-5909	132	20	4	4	NUM
ejpam-5909	132	21	.	.	PUNCT
ejpam-5909	132	22	given	give	VERB
ejpam-5909	132	23	a	a	DET
ejpam-5909	132	24	⊆	⊆	NUM
ejpam-5909	132	25	c[a	c[a	NOUN
ejpam-5909	132	26	,	,	PUNCT
ejpam-5909	132	27	b	b	NOUN
ejpam-5909	132	28	]	]	X
ejpam-5909	132	29	,	,	PUNCT
ejpam-5909	132	30	an	an	DET
ejpam-5909	132	31	operator	operator	NOUN
ejpam-5909	132	32	f	f	PROPN
ejpam-5909	132	33	mapping	mapping	NOUN
ejpam-5909	132	34	from	from	ADP
ejpam-5909	132	35	a	a	PRON
ejpam-5909	132	36	to	to	ADP
ejpam-5909	132	37	c[a	c[a	NUM
ejpam-5909	132	38	,	,	PUNCT
ejpam-5909	132	39	b	b	NOUN
ejpam-5909	132	40	]	]	X
ejpam-5909	132	41	,	,	PUNCT
ejpam-5909	132	42	and	and	CCONJ
ejpam-5909	132	43	f0	f0	VERB
ejpam-5909	132	44	as	as	ADP
ejpam-5909	132	45	a	a	DET
ejpam-5909	132	46	limit	limit	NOUN
ejpam-5909	132	47	point	point	NOUN
ejpam-5909	132	48	of	of	ADP
ejpam-5909	132	49	a	a	PRON
ejpam-5909	132	50	,	,	PUNCT
ejpam-5909	132	51	if	if	SCONJ
ejpam-5909	132	52	:	:	PUNCT
ejpam-5909	133	1	lim	lim	PROPN
ejpam-5909	133	2	f→f0	f→f0	PROPN
ejpam-5909	134	1	f	f	X
ejpam-5909	134	2	(	(	PUNCT
ejpam-5909	134	3	f	f	X
ejpam-5909	134	4	)	)	PUNCT
ejpam-5909	134	5	=	=	SYM
ejpam-5909	134	6	l	l	NOUN
ejpam-5909	134	7	and	and	CCONJ
ejpam-5909	134	8	lim	lim	PROPN
ejpam-5909	134	9	f→f0	f→f0	PROPN
ejpam-5909	135	1	f	f	X
ejpam-5909	135	2	(	(	PUNCT
ejpam-5909	135	3	f	f	X
ejpam-5909	135	4	)	)	PUNCT
ejpam-5909	135	5	=	=	SYM
ejpam-5909	135	6	m	m	PROPN
ejpam-5909	135	7	,	,	PUNCT
ejpam-5909	135	8	then	then	ADV
ejpam-5909	135	9	l	l	PROPN
ejpam-5909	135	10	=	=	NOUN
ejpam-5909	135	11	m	m	NOUN
ejpam-5909	135	12	.	.	PUNCT
ejpam-5909	136	1	proof	proof	NOUN
ejpam-5909	136	2	.	.	PUNCT
ejpam-5909	137	1	given	give	VERB
ejpam-5909	137	2	that	that	PRON
ejpam-5909	137	3	limf→f0	limf→f0	VERB
ejpam-5909	137	4	f	f	X
ejpam-5909	137	5	(	(	PUNCT
ejpam-5909	137	6	f	f	X
ejpam-5909	137	7	)	)	PUNCT
ejpam-5909	137	8	=	=	SYM
ejpam-5909	137	9	l	l	NOUN
ejpam-5909	137	10	,	,	PUNCT
ejpam-5909	137	11	it	it	PRON
ejpam-5909	137	12	follows	follow	VERB
ejpam-5909	137	13	that	that	SCONJ
ejpam-5909	137	14	for	for	ADP
ejpam-5909	137	15	every	every	DET
ejpam-5909	137	16	real	real	ADJ
ejpam-5909	137	17	number	number	NOUN
ejpam-5909	137	18	ε	ε	PROPN
ejpam-5909	137	19	>	>	X
ejpam-5909	137	20	0	0	PROPN
ejpam-5909	137	21	,	,	PUNCT
ejpam-5909	137	22	there	there	PRON
ejpam-5909	137	23	exists	exist	VERB
ejpam-5909	137	24	δ1	δ1	NOUN
ejpam-5909	137	25	>	>	X
ejpam-5909	137	26	0	0	NUM
ejpam-5909	138	1	such	such	ADJ
ejpam-5909	138	2	that	that	SCONJ
ejpam-5909	138	3	if	if	SCONJ
ejpam-5909	138	4	f	f	PROPN
ejpam-5909	138	5	∈	∈	PROPN
ejpam-5909	138	6	a	a	PRON
ejpam-5909	138	7	and	and	CCONJ
ejpam-5909	138	8	0	0	NUM
ejpam-5909	138	9	≺	≺	NOUN
ejpam-5909	138	10	|f	|f	NUM
ejpam-5909	138	11	−	−	PROPN
ejpam-5909	138	12	f0|	f0|	PROPN
ejpam-5909	138	13	≺	≺	NOUN
ejpam-5909	138	14	δ1e	δ1e	VERB
ejpam-5909	138	15	,	,	PUNCT
ejpam-5909	138	16	then	then	ADV
ejpam-5909	138	17	:	:	PUNCT
ejpam-5909	138	18	|f	|f	PROPN
ejpam-5909	139	1	(	(	PUNCT
ejpam-5909	139	2	f)−	f)−	PROPN
ejpam-5909	139	3	l|	l|	ADJ
ejpam-5909	139	4	≺	≺	NOUN
ejpam-5909	139	5	ε	ε	PROPN
ejpam-5909	139	6	2	2	NUM
ejpam-5909	139	7	e.	e.	PROPN
ejpam-5909	139	8	similarly	similarly	ADV
ejpam-5909	139	9	,	,	PUNCT
ejpam-5909	139	10	given	give	VERB
ejpam-5909	139	11	limf→f0	limf→f0	VERB
ejpam-5909	139	12	f	f	X
ejpam-5909	139	13	=	=	PUNCT
ejpam-5909	139	14	m	m	PROPN
ejpam-5909	139	15	,	,	PUNCT
ejpam-5909	139	16	for	for	ADP
ejpam-5909	139	17	every	every	DET
ejpam-5909	139	18	ε	ε	PROPN
ejpam-5909	139	19	>	>	X
ejpam-5909	139	20	0	0	PROPN
ejpam-5909	139	21	,	,	PUNCT
ejpam-5909	139	22	there	there	PRON
ejpam-5909	139	23	exists	exist	VERB
ejpam-5909	139	24	δ2	δ2	ADJ
ejpam-5909	139	25	>	>	X
ejpam-5909	139	26	0	0	NUM
ejpam-5909	140	1	such	such	ADJ
ejpam-5909	140	2	that	that	SCONJ
ejpam-5909	140	3	if	if	SCONJ
ejpam-5909	140	4	f	f	PROPN
ejpam-5909	140	5	∈	∈	PROPN
ejpam-5909	140	6	a	a	PRON
ejpam-5909	140	7	and	and	CCONJ
ejpam-5909	140	8	0	0	NUM
ejpam-5909	140	9	≺	≺	NOUN
ejpam-5909	140	10	|f	|f	NUM
ejpam-5909	140	11	−	−	PROPN
ejpam-5909	140	12	f0|	f0|	PROPN
ejpam-5909	140	13	≺	≺	NOUN
ejpam-5909	140	14	δ2e	δ2e	PROPN
ejpam-5909	140	15	,	,	PUNCT
ejpam-5909	140	16	then	then	ADV
ejpam-5909	140	17	:	:	PUNCT
ejpam-5909	140	18	|f	|f	PROPN
ejpam-5909	140	19	(	(	PUNCT
ejpam-5909	140	20	f)−m	f)−m	NOUN
ejpam-5909	140	21	|	|	ADV
ejpam-5909	140	22	≺	≺	NOUN
ejpam-5909	140	23	ε	ε	AUX
ejpam-5909	140	24	2	2	NUM
ejpam-5909	140	25	e.	e.	NOUN
ejpam-5909	140	26	choosing	choose	VERB
ejpam-5909	140	27	δ	δ	PROPN
ejpam-5909	140	28	=	=	PUNCT
ejpam-5909	140	29	min(δ1	min(δ1	PROPN
ejpam-5909	140	30	,	,	PUNCT
ejpam-5909	140	31	δ2	δ2	ADV
ejpam-5909	140	32	)	)	PUNCT
ejpam-5909	140	33	,	,	PUNCT
ejpam-5909	140	34	if	if	SCONJ
ejpam-5909	140	35	0	0	NUM
ejpam-5909	140	36	≺	≺	NOUN
ejpam-5909	140	37	|f	|f	NUM
ejpam-5909	140	38	−	−	PROPN
ejpam-5909	141	1	f0|	f0|	PROPN
ejpam-5909	141	2	≺	≺	NOUN
ejpam-5909	141	3	δe	δe	ADP
ejpam-5909	141	4	,	,	PUNCT
ejpam-5909	141	5	then	then	ADV
ejpam-5909	141	6	:	:	PUNCT
ejpam-5909	141	7	|l−m	|l−m	NOUN
ejpam-5909	141	8	|	|	ADV
ejpam-5909	141	9	=	=	PUNCT
ejpam-5909	141	10	|l−	|l−	NOUN
ejpam-5909	141	11	f	f	X
ejpam-5909	141	12	(	(	PUNCT
ejpam-5909	141	13	f	f	X
ejpam-5909	141	14	)	)	PUNCT
ejpam-5909	142	1	+	+	NOUN
ejpam-5909	142	2	f	f	X
ejpam-5909	142	3	(	(	PUNCT
ejpam-5909	142	4	f)−m	f)−m	NOUN
ejpam-5909	142	5	|	|	ADV
ejpam-5909	142	6	⪯	⪯	VERB
ejpam-5909	142	7	|l−	|l−	NOUN
ejpam-5909	142	8	f	f	PROPN
ejpam-5909	142	9	(	(	PUNCT
ejpam-5909	142	10	f)|+	f)|+	PROPN
ejpam-5909	142	11	|f	|f	PROPN
ejpam-5909	142	12	(	(	PUNCT
ejpam-5909	142	13	f)−m	f)−m	NOUN
ejpam-5909	142	14	|	|	ADV
ejpam-5909	142	15	.	.	PUNCT
ejpam-5909	143	1	by	by	ADP
ejpam-5909	143	2	substitution	substitution	NOUN
ejpam-5909	143	3	,	,	PUNCT
ejpam-5909	143	4	we	we	PRON
ejpam-5909	143	5	obtain	obtain	VERB
ejpam-5909	143	6	:	:	PUNCT
ejpam-5909	143	7	|l−m	|l−m	NOUN
ejpam-5909	143	8	|	|	ADV
ejpam-5909	143	9	≺	≺	NOUN
ejpam-5909	143	10	ε	ε	PROPN
ejpam-5909	143	11	2	2	NUM
ejpam-5909	143	12	e+	e+	PUNCT
ejpam-5909	143	13	ε	ε	PROPN
ejpam-5909	143	14	2	2	NUM
ejpam-5909	143	15	e	e	NOUN
ejpam-5909	143	16	=	=	PUNCT
ejpam-5909	143	17	εe	εe	VERB
ejpam-5909	143	18	.	.	PUNCT
ejpam-5909	144	1	this	this	PRON
ejpam-5909	144	2	holds	hold	VERB
ejpam-5909	144	3	for	for	ADP
ejpam-5909	144	4	every	every	DET
ejpam-5909	144	5	ε	ε	PROPN
ejpam-5909	144	6	>	>	X
ejpam-5909	144	7	0	0	PROPN
ejpam-5909	144	8	,	,	PUNCT
ejpam-5909	144	9	it	it	PRON
ejpam-5909	144	10	follows	follow	VERB
ejpam-5909	144	11	that	that	SCONJ
ejpam-5909	144	12	:	:	PUNCT
ejpam-5909	144	13	|l−m	|l−m	PROPN
ejpam-5909	144	14	|	|	NOUN
ejpam-5909	144	15	=	=	SYM
ejpam-5909	144	16	0	0	NUM
ejpam-5909	144	17	or	or	CCONJ
ejpam-5909	144	18	l	l	NOUN
ejpam-5909	145	1	=	=	PUNCT
ejpam-5909	145	2	m.	m.	NOUN
ejpam-5909	145	3	the	the	DET
ejpam-5909	145	4	implication	implication	NOUN
ejpam-5909	145	5	of	of	ADP
ejpam-5909	145	6	theorem	theorem	NOUN
ejpam-5909	145	7	4	4	NUM
ejpam-5909	145	8	is	be	AUX
ejpam-5909	145	9	that	that	SCONJ
ejpam-5909	145	10	if	if	SCONJ
ejpam-5909	145	11	an	an	DET
ejpam-5909	145	12	operator	operator	NOUN
ejpam-5909	145	13	f	f	PROPN
ejpam-5909	145	14	has	have	VERB
ejpam-5909	145	15	a	a	DET
ejpam-5909	145	16	limit	limit	NOUN
ejpam-5909	145	17	at	at	ADP
ejpam-5909	145	18	f0	f0	PROPN
ejpam-5909	145	19	,	,	PUNCT
ejpam-5909	145	20	then	then	ADV
ejpam-5909	145	21	the	the	DET
ejpam-5909	145	22	limit	limit	NOUN
ejpam-5909	145	23	is	be	AUX
ejpam-5909	145	24	unique	unique	ADJ
ejpam-5909	145	25	.	.	PUNCT
ejpam-5909	146	1	theorem	theorem	ADJ
ejpam-5909	146	2	5	5	NUM
ejpam-5909	146	3	.	.	PUNCT
ejpam-5909	146	4	given	give	VERB
ejpam-5909	146	5	a	a	DET
ejpam-5909	146	6	⊆	⊆	NUM
ejpam-5909	146	7	c[a	c[a	NOUN
ejpam-5909	146	8	,	,	PUNCT
ejpam-5909	146	9	b	b	NOUN
ejpam-5909	146	10	]	]	X
ejpam-5909	146	11	,	,	PUNCT
ejpam-5909	146	12	operators	operators	PROPN
ejpam-5909	146	13	f	f	PROPN
ejpam-5909	146	14	and	and	CCONJ
ejpam-5909	146	15	g	g	PROPN
ejpam-5909	146	16	,	,	PUNCT
ejpam-5909	146	17	each	each	DET
ejpam-5909	146	18	mapping	mapping	NOUN
ejpam-5909	146	19	from	from	ADP
ejpam-5909	146	20	a	a	PRON
ejpam-5909	146	21	to	to	ADP
ejpam-5909	146	22	c[a	c[a	NUM
ejpam-5909	146	23	,	,	PUNCT
ejpam-5909	146	24	b	b	NOUN
ejpam-5909	146	25	]	]	X
ejpam-5909	146	26	,	,	PUNCT
ejpam-5909	146	27	and	and	CCONJ
ejpam-5909	146	28	f0	f0	VERB
ejpam-5909	146	29	as	as	ADP
ejpam-5909	146	30	a	a	DET
ejpam-5909	146	31	limit	limit	NOUN
ejpam-5909	146	32	point	point	NOUN
ejpam-5909	146	33	of	of	ADP
ejpam-5909	146	34	the	the	DET
ejpam-5909	146	35	set	set	NOUN
ejpam-5909	146	36	a	a	PRON
ejpam-5909	146	37	,	,	PUNCT
ejpam-5909	146	38	along	along	ADP
ejpam-5909	146	39	with	with	ADP
ejpam-5909	146	40	a	a	DET
ejpam-5909	146	41	function	function	NOUN
ejpam-5909	146	42	γ	γ	X
ejpam-5909	146	43	∈	∈	PROPN
ejpam-5909	146	44	c[a	c[a	NOUN
ejpam-5909	146	45	,	,	PUNCT
ejpam-5909	146	46	b	b	NOUN
ejpam-5909	146	47	]	]	X
ejpam-5909	146	48	.	.	PUNCT
ejpam-5909	147	1	if	if	SCONJ
ejpam-5909	147	2	limf→f0	limf→f0	VERB
ejpam-5909	147	3	f	f	NOUN
ejpam-5909	147	4	=	=	SYM
ejpam-5909	147	5	l	l	PROPN
ejpam-5909	147	6	and	and	CCONJ
ejpam-5909	147	7	limf→f0	limf→f0	VERB
ejpam-5909	147	8	g	g	NOUN
ejpam-5909	147	9	=	=	PROPN
ejpam-5909	147	10	m	m	PROPN
ejpam-5909	147	11	,	,	PUNCT
ejpam-5909	147	12	then	then	ADV
ejpam-5909	147	13	:	:	PUNCT
ejpam-5909	147	14	(	(	PUNCT
ejpam-5909	147	15	i	i	NOUN
ejpam-5909	147	16	)	)	PUNCT
ejpam-5909	147	17	limf→f0(f	limf→f0(f	PROPN
ejpam-5909	147	18	(	(	PUNCT
ejpam-5909	147	19	f	f	X
ejpam-5909	147	20	)	)	PUNCT
ejpam-5909	148	1	+	+	NOUN
ejpam-5909	148	2	g(f	g(f	NOUN
ejpam-5909	148	3	)	)	PUNCT
ejpam-5909	148	4	)	)	PUNCT
ejpam-5909	149	1	=	=	SYM
ejpam-5909	149	2	l+m	l+m	X
ejpam-5909	149	3	(	(	PUNCT
ejpam-5909	149	4	ii	ii	NOUN
ejpam-5909	149	5	)	)	PUNCT
ejpam-5909	149	6	limf→f0(f	limf→f0(f	PROPN
ejpam-5909	149	7	(	(	PUNCT
ejpam-5909	149	8	f)−g(f	f)−g(f	NOUN
ejpam-5909	149	9	)	)	PUNCT
ejpam-5909	149	10	)	)	PUNCT
ejpam-5909	150	1	=	=	SYM
ejpam-5909	150	2	l−m	l−m	PROPN
ejpam-5909	150	3	(	(	PUNCT
ejpam-5909	150	4	iii	iii	NOUN
ejpam-5909	150	5	)	)	PUNCT
ejpam-5909	150	6	limf→f0(f	limf→f0(f	NOUN
ejpam-5909	150	7	(	(	PUNCT
ejpam-5909	150	8	f)g(f	f)g(f	NOUN
ejpam-5909	150	9	)	)	PUNCT
ejpam-5909	150	10	)	)	PUNCT
ejpam-5909	151	1	=	=	SYM
ejpam-5909	151	2	lm	lm	INTJ
ejpam-5909	151	3	(	(	PUNCT
ejpam-5909	151	4	iv	iv	NOUN
ejpam-5909	151	5	)	)	PUNCT
ejpam-5909	151	6	limf→f0(γf	limf→f0(γf	NOUN
ejpam-5909	151	7	(	(	PUNCT
ejpam-5909	151	8	f	f	NOUN
ejpam-5909	151	9	)	)	PUNCT
ejpam-5909	151	10	)	)	PUNCT
ejpam-5909	152	1	=	=	PRON
ejpam-5909	153	1	γl	γl	PROPN
ejpam-5909	153	2	(	(	PUNCT
ejpam-5909	153	3	v	v	NOUN
ejpam-5909	153	4	)	)	PUNCT
ejpam-5909	153	5	limf→f0	limf→f0	PART
ejpam-5909	153	6	(	(	PUNCT
ejpam-5909	153	7	f	f	X
ejpam-5909	153	8	(	(	PUNCT
ejpam-5909	153	9	f	f	X
ejpam-5909	153	10	)	)	PUNCT
ejpam-5909	153	11	g(f	g(f	PROPN
ejpam-5909	153	12	)	)	PUNCT
ejpam-5909	153	13	)	)	PUNCT
ejpam-5909	154	1	=	=	PUNCT
ejpam-5909	155	1	l	l	NOUN
ejpam-5909	155	2	m	m	VERB
ejpam-5909	155	3	,	,	PUNCT
ejpam-5909	155	4	provided	provide	VERB
ejpam-5909	155	5	that	that	SCONJ
ejpam-5909	155	6	g(f)(x	g(f)(x	NOUN
ejpam-5909	155	7	)	)	PUNCT
ejpam-5909	155	8	̸=	̸=	PROPN
ejpam-5909	155	9	0	0	NUM
ejpam-5909	155	10	and	and	CCONJ
ejpam-5909	155	11	m(x	m(x	NOUN
ejpam-5909	155	12	)	)	PUNCT
ejpam-5909	155	13	̸=	̸=	PROPN
ejpam-5909	155	14	0	0	NUM
ejpam-5909	155	15	,	,	PUNCT
ejpam-5909	155	16	for	for	ADP
ejpam-5909	155	17	all	all	DET
ejpam-5909	155	18	x	x	SYM
ejpam-5909	155	19	∈	∈	PROPN
ejpam-5909	155	20	[	[	X
ejpam-5909	155	21	a	a	X
ejpam-5909	155	22	,	,	PUNCT
ejpam-5909	155	23	b	b	NOUN
ejpam-5909	155	24	]	]	PUNCT
ejpam-5909	155	25	.	.	PUNCT
ejpam-5909	156	1	m.	m.	NOUN
ejpam-5909	156	2	alifuddin	alifuddin	VERB
ejpam-5909	156	3	et	et	PROPN
ejpam-5909	156	4	al	al	PROPN
ejpam-5909	156	5	.	.	PUNCT
ejpam-5909	156	6	/	/	SYM
ejpam-5909	156	7	eur	eur	PROPN
ejpam-5909	156	8	.	.	PUNCT
ejpam-5909	157	1	j.	j.	PROPN
ejpam-5909	157	2	pure	pure	PROPN
ejpam-5909	157	3	appl	appl	PROPN
ejpam-5909	157	4	.	.	PROPN
ejpam-5909	157	5	math	math	PROPN
ejpam-5909	157	6	,	,	PUNCT
ejpam-5909	157	7	18	18	NUM
ejpam-5909	157	8	(	(	PUNCT
ejpam-5909	157	9	2	2	NUM
ejpam-5909	157	10	)	)	PUNCT
ejpam-5909	157	11	(	(	PUNCT
ejpam-5909	157	12	2025	2025	NUM
ejpam-5909	157	13	)	)	PUNCT
ejpam-5909	157	14	,	,	PUNCT
ejpam-5909	157	15	5909	5909	NUM
ejpam-5909	157	16	8	8	NUM
ejpam-5909	157	17	of	of	ADP
ejpam-5909	157	18	17	17	NUM
ejpam-5909	157	19	proof	proof	NOUN
ejpam-5909	157	20	.	.	PUNCT
ejpam-5909	158	1	(	(	PUNCT
ejpam-5909	158	2	i	i	NOUN
ejpam-5909	158	3	)	)	PUNCT
ejpam-5909	158	4	given	give	VERB
ejpam-5909	158	5	that	that	PRON
ejpam-5909	158	6	limf→f0	limf→f0	VERB
ejpam-5909	158	7	f	f	X
ejpam-5909	158	8	(	(	PUNCT
ejpam-5909	158	9	f	f	X
ejpam-5909	158	10	)	)	PUNCT
ejpam-5909	158	11	=	=	SYM
ejpam-5909	159	1	l	l	NOUN
ejpam-5909	159	2	,	,	PUNCT
ejpam-5909	159	3	it	it	PRON
ejpam-5909	159	4	follows	follow	VERB
ejpam-5909	159	5	that	that	SCONJ
ejpam-5909	159	6	for	for	ADP
ejpam-5909	159	7	every	every	DET
ejpam-5909	159	8	real	real	ADJ
ejpam-5909	159	9	number	number	NOUN
ejpam-5909	159	10	ε	ε	PROPN
ejpam-5909	159	11	>	>	X
ejpam-5909	159	12	0	0	PROPN
ejpam-5909	159	13	,	,	PUNCT
ejpam-5909	159	14	there	there	PRON
ejpam-5909	159	15	exists	exist	VERB
ejpam-5909	159	16	a	a	DET
ejpam-5909	159	17	real	real	ADJ
ejpam-5909	159	18	number	number	NOUN
ejpam-5909	159	19	δ1	δ1	NOUN
ejpam-5909	159	20	>	>	X
ejpam-5909	159	21	0	0	NUM
ejpam-5909	160	1	such	such	ADJ
ejpam-5909	160	2	that	that	SCONJ
ejpam-5909	160	3	if	if	SCONJ
ejpam-5909	160	4	f	f	PROPN
ejpam-5909	160	5	∈	∈	PROPN
ejpam-5909	160	6	a	a	PRON
ejpam-5909	160	7	and	and	CCONJ
ejpam-5909	160	8	0	0	NUM
ejpam-5909	160	9	≺	≺	NOUN
ejpam-5909	160	10	|f	|f	NUM
ejpam-5909	160	11	−	−	PROPN
ejpam-5909	160	12	f0|	f0|	PROPN
ejpam-5909	160	13	≺	≺	NOUN
ejpam-5909	160	14	δ1e	δ1e	VERB
ejpam-5909	160	15	,	,	PUNCT
ejpam-5909	160	16	then	then	ADV
ejpam-5909	160	17	:	:	PUNCT
ejpam-5909	160	18	|f	|f	PROPN
ejpam-5909	161	1	(	(	PUNCT
ejpam-5909	161	2	f)−	f)−	PROPN
ejpam-5909	161	3	l|	l|	ADJ
ejpam-5909	161	4	≺	≺	NOUN
ejpam-5909	161	5	ε	ε	PROPN
ejpam-5909	161	6	2	2	NUM
ejpam-5909	161	7	e.	e.	PROPN
ejpam-5909	161	8	similarly	similarly	ADV
ejpam-5909	161	9	,	,	PUNCT
ejpam-5909	161	10	given	give	VERB
ejpam-5909	161	11	that	that	PRON
ejpam-5909	161	12	limf→f0	limf→f0	VERB
ejpam-5909	161	13	g(f	g(f	PROPN
ejpam-5909	161	14	)	)	PUNCT
ejpam-5909	162	1	=	=	PUNCT
ejpam-5909	162	2	m	m	X
ejpam-5909	162	3	,	,	PUNCT
ejpam-5909	162	4	it	it	PRON
ejpam-5909	162	5	follows	follow	VERB
ejpam-5909	162	6	that	that	SCONJ
ejpam-5909	162	7	for	for	ADP
ejpam-5909	162	8	every	every	DET
ejpam-5909	162	9	real	real	ADJ
ejpam-5909	162	10	number	number	NOUN
ejpam-5909	162	11	ε	ε	PROPN
ejpam-5909	162	12	>	>	X
ejpam-5909	162	13	0	0	PROPN
ejpam-5909	162	14	,	,	PUNCT
ejpam-5909	162	15	there	there	PRON
ejpam-5909	162	16	exists	exist	VERB
ejpam-5909	162	17	a	a	DET
ejpam-5909	162	18	real	real	ADJ
ejpam-5909	162	19	number	number	NOUN
ejpam-5909	162	20	δ2	δ2	VERB
ejpam-5909	162	21	>	>	X
ejpam-5909	162	22	0	0	NUM
ejpam-5909	163	1	such	such	ADJ
ejpam-5909	163	2	that	that	SCONJ
ejpam-5909	163	3	if	if	SCONJ
ejpam-5909	163	4	f	f	PROPN
ejpam-5909	163	5	∈	∈	PROPN
ejpam-5909	163	6	a	a	PRON
ejpam-5909	163	7	and	and	CCONJ
ejpam-5909	163	8	0	0	NUM
ejpam-5909	163	9	≺	≺	NOUN
ejpam-5909	163	10	|f	|f	NUM
ejpam-5909	163	11	−	−	PROPN
ejpam-5909	163	12	f0|	f0|	PROPN
ejpam-5909	163	13	≺	≺	NOUN
ejpam-5909	163	14	δ2e	δ2e	PROPN
ejpam-5909	163	15	,	,	PUNCT
ejpam-5909	163	16	then	then	ADV
ejpam-5909	163	17	:	:	PUNCT
ejpam-5909	163	18	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	163	19	|	|	ADV
ejpam-5909	163	20	≺	≺	NOUN
ejpam-5909	163	21	ε	ε	PROPN
ejpam-5909	163	22	2	2	NUM
ejpam-5909	163	23	e.	e.	NOUN
ejpam-5909	163	24	by	by	ADP
ejpam-5909	163	25	choosing	choose	VERB
ejpam-5909	163	26	δ	δ	X
ejpam-5909	163	27	=	=	PUNCT
ejpam-5909	163	28	min(δ1	min(δ1	PROPN
ejpam-5909	163	29	,	,	PUNCT
ejpam-5909	163	30	δ2	δ2	PROPN
ejpam-5909	163	31	)	)	PUNCT
ejpam-5909	163	32	,	,	PUNCT
ejpam-5909	163	33	we	we	PRON
ejpam-5909	163	34	obtain	obtain	VERB
ejpam-5909	163	35	that	that	PRON
ejpam-5909	163	36	for	for	ADP
ejpam-5909	163	37	every	every	DET
ejpam-5909	163	38	f	f	PROPN
ejpam-5909	163	39	∈	∈	PROPN
ejpam-5909	163	40	a	a	PRON
ejpam-5909	163	41	and	and	CCONJ
ejpam-5909	163	42	0	0	NUM
ejpam-5909	163	43	≺	≺	NOUN
ejpam-5909	163	44	|f	|f	NUM
ejpam-5909	163	45	−	−	PROPN
ejpam-5909	164	1	f0|	f0|	PROPN
ejpam-5909	164	2	≺	≺	NOUN
ejpam-5909	164	3	δe	δe	NOUN
ejpam-5909	164	4	,	,	PUNCT
ejpam-5909	164	5	the	the	DET
ejpam-5909	164	6	following	follow	VERB
ejpam-5909	164	7	holds	hold	NOUN
ejpam-5909	164	8	:	:	PUNCT
ejpam-5909	165	1	|[f	|[f	PROPN
ejpam-5909	165	2	(	(	PUNCT
ejpam-5909	165	3	f	f	X
ejpam-5909	165	4	)	)	PUNCT
ejpam-5909	166	1	+	+	X
ejpam-5909	166	2	g(f)]−	g(f)]−	ADJ
ejpam-5909	166	3	[	[	X
ejpam-5909	166	4	l+m	l+m	X
ejpam-5909	166	5	]	]	PUNCT
ejpam-5909	166	6	|	|	ADV
ejpam-5909	166	7	⪯	⪯	VERB
ejpam-5909	166	8	|f	|f	PROPN
ejpam-5909	167	1	(	(	PUNCT
ejpam-5909	167	2	f)−	f)−	PROPN
ejpam-5909	167	3	l|+	l|+	PROPN
ejpam-5909	167	4	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	167	5	|	|	ADV
ejpam-5909	167	6	≺	≺	NOUN
ejpam-5909	167	7	ε	ε	PROPN
ejpam-5909	167	8	2	2	NUM
ejpam-5909	167	9	e+	e+	PUNCT
ejpam-5909	167	10	ε	ε	PROPN
ejpam-5909	167	11	2	2	NUM
ejpam-5909	167	12	e	e	NOUN
ejpam-5909	167	13	=	=	PUNCT
ejpam-5909	167	14	εe	εe	PROPN
ejpam-5909	167	15	.	.	PUNCT
ejpam-5909	168	1	thus	thus	ADV
ejpam-5909	168	2	,	,	PUNCT
ejpam-5909	168	3	lim	lim	PROPN
ejpam-5909	168	4	f→f0	f→f0	PROPN
ejpam-5909	169	1	(	(	PUNCT
ejpam-5909	169	2	f	f	PROPN
ejpam-5909	169	3	(	(	PUNCT
ejpam-5909	169	4	f	f	X
ejpam-5909	169	5	)	)	PUNCT
ejpam-5909	169	6	+	+	NOUN
ejpam-5909	169	7	g(f	g(f	NOUN
ejpam-5909	169	8	)	)	PUNCT
ejpam-5909	169	9	)	)	PUNCT
ejpam-5909	170	1	=	=	SYM
ejpam-5909	170	2	l+m	l+m	X
ejpam-5909	170	3	.	.	PUNCT
ejpam-5909	170	4	(	(	PUNCT
ejpam-5909	170	5	ii	ii	NOUN
ejpam-5909	170	6	)	)	PUNCT
ejpam-5909	170	7	given	give	VERB
ejpam-5909	170	8	that	that	PRON
ejpam-5909	170	9	limf→f0	limf→f0	VERB
ejpam-5909	170	10	f	f	X
ejpam-5909	170	11	(	(	PUNCT
ejpam-5909	170	12	f	f	X
ejpam-5909	170	13	)	)	PUNCT
ejpam-5909	171	1	=	=	SYM
ejpam-5909	171	2	l	l	NOUN
ejpam-5909	171	3	,	,	PUNCT
ejpam-5909	171	4	it	it	PRON
ejpam-5909	171	5	follows	follow	VERB
ejpam-5909	171	6	that	that	SCONJ
ejpam-5909	171	7	for	for	ADP
ejpam-5909	171	8	every	every	DET
ejpam-5909	171	9	real	real	ADJ
ejpam-5909	171	10	number	number	NOUN
ejpam-5909	171	11	ε	ε	PROPN
ejpam-5909	171	12	>	>	X
ejpam-5909	171	13	0	0	PROPN
ejpam-5909	171	14	,	,	PUNCT
ejpam-5909	171	15	there	there	PRON
ejpam-5909	171	16	exists	exist	VERB
