id	sid	tid	token	lemma	pos
ejpam-6705	1	1	european	european	PROPN
ejpam-6705	1	2	journal	journal	PROPN
ejpam-6705	1	3	of	of	ADP
ejpam-6705	1	4	pure	pure	ADJ
ejpam-6705	1	5	and	and	CCONJ
ejpam-6705	1	6	applied	applied	ADJ
ejpam-6705	1	7	mathematics	mathematic	NOUN
ejpam-6705	1	8	2025	2025	NUM
ejpam-6705	1	9	,	,	PUNCT
ejpam-6705	1	10	vol	vol	NOUN
ejpam-6705	1	11	.	.	PROPN
ejpam-6705	1	12	18	18	NUM
ejpam-6705	1	13	,	,	PUNCT
ejpam-6705	1	14	issue	issue	NOUN
ejpam-6705	1	15	4	4	NUM
ejpam-6705	1	16	,	,	PUNCT
ejpam-6705	1	17	article	article	NOUN
ejpam-6705	1	18	number	number	NOUN
ejpam-6705	1	19	6705	6705	NUM
ejpam-6705	1	20	issn	issn	PROPN
ejpam-6705	1	21	1307	1307	NUM
ejpam-6705	1	22	-	-	SYM
ejpam-6705	1	23	5543	5543	NUM
ejpam-6705	1	24	–	–	PUNCT
ejpam-6705	1	25	ejpam.com	ejpam.com	X
ejpam-6705	1	26	published	publish	VERB
ejpam-6705	1	27	by	by	ADP
ejpam-6705	1	28	new	new	PROPN
ejpam-6705	1	29	york	york	PROPN
ejpam-6705	1	30	business	business	PROPN
ejpam-6705	1	31	global	global	PROPN
ejpam-6705	1	32	some	some	DET
ejpam-6705	1	33	fixed	fix	VERB
ejpam-6705	1	34	point	point	NOUN
ejpam-6705	1	35	results	result	NOUN
ejpam-6705	1	36	for	for	ADP
ejpam-6705	1	37	monotone	monotone	ADJ
ejpam-6705	1	38	multivalued	multivalued	ADJ
ejpam-6705	1	39	and	and	CCONJ
ejpam-6705	1	40	integral	integral	ADJ
ejpam-6705	1	41	type	type	NOUN
ejpam-6705	1	42	contractive	contractive	ADJ
ejpam-6705	1	43	mappings	mapping	NOUN
ejpam-6705	1	44	samina	samina	PROPN
ejpam-6705	1	45	batul1	batul1	PROPN
ejpam-6705	1	46	,	,	PUNCT
ejpam-6705	1	47	haitham	haitham	PROPN
ejpam-6705	1	48	qawaqneh2,∗	qawaqneh2,∗	PROPN
ejpam-6705	1	49	,	,	PUNCT
ejpam-6705	1	50	arbab	arbab	PROPN
ejpam-6705	1	51	sikandar1	sikandar1	PROPN
ejpam-6705	1	52	,	,	PUNCT
ejpam-6705	1	53	usman	usman	PROPN
ejpam-6705	1	54	shehzad1	shehzad1	PROPN
ejpam-6705	1	55	,	,	PUNCT
ejpam-6705	1	56	hassen	hassen	PROPN
ejpam-6705	1	57	aydi3,4	aydi3,4	PROPN
ejpam-6705	1	58	1	1	NUM
ejpam-6705	1	59	department	department	NOUN
ejpam-6705	1	60	of	of	ADP
ejpam-6705	1	61	mathematics	mathematic	NOUN
ejpam-6705	1	62	,	,	PUNCT
ejpam-6705	1	63	capital	capital	NOUN
ejpam-6705	1	64	university	university	PROPN
ejpam-6705	1	65	of	of	ADP
ejpam-6705	1	66	science	science	NOUN
ejpam-6705	1	67	and	and	CCONJ
ejpam-6705	1	68	technology	technology	NOUN
ejpam-6705	1	69	,	,	PUNCT
ejpam-6705	1	70	islamabad	islamabad	PROPN
ejpam-6705	1	71	,	,	PUNCT
ejpam-6705	1	72	pakistan	pakistan	PROPN
ejpam-6705	1	73	2	2	NUM
ejpam-6705	1	74	al	al	PROPN
ejpam-6705	1	75	-	-	PUNCT
ejpam-6705	1	76	zaytoonah	zaytoonah	PROPN
ejpam-6705	1	77	university	university	PROPN
ejpam-6705	1	78	of	of	ADP
ejpam-6705	1	79	jordan	jordan	PROPN
ejpam-6705	1	80	,	,	PUNCT
ejpam-6705	1	81	amman	amman	PROPN
ejpam-6705	1	82	11733	11733	NUM
ejpam-6705	1	83	,	,	PUNCT
ejpam-6705	1	84	jordan	jordan	PROPN
ejpam-6705	1	85	3	3	NUM
ejpam-6705	1	86	université	université	NOUN
ejpam-6705	1	87	de	de	X
ejpam-6705	1	88	sousse	sousse	PROPN
ejpam-6705	1	89	,	,	PUNCT
ejpam-6705	1	90	institut	institut	PROPN
ejpam-6705	1	91	supérieur	supérieur	PROPN
ejpam-6705	1	92	d’informatique	d’informatique	PROPN
ejpam-6705	1	93	et	et	NOUN
ejpam-6705	1	94	des	des	X
ejpam-6705	1	95	techniques	techniques	X
ejpam-6705	1	96	de	de	X
ejpam-6705	1	97	communication	communication	NOUN
ejpam-6705	1	98	,	,	PUNCT
ejpam-6705	1	99	sousse	sousse	PROPN
ejpam-6705	1	100	4000	4000	NUM
ejpam-6705	1	101	,	,	PUNCT
ejpam-6705	1	102	tunisia	tunisia	PROPN
ejpam-6705	1	103	4	4	NUM
ejpam-6705	1	104	department	department	NOUN
ejpam-6705	1	105	of	of	ADP
ejpam-6705	1	106	mathematics	mathematic	NOUN
ejpam-6705	1	107	,	,	PUNCT
ejpam-6705	1	108	sefako	sefako	VERB
ejpam-6705	1	109	makgatho	makgatho	PROPN
ejpam-6705	1	110	health	health	PROPN
ejpam-6705	1	111	sciences	sciences	PROPN
ejpam-6705	1	112	university	university	PROPN
ejpam-6705	1	113	,	,	PUNCT
ejpam-6705	1	114	ga	ga	PROPN
ejpam-6705	1	115	-	-	NOUN
ejpam-6705	1	116	rankuwa	rankuwa	PROPN
ejpam-6705	1	117	,	,	PUNCT
ejpam-6705	1	118	south	south	PROPN
ejpam-6705	1	119	africa	africa	PROPN
ejpam-6705	1	120	abstract	abstract	PROPN
ejpam-6705	1	121	.	.	PUNCT
ejpam-6705	2	1	this	this	DET
ejpam-6705	2	2	study	study	NOUN
ejpam-6705	2	3	focuses	focus	VERB
ejpam-6705	2	4	on	on	ADP
ejpam-6705	2	5	establishing	establish	VERB
ejpam-6705	2	6	fixed	fix	VERB
ejpam-6705	2	7	point	point	NOUN
ejpam-6705	2	8	results	result	NOUN
ejpam-6705	2	9	for	for	ADP
ejpam-6705	2	10	monotone	monotone	ADJ
ejpam-6705	2	11	multivalued	multivalue	VERB
ejpam-6705	2	12	mappings	mapping	NOUN
ejpam-6705	2	13	within	within	ADP
ejpam-6705	2	14	the	the	DET
ejpam-6705	2	15	framework	framework	NOUN
ejpam-6705	2	16	of	of	ADP
ejpam-6705	2	17	partially	partially	ADV
ejpam-6705	2	18	ordered	order	VERB
ejpam-6705	2	19	complete	complete	ADJ
ejpam-6705	2	20	gb	gb	ADV
ejpam-6705	2	21	-	-	PUNCT
ejpam-6705	2	22	metric	metric	ADJ
ejpam-6705	2	23	spaces	space	NOUN
ejpam-6705	2	24	.	.	PUNCT
ejpam-6705	3	1	the	the	DET
ejpam-6705	3	2	partial	partial	ADJ
ejpam-6705	3	3	order	order	NOUN
ejpam-6705	3	4	on	on	ADP
ejpam-6705	3	5	the	the	DET
ejpam-6705	3	6	set	set	NOUN
ejpam-6705	3	7	(	(	PUNCT
ejpam-6705	3	8	x	x	INTJ
ejpam-6705	3	9	,	,	PUNCT
ejpam-6705	3	10	≼	≼	PROPN
ejpam-6705	3	11	)	)	PUNCT
ejpam-6705	3	12	is	be	AUX
ejpam-6705	3	13	defined	define	VERB
ejpam-6705	3	14	through	through	ADP
ejpam-6705	3	15	a	a	DET
ejpam-6705	3	16	functional	functional	ADJ
ejpam-6705	3	17	pair	pair	NOUN
ejpam-6705	3	18	(	(	PUNCT
ejpam-6705	3	19	κ	κ	NOUN
ejpam-6705	3	20	,	,	PUNCT
ejpam-6705	3	21	θ	θ	NOUN
ejpam-6705	3	22	)	)	PUNCT
ejpam-6705	3	23	.	.	PUNCT
ejpam-6705	4	1	the	the	DET
ejpam-6705	4	2	research	research	NOUN
ejpam-6705	4	3	further	far	ADV
ejpam-6705	4	4	explores	explore	VERB
ejpam-6705	4	5	conditions	condition	NOUN
ejpam-6705	4	6	under	under	ADP
ejpam-6705	4	7	which	which	PRON
ejpam-6705	4	8	coupled	couple	VERB
ejpam-6705	4	9	fixed	fix	VERB
ejpam-6705	4	10	points	point	NOUN
ejpam-6705	4	11	exist	exist	VERB
ejpam-6705	4	12	and	and	CCONJ
ejpam-6705	4	13	are	be	AUX
ejpam-6705	4	14	unique	unique	ADJ
ejpam-6705	4	15	,	,	PUNCT
ejpam-6705	4	16	particularly	particularly	ADV
ejpam-6705	4	17	for	for	ADP
ejpam-6705	4	18	mappings	mapping	NOUN
ejpam-6705	4	19	that	that	PRON
ejpam-6705	4	20	meet	meet	VERB
ejpam-6705	4	21	certain	certain	ADJ
ejpam-6705	4	22	contractive	contractive	ADJ
ejpam-6705	4	23	requirements	requirement	NOUN
ejpam-6705	4	24	.	.	PUNCT
ejpam-6705	5	1	these	these	DET
ejpam-6705	5	2	investigations	investigation	NOUN
ejpam-6705	5	3	are	be	AUX
ejpam-6705	5	4	carried	carry	VERB
ejpam-6705	5	5	out	out	ADP
ejpam-6705	5	6	using	use	VERB
ejpam-6705	5	7	the	the	DET
ejpam-6705	5	8	notion	notion	NOUN
ejpam-6705	5	9	of	of	ADP
ejpam-6705	5	10	integral	integral	ADJ
ejpam-6705	5	11	-	-	PUNCT
ejpam-6705	5	12	type	type	NOUN
ejpam-6705	5	13	contractions	contraction	NOUN
ejpam-6705	5	14	tailored	tailor	VERB
ejpam-6705	5	15	to	to	ADP
ejpam-6705	5	16	the	the	DET
ejpam-6705	5	17	structure	structure	NOUN
ejpam-6705	5	18	of	of	ADP
ejpam-6705	5	19	partially	partially	ADV
ejpam-6705	5	20	ordered	order	VERB
ejpam-6705	5	21	gb	gb	ADV
ejpam-6705	5	22	-	-	PUNCT
ejpam-6705	5	23	metric	metric	ADJ
ejpam-6705	5	24	spaces	space	NOUN
ejpam-6705	5	25	.	.	PUNCT
ejpam-6705	6	1	in	in	ADP
ejpam-6705	6	2	addition	addition	NOUN
ejpam-6705	6	3	to	to	ADP
ejpam-6705	6	4	the	the	DET
ejpam-6705	6	5	core	core	NOUN
ejpam-6705	6	6	results	result	NOUN
ejpam-6705	6	7	,	,	PUNCT
ejpam-6705	6	8	several	several	ADJ
ejpam-6705	6	9	corollaries	corollary	NOUN
ejpam-6705	6	10	are	be	AUX
ejpam-6705	6	11	derived	derive	VERB
ejpam-6705	6	12	as	as	ADP
ejpam-6705	6	13	specific	specific	ADJ
ejpam-6705	6	14	instances	instance	NOUN
ejpam-6705	6	15	.	.	PUNCT
ejpam-6705	7	1	to	to	PART
ejpam-6705	7	2	enhance	enhance	VERB
ejpam-6705	7	3	the	the	DET
ejpam-6705	7	4	reliability	reliability	NOUN
ejpam-6705	7	5	and	and	CCONJ
ejpam-6705	7	6	relevance	relevance	NOUN
ejpam-6705	7	7	of	of	ADP
ejpam-6705	7	8	the	the	DET
ejpam-6705	7	9	findings	finding	NOUN
ejpam-6705	7	10	,	,	PUNCT
ejpam-6705	7	11	the	the	DET
ejpam-6705	7	12	paper	paper	NOUN
ejpam-6705	7	13	includes	include	VERB
ejpam-6705	7	14	a	a	DET
ejpam-6705	7	15	number	number	NOUN
ejpam-6705	7	16	of	of	ADP
ejpam-6705	7	17	illustrative	illustrative	ADJ
ejpam-6705	7	18	examples	example	NOUN
ejpam-6705	7	19	.	.	PUNCT
ejpam-6705	8	1	2020	2020	NUM
ejpam-6705	8	2	mathematics	mathematic	NOUN
ejpam-6705	8	3	subject	subject	NOUN
ejpam-6705	8	4	classifications	classification	NOUN
ejpam-6705	8	5	:	:	PUNCT
ejpam-6705	8	6	47h10	47h10	NUM
ejpam-6705	8	7	,	,	PUNCT
ejpam-6705	8	8	54h25	54h25	NUM
ejpam-6705	8	9	,	,	PUNCT
ejpam-6705	8	10	54c60	54c60	NUM
ejpam-6705	8	11	key	key	ADJ
ejpam-6705	8	12	words	word	NOUN
ejpam-6705	8	13	and	and	CCONJ
ejpam-6705	8	14	phrases	phrase	NOUN
ejpam-6705	8	15	:	:	PUNCT
ejpam-6705	8	16	fixed	fixed	ADJ
ejpam-6705	8	17	point	point	NOUN
ejpam-6705	8	18	,	,	PUNCT
ejpam-6705	8	19	gb	gb	NOUN
ejpam-6705	8	20	-	-	PUNCT
ejpam-6705	8	21	metric	metric	ADJ
ejpam-6705	8	22	space	space	NOUN
ejpam-6705	8	23	,	,	PUNCT
ejpam-6705	8	24	monotone	monotone	ADJ
ejpam-6705	8	25	multivalued	multivalue	VERB
ejpam-6705	8	26	functions	function	NOUN
ejpam-6705	8	27	1	1	NUM
ejpam-6705	8	28	.	.	PUNCT
ejpam-6705	8	29	introduction	introduction	NOUN
ejpam-6705	8	30	the	the	DET
ejpam-6705	8	31	concept	concept	NOUN
ejpam-6705	8	32	of	of	ADP
ejpam-6705	8	33	a	a	DET
ejpam-6705	8	34	metric	metric	ADJ
ejpam-6705	8	35	space	space	NOUN
ejpam-6705	8	36	was	be	AUX
ejpam-6705	8	37	first	first	ADV
ejpam-6705	8	38	introduced	introduce	VERB
ejpam-6705	8	39	by	by	ADP
ejpam-6705	8	40	fréchet	fréchet	NOUN
ejpam-6705	9	1	[	[	X
ejpam-6705	9	2	1	1	X
ejpam-6705	9	3	]	]	PUNCT
ejpam-6705	9	4	in	in	ADP
ejpam-6705	9	5	1906	1906	NUM
ejpam-6705	9	6	,	,	PUNCT
ejpam-6705	9	7	and	and	CCONJ
ejpam-6705	9	8	later	later	ADV
ejpam-6705	9	9	extended	extend	VERB
ejpam-6705	9	10	by	by	ADP
ejpam-6705	9	11	his	his	PRON
ejpam-6705	9	12	student	student	NOUN
ejpam-6705	9	13	kurepa	kurepa	NOUN
ejpam-6705	10	1	[	[	X
ejpam-6705	10	2	2	2	NUM
ejpam-6705	10	3	]	]	PUNCT
ejpam-6705	10	4	in	in	ADP
ejpam-6705	10	5	1934	1934	NUM
ejpam-6705	10	6	to	to	ADP
ejpam-6705	10	7	more	more	ADJ
ejpam-6705	10	8	abstract	abstract	ADJ
ejpam-6705	10	9	spaces	space	NOUN
ejpam-6705	10	10	where	where	SCONJ
ejpam-6705	10	11	the	the	DET
ejpam-6705	10	12	metric	metric	NOUN
ejpam-6705	10	13	takes	take	VERB
ejpam-6705	10	14	values	value	NOUN
ejpam-6705	10	15	in	in	ADP
ejpam-6705	10	16	an	an	DET
ejpam-6705	10	17	ordered	order	VERB
ejpam-6705	10	18	vector	vector	NOUN
ejpam-6705	10	19	space	space	NOUN
ejpam-6705	10	20	.	.	PUNCT
ejpam-6705	11	1	consider	consider	VERB
ejpam-6705	11	2	a	a	DET
ejpam-6705	11	3	complete	complete	ADJ
ejpam-6705	11	4	metric	metric	ADJ
ejpam-6705	11	5	space	space	NOUN
ejpam-6705	11	6	(	(	PUNCT
ejpam-6705	11	7	x	x	NOUN
ejpam-6705	11	8	,	,	PUNCT
ejpam-6705	11	9	d	d	NOUN
ejpam-6705	11	10	)	)	PUNCT
ejpam-6705	11	11	.	.	PUNCT
ejpam-6705	12	1	a	a	DET
ejpam-6705	12	2	mapping	mapping	NOUN
ejpam-6705	12	3	t	t	NOUN
ejpam-6705	12	4	:	:	PUNCT
ejpam-6705	12	5	x	x	X
ejpam-6705	12	6	→	→	PUNCT
ejpam-6705	12	7	x	x	X
ejpam-6705	12	8	is	be	AUX
ejpam-6705	12	9	said	say	VERB
ejpam-6705	12	10	to	to	PART
ejpam-6705	12	11	be	be	AUX
ejpam-6705	12	12	a	a	DET
ejpam-6705	12	13	contraction	contraction	NOUN
ejpam-6705	12	14	if	if	SCONJ
ejpam-6705	12	15	d(t	d(t	PROPN
ejpam-6705	12	16	(	(	PUNCT
ejpam-6705	12	17	u),t	u),t	PROPN
ejpam-6705	12	18	(	(	PUNCT
ejpam-6705	12	19	v	v	NOUN
ejpam-6705	12	20	)	)	PUNCT
ejpam-6705	12	21	)	)	PUNCT
ejpam-6705	12	22	≤	≤	NUM
ejpam-6705	12	23	α	α	PROPN
ejpam-6705	12	24	d(u	d(u	PROPN
ejpam-6705	12	25	,	,	PUNCT
ejpam-6705	12	26	v	v	NOUN
ejpam-6705	12	27	)	)	PUNCT
ejpam-6705	12	28	for	for	ADP
ejpam-6705	12	29	all	all	DET
ejpam-6705	12	30	u	u	NOUN
ejpam-6705	12	31	,	,	PUNCT
ejpam-6705	12	32	v	v	NOUN
ejpam-6705	12	33	∈	∈	PROPN
ejpam-6705	12	34	x	x	X
ejpam-6705	12	35	,	,	PUNCT
ejpam-6705	12	36	∗corresponding	∗corresponde	VERB
ejpam-6705	12	37	author	author	NOUN
ejpam-6705	12	38	.	.	PUNCT
ejpam-6705	13	1	doi	doi	NOUN
ejpam-6705	13	2	:	:	PUNCT
ejpam-6705	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6705	https://doi.org/10.29020/nybg.ejpam.v18i4.6705	X
ejpam-6705	13	4	email	email	NOUN
ejpam-6705	13	5	addresses	address	NOUN
ejpam-6705	13	6	:	:	PUNCT
ejpam-6705	13	7	samina.batul@cust.edu.pk	samina.batul@cust.edu.pk	PROPN
ejpam-6705	13	8	(	(	PUNCT
ejpam-6705	13	9	s.	s.	PROPN
ejpam-6705	13	10	batul	batul	PROPN
ejpam-6705	13	11	)	)	PUNCT
ejpam-6705	13	12	,	,	PUNCT
ejpam-6705	13	13	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6705	13	14	(	(	PUNCT
ejpam-6705	13	15	h.	h.	PROPN
ejpam-6705	13	16	qawaqneh	qawaqneh	PROPN
ejpam-6705	13	17	)	)	PUNCT
ejpam-6705	13	18	,	,	PUNCT
ejpam-6705	13	19	arbabsikandar873@gmail.com	arbabsikandar873@gmail.com	X
ejpam-6705	13	20	(	(	PUNCT
ejpam-6705	13	21	a.	a.	PROPN
ejpam-6705	13	22	sikandar	sikandar	PROPN
ejpam-6705	13	23	)	)	PUNCT
ejpam-6705	13	24	,	,	PUNCT
ejpam-6705	13	25	dmt211001@cust.pk	dmt211001@cust.pk	PROPN
ejpam-6705	13	26	(	(	PUNCT
ejpam-6705	13	27	u.	u.	PROPN
ejpam-6705	13	28	shehzad	shehzad	PROPN
ejpam-6705	13	29	)	)	PUNCT
ejpam-6705	13	30	,	,	PUNCT
ejpam-6705	14	1	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-6705	14	2	(	(	PUNCT
ejpam-6705	14	3	h.	h.	PROPN
ejpam-6705	14	4	aydi	aydi	ADJ
ejpam-6705	14	5	)	)	PUNCT
ejpam-6705	14	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6705	14	7	1	1	NUM
ejpam-6705	14	8	copyright	copyright	NOUN
ejpam-6705	14	9	:	:	PUNCT
ejpam-6705	14	10	©	©	PROPN
ejpam-6705	14	11	2025	2025	NUM
ejpam-6705	14	12	the	the	DET
ejpam-6705	14	13	author(s	author(s	NOUN
ejpam-6705	14	14	)	)	PUNCT
ejpam-6705	14	15	.	.	PUNCT
ejpam-6705	15	1	(	(	PUNCT
ejpam-6705	15	2	cc	cc	NOUN
ejpam-6705	15	3	by	by	ADP
ejpam-6705	15	4	-	-	PUNCT
ejpam-6705	15	5	nc	nc	PROPN
ejpam-6705	15	6	4.0	4.0	NUM
ejpam-6705	15	7	)	)	PUNCT
ejpam-6705	15	8	s.	s.	PROPN
ejpam-6705	15	9	batul	batul	PROPN
ejpam-6705	15	10	et	et	PROPN
ejpam-6705	15	11	al	al	PROPN
ejpam-6705	15	12	.	.	PUNCT
ejpam-6705	15	13	/	/	SYM
ejpam-6705	15	14	eur	eur	PROPN
ejpam-6705	15	15	.	.	PUNCT
ejpam-6705	16	1	j.	j.	PROPN
ejpam-6705	16	2	pure	pure	PROPN
ejpam-6705	16	3	appl	appl	PROPN
ejpam-6705	16	4	.	.	PROPN
ejpam-6705	16	5	math	math	PROPN
ejpam-6705	16	6	,	,	PUNCT
ejpam-6705	16	7	18	18	NUM
ejpam-6705	16	8	(	(	PUNCT
ejpam-6705	16	9	4	4	NUM
ejpam-6705	16	10	)	)	PUNCT
ejpam-6705	16	11	(	(	PUNCT
ejpam-6705	16	12	2025	2025	NUM
ejpam-6705	16	13	)	)	PUNCT
ejpam-6705	16	14	,	,	PUNCT
ejpam-6705	16	15	6705	6705	NUM
ejpam-6705	16	16	2	2	NUM
ejpam-6705	16	17	of	of	ADP
ejpam-6705	16	18	23	23	NUM
ejpam-6705	16	19	where	where	SCONJ
ejpam-6705	16	20	α	α	PROPN
ejpam-6705	16	21	∈	∈	PROPN
ejpam-6705	16	22	(	(	PUNCT
ejpam-6705	16	23	0	0	NUM
ejpam-6705	16	24	,	,	PUNCT
ejpam-6705	16	25	1	1	NUM
ejpam-6705	16	26	)	)	PUNCT
ejpam-6705	16	27	.	.	PUNCT
ejpam-6705	17	1	according	accord	VERB
ejpam-6705	17	2	to	to	ADP
ejpam-6705	17	3	the	the	DET
ejpam-6705	17	4	banach	banach	ADV
ejpam-6705	17	5	fixed	fix	VERB
ejpam-6705	17	6	point	point	NOUN
ejpam-6705	17	7	theorem	theorem	VERB
ejpam-6705	17	8	,	,	PUNCT
ejpam-6705	17	9	such	such	DET
ejpam-6705	17	10	a	a	DET
ejpam-6705	17	11	mapping	mapping	NOUN
ejpam-6705	17	12	t	t	NOUN
ejpam-6705	17	13	posseses	possese	VERB
ejpam-6705	17	14	a	a	DET
ejpam-6705	17	15	unique	unique	ADJ
ejpam-6705	17	16	fixed	fix	VERB
ejpam-6705	17	17	point	point	NOUN
ejpam-6705	17	18	in	in	ADP
ejpam-6705	17	19	x	x	X
ejpam-6705	17	20	.	.	PUNCT
ejpam-6705	18	1	the	the	DET
ejpam-6705	18	2	banach	banach	ADV
ejpam-6705	18	3	fixed	fix	VERB
ejpam-6705	18	4	point	point	NOUN
ejpam-6705	18	5	principle	principle	NOUN
ejpam-6705	18	6	has	have	AUX
ejpam-6705	18	7	undergone	undergo	VERB
ejpam-6705	18	8	significant	significant	ADJ
ejpam-6705	18	9	expansions	expansion	NOUN
ejpam-6705	18	10	due	due	ADP
ejpam-6705	18	11	to	to	ADP
ejpam-6705	18	12	its	its	PRON
ejpam-6705	18	13	efficacy	efficacy	NOUN
ejpam-6705	18	14	in	in	ADP
ejpam-6705	18	15	resolving	resolve	VERB
ejpam-6705	18	16	existence	existence	NOUN
ejpam-6705	18	17	and	and	CCONJ
ejpam-6705	18	18	uniqueness	uniqueness	NOUN
ejpam-6705	18	19	problems	problem	NOUN
ejpam-6705	18	20	in	in	ADP
ejpam-6705	18	21	integral	integral	ADJ
ejpam-6705	18	22	and	and	CCONJ
ejpam-6705	18	23	differential	differential	ADJ
ejpam-6705	18	24	equations	equation	NOUN
ejpam-6705	18	25	.	.	PUNCT
ejpam-6705	19	1	researchers	researcher	NOUN
ejpam-6705	19	2	have	have	AUX
ejpam-6705	19	3	built	build	VERB
ejpam-6705	19	4	upon	upon	SCONJ
ejpam-6705	19	5	this	this	DET
ejpam-6705	19	6	foundation	foundation	NOUN
ejpam-6705	19	7	,	,	PUNCT
ejpam-6705	19	8	introducing	introduce	VERB
ejpam-6705	19	9	novel	novel	ADJ
ejpam-6705	19	10	generalizations	generalization	NOUN
ejpam-6705	19	11	.	.	PUNCT
ejpam-6705	20	1	notably	notably	ADV
ejpam-6705	20	2	,	,	PUNCT
ejpam-6705	20	3	edelstein	edelstein	PROPN
ejpam-6705	20	4	[	[	X
ejpam-6705	20	5	3	3	NUM
ejpam-6705	20	6	]	]	PUNCT
ejpam-6705	20	7	work	work	NOUN
ejpam-6705	20	8	on	on	ADP
ejpam-6705	20	9	subsequences	subsequence	NOUN
ejpam-6705	20	10	of	of	ADP
ejpam-6705	20	11	iterates	iterate	NOUN
ejpam-6705	20	12	led	lead	VERB
ejpam-6705	20	13	to	to	ADP
ejpam-6705	20	14	a	a	DET
ejpam-6705	20	15	relaxation	relaxation	NOUN
ejpam-6705	20	16	of	of	ADP
ejpam-6705	20	17	the	the	DET
ejpam-6705	20	18	contraction	contraction	NOUN
ejpam-6705	20	19	condition	condition	NOUN
ejpam-6705	20	20	,	,	PUNCT
ejpam-6705	20	21	subsequently	subsequently	ADV
ejpam-6705	20	22	,	,	PUNCT
ejpam-6705	20	23	boyd	boyd	PROPN
ejpam-6705	20	24	and	and	CCONJ
ejpam-6705	20	25	wong	wong	PROPN
ejpam-6705	21	1	[	[	X
ejpam-6705	21	2	4	4	NUM
ejpam-6705	21	3	]	]	PUNCT
ejpam-6705	21	4	introduced	introduce	VERB
ejpam-6705	21	5	a	a	DET
ejpam-6705	21	6	continuous	continuous	ADJ
ejpam-6705	21	7	function	function	NOUN
ejpam-6705	21	8	ð	ð	X
ejpam-6705	21	9	:	:	PUNCT
ejpam-6705	22	1	[	[	X
ejpam-6705	22	2	0,∞	0,∞	NOUN
ejpam-6705	22	3	)	)	PUNCT
ejpam-6705	22	4	→	→	PUNCT
ejpam-6705	23	1	[	[	X
ejpam-6705	23	2	0,∞	0,∞	NOUN
ejpam-6705	23	3	)	)	PUNCT
ejpam-6705	23	4	,	,	PUNCT
ejpam-6705	23	5	replacing	replace	VERB
ejpam-6705	23	6	the	the	DET
ejpam-6705	23	7	linear	linear	ADJ
ejpam-6705	23	8	contraction	contraction	NOUN
ejpam-6705	23	9	condition	condition	NOUN
ejpam-6705	23	10	qd(u	qd(u	ADP
ejpam-6705	23	11	,	,	PUNCT
ejpam-6705	23	12	v	v	NOUN
ejpam-6705	23	13	)	)	PUNCT
ejpam-6705	23	14	∀	∀	PUNCT
ejpam-6705	23	15	q	q	NOUN
ejpam-6705	23	16	∈	∈	PROPN
ejpam-6705	23	17	(	(	PUNCT
ejpam-6705	23	18	0	0	NUM
ejpam-6705	23	19	,	,	PUNCT
ejpam-6705	23	20	1	1	NUM
ejpam-6705	23	21	)	)	PUNCT
ejpam-6705	23	22	with	with	ADP
ejpam-6705	23	23	ð(d(u	ð(d(u	PROPN
ejpam-6705	23	24	,	,	PUNCT
ejpam-6705	23	25	v	v	NOUN
ejpam-6705	23	26	)	)	PUNCT
ejpam-6705	23	27	)	)	PUNCT
ejpam-6705	23	28	,	,	PUNCT
ejpam-6705	23	29	thereby	thereby	ADV
ejpam-6705	23	30	presenting	present	VERB
ejpam-6705	23	31	a	a	DET
ejpam-6705	23	32	more	more	ADV
ejpam-6705	23	33	general	general	ADJ
ejpam-6705	23	34	version	version	NOUN
ejpam-6705	23	35	of	of	ADP
ejpam-6705	23	36	the	the	DET
ejpam-6705	23	37	banach	banach	ADV
ejpam-6705	23	38	fixed	fix	VERB
ejpam-6705	23	39	point	point	NOUN
ejpam-6705	23	40	theorem	theorem	VERB
ejpam-6705	23	41	.	.	PUNCT
ejpam-6705	24	1	fixed	fix	VERB
ejpam-6705	24	2	point	point	NOUN
ejpam-6705	24	3	theorems	theorem	NOUN
ejpam-6705	24	4	in	in	ADP
ejpam-6705	24	5	a	a	DET
ejpam-6705	24	6	partially	partially	ADV
ejpam-6705	24	7	ordered	order	VERB
ejpam-6705	24	8	metric	metric	ADJ
ejpam-6705	24	9	space	space	NOUN
ejpam-6705	24	10	play	play	VERB
ejpam-6705	24	11	a	a	DET
ejpam-6705	24	12	vital	vital	ADJ
ejpam-6705	24	13	role	role	NOUN
ejpam-6705	24	14	in	in	ADP
ejpam-6705	24	15	determining	determine	VERB
ejpam-6705	24	16	the	the	DET
ejpam-6705	24	17	existence	existence	NOUN
ejpam-6705	24	18	and	and	CCONJ
ejpam-6705	24	19	uniqueness	uniqueness	NOUN
ejpam-6705	24	20	of	of	ADP
ejpam-6705	24	21	solutions	solution	NOUN
ejpam-6705	24	22	to	to	ADP
ejpam-6705	24	23	specific	specific	ADJ
ejpam-6705	24	24	equations	equation	NOUN
ejpam-6705	24	25	.	.	PUNCT
ejpam-6705	25	1	moreover	moreover	ADV
ejpam-6705	25	2	,	,	PUNCT
ejpam-6705	25	3	multivalued	multivalued	ADJ
ejpam-6705	25	4	mappings	mapping	NOUN
ejpam-6705	25	5	have	have	AUX
ejpam-6705	25	6	gained	gain	VERB
ejpam-6705	25	7	significant	significant	ADJ
ejpam-6705	25	8	attention	attention	NOUN
ejpam-6705	25	9	due	due	ADP
ejpam-6705	25	10	to	to	ADP
ejpam-6705	25	11	its	its	PRON
ejpam-6705	25	12	wide	wide	ADJ
ejpam-6705	25	13	ranging	ranging	NOUN
ejpam-6705	25	14	applications	application	NOUN
ejpam-6705	25	15	in	in	ADP
ejpam-6705	25	16	fields	field	NOUN
ejpam-6705	25	17	such	such	ADJ
ejpam-6705	25	18	as	as	ADP
ejpam-6705	25	19	convex	convex	NOUN
ejpam-6705	25	20	optimization	optimization	NOUN
ejpam-6705	25	21	,	,	PUNCT
ejpam-6705	25	22	optimal	optimal	ADJ
ejpam-6705	25	23	control	control	NOUN
ejpam-6705	25	24	theory	theory	NOUN
ejpam-6705	25	25	,	,	PUNCT
ejpam-6705	25	26	and	and	CCONJ
ejpam-6705	25	27	differential	differential	ADJ
ejpam-6705	25	28	inclusions	inclusion	NOUN
ejpam-6705	25	29	.	.	PUNCT
ejpam-6705	26	1	for	for	ADP
ejpam-6705	26	2	more	more	ADV
ejpam-6705	26	3	related	related	ADJ
ejpam-6705	26	4	works	work	NOUN
ejpam-6705	26	5	,	,	PUNCT
ejpam-6705	26	6	see	see	VERB
ejpam-6705	26	7	[	[	X
ejpam-6705	26	8	5–16	5–16	NOUN
ejpam-6705	26	9	]	]	X
ejpam-6705	26	10	.	.	PUNCT
ejpam-6705	27	1	as	as	ADP
ejpam-6705	27	2	a	a	DET
ejpam-6705	27	3	generalization	generalization	NOUN
ejpam-6705	27	4	of	of	ADP
ejpam-6705	27	5	metric	metric	ADJ
ejpam-6705	27	6	space	space	NOUN
ejpam-6705	27	7	the	the	DET
ejpam-6705	27	8	concept	concept	NOUN
ejpam-6705	27	9	b	b	X
ejpam-6705	27	10	-	-	PUNCT
ejpam-6705	27	11	metric	metric	ADJ
ejpam-6705	27	12	space	space	NOUN
ejpam-6705	27	13	was	be	AUX
ejpam-6705	27	14	first	first	ADV
ejpam-6705	27	15	introduced	introduce	VERB
ejpam-6705	27	16	by	by	ADP
ejpam-6705	27	17	bakhtin	bakhtin	NOUN
ejpam-6705	27	18	[	[	X
ejpam-6705	27	19	17	17	NUM
ejpam-6705	27	20	]	]	PUNCT
ejpam-6705	27	21	.	.	PUNCT
ejpam-6705	28	1	he	he	PRON
ejpam-6705	28	2	also	also	ADV
ejpam-6705	28	3	established	establish	VERB
ejpam-6705	28	4	several	several	ADJ
ejpam-6705	28	5	fixed	fix	VERB
ejpam-6705	28	6	point	point	NOUN
ejpam-6705	28	7	results	result	NOUN
ejpam-6705	28	8	for	for	ADP
ejpam-6705	28	9	mappings	mapping	NOUN
ejpam-6705	28	10	satisfying	satisfy	VERB
ejpam-6705	28	11	specific	specific	ADJ
ejpam-6705	28	12	contractive	contractive	ADJ
ejpam-6705	28	13	conditions	condition	NOUN
ejpam-6705	28	14	within	within	ADP
ejpam-6705	28	15	this	this	DET
ejpam-6705	28	16	framework	framework	NOUN
ejpam-6705	28	17	.	.	PUNCT
ejpam-6705	29	1	later	later	ADV
ejpam-6705	29	2	on	on	ADV
ejpam-6705	29	3	,	,	PUNCT
ejpam-6705	29	4	selma	selma	PROPN
ejpam-6705	29	5	gulyaz	gulyaz	PROPN
ejpam-6705	29	6	ozyurt	ozyurt	PROPN
ejpam-6705	30	1	[	[	X
ejpam-6705	30	2	18	18	NUM
ejpam-6705	30	3	]	]	PUNCT
ejpam-6705	30	4	defined	define	VERB
ejpam-6705	30	5	α	α	PRON
ejpam-6705	30	6	-	-	ADJ
ejpam-6705	30	7	admissible	admissible	ADJ
ejpam-6705	30	8	contraction	contraction	NOUN
ejpam-6705	30	9	mappings	mapping	NOUN
ejpam-6705	30	10	on	on	ADP
ejpam-6705	30	11	branciari	branciari	ADJ
ejpam-6705	30	12	b	b	X
ejpam-6705	30	13	-	-	PUNCT
ejpam-6705	30	14	metric	metric	ADJ
ejpam-6705	30	15	spaces	space	NOUN
ejpam-6705	30	16	.	.	PUNCT
ejpam-6705	31	1	conditions	condition	NOUN
ejpam-6705	31	2	for	for	ADP
ejpam-6705	31	3	the	the	DET
ejpam-6705	31	4	existence	existence	NOUN
ejpam-6705	31	5	and	and	CCONJ
ejpam-6705	31	6	uniqueness	uniqueness	NOUN
ejpam-6705	31	7	of	of	ADP
ejpam-6705	31	8	fixed	fix	VERB
ejpam-6705	31	9	points	point	NOUN
ejpam-6705	31	10	for	for	ADP
ejpam-6705	31	11	these	these	DET
ejpam-6705	31	12	mappings	mapping	NOUN
ejpam-6705	31	13	were	be	AUX
ejpam-6705	31	14	discussed	discuss	VERB
ejpam-6705	31	15	,	,	PUNCT
ejpam-6705	31	16	and	and	CCONJ
ejpam-6705	31	17	related	related	ADJ
ejpam-6705	31	18	theorems	theorem	NOUN
ejpam-6705	31	19	were	be	AUX
ejpam-6705	31	20	proved	prove	VERB
ejpam-6705	31	21	.	.	PUNCT
ejpam-6705	32	1	aydi	aydi	VERB
ejpam-6705	32	2	et	et	PROPN
ejpam-6705	32	3	al	al	PROPN
ejpam-6705	32	4	.	.	PUNCT
ejpam-6705	33	1	[	[	X
ejpam-6705	33	2	19	19	NUM
ejpam-6705	33	3	]	]	PUNCT
ejpam-6705	33	4	established	establish	VERB
ejpam-6705	33	5	a	a	DET
ejpam-6705	33	6	fixed	fix	VERB
ejpam-6705	33	7	point	point	NOUN
ejpam-6705	33	8	theorem	theorem	NOUN
ejpam-6705	33	9	for	for	ADP
ejpam-6705	33	10	set	set	NOUN
ejpam-6705	33	11	-	-	PUNCT
ejpam-6705	33	12	valued	value	VERB
ejpam-6705	33	13	quasi	quasi	ADJ
ejpam-6705	33	14	-	-	NOUN
ejpam-6705	33	15	contraction	contraction	NOUN
ejpam-6705	33	16	mappings	mapping	NOUN
ejpam-6705	33	17	in	in	ADP
ejpam-6705	33	18	b	b	NOUN
ejpam-6705	33	19	-	-	ADJ
ejpam-6705	33	20	metric	metric	ADJ
ejpam-6705	33	21	spaces	space	NOUN
ejpam-6705	33	22	.	.	PUNCT
ejpam-6705	34	1	further	further	ADJ
ejpam-6705	34	2	generalizations	generalization	NOUN
ejpam-6705	34	3	in	in	ADP
ejpam-6705	34	4	such	such	ADJ
ejpam-6705	34	5	spaces	space	NOUN
ejpam-6705	34	6	can	can	AUX
ejpam-6705	34	7	be	be	AUX
ejpam-6705	34	8	found	find	VERB
ejpam-6705	34	9	in	in	ADP
ejpam-6705	34	10	[	[	X
ejpam-6705	34	11	20	20	NUM
ejpam-6705	34	12	,	,	PUNCT
ejpam-6705	34	13	21	21	NUM
ejpam-6705	34	14	]	]	PUNCT
ejpam-6705	34	15	.	.	PUNCT
ejpam-6705	35	1	in	in	ADP
ejpam-6705	35	2	1976	1976	NUM
ejpam-6705	35	3	,	,	PUNCT
ejpam-6705	35	4	caristi	caristi	VERB
ejpam-6705	35	5	[	[	X
ejpam-6705	35	6	22	22	NUM
ejpam-6705	35	7	]	]	PUNCT
ejpam-6705	35	8	formulated	formulate	VERB
ejpam-6705	35	9	a	a	DET
ejpam-6705	35	10	new	new	ADJ
ejpam-6705	35	11	class	class	NOUN
ejpam-6705	35	12	of	of	ADP
ejpam-6705	35	13	fixed	fix	VERB
ejpam-6705	35	14	point	point	NOUN
ejpam-6705	35	15	results	result	NOUN
ejpam-6705	35	16	based	base	VERB
ejpam-6705	35	17	on	on	ADP
ejpam-6705	35	18	the	the	DET
ejpam-6705	35	19	concept	concept	NOUN
ejpam-6705	35	20	of	of	ADP
ejpam-6705	35	21	weakly	weakly	ADJ
ejpam-6705	35	22	inward	inward	ADJ
ejpam-6705	35	23	mappings	mapping	NOUN
ejpam-6705	35	24	.	.	PUNCT
ejpam-6705	36	1	a	a	DET
ejpam-6705	36	2	variant	variant	NOUN
ejpam-6705	36	3	of	of	ADP
ejpam-6705	36	4	the	the	DET
ejpam-6705	36	5	banach	banach	NOUN
ejpam-6705	36	6	contraction	contraction	NOUN
ejpam-6705	36	7	principle	principle	NOUN
ejpam-6705	36	8	tailored	tailor	VERB
ejpam-6705	36	9	to	to	PART
ejpam-6705	36	10	partially	partially	ADV
ejpam-6705	36	11	ordered	order	VERB
ejpam-6705	36	12	sets	set	NOUN
ejpam-6705	36	13	was	be	AUX
ejpam-6705	36	14	later	later	ADV
ejpam-6705	36	15	established	establish	VERB
ejpam-6705	36	16	by	by	ADP
ejpam-6705	36	17	ran	ran	NOUN
ejpam-6705	36	18	and	and	CCONJ
ejpam-6705	36	19	reurings	reuring	NOUN
ejpam-6705	36	20	[	[	X
ejpam-6705	36	21	23	23	NUM
ejpam-6705	36	22	]	]	PUNCT
ejpam-6705	36	23	,	,	PUNCT
ejpam-6705	36	24	which	which	PRON
ejpam-6705	36	25	is	be	AUX
ejpam-6705	36	26	now	now	ADV
ejpam-6705	36	27	widely	widely	ADV
ejpam-6705	36	28	referred	refer	VERB
ejpam-6705	36	29	to	to	ADP
ejpam-6705	36	30	as	as	SCONJ
ejpam-6705	36	31	the	the	DET
ejpam-6705	36	32	ran	ran	NOUN
ejpam-6705	36	33	-	-	PUNCT
ejpam-6705	36	34	reurings	reuring	NOUN
ejpam-6705	36	35	fixed	fix	VERB
ejpam-6705	36	36	point	point	NOUN
ejpam-6705	36	37	theorem	theorem	VERB
ejpam-6705	36	38	.	.	PUNCT
ejpam-6705	37	1	however	however	ADV
ejpam-6705	37	2	,	,	PUNCT
ejpam-6705	37	3	an	an	DET
ejpam-6705	37	4	unsuccessful	unsuccessful	ADJ
ejpam-6705	37	5	attempt	attempt	NOUN
ejpam-6705	37	6	to	to	PART
ejpam-6705	37	7	generalize	generalize	VERB
ejpam-6705	37	8	the	the	DET
ejpam-6705	37	9	banach	banach	NOUN
ejpam-6705	37	10	principle	principle	NOUN
ejpam-6705	37	11	was	be	AUX
ejpam-6705	37	12	made	make	VERB
ejpam-6705	37	13	by	by	ADP
ejpam-6705	37	14	dhage	dhage	NOUN
ejpam-6705	37	15	et	et	PROPN
ejpam-6705	37	16	al	al	PROPN
ejpam-6705	37	17	.	.	PUNCT
ejpam-6705	38	1	[	[	X
ejpam-6705	38	2	24	24	NUM
ejpam-6705	38	3	]	]	PUNCT
ejpam-6705	38	4	,	,	PUNCT
ejpam-6705	38	5	who	who	PRON
ejpam-6705	38	6	gave	give	VERB
ejpam-6705	38	7	the	the	DET
ejpam-6705	38	8	concept	concept	NOUN
ejpam-6705	38	9	of	of	ADP
ejpam-6705	38	10	d	d	ADJ
ejpam-6705	38	11	-	-	ADJ
ejpam-6705	38	12	metric	metric	ADJ
ejpam-6705	38	13	space	space	NOUN
ejpam-6705	38	14	topology	topology	NOUN
ejpam-6705	38	15	.	.	PUNCT
ejpam-6705	39	1	more	more	ADV
ejpam-6705	39	2	precisely	precisely	ADV
ejpam-6705	39	3	,	,	PUNCT
ejpam-6705	39	4	sedghi	sedghi	VERB
ejpam-6705	39	5	et	et	PROPN
ejpam-6705	39	6	al	al	PROPN
ejpam-6705	39	7	.	.	PUNCT
ejpam-6705	40	1	[	[	X
ejpam-6705	40	2	25	25	NUM
ejpam-6705	40	3	]	]	PUNCT
ejpam-6705	40	4	proposed	propose	VERB
ejpam-6705	40	5	a	a	DET
ejpam-6705	40	6	revised	revise	VERB
ejpam-6705	40	7	framework	framework	NOUN
ejpam-6705	40	8	in	in	ADP
ejpam-6705	40	9	2007	2007	NUM
ejpam-6705	40	10	,	,	PUNCT
ejpam-6705	40	11	introducing	introduce	VERB
ejpam-6705	40	12	the	the	DET
ejpam-6705	40	13	notion	notion	NOUN
ejpam-6705	40	14	of	of	ADP
ejpam-6705	40	15	g	g	NOUN
ejpam-6705	40	16	-	-	PUNCT
ejpam-6705	40	17	metric	metric	ADJ
ejpam-6705	40	18	spaces	space	NOUN
ejpam-6705	40	19	as	as	ADP
ejpam-6705	40	20	a	a	DET
ejpam-6705	40	21	modification	modification	NOUN
ejpam-6705	40	22	of	of	ADP
ejpam-6705	40	23	the	the	DET
ejpam-6705	40	24	original	original	ADJ
ejpam-6705	40	25	d	d	ADJ
ejpam-6705	40	26	-	-	ADJ
ejpam-6705	40	27	metric	metric	ADJ
ejpam-6705	40	28	structure	structure	NOUN
ejpam-6705	40	29	.	.	PUNCT
ejpam-6705	41	1	since	since	SCONJ
ejpam-6705	41	2	then	then	ADV
ejpam-6705	41	3	,	,	PUNCT
ejpam-6705	41	4	numerous	numerous	ADJ
ejpam-6705	41	5	fixed	fix	VERB
ejpam-6705	41	6	point	point	NOUN
ejpam-6705	41	7	results	result	NOUN
ejpam-6705	41	8	have	have	AUX
ejpam-6705	41	9	been	be	AUX
ejpam-6705	41	10	established	establish	VERB
ejpam-6705	41	11	within	within	ADP
ejpam-6705	41	12	this	this	DET
ejpam-6705	41	13	improved	improve	VERB
ejpam-6705	41	14	framework	framework	NOUN
ejpam-6705	41	15	by	by	ADP
ejpam-6705	41	16	various	various	ADJ
ejpam-6705	41	17	authors	author	NOUN
ejpam-6705	41	18	[	[	X
ejpam-6705	41	19	26	26	NUM
ejpam-6705	41	20	,	,	PUNCT
ejpam-6705	41	21	27	27	NUM
ejpam-6705	41	22	]	]	PUNCT
ejpam-6705	41	23	.	.	PUNCT
ejpam-6705	42	1	researchers	researcher	NOUN
ejpam-6705	42	2	have	have	AUX
ejpam-6705	42	3	investigated	investigate	VERB
ejpam-6705	42	4	coupled	couple	VERB
ejpam-6705	42	5	fixed	fix	VERB
ejpam-6705	42	6	point	point	NOUN
ejpam-6705	42	7	results	result	NOUN
ejpam-6705	42	8	for	for	ADP
ejpam-6705	42	9	mixed	mixed	ADJ
ejpam-6705	42	10	monotone	monotone	ADJ
ejpam-6705	42	11	mappings	mapping	NOUN
ejpam-6705	42	12	in	in	ADP
ejpam-6705	42	13	ordered	order	VERB
ejpam-6705	42	14	metric	metric	ADJ
ejpam-6705	42	15	spaces	space	NOUN
ejpam-6705	42	16	[	[	X
ejpam-6705	42	17	28	28	NUM
ejpam-6705	42	18	,	,	PUNCT
ejpam-6705	42	19	29	29	NUM
ejpam-6705	42	20	]	]	PUNCT
ejpam-6705	42	21	.	.	PUNCT
ejpam-6705	43	1	for	for	ADP
ejpam-6705	43	2	comprehensive	comprehensive	ADJ
ejpam-6705	43	3	insights	insight	NOUN
ejpam-6705	43	4	into	into	ADP
ejpam-6705	43	5	coupled	couple	VERB
ejpam-6705	43	6	fixed	fix	VERB
ejpam-6705	43	7	points	point	NOUN
ejpam-6705	43	8	and	and	CCONJ
ejpam-6705	43	9	n	n	CCONJ
ejpam-6705	43	10	-	-	PUNCT
ejpam-6705	43	11	tupled	tuple	VERB
ejpam-6705	43	12	fixed	fix	VERB
ejpam-6705	43	13	points	point	NOUN
ejpam-6705	43	14	theorems	theorem	NOUN
ejpam-6705	43	15	,	,	PUNCT
ejpam-6705	43	16	readers	reader	NOUN
ejpam-6705	43	17	can	can	AUX
ejpam-6705	43	18	refer	refer	VERB
ejpam-6705	43	19	to	to	ADP
ejpam-6705	43	20	[	[	X
ejpam-6705	43	21	30	30	NUM
ejpam-6705	43	22	]	]	PUNCT
ejpam-6705	43	23	.	.	PUNCT
ejpam-6705	44	1	recently	recently	ADV
ejpam-6705	44	2	,	,	PUNCT
ejpam-6705	44	3	rajagopalan	rajagopalan	VERB
ejpam-6705	44	4	ramaswamy	ramaswamy	ADJ
ejpam-6705	44	5	and	and	CCONJ
ejpam-6705	44	6	gunaseelan	gunaseelan	ADJ
ejpam-6705	44	7	mani	mani	PROPN
ejpam-6705	45	1	[	[	X
ejpam-6705	45	2	31	31	NUM
ejpam-6705	45	3	]	]	PUNCT
ejpam-6705	45	4	introduced	introduce	VERB
ejpam-6705	45	5	graphical	graphical	ADJ
ejpam-6705	45	6	branciari	branciari	NOUN
ejpam-6705	45	7	ℵ-metric	ℵ-metric	ADJ
ejpam-6705	45	8	spaces	space	NOUN
ejpam-6705	45	9	and	and	CCONJ
ejpam-6705	45	10	proved	prove	VERB
ejpam-6705	45	11	a	a	DET
ejpam-6705	45	12	fixed	fix	VERB
ejpam-6705	45	13	point	point	NOUN
ejpam-6705	45	14	theorem	theorem	NOUN
ejpam-6705	45	15	for	for	ADP
ejpam-6705	45	16	ω	ω	PROPN
ejpam-6705	45	17	-	-	PUNCT
ejpam-6705	45	18	q	q	NOUN
ejpam-6705	45	19	contractions	contraction	NOUN
ejpam-6705	45	20	on	on	ADP
ejpam-6705	45	21	complete	complete	ADJ
ejpam-6705	45	22	graphical	graphical	ADJ
ejpam-6705	45	23	branciari	branciari	NOUN
ejpam-6705	45	24	ℵmetric	ℵmetric	ADJ
ejpam-6705	45	25	spaces	space	NOUN
ejpam-6705	45	26	.	.	PUNCT
ejpam-6705	46	1	additionally	additionally	ADV
ejpam-6705	46	2	,	,	PUNCT
ejpam-6705	46	3	fixed	fix	VERB
ejpam-6705	46	4	point	point	NOUN
ejpam-6705	46	5	problems	problem	NOUN
ejpam-6705	46	6	have	have	AUX
ejpam-6705	46	7	been	be	AUX
ejpam-6705	46	8	extensively	extensively	ADV
ejpam-6705	46	9	studied	study	VERB
ejpam-6705	46	10	in	in	ADP
ejpam-6705	46	11	the	the	DET
ejpam-6705	46	12	setting	setting	NOUN
ejpam-6705	46	13	of	of	ADP
ejpam-6705	46	14	partially	partially	ADV
ejpam-6705	46	15	ordered	order	VERB
ejpam-6705	46	16	complete	complete	ADJ
ejpam-6705	46	17	metric	metric	ADJ
ejpam-6705	46	18	spaces	space	NOUN
ejpam-6705	46	19	.	.	PUNCT
ejpam-6705	47	1	notably	notably	ADV
ejpam-6705	47	2	,	,	PUNCT
ejpam-6705	47	3	al	al	PROPN
ejpam-6705	47	4	-	-	PUNCT
ejpam-6705	47	5	jumaili	jumaili	PROPN
ejpam-6705	47	6	[	[	X
ejpam-6705	47	7	32	32	NUM
ejpam-6705	47	8	]	]	PUNCT
ejpam-6705	47	9	utilized	utilize	VERB
ejpam-6705	47	10	the	the	DET
ejpam-6705	47	11	concept	concept	NOUN
ejpam-6705	47	12	of	of	ADP
ejpam-6705	47	13	these	these	DET
ejpam-6705	47	14	spaces	space	NOUN
ejpam-6705	47	15	to	to	PART
ejpam-6705	47	16	establish	establish	VERB
ejpam-6705	47	17	coincidence	coincidence	NOUN
ejpam-6705	47	18	fixed	fix	VERB
ejpam-6705	47	19	point	point	NOUN
ejpam-6705	47	20	theorems	theorem	NOUN
ejpam-6705	47	21	for	for	ADP
ejpam-6705	47	22	functions	function	NOUN
ejpam-6705	47	23	satisfying	satisfy	VERB
ejpam-6705	47	24	certain	certain	ADJ
ejpam-6705	47	25	contractive	contractive	ADJ
ejpam-6705	47	26	properties	property	NOUN
ejpam-6705	47	27	involving	involve	VERB
ejpam-6705	47	28	monotone	monotone	ADJ
ejpam-6705	47	29	increasing	increase	VERB
ejpam-6705	47	30	η	η	NOUN
ejpam-6705	47	31	-	-	NOUN
ejpam-6705	47	32	mappings	mapping	NOUN
ejpam-6705	47	33	,	,	PUNCT
ejpam-6705	47	34	thereby	thereby	ADV
ejpam-6705	47	35	advancing	advance	VERB
ejpam-6705	47	36	the	the	DET
ejpam-6705	47	37	field	field	NOUN
ejpam-6705	47	38	.	.	PUNCT
ejpam-6705	48	1	ghasab	ghasab	VERB
ejpam-6705	48	2	et	et	PROPN
ejpam-6705	48	3	al	al	PROPN
ejpam-6705	48	4	.	.	PUNCT
ejpam-6705	49	1	[	[	X
ejpam-6705	49	2	33	33	NUM
ejpam-6705	49	3	]	]	PUNCT
ejpam-6705	49	4	used	use	VERB
ejpam-6705	49	5	the	the	DET
ejpam-6705	49	6	notion	notion	NOUN
ejpam-6705	49	7	of	of	ADP
ejpam-6705	49	8	integral	integral	ADJ
ejpam-6705	49	9	-	-	PUNCT
ejpam-6705	49	10	type	type	NOUN
ejpam-6705	49	11	contractions	contraction	NOUN
ejpam-6705	49	12	to	to	PART
ejpam-6705	49	13	establish	establish	VERB
ejpam-6705	49	14	coupled	couple	VERB
ejpam-6705	49	15	fixed	fix	VERB
ejpam-6705	49	16	point	point	NOUN
ejpam-6705	49	17	results	result	NOUN
ejpam-6705	49	18	in	in	ADP
ejpam-6705	49	19	ordered	order	VERB
ejpam-6705	49	20	g	g	NOUN
ejpam-6705	49	21	-	-	PUNCT
ejpam-6705	49	22	metric	metric	ADJ
ejpam-6705	49	23	spaces	space	NOUN
ejpam-6705	49	24	.	.	PUNCT
ejpam-6705	50	1	majid	majid	PROPN
ejpam-6705	50	2	et	et	PROPN
ejpam-6705	50	3	al	al	PROPN
ejpam-6705	50	4	.	.	PUNCT
ejpam-6705	51	1	[	[	X
ejpam-6705	51	2	34	34	NUM
ejpam-6705	51	3	]	]	PUNCT
ejpam-6705	51	4	developed	develop	VERB
ejpam-6705	51	5	and	and	CCONJ
ejpam-6705	51	6	investigated	investigate	VERB
ejpam-6705	51	7	new	new	ADJ
ejpam-6705	51	8	fixed	fix	VERB
ejpam-6705	51	9	point	point	NOUN
ejpam-6705	51	10	theorems	theorem	NOUN
ejpam-6705	51	11	for	for	ADP
ejpam-6705	51	12	multivalued	multivalued	ADJ
ejpam-6705	51	13	functions	function	NOUN
ejpam-6705	51	14	in	in	ADP
ejpam-6705	51	15	partially	partially	ADV
ejpam-6705	51	16	ordered	order	VERB
ejpam-6705	51	17	complete	complete	ADJ
ejpam-6705	51	18	d	d	ADJ
ejpam-6705	51	19	-	-	ADJ
ejpam-6705	51	20	metric	metric	ADJ
ejpam-6705	51	21	spaces	space	NOUN
ejpam-6705	51	22	,	,	PUNCT
ejpam-6705	51	23	where	where	SCONJ
ejpam-6705	51	24	the	the	DET
ejpam-6705	51	25	order	order	NOUN
ejpam-6705	51	26	is	be	AUX
ejpam-6705	51	27	defined	define	VERB
ejpam-6705	51	28	by	by	ADP
ejpam-6705	51	29	a	a	DET
ejpam-6705	51	30	pair	pair	NOUN
ejpam-6705	51	31	of	of	ADP
ejpam-6705	51	32	functions	function	NOUN
ejpam-6705	51	33	(	(	PUNCT
ejpam-6705	51	34	κ	κ	NOUN
ejpam-6705	51	35	,	,	PUNCT
ejpam-6705	51	36	θ	θ	NOUN
ejpam-6705	51	37	)	)	PUNCT
ejpam-6705	51	38	while	while	SCONJ
ejpam-6705	51	39	aghajani	aghajani	PROPN
ejpam-6705	51	40	et	et	PROPN
ejpam-6705	51	41	al	al	PROPN
ejpam-6705	51	42	.	.	PUNCT
ejpam-6705	52	1	[	[	X
ejpam-6705	52	2	35	35	NUM
ejpam-6705	52	3	]	]	X
ejpam-6705	52	4	s.	s.	PROPN
ejpam-6705	52	5	batul	batul	PROPN
ejpam-6705	52	6	et	et	PROPN
ejpam-6705	52	7	al	al	PROPN
ejpam-6705	52	8	.	.	PUNCT
ejpam-6705	52	9	/	/	SYM
ejpam-6705	52	10	eur	eur	PROPN
ejpam-6705	52	11	.	.	PUNCT
ejpam-6705	53	1	j.	j.	PROPN
ejpam-6705	53	2	pure	pure	PROPN
ejpam-6705	53	3	appl	appl	PROPN
ejpam-6705	53	4	.	.	PROPN
ejpam-6705	53	5	math	math	PROPN
ejpam-6705	53	6	,	,	PUNCT
ejpam-6705	53	7	18	18	NUM
ejpam-6705	53	8	(	(	PUNCT
ejpam-6705	53	9	4	4	NUM
ejpam-6705	53	10	)	)	PUNCT
ejpam-6705	53	11	(	(	PUNCT
ejpam-6705	53	12	2025	2025	NUM
ejpam-6705	53	13	)	)	PUNCT
ejpam-6705	53	14	,	,	PUNCT
ejpam-6705	53	15	6705	6705	NUM
ejpam-6705	53	16	3	3	NUM
ejpam-6705	53	17	of	of	ADP
ejpam-6705	53	18	23	23	NUM
ejpam-6705	53	19	introduced	introduce	VERB
ejpam-6705	53	20	a	a	DET
ejpam-6705	53	21	new	new	ADJ
ejpam-6705	53	22	type	type	NOUN
ejpam-6705	53	23	of	of	ADP
ejpam-6705	53	24	metric	metric	NOUN
ejpam-6705	53	25	,	,	PUNCT
ejpam-6705	53	26	called	call	VERB
ejpam-6705	53	27	the	the	DET
ejpam-6705	53	28	gb	gb	NOUN
ejpam-6705	53	29	-	-	PUNCT
ejpam-6705	53	30	metric	metric	ADJ
ejpam-6705	53	31	.	.	PUNCT
ejpam-6705	54	1	ramaswamy	ramaswamy	PROPN
ejpam-6705	54	2	et	et	PROPN
ejpam-6705	54	3	al	al	PROPN
ejpam-6705	54	4	.	.	PUNCT
ejpam-6705	55	1	[	[	X
ejpam-6705	55	2	36	36	NUM
ejpam-6705	55	3	]	]	PUNCT
ejpam-6705	55	4	introduced	introduce	VERB
ejpam-6705	55	5	a	a	DET
ejpam-6705	55	6	new	new	ADJ
ejpam-6705	55	7	notion	notion	NOUN
ejpam-6705	55	8	of	of	ADP
ejpam-6705	55	9	(	(	PUNCT
ejpam-6705	55	10	β	β	X
ejpam-6705	55	11	,	,	PUNCT
ejpam-6705	55	12	ϕ)-admissible	ϕ)-admissible	ADJ
ejpam-6705	55	13	hybrid	hybrid	ADJ
ejpam-6705	55	14	contractions	contraction	NOUN
ejpam-6705	55	15	in	in	ADP
ejpam-6705	55	16	metric	metric	ADJ
ejpam-6705	55	17	spaces	space	NOUN
ejpam-6705	55	18	and	and	CCONJ
ejpam-6705	55	19	established	establish	VERB
ejpam-6705	55	20	fixed	fix	VERB
ejpam-6705	55	21	point	point	NOUN
ejpam-6705	55	22	results	result	NOUN
ejpam-6705	55	23	in	in	ADP
ejpam-6705	55	24	this	this	DET
ejpam-6705	55	25	setting	setting	NOUN
ejpam-6705	55	26	.	.	PUNCT
ejpam-6705	56	1	recently	recently	ADV
ejpam-6705	56	2	,	,	PUNCT
ejpam-6705	56	3	samuel	samuel	PROPN
ejpam-6705	56	4	et	et	PROPN
ejpam-6705	56	5	al	al	PROPN
ejpam-6705	56	6	.	.	PUNCT
ejpam-6705	57	1	[	[	X
ejpam-6705	57	2	37	37	NUM
ejpam-6705	57	3	]	]	PUNCT
ejpam-6705	57	4	introduced	introduce	VERB
ejpam-6705	57	5	integral	integral	ADJ
ejpam-6705	57	6	-	-	PUNCT
ejpam-6705	57	7	type	type	NOUN
ejpam-6705	57	8	contractions	contraction	NOUN
ejpam-6705	57	9	on	on	ADP
ejpam-6705	57	10	orthogonal	orthogonal	ADJ
ejpam-6705	57	11	s	s	NOUN
ejpam-6705	57	12	-	-	ADJ
ejpam-6705	57	13	metric	metric	ADJ
ejpam-6705	57	14	spaces	space	NOUN
ejpam-6705	57	15	and	and	CCONJ
ejpam-6705	57	16	established	establish	VERB
ejpam-6705	57	17	common	common	ADJ
ejpam-6705	57	18	fixed	fix	VERB
ejpam-6705	57	19	point	point	NOUN
ejpam-6705	57	20	results	result	NOUN
ejpam-6705	57	21	.	.	PUNCT
ejpam-6705	58	1	in	in	ADP
ejpam-6705	58	2	this	this	DET
ejpam-6705	58	3	article	article	NOUN
ejpam-6705	58	4	,	,	PUNCT
ejpam-6705	58	5	we	we	PRON
ejpam-6705	58	6	aim	aim	VERB
ejpam-6705	58	7	to	to	PART
ejpam-6705	58	8	develop	develop	VERB
ejpam-6705	58	9	and	and	CCONJ
ejpam-6705	58	10	explore	explore	VERB
ejpam-6705	58	11	several	several	ADJ
ejpam-6705	58	12	novel	novel	ADJ
ejpam-6705	58	13	fixed	fix	VERB
ejpam-6705	58	14	point	point	NOUN
ejpam-6705	58	15	results	result	NOUN
ejpam-6705	58	16	for	for	ADP
ejpam-6705	58	17	monotone	monotone	ADJ
ejpam-6705	58	18	multivalued	multivalue	VERB
ejpam-6705	58	19	mappings	mapping	NOUN
ejpam-6705	58	20	within	within	ADP
ejpam-6705	58	21	the	the	DET
ejpam-6705	58	22	framework	framework	NOUN
ejpam-6705	58	23	of	of	ADP
ejpam-6705	58	24	partially	partially	ADV
ejpam-6705	58	25	ordered	order	VERB
ejpam-6705	58	26	complete	complete	ADJ
ejpam-6705	58	27	gb	gb	ADV
ejpam-6705	58	28	-	-	PUNCT
ejpam-6705	58	29	metric	metric	ADJ
ejpam-6705	58	30	spaces	space	NOUN
ejpam-6705	58	31	.	.	PUNCT
ejpam-6705	59	1	the	the	DET
ejpam-6705	59	2	partial	partial	ADJ
ejpam-6705	59	3	order	order	NOUN
ejpam-6705	59	4	on	on	ADP
ejpam-6705	59	5	the	the	DET
ejpam-6705	59	6	set	set	NOUN
ejpam-6705	59	7	(	(	PUNCT
ejpam-6705	59	8	x	x	INTJ
ejpam-6705	59	9	,	,	PUNCT
ejpam-6705	59	10	≼	≼	PROPN
ejpam-6705	59	11	)	)	PUNCT
ejpam-6705	59	12	is	be	AUX
ejpam-6705	59	13	defined	define	VERB
ejpam-6705	59	14	through	through	ADP
ejpam-6705	59	15	a	a	DET
ejpam-6705	59	16	functional	functional	ADJ
ejpam-6705	59	17	pair	pair	NOUN
ejpam-6705	59	18	(	(	PUNCT
ejpam-6705	59	19	κ	κ	NOUN
ejpam-6705	59	20	,	,	PUNCT
ejpam-6705	59	21	θ	θ	NOUN
ejpam-6705	59	22	)	)	PUNCT
ejpam-6705	59	23	.	.	PUNCT
ejpam-6705	60	1	additionally	additionally	ADV
ejpam-6705	60	2	,	,	PUNCT
ejpam-6705	60	3	we	we	PRON
ejpam-6705	60	4	establish	establish	VERB
ejpam-6705	60	5	existence	existence	NOUN
ejpam-6705	60	6	and	and	CCONJ
ejpam-6705	60	7	uniqueness	uniqueness	NOUN
ejpam-6705	60	8	results	result	NOUN
ejpam-6705	60	9	for	for	ADP
ejpam-6705	60	10	coupled	couple	VERB
ejpam-6705	60	11	fixed	fix	VERB
ejpam-6705	60	12	points	point	NOUN
ejpam-6705	60	13	of	of	ADP
ejpam-6705	60	14	mappings	mapping	NOUN
ejpam-6705	60	15	that	that	PRON
ejpam-6705	60	16	satisfy	satisfy	VERB
ejpam-6705	60	17	specific	specific	ADJ
ejpam-6705	60	18	contractive	contractive	ADJ
ejpam-6705	60	19	conditions	condition	NOUN
ejpam-6705	60	20	,	,	PUNCT
ejpam-6705	60	21	utilizing	utilize	VERB
ejpam-6705	60	22	the	the	DET
ejpam-6705	60	23	notion	notion	NOUN
ejpam-6705	60	24	of	of	ADP
ejpam-6705	60	25	integral	integral	ADJ
ejpam-6705	60	26	type	type	NOUN
ejpam-6705	60	27	contractions	contraction	NOUN
ejpam-6705	60	28	.	.	PUNCT
ejpam-6705	61	1	to	to	PART
ejpam-6705	61	2	support	support	VERB
ejpam-6705	61	3	our	our	PRON
ejpam-6705	61	4	findings	finding	NOUN
ejpam-6705	61	5	,	,	PUNCT
ejpam-6705	61	6	appropriate	appropriate	ADJ
ejpam-6705	61	7	examples	example	NOUN
ejpam-6705	61	8	are	be	AUX
ejpam-6705	61	9	provided	provide	VERB
ejpam-6705	61	10	as	as	ADP
ejpam-6705	61	11	practical	practical	ADJ
ejpam-6705	61	12	applications	application	NOUN
ejpam-6705	61	13	,	,	PUNCT
ejpam-6705	61	14	see	see	VERB
ejpam-6705	61	15	related	related	ADJ
ejpam-6705	61	16	application	application	NOUN
ejpam-6705	61	17	[	[	X
ejpam-6705	61	18	38	38	NUM
ejpam-6705	61	19	,	,	PUNCT
ejpam-6705	61	20	39	39	NUM
ejpam-6705	61	21	]	]	PUNCT
ejpam-6705	61	22	.	.	PUNCT
ejpam-6705	62	1	2	2	X
ejpam-6705	62	2	.	.	X
ejpam-6705	62	3	preliminaries	preliminary	NOUN
ejpam-6705	62	4	the	the	DET
ejpam-6705	62	5	following	follow	VERB
ejpam-6705	62	6	are	be	AUX
ejpam-6705	62	7	some	some	DET
ejpam-6705	62	8	definitions	definition	NOUN
