id	sid	tid	token	lemma	pos
ejpam-7013	1	1	european	european	PROPN
ejpam-7013	1	2	journal	journal	PROPN
ejpam-7013	1	3	of	of	ADP
ejpam-7013	1	4	pure	pure	ADJ
ejpam-7013	1	5	and	and	CCONJ
ejpam-7013	1	6	applied	applied	ADJ
ejpam-7013	1	7	mathematics	mathematic	NOUN
ejpam-7013	1	8	2025	2025	NUM
ejpam-7013	1	9	,	,	PUNCT
ejpam-7013	1	10	vol	vol	NOUN
ejpam-7013	1	11	.	.	PROPN
ejpam-7013	1	12	18	18	NUM
ejpam-7013	1	13	,	,	PUNCT
ejpam-7013	1	14	issue	issue	NOUN
ejpam-7013	1	15	4	4	NUM
ejpam-7013	1	16	,	,	PUNCT
ejpam-7013	1	17	article	article	NOUN
ejpam-7013	1	18	number	number	NOUN
ejpam-7013	1	19	7013	7013	NUM
ejpam-7013	1	20	issn	issn	PROPN
ejpam-7013	1	21	1307	1307	NUM
ejpam-7013	1	22	-	-	SYM
ejpam-7013	1	23	5543	5543	NUM
ejpam-7013	1	24	–	–	PUNCT
ejpam-7013	1	25	ejpam.com	ejpam.com	X
ejpam-7013	1	26	published	publish	VERB
ejpam-7013	1	27	by	by	ADP
ejpam-7013	1	28	new	new	PROPN
ejpam-7013	1	29	york	york	PROPN
ejpam-7013	1	30	business	business	PROPN
ejpam-7013	1	31	global	global	ADJ
ejpam-7013	1	32	fixed	fix	VERB
ejpam-7013	1	33	point	point	NOUN
ejpam-7013	1	34	results	result	NOUN
ejpam-7013	1	35	in	in	ADP
ejpam-7013	1	36	b	b	NOUN
ejpam-7013	1	37	-	-	PUNCT
ejpam-7013	1	38	fuzzy	fuzzy	ADJ
ejpam-7013	1	39	metric	metric	ADJ
ejpam-7013	1	40	spaces	space	NOUN
ejpam-7013	1	41	with	with	ADP
ejpam-7013	1	42	applications	application	NOUN
ejpam-7013	1	43	to	to	PART
ejpam-7013	1	44	nonlinear	nonlinear	VERB
ejpam-7013	1	45	fuzzy	fuzzy	ADJ
ejpam-7013	1	46	integral	integral	ADJ
ejpam-7013	1	47	equations	equation	NOUN
ejpam-7013	1	48	dritan	dritan	PROPN
ejpam-7013	1	49	gerbeti1	gerbeti1	PROPN
ejpam-7013	1	50	,	,	PUNCT
ejpam-7013	1	51	k.	k.	PROPN
ejpam-7013	2	1	dinesh2,∗	dinesh2,∗	PROPN
ejpam-7013	2	2	,	,	PUNCT
ejpam-7013	2	3	kastriot	kastriot	PROPN
ejpam-7013	2	4	zoto3	zoto3	PROPN
ejpam-7013	2	5	,	,	PUNCT
ejpam-7013	2	6	b.	b.	PROPN
ejpam-7013	2	7	shoba4	shoba4	PROPN
ejpam-7013	2	8	,	,	PUNCT
ejpam-7013	2	9	hawa	hawa	PROPN
ejpam-7013	2	10	ibnouf	ibnouf	PROPN
ejpam-7013	2	11	osman	osman	PROPN
ejpam-7013	2	12	ibnouf5	ibnouf5	PROPN
ejpam-7013	2	13	1	1	NUM
ejpam-7013	2	14	department	department	NOUN
ejpam-7013	2	15	of	of	ADP
ejpam-7013	2	16	mathematics	mathematic	NOUN
ejpam-7013	2	17	,	,	PUNCT
ejpam-7013	2	18	faculty	faculty	NOUN
ejpam-7013	2	19	of	of	ADP
ejpam-7013	2	20	natural	natural	ADJ
ejpam-7013	2	21	sciences	science	NOUN
ejpam-7013	2	22	,	,	PUNCT
ejpam-7013	2	23	university	university	NOUN
ejpam-7013	2	24	of	of	ADP
ejpam-7013	2	25	shkodra	shkodra	PROPN
ejpam-7013	2	26	”	"	PUNCT
ejpam-7013	2	27	luigj	luigj	PROPN
ejpam-7013	2	28	gurakuqi	gurakuqi	PROPN
ejpam-7013	2	29	”	"	PUNCT
ejpam-7013	2	30	,	,	PUNCT
ejpam-7013	2	31	4001	4001	NUM
ejpam-7013	2	32	,	,	PUNCT
ejpam-7013	2	33	shkoder	shkoder	NOUN
ejpam-7013	2	34	,	,	PUNCT
ejpam-7013	2	35	albania	albania	PROPN
ejpam-7013	2	36	2	2	NUM
ejpam-7013	2	37	department	department	NOUN
ejpam-7013	2	38	of	of	ADP
ejpam-7013	2	39	mathematics	mathematics	PROPN
ejpam-7013	2	40	,	,	PUNCT
ejpam-7013	2	41	k.	k.	PROPN
ejpam-7013	2	42	ramakrishnan	ramakrishnan	PROPN
ejpam-7013	2	43	college	college	PROPN
ejpam-7013	2	44	of	of	ADP
ejpam-7013	2	45	engineering	engineering	NOUN
ejpam-7013	2	46	(	(	PUNCT
ejpam-7013	2	47	autonomous	autonomous	ADJ
ejpam-7013	2	48	)	)	PUNCT
ejpam-7013	2	49	,	,	PUNCT
ejpam-7013	2	50	trichy	trichy	PROPN
ejpam-7013	2	51	,	,	PUNCT
ejpam-7013	2	52	india	india	PROPN
ejpam-7013	2	53	3	3	NUM
ejpam-7013	2	54	department	department	PROPN
ejpam-7013	2	55	of	of	ADP
ejpam-7013	2	56	mathematics	mathematic	NOUN
ejpam-7013	2	57	,	,	PUNCT
ejpam-7013	2	58	informatics	informatic	NOUN
ejpam-7013	2	59	and	and	CCONJ
ejpam-7013	2	60	physics	physics	PROPN
ejpam-7013	2	61	,	,	PUNCT
ejpam-7013	2	62	faculty	faculty	NOUN
ejpam-7013	2	63	of	of	ADP
ejpam-7013	2	64	natural	natural	ADJ
ejpam-7013	2	65	sciences	science	NOUN
ejpam-7013	2	66	,	,	PUNCT
ejpam-7013	2	67	university	university	NOUN
ejpam-7013	2	68	of	of	ADP
ejpam-7013	2	69	gjirokastra	gjirokastra	PROPN
ejpam-7013	2	70	6001	6001	NUM
ejpam-7013	2	71	,	,	PUNCT
ejpam-7013	2	72	gjirokastra	gjirokastra	PROPN
ejpam-7013	2	73	,	,	PUNCT
ejpam-7013	2	74	albania	albania	PROPN
ejpam-7013	2	75	4	4	NUM
ejpam-7013	2	76	department	department	NOUN
ejpam-7013	2	77	of	of	ADP
ejpam-7013	2	78	mathematics	mathematics	PROPN
ejpam-7013	2	79	,	,	PUNCT
ejpam-7013	2	80	st	st	PROPN
ejpam-7013	2	81	joseph	joseph	PROPN
ejpam-7013	2	82	’s	’s	PART
ejpam-7013	2	83	college	college	PROPN
ejpam-7013	2	84	of	of	ADP
ejpam-7013	2	85	engineering	engineering	PROPN
ejpam-7013	2	86	,	,	PUNCT
ejpam-7013	2	87	omr	omr	PROPN
ejpam-7013	2	88	chennai	chennai	NOUN
ejpam-7013	2	89	600	600	NUM
ejpam-7013	2	90	019	019	NUM
ejpam-7013	2	91	,	,	PUNCT
ejpam-7013	2	92	india	india	PROPN
ejpam-7013	2	93	5	5	NUM
ejpam-7013	2	94	department	department	NOUN
ejpam-7013	2	95	of	of	ADP
ejpam-7013	2	96	mathematics	mathematic	NOUN
ejpam-7013	2	97	,	,	PUNCT
ejpam-7013	2	98	college	college	NOUN
ejpam-7013	2	99	of	of	ADP
ejpam-7013	2	100	science	science	NOUN
ejpam-7013	2	101	,	,	PUNCT
ejpam-7013	2	102	qassim	qassim	PROPN
ejpam-7013	2	103	university	university	PROPN
ejpam-7013	2	104	,	,	PUNCT
ejpam-7013	2	105	buraydah	buraydah	PROPN
ejpam-7013	2	106	,	,	PUNCT
ejpam-7013	2	107	qassim	qassim	NOUN
ejpam-7013	2	108	,	,	PUNCT
ejpam-7013	2	109	saudi	saudi	PROPN
ejpam-7013	2	110	arabia	arabia	PROPN
ejpam-7013	2	111	abstract	abstract	NOUN
ejpam-7013	2	112	.	.	PUNCT
ejpam-7013	3	1	in	in	ADP
ejpam-7013	3	2	this	this	DET
ejpam-7013	3	3	paper	paper	NOUN
ejpam-7013	3	4	,	,	PUNCT
ejpam-7013	3	5	we	we	PRON
ejpam-7013	3	6	establish	establish	VERB
ejpam-7013	3	7	several	several	ADJ
ejpam-7013	3	8	new	new	ADJ
ejpam-7013	3	9	fixed	fix	VERB
ejpam-7013	3	10	point	point	NOUN
ejpam-7013	3	11	(	(	PUNCT
ejpam-7013	3	12	fp	fp	X
ejpam-7013	3	13	)	)	PUNCT
ejpam-7013	3	14	theorems	theorem	NOUN
ejpam-7013	3	15	for	for	ADP
ejpam-7013	3	16	fuzzy	fuzzy	ADJ
ejpam-7013	3	17	mappings	mapping	NOUN
ejpam-7013	3	18	in	in	ADP
ejpam-7013	3	19	the	the	DET
ejpam-7013	3	20	framework	framework	NOUN
ejpam-7013	3	21	of	of	ADP
ejpam-7013	3	22	complete	complete	ADJ
ejpam-7013	3	23	b	b	X
ejpam-7013	3	24	-	-	PUNCT
ejpam-7013	3	25	fuzzy	fuzzy	ADJ
ejpam-7013	3	26	metric	metric	ADJ
ejpam-7013	3	27	spaces	space	NOUN
ejpam-7013	3	28	(	(	PUNCT
ejpam-7013	3	29	fms	fms	PROPN
ejpam-7013	3	30	)	)	PUNCT
ejpam-7013	3	31	.	.	PUNCT
ejpam-7013	4	1	we	we	PRON
ejpam-7013	4	2	introduce	introduce	VERB
ejpam-7013	4	3	generalized	generalized	ADJ
ejpam-7013	4	4	contractive	contractive	ADJ
ejpam-7013	4	5	conditions	condition	NOUN
ejpam-7013	4	6	that	that	PRON
ejpam-7013	4	7	extend	extend	VERB
ejpam-7013	4	8	and	and	CCONJ
ejpam-7013	4	9	unify	unify	VERB
ejpam-7013	4	10	a	a	DET
ejpam-7013	4	11	wide	wide	ADJ
ejpam-7013	4	12	class	class	NOUN
ejpam-7013	4	13	of	of	ADP
ejpam-7013	4	14	existing	exist	VERB
ejpam-7013	4	15	fp	fp	NOUN
ejpam-7013	4	16	principles	principle	NOUN
ejpam-7013	4	17	in	in	ADP
ejpam-7013	4	18	fuzzy	fuzzy	ADJ
ejpam-7013	4	19	and	and	CCONJ
ejpam-7013	4	20	non	non	ADJ
ejpam-7013	4	21	-	-	ADJ
ejpam-7013	4	22	fuzzy	fuzzy	ADJ
ejpam-7013	4	23	settings	setting	NOUN
ejpam-7013	4	24	.	.	PUNCT
ejpam-7013	5	1	our	our	PRON
ejpam-7013	5	2	results	result	NOUN
ejpam-7013	5	3	cover	cover	VERB
ejpam-7013	5	4	and	and	CCONJ
ejpam-7013	5	5	generalize	generalize	VERB
ejpam-7013	5	6	many	many	ADJ
ejpam-7013	5	7	classical	classical	ADJ
ejpam-7013	5	8	theorems	theorem	NOUN
ejpam-7013	5	9	,	,	PUNCT
ejpam-7013	5	10	and	and	CCONJ
ejpam-7013	5	11	their	their	PRON
ejpam-7013	5	12	strength	strength	NOUN
ejpam-7013	5	13	is	be	AUX
ejpam-7013	5	14	demonstrated	demonstrate	VERB
ejpam-7013	5	15	by	by	ADP
ejpam-7013	5	16	an	an	DET
ejpam-7013	5	17	application	application	NOUN
ejpam-7013	5	18	to	to	ADP
ejpam-7013	5	19	the	the	DET
ejpam-7013	5	20	existence	existence	NOUN
ejpam-7013	5	21	of	of	ADP
ejpam-7013	5	22	fuzzy	fuzzy	ADJ
ejpam-7013	5	23	solutions	solution	NOUN
ejpam-7013	5	24	of	of	ADP
ejpam-7013	5	25	nonlinear	nonlinear	ADJ
ejpam-7013	5	26	integral	integral	ADJ
ejpam-7013	5	27	equations	equation	NOUN
ejpam-7013	5	28	.	.	PUNCT
ejpam-7013	6	1	the	the	DET
ejpam-7013	6	2	findings	finding	NOUN
ejpam-7013	6	3	highlight	highlight	VERB
ejpam-7013	6	4	the	the	DET
ejpam-7013	6	5	relevance	relevance	NOUN
ejpam-7013	6	6	of	of	ADP
ejpam-7013	6	7	b	b	NOUN
ejpam-7013	6	8	-	-	PUNCT
ejpam-7013	6	9	fmss	fmss	NOUN
ejpam-7013	6	10	in	in	ADP
ejpam-7013	6	11	handling	handle	VERB
ejpam-7013	6	12	uncertainty	uncertainty	NOUN
ejpam-7013	6	13	and	and	CCONJ
ejpam-7013	6	14	imprecision	imprecision	NOUN
ejpam-7013	6	15	arising	arise	VERB
ejpam-7013	6	16	in	in	ADP
ejpam-7013	6	17	real	real	ADJ
ejpam-7013	6	18	-	-	PUNCT
ejpam-7013	6	19	world	world	NOUN
ejpam-7013	6	20	models	model	NOUN
ejpam-7013	6	21	2020	2020	NUM
ejpam-7013	6	22	mathematics	mathematic	NOUN
ejpam-7013	6	23	subject	subject	NOUN
ejpam-7013	6	24	classifications	classification	NOUN
ejpam-7013	6	25	:	:	PUNCT
ejpam-7013	6	26	47h10	47h10	NUM
ejpam-7013	6	27	,	,	PUNCT
ejpam-7013	6	28	54h25	54h25	NUM
ejpam-7013	6	29	,	,	PUNCT
ejpam-7013	6	30	46s40	46s40	NUM
ejpam-7013	6	31	,	,	PUNCT
ejpam-7013	6	32	45g10	45g10	NUM
ejpam-7013	6	33	key	key	ADJ
ejpam-7013	6	34	words	word	NOUN
ejpam-7013	6	35	and	and	CCONJ
ejpam-7013	6	36	phrases	phrase	NOUN
ejpam-7013	6	37	:	:	PUNCT
ejpam-7013	6	38	fuzzy	fuzzy	ADJ
ejpam-7013	6	39	metric	metric	ADJ
ejpam-7013	6	40	space	space	NOUN
ejpam-7013	6	41	,	,	PUNCT
ejpam-7013	6	42	b	b	X
ejpam-7013	6	43	-	-	PUNCT
ejpam-7013	6	44	fuzzy	fuzzy	ADJ
ejpam-7013	6	45	metric	metric	ADJ
ejpam-7013	6	46	,	,	PUNCT
ejpam-7013	6	47	fuzzy	fuzzy	ADJ
ejpam-7013	6	48	mapping	mapping	NOUN
ejpam-7013	6	49	,	,	PUNCT
ejpam-7013	6	50	fuzzy	fuzzy	ADJ
ejpam-7013	6	51	contraction	contraction	NOUN
ejpam-7013	6	52	,	,	PUNCT
ejpam-7013	6	53	nonlinear	nonlinear	ADJ
ejpam-7013	6	54	fuzzy	fuzzy	ADJ
ejpam-7013	6	55	integral	integral	ADJ
ejpam-7013	6	56	equation	equation	NOUN
ejpam-7013	6	57	,	,	PUNCT
ejpam-7013	6	58	fixed	fix	VERB
ejpam-7013	6	59	point	point	NOUN
ejpam-7013	6	60	1	1	NUM
ejpam-7013	6	61	.	.	PUNCT
ejpam-7013	6	62	introduction	introduction	NOUN
ejpam-7013	6	63	fixed	fix	VERB
ejpam-7013	6	64	point	point	NOUN
ejpam-7013	6	65	theory	theory	NOUN
ejpam-7013	6	66	has	have	AUX
ejpam-7013	6	67	played	play	VERB
ejpam-7013	6	68	a	a	DET
ejpam-7013	6	69	vital	vital	ADJ
ejpam-7013	6	70	role	role	NOUN
ejpam-7013	6	71	in	in	ADP
ejpam-7013	6	72	nonlinear	nonlinear	ADJ
ejpam-7013	6	73	analysis	analysis	NOUN
ejpam-7013	6	74	,	,	PUNCT
ejpam-7013	6	75	operator	operator	NOUN
ejpam-7013	6	76	theory	theory	NOUN
ejpam-7013	6	77	,	,	PUNCT
ejpam-7013	6	78	and	and	CCONJ
ejpam-7013	6	79	applied	apply	VERB
ejpam-7013	6	80	mathematics	mathematic	NOUN
ejpam-7013	6	81	.	.	PUNCT
ejpam-7013	7	1	the	the	DET
ejpam-7013	7	2	banach	banach	NOUN
ejpam-7013	7	3	contraction	contraction	NOUN
ejpam-7013	7	4	principle	principle	NOUN
ejpam-7013	7	5	,	,	PUNCT
ejpam-7013	7	6	introduced	introduce	VERB
ejpam-7013	7	7	by	by	ADP
ejpam-7013	7	8	banach	banach	NOUN
ejpam-7013	7	9	in	in	ADP
ejpam-7013	7	10	1922	1922	NUM
ejpam-7013	7	11	,	,	PUNCT
ejpam-7013	7	12	is	be	AUX
ejpam-7013	7	13	considered	consider	VERB
ejpam-7013	7	14	a	a	DET
ejpam-7013	7	15	cornerstone	cornerstone	NOUN
ejpam-7013	7	16	of	of	ADP
ejpam-7013	7	17	this	this	DET
ejpam-7013	7	18	theory	theory	NOUN
ejpam-7013	7	19	,	,	PUNCT
ejpam-7013	7	20	and	and	CCONJ
ejpam-7013	7	21	many	many	ADJ
ejpam-7013	7	22	generalizations	generalization	NOUN
ejpam-7013	7	23	have	have	AUX
ejpam-7013	7	24	been	be	AUX
ejpam-7013	7	25	developed	develop	VERB
ejpam-7013	7	26	to	to	PART
ejpam-7013	7	27	address	address	VERB
ejpam-7013	7	28	more	more	ADJ
ejpam-7013	7	29	complex	complex	ADJ
ejpam-7013	7	30	problems	problem	NOUN
ejpam-7013	7	31	in	in	ADP
ejpam-7013	7	32	different	different	ADJ
ejpam-7013	7	33	metric	metric	ADJ
ejpam-7013	7	34	frameworks	framework	NOUN
ejpam-7013	7	35	[	[	X
ejpam-7013	7	36	1	1	NUM
ejpam-7013	7	37	,	,	PUNCT
ejpam-7013	7	38	2	2	NUM
ejpam-7013	7	39	]	]	PUNCT
ejpam-7013	7	40	.	.	PUNCT
ejpam-7013	8	1	with	with	ADP
ejpam-7013	8	2	the	the	DET
ejpam-7013	8	3	emergence	emergence	NOUN
ejpam-7013	8	4	of	of	ADP
ejpam-7013	8	5	fuzzy	fuzzy	ADJ
ejpam-7013	8	6	set	set	NOUN
ejpam-7013	8	7	theory	theory	NOUN
ejpam-7013	8	8	by	by	ADP
ejpam-7013	8	9	zadeh	zadeh	PROPN
ejpam-7013	8	10	,	,	PUNCT
ejpam-7013	8	11	researchers	researcher	NOUN
ejpam-7013	8	12	began	begin	VERB
ejpam-7013	8	13	incorporating	incorporate	VERB
ejpam-7013	8	14	fuzziness	fuzziness	NOUN
ejpam-7013	8	15	into	into	ADP
ejpam-7013	8	16	metric	metric	ADJ
ejpam-7013	8	17	spaces	space	NOUN
ejpam-7013	8	18	,	,	PUNCT
ejpam-7013	8	19	which	which	PRON
ejpam-7013	8	20	led	lead	VERB
ejpam-7013	8	21	to	to	ADP
ejpam-7013	8	22	the	the	DET
ejpam-7013	8	23	development	development	NOUN
ejpam-7013	8	24	of	of	ADP
ejpam-7013	8	25	fuzzy	fuzzy	ADJ
ejpam-7013	8	26	metric	metric	ADJ
ejpam-7013	8	27	spaces	space	NOUN
ejpam-7013	8	28	(	(	PUNCT
ejpam-7013	8	29	fmss	fmss	ADJ
ejpam-7013	8	30	)	)	PUNCT
ejpam-7013	8	31	∗corresponding	∗corresponde	VERB
ejpam-7013	8	32	author	author	NOUN
ejpam-7013	8	33	.	.	PUNCT
ejpam-7013	9	1	doi	doi	NOUN
ejpam-7013	9	2	:	:	PUNCT
ejpam-7013	9	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7013	https://doi.org/10.29020/nybg.ejpam.v18i4.7013	PROPN
ejpam-7013	9	4	email	email	NOUN
ejpam-7013	9	5	addresses	address	NOUN
ejpam-7013	9	6	:	:	PUNCT
ejpam-7013	9	7	dinesh.skksv93@gmail.com	dinesh.skksv93@gmail.com	X
ejpam-7013	9	8	(	(	PUNCT
ejpam-7013	9	9	k.	k.	PROPN
