id	sid	tid	token	lemma	pos
ejpam-5565	1	1	european	european	PROPN
ejpam-5565	1	2	journal	journal	PROPN
ejpam-5565	1	3	of	of	ADP
ejpam-5565	1	4	pure	pure	ADJ
ejpam-5565	1	5	and	and	CCONJ
ejpam-5565	1	6	applied	applied	ADJ
ejpam-5565	1	7	mathematics	mathematic	NOUN
ejpam-5565	1	8	2025	2025	NUM
ejpam-5565	1	9	,	,	PUNCT
ejpam-5565	1	10	vol	vol	NOUN
ejpam-5565	1	11	.	.	PROPN
ejpam-5565	1	12	18	18	NUM
ejpam-5565	1	13	,	,	PUNCT
ejpam-5565	1	14	issue	issue	NOUN
ejpam-5565	1	15	2	2	NUM
ejpam-5565	1	16	,	,	PUNCT
ejpam-5565	1	17	article	article	NOUN
ejpam-5565	1	18	number	number	NOUN
ejpam-5565	1	19	5565	5565	NUM
ejpam-5565	1	20	issn	issn	VERB
ejpam-5565	1	21	1307	1307	NUM
ejpam-5565	1	22	-	-	SYM
ejpam-5565	1	23	5543	5543	NUM
ejpam-5565	1	24	–	–	PUNCT
ejpam-5565	1	25	ejpam.com	ejpam.com	X
ejpam-5565	1	26	published	publish	VERB
ejpam-5565	1	27	by	by	ADP
ejpam-5565	1	28	new	new	PROPN
ejpam-5565	1	29	york	york	PROPN
ejpam-5565	1	30	business	business	PROPN
ejpam-5565	1	31	global	global	PROPN
ejpam-5565	1	32	bounded	bound	VERB
ejpam-5565	1	33	q	q	ADJ
ejpam-5565	1	34	-	-	PUNCT
ejpam-5565	1	35	variation	variation	NOUN
ejpam-5565	1	36	functions	function	NOUN
ejpam-5565	1	37	in	in	ADP
ejpam-5565	1	38	spaces	space	NOUN
ejpam-5565	1	39	with	with	ADP
ejpam-5565	1	40	indefinite	indefinite	ADJ
ejpam-5565	1	41	metric	metric	ADJ
ejpam-5565	1	42	osmin	osmin	NOUN
ejpam-5565	1	43	ferrer	ferrer	PROPN
ejpam-5565	1	44	villar1,∗	villar1,∗	PROPN
ejpam-5565	1	45	,	,	PUNCT
ejpam-5565	1	46	josé	josé	ADJ
ejpam-5565	1	47	naranjo	naranjo	PROPN
ejpam-5565	1	48	mart́ınez2	mart́ınez2	PROPN
ejpam-5565	1	49	1	1	NUM
ejpam-5565	1	50	departament	departament	NOUN
ejpam-5565	1	51	of	of	ADP
ejpam-5565	1	52	mathematics	mathematic	NOUN
ejpam-5565	1	53	,	,	PUNCT
ejpam-5565	1	54	university	university	NOUN
ejpam-5565	1	55	of	of	ADP
ejpam-5565	1	56	sucre	sucre	NOUN
ejpam-5565	1	57	,	,	PUNCT
ejpam-5565	1	58	cra	cra	PROPN
ejpam-5565	1	59	.	.	PUNCT
ejpam-5565	2	1	28	28	NUM
ejpam-5565	2	2	#	#	NOUN
ejpam-5565	2	3	5	5	NUM
ejpam-5565	2	4	-	-	SYM
ejpam-5565	2	5	267	267	NUM
ejpam-5565	2	6	,	,	PUNCT
ejpam-5565	2	7	puerta	puerta	PROPN
ejpam-5565	2	8	roja	roja	PROPN
ejpam-5565	2	9	,	,	PUNCT
ejpam-5565	2	10	sincelejo	sincelejo	ADJ
ejpam-5565	2	11	,	,	PUNCT
ejpam-5565	2	12	sucre	sucre	NOUN
ejpam-5565	2	13	,	,	PUNCT
ejpam-5565	2	14	colombia	colombia	PROPN
ejpam-5565	2	15	2	2	NUM
ejpam-5565	2	16	center	center	NOUN
ejpam-5565	2	17	for	for	ADP
ejpam-5565	2	18	basic	basic	ADJ
ejpam-5565	2	19	sciences	science	NOUN
ejpam-5565	2	20	,	,	PUNCT
ejpam-5565	2	21	school	school	NOUN
ejpam-5565	2	22	of	of	ADP
ejpam-5565	2	23	engineering	engineering	NOUN
ejpam-5565	2	24	and	and	CCONJ
ejpam-5565	2	25	architecture	architecture	NOUN
ejpam-5565	2	26	,	,	PUNCT
ejpam-5565	2	27	pontifical	pontifical	ADJ
ejpam-5565	2	28	bolivarian	bolivarian	PROPN
ejpam-5565	2	29	university	university	NOUN
ejpam-5565	2	30	,	,	PUNCT
ejpam-5565	2	31	monteria	monteria	PROPN
ejpam-5565	2	32	,	,	PUNCT
ejpam-5565	2	33	colombia	colombia	PROPN
ejpam-5565	2	34	abstract	abstract	NOUN
ejpam-5565	2	35	.	.	PUNCT
ejpam-5565	3	1	in	in	ADP
ejpam-5565	3	2	this	this	DET
ejpam-5565	3	3	paper	paper	NOUN
ejpam-5565	3	4	we	we	PRON
ejpam-5565	3	5	establish	establish	VERB
ejpam-5565	3	6	the	the	DET
ejpam-5565	3	7	definition	definition	NOUN
ejpam-5565	3	8	of	of	ADP
ejpam-5565	3	9	bounded	bounded	ADJ
ejpam-5565	3	10	q	q	ADJ
ejpam-5565	3	11	-	-	PUNCT
ejpam-5565	3	12	variation	variation	NOUN
ejpam-5565	3	13	functions	function	NOUN
ejpam-5565	3	14	on	on	ADP
ejpam-5565	3	15	krein	krein	ADJ
ejpam-5565	3	16	spaces	space	NOUN
ejpam-5565	3	17	(	(	PUNCT
ejpam-5565	3	18	definition	definition	NOUN
ejpam-5565	3	19	7	7	NUM
ejpam-5565	3	20	)	)	PUNCT
ejpam-5565	3	21	and	and	CCONJ
ejpam-5565	3	22	give	give	VERB
ejpam-5565	3	23	a	a	DET
ejpam-5565	3	24	complete	complete	ADJ
ejpam-5565	3	25	characterisation	characterisation	NOUN
ejpam-5565	3	26	by	by	ADP
ejpam-5565	3	27	comparing	compare	VERB
ejpam-5565	3	28	it	it	PRON
ejpam-5565	3	29	with	with	ADP
ejpam-5565	3	30	bounded	bounded	ADJ
ejpam-5565	3	31	q	q	ADJ
ejpam-5565	3	32	-	-	PUNCT
ejpam-5565	3	33	variation	variation	NOUN
ejpam-5565	3	34	functions	function	NOUN
ejpam-5565	3	35	on	on	ADP
ejpam-5565	3	36	classical	classical	ADJ
ejpam-5565	3	37	hilbert	hilbert	NOUN
ejpam-5565	3	38	spaces	space	NOUN
ejpam-5565	3	39	and	and	CCONJ
ejpam-5565	3	40	with	with	ADP
ejpam-5565	3	41	hilbert	hilbert	NOUN
ejpam-5565	3	42	spaces	space	NOUN
ejpam-5565	3	43	associated	associate	VERB
ejpam-5565	3	44	to	to	ADP
ejpam-5565	3	45	a	a	DET
ejpam-5565	3	46	krein	krein	ADJ
ejpam-5565	3	47	space	space	NOUN
ejpam-5565	3	48	(	(	PUNCT
ejpam-5565	3	49	theorem	theorem	NOUN
ejpam-5565	3	50	6	6	NUM
ejpam-5565	3	51	)	)	PUNCT
ejpam-5565	3	52	.	.	PUNCT
ejpam-5565	4	1	the	the	DET
ejpam-5565	4	2	fundamental	fundamental	ADJ
ejpam-5565	4	3	tools	tool	NOUN
ejpam-5565	4	4	of	of	ADP
ejpam-5565	4	5	the	the	DET
ejpam-5565	4	6	theory	theory	NOUN
ejpam-5565	4	7	of	of	ADP
ejpam-5565	4	8	bounded	bounded	ADJ
ejpam-5565	4	9	q	q	ADJ
ejpam-5565	4	10	-	-	PUNCT
ejpam-5565	4	11	variation	variation	NOUN
ejpam-5565	4	12	functions	function	NOUN
ejpam-5565	4	13	in	in	ADP
ejpam-5565	4	14	the	the	DET
ejpam-5565	4	15	formalism	formalism	NOUN
ejpam-5565	4	16	of	of	ADP
ejpam-5565	4	17	krein	krein	ADJ
ejpam-5565	4	18	spaces	space	NOUN
ejpam-5565	4	19	are	be	AUX
ejpam-5565	4	20	described	describe	VERB
ejpam-5565	4	21	(	(	PUNCT
ejpam-5565	4	22	theorems	theorem	NOUN
ejpam-5565	4	23	7	7	NUM
ejpam-5565	4	24	,	,	PUNCT
ejpam-5565	4	25	8)	8)	NUM
ejpam-5565	4	26	.	.	PUNCT
ejpam-5565	5	1	furthermore	furthermore	ADV
ejpam-5565	5	2	,	,	PUNCT
ejpam-5565	5	3	we	we	PRON
ejpam-5565	5	4	endow	endow	VERB
ejpam-5565	5	5	the	the	DET
ejpam-5565	5	6	spaces	space	NOUN
ejpam-5565	5	7	of	of	ADP
ejpam-5565	5	8	bounded	bounded	ADJ
ejpam-5565	5	9	q	q	ADJ
ejpam-5565	5	10	-	-	PUNCT
ejpam-5565	5	11	variation	variation	NOUN
ejpam-5565	5	12	functions	function	NOUN
ejpam-5565	5	13	in	in	ADP
ejpam-5565	5	14	krein	krein	ADJ
ejpam-5565	5	15	spaces	space	NOUN
ejpam-5565	5	16	with	with	ADP
ejpam-5565	5	17	a	a	DET
ejpam-5565	5	18	norm	norm	NOUN
ejpam-5565	5	19	,	,	PUNCT
ejpam-5565	5	20	which	which	PRON
ejpam-5565	5	21	we	we	PRON
ejpam-5565	5	22	have	have	AUX
ejpam-5565	5	23	called	call	VERB
ejpam-5565	5	24	q	q	NOUN
ejpam-5565	5	25	-	-	PUNCT
ejpam-5565	5	26	norm	norm	NOUN
ejpam-5565	5	27	(	(	PUNCT
ejpam-5565	5	28	theorem	theorem	NOUN
ejpam-5565	5	29	13	13	NUM
ejpam-5565	5	30	)	)	PUNCT
ejpam-5565	5	31	.	.	PUNCT
ejpam-5565	6	1	2020	2020	NUM
ejpam-5565	6	2	mathematics	mathematic	NOUN
ejpam-5565	6	3	subject	subject	NOUN
ejpam-5565	6	4	classifications	classification	NOUN
ejpam-5565	6	5	:	:	PUNCT
ejpam-5565	6	6	46c20	46c20	NUM
ejpam-5565	6	7	,	,	PUNCT
ejpam-5565	6	8	26a45	26a45	NUM
ejpam-5565	6	9	,	,	PUNCT
ejpam-5565	6	10	46b99	46b99	NUM
ejpam-5565	6	11	,	,	PUNCT
ejpam-5565	6	12	47b50	47b50	NUM
ejpam-5565	6	13	key	key	ADJ
ejpam-5565	6	14	words	word	NOUN
ejpam-5565	6	15	and	and	CCONJ
ejpam-5565	6	16	phrases	phrase	NOUN
ejpam-5565	6	17	:	:	PUNCT
ejpam-5565	6	18	krein	krein	ADJ
ejpam-5565	6	19	space	space	NOUN
ejpam-5565	6	20	,	,	PUNCT
ejpam-5565	6	21	fundamental	fundamental	ADJ
ejpam-5565	6	22	symmetry	symmetry	NOUN
ejpam-5565	6	23	,	,	PUNCT
ejpam-5565	6	24	q	q	NOUN
ejpam-5565	6	25	-	-	PUNCT
ejpam-5565	6	26	variation	variation	NOUN
ejpam-5565	6	27	,	,	PUNCT
ejpam-5565	6	28	total	total	ADJ
ejpam-5565	6	29	q	q	NOUN
ejpam-5565	6	30	-	-	PUNCT
ejpam-5565	6	31	variation	variation	NOUN
ejpam-5565	6	32	,	,	PUNCT
ejpam-5565	6	33	bounded	bound	VERB
ejpam-5565	6	34	q	q	NOUN
ejpam-5565	6	35	-	-	PUNCT
ejpam-5565	6	36	variation	variation	NOUN
ejpam-5565	6	37	,	,	PUNCT
ejpam-5565	6	38	q	q	NOUN
ejpam-5565	6	39	-	-	NOUN
ejpam-5565	6	40	norm	norm	NOUN
ejpam-5565	6	41	.	.	PUNCT
ejpam-5565	7	1	1	1	X
ejpam-5565	7	2	.	.	X
ejpam-5565	7	3	introduction	introduction	NOUN
ejpam-5565	7	4	in	in	ADP
ejpam-5565	7	5	1881	1881	NUM
ejpam-5565	7	6	,	,	PUNCT
ejpam-5565	7	7	jordan	jordan	PROPN
ejpam-5565	7	8	discovered	discover	VERB
ejpam-5565	7	9	in	in	ADP
ejpam-5565	7	10	the	the	DET
ejpam-5565	7	11	work	work	NOUN
ejpam-5565	7	12	of	of	ADP
ejpam-5565	7	13	dirichlet	dirichlet	PROPN
ejpam-5565	7	14	the	the	DET
ejpam-5565	7	15	notion	notion	NOUN
ejpam-5565	7	16	of	of	ADP
ejpam-5565	7	17	function	function	NOUN
ejpam-5565	7	18	of	of	ADP
ejpam-5565	7	19	bounded	bounded	ADJ
ejpam-5565	7	20	variation	variation	NOUN
ejpam-5565	7	21	and	and	CCONJ
ejpam-5565	7	22	proves	prove	VERB
ejpam-5565	7	23	that	that	PRON
ejpam-5565	7	24	for	for	ADP
ejpam-5565	7	25	this	this	DET
ejpam-5565	7	26	class	class	NOUN
ejpam-5565	7	27	of	of	ADP
ejpam-5565	7	28	functions	function	NOUN
ejpam-5565	7	29	the	the	DET
ejpam-5565	7	30	fourier	fourier	ADJ
ejpam-5565	7	31	conjecture	conjecture	NOUN
ejpam-5565	7	32	is	be	AUX
ejpam-5565	7	33	valid	valid	ADJ
ejpam-5565	7	34	.	.	PUNCT
ejpam-5565	8	1	he	he	PRON
ejpam-5565	8	2	also	also	ADV
ejpam-5565	8	3	shows	show	VERB
ejpam-5565	8	4	that	that	SCONJ
ejpam-5565	8	5	the	the	DET
ejpam-5565	8	6	function	function	NOUN
ejpam-5565	8	7	f	f	NOUN
ejpam-5565	8	8	:	:	PUNCT
ejpam-5565	9	1	[	[	X
ejpam-5565	9	2	a	a	X
ejpam-5565	9	3	,	,	PUNCT
ejpam-5565	9	4	b	b	NOUN
ejpam-5565	9	5	]	]	X
ejpam-5565	9	6	→	→	PUNCT
ejpam-5565	9	7	r	r	NOUN
ejpam-5565	9	8	has	have	AUX
ejpam-5565	9	9	bounded	bound	VERB
ejpam-5565	9	10	variation	variation	NOUN
ejpam-5565	9	11	on	on	ADP
ejpam-5565	9	12	[	[	X
ejpam-5565	9	13	a	a	X
ejpam-5565	9	14	,	,	PUNCT
ejpam-5565	9	15	b	b	NOUN
ejpam-5565	9	16	]	]	X
ejpam-5565	9	17	if	if	SCONJ
ejpam-5565	9	18	and	and	CCONJ
ejpam-5565	9	19	only	only	ADV
ejpam-5565	9	20	if	if	SCONJ
ejpam-5565	9	21	f	f	PROPN
ejpam-5565	9	22	is	be	AUX
ejpam-5565	9	23	the	the	DET
ejpam-5565	9	24	difference	difference	NOUN
ejpam-5565	9	25	of	of	ADP
ejpam-5565	9	26	monotone	monotone	ADJ
ejpam-5565	9	27	functions	function	NOUN
ejpam-5565	9	28	(	(	PUNCT
ejpam-5565	9	29	nowadays	nowadays	ADV
ejpam-5565	9	30	this	this	DET
ejpam-5565	9	31	result	result	NOUN
ejpam-5565	9	32	is	be	AUX
ejpam-5565	9	33	known	know	VERB
ejpam-5565	9	34	as	as	ADP
ejpam-5565	9	35	jordan	jordan	PROPN
ejpam-5565	9	36	’s	’s	PART
ejpam-5565	9	37	representation	representation	PROPN
ejpam-5565	9	38	theorem	theorem	PROPN
ejpam-5565	9	39	)	)	PUNCT
ejpam-5565	9	40	.	.	PUNCT
ejpam-5565	10	1	the	the	DET
ejpam-5565	10	2	notion	notion	NOUN
ejpam-5565	10	3	of	of	ADP
ejpam-5565	10	4	function	function	NOUN
ejpam-5565	10	5	of	of	ADP
ejpam-5565	10	6	bounded	bounded	ADJ
ejpam-5565	10	7	variation	variation	NOUN
ejpam-5565	10	8	has	have	AUX
ejpam-5565	10	9	been	be	AUX
ejpam-5565	10	10	studied	study	VERB
ejpam-5565	10	11	and	and	CCONJ
ejpam-5565	10	12	generalized	generalize	VERB
ejpam-5565	10	13	in	in	ADP
ejpam-5565	10	14	different	different	ADJ
ejpam-5565	10	15	contexts	contexts	NOUN
ejpam-5565	10	16	,	,	PUNCT
ejpam-5565	10	17	studying	study	VERB
ejpam-5565	10	18	different	different	ADJ
ejpam-5565	10	19	structures	structure	NOUN
ejpam-5565	10	20	and	and	CCONJ
ejpam-5565	10	21	properties	property	NOUN
ejpam-5565	10	22	in	in	ADP
ejpam-5565	10	23	spaces	space	NOUN
ejpam-5565	10	24	with	with	ADP
ejpam-5565	10	25	research	research	NOUN
ejpam-5565	10	26	interest	interest	NOUN
ejpam-5565	10	27	.	.	PUNCT
ejpam-5565	11	1	for	for	ADP
ejpam-5565	11	2	example	example	NOUN
ejpam-5565	11	3	,	,	PUNCT
ejpam-5565	11	4	chistyakov	chistyakov	NOUN
ejpam-5565	11	5	in	in	ADP
ejpam-5565	11	6	[	[	X
ejpam-5565	11	7	1–3	1–3	NOUN
ejpam-5565	11	8	]	]	PUNCT
ejpam-5565	11	9	studied	study	VERB
ejpam-5565	11	10	a	a	DET
ejpam-5565	11	11	concept	concept	NOUN
ejpam-5565	11	12	of	of	ADP
ejpam-5565	11	13	a	a	DET
ejpam-5565	11	14	function	function	NOUN
ejpam-5565	11	15	of	of	ADP
ejpam-5565	11	16	bounded	bounded	ADJ
ejpam-5565	11	17	generalized	generalized	ADJ
ejpam-5565	11	18	variation	variation	NOUN
ejpam-5565	11	19	in	in	ADP
ejpam-5565	11	20	the	the	DET
ejpam-5565	11	21	sense	sense	NOUN
ejpam-5565	11	22	of	of	ADP
ejpam-5565	11	23	jordan	jordan	PROPN
ejpam-5565	11	24	-	-	PUNCT
ejpam-5565	11	25	riesz	riesz	PROPN
ejpam-5565	11	26	-	-	PUNCT
ejpam-5565	11	27	orlicz	orlicz	NOUN
ejpam-5565	11	28	for	for	ADP
ejpam-5565	11	29	functions	function	NOUN
ejpam-5565	11	30	f	f	NOUN
ejpam-5565	11	31	:	:	PUNCT
ejpam-5565	12	1	[	[	X
ejpam-5565	12	2	a	a	X
ejpam-5565	12	3	,	,	PUNCT
ejpam-5565	12	4	b]→	b]→	X
ejpam-5565	12	5	x	x	NOUN
ejpam-5565	12	6	,	,	PUNCT
ejpam-5565	12	7	where	where	SCONJ
ejpam-5565	12	8	x	x	PRON
ejpam-5565	12	9	is	be	AUX
ejpam-5565	12	10	a	a	DET
ejpam-5565	12	11	normed	normed	ADJ
ejpam-5565	12	12	or	or	CCONJ
ejpam-5565	12	13	metric	metric	ADJ
ejpam-5565	12	14	space	space	NOUN
ejpam-5565	12	15	.	.	PUNCT
ejpam-5565	13	1	more	more	ADV
ejpam-5565	13	2	recently	recently	ADV
ejpam-5565	13	3	,	,	PUNCT
ejpam-5565	13	4	the	the	DET
ejpam-5565	13	5	notion	notion	NOUN
ejpam-5565	13	6	of	of	ADP
ejpam-5565	13	7	functions	function	NOUN
ejpam-5565	13	8	of	of	ADP
ejpam-5565	13	9	bounded	bounded	ADJ
ejpam-5565	13	10	variation	variation	NOUN
ejpam-5565	13	11	in	in	ADP
ejpam-5565	13	12	spaces	space	NOUN
ejpam-5565	13	13	with	with	ADP
ejpam-5565	13	14	indefinite	indefinite	ADJ
ejpam-5565	13	15	metric	metric	NOUN
ejpam-5565	13	16	was	be	AUX
ejpam-5565	13	17	introduced	introduce	VERB
ejpam-5565	13	18	by	by	ADP
ejpam-5565	13	19	ferrer	ferrer	PROPN
ejpam-5565	13	20	,	,	PUNCT
ejpam-5565	13	21	guzmán	guzmán	PROPN
ejpam-5565	13	22	and	and	CCONJ
ejpam-5565	13	23	naranjo	naranjo	VERB
ejpam-5565	13	24	in	in	ADP
ejpam-5565	13	25	[	[	X
ejpam-5565	13	26	4	4	NUM
ejpam-5565	13	27	,	,	PUNCT
ejpam-5565	13	28	5	5	NUM
ejpam-5565	13	29	]	]	PUNCT
ejpam-5565	13	30	.	.	PUNCT
ejpam-5565	14	1	furthermore	furthermore	ADV
ejpam-5565	14	2	,	,	PUNCT
ejpam-5565	14	3	functions	function	NOUN
ejpam-5565	14	4	of	of	ADP
ejpam-5565	14	5	bounded	bounded	ADJ
ejpam-5565	14	6	variation	variation	NOUN
ejpam-5565	14	7	have	have	VERB
ejpam-5565	14	8	multiple	multiple	ADJ
ejpam-5565	14	9	applications	application	NOUN
ejpam-5565	14	10	in	in	ADP
ejpam-5565	14	11	various	various	ADJ
ejpam-5565	14	12	fields	field	NOUN
ejpam-5565	14	13	,	,	PUNCT
ejpam-5565	14	14	e.g.	e.g.	ADV
ejpam-5565	14	15	in	in	ADP
ejpam-5565	14	16	image	image	NOUN
ejpam-5565	14	17	processing	processing	NOUN
ejpam-5565	14	18	,	,	PUNCT
ejpam-5565	14	19	brokman	brokman	NOUN
ejpam-5565	14	20	,	,	PUNCT
ejpam-5565	14	21	burger	burger	NOUN
ejpam-5565	14	22	and	and	CCONJ
ejpam-5565	14	23	gilboa	gilboa	NOUN
ejpam-5565	14	24	in	in	ADP
ejpam-5565	14	25	[	[	X
ejpam-5565	14	26	6	6	NUM
ejpam-5565	14	27	]	]	PUNCT
ejpam-5565	14	28	presented	present	VERB
ejpam-5565	14	29	∗corresponding	∗corresponde	VERB
ejpam-5565	14	30	author	author	NOUN
ejpam-5565	14	31	.	.	PUNCT
ejpam-5565	15	1	doi	doi	NOUN
ejpam-5565	15	2	:	:	PUNCT
ejpam-5565	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5565	https://doi.org/10.29020/nybg.ejpam.v18i2.5565	ADV
ejpam-5565	15	4	email	email	NOUN
ejpam-5565	15	5	addresses	address	VERB
ejpam-5565	15	6	:	:	PUNCT
ejpam-5565	15	7	osmin.ferrer@unisucre.edu.co	osmin.ferrer@unisucre.edu.co	INTJ
ejpam-5565	15	8	(	(	PUNCT
ejpam-5565	15	9	o.	o.	PROPN
ejpam-5565	15	10	ferrer	ferrer	PROPN
ejpam-5565	15	11	)	)	PUNCT
ejpam-5565	15	12	,	,	PUNCT
ejpam-5565	16	1	jose.naranjom@upb.edu.co	jose.naranjom@upb.edu.co	PROPN
ejpam-5565	16	2	(	(	PUNCT
ejpam-5565	16	3	j.	j.	PROPN
ejpam-5565	16	4	naranjo	naranjo	PROPN
ejpam-5565	16	5	)	)	PUNCT
ejpam-5565	16	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5565	17	1	1	1	NUM
ejpam-5565	17	2	copyright	copyright	NOUN
ejpam-5565	17	3	:	:	PUNCT
ejpam-5565	17	4	©	©	PROPN
ejpam-5565	17	5	2025	2025	NUM
ejpam-5565	17	6	the	the	DET
ejpam-5565	17	7	author(s	author(s	NOUN
ejpam-5565	17	8	)	)	PUNCT
ejpam-5565	17	9	.	.	PUNCT
ejpam-5565	18	1	(	(	PUNCT
ejpam-5565	18	2	cc	cc	NOUN
ejpam-5565	18	3	by	by	ADP
ejpam-5565	18	4	-	-	PUNCT
ejpam-5565	18	5	nc	nc	PROPN
ejpam-5565	18	6	4.0	4.0	NUM
ejpam-5565	18	7	)	)	PUNCT
ejpam-5565	18	8	o.	o.	PROPN
ejpam-5565	18	9	ferrer	ferrer	PROPN
ejpam-5565	18	10	,	,	PUNCT
ejpam-5565	18	11	j.	j.	PROPN
ejpam-5565	18	12	naranjo	naranjo	PROPN
ejpam-5565	18	13	/	/	SYM
ejpam-5565	18	14	eur	eur	PROPN
ejpam-5565	18	15	.	.	PUNCT
ejpam-5565	19	1	j.	j.	PROPN
ejpam-5565	19	2	pure	pure	PROPN
ejpam-5565	19	3	appl	appl	PROPN
ejpam-5565	19	4	.	.	PROPN
ejpam-5565	19	5	math	math	PROPN
ejpam-5565	19	6	,	,	PUNCT
ejpam-5565	19	7	18	18	NUM
ejpam-5565	19	8	(	(	PUNCT
ejpam-5565	19	9	2	2	NUM
ejpam-5565	19	10	)	)	PUNCT
ejpam-5565	19	11	(	(	PUNCT
ejpam-5565	19	12	2025	2025	NUM
ejpam-5565	19	13	)	)	PUNCT
ejpam-5565	19	14	,	,	PUNCT
ejpam-5565	19	15	5565	5565	NUM
ejpam-5565	19	16	2	2	NUM
ejpam-5565	19	17	of	of	ADP
ejpam-5565	19	18	18	18	NUM
ejpam-5565	19	19	an	an	DET
ejpam-5565	19	20	analysis	analysis	NOUN
ejpam-5565	19	21	of	of	ADP
ejpam-5565	19	22	the	the	DET
ejpam-5565	19	23	total	total	ADJ
ejpam-5565	19	24	-	-	PUNCT
ejpam-5565	19	25	variation	variation	NOUN
ejpam-5565	19	26	(	(	PUNCT
ejpam-5565	19	27	tv	tv	NOUN
ejpam-5565	19	28	)	)	PUNCT
ejpam-5565	19	29	on	on	ADP
ejpam-5565	19	30	non	non	ADJ
ejpam-5565	19	31	-	-	ADJ
ejpam-5565	19	32	euclidean	euclidean	ADJ
ejpam-5565	19	33	parametrized	parametrized	ADJ
ejpam-5565	19	34	surfaces	surface	NOUN
ejpam-5565	19	35	,	,	PUNCT
ejpam-5565	19	36	a	a	DET
ejpam-5565	19	37	natural	natural	ADJ
ejpam-5565	19	38	representation	representation	NOUN
ejpam-5565	19	39	of	of	ADP
ejpam-5565	19	40	the	the	DET
ejpam-5565	19	41	shapes	shape	NOUN
ejpam-5565	19	42	used	use	VERB
ejpam-5565	19	43	in	in	ADP
ejpam-5565	19	44	3d	3d	PROPN
ejpam-5565	19	45	graphics	graphic	NOUN
ejpam-5565	19	46	,	,	PUNCT
ejpam-5565	19	47	see	see	VERB
ejpam-5565	19	48	[	[	X
ejpam-5565	19	49	7	7	NUM
ejpam-5565	19	50	]	]	PUNCT
ejpam-5565	19	51	.	.	PUNCT
ejpam-5565	20	1	among	among	ADP
ejpam-5565	20	2	the	the	DET
ejpam-5565	20	3	results	result	NOUN
ejpam-5565	20	4	achieved	achieve	VERB
ejpam-5565	20	5	in	in	ADP
ejpam-5565	20	6	this	this	DET
ejpam-5565	20	7	research	research	NOUN
ejpam-5565	20	8	is	be	AUX
ejpam-5565	20	9	a	a	DET
ejpam-5565	20	10	new	new	ADJ
ejpam-5565	20	11	way	way	NOUN
ejpam-5565	20	12	to	to	PART
ejpam-5565	20	13	generalize	generalize	VERB
ejpam-5565	20	14	the	the	DET
ejpam-5565	20	15	convexity	convexity	NOUN
ejpam-5565	20	16	of	of	ADP
ejpam-5565	20	17	sets	set	NOUN
ejpam-5565	20	18	from	from	ADP
ejpam-5565	20	19	the	the	DET
ejpam-5565	20	20	plane	plane	NOUN
ejpam-5565	20	21	to	to	ADP
ejpam-5565	20	22	surfaces	surface	NOUN
ejpam-5565	20	23	is	be	AUX
ejpam-5565	20	24	derived	derive	VERB
ejpam-5565	20	25	by	by	ADP
ejpam-5565	20	26	characterizing	characterize	VERB
ejpam-5565	20	27	the	the	DET
ejpam-5565	20	28	tv	tv	NOUN
ejpam-5565	20	29	eigenfunctions	eigenfunction	NOUN
ejpam-5565	20	30	on	on	ADP
ejpam-5565	20	31	surfaces	surface	NOUN
ejpam-5565	20	32	.	.	PUNCT
ejpam-5565	21	1	additionally	additionally	ADV
ejpam-5565	21	2	,	,	PUNCT
ejpam-5565	21	3	bugajewska	bugajewska	NOUN
ejpam-5565	21	4	,	,	PUNCT
ejpam-5565	21	5	bugajewski	bugajewski	NOUN
ejpam-5565	21	6	and	and	CCONJ
ejpam-5565	21	7	hudzik	hudzik	ADV
ejpam-5565	21	8	in	in	ADV
ejpam-5565	21	9	[	[	X
ejpam-5565	21	10	8	8	NUM
ejpam-5565	21	11	]	]	PUNCT
ejpam-5565	21	12	they	they	PRON
ejpam-5565	21	13	investiged	investige	VERB
ejpam-5565	21	14	solutions	solution	NOUN
ejpam-5565	21	15	of	of	ADP
ejpam-5565	21	16	nonlinear	nonlinear	PROPN
ejpam-5565	21	17	hammerstein	hammerstein	PROPN
ejpam-5565	21	18	and	and	CCONJ
ejpam-5565	21	19	volterra−hammerstein	volterra−hammerstein	ADV
ejpam-5565	21	20	integral	integral	ADJ
ejpam-5565	21	21	equations	equation	NOUN
ejpam-5565	21	22	in	in	ADP
ejpam-5565	21	23	the	the	DET
ejpam-5565	21	24	space	space	NOUN
ejpam-5565	21	25	of	of	ADP
ejpam-5565	21	26	functions	function	NOUN
ejpam-5565	21	27	of	of	ADP
ejpam-5565	21	28	bounded	bounded	ADJ
ejpam-5565	21	29	ϕ-variation	ϕ-variation	NOUN
ejpam-5565	21	30	in	in	ADP
ejpam-5565	21	31	the	the	DET
ejpam-5565	21	32	sense	sense	NOUN
ejpam-5565	21	33	of	of	ADP
ejpam-5565	21	34	young	young	ADJ
ejpam-5565	21	35	.	.	PUNCT
ejpam-5565	22	1	later	later	ADV
ejpam-5565	22	2	,	,	PUNCT
ejpam-5565	22	3	bugajewska	bugajewska	NOUN
ejpam-5565	22	4	,	,	PUNCT
ejpam-5565	22	5	bugajewski	bugajewski	NOUN
ejpam-5565	22	6	and	and	CCONJ
ejpam-5565	22	7	lewicki	lewicki	VERB
ejpam-5565	22	8	in	in	ADP
ejpam-5565	22	9	[	[	PUNCT
ejpam-5565	22	10	9	9	NUM
ejpam-5565	22	11	]	]	PUNCT
ejpam-5565	22	12	explored	explore	VERB
ejpam-5565	22	13	with	with	ADP
ejpam-5565	22	14	the	the	DET
ejpam-5565	22	15	superposition	superposition	NOUN
ejpam-5565	22	16	operator	operator	NOUN
ejpam-5565	22	17	as	as	ADV
ejpam-5565	22	18	well	well	ADV
ejpam-5565	22	19	as	as	ADP
ejpam-5565	22	20	with	with	ADP
ejpam-5565	22	21	solutions	solution	NOUN
ejpam-5565	22	22	to	to	ADP
ejpam-5565	22	23	non	non	ADJ
ejpam-5565	22	24	-	-	ADJ
ejpam-5565	22	25	linear	linear	ADJ
ejpam-5565	22	26	integral	integral	ADJ
ejpam-5565	22	27	equations	equation	NOUN
ejpam-5565	22	28	in	in	ADP
ejpam-5565	22	29	spaces	space	NOUN
ejpam-5565	22	30	of	of	ADP
ejpam-5565	22	31	functions	function	NOUN
ejpam-5565	22	32	of	of	ADP
ejpam-5565	22	33	generalized	generalized	ADJ
ejpam-5565	22	34	bounded	bounded	ADJ
ejpam-5565	22	35	ϕ-variation	ϕ-variation	PROPN
ejpam-5565	22	36	.	.	PUNCT
ejpam-5565	23	1	in	in	ADP
ejpam-5565	23	2	the	the	DET
ejpam-5565	23	3	field	field	NOUN
ejpam-5565	23	4	of	of	ADP
ejpam-5565	23	5	nonlinear	nonlinear	ADJ
ejpam-5565	23	6	analysis	analysis	NOUN
ejpam-5565	23	7	,	,	PUNCT
ejpam-5565	23	8	xie	xie	PROPN
ejpam-5565	23	9	,	,	PUNCT
ejpam-5565	23	10	liu	liu	PROPN
ejpam-5565	23	11	,	,	PUNCT
ejpam-5565	23	12	li	li	PROPN
ejpam-5565	23	13	and	and	CCONJ
ejpam-5565	23	14	huang	huang	PROPN
ejpam-5565	23	15	in	in	ADP
ejpam-5565	23	16	[	[	X
ejpam-5565	23	17	10	10	NUM
ejpam-5565	23	18	]	]	PUNCT
ejpam-5565	23	19	they	they	PRON
ejpam-5565	23	20	examine	examine	VERB
ejpam-5565	23	21	the	the	DET
ejpam-5565	23	22	bounded	bounded	ADJ
ejpam-5565	23	23	variation	variation	NOUN
ejpam-5565	23	24	capacity	capacity	NOUN
ejpam-5565	23	25	(	(	PUNCT
ejpam-5565	23	26	bv	bv	NOUN
ejpam-5565	23	27	capacity	capacity	NOUN
ejpam-5565	23	28	)	)	PUNCT
ejpam-5565	23	29	and	and	CCONJ
ejpam-5565	23	30	characterise	characterise	VERB
ejpam-5565	23	31	the	the	DET
ejpam-5565	23	32	sobolev	sobolev	NOUN
ejpam-5565	23	33	-	-	PUNCT
ejpam-5565	23	34	type	type	NOUN
ejpam-5565	23	35	inequalities	inequality	NOUN
ejpam-5565	23	36	associated	associate	VERB
ejpam-5565	23	37	with	with	ADP
ejpam-5565	23	38	bv	bv	PROPN
ejpam-5565	23	39	functions	function	NOUN
ejpam-5565	23	40	within	within	ADP
ejpam-5565	23	41	a	a	DET
ejpam-5565	23	42	general	general	ADJ
ejpam-5565	23	43	framework	framework	NOUN
ejpam-5565	23	44	of	of	ADP
ejpam-5565	23	45	strictly	strictly	ADV
ejpam-5565	23	46	local	local	ADJ
ejpam-5565	23	47	dirichlet	dirichlet	NOUN
ejpam-5565	23	48	spaces	space	NOUN
ejpam-5565	23	49	with	with	ADP
ejpam-5565	23	50	a	a	DET
ejpam-5565	23	51	doubling	double	VERB
ejpam-5565	23	52	measure	measure	NOUN
ejpam-5565	23	53	,	,	PUNCT
ejpam-5565	23	54	utilising	utilise	VERB
ejpam-5565	23	55	the	the	DET
ejpam-5565	23	56	bv	bv	PROPN
ejpam-5565	23	57	capacity	capacity	NOUN
ejpam-5565	23	58	.	.	PUNCT
ejpam-5565	24	1	2	2	X
ejpam-5565	24	2	.	.	NUM
ejpam-5565	24	3	preliminaries	preliminary	NOUN
ejpam-5565	24	4	the	the	DET
ejpam-5565	24	5	following	follow	VERB
ejpam-5565	24	6	is	be	AUX
ejpam-5565	24	7	a	a	DET
ejpam-5565	24	8	type	type	NOUN
ejpam-5565	24	9	of	of	ADP
ejpam-5565	24	10	spaces	space	NOUN
ejpam-5565	24	11	with	with	ADP
ejpam-5565	24	12	indefinite	indefinite	ADJ
ejpam-5565	24	13	metric	metric	ADJ
ejpam-5565	24	14	,	,	PUNCT
ejpam-5565	24	15	called	call	VERB
ejpam-5565	24	16	krein	krein	ADJ
ejpam-5565	24	17	spaces	space	NOUN
ejpam-5565	24	18	,	,	PUNCT
ejpam-5565	24	19	which	which	PRON
ejpam-5565	24	20	are	be	AUX
ejpam-5565	24	21	a	a	DET
ejpam-5565	24	22	generalisation	generalisation	NOUN
ejpam-5565	24	23	of	of	ADP
ejpam-5565	24	24	hilbert	hilbert	PROPN
ejpam-5565	24	25	spaces	space	NOUN
ejpam-5565	24	26	.	.	PUNCT
ejpam-5565	25	1	definition	definition	NOUN
ejpam-5565	25	2	1	1	NUM
ejpam-5565	25	3	.	.	PUNCT
ejpam-5565	26	1	[	[	X
ejpam-5565	26	2	11	11	NUM
ejpam-5565	26	3	,	,	PUNCT
ejpam-5565	26	4	12	12	NUM
ejpam-5565	26	5	]	]	PUNCT
ejpam-5565	26	6	a	a	DET
ejpam-5565	26	7	space	space	NOUN
ejpam-5565	26	8	k	k	NOUN
ejpam-5565	26	9	with	with	ADP
ejpam-5565	26	10	an	an	DET
ejpam-5565	26	11	indefinite	indefinite	ADJ
ejpam-5565	26	12	inner	inner	ADJ
ejpam-5565	26	13	product	product	NOUN
ejpam-5565	26	14	[	[	X
ejpam-5565	26	15	·	·	PUNCT
ejpam-5565	26	16	,	,	PUNCT
ejpam-5565	26	17	·	·	PUNCT
ejpam-5565	26	18	]	]	PUNCT
ejpam-5565	26	19	which	which	PRON
ejpam-5565	26	20	admits	admit	VERB
ejpam-5565	26	21	a	a	DET
ejpam-5565	26	22	fundamental	fundamental	ADJ
ejpam-5565	26	23	decomposition	decomposition	NOUN
ejpam-5565	26	24	of	of	ADP
ejpam-5565	26	25	the	the	DET
ejpam-5565	26	26	form	form	NOUN
ejpam-5565	26	27	k	k	NOUN
ejpam-5565	26	28	=	=	PUNCT
ejpam-5565	26	29	k+	k+	X
ejpam-5565	26	30	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	26	31	such	such	ADJ
ejpam-5565	26	32	that	that	SCONJ
ejpam-5565	26	33	(	(	PUNCT
ejpam-5565	26	34	k+	k+	X
ejpam-5565	26	35	,	,	PUNCT
ejpam-5565	26	36	[	[	X
ejpam-5565	26	37	·	·	PUNCT
ejpam-5565	26	38	,	,	PUNCT
ejpam-5565	26	39	·	·	PUNCT
ejpam-5565	26	40	]	]	PUNCT
ejpam-5565	26	41	)	)	PUNCT
ejpam-5565	26	42	and	and	CCONJ
ejpam-5565	26	43	(	(	PUNCT
ejpam-5565	26	44	k−,−	k−,−	NOUN
ejpam-5565	26	45	[	[	X
ejpam-5565	26	46	·	·	PUNCT
ejpam-5565	26	47	,	,	PUNCT
ejpam-5565	26	48	·	·	PUNCT
ejpam-5565	26	49	]	]	PUNCT
ejpam-5565	26	50	)	)	PUNCT
ejpam-5565	26	51	are	be	AUX
ejpam-5565	26	52	hilbert	hilbert	NOUN
ejpam-5565	26	53	spaces	space	NOUN
ejpam-5565	26	54	,	,	PUNCT
ejpam-5565	26	55	is	be	AUX
ejpam-5565	26	56	called	call	VERB
ejpam-5565	26	57	a	a	DET
ejpam-5565	26	58	krein	krein	ADJ
ejpam-5565	26	59	space	space	NOUN
ejpam-5565	26	60	.	.	PUNCT
ejpam-5565	27	1	definition	definition	NOUN
ejpam-5565	27	2	2	2	NUM
ejpam-5565	27	3	.	.	PUNCT
ejpam-5565	28	1	let	let	AUX
ejpam-5565	28	2	(	(	PUNCT
ejpam-5565	28	3	k	k	NOUN
ejpam-5565	28	4	,	,	PUNCT
ejpam-5565	28	5	[	[	X
ejpam-5565	28	6	·	·	PUNCT
ejpam-5565	28	7	,	,	PUNCT
ejpam-5565	28	8	·	·	PUNCT
ejpam-5565	28	9	]	]	PUNCT
ejpam-5565	28	10	)	)	PUNCT
ejpam-5565	28	11	be	be	AUX
ejpam-5565	28	12	a	a	DET
ejpam-5565	28	13	krein	krein	ADJ
ejpam-5565	28	14	space	space	NOUN
ejpam-5565	28	15	with	with	ADP
ejpam-5565	28	16	fundamental	fundamental	ADJ
ejpam-5565	28	17	decomposition	decomposition	NOUN
ejpam-5565	28	18	k	k	NOUN
ejpam-5565	28	19	=	=	PUNCT
ejpam-5565	28	20	k+	k+	NOUN
ejpam-5565	28	21	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	28	22	,	,	PUNCT
ejpam-5565	28	23	then	then	ADV
ejpam-5565	28	24	we	we	PRON
ejpam-5565	28	25	define	define	VERB
ejpam-5565	28	26	the	the	DET
ejpam-5565	28	27	operator	operator	NOUN
ejpam-5565	28	28	j	j	NOUN
ejpam-5565	28	29	:	:	PUNCT
ejpam-5565	28	30	(	(	PUNCT
ejpam-5565	28	31	k	k	X
ejpam-5565	28	32	,	,	PUNCT
ejpam-5565	28	33	[	[	X
ejpam-5565	28	34	·	·	PUNCT
ejpam-5565	28	35	,	,	PUNCT
ejpam-5565	28	36	·	·	PUNCT
ejpam-5565	28	37	]	]	PUNCT
ejpam-5565	28	38	)	)	PUNCT
ejpam-5565	28	39	−→	−→	NOUN
ejpam-5565	28	40	(	(	PUNCT
ejpam-5565	28	41	k	k	NOUN
ejpam-5565	28	42	,	,	PUNCT
ejpam-5565	28	43	[	[	X
ejpam-5565	28	44	·	·	PUNCT
ejpam-5565	28	45	,	,	PUNCT
ejpam-5565	28	46	·	·	PUNCT
ejpam-5565	28	47	]	]	PUNCT
ejpam-5565	28	48	)	)	PUNCT
ejpam-5565	29	1	j	j	PROPN
ejpam-5565	29	2	k	k	PROPN
ejpam-5565	29	3	=	=	PUNCT
ejpam-5565	29	4	k+	k+	PROPN
ejpam-5565	30	1	−	−	PROPN
ejpam-5565	30	2	k−	k−	PROPN
ejpam-5565	30	3	,	,	PUNCT
ejpam-5565	30	4	it	it	PRON
ejpam-5565	30	5	is	be	AUX
ejpam-5565	30	6	called	call	VERB
ejpam-5565	30	7	the	the	DET
ejpam-5565	30	8	fundamental	fundamental	ADJ
ejpam-5565	30	9	symmetry	symmetry	NOUN
ejpam-5565	30	10	of	of	ADP
ejpam-5565	30	11	the	the	DET
ejpam-5565	30	12	krein	krein	PROPN
ejpam-5565	30	13	space	space	NOUN
ejpam-5565	30	14	k	k	PROPN
ejpam-5565	30	15	associated	associate	VERB
ejpam-5565	30	16	with	with	ADP
ejpam-5565	30	17	the	the	DET
ejpam-5565	30	18	fundamental	fundamental	ADJ
ejpam-5565	30	19	decomposition	decomposition	NOUN
ejpam-5565	30	20	.	.	PUNCT
ejpam-5565	31	1	from	from	ADP
ejpam-5565	31	2	now	now	ADV
ejpam-5565	31	3	on	on	ADV
ejpam-5565	31	4	we	we	PRON
ejpam-5565	31	5	will	will	AUX
ejpam-5565	31	6	write	write	VERB
ejpam-5565	31	7	(	(	PUNCT
ejpam-5565	31	8	k	k	NOUN
ejpam-5565	31	9	,	,	PUNCT
ejpam-5565	31	10	[	[	X
ejpam-5565	31	11	·	·	PUNCT
ejpam-5565	31	12	,	,	PUNCT
ejpam-5565	31	13	·	·	PUNCT
ejpam-5565	31	14	]	]	PUNCT
ejpam-5565	31	15	,	,	PUNCT
ejpam-5565	31	16	j	j	PROPN
ejpam-5565	31	17	)	)	PUNCT
ejpam-5565	31	18	to	to	PART
ejpam-5565	31	19	denote	denote	VERB
ejpam-5565	31	20	the	the	DET
ejpam-5565	31	21	krein	krein	ADJ
ejpam-5565	31	22	space	space	NOUN
ejpam-5565	31	23	with	with	ADP
ejpam-5565	31	24	fundamental	fundamental	ADJ
ejpam-5565	31	25	symmetry	symmetry	NOUN
ejpam-5565	31	26	j	j	PROPN
ejpam-5565	31	27	associated	associate	VERB
ejpam-5565	31	28	with	with	ADP
ejpam-5565	31	29	the	the	DET
ejpam-5565	31	30	fundamental	fundamental	ADJ
ejpam-5565	31	31	decomposition	decomposition	NOUN
ejpam-5565	31	32	k	k	NOUN
ejpam-5565	32	1	=	=	PUNCT
ejpam-5565	32	2	k+	k+	X
ejpam-5565	32	3	˙[+]k−.	˙[+]k−.	ADV
ejpam-5565	32	4	remark	remark	NOUN
ejpam-5565	32	5	1	1	NUM
ejpam-5565	32	6	.	.	PUNCT
ejpam-5565	33	1	let	let	VERB
ejpam-5565	33	2	(	(	PUNCT
ejpam-5565	33	3	k	k	NOUN
ejpam-5565	33	4	=	=	SYM
ejpam-5565	33	5	k+	k+	NOUN
ejpam-5565	33	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	33	7	,	,	PUNCT
ejpam-5565	33	8	[	[	X
ejpam-5565	33	9	·	·	PUNCT
ejpam-5565	33	10	,	,	PUNCT
ejpam-5565	33	11	·	·	PUNCT
ejpam-5565	33	12	]	]	PUNCT
ejpam-5565	33	13	,	,	PUNCT
ejpam-5565	33	14	j	j	PROPN
ejpam-5565	33	15	)	)	PUNCT
ejpam-5565	33	16	be	be	AUX
ejpam-5565	33	17	a	a	DET
ejpam-5565	33	18	krein	krein	ADJ
ejpam-5565	33	19	space	space	NOUN
ejpam-5565	33	20	,	,	PUNCT
ejpam-5565	33	21	and	and	CCONJ
ejpam-5565	33	22	f	f	X
ejpam-5565	33	23	:	:	PUNCT
ejpam-5565	34	1	[	[	X
ejpam-5565	34	2	a	a	X
ejpam-5565	34	3	,	,	PUNCT
ejpam-5565	34	4	b]→	b]→	ADJ
ejpam-5565	34	5	k	k	NOUN
ejpam-5565	34	6	=	=	PUNCT
ejpam-5565	34	7	k+	k+	PUNCT
ejpam-5565	34	8	˙[+]k−.	˙[+]k−.	ADV
ejpam-5565	34	9	considering	consider	VERB
ejpam-5565	34	10	that	that	SCONJ
ejpam-5565	34	11	for	for	ADP
ejpam-5565	34	12	any	any	DET
ejpam-5565	34	13	t	t	NOUN
ejpam-5565	34	14	in	in	ADP
ejpam-5565	34	15	[	[	X
ejpam-5565	34	16	a	a	PRON
ejpam-5565	34	17	,	,	PUNCT
ejpam-5565	34	18	b	b	NOUN
ejpam-5565	34	19	]	]	X
ejpam-5565	34	20	,	,	PUNCT
ejpam-5565	34	21	f(t	f(t	PROPN
ejpam-5565	34	22	)	)	PUNCT
ejpam-5565	34	23	belongs	belong	VERB
ejpam-5565	34	24	to	to	ADP
ejpam-5565	34	25	k	k	NOUN
ejpam-5565	34	26	=	=	PUNCT
ejpam-5565	34	27	k+	k+	NOUN
ejpam-5565	34	28	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	34	29	,	,	PUNCT
ejpam-5565	34	30	we	we	PRON
ejpam-5565	34	31	will	will	AUX
ejpam-5565	34	32	henceforth	henceforth	ADV
ejpam-5565	34	33	write	write	VERB
ejpam-5565	34	34	the	the	DET
ejpam-5565	34	35	image	image	NOUN
ejpam-5565	34	36	of	of	ADP
ejpam-5565	34	37	t	t	PROPN
ejpam-5565	34	38	under	under	ADP
ejpam-5565	34	39	f	f	PROPN
ejpam-5565	34	40	as	as	ADP
ejpam-5565	34	41	f(t	f(t	NOUN
ejpam-5565	34	42	)	)	PUNCT
ejpam-5565	34	43	=	=	SYM
ejpam-5565	34	44	f+(t	f+(t	PROPN
ejpam-5565	34	45	)	)	PUNCT
ejpam-5565	34	46	+	+	NUM
ejpam-5565	34	47	f−(t	f−(t	NOUN
ejpam-5565	34	48	)	)	PUNCT
ejpam-5565	34	49	,	,	PUNCT
ejpam-5565	34	50	for	for	ADP
ejpam-5565	34	51	any	any	DET
ejpam-5565	34	52	t	t	NOUN
ejpam-5565	34	53	in	in	ADP
ejpam-5565	34	54	[	[	X
ejpam-5565	34	55	a	a	PRON
ejpam-5565	34	56	,	,	PUNCT
ejpam-5565	34	57	b	b	NOUN
ejpam-5565	34	58	]	]	PUNCT
ejpam-5565	34	59	.	.	PUNCT
ejpam-5565	35	1	remark	remark	PROPN
ejpam-5565	35	2	2	2	NUM
ejpam-5565	35	3	.	.	PUNCT
ejpam-5565	36	1	let	let	VERB
ejpam-5565	36	2	(	(	PUNCT
ejpam-5565	36	3	k	k	NOUN
ejpam-5565	36	4	=	=	SYM
ejpam-5565	36	5	k+	k+	NOUN
ejpam-5565	36	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	36	7	,	,	PUNCT
ejpam-5565	36	8	[	[	X
ejpam-5565	36	9	·	·	PUNCT
ejpam-5565	36	10	,	,	PUNCT
ejpam-5565	36	11	·	·	PUNCT
ejpam-5565	36	12	]	]	PUNCT
ejpam-5565	36	13	,	,	PUNCT
ejpam-5565	36	14	j	j	PROPN
ejpam-5565	36	15	)	)	PUNCT
ejpam-5565	36	16	be	be	AUX
ejpam-5565	36	17	a	a	DET
ejpam-5565	36	18	krein	krein	ADJ
ejpam-5565	36	19	space	space	NOUN
ejpam-5565	36	20	,	,	PUNCT
ejpam-5565	36	21	and	and	CCONJ
ejpam-5565	36	22	f	f	X
ejpam-5565	36	23	:	:	PUNCT
ejpam-5565	37	1	[	[	X
ejpam-5565	37	2	a	a	X
ejpam-5565	37	3	,	,	PUNCT
ejpam-5565	37	4	b]→	b]→	ADJ
ejpam-5565	37	5	k	k	NOUN
ejpam-5565	37	6	=	=	PUNCT
ejpam-5565	37	7	k+	k+	PUNCT
ejpam-5565	37	8	˙[+]k−.	˙[+]k−.	ADV
ejpam-5565	37	9	considering	consider	VERB
ejpam-5565	37	10	that	that	SCONJ
ejpam-5565	37	11	for	for	ADP
ejpam-5565	37	12	any	any	DET
ejpam-5565	37	13	t	t	NOUN
ejpam-5565	37	14	in	in	ADP
ejpam-5565	37	15	[	[	X
ejpam-5565	37	16	a	a	PRON
ejpam-5565	37	17	,	,	PUNCT
ejpam-5565	37	18	b	b	NOUN
ejpam-5565	37	19	]	]	X
ejpam-5565	37	20	,	,	PUNCT
ejpam-5565	37	21	f(t	f(t	PROPN
ejpam-5565	37	22	)	)	PUNCT
ejpam-5565	37	23	∈	∈	PROPN
ejpam-5565	37	24	k	k	NOUN
ejpam-5565	37	25	,	,	PUNCT
ejpam-5565	37	26	therefore	therefore	ADV
ejpam-5565	37	27	there	there	PRON
ejpam-5565	37	28	exist	exist	VERB
ejpam-5565	37	29	k+	k+	X
ejpam-5565	37	30	∈	∈	PROPN
ejpam-5565	37	31	k+	k+	NOUN
ejpam-5565	37	32	and	and	CCONJ
ejpam-5565	37	33	k−	k−	PROPN
ejpam-5565	37	34	∈	∈	PROPN
ejpam-5565	37	35	k−	k−	PROPN
ejpam-5565	37	36	such	such	ADJ
ejpam-5565	37	37	that	that	SCONJ
ejpam-5565	37	38	f(t	f(t	NOUN
ejpam-5565	37	39	)	)	PUNCT
ejpam-5565	37	40	=	=	SYM
ejpam-5565	37	41	k+	k+	X
ejpam-5565	37	42	+	+	X
ejpam-5565	37	43	k−	k−	PROPN
ejpam-5565	37	44	,	,	PUNCT
ejpam-5565	37	45	we	we	PRON
ejpam-5565	37	46	will	will	AUX
ejpam-5565	37	47	write	write	VERB
ejpam-5565	37	48	k+	k+	NOUN
ejpam-5565	37	49	=	=	SYM
ejpam-5565	37	50	f+(t	f+(t	PROPN
ejpam-5565	37	51	)	)	PUNCT
ejpam-5565	37	52	and	and	CCONJ
ejpam-5565	37	53	k−	k−	PROPN
ejpam-5565	37	54	=	=	SYM
ejpam-5565	37	55	f−(t	f−(t	PROPN
ejpam-5565	37	56	)	)	PUNCT
ejpam-5565	37	57	.	.	PUNCT
ejpam-5565	38	1	therefore	therefore	ADV
ejpam-5565	38	2	,	,	PUNCT
ejpam-5565	38	3	(	(	PUNCT
ejpam-5565	38	4	j	j	PROPN
ejpam-5565	38	5	f)(t	f)(t	PROPN
ejpam-5565	38	6	)	)	PUNCT
ejpam-5565	38	7	=	=	SYM
ejpam-5565	38	8	j	j	PROPN
ejpam-5565	38	9	(	(	PUNCT
ejpam-5565	38	10	f(t	f(t	PROPN
ejpam-5565	38	11	)	)	PUNCT
ejpam-5565	38	12	)	)	PUNCT
ejpam-5565	39	1	=	=	SYM
ejpam-5565	39	2	j	j	PROPN
ejpam-5565	39	3	(	(	PUNCT
ejpam-5565	39	4	k+	k+	PROPN
ejpam-5565	39	5	+	+	NUM
ejpam-5565	39	6	k−	k−	PROPN
ejpam-5565	39	7	)	)	PUNCT
ejpam-5565	39	8	=	=	PUNCT
ejpam-5565	39	9	k+	k+	NOUN
ejpam-5565	39	10	−	−	PROPN
ejpam-5565	39	11	k−	k−	PROPN
ejpam-5565	39	12	=	=	SYM
ejpam-5565	39	13	f+(t)−	f+(t)−	PROPN
ejpam-5565	39	14	f−(t	f−(t	PROPN
ejpam-5565	39	15	)	)	PUNCT
ejpam-5565	39	16	.	.	PUNCT
ejpam-5565	40	1	definition	definition	NOUN
ejpam-5565	40	2	3	3	NUM
ejpam-5565	40	3	.	.	PUNCT
ejpam-5565	41	1	[	[	X
ejpam-5565	41	2	11	11	NUM
ejpam-5565	41	3	]	]	X
ejpam-5565	41	4	let	let	VERB
ejpam-5565	41	5	(	(	PUNCT
ejpam-5565	41	6	k	k	NOUN
ejpam-5565	41	7	=	=	SYM
ejpam-5565	41	8	k+	k+	NOUN
ejpam-5565	41	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	41	10	,	,	PUNCT
ejpam-5565	41	11	[	[	X
ejpam-5565	41	12	·	·	PUNCT
ejpam-5565	41	13	,	,	PUNCT
ejpam-5565	41	14	·	·	PUNCT
ejpam-5565	41	15	]	]	PUNCT
ejpam-5565	41	16	)	)	PUNCT
ejpam-5565	41	17	be	be	AUX
ejpam-5565	41	18	a	a	DET
ejpam-5565	41	19	krein	krein	ADJ
ejpam-5565	41	20	space	space	NOUN
ejpam-5565	41	21	and	and	CCONJ
ejpam-5565	41	22	j	j	NOUN
ejpam-5565	41	23	the	the	DET
ejpam-5565	41	24	fundamental	fundamental	ADJ
ejpam-5565	41	25	symmetry	symmetry	NOUN
ejpam-5565	41	26	associated	associate	VERB
ejpam-5565	41	27	to	to	ADP
ejpam-5565	41	28	the	the	DET
ejpam-5565	41	29	given	give	VERB
ejpam-5565	41	30	decomposition	decomposition	NOUN
ejpam-5565	41	31	.	.	PUNCT
ejpam-5565	42	1	we	we	PRON
ejpam-5565	42	2	define	define	VERB
ejpam-5565	42	3	the	the	DET
ejpam-5565	42	4	function	function	NOUN
ejpam-5565	42	5	[	[	X
ejpam-5565	42	6	·	·	PUNCT
ejpam-5565	42	7	,	,	PUNCT
ejpam-5565	42	8	·	·	PUNCT
ejpam-5565	42	9	]	]	X
ejpam-5565	42	10	j	j	X
ejpam-5565	42	11	:	:	PUNCT
ejpam-5565	42	12	k	k	X
ejpam-5565	42	13	×k	×k	VERB
ejpam-5565	42	14	−→	−→	NOUN
ejpam-5565	42	15	c	c	NOUN
ejpam-5565	42	16	by	by	ADP
ejpam-5565	42	17	[	[	X
ejpam-5565	42	18	x	x	NOUN
ejpam-5565	42	19	,	,	PUNCT
ejpam-5565	42	20	y]j	y]j	NOUN
ejpam-5565	42	21	=	=	PUNCT
ejpam-5565	43	1	[	[	X
ejpam-5565	43	2	j	j	X
ejpam-5565	43	3	x	x	PROPN