ejpam-5909	171	17	a	a	DET
ejpam-5909	171	18	real	real	ADJ
ejpam-5909	171	19	number	number	NOUN
ejpam-5909	171	20	δ1	δ1	NOUN
ejpam-5909	171	21	>	>	X
ejpam-5909	171	22	0	0	NUM
ejpam-5909	172	1	such	such	ADJ
ejpam-5909	172	2	that	that	SCONJ
ejpam-5909	172	3	if	if	SCONJ
ejpam-5909	172	4	f	f	PROPN
ejpam-5909	172	5	∈	∈	PROPN
ejpam-5909	172	6	a	a	PRON
ejpam-5909	172	7	and	and	CCONJ
ejpam-5909	172	8	0	0	NUM
ejpam-5909	172	9	≺	≺	NOUN
ejpam-5909	172	10	|f	|f	NUM
ejpam-5909	172	11	−	−	PROPN
ejpam-5909	172	12	f0|	f0|	PROPN
ejpam-5909	172	13	≺	≺	NOUN
ejpam-5909	172	14	δ1e	δ1e	VERB
ejpam-5909	172	15	,	,	PUNCT
ejpam-5909	172	16	then	then	ADV
ejpam-5909	172	17	:	:	PUNCT
ejpam-5909	172	18	|f	|f	PROPN
ejpam-5909	173	1	(	(	PUNCT
ejpam-5909	173	2	f)−	f)−	PROPN
ejpam-5909	173	3	l|	l|	ADJ
ejpam-5909	173	4	≺	≺	NOUN
ejpam-5909	173	5	ε	ε	PROPN
ejpam-5909	173	6	2	2	NUM
ejpam-5909	173	7	e.	e.	PROPN
ejpam-5909	173	8	similarly	similarly	ADV
ejpam-5909	173	9	,	,	PUNCT
ejpam-5909	173	10	given	give	VERB
ejpam-5909	173	11	that	that	PRON
ejpam-5909	173	12	limf→f0	limf→f0	VERB
ejpam-5909	173	13	g(f	g(f	PROPN
ejpam-5909	173	14	)	)	PUNCT
ejpam-5909	174	1	=	=	PUNCT
ejpam-5909	174	2	m	m	X
ejpam-5909	174	3	,	,	PUNCT
ejpam-5909	174	4	it	it	PRON
ejpam-5909	174	5	follows	follow	VERB
ejpam-5909	174	6	that	that	SCONJ
ejpam-5909	174	7	for	for	ADP
ejpam-5909	174	8	every	every	DET
ejpam-5909	174	9	real	real	ADJ
ejpam-5909	174	10	number	number	NOUN
ejpam-5909	174	11	ε	ε	PROPN
ejpam-5909	174	12	>	>	X
ejpam-5909	174	13	0	0	PROPN
ejpam-5909	174	14	,	,	PUNCT
ejpam-5909	174	15	there	there	PRON
ejpam-5909	174	16	exists	exist	VERB
ejpam-5909	174	17	a	a	DET
ejpam-5909	174	18	real	real	ADJ
ejpam-5909	174	19	number	number	NOUN
ejpam-5909	174	20	δ2	δ2	VERB
ejpam-5909	174	21	>	>	X
ejpam-5909	174	22	0	0	NUM
ejpam-5909	175	1	such	such	ADJ
ejpam-5909	175	2	that	that	SCONJ
ejpam-5909	175	3	if	if	SCONJ
ejpam-5909	175	4	f	f	PROPN
ejpam-5909	175	5	∈	∈	PROPN
ejpam-5909	175	6	a	a	PRON
ejpam-5909	175	7	and	and	CCONJ
ejpam-5909	175	8	0	0	NUM
ejpam-5909	175	9	≺	≺	NOUN
ejpam-5909	175	10	|f	|f	NUM
ejpam-5909	175	11	−	−	PROPN
ejpam-5909	175	12	f0|	f0|	PROPN
ejpam-5909	175	13	≺	≺	NOUN
ejpam-5909	175	14	δ2e	δ2e	PROPN
ejpam-5909	175	15	,	,	PUNCT
ejpam-5909	175	16	then	then	ADV
ejpam-5909	175	17	:	:	PUNCT
ejpam-5909	175	18	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	175	19	|	|	ADV
ejpam-5909	175	20	≺	≺	NOUN
ejpam-5909	175	21	ε	ε	PROPN
ejpam-5909	175	22	2	2	NUM
ejpam-5909	175	23	e.	e.	NOUN
ejpam-5909	175	24	by	by	ADP
ejpam-5909	175	25	choosing	choose	VERB
ejpam-5909	175	26	δ	δ	X
ejpam-5909	175	27	=	=	PUNCT
ejpam-5909	175	28	min(δ1	min(δ1	PROPN
ejpam-5909	175	29	,	,	PUNCT
ejpam-5909	175	30	δ2	δ2	PROPN
ejpam-5909	175	31	)	)	PUNCT
ejpam-5909	175	32	,	,	PUNCT
ejpam-5909	175	33	we	we	PRON
ejpam-5909	175	34	obtain	obtain	VERB
ejpam-5909	175	35	that	that	PRON
ejpam-5909	175	36	for	for	ADP
ejpam-5909	175	37	every	every	DET
ejpam-5909	175	38	f	f	PROPN
ejpam-5909	175	39	∈	∈	PROPN
ejpam-5909	175	40	a	a	PRON
ejpam-5909	175	41	and	and	CCONJ
ejpam-5909	175	42	0	0	NUM
ejpam-5909	175	43	≺	≺	NOUN
ejpam-5909	175	44	|f	|f	NUM
ejpam-5909	175	45	−	−	PROPN
ejpam-5909	176	1	f0|	f0|	PROPN
ejpam-5909	176	2	≺	≺	NOUN
ejpam-5909	176	3	δe	δe	NOUN
ejpam-5909	176	4	,	,	PUNCT
ejpam-5909	176	5	the	the	DET
ejpam-5909	176	6	following	follow	VERB
ejpam-5909	176	7	holds	hold	NOUN
ejpam-5909	176	8	:	:	PUNCT
ejpam-5909	176	9	|[f	|[f	PROPN
ejpam-5909	176	10	(	(	PUNCT
ejpam-5909	176	11	f)−g(f)]−	f)−g(f)]−	PROPN
ejpam-5909	176	12	[	[	X
ejpam-5909	176	13	l−m	l−m	NOUN
ejpam-5909	176	14	]	]	PUNCT
ejpam-5909	176	15	|	|	ADV
ejpam-5909	176	16	⪯	⪯	VERB
ejpam-5909	176	17	|f	|f	PROPN
ejpam-5909	177	1	(	(	PUNCT
ejpam-5909	177	2	f)−	f)−	PROPN
ejpam-5909	177	3	l|+	l|+	PROPN
ejpam-5909	177	4	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	177	5	|	|	ADV
ejpam-5909	177	6	≺	≺	NOUN
ejpam-5909	177	7	ε	ε	PROPN
ejpam-5909	177	8	2	2	NUM
ejpam-5909	177	9	e+	e+	PUNCT
ejpam-5909	177	10	ε	ε	PROPN
ejpam-5909	177	11	2	2	NUM
ejpam-5909	177	12	e	e	NOUN
ejpam-5909	177	13	=	=	PUNCT
ejpam-5909	177	14	εe	εe	PROPN
ejpam-5909	177	15	.	.	PUNCT
ejpam-5909	178	1	thus	thus	ADV
ejpam-5909	178	2	,	,	PUNCT
ejpam-5909	178	3	lim	lim	PROPN
ejpam-5909	178	4	f→f0	f→f0	PROPN
ejpam-5909	178	5	(	(	PUNCT
ejpam-5909	178	6	f	f	PROPN
ejpam-5909	178	7	−g	−g	PROPN
ejpam-5909	178	8	)	)	PUNCT
ejpam-5909	178	9	=	=	SYM
ejpam-5909	178	10	l−m	l−m	NOUN
ejpam-5909	178	11	.	.	PUNCT
ejpam-5909	179	1	(	(	PUNCT
ejpam-5909	179	2	iii	iii	NOUN
ejpam-5909	179	3	)	)	PUNCT
ejpam-5909	179	4	given	give	VERB
ejpam-5909	179	5	that	that	PRON
ejpam-5909	179	6	limf→f0	limf→f0	VERB
ejpam-5909	179	7	f	f	X
ejpam-5909	179	8	(	(	PUNCT
ejpam-5909	179	9	f	f	X
ejpam-5909	179	10	)	)	PUNCT
ejpam-5909	180	1	=	=	SYM
ejpam-5909	180	2	l	l	NOUN
ejpam-5909	180	3	,	,	PUNCT
ejpam-5909	180	4	it	it	PRON
ejpam-5909	180	5	follows	follow	VERB
ejpam-5909	180	6	that	that	SCONJ
ejpam-5909	180	7	for	for	ADP
ejpam-5909	180	8	every	every	DET
ejpam-5909	180	9	real	real	ADJ
ejpam-5909	180	10	number	number	NOUN
ejpam-5909	180	11	ε	ε	PROPN
ejpam-5909	180	12	>	>	X
ejpam-5909	180	13	0	0	PROPN
ejpam-5909	180	14	,	,	PUNCT
ejpam-5909	180	15	there	there	PRON
ejpam-5909	180	16	exists	exist	VERB
ejpam-5909	180	17	a	a	DET
ejpam-5909	180	18	real	real	ADJ
ejpam-5909	180	19	number	number	NOUN
ejpam-5909	180	20	δ1	δ1	NOUN
ejpam-5909	180	21	>	>	X
ejpam-5909	180	22	0	0	NUM
ejpam-5909	181	1	such	such	ADJ
ejpam-5909	181	2	that	that	SCONJ
ejpam-5909	181	3	if	if	SCONJ
ejpam-5909	181	4	f	f	PROPN
ejpam-5909	181	5	∈	∈	PROPN
ejpam-5909	181	6	a	a	PRON
ejpam-5909	181	7	and	and	CCONJ
ejpam-5909	181	8	0	0	NUM
ejpam-5909	181	9	≺	≺	NOUN
ejpam-5909	181	10	|f	|f	NUM
ejpam-5909	181	11	−	−	PROPN
ejpam-5909	181	12	f0|	f0|	PROPN
ejpam-5909	181	13	≺	≺	NOUN
ejpam-5909	181	14	δ1e	δ1e	VERB
ejpam-5909	181	15	,	,	PUNCT
ejpam-5909	181	16	then	then	ADV
ejpam-5909	181	17	:	:	PUNCT
ejpam-5909	181	18	|f	|f	PROPN
ejpam-5909	182	1	(	(	PUNCT
ejpam-5909	182	2	f)−	f)−	PROPN
ejpam-5909	182	3	l|	l|	ADJ
ejpam-5909	182	4	≺	≺	NOUN
ejpam-5909	182	5	ε	ε	X
ejpam-5909	182	6	(	(	PUNCT
ejpam-5909	182	7	e	e	PROPN
ejpam-5909	182	8	2|m	2|m	NUM
ejpam-5909	182	9	|+	|+	NOUN
ejpam-5909	182	10	e	e	NOUN
ejpam-5909	182	11	)	)	PUNCT
ejpam-5909	182	12	.	.	PUNCT
ejpam-5909	183	1	m.	m.	NOUN
ejpam-5909	183	2	alifuddin	alifuddin	VERB
ejpam-5909	183	3	et	et	PROPN
ejpam-5909	183	4	al	al	PROPN
ejpam-5909	183	5	.	.	PUNCT
ejpam-5909	183	6	/	/	SYM
ejpam-5909	183	7	eur	eur	PROPN
ejpam-5909	183	8	.	.	PUNCT
ejpam-5909	184	1	j.	j.	PROPN
ejpam-5909	184	2	pure	pure	PROPN
ejpam-5909	184	3	appl	appl	PROPN
ejpam-5909	184	4	.	.	PROPN
ejpam-5909	184	5	math	math	PROPN
ejpam-5909	184	6	,	,	PUNCT
ejpam-5909	184	7	18	18	NUM
ejpam-5909	184	8	(	(	PUNCT
ejpam-5909	184	9	2	2	NUM
ejpam-5909	184	10	)	)	PUNCT
ejpam-5909	184	11	(	(	PUNCT
ejpam-5909	184	12	2025	2025	NUM
ejpam-5909	184	13	)	)	PUNCT
ejpam-5909	184	14	,	,	PUNCT
ejpam-5909	184	15	5909	5909	NUM
ejpam-5909	184	16	9	9	NUM
ejpam-5909	184	17	of	of	ADP
ejpam-5909	184	18	17	17	NUM
ejpam-5909	184	19	similarly	similarly	ADV
ejpam-5909	184	20	,	,	PUNCT
ejpam-5909	184	21	given	give	VERB
ejpam-5909	184	22	that	that	DET
ejpam-5909	184	23	limf→f0	limf→f0	VERB
ejpam-5909	184	24	g(f	g(f	PROPN
ejpam-5909	184	25	)	)	PUNCT
ejpam-5909	185	1	=	=	PUNCT
ejpam-5909	185	2	m	m	X
ejpam-5909	185	3	,	,	PUNCT
ejpam-5909	185	4	it	it	PRON
ejpam-5909	185	5	follows	follow	VERB
ejpam-5909	185	6	that	that	SCONJ
ejpam-5909	185	7	for	for	ADP
ejpam-5909	185	8	every	every	DET
ejpam-5909	185	9	real	real	ADJ
ejpam-5909	185	10	number	number	NOUN
ejpam-5909	185	11	ε	ε	PROPN
ejpam-5909	185	12	>	>	X
ejpam-5909	185	13	0	0	PROPN
ejpam-5909	185	14	,	,	PUNCT
ejpam-5909	185	15	there	there	PRON
ejpam-5909	185	16	exists	exist	VERB
ejpam-5909	185	17	a	a	DET
ejpam-5909	185	18	real	real	ADJ
ejpam-5909	185	19	number	number	NOUN
ejpam-5909	185	20	δ2	δ2	VERB
ejpam-5909	185	21	>	>	X
ejpam-5909	185	22	0	0	NUM
ejpam-5909	186	1	such	such	ADJ
ejpam-5909	186	2	that	that	SCONJ
ejpam-5909	186	3	if	if	SCONJ
ejpam-5909	186	4	f	f	PROPN
ejpam-5909	186	5	∈	∈	PROPN
ejpam-5909	186	6	a	a	PRON
ejpam-5909	186	7	and	and	CCONJ
ejpam-5909	186	8	0	0	NUM
ejpam-5909	186	9	≺	≺	NOUN
ejpam-5909	186	10	|f	|f	NUM
ejpam-5909	186	11	−	−	PROPN
ejpam-5909	186	12	f0|	f0|	PROPN
ejpam-5909	186	13	≺	≺	NOUN
ejpam-5909	186	14	δ2e	δ2e	PROPN
ejpam-5909	186	15	,	,	PUNCT
ejpam-5909	186	16	then	then	ADV
ejpam-5909	186	17	:	:	PUNCT
ejpam-5909	186	18	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	186	19	|	|	ADV
ejpam-5909	186	20	≺	≺	NOUN
ejpam-5909	186	21	ε	ε	PROPN
ejpam-5909	186	22	(	(	PUNCT
ejpam-5909	186	23	e	e	PROPN
ejpam-5909	186	24	2(sup	2(sup	NUM
ejpam-5909	186	25	|f	|f	PROPN
ejpam-5909	186	26	(	(	PUNCT
ejpam-5909	186	27	f)|+	f)|+	NOUN
ejpam-5909	186	28	e	e	NOUN
ejpam-5909	186	29	)	)	PUNCT
ejpam-5909	186	30	)	)	PUNCT
ejpam-5909	186	31	,	,	PUNCT
ejpam-5909	186	32	where	where	SCONJ
ejpam-5909	186	33	sup	sup	PROPN
ejpam-5909	186	34	|f	|f	PROPN
ejpam-5909	186	35	(	(	PUNCT
ejpam-5909	186	36	f)|	f)|	VERB
ejpam-5909	186	37	is	be	AUX
ejpam-5909	186	38	the	the	DET
ejpam-5909	186	39	supremum	supremum	NOUN
ejpam-5909	186	40	of	of	ADP
ejpam-5909	186	41	|f	|f	PROPN
ejpam-5909	186	42	(	(	PUNCT
ejpam-5909	186	43	f)|	f)|	VERB
ejpam-5909	186	44	in	in	ADP
ejpam-5909	186	45	the	the	DET
ejpam-5909	186	46	neighborhood	neighborhood	NOUN
ejpam-5909	186	47	of	of	ADP
ejpam-5909	186	48	f0	f0	PROPN
ejpam-5909	186	49	where	where	SCONJ
ejpam-5909	186	50	f	f	PROPN
ejpam-5909	186	51	̸=	̸=	PROPN
ejpam-5909	186	52	f0	f0	PROPN
ejpam-5909	186	53	.	.	PUNCT
ejpam-5909	187	1	by	by	ADP
ejpam-5909	187	2	choosing	choose	VERB
ejpam-5909	187	3	δ	δ	X
ejpam-5909	187	4	=	=	PUNCT
ejpam-5909	187	5	min(δ1	min(δ1	PROPN
ejpam-5909	187	6	,	,	PUNCT
ejpam-5909	187	7	δ2	δ2	PROPN
ejpam-5909	187	8	)	)	PUNCT
ejpam-5909	187	9	,	,	PUNCT
ejpam-5909	187	10	we	we	PRON
ejpam-5909	187	11	obtain	obtain	VERB
ejpam-5909	187	12	that	that	PRON
ejpam-5909	187	13	for	for	ADP
ejpam-5909	187	14	every	every	DET
ejpam-5909	187	15	0	0	NUM
ejpam-5909	187	16	≺	≺	NOUN
ejpam-5909	187	17	|f−f0|	|f−f0|	NOUN
ejpam-5909	187	18	≺	≺	NOUN
ejpam-5909	187	19	δe	δe	ADP
ejpam-5909	187	20	,	,	PUNCT
ejpam-5909	187	21	the	the	DET
ejpam-5909	187	22	following	follow	VERB
ejpam-5909	187	23	holds	hold	VERB
ejpam-5909	187	24	:	:	PUNCT
ejpam-5909	187	25	|f	|f	PROPN
ejpam-5909	187	26	(	(	PUNCT
ejpam-5909	187	27	f)g(f)−	f)g(f)−	PROPN
ejpam-5909	188	1	lm	lm	INTJ
ejpam-5909	188	2	|	|	ADV
ejpam-5909	188	3	=	=	SYM
ejpam-5909	188	4	|f	|f	PROPN
ejpam-5909	188	5	(	(	PUNCT
ejpam-5909	188	6	f)g(f)−	f)g(f)−	PROPN
ejpam-5909	188	7	f	f	X
ejpam-5909	188	8	(	(	PUNCT
ejpam-5909	188	9	f)m	f)m	X
ejpam-5909	189	1	+	+	NUM
ejpam-5909	189	2	f	f	X
ejpam-5909	189	3	(	(	PUNCT
ejpam-5909	189	4	f)m	f)m	ADJ
ejpam-5909	189	5	−	−	NOUN
ejpam-5909	189	6	lm	lm	INTJ
ejpam-5909	190	1	|	|	ADV
ejpam-5909	190	2	=	=	SYM
ejpam-5909	190	3	|f	|f	PROPN
ejpam-5909	190	4	(	(	PUNCT
ejpam-5909	190	5	f)[g(f)−m	f)[g(f)−m	PROPN
ejpam-5909	190	6	]	]	PUNCT
ejpam-5909	191	1	+	+	NOUN
ejpam-5909	191	2	m	m	VERB
ejpam-5909	191	3	[	[	X
ejpam-5909	191	4	f	f	X
ejpam-5909	191	5	(	(	PUNCT
ejpam-5909	191	6	f)−	f)−	PROPN
ejpam-5909	191	7	l]|	l]|	PROPN
ejpam-5909	191	8	⪯	⪯	VERB
ejpam-5909	191	9	|f	|f	PROPN
ejpam-5909	192	1	(	(	PUNCT
ejpam-5909	192	2	f)|	f)|	VERB
ejpam-5909	192	3	|g(f)−m	|g(f)−m	PUNCT
ejpam-5909	192	4	|+	|+	NOUN
ejpam-5909	192	5	|m	|m	NOUN
ejpam-5909	192	6	|	|	ADV
ejpam-5909	192	7	|f	|f	PROPN
ejpam-5909	192	8	(	(	PUNCT
ejpam-5909	192	9	f)−	f)−	PROPN
ejpam-5909	192	10	l|	l|	PROPN
ejpam-5909	192	11	.	.	PUNCT
ejpam-5909	193	1	from	from	ADP
ejpam-5909	193	2	this	this	PRON
ejpam-5909	193	3	,	,	PUNCT
ejpam-5909	193	4	we	we	PRON
ejpam-5909	193	5	conclude	conclude	VERB
ejpam-5909	193	6	:	:	PUNCT
ejpam-5909	194	1	lim	lim	PROPN
ejpam-5909	194	2	f→f0	f→f0	PROPN
ejpam-5909	195	1	(	(	PUNCT
ejpam-5909	195	2	f	f	X
ejpam-5909	195	3	(	(	PUNCT
ejpam-5909	195	4	f)g(f	f)g(f	NOUN
ejpam-5909	195	5	)	)	PUNCT
ejpam-5909	195	6	)	)	PUNCT
ejpam-5909	196	1	=	=	PUNCT
ejpam-5909	196	2	lm	lm	PROPN
ejpam-5909	196	3	.	.	PUNCT
ejpam-5909	196	4	(	(	PUNCT
ejpam-5909	196	5	iv	iv	X
ejpam-5909	196	6	)	)	PUNCT
ejpam-5909	196	7	given	give	VERB
ejpam-5909	196	8	that	that	PRON
ejpam-5909	196	9	limf→f0	limf→f0	VERB
ejpam-5909	196	10	f	f	X
ejpam-5909	196	11	(	(	PUNCT
ejpam-5909	196	12	f	f	X
ejpam-5909	196	13	)	)	PUNCT
ejpam-5909	196	14	=	=	SYM
ejpam-5909	196	15	l	l	NOUN
ejpam-5909	196	16	,	,	PUNCT
ejpam-5909	196	17	it	it	PRON
ejpam-5909	196	18	follows	follow	VERB
ejpam-5909	196	19	that	that	SCONJ
ejpam-5909	196	20	for	for	ADP
ejpam-5909	196	21	every	every	DET
ejpam-5909	196	22	real	real	ADJ
ejpam-5909	196	23	number	number	NOUN
ejpam-5909	196	24	ε	ε	PROPN
ejpam-5909	196	25	>	>	X
ejpam-5909	196	26	0	0	PROPN
ejpam-5909	196	27	,	,	PUNCT
ejpam-5909	196	28	there	there	PRON
ejpam-5909	196	29	exists	exist	VERB
ejpam-5909	196	30	a	a	DET
ejpam-5909	196	31	real	real	ADJ
ejpam-5909	196	32	number	number	NOUN
ejpam-5909	196	33	δ	δ	NOUN
ejpam-5909	196	34	>	>	X
ejpam-5909	196	35	0	0	NUM
ejpam-5909	197	1	such	such	ADJ
ejpam-5909	197	2	that	that	SCONJ
ejpam-5909	197	3	if	if	SCONJ
ejpam-5909	197	4	f	f	PROPN
ejpam-5909	197	5	∈	∈	PROPN
ejpam-5909	197	6	a	a	PRON
ejpam-5909	197	7	and	and	CCONJ
ejpam-5909	197	8	0	0	NUM
ejpam-5909	197	9	≺	≺	NOUN
ejpam-5909	197	10	|f	|f	NUM
ejpam-5909	197	11	−	−	PROPN
ejpam-5909	197	12	f0|	f0|	PROPN
ejpam-5909	197	13	≺	≺	NOUN
ejpam-5909	197	14	δe	δe	ADP
ejpam-5909	197	15	,	,	PUNCT
ejpam-5909	197	16	then	then	ADV
ejpam-5909	197	17	:	:	PUNCT
ejpam-5909	197	18	|f	|f	PROPN
ejpam-5909	197	19	(	(	PUNCT
ejpam-5909	197	20	f)−	f)−	PROPN
ejpam-5909	197	21	l|	l|	ADJ
ejpam-5909	197	22	≺	≺	NOUN
ejpam-5909	197	23	εe	εe	ADP
ejpam-5909	197	24	|γ|	|γ|	PROPN
ejpam-5909	197	25	.	.	PUNCT
ejpam-5909	198	1	since	since	SCONJ
ejpam-5909	198	2	γ	γ	PROPN
ejpam-5909	198	3	∈	∈	PROPN
ejpam-5909	198	4	c[a	c[a	PROPN
ejpam-5909	198	5	,	,	PUNCT
ejpam-5909	198	6	b	b	NOUN
ejpam-5909	198	7	]	]	X
ejpam-5909	198	8	,	,	PUNCT
ejpam-5909	198	9	for	for	ADP
ejpam-5909	198	10	every	every	DET
ejpam-5909	198	11	0	0	NUM
ejpam-5909	198	12	≺	≺	NOUN
ejpam-5909	198	13	|f	|f	NUM
ejpam-5909	198	14	−	−	PROPN
ejpam-5909	198	15	f0|	f0|	PROPN
ejpam-5909	198	16	≺	≺	NOUN
ejpam-5909	198	17	δe	δe	NOUN
ejpam-5909	198	18	,	,	PUNCT
ejpam-5909	198	19	the	the	DET
ejpam-5909	198	20	following	follow	VERB
ejpam-5909	198	21	holds	hold	VERB
ejpam-5909	198	22	:	:	PUNCT
ejpam-5909	198	23	|γf	|γf	X
ejpam-5909	198	24	(	(	PUNCT
ejpam-5909	198	25	f)−	f)−	PROPN
ejpam-5909	198	26	γl|	γl|	PROPN
ejpam-5909	199	1	=	=	PUNCT
ejpam-5909	199	2	|γ|	|γ|	PROPN
ejpam-5909	199	3	|f	|f	X
ejpam-5909	199	4	(	(	PUNCT
ejpam-5909	199	5	f)−	f)−	PROPN
ejpam-5909	199	6	l|	l|	ADJ
ejpam-5909	199	7	≺	≺	NOUN
ejpam-5909	199	8	|γ|	|γ|	PRON
ejpam-5909	199	9	εe	εe	ADP
ejpam-5909	199	10	|γ|	|γ|	PROPN
ejpam-5909	199	11	=	=	PUNCT
ejpam-5909	199	12	εe	εe	PROPN
ejpam-5909	199	13	.	.	PUNCT
ejpam-5909	200	1	thus	thus	ADV
ejpam-5909	200	2	,	,	PUNCT
ejpam-5909	200	3	lim	lim	PROPN
ejpam-5909	200	4	f→f0	f→f0	PROPN
ejpam-5909	201	1	(	(	PUNCT
ejpam-5909	201	2	γf	γf	INTJ
ejpam-5909	201	3	(	(	PUNCT
ejpam-5909	201	4	f	f	NOUN
ejpam-5909	201	5	)	)	PUNCT
ejpam-5909	201	6	)	)	PUNCT
ejpam-5909	201	7	=	=	SYM
ejpam-5909	201	8	γl	γl	PROPN
ejpam-5909	201	9	.	.	PUNCT
ejpam-5909	202	1	next	next	ADV
ejpam-5909	202	2	,	,	PUNCT
ejpam-5909	202	3	the	the	DET
ejpam-5909	202	4	concept	concept	NOUN
ejpam-5909	202	5	of	of	ADP
ejpam-5909	202	6	a	a	DET
ejpam-5909	202	7	one	one	NUM
ejpam-5909	202	8	-	-	PUNCT
ejpam-5909	202	9	sided	sided	ADJ
ejpam-5909	202	10	limit	limit	NOUN
ejpam-5909	202	11	of	of	ADP
ejpam-5909	202	12	an	an	DET
ejpam-5909	202	13	operator	operator	NOUN
ejpam-5909	202	14	will	will	AUX
ejpam-5909	202	15	be	be	AUX
ejpam-5909	202	16	defined	define	VERB
ejpam-5909	202	17	in	in	ADP
ejpam-5909	202	18	more	more	ADJ
ejpam-5909	202	19	detail	detail	NOUN
ejpam-5909	202	20	.	.	PUNCT
ejpam-5909	203	1	this	this	DET
ejpam-5909	203	2	definition	definition	NOUN
ejpam-5909	203	3	will	will	AUX
ejpam-5909	203	4	be	be	AUX
ejpam-5909	203	5	used	use	VERB
ejpam-5909	203	6	to	to	PART
ejpam-5909	203	7	understand	understand	VERB
ejpam-5909	203	8	the	the	DET
ejpam-5909	203	9	behavior	behavior	NOUN
ejpam-5909	203	10	of	of	ADP
ejpam-5909	203	11	a	a	DET
ejpam-5909	203	12	function	function	NOUN
ejpam-5909	203	13	around	around	ADP
ejpam-5909	203	14	a	a	DET
ejpam-5909	203	15	specific	specific	ADJ
ejpam-5909	203	16	operator	operator	NOUN
ejpam-5909	203	17	in	in	ADP
ejpam-5909	203	18	a	a	DET
ejpam-5909	203	19	single	single	ADJ
ejpam-5909	203	20	direction	direction	NOUN
ejpam-5909	203	21	.	.	PUNCT
ejpam-5909	204	1	the	the	DET
ejpam-5909	204	2	following	follow	VERB
ejpam-5909	204	3	defines	define	VERB
ejpam-5909	204	4	a	a	DET
ejpam-5909	204	5	one	one	NUM
ejpam-5909	204	6	-	-	PUNCT
ejpam-5909	204	7	sided	sided	ADJ
ejpam-5909	204	8	limit	limit	NOUN
ejpam-5909	204	9	of	of	ADP
ejpam-5909	204	10	an	an	DET
ejpam-5909	204	11	operator	operator	NOUN
ejpam-5909	204	12	on	on	ADP
ejpam-5909	204	13	c[a	c[a	NUM
ejpam-5909	204	14	,	,	PUNCT
ejpam-5909	204	15	b	b	NOUN
ejpam-5909	204	16	]	]	PUNCT
ejpam-5909	204	17	.	.	PUNCT
ejpam-5909	205	1	definition	definition	NOUN
ejpam-5909	205	2	10	10	NUM
ejpam-5909	205	3	.	.	PUNCT
ejpam-5909	206	1	consider	consider	VERB
ejpam-5909	206	2	a	a	DET
ejpam-5909	206	3	⊆	⊆	NUM
ejpam-5909	206	4	c[a	c[a	NUM
ejpam-5909	206	5	,	,	PUNCT
ejpam-5909	206	6	b	b	NOUN
ejpam-5909	206	7	]	]	PUNCT
ejpam-5909	206	8	and	and	CCONJ
ejpam-5909	206	9	let	let	VERB
ejpam-5909	206	10	f0	f0	PROPN
ejpam-5909	206	11	be	be	AUX
ejpam-5909	206	12	a	a	DET
ejpam-5909	206	13	limit	limit	NOUN
ejpam-5909	206	14	point	point	NOUN
ejpam-5909	206	15	of	of	ADP
ejpam-5909	206	16	the	the	DET
ejpam-5909	206	17	set	set	NOUN
ejpam-5909	206	18	a.	a.	NOUN
ejpam-5909	206	19	(	(	PUNCT
ejpam-5909	206	20	i	i	NOUN
ejpam-5909	206	21	)	)	PUNCT
ejpam-5909	206	22	for	for	ADP
ejpam-5909	206	23	an	an	DET
ejpam-5909	206	24	operator	operator	NOUN
ejpam-5909	206	25	f	f	NOUN
ejpam-5909	206	26	:	:	PUNCT
ejpam-5909	206	27	a	a	DET
ejpam-5909	206	28	→	→	SYM
ejpam-5909	206	29	c[a	c[a	NUM
ejpam-5909	206	30	,	,	PUNCT
ejpam-5909	206	31	b	b	NOUN
ejpam-5909	206	32	]	]	X
ejpam-5909	206	33	,	,	PUNCT
ejpam-5909	206	34	the	the	DET
ejpam-5909	206	35	function	function	NOUN
ejpam-5909	206	36	l	l	NOUN
ejpam-5909	206	37	is	be	AUX
ejpam-5909	206	38	called	call	VERB
ejpam-5909	206	39	the	the	DET
ejpam-5909	206	40	right	right	ADJ
ejpam-5909	206	41	limit	limit	NOUN
ejpam-5909	206	42	of	of	ADP
ejpam-5909	206	43	the	the	DET
ejpam-5909	206	44	operator	operator	NOUN
ejpam-5909	206	45	f	f	PROPN
ejpam-5909	206	46	at	at	ADP
ejpam-5909	206	47	f0	f0	PROPN
ejpam-5909	206	48	if	if	SCONJ
ejpam-5909	206	49	,	,	PUNCT