ejpam-7013	9	10	dinesh	dinesh	PROPN
ejpam-7013	9	11	)	)	PUNCT
ejpam-7013	9	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7013	10	1	1	1	NUM
ejpam-7013	10	2	copyright	copyright	NOUN
ejpam-7013	10	3	:	:	PUNCT
ejpam-7013	10	4	©	©	PROPN
ejpam-7013	10	5	2025	2025	NUM
ejpam-7013	10	6	the	the	DET
ejpam-7013	10	7	author(s	author(s	NOUN
ejpam-7013	10	8	)	)	PUNCT
ejpam-7013	10	9	.	.	PUNCT
ejpam-7013	11	1	(	(	PUNCT
ejpam-7013	11	2	cc	cc	NOUN
ejpam-7013	11	3	by	by	ADP
ejpam-7013	11	4	-	-	PUNCT
ejpam-7013	11	5	nc	nc	PROPN
ejpam-7013	11	6	4.0	4.0	NUM
ejpam-7013	11	7	)	)	PUNCT
ejpam-7013	11	8	d.	d.	PROPN
ejpam-7013	11	9	gerbeti	gerbeti	PROPN
ejpam-7013	11	10	et	et	PROPN
ejpam-7013	11	11	al	al	PROPN
ejpam-7013	11	12	.	.	PUNCT
ejpam-7013	11	13	/	/	SYM
ejpam-7013	11	14	eur	eur	PROPN
ejpam-7013	11	15	.	.	PUNCT
ejpam-7013	12	1	j.	j.	PROPN
ejpam-7013	12	2	pure	pure	PROPN
ejpam-7013	12	3	appl	appl	PROPN
ejpam-7013	12	4	.	.	PROPN
ejpam-7013	12	5	math	math	PROPN
ejpam-7013	12	6	,	,	PUNCT
ejpam-7013	12	7	18	18	NUM
ejpam-7013	12	8	(	(	PUNCT
ejpam-7013	12	9	4	4	NUM
ejpam-7013	12	10	)	)	PUNCT
ejpam-7013	12	11	(	(	PUNCT
ejpam-7013	12	12	2025	2025	NUM
ejpam-7013	12	13	)	)	PUNCT
ejpam-7013	12	14	,	,	PUNCT
ejpam-7013	12	15	7013	7013	NUM
ejpam-7013	12	16	2	2	NUM
ejpam-7013	12	17	of	of	ADP
ejpam-7013	12	18	17	17	NUM
ejpam-7013	13	1	[	[	X
ejpam-7013	13	2	3–6	3–6	NUM
ejpam-7013	13	3	]	]	X
ejpam-7013	13	4	.	.	PUNCT
ejpam-7013	14	1	these	these	DET
ejpam-7013	14	2	spaces	space	NOUN
ejpam-7013	14	3	provide	provide	VERB
ejpam-7013	14	4	a	a	DET
ejpam-7013	14	5	natural	natural	ADJ
ejpam-7013	14	6	setting	setting	NOUN
ejpam-7013	14	7	to	to	AUX
ejpam-7013	14	8	model	model	NOUN
ejpam-7013	14	9	uncertainty	uncertainty	NOUN
ejpam-7013	14	10	and	and	CCONJ
ejpam-7013	14	11	vagueness	vagueness	NOUN
ejpam-7013	14	12	inherent	inherent	ADJ
ejpam-7013	14	13	in	in	ADP
ejpam-7013	14	14	many	many	ADJ
ejpam-7013	14	15	real	real	ADJ
ejpam-7013	14	16	-	-	PUNCT
ejpam-7013	14	17	world	world	NOUN
ejpam-7013	14	18	applications	application	NOUN
ejpam-7013	14	19	.	.	PUNCT
ejpam-7013	15	1	later	later	ADV
ejpam-7013	15	2	,	,	PUNCT
ejpam-7013	15	3	gregori	gregori	PROPN
ejpam-7013	15	4	and	and	CCONJ
ejpam-7013	15	5	sapena	sapena	ADJ
ejpam-7013	16	1	[	[	X
ejpam-7013	16	2	7	7	X
ejpam-7013	16	3	]	]	PUNCT
ejpam-7013	16	4	and	and	CCONJ
ejpam-7013	16	5	george	george	PROPN
ejpam-7013	16	6	&	&	CCONJ
ejpam-7013	16	7	veeramani	veeramani	PROPN
ejpam-7013	17	1	[	[	X
ejpam-7013	17	2	5	5	NUM
ejpam-7013	17	3	]	]	PUNCT
ejpam-7013	17	4	contributed	contribute	VERB
ejpam-7013	17	5	significantly	significantly	ADV
ejpam-7013	17	6	to	to	ADP
ejpam-7013	17	7	the	the	DET
ejpam-7013	17	8	theory	theory	NOUN
ejpam-7013	17	9	of	of	ADP
ejpam-7013	17	10	fuzzy	fuzzy	ADJ
ejpam-7013	17	11	fixed	fix	VERB
ejpam-7013	17	12	points	point	NOUN
ejpam-7013	17	13	.	.	PUNCT
ejpam-7013	18	1	in	in	ADP
ejpam-7013	18	2	this	this	DET
ejpam-7013	18	3	direction	direction	NOUN
ejpam-7013	18	4	,	,	PUNCT
ejpam-7013	18	5	b	b	X
ejpam-7013	18	6	-	-	PUNCT
ejpam-7013	18	7	metric	metric	ADJ
ejpam-7013	18	8	spaces	space	NOUN
ejpam-7013	18	9	,	,	PUNCT
ejpam-7013	18	10	introduced	introduce	VERB
ejpam-7013	18	11	by	by	ADP
ejpam-7013	18	12	bakhtin	bakhtin	NOUN
ejpam-7013	18	13	[	[	X
ejpam-7013	18	14	8	8	NUM
ejpam-7013	18	15	]	]	PUNCT
ejpam-7013	18	16	and	and	CCONJ
ejpam-7013	18	17	further	far	ADV
ejpam-7013	18	18	studied	study	VERB
ejpam-7013	18	19	by	by	ADP
ejpam-7013	18	20	czerwik	czerwik	PROPN
ejpam-7013	19	1	[	[	X
ejpam-7013	19	2	1	1	NUM
ejpam-7013	19	3	]	]	PUNCT
ejpam-7013	19	4	,	,	PUNCT
ejpam-7013	19	5	allow	allow	VERB
ejpam-7013	19	6	the	the	DET
ejpam-7013	19	7	relaxation	relaxation	NOUN
ejpam-7013	19	8	of	of	ADP
ejpam-7013	19	9	the	the	DET
ejpam-7013	19	10	triangle	triangle	NOUN
ejpam-7013	19	11	inequality	inequality	NOUN
ejpam-7013	19	12	through	through	ADP
ejpam-7013	19	13	a	a	DET
ejpam-7013	19	14	parameter	parameter	NOUN
ejpam-7013	19	15	b	b	PROPN
ejpam-7013	19	16	≥	≥	NUM
ejpam-7013	19	17	1	1	NUM
ejpam-7013	19	18	.	.	PUNCT
ejpam-7013	20	1	their	their	PRON
ejpam-7013	20	2	fuzzy	fuzzy	ADJ
ejpam-7013	20	3	analogues	analogue	NOUN
ejpam-7013	20	4	,	,	PUNCT
ejpam-7013	20	5	b	b	X
ejpam-7013	20	6	-	-	PUNCT
ejpam-7013	20	7	fuzzy	fuzzy	ADJ
ejpam-7013	20	8	metric	metric	ADJ
ejpam-7013	20	9	spaces	space	NOUN
ejpam-7013	20	10	,	,	PUNCT
ejpam-7013	20	11	extend	extend	VERB
ejpam-7013	20	12	this	this	DET
ejpam-7013	20	13	flexibility	flexibility	NOUN
ejpam-7013	20	14	and	and	CCONJ
ejpam-7013	20	15	have	have	AUX
ejpam-7013	20	16	been	be	AUX
ejpam-7013	20	17	investigated	investigate	VERB
ejpam-7013	20	18	for	for	ADP
ejpam-7013	20	19	fixed	fix	VERB
ejpam-7013	20	20	point	point	NOUN
ejpam-7013	20	21	results	result	NOUN
ejpam-7013	20	22	by	by	ADP
ejpam-7013	20	23	sedghi	sedghi	NOUN
ejpam-7013	20	24	and	and	CCONJ
ejpam-7013	20	25	shobe	shobe	ADV
ejpam-7013	21	1	[	[	X
ejpam-7013	21	2	9	9	NUM
ejpam-7013	21	3	,	,	PUNCT
ejpam-7013	21	4	10	10	NUM
ejpam-7013	21	5	]	]	PUNCT
ejpam-7013	21	6	.	.	PUNCT
ejpam-7013	22	1	such	such	ADJ
ejpam-7013	22	2	generalizations	generalization	NOUN
ejpam-7013	22	3	are	be	AUX
ejpam-7013	22	4	powerful	powerful	ADJ
ejpam-7013	22	5	for	for	ADP
ejpam-7013	22	6	dealing	deal	VERB
ejpam-7013	22	7	with	with	ADP
ejpam-7013	22	8	nonlinear	nonlinear	ADJ
ejpam-7013	22	9	systems	system	NOUN
ejpam-7013	22	10	,	,	PUNCT
ejpam-7013	22	11	where	where	SCONJ
ejpam-7013	22	12	classical	classical	ADJ
ejpam-7013	22	13	metric	metric	ADJ
ejpam-7013	22	14	assumptions	assumption	NOUN
ejpam-7013	22	15	may	may	AUX
ejpam-7013	22	16	be	be	AUX
ejpam-7013	22	17	too	too	ADV
ejpam-7013	22	18	restrictive	restrictive	ADJ
ejpam-7013	22	19	[	[	X
ejpam-7013	22	20	11	11	NUM
ejpam-7013	22	21	,	,	PUNCT
ejpam-7013	22	22	12	12	NUM
ejpam-7013	22	23	]	]	PUNCT
ejpam-7013	22	24	.	.	PUNCT
ejpam-7013	23	1	motivated	motivate	VERB
ejpam-7013	23	2	by	by	ADP
ejpam-7013	23	3	these	these	DET
ejpam-7013	23	4	developments	development	NOUN
ejpam-7013	23	5	,	,	PUNCT
ejpam-7013	23	6	several	several	ADJ
ejpam-7013	23	7	authors	author	NOUN
ejpam-7013	23	8	have	have	AUX
ejpam-7013	23	9	studied	study	VERB
ejpam-7013	23	10	fixed	fix	VERB
ejpam-7013	23	11	point	point	NOUN
ejpam-7013	23	12	theorems	theorem	NOUN
ejpam-7013	23	13	in	in	ADP
ejpam-7013	23	14	fuzzy	fuzzy	ADJ
ejpam-7013	23	15	and	and	CCONJ
ejpam-7013	23	16	b	b	NOUN
ejpam-7013	23	17	-	-	PUNCT
ejpam-7013	23	18	fuzzy	fuzzy	ADJ
ejpam-7013	23	19	metric	metric	ADJ
ejpam-7013	23	20	spaces	space	NOUN
ejpam-7013	23	21	with	with	ADP
ejpam-7013	23	22	applications	application	NOUN
ejpam-7013	23	23	to	to	PART
ejpam-7013	23	24	differential	differential	VERB
ejpam-7013	23	25	and	and	CCONJ
ejpam-7013	23	26	integral	integral	ADJ
ejpam-7013	23	27	equations	equation	NOUN
ejpam-7013	23	28	[	[	X
ejpam-7013	23	29	13–17	13–17	NUM
ejpam-7013	23	30	]	]	PUNCT
ejpam-7013	23	31	.	.	PUNCT
ejpam-7013	24	1	the	the	DET
ejpam-7013	24	2	purpose	purpose	NOUN
ejpam-7013	24	3	of	of	ADP
ejpam-7013	24	4	this	this	DET
ejpam-7013	24	5	paper	paper	NOUN
ejpam-7013	24	6	is	be	AUX
ejpam-7013	24	7	to	to	PART
ejpam-7013	24	8	establish	establish	VERB
ejpam-7013	24	9	new	new	ADJ
ejpam-7013	24	10	fixed	fix	VERB
ejpam-7013	24	11	point	point	NOUN
ejpam-7013	24	12	results	result	NOUN
ejpam-7013	24	13	for	for	ADP
ejpam-7013	24	14	fuzzy	fuzzy	ADJ
ejpam-7013	24	15	mappings	mapping	NOUN
ejpam-7013	24	16	in	in	ADP
ejpam-7013	24	17	complete	complete	ADJ
ejpam-7013	24	18	b	b	NOUN
ejpam-7013	24	19	-	-	PUNCT
ejpam-7013	24	20	fmss	fmss	NOUN
ejpam-7013	24	21	,	,	PUNCT
ejpam-7013	24	22	which	which	PRON
ejpam-7013	24	23	generalize	generalize	VERB
ejpam-7013	24	24	and	and	CCONJ
ejpam-7013	24	25	unify	unify	VERB
ejpam-7013	24	26	known	know	VERB
ejpam-7013	24	27	results	result	NOUN
ejpam-7013	24	28	in	in	ADP
ejpam-7013	24	29	the	the	DET
ejpam-7013	24	30	literature	literature	NOUN
ejpam-7013	24	31	.	.	PUNCT
ejpam-7013	25	1	2	2	X
ejpam-7013	25	2	.	.	X
ejpam-7013	25	3	preliminaries	preliminary	NOUN
ejpam-7013	25	4	in	in	ADP
ejpam-7013	25	5	this	this	DET
ejpam-7013	25	6	section	section	NOUN
ejpam-7013	25	7	,	,	PUNCT
ejpam-7013	25	8	we	we	PRON
ejpam-7013	25	9	recall	recall	VERB
ejpam-7013	25	10	some	some	DET
ejpam-7013	25	11	essential	essential	ADJ
ejpam-7013	25	12	concepts	concept	NOUN
ejpam-7013	25	13	and	and	CCONJ
ejpam-7013	25	14	definitions	definition	NOUN
ejpam-7013	25	15	required	require	VERB
ejpam-7013	25	16	throughout	throughout	ADP
ejpam-7013	25	17	this	this	DET
ejpam-7013	25	18	work	work	NOUN
ejpam-7013	25	19	.	.	PUNCT
ejpam-7013	26	1	definition	definition	NOUN
ejpam-7013	26	2	1	1	NUM
ejpam-7013	26	3	(	(	PUNCT
ejpam-7013	26	4	fms	fms	PROPN
ejpam-7013	26	5	[	[	X
ejpam-7013	26	6	3	3	NUM
ejpam-7013	26	7	,	,	PUNCT
ejpam-7013	26	8	4	4	NUM
ejpam-7013	26	9	]	]	NUM
ejpam-7013	26	10	)	)	PUNCT
ejpam-7013	26	11	.	.	PUNCT
ejpam-7013	27	1	a	a	DET
ejpam-7013	27	2	triple	triple	ADJ
ejpam-7013	27	3	(	(	PUNCT
ejpam-7013	27	4	x	x	NOUN
ejpam-7013	27	5	,	,	PUNCT
ejpam-7013	27	6	m	m	PROPN
ejpam-7013	27	7	,	,	PUNCT
ejpam-7013	27	8	∗	∗	NOUN
ejpam-7013	27	9	)	)	PUNCT
ejpam-7013	27	10	is	be	AUX
ejpam-7013	27	11	called	call	VERB
ejpam-7013	27	12	a	a	DET
ejpam-7013	27	13	fms	fms	PROPN
ejpam-7013	27	14	if	if	SCONJ
ejpam-7013	27	15	x	x	PRON
ejpam-7013	27	16	is	be	AUX
ejpam-7013	27	17	a	a	DET
ejpam-7013	27	18	nonempty	nonempty	ADJ
ejpam-7013	27	19	set	set	NOUN
ejpam-7013	27	20	,	,	PUNCT
ejpam-7013	27	21	∗	∗	NOUN
ejpam-7013	27	22	is	be	AUX
ejpam-7013	27	23	a	a	DET
ejpam-7013	27	24	continuous	continuous	ADJ
ejpam-7013	27	25	t	t	NOUN
ejpam-7013	27	26	-	-	PUNCT
ejpam-7013	27	27	norm	norm	NOUN
ejpam-7013	27	28	,	,	PUNCT
ejpam-7013	27	29	and	and	CCONJ
ejpam-7013	27	30	m	m	VERB
ejpam-7013	27	31	:	:	PUNCT
ejpam-7013	28	1	x	x	X
ejpam-7013	28	2	×	×	NOUN
ejpam-7013	28	3	x	x	SYM
ejpam-7013	28	4	×	×	NOUN
ejpam-7013	28	5	(	(	PUNCT
ejpam-7013	28	6	0,∞	0,∞	NOUN
ejpam-7013	28	7	)	)	PUNCT
ejpam-7013	28	8	→	→	PUNCT
ejpam-7013	29	1	[	[	X
ejpam-7013	29	2	0	0	NUM
ejpam-7013	29	3	,	,	PUNCT
ejpam-7013	29	4	1	1	NUM
ejpam-7013	29	5	]	]	PUNCT
ejpam-7013	29	6	is	be	AUX
ejpam-7013	29	7	a	a	DET
ejpam-7013	29	8	mapping	mapping	NOUN
ejpam-7013	29	9	such	such	ADJ
ejpam-7013	29	10	that	that	PRON
ejpam-7013	29	11	for	for	ADP
ejpam-7013	29	12	all	all	DET
ejpam-7013	29	13	l	l	NOUN
ejpam-7013	29	14	,	,	PUNCT
ejpam-7013	29	15	p	p	X
ejpam-7013	29	16	,	,	PUNCT
ejpam-7013	29	17	k	k	PROPN
ejpam-7013	29	18	∈	∈	PROPN
ejpam-7013	29	19	x	x	X
ejpam-7013	29	20	and	and	CCONJ
ejpam-7013	29	21	s	s	PROPN
ejpam-7013	29	22	,	,	PUNCT
ejpam-7013	29	23	t	t	X
ejpam-7013	29	24	>	>	X
ejpam-7013	29	25	0	0	PROPN
ejpam-7013	29	26	,	,	PUNCT
ejpam-7013	29	27	the	the	DET
ejpam-7013	29	28	following	follow	VERB
ejpam-7013	29	29	hold	hold	NOUN
ejpam-7013	29	30	:	:	PUNCT
ejpam-7013	29	31	(	(	PUNCT
ejpam-7013	29	32	i	i	NOUN
ejpam-7013	29	33	)	)	PUNCT
ejpam-7013	29	34	m(l	m(l	PROPN
ejpam-7013	29	35	,	,	PUNCT
ejpam-7013	29	36	p	p	X
ejpam-7013	29	37	,	,	PUNCT
ejpam-7013	29	38	t	t	PROPN
ejpam-7013	29	39	)	)	PUNCT
ejpam-7013	29	40	>	>	X
ejpam-7013	29	41	0	0	NUM
ejpam-7013	29	42	,	,	PUNCT
ejpam-7013	29	43	(	(	PUNCT
ejpam-7013	29	44	ii	ii	NOUN
ejpam-7013	29	45	)	)	PUNCT
ejpam-7013	29	46	m(l	m(l	PROPN
ejpam-7013	29	47	,	,	PUNCT
ejpam-7013	29	48	p	p	X
ejpam-7013	29	49	,	,	PUNCT
ejpam-7013	29	50	t	t	PROPN
ejpam-7013	29	51	)	)	PUNCT
ejpam-7013	29	52	=	=	SYM
ejpam-7013	29	53	1	1	NUM
ejpam-7013	29	54	⇐	⇐	ADJ
ejpam-7013	29	55	⇒	⇒	NOUN
ejpam-7013	29	56	l	l	NOUN
ejpam-7013	30	1	=	=	SYM
ejpam-7013	30	2	p	p	X
ejpam-7013	30	3	,	,	PUNCT
ejpam-7013	30	4	(	(	PUNCT
ejpam-7013	30	5	iii	iii	NOUN
ejpam-7013	30	6	)	)	PUNCT
ejpam-7013	30	7	m(l	m(l	NOUN
ejpam-7013	30	8	,	,	PUNCT
ejpam-7013	30	9	p	p	X
ejpam-7013	30	10	,	,	PUNCT
ejpam-7013	30	11	t	t	PROPN
ejpam-7013	30	12	)	)	PUNCT
ejpam-7013	30	13	=	=	PUNCT
ejpam-7013	31	1	m(p	m(p	PROPN
ejpam-7013	31	2	,	,	PUNCT
ejpam-7013	31	3	l	l	PROPN
ejpam-7013	31	4	,	,	PUNCT
ejpam-7013	31	5	t	t	PROPN
ejpam-7013	31	6	)	)	PUNCT
ejpam-7013	31	7	,	,	PUNCT
ejpam-7013	31	8	(	(	PUNCT
ejpam-7013	31	9	iv	iv	X
ejpam-7013	31	10	)	)	PUNCT
ejpam-7013	31	11	m(l	m(l	PROPN
ejpam-7013	31	12	,	,	PUNCT
ejpam-7013	31	13	k	k	NOUN
ejpam-7013	31	14	,	,	PUNCT
ejpam-7013	31	15	t+	t+	NOUN
ejpam-7013	31	16	s	s	NOUN
ejpam-7013	31	17	)	)	PUNCT
ejpam-7013	31	18	≥	≥	NOUN
ejpam-7013	31	19	m(l	m(l	NOUN
ejpam-7013	31	20	,	,	PUNCT
ejpam-7013	31	21	p	p	X
ejpam-7013	31	22	,	,	PUNCT
ejpam-7013	31	23	t	t	PROPN
ejpam-7013	31	24	)	)	PUNCT
ejpam-7013	31	25	∗m(p	∗m(p	PROPN
ejpam-7013	31	26	,	,	PUNCT
ejpam-7013	31	27	k	k	PROPN
ejpam-7013	31	28	,	,	PUNCT
ejpam-7013	31	29	s	s	PART
ejpam-7013	31	30	)	)	PUNCT
ejpam-7013	31	31	,	,	PUNCT
ejpam-7013	31	32	(	(	PUNCT
ejpam-7013	31	33	v	v	NOUN
ejpam-7013	31	34	)	)	PUNCT
ejpam-7013	31	35	m(l	m(l	NOUN
ejpam-7013	31	36	,	,	PUNCT
ejpam-7013	31	37	p	p	X
ejpam-7013	31	38	,	,	PUNCT
ejpam-7013	31	39	·	·	PUNCT
ejpam-7013	31	40	)	)	PUNCT
ejpam-7013	31	41	:	:	PUNCT
ejpam-7013	31	42	(	(	PUNCT
ejpam-7013	31	43	0,∞	0,∞	NOUN
ejpam-7013	31	44	)	)	PUNCT
ejpam-7013	31	45	→	→	PUNCT
ejpam-7013	32	1	[	[	X
ejpam-7013	32	2	0	0	NUM
ejpam-7013	32	3	,	,	PUNCT
ejpam-7013	32	4	1	1	NUM
ejpam-7013	32	5	]	]	PUNCT
ejpam-7013	32	6	is	be	AUX
ejpam-7013	32	7	continuous	continuous	ADJ
ejpam-7013	32	8	.	.	PUNCT
ejpam-7013	33	1	definition	definition	NOUN
ejpam-7013	33	2	2	2	NUM
ejpam-7013	33	3	(	(	PUNCT
ejpam-7013	33	4	b	b	NOUN
ejpam-7013	33	5	-	-	PUNCT
ejpam-7013	33	6	metric	metric	ADJ
ejpam-7013	33	7	space	space	NOUN
ejpam-7013	33	8	[	[	X
ejpam-7013	33	9	1	1	NUM
ejpam-7013	33	10	,	,	PUNCT