ejpam-5565	43	4	,	,	PUNCT
ejpam-5565	43	5	y	y	PROPN
ejpam-5565	43	6	]	]	X
ejpam-5565	43	7	,	,	PUNCT
ejpam-5565	43	8	for	for	ADP
ejpam-5565	43	9	all	all	DET
ejpam-5565	43	10	x	x	NOUN
ejpam-5565	43	11	,	,	PUNCT
ejpam-5565	43	12	y	y	PROPN
ejpam-5565	43	13	in	in	ADP
ejpam-5565	43	14	k.	k.	PROPN
ejpam-5565	43	15	o.	o.	PROPN
ejpam-5565	43	16	ferrer	ferrer	PROPN
ejpam-5565	43	17	,	,	PUNCT
ejpam-5565	43	18	j.	j.	PROPN
ejpam-5565	43	19	naranjo	naranjo	PROPN
ejpam-5565	43	20	/	/	SYM
ejpam-5565	43	21	eur	eur	PROPN
ejpam-5565	43	22	.	.	PUNCT
ejpam-5565	44	1	j.	j.	PROPN
ejpam-5565	44	2	pure	pure	PROPN
ejpam-5565	44	3	appl	appl	PROPN
ejpam-5565	44	4	.	.	PROPN
ejpam-5565	44	5	math	math	PROPN
ejpam-5565	44	6	,	,	PUNCT
ejpam-5565	44	7	18	18	NUM
ejpam-5565	44	8	(	(	PUNCT
ejpam-5565	44	9	2	2	NUM
ejpam-5565	44	10	)	)	PUNCT
ejpam-5565	44	11	(	(	PUNCT
ejpam-5565	44	12	2025	2025	NUM
ejpam-5565	44	13	)	)	PUNCT
ejpam-5565	44	14	,	,	PUNCT
ejpam-5565	44	15	5565	5565	NUM
ejpam-5565	44	16	3	3	NUM
ejpam-5565	44	17	of	of	ADP
ejpam-5565	44	18	18	18	NUM
ejpam-5565	44	19	this	this	DET
ejpam-5565	44	20	function	function	NOUN
ejpam-5565	44	21	is	be	AUX
ejpam-5565	44	22	a	a	DET
ejpam-5565	44	23	usual	usual	ADJ
ejpam-5565	44	24	inner	inner	ADJ
ejpam-5565	44	25	product	product	NOUN
ejpam-5565	44	26	and	and	CCONJ
ejpam-5565	44	27	is	be	AUX
ejpam-5565	44	28	called	call	VERB
ejpam-5565	44	29	j	j	PROPN
ejpam-5565	44	30	-inner	-inner	PROPN
ejpam-5565	44	31	product	product	NOUN
ejpam-5565	44	32	.	.	PUNCT
ejpam-5565	45	1	definition	definition	NOUN
ejpam-5565	45	2	4	4	NUM
ejpam-5565	45	3	.	.	PUNCT
ejpam-5565	46	1	[	[	X
ejpam-5565	46	2	11	11	NUM
ejpam-5565	46	3	,	,	PUNCT
ejpam-5565	46	4	12	12	NUM
ejpam-5565	46	5	]	]	PUNCT
ejpam-5565	46	6	the	the	DET
ejpam-5565	46	7	fundamental	fundamental	ADJ
ejpam-5565	46	8	symmetry	symmetry	NOUN
ejpam-5565	46	9	j	j	PROPN
ejpam-5565	46	10	associated	associate	VERB
ejpam-5565	46	11	with	with	ADP
ejpam-5565	46	12	the	the	DET
ejpam-5565	46	13	krein	krein	NOUN
ejpam-5565	46	14	space	space	NOUN
ejpam-5565	46	15	(	(	PUNCT
ejpam-5565	46	16	k	k	NOUN
ejpam-5565	46	17	=	=	SYM
ejpam-5565	46	18	k+	k+	NOUN
ejpam-5565	46	19	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	46	20	,	,	PUNCT
ejpam-5565	46	21	[	[	X
ejpam-5565	46	22	·	·	PUNCT
ejpam-5565	46	23	,	,	PUNCT
ejpam-5565	46	24	·	·	PUNCT
ejpam-5565	46	25	]	]	X
ejpam-5565	46	26	)	)	PUNCT
ejpam-5565	46	27	induces	induce	VERB
ejpam-5565	46	28	a	a	DET
ejpam-5565	46	29	norm	norm	NOUN
ejpam-5565	46	30	in	in	ADP
ejpam-5565	46	31	k	k	PROPN
ejpam-5565	46	32	defined	define	VERB
ejpam-5565	46	33	by	by	ADP
ejpam-5565	46	34	:	:	PUNCT
ejpam-5565	46	35	∥x∥j	∥x∥j	NOUN
ejpam-5565	46	36	:	:	PUNCT
ejpam-5565	46	37	=	=	PUNCT
ejpam-5565	47	1	√	√	NUM
ejpam-5565	48	1	[	[	X
ejpam-5565	48	2	x	x	X
ejpam-5565	48	3	,	,	PUNCT
ejpam-5565	48	4	x]j	x]j	INTJ
ejpam-5565	48	5	,	,	PUNCT
ejpam-5565	48	6	for	for	ADP
ejpam-5565	48	7	all	all	DET
ejpam-5565	48	8	x	x	NOUN
ejpam-5565	48	9	in	in	ADP
ejpam-5565	48	10	k	k	NOUN
ejpam-5565	48	11	,	,	PUNCT
ejpam-5565	48	12	this	this	DET
ejpam-5565	48	13	norm	norm	NOUN
ejpam-5565	48	14	is	be	AUX
ejpam-5565	48	15	called	call	VERB
ejpam-5565	48	16	the	the	DET
ejpam-5565	48	17	j	j	PROPN
ejpam-5565	48	18	-norm	-norm	PROPN
ejpam-5565	48	19	of	of	ADP
ejpam-5565	48	20	k.	k.	PROPN
ejpam-5565	48	21	explicitly	explicitly	ADV
ejpam-5565	48	22	,	,	PUNCT
ejpam-5565	48	23	∥x∥j	∥x∥j	NOUN
ejpam-5565	48	24	=	=	PUNCT
ejpam-5565	49	1	(	(	PUNCT
ejpam-5565	49	2	[	[	X
ejpam-5565	49	3	x+	x+	ADJ
ejpam-5565	49	4	,	,	PUNCT
ejpam-5565	49	5	x+]−	x+]−	PUNCT
ejpam-5565	50	1	[	[	X
ejpam-5565	50	2	x−	x−	PROPN
ejpam-5565	50	3	,	,	PUNCT
ejpam-5565	50	4	x−])1/2	x−])1/2	PROPN
ejpam-5565	50	5	,	,	PUNCT
ejpam-5565	50	6	for	for	ADP
ejpam-5565	50	7	all	all	DET
ejpam-5565	50	8	x	x	PROPN
ejpam-5565	50	9	in	in	ADP
ejpam-5565	50	10	k.	k.	PROPN
ejpam-5565	50	11	remark	remark	PROPN
ejpam-5565	50	12	3	3	NUM
ejpam-5565	50	13	.	.	PUNCT
ejpam-5565	50	14	it	it	PRON
ejpam-5565	50	15	defines	define	VERB
ejpam-5565	50	16	for	for	ADP
ejpam-5565	50	17	x+	x+	PUNCT
ejpam-5565	50	18	in	in	ADP
ejpam-5565	50	19	k+	k+	NOUN
ejpam-5565	50	20	and	and	CCONJ
ejpam-5565	50	21	x−	x−	PROPN
ejpam-5565	50	22	in	in	ADP
ejpam-5565	50	23	k−	k−	PROPN
ejpam-5565	50	24	∥x+∥+	∥x+∥+	NUM
ejpam-5565	51	1	=	=	PUNCT
ejpam-5565	51	2	√	√	PROPN
ejpam-5565	52	1	[	[	X
ejpam-5565	52	2	x+	x+	ADJ
ejpam-5565	52	3	,	,	PUNCT
ejpam-5565	52	4	x+	x+	ADJ
ejpam-5565	52	5	]	]	PUNCT
ejpam-5565	52	6	,	,	PUNCT
ejpam-5565	52	7	and	and	CCONJ
ejpam-5565	52	8	∥x−∥−	∥x−∥−	X
ejpam-5565	52	9	=	=	PUNCT
ejpam-5565	53	1	√	√	NOUN
ejpam-5565	53	2	−[x−	−[x−	NOUN
ejpam-5565	53	3	,	,	PUNCT
ejpam-5565	53	4	x−	x−	PROPN
ejpam-5565	53	5	]	]	PUNCT
ejpam-5565	53	6	from	from	ADP
ejpam-5565	53	7	now	now	ADV
ejpam-5565	53	8	on	on	ADV
ejpam-5565	53	9	,	,	PUNCT
ejpam-5565	53	10	the	the	DET
ejpam-5565	53	11	topology	topology	NOUN
ejpam-5565	53	12	studied	study	VERB
ejpam-5565	53	13	in	in	ADP
ejpam-5565	53	14	krein	krein	ADJ
ejpam-5565	53	15	spaces	space	NOUN
ejpam-5565	53	16	is	be	AUX
ejpam-5565	53	17	directly	directly	ADV
ejpam-5565	53	18	related	relate	VERB
ejpam-5565	53	19	to	to	ADP
ejpam-5565	53	20	the	the	DET
ejpam-5565	53	21	j	j	PROPN
ejpam-5565	53	22	-norm	-norm	PROPN
ejpam-5565	53	23	of	of	ADP
ejpam-5565	53	24	k.	k.	PROPN
ejpam-5565	53	25	theorem	theorem	PROPN
ejpam-5565	53	26	1	1	NUM
ejpam-5565	53	27	.	.	PUNCT
ejpam-5565	54	1	[	[	X
ejpam-5565	54	2	4	4	X
ejpam-5565	54	3	]	]	X
ejpam-5565	54	4	let	let	VERB
ejpam-5565	54	5	(	(	PUNCT
ejpam-5565	54	6	k	k	NOUN
ejpam-5565	54	7	=	=	SYM
ejpam-5565	54	8	k+	k+	NOUN
ejpam-5565	54	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	54	10	,	,	PUNCT
ejpam-5565	54	11	[	[	X
ejpam-5565	54	12	·	·	PUNCT
ejpam-5565	54	13	,	,	PUNCT
ejpam-5565	54	14	·	·	PUNCT
ejpam-5565	54	15	]	]	PUNCT
ejpam-5565	54	16	,	,	PUNCT
ejpam-5565	54	17	j	j	PROPN
ejpam-5565	54	18	)	)	PUNCT
ejpam-5565	54	19	be	be	AUX
ejpam-5565	54	20	a	a	DET
ejpam-5565	54	21	krein	krein	ADJ
ejpam-5565	54	22	space	space	NOUN
ejpam-5565	54	23	,	,	PUNCT
ejpam-5565	54	24	then	then	ADV
ejpam-5565	54	25	∥x∥j	∥x∥j	ADV
ejpam-5565	54	26	≤	≤	ADV
ejpam-5565	54	27	∥x+∥+	∥x+∥+	NUM
ejpam-5565	55	1	+	+	CCONJ
ejpam-5565	55	2	∥x−∥−	∥x−∥−	ADV
ejpam-5565	55	3	for	for	ADP
ejpam-5565	55	4	all	all	PRON
ejpam-5565	55	5	x	x	PUNCT
ejpam-5565	55	6	=	=	SYM
ejpam-5565	55	7	x+	x+	PUNCT
ejpam-5565	55	8	+	+	CCONJ
ejpam-5565	55	9	x−	x−	PROPN
ejpam-5565	55	10	in	in	ADP
ejpam-5565	55	11	k.	k.	PROPN
ejpam-5565	55	12	theorem	theorem	PROPN
ejpam-5565	55	13	2	2	NUM
ejpam-5565	55	14	.	.	PUNCT
ejpam-5565	56	1	[	[	X
ejpam-5565	56	2	11	11	NUM
ejpam-5565	56	3	,	,	PUNCT
ejpam-5565	56	4	12	12	NUM
ejpam-5565	56	5	]	]	PUNCT
ejpam-5565	56	6	let	let	NOUN
ejpam-5565	56	7	(	(	PUNCT
ejpam-5565	56	8	k	k	NOUN
ejpam-5565	56	9	,	,	PUNCT
ejpam-5565	56	10	[	[	X
ejpam-5565	56	11	·	·	PUNCT
ejpam-5565	56	12	,	,	PUNCT
ejpam-5565	56	13	·	·	PUNCT
ejpam-5565	56	14	]	]	PUNCT
ejpam-5565	56	15	)	)	PUNCT
ejpam-5565	56	16	be	be	AUX
ejpam-5565	56	17	a	a	DET
ejpam-5565	56	18	krein	krein	ADJ
ejpam-5565	56	19	space	space	NOUN
ejpam-5565	56	20	and	and	CCONJ
ejpam-5565	56	21	let	let	VERB
ejpam-5565	56	22	k	k	PROPN
ejpam-5565	56	23	=	=	PUNCT
ejpam-5565	56	24	k+	k+	NOUN
ejpam-5565	56	25	1	1	NUM
ejpam-5565	56	26	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	56	27	1	1	NUM
ejpam-5565	56	28	,	,	PUNCT
ejpam-5565	56	29	k	k	NOUN
ejpam-5565	56	30	=	=	PUNCT
ejpam-5565	56	31	k+	k+	NOUN
ejpam-5565	56	32	2	2	NUM
ejpam-5565	56	33	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	56	34	2	2	NUM
ejpam-5565	56	35	,	,	PUNCT
ejpam-5565	56	36	be	be	AUX
ejpam-5565	56	37	two	two	NUM
ejpam-5565	56	38	fundamental	fundamental	ADJ
ejpam-5565	56	39	decompositions	decomposition	NOUN
ejpam-5565	56	40	.	.	PUNCT
ejpam-5565	57	1	if	if	SCONJ
ejpam-5565	57	2	j1	j1	PROPN
ejpam-5565	57	3	and	and	CCONJ
ejpam-5565	57	4	j2	j2	PROPN
ejpam-5565	57	5	are	be	AUX
ejpam-5565	57	6	the	the	DET
ejpam-5565	57	7	respective	respective	ADJ
ejpam-5565	57	8	fundamental	fundamental	ADJ
ejpam-5565	57	9	symmetries	symmetry	NOUN
ejpam-5565	57	10	it	it	PRON
ejpam-5565	57	11	follows	follow	VERB
ejpam-5565	57	12	that	that	SCONJ
ejpam-5565	57	13	∥.∥j1	∥.∥j1	PROPN
ejpam-5565	57	14	and	and	CCONJ
ejpam-5565	57	15	∥.∥j2	∥.∥j2	PROPN
ejpam-5565	57	16	are	be	AUX
ejpam-5565	57	17	equivalent	equivalent	ADJ
ejpam-5565	57	18	norms	norm	NOUN
ejpam-5565	57	19	.	.	PUNCT
ejpam-5565	58	1	example	example	NOUN
ejpam-5565	58	2	1	1	NUM
ejpam-5565	58	3	.	.	PUNCT
ejpam-5565	59	1	let	let	VERB
ejpam-5565	59	2	us	we	PRON
ejpam-5565	59	3	consider	consider	VERB
ejpam-5565	59	4	the	the	DET
ejpam-5565	59	5	vector	vector	NOUN
ejpam-5565	59	6	space	space	NOUN
ejpam-5565	59	7	c2	c2	PROPN
ejpam-5565	59	8	,	,	PUNCT
ejpam-5565	59	9	with	with	ADP
ejpam-5565	59	10	sum	sum	NOUN
ejpam-5565	59	11	,	,	PUNCT
ejpam-5565	59	12	usual	usual	ADJ
ejpam-5565	59	13	product	product	NOUN
ejpam-5565	59	14	and	and	CCONJ
ejpam-5565	59	15	the	the	DET
ejpam-5565	59	16	mapping	mapping	NOUN
ejpam-5565	59	17	[	[	X
ejpam-5565	59	18	·	·	PUNCT
ejpam-5565	59	19	,	,	PUNCT
ejpam-5565	59	20	·	·	PUNCT
ejpam-5565	59	21	]	]	PUNCT
ejpam-5565	59	22	:	:	PUNCT
ejpam-5565	59	23	c2	c2	PROPN
ejpam-5565	59	24	×	×	PROPN
ejpam-5565	59	25	c2	c2	PROPN
ejpam-5565	59	26	−→	−→	NOUN
ejpam-5565	59	27	c	c	PROPN
ejpam-5565	59	28	given	give	VERB
ejpam-5565	59	29	by	by	ADP
ejpam-5565	59	30	:	:	PUNCT
ejpam-5565	60	1	[	[	X
ejpam-5565	60	2	(	(	PUNCT
ejpam-5565	60	3	x1	x1	PROPN
ejpam-5565	60	4	,	,	PUNCT
ejpam-5565	60	5	y1	y1	PROPN
ejpam-5565	60	6	)	)	PUNCT
ejpam-5565	60	7	,	,	PUNCT
ejpam-5565	60	8	(	(	PUNCT
ejpam-5565	60	9	x2	x2	PROPN
ejpam-5565	60	10	,	,	PUNCT
ejpam-5565	60	11	y2	y2	PROPN
ejpam-5565	60	12	)	)	PUNCT
ejpam-5565	60	13	]	]	PUNCT
ejpam-5565	61	1	=	=	PUNCT
ejpam-5565	61	2	x1x2	x1x2	X
ejpam-5565	62	1	−	−	PROPN
ejpam-5565	62	2	y1y2	y1y2	PROPN
ejpam-5565	62	3	.	.	PUNCT
ejpam-5565	63	1	(	(	PUNCT
ejpam-5565	63	2	1	1	X
ejpam-5565	63	3	)	)	PUNCT
ejpam-5565	63	4	the	the	DET
ejpam-5565	63	5	space	space	NOUN
ejpam-5565	63	6	(	(	PUNCT
ejpam-5565	63	7	c2	c2	PROPN
ejpam-5565	63	8	,	,	PUNCT
ejpam-5565	63	9	[	[	X
ejpam-5565	63	10	·	·	PUNCT
ejpam-5565	63	11	,	,	PUNCT
ejpam-5565	63	12	·	·	PUNCT
ejpam-5565	63	13	]	]	PUNCT
ejpam-5565	63	14	)	)	PUNCT
ejpam-5565	63	15	is	be	AUX
ejpam-5565	63	16	a	a	DET
ejpam-5565	63	17	krein	krein	ADJ
ejpam-5565	63	18	space	space	NOUN
ejpam-5565	63	19	with	with	ADP
ejpam-5565	63	20	fundamental	fundamental	ADJ
ejpam-5565	63	21	decomposition	decomposition	NOUN
ejpam-5565	63	22	c2	c2	PROPN
ejpam-5565	63	23	=	=	PUNCT
ejpam-5565	63	24	k+[∔]k−	k+[∔]k−	PROPN
ejpam-5565	63	25	,	,	PUNCT
ejpam-5565	63	26	where	where	SCONJ
ejpam-5565	63	27	k+	k+	NOUN
ejpam-5565	63	28	=	=	PRON
ejpam-5565	63	29	{	{	PUNCT
ejpam-5565	63	30	(	(	PUNCT
ejpam-5565	63	31	x	x	NOUN
ejpam-5565	63	32	,	,	PUNCT
ejpam-5565	63	33	0	0	NUM
ejpam-5565	63	34	)	)	PUNCT
ejpam-5565	63	35	:	:	PUNCT
ejpam-5565	64	1	x	x	X
ejpam-5565	64	2	∈	∈	NOUN
ejpam-5565	64	3	c	c	NOUN
ejpam-5565	64	4	}	}	PUNCT
ejpam-5565	64	5	and	and	CCONJ
ejpam-5565	64	6	k−	k−	PROPN
ejpam-5565	64	7	=	=	SYM
ejpam-5565	64	8	{	{	PUNCT
ejpam-5565	64	9	(	(	PUNCT
ejpam-5565	64	10	0	0	NUM
ejpam-5565	64	11	,	,	PUNCT
ejpam-5565	64	12	y	y	PROPN
ejpam-5565	64	13	)	)	PUNCT
ejpam-5565	64	14	:	:	PUNCT
ejpam-5565	65	1	y	y	PROPN
ejpam-5565	65	2	∈	∈	PROPN
ejpam-5565	65	3	c	c	X
ejpam-5565	65	4	}	}	PUNCT
ejpam-5565	65	5	,	,	PUNCT
ejpam-5565	65	6	with	with	ADP
ejpam-5565	65	7	fundamental	fundamental	ADJ
ejpam-5565	65	8	symmetry	symmetry	NOUN
ejpam-5565	65	9	j	j	PROPN
ejpam-5565	65	10	(	(	PUNCT
ejpam-5565	65	11	(	(	PUNCT
ejpam-5565	65	12	x	x	NOUN
ejpam-5565	65	13	,	,	PUNCT
ejpam-5565	65	14	y	y	NOUN
ejpam-5565	65	15	)	)	PUNCT
ejpam-5565	65	16	)	)	PUNCT
ejpam-5565	66	1	=	=	SYM
ejpam-5565	66	2	j	j	PROPN
ejpam-5565	66	3	(	(	PUNCT
ejpam-5565	66	4	(	(	PUNCT
ejpam-5565	66	5	x	x	X
ejpam-5565	66	6	,	,	PUNCT
ejpam-5565	66	7	0	0	NUM
ejpam-5565	66	8	)	)	PUNCT
ejpam-5565	66	9	+	+	CCONJ
ejpam-5565	66	10	(	(	PUNCT
ejpam-5565	66	11	0	0	NUM
ejpam-5565	66	12	,	,	PUNCT
ejpam-5565	66	13	y	y	NOUN
ejpam-5565	66	14	)	)	PUNCT
ejpam-5565	66	15	)	)	PUNCT
ejpam-5565	67	1	=	=	PRON
ejpam-5565	67	2	(	(	PUNCT
ejpam-5565	67	3	x,−y	x,−y	NOUN
ejpam-5565	67	4	)	)	PUNCT
ejpam-5565	67	5	that	that	PRON
ejpam-5565	67	6	determines	determine	VERB
ejpam-5565	67	7	the	the	DET
ejpam-5565	67	8	j	j	PROPN
ejpam-5565	67	9	-norm	-norm	PROPN
ejpam-5565	67	10	∥	∥	PUNCT
ejpam-5565	67	11	·	·	PUNCT
ejpam-5565	67	12	∥j	∥j	ADV
ejpam-5565	67	13	given	give	VERB
ejpam-5565	67	14	by	by	ADP
ejpam-5565	67	15	∥(x	∥(x	NOUN
ejpam-5565	67	16	,	,	PUNCT
ejpam-5565	67	17	y)∥j	y)∥j	X
ejpam-5565	67	18	=	=	PUNCT
ejpam-5565	68	1	[	[	X
ejpam-5565	68	2	j	j	X
ejpam-5565	68	3	(	(	PUNCT
ejpam-5565	68	4	x	x	PROPN
ejpam-5565	68	5	,	,	PUNCT
ejpam-5565	68	6	y	y	PROPN
ejpam-5565	68	7	)	)	PUNCT
ejpam-5565	68	8	,	,	PUNCT
ejpam-5565	68	9	(	(	PUNCT
ejpam-5565	68	10	x	x	X
ejpam-5565	68	11	,	,	PUNCT
ejpam-5565	68	12	y)]1/2	y)]1/2	NOUN
ejpam-5565	68	13	=	=	PUNCT
ejpam-5565	68	14	(	(	PUNCT
ejpam-5565	68	15	x	x	X
ejpam-5565	68	16	·	·	PUNCT
ejpam-5565	68	17	x−	x−	PROPN
ejpam-5565	68	18	(	(	PUNCT
ejpam-5565	68	19	−y	−y	PROPN
ejpam-5565	68	20	)	)	PUNCT
ejpam-5565	68	21	·	·	PUNCT
ejpam-5565	68	22	y)1/2	y)1/2	PUNCT
ejpam-5565	69	1	=	=	PUNCT
ejpam-5565	69	2	√	√	PROPN
ejpam-5565	69	3	|x|2	|x|2	PROPN
ejpam-5565	69	4	+	+	CCONJ
ejpam-5565	69	5	|y|2	|y|2	ADJ
ejpam-5565	69	6	.	.	PUNCT
ejpam-5565	70	1	in	in	ADP
ejpam-5565	70	2	addition	addition	NOUN
ejpam-5565	70	3	,	,	PUNCT
ejpam-5565	70	4	the	the	DET
ejpam-5565	70	5	norms	norm	NOUN
ejpam-5565	70	6	∥	∥	X
ejpam-5565	70	7	·	·	PUNCT
ejpam-5565	70	8	∥+	∥+	ADJ
ejpam-5565	70	9	:	:	PUNCT
ejpam-5565	70	10	k+	k+	X
ejpam-5565	70	11	→	→	X
ejpam-5565	70	12	r+	r+	NOUN
ejpam-5565	70	13	∪	∪	X
ejpam-5565	70	14	{	{	PUNCT
ejpam-5565	70	15	0	0	NUM
ejpam-5565	70	16	}	}	PUNCT
ejpam-5565	70	17	and	and	CCONJ
ejpam-5565	70	18	∥	∥	NUM
ejpam-5565	70	19	·	·	PUNCT
ejpam-5565	70	20	∥−	∥−	INTJ
ejpam-5565	70	21	:	:	PUNCT
ejpam-5565	70	22	k−	k−	NOUN
ejpam-5565	70	23	→	→	PUNCT
ejpam-5565	70	24	r+	r+	NOUN
ejpam-5565	70	25	∪	∪	X
ejpam-5565	70	26	{	{	PUNCT
ejpam-5565	70	27	0	0	NUM
ejpam-5565	70	28	}	}	PUNCT
ejpam-5565	70	29	are	be	AUX
ejpam-5565	70	30	given	give	VERB
ejpam-5565	70	31	by	by	ADP
ejpam-5565	70	32	:	:	PUNCT
ejpam-5565	70	33	∥(x	∥(x	NOUN
ejpam-5565	70	34	,	,	PUNCT
ejpam-5565	70	35	0)∥+	0)∥+	NOUN
ejpam-5565	70	36	=	=	SYM
ejpam-5565	71	1	√	√	NUM
ejpam-5565	72	1	[	[	X
ejpam-5565	72	2	(	(	PUNCT
ejpam-5565	72	3	x	x	X
ejpam-5565	72	4	,	,	PUNCT
ejpam-5565	72	5	0	0	NUM
ejpam-5565	72	6	)	)	PUNCT
ejpam-5565	72	7	,	,	PUNCT
ejpam-5565	72	8	(	(	PUNCT
ejpam-5565	72	9	x	x	X
ejpam-5565	72	10	,	,	PUNCT
ejpam-5565	72	11	0	0	NUM
ejpam-5565	72	12	)	)	PUNCT
ejpam-5565	72	13	]	]	PUNCT
ejpam-5565	73	1	=	=	PUNCT
ejpam-5565	73	2	√	√	NUM
ejpam-5565	73	3	|x|2	|x|2	NOUN
ejpam-5565	73	4	=	=	SYM
ejpam-5565	73	5	|x|	|x|	PROPN
ejpam-5565	73	6	∥(0	∥(0	PROPN
ejpam-5565	73	7	,	,	PUNCT
ejpam-5565	73	8	y)∥−	y)∥−	PROPN
ejpam-5565	73	9	=	=	PUNCT
ejpam-5565	73	10	√	√	PROPN
ejpam-5565	74	1	[	[	X
ejpam-5565	74	2	(	(	PUNCT
ejpam-5565	74	3	0	0	NUM
ejpam-5565	74	4	,	,	PUNCT
ejpam-5565	74	5	y	y	NOUN
ejpam-5565	74	6	)	)	PUNCT
ejpam-5565	74	7	,	,	PUNCT
ejpam-5565	74	8	(	(	PUNCT
ejpam-5565	74	9	0	0	NUM
ejpam-5565	74	10	,	,	PUNCT
ejpam-5565	74	11	y	y	NOUN
ejpam-5565	74	12	)	)	PUNCT
ejpam-5565	74	13	]	]	PUNCT
ejpam-5565	75	1	=	=	PUNCT
ejpam-5565	75	2	√	√	NUM
ejpam-5565	75	3	−y(−y	−y(−y	NOUN
ejpam-5565	75	4	)	)	PUNCT
ejpam-5565	75	5	=	=	SYM
ejpam-5565	75	6	√	√	NUM
ejpam-5565	75	7	|y|2	|y|2	PROPN
ejpam-5565	75	8	=	=	SYM
ejpam-5565	75	9	|y|	|y|	PROPN
ejpam-5565	75	10	o.	o.	PROPN
ejpam-5565	75	11	ferrer	ferrer	PROPN
ejpam-5565	75	12	,	,	PUNCT
ejpam-5565	75	13	j.	j.	PROPN
ejpam-5565	75	14	naranjo	naranjo	PROPN
ejpam-5565	75	15	/	/	SYM
ejpam-5565	75	16	eur	eur	PROPN
ejpam-5565	75	17	.	.	PUNCT
ejpam-5565	76	1	j.	j.	PROPN
ejpam-5565	76	2	pure	pure	PROPN
ejpam-5565	76	3	appl	appl	PROPN
ejpam-5565	76	4	.	.	PROPN
ejpam-5565	76	5	math	math	PROPN
ejpam-5565	76	6	,	,	PUNCT
ejpam-5565	76	7	18	18	NUM
ejpam-5565	76	8	(	(	PUNCT
ejpam-5565	76	9	2	2	NUM
ejpam-5565	76	10	)	)	PUNCT
ejpam-5565	76	11	(	(	PUNCT
ejpam-5565	76	12	2025	2025	NUM
ejpam-5565	76	13	)	)	PUNCT
ejpam-5565	76	14	,	,	PUNCT
ejpam-5565	76	15	5565	5565	NUM
ejpam-5565	76	16	4	4	NUM
ejpam-5565	76	17	of	of	ADP
ejpam-5565	76	18	18	18	NUM
ejpam-5565	76	19	3	3	NUM
ejpam-5565	76	20	.	.	PUNCT
ejpam-5565	76	21	functions	function	NOUN
ejpam-5565	76	22	of	of	ADP
ejpam-5565	76	23	bounded	bounded	ADJ
ejpam-5565	76	24	variation	variation	NOUN
ejpam-5565	76	25	in	in	ADP
ejpam-5565	76	26	krein	krein	PROPN
ejpam-5565	76	27	spaces	space	NOUN
ejpam-5565	76	28	this	this	DET
ejpam-5565	76	29	section	section	NOUN
ejpam-5565	76	30	presents	present	VERB
ejpam-5565	76	31	the	the	DET
ejpam-5565	76	32	fundamental	fundamental	ADJ
ejpam-5565	76	33	theory	theory	NOUN
ejpam-5565	76	34	of	of	ADP
ejpam-5565	76	35	bounded	bounded	ADJ
ejpam-5565	76	36	variation	variation	NOUN
ejpam-5565	76	37	functions	function	NOUN
ejpam-5565	76	38	in	in	ADP
ejpam-5565	76	39	krein	krein	ADJ
ejpam-5565	76	40	spaces	space	NOUN
ejpam-5565	76	41	,	,	PUNCT
ejpam-5565	76	42	which	which	PRON
ejpam-5565	76	43	were	be	AUX
ejpam-5565	76	44	introduced	introduce	VERB
ejpam-5565	76	45	by	by	ADP
ejpam-5565	76	46	ferrer	ferrer	PROPN
ejpam-5565	76	47	,	,	PUNCT
ejpam-5565	76	48	naranjo	naranjo	PROPN
ejpam-5565	76	49	and	and	CCONJ
ejpam-5565	76	50	guzmán	guzmán	PROPN
ejpam-5565	76	51	[	[	X
ejpam-5565	76	52	4	4	NUM
ejpam-5565	76	53	]	]	PUNCT
ejpam-5565	76	54	.	.	PUNCT
ejpam-5565	77	1	definition	definition	NOUN
ejpam-5565	77	2	5	5	NUM
ejpam-5565	77	3	.	.	PUNCT
ejpam-5565	78	1	[	[	X
ejpam-5565	78	2	4	4	X
ejpam-5565	78	3	]	]	X
ejpam-5565	78	4	let	let	VERB
ejpam-5565	78	5	(	(	PUNCT
ejpam-5565	78	6	k	k	NOUN
ejpam-5565	78	7	=	=	SYM
ejpam-5565	78	8	k+	k+	NOUN
ejpam-5565	78	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	78	10	,	,	PUNCT
ejpam-5565	78	11	[	[	X
ejpam-5565	78	12	·	·	PUNCT
ejpam-5565	78	13	,	,	PUNCT
ejpam-5565	78	14	·	·	PUNCT
ejpam-5565	78	15	]	]	PUNCT
ejpam-5565	78	16	)	)	PUNCT
ejpam-5565	78	17	be	be	AUX
ejpam-5565	78	18	a	a	DET
ejpam-5565	78	19	krein	krein	ADJ
ejpam-5565	78	20	space	space	NOUN
ejpam-5565	78	21	and	and	CCONJ
ejpam-5565	78	22	let	let	VERB
ejpam-5565	78	23	f	f	NOUN
ejpam-5565	78	24	:	:	PUNCT
ejpam-5565	79	1	[	[	X
ejpam-5565	79	2	a	a	X
ejpam-5565	79	3	,	,	PUNCT
ejpam-5565	79	4	b]→	b]→	PROPN
ejpam-5565	79	5	k	k	PROPN
ejpam-5565	79	6	defined	define	VERB
ejpam-5565	79	7	in	in	ADP
ejpam-5565	79	8	[	[	X
ejpam-5565	79	9	a	a	DET
ejpam-5565	79	10	,	,	PUNCT
ejpam-5565	79	11	b	b	NOUN
ejpam-5565	79	12	]	]	X
ejpam-5565	79	13	,	,	PUNCT
ejpam-5565	79	14	we	we	PRON
ejpam-5565	79	15	will	will	AUX
ejpam-5565	79	16	say	say	VERB
ejpam-5565	79	17	that	that	SCONJ
ejpam-5565	79	18	f	f	PROPN
ejpam-5565	79	19	is	be	AUX
ejpam-5565	79	20	strongly	strongly	ADV
ejpam-5565	79	21	of	of	ADP
ejpam-5565	79	22	bounded	bounded	ADJ
ejpam-5565	79	23	variation	variation	NOUN
ejpam-5565	79	24	in	in	ADP
ejpam-5565	79	25	[	[	X
ejpam-5565	79	26	a	a	DET
ejpam-5565	79	27	,	,	PUNCT
ejpam-5565	79	28	b	b	NOUN
ejpam-5565	79	29	]	]	X
ejpam-5565	79	30	on	on	ADP
ejpam-5565	79	31	(	(	PUNCT
ejpam-5565	79	32	k	k	NOUN
ejpam-5565	79	33	=	=	SYM
ejpam-5565	79	34	k+	k+	NOUN
ejpam-5565	79	35	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	79	36	)	)	PUNCT
ejpam-5565	79	37	if	if	SCONJ
ejpam-5565	79	38	vb	vb	PROPN
ejpam-5565	79	39	a(f	a(f	PROPN
ejpam-5565	79	40	,	,	PUNCT
ejpam-5565	79	41	(	(	PUNCT
ejpam-5565	79	42	k	k	X
ejpam-5565	79	43	,	,	PUNCT
ejpam-5565	79	44	[	[	X
ejpam-5565	79	45	·	·	PUNCT
ejpam-5565	79	46	,	,	PUNCT
ejpam-5565	79	47	·	·	PUNCT
ejpam-5565	79	48	]	]	X
ejpam-5565	79	49	)	)	PUNCT
ejpam-5565	79	50	)	)	PUNCT
ejpam-5565	80	1	=	=	SYM
ejpam-5565	80	2	sup	sup	NOUN
ejpam-5565	80	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	80	4	,	,	PUNCT
ejpam-5565	80	5	b	b	NOUN
ejpam-5565	80	6	]	]	X
ejpam-5565	80	7	{	{	PUNCT
ejpam-5565	80	8	n∑	n∑	NOUN
ejpam-5565	80	9	i=1	i=1	PROPN
ejpam-5565	80	10	(	(	PUNCT
ejpam-5565	80	11	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	80	12	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	80	13	+	+	CCONJ
ejpam-5565	80	14	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	80	15	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	80	16	)	)	PUNCT
ejpam-5565	80	17	}	}	PUNCT
ejpam-5565	80	18	is	be	AUX
ejpam-5565	80	19	finite	finite	ADJ
ejpam-5565	80	20	.	.	PUNCT
ejpam-5565	81	1	the	the	DET
ejpam-5565	81	2	set	set	NOUN
ejpam-5565	81	3	of	of	ADP
ejpam-5565	81	4	all	all	DET
ejpam-5565	81	5	functions	function	NOUN
ejpam-5565	81	6	strongly	strongly	ADV
ejpam-5565	81	7	of	of	ADP
ejpam-5565	81	8	bounded	bounded	ADJ
ejpam-5565	81	9	variation	variation	NOUN
ejpam-5565	81	10	in	in	ADP
ejpam-5565	81	11	[	[	X
ejpam-5565	81	12	a	a	DET
ejpam-5565	81	13	,	,	PUNCT
ejpam-5565	81	14	b	b	NOUN
ejpam-5565	81	15	]	]	X
ejpam-5565	81	16	on	on	ADP
ejpam-5565	81	17	(	(	PUNCT
ejpam-5565	81	18	k	k	NOUN
ejpam-5565	81	19	=	=	SYM
ejpam-5565	81	20	k+	k+	NOUN
ejpam-5565	81	21	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	81	22	,	,	PUNCT
ejpam-5565	81	23	[	[	X
ejpam-5565	81	24	·	·	PUNCT
ejpam-5565	81	25	,	,	PUNCT
ejpam-5565	81	26	·	·	PUNCT
ejpam-5565	81	27	]	]	PUNCT
ejpam-5565	81	28	)	)	PUNCT
ejpam-5565	81	29	is	be	AUX
ejpam-5565	81	30	denoted	denote	VERB
ejpam-5565	81	31	as	as	SCONJ
ejpam-5565	81	32	follows	follow	VERB
ejpam-5565	81	33	bv	bv	PROPN
ejpam-5565	81	34	(	(	PUNCT
ejpam-5565	81	35	[	[	X
ejpam-5565	81	36	a	a	X
ejpam-5565	81	37	,	,	PUNCT
ejpam-5565	81	38	b],k	b],k	X
ejpam-5565	81	39	,	,	PUNCT
ejpam-5565	81	40	[	[	X
ejpam-5565	81	41	·	·	PUNCT
ejpam-5565	81	42	,	,	PUNCT
ejpam-5565	81	43	·	·	PUNCT
ejpam-5565	81	44	]	]	PUNCT
ejpam-5565	81	45	)	)	PUNCT
ejpam-5565	81	46	definition	definition	NOUN
ejpam-5565	81	47	6	6	NUM
ejpam-5565	81	48	.	.	PUNCT
ejpam-5565	82	1	[	[	X
ejpam-5565	82	2	4	4	NUM
ejpam-5565	82	3	]	]	X
ejpam-5565	82	4	(	(	PUNCT
ejpam-5565	82	5	positive	positive	ADJ
ejpam-5565	82	6	and	and	CCONJ
ejpam-5565	82	7	negative	negative	ADJ
ejpam-5565	82	8	variations	variation	NOUN
ejpam-5565	82	9	of	of	ADP
ejpam-5565	82	10	functions	function	NOUN
ejpam-5565	82	11	in	in	ADP
ejpam-5565	82	12	krein	krein	ADJ
ejpam-5565	82	13	spaces	space	NOUN
ejpam-5565	82	14	)	)	PUNCT
ejpam-5565	82	15	let	let	VERB
ejpam-5565	82	16	(	(	PUNCT
ejpam-5565	82	17	k	k	NOUN
ejpam-5565	82	18	=	=	SYM
ejpam-5565	82	19	k+	k+	NOUN
ejpam-5565	82	20	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	82	21	,	,	PUNCT
ejpam-5565	82	22	[	[	X
ejpam-5565	82	23	·	·	PUNCT
ejpam-5565	82	24	,	,	PUNCT
ejpam-5565	82	25	·	·	PUNCT
ejpam-5565	82	26	]	]	PUNCT
ejpam-5565	82	27	,	,	PUNCT
ejpam-5565	82	28	j	j	PROPN
ejpam-5565	82	29	)	)	PUNCT
ejpam-5565	82	30	be	be	AUX
ejpam-5565	82	31	a	a	DET
ejpam-5565	82	32	krein	krein	ADJ
ejpam-5565	82	33	space	space	NOUN
ejpam-5565	82	34	,	,	PUNCT
ejpam-5565	82	35	and	and	CCONJ
ejpam-5565	82	36	f	f	X
ejpam-5565	82	37	:	:	PUNCT
ejpam-5565	83	1	[	[	X
ejpam-5565	83	2	a	a	X
ejpam-5565	83	3	,	,	PUNCT
ejpam-5565	83	4	b	b	NOUN
ejpam-5565	83	5	]	]	X
ejpam-5565	83	6	→	→	SYM
ejpam-5565	83	7	k	k	X
ejpam-5565	83	8	=	=	PUNCT
ejpam-5565	83	9	k+	k+	NOUN
ejpam-5565	83	10	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	83	11	,	,	PUNCT
ejpam-5565	83	12	with	with	ADP
ejpam-5565	83	13	f(t	f(t	NOUN
ejpam-5565	83	14	)	)	PUNCT
ejpam-5565	83	15	=	=	SYM
ejpam-5565	83	16	f+(t	f+(t	PROPN
ejpam-5565	83	17	)	)	PUNCT
ejpam-5565	83	18	+	+	NUM
ejpam-5565	83	19	f−(t	f−(t	NOUN
ejpam-5565	83	20	)	)	PUNCT
ejpam-5565	83	21	,	,	PUNCT
ejpam-5565	83	22	for	for	ADP
ejpam-5565	83	23	all	all	DET
ejpam-5565	83	24	t	t	NOUN
ejpam-5565	83	25	in	in	ADP
ejpam-5565	83	26	the	the	DET
ejpam-5565	83	27	interval	interval	NOUN
ejpam-5565	83	28	[	[	X
ejpam-5565	83	29	a	a	X
ejpam-5565	83	30	,	,	PUNCT
ejpam-5565	83	31	b	b	NOUN
ejpam-5565	83	32	]	]	X
ejpam-5565	83	33	.	.	PUNCT
ejpam-5565	84	1	the	the	DET
ejpam-5565	84	2	positive	positive	ADJ
ejpam-5565	84	3	and	and	CCONJ
ejpam-5565	84	4	negative	negative	ADJ
ejpam-5565	84	5	variation	variation	NOUN
ejpam-5565	84	6	of	of	ADP
ejpam-5565	84	7	f	f	PROPN
ejpam-5565	84	8	on	on	ADP
ejpam-5565	84	9	[	[	X
ejpam-5565	84	10	a	a	X
ejpam-5565	84	11	,	,	PUNCT
ejpam-5565	84	12	b	b	NOUN
ejpam-5565	84	13	]	]	X
ejpam-5565	84	14	with	with	ADP
ejpam-5565	84	15	respect	respect	NOUN
ejpam-5565	84	16	to	to	ADP
ejpam-5565	84	17	(	(	PUNCT
ejpam-5565	84	18	k+	k+	X
ejpam-5565	84	19	,	,	PUNCT
ejpam-5565	84	20	[	[	X
ejpam-5565	84	21	·	·	PUNCT
ejpam-5565	84	22	,	,	PUNCT
ejpam-5565	84	23	·	·	PUNCT
ejpam-5565	84	24	]	]	PUNCT
ejpam-5565	84	25	)	)	PUNCT
ejpam-5565	84	26	and	and	CCONJ
ejpam-5565	84	27	(	(	PUNCT
ejpam-5565	84	28	k−,−	k−,−	NOUN
ejpam-5565	84	29	[	[	X
ejpam-5565	84	30	·	·	PUNCT
ejpam-5565	84	31	,	,	PUNCT
ejpam-5565	84	32	·	·	PUNCT
ejpam-5565	84	33	]	]	X
ejpam-5565	84	34	)	)	PUNCT
ejpam-5565	84	35	respectively	respectively	ADV
ejpam-5565	84	36	,	,	PUNCT
ejpam-5565	84	37	are	be	AUX
ejpam-5565	84	38	defined	define	VERB
ejpam-5565	84	39	by	by	ADP
ejpam-5565	84	40	:	:	PUNCT
ejpam-5565	84	41	+	+	NUM
ejpam-5565	84	42	vb	vb	X
ejpam-5565	84	43	a(f	a(f	PROPN
ejpam-5565	84	44	,	,	PUNCT
ejpam-5565	84	45	(	(	PUNCT
ejpam-5565	84	46	k+	k+	X
ejpam-5565	84	47	,	,	PUNCT
ejpam-5565	84	48	[	[	X
ejpam-5565	84	49	·	·	PUNCT
ejpam-5565	84	50	,	,	PUNCT
ejpam-5565	84	51	·	·	PUNCT
ejpam-5565	84	52	]	]	X
ejpam-5565	84	53	)	)	PUNCT
ejpam-5565	84	54	)	)	PUNCT
ejpam-5565	85	1	=	=	SYM
ejpam-5565	85	2	sup	sup	NOUN
ejpam-5565	85	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	85	4	,	,	PUNCT
ejpam-5565	85	5	b	b	NOUN
ejpam-5565	85	6	]	]	X
ejpam-5565	85	7	{	{	PUNCT
ejpam-5565	85	8	n∑	n∑	NOUN
ejpam-5565	85	9	i=1	i=1	PROPN
ejpam-5565	85	10	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	85	11	f+(ti−1)∥+	f+(ti−1)∥+	PROPN
ejpam-5565	85	12	}	}	PUNCT
ejpam-5565	85	13	and	and	CCONJ
ejpam-5565	85	14	−	−	PROPN
ejpam-5565	85	15	vb	vb	PROPN
ejpam-5565	85	16	a(f	a(f	PROPN
ejpam-5565	85	17	,	,	PUNCT
ejpam-5565	85	18	(	(	PUNCT
ejpam-5565	85	19	k−,−	k−,−	NOUN
ejpam-5565	85	20	[	[	X
ejpam-5565	85	21	·	·	PUNCT
ejpam-5565	85	22	,	,	PUNCT
ejpam-5565	85	23	·	·	PUNCT
ejpam-5565	85	24	]	]	X
ejpam-5565	85	25	)	)	PUNCT
ejpam-5565	85	26	)	)	PUNCT
ejpam-5565	86	1	=	=	SYM
ejpam-5565	86	2	sup	sup	NOUN
ejpam-5565	86	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	86	4	,	,	PUNCT
ejpam-5565	86	5	b	b	NOUN
ejpam-5565	86	6	]	]	X
ejpam-5565	86	7	{	{	PUNCT
ejpam-5565	86	8	n∑	n∑	NOUN
ejpam-5565	86	9	i=1	i=1	PROPN
ejpam-5565	86	10	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	86	11	f−(ti−1)∥−	f−(ti−1)∥−	PROPN
ejpam-5565	86	12	}	}	PUNCT
ejpam-5565	86	13	.	.	PUNCT
ejpam-5565	87	1	theorem	theorem	NOUN
ejpam-5565	87	2	3	3	NUM
ejpam-5565	87	3	.	.	PUNCT
ejpam-5565	88	1	[	[	X
ejpam-5565	88	2	4	4	X
ejpam-5565	88	3	]	]	X
ejpam-5565	88	4	let	let	VERB
ejpam-5565	88	5	(	(	PUNCT
ejpam-5565	88	6	k	k	NOUN
ejpam-5565	88	7	=	=	SYM
ejpam-5565	88	8	k+	k+	NOUN
ejpam-5565	88	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	88	10	,	,	PUNCT
ejpam-5565	88	11	[	[	X
ejpam-5565	88	12	·	·	PUNCT
ejpam-5565	88	13	,	,	PUNCT
ejpam-5565	88	14	·	·	PUNCT
ejpam-5565	88	15	]	]	PUNCT
ejpam-5565	88	16	,	,	PUNCT
ejpam-5565	88	17	j	j	PROPN
ejpam-5565	88	18	)	)	PUNCT
ejpam-5565	88	19	be	be	AUX
ejpam-5565	88	20	a	a	DET
ejpam-5565	88	21	krein	krein	ADJ
ejpam-5565	88	22	space	space	NOUN
ejpam-5565	88	23	,	,	PUNCT
ejpam-5565	88	24	f+	f+	NOUN
ejpam-5565	88	25	:	:	PUNCT
ejpam-5565	89	1	[	[	X
ejpam-5565	89	2	a	a	PRON
ejpam-5565	89	3	,	,	PUNCT
ejpam-5565	89	4	b]→	b]→	ADJ
ejpam-5565	89	5	k+	k+	NOUN
ejpam-5565	89	6	and	and	CCONJ
ejpam-5565	89	7	f−	f−	PROPN
ejpam-5565	89	8	:	:	PUNCT
ejpam-5565	89	9	[	[	X
ejpam-5565	89	10	a	a	PRON
ejpam-5565	89	11	,	,	PUNCT
ejpam-5565	89	12	b]→	b]→	PROPN
ejpam-5565	89	13	k−	k−	PROPN
ejpam-5565	89	14	strongly	strongly	ADV
ejpam-5565	89	15	of	of	ADP
ejpam-5565	89	16	bounded	bounded	ADJ
ejpam-5565	89	17	variation	variation	NOUN
ejpam-5565	89	18	in	in	ADP
ejpam-5565	89	19	the	the	DET
ejpam-5565	89	20	hilbert	hilbert	NOUN
ejpam-5565	89	21	spaces	space	NOUN
ejpam-5565	89	22	(	(	PUNCT
ejpam-5565	89	23	k+	k+	X
ejpam-5565	89	24	,	,	PUNCT
ejpam-5565	89	25	[	[	X
ejpam-5565	89	26	·	·	PUNCT
ejpam-5565	89	27	,	,	PUNCT
ejpam-5565	89	28	·	·	PUNCT
ejpam-5565	89	29	]	]	PUNCT
ejpam-5565	89	30	)	)	PUNCT
ejpam-5565	89	31	and	and	CCONJ
ejpam-5565	89	32	(	(	PUNCT
ejpam-5565	89	33	k−,−	k−,−	NOUN
ejpam-5565	89	34	[	[	X
ejpam-5565	89	35	·	·	PUNCT
ejpam-5565	89	36	,	,	PUNCT
ejpam-5565	89	37	·	·	PUNCT
ejpam-5565	89	38	]	]	X
ejpam-5565	89	39	)	)	PUNCT
ejpam-5565	89	40	respectively	respectively	ADV
ejpam-5565	89	41	,	,	PUNCT
ejpam-5565	89	42	then	then	ADV
ejpam-5565	89	43	f	f	X
ejpam-5565	89	44	:	:	PUNCT
ejpam-5565	90	1	[	[	X
ejpam-5565	90	2	a	a	X
ejpam-5565	90	3	,	,	PUNCT
ejpam-5565	90	4	b	b	NOUN
ejpam-5565	90	5	]	]	X
ejpam-5565	90	6	→	→	SYM
ejpam-5565	90	7	k	k	PROPN
ejpam-5565	90	8	defined	define	VERB
ejpam-5565	90	9	as	as	SCONJ
ejpam-5565	90	10	follows	follow	VERB
ejpam-5565	90	11	f(t	f(t	PROPN
ejpam-5565	90	12	)	)	PUNCT
ejpam-5565	90	13	=	=	SYM
ejpam-5565	90	14	f+(t	f+(t	PROPN
ejpam-5565	90	15	)	)	PUNCT
ejpam-5565	90	16	+	+	CCONJ
ejpam-5565	90	17	f−(t	f−(t	NOUN
ejpam-5565	90	18	)	)	PUNCT
ejpam-5565	90	19	is	be	AUX
ejpam-5565	90	20	strongly	strongly	ADV
ejpam-5565	90	21	of	of	ADP
ejpam-5565	90	22	bounded	bounded	ADJ
ejpam-5565	90	23	variation	variation	NOUN
ejpam-5565	90	24	in	in	ADP
ejpam-5565	90	25	the	the	DET
ejpam-5565	90	26	hilbert	hilbert	NOUN
ejpam-5565	90	27	space	space	NOUN
ejpam-5565	90	28	(	(	PUNCT
ejpam-5565	90	29	k	k	NOUN
ejpam-5565	90	30	,	,	PUNCT
ejpam-5565	90	31	[	[	X
ejpam-5565	90	32	·	·	PUNCT
ejpam-5565	90	33	,	,	PUNCT
ejpam-5565	90	34	·	·	PUNCT
ejpam-5565	90	35	]	]	X
ejpam-5565	90	36	j	j	PROPN
ejpam-5565	90	37	)	)	PUNCT
ejpam-5565	90	38	.	.	PUNCT
ejpam-5565	91	1	theorem	theorem	ADJ
ejpam-5565	91	2	4	4	NUM
ejpam-5565	91	3	.	.	PUNCT
ejpam-5565	92	1	[	[	X
ejpam-5565	92	2	4	4	X
ejpam-5565	92	3	]	]	X
ejpam-5565	92	4	let	let	VERB
ejpam-5565	92	5	(	(	PUNCT
ejpam-5565	92	6	k	k	NOUN
ejpam-5565	92	7	=	=	SYM
ejpam-5565	92	8	k+	k+	NOUN
ejpam-5565	92	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	92	10	,	,	PUNCT
ejpam-5565	92	11	[	[	X
ejpam-5565	92	12	·	·	PUNCT
ejpam-5565	92	13	,	,	PUNCT
ejpam-5565	92	14	·	·	PUNCT
ejpam-5565	92	15	]	]	PUNCT
ejpam-5565	92	16	)	)	PUNCT
ejpam-5565	92	17	be	be	AUX
ejpam-5565	92	18	a	a	DET
ejpam-5565	92	19	krein	krein	ADJ
ejpam-5565	92	20	space	space	NOUN
ejpam-5565	92	21	,	,	PUNCT
ejpam-5565	92	22	if	if	SCONJ
ejpam-5565	92	23	f	f	X
ejpam-5565	92	24	:	:	PUNCT
ejpam-5565	93	1	[	[	X
ejpam-5565	93	2	a	a	X
ejpam-5565	93	3	,	,	PUNCT
ejpam-5565	93	4	b	b	NOUN
ejpam-5565	93	5	]	]	X
ejpam-5565	93	6	→	→	X
ejpam-5565	93	7	k	k	X
ejpam-5565	93	8	is	be	AUX
ejpam-5565	93	9	strongly	strongly	ADV
ejpam-5565	93	10	of	of	ADP
ejpam-5565	93	11	bounded	bounded	ADJ
ejpam-5565	93	12	variation	variation	NOUN
ejpam-5565	93	13	in	in	ADP
ejpam-5565	93	14	(	(	PUNCT
ejpam-5565	93	15	k	k	NOUN
ejpam-5565	93	16	=	=	SYM
ejpam-5565	93	17	k+	k+	NOUN
ejpam-5565	93	18	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	93	19	,	,	PUNCT
ejpam-5565	93	20	[	[	X
ejpam-5565	93	21	·	·	PUNCT
ejpam-5565	93	22	,	,	PUNCT
ejpam-5565	93	23	·	·	PUNCT
ejpam-5565	93	24	]	]	X
ejpam-5565	93	25	)	)	PUNCT
ejpam-5565	93	26	,	,	PUNCT
ejpam-5565	93	27	then	then	ADV
ejpam-5565	93	28	j	j	PROPN
ejpam-5565	93	29	f	f	PROPN
ejpam-5565	93	30	is	be	AUX
ejpam-5565	93	31	strongly	strongly	ADV
ejpam-5565	93	32	of	of	ADP
ejpam-5565	93	33	bounded	bounded	ADJ
ejpam-5565	93	34	variation	variation	NOUN
ejpam-5565	93	35	in	in	ADP
ejpam-5565	93	36	(	(	PUNCT
ejpam-5565	93	37	k	k	NOUN
ejpam-5565	93	38	=	=	SYM
ejpam-5565	93	39	k+	k+	NOUN
ejpam-5565	93	40	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	93	41	,	,	PUNCT
ejpam-5565	93	42	[	[	X
ejpam-5565	93	43	·	·	PUNCT
ejpam-5565	93	44	,	,	PUNCT
ejpam-5565	93	45	·	·	PUNCT
ejpam-5565	93	46	]	]	PUNCT
ejpam-5565	93	47	)	)	PUNCT
ejpam-5565	93	48	and	and	CCONJ
ejpam-5565	93	49	(	(	PUNCT
ejpam-5565	93	50	k	k	NOUN
ejpam-5565	93	51	,	,	PUNCT
ejpam-5565	93	52	[	[	X
ejpam-5565	93	53	·	·	PUNCT
ejpam-5565	93	54	,	,	PUNCT
ejpam-5565	93	55	·	·	PUNCT
ejpam-5565	93	56	]	]	X
ejpam-5565	93	57	j	j	PROPN
ejpam-5565	93	58	)	)	PUNCT
ejpam-5565	93	59	.	.	PUNCT
ejpam-5565	94	1	theorem	theorem	ADJ
ejpam-5565	94	2	5	5	NUM
ejpam-5565	94	3	.	.	PUNCT
ejpam-5565	95	1	[	[	X
ejpam-5565	95	2	4	4	X
ejpam-5565	95	3	]	]	X
ejpam-5565	95	4	let	let	VERB
ejpam-5565	95	5	(	(	PUNCT
ejpam-5565	95	6	k	k	NOUN
ejpam-5565	95	7	=	=	SYM
ejpam-5565	95	8	k+	k+	NOUN
ejpam-5565	95	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	95	10	,	,	PUNCT
ejpam-5565	95	11	[	[	X
ejpam-5565	95	12	·	·	PUNCT
ejpam-5565	95	13	,	,	PUNCT
ejpam-5565	95	14	·	·	PUNCT
ejpam-5565	95	15	]	]	PUNCT
ejpam-5565	95	16	)	)	PUNCT
ejpam-5565	95	17	be	be	AUX
ejpam-5565	95	18	a	a	DET
ejpam-5565	95	19	krein	krein	ADJ
ejpam-5565	95	20	space	space	NOUN
ejpam-5565	95	21	and	and	CCONJ
ejpam-5565	95	22	let	let	VERB
ejpam-5565	95	23	f	f	NOUN
ejpam-5565	95	24	:	:	PUNCT
ejpam-5565	96	1	[	[	X
ejpam-5565	96	2	a	a	X
ejpam-5565	96	3	,	,	PUNCT
ejpam-5565	96	4	b]→	b]→	NOUN
ejpam-5565	96	5	k	k	PROPN
ejpam-5565	96	6	a	a	DET
ejpam-5565	96	7	strongly	strongly	ADV
ejpam-5565	96	8	of	of	ADP
ejpam-5565	96	9	bounded	bounded	ADJ
ejpam-5565	96	10	variation	variation	NOUN
ejpam-5565	96	11	function	function	NOUN
ejpam-5565	96	12	in	in	ADP
ejpam-5565	96	13	[	[	X
ejpam-5565	96	14	a	a	DET
ejpam-5565	96	15	,	,	PUNCT
ejpam-5565	96	16	b	b	NOUN
ejpam-5565	96	17	]	]	X
ejpam-5565	96	18	on	on	ADP
ejpam-5565	96	19	(	(	PUNCT
ejpam-5565	96	20	k	k	NOUN
ejpam-5565	96	21	=	=	SYM
ejpam-5565	96	22	k+	k+	NOUN
ejpam-5565	96	23	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	96	24	)	)	PUNCT
ejpam-5565	96	25	,	,	PUNCT
ejpam-5565	96	26	suppose	suppose	VERB
ejpam-5565	96	27	that	that	SCONJ
ejpam-5565	96	28	c	c	PROPN
ejpam-5565	96	29	in	in	ADP
ejpam-5565	96	30	(	(	PUNCT
ejpam-5565	96	31	a	a	DET
ejpam-5565	96	32	,	,	PUNCT
ejpam-5565	96	33	b	b	NOUN
ejpam-5565	96	34	)	)	PUNCT
ejpam-5565	96	35	,	,	PUNCT
ejpam-5565	96	36	then	then	ADV
ejpam-5565	96	37	f	f	PROPN
ejpam-5565	96	38	is	be	AUX
ejpam-5565	96	39	strongly	strongly	ADV
ejpam-5565	96	40	of	of	ADP
ejpam-5565	96	41	bounded	bounded	ADJ
ejpam-5565	96	42	variation	variation	NOUN
ejpam-5565	96	43	in	in	ADP
ejpam-5565	96	44	[	[	X
ejpam-5565	96	45	a	a	X
ejpam-5565	96	46	,	,	PUNCT
ejpam-5565	96	47	c	c	NOUN
ejpam-5565	96	48	]	]	PUNCT
ejpam-5565	96	49	and	and	CCONJ
ejpam-5565	96	50	in	in	ADP
ejpam-5565	96	51	[	[	X
ejpam-5565	96	52	c	c	X
ejpam-5565	96	53	,	,	PUNCT
ejpam-5565	96	54	b	b	X
ejpam-5565	96	55	]	]	X
ejpam-5565	96	56	on	on	ADP
ejpam-5565	96	57	(	(	PUNCT
ejpam-5565	96	58	k	k	NOUN
ejpam-5565	96	59	=	=	SYM
ejpam-5565	96	60	k+	k+	NOUN
ejpam-5565	96	61	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	96	62	)	)	PUNCT
ejpam-5565	96	63	.	.	PUNCT
ejpam-5565	97	1	in	in	ADP
ejpam-5565	97	2	this	this	DET
ejpam-5565	97	3	case	case	NOUN
ejpam-5565	97	4	we	we	PRON
ejpam-5565	97	5	have	have	VERB
ejpam-5565	97	6	v	v	NUM
ejpam-5565	97	7	b	b	NOUN
ejpam-5565	97	8	a	a	DET
ejpam-5565	97	9	(	(	PUNCT
ejpam-5565	97	10	f	f	NOUN
ejpam-5565	97	11	,	,	PUNCT
ejpam-5565	97	12	(	(	PUNCT
ejpam-5565	97	13	k	k	NOUN
ejpam-5565	97	14	,	,	PUNCT
ejpam-5565	97	15	[	[	X
ejpam-5565	97	16	·	·	PUNCT
ejpam-5565	97	17	,	,	PUNCT
ejpam-5565	97	18	·	·	PUNCT
ejpam-5565	97	19	]	]	X
ejpam-5565	97	20	)	)	PUNCT
ejpam-5565	97	21	)	)	PUNCT
ejpam-5565	98	1	=	=	PUNCT
ejpam-5565	98	2	v	v	ADP
ejpam-5565	98	3	c	c	PROPN
ejpam-5565	98	4	a	a	PRON
ejpam-5565	98	5	(	(	PUNCT
ejpam-5565	98	6	f	f	X
ejpam-5565	98	7	,	,	PUNCT
ejpam-5565	98	8	k	k	NOUN
ejpam-5565	98	9	)	)	PUNCT
ejpam-5565	98	10	+	+	CCONJ
ejpam-5565	98	11	v	v	NUM
ejpam-5565	98	12	b	b	X
ejpam-5565	98	13	c	c	X
ejpam-5565	98	14	(	(	PUNCT
ejpam-5565	98	15	f	f	X
ejpam-5565	98	16	,	,	PUNCT
ejpam-5565	98	17	k	k	NOUN
ejpam-5565	98	18	)	)	PUNCT
ejpam-5565	98	19	4	4	NUM
ejpam-5565	98	20	.	.	PUNCT
ejpam-5565	98	21	functions	function	NOUN
ejpam-5565	98	22	of	of	ADP
ejpam-5565	98	23	bounded	bounded	ADJ
ejpam-5565	98	24	q	q	NOUN
ejpam-5565	98	25	-	-	PUNCT
ejpam-5565	98	26	variation	variation	NOUN
ejpam-5565	98	27	in	in	ADP
ejpam-5565	98	28	hilbert	hilbert	NOUN
ejpam-5565	98	29	spaces	space	NOUN
ejpam-5565	98	30	associated	associate	VERB
ejpam-5565	98	31	with	with	ADP
ejpam-5565	98	32	a	a	DET
ejpam-5565	98	33	krein	krein	ADJ
ejpam-5565	98	34	space	space	NOUN
ejpam-5565	98	35	given	give	VERB
ejpam-5565	98	36	a	a	DET