ejpam-6705	62	9	and	and	CCONJ
ejpam-6705	62	10	results	result	NOUN
ejpam-6705	62	11	which	which	PRON
ejpam-6705	62	12	are	be	AUX
ejpam-6705	62	13	useful	useful	ADJ
ejpam-6705	62	14	for	for	ADP
ejpam-6705	62	15	the	the	DET
ejpam-6705	62	16	proof	proof	NOUN
ejpam-6705	62	17	of	of	ADP
ejpam-6705	62	18	our	our	PRON
ejpam-6705	62	19	main	main	ADJ
ejpam-6705	62	20	theorems	theorem	NOUN
ejpam-6705	62	21	.	.	PUNCT
ejpam-6705	63	1	definition	definition	NOUN
ejpam-6705	63	2	1	1	NUM
ejpam-6705	63	3	.	.	PUNCT
ejpam-6705	64	1	[	[	X
ejpam-6705	64	2	35	35	NUM
ejpam-6705	64	3	]	]	PUNCT
ejpam-6705	64	4	a	a	DET
ejpam-6705	64	5	function	function	NOUN
ejpam-6705	64	6	gb	gb	ADP
ejpam-6705	64	7	:	:	PUNCT
ejpam-6705	64	8	x	x	PUNCT
ejpam-6705	64	9	×	×	NOUN
ejpam-6705	64	10	x	x	SYM
ejpam-6705	64	11	×	×	NOUN
ejpam-6705	64	12	x	x	INTJ
ejpam-6705	64	13	→	→	X
ejpam-6705	64	14	[	[	X
ejpam-6705	64	15	0,∞	0,∞	NUM
ejpam-6705	64	16	)	)	PUNCT
ejpam-6705	64	17	is	be	AUX
ejpam-6705	64	18	a	a	DET
ejpam-6705	64	19	gb	gb	ADV
ejpam-6705	64	20	-	-	PUNCT
ejpam-6705	64	21	metric	metric	ADJ
ejpam-6705	64	22	on	on	ADP
ejpam-6705	64	23	x	x	SYM
ejpam-6705	64	24	if	if	SCONJ
ejpam-6705	64	25	for	for	ADP
ejpam-6705	64	26	all	all	DET
ejpam-6705	64	27	u	u	NOUN
ejpam-6705	64	28	,	,	PUNCT
ejpam-6705	64	29	v	v	NOUN
ejpam-6705	64	30	,	,	PUNCT
ejpam-6705	64	31	w	w	PROPN
ejpam-6705	64	32	,	,	PUNCT
ejpam-6705	64	33	x	x	SYM
ejpam-6705	64	34	∈	∈	PROPN
ejpam-6705	64	35	x	x	X
ejpam-6705	64	36	,	,	PUNCT
ejpam-6705	64	37	the	the	DET
ejpam-6705	64	38	following	follow	VERB
ejpam-6705	64	39	conditions	condition	NOUN
ejpam-6705	64	40	are	be	AUX
ejpam-6705	64	41	satisfied	satisfied	ADJ
ejpam-6705	64	42	:	:	PUNCT
ejpam-6705	64	43	(	(	PUNCT
ejpam-6705	64	44	gb1	gb1	NOUN
ejpam-6705	64	45	)	)	PUNCT
ejpam-6705	64	46	gb(u	gb(u	NUM
ejpam-6705	64	47	,	,	PUNCT
ejpam-6705	64	48	v	v	NOUN
ejpam-6705	64	49	,	,	PUNCT
ejpam-6705	64	50	w	w	NOUN
ejpam-6705	64	51	)	)	PUNCT
ejpam-6705	64	52	=	=	SYM
ejpam-6705	64	53	0	0	NUM
ejpam-6705	64	54	⇔	⇔	X
ejpam-6705	64	55	u	u	NOUN
ejpam-6705	64	56	=	=	PROPN
ejpam-6705	64	57	v	v	PROPN
ejpam-6705	64	58	=	=	SYM
ejpam-6705	64	59	w.	w.	PROPN
ejpam-6705	64	60	(	(	PUNCT
ejpam-6705	64	61	gb2	gb2	PROPN
ejpam-6705	64	62	)	)	PUNCT
ejpam-6705	64	63	0	0	PUNCT
ejpam-6705	65	1	<	<	X
ejpam-6705	65	2	gb(u	gb(u	PROPN
ejpam-6705	65	3	,	,	PUNCT
ejpam-6705	65	4	u	u	NOUN
ejpam-6705	65	5	,	,	PUNCT
ejpam-6705	65	6	v	v	NOUN
ejpam-6705	65	7	)	)	PUNCT
ejpam-6705	65	8	for	for	ADP
ejpam-6705	65	9	all	all	DET
ejpam-6705	65	10	u	u	NOUN
ejpam-6705	65	11	,	,	PUNCT
ejpam-6705	65	12	v	v	NOUN
ejpam-6705	65	13	∈	∈	NOUN
ejpam-6705	65	14	x	x	PUNCT
ejpam-6705	65	15	with	with	ADP
ejpam-6705	65	16	u	u	NOUN
ejpam-6705	65	17	̸=	̸=	PROPN
ejpam-6705	65	18	v.	v.	ADP
ejpam-6705	65	19	(	(	PUNCT
ejpam-6705	65	20	gb3	gb3	NOUN
ejpam-6705	65	21	)	)	PUNCT
ejpam-6705	65	22	gb(u	gb(u	NUM
ejpam-6705	65	23	,	,	PUNCT
ejpam-6705	65	24	u	u	NOUN
ejpam-6705	65	25	,	,	PUNCT
ejpam-6705	65	26	v	v	NOUN
ejpam-6705	65	27	)	)	PUNCT
ejpam-6705	65	28	≤	≤	NOUN
ejpam-6705	65	29	gb(u	gb(u	NUM
ejpam-6705	65	30	,	,	PUNCT
ejpam-6705	65	31	v	v	NOUN
ejpam-6705	65	32	,	,	PUNCT
ejpam-6705	65	33	w	w	NOUN
ejpam-6705	65	34	)	)	PUNCT
ejpam-6705	65	35	for	for	ADP
ejpam-6705	65	36	all	all	DET
ejpam-6705	65	37	u	u	NOUN
ejpam-6705	65	38	,	,	PUNCT
ejpam-6705	65	39	v	v	NOUN
ejpam-6705	65	40	,	,	PUNCT
ejpam-6705	65	41	w	w	PROPN
ejpam-6705	65	42	∈	∈	PROPN
ejpam-6705	65	43	x	x	PUNCT
ejpam-6705	65	44	with	with	ADP
ejpam-6705	65	45	v	v	NOUN
ejpam-6705	65	46	̸=	̸=	PROPN
ejpam-6705	65	47	w.	w.	PROPN
ejpam-6705	65	48	(	(	PUNCT
ejpam-6705	65	49	gb4	gb4	NOUN
ejpam-6705	65	50	)	)	PUNCT
ejpam-6705	65	51	gb(u	gb(u	NUM
ejpam-6705	65	52	,	,	PUNCT
ejpam-6705	65	53	v	v	NOUN
ejpam-6705	65	54	,	,	PUNCT
ejpam-6705	65	55	w	w	NOUN
ejpam-6705	65	56	)	)	PUNCT
ejpam-6705	65	57	is	be	AUX
ejpam-6705	65	58	invariant	invariant	ADJ
ejpam-6705	65	59	under	under	ADP
ejpam-6705	65	60	permutations	permutation	NOUN
ejpam-6705	65	61	of	of	ADP
ejpam-6705	65	62	its	its	PRON
ejpam-6705	65	63	arguments	argument	NOUN
ejpam-6705	65	64	,	,	PUNCT
ejpam-6705	65	65	i.e.	i.e.	X
ejpam-6705	65	66	,	,	PUNCT
ejpam-6705	65	67	gb(u	gb(u	NUM
ejpam-6705	65	68	,	,	PUNCT
ejpam-6705	65	69	v	v	NOUN
ejpam-6705	65	70	,	,	PUNCT
ejpam-6705	65	71	w	w	NOUN
ejpam-6705	65	72	)	)	PUNCT
ejpam-6705	65	73	=	=	SYM
ejpam-6705	65	74	gb(p{u	gb(p{u	NOUN
ejpam-6705	65	75	,	,	PUNCT
ejpam-6705	65	76	v	v	NOUN
ejpam-6705	65	77	,	,	PUNCT
ejpam-6705	65	78	w	w	NOUN
ejpam-6705	65	79	}	}	PUNCT
ejpam-6705	65	80	)	)	PUNCT
ejpam-6705	65	81	for	for	ADP
ejpam-6705	65	82	any	any	DET
ejpam-6705	65	83	permutation	permutation	NOUN
ejpam-6705	66	1	p.	p.	NOUN
ejpam-6705	66	2	(	(	PUNCT
ejpam-6705	66	3	gb5	gb5	PROPN
ejpam-6705	66	4	)	)	PUNCT
ejpam-6705	66	5	gb(u	gb(u	NUM
ejpam-6705	66	6	,	,	PUNCT
ejpam-6705	66	7	v	v	NOUN
ejpam-6705	66	8	,	,	PUNCT
ejpam-6705	66	9	w	w	NOUN
ejpam-6705	66	10	)	)	PUNCT
ejpam-6705	66	11	≤	≤	NOUN
ejpam-6705	66	12	l[gb(u	l[gb(u	PROPN
ejpam-6705	66	13	,	,	PUNCT
ejpam-6705	66	14	v	v	NOUN
ejpam-6705	66	15	,	,	PUNCT
ejpam-6705	66	16	x	x	X
ejpam-6705	66	17	)	)	PUNCT
ejpam-6705	67	1	+	+	ADV
ejpam-6705	67	2	gb(x	gb(x	ADJ
ejpam-6705	67	3	,	,	PUNCT
ejpam-6705	67	4	w	w	NOUN
ejpam-6705	67	5	,	,	PUNCT
ejpam-6705	67	6	w	w	NOUN
ejpam-6705	67	7	)	)	PUNCT
ejpam-6705	67	8	]	]	PUNCT
ejpam-6705	67	9	for	for	ADP
ejpam-6705	67	10	some	some	DET
ejpam-6705	67	11	constant	constant	ADJ
ejpam-6705	67	12	l	l	NOUN
ejpam-6705	67	13	≥	≥	NUM
ejpam-6705	67	14	1	1	NUM
ejpam-6705	67	15	.	.	PUNCT
ejpam-6705	68	1	the	the	DET
ejpam-6705	68	2	pair	pair	NOUN
ejpam-6705	68	3	(	(	PUNCT
ejpam-6705	68	4	x	x	X
ejpam-6705	68	5	,	,	PUNCT
ejpam-6705	68	6	gb	gb	PROPN
ejpam-6705	68	7	)	)	PUNCT
ejpam-6705	68	8	is	be	AUX
ejpam-6705	68	9	called	call	VERB
ejpam-6705	68	10	a	a	DET
ejpam-6705	68	11	gb	gb	ADV
ejpam-6705	68	12	-	-	PUNCT
ejpam-6705	68	13	metric	metric	ADJ
ejpam-6705	68	14	space	space	NOUN
ejpam-6705	68	15	.	.	PUNCT
ejpam-6705	68	16	example	example	NOUN
ejpam-6705	69	1	1	1	NUM
ejpam-6705	69	2	.	.	PUNCT
ejpam-6705	69	3	let	let	VERB
ejpam-6705	69	4	x	x	PUNCT
ejpam-6705	69	5	=	=	PUNCT
ejpam-6705	70	1	[	[	X
ejpam-6705	70	2	0,∞	0,∞	NUM
ejpam-6705	70	3	)	)	PUNCT
ejpam-6705	70	4	and	and	CCONJ
ejpam-6705	70	5	gb	gb	PRON
ejpam-6705	70	6	:	:	PUNCT
ejpam-6705	70	7	x	x	PROPN
ejpam-6705	70	8	×x	×x	X
ejpam-6705	70	9	×x	×x	X
ejpam-6705	70	10	→	→	PUNCT
ejpam-6705	70	11	[	[	X
ejpam-6705	70	12	0,∞	0,∞	NOUN
ejpam-6705	70	13	)	)	PUNCT
ejpam-6705	70	14	be	be	VERB
ejpam-6705	70	15	a	a	DET
ejpam-6705	70	16	mapping	mapping	NOUN
ejpam-6705	70	17	defined	define	VERB
ejpam-6705	70	18	by	by	ADP
ejpam-6705	70	19	gb(u	gb(u	NUM
ejpam-6705	70	20	,	,	PUNCT
ejpam-6705	70	21	v	v	NOUN
ejpam-6705	70	22	,	,	PUNCT
ejpam-6705	70	23	w	w	NOUN
ejpam-6705	70	24	)	)	PUNCT
ejpam-6705	70	25	=	=	NOUN
ejpam-6705	70	26	|u−	|u−	NOUN
ejpam-6705	70	27	v|q	v|q	VERB
ejpam-6705	70	28	+	+	CCONJ
ejpam-6705	70	29	|u−	|u−	ADJ
ejpam-6705	70	30	w|q	w|q	NOUN
ejpam-6705	71	1	+	+	CCONJ
ejpam-6705	71	2	|v	|v	PROPN
ejpam-6705	71	3	−	−	PROPN
ejpam-6705	71	4	w|q	w|q	NOUN
ejpam-6705	71	5	,	,	PUNCT
ejpam-6705	71	6	where	where	SCONJ
ejpam-6705	71	7	q	q	PROPN
ejpam-6705	71	8	≥	≥	NUM
ejpam-6705	71	9	1	1	NUM
ejpam-6705	71	10	.	.	PUNCT
ejpam-6705	72	1	we	we	PRON
ejpam-6705	72	2	have	have	VERB
ejpam-6705	72	3	:	:	PUNCT
ejpam-6705	72	4	(	(	PUNCT
ejpam-6705	72	5	i	i	NOUN
ejpam-6705	72	6	)	)	PUNCT
ejpam-6705	72	7	gb(u	gb(u	NUM
ejpam-6705	72	8	,	,	PUNCT
ejpam-6705	72	9	v	v	NOUN
ejpam-6705	72	10	,	,	PUNCT
ejpam-6705	72	11	w	w	NOUN
ejpam-6705	72	12	)	)	PUNCT
ejpam-6705	72	13	≥	≥	NOUN
ejpam-6705	72	14	0	0	NUM
ejpam-6705	72	15	.	.	PUNCT
ejpam-6705	73	1	(	(	PUNCT
ejpam-6705	73	2	ii	ii	NOUN
ejpam-6705	73	3	)	)	PUNCT
ejpam-6705	73	4	gb(u	gb(u	NUM
ejpam-6705	73	5	,	,	PUNCT
ejpam-6705	73	6	v	v	NOUN
ejpam-6705	73	7	,	,	PUNCT
ejpam-6705	73	8	w	w	NOUN
ejpam-6705	73	9	)	)	PUNCT
ejpam-6705	73	10	=	=	SYM
ejpam-6705	73	11	0	0	NUM
ejpam-6705	73	12	⇔	⇔	PROPN
ejpam-6705	73	13	|u−	|u−	ADJ
ejpam-6705	73	14	v|q	v|q	VERB
ejpam-6705	74	1	+	+	CCONJ
ejpam-6705	74	2	|u−	|u−	ADJ
ejpam-6705	74	3	w|q	w|q	NOUN
ejpam-6705	74	4	+	+	CCONJ
ejpam-6705	74	5	|v	|v	PROPN
ejpam-6705	74	6	−	−	NOUN
ejpam-6705	74	7	w|q	w|q	NOUN
ejpam-6705	75	1	=	=	SYM
ejpam-6705	75	2	0	0	NUM
ejpam-6705	75	3	⇔	⇔	PROPN
ejpam-6705	75	4	|u−	|u−	ADJ
ejpam-6705	75	5	v|q	v|q	VERB
ejpam-6705	75	6	=	=	SYM
ejpam-6705	75	7	0	0	NUM
ejpam-6705	75	8	,	,	PUNCT
ejpam-6705	75	9	|u−	|u−	ADJ
ejpam-6705	75	10	w|q	w|q	NOUN
ejpam-6705	76	1	=	=	SYM
ejpam-6705	76	2	0	0	NUM
ejpam-6705	76	3	,	,	PUNCT
ejpam-6705	76	4	|v	|v	PROPN
ejpam-6705	76	5	−	−	PROPN
ejpam-6705	76	6	w|q	w|q	NOUN
ejpam-6705	77	1	=	=	SYM
ejpam-6705	77	2	0	0	NUM
ejpam-6705	77	3	⇔	⇔	PROPN
ejpam-6705	77	4	|u−	|u−	PROPN
ejpam-6705	77	5	v|	v|	PROPN
ejpam-6705	77	6	=	=	SYM
ejpam-6705	77	7	0	0	X
ejpam-6705	77	8	.	.	PUNCT
ejpam-6705	78	1	it	it	PRON
ejpam-6705	78	2	yields	yield	VERB
ejpam-6705	78	3	that	that	SCONJ
ejpam-6705	78	4	u	u	PRON
ejpam-6705	78	5	=	=	PUNCT
ejpam-6705	78	6	v.	v.	ADP
ejpam-6705	78	7	also	also	ADV
ejpam-6705	78	8	,	,	PUNCT
ejpam-6705	78	9	|u−	|u−	ADJ
ejpam-6705	78	10	w|	w|	NOUN
ejpam-6705	78	11	=	=	SYM
ejpam-6705	78	12	0	0	NUM
ejpam-6705	78	13	⇒	⇒	NOUN
ejpam-6705	78	14	u	u	NOUN
ejpam-6705	78	15	=	=	PROPN
ejpam-6705	78	16	w.	w.	PROPN
ejpam-6705	78	17	moreover	moreover	ADV
ejpam-6705	78	18	,	,	PUNCT
ejpam-6705	78	19	|v	|v	PROPN
ejpam-6705	78	20	−	−	NOUN
ejpam-6705	78	21	w|	w|	NOUN
ejpam-6705	78	22	=	=	SYM
ejpam-6705	78	23	0	0	NUM
ejpam-6705	78	24	⇒	⇒	NOUN
ejpam-6705	78	25	v	v	NOUN
ejpam-6705	78	26	=	=	SYM
ejpam-6705	78	27	w.	w.	NOUN
ejpam-6705	78	28	we	we	PRON
ejpam-6705	78	29	have	have	VERB
ejpam-6705	78	30	u	u	NOUN
ejpam-6705	78	31	=	=	NOUN
ejpam-6705	78	32	v	v	PROPN
ejpam-6705	78	33	=	=	SYM
ejpam-6705	78	34	w.	w.	PROPN
ejpam-6705	78	35	(	(	PUNCT
ejpam-6705	78	36	iii	iii	NOUN
ejpam-6705	78	37	)	)	PUNCT
ejpam-6705	78	38	trivial	trivial	ADJ
ejpam-6705	78	39	.	.	PUNCT
ejpam-6705	79	1	s.	s.	PROPN
ejpam-6705	79	2	batul	batul	PROPN
ejpam-6705	79	3	et	et	PROPN
ejpam-6705	79	4	al	al	PROPN
ejpam-6705	79	5	.	.	PUNCT
ejpam-6705	79	6	/	/	SYM
ejpam-6705	79	7	eur	eur	PROPN
ejpam-6705	79	8	.	.	PUNCT
ejpam-6705	80	1	j.	j.	PROPN
ejpam-6705	80	2	pure	pure	PROPN
ejpam-6705	80	3	appl	appl	PROPN
ejpam-6705	80	4	.	.	PROPN
ejpam-6705	80	5	math	math	PROPN
ejpam-6705	80	6	,	,	PUNCT
ejpam-6705	80	7	18	18	NUM
ejpam-6705	80	8	(	(	PUNCT
ejpam-6705	80	9	4	4	NUM
ejpam-6705	80	10	)	)	PUNCT
ejpam-6705	80	11	(	(	PUNCT
ejpam-6705	80	12	2025	2025	NUM
ejpam-6705	80	13	)	)	PUNCT
ejpam-6705	80	14	,	,	PUNCT
ejpam-6705	80	15	6705	6705	NUM
ejpam-6705	80	16	4	4	NUM
ejpam-6705	80	17	of	of	ADP
ejpam-6705	80	18	23	23	NUM
ejpam-6705	80	19	(	(	PUNCT
ejpam-6705	80	20	iv	iv	X
ejpam-6705	80	21	)	)	PUNCT
ejpam-6705	80	22	recall	recall	NOUN
ejpam-6705	80	23	that	that	PRON
ejpam-6705	80	24	(	(	PUNCT
ejpam-6705	80	25	a+	a+	X
ejpam-6705	80	26	b)q	b)q	NOUN
ejpam-6705	80	27	≤	≤	NUM
ejpam-6705	80	28	2q−1(aq	2q−1(aq	NUM
ejpam-6705	81	1	+	+	NUM
ejpam-6705	81	2	bq	bq	NOUN
ejpam-6705	81	3	)	)	PUNCT
ejpam-6705	81	4	,	,	PUNCT
ejpam-6705	82	1	q	q	X
ejpam-6705	82	2	≥	≥	NOUN
ejpam-6705	82	3	1	1	NUM
ejpam-6705	82	4	and	and	CCONJ
ejpam-6705	82	5	2n(a+	2n(a+	NUM
ejpam-6705	82	6	b	b	NOUN
ejpam-6705	82	7	)	)	PUNCT
ejpam-6705	83	1	+	+	NUM
ejpam-6705	83	2	c	c	NOUN
ejpam-6705	83	3	≤	≤	NOUN
ejpam-6705	83	4	2n(a+	2n(a+	NUM
ejpam-6705	83	5	b+	b+	X
ejpam-6705	83	6	c	c	NOUN
ejpam-6705	83	7	)	)	PUNCT
ejpam-6705	83	8	,	,	PUNCT
ejpam-6705	83	9	n	n	X
ejpam-6705	83	10	≥	≥	NOUN
ejpam-6705	83	11	1	1	NUM
ejpam-6705	83	12	.	.	PUNCT
ejpam-6705	84	1	now	now	ADV
ejpam-6705	84	2	,	,	PUNCT
ejpam-6705	84	3	gb(u	gb(u	NUM
ejpam-6705	84	4	,	,	PUNCT
ejpam-6705	84	5	v	v	NOUN
ejpam-6705	84	6	,	,	PUNCT
ejpam-6705	84	7	w	w	NOUN
ejpam-6705	84	8	)	)	PUNCT
ejpam-6705	84	9	=	=	NOUN
ejpam-6705	84	10	|u−	|u−	NOUN
ejpam-6705	84	11	v|q	v|q	VERB
ejpam-6705	85	1	+	+	CCONJ
ejpam-6705	85	2	|u−	|u−	ADJ
ejpam-6705	85	3	w|q	w|q	NOUN
ejpam-6705	85	4	+	+	CCONJ
ejpam-6705	85	5	|v	|v	PROPN
ejpam-6705	85	6	−	−	PROPN
ejpam-6705	85	7	w|q	w|q	NOUN
ejpam-6705	85	8	=	=	SYM
ejpam-6705	85	9	|u−	|u−	NOUN
ejpam-6705	85	10	v|q	v|q	VERB
ejpam-6705	86	1	+	+	CCONJ
ejpam-6705	86	2	|v	|v	PROPN
ejpam-6705	86	3	−	−	PROPN
ejpam-6705	86	4	x+	x+	ADJ
ejpam-6705	86	5	x−	x−	PROPN
ejpam-6705	86	6	w|q	w|q	PROPN
ejpam-6705	87	1	+	+	CCONJ
ejpam-6705	87	2	|w	|w	ADJ
ejpam-6705	87	3	−	−	PROPN
ejpam-6705	87	4	x+	x+	ADJ
ejpam-6705	87	5	x−	x−	PROPN
ejpam-6705	87	6	u|q	u|q	PROPN
ejpam-6705	88	1	≤	≤	ADJ
ejpam-6705	88	2	|u−	|u−	ADJ
ejpam-6705	88	3	v|q	v|q	VERB
ejpam-6705	89	1	+	+	CCONJ
ejpam-6705	90	1	2q−1(|v	2q−1(|v	NUM
ejpam-6705	90	2	−	−	NOUN
ejpam-6705	90	3	x|q	x|q	PUNCT
ejpam-6705	91	1	+	+	NUM
ejpam-6705	91	2	|x−	|x−	PROPN
ejpam-6705	91	3	w|q	w|q	NOUN
ejpam-6705	91	4	)	)	PUNCT
ejpam-6705	92	1	+	+	CCONJ
ejpam-6705	92	2	2q−1(|w	2q−1(|w	NUM
ejpam-6705	92	3	−	−	NOUN
ejpam-6705	92	4	x|q	x|q	PUNCT
ejpam-6705	93	1	+	+	CCONJ
ejpam-6705	93	2	|x−	|x−	NOUN
ejpam-6705	93	3	u|q	u|q	ADJ
ejpam-6705	93	4	)	)	PUNCT
ejpam-6705	93	5	≤	≤	NOUN
ejpam-6705	93	6	2q−1(|u−	2q−1(|u−	NUM
ejpam-6705	93	7	v|q	v|q	NOUN
ejpam-6705	93	8	+	+	CCONJ
ejpam-6705	93	9	|v	|v	PROPN
ejpam-6705	93	10	−	−	PROPN
ejpam-6705	93	11	x|q	x|q	PUNCT
ejpam-6705	94	1	+	+	CCONJ
ejpam-6705	94	2	|x−	|x−	ADJ
ejpam-6705	94	3	w|q	w|q	NOUN
ejpam-6705	95	1	+	+	CCONJ
ejpam-6705	95	2	|w	|w	ADJ
ejpam-6705	95	3	−	−	PROPN
ejpam-6705	95	4	x|q	x|q	PUNCT
ejpam-6705	96	1	+	+	CCONJ
ejpam-6705	96	2	|x−	|x−	NOUN
ejpam-6705	96	3	u|q	u|q	NOUN
ejpam-6705	96	4	)	)	PUNCT
ejpam-6705	97	1	=	=	SYM
ejpam-6705	97	2	2q−1(gb(u	2q−1(gb(u	NUM
ejpam-6705	97	3	,	,	PUNCT
ejpam-6705	97	4	v	v	NOUN
ejpam-6705	97	5	,	,	PUNCT
ejpam-6705	97	6	x	x	X
ejpam-6705	97	7	)	)	PUNCT
ejpam-6705	98	1	+	+	ADV
ejpam-6705	98	2	gb(x	gb(x	ADJ
ejpam-6705	98	3	,	,	PUNCT
ejpam-6705	98	4	w	w	NOUN
ejpam-6705	98	5	,	,	PUNCT
ejpam-6705	98	6	w	w	NOUN
ejpam-6705	98	7	)	)	PUNCT
ejpam-6705	98	8	)	)	PUNCT
ejpam-6705	99	1	=	=	PUNCT
ejpam-6705	99	2	l(gb(u	l(gb(u	PROPN
ejpam-6705	99	3	,	,	PUNCT
ejpam-6705	99	4	v	v	NOUN
ejpam-6705	99	5	,	,	PUNCT
ejpam-6705	99	6	x	x	X
ejpam-6705	99	7	)	)	PUNCT
ejpam-6705	99	8	+	+	ADV
ejpam-6705	99	9	gb(x	gb(x	ADJ
ejpam-6705	99	10	,	,	PUNCT
ejpam-6705	99	11	w	w	NOUN
ejpam-6705	99	12	,	,	PUNCT
ejpam-6705	99	13	w	w	NOUN
ejpam-6705	99	14	)	)	PUNCT
ejpam-6705	99	15	)	)	PUNCT
ejpam-6705	99	16	.	.	PUNCT
ejpam-6705	100	1	since	since	SCONJ
ejpam-6705	100	2	all	all	DET
ejpam-6705	100	3	conditions	condition	NOUN
ejpam-6705	100	4	are	be	AUX
ejpam-6705	100	5	satisfied	satisfied	ADJ
ejpam-6705	100	6	,	,	PUNCT
ejpam-6705	100	7	therefore	therefore	ADV
ejpam-6705	100	8	(	(	PUNCT
ejpam-6705	100	9	x	x	X
ejpam-6705	100	10	,	,	PUNCT
ejpam-6705	100	11	gb	gb	PROPN
ejpam-6705	100	12	)	)	PUNCT
ejpam-6705	100	13	is	be	AUX
ejpam-6705	100	14	a	a	DET
ejpam-6705	100	15	gb	gb	ADV
ejpam-6705	100	16	-	-	PUNCT
ejpam-6705	100	17	metric	metric	ADJ
ejpam-6705	100	18	space	space	NOUN
ejpam-6705	100	19	.	.	PUNCT
ejpam-6705	101	1	definition	definition	NOUN
ejpam-6705	101	2	2	2	NUM
ejpam-6705	101	3	.	.	PUNCT
ejpam-6705	102	1	[	[	X
ejpam-6705	102	2	35	35	NUM
ejpam-6705	102	3	]	]	X
ejpam-6705	102	4	let	let	AUX
ejpam-6705	102	5	(	(	PUNCT
ejpam-6705	102	6	x	x	X
ejpam-6705	102	7	,	,	PUNCT
ejpam-6705	102	8	gb	gb	PROPN
ejpam-6705	102	9	)	)	PUNCT
ejpam-6705	102	10	be	be	AUX
ejpam-6705	102	11	a	a	DET
ejpam-6705	102	12	gb	gb	ADV
ejpam-6705	102	13	-	-	PUNCT
ejpam-6705	102	14	metric	metric	ADJ
ejpam-6705	102	15	space	space	NOUN
ejpam-6705	102	16	.	.	PUNCT
ejpam-6705	103	1	a	a	DET
ejpam-6705	103	2	sequence	sequence	NOUN
ejpam-6705	103	3	(	(	PUNCT
ejpam-6705	103	4	us	us	PROPN
ejpam-6705	103	5	)	)	PUNCT
ejpam-6705	103	6	in	in	ADP
ejpam-6705	103	7	x	x	VERB
ejpam-6705	103	8	is	be	AUX
ejpam-6705	103	9	said	say	VERB
ejpam-6705	103	10	to	to	PART
ejpam-6705	103	11	converge	converge	VERB
ejpam-6705	103	12	to	to	ADP
ejpam-6705	103	13	u	u	PROPN
ejpam-6705	103	14	∈	∈	PROPN
ejpam-6705	103	15	x	x	SYM
ejpam-6705	103	16	if	if	SCONJ
ejpam-6705	103	17	and	and	CCONJ
ejpam-6705	103	18	only	only	ADV
ejpam-6705	103	19	if	if	SCONJ
ejpam-6705	103	20	gb(us	gb(us	PROPN
ejpam-6705	103	21	,	,	PUNCT
ejpam-6705	103	22	us	we	PRON
ejpam-6705	103	23	,	,	PUNCT
ejpam-6705	103	24	u	u	NOUN
ejpam-6705	103	25	)	)	PUNCT
ejpam-6705	103	26	=	=	SYM
ejpam-6705	104	1	gb(u	gb(u	X
ejpam-6705	104	2	,	,	PUNCT
ejpam-6705	104	3	u	u	NOUN
ejpam-6705	104	4	,	,	PUNCT
ejpam-6705	104	5	us	we	PRON
ejpam-6705	104	6	)	)	PUNCT
ejpam-6705	104	7	→	→	SYM
ejpam-6705	104	8	0	0	PUNCT
ejpam-6705	104	9	as	as	ADP
ejpam-6705	104	10	s→	s→	PROPN
ejpam-6705	104	11	∞.	∞.	PROPN
ejpam-6705	104	12	definition	definition	NOUN
ejpam-6705	104	13	3	3	NUM
ejpam-6705	104	14	.	.	PUNCT
ejpam-6705	105	1	[	[	X
ejpam-6705	105	2	35	35	NUM
ejpam-6705	105	3	]	]	PUNCT
ejpam-6705	105	4	a	a	DET
ejpam-6705	105	5	sequence	sequence	NOUN
ejpam-6705	105	6	(	(	PUNCT
ejpam-6705	105	7	us	us	PROPN
ejpam-6705	105	8	)	)	PUNCT
ejpam-6705	105	9	∈	∈	PROPN
ejpam-6705	105	10	x	x	PUNCT
ejpam-6705	105	11	is	be	AUX
ejpam-6705	105	12	called	call	VERB
ejpam-6705	105	13	a	a	DET
ejpam-6705	105	14	cauchy	cauchy	ADJ
ejpam-6705	105	15	sequence	sequence	NOUN
ejpam-6705	105	16	if	if	SCONJ
ejpam-6705	105	17	for	for	ADP
ejpam-6705	105	18	any	any	PRON
ejpam-6705	105	19	ϵ	ϵ	X
ejpam-6705	105	20	>	>	SYM
ejpam-6705	105	21	0	0	PUNCT
ejpam-6705	105	22	there	there	PRON
ejpam-6705	105	23	exists	exist	VERB
ejpam-6705	105	24	a	a	DET
ejpam-6705	105	25	positive	positive	ADJ
ejpam-6705	105	26	integer	integer	NOUN
ejpam-6705	105	27	s0	s0	NOUN
ejpam-6705	105	28	such	such	ADJ
ejpam-6705	105	29	that	that	PRON
ejpam-6705	105	30	for	for	ADP
ejpam-6705	105	31	all	all	DET
ejpam-6705	105	32	s	s	NOUN
ejpam-6705	105	33	,	,	PUNCT
ejpam-6705	105	34	r	r	NOUN
ejpam-6705	105	35	≥	≥	NOUN
ejpam-6705	105	36	s0,gb(us	s0,gb(us	PROPN
ejpam-6705	105	37	,	,	PUNCT
ejpam-6705	105	38	us	we	PRON
ejpam-6705	105	39	,	,	PUNCT
ejpam-6705	105	40	ur	ur	INTJ
ejpam-6705	105	41	)	)	PUNCT
ejpam-6705	105	42	<	<	X
ejpam-6705	105	43	ϵ.	ϵ.	NOUN
ejpam-6705	105	44	definition	definition	NOUN
ejpam-6705	105	45	4	4	NUM
ejpam-6705	105	46	.	.	PUNCT
ejpam-6705	106	1	[	[	X
ejpam-6705	106	2	35	35	NUM
ejpam-6705	106	3	]	]	PUNCT
ejpam-6705	106	4	a	a	DET
ejpam-6705	106	5	gb	gb	ADV
ejpam-6705	106	6	-	-	PUNCT
ejpam-6705	106	7	metric	metric	ADJ
ejpam-6705	106	8	space	space	NOUN
ejpam-6705	106	9	(	(	PUNCT
ejpam-6705	106	10	x	x	X
ejpam-6705	106	11	,	,	PUNCT
ejpam-6705	106	12	gb	gb	PROPN
ejpam-6705	106	13	)	)	PUNCT
ejpam-6705	106	14	is	be	AUX
ejpam-6705	106	15	a	a	DET
ejpam-6705	106	16	complete	complete	ADJ
ejpam-6705	106	17	gb	gb	NOUN
ejpam-6705	106	18	-	-	PUNCT
ejpam-6705	106	19	metric	metric	ADJ
ejpam-6705	106	20	if	if	SCONJ
ejpam-6705	106	21	every	every	DET
ejpam-6705	106	22	cauchy	cauchy	ADJ
ejpam-6705	106	23	sequence	sequence	NOUN
ejpam-6705	106	24	in	in	ADP
ejpam-6705	106	25	(	(	PUNCT
ejpam-6705	106	26	x	x	INTJ
ejpam-6705	106	27	,	,	PUNCT
ejpam-6705	106	28	gb	gb	NOUN
ejpam-6705	106	29	)	)	PUNCT
ejpam-6705	106	30	converges	converge	VERB
ejpam-6705	106	31	in	in	ADP
ejpam-6705	106	32	(	(	PUNCT
ejpam-6705	106	33	x	x	NOUN
ejpam-6705	106	34	,	,	PUNCT
ejpam-6705	106	35	gb	gb	NOUN
ejpam-6705	106	36	)	)	PUNCT
ejpam-6705	106	37	.	.	PUNCT
ejpam-6705	107	1	definition	definition	NOUN
ejpam-6705	107	2	5	5	NUM
ejpam-6705	107	3	.	.	PUNCT
ejpam-6705	108	1	let	let	AUX
ejpam-6705	108	2	(	(	PUNCT
ejpam-6705	108	3	x	x	X
ejpam-6705	108	4	,	,	PUNCT
ejpam-6705	108	5	gb,≼	gb,≼	NOUN
ejpam-6705	108	6	)	)	PUNCT
ejpam-6705	108	7	be	be	AUX
ejpam-6705	108	8	a	a	DET
ejpam-6705	108	9	gb	gb	ADV
ejpam-6705	108	10	-	-	PUNCT
ejpam-6705	108	11	metric	metric	ADJ
ejpam-6705	108	12	space	space	NOUN
ejpam-6705	108	13	,	,	PUNCT
ejpam-6705	108	14	and	and	CCONJ
ejpam-6705	108	15	θ	θ	NOUN
ejpam-6705	108	16	:	:	PUNCT
ejpam-6705	109	1	x	x	X
ejpam-6705	109	2	→	→	PUNCT
ejpam-6705	109	3	[	[	X
ejpam-6705	109	4	0,∞	0,∞	NOUN
ejpam-6705	109	5	)	)	PUNCT
ejpam-6705	109	6	be	be	AUX
ejpam-6705	109	7	a	a	DET
ejpam-6705	109	8	functional	functional	ADJ
ejpam-6705	109	9	.	.	PUNCT
ejpam-6705	110	1	we	we	PRON
ejpam-6705	110	2	define	define	VERB
ejpam-6705	110	3	the	the	DET
ejpam-6705	110	4	relation	relation	NOUN
ejpam-6705	110	5	≼	≼	ADV
ejpam-6705	110	6	as	as	SCONJ
ejpam-6705	110	7	follows	follow	VERB
ejpam-6705	110	8	:	:	PUNCT
ejpam-6705	110	9	u	u	NOUN
ejpam-6705	110	10	≼	≼	PROPN
ejpam-6705	110	11	v	v	ADP
ejpam-6705	110	12	⇔	⇔	PROPN
ejpam-6705	110	13	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	110	14	,	,	PUNCT
ejpam-6705	110	15	u	u	NOUN
ejpam-6705	110	16	,	,	PUNCT
ejpam-6705	110	17	v	v	NOUN
ejpam-6705	110	18	)	)	PUNCT
ejpam-6705	110	19	)	)	PUNCT
ejpam-6705	110	20	≤	≤	NUM
ejpam-6705	110	21	θ(u)−θ(v	θ(u)−θ(v	NOUN
ejpam-6705	110	22	)	)	PUNCT
ejpam-6705	110	23	∀	∀	X
ejpam-6705	110	24	u	u	NOUN
ejpam-6705	110	25	,	,	PUNCT
ejpam-6705	110	26	v	v	NOUN
ejpam-6705	110	27	∈	∈	PROPN
ejpam-6705	110	28	x	x	X
ejpam-6705	110	29	,	,	PUNCT
ejpam-6705	110	30	where	where	SCONJ
ejpam-6705	110	31	κ	κ	NOUN
ejpam-6705	110	32	:	:	PUNCT
ejpam-6705	111	1	[	[	X
ejpam-6705	111	2	0,∞	0,∞	NOUN
ejpam-6705	111	3	)	)	PUNCT
ejpam-6705	111	4	→	→	PUNCT
ejpam-6705	112	1	[	[	X
ejpam-6705	112	2	0,∞	0,∞	NUM
ejpam-6705	112	3	)	)	PUNCT
ejpam-6705	112	4	is	be	AUX
ejpam-6705	112	5	so	so	SCONJ
ejpam-6705	112	6	that	that	SCONJ
ejpam-6705	112	7	(	(	PUNCT
ejpam-6705	112	8	i	i	NOUN
ejpam-6705	112	9	)	)	PUNCT
ejpam-6705	112	10	κ	κ	PROPN
ejpam-6705	112	11	is	be	AUX
ejpam-6705	112	12	increasing	increase	VERB
ejpam-6705	112	13	and	and	CCONJ
ejpam-6705	112	14	continuous	continuous	ADJ
ejpam-6705	112	15	.	.	PUNCT
ejpam-6705	113	1	(	(	PUNCT
ejpam-6705	113	2	ii	ii	NOUN
ejpam-6705	113	3	)	)	PUNCT
ejpam-6705	113	4	κ−1({0	κ−1({0	NOUN
ejpam-6705	113	5	}	}	PUNCT
ejpam-6705	113	6	)	)	PUNCT
ejpam-6705	114	1	=	=	PUNCT
ejpam-6705	114	2	{	{	PUNCT
ejpam-6705	114	3	0	0	NUM
ejpam-6705	114	4	}	}	PUNCT
ejpam-6705	114	5	.	.	PUNCT
ejpam-6705	115	1	(	(	PUNCT
ejpam-6705	115	2	iii	iii	X
ejpam-6705	115	3	)	)	PUNCT
ejpam-6705	115	4	κ(l(k+	κ(l(k+	PROPN
ejpam-6705	115	5	j	j	PROPN
ejpam-6705	115	6	)	)	PUNCT
ejpam-6705	115	7	)	)	PUNCT
ejpam-6705	116	1	≤	≤	PROPN
ejpam-6705	116	2	κ(k	κ(k	PROPN
ejpam-6705	116	3	)	)	PUNCT
ejpam-6705	117	1	+	+	X
ejpam-6705	117	2	κ(j	κ(j	NOUN
ejpam-6705	117	3	)	)	PUNCT
ejpam-6705	117	4	∀	∀	PUNCT
ejpam-6705	118	1	k	k	X
ejpam-6705	118	2	,	,	PUNCT
ejpam-6705	118	3	j	j	PROPN
ejpam-6705	118	4	∈	∈	PROPN
ejpam-6705	119	1	[	[	X
ejpam-6705	119	2	0,∞	0,∞	NOUN
ejpam-6705	119	3	)	)	PUNCT
ejpam-6705	119	4	.	.	PUNCT
ejpam-6705	120	1	the	the	DET
ejpam-6705	120	2	triplet	triplet	NOUN
ejpam-6705	120	3	(	(	PUNCT
ejpam-6705	120	4	x	x	NOUN
ejpam-6705	120	5	,	,	PUNCT
ejpam-6705	120	6	gb,≼	gb,≼	NOUN
ejpam-6705	120	7	)	)	PUNCT
ejpam-6705	120	8	with	with	ADP
ejpam-6705	120	9	this	this	DET
ejpam-6705	120	10	partial	partial	ADJ
ejpam-6705	120	11	order	order	NOUN
ejpam-6705	120	12	is	be	AUX
ejpam-6705	120	13	called	call	VERB
ejpam-6705	120	14	an	an	DET
ejpam-6705	120	15	ordered	order	VERB
ejpam-6705	120	16	gb	gb	NOUN
ejpam-6705	120	17	-	-	PUNCT
ejpam-6705	120	18	metric	metric	ADJ
ejpam-6705	120	19	space	space	NOUN
ejpam-6705	120	20	induced	induce	VERB
ejpam-6705	120	21	via	via	ADP
ejpam-6705	120	22	(	(	PUNCT
ejpam-6705	120	23	κ	κ	NOUN
ejpam-6705	120	24	,	,	PUNCT
ejpam-6705	120	25	θ	θ	NOUN
ejpam-6705	120	26	)	)	PUNCT
ejpam-6705	120	27	.	.	PUNCT
ejpam-6705	121	1	proposition	proposition	NOUN
ejpam-6705	121	2	1	1	NUM
ejpam-6705	121	3	.	.	PUNCT
ejpam-6705	121	4	suppose	suppose	VERB
ejpam-6705	121	5	that	that	SCONJ
ejpam-6705	121	6	(	(	PUNCT
ejpam-6705	121	7	x	x	X
ejpam-6705	121	8	,	,	PUNCT
ejpam-6705	121	9	gb	gb	PROPN
ejpam-6705	121	10	)	)	PUNCT
ejpam-6705	121	11	is	be	AUX
ejpam-6705	121	12	a	a	DET
ejpam-6705	121	13	gb	gb	ADV
ejpam-6705	121	14	-	-	PUNCT
ejpam-6705	121	15	metric	metric	ADJ
ejpam-6705	121	16	space	space	NOUN
ejpam-6705	121	17	,	,	PUNCT
ejpam-6705	121	18	then	then	ADV
ejpam-6705	121	19	≼	≼	PROPN
ejpam-6705	121	20	is	be	AUX
ejpam-6705	121	21	a	a	DET
ejpam-6705	121	22	partial	partial	ADJ
ejpam-6705	121	23	order	order	NOUN
ejpam-6705	121	24	on	on	ADP
ejpam-6705	121	25	x	x	PUNCT
ejpam-6705	121	26	and	and	CCONJ
ejpam-6705	121	27	(	(	PUNCT
ejpam-6705	121	28	x	x	X
ejpam-6705	121	29	,	,	PUNCT
ejpam-6705	121	30	≼	≼	PROPN
ejpam-6705	121	31	)	)	PUNCT
ejpam-6705	121	32	is	be	AUX
ejpam-6705	121	33	a	a	DET
ejpam-6705	121	34	partially	partially	ADV
ejpam-6705	121	35	ordered	order	VERB
ejpam-6705	121	36	set	set	NOUN
ejpam-6705	121	37	.	.	PUNCT
ejpam-6705	122	1	proof	proof	NOUN
ejpam-6705	122	2	.	.	PUNCT
ejpam-6705	123	1	let	let	AUX
ejpam-6705	123	2	start	start	VERB
ejpam-6705	123	3	by	by	ADP
ejpam-6705	123	4	showing	show	VERB
ejpam-6705	123	5	that	that	SCONJ
ejpam-6705	123	6	the	the	DET
ejpam-6705	123	7	relation	relation	NOUN
ejpam-6705	123	8	≼	≼	ADV
ejpam-6705	123	9	is	be	AUX
ejpam-6705	123	10	reflexive	reflexive	ADJ
ejpam-6705	123	11	,	,	PUNCT
ejpam-6705	123	12	meaning	mean	VERB
ejpam-6705	123	13	that	that	SCONJ
ejpam-6705	123	14	every	every	DET
ejpam-6705	123	15	element	element	NOUN
ejpam-6705	123	16	is	be	AUX
ejpam-6705	123	17	≼	≼	PROPN
ejpam-6705	123	18	itself	itself	PRON
ejpam-6705	123	19	.	.	PUNCT
ejpam-6705	124	1	s.	s.	PROPN
ejpam-6705	124	2	batul	batul	PROPN
ejpam-6705	124	3	et	et	PROPN
ejpam-6705	124	4	al	al	PROPN
ejpam-6705	124	5	.	.	PUNCT
ejpam-6705	124	6	/	/	SYM
ejpam-6705	124	7	eur	eur	PROPN
ejpam-6705	124	8	.	.	PUNCT
ejpam-6705	125	1	j.	j.	PROPN
ejpam-6705	125	2	pure	pure	PROPN
ejpam-6705	125	3	appl	appl	PROPN
ejpam-6705	125	4	.	.	PROPN
ejpam-6705	125	5	math	math	PROPN
ejpam-6705	125	6	,	,	PUNCT
ejpam-6705	125	7	18	18	NUM
ejpam-6705	125	8	(	(	PUNCT
ejpam-6705	125	9	4	4	NUM
ejpam-6705	125	10	)	)	PUNCT
ejpam-6705	125	11	(	(	PUNCT
ejpam-6705	125	12	2025	2025	NUM
ejpam-6705	125	13	)	)	PUNCT
ejpam-6705	125	14	,	,	PUNCT
ejpam-6705	125	15	6705	6705	NUM
ejpam-6705	125	16	5	5	NUM
ejpam-6705	125	17	of	of	ADP
ejpam-6705	125	18	23	23	NUM
ejpam-6705	125	19	since	since	SCONJ
ejpam-6705	125	20	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	125	21	,	,	PUNCT
ejpam-6705	125	22	u	u	NOUN
ejpam-6705	125	23	,	,	PUNCT
ejpam-6705	125	24	u	u	NOUN
ejpam-6705	125	25	)	)	PUNCT
ejpam-6705	125	26	)	)	PUNCT
ejpam-6705	126	1	=	=	SYM
ejpam-6705	126	2	θ(u)−θ(u	θ(u)−θ(u	NOUN
ejpam-6705	126	3	)	)	PUNCT
ejpam-6705	126	4	for	for	ADP
ejpam-6705	126	5	all	all	DET
ejpam-6705	126	6	u	u	NOUN
ejpam-6705	126	7	∈	∈	PROPN
ejpam-6705	126	8	x	x	X
ejpam-6705	126	9	,	,	PUNCT
ejpam-6705	126	10	this	this	PRON
ejpam-6705	126	11	implies	imply	VERB
ejpam-6705	126	12	that	that	SCONJ
ejpam-6705	126	13	≼	≼	PROPN
ejpam-6705	126	14	is	be	AUX
ejpam-6705	126	15	reflexive	reflexive	ADJ
ejpam-6705	126	16	.	.	PUNCT
ejpam-6705	127	1	next	next	ADJ
ejpam-6705	127	2	to	to	PART
ejpam-6705	127	3	show	show	VERB
ejpam-6705	127	4	that	that	SCONJ
ejpam-6705	127	5	the	the	DET
ejpam-6705	127	6	relation	relation	NOUN
ejpam-6705	127	7	≼	≼	PROPN
ejpam-6705	127	8	is	be	AUX
ejpam-6705	127	9	antisymmetric	antisymmetric	ADJ
ejpam-6705	127	10	.	.	PUNCT
ejpam-6705	128	1	if	if	SCONJ
ejpam-6705	128	2	u	u	PROPN
ejpam-6705	128	3	,	,	PUNCT
ejpam-6705	128	4	v	v	PROPN
ejpam-6705	128	5	∈	∈	NOUN
ejpam-6705	128	6	x	x	PUNCT
ejpam-6705	128	7	with	with	ADP
ejpam-6705	128	8	u	u	PRON
ejpam-6705	128	9	≼	≼	PROPN
ejpam-6705	128	10	v	v	NOUN
ejpam-6705	128	11	and	and	CCONJ
ejpam-6705	128	12	v	v	ADP
ejpam-6705	128	13	≼	≼	PROPN
ejpam-6705	128	14	u	u	NOUN
ejpam-6705	128	15	,	,	PUNCT
ejpam-6705	128	16	then	then	ADV
ejpam-6705	128	17	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	128	18	,	,	PUNCT
ejpam-6705	128	19	u	u	NOUN
ejpam-6705	128	20	,	,	PUNCT
ejpam-6705	128	21	v	v	NOUN
ejpam-6705	128	22	)	)	PUNCT
ejpam-6705	128	23	)	)	PUNCT
ejpam-6705	128	24	≤	≤	NOUN
ejpam-6705	128	25	θ(u)−θ(v	θ(u)−θ(v	NOUN
ejpam-6705	128	26	)	)	PUNCT
ejpam-6705	128	27	and	and	CCONJ
ejpam-6705	128	28	κ(gb(v	κ(gb(v	PROPN
ejpam-6705	128	29	,	,	PUNCT
ejpam-6705	128	30	v	v	NOUN
ejpam-6705	128	31	,	,	PUNCT
ejpam-6705	128	32	u	u	NOUN
ejpam-6705	128	33	)	)	PUNCT
ejpam-6705	128	34	)	)	PUNCT
ejpam-6705	128	35	≤	≤	NOUN
ejpam-6705	128	36	θ(v)−θ(u	θ(v)−θ(u	PRON
ejpam-6705	128	37	)	)	PUNCT
ejpam-6705	128	38	.	.	PUNCT
ejpam-6705	129	1	it	it	PRON
ejpam-6705	129	2	implies	imply	VERB
ejpam-6705	129	3	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	129	4	,	,	PUNCT
ejpam-6705	129	5	u	u	NOUN
ejpam-6705	129	6	,	,	PUNCT
ejpam-6705	129	7	v	v	NOUN
ejpam-6705	129	8	)	)	PUNCT
ejpam-6705	129	9	)	)	PUNCT
ejpam-6705	130	1	+	+	CCONJ
ejpam-6705	131	1	κ(gb(v	κ(gb(v	PROPN
ejpam-6705	131	2	,	,	PUNCT
ejpam-6705	131	3	v	v	NOUN
ejpam-6705	131	4	,	,	PUNCT
ejpam-6705	131	5	u	u	NOUN
ejpam-6705	131	6	)	)	PUNCT
ejpam-6705	131	7	)	)	PUNCT
ejpam-6705	132	1	=	=	PUNCT
ejpam-6705	132	2	0	0	X
ejpam-6705	132	3	.	.	PUNCT
ejpam-6705	133	1	thus	thus	ADV
ejpam-6705	133	2	,	,	PUNCT
ejpam-6705	133	3	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	133	4	,	,	PUNCT
ejpam-6705	133	5	u	u	NOUN
ejpam-6705	133	6	,	,	PUNCT
ejpam-6705	133	7	v	v	NOUN
ejpam-6705	133	8	)	)	PUNCT
ejpam-6705	133	9	)	)	PUNCT
ejpam-6705	134	1	=	=	SYM
ejpam-6705	134	2	κ(gb(v	κ(gb(v	PROPN
ejpam-6705	134	3	,	,	PUNCT
ejpam-6705	134	4	v	v	NOUN
ejpam-6705	134	5	,	,	PUNCT
ejpam-6705	134	6	u	u	NOUN
ejpam-6705	134	7	)	)	PUNCT
ejpam-6705	134	8	)	)	PUNCT
ejpam-6705	135	1	=	=	PUNCT
ejpam-6705	135	2	0	0	X
ejpam-6705	135	3	.	.	PUNCT
ejpam-6705	136	1	that	that	PRON
ejpam-6705	136	2	is	be	AUX
ejpam-6705	136	3	,	,	PUNCT
ejpam-6705	136	4	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	136	5	,	,	PUNCT
ejpam-6705	136	6	u	u	NOUN
ejpam-6705	136	7	,	,	PUNCT
ejpam-6705	136	8	v	v	NOUN
ejpam-6705	136	9	)	)	PUNCT
ejpam-6705	136	10	)	)	PUNCT
ejpam-6705	137	1	=	=	PUNCT
ejpam-6705	137	2	0	0	NUM
ejpam-6705	137	3	,	,	PUNCT
ejpam-6705	137	4	and	and	CCONJ
ejpam-6705	137	5	so	so	ADV
ejpam-6705	137	6	u	u	X
ejpam-6705	137	7	=	=	PROPN
ejpam-6705	137	8	v	v	PROPN
ejpam-6705	137	9	,	,	PUNCT
ejpam-6705	137	10	which	which	PRON
ejpam-6705	137	11	shows	show	VERB
ejpam-6705	137	12	that	that	SCONJ
ejpam-6705	137	13	≼	≼	PROPN
ejpam-6705	137	14	is	be	AUX
ejpam-6705	137	15	antisymmetric	antisymmetric	ADJ
ejpam-6705	137	16	.	.	PUNCT
ejpam-6705	138	1	lastly	lastly	ADV
ejpam-6705	138	2	,	,	PUNCT
ejpam-6705	138	3	we	we	PRON
ejpam-6705	138	4	prove	prove	VERB
ejpam-6705	138	5	that	that	SCONJ
ejpam-6705	138	6	≼	≼	PROPN
ejpam-6705	138	7	is	be	AUX
ejpam-6705	138	8	transitive	transitive	ADJ
ejpam-6705	138	9	.	.	PUNCT
ejpam-6705	139	1	if	if	SCONJ
ejpam-6705	139	2	u	u	PROPN
ejpam-6705	139	3	,	,	PUNCT
ejpam-6705	139	4	v	v	NOUN
ejpam-6705	139	5	,	,	PUNCT
ejpam-6705	139	6	w	w	PROPN
ejpam-6705	139	7	∈	∈	PROPN
ejpam-6705	139	8	x	x	PUNCT
ejpam-6705	139	9	such	such	ADJ
ejpam-6705	139	10	that	that	SCONJ
ejpam-6705	139	11	u	u	PROPN
ejpam-6705	139	12	≼	≼	ADJ
ejpam-6705	139	13	v	v	NOUN
ejpam-6705	139	14	and	and	CCONJ
ejpam-6705	139	15	v	v	ADP
ejpam-6705	139	16	≼	≼	PROPN
ejpam-6705	139	17	w	w	PROPN
ejpam-6705	139	18	,	,	PUNCT
ejpam-6705	139	19	then	then	ADV
ejpam-6705	139	20	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	139	21	,	,	PUNCT
ejpam-6705	139	22	u	u	NOUN
ejpam-6705	139	23	,	,	PUNCT
ejpam-6705	139	24	v	v	NOUN
ejpam-6705	139	25	)	)	PUNCT
ejpam-6705	139	26	)	)	PUNCT
ejpam-6705	139	27	≤	≤	NOUN
ejpam-6705	139	28	θ(u)−θ(v	θ(u)−θ(v	NOUN
ejpam-6705	139	29	)	)	PUNCT
ejpam-6705	139	30	.	.	PUNCT
ejpam-6705	140	1	(	(	PUNCT
ejpam-6705	140	2	1	1	X
ejpam-6705	140	3	)	)	PUNCT
ejpam-6705	140	4	also	also	ADV
ejpam-6705	140	5	,	,	PUNCT
ejpam-6705	140	6	κ(gb(v	κ(gb(v	PROPN
ejpam-6705	140	7	,	,	PUNCT
ejpam-6705	140	8	v	v	NOUN
ejpam-6705	140	9	,	,	PUNCT
ejpam-6705	140	10	u	u	NOUN
ejpam-6705	140	11	)	)	PUNCT
ejpam-6705	140	12	)	)	PUNCT
ejpam-6705	140	13	≤	≤	NOUN
ejpam-6705	140	14	θ(v)−θ(u	θ(v)−θ(u	PRON
ejpam-6705	140	15	)	)	PUNCT
ejpam-6705	140	16	.	.	PUNCT
ejpam-6705	141	1	(	(	PUNCT
ejpam-6705	141	2	2	2	X
ejpam-6705	141	3	)	)	PUNCT
ejpam-6705	141	4	hence	hence	ADV
ejpam-6705	141	5	,	,	PUNCT
ejpam-6705	141	6	combining	combine	VERB
ejpam-6705	141	7	(	(	PUNCT
ejpam-6705	141	8	1	1	NUM
ejpam-6705	141	9	)	)	PUNCT
ejpam-6705	141	10	and	and	CCONJ
ejpam-6705	141	11	(	(	PUNCT
ejpam-6705	141	12	2	2	NUM
ejpam-6705	141	13	)	)	PUNCT
ejpam-6705	141	14	,	,	PUNCT
ejpam-6705	141	15	one	one	PRON
ejpam-6705	141	16	writes	write	VERB
ejpam-6705	141	17	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	141	18	,	,	PUNCT
ejpam-6705	141	19	u	u	NOUN
ejpam-6705	141	20	,	,	PUNCT
ejpam-6705	141	21	v	v	NOUN
ejpam-6705	141	22	)	)	PUNCT
ejpam-6705	141	23	)	)	PUNCT
ejpam-6705	142	1	+	+	CCONJ
ejpam-6705	143	1	κ(gb(v	κ(gb(v	PROPN
ejpam-6705	143	2	,	,	PUNCT
ejpam-6705	143	3	v	v	NOUN
ejpam-6705	143	4	,	,	PUNCT
ejpam-6705	143	5	u	u	NOUN
ejpam-6705	143	6	)	)	PUNCT
ejpam-6705	143	7	)	)	PUNCT
ejpam-6705	143	8	≤	≤	NUM
ejpam-6705	143	9	θ(u)−θ(w	θ(u)−θ(w	X
ejpam-6705	143	10	)	)	PUNCT
ejpam-6705	143	11	.	.	PUNCT
ejpam-6705	144	1	by	by	ADP
ejpam-6705	144	2	the	the	DET
ejpam-6705	144	3	definition	definition	NOUN
ejpam-6705	144	4	of	of	ADP
ejpam-6705	144	5	gb	gb	ADV
ejpam-6705	144	6	-	-	PUNCT
ejpam-6705	144	7	metric	metric	ADJ
ejpam-6705	144	8	space	space	NOUN
ejpam-6705	144	9	,	,	PUNCT
ejpam-6705	144	10	one	one	PRON
ejpam-6705	144	11	has	have	VERB
ejpam-6705	144	12	κ(gb(u	κ(gb(u	PROPN
ejpam-6705	144	13	,	,	PUNCT
ejpam-6705	144	14	u	u	NOUN
ejpam-6705	144	15	,	,	PUNCT
ejpam-6705	144	16	w	w	NOUN
ejpam-6705	144	17	)	)	PUNCT
ejpam-6705	144	18	)	)	PUNCT
ejpam-6705	145	1	=	=	SYM
ejpam-6705	145	2	κ[l	κ[l	PROPN
ejpam-6705	145	3	(	(	PUNCT
ejpam-6705	145	4	gb(u	gb(u	X
ejpam-6705	145	5	,	,	PUNCT
ejpam-6705	145	6	u	u	NOUN
ejpam-6705	145	7	,	,	PUNCT
ejpam-6705	145	8	v	v	NOUN
ejpam-6705	145	9	)	)	PUNCT
ejpam-6705	145	10	+	+	NOUN
ejpam-6705	145	11	gb(v	gb(v	ADJ
ejpam-6705	145	12	,	,	PUNCT
ejpam-6705	145	13	v	v	NOUN
ejpam-6705	145	14	,	,	PUNCT
ejpam-6705	145	15	w	w	NOUN
ejpam-6705	145	16	)	)	PUNCT
ejpam-6705	145	17	)	)	PUNCT
ejpam-6705	145	18	]	]	PUNCT
ejpam-6705	145	19	≤	≤	NUM
ejpam-6705	145	20	κ	κ	X
ejpam-6705	145	21	(	(	PUNCT
ejpam-6705	145	22	gb(u	gb(u	NUM
ejpam-6705	145	23	,	,	PUNCT
ejpam-6705	145	24	u	u	NOUN
ejpam-6705	145	25	,	,	PUNCT
ejpam-6705	145	26	v	v	NOUN
ejpam-6705	145	27	)	)	PUNCT
ejpam-6705	145	28	)	)	PUNCT
ejpam-6705	146	1	+	+	CCONJ
ejpam-6705	146	2	κ	κ	X
ejpam-6705	146	3	(	(	PUNCT
ejpam-6705	146	4	gb(v	gb(v	NOUN
ejpam-6705	146	5	,	,	PUNCT
ejpam-6705	146	6	v	v	NOUN
ejpam-6705	146	7	,	,	PUNCT
ejpam-6705	146	8	w	w	NOUN
ejpam-6705	146	9	)	)	PUNCT
ejpam-6705	146	10	)	)	PUNCT
ejpam-6705	146	11	=	=	SYM
ejpam-6705	146	12	θ(u)−θ(v	θ(u)−θ(v	X
ejpam-6705	146	13	)	)	PUNCT
ejpam-6705	146	14	+	+	NUM
ejpam-6705	146	15	θ(v)−θ(w	θ(v)−θ(w	X
ejpam-6705	146	16	)	)	PUNCT
ejpam-6705	146	17	≤	≤	NOUN
ejpam-6705	146	18	θ(u)−θ(w	θ(u)−θ(w	NOUN
ejpam-6705	146	19	)	)	PUNCT
ejpam-6705	146	20	.	.	PUNCT
ejpam-6705	147	1	thus	thus	ADV
ejpam-6705	147	2	,	,	PUNCT
ejpam-6705	147	3	u	u	PROPN
ejpam-6705	147	4	≼	≼	PROPN
ejpam-6705	147	5	w.	w.	PROPN
ejpam-6705	147	6	the	the	DET
ejpam-6705	147	7	triplet	triplet	NOUN
ejpam-6705	147	8	(	(	PUNCT
ejpam-6705	147	9	x	x	NOUN
ejpam-6705	147	10	,	,	PUNCT
ejpam-6705	147	11	gb,≼	gb,≼	NOUN
ejpam-6705	147	12	)	)	PUNCT
ejpam-6705	147	13	is	be	AUX
ejpam-6705	147	14	called	call	VERB
ejpam-6705	147	15	partially	partially	ADV
ejpam-6705	147	16	ordered	order	VERB
ejpam-6705	147	17	gb	gb	ADV
ejpam-6705	147	18	-	-	PUNCT
ejpam-6705	147	19	metric	metric	ADJ
ejpam-6705	147	20	space	space	NOUN
ejpam-6705	147	21	induced	induce	VERB
ejpam-6705	147	22	via	via	ADP
ejpam-6705	147	23	(	(	PUNCT
ejpam-6705	147	24	κ	κ	NOUN
ejpam-6705	147	25	,	,	PUNCT
ejpam-6705	147	26	θ	θ	NOUN
ejpam-6705	147	27	)	)	PUNCT
ejpam-6705	147	28	.	.	PUNCT
ejpam-6705	148	1	definition	definition	NOUN
ejpam-6705	148	2	6	6	NUM
ejpam-6705	148	3	.	.	PUNCT
ejpam-6705	149	1	let	let	VERB
ejpam-6705	149	2	(	(	PUNCT
ejpam-6705	149	3	x	x	X
ejpam-6705	149	4	,	,	PUNCT
ejpam-6705	149	5	gb,≼	gb,≼	NOUN
ejpam-6705	149	6	)	)	PUNCT
ejpam-6705	149	7	be	be	AUX
ejpam-6705	149	8	an	an	DET
ejpam-6705	149	9	ordered	order	VERB
ejpam-6705	149	10	gb	gb	ADV
ejpam-6705	149	11	-	-	PUNCT
ejpam-6705	149	12	metric	metric	ADJ
ejpam-6705	149	13	space	space	NOUN
ejpam-6705	149	14	induced	induce	VERB
ejpam-6705	149	15	by	by	ADP
ejpam-6705	149	16	(	(	PUNCT
ejpam-6705	149	17	κ	κ	NOUN
ejpam-6705	149	18	,	,	PUNCT
ejpam-6705	149	19	θ	θ	NOUN
ejpam-6705	149	20	)	)	PUNCT
ejpam-6705	149	21	.	.	PUNCT
ejpam-6705	150	1	the	the	DET
ejpam-6705	150	2	following	follow	VERB
ejpam-6705	150	3	defines	define	VERB
ejpam-6705	150	4	the	the	DET
ejpam-6705	150	5	ordered	order	VERB
ejpam-6705	150	6	intervals	interval	NOUN
ejpam-6705	150	7	in	in	ADP
ejpam-6705	150	8	x	x	X
ejpam-6705	150	9	:	:	PUNCT
ejpam-6705	150	10	(	(	PUNCT
ejpam-6705	150	11	i	i	NOUN
ejpam-6705	150	12	)	)	PUNCT
ejpam-6705	151	1	[	[	X
ejpam-6705	151	2	u	u	NOUN
ejpam-6705	151	3	,	,	PUNCT
ejpam-6705	151	4	v	v	NOUN
ejpam-6705	151	5	]	]	X
ejpam-6705	151	6	=	=	PUNCT
ejpam-6705	151	7	{	{	PUNCT
ejpam-6705	151	8	w	w	NOUN
ejpam-6705	151	9	∈	∈	PROPN
ejpam-6705	151	10	x	x	X
ejpam-6705	151	11	:	:	PUNCT
ejpam-6705	151	12	u	u	NOUN
ejpam-6705	151	13	≼	≼	PROPN
ejpam-6705	151	14	w	w	PROPN
ejpam-6705	151	15	≼	≼	ADJ
ejpam-6705	151	16	v	v	ADP
ejpam-6705	151	17	}	}	PUNCT
ejpam-6705	151	18	.	.	PUNCT
ejpam-6705	152	1	(	(	PUNCT
ejpam-6705	152	2	ii	ii	NOUN
ejpam-6705	152	3	)	)	PUNCT
ejpam-6705	153	1	[	[	X
ejpam-6705	153	2	u,∞	u,∞	NOUN
ejpam-6705	153	3	)	)	PUNCT
ejpam-6705	153	4	=	=	PRON
ejpam-6705	153	5	{	{	PUNCT
ejpam-6705	153	6	w	w	NOUN
ejpam-6705	153	7	∈	∈	PROPN
ejpam-6705	153	8	x	x	X
ejpam-6705	153	9	:	:	PUNCT
ejpam-6705	153	10	u	u	NOUN
ejpam-6705	153	11	≼	≼	PROPN
ejpam-6705	153	12	w	w	PROPN
ejpam-6705	153	13	}	}	PUNCT
ejpam-6705	153	14	.	.	PUNCT
ejpam-6705	154	1	(	(	PUNCT
ejpam-6705	154	2	iii	iii	X
ejpam-6705	154	3	)	)	PUNCT
ejpam-6705	154	4	(	(	PUNCT
ejpam-6705	154	5	−∞	−∞	NOUN
ejpam-6705	154	6	,	,	PUNCT
ejpam-6705	154	7	u	u	NOUN
ejpam-6705	154	8	]	]	X
ejpam-6705	154	9	=	=	PUNCT
ejpam-6705	154	10	{	{	PUNCT
ejpam-6705	154	11	w	w	NOUN
ejpam-6705	154	12	∈	∈	PROPN
ejpam-6705	154	13	x	x	X
ejpam-6705	154	14	:	:	PUNCT
ejpam-6705	154	15	w	w	X
ejpam-6705	154	16	≼	≼	PROPN
ejpam-6705	154	17	u	u	NOUN
ejpam-6705	154	18	}	}	PUNCT
ejpam-6705	154	19	.	.	PUNCT
ejpam-6705	155	1	s.	s.	PROPN
ejpam-6705	155	2	batul	batul	PROPN
ejpam-6705	155	3	et	et	PROPN
ejpam-6705	155	4	al	al	PROPN
ejpam-6705	155	5	.	.	PUNCT
ejpam-6705	155	6	/	/	SYM
ejpam-6705	155	7	eur	eur	PROPN
ejpam-6705	155	8	.	.	PUNCT
ejpam-6705	156	1	j.	j.	PROPN
ejpam-6705	156	2	pure	pure	PROPN
ejpam-6705	156	3	appl	appl	PROPN
ejpam-6705	156	4	.	.	PROPN
ejpam-6705	156	5	math	math	PROPN
ejpam-6705	156	6	,	,	PUNCT
ejpam-6705	156	7	18	18	NUM
ejpam-6705	156	8	(	(	PUNCT
ejpam-6705	156	9	4	4	NUM
ejpam-6705	156	10	)	)	PUNCT
ejpam-6705	156	11	(	(	PUNCT
ejpam-6705	156	12	2025	2025	NUM
ejpam-6705	156	13	)	)	PUNCT
ejpam-6705	156	14	,	,	PUNCT
ejpam-6705	156	15	6705	6705	NUM
ejpam-6705	156	16	6	6	NUM
ejpam-6705	156	17	of	of	ADP
ejpam-6705	156	18	23	23	NUM
ejpam-6705	156	19	definition	definition	NOUN
ejpam-6705	156	20	7	7	NUM
ejpam-6705	156	21	.	.	PUNCT
ejpam-6705	157	1	[	[	X
ejpam-6705	157	2	40	40	NUM
ejpam-6705	157	3	]	]	PUNCT
ejpam-6705	157	4	let	let	VERB
ejpam-6705	157	5	u	u	PRON
ejpam-6705	157	6	∈	∈	PROPN
ejpam-6705	157	7	x	x	X
ejpam-6705	157	8	.	.	PUNCT
ejpam-6705	158	1	u	u	NOUN
ejpam-6705	158	2	is	be	AUX
ejpam-6705	158	3	said	say	VERB
ejpam-6705	158	4	to	to	PART
ejpam-6705	158	5	be	be	AUX
ejpam-6705	158	6	a	a	DET
ejpam-6705	158	7	fixed	fixed	ADJ
ejpam-6705	158	8	point	point	NOUN
ejpam-6705	158	9	of	of	ADP
ejpam-6705	158	10	a	a	DET
ejpam-6705	158	11	multivalued	multivalue	VERB
ejpam-6705	158	12	mapping	mapping	NOUN
ejpam-6705	158	13	t	t	NOUN
ejpam-6705	158	14	:	:	PUNCT
ejpam-6705	158	15	x	x	X
ejpam-6705	158	16	→	→	SYM
ejpam-6705	158	17	2x	2x	NUM
ejpam-6705	158	18	if	if	SCONJ
ejpam-6705	158	19	u	u	PROPN
ejpam-6705	158	20	∈	∈	PROPN
ejpam-6705	158	21	t	t	PROPN
ejpam-6705	158	22	(	(	PUNCT
ejpam-6705	158	23	u	u	NOUN
ejpam-6705	158	24	)	)	PUNCT
ejpam-6705	158	25	.	.	PUNCT
ejpam-6705	159	1	definition	definition	NOUN
ejpam-6705	159	2	8	8	NUM
ejpam-6705	159	3	.	.	PUNCT
ejpam-6705	160	1	[	[	X
ejpam-6705	160	2	40	40	NUM
ejpam-6705	160	3	]	]	PUNCT
ejpam-6705	160	4	let	let	VERB
ejpam-6705	160	5	t	t	NOUN
ejpam-6705	160	6	:	:	PUNCT
ejpam-6705	160	7	x	x	X
ejpam-6705	160	8	→	→	X
ejpam-6705	160	9	2x	2x	NUM
ejpam-6705	160	10	be	be	AUX
ejpam-6705	160	11	a	a	DET
ejpam-6705	160	12	multivalued	multivalue	VERB
ejpam-6705	160	13	mapping	mapping	NOUN
ejpam-6705	160	14	,	,	PUNCT
ejpam-6705	160	15	then	then	ADV
ejpam-6705	160	16	t	t	PROPN
ejpam-6705	160	17	is	be	AUX
ejpam-6705	160	18	termed	term	VERB
ejpam-6705	160	19	as	as	ADP
ejpam-6705	160	20	upper	upper	ADJ
ejpam-6705	160	21	semi	semi	ADJ
ejpam-6705	160	22	-	-	ADJ
ejpam-6705	160	23	continuous	continuous	ADJ
ejpam-6705	160	24	if	if	SCONJ
ejpam-6705	160	25	whenever	whenever	SCONJ
ejpam-6705	160	26	(	(	PUNCT
ejpam-6705	160	27	us	we	PRON
ejpam-6705	160	28	)	)	PUNCT
ejpam-6705	160	29	∈	∈	PROPN
ejpam-6705	160	30	x	x	X
ejpam-6705	160	31	and	and	CCONJ
ejpam-6705	160	32	(	(	PUNCT
ejpam-6705	160	33	vs	vs	NOUN
ejpam-6705	160	34	)	)	PUNCT
ejpam-6705	160	35	∈	∈	PROPN
ejpam-6705	160	36	t	t	PROPN
ejpam-6705	160	37	(	(	PUNCT
ejpam-6705	160	38	us	us	PROPN
ejpam-6705	160	39	)	)	PUNCT
ejpam-6705	160	40	with	with	ADP
ejpam-6705	160	41	us	we	PRON
ejpam-6705	160	42	→	→	SYM
ejpam-6705	160	43	m	m	NOUN
ejpam-6705	160	44	∈	∈	NOUN
ejpam-6705	160	45	x	x	X
ejpam-6705	160	46	and	and	CCONJ
ejpam-6705	160	47	vs	vs	ADP
ejpam-6705	160	48	→	→	ADP
ejpam-6705	160	49	e	e	X
ejpam-6705	160	50	∈	∈	PROPN
ejpam-6705	160	51	x	x	X
ejpam-6705	160	52	,	,	PUNCT
ejpam-6705	160	53	then	then	ADV
ejpam-6705	160	54	e	e	PROPN
ejpam-6705	160	55	∈	∈	PROPN
ejpam-6705	160	56	t	t	PROPN
ejpam-6705	160	57	(	(	PUNCT
ejpam-6705	160	58	m	m	PROPN
ejpam-6705	160	59	)	)	PUNCT
ejpam-6705	160	60	.	.	PUNCT
ejpam-6705	161	1	definition	definition	NOUN
ejpam-6705	161	2	9	9	NUM
ejpam-6705	161	3	.	.	PUNCT
ejpam-6705	162	1	[	[	X
ejpam-6705	162	2	41	41	NUM
ejpam-6705	162	3	]	]	PUNCT
ejpam-6705	162	4	an	an	DET
ejpam-6705	162	5	element	element	NOUN
ejpam-6705	162	6	(	(	PUNCT
ejpam-6705	162	7	a	a	PRON
ejpam-6705	162	8	,	,	PUNCT
ejpam-6705	162	9	b	b	NOUN
ejpam-6705	162	10	)	)	PUNCT
ejpam-6705	162	11	∈	∈	NOUN
ejpam-6705	162	12	x	x	X
ejpam-6705	162	13	×	×	NOUN
ejpam-6705	162	14	x	x	VERB
ejpam-6705	162	15	is	be	AUX
ejpam-6705	162	16	said	say	VERB
ejpam-6705	162	17	to	to	PART
ejpam-6705	162	18	be	be	AUX
ejpam-6705	162	19	a	a	DET
ejpam-6705	162	20	coupled	couple	VERB
ejpam-6705	162	21	fixed	fix	VERB
ejpam-6705	162	22	point	point	NOUN
ejpam-6705	162	23	of	of	ADP
ejpam-6705	162	24	a	a	DET
ejpam-6705	162	25	mapping	mapping	NOUN
ejpam-6705	162	26	t	t	NOUN
ejpam-6705	162	27	:	:	PUNCT
ejpam-6705	162	28	x	x	X
ejpam-6705	162	29	×x	×x	PROPN
ejpam-6705	162	30	→	→	SYM
ejpam-6705	162	31	x	x	X
ejpam-6705	162	32	if	if	SCONJ
ejpam-6705	162	33	t	t	PROPN
ejpam-6705	162	34	(	(	PUNCT
ejpam-6705	162	35	a	a	DET
ejpam-6705	162	36	,	,	PUNCT
ejpam-6705	162	37	b	b	NOUN
ejpam-6705	162	38	)	)	PUNCT
ejpam-6705	162	39	=	=	PUNCT
ejpam-6705	162	40	a	a	PROPN
ejpam-6705	162	41	and	and	CCONJ
ejpam-6705	162	42	t	t	PROPN
ejpam-6705	162	43	(	(	PUNCT
ejpam-6705	162	44	b	b	PROPN
ejpam-6705	162	45	,	,	PUNCT
ejpam-6705	162	46	a	a	PRON
ejpam-6705	162	47	)	)	PUNCT
ejpam-6705	162	48	=	=	SYM
ejpam-6705	162	49	b.	b.	NOUN
ejpam-6705	162	50	definition	definition	NOUN
ejpam-6705	162	51	10	10	NUM
ejpam-6705	162	52	.	.	PUNCT
ejpam-6705	163	1	[	[	X
ejpam-6705	163	2	40	40	NUM
ejpam-6705	163	3	]	]	PUNCT
ejpam-6705	163	4	a	a	DET
ejpam-6705	163	5	function	function	NOUN
ejpam-6705	163	6	u	u	NOUN
ejpam-6705	163	7	:	:	PUNCT
ejpam-6705	163	8	x	x	X
ejpam-6705	163	9	→	→	SYM
ejpam-6705	163	10	r	r	NOUN
ejpam-6705	163	11	is	be	AUX
ejpam-6705	163	12	called	call	VERB
ejpam-6705	163	13	a	a	DET
ejpam-6705	163	14	lower	low	ADJ
ejpam-6705	163	15	semi	semi	ADJ
ejpam-6705	163	16	-	-	ADJ