ejpam-7013	33	11	8	8	NUM
ejpam-7013	33	12	]	]	NUM
ejpam-7013	33	13	)	)	PUNCT
ejpam-7013	33	14	.	.	PUNCT
ejpam-7013	34	1	a	a	DET
ejpam-7013	34	2	pair	pair	NOUN
ejpam-7013	34	3	(	(	PUNCT
ejpam-7013	34	4	x	x	NOUN
ejpam-7013	34	5	,	,	PUNCT
ejpam-7013	34	6	db	db	PROPN
ejpam-7013	34	7	)	)	PUNCT
ejpam-7013	34	8	is	be	AUX
ejpam-7013	34	9	called	call	VERB
ejpam-7013	34	10	a	a	DET
ejpam-7013	34	11	b	b	NOUN
ejpam-7013	34	12	-	-	PUNCT
ejpam-7013	34	13	metric	metric	ADJ
ejpam-7013	34	14	space	space	NOUN
ejpam-7013	34	15	if	if	SCONJ
ejpam-7013	34	16	x	x	PRON
ejpam-7013	34	17	is	be	AUX
ejpam-7013	34	18	a	a	DET
ejpam-7013	34	19	nonempty	nonempty	ADV
ejpam-7013	34	20	set	set	VERB
ejpam-7013	34	21	and	and	CCONJ
ejpam-7013	34	22	db	db	VERB
ejpam-7013	34	23	:	:	PUNCT
ejpam-7013	34	24	x×x	x×x	PROPN
ejpam-7013	34	25	→	→	PUNCT
ejpam-7013	34	26	[	[	X
ejpam-7013	34	27	0,∞	0,∞	NUM
ejpam-7013	34	28	)	)	PUNCT
ejpam-7013	34	29	is	be	AUX
ejpam-7013	34	30	a	a	DET
ejpam-7013	34	31	function	function	NOUN
ejpam-7013	34	32	such	such	ADJ
ejpam-7013	34	33	that	that	SCONJ
ejpam-7013	34	34	there	there	PRON
ejpam-7013	34	35	exists	exist	VERB
ejpam-7013	34	36	a	a	DET
ejpam-7013	34	37	constant	constant	ADJ
ejpam-7013	34	38	b	b	NOUN
ejpam-7013	34	39	≥	≥	NUM
ejpam-7013	34	40	1	1	NUM
ejpam-7013	34	41	with	with	ADP
ejpam-7013	34	42	(	(	PUNCT
ejpam-7013	34	43	i	i	NOUN
ejpam-7013	34	44	)	)	PUNCT
ejpam-7013	34	45	db(l	db(l	PROPN
ejpam-7013	34	46	,	,	PUNCT
ejpam-7013	34	47	p	p	X
ejpam-7013	34	48	)	)	PUNCT
ejpam-7013	34	49	=	=	SYM
ejpam-7013	34	50	0	0	NUM
ejpam-7013	35	1	⇐	⇐	ADJ
ejpam-7013	35	2	⇒	⇒	NOUN
ejpam-7013	35	3	l	l	NOUN
ejpam-7013	36	1	=	=	SYM
ejpam-7013	36	2	p	p	X
ejpam-7013	36	3	,	,	PUNCT
ejpam-7013	36	4	(	(	PUNCT
ejpam-7013	36	5	ii	ii	NOUN
ejpam-7013	36	6	)	)	PUNCT
ejpam-7013	36	7	db(l	db(l	PROPN
ejpam-7013	36	8	,	,	PUNCT
ejpam-7013	36	9	p	p	X
ejpam-7013	36	10	)	)	PUNCT
ejpam-7013	36	11	=	=	SYM
ejpam-7013	36	12	db(p	db(p	ADJ
ejpam-7013	36	13	,	,	PUNCT
ejpam-7013	36	14	l	l	NOUN
ejpam-7013	36	15	)	)	PUNCT
ejpam-7013	36	16	,	,	PUNCT
ejpam-7013	36	17	(	(	PUNCT
ejpam-7013	36	18	iii	iii	X
ejpam-7013	36	19	)	)	PUNCT
ejpam-7013	36	20	db(l	db(l	PROPN
ejpam-7013	36	21	,	,	PUNCT
ejpam-7013	36	22	k	k	NOUN
ejpam-7013	36	23	)	)	PUNCT
ejpam-7013	36	24	≤	≤	NOUN
ejpam-7013	36	25	b	b	X
ejpam-7013	36	26	(	(	PUNCT
ejpam-7013	36	27	db(l	db(l	PROPN
ejpam-7013	36	28	,	,	PUNCT
ejpam-7013	36	29	p	p	X
ejpam-7013	36	30	)	)	PUNCT
ejpam-7013	36	31	+	+	X
ejpam-7013	36	32	db(p	db(p	ADJ
ejpam-7013	36	33	,	,	PUNCT
ejpam-7013	36	34	k	k	NOUN
ejpam-7013	36	35	)	)	PUNCT
ejpam-7013	36	36	)	)	PUNCT
ejpam-7013	36	37	.	.	PUNCT
ejpam-7013	37	1	for	for	ADP
ejpam-7013	37	2	all	all	DET
ejpam-7013	37	3	l	l	NOUN
ejpam-7013	37	4	,	,	PUNCT
ejpam-7013	37	5	p	p	X
ejpam-7013	37	6	,	,	PUNCT
ejpam-7013	37	7	k	k	PROPN
ejpam-7013	37	8	∈	∈	PROPN
ejpam-7013	37	9	x.	x.	NOUN
ejpam-7013	37	10	definition	definition	NOUN
ejpam-7013	37	11	3	3	NUM
ejpam-7013	37	12	(	(	PUNCT
ejpam-7013	37	13	b	b	NOUN
ejpam-7013	37	14	-	-	PUNCT
ejpam-7013	37	15	fms	fms	PROPN
ejpam-7013	37	16	)	)	PUNCT
ejpam-7013	37	17	.	.	PUNCT
ejpam-7013	38	1	a	a	DET
ejpam-7013	38	2	triple	triple	ADJ
ejpam-7013	38	3	(	(	PUNCT
ejpam-7013	38	4	x	x	NOUN
ejpam-7013	38	5	,	,	PUNCT
ejpam-7013	38	6	mb	mb	NOUN
ejpam-7013	38	7	,	,	PUNCT
ejpam-7013	38	8	∗	∗	NOUN
ejpam-7013	38	9	)	)	PUNCT
ejpam-7013	38	10	is	be	AUX
ejpam-7013	38	11	said	say	VERB
ejpam-7013	38	12	to	to	PART
ejpam-7013	38	13	be	be	AUX
ejpam-7013	38	14	a	a	DET
ejpam-7013	38	15	b	b	NOUN
ejpam-7013	38	16	-	-	PUNCT
ejpam-7013	38	17	fms	fms	PROPN
ejpam-7013	38	18	if	if	SCONJ
ejpam-7013	38	19	x	x	PRON
ejpam-7013	38	20	is	be	AUX
ejpam-7013	38	21	a	a	DET
ejpam-7013	38	22	nonempty	nonempty	ADJ
ejpam-7013	38	23	set	set	NOUN
ejpam-7013	38	24	,	,	PUNCT
ejpam-7013	38	25	∗	∗	NOUN
ejpam-7013	38	26	is	be	AUX
ejpam-7013	38	27	a	a	DET
ejpam-7013	38	28	continuous	continuous	ADJ
ejpam-7013	38	29	t	t	NOUN
ejpam-7013	38	30	-	-	PUNCT
ejpam-7013	38	31	norm	norm	NOUN
ejpam-7013	38	32	,	,	PUNCT
ejpam-7013	38	33	and	and	CCONJ
ejpam-7013	38	34	mb	mb	ADP
ejpam-7013	38	35	:	:	PUNCT
ejpam-7013	39	1	x×	x×	X
ejpam-7013	39	2	x×	x×	PUNCT
ejpam-7013	39	3	(	(	PUNCT
ejpam-7013	39	4	0,∞	0,∞	NOUN
ejpam-7013	39	5	)	)	PUNCT
ejpam-7013	39	6	→	→	PUNCT
ejpam-7013	40	1	[	[	X
ejpam-7013	40	2	0	0	NUM
ejpam-7013	40	3	,	,	PUNCT
ejpam-7013	40	4	1	1	NUM
ejpam-7013	40	5	]	]	PUNCT
ejpam-7013	40	6	is	be	AUX
ejpam-7013	40	7	a	a	DET
ejpam-7013	40	8	fuzzy	fuzzy	ADJ
ejpam-7013	40	9	set	set	NOUN
ejpam-7013	40	10	satisfying	satisfy	VERB
ejpam-7013	40	11	:	:	PUNCT
ejpam-7013	40	12	d.	d.	PROPN
ejpam-7013	40	13	gerbeti	gerbeti	PROPN
ejpam-7013	40	14	et	et	PROPN
ejpam-7013	40	15	al	al	PROPN
ejpam-7013	40	16	.	.	PUNCT
ejpam-7013	40	17	/	/	SYM
ejpam-7013	40	18	eur	eur	PROPN
ejpam-7013	40	19	.	.	PUNCT
ejpam-7013	41	1	j.	j.	PROPN
ejpam-7013	41	2	pure	pure	PROPN
ejpam-7013	41	3	appl	appl	PROPN
ejpam-7013	41	4	.	.	PROPN
ejpam-7013	41	5	math	math	PROPN
ejpam-7013	41	6	,	,	PUNCT
ejpam-7013	41	7	18	18	NUM
ejpam-7013	41	8	(	(	PUNCT
ejpam-7013	41	9	4	4	NUM
ejpam-7013	41	10	)	)	PUNCT
ejpam-7013	41	11	(	(	PUNCT
ejpam-7013	41	12	2025	2025	NUM
ejpam-7013	41	13	)	)	PUNCT
ejpam-7013	41	14	,	,	PUNCT
ejpam-7013	41	15	7013	7013	NUM
ejpam-7013	41	16	3	3	NUM
ejpam-7013	41	17	of	of	ADP
ejpam-7013	41	18	17	17	NUM
ejpam-7013	41	19	(	(	PUNCT
ejpam-7013	41	20	i	i	NOUN
ejpam-7013	41	21	)	)	PUNCT
ejpam-7013	41	22	mb(l	mb(l	PROPN
ejpam-7013	41	23	,	,	PUNCT
ejpam-7013	41	24	p	p	X
ejpam-7013	41	25	,	,	PUNCT
ejpam-7013	41	26	t	t	PROPN
ejpam-7013	41	27	)	)	PUNCT
ejpam-7013	41	28	>	>	X
ejpam-7013	41	29	0	0	NUM
ejpam-7013	41	30	,	,	PUNCT
ejpam-7013	41	31	(	(	PUNCT
ejpam-7013	41	32	ii	ii	NOUN
ejpam-7013	41	33	)	)	PUNCT
ejpam-7013	41	34	mb(l	mb(l	PROPN
ejpam-7013	41	35	,	,	PUNCT
ejpam-7013	41	36	p	p	X
ejpam-7013	41	37	,	,	PUNCT
ejpam-7013	41	38	t	t	PROPN
ejpam-7013	41	39	)	)	PUNCT
ejpam-7013	41	40	=	=	SYM
ejpam-7013	41	41	1	1	NUM
ejpam-7013	41	42	⇐	⇐	ADJ
ejpam-7013	41	43	⇒	⇒	NOUN
ejpam-7013	41	44	l	l	NOUN
ejpam-7013	42	1	=	=	SYM
ejpam-7013	42	2	p	p	X
ejpam-7013	42	3	,	,	PUNCT
ejpam-7013	42	4	(	(	PUNCT
ejpam-7013	42	5	iii	iii	NOUN
ejpam-7013	42	6	)	)	PUNCT
ejpam-7013	42	7	mb(l	mb(l	PROPN
ejpam-7013	42	8	,	,	PUNCT
ejpam-7013	42	9	p	p	X
ejpam-7013	42	10	,	,	PUNCT
ejpam-7013	42	11	t	t	PROPN
ejpam-7013	42	12	)	)	PUNCT
ejpam-7013	42	13	=	=	SYM
ejpam-7013	42	14	mb(p	mb(p	X
ejpam-7013	42	15	,	,	PUNCT
ejpam-7013	42	16	l	l	PROPN
ejpam-7013	42	17	,	,	PUNCT
ejpam-7013	42	18	t	t	PROPN
ejpam-7013	42	19	)	)	PUNCT
ejpam-7013	42	20	,	,	PUNCT
ejpam-7013	42	21	(	(	PUNCT
ejpam-7013	42	22	iv	iv	X
ejpam-7013	42	23	)	)	PUNCT
ejpam-7013	42	24	mb(l	mb(l	PROPN
ejpam-7013	42	25	,	,	PUNCT
ejpam-7013	42	26	k	k	NOUN
ejpam-7013	42	27	,	,	PUNCT
ejpam-7013	42	28	t+	t+	NOUN
ejpam-7013	42	29	s	s	NOUN
ejpam-7013	42	30	)	)	PUNCT
ejpam-7013	42	31	≥	≥	NOUN
ejpam-7013	42	32	mb(l	mb(l	PROPN
ejpam-7013	42	33	,	,	PUNCT
ejpam-7013	42	34	p	p	X
ejpam-7013	42	35	,	,	PUNCT
ejpam-7013	42	36	t	t	PROPN
ejpam-7013	42	37	)	)	PUNCT
ejpam-7013	42	38	∗mb(p	∗mb(p	PROPN
ejpam-7013	42	39	,	,	PUNCT
ejpam-7013	42	40	k	k	X
ejpam-7013	42	41	,	,	PUNCT
ejpam-7013	42	42	s	s	PART
ejpam-7013	42	43	)	)	PUNCT
ejpam-7013	42	44	,	,	PUNCT
ejpam-7013	42	45	(	(	PUNCT
ejpam-7013	42	46	v	v	NOUN
ejpam-7013	42	47	)	)	PUNCT
ejpam-7013	42	48	mb(l	mb(l	PROPN
ejpam-7013	42	49	,	,	PUNCT
ejpam-7013	42	50	p	p	X
ejpam-7013	42	51	,	,	PUNCT
ejpam-7013	42	52	·	·	PUNCT
ejpam-7013	42	53	)	)	PUNCT
ejpam-7013	42	54	is	be	AUX
ejpam-7013	42	55	continuous	continuous	ADJ
ejpam-7013	42	56	in	in	ADP
ejpam-7013	42	57	t	t	PROPN
ejpam-7013	42	58	,	,	PUNCT
ejpam-7013	42	59	(	(	PUNCT
ejpam-7013	42	60	vi	vi	NOUN
ejpam-7013	42	61	)	)	PUNCT
ejpam-7013	42	62	mb(l	mb(l	PROPN
ejpam-7013	42	63	,	,	PUNCT
ejpam-7013	42	64	k	k	PROPN
ejpam-7013	42	65	,	,	PUNCT
ejpam-7013	42	66	t	t	PROPN
ejpam-7013	42	67	)	)	PUNCT
ejpam-7013	42	68	≤	≤	PROPN
ejpam-7013	42	69	b	b	X
ejpam-7013	42	70	(	(	PUNCT
ejpam-7013	42	71	mb(l	mb(l	PROPN
ejpam-7013	42	72	,	,	PUNCT
ejpam-7013	42	73	p	p	X
ejpam-7013	42	74	,	,	PUNCT
ejpam-7013	42	75	t	t	PROPN
ejpam-7013	42	76	)	)	PUNCT
ejpam-7013	42	77	∗mb(p	∗mb(p	PROPN
ejpam-7013	42	78	,	,	PUNCT
ejpam-7013	42	79	k	k	PROPN
ejpam-7013	42	80	,	,	PUNCT
ejpam-7013	42	81	t	t	PROPN
ejpam-7013	42	82	)	)	PUNCT
ejpam-7013	42	83	)	)	PUNCT
ejpam-7013	42	84	.	.	PUNCT
ejpam-7013	43	1	definition	definition	NOUN
ejpam-7013	43	2	4	4	NUM
ejpam-7013	43	3	.	.	PUNCT
ejpam-7013	44	1	let	let	AUX
ejpam-7013	44	2	(	(	PUNCT
ejpam-7013	44	3	x	x	X
ejpam-7013	44	4	,	,	PUNCT
ejpam-7013	44	5	m	m	PROPN
ejpam-7013	44	6	,	,	PUNCT
ejpam-7013	44	7	∗	∗	NOUN
ejpam-7013	44	8	)	)	PUNCT
ejpam-7013	44	9	be	be	VERB
ejpam-7013	44	10	a	a	DET
ejpam-7013	44	11	fuzzy	fuzzy	ADJ
ejpam-7013	44	12	metric	metric	ADJ
ejpam-7013	44	13	space	space	NOUN
ejpam-7013	44	14	.	.	PUNCT
ejpam-7013	45	1	a	a	DET
ejpam-7013	45	2	mapping	mapping	NOUN
ejpam-7013	45	3	t	t	NOUN
ejpam-7013	45	4	:	:	PUNCT
ejpam-7013	45	5	x	x	X
ejpam-7013	45	6	→	→	SYM
ejpam-7013	45	7	f(x	f(x	PROPN
ejpam-7013	45	8	)	)	PUNCT
ejpam-7013	45	9	is	be	AUX
ejpam-7013	45	10	called	call	VERB
ejpam-7013	45	11	a	a	DET
ejpam-7013	45	12	fuzzy	fuzzy	ADJ
ejpam-7013	45	13	mapping	mapping	NOUN
ejpam-7013	45	14	if	if	SCONJ
ejpam-7013	45	15	for	for	ADP
ejpam-7013	45	16	each	each	DET
ejpam-7013	45	17	x	x	SYM
ejpam-7013	45	18	∈	∈	PROPN
ejpam-7013	45	19	x	x	X
ejpam-7013	45	20	,	,	PUNCT
ejpam-7013	45	21	t	t	PROPN
ejpam-7013	45	22	(	(	PUNCT
ejpam-7013	45	23	x	x	X
ejpam-7013	45	24	)	)	PUNCT
ejpam-7013	45	25	is	be	AUX
ejpam-7013	45	26	a	a	DET
ejpam-7013	45	27	fuzzy	fuzzy	ADJ
ejpam-7013	45	28	subset	subset	NOUN
ejpam-7013	45	29	of	of	ADP
ejpam-7013	45	30	x	x	PRON
ejpam-7013	45	31	,	,	PUNCT
ejpam-7013	45	32	i.e.	i.e.	X
ejpam-7013	45	33	,	,	PUNCT
ejpam-7013	45	34	t	t	PROPN
ejpam-7013	45	35	(	(	PUNCT
ejpam-7013	45	36	x	x	NOUN
ejpam-7013	45	37	)	)	PUNCT
ejpam-7013	45	38	:	:	PUNCT
ejpam-7013	46	1	x	x	X
ejpam-7013	46	2	→	→	PUNCT
ejpam-7013	46	3	[	[	X
ejpam-7013	46	4	0	0	NUM
ejpam-7013	46	5	,	,	PUNCT
ejpam-7013	46	6	1	1	NUM
ejpam-7013	46	7	]	]	PUNCT
ejpam-7013	46	8	assigns	assign	NOUN
ejpam-7013	46	9	to	to	ADP
ejpam-7013	46	10	each	each	DET
ejpam-7013	46	11	y	y	PROPN
ejpam-7013	46	12	∈	∈	PROPN
ejpam-7013	46	13	x	x	PUNCT
ejpam-7013	46	14	a	a	DET
ejpam-7013	46	15	membership	membership	NOUN
ejpam-7013	46	16	degree	degree	NOUN
ejpam-7013	46	17	t	t	PROPN
ejpam-7013	46	18	(	(	PUNCT
ejpam-7013	46	19	x)(y	x)(y	PROPN
ejpam-7013	46	20	)	)	PUNCT
ejpam-7013	46	21	∈	∈	PROPN
ejpam-7013	47	1	[	[	X
ejpam-7013	47	2	0	0	NUM
ejpam-7013	47	3	,	,	PUNCT
ejpam-7013	47	4	1	1	NUM
ejpam-7013	47	5	]	]	PUNCT
ejpam-7013	47	6	.	.	PUNCT
ejpam-7013	48	1	definition	definition	NOUN
ejpam-7013	48	2	5	5	NUM
ejpam-7013	48	3	.	.	PUNCT
ejpam-7013	49	1	for	for	ADP
ejpam-7013	49	2	a	a	DET
ejpam-7013	49	3	fuzzy	fuzzy	ADJ
ejpam-7013	49	4	mapping	mapping	NOUN
ejpam-7013	49	5	t	t	NOUN
ejpam-7013	49	6	:	:	PUNCT
ejpam-7013	49	7	x	x	X
ejpam-7013	49	8	→	→	SYM
ejpam-7013	49	9	w	w	PROPN
ejpam-7013	49	10	(	(	PUNCT
ejpam-7013	49	11	x	x	NOUN
ejpam-7013	49	12	)	)	PUNCT
ejpam-7013	49	13	,	,	PUNCT
ejpam-7013	49	14	where	where	SCONJ
ejpam-7013	49	15	w	w	X
ejpam-7013	49	16	(	(	PUNCT
ejpam-7013	49	17	x	x	NOUN
ejpam-7013	49	18	)	)	PUNCT
ejpam-7013	49	19	denotes	denote	VERB
ejpam-7013	49	20	the	the	DET
ejpam-7013	49	21	set	set	NOUN
ejpam-7013	49	22	of	of	ADP
ejpam-7013	49	23	all	all	PRON
ejpam-7013	49	24	nonempty	nonempty	ADV
ejpam-7013	49	25	closed	close	VERB
ejpam-7013	49	26	and	and	CCONJ
ejpam-7013	49	27	bounded	bound	VERB
ejpam-7013	49	28	subsets	subset	NOUN
ejpam-7013	49	29	of	of	ADP
ejpam-7013	49	30	x	x	PRON
ejpam-7013	49	31	,	,	PUNCT
ejpam-7013	49	32	the	the	DET
ejpam-7013	49	33	fuzzy	fuzzy	ADJ
ejpam-7013	49	34	hausdorff	hausdorff	NOUN
ejpam-7013	49	35	metric	metric	ADJ
ejpam-7013	49	36	h	h	NOUN
ejpam-7013	49	37	between	between	ADP
ejpam-7013	49	38	a	a	DET
ejpam-7013	49	39	,	,	PUNCT
ejpam-7013	49	40	b	b	PROPN
ejpam-7013	49	41	∈	∈	PROPN
ejpam-7013	49	42	w	w	PROPN
ejpam-7013	49	43	(	(	PUNCT
ejpam-7013	49	44	x	x	X
ejpam-7013	49	45	)	)	PUNCT
ejpam-7013	49	46	is	be	AUX
ejpam-7013	49	47	defined	define	VERB
ejpam-7013	49	48	as	as	ADP
ejpam-7013	49	49	h(a	h(a	PROPN
ejpam-7013	49	50	,	,	PUNCT
ejpam-7013	49	51	b	b	NOUN
ejpam-7013	49	52	)	)	PUNCT
ejpam-7013	49	53	=	=	SYM
ejpam-7013	49	54	max	max	PROPN
ejpam-7013	49	55	{	{	PUNCT
ejpam-7013	49	56	sup	sup	PROPN
ejpam-7013	49	57	l∈a	l∈a	VERB
ejpam-7013	49	58	dα(l	dα(l	PROPN
ejpam-7013	49	59	,	,	PUNCT
ejpam-7013	49	60	b	b	NOUN
ejpam-7013	49	61	)	)	PUNCT
ejpam-7013	49	62	,	,	PUNCT
ejpam-7013	49	63	sup	sup	NOUN
ejpam-7013	49	64	p∈b	p∈b	NOUN
ejpam-7013	49	65	dα(p	dα(p	NOUN
ejpam-7013	49	66	,	,	PUNCT
ejpam-7013	49	67	a	a	PRON
ejpam-7013	49	68	)	)	PUNCT
ejpam-7013	49	69	}	}	PUNCT
ejpam-7013	49	70	,	,	PUNCT
ejpam-7013	49	71	where	where	SCONJ
ejpam-7013	49	72	the	the	DET
ejpam-7013	49	73	α	α	NOUN
ejpam-7013	49	74	-	-	PUNCT
ejpam-7013	49	75	level	level	NOUN
ejpam-7013	49	76	distance	distance	NOUN
ejpam-7013	49	77	dα(l	dα(l	NOUN
ejpam-7013	49	78	,	,	PUNCT
ejpam-7013	49	79	b	b	NOUN
ejpam-7013	49	80	)	)	PUNCT
ejpam-7013	49	81	is	be	AUX
ejpam-7013	49	82	given	give	VERB
ejpam-7013	49	83	by	by	ADP
ejpam-7013	49	84	dα(l	dα(l	ADJ
ejpam-7013	49	85	,	,	PUNCT
ejpam-7013	49	86	b	b	NOUN
ejpam-7013	49	87	)	)	PUNCT
ejpam-7013	49	88	=	=	SYM
ejpam-7013	49	89	inf	inf	NOUN
ejpam-7013	49	90	{	{	PUNCT
ejpam-7013	49	91	d(l	d(l	ADJ
ejpam-7013	49	92	,	,	PUNCT
ejpam-7013	49	93	k	k	NOUN
ejpam-7013	49	94	)	)	PUNCT