ejpam-5565	98	37	krein	krein	ADJ
ejpam-5565	98	38	space	space	NOUN
ejpam-5565	98	39	(	(	PUNCT
ejpam-5565	98	40	k	k	NOUN
ejpam-5565	98	41	=	=	SYM
ejpam-5565	98	42	k+	k+	NOUN
ejpam-5565	98	43	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	98	44	,	,	PUNCT
ejpam-5565	98	45	[	[	X
ejpam-5565	98	46	·	·	PUNCT
ejpam-5565	98	47	,	,	PUNCT
ejpam-5565	98	48	·	·	PUNCT
ejpam-5565	98	49	]	]	PUNCT
ejpam-5565	98	50	,	,	PUNCT
ejpam-5565	98	51	j	j	PROPN
ejpam-5565	98	52	)	)	PUNCT
ejpam-5565	98	53	and	and	CCONJ
ejpam-5565	98	54	f	f	X
ejpam-5565	98	55	:	:	PUNCT
ejpam-5565	99	1	[	[	X
ejpam-5565	99	2	a	a	X
ejpam-5565	99	3	,	,	PUNCT
ejpam-5565	99	4	b	b	NOUN
ejpam-5565	99	5	]	]	X
ejpam-5565	99	6	→	→	SYM
ejpam-5565	99	7	k	k	X
ejpam-5565	99	8	=	=	PUNCT
ejpam-5565	99	9	k+	k+	NOUN
ejpam-5565	99	10	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	99	11	,	,	PUNCT
ejpam-5565	99	12	for	for	ADP
ejpam-5565	99	13	t	t	PROPN
ejpam-5565	99	14	in	in	ADP
ejpam-5565	99	15	[	[	X
ejpam-5565	99	16	a	a	PRON
ejpam-5565	99	17	,	,	PUNCT
ejpam-5565	99	18	b	b	NOUN
ejpam-5565	99	19	]	]	X
ejpam-5565	99	20	,	,	PUNCT
ejpam-5565	99	21	as	as	ADP
ejpam-5565	99	22	f(t	f(t	NOUN
ejpam-5565	99	23	)	)	PUNCT
ejpam-5565	99	24	in	in	ADP
ejpam-5565	99	25	k	k	PROPN
ejpam-5565	99	26	,	,	PUNCT
ejpam-5565	99	27	we	we	PRON
ejpam-5565	99	28	can	can	AUX
ejpam-5565	99	29	write	write	VERB
ejpam-5565	99	30	f(t	f(t	NOUN
ejpam-5565	99	31	)	)	PUNCT
ejpam-5565	99	32	=	=	SYM
ejpam-5565	99	33	f+(t	f+(t	PROPN
ejpam-5565	99	34	)	)	PUNCT
ejpam-5565	99	35	+	+	NUM
ejpam-5565	99	36	f−(t	f−(t	NOUN
ejpam-5565	99	37	)	)	PUNCT
ejpam-5565	99	38	,	,	PUNCT
ejpam-5565	99	39	where	where	SCONJ
ejpam-5565	99	40	f+(t	f+(t	NOUN
ejpam-5565	99	41	)	)	PUNCT
ejpam-5565	99	42	in	in	ADP
ejpam-5565	99	43	k+	k+	NOUN
ejpam-5565	99	44	and	and	CCONJ
ejpam-5565	99	45	f−(t	f−(t	NOUN
ejpam-5565	99	46	)	)	PUNCT
ejpam-5565	99	47	in	in	ADP
ejpam-5565	99	48	o.	o.	PROPN
ejpam-5565	99	49	ferrer	ferrer	PROPN
ejpam-5565	99	50	,	,	PUNCT
ejpam-5565	99	51	j.	j.	PROPN
ejpam-5565	99	52	naranjo	naranjo	PROPN
ejpam-5565	99	53	/	/	SYM
ejpam-5565	99	54	eur	eur	PROPN
ejpam-5565	99	55	.	.	PUNCT
ejpam-5565	100	1	j.	j.	PROPN
ejpam-5565	100	2	pure	pure	PROPN
ejpam-5565	100	3	appl	appl	PROPN
ejpam-5565	100	4	.	.	PROPN
ejpam-5565	100	5	math	math	PROPN
ejpam-5565	100	6	,	,	PUNCT
ejpam-5565	100	7	18	18	NUM
ejpam-5565	100	8	(	(	PUNCT
ejpam-5565	100	9	2	2	NUM
ejpam-5565	100	10	)	)	PUNCT
ejpam-5565	100	11	(	(	PUNCT
ejpam-5565	100	12	2025	2025	NUM
ejpam-5565	100	13	)	)	PUNCT
ejpam-5565	100	14	,	,	PUNCT
ejpam-5565	100	15	5565	5565	NUM
ejpam-5565	100	16	5	5	NUM
ejpam-5565	100	17	of	of	ADP
ejpam-5565	100	18	18	18	NUM
ejpam-5565	100	19	k−.	k−.	NOUN
ejpam-5565	100	20	now	now	ADV
ejpam-5565	100	21	,	,	PUNCT
ejpam-5565	100	22	since	since	SCONJ
ejpam-5565	100	23	(	(	PUNCT
ejpam-5565	100	24	k+	k+	X
ejpam-5565	100	25	,	,	PUNCT
ejpam-5565	100	26	[	[	X
ejpam-5565	100	27	·	·	PUNCT
ejpam-5565	100	28	,	,	PUNCT
ejpam-5565	100	29	·	·	PUNCT
ejpam-5565	100	30	]	]	PUNCT
ejpam-5565	100	31	)	)	PUNCT
ejpam-5565	100	32	and	and	CCONJ
ejpam-5565	100	33	(	(	PUNCT
ejpam-5565	100	34	k−,−	k−,−	NOUN
ejpam-5565	100	35	[	[	X
ejpam-5565	100	36	·	·	PUNCT
ejpam-5565	100	37	,	,	PUNCT
ejpam-5565	100	38	·	·	PUNCT
ejpam-5565	100	39	]	]	PUNCT
ejpam-5565	100	40	)	)	PUNCT
ejpam-5565	100	41	are	be	AUX
ejpam-5565	100	42	hilbert	hilbert	NOUN
ejpam-5565	100	43	spaces	space	NOUN
ejpam-5565	100	44	,	,	PUNCT
ejpam-5565	100	45	the	the	DET
ejpam-5565	100	46	q−variations	q−variation	NOUN
ejpam-5565	100	47	of	of	ADP
ejpam-5565	100	48	f	f	PROPN
ejpam-5565	100	49	on	on	ADP
ejpam-5565	100	50	[	[	X
ejpam-5565	100	51	a	a	DET
ejpam-5565	100	52	,	,	PUNCT
ejpam-5565	100	53	b	b	NOUN
ejpam-5565	100	54	]	]	PUNCT
ejpam-5565	100	55	denoted	denote	VERB
ejpam-5565	100	56	by	by	ADP
ejpam-5565	100	57	q+	q+	ADV
ejpam-5565	100	58	vb	vb	PROPN
ejpam-5565	100	59	a(f	a(f	PROPN
ejpam-5565	100	60	,	,	PUNCT
ejpam-5565	100	61	(	(	PUNCT
ejpam-5565	100	62	k+	k+	X
ejpam-5565	100	63	,	,	PUNCT
ejpam-5565	100	64	[	[	X
ejpam-5565	100	65	·	·	PUNCT
ejpam-5565	100	66	,	,	PUNCT
ejpam-5565	100	67	·	·	PUNCT
ejpam-5565	100	68	]	]	X
ejpam-5565	100	69	)	)	PUNCT
ejpam-5565	100	70	)	)	PUNCT
ejpam-5565	100	71	and	and	CCONJ
ejpam-5565	100	72	q−	q−	PROPN
ejpam-5565	100	73	vb	vb	PROPN
ejpam-5565	100	74	a(f	a(f	PROPN
ejpam-5565	100	75	,	,	PUNCT
ejpam-5565	100	76	(	(	PUNCT
ejpam-5565	100	77	k−	k−	PROPN
ejpam-5565	100	78	,	,	PUNCT
ejpam-5565	100	79	[	[	X
ejpam-5565	100	80	·	·	PUNCT
ejpam-5565	100	81	,	,	PUNCT
ejpam-5565	100	82	·	·	PUNCT
ejpam-5565	100	83	]	]	X
ejpam-5565	100	84	)	)	PUNCT
ejpam-5565	100	85	)	)	PUNCT
ejpam-5565	100	86	are	be	AUX
ejpam-5565	100	87	given	give	VERB
ejpam-5565	100	88	as	as	SCONJ
ejpam-5565	100	89	follows	follow	VERB
ejpam-5565	100	90	:	:	PUNCT
ejpam-5565	100	91	q+	q+	ADV
ejpam-5565	100	92	vb	vb	ADP
ejpam-5565	100	93	a(f	a(f	PROPN
ejpam-5565	100	94	,	,	PUNCT
ejpam-5565	100	95	(	(	PUNCT
ejpam-5565	100	96	k+	k+	X
ejpam-5565	100	97	,	,	PUNCT
ejpam-5565	100	98	[	[	X
ejpam-5565	100	99	·	·	PUNCT
ejpam-5565	100	100	,	,	PUNCT
ejpam-5565	100	101	·	·	PUNCT
ejpam-5565	100	102	]	]	X
ejpam-5565	100	103	)	)	PUNCT
ejpam-5565	100	104	)	)	PUNCT
ejpam-5565	101	1	=	=	SYM
ejpam-5565	101	2	sup	sup	NOUN
ejpam-5565	101	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	101	4	,	,	PUNCT
ejpam-5565	101	5	b	b	NOUN
ejpam-5565	101	6	]	]	PUNCT
ejpam-5565	101	7			PUNCT
ejpam-5565	101	8	(	(	PUNCT
ejpam-5565	101	9	n∑	n∑	NOUN
ejpam-5565	101	10	i=1	i=1	PROPN
ejpam-5565	101	11	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	101	12	f+(ti−1)∥q+	f+(ti−1)∥q+	PUNCT
ejpam-5565	101	13	)	)	PUNCT
ejpam-5565	101	14	1	1	X
ejpam-5565	101	15	/	/	SYM
ejpam-5565	101	16	q	q	NOUN
ejpam-5565	101	17			NOUN
ejpam-5565	101	18	and	and	CCONJ
ejpam-5565	101	19	q−	q−	PROPN
ejpam-5565	101	20	vb	vb	PROPN
ejpam-5565	101	21	a(f	a(f	PROPN
ejpam-5565	101	22	,	,	PUNCT
ejpam-5565	101	23	(	(	PUNCT
ejpam-5565	101	24	k−,−	k−,−	NOUN
ejpam-5565	101	25	[	[	X
ejpam-5565	101	26	·	·	PUNCT
ejpam-5565	101	27	,	,	PUNCT
ejpam-5565	101	28	·	·	PUNCT
ejpam-5565	101	29	]	]	X
ejpam-5565	101	30	)	)	PUNCT
ejpam-5565	101	31	)	)	PUNCT
ejpam-5565	102	1	=	=	SYM
ejpam-5565	102	2	sup	sup	NOUN
ejpam-5565	102	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	102	4	,	,	PUNCT
ejpam-5565	102	5	b	b	NOUN
ejpam-5565	102	6	]	]	PUNCT
ejpam-5565	102	7			PUNCT
ejpam-5565	102	8	(	(	PUNCT
ejpam-5565	102	9	n∑	n∑	NOUN
ejpam-5565	102	10	i=1	i=1	PROPN
ejpam-5565	102	11	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	102	12	f−(ti−1)∥q−	f−(ti−1)∥q−	X
ejpam-5565	102	13	)	)	PUNCT
ejpam-5565	102	14	1	1	X
ejpam-5565	102	15	/	/	SYM
ejpam-5565	102	16	q	q	X
ejpam-5565	102	17			NOUN
ejpam-5565	102	18	.	.	PUNCT
ejpam-5565	103	1	where	where	SCONJ
ejpam-5565	103	2	the	the	DET
ejpam-5565	103	3	supreme	supreme	NOUN
ejpam-5565	103	4	is	be	AUX
ejpam-5565	103	5	taken	take	VERB
ejpam-5565	103	6	over	over	ADP
ejpam-5565	103	7	the	the	DET
ejpam-5565	103	8	entire	entire	ADJ
ejpam-5565	103	9	set	set	NOUN
ejpam-5565	103	10	of	of	ADP
ejpam-5565	103	11	partitions	partition	NOUN
ejpam-5565	103	12	{	{	PUNCT
ejpam-5565	103	13	t0	t0	NOUN
ejpam-5565	103	14	,	,	PUNCT
ejpam-5565	103	15	t1	t1	NOUN
ejpam-5565	103	16	,	,	PUNCT
ejpam-5565	103	17	t2	t2	NOUN
ejpam-5565	103	18	,	,	PUNCT
ejpam-5565	103	19	.	.	PUNCT
ejpam-5565	103	20	.	.	PUNCT
ejpam-5565	104	1	.	.	PUNCT
ejpam-5565	105	1	,	,	PUNCT
ejpam-5565	105	2	tn	tn	NOUN
ejpam-5565	105	3	}	}	PUNCT
ejpam-5565	105	4	of	of	ADP
ejpam-5565	105	5	the	the	DET
ejpam-5565	105	6	interval	interval	NOUN
ejpam-5565	106	1	[	[	X
ejpam-5565	106	2	a	a	X
ejpam-5565	106	3	,	,	PUNCT
ejpam-5565	106	4	b	b	NOUN
ejpam-5565	106	5	]	]	X
ejpam-5565	106	6	.	.	PUNCT
ejpam-5565	107	1	we	we	PRON
ejpam-5565	107	2	will	will	AUX
ejpam-5565	107	3	call	call	VERB
ejpam-5565	107	4	these	these	DET
ejpam-5565	107	5	q−variations	q−variation	NOUN
ejpam-5565	107	6	positive	positive	ADJ
ejpam-5565	107	7	and	and	CCONJ
ejpam-5565	107	8	negative	negative	ADJ
ejpam-5565	107	9	q−variations	q−variation	NOUN
ejpam-5565	107	10	respectively	respectively	ADV
ejpam-5565	107	11	.	.	PUNCT
ejpam-5565	108	1	remark	remark	PROPN
ejpam-5565	108	2	4	4	NUM
ejpam-5565	108	3	.	.	PUNCT
ejpam-5565	109	1	note	note	VERB
ejpam-5565	109	2	that	that	SCONJ
ejpam-5565	109	3	(	(	PUNCT
ejpam-5565	109	4	i	i	NOUN
ejpam-5565	109	5	)	)	PUNCT
ejpam-5565	109	6	q+	q+	ADV
ejpam-5565	109	7	vb	vb	ADP
ejpam-5565	109	8	a(f	a(f	PROPN
ejpam-5565	109	9	,	,	PUNCT
ejpam-5565	109	10	(	(	PUNCT
ejpam-5565	109	11	k+	k+	X
ejpam-5565	109	12	,	,	PUNCT
ejpam-5565	109	13	[	[	X
ejpam-5565	109	14	·	·	PUNCT
ejpam-5565	109	15	,	,	PUNCT
ejpam-5565	109	16	·	·	PUNCT
ejpam-5565	109	17	]	]	X
ejpam-5565	109	18	)	)	PUNCT
ejpam-5565	109	19	)	)	PUNCT
ejpam-5565	109	20	≥	≥	NOUN
ejpam-5565	109	21	0	0	NUM
ejpam-5565	109	22	,	,	PUNCT
ejpam-5565	109	23	q−	q−	PROPN
ejpam-5565	109	24	vb	vb	PROPN
ejpam-5565	109	25	a(f	a(f	PROPN
ejpam-5565	109	26	,	,	PUNCT
ejpam-5565	109	27	(	(	PUNCT
ejpam-5565	109	28	k−,−	k−,−	NOUN
ejpam-5565	109	29	[	[	X
ejpam-5565	109	30	·	·	PUNCT
ejpam-5565	109	31	,	,	PUNCT
ejpam-5565	109	32	·	·	PUNCT
ejpam-5565	109	33	]	]	X
ejpam-5565	109	34	)	)	PUNCT
ejpam-5565	109	35	)	)	PUNCT
ejpam-5565	110	1	≥	≥	NOUN
ejpam-5565	110	2	0	0	NUM
ejpam-5565	110	3	and	and	CCONJ
ejpam-5565	110	4	q	q	ADJ
ejpam-5565	110	5	vb	vb	PROPN
ejpam-5565	110	6	a(f	a(f	PROPN
ejpam-5565	110	7	,	,	PUNCT
ejpam-5565	110	8	(	(	PUNCT
ejpam-5565	110	9	k	k	X
ejpam-5565	110	10	,	,	PUNCT
ejpam-5565	110	11	[	[	X
ejpam-5565	110	12	·	·	PUNCT
ejpam-5565	110	13	,	,	PUNCT
ejpam-5565	110	14	·	·	PUNCT
ejpam-5565	110	15	]	]	X
ejpam-5565	110	16	)	)	PUNCT
ejpam-5565	110	17	)	)	PUNCT
ejpam-5565	110	18	≥	≥	NOUN
ejpam-5565	110	19	0	0	NUM
ejpam-5565	110	20	.	.	PUNCT
ejpam-5565	111	1	(	(	PUNCT
ejpam-5565	111	2	ii	ii	NOUN
ejpam-5565	111	3	)	)	PUNCT
ejpam-5565	111	4	since	since	SCONJ
ejpam-5565	111	5	(	(	PUNCT
ejpam-5565	111	6	k+	k+	X
ejpam-5565	111	7	,	,	PUNCT
ejpam-5565	111	8	[	[	X
ejpam-5565	111	9	·	·	PUNCT
ejpam-5565	111	10	,	,	PUNCT
ejpam-5565	111	11	·	·	PUNCT
ejpam-5565	111	12	]	]	PUNCT
ejpam-5565	111	13	)	)	PUNCT
ejpam-5565	112	1	and	and	CCONJ
ejpam-5565	112	2	(	(	PUNCT
ejpam-5565	112	3	k−,−	k−,−	NOUN
ejpam-5565	112	4	[	[	X
ejpam-5565	112	5	·	·	PUNCT
ejpam-5565	112	6	,	,	PUNCT
ejpam-5565	112	7	·	·	PUNCT
ejpam-5565	112	8	]	]	PUNCT
ejpam-5565	112	9	)	)	PUNCT
ejpam-5565	112	10	are	be	AUX
ejpam-5565	112	11	hilbert	hilbert	NOUN
ejpam-5565	112	12	space	space	NOUN
ejpam-5565	112	13	.	.	PUNCT
ejpam-5565	113	1	given	give	VERB
ejpam-5565	113	2	α	α	PROPN
ejpam-5565	113	3	∈	∈	PROPN
ejpam-5565	113	4	c	c	NOUN
ejpam-5565	113	5	and	and	CCONJ
ejpam-5565	113	6	f	f	NOUN
ejpam-5565	113	7	,	,	PUNCT
ejpam-5565	113	8	g	g	PROPN
ejpam-5565	113	9	functions	function	NOUN
ejpam-5565	113	10	functions	function	NOUN
ejpam-5565	113	11	of	of	ADP
ejpam-5565	113	12	bounded	bounded	ADJ
ejpam-5565	113	13	q	q	NOUN
ejpam-5565	113	14	-	-	NOUN
ejpam-5565	113	15	variation	variation	NOUN
ejpam-5565	113	16	,	,	PUNCT
ejpam-5565	113	17	for	for	ADP
ejpam-5565	113	18	[	[	X
ejpam-5565	113	19	13	13	NUM
ejpam-5565	113	20	]	]	X
ejpam-5565	113	21	it	it	PRON
ejpam-5565	113	22	is	be	AUX
ejpam-5565	113	23	satisfied	satisfied	ADJ
ejpam-5565	113	24	that	that	SCONJ
ejpam-5565	113	25	:	:	PUNCT
ejpam-5565	113	26	i	i	NOUN
ejpam-5565	113	27	)	)	PUNCT
ejpam-5565	113	28	q+	q+	VERB
ejpam-5565	113	29	vb	vb	ADP
ejpam-5565	113	30	a(αf	a(αf	NOUN
ejpam-5565	113	31	,	,	PUNCT
ejpam-5565	113	32	(	(	PUNCT
ejpam-5565	113	33	k+	k+	X
ejpam-5565	113	34	,	,	PUNCT
ejpam-5565	113	35	[	[	X
ejpam-5565	113	36	·	·	PUNCT
ejpam-5565	113	37	,	,	PUNCT
ejpam-5565	113	38	·	·	PUNCT
ejpam-5565	113	39	]	]	X
ejpam-5565	113	40	)	)	PUNCT
ejpam-5565	113	41	)	)	PUNCT
ejpam-5565	114	1	=	=	SYM
ejpam-5565	114	2	|α|	|α|	PROPN
ejpam-5565	114	3	q+	q+	PUNCT
ejpam-5565	114	4	vb	vb	PROPN
ejpam-5565	114	5	a(f	a(f	PROPN
ejpam-5565	114	6	,	,	PUNCT
ejpam-5565	114	7	(	(	PUNCT
ejpam-5565	114	8	k+	k+	X
ejpam-5565	114	9	,	,	PUNCT
ejpam-5565	114	10	[	[	X
ejpam-5565	114	11	·	·	PUNCT
ejpam-5565	114	12	,	,	PUNCT
ejpam-5565	114	13	·	·	PUNCT
ejpam-5565	114	14	]	]	X
ejpam-5565	114	15	)	)	PUNCT
ejpam-5565	114	16	)	)	PUNCT
ejpam-5565	114	17	ii	ii	PROPN
ejpam-5565	114	18	)	)	PUNCT
ejpam-5565	114	19	q+	q+	PUNCT
ejpam-5565	114	20	vb	vb	NOUN
ejpam-5565	114	21	a((f	a((f	PUNCT
ejpam-5565	114	22	+	+	CCONJ
ejpam-5565	114	23	g	g	NOUN
ejpam-5565	114	24	)	)	PUNCT
ejpam-5565	114	25	,	,	PUNCT
ejpam-5565	114	26	(	(	PUNCT
ejpam-5565	114	27	k+	k+	X
ejpam-5565	114	28	,	,	PUNCT
ejpam-5565	114	29	[	[	X
ejpam-5565	114	30	·	·	PUNCT
ejpam-5565	114	31	,	,	PUNCT
ejpam-5565	114	32	·	·	PUNCT
ejpam-5565	114	33	]	]	X
ejpam-5565	114	34	)	)	PUNCT
ejpam-5565	114	35	)	)	PUNCT
ejpam-5565	115	1	=	=	PRON
ejpam-5565	115	2	q+	q+	PUNCT
ejpam-5565	115	3	vb	vb	ADP
ejpam-5565	115	4	a(f	a(f	PROPN
ejpam-5565	115	5	,	,	PUNCT
ejpam-5565	115	6	(	(	PUNCT
ejpam-5565	115	7	k+	k+	X
ejpam-5565	115	8	,	,	PUNCT
ejpam-5565	115	9	[	[	X
ejpam-5565	115	10	·	·	PUNCT
ejpam-5565	115	11	,	,	PUNCT
ejpam-5565	115	12	·	·	PUNCT
ejpam-5565	115	13	]	]	X
ejpam-5565	115	14	)	)	PUNCT
ejpam-5565	115	15	)	)	PUNCT
ejpam-5565	116	1	+	+	CCONJ
ejpam-5565	116	2	q+	q+	ADP
ejpam-5565	116	3	vb	vb	ADP
ejpam-5565	116	4	a(g	a(g	PROPN
ejpam-5565	116	5	,	,	PUNCT
ejpam-5565	116	6	(	(	PUNCT
ejpam-5565	116	7	k+	k+	X
ejpam-5565	116	8	,	,	PUNCT
ejpam-5565	116	9	[	[	X
ejpam-5565	116	10	·	·	PUNCT
ejpam-5565	116	11	,	,	PUNCT
ejpam-5565	116	12	·	·	PUNCT
ejpam-5565	116	13	]	]	X
ejpam-5565	116	14	)	)	PUNCT
ejpam-5565	116	15	)	)	PUNCT
ejpam-5565	116	16	iii	iii	X
ejpam-5565	116	17	)	)	PUNCT
ejpam-5565	116	18	q−	q−	PROPN
ejpam-5565	116	19	vb	vb	NOUN
ejpam-5565	116	20	a(αf	a(αf	NOUN
ejpam-5565	116	21	,	,	PUNCT
ejpam-5565	116	22	(	(	PUNCT
ejpam-5565	116	23	k−	k−	PROPN
ejpam-5565	116	24	,	,	PUNCT
ejpam-5565	116	25	[	[	X
ejpam-5565	116	26	·	·	PUNCT
ejpam-5565	116	27	,	,	PUNCT
ejpam-5565	116	28	·	·	PUNCT
ejpam-5565	116	29	]	]	X
ejpam-5565	116	30	)	)	PUNCT
ejpam-5565	116	31	)	)	PUNCT
ejpam-5565	117	1	=	=	PUNCT
ejpam-5565	117	2	|α|	|α|	X
ejpam-5565	117	3	q−	q−	PROPN
ejpam-5565	117	4	vb	vb	PROPN
ejpam-5565	117	5	a(f	a(f	PROPN
ejpam-5565	117	6	,	,	PUNCT
ejpam-5565	117	7	(	(	PUNCT
ejpam-5565	117	8	k−	k−	PROPN
ejpam-5565	117	9	,	,	PUNCT
ejpam-5565	117	10	[	[	X
ejpam-5565	117	11	·	·	PUNCT
ejpam-5565	117	12	,	,	PUNCT
ejpam-5565	117	13	·	·	PUNCT
ejpam-5565	117	14	]	]	X
ejpam-5565	117	15	)	)	PUNCT
ejpam-5565	117	16	)	)	PUNCT
ejpam-5565	117	17	iv	iv	X
ejpam-5565	117	18	)	)	PUNCT
ejpam-5565	117	19	q−	q−	PROPN
ejpam-5565	117	20	vb	vb	NOUN
ejpam-5565	117	21	a((f	a((f	PUNCT
ejpam-5565	117	22	+	+	CCONJ
ejpam-5565	117	23	g	g	NOUN
ejpam-5565	117	24	)	)	PUNCT
ejpam-5565	117	25	,	,	PUNCT
ejpam-5565	117	26	(	(	PUNCT
ejpam-5565	117	27	k−	k−	PROPN
ejpam-5565	117	28	,	,	PUNCT
ejpam-5565	117	29	[	[	X
ejpam-5565	117	30	·	·	PUNCT
ejpam-5565	117	31	,	,	PUNCT
ejpam-5565	117	32	·	·	PUNCT
ejpam-5565	117	33	]	]	X
ejpam-5565	117	34	)	)	PUNCT
ejpam-5565	117	35	)	)	PUNCT
ejpam-5565	118	1	=	=	SYM
ejpam-5565	118	2	q−	q−	PROPN
ejpam-5565	118	3	vb	vb	PROPN
ejpam-5565	118	4	a(f	a(f	PROPN
ejpam-5565	118	5	,	,	PUNCT
ejpam-5565	118	6	(	(	PUNCT
ejpam-5565	118	7	k−	k−	PROPN
ejpam-5565	118	8	,	,	PUNCT
ejpam-5565	118	9	[	[	X
ejpam-5565	118	10	·	·	PUNCT
ejpam-5565	118	11	,	,	PUNCT
ejpam-5565	118	12	·	·	PUNCT
ejpam-5565	118	13	]	]	X
ejpam-5565	118	14	)	)	PUNCT
ejpam-5565	118	15	)	)	PUNCT
ejpam-5565	119	1	+	+	CCONJ
ejpam-5565	119	2	q−	q−	PROPN
ejpam-5565	119	3	vb	vb	NOUN
ejpam-5565	119	4	a(g	a(g	PROPN
ejpam-5565	119	5	,	,	PUNCT
ejpam-5565	119	6	(	(	PUNCT
ejpam-5565	119	7	k−	k−	PROPN
ejpam-5565	119	8	,	,	PUNCT
ejpam-5565	119	9	[	[	X
ejpam-5565	119	10	·	·	PUNCT
ejpam-5565	119	11	,	,	PUNCT
ejpam-5565	119	12	·	·	PUNCT
ejpam-5565	119	13	]	]	X
ejpam-5565	119	14	)	)	PUNCT
ejpam-5565	119	15	)	)	PUNCT
ejpam-5565	119	16	example	example	NOUN
ejpam-5565	119	17	2	2	NUM
ejpam-5565	119	18	.	.	X
ejpam-5565	119	19	consider	consider	VERB
ejpam-5565	119	20	example	example	NOUN
ejpam-5565	120	1	1	1	NUM
ejpam-5565	120	2	and	and	CCONJ
ejpam-5565	120	3	the	the	DET
ejpam-5565	120	4	function	function	NOUN
ejpam-5565	120	5	f	f	NOUN
ejpam-5565	121	1	:	:	PUNCT
ejpam-5565	122	1	[	[	X
ejpam-5565	122	2	2	2	NUM
ejpam-5565	122	3	,	,	PUNCT
ejpam-5565	122	4	3]→	3]→	PROPN
ejpam-5565	122	5	c2	c2	PROPN
ejpam-5565	122	6	defined	define	VERB
ejpam-5565	122	7	by	by	ADP
ejpam-5565	122	8	f(t	f(t	NOUN
ejpam-5565	122	9	)	)	PUNCT
ejpam-5565	122	10	=	=	SYM
ejpam-5565	122	11	(	(	PUNCT
ejpam-5565	122	12	ti,−ti	ti,−ti	NOUN
ejpam-5565	122	13	)	)	PUNCT
ejpam-5565	122	14	=	=	SYM
ejpam-5565	122	15	(	(	PUNCT
ejpam-5565	122	16	ti	ti	NOUN
ejpam-5565	122	17	,	,	PUNCT
ejpam-5565	122	18	0	0	NUM
ejpam-5565	122	19	)	)	PUNCT
ejpam-5565	122	20	+	+	CCONJ
ejpam-5565	122	21	(	(	PUNCT
ejpam-5565	122	22	0,−ti	0,−ti	NUM
ejpam-5565	122	23	)	)	PUNCT
ejpam-5565	122	24	.	.	PUNCT
ejpam-5565	123	1	aśı	aśı	NOUN
ejpam-5565	123	2	,	,	PUNCT
ejpam-5565	123	3	f+(t	f+(t	NOUN
ejpam-5565	123	4	)	)	PUNCT
ejpam-5565	123	5	=	=	SYM
ejpam-5565	123	6	(	(	PUNCT
ejpam-5565	123	7	ti	ti	NOUN
ejpam-5565	123	8	,	,	PUNCT
ejpam-5565	123	9	0	0	NUM
ejpam-5565	123	10	)	)	PUNCT
ejpam-5565	123	11	,	,	PUNCT
ejpam-5565	123	12	f+(t	f+(t	X
ejpam-5565	123	13	)	)	PUNCT
ejpam-5565	123	14	=	=	SYM
ejpam-5565	123	15	(	(	PUNCT
ejpam-5565	123	16	ti	ti	NOUN
ejpam-5565	123	17	,	,	PUNCT
ejpam-5565	123	18	0	0	NUM
ejpam-5565	123	19	)	)	PUNCT
ejpam-5565	123	20	and	and	CCONJ
ejpam-5565	123	21	f−(t	f−(t	PROPN
ejpam-5565	123	22	)	)	PUNCT
ejpam-5565	123	23	=	=	PRON
ejpam-5565	123	24	(	(	PUNCT
ejpam-5565	123	25	0,−ti	0,−ti	NUM
ejpam-5565	123	26	)	)	PUNCT
ejpam-5565	123	27	.	.	PUNCT
ejpam-5565	124	1	then	then	ADV
ejpam-5565	124	2	the	the	DET
ejpam-5565	124	3	positive	positive	ADJ
ejpam-5565	124	4	and	and	CCONJ
ejpam-5565	124	5	negative	negative	ADJ
ejpam-5565	124	6	q−variations	q−variation	NOUN
ejpam-5565	124	7	are	be	AUX
ejpam-5565	124	8	given	give	VERB
ejpam-5565	124	9	by	by	ADP
ejpam-5565	124	10	:	:	PUNCT
ejpam-5565	124	11	q+	q+	ADV
ejpam-5565	124	12	vb	vb	ADP
ejpam-5565	124	13	a(f	a(f	PROPN
ejpam-5565	124	14	,	,	PUNCT
ejpam-5565	124	15	(	(	PUNCT
ejpam-5565	124	16	k+	k+	X
ejpam-5565	124	17	,	,	PUNCT
ejpam-5565	124	18	[	[	X
ejpam-5565	124	19	·	·	PUNCT
ejpam-5565	124	20	,	,	PUNCT
ejpam-5565	124	21	·	·	PUNCT
ejpam-5565	124	22	]	]	X
ejpam-5565	124	23	)	)	PUNCT
ejpam-5565	124	24	)	)	PUNCT
ejpam-5565	125	1	=	=	SYM
ejpam-5565	125	2	sup	sup	NOUN
ejpam-5565	125	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	125	4	,	,	PUNCT
ejpam-5565	125	5	b	b	NOUN
ejpam-5565	125	6	]	]	X
ejpam-5565	125	7			PROPN
ejpam-5565	125	8			PROPN
ejpam-5565	125	9	n∑	n∑	PROPN
ejpam-5565	125	10	j=1	j=1	PROPN
ejpam-5565	125	11	(	(	PUNCT
ejpam-5565	125	12	tj	tj	NOUN
ejpam-5565	125	13	−	−	PROPN
ejpam-5565	125	14	tj−1	tj−1	PROPN
ejpam-5565	125	15	)	)	PUNCT
ejpam-5565	125	16	q	q	NOUN
ejpam-5565	125	17	1	1	PROPN
ejpam-5565	125	18	/	/	SYM
ejpam-5565	125	19	q	q	NOUN
ejpam-5565	125	20			PROPN
ejpam-5565	125	21	=	=	SYM
ejpam-5565	125	22	q−	q−	PROPN
ejpam-5565	125	23	vb	vb	PROPN
ejpam-5565	125	24	a(f	a(f	PROPN
ejpam-5565	125	25	,	,	PUNCT
ejpam-5565	125	26	(	(	PUNCT
ejpam-5565	125	27	k−	k−	PROPN
ejpam-5565	125	28	,	,	PUNCT
ejpam-5565	125	29	[	[	X
ejpam-5565	125	30	·	·	PUNCT
ejpam-5565	125	31	,	,	PUNCT
ejpam-5565	125	32	·	·	PUNCT
ejpam-5565	125	33	]	]	X
ejpam-5565	125	34	)	)	PUNCT
ejpam-5565	125	35	)	)	PUNCT
ejpam-5565	126	1	the	the	DET
ejpam-5565	126	2	existence	existence	NOUN
ejpam-5565	126	3	of	of	ADP
ejpam-5565	126	4	functions	function	NOUN
ejpam-5565	126	5	of	of	ADP
ejpam-5565	126	6	bounded	bounded	ADJ
ejpam-5565	126	7	q−variation	q−variation	NOUN
ejpam-5565	126	8	on	on	ADP
ejpam-5565	126	9	hilbert	hilbert	NOUN
ejpam-5565	126	10	spaces	space	NOUN
ejpam-5565	126	11	associated	associate	VERB
ejpam-5565	126	12	to	to	ADP
ejpam-5565	126	13	a	a	DET
ejpam-5565	126	14	krein	krein	ADJ
ejpam-5565	126	15	space	space	NOUN
ejpam-5565	126	16	led	lead	VERB
ejpam-5565	126	17	us	we	PRON
ejpam-5565	126	18	to	to	PART
ejpam-5565	126	19	think	think	VERB
ejpam-5565	126	20	about	about	ADP
ejpam-5565	126	21	the	the	DET
ejpam-5565	126	22	definition	definition	NOUN
ejpam-5565	126	23	of	of	ADP
ejpam-5565	126	24	functions	function	NOUN
ejpam-5565	126	25	of	of	ADP
ejpam-5565	126	26	bounded	bounded	ADJ
ejpam-5565	126	27	q−variation	q−variation	NOUN
ejpam-5565	126	28	on	on	ADP
ejpam-5565	126	29	krein	krein	ADJ
ejpam-5565	126	30	spaces	space	NOUN
ejpam-5565	126	31	studied	study	VERB
ejpam-5565	126	32	in	in	ADP
ejpam-5565	126	33	the	the	DET
ejpam-5565	126	34	next	next	ADJ
ejpam-5565	126	35	section	section	NOUN
ejpam-5565	126	36	.	.	PUNCT
ejpam-5565	127	1	o.	o.	PROPN
ejpam-5565	127	2	ferrer	ferrer	PROPN
ejpam-5565	127	3	,	,	PUNCT
ejpam-5565	127	4	j.	j.	PROPN
ejpam-5565	127	5	naranjo	naranjo	PROPN
ejpam-5565	127	6	/	/	SYM
ejpam-5565	127	7	eur	eur	PROPN
ejpam-5565	127	8	.	.	PUNCT
ejpam-5565	128	1	j.	j.	PROPN
ejpam-5565	128	2	pure	pure	PROPN
ejpam-5565	128	3	appl	appl	PROPN
ejpam-5565	128	4	.	.	PROPN
ejpam-5565	128	5	math	math	PROPN
ejpam-5565	128	6	,	,	PUNCT
ejpam-5565	128	7	18	18	NUM
ejpam-5565	128	8	(	(	PUNCT
ejpam-5565	128	9	2	2	NUM
ejpam-5565	128	10	)	)	PUNCT
ejpam-5565	128	11	(	(	PUNCT
ejpam-5565	128	12	2025	2025	NUM
ejpam-5565	128	13	)	)	PUNCT
ejpam-5565	128	14	,	,	PUNCT
ejpam-5565	128	15	5565	5565	NUM
ejpam-5565	128	16	6	6	NUM
ejpam-5565	128	17	of	of	ADP
ejpam-5565	128	18	18	18	NUM
ejpam-5565	128	19	5	5	NUM
ejpam-5565	128	20	.	.	PUNCT
ejpam-5565	128	21	functions	function	NOUN
ejpam-5565	128	22	of	of	ADP
ejpam-5565	128	23	bounded	bounded	ADJ
ejpam-5565	128	24	q	q	NOUN
ejpam-5565	128	25	-	-	PUNCT
ejpam-5565	128	26	variation	variation	NOUN
ejpam-5565	128	27	in	in	ADP
ejpam-5565	128	28	krein	krein	ADJ
ejpam-5565	128	29	spaces	space	NOUN
ejpam-5565	128	30	in	in	ADP
ejpam-5565	128	31	this	this	DET
ejpam-5565	128	32	section	section	NOUN
ejpam-5565	128	33	we	we	PRON
ejpam-5565	128	34	will	will	AUX
ejpam-5565	128	35	introduce	introduce	VERB
ejpam-5565	128	36	in	in	ADP
ejpam-5565	128	37	krein	krein	PROPN
ejpam-5565	128	38	spaces	space	NOUN
ejpam-5565	128	39	the	the	DET
ejpam-5565	128	40	concepts	concept	NOUN
ejpam-5565	128	41	of	of	ADP
ejpam-5565	128	42	total	total	ADJ
ejpam-5565	128	43	q	q	ADJ
ejpam-5565	128	44	-	-	PUNCT
ejpam-5565	128	45	variation	variation	NOUN
ejpam-5565	128	46	and	and	CCONJ
ejpam-5565	128	47	give	give	VERB
ejpam-5565	128	48	the	the	DET
ejpam-5565	128	49	notion	notion	NOUN
ejpam-5565	128	50	of	of	ADP
ejpam-5565	128	51	a	a	DET
ejpam-5565	128	52	bounded	bounded	ADJ
ejpam-5565	128	53	q	q	ADJ
ejpam-5565	128	54	-	-	PUNCT
ejpam-5565	128	55	variation	variation	NOUN
ejpam-5565	128	56	function	function	NOUN
ejpam-5565	128	57	,	,	PUNCT
ejpam-5565	128	58	notions	notion	NOUN
ejpam-5565	128	59	that	that	PRON
ejpam-5565	128	60	generalise	generalise	VERB
ejpam-5565	128	61	the	the	DET
ejpam-5565	128	62	results	result	NOUN
ejpam-5565	128	63	given	give	VERB
ejpam-5565	128	64	in	in	ADP
ejpam-5565	128	65	[	[	NOUN
ejpam-5565	128	66	4	4	NUM
ejpam-5565	128	67	]	]	PUNCT
ejpam-5565	128	68	and	and	CCONJ
ejpam-5565	128	69	[	[	X
ejpam-5565	128	70	13	13	NUM
ejpam-5565	128	71	]	]	PUNCT
ejpam-5565	128	72	definition	definition	NOUN
ejpam-5565	128	73	7	7	NUM
ejpam-5565	128	74	.	.	PUNCT
ejpam-5565	129	1	let	let	VERB
ejpam-5565	129	2	(	(	PUNCT
ejpam-5565	129	3	k	k	NOUN
ejpam-5565	129	4	=	=	SYM
ejpam-5565	129	5	k+	k+	NOUN
ejpam-5565	129	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	129	7	,	,	PUNCT
ejpam-5565	129	8	[	[	X
ejpam-5565	129	9	·	·	PUNCT
ejpam-5565	129	10	,	,	PUNCT
ejpam-5565	129	11	·	·	PUNCT
ejpam-5565	129	12	]	]	PUNCT
ejpam-5565	129	13	)	)	PUNCT
ejpam-5565	129	14	be	be	AUX
ejpam-5565	129	15	a	a	DET
ejpam-5565	129	16	krein	krein	ADJ
ejpam-5565	129	17	space	space	NOUN
ejpam-5565	129	18	,	,	PUNCT
ejpam-5565	129	19	f	f	X
ejpam-5565	129	20	:	:	PUNCT
ejpam-5565	130	1	[	[	X
ejpam-5565	130	2	a	a	X
ejpam-5565	130	3	,	,	PUNCT
ejpam-5565	130	4	b]→	b]→	X
ejpam-5565	130	5	k	k	PROPN
ejpam-5565	130	6	and	and	CCONJ
ejpam-5565	130	7	q	q	ADJ
ejpam-5565	130	8	≥	≥	NOUN
ejpam-5565	130	9	1.at	1.at	NUM
ejpam-5565	130	10	the	the	DET
ejpam-5565	130	11	number	number	NOUN
ejpam-5565	130	12	q	q	X
ejpam-5565	130	13	vb	vb	PROPN
ejpam-5565	130	14	a(f	a(f	PROPN
ejpam-5565	130	15	,	,	PUNCT
ejpam-5565	130	16	(	(	PUNCT
ejpam-5565	130	17	k	k	X
ejpam-5565	130	18	,	,	PUNCT
ejpam-5565	130	19	[	[	X
ejpam-5565	130	20	·	·	PUNCT
ejpam-5565	130	21	,	,	PUNCT
ejpam-5565	130	22	·	·	PUNCT
ejpam-5565	130	23	]	]	X
ejpam-5565	130	24	)	)	PUNCT
ejpam-5565	130	25	)	)	PUNCT
ejpam-5565	131	1	=	=	SYM
ejpam-5565	131	2	sup	sup	NOUN
ejpam-5565	131	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	131	4	,	,	PUNCT
ejpam-5565	131	5	b	b	NOUN
ejpam-5565	131	6	]	]	PUNCT
ejpam-5565	131	7			PUNCT
ejpam-5565	131	8	(	(	PUNCT
ejpam-5565	131	9	n∑	n∑	NOUN
ejpam-5565	131	10	i=1	i=1	PROPN
ejpam-5565	131	11	(	(	PUNCT
ejpam-5565	131	12	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	131	13	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	131	14	+	+	CCONJ
ejpam-5565	131	15	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	131	16	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	131	17	)	)	PUNCT
ejpam-5565	131	18	1	1	X
ejpam-5565	131	19	/	/	SYM
ejpam-5565	131	20	q	q	NOUN
ejpam-5565	131	21			NOUN
ejpam-5565	131	22	where	where	SCONJ
ejpam-5565	131	23	the	the	DET
ejpam-5565	131	24	supremum	supremum	NOUN
ejpam-5565	131	25	is	be	AUX
ejpam-5565	131	26	taken	take	VERB
ejpam-5565	131	27	over	over	ADP
ejpam-5565	131	28	the	the	DET
ejpam-5565	131	29	set	set	NOUN
ejpam-5565	131	30	of	of	ADP
ejpam-5565	131	31	all	all	DET
ejpam-5565	131	32	partitions	partition	NOUN
ejpam-5565	131	33	p	p	X
ejpam-5565	131	34	=	=	X
ejpam-5565	131	35	{	{	PUNCT
ejpam-5565	131	36	t0	t0	PROPN
ejpam-5565	131	37	,	,	PUNCT
ejpam-5565	131	38	t1	t1	PROPN
ejpam-5565	131	39	,	,	PUNCT
ejpam-5565	131	40	.	.	PUNCT
ejpam-5565	131	41	.	.	PUNCT
ejpam-5565	131	42	.	.	PUNCT
ejpam-5565	131	43	,	,	PUNCT
ejpam-5565	131	44	tn	tn	NOUN
ejpam-5565	131	45	}	}	PUNCT
ejpam-5565	131	46	of	of	ADP
ejpam-5565	131	47	the	the	DET
ejpam-5565	131	48	interval	interval	NOUN
ejpam-5565	131	49	[	[	X
ejpam-5565	131	50	a	a	X
ejpam-5565	131	51	,	,	PUNCT
ejpam-5565	131	52	b	b	NOUN
ejpam-5565	131	53	]	]	X
ejpam-5565	131	54	,	,	PUNCT
ejpam-5565	131	55	we	we	PRON
ejpam-5565	131	56	will	will	AUX
ejpam-5565	131	57	call	call	VERB
ejpam-5565	131	58	total	total	ADJ
ejpam-5565	131	59	q	q	NOUN
ejpam-5565	131	60	-	-	PUNCT
ejpam-5565	131	61	variation	variation	NOUN
ejpam-5565	131	62	of	of	ADP
ejpam-5565	131	63	f	f	PROPN
ejpam-5565	131	64	in	in	ADP
ejpam-5565	131	65	[	[	X
ejpam-5565	131	66	a	a	DET
ejpam-5565	131	67	,	,	PUNCT
ejpam-5565	131	68	b	b	NOUN
ejpam-5565	131	69	]	]	X
ejpam-5565	131	70	on	on	ADP
ejpam-5565	131	71	k.	k.	PROPN
ejpam-5565	131	72	moreover	moreover	ADV
ejpam-5565	131	73	,	,	PUNCT
ejpam-5565	131	74	if	if	SCONJ
ejpam-5565	131	75	there	there	PRON
ejpam-5565	131	76	is	be	VERB
ejpam-5565	131	77	a	a	DET
ejpam-5565	131	78	constant	constant	ADJ
ejpam-5565	131	79	m	m	NOUN
ejpam-5565	131	80	>	>	X
ejpam-5565	131	81	0	0	NUM
ejpam-5565	132	1	such	such	ADJ
ejpam-5565	132	2	that	that	SCONJ
ejpam-5565	132	3	q	q	PROPN
ejpam-5565	132	4	vb	vb	PROPN
ejpam-5565	132	5	a(f	a(f	PROPN
ejpam-5565	132	6	,	,	PUNCT
ejpam-5565	132	7	(	(	PUNCT
ejpam-5565	132	8	k	k	X
ejpam-5565	132	9	,	,	PUNCT
ejpam-5565	132	10	[	[	X
ejpam-5565	132	11	·	·	PUNCT
ejpam-5565	132	12	,	,	PUNCT
ejpam-5565	132	13	·	·	PUNCT
ejpam-5565	132	14	]	]	X
ejpam-5565	132	15	)	)	PUNCT
ejpam-5565	132	16	)	)	PUNCT
ejpam-5565	132	17	≤m	≤m	NOUN
ejpam-5565	132	18	we	we	PRON
ejpam-5565	132	19	will	will	AUX
ejpam-5565	132	20	say	say	VERB
ejpam-5565	132	21	that	that	SCONJ
ejpam-5565	132	22	f	f	PROPN
ejpam-5565	132	23	is	be	AUX
ejpam-5565	132	24	of	of	ADP
ejpam-5565	132	25	bounded	bounded	ADJ
ejpam-5565	132	26	q	q	NOUN
ejpam-5565	132	27	-	-	NOUN
ejpam-5565	132	28	variation	variation	NOUN
ejpam-5565	132	29	in	in	ADP
ejpam-5565	132	30	[	[	X
ejpam-5565	132	31	a	a	DET
ejpam-5565	132	32	,	,	PUNCT
ejpam-5565	132	33	b	b	NOUN
ejpam-5565	132	34	]	]	X
ejpam-5565	132	35	on	on	ADP
ejpam-5565	132	36	k.	k.	PROPN
ejpam-5565	132	37	remark	remark	PROPN
ejpam-5565	132	38	5	5	NUM
ejpam-5565	132	39	.	.	PUNCT
ejpam-5565	133	1	the	the	DET
ejpam-5565	133	2	set	set	NOUN
ejpam-5565	133	3	of	of	ADP
ejpam-5565	133	4	all	all	DET
ejpam-5565	133	5	functions	function	NOUN
ejpam-5565	133	6	of	of	ADP
ejpam-5565	133	7	bounded	bounded	ADJ
ejpam-5565	133	8	q	q	NOUN
ejpam-5565	133	9	-	-	NOUN
ejpam-5565	133	10	variation	variation	NOUN
ejpam-5565	133	11	in	in	ADP
ejpam-5565	133	12	[	[	X
ejpam-5565	133	13	a	a	DET
ejpam-5565	133	14	,	,	PUNCT
ejpam-5565	133	15	b	b	NOUN
ejpam-5565	133	16	]	]	X
ejpam-5565	133	17	on	on	ADP
ejpam-5565	133	18	(	(	PUNCT
ejpam-5565	133	19	k	k	NOUN
ejpam-5565	133	20	=	=	SYM
ejpam-5565	133	21	k+	k+	NOUN
ejpam-5565	133	22	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	133	23	,	,	PUNCT
ejpam-5565	133	24	[	[	X
ejpam-5565	133	25	·	·	PUNCT
ejpam-5565	133	26	,	,	PUNCT
ejpam-5565	133	27	·	·	PUNCT
ejpam-5565	133	28	]	]	PUNCT
ejpam-5565	133	29	)	)	PUNCT
ejpam-5565	133	30	will	will	AUX
ejpam-5565	133	31	be	be	AUX
ejpam-5565	133	32	denoted	denote	VERB
ejpam-5565	133	33	as	as	SCONJ
ejpam-5565	133	34	follows	follow	VERB
ejpam-5565	133	35	b	b	PROPN
ejpam-5565	133	36	q	q	X
ejpam-5565	133	37	v	v	PROPN
ejpam-5565	133	38	b	b	PROPN
ejpam-5565	133	39	a	a	PRON
ejpam-5565	133	40	(	(	PUNCT
ejpam-5565	133	41	k	k	NOUN
ejpam-5565	133	42	,	,	PUNCT
ejpam-5565	133	43	[	[	X
ejpam-5565	133	44	·	·	PUNCT
ejpam-5565	133	45	,	,	PUNCT
ejpam-5565	133	46	·	·	PUNCT
ejpam-5565	133	47	]	]	X
ejpam-5565	133	48	)	)	PUNCT
ejpam-5565	133	49	.	.	PUNCT
ejpam-5565	134	1	(	(	PUNCT
ejpam-5565	134	2	i	i	NOUN
ejpam-5565	134	3	)	)	PUNCT
ejpam-5565	134	4	note	note	VERB
ejpam-5565	134	5	that	that	SCONJ
ejpam-5565	134	6	when	when	SCONJ
ejpam-5565	134	7	q	q	NOUN
ejpam-5565	134	8	=	=	NOUN
ejpam-5565	134	9	1	1	NUM
ejpam-5565	134	10	we	we	PRON
ejpam-5565	134	11	are	be	AUX
ejpam-5565	134	12	dealing	deal	VERB
ejpam-5565	134	13	with	with	ADP
ejpam-5565	134	14	definition	definition	NOUN
ejpam-5565	134	15	4.3	4.3	NUM
ejpam-5565	134	16	given	give	VERB
ejpam-5565	134	17	in	in	ADP
ejpam-5565	134	18	[	[	X
ejpam-5565	134	19	4	4	NUM
ejpam-5565	134	20	]	]	PUNCT
ejpam-5565	134	21	.	.	PUNCT
ejpam-5565	135	1	(	(	PUNCT
ejpam-5565	135	2	ii	ii	NOUN
ejpam-5565	135	3	)	)	PUNCT
ejpam-5565	135	4	in	in	ADP
ejpam-5565	135	5	the	the	DET
ejpam-5565	135	6	case	case	NOUN
ejpam-5565	135	7	of	of	ADP
ejpam-5565	135	8	a	a	DET
ejpam-5565	135	9	hilbert	hilbert	NOUN
ejpam-5565	135	10	space	space	NOUN
ejpam-5565	135	11	,	,	PUNCT
ejpam-5565	135	12	we	we	PRON
ejpam-5565	135	13	have	have	VERB
ejpam-5565	135	14	that	that	DET
ejpam-5565	135	15	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	135	16	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	135	17	=	=	SYM
ejpam-5565	135	18	0	0	NUM
ejpam-5565	136	1	and	and	CCONJ
ejpam-5565	136	2	so	so	ADV
ejpam-5565	136	3	q	q	X
ejpam-5565	136	4	v	v	PROPN
ejpam-5565	136	5	b	b	PROPN
ejpam-5565	136	6	a	a	DET
ejpam-5565	136	7	(	(	PUNCT
ejpam-5565	136	8	f	f	X
ejpam-5565	136	9	,	,	PUNCT
ejpam-5565	136	10	k	k	NOUN
ejpam-5565	136	11	,	,	PUNCT
ejpam-5565	136	12	[	[	X
ejpam-5565	136	13	·	·	PUNCT
ejpam-5565	136	14	,	,	PUNCT
ejpam-5565	136	15	·	·	PUNCT
ejpam-5565	136	16	]	]	PUNCT
ejpam-5565	136	17	)	)	PUNCT
ejpam-5565	136	18	=	=	SYM
ejpam-5565	136	19	sup	sup	NOUN
ejpam-5565	136	20	p∈p[a	p∈p[a	NOUN
ejpam-5565	136	21	,	,	PUNCT
ejpam-5565	136	22	b	b	NOUN
ejpam-5565	136	23	]	]	X
ejpam-5565	136	24	{	{	PUNCT
ejpam-5565	136	25	(	(	PUNCT
ejpam-5565	136	26	∑n	∑n	PROPN
ejpam-5565	136	27	i=1	i=1	PROPN
ejpam-5565	136	28	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	136	29	f+(ti−1)∥q+	f+(ti−1)∥q+	VERB
ejpam-5565	136	30	)	)	PUNCT
ejpam-5565	136	31	1	1	NUM
ejpam-5565	136	32	/	/	SYM
ejpam-5565	136	33	q	q	NOUN
ejpam-5565	136	34	}	}	PUNCT
ejpam-5565	136	35	=	=	PUNCT
ejpam-5565	136	36	vq(f	vq(f	X
ejpam-5565	136	37	)	)	PUNCT
ejpam-5565	136	38	which	which	PRON
ejpam-5565	136	39	is	be	AUX
ejpam-5565	136	40	the	the	DET
ejpam-5565	136	41	definition	definition	NOUN
ejpam-5565	136	42	of	of	ADP
ejpam-5565	136	43	a	a	DET
ejpam-5565	136	44	function	function	NOUN
ejpam-5565	136	45	of	of	ADP
ejpam-5565	136	46	q	q	NOUN
ejpam-5565	136	47	-	-	PUNCT
ejpam-5565	136	48	variation	variation	NOUN
ejpam-5565	136	49	on	on	ADP
ejpam-5565	136	50	a	a	DET
ejpam-5565	136	51	hilbert	hilbert	NOUN
ejpam-5565	136	52	space	space	NOUN
ejpam-5565	136	53	in	in	ADP
ejpam-5565	136	54	the	the	DET
ejpam-5565	136	55	weiner	weiner	NOUN
ejpam-5565	136	56	sense	sense	NOUN
ejpam-5565	136	57	[	[	X
ejpam-5565	136	58	13	13	NUM
ejpam-5565	136	59	]	]	PUNCT
ejpam-5565	136	60	.	.	PUNCT
ejpam-5565	137	1	(	(	PUNCT
ejpam-5565	137	2	iii	iii	X
ejpam-5565	137	3	)	)	PUNCT
ejpam-5565	137	4	if	if	SCONJ
ejpam-5565	137	5	f	f	PROPN
ejpam-5565	137	6	∈	∈	PROPN
ejpam-5565	138	1	b	b	X
ejpam-5565	138	2	q	q	X
ejpam-5565	138	3	v	v	PROPN
ejpam-5565	138	4	b	b	PROPN
ejpam-5565	138	5	a	a	DET
ejpam-5565	138	6	(	(	PUNCT
ejpam-5565	138	7	k	k	NOUN
ejpam-5565	138	8	,	,	PUNCT
ejpam-5565	138	9	[	[	X
ejpam-5565	138	10	·	·	PUNCT
ejpam-5565	138	11	,	,	PUNCT
ejpam-5565	138	12	·	·	PUNCT
ejpam-5565	138	13	]	]	X
ejpam-5565	138	14	)	)	PUNCT
ejpam-5565	139	1	,	,	PUNCT
ejpam-5565	139	2	then	then	ADV
ejpam-5565	139	3	f	f	PROPN
ejpam-5565	139	4	∈	∈	PROPN
ejpam-5565	139	5	b	b	X
ejpam-5565	139	6	q	q	X
ejpam-5565	139	7	v	v	PROPN
ejpam-5565	139	8	b	b	PROPN
ejpam-5565	139	9	a	a	DET
ejpam-5565	139	10	(	(	PUNCT
ejpam-5565	139	11	k+	k+	NOUN
ejpam-5565	139	12	,	,	PUNCT
ejpam-5565	139	13	[	[	X
ejpam-5565	139	14	·	·	PUNCT
ejpam-5565	139	15	,	,	PUNCT
ejpam-5565	139	16	·	·	PUNCT
ejpam-5565	139	17	]	]	PUNCT
ejpam-5565	139	18	)	)	PUNCT
ejpam-5565	139	19	and	and	CCONJ
ejpam-5565	139	20	f	f	PROPN
ejpam-5565	139	21	∈	∈	PROPN
ejpam-5565	140	1	b	b	X
ejpam-5565	140	2	q	q	X
ejpam-5565	140	3	v	v	PROPN
ejpam-5565	140	4	b	b	PROPN
ejpam-5565	140	5	a	a	DET
ejpam-5565	140	6	(	(	PUNCT
ejpam-5565	140	7	k−,−	k−,−	NOUN
ejpam-5565	140	8	[	[	X
ejpam-5565	140	9	·	·	PUNCT
ejpam-5565	140	10	,	,	PUNCT
ejpam-5565	140	11	·	·	PUNCT
ejpam-5565	140	12	]	]	X
ejpam-5565	140	13	)	)	PUNCT
ejpam-5565	140	14	,	,	PUNCT
ejpam-5565	140	15	since	since	SCONJ
ejpam-5565	140	16	that	that	DET
ejpam-5565	140	17	∥f+(ti	∥f+(ti	NOUN
ejpam-5565	140	18	)	)	PUNCT
ejpam-5565	140	19	−	−	PROPN
ejpam-5565	141	1	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	141	2	,	,	PUNCT
ejpam-5565	141	3	∥f−(ti	∥f−(ti	NOUN
ejpam-5565	141	4	)	)	PUNCT
ejpam-5565	141	5	−	−	NOUN
ejpam-5565	141	6	f−(ti−1)∥−	f−(ti−1)∥−	ADJ
ejpam-5565	141	7	≤	≤	PROPN
ejpam-5565	141	8	∥f+(ti	∥f+(ti	NOUN
ejpam-5565	141	9	)	)	PUNCT
ejpam-5565	141	10	−	−	NOUN
ejpam-5565	142	1	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	142	2	+	+	CCONJ
ejpam-5565	142	3	∥f−(ti	∥f−(ti	NOUN
ejpam-5565	142	4	)	)	PUNCT
ejpam-5565	142	5	−	−	NOUN
ejpam-5565	142	6	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	142	7	the	the	DET
ejpam-5565	142	8	observation3	observation3	NOUN
ejpam-5565	142	9	is	be	AUX
ejpam-5565	142	10	of	of	ADP
ejpam-5565	142	11	utmost	utmost	ADJ
ejpam-5565	142	12	relevance	relevance	NOUN
ejpam-5565	142	13	,	,	PUNCT
ejpam-5565	142	14	since	since	SCONJ
ejpam-5565	142	15	it	it	PRON
ejpam-5565	142	16	guarantees	guarantee	VERB
ejpam-5565	142	17	that	that	SCONJ
ejpam-5565	142	18	every	every	DET
ejpam-5565	142	19	bounded	bounded	ADJ
ejpam-5565	142	20	q	q	ADJ
ejpam-5565	142	21	-	-	PUNCT
ejpam-5565	142	22	variation	variation	NOUN
ejpam-5565	142	23	function	function	NOUN
ejpam-5565	142	24	on	on	ADP
ejpam-5565	142	25	krein	krein	ADJ
ejpam-5565	142	26	space	space	NOUN
ejpam-5565	142	27	k	k	PROPN
ejpam-5565	142	28	=	=	PUNCT
ejpam-5565	142	29	k+	k+	PROPN
ejpam-5565	142	30	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	142	31	is	be	AUX
ejpam-5565	142	32	of	of	ADP
ejpam-5565	142	33	bounded	bounded	ADJ
ejpam-5565	142	34	q	q	NOUN
ejpam-5565	142	35	-	-	NOUN
ejpam-5565	142	36	variation	variation	NOUN
ejpam-5565	142	37	on	on	ADP
ejpam-5565	142	38	the	the	DET
ejpam-5565	142	39	associated	associated	ADJ
ejpam-5565	142	40	hilbert	hilbert	NOUN
ejpam-5565	142	41	spaces	space	NOUN
ejpam-5565	142	42	k+	k+	NOUN
ejpam-5565	142	43	and	and	CCONJ
ejpam-5565	142	44	k−.	k−.	PROPN
ejpam-5565	142	45	remark	remark	VERB
ejpam-5565	142	46	6	6	NUM
ejpam-5565	142	47	.	.	PUNCT
ejpam-5565	143	1	note	note	VERB
ejpam-5565	143	2	that	that	SCONJ
ejpam-5565	143	3	for	for	ADP
ejpam-5565	143	4	the	the	DET
ejpam-5565	143	5	associated	associated	ADJ
ejpam-5565	143	6	hilbert	hilbert	NOUN