ejpam-5909	206	50	for	for	ADP
ejpam-5909	206	51	every	every	DET
ejpam-5909	206	52	positive	positive	ADJ
ejpam-5909	206	53	real	real	ADJ
ejpam-5909	206	54	number	number	NOUN
ejpam-5909	206	55	ε	ε	PROPN
ejpam-5909	206	56	,	,	PUNCT
ejpam-5909	206	57	there	there	PRON
ejpam-5909	206	58	exists	exist	VERB
ejpam-5909	206	59	a	a	DET
ejpam-5909	206	60	positive	positive	ADJ
ejpam-5909	206	61	real	real	ADJ
ejpam-5909	206	62	number	number	NOUN
ejpam-5909	206	63	δ	δ	NOUN
ejpam-5909	206	64	such	such	ADJ
ejpam-5909	206	65	that	that	PRON
ejpam-5909	206	66	for	for	ADP
ejpam-5909	206	67	every	every	DET
ejpam-5909	206	68	function	function	NOUN
ejpam-5909	206	69	f	f	PROPN
ejpam-5909	206	70	∈	∈	PROPN
ejpam-5909	206	71	a	a	DET
ejpam-5909	206	72	∩	∩	NOUN
ejpam-5909	206	73	{	{	PUNCT
ejpam-5909	206	74	f	f	PROPN
ejpam-5909	206	75	∈	∈	PROPN
ejpam-5909	206	76	c[a	c[a	PROPN
ejpam-5909	206	77	,	,	PUNCT
ejpam-5909	206	78	b	b	X
ejpam-5909	206	79	]	]	X
ejpam-5909	206	80	:	:	PUNCT
ejpam-5909	206	81	f	f	PROPN
ejpam-5909	206	82	≻	≻	PROPN
ejpam-5909	206	83	f0	f0	PROPN
ejpam-5909	206	84	}	}	PUNCT
ejpam-5909	206	85	and	and	CCONJ
ejpam-5909	206	86	0	0	NUM
ejpam-5909	206	87	≺	≺	NOUN
ejpam-5909	206	88	|f	|f	NUM
ejpam-5909	206	89	−	−	PROPN
ejpam-5909	206	90	f0|	f0|	PROPN
ejpam-5909	206	91	≺	≺	NOUN
ejpam-5909	206	92	δe	δe	NOUN
ejpam-5909	206	93	,	,	PUNCT
ejpam-5909	206	94	the	the	DET
ejpam-5909	206	95	following	follow	VERB
ejpam-5909	206	96	holds	hold	VERB
ejpam-5909	206	97	:	:	PUNCT
ejpam-5909	206	98	|f	|f	PROPN
ejpam-5909	206	99	(	(	PUNCT
ejpam-5909	206	100	f)−	f)−	PROPN
ejpam-5909	206	101	f	f	X
ejpam-5909	206	102	(	(	PUNCT
ejpam-5909	206	103	f0)|	f0)|	NOUN
ejpam-5909	206	104	≺	≺	NOUN
ejpam-5909	206	105	εe	εe	NOUN
ejpam-5909	206	106	.	.	PUNCT
ejpam-5909	207	1	if	if	SCONJ
ejpam-5909	207	2	l	l	NOUN
ejpam-5909	207	3	is	be	AUX
ejpam-5909	207	4	the	the	DET
ejpam-5909	207	5	right	right	ADJ
ejpam-5909	207	6	limit	limit	NOUN
ejpam-5909	207	7	of	of	ADP
ejpam-5909	207	8	the	the	DET
ejpam-5909	207	9	operator	operator	NOUN
ejpam-5909	207	10	f	f	PROPN
ejpam-5909	207	11	at	at	ADP
ejpam-5909	207	12	f0	f0	PROPN
ejpam-5909	207	13	,	,	PUNCT
ejpam-5909	207	14	it	it	PRON
ejpam-5909	207	15	is	be	AUX
ejpam-5909	207	16	written	write	VERB
ejpam-5909	207	17	as	as	ADP
ejpam-5909	207	18	l	l	NOUN
ejpam-5909	207	19	=	=	PROPN
ejpam-5909	207	20	lim	lim	PROPN
ejpam-5909	207	21	f→f+	f→f+	PROPN
ejpam-5909	208	1	0	0	NUM
ejpam-5909	208	2	f	f	PROPN
ejpam-5909	208	3	(	(	PUNCT
ejpam-5909	208	4	f	f	NOUN
ejpam-5909	208	5	)	)	PUNCT
ejpam-5909	208	6	.	.	PUNCT
ejpam-5909	209	1	m.	m.	NOUN
ejpam-5909	209	2	alifuddin	alifuddin	VERB
ejpam-5909	209	3	et	et	PROPN
ejpam-5909	209	4	al	al	PROPN
ejpam-5909	209	5	.	.	PUNCT
ejpam-5909	209	6	/	/	SYM
ejpam-5909	209	7	eur	eur	PROPN
ejpam-5909	209	8	.	.	PUNCT
ejpam-5909	210	1	j.	j.	PROPN
ejpam-5909	210	2	pure	pure	PROPN
ejpam-5909	210	3	appl	appl	PROPN
ejpam-5909	210	4	.	.	PROPN
ejpam-5909	210	5	math	math	PROPN
ejpam-5909	210	6	,	,	PUNCT
ejpam-5909	210	7	18	18	NUM
ejpam-5909	210	8	(	(	PUNCT
ejpam-5909	210	9	2	2	NUM
ejpam-5909	210	10	)	)	PUNCT
ejpam-5909	210	11	(	(	PUNCT
ejpam-5909	210	12	2025	2025	NUM
ejpam-5909	210	13	)	)	PUNCT
ejpam-5909	210	14	,	,	PUNCT
ejpam-5909	210	15	5909	5909	NUM
ejpam-5909	210	16	10	10	NUM
ejpam-5909	210	17	of	of	ADP
ejpam-5909	210	18	17	17	NUM
ejpam-5909	210	19	(	(	PUNCT
ejpam-5909	210	20	ii	ii	NOUN
ejpam-5909	210	21	)	)	PUNCT
ejpam-5909	210	22	for	for	ADP
ejpam-5909	210	23	an	an	DET
ejpam-5909	210	24	operator	operator	NOUN
ejpam-5909	210	25	f	f	NOUN
ejpam-5909	210	26	:	:	PUNCT
ejpam-5909	210	27	a	a	DET
ejpam-5909	210	28	→	→	SYM
ejpam-5909	210	29	c[a	c[a	NUM
ejpam-5909	210	30	,	,	PUNCT
ejpam-5909	210	31	b	b	NOUN
ejpam-5909	210	32	]	]	X
ejpam-5909	210	33	,	,	PUNCT
ejpam-5909	210	34	the	the	DET
ejpam-5909	210	35	function	function	NOUN
ejpam-5909	210	36	l	l	NOUN
ejpam-5909	210	37	is	be	AUX
ejpam-5909	210	38	called	call	VERB
ejpam-5909	210	39	the	the	DET
ejpam-5909	210	40	left	left	ADJ
ejpam-5909	210	41	limit	limit	NOUN
ejpam-5909	210	42	of	of	ADP
ejpam-5909	210	43	the	the	DET
ejpam-5909	210	44	operator	operator	NOUN
ejpam-5909	210	45	f	f	PROPN
ejpam-5909	210	46	at	at	ADP
ejpam-5909	210	47	f0	f0	PROPN
ejpam-5909	210	48	if	if	SCONJ
ejpam-5909	210	49	,	,	PUNCT
ejpam-5909	210	50	for	for	ADP
ejpam-5909	210	51	every	every	DET
ejpam-5909	210	52	real	real	ADJ
ejpam-5909	210	53	number	number	NOUN
ejpam-5909	210	54	ε	ε	PROPN
ejpam-5909	210	55	>	>	X
ejpam-5909	210	56	0	0	PROPN
ejpam-5909	210	57	,	,	PUNCT
ejpam-5909	210	58	there	there	PRON
ejpam-5909	210	59	exists	exist	VERB
ejpam-5909	210	60	a	a	DET
ejpam-5909	210	61	real	real	ADJ
ejpam-5909	210	62	number	number	NOUN
ejpam-5909	210	63	δ	δ	NOUN
ejpam-5909	210	64	>	>	X
ejpam-5909	210	65	0	0	NUM
ejpam-5909	210	66	such	such	ADJ
ejpam-5909	210	67	that	that	PRON
ejpam-5909	210	68	for	for	ADP
ejpam-5909	210	69	every	every	DET
ejpam-5909	210	70	f	f	PROPN
ejpam-5909	210	71	∈	∈	PROPN
ejpam-5909	210	72	a	a	DET
ejpam-5909	210	73	∩	∩	NOUN
ejpam-5909	210	74	{	{	PUNCT
ejpam-5909	210	75	f	f	PROPN
ejpam-5909	210	76	∈	∈	PROPN
ejpam-5909	210	77	c[a	c[a	PROPN
ejpam-5909	210	78	,	,	PUNCT
ejpam-5909	210	79	b	b	X
ejpam-5909	210	80	]	]	X
ejpam-5909	210	81	:	:	PUNCT
ejpam-5909	210	82	f	f	PROPN
ejpam-5909	210	83	≺	≺	NOUN
ejpam-5909	210	84	f0	f0	PROPN
ejpam-5909	210	85	}	}	PUNCT
ejpam-5909	210	86	and	and	CCONJ
ejpam-5909	210	87	0	0	NUM
ejpam-5909	210	88	≺	≺	NOUN
ejpam-5909	210	89	|f	|f	NUM
ejpam-5909	210	90	−	−	PROPN
ejpam-5909	210	91	f0|	f0|	PROPN
ejpam-5909	210	92	≺	≺	NOUN
ejpam-5909	210	93	δe	δe	NOUN
ejpam-5909	210	94	,	,	PUNCT
ejpam-5909	210	95	the	the	DET
ejpam-5909	210	96	following	follow	VERB
ejpam-5909	210	97	holds	hold	VERB
ejpam-5909	210	98	:	:	PUNCT
ejpam-5909	210	99	|f	|f	PROPN
ejpam-5909	210	100	(	(	PUNCT
ejpam-5909	210	101	f)−	f)−	PROPN
ejpam-5909	210	102	f	f	X
ejpam-5909	210	103	(	(	PUNCT
ejpam-5909	210	104	f0)|	f0)|	NOUN
ejpam-5909	210	105	≺	≺	NOUN
ejpam-5909	210	106	εe	εe	NOUN
ejpam-5909	210	107	.	.	PUNCT
ejpam-5909	211	1	if	if	SCONJ
ejpam-5909	211	2	l	l	NOUN
ejpam-5909	211	3	is	be	AUX
ejpam-5909	211	4	the	the	DET
ejpam-5909	211	5	left	left	ADJ
ejpam-5909	211	6	limit	limit	NOUN
ejpam-5909	211	7	of	of	ADP
ejpam-5909	211	8	the	the	DET
ejpam-5909	211	9	operator	operator	NOUN
ejpam-5909	211	10	f	f	PROPN
ejpam-5909	211	11	at	at	ADP
ejpam-5909	211	12	f0	f0	PROPN
ejpam-5909	211	13	,	,	PUNCT
ejpam-5909	211	14	it	it	PRON
ejpam-5909	211	15	is	be	AUX
ejpam-5909	211	16	written	write	VERB
ejpam-5909	211	17	as	as	ADP
ejpam-5909	211	18	l	l	NOUN
ejpam-5909	211	19	=	=	PROPN
ejpam-5909	211	20	lim	lim	PROPN
ejpam-5909	211	21	f→f−	f→f−	X
ejpam-5909	212	1	0	0	NUM
ejpam-5909	212	2	f	f	X
ejpam-5909	212	3	(	(	PUNCT
ejpam-5909	212	4	f	f	PROPN
ejpam-5909	212	5	)	)	PUNCT
ejpam-5909	212	6	.	.	PUNCT
ejpam-5909	213	1	example	example	NOUN
ejpam-5909	214	1	4	4	X
ejpam-5909	214	2	.	.	PUNCT
ejpam-5909	214	3	consider	consider	VERB
ejpam-5909	214	4	f	f	NOUN
ejpam-5909	214	5	:	:	PUNCT
ejpam-5909	214	6	c[a	c[a	NUM
ejpam-5909	214	7	,	,	PUNCT
ejpam-5909	214	8	b	b	X
ejpam-5909	214	9	]	]	X
ejpam-5909	214	10	→	→	SYM
ejpam-5909	214	11	c[a	c[a	NUM
ejpam-5909	214	12	,	,	PUNCT
ejpam-5909	214	13	b	b	NOUN
ejpam-5909	214	14	]	]	PUNCT
ejpam-5909	214	15	defined	define	VERB
ejpam-5909	214	16	by	by	ADP
ejpam-5909	214	17	:	:	PUNCT
ejpam-5909	214	18	f	f	PROPN
ejpam-5909	214	19	(	(	PUNCT
ejpam-5909	214	20	f	f	X
ejpam-5909	214	21	)	)	PUNCT
ejpam-5909	214	22	=	=	PRON
ejpam-5909	214	23	{	{	PUNCT
ejpam-5909	214	24	e	e	X
ejpam-5909	214	25	,	,	PUNCT
ejpam-5909	214	26	if	if	SCONJ
ejpam-5909	214	27	f	f	PROPN
ejpam-5909	214	28	⪯	⪯	PROPN
ejpam-5909	214	29	0	0	NUM
ejpam-5909	214	30	,	,	PUNCT
ejpam-5909	214	31	2e	2e	NUM
ejpam-5909	214	32	,	,	PUNCT
ejpam-5909	214	33	if	if	SCONJ
ejpam-5909	214	34	f	f	PROPN
ejpam-5909	214	35	≻	≻	PROPN
ejpam-5909	214	36	0	0	NUM
ejpam-5909	214	37	.	.	PUNCT
ejpam-5909	215	1	we	we	PRON
ejpam-5909	215	2	will	will	AUX
ejpam-5909	215	3	show	show	VERB
ejpam-5909	215	4	that	that	SCONJ
ejpam-5909	215	5	lim	lim	PROPN
ejpam-5909	215	6	f→0	f→0	PROPN
ejpam-5909	215	7	+	+	PROPN
ejpam-5909	215	8	f	f	X
ejpam-5909	215	9	(	(	PUNCT
ejpam-5909	215	10	f	f	X
ejpam-5909	215	11	)	)	PUNCT
ejpam-5909	215	12	=	=	SYM
ejpam-5909	215	13	2e	2e	NOUN
ejpam-5909	215	14	and	and	CCONJ
ejpam-5909	215	15	lim	lim	PROPN
ejpam-5909	215	16	f→0−	f→0−	PROPN
ejpam-5909	216	1	f	f	PROPN
ejpam-5909	216	2	(	(	PUNCT
ejpam-5909	216	3	f	f	X
ejpam-5909	216	4	)	)	PUNCT
ejpam-5909	217	1	=	=	SYM
ejpam-5909	217	2	e.	e.	PROPN
ejpam-5909	217	3	(	(	PUNCT
ejpam-5909	217	4	i	i	NOUN
ejpam-5909	217	5	)	)	PUNCT
ejpam-5909	217	6	take	take	VERB
ejpam-5909	217	7	any	any	DET
ejpam-5909	217	8	positive	positive	ADJ
ejpam-5909	217	9	real	real	ADJ
ejpam-5909	217	10	number	number	NOUN
ejpam-5909	217	11	ε	ε	PROPN
ejpam-5909	217	12	,	,	PUNCT
ejpam-5909	217	13	and	and	CCONJ
ejpam-5909	217	14	choose	choose	VERB
ejpam-5909	217	15	a	a	DET
ejpam-5909	217	16	positive	positive	ADJ
ejpam-5909	217	17	real	real	ADJ
ejpam-5909	217	18	number	number	NOUN
ejpam-5909	217	19	δ	δ	NOUN
ejpam-5909	217	20	=	=	NOUN
ejpam-5909	217	21	5	5	NUM
ejpam-5909	217	22	such	such	ADJ
ejpam-5909	217	23	that	that	PRON
ejpam-5909	217	24	for	for	ADP
ejpam-5909	217	25	every	every	DET
ejpam-5909	217	26	f	f	PROPN
ejpam-5909	217	27	∈	∈	PROPN
ejpam-5909	217	28	c[a	c[a	PROPN
ejpam-5909	217	29	,	,	PUNCT
ejpam-5909	217	30	b	b	X
ejpam-5909	217	31	]	]	X
ejpam-5909	217	32	∩	∩	NOUN
ejpam-5909	217	33	{	{	PUNCT
ejpam-5909	217	34	f	f	PROPN
ejpam-5909	217	35	∈	∈	PROPN
ejpam-5909	217	36	c[a	c[a	PROPN
ejpam-5909	217	37	,	,	PUNCT
ejpam-5909	217	38	b	b	X
ejpam-5909	217	39	]	]	X
ejpam-5909	217	40	:	:	PUNCT
ejpam-5909	217	41	f	f	PROPN
ejpam-5909	217	42	≻	≻	PROPN
ejpam-5909	217	43	0	0	NUM
ejpam-5909	217	44	}	}	PUNCT
ejpam-5909	217	45	and	and	CCONJ
ejpam-5909	217	46	0	0	NUM
ejpam-5909	217	47	≺	≺	NOUN
ejpam-5909	217	48	|f	|f	ADP
ejpam-5909	217	49	−	−	PROPN
ejpam-5909	217	50	0|	0|	NOUN
ejpam-5909	217	51	≺	≺	NOUN
ejpam-5909	217	52	δe	δe	ADP
ejpam-5909	217	53	,	,	PUNCT
ejpam-5909	217	54	we	we	PRON
ejpam-5909	217	55	obtain	obtain	VERB
ejpam-5909	217	56	:	:	PUNCT
ejpam-5909	217	57	|f	|f	PROPN
ejpam-5909	218	1	(	(	PUNCT
ejpam-5909	218	2	f)−	f)−	PROPN
ejpam-5909	218	3	2e|	2e|	NUM
ejpam-5909	218	4	=	=	SYM
ejpam-5909	218	5	|2e−	|2e−	PROPN
ejpam-5909	218	6	2e|	2e|	NUM
ejpam-5909	218	7	=	=	SYM
ejpam-5909	218	8	|0|	|0|	X
ejpam-5909	218	9	=	=	NOUN
ejpam-5909	218	10	0	0	PUNCT
ejpam-5909	218	11	<	<	X
ejpam-5909	218	12	εe	εe	NOUN
ejpam-5909	218	13	.	.	PUNCT
ejpam-5909	219	1	thus	thus	ADV
ejpam-5909	219	2	:	:	PUNCT
ejpam-5909	219	3	lim	lim	PROPN
ejpam-5909	219	4	f→0	f→0	PROPN
ejpam-5909	219	5	+	+	CCONJ
ejpam-5909	219	6	f	f	X
ejpam-5909	219	7	(	(	PUNCT
ejpam-5909	219	8	f	f	X
ejpam-5909	219	9	)	)	PUNCT
ejpam-5909	219	10	=	=	SYM
ejpam-5909	219	11	2e	2e	NOUN
ejpam-5909	219	12	.	.	PUNCT
ejpam-5909	220	1	(	(	PUNCT
ejpam-5909	220	2	ii	ii	NOUN
ejpam-5909	220	3	)	)	PUNCT
ejpam-5909	220	4	take	take	VERB
ejpam-5909	220	5	any	any	DET
ejpam-5909	220	6	positive	positive	ADJ
ejpam-5909	220	7	real	real	ADJ
ejpam-5909	220	8	number	number	NOUN
ejpam-5909	220	9	ε	ε	PROPN
ejpam-5909	220	10	,	,	PUNCT
ejpam-5909	220	11	and	and	CCONJ
ejpam-5909	220	12	choose	choose	VERB
ejpam-5909	220	13	a	a	DET
ejpam-5909	220	14	positive	positive	ADJ
ejpam-5909	220	15	real	real	ADJ
ejpam-5909	220	16	number	number	NOUN
ejpam-5909	220	17	δ	δ	NOUN
ejpam-5909	220	18	=	=	NOUN
ejpam-5909	220	19	5	5	NUM
ejpam-5909	220	20	such	such	ADJ
ejpam-5909	220	21	that	that	PRON
ejpam-5909	220	22	for	for	ADP
ejpam-5909	220	23	every	every	DET
ejpam-5909	220	24	f	f	PROPN
ejpam-5909	220	25	∈	∈	PROPN
ejpam-5909	220	26	c[a	c[a	PROPN
ejpam-5909	220	27	,	,	PUNCT
ejpam-5909	220	28	b	b	X
ejpam-5909	220	29	]	]	X
ejpam-5909	220	30	∩	∩	NOUN
ejpam-5909	220	31	{	{	PUNCT
ejpam-5909	220	32	f	f	PROPN
ejpam-5909	220	33	∈	∈	PROPN
ejpam-5909	220	34	c[a	c[a	PROPN
ejpam-5909	220	35	,	,	PUNCT
ejpam-5909	220	36	b	b	X
ejpam-5909	220	37	]	]	X
ejpam-5909	220	38	:	:	PUNCT
ejpam-5909	220	39	f	f	PROPN
ejpam-5909	220	40	≺	≺	NOUN
ejpam-5909	220	41	0	0	NUM
ejpam-5909	220	42	}	}	PUNCT
ejpam-5909	220	43	and	and	CCONJ
ejpam-5909	220	44	0	0	NUM
ejpam-5909	220	45	≺	≺	NOUN
ejpam-5909	220	46	|f	|f	ADP
ejpam-5909	220	47	−	−	PROPN
ejpam-5909	221	1	0|	0|	NOUN
ejpam-5909	221	2	≺	≺	NOUN
ejpam-5909	221	3	δe	δe	ADP
ejpam-5909	221	4	,	,	PUNCT
ejpam-5909	221	5	we	we	PRON
ejpam-5909	221	6	obtain	obtain	VERB
ejpam-5909	221	7	:	:	PUNCT
ejpam-5909	221	8	|f	|f	PROPN
ejpam-5909	221	9	(	(	PUNCT
ejpam-5909	221	10	f)−	f)−	PROPN
ejpam-5909	221	11	e|	e|	PROPN
ejpam-5909	221	12	=	=	PUNCT
ejpam-5909	221	13	|e−	|e−	PROPN
ejpam-5909	221	14	e|	e|	PROPN
ejpam-5909	221	15	=	=	SYM
ejpam-5909	221	16	|0|	|0|	PROPN
ejpam-5909	222	1	=	=	NOUN
ejpam-5909	222	2	0	0	PUNCT
ejpam-5909	222	3	<	<	X
ejpam-5909	222	4	εe	εe	NOUN
ejpam-5909	222	5	.	.	PUNCT
ejpam-5909	223	1	thus	thus	ADV
ejpam-5909	223	2	:	:	PUNCT
ejpam-5909	223	3	lim	lim	PROPN
ejpam-5909	223	4	f→0−	f→0−	PROPN
ejpam-5909	223	5	f	f	PROPN
ejpam-5909	223	6	(	(	PUNCT
ejpam-5909	223	7	f	f	X
ejpam-5909	223	8	)	)	PUNCT
ejpam-5909	223	9	=	=	SYM
ejpam-5909	223	10	e.	e.	PROPN
ejpam-5909	223	11	m.	m.	PROPN
ejpam-5909	223	12	alifuddin	alifuddin	VERB
ejpam-5909	223	13	et	et	PROPN
ejpam-5909	223	14	al	al	PROPN
ejpam-5909	223	15	.	.	PUNCT
ejpam-5909	223	16	/	/	SYM
ejpam-5909	223	17	eur	eur	PROPN
ejpam-5909	223	18	.	.	PUNCT
ejpam-5909	224	1	j.	j.	PROPN
ejpam-5909	224	2	pure	pure	PROPN
ejpam-5909	224	3	appl	appl	PROPN
ejpam-5909	224	4	.	.	PROPN
ejpam-5909	224	5	math	math	PROPN
ejpam-5909	224	6	,	,	PUNCT
ejpam-5909	224	7	18	18	NUM
ejpam-5909	224	8	(	(	PUNCT
ejpam-5909	224	9	2	2	NUM
ejpam-5909	224	10	)	)	PUNCT
ejpam-5909	224	11	(	(	PUNCT
ejpam-5909	224	12	2025	2025	NUM
ejpam-5909	224	13	)	)	PUNCT
ejpam-5909	224	14	,	,	PUNCT
ejpam-5909	224	15	5909	5909	NUM
ejpam-5909	224	16	11	11	NUM
ejpam-5909	224	17	of	of	ADP
ejpam-5909	224	18	17	17	NUM
ejpam-5909	224	19	next	next	ADV
ejpam-5909	225	1	,	,	PUNCT
ejpam-5909	225	2	we	we	PRON
ejpam-5909	225	3	discuss	discuss	VERB
ejpam-5909	225	4	a	a	DET
ejpam-5909	225	5	theorem	theorem	NOUN
ejpam-5909	225	6	that	that	PRON
ejpam-5909	225	7	establishes	establish	VERB
ejpam-5909	225	8	the	the	DET
ejpam-5909	225	9	relationship	relationship	NOUN
ejpam-5909	225	10	between	between	ADP
ejpam-5909	225	11	the	the	DET
ejpam-5909	225	12	general	general	ADJ
ejpam-5909	225	13	definition	definition	NOUN
ejpam-5909	225	14	of	of	ADP
ejpam-5909	225	15	the	the	DET
ejpam-5909	225	16	limit	limit	NOUN
ejpam-5909	225	17	of	of	ADP
ejpam-5909	225	18	an	an	DET
ejpam-5909	225	19	operator	operator	NOUN
ejpam-5909	225	20	and	and	CCONJ
ejpam-5909	225	21	the	the	DET
ejpam-5909	225	22	definition	definition	NOUN
ejpam-5909	225	23	of	of	ADP
ejpam-5909	225	24	the	the	DET
ejpam-5909	225	25	one	one	NUM
ejpam-5909	225	26	-	-	PUNCT
ejpam-5909	225	27	sided	sided	ADJ
ejpam-5909	225	28	limit	limit	NOUN
ejpam-5909	225	29	of	of	ADP
ejpam-5909	225	30	an	an	DET
ejpam-5909	225	31	operator	operator	NOUN
ejpam-5909	225	32	(	(	PUNCT
ejpam-5909	225	33	right	right	ADJ
ejpam-5909	225	34	-	-	PUNCT
ejpam-5909	225	35	hand	hand	NOUN
ejpam-5909	225	36	limit	limit	NOUN
ejpam-5909	225	37	or	or	CCONJ
ejpam-5909	225	38	left	left	ADJ
ejpam-5909	225	39	-	-	PUNCT
ejpam-5909	225	40	hand	hand	NOUN
ejpam-5909	225	41	limit	limit	NOUN
ejpam-5909	225	42	)	)	PUNCT
ejpam-5909	225	43	,	,	PUNCT
ejpam-5909	225	44	as	as	SCONJ
ejpam-5909	225	45	described	describe	VERB
ejpam-5909	225	46	below	below	ADV
ejpam-5909	225	47	.	.	PUNCT
ejpam-5909	226	1	theorem	theorem	NOUN
ejpam-5909	226	2	6	6	NUM
ejpam-5909	226	3	.	.	PUNCT
ejpam-5909	227	1	consider	consider	VERB
ejpam-5909	227	2	f	f	NOUN
ejpam-5909	227	3	:	:	PUNCT
ejpam-5909	227	4	a	a	DET
ejpam-5909	227	5	⊆	⊆	NUM
ejpam-5909	227	6	c[a	c[a	NOUN
ejpam-5909	227	7	,	,	PUNCT
ejpam-5909	227	8	b	b	X
ejpam-5909	227	9	]	]	X
ejpam-5909	227	10	→	→	SYM
ejpam-5909	227	11	c[a	c[a	NUM
ejpam-5909	227	12	,	,	PUNCT
ejpam-5909	227	13	b	b	NOUN
ejpam-5909	227	14	]	]	PUNCT
ejpam-5909	227	15	and	and	CCONJ
ejpam-5909	227	16	let	let	VERB
ejpam-5909	227	17	f0	f0	PROPN
ejpam-5909	227	18	∈	∈	PROPN
ejpam-5909	227	19	a	a	DET
ejpam-5909	227	20	be	be	AUX
ejpam-5909	227	21	a	a	DET
ejpam-5909	227	22	limit	limit	NOUN
ejpam-5909	227	23	point	point	NOUN
ejpam-5909	227	24	of	of	ADP
ejpam-5909	227	25	the	the	DET
ejpam-5909	227	26	set	set	NOUN
ejpam-5909	227	27	a	a	DET
ejpam-5909	227	28	∩	∩	NOUN
ejpam-5909	227	29	{	{	PUNCT
ejpam-5909	227	30	f	f	PROPN
ejpam-5909	227	31	∈	∈	PROPN
ejpam-5909	227	32	c[a	c[a	PROPN
ejpam-5909	227	33	,	,	PUNCT
ejpam-5909	227	34	b	b	X
ejpam-5909	227	35	]	]	X
ejpam-5909	227	36	:	:	PUNCT
ejpam-5909	227	37	f	f	PROPN
ejpam-5909	227	38	≻	≻	PROPN
ejpam-5909	227	39	f0	f0	PROPN
ejpam-5909	227	40	}	}	PUNCT
ejpam-5909	227	41	and	and	CCONJ
ejpam-5909	227	42	the	the	DET
ejpam-5909	227	43	set	set	NOUN
ejpam-5909	227	44	a	a	DET
ejpam-5909	227	45	∩	∩	NOUN
ejpam-5909	227	46	{	{	PUNCT
ejpam-5909	227	47	f	f	PROPN
ejpam-5909	227	48	∈	∈	PROPN
ejpam-5909	227	49	c[a	c[a	PROPN
ejpam-5909	227	50	,	,	PUNCT
ejpam-5909	227	51	b	b	X
ejpam-5909	227	52	]	]	X
ejpam-5909	227	53	:	:	PUNCT
ejpam-5909	227	54	f	f	PROPN
ejpam-5909	227	55	≺	≺	VERB
ejpam-5909	227	56	f0	f0	PROPN
ejpam-5909	227	57	}	}	PUNCT
ejpam-5909	227	58	.	.	PUNCT
ejpam-5909	228	1	we	we	PRON
ejpam-5909	228	2	obtain	obtain	VERB
ejpam-5909	228	3	limf→f0	limf→f0	VERB
ejpam-5909	228	4	f	f	X
ejpam-5909	228	5	(	(	PUNCT
ejpam-5909	228	6	f	f	X
ejpam-5909	228	7	)	)	PUNCT
ejpam-5909	228	8	=	=	SYM
ejpam-5909	229	1	l	l	NOUN
ejpam-5909	229	2	if	if	SCONJ
ejpam-5909	229	3	and	and	CCONJ
ejpam-5909	229	4	only	only	ADV
ejpam-5909	229	5	if	if	SCONJ
ejpam-5909	229	6	lim	lim	PROPN
ejpam-5909	229	7	f→f+	f→f+	VERB
ejpam-5909	229	8	0	0	PROPN
ejpam-5909	230	1	f	f	PROPN
ejpam-5909	230	2	(	(	PUNCT
ejpam-5909	230	3	f	f	X
ejpam-5909	230	4	)	)	PUNCT
ejpam-5909	230	5	=	=	SYM
ejpam-5909	230	6	l	l	NOUN
ejpam-5909	231	1	=	=	SYM
ejpam-5909	231	2	lim	lim	PROPN
ejpam-5909	231	3	f→f−	f→f−	X
ejpam-5909	231	4	0	0	NUM
ejpam-5909	231	5	f	f	X
ejpam-5909	231	6	(	(	PUNCT
ejpam-5909	231	7	f	f	NOUN
ejpam-5909	231	8	)	)	PUNCT
ejpam-5909	231	9	.	.	PUNCT
ejpam-5909	232	1	proof	proof	NOUN
ejpam-5909	232	2	.	.	PUNCT
ejpam-5909	233	1	consider	consider	VERB
ejpam-5909	233	2	f	f	NOUN
ejpam-5909	233	3	:	:	PUNCT
ejpam-5909	233	4	a	a	DET
ejpam-5909	233	5	⊆	⊆	NUM
ejpam-5909	233	6	c[a	c[a	NOUN
ejpam-5909	233	7	,	,	PUNCT
ejpam-5909	233	8	b	b	X
ejpam-5909	233	9	]	]	X
ejpam-5909	233	10	→	→	SYM
ejpam-5909	233	11	c[a	c[a	NUM
ejpam-5909	233	12	,	,	PUNCT
ejpam-5909	233	13	b	b	NOUN
ejpam-5909	233	14	]	]	PUNCT
ejpam-5909	233	15	and	and	CCONJ
ejpam-5909	233	16	let	let	VERB
ejpam-5909	233	17	f0	f0	PROPN
ejpam-5909	233	18	∈	∈	PROPN
ejpam-5909	233	19	a	a	DET
ejpam-5909	233	20	be	be	AUX