ejpam-7013	49	95	:	:	PUNCT
ejpam-7013	49	96	k	k	PROPN
ejpam-7013	49	97	∈	∈	PROPN
ejpam-7013	49	98	b	b	PROPN
ejpam-7013	49	99	}	}	PUNCT
ejpam-7013	49	100	.	.	PUNCT
ejpam-7013	50	1	definition	definition	NOUN
ejpam-7013	50	2	6	6	NUM
ejpam-7013	50	3	.	.	PUNCT
ejpam-7013	51	1	let	let	AUX
ejpam-7013	51	2	(	(	PUNCT
ejpam-7013	51	3	x	x	X
ejpam-7013	51	4	,	,	PUNCT
ejpam-7013	51	5	m	m	PROPN
ejpam-7013	51	6	,	,	PUNCT
ejpam-7013	51	7	∗	∗	NOUN
ejpam-7013	51	8	)	)	PUNCT
ejpam-7013	51	9	be	be	VERB
ejpam-7013	51	10	a	a	DET
ejpam-7013	51	11	b	b	PROPN
ejpam-7013	51	12	-	-	PUNCT
ejpam-7013	51	13	fms	fms	PROPN
ejpam-7013	51	14	.	.	PUNCT
ejpam-7013	52	1	a	a	DET
ejpam-7013	52	2	sequence	sequence	NOUN
ejpam-7013	52	3	{	{	PUNCT
ejpam-7013	52	4	ln	ln	ADJ
ejpam-7013	52	5	}	}	PUNCT
ejpam-7013	52	6	in	in	ADP
ejpam-7013	52	7	x	x	VERB
ejpam-7013	52	8	is	be	AUX
ejpam-7013	52	9	said	say	VERB
ejpam-7013	52	10	to	to	PART
ejpam-7013	52	11	be	be	AUX
ejpam-7013	52	12	:	:	PUNCT
ejpam-7013	52	13	(	(	PUNCT
ejpam-7013	52	14	i	i	NOUN
ejpam-7013	52	15	)	)	PUNCT
ejpam-7013	52	16	convergent	convergent	NOUN
ejpam-7013	52	17	to	to	ADP
ejpam-7013	52	18	l	l	NOUN
ejpam-7013	52	19	∈	∈	PROPN
ejpam-7013	52	20	x	x	INTJ
ejpam-7013	52	21	if	if	SCONJ
ejpam-7013	52	22	for	for	ADP
ejpam-7013	52	23	every	every	DET
ejpam-7013	52	24	ε	ε	PROPN
ejpam-7013	52	25	>	>	X
ejpam-7013	52	26	0	0	PUNCT
ejpam-7013	53	1	and	and	CCONJ
ejpam-7013	53	2	λ	λ	PROPN
ejpam-7013	53	3	∈	∈	PROPN
ejpam-7013	53	4	(	(	PUNCT
ejpam-7013	53	5	0	0	NUM
ejpam-7013	53	6	,	,	PUNCT
ejpam-7013	53	7	1	1	NUM
ejpam-7013	53	8	)	)	PUNCT
ejpam-7013	53	9	there	there	PRON
ejpam-7013	53	10	exists	exist	VERB
ejpam-7013	53	11	n	n	PRON
ejpam-7013	53	12	∈	∈	PROPN
ejpam-7013	53	13	n	n	PRON
ejpam-7013	53	14	such	such	ADJ
ejpam-7013	53	15	that	that	SCONJ
ejpam-7013	53	16	m(ln	m(ln	PROPN
ejpam-7013	53	17	,	,	PUNCT
ejpam-7013	53	18	l	l	PROPN
ejpam-7013	53	19	,	,	PUNCT
ejpam-7013	53	20	t	t	PROPN
ejpam-7013	53	21	)	)	PUNCT
ejpam-7013	53	22	>	>	X
ejpam-7013	54	1	1−	1−	NUM
ejpam-7013	54	2	λ	λ	NOUN
ejpam-7013	54	3	for	for	ADP
ejpam-7013	54	4	all	all	DET
ejpam-7013	54	5	n	n	DET
ejpam-7013	54	6	≥	≥	NOUN
ejpam-7013	54	7	n	n	NOUN
ejpam-7013	54	8	and	and	CCONJ
ejpam-7013	54	9	t	t	PROPN
ejpam-7013	54	10	>	>	X
ejpam-7013	54	11	0	0	NUM
ejpam-7013	54	12	.	.	PUNCT
ejpam-7013	54	13	(	(	PUNCT
ejpam-7013	54	14	ii	ii	NOUN
ejpam-7013	54	15	)	)	PUNCT
ejpam-7013	54	16	cauchy	cauchy	NOUN
ejpam-7013	54	17	if	if	SCONJ
ejpam-7013	54	18	for	for	ADP
ejpam-7013	54	19	every	every	DET
ejpam-7013	54	20	ε	ε	PROPN
ejpam-7013	54	21	>	>	X
ejpam-7013	54	22	0	0	PUNCT
ejpam-7013	54	23	and	and	CCONJ
ejpam-7013	54	24	λ	λ	PROPN
ejpam-7013	54	25	∈	∈	PROPN
ejpam-7013	54	26	(	(	PUNCT
ejpam-7013	54	27	0	0	NUM
ejpam-7013	54	28	,	,	PUNCT
ejpam-7013	54	29	1	1	NUM
ejpam-7013	54	30	)	)	PUNCT
ejpam-7013	54	31	there	there	PRON
ejpam-7013	54	32	exists	exist	VERB
ejpam-7013	54	33	n	n	PRON
ejpam-7013	54	34	∈	∈	PROPN
ejpam-7013	54	35	n	n	PRON
ejpam-7013	54	36	such	such	ADJ
ejpam-7013	54	37	that	that	SCONJ
ejpam-7013	54	38	m(ln	m(ln	PROPN
ejpam-7013	54	39	,	,	PUNCT
ejpam-7013	54	40	lm	lm	PROPN
ejpam-7013	54	41	,	,	PUNCT
ejpam-7013	54	42	t	t	PROPN
ejpam-7013	54	43	)	)	PUNCT
ejpam-7013	54	44	>	>	X
ejpam-7013	55	1	1−	1−	NUM
ejpam-7013	55	2	λ	λ	NOUN
ejpam-7013	55	3	for	for	ADP
ejpam-7013	55	4	all	all	DET
ejpam-7013	55	5	n	n	CCONJ
ejpam-7013	55	6	,	,	PUNCT
ejpam-7013	55	7	m	m	VERB
ejpam-7013	55	8	≥	≥	NOUN
ejpam-7013	55	9	n	n	NOUN
ejpam-7013	55	10	and	and	CCONJ
ejpam-7013	55	11	t	t	PROPN
ejpam-7013	55	12	>	>	X
ejpam-7013	55	13	0	0	X
ejpam-7013	55	14	.	.	PUNCT
ejpam-7013	56	1	definition	definition	NOUN
ejpam-7013	56	2	7	7	NUM
ejpam-7013	56	3	.	.	PUNCT
ejpam-7013	57	1	a	a	DET
ejpam-7013	57	2	b	b	X
ejpam-7013	57	3	-	-	PUNCT
ejpam-7013	57	4	fms	fms	PROPN
ejpam-7013	57	5	(	(	PUNCT
ejpam-7013	57	6	x	x	X
ejpam-7013	57	7	,	,	PUNCT
ejpam-7013	57	8	m	m	PROPN
ejpam-7013	57	9	,	,	PUNCT
ejpam-7013	57	10	∗	∗	NOUN
ejpam-7013	57	11	)	)	PUNCT
ejpam-7013	57	12	is	be	AUX
ejpam-7013	57	13	said	say	VERB
ejpam-7013	57	14	to	to	PART
ejpam-7013	57	15	be	be	AUX
ejpam-7013	57	16	complete	complete	ADJ
ejpam-7013	57	17	if	if	SCONJ
ejpam-7013	57	18	every	every	DET
ejpam-7013	57	19	cauchy	cauchy	ADJ
ejpam-7013	57	20	sequence	sequence	NOUN
ejpam-7013	57	21	in	in	ADP
ejpam-7013	57	22	x	x	PUNCT
ejpam-7013	57	23	converges	converge	NOUN
ejpam-7013	57	24	to	to	ADP
ejpam-7013	57	25	a	a	DET
ejpam-7013	57	26	point	point	NOUN
ejpam-7013	57	27	l	l	NOUN
ejpam-7013	57	28	∈	∈	PROPN
ejpam-7013	57	29	x.	x.	NOUN
ejpam-7013	57	30	d.	d.	PROPN
ejpam-7013	57	31	gerbeti	gerbeti	PROPN
ejpam-7013	57	32	et	et	PROPN
ejpam-7013	57	33	al	al	PROPN
ejpam-7013	57	34	.	.	PUNCT
ejpam-7013	57	35	/	/	SYM
ejpam-7013	57	36	eur	eur	PROPN
ejpam-7013	57	37	.	.	PUNCT
ejpam-7013	58	1	j.	j.	PROPN
ejpam-7013	58	2	pure	pure	PROPN
ejpam-7013	58	3	appl	appl	PROPN
ejpam-7013	58	4	.	.	PROPN
ejpam-7013	58	5	math	math	PROPN
ejpam-7013	58	6	,	,	PUNCT
ejpam-7013	58	7	18	18	NUM
ejpam-7013	58	8	(	(	PUNCT
ejpam-7013	58	9	4	4	NUM
ejpam-7013	58	10	)	)	PUNCT
ejpam-7013	58	11	(	(	PUNCT
ejpam-7013	58	12	2025	2025	NUM
ejpam-7013	58	13	)	)	PUNCT
ejpam-7013	58	14	,	,	PUNCT
ejpam-7013	58	15	7013	7013	NUM
ejpam-7013	58	16	4	4	NUM
ejpam-7013	58	17	of	of	ADP
ejpam-7013	58	18	17	17	NUM
ejpam-7013	58	19	3	3	NUM
ejpam-7013	58	20	.	.	PUNCT
ejpam-7013	58	21	main	main	ADJ
ejpam-7013	58	22	results	result	NOUN
ejpam-7013	58	23	the	the	DET
ejpam-7013	58	24	following	follow	VERB
ejpam-7013	58	25	theorems	theorem	NOUN
ejpam-7013	58	26	present	present	VERB
ejpam-7013	58	27	the	the	DET
ejpam-7013	58	28	core	core	ADJ
ejpam-7013	58	29	contributions	contribution	NOUN
ejpam-7013	58	30	of	of	ADP
ejpam-7013	58	31	this	this	DET
ejpam-7013	58	32	paper	paper	NOUN
ejpam-7013	58	33	in	in	ADP
ejpam-7013	58	34	the	the	DET
ejpam-7013	58	35	framework	framework	NOUN
ejpam-7013	58	36	of	of	ADP
ejpam-7013	58	37	complete	complete	ADJ
ejpam-7013	58	38	b	b	X
ejpam-7013	58	39	-	-	PUNCT
ejpam-7013	58	40	fuzzy	fuzzy	ADJ
ejpam-7013	58	41	metric	metric	ADJ
ejpam-7013	58	42	spaces	space	NOUN
ejpam-7013	58	43	.	.	PUNCT
ejpam-7013	59	1	theorem	theorem	NOUN
ejpam-7013	59	2	1	1	NUM
ejpam-7013	59	3	.	.	PUNCT
ejpam-7013	60	1	let	let	AUX
ejpam-7013	60	2	(	(	PUNCT
ejpam-7013	60	3	x	x	X
ejpam-7013	60	4	,	,	PUNCT
ejpam-7013	60	5	m	m	PROPN
ejpam-7013	60	6	,	,	PUNCT
ejpam-7013	60	7	∗	∗	NOUN
ejpam-7013	60	8	)	)	PUNCT
ejpam-7013	60	9	be	be	VERB
ejpam-7013	60	10	a	a	DET
ejpam-7013	60	11	complete	complete	ADJ
ejpam-7013	60	12	b	b	NOUN
ejpam-7013	60	13	-	-	PUNCT
ejpam-7013	60	14	fms	fms	PROPN
ejpam-7013	60	15	and	and	CCONJ
ejpam-7013	60	16	let	let	VERB
ejpam-7013	60	17	t	t	NOUN
ejpam-7013	60	18	:	:	PUNCT
ejpam-7013	60	19	x	x	X
ejpam-7013	60	20	→	→	SYM
ejpam-7013	60	21	w	w	PROPN
ejpam-7013	60	22	(	(	PUNCT
ejpam-7013	60	23	x	x	X
ejpam-7013	60	24	)	)	PUNCT
ejpam-7013	60	25	be	be	AUX
ejpam-7013	60	26	a	a	DET
ejpam-7013	60	27	fuzzy	fuzzy	ADJ
ejpam-7013	60	28	mapping	mapping	NOUN
ejpam-7013	60	29	.	.	PUNCT
ejpam-7013	61	1	suppose	suppose	VERB
ejpam-7013	61	2	there	there	PRON
ejpam-7013	61	3	exist	exist	VERB
ejpam-7013	61	4	nonnegative	nonnegative	ADJ
ejpam-7013	61	5	constants	constant	NOUN
ejpam-7013	61	6	λ1,λ2,λ3,λ4	λ1,λ2,λ3,λ4	PROPN
ejpam-7013	61	7	≥	≥	NOUN
ejpam-7013	61	8	0	0	NUM
ejpam-7013	61	9	such	such	ADJ
ejpam-7013	61	10	that	that	PRON
ejpam-7013	61	11	for	for	ADP
ejpam-7013	61	12	all	all	DET
ejpam-7013	61	13	l	l	NOUN
ejpam-7013	61	14	,	,	PUNCT
ejpam-7013	61	15	p	p	PROPN
ejpam-7013	61	16	∈	∈	PROPN
ejpam-7013	61	17	x	x	PRON
ejpam-7013	61	18	,	,	PUNCT
ejpam-7013	61	19	the	the	DET
ejpam-7013	61	20	inequality	inequality	NOUN
ejpam-7013	61	21	h(t	h(t	PROPN
ejpam-7013	61	22	(	(	PUNCT
ejpam-7013	61	23	l	l	NOUN
ejpam-7013	61	24	)	)	PUNCT
ejpam-7013	61	25	,	,	PUNCT
ejpam-7013	61	26	t	t	PROPN
ejpam-7013	61	27	(	(	PUNCT
ejpam-7013	61	28	p	p	NOUN
ejpam-7013	61	29	)	)	PUNCT
ejpam-7013	61	30	)	)	PUNCT
ejpam-7013	62	1	+	+	CCONJ
ejpam-7013	63	1	λ3dα(l	λ3dα(l	PROPN
ejpam-7013	63	2	,	,	PUNCT
ejpam-7013	63	3	t	t	PROPN
ejpam-7013	63	4	(	(	PUNCT
ejpam-7013	63	5	l	l	NOUN
ejpam-7013	63	6	)	)	PUNCT
ejpam-7013	63	7	)	)	PUNCT
ejpam-7013	63	8	≤	≤	NOUN
ejpam-7013	64	1	λ1dα(l	λ1dα(l	PROPN
ejpam-7013	64	2	,	,	PUNCT
ejpam-7013	64	3	t	t	PROPN
ejpam-7013	64	4	(	(	PUNCT
ejpam-7013	64	5	p	p	NOUN
ejpam-7013	64	6	)	)	PUNCT
ejpam-7013	64	7	)	)	PUNCT
ejpam-7013	65	1	+	+	CCONJ
ejpam-7013	65	2	λ2dα(p	λ2dα(p	PROPN
ejpam-7013	65	3	,	,	PUNCT
ejpam-7013	65	4	t	t	PROPN
ejpam-7013	65	5	(	(	PUNCT
ejpam-7013	65	6	l	l	NOUN
ejpam-7013	65	7	)	)	PUNCT
ejpam-7013	65	8	)	)	PUNCT
ejpam-7013	66	1	+	+	CCONJ
ejpam-7013	66	2	λ4d(l	λ4d(l	PROPN
ejpam-7013	66	3	,	,	PUNCT
ejpam-7013	66	4	p	p	NOUN
ejpam-7013	66	5	)	)	PUNCT
ejpam-7013	66	6	,	,	PUNCT
ejpam-7013	66	7	holds	hold	VERB
ejpam-7013	66	8	,	,	PUNCT
ejpam-7013	66	9	where	where	SCONJ
ejpam-7013	66	10	λ1	λ1	ADJ
ejpam-7013	66	11	+	+	NUM
ejpam-7013	66	12	λ2	λ2	NOUN
ejpam-7013	66	13	+	+	CCONJ
ejpam-7013	66	14	λ4	λ4	ADJ
ejpam-7013	66	15	<	<	X
ejpam-7013	66	16	1	1	NUM
ejpam-7013	66	17	,	,	PUNCT
ejpam-7013	66	18	λ2	λ2	NOUN
ejpam-7013	66	19	+	+	CCONJ
ejpam-7013	66	20	λ3	λ3	PROPN
ejpam-7013	66	21	<	<	X
ejpam-7013	66	22	1	1	NUM
ejpam-7013	66	23	,	,	PUNCT
ejpam-7013	66	24	λ3	λ3	PROPN
ejpam-7013	67	1	+	+	X
ejpam-7013	67	2	λ4	λ4	PROPN
ejpam-7013	67	3	<	<	X
ejpam-7013	67	4	1	1	X
ejpam-7013	67	5	.	.	PUNCT
ejpam-7013	68	1	then	then	ADV
ejpam-7013	68	2	t	t	PROPN
ejpam-7013	68	3	has	have	VERB
ejpam-7013	68	4	a	a	DET
ejpam-7013	68	5	fuzzy	fuzzy	ADJ
ejpam-7013	68	6	fixed	fix	VERB
ejpam-7013	68	7	point	point	NOUN
ejpam-7013	68	8	,	,	PUNCT
ejpam-7013	68	9	i.e.	i.e.	X
ejpam-7013	68	10	,	,	PUNCT
ejpam-7013	68	11	there	there	PRON
ejpam-7013	68	12	exists	exist	VERB
ejpam-7013	68	13	k	k	PROPN
ejpam-7013	68	14	∈	∈	PROPN
ejpam-7013	68	15	x	x	PUNCT
ejpam-7013	69	1	such	such	ADJ
ejpam-7013	69	2	that	that	SCONJ
ejpam-7013	69	3	{	{	PUNCT
ejpam-7013	69	4	k	k	NOUN
ejpam-7013	69	5	}	}	PUNCT
ejpam-7013	69	6	⊆	⊆	NUM
ejpam-7013	69	7	t	t	NOUN
ejpam-7013	69	8	(	(	PUNCT
ejpam-7013	69	9	k	k	NOUN
ejpam-7013	69	10	)	)	PUNCT
ejpam-7013	69	11	.	.	PUNCT
ejpam-7013	69	12	proof	proof	NOUN
ejpam-7013	69	13	.	.	PUNCT
ejpam-7013	70	1	let	let	VERB
ejpam-7013	70	2	l0	l0	PROPN
ejpam-7013	70	3	∈	∈	PROPN
ejpam-7013	70	4	x	x	AUX
ejpam-7013	70	5	be	be	AUX
ejpam-7013	70	6	arbitrary	arbitrary	ADJ
ejpam-7013	70	7	.	.	PUNCT
ejpam-7013	71	1	define	define	VERB
ejpam-7013	71	2	a	a	DET
ejpam-7013	71	3	sequence	sequence	NOUN
ejpam-7013	71	4	{	{	PUNCT
ejpam-7013	71	5	ln	ln	ADJ
ejpam-7013	71	6	}	}	PUNCT
ejpam-7013	71	7	in	in	ADP
ejpam-7013	71	8	x	x	PUNCT
ejpam-7013	71	9	by	by	ADP
ejpam-7013	71	10	choosing	choose	VERB
ejpam-7013	71	11	ln+1	ln+1	PROPN
ejpam-7013	71	12	∈	∈	PROPN
ejpam-7013	71	13	t	t	PROPN
ejpam-7013	71	14	(	(	PUNCT
ejpam-7013	71	15	ln	ln	ADJ
ejpam-7013	71	16	)	)	PUNCT
ejpam-7013	71	17	for	for	ADP
ejpam-7013	71	18	each	each	DET
ejpam-7013	71	19	n	n	PRON
ejpam-7013	71	20	≥	≥	NOUN
ejpam-7013	71	21	0	0	NUM
ejpam-7013	71	22	.	.	PUNCT
ejpam-7013	72	1	by	by	ADP
ejpam-7013	72	2	the	the	DET
ejpam-7013	72	3	assumed	assume	VERB
ejpam-7013	72	4	contractive	contractive	ADJ
ejpam-7013	72	5	condition	condition	NOUN
ejpam-7013	72	6	,	,	PUNCT
ejpam-7013	72	7	we	we	PRON
ejpam-7013	72	8	obtain	obtain	VERB
ejpam-7013	72	9	h(t	h(t	PROPN
ejpam-7013	72	10	(	(	PUNCT
ejpam-7013	72	11	ln	ln	ADJ
ejpam-7013	72	12	)	)	PUNCT
ejpam-7013	72	13	,	,	PUNCT
ejpam-7013	72	14	t	t	PROPN
ejpam-7013	72	15	(	(	PUNCT
ejpam-7013	72	16	ln+1))+λ3dα(ln	ln+1))+λ3dα(ln	PROPN
ejpam-7013	72	17	,	,	PUNCT
ejpam-7013	72	18	t	t	PROPN
ejpam-7013	72	19	(	(	PUNCT
ejpam-7013	72	20	ln	ln	ADJ
ejpam-7013	72	21	)	)	PUNCT
ejpam-7013	72	22	)	)	PUNCT
ejpam-7013	72	23	≤	≤	ADV
ejpam-7013	73	1	λ1dα(ln	λ1dα(ln	PROPN
ejpam-7013	73	2	,	,	PUNCT
ejpam-7013	73	3	t	t	PROPN
ejpam-7013	73	4	(	(	PUNCT
ejpam-7013	73	5	ln+1))+λ2dα(ln+1	ln+1))+λ2dα(ln+1	PROPN
ejpam-7013	73	6	,	,	PUNCT
ejpam-7013	73	7	t	t	PROPN
ejpam-7013	73	8	(	(	PUNCT
ejpam-7013	73	9	ln))+λ4d(ln	ln))+λ4d(ln	PROPN
ejpam-7013	73	10	,	,	PUNCT
ejpam-7013	73	11	ln+1	ln+1	ADJ
ejpam-7013	73	12	)	)	PUNCT
ejpam-7013	73	13	.	.	PUNCT
ejpam-7013	74	1	since	since	SCONJ
ejpam-7013	74	2	ln+1	ln+1	PROPN
ejpam-7013	74	3	∈	∈	PROPN
ejpam-7013	74	4	t	t	PROPN
ejpam-7013	74	5	(	(	PUNCT
ejpam-7013	74	6	ln	ln	PROPN
ejpam-7013	74	7	)	)	PUNCT
ejpam-7013	74	8	,	,	PUNCT
ejpam-7013	74	9	we	we	PRON
ejpam-7013	74	10	have	have	VERB
ejpam-7013	74	11	dα(ln	dα(ln	PROPN
ejpam-7013	74	12	,	,	PUNCT
ejpam-7013	74	13	t	t	PROPN
ejpam-7013	74	14	(	(	PUNCT
ejpam-7013	74	15	ln	ln	ADJ
ejpam-7013	74	16	)	)	PUNCT
ejpam-7013	74	17	)	)	PUNCT
ejpam-7013	75	1	≤	≤	PROPN
ejpam-7013	75	2	d(ln	d(ln	PROPN
ejpam-7013	75	3	,	,	PUNCT
ejpam-7013	75	4	ln+1	ln+1	PROPN
ejpam-7013	75	5	)	)	PUNCT
ejpam-7013	75	6	.	.	PUNCT
ejpam-7013	76	1	similarly	similarly	ADV
ejpam-7013	76	2	,	,	PUNCT
ejpam-7013	76	3	dα(ln	dα(ln	PROPN
ejpam-7013	76	4	,	,	PUNCT
ejpam-7013	76	5	t	t	PROPN
ejpam-7013	76	6	(	(	PUNCT
ejpam-7013	76	7	ln+1	ln+1	PROPN
ejpam-7013	76	8	)	)	PUNCT
ejpam-7013	76	9	)	)	PUNCT
ejpam-7013	77	1	≤	≤	PROPN
ejpam-7013	77	2	d(ln	d(ln	PROPN
ejpam-7013	77	3	,	,	PUNCT
ejpam-7013	77	4	ln+1	ln+1	ADJ
ejpam-7013	77	5	)	)	PUNCT
ejpam-7013	77	6	and	and	CCONJ
ejpam-7013	77	7	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	77	8	,	,	PUNCT
ejpam-7013	77	9	t	t	PROPN
ejpam-7013	77	10	(	(	PUNCT
ejpam-7013	77	11	ln	ln	ADJ
ejpam-7013	77	12	)	)	PUNCT
ejpam-7013	77	13	)	)	PUNCT
ejpam-7013	77	14	≤	≤	PROPN
ejpam-7013	77	15	d(ln	d(ln	PROPN
ejpam-7013	77	16	,	,	PUNCT