ejpam-5565	143	7	space	space	NOUN
ejpam-5565	143	8	(	(	PUNCT
ejpam-5565	143	9	k	k	NOUN
ejpam-5565	143	10	,	,	PUNCT
ejpam-5565	143	11	[	[	X
ejpam-5565	143	12	·	·	PUNCT
ejpam-5565	143	13	,	,	PUNCT
ejpam-5565	143	14	·	·	PUNCT
ejpam-5565	143	15	]	]	X
ejpam-5565	143	16	j	j	X
ejpam-5565	143	17	)	)	PUNCT
ejpam-5565	143	18	the	the	DET
ejpam-5565	143	19	total	total	ADJ
ejpam-5565	143	20	q	q	NOUN
ejpam-5565	143	21	-	-	PUNCT
ejpam-5565	143	22	variation	variation	NOUN
ejpam-5565	143	23	of	of	ADP
ejpam-5565	143	24	f	f	PROPN
ejpam-5565	143	25	is	be	AUX
ejpam-5565	143	26	:	:	PUNCT
ejpam-5565	143	27	q	q	ADJ
ejpam-5565	143	28	vb	vb	PROPN
ejpam-5565	143	29	a(f	a(f	PROPN
ejpam-5565	143	30	,	,	PUNCT
ejpam-5565	143	31	(	(	PUNCT
ejpam-5565	143	32	k	k	X
ejpam-5565	143	33	,	,	PUNCT
ejpam-5565	143	34	[	[	X
ejpam-5565	143	35	·	·	PUNCT
ejpam-5565	143	36	,	,	PUNCT
ejpam-5565	143	37	·	·	PUNCT
ejpam-5565	143	38	]	]	X
ejpam-5565	143	39	j	j	NOUN
ejpam-5565	143	40	)	)	PUNCT
ejpam-5565	143	41	)	)	PUNCT
ejpam-5565	144	1	=	=	SYM
ejpam-5565	144	2	sup	sup	NOUN
ejpam-5565	144	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	144	4	,	,	PUNCT
ejpam-5565	144	5	b	b	NOUN
ejpam-5565	144	6	]	]	PUNCT
ejpam-5565	144	7			PUNCT
ejpam-5565	144	8	(	(	PUNCT
ejpam-5565	144	9	n∑	n∑	NOUN
ejpam-5565	144	10	i=1	i=1	PROPN
ejpam-5565	144	11	∥f(ti)−	∥f(ti)−	PROPN
ejpam-5565	144	12	f(ti−1)∥qj	f(ti−1)∥qj	PROPN
ejpam-5565	144	13	)	)	PUNCT
ejpam-5565	144	14	1	1	X
ejpam-5565	144	15	/	/	SYM
ejpam-5565	144	16	q	q	NOUN
ejpam-5565	144	17			PROPN
ejpam-5565	144	18	next	next	ADV
ejpam-5565	144	19	,	,	PUNCT
ejpam-5565	144	20	we	we	PRON
ejpam-5565	144	21	show	show	VERB
ejpam-5565	144	22	an	an	DET
ejpam-5565	144	23	example	example	NOUN
ejpam-5565	144	24	of	of	ADP
ejpam-5565	144	25	a	a	DET
ejpam-5565	144	26	bounded	bounded	ADJ
ejpam-5565	144	27	q	q	ADJ
ejpam-5565	144	28	-	-	PUNCT
ejpam-5565	144	29	variation	variation	NOUN
ejpam-5565	144	30	function	function	NOUN
ejpam-5565	144	31	in	in	ADP
ejpam-5565	144	32	a	a	DET
ejpam-5565	144	33	krein	krein	ADJ
ejpam-5565	144	34	space	space	NOUN
ejpam-5565	144	35	.	.	PUNCT
ejpam-5565	145	1	o.	o.	PROPN
ejpam-5565	145	2	ferrer	ferrer	PROPN
ejpam-5565	145	3	,	,	PUNCT
ejpam-5565	145	4	j.	j.	PROPN
ejpam-5565	145	5	naranjo	naranjo	PROPN
ejpam-5565	145	6	/	/	SYM
ejpam-5565	145	7	eur	eur	PROPN
ejpam-5565	145	8	.	.	PUNCT
ejpam-5565	146	1	j.	j.	PROPN
ejpam-5565	146	2	pure	pure	PROPN
ejpam-5565	146	3	appl	appl	PROPN
ejpam-5565	146	4	.	.	PROPN
ejpam-5565	146	5	math	math	PROPN
ejpam-5565	146	6	,	,	PUNCT
ejpam-5565	146	7	18	18	NUM
ejpam-5565	146	8	(	(	PUNCT
ejpam-5565	146	9	2	2	NUM
ejpam-5565	146	10	)	)	PUNCT
ejpam-5565	146	11	(	(	PUNCT
ejpam-5565	146	12	2025	2025	NUM
ejpam-5565	146	13	)	)	PUNCT
ejpam-5565	146	14	,	,	PUNCT
ejpam-5565	146	15	5565	5565	NUM
ejpam-5565	146	16	7	7	NUM
ejpam-5565	146	17	of	of	ADP
ejpam-5565	146	18	18	18	NUM
ejpam-5565	146	19	example	example	NOUN
ejpam-5565	146	20	3	3	NUM
ejpam-5565	146	21	.	.	X
ejpam-5565	146	22	consider	consider	VERB
ejpam-5565	146	23	example	example	NOUN
ejpam-5565	146	24	1	1	NUM
ejpam-5565	146	25	and	and	CCONJ
ejpam-5565	146	26	the	the	DET
ejpam-5565	146	27	function	function	NOUN
ejpam-5565	146	28	f	f	NOUN
ejpam-5565	146	29	:	:	PUNCT
ejpam-5565	147	1	[	[	X
ejpam-5565	147	2	2	2	NUM
ejpam-5565	147	3	,	,	PUNCT
ejpam-5565	147	4	3]→	3]→	PROPN
ejpam-5565	147	5	c2	c2	PROPN
ejpam-5565	147	6	defined	define	VERB
ejpam-5565	147	7	by	by	ADP
ejpam-5565	147	8	f(t	f(t	NOUN
ejpam-5565	147	9	)	)	PUNCT
ejpam-5565	147	10	=	=	SYM
ejpam-5565	147	11	(	(	PUNCT
ejpam-5565	147	12	ti,−ti	ti,−ti	NOUN
ejpam-5565	147	13	)	)	PUNCT
ejpam-5565	147	14	.	.	PUNCT
ejpam-5565	148	1	let	let	VERB
ejpam-5565	148	2	us	we	PRON
ejpam-5565	148	3	see	see	VERB
ejpam-5565	148	4	that	that	SCONJ
ejpam-5565	148	5	f	f	PROPN
ejpam-5565	148	6	is	be	AUX
ejpam-5565	148	7	a	a	DET
ejpam-5565	148	8	function	function	NOUN
ejpam-5565	148	9	of	of	ADP
ejpam-5565	148	10	bounded	bounded	ADJ
ejpam-5565	148	11	2	2	NUM
ejpam-5565	148	12	-	-	PUNCT
ejpam-5565	148	13	variation	variation	NOUN
ejpam-5565	148	14	.	.	PUNCT
ejpam-5565	149	1	in	in	ADP
ejpam-5565	149	2	fact	fact	NOUN
ejpam-5565	149	3	,	,	PUNCT
ejpam-5565	149	4	let	let	VERB
ejpam-5565	149	5	p	p	NOUN
ejpam-5565	149	6	=	=	X
ejpam-5565	149	7	{	{	PUNCT
ejpam-5565	149	8	t0	t0	PROPN
ejpam-5565	149	9	,	,	PUNCT
ejpam-5565	149	10	t1	t1	PROPN
ejpam-5565	149	11	,	,	PUNCT
ejpam-5565	149	12	.	.	PUNCT
ejpam-5565	149	13	.	.	PUNCT
ejpam-5565	150	1	.	.	PUNCT
ejpam-5565	151	1	,	,	PUNCT
ejpam-5565	151	2	tn	tn	PROPN
ejpam-5565	151	3	}	}	PUNCT
ejpam-5565	151	4	be	be	VERB
ejpam-5565	151	5	a	a	DET
ejpam-5565	151	6	partition	partition	NOUN
ejpam-5565	151	7	of	of	ADP
ejpam-5565	151	8	[	[	X
ejpam-5565	151	9	2	2	NUM
ejpam-5565	151	10	,	,	PUNCT
ejpam-5565	151	11	3	3	NUM
ejpam-5565	151	12	]	]	PUNCT
ejpam-5565	151	13	.	.	PUNCT
ejpam-5565	152	1	then	then	ADV
ejpam-5565	152	2	,	,	PUNCT
ejpam-5565	152	3	∥f+(tj)−	∥f+(tj)−	NOUN
ejpam-5565	152	4	f+(tj−1)∥+	f+(tj−1)∥+	NOUN
ejpam-5565	152	5	=	=	SYM
ejpam-5565	152	6	∥(tji−	∥(tji−	NUM
ejpam-5565	152	7	tj−1i	tj−1i	NUM
ejpam-5565	152	8	,	,	PUNCT
ejpam-5565	152	9	0)∥+	0)∥+	NOUN
ejpam-5565	152	10	=	=	SYM
ejpam-5565	152	11	|tji−	|tji−	ADP
ejpam-5565	152	12	tj−1i|	tj−1i|	NOUN
ejpam-5565	152	13	=	=	PUNCT
ejpam-5565	153	1	|tj	|tj	NOUN
ejpam-5565	153	2	−	−	NOUN
ejpam-5565	153	3	tj−1|	tj−1|	NOUN
ejpam-5565	153	4	·	·	PUNCT
ejpam-5565	153	5	|i|	|i|	INTJ
ejpam-5565	153	6	=	=	SYM
ejpam-5565	153	7	tj	tj	PROPN
ejpam-5565	153	8	−	−	PROPN
ejpam-5565	153	9	tj−1	tj−1	NOUN
ejpam-5565	153	10	∥f−(ji)−	∥f−(ji)−	ADJ
ejpam-5565	153	11	f−(tj−1)∥−	f−(tj−1)∥−	NOUN
ejpam-5565	153	12	=	=	SYM
ejpam-5565	153	13	∥(0	∥(0	PROPN
ejpam-5565	153	14	,	,	PUNCT
ejpam-5565	153	15	tj−1i−	tj−1i−	X
ejpam-5565	153	16	tji)∥−	tji)∥−	NOUN
ejpam-5565	153	17	=	=	SYM
ejpam-5565	153	18	|tj−1i−	|tj−1i−	NUM
ejpam-5565	153	19	tji|	tji|	NOUN
ejpam-5565	153	20	=	=	PUNCT
ejpam-5565	154	1	|tj−1	|tj−1	NUM
ejpam-5565	154	2	−	−	NOUN
ejpam-5565	154	3	tj	tj	NOUN
ejpam-5565	154	4	|	|	ADV
ejpam-5565	154	5	·	·	PUNCT
ejpam-5565	155	1	|i|	|i|	INTJ
ejpam-5565	155	2	=	=	SYM
ejpam-5565	155	3	tj	tj	PROPN
ejpam-5565	155	4	−	−	PROPN
ejpam-5565	155	5	tj−1	tj−1	PROPN
ejpam-5565	155	6	.	.	PUNCT
ejpam-5565	156	1	thus	thus	ADV
ejpam-5565	156	2	,	,	PUNCT
ejpam-5565	156	3	(	(	PUNCT
ejpam-5565	156	4	∥f+(tj)−	∥f+(tj)−	NOUN
ejpam-5565	156	5	f+(tj−1)∥+	f+(tj−1)∥+	ADJ
ejpam-5565	156	6	+	+	NUM
ejpam-5565	156	7	∥f−(tj)−	∥f−(tj)−	NOUN
ejpam-5565	156	8	f−(tj−1)∥−)2	f−(tj−1)∥−)2	NOUN
ejpam-5565	156	9	=	=	SYM
ejpam-5565	156	10	(	(	PUNCT
ejpam-5565	156	11	2(tj	2(tj	NUM
ejpam-5565	156	12	−	−	PROPN
ejpam-5565	156	13	tj−1	tj−1	NOUN
ejpam-5565	156	14	)	)	PUNCT
ejpam-5565	156	15	)	)	PUNCT
ejpam-5565	156	16	2	2	NUM
ejpam-5565	156	17	=	=	SYM
ejpam-5565	156	18	4(tj	4(tj	NOUN
ejpam-5565	156	19	−	−	PROPN
ejpam-5565	156	20	tj−1	tj−1	PROPN
ejpam-5565	156	21	)	)	PUNCT
ejpam-5565	156	22	2	2	NUM
ejpam-5565	156	23	now	now	ADV
ejpam-5565	156	24	,	,	PUNCT
ejpam-5565	156	25	since	since	SCONJ
ejpam-5565	156	26	t	t	PROPN
ejpam-5565	156	27	∈	∈	PROPN
ejpam-5565	157	1	[	[	X
ejpam-5565	157	2	2	2	NUM
ejpam-5565	157	3	,	,	PUNCT
ejpam-5565	157	4	3	3	NUM
ejpam-5565	157	5	]	]	PUNCT
ejpam-5565	157	6	,	,	PUNCT
ejpam-5565	157	7	then	then	ADV
ejpam-5565	157	8	0	0	NUM
ejpam-5565	157	9	≤	≤	NUM
ejpam-5565	157	10	tj	tj	NOUN
ejpam-5565	157	11	−	−	PROPN
ejpam-5565	157	12	tj−1	tj−1	NOUN
ejpam-5565	157	13	≤	≤	ADJ
ejpam-5565	157	14	1	1	NUM
ejpam-5565	157	15	.	.	PUNCT
ejpam-5565	158	1	then	then	ADV
ejpam-5565	158	2	,	,	PUNCT
ejpam-5565	158	3	(	(	PUNCT
ejpam-5565	158	4	tj	tj	NOUN
ejpam-5565	158	5	−	−	PROPN
ejpam-5565	158	6	tj−1	tj−1	PROPN
ejpam-5565	158	7	)	)	PUNCT
ejpam-5565	158	8	2	2	NUM
ejpam-5565	158	9	≤	≤	NOUN
ejpam-5565	158	10	tj	tj	NOUN
ejpam-5565	158	11	−	−	PROPN
ejpam-5565	158	12	tj−1	tj−1	PROPN
ejpam-5565	158	13	,	,	PUNCT
ejpam-5565	158	14	so	so	ADV
ejpam-5565	158	15	0	0	NUM
ejpam-5565	158	16	≤	≤	NUM
ejpam-5565	158	17	n∑	n∑	PUNCT
ejpam-5565	158	18	j=1	j=1	PROPN
ejpam-5565	158	19	4(tj	4(tj	NOUN
ejpam-5565	158	20	−	−	PROPN
ejpam-5565	158	21	tj−1	tj−1	PROPN
ejpam-5565	158	22	)	)	PUNCT
ejpam-5565	158	23	2	2	NUM
ejpam-5565	158	24	≤	≤	NUM
ejpam-5565	158	25	n∑	n∑	PRON
ejpam-5565	158	26	j=1	j=1	PROPN
ejpam-5565	158	27	4(tj	4(tj	NOUN
ejpam-5565	159	1	−	−	PROPN
ejpam-5565	159	2	tj−1	tj−1	PROPN
ejpam-5565	159	3	)	)	PUNCT
ejpam-5565	160	1	,	,	PUNCT
ejpam-5565	160	2	it	it	PRON
ejpam-5565	160	3	follows	follow	VERB
ejpam-5565	160	4	that	that	SCONJ
ejpam-5565	160	5			PROPN
ejpam-5565	160	6	n∑	n∑	PROPN
ejpam-5565	160	7	j=1	j=1	PROPN
ejpam-5565	160	8	4(tj	4(tj	PROPN
ejpam-5565	160	9	−	−	PROPN
ejpam-5565	160	10	tj−1	tj−1	PROPN
ejpam-5565	160	11	)	)	PUNCT
ejpam-5565	160	12	2	2	NUM
ejpam-5565	160	13	1/2	1/2	PROPN
ejpam-5565	160	14	≤	≤	PUNCT
ejpam-5565	161	1			PROPN
ejpam-5565	161	2	n∑	n∑	PROPN
ejpam-5565	161	3	j=1	j=1	PROPN
ejpam-5565	161	4	4(tj	4(tj	PROPN
ejpam-5565	161	5	−	−	PROPN
ejpam-5565	161	6	tj−1	tj−1	PROPN
ejpam-5565	161	7	)	)	PUNCT
ejpam-5565	161	8	1/2	1/2	PROPN
ejpam-5565	161	9	≤	≤	ADJ
ejpam-5565	161	10	2	2	NUM
ejpam-5565	161	11	(	(	PUNCT
ejpam-5565	161	12	tn	tn	NOUN
ejpam-5565	161	13	−	−	PROPN
ejpam-5565	161	14	t0	t0	PROPN
ejpam-5565	161	15	)	)	PUNCT
ejpam-5565	161	16	1/2	1/2	NUM
ejpam-5565	161	17	=	=	SYM
ejpam-5565	161	18	2(3−	2(3−	NUM
ejpam-5565	161	19	2)1/2	2)1/2	NUM
ejpam-5565	161	20	=	=	SYM
ejpam-5565	161	21	2	2	NUM
ejpam-5565	161	22	therefore	therefore	ADV
ejpam-5565	161	23	,	,	PUNCT
ejpam-5565	161	24	we	we	PRON
ejpam-5565	161	25	have	have	VERB
ejpam-5565	161	26	to	to	ADP
ejpam-5565	161	27	2	2	NUM
ejpam-5565	161	28	v3	v3	PROPN
ejpam-5565	161	29	2(f	2(f	NUM
ejpam-5565	161	30	,	,	PUNCT
ejpam-5565	161	31	(	(	PUNCT
ejpam-5565	161	32	c2	c2	PROPN
ejpam-5565	161	33	,	,	PUNCT
ejpam-5565	161	34	[	[	X
ejpam-5565	161	35	·	·	PUNCT
ejpam-5565	161	36	,	,	PUNCT
ejpam-5565	161	37	·	·	PUNCT
ejpam-5565	161	38	]	]	X
ejpam-5565	161	39	)	)	PUNCT
ejpam-5565	161	40	)	)	PUNCT
ejpam-5565	161	41	is	be	AUX
ejpam-5565	161	42	bounded	bound	VERB
ejpam-5565	161	43	,	,	PUNCT
ejpam-5565	161	44	thus	thus	ADV
ejpam-5565	161	45	it	it	PRON
ejpam-5565	161	46	follows	follow	VERB
ejpam-5565	161	47	that	that	SCONJ
ejpam-5565	161	48	f	f	PROPN
ejpam-5565	161	49	is	be	AUX
ejpam-5565	161	50	of	of	ADP
ejpam-5565	161	51	bounded	bounded	ADJ
ejpam-5565	161	52	2	2	NUM
ejpam-5565	161	53	-	-	PUNCT
ejpam-5565	161	54	variation	variation	NOUN
ejpam-5565	161	55	function	function	NOUN
ejpam-5565	161	56	.	.	PUNCT
ejpam-5565	162	1	in	in	ADP
ejpam-5565	162	2	definition	definition	NOUN
ejpam-5565	162	3	7	7	NUM
ejpam-5565	162	4	we	we	PRON
ejpam-5565	162	5	introduce	introduce	VERB
ejpam-5565	162	6	the	the	DET
ejpam-5565	162	7	concept	concept	NOUN
ejpam-5565	162	8	of	of	ADP
ejpam-5565	162	9	a	a	DET
ejpam-5565	162	10	bounded	bounded	ADJ
ejpam-5565	162	11	q	q	ADJ
ejpam-5565	162	12	-	-	PUNCT
ejpam-5565	162	13	variation	variation	NOUN
ejpam-5565	162	14	function	function	NOUN
ejpam-5565	162	15	in	in	ADP
ejpam-5565	162	16	krein	krein	ADJ
ejpam-5565	162	17	spaces	space	NOUN
ejpam-5565	162	18	.	.	PUNCT
ejpam-5565	163	1	in	in	ADP
ejpam-5565	163	2	the	the	DET
ejpam-5565	163	3	following	following	NOUN
ejpam-5565	163	4	,	,	PUNCT
ejpam-5565	163	5	we	we	PRON
ejpam-5565	163	6	show	show	VERB
ejpam-5565	163	7	that	that	SCONJ
ejpam-5565	163	8	this	this	DET
ejpam-5565	163	9	concept	concept	NOUN
ejpam-5565	163	10	is	be	AUX
ejpam-5565	163	11	broader	broad	ADJ
ejpam-5565	163	12	than	than	ADP
ejpam-5565	163	13	the	the	DET
ejpam-5565	163	14	one	one	NOUN
ejpam-5565	163	15	given	give	VERB
ejpam-5565	163	16	in	in	ADP
ejpam-5565	163	17	[	[	PUNCT
ejpam-5565	163	18	13	13	NUM
ejpam-5565	163	19	]	]	PUNCT
ejpam-5565	163	20	.	.	PUNCT
ejpam-5565	164	1	theorem	theorem	ADJ
ejpam-5565	164	2	6	6	NUM
ejpam-5565	164	3	.	.	PUNCT
ejpam-5565	165	1	let	let	VERB
ejpam-5565	165	2	(	(	PUNCT
ejpam-5565	165	3	k	k	NOUN
ejpam-5565	165	4	=	=	SYM
ejpam-5565	165	5	k+	k+	NOUN
ejpam-5565	165	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	165	7	,	,	PUNCT
ejpam-5565	165	8	[	[	X
ejpam-5565	165	9	·	·	PUNCT
ejpam-5565	165	10	,	,	PUNCT
ejpam-5565	165	11	·	·	PUNCT
ejpam-5565	165	12	]	]	PUNCT
ejpam-5565	165	13	)	)	PUNCT
ejpam-5565	165	14	be	be	AUX
ejpam-5565	165	15	a	a	DET
ejpam-5565	165	16	krein	krein	ADJ
ejpam-5565	165	17	space	space	NOUN
ejpam-5565	165	18	and	and	CCONJ
ejpam-5565	165	19	f	f	NOUN
ejpam-5565	165	20	:	:	PUNCT
ejpam-5565	166	1	[	[	X
ejpam-5565	166	2	a	a	X
ejpam-5565	166	3	,	,	PUNCT
ejpam-5565	166	4	b	b	NOUN
ejpam-5565	166	5	]	]	X
ejpam-5565	166	6	→	→	SYM
ejpam-5565	166	7	k	k	PROPN
ejpam-5565	166	8	of	of	ADP
ejpam-5565	166	9	bounded	bounded	ADJ
ejpam-5565	166	10	q	q	ADJ
ejpam-5565	166	11	-	-	PUNCT
ejpam-5565	166	12	variation	variation	NOUN
ejpam-5565	166	13	function	function	NOUN
ejpam-5565	166	14	in	in	ADP
ejpam-5565	166	15	(	(	PUNCT
ejpam-5565	166	16	k	k	NOUN
ejpam-5565	166	17	=	=	SYM
ejpam-5565	166	18	k+	k+	NOUN
ejpam-5565	166	19	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	166	20	,	,	PUNCT
ejpam-5565	166	21	[	[	X
ejpam-5565	166	22	·	·	PUNCT
ejpam-5565	166	23	,	,	PUNCT
ejpam-5565	166	24	·	·	PUNCT
ejpam-5565	166	25	]	]	X
ejpam-5565	166	26	)	)	PUNCT
ejpam-5565	166	27	,	,	PUNCT
ejpam-5565	166	28	then	then	ADV
ejpam-5565	166	29	f	f	PROPN
ejpam-5565	166	30	is	be	AUX
ejpam-5565	166	31	of	of	ADP
ejpam-5565	166	32	bounded	bounded	ADJ
ejpam-5565	166	33	q	q	ADJ
ejpam-5565	166	34	-	-	PUNCT
ejpam-5565	166	35	variation	variation	NOUN
ejpam-5565	166	36	function	function	NOUN
ejpam-5565	166	37	in	in	ADP
ejpam-5565	166	38	the	the	DET
ejpam-5565	166	39	hilbert	hilbert	NOUN
ejpam-5565	166	40	space	space	NOUN
ejpam-5565	166	41	(	(	PUNCT
ejpam-5565	166	42	k	k	NOUN
ejpam-5565	166	43	,	,	PUNCT
ejpam-5565	166	44	[	[	X
ejpam-5565	166	45	·	·	PUNCT
ejpam-5565	166	46	,	,	PUNCT
ejpam-5565	166	47	·	·	PUNCT
ejpam-5565	166	48	]	]	X
ejpam-5565	166	49	j	j	NOUN
ejpam-5565	166	50	)	)	PUNCT
ejpam-5565	166	51	.	.	PUNCT
ejpam-5565	167	1	proof	proof	NOUN
ejpam-5565	167	2	.	.	PUNCT
ejpam-5565	168	1	if	if	SCONJ
ejpam-5565	168	2	f	f	PROPN
ejpam-5565	168	3	is	be	AUX
ejpam-5565	168	4	of	of	ADP
ejpam-5565	168	5	bounded	bounded	ADJ
ejpam-5565	168	6	q	q	NOUN
ejpam-5565	168	7	-	-	NOUN
ejpam-5565	168	8	variation	variation	NOUN
ejpam-5565	168	9	in	in	ADP
ejpam-5565	168	10	[	[	X
ejpam-5565	168	11	a	a	DET
ejpam-5565	168	12	,	,	PUNCT
ejpam-5565	168	13	b	b	NOUN
ejpam-5565	168	14	]	]	X
ejpam-5565	168	15	on	on	ADP
ejpam-5565	168	16	(	(	PUNCT
ejpam-5565	168	17	k	k	NOUN
ejpam-5565	168	18	=	=	SYM
ejpam-5565	168	19	k+	k+	NOUN
ejpam-5565	168	20	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	168	21	,	,	PUNCT
ejpam-5565	168	22	[	[	X
ejpam-5565	168	23	·	·	PUNCT
ejpam-5565	168	24	,	,	PUNCT
ejpam-5565	168	25	·	·	PUNCT
ejpam-5565	168	26	]	]	X
ejpam-5565	168	27	)	)	PUNCT
ejpam-5565	168	28	,	,	PUNCT
ejpam-5565	168	29	then	then	ADV
ejpam-5565	168	30	exists	exist	VERB
ejpam-5565	168	31	m	m	VERB
ejpam-5565	168	32	>	>	X
ejpam-5565	168	33	0	0	NUM
ejpam-5565	169	1	such	such	ADJ
ejpam-5565	169	2	that	that	SCONJ
ejpam-5565	169	3	:	:	PUNCT
ejpam-5565	169	4	q	q	X
ejpam-5565	169	5	vb	vb	PROPN
ejpam-5565	169	6	a(f	a(f	PROPN
ejpam-5565	169	7	,	,	PUNCT
ejpam-5565	169	8	(	(	PUNCT
ejpam-5565	169	9	k	k	X
ejpam-5565	169	10	,	,	PUNCT
ejpam-5565	169	11	[	[	X
ejpam-5565	169	12	·	·	PUNCT
ejpam-5565	169	13	,	,	PUNCT
ejpam-5565	169	14	·	·	PUNCT
ejpam-5565	169	15	]	]	X
ejpam-5565	169	16	)	)	PUNCT
ejpam-5565	169	17	)	)	PUNCT
ejpam-5565	169	18	=	=	SYM
ejpam-5565	169	19	sup	sup	NOUN
ejpam-5565	169	20	p∈p[a	p∈p[a	NOUN
ejpam-5565	169	21	,	,	PUNCT
ejpam-5565	169	22	b	b	NOUN
ejpam-5565	169	23	]	]	X
ejpam-5565	169	24	{	{	PUNCT
ejpam-5565	169	25	(	(	PUNCT
ejpam-5565	169	26	n∑	n∑	NOUN
ejpam-5565	169	27	i=1	i=1	PROPN
ejpam-5565	169	28	(	(	PUNCT
ejpam-5565	169	29	∥f+(ti)−f+(ti−1)∥++∥f−(ti)−f−(ti−1)∥−)q	∥f+(ti)−f+(ti−1)∥++∥f−(ti)−f−(ti−1)∥−)q	PROPN
ejpam-5565	169	30	)	)	PUNCT
ejpam-5565	169	31	1	1	NUM
ejpam-5565	169	32	/	/	SYM
ejpam-5565	169	33	q	q	NOUN
ejpam-5565	169	34	}	}	PUNCT
ejpam-5565	169	35	≤m	≤m	NOUN
ejpam-5565	169	36	by	by	ADP
ejpam-5565	169	37	theorem	theorem	NOUN
ejpam-5565	169	38	1	1	NUM
ejpam-5565	169	39	we	we	PRON
ejpam-5565	169	40	have	have	VERB
ejpam-5565	169	41	that	that	PRON
ejpam-5565	169	42	:	:	PUNCT
ejpam-5565	169	43	∥f(ti)−	∥f(ti)−	PROPN
ejpam-5565	169	44	f(ti−1)∥j	f(ti−1)∥j	NOUN
ejpam-5565	169	45	≤	≤	NUM
ejpam-5565	169	46	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	169	47	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	169	48	+	+	CCONJ
ejpam-5565	169	49	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	169	50	f−(ti−1)∥−	f−(ti−1)∥−	VERB
ejpam-5565	169	51	therefore	therefore	ADV
ejpam-5565	169	52	,	,	PUNCT
ejpam-5565	169	53	for	for	ADP
ejpam-5565	169	54	q	q	PRON
ejpam-5565	169	55	≥	≥	NUM
ejpam-5565	169	56	1	1	NUM
ejpam-5565	169	57	,	,	PUNCT
ejpam-5565	169	58	it	it	PRON
ejpam-5565	169	59	is	be	AUX
ejpam-5565	169	60	satisfied	satisfied	ADJ
ejpam-5565	169	61	that	that	SCONJ
ejpam-5565	169	62	:	:	PUNCT
ejpam-5565	169	63	∥f(ti)−	∥f(ti)−	PROPN
ejpam-5565	169	64	f(ti−1)∥qj	f(ti−1)∥qj	PROPN
ejpam-5565	169	65	≤	≤	NUM
ejpam-5565	169	66	(	(	PUNCT
ejpam-5565	169	67	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	169	68	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	169	69	+	+	CCONJ
ejpam-5565	169	70	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	169	71	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	169	72	whence	whence	NOUN
ejpam-5565	169	73	:	:	PUNCT
ejpam-5565	169	74	q	q	X
ejpam-5565	169	75	vb	vb	PROPN
ejpam-5565	169	76	a(f	a(f	PROPN
ejpam-5565	169	77	,	,	PUNCT
ejpam-5565	169	78	(	(	PUNCT
ejpam-5565	169	79	k	k	X
ejpam-5565	169	80	,	,	PUNCT
ejpam-5565	169	81	[	[	X
ejpam-5565	169	82	·	·	PUNCT
ejpam-5565	169	83	,	,	PUNCT
ejpam-5565	169	84	·	·	PUNCT
ejpam-5565	169	85	]	]	X
ejpam-5565	169	86	j	j	NOUN
ejpam-5565	169	87	)	)	PUNCT
ejpam-5565	169	88	)	)	PUNCT
ejpam-5565	169	89	≤m	≤m	PROPN
ejpam-5565	169	90	o.	o.	PROPN
ejpam-5565	169	91	ferrer	ferrer	PROPN
ejpam-5565	169	92	,	,	PUNCT
ejpam-5565	169	93	j.	j.	PROPN
ejpam-5565	169	94	naranjo	naranjo	PROPN
ejpam-5565	169	95	/	/	SYM
ejpam-5565	169	96	eur	eur	PROPN
ejpam-5565	169	97	.	.	PUNCT
ejpam-5565	170	1	j.	j.	PROPN
ejpam-5565	170	2	pure	pure	PROPN
ejpam-5565	170	3	appl	appl	PROPN
ejpam-5565	170	4	.	.	PROPN
ejpam-5565	170	5	math	math	PROPN
ejpam-5565	170	6	,	,	PUNCT
ejpam-5565	170	7	18	18	NUM
ejpam-5565	170	8	(	(	PUNCT
ejpam-5565	170	9	2	2	NUM
ejpam-5565	170	10	)	)	PUNCT
ejpam-5565	170	11	(	(	PUNCT
ejpam-5565	170	12	2025	2025	NUM
ejpam-5565	170	13	)	)	PUNCT
ejpam-5565	170	14	,	,	PUNCT
ejpam-5565	170	15	5565	5565	NUM
ejpam-5565	170	16	8	8	NUM
ejpam-5565	170	17	of	of	ADP
ejpam-5565	170	18	18	18	NUM
ejpam-5565	170	19	therefore	therefore	ADV
ejpam-5565	170	20	,	,	PUNCT
ejpam-5565	170	21	f	f	PROPN
ejpam-5565	170	22	is	be	AUX
ejpam-5565	170	23	of	of	ADP
ejpam-5565	170	24	bounded	bounded	ADJ
ejpam-5565	170	25	q	q	NOUN
ejpam-5565	170	26	-	-	NOUN
ejpam-5565	170	27	variation	variation	NOUN
ejpam-5565	170	28	in	in	ADP
ejpam-5565	170	29	[	[	X
ejpam-5565	170	30	a	a	DET
ejpam-5565	170	31	,	,	PUNCT
ejpam-5565	170	32	b	b	NOUN
ejpam-5565	170	33	]	]	X
ejpam-5565	170	34	on	on	ADP
ejpam-5565	170	35	the	the	DET
ejpam-5565	170	36	hilbert	hilbert	NOUN
ejpam-5565	170	37	space	space	NOUN
ejpam-5565	170	38	(	(	PUNCT
ejpam-5565	170	39	k	k	NOUN
ejpam-5565	170	40	,	,	PUNCT
ejpam-5565	170	41	[	[	X
ejpam-5565	170	42	·	·	PUNCT
ejpam-5565	170	43	,	,	PUNCT
ejpam-5565	170	44	·	·	PUNCT
ejpam-5565	170	45	]	]	X
ejpam-5565	170	46	j	j	PROPN
ejpam-5565	170	47	)	)	PUNCT
ejpam-5565	170	48	.	.	PUNCT
ejpam-5565	171	1	the	the	DET
ejpam-5565	171	2	following	follow	VERB
ejpam-5565	171	3	result	result	NOUN
ejpam-5565	171	4	is	be	AUX
ejpam-5565	171	5	very	very	ADV
ejpam-5565	171	6	significant	significant	ADJ
ejpam-5565	171	7	in	in	ADP
ejpam-5565	171	8	this	this	DET
ejpam-5565	171	9	research	research	NOUN
ejpam-5565	171	10	,	,	PUNCT
ejpam-5565	171	11	as	as	SCONJ
ejpam-5565	171	12	it	it	PRON
ejpam-5565	171	13	shows	show	VERB
ejpam-5565	171	14	the	the	DET
ejpam-5565	171	15	robustness	robustness	NOUN
ejpam-5565	171	16	of	of	ADP
ejpam-5565	171	17	the	the	DET
ejpam-5565	171	18	definition	definition	NOUN
ejpam-5565	171	19	7	7	NUM
ejpam-5565	171	20	introduced	introduce	VERB
ejpam-5565	171	21	in	in	ADP
ejpam-5565	171	22	this	this	DET
ejpam-5565	171	23	paper	paper	NOUN
ejpam-5565	171	24	,	,	PUNCT
ejpam-5565	171	25	more	more	ADV
ejpam-5565	171	26	precisely	precisely	ADV
ejpam-5565	171	27	it	it	PRON
ejpam-5565	171	28	shows	show	VERB
ejpam-5565	171	29	that	that	SCONJ
ejpam-5565	171	30	the	the	DET
ejpam-5565	171	31	bounded	bounded	ADJ
ejpam-5565	171	32	qvariation	qvariation	NOUN
ejpam-5565	171	33	functions	function	NOUN
ejpam-5565	171	34	on	on	ADP
ejpam-5565	171	35	a	a	DET
ejpam-5565	171	36	krein	krein	ADJ
ejpam-5565	171	37	space	space	NOUN
ejpam-5565	171	38	are	be	AUX
ejpam-5565	171	39	independent	independent	ADJ
ejpam-5565	171	40	of	of	ADP
ejpam-5565	171	41	the	the	DET
ejpam-5565	171	42	fundamental	fundamental	ADJ
ejpam-5565	171	43	decomposition	decomposition	NOUN
ejpam-5565	171	44	of	of	ADP
ejpam-5565	171	45	the	the	DET
ejpam-5565	171	46	space	space	NOUN
ejpam-5565	171	47	.	.	PUNCT
ejpam-5565	172	1	this	this	DET
ejpam-5565	172	2	finding	finding	NOUN
ejpam-5565	172	3	is	be	AUX
ejpam-5565	172	4	remarkable	remarkable	ADJ
ejpam-5565	172	5	as	as	SCONJ
ejpam-5565	172	6	it	it	PRON
ejpam-5565	172	7	reinforces	reinforce	VERB
ejpam-5565	172	8	the	the	DET
ejpam-5565	172	9	robustness	robustness	NOUN
ejpam-5565	172	10	of	of	ADP
ejpam-5565	172	11	these	these	DET
ejpam-5565	172	12	functions	function	NOUN
ejpam-5565	172	13	in	in	ADP
ejpam-5565	172	14	different	different	ADJ
ejpam-5565	172	15	decomposition	decomposition	NOUN
ejpam-5565	172	16	structures	structure	NOUN
ejpam-5565	172	17	,	,	PUNCT
ejpam-5565	172	18	this	this	PRON
ejpam-5565	172	19	not	not	PART
ejpam-5565	172	20	only	only	ADV
ejpam-5565	172	21	challenges	challenge	VERB
ejpam-5565	172	22	traditional	traditional	ADJ
ejpam-5565	172	23	conceptions	conception	NOUN
ejpam-5565	172	24	,	,	PUNCT
ejpam-5565	172	25	but	but	CCONJ
ejpam-5565	172	26	also	also	ADV
ejpam-5565	172	27	opens	open	VERB
ejpam-5565	172	28	new	new	ADJ
ejpam-5565	172	29	perspectives	perspective	NOUN
ejpam-5565	172	30	in	in	ADP
ejpam-5565	172	31	functional	functional	ADJ
ejpam-5565	172	32	analysis	analysis	NOUN
ejpam-5565	172	33	,	,	PUNCT
ejpam-5565	172	34	providing	provide	VERB
ejpam-5565	172	35	a	a	DET
ejpam-5565	172	36	solid	solid	ADJ
ejpam-5565	172	37	basis	basis	NOUN
ejpam-5565	172	38	for	for	ADP
ejpam-5565	172	39	future	future	ADJ
ejpam-5565	172	40	research	research	NOUN
ejpam-5565	172	41	and	and	CCONJ
ejpam-5565	172	42	applications	application	NOUN
ejpam-5565	172	43	in	in	ADP
ejpam-5565	172	44	economics	economic	NOUN
ejpam-5565	172	45	,	,	PUNCT
ejpam-5565	172	46	quantum	quantum	NOUN
ejpam-5565	172	47	mechanics	mechanic	NOUN
ejpam-5565	172	48	,	,	PUNCT
ejpam-5565	172	49	signal	signal	NOUN
ejpam-5565	172	50	processing[14–17	processing[14–17	PROPN
ejpam-5565	172	51	]	]	PUNCT
ejpam-5565	172	52	where	where	SCONJ
ejpam-5565	172	53	the	the	DET
ejpam-5565	172	54	bounded	bounded	ADJ
ejpam-5565	172	55	q	q	NOUN
ejpam-5565	172	56	-	-	PUNCT
ejpam-5565	172	57	variation	variation	NOUN
ejpam-5565	172	58	plays	play	VERB
ejpam-5565	172	59	a	a	DET
ejpam-5565	172	60	very	very	ADV
ejpam-5565	172	61	important	important	ADJ
ejpam-5565	172	62	role	role	NOUN
ejpam-5565	172	63	.	.	PUNCT
ejpam-5565	173	1	theorem	theorem	ADJ
ejpam-5565	173	2	7	7	NUM
ejpam-5565	173	3	.	.	PUNCT
ejpam-5565	174	1	let	let	VERB
ejpam-5565	174	2	(	(	PUNCT
ejpam-5565	174	3	k	k	NOUN
ejpam-5565	174	4	,	,	PUNCT
ejpam-5565	174	5	[	[	X
ejpam-5565	174	6	·	·	PUNCT
ejpam-5565	174	7	,	,	PUNCT
ejpam-5565	174	8	·	·	PUNCT
ejpam-5565	174	9	]	]	PUNCT
ejpam-5565	174	10	)	)	PUNCT
ejpam-5565	174	11	be	be	AUX
ejpam-5565	174	12	a	a	DET
ejpam-5565	174	13	krein	krein	ADJ
ejpam-5565	174	14	space	space	NOUN
ejpam-5565	174	15	with	with	ADP
ejpam-5565	174	16	decompositions	decomposition	NOUN
ejpam-5565	174	17	(	(	PUNCT
ejpam-5565	174	18	k	k	NOUN
ejpam-5565	174	19	=	=	SYM
ejpam-5565	174	20	k1	k1	PROPN
ejpam-5565	174	21	+	+	CCONJ
ejpam-5565	174	22	˙[+]k1−	˙[+]k1−	NOUN
ejpam-5565	174	23	,	,	PUNCT
ejpam-5565	174	24	j1	j1	PROPN
ejpam-5565	174	25	)	)	PUNCT
ejpam-5565	174	26	,	,	PUNCT
ejpam-5565	174	27	(	(	PUNCT
ejpam-5565	174	28	k	k	NOUN
ejpam-5565	174	29	=	=	SYM
ejpam-5565	174	30	k2	k2	PROPN
ejpam-5565	174	31	+	+	CCONJ
ejpam-5565	174	32	˙[+]k2−	˙[+]k2−	NOUN
ejpam-5565	174	33	,	,	PUNCT
ejpam-5565	174	34	j2	j2	PROPN
ejpam-5565	174	35	)	)	PUNCT
ejpam-5565	174	36	and	and	CCONJ
ejpam-5565	174	37	f	f	NOUN
ejpam-5565	174	38	:	:	PUNCT
ejpam-5565	175	1	[	[	X
ejpam-5565	175	2	a	a	X
ejpam-5565	175	3	,	,	PUNCT
ejpam-5565	175	4	b	b	NOUN
ejpam-5565	175	5	]	]	X
ejpam-5565	175	6	→	→	SYM
ejpam-5565	175	7	k	k	PROPN
ejpam-5565	175	8	of	of	ADP
ejpam-5565	175	9	bounded	bounded	ADJ
ejpam-5565	175	10	q	q	ADJ
ejpam-5565	175	11	-	-	PUNCT
ejpam-5565	175	12	variation	variation	NOUN
ejpam-5565	175	13	function	function	NOUN
ejpam-5565	175	14	in	in	ADP
ejpam-5565	175	15	[	[	X
ejpam-5565	175	16	a	a	DET
ejpam-5565	175	17	,	,	PUNCT
ejpam-5565	175	18	b	b	NOUN
ejpam-5565	175	19	]	]	X
ejpam-5565	175	20	on	on	ADP
ejpam-5565	175	21	(	(	PUNCT
ejpam-5565	175	22	k	k	NOUN
ejpam-5565	175	23	=	=	SYM
ejpam-5565	175	24	k1	k1	PROPN
ejpam-5565	175	25	+	+	CCONJ
ejpam-5565	175	26	˙[+]k1−	˙[+]k1−	NOUN
ejpam-5565	175	27	)	)	PUNCT
ejpam-5565	175	28	,	,	PUNCT
ejpam-5565	175	29	then	then	ADV
ejpam-5565	175	30	f	f	PROPN
ejpam-5565	175	31	is	be	AUX
ejpam-5565	175	32	of	of	ADP
ejpam-5565	175	33	bounded	bounded	ADJ
ejpam-5565	175	34	q	q	NOUN
ejpam-5565	175	35	-	-	NOUN
ejpam-5565	175	36	variation	variation	NOUN
ejpam-5565	175	37	in	in	ADP
ejpam-5565	175	38	[	[	X
ejpam-5565	175	39	a	a	DET
ejpam-5565	175	40	,	,	PUNCT
ejpam-5565	175	41	b	b	NOUN
ejpam-5565	175	42	]	]	X
ejpam-5565	175	43	on	on	ADP
ejpam-5565	175	44	(	(	PUNCT
ejpam-5565	175	45	k	k	NOUN
ejpam-5565	175	46	=	=	SYM
ejpam-5565	175	47	k2	k2	PROPN
ejpam-5565	175	48	+	+	CCONJ
ejpam-5565	175	49	˙[+]k2−	˙[+]k2−	NUM
ejpam-5565	175	50	)	)	PUNCT
ejpam-5565	175	51	.	.	PUNCT
ejpam-5565	176	1	proof	proof	NOUN
ejpam-5565	176	2	.	.	PUNCT
ejpam-5565	177	1	if	if	SCONJ
ejpam-5565	177	2	f	f	PROPN
ejpam-5565	177	3	is	be	AUX
ejpam-5565	177	4	of	of	ADP
ejpam-5565	177	5	bounded	bounded	ADJ
ejpam-5565	177	6	q	q	NOUN
ejpam-5565	177	7	-	-	NOUN
ejpam-5565	177	8	variation	variation	NOUN
ejpam-5565	177	9	in	in	ADP
ejpam-5565	177	10	[	[	X
ejpam-5565	177	11	a	a	DET
ejpam-5565	177	12	,	,	PUNCT
ejpam-5565	177	13	b	b	NOUN
ejpam-5565	177	14	]	]	X
ejpam-5565	177	15	on	on	ADP
ejpam-5565	177	16	(	(	PUNCT
ejpam-5565	177	17	k	k	NOUN
ejpam-5565	177	18	=	=	SYM
ejpam-5565	177	19	k1	k1	PROPN
ejpam-5565	177	20	+	+	CCONJ
ejpam-5565	177	21	˙[+]k1−	˙[+]k1−	NOUN
ejpam-5565	177	22	,	,	PUNCT
ejpam-5565	177	23	[	[	X
ejpam-5565	177	24	·	·	PUNCT
ejpam-5565	177	25	,	,	PUNCT
ejpam-5565	177	26	·	·	PUNCT
ejpam-5565	177	27	]	]	X
ejpam-5565	177	28	)	)	PUNCT
ejpam-5565	177	29	,	,	PUNCT
ejpam-5565	177	30	then	then	ADV
ejpam-5565	177	31	exists	exist	VERB
ejpam-5565	177	32	m	m	VERB
ejpam-5565	177	33	>	>	X
ejpam-5565	177	34	0	0	NUM
ejpam-5565	178	1	such	such	ADJ
ejpam-5565	178	2	that	that	SCONJ
ejpam-5565	178	3	:	:	PUNCT
ejpam-5565	178	4	q	q	X
ejpam-5565	178	5	vb	vb	PROPN
ejpam-5565	178	6	a(f	a(f	PROPN
ejpam-5565	178	7	,	,	PUNCT
ejpam-5565	178	8	(	(	PUNCT
ejpam-5565	178	9	k	k	X
ejpam-5565	178	10	,	,	PUNCT
ejpam-5565	178	11	[	[	X
ejpam-5565	178	12	·	·	PUNCT
ejpam-5565	178	13	,	,	PUNCT
ejpam-5565	178	14	·	·	PUNCT
ejpam-5565	178	15	]	]	X
ejpam-5565	178	16	)	)	PUNCT
ejpam-5565	178	17	)	)	PUNCT
ejpam-5565	178	18	=	=	SYM
ejpam-5565	178	19	sup	sup	NOUN
ejpam-5565	178	20	p∈p[a	p∈p[a	NOUN
ejpam-5565	178	21	,	,	PUNCT
ejpam-5565	178	22	b	b	NOUN
ejpam-5565	178	23	]	]	X
ejpam-5565	178	24	{	{	PUNCT
ejpam-5565	178	25	(	(	PUNCT
ejpam-5565	178	26	n∑	n∑	INTJ
ejpam-5565	178	27	i=1	i=1	PROPN
ejpam-5565	178	28	(	(	PUNCT
ejpam-5565	178	29	∥f+(ti)−f+(ti−1)∥1++∥f−(ti)−f−(ti−1)∥1−)q	∥f+(ti)−f+(ti−1)∥1++∥f−(ti)−f−(ti−1)∥1−)q	PROPN
ejpam-5565	178	30	)	)	PUNCT
ejpam-5565	178	31	1	1	NUM
ejpam-5565	178	32	/	/	SYM
ejpam-5565	178	33	q	q	NOUN
ejpam-5565	178	34	}	}	PUNCT
ejpam-5565	178	35	≤m	≤m	NOUN
ejpam-5565	178	36	moreover	moreover	ADV
ejpam-5565	178	37	,	,	PUNCT
ejpam-5565	178	38	as	as	SCONJ
ejpam-5565	178	39	∥	∥	X
ejpam-5565	178	40	·	·	PUNCT
ejpam-5565	178	41	∥j1	∥j1	NOUN
ejpam-5565	178	42	and∥	and∥	SYM
ejpam-5565	178	43	·	·	PUNCT
ejpam-5565	178	44	∥j2	∥j2	NOUN
ejpam-5565	178	45	are	be	AUX
ejpam-5565	178	46	equivalent	equivalent	ADJ
ejpam-5565	178	47	norms	norm	NOUN
ejpam-5565	178	48	[	[	X
ejpam-5565	178	49	12	12	NUM
ejpam-5565	178	50	]	]	PUNCT
ejpam-5565	178	51	,	,	PUNCT
ejpam-5565	178	52	then	then	ADV
ejpam-5565	178	53	there	there	PRON
ejpam-5565	178	54	are	be	VERB
ejpam-5565	178	55	a	a	DET
ejpam-5565	178	56	,	,	PUNCT
ejpam-5565	178	57	b	b	X
ejpam-5565	178	58	>	>	X
ejpam-5565	178	59	0	0	NUM
ejpam-5565	179	1	such	such	ADJ
ejpam-5565	179	2	that	that	SCONJ
ejpam-5565	179	3	a∥	a∥	PROPN
ejpam-5565	179	4	·	·	PUNCT
ejpam-5565	179	5	∥j2	∥j2	X
ejpam-5565	179	6	≤	≤	X
ejpam-5565	179	7	∥	∥	PUNCT
ejpam-5565	179	8	·	·	PUNCT
ejpam-5565	179	9	∥j1	∥j1	VERB
ejpam-5565	179	10	≤	≤	ADJ
ejpam-5565	179	11	b∥	b∥	NOUN
ejpam-5565	179	12	·	·	PUNCT
ejpam-5565	179	13	∥j2	∥j2	X
ejpam-5565	179	14	.	.	PUNCT
ejpam-5565	180	1	therefore	therefore	ADV
ejpam-5565	180	2	,	,	PUNCT
ejpam-5565	180	3	(	(	PUNCT
ejpam-5565	180	4	a∥f(ti)−	a∥f(ti)−	ADP
ejpam-5565	180	5	f(ti−1)∥j2	f(ti−1)∥j2	PROPN
ejpam-5565	180	6	)	)	PUNCT
ejpam-5565	180	7	q	q	PROPN
ejpam-5565	180	8	≤	≤	ADJ
ejpam-5565	180	9	∥f(ti)−	∥f(ti)−	NOUN
ejpam-5565	180	10	f(ti−1)∥qj1	f(ti−1)∥qj1	PROPN
ejpam-5565	180	11	≤	≤	X
ejpam-5565	180	12	(	(	PUNCT
ejpam-5565	180	13	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	180	14	f+(ti−1)∥1	f+(ti−1)∥1	NOUN
ejpam-5565	180	15	+	+	CCONJ
ejpam-5565	180	16	+	+	NUM
ejpam-5565	180	17	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	180	18	f−(ti−1)∥1−)q	f−(ti−1)∥1−)q	NOUN
ejpam-5565	180	19	the	the	DET
ejpam-5565	180	20	last	last	ADJ
ejpam-5565	180	21	inequality	inequality	NOUN
ejpam-5565	180	22	is	be	AUX
ejpam-5565	180	23	obtained	obtain	VERB
ejpam-5565	180	24	thanks	thank	NOUN
ejpam-5565	180	25	to	to	ADP
ejpam-5565	180	26	theorem	theorem	NOUN
ejpam-5565	180	27	1	1	NUM
ejpam-5565	180	28	.	.	PUNCT
ejpam-5565	180	29	later,∑n	later,∑n	PROPN
ejpam-5565	180	30	i=1(a∥f(ti)−	i=1(a∥f(ti)−	PROPN
ejpam-5565	180	31	f(ti−1)∥j2	f(ti−1)∥j2	PROPN
ejpam-5565	180	32	)	)	PUNCT
ejpam-5565	180	33	q	q	PROPN
ejpam-5565	180	34	≤	≤	ADJ
ejpam-5565	180	35	∑n	∑n	PROPN
ejpam-5565	180	36	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	180	37	f+(ti−1)∥1	f+(ti−1)∥1	NOUN
ejpam-5565	180	38	+	+	CCONJ
ejpam-5565	180	39	+	+	NUM
ejpam-5565	180	40	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	180	41	f−(ti−1)∥1−)q	f−(ti−1)∥1−)q	NOUN
ejpam-5565	180	42	(	(	PUNCT
ejpam-5565	180	43	aq	aq	PROPN
ejpam-5565	180	44	∑n	∑n	PROPN
ejpam-5565	180	45	i=1(∥f(ti)−	i=1(∥f(ti)−	PROPN
ejpam-5565	180	46	f(ti−1)∥j2	f(ti−1)∥j2	PROPN
ejpam-5565	180	47	)	)	PUNCT
ejpam-5565	180	48	q)1	q)1	PROPN
ejpam-5565	180	49	/	/	SYM
ejpam-5565	180	50	q	q	PROPN
ejpam-5565	180	51	≤	≤	NUM
ejpam-5565	180	52	(	(	PUNCT
ejpam-5565	180	53	∑n	∑n	PROPN
ejpam-5565	180	54	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	180	55	f+(ti−1)∥1	f+(ti−1)∥1	NOUN
ejpam-5565	180	56	+	+	CCONJ
ejpam-5565	180	57	+	+	NUM
ejpam-5565	180	58	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	180	59	f−(ti−1)∥1−)q)1	f−(ti−1)∥1−)q)1	NOUN
ejpam-5565	180	60	/	/	SYM
ejpam-5565	180	61	q	q	NOUN
ejpam-5565	180	62	a	a	PROPN
ejpam-5565	180	63	(	(	PUNCT
ejpam-5565	180	64	∑n	∑n	PROPN
ejpam-5565	180	65	i=1(∥f(ti)−	i=1(∥f(ti)−	PROPN
ejpam-5565	180	66	f(ti−1)∥j2	f(ti−1)∥j2	PROPN
ejpam-5565	180	67	)	)	PUNCT
ejpam-5565	180	68	q)1	q)1	PROPN
ejpam-5565	180	69	/	/	SYM
ejpam-5565	180	70	q	q	PROPN
ejpam-5565	180	71	≤	≤	NUM
ejpam-5565	180	72	(	(	PUNCT
ejpam-5565	180	73	∑n	∑n	PROPN
ejpam-5565	180	74	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	180	75	f+(ti−1)∥1	f+(ti−1)∥1	NOUN
ejpam-5565	180	76	+	+	CCONJ
ejpam-5565	180	77	+	+	NUM
ejpam-5565	180	78	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	180	79	f−(ti−1)∥1−)q)1	f−(ti−1)∥1−)q)1	NOUN
ejpam-5565	180	80	/	/	SYM
ejpam-5565	180	81	q	q	NOUN
ejpam-5565	180	82	≤m	≤m	NOUN
ejpam-5565	180	83	it	it	PRON
ejpam-5565	180	84	follows	follow	VERB
ejpam-5565	180	85	that	that	SCONJ
ejpam-5565	180	86	:	:	PUNCT
ejpam-5565	180	87	q	q	X
ejpam-5565	180	88	vb	vb	PROPN
ejpam-5565	180	89	a(f	a(f	PROPN
ejpam-5565	180	90	,	,	PUNCT
ejpam-5565	180	91	(	(	PUNCT
ejpam-5565	180	92	k	k	X
ejpam-5565	180	93	,	,	PUNCT
ejpam-5565	180	94	[	[	X
ejpam-5565	180	95	·	·	PUNCT
ejpam-5565	180	96	,	,	PUNCT
ejpam-5565	180	97	·	·	PUNCT
ejpam-5565	180	98	]	]	X
ejpam-5565	180	99	j2	j2	NOUN
ejpam-5565	180	100	)	)	PUNCT
ejpam-5565	180	101	)	)	PUNCT
ejpam-5565	181	1	=	=	SYM
ejpam-5565	181	2	sup	sup	NOUN
ejpam-5565	181	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	181	4	,	,	PUNCT
ejpam-5565	181	5	b	b	NOUN
ejpam-5565	181	6	]	]	X
ejpam-5565	181	7	{	{	PUNCT
ejpam-5565	181	8	(	(	PUNCT
ejpam-5565	181	9	n∑	n∑	NOUN
ejpam-5565	181	10	i=1	i=1	PROPN
ejpam-5565	181	11	(	(	PUNCT
ejpam-5565	181	12	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	181	13	f+(ti−1)∥2	f+(ti−1)∥2	PROPN
ejpam-5565	181	14	+	+	CCONJ
ejpam-5565	181	15	+	+	NUM
ejpam-5565	181	16	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	181	17	f−(ti−1)∥2−)q)1	f−(ti−1)∥2−)q)1	NOUN
ejpam-5565	181	18	/	/	SYM
ejpam-5565	181	19	q	q	NOUN
ejpam-5565	181	20	}	}	PUNCT
ejpam-5565	181	21	≤m	≤m	NOUN
ejpam-5565	181	22	/	/	SYM
ejpam-5565	181	23	a	a	PRON
ejpam-5565	181	24	this	this	PRON
ejpam-5565	181	25	implies	imply	VERB
ejpam-5565	181	26	thatf	thatf	NOUN
ejpam-5565	181	27	is	be	AUX
ejpam-5565	181	28	of	of	ADP
ejpam-5565	181	29	bounded	bounded	ADJ
ejpam-5565	181	30	q	q	NOUN
ejpam-5565	181	31	-	-	NOUN
ejpam-5565	181	32	variation	variation	NOUN
ejpam-5565	181	33	in	in	ADP
ejpam-5565	181	34	[	[	X
ejpam-5565	181	35	a	a	DET
ejpam-5565	181	36	,	,	PUNCT
ejpam-5565	181	37	b	b	NOUN
ejpam-5565	181	38	]	]	X
ejpam-5565	181	39	on	on	ADP
ejpam-5565	181	40	(	(	PUNCT
ejpam-5565	181	41	k	k	NOUN
ejpam-5565	181	42	=	=	SYM
ejpam-5565	181	43	k2	k2	PROPN
ejpam-5565	181	44	+	+	X
ejpam-5565	181	45	˙[+]k2−	˙[+]k2−	PUNCT
ejpam-5565	181	46	,	,	PUNCT
ejpam-5565	181	47	[	[	X
ejpam-5565	181	48	·	·	PUNCT
ejpam-5565	181	49	,	,	PUNCT
ejpam-5565	181	50	·	·	PUNCT
ejpam-5565	181	51	]	]	X
ejpam-5565	181	52	j2	j2	PROPN
ejpam-5565	181	53	)	)	PUNCT
ejpam-5565	181	54	.	.	PUNCT
ejpam-5565	182	1	o.	o.	PROPN
ejpam-5565	182	2	ferrer	ferrer	PROPN
ejpam-5565	182	3	,	,	PUNCT
ejpam-5565	182	4	j.	j.	PROPN
ejpam-5565	182	5	naranjo	naranjo	PROPN
ejpam-5565	182	6	/	/	SYM
ejpam-5565	182	7	eur	eur	PROPN
ejpam-5565	182	8	.	.	PUNCT
ejpam-5565	183	1	j.	j.	PROPN
ejpam-5565	183	2	pure	pure	PROPN
ejpam-5565	183	3	appl	appl	PROPN
ejpam-5565	183	4	.	.	PROPN
ejpam-5565	183	5	math	math	PROPN
ejpam-5565	183	6	,	,	PUNCT
ejpam-5565	183	7	18	18	NUM
ejpam-5565	183	8	(	(	PUNCT
ejpam-5565	183	9	2	2	NUM
ejpam-5565	183	10	)	)	PUNCT
ejpam-5565	183	11	(	(	PUNCT
ejpam-5565	183	12	2025	2025	NUM
ejpam-5565	183	13	)	)	PUNCT
ejpam-5565	183	14	,	,	PUNCT
ejpam-5565	183	15	5565	5565	NUM
ejpam-5565	183	16	9	9	NUM
ejpam-5565	183	17	of	of	ADP
ejpam-5565	183	18	18	18	NUM
ejpam-5565	183	19	theorem	theorem	NOUN
ejpam-5565	183	20	8	8	NUM
ejpam-5565	183	21	.	.	PUNCT
ejpam-5565	184	1	let	let	VERB
ejpam-5565	184	2	(	(	PUNCT
ejpam-5565	184	3	k	k	NOUN
ejpam-5565	184	4	=	=	SYM
ejpam-5565	184	5	k+	k+	NOUN
ejpam-5565	184	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	184	7	,	,	PUNCT
ejpam-5565	184	8	[	[	X
ejpam-5565	184	9	·	·	PUNCT
ejpam-5565	184	10	,	,	PUNCT
ejpam-5565	184	11	·	·	PUNCT
ejpam-5565	184	12	]	]	PUNCT
ejpam-5565	184	13	)	)	PUNCT
ejpam-5565	184	14	be	be	AUX
ejpam-5565	184	15	a	a	DET
ejpam-5565	184	16	krein	krein	ADJ
ejpam-5565	184	17	space	space	NOUN
ejpam-5565	184	18	and	and	CCONJ
ejpam-5565	184	19	f	f	NOUN
ejpam-5565	184	20	:	:	PUNCT
ejpam-5565	185	1	[	[	X
ejpam-5565	185	2	a	a	X
ejpam-5565	185	3	,	,	PUNCT
ejpam-5565	185	4	b	b	NOUN
ejpam-5565	185	5	]	]	X
ejpam-5565	185	6	→	→	SYM
ejpam-5565	185	7	k	k	PROPN
ejpam-5565	185	8	of	of	ADP
ejpam-5565	185	9	bounded	bounded	ADJ
ejpam-5565	185	10	q	q	ADJ
ejpam-5565	185	11	-	-	PUNCT
ejpam-5565	185	12	variation	variation	NOUN
ejpam-5565	185	13	function	function	NOUN
ejpam-5565	185	14	in	in	ADP
ejpam-5565	185	15	[	[	X
ejpam-5565	185	16	a	a	DET