ejpam-6705	163	17	continuous	continuous	ADJ
ejpam-6705	163	18	if	if	SCONJ
ejpam-6705	163	19	for	for	ADP
ejpam-6705	163	20	any	any	DET
ejpam-6705	163	21	{	{	PUNCT
ejpam-6705	163	22	un	un	PROPN
ejpam-6705	163	23	}	}	PUNCT
ejpam-6705	163	24	⊂	⊂	NOUN
ejpam-6705	163	25	x	x	X
ejpam-6705	163	26	and	and	CCONJ
ejpam-6705	163	27	u	u	PROPN
ejpam-6705	163	28	∈	∈	PROPN
ejpam-6705	163	29	x	x	SYM
ejpam-6705	163	30	un	un	PROPN
ejpam-6705	163	31	→	→	NOUN
ejpam-6705	163	32	u⇒	u⇒	NOUN
ejpam-6705	163	33	u(u	u(u	NOUN
ejpam-6705	163	34	)	)	PUNCT
ejpam-6705	163	35	≤	≤	NOUN
ejpam-6705	163	36	lim	lim	PROPN
ejpam-6705	163	37	n→∞	n→∞	NUM
ejpam-6705	163	38	inf	inf	PROPN
ejpam-6705	163	39	u(un	u(un	PROPN
ejpam-6705	163	40	)	)	PUNCT
ejpam-6705	163	41	.	.	PUNCT
ejpam-6705	164	1	definition	definition	NOUN
ejpam-6705	164	2	11	11	NUM
ejpam-6705	164	3	.	.	PUNCT
ejpam-6705	165	1	[	[	X
ejpam-6705	165	2	41	41	NUM
ejpam-6705	165	3	]	]	X
ejpam-6705	165	4	let	let	AUX
ejpam-6705	165	5	(	(	PUNCT
ejpam-6705	165	6	x	x	X
ejpam-6705	165	7	,	,	PUNCT
ejpam-6705	165	8	≼	≼	PROPN
ejpam-6705	165	9	)	)	PUNCT
ejpam-6705	165	10	be	be	AUX
ejpam-6705	165	11	a	a	DET
ejpam-6705	165	12	partial	partial	ADJ
ejpam-6705	165	13	order	order	NOUN
ejpam-6705	165	14	set	set	NOUN
ejpam-6705	165	15	,	,	PUNCT
ejpam-6705	165	16	then	then	ADV
ejpam-6705	165	17	t	t	X
ejpam-6705	165	18	:	:	PUNCT
ejpam-6705	165	19	x	x	PUNCT
ejpam-6705	165	20	×	×	NOUN
ejpam-6705	165	21	x	x	PUNCT
ejpam-6705	165	22	→	→	PUNCT
ejpam-6705	165	23	x	x	X
ejpam-6705	165	24	is	be	AUX
ejpam-6705	165	25	said	say	VERB
ejpam-6705	165	26	to	to	PART
ejpam-6705	165	27	have	have	VERB
ejpam-6705	165	28	mixed	mix	VERB
ejpam-6705	165	29	monotone	monotone	ADJ
ejpam-6705	165	30	property	property	NOUN
ejpam-6705	165	31	if	if	SCONJ
ejpam-6705	165	32	t	t	PROPN
ejpam-6705	165	33	(	(	PUNCT
ejpam-6705	165	34	u	u	NOUN
ejpam-6705	165	35	,	,	PUNCT
ejpam-6705	165	36	v	v	NOUN
ejpam-6705	165	37	)	)	PUNCT
ejpam-6705	165	38	is	be	AUX
ejpam-6705	165	39	monotone	monotone	ADJ
ejpam-6705	165	40	non	non	ADJ
ejpam-6705	165	41	-	-	ADJ
ejpam-6705	165	42	decreasing	decrease	VERB
ejpam-6705	165	43	in	in	ADP
ejpam-6705	165	44	its	its	PRON
ejpam-6705	165	45	first	first	ADJ
ejpam-6705	165	46	argument	argument	NOUN
ejpam-6705	165	47	and	and	CCONJ
ejpam-6705	165	48	is	be	AUX
ejpam-6705	165	49	monotone	monotone	ADJ
ejpam-6705	165	50	non	non	ADJ
ejpam-6705	165	51	-	-	ADJ
ejpam-6705	165	52	increasing	increase	VERB
ejpam-6705	165	53	in	in	ADP
ejpam-6705	165	54	its	its	PRON
ejpam-6705	165	55	second	second	ADJ
ejpam-6705	165	56	argument	argument	NOUN
ejpam-6705	165	57	;	;	PUNCT
ejpam-6705	165	58	i.e	i.e	X
ejpam-6705	165	59	,	,	PUNCT
ejpam-6705	165	60	for	for	ADP
ejpam-6705	165	61	all	all	DET
ejpam-6705	165	62	u1	u1	NOUN
ejpam-6705	165	63	,	,	PUNCT
ejpam-6705	165	64	u2	u2	PROPN
ejpam-6705	165	65	∈	∈	PROPN
ejpam-6705	165	66	x	x	X
ejpam-6705	165	67	,	,	PUNCT
ejpam-6705	165	68	u1	u1	VERB
ejpam-6705	165	69	≼	≼	PROPN
ejpam-6705	165	70	u2	u2	PROPN
ejpam-6705	165	71	⇒	⇒	PROPN
ejpam-6705	165	72	t	t	PROPN
ejpam-6705	165	73	(	(	PUNCT
ejpam-6705	165	74	u1	u1	PROPN
ejpam-6705	165	75	,	,	PUNCT
ejpam-6705	165	76	v	v	NOUN
ejpam-6705	165	77	)	)	PUNCT
ejpam-6705	165	78	≼	≼	PROPN
ejpam-6705	165	79	t	t	PROPN
ejpam-6705	165	80	(	(	PUNCT
ejpam-6705	165	81	u2	u2	PROPN
ejpam-6705	165	82	,	,	PUNCT
ejpam-6705	165	83	v	v	NOUN
ejpam-6705	165	84	)	)	PUNCT
ejpam-6705	165	85	∀	∀	PUNCT
ejpam-6705	165	86	v	v	ADP
ejpam-6705	165	87	∈	∈	PROPN
ejpam-6705	165	88	x	x	X
ejpam-6705	165	89	and	and	CCONJ
ejpam-6705	165	90	for	for	ADP
ejpam-6705	165	91	all	all	DET
ejpam-6705	165	92	v1	v1	NOUN
ejpam-6705	165	93	,	,	PUNCT
ejpam-6705	165	94	v2	v2	PROPN
ejpam-6705	165	95	∈	∈	PROPN
ejpam-6705	165	96	x	x	X
ejpam-6705	165	97	,	,	PUNCT
ejpam-6705	165	98	v1	v1	VERB
ejpam-6705	165	99	≼	≼	ADJ
ejpam-6705	165	100	v2	v2	PROPN
ejpam-6705	165	101	⇒	⇒	NOUN
ejpam-6705	165	102	t	t	PROPN
ejpam-6705	165	103	(	(	PUNCT
ejpam-6705	165	104	u	u	NOUN
ejpam-6705	165	105	,	,	PUNCT
ejpam-6705	165	106	v1	v1	NOUN
ejpam-6705	165	107	)	)	PUNCT
ejpam-6705	165	108	≽	≽	PROPN
ejpam-6705	165	109	t	t	PROPN
ejpam-6705	165	110	(	(	PUNCT
ejpam-6705	165	111	u	u	NOUN
ejpam-6705	165	112	,	,	PUNCT
ejpam-6705	165	113	v2	v2	PROPN
ejpam-6705	165	114	)	)	PUNCT
ejpam-6705	165	115	∀	∀	PUNCT
ejpam-6705	165	116	u	u	NOUN
ejpam-6705	165	117	∈	∈	NOUN
ejpam-6705	165	118	t.	t.	NOUN
ejpam-6705	165	119	definition	definition	NOUN
ejpam-6705	165	120	12	12	NUM
ejpam-6705	165	121	.	.	PUNCT
ejpam-6705	166	1	[	[	X
ejpam-6705	166	2	42	42	NUM
ejpam-6705	166	3	]	]	PUNCT
ejpam-6705	166	4	denote	denote	NOUN
ejpam-6705	166	5	by	by	ADP
ejpam-6705	166	6	σ	σ	NOUN
ejpam-6705	166	7	the	the	DET
ejpam-6705	166	8	collection	collection	NOUN
ejpam-6705	166	9	of	of	ADP
ejpam-6705	166	10	all	all	DET
ejpam-6705	166	11	functions	function	NOUN
ejpam-6705	166	12	κ	κ	X
ejpam-6705	166	13	:	:	PUNCT
ejpam-6705	167	1	[	[	X
ejpam-6705	167	2	0,∞	0,∞	NOUN
ejpam-6705	167	3	)	)	PUNCT
ejpam-6705	167	4	→	→	PUNCT
ejpam-6705	168	1	[	[	X
ejpam-6705	168	2	0,∞	0,∞	NUM
ejpam-6705	168	3	)	)	PUNCT
ejpam-6705	168	4	such	such	ADJ
ejpam-6705	168	5	that	that	SCONJ
ejpam-6705	168	6	:	:	PUNCT
ejpam-6705	168	7	(	(	PUNCT
ejpam-6705	168	8	i	i	NOUN
ejpam-6705	168	9	)	)	PUNCT
ejpam-6705	168	10	κ	κ	PROPN
ejpam-6705	168	11	is	be	AUX
ejpam-6705	168	12	continuous	continuous	ADJ
ejpam-6705	168	13	.	.	PUNCT
ejpam-6705	169	1	(	(	PUNCT
ejpam-6705	169	2	ii	ii	NOUN
ejpam-6705	169	3	)	)	PUNCT
ejpam-6705	169	4	κ	κ	PROPN
ejpam-6705	169	5	is	be	AUX
ejpam-6705	169	6	non	non	ADJ
ejpam-6705	169	7	-	-	ADJ
ejpam-6705	169	8	decreasing	decrease	VERB
ejpam-6705	169	9	with	with	ADP
ejpam-6705	169	10	κ(τ	κ(τ	NOUN
ejpam-6705	169	11	)	)	PUNCT
ejpam-6705	169	12	=	=	SYM
ejpam-6705	169	13	0	0	NUM
ejpam-6705	169	14	⇔	⇔	X
ejpam-6705	169	15	τ	τ	X
ejpam-6705	169	16	=	=	SYM
ejpam-6705	169	17	0	0	PROPN
ejpam-6705	169	18	.	.	PUNCT
ejpam-6705	170	1	definition	definition	NOUN
ejpam-6705	170	2	13	13	NUM
ejpam-6705	170	3	.	.	PUNCT
ejpam-6705	171	1	[	[	X
ejpam-6705	171	2	42	42	NUM
ejpam-6705	171	3	]	]	PUNCT
ejpam-6705	171	4	denote	denote	VERB
ejpam-6705	171	5	by	by	ADP
ejpam-6705	171	6	ℵ	ℵ	ADP
ejpam-6705	171	7	the	the	DET
ejpam-6705	171	8	collection	collection	NOUN
ejpam-6705	171	9	of	of	ADP
ejpam-6705	171	10	all	all	DET
ejpam-6705	171	11	functions	function	NOUN
ejpam-6705	171	12	θ	θ	NOUN
ejpam-6705	171	13	:	:	PUNCT
ejpam-6705	172	1	[	[	X
ejpam-6705	172	2	0,∞	0,∞	NOUN
ejpam-6705	172	3	)	)	PUNCT
ejpam-6705	172	4	→	→	PUNCT
ejpam-6705	173	1	[	[	X
ejpam-6705	173	2	0,∞	0,∞	NUM
ejpam-6705	173	3	)	)	PUNCT
ejpam-6705	173	4	such	such	ADJ
ejpam-6705	173	5	that	that	SCONJ
ejpam-6705	173	6	:	:	PUNCT
ejpam-6705	173	7	(	(	PUNCT
ejpam-6705	173	8	i	i	NOUN
ejpam-6705	173	9	)	)	PUNCT
ejpam-6705	173	10	θ	θ	PROPN
ejpam-6705	173	11	is	be	AUX
ejpam-6705	173	12	lower	low	ADJ
ejpam-6705	173	13	semi	semi	ADJ
ejpam-6705	173	14	-	-	ADJ
ejpam-6705	173	15	continuous	continuous	ADJ
ejpam-6705	173	16	.	.	PUNCT
ejpam-6705	174	1	(	(	PUNCT
ejpam-6705	174	2	ii	ii	NOUN
ejpam-6705	174	3	)	)	PUNCT
ejpam-6705	174	4	θ(τ	θ(τ	PROPN
ejpam-6705	174	5	)	)	PUNCT
ejpam-6705	174	6	>	>	X
ejpam-6705	174	7	0	0	PUNCT
ejpam-6705	175	1	for	for	ADP
ejpam-6705	175	2	all	all	DET
ejpam-6705	175	3	τ	τ	PROPN
ejpam-6705	175	4	>	>	X
ejpam-6705	175	5	0	0	PUNCT
ejpam-6705	175	6	and	and	CCONJ
ejpam-6705	175	7	θ(0	θ(0	PROPN
ejpam-6705	175	8	)	)	PUNCT
ejpam-6705	175	9	=	=	PUNCT
ejpam-6705	175	10	0	0	NUM
ejpam-6705	175	11	.	.	NOUN
ejpam-6705	175	12	3	3	X
ejpam-6705	175	13	.	.	NUM
ejpam-6705	175	14	multivalued	multivalue	VERB
ejpam-6705	175	15	functions	function	NOUN
ejpam-6705	175	16	and	and	CCONJ
ejpam-6705	175	17	gb	gb	NOUN
ejpam-6705	175	18	-	-	PUNCT
ejpam-6705	175	19	metric	metric	ADJ
ejpam-6705	175	20	spaces	space	NOUN
ejpam-6705	175	21	this	this	DET
ejpam-6705	175	22	section	section	NOUN
ejpam-6705	175	23	introduces	introduce	NOUN
ejpam-6705	175	24	and	and	CCONJ
ejpam-6705	175	25	explores	explore	VERB
ejpam-6705	175	26	new	new	ADJ
ejpam-6705	175	27	fixed	fix	VERB
ejpam-6705	175	28	point	point	NOUN
ejpam-6705	175	29	theorems	theorem	NOUN
ejpam-6705	175	30	for	for	ADP
ejpam-6705	175	31	monotone	monotone	ADJ
ejpam-6705	175	32	multivalued	multivalued	ADJ
ejpam-6705	175	33	functions	function	NOUN
ejpam-6705	175	34	,	,	PUNCT
ejpam-6705	175	35	with	with	ADP
ejpam-6705	175	36	a	a	DET
ejpam-6705	175	37	specific	specific	ADJ
ejpam-6705	175	38	focus	focus	NOUN
ejpam-6705	175	39	on	on	ADP
ejpam-6705	175	40	their	their	PRON
ejpam-6705	175	41	applications	application	NOUN
ejpam-6705	175	42	within	within	ADP
ejpam-6705	175	43	partially	partially	ADV
ejpam-6705	175	44	ordered	order	VERB
ejpam-6705	175	45	complete	complete	ADJ
ejpam-6705	175	46	gb	gb	ADV
ejpam-6705	175	47	-	-	PUNCT
ejpam-6705	175	48	metric	metric	ADJ
ejpam-6705	175	49	spaces	space	NOUN
ejpam-6705	175	50	.	.	PUNCT
ejpam-6705	176	1	theorem	theorem	NOUN
ejpam-6705	176	2	1	1	NUM
ejpam-6705	176	3	.	.	PUNCT
ejpam-6705	177	1	let	let	AUX
ejpam-6705	177	2	(	(	PUNCT
ejpam-6705	177	3	x	x	X
ejpam-6705	177	4	,	,	PUNCT
ejpam-6705	177	5	gb,≼	gb,≼	NOUN
ejpam-6705	177	6	)	)	PUNCT
ejpam-6705	177	7	be	be	AUX
ejpam-6705	177	8	a	a	DET
ejpam-6705	177	9	partially	partially	ADV
ejpam-6705	177	10	ordered	order	VERB
ejpam-6705	177	11	complete	complete	ADJ
ejpam-6705	177	12	gb	gb	ADV
ejpam-6705	177	13	-	-	PUNCT
ejpam-6705	177	14	metric	metric	ADJ
ejpam-6705	177	15	space	space	NOUN
ejpam-6705	177	16	generated	generate	VERB
ejpam-6705	177	17	by	by	ADP
ejpam-6705	177	18	(	(	PUNCT
ejpam-6705	177	19	κ	κ	NOUN
ejpam-6705	177	20	,	,	PUNCT
ejpam-6705	177	21	θ	θ	NOUN
ejpam-6705	177	22	)	)	PUNCT
ejpam-6705	177	23	,	,	PUNCT
ejpam-6705	177	24	where	where	SCONJ
ejpam-6705	177	25	θ	θ	NOUN
ejpam-6705	177	26	:	:	PUNCT
ejpam-6705	177	27	x	x	X
ejpam-6705	178	1	→	→	PUNCT
ejpam-6705	178	2	[	[	X
ejpam-6705	178	3	0,∞	0,∞	NUM
ejpam-6705	178	4	)	)	PUNCT
ejpam-6705	178	5	is	be	AUX
ejpam-6705	178	6	a	a	DET
ejpam-6705	178	7	mapping	mapping	NOUN
ejpam-6705	178	8	which	which	PRON
ejpam-6705	178	9	is	be	AUX
ejpam-6705	178	10	bounded	bound	VERB
ejpam-6705	178	11	below	below	ADV
ejpam-6705	178	12	.	.	PUNCT
ejpam-6705	179	1	let	let	VERB
ejpam-6705	179	2	t	t	NOUN
ejpam-6705	179	3	:	:	PUNCT
ejpam-6705	179	4	x	x	X
ejpam-6705	179	5	→	→	X
ejpam-6705	179	6	2x	2x	NUM
ejpam-6705	179	7	be	be	AUX
ejpam-6705	179	8	a	a	DET
ejpam-6705	179	9	multivalued	multivalue	VERB
ejpam-6705	179	10	mapping	mapping	NOUN
ejpam-6705	179	11	and	and	CCONJ
ejpam-6705	179	12	m	m	PROPN
ejpam-6705	179	13	=	=	PUNCT
ejpam-6705	179	14	{	{	PUNCT
ejpam-6705	179	15	u	u	NOUN
ejpam-6705	179	16	∈	∈	PROPN
ejpam-6705	179	17	x	x	X
ejpam-6705	179	18	:	:	PUNCT
ejpam-6705	179	19	t	t	PROPN
ejpam-6705	179	20	(	(	PUNCT
ejpam-6705	179	21	u	u	NOUN
ejpam-6705	179	22	)	)	PUNCT
ejpam-6705	179	23	∩	∩	NOUN
ejpam-6705	179	24	[	[	X
ejpam-6705	179	25	u,∞	u,∞	NOUN
ejpam-6705	179	26	)	)	PUNCT
ejpam-6705	179	27	̸=	̸=	PROPN
ejpam-6705	179	28	∅	∅	NOUN
ejpam-6705	179	29	}	}	PUNCT
ejpam-6705	179	30	.	.	PUNCT
ejpam-6705	180	1	assume	assume	VERB
ejpam-6705	180	2	that	that	SCONJ
ejpam-6705	180	3	:	:	PUNCT
ejpam-6705	180	4	(	(	PUNCT
ejpam-6705	180	5	i	i	NOUN
ejpam-6705	180	6	)	)	PUNCT
ejpam-6705	180	7	t	t	PROPN
ejpam-6705	180	8	is	be	AUX
ejpam-6705	180	9	upper	upper	ADJ
ejpam-6705	180	10	semi	semi	ADJ
ejpam-6705	180	11	-	-	ADJ
ejpam-6705	180	12	continuous	continuous	ADJ
ejpam-6705	180	13	.	.	PUNCT
ejpam-6705	181	1	(	(	PUNCT
ejpam-6705	181	2	ii	ii	NOUN
ejpam-6705	181	3	)	)	PUNCT
ejpam-6705	181	4	if	if	SCONJ
ejpam-6705	181	5	u	u	PROPN
ejpam-6705	181	6	∈	∈	PROPN
ejpam-6705	181	7	m	m	PROPN
ejpam-6705	181	8	,	,	PUNCT
ejpam-6705	181	9	then	then	ADV
ejpam-6705	181	10	v	v	AUX
ejpam-6705	181	11	∈	∈	NOUN
ejpam-6705	181	12	m	m	VERB
ejpam-6705	181	13	for	for	ADP
ejpam-6705	181	14	all	all	DET
ejpam-6705	181	15	v	v	ADP
ejpam-6705	181	16	∈	∈	NOUN
ejpam-6705	181	17	t	t	NOUN
ejpam-6705	181	18	(	(	PUNCT
ejpam-6705	181	19	u	u	NOUN
ejpam-6705	181	20	)	)	PUNCT
ejpam-6705	181	21	∩	∩	NOUN
ejpam-6705	181	22	[	[	X
ejpam-6705	181	23	u,∞	u,∞	PROPN
ejpam-6705	181	24	)	)	PUNCT
ejpam-6705	181	25	.	.	PUNCT
ejpam-6705	182	1	s.	s.	PROPN
ejpam-6705	182	2	batul	batul	PROPN
ejpam-6705	182	3	et	et	PROPN
ejpam-6705	182	4	al	al	PROPN
ejpam-6705	182	5	.	.	PUNCT
ejpam-6705	182	6	/	/	SYM
ejpam-6705	182	7	eur	eur	PROPN
ejpam-6705	182	8	.	.	PUNCT
ejpam-6705	183	1	j.	j.	PROPN
ejpam-6705	183	2	pure	pure	PROPN
ejpam-6705	183	3	appl	appl	PROPN
ejpam-6705	183	4	.	.	PROPN
ejpam-6705	183	5	math	math	PROPN
ejpam-6705	183	6	,	,	PUNCT
ejpam-6705	183	7	18	18	NUM
ejpam-6705	183	8	(	(	PUNCT
ejpam-6705	183	9	4	4	NUM
ejpam-6705	183	10	)	)	PUNCT
ejpam-6705	183	11	(	(	PUNCT
ejpam-6705	183	12	2025	2025	NUM
ejpam-6705	183	13	)	)	PUNCT
ejpam-6705	183	14	,	,	PUNCT
ejpam-6705	183	15	6705	6705	NUM
ejpam-6705	183	16	7	7	NUM
ejpam-6705	183	17	of	of	ADP
ejpam-6705	183	18	23	23	NUM
ejpam-6705	183	19	(	(	PUNCT
ejpam-6705	183	20	iii	iii	NOUN
ejpam-6705	183	21	)	)	PUNCT
ejpam-6705	183	22	t	t	PROPN
ejpam-6705	183	23	(	(	PUNCT
ejpam-6705	183	24	m	m	NOUN
ejpam-6705	183	25	)	)	PUNCT
ejpam-6705	183	26	∩	∩	NOUN
ejpam-6705	183	27	[	[	X
ejpam-6705	183	28	m,∞	m,∞	NOUN
ejpam-6705	183	29	)	)	PUNCT
ejpam-6705	183	30	̸=	̸=	PROPN
ejpam-6705	183	31	∅	∅	NOUN
ejpam-6705	183	32	for	for	ADP
ejpam-6705	183	33	some	some	DET
ejpam-6705	183	34	m	m	NOUN
ejpam-6705	183	35	∈	∈	NOUN
ejpam-6705	183	36	x	x	X
ejpam-6705	183	37	.	.	PUNCT
ejpam-6705	184	1	then	then	ADV
ejpam-6705	184	2	there	there	PRON
ejpam-6705	184	3	is	be	VERB
ejpam-6705	184	4	a	a	DET
ejpam-6705	184	5	sequence	sequence	NOUN
ejpam-6705	184	6	(	(	PUNCT
ejpam-6705	184	7	us	we	PRON
ejpam-6705	184	8	)	)	PUNCT
ejpam-6705	184	9	such	such	ADJ
ejpam-6705	184	10	that	that	SCONJ
ejpam-6705	184	11	us−1	us−1	PROPN
ejpam-6705	184	12	≼	≼	VERB
ejpam-6705	184	13	us	us	PROPN
ejpam-6705	184	14	∈	∈	PROPN
ejpam-6705	184	15	t	t	PROPN
ejpam-6705	184	16	(	(	PUNCT
ejpam-6705	184	17	us−1	us−1	PROPN
ejpam-6705	184	18	)	)	PUNCT
ejpam-6705	184	19	for	for	ADP
ejpam-6705	184	20	all	all	DET
ejpam-6705	184	21	s	s	PROPN
ejpam-6705	184	22	∈	∈	NOUN
ejpam-6705	184	23	n	n	CCONJ
ejpam-6705	184	24	,	,	PUNCT
ejpam-6705	184	25	and	and	CCONJ
ejpam-6705	184	26	t	t	PROPN
ejpam-6705	184	27	has	have	VERB
ejpam-6705	184	28	a	a	DET
ejpam-6705	184	29	fixed	fix	VERB
ejpam-6705	184	30	point	point	NOUN
ejpam-6705	184	31	u0	u0	ADJ
ejpam-6705	184	32	such	such	ADJ
ejpam-6705	184	33	that	that	SCONJ
ejpam-6705	184	34	us	we	PRON
ejpam-6705	184	35	→	→	SYM
ejpam-6705	184	36	u0	u0	PROPN
ejpam-6705	184	37	.	.	PUNCT
ejpam-6705	185	1	in	in	ADP
ejpam-6705	185	2	addition	addition	NOUN
ejpam-6705	185	3	,	,	PUNCT
ejpam-6705	185	4	if	if	SCONJ
ejpam-6705	185	5	θ	θ	PROPN
ejpam-6705	185	6	is	be	AUX
ejpam-6705	185	7	lower	low	ADJ
ejpam-6705	185	8	semi	semi	ADJ
ejpam-6705	185	9	-	-	ADJ
ejpam-6705	185	10	continuous	continuous	ADJ
ejpam-6705	185	11	,	,	PUNCT
ejpam-6705	185	12	then	then	ADV
ejpam-6705	185	13	us	we	PRON
ejpam-6705	185	14	≼	≼	PROPN
ejpam-6705	185	15	u0	u0	ADJ
ejpam-6705	185	16	for	for	ADP
ejpam-6705	185	17	all	all	DET
ejpam-6705	185	18	s.	s.	PROPN
ejpam-6705	185	19	proof	proof	NOUN
ejpam-6705	185	20	.	.	PUNCT
ejpam-6705	186	1	by	by	ADP
ejpam-6705	186	2	using	use	VERB
ejpam-6705	186	3	(	(	PUNCT
ejpam-6705	186	4	iii	iii	NOUN
ejpam-6705	186	5	)	)	PUNCT
ejpam-6705	186	6	,	,	PUNCT
ejpam-6705	186	7	there	there	PRON
ejpam-6705	186	8	is	be	VERB
ejpam-6705	186	9	m	m	PROPN
ejpam-6705	186	10	∈	∈	ADJ
ejpam-6705	186	11	x	x	SYM
ejpam-6705	186	12	that	that	PRON
ejpam-6705	186	13	belongs	belong	VERB
ejpam-6705	186	14	to	to	ADP
ejpam-6705	186	15	m.	m.	NOUN
ejpam-6705	186	16	then	then	ADV
ejpam-6705	186	17	choose	choose	VERB
ejpam-6705	186	18	n	n	PRON
ejpam-6705	186	19	∈	∈	PROPN
ejpam-6705	186	20	t	t	PROPN
ejpam-6705	186	21	(	(	PUNCT
ejpam-6705	186	22	m	m	NOUN
ejpam-6705	186	23	)	)	PUNCT
ejpam-6705	186	24	∩	∩	NOUN
ejpam-6705	186	25	[	[	X
ejpam-6705	186	26	m,∞	m,∞	NOUN
ejpam-6705	186	27	)	)	PUNCT
ejpam-6705	186	28	,	,	PUNCT
ejpam-6705	186	29	and	and	CCONJ
ejpam-6705	186	30	we	we	PRON
ejpam-6705	186	31	have	have	VERB
ejpam-6705	186	32	m	m	VERB
ejpam-6705	186	33	≼	≼	ADJ
ejpam-6705	186	34	n.	n.	NOUN
ejpam-6705	186	35	by	by	ADP
ejpam-6705	186	36	condition	condition	NOUN
ejpam-6705	186	37	(	(	PUNCT
ejpam-6705	186	38	ii	ii	NOUN
ejpam-6705	186	39	)	)	PUNCT
ejpam-6705	186	40	,	,	PUNCT
ejpam-6705	186	41	n	n	PROPN
ejpam-6705	186	42	∈	∈	PROPN
ejpam-6705	186	43	m.	m.	NOUN
ejpam-6705	186	44	choose	choose	VERB
ejpam-6705	186	45	τ	τ	PROPN
ejpam-6705	186	46	∈	∈	PROPN
ejpam-6705	186	47	t	t	PROPN
ejpam-6705	186	48	(	(	PUNCT
ejpam-6705	186	49	n	n	CCONJ
ejpam-6705	186	50	)	)	PUNCT
ejpam-6705	186	51	∩	∩	NOUN
ejpam-6705	187	1	[	[	X
ejpam-6705	187	2	n,∞	n,∞	NOUN
ejpam-6705	187	3	)	)	PUNCT
ejpam-6705	187	4	such	such	ADJ
ejpam-6705	187	5	that	that	SCONJ
ejpam-6705	187	6	n	n	PRON
ejpam-6705	187	7	≼	≼	NOUN
ejpam-6705	187	8	τ	τ	PROPN
ejpam-6705	187	9	.	.	PUNCT
ejpam-6705	188	1	by	by	ADP
ejpam-6705	188	2	repeating	repeat	VERB
ejpam-6705	188	3	the	the	DET
ejpam-6705	188	4	process	process	NOUN
ejpam-6705	188	5	,	,	PUNCT
ejpam-6705	188	6	we	we	PRON
ejpam-6705	188	7	get	get	VERB
ejpam-6705	188	8	a	a	DET
ejpam-6705	188	9	sequence	sequence	NOUN
ejpam-6705	188	10	(	(	PUNCT
ejpam-6705	188	11	us	us	PROPN
ejpam-6705	188	12	)	)	PUNCT
ejpam-6705	188	13	∈	∈	PROPN
ejpam-6705	188	14	x	x	PUNCT
ejpam-6705	188	15	such	such	ADJ
ejpam-6705	188	16	that	that	SCONJ
ejpam-6705	188	17	us−1	us−1	PROPN
ejpam-6705	188	18	≼	≼	VERB
ejpam-6705	188	19	us	us	PROPN
ejpam-6705	188	20	∈	∈	PROPN
ejpam-6705	188	21	t	t	PROPN
ejpam-6705	188	22	(	(	PUNCT
ejpam-6705	188	23	us−1	us−1	PROPN
ejpam-6705	188	24	)	)	PUNCT
ejpam-6705	188	25	∀	∀	PUNCT
ejpam-6705	188	26	s	s	NOUN
ejpam-6705	188	27	∈	∈	PROPN
ejpam-6705	188	28	n.	n.	NOUN
ejpam-6705	188	29	since	since	SCONJ
ejpam-6705	188	30	(	(	PUNCT
ejpam-6705	188	31	x	x	INTJ
ejpam-6705	188	32	,	,	PUNCT
ejpam-6705	188	33	gb,≼	gb,≼	NOUN
ejpam-6705	188	34	)	)	PUNCT
ejpam-6705	188	35	is	be	AUX
ejpam-6705	188	36	a	a	DET
ejpam-6705	188	37	partially	partially	ADV
ejpam-6705	188	38	ordered	order	VERB
ejpam-6705	188	39	gb	gb	ADV
ejpam-6705	188	40	-	-	PUNCT
ejpam-6705	188	41	metric	metric	ADJ
ejpam-6705	188	42	space	space	NOUN
ejpam-6705	188	43	induced	induce	VERB
ejpam-6705	188	44	via	via	ADP
ejpam-6705	188	45	(	(	PUNCT
ejpam-6705	188	46	κ	κ	NOUN
ejpam-6705	188	47	,	,	PUNCT
ejpam-6705	188	48	θ	θ	NOUN
ejpam-6705	188	49	)	)	PUNCT
ejpam-6705	188	50	κ(gb(us−1	κ(gb(us−1	PROPN
ejpam-6705	188	51	,	,	PUNCT
ejpam-6705	188	52	us−1	us−1	PROPN
ejpam-6705	188	53	,	,	PUNCT
ejpam-6705	188	54	us	we	PRON
ejpam-6705	188	55	)	)	PUNCT
ejpam-6705	188	56	)	)	PUNCT
ejpam-6705	189	1	≤	≤	ADV
ejpam-6705	189	2	θ(us−1)−θ(us	θ(us−1)−θ(us	ADV
ejpam-6705	189	3	)	)	PUNCT
ejpam-6705	189	4	.	.	PUNCT
ejpam-6705	190	1	(	(	PUNCT
ejpam-6705	190	2	3	3	X
ejpam-6705	190	3	)	)	PUNCT
ejpam-6705	190	4	the	the	DET
ejpam-6705	190	5	mapping	mapping	NOUN
ejpam-6705	190	6	κ	κ	NOUN
ejpam-6705	190	7	is	be	AUX
ejpam-6705	190	8	non	non	ADJ
ejpam-6705	190	9	-	-	ADJ
ejpam-6705	190	10	negative	negative	ADJ
ejpam-6705	190	11	,	,	PUNCT
ejpam-6705	190	12	so	so	SCONJ
ejpam-6705	190	13	for	for	SCONJ
ejpam-6705	190	14	all	all	PRON
ejpam-6705	190	15	s	s	PART
ejpam-6705	190	16	∈	∈	PROPN
ejpam-6705	190	17	n	n	CCONJ
ejpam-6705	190	18	,	,	PUNCT
ejpam-6705	190	19	θ(us−1)−θ(us	θ(us−1)−θ(us	NOUN
ejpam-6705	190	20	)	)	PUNCT
ejpam-6705	190	21	≥	≥	NOUN
ejpam-6705	190	22	0	0	NUM
ejpam-6705	190	23	.	.	PUNCT
ejpam-6705	191	1	that	that	PRON
ejpam-6705	191	2	is	be	AUX
ejpam-6705	191	3	,	,	PUNCT
ejpam-6705	191	4	for	for	ADP
ejpam-6705	192	1	all	all	PRON
ejpam-6705	192	2	s	s	PART
ejpam-6705	192	3	∈	∈	NOUN
ejpam-6705	192	4	n	n	CCONJ
ejpam-6705	192	5	,	,	PUNCT
ejpam-6705	192	6	θ(us−1	θ(us−1	NOUN
ejpam-6705	192	7	)	)	PUNCT
ejpam-6705	192	8	≥	≥	NOUN
ejpam-6705	192	9	θ(us	θ(us	PROPN
ejpam-6705	192	10	)	)	PUNCT
ejpam-6705	192	11	.	.	PUNCT
ejpam-6705	193	1	since	since	SCONJ
ejpam-6705	193	2	θ	θ	PROPN
ejpam-6705	193	3	is	be	AUX
ejpam-6705	193	4	bounded	bound	VERB
ejpam-6705	193	5	below	below	ADV
ejpam-6705	193	6	,	,	PUNCT
ejpam-6705	193	7	the	the	DET
ejpam-6705	193	8	sequence	sequence	NOUN
ejpam-6705	193	9	θ(us	θ(us	PROPN
ejpam-6705	193	10	)	)	PUNCT
ejpam-6705	193	11	is	be	AUX
ejpam-6705	193	12	both	both	PRON
ejpam-6705	193	13	decreasing	decrease	VERB
ejpam-6705	193	14	and	and	CCONJ
ejpam-6705	193	15	bounded	bound	VERB
ejpam-6705	193	16	below	below	ADV
ejpam-6705	193	17	.	.	PUNCT
ejpam-6705	194	1	therefore	therefore	ADV
ejpam-6705	194	2	,	,	PUNCT
ejpam-6705	194	3	by	by	ADP
ejpam-6705	194	4	the	the	DET
ejpam-6705	194	5	completeness	completeness	NOUN
ejpam-6705	194	6	property	property	NOUN
ejpam-6705	194	7	of	of	ADP
ejpam-6705	194	8	r	r	NOUN
ejpam-6705	194	9	,	,	PUNCT
ejpam-6705	194	10	lim	lim	PROPN
ejpam-6705	194	11	s→∞	s→∞	PROPN
ejpam-6705	194	12	θ(us	θ(us	PROPN
ejpam-6705	194	13	)	)	PUNCT
ejpam-6705	194	14	=	=	SYM
ejpam-6705	194	15	inf{us	inf{us	NOUN
ejpam-6705	194	16	:	:	PUNCT
ejpam-6705	194	17	s	s	X
ejpam-6705	194	18	∈	∈	PROPN
ejpam-6705	194	19	n	n	CCONJ
ejpam-6705	194	20	}	}	PUNCT
ejpam-6705	194	21	.	.	PUNCT
ejpam-6705	195	1	thus	thus	ADV
ejpam-6705	195	2	,	,	PUNCT
ejpam-6705	195	3	by	by	ADP
ejpam-6705	195	4	equation	equation	NOUN
ejpam-6705	195	5	(	(	PUNCT
ejpam-6705	195	6	3	3	NUM
ejpam-6705	195	7	)	)	PUNCT
ejpam-6705	195	8	,	,	PUNCT
ejpam-6705	195	9	lim	lim	PROPN
ejpam-6705	195	10	s	s	PROPN
ejpam-6705	195	11	,	,	PUNCT
ejpam-6705	195	12	r→∞	r→∞	PROPN
ejpam-6705	195	13	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	195	14	,	,	PUNCT
ejpam-6705	195	15	us	we	PRON
ejpam-6705	195	16	,	,	PUNCT
ejpam-6705	195	17	ur	ur	INTJ
ejpam-6705	195	18	)	)	PUNCT
ejpam-6705	195	19	)	)	PUNCT
ejpam-6705	195	20	≤	≤	PROPN
ejpam-6705	195	21	lim	lim	PROPN
ejpam-6705	195	22	s→∞	s→∞	PROPN
ejpam-6705	195	23	θ(us)−	θ(us)−	ADP
ejpam-6705	195	24	lim	lim	PROPN
ejpam-6705	195	25	r→∞	r→∞	PUNCT
ejpam-6705	195	26	θ(ur	θ(ur	PROPN
ejpam-6705	195	27	)	)	PUNCT
ejpam-6705	195	28	.	.	PUNCT
ejpam-6705	196	1	therefore	therefore	ADV
ejpam-6705	196	2	,	,	PUNCT
ejpam-6705	196	3	lim	lim	PROPN
ejpam-6705	196	4	s	s	PROPN
ejpam-6705	196	5	,	,	PUNCT
ejpam-6705	196	6	r→∞	r→∞	PROPN
ejpam-6705	196	7	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	196	8	,	,	PUNCT
ejpam-6705	196	9	us	we	PRON
ejpam-6705	196	10	,	,	PUNCT
ejpam-6705	196	11	ur	ur	INTJ
ejpam-6705	196	12	)	)	PUNCT
ejpam-6705	196	13	)	)	PUNCT
ejpam-6705	197	1	=	=	PUNCT
ejpam-6705	197	2	0	0	X
ejpam-6705	197	3	.	.	PUNCT
ejpam-6705	197	4	by	by	ADP
ejpam-6705	197	5	exploiting	exploit	VERB
ejpam-6705	197	6	the	the	DET
ejpam-6705	197	7	continuity	continuity	NOUN
ejpam-6705	197	8	of	of	ADP
ejpam-6705	197	9	κ	κ	NOUN
ejpam-6705	197	10	and	and	CCONJ
ejpam-6705	197	11	the	the	DET
ejpam-6705	197	12	fact	fact	NOUN
ejpam-6705	197	13	that	that	SCONJ
ejpam-6705	197	14	κ−1({0	κ−1({0	NOUN
ejpam-6705	197	15	}	}	PUNCT
ejpam-6705	197	16	)	)	PUNCT
ejpam-6705	197	17	=	=	PUNCT
ejpam-6705	197	18	{	{	PUNCT
ejpam-6705	197	19	0	0	NUM
ejpam-6705	197	20	}	}	PUNCT
ejpam-6705	197	21	,	,	PUNCT
ejpam-6705	197	22	it	it	PRON
ejpam-6705	197	23	follows	follow	VERB
ejpam-6705	197	24	that	that	SCONJ
ejpam-6705	197	25	lim	lim	PROPN
ejpam-6705	197	26	s	s	PROPN
ejpam-6705	197	27	,	,	PUNCT
ejpam-6705	197	28	r→∞	r→∞	X
ejpam-6705	197	29	gb(us	gb(us	PROPN
ejpam-6705	197	30	,	,	PUNCT
ejpam-6705	197	31	us	we	PRON
ejpam-6705	197	32	,	,	PUNCT
ejpam-6705	197	33	ur	ur	INTJ
ejpam-6705	197	34	)	)	PUNCT
ejpam-6705	197	35	=	=	SYM
ejpam-6705	198	1	0	0	X
ejpam-6705	198	2	.	.	PUNCT
ejpam-6705	199	1	therefore	therefore	ADV
ejpam-6705	199	2	,	,	PUNCT
ejpam-6705	199	3	(	(	PUNCT
ejpam-6705	199	4	us	us	PROPN
ejpam-6705	199	5	)	)	PUNCT
ejpam-6705	199	6	is	be	AUX
ejpam-6705	199	7	a	a	DET
ejpam-6705	199	8	cauchy	cauchy	ADJ
ejpam-6705	199	9	sequence	sequence	NOUN
ejpam-6705	199	10	in	in	ADP
ejpam-6705	199	11	x	x	X
ejpam-6705	199	12	.	.	PUNCT
ejpam-6705	200	1	since	since	SCONJ
ejpam-6705	200	2	x	x	PRON
ejpam-6705	200	3	is	be	AUX
ejpam-6705	200	4	a	a	DET
ejpam-6705	200	5	complete	complete	ADJ
ejpam-6705	200	6	gb	gb	ADV
ejpam-6705	200	7	-	-	PUNCT
ejpam-6705	200	8	metric	metric	ADJ
ejpam-6705	200	9	space	space	NOUN
ejpam-6705	200	10	,	,	PUNCT
ejpam-6705	200	11	there	there	PRON
ejpam-6705	200	12	is	be	VERB
ejpam-6705	200	13	∃	∃	PROPN
ejpam-6705	200	14	u0	u0	PROPN
ejpam-6705	200	15	∈	∈	PROPN
ejpam-6705	200	16	x	x	PUNCT
ejpam-6705	200	17	such	such	ADJ
ejpam-6705	200	18	that	that	SCONJ
ejpam-6705	200	19	(	(	PUNCT
ejpam-6705	200	20	us	we	PRON
ejpam-6705	200	21	)	)	PUNCT
ejpam-6705	200	22	is	be	AUX
ejpam-6705	200	23	gb	gb	NOUN
ejpam-6705	200	24	-	-	PUNCT
ejpam-6705	200	25	convergent	convergent	NOUN
ejpam-6705	200	26	to	to	PART
ejpam-6705	200	27	u0	u0	VERB
ejpam-6705	200	28	.	.	PUNCT
ejpam-6705	201	1	since	since	SCONJ
ejpam-6705	201	2	us−1	us−1	PROPN
ejpam-6705	201	3	∈	∈	PROPN
ejpam-6705	201	4	x	x	X
ejpam-6705	201	5	,	,	PUNCT
ejpam-6705	201	6	us	us	PROPN
ejpam-6705	201	7	∈	∈	PROPN
ejpam-6705	201	8	t	t	PROPN
ejpam-6705	201	9	(	(	PUNCT
ejpam-6705	201	10	us−1	us−1	PROPN
ejpam-6705	201	11	)	)	PUNCT
ejpam-6705	201	12	,	,	PUNCT
ejpam-6705	201	13	us−1	us−1	PROPN
ejpam-6705	201	14	→	→	SYM
ejpam-6705	201	15	u0	u0	ADJ
ejpam-6705	201	16	,	,	PUNCT
ejpam-6705	201	17	and	and	CCONJ
ejpam-6705	201	18	us	we	PRON
ejpam-6705	201	19	→	→	SYM
ejpam-6705	201	20	u0	u0	PROPN
ejpam-6705	201	21	,	,	PUNCT
ejpam-6705	201	22	via	via	ADP
ejpam-6705	201	23	the	the	DET
ejpam-6705	201	24	definition	definition	NOUN
ejpam-6705	201	25	of	of	ADP
ejpam-6705	201	26	upper	upper	ADJ
ejpam-6705	201	27	semi	semi	NOUN
ejpam-6705	201	28	-	-	NOUN
ejpam-6705	201	29	continuity	continuity	NOUN
ejpam-6705	201	30	of	of	ADP
ejpam-6705	201	31	t	t	PROPN
ejpam-6705	201	32	,	,	PUNCT
ejpam-6705	201	33	we	we	PRON
ejpam-6705	201	34	have	have	VERB
ejpam-6705	201	35	u0	u0	PROPN
ejpam-6705	201	36	∈	∈	PROPN
ejpam-6705	201	37	t	t	PROPN
ejpam-6705	201	38	(	(	PUNCT
ejpam-6705	201	39	u0	u0	PROPN
ejpam-6705	201	40	)	)	PUNCT
ejpam-6705	201	41	.	.	PUNCT
ejpam-6705	202	1	now	now	ADV
ejpam-6705	202	2	,	,	PUNCT
ejpam-6705	202	3	assuming	assume	VERB
ejpam-6705	202	4	θ	θ	PROPN
ejpam-6705	202	5	is	be	AUX
ejpam-6705	202	6	lower	low	ADJ
ejpam-6705	202	7	semi	semi	ADJ
ejpam-6705	202	8	-	-	ADJ
ejpam-6705	202	9	continuous	continuous	ADJ
ejpam-6705	202	10	,	,	PUNCT
ejpam-6705	202	11	then	then	ADV
ejpam-6705	202	12	for	for	ADP
ejpam-6705	202	13	each	each	DET
ejpam-6705	202	14	s	s	PROPN
ejpam-6705	202	15	∈	∈	PROPN
ejpam-6705	202	16	n	n	CCONJ
ejpam-6705	202	17	,	,	PUNCT
ejpam-6705	202	18	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	202	19	,	,	PUNCT
ejpam-6705	202	20	us	we	PRON
ejpam-6705	202	21	,	,	PUNCT
ejpam-6705	202	22	u0	u0	ADJ
ejpam-6705	202	23	)	)	PUNCT
ejpam-6705	202	24	)	)	PUNCT
ejpam-6705	203	1	=	=	SYM
ejpam-6705	203	2	lim	lim	PROPN
ejpam-6705	203	3	r→∞	r→∞	PRON
ejpam-6705	203	4	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	203	5	,	,	PUNCT
ejpam-6705	203	6	us	we	PRON
ejpam-6705	203	7	,	,	PUNCT
ejpam-6705	203	8	ur	ur	INTJ
ejpam-6705	203	9	)	)	PUNCT
ejpam-6705	203	10	)	)	PUNCT
ejpam-6705	203	11	≤	≤	PROPN
ejpam-6705	203	12	lim	lim	PROPN
ejpam-6705	203	13	r→∞	r→∞	NUM
ejpam-6705	203	14	inf{θ(us)−θ(ur	inf{θ(us)−θ(ur	ADV
ejpam-6705	203	15	)	)	PUNCT
ejpam-6705	203	16	}	}	PUNCT
ejpam-6705	203	17	=	=	PUNCT
ejpam-6705	203	18	θ(us)−	θ(us)−	ADP
ejpam-6705	203	19	lim	lim	PROPN
ejpam-6705	203	20	r→∞	r→∞	PROPN
ejpam-6705	203	21	inf	inf	PROPN
ejpam-6705	203	22	θ(ur	θ(ur	PROPN
ejpam-6705	203	23	)	)	PUNCT
ejpam-6705	203	24	≤	≤	NUM
ejpam-6705	203	25	θ(us)−θ(u0	θ(us)−θ(u0	NOUN
ejpam-6705	203	26	)	)	PUNCT
ejpam-6705	203	27	.	.	PUNCT
ejpam-6705	204	1	thus	thus	ADV
ejpam-6705	204	2	,	,	PUNCT
ejpam-6705	204	3	us	us	PROPN
ejpam-6705	204	4	≤	≤	PROPN
ejpam-6705	204	5	u0	u0	ADJ
ejpam-6705	204	6	for	for	ADP
ejpam-6705	204	7	all	all	DET
ejpam-6705	204	8	s	s	PROPN
ejpam-6705	204	9	∈	∈	PROPN
ejpam-6705	204	10	n.	n.	PROPN
ejpam-6705	204	11	s.	s.	PROPN
ejpam-6705	204	12	batul	batul	PROPN
ejpam-6705	204	13	et	et	PROPN
ejpam-6705	204	14	al	al	PROPN
ejpam-6705	204	15	.	.	PUNCT
ejpam-6705	204	16	/	/	SYM
ejpam-6705	204	17	eur	eur	PROPN
ejpam-6705	204	18	.	.	PUNCT
ejpam-6705	205	1	j.	j.	PROPN
ejpam-6705	205	2	pure	pure	PROPN
ejpam-6705	205	3	appl	appl	PROPN
ejpam-6705	205	4	.	.	PROPN
ejpam-6705	205	5	math	math	PROPN
ejpam-6705	205	6	,	,	PUNCT
ejpam-6705	205	7	18	18	NUM
ejpam-6705	205	8	(	(	PUNCT
ejpam-6705	205	9	4	4	NUM
ejpam-6705	205	10	)	)	PUNCT
ejpam-6705	205	11	(	(	PUNCT
ejpam-6705	205	12	2025	2025	NUM
ejpam-6705	205	13	)	)	PUNCT
ejpam-6705	205	14	,	,	PUNCT
ejpam-6705	205	15	6705	6705	NUM
ejpam-6705	205	16	8	8	NUM
ejpam-6705	205	17	of	of	ADP
ejpam-6705	205	18	23	23	NUM
ejpam-6705	205	19	corollary	corollary	ADJ
ejpam-6705	205	20	1	1	NUM
ejpam-6705	205	21	.	.	PUNCT
ejpam-6705	205	22	suppose	suppose	VERB
ejpam-6705	205	23	that	that	SCONJ
ejpam-6705	205	24	(	(	PUNCT
ejpam-6705	205	25	x	x	X
ejpam-6705	205	26	,	,	PUNCT
ejpam-6705	205	27	gb,≼	gb,≼	NOUN
ejpam-6705	205	28	)	)	PUNCT
ejpam-6705	205	29	is	be	AUX
ejpam-6705	205	30	a	a	DET
ejpam-6705	205	31	partially	partially	ADV
ejpam-6705	205	32	ordered	order	VERB
ejpam-6705	205	33	complete	complete	ADJ
ejpam-6705	205	34	gb	gb	ADV
ejpam-6705	205	35	-	-	PUNCT
ejpam-6705	205	36	induced	induce	VERB
ejpam-6705	205	37	via	via	ADP
ejpam-6705	205	38	(	(	PUNCT
ejpam-6705	205	39	κ	κ	NOUN
ejpam-6705	205	40	,	,	PUNCT
ejpam-6705	205	41	θ	θ	NOUN
ejpam-6705	205	42	)	)	PUNCT
ejpam-6705	205	43	,	,	PUNCT
ejpam-6705	205	44	where	where	SCONJ
ejpam-6705	205	45	θ	θ	NOUN
ejpam-6705	205	46	:	:	PUNCT
ejpam-6705	205	47	x	x	X
ejpam-6705	205	48	→	→	PUNCT
ejpam-6705	205	49	[	[	X
ejpam-6705	205	50	0,∞	0,∞	NUM
ejpam-6705	205	51	)	)	PUNCT
ejpam-6705	205	52	is	be	AUX
ejpam-6705	205	53	a	a	DET
ejpam-6705	205	54	bounded	bound	VERB
ejpam-6705	205	55	below	below	ADP
ejpam-6705	205	56	mapping	mapping	NOUN
ejpam-6705	205	57	,	,	PUNCT
ejpam-6705	205	58	and	and	CCONJ
ejpam-6705	205	59	let	let	VERB
ejpam-6705	205	60	t	t	NOUN
ejpam-6705	205	61	:	:	PUNCT
ejpam-6705	205	62	x	x	X
ejpam-6705	205	63	→	→	X
ejpam-6705	205	64	2x	2x	NUM
ejpam-6705	205	65	be	be	AUX
ejpam-6705	205	66	a	a	DET
ejpam-6705	205	67	multivalued	multivalue	VERB
ejpam-6705	205	68	mapping	mapping	NOUN
ejpam-6705	205	69	be	be	AUX
ejpam-6705	205	70	so	so	SCONJ
ejpam-6705	205	71	that	that	SCONJ
ejpam-6705	205	72	:	:	PUNCT
ejpam-6705	205	73	(	(	PUNCT
ejpam-6705	205	74	i	i	NOUN
ejpam-6705	205	75	)	)	PUNCT
ejpam-6705	205	76	t	t	PROPN
ejpam-6705	205	77	is	be	AUX
ejpam-6705	205	78	upper	upper	ADJ
ejpam-6705	205	79	semi	semi	ADJ
ejpam-6705	205	80	-	-	ADJ
ejpam-6705	205	81	continuous	continuous	ADJ
ejpam-6705	205	82	.	.	PUNCT
ejpam-6705	206	1	(	(	PUNCT
ejpam-6705	206	2	ii	ii	NOUN
ejpam-6705	206	3	)	)	PUNCT
ejpam-6705	206	4	t	t	PROPN
ejpam-6705	206	5	satisfies	satisfy	VERB
ejpam-6705	206	6	the	the	DET
ejpam-6705	206	7	condition	condition	NOUN
ejpam-6705	206	8	of	of	ADP
ejpam-6705	206	9	monotonic	monotonic	ADJ
ejpam-6705	206	10	sequence	sequence	NOUN
ejpam-6705	206	11	:	:	PUNCT
ejpam-6705	206	12	for	for	ADP
ejpam-6705	206	13	all	all	DET
ejpam-6705	206	14	u	u	NOUN
ejpam-6705	206	15	,	,	PUNCT
ejpam-6705	206	16	v	v	NOUN
ejpam-6705	206	17	∈	∈	NOUN
ejpam-6705	206	18	x	x	X
ejpam-6705	206	19	and	and	CCONJ
ejpam-6705	206	20	u	u	NOUN
ejpam-6705	206	21	≼	≼	PROPN
ejpam-6705	206	22	v	v	NOUN
ejpam-6705	206	23	and	and	CCONJ
ejpam-6705	206	24	every	every	DET
ejpam-6705	206	25	α	α	PROPN
ejpam-6705	206	26	≼	≼	PROPN
ejpam-6705	206	27	t	t	PROPN
ejpam-6705	206	28	(	(	PUNCT
ejpam-6705	206	29	u	u	NOUN
ejpam-6705	206	30	)	)	PUNCT
ejpam-6705	206	31	,	,	PUNCT
ejpam-6705	206	32	there	there	PRON
ejpam-6705	206	33	exists	exist	VERB
ejpam-6705	206	34	β	β	X
ejpam-6705	206	35	≼	≼	PROPN
ejpam-6705	206	36	t	t	PROPN
ejpam-6705	206	37	(	(	PUNCT
ejpam-6705	206	38	v	v	NOUN
ejpam-6705	206	39	)	)	PUNCT
ejpam-6705	206	40	such	such	ADJ
ejpam-6705	206	41	that	that	SCONJ
ejpam-6705	206	42	α	α	PRON
ejpam-6705	206	43	≼	≼	NOUN
ejpam-6705	206	44	β	β	NOUN
ejpam-6705	206	45	.	.	PUNCT
ejpam-6705	207	1	(	(	PUNCT
ejpam-6705	207	2	iii	iii	X
ejpam-6705	207	3	)	)	PUNCT
ejpam-6705	207	4	there	there	PRON
ejpam-6705	207	5	is	be	VERB
ejpam-6705	207	6	∃	∃	PROPN
ejpam-6705	207	7	m	m	NOUN
ejpam-6705	207	8	∈	∈	NOUN
ejpam-6705	207	9	x	x	PUNCT
ejpam-6705	207	10	such	such	ADJ
ejpam-6705	207	11	that	that	SCONJ
ejpam-6705	207	12	t	t	PROPN
ejpam-6705	207	13	(	(	PUNCT
ejpam-6705	207	14	m	m	NOUN
ejpam-6705	207	15	)	)	PUNCT
ejpam-6705	207	16	∩	∩	NOUN
ejpam-6705	208	1	[	[	X
ejpam-6705	208	2	0,∞	0,∞	NOUN
ejpam-6705	208	3	)	)	PUNCT
ejpam-6705	208	4	̸=	̸=	PROPN
ejpam-6705	208	5	∅.	∅.	ADV
ejpam-6705	208	6	then	then	ADV
ejpam-6705	208	7	there	there	PRON
ejpam-6705	208	8	exists	exist	VERB
ejpam-6705	208	9	a	a	DET
ejpam-6705	208	10	sequence	sequence	NOUN
ejpam-6705	208	11	(	(	PUNCT
ejpam-6705	208	12	us	us	PROPN
ejpam-6705	208	13	)	)	PUNCT
ejpam-6705	208	14	∈	∈	PROPN
ejpam-6705	208	15	x	x	PUNCT
ejpam-6705	208	16	with	with	ADP
ejpam-6705	208	17	us−1	us−1	PROPN
ejpam-6705	208	18	≼	≼	ADV
ejpam-6705	208	19	us	us	PROPN
ejpam-6705	208	20	∈	∈	PROPN
ejpam-6705	208	21	t	t	PROPN
ejpam-6705	208	22	(	(	PUNCT
ejpam-6705	208	23	us−1	us−1	PROPN
ejpam-6705	208	24	)	)	PUNCT
ejpam-6705	208	25	for	for	ADP
ejpam-6705	208	26	all	all	DET
ejpam-6705	208	27	s	s	PROPN
ejpam-6705	208	28	∈	∈	NOUN
ejpam-6705	208	29	n	n	CCONJ
ejpam-6705	208	30	,	,	PUNCT
ejpam-6705	208	31	and	and	CCONJ
ejpam-6705	208	32	t	t	PROPN
ejpam-6705	208	33	has	have	VERB
ejpam-6705	208	34	a	a	DET
ejpam-6705	208	35	fixed	fix	VERB
ejpam-6705	208	36	point	point	NOUN
ejpam-6705	208	37	u0	u0	ADJ
ejpam-6705	208	38	such	such	ADJ
ejpam-6705	208	39	that	that	SCONJ
ejpam-6705	208	40	us	we	PRON
ejpam-6705	208	41	→	→	SYM
ejpam-6705	208	42	u0	u0	PROPN
ejpam-6705	208	43	.	.	PUNCT
ejpam-6705	209	1	furthermore	furthermore	ADV
ejpam-6705	209	2	,	,	PUNCT
ejpam-6705	209	3	if	if	SCONJ
ejpam-6705	209	4	θ	θ	PROPN
ejpam-6705	209	5	is	be	AUX
ejpam-6705	209	6	lower	low	ADJ
ejpam-6705	209	7	semi	semi	ADJ
ejpam-6705	209	8	-	-	ADJ
ejpam-6705	209	9	continuous	continuous	ADJ
ejpam-6705	209	10	,	,	PUNCT
ejpam-6705	209	11	then	then	ADV
ejpam-6705	209	12	us	we	PRON
ejpam-6705	209	13	≼	≼	PROPN
ejpam-6705	209	14	u0	u0	ADJ
ejpam-6705	209	15	for	for	ADP
ejpam-6705	209	16	all	all	DET
ejpam-6705	209	17	s.	s.	PROPN
ejpam-6705	209	18	proof	proof	NOUN
ejpam-6705	209	19	.	.	PUNCT
ejpam-6705	210	1	by	by	ADP
ejpam-6705	210	2	property	property	NOUN
ejpam-6705	210	3	(	(	PUNCT
ejpam-6705	210	4	ii	ii	NOUN
ejpam-6705	210	5	)	)	PUNCT
ejpam-6705	210	6	,	,	PUNCT
ejpam-6705	210	7	m	m	PROPN
ejpam-6705	210	8	∈	∈	NOUN
ejpam-6705	210	9	m.	m.	NOUN
ejpam-6705	210	10	now	now	ADV
ejpam-6705	210	11	,	,	PUNCT
ejpam-6705	210	12	consider	consider	VERB
ejpam-6705	210	13	v	v	ADP
ejpam-6705	210	14	∈	∈	PROPN
ejpam-6705	210	15	t	t	PROPN
ejpam-6705	210	16	(	(	PUNCT
ejpam-6705	210	17	m	m	NOUN
ejpam-6705	210	18	)	)	PUNCT
ejpam-6705	210	19	∩	∩	NOUN
ejpam-6705	211	1	[	[	X
ejpam-6705	211	2	0,∞	0,∞	NOUN
ejpam-6705	211	3	)	)	PUNCT
ejpam-6705	211	4	,	,	PUNCT
ejpam-6705	211	5	then	then	ADV
ejpam-6705	211	6	by	by	ADP
ejpam-6705	211	7	the	the	DET
ejpam-6705	211	8	condition	condition	NOUN
ejpam-6705	211	9	of	of	ADP
ejpam-6705	211	10	t	t	PROPN
ejpam-6705	211	11	,	,	PUNCT
ejpam-6705	211	12	there	there	PRON
ejpam-6705	211	13	exists	exist	VERB
ejpam-6705	211	14	w	w	PROPN
ejpam-6705	211	15	∈	∈	PROPN
ejpam-6705	211	16	t	t	PROPN
ejpam-6705	211	17	(	(	PUNCT
ejpam-6705	211	18	v	v	NOUN
ejpam-6705	211	19	)	)	PUNCT
ejpam-6705	211	20	such	such	ADJ
ejpam-6705	211	21	that	that	PRON
ejpam-6705	211	22	v	v	ADP
ejpam-6705	211	23	≼	≼	PROPN
ejpam-6705	211	24	w.	w.	PROPN
ejpam-6705	211	25	equivalently	equivalently	PROPN
ejpam-6705	211	26	,	,	PUNCT
ejpam-6705	211	27	w	w	PROPN
ejpam-6705	211	28	∈	∈	PROPN
ejpam-6705	211	29	t	t	PROPN
ejpam-6705	211	30	(	(	PUNCT
ejpam-6705	211	31	v)∩	v)∩	X
ejpam-6705	212	1	[	[	X
ejpam-6705	212	2	0,∞	0,∞	NOUN
ejpam-6705	212	3	)	)	PUNCT
ejpam-6705	212	4	̸=	̸=	PROPN
ejpam-6705	212	5	∅.	∅.	ADP
ejpam-6705	212	6	this	this	PRON
ejpam-6705	212	7	implies	imply	VERB
ejpam-6705	212	8	that	that	SCONJ
ejpam-6705	212	9	v	v	NUM
ejpam-6705	212	10	∈	∈	NOUN
ejpam-6705	212	11	m	m	VERB
ejpam-6705	212	12	and	and	CCONJ
ejpam-6705	212	13	then	then	ADV
ejpam-6705	212	14	by	by	ADP
ejpam-6705	212	15	theorem	theorem	NOUN
ejpam-6705	212	16	1	1	NUM
ejpam-6705	212	17	,	,	PUNCT
ejpam-6705	212	18	the	the	DET
ejpam-6705	212	19	proof	proof	NOUN
ejpam-6705	212	20	is	be	AUX
ejpam-6705	212	21	completed	complete	VERB
ejpam-6705	212	22	.	.	PUNCT
ejpam-6705	213	1	corollary	corollary	ADJ
ejpam-6705	213	2	2	2	NUM
ejpam-6705	213	3	.	.	PUNCT
ejpam-6705	214	1	let	let	AUX
ejpam-6705	214	2	(	(	PUNCT
ejpam-6705	214	3	x	x	X
ejpam-6705	214	4	,	,	PUNCT
ejpam-6705	214	5	gb,≼	gb,≼	NOUN
ejpam-6705	214	6	)	)	PUNCT
ejpam-6705	214	7	be	be	AUX
ejpam-6705	214	8	a	a	DET
ejpam-6705	214	9	partially	partially	ADV
ejpam-6705	214	10	ordered	order	VERB
ejpam-6705	214	11	complete	complete	ADJ
ejpam-6705	214	12	gb	gb	ADV
ejpam-6705	214	13	-	-	PUNCT
ejpam-6705	214	14	metric	metric	ADJ
ejpam-6705	214	15	space	space	NOUN
ejpam-6705	214	16	induced	induce	VERB
ejpam-6705	214	17	by	by	ADP
ejpam-6705	214	18	(	(	PUNCT
ejpam-6705	214	19	κ	κ	NOUN
ejpam-6705	214	20	,	,	PUNCT
ejpam-6705	214	21	θ	θ	NOUN
ejpam-6705	214	22	)	)	PUNCT
ejpam-6705	214	23	such	such	ADJ
ejpam-6705	214	24	that	that	SCONJ
ejpam-6705	214	25	θ	θ	NOUN
ejpam-6705	214	26	:	:	PUNCT
ejpam-6705	214	27	x	x	X
ejpam-6705	215	1	→	→	PUNCT
ejpam-6705	215	2	[	[	X
ejpam-6705	215	3	0,∞	0,∞	NUM
ejpam-6705	215	4	)	)	PUNCT
ejpam-6705	215	5	is	be	AUX
ejpam-6705	215	6	a	a	DET
ejpam-6705	215	7	bounded	bound	VERB
ejpam-6705	215	8	below	below	ADP
ejpam-6705	215	9	mapping	mapping	NOUN
ejpam-6705	215	10	,	,	PUNCT
ejpam-6705	215	11	and	and	CCONJ
ejpam-6705	215	12	let	let	VERB
ejpam-6705	215	13	s	s	PRON
ejpam-6705	215	14	:	:	PUNCT
ejpam-6705	215	15	x	x	SYM
ejpam-6705	215	16	→	→	PUNCT
ejpam-6705	215	17	x	x	PUNCT
ejpam-6705	215	18	satisfy	satisfy	VERB
ejpam-6705	215	19	the	the	DET
ejpam-6705	215	20	following	following	NOUN
ejpam-6705	215	21	:	:	PUNCT
ejpam-6705	215	22	(	(	PUNCT
ejpam-6705	215	23	i	i	NOUN
ejpam-6705	215	24	)	)	PUNCT
ejpam-6705	215	25	s	s	AUX
ejpam-6705	215	26	is	be	AUX
ejpam-6705	215	27	a	a	DET
ejpam-6705	215	28	continuous	continuous	ADJ
ejpam-6705	215	29	function	function	NOUN
ejpam-6705	215	30	.	.	PUNCT
ejpam-6705	216	1	(	(	PUNCT
ejpam-6705	216	2	ii	ii	NOUN
ejpam-6705	216	3	)	)	PUNCT
ejpam-6705	216	4	for	for	ADP
ejpam-6705	216	5	any	any	DET
ejpam-6705	216	6	α	α	NOUN
ejpam-6705	216	7	∈	∈	NOUN
ejpam-6705	216	8	s	s	PART
ejpam-6705	216	9	(	(	PUNCT
ejpam-6705	216	10	u	u	NOUN
ejpam-6705	216	11	)	)	PUNCT
ejpam-6705	216	12	,	,	PUNCT
ejpam-6705	216	13	there	there	PRON
ejpam-6705	216	14	is	be	VERB
ejpam-6705	216	15	β	β	X
ejpam-6705	216	16	∈	∈	PROPN
ejpam-6705	216	17	s	s	X
ejpam-6705	216	18	(	(	PUNCT
ejpam-6705	216	19	v	v	NOUN
ejpam-6705	216	20	)	)	PUNCT
ejpam-6705	216	21	such	such	ADJ
ejpam-6705	216	22	that	that	SCONJ
ejpam-6705	216	23	α	α	PRON
ejpam-6705	216	24	≼	≼	NOUN
ejpam-6705	216	25	β	β	NOUN
ejpam-6705	216	26	.	.	PUNCT
ejpam-6705	217	1	(	(	PUNCT
ejpam-6705	217	2	iii	iii	X
ejpam-6705	217	3	)	)	PUNCT
ejpam-6705	217	4	there	there	PRON
ejpam-6705	217	5	is	be	VERB
ejpam-6705	217	6	m	m	PROPN
ejpam-6705	217	7	∈	∈	ADJ
ejpam-6705	217	8	x	x	PUNCT
ejpam-6705	217	9	such	such	ADJ
ejpam-6705	217	10	that	that	SCONJ
ejpam-6705	217	11	m	m	VERB
ejpam-6705	217	12	≼	≼	NOUN
ejpam-6705	217	13	s	s	X
ejpam-6705	217	14	(	(	PUNCT
ejpam-6705	217	15	m	m	NOUN
ejpam-6705	217	16	)	)	PUNCT
ejpam-6705	217	17	.	.	PUNCT
ejpam-6705	218	1	then	then	ADV
ejpam-6705	218	2	there	there	PRON
ejpam-6705	218	3	is	be	VERB
ejpam-6705	218	4	a	a	DET
ejpam-6705	218	5	sequence	sequence	NOUN
ejpam-6705	218	6	(	(	PUNCT
ejpam-6705	218	7	us	us	PROPN
ejpam-6705	218	8	)	)	PUNCT
ejpam-6705	218	9	∈	∈	PROPN
ejpam-6705	218	10	x	x	PUNCT
ejpam-6705	218	11	with	with	ADP
ejpam-6705	218	12	us−1	us−1	PROPN
ejpam-6705	218	13	≼	≼	ADV
ejpam-6705	218	14	us	us	PROPN
ejpam-6705	218	15	∈	∈	PROPN
ejpam-6705	218	16	s	s	X
ejpam-6705	218	17	(	(	PUNCT
ejpam-6705	218	18	us−1	us−1	PROPN
ejpam-6705	218	19	)	)	PUNCT
ejpam-6705	218	20	for	for	ADP
ejpam-6705	218	21	all	all	DET
ejpam-6705	218	22	s	s	PROPN
ejpam-6705	218	23	∈	∈	NOUN
ejpam-6705	218	24	n	n	CCONJ
ejpam-6705	218	25	,	,	PUNCT
ejpam-6705	218	26	and	and	CCONJ
ejpam-6705	218	27	s	s	VERB
ejpam-6705	218	28	has	have	VERB
ejpam-6705	218	29	a	a	DET
ejpam-6705	218	30	fixed	fix	VERB
ejpam-6705	218	31	point	point	NOUN
ejpam-6705	218	32	u0	u0	ADJ
ejpam-6705	218	33	such	such	ADJ
ejpam-6705	218	34	that	that	SCONJ
ejpam-6705	218	35	us	we	PRON
ejpam-6705	218	36	→	→	SYM
ejpam-6705	218	37	u0	u0	PROPN
ejpam-6705	218	38	.	.	PUNCT
ejpam-6705	219	1	also	also	ADV
ejpam-6705	219	2	,	,	PUNCT
ejpam-6705	219	3	if	if	SCONJ
ejpam-6705	219	4	θ	θ	PROPN
ejpam-6705	219	5	is	be	AUX
ejpam-6705	219	6	lower	low	ADJ
ejpam-6705	219	7	semi	semi	ADJ
ejpam-6705	219	8	-	-	ADJ
ejpam-6705	219	9	continuous	continuous	ADJ
ejpam-6705	219	10	,	,	PUNCT
ejpam-6705	219	11	then	then	ADV
ejpam-6705	219	12	us	we	PRON
ejpam-6705	219	13	≼	≼	PROPN
ejpam-6705	219	14	u0	u0	ADJ
ejpam-6705	219	15	for	for	ADP
ejpam-6705	219	16	all	all	DET
ejpam-6705	219	17	s.	s.	PROPN
ejpam-6705	219	18	proof	proof	NOUN
ejpam-6705	219	19	.	.	PUNCT
ejpam-6705	220	1	define	define	VERB
ejpam-6705	220	2	the	the	DET
ejpam-6705	220	3	multivalued	multivalue	VERB
ejpam-6705	220	4	mapping	mapping	NOUN
ejpam-6705	220	5	t	t	NOUN
ejpam-6705	220	6	:	:	PUNCT
ejpam-6705	220	7	x	x	X
ejpam-6705	220	8	→	→	SYM
ejpam-6705	220	9	2x	2x	NUM
ejpam-6705	220	10	via	via	ADP
ejpam-6705	220	11	t	t	PROPN
ejpam-6705	220	12	(	(	PUNCT
ejpam-6705	220	13	u	u	NOUN
ejpam-6705	220	14	)	)	PUNCT
ejpam-6705	220	15	=	=	PUNCT
ejpam-6705	220	16	{	{	PUNCT
ejpam-6705	220	17	s	s	X
ejpam-6705	220	18	(	(	PUNCT
ejpam-6705	220	19	u	u	NOUN
ejpam-6705	220	20	)	)	PUNCT
ejpam-6705	220	21	}	}	PUNCT
ejpam-6705	220	22	,	,	PUNCT
ejpam-6705	220	23	then	then	ADV
ejpam-6705	220	24	t	t	PROPN
ejpam-6705	220	25	and	and	CCONJ
ejpam-6705	220	26	x	x	PART
ejpam-6705	220	27	satisfy	satisfy	VERB
ejpam-6705	220	28	all	all	DET
ejpam-6705	220	29	the	the	DET
ejpam-6705	220	30	conditions	condition	NOUN
ejpam-6705	220	31	of	of	ADP
ejpam-6705	220	32	theorem	theorem	NOUN
ejpam-6705	220	33	1	1	NUM
ejpam-6705	220	34	.	.	PUNCT
ejpam-6705	221	1	therefore	therefore	ADV
ejpam-6705	221	2	,	,	PUNCT
ejpam-6705	221	3	the	the	DET
ejpam-6705	221	4	proof	proof	NOUN
ejpam-6705	221	5	follows	follow	VERB
ejpam-6705	221	6	from	from	ADP
ejpam-6705	221	7	theorem	theorem	ADJ
ejpam-6705	221	8	1	1	NUM
ejpam-6705	221	9	.	.	PUNCT
ejpam-6705	221	10	by	by	ADP
ejpam-6705	221	11	replacing	replace	VERB
ejpam-6705	221	12	the	the	DET
ejpam-6705	221	13	conditions	condition	NOUN
ejpam-6705	221	14	bounded	bound	VERB
ejpam-6705	221	15	below	below	ADV
ejpam-6705	221	16	with	with	ADP
ejpam-6705	221	17	the	the	DET
ejpam-6705	221	18	conditions	condition	NOUN
ejpam-6705	221	19	of	of	ADP
ejpam-6705	221	20	bounded	bounded	ADJ
ejpam-6705	221	21	above	above	ADV
ejpam-6705	221	22	,	,	PUNCT
ejpam-6705	221	23	we	we	PRON
ejpam-6705	221	24	obtain	obtain	VERB
ejpam-6705	221	25	the	the	DET
ejpam-6705	221	26	following	follow	VERB
ejpam-6705	221	27	results	result	NOUN
ejpam-6705	221	28	.	.	PUNCT
ejpam-6705	222	1	theorem	theorem	NOUN
ejpam-6705	222	2	2	2	NUM
ejpam-6705	222	3	.	.	X
ejpam-6705	223	1	let	let	AUX
ejpam-6705	223	2	(	(	PUNCT
ejpam-6705	223	3	x	x	X
ejpam-6705	223	4	,	,	PUNCT
ejpam-6705	223	5	gb,≼	gb,≼	NOUN
ejpam-6705	223	6	)	)	PUNCT
ejpam-6705	223	7	be	be	AUX
ejpam-6705	223	8	a	a	DET
ejpam-6705	223	9	partially	partially	ADV
ejpam-6705	223	10	ordered	order	VERB
ejpam-6705	223	11	complete	complete	ADJ
ejpam-6705	223	12	gb	gb	ADV
ejpam-6705	223	13	-	-	PUNCT
ejpam-6705	223	14	metric	metric	ADJ
ejpam-6705	223	15	space	space	NOUN
ejpam-6705	223	16	induced	induce	VERB
ejpam-6705	223	17	via	via	ADP
ejpam-6705	223	18	(	(	PUNCT
ejpam-6705	223	19	κ	κ	NOUN
ejpam-6705	223	20	,	,	PUNCT