ejpam-7013	77	17	ln+1	ln+1	PROPN
ejpam-7013	77	18	)	)	PUNCT
ejpam-7013	77	19	.	.	PUNCT
ejpam-7013	78	1	thus	thus	ADV
ejpam-7013	78	2	the	the	DET
ejpam-7013	78	3	inequality	inequality	NOUN
ejpam-7013	78	4	reduces	reduce	VERB
ejpam-7013	78	5	to	to	ADP
ejpam-7013	78	6	h(t	h(t	PROPN
ejpam-7013	78	7	(	(	PUNCT
ejpam-7013	78	8	ln	ln	ADJ
ejpam-7013	78	9	)	)	PUNCT
ejpam-7013	78	10	,	,	PUNCT
ejpam-7013	78	11	t	t	PROPN
ejpam-7013	78	12	(	(	PUNCT
ejpam-7013	78	13	ln+1	ln+1	PROPN
ejpam-7013	78	14	)	)	PUNCT
ejpam-7013	78	15	)	)	PUNCT
ejpam-7013	78	16	≤	≤	NOUN
ejpam-7013	78	17	(	(	PUNCT
ejpam-7013	78	18	λ1	λ1	ADJ
ejpam-7013	78	19	+	+	NUM
ejpam-7013	78	20	λ2	λ2	NOUN
ejpam-7013	78	21	+	+	CCONJ
ejpam-7013	78	22	λ4	λ4	PROPN
ejpam-7013	78	23	)	)	PUNCT
ejpam-7013	78	24	d(ln	d(ln	PROPN
ejpam-7013	78	25	,	,	PUNCT
ejpam-7013	78	26	ln+1	ln+1	ADJ
ejpam-7013	78	27	)	)	PUNCT
ejpam-7013	79	1	+	+	CCONJ
ejpam-7013	79	2	λ3d(ln	λ3d(ln	PROPN
ejpam-7013	79	3	,	,	PUNCT
ejpam-7013	79	4	ln+1	ln+1	PROPN
ejpam-7013	79	5	)	)	PUNCT
ejpam-7013	79	6	.	.	PUNCT
ejpam-7013	80	1	by	by	ADP
ejpam-7013	80	2	the	the	DET
ejpam-7013	80	3	conditions	condition	NOUN
ejpam-7013	80	4	λ1	λ1	VERB
ejpam-7013	81	1	+	+	SYM
ejpam-7013	81	2	λ2	λ2	NOUN
ejpam-7013	81	3	+	+	ADJ
ejpam-7013	81	4	λ4	λ4	ADJ
ejpam-7013	81	5	<	<	X
ejpam-7013	81	6	1	1	NUM
ejpam-7013	81	7	and	and	CCONJ
ejpam-7013	81	8	λ2	λ2	NOUN
ejpam-7013	82	1	+	+	NOUN
ejpam-7013	82	2	λ3	λ3	PROPN
ejpam-7013	82	3	<	<	X
ejpam-7013	82	4	1	1	NUM
ejpam-7013	82	5	,	,	PUNCT
ejpam-7013	82	6	one	one	PRON
ejpam-7013	82	7	can	can	AUX
ejpam-7013	82	8	set	set	VERB
ejpam-7013	82	9	η	η	NOUN
ejpam-7013	82	10	=	=	NOUN
ejpam-7013	82	11	max{λ1	max{λ1	PROPN
ejpam-7013	82	12	+	+	NOUN
ejpam-7013	82	13	λ2	λ2	NOUN
ejpam-7013	82	14	+	+	CCONJ
ejpam-7013	82	15	λ4	λ4	ADJ
ejpam-7013	82	16	,	,	PUNCT
ejpam-7013	82	17	λ2	λ2	PROPN
ejpam-7013	82	18	+	+	CCONJ
ejpam-7013	82	19	λ3	λ3	PROPN
ejpam-7013	82	20	,	,	PUNCT
ejpam-7013	82	21	λ3	λ3	PROPN
ejpam-7013	82	22	+	+	PROPN
ejpam-7013	82	23	λ4	λ4	ADJ
ejpam-7013	82	24	}	}	PUNCT
ejpam-7013	82	25	<	<	X
ejpam-7013	83	1	1	1	NUM
ejpam-7013	83	2	.	.	PUNCT
ejpam-7013	84	1	hence	hence	ADV
ejpam-7013	84	2	,	,	PUNCT
ejpam-7013	84	3	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	84	4	)	)	PUNCT
ejpam-7013	84	5	≤	≤	PROPN
ejpam-7013	84	6	η	η	PROPN
ejpam-7013	84	7	d(ln	d(ln	PROPN
ejpam-7013	84	8	,	,	PUNCT
ejpam-7013	84	9	ln+1	ln+1	PROPN
ejpam-7013	84	10	)	)	PUNCT
ejpam-7013	84	11	.	.	PUNCT
ejpam-7013	85	1	by	by	ADP
ejpam-7013	85	2	induction	induction	NOUN
ejpam-7013	85	3	,	,	PUNCT
ejpam-7013	85	4	this	this	DET
ejpam-7013	85	5	yields	yield	NOUN
ejpam-7013	85	6	d(ln	d(ln	PROPN
ejpam-7013	85	7	,	,	PUNCT
ejpam-7013	85	8	ln+1	ln+1	PROPN
ejpam-7013	85	9	)	)	PUNCT
ejpam-7013	85	10	≤	≤	NOUN
ejpam-7013	85	11	ηnd(l0,l1	ηnd(l0,l1	PROPN
ejpam-7013	85	12	)	)	PUNCT
ejpam-7013	85	13	.	.	PUNCT
ejpam-7013	86	1	thus	thus	ADV
ejpam-7013	86	2	{	{	PUNCT
ejpam-7013	86	3	ln	ln	ADJ
ejpam-7013	86	4	}	}	PUNCT
ejpam-7013	86	5	is	be	AUX
ejpam-7013	86	6	a	a	DET
ejpam-7013	86	7	cauchy	cauchy	ADJ
ejpam-7013	86	8	sequence	sequence	NOUN
ejpam-7013	86	9	in	in	ADP
ejpam-7013	86	10	x.	x.	NOUN
ejpam-7013	86	11	since	since	SCONJ
ejpam-7013	86	12	(	(	PUNCT
ejpam-7013	86	13	x	x	X
ejpam-7013	86	14	,	,	PUNCT
ejpam-7013	86	15	m	m	PROPN
ejpam-7013	86	16	,	,	PUNCT
ejpam-7013	86	17	∗	∗	NOUN
ejpam-7013	86	18	)	)	PUNCT
ejpam-7013	86	19	is	be	AUX
ejpam-7013	86	20	complete	complete	ADJ
ejpam-7013	86	21	,	,	PUNCT
ejpam-7013	86	22	there	there	PRON
ejpam-7013	86	23	exists	exist	VERB
ejpam-7013	86	24	k	k	PROPN
ejpam-7013	86	25	∈	∈	PROPN
ejpam-7013	86	26	x	x	PUNCT
ejpam-7013	86	27	such	such	ADJ
ejpam-7013	86	28	that	that	DET
ejpam-7013	86	29	ln	ln	NOUN
ejpam-7013	86	30	→	→	SYM
ejpam-7013	86	31	k	k	PROPN
ejpam-7013	86	32	as	as	ADP
ejpam-7013	86	33	n	n	PROPN
ejpam-7013	86	34	→	→	SYM
ejpam-7013	86	35	∞.	∞.	PROPN
ejpam-7013	86	36	it	it	PRON
ejpam-7013	86	37	remains	remain	VERB
ejpam-7013	86	38	to	to	PART
ejpam-7013	86	39	show	show	VERB
ejpam-7013	86	40	k	k	PROPN
ejpam-7013	86	41	is	be	AUX
ejpam-7013	86	42	a	a	DET
ejpam-7013	86	43	fuzzy	fuzzy	ADJ
ejpam-7013	86	44	fp	fp	NOUN
ejpam-7013	86	45	.	.	PROPN
ejpam-7013	86	46	from	from	ADP
ejpam-7013	86	47	the	the	DET
ejpam-7013	86	48	contractive	contractive	ADJ
ejpam-7013	86	49	inequality	inequality	NOUN
ejpam-7013	86	50	and	and	CCONJ
ejpam-7013	86	51	the	the	DET
ejpam-7013	86	52	continuity	continuity	NOUN
ejpam-7013	86	53	of	of	ADP
ejpam-7013	86	54	m	m	PRON
ejpam-7013	86	55	,	,	PUNCT
ejpam-7013	86	56	we	we	PRON
ejpam-7013	86	57	deduce	deduce	VERB
ejpam-7013	86	58	lim	lim	PROPN
ejpam-7013	86	59	n→∞	n→∞	PRON
ejpam-7013	86	60	h(t	h(t	PROPN
ejpam-7013	86	61	(	(	PUNCT
ejpam-7013	86	62	ln	ln	PROPN
ejpam-7013	86	63	)	)	PUNCT
ejpam-7013	86	64	,	,	PUNCT
ejpam-7013	86	65	t	t	PROPN
ejpam-7013	86	66	(	(	PUNCT
ejpam-7013	86	67	k	k	NOUN
ejpam-7013	86	68	)	)	PUNCT
ejpam-7013	86	69	)	)	PUNCT
ejpam-7013	87	1	=	=	PUNCT
ejpam-7013	87	2	0	0	X
ejpam-7013	87	3	.	.	PUNCT
ejpam-7013	88	1	since	since	SCONJ
ejpam-7013	88	2	ln+1	ln+1	PROPN
ejpam-7013	88	3	∈	∈	PROPN
ejpam-7013	88	4	t	t	PROPN
ejpam-7013	88	5	(	(	PUNCT
ejpam-7013	88	6	ln	ln	ADJ
ejpam-7013	88	7	)	)	PUNCT
ejpam-7013	88	8	and	and	CCONJ
ejpam-7013	88	9	ln+1	ln+1	PROPN
ejpam-7013	88	10	→	→	SYM
ejpam-7013	89	1	k	k	X
ejpam-7013	89	2	,	,	PUNCT
ejpam-7013	89	3	we	we	PRON
ejpam-7013	89	4	obtain	obtain	VERB
ejpam-7013	89	5	k	k	PROPN
ejpam-7013	89	6	∈	∈	PROPN
ejpam-7013	89	7	t	t	PROPN
ejpam-7013	89	8	(	(	PUNCT
ejpam-7013	89	9	k	k	NOUN
ejpam-7013	89	10	)	)	PUNCT
ejpam-7013	89	11	.	.	PUNCT
ejpam-7013	90	1	therefore	therefore	ADV
ejpam-7013	90	2	,	,	PUNCT
ejpam-7013	90	3	{	{	PUNCT
ejpam-7013	90	4	k	k	NOUN
ejpam-7013	90	5	}	}	PUNCT
ejpam-7013	90	6	⊆	⊆	NUM
ejpam-7013	90	7	t	t	NOUN
ejpam-7013	90	8	(	(	PUNCT
ejpam-7013	90	9	k	k	NOUN
ejpam-7013	90	10	)	)	PUNCT
ejpam-7013	90	11	,	,	PUNCT
ejpam-7013	90	12	proving	prove	VERB
ejpam-7013	90	13	the	the	DET
ejpam-7013	90	14	theorem	theorem	NOUN
ejpam-7013	90	15	.	.	PUNCT
ejpam-7013	91	1	d.	d.	PROPN
ejpam-7013	91	2	gerbeti	gerbeti	PROPN
ejpam-7013	91	3	et	et	PROPN
ejpam-7013	91	4	al	al	PROPN
ejpam-7013	91	5	.	.	PUNCT
ejpam-7013	91	6	/	/	SYM
ejpam-7013	91	7	eur	eur	PROPN
ejpam-7013	91	8	.	.	PUNCT
ejpam-7013	92	1	j.	j.	PROPN
ejpam-7013	92	2	pure	pure	PROPN
ejpam-7013	92	3	appl	appl	PROPN
ejpam-7013	92	4	.	.	PROPN
ejpam-7013	92	5	math	math	PROPN
ejpam-7013	92	6	,	,	PUNCT
ejpam-7013	92	7	18	18	NUM
ejpam-7013	92	8	(	(	PUNCT
ejpam-7013	92	9	4	4	NUM
ejpam-7013	92	10	)	)	PUNCT
ejpam-7013	92	11	(	(	PUNCT
ejpam-7013	92	12	2025	2025	NUM
ejpam-7013	92	13	)	)	PUNCT
ejpam-7013	92	14	,	,	PUNCT
ejpam-7013	92	15	7013	7013	NUM
ejpam-7013	92	16	5	5	NUM
ejpam-7013	92	17	of	of	ADP
ejpam-7013	92	18	17	17	NUM
ejpam-7013	92	19	corollary	corollary	ADJ
ejpam-7013	92	20	1	1	NUM
ejpam-7013	92	21	.	.	PUNCT
ejpam-7013	93	1	if	if	SCONJ
ejpam-7013	93	2	the	the	DET
ejpam-7013	93	3	multivalued	multivalue	VERB
ejpam-7013	93	4	mapping	mapping	NOUN
ejpam-7013	93	5	t	t	NOUN
ejpam-7013	93	6	:	:	PUNCT
ejpam-7013	93	7	x	x	X
ejpam-7013	93	8	→	→	SYM
ejpam-7013	93	9	w	w	PROPN
ejpam-7013	93	10	(	(	PUNCT
ejpam-7013	93	11	x	x	NOUN
ejpam-7013	93	12	)	)	PUNCT
ejpam-7013	93	13	satisfies	satisfy	VERB
ejpam-7013	93	14	the	the	DET
ejpam-7013	93	15	simple	simple	ADJ
ejpam-7013	93	16	hausdorfftype	hausdorfftype	NOUN
ejpam-7013	93	17	contraction	contraction	NOUN
ejpam-7013	93	18	h	h	PROPN
ejpam-7013	93	19	(	(	PUNCT
ejpam-7013	93	20	t	t	PROPN
ejpam-7013	93	21	(	(	PUNCT
ejpam-7013	93	22	l	l	NOUN
ejpam-7013	93	23	)	)	PUNCT
ejpam-7013	93	24	,	,	PUNCT
ejpam-7013	93	25	t	t	PROPN
ejpam-7013	93	26	(	(	PUNCT
ejpam-7013	93	27	p	p	NOUN
ejpam-7013	93	28	)	)	PUNCT
ejpam-7013	93	29	)	)	PUNCT
ejpam-7013	93	30	≤	≤	NOUN
ejpam-7013	93	31	κ	κ	NOUN
ejpam-7013	93	32	d(l	d(l	ADJ
ejpam-7013	93	33	,	,	PUNCT
ejpam-7013	93	34	p	p	NOUN
ejpam-7013	93	35	)	)	PUNCT
ejpam-7013	93	36	for	for	ADP
ejpam-7013	93	37	all	all	DET
ejpam-7013	93	38	l	l	NOUN
ejpam-7013	93	39	,	,	PUNCT
ejpam-7013	93	40	p	p	PROPN
ejpam-7013	93	41	∈	∈	PROPN
ejpam-7013	93	42	x	x	X
ejpam-7013	93	43	,	,	PUNCT
ejpam-7013	93	44	for	for	ADP
ejpam-7013	93	45	some	some	DET
ejpam-7013	93	46	constant	constant	ADJ
ejpam-7013	93	47	0	0	NUM
ejpam-7013	93	48	≤	≤	NUM
ejpam-7013	93	49	κ	κ	X
ejpam-7013	93	50	<	<	X
ejpam-7013	93	51	1	1	NUM
ejpam-7013	93	52	,	,	PUNCT
ejpam-7013	93	53	then	then	ADV
ejpam-7013	93	54	t	t	PROPN
ejpam-7013	93	55	has	have	VERB
ejpam-7013	93	56	a	a	DET
ejpam-7013	93	57	fuzzy	fuzzy	ADJ
ejpam-7013	93	58	fp	fp	X
ejpam-7013	93	59	(	(	PUNCT
ejpam-7013	93	60	i.e.	i.e.	X
ejpam-7013	93	61	there	there	PRON
ejpam-7013	93	62	exists	exist	VERB
ejpam-7013	93	63	k	k	PROPN
ejpam-7013	93	64	∈	∈	PROPN
ejpam-7013	93	65	x	x	PUNCT
ejpam-7013	93	66	with	with	ADP
ejpam-7013	93	67	{	{	PUNCT
ejpam-7013	93	68	k	k	NOUN
ejpam-7013	93	69	}	}	PUNCT
ejpam-7013	93	70	⊆	⊆	NUM
ejpam-7013	93	71	t	t	NOUN
ejpam-7013	93	72	(	(	PUNCT
ejpam-7013	93	73	k	k	NOUN
ejpam-7013	93	74	)	)	PUNCT
ejpam-7013	93	75	)	)	PUNCT
ejpam-7013	93	76	.	.	PUNCT
ejpam-7013	94	1	proof	proof	NOUN
ejpam-7013	94	2	.	.	PUNCT
ejpam-7013	95	1	choose	choose	VERB
ejpam-7013	95	2	constants	constant	NOUN
ejpam-7013	95	3	in	in	ADP
ejpam-7013	95	4	the	the	DET
ejpam-7013	95	5	theorem	theorem	NOUN
ejpam-7013	95	6	as	as	ADP
ejpam-7013	95	7	λ1	λ1	PROPN
ejpam-7013	95	8	=	=	SYM
ejpam-7013	95	9	λ2	λ2	PROPN
ejpam-7013	95	10	=	=	SYM
ejpam-7013	95	11	λ3	λ3	PROPN
ejpam-7013	95	12	=	=	SYM
ejpam-7013	95	13	0	0	NUM
ejpam-7013	95	14	and	and	CCONJ
ejpam-7013	95	15	λ4	λ4	PROPN
ejpam-7013	95	16	=	=	SYM
ejpam-7013	96	1	κ	κ	X
ejpam-7013	96	2	.	.	PUNCT
ejpam-7013	97	1	the	the	DET
ejpam-7013	97	2	hypotheses	hypothesis	NOUN
ejpam-7013	97	3	of	of	ADP
ejpam-7013	97	4	the	the	DET
ejpam-7013	97	5	theorem	theorem	NOUN
ejpam-7013	97	6	are	be	AUX
ejpam-7013	97	7	satisfied	satisfied	ADJ
ejpam-7013	97	8	because	because	SCONJ
ejpam-7013	97	9	λ4	λ4	PROPN
ejpam-7013	97	10	=	=	PROPN
ejpam-7013	97	11	κ	κ	X
ejpam-7013	97	12	<	<	X
ejpam-7013	97	13	1	1	NUM
ejpam-7013	97	14	and	and	CCONJ
ejpam-7013	97	15	the	the	DET
ejpam-7013	97	16	other	other	ADJ
ejpam-7013	97	17	inequalities	inequality	NOUN
ejpam-7013	97	18	reduce	reduce	VERB
ejpam-7013	97	19	trivially	trivially	ADV
ejpam-7013	97	20	.	.	PUNCT
ejpam-7013	98	1	the	the	DET
ejpam-7013	98	2	contractive	contractive	ADJ
ejpam-7013	98	3	condition	condition	NOUN
ejpam-7013	98	4	in	in	ADP
ejpam-7013	98	5	the	the	DET
ejpam-7013	98	6	theorem	theorem	NOUN
ejpam-7013	98	7	becomes	become	VERB
ejpam-7013	98	8	the	the	DET
ejpam-7013	98	9	displayed	displayed	ADJ
ejpam-7013	98	10	inequality	inequality	NOUN
ejpam-7013	98	11	above	above	ADV
ejpam-7013	98	12	.	.	PUNCT
ejpam-7013	99	1	hence	hence	ADV
ejpam-7013	99	2	the	the	DET
ejpam-7013	99	3	conclusion	conclusion	NOUN
ejpam-7013	99	4	of	of	ADP
ejpam-7013	99	5	the	the	DET
ejpam-7013	99	6	theorem	theorem	NOUN
ejpam-7013	99	7	applies	applie	NOUN
ejpam-7013	99	8	and	and	CCONJ
ejpam-7013	99	9	t	t	PROPN
ejpam-7013	99	10	admits	admit	VERB
ejpam-7013	99	11	a	a	DET
ejpam-7013	99	12	fuzzy	fuzzy	ADJ
ejpam-7013	99	13	fp	fp	NOUN
ejpam-7013	99	14	.	.	PROPN
ejpam-7013	99	15	theorem	theorem	PROPN
ejpam-7013	99	16	2	2	NUM
ejpam-7013	99	17	.	.	PUNCT
ejpam-7013	100	1	let	let	VERB
ejpam-7013	100	2	(	(	PUNCT
ejpam-7013	100	3	x	x	X
ejpam-7013	100	4	,	,	PUNCT
ejpam-7013	100	5	m	m	PROPN
ejpam-7013	100	6	,	,	PUNCT
ejpam-7013	100	7	∗	∗	NOUN
ejpam-7013	100	8	)	)	PUNCT
ejpam-7013	100	9	be	be	VERB
ejpam-7013	100	10	a	a	DET
ejpam-7013	100	11	complete	complete	ADJ
ejpam-7013	100	12	b	b	NOUN
ejpam-7013	100	13	-	-	PUNCT
ejpam-7013	100	14	fms	fms	PROPN
ejpam-7013	100	15	whose	whose	DET
ejpam-7013	100	16	underlying	underlying	ADJ
ejpam-7013	100	17	b	b	X
ejpam-7013	100	18	-	-	ADJ
ejpam-7013	100	19	metric	metric	ADJ
ejpam-7013	100	20	is	be	AUX
ejpam-7013	100	21	d	d	NOUN
ejpam-7013	100	22	:	:	PUNCT
ejpam-7013	100	23	x×x	x×x	PROPN
ejpam-7013	100	24	→	→	PUNCT
ejpam-7013	100	25	[	[	X
ejpam-7013	100	26	0,∞	0,∞	NOUN
ejpam-7013	100	27	)	)	PUNCT
ejpam-7013	100	28	with	with	ADP
ejpam-7013	100	29	constant	constant	ADJ
ejpam-7013	100	30	s	s	PART
ejpam-7013	100	31	≥	≥	NOUN
ejpam-7013	100	32	1	1	NUM
ejpam-7013	100	33	.	.	PUNCT
ejpam-7013	101	1	let	let	VERB
ejpam-7013	101	2	t	t	NOUN
ejpam-7013	101	3	:	:	PUNCT
ejpam-7013	101	4	x	x	X
ejpam-7013	101	5	→	→	SYM
ejpam-7013	101	6	w(x	w(x	NOUN
ejpam-7013	101	7	)	)	PUNCT
ejpam-7013	101	8	be	be	AUX
ejpam-7013	101	9	a	a	DET
ejpam-7013	101	10	multivalued	multivalued	ADJ
ejpam-7013	101	11	(	(	PUNCT
ejpam-7013	101	12	fuzzy	fuzzy	ADJ
ejpam-7013	101	13	)	)	PUNCT
ejpam-7013	101	14	mapping	mapping	NOUN
ejpam-7013	101	15	.	.	PUNCT
ejpam-7013	102	1	assume	assume	VERB
ejpam-7013	102	2	there	there	PRON
ejpam-7013	102	3	exist	exist	VERB
ejpam-7013	102	4	constants	constant	NOUN
ejpam-7013	102	5	λ1,λ2,λ3	λ1,λ2,λ3	X
ejpam-7013	102	6	≥	≥	X
ejpam-7013	102	7	0	0	NUM
ejpam-7013	102	8	such	such	ADJ
ejpam-7013	102	9	that	that	PRON
ejpam-7013	102	10	for	for	ADP
ejpam-7013	102	11	all	all	DET
ejpam-7013	102	12	l	l	NOUN
ejpam-7013	102	13	,	,	PUNCT
ejpam-7013	103	1	p	p	PROPN
ejpam-7013	103	2	∈	∈	PROPN
ejpam-7013	103	3	x	x	INTJ
ejpam-7013	103	4	h	h	NOUN
ejpam-7013	103	5	(	(	PUNCT
ejpam-7013	103	6	t	t	PROPN
ejpam-7013	103	7	(	(	PUNCT
ejpam-7013	103	8	l	l	NOUN
ejpam-7013	103	9	)	)	PUNCT
ejpam-7013	103	10	,	,	PUNCT
ejpam-7013	103	11	t	t	PROPN
ejpam-7013	103	12	(	(	PUNCT
ejpam-7013	103	13	p	p	NOUN
ejpam-7013	103	14	)	)	PUNCT
ejpam-7013	103	15	)	)	PUNCT
ejpam-7013	103	16	≤	≤	NOUN