ejpam-5909	233	21	a	a	DET
ejpam-5909	233	22	limit	limit	NOUN
ejpam-5909	233	23	point	point	NOUN
ejpam-5909	233	24	of	of	ADP
ejpam-5909	233	25	the	the	DET
ejpam-5909	233	26	set	set	NOUN
ejpam-5909	233	27	a	a	DET
ejpam-5909	233	28	∩	∩	NOUN
ejpam-5909	233	29	{	{	PUNCT
ejpam-5909	233	30	f	f	PROPN
ejpam-5909	233	31	∈	∈	PROPN
ejpam-5909	233	32	c[a	c[a	PROPN
ejpam-5909	233	33	,	,	PUNCT
ejpam-5909	233	34	b	b	X
ejpam-5909	233	35	]	]	X
ejpam-5909	233	36	:	:	PUNCT
ejpam-5909	233	37	f	f	PROPN
ejpam-5909	233	38	≻	≻	PROPN
ejpam-5909	233	39	f0	f0	PROPN
ejpam-5909	233	40	}	}	PUNCT
ejpam-5909	233	41	and	and	CCONJ
ejpam-5909	233	42	the	the	DET
ejpam-5909	233	43	set	set	NOUN
ejpam-5909	233	44	a	a	DET
ejpam-5909	233	45	∩	∩	NOUN
ejpam-5909	233	46	{	{	PUNCT
ejpam-5909	233	47	f	f	PROPN
ejpam-5909	233	48	∈	∈	PROPN
ejpam-5909	233	49	c[a	c[a	PROPN
ejpam-5909	233	50	,	,	PUNCT
ejpam-5909	233	51	b	b	X
ejpam-5909	233	52	]	]	X
ejpam-5909	233	53	:	:	PUNCT
ejpam-5909	233	54	f	f	PROPN
ejpam-5909	233	55	≺	≺	VERB
ejpam-5909	233	56	f0	f0	PROPN
ejpam-5909	233	57	}	}	PUNCT
ejpam-5909	233	58	.	.	PUNCT
ejpam-5909	234	1	(	(	PUNCT
ejpam-5909	234	2	⇒	⇒	PROPN
ejpam-5909	234	3	)	)	PUNCT
ejpam-5909	234	4	suppose	suppose	VERB
ejpam-5909	234	5	limf→f0	limf→f0	X
ejpam-5909	234	6	f	f	X
ejpam-5909	234	7	=	=	SYM
ejpam-5909	234	8	l	l	PROPN
ejpam-5909	234	9	,	,	PUNCT
ejpam-5909	234	10	meaning	mean	VERB
ejpam-5909	234	11	that	that	SCONJ
ejpam-5909	234	12	for	for	ADP
ejpam-5909	234	13	every	every	DET
ejpam-5909	234	14	real	real	ADJ
ejpam-5909	234	15	number	number	NOUN
ejpam-5909	234	16	ε	ε	PROPN
ejpam-5909	234	17	>	>	X
ejpam-5909	234	18	0	0	PROPN
ejpam-5909	234	19	,	,	PUNCT
ejpam-5909	234	20	there	there	PRON
ejpam-5909	234	21	exists	exist	VERB
ejpam-5909	234	22	a	a	DET
ejpam-5909	234	23	real	real	ADJ
ejpam-5909	234	24	number	number	NOUN
ejpam-5909	234	25	δ	δ	NOUN
ejpam-5909	234	26	>	>	X
ejpam-5909	234	27	0	0	NUM
ejpam-5909	234	28	such	such	ADJ
ejpam-5909	234	29	that	that	PRON
ejpam-5909	234	30	for	for	ADP
ejpam-5909	234	31	every	every	DET
ejpam-5909	234	32	f	f	PROPN
ejpam-5909	234	33	∈	∈	PROPN
ejpam-5909	234	34	a	a	PRON
ejpam-5909	234	35	and	and	CCONJ
ejpam-5909	234	36	0	0	NUM
ejpam-5909	234	37	≺	≺	NOUN
ejpam-5909	234	38	|f	|f	NUM
ejpam-5909	234	39	−	−	PROPN
ejpam-5909	234	40	f0|	f0|	PROPN
ejpam-5909	234	41	≺	≺	NOUN
ejpam-5909	234	42	δe	δe	NOUN
ejpam-5909	234	43	,	,	PUNCT
ejpam-5909	234	44	we	we	PRON
ejpam-5909	234	45	have	have	VERB
ejpam-5909	234	46	:	:	PUNCT
ejpam-5909	234	47	|f	|f	PROPN
ejpam-5909	234	48	(	(	PUNCT
ejpam-5909	234	49	f)−	f)−	PROPN
ejpam-5909	234	50	l|	l|	ADJ
ejpam-5909	234	51	≺	≺	NOUN
ejpam-5909	234	52	εe	εe	NOUN
ejpam-5909	234	53	.	.	PUNCT
ejpam-5909	235	1	since	since	SCONJ
ejpam-5909	235	2	a	a	DET
ejpam-5909	235	3	∩	∩	NOUN
ejpam-5909	235	4	{	{	PUNCT
ejpam-5909	235	5	f	f	PROPN
ejpam-5909	235	6	∈	∈	PROPN
ejpam-5909	235	7	c[a	c[a	PROPN
ejpam-5909	235	8	,	,	PUNCT
ejpam-5909	235	9	b	b	X
ejpam-5909	235	10	]	]	X
ejpam-5909	235	11	:	:	PUNCT
ejpam-5909	236	1	f	f	PROPN
ejpam-5909	236	2	≻	≻	PROPN
ejpam-5909	236	3	f0	f0	PROPN
ejpam-5909	236	4	}	}	PUNCT
ejpam-5909	236	5	⊆	⊆	NUM
ejpam-5909	236	6	a	a	PRON
ejpam-5909	236	7	and	and	CCONJ
ejpam-5909	236	8	a	a	DET
ejpam-5909	236	9	∩	∩	NOUN
ejpam-5909	236	10	{	{	PUNCT
ejpam-5909	236	11	f	f	PROPN
ejpam-5909	236	12	∈	∈	PROPN
ejpam-5909	236	13	c[a	c[a	PROPN
ejpam-5909	236	14	,	,	PUNCT
ejpam-5909	236	15	b	b	X
ejpam-5909	236	16	]	]	X
ejpam-5909	236	17	:	:	PUNCT
ejpam-5909	236	18	f	f	PROPN
ejpam-5909	236	19	≺	≺	VERB
ejpam-5909	236	20	f0	f0	PROPN
ejpam-5909	236	21	}	}	PUNCT
ejpam-5909	236	22	⊆	⊆	NUM
ejpam-5909	236	23	a	a	PRON
ejpam-5909	236	24	,	,	PUNCT
ejpam-5909	236	25	it	it	PRON
ejpam-5909	236	26	follows	follow	VERB
ejpam-5909	236	27	that	that	SCONJ
ejpam-5909	236	28	for	for	ADP
ejpam-5909	236	29	every	every	DET
ejpam-5909	236	30	real	real	ADJ
ejpam-5909	236	31	number	number	NOUN
ejpam-5909	236	32	ε	ε	PROPN
ejpam-5909	236	33	>	>	X
ejpam-5909	236	34	0	0	PROPN
ejpam-5909	236	35	,	,	PUNCT
ejpam-5909	236	36	there	there	PRON
ejpam-5909	236	37	exists	exist	VERB
ejpam-5909	236	38	a	a	DET
ejpam-5909	236	39	real	real	ADJ
ejpam-5909	236	40	number	number	NOUN
ejpam-5909	236	41	δ	δ	NOUN
ejpam-5909	236	42	>	>	X
ejpam-5909	236	43	0	0	NUM
ejpam-5909	236	44	such	such	ADJ
ejpam-5909	236	45	that	that	PRON
ejpam-5909	236	46	for	for	ADP
ejpam-5909	236	47	every	every	DET
ejpam-5909	236	48	f	f	PROPN
ejpam-5909	236	49	∈	∈	PROPN
ejpam-5909	236	50	a	a	DET
ejpam-5909	236	51	∩	∩	NOUN
ejpam-5909	236	52	{	{	PUNCT
ejpam-5909	236	53	f	f	PROPN
ejpam-5909	236	54	∈	∈	PROPN
ejpam-5909	236	55	c[a	c[a	PROPN
ejpam-5909	236	56	,	,	PUNCT
ejpam-5909	236	57	b	b	X
ejpam-5909	236	58	]	]	X
ejpam-5909	236	59	:	:	PUNCT
ejpam-5909	236	60	f	f	PROPN
ejpam-5909	236	61	≻	≻	PROPN
ejpam-5909	236	62	f0	f0	PROPN
ejpam-5909	236	63	}	}	PUNCT
ejpam-5909	236	64	and	and	CCONJ
ejpam-5909	236	65	0	0	NUM
ejpam-5909	236	66	≺	≺	NOUN
ejpam-5909	236	67	|f	|f	NUM
ejpam-5909	236	68	−	−	PROPN
ejpam-5909	236	69	f0|	f0|	PROPN
ejpam-5909	236	70	≺	≺	NOUN
ejpam-5909	236	71	δe	δe	NOUN
ejpam-5909	236	72	,	,	PUNCT
ejpam-5909	236	73	we	we	PRON
ejpam-5909	236	74	obtain	obtain	VERB
ejpam-5909	236	75	:	:	PUNCT
ejpam-5909	236	76	|f	|f	PROPN
ejpam-5909	237	1	(	(	PUNCT
ejpam-5909	237	2	f)−	f)−	PROPN
ejpam-5909	237	3	l|	l|	ADJ
ejpam-5909	237	4	≺	≺	NOUN
ejpam-5909	237	5	εe	εe	NOUN
ejpam-5909	237	6	.	.	PROPN
ejpam-5909	237	7	similarly	similarly	ADV
ejpam-5909	237	8	,	,	PUNCT
ejpam-5909	237	9	for	for	SCONJ
ejpam-5909	237	10	every	every	DET
ejpam-5909	237	11	f	f	PROPN
ejpam-5909	237	12	∈	∈	PROPN
ejpam-5909	237	13	a	a	DET
ejpam-5909	237	14	∩	∩	NOUN
ejpam-5909	237	15	{	{	PUNCT
ejpam-5909	237	16	f	f	PROPN
ejpam-5909	237	17	∈	∈	PROPN
ejpam-5909	237	18	c[a	c[a	PROPN
ejpam-5909	237	19	,	,	PUNCT
ejpam-5909	237	20	b	b	X
ejpam-5909	237	21	]	]	X
ejpam-5909	237	22	:	:	PUNCT
ejpam-5909	237	23	f	f	PROPN
ejpam-5909	237	24	≺	≺	NOUN
ejpam-5909	237	25	f0	f0	PROPN
ejpam-5909	237	26	}	}	PUNCT
ejpam-5909	237	27	and	and	CCONJ
ejpam-5909	237	28	0	0	NUM
ejpam-5909	237	29	≺	≺	NOUN
ejpam-5909	237	30	|f	|f	NUM
ejpam-5909	237	31	−	−	PROPN
ejpam-5909	237	32	f0|	f0|	PROPN
ejpam-5909	237	33	≺	≺	NOUN
ejpam-5909	237	34	δe	δe	NOUN
ejpam-5909	237	35	,	,	PUNCT
ejpam-5909	237	36	we	we	PRON
ejpam-5909	237	37	have	have	VERB
ejpam-5909	237	38	:	:	PUNCT
ejpam-5909	237	39	|f	|f	PROPN
ejpam-5909	237	40	(	(	PUNCT
ejpam-5909	237	41	f)−	f)−	PROPN
ejpam-5909	237	42	l|	l|	ADJ
ejpam-5909	237	43	≺	≺	NOUN
ejpam-5909	237	44	εe	εe	NOUN
ejpam-5909	237	45	.	.	PUNCT
ejpam-5909	238	1	thus	thus	ADV
ejpam-5909	238	2	,	,	PUNCT
ejpam-5909	238	3	we	we	PRON
ejpam-5909	238	4	conclude	conclude	VERB
ejpam-5909	238	5	:	:	PUNCT
ejpam-5909	238	6	lim	lim	PROPN
ejpam-5909	238	7	f→f+	f→f+	VERB
ejpam-5909	238	8	0	0	NUM
ejpam-5909	238	9	f	f	PROPN
ejpam-5909	238	10	(	(	PUNCT
ejpam-5909	238	11	f	f	X
ejpam-5909	238	12	)	)	PUNCT
ejpam-5909	238	13	=	=	SYM
ejpam-5909	238	14	l	l	NOUN
ejpam-5909	238	15	and	and	CCONJ
ejpam-5909	238	16	lim	lim	PROPN
ejpam-5909	239	1	f→f−	f→f−	PUNCT
ejpam-5909	239	2	0	0	NUM
ejpam-5909	239	3	f	f	X
ejpam-5909	239	4	(	(	PUNCT
ejpam-5909	239	5	f	f	X
ejpam-5909	239	6	)	)	PUNCT
ejpam-5909	239	7	=	=	SYM
ejpam-5909	239	8	l.	l.	PROPN
ejpam-5909	239	9	(	(	PUNCT
ejpam-5909	239	10	⇐	⇐	PROPN
ejpam-5909	239	11	)	)	PUNCT
ejpam-5909	239	12	suppose	suppose	VERB
ejpam-5909	239	13	limf→f+	limf→f+	PRON
ejpam-5909	239	14	0	0	NUM
ejpam-5909	239	15	f	f	X
ejpam-5909	239	16	(	(	PUNCT
ejpam-5909	239	17	f	f	X
ejpam-5909	239	18	)	)	PUNCT
ejpam-5909	239	19	=	=	SYM
ejpam-5909	239	20	l	l	NOUN
ejpam-5909	239	21	,	,	PUNCT
ejpam-5909	239	22	meaning	mean	VERB
ejpam-5909	239	23	that	that	SCONJ
ejpam-5909	239	24	for	for	ADP
ejpam-5909	239	25	every	every	DET
ejpam-5909	239	26	real	real	ADJ
ejpam-5909	239	27	number	number	NOUN
ejpam-5909	239	28	ε	ε	PROPN
ejpam-5909	239	29	>	>	X
ejpam-5909	239	30	0	0	PROPN
ejpam-5909	239	31	,	,	PUNCT
ejpam-5909	239	32	there	there	PRON
ejpam-5909	239	33	exists	exist	VERB
ejpam-5909	239	34	a	a	DET
ejpam-5909	239	35	real	real	ADJ
ejpam-5909	239	36	number	number	NOUN
ejpam-5909	239	37	δ1	δ1	NOUN
ejpam-5909	239	38	>	>	X
ejpam-5909	239	39	0	0	NUM
ejpam-5909	239	40	such	such	ADJ
ejpam-5909	239	41	that	that	PRON
ejpam-5909	239	42	for	for	ADP
ejpam-5909	239	43	every	every	DET
ejpam-5909	239	44	f	f	PROPN
ejpam-5909	239	45	∈	∈	PROPN
ejpam-5909	239	46	a	a	DET
ejpam-5909	239	47	∩	∩	NOUN
ejpam-5909	239	48	{	{	PUNCT
ejpam-5909	239	49	f	f	PROPN
ejpam-5909	239	50	∈	∈	PROPN
ejpam-5909	239	51	c[a	c[a	PROPN
ejpam-5909	239	52	,	,	PUNCT
ejpam-5909	239	53	b	b	X
ejpam-5909	239	54	]	]	X
ejpam-5909	239	55	:	:	PUNCT
ejpam-5909	239	56	f	f	PROPN
ejpam-5909	239	57	≻	≻	PROPN
ejpam-5909	239	58	f0	f0	PROPN
ejpam-5909	239	59	}	}	PUNCT
ejpam-5909	239	60	and	and	CCONJ
ejpam-5909	239	61	0	0	NUM
ejpam-5909	239	62	≺	≺	NOUN
ejpam-5909	239	63	|f	|f	NUM
ejpam-5909	239	64	−	−	PROPN
ejpam-5909	239	65	f0|	f0|	PROPN
ejpam-5909	239	66	≺	≺	NOUN
ejpam-5909	239	67	δ1e	δ1e	VERB
ejpam-5909	239	68	,	,	PUNCT
ejpam-5909	239	69	we	we	PRON
ejpam-5909	239	70	obtain	obtain	VERB
ejpam-5909	239	71	:	:	PUNCT
ejpam-5909	239	72	|f	|f	PROPN
ejpam-5909	239	73	(	(	PUNCT
ejpam-5909	239	74	f)−	f)−	PROPN
ejpam-5909	239	75	l|	l|	ADJ
ejpam-5909	239	76	≺	≺	NOUN
ejpam-5909	239	77	εe	εe	NOUN
ejpam-5909	239	78	.	.	PROPN
ejpam-5909	239	79	similarly	similarly	ADV
ejpam-5909	239	80	,	,	PUNCT
ejpam-5909	239	81	since	since	SCONJ
ejpam-5909	239	82	limf→f−	limf→f−	PROPN
ejpam-5909	239	83	0	0	NUM
ejpam-5909	239	84	f	f	PROPN
ejpam-5909	239	85	(	(	PUNCT
ejpam-5909	239	86	f	f	X
ejpam-5909	239	87	)	)	PUNCT
ejpam-5909	239	88	=	=	SYM
ejpam-5909	240	1	l	l	NOUN
ejpam-5909	240	2	,	,	PUNCT
ejpam-5909	240	3	for	for	ADP
ejpam-5909	240	4	every	every	DET
ejpam-5909	240	5	real	real	ADJ
ejpam-5909	240	6	number	number	NOUN
ejpam-5909	240	7	ε	ε	PROPN
ejpam-5909	240	8	>	>	X
ejpam-5909	240	9	0	0	PROPN
ejpam-5909	240	10	,	,	PUNCT
ejpam-5909	240	11	there	there	PRON
ejpam-5909	240	12	exists	exist	VERB
ejpam-5909	240	13	a	a	DET
ejpam-5909	240	14	real	real	ADJ
ejpam-5909	240	15	number	number	NOUN
ejpam-5909	240	16	δ2	δ2	VERB
ejpam-5909	240	17	>	>	X
ejpam-5909	240	18	0	0	NUM
ejpam-5909	240	19	such	such	ADJ
ejpam-5909	240	20	that	that	PRON
ejpam-5909	240	21	for	for	ADP
ejpam-5909	240	22	every	every	DET
ejpam-5909	240	23	f	f	PROPN
ejpam-5909	240	24	∈	∈	PROPN
ejpam-5909	240	25	a∩{f	a∩{f	PROPN
ejpam-5909	240	26	∈	∈	PROPN
ejpam-5909	240	27	c[a	c[a	PROPN
ejpam-5909	240	28	,	,	PUNCT
ejpam-5909	240	29	b	b	X
ejpam-5909	240	30	]	]	X
ejpam-5909	240	31	:	:	PUNCT
ejpam-5909	240	32	f	f	PROPN
ejpam-5909	240	33	≺	≺	NOUN
ejpam-5909	240	34	f0	f0	PROPN
ejpam-5909	240	35	}	}	PUNCT
ejpam-5909	240	36	and	and	CCONJ
ejpam-5909	240	37	0	0	NUM
ejpam-5909	240	38	≺	≺	NOUN
ejpam-5909	240	39	|f	|f	PROPN
ejpam-5909	240	40	−f0|	−f0|	PROPN
ejpam-5909	240	41	≺	≺	NOUN
ejpam-5909	240	42	δ2e	δ2e	PROPN
ejpam-5909	240	43	,	,	PUNCT
ejpam-5909	240	44	we	we	PRON
ejpam-5909	240	45	obtain	obtain	VERB
ejpam-5909	240	46	:	:	PUNCT
ejpam-5909	240	47	|f	|f	PROPN
ejpam-5909	240	48	(	(	PUNCT
ejpam-5909	240	49	f)−	f)−	PROPN
ejpam-5909	240	50	l|	l|	ADJ
ejpam-5909	240	51	≺	≺	NOUN
ejpam-5909	240	52	εe	εe	NOUN
ejpam-5909	240	53	.	.	PUNCT
ejpam-5909	240	54	choosing	choose	VERB
ejpam-5909	240	55	δ	δ	PROPN
ejpam-5909	240	56	=	=	PROPN
ejpam-5909	240	57	min{δ1	min{δ1	NOUN
ejpam-5909	240	58	,	,	PUNCT
ejpam-5909	240	59	δ2	δ2	ADV
ejpam-5909	240	60	}	}	PUNCT
ejpam-5909	240	61	,	,	PUNCT
ejpam-5909	240	62	we	we	PRON
ejpam-5909	240	63	conclude	conclude	VERB
ejpam-5909	240	64	that	that	SCONJ
ejpam-5909	240	65	for	for	ADP
ejpam-5909	240	66	every	every	DET
ejpam-5909	240	67	real	real	ADJ
ejpam-5909	240	68	number	number	NOUN
ejpam-5909	240	69	ε	ε	PROPN
ejpam-5909	240	70	>	>	X
ejpam-5909	240	71	0	0	PROPN
ejpam-5909	240	72	,	,	PUNCT
ejpam-5909	240	73	there	there	PRON
ejpam-5909	240	74	exists	exist	VERB
ejpam-5909	240	75	a	a	DET
ejpam-5909	240	76	real	real	ADJ
ejpam-5909	240	77	number	number	NOUN
ejpam-5909	240	78	δ	δ	NOUN
ejpam-5909	240	79	>	>	X
ejpam-5909	240	80	0	0	NUM
ejpam-5909	240	81	such	such	ADJ
ejpam-5909	240	82	that	that	PRON
ejpam-5909	240	83	for	for	ADP
ejpam-5909	240	84	every	every	DET
ejpam-5909	240	85	f	f	PROPN
ejpam-5909	240	86	∈	∈	PROPN
ejpam-5909	240	87	a	a	PRON
ejpam-5909	240	88	and	and	CCONJ
ejpam-5909	240	89	0	0	NUM
ejpam-5909	240	90	≺	≺	NOUN
ejpam-5909	240	91	|f	|f	NUM
ejpam-5909	240	92	−	−	PROPN
ejpam-5909	240	93	f0|	f0|	PROPN
ejpam-5909	240	94	≺	≺	NOUN
ejpam-5909	240	95	δe	δe	NOUN
ejpam-5909	240	96	,	,	PUNCT
ejpam-5909	240	97	the	the	DET
ejpam-5909	240	98	following	follow	VERB
ejpam-5909	240	99	holds	hold	VERB
ejpam-5909	240	100	:	:	PUNCT
ejpam-5909	240	101	|f	|f	PROPN
ejpam-5909	240	102	(	(	PUNCT
ejpam-5909	240	103	f)−	f)−	PROPN
ejpam-5909	240	104	l|	l|	VERB
ejpam-5909	240	105	<	<	X
ejpam-5909	240	106	εe	εe	PROPN
ejpam-5909	240	107	.	.	PROPN
ejpam-5909	240	108	m.	m.	PROPN
ejpam-5909	240	109	alifuddin	alifuddin	VERB
ejpam-5909	241	1	et	et	PROPN
ejpam-5909	241	2	al	al	PROPN
ejpam-5909	241	3	.	.	PUNCT
ejpam-5909	241	4	/	/	SYM
ejpam-5909	241	5	eur	eur	PROPN
ejpam-5909	241	6	.	.	PUNCT
ejpam-5909	242	1	j.	j.	PROPN
ejpam-5909	242	2	pure	pure	PROPN
ejpam-5909	242	3	appl	appl	PROPN
ejpam-5909	242	4	.	.	PROPN
ejpam-5909	242	5	math	math	PROPN
ejpam-5909	242	6	,	,	PUNCT
ejpam-5909	242	7	18	18	NUM
ejpam-5909	242	8	(	(	PUNCT
ejpam-5909	242	9	2	2	NUM
ejpam-5909	242	10	)	)	PUNCT
ejpam-5909	242	11	(	(	PUNCT
ejpam-5909	242	12	2025	2025	NUM
ejpam-5909	242	13	)	)	PUNCT
ejpam-5909	242	14	,	,	PUNCT
ejpam-5909	242	15	5909	5909	NUM
ejpam-5909	242	16	12	12	NUM
ejpam-5909	242	17	of	of	ADP
ejpam-5909	242	18	17	17	NUM
ejpam-5909	242	19	thus	thus	ADV
ejpam-5909	242	20	,	,	PUNCT
ejpam-5909	242	21	lim	lim	PROPN
ejpam-5909	242	22	f→f0	f→f0	PROPN
ejpam-5909	243	1	f	f	X
ejpam-5909	243	2	(	(	PUNCT
ejpam-5909	243	3	f	f	X
ejpam-5909	243	4	)	)	PUNCT
ejpam-5909	243	5	=	=	VERB
ejpam-5909	244	1	l.	l.	PROPN
ejpam-5909	244	2	next	next	ADV
ejpam-5909	244	3	,	,	PUNCT
ejpam-5909	244	4	we	we	PRON
ejpam-5909	244	5	define	define	VERB
ejpam-5909	244	6	the	the	DET
ejpam-5909	244	7	concept	concept	NOUN
ejpam-5909	244	8	of	of	ADP
ejpam-5909	244	9	operator	operator	NOUN
ejpam-5909	244	10	continuity	continuity	NOUN
ejpam-5909	244	11	at	at	ADP
ejpam-5909	244	12	f0	f0	PROPN
ejpam-5909	244	13	∈	∈	PROPN
ejpam-5909	244	14	a	a	DET
ejpam-5909	244	15	⊆	⊆	NUM
ejpam-5909	244	16	c[a	c[a	NOUN
ejpam-5909	244	17	,	,	PUNCT
ejpam-5909	244	18	b	b	NOUN
ejpam-5909	244	19	]	]	PUNCT
ejpam-5909	244	20	or	or	CCONJ
ejpam-5909	244	21	over	over	ADP
ejpam-5909	244	22	b	b	NOUN
ejpam-5909	244	23	⊆	⊆	NUM
ejpam-5909	244	24	c[a	c[a	NUM
ejpam-5909	244	25	,	,	PUNCT
ejpam-5909	244	26	b	b	NOUN
ejpam-5909	244	27	]	]	X
ejpam-5909	244	28	,	,	PUNCT
ejpam-5909	244	29	which	which	PRON
ejpam-5909	244	30	is	be	AUX
ejpam-5909	244	31	frequently	frequently	ADV
ejpam-5909	244	32	used	use	VERB
ejpam-5909	244	33	in	in	ADP
ejpam-5909	244	34	subsequent	subsequent	ADJ
ejpam-5909	244	35	subsections	subsection	NOUN
ejpam-5909	244	36	.	.	PUNCT
ejpam-5909	245	1	definition	definition	NOUN
ejpam-5909	245	2	11	11	NUM
ejpam-5909	245	3	.	.	PUNCT
ejpam-5909	246	1	given	give	VERB
ejpam-5909	246	2	a	a	DET
ejpam-5909	246	3	⊆	⊆	NUM
ejpam-5909	246	4	c[a	c[a	NUM
ejpam-5909	246	5	,	,	PUNCT
ejpam-5909	246	6	b	b	NOUN
ejpam-5909	246	7	]	]	PUNCT
ejpam-5909	246	8	and	and	CCONJ
ejpam-5909	246	9	an	an	DET
ejpam-5909	246	10	operator	operator	NOUN
ejpam-5909	246	11	r	r	NOUN
ejpam-5909	246	12	:	:	PUNCT
ejpam-5909	246	13	a	a	DET
ejpam-5909	246	14	→	→	SYM
ejpam-5909	246	15	c[a	c[a	NUM
ejpam-5909	246	16	,	,	PUNCT
ejpam-5909	246	17	b	b	NOUN
ejpam-5909	246	18	]	]	X
ejpam-5909	246	19	,	,	PUNCT
ejpam-5909	246	20	the	the	DET
ejpam-5909	246	21	operator	operator	NOUN
ejpam-5909	246	22	r	r	NOUN
ejpam-5909	246	23	is	be	AUX
ejpam-5909	246	24	said	say	VERB
ejpam-5909	246	25	to	to	PART
ejpam-5909	246	26	be	be	AUX
ejpam-5909	246	27	continuous	continuous	ADJ
ejpam-5909	246	28	at	at	ADP
ejpam-5909	246	29	f0	f0	PROPN
ejpam-5909	246	30	if	if	SCONJ
ejpam-5909	246	31	,	,	PUNCT
ejpam-5909	246	32	for	for	ADP
ejpam-5909	246	33	every	every	DET
ejpam-5909	246	34	real	real	ADJ
ejpam-5909	246	35	number	number	NOUN
ejpam-5909	246	36	ε	ε	PROPN
ejpam-5909	246	37	>	>	X
ejpam-5909	246	38	0	0	PROPN
ejpam-5909	246	39	,	,	PUNCT
ejpam-5909	246	40	there	there	PRON
ejpam-5909	246	41	exists	exist	VERB
ejpam-5909	246	42	δ	δ	PROPN
ejpam-5909	246	43	>	>	X
ejpam-5909	246	44	0	0	NUM
ejpam-5909	246	45	such	such	ADJ
ejpam-5909	246	46	that	that	PRON
ejpam-5909	246	47	for	for	ADP
ejpam-5909	246	48	every	every	DET
ejpam-5909	246	49	f	f	PROPN
ejpam-5909	246	50	∈	∈	PROPN
ejpam-5909	246	51	a	a	PRON
ejpam-5909	246	52	with	with	ADP
ejpam-5909	246	53	|f	|f	ADP
ejpam-5909	246	54	−	−	PROPN
ejpam-5909	247	1	f0|	f0|	PROPN
ejpam-5909	247	2	≺	≺	VERB
ejpam-5909	247	3	δe	δe	NOUN
ejpam-5909	247	4	,	,	PUNCT
ejpam-5909	247	5	the	the	DET
ejpam-5909	247	6	following	follow	VERB
ejpam-5909	247	7	holds	hold	VERB
ejpam-5909	247	8	:	:	PUNCT
ejpam-5909	247	9	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	247	10	≺	≺	NOUN
ejpam-5909	247	11	εe	εe	NOUN
ejpam-5909	247	12	.	.	PUNCT
ejpam-5909	248	1	furthermore	furthermore	ADV
ejpam-5909	248	2	,	,	PUNCT
ejpam-5909	248	3	the	the	DET
ejpam-5909	248	4	operator	operator	NOUN
ejpam-5909	248	5	r	r	NOUN
ejpam-5909	248	6	is	be	AUX
ejpam-5909	248	7	said	say	VERB
ejpam-5909	248	8	to	to	PART
ejpam-5909	248	9	be	be	AUX
ejpam-5909	248	10	continuous	continuous	ADJ
ejpam-5909	248	11	on	on	ADP
ejpam-5909	248	12	the	the	DET
ejpam-5909	248	13	set	set	PROPN
ejpam-5909	248	14	b	b	NOUN
ejpam-5909	248	15	if	if	SCONJ
ejpam-5909	248	16	r	r	NOUN
ejpam-5909	248	17	is	be	AUX
ejpam-5909	248	18	continuous	continuous	ADJ
ejpam-5909	248	19	at	at	ADP
ejpam-5909	248	20	every	every	DET
ejpam-5909	248	21	f	f	PROPN
ejpam-5909	248	22	∈	∈	PROPN
ejpam-5909	248	23	b.	b.	PROPN
ejpam-5909	248	24	3.2	3.2	NUM
ejpam-5909	248	25	.	.	PUNCT
ejpam-5909	249	1	stieltjes	stieltjes	PROPN
ejpam-5909	249	2	limit	limit	VERB
ejpam-5909	249	3	on	on	ADP
ejpam-5909	249	4	c[a	c[a	NUM
ejpam-5909	249	5	,	,	PUNCT
ejpam-5909	249	6	b	b	X
ejpam-5909	249	7	]	]	PUNCT
ejpam-5909	249	8	before	before	ADP
ejpam-5909	249	9	defining	define	VERB
ejpam-5909	249	10	the	the	DET
ejpam-5909	249	11	stieltjes	stieltjes	NOUN
ejpam-5909	249	12	limit	limit	VERB
ejpam-5909	249	13	on	on	ADP
ejpam-5909	249	14	c[a	c[a	NUM
ejpam-5909	249	15	,	,	PUNCT
ejpam-5909	249	16	b	b	NOUN
ejpam-5909	249	17	]	]	X
ejpam-5909	249	18	,	,	PUNCT
ejpam-5909	249	19	it	it	PRON
ejpam-5909	249	20	is	be	AUX
ejpam-5909	249	21	important	important	ADJ
ejpam-5909	249	22	to	to	PART
ejpam-5909	249	23	first	first	ADV
ejpam-5909	249	24	establish	establish	VERB
ejpam-5909	249	25	the	the	DET
ejpam-5909	249	26	definition	definition	NOUN