ejpam-5565	185	17	,	,	PUNCT
ejpam-5565	185	18	b	b	NOUN
ejpam-5565	185	19	]	]	X
ejpam-5565	185	20	on	on	ADP
ejpam-5565	185	21	(	(	PUNCT
ejpam-5565	185	22	k	k	NOUN
ejpam-5565	185	23	=	=	SYM
ejpam-5565	185	24	k+	k+	NOUN
ejpam-5565	185	25	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	185	26	,	,	PUNCT
ejpam-5565	185	27	[	[	X
ejpam-5565	185	28	·	·	PUNCT
ejpam-5565	185	29	,	,	PUNCT
ejpam-5565	185	30	·	·	PUNCT
ejpam-5565	185	31	]	]	X
ejpam-5565	185	32	)	)	PUNCT
ejpam-5565	185	33	,	,	PUNCT
ejpam-5565	185	34	then	then	ADV
ejpam-5565	185	35	f	f	PROPN
ejpam-5565	185	36	is	be	AUX
ejpam-5565	185	37	bounded	bound	VERB
ejpam-5565	185	38	.	.	PUNCT
ejpam-5565	186	1	proof	proof	NOUN
ejpam-5565	186	2	.	.	PUNCT
ejpam-5565	187	1	suppose	suppose	VERB
ejpam-5565	187	2	that	that	SCONJ
ejpam-5565	187	3	f	f	PROPN
ejpam-5565	187	4	is	be	AUX
ejpam-5565	187	5	of	of	ADP
ejpam-5565	187	6	bounded	bounded	ADJ
ejpam-5565	187	7	q	q	NOUN
ejpam-5565	187	8	-	-	NOUN
ejpam-5565	187	9	variation	variation	NOUN
ejpam-5565	187	10	on	on	ADP
ejpam-5565	187	11	[	[	X
ejpam-5565	187	12	a	a	X
ejpam-5565	187	13	,	,	PUNCT
ejpam-5565	187	14	b	b	NOUN
ejpam-5565	187	15	]	]	X
ejpam-5565	187	16	,	,	PUNCT
ejpam-5565	187	17	then	then	ADV
ejpam-5565	187	18	there	there	PRON
ejpam-5565	187	19	exists	exist	VERB
ejpam-5565	187	20	m	m	VERB
ejpam-5565	187	21	>	>	X
ejpam-5565	187	22	0	0	NUM
ejpam-5565	188	1	such	such	ADJ
ejpam-5565	188	2	that	that	SCONJ
ejpam-5565	188	3	q	q	PROPN
ejpam-5565	188	4	vb	vb	PROPN
ejpam-5565	188	5	a(f	a(f	PROPN
ejpam-5565	188	6	,	,	PUNCT
ejpam-5565	188	7	(	(	PUNCT
ejpam-5565	188	8	k	k	X
ejpam-5565	188	9	,	,	PUNCT
ejpam-5565	188	10	[	[	X
ejpam-5565	188	11	·	·	PUNCT
ejpam-5565	188	12	,	,	PUNCT
ejpam-5565	188	13	·	·	PUNCT
ejpam-5565	188	14	]	]	X
ejpam-5565	188	15	j	j	NOUN
ejpam-5565	188	16	)	)	PUNCT
ejpam-5565	188	17	)	)	PUNCT
ejpam-5565	188	18	≤	≤	NUM
ejpam-5565	188	19	m	m	VERB
ejpam-5565	188	20	for	for	ADP
ejpam-5565	188	21	all	all	DET
ejpam-5565	188	22	partition	partition	NOUN
ejpam-5565	188	23	p	p	NOUN
ejpam-5565	188	24	of	of	ADP
ejpam-5565	188	25	[	[	X
ejpam-5565	188	26	a	a	X
ejpam-5565	188	27	,	,	PUNCT
ejpam-5565	188	28	b	b	NOUN
ejpam-5565	188	29	]	]	PUNCT
ejpam-5565	188	30	.	.	PUNCT
ejpam-5565	189	1	let	let	AUX
ejpam-5565	189	2	be	be	AUX
ejpam-5565	189	3	t	t	PRON
ejpam-5565	189	4	∈	∈	PROPN
ejpam-5565	189	5	(	(	PUNCT
ejpam-5565	189	6	a	a	DET
ejpam-5565	189	7	,	,	PUNCT
ejpam-5565	189	8	b	b	NOUN
ejpam-5565	189	9	)	)	PUNCT
ejpam-5565	189	10	and	and	CCONJ
ejpam-5565	189	11	consider	consider	VERB
ejpam-5565	189	12	the	the	DET
ejpam-5565	189	13	partition	partition	NOUN
ejpam-5565	189	14	p	p	NOUN
ejpam-5565	189	15	=	=	X
ejpam-5565	189	16	{	{	PUNCT
ejpam-5565	189	17	a	a	PROPN
ejpam-5565	189	18	,	,	PUNCT
ejpam-5565	189	19	t	t	PROPN
ejpam-5565	189	20	,	,	PUNCT
ejpam-5565	189	21	b	b	PROPN
ejpam-5565	189	22	}	}	PUNCT
ejpam-5565	189	23	,	,	PUNCT
ejpam-5565	189	24	then	then	ADV
ejpam-5565	189	25	,	,	PUNCT
ejpam-5565	189	26	(	(	PUNCT
ejpam-5565	189	27	2∑	2∑	X
ejpam-5565	189	28	i=1	i=1	X
ejpam-5565	189	29	(	(	PUNCT
ejpam-5565	189	30	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	189	31	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	189	32	+	+	CCONJ
ejpam-5565	189	33	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	189	34	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	189	35	)	)	PUNCT
ejpam-5565	189	36	1	1	NUM
ejpam-5565	189	37	/	/	SYM
ejpam-5565	189	38	q	q	NOUN
ejpam-5565	189	39	=	=	PUNCT
ejpam-5565	189	40	(	(	PUNCT
ejpam-5565	189	41	(	(	PUNCT
ejpam-5565	189	42	∥f+(t)−	∥f+(t)−	PROPN
ejpam-5565	189	43	f+(a)∥+	f+(a)∥+	ADV
ejpam-5565	189	44	+	+	CCONJ
ejpam-5565	189	45	∥f−(t)−	∥f−(t)−	PROPN
ejpam-5565	189	46	f−(a)∥−	f−(a)∥−	NOUN
ejpam-5565	189	47	)	)	PUNCT
ejpam-5565	189	48	q	q	PROPN
ejpam-5565	190	1	+	+	CCONJ
ejpam-5565	190	2	(	(	PUNCT
ejpam-5565	190	3	∥f+(b)−	∥f+(b)−	PROPN
ejpam-5565	190	4	f+(t)∥+	f+(t)∥+	ADJ
ejpam-5565	190	5	+	+	CCONJ
ejpam-5565	190	6	∥f−(b)−	∥f−(b)−	NOUN
ejpam-5565	190	7	f−(t)∥−	f−(t)∥−	NUM
ejpam-5565	190	8	)	)	PUNCT
ejpam-5565	190	9	q)1	q)1	PROPN
ejpam-5565	190	10	/	/	SYM
ejpam-5565	190	11	q	q	PROPN
ejpam-5565	190	12	≤	≤	NUM
ejpam-5565	190	13	sup	sup	NOUN
ejpam-5565	190	14	p∈p[a	p∈p[a	NOUN
ejpam-5565	190	15	,	,	PUNCT
ejpam-5565	190	16	b	b	NOUN
ejpam-5565	190	17	]	]	PUNCT
ejpam-5565	190	18			PUNCT
ejpam-5565	190	19	(	(	PUNCT
ejpam-5565	190	20	n∑	n∑	NOUN
ejpam-5565	190	21	i=1	i=1	PROPN
ejpam-5565	190	22	(	(	PUNCT
ejpam-5565	190	23	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	190	24	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	190	25	+	+	CCONJ
ejpam-5565	190	26	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	190	27	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	190	28	)	)	PUNCT
ejpam-5565	190	29	1	1	X
ejpam-5565	190	30	/	/	SYM
ejpam-5565	190	31	q	q	NOUN
ejpam-5565	190	32			PROPN
ejpam-5565	190	33	≤m	≤m	PROPN
ejpam-5565	190	34	thus	thus	ADV
ejpam-5565	190	35	,	,	PUNCT
ejpam-5565	190	36	(	(	PUNCT
ejpam-5565	190	37	(	(	PUNCT
ejpam-5565	190	38	∥f+(t)−f+(a)∥++∥f−(t)−f−(a)∥−)q+(∥f+(b)−f+(t)∥++∥f−(b)−f−(t)∥−)q)1	∥f+(t)−f+(a)∥++∥f−(t)−f−(a)∥−)q+(∥f+(b)−f+(t)∥++∥f−(b)−f−(t)∥−)q)1	NOUN
ejpam-5565	190	39	/	/	SYM
ejpam-5565	190	40	q	q	NOUN
ejpam-5565	190	41	≤m	≤m	NOUN
ejpam-5565	190	42	therefore	therefore	ADV
ejpam-5565	190	43	,	,	PUNCT
ejpam-5565	190	44	(	(	PUNCT
ejpam-5565	190	45	∥f+(t)−f+(a)∥++∥f−(t)−f−(a)∥−)q+	∥f+(t)−f+(a)∥++∥f−(t)−f−(a)∥−)q+	NOUN
ejpam-5565	190	46	(	(	PUNCT
ejpam-5565	190	47	∥f+(b)−	∥f+(b)−	PROPN
ejpam-5565	190	48	f+(t)∥+	f+(t)∥+	ADJ
ejpam-5565	190	49	+	+	CCONJ
ejpam-5565	190	50	∥f−(b)−	∥f−(b)−	NOUN
ejpam-5565	190	51	f−(t)∥−	f−(t)∥−	NOUN
ejpam-5565	190	52	)	)	PUNCT
ejpam-5565	190	53	q	q	PROPN
ejpam-5565	191	1	≤	≤	NUM
ejpam-5565	191	2	m	m	VERB
ejpam-5565	191	3	q	q	NOUN
ejpam-5565	191	4	whence	whence	NOUN
ejpam-5565	191	5	,	,	PUNCT
ejpam-5565	191	6	(	(	PUNCT
ejpam-5565	191	7	∥f+(t)−	∥f+(t)−	PROPN
ejpam-5565	191	8	f+(a)∥++	f+(a)∥++	PROPN
ejpam-5565	191	9	∥f−(t)−	∥f−(t)−	PROPN
ejpam-5565	191	10	f−(a)∥−)q	f−(a)∥−)q	VERB
ejpam-5565	191	11	,	,	PUNCT
ejpam-5565	191	12	(	(	PUNCT
ejpam-5565	191	13	∥f+(b)−	∥f+(b)−	PROPN
ejpam-5565	191	14	f+(t)∥++	f+(t)∥++	X
ejpam-5565	191	15	∥f−(b)−	∥f−(b)−	NOUN
ejpam-5565	191	16	f−(t)∥−)q	f−(t)∥−)q	VERB
ejpam-5565	191	17	≤m	≤m	PROPN
ejpam-5565	191	18	q	q	X
ejpam-5565	191	19	since	since	SCONJ
ejpam-5565	191	20	(	(	PUNCT
ejpam-5565	191	21	∥f+(t)−	∥f+(t)−	PROPN
ejpam-5565	191	22	f+(a)∥+	f+(a)∥+	ADJ
ejpam-5565	191	23	+	+	CCONJ
ejpam-5565	191	24	∥f−(t)−	∥f−(t)−	PROPN
ejpam-5565	191	25	f−(a)∥−)q	f−(a)∥−)q	VERB
ejpam-5565	191	26	≤	≤	NUM
ejpam-5565	191	27	m	m	VERB
ejpam-5565	191	28	q	q	NOUN
ejpam-5565	191	29	,	,	PUNCT
ejpam-5565	191	30	then	then	ADV
ejpam-5565	191	31	,	,	PUNCT
ejpam-5565	191	32	∥f+(t)−	∥f+(t)−	PROPN
ejpam-5565	191	33	f+(a)∥+	f+(a)∥+	ADV
ejpam-5565	191	34	+	+	CCONJ
ejpam-5565	191	35	∥f−(t)−	∥f−(t)−	PROPN
ejpam-5565	191	36	f−(a)∥−	f−(a)∥−	NOUN
ejpam-5565	191	37	≤	≤	NUM
ejpam-5565	191	38	m	m	VERB
ejpam-5565	191	39	then	then	ADV
ejpam-5565	191	40	,	,	PUNCT
ejpam-5565	191	41	using	use	VERB
ejpam-5565	191	42	the	the	DET
ejpam-5565	191	43	theorem	theorem	NOUN
ejpam-5565	191	44	1	1	NUM
ejpam-5565	191	45	,	,	PUNCT
ejpam-5565	191	46	it	it	PRON
ejpam-5565	191	47	follows	follow	VERB
ejpam-5565	191	48	that	that	SCONJ
ejpam-5565	191	49	:	:	PUNCT
ejpam-5565	191	50	∥f(t)−	∥f(t)−	PROPN
ejpam-5565	191	51	f(a)∥j	f(a)∥j	VERB
ejpam-5565	191	52	≤	≤	NOUN
ejpam-5565	191	53	∥f+(t)−	∥f+(t)−	PROPN
ejpam-5565	191	54	f+(a)∥+	f+(a)∥+	ADV
ejpam-5565	191	55	+	+	CCONJ
ejpam-5565	192	1	∥f−(t)−	∥f−(t)−	PROPN
ejpam-5565	192	2	f−(a)∥−	f−(a)∥−	NOUN
ejpam-5565	192	3	≤	≤	NUM
ejpam-5565	192	4	m	m	VERB
ejpam-5565	192	5	since	since	SCONJ
ejpam-5565	192	6	,	,	PUNCT
ejpam-5565	192	7	∥f(t)∥j	∥f(t)∥j	PROPN
ejpam-5565	192	8	−	−	ADP
ejpam-5565	192	9	∥f(a)∥j	∥f(a)∥j	PROPN
ejpam-5565	192	10	≤	≤	PROPN
ejpam-5565	192	11	∥f(t)−	∥f(t)−	PROPN
ejpam-5565	192	12	f(a)∥j	f(a)∥j	PROPN
ejpam-5565	192	13	,	,	PUNCT
ejpam-5565	192	14	then	then	ADV
ejpam-5565	192	15	∥f(t)∥j	∥f(t)∥j	PROPN
ejpam-5565	192	16	≤	≤	NUM
ejpam-5565	192	17	m	m	VERB
ejpam-5565	193	1	+	+	NUM
ejpam-5565	193	2	∥f(a)∥j	∥f(a)∥j	PROPN
ejpam-5565	193	3	≤	≤	NOUN
ejpam-5565	193	4	m	m	VERB
ejpam-5565	193	5	+	+	NUM
ejpam-5565	193	6	∥f(a)∥j	∥f(a)∥j	PROPN
ejpam-5565	193	7	+	+	CCONJ
ejpam-5565	193	8	∥f(b)∥j	∥f(b)∥j	PROPN
ejpam-5565	193	9	=	=	SYM
ejpam-5565	193	10	d.	d.	PROPN
ejpam-5565	193	11	therefore	therefore	ADV
ejpam-5565	193	12	for	for	ADP
ejpam-5565	193	13	all	all	DET
ejpam-5565	193	14	t	t	NOUN
ejpam-5565	193	15	∈	∈	PROPN
ejpam-5565	194	1	[	[	X
ejpam-5565	194	2	a	a	X
ejpam-5565	194	3	,	,	PUNCT
ejpam-5565	194	4	b	b	NOUN
ejpam-5565	194	5	]	]	X
ejpam-5565	194	6	,	,	PUNCT
ejpam-5565	194	7	it	it	PRON
ejpam-5565	194	8	follows	follow	VERB
ejpam-5565	194	9	that	that	SCONJ
ejpam-5565	194	10	∥f(t)∥j	∥f(t)∥j	PROPN
ejpam-5565	194	11	≤	≤	PROPN
ejpam-5565	194	12	d.	d.	PROPN
ejpam-5565	194	13	this	this	PRON
ejpam-5565	194	14	implies	imply	VERB
ejpam-5565	194	15	that	that	SCONJ
ejpam-5565	194	16	f	f	PROPN
ejpam-5565	194	17	is	be	AUX
ejpam-5565	194	18	bounded	bound	VERB
ejpam-5565	194	19	in	in	ADP
ejpam-5565	194	20	[	[	X
ejpam-5565	194	21	a	a	DET
ejpam-5565	194	22	,	,	PUNCT
ejpam-5565	194	23	b	b	NOUN
ejpam-5565	194	24	]	]	X
ejpam-5565	194	25	.	.	PUNCT
ejpam-5565	195	1	we	we	PRON
ejpam-5565	195	2	show	show	VERB
ejpam-5565	195	3	below	below	ADP
ejpam-5565	195	4	that	that	PRON
ejpam-5565	195	5	the	the	DET
ejpam-5565	195	6	reciprocal	reciprocal	NOUN
ejpam-5565	195	7	of	of	ADP
ejpam-5565	195	8	8	8	NUM
ejpam-5565	195	9	is	be	AUX
ejpam-5565	195	10	not	not	PART
ejpam-5565	195	11	true	true	ADJ
ejpam-5565	195	12	.	.	PUNCT
ejpam-5565	196	1	o.	o.	PROPN
ejpam-5565	196	2	ferrer	ferrer	PROPN
ejpam-5565	196	3	,	,	PUNCT
ejpam-5565	196	4	j.	j.	PROPN
ejpam-5565	196	5	naranjo	naranjo	PROPN
ejpam-5565	196	6	/	/	SYM
ejpam-5565	196	7	eur	eur	PROPN
ejpam-5565	196	8	.	.	PUNCT
ejpam-5565	197	1	j.	j.	PROPN
ejpam-5565	197	2	pure	pure	PROPN
ejpam-5565	197	3	appl	appl	PROPN
ejpam-5565	197	4	.	.	PROPN
ejpam-5565	197	5	math	math	PROPN
ejpam-5565	197	6	,	,	PUNCT
ejpam-5565	197	7	18	18	NUM
ejpam-5565	197	8	(	(	PUNCT
ejpam-5565	197	9	2	2	NUM
ejpam-5565	197	10	)	)	PUNCT
ejpam-5565	197	11	(	(	PUNCT
ejpam-5565	197	12	2025	2025	NUM
ejpam-5565	197	13	)	)	PUNCT
ejpam-5565	197	14	,	,	PUNCT
ejpam-5565	197	15	5565	5565	NUM
ejpam-5565	197	16	10	10	NUM
ejpam-5565	197	17	of	of	ADP
ejpam-5565	197	18	18	18	NUM
ejpam-5565	197	19	example	example	NOUN
ejpam-5565	197	20	4	4	NUM
ejpam-5565	197	21	.	.	PUNCT
ejpam-5565	197	22	consider	consider	VERB
ejpam-5565	197	23	the	the	DET
ejpam-5565	197	24	krein	krein	NOUN
ejpam-5565	197	25	space	space	NOUN
ejpam-5565	197	26	given	give	VERB
ejpam-5565	197	27	in	in	ADP
ejpam-5565	197	28	example	example	NOUN
ejpam-5565	197	29	1	1	NUM
ejpam-5565	197	30	and	and	CCONJ
ejpam-5565	197	31	the	the	DET
ejpam-5565	197	32	function	function	NOUN
ejpam-5565	197	33	f	f	NOUN
ejpam-5565	197	34	:	:	PUNCT
ejpam-5565	197	35	[	[	PUNCT
ejpam-5565	197	36	√	√	NUM
ejpam-5565	197	37	3	3	NUM
ejpam-5565	197	38	,	,	PUNCT
ejpam-5565	197	39	4]→	4]→	PROPN
ejpam-5565	197	40	c2	c2	PROPN
ejpam-5565	197	41	defined	define	VERB
ejpam-5565	197	42	by	by	ADP
ejpam-5565	197	43	f(t	f(t	NOUN
ejpam-5565	197	44	)	)	PUNCT
ejpam-5565	197	45	=	=	PUNCT
ejpam-5565	198	1			PUNCT
ejpam-5565	198	2	(	(	PUNCT
ejpam-5565	198	3	i	i	PROPN
ejpam-5565	198	4	,	,	PUNCT
ejpam-5565	198	5	i	i	PROPN
ejpam-5565	198	6	)	)	PUNCT
ejpam-5565	198	7	,	,	PUNCT
ejpam-5565	198	8	if	if	SCONJ
ejpam-5565	198	9	t	t	PROPN
ejpam-5565	198	10	is	be	AUX
ejpam-5565	198	11	rational	rational	ADJ
ejpam-5565	198	12	,	,	PUNCT
ejpam-5565	198	13	t	t	PROPN
ejpam-5565	198	14	∈	∈	PROPN
ejpam-5565	198	15	[	[	PUNCT
ejpam-5565	198	16	√	√	NOUN
ejpam-5565	198	17	3	3	NUM
ejpam-5565	198	18	,	,	PUNCT
ejpam-5565	198	19	4	4	NUM
ejpam-5565	198	20	]	]	PUNCT
ejpam-5565	198	21	,	,	PUNCT
ejpam-5565	198	22	(	(	PUNCT
ejpam-5565	198	23	0	0	NUM
ejpam-5565	198	24	,	,	PUNCT
ejpam-5565	198	25	0	0	NUM
ejpam-5565	198	26	)	)	PUNCT
ejpam-5565	198	27	,	,	PUNCT
ejpam-5565	198	28	if	if	SCONJ
ejpam-5565	198	29	t	t	PROPN
ejpam-5565	198	30	is	be	AUX
ejpam-5565	198	31	irrational	irrational	ADJ
ejpam-5565	198	32	,	,	PUNCT
ejpam-5565	198	33	t	t	PROPN
ejpam-5565	198	34	∈	∈	PROPN
ejpam-5565	198	35	[	[	PUNCT
ejpam-5565	198	36	√	√	NOUN
ejpam-5565	198	37	3	3	NUM
ejpam-5565	198	38	,	,	PUNCT
ejpam-5565	198	39	4	4	NUM
ejpam-5565	198	40	]	]	PUNCT
ejpam-5565	198	41	.	.	PUNCT
ejpam-5565	199	1	let	let	VERB
ejpam-5565	199	2	’s	’s	NOUN
ejpam-5565	199	3	see	see	VERB
ejpam-5565	199	4	that	that	SCONJ
ejpam-5565	199	5	f	f	PROPN
ejpam-5565	199	6	is	be	AUX
ejpam-5565	199	7	bounded	bound	VERB
ejpam-5565	199	8	on	on	ADP
ejpam-5565	199	9	[	[	PUNCT
ejpam-5565	199	10	√	√	NUM
ejpam-5565	199	11	3	3	NUM
ejpam-5565	199	12	,	,	PUNCT
ejpam-5565	199	13	4	4	NUM
ejpam-5565	199	14	]	]	PUNCT
ejpam-5565	199	15	.	.	PUNCT
ejpam-5565	200	1	in	in	ADP
ejpam-5565	200	2	fact	fact	NOUN
ejpam-5565	200	3	,	,	PUNCT
ejpam-5565	200	4	∥f(t)∥j	∥f(t)∥j	PROPN
ejpam-5565	200	5	=	=	PUNCT
ejpam-5565	200	6			PUNCT
ejpam-5565	200	7	√	√	NUM
ejpam-5565	200	8	2	2	NUM
ejpam-5565	200	9	,	,	PUNCT
ejpam-5565	200	10	if	if	SCONJ
ejpam-5565	200	11	t	t	PROPN
ejpam-5565	200	12	is	be	AUX
ejpam-5565	200	13	rational	rational	ADJ
ejpam-5565	200	14	,	,	PUNCT
ejpam-5565	200	15	t	t	PROPN
ejpam-5565	200	16	∈	∈	PROPN
ejpam-5565	200	17	[	[	PUNCT
ejpam-5565	200	18	√	√	NOUN
ejpam-5565	200	19	3	3	NUM
ejpam-5565	200	20	,	,	PUNCT
ejpam-5565	200	21	4	4	NUM
ejpam-5565	200	22	]	]	PUNCT
ejpam-5565	200	23	,	,	PUNCT
ejpam-5565	200	24	0	0	NUM
ejpam-5565	200	25	,	,	PUNCT
ejpam-5565	200	26	if	if	SCONJ
ejpam-5565	200	27	t	t	PROPN
ejpam-5565	200	28	is	be	AUX
ejpam-5565	200	29	irrational	irrational	ADJ
ejpam-5565	200	30	,	,	PUNCT
ejpam-5565	200	31	t	t	PROPN
ejpam-5565	200	32	∈	∈	PROPN
ejpam-5565	200	33	[	[	PUNCT
ejpam-5565	200	34	√	√	NOUN
ejpam-5565	200	35	3	3	NUM
ejpam-5565	200	36	,	,	PUNCT
ejpam-5565	200	37	4	4	NUM
ejpam-5565	200	38	]	]	PUNCT
ejpam-5565	200	39	.	.	PUNCT
ejpam-5565	201	1	therefore	therefore	ADV
ejpam-5565	201	2	,	,	PUNCT
ejpam-5565	201	3	∥f(t)∥j	∥f(t)∥j	PROPN
ejpam-5565	201	4	≤	≤	NOUN
ejpam-5565	201	5	√	√	ADP
ejpam-5565	201	6	2	2	NUM
ejpam-5565	201	7	for	for	ADP
ejpam-5565	201	8	all	all	DET
ejpam-5565	201	9	t	t	NOUN
ejpam-5565	201	10	∈	∈	PROPN
ejpam-5565	201	11	[	[	PUNCT
ejpam-5565	201	12	√	√	NOUN
ejpam-5565	201	13	3	3	NUM
ejpam-5565	201	14	,	,	PUNCT
ejpam-5565	201	15	4	4	NUM
ejpam-5565	201	16	]	]	PUNCT
ejpam-5565	201	17	.	.	PUNCT
ejpam-5565	202	1	thus	thus	ADV
ejpam-5565	202	2	f	f	PROPN
ejpam-5565	202	3	is	be	AUX
ejpam-5565	202	4	bounded	bound	VERB
ejpam-5565	202	5	.	.	PUNCT
ejpam-5565	203	1	now	now	ADV
ejpam-5565	203	2	,	,	PUNCT
ejpam-5565	203	3	let	let	VERB
ejpam-5565	203	4	’s	’s	NOUN
ejpam-5565	203	5	see	see	VERB
ejpam-5565	203	6	that	that	SCONJ
ejpam-5565	203	7	f	f	PROPN
ejpam-5565	203	8	is	be	AUX
ejpam-5565	203	9	not	not	PART
ejpam-5565	203	10	of	of	ADP
ejpam-5565	203	11	q−bounded	q−bounded	ADJ
ejpam-5565	203	12	variation	variation	NOUN
ejpam-5565	203	13	.	.	PUNCT
ejpam-5565	204	1	let	let	VERB
ejpam-5565	204	2	t0	t0	NOUN
ejpam-5565	204	3	=	=	PUNCT
ejpam-5565	204	4	√	√	PROPN
ejpam-5565	204	5	3	3	NUM
ejpam-5565	204	6	,	,	PUNCT
ejpam-5565	204	7	as	as	ADP
ejpam-5565	204	8	between	between	ADP
ejpam-5565	204	9	any	any	DET
ejpam-5565	204	10	two	two	NUM
ejpam-5565	204	11	reals	real	NOUN
ejpam-5565	204	12	there	there	PRON
ejpam-5565	204	13	is	be	VERB
ejpam-5565	204	14	a	a	DET
ejpam-5565	204	15	rational	rational	ADJ
ejpam-5565	204	16	number	number	NOUN
ejpam-5565	204	17	and	and	CCONJ
ejpam-5565	204	18	an	an	DET
ejpam-5565	204	19	irrational	irrational	ADJ
ejpam-5565	204	20	number	number	NOUN
ejpam-5565	204	21	,	,	PUNCT
ejpam-5565	204	22	we	we	PRON
ejpam-5565	204	23	can	can	AUX
ejpam-5565	204	24	choose	choose	VERB
ejpam-5565	204	25	t1	t1	NOUN
ejpam-5565	204	26	as	as	ADP
ejpam-5565	204	27	a	a	DET
ejpam-5565	204	28	rational	rational	ADJ
ejpam-5565	204	29	number	number	NOUN
ejpam-5565	204	30	between	between	ADP
ejpam-5565	204	31	√	√	NUM
ejpam-5565	204	32	3	3	NUM
ejpam-5565	204	33	and	and	CCONJ
ejpam-5565	204	34	4	4	NUM
ejpam-5565	204	35	,	,	PUNCT
ejpam-5565	204	36	t2	t2	NOUN
ejpam-5565	204	37	as	as	ADP
ejpam-5565	204	38	an	an	DET
ejpam-5565	204	39	irrational	irrational	ADJ
ejpam-5565	204	40	number	number	NOUN
ejpam-5565	204	41	between	between	ADP
ejpam-5565	204	42	t1	t1	NOUN
ejpam-5565	204	43	and	and	CCONJ
ejpam-5565	204	44	4	4	NUM
ejpam-5565	204	45	,	,	PUNCT
ejpam-5565	204	46	t3	t3	NOUN
ejpam-5565	204	47	as	as	ADP
ejpam-5565	204	48	a	a	DET
ejpam-5565	204	49	rational	rational	ADJ
ejpam-5565	204	50	number	number	NOUN
ejpam-5565	204	51	between	between	ADP
ejpam-5565	204	52	t2	t2	NOUN
ejpam-5565	204	53	and	and	CCONJ
ejpam-5565	204	54	4	4	NUM
ejpam-5565	204	55	,	,	PUNCT
ejpam-5565	204	56	and	and	CCONJ
ejpam-5565	204	57	so	so	ADV
ejpam-5565	204	58	on	on	ADV
ejpam-5565	204	59	t2i	t2i	PUNCT
ejpam-5565	204	60	would	would	AUX
ejpam-5565	204	61	be	be	AUX
ejpam-5565	204	62	an	an	DET
ejpam-5565	204	63	irrational	irrational	ADJ
ejpam-5565	204	64	number	number	NOUN
ejpam-5565	204	65	between	between	ADP
ejpam-5565	204	66	t2i−1	t2i−1	PROPN
ejpam-5565	204	67	and	and	CCONJ
ejpam-5565	204	68	4	4	NUM
ejpam-5565	204	69	,	,	PUNCT
ejpam-5565	204	70	t2i+1	t2i+1	PRON
ejpam-5565	204	71	would	would	AUX
ejpam-5565	204	72	be	be	AUX
ejpam-5565	204	73	a	a	DET
ejpam-5565	204	74	rational	rational	ADJ
ejpam-5565	204	75	number	number	NOUN
ejpam-5565	204	76	between	between	ADP
ejpam-5565	204	77	t2i	t2i	PUNCT
ejpam-5565	204	78	and	and	CCONJ
ejpam-5565	204	79	4	4	NUM
ejpam-5565	204	80	,	,	PUNCT
ejpam-5565	204	81	finally	finally	ADV
ejpam-5565	204	82	we	we	PRON
ejpam-5565	204	83	choose	choose	VERB
ejpam-5565	204	84	tn	tn	NOUN
ejpam-5565	204	85	=	=	SYM
ejpam-5565	204	86	4	4	NUM
ejpam-5565	204	87	.	.	PUNCT
ejpam-5565	205	1	then	then	ADV
ejpam-5565	205	2	,	,	PUNCT
ejpam-5565	205	3	f+(t	f+(t	NOUN
ejpam-5565	205	4	)	)	PUNCT
ejpam-5565	205	5	=	=	PUNCT
ejpam-5565	205	6	(	(	PUNCT
ejpam-5565	205	7	i	i	INTJ
ejpam-5565	205	8	,	,	PUNCT
ejpam-5565	205	9	0	0	NUM
ejpam-5565	205	10	)	)	PUNCT
ejpam-5565	205	11	and	and	CCONJ
ejpam-5565	205	12	f−(t	f−(t	PROPN
ejpam-5565	205	13	)	)	PUNCT
ejpam-5565	205	14	=	=	PUNCT
ejpam-5565	206	1	(	(	PUNCT
ejpam-5565	206	2	0	0	NUM
ejpam-5565	206	3	,	,	PUNCT
ejpam-5565	206	4	i	i	NOUN
ejpam-5565	206	5	)	)	PUNCT
ejpam-5565	206	6	furthermore	furthermore	ADV
ejpam-5565	206	7	,	,	PUNCT
ejpam-5565	206	8	2	2	NUM
ejpam-5565	206	9	v4√	v4√	NOUN
ejpam-5565	206	10	3(f	3(f	NUM
ejpam-5565	206	11	,	,	PUNCT
ejpam-5565	206	12	(	(	PUNCT
ejpam-5565	206	13	c2	c2	PROPN
ejpam-5565	206	14	,	,	PUNCT
ejpam-5565	206	15	[	[	X
ejpam-5565	206	16	·	·	PUNCT
ejpam-5565	206	17	,	,	PUNCT
ejpam-5565	206	18	·	·	PUNCT
ejpam-5565	206	19	]	]	X
ejpam-5565	206	20	)	)	PUNCT
ejpam-5565	206	21	)	)	PUNCT
ejpam-5565	207	1	≥	≥	NOUN
ejpam-5565	208	1			PROPN
ejpam-5565	208	2	n∑	n∑	PROPN
ejpam-5565	208	3	j=1	j=1	NOUN
ejpam-5565	208	4	(	(	PUNCT
ejpam-5565	208	5	∥f+(tj)−	∥f+(tj)−	NOUN
ejpam-5565	208	6	f+(tj−1)∥+	f+(tj−1)∥+	ADJ
ejpam-5565	208	7	+	+	NUM
ejpam-5565	208	8	∥f−(tj)−	∥f−(tj)−	NOUN
ejpam-5565	208	9	f−(tj−1)∥−	f−(tj−1)∥−	NOUN
ejpam-5565	208	10	)	)	PUNCT
ejpam-5565	208	11	21/2	21/2	NUM
ejpam-5565	208	12	=	=	SYM
ejpam-5565	208	13	(	(	PUNCT
ejpam-5565	208	14	(	(	PUNCT
ejpam-5565	208	15	∥	∥	X
ejpam-5565	208	16	−	−	PROPN
ejpam-5565	208	17	(	(	PUNCT
ejpam-5565	208	18	i	i	NOUN
ejpam-5565	208	19	,	,	PUNCT
ejpam-5565	208	20	i)∥+	i)∥+	ADV
ejpam-5565	208	21	+	+	CCONJ
ejpam-5565	208	22	∥(i	∥(i	ADJ
ejpam-5565	208	23	,	,	PUNCT
ejpam-5565	208	24	i)∥−)2	i)∥−)2	PRON
ejpam-5565	208	25	+	+	PUNCT
ejpam-5565	208	26	·	·	PUNCT
ejpam-5565	208	27	·	·	PUNCT
ejpam-5565	208	28	·	·	PUNCT
ejpam-5565	209	1	+	+	PUNCT
ejpam-5565	209	2	(	(	PUNCT
ejpam-5565	209	3	∥	∥	X
ejpam-5565	209	4	−	−	PROPN
ejpam-5565	209	5	(	(	PUNCT
ejpam-5565	209	6	i	i	NOUN
ejpam-5565	209	7	,	,	PUNCT
ejpam-5565	209	8	i)∥+	i)∥+	ADV
ejpam-5565	209	9	+	+	CCONJ
ejpam-5565	209	10	∥(i	∥(i	ADJ
ejpam-5565	209	11	,	,	PUNCT
ejpam-5565	209	12	i)∥−)2	i)∥−)2	NOUN
ejpam-5565	209	13	)	)	PUNCT
ejpam-5565	209	14	1/2	1/2	NUM
ejpam-5565	209	15	=	=	SYM
ejpam-5565	209	16	(	(	PUNCT
ejpam-5565	209	17	(	(	PUNCT
ejpam-5565	209	18	∥(i	∥(i	ADJ
ejpam-5565	209	19	,	,	PUNCT
ejpam-5565	209	20	i)∥+	i)∥+	ADV
ejpam-5565	209	21	+	+	CCONJ
ejpam-5565	209	22	∥(i	∥(i	ADJ
ejpam-5565	209	23	,	,	PUNCT
ejpam-5565	209	24	i)∥−)2	i)∥−)2	PRON
ejpam-5565	209	25	+	+	PUNCT
ejpam-5565	209	26	·	·	PUNCT
ejpam-5565	209	27	·	·	PUNCT
ejpam-5565	209	28	·	·	PUNCT
ejpam-5565	209	29	+	+	CCONJ
ejpam-5565	209	30	(	(	PUNCT
ejpam-5565	209	31	∥(i	∥(i	ADJ
ejpam-5565	209	32	,	,	PUNCT
ejpam-5565	209	33	i)∥+	i)∥+	ADV
ejpam-5565	209	34	+	+	CCONJ
ejpam-5565	209	35	∥(i	∥(i	ADJ
ejpam-5565	209	36	,	,	PUNCT
ejpam-5565	209	37	i)∥−)2	i)∥−)2	NOUN
ejpam-5565	209	38	)	)	PUNCT
ejpam-5565	209	39	1/2	1/2	NUM
ejpam-5565	209	40	≥	≥	NOUN
ejpam-5565	209	41	(	(	PUNCT
ejpam-5565	209	42	∥(i	∥(i	ADJ
ejpam-5565	209	43	,	,	PUNCT
ejpam-5565	209	44	i)∥2j	i)∥2j	VERB
ejpam-5565	209	45	+	+	X
ejpam-5565	209	46	·	·	PUNCT
ejpam-5565	209	47	·	·	PUNCT
ejpam-5565	209	48	·	·	PUNCT
ejpam-5565	209	49	+	+	CCONJ
ejpam-5565	209	50	∥(i	∥(i	ADJ
ejpam-5565	209	51	,	,	PUNCT
ejpam-5565	209	52	i)∥2j	i)∥2j	ADJ
ejpam-5565	209	53	)	)	PUNCT
ejpam-5565	209	54	1/2	1/2	NUM
ejpam-5565	209	55	=	=	SYM
ejpam-5565	209	56	(	(	PUNCT
ejpam-5565	209	57	(	(	PUNCT
ejpam-5565	209	58	√	√	ADP
ejpam-5565	209	59	2)2	2)2	NUM
ejpam-5565	209	60	+	+	CCONJ
ejpam-5565	209	61	·	·	PUNCT
ejpam-5565	209	62	·	·	PUNCT
ejpam-5565	209	63	·	·	PUNCT
ejpam-5565	209	64	+	+	CCONJ
ejpam-5565	209	65	(	(	PUNCT
ejpam-5565	209	66	√	√	NUM
ejpam-5565	209	67	2)2	2)2	NUM
ejpam-5565	209	68	)	)	PUNCT
ejpam-5565	209	69	1/2	1/2	NUM
ejpam-5565	209	70	=	=	SYM
ejpam-5565	209	71	(	(	PUNCT
ejpam-5565	209	72	2	2	NUM
ejpam-5565	209	73	+	+	CCONJ
ejpam-5565	209	74	·	·	PUNCT
ejpam-5565	209	75	·	·	PUNCT
ejpam-5565	209	76	·	·	PUNCT
ejpam-5565	209	77	+	+	NUM
ejpam-5565	209	78	2)1/2	2)1/2	NUM
ejpam-5565	209	79	=	=	SYM
ejpam-5565	209	80	√	√	NUM
ejpam-5565	209	81	2n	2n	NUM
ejpam-5565	209	82	note	note	VERB
ejpam-5565	209	83	that	that	SCONJ
ejpam-5565	209	84	a	a	DET
ejpam-5565	209	85	partition	partition	NOUN
ejpam-5565	209	86	of	of	ADP
ejpam-5565	209	87	the	the	DET
ejpam-5565	209	88	interval	interval	NOUN
ejpam-5565	209	89	[	[	PUNCT
ejpam-5565	209	90	√	√	NUM
ejpam-5565	209	91	3	3	NUM
ejpam-5565	209	92	,	,	PUNCT
ejpam-5565	209	93	4	4	NUM
ejpam-5565	209	94	]	]	PUNCT
ejpam-5565	209	95	was	be	AUX
ejpam-5565	209	96	constructed	construct	VERB
ejpam-5565	209	97	,	,	PUNCT
ejpam-5565	209	98	starting	start	VERB
ejpam-5565	209	99	at	at	ADP
ejpam-5565	209	100	√	√	NUM
ejpam-5565	209	101	3	3	NUM
ejpam-5565	209	102	,	,	PUNCT
ejpam-5565	209	103	then	then	ADV
ejpam-5565	209	104	alternating	alternate	VERB
ejpam-5565	209	105	between	between	ADP
ejpam-5565	209	106	rational	rational	ADJ
ejpam-5565	209	107	and	and	CCONJ
ejpam-5565	209	108	irrational	irrational	ADJ
ejpam-5565	209	109	numbers	number	NOUN
ejpam-5565	209	110	until	until	SCONJ
ejpam-5565	209	111	it	it	PRON
ejpam-5565	209	112	ends	end	VERB
ejpam-5565	209	113	at	at	ADP
ejpam-5565	209	114	4	4	NUM
ejpam-5565	209	115	,	,	PUNCT
ejpam-5565	209	116	for	for	ADP
ejpam-5565	209	117	which	which	PRON
ejpam-5565	209	118	2	2	NUM
ejpam-5565	209	119	v4√	v4√	NOUN
ejpam-5565	209	120	3(f	3(f	NUM
ejpam-5565	209	121	,	,	PUNCT
ejpam-5565	209	122	(	(	PUNCT
ejpam-5565	209	123	c2	c2	PROPN
ejpam-5565	209	124	,	,	PUNCT
ejpam-5565	209	125	[	[	X
ejpam-5565	209	126	·	·	PUNCT
ejpam-5565	209	127	,	,	PUNCT
ejpam-5565	209	128	·	·	PUNCT
ejpam-5565	209	129	]	]	X
ejpam-5565	209	130	)	)	PUNCT
ejpam-5565	209	131	)	)	PUNCT
ejpam-5565	209	132	is	be	AUX
ejpam-5565	209	133	not	not	PART
ejpam-5565	209	134	finite	finite	ADJ
ejpam-5565	209	135	,	,	PUNCT
ejpam-5565	209	136	thus	thus	ADV
ejpam-5565	209	137	f	f	PROPN
ejpam-5565	209	138	is	be	AUX
ejpam-5565	209	139	not	not	PART
ejpam-5565	209	140	of	of	ADP
ejpam-5565	209	141	bounded	bounded	ADJ
ejpam-5565	209	142	2	2	NUM
ejpam-5565	209	143	-	-	PUNCT
ejpam-5565	209	144	variation	variation	NOUN
ejpam-5565	209	145	in	in	ADP
ejpam-5565	209	146	(	(	PUNCT
ejpam-5565	209	147	c2	c2	PROPN
ejpam-5565	209	148	,	,	PUNCT
ejpam-5565	209	149	[	[	X
ejpam-5565	209	150	·	·	PUNCT
ejpam-5565	209	151	,	,	PUNCT
ejpam-5565	209	152	·	·	PUNCT
ejpam-5565	209	153	]	]	X
ejpam-5565	209	154	)	)	PUNCT
ejpam-5565	209	155	.	.	PUNCT
ejpam-5565	210	1	theorem	theorem	NOUN
ejpam-5565	210	2	9	9	NUM
ejpam-5565	210	3	.	.	PUNCT
ejpam-5565	211	1	let	let	VERB
ejpam-5565	211	2	(	(	PUNCT
ejpam-5565	211	3	k	k	NOUN
ejpam-5565	211	4	=	=	SYM
ejpam-5565	211	5	k+	k+	NOUN
ejpam-5565	211	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	211	7	,	,	PUNCT
ejpam-5565	211	8	[	[	X
ejpam-5565	211	9	·	·	PUNCT
ejpam-5565	211	10	,	,	PUNCT
ejpam-5565	211	11	·	·	PUNCT
ejpam-5565	211	12	]	]	PUNCT
ejpam-5565	211	13	)	)	PUNCT
ejpam-5565	211	14	be	be	AUX
ejpam-5565	211	15	a	a	DET
ejpam-5565	211	16	krein	krein	ADJ
ejpam-5565	211	17	space	space	NOUN
ejpam-5565	211	18	,	,	PUNCT
ejpam-5565	211	19	f	f	X
ejpam-5565	211	20	:	:	PUNCT
ejpam-5565	212	1	[	[	X
ejpam-5565	212	2	a	a	X
ejpam-5565	212	3	,	,	PUNCT
ejpam-5565	212	4	b	b	NOUN
ejpam-5565	212	5	]	]	X
ejpam-5565	212	6	→	→	SYM
ejpam-5565	212	7	k	k	X
ejpam-5565	212	8	,	,	PUNCT
ejpam-5565	212	9	is	be	AUX
ejpam-5565	212	10	of	of	ADP
ejpam-5565	212	11	bounded	bounded	ADJ
ejpam-5565	212	12	q	q	NOUN
ejpam-5565	212	13	-	-	NOUN
ejpam-5565	212	14	variation	variation	NOUN
ejpam-5565	212	15	in	in	ADP
ejpam-5565	212	16	[	[	X
ejpam-5565	212	17	a	a	DET
ejpam-5565	212	18	,	,	PUNCT
ejpam-5565	212	19	b	b	NOUN
ejpam-5565	212	20	]	]	X
ejpam-5565	212	21	on	on	ADP
ejpam-5565	212	22	(	(	PUNCT
ejpam-5565	212	23	k	k	NOUN
ejpam-5565	212	24	=	=	SYM
ejpam-5565	212	25	k+	k+	NOUN
ejpam-5565	212	26	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	212	27	)	)	PUNCT
ejpam-5565	212	28	,	,	PUNCT
ejpam-5565	212	29	then	then	ADV
ejpam-5565	212	30	f	f	PROPN
ejpam-5565	212	31	is	be	AUX
ejpam-5565	212	32	of	of	ADP
ejpam-5565	212	33	bounded	bounded	ADJ
ejpam-5565	212	34	q	q	NOUN
ejpam-5565	212	35	-	-	NOUN
ejpam-5565	212	36	variation	variation	NOUN
ejpam-5565	212	37	in	in	ADP
ejpam-5565	212	38	[	[	X
ejpam-5565	212	39	a	a	DET
ejpam-5565	212	40	,	,	PUNCT
ejpam-5565	212	41	b	b	NOUN
ejpam-5565	212	42	]	]	X
ejpam-5565	212	43	on	on	ADP
ejpam-5565	212	44	the	the	DET
ejpam-5565	212	45	hilbert	hilbert	NOUN
ejpam-5565	212	46	spaces	space	NOUN
ejpam-5565	212	47	(	(	PUNCT
ejpam-5565	212	48	k+	k+	X
ejpam-5565	212	49	,	,	PUNCT
ejpam-5565	212	50	[	[	X
ejpam-5565	212	51	·	·	PUNCT
ejpam-5565	212	52	,	,	PUNCT
ejpam-5565	212	53	·	·	PUNCT
ejpam-5565	212	54	]	]	PUNCT
ejpam-5565	212	55	)	)	PUNCT
ejpam-5565	212	56	and	and	CCONJ
ejpam-5565	212	57	(	(	PUNCT
ejpam-5565	212	58	k−,−	k−,−	NOUN
ejpam-5565	212	59	[	[	X
ejpam-5565	212	60	·	·	PUNCT
ejpam-5565	212	61	,	,	PUNCT
ejpam-5565	212	62	·	·	PUNCT
ejpam-5565	212	63	]	]	X
ejpam-5565	212	64	)	)	PUNCT
ejpam-5565	212	65	.	.	PUNCT
ejpam-5565	213	1	proof	proof	NOUN
ejpam-5565	213	2	.	.	PUNCT
ejpam-5565	214	1	consider	consider	VERB
ejpam-5565	214	2	the	the	DET
ejpam-5565	214	3	partition	partition	NOUN
ejpam-5565	214	4	p	p	NOUN
ejpam-5565	214	5	=	=	X
ejpam-5565	214	6	{	{	PUNCT
ejpam-5565	214	7	a	a	PRON
ejpam-5565	214	8	,	,	PUNCT
ejpam-5565	214	9	t1	t1	NOUN
ejpam-5565	214	10	,	,	PUNCT
ejpam-5565	214	11	t2	t2	NOUN
ejpam-5565	214	12	,	,	PUNCT
ejpam-5565	214	13	·	·	PUNCT
ejpam-5565	214	14	·	·	PUNCT
ejpam-5565	214	15	·	·	PUNCT
ejpam-5565	214	16	,	,	PUNCT
ejpam-5565	214	17	ti−1	ti−1	NOUN
ejpam-5565	214	18	,	,	PUNCT
ejpam-5565	214	19	ti	ti	NOUN
ejpam-5565	214	20	,	,	PUNCT
ejpam-5565	214	21	·	·	PUNCT
ejpam-5565	214	22	·	·	PUNCT
ejpam-5565	214	23	·	·	PUNCT
ejpam-5565	214	24	,	,	PUNCT
ejpam-5565	214	25	tn−1	tn−1	PROPN
ejpam-5565	214	26	,	,	PUNCT
ejpam-5565	214	27	b	b	NOUN
ejpam-5565	214	28	}	}	PUNCT
ejpam-5565	214	29	∈	∈	PROPN
ejpam-5565	214	30	p[a	p[a	PROPN
ejpam-5565	214	31	,	,	PUNCT
ejpam-5565	214	32	b	b	X
ejpam-5565	214	33	]	]	X
ejpam-5565	214	34	y	y	PROPN
ejpam-5565	214	35	q	q	X
ejpam-5565	214	36	≥	≥	PROPN
ejpam-5565	214	37	1	1	NUM
ejpam-5565	214	38	.	.	PUNCT
ejpam-5565	215	1	the	the	DET
ejpam-5565	215	2	proof	proof	NOUN
ejpam-5565	215	3	is	be	AUX
ejpam-5565	215	4	a	a	DET
ejpam-5565	215	5	consequence	consequence	NOUN
ejpam-5565	215	6	of	of	ADP
ejpam-5565	215	7	:	:	PUNCT
ejpam-5565	215	8	∥f−(ti)−f−(ti−1)∥q−	∥f−(ti)−f−(ti−1)∥q−	PROPN
ejpam-5565	215	9	,	,	PUNCT
ejpam-5565	215	10	∥f+(ti)−f+(ti−1)∥q+	∥f+(ti)−f+(ti−1)∥q+	PUNCT
ejpam-5565	215	11	≤	≤	NOUN
ejpam-5565	215	12	(	(	PUNCT
ejpam-5565	215	13	∥f+(ti)−f+(ti−1)∥++∥f−(ti)−f−(ti−1)∥−)q	∥f+(ti)−f+(ti−1)∥++∥f−(ti)−f−(ti−1)∥−)q	PROPN
ejpam-5565	215	14	o.	o.	PROPN
ejpam-5565	215	15	ferrer	ferrer	PROPN
ejpam-5565	215	16	,	,	PUNCT
ejpam-5565	215	17	j.	j.	PROPN
ejpam-5565	215	18	naranjo	naranjo	PROPN
ejpam-5565	215	19	/	/	SYM
ejpam-5565	215	20	eur	eur	PROPN
ejpam-5565	215	21	.	.	PUNCT
ejpam-5565	216	1	j.	j.	PROPN
ejpam-5565	216	2	pure	pure	PROPN
ejpam-5565	216	3	appl	appl	PROPN
ejpam-5565	216	4	.	.	PROPN
ejpam-5565	216	5	math	math	PROPN
ejpam-5565	216	6	,	,	PUNCT
ejpam-5565	216	7	18	18	NUM
ejpam-5565	216	8	(	(	PUNCT
ejpam-5565	216	9	2	2	NUM
ejpam-5565	216	10	)	)	PUNCT
ejpam-5565	216	11	(	(	PUNCT
ejpam-5565	216	12	2025	2025	NUM
ejpam-5565	216	13	)	)	PUNCT
ejpam-5565	216	14	,	,	PUNCT
ejpam-5565	216	15	5565	5565	NUM
ejpam-5565	216	16	11	11	NUM
ejpam-5565	216	17	of	of	ADP
ejpam-5565	216	18	18	18	NUM
ejpam-5565	216	19	theorem	theorem	VERB
ejpam-5565	216	20	10	10	NUM
ejpam-5565	216	21	.	.	PUNCT
ejpam-5565	217	1	let	let	VERB
ejpam-5565	217	2	(	(	PUNCT
ejpam-5565	217	3	k	k	NOUN
ejpam-5565	217	4	=	=	SYM
ejpam-5565	217	5	k+	k+	NOUN
ejpam-5565	217	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	217	7	,	,	PUNCT
ejpam-5565	217	8	[	[	X
ejpam-5565	217	9	·	·	PUNCT
ejpam-5565	217	10	,	,	PUNCT
ejpam-5565	217	11	·	·	PUNCT
ejpam-5565	217	12	]	]	PUNCT
ejpam-5565	217	13	)	)	PUNCT
ejpam-5565	217	14	be	be	AUX
ejpam-5565	217	15	a	a	DET
ejpam-5565	217	16	krein	krein	ADJ
ejpam-5565	217	17	space	space	NOUN
ejpam-5565	217	18	and	and	CCONJ
ejpam-5565	217	19	f	f	NOUN
ejpam-5565	217	20	:	:	PUNCT
ejpam-5565	218	1	[	[	X
ejpam-5565	218	2	a	a	X
ejpam-5565	218	3	,	,	PUNCT
ejpam-5565	218	4	b	b	NOUN
ejpam-5565	218	5	]	]	X
ejpam-5565	218	6	→	→	SYM
ejpam-5565	218	7	k	k	X
ejpam-5565	218	8	=	=	PUNCT
ejpam-5565	218	9	k+	k+	PROPN
ejpam-5565	218	10	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	218	11	a	a	DET
ejpam-5565	218	12	function	function	NOUN
ejpam-5565	218	13	,	,	PUNCT
ejpam-5565	218	14	f	f	PROPN
ejpam-5565	218	15	∈	∈	PROPN
ejpam-5565	218	16	b	b	X
ejpam-5565	218	17	q	q	X
ejpam-5565	218	18	v	v	NOUN
ejpam-5565	218	19	(	(	PUNCT
ejpam-5565	218	20	[	[	X
ejpam-5565	218	21	a	a	PRON
ejpam-5565	218	22	,	,	PUNCT
ejpam-5565	218	23	b],k	b],k	NOUN
ejpam-5565	218	24	)	)	PUNCT
ejpam-5565	218	25	,	,	PUNCT
ejpam-5565	218	26	then	then	ADV
ejpam-5565	218	27	q+	q+	ADV
ejpam-5565	218	28	vb	vb	ADP
ejpam-5565	218	29	a(f	a(f	PROPN
ejpam-5565	218	30	,	,	PUNCT
ejpam-5565	218	31	(	(	PUNCT
ejpam-5565	218	32	k+	k+	X
ejpam-5565	218	33	,	,	PUNCT
ejpam-5565	218	34	[	[	X
ejpam-5565	218	35	·	·	PUNCT
ejpam-5565	218	36	,	,	PUNCT
ejpam-5565	218	37	·	·	PUNCT
ejpam-5565	218	38	]	]	X
ejpam-5565	218	39	)	)	PUNCT
ejpam-5565	218	40	)	)	PUNCT
ejpam-5565	219	1	=	=	SYM
ejpam-5565	219	2	0	0	PUNCT
ejpam-5565	220	1	=	=	SYM
ejpam-5565	220	2	q−	q−	PROPN
ejpam-5565	220	3	vb	vb	PROPN
ejpam-5565	220	4	a(f	a(f	PROPN
ejpam-5565	220	5	,	,	PUNCT
ejpam-5565	220	6	(	(	PUNCT
ejpam-5565	220	7	k−,−	k−,−	NOUN
ejpam-5565	220	8	[	[	X
ejpam-5565	220	9	·	·	PUNCT
ejpam-5565	220	10	,	,	PUNCT
ejpam-5565	220	11	·	·	PUNCT
ejpam-5565	220	12	]	]	X
ejpam-5565	220	13	)	)	PUNCT
ejpam-5565	220	14	)	)	PUNCT
ejpam-5565	221	1	if	if	SCONJ
ejpam-5565	221	2	and	and	CCONJ
ejpam-5565	221	3	only	only	ADV
ejpam-5565	221	4	if	if	SCONJ
ejpam-5565	221	5	f	f	PROPN
ejpam-5565	221	6	is	be	AUX
ejpam-5565	221	7	constant	constant	ADJ
ejpam-5565	221	8	in	in	ADP
ejpam-5565	221	9	[	[	X
ejpam-5565	221	10	a	a	DET
ejpam-5565	221	11	,	,	PUNCT
ejpam-5565	221	12	b	b	NOUN
ejpam-5565	221	13	]	]	X
ejpam-5565	221	14	with	with	ADP
ejpam-5565	221	15	respect	respect	NOUN
ejpam-5565	221	16	to	to	ADP
ejpam-5565	221	17	(	(	PUNCT
ejpam-5565	221	18	k	k	X
ejpam-5565	221	19	=	=	SYM
ejpam-5565	221	20	k+	k+	NOUN
ejpam-5565	221	21	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	221	22	)	)	PUNCT
ejpam-5565	221	23	.	.	PUNCT
ejpam-5565	222	1	proof	proof	NOUN
ejpam-5565	222	2	.	.	PUNCT
ejpam-5565	223	1	(	(	PUNCT
ejpam-5565	223	2	→	→	NOUN
ejpam-5565	223	3	)	)	PUNCT
ejpam-5565	223	4	suppose	suppose	VERB
ejpam-5565	223	5	that	that	SCONJ
ejpam-5565	223	6	q+	q+	ADP
ejpam-5565	223	7	vb	vb	ADP
ejpam-5565	223	8	a(f	a(f	PROPN
ejpam-5565	223	9	,	,	PUNCT
ejpam-5565	223	10	(	(	PUNCT
ejpam-5565	223	11	k+	k+	X
ejpam-5565	223	12	,	,	PUNCT
ejpam-5565	223	13	[	[	X
ejpam-5565	223	14	·	·	PUNCT
ejpam-5565	223	15	,	,	PUNCT
ejpam-5565	223	16	·	·	PUNCT
ejpam-5565	223	17	]	]	X
ejpam-5565	223	18	)	)	PUNCT
ejpam-5565	223	19	)	)	PUNCT
ejpam-5565	223	20	=	=	SYM
ejpam-5565	224	1	0	0	PUNCT
ejpam-5565	225	1	=	=	SYM
ejpam-5565	225	2	q−	q−	PROPN
ejpam-5565	225	3	vb	vb	PROPN
ejpam-5565	225	4	a(f	a(f	PROPN
ejpam-5565	225	5	,	,	PUNCT
ejpam-5565	225	6	(	(	PUNCT
ejpam-5565	225	7	k−,−	k−,−	NOUN
ejpam-5565	225	8	[	[	X
ejpam-5565	225	9	·	·	PUNCT
ejpam-5565	225	10	,	,	PUNCT
ejpam-5565	225	11	·	·	PUNCT
ejpam-5565	225	12	]	]	X
ejpam-5565	225	13	)	)	PUNCT
ejpam-5565	225	14	)	)	PUNCT
ejpam-5565	225	15	,	,	PUNCT
ejpam-5565	225	16	that	that	ADV
ejpam-5565	225	17	is	is	ADV
ejpam-5565	225	18	,	,	PUNCT
ejpam-5565	225	19	q+	q+	ADV
ejpam-5565	225	20	vb	vb	ADP
ejpam-5565	225	21	a(f	a(f	PROPN
ejpam-5565	225	22	,	,	PUNCT
ejpam-5565	225	23	(	(	PUNCT
ejpam-5565	225	24	k+	k+	X
ejpam-5565	225	25	,	,	PUNCT
ejpam-5565	225	26	[	[	X
ejpam-5565	225	27	·	·	PUNCT
ejpam-5565	225	28	,	,	PUNCT
ejpam-5565	225	29	·	·	PUNCT
ejpam-5565	225	30	]	]	X
ejpam-5565	225	31	)	)	PUNCT
ejpam-5565	225	32	)	)	PUNCT
ejpam-5565	226	1	=	=	SYM
ejpam-5565	226	2	sup	sup	NOUN
ejpam-5565	226	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	226	4	,	,	PUNCT
ejpam-5565	226	5	b	b	NOUN
ejpam-5565	226	6	]	]	PUNCT
ejpam-5565	226	7			PUNCT
ejpam-5565	226	8	(	(	PUNCT
ejpam-5565	226	9	n∑	n∑	NOUN
ejpam-5565	226	10	i=1	i=1	PROPN
ejpam-5565	226	11	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	226	12	f+(ti−1)∥q+	f+(ti−1)∥q+	PUNCT
ejpam-5565	226	13	)	)	PUNCT
ejpam-5565	226	14	1	1	X
ejpam-5565	226	15	/	/	SYM
ejpam-5565	226	16	q	q	X
ejpam-5565	226	17			NOUN
ejpam-5565	226	18	=	=	PUNCT
ejpam-5565	226	19	0	0	PUNCT
ejpam-5565	226	20	and	and	CCONJ
ejpam-5565	226	21	q−	q−	PROPN
ejpam-5565	226	22	vb	vb	PROPN
ejpam-5565	226	23	a(f	a(f	PROPN
ejpam-5565	226	24	,	,	PUNCT
ejpam-5565	226	25	(	(	PUNCT
ejpam-5565	226	26	k−,−	k−,−	NOUN
ejpam-5565	226	27	[	[	X
ejpam-5565	226	28	·	·	PUNCT
ejpam-5565	226	29	,	,	PUNCT
ejpam-5565	226	30	·	·	PUNCT
ejpam-5565	226	31	]	]	X
ejpam-5565	226	32	)	)	PUNCT
ejpam-5565	226	33	)	)	PUNCT
ejpam-5565	227	1	=	=	SYM
ejpam-5565	227	2	sup	sup	NOUN
ejpam-5565	227	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	227	4	,	,	PUNCT
ejpam-5565	227	5	b	b	NOUN
ejpam-5565	227	6	]	]	PUNCT
ejpam-5565	227	7			PUNCT
ejpam-5565	227	8	(	(	PUNCT
ejpam-5565	227	9	n∑	n∑	NOUN
ejpam-5565	227	10	i=1	i=1	PROPN
ejpam-5565	227	11	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	227	12	f−(ti−1)∥q−	f−(ti−1)∥q−	X
ejpam-5565	227	13	)	)	PUNCT
ejpam-5565	227	14	1	1	X
ejpam-5565	227	15	/	/	SYM
ejpam-5565	227	16	q	q	X
ejpam-5565	227	17			NOUN
ejpam-5565	227	18	=	=	NOUN
ejpam-5565	227	19	0	0	X
ejpam-5565	227	20	.	.	PUNCT
ejpam-5565	228	1	then	then	ADV
ejpam-5565	228	2	,	,	PUNCT
ejpam-5565	228	3	(	(	PUNCT
ejpam-5565	228	4	n∑	n∑	NOUN
ejpam-5565	228	5	i=1	i=1	PROPN
ejpam-5565	228	6	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	228	7	f+(ti−1)∥q+	f+(ti−1)∥q+	PUNCT
ejpam-5565	228	8	)	)	PUNCT
ejpam-5565	228	9	1	1	X
ejpam-5565	228	10	/	/	SYM
ejpam-5565	228	11	q	q	NOUN
ejpam-5565	228	12	=	=	SYM
ejpam-5565	228	13	0	0	NUM
ejpam-5565	228	14	and	and	CCONJ
ejpam-5565	228	15	(	(	PUNCT
ejpam-5565	228	16	n∑	n∑	NOUN
ejpam-5565	228	17	i=1	i=1	PROPN
ejpam-5565	228	18	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	228	19	f−(ti−1)∥q−	f−(ti−1)∥q−	X
ejpam-5565	228	20	)	)	PUNCT
ejpam-5565	228	21	1	1	X
ejpam-5565	228	22	/	/	SYM
ejpam-5565	228	23	q	q	NOUN
ejpam-5565	228	24	=	=	NOUN
ejpam-5565	228	25	0	0	X
ejpam-5565	228	26	.	.	PUNCT
ejpam-5565	229	1	let	let	VERB
ejpam-5565	229	2	x	x	PUNCT