ejpam-7013	104	1	λ1	λ1	PROPN
ejpam-7013	104	2	(	(	PUNCT
ejpam-7013	104	3	dα(l	dα(l	PROPN
ejpam-7013	104	4	,	,	PUNCT
ejpam-7013	104	5	t	t	PROPN
ejpam-7013	104	6	(	(	PUNCT
ejpam-7013	104	7	p	p	NOUN
ejpam-7013	104	8	)	)	PUNCT
ejpam-7013	104	9	)	)	PUNCT
ejpam-7013	105	1	+	+	ADV
ejpam-7013	105	2	dα(p	dα(p	NOUN
ejpam-7013	105	3	,	,	PUNCT
ejpam-7013	105	4	t	t	PROPN
ejpam-7013	105	5	(	(	PUNCT
ejpam-7013	105	6	l	l	NOUN
ejpam-7013	105	7	)	)	PUNCT
ejpam-7013	105	8	)	)	PUNCT
ejpam-7013	105	9	)	)	PUNCT
ejpam-7013	106	1	+	+	CCONJ
ejpam-7013	106	2	λ2dα(l	λ2dα(l	PROPN
ejpam-7013	106	3	,	,	PUNCT
ejpam-7013	106	4	t	t	PROPN
ejpam-7013	106	5	(	(	PUNCT
ejpam-7013	106	6	l	l	NOUN
ejpam-7013	106	7	)	)	PUNCT
ejpam-7013	106	8	)	)	PUNCT
ejpam-7013	107	1	+	+	CCONJ
ejpam-7013	107	2	λ3	λ3	PROPN
ejpam-7013	107	3	d(l	d(l	ADJ
ejpam-7013	107	4	,	,	PUNCT
ejpam-7013	107	5	p	p	NOUN
ejpam-7013	107	6	)	)	PUNCT
ejpam-7013	107	7	,	,	PUNCT
ejpam-7013	107	8	and	and	CCONJ
ejpam-7013	107	9	suppose	suppose	VERB
ejpam-7013	107	10	the	the	DET
ejpam-7013	107	11	parameters	parameter	NOUN
ejpam-7013	107	12	satisfy	satisfy	VERB
ejpam-7013	107	13	λ1s	λ1s	X
ejpam-7013	107	14	<	<	X
ejpam-7013	107	15	1	1	NUM
ejpam-7013	107	16	,	,	PUNCT
ejpam-7013	107	17	2λ1s+	2λ1s+	NUM
ejpam-7013	107	18	λ2	λ2	NOUN
ejpam-7013	108	1	+	+	CCONJ
ejpam-7013	109	1	λ3	λ3	PROPN
ejpam-7013	109	2	<	<	X
ejpam-7013	109	3	1	1	NUM
ejpam-7013	109	4	.	.	PUNCT
ejpam-7013	110	1	then	then	ADV
ejpam-7013	110	2	t	t	PROPN
ejpam-7013	110	3	has	have	VERB
ejpam-7013	110	4	a	a	DET
ejpam-7013	110	5	fuzzy	fuzzy	ADJ
ejpam-7013	110	6	fp	fp	NOUN
ejpam-7013	110	7	:	:	PUNCT
ejpam-7013	110	8	there	there	PRON
ejpam-7013	110	9	exists	exist	VERB
ejpam-7013	110	10	k	k	PROPN
ejpam-7013	110	11	∈	∈	PROPN
ejpam-7013	110	12	x	x	PUNCT
ejpam-7013	110	13	with	with	ADP
ejpam-7013	110	14	{	{	PUNCT
ejpam-7013	110	15	k	k	NOUN
ejpam-7013	110	16	}	}	PUNCT
ejpam-7013	110	17	⊆	⊆	NUM
ejpam-7013	110	18	t	t	NOUN
ejpam-7013	110	19	(	(	PUNCT
ejpam-7013	110	20	k	k	NOUN
ejpam-7013	110	21	)	)	PUNCT
ejpam-7013	110	22	.	.	PUNCT
ejpam-7013	111	1	proof	proof	NOUN
ejpam-7013	111	2	.	.	PUNCT
ejpam-7013	112	1	let	let	VERB
ejpam-7013	112	2	l0	l0	PROPN
ejpam-7013	112	3	∈	∈	PROPN
ejpam-7013	112	4	x	x	AUX
ejpam-7013	112	5	be	be	AUX
ejpam-7013	112	6	arbitrary	arbitrary	ADJ
ejpam-7013	112	7	and	and	CCONJ
ejpam-7013	112	8	choose	choose	VERB
ejpam-7013	112	9	l1	l1	PROPN
ejpam-7013	112	10	∈	∈	PROPN
ejpam-7013	112	11	t	t	PROPN
ejpam-7013	112	12	(	(	PUNCT
ejpam-7013	112	13	l0	l0	PROPN
ejpam-7013	112	14	)	)	PUNCT
ejpam-7013	112	15	.	.	PUNCT
ejpam-7013	113	1	having	having	AUX
ejpam-7013	113	2	chosen	choose	VERB
ejpam-7013	113	3	ln	ln	PROPN
ejpam-7013	113	4	∈	∈	PROPN
ejpam-7013	113	5	x	x	PUNCT
ejpam-7013	113	6	pick	pick	VERB
ejpam-7013	113	7	ln+1	ln+1	PROPN
ejpam-7013	113	8	∈	∈	PROPN
ejpam-7013	113	9	t	t	PROPN
ejpam-7013	113	10	(	(	PUNCT
ejpam-7013	113	11	ln	ln	ADJ
ejpam-7013	113	12	)	)	PUNCT
ejpam-7013	113	13	for	for	ADP
ejpam-7013	113	14	each	each	DET
ejpam-7013	113	15	n	n	PRON
ejpam-7013	113	16	≥	≥	NOUN
ejpam-7013	113	17	0	0	NUM
ejpam-7013	113	18	.	.	PUNCT
ejpam-7013	114	1	additionally	additionally	ADV
ejpam-7013	114	2	,	,	PUNCT
ejpam-7013	114	3	for	for	SCONJ
ejpam-7013	114	4	every	every	DET
ejpam-7013	114	5	n	n	NOUN
ejpam-7013	114	6	choose	choose	VERB
ejpam-7013	114	7	ln+2	ln+2	NUM
ejpam-7013	114	8	∈	∈	PROPN
ejpam-7013	114	9	t	t	PROPN
ejpam-7013	114	10	(	(	PUNCT
ejpam-7013	114	11	ln+1	ln+1	PROPN
ejpam-7013	114	12	)	)	PUNCT
ejpam-7013	114	13	so	so	SCONJ
ejpam-7013	114	14	that	that	SCONJ
ejpam-7013	114	15	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	114	16	)	)	PUNCT
ejpam-7013	114	17	≤	≤	NUM
ejpam-7013	114	18	h	h	NOUN
ejpam-7013	114	19	(	(	PUNCT
ejpam-7013	114	20	t	t	PROPN
ejpam-7013	114	21	(	(	PUNCT
ejpam-7013	114	22	ln	ln	PROPN
ejpam-7013	114	23	)	)	PUNCT
ejpam-7013	114	24	,	,	PUNCT
ejpam-7013	114	25	t	t	PROPN
ejpam-7013	114	26	(	(	PUNCT
ejpam-7013	114	27	ln+1	ln+1	PROPN
ejpam-7013	114	28	)	)	PUNCT
ejpam-7013	114	29	)	)	PUNCT
ejpam-7013	115	1	+	+	CCONJ
ejpam-7013	116	1	εn	εn	ADJ
ejpam-7013	116	2	,	,	PUNCT
ejpam-7013	116	3	(	(	PUNCT
ejpam-7013	116	4	1	1	X
ejpam-7013	116	5	)	)	PUNCT
ejpam-7013	116	6	where	where	SCONJ
ejpam-7013	116	7	(	(	PUNCT
ejpam-7013	116	8	εn	εn	ADJ
ejpam-7013	116	9	)	)	PUNCT
ejpam-7013	116	10	is	be	AUX
ejpam-7013	116	11	a	a	DET
ejpam-7013	116	12	sequence	sequence	NOUN
ejpam-7013	116	13	of	of	ADP
ejpam-7013	116	14	positive	positive	ADJ
ejpam-7013	116	15	numbers	number	NOUN
ejpam-7013	116	16	tending	tend	VERB
ejpam-7013	116	17	to	to	ADP
ejpam-7013	116	18	0	0	NUM
ejpam-7013	116	19	.	.	PUNCT
ejpam-7013	117	1	such	such	DET
ejpam-7013	117	2	a	a	DET
ejpam-7013	117	3	choice	choice	NOUN
ejpam-7013	117	4	is	be	AUX
ejpam-7013	117	5	always	always	ADV
ejpam-7013	117	6	possible	possible	ADJ
ejpam-7013	117	7	by	by	ADP
ejpam-7013	117	8	definition	definition	NOUN
ejpam-7013	117	9	of	of	ADP
ejpam-7013	117	10	the	the	DET
ejpam-7013	117	11	hausdorff	hausdorff	NOUN
ejpam-7013	117	12	distance	distance	NOUN
ejpam-7013	117	13	(	(	PUNCT
ejpam-7013	117	14	for	for	ADP
ejpam-7013	117	15	each	each	DET
ejpam-7013	117	16	point	point	NOUN
ejpam-7013	117	17	of	of	ADP
ejpam-7013	117	18	t	t	PROPN
ejpam-7013	117	19	(	(	PUNCT
ejpam-7013	117	20	ln	ln	ADJ
ejpam-7013	117	21	)	)	PUNCT
ejpam-7013	117	22	there	there	PRON
ejpam-7013	117	23	exists	exist	VERB
ejpam-7013	117	24	a	a	DET
ejpam-7013	117	25	point	point	NOUN
ejpam-7013	117	26	of	of	ADP
ejpam-7013	117	27	t	t	PROPN
ejpam-7013	117	28	(	(	PUNCT
ejpam-7013	117	29	ln+1	ln+1	PROPN
ejpam-7013	117	30	)	)	PUNCT
ejpam-7013	117	31	within	within	ADP
ejpam-7013	117	32	h(t	h(t	PROPN
ejpam-7013	117	33	(	(	PUNCT
ejpam-7013	117	34	ln	ln	PROPN
ejpam-7013	117	35	)	)	PUNCT
ejpam-7013	117	36	,	,	PUNCT
ejpam-7013	117	37	t	t	PROPN
ejpam-7013	117	38	(	(	PUNCT
ejpam-7013	117	39	ln+1	ln+1	PROPN
ejpam-7013	117	40	)	)	PUNCT
ejpam-7013	117	41	)	)	PUNCT
ejpam-7013	118	1	+	+	CCONJ
ejpam-7013	118	2	εn	εn	ADJ
ejpam-7013	118	3	)	)	PUNCT
ejpam-7013	118	4	.	.	PUNCT
ejpam-7013	119	1	put	put	VERB
ejpam-7013	119	2	sn	sn	PROPN
ejpam-7013	119	3	:	:	PUNCT
ejpam-7013	119	4	=	=	SYM
ejpam-7013	119	5	d(ln	d(ln	PROPN
ejpam-7013	119	6	,	,	PUNCT
ejpam-7013	119	7	ln+1	ln+1	PROPN
ejpam-7013	119	8	)	)	PUNCT
ejpam-7013	119	9	for	for	ADP
ejpam-7013	119	10	n	n	PRON
ejpam-7013	119	11	≥	≥	NOUN
ejpam-7013	119	12	0	0	NUM
ejpam-7013	119	13	.	.	PUNCT
ejpam-7013	119	14	apply	apply	VERB
ejpam-7013	119	15	the	the	DET
ejpam-7013	119	16	contractive	contractive	ADJ
ejpam-7013	119	17	hypothesis	hypothesis	NOUN
ejpam-7013	119	18	with	with	ADP
ejpam-7013	119	19	l	l	NOUN
ejpam-7013	119	20	=	=	PUNCT
ejpam-7013	119	21	ln	ln	ADJ
ejpam-7013	119	22	and	and	CCONJ
ejpam-7013	119	23	p	p	X
ejpam-7013	119	24	=	=	PUNCT
ejpam-7013	119	25	ln+1	ln+1	ADJ
ejpam-7013	119	26	to	to	PART
ejpam-7013	119	27	get	get	VERB
ejpam-7013	119	28	h	h	NOUN
ejpam-7013	119	29	(	(	PUNCT
ejpam-7013	119	30	t	t	PROPN
ejpam-7013	119	31	(	(	PUNCT
ejpam-7013	119	32	ln	ln	PROPN
ejpam-7013	119	33	)	)	PUNCT
ejpam-7013	119	34	,	,	PUNCT
ejpam-7013	119	35	t	t	PROPN
ejpam-7013	119	36	(	(	PUNCT
ejpam-7013	119	37	ln+1	ln+1	PROPN
ejpam-7013	119	38	)	)	PUNCT
ejpam-7013	119	39	)	)	PUNCT
ejpam-7013	120	1	≤	≤	NOUN
ejpam-7013	120	2	λ1	λ1	PROPN
ejpam-7013	120	3	(	(	PUNCT
ejpam-7013	120	4	dα(ln	dα(ln	PROPN
ejpam-7013	120	5	,	,	PUNCT
ejpam-7013	120	6	t	t	PROPN
ejpam-7013	120	7	(	(	PUNCT
ejpam-7013	120	8	ln+1))+dα(ln+1	ln+1))+dα(ln+1	PROPN
ejpam-7013	120	9	,	,	PUNCT
ejpam-7013	120	10	t	t	PROPN
ejpam-7013	120	11	(	(	PUNCT
ejpam-7013	120	12	ln	ln	ADJ
ejpam-7013	120	13	)	)	PUNCT
ejpam-7013	120	14	)	)	PUNCT
ejpam-7013	120	15	)	)	PUNCT
ejpam-7013	121	1	+	+	PUNCT
ejpam-7013	121	2	λ2dα(ln	λ2dα(ln	NOUN
ejpam-7013	121	3	,	,	PUNCT
ejpam-7013	121	4	t	t	PROPN
ejpam-7013	121	5	(	(	PUNCT
ejpam-7013	121	6	ln))+λ3sn	ln))+λ3sn	PROPN
ejpam-7013	121	7	.	.	PUNCT
ejpam-7013	121	8	since	since	SCONJ
ejpam-7013	121	9	ln+1	ln+1	PROPN
ejpam-7013	121	10	∈	∈	PROPN
ejpam-7013	121	11	t	t	PROPN
ejpam-7013	121	12	(	(	PUNCT
ejpam-7013	121	13	ln	ln	X
ejpam-7013	121	14	)	)	PUNCT
ejpam-7013	121	15	we	we	PRON
ejpam-7013	121	16	have	have	VERB
ejpam-7013	121	17	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	121	18	,	,	PUNCT
ejpam-7013	121	19	t	t	PROPN
ejpam-7013	121	20	(	(	PUNCT
ejpam-7013	121	21	ln	ln	ADJ
ejpam-7013	121	22	)	)	PUNCT
ejpam-7013	121	23	)	)	PUNCT
ejpam-7013	122	1	=	=	PUNCT
ejpam-7013	122	2	0	0	X
ejpam-7013	122	3	.	.	PUNCT
ejpam-7013	122	4	also	also	ADV
ejpam-7013	122	5	dα(ln	dα(ln	PROPN
ejpam-7013	122	6	,	,	PUNCT
ejpam-7013	122	7	t	t	PROPN
ejpam-7013	122	8	(	(	PUNCT
ejpam-7013	122	9	ln	ln	ADJ
ejpam-7013	122	10	)	)	PUNCT
ejpam-7013	122	11	)	)	PUNCT
ejpam-7013	122	12	≤	≤	NUM
ejpam-7013	122	13	sn	sn	PROPN
ejpam-7013	122	14	.	.	PUNCT
ejpam-7013	123	1	moreover	moreover	ADV
ejpam-7013	123	2	,	,	PUNCT
ejpam-7013	123	3	because	because	SCONJ
ejpam-7013	123	4	ln+2	ln+2	NUM
ejpam-7013	123	5	∈	∈	PROPN
ejpam-7013	123	6	t	t	PROPN
ejpam-7013	123	7	(	(	PUNCT
ejpam-7013	123	8	ln+1	ln+1	PROPN
ejpam-7013	123	9	)	)	PUNCT
ejpam-7013	123	10	,	,	PUNCT
ejpam-7013	123	11	dα(ln	dα(ln	PROPN
ejpam-7013	123	12	,	,	PUNCT
ejpam-7013	123	13	t	t	PROPN
ejpam-7013	123	14	(	(	PUNCT
ejpam-7013	123	15	ln+1	ln+1	PROPN
ejpam-7013	123	16	)	)	PUNCT
ejpam-7013	123	17	)	)	PUNCT
ejpam-7013	124	1	≤	≤	PROPN
ejpam-7013	124	2	d(ln	d(ln	PROPN
ejpam-7013	124	3	,	,	PUNCT
ejpam-7013	124	4	ln+2	ln+2	NUM
ejpam-7013	124	5	)	)	PUNCT
ejpam-7013	124	6	.	.	PUNCT
ejpam-7013	125	1	using	use	VERB
ejpam-7013	125	2	the	the	DET
ejpam-7013	125	3	b	b	NOUN
ejpam-7013	125	4	-	-	PUNCT
ejpam-7013	125	5	metric	metric	ADJ
ejpam-7013	125	6	inequality	inequality	PROPN
ejpam-7013	125	7	d(ln	d(ln	PROPN
ejpam-7013	125	8	,	,	PUNCT
ejpam-7013	125	9	ln+2	ln+2	NUM
ejpam-7013	125	10	)	)	PUNCT
ejpam-7013	125	11	≤	≤	NOUN
ejpam-7013	125	12	s	s	PART
ejpam-7013	125	13	(	(	PUNCT
ejpam-7013	125	14	d(ln	d(ln	PROPN
ejpam-7013	125	15	,	,	PUNCT
ejpam-7013	125	16	ln+1	ln+1	ADJ
ejpam-7013	125	17	)	)	PUNCT
ejpam-7013	125	18	+	+	CCONJ
ejpam-7013	125	19	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	125	20	)	)	PUNCT
ejpam-7013	125	21	)	)	PUNCT
ejpam-7013	126	1	=	=	PUNCT
ejpam-7013	126	2	s(sn	s(sn	PROPN
ejpam-7013	126	3	+	+	CCONJ
ejpam-7013	126	4	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	126	5	)	)	PUNCT
ejpam-7013	126	6	)	)	PUNCT
ejpam-7013	126	7	,	,	PUNCT
ejpam-7013	126	8	we	we	PRON
ejpam-7013	126	9	obtain	obtain	VERB
ejpam-7013	126	10	h	h	NOUN
ejpam-7013	126	11	(	(	PUNCT
ejpam-7013	126	12	t	t	PROPN
ejpam-7013	126	13	(	(	PUNCT
ejpam-7013	126	14	ln	ln	PROPN
ejpam-7013	126	15	)	)	PUNCT
ejpam-7013	126	16	,	,	PUNCT
ejpam-7013	126	17	t	t	PROPN
ejpam-7013	126	18	(	(	PUNCT
ejpam-7013	126	19	ln+1	ln+1	PROPN
ejpam-7013	126	20	)	)	PUNCT
ejpam-7013	126	21	)	)	PUNCT
ejpam-7013	127	1	≤	≤	NUM
ejpam-7013	127	2	λ1s	λ1s	NOUN
ejpam-7013	127	3	(	(	PUNCT
ejpam-7013	127	4	sn	sn	PROPN
ejpam-7013	127	5	+	+	CCONJ
ejpam-7013	127	6	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	127	7	)	)	PUNCT
ejpam-7013	127	8	)	)	PUNCT
ejpam-7013	128	1	+	+	CCONJ
ejpam-7013	128	2	λ2sn	λ2sn	X
ejpam-7013	128	3	+	+	CCONJ
ejpam-7013	128	4	λ3sn	λ3sn	PUNCT
ejpam-7013	128	5	.	.	PUNCT
ejpam-7013	129	1	d.	d.	PROPN
ejpam-7013	129	2	gerbeti	gerbeti	PROPN
ejpam-7013	129	3	et	et	PROPN
ejpam-7013	129	4	al	al	PROPN
ejpam-7013	129	5	.	.	PUNCT
ejpam-7013	129	6	/	/	SYM
ejpam-7013	129	7	eur	eur	PROPN
ejpam-7013	129	8	.	.	PUNCT
ejpam-7013	130	1	j.	j.	PROPN
ejpam-7013	130	2	pure	pure	PROPN
ejpam-7013	130	3	appl	appl	PROPN
ejpam-7013	130	4	.	.	PROPN
ejpam-7013	130	5	math	math	PROPN
ejpam-7013	130	6	,	,	PUNCT
ejpam-7013	130	7	18	18	NUM
ejpam-7013	130	8	(	(	PUNCT
ejpam-7013	130	9	4	4	NUM
ejpam-7013	130	10	)	)	PUNCT
ejpam-7013	130	11	(	(	PUNCT
ejpam-7013	130	12	2025	2025	NUM
ejpam-7013	130	13	)	)	PUNCT
ejpam-7013	130	14	,	,	PUNCT
ejpam-7013	130	15	7013	7013	NUM
ejpam-7013	130	16	6	6	NUM
ejpam-7013	130	17	of	of	ADP
ejpam-7013	130	18	17	17	NUM
ejpam-7013	130	19	combine	combine	VERB
ejpam-7013	130	20	this	this	PRON
ejpam-7013	130	21	with	with	ADP
ejpam-7013	130	22	(	(	PUNCT
ejpam-7013	130	23	1	1	NUM
ejpam-7013	130	24	)	)	PUNCT
ejpam-7013	130	25	to	to	ADP
ejpam-7013	130	26	bound	bind	VERB
ejpam-7013	130	27	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	130	28	):	):	PUNCT
ejpam-7013	130	29	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	130	30	)	)	PUNCT
ejpam-7013	130	31	≤	≤	NOUN
ejpam-7013	130	32	λ1s	λ1s	PROPN
ejpam-7013	130	33	(	(	PUNCT
ejpam-7013	130	34	sn	sn	PROPN
ejpam-7013	130	35	+	+	CCONJ
ejpam-7013	130	36	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	130	37	)	)	PUNCT
ejpam-7013	130	38	)	)	PUNCT
ejpam-7013	131	1	+	+	CCONJ
ejpam-7013	131	2	(	(	PUNCT
ejpam-7013	131	3	λ2	λ2	NOUN
ejpam-7013	131	4	+	+	CCONJ
ejpam-7013	131	5	λ3)sn	λ3)sn	PROPN
ejpam-7013	131	6	+	+	CCONJ
ejpam-7013	131	7	εn	εn	ADJ
ejpam-7013	131	8	.	.	PUNCT
ejpam-7013	131	9	collect	collect	VERB
ejpam-7013	131	10	terms	term	NOUN
ejpam-7013	131	11	with	with	ADP
ejpam-7013	131	12	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	131	13	)	)	PUNCT
ejpam-7013	131	14	on	on	ADP
ejpam-7013	131	15	the	the	DET
ejpam-7013	131	16	left	left	NOUN
ejpam-7013	131	17	:(	:(	X
ejpam-7013	131	18	1−	1−	NUM
ejpam-7013	131	19	λ1s	λ1s	NOUN
ejpam-7013	131	20	)	)	PUNCT
ejpam-7013	131	21	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	131	22	)	)	PUNCT
ejpam-7013	131	23	≤	≤	NOUN
ejpam-7013	131	24	(	(	PUNCT
ejpam-7013	131	25	λ1s+	λ1s+	X
ejpam-7013	131	26	λ2	λ2	NOUN
ejpam-7013	131	27	+	+	CCONJ