ejpam-5909	249	27	of	of	ADP
ejpam-5909	249	28	increasing	increase	VERB
ejpam-5909	249	29	,	,	PUNCT
ejpam-5909	249	30	strictly	strictly	ADV
ejpam-5909	249	31	increasing	increase	VERB
ejpam-5909	249	32	,	,	PUNCT
ejpam-5909	249	33	decreasing	decrease	VERB
ejpam-5909	249	34	,	,	PUNCT
ejpam-5909	249	35	and	and	CCONJ
ejpam-5909	249	36	strictly	strictly	ADV
ejpam-5909	249	37	decreasing	decrease	VERB
ejpam-5909	249	38	operators	operator	NOUN
ejpam-5909	249	39	.	.	PUNCT
ejpam-5909	250	1	these	these	DET
ejpam-5909	250	2	fundamental	fundamental	ADJ
ejpam-5909	250	3	concepts	concept	NOUN
ejpam-5909	250	4	serve	serve	VERB
ejpam-5909	250	5	as	as	ADP
ejpam-5909	250	6	a	a	DET
ejpam-5909	250	7	crucial	crucial	ADJ
ejpam-5909	250	8	foundation	foundation	NOUN
ejpam-5909	250	9	for	for	ADP
ejpam-5909	250	10	understanding	understand	VERB
ejpam-5909	250	11	the	the	DET
ejpam-5909	250	12	definition	definition	NOUN
ejpam-5909	250	13	and	and	CCONJ
ejpam-5909	250	14	properties	property	NOUN
ejpam-5909	250	15	of	of	ADP
ejpam-5909	250	16	the	the	DET
ejpam-5909	250	17	stieltjes	stieltjes	NOUN
ejpam-5909	250	18	limit	limit	NOUN
ejpam-5909	250	19	on	on	ADP
ejpam-5909	250	20	c[a	c[a	NUM
ejpam-5909	250	21	,	,	PUNCT
ejpam-5909	250	22	b	b	NOUN
ejpam-5909	250	23	]	]	X
ejpam-5909	250	24	.	.	PUNCT
ejpam-5909	251	1	the	the	DET
ejpam-5909	251	2	following	follow	VERB
ejpam-5909	251	3	definitions	definition	NOUN
ejpam-5909	251	4	describe	describe	VERB
ejpam-5909	251	5	increasing	increase	VERB
ejpam-5909	251	6	,	,	PUNCT
ejpam-5909	251	7	strictly	strictly	ADV
ejpam-5909	251	8	increasing	increase	VERB
ejpam-5909	251	9	,	,	PUNCT
ejpam-5909	251	10	decreasing	decrease	VERB
ejpam-5909	251	11	,	,	PUNCT
ejpam-5909	251	12	and	and	CCONJ
ejpam-5909	251	13	strictly	strictly	ADV
ejpam-5909	251	14	decreasing	decrease	VERB
ejpam-5909	251	15	operators	operator	NOUN
ejpam-5909	251	16	:	:	PUNCT
ejpam-5909	251	17	definition	definition	NOUN
ejpam-5909	251	18	12	12	NUM
ejpam-5909	251	19	.	.	PUNCT
ejpam-5909	252	1	(	(	PUNCT
ejpam-5909	252	2	i	i	NOUN
ejpam-5909	252	3	)	)	PUNCT
ejpam-5909	252	4	an	an	DET
ejpam-5909	252	5	operator	operator	NOUN
ejpam-5909	252	6	r	r	NOUN
ejpam-5909	252	7	is	be	AUX
ejpam-5909	252	8	said	say	VERB
ejpam-5909	252	9	to	to	PART
ejpam-5909	252	10	be	be	AUX
ejpam-5909	252	11	increasing	increase	VERB
ejpam-5909	252	12	on	on	ADP
ejpam-5909	252	13	a	a	DET
ejpam-5909	252	14	if	if	NOUN
ejpam-5909	252	15	for	for	ADP
ejpam-5909	252	16	every	every	DET
ejpam-5909	252	17	t	t	PROPN
ejpam-5909	252	18	,	,	PUNCT
ejpam-5909	252	19	v	v	ADP
ejpam-5909	252	20	∈	∈	PRON
ejpam-5909	252	21	a	a	PRON
ejpam-5909	252	22	with	with	ADP
ejpam-5909	252	23	t	t	NOUN
ejpam-5909	252	24	≺	≺	NOUN
ejpam-5909	252	25	v	v	NOUN
ejpam-5909	252	26	,	,	PUNCT
ejpam-5909	252	27	then	then	ADV
ejpam-5909	252	28	r(t	r(t	NOUN
ejpam-5909	252	29	)	)	PUNCT
ejpam-5909	252	30	⪯	⪯	PROPN
ejpam-5909	252	31	r(v	r(v	PROPN
ejpam-5909	252	32	)	)	PUNCT
ejpam-5909	252	33	.	.	PUNCT
ejpam-5909	253	1	(	(	PUNCT
ejpam-5909	253	2	ii	ii	NOUN
ejpam-5909	253	3	)	)	PUNCT
ejpam-5909	253	4	an	an	DET
ejpam-5909	253	5	operator	operator	NOUN
ejpam-5909	253	6	r	r	NOUN
ejpam-5909	253	7	is	be	AUX
ejpam-5909	253	8	said	say	VERB
ejpam-5909	253	9	to	to	PART
ejpam-5909	253	10	be	be	AUX
ejpam-5909	253	11	strictly	strictly	ADV
ejpam-5909	253	12	increasing	increase	VERB
ejpam-5909	253	13	on	on	ADP
ejpam-5909	253	14	a	a	DET
ejpam-5909	253	15	if	if	NOUN
ejpam-5909	253	16	for	for	ADP
ejpam-5909	253	17	every	every	DET
ejpam-5909	253	18	t	t	PROPN
ejpam-5909	253	19	,	,	PUNCT
ejpam-5909	253	20	v	v	ADP
ejpam-5909	253	21	∈	∈	PRON
ejpam-5909	253	22	a	a	PRON
ejpam-5909	253	23	with	with	ADP
ejpam-5909	253	24	t	t	NOUN
ejpam-5909	253	25	≺	≺	NOUN
ejpam-5909	253	26	v	v	NOUN
ejpam-5909	253	27	,	,	PUNCT
ejpam-5909	253	28	then	then	ADV
ejpam-5909	253	29	r(t	r(t	NOUN
ejpam-5909	253	30	)	)	PUNCT
ejpam-5909	253	31	≺	≺	VERB
ejpam-5909	253	32	r(v	r(v	PROPN
ejpam-5909	253	33	)	)	PUNCT
ejpam-5909	253	34	.	.	PUNCT
ejpam-5909	254	1	(	(	PUNCT
ejpam-5909	254	2	iii	iii	X
ejpam-5909	254	3	)	)	PUNCT
ejpam-5909	254	4	an	an	DET
ejpam-5909	254	5	operator	operator	NOUN
ejpam-5909	254	6	r	r	NOUN
ejpam-5909	254	7	is	be	AUX
ejpam-5909	254	8	said	say	VERB
ejpam-5909	254	9	to	to	PART
ejpam-5909	254	10	be	be	AUX
ejpam-5909	254	11	decreasing	decrease	VERB
ejpam-5909	254	12	on	on	ADP
ejpam-5909	254	13	a	a	DET
ejpam-5909	254	14	if	if	NOUN
ejpam-5909	254	15	for	for	ADP
ejpam-5909	254	16	every	every	DET
ejpam-5909	254	17	t	t	PROPN
ejpam-5909	254	18	,	,	PUNCT
ejpam-5909	254	19	v	v	ADP
ejpam-5909	254	20	∈	∈	PRON
ejpam-5909	254	21	a	a	PRON
ejpam-5909	254	22	with	with	ADP
ejpam-5909	254	23	t	t	NOUN
ejpam-5909	254	24	≺	≺	NOUN
ejpam-5909	254	25	v	v	NOUN
ejpam-5909	254	26	,	,	PUNCT
ejpam-5909	254	27	then	then	ADV
ejpam-5909	254	28	r(t	r(t	NOUN
ejpam-5909	254	29	)	)	PUNCT
ejpam-5909	254	30	⪰	⪰	VERB
ejpam-5909	254	31	r(v	r(v	PROPN
ejpam-5909	254	32	)	)	PUNCT
ejpam-5909	254	33	.	.	PUNCT
ejpam-5909	255	1	(	(	PUNCT
ejpam-5909	255	2	iv	iv	X
ejpam-5909	255	3	)	)	PUNCT
ejpam-5909	255	4	an	an	DET
ejpam-5909	255	5	operator	operator	NOUN
ejpam-5909	255	6	r	r	NOUN
ejpam-5909	255	7	is	be	AUX
ejpam-5909	255	8	said	say	VERB
ejpam-5909	255	9	to	to	PART
ejpam-5909	255	10	be	be	AUX
ejpam-5909	255	11	strictly	strictly	ADV
ejpam-5909	255	12	decreasing	decrease	VERB
ejpam-5909	255	13	on	on	ADP
ejpam-5909	255	14	a	a	DET
ejpam-5909	255	15	if	if	NOUN
ejpam-5909	255	16	for	for	ADP
ejpam-5909	255	17	every	every	DET
ejpam-5909	255	18	t	t	PROPN
ejpam-5909	255	19	,	,	PUNCT
ejpam-5909	255	20	v	v	ADP
ejpam-5909	255	21	∈	∈	PRON
ejpam-5909	255	22	a	a	PRON
ejpam-5909	255	23	with	with	ADP
ejpam-5909	255	24	t	t	NOUN
ejpam-5909	255	25	≺	≺	NOUN
ejpam-5909	255	26	v	v	NOUN
ejpam-5909	255	27	,	,	PUNCT
ejpam-5909	255	28	then	then	ADV
ejpam-5909	255	29	r(t	r(t	NOUN
ejpam-5909	255	30	)	)	PUNCT
ejpam-5909	255	31	≻	≻	PART
ejpam-5909	255	32	r(v	r(v	PROPN
ejpam-5909	255	33	)	)	PUNCT
ejpam-5909	255	34	.	.	PUNCT
ejpam-5909	256	1	next	next	ADV
ejpam-5909	256	2	,	,	PUNCT
ejpam-5909	256	3	we	we	PRON
ejpam-5909	256	4	define	define	VERB
ejpam-5909	256	5	and	and	CCONJ
ejpam-5909	256	6	discuss	discuss	VERB
ejpam-5909	256	7	the	the	DET
ejpam-5909	256	8	stieltjes	stieltjes	PROPN
ejpam-5909	256	9	limit	limit	NOUN
ejpam-5909	256	10	theorem	theorem	NOUN
ejpam-5909	256	11	for	for	ADP
ejpam-5909	256	12	an	an	DET
ejpam-5909	256	13	operator	operator	NOUN
ejpam-5909	256	14	r	r	NOUN
ejpam-5909	256	15	in	in	ADP
ejpam-5909	256	16	the	the	DET
ejpam-5909	256	17	space	space	NOUN
ejpam-5909	256	18	of	of	ADP
ejpam-5909	256	19	continuous	continuous	ADJ
ejpam-5909	256	20	functions	function	NOUN
ejpam-5909	256	21	c[a	c[a	NUM
ejpam-5909	256	22	,	,	PUNCT
ejpam-5909	256	23	b	b	NOUN
ejpam-5909	256	24	]	]	X
ejpam-5909	256	25	.	.	PUNCT
ejpam-5909	257	1	the	the	DET
ejpam-5909	257	2	stieltjes	stieltjes	PROPN
ejpam-5909	257	3	limit	limit	NOUN
ejpam-5909	257	4	of	of	ADP
ejpam-5909	257	5	an	an	DET
ejpam-5909	257	6	operator	operator	NOUN
ejpam-5909	257	7	with	with	ADP
ejpam-5909	257	8	continuous	continuous	ADJ
ejpam-5909	257	9	function	function	NOUN
ejpam-5909	257	10	values	value	NOUN
ejpam-5909	257	11	generalizes	generalize	VERB
ejpam-5909	257	12	the	the	DET
ejpam-5909	257	13	concept	concept	NOUN
ejpam-5909	257	14	of	of	ADP
ejpam-5909	257	15	the	the	DET
ejpam-5909	257	16	limit	limit	NOUN
ejpam-5909	257	17	of	of	ADP
ejpam-5909	257	18	an	an	DET
ejpam-5909	257	19	operator	operator	NOUN
ejpam-5909	257	20	with	with	ADP
ejpam-5909	257	21	continuous	continuous	ADJ
ejpam-5909	257	22	function	function	NOUN
ejpam-5909	257	23	values	value	NOUN
ejpam-5909	257	24	.	.	PUNCT
ejpam-5909	258	1	definition	definition	NOUN
ejpam-5909	258	2	13	13	NUM
ejpam-5909	258	3	.	.	PUNCT
ejpam-5909	259	1	given	give	VERB
ejpam-5909	259	2	a	a	DET
ejpam-5909	259	3	⊆	⊆	NUM
ejpam-5909	259	4	c[a	c[a	NUM
ejpam-5909	259	5	,	,	PUNCT
ejpam-5909	259	6	b	b	NOUN
ejpam-5909	259	7	]	]	PUNCT
ejpam-5909	259	8	and	and	CCONJ
ejpam-5909	259	9	a	a	DET
ejpam-5909	259	10	function	function	NOUN
ejpam-5909	259	11	f0	f0	NOUN
ejpam-5909	259	12	as	as	ADP
ejpam-5909	259	13	a	a	DET
ejpam-5909	259	14	limit	limit	NOUN
ejpam-5909	259	15	point	point	NOUN
ejpam-5909	259	16	of	of	ADP
ejpam-5909	259	17	the	the	DET
ejpam-5909	259	18	set	set	NOUN
ejpam-5909	259	19	a	a	NOUN
ejpam-5909	259	20	,	,	PUNCT
ejpam-5909	259	21	an	an	DET
ejpam-5909	259	22	operator	operator	NOUN
ejpam-5909	259	23	f	f	NOUN
ejpam-5909	259	24	:	:	PUNCT
ejpam-5909	259	25	a	a	DET
ejpam-5909	259	26	→	→	SYM
ejpam-5909	259	27	c[a	c[a	NUM
ejpam-5909	259	28	,	,	PUNCT
ejpam-5909	259	29	b	b	NOUN
ejpam-5909	259	30	]	]	X
ejpam-5909	259	31	,	,	PUNCT
ejpam-5909	259	32	and	and	CCONJ
ejpam-5909	259	33	an	an	DET
ejpam-5909	259	34	operator	operator	NOUN
ejpam-5909	259	35	r	r	NOUN
ejpam-5909	259	36	:	:	PUNCT
ejpam-5909	259	37	a	a	PRON
ejpam-5909	259	38	→	→	SYM
ejpam-5909	259	39	c[a	c[a	NUM
ejpam-5909	259	40	,	,	PUNCT
ejpam-5909	259	41	b	b	NOUN
ejpam-5909	259	42	]	]	X
ejpam-5909	259	43	that	that	PRON
ejpam-5909	259	44	is	be	AUX
ejpam-5909	259	45	continuous	continuous	ADJ
ejpam-5909	259	46	and	and	CCONJ
ejpam-5909	259	47	increasing	increase	VERB
ejpam-5909	259	48	,	,	PUNCT
ejpam-5909	259	49	a	a	DET
ejpam-5909	259	50	function	function	NOUN
ejpam-5909	259	51	l	l	NOUN
ejpam-5909	259	52	is	be	AUX
ejpam-5909	259	53	called	call	VERB
ejpam-5909	259	54	the	the	DET
ejpam-5909	259	55	limit	limit	NOUN
ejpam-5909	259	56	operator	operator	NOUN
ejpam-5909	259	57	of	of	ADP
ejpam-5909	259	58	f	f	PROPN
ejpam-5909	259	59	at	at	ADP
ejpam-5909	259	60	f0	f0	PROPN
ejpam-5909	259	61	with	with	ADP
ejpam-5909	259	62	respect	respect	NOUN
ejpam-5909	259	63	to	to	ADP
ejpam-5909	259	64	r	r	NOUN
ejpam-5909	259	65	if	if	SCONJ
ejpam-5909	259	66	,	,	PUNCT
ejpam-5909	259	67	for	for	ADP
ejpam-5909	259	68	every	every	DET
ejpam-5909	259	69	real	real	ADJ
ejpam-5909	259	70	number	number	NOUN
ejpam-5909	259	71	ε	ε	PROPN
ejpam-5909	259	72	>	>	X
ejpam-5909	259	73	0	0	PROPN
ejpam-5909	259	74	,	,	PUNCT
ejpam-5909	259	75	there	there	PRON
ejpam-5909	259	76	exists	exist	VERB
ejpam-5909	259	77	a	a	DET
ejpam-5909	259	78	real	real	ADJ
ejpam-5909	259	79	number	number	NOUN
ejpam-5909	259	80	δ	δ	NOUN
ejpam-5909	259	81	>	>	X
ejpam-5909	259	82	0	0	NUM
ejpam-5909	259	83	such	such	ADJ
ejpam-5909	259	84	that	that	PRON
ejpam-5909	259	85	for	for	ADP
ejpam-5909	259	86	every	every	DET
ejpam-5909	259	87	f	f	PROPN
ejpam-5909	259	88	∈	∈	PROPN
ejpam-5909	259	89	a	a	DET
ejpam-5909	259	90	satisfying	satisfying	ADJ
ejpam-5909	259	91	0	0	NUM
ejpam-5909	259	92	≺	≺	NOUN
ejpam-5909	259	93	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	259	94	≺	≺	NOUN
ejpam-5909	259	95	δe	δe	ADP
ejpam-5909	259	96	,	,	PUNCT
ejpam-5909	259	97	the	the	DET
ejpam-5909	259	98	following	follow	VERB
ejpam-5909	259	99	holds	hold	VERB
ejpam-5909	259	100	:	:	PUNCT
ejpam-5909	259	101	|f	|f	PROPN
ejpam-5909	259	102	(	(	PUNCT
ejpam-5909	259	103	f)−	f)−	PROPN
ejpam-5909	259	104	l|	l|	ADJ
ejpam-5909	259	105	≺	≺	NOUN
ejpam-5909	259	106	εe	εe	NOUN
ejpam-5909	259	107	.	.	PROPN
ejpam-5909	259	108	m.	m.	NOUN
ejpam-5909	259	109	alifuddin	alifuddin	VERB
ejpam-5909	260	1	et	et	PROPN
ejpam-5909	260	2	al	al	PROPN
ejpam-5909	260	3	.	.	PUNCT
ejpam-5909	260	4	/	/	SYM
ejpam-5909	260	5	eur	eur	PROPN
ejpam-5909	260	6	.	.	PUNCT
ejpam-5909	261	1	j.	j.	PROPN
ejpam-5909	261	2	pure	pure	PROPN
ejpam-5909	261	3	appl	appl	PROPN
ejpam-5909	261	4	.	.	PROPN
ejpam-5909	261	5	math	math	PROPN
ejpam-5909	261	6	,	,	PUNCT
ejpam-5909	261	7	18	18	NUM
ejpam-5909	261	8	(	(	PUNCT
ejpam-5909	261	9	2	2	NUM
ejpam-5909	261	10	)	)	PUNCT
ejpam-5909	261	11	(	(	PUNCT
ejpam-5909	261	12	2025	2025	NUM
ejpam-5909	261	13	)	)	PUNCT
ejpam-5909	261	14	,	,	PUNCT
ejpam-5909	261	15	5909	5909	NUM
ejpam-5909	261	16	13	13	NUM
ejpam-5909	261	17	of	of	ADP
ejpam-5909	261	18	17	17	NUM
ejpam-5909	261	19	if	if	SCONJ
ejpam-5909	261	20	l	l	NOUN
ejpam-5909	261	21	is	be	AUX
ejpam-5909	261	22	the	the	DET
ejpam-5909	261	23	limit	limit	NOUN
ejpam-5909	261	24	operator	operator	NOUN
ejpam-5909	261	25	of	of	ADP
ejpam-5909	261	26	f	f	PROPN
ejpam-5909	261	27	with	with	ADP
ejpam-5909	261	28	respect	respect	NOUN
ejpam-5909	261	29	to	to	ADP
ejpam-5909	261	30	r	r	NOUN
ejpam-5909	261	31	at	at	ADP
ejpam-5909	261	32	f0	f0	PROPN
ejpam-5909	261	33	,	,	PUNCT
ejpam-5909	261	34	it	it	PRON
ejpam-5909	261	35	is	be	AUX
ejpam-5909	261	36	written	write	VERB
ejpam-5909	261	37	as	as	ADP
ejpam-5909	261	38	:	:	PUNCT
ejpam-5909	261	39	l	l	NOUN
ejpam-5909	261	40	=	=	SYM
ejpam-5909	261	41	lim	lim	PROPN
ejpam-5909	261	42	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	261	43	)	)	PUNCT
ejpam-5909	261	44	f	f	PROPN
ejpam-5909	261	45	(	(	PUNCT
ejpam-5909	261	46	f	f	NOUN
ejpam-5909	261	47	)	)	PUNCT
ejpam-5909	261	48	.	.	PUNCT
ejpam-5909	262	1	next	next	ADV
ejpam-5909	262	2	,	,	PUNCT
ejpam-5909	262	3	in	in	ADP
ejpam-5909	262	4	this	this	DET
ejpam-5909	262	5	subsection	subsection	NOUN
ejpam-5909	262	6	,	,	PUNCT
ejpam-5909	262	7	each	each	DET
ejpam-5909	262	8	operator	operator	NOUN
ejpam-5909	262	9	f	f	PROPN
ejpam-5909	262	10	and	and	CCONJ
ejpam-5909	262	11	r	r	PROPN
ejpam-5909	262	12	considered	consider	VERB
ejpam-5909	262	13	is	be	AUX
ejpam-5909	262	14	an	an	DET
ejpam-5909	262	15	operator	operator	NOUN
ejpam-5909	262	16	mapping	mapping	NOUN
ejpam-5909	262	17	from	from	ADP
ejpam-5909	262	18	a	a	DET
ejpam-5909	262	19	⊆	⊆	NUM
ejpam-5909	262	20	c[a	c[a	NOUN
ejpam-5909	262	21	,	,	PUNCT
ejpam-5909	262	22	b	b	X
ejpam-5909	262	23	]	]	X
ejpam-5909	262	24	to	to	ADP
ejpam-5909	262	25	c[a	c[a	NUM
ejpam-5909	262	26	,	,	PUNCT
ejpam-5909	262	27	b	b	AUX
ejpam-5909	262	28	]	]	X
ejpam-5909	262	29	that	that	PRON
ejpam-5909	262	30	is	be	AUX
ejpam-5909	262	31	defined	define	VERB
ejpam-5909	262	32	on	on	ADP
ejpam-5909	262	33	an	an	DET
ejpam-5909	262	34	open	open	ADJ
ejpam-5909	262	35	interval	interval	NOUN
ejpam-5909	262	36	,	,	PUNCT
ejpam-5909	262	37	with	with	ADP
ejpam-5909	262	38	r	r	NOUN
ejpam-5909	262	39	being	be	AUX
ejpam-5909	262	40	a	a	DET
ejpam-5909	262	41	continuous	continuous	ADJ
ejpam-5909	262	42	and	and	CCONJ
ejpam-5909	262	43	increasing	increase	VERB
ejpam-5909	262	44	operator	operator	NOUN
ejpam-5909	262	45	.	.	PUNCT
ejpam-5909	262	46	example	example	NOUN
ejpam-5909	263	1	5	5	NUM
ejpam-5909	263	2	.	.	PUNCT
ejpam-5909	263	3	given	give	VERB
ejpam-5909	263	4	r(f	r(f	PROPN
ejpam-5909	263	5	)	)	PUNCT
ejpam-5909	263	6	=	=	SYM
ejpam-5909	263	7	2f	2f	NUM
ejpam-5909	263	8	and	and	CCONJ
ejpam-5909	263	9	f	f	X
ejpam-5909	263	10	(	(	PUNCT
ejpam-5909	263	11	f	f	X
ejpam-5909	263	12	)	)	PUNCT
ejpam-5909	263	13	=	=	NOUN
ejpam-5909	263	14	2f	2f	NOUN
ejpam-5909	264	1	+	+	CCONJ
ejpam-5909	264	2	e	e	X
ejpam-5909	264	3	,	,	PUNCT
ejpam-5909	264	4	we	we	PRON
ejpam-5909	264	5	will	will	AUX
ejpam-5909	264	6	show	show	VERB
ejpam-5909	264	7	that	that	SCONJ
ejpam-5909	264	8	:	:	PUNCT
ejpam-5909	264	9	lim	lim	PROPN
ejpam-5909	264	10	r(f)→r(e	r(f)→r(e	PROPN
ejpam-5909	264	11	)	)	PUNCT
ejpam-5909	264	12	(	(	PUNCT
ejpam-5909	264	13	2f	2f	NOUN
ejpam-5909	264	14	+	+	CCONJ
ejpam-5909	264	15	e	e	X
ejpam-5909	264	16	)	)	PUNCT
ejpam-5909	264	17	=	=	SYM
ejpam-5909	264	18	3e	3e	NOUN
ejpam-5909	264	19	.	.	PUNCT
ejpam-5909	265	1	taking	take	VERB
ejpam-5909	265	2	any	any	DET
ejpam-5909	265	3	positive	positive	ADJ
ejpam-5909	265	4	real	real	ADJ
ejpam-5909	265	5	number	number	NOUN
ejpam-5909	265	6	ε	ε	PROPN
ejpam-5909	265	7	,	,	PUNCT
ejpam-5909	265	8	we	we	PRON
ejpam-5909	265	9	choose	choose	VERB
ejpam-5909	265	10	a	a	DET
ejpam-5909	265	11	positive	positive	ADJ
ejpam-5909	265	12	real	real	ADJ
ejpam-5909	265	13	number	number	NOUN
ejpam-5909	265	14	δ	δ	NOUN
ejpam-5909	265	15	=	=	PUNCT
ejpam-5909	265	16	ε	ε	PROPN
ejpam-5909	265	17	such	such	ADJ
ejpam-5909	265	18	that	that	PRON
ejpam-5909	265	19	for	for	ADP
ejpam-5909	265	20	every	every	DET
ejpam-5909	265	21	f	f	PROPN
ejpam-5909	265	22	∈	∈	PROPN
ejpam-5909	265	23	a	a	DET
ejpam-5909	265	24	satisfying	satisfy	VERB
ejpam-5909	265	25	0	0	NUM
ejpam-5909	265	26	≺	≺	NOUN
ejpam-5909	265	27	|r(f)−r(e)|	|r(f)−r(e)|	NOUN
ejpam-5909	265	28	=	=	SYM
ejpam-5909	265	29	|2f	|2f	NOUN
ejpam-5909	265	30	−	−	PROPN
ejpam-5909	265	31	2e|	2e|	NUM
ejpam-5909	265	32	≺	≺	NOUN
ejpam-5909	265	33	δe	δe	ADP
ejpam-5909	265	34	,	,	PUNCT
ejpam-5909	265	35	we	we	PRON
ejpam-5909	265	36	obtain	obtain	VERB
ejpam-5909	265	37	:	:	PUNCT
ejpam-5909	265	38	|(2f	|(2f	X
ejpam-5909	266	1	+	+	X
ejpam-5909	266	2	e)−	e)−	PROPN
ejpam-5909	266	3	(	(	PUNCT
ejpam-5909	266	4	3e)|	3e)|	NOUN
ejpam-5909	266	5	≺	≺	NOUN
ejpam-5909	266	6	|2f	|2f	X
ejpam-5909	267	1	−	−	PROPN
ejpam-5909	267	2	2e|	2e|	NUM
ejpam-5909	267	3	≺	≺	NOUN
ejpam-5909	267	4	δe	δe	NOUN
ejpam-5909	267	5	=	=	NOUN
ejpam-5909	267	6	εe	εe	NOUN
ejpam-5909	267	7	.	.	PUNCT
ejpam-5909	268	1	thus	thus	ADV
ejpam-5909	268	2	:	:	PUNCT
ejpam-5909	268	3	lim	lim	PROPN
ejpam-5909	268	4	f→2e	f→2e	NOUN
ejpam-5909	268	5	(	(	PUNCT
ejpam-5909	268	6	2f	2f	NOUN
ejpam-5909	268	7	+	+	CCONJ
ejpam-5909	268	8	e	e	NOUN
ejpam-5909	268	9	)	)	PUNCT
ejpam-5909	268	10	=	=	SYM
ejpam-5909	268	11	3e	3e	X
ejpam-5909	268	12	.	.	PUNCT
ejpam-5909	268	13	theorem	theorem	NOUN
ejpam-5909	268	14	7	7	NUM
ejpam-5909	268	15	.	.	PUNCT
ejpam-5909	268	16	given	give	VERB
ejpam-5909	268	17	a	a	DET
ejpam-5909	268	18	⊆	⊆	NUM
ejpam-5909	268	19	c[a	c[a	NOUN
ejpam-5909	268	20	,	,	PUNCT
ejpam-5909	268	21	b	b	NOUN
ejpam-5909	268	22	]	]	X
ejpam-5909	268	23	,	,	PUNCT
ejpam-5909	268	24	an	an	DET
ejpam-5909	268	25	operator	operator	NOUN
ejpam-5909	268	26	f	f	PROPN
ejpam-5909	268	27	mapping	mapping	NOUN
ejpam-5909	268	28	from	from	ADP
ejpam-5909	268	29	a	a	PRON
ejpam-5909	268	30	to	to	ADP
ejpam-5909	268	31	c[a	c[a	NUM
ejpam-5909	268	32	,	,	PUNCT
ejpam-5909	268	33	b	b	NOUN
ejpam-5909	268	34	]	]	X
ejpam-5909	268	35	,	,	PUNCT
ejpam-5909	268	36	and	and	CCONJ
ejpam-5909	268	37	f0	f0	VERB
ejpam-5909	268	38	as	as	ADP
ejpam-5909	268	39	a	a	DET
ejpam-5909	268	40	limit	limit	NOUN
ejpam-5909	268	41	point	point	NOUN
ejpam-5909	268	42	of	of	ADP
ejpam-5909	268	43	the	the	DET
ejpam-5909	268	44	set	set	NOUN
ejpam-5909	268	45	a	a	PRON
ejpam-5909	268	46	,	,	PUNCT
ejpam-5909	268	47	if	if	SCONJ
ejpam-5909	268	48	:	:	PUNCT
ejpam-5909	268	49	lim	lim	PROPN
ejpam-5909	268	50	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	268	51	)	)	PUNCT
ejpam-5909	268	52	f	f	PROPN
ejpam-5909	268	53	(	(	PUNCT
ejpam-5909	268	54	f	f	X
ejpam-5909	268	55	)	)	PUNCT
ejpam-5909	268	56	=	=	SYM
ejpam-5909	268	57	l	l	NOUN
ejpam-5909	268	58	and	and	CCONJ
ejpam-5909	268	59	lim	lim	PROPN
ejpam-5909	268	60	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	269	1	)	)	PUNCT
ejpam-5909	269	2	f	f	PROPN
ejpam-5909	270	1	(	(	PUNCT
ejpam-5909	270	2	f	f	X
ejpam-5909	270	3	)	)	PUNCT
ejpam-5909	270	4	=	=	SYM
ejpam-5909	270	5	m	m	PROPN
ejpam-5909	270	6	,	,	PUNCT