ejpam-6705	223	21	θ	θ	NOUN
ejpam-6705	223	22	)	)	PUNCT
ejpam-6705	223	23	,	,	PUNCT
ejpam-6705	223	24	where	where	SCONJ
ejpam-6705	223	25	θ	θ	NOUN
ejpam-6705	223	26	:	:	PUNCT
ejpam-6705	223	27	x	x	X
ejpam-6705	223	28	→	→	X
ejpam-6705	223	29	(	(	PUNCT
ejpam-6705	223	30	−∞	−∞	NOUN
ejpam-6705	223	31	,	,	PUNCT
ejpam-6705	223	32	0	0	NUM
ejpam-6705	223	33	]	]	PUNCT
ejpam-6705	223	34	is	be	AUX
ejpam-6705	223	35	a	a	DET
ejpam-6705	223	36	bounded	bound	VERB
ejpam-6705	223	37	above	above	ADP
ejpam-6705	223	38	mapping	mapping	NOUN
ejpam-6705	223	39	.	.	PUNCT
ejpam-6705	224	1	presume	presume	VERB
ejpam-6705	224	2	that	that	SCONJ
ejpam-6705	224	3	t	t	NOUN
ejpam-6705	224	4	:	:	PUNCT
ejpam-6705	224	5	x	x	X
ejpam-6705	224	6	→	→	SYM
ejpam-6705	224	7	2x	2x	NUM
ejpam-6705	224	8	is	be	AUX
ejpam-6705	224	9	a	a	DET
ejpam-6705	224	10	multivalued	multivalue	VERB
ejpam-6705	224	11	mapping	mapping	NOUN
ejpam-6705	224	12	and	and	CCONJ
ejpam-6705	224	13	m	m	PROPN
ejpam-6705	224	14	=	=	PUNCT
ejpam-6705	224	15	{	{	PUNCT
ejpam-6705	224	16	u	u	NOUN
ejpam-6705	224	17	∈	∈	PROPN
ejpam-6705	224	18	x	x	X
ejpam-6705	224	19	:	:	PUNCT
ejpam-6705	224	20	t	t	PROPN
ejpam-6705	224	21	(	(	PUNCT
ejpam-6705	224	22	u	u	NOUN
ejpam-6705	224	23	)	)	PUNCT
ejpam-6705	224	24	∩	∩	NOUN
ejpam-6705	224	25	(	(	PUNCT
ejpam-6705	224	26	−∞	−∞	NOUN
ejpam-6705	224	27	,	,	PUNCT
ejpam-6705	224	28	u	u	NOUN
ejpam-6705	224	29	]	]	X
ejpam-6705	224	30	̸=	̸=	PROPN
ejpam-6705	224	31	∅	∅	NOUN
ejpam-6705	224	32	}	}	PUNCT
ejpam-6705	224	33	.	.	PUNCT
ejpam-6705	225	1	assume	assume	VERB
ejpam-6705	225	2	that	that	SCONJ
ejpam-6705	225	3	(	(	PUNCT
ejpam-6705	225	4	i	i	NOUN
ejpam-6705	225	5	)	)	PUNCT
ejpam-6705	225	6	t	t	PROPN
ejpam-6705	225	7	is	be	AUX
ejpam-6705	225	8	upper	upper	ADJ
ejpam-6705	225	9	semi	semi	ADJ
ejpam-6705	225	10	-	-	ADJ
ejpam-6705	225	11	continuous	continuous	ADJ
ejpam-6705	225	12	.	.	PUNCT
ejpam-6705	226	1	(	(	PUNCT
ejpam-6705	226	2	ii	ii	NOUN
ejpam-6705	226	3	)	)	PUNCT
ejpam-6705	226	4	for	for	ADP
ejpam-6705	226	5	all	all	DET
ejpam-6705	226	6	u	u	PROPN
ejpam-6705	226	7	∈	∈	PROPN
ejpam-6705	226	8	m	m	PROPN
ejpam-6705	226	9	,	,	PUNCT
ejpam-6705	226	10	t	t	PROPN
ejpam-6705	226	11	(	(	PUNCT
ejpam-6705	226	12	u	u	NOUN
ejpam-6705	226	13	)	)	PUNCT
ejpam-6705	226	14	∩m∩	∩m∩	PROPN
ejpam-6705	226	15	(	(	PUNCT
ejpam-6705	226	16	−∞	−∞	NOUN
ejpam-6705	226	17	,	,	PUNCT
ejpam-6705	226	18	u	u	NOUN
ejpam-6705	226	19	]	]	X
ejpam-6705	226	20	̸=	̸=	PROPN
ejpam-6705	226	21	∅.	∅.	ADP
ejpam-6705	226	22	s.	s.	PROPN
ejpam-6705	226	23	batul	batul	PROPN
ejpam-6705	226	24	et	et	PROPN
ejpam-6705	226	25	al	al	PROPN
ejpam-6705	226	26	.	.	PUNCT
ejpam-6705	226	27	/	/	SYM
ejpam-6705	226	28	eur	eur	PROPN
ejpam-6705	226	29	.	.	PUNCT
ejpam-6705	227	1	j.	j.	PROPN
ejpam-6705	227	2	pure	pure	PROPN
ejpam-6705	227	3	appl	appl	PROPN
ejpam-6705	227	4	.	.	PROPN
ejpam-6705	227	5	math	math	PROPN
ejpam-6705	227	6	,	,	PUNCT
ejpam-6705	227	7	18	18	NUM
ejpam-6705	227	8	(	(	PUNCT
ejpam-6705	227	9	4	4	NUM
ejpam-6705	227	10	)	)	PUNCT
ejpam-6705	227	11	(	(	PUNCT
ejpam-6705	227	12	2025	2025	NUM
ejpam-6705	227	13	)	)	PUNCT
ejpam-6705	227	14	,	,	PUNCT
ejpam-6705	227	15	6705	6705	NUM
ejpam-6705	227	16	9	9	NUM
ejpam-6705	227	17	of	of	ADP
ejpam-6705	227	18	23	23	NUM
ejpam-6705	227	19	then	then	ADV
ejpam-6705	227	20	there	there	PRON
ejpam-6705	227	21	is	be	VERB
ejpam-6705	227	22	a	a	DET
ejpam-6705	227	23	sequence	sequence	NOUN
ejpam-6705	227	24	(	(	PUNCT
ejpam-6705	227	25	us	we	PRON
ejpam-6705	227	26	)	)	PUNCT
ejpam-6705	227	27	such	such	ADJ
ejpam-6705	227	28	that	that	SCONJ
ejpam-6705	227	29	us−1	us−1	PROPN
ejpam-6705	227	30	≽	≽	PROPN
ejpam-6705	227	31	us	us	PROPN
ejpam-6705	227	32	∈	∈	PROPN
ejpam-6705	227	33	t	t	PROPN
ejpam-6705	227	34	(	(	PUNCT
ejpam-6705	227	35	us−1	us−1	PROPN
ejpam-6705	227	36	)	)	PUNCT
ejpam-6705	227	37	for	for	ADP
ejpam-6705	227	38	all	all	DET
ejpam-6705	227	39	s	s	PROPN
ejpam-6705	227	40	∈	∈	NOUN
ejpam-6705	227	41	n	n	CCONJ
ejpam-6705	227	42	,	,	PUNCT
ejpam-6705	227	43	and	and	CCONJ
ejpam-6705	227	44	t	t	PROPN
ejpam-6705	227	45	has	have	VERB
ejpam-6705	227	46	a	a	DET
ejpam-6705	227	47	fixed	fix	VERB
ejpam-6705	227	48	point	point	NOUN
ejpam-6705	227	49	u0	u0	ADJ
ejpam-6705	227	50	such	such	ADJ
ejpam-6705	227	51	that	that	SCONJ
ejpam-6705	227	52	us	we	PRON
ejpam-6705	227	53	→	→	SYM
ejpam-6705	227	54	u0	u0	PROPN
ejpam-6705	227	55	.	.	PUNCT
ejpam-6705	228	1	also	also	ADV
ejpam-6705	228	2	,	,	PUNCT
ejpam-6705	228	3	if	if	SCONJ
ejpam-6705	228	4	θ	θ	PROPN
ejpam-6705	228	5	is	be	AUX
ejpam-6705	228	6	lower	low	ADJ
ejpam-6705	228	7	semi	semi	ADJ
ejpam-6705	228	8	-	-	ADJ
ejpam-6705	228	9	continuous	continuous	ADJ
ejpam-6705	228	10	,	,	PUNCT
ejpam-6705	228	11	then	then	ADV
ejpam-6705	228	12	us	us	PROPN
ejpam-6705	228	13	≽	≽	PROPN
ejpam-6705	228	14	u0	u0	ADJ
ejpam-6705	228	15	for	for	ADP
ejpam-6705	228	16	all	all	DET
ejpam-6705	228	17	s.	s.	PROPN
ejpam-6705	228	18	proof	proof	NOUN
ejpam-6705	228	19	.	.	PUNCT
ejpam-6705	229	1	by	by	ADP
ejpam-6705	229	2	using	use	VERB
ejpam-6705	229	3	condition	condition	NOUN
ejpam-6705	229	4	(	(	PUNCT
ejpam-6705	229	5	ii	ii	NOUN
ejpam-6705	229	6	)	)	PUNCT
ejpam-6705	229	7	,	,	PUNCT
ejpam-6705	229	8	there	there	PRON
ejpam-6705	229	9	exists	exist	VERB
ejpam-6705	229	10	m	m	VERB
ejpam-6705	229	11	∈	∈	ADJ
ejpam-6705	229	12	x	x	PUNCT
ejpam-6705	229	13	such	such	ADJ
ejpam-6705	229	14	that	that	SCONJ
ejpam-6705	229	15	m	m	PROPN
ejpam-6705	229	16	∈	∈	NOUN
ejpam-6705	229	17	m.	m.	NOUN
ejpam-6705	229	18	by	by	ADP
ejpam-6705	229	19	choosing	choose	VERB
ejpam-6705	229	20	n	n	PROPN
ejpam-6705	229	21	∈	∈	PROPN
ejpam-6705	229	22	t	t	PROPN
ejpam-6705	229	23	(	(	PUNCT
ejpam-6705	229	24	m	m	NOUN
ejpam-6705	229	25	)	)	PUNCT
ejpam-6705	229	26	∩	∩	NOUN
ejpam-6705	229	27	(	(	PUNCT
ejpam-6705	229	28	−∞,m	−∞,m	X
ejpam-6705	229	29	]	]	PUNCT
ejpam-6705	229	30	,	,	PUNCT
ejpam-6705	229	31	and	and	CCONJ
ejpam-6705	229	32	we	we	PRON
ejpam-6705	229	33	get	get	VERB
ejpam-6705	229	34	m	m	VERB
ejpam-6705	229	35	≽	≽	NOUN
ejpam-6705	229	36	n.	n.	NOUN
ejpam-6705	229	37	by	by	ADP
ejpam-6705	229	38	condition	condition	NOUN
ejpam-6705	229	39	(	(	PUNCT
ejpam-6705	229	40	ii	ii	NOUN
ejpam-6705	229	41	)	)	PUNCT
ejpam-6705	229	42	,	,	PUNCT
ejpam-6705	229	43	n	n	PROPN
ejpam-6705	229	44	∈	∈	PROPN
ejpam-6705	229	45	m.	m.	NOUN
ejpam-6705	229	46	choose	choose	VERB
ejpam-6705	229	47	τ	τ	PROPN
ejpam-6705	229	48	∈	∈	PROPN
ejpam-6705	229	49	t	t	PROPN
ejpam-6705	229	50	(	(	PUNCT
ejpam-6705	229	51	n	n	CCONJ
ejpam-6705	229	52	)	)	PUNCT
ejpam-6705	229	53	∩	∩	NOUN
ejpam-6705	229	54	(	(	PUNCT
ejpam-6705	229	55	−∞	−∞	NOUN
ejpam-6705	229	56	,	,	PUNCT
ejpam-6705	229	57	n	n	CCONJ
ejpam-6705	229	58	]	]	PUNCT
ejpam-6705	229	59	,	,	PUNCT
ejpam-6705	229	60	⇒	⇒	NOUN
ejpam-6705	229	61	n	n	PRON
ejpam-6705	229	62	≽	≽	PROPN
ejpam-6705	229	63	τ	τ	PROPN
ejpam-6705	229	64	.	.	PUNCT
ejpam-6705	230	1	by	by	ADP
ejpam-6705	230	2	proceeding	proceed	VERB
ejpam-6705	230	3	in	in	ADP
ejpam-6705	230	4	this	this	DET
ejpam-6705	230	5	way	way	NOUN
ejpam-6705	230	6	,	,	PUNCT
ejpam-6705	230	7	there	there	PRON
ejpam-6705	230	8	is	be	VERB
ejpam-6705	230	9	a	a	DET
ejpam-6705	230	10	sequence	sequence	NOUN
ejpam-6705	230	11	(	(	PUNCT
ejpam-6705	230	12	us	we	PRON
ejpam-6705	230	13	)	)	PUNCT
ejpam-6705	230	14	∈	∈	PROPN
ejpam-6705	230	15	x	x	SYM
ejpam-6705	230	16	s.t	s.t	PROPN
ejpam-6705	230	17	.	.	PUNCT
ejpam-6705	231	1	us−1	us−1	PROPN
ejpam-6705	231	2	≽	≽	PROPN
ejpam-6705	231	3	us	us	PROPN
ejpam-6705	231	4	∈	∈	PROPN
ejpam-6705	231	5	t	t	PROPN
ejpam-6705	231	6	(	(	PUNCT
ejpam-6705	231	7	us−1	us−1	PROPN
ejpam-6705	231	8	)	)	PUNCT
ejpam-6705	231	9	for	for	ADP
ejpam-6705	231	10	all	all	DET
ejpam-6705	231	11	s	s	PROPN
ejpam-6705	231	12	∈	∈	PROPN
ejpam-6705	231	13	n.	n.	NOUN
ejpam-6705	231	14	since	since	SCONJ
ejpam-6705	231	15	(	(	PUNCT
ejpam-6705	231	16	x	x	INTJ
ejpam-6705	231	17	,	,	PUNCT
ejpam-6705	231	18	gb,≼	gb,≼	NOUN
ejpam-6705	231	19	)	)	PUNCT
ejpam-6705	231	20	is	be	AUX
ejpam-6705	231	21	a	a	DET
ejpam-6705	231	22	partially	partially	ADV
ejpam-6705	231	23	ordered	order	VERB
ejpam-6705	231	24	gb	gb	ADP
ejpam-6705	231	25	metric	metric	ADJ
ejpam-6705	231	26	space	space	NOUN
ejpam-6705	231	27	induced	induce	VERB
ejpam-6705	231	28	via	via	ADP
ejpam-6705	231	29	(	(	PUNCT
ejpam-6705	231	30	κ	κ	NOUN
ejpam-6705	231	31	,	,	PUNCT
ejpam-6705	231	32	θ	θ	NOUN
ejpam-6705	231	33	)	)	PUNCT
ejpam-6705	231	34	,	,	PUNCT
ejpam-6705	231	35	⇒	⇒	VERB
ejpam-6705	231	36	κ(gb(us−1	κ(gb(us−1	PROPN
ejpam-6705	231	37	,	,	PUNCT
ejpam-6705	231	38	us−1	us−1	PROPN
ejpam-6705	231	39	,	,	PUNCT
ejpam-6705	231	40	us	we	PRON
ejpam-6705	231	41	)	)	PUNCT
ejpam-6705	231	42	)	)	PUNCT
ejpam-6705	231	43	≤	≤	ADV
ejpam-6705	231	44	θ(us−1)−θ(us	θ(us−1)−θ(us	ADV
ejpam-6705	231	45	)	)	PUNCT
ejpam-6705	231	46	.	.	PUNCT
ejpam-6705	232	1	given	give	VERB
ejpam-6705	232	2	that	that	PRON
ejpam-6705	232	3	κ	κ	NOUN
ejpam-6705	232	4	is	be	AUX
ejpam-6705	232	5	non	non	ADJ
ejpam-6705	232	6	-	-	ADJ
ejpam-6705	232	7	negative	negative	ADJ
ejpam-6705	232	8	mapping	mapping	NOUN
ejpam-6705	232	9	,	,	PUNCT
ejpam-6705	232	10	θ(us−1)−θ(us	θ(us−1)−θ(us	PROPN
ejpam-6705	232	11	)	)	PUNCT
ejpam-6705	232	12	≥	≥	NOUN
ejpam-6705	232	13	0	0	NUM
ejpam-6705	232	14	∀	∀	NOUN
ejpam-6705	232	15	s	s	NOUN
ejpam-6705	232	16	∈	∈	PROPN
ejpam-6705	232	17	n.	n.	PROPN
ejpam-6705	232	18	⇒	⇒	PROPN
ejpam-6705	232	19	θ(us−1	θ(us−1	PROPN
ejpam-6705	232	20	)	)	PUNCT
ejpam-6705	232	21	≥	≥	NOUN
ejpam-6705	232	22	θ(us	θ(us	X
ejpam-6705	232	23	)	)	PUNCT
ejpam-6705	232	24	∀	∀	PUNCT
ejpam-6705	232	25	s	s	NOUN
ejpam-6705	232	26	∈	∈	PROPN
ejpam-6705	232	27	n.	n.	NOUN
ejpam-6705	232	28	as	as	SCONJ
ejpam-6705	232	29	θ	θ	PROPN
ejpam-6705	232	30	is	be	AUX
ejpam-6705	232	31	bounded	bound	VERB
ejpam-6705	232	32	above	above	ADV
ejpam-6705	232	33	,	,	PUNCT
ejpam-6705	232	34	we	we	PRON
ejpam-6705	232	35	get	get	VERB
ejpam-6705	232	36	θ(us	θ(us	PROPN
ejpam-6705	232	37	)	)	PUNCT
ejpam-6705	232	38	is	be	AUX
ejpam-6705	232	39	an	an	DET
ejpam-6705	232	40	increasing	increase	VERB
ejpam-6705	232	41	sequence	sequence	NOUN
ejpam-6705	232	42	which	which	PRON
ejpam-6705	232	43	is	be	AUX
ejpam-6705	232	44	bounded	bound	VERB
ejpam-6705	232	45	above	above	ADV
ejpam-6705	232	46	.	.	PUNCT
ejpam-6705	233	1	by	by	ADP
ejpam-6705	233	2	the	the	DET
ejpam-6705	233	3	completeness	completeness	NOUN
ejpam-6705	233	4	of	of	ADP
ejpam-6705	233	5	r	r	PROPN
ejpam-6705	233	6	,	,	PUNCT
ejpam-6705	233	7	lim	lim	PROPN
ejpam-6705	233	8	s→−∞	s→−∞	PROPN
ejpam-6705	233	9	θ(us	θ(us	PROPN
ejpam-6705	233	10	)	)	PUNCT
ejpam-6705	234	1	=	=	SYM
ejpam-6705	234	2	inf{us	inf{us	NOUN
ejpam-6705	234	3	:	:	PUNCT
ejpam-6705	234	4	s	s	X
ejpam-6705	234	5	∈	∈	PROPN
ejpam-6705	234	6	n	n	CCONJ
ejpam-6705	234	7	}	}	PUNCT
ejpam-6705	234	8	,	,	PUNCT
ejpam-6705	234	9	thus	thus	ADV
ejpam-6705	234	10	lim	lim	PROPN
ejpam-6705	234	11	s	s	PROPN
ejpam-6705	234	12	,	,	PUNCT
ejpam-6705	234	13	r→−∞	r→−∞	PROPN
ejpam-6705	234	14	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	234	15	,	,	PUNCT
ejpam-6705	234	16	us	we	PRON
ejpam-6705	234	17	,	,	PUNCT
ejpam-6705	234	18	ur	ur	INTJ
ejpam-6705	234	19	)	)	PUNCT
ejpam-6705	234	20	)	)	PUNCT
ejpam-6705	234	21	≤	≤	PROPN
ejpam-6705	234	22	lim	lim	PROPN
ejpam-6705	234	23	s→−∞	s→−∞	PROPN
ejpam-6705	234	24	θ(us)−	θ(us)−	VERB
ejpam-6705	234	25	lim	lim	PROPN
ejpam-6705	234	26	r→−∞	r→−∞	PROPN
ejpam-6705	234	27	θ(ur	θ(ur	PROPN
ejpam-6705	234	28	)	)	PUNCT
ejpam-6705	234	29	.	.	PUNCT
ejpam-6705	235	1	therefore	therefore	ADV
ejpam-6705	235	2	,	,	PUNCT
ejpam-6705	235	3	lim	lim	PROPN
ejpam-6705	235	4	s	s	PROPN
ejpam-6705	235	5	,	,	PUNCT
ejpam-6705	235	6	r→−∞	r→−∞	PROPN
ejpam-6705	235	7	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	235	8	,	,	PUNCT
ejpam-6705	235	9	us	we	PRON
ejpam-6705	235	10	,	,	PUNCT
ejpam-6705	235	11	ur	ur	INTJ
ejpam-6705	235	12	)	)	PUNCT
ejpam-6705	235	13	)	)	PUNCT
ejpam-6705	236	1	=	=	PUNCT
ejpam-6705	236	2	0	0	X
ejpam-6705	236	3	.	.	PUNCT
ejpam-6705	237	1	now	now	ADV
ejpam-6705	237	2	,	,	PUNCT
ejpam-6705	237	3	since	since	SCONJ
ejpam-6705	237	4	κ	κ	NOUN
ejpam-6705	237	5	is	be	AUX
ejpam-6705	237	6	continuous	continuous	ADJ
ejpam-6705	237	7	κ−1({0	κ−1({0	NOUN
ejpam-6705	237	8	}	}	PUNCT
ejpam-6705	237	9	)	)	PUNCT
ejpam-6705	238	1	=	=	PUNCT
ejpam-6705	238	2	{	{	PUNCT
ejpam-6705	238	3	0	0	NUM
ejpam-6705	238	4	}	}	PUNCT
ejpam-6705	238	5	,	,	PUNCT
ejpam-6705	238	6	we	we	PRON
ejpam-6705	238	7	get	get	VERB
ejpam-6705	238	8	lim	lim	PROPN
ejpam-6705	238	9	s	s	PART
ejpam-6705	238	10	,	,	PUNCT
ejpam-6705	238	11	r→−∞	r→−∞	PROPN
ejpam-6705	238	12	gb(us	gb(us	PROPN
ejpam-6705	238	13	,	,	PUNCT
ejpam-6705	238	14	us	we	PRON
ejpam-6705	238	15	,	,	PUNCT
ejpam-6705	238	16	ur	ur	INTJ
ejpam-6705	238	17	)	)	PUNCT
ejpam-6705	238	18	=	=	SYM
ejpam-6705	239	1	0	0	X
ejpam-6705	239	2	.	.	PUNCT
ejpam-6705	240	1	therefore	therefore	ADV
ejpam-6705	240	2	,	,	PUNCT
ejpam-6705	240	3	(	(	PUNCT
ejpam-6705	240	4	us	us	PROPN
ejpam-6705	240	5	)	)	PUNCT
ejpam-6705	240	6	is	be	AUX
ejpam-6705	240	7	a	a	DET
ejpam-6705	240	8	cauchy	cauchy	ADJ
ejpam-6705	240	9	sequence	sequence	NOUN
ejpam-6705	240	10	in	in	ADP
ejpam-6705	240	11	x	x	X
ejpam-6705	240	12	.	.	PUNCT
ejpam-6705	241	1	since	since	SCONJ
ejpam-6705	241	2	x	x	PRON
ejpam-6705	241	3	is	be	AUX
ejpam-6705	241	4	complete	complete	ADJ
ejpam-6705	241	5	,	,	PUNCT
ejpam-6705	241	6	there	there	PRON
ejpam-6705	241	7	exists	exist	VERB
ejpam-6705	241	8	u0	u0	ADJ
ejpam-6705	241	9	∈	∈	PROPN
ejpam-6705	241	10	x	x	PUNCT
ejpam-6705	241	11	such	such	ADJ
ejpam-6705	241	12	that	that	SCONJ
ejpam-6705	241	13	(	(	PUNCT
ejpam-6705	241	14	us	we	PRON
ejpam-6705	241	15	)	)	PUNCT
ejpam-6705	241	16	is	be	AUX
ejpam-6705	241	17	gb	gb	ADP
ejpam-6705	241	18	convergent	convergent	NOUN
ejpam-6705	241	19	.	.	PUNCT
ejpam-6705	242	1	to	to	PART
ejpam-6705	242	2	u0	u0	VERB
ejpam-6705	242	3	.	.	PUNCT
ejpam-6705	243	1	since	since	SCONJ
ejpam-6705	243	2	us−1	us−1	PROPN
ejpam-6705	243	3	∈	∈	PROPN
ejpam-6705	243	4	x	x	X
ejpam-6705	243	5	,	,	PUNCT
ejpam-6705	243	6	us	us	PROPN
ejpam-6705	243	7	∈	∈	PROPN
ejpam-6705	243	8	t	t	PROPN
ejpam-6705	243	9	(	(	PUNCT
ejpam-6705	243	10	us−1	us−1	PROPN
ejpam-6705	243	11	)	)	PUNCT
ejpam-6705	243	12	,	,	PUNCT
ejpam-6705	243	13	us−1	us−1	PROPN
ejpam-6705	243	14	→	→	SYM
ejpam-6705	243	15	u0	u0	ADJ
ejpam-6705	243	16	,	,	PUNCT
ejpam-6705	243	17	and	and	CCONJ
ejpam-6705	243	18	us	we	PRON
ejpam-6705	243	19	→	→	SYM
ejpam-6705	243	20	u0	u0	PROPN
ejpam-6705	243	21	,	,	PUNCT
ejpam-6705	243	22	via	via	ADP
ejpam-6705	243	23	the	the	DET
ejpam-6705	243	24	definition	definition	NOUN
ejpam-6705	243	25	of	of	ADP
ejpam-6705	243	26	upper	upper	ADJ
ejpam-6705	243	27	semi	semi	NOUN
ejpam-6705	243	28	-	-	NOUN
ejpam-6705	243	29	continuity	continuity	NOUN
ejpam-6705	243	30	of	of	ADP
ejpam-6705	243	31	t	t	PROPN
ejpam-6705	243	32	,	,	PUNCT
ejpam-6705	243	33	we	we	PRON
ejpam-6705	243	34	have	have	VERB
ejpam-6705	243	35	u0	u0	PROPN
ejpam-6705	243	36	∈	∈	PROPN
ejpam-6705	243	37	t	t	PROPN
ejpam-6705	243	38	(	(	PUNCT
ejpam-6705	243	39	u0	u0	PROPN
ejpam-6705	243	40	)	)	PUNCT
ejpam-6705	243	41	.	.	PUNCT
ejpam-6705	244	1	now	now	ADV
ejpam-6705	244	2	,	,	PUNCT
ejpam-6705	244	3	if	if	SCONJ
ejpam-6705	244	4	θ	θ	PROPN
ejpam-6705	244	5	is	be	AUX
ejpam-6705	244	6	lower	low	ADJ
ejpam-6705	244	7	semi	semi	ADJ
ejpam-6705	244	8	-	-	ADJ
ejpam-6705	244	9	continuous	continuous	ADJ
ejpam-6705	244	10	,	,	PUNCT
ejpam-6705	244	11	then	then	ADV
ejpam-6705	244	12	for	for	ADP
ejpam-6705	244	13	all	all	DET
ejpam-6705	244	14	s	s	PART
ejpam-6705	244	15	∈	∈	PROPN
ejpam-6705	244	16	n	n	CCONJ
ejpam-6705	244	17	,	,	PUNCT
ejpam-6705	244	18	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	244	19	,	,	PUNCT
ejpam-6705	244	20	us	we	PRON
ejpam-6705	244	21	,	,	PUNCT
ejpam-6705	244	22	u0	u0	ADJ
ejpam-6705	244	23	)	)	PUNCT
ejpam-6705	244	24	)	)	PUNCT
ejpam-6705	245	1	=	=	SYM
ejpam-6705	245	2	lim	lim	PROPN
ejpam-6705	245	3	r→∞	r→∞	PRON
ejpam-6705	245	4	κ(gb(us	κ(gb(us	PROPN
ejpam-6705	245	5	,	,	PUNCT
ejpam-6705	245	6	us	we	PRON
ejpam-6705	245	7	,	,	PUNCT
ejpam-6705	245	8	ur	ur	INTJ
ejpam-6705	245	9	)	)	PUNCT
ejpam-6705	245	10	)	)	PUNCT
ejpam-6705	245	11	≤	≤	PROPN
ejpam-6705	246	1	lim	lim	PROPN
ejpam-6705	246	2	r→∞	r→∞	NUM
ejpam-6705	246	3	{	{	PUNCT
ejpam-6705	246	4	inf	inf	NOUN
ejpam-6705	246	5	θ(us)−θ(ur	θ(us)−θ(ur	ADJ
ejpam-6705	246	6	)	)	PUNCT
ejpam-6705	246	7	}	}	PUNCT
ejpam-6705	246	8	=	=	PUNCT
ejpam-6705	246	9	θ(us)−	θ(us)−	ADP
ejpam-6705	246	10	lim	lim	PROPN
ejpam-6705	246	11	r→∞	r→∞	PUNCT
ejpam-6705	246	12	θ(ur	θ(ur	PROPN
ejpam-6705	246	13	)	)	PUNCT
ejpam-6705	246	14	≤	≤	NUM
ejpam-6705	246	15	θ(us)−θ(u0	θ(us)−θ(u0	NOUN
ejpam-6705	246	16	)	)	PUNCT
ejpam-6705	246	17	.	.	PUNCT
ejpam-6705	247	1	thus	thus	ADV
ejpam-6705	247	2	,	,	PUNCT
ejpam-6705	247	3	us	us	PROPN
ejpam-6705	247	4	≽	≽	PROPN
ejpam-6705	247	5	u0	u0	ADJ
ejpam-6705	247	6	for	for	ADP
ejpam-6705	247	7	all	all	DET
ejpam-6705	247	8	s	s	PROPN
ejpam-6705	247	9	∈	∈	PROPN
ejpam-6705	247	10	n.	n.	NOUN
ejpam-6705	247	11	corollary	corollary	NOUN
ejpam-6705	247	12	3	3	PROPN
ejpam-6705	247	13	.	.	PUNCT
ejpam-6705	247	14	suppose	suppose	VERB
ejpam-6705	247	15	that	that	SCONJ
ejpam-6705	247	16	(	(	PUNCT
ejpam-6705	247	17	x	x	X
ejpam-6705	247	18	,	,	PUNCT
ejpam-6705	247	19	gb,≼	gb,≼	NOUN
ejpam-6705	247	20	)	)	PUNCT
ejpam-6705	247	21	is	be	AUX
ejpam-6705	247	22	a	a	DET
ejpam-6705	247	23	partially	partially	ADV
ejpam-6705	247	24	ordered	order	VERB
ejpam-6705	247	25	complete	complete	ADJ
ejpam-6705	247	26	gb	gb	ADV
ejpam-6705	247	27	-	-	PUNCT
ejpam-6705	247	28	metric	metric	ADJ
ejpam-6705	247	29	space	space	NOUN
ejpam-6705	247	30	induced	induce	VERB
ejpam-6705	247	31	via	via	ADP
ejpam-6705	247	32	(	(	PUNCT
ejpam-6705	247	33	κ	κ	NOUN
ejpam-6705	247	34	,	,	PUNCT
ejpam-6705	247	35	θ	θ	NOUN
ejpam-6705	247	36	)	)	PUNCT
ejpam-6705	247	37	,	,	PUNCT
ejpam-6705	247	38	where	where	SCONJ
ejpam-6705	247	39	θ	θ	NOUN
ejpam-6705	247	40	:	:	PUNCT
ejpam-6705	247	41	x	x	X
ejpam-6705	247	42	→	→	X
ejpam-6705	247	43	(	(	PUNCT
ejpam-6705	247	44	−∞	−∞	NOUN
ejpam-6705	247	45	,	,	PUNCT
ejpam-6705	247	46	0	0	NUM
ejpam-6705	247	47	]	]	PUNCT
ejpam-6705	247	48	is	be	AUX
ejpam-6705	247	49	bounded	bound	VERB
ejpam-6705	247	50	above	above	ADV
ejpam-6705	247	51	,	,	PUNCT
ejpam-6705	247	52	and	and	CCONJ
ejpam-6705	247	53	let	let	VERB
ejpam-6705	247	54	t	t	NOUN
ejpam-6705	247	55	:	:	PUNCT
ejpam-6705	247	56	x	x	X
ejpam-6705	247	57	→	→	X
ejpam-6705	247	58	2x	2x	NUM
ejpam-6705	247	59	be	be	AUX
ejpam-6705	247	60	a	a	DET
ejpam-6705	247	61	multivalued	multivalue	VERB
ejpam-6705	247	62	mapping	mapping	NOUN
ejpam-6705	247	63	so	so	SCONJ
ejpam-6705	247	64	that	that	SCONJ
ejpam-6705	247	65	:	:	PUNCT
ejpam-6705	247	66	(	(	PUNCT
ejpam-6705	247	67	i	i	NOUN
ejpam-6705	247	68	)	)	PUNCT
ejpam-6705	247	69	t	t	PROPN
ejpam-6705	247	70	is	be	AUX
ejpam-6705	247	71	upper	upper	ADJ
ejpam-6705	247	72	semi	semi	ADJ
ejpam-6705	247	73	-	-	ADJ
ejpam-6705	247	74	continuous	continuous	ADJ
ejpam-6705	247	75	.	.	PUNCT
ejpam-6705	248	1	(	(	PUNCT
ejpam-6705	248	2	ii	ii	NOUN
ejpam-6705	248	3	)	)	PUNCT
ejpam-6705	248	4	for	for	ADP
ejpam-6705	248	5	all	all	DET
ejpam-6705	248	6	u	u	NOUN
ejpam-6705	248	7	,	,	PUNCT
ejpam-6705	248	8	v	v	NOUN
ejpam-6705	248	9	∈	∈	NOUN
ejpam-6705	248	10	x	x	X
ejpam-6705	248	11	and	and	CCONJ
ejpam-6705	248	12	u	u	X
ejpam-6705	248	13	≽	≽	PROPN
ejpam-6705	248	14	v	v	NOUN
ejpam-6705	248	15	and	and	CCONJ
ejpam-6705	248	16	every	every	DET
ejpam-6705	248	17	α	α	PROPN
ejpam-6705	248	18	∈	∈	PROPN
ejpam-6705	248	19	t	t	PROPN
ejpam-6705	248	20	(	(	PUNCT
ejpam-6705	248	21	u	u	NOUN
ejpam-6705	248	22	)	)	PUNCT
ejpam-6705	248	23	,	,	PUNCT
ejpam-6705	248	24	there	there	PRON
ejpam-6705	248	25	exists	exist	VERB
ejpam-6705	248	26	β	β	PROPN
ejpam-6705	248	27	∈	∈	PROPN
ejpam-6705	248	28	t	t	PROPN
ejpam-6705	248	29	(	(	PUNCT
ejpam-6705	248	30	v	v	NOUN
ejpam-6705	248	31	)	)	PUNCT
ejpam-6705	248	32	such	such	ADJ
ejpam-6705	248	33	that	that	SCONJ
ejpam-6705	248	34	α	α	PROPN
ejpam-6705	248	35	≽	≽	PROPN
ejpam-6705	248	36	β	β	X
ejpam-6705	248	37	.	.	PUNCT
ejpam-6705	249	1	s.	s.	PROPN
ejpam-6705	249	2	batul	batul	PROPN
ejpam-6705	249	3	et	et	PROPN
ejpam-6705	249	4	al	al	PROPN
ejpam-6705	249	5	.	.	PUNCT
ejpam-6705	249	6	/	/	SYM
ejpam-6705	249	7	eur	eur	PROPN
ejpam-6705	249	8	.	.	PUNCT
ejpam-6705	250	1	j.	j.	PROPN
ejpam-6705	250	2	pure	pure	PROPN
ejpam-6705	250	3	appl	appl	PROPN
ejpam-6705	250	4	.	.	PROPN
ejpam-6705	250	5	math	math	PROPN
ejpam-6705	250	6	,	,	PUNCT
ejpam-6705	250	7	18	18	NUM
ejpam-6705	250	8	(	(	PUNCT
ejpam-6705	250	9	4	4	NUM
ejpam-6705	250	10	)	)	PUNCT
ejpam-6705	250	11	(	(	PUNCT
ejpam-6705	250	12	2025	2025	NUM
ejpam-6705	250	13	)	)	PUNCT
ejpam-6705	250	14	,	,	PUNCT
ejpam-6705	250	15	6705	6705	NUM
ejpam-6705	250	16	10	10	NUM
ejpam-6705	250	17	of	of	ADP
ejpam-6705	250	18	23	23	NUM
ejpam-6705	250	19	(	(	PUNCT
ejpam-6705	250	20	iii	iii	NOUN
ejpam-6705	250	21	)	)	PUNCT
ejpam-6705	250	22	there	there	PRON
ejpam-6705	250	23	is	be	VERB
ejpam-6705	250	24	m	m	PROPN
ejpam-6705	250	25	∈	∈	ADJ
ejpam-6705	250	26	x	x	PUNCT
ejpam-6705	250	27	such	such	ADJ
ejpam-6705	250	28	that	that	SCONJ
ejpam-6705	250	29	t	t	PROPN
ejpam-6705	250	30	(	(	PUNCT
ejpam-6705	250	31	m	m	NOUN
ejpam-6705	250	32	)	)	PUNCT
ejpam-6705	250	33	∩	∩	NOUN
ejpam-6705	250	34	[	[	X
ejpam-6705	250	35	0,∞	0,∞	NOUN
ejpam-6705	250	36	)	)	PUNCT
ejpam-6705	250	37	̸=	̸=	PROPN
ejpam-6705	250	38	∅.	∅.	ADV
ejpam-6705	250	39	then	then	ADV
ejpam-6705	250	40	there	there	PRON
ejpam-6705	250	41	exists	exist	VERB
ejpam-6705	250	42	a	a	DET
ejpam-6705	250	43	sequence	sequence	NOUN
ejpam-6705	250	44	(	(	PUNCT
ejpam-6705	250	45	us	us	PROPN
ejpam-6705	250	46	)	)	PUNCT
ejpam-6705	250	47	∈	∈	PROPN
ejpam-6705	250	48	x	x	PUNCT
ejpam-6705	250	49	with	with	ADP
ejpam-6705	250	50	us−1	us−1	NOUN
ejpam-6705	250	51	≽	≽	PROPN
ejpam-6705	250	52	us	us	PROPN
ejpam-6705	250	53	∈	∈	PROPN
ejpam-6705	250	54	t	t	PROPN
ejpam-6705	250	55	(	(	PUNCT
ejpam-6705	250	56	us−1	us−1	PROPN
ejpam-6705	250	57	)	)	PUNCT
ejpam-6705	250	58	∀	∀	PUNCT
ejpam-6705	250	59	s	s	NOUN
ejpam-6705	250	60	∈	∈	PROPN
ejpam-6705	250	61	n	n	CCONJ
ejpam-6705	250	62	,	,	PUNCT
ejpam-6705	250	63	and	and	CCONJ
ejpam-6705	250	64	t	t	PROPN
ejpam-6705	250	65	has	have	VERB
ejpam-6705	250	66	a	a	DET
ejpam-6705	250	67	fixed	fix	VERB
ejpam-6705	250	68	point	point	NOUN
ejpam-6705	250	69	u0	u0	ADJ
ejpam-6705	250	70	such	such	ADJ
ejpam-6705	250	71	that	that	SCONJ
ejpam-6705	250	72	us	we	PRON
ejpam-6705	250	73	→	→	SYM
ejpam-6705	250	74	u0	u0	PROPN
ejpam-6705	250	75	.	.	PUNCT
ejpam-6705	251	1	furthermore	furthermore	ADV
ejpam-6705	251	2	,	,	PUNCT
ejpam-6705	251	3	if	if	SCONJ
ejpam-6705	251	4	θ	θ	PROPN
ejpam-6705	251	5	is	be	AUX
ejpam-6705	251	6	lower	low	ADJ
ejpam-6705	251	7	semi	semi	ADJ
ejpam-6705	251	8	-	-	ADJ
ejpam-6705	251	9	continuous	continuous	ADJ
ejpam-6705	251	10	,	,	PUNCT
ejpam-6705	251	11	then	then	ADV
ejpam-6705	251	12	us	us	PROPN
ejpam-6705	251	13	≽	≽	PROPN
ejpam-6705	251	14	u0	u0	ADJ
ejpam-6705	251	15	for	for	ADP
ejpam-6705	251	16	all	all	DET
ejpam-6705	251	17	s.	s.	PROPN
ejpam-6705	251	18	corollary	corollary	NOUN
ejpam-6705	251	19	4	4	NUM
ejpam-6705	251	20	.	.	PUNCT
ejpam-6705	252	1	assume	assume	VERB
ejpam-6705	252	2	that	that	SCONJ
ejpam-6705	252	3	(	(	PUNCT
ejpam-6705	252	4	x	x	X
ejpam-6705	252	5	,	,	PUNCT
ejpam-6705	252	6	gb,≼	gb,≼	NOUN
ejpam-6705	252	7	)	)	PUNCT
ejpam-6705	252	8	is	be	AUX
ejpam-6705	252	9	a	a	DET
ejpam-6705	252	10	partially	partially	ADV
ejpam-6705	252	11	ordered	order	VERB
ejpam-6705	252	12	complete	complete	ADJ
ejpam-6705	252	13	gb	gb	ADV
ejpam-6705	252	14	-	-	PUNCT
ejpam-6705	252	15	metric	metric	ADJ
ejpam-6705	252	16	space	space	NOUN
ejpam-6705	252	17	induced	induce	VERB
ejpam-6705	252	18	via	via	ADP
ejpam-6705	252	19	(	(	PUNCT
ejpam-6705	252	20	κ	κ	NOUN
ejpam-6705	252	21	,	,	PUNCT
ejpam-6705	252	22	θ	θ	NOUN
ejpam-6705	252	23	)	)	PUNCT
ejpam-6705	252	24	such	such	ADJ
ejpam-6705	252	25	that	that	SCONJ
ejpam-6705	252	26	θ	θ	NOUN
ejpam-6705	252	27	:	:	PUNCT
ejpam-6705	252	28	x	x	X
ejpam-6705	252	29	→	→	X
ejpam-6705	252	30	(	(	PUNCT
ejpam-6705	252	31	−∞	−∞	NOUN
ejpam-6705	252	32	,	,	PUNCT
ejpam-6705	252	33	0	0	NUM
ejpam-6705	252	34	]	]	PUNCT
ejpam-6705	252	35	is	be	AUX
ejpam-6705	252	36	bounded	bound	VERB
ejpam-6705	252	37	above	above	ADV
ejpam-6705	252	38	,	,	PUNCT
ejpam-6705	252	39	and	and	CCONJ
ejpam-6705	252	40	let	let	VERB
ejpam-6705	252	41	s	s	PRON
ejpam-6705	252	42	:	:	PUNCT
ejpam-6705	252	43	x	x	SYM
ejpam-6705	252	44	→	→	PUNCT
ejpam-6705	252	45	x	x	PUNCT
ejpam-6705	252	46	satisfy	satisfy	VERB
ejpam-6705	252	47	the	the	DET
ejpam-6705	252	48	following	following	NOUN
ejpam-6705	252	49	:	:	PUNCT
ejpam-6705	252	50	(	(	PUNCT
ejpam-6705	252	51	i	i	NOUN
ejpam-6705	252	52	)	)	PUNCT
ejpam-6705	252	53	s	s	AUX
ejpam-6705	252	54	is	be	AUX
ejpam-6705	252	55	continuous	continuous	ADJ
ejpam-6705	252	56	.	.	PUNCT
ejpam-6705	253	1	(	(	PUNCT
ejpam-6705	253	2	ii	ii	NOUN
ejpam-6705	253	3	)	)	PUNCT
ejpam-6705	253	4	for	for	ADP
ejpam-6705	253	5	any	any	DET
ejpam-6705	253	6	α	α	NOUN
ejpam-6705	253	7	∈	∈	NOUN
ejpam-6705	253	8	s	s	PART
ejpam-6705	253	9	(	(	PUNCT
ejpam-6705	253	10	u	u	NOUN
ejpam-6705	253	11	)	)	PUNCT
ejpam-6705	253	12	,	,	PUNCT
ejpam-6705	253	13	there	there	PRON
ejpam-6705	253	14	exists	exist	VERB
ejpam-6705	253	15	β	β	X
ejpam-6705	253	16	∈	∈	PROPN
ejpam-6705	253	17	s	s	X
ejpam-6705	253	18	(	(	PUNCT
ejpam-6705	253	19	v	v	NOUN
ejpam-6705	253	20	)	)	PUNCT
ejpam-6705	253	21	such	such	ADJ
ejpam-6705	253	22	that	that	SCONJ
ejpam-6705	253	23	α	α	PROPN
ejpam-6705	253	24	≽	≽	PROPN
ejpam-6705	253	25	β	β	X
ejpam-6705	253	26	.	.	PUNCT
ejpam-6705	254	1	(	(	PUNCT
ejpam-6705	254	2	iii	iii	X
ejpam-6705	254	3	)	)	PUNCT
ejpam-6705	254	4	there	there	PRON
ejpam-6705	254	5	is	be	VERB
ejpam-6705	254	6	m	m	PROPN
ejpam-6705	254	7	∈	∈	ADJ
ejpam-6705	254	8	x	x	PUNCT
ejpam-6705	254	9	such	such	ADJ
ejpam-6705	254	10	that	that	SCONJ
ejpam-6705	254	11	m	m	VERB
ejpam-6705	254	12	≽	≽	NOUN
ejpam-6705	254	13	s	s	X
ejpam-6705	254	14	(	(	PUNCT
ejpam-6705	254	15	m	m	NOUN
ejpam-6705	254	16	)	)	PUNCT
ejpam-6705	254	17	.	.	PUNCT
ejpam-6705	255	1	then	then	ADV
ejpam-6705	255	2	there	there	PRON
ejpam-6705	255	3	is	be	VERB
ejpam-6705	255	4	a	a	DET
ejpam-6705	255	5	sequence	sequence	NOUN
ejpam-6705	255	6	(	(	PUNCT
ejpam-6705	255	7	us	us	PROPN
ejpam-6705	255	8	)	)	PUNCT
ejpam-6705	255	9	∈	∈	PROPN
ejpam-6705	255	10	x	x	PUNCT
ejpam-6705	255	11	with	with	ADP
ejpam-6705	255	12	us−1	us−1	NOUN
ejpam-6705	255	13	≽	≽	PROPN
ejpam-6705	255	14	us	us	PROPN
ejpam-6705	255	15	∈	∈	PROPN
ejpam-6705	255	16	s	s	X
ejpam-6705	255	17	(	(	PUNCT
ejpam-6705	255	18	us−1	us−1	PROPN
ejpam-6705	255	19	)	)	PUNCT
ejpam-6705	255	20	for	for	ADP
ejpam-6705	255	21	all	all	DET
ejpam-6705	255	22	s	s	PROPN
ejpam-6705	255	23	∈	∈	NOUN
ejpam-6705	255	24	n	n	CCONJ
ejpam-6705	255	25	,	,	PUNCT
ejpam-6705	255	26	and	and	CCONJ
ejpam-6705	255	27	t	t	PROPN
ejpam-6705	255	28	has	have	VERB
ejpam-6705	255	29	a	a	DET
ejpam-6705	255	30	fixed	fix	VERB
ejpam-6705	255	31	point	point	NOUN
ejpam-6705	255	32	u0	u0	ADJ
ejpam-6705	255	33	such	such	ADJ
ejpam-6705	255	34	that	that	SCONJ
ejpam-6705	255	35	us	we	PRON
ejpam-6705	255	36	→	→	SYM
ejpam-6705	255	37	u0	u0	PROPN
ejpam-6705	255	38	.	.	PUNCT
ejpam-6705	256	1	also	also	ADV
ejpam-6705	256	2	,	,	PUNCT
ejpam-6705	256	3	if	if	SCONJ
ejpam-6705	256	4	θ	θ	PROPN
ejpam-6705	256	5	is	be	AUX
ejpam-6705	256	6	lower	low	ADJ
ejpam-6705	256	7	semi	semi	ADJ
ejpam-6705	256	8	-	-	ADJ
ejpam-6705	256	9	continuous	continuous	ADJ
ejpam-6705	256	10	,	,	PUNCT
ejpam-6705	256	11	then	then	ADV
ejpam-6705	256	12	us	us	PROPN
ejpam-6705	256	13	≽	≽	PROPN
ejpam-6705	256	14	u0	u0	ADJ
ejpam-6705	256	15	for	for	ADP
ejpam-6705	256	16	all	all	DET
ejpam-6705	256	17	s.	s.	PROPN
ejpam-6705	256	18	4	4	NUM
ejpam-6705	256	19	.	.	PUNCT
ejpam-6705	256	20	coupled	couple	VERB
ejpam-6705	256	21	fixed	fix	VERB
ejpam-6705	256	22	point	point	NOUN
ejpam-6705	256	23	theorems	theorem	NOUN
ejpam-6705	256	24	in	in	ADP
ejpam-6705	256	25	gb	gb	ADV
ejpam-6705	256	26	-	-	PUNCT
ejpam-6705	256	27	metric	metric	ADJ
ejpam-6705	256	28	spaces	space	NOUN
ejpam-6705	256	29	theorem	theorem	VERB
ejpam-6705	256	30	3	3	X
ejpam-6705	256	31	.	.	PUNCT
ejpam-6705	256	32	assume	assume	VERB
ejpam-6705	256	33	that	that	SCONJ
ejpam-6705	256	34	(	(	PUNCT
ejpam-6705	256	35	x	x	X
ejpam-6705	256	36	,	,	PUNCT
ejpam-6705	256	37	gb,≼	gb,≼	NOUN
ejpam-6705	256	38	)	)	PUNCT
ejpam-6705	256	39	is	be	AUX
ejpam-6705	256	40	a	a	DET
ejpam-6705	256	41	partially	partially	ADV
ejpam-6705	256	42	ordered	order	VERB
ejpam-6705	256	43	complete	complete	ADJ
ejpam-6705	256	44	gb	gb	ADV
ejpam-6705	256	45	-	-	PUNCT
ejpam-6705	256	46	metric	metric	ADJ
ejpam-6705	256	47	space	space	NOUN
ejpam-6705	256	48	,	,	PUNCT
ejpam-6705	256	49	and	and	CCONJ
ejpam-6705	256	50	let	let	VERB
ejpam-6705	256	51	t	t	NOUN
ejpam-6705	256	52	:	:	PUNCT
ejpam-6705	256	53	x	x	PUNCT
ejpam-6705	256	54	×	×	NOUN
ejpam-6705	256	55	x	x	INTJ
ejpam-6705	256	56	→	→	PUNCT
ejpam-6705	256	57	x	x	PUNCT
ejpam-6705	256	58	be	be	AUX
ejpam-6705	256	59	a	a	DET
ejpam-6705	256	60	continuous	continuous	ADJ
ejpam-6705	256	61	mapping	mapping	NOUN
ejpam-6705	256	62	with	with	ADP
ejpam-6705	256	63	the	the	DET
ejpam-6705	256	64	mixed	mixed	ADJ
ejpam-6705	256	65	monotone	monotone	ADJ
ejpam-6705	256	66	property	property	NOUN
ejpam-6705	256	67	on	on	ADP
ejpam-6705	256	68	x	x	SYM
ejpam-6705	256	69	such	such	ADJ
ejpam-6705	256	70	that	that	DET
ejpam-6705	256	71	∫	∫	PROPN
ejpam-6705	256	72	gb(t	gb(t	X
ejpam-6705	256	73	(	(	PUNCT
ejpam-6705	256	74	u	u	NOUN
ejpam-6705	256	75	,	,	PUNCT
ejpam-6705	256	76	v),t	v),t	PROPN
ejpam-6705	256	77	(	(	PUNCT
ejpam-6705	256	78	m	m	PROPN
ejpam-6705	256	79	,	,	PUNCT
ejpam-6705	256	80	n),t	n),t	PROPN
ejpam-6705	256	81	(	(	PUNCT
ejpam-6705	256	82	f	f	X
ejpam-6705	256	83	,	,	PUNCT
ejpam-6705	256	84	w	w	NOUN
ejpam-6705	256	85	)	)	PUNCT
ejpam-6705	256	86	)	)	PUNCT
ejpam-6705	256	87	0	0	NUM
ejpam-6705	257	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	257	2	≤	≤	PROPN
ejpam-6705	257	3	σ	σ	PROPN
ejpam-6705	257	4	(	(	PUNCT
ejpam-6705	257	5	∫	∫	PROPN
ejpam-6705	257	6	gb(u	gb(u	PROPN
ejpam-6705	257	7	,	,	PUNCT
ejpam-6705	257	8	m	m	NOUN
ejpam-6705	257	9	,	,	PUNCT
ejpam-6705	257	10	f)+gb(v	f)+gb(v	NOUN
ejpam-6705	257	11	,	,	PUNCT
ejpam-6705	257	12	n	n	CCONJ
ejpam-6705	257	13	,	,	PUNCT
ejpam-6705	257	14	w	w	NOUN
ejpam-6705	257	15	)	)	PUNCT
ejpam-6705	257	16	0	0	NUM
ejpam-6705	257	17	g(t)dt	g(t)dt	PROPN
ejpam-6705	257	18	)	)	PUNCT
ejpam-6705	257	19	,	,	PUNCT
ejpam-6705	257	20	(	(	PUNCT
ejpam-6705	257	21	4	4	X
ejpam-6705	257	22	)	)	PUNCT
ejpam-6705	257	23	where	where	SCONJ
ejpam-6705	257	24	u	u	NOUN
ejpam-6705	257	25	,	,	PUNCT
ejpam-6705	257	26	v	v	NOUN
ejpam-6705	257	27	,	,	PUNCT
ejpam-6705	257	28	w	w	PROPN
ejpam-6705	257	29	,	,	PUNCT
ejpam-6705	257	30	m	m	PROPN
ejpam-6705	257	31	,	,	PUNCT
ejpam-6705	257	32	n	n	CCONJ
ejpam-6705	257	33	,	,	PUNCT
ejpam-6705	257	34	f	f	PROPN
ejpam-6705	257	35	∈	∈	PROPN
ejpam-6705	257	36	x	x	X
ejpam-6705	257	37	and	and	CCONJ
ejpam-6705	257	38	g	g	NOUN
ejpam-6705	257	39	:	:	PUNCT
ejpam-6705	258	1	[	[	X
ejpam-6705	258	2	0,∞	0,∞	NOUN
ejpam-6705	258	3	)	)	PUNCT
ejpam-6705	258	4	→	→	PUNCT
ejpam-6705	259	1	[	[	X
ejpam-6705	259	2	0,∞	0,∞	NUM
ejpam-6705	259	3	)	)	PUNCT
ejpam-6705	259	4	is	be	AUX
ejpam-6705	259	5	a	a	DET
ejpam-6705	259	6	lebesgue	lebesgue	NOUN
ejpam-6705	259	7	integrable	integrable	ADJ
ejpam-6705	259	8	mapping	mapping	NOUN
ejpam-6705	259	9	with	with	ADP
ejpam-6705	259	10	f	f	PROPN
ejpam-6705	259	11	≼	≼	PROPN
ejpam-6705	259	12	m	m	VERB
ejpam-6705	259	13	≼	≼	ADJ
ejpam-6705	259	14	u	u	NOUN
ejpam-6705	259	15	and	and	CCONJ
ejpam-6705	259	16	v	v	ADP
ejpam-6705	259	17	≼	≼	NOUN
ejpam-6705	259	18	n	n	PROPN
ejpam-6705	259	19	≼	≼	PROPN
ejpam-6705	259	20	w	w	PROPN
ejpam-6705	259	21	,	,	PUNCT
ejpam-6705	259	22	where	where	SCONJ
ejpam-6705	259	23	either	either	CCONJ
ejpam-6705	259	24	m	m	VERB
ejpam-6705	259	25	̸=	̸=	PROPN
ejpam-6705	259	26	f	f	PROPN
ejpam-6705	259	27	or	or	CCONJ
ejpam-6705	259	28	n	n	PRON
ejpam-6705	259	29	̸=	̸=	PROPN
ejpam-6705	259	30	w.	w.	NOUN
ejpam-6705	259	31	if	if	SCONJ
ejpam-6705	259	32	there	there	PRON
ejpam-6705	259	33	exist	exist	VERB
ejpam-6705	259	34	u0	u0	ADJ
ejpam-6705	259	35	,	,	PUNCT
ejpam-6705	259	36	v0	v0	NOUN
ejpam-6705	259	37	∈	∈	PROPN
ejpam-6705	259	38	x	x	PUNCT
ejpam-6705	259	39	such	such	ADJ
ejpam-6705	259	40	that	that	DET
ejpam-6705	259	41	u0	u0	ADJ
ejpam-6705	259	42	≼	≼	PROPN
ejpam-6705	259	43	t	t	PROPN
ejpam-6705	259	44	(	(	PUNCT
ejpam-6705	259	45	u0	u0	PROPN
ejpam-6705	259	46	,	,	PUNCT
ejpam-6705	259	47	v0	v0	PROPN
ejpam-6705	259	48	)	)	PUNCT
ejpam-6705	259	49	and	and	CCONJ
ejpam-6705	259	50	t	t	PROPN
ejpam-6705	259	51	(	(	PUNCT
ejpam-6705	259	52	v0	v0	PROPN
ejpam-6705	259	53	,	,	PUNCT
ejpam-6705	259	54	u0	u0	ADJ
ejpam-6705	259	55	)	)	PUNCT
ejpam-6705	259	56	≼	≼	ADJ
ejpam-6705	259	57	v0	v0	NOUN
ejpam-6705	259	58	,	,	PUNCT
ejpam-6705	259	59	then	then	ADV
ejpam-6705	259	60	t	t	PROPN
ejpam-6705	259	61	has	have	VERB
ejpam-6705	259	62	a	a	DET
ejpam-6705	259	63	coupled	couple	VERB
ejpam-6705	259	64	fixed	fix	VERB
ejpam-6705	259	65	point	point	NOUN
ejpam-6705	259	66	in	in	ADP
ejpam-6705	259	67	x	x	X
ejpam-6705	259	68	.	.	PUNCT
ejpam-6705	260	1	proof	proof	NOUN
ejpam-6705	260	2	.	.	PUNCT
ejpam-6705	261	1	by	by	ADP
ejpam-6705	261	2	hypothesis	hypothesis	NOUN
ejpam-6705	261	3	,	,	PUNCT
ejpam-6705	261	4	there	there	PRON
ejpam-6705	261	5	are	be	VERB
ejpam-6705	261	6	u0	u0	ADJ
ejpam-6705	261	7	,	,	PUNCT
ejpam-6705	261	8	v0	v0	NOUN
ejpam-6705	261	9	∈	∈	PROPN
ejpam-6705	261	10	x	x	PUNCT
ejpam-6705	261	11	such	such	ADJ
ejpam-6705	261	12	that	that	DET
ejpam-6705	261	13	u0	u0	ADJ
ejpam-6705	261	14	≼	≼	PROPN
ejpam-6705	261	15	t	t	PROPN
ejpam-6705	261	16	(	(	PUNCT
ejpam-6705	261	17	u0	u0	PROPN
ejpam-6705	261	18	,	,	PUNCT
ejpam-6705	261	19	v0	v0	PROPN
ejpam-6705	261	20	)	)	PUNCT
ejpam-6705	261	21	and	and	CCONJ
ejpam-6705	261	22	t	t	PROPN
ejpam-6705	261	23	(	(	PUNCT
ejpam-6705	261	24	v0	v0	PROPN
ejpam-6705	261	25	,	,	PUNCT
ejpam-6705	261	26	u0	u0	ADJ
ejpam-6705	261	27	)	)	PUNCT
ejpam-6705	261	28	≼	≼	PROPN
ejpam-6705	261	29	v0	v0	PROPN
ejpam-6705	261	30	.	.	PUNCT
ejpam-6705	262	1	define	define	PROPN
ejpam-6705	262	2	u1	u1	NOUN
ejpam-6705	262	3	,	,	PUNCT
ejpam-6705	262	4	v1	v1	NOUN
ejpam-6705	262	5	∈	∈	NOUN
ejpam-6705	262	6	x	x	PUNCT
ejpam-6705	262	7	as	as	ADP
ejpam-6705	262	8	u0	u0	ADJ
ejpam-6705	262	9	≼	≼	PROPN
ejpam-6705	262	10	t	t	PROPN
ejpam-6705	262	11	(	(	PUNCT
ejpam-6705	262	12	u0	u0	PROPN
ejpam-6705	262	13	,	,	PUNCT
ejpam-6705	262	14	v0	v0	NOUN
ejpam-6705	262	15	)	)	PUNCT
ejpam-6705	262	16	=	=	SYM
ejpam-6705	262	17	u1	u1	NOUN
ejpam-6705	262	18	and	and	CCONJ
ejpam-6705	262	19	v1	v1	PROPN
ejpam-6705	262	20	=	=	SYM
ejpam-6705	262	21	t	t	PROPN
ejpam-6705	262	22	(	(	PUNCT
ejpam-6705	262	23	v0	v0	PROPN
ejpam-6705	262	24	,	,	PUNCT
ejpam-6705	262	25	u0	u0	ADJ
ejpam-6705	262	26	)	)	PUNCT
ejpam-6705	262	27	≼	≼	PROPN
ejpam-6705	262	28	v0	v0	PROPN
ejpam-6705	262	29	.	.	PUNCT
ejpam-6705	262	30	suppose	suppose	VERB
ejpam-6705	262	31	that	that	SCONJ
ejpam-6705	262	32	u2	u2	PROPN
ejpam-6705	262	33	=	=	PROPN
ejpam-6705	262	34	t	t	PROPN
ejpam-6705	262	35	(	(	PUNCT
ejpam-6705	262	36	u1	u1	NOUN
ejpam-6705	262	37	,	,	PUNCT
ejpam-6705	262	38	v1	v1	NOUN
ejpam-6705	262	39	)	)	PUNCT
ejpam-6705	262	40	and	and	CCONJ
ejpam-6705	262	41	v2	v2	PROPN
ejpam-6705	262	42	=	=	SYM
ejpam-6705	262	43	t	t	PROPN
ejpam-6705	262	44	(	(	PUNCT
ejpam-6705	262	45	v1	v1	PROPN
ejpam-6705	262	46	,	,	PUNCT
ejpam-6705	262	47	u1	u1	NOUN
ejpam-6705	262	48	)	)	PUNCT
ejpam-6705	262	49	,	,	PUNCT
ejpam-6705	262	50	therefore	therefore	ADV
ejpam-6705	262	51	u2	u2	PROPN
ejpam-6705	262	52	=	=	PROPN
ejpam-6705	262	53	t	t	PROPN
ejpam-6705	262	54	(	(	PUNCT
ejpam-6705	262	55	u1	u1	NOUN
ejpam-6705	262	56	,	,	PUNCT
ejpam-6705	262	57	v1	v1	NOUN
ejpam-6705	262	58	)	)	PUNCT
ejpam-6705	262	59	=	=	SYM
ejpam-6705	262	60	t	t	PROPN
ejpam-6705	262	61	(	(	PUNCT
ejpam-6705	262	62	t	t	PROPN
ejpam-6705	262	63	(	(	PUNCT
ejpam-6705	262	64	u0	u0	PROPN
ejpam-6705	262	65	,	,	PUNCT
ejpam-6705	262	66	v0),t	v0),t	X
ejpam-6705	262	67	(	(	PUNCT
ejpam-6705	262	68	v0	v0	NOUN
ejpam-6705	262	69	,	,	PUNCT
ejpam-6705	262	70	u0	u0	ADJ
ejpam-6705	262	71	)	)	PUNCT
ejpam-6705	262	72	)	)	PUNCT
ejpam-6705	263	1	=	=	SYM
ejpam-6705	263	2	t	t	PROPN
ejpam-6705	263	3	2(u0	2(u0	NUM
ejpam-6705	263	4	,	,	PUNCT
ejpam-6705	263	5	v0	v0	PROPN
ejpam-6705	263	6	)	)	PUNCT
ejpam-6705	263	7	.	.	PUNCT
ejpam-6705	264	1	v2	v2	PROPN
ejpam-6705	264	2	=	=	SYM
ejpam-6705	264	3	t	t	PROPN
ejpam-6705	264	4	(	(	PUNCT
ejpam-6705	264	5	v1	v1	PROPN
ejpam-6705	264	6	,	,	PUNCT
ejpam-6705	264	7	u1	u1	NOUN
ejpam-6705	264	8	)	)	PUNCT
ejpam-6705	264	9	=	=	SYM
ejpam-6705	264	10	t	t	PROPN
ejpam-6705	264	11	(	(	PUNCT
ejpam-6705	264	12	t	t	PROPN
ejpam-6705	264	13	(	(	PUNCT
ejpam-6705	264	14	v0	v0	PROPN
ejpam-6705	264	15	,	,	PUNCT
ejpam-6705	264	16	u0),t	u0),t	X
ejpam-6705	264	17	(	(	PUNCT
ejpam-6705	264	18	u0	u0	PROPN
ejpam-6705	264	19	,	,	PUNCT
ejpam-6705	264	20	v0	v0	NOUN
ejpam-6705	264	21	)	)	PUNCT
ejpam-6705	264	22	)	)	PUNCT
ejpam-6705	265	1	=	=	SYM
ejpam-6705	265	2	t	t	PROPN
ejpam-6705	265	3	2(v0	2(v0	NUM
ejpam-6705	265	4	,	,	PUNCT
ejpam-6705	265	5	u0	u0	PROPN
ejpam-6705	265	6	)	)	PUNCT
ejpam-6705	265	7	.	.	PUNCT
ejpam-6705	266	1	utilizing	utilize	VERB
ejpam-6705	266	2	the	the	DET
ejpam-6705	266	3	mixed	mixed	ADJ
ejpam-6705	266	4	monotonicity	monotonicity	NOUN
ejpam-6705	266	5	for	for	ADP
ejpam-6705	266	6	the	the	DET
ejpam-6705	266	7	mapping	mapping	NOUN
ejpam-6705	266	8	t	t	NOUN
ejpam-6705	266	9	,	,	PUNCT
ejpam-6705	266	10	one	one	PRON
ejpam-6705	266	11	writes	write	VERB
ejpam-6705	266	12	u2	u2	PROPN
ejpam-6705	266	13	=	=	PROPN
ejpam-6705	266	14	t	t	PROPN
ejpam-6705	266	15	2(u0	2(u0	NUM
ejpam-6705	266	16	,	,	PUNCT
ejpam-6705	266	17	v0	v0	NOUN
ejpam-6705	266	18	)	)	PUNCT
ejpam-6705	266	19	=	=	SYM
ejpam-6705	266	20	t	t	PROPN
ejpam-6705	266	21	(	(	PUNCT
ejpam-6705	266	22	u1	u1	NOUN
ejpam-6705	266	23	,	,	PUNCT
ejpam-6705	266	24	v1	v1	NOUN
ejpam-6705	266	25	)	)	PUNCT
ejpam-6705	266	26	≽	≽	PROPN
ejpam-6705	266	27	t	t	PROPN
ejpam-6705	266	28	(	(	PUNCT
ejpam-6705	266	29	u0	u0	PROPN
ejpam-6705	266	30	,	,	PUNCT
ejpam-6705	266	31	v0	v0	NOUN
ejpam-6705	266	32	)	)	PUNCT
ejpam-6705	266	33	=	=	SYM
ejpam-6705	266	34	u1	u1	PROPN
ejpam-6705	266	35	≽	≽	PROPN
ejpam-6705	266	36	u0	u0	PROPN
ejpam-6705	266	37	,	,	PUNCT
ejpam-6705	266	38	v2	v2	PROPN
ejpam-6705	266	39	=	=	SYM
ejpam-6705	266	40	t	t	PROPN
ejpam-6705	266	41	2(v0	2(v0	NUM
ejpam-6705	266	42	,	,	PUNCT
ejpam-6705	266	43	u0	u0	ADJ
ejpam-6705	266	44	)	)	PUNCT
ejpam-6705	266	45	=	=	SYM
ejpam-6705	266	46	t	t	PROPN
ejpam-6705	266	47	(	(	PUNCT
ejpam-6705	266	48	v1	v1	NOUN
ejpam-6705	266	49	,	,	PUNCT
ejpam-6705	266	50	u1	u1	NOUN
ejpam-6705	266	51	)	)	PUNCT
ejpam-6705	266	52	≼	≼	PROPN
ejpam-6705	266	53	t	t	PROPN
ejpam-6705	266	54	(	(	PUNCT
ejpam-6705	266	55	v0	v0	PROPN
ejpam-6705	266	56	,	,	PUNCT
ejpam-6705	266	57	u0	u0	ADJ
ejpam-6705	266	58	)	)	PUNCT
ejpam-6705	266	59	=	=	SYM
ejpam-6705	266	60	v1	v1	PROPN
ejpam-6705	266	61	≼	≼	PROPN
ejpam-6705	266	62	v0	v0	NOUN
ejpam-6705	266	63	.	.	PUNCT
ejpam-6705	267	1	repeatedly	repeatedly	ADV
ejpam-6705	267	2	applying	apply	VERB
ejpam-6705	267	3	the	the	DET
ejpam-6705	267	4	above	above	ADJ
ejpam-6705	267	5	process	process	NOUN
ejpam-6705	267	6	for	for	ADP
ejpam-6705	267	7	all	all	PRON
ejpam-6705	267	8	s	s	PART
ejpam-6705	267	9	≥	≥	NOUN
ejpam-6705	267	10	0	0	NUM
ejpam-6705	267	11	leads	lead	VERB
ejpam-6705	267	12	to	to	ADP
ejpam-6705	267	13	s.	s.	PROPN
ejpam-6705	267	14	batul	batul	PROPN
ejpam-6705	267	15	et	et	PROPN
ejpam-6705	267	16	al	al	PROPN
ejpam-6705	267	17	.	.	PUNCT
ejpam-6705	267	18	/	/	SYM
ejpam-6705	267	19	eur	eur	PROPN
ejpam-6705	267	20	.	.	PUNCT
ejpam-6705	268	1	j.	j.	PROPN
ejpam-6705	268	2	pure	pure	PROPN
ejpam-6705	268	3	appl	appl	PROPN
ejpam-6705	268	4	.	.	PROPN
ejpam-6705	268	5	math	math	PROPN
ejpam-6705	268	6	,	,	PUNCT
ejpam-6705	268	7	18	18	NUM
ejpam-6705	268	8	(	(	PUNCT
ejpam-6705	268	9	4	4	NUM
ejpam-6705	268	10	)	)	PUNCT
ejpam-6705	268	11	(	(	PUNCT
ejpam-6705	268	12	2025	2025	NUM
ejpam-6705	268	13	)	)	PUNCT
ejpam-6705	268	14	,	,	PUNCT
ejpam-6705	268	15	6705	6705	NUM
ejpam-6705	268	16	11	11	NUM
ejpam-6705	268	17	of	of	ADP
ejpam-6705	268	18	23	23	NUM
ejpam-6705	268	19	u0	u0	ADJ
ejpam-6705	268	20	≤	≤	NUM
ejpam-6705	268	21	u1	u1	NOUN
ejpam-6705	268	22	≼	≼	PROPN
ejpam-6705	268	23	u2	u2	PROPN
ejpam-6705	269	1	≼	≼	PROPN
ejpam-6705	269	2	...	...	PUNCT
ejpam-6705	270	1	≼	≼	ADV
ejpam-6705	270	2	us+1	us+1	PROPN
ejpam-6705	270	3	≼	≼	ADV
ejpam-6705	270	4	...	...	PUNCT
ejpam-6705	270	5	,	,	PUNCT
ejpam-6705	270	6	v0	v0	PROPN
ejpam-6705	270	7	≽	≽	PROPN
ejpam-6705	270	8	v1	v1	PROPN
ejpam-6705	270	9	≽	≽	PROPN
ejpam-6705	270	10	v2	v2	PROPN
ejpam-6705	270	11	≽	≽	PROPN
ejpam-6705	270	12	...	...	PUNCT
ejpam-6705	271	1	≽	≽	PROPN
ejpam-6705	271	2	vs+1	vs+1	PROPN
ejpam-6705	271	3	≽	≽	PROPN
ejpam-6705	271	4	...	...	PUNCT
ejpam-6705	271	5	such	such	ADJ
ejpam-6705	271	6	that	that	SCONJ
ejpam-6705	271	7	us+1	us+1	PROPN
ejpam-6705	271	8	=	=	SYM
ejpam-6705	271	9	t	t	PROPN
ejpam-6705	271	10	s+1(u0	s+1(u0	PROPN
ejpam-6705	271	11	,	,	PUNCT
ejpam-6705	271	12	v0	v0	PROPN
ejpam-6705	271	13	)	)	PUNCT
ejpam-6705	271	14	=	=	SYM
ejpam-6705	271	15	t	t	PROPN
ejpam-6705	271	16	(	(	PUNCT
ejpam-6705	271	17	t	t	PROPN
ejpam-6705	271	18	s(u0	s(u0	PROPN
ejpam-6705	271	19	,	,	PUNCT
ejpam-6705	271	20	v0),t	v0),t	X
ejpam-6705	271	21	s(v0	s(v0	NOUN
ejpam-6705	271	22	,	,	PUNCT
ejpam-6705	271	23	u0	u0	ADJ
ejpam-6705	271	24	)	)	PUNCT
ejpam-6705	271	25	)	)	PUNCT
ejpam-6705	271	26	,	,	PUNCT
ejpam-6705	271	27	vs+1	vs+1	PROPN
ejpam-6705	271	28	=	=	SYM
ejpam-6705	271	29	t	t	PROPN
ejpam-6705	271	30	s+1(v0	s+1(v0	PROPN
ejpam-6705	271	31	,	,	PUNCT
ejpam-6705	271	32	u0	u0	ADJ
ejpam-6705	271	33	)	)	PUNCT
ejpam-6705	271	34	=	=	SYM
ejpam-6705	271	35	t	t	PROPN
ejpam-6705	271	36	(	(	PUNCT
ejpam-6705	271	37	t	t	PROPN
ejpam-6705	271	38	s(v0	s(v0	NOUN
ejpam-6705	271	39	,	,	PUNCT
ejpam-6705	271	40	u0),t	u0),t	PROPN
ejpam-6705	271	41	s(u0	s(u0	PROPN
ejpam-6705	271	42	,	,	PUNCT
ejpam-6705	271	43	v0	v0	PROPN
ejpam-6705	271	44	)	)	PUNCT
ejpam-6705	271	45	)	)	PUNCT
ejpam-6705	271	46	.	.	PUNCT
ejpam-6705	272	1	if	if	SCONJ
ejpam-6705	272	2	(	(	PUNCT
ejpam-6705	272	3	us+1	us+1	ADJ
ejpam-6705	272	4	,	,	PUNCT
ejpam-6705	272	5	vs+1	vs+1	NOUN
ejpam-6705	272	6	)	)	PUNCT
ejpam-6705	272	7	=	=	SYM
ejpam-6705	272	8	(	(	PUNCT
ejpam-6705	272	9	u0	u0	PROPN
ejpam-6705	272	10	,	,	PUNCT
ejpam-6705	272	11	v0	v0	PROPN
ejpam-6705	272	12	)	)	PUNCT
ejpam-6705	272	13	,	,	PUNCT
ejpam-6705	272	14	then	then	ADV
ejpam-6705	272	15	a	a	DET
ejpam-6705	272	16	coupled	couple	VERB
ejpam-6705	272	17	fixed	fix	VERB
ejpam-6705	272	18	point	point	NOUN
ejpam-6705	272	19	exists	exist	VERB
ejpam-6705	272	20	for	for	ADP
ejpam-6705	272	21	the	the	DET
ejpam-6705	272	22	mapping	mapping	NOUN
ejpam-6705	272	23	t	t	NOUN
ejpam-6705	272	24	.	.	PUNCT
ejpam-6705	273	1	now	now	ADV
ejpam-6705	273	2	,	,	PUNCT
ejpam-6705	273	3	we	we	PRON
ejpam-6705	273	4	assume	assume	VERB
ejpam-6705	273	5	that	that	SCONJ
ejpam-6705	273	6	(	(	PUNCT
ejpam-6705	273	7	us+1	us+1	ADJ
ejpam-6705	273	8	,	,	PUNCT
ejpam-6705	273	9	vs+1	vs+1	NOUN
ejpam-6705	273	10	)	)	PUNCT
ejpam-6705	273	11	̸=	̸=	PROPN
ejpam-6705	273	12	(	(	PUNCT
ejpam-6705	273	13	us	us	PROPN
ejpam-6705	273	14	,	,	PUNCT
ejpam-6705	273	15	vs	vs	ADP
ejpam-6705	273	16	)	)	PUNCT
ejpam-6705	273	17	for	for	ADP
ejpam-6705	273	18	all	all	PRON
ejpam-6705	273	19	s	s	PART
ejpam-6705	273	20	≥	≥	NOUN
ejpam-6705	273	21	0	0	NUM
ejpam-6705	273	22	,	,	PUNCT
ejpam-6705	273	23	that	that	ADV
ejpam-6705	273	24	is	is	ADV
ejpam-6705	273	25	,	,	PUNCT
ejpam-6705	273	26	let	let	VERB
ejpam-6705	273	27	either	either	CCONJ
ejpam-6705	273	28	us+1	us+1	PRON
ejpam-6705	273	29	=	=	SYM
ejpam-6705	273	30	t	t	PROPN