ejpam-7013	131	28	λ3	λ3	PROPN
ejpam-7013	131	29	)	)	PUNCT
ejpam-7013	131	30	sn	sn	PROPN
ejpam-7013	131	31	+	+	CCONJ
ejpam-7013	131	32	εn	εn	ADJ
ejpam-7013	131	33	.	.	PUNCT
ejpam-7013	132	1	by	by	ADP
ejpam-7013	132	2	the	the	DET
ejpam-7013	132	3	assumption	assumption	NOUN
ejpam-7013	132	4	λ1s	λ1s	X
ejpam-7013	132	5	<	<	X
ejpam-7013	132	6	1	1	NUM
ejpam-7013	132	7	we	we	PRON
ejpam-7013	132	8	may	may	AUX
ejpam-7013	132	9	divide	divide	VERB
ejpam-7013	132	10	by	by	ADP
ejpam-7013	132	11	1−	1−	NUM
ejpam-7013	132	12	λ1s	λ1s	NOUN
ejpam-7013	132	13	>	>	X
ejpam-7013	132	14	0	0	NUM
ejpam-7013	132	15	to	to	PART
ejpam-7013	132	16	obtain	obtain	VERB
ejpam-7013	132	17	sn+1	sn+1	NOUN
ejpam-7013	132	18	≤	≤	PUNCT
ejpam-7013	132	19	q	q	PROPN
ejpam-7013	132	20	sn	sn	PROPN
ejpam-7013	132	21	+	+	CCONJ
ejpam-7013	132	22	εn	εn	ADJ
ejpam-7013	132	23	1−	1−	NUM
ejpam-7013	132	24	λ1s	λ1s	NOUN
ejpam-7013	132	25	,	,	PUNCT
ejpam-7013	132	26	where	where	SCONJ
ejpam-7013	132	27	q	q	X
ejpam-7013	132	28	:	:	PUNCT
ejpam-7013	133	1	=	=	SYM
ejpam-7013	133	2	λ1s+	λ1s+	X
ejpam-7013	133	3	λ2	λ2	NOUN
ejpam-7013	134	1	+	+	CCONJ
ejpam-7013	135	1	λ3	λ3	PROPN
ejpam-7013	135	2	1−	1−	NUM
ejpam-7013	135	3	λ1s	λ1s	NOUN
ejpam-7013	135	4	.	.	PUNCT
ejpam-7013	136	1	the	the	DET
ejpam-7013	136	2	parameter	parameter	NOUN
ejpam-7013	136	3	condition	condition	NOUN
ejpam-7013	136	4	2λ1s+	2λ1s+	NUM
ejpam-7013	137	1	λ2	λ2	NOUN
ejpam-7013	138	1	+	+	CCONJ
ejpam-7013	139	1	λ3	λ3	PROPN
ejpam-7013	139	2	<	<	X
ejpam-7013	139	3	1	1	NUM
ejpam-7013	139	4	ensures	ensure	VERB
ejpam-7013	139	5	that	that	SCONJ
ejpam-7013	139	6	q	q	PUNCT
ejpam-7013	139	7	∈	∈	PROPN
ejpam-7013	140	1	[	[	X
ejpam-7013	140	2	0	0	NUM
ejpam-7013	140	3	,	,	PUNCT
ejpam-7013	140	4	1	1	NUM
ejpam-7013	140	5	)	)	PUNCT
ejpam-7013	140	6	.	.	PUNCT
ejpam-7013	141	1	indeed	indeed	ADV
ejpam-7013	141	2	,	,	PUNCT
ejpam-7013	141	3	q	q	X
ejpam-7013	141	4	<	<	X
ejpam-7013	141	5	1	1	NUM
ejpam-7013	141	6	⇐	⇐	ADJ
ejpam-7013	141	7	⇒	⇒	NOUN
ejpam-7013	141	8	λ1s+	λ1s+	X
ejpam-7013	141	9	λ2	λ2	NOUN
ejpam-7013	141	10	+	+	CCONJ
ejpam-7013	141	11	λ3	λ3	PROPN
ejpam-7013	141	12	<	<	X
ejpam-7013	141	13	1−	1−	NUM
ejpam-7013	141	14	λ1s	λ1s	ADJ
ejpam-7013	141	15	⇐	⇐	ADJ
ejpam-7013	141	16	⇒	⇒	NOUN
ejpam-7013	141	17	2λ1s+	2λ1s+	NUM
ejpam-7013	141	18	λ2	λ2	NOUN
ejpam-7013	142	1	+	+	CCONJ
ejpam-7013	143	1	λ3	λ3	PROPN
ejpam-7013	143	2	<	<	X
ejpam-7013	143	3	1	1	NUM
ejpam-7013	143	4	.	.	PUNCT
ejpam-7013	144	1	since	since	SCONJ
ejpam-7013	144	2	εn	εn	ADJ
ejpam-7013	144	3	→	→	SYM
ejpam-7013	144	4	0	0	NUM
ejpam-7013	144	5	and	and	CCONJ
ejpam-7013	144	6	q	q	NOUN
ejpam-7013	144	7	∈	∈	PROPN
ejpam-7013	144	8	[	[	X
ejpam-7013	144	9	0	0	NUM
ejpam-7013	144	10	,	,	PUNCT
ejpam-7013	144	11	1	1	NUM
ejpam-7013	144	12	)	)	PUNCT
ejpam-7013	144	13	,	,	PUNCT
ejpam-7013	144	14	iteration	iteration	NOUN
ejpam-7013	144	15	gives	give	VERB
ejpam-7013	144	16	for	for	ADP
ejpam-7013	144	17	each	each	DET
ejpam-7013	144	18	fixed	fix	VERB
ejpam-7013	144	19	n	n	PROPN
ejpam-7013	144	20	and	and	CCONJ
ejpam-7013	144	21	k	k	PROPN
ejpam-7013	144	22	≥	≥	NUM
ejpam-7013	144	23	1	1	NUM
ejpam-7013	144	24	,	,	PUNCT
ejpam-7013	144	25	sn+k	sn+k	VERB
ejpam-7013	144	26	≤	≤	NUM
ejpam-7013	144	27	qksn	qksn	NOUN
ejpam-7013	145	1	+	+	CCONJ
ejpam-7013	145	2	k−1∑	k−1∑	PROPN
ejpam-7013	145	3	j=0	j=0	PROPN
ejpam-7013	145	4	q	q	PROPN
ejpam-7013	145	5	k−1−j	k−1−j	PROPN
ejpam-7013	145	6	εn+j	εn+j	PROPN
ejpam-7013	145	7	1−	1−	NUM
ejpam-7013	145	8	λ1s	λ1s	NOUN
ejpam-7013	145	9	.	.	PUNCT
ejpam-7013	146	1	letting	let	VERB
ejpam-7013	146	2	k	k	PRON
ejpam-7013	146	3	→	→	SYM
ejpam-7013	146	4	∞	∞	NUM
ejpam-7013	146	5	yields	yield	NOUN
ejpam-7013	146	6	sn+k	sn+k	PROPN
ejpam-7013	146	7	→	→	SYM
ejpam-7013	146	8	0	0	X
ejpam-7013	146	9	.	.	PUNCT
ejpam-7013	147	1	hence	hence	ADV
ejpam-7013	147	2	sn	sn	PROPN
ejpam-7013	147	3	→	→	SYM
ejpam-7013	147	4	0	0	PUNCT
ejpam-7013	147	5	as	as	ADP
ejpam-7013	147	6	n	n	PROPN
ejpam-7013	147	7	→	→	SYM
ejpam-7013	147	8	∞.	∞.	PROPN
ejpam-7013	147	9	in	in	ADP
ejpam-7013	147	10	particular	particular	ADJ
ejpam-7013	147	11	ln	ln	NOUN
ejpam-7013	147	12	is	be	AUX
ejpam-7013	147	13	a	a	DET
ejpam-7013	147	14	cauchy	cauchy	ADJ
ejpam-7013	147	15	sequence	sequence	NOUN
ejpam-7013	147	16	with	with	ADP
ejpam-7013	147	17	respect	respect	NOUN
ejpam-7013	147	18	to	to	ADP
ejpam-7013	147	19	d.	d.	PROPN
ejpam-7013	147	20	to	to	PART
ejpam-7013	147	21	check	check	VERB
ejpam-7013	147	22	this	this	PRON
ejpam-7013	147	23	directly	directly	ADV
ejpam-7013	147	24	,	,	PUNCT
ejpam-7013	147	25	for	for	ADP
ejpam-7013	147	26	m	m	PROPN
ejpam-7013	147	27	<	<	X
ejpam-7013	147	28	n	n	CCONJ
ejpam-7013	147	29	,	,	PUNCT
ejpam-7013	147	30	d(lm	d(lm	NUM
ejpam-7013	147	31	,	,	PUNCT
ejpam-7013	147	32	ln	ln	ADJ
ejpam-7013	147	33	)	)	PUNCT
ejpam-7013	147	34	≤	≤	PROPN
ejpam-7013	147	35	s	s	PART
ejpam-7013	147	36	n−1∑	n−1∑	PROPN
ejpam-7013	147	37	k	k	NOUN
ejpam-7013	147	38	=	=	NOUN
ejpam-7013	147	39	m	m	VERB
ejpam-7013	147	40	d(lk	d(lk	ADJ
ejpam-7013	147	41	,	,	PUNCT
ejpam-7013	147	42	lk+1	lk+1	X
ejpam-7013	147	43	)	)	PUNCT
ejpam-7013	147	44	=	=	SYM
ejpam-7013	147	45	s	s	VERB
ejpam-7013	147	46	n−1∑	n−1∑	PROPN
ejpam-7013	147	47	k	k	NOUN
ejpam-7013	148	1	=	=	NOUN
ejpam-7013	148	2	m	m	VERB
ejpam-7013	148	3	sk	sk	ADJ
ejpam-7013	148	4	,	,	PUNCT
ejpam-7013	148	5	and	and	CCONJ
ejpam-7013	148	6	since	since	SCONJ
ejpam-7013	148	7	sk	sk	INTJ
ejpam-7013	148	8	→	→	SYM
ejpam-7013	148	9	0	0	NUM
ejpam-7013	148	10	at	at	ADP
ejpam-7013	148	11	a	a	DET
ejpam-7013	148	12	geometric	geometric	ADJ
ejpam-7013	148	13	rate	rate	NOUN
ejpam-7013	148	14	the	the	DET
ejpam-7013	148	15	series	series	NOUN
ejpam-7013	148	16	∑	∑	PUNCT
ejpam-7013	148	17	sk	sk	ADP
ejpam-7013	148	18	converges	converge	NOUN
ejpam-7013	148	19	,	,	PUNCT
ejpam-7013	148	20	showing	show	VERB
ejpam-7013	148	21	d(lm	d(lm	NOUN
ejpam-7013	148	22	,	,	PUNCT
ejpam-7013	148	23	ln	ln	ADJ
ejpam-7013	148	24	)	)	PUNCT
ejpam-7013	148	25	→	→	SYM
ejpam-7013	148	26	0	0	NUM
ejpam-7013	148	27	as	as	ADP
ejpam-7013	148	28	m	m	PROPN
ejpam-7013	148	29	,	,	PUNCT
ejpam-7013	148	30	n	n	PROPN
ejpam-7013	148	31	→	→	SYM
ejpam-7013	148	32	∞.	∞.	PROPN
ejpam-7013	148	33	completeness	completeness	NOUN
ejpam-7013	148	34	of	of	ADP
ejpam-7013	148	35	(	(	PUNCT
ejpam-7013	148	36	x	x	NOUN
ejpam-7013	148	37	,	,	PUNCT
ejpam-7013	148	38	d	d	NOUN
ejpam-7013	148	39	)	)	PUNCT
ejpam-7013	148	40	yields	yield	VERB
ejpam-7013	148	41	a	a	DET
ejpam-7013	148	42	limit	limit	NOUN
ejpam-7013	148	43	k	k	X
ejpam-7013	148	44	∈	∈	PROPN
ejpam-7013	148	45	x	x	PUNCT
ejpam-7013	148	46	with	with	ADP
ejpam-7013	148	47	ln	ln	NOUN
ejpam-7013	148	48	→	→	PUNCT
ejpam-7013	148	49	k.	k.	NOUN
ejpam-7013	148	50	it	it	PRON
ejpam-7013	148	51	remains	remain	VERB
ejpam-7013	148	52	to	to	PART
ejpam-7013	148	53	show	show	VERB
ejpam-7013	148	54	k	k	PROPN
ejpam-7013	148	55	∈	∈	PROPN
ejpam-7013	148	56	t	t	PROPN
ejpam-7013	148	57	(	(	PUNCT
ejpam-7013	148	58	k	k	NOUN
ejpam-7013	148	59	)	)	PUNCT
ejpam-7013	148	60	.	.	PUNCT
ejpam-7013	149	1	we	we	PRON
ejpam-7013	149	2	first	first	ADV
ejpam-7013	149	3	observe	observe	VERB
ejpam-7013	149	4	that	that	SCONJ
ejpam-7013	149	5	h	h	NOUN
ejpam-7013	149	6	(	(	PUNCT
ejpam-7013	149	7	t	t	PROPN
ejpam-7013	149	8	(	(	PUNCT
ejpam-7013	149	9	ln	ln	PROPN
ejpam-7013	149	10	)	)	PUNCT
ejpam-7013	149	11	,	,	PUNCT
ejpam-7013	149	12	t	t	PROPN
ejpam-7013	149	13	(	(	PUNCT
ejpam-7013	149	14	ln+1	ln+1	PROPN
ejpam-7013	149	15	)	)	PUNCT
ejpam-7013	149	16	)	)	PUNCT
ejpam-7013	149	17	≤	≤	NOUN
ejpam-7013	149	18	λ1	λ1	PROPN
ejpam-7013	149	19	(	(	PUNCT
ejpam-7013	149	20	dα(ln	dα(ln	PROPN
ejpam-7013	149	21	,	,	PUNCT
ejpam-7013	149	22	t	t	PROPN
ejpam-7013	149	23	(	(	PUNCT
ejpam-7013	149	24	ln+1	ln+1	PROPN
ejpam-7013	149	25	)	)	PUNCT
ejpam-7013	149	26	)	)	PUNCT
ejpam-7013	149	27	)	)	PUNCT
ejpam-7013	150	1	+	+	CCONJ
ejpam-7013	150	2	λ2sn	λ2sn	X
ejpam-7013	150	3	+	+	CCONJ
ejpam-7013	150	4	λ3sn	λ3sn	PUNCT
ejpam-7013	150	5	,	,	PUNCT
ejpam-7013	150	6	and	and	CCONJ
ejpam-7013	150	7	since	since	SCONJ
ejpam-7013	150	8	dα(ln	dα(ln	PROPN
ejpam-7013	150	9	,	,	PUNCT
ejpam-7013	150	10	t	t	PROPN
ejpam-7013	150	11	(	(	PUNCT
ejpam-7013	150	12	ln+1	ln+1	PROPN
ejpam-7013	150	13	)	)	PUNCT
ejpam-7013	150	14	)	)	PUNCT
ejpam-7013	150	15	≤	≤	PROPN
ejpam-7013	150	16	d(ln	d(ln	PROPN
ejpam-7013	150	17	,	,	PUNCT
ejpam-7013	150	18	ln+2	ln+2	NUM
ejpam-7013	150	19	)	)	PUNCT
ejpam-7013	150	20	→	→	SYM
ejpam-7013	150	21	0	0	NUM
ejpam-7013	150	22	and	and	CCONJ
ejpam-7013	150	23	sn	sn	PROPN
ejpam-7013	150	24	→	→	SYM
ejpam-7013	150	25	0	0	NUM
ejpam-7013	150	26	,	,	PUNCT
ejpam-7013	150	27	we	we	PRON
ejpam-7013	150	28	deduce	deduce	VERB
ejpam-7013	150	29	h(t	h(t	PROPN
ejpam-7013	150	30	(	(	PUNCT
ejpam-7013	150	31	ln	ln	ADJ
ejpam-7013	150	32	)	)	PUNCT
ejpam-7013	150	33	,	,	PUNCT
ejpam-7013	150	34	t	t	PROPN
ejpam-7013	150	35	(	(	PUNCT
ejpam-7013	150	36	ln+1	ln+1	PROPN
ejpam-7013	150	37	)	)	PUNCT
ejpam-7013	150	38	)	)	PUNCT
ejpam-7013	151	1	→	→	SYM
ejpam-7013	151	2	0	0	X
ejpam-7013	151	3	.	.	PUNCT
ejpam-7013	152	1	the	the	DET
ejpam-7013	152	2	triangle	triangle	NOUN
ejpam-7013	152	3	inequality	inequality	NOUN
ejpam-7013	152	4	for	for	ADP
ejpam-7013	152	5	h	h	NOUN
ejpam-7013	152	6	then	then	ADV
ejpam-7013	152	7	implies	imply	VERB
ejpam-7013	152	8	h(t	h(t	PROPN
ejpam-7013	152	9	(	(	PUNCT
ejpam-7013	152	10	ln	ln	ADJ
ejpam-7013	152	11	)	)	PUNCT
ejpam-7013	152	12	,	,	PUNCT
ejpam-7013	152	13	t	t	PROPN
ejpam-7013	152	14	(	(	PUNCT
ejpam-7013	152	15	k	k	NOUN
ejpam-7013	152	16	)	)	PUNCT
ejpam-7013	152	17	)	)	PUNCT
ejpam-7013	153	1	→	→	SYM
ejpam-7013	153	2	0	0	NUM
ejpam-7013	153	3	,	,	PUNCT
ejpam-7013	153	4	because	because	SCONJ
ejpam-7013	153	5	h(t	h(t	PROPN
ejpam-7013	153	6	(	(	PUNCT
ejpam-7013	153	7	ln	ln	ADJ
ejpam-7013	153	8	)	)	PUNCT
ejpam-7013	153	9	,	,	PUNCT
ejpam-7013	153	10	t	t	PROPN
ejpam-7013	153	11	(	(	PUNCT
ejpam-7013	153	12	k	k	NOUN
ejpam-7013	153	13	)	)	PUNCT
ejpam-7013	153	14	)	)	PUNCT
ejpam-7013	153	15	≤	≤	NUM
ejpam-7013	153	16	h(t	h(t	PROPN
ejpam-7013	153	17	(	(	PUNCT
ejpam-7013	153	18	ln	ln	ADJ
ejpam-7013	153	19	)	)	PUNCT
ejpam-7013	153	20	,	,	PUNCT
ejpam-7013	153	21	t	t	PROPN
ejpam-7013	153	22	(	(	PUNCT
ejpam-7013	153	23	ln+1	ln+1	PROPN
ejpam-7013	153	24	)	)	PUNCT
ejpam-7013	153	25	)	)	PUNCT
ejpam-7013	154	1	+	+	VERB
ejpam-7013	154	2	h(t	h(t	PROPN
ejpam-7013	154	3	(	(	PUNCT
ejpam-7013	154	4	ln+1	ln+1	PROPN
ejpam-7013	154	5	)	)	PUNCT
ejpam-7013	154	6	,	,	PUNCT
ejpam-7013	154	7	t	t	PROPN
ejpam-7013	154	8	(	(	PUNCT
ejpam-7013	154	9	ln+2	ln+2	NUM
ejpam-7013	154	10	)	)	PUNCT
ejpam-7013	154	11	)	)	PUNCT
ejpam-7013	154	12	+	+	CCONJ
ejpam-7013	154	13	·	·	PUNCT
ejpam-7013	154	14	·	·	PUNCT
ejpam-7013	154	15	·	·	PUNCT
ejpam-7013	154	16	and	and	CCONJ
ejpam-7013	154	17	the	the	DET
ejpam-7013	154	18	tail	tail	NOUN
ejpam-7013	154	19	of	of	ADP
ejpam-7013	154	20	these	these	DET
ejpam-7013	154	21	terms	term	NOUN
ejpam-7013	154	22	tends	tend	VERB
ejpam-7013	154	23	to	to	ADP
ejpam-7013	154	24	0	0	NUM
ejpam-7013	154	25	.	.	PUNCT
ejpam-7013	155	1	now	now	ADV
ejpam-7013	155	2	apply	apply	VERB
ejpam-7013	155	3	the	the	DET
ejpam-7013	155	4	contractive	contractive	ADJ
ejpam-7013	155	5	inequality	inequality	NOUN
ejpam-7013	155	6	with	with	ADP
ejpam-7013	155	7	l	l	NOUN
ejpam-7013	155	8	=	=	PUNCT
ejpam-7013	155	9	k	k	PROPN
ejpam-7013	155	10	and	and	CCONJ
ejpam-7013	155	11	p	p	NOUN
ejpam-7013	155	12	=	=	NOUN
ejpam-7013	155	13	ln	ln	ADJ
ejpam-7013	155	14	:	:	PUNCT
ejpam-7013	155	15	h	h	PROPN
ejpam-7013	155	16	(	(	PUNCT
ejpam-7013	155	17	t	t	PROPN
ejpam-7013	155	18	(	(	PUNCT
ejpam-7013	155	19	k	k	NOUN
ejpam-7013	155	20	)	)	PUNCT
ejpam-7013	155	21	,	,	PUNCT
ejpam-7013	155	22	t	t	PROPN
ejpam-7013	155	23	(	(	PUNCT
ejpam-7013	155	24	ln	ln	ADJ
ejpam-7013	155	25	)	)	PUNCT
ejpam-7013	155	26	)	)	PUNCT
ejpam-7013	156	1	≤	≤	NOUN
ejpam-7013	156	2	λ1	λ1	PROPN
ejpam-7013	156	3	(	(	PUNCT
ejpam-7013	156	4	dα(k	dα(k	PROPN
ejpam-7013	156	5	,	,	PUNCT
ejpam-7013	156	6	t	t	PROPN
ejpam-7013	156	7	(	(	PUNCT
ejpam-7013	156	8	ln	ln	ADJ
ejpam-7013	156	9	)	)	PUNCT
ejpam-7013	156	10	)	)	PUNCT
ejpam-7013	157	1	+	+	VERB
ejpam-7013	157	2	dα(ln	dα(ln	ADJ
ejpam-7013	157	3	,	,	PUNCT
ejpam-7013	157	4	t	t	PROPN
ejpam-7013	157	5	(	(	PUNCT
ejpam-7013	157	6	k	k	NOUN
ejpam-7013	157	7	)	)	PUNCT
ejpam-7013	157	8	)	)	PUNCT
ejpam-7013	157	9	)	)	PUNCT
ejpam-7013	158	1	+	+	PUNCT
ejpam-7013	158	2	λ2dα(k	λ2dα(k	NOUN
ejpam-7013	158	3	,	,	PUNCT
ejpam-7013	158	4	t	t	PROPN
ejpam-7013	158	5	(	(	PUNCT
ejpam-7013	158	6	k	k	NOUN
ejpam-7013	158	7	)	)	PUNCT
ejpam-7013	158	8	)	)	PUNCT
ejpam-7013	159	1	+	+	CCONJ
ejpam-7013	160	1	λ3d(k	λ3d(k	PROPN
ejpam-7013	160	2	,	,	PUNCT
ejpam-7013	160	3	ln	ln	ADJ
ejpam-7013	160	4	)	)	PUNCT
ejpam-7013	160	5	.	.	PUNCT
ejpam-7013	161	1	we	we	PRON
ejpam-7013	161	2	already	already	ADV
ejpam-7013	161	3	know	know	VERB
ejpam-7013	161	4	h(t	h(t	PROPN
ejpam-7013	161	5	(	(	PUNCT
ejpam-7013	161	6	k	k	NOUN
ejpam-7013	161	7	)	)	PUNCT
ejpam-7013	161	8	,	,	PUNCT
ejpam-7013	161	9	t	t	PROPN
ejpam-7013	161	10	(	(	PUNCT
ejpam-7013	161	11	ln	ln	ADJ
ejpam-7013	161	12	)	)	PUNCT
ejpam-7013	161	13	)	)	PUNCT
ejpam-7013	161	14	→	→	SYM
ejpam-7013	161	15	0	0	NUM
ejpam-7013	161	16	and	and	CCONJ
ejpam-7013	161	17	d(k	d(k	PROPN
ejpam-7013	161	18	,	,	PUNCT
ejpam-7013	161	19	ln	ln	ADJ
ejpam-7013	161	20	)	)	PUNCT
ejpam-7013	161	21	→	→	SYM
ejpam-7013	161	22	0	0	X
ejpam-7013	161	23	.	.	PUNCT
ejpam-7013	161	24	also	also	ADV
ejpam-7013	161	25	dα(k	dα(k	PROPN
ejpam-7013	161	26	,	,	PUNCT
ejpam-7013	161	27	t	t	PROPN
ejpam-7013	161	28	(	(	PUNCT