ejpam-5909	270	7	then	then	ADV
ejpam-5909	270	8	l	l	PROPN
ejpam-5909	270	9	=	=	NOUN
ejpam-5909	270	10	m	m	NOUN
ejpam-5909	270	11	.	.	PUNCT
ejpam-5909	271	1	proof	proof	NOUN
ejpam-5909	271	2	.	.	PUNCT
ejpam-5909	272	1	given	give	VERB
ejpam-5909	272	2	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	272	3	)	)	PUNCT
ejpam-5909	272	4	f	f	NOUN
ejpam-5909	272	5	(	(	PUNCT
ejpam-5909	272	6	f	f	X
ejpam-5909	272	7	)	)	PUNCT
ejpam-5909	272	8	=	=	SYM
ejpam-5909	272	9	l	l	NOUN
ejpam-5909	272	10	,	,	PUNCT
ejpam-5909	272	11	meaning	mean	VERB
ejpam-5909	272	12	that	that	SCONJ
ejpam-5909	272	13	for	for	ADP
ejpam-5909	272	14	every	every	DET
ejpam-5909	272	15	real	real	ADJ
ejpam-5909	272	16	number	number	NOUN
ejpam-5909	272	17	ε	ε	PROPN
ejpam-5909	272	18	>	>	X
ejpam-5909	272	19	0	0	PROPN
ejpam-5909	272	20	,	,	PUNCT
ejpam-5909	272	21	there	there	PRON
ejpam-5909	272	22	exists	exist	VERB
ejpam-5909	272	23	δ1	δ1	NOUN
ejpam-5909	272	24	>	>	X
ejpam-5909	272	25	0	0	NUM
ejpam-5909	273	1	such	such	ADJ
ejpam-5909	273	2	that	that	SCONJ
ejpam-5909	273	3	if	if	SCONJ
ejpam-5909	273	4	f	f	PROPN
ejpam-5909	273	5	∈	∈	PROPN
ejpam-5909	273	6	a	a	DET
ejpam-5909	273	7	and	and	CCONJ
ejpam-5909	273	8	0	0	NUM
ejpam-5909	273	9	≺	≺	NOUN
ejpam-5909	273	10	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	273	11	≺	≺	NOUN
ejpam-5909	273	12	δ1e	δ1e	VERB
ejpam-5909	273	13	,	,	PUNCT
ejpam-5909	273	14	then	then	ADV
ejpam-5909	273	15	:	:	PUNCT
ejpam-5909	273	16	|f	|f	PROPN
ejpam-5909	274	1	(	(	PUNCT
ejpam-5909	274	2	f)−	f)−	PROPN
ejpam-5909	274	3	l|	l|	ADJ
ejpam-5909	274	4	≺	≺	NOUN
ejpam-5909	274	5	ε	ε	PROPN
ejpam-5909	274	6	2	2	NUM
ejpam-5909	274	7	e.	e.	PROPN
ejpam-5909	274	8	similarly	similarly	ADV
ejpam-5909	274	9	,	,	PUNCT
ejpam-5909	274	10	given	give	VERB
ejpam-5909	274	11	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	274	12	)	)	PUNCT
ejpam-5909	274	13	f	f	NOUN
ejpam-5909	274	14	(	(	PUNCT
ejpam-5909	274	15	f	f	X
ejpam-5909	274	16	)	)	PUNCT
ejpam-5909	274	17	=	=	NOUN
ejpam-5909	274	18	m	m	PROPN
ejpam-5909	274	19	,	,	PUNCT
ejpam-5909	274	20	meaning	mean	VERB
ejpam-5909	274	21	that	that	SCONJ
ejpam-5909	274	22	for	for	ADP
ejpam-5909	274	23	every	every	DET
ejpam-5909	274	24	ε	ε	PROPN
ejpam-5909	274	25	>	>	X
ejpam-5909	274	26	0	0	PROPN
ejpam-5909	274	27	,	,	PUNCT
ejpam-5909	274	28	there	there	PRON
ejpam-5909	274	29	exists	exist	VERB
ejpam-5909	274	30	δ2	δ2	ADJ
ejpam-5909	274	31	>	>	X
ejpam-5909	274	32	0	0	NUM
ejpam-5909	274	33	such	such	ADJ
ejpam-5909	274	34	that	that	SCONJ
ejpam-5909	274	35	if	if	SCONJ
ejpam-5909	274	36	f	f	PROPN
ejpam-5909	274	37	∈	∈	PROPN
ejpam-5909	274	38	a	a	DET
ejpam-5909	274	39	and	and	CCONJ
ejpam-5909	274	40	0	0	NUM
ejpam-5909	274	41	≺	≺	NOUN
ejpam-5909	274	42	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	274	43	≺	≺	NOUN
ejpam-5909	274	44	δ2e	δ2e	PROPN
ejpam-5909	274	45	,	,	PUNCT
ejpam-5909	274	46	then	then	ADV
ejpam-5909	274	47	:	:	PUNCT
ejpam-5909	274	48	|f	|f	PROPN
ejpam-5909	274	49	(	(	PUNCT
ejpam-5909	274	50	f)−m	f)−m	NOUN
ejpam-5909	274	51	|	|	ADV
ejpam-5909	274	52	≺	≺	NOUN
ejpam-5909	274	53	ε	ε	AUX
ejpam-5909	274	54	2	2	NUM
ejpam-5909	274	55	e.	e.	NOUN
ejpam-5909	274	56	choosing	choose	VERB
ejpam-5909	274	57	δ	δ	PROPN
ejpam-5909	274	58	=	=	PUNCT
ejpam-5909	274	59	min(δ1	min(δ1	PROPN
ejpam-5909	274	60	,	,	PUNCT
ejpam-5909	274	61	δ2	δ2	ADV
ejpam-5909	274	62	)	)	PUNCT
ejpam-5909	274	63	,	,	PUNCT
ejpam-5909	274	64	if	if	SCONJ
ejpam-5909	274	65	0	0	NUM
ejpam-5909	274	66	≺	≺	NOUN
ejpam-5909	274	67	|f	|f	NUM
ejpam-5909	274	68	−	−	PROPN
ejpam-5909	274	69	f0|	f0|	PROPN
ejpam-5909	274	70	≺	≺	NOUN
ejpam-5909	274	71	δe	δe	ADP
ejpam-5909	274	72	,	,	PUNCT
ejpam-5909	274	73	then	then	ADV
ejpam-5909	274	74	:	:	PUNCT
ejpam-5909	275	1	|l−m	|l−m	NOUN
ejpam-5909	275	2	|	|	ADV
ejpam-5909	275	3	=	=	PUNCT
ejpam-5909	275	4	|l−	|l−	NOUN
ejpam-5909	275	5	f	f	X
ejpam-5909	275	6	(	(	PUNCT
ejpam-5909	275	7	f	f	X
ejpam-5909	275	8	)	)	PUNCT
ejpam-5909	276	1	+	+	NOUN
ejpam-5909	276	2	f	f	X
ejpam-5909	276	3	(	(	PUNCT
ejpam-5909	276	4	f)−m	f)−m	NOUN
ejpam-5909	276	5	|	|	ADV
ejpam-5909	276	6	⪯	⪯	VERB
ejpam-5909	276	7	|l−	|l−	NOUN
ejpam-5909	276	8	f	f	PROPN
ejpam-5909	276	9	(	(	PUNCT
ejpam-5909	276	10	f)|+	f)|+	PROPN
ejpam-5909	276	11	|f	|f	PROPN
ejpam-5909	276	12	(	(	PUNCT
ejpam-5909	276	13	f)−m	f)−m	NOUN
ejpam-5909	276	14	|	|	ADV
ejpam-5909	276	15	.	.	PUNCT
ejpam-5909	277	1	by	by	ADP
ejpam-5909	277	2	substitution	substitution	NOUN
ejpam-5909	277	3	,	,	PUNCT
ejpam-5909	277	4	we	we	PRON
ejpam-5909	277	5	obtain	obtain	VERB
ejpam-5909	277	6	:	:	PUNCT
ejpam-5909	277	7	|l−m	|l−m	NOUN
ejpam-5909	277	8	|	|	ADV
ejpam-5909	277	9	≺	≺	NOUN
ejpam-5909	277	10	ε	ε	PROPN
ejpam-5909	277	11	2	2	NUM
ejpam-5909	277	12	e+	e+	PUNCT
ejpam-5909	277	13	ε	ε	PROPN
ejpam-5909	277	14	2	2	NUM
ejpam-5909	277	15	e	e	NOUN
ejpam-5909	277	16	=	=	PUNCT
ejpam-5909	277	17	εe	εe	VERB
ejpam-5909	277	18	.	.	PUNCT
ejpam-5909	278	1	this	this	PRON
ejpam-5909	278	2	holds	hold	VERB
ejpam-5909	278	3	for	for	ADP
ejpam-5909	278	4	every	every	DET
ejpam-5909	278	5	ε	ε	PROPN
ejpam-5909	278	6	>	>	X
ejpam-5909	278	7	0	0	PROPN
ejpam-5909	278	8	,	,	PUNCT
ejpam-5909	278	9	by	by	ADP
ejpam-5909	278	10	theorem	theorem	NOUN
ejpam-5909	278	11	4.1.11	4.1.11	NUM
ejpam-5909	278	12	:	:	PUNCT
ejpam-5909	278	13	|l−m	|l−m	NOUN
ejpam-5909	278	14	|	|	NOUN
ejpam-5909	278	15	=	=	SYM
ejpam-5909	278	16	0	0	NUM
ejpam-5909	278	17	or	or	CCONJ
ejpam-5909	278	18	l	l	NOUN
ejpam-5909	278	19	=	=	NOUN
ejpam-5909	278	20	m.	m.	NOUN
ejpam-5909	278	21	the	the	DET
ejpam-5909	278	22	significance	significance	NOUN
ejpam-5909	278	23	of	of	ADP
ejpam-5909	278	24	theorem	theorem	ADJ
ejpam-5909	278	25	4.5.4	4.5.4	PROPN
ejpam-5909	278	26	is	be	AUX
ejpam-5909	278	27	that	that	SCONJ
ejpam-5909	278	28	if	if	SCONJ
ejpam-5909	278	29	an	an	DET
ejpam-5909	278	30	operator	operator	NOUN
ejpam-5909	278	31	f	f	PROPN
ejpam-5909	278	32	has	have	VERB
ejpam-5909	278	33	a	a	DET
ejpam-5909	278	34	limit	limit	NOUN
ejpam-5909	278	35	at	at	ADP
ejpam-5909	278	36	f0	f0	PROPN
ejpam-5909	278	37	with	with	ADP
ejpam-5909	278	38	respect	respect	NOUN
ejpam-5909	278	39	to	to	ADP
ejpam-5909	278	40	r	r	NOUN
ejpam-5909	278	41	,	,	PUNCT
ejpam-5909	278	42	then	then	ADV
ejpam-5909	278	43	the	the	DET
ejpam-5909	278	44	limit	limit	NOUN
ejpam-5909	278	45	is	be	AUX
ejpam-5909	278	46	unique	unique	ADJ
ejpam-5909	278	47	.	.	PUNCT
ejpam-5909	279	1	m.	m.	NOUN
ejpam-5909	279	2	alifuddin	alifuddin	VERB
ejpam-5909	279	3	et	et	PROPN
ejpam-5909	279	4	al	al	PROPN
ejpam-5909	279	5	.	.	PUNCT
ejpam-5909	279	6	/	/	SYM
ejpam-5909	279	7	eur	eur	PROPN
ejpam-5909	279	8	.	.	PUNCT
ejpam-5909	280	1	j.	j.	PROPN
ejpam-5909	280	2	pure	pure	PROPN
ejpam-5909	280	3	appl	appl	PROPN
ejpam-5909	280	4	.	.	PROPN
ejpam-5909	280	5	math	math	PROPN
ejpam-5909	280	6	,	,	PUNCT
ejpam-5909	280	7	18	18	NUM
ejpam-5909	280	8	(	(	PUNCT
ejpam-5909	280	9	2	2	NUM
ejpam-5909	280	10	)	)	PUNCT
ejpam-5909	280	11	(	(	PUNCT
ejpam-5909	280	12	2025	2025	NUM
ejpam-5909	280	13	)	)	PUNCT
ejpam-5909	280	14	,	,	PUNCT
ejpam-5909	280	15	5909	5909	NUM
ejpam-5909	280	16	14	14	NUM
ejpam-5909	280	17	of	of	ADP
ejpam-5909	280	18	17	17	NUM
ejpam-5909	280	19	theorem	theorem	NOUN
ejpam-5909	280	20	8	8	NUM
ejpam-5909	280	21	.	.	PUNCT
ejpam-5909	280	22	given	give	VERB
ejpam-5909	280	23	a	a	DET
ejpam-5909	280	24	⊆	⊆	NUM
ejpam-5909	280	25	c[a	c[a	NOUN
ejpam-5909	280	26	,	,	PUNCT
ejpam-5909	280	27	b	b	NOUN
ejpam-5909	280	28	]	]	X
ejpam-5909	280	29	,	,	PUNCT
ejpam-5909	280	30	operators	operators	PROPN
ejpam-5909	280	31	f	f	PROPN
ejpam-5909	280	32	,	,	PUNCT
ejpam-5909	280	33	g	g	PROPN
ejpam-5909	280	34	,	,	PUNCT
ejpam-5909	280	35	and	and	CCONJ
ejpam-5909	280	36	r	r	NOUN
ejpam-5909	280	37	,	,	PUNCT
ejpam-5909	280	38	each	each	DET
ejpam-5909	280	39	mapping	mapping	NOUN
ejpam-5909	280	40	from	from	ADP
ejpam-5909	280	41	a	a	PRON
ejpam-5909	280	42	to	to	ADP
ejpam-5909	280	43	c[a	c[a	NUM
ejpam-5909	280	44	,	,	PUNCT
ejpam-5909	280	45	b	b	NOUN
ejpam-5909	280	46	]	]	X
ejpam-5909	280	47	,	,	PUNCT
ejpam-5909	280	48	with	with	ADP
ejpam-5909	280	49	r	r	NOUN
ejpam-5909	280	50	being	be	AUX
ejpam-5909	280	51	an	an	DET
ejpam-5909	280	52	increasing	increase	VERB
ejpam-5909	280	53	operator	operator	NOUN
ejpam-5909	280	54	,	,	PUNCT
ejpam-5909	280	55	and	and	CCONJ
ejpam-5909	280	56	f0	f0	PROPN
ejpam-5909	280	57	as	as	ADP
ejpam-5909	280	58	a	a	DET
ejpam-5909	280	59	limit	limit	NOUN
ejpam-5909	280	60	point	point	NOUN
ejpam-5909	280	61	of	of	ADP
ejpam-5909	280	62	the	the	DET
ejpam-5909	280	63	set	set	NOUN
ejpam-5909	280	64	a	a	PRON
ejpam-5909	280	65	,	,	PUNCT
ejpam-5909	280	66	along	along	ADP
ejpam-5909	280	67	with	with	ADP
ejpam-5909	280	68	a	a	DET
ejpam-5909	280	69	function	function	NOUN
ejpam-5909	280	70	γ	γ	X
ejpam-5909	280	71	∈	∈	PROPN
ejpam-5909	280	72	c[a	c[a	NOUN
ejpam-5909	280	73	,	,	PUNCT
ejpam-5909	280	74	b	b	NOUN
ejpam-5909	280	75	]	]	X
ejpam-5909	280	76	.	.	PUNCT
ejpam-5909	281	1	if	if	SCONJ
ejpam-5909	281	2	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	282	1	)	)	PUNCT
ejpam-5909	282	2	f	f	NOUN
ejpam-5909	282	3	(	(	PUNCT
ejpam-5909	282	4	f	f	X
ejpam-5909	282	5	)	)	PUNCT
ejpam-5909	282	6	=	=	SYM
ejpam-5909	282	7	l	l	NOUN
ejpam-5909	282	8	and	and	CCONJ
ejpam-5909	282	9	limr(f)→r(f0)g(f	limr(f)→r(f0)g(f	NOUN
ejpam-5909	282	10	)	)	PUNCT
ejpam-5909	283	1	=	=	NOUN
ejpam-5909	283	2	m	m	NOUN
ejpam-5909	283	3	,	,	PUNCT
ejpam-5909	283	4	then	then	ADV
ejpam-5909	283	5	:	:	PUNCT
ejpam-5909	283	6	(	(	PUNCT
ejpam-5909	283	7	i	i	NOUN
ejpam-5909	283	8	)	)	PUNCT
ejpam-5909	283	9	limr(f)→r(f0)(f	limr(f)→r(f0)(f	PROPN
ejpam-5909	283	10	+	+	NOUN
ejpam-5909	283	11	g)(f	g)(f	ADV
ejpam-5909	283	12	)	)	PUNCT
ejpam-5909	284	1	=	=	SYM
ejpam-5909	284	2	l+m	l+m	X
ejpam-5909	284	3	(	(	PUNCT
ejpam-5909	284	4	ii	ii	NOUN
ejpam-5909	284	5	)	)	PUNCT
ejpam-5909	284	6	limr(f)→r(f0)(f	limr(f)→r(f0)(f	PROPN
ejpam-5909	284	7	−g	−g	NOUN
ejpam-5909	284	8	)	)	PUNCT
ejpam-5909	285	1	=	=	SYM
ejpam-5909	285	2	l−m	l−m	NOUN
ejpam-5909	285	3	(	(	PUNCT
ejpam-5909	285	4	iii	iii	NOUN
ejpam-5909	285	5	)	)	PUNCT
ejpam-5909	285	6	limr(f)→r(f0)(fg)(f	limr(f)→r(f0)(fg)(f	PROPN
ejpam-5909	285	7	)	)	PUNCT
ejpam-5909	285	8	=	=	SYM
ejpam-5909	286	1	lm	lm	INTJ
ejpam-5909	286	2	(	(	PUNCT
ejpam-5909	286	3	iv	iv	X
ejpam-5909	286	4	)	)	PUNCT
ejpam-5909	286	5	limr(f)→r(f0)(γf	limr(f)→r(f0)(γf	PROPN
ejpam-5909	286	6	(	(	PUNCT
ejpam-5909	286	7	f	f	NOUN
ejpam-5909	286	8	)	)	PUNCT
ejpam-5909	286	9	)	)	PUNCT
ejpam-5909	287	1	=	=	PRON
ejpam-5909	287	2	γl	γl	PROPN
ejpam-5909	287	3	(	(	PUNCT
ejpam-5909	287	4	v	v	NOUN
ejpam-5909	287	5	)	)	PUNCT
ejpam-5909	287	6	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	287	7	)	)	PUNCT
ejpam-5909	288	1	(	(	PUNCT
ejpam-5909	288	2	f	f	PROPN
ejpam-5909	288	3	g	g	PROPN
ejpam-5909	288	4	)	)	PUNCT
ejpam-5909	288	5	(	(	PUNCT
ejpam-5909	288	6	f	f	X
ejpam-5909	288	7	)	)	PUNCT
ejpam-5909	288	8	=	=	PUNCT
ejpam-5909	289	1	l	l	NOUN
ejpam-5909	289	2	m	m	VERB
ejpam-5909	289	3	,	,	PUNCT
ejpam-5909	289	4	provided	provide	VERB
ejpam-5909	289	5	that	that	SCONJ
ejpam-5909	289	6	m(x	m(x	NOUN
ejpam-5909	289	7	)	)	PUNCT
ejpam-5909	289	8	̸=	̸=	PROPN
ejpam-5909	289	9	0	0	NUM
ejpam-5909	289	10	for	for	ADP
ejpam-5909	289	11	all	all	DET
ejpam-5909	289	12	x	x	SYM
ejpam-5909	289	13	∈	∈	PROPN
ejpam-5909	289	14	[	[	X
ejpam-5909	289	15	a	a	X
ejpam-5909	289	16	,	,	PUNCT
ejpam-5909	289	17	b	b	NOUN
ejpam-5909	289	18	]	]	PUNCT
ejpam-5909	289	19	.	.	PUNCT
ejpam-5909	290	1	proof	proof	NOUN
ejpam-5909	290	2	.	.	PUNCT
ejpam-5909	291	1	(	(	PUNCT
ejpam-5909	291	2	i	i	NOUN
ejpam-5909	291	3	)	)	PUNCT
ejpam-5909	291	4	given	give	VERB
ejpam-5909	291	5	that	that	DET
ejpam-5909	291	6	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	291	7	)	)	PUNCT
ejpam-5909	291	8	f	f	NOUN
ejpam-5909	291	9	=	=	SYM
ejpam-5909	291	10	l	l	PROPN
ejpam-5909	291	11	,	,	PUNCT
ejpam-5909	291	12	meaning	mean	VERB
ejpam-5909	291	13	that	that	SCONJ
ejpam-5909	291	14	for	for	ADP
ejpam-5909	291	15	every	every	DET
ejpam-5909	291	16	real	real	ADJ
ejpam-5909	291	17	number	number	NOUN
ejpam-5909	291	18	ε	ε	PROPN
ejpam-5909	291	19	>	>	X
ejpam-5909	291	20	0	0	PROPN
ejpam-5909	291	21	,	,	PUNCT
ejpam-5909	291	22	there	there	PRON
ejpam-5909	291	23	exists	exist	VERB
ejpam-5909	291	24	a	a	DET
ejpam-5909	291	25	real	real	ADJ
ejpam-5909	291	26	number	number	NOUN
ejpam-5909	291	27	δ1	δ1	NOUN
ejpam-5909	291	28	>	>	X
ejpam-5909	291	29	0	0	NUM
ejpam-5909	291	30	such	such	ADJ
ejpam-5909	291	31	that	that	SCONJ
ejpam-5909	291	32	if	if	SCONJ
ejpam-5909	291	33	f	f	PROPN
ejpam-5909	291	34	∈	∈	PROPN
ejpam-5909	291	35	a	a	DET
ejpam-5909	291	36	and	and	CCONJ
ejpam-5909	291	37	0	0	NUM
ejpam-5909	291	38	≺	≺	NOUN
ejpam-5909	291	39	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	291	40	≺	≺	NOUN
ejpam-5909	291	41	δ1e	δ1e	VERB
ejpam-5909	291	42	,	,	PUNCT
ejpam-5909	291	43	then	then	ADV
ejpam-5909	291	44	:	:	PUNCT
ejpam-5909	291	45	|f	|f	PROPN
ejpam-5909	291	46	(	(	PUNCT
ejpam-5909	291	47	f)−	f)−	PROPN
ejpam-5909	291	48	l|	l|	ADJ
ejpam-5909	291	49	≺	≺	NOUN
ejpam-5909	291	50	ε	ε	PROPN
ejpam-5909	291	51	2	2	NUM
ejpam-5909	291	52	e.	e.	PROPN
ejpam-5909	291	53	similarly	similarly	ADV
ejpam-5909	291	54	,	,	PUNCT
ejpam-5909	291	55	given	give	VERB
ejpam-5909	291	56	that	that	PRON
ejpam-5909	291	57	limr(f)→r(f0)g	limr(f)→r(f0)g	NOUN
ejpam-5909	291	58	=	=	SYM
ejpam-5909	291	59	m	m	NOUN
ejpam-5909	291	60	,	,	PUNCT
ejpam-5909	291	61	meaning	mean	VERB
ejpam-5909	291	62	that	that	SCONJ
ejpam-5909	291	63	for	for	ADP
ejpam-5909	291	64	every	every	DET
ejpam-5909	291	65	real	real	ADJ
ejpam-5909	291	66	number	number	NOUN
ejpam-5909	291	67	ε	ε	PROPN
ejpam-5909	291	68	>	>	X
ejpam-5909	291	69	0	0	PROPN
ejpam-5909	291	70	,	,	PUNCT
ejpam-5909	291	71	there	there	PRON
ejpam-5909	291	72	exists	exist	VERB
ejpam-5909	291	73	a	a	DET
ejpam-5909	291	74	real	real	ADJ
ejpam-5909	291	75	number	number	NOUN
ejpam-5909	291	76	δ2	δ2	VERB
ejpam-5909	291	77	>	>	X
ejpam-5909	291	78	0	0	NUM
ejpam-5909	291	79	such	such	ADJ
ejpam-5909	291	80	that	that	SCONJ
ejpam-5909	291	81	if	if	SCONJ
ejpam-5909	291	82	f	f	PROPN
ejpam-5909	291	83	∈	∈	PROPN
ejpam-5909	291	84	a	a	PRON
ejpam-5909	291	85	and	and	CCONJ
ejpam-5909	291	86	0	0	NUM
ejpam-5909	291	87	≺	≺	NOUN
ejpam-5909	291	88	|r(f)−	|r(f)−	NOUN
ejpam-5909	291	89	r(f0)|	r(f0)|	PROPN
ejpam-5909	291	90	≺	≺	NOUN
ejpam-5909	291	91	δ2e	δ2e	PROPN
ejpam-5909	291	92	,	,	PUNCT
ejpam-5909	291	93	then	then	ADV
ejpam-5909	291	94	:	:	PUNCT
ejpam-5909	291	95	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	291	96	|	|	ADV
ejpam-5909	291	97	≺	≺	NOUN
ejpam-5909	291	98	ε	ε	AUX
ejpam-5909	291	99	2	2	NUM
ejpam-5909	291	100	e.	e.	NOUN
ejpam-5909	291	101	choosing	choose	VERB
ejpam-5909	291	102	δ	δ	PROPN
ejpam-5909	291	103	=	=	PUNCT
ejpam-5909	291	104	min(δ1	min(δ1	PROPN
ejpam-5909	291	105	,	,	PUNCT
ejpam-5909	291	106	δ2	δ2	PROPN
ejpam-5909	291	107	)	)	PUNCT
ejpam-5909	291	108	,	,	PUNCT
ejpam-5909	291	109	we	we	PRON
ejpam-5909	291	110	obtain	obtain	VERB
ejpam-5909	291	111	that	that	PRON
ejpam-5909	291	112	for	for	ADP
ejpam-5909	291	113	every	every	DET
ejpam-5909	291	114	f	f	PROPN
ejpam-5909	291	115	∈	∈	PROPN
ejpam-5909	291	116	a	a	PRON
ejpam-5909	291	117	and	and	CCONJ
ejpam-5909	291	118	0	0	NUM
ejpam-5909	291	119	≺	≺	NOUN
ejpam-5909	291	120	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	291	121	≺	≺	NOUN
ejpam-5909	291	122	δe	δe	ADP
ejpam-5909	291	123	,	,	PUNCT
ejpam-5909	291	124	the	the	DET
ejpam-5909	291	125	following	follow	VERB
ejpam-5909	291	126	holds	hold	NOUN
ejpam-5909	291	127	:	:	PUNCT
ejpam-5909	292	1	|[f	|[f	PROPN
ejpam-5909	292	2	(	(	PUNCT
ejpam-5909	292	3	f	f	X
ejpam-5909	292	4	)	)	PUNCT
ejpam-5909	293	1	+	+	X
ejpam-5909	293	2	g(f)]−	g(f)]−	ADJ
ejpam-5909	293	3	[	[	X
ejpam-5909	293	4	l+m	l+m	X
ejpam-5909	293	5	]	]	PUNCT
ejpam-5909	293	6	|	|	ADV
ejpam-5909	293	7	⪯	⪯	VERB
ejpam-5909	293	8	|f	|f	PROPN
ejpam-5909	294	1	(	(	PUNCT
ejpam-5909	294	2	f)−	f)−	PROPN
ejpam-5909	294	3	l|+	l|+	PROPN
ejpam-5909	294	4	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	294	5	|	|	ADV
ejpam-5909	294	6	≺	≺	NOUN
ejpam-5909	294	7	ε	ε	PROPN
ejpam-5909	294	8	2	2	NUM
ejpam-5909	294	9	e+	e+	PUNCT
ejpam-5909	294	10	ε	ε	PROPN
ejpam-5909	294	11	2	2	NUM
ejpam-5909	294	12	e	e	NOUN
ejpam-5909	294	13	=	=	PUNCT
ejpam-5909	294	14	εe	εe	PROPN
ejpam-5909	294	15	.	.	PUNCT
ejpam-5909	295	1	thus	thus	ADV
ejpam-5909	295	2	,	,	PUNCT
ejpam-5909	295	3	lim	lim	PROPN
ejpam-5909	295	4	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	295	5	)	)	PUNCT
ejpam-5909	295	6	(	(	PUNCT
ejpam-5909	296	1	f	f	X
ejpam-5909	296	2	+	+	ADJ
ejpam-5909	296	3	g)(f	g)(f	ADV
ejpam-5909	296	4	)	)	PUNCT
ejpam-5909	296	5	=	=	SYM
ejpam-5909	297	1	l+m	l+m	X
ejpam-5909	297	2	.	.	PUNCT
ejpam-5909	297	3	(	(	PUNCT
ejpam-5909	297	4	ii	ii	NOUN
ejpam-5909	297	5	)	)	PUNCT
ejpam-5909	297	6	given	give	VERB
ejpam-5909	297	7	that	that	DET
ejpam-5909	297	8	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	297	9	)	)	PUNCT
ejpam-5909	297	10	f	f	NOUN
ejpam-5909	297	11	(	(	PUNCT
ejpam-5909	297	12	f	f	X
ejpam-5909	297	13	)	)	PUNCT
ejpam-5909	297	14	=	=	SYM
ejpam-5909	297	15	l	l	NOUN
ejpam-5909	297	16	,	,	PUNCT
ejpam-5909	297	17	meaning	mean	VERB
ejpam-5909	297	18	that	that	SCONJ
ejpam-5909	297	19	for	for	ADP
ejpam-5909	297	20	every	every	DET
ejpam-5909	297	21	real	real	ADJ
ejpam-5909	297	22	number	number	NOUN
ejpam-5909	297	23	ε	ε	PROPN
ejpam-5909	297	24	>	>	X
ejpam-5909	297	25	0	0	PROPN
ejpam-5909	297	26	,	,	PUNCT
ejpam-5909	297	27	there	there	PRON
ejpam-5909	297	28	exists	exist	VERB
ejpam-5909	297	29	a	a	DET
ejpam-5909	297	30	real	real	ADJ
ejpam-5909	297	31	number	number	NOUN
ejpam-5909	297	32	δ1	δ1	NOUN
ejpam-5909	297	33	>	>	X
ejpam-5909	297	34	0	0	NUM
ejpam-5909	297	35	such	such	ADJ
ejpam-5909	297	36	that	that	SCONJ
ejpam-5909	297	37	if	if	SCONJ
ejpam-5909	297	38	f	f	PROPN
ejpam-5909	297	39	∈	∈	PROPN
ejpam-5909	297	40	a	a	DET
ejpam-5909	297	41	and	and	CCONJ
ejpam-5909	297	42	0	0	NUM
ejpam-5909	297	43	≺	≺	NOUN
ejpam-5909	297	44	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	297	45	≺	≺	NOUN
ejpam-5909	297	46	δ1e	δ1e	VERB
ejpam-5909	297	47	,	,	PUNCT
ejpam-5909	297	48	then	then	ADV
ejpam-5909	297	49	:	:	PUNCT
ejpam-5909	297	50	|f	|f	PROPN
ejpam-5909	297	51	(	(	PUNCT
ejpam-5909	297	52	f)−	f)−	PROPN
ejpam-5909	297	53	l|	l|	ADJ
ejpam-5909	297	54	≺	≺	NOUN
ejpam-5909	297	55	ε	ε	PROPN
ejpam-5909	297	56	2	2	NUM
ejpam-5909	297	57	e.	e.	PROPN
ejpam-5909	297	58	similarly	similarly	ADV
ejpam-5909	297	59	,	,	PUNCT
ejpam-5909	297	60	given	give	VERB
ejpam-5909	297	61	that	that	DET
ejpam-5909	297	62	limr(f)→r(f0)g(f	limr(f)→r(f0)g(f	NOUN
ejpam-5909	297	63	)	)	PUNCT
ejpam-5909	297	64	=	=	SYM
ejpam-5909	298	1	m	m	NOUN
ejpam-5909	298	2	,	,	PUNCT
ejpam-5909	298	3	meaning	mean	VERB
ejpam-5909	298	4	that	that	SCONJ