ejpam-6705	273	31	(	(	PUNCT
ejpam-6705	273	32	us	us	PROPN
ejpam-6705	273	33	,	,	PUNCT
ejpam-6705	273	34	vs	vs	ADJ
ejpam-6705	273	35	)	)	PUNCT
ejpam-6705	273	36	̸=	̸=	PROPN
ejpam-6705	273	37	us	we	PRON
ejpam-6705	273	38	or	or	CCONJ
ejpam-6705	273	39	vs+1	vs+1	PRON
ejpam-6705	273	40	=	=	SYM
ejpam-6705	273	41	t	t	PROPN
ejpam-6705	273	42	(	(	PUNCT
ejpam-6705	273	43	v0	v0	PROPN
ejpam-6705	273	44	,	,	PUNCT
ejpam-6705	273	45	u0	u0	ADJ
ejpam-6705	273	46	)	)	PUNCT
ejpam-6705	273	47	̸=	̸=	PROPN
ejpam-6705	273	48	vs.	vs.	X
ejpam-6705	273	49	by	by	ADP
ejpam-6705	273	50	equation	equation	NOUN
ejpam-6705	273	51	(	(	PUNCT
ejpam-6705	273	52	4	4	NUM
ejpam-6705	273	53	)	)	PUNCT
ejpam-6705	273	54	,	,	PUNCT
ejpam-6705	273	55	it	it	PRON
ejpam-6705	273	56	follows	follow	VERB
ejpam-6705	273	57	that∫	that∫	PROPN
ejpam-6705	273	58	gb(us	gb(us	PROPN
ejpam-6705	273	59	,	,	PUNCT
ejpam-6705	273	60	us	we	PRON
ejpam-6705	273	61	,	,	PUNCT
ejpam-6705	273	62	us+1	us+1	PROPN
ejpam-6705	273	63	)	)	PUNCT
ejpam-6705	273	64	0	0	NUM
ejpam-6705	274	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	274	2	=	=	SYM
ejpam-6705	274	3	∫	∫	PROPN
ejpam-6705	274	4	gb(t	gb(t	PROPN
ejpam-6705	274	5	(	(	PUNCT
ejpam-6705	274	6	us−1,vs−1),t	us−1,vs−1),t	PROPN
ejpam-6705	274	7	(	(	PUNCT
ejpam-6705	274	8	us−1,vs−1),t	us−1,vs−1),t	PROPN
ejpam-6705	274	9	(	(	PUNCT
ejpam-6705	274	10	us	us	PROPN
ejpam-6705	274	11	,	,	PUNCT
ejpam-6705	274	12	vs	vs	ADJ
ejpam-6705	274	13	)	)	PUNCT
ejpam-6705	274	14	)	)	PUNCT
ejpam-6705	274	15	0	0	NUM
ejpam-6705	275	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	275	2	≤	≤	PROPN
ejpam-6705	275	3	σ	σ	PROPN
ejpam-6705	275	4	(	(	PUNCT
ejpam-6705	275	5	∫	∫	PROPN
ejpam-6705	275	6	gb(us−1,us−1,us),gb(vs−1,vs−1,vs	gb(us−1,us−1,us),gb(vs−1,vs−1,vs	PROPN
ejpam-6705	275	7	)	)	PUNCT
ejpam-6705	275	8	0	0	NUM
ejpam-6705	276	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	276	2	)	)	PUNCT
ejpam-6705	276	3	.	.	PUNCT
ejpam-6705	277	1	(	(	PUNCT
ejpam-6705	277	2	5	5	X
ejpam-6705	277	3	)	)	PUNCT
ejpam-6705	277	4	in	in	ADP
ejpam-6705	277	5	the	the	DET
ejpam-6705	277	6	same	same	ADJ
ejpam-6705	277	7	way	way	NOUN
ejpam-6705	277	8	,	,	PUNCT
ejpam-6705	277	9	it	it	PRON
ejpam-6705	277	10	can	can	AUX
ejpam-6705	277	11	be	be	AUX
ejpam-6705	277	12	proved	prove	VERB
ejpam-6705	277	13	that∫	that∫	PROPN
ejpam-6705	277	14	gb(vs	gb(vs	PROPN
ejpam-6705	277	15	,	,	PUNCT
ejpam-6705	277	16	vs	vs	ADP
ejpam-6705	277	17	,	,	PUNCT
ejpam-6705	277	18	vs+1	vs+1	NOUN
ejpam-6705	277	19	)	)	PUNCT
ejpam-6705	277	20	0	0	NUM
ejpam-6705	278	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	278	2	=	=	SYM
ejpam-6705	278	3	∫	∫	PROPN
ejpam-6705	278	4	gb(t	gb(t	PROPN
ejpam-6705	278	5	(	(	PUNCT
ejpam-6705	278	6	vs−1,us−1),t	vs−1,us−1),t	X
ejpam-6705	278	7	(	(	PUNCT
ejpam-6705	278	8	vs−1,us−1),t	vs−1,us−1),t	X
ejpam-6705	278	9	(	(	PUNCT
ejpam-6705	278	10	vs	vs	X
ejpam-6705	278	11	,	,	PUNCT
ejpam-6705	278	12	us	we	PRON
ejpam-6705	278	13	)	)	PUNCT
ejpam-6705	278	14	)	)	PUNCT
ejpam-6705	278	15	0	0	NUM
ejpam-6705	279	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	279	2	≤	≤	PROPN
ejpam-6705	279	3	σ	σ	PROPN
ejpam-6705	279	4	(	(	PUNCT
ejpam-6705	279	5	∫	∫	PROPN
ejpam-6705	279	6	gb(us−1,us−1,us),gb(vs−1,vs−1,vs	gb(us−1,us−1,us),gb(vs−1,vs−1,vs	PROPN
ejpam-6705	279	7	)	)	PUNCT
ejpam-6705	279	8	0	0	NUM
ejpam-6705	280	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	280	2	)	)	PUNCT
ejpam-6705	280	3	.	.	PUNCT
ejpam-6705	281	1	(	(	PUNCT
ejpam-6705	281	2	6	6	NUM
ejpam-6705	281	3	)	)	PUNCT
ejpam-6705	281	4	since	since	SCONJ
ejpam-6705	281	5	g	g	PROPN
ejpam-6705	281	6	is	be	AUX
ejpam-6705	281	7	non	non	ADJ
ejpam-6705	281	8	-	-	ADJ
ejpam-6705	281	9	increasing	increase	VERB
ejpam-6705	281	10	mapping	mapping	NOUN
ejpam-6705	281	11	,	,	PUNCT
ejpam-6705	281	12	then	then	ADV
ejpam-6705	281	13	for	for	ADP
ejpam-6705	281	14	each	each	DET
ejpam-6705	281	15	k	k	PROPN
ejpam-6705	281	16	,	,	PUNCT
ejpam-6705	281	17	j	j	PROPN
ejpam-6705	281	18	≥	≥	NUM
ejpam-6705	281	19	0,∫	0,∫	NOUN
ejpam-6705	281	20	k+j	k+j	PROPN
ejpam-6705	281	21	0	0	NUM
ejpam-6705	282	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	283	1	≤	≤	PUNCT
ejpam-6705	283	2	∫	∫	PROPN
ejpam-6705	284	1	k	k	PROPN
ejpam-6705	284	2	0	0	NUM
ejpam-6705	285	1	g(t)dt+	g(t)dt+	PROPN
ejpam-6705	285	2	∫	∫	PROPN
ejpam-6705	285	3	j	j	PROPN
ejpam-6705	285	4	0	0	PROPN
ejpam-6705	285	5	g(t)dt	g(t)dt	PROPN
ejpam-6705	285	6	.	.	PUNCT
ejpam-6705	286	1	(	(	PUNCT
ejpam-6705	286	2	7	7	NUM
ejpam-6705	286	3	)	)	PUNCT
ejpam-6705	286	4	additionally	additionally	ADV
ejpam-6705	286	5	,	,	PUNCT
ejpam-6705	286	6	since	since	SCONJ
ejpam-6705	286	7	σ	σ	PROPN
ejpam-6705	286	8	is	be	AUX
ejpam-6705	286	9	a	a	DET
ejpam-6705	286	10	linear	linear	NOUN
ejpam-6705	286	11	and	and	CCONJ
ejpam-6705	286	12	monotonically	monotonically	ADV
ejpam-6705	286	13	increasing	increase	VERB
ejpam-6705	286	14	mapping	mapping	NOUN
ejpam-6705	286	15	,	,	PUNCT
ejpam-6705	286	16	it	it	PRON
ejpam-6705	286	17	follows	follow	VERB
ejpam-6705	286	18	from	from	ADP
ejpam-6705	286	19	(	(	PUNCT
ejpam-6705	286	20	4	4	NUM
ejpam-6705	286	21	)	)	PUNCT
ejpam-6705	286	22	,	,	PUNCT
ejpam-6705	286	23	(	(	PUNCT
ejpam-6705	286	24	5	5	NUM
ejpam-6705	286	25	)	)	PUNCT
ejpam-6705	286	26	and	and	CCONJ
ejpam-6705	286	27	(	(	PUNCT
ejpam-6705	286	28	7	7	X
ejpam-6705	286	29	)	)	PUNCT
ejpam-6705	287	1	that	that	SCONJ
ejpam-6705	287	2	for	for	ADP
ejpam-6705	287	3	all	all	DET
ejpam-6705	287	4	s	s	PART
ejpam-6705	287	5	≥	≥	NOUN
ejpam-6705	287	6	0∫	0∫	NUM
ejpam-6705	287	7	gb(us	gb(us	PROPN
ejpam-6705	287	8	,	,	PUNCT
ejpam-6705	287	9	us	we	PRON
ejpam-6705	287	10	,	,	PUNCT
ejpam-6705	287	11	us+1	us+1	PROPN
ejpam-6705	287	12	)	)	PUNCT
ejpam-6705	287	13	0	0	NUM
ejpam-6705	287	14	g(t)dt	g(t)dt	PROPN
ejpam-6705	287	15	=	=	SYM
ejpam-6705	287	16	∫	∫	PROPN
ejpam-6705	287	17	gb(t	gb(t	PROPN
ejpam-6705	287	18	(	(	PUNCT
ejpam-6705	287	19	us−1,vs−1),t	us−1,vs−1),t	PROPN
ejpam-6705	287	20	(	(	PUNCT
ejpam-6705	287	21	us−1,vs−1),t	us−1,vs−1),t	PROPN
ejpam-6705	287	22	(	(	PUNCT
ejpam-6705	287	23	us	us	PROPN
ejpam-6705	287	24	,	,	PUNCT
ejpam-6705	287	25	vs	vs	ADJ
ejpam-6705	287	26	)	)	PUNCT
ejpam-6705	287	27	)	)	PUNCT
ejpam-6705	287	28	0	0	NUM
ejpam-6705	287	29	g(t)dt	g(t)dt	PROPN
ejpam-6705	287	30	≤	≤	PROPN
ejpam-6705	287	31	σ	σ	PROPN
ejpam-6705	287	32	(	(	PUNCT
ejpam-6705	287	33	∫	∫	PROPN
ejpam-6705	287	34	gb(us−1,us−1,us)+gb(vs−1,vs−1,vs	gb(us−1,us−1,us)+gb(vs−1,vs−1,vs	PROPN
ejpam-6705	287	35	)	)	PUNCT
ejpam-6705	287	36	0	0	NUM
ejpam-6705	287	37	g(t)dt	g(t)dt	PROPN
ejpam-6705	287	38	)	)	PUNCT
ejpam-6705	287	39	≤	≤	PROPN
ejpam-6705	287	40	σ	σ	PROPN
ejpam-6705	287	41	(	(	PUNCT
ejpam-6705	287	42	∫	∫	PROPN
ejpam-6705	287	43	gb(us−1,us−1,us	gb(us−1,us−1,us	PROPN
ejpam-6705	287	44	)	)	PUNCT
ejpam-6705	287	45	0	0	NUM
ejpam-6705	287	46	g(t)dt	g(t)dt	PROPN
ejpam-6705	287	47	)	)	PUNCT
ejpam-6705	288	1	+	+	CCONJ
ejpam-6705	289	1	σ	σ	PROPN
ejpam-6705	289	2	(	(	PUNCT
ejpam-6705	289	3	∫	∫	PROPN
ejpam-6705	289	4	gb(vs−1,vs−1,vs	gb(vs−1,vs−1,vs	PROPN
ejpam-6705	289	5	)	)	PUNCT
ejpam-6705	289	6	0	0	NUM
ejpam-6705	290	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	290	2	)	)	PUNCT
ejpam-6705	291	1	=	=	SYM
ejpam-6705	291	2	σ	σ	PROPN
ejpam-6705	291	3	(	(	PUNCT
ejpam-6705	291	4	∫	∫	PROPN
ejpam-6705	291	5	gb(t	gb(t	PROPN
ejpam-6705	291	6	(	(	PUNCT
ejpam-6705	291	7	us−2,vs−2),t	us−2,vs−2),t	PROPN
ejpam-6705	291	8	(	(	PUNCT
ejpam-6705	291	9	us−2,vs−2),t	us−2,vs−2),t	PROPN
ejpam-6705	291	10	(	(	PUNCT
ejpam-6705	291	11	us−1,vs−1	us−1,vs−1	PROPN
ejpam-6705	291	12	)	)	PUNCT
ejpam-6705	291	13	)	)	PUNCT
ejpam-6705	291	14	0	0	NUM
ejpam-6705	292	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	292	2	)	)	PUNCT
ejpam-6705	293	1	+	+	CCONJ
ejpam-6705	293	2	σ	σ	PROPN
ejpam-6705	293	3	(	(	PUNCT
ejpam-6705	293	4	∫	∫	PROPN
ejpam-6705	293	5	gb(t	gb(t	X
ejpam-6705	293	6	(	(	PUNCT
ejpam-6705	293	7	vs−2,us−2),t	vs−2,us−2),t	X
ejpam-6705	293	8	(	(	PUNCT
ejpam-6705	293	9	vs−2,us−2),t	vs−2,us−2),t	X
ejpam-6705	293	10	(	(	PUNCT
ejpam-6705	293	11	vs−1,us−1	vs−1,us−1	NOUN
ejpam-6705	293	12	)	)	PUNCT
ejpam-6705	293	13	)	)	PUNCT
ejpam-6705	293	14	0	0	NUM
ejpam-6705	294	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	294	2	)	)	PUNCT
ejpam-6705	295	1	s.	s.	PROPN
ejpam-6705	295	2	batul	batul	PROPN
ejpam-6705	295	3	et	et	PROPN
ejpam-6705	295	4	al	al	PROPN
ejpam-6705	295	5	.	.	PUNCT
ejpam-6705	295	6	/	/	SYM
ejpam-6705	295	7	eur	eur	PROPN
ejpam-6705	295	8	.	.	PUNCT
ejpam-6705	296	1	j.	j.	PROPN
ejpam-6705	296	2	pure	pure	PROPN
ejpam-6705	296	3	appl	appl	PROPN
ejpam-6705	296	4	.	.	PROPN
ejpam-6705	296	5	math	math	PROPN
ejpam-6705	296	6	,	,	PUNCT
ejpam-6705	296	7	18	18	NUM
ejpam-6705	296	8	(	(	PUNCT
ejpam-6705	296	9	4	4	NUM
ejpam-6705	296	10	)	)	PUNCT
ejpam-6705	296	11	(	(	PUNCT
ejpam-6705	296	12	2025	2025	NUM
ejpam-6705	296	13	)	)	PUNCT
ejpam-6705	296	14	,	,	PUNCT
ejpam-6705	296	15	6705	6705	NUM
ejpam-6705	296	16	12	12	NUM
ejpam-6705	296	17	of	of	ADP
ejpam-6705	296	18	23	23	NUM
ejpam-6705	296	19	≤	≤	NUM
ejpam-6705	296	20	σ	σ	NOUN
ejpam-6705	296	21	(	(	PUNCT
ejpam-6705	296	22	σ	σ	PROPN
ejpam-6705	296	23	(	(	PUNCT
ejpam-6705	296	24	∫	∫	PROPN
ejpam-6705	296	25	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	296	26	)	)	PUNCT
ejpam-6705	296	27	0	0	NUM
ejpam-6705	296	28	g(t)dt	g(t)dt	PROPN
ejpam-6705	296	29	)	)	PUNCT
ejpam-6705	296	30	)	)	PUNCT
ejpam-6705	297	1	+	+	CCONJ
ejpam-6705	298	1	σ	σ	NOUN
ejpam-6705	298	2	(	(	PUNCT
ejpam-6705	298	3	σ	σ	PROPN
ejpam-6705	298	4	(	(	PUNCT
ejpam-6705	298	5	∫	∫	PROPN
ejpam-6705	298	6	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	NUM
ejpam-6705	298	7	)	)	PUNCT
ejpam-6705	298	8	0	0	NUM
ejpam-6705	299	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	299	2	)	)	PUNCT
ejpam-6705	299	3	)	)	PUNCT
ejpam-6705	300	1	≤	≤	PROPN
ejpam-6705	300	2	σ2	σ2	PROPN
ejpam-6705	300	3	(	(	PUNCT
ejpam-6705	300	4	∫	∫	PROPN
ejpam-6705	300	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	300	6	)	)	PUNCT
ejpam-6705	300	7	0	0	NUM
ejpam-6705	300	8	g(t)dt	g(t)dt	PROPN
ejpam-6705	300	9	)	)	PUNCT
ejpam-6705	301	1	+	+	NUM
ejpam-6705	301	2	σ2	σ2	PROPN
ejpam-6705	301	3	(	(	PUNCT
ejpam-6705	301	4	∫	∫	PROPN
ejpam-6705	301	5	g(vs−2,vs−2,vs−1	g(vs−2,vs−2,vs−1	PROPN
ejpam-6705	301	6	)	)	PUNCT
ejpam-6705	301	7	0	0	NUM
ejpam-6705	302	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	302	2	)	)	PUNCT
ejpam-6705	303	1	+	+	NUM
ejpam-6705	303	2	σ2	σ2	PROPN
ejpam-6705	303	3	(	(	PUNCT
ejpam-6705	303	4	∫	∫	PROPN
ejpam-6705	303	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	303	6	)	)	PUNCT
ejpam-6705	303	7	0	0	NUM
ejpam-6705	304	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	304	2	)	)	PUNCT
ejpam-6705	305	1	+	+	NUM
ejpam-6705	305	2	σ2	σ2	PROPN
ejpam-6705	305	3	(	(	PUNCT
ejpam-6705	305	4	∫	∫	PROPN
ejpam-6705	305	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	305	6	)	)	PUNCT
ejpam-6705	305	7	0	0	NUM
ejpam-6705	306	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	306	2	)	)	PUNCT
ejpam-6705	307	1	=	=	SYM
ejpam-6705	307	2	2σ2	2σ2	NUM
ejpam-6705	307	3	(	(	PUNCT
ejpam-6705	307	4	∫	∫	PROPN
ejpam-6705	307	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	307	6	)	)	PUNCT
ejpam-6705	307	7	0	0	NUM
ejpam-6705	308	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	308	2	)	)	PUNCT
ejpam-6705	309	1	+	+	CCONJ
ejpam-6705	309	2	2σ2	2σ2	NUM
ejpam-6705	309	3	(	(	PUNCT
ejpam-6705	309	4	∫	∫	PROPN
ejpam-6705	309	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	309	6	)	)	PUNCT
ejpam-6705	309	7	0	0	NUM
ejpam-6705	310	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	310	2	)	)	PUNCT
ejpam-6705	311	1	=	=	SYM
ejpam-6705	311	2	2σ2	2σ2	NUM
ejpam-6705	311	3	(	(	PUNCT
ejpam-6705	311	4	∫	∫	PROPN
ejpam-6705	311	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	311	6	)	)	PUNCT
ejpam-6705	311	7	0	0	NUM
ejpam-6705	312	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	312	2	∫	∫	PROPN
ejpam-6705	312	3	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	312	4	)	)	PUNCT
ejpam-6705	312	5	0	0	NUM
ejpam-6705	312	6	g(t)dt	g(t)dt	PROPN
ejpam-6705	312	7	)	)	PUNCT
ejpam-6705	312	8	≤	≤	NOUN
ejpam-6705	312	9	2σ2	2σ2	NUM
ejpam-6705	313	1	(	(	PUNCT
ejpam-6705	313	2	∫	∫	PROPN
ejpam-6705	313	3	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	313	4	)	)	PUNCT
ejpam-6705	313	5	0	0	NUM
ejpam-6705	313	6	g(t)dt	g(t)dt	PROPN
ejpam-6705	313	7	)	)	PUNCT
ejpam-6705	313	8	...	...	PUNCT
ejpam-6705	314	1	≤	≤	NUM
ejpam-6705	314	2	sσs	sσs	NOUN
ejpam-6705	314	3	(	(	PUNCT
ejpam-6705	314	4	∫	∫	PROPN
ejpam-6705	314	5	gb(u0,u0,u1)+gb(v0,v0,v1	gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	314	6	)	)	PUNCT
ejpam-6705	314	7	0	0	NUM
ejpam-6705	315	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	315	2	)	)	PUNCT
ejpam-6705	315	3	.	.	PUNCT
ejpam-6705	316	1	following	follow	VERB
ejpam-6705	316	2	the	the	DET
ejpam-6705	316	3	same	same	ADJ
ejpam-6705	316	4	steps	step	NOUN
ejpam-6705	316	5	,	,	PUNCT
ejpam-6705	316	6	it	it	PRON
ejpam-6705	316	7	can	can	AUX
ejpam-6705	316	8	be	be	AUX
ejpam-6705	316	9	proved	prove	VERB
ejpam-6705	316	10	that∫	that∫	PROPN
ejpam-6705	316	11	gb(vs	gb(vs	PROPN
ejpam-6705	316	12	,	,	PUNCT
ejpam-6705	316	13	vs	vs	ADP
ejpam-6705	316	14	,	,	PUNCT
ejpam-6705	316	15	vs+1	vs+1	NOUN
ejpam-6705	316	16	)	)	PUNCT
ejpam-6705	316	17	0	0	NUM
ejpam-6705	317	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	317	2	=	=	SYM
ejpam-6705	317	3	∫	∫	PROPN
ejpam-6705	317	4	gb(t	gb(t	PROPN
ejpam-6705	317	5	(	(	PUNCT
ejpam-6705	317	6	vs−1,us−1),t	vs−1,us−1),t	X
ejpam-6705	317	7	(	(	PUNCT
ejpam-6705	317	8	vs−1,us−1),t	vs−1,us−1),t	X
ejpam-6705	317	9	(	(	PUNCT
ejpam-6705	317	10	vs	vs	X
ejpam-6705	317	11	,	,	PUNCT
ejpam-6705	317	12	us	we	PRON
ejpam-6705	317	13	)	)	PUNCT
ejpam-6705	317	14	)	)	PUNCT
ejpam-6705	317	15	0	0	NUM
ejpam-6705	318	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	318	2	≤	≤	PROPN
ejpam-6705	318	3	σ	σ	PROPN
ejpam-6705	318	4	(	(	PUNCT
ejpam-6705	318	5	∫	∫	PROPN
ejpam-6705	318	6	gb(vs−1,vs−1,vs)+gb(us−1,us−1,us	gb(vs−1,vs−1,vs)+gb(us−1,us−1,us	PROPN
ejpam-6705	318	7	)	)	PUNCT
ejpam-6705	318	8	0	0	NUM
ejpam-6705	319	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	319	2	)	)	PUNCT
ejpam-6705	320	1	≤	≤	PROPN
ejpam-6705	320	2	σ	σ	PROPN
ejpam-6705	320	3	(	(	PUNCT
ejpam-6705	320	4	∫	∫	PROPN
ejpam-6705	320	5	gb(vs−1,vs−1,vs	gb(vs−1,vs−1,vs	PROPN
ejpam-6705	320	6	)	)	PUNCT
ejpam-6705	320	7	0	0	NUM
ejpam-6705	321	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	321	2	)	)	PUNCT
ejpam-6705	322	1	+	+	CCONJ
ejpam-6705	323	1	σ	σ	NOUN
ejpam-6705	323	2	(	(	PUNCT
ejpam-6705	323	3	∫	∫	PROPN
ejpam-6705	323	4	gb(us−1,us−1,us	gb(us−1,us−1,us	PROPN
ejpam-6705	323	5	)	)	PUNCT
ejpam-6705	323	6	0	0	NUM
ejpam-6705	324	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	324	2	)	)	PUNCT
ejpam-6705	325	1	=	=	SYM
ejpam-6705	325	2	σ	σ	PROPN
ejpam-6705	325	3	(	(	PUNCT
ejpam-6705	325	4	∫	∫	PROPN
ejpam-6705	325	5	gb(t	gb(t	PROPN
ejpam-6705	325	6	(	(	PUNCT
ejpam-6705	325	7	vs−2,us−2),t	vs−2,us−2),t	X
ejpam-6705	325	8	(	(	PUNCT
ejpam-6705	325	9	vs−2,us−2),t	vs−2,us−2),t	X
ejpam-6705	325	10	(	(	PUNCT
ejpam-6705	325	11	vs−1,us−1	vs−1,us−1	NOUN
ejpam-6705	325	12	)	)	PUNCT
ejpam-6705	325	13	)	)	PUNCT
ejpam-6705	325	14	0	0	NUM
ejpam-6705	326	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	326	2	)	)	PUNCT
ejpam-6705	327	1	s.	s.	PROPN
ejpam-6705	327	2	batul	batul	PROPN
ejpam-6705	327	3	et	et	PROPN
ejpam-6705	327	4	al	al	PROPN
ejpam-6705	327	5	.	.	PUNCT
ejpam-6705	327	6	/	/	SYM
ejpam-6705	327	7	eur	eur	PROPN
ejpam-6705	327	8	.	.	PUNCT
ejpam-6705	328	1	j.	j.	PROPN
ejpam-6705	328	2	pure	pure	PROPN
ejpam-6705	328	3	appl	appl	PROPN
ejpam-6705	328	4	.	.	PROPN
ejpam-6705	328	5	math	math	PROPN
ejpam-6705	328	6	,	,	PUNCT
ejpam-6705	328	7	18	18	NUM
ejpam-6705	328	8	(	(	PUNCT
ejpam-6705	328	9	4	4	NUM
ejpam-6705	328	10	)	)	PUNCT
ejpam-6705	328	11	(	(	PUNCT
ejpam-6705	328	12	2025	2025	NUM
ejpam-6705	328	13	)	)	PUNCT
ejpam-6705	328	14	,	,	PUNCT
ejpam-6705	328	15	6705	6705	NUM
ejpam-6705	328	16	13	13	NUM
ejpam-6705	328	17	of	of	ADP
ejpam-6705	328	18	23	23	NUM
ejpam-6705	328	19	+	+	NUM
ejpam-6705	328	20	σ	σ	PROPN
ejpam-6705	328	21	(	(	PUNCT
ejpam-6705	328	22	∫	∫	PROPN
ejpam-6705	328	23	gb(t	gb(t	PROPN
ejpam-6705	328	24	(	(	PUNCT
ejpam-6705	328	25	us−2,vs−2),t	us−2,vs−2),t	PROPN
ejpam-6705	328	26	(	(	PUNCT
ejpam-6705	328	27	us−2,vs−2),t	us−2,vs−2),t	PROPN
ejpam-6705	328	28	(	(	PUNCT
ejpam-6705	328	29	us−1,vs−1	us−1,vs−1	PROPN
ejpam-6705	328	30	)	)	PUNCT
ejpam-6705	328	31	)	)	PUNCT
ejpam-6705	328	32	0	0	NUM
ejpam-6705	329	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	329	2	)	)	PUNCT
ejpam-6705	330	1	≤	≤	PROPN
ejpam-6705	330	2	σ	σ	PROPN
ejpam-6705	330	3	(	(	PUNCT
ejpam-6705	330	4	σ	σ	PROPN
ejpam-6705	330	5	(	(	PUNCT
ejpam-6705	330	6	∫	∫	PROPN
ejpam-6705	330	7	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	NUM
ejpam-6705	330	8	)	)	PUNCT
ejpam-6705	330	9	0	0	NUM
ejpam-6705	330	10	g(t)dt	g(t)dt	PROPN
ejpam-6705	330	11	)	)	PUNCT
ejpam-6705	330	12	)	)	PUNCT
ejpam-6705	331	1	+	+	CCONJ
ejpam-6705	332	1	σ	σ	NOUN
ejpam-6705	332	2	(	(	PUNCT
ejpam-6705	332	3	σ	σ	PROPN
ejpam-6705	332	4	(	(	PUNCT
ejpam-6705	332	5	∫	∫	PROPN
ejpam-6705	332	6	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	gb(us−2,us−2,us−1)+gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	332	7	)	)	PUNCT
ejpam-6705	332	8	0	0	NUM
ejpam-6705	333	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	333	2	)	)	PUNCT
ejpam-6705	333	3	)	)	PUNCT
ejpam-6705	334	1	≤	≤	PROPN
ejpam-6705	334	2	σ2	σ2	PROPN
ejpam-6705	334	3	(	(	PUNCT
ejpam-6705	334	4	∫	∫	PROPN
ejpam-6705	334	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	334	6	)	)	PUNCT
ejpam-6705	334	7	0	0	NUM
ejpam-6705	334	8	g(t)dt	g(t)dt	PROPN
ejpam-6705	334	9	)	)	PUNCT
ejpam-6705	335	1	+	+	NUM
ejpam-6705	335	2	σ2	σ2	PROPN
ejpam-6705	335	3	(	(	PUNCT
ejpam-6705	335	4	∫	∫	PROPN
ejpam-6705	335	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	335	6	)	)	PUNCT
ejpam-6705	335	7	0	0	NUM
ejpam-6705	336	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	336	2	)	)	PUNCT
ejpam-6705	337	1	+	+	NUM
ejpam-6705	337	2	σ2	σ2	PROPN
ejpam-6705	337	3	(	(	PUNCT
ejpam-6705	337	4	∫	∫	PROPN
ejpam-6705	337	5	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	337	6	)	)	PUNCT
ejpam-6705	337	7	0	0	NUM
ejpam-6705	338	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	338	2	)	)	PUNCT
ejpam-6705	339	1	+	+	NUM
ejpam-6705	339	2	σ2	σ2	PROPN
ejpam-6705	339	3	(	(	PUNCT
ejpam-6705	339	4	∫	∫	PROPN
ejpam-6705	339	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	339	6	)	)	PUNCT
ejpam-6705	339	7	0	0	NUM
ejpam-6705	340	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	340	2	)	)	PUNCT
ejpam-6705	341	1	=	=	SYM
ejpam-6705	341	2	2σ2	2σ2	NUM
ejpam-6705	341	3	(	(	PUNCT
ejpam-6705	341	4	∫	∫	PROPN
ejpam-6705	341	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	341	6	)	)	PUNCT
ejpam-6705	341	7	0	0	NUM
ejpam-6705	342	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	342	2	)	)	PUNCT
ejpam-6705	343	1	+	+	CCONJ
ejpam-6705	344	1	2σ2	2σ2	NUM
ejpam-6705	344	2	(	(	PUNCT
ejpam-6705	344	3	∫	∫	PROPN
ejpam-6705	344	4	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	344	5	)	)	PUNCT
ejpam-6705	344	6	0	0	NUM
ejpam-6705	344	7	g(t)dt	g(t)dt	NOUN
ejpam-6705	344	8	)	)	PUNCT
ejpam-6705	345	1	=	=	SYM
ejpam-6705	345	2	2σ2	2σ2	NUM
ejpam-6705	345	3	(	(	PUNCT
ejpam-6705	345	4	∫	∫	PROPN
ejpam-6705	345	5	gb(vs−2,vs−2,vs−1	gb(vs−2,vs−2,vs−1	PROPN
ejpam-6705	345	6	)	)	PUNCT
ejpam-6705	345	7	0	0	NUM
ejpam-6705	346	1	g(t)dt+	g(t)dt+	PROPN
ejpam-6705	346	2	∫	∫	PROPN
ejpam-6705	346	3	gb(us−2,us−2,us−1	gb(us−2,us−2,us−1	PROPN
ejpam-6705	346	4	)	)	PUNCT
ejpam-6705	346	5	0	0	NUM
ejpam-6705	346	6	g(t)dt	g(t)dt	PROPN
ejpam-6705	346	7	)	)	PUNCT
ejpam-6705	346	8	≤	≤	NOUN
ejpam-6705	346	9	2σ2	2σ2	NUM
ejpam-6705	346	10	(	(	PUNCT
ejpam-6705	346	11	∫	∫	PROPN
ejpam-6705	346	12	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	gb(vs−2,vs−2,vs−1)+gb(us−2,us−2,us−1	NUM
ejpam-6705	346	13	)	)	PUNCT
ejpam-6705	346	14	0	0	NUM
ejpam-6705	346	15	g(t)dt	g(t)dt	PROPN
ejpam-6705	346	16	)	)	PUNCT
ejpam-6705	346	17	...	...	PUNCT
ejpam-6705	347	1	≤	≤	NUM
ejpam-6705	347	2	sσs	sσs	NOUN
ejpam-6705	347	3	(	(	PUNCT
ejpam-6705	347	4	∫	∫	PROPN
ejpam-6705	347	5	gb(v0,v0,v1)+gb(u0,u0,u1	gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	347	6	)	)	PUNCT
ejpam-6705	347	7	0	0	NUM
ejpam-6705	347	8	g(t)dt	g(t)dt	PROPN
ejpam-6705	347	9	)	)	PUNCT
ejpam-6705	347	10	.	.	PUNCT
ejpam-6705	348	1	let	let	VERB
ejpam-6705	348	2	r	r	NOUN
ejpam-6705	348	3	,	,	PUNCT
ejpam-6705	348	4	s	s	PART
ejpam-6705	348	5	∈	∈	PROPN
ejpam-6705	348	6	n	n	PRON
ejpam-6705	348	7	such	such	ADJ
ejpam-6705	349	1	that	that	SCONJ
ejpam-6705	349	2	r	r	NOUN
ejpam-6705	349	3	>	>	X
ejpam-6705	349	4	s	s	PROPN
ejpam-6705	349	5	,	,	PUNCT
ejpam-6705	349	6	then	then	ADV
ejpam-6705	349	7	from	from	ADP
ejpam-6705	349	8	the	the	DET
ejpam-6705	349	9	definition	definition	NOUN
ejpam-6705	349	10	of	of	ADP
ejpam-6705	349	11	gb	gb	ADV
ejpam-6705	349	12	-	-	PUNCT
ejpam-6705	349	13	metric	metric	ADJ
ejpam-6705	349	14	space,∫	space,∫	NOUN
ejpam-6705	349	15	gb(us	gb(us	PROPN
ejpam-6705	349	16	,	,	PUNCT
ejpam-6705	349	17	us	we	PRON
ejpam-6705	349	18	,	,	PUNCT
ejpam-6705	349	19	ur	ur	INTJ
ejpam-6705	349	20	)	)	PUNCT
ejpam-6705	349	21	0	0	NUM
ejpam-6705	349	22	g(t)dt	g(t)dt	PROPN
ejpam-6705	349	23	≤	≤	PROPN
ejpam-6705	349	24	∫	∫	PROPN
ejpam-6705	349	25	l[gb(us	l[gb(us	PROPN
ejpam-6705	349	26	,	,	PUNCT
ejpam-6705	349	27	us	we	PRON
ejpam-6705	349	28	,	,	PUNCT
ejpam-6705	349	29	us+1)+gb(us+1,us+1,ur	us+1)+gb(us+1,us+1,ur	NUM
ejpam-6705	349	30	)	)	PUNCT
ejpam-6705	349	31	]	]	PUNCT
ejpam-6705	349	32	0	0	NUM
ejpam-6705	349	33	g(t)dt	g(t)dt	NOUN
ejpam-6705	349	34	=	=	SYM
ejpam-6705	349	35	∫	∫	PROPN
ejpam-6705	349	36	lgb(us	lgb(us	PROPN
ejpam-6705	349	37	,	,	PUNCT
ejpam-6705	349	38	us	we	PRON
ejpam-6705	349	39	,	,	PUNCT
ejpam-6705	349	40	us+1)+lgb(us+1,us+1,ur	us+1)+lgb(us+1,us+1,ur	ADJ
ejpam-6705	349	41	)	)	PUNCT
ejpam-6705	349	42	0	0	NUM
ejpam-6705	349	43	g(t)dt	g(t)dt	PROPN
ejpam-6705	349	44	≤	≤	NUM
ejpam-6705	349	45	∫	∫	PROPN
ejpam-6705	349	46	lgb(us	lgb(us	PROPN
ejpam-6705	349	47	,	,	PUNCT
ejpam-6705	349	48	us	we	PRON
ejpam-6705	349	49	,	,	PUNCT
ejpam-6705	349	50	us+1	us+1	ADJ
ejpam-6705	349	51	)	)	PUNCT
ejpam-6705	349	52	0	0	NUM
ejpam-6705	350	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	350	2	∫	∫	PROPN
ejpam-6705	350	3	lgb(us+1,us+1,ur	lgb(us+1,us+1,ur	PROPN
ejpam-6705	350	4	)	)	PUNCT
ejpam-6705	350	5	0	0	NUM
ejpam-6705	351	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	351	2	s.	s.	PROPN
ejpam-6705	351	3	batul	batul	PROPN
ejpam-6705	351	4	et	et	PROPN
ejpam-6705	351	5	al	al	PROPN
ejpam-6705	351	6	.	.	PUNCT
ejpam-6705	351	7	/	/	SYM
ejpam-6705	351	8	eur	eur	PROPN
ejpam-6705	351	9	.	.	PUNCT
ejpam-6705	352	1	j.	j.	PROPN
ejpam-6705	352	2	pure	pure	PROPN
ejpam-6705	352	3	appl	appl	PROPN
ejpam-6705	352	4	.	.	PROPN
ejpam-6705	352	5	math	math	PROPN
ejpam-6705	352	6	,	,	PUNCT
ejpam-6705	352	7	18	18	NUM
ejpam-6705	352	8	(	(	PUNCT
ejpam-6705	352	9	4	4	NUM
ejpam-6705	352	10	)	)	PUNCT
ejpam-6705	352	11	(	(	PUNCT
ejpam-6705	352	12	2025	2025	NUM
ejpam-6705	352	13	)	)	PUNCT
ejpam-6705	352	14	,	,	PUNCT
ejpam-6705	352	15	6705	6705	NUM
ejpam-6705	352	16	14	14	NUM
ejpam-6705	352	17	of	of	ADP
ejpam-6705	352	18	23	23	NUM
ejpam-6705	352	19	≤	≤	NUM
ejpam-6705	352	20	∫	∫	PROPN
ejpam-6705	353	1	lgb(us	lgb(us	PROPN
ejpam-6705	353	2	,	,	PUNCT
ejpam-6705	353	3	us	we	PRON
ejpam-6705	353	4	,	,	PUNCT
ejpam-6705	353	5	us+1	us+1	PROPN
ejpam-6705	353	6	)	)	PUNCT
ejpam-6705	353	7	0	0	NUM
ejpam-6705	354	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	354	2	+	+	CCONJ
ejpam-6705	354	3	∫	∫	PROPN
ejpam-6705	354	4	l[l(gb(us+1,us+1,us+2)+gb(us+2,us+2,ur	l[l(gb(us+1,us+1,us+2)+gb(us+2,us+2,ur	NUM
ejpam-6705	354	5	)	)	PUNCT
ejpam-6705	354	6	)	)	PUNCT
ejpam-6705	354	7	]	]	PUNCT
ejpam-6705	354	8	0	0	NUM
ejpam-6705	355	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	355	2	≤	≤	NUM
ejpam-6705	355	3	∫	∫	PROPN
ejpam-6705	355	4	lgb(us	lgb(us	PROPN
ejpam-6705	355	5	,	,	PUNCT
ejpam-6705	355	6	us	we	PRON
ejpam-6705	355	7	,	,	PUNCT
ejpam-6705	355	8	us+1	us+1	ADJ
ejpam-6705	355	9	)	)	PUNCT
ejpam-6705	355	10	0	0	NUM
ejpam-6705	356	1	g(t)dt+	g(t)dt+	PROPN
ejpam-6705	356	2	∫	∫	PROPN
ejpam-6705	356	3	l2gb(us+1,us+1,us+2	l2gb(us+1,us+1,us+2	PROPN
ejpam-6705	356	4	)	)	PUNCT
ejpam-6705	356	5	0	0	NUM
ejpam-6705	357	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	357	2	+	+	CCONJ
ejpam-6705	357	3	∫	∫	PROPN
ejpam-6705	357	4	l2gb(us+2,us+2,ur	l2gb(us+2,us+2,ur	PROPN
ejpam-6705	357	5	)	)	PUNCT
ejpam-6705	357	6	0	0	NUM
ejpam-6705	358	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	358	2	≤	≤	NUM
ejpam-6705	358	3	∫	∫	PROPN
ejpam-6705	358	4	lgb(us	lgb(us	PROPN
ejpam-6705	358	5	,	,	PUNCT
ejpam-6705	358	6	us	we	PRON
ejpam-6705	358	7	,	,	PUNCT
ejpam-6705	358	8	us+1	us+1	ADJ
ejpam-6705	358	9	)	)	PUNCT
ejpam-6705	358	10	0	0	NUM
ejpam-6705	359	1	g(t)dt+	g(t)dt+	PROPN
ejpam-6705	359	2	∫	∫	PROPN
ejpam-6705	359	3	l2gb(us+1,us+1,us+2	l2gb(us+1,us+1,us+2	PROPN
ejpam-6705	359	4	)	)	PUNCT
ejpam-6705	359	5	0	0	NUM
ejpam-6705	360	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	360	2	+	+	CCONJ
ejpam-6705	360	3	∫	∫	PROPN
ejpam-6705	360	4	l3gb(us+2,us+2,us+3	l3gb(us+2,us+2,us+3	PROPN
ejpam-6705	360	5	)	)	PUNCT
ejpam-6705	360	6	0	0	NUM
ejpam-6705	360	7	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	360	8	.	.	PUNCT
ejpam-6705	360	9	.	.	PUNCT
ejpam-6705	361	1	.+	.+	NOUN
ejpam-6705	361	2	∫	∫	PROPN
ejpam-6705	362	1	lr−sgb(ur−2,ur−2,ur−1	lr−sgb(ur−2,ur−2,ur−1	PROPN
ejpam-6705	362	2	)	)	PUNCT
ejpam-6705	362	3	0	0	NUM
ejpam-6705	363	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	363	2	+	+	CCONJ
ejpam-6705	363	3	∫	∫	PROPN
ejpam-6705	363	4	lr−sgb(ur−1,ur−1,ur	lr−sgb(ur−1,ur−1,ur	X
ejpam-6705	363	5	)	)	PUNCT
ejpam-6705	363	6	0	0	NUM
ejpam-6705	364	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	364	2	≤	≤	X
ejpam-6705	364	3	sσs	sσs	NOUN
ejpam-6705	364	4	(	(	PUNCT
ejpam-6705	364	5	∫	∫	PROPN
ejpam-6705	364	6	l[gb(u0,u0,u1)+gb(v0,v0,v1	l[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	364	7	)	)	PUNCT
ejpam-6705	364	8	]	]	PUNCT
ejpam-6705	364	9	0	0	NUM
ejpam-6705	364	10	g(t)dt	g(t)dt	PROPN
ejpam-6705	364	11	)	)	PUNCT
ejpam-6705	365	1	+	+	CCONJ
ejpam-6705	365	2	(	(	PUNCT
ejpam-6705	365	3	s+	s+	X
ejpam-6705	365	4	1)σs+1	1)σs+1	NUM
ejpam-6705	365	5	(	(	PUNCT
ejpam-6705	365	6	∫	∫	PROPN
ejpam-6705	365	7	l2[gb(u0,u0,u1)+gb(v0,v0,v1	l2[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	365	8	)	)	PUNCT
ejpam-6705	365	9	]	]	PUNCT
ejpam-6705	365	10	0	0	NUM
ejpam-6705	365	11	g(t)dt	g(t)dt	PROPN
ejpam-6705	365	12	)	)	PUNCT
ejpam-6705	366	1	+	+	CCONJ
ejpam-6705	366	2	(	(	PUNCT
ejpam-6705	366	3	s+	s+	NUM
ejpam-6705	366	4	2)σs+2	2)σs+2	NUM
ejpam-6705	366	5	(	(	PUNCT
ejpam-6705	366	6	∫	∫	PROPN
ejpam-6705	366	7	l3[gb(u0,u0,u1)+gb(v0,v0,v1	l3[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	366	8	)	)	PUNCT
ejpam-6705	366	9	]	]	PUNCT
ejpam-6705	367	1	o	o	X
ejpam-6705	367	2	g(t)dt	g(t)dt	PROPN
ejpam-6705	367	3	)	)	PUNCT
ejpam-6705	368	1	+	+	CCONJ
ejpam-6705	368	2	.	.	PUNCT
ejpam-6705	368	3	.	.	PUNCT
ejpam-6705	369	1	.+	.+	NOUN
ejpam-6705	369	2	(	(	PUNCT
ejpam-6705	369	3	r	r	NOUN
ejpam-6705	369	4	−	−	PROPN
ejpam-6705	369	5	2)σr−2	2)σr−2	NUM
ejpam-6705	369	6	(	(	PUNCT
ejpam-6705	369	7	∫	∫	PROPN
ejpam-6705	369	8	lr−s[gb(u0,u0,u1)+gb(v0,v0,v1	lr−s[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	369	9	)	)	PUNCT
ejpam-6705	369	10	]	]	PUNCT
ejpam-6705	369	11	0	0	NUM
ejpam-6705	369	12	g(t)dt	g(t)dt	PROPN
ejpam-6705	369	13	)	)	PUNCT
ejpam-6705	370	1	+	+	CCONJ
ejpam-6705	370	2	(	(	PUNCT
ejpam-6705	370	3	r	r	NOUN
ejpam-6705	370	4	−	−	PROPN
ejpam-6705	370	5	1)σr−1	1)σr−1	PROPN
ejpam-6705	370	6	(	(	PUNCT
ejpam-6705	370	7	∫	∫	PROPN
ejpam-6705	370	8	lr−s[gb(u0,u0,u1)+gb(v0,v0,v1	lr−s[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	370	9	)	)	PUNCT
ejpam-6705	370	10	]	]	PUNCT
ejpam-6705	370	11	0	0	NUM
ejpam-6705	370	12	g(t)dt	g(t)dt	NOUN
ejpam-6705	370	13	)	)	PUNCT
ejpam-6705	371	1	=	=	PUNCT
ejpam-6705	372	1	i	i	PRON
ejpam-6705	372	2	=	=	PROPN
ejpam-6705	372	3	r−1∑	r−1∑	PROPN
ejpam-6705	372	4	i	i	PROPN
ejpam-6705	372	5	=	=	PROPN
ejpam-6705	372	6	s	s	PART
ejpam-6705	372	7	iσi	iσi	NOUN
ejpam-6705	372	8	(	(	PUNCT
ejpam-6705	372	9	∫	∫	PROPN
ejpam-6705	372	10	li−s+1[gb(u0,u0,u1)+gb(v0,v0,v1	li−s+1[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	372	11	)	)	PUNCT
ejpam-6705	372	12	]	]	PUNCT
ejpam-6705	372	13	0	0	NUM
ejpam-6705	372	14	g(t)dt	g(t)dt	PROPN
ejpam-6705	372	15	)	)	PUNCT
ejpam-6705	372	16	≤	≤	NOUN
ejpam-6705	373	1	∞∑	∞∑	NUM
ejpam-6705	373	2	i	i	PRON
ejpam-6705	373	3	=	=	NOUN
ejpam-6705	373	4	s	s	PART
ejpam-6705	373	5	iσi	iσi	NOUN
ejpam-6705	373	6	(	(	PUNCT
ejpam-6705	373	7	∫	∫	PROPN
ejpam-6705	373	8	li−s+1[gb(u0,u0,u1)+gb(v0,v0,v1	li−s+1[gb(u0,u0,u1)+gb(v0,v0,v1	PROPN
ejpam-6705	373	9	)	)	PUNCT
ejpam-6705	373	10	]	]	PUNCT
ejpam-6705	373	11	0	0	NUM
ejpam-6705	373	12	g(t)dt	g(t)dt	PROPN
ejpam-6705	373	13	)	)	PUNCT
ejpam-6705	373	14	.	.	PUNCT
ejpam-6705	374	1	since	since	SCONJ
ejpam-6705	374	2	∞∑	∞∑	NUM
ejpam-6705	374	3	i	i	NOUN
ejpam-6705	374	4	=	=	NOUN
ejpam-6705	374	5	s	s	PART
ejpam-6705	374	6	iσi(t	iσi(t	NOUN
ejpam-6705	374	7	)	)	PUNCT
ejpam-6705	374	8	<	<	X
ejpam-6705	374	9	∞	∞	PROPN
ejpam-6705	374	10	for	for	ADP
ejpam-6705	374	11	all	all	DET
ejpam-6705	374	12	t	t	PROPN
ejpam-6705	374	13	>	>	X
ejpam-6705	374	14	0	0	PROPN
ejpam-6705	374	15	,	,	PUNCT
ejpam-6705	374	16	this	this	PRON
ejpam-6705	374	17	implies	imply	VERB
ejpam-6705	374	18	that	that	SCONJ
ejpam-6705	374	19	lim	lim	PROPN
ejpam-6705	374	20	s	s	PROPN
ejpam-6705	374	21	,	,	PUNCT
ejpam-6705	374	22	r→∞	r→∞	X
ejpam-6705	374	23	gb(us	gb(us	PROPN
ejpam-6705	374	24	,	,	PUNCT
ejpam-6705	374	25	us	we	PRON
ejpam-6705	374	26	,	,	PUNCT
ejpam-6705	374	27	ur	ur	INTJ
ejpam-6705	374	28	)	)	PUNCT
ejpam-6705	374	29	=	=	SYM
ejpam-6705	374	30	0	0	NUM
ejpam-6705	375	1	and	and	CCONJ
ejpam-6705	375	2	(	(	PUNCT
ejpam-6705	375	3	us	us	PROPN
ejpam-6705	375	4	)	)	PUNCT
ejpam-6705	375	5	is	be	AUX
ejpam-6705	375	6	a	a	DET
ejpam-6705	375	7	cauchy	cauchy	ADJ
ejpam-6705	375	8	sequence	sequence	NOUN
ejpam-6705	375	9	in	in	ADP
ejpam-6705	375	10	x	x	X
ejpam-6705	375	11	.	.	PUNCT
ejpam-6705	376	1	in	in	ADP
ejpam-6705	376	2	a	a	DET
ejpam-6705	376	3	similar	similar	ADJ
ejpam-6705	376	4	manner	manner	NOUN
ejpam-6705	376	5	,	,	PUNCT
ejpam-6705	376	6	the	the	DET
ejpam-6705	376	7	following	following	ADJ
ejpam-6705	376	8	result	result	NOUN
ejpam-6705	376	9	can	can	AUX
ejpam-6705	376	10	be	be	AUX
ejpam-6705	376	11	obtained∫	obtained∫	ADJ
ejpam-6705	376	12	gb(vs	gb(vs	ADJ
ejpam-6705	376	13	,	,	PUNCT
ejpam-6705	376	14	vs	vs	ADP
ejpam-6705	376	15	,	,	PUNCT
ejpam-6705	376	16	vr	vr	NOUN
ejpam-6705	376	17	)	)	PUNCT
ejpam-6705	376	18	0	0	NUM
ejpam-6705	377	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	377	2	≤	≤	PROPN
ejpam-6705	377	3	∫	∫	PROPN
ejpam-6705	377	4	l[gb(vs	l[gb(vs	PROPN
ejpam-6705	377	5	,	,	PUNCT
ejpam-6705	377	6	vs	vs	ADP
ejpam-6705	377	7	,	,	PUNCT
ejpam-6705	377	8	vs+1)+gb(vs+1,vs+1,vr	vs+1)+gb(vs+1,vs+1,vr	NUM
ejpam-6705	377	9	)	)	PUNCT
ejpam-6705	377	10	]	]	PUNCT
ejpam-6705	377	11	0	0	NUM
ejpam-6705	378	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	378	2	s.	s.	PROPN
ejpam-6705	378	3	batul	batul	PROPN
ejpam-6705	378	4	et	et	PROPN
ejpam-6705	378	5	al	al	PROPN
ejpam-6705	378	6	.	.	PUNCT
ejpam-6705	378	7	/	/	SYM
ejpam-6705	378	8	eur	eur	PROPN
ejpam-6705	378	9	.	.	PUNCT
ejpam-6705	379	1	j.	j.	PROPN
ejpam-6705	379	2	pure	pure	PROPN
ejpam-6705	379	3	appl	appl	PROPN
ejpam-6705	379	4	.	.	PROPN
ejpam-6705	379	5	math	math	PROPN
ejpam-6705	379	6	,	,	PUNCT
ejpam-6705	379	7	18	18	NUM
ejpam-6705	379	8	(	(	PUNCT
ejpam-6705	379	9	4	4	NUM
ejpam-6705	379	10	)	)	PUNCT
ejpam-6705	379	11	(	(	PUNCT
ejpam-6705	379	12	2025	2025	NUM
ejpam-6705	379	13	)	)	PUNCT
ejpam-6705	379	14	,	,	PUNCT
ejpam-6705	379	15	6705	6705	NUM
ejpam-6705	379	16	15	15	NUM
ejpam-6705	379	17	of	of	ADP
ejpam-6705	379	18	23	23	NUM
ejpam-6705	379	19	=	=	SYM
ejpam-6705	379	20	∫	∫	PROPN
ejpam-6705	379	21	lgb(vs	lgb(vs	NOUN
ejpam-6705	379	22	,	,	PUNCT
ejpam-6705	379	23	vs	vs	ADP
ejpam-6705	379	24	,	,	PUNCT
ejpam-6705	379	25	vs+1)+lgb(vs+1,vs+1,vr	vs+1)+lgb(vs+1,vs+1,vr	NOUN
ejpam-6705	379	26	)	)	PUNCT
ejpam-6705	379	27	0	0	NUM
ejpam-6705	380	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	380	2	≤	≤	PROPN
ejpam-6705	380	3	∫	∫	PROPN
ejpam-6705	380	4	lgb(vs	lgb(vs	PROPN
ejpam-6705	380	5	,	,	PUNCT
ejpam-6705	380	6	vs	vs	ADP
ejpam-6705	380	7	,	,	PUNCT
ejpam-6705	380	8	vs+1	vs+1	NOUN
ejpam-6705	380	9	)	)	PUNCT
ejpam-6705	380	10	0	0	NUM
ejpam-6705	381	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	381	2	∫	∫	NOUN
ejpam-6705	381	3	lgb(vs+1,vs+1,vr	lgb(vs+1,vs+1,vr	PROPN
ejpam-6705	381	4	)	)	PUNCT
ejpam-6705	381	5	0	0	NUM
ejpam-6705	382	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	382	2	≤	≤	PROPN
ejpam-6705	382	3	∫	∫	PROPN
ejpam-6705	382	4	lgb(vs	lgb(vs	PROPN
ejpam-6705	382	5	,	,	PUNCT
ejpam-6705	382	6	vs	vs	ADP
ejpam-6705	382	7	,	,	PUNCT
ejpam-6705	382	8	vs+1	vs+1	NOUN
ejpam-6705	382	9	)	)	PUNCT
ejpam-6705	382	10	0	0	NUM
ejpam-6705	383	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	383	2	+	+	CCONJ
ejpam-6705	383	3	∫	∫	PROPN
ejpam-6705	383	4	l[l(gb(vs+1,vs+1,vs+2)+gb(vs+2,vs+2,vr	l[l(gb(vs+1,vs+1,vs+2)+gb(vs+2,vs+2,vr	NUM
ejpam-6705	383	5	)	)	PUNCT
ejpam-6705	383	6	)	)	PUNCT
ejpam-6705	383	7	]	]	PUNCT
ejpam-6705	384	1	0	0	NUM
ejpam-6705	385	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	385	2	≤	≤	PROPN
ejpam-6705	385	3	∫	∫	PROPN
ejpam-6705	385	4	lgb(vs	lgb(vs	PROPN
ejpam-6705	385	5	,	,	PUNCT
ejpam-6705	385	6	vs	vs	ADP
ejpam-6705	385	7	,	,	PUNCT
ejpam-6705	385	8	vs+1	vs+1	NOUN
ejpam-6705	385	9	)	)	PUNCT
ejpam-6705	385	10	0	0	NUM
ejpam-6705	386	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	386	2	∫	∫	PROPN
ejpam-6705	386	3	l2gb(vs+1,vs+1,vs+2	l2gb(vs+1,vs+1,vs+2	PROPN
ejpam-6705	386	4	)	)	PUNCT
ejpam-6705	386	5	0	0	NUM
ejpam-6705	387	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	387	2	+	+	CCONJ
ejpam-6705	387	3	∫	∫	PROPN
ejpam-6705	387	4	l2gb(vs+2,vs+2,vr	l2gb(vs+2,vs+2,vr	NOUN
ejpam-6705	387	5	)	)	PUNCT
ejpam-6705	387	6	0	0	NUM
ejpam-6705	388	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	388	2	≤	≤	PROPN
ejpam-6705	388	3	∫	∫	PROPN
ejpam-6705	388	4	lgb(vs	lgb(vs	PROPN
ejpam-6705	388	5	,	,	PUNCT
ejpam-6705	388	6	vs	vs	ADP
ejpam-6705	388	7	,	,	PUNCT
ejpam-6705	388	8	vs+1	vs+1	NOUN
ejpam-6705	388	9	)	)	PUNCT
ejpam-6705	388	10	0	0	NUM
ejpam-6705	389	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	389	2	∫	∫	PROPN
ejpam-6705	389	3	l2gb(vs+1,vs+1,vs+2	l2gb(vs+1,vs+1,vs+2	PROPN
ejpam-6705	389	4	)	)	PUNCT
ejpam-6705	389	5	0	0	NUM
ejpam-6705	390	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	390	2	+	+	CCONJ
ejpam-6705	390	3	∫	∫	PROPN
ejpam-6705	390	4	l3gb(vs+2,vs+2,vs+3	l3gb(vs+2,vs+2,vs+3	NOUN
ejpam-6705	390	5	)	)	PUNCT
ejpam-6705	390	6	0	0	NUM
ejpam-6705	390	7	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	390	8	.	.	PUNCT
ejpam-6705	390	9	.	.	PUNCT
ejpam-6705	391	1	.+	.+	NOUN
ejpam-6705	391	2	∫	∫	PROPN
ejpam-6705	391	3	lr−sgb(vr−2,vr−2,vr−1	lr−sgb(vr−2,vr−2,vr−1	PROPN
ejpam-6705	391	4	)	)	PUNCT
ejpam-6705	391	5	0	0	NUM
ejpam-6705	392	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	392	2	+	+	CCONJ
ejpam-6705	392	3	∫	∫	PROPN
ejpam-6705	392	4	lr−sgb(vr−1,vr−1,vr	lr−sgb(vr−1,vr−1,vr	PROPN
ejpam-6705	392	5	)	)	PUNCT
ejpam-6705	392	6	0	0	NUM
ejpam-6705	393	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	393	2	≤	≤	NUM
ejpam-6705	393	3	sσs	sσs	NOUN
ejpam-6705	393	4	(	(	PUNCT
ejpam-6705	393	5	∫	∫	PROPN
ejpam-6705	393	6	l[gb(v0,v0,v1)+gb(u0,u0,u1	l[gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	393	7	)	)	PUNCT
ejpam-6705	393	8	]	]	PUNCT
ejpam-6705	393	9	0	0	NUM
ejpam-6705	393	10	g(t)dt	g(t)dt	PROPN
ejpam-6705	393	11	)	)	PUNCT
ejpam-6705	394	1	+	+	CCONJ
ejpam-6705	394	2	(	(	PUNCT
ejpam-6705	394	3	s+	s+	X
ejpam-6705	394	4	1)σs+1	1)σs+1	NUM
ejpam-6705	394	5	(	(	PUNCT
ejpam-6705	394	6	∫	∫	PROPN
ejpam-6705	394	7	l2[gb(v0,v0,v1)+gb(u0,u0,u1	l2[gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	394	8	)	)	PUNCT
ejpam-6705	394	9	]	]	PUNCT
ejpam-6705	394	10	0	0	NUM
ejpam-6705	394	11	g(t)dt	g(t)dt	PROPN
ejpam-6705	394	12	)	)	PUNCT
ejpam-6705	395	1	+	+	CCONJ
ejpam-6705	395	2	(	(	PUNCT
ejpam-6705	395	3	s+	s+	NUM
ejpam-6705	395	4	2)σs+2	2)σs+2	NUM
ejpam-6705	395	5	(	(	PUNCT
ejpam-6705	395	6	∫	∫	PROPN
ejpam-6705	395	7	l3[gb(v0,v0,v1)+gb(u0,u0,u1	l3[gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	395	8	)	)	PUNCT
ejpam-6705	395	9	]	]	PUNCT
ejpam-6705	396	1	o	o	X
ejpam-6705	396	2	g(t)dt	g(t)dt	PROPN
ejpam-6705	396	3	)	)	PUNCT
ejpam-6705	397	1	+	+	CCONJ
ejpam-6705	397	2	.	.	PUNCT
ejpam-6705	397	3	.	.	PUNCT
ejpam-6705	398	1	.+	.+	NOUN
ejpam-6705	398	2	(	(	PUNCT
ejpam-6705	398	3	r	r	NOUN
ejpam-6705	398	4	−	−	PROPN
ejpam-6705	398	5	2)σr−2	2)σr−2	NUM
ejpam-6705	398	6	(	(	PUNCT
ejpam-6705	398	7	∫	∫	PROPN
ejpam-6705	398	8	lr−s[gb(v0,v0,v1)+gb(u0,u0,u1	lr−s[gb(v0,v0,v1)+gb(u0,u0,u1	X
ejpam-6705	398	9	)	)	PUNCT
ejpam-6705	398	10	]	]	PUNCT
ejpam-6705	398	11	0	0	NUM
ejpam-6705	398	12	g(t)dt	g(t)dt	PROPN
ejpam-6705	398	13	)	)	PUNCT
ejpam-6705	399	1	+	+	CCONJ
ejpam-6705	399	2	(	(	PUNCT
ejpam-6705	399	3	r	r	NOUN
ejpam-6705	399	4	−	−	PROPN
ejpam-6705	399	5	1)σr−1	1)σr−1	PROPN
ejpam-6705	399	6	(	(	PUNCT
ejpam-6705	399	7	∫	∫	PROPN
ejpam-6705	399	8	lr−s[gb(v0,v0,v1)+gb(u0,u0,u1	lr−s[gb(v0,v0,v1)+gb(u0,u0,u1	PUNCT
ejpam-6705	399	9	)	)	PUNCT
ejpam-6705	399	10	]	]	PUNCT
ejpam-6705	399	11	0	0	NUM
ejpam-6705	399	12	g(t)dt	g(t)dt	NOUN
ejpam-6705	399	13	)	)	PUNCT
ejpam-6705	400	1	=	=	PUNCT
ejpam-6705	401	1	i	i	PRON
ejpam-6705	401	2	=	=	PROPN
ejpam-6705	401	3	r−1∑	r−1∑	PROPN
ejpam-6705	401	4	i	i	PROPN
ejpam-6705	401	5	=	=	PROPN
ejpam-6705	401	6	s	s	PART
ejpam-6705	401	7	iσi	iσi	NOUN
ejpam-6705	401	8	(	(	PUNCT
ejpam-6705	401	9	∫	∫	PROPN
ejpam-6705	401	10	li−s+1[gb(v0,v0,v1)+gb(u0,u0,u1	li−s+1[gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	401	11	)	)	PUNCT
ejpam-6705	401	12	]	]	PUNCT
ejpam-6705	401	13	0	0	NUM
ejpam-6705	401	14	g(t)dt	g(t)dt	PROPN
ejpam-6705	401	15	)	)	PUNCT
ejpam-6705	401	16	≤	≤	NOUN
ejpam-6705	402	1	∞∑	∞∑	NUM
ejpam-6705	402	2	i	i	PRON
ejpam-6705	402	3	=	=	NOUN
ejpam-6705	402	4	s	s	PART
ejpam-6705	402	5	iσi	iσi	NOUN
ejpam-6705	402	6	(	(	PUNCT
ejpam-6705	402	7	∫	∫	PROPN
ejpam-6705	402	8	li−s+1[gb(v0,v0,v1)+gb(u0,u0,u1	li−s+1[gb(v0,v0,v1)+gb(u0,u0,u1	PROPN
ejpam-6705	402	9	)	)	PUNCT
ejpam-6705	402	10	]	]	PUNCT
ejpam-6705	402	11	0	0	NUM
ejpam-6705	402	12	g(t)dt	g(t)dt	PROPN
ejpam-6705	402	13	)	)	PUNCT
ejpam-6705	402	14	.	.	PUNCT
ejpam-6705	403	1	since	since	SCONJ
ejpam-6705	403	2	∞∑	∞∑	NUM
ejpam-6705	403	3	i	i	NOUN
ejpam-6705	403	4	=	=	NOUN
ejpam-6705	403	5	s	s	PART
ejpam-6705	403	6	iσi(t	iσi(t	NOUN
ejpam-6705	403	7	)	)	PUNCT
ejpam-6705	403	8	<	<	X
ejpam-6705	403	9	∞	∞	PROPN
ejpam-6705	403	10	for	for	ADP
ejpam-6705	403	11	all	all	DET
ejpam-6705	403	12	t	t	NOUN
ejpam-6705	403	13	∈	∈	PROPN
ejpam-6705	404	1	[	[	X
ejpam-6705	404	2	0,+∞	0,+∞	NUM
ejpam-6705	404	3	)	)	PUNCT
ejpam-6705	404	4	,	,	PUNCT
ejpam-6705	404	5	then	then	ADV
ejpam-6705	404	6	lim	lim	PROPN
ejpam-6705	404	7	s	s	PROPN
ejpam-6705	404	8	,	,	PUNCT
ejpam-6705	404	9	r→∞	r→∞	PROPN
ejpam-6705	404	10	gb(vs	gb(vs	PROPN
ejpam-6705	404	11	,	,	PUNCT
ejpam-6705	404	12	vs	vs	ADP
ejpam-6705	404	13	,	,	PUNCT
ejpam-6705	404	14	vr	vr	NOUN
ejpam-6705	404	15	)	)	PUNCT
ejpam-6705	404	16	=	=	SYM
ejpam-6705	404	17	0	0	NUM
ejpam-6705	405	1	and	and	CCONJ
ejpam-6705	405	2	(	(	PUNCT
ejpam-6705	405	3	vs	vs	ADP
ejpam-6705	405	4	)	)	PUNCT
ejpam-6705	405	5	is	be	AUX
ejpam-6705	405	6	a	a	DET
ejpam-6705	405	7	s.	s.	PROPN
ejpam-6705	405	8	batul	batul	PROPN
ejpam-6705	405	9	et	et	PROPN
ejpam-6705	405	10	al	al	PROPN
ejpam-6705	405	11	.	.	PUNCT
ejpam-6705	405	12	/	/	SYM
ejpam-6705	405	13	eur	eur	PROPN
ejpam-6705	405	14	.	.	PUNCT
ejpam-6705	406	1	j.	j.	PROPN
ejpam-6705	406	2	pure	pure	PROPN
ejpam-6705	406	3	appl	appl	PROPN
ejpam-6705	406	4	.	.	PROPN
ejpam-6705	406	5	math	math	PROPN
ejpam-6705	406	6	,	,	PUNCT
ejpam-6705	406	7	18	18	NUM
ejpam-6705	406	8	(	(	PUNCT
ejpam-6705	406	9	4	4	NUM
ejpam-6705	406	10	)	)	PUNCT
ejpam-6705	406	11	(	(	PUNCT
ejpam-6705	406	12	2025	2025	NUM
ejpam-6705	406	13	)	)	PUNCT
ejpam-6705	406	14	,	,	PUNCT
ejpam-6705	406	15	6705	6705	NUM
ejpam-6705	406	16	16	16	NUM
ejpam-6705	406	17	of	of	ADP
ejpam-6705	406	18	23	23	NUM
ejpam-6705	406	19	cauchy	cauchy	NOUN
ejpam-6705	406	20	sequence	sequence	NOUN
ejpam-6705	406	21	in	in	ADP
ejpam-6705	406	22	x	x	X
ejpam-6705	406	23	,	,	PUNCT
ejpam-6705	406	24	which	which	PRON
ejpam-6705	406	25	is	be	AUX
ejpam-6705	406	26	a	a	DET
ejpam-6705	406	27	complete	complete	ADJ
ejpam-6705	406	28	gb	gb	ADV
ejpam-6705	406	29	-	-	PUNCT
ejpam-6705	406	30	metric	metric	ADJ
ejpam-6705	406	31	space	space	NOUN
ejpam-6705	406	32	,	,	PUNCT
ejpam-6705	406	33	there	there	PRON
ejpam-6705	406	34	exist	exist	VERB
ejpam-6705	406	35	u	u	NOUN
ejpam-6705	406	36	,	,	PUNCT
ejpam-6705	406	37	v	v	NOUN
ejpam-6705	406	38	∈	∈	NOUN
ejpam-6705	406	39	x	x	PUNCT
ejpam-6705	406	40	such	such	ADJ
ejpam-6705	406	41	that	that	SCONJ
ejpam-6705	406	42	lim	lim	PROPN
ejpam-6705	406	43	s→∞	s→∞	VERB
ejpam-6705	406	44	us	we	PRON
ejpam-6705	407	1	=	=	PUNCT
ejpam-6705	407	2	u	u	PROPN
ejpam-6705	407	3	and	and	CCONJ
ejpam-6705	407	4	lim	lim	PROPN
ejpam-6705	407	5	s→∞	s→∞	PROPN
ejpam-6705	407	6	vs	vs	ADP
ejpam-6705	407	7	=	=	PUNCT
ejpam-6705	408	1	v.	v.	ADV
ejpam-6705	408	2	since	since	SCONJ
ejpam-6705	408	3	t	t	PROPN
ejpam-6705	408	4	is	be	AUX
ejpam-6705	408	5	continuous	continuous	ADJ
ejpam-6705	408	6	,	,	PUNCT
ejpam-6705	408	7	it	it	PRON
ejpam-6705	408	8	follows	follow	VERB
ejpam-6705	408	9	that	that	SCONJ
ejpam-6705	408	10	t	t	PROPN
ejpam-6705	408	11	(	(	PUNCT
ejpam-6705	408	12	u	u	NOUN
ejpam-6705	408	13	,	,	PUNCT
ejpam-6705	408	14	v	v	NOUN
ejpam-6705	408	15	)	)	PUNCT
ejpam-6705	408	16	=	=	SYM
ejpam-6705	408	17	u	u	NOUN
ejpam-6705	408	18	and	and	CCONJ
ejpam-6705	408	19	t	t	PROPN
ejpam-6705	408	20	(	(	PUNCT
ejpam-6705	408	21	v	v	NOUN
ejpam-6705	408	22	,	,	PUNCT
ejpam-6705	408	23	u	u	NOUN
ejpam-6705	408	24	)	)	PUNCT
ejpam-6705	408	25	=	=	SYM
ejpam-6705	408	26	v	v	NOUN
ejpam-6705	408	27	,	,	PUNCT
ejpam-6705	408	28	that	that	ADV
ejpam-6705	408	29	is	is	ADV
ejpam-6705	408	30	,	,	PUNCT
ejpam-6705	408	31	(	(	PUNCT
ejpam-6705	408	32	u	u	NOUN
ejpam-6705	408	33	,	,	PUNCT
ejpam-6705	408	34	v	v	NOUN
ejpam-6705	408	35	)	)	PUNCT
ejpam-6705	408	36	is	be	AUX
ejpam-6705	408	37	a	a	DET
ejpam-6705	408	38	coupled	couple	VERB
ejpam-6705	408	39	fixed	fix	VERB
ejpam-6705	408	40	point	point	NOUN
ejpam-6705	408	41	of	of	ADP
ejpam-6705	408	42	t	t	PROPN
ejpam-6705	408	43	.	.	PUNCT
ejpam-6705	409	1	theorem	theorem	ADJ
ejpam-6705	409	2	4	4	NUM
ejpam-6705	409	3	.	.	PUNCT
ejpam-6705	410	1	let	let	AUX
ejpam-6705	410	2	(	(	PUNCT
ejpam-6705	410	3	x	x	X
ejpam-6705	410	4	,	,	PUNCT
ejpam-6705	410	5	gb,≼	gb,≼	NOUN
ejpam-6705	410	6	)	)	PUNCT
ejpam-6705	410	7	be	be	AUX
ejpam-6705	410	8	a	a	DET
ejpam-6705	410	9	partially	partially	ADV
ejpam-6705	410	10	ordered	order	VERB
ejpam-6705	410	11	complete	complete	ADJ
ejpam-6705	410	12	gb	gb	ADV
ejpam-6705	410	13	-	-	PUNCT
ejpam-6705	410	14	metric	metric	ADJ
ejpam-6705	410	15	space	space	NOUN
ejpam-6705	410	16	satisfying	satisfy	VERB
ejpam-6705	410	17	the	the	DET
ejpam-6705	410	18	following	follow	VERB
ejpam-6705	410	19	conditions	condition	NOUN
ejpam-6705	410	20	:	:	PUNCT
ejpam-6705	410	21	(	(	PUNCT
ejpam-6705	410	22	i	i	NOUN
ejpam-6705	410	23	)	)	PUNCT
ejpam-6705	410	24	if	if	SCONJ
ejpam-6705	410	25	(	(	PUNCT
ejpam-6705	410	26	us	we	PRON
ejpam-6705	410	27	)	)	PUNCT
ejpam-6705	410	28	is	be	AUX
ejpam-6705	410	29	non	non	ADJ
ejpam-6705	410	30	-	-	ADJ