ejpam-5565	229	3	∈	∈	PROPN
ejpam-5565	229	4	[	[	X
ejpam-5565	229	5	a	a	X
ejpam-5565	229	6	,	,	PUNCT
ejpam-5565	229	7	b	b	NOUN
ejpam-5565	229	8	]	]	X
ejpam-5565	229	9	.	.	PUNCT
ejpam-5565	230	1	then	then	ADV
ejpam-5565	230	2	,	,	PUNCT
ejpam-5565	230	3	in	in	ADP
ejpam-5565	230	4	particular	particular	ADJ
ejpam-5565	230	5	,	,	PUNCT
ejpam-5565	230	6	for	for	ADP
ejpam-5565	230	7	the	the	DET
ejpam-5565	230	8	partition	partition	NOUN
ejpam-5565	230	9	p	p	NOUN
ejpam-5565	230	10	=	=	X
ejpam-5565	230	11	{	{	PUNCT
ejpam-5565	230	12	a	a	NOUN
ejpam-5565	230	13	,	,	PUNCT
ejpam-5565	230	14	x	x	NOUN
ejpam-5565	230	15	,	,	PUNCT
ejpam-5565	230	16	b	b	PROPN
ejpam-5565	230	17	}	}	PUNCT
ejpam-5565	230	18	,	,	PUNCT
ejpam-5565	230	19	we	we	PRON
ejpam-5565	230	20	have	have	VERB
ejpam-5565	230	21	that	that	PRON
ejpam-5565	230	22	(	(	PUNCT
ejpam-5565	230	23	∥f+(x)−	∥f+(x)−	PROPN
ejpam-5565	230	24	f+(a)∥q+	f+(a)∥q+	PROPN
ejpam-5565	230	25	+	+	CCONJ
ejpam-5565	230	26	∥f+(b)−	∥f+(b)−	PROPN
ejpam-5565	230	27	f+(x)∥q+	f+(x)∥q+	PROPN
ejpam-5565	230	28	)	)	PUNCT
ejpam-5565	231	1	1	1	X
ejpam-5565	231	2	/	/	SYM
ejpam-5565	231	3	q	q	NOUN
ejpam-5565	231	4	=	=	SYM
ejpam-5565	231	5	0	0	PUNCT
ejpam-5565	232	1	and	and	CCONJ
ejpam-5565	232	2	(	(	PUNCT
ejpam-5565	232	3	∥f−(x)−	∥f−(x)−	PROPN
ejpam-5565	232	4	f−(a)∥q−	f−(a)∥q−	PROPN
ejpam-5565	232	5	+	+	CCONJ
ejpam-5565	232	6	∥f−(b)−	∥f−(b)−	PROPN
ejpam-5565	232	7	f−(x)∥q−	f−(x)∥q−	NOUN
ejpam-5565	232	8	)	)	PUNCT
ejpam-5565	232	9	1	1	X
ejpam-5565	232	10	/	/	SYM
ejpam-5565	232	11	q	q	NOUN
ejpam-5565	232	12	=	=	NOUN
ejpam-5565	232	13	0	0	NUM
ejpam-5565	232	14	.	.	PUNCT
ejpam-5565	232	15	whence	whence	NOUN
ejpam-5565	232	16	,	,	PUNCT
ejpam-5565	232	17	∥f+(x)−f+(a)∥q++∥f+(b)−f+(x)∥q+	∥f+(x)−f+(a)∥q++∥f+(b)−f+(x)∥q+	PROPN
ejpam-5565	232	18	=	=	PUNCT
ejpam-5565	232	19	0	0	PROPN
ejpam-5565	232	20	,	,	PUNCT
ejpam-5565	232	21	∥f−(x)−f−(a)∥q−+∥f−(b)−f−(x)∥q−	∥f−(x)−f−(a)∥q−+∥f−(b)−f−(x)∥q−	PUNCT
ejpam-5565	232	22	=	=	SYM
ejpam-5565	232	23	0	0	NUM
ejpam-5565	232	24	.	.	PUNCT
ejpam-5565	233	1	thus	thus	ADV
ejpam-5565	233	2	,	,	PUNCT
ejpam-5565	233	3	∥f+(x)−	∥f+(x)−	PROPN
ejpam-5565	233	4	f+(a)∥q+	f+(a)∥q+	PROPN
ejpam-5565	233	5	=	=	SYM
ejpam-5565	233	6	0	0	PROPN
ejpam-5565	233	7	,	,	PUNCT
ejpam-5565	233	8	∥f+(b)−	∥f+(b)−	PROPN
ejpam-5565	233	9	f+(x)∥q+	f+(x)∥q+	PROPN
ejpam-5565	233	10	=	=	SYM
ejpam-5565	233	11	0	0	PROPN
ejpam-5565	233	12	,	,	PUNCT
ejpam-5565	233	13	∥f−(x)−	∥f−(x)−	PROPN
ejpam-5565	233	14	f−(a)∥q−	f−(a)∥q−	PROPN
ejpam-5565	233	15	=	=	SYM
ejpam-5565	233	16	0	0	NUM
ejpam-5565	233	17	,	,	PUNCT
ejpam-5565	233	18	∥f−(b)−	∥f−(b)−	VERB
ejpam-5565	233	19	f−(x)∥q−	f−(x)∥q−	NOUN
ejpam-5565	233	20	=	=	SYM
ejpam-5565	233	21	0	0	X
ejpam-5565	233	22	.	.	PUNCT
ejpam-5565	234	1	therefore	therefore	ADV
ejpam-5565	234	2	,	,	PUNCT
ejpam-5565	234	3	(	(	PUNCT
ejpam-5565	234	4	f+(x)−f+(a	f+(x)−f+(a	PROPN
ejpam-5565	234	5	)	)	PUNCT
ejpam-5565	234	6	=	=	SYM
ejpam-5565	234	7	0	0	NUM
ejpam-5565	234	8	,	,	PUNCT
ejpam-5565	234	9	f+(b)−f+(x	f+(b)−f+(x	PROPN
ejpam-5565	234	10	)	)	PUNCT
ejpam-5565	234	11	=	=	SYM
ejpam-5565	234	12	0	0	X
ejpam-5565	234	13	)	)	PUNCT
ejpam-5565	234	14	and	and	CCONJ
ejpam-5565	234	15	(	(	PUNCT
ejpam-5565	234	16	f−(x)−f−(a	f−(x)−f−(a	NOUN
ejpam-5565	234	17	)	)	PUNCT
ejpam-5565	234	18	=	=	SYM
ejpam-5565	234	19	0	0	NUM
ejpam-5565	234	20	,	,	PUNCT
ejpam-5565	234	21	f−(b)−f−(x	f−(b)−f−(x	NOUN
ejpam-5565	234	22	)	)	PUNCT
ejpam-5565	234	23	=	=	SYM
ejpam-5565	234	24	0	0	NUM
ejpam-5565	234	25	)	)	PUNCT
ejpam-5565	234	26	.	.	PUNCT
ejpam-5565	235	1	next	next	ADV
ejpam-5565	235	2	,	,	PUNCT
ejpam-5565	235	3	(	(	PUNCT
ejpam-5565	235	4	f+(x	f+(x	X
ejpam-5565	235	5	)	)	PUNCT
ejpam-5565	235	6	=	=	SYM
ejpam-5565	235	7	f+(a	f+(a	NOUN
ejpam-5565	235	8	)	)	PUNCT
ejpam-5565	235	9	,	,	PUNCT
ejpam-5565	235	10	f+(b	f+(b	NOUN
ejpam-5565	235	11	)	)	PUNCT
ejpam-5565	235	12	=	=	SYM
ejpam-5565	235	13	f+(x	f+(x	PROPN
ejpam-5565	235	14	)	)	PUNCT
ejpam-5565	235	15	)	)	PUNCT
ejpam-5565	235	16	and	and	CCONJ
ejpam-5565	235	17	(	(	PUNCT
ejpam-5565	235	18	f−(x	f−(x	PROPN
ejpam-5565	235	19	)	)	PUNCT
ejpam-5565	235	20	=	=	SYM
ejpam-5565	235	21	f−(a	f−(a	NOUN
ejpam-5565	235	22	)	)	PUNCT
ejpam-5565	235	23	,	,	PUNCT
ejpam-5565	235	24	f−(b	f−(b	PROPN
ejpam-5565	235	25	)	)	PUNCT
ejpam-5565	235	26	=	=	SYM
ejpam-5565	235	27	f−(x	f−(x	PROPN
ejpam-5565	235	28	)	)	PUNCT
ejpam-5565	235	29	)	)	PUNCT
ejpam-5565	235	30	follows	follow	VERB
ejpam-5565	235	31	,	,	PUNCT
ejpam-5565	235	32	f+(x	f+(x	X
ejpam-5565	235	33	)	)	PUNCT
ejpam-5565	235	34	=	=	SYM
ejpam-5565	235	35	f+(a	f+(a	ADJ
ejpam-5565	235	36	)	)	PUNCT
ejpam-5565	235	37	=	=	SYM
ejpam-5565	235	38	f+(b	f+(b	PROPN
ejpam-5565	235	39	)	)	PUNCT
ejpam-5565	235	40	and	and	CCONJ
ejpam-5565	235	41	f−(x	f−(x	PROPN
ejpam-5565	235	42	)	)	PUNCT
ejpam-5565	236	1	=	=	SYM
ejpam-5565	236	2	f−(a	f−(a	NOUN
ejpam-5565	236	3	)	)	PUNCT
ejpam-5565	236	4	=	=	SYM
ejpam-5565	236	5	f−(b	f−(b	PROPN
ejpam-5565	236	6	)	)	PUNCT
ejpam-5565	236	7	.	.	PUNCT
ejpam-5565	237	1	therefore	therefore	ADV
ejpam-5565	237	2	,	,	PUNCT
ejpam-5565	237	3	f(x	f(x	PROPN
ejpam-5565	237	4	)	)	PUNCT
ejpam-5565	237	5	=	=	SYM
ejpam-5565	238	1	f+(x	f+(x	X
ejpam-5565	238	2	)	)	PUNCT
ejpam-5565	238	3	+	+	NUM
ejpam-5565	238	4	f−(x	f−(x	NOUN
ejpam-5565	238	5	)	)	PUNCT
ejpam-5565	238	6	=	=	SYM
ejpam-5565	239	1	f+(a	f+(a	NOUN
ejpam-5565	239	2	)	)	PUNCT
ejpam-5565	239	3	+	+	CCONJ
ejpam-5565	239	4	f−(a	f−(a	ADV
ejpam-5565	239	5	)	)	PUNCT
ejpam-5565	239	6	=	=	SYM
ejpam-5565	239	7	f+(b	f+(b	PROPN
ejpam-5565	239	8	)	)	PUNCT
ejpam-5565	239	9	+	+	NUM
ejpam-5565	239	10	f−(b	f−(b	NOUN
ejpam-5565	239	11	)	)	PUNCT
ejpam-5565	239	12	.	.	PUNCT
ejpam-5565	240	1	thus	thus	ADV
ejpam-5565	240	2	,	,	PUNCT
ejpam-5565	240	3	f	f	PROPN
ejpam-5565	240	4	is	be	AUX
ejpam-5565	240	5	constant	constant	ADJ
ejpam-5565	240	6	in	in	ADP
ejpam-5565	240	7	the	the	DET
ejpam-5565	240	8	interval	interval	NOUN
ejpam-5565	240	9	[	[	X
ejpam-5565	240	10	a	a	X
ejpam-5565	240	11	,	,	PUNCT
ejpam-5565	240	12	b	b	NOUN
ejpam-5565	240	13	]	]	PUNCT
ejpam-5565	240	14	.	.	PUNCT
ejpam-5565	241	1	o.	o.	PROPN
ejpam-5565	241	2	ferrer	ferrer	PROPN
ejpam-5565	241	3	,	,	PUNCT
ejpam-5565	241	4	j.	j.	PROPN
ejpam-5565	241	5	naranjo	naranjo	PROPN
ejpam-5565	241	6	/	/	SYM
ejpam-5565	241	7	eur	eur	PROPN
ejpam-5565	241	8	.	.	PUNCT
ejpam-5565	242	1	j.	j.	PROPN
ejpam-5565	242	2	pure	pure	PROPN
ejpam-5565	242	3	appl	appl	PROPN
ejpam-5565	242	4	.	.	PROPN
ejpam-5565	242	5	math	math	PROPN
ejpam-5565	242	6	,	,	PUNCT
ejpam-5565	242	7	18	18	NUM
ejpam-5565	242	8	(	(	PUNCT
ejpam-5565	242	9	2	2	NUM
ejpam-5565	242	10	)	)	PUNCT
ejpam-5565	242	11	(	(	PUNCT
ejpam-5565	242	12	2025	2025	NUM
ejpam-5565	242	13	)	)	PUNCT
ejpam-5565	242	14	,	,	PUNCT
ejpam-5565	242	15	5565	5565	NUM
ejpam-5565	242	16	12	12	NUM
ejpam-5565	242	17	of	of	ADP
ejpam-5565	242	18	18	18	NUM
ejpam-5565	242	19	(	(	PUNCT
ejpam-5565	242	20	←	←	PROPN
ejpam-5565	242	21	)	)	PUNCT
ejpam-5565	242	22	suppose	suppose	VERB
ejpam-5565	242	23	that	that	SCONJ
ejpam-5565	242	24	f	f	PROPN
ejpam-5565	242	25	is	be	AUX
ejpam-5565	242	26	constant	constant	ADJ
ejpam-5565	242	27	in	in	ADP
ejpam-5565	242	28	[	[	X
ejpam-5565	242	29	a	a	DET
ejpam-5565	242	30	,	,	PUNCT
ejpam-5565	242	31	b	b	NOUN
ejpam-5565	242	32	]	]	X
ejpam-5565	242	33	,	,	PUNCT
ejpam-5565	242	34	then	then	ADV
ejpam-5565	242	35	exists	exist	VERB
ejpam-5565	242	36	c	c	PROPN
ejpam-5565	242	37	∈	∈	PROPN
ejpam-5565	242	38	k	k	ADJ
ejpam-5565	242	39	such	such	ADJ
ejpam-5565	242	40	that	that	PRON
ejpam-5565	242	41	for	for	ADP
ejpam-5565	242	42	any	any	DET
ejpam-5565	242	43	x	x	SYM
ejpam-5565	242	44	∈	∈	PROPN
ejpam-5565	242	45	[	[	X
ejpam-5565	242	46	a	a	X
ejpam-5565	242	47	,	,	PUNCT
ejpam-5565	242	48	b	b	NOUN
ejpam-5565	242	49	]	]	X
ejpam-5565	242	50	,	,	PUNCT
ejpam-5565	242	51	f(x	f(x	PROPN
ejpam-5565	242	52	)	)	PUNCT
ejpam-5565	243	1	=	=	SYM
ejpam-5565	243	2	c.	c.	NOUN
ejpam-5565	243	3	since	since	SCONJ
ejpam-5565	243	4	c	c	PROPN
ejpam-5565	243	5	∈	∈	PROPN
ejpam-5565	243	6	k	k	NOUN
ejpam-5565	243	7	=	=	PUNCT
ejpam-5565	243	8	k+	k+	NOUN
ejpam-5565	243	9	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	243	10	,	,	PUNCT
ejpam-5565	243	11	there	there	PRON
ejpam-5565	243	12	are	be	VERB
ejpam-5565	243	13	c+	c+	NOUN
ejpam-5565	243	14	∈	∈	NOUN
ejpam-5565	243	15	k+	k+	NOUN
ejpam-5565	243	16	and	and	CCONJ
ejpam-5565	243	17	c−	c−	NOUN
ejpam-5565	243	18	∈	∈	PROPN
ejpam-5565	243	19	k−	k−	PROPN
ejpam-5565	243	20	such	such	ADJ
ejpam-5565	243	21	that	that	SCONJ
ejpam-5565	243	22	c	c	NOUN
ejpam-5565	243	23	=	=	PRON
ejpam-5565	243	24	c+	c+	VERB
ejpam-5565	243	25	+	+	CCONJ
ejpam-5565	243	26	c−.	c−.	VERB
ejpam-5565	243	27	furthermore	furthermore	ADV
ejpam-5565	243	28	,	,	PUNCT
ejpam-5565	243	29	as	as	ADP
ejpam-5565	243	30	f(x	f(x	PROPN
ejpam-5565	243	31	)	)	PUNCT
ejpam-5565	243	32	=	=	SYM
ejpam-5565	243	33	f+(x	f+(x	X
ejpam-5565	243	34	)	)	PUNCT
ejpam-5565	243	35	+	+	NUM
ejpam-5565	243	36	f−(x	f−(x	PROPN
ejpam-5565	243	37	)	)	PUNCT
ejpam-5565	243	38	,	,	PUNCT
ejpam-5565	243	39	it	it	PRON
ejpam-5565	243	40	follows	follow	VERB
ejpam-5565	243	41	that	that	SCONJ
ejpam-5565	243	42	:	:	PUNCT
ejpam-5565	243	43	f+(x	f+(x	X
ejpam-5565	243	44	)	)	PUNCT
ejpam-5565	243	45	+	+	NUM
ejpam-5565	243	46	f−(x	f−(x	NOUN
ejpam-5565	243	47	)	)	PUNCT
ejpam-5565	243	48	=	=	SYM
ejpam-5565	244	1	c+	c+	X
ejpam-5565	244	2	+	+	CCONJ
ejpam-5565	244	3	c−	c−	ADJ
ejpam-5565	244	4	,	,	PUNCT
ejpam-5565	244	5	whence	whence	ADP
ejpam-5565	244	6	f+(x)−	f+(x)−	PROPN
ejpam-5565	244	7	c+	c+	NOUN
ejpam-5565	244	8	=	=	SYM
ejpam-5565	244	9	c−	c−	PROPN
ejpam-5565	244	10	−	−	PROPN
ejpam-5565	244	11	f−(x	f−(x	PROPN
ejpam-5565	244	12	)	)	PUNCT
ejpam-5565	244	13	∈	∈	PROPN
ejpam-5565	244	14	k+	k+	NOUN
ejpam-5565	244	15	∩	∩	ADJ
ejpam-5565	244	16	k−	k−	PROPN
ejpam-5565	244	17	=	=	SYM
ejpam-5565	244	18	{	{	PUNCT
ejpam-5565	244	19	0	0	NUM
ejpam-5565	244	20	}	}	PUNCT
ejpam-5565	244	21	thus	thus	ADV
ejpam-5565	244	22	,	,	PUNCT
ejpam-5565	244	23	f+(x)−	f+(x)−	PROPN
ejpam-5565	244	24	c+	c+	VERB
ejpam-5565	244	25	=	=	SYM
ejpam-5565	244	26	0	0	NUM
ejpam-5565	244	27	and	and	CCONJ
ejpam-5565	244	28	c−	c−	NOUN
ejpam-5565	244	29	−	−	PROPN
ejpam-5565	244	30	f−(x	f−(x	PROPN
ejpam-5565	244	31	)	)	PUNCT
ejpam-5565	245	1	=	=	SYM
ejpam-5565	245	2	0	0	NUM
ejpam-5565	245	3	,	,	PUNCT
ejpam-5565	245	4	therefore	therefore	ADV
ejpam-5565	245	5	,	,	PUNCT
ejpam-5565	245	6	f+(x	f+(x	X
ejpam-5565	245	7	)	)	PUNCT
ejpam-5565	245	8	=	=	SYM
ejpam-5565	245	9	c+	c+	NOUN
ejpam-5565	245	10	and	and	CCONJ
ejpam-5565	245	11	c−	c−	ADJ
ejpam-5565	245	12	=	=	SYM
ejpam-5565	245	13	f−(x	f−(x	PROPN
ejpam-5565	245	14	)	)	PUNCT
ejpam-5565	245	15	,	,	PUNCT
ejpam-5565	245	16	thus	thus	ADV
ejpam-5565	245	17	,	,	PUNCT
ejpam-5565	245	18	q+	q+	ADV
ejpam-5565	245	19	vb	vb	ADP
ejpam-5565	245	20	a(f	a(f	PROPN
ejpam-5565	245	21	,	,	PUNCT
ejpam-5565	245	22	(	(	PUNCT
ejpam-5565	245	23	k+	k+	X
ejpam-5565	245	24	,	,	PUNCT
ejpam-5565	245	25	[	[	X
ejpam-5565	245	26	·	·	PUNCT
ejpam-5565	245	27	,	,	PUNCT
ejpam-5565	245	28	·	·	PUNCT
ejpam-5565	245	29	]	]	X
ejpam-5565	245	30	)	)	PUNCT
ejpam-5565	245	31	)	)	PUNCT
ejpam-5565	246	1	=	=	SYM
ejpam-5565	246	2	sup	sup	NOUN
ejpam-5565	246	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	246	4	,	,	PUNCT
ejpam-5565	246	5	b	b	NOUN
ejpam-5565	246	6	]	]	PUNCT
ejpam-5565	246	7			PUNCT
ejpam-5565	246	8	(	(	PUNCT
ejpam-5565	246	9	n∑	n∑	NOUN
ejpam-5565	246	10	i=1	i=1	PROPN
ejpam-5565	246	11	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	246	12	f+(ti−1)∥q+	f+(ti−1)∥q+	PUNCT
ejpam-5565	246	13	)	)	PUNCT
ejpam-5565	246	14	1	1	X
ejpam-5565	246	15	/	/	SYM
ejpam-5565	246	16	q	q	X
ejpam-5565	246	17			NOUN
ejpam-5565	246	18	=	=	NOUN
ejpam-5565	246	19	sup	sup	NOUN
ejpam-5565	246	20	p∈p[a	p∈p[a	NOUN
ejpam-5565	246	21	,	,	PUNCT
ejpam-5565	246	22	b	b	NOUN
ejpam-5565	246	23	]	]	PUNCT
ejpam-5565	246	24			PUNCT
ejpam-5565	246	25	(	(	PUNCT
ejpam-5565	246	26	n∑	n∑	INTJ
ejpam-5565	246	27	i=1	i=1	PROPN
ejpam-5565	247	1	∥c+	∥c+	PROPN
ejpam-5565	247	2	−	−	PROPN
ejpam-5565	247	3	c+∥q−	c+∥q−	X
ejpam-5565	247	4	)	)	PUNCT
ejpam-5565	247	5	1	1	NUM
ejpam-5565	247	6	/	/	SYM
ejpam-5565	247	7	q	q	NOUN
ejpam-5565	247	8			NOUN
ejpam-5565	247	9	=	=	SYM
ejpam-5565	247	10	sup{0	sup{0	NOUN
ejpam-5565	247	11	}	}	PUNCT
ejpam-5565	247	12	=	=	SYM
ejpam-5565	247	13	0	0	NUM
ejpam-5565	248	1	and	and	CCONJ
ejpam-5565	248	2	q−	q−	PROPN
ejpam-5565	248	3	vb	vb	PROPN
ejpam-5565	248	4	a(f	a(f	PROPN
ejpam-5565	248	5	,	,	PUNCT
ejpam-5565	248	6	(	(	PUNCT
ejpam-5565	248	7	k−,−	k−,−	NOUN
ejpam-5565	248	8	[	[	X
ejpam-5565	248	9	·	·	PUNCT
ejpam-5565	248	10	,	,	PUNCT
ejpam-5565	248	11	·	·	PUNCT
ejpam-5565	248	12	]	]	X
ejpam-5565	248	13	)	)	PUNCT
ejpam-5565	248	14	)	)	PUNCT
ejpam-5565	249	1	=	=	SYM
ejpam-5565	249	2	sup	sup	NOUN
ejpam-5565	249	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	249	4	,	,	PUNCT
ejpam-5565	249	5	b	b	NOUN
ejpam-5565	249	6	]	]	PUNCT
ejpam-5565	249	7			PUNCT
ejpam-5565	249	8	(	(	PUNCT
ejpam-5565	249	9	n∑	n∑	NOUN
ejpam-5565	249	10	i=1	i=1	PROPN
ejpam-5565	249	11	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	249	12	f−(ti−1)∥q−	f−(ti−1)∥q−	X
ejpam-5565	249	13	)	)	PUNCT
ejpam-5565	249	14	1	1	X
ejpam-5565	249	15	/	/	SYM
ejpam-5565	249	16	q	q	X
ejpam-5565	249	17			NOUN
ejpam-5565	249	18	=	=	NOUN
ejpam-5565	249	19	sup	sup	NOUN
ejpam-5565	249	20	p∈p[a	p∈p[a	NOUN
ejpam-5565	249	21	,	,	PUNCT
ejpam-5565	249	22	b	b	NOUN
ejpam-5565	249	23	]	]	PUNCT
ejpam-5565	249	24			PUNCT
ejpam-5565	249	25	(	(	PUNCT
ejpam-5565	249	26	n∑	n∑	NOUN
ejpam-5565	249	27	i=1	i=1	PROPN
ejpam-5565	249	28	∥c−	∥c−	PRON
ejpam-5565	249	29	−	−	PROPN
ejpam-5565	249	30	c−∥q−	c−∥q−	PROPN
ejpam-5565	249	31	)	)	PUNCT
ejpam-5565	249	32	1	1	X
ejpam-5565	249	33	/	/	SYM
ejpam-5565	249	34	q	q	NOUN
ejpam-5565	249	35			NOUN
ejpam-5565	249	36	=	=	SYM
ejpam-5565	249	37	sup{0	sup{0	NOUN
ejpam-5565	249	38	}	}	PUNCT
ejpam-5565	249	39	=	=	SYM
ejpam-5565	249	40	0	0	NUM
ejpam-5565	249	41	5.1	5.1	NUM
ejpam-5565	249	42	.	.	PUNCT
ejpam-5565	250	1	algebra	algebra	NOUN
ejpam-5565	250	2	of	of	ADP
ejpam-5565	250	3	bounded	bounded	ADJ
ejpam-5565	250	4	q	q	ADJ
ejpam-5565	250	5	-	-	PUNCT
ejpam-5565	250	6	variation	variation	NOUN
ejpam-5565	250	7	functions	function	NOUN
ejpam-5565	250	8	in	in	ADP
ejpam-5565	250	9	krein	krein	ADJ
ejpam-5565	250	10	spaces	space	NOUN
ejpam-5565	250	11	theorem	theorem	VERB
ejpam-5565	250	12	11	11	NUM
ejpam-5565	250	13	.	.	PUNCT
ejpam-5565	251	1	let	let	VERB
ejpam-5565	251	2	(	(	PUNCT
ejpam-5565	251	3	k	k	NOUN
ejpam-5565	251	4	=	=	SYM
ejpam-5565	251	5	k+	k+	NOUN
ejpam-5565	251	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	251	7	,	,	PUNCT
ejpam-5565	251	8	[	[	X
ejpam-5565	251	9	·	·	PUNCT
ejpam-5565	251	10	,	,	PUNCT
ejpam-5565	251	11	·	·	PUNCT
ejpam-5565	251	12	]	]	PUNCT
ejpam-5565	251	13	)	)	PUNCT
ejpam-5565	251	14	be	be	AUX
ejpam-5565	251	15	a	a	DET
ejpam-5565	251	16	krein	krein	ADJ
ejpam-5565	251	17	space	space	NOUN
ejpam-5565	251	18	,	,	PUNCT
ejpam-5565	251	19	if	if	SCONJ
ejpam-5565	251	20	f	f	X
ejpam-5565	251	21	,	,	PUNCT
ejpam-5565	251	22	g	g	NOUN
ejpam-5565	251	23	:	:	PUNCT
ejpam-5565	251	24	[	[	X
ejpam-5565	251	25	a	a	X
ejpam-5565	251	26	,	,	PUNCT
ejpam-5565	251	27	b]→	b]→	PROPN
ejpam-5565	251	28	k	k	PROPN
ejpam-5565	251	29	be	be	AUX
ejpam-5565	251	30	of	of	ADP
ejpam-5565	251	31	bounded	bounded	ADJ
ejpam-5565	251	32	q	q	ADJ
ejpam-5565	251	33	-	-	PUNCT
ejpam-5565	251	34	variation	variation	NOUN
ejpam-5565	251	35	functions	function	NOUN
ejpam-5565	251	36	in	in	ADP
ejpam-5565	251	37	[	[	X
ejpam-5565	251	38	a	a	DET
ejpam-5565	251	39	,	,	PUNCT
ejpam-5565	251	40	b	b	NOUN
ejpam-5565	251	41	]	]	X
ejpam-5565	251	42	on	on	ADP
ejpam-5565	251	43	(	(	PUNCT
ejpam-5565	251	44	k	k	NOUN
ejpam-5565	251	45	=	=	SYM
ejpam-5565	251	46	k+	k+	NOUN
ejpam-5565	251	47	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	251	48	)	)	PUNCT
ejpam-5565	251	49	and	and	CCONJ
ejpam-5565	251	50	α	α	PRON
ejpam-5565	251	51	a	a	DET
ejpam-5565	251	52	scalar	scalar	ADJ
ejpam-5565	251	53	,	,	PUNCT
ejpam-5565	251	54	then	then	ADV
ejpam-5565	251	55	αf	αf	VERB
ejpam-5565	251	56	and	and	CCONJ
ejpam-5565	251	57	f	f	PROPN
ejpam-5565	252	1	+	+	CCONJ
ejpam-5565	252	2	g	g	NOUN
ejpam-5565	252	3	are	be	AUX
ejpam-5565	252	4	also	also	ADV
ejpam-5565	252	5	of	of	ADP
ejpam-5565	252	6	bounded	bounded	ADJ
ejpam-5565	252	7	q	q	ADJ
ejpam-5565	252	8	-	-	PUNCT
ejpam-5565	252	9	variation	variation	NOUN
ejpam-5565	252	10	functions	function	NOUN
ejpam-5565	252	11	in	in	ADP
ejpam-5565	252	12	[	[	X
ejpam-5565	252	13	a	a	DET
ejpam-5565	252	14	,	,	PUNCT
ejpam-5565	252	15	b	b	NOUN
ejpam-5565	252	16	]	]	X
ejpam-5565	252	17	on	on	ADP
ejpam-5565	252	18	(	(	PUNCT
ejpam-5565	252	19	k	k	NOUN
ejpam-5565	252	20	=	=	SYM
ejpam-5565	252	21	k+	k+	NOUN
ejpam-5565	252	22	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	252	23	)	)	PUNCT
ejpam-5565	252	24	.	.	PUNCT
ejpam-5565	253	1	proof	proof	NOUN
ejpam-5565	253	2	.	.	PUNCT
ejpam-5565	254	1	if	if	SCONJ
ejpam-5565	254	2	f	f	PROPN
ejpam-5565	254	3	and	and	CCONJ
ejpam-5565	254	4	g	g	PROPN
ejpam-5565	254	5	are	be	AUX
ejpam-5565	254	6	functions	function	NOUN
ejpam-5565	254	7	of	of	ADP
ejpam-5565	254	8	bounded	bounded	ADJ
ejpam-5565	254	9	q	q	NOUN
ejpam-5565	254	10	-	-	NOUN
ejpam-5565	254	11	variation	variation	NOUN
ejpam-5565	254	12	in	in	ADP
ejpam-5565	254	13	[	[	X
ejpam-5565	254	14	a	a	DET
ejpam-5565	254	15	,	,	PUNCT
ejpam-5565	254	16	b	b	NOUN
ejpam-5565	254	17	]	]	X
ejpam-5565	254	18	on	on	ADP
ejpam-5565	254	19	(	(	PUNCT
ejpam-5565	254	20	k	k	NOUN
ejpam-5565	254	21	=	=	SYM
ejpam-5565	254	22	k+	k+	NOUN
ejpam-5565	254	23	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	254	24	,	,	PUNCT
ejpam-5565	254	25	[	[	X
ejpam-5565	254	26	·	·	PUNCT
ejpam-5565	254	27	,	,	PUNCT
ejpam-5565	254	28	·	·	PUNCT
ejpam-5565	254	29	]	]	X
ejpam-5565	254	30	)	)	PUNCT
ejpam-5565	254	31	,	,	PUNCT
ejpam-5565	254	32	then	then	ADV
ejpam-5565	254	33	exists	exist	VERB
ejpam-5565	254	34	l	l	NOUN
ejpam-5565	254	35	,	,	PUNCT
ejpam-5565	254	36	m	m	VERB
ejpam-5565	254	37	>	>	X
ejpam-5565	254	38	0	0	NUM
ejpam-5565	255	1	such	such	ADJ
ejpam-5565	255	2	that	that	SCONJ
ejpam-5565	255	3	q	q	PROPN
ejpam-5565	255	4	vb	vb	PROPN
ejpam-5565	255	5	a(f	a(f	PROPN
ejpam-5565	255	6	,	,	PUNCT
ejpam-5565	255	7	(	(	PUNCT
ejpam-5565	255	8	k	k	X
ejpam-5565	255	9	,	,	PUNCT
ejpam-5565	255	10	[	[	X
ejpam-5565	255	11	·	·	PUNCT
ejpam-5565	255	12	,	,	PUNCT
ejpam-5565	255	13	·	·	PUNCT
ejpam-5565	255	14	]	]	X
ejpam-5565	255	15	)	)	PUNCT
ejpam-5565	255	16	)	)	PUNCT
ejpam-5565	255	17	≤	≤	NUM
ejpam-5565	255	18	l	l	NOUN
ejpam-5565	255	19	and	and	CCONJ
ejpam-5565	255	20	q	q	ADJ
ejpam-5565	255	21	vb	vb	PROPN
ejpam-5565	255	22	a(g	a(g	PROPN
ejpam-5565	255	23	,	,	PUNCT
ejpam-5565	255	24	(	(	PUNCT
ejpam-5565	255	25	k	k	X
ejpam-5565	255	26	,	,	PUNCT
ejpam-5565	255	27	[	[	X
ejpam-5565	255	28	·	·	PUNCT
ejpam-5565	255	29	,	,	PUNCT
ejpam-5565	255	30	·	·	PUNCT
ejpam-5565	255	31	]	]	X
ejpam-5565	255	32	)	)	PUNCT
ejpam-5565	255	33	)	)	PUNCT
ejpam-5565	255	34	≤m	≤m	NOUN
ejpam-5565	255	35	(	(	PUNCT
ejpam-5565	255	36	i	i	NOUN
ejpam-5565	255	37	)	)	PUNCT
ejpam-5565	255	38	if	if	SCONJ
ejpam-5565	255	39	α	α	PRON
ejpam-5565	255	40	is	be	AUX
ejpam-5565	255	41	a	a	DET
ejpam-5565	255	42	scalar	scalar	ADJ
ejpam-5565	255	43	,	,	PUNCT
ejpam-5565	255	44	considering	consider	VERB
ejpam-5565	255	45	part	part	NOUN
ejpam-5565	255	46	two	two	NUM
ejpam-5565	255	47	(	(	PUNCT
ejpam-5565	255	48	i	i	NOUN
ejpam-5565	255	49	)	)	PUNCT
ejpam-5565	255	50	and	and	CCONJ
ejpam-5565	255	51	(	(	PUNCT
ejpam-5565	255	52	iii	iii	NOUN
ejpam-5565	255	53	)	)	PUNCT
ejpam-5565	255	54	of	of	ADP
ejpam-5565	255	55	the	the	DET
ejpam-5565	255	56	remark	remark	NOUN
ejpam-5565	255	57	4	4	NUM
ejpam-5565	255	58	,	,	PUNCT
ejpam-5565	255	59	for	for	ADP
ejpam-5565	255	60	all	all	DET
ejpam-5565	255	61	partition	partition	NOUN
ejpam-5565	255	62	p	p	X
ejpam-5565	255	63	∈	∈	PROPN
ejpam-5565	255	64	p[a	p[a	PROPN
ejpam-5565	255	65	,	,	PUNCT
ejpam-5565	255	66	b	b	NOUN
ejpam-5565	255	67	]	]	X
ejpam-5565	255	68	,	,	PUNCT
ejpam-5565	255	69	it	it	PRON
ejpam-5565	255	70	follows	follow	VERB
ejpam-5565	255	71	that	that	PRON
ejpam-5565	255	72	:	:	PUNCT
ejpam-5565	255	73	o.	o.	PROPN
ejpam-5565	255	74	ferrer	ferrer	PROPN
ejpam-5565	255	75	,	,	PUNCT
ejpam-5565	255	76	j.	j.	PROPN
ejpam-5565	255	77	naranjo	naranjo	PROPN
ejpam-5565	255	78	/	/	SYM
ejpam-5565	255	79	eur	eur	PROPN
ejpam-5565	255	80	.	.	PUNCT
ejpam-5565	256	1	j.	j.	PROPN
ejpam-5565	256	2	pure	pure	PROPN
ejpam-5565	256	3	appl	appl	PROPN
ejpam-5565	256	4	.	.	PROPN
ejpam-5565	256	5	math	math	PROPN
ejpam-5565	256	6	,	,	PUNCT
ejpam-5565	256	7	18	18	NUM
ejpam-5565	256	8	(	(	PUNCT
ejpam-5565	256	9	2	2	NUM
ejpam-5565	256	10	)	)	PUNCT
ejpam-5565	256	11	(	(	PUNCT
ejpam-5565	256	12	2025	2025	NUM
ejpam-5565	256	13	)	)	PUNCT
ejpam-5565	256	14	,	,	PUNCT
ejpam-5565	256	15	5565	5565	NUM
ejpam-5565	256	16	13	13	NUM
ejpam-5565	256	17	of	of	ADP
ejpam-5565	256	18	18	18	NUM
ejpam-5565	256	19	q	q	NOUN
ejpam-5565	256	20	vb	vb	NOUN
ejpam-5565	256	21	a(αf	a(αf	NOUN
ejpam-5565	256	22	,	,	PUNCT
ejpam-5565	256	23	(	(	PUNCT
ejpam-5565	256	24	k	k	X
ejpam-5565	256	25	,	,	PUNCT
ejpam-5565	256	26	[	[	X
ejpam-5565	256	27	·	·	PUNCT
ejpam-5565	256	28	,	,	PUNCT
ejpam-5565	256	29	·	·	PUNCT
ejpam-5565	256	30	]	]	X
ejpam-5565	256	31	)	)	PUNCT
ejpam-5565	256	32	)	)	PUNCT
ejpam-5565	257	1	=	=	SYM
ejpam-5565	257	2	sup	sup	NOUN
ejpam-5565	257	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	257	4	,	,	PUNCT
ejpam-5565	257	5	b	b	NOUN
ejpam-5565	257	6	]	]	X
ejpam-5565	257	7	{	{	PUNCT
ejpam-5565	257	8	(	(	PUNCT
ejpam-5565	257	9	n∑	n∑	NOUN
ejpam-5565	257	10	i=1	i=1	PROPN
ejpam-5565	257	11	(	(	PUNCT
ejpam-5565	257	12	∥αf+(ti)−	∥αf+(ti)−	NOUN
ejpam-5565	257	13	αf+(ti−1)∥+	αf+(ti−1)∥+	NOUN
ejpam-5565	257	14	+	+	CCONJ
ejpam-5565	257	15	∥αf−(ti)−	∥αf−(ti)−	NOUN
ejpam-5565	257	16	αf−(ti−1)∥−	αf−(ti−1)∥−	NUM
ejpam-5565	257	17	)	)	PUNCT
ejpam-5565	257	18	q	q	X
ejpam-5565	257	19	)	)	PUNCT
ejpam-5565	257	20	1	1	NUM
ejpam-5565	257	21	/	/	SYM
ejpam-5565	257	22	q	q	NOUN
ejpam-5565	257	23	}	}	PUNCT
ejpam-5565	257	24	=	=	SYM
ejpam-5565	257	25	sup	sup	NOUN
ejpam-5565	257	26	p∈p[a	p∈p[a	NOUN
ejpam-5565	257	27	,	,	PUNCT
ejpam-5565	257	28	b	b	NOUN
ejpam-5565	257	29	]	]	X
ejpam-5565	257	30	{	{	PUNCT
ejpam-5565	257	31	(	(	PUNCT
ejpam-5565	257	32	n∑	n∑	NOUN
ejpam-5565	257	33	i=1	i=1	PROPN
ejpam-5565	258	1	(	(	PUNCT
ejpam-5565	258	2	∥α	∥α	NOUN
ejpam-5565	258	3	(	(	PUNCT
ejpam-5565	258	4	f+(ti)−	f+(ti)−	NOUN
ejpam-5565	258	5	f+(ti−1))∥+	f+(ti−1))∥+	ADV
ejpam-5565	258	6	+	+	CCONJ
ejpam-5565	258	7	∥α(f−(ti)−	∥α(f−(ti)−	PROPN
ejpam-5565	258	8	f−(ti−1	f−(ti−1	PROPN
ejpam-5565	258	9	)	)	PUNCT
ejpam-5565	258	10	)	)	PUNCT
ejpam-5565	258	11	∥−	∥−	NOUN
ejpam-5565	258	12	)	)	PUNCT
ejpam-5565	258	13	q)1	q)1	PROPN
ejpam-5565	258	14	/	/	SYM
ejpam-5565	258	15	q	q	NOUN
ejpam-5565	258	16	}	}	PUNCT
ejpam-5565	258	17	=	=	SYM
ejpam-5565	258	18	sup	sup	NOUN
ejpam-5565	258	19	p∈p[a	p∈p[a	NOUN
ejpam-5565	258	20	,	,	PUNCT
ejpam-5565	258	21	b	b	NOUN
ejpam-5565	258	22	]	]	X
ejpam-5565	258	23	{	{	PUNCT
ejpam-5565	258	24	(	(	PUNCT
ejpam-5565	258	25	n∑	n∑	NOUN
ejpam-5565	258	26	i=1	i=1	PROPN
ejpam-5565	258	27	(	(	PUNCT
ejpam-5565	258	28	|α|∥f+(ti)−	|α|∥f+(ti)−	NOUN
ejpam-5565	258	29	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	258	30	+	+	CCONJ
ejpam-5565	258	31	|α|∥f−(ti)−	|α|∥f−(ti)−	NOUN
ejpam-5565	258	32	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	258	33	)	)	PUNCT
ejpam-5565	258	34	q)1	q)1	PROPN
ejpam-5565	258	35	/	/	SYM
ejpam-5565	258	36	q	q	NOUN
ejpam-5565	258	37	}	}	PUNCT
ejpam-5565	258	38	=	=	SYM
ejpam-5565	258	39	sup	sup	NOUN
ejpam-5565	258	40	p∈p[a	p∈p[a	NOUN
ejpam-5565	258	41	,	,	PUNCT
ejpam-5565	258	42	b	b	NOUN
ejpam-5565	258	43	]	]	X
ejpam-5565	258	44	{	{	PUNCT
ejpam-5565	258	45	(	(	PUNCT
ejpam-5565	258	46	|α|q	|α|q	PROPN
ejpam-5565	258	47	n∑	n∑	NOUN
ejpam-5565	258	48	i=1	i=1	PROPN
ejpam-5565	258	49	(	(	PUNCT
ejpam-5565	258	50	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	258	51	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	258	52	+	+	CCONJ
ejpam-5565	258	53	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	258	54	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	258	55	)	)	PUNCT
ejpam-5565	258	56	q)1	q)1	PROPN
ejpam-5565	258	57	/	/	SYM
ejpam-5565	258	58	q	q	NOUN
ejpam-5565	258	59	}	}	PUNCT
ejpam-5565	258	60	=	=	PUNCT
ejpam-5565	258	61	|α|	|α|	NUM
ejpam-5565	258	62	sup	sup	NOUN
ejpam-5565	258	63	p∈p[a	p∈p[a	NOUN
ejpam-5565	258	64	,	,	PUNCT
ejpam-5565	258	65	b	b	NOUN
ejpam-5565	258	66	]	]	X
ejpam-5565	258	67	{	{	PUNCT
ejpam-5565	258	68	(	(	PUNCT
ejpam-5565	258	69	n∑	n∑	NOUN
ejpam-5565	258	70	i=1	i=1	PROPN
ejpam-5565	258	71	(	(	PUNCT
ejpam-5565	258	72	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	258	73	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	258	74	+	+	CCONJ
ejpam-5565	258	75	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	258	76	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	258	77	)	)	PUNCT
ejpam-5565	258	78	q)1	q)1	PROPN
ejpam-5565	258	79	/	/	SYM
ejpam-5565	258	80	q	q	NOUN
ejpam-5565	258	81	}	}	PUNCT
ejpam-5565	258	82	=	=	PUNCT
ejpam-5565	258	83	|α|	|α|	PART
ejpam-5565	258	84	q	q	X
ejpam-5565	258	85	vb	vb	PROPN
ejpam-5565	258	86	a(f	a(f	PROPN
ejpam-5565	258	87	,	,	PUNCT
ejpam-5565	258	88	(	(	PUNCT
ejpam-5565	258	89	k	k	X
ejpam-5565	258	90	,	,	PUNCT
ejpam-5565	258	91	[	[	X
ejpam-5565	258	92	·	·	PUNCT
ejpam-5565	258	93	,	,	PUNCT
ejpam-5565	258	94	·	·	PUNCT
ejpam-5565	258	95	]	]	X
ejpam-5565	258	96	)	)	PUNCT
ejpam-5565	258	97	)	)	PUNCT
ejpam-5565	258	98	≤	≤	NUM
ejpam-5565	258	99	|α|l	|α|l	PROPN
ejpam-5565	258	100	.	.	PUNCT
ejpam-5565	259	1	therefore	therefore	ADV
ejpam-5565	259	2	,	,	PUNCT
ejpam-5565	259	3	q	q	NOUN
ejpam-5565	259	4	vb	vb	NOUN
ejpam-5565	259	5	a(αf	a(αf	NOUN
ejpam-5565	259	6	,	,	PUNCT
ejpam-5565	259	7	(	(	PUNCT
ejpam-5565	259	8	k	k	X
ejpam-5565	259	9	,	,	PUNCT
ejpam-5565	259	10	[	[	X
ejpam-5565	259	11	·	·	PUNCT
ejpam-5565	259	12	,	,	PUNCT
ejpam-5565	259	13	·	·	PUNCT
ejpam-5565	259	14	]	]	X
ejpam-5565	259	15	)	)	PUNCT
ejpam-5565	259	16	)	)	PUNCT
ejpam-5565	259	17	is	be	AUX
ejpam-5565	259	18	finite	finite	PROPN
ejpam-5565	259	19	,	,	PUNCT
ejpam-5565	259	20	which	which	PRON
ejpam-5565	259	21	implies	imply	VERB
ejpam-5565	259	22	that	that	SCONJ
ejpam-5565	259	23	αf	αf	NOUN
ejpam-5565	259	24	is	be	AUX
ejpam-5565	259	25	of	of	ADP
ejpam-5565	259	26	bounded	bounded	ADJ
ejpam-5565	259	27	q	q	NOUN
ejpam-5565	259	28	-	-	NOUN
ejpam-5565	259	29	variation	variation	NOUN
ejpam-5565	259	30	in	in	ADP
ejpam-5565	259	31	[	[	X
ejpam-5565	259	32	a	a	DET
ejpam-5565	259	33	,	,	PUNCT
ejpam-5565	259	34	b	b	NOUN
ejpam-5565	259	35	]	]	X
ejpam-5565	259	36	on	on	ADP
ejpam-5565	259	37	(	(	PUNCT
ejpam-5565	259	38	k	k	NOUN
ejpam-5565	259	39	=	=	SYM
ejpam-5565	259	40	k+	k+	NOUN
ejpam-5565	259	41	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	259	42	,	,	PUNCT
ejpam-5565	259	43	[	[	X
ejpam-5565	259	44	·	·	PUNCT
ejpam-5565	259	45	,	,	PUNCT
ejpam-5565	259	46	·	·	PUNCT
ejpam-5565	259	47	]	]	X
ejpam-5565	259	48	)	)	PUNCT
ejpam-5565	259	49	.	.	PUNCT
ejpam-5565	260	1	(	(	PUNCT
ejpam-5565	260	2	ii	ii	NOUN
ejpam-5565	260	3	)	)	PUNCT
ejpam-5565	260	4	using	use	VERB
ejpam-5565	260	5	(	(	PUNCT
ejpam-5565	260	6	ii	ii	NOUN
ejpam-5565	260	7	)	)	PUNCT
ejpam-5565	260	8	and	and	CCONJ
ejpam-5565	260	9	(	(	PUNCT
ejpam-5565	260	10	iv	iv	X
ejpam-5565	260	11	)	)	PUNCT
ejpam-5565	260	12	in	in	ADP
ejpam-5565	260	13	part	part	NOUN
ejpam-5565	260	14	two	two	NUM
ejpam-5565	260	15	of	of	ADP
ejpam-5565	260	16	remark	remark	NOUN
ejpam-5565	260	17	4	4	NUM
ejpam-5565	260	18	it	it	PRON
ejpam-5565	260	19	follows	follow	VERB
ejpam-5565	260	20	that	that	SCONJ
ejpam-5565	260	21	for	for	ADP
ejpam-5565	260	22	any	any	DET
ejpam-5565	260	23	partition	partition	NOUN
ejpam-5565	260	24	p	p	X
ejpam-5565	260	25	∈	∈	PROPN
ejpam-5565	260	26	p[a	p[a	PROPN
ejpam-5565	260	27	,	,	PUNCT
ejpam-5565	260	28	b	b	NOUN
ejpam-5565	260	29	]	]	X
ejpam-5565	260	30	,	,	PUNCT
ejpam-5565	260	31	it	it	PRON
ejpam-5565	260	32	is	be	AUX
ejpam-5565	260	33	satisfied	satisfied	ADJ
ejpam-5565	260	34	that	that	SCONJ
ejpam-5565	260	35	:	:	PUNCT
ejpam-5565	260	36	(	(	PUNCT
ejpam-5565	260	37	n∑	n∑	INTJ
ejpam-5565	260	38	i=1	i=1	PROPN
ejpam-5565	260	39	(	(	PUNCT
ejpam-5565	260	40	∥(f	∥(f	NOUN
ejpam-5565	260	41	+	+	CCONJ
ejpam-5565	260	42	g)+(ti)−	g)+(ti)−	NOUN
ejpam-5565	260	43	(	(	PUNCT
ejpam-5565	260	44	f	f	X
ejpam-5565	260	45	+	+	PUNCT
ejpam-5565	260	46	g)+(ti−1)∥+	g)+(ti−1)∥+	ADJ
ejpam-5565	260	47	+	+	CCONJ
ejpam-5565	260	48	∥(f	∥(f	ADJ
ejpam-5565	260	49	+	+	CCONJ
ejpam-5565	260	50	g)−(ti)−	g)−(ti)−	NOUN
ejpam-5565	260	51	(	(	PUNCT
ejpam-5565	260	52	f	f	NOUN
ejpam-5565	260	53	+	+	CCONJ
ejpam-5565	260	54	g)−(ti−1)∥−	g)−(ti−1)∥−	NOUN
ejpam-5565	260	55	)	)	PUNCT
ejpam-5565	260	56	q)1	q)1	PROPN
ejpam-5565	260	57	/	/	SYM
ejpam-5565	260	58	q	q	NOUN
ejpam-5565	260	59	=	=	PUNCT
ejpam-5565	260	60	(	(	PUNCT
ejpam-5565	260	61	n∑	n∑	INTJ
ejpam-5565	260	62	i=1	i=1	PROPN
ejpam-5565	260	63	(	(	PUNCT
ejpam-5565	260	64	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	260	65	f+(ti−1	f+(ti−1	NOUN
ejpam-5565	260	66	)	)	PUNCT
ejpam-5565	261	1	+	+	NUM
ejpam-5565	261	2	g+(ti)−	g+(ti)−	NOUN
ejpam-5565	261	3	g+(ti−1)∥+	g+(ti−1)∥+	NOUN
ejpam-5565	261	4	+	+	CCONJ
ejpam-5565	261	5	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	261	6	f−(ti−1	f−(ti−1	NUM
ejpam-5565	261	7	)	)	PUNCT
ejpam-5565	262	1	+	+	CCONJ
ejpam-5565	262	2	g−(ti)−	g−(ti)−	PROPN
ejpam-5565	262	3	g−(ti−1)∥−)q)1	g−(ti−1)∥−)q)1	PROPN
ejpam-5565	262	4	/	/	SYM
ejpam-5565	262	5	q	q	NOUN
ejpam-5565	262	6	≤	≤	NOUN
ejpam-5565	262	7	(	(	PUNCT
ejpam-5565	262	8	n∑	n∑	NOUN
ejpam-5565	262	9	i=1	i=1	PROPN
ejpam-5565	263	1	(	(	PUNCT
ejpam-5565	263	2	(	(	PUNCT
ejpam-5565	263	3	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	263	4	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	263	5	+	+	CCONJ
ejpam-5565	263	6	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	263	7	f−(ti−1∥−	f−(ti−1∥−	ADJ
ejpam-5565	263	8	)	)	PUNCT
ejpam-5565	264	1	+	+	CCONJ
ejpam-5565	264	2	(	(	PUNCT
ejpam-5565	264	3	∥g+(ti)−	∥g+(ti)−	ADJ
ejpam-5565	264	4	g+(ti−1)∥+	g+(ti−1)∥+	VERB
ejpam-5565	264	5	+	+	CCONJ
ejpam-5565	264	6	∥g−(ti)−	∥g−(ti)−	DET
ejpam-5565	264	7	g−(ti−1)∥−	g−(ti−1)∥−	NOUN
ejpam-5565	264	8	)	)	PUNCT
ejpam-5565	264	9	)	)	PUNCT
ejpam-5565	264	10	q)1	q)1	PROPN
ejpam-5565	264	11	/	/	SYM
ejpam-5565	264	12	q	q	PROPN
ejpam-5565	264	13	then	then	ADV
ejpam-5565	264	14	by	by	ADP
ejpam-5565	264	15	the	the	DET
ejpam-5565	264	16	minkowski	minkowski	ADJ
ejpam-5565	264	17	inequality	inequality	NOUN
ejpam-5565	264	18	[	[	X
ejpam-5565	264	19	7	7	NUM
ejpam-5565	264	20	]	]	PUNCT
ejpam-5565	264	21	,	,	PUNCT
ejpam-5565	264	22	it	it	PRON
ejpam-5565	264	23	follows	follow	VERB
ejpam-5565	264	24	that	that	SCONJ
ejpam-5565	264	25	:(	:(	PUNCT
ejpam-5565	265	1	n∑	n∑	PROPN
ejpam-5565	266	1	i=1	i=1	PROPN
ejpam-5565	266	2	(	(	PUNCT
ejpam-5565	266	3	∥(f	∥(f	NOUN
ejpam-5565	266	4	+	+	CCONJ
ejpam-5565	266	5	g)+(ti)−	g)+(ti)−	NOUN
ejpam-5565	266	6	(	(	PUNCT
ejpam-5565	266	7	f	f	X
ejpam-5565	266	8	+	+	PUNCT
ejpam-5565	266	9	g)+(ti−1)∥+	g)+(ti−1)∥+	ADJ
ejpam-5565	266	10	+	+	CCONJ
ejpam-5565	266	11	∥(f	∥(f	ADJ
ejpam-5565	266	12	+	+	CCONJ
ejpam-5565	266	13	g)−(ti)−	g)−(ti)−	NOUN
ejpam-5565	266	14	(	(	PUNCT
ejpam-5565	266	15	f	f	NOUN
ejpam-5565	266	16	+	+	CCONJ
ejpam-5565	266	17	g)−(ti−1)∥−	g)−(ti−1)∥−	NOUN
ejpam-5565	266	18	)	)	PUNCT
ejpam-5565	266	19	q)1	q)1	PROPN
ejpam-5565	266	20	/	/	SYM
ejpam-5565	266	21	q	q	PROPN
ejpam-5565	266	22	o.	o.	PROPN
ejpam-5565	266	23	ferrer	ferrer	PROPN
ejpam-5565	266	24	,	,	PUNCT
ejpam-5565	266	25	j.	j.	PROPN
ejpam-5565	266	26	naranjo	naranjo	PROPN
ejpam-5565	266	27	/	/	SYM
ejpam-5565	266	28	eur	eur	PROPN
ejpam-5565	266	29	.	.	PUNCT
ejpam-5565	267	1	j.	j.	PROPN
ejpam-5565	267	2	pure	pure	PROPN
ejpam-5565	267	3	appl	appl	PROPN
ejpam-5565	267	4	.	.	PROPN
ejpam-5565	267	5	math	math	PROPN
ejpam-5565	267	6	,	,	PUNCT
ejpam-5565	267	7	18	18	NUM
ejpam-5565	267	8	(	(	PUNCT
ejpam-5565	267	9	2	2	NUM
ejpam-5565	267	10	)	)	PUNCT
ejpam-5565	267	11	(	(	PUNCT
ejpam-5565	267	12	2025	2025	NUM
ejpam-5565	267	13	)	)	PUNCT
ejpam-5565	267	14	,	,	PUNCT
ejpam-5565	267	15	5565	5565	NUM
ejpam-5565	267	16	14	14	NUM
ejpam-5565	267	17	of	of	ADP
ejpam-5565	267	18	18	18	NUM
ejpam-5565	267	19	≤	≤	NOUN
ejpam-5565	267	20	(	(	PUNCT
ejpam-5565	267	21	n∑	n∑	NOUN
ejpam-5565	267	22	i=1	i=1	PROPN
ejpam-5565	268	1	(	(	PUNCT
ejpam-5565	268	2	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	268	3	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	268	4	+	+	CCONJ
ejpam-5565	268	5	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	268	6	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	268	7	)	)	PUNCT
ejpam-5565	268	8	q)1	q)1	PROPN
ejpam-5565	268	9	/	/	SYM
ejpam-5565	268	10	q	q	PROPN
ejpam-5565	269	1	+	+	CCONJ
ejpam-5565	269	2	(	(	PUNCT
ejpam-5565	269	3	n∑	n∑	INTJ
ejpam-5565	269	4	i=1	i=1	PROPN
ejpam-5565	269	5	(	(	PUNCT
ejpam-5565	269	6	∥g+(ti)−	∥g+(ti)−	NOUN
ejpam-5565	269	7	g+(ti−1)∥+	g+(ti−1)∥+	VERB
ejpam-5565	269	8	+	+	CCONJ
ejpam-5565	269	9	∥g−(ti)−	∥g−(ti)−	DET
ejpam-5565	269	10	g−(ti−1)∥−	g−(ti−1)∥−	NOUN
ejpam-5565	269	11	)	)	PUNCT
ejpam-5565	269	12	q)1	q)1	PROPN
ejpam-5565	269	13	/	/	SYM
ejpam-5565	269	14	q	q	PROPN
ejpam-5565	269	15	whence	whence	NOUN
ejpam-5565	269	16	,	,	PUNCT
ejpam-5565	269	17	q	q	ADJ
ejpam-5565	269	18	vb	vb	NOUN
ejpam-5565	269	19	a((f	a((f	VERB
ejpam-5565	269	20	+	+	CCONJ
ejpam-5565	269	21	g	g	NOUN
ejpam-5565	269	22	)	)	PUNCT
ejpam-5565	269	23	,	,	PUNCT
ejpam-5565	269	24	(	(	PUNCT
ejpam-5565	269	25	k	k	X
ejpam-5565	269	26	,	,	PUNCT
ejpam-5565	269	27	[	[	X
ejpam-5565	269	28	·	·	PUNCT
ejpam-5565	269	29	,	,	PUNCT
ejpam-5565	269	30	·	·	PUNCT
ejpam-5565	269	31	]	]	X
ejpam-5565	269	32	)	)	PUNCT
ejpam-5565	269	33	)	)	PUNCT
ejpam-5565	269	34	≤	≤	NUM
ejpam-5565	269	35	q	q	X
ejpam-5565	269	36	vb	vb	PROPN
ejpam-5565	269	37	a(f	a(f	PROPN
ejpam-5565	269	38	,	,	PUNCT
ejpam-5565	269	39	(	(	PUNCT
ejpam-5565	269	40	k	k	X
ejpam-5565	269	41	,	,	PUNCT
ejpam-5565	269	42	[	[	X
ejpam-5565	269	43	·	·	PUNCT
ejpam-5565	269	44	,	,	PUNCT
ejpam-5565	269	45	·	·	PUNCT
ejpam-5565	269	46	]	]	X
ejpam-5565	269	47	)	)	PUNCT
ejpam-5565	269	48	)	)	PUNCT
ejpam-5565	270	1	+	+	CCONJ
ejpam-5565	270	2	q	q	ADJ
ejpam-5565	270	3	vb	vb	PROPN
ejpam-5565	270	4	a(g	a(g	PROPN
ejpam-5565	270	5	,	,	PUNCT
ejpam-5565	270	6	(	(	PUNCT
ejpam-5565	270	7	k	k	X
ejpam-5565	270	8	,	,	PUNCT
ejpam-5565	270	9	[	[	X
ejpam-5565	270	10	·	·	PUNCT
ejpam-5565	270	11	,	,	PUNCT
ejpam-5565	270	12	·	·	PUNCT
ejpam-5565	270	13	]	]	X
ejpam-5565	270	14	)	)	PUNCT
ejpam-5565	270	15	)	)	PUNCT
ejpam-5565	270	16	≤	≤	NOUN
ejpam-5565	270	17	l+m	l+m	NUM
ejpam-5565	270	18	.	.	PUNCT
ejpam-5565	271	1	therefore	therefore	ADV
ejpam-5565	271	2	,	,	PUNCT
ejpam-5565	271	3	f+g	f+g	PROPN
ejpam-5565	271	4	is	be	AUX
ejpam-5565	271	5	of	of	ADP
ejpam-5565	271	6	bounded	bounded	ADJ
ejpam-5565	271	7	q	q	NOUN
ejpam-5565	271	8	-	-	NOUN
ejpam-5565	271	9	variation	variation	NOUN
ejpam-5565	271	10	in	in	ADP
ejpam-5565	271	11	[	[	X
ejpam-5565	271	12	a	a	DET
ejpam-5565	271	13	,	,	PUNCT
ejpam-5565	271	14	b	b	NOUN
ejpam-5565	271	15	]	]	X
ejpam-5565	271	16	on	on	ADP
ejpam-5565	271	17	the	the	DET
ejpam-5565	271	18	krein	krein	NOUN
ejpam-5565	271	19	space	space	NOUN
ejpam-5565	271	20	(	(	PUNCT
ejpam-5565	271	21	k	k	NOUN
ejpam-5565	271	22	=	=	SYM
ejpam-5565	271	23	k+	k+	NOUN
ejpam-5565	271	24	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	271	25	,	,	PUNCT
ejpam-5565	271	26	[	[	X
ejpam-5565	271	27	·	·	PUNCT
ejpam-5565	271	28	,	,	PUNCT
ejpam-5565	271	29	·	·	PUNCT
ejpam-5565	271	30	]	]	X
ejpam-5565	271	31	)	)	PUNCT
ejpam-5565	271	32	.	.	PUNCT
ejpam-5565	272	1	theorem	theorem	NOUN
ejpam-5565	272	2	12	12	NUM
ejpam-5565	272	3	.	.	PUNCT
ejpam-5565	273	1	let	let	VERB
ejpam-5565	273	2	(	(	PUNCT
ejpam-5565	273	3	k	k	NOUN
ejpam-5565	273	4	=	=	SYM
ejpam-5565	273	5	k+	k+	NOUN
ejpam-5565	273	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	273	7	,	,	PUNCT
ejpam-5565	273	8	[	[	X
ejpam-5565	273	9	·	·	PUNCT
ejpam-5565	273	10	,	,	PUNCT
ejpam-5565	273	11	·	·	PUNCT
ejpam-5565	273	12	]	]	PUNCT
ejpam-5565	273	13	)	)	PUNCT
ejpam-5565	273	14	be	be	AUX
ejpam-5565	273	15	a	a	DET
ejpam-5565	273	16	krein	krein	ADJ
ejpam-5565	273	17	space	space	NOUN
ejpam-5565	273	18	and	and	CCONJ
ejpam-5565	273	19	f	f	NOUN
ejpam-5565	273	20	:	:	PUNCT
ejpam-5565	274	1	[	[	X
ejpam-5565	274	2	a	a	X
ejpam-5565	274	3	,	,	PUNCT
ejpam-5565	274	4	b	b	NOUN