ejpam-5909	298	5	for	for	ADP
ejpam-5909	298	6	every	every	DET
ejpam-5909	298	7	real	real	ADJ
ejpam-5909	298	8	number	number	NOUN
ejpam-5909	298	9	ε	ε	PROPN
ejpam-5909	298	10	>	>	X
ejpam-5909	298	11	0	0	PROPN
ejpam-5909	298	12	,	,	PUNCT
ejpam-5909	298	13	there	there	PRON
ejpam-5909	298	14	exists	exist	VERB
ejpam-5909	298	15	a	a	DET
ejpam-5909	298	16	real	real	ADJ
ejpam-5909	298	17	number	number	NOUN
ejpam-5909	298	18	δ2	δ2	VERB
ejpam-5909	298	19	>	>	X
ejpam-5909	298	20	0	0	NUM
ejpam-5909	298	21	such	such	ADJ
ejpam-5909	298	22	that	that	SCONJ
ejpam-5909	298	23	if	if	SCONJ
ejpam-5909	298	24	f	f	PROPN
ejpam-5909	298	25	∈	∈	PROPN
ejpam-5909	298	26	a	a	DET
ejpam-5909	298	27	and	and	CCONJ
ejpam-5909	298	28	0	0	NUM
ejpam-5909	298	29	≺	≺	NOUN
ejpam-5909	298	30	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	298	31	≺	≺	NOUN
ejpam-5909	298	32	δ2e	δ2e	PROPN
ejpam-5909	298	33	,	,	PUNCT
ejpam-5909	298	34	then	then	ADV
ejpam-5909	298	35	:	:	PUNCT
ejpam-5909	298	36	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	298	37	|	|	ADV
ejpam-5909	298	38	≺	≺	NOUN
ejpam-5909	298	39	ε	ε	PROPN
ejpam-5909	298	40	2	2	NUM
ejpam-5909	298	41	e.	e.	PROPN
ejpam-5909	298	42	m.	m.	PROPN
ejpam-5909	298	43	alifuddin	alifuddin	VERB
ejpam-5909	298	44	et	et	PROPN
ejpam-5909	298	45	al	al	PROPN
ejpam-5909	298	46	.	.	PUNCT
ejpam-5909	298	47	/	/	SYM
ejpam-5909	298	48	eur	eur	PROPN
ejpam-5909	298	49	.	.	PUNCT
ejpam-5909	299	1	j.	j.	PROPN
ejpam-5909	299	2	pure	pure	PROPN
ejpam-5909	299	3	appl	appl	PROPN
ejpam-5909	299	4	.	.	PROPN
ejpam-5909	299	5	math	math	PROPN
ejpam-5909	299	6	,	,	PUNCT
ejpam-5909	299	7	18	18	NUM
ejpam-5909	299	8	(	(	PUNCT
ejpam-5909	299	9	2	2	NUM
ejpam-5909	299	10	)	)	PUNCT
ejpam-5909	299	11	(	(	PUNCT
ejpam-5909	299	12	2025	2025	NUM
ejpam-5909	299	13	)	)	PUNCT
ejpam-5909	299	14	,	,	PUNCT
ejpam-5909	299	15	5909	5909	NUM
ejpam-5909	299	16	15	15	NUM
ejpam-5909	299	17	of	of	ADP
ejpam-5909	299	18	17	17	NUM
ejpam-5909	299	19	choosing	choose	VERB
ejpam-5909	299	20	δ	δ	X
ejpam-5909	299	21	=	=	PUNCT
ejpam-5909	299	22	min(δ1	min(δ1	PROPN
ejpam-5909	299	23	,	,	PUNCT
ejpam-5909	299	24	δ2	δ2	PROPN
ejpam-5909	299	25	)	)	PUNCT
ejpam-5909	299	26	,	,	PUNCT
ejpam-5909	299	27	we	we	PRON
ejpam-5909	299	28	obtain	obtain	VERB
ejpam-5909	299	29	that	that	PRON
ejpam-5909	299	30	for	for	ADP
ejpam-5909	299	31	every	every	DET
ejpam-5909	299	32	f	f	PROPN
ejpam-5909	299	33	∈	∈	PROPN
ejpam-5909	299	34	a	a	PRON
ejpam-5909	299	35	and	and	CCONJ
ejpam-5909	299	36	0	0	NUM
ejpam-5909	299	37	≺	≺	NOUN
ejpam-5909	299	38	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	299	39	≺	≺	NOUN
ejpam-5909	299	40	δe	δe	ADP
ejpam-5909	299	41	,	,	PUNCT
ejpam-5909	299	42	the	the	DET
ejpam-5909	299	43	following	follow	VERB
ejpam-5909	299	44	holds	hold	NOUN
ejpam-5909	299	45	:	:	PUNCT
ejpam-5909	299	46	|[f	|[f	PROPN
ejpam-5909	299	47	(	(	PUNCT
ejpam-5909	299	48	f)−g(f)]−	f)−g(f)]−	PROPN
ejpam-5909	300	1	[	[	X
ejpam-5909	300	2	l−m	l−m	NOUN
ejpam-5909	300	3	]	]	PUNCT
ejpam-5909	300	4	|	|	ADV
ejpam-5909	300	5	⪯	⪯	VERB
ejpam-5909	300	6	|f	|f	PROPN
ejpam-5909	301	1	(	(	PUNCT
ejpam-5909	301	2	f)−	f)−	PROPN
ejpam-5909	301	3	l|+	l|+	PROPN
ejpam-5909	301	4	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	301	5	|	|	ADV
ejpam-5909	301	6	≺	≺	NOUN
ejpam-5909	301	7	ε	ε	PROPN
ejpam-5909	301	8	2	2	NUM
ejpam-5909	301	9	e+	e+	PUNCT
ejpam-5909	301	10	ε	ε	PROPN
ejpam-5909	301	11	2	2	NUM
ejpam-5909	301	12	e	e	NOUN
ejpam-5909	301	13	=	=	PUNCT
ejpam-5909	301	14	εe	εe	PROPN
ejpam-5909	301	15	.	.	PUNCT
ejpam-5909	302	1	thus	thus	ADV
ejpam-5909	302	2	,	,	PUNCT
ejpam-5909	302	3	lim	lim	PROPN
ejpam-5909	302	4	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	302	5	)	)	PUNCT
ejpam-5909	302	6	(	(	PUNCT
ejpam-5909	303	1	f	f	PROPN
ejpam-5909	303	2	−g)(f	−g)(f	PROPN
ejpam-5909	303	3	)	)	PUNCT
ejpam-5909	303	4	=	=	SYM
ejpam-5909	303	5	l−m	l−m	NOUN
ejpam-5909	303	6	.	.	PUNCT
ejpam-5909	304	1	(	(	PUNCT
ejpam-5909	304	2	iii	iii	NOUN
ejpam-5909	304	3	)	)	PUNCT
ejpam-5909	304	4	given	give	VERB
ejpam-5909	304	5	that	that	DET
ejpam-5909	304	6	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	304	7	)	)	PUNCT
ejpam-5909	304	8	f	f	NOUN
ejpam-5909	304	9	(	(	PUNCT
ejpam-5909	304	10	f	f	X
ejpam-5909	304	11	)	)	PUNCT
ejpam-5909	304	12	=	=	SYM
ejpam-5909	304	13	l	l	NOUN
ejpam-5909	304	14	,	,	PUNCT
ejpam-5909	304	15	meaning	mean	VERB
ejpam-5909	304	16	that	that	SCONJ
ejpam-5909	304	17	for	for	ADP
ejpam-5909	304	18	every	every	DET
ejpam-5909	304	19	real	real	ADJ
ejpam-5909	304	20	number	number	NOUN
ejpam-5909	304	21	ε	ε	PROPN
ejpam-5909	304	22	>	>	X
ejpam-5909	304	23	0	0	PROPN
ejpam-5909	304	24	,	,	PUNCT
ejpam-5909	304	25	there	there	PRON
ejpam-5909	304	26	exists	exist	VERB
ejpam-5909	304	27	a	a	DET
ejpam-5909	304	28	real	real	ADJ
ejpam-5909	304	29	number	number	NOUN
ejpam-5909	304	30	δ1	δ1	NOUN
ejpam-5909	304	31	>	>	X
ejpam-5909	304	32	0	0	NUM
ejpam-5909	304	33	such	such	ADJ
ejpam-5909	304	34	that	that	SCONJ
ejpam-5909	304	35	if	if	SCONJ
ejpam-5909	304	36	f	f	PROPN
ejpam-5909	304	37	∈	∈	PROPN
ejpam-5909	304	38	a	a	DET
ejpam-5909	304	39	and	and	CCONJ
ejpam-5909	304	40	0	0	NUM
ejpam-5909	304	41	≺	≺	NOUN
ejpam-5909	304	42	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	304	43	≺	≺	NOUN
ejpam-5909	304	44	δ1e	δ1e	VERB
ejpam-5909	304	45	,	,	PUNCT
ejpam-5909	304	46	then	then	ADV
ejpam-5909	304	47	:	:	PUNCT
ejpam-5909	304	48	|f	|f	PROPN
ejpam-5909	304	49	(	(	PUNCT
ejpam-5909	304	50	f)−	f)−	PROPN
ejpam-5909	304	51	l|	l|	ADJ
ejpam-5909	304	52	≺	≺	NOUN
ejpam-5909	304	53	ε	ε	X
ejpam-5909	304	54	(	(	PUNCT
ejpam-5909	304	55	e	e	PROPN
ejpam-5909	304	56	2|m	2|m	NUM
ejpam-5909	304	57	|+	|+	NOUN
ejpam-5909	304	58	e	e	NOUN
ejpam-5909	304	59	)	)	PUNCT
ejpam-5909	304	60	.	.	PUNCT
ejpam-5909	305	1	similarly	similarly	ADV
ejpam-5909	305	2	,	,	PUNCT
ejpam-5909	305	3	given	give	VERB
ejpam-5909	305	4	that	that	DET
ejpam-5909	305	5	limr(f)→r(f0)g(f	limr(f)→r(f0)g(f	NOUN
ejpam-5909	305	6	)	)	PUNCT
ejpam-5909	305	7	=	=	SYM
ejpam-5909	305	8	m	m	NOUN
ejpam-5909	305	9	,	,	PUNCT
ejpam-5909	305	10	meaning	mean	VERB
ejpam-5909	305	11	that	that	SCONJ
ejpam-5909	305	12	for	for	ADP
ejpam-5909	305	13	every	every	DET
ejpam-5909	305	14	real	real	ADJ
ejpam-5909	305	15	number	number	NOUN
ejpam-5909	305	16	ε	ε	PROPN
ejpam-5909	305	17	>	>	X
ejpam-5909	305	18	0	0	PROPN
ejpam-5909	305	19	,	,	PUNCT
ejpam-5909	305	20	there	there	PRON
ejpam-5909	305	21	exists	exist	VERB
ejpam-5909	305	22	a	a	DET
ejpam-5909	305	23	real	real	ADJ
ejpam-5909	305	24	number	number	NOUN
ejpam-5909	305	25	δ2	δ2	VERB
ejpam-5909	305	26	>	>	X
ejpam-5909	305	27	0	0	NUM
ejpam-5909	305	28	such	such	ADJ
ejpam-5909	305	29	that	that	SCONJ
ejpam-5909	305	30	if	if	SCONJ
ejpam-5909	305	31	f	f	PROPN
ejpam-5909	305	32	∈	∈	PROPN
ejpam-5909	305	33	a	a	DET
ejpam-5909	305	34	and	and	CCONJ
ejpam-5909	305	35	0	0	NUM
ejpam-5909	305	36	≺	≺	NOUN
ejpam-5909	305	37	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	305	38	≺	≺	NOUN
ejpam-5909	305	39	δ2e	δ2e	PROPN
ejpam-5909	305	40	,	,	PUNCT
ejpam-5909	305	41	then	then	ADV
ejpam-5909	305	42	:	:	PUNCT
ejpam-5909	305	43	|g(f)−m	|g(f)−m	NOUN
ejpam-5909	305	44	|	|	ADV
ejpam-5909	305	45	≺	≺	NOUN
ejpam-5909	305	46	ε	ε	PROPN
ejpam-5909	305	47	(	(	PUNCT
ejpam-5909	305	48	e	e	PROPN
ejpam-5909	305	49	2(sup	2(sup	NUM
ejpam-5909	305	50	|f	|f	PROPN
ejpam-5909	305	51	(	(	PUNCT
ejpam-5909	305	52	f)|+	f)|+	NOUN
ejpam-5909	305	53	e	e	NOUN
ejpam-5909	305	54	)	)	PUNCT
ejpam-5909	305	55	)	)	PUNCT
ejpam-5909	305	56	,	,	PUNCT
ejpam-5909	305	57	where	where	SCONJ
ejpam-5909	305	58	sup	sup	PROPN
ejpam-5909	305	59	|f	|f	PROPN
ejpam-5909	305	60	(	(	PUNCT
ejpam-5909	305	61	f)|	f)|	VERB
ejpam-5909	305	62	is	be	AUX
ejpam-5909	305	63	the	the	DET
ejpam-5909	305	64	supremum	supremum	NOUN
ejpam-5909	305	65	of	of	ADP
ejpam-5909	305	66	|f	|f	PROPN
ejpam-5909	305	67	(	(	PUNCT
ejpam-5909	305	68	f)|	f)|	VERB
ejpam-5909	305	69	in	in	ADP
ejpam-5909	305	70	the	the	DET
ejpam-5909	305	71	neighborhood	neighborhood	NOUN
ejpam-5909	305	72	of	of	ADP
ejpam-5909	305	73	f0	f0	PROPN
ejpam-5909	305	74	where	where	SCONJ
ejpam-5909	305	75	f	f	PROPN
ejpam-5909	305	76	̸=	̸=	PROPN
ejpam-5909	305	77	f0	f0	PROPN
ejpam-5909	305	78	.	.	PUNCT
ejpam-5909	306	1	choosing	choose	VERB
ejpam-5909	306	2	δ	δ	X
ejpam-5909	306	3	=	=	PUNCT
ejpam-5909	306	4	min(δ1	min(δ1	PROPN
ejpam-5909	306	5	,	,	PUNCT
ejpam-5909	306	6	δ2	δ2	PROPN
ejpam-5909	306	7	)	)	PUNCT
ejpam-5909	306	8	,	,	PUNCT
ejpam-5909	306	9	we	we	PRON
ejpam-5909	306	10	obtain	obtain	VERB
ejpam-5909	306	11	that	that	PRON
ejpam-5909	306	12	for	for	ADP
ejpam-5909	306	13	every	every	DET
ejpam-5909	306	14	0	0	NUM
ejpam-5909	306	15	≺	≺	NOUN
ejpam-5909	306	16	|r(f	|r(f	NOUN
ejpam-5909	306	17	)	)	PUNCT
ejpam-5909	306	18	−	−	PROPN
ejpam-5909	306	19	r(f0)|	r(f0)|	NOUN
ejpam-5909	306	20	≺	≺	NOUN
ejpam-5909	306	21	δe	δe	ADP
ejpam-5909	306	22	,	,	PUNCT
ejpam-5909	306	23	the	the	DET
ejpam-5909	306	24	following	follow	VERB
ejpam-5909	306	25	holds	hold	VERB
ejpam-5909	306	26	:	:	PUNCT
ejpam-5909	306	27	|f	|f	PROPN
ejpam-5909	306	28	(	(	PUNCT
ejpam-5909	306	29	f)g(f)−	f)g(f)−	PROPN
ejpam-5909	307	1	lm	lm	INTJ
ejpam-5909	307	2	|	|	ADV
ejpam-5909	307	3	=	=	SYM
ejpam-5909	307	4	|f	|f	PROPN
ejpam-5909	307	5	(	(	PUNCT
ejpam-5909	307	6	f)g(f)−	f)g(f)−	PROPN
ejpam-5909	307	7	f	f	X
ejpam-5909	307	8	(	(	PUNCT
ejpam-5909	307	9	f)m	f)m	X
ejpam-5909	308	1	+	+	NUM
ejpam-5909	308	2	f	f	X
ejpam-5909	308	3	(	(	PUNCT
ejpam-5909	308	4	f)m	f)m	ADJ
ejpam-5909	308	5	−	−	NOUN
ejpam-5909	308	6	lm	lm	INTJ
ejpam-5909	309	1	|	|	ADV
ejpam-5909	309	2	=	=	SYM
ejpam-5909	309	3	|f	|f	PROPN
ejpam-5909	309	4	(	(	PUNCT
ejpam-5909	309	5	f)[g(f)−m	f)[g(f)−m	PROPN
ejpam-5909	309	6	]	]	PUNCT
ejpam-5909	310	1	+	+	NOUN
ejpam-5909	310	2	m	m	VERB
ejpam-5909	310	3	[	[	X
ejpam-5909	310	4	f	f	X
ejpam-5909	310	5	(	(	PUNCT
ejpam-5909	310	6	f)−	f)−	PROPN
ejpam-5909	310	7	l]|	l]|	PROPN
ejpam-5909	310	8	⪯	⪯	VERB
ejpam-5909	310	9	|f	|f	PROPN
ejpam-5909	311	1	(	(	PUNCT
ejpam-5909	311	2	f)|	f)|	VERB
ejpam-5909	311	3	|g(f)−m	|g(f)−m	PUNCT
ejpam-5909	311	4	|+	|+	NOUN
ejpam-5909	311	5	|m	|m	NOUN
ejpam-5909	311	6	|	|	ADV
ejpam-5909	311	7	|f	|f	PROPN
ejpam-5909	311	8	(	(	PUNCT
ejpam-5909	311	9	f)−	f)−	PROPN
ejpam-5909	311	10	l|	l|	PROPN
ejpam-5909	311	11	.	.	PUNCT
ejpam-5909	312	1	thus	thus	ADV
ejpam-5909	312	2	,	,	PUNCT
ejpam-5909	312	3	lim	lim	PROPN
ejpam-5909	312	4	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	312	5	)	)	PUNCT
ejpam-5909	312	6	(	(	PUNCT
ejpam-5909	312	7	fg)(f	fg)(f	PROPN
ejpam-5909	312	8	)	)	PUNCT
ejpam-5909	312	9	=	=	SYM
ejpam-5909	313	1	lm	lm	PROPN
ejpam-5909	313	2	.	.	PUNCT
ejpam-5909	313	3	(	(	PUNCT
ejpam-5909	313	4	iv	iv	X
ejpam-5909	313	5	)	)	PUNCT
ejpam-5909	313	6	given	give	VERB
ejpam-5909	313	7	that	that	DET
ejpam-5909	313	8	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	313	9	)	)	PUNCT
ejpam-5909	313	10	f	f	NOUN
ejpam-5909	313	11	(	(	PUNCT
ejpam-5909	313	12	f	f	X
ejpam-5909	313	13	)	)	PUNCT
ejpam-5909	313	14	=	=	SYM
ejpam-5909	313	15	l	l	NOUN
ejpam-5909	313	16	,	,	PUNCT
ejpam-5909	313	17	meaning	mean	VERB
ejpam-5909	313	18	that	that	SCONJ
ejpam-5909	313	19	for	for	ADP
ejpam-5909	313	20	every	every	DET
ejpam-5909	313	21	real	real	ADJ
ejpam-5909	313	22	number	number	NOUN
ejpam-5909	313	23	ε	ε	PROPN
ejpam-5909	313	24	>	>	X
ejpam-5909	313	25	0	0	PROPN
ejpam-5909	313	26	,	,	PUNCT
ejpam-5909	313	27	there	there	PRON
ejpam-5909	313	28	exists	exist	VERB
ejpam-5909	313	29	a	a	DET
ejpam-5909	313	30	real	real	ADJ
ejpam-5909	313	31	number	number	NOUN
ejpam-5909	313	32	δ	δ	NOUN
ejpam-5909	313	33	>	>	X
ejpam-5909	313	34	0	0	NUM
ejpam-5909	313	35	such	such	ADJ
ejpam-5909	313	36	that	that	SCONJ
ejpam-5909	313	37	if	if	SCONJ
ejpam-5909	313	38	f	f	PROPN
ejpam-5909	313	39	∈	∈	PROPN
ejpam-5909	313	40	a	a	PRON
ejpam-5909	313	41	and	and	CCONJ
ejpam-5909	313	42	0	0	NUM
ejpam-5909	313	43	≺	≺	NOUN
ejpam-5909	313	44	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	313	45	≺	≺	NOUN
ejpam-5909	313	46	δe	δe	ADP
ejpam-5909	313	47	,	,	PUNCT
ejpam-5909	313	48	then	then	ADV
ejpam-5909	313	49	:	:	PUNCT
ejpam-5909	313	50	|γf	|γf	X
ejpam-5909	313	51	(	(	PUNCT
ejpam-5909	313	52	f)−	f)−	PROPN
ejpam-5909	313	53	γl|	γl|	PROPN
ejpam-5909	313	54	=	=	PUNCT
ejpam-5909	314	1	|γ|	|γ|	PROPN
ejpam-5909	314	2	|f	|f	X
ejpam-5909	314	3	(	(	PUNCT
ejpam-5909	314	4	f)−	f)−	PROPN
ejpam-5909	314	5	l|	l|	ADJ
ejpam-5909	314	6	≺	≺	NOUN
ejpam-5909	314	7	|γ|	|γ|	PRON
ejpam-5909	314	8	εe	εe	ADP
ejpam-5909	314	9	|γ|	|γ|	PROPN
ejpam-5909	314	10	=	=	PUNCT
ejpam-5909	314	11	εe	εe	PROPN
ejpam-5909	314	12	.	.	PUNCT
ejpam-5909	315	1	thus	thus	ADV
ejpam-5909	315	2	,	,	PUNCT
ejpam-5909	315	3	lim	lim	PROPN
ejpam-5909	315	4	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	315	5	)	)	PUNCT
ejpam-5909	315	6	(	(	PUNCT
ejpam-5909	315	7	γf	γf	INTJ
ejpam-5909	315	8	(	(	PUNCT
ejpam-5909	315	9	f	f	NOUN
ejpam-5909	315	10	)	)	PUNCT
ejpam-5909	315	11	)	)	PUNCT
ejpam-5909	316	1	=	=	SYM
ejpam-5909	316	2	γl	γl	PROPN
ejpam-5909	316	3	.	.	PROPN
ejpam-5909	316	4	m.	m.	NOUN
ejpam-5909	316	5	alifuddin	alifuddin	VERB
ejpam-5909	316	6	et	et	PROPN
ejpam-5909	316	7	al	al	PROPN
ejpam-5909	316	8	.	.	PUNCT
ejpam-5909	316	9	/	/	SYM
ejpam-5909	316	10	eur	eur	PROPN
ejpam-5909	316	11	.	.	PUNCT
ejpam-5909	317	1	j.	j.	PROPN
ejpam-5909	317	2	pure	pure	PROPN
ejpam-5909	317	3	appl	appl	PROPN
ejpam-5909	317	4	.	.	PROPN
ejpam-5909	317	5	math	math	PROPN
ejpam-5909	317	6	,	,	PUNCT
ejpam-5909	317	7	18	18	NUM
ejpam-5909	317	8	(	(	PUNCT
ejpam-5909	317	9	2	2	NUM
ejpam-5909	317	10	)	)	PUNCT
ejpam-5909	317	11	(	(	PUNCT
ejpam-5909	317	12	2025	2025	NUM
ejpam-5909	317	13	)	)	PUNCT
ejpam-5909	317	14	,	,	PUNCT
ejpam-5909	317	15	5909	5909	NUM
ejpam-5909	317	16	16	16	NUM
ejpam-5909	317	17	of	of	ADP
ejpam-5909	317	18	17	17	NUM
ejpam-5909	317	19	(	(	PUNCT
ejpam-5909	317	20	v	v	NOUN
ejpam-5909	317	21	)	)	PUNCT
ejpam-5909	317	22	given	give	VERB
ejpam-5909	317	23	that	that	DET
ejpam-5909	317	24	limr(f)→r(f0	limr(f)→r(f0	NOUN
ejpam-5909	317	25	)	)	PUNCT
ejpam-5909	317	26	f	f	NOUN
ejpam-5909	317	27	(	(	PUNCT
ejpam-5909	317	28	f	f	X
ejpam-5909	317	29	)	)	PUNCT
ejpam-5909	317	30	=	=	SYM
ejpam-5909	317	31	l	l	NOUN
ejpam-5909	317	32	,	,	PUNCT
ejpam-5909	317	33	meaning	mean	VERB
ejpam-5909	317	34	that	that	SCONJ
ejpam-5909	317	35	for	for	ADP
ejpam-5909	317	36	every	every	DET
ejpam-5909	317	37	real	real	ADJ
ejpam-5909	317	38	number	number	NOUN
ejpam-5909	317	39	ε	ε	PROPN
ejpam-5909	317	40	>	>	X
ejpam-5909	317	41	0	0	PROPN
ejpam-5909	317	42	,	,	PUNCT
ejpam-5909	317	43	there	there	PRON
ejpam-5909	317	44	exists	exist	VERB
ejpam-5909	317	45	a	a	DET
ejpam-5909	317	46	real	real	ADJ
ejpam-5909	317	47	number	number	NOUN
ejpam-5909	317	48	δ1	δ1	NOUN
ejpam-5909	317	49	>	>	X
ejpam-5909	317	50	0	0	NUM
ejpam-5909	318	1	such	such	ADJ
ejpam-5909	318	2	that	that	SCONJ
ejpam-5909	318	3	if	if	SCONJ
ejpam-5909	318	4	f	f	PROPN
ejpam-5909	318	5	∈	∈	PROPN
ejpam-5909	318	6	a	a	DET
ejpam-5909	318	7	and	and	CCONJ
ejpam-5909	318	8	0	0	NUM
ejpam-5909	318	9	≺	≺	NOUN
ejpam-5909	318	10	|r(f)−r(f0)|	|r(f)−r(f0)|	NOUN
ejpam-5909	318	11	≺	≺	NOUN
ejpam-5909	318	12	δ1e	δ1e	VERB
ejpam-5909	318	13	,	,	PUNCT
ejpam-5909	318	14	then	then	ADV
ejpam-5909	318	15	:	:	PUNCT
ejpam-5909	318	16	|f	|f	PROPN
ejpam-5909	319	1	(	(	PUNCT
ejpam-5909	319	2	f)−	f)−	PROPN
ejpam-5909	319	3	l|	l|	ADJ
ejpam-5909	319	4	≺	≺	NOUN
ejpam-5909	319	5	|m	|m	NOUN
ejpam-5909	319	6	|	|	ADV
ejpam-5909	319	7	4	4	NUM
ejpam-5909	319	8	e.	e.	PROPN
ejpam-5909	319	9	similarly	similarly	ADV
ejpam-5909	319	10	,	,	PUNCT
ejpam-5909	319	11	given	give	VERB
ejpam-5909	319	12	limr(f)→r(f0)g	limr(f)→r(f0)g	NOUN
ejpam-5909	319	13	=	=	NOUN
ejpam-5909	319	14	m	m	NOUN
ejpam-5909	319	15	,	,	PUNCT
ejpam-5909	319	16	the	the	DET
ejpam-5909	319	17	same	same	ADJ
ejpam-5909	319	18	holds	hold	VERB
ejpam-5909	319	19	,	,	PUNCT
ejpam-5909	319	20	ensuring	ensure	VERB
ejpam-5909	319	21	:	:	PUNCT
ejpam-5909	319	22	lim	lim	PROPN
ejpam-5909	319	23	r(f)→r(f0	r(f)→r(f0	PROPN
ejpam-5909	319	24	)	)	PUNCT
ejpam-5909	319	25	(	(	PUNCT
ejpam-5909	319	26	f	f	PROPN
ejpam-5909	319	27	g	g	PROPN
ejpam-5909	319	28	)	)	PUNCT
ejpam-5909	319	29	(	(	PUNCT
ejpam-5909	319	30	f	f	X
ejpam-5909	319	31	)	)	PUNCT
ejpam-5909	319	32	=	=	PUNCT
ejpam-5909	320	1	l	l	NOUN
ejpam-5909	320	2	m	m	NOUN
ejpam-5909	320	3	.	.	PUNCT
ejpam-5909	321	1	4	4	X
ejpam-5909	321	2	.	.	X
ejpam-5909	321	3	conclusion	conclusion	VERB
ejpam-5909	321	4	the	the	DET
ejpam-5909	321	5	findings	finding	NOUN
ejpam-5909	321	6	of	of	ADP
ejpam-5909	321	7	this	this	DET
ejpam-5909	321	8	study	study	NOUN
ejpam-5909	321	9	indicate	indicate	VERB
ejpam-5909	321	10	that	that	SCONJ
ejpam-5909	321	11	the	the	DET
ejpam-5909	321	12	characteristics	characteristic	NOUN
ejpam-5909	321	13	of	of	ADP
ejpam-5909	321	14	the	the	DET
ejpam-5909	321	15	limit	limit	NOUN
ejpam-5909	321	16	and	and	CCONJ
ejpam-5909	321	17	the	the	DET
ejpam-5909	321	18	stieltjes	stieltjes	NOUN
ejpam-5909	321	19	limit	limit	NOUN
ejpam-5909	321	20	of	of	ADP
ejpam-5909	321	21	function	function	NOUN
ejpam-5909	321	22	-	-	PUNCT
ejpam-5909	321	23	valued	value	VERB
ejpam-5909	321	24	continuous	continuous	ADJ
ejpam-5909	321	25	functions	function	NOUN
ejpam-5909	321	26	are	be	AUX
ejpam-5909	321	27	comparable	comparable	ADJ
ejpam-5909	321	28	to	to	ADP
ejpam-5909	321	29	those	those	PRON
ejpam-5909	321	30	of	of	ADP
ejpam-5909	321	31	the	the	DET
ejpam-5909	321	32	limit	limit	NOUN
ejpam-5909	321	33	and	and	CCONJ
ejpam-5909	321	34	the	the	DET
ejpam-5909	321	35	stieltjes	stieltjes	NOUN
ejpam-5909	321	36	limit	limit	NOUN
ejpam-5909	321	37	of	of	ADP
ejpam-5909	321	38	real	real	ADV
ejpam-5909	321	39	-	-	PUNCT
ejpam-5909	321	40	valued	value	VERB
ejpam-5909	321	41	functions	function	NOUN
ejpam-5909	321	42	.	.	PUNCT
ejpam-5909	322	1	acknowledgements	acknowledgement	VERB
ejpam-5909	322	2	the	the	DET
ejpam-5909	322	3	author(s	author(s	NOUN
ejpam-5909	322	4	)	)	PUNCT
ejpam-5909	322	5	would	would	AUX
ejpam-5909	322	6	like	like	VERB
ejpam-5909	322	7	to	to	PART
ejpam-5909	322	8	thank	thank	VERB
ejpam-5909	322	9	the	the	DET
ejpam-5909	322	10	department	department	NOUN
ejpam-5909	322	11	of	of	ADP
ejpam-5909	322	12	mathematics	mathematics	PROPN
ejpam-5909	322	13	,	,	PUNCT
ejpam-5909	322	14	institut	institut	PROPN
ejpam-5909	322	15	teknologi	teknologi	PROPN
ejpam-5909	322	16	sepuluh	sepuluh	PROPN
ejpam-5909	322	17	nopember	nopember	PROPN
ejpam-5909	322	18	(	(	PUNCT
ejpam-5909	322	19	its	its	PRON
ejpam-5909	322	20	)	)	PUNCT
ejpam-5909	322	21	,	,	PUNCT
ejpam-5909	322	22	surabaya	surabaya	PROPN
ejpam-5909	322	23	,	,	PUNCT
ejpam-5909	322	24	indonesia	indonesia	PROPN
ejpam-5909	322	25	,	,	PUNCT
ejpam-5909	322	26	for	for	ADP
ejpam-5909	322	27	supporting	support	VERB
ejpam-5909	322	28	this	this	DET