ejpam-6705	410	31	decreasing	decrease	VERB
ejpam-6705	410	32	sequence	sequence	NOUN
ejpam-6705	410	33	which	which	PRON
ejpam-6705	410	34	converges	converge	VERB
ejpam-6705	410	35	to	to	ADP
ejpam-6705	410	36	u	u	PROPN
ejpam-6705	410	37	∈	∈	PROPN
ejpam-6705	411	1	x	x	X
ejpam-6705	411	2	,	,	PUNCT
ejpam-6705	411	3	then	then	ADV
ejpam-6705	411	4	us	we	PRON
ejpam-6705	411	5	≼	≼	ADJ
ejpam-6705	411	6	u	u	NOUN
ejpam-6705	411	7	∀	∀	X
ejpam-6705	411	8	s.	s.	PROPN
ejpam-6705	411	9	(	(	PUNCT
ejpam-6705	411	10	ii	ii	PROPN
ejpam-6705	411	11	)	)	PUNCT
ejpam-6705	411	12	if	if	SCONJ
ejpam-6705	411	13	(	(	PUNCT
ejpam-6705	411	14	vs	vs	NOUN
ejpam-6705	411	15	)	)	PUNCT
ejpam-6705	411	16	is	be	AUX
ejpam-6705	411	17	non	non	ADJ
ejpam-6705	411	18	-	-	ADJ
ejpam-6705	411	19	increasing	increasing	ADJ
ejpam-6705	411	20	sequence	sequence	NOUN
ejpam-6705	411	21	which	which	PRON
ejpam-6705	411	22	converges	converge	VERB
ejpam-6705	411	23	to	to	ADP
ejpam-6705	411	24	v	v	NUM
ejpam-6705	411	25	∈	∈	PROPN
ejpam-6705	411	26	x	x	X
ejpam-6705	411	27	,	,	PUNCT
ejpam-6705	411	28	then	then	ADV
ejpam-6705	411	29	vs	vs	ADP
ejpam-6705	411	30	≽	≽	PROPN
ejpam-6705	411	31	v	v	PROPN
ejpam-6705	411	32	∀	∀	NOUN
ejpam-6705	411	33	s.	s.	PROPN
ejpam-6705	411	34	also	also	ADV
ejpam-6705	411	35	suppose	suppose	VERB
ejpam-6705	411	36	that	that	SCONJ
ejpam-6705	411	37	t	t	NOUN
ejpam-6705	411	38	:	:	PUNCT
ejpam-6705	411	39	x	x	PUNCT
ejpam-6705	411	40	×	×	NOUN
ejpam-6705	411	41	x	x	PUNCT
ejpam-6705	411	42	→	→	PUNCT
ejpam-6705	411	43	x	x	X
ejpam-6705	411	44	is	be	AUX
ejpam-6705	411	45	a	a	DET
ejpam-6705	411	46	continuous	continuous	ADJ
ejpam-6705	411	47	function	function	NOUN
ejpam-6705	411	48	having	have	VERB
ejpam-6705	411	49	the	the	DET
ejpam-6705	411	50	mixed	mixed	ADJ
ejpam-6705	411	51	monotone	monotone	ADJ
ejpam-6705	411	52	property	property	NOUN
ejpam-6705	411	53	on	on	ADP
ejpam-6705	411	54	x	x	SYM
ejpam-6705	411	55	such	such	ADJ
ejpam-6705	411	56	that	that	DET
ejpam-6705	411	57	∫	∫	PROPN
ejpam-6705	411	58	gb(t	gb(t	X
ejpam-6705	411	59	(	(	PUNCT
ejpam-6705	411	60	u	u	NOUN
ejpam-6705	411	61	,	,	PUNCT
ejpam-6705	411	62	v),t	v),t	PROPN
ejpam-6705	411	63	(	(	PUNCT
ejpam-6705	411	64	m	m	PROPN
ejpam-6705	411	65	,	,	PUNCT
ejpam-6705	411	66	n),t	n),t	PROPN
ejpam-6705	411	67	(	(	PUNCT
ejpam-6705	411	68	f	f	X
ejpam-6705	411	69	,	,	PUNCT
ejpam-6705	411	70	w	w	NOUN
ejpam-6705	411	71	)	)	PUNCT
ejpam-6705	411	72	)	)	PUNCT
ejpam-6705	411	73	0	0	NUM
ejpam-6705	412	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	412	2	≤	≤	PROPN
ejpam-6705	412	3	σ	σ	PROPN
ejpam-6705	412	4	(	(	PUNCT
ejpam-6705	412	5	∫	∫	PROPN
ejpam-6705	412	6	gb(u	gb(u	PROPN
ejpam-6705	412	7	,	,	PUNCT
ejpam-6705	412	8	m	m	NOUN
ejpam-6705	412	9	,	,	PUNCT
ejpam-6705	412	10	f)+gb(v	f)+gb(v	NOUN
ejpam-6705	412	11	,	,	PUNCT
ejpam-6705	412	12	n	n	CCONJ
ejpam-6705	412	13	,	,	PUNCT
ejpam-6705	412	14	w	w	NOUN
ejpam-6705	412	15	)	)	PUNCT
ejpam-6705	412	16	0	0	NUM
ejpam-6705	412	17	g(t)dt	g(t)dt	PROPN
ejpam-6705	412	18	)	)	PUNCT
ejpam-6705	412	19	,	,	PUNCT
ejpam-6705	412	20	(	(	PUNCT
ejpam-6705	412	21	8)	8)	NUM
ejpam-6705	412	22	where	where	SCONJ
ejpam-6705	412	23	u	u	NOUN
ejpam-6705	412	24	,	,	PUNCT
ejpam-6705	412	25	v	v	NOUN
ejpam-6705	412	26	,	,	PUNCT
ejpam-6705	412	27	w	w	PROPN
ejpam-6705	412	28	,	,	PUNCT
ejpam-6705	412	29	m	m	PROPN
ejpam-6705	412	30	,	,	PUNCT
ejpam-6705	412	31	n	n	CCONJ
ejpam-6705	412	32	,	,	PUNCT
ejpam-6705	412	33	f	f	PROPN
ejpam-6705	412	34	∈	∈	PROPN
ejpam-6705	412	35	x	x	X
ejpam-6705	412	36	and	and	CCONJ
ejpam-6705	412	37	g	g	NOUN
ejpam-6705	412	38	:	:	PUNCT
ejpam-6705	413	1	[	[	X
ejpam-6705	413	2	0,∞	0,∞	NOUN
ejpam-6705	413	3	)	)	PUNCT
ejpam-6705	413	4	→	→	PUNCT
ejpam-6705	414	1	[	[	X
ejpam-6705	414	2	0,∞	0,∞	NUM
ejpam-6705	414	3	)	)	PUNCT
ejpam-6705	414	4	is	be	AUX
ejpam-6705	414	5	a	a	DET
ejpam-6705	414	6	lebesgue	lebesgue	NOUN
ejpam-6705	414	7	integrable	integrable	ADJ
ejpam-6705	414	8	mapping	mapping	NOUN
ejpam-6705	414	9	with	with	ADP
ejpam-6705	414	10	f	f	PROPN
ejpam-6705	414	11	≼	≼	PROPN
ejpam-6705	414	12	m	m	VERB
ejpam-6705	414	13	≼	≼	ADJ
ejpam-6705	414	14	u	u	NOUN
ejpam-6705	414	15	and	and	CCONJ
ejpam-6705	414	16	v	v	ADP
ejpam-6705	414	17	≼	≼	NOUN
ejpam-6705	414	18	n	n	PROPN
ejpam-6705	414	19	≼	≼	PROPN
ejpam-6705	414	20	w	w	PROPN
ejpam-6705	414	21	,	,	PUNCT
ejpam-6705	414	22	where	where	SCONJ
ejpam-6705	414	23	either	either	CCONJ
ejpam-6705	414	24	m	m	VERB
ejpam-6705	414	25	̸=	̸=	PROPN
ejpam-6705	414	26	f	f	PROPN
ejpam-6705	414	27	or	or	CCONJ
ejpam-6705	414	28	n	n	PRON
ejpam-6705	414	29	̸=	̸=	PROPN
ejpam-6705	414	30	w.	w.	NOUN
ejpam-6705	414	31	if	if	SCONJ
ejpam-6705	414	32	there	there	PRON
ejpam-6705	414	33	exist	exist	VERB
ejpam-6705	414	34	u0	u0	ADJ
ejpam-6705	414	35	,	,	PUNCT
ejpam-6705	414	36	v0	v0	NOUN
ejpam-6705	414	37	∈	∈	PROPN
ejpam-6705	414	38	x	x	PUNCT
ejpam-6705	414	39	such	such	ADJ
ejpam-6705	414	40	that	that	DET
ejpam-6705	414	41	u0	u0	ADJ
ejpam-6705	414	42	≼	≼	PROPN
ejpam-6705	414	43	h(u0	h(u0	PROPN
ejpam-6705	414	44	,	,	PUNCT
ejpam-6705	414	45	v0	v0	PROPN
ejpam-6705	414	46	)	)	PUNCT
ejpam-6705	414	47	and	and	CCONJ
ejpam-6705	414	48	(	(	PUNCT
ejpam-6705	414	49	v0	v0	PROPN
ejpam-6705	414	50	,	,	PUNCT
ejpam-6705	414	51	u0	u0	ADJ
ejpam-6705	414	52	)	)	PUNCT
ejpam-6705	414	53	≼	≼	ADJ
ejpam-6705	414	54	v0	v0	NOUN
ejpam-6705	414	55	,	,	PUNCT
ejpam-6705	414	56	then	then	ADV
ejpam-6705	414	57	t	t	PROPN
ejpam-6705	414	58	has	have	VERB
ejpam-6705	414	59	a	a	DET
ejpam-6705	414	60	coupled	couple	VERB
ejpam-6705	414	61	fixed	fix	VERB
ejpam-6705	414	62	point	point	NOUN
ejpam-6705	414	63	in	in	ADP
ejpam-6705	414	64	x	x	X
ejpam-6705	414	65	.	.	PUNCT
ejpam-6705	415	1	proof	proof	NOUN
ejpam-6705	415	2	.	.	PUNCT
ejpam-6705	416	1	using	use	VERB
ejpam-6705	416	2	the	the	DET
ejpam-6705	416	3	similar	similar	ADJ
ejpam-6705	416	4	approach	approach	NOUN
ejpam-6705	416	5	to	to	ADP
ejpam-6705	416	6	that	that	PRON
ejpam-6705	416	7	in	in	ADP
ejpam-6705	416	8	the	the	DET
ejpam-6705	416	9	proof	proof	NOUN
ejpam-6705	416	10	of	of	ADP
ejpam-6705	416	11	theorem	theorem	NOUN
ejpam-6705	416	12	3	3	NUM
ejpam-6705	416	13	,	,	PUNCT
ejpam-6705	416	14	gives	give	VERB
ejpam-6705	416	15	two	two	NUM
ejpam-6705	416	16	cauchy	cauchy	ADJ
ejpam-6705	416	17	sequences	sequence	NOUN
ejpam-6705	416	18	(	(	PUNCT
ejpam-6705	416	19	us	us	PROPN
ejpam-6705	416	20	)	)	PUNCT
ejpam-6705	416	21	and	and	CCONJ
ejpam-6705	416	22	(	(	PUNCT
ejpam-6705	416	23	vs	vs	NOUN
ejpam-6705	416	24	)	)	PUNCT
ejpam-6705	416	25	∈	∈	PROPN
ejpam-6705	416	26	x	x	X
ejpam-6705	416	27	.	.	PUNCT
ejpam-6705	417	1	conditions	condition	NOUN
ejpam-6705	417	2	(	(	PUNCT
ejpam-6705	417	3	i	i	NOUN
ejpam-6705	417	4	)	)	PUNCT
ejpam-6705	417	5	and	and	CCONJ
ejpam-6705	417	6	(	(	PUNCT
ejpam-6705	417	7	ii	ii	NOUN
ejpam-6705	417	8	)	)	PUNCT
ejpam-6705	417	9	implies	imply	VERB
ejpam-6705	417	10	that	that	SCONJ
ejpam-6705	417	11	there	there	PRON
ejpam-6705	417	12	exist	exist	VERB
ejpam-6705	417	13	u	u	NOUN
ejpam-6705	417	14	,	,	PUNCT
ejpam-6705	417	15	v	v	NOUN
ejpam-6705	417	16	∈	∈	NOUN
ejpam-6705	417	17	x	x	PUNCT
ejpam-6705	417	18	such	such	ADJ
ejpam-6705	417	19	that	that	SCONJ
ejpam-6705	417	20	us	we	PRON
ejpam-6705	417	21	≼	≼	ADJ
ejpam-6705	417	22	u	u	NOUN
ejpam-6705	417	23	and	and	CCONJ
ejpam-6705	417	24	vs	vs	ADP
ejpam-6705	417	25	≽	≽	PROPN
ejpam-6705	417	26	v	v	NOUN
ejpam-6705	417	27	for	for	ADP
ejpam-6705	417	28	all	all	DET
ejpam-6705	417	29	s	s	PART
ejpam-6705	417	30	≥	≥	NOUN
ejpam-6705	417	31	0	0	NUM
ejpam-6705	417	32	.	.	PUNCT
ejpam-6705	418	1	if	if	SCONJ
ejpam-6705	418	2	us	we	PRON
ejpam-6705	418	3	=	=	PUNCT
ejpam-6705	418	4	u	u	NOUN
ejpam-6705	418	5	and	and	CCONJ
ejpam-6705	418	6	vs	vs	ADP
ejpam-6705	418	7	=	=	ADJ
ejpam-6705	418	8	v	v	NOUN
ejpam-6705	418	9	for	for	ADP
ejpam-6705	418	10	some	some	DET
ejpam-6705	418	11	s	s	NOUN
ejpam-6705	418	12	,	,	PUNCT
ejpam-6705	418	13	then	then	ADV
ejpam-6705	418	14	us+1	us+1	PROPN
ejpam-6705	418	15	=	=	SYM
ejpam-6705	418	16	u	u	NOUN
ejpam-6705	418	17	and	and	CCONJ
ejpam-6705	418	18	vs+1	vs+1	NOUN
ejpam-6705	418	19	=	=	PUNCT
ejpam-6705	418	20	v	v	NOUN
ejpam-6705	418	21	;	;	PUNCT
ejpam-6705	418	22	that	that	PRON
ejpam-6705	418	23	is	is	ADV
ejpam-6705	418	24	,	,	PUNCT
ejpam-6705	418	25	(	(	PUNCT
ejpam-6705	418	26	u	u	NOUN
ejpam-6705	418	27	,	,	PUNCT
ejpam-6705	418	28	v	v	NOUN
ejpam-6705	418	29	)	)	PUNCT
ejpam-6705	418	30	is	be	AUX
ejpam-6705	418	31	a	a	DET
ejpam-6705	418	32	coupled	couple	VERB
ejpam-6705	418	33	fixed	fix	VERB
ejpam-6705	418	34	point	point	NOUN
ejpam-6705	418	35	.	.	PUNCT
ejpam-6705	419	1	now	now	ADV
ejpam-6705	419	2	,	,	PUNCT
ejpam-6705	419	3	without	without	ADP
ejpam-6705	419	4	loss	loss	NOUN
ejpam-6705	419	5	of	of	ADP
ejpam-6705	419	6	generality	generality	NOUN
ejpam-6705	419	7	,	,	PUNCT
ejpam-6705	419	8	let	let	VERB
ejpam-6705	419	9	either	either	CCONJ
ejpam-6705	419	10	us	we	PRON
ejpam-6705	419	11	̸=	̸=	PROPN
ejpam-6705	419	12	u	u	NOUN
ejpam-6705	419	13	or	or	CCONJ
ejpam-6705	419	14	vs	vs	ADP
ejpam-6705	419	15	̸=	̸=	PROPN
ejpam-6705	419	16	v.	v.	ADV
ejpam-6705	419	17	by	by	ADP
ejpam-6705	419	18	using	use	VERB
ejpam-6705	419	19	(	(	PUNCT
ejpam-6705	419	20	8),∫	8),∫	NUM
ejpam-6705	419	21	gb(t	gb(t	NOUN
ejpam-6705	419	22	(	(	PUNCT
ejpam-6705	419	23	u	u	NOUN
ejpam-6705	419	24	,	,	PUNCT
ejpam-6705	419	25	v),t	v),t	PROPN
ejpam-6705	419	26	(	(	PUNCT
ejpam-6705	419	27	u	u	NOUN
ejpam-6705	419	28	,	,	PUNCT
ejpam-6705	419	29	v),u	v),u	NOUN
ejpam-6705	419	30	)	)	PUNCT
ejpam-6705	419	31	0	0	NUM
ejpam-6705	420	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	420	2	≤	≤	NUM
ejpam-6705	420	3	∫	∫	PROPN
ejpam-6705	420	4	gb(t	gb(t	NOUN
ejpam-6705	420	5	(	(	PUNCT
ejpam-6705	420	6	u	u	NOUN
ejpam-6705	420	7	,	,	PUNCT
ejpam-6705	420	8	v),t	v),t	PROPN
ejpam-6705	420	9	(	(	PUNCT
ejpam-6705	420	10	u	u	NOUN
ejpam-6705	420	11	,	,	PUNCT
ejpam-6705	420	12	v),t	v),t	PROPN
ejpam-6705	420	13	(	(	PUNCT
ejpam-6705	420	14	us	us	PROPN
ejpam-6705	420	15	,	,	PUNCT
ejpam-6705	420	16	vs))+gb(t	vs))+gb(t	X
ejpam-6705	420	17	(	(	PUNCT
ejpam-6705	420	18	us	us	PROPN
ejpam-6705	420	19	,	,	PUNCT
ejpam-6705	420	20	vs),t	vs),t	X
ejpam-6705	420	21	(	(	PUNCT
ejpam-6705	420	22	us	we	PRON
ejpam-6705	420	23	,	,	PUNCT
ejpam-6705	420	24	vs),u	vs),u	ADJ
ejpam-6705	420	25	)	)	PUNCT
ejpam-6705	420	26	0	0	NUM
ejpam-6705	421	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	421	2	≤	≤	NUM
ejpam-6705	421	3	∫	∫	PROPN
ejpam-6705	421	4	gb(t	gb(t	NOUN
ejpam-6705	422	1	(	(	PUNCT
ejpam-6705	422	2	u	u	NOUN
ejpam-6705	422	3	,	,	PUNCT
ejpam-6705	422	4	v),t	v),t	PROPN
ejpam-6705	422	5	(	(	PUNCT
ejpam-6705	422	6	u	u	NOUN
ejpam-6705	422	7	,	,	PUNCT
ejpam-6705	422	8	v),t	v),t	PROPN
ejpam-6705	422	9	(	(	PUNCT
ejpam-6705	422	10	us	we	PRON
ejpam-6705	422	11	,	,	PUNCT
ejpam-6705	422	12	vs	vs	ADJ
ejpam-6705	422	13	)	)	PUNCT
ejpam-6705	422	14	)	)	PUNCT
ejpam-6705	422	15	0	0	NUM
ejpam-6705	423	1	g(t)dt+	g(t)dt+	NOUN
ejpam-6705	423	2	∫	∫	PROPN
ejpam-6705	423	3	gb(t	gb(t	PROPN
ejpam-6705	423	4	(	(	PUNCT
ejpam-6705	423	5	us	us	PROPN
ejpam-6705	423	6	,	,	PUNCT
ejpam-6705	423	7	vs),t	vs),t	X
ejpam-6705	423	8	(	(	PUNCT
ejpam-6705	423	9	us	we	PRON
ejpam-6705	423	10	,	,	PUNCT
ejpam-6705	423	11	vs),u	vs),u	ADJ
ejpam-6705	423	12	)	)	PUNCT
ejpam-6705	423	13	0	0	NUM
ejpam-6705	424	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	424	2	≤	≤	PROPN
ejpam-6705	424	3	σ	σ	PROPN
ejpam-6705	424	4	(	(	PUNCT
ejpam-6705	424	5	∫	∫	PROPN
ejpam-6705	424	6	gb(u	gb(u	PROPN
ejpam-6705	424	7	,	,	PUNCT
ejpam-6705	424	8	u	u	NOUN
ejpam-6705	424	9	,	,	PUNCT
ejpam-6705	424	10	us)+gb(v	us)+gb(v	PROPN
ejpam-6705	424	11	,	,	PUNCT
ejpam-6705	424	12	v	v	NOUN
ejpam-6705	424	13	,	,	PUNCT
ejpam-6705	424	14	vs	vs	ADJ
ejpam-6705	424	15	)	)	PUNCT
ejpam-6705	424	16	0	0	NUM
ejpam-6705	424	17	g(t)dt	g(t)dt	PROPN
ejpam-6705	424	18	)	)	PUNCT
ejpam-6705	425	1	+	+	CCONJ
ejpam-6705	425	2	∫	∫	PROPN
ejpam-6705	425	3	gb(us+1,us+1,u	gb(us+1,us+1,u	PROPN
ejpam-6705	425	4	)	)	PUNCT
ejpam-6705	425	5	0	0	NUM
ejpam-6705	426	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	426	2	.	.	PUNCT
ejpam-6705	427	1	hence	hence	ADV
ejpam-6705	427	2	,	,	PUNCT
ejpam-6705	427	3	from	from	ADP
ejpam-6705	427	4	above	above	ADP
ejpam-6705	427	5	with	with	ADP
ejpam-6705	427	6	s	s	PROPN
ejpam-6705	427	7	→	→	SYM
ejpam-6705	427	8	∞	∞	PROPN
ejpam-6705	427	9	,	,	PUNCT
ejpam-6705	427	10	we	we	PRON
ejpam-6705	427	11	get	get	VERB
ejpam-6705	427	12	g(t	g(t	PROPN
ejpam-6705	427	13	(	(	PUNCT
ejpam-6705	427	14	u	u	NOUN
ejpam-6705	427	15	,	,	PUNCT
ejpam-6705	427	16	v),t	v),t	PROPN
ejpam-6705	427	17	(	(	PUNCT
ejpam-6705	427	18	u	u	NOUN
ejpam-6705	427	19	,	,	PUNCT
ejpam-6705	427	20	v	v	NOUN
ejpam-6705	427	21	)	)	PUNCT
ejpam-6705	427	22	,	,	PUNCT
ejpam-6705	427	23	u	u	NOUN
ejpam-6705	427	24	)	)	PUNCT
ejpam-6705	427	25	=	=	SYM
ejpam-6705	427	26	0	0	NUM
ejpam-6705	427	27	,	,	PUNCT
ejpam-6705	427	28	which	which	PRON
ejpam-6705	427	29	gives	give	VERB
ejpam-6705	427	30	that	that	DET
ejpam-6705	427	31	t	t	NOUN
ejpam-6705	427	32	(	(	PUNCT
ejpam-6705	427	33	u	u	NOUN
ejpam-6705	427	34	,	,	PUNCT
ejpam-6705	427	35	v	v	NOUN
ejpam-6705	427	36	)	)	PUNCT
ejpam-6705	427	37	=	=	VERB
ejpam-6705	428	1	u.	u.	VERB
ejpam-6705	428	2	likewise	likewise	ADV
ejpam-6705	428	3	,	,	PUNCT
ejpam-6705	428	4	the	the	DET
ejpam-6705	428	5	same	same	ADJ
ejpam-6705	428	6	approach	approach	NOUN
ejpam-6705	428	7	can	can	AUX
ejpam-6705	428	8	be	be	AUX
ejpam-6705	428	9	applied	apply	VERB
ejpam-6705	428	10	to	to	PART
ejpam-6705	428	11	write	write	VERB
ejpam-6705	428	12	s.	s.	PROPN
ejpam-6705	428	13	batul	batul	PROPN
ejpam-6705	428	14	et	et	PROPN
ejpam-6705	428	15	al	al	PROPN
ejpam-6705	428	16	.	.	PUNCT
ejpam-6705	428	17	/	/	SYM
ejpam-6705	428	18	eur	eur	PROPN
ejpam-6705	428	19	.	.	PUNCT
ejpam-6705	429	1	j.	j.	PROPN
ejpam-6705	429	2	pure	pure	PROPN
ejpam-6705	429	3	appl	appl	PROPN
ejpam-6705	429	4	.	.	PROPN
ejpam-6705	429	5	math	math	PROPN
ejpam-6705	429	6	,	,	PUNCT
ejpam-6705	429	7	18	18	NUM
ejpam-6705	429	8	(	(	PUNCT
ejpam-6705	429	9	4	4	NUM
ejpam-6705	429	10	)	)	PUNCT
ejpam-6705	429	11	(	(	PUNCT
ejpam-6705	429	12	2025	2025	NUM
ejpam-6705	429	13	)	)	PUNCT
ejpam-6705	429	14	,	,	PUNCT
ejpam-6705	429	15	6705	6705	NUM
ejpam-6705	429	16	17	17	NUM
ejpam-6705	429	17	of	of	ADP
ejpam-6705	429	18	23	23	NUM
ejpam-6705	429	19	∫	∫	NOUN
ejpam-6705	429	20	gb(t	gb(t	NOUN
ejpam-6705	429	21	(	(	PUNCT
ejpam-6705	429	22	v	v	NOUN
ejpam-6705	429	23	,	,	PUNCT
ejpam-6705	429	24	u),t	u),t	PROPN
ejpam-6705	429	25	(	(	PUNCT
ejpam-6705	429	26	v	v	NOUN
ejpam-6705	429	27	,	,	PUNCT
ejpam-6705	429	28	u),v	u),v	NOUN
ejpam-6705	429	29	)	)	PUNCT
ejpam-6705	429	30	0	0	NUM
ejpam-6705	430	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	430	2	≤	≤	NUM
ejpam-6705	430	3	∫	∫	PROPN
ejpam-6705	430	4	gb(t	gb(t	X
ejpam-6705	431	1	(	(	PUNCT
ejpam-6705	431	2	v	v	NOUN
ejpam-6705	431	3	,	,	PUNCT
ejpam-6705	431	4	u),t	u),t	PROPN
ejpam-6705	431	5	(	(	PUNCT
ejpam-6705	431	6	v	v	NOUN
ejpam-6705	431	7	,	,	PUNCT
ejpam-6705	431	8	u),t	u),t	PROPN
ejpam-6705	431	9	(	(	PUNCT
ejpam-6705	431	10	vs	vs	X
ejpam-6705	431	11	,	,	PUNCT
ejpam-6705	431	12	us))+gb(t	us))+gb(t	X
ejpam-6705	431	13	(	(	PUNCT
ejpam-6705	431	14	vs	vs	ADP
ejpam-6705	431	15	,	,	PUNCT
ejpam-6705	431	16	us),t	us),t	X
ejpam-6705	431	17	(	(	PUNCT
ejpam-6705	431	18	vs	vs	X
ejpam-6705	431	19	,	,	PUNCT
ejpam-6705	431	20	us),v	us),v	NOUN
ejpam-6705	431	21	)	)	PUNCT
ejpam-6705	431	22	0	0	NUM
ejpam-6705	432	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	432	2	≤	≤	NUM
ejpam-6705	432	3	∫	∫	PROPN
ejpam-6705	433	1	gb(h(v	gb(h(v	NOUN
ejpam-6705	433	2	,	,	PUNCT
ejpam-6705	433	3	u),h(v	u),h(v	NUM
ejpam-6705	433	4	,	,	PUNCT
ejpam-6705	433	5	u),h(vs	u),h(vs	ADJ
ejpam-6705	433	6	,	,	PUNCT
ejpam-6705	433	7	us	we	PRON
ejpam-6705	433	8	)	)	PUNCT
ejpam-6705	433	9	)	)	PUNCT
ejpam-6705	434	1	0	0	NUM
ejpam-6705	435	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	435	2	+	+	CCONJ
ejpam-6705	435	3	∫	∫	PROPN
ejpam-6705	435	4	gb(t	gb(t	X
ejpam-6705	435	5	(	(	PUNCT
ejpam-6705	435	6	vs	vs	ADP
ejpam-6705	435	7	,	,	PUNCT
ejpam-6705	435	8	us),t	us),t	X
ejpam-6705	435	9	(	(	PUNCT
ejpam-6705	435	10	vs	vs	X
ejpam-6705	435	11	,	,	PUNCT
ejpam-6705	435	12	us),v	us),v	NOUN
ejpam-6705	435	13	)	)	PUNCT
ejpam-6705	435	14	0	0	NUM
ejpam-6705	436	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	436	2	≤	≤	PROPN
ejpam-6705	436	3	σ	σ	PROPN
ejpam-6705	436	4	(	(	PUNCT
ejpam-6705	436	5	∫	∫	PROPN
ejpam-6705	436	6	gb(v	gb(v	PROPN
ejpam-6705	436	7	,	,	PUNCT
ejpam-6705	436	8	v	v	NOUN
ejpam-6705	436	9	,	,	PUNCT
ejpam-6705	436	10	vs)+gb(u	vs)+gb(u	PROPN
ejpam-6705	436	11	,	,	PUNCT
ejpam-6705	436	12	u	u	NOUN
ejpam-6705	436	13	,	,	PUNCT
ejpam-6705	436	14	us	we	PRON
ejpam-6705	436	15	)	)	PUNCT
ejpam-6705	436	16	0	0	NUM
ejpam-6705	437	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	437	2	)	)	PUNCT
ejpam-6705	438	1	+	+	NUM
ejpam-6705	438	2	∫	∫	PROPN
ejpam-6705	438	3	gb(vs+1,vs+1,v	gb(vs+1,vs+1,v	PROPN
ejpam-6705	438	4	)	)	PUNCT
ejpam-6705	438	5	0	0	NUM
ejpam-6705	439	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	439	2	.	.	PUNCT
ejpam-6705	440	1	(	(	PUNCT
ejpam-6705	440	2	9	9	NUM
ejpam-6705	440	3	)	)	PUNCT
ejpam-6705	440	4	hence	hence	ADV
ejpam-6705	440	5	,	,	PUNCT
ejpam-6705	440	6	via	via	ADP
ejpam-6705	440	7	(	(	PUNCT
ejpam-6705	440	8	9	9	NUM
ejpam-6705	440	9	)	)	PUNCT
ejpam-6705	440	10	with	with	ADP
ejpam-6705	440	11	s	s	PROPN
ejpam-6705	440	12	→	→	SYM
ejpam-6705	440	13	∞	∞	PROPN
ejpam-6705	440	14	,	,	PUNCT
ejpam-6705	440	15	we	we	PRON
ejpam-6705	440	16	get	get	VERB
ejpam-6705	440	17	gb(t	gb(t	NOUN
ejpam-6705	440	18	(	(	PUNCT
ejpam-6705	440	19	v	v	NOUN
ejpam-6705	440	20	,	,	PUNCT
ejpam-6705	440	21	u	u	NOUN
ejpam-6705	440	22	)	)	PUNCT
ejpam-6705	440	23	,	,	PUNCT
ejpam-6705	440	24	h(v	h(v	PROPN
ejpam-6705	440	25	,	,	PUNCT
ejpam-6705	440	26	u	u	NOUN
ejpam-6705	440	27	)	)	PUNCT
ejpam-6705	440	28	,	,	PUNCT
ejpam-6705	440	29	v	v	NOUN
ejpam-6705	440	30	)	)	PUNCT
ejpam-6705	440	31	=	=	SYM
ejpam-6705	440	32	0	0	NUM
ejpam-6705	440	33	and	and	CCONJ
ejpam-6705	440	34	thus	thus	ADV
ejpam-6705	440	35	h(v	h(v	PROPN
ejpam-6705	440	36	,	,	PUNCT
ejpam-6705	440	37	u	u	NOUN
ejpam-6705	440	38	)	)	PUNCT
ejpam-6705	440	39	=	=	PUNCT
ejpam-6705	441	1	v.	v.	CCONJ
ejpam-6705	441	2	therefore	therefore	ADV
ejpam-6705	441	3	,	,	PUNCT
ejpam-6705	441	4	(	(	PUNCT
ejpam-6705	441	5	u	u	NOUN
ejpam-6705	441	6	,	,	PUNCT
ejpam-6705	441	7	v	v	NOUN
ejpam-6705	441	8	)	)	PUNCT
ejpam-6705	441	9	is	be	AUX
ejpam-6705	441	10	a	a	DET
ejpam-6705	441	11	coupled	couple	VERB
ejpam-6705	441	12	fixed	fix	VERB
ejpam-6705	441	13	point	point	NOUN
ejpam-6705	441	14	of	of	ADP
ejpam-6705	441	15	the	the	DET
ejpam-6705	441	16	mapping	mapping	NOUN
ejpam-6705	441	17	t.	t.	NOUN
ejpam-6705	441	18	the	the	DET
ejpam-6705	441	19	following	follow	VERB
ejpam-6705	441	20	theorem	theorem	NOUN
ejpam-6705	441	21	shows	show	VERB
ejpam-6705	441	22	that	that	SCONJ
ejpam-6705	441	23	the	the	DET
ejpam-6705	441	24	coupled	couple	VERB
ejpam-6705	441	25	fixed	fix	VERB
ejpam-6705	441	26	point	point	NOUN
ejpam-6705	441	27	of	of	ADP
ejpam-6705	441	28	t	t	PROPN
ejpam-6705	441	29	can	can	AUX
ejpam-6705	441	30	be	be	AUX
ejpam-6705	441	31	unique	unique	ADJ
ejpam-6705	441	32	.	.	PUNCT
ejpam-6705	442	1	theorem	theorem	NOUN
ejpam-6705	442	2	5	5	NUM
ejpam-6705	442	3	.	.	PUNCT
ejpam-6705	442	4	suppose	suppose	VERB
ejpam-6705	442	5	that	that	SCONJ
ejpam-6705	442	6	(	(	PUNCT
ejpam-6705	442	7	x	x	X
ejpam-6705	442	8	,	,	PUNCT
ejpam-6705	442	9	gb,≼	gb,≼	NOUN
ejpam-6705	442	10	)	)	PUNCT
ejpam-6705	442	11	is	be	AUX
ejpam-6705	442	12	a	a	DET
ejpam-6705	442	13	partially	partially	ADV
ejpam-6705	442	14	ordered	order	VERB
ejpam-6705	442	15	complete	complete	ADJ
ejpam-6705	442	16	gb	gb	ADV
ejpam-6705	442	17	-	-	PUNCT
ejpam-6705	442	18	metric	metric	ADJ
ejpam-6705	442	19	space	space	NOUN
ejpam-6705	442	20	satisfying	satisfy	VERB
ejpam-6705	442	21	the	the	DET
ejpam-6705	442	22	following	following	NOUN
ejpam-6705	442	23	:	:	PUNCT
ejpam-6705	442	24	(	(	PUNCT
ejpam-6705	442	25	i	i	NOUN
ejpam-6705	442	26	)	)	PUNCT
ejpam-6705	442	27	if	if	SCONJ
ejpam-6705	442	28	(	(	PUNCT
ejpam-6705	442	29	us	we	PRON
ejpam-6705	442	30	)	)	PUNCT
ejpam-6705	442	31	is	be	AUX
ejpam-6705	442	32	a	a	DET
ejpam-6705	442	33	non	non	ADJ
ejpam-6705	442	34	-	-	ADJ
ejpam-6705	442	35	decreasing	decrease	VERB
ejpam-6705	442	36	sequence	sequence	NOUN
ejpam-6705	442	37	that	that	PRON
ejpam-6705	442	38	converges	converge	VERB
ejpam-6705	442	39	to	to	ADP
ejpam-6705	442	40	some	some	DET
ejpam-6705	442	41	point	point	NOUN
ejpam-6705	442	42	u	u	NOUN
ejpam-6705	442	43	∈	∈	PROPN
ejpam-6705	442	44	x	x	X
ejpam-6705	442	45	,	,	PUNCT
ejpam-6705	442	46	then	then	ADV
ejpam-6705	442	47	us	we	PRON
ejpam-6705	442	48	≼	≼	ADJ
ejpam-6705	442	49	u	u	NOUN
ejpam-6705	442	50	for	for	ADP
ejpam-6705	442	51	all	all	DET
ejpam-6705	442	52	s	s	PROPN
ejpam-6705	442	53	∈	∈	PROPN
ejpam-6705	442	54	n.	n.	NOUN
ejpam-6705	442	55	(	(	PUNCT
ejpam-6705	442	56	ii	ii	NOUN
ejpam-6705	442	57	)	)	PUNCT
ejpam-6705	442	58	if	if	SCONJ
ejpam-6705	442	59	(	(	PUNCT
ejpam-6705	442	60	vs	vs	NOUN
ejpam-6705	442	61	)	)	PUNCT
ejpam-6705	442	62	is	be	AUX
ejpam-6705	442	63	a	a	DET
ejpam-6705	442	64	non	non	ADJ
ejpam-6705	442	65	-	-	ADJ
ejpam-6705	442	66	increasing	increasing	ADJ
ejpam-6705	442	67	sequence	sequence	NOUN
ejpam-6705	442	68	that	that	PRON
ejpam-6705	442	69	converges	converge	VERB
ejpam-6705	442	70	to	to	ADP
ejpam-6705	442	71	a	a	DET
ejpam-6705	442	72	point	point	NOUN
ejpam-6705	442	73	v	v	ADP
ejpam-6705	442	74	∈	∈	NOUN
ejpam-6705	442	75	x	x	X
ejpam-6705	442	76	,	,	PUNCT
ejpam-6705	442	77	then	then	ADV
ejpam-6705	442	78	vs	vs	ADP
ejpam-6705	442	79	≽	≽	PROPN
ejpam-6705	442	80	v	v	NOUN
ejpam-6705	442	81	for	for	ADP
ejpam-6705	442	82	all	all	DET
ejpam-6705	442	83	s	s	PROPN
ejpam-6705	442	84	∈	∈	PROPN
ejpam-6705	442	85	n.	n.	NOUN
ejpam-6705	442	86	(	(	PUNCT
ejpam-6705	442	87	iii	iii	NOUN
ejpam-6705	442	88	)	)	PUNCT
ejpam-6705	442	89	for	for	ADP
ejpam-6705	442	90	any	any	DET
ejpam-6705	442	91	two	two	NUM
ejpam-6705	442	92	pairs	pair	NOUN
ejpam-6705	442	93	(	(	PUNCT
ejpam-6705	442	94	u	u	NOUN
ejpam-6705	442	95	,	,	PUNCT
ejpam-6705	442	96	v	v	NOUN
ejpam-6705	442	97	)	)	PUNCT
ejpam-6705	442	98	,	,	PUNCT
ejpam-6705	442	99	(	(	PUNCT
ejpam-6705	442	100	u1	u1	NOUN
ejpam-6705	442	101	,	,	PUNCT
ejpam-6705	442	102	v1	v1	NOUN
ejpam-6705	442	103	)	)	PUNCT
ejpam-6705	442	104	∈	∈	PROPN
ejpam-6705	442	105	x	x	X
ejpam-6705	442	106	×x	×x	NUM
ejpam-6705	442	107	,	,	PUNCT
ejpam-6705	442	108	there	there	PRON
ejpam-6705	442	109	exists	exist	VERB
ejpam-6705	442	110	a	a	DET
ejpam-6705	442	111	pair	pair	NOUN
ejpam-6705	442	112	(	(	PUNCT
ejpam-6705	442	113	w1	w1	NOUN
ejpam-6705	442	114	,	,	PUNCT
ejpam-6705	442	115	w2	w2	NOUN
ejpam-6705	442	116	)	)	PUNCT
ejpam-6705	442	117	∈	∈	PROPN
ejpam-6705	442	118	x	x	X
ejpam-6705	442	119	×x	×x	VERB
ejpam-6705	442	120	that	that	PRON
ejpam-6705	442	121	is	be	AUX
ejpam-6705	442	122	comparable	comparable	ADJ
ejpam-6705	442	123	with	with	ADP
ejpam-6705	442	124	both	both	DET
ejpam-6705	442	125	(	(	PUNCT
ejpam-6705	442	126	u	u	NOUN
ejpam-6705	442	127	,	,	PUNCT
ejpam-6705	442	128	v	v	NOUN
ejpam-6705	442	129	)	)	PUNCT
ejpam-6705	442	130	and	and	CCONJ
ejpam-6705	442	131	(	(	PUNCT
ejpam-6705	442	132	u1	u1	NOUN
ejpam-6705	442	133	,	,	PUNCT
ejpam-6705	442	134	v1	v1	NOUN
ejpam-6705	442	135	)	)	PUNCT
ejpam-6705	442	136	.	.	PUNCT
ejpam-6705	443	1	assume	assume	VERB
ejpam-6705	443	2	that	that	SCONJ
ejpam-6705	443	3	t	t	NOUN
ejpam-6705	443	4	:	:	PUNCT
ejpam-6705	443	5	x	x	PROPN
ejpam-6705	443	6	×x	×x	ADP
ejpam-6705	443	7	→	→	SYM
ejpam-6705	443	8	x	x	X
ejpam-6705	443	9	is	be	AUX
ejpam-6705	443	10	a	a	DET
ejpam-6705	443	11	continuous	continuous	ADJ
ejpam-6705	443	12	mapping	mapping	NOUN
ejpam-6705	443	13	which	which	PRON
ejpam-6705	443	14	satisfies	satisfy	VERB
ejpam-6705	443	15	the	the	DET
ejpam-6705	443	16	mixed	mixed	ADJ
ejpam-6705	443	17	monotone	monotone	ADJ
ejpam-6705	443	18	property	property	NOUN
ejpam-6705	443	19	on	on	ADP
ejpam-6705	443	20	x	x	SYM
ejpam-6705	443	21	such	such	ADJ
ejpam-6705	443	22	that∫	that∫	NOUN
ejpam-6705	443	23	gb(t	gb(t	X
ejpam-6705	443	24	(	(	PUNCT
ejpam-6705	443	25	u	u	NOUN
ejpam-6705	443	26	,	,	PUNCT
ejpam-6705	443	27	v),t	v),t	PROPN
ejpam-6705	443	28	(	(	PUNCT
ejpam-6705	443	29	m	m	PROPN
ejpam-6705	443	30	,	,	PUNCT
ejpam-6705	443	31	n),t	n),t	PROPN
ejpam-6705	443	32	(	(	PUNCT
ejpam-6705	443	33	f	f	X
ejpam-6705	443	34	,	,	PUNCT
ejpam-6705	443	35	w	w	NOUN
ejpam-6705	443	36	)	)	PUNCT
ejpam-6705	443	37	)	)	PUNCT
ejpam-6705	443	38	0	0	NUM
ejpam-6705	444	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	444	2	≤	≤	PROPN
ejpam-6705	444	3	σ	σ	PROPN
ejpam-6705	444	4	(	(	PUNCT
ejpam-6705	444	5	∫	∫	PROPN
ejpam-6705	444	6	gb(u	gb(u	PROPN
ejpam-6705	444	7	,	,	PUNCT
ejpam-6705	444	8	m	m	NOUN
ejpam-6705	444	9	,	,	PUNCT
ejpam-6705	444	10	f)+gb(v	f)+gb(v	NOUN
ejpam-6705	444	11	,	,	PUNCT
ejpam-6705	444	12	n	n	CCONJ
ejpam-6705	444	13	,	,	PUNCT
ejpam-6705	444	14	w	w	NOUN
ejpam-6705	444	15	)	)	PUNCT
ejpam-6705	444	16	0	0	NUM
ejpam-6705	444	17	g(t)dt	g(t)dt	PROPN
ejpam-6705	444	18	)	)	PUNCT
ejpam-6705	444	19	,	,	PUNCT
ejpam-6705	444	20	(	(	PUNCT
ejpam-6705	444	21	10	10	NUM
ejpam-6705	444	22	)	)	PUNCT
ejpam-6705	445	1	where	where	SCONJ
ejpam-6705	445	2	u	u	NOUN
ejpam-6705	445	3	,	,	PUNCT
ejpam-6705	445	4	v	v	NOUN
ejpam-6705	445	5	,	,	PUNCT
ejpam-6705	445	6	w	w	PROPN
ejpam-6705	445	7	,	,	PUNCT
ejpam-6705	445	8	m	m	PROPN
ejpam-6705	445	9	,	,	PUNCT
ejpam-6705	445	10	n	n	CCONJ
ejpam-6705	445	11	,	,	PUNCT
ejpam-6705	445	12	f	f	PROPN
ejpam-6705	445	13	∈	∈	PROPN
ejpam-6705	445	14	x	x	X
ejpam-6705	445	15	and	and	CCONJ
ejpam-6705	445	16	g	g	NOUN
ejpam-6705	445	17	:	:	PUNCT
ejpam-6705	446	1	[	[	X
ejpam-6705	446	2	0,∞	0,∞	NOUN
ejpam-6705	446	3	)	)	PUNCT
ejpam-6705	446	4	→	→	PUNCT
ejpam-6705	447	1	[	[	X
ejpam-6705	447	2	0,∞	0,∞	NUM
ejpam-6705	447	3	)	)	PUNCT
ejpam-6705	447	4	is	be	AUX
ejpam-6705	447	5	a	a	DET
ejpam-6705	447	6	lebesgue	lebesgue	NOUN
ejpam-6705	447	7	integrable	integrable	ADJ
ejpam-6705	447	8	mapping	mapping	NOUN
ejpam-6705	447	9	with	with	ADP
ejpam-6705	447	10	f	f	PROPN
ejpam-6705	447	11	≼	≼	PROPN
ejpam-6705	447	12	m	m	VERB
ejpam-6705	447	13	≼	≼	ADJ
ejpam-6705	447	14	u	u	NOUN
ejpam-6705	447	15	and	and	CCONJ
ejpam-6705	447	16	v	v	ADP
ejpam-6705	447	17	≼	≼	NOUN
ejpam-6705	447	18	n	n	PROPN
ejpam-6705	447	19	≼	≼	PROPN
ejpam-6705	447	20	w	w	PROPN
ejpam-6705	447	21	,	,	PUNCT
ejpam-6705	447	22	where	where	SCONJ
ejpam-6705	447	23	either	either	CCONJ
ejpam-6705	447	24	m	m	VERB
ejpam-6705	447	25	̸=	̸=	PROPN
ejpam-6705	447	26	f	f	PROPN
ejpam-6705	447	27	or	or	CCONJ
ejpam-6705	447	28	n	n	PRON
ejpam-6705	447	29	̸=	̸=	PROPN
ejpam-6705	447	30	w.	w.	NOUN
ejpam-6705	447	31	if	if	SCONJ
ejpam-6705	447	32	∃	∃	PROPN
ejpam-6705	447	33	u0	u0	PROPN
ejpam-6705	447	34	,	,	PUNCT
ejpam-6705	447	35	v0	v0	PROPN
ejpam-6705	447	36	∈	∈	PROPN
ejpam-6705	447	37	x	x	PUNCT
ejpam-6705	447	38	such	such	ADJ
ejpam-6705	447	39	that	that	DET
ejpam-6705	447	40	u0	u0	ADJ
ejpam-6705	447	41	≼	≼	PROPN
ejpam-6705	447	42	t	t	PROPN
ejpam-6705	447	43	(	(	PUNCT
ejpam-6705	447	44	u0	u0	PROPN
ejpam-6705	447	45	,	,	PUNCT
ejpam-6705	447	46	v0	v0	PROPN
ejpam-6705	447	47	)	)	PUNCT
ejpam-6705	447	48	and	and	CCONJ
ejpam-6705	447	49	t	t	PROPN
ejpam-6705	447	50	(	(	PUNCT
ejpam-6705	447	51	v0	v0	PROPN
ejpam-6705	447	52	,	,	PUNCT
ejpam-6705	447	53	u0	u0	ADJ
ejpam-6705	447	54	)	)	PUNCT
ejpam-6705	447	55	≼	≼	ADJ
ejpam-6705	447	56	v0	v0	NOUN
ejpam-6705	447	57	,	,	PUNCT
ejpam-6705	447	58	then	then	ADV
ejpam-6705	447	59	t	t	PROPN
ejpam-6705	447	60	has	have	VERB
ejpam-6705	447	61	a	a	DET
ejpam-6705	447	62	unique	unique	ADJ
ejpam-6705	447	63	coupled	couple	VERB
ejpam-6705	447	64	fixed	fix	VERB
ejpam-6705	447	65	point	point	NOUN
ejpam-6705	447	66	in	in	ADP
ejpam-6705	447	67	(	(	PUNCT
ejpam-6705	447	68	x	x	INTJ
ejpam-6705	447	69	,	,	PUNCT
ejpam-6705	447	70	g	g	NOUN
ejpam-6705	447	71	)	)	PUNCT
ejpam-6705	447	72	.	.	PUNCT
ejpam-6705	448	1	s.	s.	PROPN
ejpam-6705	448	2	batul	batul	PROPN
ejpam-6705	448	3	et	et	PROPN
ejpam-6705	448	4	al	al	PROPN
ejpam-6705	448	5	.	.	PUNCT
ejpam-6705	448	6	/	/	SYM
ejpam-6705	448	7	eur	eur	PROPN
ejpam-6705	448	8	.	.	PUNCT
ejpam-6705	449	1	j.	j.	PROPN
ejpam-6705	449	2	pure	pure	PROPN
ejpam-6705	449	3	appl	appl	PROPN
ejpam-6705	449	4	.	.	PROPN
ejpam-6705	449	5	math	math	PROPN
ejpam-6705	449	6	,	,	PUNCT
ejpam-6705	449	7	18	18	NUM
ejpam-6705	449	8	(	(	PUNCT
ejpam-6705	449	9	4	4	NUM
ejpam-6705	449	10	)	)	PUNCT
ejpam-6705	449	11	(	(	PUNCT
ejpam-6705	449	12	2025	2025	NUM
ejpam-6705	449	13	)	)	PUNCT
ejpam-6705	449	14	,	,	PUNCT
ejpam-6705	449	15	6705	6705	NUM
ejpam-6705	449	16	18	18	NUM
ejpam-6705	449	17	of	of	ADP
ejpam-6705	449	18	23	23	NUM
ejpam-6705	449	19	proof	proof	NOUN
ejpam-6705	449	20	.	.	PUNCT
ejpam-6705	449	21	suppose	suppose	VERB
ejpam-6705	449	22	that	that	SCONJ
ejpam-6705	449	23	(	(	PUNCT
ejpam-6705	449	24	u1	u1	NOUN
ejpam-6705	449	25	,	,	PUNCT
ejpam-6705	449	26	v1	v1	NOUN
ejpam-6705	449	27	)	)	PUNCT
ejpam-6705	449	28	is	be	AUX
ejpam-6705	449	29	another	another	DET
ejpam-6705	449	30	fixed	fix	VERB
ejpam-6705	449	31	point	point	NOUN
ejpam-6705	449	32	of	of	ADP
ejpam-6705	449	33	t	t	PROPN
ejpam-6705	449	34	.	.	PUNCT
ejpam-6705	450	1	the	the	DET
ejpam-6705	450	2	following	follow	VERB
ejpam-6705	450	3	cases	case	NOUN
ejpam-6705	450	4	are	be	AUX
ejpam-6705	450	5	now	now	ADV
ejpam-6705	450	6	considered	consider	VERB
ejpam-6705	450	7	.	.	PUNCT
ejpam-6705	451	1	case	case	NOUN
ejpam-6705	451	2	1	1	NUM
ejpam-6705	451	3	:	:	PUNCT
ejpam-6705	451	4	let	let	VERB
ejpam-6705	451	5	(	(	PUNCT
ejpam-6705	451	6	u	u	NOUN
ejpam-6705	451	7	,	,	PUNCT
ejpam-6705	451	8	v	v	NOUN
ejpam-6705	451	9	)	)	PUNCT
ejpam-6705	451	10	and	and	CCONJ
ejpam-6705	451	11	(	(	PUNCT
ejpam-6705	451	12	u1	u1	NOUN
ejpam-6705	451	13	,	,	PUNCT
ejpam-6705	451	14	v1	v1	NOUN
ejpam-6705	451	15	)	)	PUNCT
ejpam-6705	451	16	be	be	AUX
ejpam-6705	451	17	elements	element	NOUN
ejpam-6705	451	18	in	in	ADP
ejpam-6705	451	19	x	x	X
ejpam-6705	451	20	×	×	NOUN
ejpam-6705	451	21	x	x	PUNCT
ejpam-6705	451	22	that	that	PRON
ejpam-6705	451	23	are	be	AUX
ejpam-6705	451	24	comparable	comparable	ADJ
ejpam-6705	451	25	that	that	SCONJ
ejpam-6705	451	26	(	(	PUNCT
ejpam-6705	451	27	u	u	NOUN
ejpam-6705	451	28	,	,	PUNCT
ejpam-6705	451	29	v	v	NOUN
ejpam-6705	451	30	)	)	PUNCT
ejpam-6705	451	31	≼	≼	NOUN
ejpam-6705	451	32	(	(	PUNCT
ejpam-6705	451	33	u1	u1	NOUN
ejpam-6705	451	34	,	,	PUNCT
ejpam-6705	451	35	v1	v1	NOUN
ejpam-6705	451	36	)	)	PUNCT
ejpam-6705	451	37	i.e.	i.e.	X
ejpam-6705	451	38	u	u	X
ejpam-6705	451	39	≼	≼	ADJ
ejpam-6705	451	40	u1	u1	NOUN
ejpam-6705	451	41	and	and	CCONJ
ejpam-6705	451	42	v	v	ADP
ejpam-6705	451	43	≼	≼	PROPN
ejpam-6705	451	44	v1	v1	NOUN
ejpam-6705	451	45	.	.	PUNCT
ejpam-6705	452	1	now	now	ADV
ejpam-6705	452	2	,	,	PUNCT
ejpam-6705	452	3	by	by	ADP
ejpam-6705	452	4	using	use	VERB
ejpam-6705	452	5	(	(	PUNCT
ejpam-6705	452	6	10),∫	10),∫	NUM
ejpam-6705	452	7	gb(t	gb(t	NOUN
ejpam-6705	452	8	s(u	s(u	PROPN
ejpam-6705	452	9	,	,	PUNCT
ejpam-6705	452	10	v),ts(u1,v1),ts(u1,v1	v),ts(u1,v1),ts(u1,v1	NUM
ejpam-6705	452	11	)	)	PUNCT
ejpam-6705	452	12	)	)	PUNCT
ejpam-6705	452	13	0	0	NUM
ejpam-6705	453	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	453	2	≤	≤	NOUN
ejpam-6705	453	3	∞∑	∞∑	NUM
ejpam-6705	453	4	s=0	s=0	PROPN
ejpam-6705	453	5	sσs	sσs	NOUN
ejpam-6705	453	6	(	(	PUNCT
ejpam-6705	453	7	∫	∫	PROPN
ejpam-6705	453	8	gb(u	gb(u	PROPN
ejpam-6705	453	9	,	,	PUNCT
ejpam-6705	453	10	u1,u1)+gb(v	u1,u1)+gb(v	NOUN
ejpam-6705	453	11	,	,	PUNCT
ejpam-6705	453	12	v1,v1	v1,v1	PROPN
ejpam-6705	453	13	)	)	PUNCT
ejpam-6705	453	14	0	0	NUM
ejpam-6705	454	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	454	2	)	)	PUNCT
ejpam-6705	454	3	.	.	PUNCT
ejpam-6705	455	1	(	(	PUNCT
ejpam-6705	455	2	11	11	X
ejpam-6705	455	3	)	)	PUNCT
ejpam-6705	455	4	taking	take	VERB
ejpam-6705	455	5	lim	lim	PROPN
ejpam-6705	455	6	s→∞	s→∞	PROPN
ejpam-6705	455	7	and	and	CCONJ
ejpam-6705	455	8	by	by	ADP
ejpam-6705	455	9	the	the	DET
ejpam-6705	455	10	use	use	NOUN
ejpam-6705	455	11	of	of	ADP
ejpam-6705	455	12	(	(	PUNCT
ejpam-6705	455	13	11	11	NUM
ejpam-6705	455	14	)	)	PUNCT
ejpam-6705	455	15	,	,	PUNCT
ejpam-6705	455	16	u	u	NOUN
ejpam-6705	455	17	=	=	NOUN
ejpam-6705	455	18	u1	u1	PROPN
ejpam-6705	455	19	.	.	PUNCT
ejpam-6705	456	1	following	follow	VERB
ejpam-6705	456	2	a	a	DET
ejpam-6705	456	3	similar	similar	ADJ
ejpam-6705	456	4	pattern	pattern	NOUN
ejpam-6705	456	5	,	,	PUNCT
ejpam-6705	456	6	it	it	PRON
ejpam-6705	456	7	is	be	AUX
ejpam-6705	456	8	clear	clear	ADJ
ejpam-6705	456	9	that	that	SCONJ
ejpam-6705	456	10	∫	∫	PROPN
ejpam-6705	456	11	gb(t	gb(t	PROPN
ejpam-6705	456	12	s(v	s(v	PROPN
ejpam-6705	456	13	,	,	PUNCT
ejpam-6705	456	14	u),ts(v1,u1),ts(v1,u1	u),ts(v1,u1),ts(v1,u1	PROPN
ejpam-6705	456	15	)	)	PUNCT
ejpam-6705	456	16	)	)	PUNCT
ejpam-6705	456	17	0	0	NUM
ejpam-6705	457	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	457	2	≤	≤	NOUN
ejpam-6705	457	3	∞∑	∞∑	NUM
ejpam-6705	457	4	s=0	s=0	PROPN
ejpam-6705	457	5	sσs	sσs	NOUN
ejpam-6705	457	6	(	(	PUNCT
ejpam-6705	457	7	∫	∫	PROPN
ejpam-6705	457	8	gb(v	gb(v	NOUN
ejpam-6705	457	9	,	,	PUNCT
ejpam-6705	457	10	v1,v1)+gb(u	v1,v1)+gb(u	ADJ
ejpam-6705	457	11	,	,	PUNCT
ejpam-6705	457	12	u1,u1	u1,u1	PROPN
ejpam-6705	457	13	)	)	PUNCT
ejpam-6705	457	14	0	0	NUM
ejpam-6705	458	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	458	2	)	)	PUNCT
ejpam-6705	458	3	.	.	PUNCT
ejpam-6705	459	1	(	(	PUNCT
ejpam-6705	459	2	12	12	X
ejpam-6705	459	3	)	)	PUNCT
ejpam-6705	459	4	taking	take	VERB
ejpam-6705	459	5	lim	lim	PROPN
ejpam-6705	459	6	s→∞	s→∞	PROPN
ejpam-6705	459	7	and	and	CCONJ
ejpam-6705	459	8	by	by	ADP
ejpam-6705	459	9	the	the	DET
ejpam-6705	459	10	use	use	NOUN
ejpam-6705	459	11	of	of	ADP
ejpam-6705	459	12	(	(	PUNCT
ejpam-6705	459	13	12	12	NUM
ejpam-6705	459	14	)	)	PUNCT
ejpam-6705	459	15	,	,	PUNCT
ejpam-6705	459	16	we	we	PRON
ejpam-6705	459	17	obtain	obtain	VERB
ejpam-6705	459	18	u	u	NOUN
ejpam-6705	459	19	=	=	NOUN
ejpam-6705	459	20	u1	u1	NOUN
ejpam-6705	459	21	.	.	PUNCT
ejpam-6705	460	1	case	case	NOUN
ejpam-6705	460	2	2	2	NUM
ejpam-6705	460	3	:	:	PUNCT
ejpam-6705	460	4	let	let	VERB
ejpam-6705	460	5	(	(	PUNCT
ejpam-6705	460	6	u	u	NOUN
ejpam-6705	460	7	,	,	PUNCT
ejpam-6705	460	8	v	v	NOUN
ejpam-6705	460	9	)	)	PUNCT
ejpam-6705	460	10	be	be	AUX
ejpam-6705	460	11	not	not	PART
ejpam-6705	460	12	comparable	comparable	ADJ
ejpam-6705	460	13	with	with	ADP
ejpam-6705	460	14	(	(	PUNCT
ejpam-6705	460	15	u1	u1	NOUN
ejpam-6705	460	16	,	,	PUNCT
ejpam-6705	460	17	v1	v1	NOUN
ejpam-6705	460	18	)	)	PUNCT
ejpam-6705	460	19	.	.	PUNCT
ejpam-6705	461	1	so	so	ADV
ejpam-6705	461	2	by	by	ADP
ejpam-6705	461	3	condition	condition	NOUN
ejpam-6705	461	4	(	(	PUNCT
ejpam-6705	461	5	iii	iii	NOUN
ejpam-6705	461	6	)	)	PUNCT
ejpam-6705	461	7	there	there	PRON
ejpam-6705	461	8	exist	exist	VERB
ejpam-6705	461	9	(	(	PUNCT
ejpam-6705	461	10	w1	w1	NOUN
ejpam-6705	461	11	,	,	PUNCT
ejpam-6705	461	12	w2	w2	NOUN
ejpam-6705	461	13	)	)	PUNCT
ejpam-6705	461	14	∈	∈	PROPN
ejpam-6705	462	1	x	x	X
ejpam-6705	462	2	×	×	NOUN
ejpam-6705	462	3	x	x	X
ejpam-6705	462	4	,	,	PUNCT
ejpam-6705	462	5	which	which	PRON
ejpam-6705	462	6	is	be	AUX
ejpam-6705	462	7	comparable	comparable	ADJ
ejpam-6705	462	8	to	to	ADP
ejpam-6705	462	9	(	(	PUNCT
ejpam-6705	462	10	u	u	NOUN
ejpam-6705	462	11	,	,	PUNCT
ejpam-6705	462	12	v	v	NOUN
ejpam-6705	462	13	)	)	PUNCT
ejpam-6705	462	14	and	and	CCONJ
ejpam-6705	462	15	(	(	PUNCT
ejpam-6705	462	16	u1	u1	NOUN
ejpam-6705	462	17	,	,	PUNCT
ejpam-6705	462	18	v1	v1	NOUN
ejpam-6705	462	19	)	)	PUNCT
ejpam-6705	462	20	.	.	PUNCT
ejpam-6705	463	1	we	we	PRON
ejpam-6705	463	2	can	can	AUX
ejpam-6705	463	3	assume	assume	VERB
ejpam-6705	463	4	that	that	SCONJ
ejpam-6705	463	5	w1	w1	NOUN
ejpam-6705	463	6	≼	≼	PROPN
ejpam-6705	463	7	u	u	PROPN
ejpam-6705	463	8	,	,	PUNCT
ejpam-6705	463	9	w2	w2	NOUN
ejpam-6705	463	10	≼	≼	PROPN
ejpam-6705	463	11	v	v	PROPN
ejpam-6705	463	12	,	,	PUNCT
ejpam-6705	463	13	w1	w1	NOUN
ejpam-6705	463	14	≼	≼	ADJ
ejpam-6705	463	15	u1	u1	NOUN
ejpam-6705	463	16	and	and	CCONJ
ejpam-6705	463	17	w2	w2	NOUN
ejpam-6705	463	18	≼	≼	PROPN
ejpam-6705	463	19	v1	v1	PROPN
ejpam-6705	463	20	.	.	PUNCT
ejpam-6705	464	1	again	again	ADV
ejpam-6705	464	2	,	,	PUNCT
ejpam-6705	464	3	by	by	ADP
ejpam-6705	464	4	using	use	VERB
ejpam-6705	464	5	(	(	PUNCT
ejpam-6705	464	6	10),∫	10),∫	NUM
ejpam-6705	464	7	gb(t	gb(t	NOUN
ejpam-6705	464	8	s(u	s(u	PROPN
ejpam-6705	464	9	,	,	PUNCT
ejpam-6705	464	10	v),ts(w1,w2),ts(w1,w2	v),ts(w1,w2),ts(w1,w2	NUM
ejpam-6705	464	11	)	)	PUNCT
ejpam-6705	464	12	)	)	PUNCT
ejpam-6705	464	13	0	0	NUM
ejpam-6705	464	14	g(t)dt	g(t)dt	NOUN
ejpam-6705	464	15	≤	≤	NOUN
ejpam-6705	464	16	∞∑	∞∑	NUM
ejpam-6705	464	17	s=0	s=0	PROPN
ejpam-6705	464	18	sσs	sσs	NOUN
ejpam-6705	464	19	(	(	PUNCT
ejpam-6705	464	20	∫	∫	PROPN
ejpam-6705	464	21	gb(u	gb(u	PROPN
ejpam-6705	464	22	,	,	PUNCT
ejpam-6705	464	23	w1,w1)+gb(v	w1,w1)+gb(v	NOUN
ejpam-6705	464	24	,	,	PUNCT
ejpam-6705	464	25	w2,w2	w2,w2	PROPN
ejpam-6705	464	26	)	)	PUNCT
ejpam-6705	464	27	0	0	NUM
ejpam-6705	464	28	g(t)dt	g(t)dt	PROPN
ejpam-6705	464	29	)	)	PUNCT
ejpam-6705	464	30	.	.	PUNCT
ejpam-6705	465	1	(	(	PUNCT
ejpam-6705	465	2	13	13	X
ejpam-6705	465	3	)	)	PUNCT
ejpam-6705	465	4	taking	take	VERB
ejpam-6705	465	5	s→	s→	PRON
ejpam-6705	465	6	∞	∞	NOUN
ejpam-6705	465	7	and	and	CCONJ
ejpam-6705	465	8	by	by	ADP
ejpam-6705	465	9	(	(	PUNCT
ejpam-6705	465	10	13	13	NUM
ejpam-6705	465	11	)	)	PUNCT
ejpam-6705	465	12	,	,	PUNCT
ejpam-6705	465	13	gb(t	gb(t	NOUN
ejpam-6705	465	14	s(u	s(u	PROPN
ejpam-6705	465	15	,	,	PUNCT
ejpam-6705	465	16	v),t	v),t	X
ejpam-6705	465	17	s(w1	s(w1	PROPN
ejpam-6705	465	18	,	,	PUNCT
ejpam-6705	465	19	w2),t	w2),t	X
ejpam-6705	465	20	s(w1	s(w1	VERB
ejpam-6705	465	21	,	,	PUNCT
ejpam-6705	465	22	w2	w2	NOUN
ejpam-6705	465	23	)	)	PUNCT
ejpam-6705	465	24	)	)	PUNCT
ejpam-6705	466	1	=	=	PUNCT
ejpam-6705	466	2	0	0	X
ejpam-6705	466	3	.	.	PUNCT
ejpam-6705	467	1	that	that	PRON
ejpam-6705	467	2	is	is	ADV
ejpam-6705	467	3	,	,	PUNCT
ejpam-6705	467	4	lim	lim	PROPN
ejpam-6705	467	5	s→∞	s→∞	PROPN
ejpam-6705	467	6	t	t	PROPN
ejpam-6705	467	7	s(u	s(u	PROPN
ejpam-6705	467	8	,	,	PUNCT
ejpam-6705	467	9	v	v	NOUN
ejpam-6705	467	10	)	)	PUNCT
ejpam-6705	468	1	=	=	SYM
ejpam-6705	468	2	lim	lim	PROPN
ejpam-6705	468	3	s→∞	s→∞	PROPN
ejpam-6705	468	4	t	t	PROPN
ejpam-6705	468	5	s(w1	s(w1	PROPN
ejpam-6705	468	6	,	,	PUNCT
ejpam-6705	468	7	w2	w2	NOUN
ejpam-6705	468	8	)	)	PUNCT
ejpam-6705	468	9	=	=	PUNCT
ejpam-6705	469	1	u.∫	u.∫	NOUN
ejpam-6705	469	2	gb(t	gb(t	NOUN
ejpam-6705	469	3	s(u1,v1),ts(w1,w2),ts(w1,w2	s(u1,v1),ts(w1,w2),ts(w1,w2	PROPN
ejpam-6705	469	4	)	)	PUNCT
ejpam-6705	469	5	)	)	PUNCT
ejpam-6705	469	6	0	0	NUM
ejpam-6705	470	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	470	2	≤	≤	NOUN
ejpam-6705	470	3	∞∑	∞∑	NUM
ejpam-6705	470	4	s=0	s=0	PROPN
ejpam-6705	470	5	sσs	sσs	NOUN
ejpam-6705	470	6	(	(	PUNCT
ejpam-6705	470	7	∫	∫	PROPN
ejpam-6705	470	8	gb(u1,w1,w1)+gb(v1,w2,w2	gb(u1,w1,w1)+gb(v1,w2,w2	NOUN
ejpam-6705	470	9	)	)	PUNCT
ejpam-6705	470	10	0	0	NUM
ejpam-6705	471	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	471	2	)	)	PUNCT
ejpam-6705	471	3	.	.	PUNCT
ejpam-6705	472	1	(	(	PUNCT
ejpam-6705	472	2	14	14	NUM
ejpam-6705	472	3	)	)	PUNCT
ejpam-6705	472	4	from	from	ADP
ejpam-6705	472	5	(	(	PUNCT
ejpam-6705	472	6	14	14	NUM
ejpam-6705	472	7	)	)	PUNCT
ejpam-6705	472	8	lim	lim	PROPN
ejpam-6705	472	9	s→∞	s→∞	PROPN
ejpam-6705	472	10	t	t	PROPN
ejpam-6705	472	11	s(u1	s(u1	NOUN
ejpam-6705	472	12	,	,	PUNCT
ejpam-6705	472	13	v1	v1	NOUN
ejpam-6705	472	14	)	)	PUNCT
ejpam-6705	472	15	=	=	SYM
ejpam-6705	472	16	lim	lim	PROPN
ejpam-6705	472	17	s→∞	s→∞	PROPN
ejpam-6705	472	18	t	t	PROPN
ejpam-6705	472	19	s(w1	s(w1	PROPN
ejpam-6705	472	20	,	,	PUNCT
ejpam-6705	472	21	w2	w2	NOUN
ejpam-6705	472	22	)	)	PUNCT
ejpam-6705	472	23	=	=	SYM
ejpam-6705	472	24	u1	u1	NOUN
ejpam-6705	472	25	,	,	PUNCT
ejpam-6705	472	26	and	and	CCONJ
ejpam-6705	472	27	so	so	ADV
ejpam-6705	472	28	u	u	NOUN
ejpam-6705	472	29	=	=	NOUN
ejpam-6705	472	30	u1	u1	PROPN
ejpam-6705	472	31	.	.	PUNCT
ejpam-6705	473	1	preceding	precede	VERB
ejpam-6705	473	2	in	in	ADP
ejpam-6705	473	3	the	the	DET
ejpam-6705	473	4	same	same	ADJ
ejpam-6705	473	5	way	way	NOUN
ejpam-6705	473	6	,	,	PUNCT
ejpam-6705	473	7	one	one	NUM
ejpam-6705	473	8	has∫	has∫	NOUN
ejpam-6705	473	9	gb(t	gb(t	NOUN
ejpam-6705	473	10	s(v	s(v	PROPN
ejpam-6705	473	11	,	,	PUNCT
ejpam-6705	473	12	u),ts(w2,w1),ts(w2,w1	u),ts(w2,w1),ts(w2,w1	NUM
ejpam-6705	473	13	)	)	PUNCT
ejpam-6705	473	14	)	)	PUNCT
ejpam-6705	473	15	0	0	NUM
ejpam-6705	474	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	474	2	≤	≤	NOUN
ejpam-6705	474	3	∞∑	∞∑	NUM
ejpam-6705	474	4	s=0	s=0	PROPN
ejpam-6705	474	5	sσs	sσs	NOUN
ejpam-6705	474	6	(	(	PUNCT
ejpam-6705	474	7	∫	∫	PROPN
ejpam-6705	474	8	gb(v	gb(v	PROPN
ejpam-6705	474	9	,	,	PUNCT
ejpam-6705	474	10	w2,w2)+gb(u	w2,w2)+gb(u	PROPN
ejpam-6705	474	11	,	,	PUNCT
ejpam-6705	474	12	w1,w1	w1,w1	PROPN
ejpam-6705	474	13	)	)	PUNCT
ejpam-6705	474	14	0	0	NUM
ejpam-6705	475	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	475	2	)	)	PUNCT
ejpam-6705	475	3	.	.	PUNCT
ejpam-6705	476	1	(	(	PUNCT
ejpam-6705	476	2	15	15	X
ejpam-6705	476	3	)	)	PUNCT
ejpam-6705	476	4	assume	assume	VERB
ejpam-6705	476	5	that	that	SCONJ
ejpam-6705	476	6	s→	s→	PROPN
ejpam-6705	477	1	∞	∞	NOUN
ejpam-6705	477	2	,	,	PUNCT
ejpam-6705	477	3	then	then	ADV
ejpam-6705	477	4	(	(	PUNCT
ejpam-6705	477	5	15	15	X
ejpam-6705	477	6	)	)	PUNCT
ejpam-6705	477	7	gives	give	VERB
ejpam-6705	477	8	gb(t	gb(t	NOUN
ejpam-6705	477	9	s(v	s(v	PROPN
ejpam-6705	477	10	,	,	PUNCT
ejpam-6705	477	11	u),t	u),t	NOUN
ejpam-6705	477	12	s(w2	s(w2	NOUN
ejpam-6705	477	13	,	,	PUNCT
ejpam-6705	477	14	w1),t	w1),t	NOUN
ejpam-6705	477	15	s(w2	s(w2	NOUN
ejpam-6705	477	16	,	,	PUNCT
ejpam-6705	477	17	w1	w1	NOUN
ejpam-6705	477	18	)	)	PUNCT
ejpam-6705	477	19	)	)	PUNCT
ejpam-6705	478	1	=	=	PUNCT
ejpam-6705	478	2	0	0	X
ejpam-6705	478	3	.	.	PUNCT
ejpam-6705	479	1	we	we	PRON
ejpam-6705	479	2	have	have	VERB
ejpam-6705	479	3	lim	lim	PROPN
ejpam-6705	479	4	s→∞	s→∞	PROPN
ejpam-6705	479	5	t	t	PROPN
ejpam-6705	479	6	s(v	s(v	PROPN
ejpam-6705	479	7	,	,	PUNCT
ejpam-6705	479	8	u	u	NOUN
ejpam-6705	479	9	)	)	PUNCT
ejpam-6705	479	10	=	=	SYM
ejpam-6705	480	1	lim	lim	PROPN
ejpam-6705	480	2	s→∞	s→∞	PROPN
ejpam-6705	480	3	t	t	PROPN
ejpam-6705	480	4	s(w2	s(w2	NOUN
ejpam-6705	480	5	,	,	PUNCT
ejpam-6705	480	6	w1	w1	NOUN
ejpam-6705	480	7	)	)	PUNCT
ejpam-6705	480	8	=	=	PUNCT
ejpam-6705	481	1	v.	v.	CCONJ
ejpam-6705	481	2	similarly	similarly	ADV
ejpam-6705	481	3	,	,	PUNCT
ejpam-6705	481	4	it	it	PRON
ejpam-6705	481	5	can	can	AUX
ejpam-6705	481	6	be	be	AUX
ejpam-6705	481	7	proved	prove	VERB
ejpam-6705	481	8	that∫	that∫	NOUN
ejpam-6705	481	9	gb(t	gb(t	X
ejpam-6705	481	10	s(v1,u1),ts(w2,w1),ts(w2,w1	s(v1,u1),ts(w2,w1),ts(w2,w1	PROPN
ejpam-6705	481	11	)	)	PUNCT
ejpam-6705	481	12	)	)	PUNCT
ejpam-6705	481	13	0	0	NUM
ejpam-6705	482	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	482	2	≤	≤	NOUN
ejpam-6705	482	3	∞∑	∞∑	NUM
ejpam-6705	482	4	s=0	s=0	PROPN
ejpam-6705	482	5	sσs	sσs	NOUN
ejpam-6705	482	6	(	(	PUNCT
ejpam-6705	482	7	∫	∫	PROPN
ejpam-6705	482	8	gb(v1,w2,w2)+gb(u1,w1,w1	gb(v1,w2,w2)+gb(u1,w1,w1	X
ejpam-6705	482	9	)	)	PUNCT
ejpam-6705	482	10	0	0	NUM
ejpam-6705	483	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	483	2	)	)	PUNCT
ejpam-6705	483	3	.	.	PUNCT
ejpam-6705	484	1	(	(	PUNCT
ejpam-6705	484	2	16	16	NUM
ejpam-6705	484	3	)	)	PUNCT
ejpam-6705	484	4	s.	s.	PROPN
ejpam-6705	484	5	batul	batul	PROPN
ejpam-6705	484	6	et	et	PROPN
ejpam-6705	484	7	al	al	PROPN
ejpam-6705	484	8	.	.	PUNCT
ejpam-6705	484	9	/	/	SYM
ejpam-6705	484	10	eur	eur	PROPN
ejpam-6705	484	11	.	.	PUNCT
ejpam-6705	485	1	j.	j.	PROPN
ejpam-6705	485	2	pure	pure	PROPN
ejpam-6705	485	3	appl	appl	PROPN
ejpam-6705	485	4	.	.	PROPN
ejpam-6705	485	5	math	math	PROPN