ejpam-5565	274	5	]	]	X
ejpam-5565	274	6	→	→	SYM
ejpam-5565	274	7	k	k	X
ejpam-5565	274	8	=	=	PUNCT
ejpam-5565	274	9	k+	k+	PROPN
ejpam-5565	274	10	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	274	11	a	a	DET
ejpam-5565	274	12	function	function	NOUN
ejpam-5565	274	13	,	,	PUNCT
ejpam-5565	274	14	if	if	SCONJ
ejpam-5565	274	15	f	f	PROPN
ejpam-5565	274	16	∈	∈	PROPN
ejpam-5565	275	1	b	b	X
ejpam-5565	275	2	q	q	X
ejpam-5565	275	3	v	v	PROPN
ejpam-5565	275	4	b	b	PROPN
ejpam-5565	275	5	a	a	DET
ejpam-5565	275	6	(	(	PUNCT
ejpam-5565	275	7	k	k	NOUN
ejpam-5565	275	8	,	,	PUNCT
ejpam-5565	275	9	[	[	X
ejpam-5565	275	10	·	·	PUNCT
ejpam-5565	275	11	,	,	PUNCT
ejpam-5565	275	12	·	·	PUNCT
ejpam-5565	275	13	]	]	X
ejpam-5565	275	14	)	)	PUNCT
ejpam-5565	275	15	,	,	PUNCT
ejpam-5565	275	16	then	then	ADV
ejpam-5565	275	17	f	f	PROPN
ejpam-5565	275	18	∈	∈	PROPN
ejpam-5565	275	19	b	b	PROPN
ejpam-5565	275	20	p	p	X
ejpam-5565	275	21	v	v	ADP
ejpam-5565	275	22	b	b	PROPN
ejpam-5565	275	23	a	a	DET
ejpam-5565	275	24	(	(	PUNCT
ejpam-5565	275	25	k	k	NOUN
ejpam-5565	275	26	,	,	PUNCT
ejpam-5565	275	27	[	[	X
ejpam-5565	275	28	·	·	PUNCT
ejpam-5565	275	29	,	,	PUNCT
ejpam-5565	275	30	·	·	PUNCT
ejpam-5565	275	31	]	]	PUNCT
ejpam-5565	275	32	)	)	PUNCT
ejpam-5565	275	33	para	para	NOUN
ejpam-5565	275	34	p	p	X
ejpam-5565	275	35	>	>	X
ejpam-5565	275	36	q.	q.	PROPN
ejpam-5565	275	37	proof	proof	NOUN
ejpam-5565	275	38	.	.	PUNCT
ejpam-5565	276	1	suppose	suppose	VERB
ejpam-5565	276	2	that	that	SCONJ
ejpam-5565	276	3	f	f	PROPN
ejpam-5565	276	4	∈	∈	PROPN
ejpam-5565	276	5	q	q	PROPN
ejpam-5565	276	6	v	v	PROPN
ejpam-5565	276	7	b	b	PROPN
ejpam-5565	276	8	a	a	DET
ejpam-5565	276	9	(	(	PUNCT
ejpam-5565	276	10	k	k	NOUN
ejpam-5565	276	11	,	,	PUNCT
ejpam-5565	276	12	[	[	X
ejpam-5565	276	13	·	·	PUNCT
ejpam-5565	276	14	,	,	PUNCT
ejpam-5565	276	15	·	·	PUNCT
ejpam-5565	276	16	]	]	X
ejpam-5565	276	17	)	)	PUNCT
ejpam-5565	276	18	,	,	PUNCT
ejpam-5565	276	19	then	then	ADV
ejpam-5565	276	20	existsm	existsm	VERB
ejpam-5565	276	21	>	>	X
ejpam-5565	276	22	0	0	NUM
ejpam-5565	276	23	such	such	ADJ
ejpam-5565	276	24	that	that	SCONJ
ejpam-5565	276	25	q	q	PROPN
ejpam-5565	276	26	vb	vb	PROPN
ejpam-5565	276	27	a(f	a(f	PROPN
ejpam-5565	276	28	,	,	PUNCT
ejpam-5565	276	29	(	(	PUNCT
ejpam-5565	276	30	k	k	X
ejpam-5565	276	31	,	,	PUNCT
ejpam-5565	276	32	[	[	X
ejpam-5565	276	33	·	·	PUNCT
ejpam-5565	276	34	,	,	PUNCT
ejpam-5565	276	35	·	·	PUNCT
ejpam-5565	276	36	]	]	X
ejpam-5565	276	37	)	)	PUNCT
ejpam-5565	276	38	)	)	PUNCT
ejpam-5565	276	39	≤m	≤m	NOUN
ejpam-5565	276	40	now	now	ADV
ejpam-5565	276	41	,	,	PUNCT
ejpam-5565	276	42	for	for	ADP
ejpam-5565	276	43	p	p	PROPN
ejpam-5565	276	44	>	>	X
ejpam-5565	276	45	q	q	X
ejpam-5565	276	46	,	,	PUNCT
ejpam-5565	276	47	let	let	VERB
ejpam-5565	276	48	us	we	PRON
ejpam-5565	276	49	consider	consider	VERB
ejpam-5565	276	50	two	two	NUM
ejpam-5565	276	51	cases	case	NOUN
ejpam-5565	276	52	:	:	PUNCT
ejpam-5565	276	53	i	i	PRON
ejpam-5565	276	54	)	)	PUNCT
ejpam-5565	276	55	∥f+(ti)−	∥f+(ti)−	VERB
ejpam-5565	276	56	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	276	57	+	+	CCONJ
ejpam-5565	276	58	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	276	59	f−(ti−1)∥−	f−(ti−1)∥−	ADJ
ejpam-5565	276	60	≥	≥	NOUN
ejpam-5565	276	61	1	1	NUM
ejpam-5565	276	62	.	.	PUNCT
ejpam-5565	277	1	then	then	ADV
ejpam-5565	277	2	,	,	PUNCT
ejpam-5565	277	3	(	(	PUNCT
ejpam-5565	277	4	∥f+(ti	∥f+(ti	NOUN
ejpam-5565	277	5	)	)	PUNCT
ejpam-5565	277	6	−	−	NOUN
ejpam-5565	278	1	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	278	2	+	+	CCONJ
ejpam-5565	278	3	∥f−(ti	∥f−(ti	NUM
ejpam-5565	278	4	)	)	PUNCT
ejpam-5565	278	5	−	−	ADP
ejpam-5565	278	6	f−(ti−1)∥−)q	f−(ti−1)∥−)q	VERB
ejpam-5565	278	7	≤	≤	NOUN
ejpam-5565	278	8	(	(	PUNCT
ejpam-5565	278	9	∥f+(ti	∥f+(ti	NOUN
ejpam-5565	278	10	)	)	PUNCT
ejpam-5565	278	11	−	−	NOUN
ejpam-5565	279	1	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	279	2	+	+	CCONJ
ejpam-5565	279	3	∥f−(ti	∥f−(ti	NOUN
ejpam-5565	279	4	)	)	PUNCT
ejpam-5565	279	5	−	−	ADP
ejpam-5565	279	6	f−(ti−1)∥−)p	f−(ti−1)∥−)p	NOUN
ejpam-5565	279	7	.	.	PUNCT
ejpam-5565	280	1	later,∑n	later,∑n	NOUN
ejpam-5565	280	2	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	280	3	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	280	4	+	+	CCONJ
ejpam-5565	280	5	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	280	6	f−(ti−1)∥−)q	f−(ti−1)∥−)q	VERB
ejpam-5565	280	7	≤	≤	ADJ
ejpam-5565	280	8	∑n	∑n	NUM
ejpam-5565	280	9	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	280	10	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	280	11	+	+	NUM
ejpam-5565	280	12	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	280	13	f−(ti−1)∥−)p	f−(ti−1)∥−)p	NOUN
ejpam-5565	280	14	since	since	SCONJ
ejpam-5565	280	15	p	p	PROPN
ejpam-5565	280	16	>	>	X
ejpam-5565	280	17	q	q	X
ejpam-5565	280	18	,	,	PUNCT
ejpam-5565	280	19	then	then	ADV
ejpam-5565	280	20	1	1	NUM
ejpam-5565	280	21	p	p	NOUN
ejpam-5565	280	22	<	<	X
ejpam-5565	280	23	1	1	NUM
ejpam-5565	280	24	q	q	NOUN
ejpam-5565	280	25	and	and	CCONJ
ejpam-5565	280	26	thus	thus	ADV
ejpam-5565	280	27	:	:	PUNCT
ejpam-5565	280	28	p	p	X
ejpam-5565	280	29	vb	vb	ADP
ejpam-5565	280	30	a(f	a(f	PROPN
ejpam-5565	280	31	,	,	PUNCT
ejpam-5565	280	32	(	(	PUNCT
ejpam-5565	280	33	k	k	X
ejpam-5565	280	34	,	,	PUNCT
ejpam-5565	280	35	[	[	X
ejpam-5565	280	36	·	·	PUNCT
ejpam-5565	280	37	,	,	PUNCT
ejpam-5565	280	38	·	·	PUNCT
ejpam-5565	280	39	]	]	X
ejpam-5565	280	40	)	)	PUNCT
ejpam-5565	280	41	)	)	PUNCT
ejpam-5565	281	1	=	=	SYM
ejpam-5565	281	2	sup	sup	NOUN
ejpam-5565	281	3	p∈p[a	p∈p[a	NOUN
ejpam-5565	281	4	,	,	PUNCT
ejpam-5565	281	5	b	b	NOUN
ejpam-5565	281	6	]	]	PUNCT
ejpam-5565	281	7			PUNCT
ejpam-5565	281	8	(	(	PUNCT
ejpam-5565	281	9	n∑	n∑	NOUN
ejpam-5565	281	10	i=1	i=1	PROPN
ejpam-5565	281	11	(	(	PUNCT
ejpam-5565	281	12	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	281	13	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	281	14	+	+	CCONJ
ejpam-5565	281	15	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	281	16	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	281	17	)	)	PUNCT
ejpam-5565	281	18	p)1	p)1	VERB
ejpam-5565	281	19	/	/	SYM
ejpam-5565	281	20	p	p	X
ejpam-5565	281	21			PROPN
ejpam-5565	281	22	≤	≤	NUM
ejpam-5565	281	23	sup	sup	NOUN
ejpam-5565	281	24	p∈p[a	p∈p[a	NOUN
ejpam-5565	281	25	,	,	PUNCT
ejpam-5565	281	26	b	b	NOUN
ejpam-5565	281	27	]	]	PUNCT
ejpam-5565	281	28			PUNCT
ejpam-5565	281	29	(	(	PUNCT
ejpam-5565	281	30	n∑	n∑	NOUN
ejpam-5565	281	31	i=1	i=1	PROPN
ejpam-5565	281	32	(	(	PUNCT
ejpam-5565	281	33	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	281	34	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	281	35	+	+	CCONJ
ejpam-5565	281	36	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	281	37	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	281	38	)	)	PUNCT
ejpam-5565	281	39	q)1	q)1	PROPN
ejpam-5565	281	40	/	/	SYM
ejpam-5565	281	41	q	q	PROPN
ejpam-5565	281	42			PROPN
ejpam-5565	281	43	≤m	≤m	PROPN
ejpam-5565	281	44	ii	ii	PROPN
ejpam-5565	281	45	)	)	PUNCT
ejpam-5565	281	46	0	0	NUM
ejpam-5565	282	1	≤	≤	NOUN
ejpam-5565	282	2	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	282	3	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	282	4	+	+	CCONJ
ejpam-5565	282	5	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	282	6	f−(ti−1)∥−	f−(ti−1)∥−	VERB
ejpam-5565	282	7	<	<	X
ejpam-5565	282	8	1	1	NUM
ejpam-5565	282	9	.	.	PUNCT
ejpam-5565	283	1	then	then	ADV
ejpam-5565	283	2	(	(	PUNCT
ejpam-5565	283	3	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	283	4	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	283	5	+	+	CCONJ
ejpam-5565	283	6	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	283	7	f−(ti−1)∥−)p	f−(ti−1)∥−)p	NOUN
ejpam-5565	283	8	≤	≤	NOUN
ejpam-5565	283	9	(	(	PUNCT
ejpam-5565	283	10	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	283	11	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	283	12	+	+	CCONJ
ejpam-5565	283	13	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	283	14	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	283	15	.	.	PUNCT
ejpam-5565	284	1	whence	whence	NOUN
ejpam-5565	284	2	,	,	PUNCT
ejpam-5565	284	3	o.	o.	PROPN
ejpam-5565	284	4	ferrer	ferrer	PROPN
ejpam-5565	284	5	,	,	PUNCT
ejpam-5565	284	6	j.	j.	PROPN
ejpam-5565	284	7	naranjo	naranjo	PROPN
ejpam-5565	284	8	/	/	SYM
ejpam-5565	284	9	eur	eur	PROPN
ejpam-5565	284	10	.	.	PUNCT
ejpam-5565	285	1	j.	j.	PROPN
ejpam-5565	285	2	pure	pure	PROPN
ejpam-5565	285	3	appl	appl	PROPN
ejpam-5565	285	4	.	.	PROPN
ejpam-5565	285	5	math	math	PROPN
ejpam-5565	285	6	,	,	PUNCT
ejpam-5565	285	7	18	18	NUM
ejpam-5565	285	8	(	(	PUNCT
ejpam-5565	285	9	2	2	NUM
ejpam-5565	285	10	)	)	PUNCT
ejpam-5565	285	11	(	(	PUNCT
ejpam-5565	285	12	2025	2025	NUM
ejpam-5565	285	13	)	)	PUNCT
ejpam-5565	285	14	,	,	PUNCT
ejpam-5565	285	15	5565	5565	NUM
ejpam-5565	285	16	15	15	NUM
ejpam-5565	285	17	of	of	ADP
ejpam-5565	285	18	18∑n	18∑n	NUM
ejpam-5565	285	19	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	285	20	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	285	21	+	+	NUM
ejpam-5565	285	22	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	285	23	f−(ti−1)∥−)p	f−(ti−1)∥−)p	NOUN
ejpam-5565	285	24	≤	≤	NUM
ejpam-5565	285	25	∑n	∑n	PROPN
ejpam-5565	285	26	i=1(∥f+(ti)−	i=1(∥f+(ti)−	NOUN
ejpam-5565	285	27	f+(ti−1)∥+	f+(ti−1)∥+	NOUN
ejpam-5565	285	28	+	+	CCONJ
ejpam-5565	285	29	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	285	30	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	285	31	and	and	CCONJ
ejpam-5565	285	32	therefore	therefore	ADV
ejpam-5565	285	33	,	,	PUNCT
ejpam-5565	285	34	(	(	PUNCT
ejpam-5565	285	35	n∑	n∑	INTJ
ejpam-5565	285	36	i=1	i=1	PROPN
ejpam-5565	285	37	(	(	PUNCT
ejpam-5565	285	38	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	285	39	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	285	40	+	+	CCONJ
ejpam-5565	285	41	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	285	42	f−(ti−1)∥−	f−(ti−1)∥−	NOUN
ejpam-5565	285	43	)	)	PUNCT
ejpam-5565	285	44	p)1	p)1	VERB
ejpam-5565	285	45	/	/	SYM
ejpam-5565	285	46	p	p	PRON
ejpam-5565	285	47	is	be	AUX
ejpam-5565	285	48	less	less	ADJ
ejpam-5565	285	49	than	than	ADP
ejpam-5565	285	50	or	or	CCONJ
ejpam-5565	285	51	equal	equal	ADJ
ejpam-5565	285	52	to	to	ADP
ejpam-5565	285	53	(	(	PUNCT
ejpam-5565	285	54	n∑	n∑	INTJ
ejpam-5565	285	55	i=1	i=1	PROPN
ejpam-5565	285	56	(	(	PUNCT
ejpam-5565	285	57	∥f+(ti)−	∥f+(ti)−	NOUN
ejpam-5565	285	58	f+(ti−1)∥+	f+(ti−1)∥+	ADJ
ejpam-5565	285	59	+	+	CCONJ
ejpam-5565	285	60	∥f−(ti)−	∥f−(ti)−	NOUN
ejpam-5565	285	61	f−(ti−1)∥−)q	f−(ti−1)∥−)q	NOUN
ejpam-5565	285	62	)	)	PUNCT
ejpam-5565	285	63	1	1	NUM
ejpam-5565	285	64	/	/	SYM
ejpam-5565	285	65	q	q	NOUN
ejpam-5565	285	66	,	,	PUNCT
ejpam-5565	285	67	it	it	PRON
ejpam-5565	285	68	follows	follow	VERB
ejpam-5565	285	69	that	that	SCONJ
ejpam-5565	285	70	:	:	PUNCT
ejpam-5565	286	1	p	p	X
ejpam-5565	286	2	vb	vb	ADP
ejpam-5565	286	3	a(f	a(f	PROPN
ejpam-5565	286	4	,	,	PUNCT
ejpam-5565	286	5	(	(	PUNCT
ejpam-5565	286	6	k	k	X
ejpam-5565	286	7	,	,	PUNCT
ejpam-5565	286	8	[	[	X
ejpam-5565	286	9	·	·	PUNCT
ejpam-5565	286	10	,	,	PUNCT
ejpam-5565	286	11	·	·	PUNCT
ejpam-5565	286	12	]	]	X
ejpam-5565	286	13	)	)	PUNCT
ejpam-5565	286	14	)	)	PUNCT
ejpam-5565	286	15	≤	≤	NUM
ejpam-5565	286	16	q	q	X
ejpam-5565	286	17	vb	vb	PROPN
ejpam-5565	286	18	a(f	a(f	PROPN
ejpam-5565	286	19	,	,	PUNCT
ejpam-5565	286	20	(	(	PUNCT
ejpam-5565	286	21	k	k	X
ejpam-5565	286	22	,	,	PUNCT
ejpam-5565	286	23	[	[	X
ejpam-5565	286	24	·	·	PUNCT
ejpam-5565	286	25	,	,	PUNCT
ejpam-5565	286	26	·	·	PUNCT
ejpam-5565	286	27	]	]	X
ejpam-5565	286	28	)	)	PUNCT
ejpam-5565	286	29	)	)	PUNCT
ejpam-5565	286	30	from	from	ADP
ejpam-5565	286	31	which	which	PRON
ejpam-5565	286	32	it	it	PRON
ejpam-5565	286	33	follows	follow	VERB
ejpam-5565	286	34	for	for	ADP
ejpam-5565	286	35	cases	case	NOUN
ejpam-5565	286	36	i	i	PRON
ejpam-5565	286	37	)	)	PUNCT
ejpam-5565	286	38	y	y	PROPN
ejpam-5565	286	39	ii	ii	PROPN
ejpam-5565	286	40	)	)	PUNCT
ejpam-5565	286	41	that	that	SCONJ
ejpam-5565	286	42	p	p	PROPN
ejpam-5565	286	43	vb	vb	ADP
ejpam-5565	286	44	a(f	a(f	PROPN
ejpam-5565	286	45	,	,	PUNCT
ejpam-5565	286	46	(	(	PUNCT
ejpam-5565	286	47	k	k	X
ejpam-5565	286	48	,	,	PUNCT
ejpam-5565	286	49	[	[	X
ejpam-5565	286	50	·	·	PUNCT
ejpam-5565	286	51	,	,	PUNCT
ejpam-5565	286	52	·	·	PUNCT
ejpam-5565	286	53	]	]	X
ejpam-5565	286	54	)	)	PUNCT
ejpam-5565	286	55	)	)	PUNCT
ejpam-5565	286	56	is	be	AUX
ejpam-5565	286	57	finite	finite	ADJ
ejpam-5565	286	58	,	,	PUNCT
ejpam-5565	286	59	therefore	therefore	ADV
ejpam-5565	286	60	f	f	PROPN
ejpam-5565	286	61	∈	∈	PROPN
ejpam-5565	286	62	b	b	PROPN
ejpam-5565	286	63	p	p	X
ejpam-5565	286	64	v	v	ADP
ejpam-5565	286	65	b	b	PROPN
ejpam-5565	286	66	a	a	DET
ejpam-5565	286	67	(	(	PUNCT
ejpam-5565	286	68	k	k	NOUN
ejpam-5565	286	69	,	,	PUNCT
ejpam-5565	286	70	[	[	X
ejpam-5565	286	71	·	·	PUNCT
ejpam-5565	286	72	,	,	PUNCT
ejpam-5565	286	73	·	·	PUNCT
ejpam-5565	286	74	]	]	X
ejpam-5565	286	75	)	)	PUNCT
ejpam-5565	286	76	.	.	PUNCT
ejpam-5565	287	1	next	next	ADV
ejpam-5565	287	2	,	,	PUNCT
ejpam-5565	287	3	the	the	DET
ejpam-5565	287	4	set	set	NOUN
ejpam-5565	287	5	of	of	ADP
ejpam-5565	287	6	bounded	bounded	ADJ
ejpam-5565	287	7	q−variation	q−variation	NOUN
ejpam-5565	287	8	functions	function	NOUN
ejpam-5565	287	9	on	on	ADP
ejpam-5565	287	10	krein	krein	ADJ
ejpam-5565	287	11	space	space	NOUN
ejpam-5565	287	12	,	,	PUNCT
ejpam-5565	287	13	que	que	X
ejpam-5565	287	14	which	which	PRON
ejpam-5565	287	15	we	we	PRON
ejpam-5565	287	16	introduce	introduce	VERB
ejpam-5565	287	17	in	in	ADP
ejpam-5565	287	18	7	7	NUM
ejpam-5565	287	19	will	will	AUX
ejpam-5565	287	20	be	be	AUX
ejpam-5565	287	21	given	give	VERB
ejpam-5565	287	22	a	a	DET
ejpam-5565	287	23	norm	norm	NOUN
ejpam-5565	287	24	,	,	PUNCT
ejpam-5565	287	25	which	which	PRON
ejpam-5565	287	26	we	we	PRON
ejpam-5565	287	27	will	will	AUX
ejpam-5565	287	28	call	call	VERB
ejpam-5565	287	29	q−norm	q−norm	NOUN
ejpam-5565	287	30	and	and	CCONJ
ejpam-5565	287	31	denote	denote	VERB
ejpam-5565	287	32	by	by	ADP
ejpam-5565	287	33	∥	∥	X
ejpam-5565	287	34	·	·	PUNCT
ejpam-5565	288	1	∥q	∥q	ADJ
ejpam-5565	288	2	theorem	theorem	VERB
ejpam-5565	288	3	13	13	NUM
ejpam-5565	288	4	.	.	PUNCT
ejpam-5565	289	1	let	let	VERB
ejpam-5565	289	2	(	(	PUNCT
ejpam-5565	289	3	k	k	NOUN
ejpam-5565	289	4	=	=	SYM
ejpam-5565	289	5	k+	k+	NOUN
ejpam-5565	289	6	˙[+]k−	˙[+]k−	NOUN
ejpam-5565	289	7	,	,	PUNCT
ejpam-5565	289	8	[	[	X
ejpam-5565	289	9	·	·	PUNCT
ejpam-5565	289	10	,	,	PUNCT
ejpam-5565	289	11	·	·	PUNCT
ejpam-5565	289	12	]	]	PUNCT
ejpam-5565	289	13	)	)	PUNCT
ejpam-5565	289	14	be	be	AUX
ejpam-5565	289	15	a	a	DET
ejpam-5565	289	16	krein	krein	ADJ
ejpam-5565	289	17	space	space	NOUN
ejpam-5565	289	18	,	,	PUNCT
ejpam-5565	289	19	the	the	DET
ejpam-5565	289	20	function	function	NOUN
ejpam-5565	289	21	||	||	NOUN
ejpam-5565	290	1	·	·	PUNCT
ejpam-5565	291	1	||q	||q	ADV
ejpam-5565	291	2	:	:	PUNCT
ejpam-5565	291	3	b	b	X
ejpam-5565	291	4	q	q	X
ejpam-5565	291	5	v	v	ADP
ejpam-5565	291	6	b	b	NOUN
ejpam-5565	291	7	a	a	PRON
ejpam-5565	291	8	(	(	PUNCT
ejpam-5565	291	9	k	k	NOUN
ejpam-5565	291	10	,	,	PUNCT
ejpam-5565	291	11	[	[	X
ejpam-5565	291	12	·	·	PUNCT
ejpam-5565	291	13	,	,	PUNCT
ejpam-5565	291	14	·	·	PUNCT
ejpam-5565	291	15	]	]	X
ejpam-5565	291	16	)	)	PUNCT
ejpam-5565	291	17	→	→	SYM
ejpam-5565	292	1	r	r	NOUN
ejpam-5565	292	2	defined	define	VERB
ejpam-5565	292	3	by	by	ADP
ejpam-5565	292	4	∥f∥q	∥f∥q	NOUN
ejpam-5565	292	5	=	=	NOUN
ejpam-5565	292	6	∥f+(x)∥+	∥f+(x)∥+	X
ejpam-5565	292	7	+	+	CCONJ
ejpam-5565	292	8	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	292	9	+	+	CCONJ
ejpam-5565	292	10	q+	q+	ADV
ejpam-5565	292	11	vb	vb	ADP
ejpam-5565	292	12	a(f	a(f	PROPN
ejpam-5565	292	13	,	,	PUNCT
ejpam-5565	292	14	(	(	PUNCT
ejpam-5565	292	15	k+	k+	X
ejpam-5565	292	16	,	,	PUNCT
ejpam-5565	292	17	[	[	X
ejpam-5565	292	18	·	·	PUNCT
ejpam-5565	292	19	,	,	PUNCT
ejpam-5565	292	20	·	·	PUNCT
ejpam-5565	292	21	]	]	X
ejpam-5565	292	22	)	)	PUNCT
ejpam-5565	292	23	)	)	PUNCT
ejpam-5565	293	1	+	+	CCONJ
ejpam-5565	293	2	q−	q−	PROPN
ejpam-5565	293	3	vb	vb	PROPN
ejpam-5565	293	4	a(f	a(f	PROPN
ejpam-5565	293	5	,	,	PUNCT
ejpam-5565	293	6	(	(	PUNCT
ejpam-5565	293	7	k−,−	k−,−	NOUN
ejpam-5565	293	8	[	[	X
ejpam-5565	293	9	·	·	PUNCT
ejpam-5565	293	10	,	,	PUNCT
ejpam-5565	293	11	·	·	PUNCT
ejpam-5565	293	12	]	]	X
ejpam-5565	293	13	)	)	PUNCT
ejpam-5565	293	14	)	)	PUNCT
ejpam-5565	293	15	,	,	PUNCT
ejpam-5565	293	16	is	be	AUX
ejpam-5565	293	17	a	a	DET
ejpam-5565	293	18	norm	norm	NOUN
ejpam-5565	293	19	in	in	ADP
ejpam-5565	293	20	b	b	PROPN
ejpam-5565	293	21	q	q	X
ejpam-5565	293	22	v	v	PROPN
ejpam-5565	293	23	b	b	PROPN
ejpam-5565	293	24	a	a	DET
ejpam-5565	293	25	(	(	PUNCT
ejpam-5565	293	26	k	k	NOUN
ejpam-5565	293	27	,	,	PUNCT
ejpam-5565	293	28	[	[	X
ejpam-5565	293	29	·	·	PUNCT
ejpam-5565	293	30	,	,	PUNCT
ejpam-5565	293	31	·	·	PUNCT
ejpam-5565	293	32	]	]	X
ejpam-5565	293	33	)	)	PUNCT
ejpam-5565	293	34	.	.	PUNCT
ejpam-5565	294	1	proof	proof	NOUN
ejpam-5565	294	2	.	.	PUNCT
ejpam-5565	295	1	let	let	VERB
ejpam-5565	295	2	f	f	X
ejpam-5565	295	3	,	,	PUNCT
ejpam-5565	295	4	g	g	PROPN
ejpam-5565	295	5	∈	∈	PROPN
ejpam-5565	295	6	b	b	X
ejpam-5565	295	7	q	q	X
ejpam-5565	295	8	v	v	PROPN
ejpam-5565	295	9	b	b	PROPN
ejpam-5565	295	10	a	a	PRON
ejpam-5565	295	11	(	(	PUNCT
ejpam-5565	295	12	k	k	NOUN
ejpam-5565	295	13	,	,	PUNCT
ejpam-5565	295	14	[	[	X
ejpam-5565	295	15	·	·	PUNCT
ejpam-5565	295	16	,	,	PUNCT
ejpam-5565	295	17	·	·	PUNCT
ejpam-5565	295	18	]	]	X
ejpam-5565	295	19	)	)	PUNCT
ejpam-5565	295	20	,	,	PUNCT
ejpam-5565	295	21	λ	λ	PROPN
ejpam-5565	295	22	∈	∈	PROPN
ejpam-5565	295	23	r.	r.	NOUN
ejpam-5565	295	24	if	if	SCONJ
ejpam-5565	295	25	x	x	SYM
ejpam-5565	295	26	∈	∈	PROPN
ejpam-5565	295	27	[	[	X
ejpam-5565	295	28	a	a	X
ejpam-5565	295	29	,	,	PUNCT
ejpam-5565	295	30	b	b	NOUN
ejpam-5565	295	31	]	]	X
ejpam-5565	295	32	,	,	PUNCT
ejpam-5565	295	33	then	then	ADV
ejpam-5565	295	34	we	we	PRON
ejpam-5565	295	35	have	have	VERB
ejpam-5565	295	36	:	:	PUNCT
ejpam-5565	295	37	(	(	PUNCT
ejpam-5565	295	38	i	i	NOUN
ejpam-5565	295	39	)	)	PUNCT
ejpam-5565	295	40	∥f+(x)∥+	∥f+(x)∥+	PROPN
ejpam-5565	295	41	≥	≥	NUM
ejpam-5565	295	42	0	0	NUM
ejpam-5565	295	43	,	,	PUNCT
ejpam-5565	295	44	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	295	45	≥	≥	NOUN
ejpam-5565	295	46	0	0	NUM
ejpam-5565	295	47	.	.	PUNCT
ejpam-5565	296	1	also	also	ADV
ejpam-5565	296	2	satisfied	satisfied	ADJ
ejpam-5565	296	3	that	that	SCONJ
ejpam-5565	296	4	q+	q+	ADP
ejpam-5565	296	5	vb	vb	ADP
ejpam-5565	296	6	a(f	a(f	PROPN
ejpam-5565	296	7	,	,	PUNCT
ejpam-5565	296	8	(	(	PUNCT
ejpam-5565	296	9	k+	k+	X
ejpam-5565	296	10	,	,	PUNCT
ejpam-5565	296	11	[	[	X
ejpam-5565	296	12	·	·	PUNCT
ejpam-5565	296	13	,	,	PUNCT
ejpam-5565	296	14	·	·	PUNCT
ejpam-5565	296	15	]	]	X
ejpam-5565	296	16	)	)	PUNCT
ejpam-5565	296	17	)	)	PUNCT
ejpam-5565	297	1	≥	≥	NOUN
ejpam-5565	297	2	0	0	NUM
ejpam-5565	297	3	and	and	CCONJ
ejpam-5565	297	4	q−	q−	PROPN
ejpam-5565	297	5	vb	vb	PROPN
ejpam-5565	297	6	a(f	a(f	PROPN
ejpam-5565	297	7	,	,	PUNCT
ejpam-5565	297	8	(	(	PUNCT
ejpam-5565	297	9	k−,−	k−,−	NOUN
ejpam-5565	297	10	[	[	X
ejpam-5565	297	11	·	·	PUNCT
ejpam-5565	297	12	,	,	PUNCT
ejpam-5565	297	13	·	·	PUNCT
ejpam-5565	297	14	]	]	X
ejpam-5565	297	15	)	)	PUNCT
ejpam-5565	297	16	)	)	PUNCT
ejpam-5565	297	17	≥	≥	NOUN
ejpam-5565	297	18	0	0	NUM
ejpam-5565	297	19	.	.	PUNCT
ejpam-5565	298	1	therefore	therefore	ADV
ejpam-5565	298	2	,	,	PUNCT
ejpam-5565	298	3	∥f∥	∥f∥	PROPN
ejpam-5565	298	4	b	b	PROPN
ejpam-5565	298	5	q	q	X
ejpam-5565	298	6	v	v	PROPN
ejpam-5565	298	7	b	b	PROPN
ejpam-5565	298	8	a	a	PRON
ejpam-5565	298	9	(	(	PUNCT
ejpam-5565	298	10	k	k	NOUN
ejpam-5565	298	11	,	,	PUNCT
ejpam-5565	298	12	[	[	X
ejpam-5565	298	13	·	·	PUNCT
ejpam-5565	298	14	,	,	PUNCT
ejpam-5565	298	15	·	·	PUNCT
ejpam-5565	298	16	]	]	X
ejpam-5565	298	17	)	)	PUNCT
ejpam-5565	298	18	≥	≥	NOUN
ejpam-5565	298	19	0	0	NUM
ejpam-5565	298	20	.	.	PUNCT
ejpam-5565	298	21	(	(	PUNCT
ejpam-5565	298	22	ii	ii	NOUN
ejpam-5565	298	23	)	)	PUNCT
ejpam-5565	298	24	if	if	SCONJ
ejpam-5565	298	25	∥f∥	∥f∥	PROPN
ejpam-5565	298	26	b	b	PROPN
ejpam-5565	298	27	q	q	X
ejpam-5565	298	28	v	v	PROPN
ejpam-5565	298	29	b	b	PROPN
ejpam-5565	298	30	a	a	PRON
ejpam-5565	298	31	(	(	PUNCT
ejpam-5565	298	32	k	k	NOUN
ejpam-5565	298	33	,	,	PUNCT
ejpam-5565	298	34	[	[	X
ejpam-5565	298	35	·	·	PUNCT
ejpam-5565	298	36	,	,	PUNCT
ejpam-5565	298	37	·	·	PUNCT
ejpam-5565	298	38	]	]	X
ejpam-5565	298	39	)	)	PUNCT
ejpam-5565	298	40	=	=	SYM
ejpam-5565	298	41	0	0	NUM
ejpam-5565	298	42	,	,	PUNCT
ejpam-5565	298	43	then	then	ADV
ejpam-5565	298	44	q+	q+	ADP
ejpam-5565	298	45	v	v	ADP
ejpam-5565	298	46	b	b	X
ejpam-5565	298	47	a	a	PRON
ejpam-5565	298	48	(	(	PUNCT
ejpam-5565	298	49	f	f	NOUN
ejpam-5565	298	50	,	,	PUNCT
ejpam-5565	298	51	(	(	PUNCT
ejpam-5565	298	52	k+	k+	X
ejpam-5565	298	53	,	,	PUNCT
ejpam-5565	298	54	[	[	X
ejpam-5565	298	55	·	·	PUNCT
ejpam-5565	298	56	,	,	PUNCT
ejpam-5565	298	57	·	·	PUNCT
ejpam-5565	298	58	]	]	X
ejpam-5565	298	59	)	)	PUNCT
ejpam-5565	298	60	)	)	PUNCT
ejpam-5565	299	1	+	+	CCONJ
ejpam-5565	299	2	q−	q−	PROPN
ejpam-5565	299	3	v	v	NOUN
ejpam-5565	299	4	b	b	NOUN
ejpam-5565	299	5	a	a	DET
ejpam-5565	299	6	(	(	PUNCT
ejpam-5565	299	7	f	f	NOUN
ejpam-5565	299	8	,	,	PUNCT
ejpam-5565	299	9	(	(	PUNCT
ejpam-5565	299	10	k−,−	k−,−	NOUN
ejpam-5565	299	11	[	[	X
ejpam-5565	299	12	·	·	PUNCT
ejpam-5565	299	13	,	,	PUNCT
ejpam-5565	299	14	·	·	PUNCT
ejpam-5565	299	15	]	]	X
ejpam-5565	299	16	)	)	PUNCT
ejpam-5565	299	17	)	)	PUNCT
ejpam-5565	300	1	+	+	CCONJ
ejpam-5565	300	2	∥f+(x)∥+	∥f+(x)∥+	ADJ
ejpam-5565	300	3	+	+	CCONJ
ejpam-5565	300	4	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	300	5	=	=	SYM
ejpam-5565	300	6	0	0	PROPN
ejpam-5565	300	7	.	.	PUNCT
ejpam-5565	300	8	o.	o.	PROPN
ejpam-5565	300	9	ferrer	ferrer	PROPN
ejpam-5565	300	10	,	,	PUNCT
ejpam-5565	300	11	j.	j.	PROPN
ejpam-5565	300	12	naranjo	naranjo	PROPN
ejpam-5565	300	13	/	/	SYM
ejpam-5565	300	14	eur	eur	PROPN
ejpam-5565	300	15	.	.	PUNCT
ejpam-5565	301	1	j.	j.	PROPN
ejpam-5565	301	2	pure	pure	PROPN
ejpam-5565	301	3	appl	appl	PROPN
ejpam-5565	301	4	.	.	PROPN
ejpam-5565	301	5	math	math	PROPN
ejpam-5565	301	6	,	,	PUNCT
ejpam-5565	301	7	18	18	NUM
ejpam-5565	301	8	(	(	PUNCT
ejpam-5565	301	9	2	2	NUM
ejpam-5565	301	10	)	)	PUNCT
ejpam-5565	301	11	(	(	PUNCT
ejpam-5565	301	12	2025	2025	NUM
ejpam-5565	301	13	)	)	PUNCT
ejpam-5565	301	14	,	,	PUNCT
ejpam-5565	301	15	5565	5565	NUM
ejpam-5565	301	16	16	16	NUM
ejpam-5565	301	17	of	of	ADP
ejpam-5565	301	18	18	18	NUM
ejpam-5565	301	19	since	since	SCONJ
ejpam-5565	301	20	q+	q+	ADP
ejpam-5565	301	21	v	v	NOUN
ejpam-5565	301	22	b	b	NOUN
ejpam-5565	301	23	a	a	PRON
ejpam-5565	301	24	(	(	PUNCT
ejpam-5565	301	25	f	f	NOUN
ejpam-5565	301	26	,	,	PUNCT
ejpam-5565	301	27	(	(	PUNCT
ejpam-5565	301	28	k+	k+	X
ejpam-5565	301	29	,	,	PUNCT
ejpam-5565	301	30	[	[	X
ejpam-5565	301	31	·	·	PUNCT
ejpam-5565	301	32	,	,	PUNCT
ejpam-5565	301	33	·	·	PUNCT
ejpam-5565	301	34	]	]	X
ejpam-5565	301	35	)	)	PUNCT
ejpam-5565	301	36	)	)	PUNCT
ejpam-5565	301	37	,	,	PUNCT
ejpam-5565	301	38	q−	q−	PROPN
ejpam-5565	301	39	v	v	NOUN
ejpam-5565	301	40	b	b	NOUN
ejpam-5565	301	41	a	a	DET
ejpam-5565	301	42	(	(	PUNCT
ejpam-5565	301	43	f	f	NOUN
ejpam-5565	301	44	,	,	PUNCT
ejpam-5565	301	45	(	(	PUNCT
ejpam-5565	301	46	k−,−	k−,−	NOUN
ejpam-5565	301	47	[	[	X
ejpam-5565	301	48	·	·	PUNCT
ejpam-5565	301	49	,	,	PUNCT
ejpam-5565	301	50	·	·	PUNCT
ejpam-5565	301	51	]	]	X
ejpam-5565	301	52	)	)	PUNCT
ejpam-5565	301	53	)	)	PUNCT
ejpam-5565	301	54	,	,	PUNCT
ejpam-5565	301	55	∥f+(x)∥+	∥f+(x)∥+	NOUN
ejpam-5565	301	56	,	,	PUNCT
ejpam-5565	301	57	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	301	58	≥	≥	NOUN
ejpam-5565	301	59	0	0	NUM
ejpam-5565	301	60	,	,	PUNCT
ejpam-5565	301	61	then	then	ADV
ejpam-5565	301	62	q+	q+	ADP
ejpam-5565	301	63	v	v	ADP
ejpam-5565	301	64	b	b	X
ejpam-5565	301	65	a	a	PRON
ejpam-5565	301	66	(	(	PUNCT
ejpam-5565	301	67	f	f	NOUN
ejpam-5565	301	68	,	,	PUNCT
ejpam-5565	301	69	(	(	PUNCT
ejpam-5565	301	70	k+	k+	X
ejpam-5565	301	71	,	,	PUNCT
ejpam-5565	301	72	[	[	X
ejpam-5565	301	73	·	·	PUNCT
ejpam-5565	301	74	,	,	PUNCT
ejpam-5565	301	75	·	·	PUNCT
ejpam-5565	301	76	]	]	X
ejpam-5565	301	77	)	)	PUNCT
ejpam-5565	301	78	)	)	PUNCT
ejpam-5565	302	1	=	=	PUNCT
ejpam-5565	302	2	q−	q−	PROPN
ejpam-5565	302	3	v	v	NOUN
ejpam-5565	302	4	b	b	NOUN
ejpam-5565	302	5	a	a	DET
ejpam-5565	302	6	(	(	PUNCT
ejpam-5565	302	7	f	f	NOUN
ejpam-5565	302	8	,	,	PUNCT
ejpam-5565	302	9	(	(	PUNCT
ejpam-5565	302	10	k−,−	k−,−	NOUN
ejpam-5565	302	11	[	[	X
ejpam-5565	302	12	·	·	PUNCT
ejpam-5565	302	13	,	,	PUNCT
ejpam-5565	302	14	·	·	PUNCT
ejpam-5565	302	15	]	]	X
ejpam-5565	302	16	)	)	PUNCT
ejpam-5565	302	17	)	)	PUNCT
ejpam-5565	303	1	=	=	SYM
ejpam-5565	303	2	∥f+(x)∥+	∥f+(x)∥+	ADJ
ejpam-5565	303	3	=	=	PUNCT
ejpam-5565	303	4	∥f−(x)∥−	∥f−(x)∥−	NOUN
ejpam-5565	303	5	=	=	SYM
ejpam-5565	303	6	0	0	NUM
ejpam-5565	303	7	.	.	PUNCT
ejpam-5565	303	8	(	(	PUNCT
ejpam-5565	303	9	2	2	X
ejpam-5565	303	10	)	)	PUNCT
ejpam-5565	303	11	as	as	ADP
ejpam-5565	303	12	the	the	DET
ejpam-5565	303	13	positive	positive	ADJ
ejpam-5565	303	14	and	and	CCONJ
ejpam-5565	303	15	negative	negative	ADJ
ejpam-5565	303	16	variations	variation	NOUN
ejpam-5565	303	17	are	be	AUX
ejpam-5565	303	18	zero	zero	NUM
ejpam-5565	303	19	,	,	PUNCT
ejpam-5565	303	20	then	then	ADV
ejpam-5565	303	21	by	by	ADP
ejpam-5565	303	22	theorem	theorem	NOUN
ejpam-5565	303	23	10	10	NUM
ejpam-5565	303	24	f	f	NOUN
ejpam-5565	303	25	is	be	AUX
ejpam-5565	303	26	constant	constant	ADJ
ejpam-5565	303	27	in	in	ADP
ejpam-5565	303	28	k+	k+	NOUN
ejpam-5565	303	29	and	and	CCONJ
ejpam-5565	303	30	in	in	ADP
ejpam-5565	303	31	k−	k−	PROPN
ejpam-5565	303	32	,	,	PUNCT
ejpam-5565	303	33	so	so	SCONJ
ejpam-5565	303	34	there	there	PRON
ejpam-5565	303	35	exist	exist	VERB
ejpam-5565	303	36	c+	c+	X
ejpam-5565	303	37	∈	∈	NOUN
ejpam-5565	303	38	k+	k+	NOUN
ejpam-5565	303	39	and	and	CCONJ
ejpam-5565	303	40	c−	c−	NOUN
ejpam-5565	303	41	∈	∈	PROPN
ejpam-5565	303	42	k−	k−	PROPN
ejpam-5565	303	43	such	such	ADJ
ejpam-5565	303	44	that	that	SCONJ
ejpam-5565	303	45	:	:	PUNCT
ejpam-5565	303	46	f+(x	f+(x	X
ejpam-5565	303	47	)	)	PUNCT
ejpam-5565	303	48	=	=	SYM
ejpam-5565	303	49	c+	c+	NOUN
ejpam-5565	303	50	and	and	CCONJ
ejpam-5565	303	51	f−(x	f−(x	PROPN
ejpam-5565	303	52	)	)	PUNCT
ejpam-5565	303	53	=	=	SYM
ejpam-5565	303	54	c−	c−	PROPN
ejpam-5565	303	55	,	,	PUNCT
ejpam-5565	303	56	∀x	∀x	X
ejpam-5565	303	57	∈	∈	PROPN
ejpam-5565	304	1	[	[	X
ejpam-5565	304	2	a	a	X
ejpam-5565	304	3	,	,	PUNCT
ejpam-5565	304	4	b	b	NOUN
ejpam-5565	304	5	]	]	X
ejpam-5565	304	6	then	then	ADV
ejpam-5565	304	7	,	,	PUNCT
ejpam-5565	304	8	using	use	VERB
ejpam-5565	304	9	the	the	DET
ejpam-5565	304	10	above	above	NOUN
ejpam-5565	304	11	and	and	CCONJ
ejpam-5565	304	12	equation	equation	NOUN
ejpam-5565	304	13	2	2	NUM
ejpam-5565	304	14	it	it	PRON
ejpam-5565	304	15	follows	follow	VERB
ejpam-5565	304	16	that	that	SCONJ
ejpam-5565	304	17	:	:	PUNCT
ejpam-5565	304	18	∥f+(x)∥+	∥f+(x)∥+	PROPN
ejpam-5565	304	19	=	=	SYM
ejpam-5565	304	20	∥c+∥+	∥c+∥+	NUM
ejpam-5565	304	21	=	=	SYM
ejpam-5565	304	22	0	0	NUM
ejpam-5565	304	23	and	and	CCONJ
ejpam-5565	304	24	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	304	25	=	=	SYM
ejpam-5565	304	26	∥c−∥−	∥c−∥−	NOUN
ejpam-5565	304	27	=	=	SYM
ejpam-5565	304	28	0	0	NUM
ejpam-5565	305	1	it	it	PRON
ejpam-5565	305	2	implies	imply	VERB
ejpam-5565	305	3	that	that	SCONJ
ejpam-5565	305	4	c+	c+	VERB
ejpam-5565	305	5	=	=	SYM
ejpam-5565	305	6	0	0	NUM
ejpam-5565	305	7	and	and	CCONJ
ejpam-5565	305	8	c−	c−	NOUN
ejpam-5565	305	9	=	=	SYM
ejpam-5565	305	10	0	0	X
ejpam-5565	305	11	.	.	PUNCT
ejpam-5565	306	1	therefore	therefore	ADV
ejpam-5565	306	2	,	,	PUNCT
ejpam-5565	306	3	f(x	f(x	PROPN
ejpam-5565	306	4	)	)	PUNCT
ejpam-5565	306	5	=	=	PUNCT
ejpam-5565	306	6	0	0	PUNCT
ejpam-5565	307	1	+	+	CCONJ
ejpam-5565	307	2	0	0	NUM
ejpam-5565	307	3	=	=	SYM
ejpam-5565	307	4	0	0	NUM
ejpam-5565	307	5	for	for	ADP
ejpam-5565	307	6	all	all	DET
ejpam-5565	307	7	x	x	SYM
ejpam-5565	307	8	∈	∈	PROPN
ejpam-5565	307	9	[	[	X
ejpam-5565	307	10	a	a	X
ejpam-5565	307	11	,	,	PUNCT
ejpam-5565	307	12	b	b	NOUN
ejpam-5565	307	13	]	]	X
ejpam-5565	307	14	,	,	PUNCT
ejpam-5565	307	15	then	then	ADV
ejpam-5565	307	16	f	f	PROPN
ejpam-5565	307	17	is	be	AUX
ejpam-5565	307	18	the	the	DET
ejpam-5565	307	19	null	null	ADJ
ejpam-5565	307	20	function	function	NOUN
ejpam-5565	307	21	.	.	PUNCT
ejpam-5565	308	1	(	(	PUNCT
ejpam-5565	308	2	iii	iii	X
ejpam-5565	308	3	)	)	PUNCT
ejpam-5565	308	4	since	since	SCONJ
ejpam-5565	308	5	f	f	PROPN
ejpam-5565	308	6	∈	∈	PROPN
ejpam-5565	308	7	b	b	PROPN
ejpam-5565	308	8	q	q	X
ejpam-5565	308	9	v	v	PROPN
ejpam-5565	308	10	b	b	PROPN
ejpam-5565	308	11	a	a	DET
ejpam-5565	308	12	(	(	PUNCT
ejpam-5565	308	13	k	k	NOUN
ejpam-5565	308	14	,	,	PUNCT
ejpam-5565	308	15	[	[	X
ejpam-5565	308	16	·	·	PUNCT
ejpam-5565	308	17	,	,	PUNCT
ejpam-5565	308	18	·	·	PUNCT
ejpam-5565	308	19	]	]	PUNCT
ejpam-5565	308	20	)	)	PUNCT
ejpam-5565	308	21	and	and	CCONJ
ejpam-5565	308	22	λ	λ	X
ejpam-5565	308	23	∈	∈	PROPN
ejpam-5565	308	24	c	c	NOUN
ejpam-5565	308	25	,	,	PUNCT
ejpam-5565	308	26	using	use	VERB
ejpam-5565	308	27	(	(	PUNCT
ejpam-5565	308	28	i	i	NOUN
ejpam-5565	308	29	)	)	PUNCT
ejpam-5565	308	30	and	and	CCONJ
ejpam-5565	308	31	(	(	PUNCT
ejpam-5565	308	32	iii	iii	NOUN
ejpam-5565	308	33	)	)	PUNCT
ejpam-5565	308	34	of	of	ADP
ejpam-5565	308	35	the	the	DET
ejpam-5565	308	36	remark	remark	NOUN
ejpam-5565	308	37	4	4	NUM
ejpam-5565	308	38	,	,	PUNCT
ejpam-5565	308	39	then	then	ADV
ejpam-5565	308	40	∥λf∥	∥λf∥	PROPN
ejpam-5565	309	1	b	b	PROPN
ejpam-5565	309	2	q	q	X
ejpam-5565	309	3	v	v	PROPN
ejpam-5565	309	4	b	b	PROPN
ejpam-5565	309	5	a	a	PRON
ejpam-5565	309	6	(	(	PUNCT
ejpam-5565	309	7	k	k	NOUN
ejpam-5565	309	8	,	,	PUNCT
ejpam-5565	309	9	[	[	X
ejpam-5565	309	10	·	·	PUNCT
ejpam-5565	309	11	,	,	PUNCT
ejpam-5565	309	12	·	·	PUNCT
ejpam-5565	309	13	]	]	X
ejpam-5565	309	14	)	)	PUNCT
ejpam-5565	309	15	=	=	SYM
ejpam-5565	309	16	∥λf+(x)∥+	∥λf+(x)∥+	PROPN
ejpam-5565	309	17	+	+	CCONJ
ejpam-5565	309	18	∥λf−(x)∥−	∥λf−(x)∥−	NOUN
ejpam-5565	309	19	+	+	CCONJ
ejpam-5565	309	20	q+	q+	ADP
ejpam-5565	309	21	v	v	NOUN
ejpam-5565	309	22	b	b	NOUN
ejpam-5565	309	23	a	a	DET
ejpam-5565	309	24	(	(	PUNCT
ejpam-5565	309	25	λf	λf	PROPN
ejpam-5565	309	26	,	,	PUNCT
ejpam-5565	309	27	(	(	PUNCT
ejpam-5565	309	28	k+	k+	X
ejpam-5565	309	29	,	,	PUNCT
ejpam-5565	309	30	[	[	X
ejpam-5565	309	31	·	·	PUNCT
ejpam-5565	309	32	,	,	PUNCT
ejpam-5565	309	33	·	·	PUNCT
ejpam-5565	309	34	]	]	X
ejpam-5565	309	35	)	)	PUNCT
ejpam-5565	309	36	)	)	PUNCT
ejpam-5565	310	1	+	+	CCONJ
ejpam-5565	310	2	q−	q−	PROPN
ejpam-5565	310	3	v	v	NOUN
ejpam-5565	310	4	b	b	NOUN
ejpam-5565	310	5	a	a	DET
ejpam-5565	310	6	(	(	PUNCT
ejpam-5565	310	7	λf	λf	PROPN
ejpam-5565	310	8	,	,	PUNCT
ejpam-5565	310	9	(	(	PUNCT
ejpam-5565	310	10	k−,−	k−,−	NOUN
ejpam-5565	310	11	[	[	X
ejpam-5565	310	12	·	·	PUNCT
ejpam-5565	310	13	,	,	PUNCT
ejpam-5565	310	14	·	·	PUNCT
ejpam-5565	310	15	]	]	X
ejpam-5565	310	16	)	)	PUNCT
ejpam-5565	310	17	)	)	PUNCT
ejpam-5565	311	1	=	=	PUNCT
ejpam-5565	312	1	|λ|∥f+(x)∥+	|λ|∥f+(x)∥+	NUM
ejpam-5565	312	2	+	+	CCONJ
ejpam-5565	312	3	|λ|∥f−(x)∥−	|λ|∥f−(x)∥−	PROPN
ejpam-5565	312	4	+	+	NUM
ejpam-5565	312	5	|λ|	|λ|	PROPN
ejpam-5565	312	6	q+	q+	ADP
ejpam-5565	312	7	v	v	NOUN
ejpam-5565	312	8	b	b	NOUN
ejpam-5565	312	9	a	a	PRON
ejpam-5565	312	10	(	(	PUNCT
ejpam-5565	312	11	f	f	NOUN
ejpam-5565	312	12	,	,	PUNCT
ejpam-5565	312	13	(	(	PUNCT
ejpam-5565	312	14	k+	k+	X
ejpam-5565	312	15	,	,	PUNCT
ejpam-5565	312	16	[	[	X
ejpam-5565	312	17	·	·	PUNCT
ejpam-5565	312	18	,	,	PUNCT
ejpam-5565	312	19	·	·	PUNCT
ejpam-5565	312	20	]	]	X
ejpam-5565	312	21	)	)	PUNCT
ejpam-5565	312	22	)	)	PUNCT
ejpam-5565	313	1	+	+	CCONJ
ejpam-5565	313	2	|λ|	|λ|	NOUN
ejpam-5565	313	3	q−	q−	PROPN
ejpam-5565	313	4	v	v	NOUN
ejpam-5565	313	5	b	b	NOUN
ejpam-5565	313	6	a	a	DET
ejpam-5565	313	7	(	(	PUNCT
ejpam-5565	313	8	f	f	NOUN
ejpam-5565	313	9	,	,	PUNCT
ejpam-5565	313	10	(	(	PUNCT
ejpam-5565	313	11	k−,−	k−,−	NOUN
ejpam-5565	313	12	[	[	X
ejpam-5565	313	13	·	·	PUNCT
ejpam-5565	313	14	,	,	PUNCT
ejpam-5565	313	15	·	·	PUNCT
ejpam-5565	313	16	]	]	X
ejpam-5565	313	17	)	)	PUNCT
ejpam-5565	313	18	)	)	PUNCT
ejpam-5565	314	1	=	=	PUNCT
ejpam-5565	315	1	|λ|(∥f+(x)∥+	|λ|(∥f+(x)∥+	PUNCT
ejpam-5565	315	2	+	+	CCONJ
ejpam-5565	315	3	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	315	4	+	+	NUM
ejpam-5565	315	5	q+	q+	NUM
ejpam-5565	315	6	v	v	NOUN
ejpam-5565	315	7	b	b	NOUN
ejpam-5565	315	8	a	a	PRON
ejpam-5565	315	9	(	(	PUNCT
ejpam-5565	315	10	f	f	NOUN
ejpam-5565	315	11	,	,	PUNCT
ejpam-5565	315	12	(	(	PUNCT
ejpam-5565	315	13	k+	k+	X
ejpam-5565	315	14	,	,	PUNCT
ejpam-5565	315	15	[	[	X
ejpam-5565	315	16	·	·	PUNCT
ejpam-5565	315	17	,	,	PUNCT
ejpam-5565	315	18	·	·	PUNCT
ejpam-5565	315	19	]	]	X
ejpam-5565	315	20	)	)	PUNCT
ejpam-5565	315	21	)	)	PUNCT
ejpam-5565	316	1	+	+	CCONJ
ejpam-5565	316	2	q−	q−	PROPN
ejpam-5565	316	3	v	v	NOUN
ejpam-5565	316	4	b	b	NOUN
ejpam-5565	316	5	a	a	DET
ejpam-5565	316	6	(	(	PUNCT
ejpam-5565	316	7	f	f	NOUN
ejpam-5565	316	8	,	,	PUNCT
ejpam-5565	316	9	(	(	PUNCT
ejpam-5565	316	10	k−,−	k−,−	NOUN
ejpam-5565	316	11	[	[	X
ejpam-5565	316	12	·	·	PUNCT
ejpam-5565	316	13	,	,	PUNCT
ejpam-5565	316	14	·	·	PUNCT
ejpam-5565	316	15	]	]	X
ejpam-5565	316	16	)	)	PUNCT
ejpam-5565	316	17	)	)	PUNCT
ejpam-5565	316	18	)	)	PUNCT
ejpam-5565	317	1	=	=	PUNCT
ejpam-5565	318	1	|λ|∥f∥	|λ|∥f∥	NOUN
ejpam-5565	318	2	b	b	PROPN
ejpam-5565	318	3	q	q	X
ejpam-5565	318	4	v	v	PROPN
ejpam-5565	318	5	b	b	PROPN
ejpam-5565	318	6	a	a	PRON
ejpam-5565	318	7	(	(	PUNCT
ejpam-5565	318	8	k	k	NOUN
ejpam-5565	318	9	,	,	PUNCT
ejpam-5565	318	10	[	[	X
ejpam-5565	318	11	·	·	PUNCT
ejpam-5565	318	12	,	,	PUNCT
ejpam-5565	318	13	·	·	PUNCT
ejpam-5565	318	14	]	]	X
ejpam-5565	318	15	)	)	PUNCT
ejpam-5565	318	16	.	.	PUNCT
ejpam-5565	319	1	(	(	PUNCT
ejpam-5565	319	2	iv	iv	X
ejpam-5565	319	3	)	)	PUNCT
ejpam-5565	319	4	(	(	PUNCT
ejpam-5565	319	5	triangular	triangular	NOUN
ejpam-5565	319	6	inequality	inequality	NOUN
ejpam-5565	319	7	)	)	PUNCT
ejpam-5565	319	8	let	let	VERB
ejpam-5565	319	9	f	f	X
ejpam-5565	319	10	,	,	PUNCT
ejpam-5565	319	11	g	g	PROPN
ejpam-5565	319	12	∈	∈	PROPN
ejpam-5565	319	13	b	b	X
ejpam-5565	319	14	q	q	X
ejpam-5565	319	15	v	v	PROPN
ejpam-5565	319	16	b	b	PROPN
ejpam-5565	319	17	a	a	DET
ejpam-5565	319	18	(	(	PUNCT
ejpam-5565	319	19	k	k	NOUN
ejpam-5565	319	20	,	,	PUNCT
ejpam-5565	319	21	[	[	X
ejpam-5565	319	22	·	·	PUNCT
ejpam-5565	319	23	,	,	PUNCT
ejpam-5565	319	24	·	·	PUNCT
ejpam-5565	319	25	]	]	X
ejpam-5565	319	26	)	)	PUNCT
ejpam-5565	319	27	,	,	PUNCT
ejpam-5565	319	28	using	use	VERB
ejpam-5565	319	29	(	(	PUNCT
ejpam-5565	319	30	ii	ii	NOUN
ejpam-5565	319	31	)	)	PUNCT
ejpam-5565	319	32	and	and	CCONJ
ejpam-5565	319	33	(	(	PUNCT
ejpam-5565	319	34	iv	iv	X
ejpam-5565	319	35	)	)	PUNCT
ejpam-5565	319	36	of	of	ADP
ejpam-5565	319	37	the	the	DET
ejpam-5565	319	38	remark	remark	NOUN
ejpam-5565	319	39	4	4	NUM
ejpam-5565	319	40	,	,	PUNCT
ejpam-5565	319	41	it	it	PRON
ejpam-5565	319	42	follows	follow	VERB
ejpam-5565	319	43	that	that	SCONJ
ejpam-5565	319	44	:	:	PUNCT
ejpam-5565	320	1	∥f	∥f	PROPN
ejpam-5565	321	1	+	+	NUM
ejpam-5565	321	2	g∥	g∥	PROPN
ejpam-5565	321	3	b	b	PROPN
ejpam-5565	321	4	q	q	X
ejpam-5565	321	5	v	v	ADP
ejpam-5565	321	6	b	b	NOUN
ejpam-5565	321	7	a	a	PRON
ejpam-5565	321	8	(	(	PUNCT
ejpam-5565	321	9	k	k	NOUN
ejpam-5565	321	10	,	,	PUNCT
ejpam-5565	321	11	[	[	X
ejpam-5565	321	12	·	·	PUNCT
ejpam-5565	321	13	,	,	PUNCT
ejpam-5565	321	14	·	·	PUNCT
ejpam-5565	321	15	]	]	X
ejpam-5565	321	16	)	)	PUNCT
ejpam-5565	321	17	=	=	SYM
ejpam-5565	321	18	∥(f	∥(f	ADJ
ejpam-5565	321	19	+	+	CCONJ
ejpam-5565	321	20	g)+(x)∥+	g)+(x)∥+	ADJ
ejpam-5565	321	21	+	+	CCONJ
ejpam-5565	321	22	∥(f	∥(f	NOUN
ejpam-5565	321	23	+	+	CCONJ
ejpam-5565	321	24	g)−(x)∥−	g)−(x)∥−	NOUN
ejpam-5565	321	25	+	+	CCONJ
ejpam-5565	321	26	q+	q+	ADP
ejpam-5565	321	27	v	v	NOUN
ejpam-5565	321	28	b	b	NOUN
ejpam-5565	321	29	a	a	PRON
ejpam-5565	321	30	(	(	PUNCT
ejpam-5565	321	31	f	f	PROPN
ejpam-5565	321	32	+	+	CCONJ
ejpam-5565	321	33	g	g	PROPN
ejpam-5565	321	34	,	,	PUNCT
ejpam-5565	321	35	(	(	PUNCT
ejpam-5565	321	36	k+	k+	X
ejpam-5565	321	37	,	,	PUNCT
ejpam-5565	321	38	[	[	X
ejpam-5565	321	39	·	·	PUNCT
ejpam-5565	321	40	,	,	PUNCT
ejpam-5565	321	41	·	·	PUNCT
ejpam-5565	321	42	]	]	X
ejpam-5565	321	43	)	)	PUNCT
ejpam-5565	321	44	)	)	PUNCT
ejpam-5565	322	1	+	+	CCONJ
ejpam-5565	323	1	q−	q−	PROPN
ejpam-5565	323	2	v	v	NOUN