ejpam-5909	322	29	research	research	NOUN
ejpam-5909	322	30	.	.	PUNCT
ejpam-5909	323	1	additionally	additionally	ADV
ejpam-5909	323	2	,	,	PUNCT
ejpam-5909	323	3	the	the	DET
ejpam-5909	323	4	author(s	author(s	NOUN
ejpam-5909	323	5	)	)	PUNCT
ejpam-5909	323	6	express	express	VERB
ejpam-5909	323	7	their	their	PRON
ejpam-5909	323	8	gratitude	gratitude	NOUN
ejpam-5909	323	9	to	to	ADP
ejpam-5909	323	10	lembaga	lembaga	PROPN
ejpam-5909	323	11	pengelola	pengelola	PROPN
ejpam-5909	323	12	dana	dana	PROPN
ejpam-5909	323	13	pendidikan	pendidikan	PROPN
ejpam-5909	323	14	(	(	PUNCT
ejpam-5909	323	15	lpdp	lpdp	ADJ
ejpam-5909	323	16	)	)	PUNCT
ejpam-5909	323	17	and	and	CCONJ
ejpam-5909	323	18	balai	balai	PROPN
ejpam-5909	323	19	pembiayaan	pembiayaan	PROPN
ejpam-5909	323	20	pendidikan	pendidikan	PROPN
ejpam-5909	323	21	tinggi	tinggi	PROPN
ejpam-5909	323	22	(	(	PUNCT
ejpam-5909	323	23	bppt	bppt	PROPN
ejpam-5909	323	24	)	)	PUNCT
ejpam-5909	323	25	indonesia	indonesia	PROPN
ejpam-5909	323	26	for	for	ADP
ejpam-5909	323	27	their	their	PRON
ejpam-5909	323	28	financial	financial	ADJ
ejpam-5909	323	29	support	support	NOUN
ejpam-5909	323	30	of	of	ADP
ejpam-5909	323	31	this	this	DET
ejpam-5909	323	32	research	research	NOUN
ejpam-5909	323	33	.	.	PUNCT
ejpam-5909	324	1	references	reference	NOUN
ejpam-5909	324	2	[	[	X
ejpam-5909	324	3	1	1	NUM
ejpam-5909	324	4	]	]	X
ejpam-5909	324	5	umi	umi	PROPN
ejpam-5909	324	6	mahnuna	mahnuna	PROPN
ejpam-5909	324	7	hanung	hanung	PROPN
ejpam-5909	324	8	and	and	CCONJ
ejpam-5909	324	9	ch	ch	PROPN
ejpam-5909	324	10	rini	rini	PROPN
ejpam-5909	324	11	indrati	indrati	PROPN
ejpam-5909	324	12	.	.	PUNCT
ejpam-5909	325	1	integral	integral	ADJ
ejpam-5909	325	2	henstock	henstock	NOUN
ejpam-5909	325	3	-	-	PUNCT
ejpam-5909	325	4	stieltjes	stieltjes	PROPN
ejpam-5909	325	5	fungsi	fungsi	PROPN
ejpam-5909	325	6	bernilai	bernilai	PROPN
ejpam-5909	325	7	vektor	vektor	PROPN
ejpam-5909	325	8	.	.	PUNCT
ejpam-5909	326	1	pythagoras	pythagoras	PROPN
ejpam-5909	326	2	jurnal	jurnal	PROPN
ejpam-5909	326	3	pendidikan	pendidikan	PROPN
ejpam-5909	326	4	matematika	matematika	PROPN
ejpam-5909	326	5	,	,	PUNCT
ejpam-5909	326	6	5(2	5(2	NUM
ejpam-5909	326	7	)	)	PUNCT
ejpam-5909	326	8	,	,	PUNCT
ejpam-5909	326	9	2009	2009	NUM
ejpam-5909	326	10	.	.	PUNCT
ejpam-5909	327	1	[	[	X
ejpam-5909	327	2	2	2	NUM
ejpam-5909	327	3	]	]	X
ejpam-5909	327	4	neva	neva	PROPN
ejpam-5909	327	5	satyahadewi	satyahadewi	PROPN
ejpam-5909	327	6	widyawati	widyawati	PROPN
ejpam-5909	327	7	,	,	PUNCT
ejpam-5909	327	8	evy	evy	PROPN
ejpam-5909	327	9	sulistianingsih	sulistianingsih	PROPN
ejpam-5909	327	10	,	,	PUNCT
ejpam-5909	327	11	et	et	PROPN
ejpam-5909	327	12	al	al	PROPN
ejpam-5909	327	13	.	.	PROPN
ejpam-5909	327	14	penggunaan	penggunaan	PROPN
ejpam-5909	327	15	model	model	PROPN
ejpam-5909	327	16	black	black	PROPN
ejpam-5909	327	17	scholes	scholes	PROPN
ejpam-5909	327	18	untuk	untuk	PROPN
ejpam-5909	327	19	penentuan	penentuan	PROPN
ejpam-5909	328	1	harga	harga	PROPN
ejpam-5909	328	2	opsi	opsi	PROPN
ejpam-5909	328	3	jual	jual	PROPN
ejpam-5909	328	4	tipe	tipe	PROPN
ejpam-5909	328	5	eropa	eropa	PROPN
ejpam-5909	328	6	.	.	PUNCT
ejpam-5909	329	1	bimaster	bimaster	NOUN
ejpam-5909	329	2	:	:	PUNCT
ejpam-5909	329	3	buletin	buletin	PROPN
ejpam-5909	329	4	ilmiah	ilmiah	PROPN
ejpam-5909	329	5	matematika	matematika	PROPN
ejpam-5909	329	6	,	,	PUNCT
ejpam-5909	329	7	statistika	statistika	PROPN
ejpam-5909	329	8	dan	dan	PROPN
ejpam-5909	329	9	terapannya	terapannya	PROPN
ejpam-5909	329	10	,	,	PUNCT
ejpam-5909	329	11	2(1	2(1	NUM
ejpam-5909	329	12	)	)	PUNCT
ejpam-5909	329	13	,	,	PUNCT
ejpam-5909	329	14	2013	2013	NUM
ejpam-5909	329	15	.	.	PUNCT
ejpam-5909	330	1	[	[	X
ejpam-5909	330	2	3	3	X
ejpam-5909	330	3	]	]	X
ejpam-5909	330	4	toto	toto	NOUN
ejpam-5909	330	5	supriyono	supriyono	PROPN
ejpam-5909	330	6	.	.	PUNCT
ejpam-5909	331	1	mekanika	mekanika	PROPN
ejpam-5909	331	2	fluida	fluida	PROPN
ejpam-5909	331	3	lanjut	lanjut	PROPN
ejpam-5909	331	4	,	,	PUNCT
ejpam-5909	331	5	2021	2021	NUM
ejpam-5909	331	6	.	.	PUNCT
ejpam-5909	332	1	[	[	X
ejpam-5909	332	2	4	4	NUM
ejpam-5909	332	3	]	]	SYM
ejpam-5909	332	4	s	s	PROPN
ejpam-5909	332	5	pd	pd	PROPN
ejpam-5909	332	6	usman	usman	PROPN
ejpam-5909	332	7	,	,	PUNCT
ejpam-5909	332	8	m	m	PROPN
ejpam-5909	332	9	patima	patima	PROPN
ejpam-5909	332	10	,	,	PUNCT
ejpam-5909	332	11	s	s	PART
ejpam-5909	332	12	pd	pd	PROPN
ejpam-5909	332	13	puspapratiwi	puspapratiwi	PROPN
ejpam-5909	332	14	,	,	PUNCT
ejpam-5909	332	15	et	et	PROPN
ejpam-5909	332	16	al	al	PROPN
ejpam-5909	332	17	.	.	PUNCT
ejpam-5909	333	1	buku	buku	PROPN
ejpam-5909	333	2	referensi	referensi	PROPN
ejpam-5909	333	3	matematika	matematika	PROPN
ejpam-5909	333	4	terapan	terapan	PROPN
ejpam-5909	333	5	,	,	PUNCT
ejpam-5909	333	6	2024	2024	NUM
ejpam-5909	333	7	.	.	PUNCT
ejpam-5909	334	1	[	[	X
ejpam-5909	334	2	5	5	NUM
ejpam-5909	334	3	]	]	PUNCT
ejpam-5909	334	4	miftahul	miftahul	PROPN
ejpam-5909	334	5	fikri	fikri	PROPN
ejpam-5909	334	6	,	,	PUNCT
ejpam-5909	334	7	samsurizal	samsurizal	PROPN
ejpam-5909	334	8	samsurizal	samsurizal	PROPN
ejpam-5909	334	9	,	,	PUNCT
ejpam-5909	334	10	and	and	CCONJ
ejpam-5909	334	11	andi	andi	PROPN
ejpam-5909	334	12	makkulau	makkulau	PROPN
ejpam-5909	334	13	.	.	PUNCT
ejpam-5909	335	1	perbandingan	perbandingan	ADJ
ejpam-5909	335	2	penyelesaian	penyelesaian	PROPN
ejpam-5909	335	3	integral	integral	ADJ
ejpam-5909	335	4	riemann	riemann	PROPN
ejpam-5909	335	5	,	,	PUNCT
ejpam-5909	335	6	lebesgue	lebesgue	PROPN
ejpam-5909	335	7	dan	dan	PROPN
ejpam-5909	335	8	hk	hk	PROPN
ejpam-5909	335	9	berdasarkan	berdasarkan	PROPN
ejpam-5909	335	10	definisi	definisi	PROPN
ejpam-5909	335	11	.	.	PUNCT
ejpam-5909	336	1	limits	limit	NOUN
ejpam-5909	336	2	:	:	PUNCT
ejpam-5909	336	3	journal	journal	NOUN
ejpam-5909	336	4	of	of	ADP
ejpam-5909	336	5	mathematics	mathematic	NOUN
ejpam-5909	336	6	and	and	CCONJ
ejpam-5909	336	7	its	its	PRON
ejpam-5909	336	8	applications	application	NOUN
ejpam-5909	336	9	,	,	PUNCT
ejpam-5909	336	10	18(2):169–186	18(2):169–186	PROPN
ejpam-5909	336	11	,	,	PUNCT
ejpam-5909	336	12	2021	2021	NUM
ejpam-5909	336	13	.	.	PUNCT
ejpam-5909	337	1	[	[	X
ejpam-5909	337	2	6	6	NUM
ejpam-5909	337	3	]	]	X
ejpam-5909	337	4	firdaus	firdaus	PROPN
ejpam-5909	337	5	ubaidillah	ubaidillah	PROPN
ejpam-5909	337	6	,	,	PUNCT
ejpam-5909	337	7	soeparna	soeparna	NOUN
ejpam-5909	337	8	darmawijaya	darmawijaya	NOUN
ejpam-5909	337	9	,	,	PUNCT
ejpam-5909	337	10	and	and	CCONJ
ejpam-5909	337	11	r	r	NOUN
ejpam-5909	337	12	indrati	indrati	NOUN
ejpam-5909	337	13	.	.	PUNCT
ejpam-5909	338	1	integral	integral	ADJ
ejpam-5909	338	2	henstockkurzweil	henstockkurzweil	PROPN
ejpam-5909	338	3	fungsi	fungsi	PROPN
ejpam-5909	338	4	bernilai	bernilai	PROPN
ejpam-5909	338	5	c	c	PROPN
ejpam-5909	339	1	[	[	X
ejpam-5909	339	2	a	a	X
ejpam-5909	339	3	,	,	PUNCT
ejpam-5909	339	4	b	b	NOUN
ejpam-5909	339	5	]	]	X
ejpam-5909	339	6	:	:	PUNCT
ejpam-5909	339	7	teorema	teorema	PROPN
ejpam-5909	339	8	kekonvergenan	kekonvergenan	VERB
ejpam-5909	339	9	seragam	seragam	PROPN
ejpam-5909	339	10	.	.	PUNCT
ejpam-5909	340	1	prosiding	proside	VERB
ejpam-5909	340	2	knm	knm	PROPN
ejpam-5909	340	3	xvii	xvii	PROPN
ejpam-5909	340	4	,	,	PUNCT
ejpam-5909	340	5	pages	page	NOUN
ejpam-5909	340	6	1–7	1–7	NUM
ejpam-5909	340	7	,	,	PUNCT
ejpam-5909	340	8	2014	2014	NUM
ejpam-5909	340	9	.	.	PUNCT
ejpam-5909	341	1	m.	m.	NOUN
ejpam-5909	341	2	alifuddin	alifuddin	VERB
ejpam-5909	341	3	et	et	PROPN
ejpam-5909	341	4	al	al	PROPN
ejpam-5909	341	5	.	.	PUNCT
ejpam-5909	341	6	/	/	SYM
ejpam-5909	341	7	eur	eur	PROPN
ejpam-5909	341	8	.	.	PUNCT
ejpam-5909	342	1	j.	j.	PROPN
ejpam-5909	342	2	pure	pure	PROPN
ejpam-5909	342	3	appl	appl	PROPN
ejpam-5909	342	4	.	.	PROPN
ejpam-5909	342	5	math	math	PROPN
ejpam-5909	342	6	,	,	PUNCT
ejpam-5909	342	7	18	18	NUM
ejpam-5909	342	8	(	(	PUNCT
ejpam-5909	342	9	2	2	NUM
ejpam-5909	342	10	)	)	PUNCT
ejpam-5909	342	11	(	(	PUNCT
ejpam-5909	342	12	2025	2025	NUM
ejpam-5909	342	13	)	)	PUNCT
ejpam-5909	342	14	,	,	PUNCT
ejpam-5909	342	15	5909	5909	NUM
ejpam-5909	342	16	17	17	NUM
ejpam-5909	342	17	of	of	ADP
ejpam-5909	342	18	17	17	NUM
ejpam-5909	342	19	[	[	SYM
ejpam-5909	342	20	7	7	NUM
ejpam-5909	342	21	]	]	X
ejpam-5909	342	22	riva	riva	PROPN
ejpam-5909	342	23	yasin	yasin	PROPN
ejpam-5909	342	24	nurandini	nurandini	PROPN
ejpam-5909	342	25	,	,	PUNCT
ejpam-5909	342	26	encum	encum	PROPN
ejpam-5909	342	27	sumiaty	sumiaty	PROPN
ejpam-5909	342	28	,	,	PUNCT
ejpam-5909	342	29	and	and	CCONJ
ejpam-5909	342	30	cece	cece	PROPN
ejpam-5909	342	31	kustiawan	kustiawan	PROPN
ejpam-5909	342	32	.	.	PUNCT
ejpam-5909	343	1	integral	integral	ADJ
ejpam-5909	343	2	perron	perron	PROPN
ejpam-5909	343	3	dan	dan	PROPN
ejpam-5909	343	4	ekuivalensinya	ekuivalensinya	PROPN
ejpam-5909	343	5	dengan	dengan	PROPN
ejpam-5909	343	6	integral	integral	ADJ
ejpam-5909	343	7	denjoy	denjoy	PROPN
ejpam-5909	343	8	.	.	PUNCT
ejpam-5909	344	1	jurnal	jurnal	ADJ
ejpam-5909	344	2	eurekamatika	eurekamatika	PROPN
ejpam-5909	344	3	,	,	PUNCT
ejpam-5909	344	4	6(2):12–24	6(2):12–24	NUM
ejpam-5909	344	5	,	,	PUNCT
ejpam-5909	344	6	2018	2018	NUM
ejpam-5909	344	7	.	.	PUNCT
ejpam-5909	345	1	[	[	X
ejpam-5909	345	2	8	8	NUM
ejpam-5909	345	3	]	]	X
ejpam-5909	345	4	develin	develin	NOUN
ejpam-5909	345	5	o	o	NOUN
ejpam-5909	345	6	omayan	omayan	NOUN
ejpam-5909	345	7	and	and	CCONJ
ejpam-5909	345	8	greig	greig	PROPN
ejpam-5909	345	9	bates	bates	PROPN
ejpam-5909	345	10	c	c	PROPN
ejpam-5909	345	11	flores	flores	PROPN
ejpam-5909	345	12	.	.	PUNCT
ejpam-5909	346	1	some	some	DET
ejpam-5909	346	2	fundamental	fundamental	ADJ
ejpam-5909	346	3	properties	property	NOUN
ejpam-5909	346	4	of	of	ADP
ejpam-5909	346	5	variational	variational	ADJ
ejpam-5909	346	6	kurzweil	kurzweil	NOUN
ejpam-5909	346	7	-	-	PUNCT
ejpam-5909	346	8	henstock	henstock	NOUN
ejpam-5909	346	9	-	-	PUNCT
ejpam-5909	346	10	stieltjes	stieltjes	NOUN
ejpam-5909	346	11	integral	integral	ADJ
ejpam-5909	346	12	on	on	ADP
ejpam-5909	346	13	a	a	DET
ejpam-5909	346	14	compact	compact	ADJ
ejpam-5909	346	15	interval	interval	NOUN
ejpam-5909	346	16	in	in	ADP
ejpam-5909	346	17	rn.asianresearchjournalofmathematics	rn.asianresearchjournalofmathematic	NOUN
ejpam-5909	346	18	,	,	PUNCT
ejpam-5909	346	19	18(9	18(9	NOUN
ejpam-5909	346	20	)	)	PUNCT
ejpam-5909	346	21	:	:	PUNCT
ejpam-5909	346	22	69−−81	69−−81	NUM
ejpam-5909	346	23	,	,	PUNCT
ejpam-5909	346	24	2022	2022	NUM
ejpam-5909	346	25	.	.	PUNCT
ejpam-5909	347	1	[	[	X
ejpam-5909	347	2	9	9	NUM
ejpam-5909	347	3	]	]	X
ejpam-5909	347	4	septian	septian	ADJ
ejpam-5909	347	5	pirade	pirade	NOUN
ejpam-5909	347	6	,	,	PUNCT
ejpam-5909	347	7	tohap	tohap	NOUN
ejpam-5909	347	8	manurung	manurung	PROPN
ejpam-5909	347	9	,	,	PUNCT
ejpam-5909	347	10	and	and	CCONJ
ejpam-5909	347	11	jullia	jullia	PROPN
ejpam-5909	347	12	titaley	titaley	PROPN
ejpam-5909	347	13	.	.	PUNCT
ejpam-5909	348	1	integral	integral	ADJ
ejpam-5909	348	2	riemann	riemann	PROPN
ejpam-5909	348	3	-	-	PUNCT
ejpam-5909	348	4	stieltjes	stieltjes	PROPN
ejpam-5909	348	5	pada	pada	PROPN
ejpam-5909	348	6	fungsi	fungsi	PROPN
ejpam-5909	348	7	bernilai	bernilai	PROPN
ejpam-5909	348	8	real	real	PROPN
ejpam-5909	348	9	.	.	PUNCT
ejpam-5909	349	1	d’cartesian	d’cartesian	ADJ
ejpam-5909	349	2	:	:	PUNCT
ejpam-5909	349	3	jurnal	jurnal	ADJ
ejpam-5909	349	4	matematika	matematika	PROPN
ejpam-5909	349	5	dan	dan	PROPN
ejpam-5909	349	6	aplikasi	aplikasi	PROPN
ejpam-5909	349	7	,	,	PUNCT
ejpam-5909	349	8	6(1):1–7	6(1):1–7	NUM
ejpam-5909	349	9	,	,	PUNCT
ejpam-5909	349	10	2017	2017	NUM
ejpam-5909	349	11	.	.	PUNCT
ejpam-5909	350	1	[	[	X
ejpam-5909	350	2	10	10	NUM
ejpam-5909	350	3	]	]	X
ejpam-5909	350	4	kalfin	kalfin	NOUN
ejpam-5909	350	5	muchtar	muchtar	PROPN
ejpam-5909	350	6	,	,	PUNCT
ejpam-5909	350	7	jullia	jullia	PROPN
ejpam-5909	350	8	titaley	titaley	NOUN
ejpam-5909	350	9	,	,	PUNCT
ejpam-5909	350	10	and	and	CCONJ
ejpam-5909	350	11	mans	mans	PROPN
ejpam-5909	350	12	mananohas	mananoha	NOUN
ejpam-5909	350	13	.	.	PUNCT
ejpam-5909	351	1	integral	integral	ADJ
ejpam-5909	351	2	baire-1	baire-1	PROPN
ejpam-5909	351	3	stieltjes	stieltjes	PROPN
ejpam-5909	351	4	,	,	PUNCT
ejpam-5909	351	5	henstock	henstock	NOUN
ejpam-5909	351	6	-	-	PUNCT
ejpam-5909	351	7	stieltjes	stieltjes	PROPN
ejpam-5909	351	8	dan	dan	PROPN
ejpam-5909	351	9	riemann	riemann	PROPN
ejpam-5909	351	10	-	-	PUNCT
ejpam-5909	351	11	stieltjes	stieltjes	PROPN
ejpam-5909	351	12	.	.	PUNCT
ejpam-5909	352	1	d’cartesian	d’cartesian	NOUN
ejpam-5909	352	2	,	,	PUNCT
ejpam-5909	352	3	5(1):7–12	5(1):7–12	NUM
ejpam-5909	352	4	,	,	PUNCT
ejpam-5909	352	5	2016	2016	NUM
ejpam-5909	352	6	.	.	PUNCT
ejpam-5909	353	1	[	[	X
ejpam-5909	353	2	11	11	NUM
ejpam-5909	353	3	]	]	PUNCT
ejpam-5909	353	4	gregory	gregory	PROPN
ejpam-5909	353	5	convertito	convertito	PROPN
ejpam-5909	353	6	and	and	CCONJ
ejpam-5909	353	7	david	david	PROPN
ejpam-5909	353	8	cruz	cruz	PROPN
ejpam-5909	353	9	-	-	PUNCT
ejpam-5909	353	10	uribe	uribe	PROPN
ejpam-5909	353	11	.	.	PUNCT
ejpam-5909	354	1	the	the	DET
ejpam-5909	354	2	stieltjes	stieltjes	PROPN
ejpam-5909	354	3	integral	integral	ADJ
ejpam-5909	354	4	.	.	PUNCT
ejpam-5909	355	1	chapman	chapman	NOUN
ejpam-5909	355	2	and	and	CCONJ
ejpam-5909	355	3	hall	hall	PROPN
ejpam-5909	355	4	/	/	SYM
ejpam-5909	355	5	crc	crc	NOUN
ejpam-5909	355	6	,	,	PUNCT
ejpam-5909	355	7	2023	2023	NUM
ejpam-5909	355	8	.	.	PUNCT
ejpam-5909	356	1	[	[	X
ejpam-5909	356	2	12	12	NUM
ejpam-5909	356	3	]	]	X
ejpam-5909	356	4	joong	joong	PROPN
ejpam-5909	356	5	kwoen	kwoen	PROPN
ejpam-5909	356	6	lee	lee	PROPN
ejpam-5909	356	7	and	and	CCONJ
ejpam-5909	356	8	han	han	PROPN
ejpam-5909	356	9	ju	ju	PROPN
ejpam-5909	356	10	lee	lee	PROPN
ejpam-5909	356	11	.	.	PUNCT
ejpam-5909	357	1	riemann	riemann	PROPN
ejpam-5909	357	2	-	-	PUNCT
ejpam-5909	357	3	stieltjes	stieltjes	PROPN
ejpam-5909	357	4	integrals	integral	NOUN
ejpam-5909	357	5	and	and	CCONJ
ejpam-5909	357	6	their	their	PRON
ejpam-5909	357	7	representing	represent	VERB
ejpam-5909	357	8	measures	measure	NOUN
ejpam-5909	357	9	.	.	PUNCT
ejpam-5909	358	1	the	the	DET
ejpam-5909	358	2	pure	pure	ADJ
ejpam-5909	358	3	and	and	CCONJ
ejpam-5909	358	4	applied	applied	ADJ
ejpam-5909	358	5	mathematics	mathematic	NOUN
ejpam-5909	358	6	,	,	PUNCT
ejpam-5909	358	7	31(4):453–476	31(4):453–476	PROPN
ejpam-5909	358	8	,	,	PUNCT
ejpam-5909	358	9	2024	2024	NUM
ejpam-5909	358	10	.	.	PUNCT
ejpam-5909	359	1	[	[	X
ejpam-5909	359	2	13	13	NUM
ejpam-5909	359	3	]	]	X
ejpam-5909	359	4	andrew	andrew	PROPN
ejpam-5909	359	5	felix	felix	PROPN
ejpam-5909	359	6	iv	iv	PROPN
ejpam-5909	359	7	suarez	suarez	PROPN
ejpam-5909	359	8	cunanan	cunanan	PROPN
ejpam-5909	359	9	and	and	CCONJ
ejpam-5909	359	10	julius	julius	PROPN
ejpam-5909	359	11	benitez	benitez	PROPN
ejpam-5909	359	12	.	.	PUNCT
ejpam-5909	360	1	simple	simple	ADJ
ejpam-5909	360	2	properties	property	NOUN
ejpam-5909	360	3	and	and	CCONJ
ejpam-5909	360	4	existence	existence	NOUN
ejpam-5909	360	5	theorem	theorem	VERB
ejpam-5909	360	6	for	for	ADP
ejpam-5909	360	7	the	the	DET
ejpam-5909	360	8	henstock	henstock	NOUN
ejpam-5909	360	9	-	-	PUNCT
ejpam-5909	360	10	kurzweil	kurzweil	NOUN
ejpam-5909	360	11	-	-	PUNCT
ejpam-5909	360	12	stieltjes	stieltjes	NOUN
ejpam-5909	360	13	integral	integral	ADJ
ejpam-5909	360	14	of	of	ADP
ejpam-5909	360	15	functions	function	NOUN
ejpam-5909	360	16	taking	take	VERB
ejpam-5909	360	17	values	value	NOUN
ejpam-5909	360	18	on	on	ADP
ejpam-5909	360	19	c	c	PROPN
ejpam-5909	360	20	[	[	X
ejpam-5909	360	21	a	a	X
ejpam-5909	360	22	,	,	PUNCT
ejpam-5909	360	23	b	b	NOUN
ejpam-5909	360	24	]	]	X
ejpam-5909	360	25	space	space	NOUN
ejpam-5909	360	26	-	-	PUNCT
ejpam-5909	360	27	valued	value	VERB
ejpam-5909	360	28	functions	function	NOUN
ejpam-5909	360	29	.	.	PUNCT
ejpam-5909	361	1	european	european	ADJ
ejpam-5909	361	2	journal	journal	PROPN
ejpam-5909	361	3	of	of	ADP
ejpam-5909	361	4	pure	pure	ADJ
ejpam-5909	361	5	and	and	CCONJ
ejpam-5909	361	6	applied	applied	ADJ
ejpam-5909	361	7	mathematics	mathematic	NOUN
ejpam-5909	361	8	,	,	PUNCT
ejpam-5909	361	9	13(1):130–143	13(1):130–143	PROPN
ejpam-5909	361	10	,	,	PUNCT
ejpam-5909	361	11	2020	2020	NUM
ejpam-5909	361	12	.	.	PUNCT
ejpam-5909	362	1	[	[	X
ejpam-5909	362	2	14	14	NUM
ejpam-5909	362	3	]	]	X
ejpam-5909	362	4	firdaus	firdaus	PROPN
ejpam-5909	362	5	ubaidillah	ubaidillah	PROPN
ejpam-5909	362	6	,	,	PUNCT
ejpam-5909	362	7	soeparna	soeparna	NOUN
ejpam-5909	362	8	darmawijaya	darmawijaya	NOUN
ejpam-5909	362	9	,	,	PUNCT
ejpam-5909	362	10	and	and	CCONJ
ejpam-5909	362	11	ch	ch	NOUN
ejpam-5909	362	12	i	i	PROPN
ejpam-5909	362	13	rini	rini	PROPN
ejpam-5909	362	14	.	.	PROPN
ejpam-5909	363	1	on	on	ADP
ejpam-5909	363	2	the	the	DET
ejpam-5909	363	3	henstock	henstock	NOUN
ejpam-5909	363	4	-	-	PUNCT
ejpam-5909	363	5	kurzweil	kurzweil	NOUN
ejpam-5909	363	6	integral	integral	ADJ
ejpam-5909	363	7	of	of	ADP
ejpam-5909	363	8	c	c	PROPN
ejpam-5909	363	9	[	[	X
ejpam-5909	363	10	a	a	X
ejpam-5909	363	11	;	;	PUNCT
ejpam-5909	363	12	b	b	X
ejpam-5909	363	13	]	]	X
ejpam-5909	363	14	space	space	NOUN
ejpam-5909	363	15	-	-	PUNCT
ejpam-5909	363	16	valued	value	VERB
ejpam-5909	363	17	functions	function	NOUN
ejpam-5909	363	18	.	.	PUNCT
ejpam-5909	364	1	int	int	NOUN
ejpam-5909	364	2	.	.	PUNCT
ejpam-5909	365	1	j.	j.	PROPN
ejpam-5909	365	2	math	math	PROPN
ejpam-5909	365	3	.	.	PUNCT
ejpam-5909	366	1	an	an	PRON
ejpam-5909	366	2	,	,	PUNCT
ejpam-5909	366	3	9(37):1831–1846	9(37):1831–1846	NUM
ejpam-5909	366	4	,	,	PUNCT
ejpam-5909	366	5	2015	2015	NUM
ejpam-5909	366	6	.	.	PUNCT
ejpam-5909	367	1	[	[	X
ejpam-5909	367	2	15	15	NUM
ejpam-5909	367	3	]	]	X
ejpam-5909	367	4	firdaus	firdaus	PROPN
ejpam-5909	367	5	ubaidillah	ubaidillah	PROPN
ejpam-5909	367	6	,	,	PUNCT
ejpam-5909	367	7	soeparna	soeparna	NOUN
ejpam-5909	367	8	darmawijaya	darmawijaya	NOUN
ejpam-5909	367	9	,	,	PUNCT
ejpam-5909	367	10	and	and	CCONJ
ejpam-5909	367	11	rini	rini	PROPN
ejpam-5909	367	12	indrati	indrati	PROPN
ejpam-5909	367	13	.	.	PUNCT
ejpam-5909	368	1	kekonvergenan	kekonvergenan	PROPN
ejpam-5909	368	2	barisan	barisan	PROPN
ejpam-5909	368	3	di	di	PROPN
ejpam-5909	368	4	dalam	dalam	PROPN
ejpam-5909	368	5	ruang	ruang	PROPN
ejpam-5909	368	6	fungsi	fungsi	PROPN
ejpam-5909	368	7	kontinu	kontinu	PROPN
ejpam-5909	368	8	c	c	PROPN
ejpam-5909	369	1	[	[	X
ejpam-5909	369	2	a	a	X
ejpam-5909	369	3	,	,	PUNCT
ejpam-5909	369	4	b	b	NOUN
ejpam-5909	369	5	]	]	PUNCT
ejpam-5909	369	6	.	.	PUNCT
ejpam-5909	370	1	cauchy	cauchy	PROPN
ejpam-5909	370	2	:	:	PUNCT
ejpam-5909	370	3	jurnal	jurnal	ADJ
ejpam-5909	370	4	matematika	matematika	PROPN
ejpam-5909	370	5	murni	murni	PROPN
ejpam-5909	370	6	dan	dan	PROPN
ejpam-5909	370	7	aplikasi	aplikasi	PROPN
ejpam-5909	370	8	,	,	PUNCT
ejpam-5909	370	9	2(4):184–188	2(4):184–188	NUM
ejpam-5909	370	10	,	,	PUNCT
ejpam-5909	370	11	2013	2013	NUM
ejpam-5909	370	12	.	.	PUNCT