ejpam-6705	485	6	,	,	PUNCT
ejpam-6705	485	7	18	18	NUM
ejpam-6705	485	8	(	(	PUNCT
ejpam-6705	485	9	4	4	NUM
ejpam-6705	485	10	)	)	PUNCT
ejpam-6705	485	11	(	(	PUNCT
ejpam-6705	485	12	2025	2025	NUM
ejpam-6705	485	13	)	)	PUNCT
ejpam-6705	485	14	,	,	PUNCT
ejpam-6705	485	15	6705	6705	NUM
ejpam-6705	485	16	19	19	NUM
ejpam-6705	485	17	of	of	ADP
ejpam-6705	485	18	23	23	NUM
ejpam-6705	485	19	also	also	ADV
ejpam-6705	485	20	lim	lim	PROPN
ejpam-6705	485	21	s→∞	s→∞	PROPN
ejpam-6705	485	22	t	t	PROPN
ejpam-6705	485	23	s(v1	s(v1	NOUN
ejpam-6705	485	24	,	,	PUNCT
ejpam-6705	485	25	u1	u1	NOUN
ejpam-6705	485	26	)	)	PUNCT
ejpam-6705	486	1	=	=	SYM
ejpam-6705	486	2	lim	lim	PROPN
ejpam-6705	486	3	s→∞	s→∞	PROPN
ejpam-6705	486	4	t	t	PROPN
ejpam-6705	486	5	s(w2	s(w2	NOUN
ejpam-6705	486	6	,	,	PUNCT
ejpam-6705	486	7	w1	w1	NOUN
ejpam-6705	486	8	)	)	PUNCT
ejpam-6705	486	9	=	=	SYM
ejpam-6705	486	10	v1	v1	NOUN
ejpam-6705	486	11	by	by	ADP
ejpam-6705	486	12	using	use	VERB
ejpam-6705	486	13	(	(	PUNCT
ejpam-6705	486	14	16	16	NUM
ejpam-6705	486	15	)	)	PUNCT
ejpam-6705	486	16	.	.	PUNCT
ejpam-6705	487	1	that	that	PRON
ejpam-6705	487	2	is	be	AUX
ejpam-6705	487	3	,	,	PUNCT
ejpam-6705	487	4	v	v	NOUN
ejpam-6705	487	5	=	=	SYM
ejpam-6705	487	6	v1	v1	NOUN
ejpam-6705	487	7	.	.	PUNCT
ejpam-6705	488	1	hence	hence	ADV
ejpam-6705	488	2	,	,	PUNCT
ejpam-6705	488	3	in	in	ADP
ejpam-6705	488	4	all	all	DET
ejpam-6705	488	5	cases	case	NOUN
ejpam-6705	488	6	,	,	PUNCT
ejpam-6705	488	7	(	(	PUNCT
ejpam-6705	488	8	u	u	NOUN
ejpam-6705	488	9	,	,	PUNCT
ejpam-6705	488	10	v	v	NOUN
ejpam-6705	488	11	)	)	PUNCT
ejpam-6705	488	12	=	=	SYM
ejpam-6705	488	13	(	(	PUNCT
ejpam-6705	488	14	u1	u1	NOUN
ejpam-6705	488	15	,	,	PUNCT
ejpam-6705	488	16	v1	v1	NOUN
ejpam-6705	488	17	)	)	PUNCT
ejpam-6705	488	18	,	,	PUNCT
ejpam-6705	488	19	which	which	PRON
ejpam-6705	488	20	means	mean	VERB
ejpam-6705	488	21	that	that	SCONJ
ejpam-6705	488	22	the	the	DET
ejpam-6705	488	23	coupled	couple	VERB
ejpam-6705	488	24	fixed	fix	VERB
ejpam-6705	488	25	point	point	NOUN
ejpam-6705	488	26	of	of	ADP
ejpam-6705	488	27	the	the	DET
ejpam-6705	488	28	mapping	mapping	NOUN
ejpam-6705	488	29	t	t	PROPN
ejpam-6705	488	30	is	be	AUX
ejpam-6705	488	31	unique	unique	ADJ
ejpam-6705	488	32	.	.	PUNCT
ejpam-6705	489	1	theorem	theorem	ADJ
ejpam-6705	489	2	6	6	NUM
ejpam-6705	489	3	.	.	PUNCT
ejpam-6705	490	1	let	let	AUX
ejpam-6705	490	2	(	(	PUNCT
ejpam-6705	490	3	x	x	X
ejpam-6705	490	4	,	,	PUNCT
ejpam-6705	490	5	gb,≼	gb,≼	NOUN
ejpam-6705	490	6	)	)	PUNCT
ejpam-6705	490	7	be	be	AUX
ejpam-6705	490	8	a	a	DET
ejpam-6705	490	9	partially	partially	ADV
ejpam-6705	490	10	ordered	order	VERB
ejpam-6705	490	11	complete	complete	ADJ
ejpam-6705	490	12	gb	gb	ADV
ejpam-6705	490	13	-	-	PUNCT
ejpam-6705	490	14	metric	metric	ADJ
ejpam-6705	490	15	space	space	NOUN
ejpam-6705	490	16	satisfying	satisfy	VERB
ejpam-6705	490	17	the	the	DET
ejpam-6705	490	18	following	follow	VERB
ejpam-6705	490	19	conditions	condition	NOUN
ejpam-6705	490	20	:	:	PUNCT
ejpam-6705	490	21	(	(	PUNCT
ejpam-6705	490	22	i	i	NOUN
ejpam-6705	490	23	)	)	PUNCT
ejpam-6705	490	24	if	if	SCONJ
ejpam-6705	490	25	(	(	PUNCT
ejpam-6705	490	26	us	we	PRON
ejpam-6705	490	27	)	)	PUNCT
ejpam-6705	490	28	is	be	AUX
ejpam-6705	490	29	a	a	DET
ejpam-6705	490	30	non	non	ADJ
ejpam-6705	490	31	-	-	ADJ
ejpam-6705	490	32	decreasing	decrease	VERB
ejpam-6705	490	33	sequence	sequence	NOUN
ejpam-6705	490	34	which	which	PRON
ejpam-6705	490	35	converges	converge	VERB
ejpam-6705	490	36	to	to	ADP
ejpam-6705	490	37	u	u	PROPN
ejpam-6705	490	38	∈	∈	PROPN
ejpam-6705	491	1	x	x	X
ejpam-6705	491	2	,	,	PUNCT
ejpam-6705	491	3	then	then	ADV
ejpam-6705	491	4	us	we	PRON
ejpam-6705	491	5	≼	≼	ADJ
ejpam-6705	491	6	u	u	NOUN
ejpam-6705	491	7	∀	∀	X
ejpam-6705	491	8	s.	s.	PROPN
ejpam-6705	491	9	(	(	PUNCT
ejpam-6705	491	10	ii	ii	PROPN
ejpam-6705	491	11	)	)	PUNCT
ejpam-6705	491	12	if	if	SCONJ
ejpam-6705	491	13	(	(	PUNCT
ejpam-6705	491	14	vs	vs	NOUN
ejpam-6705	491	15	)	)	PUNCT
ejpam-6705	491	16	is	be	AUX
ejpam-6705	491	17	a	a	DET
ejpam-6705	491	18	non	non	ADJ
ejpam-6705	491	19	-	-	ADJ
ejpam-6705	491	20	increasing	increasing	ADJ
ejpam-6705	491	21	sequence	sequence	NOUN
ejpam-6705	491	22	which	which	PRON
ejpam-6705	491	23	converges	converge	VERB
ejpam-6705	491	24	to	to	ADP
ejpam-6705	491	25	v	v	NUM
ejpam-6705	491	26	∈	∈	PROPN
ejpam-6705	491	27	x	x	X
ejpam-6705	491	28	,	,	PUNCT
ejpam-6705	491	29	then	then	ADV
ejpam-6705	491	30	vs	vs	ADP
ejpam-6705	491	31	≽	≽	PROPN
ejpam-6705	491	32	v	v	PROPN
ejpam-6705	491	33	∀	∀	NOUN
ejpam-6705	491	34	s.	s.	PROPN
ejpam-6705	491	35	(	(	PUNCT
ejpam-6705	491	36	iii	iii	NOUN
ejpam-6705	491	37	)	)	PUNCT
ejpam-6705	491	38	every	every	DET
ejpam-6705	491	39	pair	pair	NOUN
ejpam-6705	491	40	of	of	ADP
ejpam-6705	491	41	the	the	DET
ejpam-6705	491	42	element	element	NOUN
ejpam-6705	491	43	x	x	PUNCT
ejpam-6705	491	44	has	have	VERB
ejpam-6705	491	45	an	an	DET
ejpam-6705	491	46	upper	upper	ADJ
ejpam-6705	491	47	bound	bind	VERB
ejpam-6705	491	48	and	and	CCONJ
ejpam-6705	491	49	a	a	DET
ejpam-6705	491	50	lower	lower	ADV
ejpam-6705	491	51	bound	bind	VERB
ejpam-6705	491	52	in	in	ADP
ejpam-6705	491	53	x	x	X
ejpam-6705	491	54	.	.	PUNCT
ejpam-6705	492	1	also	also	ADV
ejpam-6705	492	2	,	,	PUNCT
ejpam-6705	492	3	let	let	VERB
ejpam-6705	492	4	t	t	NOUN
ejpam-6705	492	5	:	:	PUNCT
ejpam-6705	492	6	x	x	PROPN
ejpam-6705	492	7	×x	×x	ADP
ejpam-6705	492	8	→	→	SYM
ejpam-6705	492	9	x	x	PART
ejpam-6705	492	10	be	be	AUX
ejpam-6705	492	11	a	a	DET
ejpam-6705	492	12	continuous	continuous	ADJ
ejpam-6705	492	13	having	have	VERB
ejpam-6705	492	14	the	the	DET
ejpam-6705	492	15	mixed	mixed	ADJ
ejpam-6705	492	16	monotone	monotone	ADJ
ejpam-6705	492	17	property	property	NOUN
ejpam-6705	492	18	on	on	ADP
ejpam-6705	492	19	x	x	SYM
ejpam-6705	492	20	such	such	ADJ
ejpam-6705	492	21	that	that	DET
ejpam-6705	492	22	∫	∫	PROPN
ejpam-6705	492	23	gb(t	gb(t	X
ejpam-6705	492	24	(	(	PUNCT
ejpam-6705	492	25	u	u	NOUN
ejpam-6705	492	26	,	,	PUNCT
ejpam-6705	492	27	v),t	v),t	PROPN
ejpam-6705	492	28	(	(	PUNCT
ejpam-6705	492	29	m	m	PROPN
ejpam-6705	492	30	,	,	PUNCT
ejpam-6705	492	31	n),t	n),t	PROPN
ejpam-6705	492	32	(	(	PUNCT
ejpam-6705	492	33	f	f	X
ejpam-6705	492	34	,	,	PUNCT
ejpam-6705	492	35	w	w	NOUN
ejpam-6705	492	36	)	)	PUNCT
ejpam-6705	492	37	)	)	PUNCT
ejpam-6705	492	38	0	0	NUM
ejpam-6705	493	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	493	2	≤	≤	PROPN
ejpam-6705	493	3	σ	σ	PROPN
ejpam-6705	493	4	(	(	PUNCT
ejpam-6705	493	5	∫	∫	PROPN
ejpam-6705	493	6	gb(u	gb(u	PROPN
ejpam-6705	493	7	,	,	PUNCT
ejpam-6705	493	8	m	m	NOUN
ejpam-6705	493	9	,	,	PUNCT
ejpam-6705	493	10	f)+gb(v	f)+gb(v	NOUN
ejpam-6705	493	11	,	,	PUNCT
ejpam-6705	493	12	n	n	CCONJ
ejpam-6705	493	13	,	,	PUNCT
ejpam-6705	493	14	w	w	NOUN
ejpam-6705	493	15	)	)	PUNCT
ejpam-6705	493	16	0	0	NUM
ejpam-6705	493	17	g(t)dt	g(t)dt	PROPN
ejpam-6705	493	18	)	)	PUNCT
ejpam-6705	493	19	,	,	PUNCT
ejpam-6705	493	20	(	(	PUNCT
ejpam-6705	493	21	17	17	NUM
ejpam-6705	493	22	)	)	PUNCT
ejpam-6705	494	1	where	where	SCONJ
ejpam-6705	494	2	u	u	NOUN
ejpam-6705	494	3	,	,	PUNCT
ejpam-6705	494	4	v	v	NOUN
ejpam-6705	494	5	,	,	PUNCT
ejpam-6705	494	6	w	w	PROPN
ejpam-6705	494	7	,	,	PUNCT
ejpam-6705	494	8	m	m	PROPN
ejpam-6705	494	9	,	,	PUNCT
ejpam-6705	494	10	n	n	CCONJ
ejpam-6705	494	11	,	,	PUNCT
ejpam-6705	494	12	f	f	PROPN
ejpam-6705	494	13	∈	∈	PROPN
ejpam-6705	494	14	x	x	X
ejpam-6705	494	15	and	and	CCONJ
ejpam-6705	494	16	g	g	NOUN
ejpam-6705	494	17	:	:	PUNCT
ejpam-6705	495	1	[	[	X
ejpam-6705	495	2	0,∞	0,∞	NOUN
ejpam-6705	495	3	)	)	PUNCT
ejpam-6705	495	4	→	→	PUNCT
ejpam-6705	496	1	[	[	X
ejpam-6705	496	2	0,∞	0,∞	NUM
ejpam-6705	496	3	)	)	PUNCT
ejpam-6705	496	4	is	be	AUX
ejpam-6705	496	5	a	a	DET
ejpam-6705	496	6	lebesgue	lebesgue	NOUN
ejpam-6705	496	7	integrable	integrable	ADJ
ejpam-6705	496	8	mapping	mapping	NOUN
ejpam-6705	496	9	with	with	ADP
ejpam-6705	496	10	f	f	PROPN
ejpam-6705	496	11	≼	≼	PROPN
ejpam-6705	496	12	m	m	VERB
ejpam-6705	496	13	≼	≼	ADJ
ejpam-6705	496	14	u	u	NOUN
ejpam-6705	496	15	and	and	CCONJ
ejpam-6705	496	16	v	v	ADP
ejpam-6705	496	17	≼	≼	NOUN
ejpam-6705	496	18	n	n	PROPN
ejpam-6705	496	19	≼	≼	PROPN
ejpam-6705	496	20	w	w	PROPN
ejpam-6705	496	21	,	,	PUNCT
ejpam-6705	496	22	where	where	SCONJ
ejpam-6705	496	23	either	either	CCONJ
ejpam-6705	496	24	m	m	VERB
ejpam-6705	496	25	̸=	̸=	PROPN
ejpam-6705	496	26	f	f	PROPN
ejpam-6705	496	27	or	or	CCONJ
ejpam-6705	496	28	n	n	PRON
ejpam-6705	496	29	̸=	̸=	PROPN
ejpam-6705	496	30	w.	w.	NOUN
ejpam-6705	496	31	if	if	SCONJ
ejpam-6705	496	32	there	there	PRON
ejpam-6705	496	33	exist	exist	VERB
ejpam-6705	496	34	u0	u0	ADJ
ejpam-6705	496	35	,	,	PUNCT
ejpam-6705	496	36	v0	v0	NOUN
ejpam-6705	496	37	∈	∈	PROPN
ejpam-6705	496	38	x	x	PUNCT
ejpam-6705	496	39	such	such	ADJ
ejpam-6705	496	40	that	that	DET
ejpam-6705	496	41	u0	u0	ADJ
ejpam-6705	496	42	≼	≼	PROPN
ejpam-6705	496	43	t	t	PROPN
ejpam-6705	496	44	(	(	PUNCT
ejpam-6705	496	45	u0	u0	PROPN
ejpam-6705	496	46	,	,	PUNCT
ejpam-6705	496	47	v0	v0	PROPN
ejpam-6705	496	48	)	)	PUNCT
ejpam-6705	496	49	and	and	CCONJ
ejpam-6705	496	50	t	t	PROPN
ejpam-6705	496	51	(	(	PUNCT
ejpam-6705	496	52	v0	v0	PROPN
ejpam-6705	496	53	,	,	PUNCT
ejpam-6705	496	54	u0	u0	ADJ
ejpam-6705	496	55	)	)	PUNCT
ejpam-6705	496	56	≼	≼	PROPN
ejpam-6705	496	57	v0	v0	PROPN
ejpam-6705	496	58	,	,	PUNCT
ejpam-6705	496	59	then	then	ADV
ejpam-6705	496	60	u	u	X
ejpam-6705	496	61	=	=	PUNCT
ejpam-6705	496	62	v.	v.	ADP
ejpam-6705	496	63	proof	proof	NOUN
ejpam-6705	496	64	.	.	PUNCT
ejpam-6705	497	1	assume	assume	VERB
ejpam-6705	497	2	that	that	SCONJ
ejpam-6705	497	3	u	u	PROPN
ejpam-6705	497	4	and	and	CCONJ
ejpam-6705	497	5	v	v	NOUN
ejpam-6705	497	6	are	be	AUX
ejpam-6705	497	7	comparable	comparable	ADJ
ejpam-6705	497	8	under	under	ADP
ejpam-6705	497	9	the	the	DET
ejpam-6705	497	10	partial	partial	ADJ
ejpam-6705	497	11	ordering	ordering	NOUN
ejpam-6705	497	12	≼	≼	ADV
ejpam-6705	497	13	in	in	ADP
ejpam-6705	497	14	x	x	X
ejpam-6705	497	15	,	,	PUNCT
ejpam-6705	497	16	allowing	allow	VERB
ejpam-6705	497	17	us	we	PRON
ejpam-6705	497	18	to	to	PART
ejpam-6705	497	19	assume	assume	VERB
ejpam-6705	497	20	that	that	SCONJ
ejpam-6705	497	21	u	u	PROPN
ejpam-6705	497	22	≼	≼	ADJ
ejpam-6705	497	23	v	v	NOUN
ejpam-6705	497	24	and	and	CCONJ
ejpam-6705	497	25	v	v	ADP
ejpam-6705	497	26	≼	≼	ADV
ejpam-6705	497	27	v.	v.	ADP
ejpam-6705	497	28	using	use	VERB
ejpam-6705	497	29	the	the	DET
ejpam-6705	497	30	same	same	ADJ
ejpam-6705	497	31	argument	argument	NOUN
ejpam-6705	497	32	as	as	ADP
ejpam-6705	497	33	in	in	ADP
ejpam-6705	497	34	theorem	theorem	NOUN
ejpam-6705	497	35	3	3	NUM
ejpam-6705	497	36	,	,	PUNCT
ejpam-6705	497	37	we	we	PRON
ejpam-6705	497	38	arrive	arrive	VERB
ejpam-6705	497	39	at	at	ADP
ejpam-6705	497	40	u	u	NOUN
ejpam-6705	497	41	=	=	PROPN
ejpam-6705	498	1	v.	v.	CCONJ
ejpam-6705	498	2	next	next	ADJ
ejpam-6705	498	3	assume	assume	VERB
ejpam-6705	498	4	that	that	SCONJ
ejpam-6705	498	5	u	u	PROPN
ejpam-6705	498	6	and	and	CCONJ
ejpam-6705	498	7	v	v	NOUN
ejpam-6705	498	8	are	be	AUX
ejpam-6705	498	9	incomparable	incomparable	ADJ
ejpam-6705	498	10	.	.	PUNCT
ejpam-6705	499	1	then	then	ADV
ejpam-6705	499	2	there	there	PRON
ejpam-6705	499	3	is	be	VERB
ejpam-6705	499	4	a	a	DET
ejpam-6705	499	5	common	common	ADJ
ejpam-6705	499	6	upper	upper	ADJ
ejpam-6705	499	7	bound	bind	VERB
ejpam-6705	499	8	w	w	PROPN
ejpam-6705	499	9	∈	∈	PROPN
ejpam-6705	499	10	x	x	PUNCT
ejpam-6705	499	11	that	that	PRON
ejpam-6705	499	12	is	be	AUX
ejpam-6705	499	13	comparable	comparable	ADJ
ejpam-6705	499	14	with	with	ADP
ejpam-6705	499	15	both	both	CCONJ
ejpam-6705	499	16	u	u	NOUN
ejpam-6705	499	17	and	and	CCONJ
ejpam-6705	499	18	v.	v.	CCONJ
ejpam-6705	499	19	so	so	ADV
ejpam-6705	499	20	suppose	suppose	VERB
ejpam-6705	499	21	that	that	SCONJ
ejpam-6705	499	22	u	u	PROPN
ejpam-6705	499	23	≼	≼	PROPN
ejpam-6705	499	24	w	w	PROPN
ejpam-6705	499	25	and	and	CCONJ
ejpam-6705	499	26	v	v	ADP
ejpam-6705	499	27	≼	≼	PROPN
ejpam-6705	499	28	w.	w.	NOUN
ejpam-6705	499	29	by	by	ADP
ejpam-6705	499	30	applying	apply	VERB
ejpam-6705	499	31	theorem	theorem	NOUN
ejpam-6705	499	32	3	3	NUM
ejpam-6705	499	33	,	,	PUNCT
ejpam-6705	499	34	(	(	PUNCT
ejpam-6705	499	35	u	u	NOUN
ejpam-6705	499	36	,	,	PUNCT
ejpam-6705	499	37	v	v	NOUN
ejpam-6705	499	38	)	)	PUNCT
ejpam-6705	499	39	=	=	SYM
ejpam-6705	499	40	(	(	PUNCT
ejpam-6705	499	41	w	w	PROPN
ejpam-6705	499	42	,	,	PUNCT
ejpam-6705	499	43	w	w	NOUN
ejpam-6705	499	44	)	)	PUNCT
ejpam-6705	499	45	.	.	PUNCT
ejpam-6705	500	1	thus	thus	ADV
ejpam-6705	500	2	,	,	PUNCT
ejpam-6705	500	3	w	w	PROPN
ejpam-6705	500	4	=	=	PUNCT
ejpam-6705	500	5	v.	v.	ADP
ejpam-6705	500	6	the	the	DET
ejpam-6705	500	7	following	follow	VERB
ejpam-6705	500	8	examples	example	NOUN
ejpam-6705	500	9	validate	validate	VERB
ejpam-6705	500	10	our	our	PRON
ejpam-6705	500	11	result	result	NOUN
ejpam-6705	500	12	.	.	PUNCT
ejpam-6705	501	1	example	example	NOUN
ejpam-6705	501	2	2	2	NUM
ejpam-6705	501	3	.	.	X
ejpam-6705	502	1	consider	consider	VERB
ejpam-6705	502	2	the	the	DET
ejpam-6705	502	3	set	set	NOUN
ejpam-6705	502	4	x	x	PUNCT
ejpam-6705	502	5	=	=	PUNCT
ejpam-6705	503	1	[	[	X
ejpam-6705	503	2	0	0	NUM
ejpam-6705	503	3	,	,	PUNCT
ejpam-6705	503	4	1	1	NUM
ejpam-6705	503	5	]	]	PUNCT
ejpam-6705	503	6	and	and	CCONJ
ejpam-6705	503	7	define	define	VERB
ejpam-6705	503	8	a	a	DET
ejpam-6705	503	9	mapping	mapping	NOUN
ejpam-6705	503	10	gb	gb	NOUN
ejpam-6705	503	11	:	:	PUNCT
ejpam-6705	503	12	x	x	PROPN
ejpam-6705	503	13	×x	×x	X
ejpam-6705	503	14	×x	×x	X
ejpam-6705	503	15	→	→	SYM
ejpam-6705	503	16	r+	r+	NOUN
ejpam-6705	503	17	by	by	ADP
ejpam-6705	503	18	gb(u	gb(u	NUM
ejpam-6705	503	19	,	,	PUNCT
ejpam-6705	503	20	v	v	NOUN
ejpam-6705	503	21	,	,	PUNCT
ejpam-6705	503	22	w	w	NOUN
ejpam-6705	503	23	)	)	PUNCT
ejpam-6705	503	24	=	=	SYM
ejpam-6705	503	25	|u−	|u−	NOUN
ejpam-6705	503	26	v|2	v|2	PROPN
ejpam-6705	503	27	+	+	NOUN
ejpam-6705	503	28	|u−w|2	|u−w|2	NOUN
ejpam-6705	503	29	+	+	CCONJ
ejpam-6705	503	30	|v−w|2	|v−w|2	NOUN
ejpam-6705	503	31	∀	∀	X
ejpam-6705	503	32	u	u	NOUN
ejpam-6705	503	33	,	,	PUNCT
ejpam-6705	503	34	v	v	NOUN
ejpam-6705	503	35	,	,	PUNCT
ejpam-6705	503	36	w	w	PROPN
ejpam-6705	503	37	∈	∈	PROPN
ejpam-6705	503	38	x	x	X
ejpam-6705	503	39	.	.	PUNCT
ejpam-6705	504	1	therefore	therefore	ADV
ejpam-6705	504	2	(	(	PUNCT
ejpam-6705	504	3	x	x	X
ejpam-6705	504	4	,	,	PUNCT
ejpam-6705	504	5	gb	gb	PROPN
ejpam-6705	504	6	)	)	PUNCT
ejpam-6705	504	7	is	be	AUX
ejpam-6705	504	8	a	a	DET
ejpam-6705	504	9	complete	complete	ADJ
ejpam-6705	504	10	gb	gb	ADV
ejpam-6705	504	11	-	-	PUNCT
ejpam-6705	504	12	metric	metric	ADJ
ejpam-6705	504	13	space	space	NOUN
ejpam-6705	504	14	.	.	PUNCT
ejpam-6705	505	1	now	now	ADV
ejpam-6705	505	2	,	,	PUNCT
ejpam-6705	505	3	assume	assume	VERB
ejpam-6705	505	4	that	that	SCONJ
ejpam-6705	505	5	σ(t	σ(t	PROPN
ejpam-6705	505	6	)	)	PUNCT
ejpam-6705	506	1	=	=	SYM
ejpam-6705	506	2	t	t	PROPN
ejpam-6705	506	3	2	2	NUM
ejpam-6705	506	4	for	for	ADP
ejpam-6705	506	5	all	all	DET
ejpam-6705	506	6	t	t	NOUN
ejpam-6705	506	7	∈	∈	PROPN
ejpam-6705	507	1	[	[	X
ejpam-6705	507	2	0,∞	0,∞	NOUN
ejpam-6705	507	3	)	)	PUNCT
ejpam-6705	507	4	,	,	PUNCT
ejpam-6705	507	5	and	and	CCONJ
ejpam-6705	507	6	let	let	VERB
ejpam-6705	507	7	t	t	NOUN
ejpam-6705	507	8	:	:	PUNCT
ejpam-6705	507	9	x	x	PUNCT
ejpam-6705	507	10	×	×	NOUN
ejpam-6705	507	11	x	x	INTJ
ejpam-6705	507	12	→	→	PUNCT
ejpam-6705	507	13	x	x	AUX
ejpam-6705	507	14	be	be	AUX
ejpam-6705	507	15	a	a	DET
ejpam-6705	507	16	mapping	mapping	NOUN
ejpam-6705	507	17	defined	define	VERB
ejpam-6705	507	18	by	by	ADP
ejpam-6705	507	19	t	t	PROPN
ejpam-6705	507	20	(	(	PUNCT
ejpam-6705	507	21	g	g	PROPN
ejpam-6705	507	22	,	,	PUNCT
ejpam-6705	507	23	h	h	NOUN
ejpam-6705	507	24	)	)	PUNCT
ejpam-6705	508	1	=	=	SYM
ejpam-6705	508	2	3(g+h	3(g+h	NUM
ejpam-6705	508	3	)	)	PUNCT
ejpam-6705	508	4	16	16	NUM
ejpam-6705	508	5	.	.	PUNCT
ejpam-6705	509	1	thus	thus	ADV
ejpam-6705	509	2	the	the	DET
ejpam-6705	509	3	conditions	condition	NOUN
ejpam-6705	509	4	of	of	ADP
ejpam-6705	509	5	theorem	theorem	ADJ
ejpam-6705	509	6	3	3	NUM
ejpam-6705	509	7	are	be	AUX
ejpam-6705	509	8	satisfied	satisfied	ADJ
ejpam-6705	509	9	.	.	PUNCT
ejpam-6705	510	1	that	that	PRON
ejpam-6705	510	2	is,∫	is,∫	VERB
ejpam-6705	510	3	gb(t	gb(t	X
ejpam-6705	510	4	(	(	PUNCT
ejpam-6705	510	5	g	g	NOUN
ejpam-6705	510	6	,	,	PUNCT
ejpam-6705	510	7	h),t	h),t	PROPN
ejpam-6705	510	8	(	(	PUNCT
ejpam-6705	510	9	m	m	PROPN
ejpam-6705	510	10	,	,	PUNCT
ejpam-6705	510	11	n),t	n),t	X
ejpam-6705	510	12	(	(	PUNCT
ejpam-6705	510	13	c	c	X
ejpam-6705	510	14	,	,	PUNCT
ejpam-6705	510	15	k	k	NOUN
ejpam-6705	510	16	)	)	PUNCT
ejpam-6705	510	17	)	)	PUNCT
ejpam-6705	510	18	0	0	NUM
ejpam-6705	511	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	511	2	=	=	SYM
ejpam-6705	511	3	∫	∫	PROPN
ejpam-6705	511	4	|t	|t	PROPN
ejpam-6705	512	1	(	(	PUNCT
ejpam-6705	512	2	g	g	PROPN
ejpam-6705	512	3	,	,	PUNCT
ejpam-6705	512	4	h)−t	h)−t	PROPN
ejpam-6705	512	5	(	(	PUNCT
ejpam-6705	512	6	m	m	PROPN
ejpam-6705	512	7	,	,	PUNCT
ejpam-6705	512	8	n)|2+|t	n)|2+|t	PROPN
ejpam-6705	512	9	(	(	PUNCT
ejpam-6705	512	10	g	g	PROPN
ejpam-6705	512	11	,	,	PUNCT
ejpam-6705	512	12	h)−t	h)−t	PROPN
ejpam-6705	512	13	(	(	PUNCT
ejpam-6705	512	14	c	c	NOUN
ejpam-6705	512	15	,	,	PUNCT
ejpam-6705	512	16	k)|2+|t	k)|2+|t	PROPN
ejpam-6705	512	17	(	(	PUNCT
ejpam-6705	512	18	m	m	PROPN
ejpam-6705	512	19	,	,	PUNCT
ejpam-6705	512	20	n)−t	n)−t	PROPN
ejpam-6705	512	21	(	(	PUNCT
ejpam-6705	512	22	c	c	X
ejpam-6705	512	23	,	,	PUNCT
ejpam-6705	512	24	k)|2	k)|2	PROPN
ejpam-6705	512	25	0	0	NUM
ejpam-6705	512	26	g(t)dt	g(t)dt	PROPN
ejpam-6705	513	1	=	=	SYM
ejpam-6705	513	2	∫	∫	PROPN
ejpam-6705	514	1	|	|	ADV
ejpam-6705	514	2	3(g+h	3(g+h	NUM
ejpam-6705	514	3	)	)	PUNCT
ejpam-6705	515	1	16	16	NUM
ejpam-6705	516	1	−	−	PROPN
ejpam-6705	516	2	3(m+n	3(m+n	NUM
ejpam-6705	516	3	)	)	PUNCT
ejpam-6705	516	4	16	16	NUM
ejpam-6705	516	5	|2+|	|2+|	NOUN
ejpam-6705	516	6	3(g+h	3(g+h	NUM
ejpam-6705	516	7	)	)	PUNCT
ejpam-6705	516	8	16	16	NUM
ejpam-6705	516	9	−	−	PROPN
ejpam-6705	516	10	3(c+l	3(c+l	NUM
ejpam-6705	516	11	)	)	PUNCT
ejpam-6705	516	12	16	16	NUM
ejpam-6705	516	13	|2+|	|2+|	NOUN
ejpam-6705	516	14	3(m+n	3(m+n	NUM
ejpam-6705	516	15	)	)	PUNCT
ejpam-6705	516	16	16	16	NUM
ejpam-6705	516	17	−	−	PROPN
ejpam-6705	516	18	3(c+k	3(c+k	NUM
ejpam-6705	516	19	)	)	PUNCT
ejpam-6705	516	20	16	16	NUM
ejpam-6705	516	21	|2	|2	NUM
ejpam-6705	516	22	0	0	NUM
ejpam-6705	516	23	g(t)dt	g(t)dt	PROPN
ejpam-6705	516	24	≤	≤	NUM
ejpam-6705	516	25	∫	∫	PROPN
ejpam-6705	516	26	9(2	9(2	NUM
ejpam-6705	516	27	)	)	PUNCT
ejpam-6705	516	28	256	256	NUM
ejpam-6705	516	29	(	(	PUNCT
ejpam-6705	516	30	|g−m|2+|h−n|2+|g−c|2+|h−k|2+|m−c|2+|n−k|2	|g−m|2+|h−n|2+|g−c|2+|h−k|2+|m−c|2+|n−k|2	NOUN
ejpam-6705	516	31	)	)	PUNCT
ejpam-6705	516	32	0	0	NUM
ejpam-6705	517	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	517	2	≤	≤	NOUN
ejpam-6705	517	3	1	1	NUM
ejpam-6705	517	4	256	256	NUM
ejpam-6705	517	5	∫	∫	NOUN
ejpam-6705	517	6	l[|g−m|2+|h−n|2+|g−c|2+|h−k|2+|m−c|2+|n−k|2	l[|g−m|2+|h−n|2+|g−c|2+|h−k|2+|m−c|2+|n−k|2	X
ejpam-6705	517	7	]	]	PUNCT
ejpam-6705	517	8	0	0	NUM
ejpam-6705	517	9	g(t)dt	g(t)dt	PROPN
ejpam-6705	517	10	≤	≤	PROPN
ejpam-6705	517	11	σ	σ	PROPN
ejpam-6705	518	1	(	(	PUNCT
ejpam-6705	518	2	∫	∫	PROPN
ejpam-6705	518	3	l[gb(g	l[gb(g	PROPN
ejpam-6705	518	4	,	,	PUNCT
ejpam-6705	518	5	m	m	PROPN
ejpam-6705	518	6	,	,	PUNCT
ejpam-6705	518	7	c)+gb(h	c)+gb(h	PROPN
ejpam-6705	518	8	,	,	PUNCT
ejpam-6705	518	9	n	n	CCONJ
ejpam-6705	518	10	,	,	PUNCT
ejpam-6705	518	11	k	k	NOUN
ejpam-6705	518	12	)	)	PUNCT
ejpam-6705	518	13	]	]	PUNCT
ejpam-6705	518	14	0	0	NUM
ejpam-6705	519	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	519	2	)	)	PUNCT
ejpam-6705	520	1	s.	s.	PROPN
ejpam-6705	520	2	batul	batul	PROPN
ejpam-6705	520	3	et	et	PROPN
ejpam-6705	520	4	al	al	PROPN
ejpam-6705	520	5	.	.	PUNCT
ejpam-6705	520	6	/	/	SYM
ejpam-6705	520	7	eur	eur	PROPN
ejpam-6705	520	8	.	.	PUNCT
ejpam-6705	521	1	j.	j.	PROPN
ejpam-6705	521	2	pure	pure	PROPN
ejpam-6705	521	3	appl	appl	PROPN
ejpam-6705	521	4	.	.	PROPN
ejpam-6705	521	5	math	math	PROPN
ejpam-6705	521	6	,	,	PUNCT
ejpam-6705	521	7	18	18	NUM
ejpam-6705	521	8	(	(	PUNCT
ejpam-6705	521	9	4	4	NUM
ejpam-6705	521	10	)	)	PUNCT
ejpam-6705	521	11	(	(	PUNCT
ejpam-6705	521	12	2025	2025	NUM
ejpam-6705	521	13	)	)	PUNCT
ejpam-6705	521	14	,	,	PUNCT
ejpam-6705	521	15	6705	6705	NUM
ejpam-6705	521	16	20	20	NUM
ejpam-6705	521	17	of	of	ADP
ejpam-6705	521	18	23	23	NUM
ejpam-6705	521	19	where	where	SCONJ
ejpam-6705	521	20	g	g	NOUN
ejpam-6705	521	21	,	,	PUNCT
ejpam-6705	521	22	h	h	NOUN
ejpam-6705	521	23	,	,	PUNCT
ejpam-6705	521	24	c	c	X
ejpam-6705	521	25	,	,	PUNCT
ejpam-6705	521	26	m	m	PROPN
ejpam-6705	521	27	,	,	PUNCT
ejpam-6705	521	28	n	n	CCONJ
ejpam-6705	521	29	,	,	PUNCT
ejpam-6705	521	30	k	k	PROPN
ejpam-6705	521	31	∈	∈	PROPN
ejpam-6705	521	32	x	x	X
ejpam-6705	521	33	.	.	PUNCT
ejpam-6705	522	1	thus	thus	ADV
ejpam-6705	522	2	t	t	PROPN
ejpam-6705	522	3	has	have	VERB
ejpam-6705	522	4	a	a	DET
ejpam-6705	522	5	coupled	couple	VERB
ejpam-6705	522	6	fixed	fix	VERB
ejpam-6705	522	7	point	point	NOUN
ejpam-6705	522	8	.	.	PUNCT
ejpam-6705	523	1	example	example	NOUN
ejpam-6705	524	1	3	3	X
ejpam-6705	524	2	.	.	PUNCT
ejpam-6705	524	3	let	let	VERB
ejpam-6705	524	4	x	x	PUNCT
ejpam-6705	524	5	=	=	PUNCT
ejpam-6705	525	1	[	[	X
ejpam-6705	525	2	0,∞	0,∞	NUM
ejpam-6705	525	3	)	)	PUNCT
ejpam-6705	525	4	and	and	CCONJ
ejpam-6705	525	5	gb	gb	PRON
ejpam-6705	525	6	:	:	PUNCT
ejpam-6705	525	7	x	x	PROPN
ejpam-6705	525	8	×x	×x	X
ejpam-6705	525	9	×x	×x	X
ejpam-6705	525	10	→	→	SYM
ejpam-6705	525	11	r+	r+	X
ejpam-6705	525	12	be	be	AUX
ejpam-6705	525	13	a	a	DET
ejpam-6705	525	14	mapping	mapping	NOUN
ejpam-6705	525	15	defined	define	VERB
ejpam-6705	525	16	by	by	ADP
ejpam-6705	525	17	:	:	PUNCT
ejpam-6705	525	18	gb(u	gb(u	NUM
ejpam-6705	525	19	,	,	PUNCT
ejpam-6705	525	20	v	v	NOUN
ejpam-6705	525	21	,	,	PUNCT
ejpam-6705	525	22	w	w	NOUN
ejpam-6705	525	23	)	)	PUNCT
ejpam-6705	525	24	=	=	NOUN
ejpam-6705	525	25	|u−	|u−	NOUN
ejpam-6705	525	26	v|q	v|q	VERB
ejpam-6705	525	27	+	+	CCONJ
ejpam-6705	525	28	|v	|v	PROPN
ejpam-6705	525	29	−	−	NOUN
ejpam-6705	525	30	w|q	w|q	NOUN
ejpam-6705	526	1	+	+	CCONJ
ejpam-6705	526	2	|w	|w	ADJ
ejpam-6705	526	3	−	−	NOUN
ejpam-6705	526	4	u|q	u|q	PROPN
ejpam-6705	526	5	.	.	PUNCT
ejpam-6705	527	1	then	then	ADV
ejpam-6705	527	2	gb	gb	PRON
ejpam-6705	527	3	is	be	AUX
ejpam-6705	527	4	gb	gb	ADV
ejpam-6705	527	5	-	-	PUNCT
ejpam-6705	527	6	metric	metric	ADJ
ejpam-6705	527	7	space	space	NOUN
ejpam-6705	527	8	(	(	PUNCT
ejpam-6705	527	9	by	by	ADP
ejpam-6705	527	10	example	example	NOUN
ejpam-6705	527	11	1	1	NUM
ejpam-6705	527	12	)	)	PUNCT
ejpam-6705	527	13	.	.	PUNCT
ejpam-6705	528	1	now	now	ADV
ejpam-6705	528	2	,	,	PUNCT
ejpam-6705	528	3	suppose	suppose	VERB
ejpam-6705	528	4	that	that	SCONJ
ejpam-6705	528	5	σ(t	σ(t	PROPN
ejpam-6705	528	6	)	)	PUNCT
ejpam-6705	528	7	=	=	SYM
ejpam-6705	528	8	1	1	NUM
ejpam-6705	528	9	2	2	NUM
ejpam-6705	528	10	t	t	NOUN
ejpam-6705	528	11	for	for	ADP
ejpam-6705	528	12	all	all	DET
ejpam-6705	528	13	t	t	NOUN
ejpam-6705	528	14	∈	∈	PROPN
ejpam-6705	529	1	[	[	X
ejpam-6705	529	2	0,∞	0,∞	X
ejpam-6705	529	3	]	]	PUNCT
ejpam-6705	529	4	,	,	PUNCT
ejpam-6705	529	5	and	and	CCONJ
ejpam-6705	529	6	let	let	VERB
ejpam-6705	529	7	t	t	NOUN
ejpam-6705	529	8	:	:	PUNCT
ejpam-6705	529	9	x	x	PROPN
ejpam-6705	529	10	×x	×x	ADP
ejpam-6705	529	11	→	→	SYM
ejpam-6705	529	12	x	x	PART
ejpam-6705	529	13	be	be	AUX
ejpam-6705	529	14	a	a	DET
ejpam-6705	529	15	mapping	mapping	NOUN
ejpam-6705	529	16	defined	define	VERB
ejpam-6705	529	17	by	by	ADP
ejpam-6705	529	18	t	t	PROPN
ejpam-6705	529	19	(	(	PUNCT
ejpam-6705	529	20	g	g	PROPN
ejpam-6705	529	21	,	,	PUNCT
ejpam-6705	529	22	h	h	NOUN
ejpam-6705	529	23	)	)	PUNCT
ejpam-6705	529	24	=	=	SYM
ejpam-6705	530	1	g+h	g+h	NUM
ejpam-6705	530	2	16	16	NUM
ejpam-6705	530	3	.	.	PUNCT
ejpam-6705	531	1	we	we	PRON
ejpam-6705	531	2	have∫	have∫	VERB
ejpam-6705	531	3	gb(t	gb(t	NOUN
ejpam-6705	532	1	(	(	PUNCT
ejpam-6705	532	2	g	g	NOUN
ejpam-6705	532	3	,	,	PUNCT
ejpam-6705	532	4	h),t	h),t	PROPN
ejpam-6705	532	5	(	(	PUNCT
ejpam-6705	532	6	m	m	PROPN
ejpam-6705	532	7	,	,	PUNCT
ejpam-6705	532	8	n),t	n),t	X
ejpam-6705	532	9	(	(	PUNCT
ejpam-6705	532	10	c	c	X
ejpam-6705	532	11	,	,	PUNCT
ejpam-6705	532	12	k	k	NOUN
ejpam-6705	532	13	)	)	PUNCT
ejpam-6705	532	14	)	)	PUNCT
ejpam-6705	532	15	0	0	NUM
ejpam-6705	533	1	g(t)dt	g(t)dt	NOUN
ejpam-6705	533	2	=	=	SYM
ejpam-6705	533	3	∫	∫	PROPN
ejpam-6705	533	4	|t	|t	PROPN
ejpam-6705	534	1	(	(	PUNCT
ejpam-6705	534	2	g	g	PROPN
ejpam-6705	534	3	,	,	PUNCT
ejpam-6705	534	4	h)−t	h)−t	PROPN
ejpam-6705	534	5	(	(	PUNCT
ejpam-6705	534	6	m	m	PROPN
ejpam-6705	534	7	,	,	PUNCT
ejpam-6705	534	8	n)|q+|t	n)|q+|t	X
ejpam-6705	534	9	(	(	PUNCT
ejpam-6705	534	10	g	g	NOUN
ejpam-6705	534	11	,	,	PUNCT
ejpam-6705	534	12	h)−t	h)−t	PROPN
ejpam-6705	534	13	(	(	PUNCT
ejpam-6705	534	14	c	c	X
ejpam-6705	534	15	,	,	PUNCT
ejpam-6705	534	16	k)|q+|t	k)|q+|t	PROPN
ejpam-6705	534	17	(	(	PUNCT
ejpam-6705	534	18	m	m	PROPN
ejpam-6705	534	19	,	,	PUNCT
ejpam-6705	534	20	n)−t	n)−t	PROPN
ejpam-6705	534	21	(	(	PUNCT
ejpam-6705	534	22	c	c	X
ejpam-6705	534	23	,	,	PUNCT
ejpam-6705	534	24	k)|q	k)|q	NOUN
ejpam-6705	534	25	0	0	NUM
ejpam-6705	535	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	535	2	=	=	SYM
ejpam-6705	535	3	∫	∫	PROPN
ejpam-6705	536	1	|	|	INTJ
ejpam-6705	536	2	g+h	g+h	PROPN
ejpam-6705	537	1	16	16	NUM
ejpam-6705	537	2	−m+n	−m+n	NOUN
ejpam-6705	537	3	16	16	NUM
ejpam-6705	538	1	|q+|	|q+|	PROPN
ejpam-6705	538	2	g+h	g+h	PROPN
ejpam-6705	538	3	16	16	NUM
ejpam-6705	538	4	−	−	NOUN
ejpam-6705	538	5	c+k	c+k	NUM
ejpam-6705	538	6	16	16	NUM
ejpam-6705	538	7	|q+|m+n	|q+|m+n	NOUN
ejpam-6705	538	8	16	16	NUM
ejpam-6705	538	9	−	−	NOUN
ejpam-6705	538	10	c+k	c+k	NUM
ejpam-6705	538	11	16	16	NUM
ejpam-6705	538	12	|q	|q	NOUN
ejpam-6705	538	13	0	0	PUNCT
ejpam-6705	539	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	540	1	≤	≤	PROPN
ejpam-6705	540	2	∫	∫	PROPN
ejpam-6705	540	3	(	(	PUNCT
ejpam-6705	540	4	1	1	NUM
ejpam-6705	540	5	16	16	NUM
ejpam-6705	540	6	)	)	PUNCT
ejpam-6705	540	7	q(2)q−1(|g−m|q+|h−n|q+|g−c|q+|h−k|q+|m−c|q+|n−k|q	q(2)q−1(|g−m|q+|h−n|q+|g−c|q+|h−k|q+|m−c|q+|n−k|q	NUM
ejpam-6705	540	8	)	)	PUNCT
ejpam-6705	540	9	0	0	NUM
ejpam-6705	541	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	541	2	≤	≤	NOUN
ejpam-6705	541	3	(	(	PUNCT
ejpam-6705	541	4	1	1	NUM
ejpam-6705	541	5	16	16	NUM
ejpam-6705	541	6	)	)	PUNCT
ejpam-6705	541	7	q	q	NOUN
ejpam-6705	541	8	∫	∫	PROPN
ejpam-6705	541	9	l(|g−m|q+|h−n|q+|g−c|q+|h−k|q+|m−c|q+|n−k|q	l(|g−m|q+|h−n|q+|g−c|q+|h−k|q+|m−c|q+|n−k|q	X
ejpam-6705	541	10	)	)	PUNCT
ejpam-6705	541	11	0	0	NUM
ejpam-6705	542	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	542	2	≤	≤	PROPN
ejpam-6705	542	3	σ	σ	PROPN
ejpam-6705	542	4	(	(	PUNCT
ejpam-6705	542	5	∫	∫	PROPN
ejpam-6705	542	6	l[gb(g	l[gb(g	PROPN
ejpam-6705	542	7	,	,	PUNCT
ejpam-6705	542	8	m	m	PROPN
ejpam-6705	542	9	,	,	PUNCT
ejpam-6705	542	10	c)+gb(h	c)+gb(h	PROPN
ejpam-6705	542	11	,	,	PUNCT
ejpam-6705	542	12	n	n	CCONJ
ejpam-6705	542	13	,	,	PUNCT
ejpam-6705	542	14	k	k	NOUN
ejpam-6705	542	15	)	)	PUNCT
ejpam-6705	542	16	]	]	PUNCT
ejpam-6705	542	17	0	0	NUM
ejpam-6705	543	1	g(t)dt	g(t)dt	PROPN
ejpam-6705	543	2	)	)	PUNCT
ejpam-6705	544	1	where	where	SCONJ
ejpam-6705	544	2	g	g	NOUN
ejpam-6705	544	3	,	,	PUNCT
ejpam-6705	544	4	h	h	NOUN
ejpam-6705	544	5	,	,	PUNCT
ejpam-6705	544	6	c	c	X
ejpam-6705	544	7	,	,	PUNCT
ejpam-6705	544	8	m	m	PROPN
ejpam-6705	544	9	,	,	PUNCT
ejpam-6705	544	10	n	n	CCONJ
ejpam-6705	544	11	,	,	PUNCT
ejpam-6705	544	12	k	k	PROPN
ejpam-6705	544	13	∈	∈	PROPN
ejpam-6705	544	14	x	x	X
ejpam-6705	544	15	.	.	PUNCT
ejpam-6705	544	16	clearly	clearly	ADV
ejpam-6705	544	17	,	,	PUNCT
ejpam-6705	544	18	t	t	PROPN
ejpam-6705	544	19	fulfills	fulfill	VERB
ejpam-6705	544	20	all	all	DET
ejpam-6705	544	21	the	the	DET
ejpam-6705	544	22	axioms	axiom	NOUN
ejpam-6705	544	23	of	of	ADP
ejpam-6705	544	24	theorem	theorem	ADJ
ejpam-6705	544	25	3	3	NUM
ejpam-6705	544	26	,	,	PUNCT
ejpam-6705	544	27	so	so	SCONJ
ejpam-6705	544	28	t	t	PROPN
ejpam-6705	544	29	possesses	possess	VERB
ejpam-6705	544	30	a	a	DET
ejpam-6705	544	31	coupled	couple	VERB
ejpam-6705	544	32	fixed	fix	VERB
ejpam-6705	544	33	point	point	NOUN
ejpam-6705	544	34	.	.	PUNCT
ejpam-6705	545	1	5	5	X
ejpam-6705	545	2	.	.	X
ejpam-6705	545	3	conclusion	conclusion	NOUN
ejpam-6705	545	4	the	the	DET
ejpam-6705	545	5	concepts	concept	NOUN
ejpam-6705	545	6	of	of	ADP
ejpam-6705	545	7	partial	partial	ADJ
ejpam-6705	545	8	order	order	NOUN
ejpam-6705	545	9	and	and	CCONJ
ejpam-6705	545	10	contractive	contractive	ADJ
ejpam-6705	545	11	conditions	condition	NOUN
ejpam-6705	545	12	are	be	AUX
ejpam-6705	545	13	redefined	redefine	VERB
ejpam-6705	545	14	within	within	ADP
ejpam-6705	545	15	the	the	DET
ejpam-6705	545	16	framework	framework	NOUN
ejpam-6705	545	17	of	of	ADP
ejpam-6705	545	18	gb	gb	ADV
ejpam-6705	545	19	-	-	PUNCT
ejpam-6705	545	20	metric	metric	ADJ
ejpam-6705	545	21	spaces	space	NOUN
ejpam-6705	545	22	and	and	CCONJ
ejpam-6705	545	23	it	it	PRON
ejpam-6705	545	24	is	be	AUX
ejpam-6705	545	25	observed	observe	VERB
ejpam-6705	545	26	that	that	SCONJ
ejpam-6705	545	27	the	the	DET
ejpam-6705	545	28	contractive	contractive	ADJ
ejpam-6705	545	29	condition	condition	NOUN
ejpam-6705	545	30	of	of	ADP
ejpam-6705	545	31	majid	majid	PROPN
ejpam-6705	545	32	et	et	PROPN
ejpam-6705	545	33	al	al	PROPN
ejpam-6705	545	34	.	.	PUNCT
ejpam-6705	546	1	[	[	X
ejpam-6705	546	2	43	43	NUM
ejpam-6705	546	3	]	]	PUNCT
ejpam-6705	546	4	is	be	AUX
ejpam-6705	546	5	a	a	DET
ejpam-6705	546	6	special	special	ADJ
ejpam-6705	546	7	case	case	NOUN
ejpam-6705	546	8	of	of	ADP
ejpam-6705	546	9	our	our	PRON
ejpam-6705	546	10	results	result	NOUN
ejpam-6705	546	11	.	.	PUNCT
ejpam-6705	547	1	in	in	ADP
ejpam-6705	547	2	order	order	NOUN
ejpam-6705	547	3	to	to	PART
ejpam-6705	547	4	show	show	VERB
ejpam-6705	547	5	the	the	DET
ejpam-6705	547	6	applicability	applicability	NOUN
ejpam-6705	547	7	of	of	ADP
ejpam-6705	547	8	our	our	PRON
ejpam-6705	547	9	results	result	NOUN
ejpam-6705	547	10	,	,	PUNCT
ejpam-6705	547	11	nontrivial	nontrivial	ADJ
ejpam-6705	547	12	examples	example	NOUN
ejpam-6705	547	13	are	be	AUX
ejpam-6705	547	14	provided	provide	VERB
ejpam-6705	547	15	.	.	PUNCT
ejpam-6705	548	1	in	in	ADP
ejpam-6705	548	2	future	future	ADJ
ejpam-6705	548	3	the	the	DET
ejpam-6705	548	4	generalization	generalization	NOUN
ejpam-6705	548	5	of	of	ADP
ejpam-6705	548	6	this	this	DET
ejpam-6705	548	7	work	work	NOUN
ejpam-6705	548	8	can	can	AUX
ejpam-6705	548	9	be	be	AUX
ejpam-6705	548	10	done	do	VERB
ejpam-6705	548	11	by	by	ADP
ejpam-6705	548	12	using	use	VERB
ejpam-6705	548	13	doubled	double	VERB
ejpam-6705	548	14	controlled	control	VERB
ejpam-6705	548	15	metric	metric	ADJ
ejpam-6705	548	16	spaces	space	NOUN
ejpam-6705	548	17	or	or	CCONJ
ejpam-6705	548	18	triple	triple	ADV
ejpam-6705	548	19	controlled	control	VERB
ejpam-6705	548	20	metric	metric	ADJ
ejpam-6705	548	21	spaces	space	NOUN
ejpam-6705	548	22	.	.	PUNCT
ejpam-6705	549	1	one	one	PRON
ejpam-6705	549	2	can	can	AUX
ejpam-6705	549	3	also	also	ADV
ejpam-6705	549	4	modify	modify	VERB
ejpam-6705	549	5	the	the	DET
ejpam-6705	549	6	contractive	contractive	ADJ
ejpam-6705	549	7	condition	condition	NOUN
ejpam-6705	549	8	to	to	PART
ejpam-6705	549	9	obtain	obtain	VERB
ejpam-6705	549	10	more	more	ADJ
ejpam-6705	549	11	general	general	ADJ
ejpam-6705	549	12	results	result	NOUN
ejpam-6705	549	13	.	.	PUNCT
ejpam-6705	550	1	acknowledgements	acknowledgement	NOUN
ejpam-6705	550	2	we	we	PRON
ejpam-6705	550	3	acknowledge	acknowledge	VERB
ejpam-6705	550	4	the	the	DET
ejpam-6705	550	5	support	support	NOUN
ejpam-6705	550	6	of	of	ADP
ejpam-6705	550	7	this	this	DET
ejpam-6705	550	8	research	research	NOUN
ejpam-6705	550	9	from	from	ADP
ejpam-6705	550	10	al	al	PROPN
ejpam-6705	550	11	-	-	PROPN
ejpam-6705	550	12	zaytoonah	zaytoonah	PROPN
ejpam-6705	550	13	university	university	PROPN
ejpam-6705	550	14	.	.	PUNCT
ejpam-6705	551	1	authors	author	NOUN
ejpam-6705	551	2	’	'	PUNCT
ejpam-6705	551	3	contributions	contribution	NOUN
ejpam-6705	551	4	all	all	DET
ejpam-6705	551	5	authors	author	NOUN
ejpam-6705	551	6	contribute	contribute	VERB
ejpam-6705	551	7	equally	equally	ADV
ejpam-6705	551	8	in	in	ADP
ejpam-6705	551	9	this	this	DET
ejpam-6705	551	10	paper	paper	NOUN
ejpam-6705	551	11	.	.	PUNCT
ejpam-6705	552	1	conflict	conflict	NOUN
ejpam-6705	552	2	of	of	ADP
ejpam-6705	552	3	interest	interest	NOUN
ejpam-6705	552	4	the	the	DET
ejpam-6705	552	5	authors	author	NOUN
ejpam-6705	552	6	declare	declare	VERB
ejpam-6705	552	7	that	that	SCONJ
ejpam-6705	552	8	they	they	PRON
ejpam-6705	552	9	have	have	VERB
ejpam-6705	552	10	no	no	DET
ejpam-6705	552	11	conflict	conflict	NOUN
ejpam-6705	552	12	of	of	ADP
ejpam-6705	552	13	interest	interest	NOUN
ejpam-6705	552	14	.	.	PUNCT
ejpam-6705	553	1	s.	s.	PROPN
ejpam-6705	553	2	batul	batul	PROPN
ejpam-6705	553	3	et	et	PROPN
ejpam-6705	553	4	al	al	PROPN
ejpam-6705	553	5	.	.	PUNCT
ejpam-6705	553	6	/	/	SYM
ejpam-6705	553	7	eur	eur	PROPN
ejpam-6705	553	8	.	.	PUNCT
ejpam-6705	554	1	j.	j.	PROPN
ejpam-6705	554	2	pure	pure	PROPN
ejpam-6705	554	3	appl	appl	PROPN
ejpam-6705	554	4	.	.	PROPN
ejpam-6705	554	5	math	math	PROPN
ejpam-6705	554	6	,	,	PUNCT
ejpam-6705	554	7	18	18	NUM
ejpam-6705	554	8	(	(	PUNCT
ejpam-6705	554	9	4	4	NUM
ejpam-6705	554	10	)	)	PUNCT
ejpam-6705	554	11	(	(	PUNCT
ejpam-6705	554	12	2025	2025	NUM
ejpam-6705	554	13	)	)	PUNCT
ejpam-6705	554	14	,	,	PUNCT
ejpam-6705	554	15	6705	6705	NUM
ejpam-6705	554	16	21	21	NUM
ejpam-6705	554	17	of	of	ADP
ejpam-6705	554	18	23	23	NUM
ejpam-6705	554	19	references	reference	NOUN
ejpam-6705	554	20	[	[	X
ejpam-6705	554	21	1	1	NUM
ejpam-6705	554	22	]	]	PUNCT
ejpam-6705	554	23	maurice	maurice	PROPN
ejpam-6705	554	24	fréchet	fréchet	PROPN
ejpam-6705	554	25	.	.	PUNCT
ejpam-6705	555	1	sur	sur	PROPN
ejpam-6705	555	2	quelques	quelques	PROPN
ejpam-6705	555	3	points	point	NOUN
ejpam-6705	555	4	du	du	PROPN
ejpam-6705	555	5	calcul	calcul	PROPN
ejpam-6705	555	6	fonctionnel	fonctionnel	PROPN
ejpam-6705	555	7	.	.	PUNCT
ejpam-6705	555	8	1906	1906	NUM
ejpam-6705	555	9	.	.	PUNCT
ejpam-6705	556	1	[	[	X
ejpam-6705	556	2	2	2	NUM
ejpam-6705	556	3	]	]	SYM
ejpam-6705	556	4	djuro	djuro	NOUN
ejpam-6705	556	5	r	r	NOUN
ejpam-6705	556	6	kurepa	kurepa	NOUN
ejpam-6705	556	7	.	.	PUNCT
ejpam-6705	557	1	tableaux	tableaux	PROPN
ejpam-6705	557	2	ramifiés	ramifiés	PROPN
ejpam-6705	557	3	d’ensembles	d’ensemble	NOUN
ejpam-6705	557	4	.	.	PUNCT
ejpam-6705	557	5	espaces	espace	VERB
ejpam-6705	557	6	pseudo	pseudo	NOUN
ejpam-6705	557	7	-	-	NOUN
ejpam-6705	557	8	distanciés	distancié	NOUN
ejpam-6705	557	9	.	.	PUNCT
ejpam-6705	558	1	cr	cr	PROPN
ejpam-6705	558	2	acad	acad	PROPN
ejpam-6705	558	3	.	.	PUNCT
ejpam-6705	559	1	sci	sci	PROPN
ejpam-6705	559	2	.	.	PROPN
ejpam-6705	559	3	paris	paris	PROPN
ejpam-6705	559	4	,	,	PUNCT
ejpam-6705	559	5	198(2):1563–1565	198(2):1563–1565	NUM
ejpam-6705	559	6	,	,	PUNCT
ejpam-6705	559	7	1934	1934	NUM
ejpam-6705	559	8	.	.	PUNCT
ejpam-6705	560	1	[	[	X
ejpam-6705	560	2	3	3	X
ejpam-6705	560	3	]	]	X
ejpam-6705	560	4	michael	michael	PROPN
ejpam-6705	560	5	edelstein	edelstein	PROPN
ejpam-6705	560	6	.	.	PUNCT
ejpam-6705	561	1	on	on	ADP
ejpam-6705	561	2	fixed	fix	VERB
ejpam-6705	561	3	and	and	CCONJ
ejpam-6705	561	4	periodic	periodic	ADJ
ejpam-6705	561	5	points	point	NOUN
ejpam-6705	561	6	under	under	ADP
ejpam-6705	561	7	contractive	contractive	ADJ
ejpam-6705	561	8	mappings	mapping	NOUN
ejpam-6705	561	9	.	.	PUNCT
ejpam-6705	562	1	journal	journal	NOUN
ejpam-6705	562	2	of	of	ADP
ejpam-6705	562	3	the	the	DET
ejpam-6705	562	4	london	london	PROPN
ejpam-6705	562	5	mathematical	mathematical	ADJ
ejpam-6705	562	6	society	society	NOUN
ejpam-6705	562	7	,	,	PUNCT
ejpam-6705	562	8	1(1):74–79	1(1):74–79	NUM
ejpam-6705	562	9	,	,	PUNCT
ejpam-6705	562	10	1962	1962	NUM
ejpam-6705	562	11	.	.	PUNCT
ejpam-6705	563	1	[	[	X
ejpam-6705	563	2	4	4	X
ejpam-6705	563	3	]	]	X
ejpam-6705	563	4	david	david	PROPN
ejpam-6705	563	5	william	william	PROPN
ejpam-6705	563	6	boyd	boyd	PROPN
ejpam-6705	563	7	and	and	CCONJ
ejpam-6705	563	8	james	james	PROPN
ejpam-6705	563	9	sw	sw	PROPN
ejpam-6705	563	10	wong	wong	PROPN
ejpam-6705	563	11	.	.	PUNCT
ejpam-6705	564	1	on	on	ADP
ejpam-6705	564	2	nonlinear	nonlinear	ADJ
ejpam-6705	564	3	contractions	contraction	NOUN
ejpam-6705	564	4	.	.	PUNCT
ejpam-6705	565	1	proceedings	proceeding	NOUN
ejpam-6705	565	2	of	of	ADP
ejpam-6705	565	3	the	the	DET
ejpam-6705	565	4	american	american	PROPN
ejpam-6705	565	5	mathematical	mathematical	PROPN
ejpam-6705	565	6	society	society	NOUN
ejpam-6705	565	7	,	,	PUNCT
ejpam-6705	565	8	20(2):458–464	20(2):458–464	NUM
ejpam-6705	565	9	,	,	PUNCT
ejpam-6705	565	10	1969	1969	NUM
ejpam-6705	565	11	.	.	PUNCT
ejpam-6705	566	1	[	[	X
ejpam-6705	566	2	5	5	X
ejpam-6705	566	3	]	]	PUNCT
ejpam-6705	566	4	haitham	haitham	PROPN
ejpam-6705	566	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	566	6	,	,	PUNCT
ejpam-6705	566	7	mohd	mohd	PROPN
ejpam-6705	566	8	salmi	salmi	PROPN
ejpam-6705	566	9	noorani	noorani	PROPN
ejpam-6705	566	10	,	,	PUNCT
ejpam-6705	566	11	hassen	hassen	PROPN
ejpam-6705	566	12	aydi	aydi	ADV
ejpam-6705	566	13	,	,	PUNCT
ejpam-6705	566	14	and	and	CCONJ
ejpam-6705	566	15	wasfi	wasfi	ADV
ejpam-6705	566	16	shatanawi	shatanawi	ADJ
ejpam-6705	566	17	.	.	PUNCT
ejpam-6705	567	1	on	on	ADP
ejpam-6705	567	2	common	common	ADJ
ejpam-6705	567	3	fixed	fix	VERB
ejpam-6705	567	4	point	point	NOUN
ejpam-6705	567	5	results	result	NOUN
ejpam-6705	567	6	for	for	ADP
ejpam-6705	567	7	new	new	ADJ
ejpam-6705	567	8	contractions	contraction	NOUN
ejpam-6705	567	9	with	with	ADP
ejpam-6705	567	10	applications	application	NOUN
ejpam-6705	567	11	to	to	PART
ejpam-6705	567	12	graph	graph	VERB
ejpam-6705	567	13	and	and	CCONJ
ejpam-6705	567	14	integral	integral	ADJ
ejpam-6705	567	15	equations	equation	NOUN
ejpam-6705	567	16	.	.	PUNCT
ejpam-6705	568	1	mathematics	mathematic	NOUN
ejpam-6705	568	2	,	,	PUNCT
ejpam-6705	568	3	7(11	7(11	NUM
ejpam-6705	568	4	)	)	PUNCT
ejpam-6705	568	5	,	,	PUNCT
ejpam-6705	568	6	2019	2019	NUM
ejpam-6705	568	7	.	.	PUNCT
ejpam-6705	569	1	[	[	X
ejpam-6705	569	2	6	6	NUM
ejpam-6705	569	3	]	]	PUNCT
ejpam-6705	569	4	haitham	haitham	PROPN
ejpam-6705	569	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	569	6	.	.	PUNCT
ejpam-6705	570	1	fractional	fractional	ADJ
ejpam-6705	570	2	analytic	analytic	ADJ
ejpam-6705	570	3	solutions	solution	NOUN
ejpam-6705	570	4	and	and	CCONJ
ejpam-6705	570	5	fixed	fix	VERB
ejpam-6705	570	6	point	point	NOUN
ejpam-6705	570	7	results	result	NOUN
ejpam-6705	570	8	with	with	ADP
ejpam-6705	570	9	some	some	DET
ejpam-6705	570	10	applications	application	NOUN
ejpam-6705	570	11	.	.	PUNCT
ejpam-6705	571	1	adv	adv	PROPN
ejpam-6705	571	2	.	.	PUNCT
ejpam-6705	571	3	fixed	fix	VERB
ejpam-6705	571	4	point	point	NOUN
ejpam-6705	571	5	theory	theory	NOUN
ejpam-6705	571	6	,	,	PUNCT
ejpam-6705	571	7	14(1	14(1	NUM
ejpam-6705	571	8	)	)	PUNCT
ejpam-6705	571	9	,	,	PUNCT
ejpam-6705	571	10	2024	2024	NUM
ejpam-6705	571	11	.	.	PUNCT
ejpam-6705	572	1	[	[	X
ejpam-6705	572	2	7	7	X
ejpam-6705	572	3	]	]	X
ejpam-6705	572	4	haitham	haitham	PROPN
ejpam-6705	572	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	572	6	,	,	PUNCT
ejpam-6705	572	7	mohd	mohd	PROPN
ejpam-6705	572	8	salmi	salmi	PROPN
ejpam-6705	572	9	md	md	PROPN
ejpam-6705	572	10	noorani	noorani	PROPN
ejpam-6705	572	11	,	,	PUNCT
ejpam-6705	572	12	and	and	CCONJ
ejpam-6705	572	13	hassen	hassen	PROPN
ejpam-6705	572	14	aydi	aydi	VERB
ejpam-6705	572	15	.	.	PUNCT
ejpam-6705	573	1	some	some	DET
ejpam-6705	573	2	new	new	ADJ
ejpam-6705	573	3	characterizations	characterization	NOUN
ejpam-6705	573	4	and	and	CCONJ
ejpam-6705	573	5	results	result	NOUN
ejpam-6705	573	6	for	for	ADP
ejpam-6705	573	7	fuzzy	fuzzy	ADJ
ejpam-6705	573	8	contractions	contraction	NOUN
ejpam-6705	573	9	in	in	ADP
ejpam-6705	573	10	fuzzy	fuzzy	ADJ
ejpam-6705	573	11	b	b	X
ejpam-6705	573	12	-	-	PUNCT
ejpam-6705	573	13	metric	metric	ADJ
ejpam-6705	573	14	spaces	space	NOUN
ejpam-6705	573	15	and	and	CCONJ
ejpam-6705	573	16	applications	application	NOUN
ejpam-6705	573	17	.	.	PUNCT
ejpam-6705	574	1	aims	aim	VERB
ejpam-6705	574	2	mathematics	mathematics	PROPN
ejpam-6705	574	3	,	,	PUNCT
ejpam-6705	574	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6705	574	5	,	,	PUNCT
ejpam-6705	574	6	2023	2023	NUM
ejpam-6705	574	7	.	.	PUNCT
ejpam-6705	575	1	[	[	X
ejpam-6705	575	2	8	8	X
ejpam-6705	575	3	]	]	X
ejpam-6705	575	4	muhammad	muhammad	PROPN
ejpam-6705	575	5	nazam	nazam	PROPN
ejpam-6705	575	6	,	,	PUNCT
ejpam-6705	575	7	hassen	hassen	PROPN
ejpam-6705	575	8	aydi	aydi	ADV
ejpam-6705	575	9	,	,	PUNCT
ejpam-6705	575	10	mohd	mohd	PROPN
ejpam-6705	575	11	salmi	salmi	PROPN
ejpam-6705	575	12	noorani	noorani	PROPN
ejpam-6705	575	13	,	,	PUNCT
ejpam-6705	575	14	and	and	CCONJ
ejpam-6705	575	15	haitham	haitham	PROPN
ejpam-6705	575	16	qawaqneh	qawaqneh	PROPN
ejpam-6705	575	17	.	.	PUNCT
ejpam-6705	576	1	existence	existence	NOUN
ejpam-6705	576	2	of	of	ADP
ejpam-6705	576	3	fixed	fix	VERB
ejpam-6705	576	4	points	point	NOUN
ejpam-6705	576	5	of	of	ADP
ejpam-6705	576	6	four	four	NUM
ejpam-6705	576	7	maps	map	NOUN
ejpam-6705	576	8	for	for	ADP
ejpam-6705	576	9	a	a	DET
ejpam-6705	576	10	new	new	ADJ
ejpam-6705	576	11	generalized	generalized	ADJ
ejpam-6705	576	12	f	f	NOUN
ejpam-6705	576	13	-	-	PUNCT
ejpam-6705	576	14	contraction	contraction	NOUN
ejpam-6705	576	15	and	and	CCONJ
ejpam-6705	576	16	an	an	DET
ejpam-6705	576	17	application	application	NOUN
ejpam-6705	576	18	.	.	PUNCT
ejpam-6705	577	1	journal	journal	NOUN
ejpam-6705	577	2	of	of	ADP
ejpam-6705	577	3	function	function	NOUN
ejpam-6705	577	4	spaces	space	NOUN
ejpam-6705	577	5	,	,	PUNCT
ejpam-6705	577	6	2019(1):5980312	2019(1):5980312	NUM
ejpam-6705	577	7	,	,	PUNCT
ejpam-6705	577	8	2019	2019	NUM
ejpam-6705	577	9	.	.	PUNCT
ejpam-6705	578	1	[	[	X
ejpam-6705	578	2	9	9	NUM
ejpam-6705	578	3	]	]	PUNCT
ejpam-6705	578	4	haitham	haitham	PROPN
ejpam-6705	578	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	578	6	,	,	PUNCT
ejpam-6705	578	7	hasanen	hasanen	PROPN
ejpam-6705	578	8	hammad	hammad	PROPN
ejpam-6705	578	9	,	,	PUNCT
ejpam-6705	578	10	and	and	CCONJ
ejpam-6705	578	11	hassen	hassen	PROPN
ejpam-6705	578	12	aydi	aydi	VERB
ejpam-6705	578	13	.	.	PUNCT
ejpam-6705	579	1	exploring	explore	VERB
ejpam-6705	579	2	new	new	ADJ
ejpam-6705	579	3	geometric	geometric	ADJ
ejpam-6705	579	4	contraction	contraction	NOUN
ejpam-6705	579	5	mappings	mapping	NOUN
ejpam-6705	579	6	and	and	CCONJ
ejpam-6705	579	7	their	their	PRON
ejpam-6705	579	8	applications	application	NOUN
ejpam-6705	579	9	in	in	ADP
ejpam-6705	579	10	fractional	fractional	ADJ
ejpam-6705	579	11	metric	metric	ADJ
ejpam-6705	579	12	spaces	space	NOUN
ejpam-6705	579	13	.	.	PUNCT
ejpam-6705	580	1	aims	aim	VERB
ejpam-6705	580	2	mathematics	mathematic	NOUN
ejpam-6705	580	3	,	,	PUNCT
ejpam-6705	580	4	9(1):521–541	9(1):521–541	NUM
ejpam-6705	580	5	,	,	PUNCT
ejpam-6705	580	6	2024	2024	NUM
ejpam-6705	580	7	.	.	PUNCT
ejpam-6705	581	1	[	[	X
ejpam-6705	581	2	10	10	NUM
ejpam-6705	581	3	]	]	X
ejpam-6705	581	4	haitham	haitham	PROPN
ejpam-6705	581	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	581	6	.	.	PUNCT
ejpam-6705	582	1	new	new	ADJ
ejpam-6705	582	2	functions	function	NOUN
ejpam-6705	582	3	for	for	ADP
ejpam-6705	582	4	fixed	fix	VERB
ejpam-6705	582	5	point	point	NOUN
ejpam-6705	582	6	results	result	NOUN
ejpam-6705	582	7	in	in	ADP
ejpam-6705	582	8	metric	metric	ADJ
ejpam-6705	582	9	spaces	space	NOUN
ejpam-6705	582	10	with	with	ADP
ejpam-6705	582	11	some	some	DET
ejpam-6705	582	12	applications	application	NOUN
ejpam-6705	582	13	.	.	PUNCT
ejpam-6705	583	1	indian	indian	ADJ
ejpam-6705	583	2	journal	journal	PROPN
ejpam-6705	583	3	of	of	ADP
ejpam-6705	583	4	mathematics	mathematic	NOUN
ejpam-6705	583	5	,	,	PUNCT