ejpam-5565	323	3	b	b	NOUN
ejpam-5565	323	4	a	a	PRON
ejpam-5565	323	5	(	(	PUNCT
ejpam-5565	323	6	f	f	PROPN
ejpam-5565	323	7	+	+	CCONJ
ejpam-5565	323	8	g	g	PROPN
ejpam-5565	323	9	,	,	PUNCT
ejpam-5565	323	10	(	(	PUNCT
ejpam-5565	323	11	k−,−	k−,−	NOUN
ejpam-5565	323	12	[	[	X
ejpam-5565	323	13	·	·	PUNCT
ejpam-5565	323	14	,	,	PUNCT
ejpam-5565	323	15	·	·	PUNCT
ejpam-5565	323	16	]	]	X
ejpam-5565	323	17	)	)	PUNCT
ejpam-5565	323	18	)	)	PUNCT
ejpam-5565	324	1	≤	≤	NUM
ejpam-5565	324	2	∥f+(x)∥+	∥f+(x)∥+	NOUN
ejpam-5565	324	3	+	+	CCONJ
ejpam-5565	324	4	∥g+(x)∥+	∥g+(x)∥+	NOUN
ejpam-5565	324	5	+	+	CCONJ
ejpam-5565	324	6	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	324	7	+	+	X
ejpam-5565	324	8	∥g−(x)∥−	∥g−(x)∥−	PRON
ejpam-5565	324	9	+	+	CCONJ
ejpam-5565	324	10	q+	q+	ADP
ejpam-5565	324	11	v	v	NOUN
ejpam-5565	324	12	b	b	NOUN
ejpam-5565	324	13	a	a	PRON
ejpam-5565	324	14	(	(	PUNCT
ejpam-5565	324	15	f	f	NOUN
ejpam-5565	324	16	,	,	PUNCT
ejpam-5565	324	17	(	(	PUNCT
ejpam-5565	324	18	k+	k+	X
ejpam-5565	324	19	,	,	PUNCT
ejpam-5565	324	20	[	[	X
ejpam-5565	324	21	·	·	PUNCT
ejpam-5565	324	22	,	,	PUNCT
ejpam-5565	324	23	·	·	PUNCT
ejpam-5565	324	24	]	]	X
ejpam-5565	324	25	)	)	PUNCT
ejpam-5565	324	26	)	)	PUNCT
ejpam-5565	325	1	+	+	CCONJ
ejpam-5565	325	2	q+	q+	ADP
ejpam-5565	325	3	v	v	NOUN
ejpam-5565	325	4	b	b	NOUN
ejpam-5565	325	5	a	a	DET
ejpam-5565	325	6	(	(	PUNCT
ejpam-5565	325	7	g	g	NOUN
ejpam-5565	325	8	,	,	PUNCT
ejpam-5565	325	9	(	(	PUNCT
ejpam-5565	325	10	k+	k+	X
ejpam-5565	325	11	,	,	PUNCT
ejpam-5565	325	12	[	[	X
ejpam-5565	325	13	·	·	PUNCT
ejpam-5565	325	14	,	,	PUNCT
ejpam-5565	325	15	·	·	PUNCT
ejpam-5565	325	16	]	]	X
ejpam-5565	325	17	)	)	PUNCT
ejpam-5565	325	18	)	)	PUNCT
ejpam-5565	326	1	+	+	CCONJ
ejpam-5565	326	2	q−	q−	PROPN
ejpam-5565	326	3	v	v	NOUN
ejpam-5565	326	4	b	b	NOUN
ejpam-5565	326	5	a	a	DET
ejpam-5565	326	6	(	(	PUNCT
ejpam-5565	326	7	f	f	NOUN
ejpam-5565	326	8	,	,	PUNCT
ejpam-5565	326	9	(	(	PUNCT
ejpam-5565	326	10	k−,−	k−,−	NOUN
ejpam-5565	326	11	[	[	X
ejpam-5565	326	12	·	·	PUNCT
ejpam-5565	326	13	,	,	PUNCT
ejpam-5565	326	14	·	·	PUNCT
ejpam-5565	326	15	]	]	X
ejpam-5565	326	16	)	)	PUNCT
ejpam-5565	326	17	)	)	PUNCT
ejpam-5565	327	1	+	+	CCONJ
ejpam-5565	327	2	q−	q−	PROPN
ejpam-5565	327	3	v	v	NOUN
ejpam-5565	327	4	b	b	NOUN
ejpam-5565	327	5	a	a	DET
ejpam-5565	327	6	(	(	PUNCT
ejpam-5565	327	7	g	g	NOUN
ejpam-5565	327	8	,	,	PUNCT
ejpam-5565	327	9	(	(	PUNCT
ejpam-5565	327	10	k−,−	k−,−	NOUN
ejpam-5565	327	11	[	[	X
ejpam-5565	327	12	·	·	PUNCT
ejpam-5565	327	13	,	,	PUNCT
ejpam-5565	327	14	·	·	PUNCT
ejpam-5565	327	15	]	]	X
ejpam-5565	327	16	)	)	PUNCT
ejpam-5565	327	17	)	)	PUNCT
ejpam-5565	328	1	=	=	SYM
ejpam-5565	328	2	∥f+(x)∥+	∥f+(x)∥+	X
ejpam-5565	328	3	+	+	CCONJ
ejpam-5565	328	4	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	328	5	+	+	NUM
ejpam-5565	328	6	q+	q+	NUM
ejpam-5565	328	7	v	v	NOUN
ejpam-5565	328	8	b	b	NOUN
ejpam-5565	328	9	a	a	PRON
ejpam-5565	328	10	(	(	PUNCT
ejpam-5565	328	11	f	f	NOUN
ejpam-5565	328	12	,	,	PUNCT
ejpam-5565	328	13	(	(	PUNCT
ejpam-5565	328	14	k+	k+	X
ejpam-5565	328	15	,	,	PUNCT
ejpam-5565	328	16	[	[	X
ejpam-5565	328	17	·	·	PUNCT
ejpam-5565	328	18	,	,	PUNCT
ejpam-5565	328	19	·	·	PUNCT
ejpam-5565	328	20	]	]	X
ejpam-5565	328	21	)	)	PUNCT
ejpam-5565	328	22	)	)	PUNCT
ejpam-5565	329	1	+	+	CCONJ
ejpam-5565	329	2	q−	q−	PROPN
ejpam-5565	329	3	v	v	NOUN
ejpam-5565	329	4	b	b	NOUN
ejpam-5565	329	5	a	a	DET
ejpam-5565	329	6	(	(	PUNCT
ejpam-5565	329	7	f	f	NOUN
ejpam-5565	329	8	,	,	PUNCT
ejpam-5565	329	9	(	(	PUNCT
ejpam-5565	329	10	k−,−	k−,−	NOUN
ejpam-5565	329	11	[	[	X
ejpam-5565	329	12	·	·	PUNCT
ejpam-5565	329	13	,	,	PUNCT
ejpam-5565	329	14	·	·	PUNCT
ejpam-5565	329	15	]	]	X
ejpam-5565	329	16	)	)	PUNCT
ejpam-5565	329	17	)	)	PUNCT
ejpam-5565	330	1	+	+	NUM
ejpam-5565	330	2	∥g+(x)∥++	∥g+(x)∥++	NOUN
ejpam-5565	330	3	∥g−(x)∥−	∥g−(x)∥−	NOUN
ejpam-5565	330	4	+	+	CCONJ
ejpam-5565	330	5	q+	q+	ADP
ejpam-5565	330	6	v	v	NOUN
ejpam-5565	330	7	b	b	NOUN
ejpam-5565	330	8	a	a	PRON
ejpam-5565	330	9	(	(	PUNCT
ejpam-5565	330	10	g	g	NOUN
ejpam-5565	330	11	,	,	PUNCT
ejpam-5565	330	12	(	(	PUNCT
ejpam-5565	330	13	k+	k+	X
ejpam-5565	330	14	,	,	PUNCT
ejpam-5565	330	15	[	[	X
ejpam-5565	330	16	·	·	PUNCT
ejpam-5565	330	17	,	,	PUNCT
ejpam-5565	330	18	·	·	PUNCT
ejpam-5565	330	19	]	]	X
ejpam-5565	330	20	)	)	PUNCT
ejpam-5565	330	21	)	)	PUNCT
ejpam-5565	331	1	+	+	CCONJ
ejpam-5565	331	2	q−	q−	PROPN
ejpam-5565	331	3	v	v	NOUN
ejpam-5565	331	4	b	b	NOUN
ejpam-5565	331	5	a	a	DET
ejpam-5565	331	6	(	(	PUNCT
ejpam-5565	331	7	g	g	NOUN
ejpam-5565	331	8	,	,	PUNCT
ejpam-5565	331	9	(	(	PUNCT
ejpam-5565	331	10	k−,−	k−,−	NOUN
ejpam-5565	331	11	[	[	X
ejpam-5565	331	12	·	·	PUNCT
ejpam-5565	331	13	,	,	PUNCT
ejpam-5565	331	14	·	·	PUNCT
ejpam-5565	331	15	]	]	X
ejpam-5565	331	16	)	)	PUNCT
ejpam-5565	331	17	)	)	PUNCT
ejpam-5565	332	1	=	=	PUNCT
ejpam-5565	332	2	∥f∥	∥f∥	NUM
ejpam-5565	332	3	b	b	X
ejpam-5565	332	4	q	q	X
ejpam-5565	332	5	v	v	PROPN
ejpam-5565	332	6	b	b	NOUN
ejpam-5565	332	7	a(k	a(k	PROPN
ejpam-5565	332	8	,	,	PUNCT
ejpam-5565	332	9	[	[	X
ejpam-5565	332	10	·	·	PUNCT
ejpam-5565	332	11	,	,	PUNCT
ejpam-5565	332	12	·	·	PUNCT
ejpam-5565	332	13	]	]	PUNCT
ejpam-5565	332	14	)	)	PUNCT
ejpam-5565	333	1	+	+	CCONJ
ejpam-5565	333	2	∥g∥	∥g∥	PROPN
ejpam-5565	333	3	b	b	X
ejpam-5565	333	4	q	q	X
ejpam-5565	333	5	v	v	PROPN
ejpam-5565	333	6	b	b	NOUN
ejpam-5565	333	7	a(k	a(k	PROPN
ejpam-5565	333	8	,	,	PUNCT
ejpam-5565	333	9	[	[	X
ejpam-5565	333	10	·	·	PUNCT
ejpam-5565	333	11	,	,	PUNCT
ejpam-5565	333	12	·	·	PUNCT
ejpam-5565	333	13	]	]	PUNCT
ejpam-5565	333	14	)	)	PUNCT
ejpam-5565	333	15	o.	o.	PROPN
ejpam-5565	333	16	ferrer	ferrer	PROPN
ejpam-5565	333	17	,	,	PUNCT
ejpam-5565	333	18	j.	j.	PROPN
ejpam-5565	333	19	naranjo	naranjo	PROPN
ejpam-5565	333	20	/	/	SYM
ejpam-5565	333	21	eur	eur	PROPN
ejpam-5565	333	22	.	.	PUNCT
ejpam-5565	334	1	j.	j.	PROPN
ejpam-5565	334	2	pure	pure	PROPN
ejpam-5565	334	3	appl	appl	PROPN
ejpam-5565	334	4	.	.	PROPN
ejpam-5565	334	5	math	math	PROPN
ejpam-5565	334	6	,	,	PUNCT
ejpam-5565	334	7	18	18	NUM
ejpam-5565	334	8	(	(	PUNCT
ejpam-5565	334	9	2	2	NUM
ejpam-5565	334	10	)	)	PUNCT
ejpam-5565	334	11	(	(	PUNCT
ejpam-5565	334	12	2025	2025	NUM
ejpam-5565	334	13	)	)	PUNCT
ejpam-5565	334	14	,	,	PUNCT
ejpam-5565	334	15	5565	5565	NUM
ejpam-5565	334	16	17	17	NUM
ejpam-5565	334	17	of	of	ADP
ejpam-5565	334	18	18	18	NUM
ejpam-5565	334	19	thus	thus	ADV
ejpam-5565	334	20	,	,	PUNCT
ejpam-5565	334	21	∥f∥	∥f∥	PROPN
ejpam-5565	334	22	b	b	PROPN
ejpam-5565	334	23	q	q	X
ejpam-5565	334	24	v	v	PROPN
ejpam-5565	334	25	b	b	PROPN
ejpam-5565	334	26	a	a	PRON
ejpam-5565	334	27	(	(	PUNCT
ejpam-5565	334	28	k	k	NOUN
ejpam-5565	334	29	,	,	PUNCT
ejpam-5565	334	30	[	[	X
ejpam-5565	334	31	·	·	PUNCT
ejpam-5565	334	32	,	,	PUNCT
ejpam-5565	334	33	·	·	PUNCT
ejpam-5565	334	34	]	]	X
ejpam-5565	334	35	)	)	PUNCT
ejpam-5565	335	1	=	=	SYM
ejpam-5565	335	2	∥f+(x)∥+	∥f+(x)∥+	X
ejpam-5565	335	3	+	+	CCONJ
ejpam-5565	335	4	∥f−(x)∥−	∥f−(x)∥−	X
ejpam-5565	335	5	+	+	NUM
ejpam-5565	335	6	q+	q+	NUM
ejpam-5565	335	7	v	v	NOUN
ejpam-5565	335	8	b	b	NOUN
ejpam-5565	335	9	a	a	PRON
ejpam-5565	335	10	(	(	PUNCT
ejpam-5565	335	11	f	f	NOUN
ejpam-5565	335	12	,	,	PUNCT
ejpam-5565	335	13	(	(	PUNCT
ejpam-5565	335	14	k+	k+	X
ejpam-5565	335	15	,	,	PUNCT
ejpam-5565	335	16	[	[	X
ejpam-5565	335	17	·	·	PUNCT
ejpam-5565	335	18	,	,	PUNCT
ejpam-5565	335	19	·	·	PUNCT
ejpam-5565	335	20	]	]	X
ejpam-5565	335	21	)	)	PUNCT
ejpam-5565	335	22	)	)	PUNCT
ejpam-5565	336	1	+	+	CCONJ
ejpam-5565	336	2	q−	q−	PROPN
ejpam-5565	336	3	v	v	NOUN
ejpam-5565	336	4	b	b	NOUN
ejpam-5565	336	5	a	a	DET
ejpam-5565	336	6	(	(	PUNCT
ejpam-5565	336	7	f	f	NOUN
ejpam-5565	336	8	,	,	PUNCT
ejpam-5565	336	9	(	(	PUNCT
ejpam-5565	336	10	k−,−	k−,−	NOUN
ejpam-5565	336	11	[	[	X
ejpam-5565	336	12	·	·	PUNCT
ejpam-5565	336	13	,	,	PUNCT
ejpam-5565	336	14	·	·	PUNCT
ejpam-5565	336	15	]	]	X
ejpam-5565	336	16	)	)	PUNCT
ejpam-5565	336	17	)	)	PUNCT
ejpam-5565	336	18	is	be	AUX
ejpam-5565	336	19	a	a	DET
ejpam-5565	336	20	norm	norm	NOUN
ejpam-5565	336	21	in	in	ADP
ejpam-5565	336	22	b	b	PROPN
ejpam-5565	336	23	q	q	X
ejpam-5565	336	24	v	v	PROPN
ejpam-5565	336	25	b	b	PROPN
ejpam-5565	336	26	a	a	DET
ejpam-5565	336	27	(	(	PUNCT
ejpam-5565	336	28	k	k	NOUN
ejpam-5565	336	29	,	,	PUNCT
ejpam-5565	336	30	[	[	X
ejpam-5565	336	31	·	·	PUNCT
ejpam-5565	336	32	,	,	PUNCT
ejpam-5565	336	33	·	·	PUNCT
ejpam-5565	336	34	]	]	X
ejpam-5565	336	35	)	)	PUNCT
ejpam-5565	336	36	.	.	PUNCT
ejpam-5565	337	1	6	6	X
ejpam-5565	337	2	.	.	X
ejpam-5565	337	3	conclusion	conclusion	NOUN
ejpam-5565	337	4	and	and	CCONJ
ejpam-5565	337	5	future	future	ADJ
ejpam-5565	337	6	work	work	NOUN
ejpam-5565	337	7	in	in	ADP
ejpam-5565	337	8	this	this	DET
ejpam-5565	337	9	study	study	NOUN
ejpam-5565	337	10	,	,	PUNCT
ejpam-5565	337	11	the	the	DET
ejpam-5565	337	12	concept	concept	NOUN
ejpam-5565	337	13	of	of	ADP
ejpam-5565	337	14	bounded	bounded	ADJ
ejpam-5565	337	15	qvariation	qvariation	NOUN
ejpam-5565	337	16	function	function	NOUN
ejpam-5565	337	17	in	in	ADP
ejpam-5565	337	18	krein	krein	ADJ
ejpam-5565	337	19	spaces	space	NOUN
ejpam-5565	337	20	was	be	AUX
ejpam-5565	337	21	defined	define	VERB
ejpam-5565	337	22	(	(	PUNCT
ejpam-5565	337	23	definition	definition	NOUN
ejpam-5565	337	24	7	7	NUM
ejpam-5565	337	25	)	)	PUNCT
ejpam-5565	337	26	and	and	CCONJ
ejpam-5565	337	27	exemplified	exemplify	VERB
ejpam-5565	337	28	(	(	PUNCT
ejpam-5565	337	29	example	example	NOUN
ejpam-5565	337	30	3	3	NUM
ejpam-5565	337	31	)	)	PUNCT
ejpam-5565	337	32	,	,	PUNCT
ejpam-5565	337	33	extending	extend	VERB
ejpam-5565	337	34	the	the	DET
ejpam-5565	337	35	existing	exist	VERB
ejpam-5565	337	36	notion	notion	NOUN
ejpam-5565	337	37	of	of	ADP
ejpam-5565	337	38	these	these	DET
ejpam-5565	337	39	functions	function	NOUN
ejpam-5565	337	40	in	in	ADP
ejpam-5565	337	41	hilbert	hilbert	PROPN
ejpam-5565	337	42	spaces	space	NOUN
ejpam-5565	337	43	.	.	PUNCT
ejpam-5565	338	1	classical	classical	ADJ
ejpam-5565	338	2	results	result	NOUN
ejpam-5565	338	3	were	be	AUX
ejpam-5565	338	4	extended	extend	VERB
ejpam-5565	338	5	(	(	PUNCT
ejpam-5565	338	6	theorem	theorem	VERB
ejpam-5565	338	7	6	6	NUM
ejpam-5565	338	8	,	,	PUNCT
ejpam-5565	338	9	theorem	theorem	VERB
ejpam-5565	338	10	7	7	NUM
ejpam-5565	338	11	,	,	PUNCT
ejpam-5565	338	12	theorem	theorem	ADJ
ejpam-5565	338	13	8	8	NUM
ejpam-5565	338	14	,	,	PUNCT
ejpam-5565	338	15	theorem	theorem	VERB
ejpam-5565	338	16	9	9	NUM
ejpam-5565	338	17	,	,	PUNCT
ejpam-5565	338	18	theorem	theorem	VERB
ejpam-5565	338	19	10	10	NUM
ejpam-5565	338	20	,	,	PUNCT
ejpam-5565	338	21	theorem	theorem	VERB
ejpam-5565	338	22	11	11	NUM
ejpam-5565	338	23	,	,	PUNCT
ejpam-5565	338	24	theorem	theorem	VERB
ejpam-5565	338	25	12	12	NUM
ejpam-5565	338	26	,	,	PUNCT
ejpam-5565	338	27	theorem	theorem	VERB
ejpam-5565	338	28	13	13	NUM
ejpam-5565	338	29	)	)	PUNCT
ejpam-5565	338	30	,	,	PUNCT
ejpam-5565	338	31	showing	show	VERB
ejpam-5565	338	32	the	the	DET
ejpam-5565	338	33	potential	potential	NOUN
ejpam-5565	338	34	that	that	SCONJ
ejpam-5565	338	35	this	this	DET
ejpam-5565	338	36	research	research	NOUN
ejpam-5565	338	37	has	have	VERB
ejpam-5565	338	38	for	for	ADP
ejpam-5565	338	39	further	further	ADJ
ejpam-5565	338	40	extensions	extension	NOUN
ejpam-5565	338	41	and	and	CCONJ
ejpam-5565	338	42	applications	application	NOUN
ejpam-5565	338	43	.	.	PUNCT
ejpam-5565	339	1	future	future	ADJ
ejpam-5565	339	2	research	research	NOUN
ejpam-5565	339	3	could	could	AUX
ejpam-5565	339	4	focus	focus	VERB
ejpam-5565	339	5	on	on	ADP
ejpam-5565	339	6	extending	extend	VERB
ejpam-5565	339	7	work	work	NOUN
ejpam-5565	339	8	presented	present	VERB
ejpam-5565	339	9	in	in	ADP
ejpam-5565	339	10	[	[	X
ejpam-5565	339	11	18	18	NUM
ejpam-5565	339	12	]	]	PUNCT
ejpam-5565	339	13	to	to	ADP
ejpam-5565	339	14	spaces	space	NOUN
ejpam-5565	339	15	with	with	ADP
ejpam-5565	339	16	indefinite	indefinite	ADJ
ejpam-5565	339	17	metrics	metric	NOUN
ejpam-5565	339	18	.	.	PUNCT
ejpam-5565	340	1	in	in	ADP
ejpam-5565	340	2	addition	addition	NOUN
ejpam-5565	340	3	,	,	PUNCT
ejpam-5565	340	4	investigate	investigate	VERB
ejpam-5565	340	5	the	the	DET
ejpam-5565	340	6	interaction	interaction	NOUN
ejpam-5565	340	7	between	between	ADP
ejpam-5565	340	8	bounded	bounded	ADJ
ejpam-5565	340	9	q	q	ADJ
ejpam-5565	340	10	-	-	PUNCT
ejpam-5565	340	11	variational	variational	ADJ
ejpam-5565	340	12	functions	function	NOUN
ejpam-5565	340	13	on	on	ADP
ejpam-5565	340	14	spaces	space	NOUN
ejpam-5565	340	15	with	with	ADP
ejpam-5565	340	16	indefinite	indefinite	ADJ
ejpam-5565	340	17	metrics	metric	NOUN
ejpam-5565	340	18	and	and	CCONJ
ejpam-5565	340	19	fixed	fix	VERB
ejpam-5565	340	20	point	point	NOUN
ejpam-5565	340	21	theory	theory	NOUN
ejpam-5565	340	22	.	.	PUNCT
ejpam-5565	341	1	knowing	know	VERB
ejpam-5565	341	2	the	the	DET
ejpam-5565	341	3	importance	importance	NOUN
ejpam-5565	341	4	of	of	ADP
ejpam-5565	341	5	spaces	space	NOUN
ejpam-5565	341	6	of	of	ADP
ejpam-5565	341	7	indefinite	indefinite	ADJ
ejpam-5565	341	8	metric	metric	ADJ
ejpam-5565	341	9	[	[	X
ejpam-5565	341	10	19	19	NUM
ejpam-5565	341	11	]	]	X
ejpam-5565	341	12	,	,	PUNCT
ejpam-5565	341	13	in	in	ADP
ejpam-5565	341	14	quantum	quantum	ADJ
ejpam-5565	341	15	mechanics	mechanic	NOUN
ejpam-5565	341	16	[	[	X
ejpam-5565	341	17	15	15	NUM
ejpam-5565	341	18	]	]	PUNCT
ejpam-5565	341	19	,	,	PUNCT
ejpam-5565	341	20	introducing	introduce	VERB
ejpam-5565	341	21	a	a	DET
ejpam-5565	341	22	q	q	NOUN
ejpam-5565	341	23	-	-	PUNCT
ejpam-5565	341	24	norm	norm	NOUN
ejpam-5565	341	25	(	(	PUNCT
ejpam-5565	341	26	theorem	theorem	NOUN
ejpam-5565	341	27	13	13	NUM
ejpam-5565	341	28	)	)	PUNCT
ejpam-5565	341	29	for	for	ADP
ejpam-5565	341	30	bounded	bounded	ADJ
ejpam-5565	341	31	variation	variation	NOUN
ejpam-5565	341	32	functions	function	NOUN
ejpam-5565	341	33	in	in	ADP
ejpam-5565	341	34	spaces	space	NOUN
ejpam-5565	341	35	with	with	ADP
ejpam-5565	341	36	an	an	DET
ejpam-5565	341	37	indefinite	indefinite	ADJ
ejpam-5565	341	38	metric	metric	NOUN
ejpam-5565	341	39	can	can	AUX
ejpam-5565	341	40	provide	provide	VERB
ejpam-5565	341	41	applications	application	NOUN
ejpam-5565	341	42	such	such	ADJ
ejpam-5565	341	43	as	as	ADP
ejpam-5565	341	44	those	those	PRON
ejpam-5565	341	45	given	give	VERB
ejpam-5565	341	46	in	in	ADP
ejpam-5565	341	47	which	which	PRON
ejpam-5565	341	48	gives	give	VERB
ejpam-5565	341	49	insight	insight	NOUN
ejpam-5565	341	50	into	into	ADP
ejpam-5565	341	51	the	the	DET
ejpam-5565	341	52	future	future	ADJ
ejpam-5565	341	53	impact	impact	NOUN
ejpam-5565	341	54	of	of	ADP
ejpam-5565	341	55	this	this	DET
ejpam-5565	341	56	work	work	NOUN
ejpam-5565	341	57	.	.	PUNCT
ejpam-5565	342	1	acknowledgements	acknowledgement	NOUN
ejpam-5565	342	2	the	the	DET
ejpam-5565	342	3	authors	author	NOUN
ejpam-5565	342	4	are	be	AUX
ejpam-5565	342	5	gratefully	gratefully	ADV
ejpam-5565	342	6	acknowledged	acknowledge	VERB
ejpam-5565	342	7	for	for	ADP
ejpam-5565	342	8	contributing	contribute	VERB
ejpam-5565	342	9	equally	equally	ADV
ejpam-5565	342	10	to	to	ADP
ejpam-5565	342	11	the	the	DET
ejpam-5565	342	12	manuscript	manuscript	NOUN
ejpam-5565	342	13	.	.	PUNCT
ejpam-5565	343	1	the	the	DET
ejpam-5565	343	2	authors	author	NOUN
ejpam-5565	343	3	thank	thank	VERB
ejpam-5565	343	4	the	the	DET
ejpam-5565	343	5	universities	university	NOUN
ejpam-5565	343	6	of	of	ADP
ejpam-5565	343	7	sucre	sucre	NOUN
ejpam-5565	343	8	and	and	CCONJ
ejpam-5565	343	9	pontificia	pontificia	PROPN
ejpam-5565	343	10	bolivariana	bolivariana	PROPN
ejpam-5565	343	11	for	for	ADP
ejpam-5565	343	12	their	their	PRON
ejpam-5565	343	13	support	support	NOUN
ejpam-5565	343	14	.	.	PUNCT
ejpam-5565	344	1	strong	strong	ADJ
ejpam-5565	344	2	thanks	thank	NOUN
ejpam-5565	344	3	are	be	AUX
ejpam-5565	344	4	also	also	ADV
ejpam-5565	344	5	due	due	ADJ
ejpam-5565	344	6	to	to	ADP
ejpam-5565	344	7	the	the	DET
ejpam-5565	344	8	editor	editor	NOUN
ejpam-5565	344	9	and	and	CCONJ
ejpam-5565	344	10	referees	referee	NOUN
ejpam-5565	344	11	of	of	ADP
ejpam-5565	344	12	the	the	DET
ejpam-5565	344	13	journal	journal	NOUN
ejpam-5565	344	14	for	for	ADP
ejpam-5565	344	15	their	their	PRON
ejpam-5565	344	16	helpful	helpful	ADJ
ejpam-5565	344	17	suggestions	suggestion	NOUN
ejpam-5565	344	18	that	that	PRON
ejpam-5565	344	19	allowed	allow	VERB
ejpam-5565	344	20	us	we	PRON
ejpam-5565	344	21	to	to	PART
ejpam-5565	344	22	improve	improve	VERB
ejpam-5565	344	23	this	this	DET
ejpam-5565	344	24	manuscript	manuscript	NOUN
ejpam-5565	344	25	.	.	PUNCT
ejpam-5565	345	1	conflict	conflict	NOUN
ejpam-5565	345	2	of	of	ADP
ejpam-5565	345	3	interest	interest	NOUN
ejpam-5565	345	4	the	the	DET
ejpam-5565	345	5	authors	author	NOUN
ejpam-5565	345	6	declare	declare	VERB
ejpam-5565	345	7	that	that	SCONJ
ejpam-5565	345	8	they	they	PRON
ejpam-5565	345	9	have	have	VERB
ejpam-5565	345	10	no	no	DET
ejpam-5565	345	11	conflict	conflict	NOUN
ejpam-5565	345	12	of	of	ADP
ejpam-5565	345	13	interest	interest	NOUN
ejpam-5565	345	14	in	in	ADP
ejpam-5565	345	15	this	this	DET
ejpam-5565	345	16	work	work	NOUN
ejpam-5565	345	17	.	.	PUNCT
ejpam-5565	346	1	references	reference	NOUN
ejpam-5565	346	2	[	[	X
ejpam-5565	346	3	1	1	X
ejpam-5565	346	4	]	]	X
ejpam-5565	346	5	v.	v.	PROPN
ejpam-5565	346	6	v.	v.	ADP
ejpam-5565	346	7	chistyakov	chistyakov	PROPN
ejpam-5565	346	8	.	.	PUNCT
ejpam-5565	347	1	on	on	ADP
ejpam-5565	347	2	mappings	mapping	NOUN
ejpam-5565	347	3	of	of	ADP
ejpam-5565	347	4	bounded	bounded	ADJ
ejpam-5565	347	5	variation	variation	NOUN
ejpam-5565	347	6	.	.	PUNCT
ejpam-5565	348	1	j	j	PROPN
ejpam-5565	348	2	dyn	dyn	PROPN
ejpam-5565	348	3	control	control	PROPN
ejpam-5565	348	4	syst	syst	PROPN
ejpam-5565	348	5	,	,	PUNCT
ejpam-5565	348	6	2:261–289	2:261–289	NUM
ejpam-5565	348	7	,	,	PUNCT
ejpam-5565	348	8	1997	1997	NUM
ejpam-5565	348	9	.	.	PUNCT
ejpam-5565	349	1	[	[	X
ejpam-5565	349	2	2	2	X
ejpam-5565	349	3	]	]	PUNCT
ejpam-5565	349	4	v.	v.	PROPN
ejpam-5565	349	5	v.	v.	ADP
ejpam-5565	349	6	chistyakov	chistyakov	PROPN
ejpam-5565	349	7	.	.	PUNCT
ejpam-5565	350	1	on	on	ADP
ejpam-5565	350	2	the	the	DET
ejpam-5565	350	3	theory	theory	NOUN
ejpam-5565	350	4	of	of	ADP
ejpam-5565	350	5	multivalued	multivalued	ADJ
ejpam-5565	350	6	mappings	mapping	NOUN
ejpam-5565	350	7	of	of	ADP
ejpam-5565	350	8	bounded	bounded	ADJ
ejpam-5565	350	9	variation	variation	NOUN
ejpam-5565	350	10	of	of	ADP
ejpam-5565	350	11	one	one	NUM
ejpam-5565	350	12	real	real	ADJ
ejpam-5565	350	13	variable	variable	NOUN
ejpam-5565	350	14	.	.	PUNCT
ejpam-5565	351	1	sb	sb	PROPN
ejpam-5565	351	2	math	math	PROPN
ejpam-5565	351	3	,	,	PUNCT
ejpam-5565	351	4	189:153–176	189:153–176	NUM
ejpam-5565	351	5	,	,	PUNCT
ejpam-5565	351	6	1998	1998	NUM
ejpam-5565	351	7	.	.	PUNCT
ejpam-5565	352	1	[	[	X
ejpam-5565	352	2	3	3	X
ejpam-5565	352	3	]	]	X
ejpam-5565	352	4	v.	v.	PROPN
ejpam-5565	352	5	v.	v.	ADP
ejpam-5565	352	6	chistyakov	chistyakov	PROPN
ejpam-5565	352	7	.	.	PUNCT
ejpam-5565	353	1	metric	metric	ADJ
ejpam-5565	353	2	-	-	PUNCT
ejpam-5565	353	3	valued	value	VERB
ejpam-5565	353	4	mappings	mapping	NOUN
ejpam-5565	353	5	of	of	ADP
ejpam-5565	353	6	bounded	bounded	ADJ
ejpam-5565	353	7	variation	variation	NOUN
ejpam-5565	353	8	.	.	PUNCT
ejpam-5565	354	1	j	j	PROPN
ejpam-5565	354	2	math	math	PROPN
ejpam-5565	354	3	sci	sci	PROPN
ejpam-5565	354	4	(	(	PUNCT
ejpam-5565	354	5	n.y	n.y	PROPN
ejpam-5565	354	6	.	.	PROPN
ejpam-5565	354	7	)	)	PUNCT
ejpam-5565	354	8	,	,	PUNCT
ejpam-5565	354	9	111:3387–3429	111:3387–3429	NOUN
ejpam-5565	354	10	,	,	PUNCT
ejpam-5565	354	11	2002	2002	NUM
ejpam-5565	354	12	.	.	PUNCT
ejpam-5565	355	1	[	[	X
ejpam-5565	355	2	4	4	X
ejpam-5565	355	3	]	]	X
ejpam-5565	355	4	o.	o.	PROPN
ejpam-5565	355	5	ferrer	ferrer	PROPN
ejpam-5565	355	6	,	,	PUNCT
ejpam-5565	355	7	j.	j.	PROPN
ejpam-5565	355	8	naranjo	naranjo	PROPN
ejpam-5565	355	9	,	,	PUNCT
ejpam-5565	355	10	and	and	CCONJ
ejpam-5565	355	11	c.	c.	PROPN
ejpam-5565	355	12	guzmán	guzmán	PROPN
ejpam-5565	355	13	.	.	PUNCT
ejpam-5565	356	1	strongly	strongly	ADV
ejpam-5565	356	2	bounded	bound	VERB
ejpam-5565	356	3	variation	variation	NOUN
ejpam-5565	356	4	in	in	ADP
ejpam-5565	356	5	krein	krein	PROPN
ejpam-5565	356	6	spaces	space	NOUN
ejpam-5565	356	7	.	.	PUNCT
ejpam-5565	357	1	journal	journal	NOUN
ejpam-5565	357	2	of	of	ADP
ejpam-5565	357	3	mathematics	mathematic	NOUN
ejpam-5565	357	4	and	and	CCONJ
ejpam-5565	357	5	computer	computer	NOUN
ejpam-5565	357	6	science	science	NOUN
ejpam-5565	357	7	,	,	PUNCT
ejpam-5565	357	8	36(2):237–250	36(2):237–250	PROPN
ejpam-5565	357	9	,	,	PUNCT
ejpam-5565	357	10	2024	2024	NUM
ejpam-5565	357	11	.	.	PUNCT
ejpam-5565	358	1	[	[	X
ejpam-5565	358	2	5	5	X
ejpam-5565	358	3	]	]	PUNCT
ejpam-5565	358	4	j.	j.	PROPN
ejpam-5565	358	5	cure	cure	PROPN
ejpam-5565	358	6	,	,	PUNCT
ejpam-5565	358	7	k.	k.	PROPN
ejpam-5565	358	8	ferrer	ferrer	PROPN
ejpam-5565	358	9	,	,	PUNCT
ejpam-5565	358	10	and	and	CCONJ
ejpam-5565	358	11	o.	o.	PROPN
ejpam-5565	358	12	ferrer	ferrer	PROPN
ejpam-5565	358	13	.	.	PUNCT
ejpam-5565	358	14	functions	function	NOUN
ejpam-5565	358	15	of	of	ADP
ejpam-5565	358	16	bounded	bounded	ADJ
ejpam-5565	358	17	(	(	PUNCT
ejpam-5565	358	18	2	2	NUM
ejpam-5565	358	19	,	,	PUNCT
ejpam-5565	358	20	k)-variation	k)-variation	NOUN
ejpam-5565	358	21	in	in	ADP
ejpam-5565	358	22	2	2	NUM
ejpam-5565	358	23	-	-	PUNCT
ejpam-5565	358	24	normed	norme	VERB
ejpam-5565	358	25	spaces	space	NOUN
ejpam-5565	358	26	.	.	PUNCT
ejpam-5565	359	1	aims	aim	VERB
ejpam-5565	359	2	mathematics	mathematic	NOUN
ejpam-5565	359	3	,	,	PUNCT
ejpam-5565	359	4	9(9):24166–24183	9(9):24166–24183	PROPN
ejpam-5565	359	5	,	,	PUNCT
ejpam-5565	359	6	2024	2024	NUM
ejpam-5565	359	7	.	.	PUNCT
ejpam-5565	360	1	o.	o.	PROPN
ejpam-5565	360	2	ferrer	ferrer	PROPN
ejpam-5565	360	3	,	,	PUNCT
ejpam-5565	360	4	j.	j.	PROPN
ejpam-5565	360	5	naranjo	naranjo	PROPN
ejpam-5565	360	6	/	/	SYM
ejpam-5565	360	7	eur	eur	PROPN
ejpam-5565	360	8	.	.	PUNCT
ejpam-5565	361	1	j.	j.	PROPN
ejpam-5565	361	2	pure	pure	PROPN
ejpam-5565	361	3	appl	appl	PROPN
ejpam-5565	361	4	.	.	PROPN
ejpam-5565	361	5	math	math	PROPN
ejpam-5565	361	6	,	,	PUNCT
ejpam-5565	361	7	18	18	NUM
ejpam-5565	361	8	(	(	PUNCT
ejpam-5565	361	9	2	2	NUM
ejpam-5565	361	10	)	)	PUNCT
ejpam-5565	361	11	(	(	PUNCT
ejpam-5565	361	12	2025	2025	NUM
ejpam-5565	361	13	)	)	PUNCT
ejpam-5565	361	14	,	,	PUNCT
ejpam-5565	361	15	5565	5565	NUM
ejpam-5565	361	16	18	18	NUM
ejpam-5565	361	17	of	of	ADP
ejpam-5565	361	18	18	18	NUM
ejpam-5565	361	19	[	[	SYM
ejpam-5565	361	20	6	6	NUM
ejpam-5565	361	21	]	]	PUNCT
ejpam-5565	361	22	j.	j.	PROPN
ejpam-5565	361	23	brokman	brokman	PROPN
ejpam-5565	361	24	,	,	PUNCT
ejpam-5565	361	25	m.	m.	NOUN
ejpam-5565	361	26	burger	burger	NOUN
ejpam-5565	361	27	,	,	PUNCT
ejpam-5565	361	28	and	and	CCONJ
ejpam-5565	361	29	g.	g.	PROPN
ejpam-5565	361	30	gilboa	gilboa	PROPN
ejpam-5565	361	31	.	.	PUNCT
ejpam-5565	362	1	spectral	spectral	ADJ
ejpam-5565	362	2	total	total	ADJ
ejpam-5565	362	3	-	-	PUNCT
ejpam-5565	362	4	variation	variation	NOUN
ejpam-5565	362	5	processing	processing	NOUN
ejpam-5565	362	6	of	of	ADP
ejpam-5565	362	7	shapestheory	shapestheory	NOUN
ejpam-5565	362	8	and	and	CCONJ
ejpam-5565	362	9	applications	application	NOUN
ejpam-5565	362	10	.	.	PUNCT
ejpam-5565	363	1	acm	acm	PROPN
ejpam-5565	363	2	transactions	transaction	NOUN
ejpam-5565	363	3	on	on	ADP
ejpam-5565	363	4	graphics	graphic	NOUN
ejpam-5565	363	5	,	,	PUNCT
ejpam-5565	363	6	43(2	43(2	NUM
ejpam-5565	363	7	)	)	PUNCT
ejpam-5565	363	8	,	,	PUNCT
ejpam-5565	363	9	2024	2024	NUM
ejpam-5565	363	10	.	.	PUNCT
ejpam-5565	364	1	[	[	X
ejpam-5565	364	2	7	7	X
ejpam-5565	364	3	]	]	X
ejpam-5565	364	4	m.	m.	NOUN
ejpam-5565	364	5	di	di	X
ejpam-5565	364	6	francesco	francesco	PROPN
ejpam-5565	364	7	.	.	PUNCT
ejpam-5565	365	1	functional	functional	ADJ
ejpam-5565	365	2	analysis	analysis	NOUN
ejpam-5565	365	3	in	in	ADP
ejpam-5565	365	4	applied	applied	ADJ
ejpam-5565	365	5	mathematics	mathematic	NOUN
ejpam-5565	365	6	and	and	CCONJ
ejpam-5565	365	7	engineering	engineering	NOUN
ejpam-5565	365	8	.	.	PUNCT
ejpam-5565	366	1	2019	2019	NUM
ejpam-5565	366	2	.	.	PUNCT
ejpam-5565	367	1	[	[	X
ejpam-5565	367	2	8	8	NUM
ejpam-5565	367	3	]	]	X
ejpam-5565	367	4	d.	d.	PROPN
ejpam-5565	367	5	bugajewska	bugajewska	PROPN
ejpam-5565	367	6	,	,	PUNCT
ejpam-5565	367	7	d.	d.	PROPN
ejpam-5565	367	8	bugajewski	bugajewski	PROPN
ejpam-5565	367	9	,	,	PUNCT
ejpam-5565	367	10	and	and	CCONJ
ejpam-5565	367	11	h.	h.	PROPN
ejpam-5565	367	12	hudzik	hudzik	PROPN
ejpam-5565	367	13	.	.	PUNCT
ejpam-5565	368	1	bvϕ-solutions	bvϕ-solution	NOUN
ejpam-5565	368	2	of	of	ADP
ejpam-5565	368	3	nonlinear	nonlinear	ADJ
ejpam-5565	368	4	integral	integral	ADJ
ejpam-5565	368	5	equations	equation	NOUN
ejpam-5565	368	6	.	.	PUNCT
ejpam-5565	369	1	journal	journal	PROPN
ejpam-5565	369	2	of	of	ADP
ejpam-5565	369	3	mathematical	mathematical	ADJ
ejpam-5565	369	4	analysis	analysis	NOUN
ejpam-5565	369	5	and	and	CCONJ
ejpam-5565	369	6	applications	application	NOUN
ejpam-5565	369	7	,	,	PUNCT
ejpam-5565	369	8	287(1):265–278	287(1):265–278	NUM
ejpam-5565	369	9	,	,	PUNCT
ejpam-5565	369	10	2003	2003	NUM
ejpam-5565	369	11	.	.	PUNCT
ejpam-5565	370	1	[	[	X
ejpam-5565	370	2	9	9	NUM
ejpam-5565	370	3	]	]	PUNCT
ejpam-5565	370	4	d.	d.	PROPN
ejpam-5565	370	5	bugajewska	bugajewska	PROPN
ejpam-5565	370	6	,	,	PUNCT
ejpam-5565	370	7	d.	d.	PROPN
ejpam-5565	370	8	bugajewski	bugajewski	PROPN
ejpam-5565	370	9	,	,	PUNCT
ejpam-5565	370	10	and	and	CCONJ
ejpam-5565	370	11	g.	g.	PROPN
ejpam-5565	370	12	lewicki	lewicki	PROPN
ejpam-5565	370	13	.	.	PUNCT
ejpam-5565	371	1	on	on	ADP
ejpam-5565	371	2	nonlinear	nonlinear	ADJ
ejpam-5565	371	3	integral	integral	ADJ
ejpam-5565	371	4	equations	equation	NOUN
ejpam-5565	371	5	in	in	ADP
ejpam-5565	371	6	the	the	DET
ejpam-5565	371	7	space	space	NOUN
ejpam-5565	371	8	of	of	ADP
ejpam-5565	371	9	functions	function	NOUN
ejpam-5565	371	10	of	of	ADP
ejpam-5565	371	11	bounded	bounded	ADJ
ejpam-5565	371	12	generalized	generalized	ADJ
ejpam-5565	371	13	ϕ-variation	ϕ-variation	NOUN
ejpam-5565	371	14	.	.	PUNCT
ejpam-5565	372	1	the	the	DET
ejpam-5565	372	2	journal	journal	NOUN
ejpam-5565	372	3	of	of	ADP
ejpam-5565	372	4	integral	integral	ADJ
ejpam-5565	372	5	equations	equation	NOUN
ejpam-5565	372	6	and	and	CCONJ
ejpam-5565	372	7	applications	application	NOUN
ejpam-5565	372	8	,	,	PUNCT
ejpam-5565	372	9	21(1):1–20	21(1):1–20	NUM
ejpam-5565	372	10	,	,	PUNCT
ejpam-5565	372	11	2009	2009	NUM
ejpam-5565	372	12	.	.	PUNCT
ejpam-5565	373	1	[	[	X
ejpam-5565	373	2	10	10	NUM
ejpam-5565	373	3	]	]	PUNCT
ejpam-5565	373	4	x.	x.	PROPN
ejpam-5565	373	5	xie	xie	PROPN
ejpam-5565	373	6	,	,	PUNCT
ejpam-5565	373	7	y.	y.	PROPN
ejpam-5565	373	8	liu	liu	PROPN
ejpam-5565	373	9	,	,	PUNCT
ejpam-5565	373	10	p.	p.	PROPN
ejpam-5565	373	11	li	li	PROPN
ejpam-5565	373	12	,	,	PUNCT
ejpam-5565	373	13	and	and	CCONJ
ejpam-5565	373	14	j.	j.	PROPN
ejpam-5565	373	15	huang	huang	PROPN
ejpam-5565	373	16	.	.	PUNCT
ejpam-5565	374	1	the	the	DET
ejpam-5565	374	2	bounded	bounded	ADJ
ejpam-5565	374	3	variation	variation	NOUN
ejpam-5565	374	4	capacity	capacity	NOUN
ejpam-5565	374	5	and	and	CCONJ
ejpam-5565	374	6	sobolev	sobolev	NOUN
ejpam-5565	374	7	-	-	PUNCT
ejpam-5565	374	8	type	type	NOUN
ejpam-5565	374	9	inequalities	inequality	NOUN
ejpam-5565	374	10	on	on	ADP
ejpam-5565	374	11	dirichlet	dirichlet	PROPN
ejpam-5565	374	12	spaces	space	NOUN
ejpam-5565	374	13	.	.	PUNCT
ejpam-5565	375	1	advances	advance	NOUN
ejpam-5565	375	2	in	in	ADP
ejpam-5565	375	3	nonlinear	nonlinear	ADJ
ejpam-5565	375	4	analysis	analysis	NOUN
ejpam-5565	375	5	,	,	PUNCT
ejpam-5565	375	6	13(1	13(1	NUM
ejpam-5565	375	7	)	)	PUNCT
ejpam-5565	375	8	,	,	PUNCT
ejpam-5565	375	9	2024	2024	NUM
ejpam-5565	375	10	.	.	PUNCT
ejpam-5565	376	1	[	[	X
ejpam-5565	376	2	11	11	NUM
ejpam-5565	376	3	]	]	PUNCT
ejpam-5565	376	4	t.	t.	PROPN
ejpam-5565	376	5	azizov	azizov	PROPN
ejpam-5565	376	6	and	and	CCONJ
ejpam-5565	376	7	i.	i.	PROPN
ejpam-5565	376	8	iokhvidov	iokhvidov	PROPN
ejpam-5565	376	9	.	.	PUNCT
ejpam-5565	377	1	linear	linear	PROPN
ejpam-5565	377	2	operators	operator	NOUN
ejpam-5565	377	3	in	in	ADP
ejpam-5565	377	4	spaces	space	NOUN
ejpam-5565	377	5	with	with	ADP
ejpam-5565	377	6	an	an	DET
ejpam-5565	377	7	indefinite	indefinite	ADJ
ejpam-5565	377	8	metric	metric	NOUN
ejpam-5565	377	9	.	.	PUNCT
ejpam-5565	378	1	john	john	PROPN
ejpam-5565	378	2	wiley	wiley	PROPN
ejpam-5565	378	3	and	and	CCONJ
ejpam-5565	378	4	sons	sons	PROPN
ejpam-5565	378	5	ltd	ltd	PROPN
ejpam-5565	378	6	,	,	PUNCT
ejpam-5565	378	7	chichester	chichester	PROPN
ejpam-5565	378	8	,	,	PUNCT
ejpam-5565	378	9	1989	1989	NUM
ejpam-5565	378	10	.	.	PUNCT
ejpam-5565	379	1	[	[	X
ejpam-5565	379	2	12	12	NUM
ejpam-5565	379	3	]	]	X
ejpam-5565	379	4	j.	j.	PROPN
ejpam-5565	379	5	bognar	bognar	PROPN
ejpam-5565	379	6	.	.	PUNCT
ejpam-5565	380	1	indefinite	indefinite	ADJ
ejpam-5565	380	2	inner	inner	ADJ
ejpam-5565	380	3	product	product	NOUN
ejpam-5565	380	4	spaces	space	NOUN
ejpam-5565	380	5	.	.	PUNCT
ejpam-5565	381	1	springer	springer	NOUN
ejpam-5565	381	2	,	,	PUNCT
ejpam-5565	381	3	berlin	berlin	PROPN
ejpam-5565	381	4	,	,	PUNCT
ejpam-5565	381	5	1974	1974	NUM
ejpam-5565	381	6	.	.	PUNCT
ejpam-5565	382	1	[	[	X
ejpam-5565	382	2	13	13	NUM
ejpam-5565	382	3	]	]	PUNCT
ejpam-5565	382	4	n.	n.	NOUN
ejpam-5565	382	5	weiner	weiner	NOUN
ejpam-5565	382	6	.	.	PUNCT
ejpam-5565	383	1	the	the	DET
ejpam-5565	383	2	quadratic	quadratic	ADJ
ejpam-5565	383	3	variation	variation	NOUN
ejpam-5565	383	4	of	of	ADP
ejpam-5565	383	5	function	function	NOUN
ejpam-5565	383	6	and	and	CCONJ
ejpam-5565	383	7	its	its	PRON
ejpam-5565	383	8	fourier	fourier	ADJ
ejpam-5565	383	9	coefficients	coefficient	NOUN
ejpam-5565	383	10	.	.	PUNCT
ejpam-5565	384	1	massachusett	massachusett	PROPN
ejpam-5565	384	2	j.	j.	PROPN
ejpam-5565	384	3	math	math	PROPN
ejpam-5565	384	4	.	.	PUNCT
ejpam-5565	385	1	phys	phy	NOUN
ejpam-5565	385	2	.	.	PUNCT
ejpam-5565	385	3	,	,	PUNCT
ejpam-5565	385	4	3:72–94	3:72–94	NUM
ejpam-5565	385	5	,	,	PUNCT
ejpam-5565	385	6	1924	1924	NUM
ejpam-5565	385	7	.	.	PUNCT
ejpam-5565	386	1	[	[	X
ejpam-5565	386	2	14	14	NUM
ejpam-5565	386	3	]	]	X
ejpam-5565	386	4	y.	y.	PROPN
ejpam-5565	386	5	abramovich	abramovich	PROPN
ejpam-5565	386	6	,	,	PUNCT
ejpam-5565	386	7	e.	e.	PROPN
ejpam-5565	386	8	avgerinos	avgerinos	PROPN
ejpam-5565	386	9	,	,	PUNCT
ejpam-5565	386	10	and	and	CCONJ
ejpam-5565	386	11	a.c	a.c	PROPN
ejpam-5565	386	12	.	.	PROPN
ejpam-5565	386	13	yannelis	yannelis	PROPN
ejpam-5565	386	14	.	.	PUNCT
ejpam-5565	387	1	functional	functional	ADJ
ejpam-5565	387	2	analysis	analysis	NOUN
ejpam-5565	387	3	and	and	CCONJ
ejpam-5565	387	4	economic	economic	ADJ
ejpam-5565	387	5	theory	theory	NOUN
ejpam-5565	387	6	.	.	PUNCT
ejpam-5565	388	1	springer	springer	NOUN
ejpam-5565	388	2	-	-	PUNCT
ejpam-5565	388	3	verlag	verlag	PROPN
ejpam-5565	388	4	,	,	PUNCT
ejpam-5565	388	5	berlin	berlin	PROPN
ejpam-5565	388	6	,	,	PUNCT
ejpam-5565	388	7	heidelberg	heidelberg	PROPN
ejpam-5565	388	8	,	,	PUNCT
ejpam-5565	388	9	1998	1998	NUM
ejpam-5565	388	10	.	.	PUNCT
ejpam-5565	389	1	[	[	X
ejpam-5565	389	2	15	15	NUM
ejpam-5565	389	3	]	]	X
ejpam-5565	389	4	p.	p.	NOUN
ejpam-5565	389	5	a.	a.	PROPN
ejpam-5565	389	6	m.	m.	PROPN
ejpam-5565	389	7	dirac	dirac	PROPN
ejpam-5565	389	8	.	.	PUNCT
ejpam-5565	390	1	the	the	DET
ejpam-5565	390	2	physical	physical	ADJ
ejpam-5565	390	3	interpretation	interpretation	NOUN
ejpam-5565	390	4	of	of	ADP
ejpam-5565	390	5	the	the	DET
ejpam-5565	390	6	quantum	quantum	NOUN
ejpam-5565	390	7	dynamics	dynamic	NOUN
ejpam-5565	390	8	.	.	PUNCT
ejpam-5565	391	1	proceedings	proceeding	NOUN
ejpam-5565	391	2	of	of	ADP
ejpam-5565	391	3	the	the	DET
ejpam-5565	391	4	royal	royal	ADJ
ejpam-5565	391	5	society	society	NOUN
ejpam-5565	391	6	of	of	ADP
ejpam-5565	391	7	london	london	PROPN
ejpam-5565	391	8	.	.	PUNCT
ejpam-5565	392	1	series	series	PROPN
ejpam-5565	392	2	a	a	PROPN
ejpam-5565	392	3	,	,	PUNCT
ejpam-5565	392	4	containing	contain	VERB
ejpam-5565	392	5	papers	paper	NOUN
ejpam-5565	392	6	of	of	ADP
ejpam-5565	392	7	a	a	DET
ejpam-5565	392	8	mathematical	mathematical	ADJ
ejpam-5565	392	9	and	and	CCONJ
ejpam-5565	392	10	physical	physical	ADJ
ejpam-5565	392	11	character	character	NOUN
ejpam-5565	392	12	,	,	PUNCT
ejpam-5565	392	13	113(765):621–641	113(765):621–641	NUM
ejpam-5565	392	14	,	,	PUNCT
ejpam-5565	392	15	1927	1927	NUM
ejpam-5565	392	16	.	.	PUNCT
ejpam-5565	393	1	[	[	X
ejpam-5565	393	2	16	16	NUM
ejpam-5565	393	3	]	]	X
ejpam-5565	393	4	j.	j.	PROPN
ejpam-5565	393	5	krvavych	krvavych	PROPN
ejpam-5565	393	6	.	.	PUNCT
ejpam-5565	394	1	stock	stock	NOUN
ejpam-5565	394	2	price	price	NOUN
ejpam-5565	394	3	modelling	modelling	NOUN
ejpam-5565	394	4	by	by	ADP
ejpam-5565	394	5	long	long	ADJ
ejpam-5565	394	6	-	-	PUNCT
ejpam-5565	394	7	memory	memory	NOUN
ejpam-5565	394	8	processes	process	NOUN
ejpam-5565	394	9	:	:	PUNCT
ejpam-5565	394	10	overview	overview	NOUN
ejpam-5565	394	11	of	of	ADP
ejpam-5565	394	12	the	the	DET
ejpam-5565	394	13	fractional	fractional	ADJ
ejpam-5565	394	14	brownian	brownian	ADJ
ejpam-5565	394	15	approach	approach	NOUN
ejpam-5565	394	16	.	.	PUNCT
ejpam-5565	395	1	in	in	ADP
ejpam-5565	395	2	actuarial	actuarial	ADJ
ejpam-5565	395	3	studies	study	NOUN
ejpam-5565	395	4	research	research	NOUN
ejpam-5565	395	5	symposium	symposium	NOUN
ejpam-5565	395	6	,	,	PUNCT
ejpam-5565	395	7	unsw	unsw	PROPN
ejpam-5565	395	8	,	,	PUNCT
ejpam-5565	395	9	nov	nov	PROPN
ejpam-5565	395	10	.	.	PROPN
ejpam-5565	395	11	,	,	PUNCT
ejpam-5565	395	12	2002	2002	NUM
ejpam-5565	395	13	.	.	PUNCT
ejpam-5565	396	1	[	[	X
ejpam-5565	396	2	17	17	NUM
ejpam-5565	396	3	]	]	PUNCT
ejpam-5565	396	4	s.	s.	PROPN
ejpam-5565	396	5	osher	osher	PROPN
ejpam-5565	396	6	,	,	PUNCT
ejpam-5565	396	7	a.	a.	NOUN
ejpam-5565	396	8	solé	solé	NOUN
ejpam-5565	396	9	,	,	PUNCT
ejpam-5565	396	10	and	and	CCONJ
ejpam-5565	396	11	l.	l.	PROPN
ejpam-5565	396	12	vese	vese	PROPN
ejpam-5565	396	13	.	.	PUNCT
ejpam-5565	397	1	image	image	NOUN
ejpam-5565	397	2	decomposition	decomposition	NOUN
ejpam-5565	397	3	,	,	PUNCT
ejpam-5565	397	4	image	image	NOUN
ejpam-5565	397	5	restoration	restoration	NOUN
ejpam-5565	397	6	,	,	PUNCT
ejpam-5565	397	7	and	and	CCONJ
ejpam-5565	397	8	texture	texture	NOUN
ejpam-5565	397	9	modeling	modeling	NOUN
ejpam-5565	397	10	using	use	VERB
ejpam-5565	397	11	total	total	ADJ
ejpam-5565	397	12	variation	variation	NOUN
ejpam-5565	397	13	minimization	minimization	NOUN
ejpam-5565	397	14	and	and	CCONJ
ejpam-5565	397	15	the	the	DET
ejpam-5565	397	16	h−1	h−1	PROPN
ejpam-5565	397	17	norm	norm	NOUN
ejpam-5565	397	18	.	.	PUNCT
ejpam-5565	398	1	icip	icip	PROPN
ejpam-5565	398	2	,	,	PUNCT
ejpam-5565	398	3	2003	2003	NUM
ejpam-5565	398	4	.	.	PUNCT
ejpam-5565	399	1	[	[	X
ejpam-5565	399	2	18	18	NUM
ejpam-5565	399	3	]	]	PUNCT
ejpam-5565	399	4	p.	p.	NOUN
ejpam-5565	399	5	debnath	debnath	NOUN
ejpam-5565	399	6	,	,	PUNCT
ejpam-5565	399	7	n.	n.	PROPN
ejpam-5565	399	8	konwar	konwar	PROPN
ejpam-5565	399	9	,	,	PUNCT
ejpam-5565	399	10	and	and	CCONJ
ejpam-5565	399	11	s.	s.	PROPN
ejpam-5565	399	12	radenović.	radenović.	PROPN
ejpam-5565	399	13	metric	metric	ADJ
ejpam-5565	399	14	fixed	fix	VERB
ejpam-5565	399	15	point	point	NOUN
ejpam-5565	399	16	theory	theory	NOUN
ejpam-5565	399	17	.	.	PUNCT
ejpam-5565	400	1	springer	springer	PROPN
ejpam-5565	400	2	,	,	PUNCT
ejpam-5565	400	3	singapore	singapore	PROPN
ejpam-5565	400	4	,	,	PUNCT
ejpam-5565	400	5	2021	2021	NUM
ejpam-5565	400	6	.	.	PUNCT
ejpam-5565	401	1	[	[	X
ejpam-5565	401	2	19	19	NUM
ejpam-5565	401	3	]	]	SYM
ejpam-5565	401	4	m.langer	m.langer	NOUN
ejpam-5565	401	5	and	and	CCONJ
ejpam-5565	401	6	a.	a.	NOUN
ejpam-5565	401	7	luger	luger	PROPN
ejpam-5565	401	8	.	.	PUNCT
ejpam-5565	402	1	on	on	ADP
ejpam-5565	402	2	norms	norm	NOUN
ejpam-5565	402	3	in	in	ADP
ejpam-5565	402	4	indefinite	indefinite	ADJ
ejpam-5565	402	5	inner	inner	ADJ
ejpam-5565	402	6	product	product	NOUN
ejpam-5565	402	7	spaces	space	VERB
ejpam-5565	402	8	.	.	PUNCT
ejpam-5565	403	1	in	in	ADP
ejpam-5565	403	2	:	:	PUNCT
ejpam-5565	403	3	recent	recent	ADJ
ejpam-5565	403	4	advances	advance	NOUN
ejpam-5565	403	5	in	in	ADP
ejpam-5565	403	6	operator	operator	NOUN
ejpam-5565	403	7	theory	theory	NOUN
ejpam-5565	403	8	in	in	ADP
ejpam-5565	403	9	hilbert	hilbert	PROPN
ejpam-5565	403	10	and	and	CCONJ
ejpam-5565	403	11	krein	krein	PROPN
ejpam-5565	403	12	spaces	space	NOUN
ejpam-5565	403	13	.	.	PUNCT
ejpam-5565	404	1	oper	oper	PROPN
ejpam-5565	404	2	.	.	PROPN
ejpam-5565	404	3	theory	theory	PROPN
ejpam-5565	404	4	adv	adv	PROPN
ejpam-5565	404	5	.	.	PUNCT
ejpam-5565	404	6	appl	appl	PROPN
ejpam-5565	404	7	,	,	PUNCT
ejpam-5565	404	8	2010	2010	NUM
ejpam-5565	404	9	.	.	PUNCT