ejpam-6705	583	6	66(1):55–84	66(1):55–84	NOUN
ejpam-6705	583	7	,	,	PUNCT
ejpam-6705	583	8	2024	2024	NUM
ejpam-6705	583	9	.	.	PUNCT
ejpam-6705	584	1	[	[	X
ejpam-6705	584	2	11	11	NUM
ejpam-6705	584	3	]	]	PUNCT
ejpam-6705	584	4	haitham	haitham	PROPN
ejpam-6705	584	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	584	6	,	,	PUNCT
ejpam-6705	584	7	mohd	mohd	PROPN
ejpam-6705	584	8	salmi	salmi	PROPN
ejpam-6705	584	9	noorani	noorani	PROPN
ejpam-6705	584	10	,	,	PUNCT
ejpam-6705	584	11	and	and	CCONJ
ejpam-6705	584	12	wasfi	wasfi	ADV
ejpam-6705	584	13	shatanawi	shatanawi	PROPN
ejpam-6705	584	14	.	.	PUNCT
ejpam-6705	585	1	fixed	fix	VERB
ejpam-6705	585	2	point	point	NOUN
ejpam-6705	585	3	results	result	NOUN
ejpam-6705	585	4	for	for	ADP
ejpam-6705	585	5	geraghty	geraghty	PROPN
ejpam-6705	585	6	type	type	NOUN
ejpam-6705	585	7	generalized	generalize	VERB
ejpam-6705	585	8	f	f	NOUN
ejpam-6705	585	9	-	-	PUNCT
ejpam-6705	585	10	contraction	contraction	NOUN
ejpam-6705	585	11	for	for	ADP
ejpam-6705	585	12	weak	weak	ADJ
ejpam-6705	585	13	admissible	admissible	ADJ
ejpam-6705	585	14	mappings	mapping	NOUN
ejpam-6705	585	15	in	in	ADP
ejpam-6705	585	16	metriclike	metriclike	ADJ
ejpam-6705	585	17	spaces	space	NOUN
ejpam-6705	585	18	.	.	PUNCT
ejpam-6705	586	1	eur	eur	PROPN
ejpam-6705	586	2	.	.	PUNCT
ejpam-6705	587	1	j.	j.	PROPN
ejpam-6705	587	2	pure	pure	PROPN
ejpam-6705	587	3	appl	appl	PROPN
ejpam-6705	587	4	.	.	PUNCT
ejpam-6705	587	5	math	math	PROPN
ejpam-6705	587	6	.	.	PUNCT
ejpam-6705	587	7	,	,	PUNCT
ejpam-6705	587	8	11(3):702–716	11(3):702–716	PROPN
ejpam-6705	587	9	,	,	PUNCT
ejpam-6705	587	10	2018	2018	NUM
ejpam-6705	587	11	.	.	PUNCT
ejpam-6705	588	1	[	[	X
ejpam-6705	588	2	12	12	NUM
ejpam-6705	588	3	]	]	PUNCT
ejpam-6705	588	4	haitham	haitham	PROPN
ejpam-6705	588	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	588	6	,	,	PUNCT
ejpam-6705	588	7	mohd	mohd	PROPN
ejpam-6705	588	8	salmi	salmi	PROPN
ejpam-6705	588	9	noorani	noorani	PROPN
ejpam-6705	588	10	,	,	PUNCT
ejpam-6705	588	11	and	and	CCONJ
ejpam-6705	588	12	wasfi	wasfi	ADV
ejpam-6705	588	13	shatanawi	shatanawi	PROPN
ejpam-6705	588	14	.	.	PUNCT
ejpam-6705	589	1	fixed	fix	VERB
ejpam-6705	589	2	point	point	NOUN
ejpam-6705	589	3	theorems	theorem	NOUN
ejpam-6705	589	4	for	for	ADP
ejpam-6705	589	5	(	(	PUNCT
ejpam-6705	589	6	α	α	X
ejpam-6705	589	7	,	,	PUNCT
ejpam-6705	589	8	k	k	NOUN
ejpam-6705	589	9	,	,	PUNCT
ejpam-6705	589	10	θ)-contractive	θ)-contractive	PUNCT
ejpam-6705	589	11	multi	multi	ADJ
ejpam-6705	589	12	-	-	ADJ
ejpam-6705	589	13	valued	value	VERB
ejpam-6705	589	14	mapping	mapping	NOUN
ejpam-6705	589	15	in	in	ADP
ejpam-6705	589	16	b	b	NOUN
ejpam-6705	589	17	-	-	PUNCT
ejpam-6705	589	18	metric	metric	ADJ
ejpam-6705	589	19	space	space	NOUN
ejpam-6705	589	20	and	and	CCONJ
ejpam-6705	589	21	applications	application	NOUN
ejpam-6705	589	22	.	.	PUNCT
ejpam-6705	590	1	international	international	ADJ
ejpam-6705	590	2	journal	journal	PROPN
ejpam-6705	590	3	of	of	ADP
ejpam-6705	590	4	mathematics	mathematic	NOUN
ejpam-6705	590	5	and	and	CCONJ
ejpam-6705	590	6	computer	computer	NOUN
ejpam-6705	590	7	science	science	NOUN
ejpam-6705	590	8	,	,	PUNCT
ejpam-6705	590	9	14(1):263–283	14(1):263–283	NUM
ejpam-6705	590	10	,	,	PUNCT
ejpam-6705	590	11	2019	2019	NUM
ejpam-6705	590	12	.	.	PUNCT
ejpam-6705	591	1	[	[	X
ejpam-6705	591	2	13	13	NUM
ejpam-6705	591	3	]	]	PUNCT
ejpam-6705	591	4	m.	m.	NOUN
ejpam-6705	591	5	meneceur	meneceur	PROPN
ejpam-6705	591	6	,	,	PUNCT
ejpam-6705	591	7	h.	h.	PROPN
ejpam-6705	591	8	qawaqneh	qawaqneh	PROPN
ejpam-6705	591	9	,	,	PUNCT
ejpam-6705	591	10	alsamir	alsamir	VERB
ejpam-6705	591	11	h.	h.	PROPN
ejpam-6705	591	12	,	,	PUNCT
ejpam-6705	591	13	and	and	CCONJ
ejpam-6705	591	14	g.	g.	PROPN
ejpam-6705	591	15	al	al	PROPN
ejpam-6705	591	16	-	-	PUNCT
ejpam-6705	591	17	musannef	musannef	NOUN
ejpam-6705	591	18	.	.	PUNCT
ejpam-6705	592	1	common	common	ADJ
ejpam-6705	592	2	fixed	fix	VERB
ejpam-6705	592	3	point	point	NOUN
ejpam-6705	592	4	of	of	ADP
ejpam-6705	592	5	generalized	generalized	ADJ
ejpam-6705	592	6	berinde	berinde	NOUN
ejpam-6705	592	7	type	type	NOUN
ejpam-6705	592	8	contraction	contraction	NOUN
ejpam-6705	592	9	and	and	CCONJ
ejpam-6705	592	10	an	an	DET
ejpam-6705	592	11	application	application	NOUN
ejpam-6705	592	12	.	.	PUNCT
ejpam-6705	593	1	eur	eur	PROPN
ejpam-6705	593	2	.	.	PUNCT
ejpam-6705	594	1	j.	j.	PROPN
ejpam-6705	594	2	pure	pure	PROPN
ejpam-6705	594	3	appl	appl	PROPN
ejpam-6705	594	4	.	.	PUNCT
ejpam-6705	594	5	math	math	PROPN
ejpam-6705	594	6	.	.	PUNCT
ejpam-6705	594	7	,	,	PUNCT
ejpam-6705	594	8	17(4):3093–3108	17(4):3093–3108	NUM
ejpam-6705	594	9	,	,	PUNCT
ejpam-6705	594	10	2024	2024	NUM
ejpam-6705	594	11	.	.	PUNCT
ejpam-6705	595	1	[	[	X
ejpam-6705	595	2	14	14	NUM
ejpam-6705	595	3	]	]	X
ejpam-6705	595	4	d.	d.	PROPN
ejpam-6705	595	5	judeh	judeh	PROPN
ejpam-6705	595	6	and	and	CCONJ
ejpam-6705	595	7	m.	m.	PROPN
ejpam-6705	595	8	abu	abu	PROPN
ejpam-6705	595	9	hammad	hammad	PROPN
ejpam-6705	595	10	.	.	PUNCT
ejpam-6705	596	1	applications	application	NOUN
ejpam-6705	596	2	of	of	ADP
ejpam-6705	596	3	conformable	conformable	ADJ
ejpam-6705	596	4	fractional	fractional	ADJ
ejpam-6705	596	5	pareto	pareto	ADJ
ejpam-6705	596	6	probability	probability	NOUN
ejpam-6705	596	7	distribution	distribution	NOUN
ejpam-6705	596	8	.	.	PUNCT
ejpam-6705	597	1	international	international	ADJ
ejpam-6705	597	2	journal	journal	NOUN
ejpam-6705	597	3	of	of	ADP
ejpam-6705	597	4	advances	advance	NOUN
ejpam-6705	597	5	in	in	ADP
ejpam-6705	597	6	soft	soft	ADJ
ejpam-6705	597	7	computing	computing	NOUN
ejpam-6705	597	8	and	and	CCONJ
ejpam-6705	597	9	its	its	PRON
ejpam-6705	597	10	applications	application	NOUN
ejpam-6705	597	11	,	,	PUNCT
ejpam-6705	597	12	14(2):116–124	14(2):116–124	PROPN
ejpam-6705	597	13	,	,	PUNCT
ejpam-6705	597	14	2022	2022	NUM
ejpam-6705	597	15	.	.	PUNCT
ejpam-6705	598	1	[	[	X
ejpam-6705	598	2	15	15	NUM
ejpam-6705	598	3	]	]	PUNCT
ejpam-6705	598	4	t.	t.	PROPN
ejpam-6705	598	5	kanan	kanan	PROPN
ejpam-6705	598	6	,	,	PUNCT
ejpam-6705	598	7	m.	m.	NOUN
ejpam-6705	598	8	elbes	elbes	PROPN
ejpam-6705	598	9	,	,	PUNCT
ejpam-6705	598	10	k.	k.	PROPN
ejpam-6705	598	11	abu	abu	PROPN
ejpam-6705	598	12	maria	maria	PROPN
ejpam-6705	598	13	,	,	PUNCT
ejpam-6705	598	14	and	and	CCONJ
ejpam-6705	598	15	m.	m.	NOUN
ejpam-6705	598	16	alia	alia	PROPN
ejpam-6705	598	17	.	.	PUNCT
ejpam-6705	599	1	exploring	explore	VERB
ejpam-6705	599	2	the	the	DET
ejpam-6705	599	3	potential	potential	NOUN
ejpam-6705	599	4	of	of	ADP
ejpam-6705	599	5	iotbased	iotbase	VERB
ejpam-6705	599	6	learning	learn	VERB
ejpam-6705	599	7	environments	environment	NOUN
ejpam-6705	599	8	in	in	ADP
ejpam-6705	599	9	education	education	NOUN
ejpam-6705	599	10	.	.	PUNCT
ejpam-6705	600	1	international	international	ADJ
ejpam-6705	600	2	journal	journal	NOUN
ejpam-6705	600	3	of	of	ADP
ejpam-6705	600	4	advances	advance	NOUN
ejpam-6705	600	5	in	in	ADP
ejpam-6705	600	6	soft	soft	ADJ
ejpam-6705	600	7	computing	computing	NOUN
ejpam-6705	600	8	and	and	CCONJ
ejpam-6705	600	9	its	its	PRON
ejpam-6705	600	10	applications	application	NOUN
ejpam-6705	600	11	,	,	PUNCT
ejpam-6705	600	12	2023	2023	NUM
ejpam-6705	600	13	.	.	PUNCT
ejpam-6705	601	1	[	[	X
ejpam-6705	601	2	16	16	NUM
ejpam-6705	601	3	]	]	X
ejpam-6705	601	4	m.	m.	NOUN
ejpam-6705	601	5	elbes	elbes	PROPN
ejpam-6705	601	6	,	,	PUNCT
ejpam-6705	601	7	kanan	kanan	PROPN
ejpam-6705	601	8	t.	t.	PROPN
ejpam-6705	601	9	,	,	PUNCT
ejpam-6705	601	10	m.	m.	NOUN
ejpam-6705	601	11	alia	alia	PROPN
ejpam-6705	601	12	,	,	PUNCT
ejpam-6705	601	13	and	and	CCONJ
ejpam-6705	601	14	ziad	ziad	PROPN
ejpam-6705	601	15	m.	m.	NOUN
ejpam-6705	601	16	covd-19	covd-19	PROPN
ejpam-6705	601	17	detection	detection	NOUN
ejpam-6705	601	18	platform	platform	NOUN
ejpam-6705	601	19	from	from	ADP
ejpam-6705	601	20	x	x	ADJ
ejpam-6705	601	21	-	-	NOUN
ejpam-6705	601	22	ray	ray	NOUN
ejpam-6705	601	23	images	image	NOUN
ejpam-6705	601	24	using	use	VERB
ejpam-6705	601	25	deep	deep	ADJ
ejpam-6705	601	26	learning	learning	NOUN
ejpam-6705	601	27	.	.	PUNCT
ejpam-6705	602	1	international	international	ADJ
ejpam-6705	602	2	journal	journal	NOUN
ejpam-6705	602	3	of	of	ADP
ejpam-6705	602	4	advances	advance	NOUN
ejpam-6705	602	5	in	in	ADP
ejpam-6705	602	6	soft	soft	ADJ
ejpam-6705	602	7	computing	computing	NOUN
ejpam-6705	602	8	and	and	CCONJ
ejpam-6705	602	9	its	its	PRON
ejpam-6705	602	10	applications	application	NOUN
ejpam-6705	602	11	,	,	PUNCT
ejpam-6705	602	12	14(1	14(1	NUM
ejpam-6705	602	13	)	)	PUNCT
ejpam-6705	602	14	,	,	PUNCT
ejpam-6705	602	15	2022	2022	NUM
ejpam-6705	602	16	.	.	PUNCT
ejpam-6705	603	1	s.	s.	PROPN
ejpam-6705	603	2	batul	batul	PROPN
ejpam-6705	603	3	et	et	PROPN
ejpam-6705	603	4	al	al	PROPN
ejpam-6705	603	5	.	.	PUNCT
ejpam-6705	603	6	/	/	SYM
ejpam-6705	603	7	eur	eur	PROPN
ejpam-6705	603	8	.	.	PUNCT
ejpam-6705	604	1	j.	j.	PROPN
ejpam-6705	604	2	pure	pure	PROPN
ejpam-6705	604	3	appl	appl	PROPN
ejpam-6705	604	4	.	.	PROPN
ejpam-6705	604	5	math	math	PROPN
ejpam-6705	604	6	,	,	PUNCT
ejpam-6705	604	7	18	18	NUM
ejpam-6705	604	8	(	(	PUNCT
ejpam-6705	604	9	4	4	NUM
ejpam-6705	604	10	)	)	PUNCT
ejpam-6705	604	11	(	(	PUNCT
ejpam-6705	604	12	2025	2025	NUM
ejpam-6705	604	13	)	)	PUNCT
ejpam-6705	604	14	,	,	PUNCT
ejpam-6705	604	15	6705	6705	NUM
ejpam-6705	604	16	22	22	NUM
ejpam-6705	604	17	of	of	ADP
ejpam-6705	604	18	23	23	NUM
ejpam-6705	604	19	[	[	SYM
ejpam-6705	604	20	17	17	NUM
ejpam-6705	604	21	]	]	X
ejpam-6705	604	22	ia	ia	PROPN
ejpam-6705	604	23	bakhtin	bakhtin	NOUN
ejpam-6705	604	24	.	.	PUNCT
ejpam-6705	605	1	the	the	DET
ejpam-6705	605	2	contraction	contraction	NOUN
ejpam-6705	605	3	mapping	map	VERB
ejpam-6705	605	4	principle	principle	NOUN
ejpam-6705	605	5	in	in	ADP
ejpam-6705	605	6	quasimetric	quasimetric	ADJ
ejpam-6705	605	7	spaces	space	NOUN
ejpam-6705	605	8	.	.	PUNCT
ejpam-6705	606	1	functional	functional	ADJ
ejpam-6705	606	2	analysis	analysis	NOUN
ejpam-6705	606	3	,	,	PUNCT
ejpam-6705	606	4	30:26–37	30:26–37	PROPN
ejpam-6705	606	5	,	,	PUNCT
ejpam-6705	606	6	1989	1989	NUM
ejpam-6705	606	7	.	.	PUNCT
ejpam-6705	607	1	[	[	X
ejpam-6705	607	2	18	18	NUM
ejpam-6705	607	3	]	]	X
ejpam-6705	607	4	selma	selma	PROPN
ejpam-6705	607	5	gülyaz	gülyaz	PROPN
ejpam-6705	607	6	-	-	PUNCT
ejpam-6705	607	7	özyurt	özyurt	PROPN
ejpam-6705	607	8	.	.	PUNCT
ejpam-6705	608	1	on	on	ADP
ejpam-6705	608	2	some	some	DET
ejpam-6705	608	3	alpha	alpha	NOUN
ejpam-6705	608	4	-	-	PUNCT
ejpam-6705	608	5	admissible	admissible	ADJ
ejpam-6705	608	6	contraction	contraction	NOUN
ejpam-6705	608	7	mappings	mapping	NOUN
ejpam-6705	608	8	on	on	ADP
ejpam-6705	608	9	branciari	branciari	ADJ
ejpam-6705	608	10	b	b	X
ejpam-6705	608	11	-	-	PUNCT
ejpam-6705	608	12	metric	metric	ADJ
ejpam-6705	608	13	spaces	space	NOUN
ejpam-6705	608	14	.	.	PUNCT
ejpam-6705	609	1	advances	advance	NOUN
ejpam-6705	609	2	in	in	ADP
ejpam-6705	609	3	the	the	DET
ejpam-6705	609	4	theory	theory	NOUN
ejpam-6705	609	5	of	of	ADP
ejpam-6705	609	6	nonlinear	nonlinear	ADJ
ejpam-6705	609	7	analysis	analysis	NOUN
ejpam-6705	609	8	and	and	CCONJ
ejpam-6705	609	9	its	its	PRON
ejpam-6705	609	10	application	application	NOUN
ejpam-6705	609	11	,	,	PUNCT
ejpam-6705	609	12	1(1):1–13	1(1):1–13	NUM
ejpam-6705	609	13	,	,	PUNCT
ejpam-6705	609	14	2017	2017	NUM
ejpam-6705	609	15	.	.	PUNCT
ejpam-6705	610	1	[	[	X
ejpam-6705	610	2	19	19	NUM
ejpam-6705	610	3	]	]	X
ejpam-6705	610	4	hassen	hassen	PROPN
ejpam-6705	610	5	aydi	aydi	VERB
ejpam-6705	610	6	,	,	PUNCT
ejpam-6705	610	7	monica	monica	PROPN
ejpam-6705	610	8	-	-	PUNCT
ejpam-6705	610	9	felicia	felicia	PROPN
ejpam-6705	610	10	bota	bota	NOUN
ejpam-6705	610	11	,	,	PUNCT
ejpam-6705	610	12	erdal	erdal	PROPN
ejpam-6705	610	13	karapınar	karapınar	PROPN
ejpam-6705	610	14	,	,	PUNCT
ejpam-6705	610	15	and	and	CCONJ
ejpam-6705	610	16	slobodanka	slobodanka	NOUN
ejpam-6705	610	17	mitrović.	mitrović.	PROPN
ejpam-6705	610	18	a	a	DET
ejpam-6705	610	19	fixed	fix	VERB
ejpam-6705	610	20	point	point	NOUN
ejpam-6705	610	21	theorem	theorem	NOUN
ejpam-6705	610	22	for	for	ADP
ejpam-6705	610	23	set	set	NOUN
ejpam-6705	610	24	-	-	PUNCT
ejpam-6705	610	25	valued	value	VERB
ejpam-6705	610	26	quasi	quasi	NOUN
ejpam-6705	610	27	-	-	NOUN
ejpam-6705	610	28	contractions	contraction	NOUN
ejpam-6705	610	29	in	in	ADP
ejpam-6705	610	30	b	b	NOUN
ejpam-6705	610	31	-	-	ADJ
ejpam-6705	610	32	metric	metric	ADJ
ejpam-6705	610	33	spaces	space	NOUN
ejpam-6705	610	34	.	.	PUNCT
ejpam-6705	611	1	fixed	fix	VERB
ejpam-6705	611	2	point	point	NOUN
ejpam-6705	611	3	theory	theory	NOUN
ejpam-6705	611	4	and	and	CCONJ
ejpam-6705	611	5	applications	application	NOUN
ejpam-6705	611	6	,	,	PUNCT
ejpam-6705	611	7	2012(1):88	2012(1):88	NUM
ejpam-6705	611	8	,	,	PUNCT
ejpam-6705	611	9	2012	2012	NUM
ejpam-6705	611	10	.	.	PUNCT
ejpam-6705	612	1	[	[	X
ejpam-6705	612	2	20	20	NUM
ejpam-6705	612	3	]	]	X
ejpam-6705	612	4	hassen	hassen	PROPN
ejpam-6705	612	5	aydi	aydi	VERB
ejpam-6705	612	6	,	,	PUNCT
ejpam-6705	612	7	monica	monica	PROPN
ejpam-6705	612	8	-	-	PUNCT
ejpam-6705	612	9	felicia	felicia	PROPN
ejpam-6705	612	10	bota	bota	NOUN
ejpam-6705	612	11	,	,	PUNCT
ejpam-6705	612	12	erdal	erdal	PROPN
ejpam-6705	612	13	karapinar	karapinar	PROPN
ejpam-6705	612	14	,	,	PUNCT
ejpam-6705	612	15	and	and	CCONJ
ejpam-6705	612	16	sirous	sirous	ADJ
ejpam-6705	612	17	moradi	moradi	NOUN
ejpam-6705	612	18	.	.	PUNCT
ejpam-6705	613	1	a	a	DET
ejpam-6705	613	2	common	common	ADJ
ejpam-6705	613	3	fixed	fix	VERB
ejpam-6705	613	4	point	point	NOUN
ejpam-6705	613	5	for	for	ADP
ejpam-6705	613	6	weak	weak	ADJ
ejpam-6705	613	7	φ	φ	NOUN
ejpam-6705	613	8	-	-	NOUN
ejpam-6705	613	9	contractions	contraction	NOUN
ejpam-6705	613	10	on	on	ADP
ejpam-6705	613	11	b	b	X
ejpam-6705	613	12	-	-	PUNCT
ejpam-6705	613	13	metric	metric	ADJ
ejpam-6705	613	14	spaces	space	NOUN
ejpam-6705	613	15	.	.	PUNCT
ejpam-6705	614	1	fixed	fix	VERB
ejpam-6705	614	2	point	point	NOUN
ejpam-6705	614	3	theory	theory	NOUN
ejpam-6705	614	4	,	,	PUNCT
ejpam-6705	614	5	13(2):337	13(2):337	NUM
ejpam-6705	614	6	–	–	PUNCT
ejpam-6705	614	7	346	346	NUM
ejpam-6705	614	8	,	,	PUNCT
ejpam-6705	614	9	2012	2012	NUM
ejpam-6705	614	10	.	.	PUNCT
ejpam-6705	615	1	[	[	X
ejpam-6705	615	2	21	21	NUM
ejpam-6705	615	3	]	]	X
ejpam-6705	615	4	hojjat	hojjat	NOUN
ejpam-6705	615	5	afshari	afshari	PROPN
ejpam-6705	615	6	,	,	PUNCT
ejpam-6705	615	7	hassen	hassen	PROPN
ejpam-6705	615	8	aydi	aydi	ADV
ejpam-6705	615	9	,	,	PUNCT
ejpam-6705	615	10	and	and	CCONJ
ejpam-6705	615	11	erdal	erdal	PROPN
ejpam-6705	615	12	karapınar	karapınar	PROPN
ejpam-6705	615	13	.	.	PUNCT
ejpam-6705	616	1	on	on	ADP
ejpam-6705	616	2	generalized	generalized	ADJ
ejpam-6705	616	3	α	α	PROPN
ejpam-6705	616	4	-	-	PUNCT
ejpam-6705	616	5	ψ	ψ	NOUN
ejpam-6705	616	6	-	-	ADJ
ejpam-6705	616	7	geraghty	geraghty	ADJ
ejpam-6705	616	8	contractions	contraction	NOUN
ejpam-6705	616	9	on	on	ADP
ejpam-6705	616	10	b	b	X
ejpam-6705	616	11	-	-	PUNCT
ejpam-6705	616	12	metric	metric	ADJ
ejpam-6705	616	13	spaces	space	NOUN
ejpam-6705	616	14	.	.	PUNCT
ejpam-6705	617	1	georgian	georgian	PROPN
ejpam-6705	617	2	mathematical	mathematical	PROPN
ejpam-6705	617	3	journal	journal	PROPN
ejpam-6705	617	4	,	,	PUNCT
ejpam-6705	617	5	27(1):9–21	27(1):9–21	NUM
ejpam-6705	617	6	,	,	PUNCT
ejpam-6705	617	7	2020	2020	NUM
ejpam-6705	617	8	.	.	PUNCT
ejpam-6705	618	1	[	[	X
ejpam-6705	618	2	22	22	NUM
ejpam-6705	618	3	]	]	X
ejpam-6705	618	4	james	james	PROPN
ejpam-6705	618	5	caristi	caristi	PROPN
ejpam-6705	618	6	.	.	PUNCT
ejpam-6705	619	1	fixed	fix	VERB
ejpam-6705	619	2	point	point	NOUN
ejpam-6705	619	3	theorems	theorem	NOUN
ejpam-6705	619	4	for	for	ADP
ejpam-6705	619	5	mappings	mapping	NOUN
ejpam-6705	619	6	satisfying	satisfy	VERB
ejpam-6705	619	7	inwardness	inwardness	NOUN
ejpam-6705	619	8	conditions	condition	NOUN
ejpam-6705	619	9	.	.	PUNCT
ejpam-6705	620	1	transactions	transaction	NOUN
ejpam-6705	620	2	of	of	ADP
ejpam-6705	620	3	the	the	DET
ejpam-6705	620	4	american	american	PROPN
ejpam-6705	620	5	mathematical	mathematical	PROPN
ejpam-6705	620	6	society	society	NOUN
ejpam-6705	620	7	,	,	PUNCT
ejpam-6705	620	8	215:241–251	215:241–251	NUM
ejpam-6705	620	9	,	,	PUNCT
ejpam-6705	620	10	1976	1976	NUM
ejpam-6705	620	11	.	.	PUNCT
ejpam-6705	621	1	[	[	X
ejpam-6705	621	2	23	23	NUM
ejpam-6705	621	3	]	]	X
ejpam-6705	621	4	andre	andre	PROPN
ejpam-6705	621	5	cm	cm	PROPN
ejpam-6705	621	6	ran	run	VERB
ejpam-6705	621	7	and	and	CCONJ
ejpam-6705	621	8	martine	martine	PROPN
ejpam-6705	621	9	cb	cb	PROPN
ejpam-6705	621	10	reurings	reurings	PROPN
ejpam-6705	621	11	.	.	PUNCT
ejpam-6705	622	1	a	a	DET
ejpam-6705	622	2	fixed	fix	VERB
ejpam-6705	622	3	point	point	NOUN
ejpam-6705	622	4	theorem	theorem	VERB
ejpam-6705	622	5	in	in	ADP
ejpam-6705	622	6	partially	partially	ADV
ejpam-6705	622	7	ordered	order	VERB
ejpam-6705	622	8	sets	set	NOUN
ejpam-6705	622	9	and	and	CCONJ
ejpam-6705	622	10	some	some	DET
ejpam-6705	622	11	applications	application	NOUN
ejpam-6705	622	12	to	to	PART
ejpam-6705	622	13	matrix	matrix	VERB
ejpam-6705	622	14	equations	equation	NOUN
ejpam-6705	622	15	.	.	PUNCT
ejpam-6705	623	1	proceedings	proceeding	NOUN
ejpam-6705	623	2	of	of	ADP
ejpam-6705	623	3	the	the	DET
ejpam-6705	623	4	american	american	PROPN
ejpam-6705	623	5	mathematical	mathematical	PROPN
ejpam-6705	623	6	society	society	NOUN
ejpam-6705	623	7	,	,	PUNCT
ejpam-6705	623	8	pages	page	NOUN
ejpam-6705	623	9	1435–1443	1435–1443	NUM
ejpam-6705	623	10	,	,	PUNCT
ejpam-6705	623	11	2004	2004	NUM
ejpam-6705	623	12	.	.	PUNCT
ejpam-6705	624	1	[	[	X
ejpam-6705	624	2	24	24	NUM
ejpam-6705	624	3	]	]	PUNCT
ejpam-6705	624	4	bapurao	bapurao	NOUN
ejpam-6705	624	5	c	c	PROPN
ejpam-6705	624	6	dhage	dhage	NOUN
ejpam-6705	624	7	.	.	PUNCT
ejpam-6705	625	1	generalised	generalise	VERB
ejpam-6705	625	2	metric	metric	ADJ
ejpam-6705	625	3	space	space	NOUN
ejpam-6705	625	4	and	and	CCONJ
ejpam-6705	625	5	mappings	mapping	NOUN
ejpam-6705	625	6	with	with	ADP
ejpam-6705	625	7	fixed	fix	VERB
ejpam-6705	625	8	point	point	NOUN
ejpam-6705	625	9	.	.	PUNCT
ejpam-6705	626	1	1992	1992	NUM
ejpam-6705	626	2	.	.	PUNCT
ejpam-6705	627	1	[	[	X
ejpam-6705	627	2	25	25	NUM
ejpam-6705	627	3	]	]	X
ejpam-6705	627	4	shaban	shaban	PROPN
ejpam-6705	627	5	sedghi	sedghi	PROPN
ejpam-6705	627	6	,	,	PUNCT
ejpam-6705	627	7	nabi	nabi	PROPN
ejpam-6705	627	8	shobe	shobe	PROPN
ejpam-6705	627	9	,	,	PUNCT
ejpam-6705	627	10	and	and	CCONJ
ejpam-6705	627	11	haiyun	haiyun	VERB
ejpam-6705	627	12	zhou	zhou	PROPN
ejpam-6705	627	13	.	.	PUNCT
ejpam-6705	628	1	a	a	DET
ejpam-6705	628	2	common	common	ADJ
ejpam-6705	628	3	fixed	fix	VERB
ejpam-6705	628	4	point	point	NOUN
ejpam-6705	628	5	theorem	theorem	VERB
ejpam-6705	628	6	inmetric	inmetric	ADJ
ejpam-6705	628	7	spaces	space	NOUN
ejpam-6705	628	8	.	.	PUNCT
ejpam-6705	629	1	fixed	fix	VERB
ejpam-6705	629	2	point	point	NOUN
ejpam-6705	629	3	theory	theory	NOUN
ejpam-6705	629	4	and	and	CCONJ
ejpam-6705	629	5	applications	application	NOUN
ejpam-6705	629	6	,	,	PUNCT
ejpam-6705	629	7	13(1):027906	13(1):027906	NUM
ejpam-6705	629	8	,	,	PUNCT
ejpam-6705	629	9	2007	2007	NUM
ejpam-6705	629	10	.	.	PUNCT
ejpam-6705	630	1	[	[	X
ejpam-6705	630	2	26	26	NUM
ejpam-6705	630	3	]	]	X
ejpam-6705	630	4	nguyen	nguyen	PROPN
ejpam-6705	630	5	van	van	PROPN
ejpam-6705	630	6	luong	luong	PROPN
ejpam-6705	630	7	and	and	CCONJ
ejpam-6705	630	8	nguyen	nguyen	PROPN
ejpam-6705	630	9	xuan	xuan	PROPN
ejpam-6705	630	10	thuan	thuan	PROPN
ejpam-6705	630	11	.	.	PUNCT
ejpam-6705	631	1	common	common	ADJ
ejpam-6705	631	2	fixed	fix	VERB
ejpam-6705	631	3	point	point	NOUN
ejpam-6705	631	4	theorem	theorem	VERB
ejpam-6705	631	5	in	in	ADP
ejpam-6705	631	6	compact	compact	ADJ
ejpam-6705	631	7	d	d	ADJ
ejpam-6705	631	8	-	-	ADJ
ejpam-6705	631	9	metric	metric	ADJ
ejpam-6705	631	10	spaces	space	NOUN
ejpam-6705	631	11	.	.	PUNCT
ejpam-6705	632	1	international	international	ADJ
ejpam-6705	632	2	mathematical	mathematical	PROPN
ejpam-6705	632	3	forum	forum	PROPN
ejpam-6705	632	4	,	,	PUNCT
ejpam-6705	632	5	6(13):605–612	6(13):605–612	NUM
ejpam-6705	632	6	,	,	PUNCT
ejpam-6705	632	7	2011	2011	NUM
ejpam-6705	632	8	.	.	PUNCT
ejpam-6705	633	1	[	[	X
ejpam-6705	633	2	27	27	NUM
ejpam-6705	633	3	]	]	X
ejpam-6705	633	4	t	t	PROPN
ejpam-6705	633	5	veerapandi	veerapandi	PROPN
ejpam-6705	633	6	and	and	CCONJ
ejpam-6705	633	7	aji	aji	PROPN
ejpam-6705	633	8	m	m	PROPN
ejpam-6705	633	9	pillai	pillai	PROPN
ejpam-6705	633	10	.	.	PUNCT
ejpam-6705	634	1	some	some	DET
ejpam-6705	634	2	common	common	ADJ
ejpam-6705	634	3	fixed	fix	VERB
ejpam-6705	634	4	point	point	NOUN
ejpam-6705	634	5	theorems	theorem	NOUN
ejpam-6705	634	6	in	in	ADP
ejpam-6705	634	7	d∗-metric	d∗-metric	ADJ
ejpam-6705	634	8	spaces	space	NOUN
ejpam-6705	634	9	.	.	PUNCT
ejpam-6705	635	1	african	african	ADJ
ejpam-6705	635	2	journal	journal	PROPN
ejpam-6705	635	3	of	of	ADP
ejpam-6705	635	4	mathematics	mathematics	PROPN
ejpam-6705	635	5	and	and	CCONJ
ejpam-6705	635	6	computer	computer	NOUN
ejpam-6705	635	7	science	science	NOUN
ejpam-6705	635	8	research	research	NOUN
ejpam-6705	635	9	,	,	PUNCT
ejpam-6705	635	10	4(12):357	4(12):357	PROPN
ejpam-6705	635	11	–	–	PUNCT
ejpam-6705	635	12	357	357	NUM
ejpam-6705	635	13	,	,	PUNCT
ejpam-6705	635	14	2011	2011	NUM
ejpam-6705	635	15	.	.	PUNCT
ejpam-6705	636	1	[	[	X
ejpam-6705	636	2	28	28	NUM
ejpam-6705	636	3	]	]	X
ejpam-6705	636	4	ravi	ravi	NOUN
ejpam-6705	636	5	p	p	PROPN
ejpam-6705	636	6	agarwal	agarwal	PROPN
ejpam-6705	636	7	,	,	PUNCT
ejpam-6705	636	8	zoran	zoran	PROPN
ejpam-6705	636	9	kadelburg	kadelburg	PROPN
ejpam-6705	636	10	,	,	PUNCT
ejpam-6705	636	11	and	and	CCONJ
ejpam-6705	636	12	stojan	stojan	ADP
ejpam-6705	636	13	radenović.	radenović.	PROPN
ejpam-6705	636	14	on	on	ADP
ejpam-6705	636	15	coupled	couple	VERB
ejpam-6705	636	16	fixed	fix	VERB
ejpam-6705	636	17	point	point	NOUN
ejpam-6705	636	18	results	result	NOUN
ejpam-6705	636	19	in	in	ADP
ejpam-6705	636	20	asymmetric	asymmetric	ADJ
ejpam-6705	636	21	g	g	NOUN
ejpam-6705	636	22	-	-	PUNCT
ejpam-6705	636	23	metric	metric	ADJ
ejpam-6705	636	24	spaces	space	NOUN
ejpam-6705	636	25	.	.	PUNCT
ejpam-6705	637	1	journal	journal	PROPN
ejpam-6705	637	2	of	of	ADP
ejpam-6705	637	3	inequalities	inequality	NOUN
ejpam-6705	637	4	and	and	CCONJ
ejpam-6705	637	5	applications	application	NOUN
ejpam-6705	637	6	,	,	PUNCT
ejpam-6705	637	7	2013(1):528	2013(1):528	NUM
ejpam-6705	637	8	,	,	PUNCT
ejpam-6705	637	9	2013	2013	NUM
ejpam-6705	637	10	.	.	PUNCT
ejpam-6705	638	1	[	[	X
ejpam-6705	638	2	29	29	NUM
ejpam-6705	638	3	]	]	PUNCT
ejpam-6705	638	4	stojan	stojan	ADP
ejpam-6705	638	5	radenović.	radenović.	PROPN
ejpam-6705	638	6	coupled	couple	VERB
ejpam-6705	638	7	fixed	fix	VERB
ejpam-6705	638	8	point	point	NOUN
ejpam-6705	638	9	theorems	theorem	NOUN
ejpam-6705	638	10	for	for	ADP
ejpam-6705	638	11	monotone	monotone	ADJ
ejpam-6705	638	12	mappings	mapping	NOUN
ejpam-6705	638	13	in	in	ADP
ejpam-6705	638	14	partially	partially	ADV
ejpam-6705	638	15	ordered	order	VERB
ejpam-6705	638	16	metric	metric	ADJ
ejpam-6705	638	17	spaces	space	NOUN
ejpam-6705	638	18	.	.	PUNCT
ejpam-6705	639	1	kragujevac	kragujevac	PROPN
ejpam-6705	639	2	journal	journal	PROPN
ejpam-6705	639	3	of	of	ADP
ejpam-6705	639	4	mathematics	mathematic	NOUN
ejpam-6705	639	5	,	,	PUNCT
ejpam-6705	639	6	38(2):249–257	38(2):249–257	PROPN
ejpam-6705	639	7	,	,	PUNCT
ejpam-6705	639	8	2014	2014	NUM
ejpam-6705	639	9	.	.	PUNCT
ejpam-6705	640	1	[	[	X
ejpam-6705	640	2	30	30	NUM
ejpam-6705	640	3	]	]	X
ejpam-6705	640	4	ghasem	ghasem	PROPN
ejpam-6705	640	5	soleimani	soleimani	PROPN
ejpam-6705	640	6	rad	rad	PROPN
ejpam-6705	640	7	,	,	PUNCT
ejpam-6705	640	8	satish	satish	ADJ
ejpam-6705	640	9	shukla	shukla	NOUN
ejpam-6705	640	10	,	,	PUNCT
ejpam-6705	640	11	and	and	CCONJ
ejpam-6705	640	12	hamidreza	hamidreza	PROPN
ejpam-6705	640	13	rahimi	rahimi	NOUN
ejpam-6705	640	14	.	.	PUNCT
ejpam-6705	641	1	some	some	DET
ejpam-6705	641	2	relations	relation	NOUN
ejpam-6705	641	3	between	between	ADP
ejpam-6705	641	4	n	n	CCONJ
ejpam-6705	641	5	-	-	PUNCT
ejpam-6705	641	6	tuple	tuple	NOUN
ejpam-6705	641	7	fixed	fix	VERB
ejpam-6705	641	8	point	point	NOUN
ejpam-6705	641	9	and	and	CCONJ
ejpam-6705	641	10	fixed	fix	VERB
ejpam-6705	641	11	point	point	NOUN
ejpam-6705	641	12	results	result	NOUN
ejpam-6705	641	13	.	.	PUNCT
ejpam-6705	642	1	revista	revista	PROPN
ejpam-6705	642	2	de	de	X
ejpam-6705	642	3	la	la	PROPN
ejpam-6705	642	4	real	real	PROPN
ejpam-6705	642	5	academia	academia	PROPN
ejpam-6705	642	6	de	de	PROPN
ejpam-6705	642	7	ciencias	ciencias	PROPN
ejpam-6705	642	8	exactas	exacta	NOUN
ejpam-6705	642	9	,	,	PUNCT
ejpam-6705	642	10	f́ısicas	f́ısicas	PROPN
ejpam-6705	642	11	y	y	PROPN
ejpam-6705	642	12	naturales	naturale	NOUN
ejpam-6705	642	13	.	.	PUNCT
ejpam-6705	643	1	serie	serie	PROPN
ejpam-6705	643	2	a.	a.	PROPN
ejpam-6705	643	3	matemáticas	matemáticas	PROPN
ejpam-6705	643	4	,	,	PUNCT
ejpam-6705	643	5	109(2):471–481	109(2):471–481	NUM
ejpam-6705	643	6	,	,	PUNCT
ejpam-6705	643	7	2015	2015	NUM
ejpam-6705	643	8	.	.	PUNCT
ejpam-6705	644	1	[	[	X
ejpam-6705	644	2	31	31	NUM
ejpam-6705	644	3	]	]	PUNCT
ejpam-6705	644	4	rajagopalan	rajagopalan	VERB
ejpam-6705	644	5	ramaswamy	ramaswamy	ADJ
ejpam-6705	644	6	and	and	CCONJ
ejpam-6705	644	7	gunaseelan	gunaseelan	PROPN
ejpam-6705	644	8	mani	mani	PROPN
ejpam-6705	644	9	.	.	PUNCT
ejpam-6705	645	1	application	application	NOUN
ejpam-6705	645	2	of	of	ADP
ejpam-6705	645	3	fixed	fix	VERB
ejpam-6705	645	4	point	point	NOUN
ejpam-6705	645	5	result	result	VERB
ejpam-6705	645	6	to	to	PART
ejpam-6705	645	7	solve	solve	VERB
ejpam-6705	645	8	integral	integral	ADJ
ejpam-6705	645	9	equation	equation	NOUN
ejpam-6705	645	10	in	in	ADP
ejpam-6705	645	11	the	the	DET
ejpam-6705	645	12	setting	setting	NOUN
ejpam-6705	645	13	of	of	ADP
ejpam-6705	645	14	graphical	graphical	ADJ
ejpam-6705	645	15	branciari	branciari	NOUN
ejpam-6705	645	16	ℵ-metric	ℵ-metric	ADJ
ejpam-6705	645	17	spaces	space	NOUN
ejpam-6705	645	18	.	.	PUNCT
ejpam-6705	646	1	aims	aim	VERB
ejpam-6705	646	2	mathematics	mathematic	NOUN
ejpam-6705	646	3	,	,	PUNCT
ejpam-6705	646	4	9(11):32945–32961	9(11):32945–32961	NUM
ejpam-6705	646	5	,	,	PUNCT
ejpam-6705	646	6	2024	2024	NUM
ejpam-6705	646	7	.	.	PUNCT
ejpam-6705	647	1	[	[	X
ejpam-6705	647	2	32	32	NUM
ejpam-6705	647	3	]	]	PUNCT
ejpam-6705	647	4	alaa	alaa	PROPN
ejpam-6705	647	5	mahmood	mahmood	PROPN
ejpam-6705	647	6	al	al	PROPN
ejpam-6705	647	7	jumaili	jumaili	PROPN
ejpam-6705	647	8	.	.	PUNCT
ejpam-6705	648	1	some	some	DET
ejpam-6705	648	2	coincidence	coincidence	NOUN
ejpam-6705	648	3	and	and	CCONJ
ejpam-6705	648	4	fixed	fix	VERB
ejpam-6705	648	5	point	point	NOUN
ejpam-6705	648	6	results	result	NOUN
ejpam-6705	648	7	in	in	ADP
ejpam-6705	648	8	partially	partially	ADV
ejpam-6705	648	9	ordered	order	VERB
ejpam-6705	648	10	complete	complete	ADJ
ejpam-6705	648	11	generalized	generalize	VERB
ejpam-6705	648	12	d∗metric	d∗metric	PROPN
ejpam-6705	648	13	spaces	space	NOUN
ejpam-6705	648	14	.	.	PUNCT
ejpam-6705	649	1	european	european	ADJ
ejpam-6705	649	2	journal	journal	PROPN
ejpam-6705	649	3	of	of	ADP
ejpam-6705	649	4	pure	pure	ADJ
ejpam-6705	649	5	and	and	CCONJ
ejpam-6705	649	6	applied	applied	ADJ
ejpam-6705	649	7	mathematics	mathematic	NOUN
ejpam-6705	649	8	,	,	PUNCT
ejpam-6705	649	9	10(5):1023–1034	10(5):1023–1034	NUM
ejpam-6705	649	10	,	,	PUNCT
ejpam-6705	649	11	2017	2017	NUM
ejpam-6705	649	12	.	.	PUNCT
ejpam-6705	650	1	[	[	X
ejpam-6705	650	2	33	33	NUM
ejpam-6705	650	3	]	]	X
ejpam-6705	650	4	e	e	X
ejpam-6705	650	5	lotfali	lotfali	PROPN
ejpam-6705	650	6	ghasab	ghasab	VERB
ejpam-6705	650	7	,	,	PUNCT
ejpam-6705	650	8	h	h	NOUN
ejpam-6705	650	9	majani	majani	NOUN
ejpam-6705	650	10	,	,	PUNCT
ejpam-6705	650	11	and	and	CCONJ
ejpam-6705	650	12	g	g	PROPN
ejpam-6705	650	13	soleimani	soleimani	PROPN
ejpam-6705	650	14	rad	rad	PROPN
ejpam-6705	650	15	.	.	PROPN
ejpam-6705	650	16	integral	integral	ADJ
ejpam-6705	650	17	type	type	NOUN
ejpam-6705	650	18	contraction	contraction	NOUN
ejpam-6705	650	19	and	and	CCONJ
ejpam-6705	650	20	coupled	couple	VERB
ejpam-6705	650	21	fixed	fix	VERB
ejpam-6705	650	22	point	point	NOUN
ejpam-6705	650	23	theorems	theorem	NOUN
ejpam-6705	650	24	in	in	ADP
ejpam-6705	650	25	ordered	order	VERB
ejpam-6705	650	26	g	g	NOUN
ejpam-6705	650	27	-	-	PUNCT
ejpam-6705	650	28	metric	metric	ADJ
ejpam-6705	650	29	spaces	space	NOUN
ejpam-6705	650	30	.	.	PUNCT
ejpam-6705	651	1	journal	journal	NOUN
ejpam-6705	651	2	of	of	ADP
ejpam-6705	651	3	linear	linear	PROPN
ejpam-6705	651	4	and	and	CCONJ
ejpam-6705	651	5	topological	topological	ADJ
ejpam-6705	651	6	algebra	algebra	NOUN
ejpam-6705	651	7	,	,	PUNCT
ejpam-6705	651	8	9(02):113–120	9(02):113–120	NUM
ejpam-6705	651	9	,	,	PUNCT
ejpam-6705	651	10	2020	2020	NUM
ejpam-6705	651	11	.	.	PUNCT
ejpam-6705	652	1	s.	s.	PROPN
ejpam-6705	652	2	batul	batul	PROPN
ejpam-6705	652	3	et	et	PROPN
ejpam-6705	652	4	al	al	PROPN
ejpam-6705	652	5	.	.	PUNCT
ejpam-6705	652	6	/	/	SYM
ejpam-6705	652	7	eur	eur	PROPN
ejpam-6705	652	8	.	.	PUNCT
ejpam-6705	653	1	j.	j.	PROPN
ejpam-6705	653	2	pure	pure	PROPN
ejpam-6705	653	3	appl	appl	PROPN
ejpam-6705	653	4	.	.	PROPN
ejpam-6705	653	5	math	math	PROPN
ejpam-6705	653	6	,	,	PUNCT
ejpam-6705	653	7	18	18	NUM
ejpam-6705	653	8	(	(	PUNCT
ejpam-6705	653	9	4	4	NUM
ejpam-6705	653	10	)	)	PUNCT
ejpam-6705	653	11	(	(	PUNCT
ejpam-6705	653	12	2025	2025	NUM
ejpam-6705	653	13	)	)	PUNCT
ejpam-6705	653	14	,	,	PUNCT
ejpam-6705	653	15	6705	6705	NUM
ejpam-6705	653	16	23	23	NUM
ejpam-6705	653	17	of	of	ADP
ejpam-6705	653	18	23	23	NUM
ejpam-6705	654	1	[	[	SYM
ejpam-6705	654	2	34	34	NUM
ejpam-6705	654	3	]	]	X
ejpam-6705	654	4	nassar	nassar	PROPN
ejpam-6705	654	5	aiman	aiman	PROPN
ejpam-6705	654	6	majid	majid	PROPN
ejpam-6705	654	7	,	,	PUNCT
ejpam-6705	654	8	alaa	alaa	PROPN
ejpam-6705	654	9	al	al	PROPN
ejpam-6705	654	10	jumaili	jumaili	PROPN
ejpam-6705	654	11	,	,	PUNCT
ejpam-6705	654	12	zhen	zhen	PROPN
ejpam-6705	654	13	chuan	chuan	PROPN
ejpam-6705	654	14	ng	ng	PROPN
ejpam-6705	654	15	,	,	PUNCT
ejpam-6705	654	16	and	and	CCONJ
ejpam-6705	654	17	see	see	VERB
ejpam-6705	654	18	keong	keong	PROPN
ejpam-6705	654	19	lee	lee	PROPN
ejpam-6705	654	20	.	.	PUNCT
ejpam-6705	655	1	some	some	DET
ejpam-6705	655	2	applications	application	NOUN
ejpam-6705	655	3	of	of	ADP
ejpam-6705	655	4	fixed	fix	VERB
ejpam-6705	655	5	point	point	NOUN
ejpam-6705	655	6	results	result	NOUN
ejpam-6705	655	7	for	for	ADP
ejpam-6705	655	8	monotone	monotone	ADJ
ejpam-6705	655	9	multivalued	multivalued	ADJ
ejpam-6705	655	10	and	and	CCONJ
ejpam-6705	655	11	integral	integral	ADJ
ejpam-6705	655	12	type	type	NOUN
ejpam-6705	655	13	contractive	contractive	ADJ
ejpam-6705	655	14	mappings	mapping	NOUN
ejpam-6705	655	15	.	.	PUNCT
ejpam-6705	656	1	fixed	fix	VERB
ejpam-6705	656	2	point	point	NOUN
ejpam-6705	656	3	theory	theory	NOUN
ejpam-6705	656	4	and	and	CCONJ
ejpam-6705	656	5	algorithms	algorithm	NOUN
ejpam-6705	656	6	for	for	ADP
ejpam-6705	656	7	sciences	science	NOUN
ejpam-6705	656	8	and	and	CCONJ
ejpam-6705	656	9	engineering	engineering	NOUN
ejpam-6705	656	10	,	,	PUNCT
ejpam-6705	656	11	2023(1):11	2023(1):11	NUM
ejpam-6705	656	12	,	,	PUNCT
ejpam-6705	656	13	2023	2023	NUM
ejpam-6705	656	14	.	.	PUNCT
ejpam-6705	657	1	[	[	X
ejpam-6705	657	2	35	35	NUM
ejpam-6705	657	3	]	]	X
ejpam-6705	657	4	asadollah	asadollah	PROPN
ejpam-6705	657	5	aghajani	aghajani	PROPN
ejpam-6705	657	6	,	,	PUNCT
ejpam-6705	657	7	mujahid	mujahid	NOUN
ejpam-6705	657	8	abbas	abbas	NOUN
ejpam-6705	657	9	,	,	PUNCT
ejpam-6705	657	10	and	and	CCONJ
ejpam-6705	657	11	jamal	jamal	PROPN
ejpam-6705	657	12	rezaei	rezaei	PROPN
ejpam-6705	657	13	roshan	roshan	PROPN
ejpam-6705	657	14	.	.	PUNCT
ejpam-6705	658	1	common	common	ADJ
ejpam-6705	658	2	fixed	fix	VERB
ejpam-6705	658	3	point	point	NOUN
ejpam-6705	658	4	of	of	ADP
ejpam-6705	658	5	generalized	generalized	ADJ
ejpam-6705	658	6	weak	weak	ADJ
ejpam-6705	658	7	contractive	contractive	ADJ
ejpam-6705	658	8	mappings	mapping	NOUN
ejpam-6705	658	9	in	in	ADP
ejpam-6705	658	10	partially	partially	ADV
ejpam-6705	658	11	ordered	order	VERB
ejpam-6705	658	12	gb	gb	ADV
ejpam-6705	658	13	-	-	PUNCT
ejpam-6705	658	14	metric	metric	ADJ
ejpam-6705	658	15	spaces	space	NOUN
ejpam-6705	658	16	.	.	PUNCT
ejpam-6705	659	1	filomat	filomat	PROPN
ejpam-6705	659	2	,	,	PUNCT
ejpam-6705	659	3	28(6):1087–1101	28(6):1087–1101	NUM
ejpam-6705	659	4	,	,	PUNCT
ejpam-6705	659	5	2014	2014	NUM
ejpam-6705	659	6	.	.	PUNCT
ejpam-6705	660	1	[	[	X
ejpam-6705	660	2	36	36	NUM
ejpam-6705	660	3	]	]	PUNCT
ejpam-6705	660	4	rajagopalan	rajagopalan	VERB
ejpam-6705	660	5	ramaswamy	ramaswamy	PROPN
ejpam-6705	660	6	,	,	PUNCT
ejpam-6705	660	7	manoj	manoj	PROPN
ejpam-6705	660	8	kumar	kumar	PROPN
ejpam-6705	660	9	,	,	PUNCT
ejpam-6705	660	10	prem	prem	PROPN
ejpam-6705	660	11	lata	lata	PROPN
ejpam-6705	660	12	sharma	sharma	PROPN
ejpam-6705	660	13	,	,	PUNCT
ejpam-6705	660	14	rayan	rayan	PROPN
ejpam-6705	660	15	abdulrahman	abdulrahman	PROPN
ejpam-6705	660	16	alkhowaiter	alkhowaiter	PROPN
ejpam-6705	660	17	,	,	PUNCT
ejpam-6705	660	18	hossam	hossam	NOUN
ejpam-6705	660	19	a	a	DET
ejpam-6705	660	20	nabway	nabway	NOUN
ejpam-6705	660	21	,	,	PUNCT
ejpam-6705	660	22	ola	ola	PROPN
ejpam-6705	660	23	ashour	ashour	VERB
ejpam-6705	660	24	a	a	DET
ejpam-6705	660	25	abdelnaby	abdelnaby	NOUN
ejpam-6705	660	26	,	,	PUNCT
ejpam-6705	660	27	and	and	CCONJ
ejpam-6705	660	28	gunaseelan	gunaseelan	PROPN
ejpam-6705	660	29	mani	mani	PROPN
ejpam-6705	660	30	.	.	PUNCT
ejpam-6705	661	1	some	some	DET
ejpam-6705	661	2	fixed	fix	VERB
ejpam-6705	661	3	point	point	NOUN
ejpam-6705	661	4	results	result	NOUN
ejpam-6705	661	5	for	for	ADP
ejpam-6705	661	6	hybrid	hybrid	ADJ
ejpam-6705	661	7	contraction	contraction	NOUN
ejpam-6705	661	8	in	in	ADP
ejpam-6705	661	9	metric	metric	ADJ
ejpam-6705	661	10	spaces	space	NOUN
ejpam-6705	661	11	and	and	CCONJ
ejpam-6705	661	12	ulam	ulam	NOUN
ejpam-6705	661	13	-	-	PUNCT
ejpam-6705	661	14	hyers	hyer	NOUN
ejpam-6705	661	15	stability	stability	NOUN
ejpam-6705	661	16	.	.	PUNCT
ejpam-6705	662	1	european	european	ADJ
ejpam-6705	662	2	journal	journal	PROPN
ejpam-6705	662	3	of	of	ADP
ejpam-6705	662	4	pure	pure	ADJ
ejpam-6705	662	5	and	and	CCONJ
ejpam-6705	662	6	applied	applied	ADJ
ejpam-6705	662	7	mathematics	mathematic	NOUN
ejpam-6705	662	8	,	,	PUNCT
ejpam-6705	662	9	18(3):6243–6243	18(3):6243–6243	NUM
ejpam-6705	662	10	,	,	PUNCT
ejpam-6705	662	11	2025	2025	NUM
ejpam-6705	662	12	.	.	PUNCT
ejpam-6705	663	1	[	[	X
ejpam-6705	663	2	37	37	NUM
ejpam-6705	663	3	]	]	X
ejpam-6705	663	4	benitha	benitha	NOUN
ejpam-6705	663	5	wises	wise	VERB
ejpam-6705	663	6	samuel	samuel	PROPN
ejpam-6705	663	7	,	,	PUNCT
ejpam-6705	663	8	gunaseelan	gunaseelan	PROPN
ejpam-6705	663	9	mani	mani	PROPN
ejpam-6705	663	10	,	,	PUNCT
ejpam-6705	663	11	shoba	shoba	VERB
ejpam-6705	663	12	sree	sree	PROPN
ejpam-6705	663	13	ramulu	ramulu	PROPN
ejpam-6705	663	14	,	,	PUNCT
ejpam-6705	663	15	sabri	sabri	NOUN
ejpam-6705	663	16	tm	tm	PROPN
ejpam-6705	663	17	thabet	thabet	PROPN
ejpam-6705	663	18	,	,	PUNCT
ejpam-6705	663	19	and	and	CCONJ
ejpam-6705	663	20	imed	imed	PROPN
ejpam-6705	663	21	kedim	kedim	PROPN
ejpam-6705	663	22	.	.	PUNCT
ejpam-6705	664	1	integral	integral	ADJ
ejpam-6705	664	2	-	-	PUNCT
ejpam-6705	664	3	type	type	NOUN
ejpam-6705	664	4	contraction	contraction	NOUN
ejpam-6705	664	5	on	on	ADP
ejpam-6705	664	6	orthogonal	orthogonal	ADJ
ejpam-6705	664	7	s	s	NOUN
ejpam-6705	664	8	-	-	ADJ
ejpam-6705	664	9	metric	metric	ADJ
ejpam-6705	664	10	spaces	space	NOUN
ejpam-6705	664	11	with	with	ADP
ejpam-6705	664	12	common	common	ADJ
ejpam-6705	664	13	fixed	fix	VERB
ejpam-6705	664	14	-	-	PUNCT
ejpam-6705	664	15	point	point	NOUN
ejpam-6705	664	16	results	result	NOUN
ejpam-6705	664	17	and	and	CCONJ
ejpam-6705	664	18	applications	application	NOUN
ejpam-6705	664	19	to	to	PART
ejpam-6705	664	20	fractional	fractional	ADJ
ejpam-6705	664	21	integral	integral	ADJ
ejpam-6705	664	22	equations	equation	NOUN
ejpam-6705	664	23	.	.	PUNCT
ejpam-6705	665	1	fixed	fix	VERB
ejpam-6705	665	2	point	point	NOUN
ejpam-6705	665	3	theory	theory	NOUN
ejpam-6705	665	4	and	and	CCONJ
ejpam-6705	665	5	algorithms	algorithm	NOUN
ejpam-6705	665	6	for	for	ADP
ejpam-6705	665	7	sciences	science	NOUN
ejpam-6705	665	8	and	and	CCONJ
ejpam-6705	665	9	engineering	engineering	NOUN
ejpam-6705	665	10	,	,	PUNCT
ejpam-6705	665	11	2025(1):10	2025(1):10	NUM
ejpam-6705	665	12	,	,	PUNCT
ejpam-6705	665	13	2025	2025	NUM
ejpam-6705	665	14	.	.	PUNCT
ejpam-6705	666	1	[	[	X
ejpam-6705	666	2	38	38	NUM
ejpam-6705	666	3	]	]	PUNCT
ejpam-6705	666	4	haitham	haitham	PROPN
ejpam-6705	666	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	666	6	and	and	CCONJ
ejpam-6705	666	7	yasser	yasser	PROPN
ejpam-6705	666	8	alrashedi	alrashedi	PROPN
ejpam-6705	666	9	.	.	PUNCT
ejpam-6705	667	1	mathematical	mathematical	ADJ
ejpam-6705	667	2	and	and	CCONJ
ejpam-6705	667	3	physical	physical	ADJ
ejpam-6705	667	4	analysis	analysis	NOUN
ejpam-6705	667	5	of	of	ADP
ejpam-6705	667	6	fractional	fractional	ADJ
ejpam-6705	667	7	estevez	estevez	PROPN
ejpam-6705	667	8	–	–	PUNCT
ejpam-6705	667	9	mansfield	mansfield	PROPN
ejpam-6705	667	10	–	–	PUNCT
ejpam-6705	667	11	clarkson	clarkson	PROPN
ejpam-6705	667	12	equation	equation	NOUN
ejpam-6705	667	13	.	.	PUNCT
ejpam-6705	668	1	fractal	fractal	PROPN
ejpam-6705	668	2	and	and	CCONJ
ejpam-6705	668	3	fractional	fractional	ADJ
ejpam-6705	668	4	,	,	PUNCT
ejpam-6705	668	5	8(8	8(8	NUM
ejpam-6705	668	6	)	)	PUNCT
ejpam-6705	668	7	,	,	PUNCT
ejpam-6705	668	8	2024	2024	NUM
ejpam-6705	668	9	.	.	PUNCT
ejpam-6705	669	1	[	[	X
ejpam-6705	669	2	39	39	NUM
ejpam-6705	669	3	]	]	PUNCT
ejpam-6705	669	4	haitham	haitham	PROPN
ejpam-6705	669	5	qawaqneh	qawaqneh	PROPN
ejpam-6705	669	6	,	,	PUNCT
ejpam-6705	669	7	khalil	khalil	PROPN
ejpam-6705	669	8	hakami	hakami	PROPN
ejpam-6705	669	9	,	,	PUNCT
ejpam-6705	669	10	ali	ali	PROPN
ejpam-6705	669	11	altalbe	altalbe	NOUN
ejpam-6705	669	12	,	,	PUNCT
ejpam-6705	669	13	and	and	CCONJ
ejpam-6705	669	14	mustafa	mustafa	PROPN
ejpam-6705	669	15	bayram	bayram	PROPN
ejpam-6705	669	16	.	.	PUNCT
ejpam-6705	670	1	the	the	DET
ejpam-6705	670	2	discovery	discovery	PROPN
ejpam-6705	670	3	of	of	ADP
ejpam-6705	670	4	truncated	truncated	ADJ
ejpam-6705	670	5	m	m	PROPN
ejpam-6705	670	6	-	-	ADJ
ejpam-6705	670	7	fractional	fractional	ADJ
ejpam-6705	670	8	exact	exact	ADJ
ejpam-6705	670	9	solitons	soliton	NOUN
ejpam-6705	670	10	and	and	CCONJ
ejpam-6705	670	11	a	a	DET
ejpam-6705	670	12	qualitative	qualitative	ADJ
ejpam-6705	670	13	analysis	analysis	NOUN
ejpam-6705	670	14	of	of	ADP
ejpam-6705	670	15	the	the	DET
ejpam-6705	670	16	generalized	generalized	ADJ
ejpam-6705	670	17	bretherton	bretherton	PROPN
ejpam-6705	670	18	model	model	NOUN
ejpam-6705	670	19	.	.	PUNCT
ejpam-6705	671	1	mathematics	mathematic	NOUN
ejpam-6705	671	2	,	,	PUNCT
ejpam-6705	671	3	12(17	12(17	NUM
ejpam-6705	671	4	)	)	PUNCT
ejpam-6705	671	5	,	,	PUNCT
ejpam-6705	671	6	2024	2024	NUM
ejpam-6705	671	7	.	.	PUNCT
ejpam-6705	672	1	[	[	X
ejpam-6705	672	2	40	40	NUM
ejpam-6705	672	3	]	]	X
ejpam-6705	672	4	yuqiang	yuqiang	PROPN
ejpam-6705	672	5	feng	feng	PROPN
ejpam-6705	672	6	and	and	CCONJ
ejpam-6705	672	7	sanyang	sanyang	PROPN
ejpam-6705	672	8	liu	liu	PROPN
ejpam-6705	672	9	.	.	PUNCT
ejpam-6705	673	1	fixed	fix	VERB
ejpam-6705	673	2	point	point	NOUN
ejpam-6705	673	3	theorems	theorem	NOUN
ejpam-6705	673	4	for	for	ADP
ejpam-6705	673	5	multi	multi	ADJ
ejpam-6705	673	6	-	-	ADJ
ejpam-6705	673	7	valued	value	VERB
ejpam-6705	673	8	contractive	contractive	ADJ
ejpam-6705	673	9	mappings	mapping	NOUN
ejpam-6705	673	10	and	and	CCONJ
ejpam-6705	673	11	multi	multi	ADJ
ejpam-6705	673	12	-	-	ADJ
ejpam-6705	673	13	valued	value	VERB
ejpam-6705	673	14	caristi	caristi	NOUN
ejpam-6705	673	15	type	type	NOUN
ejpam-6705	673	16	mappings	mapping	NOUN
ejpam-6705	673	17	.	.	PUNCT
ejpam-6705	674	1	journal	journal	PROPN
ejpam-6705	674	2	of	of	ADP
ejpam-6705	674	3	mathematical	mathematical	ADJ
ejpam-6705	674	4	analysis	analysis	NOUN
ejpam-6705	674	5	and	and	CCONJ
ejpam-6705	674	6	applications	application	NOUN
ejpam-6705	674	7	,	,	PUNCT
ejpam-6705	674	8	317(1):103–112	317(1):103–112	NUM
ejpam-6705	674	9	,	,	PUNCT
ejpam-6705	674	10	2006	2006	NUM
ejpam-6705	674	11	.	.	PUNCT
ejpam-6705	675	1	[	[	X
ejpam-6705	675	2	41	41	NUM
ejpam-6705	675	3	]	]	PUNCT
ejpam-6705	675	4	t	t	PROPN
ejpam-6705	675	5	gnana	gnana	PROPN
ejpam-6705	675	6	bhaskar	bhaskar	NOUN
ejpam-6705	675	7	and	and	CCONJ
ejpam-6705	675	8	vangipuram	vangipuram	PROPN
ejpam-6705	675	9	lakshmikantham	lakshmikantham	VERB
ejpam-6705	675	10	.	.	PUNCT
ejpam-6705	676	1	fixed	fix	VERB
ejpam-6705	676	2	point	point	NOUN
ejpam-6705	676	3	theorems	theorem	NOUN
ejpam-6705	676	4	in	in	ADP
ejpam-6705	676	5	partially	partially	ADV
ejpam-6705	676	6	ordered	order	VERB
ejpam-6705	676	7	metric	metric	ADJ
ejpam-6705	676	8	spaces	space	NOUN
ejpam-6705	676	9	and	and	CCONJ
ejpam-6705	676	10	applications	application	NOUN
ejpam-6705	676	11	.	.	PUNCT
ejpam-6705	677	1	nonlinear	nonlinear	ADJ
ejpam-6705	677	2	analysis	analysis	NOUN
ejpam-6705	677	3	:	:	PUNCT
ejpam-6705	677	4	theory	theory	NOUN
ejpam-6705	677	5	,	,	PUNCT
ejpam-6705	677	6	methods	method	NOUN
ejpam-6705	677	7	&	&	CCONJ
ejpam-6705	677	8	applications	application	NOUN
ejpam-6705	677	9	,	,	PUNCT
ejpam-6705	677	10	65(7):1379–1393	65(7):1379–1393	NUM
ejpam-6705	677	11	,	,	PUNCT
ejpam-6705	677	12	2006	2006	NUM
ejpam-6705	677	13	.	.	PUNCT
ejpam-6705	678	1	[	[	X
ejpam-6705	678	2	42	42	NUM
ejpam-6705	678	3	]	]	X
ejpam-6705	678	4	james	james	PROPN
ejpam-6705	678	5	caristi	caristi	PROPN
ejpam-6705	678	6	.	.	PUNCT
ejpam-6705	679	1	fixed	fix	VERB
ejpam-6705	679	2	point	point	NOUN
ejpam-6705	679	3	theorems	theorem	NOUN
ejpam-6705	679	4	for	for	ADP
ejpam-6705	679	5	mappings	mapping	NOUN
ejpam-6705	679	6	satisfying	satisfy	VERB
ejpam-6705	679	7	inwardness	inwardness	NOUN
ejpam-6705	679	8	conditions	condition	NOUN
ejpam-6705	679	9	.	.	PUNCT
ejpam-6705	680	1	transactions	transaction	NOUN
ejpam-6705	680	2	of	of	ADP
ejpam-6705	680	3	the	the	DET
ejpam-6705	680	4	american	american	PROPN
ejpam-6705	680	5	mathematical	mathematical	PROPN
ejpam-6705	680	6	society	society	NOUN
ejpam-6705	680	7	,	,	PUNCT
ejpam-6705	680	8	215:241–251	215:241–251	NUM
ejpam-6705	680	9	,	,	PUNCT
ejpam-6705	680	10	1976	1976	NUM
ejpam-6705	680	11	.	.	PUNCT
ejpam-6705	681	1	[	[	X
ejpam-6705	681	2	43	43	NUM
ejpam-6705	681	3	]	]	X
ejpam-6705	681	4	nassar	nassar	PROPN
ejpam-6705	681	5	aiman	aiman	PROPN
ejpam-6705	681	6	majid	majid	PROPN
ejpam-6705	681	7	,	,	PUNCT
ejpam-6705	681	8	alaa	alaa	PROPN
ejpam-6705	681	9	al	al	PROPN
ejpam-6705	681	10	jumaili	jumaili	PROPN
ejpam-6705	681	11	,	,	PUNCT
ejpam-6705	681	12	zhen	zhen	PROPN
ejpam-6705	681	13	chuan	chuan	PROPN
ejpam-6705	681	14	ng	ng	PROPN
ejpam-6705	681	15	,	,	PUNCT
ejpam-6705	681	16	and	and	CCONJ
ejpam-6705	681	17	see	see	VERB
ejpam-6705	681	18	keong	keong	PROPN
ejpam-6705	681	19	lee	lee	PROPN
ejpam-6705	681	20	.	.	PUNCT
ejpam-6705	682	1	some	some	DET
ejpam-6705	682	2	applications	application	NOUN
ejpam-6705	682	3	of	of	ADP
ejpam-6705	682	4	fixed	fix	VERB
ejpam-6705	682	5	point	point	NOUN
ejpam-6705	682	6	results	result	NOUN
ejpam-6705	682	7	for	for	ADP
ejpam-6705	682	8	monotone	monotone	ADJ
ejpam-6705	682	9	multivalued	multivalued	ADJ
ejpam-6705	682	10	and	and	CCONJ
ejpam-6705	682	11	integral	integral	ADJ
ejpam-6705	682	12	type	type	NOUN
ejpam-6705	682	13	contractive	contractive	ADJ
ejpam-6705	682	14	mappings	mapping	NOUN
ejpam-6705	682	15	.	.	PUNCT
ejpam-6705	683	1	fixed	fix	VERB
ejpam-6705	683	2	point	point	NOUN
ejpam-6705	683	3	theory	theory	NOUN
ejpam-6705	683	4	and	and	CCONJ
ejpam-6705	683	5	algorithms	algorithm	NOUN
ejpam-6705	683	6	for	for	ADP
ejpam-6705	683	7	sciences	science	NOUN
ejpam-6705	683	8	and	and	CCONJ
ejpam-6705	683	9	engineering	engineering	NOUN
ejpam-6705	683	10	,	,	PUNCT
ejpam-6705	683	11	2023(1):11	2023(1):11	NUM
ejpam-6705	683	12	,	,	PUNCT
ejpam-6705	683	13	2023	2023	NUM
ejpam-6705	683	14	.	.	PUNCT