ejpam-7013	161	29	ln	ln	ADJ
ejpam-7013	161	30	)	)	PUNCT
ejpam-7013	161	31	)	)	PUNCT
ejpam-7013	161	32	≤	≤	NOUN
ejpam-7013	162	1	d(k	d(k	PROPN
ejpam-7013	162	2	,	,	PUNCT
ejpam-7013	162	3	ln+1	ln+1	PROPN
ejpam-7013	162	4	)	)	PUNCT
ejpam-7013	162	5	→	→	SYM
ejpam-7013	162	6	0	0	X
ejpam-7013	162	7	.	.	X
ejpam-7013	162	8	for	for	ADP
ejpam-7013	162	9	dα(ln	dα(ln	PROPN
ejpam-7013	162	10	,	,	PUNCT
ejpam-7013	162	11	t	t	PROPN
ejpam-7013	162	12	(	(	PUNCT
ejpam-7013	162	13	k	k	NOUN
ejpam-7013	162	14	)	)	PUNCT
ejpam-7013	162	15	)	)	PUNCT
ejpam-7013	162	16	note	note	VERB
ejpam-7013	162	17	that	that	SCONJ
ejpam-7013	162	18	for	for	ADP
ejpam-7013	162	19	any	any	DET
ejpam-7013	162	20	y	y	PROPN
ejpam-7013	162	21	∈	∈	PROPN
ejpam-7013	162	22	t	t	PROPN
ejpam-7013	162	23	(	(	PUNCT
ejpam-7013	162	24	k	k	NOUN
ejpam-7013	162	25	)	)	PUNCT
ejpam-7013	162	26	,	,	PUNCT
ejpam-7013	162	27	d(ln	d(ln	PROPN
ejpam-7013	162	28	,	,	PUNCT
ejpam-7013	162	29	y	y	PROPN
ejpam-7013	162	30	)	)	PUNCT
ejpam-7013	162	31	≤	≤	PROPN
ejpam-7013	162	32	d(ln	d(ln	PROPN
ejpam-7013	162	33	,	,	PUNCT
ejpam-7013	162	34	k	k	NOUN
ejpam-7013	162	35	)	)	PUNCT
ejpam-7013	162	36	+	+	CCONJ
ejpam-7013	163	1	d(k	d(k	PROPN
ejpam-7013	163	2	,	,	PUNCT
ejpam-7013	163	3	y	y	PROPN
ejpam-7013	163	4	)	)	PUNCT
ejpam-7013	163	5	,	,	PUNCT
ejpam-7013	163	6	d.	d.	PROPN
ejpam-7013	163	7	gerbeti	gerbeti	PROPN
ejpam-7013	163	8	et	et	PROPN
ejpam-7013	163	9	al	al	PROPN
ejpam-7013	163	10	.	.	PUNCT
ejpam-7013	163	11	/	/	SYM
ejpam-7013	163	12	eur	eur	PROPN
ejpam-7013	163	13	.	.	PUNCT
ejpam-7013	164	1	j.	j.	PROPN
ejpam-7013	164	2	pure	pure	PROPN
ejpam-7013	164	3	appl	appl	PROPN
ejpam-7013	164	4	.	.	PROPN
ejpam-7013	164	5	math	math	PROPN
ejpam-7013	164	6	,	,	PUNCT
ejpam-7013	164	7	18	18	NUM
ejpam-7013	164	8	(	(	PUNCT
ejpam-7013	164	9	4	4	NUM
ejpam-7013	164	10	)	)	PUNCT
ejpam-7013	164	11	(	(	PUNCT
ejpam-7013	164	12	2025	2025	NUM
ejpam-7013	164	13	)	)	PUNCT
ejpam-7013	164	14	,	,	PUNCT
ejpam-7013	164	15	7013	7013	NUM
ejpam-7013	164	16	7	7	NUM
ejpam-7013	164	17	of	of	ADP
ejpam-7013	164	18	17	17	NUM
ejpam-7013	164	19	hence	hence	ADV
ejpam-7013	164	20	dα(ln	dα(ln	PROPN
ejpam-7013	164	21	,	,	PUNCT
ejpam-7013	164	22	t	t	PROPN
ejpam-7013	164	23	(	(	PUNCT
ejpam-7013	164	24	k	k	NOUN
ejpam-7013	164	25	)	)	PUNCT
ejpam-7013	164	26	)	)	PUNCT
ejpam-7013	165	1	≤	≤	PROPN
ejpam-7013	165	2	d(ln	d(ln	PROPN
ejpam-7013	165	3	,	,	PUNCT
ejpam-7013	165	4	k)+dα(k	k)+dα(k	PROPN
ejpam-7013	165	5	,	,	PUNCT
ejpam-7013	165	6	t	t	PROPN
ejpam-7013	165	7	(	(	PUNCT
ejpam-7013	165	8	k	k	NOUN
ejpam-7013	165	9	)	)	PUNCT
ejpam-7013	165	10	)	)	PUNCT
ejpam-7013	165	11	,	,	PUNCT
ejpam-7013	165	12	so	so	ADV
ejpam-7013	165	13	lim	lim	PROPN
ejpam-7013	165	14	supn→∞dα(ln	supn→∞dα(ln	PROPN
ejpam-7013	165	15	,	,	PUNCT
ejpam-7013	165	16	t	t	PROPN
ejpam-7013	165	17	(	(	PUNCT
ejpam-7013	165	18	k	k	NOUN
ejpam-7013	165	19	)	)	PUNCT
ejpam-7013	165	20	)	)	PUNCT
ejpam-7013	165	21	≤	≤	NOUN
ejpam-7013	165	22	dα(k	dα(k	NOUN
ejpam-7013	165	23	,	,	PUNCT
ejpam-7013	165	24	t	t	PROPN
ejpam-7013	165	25	(	(	PUNCT
ejpam-7013	165	26	k	k	NOUN
ejpam-7013	165	27	)	)	PUNCT
ejpam-7013	165	28	)	)	PUNCT
ejpam-7013	165	29	.	.	PUNCT
ejpam-7013	166	1	passing	pass	VERB
ejpam-7013	166	2	to	to	ADP
ejpam-7013	166	3	the	the	DET
ejpam-7013	166	4	limit	limit	NOUN
ejpam-7013	166	5	superior	superior	ADJ
ejpam-7013	166	6	as	as	ADP
ejpam-7013	166	7	n	n	PROPN
ejpam-7013	166	8	→	→	SYM
ejpam-7013	166	9	∞	∞	PROPN
ejpam-7013	166	10	in	in	ADP
ejpam-7013	166	11	the	the	DET
ejpam-7013	166	12	previous	previous	ADJ
ejpam-7013	166	13	displayed	display	VERB
ejpam-7013	166	14	inequality	inequality	NOUN
ejpam-7013	166	15	yields	yield	NOUN
ejpam-7013	166	16	0	0	NUM
ejpam-7013	166	17	≤	≤	NOUN
ejpam-7013	166	18	λ1	λ1	PROPN
ejpam-7013	166	19	(	(	PUNCT
ejpam-7013	166	20	0	0	NUM
ejpam-7013	166	21	+	+	NOUN
ejpam-7013	166	22	dα(k	dα(k	NOUN
ejpam-7013	166	23	,	,	PUNCT
ejpam-7013	166	24	t	t	PROPN
ejpam-7013	166	25	(	(	PUNCT
ejpam-7013	166	26	k	k	NOUN
ejpam-7013	166	27	)	)	PUNCT
ejpam-7013	166	28	)	)	PUNCT
ejpam-7013	166	29	)	)	PUNCT
ejpam-7013	167	1	+	+	PUNCT
ejpam-7013	167	2	λ2dα(k	λ2dα(k	NOUN
ejpam-7013	167	3	,	,	PUNCT
ejpam-7013	167	4	t	t	PROPN
ejpam-7013	167	5	(	(	PUNCT
ejpam-7013	167	6	k	k	NOUN
ejpam-7013	167	7	)	)	PUNCT
ejpam-7013	167	8	)	)	PUNCT
ejpam-7013	168	1	+	+	CCONJ
ejpam-7013	168	2	0	0	NUM
ejpam-7013	168	3	,	,	PUNCT
ejpam-7013	168	4	i.e.	i.e.	X
ejpam-7013	168	5	0	0	NUM
ejpam-7013	168	6	≤	≤	NOUN
ejpam-7013	168	7	(	(	PUNCT
ejpam-7013	168	8	λ1	λ1	ADJ
ejpam-7013	168	9	+	+	CCONJ
ejpam-7013	168	10	λ2)dα(k	λ2)dα(k	PROPN
ejpam-7013	168	11	,	,	PUNCT
ejpam-7013	168	12	t	t	PROPN
ejpam-7013	168	13	(	(	PUNCT
ejpam-7013	168	14	k	k	NOUN
ejpam-7013	168	15	)	)	PUNCT
ejpam-7013	168	16	)	)	PUNCT
ejpam-7013	168	17	.	.	PUNCT
ejpam-7013	169	1	this	this	DET
ejpam-7013	169	2	estimate	estimate	NOUN
ejpam-7013	169	3	alone	alone	ADV
ejpam-7013	169	4	does	do	AUX
ejpam-7013	169	5	not	not	PART
ejpam-7013	169	6	immediately	immediately	ADV
ejpam-7013	169	7	force	force	VERB
ejpam-7013	169	8	dα(k	dα(k	PROPN
ejpam-7013	169	9	,	,	PUNCT
ejpam-7013	169	10	t	t	PROPN
ejpam-7013	169	11	(	(	PUNCT
ejpam-7013	169	12	k	k	NOUN
ejpam-7013	169	13	)	)	PUNCT
ejpam-7013	169	14	)	)	PUNCT
ejpam-7013	170	1	=	=	PUNCT
ejpam-7013	170	2	0	0	X
ejpam-7013	170	3	.	.	PUNCT
ejpam-7013	170	4	to	to	PART
ejpam-7013	170	5	obtain	obtain	VERB
ejpam-7013	170	6	the	the	DET
ejpam-7013	170	7	stronger	strong	ADJ
ejpam-7013	170	8	conclusion	conclusion	NOUN
ejpam-7013	170	9	,	,	PUNCT
ejpam-7013	170	10	revisit	revisit	VERB
ejpam-7013	170	11	the	the	DET
ejpam-7013	170	12	contractive	contractive	ADJ
ejpam-7013	170	13	inequality	inequality	NOUN
ejpam-7013	170	14	with	with	ADP
ejpam-7013	170	15	l	l	NOUN
ejpam-7013	170	16	=	=	PUNCT
ejpam-7013	170	17	ln	ln	ADJ
ejpam-7013	170	18	and	and	CCONJ
ejpam-7013	170	19	p	p	NOUN
ejpam-7013	170	20	=	=	ADJ
ejpam-7013	170	21	k	k	NOUN
ejpam-7013	170	22	:	:	PUNCT
ejpam-7013	170	23	h	h	PROPN
ejpam-7013	170	24	(	(	PUNCT
ejpam-7013	170	25	t	t	PROPN
ejpam-7013	170	26	(	(	PUNCT
ejpam-7013	170	27	ln	ln	PROPN
ejpam-7013	170	28	)	)	PUNCT
ejpam-7013	170	29	,	,	PUNCT
ejpam-7013	170	30	t	t	PROPN
ejpam-7013	170	31	(	(	PUNCT
ejpam-7013	170	32	k	k	NOUN
ejpam-7013	170	33	)	)	PUNCT
ejpam-7013	170	34	)	)	PUNCT
ejpam-7013	171	1	≤	≤	NOUN
ejpam-7013	171	2	λ1	λ1	PROPN
ejpam-7013	171	3	(	(	PUNCT
ejpam-7013	171	4	dα(ln	dα(ln	PROPN
ejpam-7013	171	5	,	,	PUNCT
ejpam-7013	171	6	t	t	PROPN
ejpam-7013	171	7	(	(	PUNCT
ejpam-7013	171	8	k	k	NOUN
ejpam-7013	171	9	)	)	PUNCT
ejpam-7013	171	10	)	)	PUNCT
ejpam-7013	172	1	+	+	NOUN
ejpam-7013	172	2	dα(k	dα(k	NOUN
ejpam-7013	172	3	,	,	PUNCT
ejpam-7013	172	4	t	t	PROPN
ejpam-7013	172	5	(	(	PUNCT
ejpam-7013	172	6	ln	ln	ADJ
ejpam-7013	172	7	)	)	PUNCT
ejpam-7013	172	8	)	)	PUNCT
ejpam-7013	172	9	)	)	PUNCT
ejpam-7013	173	1	+	+	PUNCT
ejpam-7013	173	2	λ2dα(ln	λ2dα(ln	NOUN
ejpam-7013	173	3	,	,	PUNCT
ejpam-7013	173	4	t	t	PROPN
ejpam-7013	173	5	(	(	PUNCT
ejpam-7013	173	6	ln	ln	ADJ
ejpam-7013	173	7	)	)	PUNCT
ejpam-7013	173	8	)	)	PUNCT
ejpam-7013	174	1	+	+	CCONJ
ejpam-7013	174	2	λ3d(ln	λ3d(ln	PROPN
ejpam-7013	174	3	,	,	PUNCT
ejpam-7013	174	4	k	k	NOUN
ejpam-7013	174	5	)	)	PUNCT
ejpam-7013	174	6	.	.	PUNCT
ejpam-7013	175	1	we	we	PRON
ejpam-7013	175	2	know	know	VERB
ejpam-7013	175	3	the	the	DET
ejpam-7013	175	4	left	left	ADJ
ejpam-7013	175	5	-	-	PUNCT
ejpam-7013	175	6	hand	hand	NOUN
ejpam-7013	175	7	side	side	NOUN
ejpam-7013	175	8	tends	tend	VERB
ejpam-7013	175	9	to	to	ADP
ejpam-7013	175	10	0	0	NUM
ejpam-7013	175	11	,	,	PUNCT
ejpam-7013	175	12	dα(k	dα(k	NOUN
ejpam-7013	175	13	,	,	PUNCT
ejpam-7013	175	14	t	t	PROPN
ejpam-7013	175	15	(	(	PUNCT
ejpam-7013	175	16	ln	ln	ADJ
ejpam-7013	175	17	)	)	PUNCT
ejpam-7013	175	18	)	)	PUNCT
ejpam-7013	175	19	→	→	SYM
ejpam-7013	175	20	0	0	NUM
ejpam-7013	175	21	and	and	CCONJ
ejpam-7013	175	22	dα(ln	dα(ln	PROPN
ejpam-7013	175	23	,	,	PUNCT
ejpam-7013	175	24	t	t	PROPN
ejpam-7013	175	25	(	(	PUNCT
ejpam-7013	175	26	ln	ln	ADJ
ejpam-7013	175	27	)	)	PUNCT
ejpam-7013	175	28	)	)	PUNCT
ejpam-7013	175	29	≤	≤	NUM
ejpam-7013	175	30	sn	sn	PROPN
ejpam-7013	175	31	→	→	SYM
ejpam-7013	175	32	0	0	X
ejpam-7013	175	33	.	.	PUNCT
ejpam-7013	176	1	thus	thus	ADV
ejpam-7013	176	2	taking	take	VERB
ejpam-7013	176	3	limits	limit	NOUN
ejpam-7013	176	4	yields	yield	NOUN
ejpam-7013	176	5	0	0	NUM
ejpam-7013	176	6	≤	≤	NOUN
ejpam-7013	176	7	λ1	λ1	PROPN
ejpam-7013	176	8	lim	lim	PROPN
ejpam-7013	176	9	sup	sup	X
ejpam-7013	176	10	n→∞	n→∞	X
ejpam-7013	176	11	dα(ln	dα(ln	ADJ
ejpam-7013	176	12	,	,	PUNCT
ejpam-7013	176	13	t	t	PROPN
ejpam-7013	176	14	(	(	PUNCT
ejpam-7013	176	15	k	k	NOUN
ejpam-7013	176	16	)	)	PUNCT
ejpam-7013	176	17	)	)	PUNCT
ejpam-7013	176	18	.	.	PUNCT
ejpam-7013	177	1	combining	combine	VERB
ejpam-7013	177	2	with	with	ADP
ejpam-7013	177	3	the	the	DET
ejpam-7013	177	4	previous	previous	ADJ
ejpam-7013	177	5	bound	bind	VERB
ejpam-7013	177	6	lim	lim	PROPN
ejpam-7013	177	7	supn→∞dα(ln	supn→∞dα(ln	PROPN
ejpam-7013	177	8	,	,	PUNCT
ejpam-7013	177	9	t	t	PROPN
ejpam-7013	177	10	(	(	PUNCT
ejpam-7013	177	11	k	k	NOUN
ejpam-7013	177	12	)	)	PUNCT
ejpam-7013	177	13	)	)	PUNCT
ejpam-7013	177	14	≤	≤	NOUN
ejpam-7013	177	15	dα(k	dα(k	NOUN
ejpam-7013	177	16	,	,	PUNCT
ejpam-7013	177	17	t	t	PROPN
ejpam-7013	177	18	(	(	PUNCT
ejpam-7013	177	19	k	k	NOUN
ejpam-7013	177	20	)	)	PUNCT
ejpam-7013	177	21	)	)	PUNCT
ejpam-7013	177	22	,	,	PUNCT
ejpam-7013	177	23	we	we	PRON
ejpam-7013	177	24	obtain	obtain	VERB
ejpam-7013	177	25	0	0	NUM
ejpam-7013	177	26	≤	≤	NOUN
ejpam-7013	177	27	λ1dα(k	λ1dα(k	PROPN
ejpam-7013	177	28	,	,	PUNCT
ejpam-7013	177	29	t	t	PROPN
ejpam-7013	177	30	(	(	PUNCT
ejpam-7013	177	31	k	k	NOUN
ejpam-7013	177	32	)	)	PUNCT
ejpam-7013	177	33	)	)	PUNCT
ejpam-7013	177	34	.	.	PUNCT
ejpam-7013	178	1	now	now	ADV
ejpam-7013	178	2	consider	consider	VERB
ejpam-7013	178	3	the	the	DET
ejpam-7013	178	4	original	original	ADJ
ejpam-7013	178	5	inequality	inequality	NOUN
ejpam-7013	178	6	with	with	ADP
ejpam-7013	178	7	both	both	DET
ejpam-7013	178	8	arguments	argument	NOUN
ejpam-7013	178	9	equal	equal	ADJ
ejpam-7013	178	10	to	to	ADP
ejpam-7013	178	11	k	k	NOUN
ejpam-7013	178	12	:	:	PUNCT
ejpam-7013	178	13	h	h	PROPN
ejpam-7013	178	14	(	(	PUNCT
ejpam-7013	178	15	t	t	PROPN
ejpam-7013	178	16	(	(	PUNCT
ejpam-7013	178	17	k	k	NOUN
ejpam-7013	178	18	)	)	PUNCT
ejpam-7013	178	19	,	,	PUNCT
ejpam-7013	178	20	t	t	PROPN
ejpam-7013	178	21	(	(	PUNCT
ejpam-7013	178	22	k	k	NOUN
ejpam-7013	178	23	)	)	PUNCT
ejpam-7013	178	24	)	)	PUNCT
ejpam-7013	178	25	≤	≤	NOUN
ejpam-7013	178	26	λ1	λ1	PROPN
ejpam-7013	178	27	(	(	PUNCT
ejpam-7013	178	28	dα(k	dα(k	PROPN
ejpam-7013	178	29	,	,	PUNCT
ejpam-7013	178	30	t	t	PROPN
ejpam-7013	178	31	(	(	PUNCT
ejpam-7013	178	32	k	k	NOUN
ejpam-7013	178	33	)	)	PUNCT
ejpam-7013	178	34	)	)	PUNCT
ejpam-7013	179	1	+	+	NOUN
ejpam-7013	179	2	dα(k	dα(k	NOUN
ejpam-7013	179	3	,	,	PUNCT
ejpam-7013	179	4	t	t	PROPN
ejpam-7013	179	5	(	(	PUNCT
ejpam-7013	179	6	k	k	NOUN
ejpam-7013	179	7	)	)	PUNCT
ejpam-7013	179	8	)	)	PUNCT
ejpam-7013	179	9	)	)	PUNCT
ejpam-7013	180	1	+	+	PUNCT
ejpam-7013	180	2	λ2dα(k	λ2dα(k	NOUN
ejpam-7013	180	3	,	,	PUNCT
ejpam-7013	180	4	t	t	PROPN
ejpam-7013	180	5	(	(	PUNCT
ejpam-7013	180	6	k	k	NOUN
ejpam-7013	180	7	)	)	PUNCT
ejpam-7013	180	8	)	)	PUNCT
ejpam-7013	181	1	+	+	CCONJ
ejpam-7013	181	2	λ3	λ3	PROPN
ejpam-7013	181	3	·	·	PUNCT
ejpam-7013	181	4	0	0	NUM
ejpam-7013	181	5	,	,	PUNCT
ejpam-7013	181	6	which	which	PRON
ejpam-7013	181	7	simplifies	simplify	VERB
ejpam-7013	181	8	to	to	ADP
ejpam-7013	181	9	0	0	NUM
ejpam-7013	181	10	≤	≤	NOUN
ejpam-7013	181	11	(	(	PUNCT
ejpam-7013	181	12	2λ1	2λ1	NUM
ejpam-7013	181	13	+	+	SYM
ejpam-7013	181	14	λ2)dα(k	λ2)dα(k	PROPN
ejpam-7013	181	15	,	,	PUNCT
ejpam-7013	181	16	t	t	PROPN
ejpam-7013	181	17	(	(	PUNCT
ejpam-7013	181	18	k	k	NOUN
ejpam-7013	181	19	)	)	PUNCT
ejpam-7013	181	20	)	)	PUNCT
ejpam-7013	181	21	.	.	PUNCT
ejpam-7013	182	1	combining	combine	VERB
ejpam-7013	182	2	the	the	DET
ejpam-7013	182	3	inequalities	inequality	NOUN
ejpam-7013	182	4	and	and	CCONJ
ejpam-7013	182	5	using	use	VERB
ejpam-7013	182	6	the	the	DET
ejpam-7013	182	7	parameter	parameter	NOUN
ejpam-7013	182	8	condition	condition	NOUN
ejpam-7013	182	9	2λ1s+	2λ1s+	NUM
ejpam-7013	182	10	λ2	λ2	NOUN
ejpam-7013	183	1	+	+	CCONJ
ejpam-7013	183	2	λ3	λ3	PROPN
ejpam-7013	183	3	<	<	X
ejpam-7013	183	4	1	1	NUM
ejpam-7013	183	5	along	along	ADP
ejpam-7013	183	6	with	with	ADP
ejpam-7013	183	7	λ1s	λ1s	PROPN
ejpam-7013	183	8	<	<	X
ejpam-7013	183	9	1	1	NUM
ejpam-7013	183	10	,	,	PUNCT
ejpam-7013	183	11	a	a	DET
ejpam-7013	183	12	standard	standard	ADJ
ejpam-7013	183	13	contradiction	contradiction	NOUN
ejpam-7013	183	14	argument	argument	NOUN
ejpam-7013	183	15	(	(	PUNCT
ejpam-7013	183	16	if	if	SCONJ
ejpam-7013	183	17	dα(k	dα(k	NOUN
ejpam-7013	183	18	,	,	PUNCT
ejpam-7013	183	19	t	t	PROPN
ejpam-7013	183	20	(	(	PUNCT
ejpam-7013	183	21	k	k	NOUN
ejpam-7013	183	22	)	)	PUNCT
ejpam-7013	183	23	)	)	PUNCT
ejpam-7013	183	24	>	>	X
ejpam-7013	183	25	0	0	PUNCT
ejpam-7013	184	1	the	the	DET
ejpam-7013	184	2	contraction	contraction	NOUN
ejpam-7013	184	3	applied	apply	VERB
ejpam-7013	184	4	to	to	ADP
ejpam-7013	184	5	nearby	nearby	ADJ
ejpam-7013	184	6	iterates	iterate	NOUN
ejpam-7013	184	7	produces	produce	VERB
ejpam-7013	184	8	a	a	DET
ejpam-7013	184	9	strict	strict	ADJ
ejpam-7013	184	10	contraction	contraction	NOUN
ejpam-7013	184	11	of	of	ADP
ejpam-7013	184	12	a	a	DET
ejpam-7013	184	13	positive	positive	ADJ
ejpam-7013	184	14	number	number	NOUN
ejpam-7013	184	15	contradicting	contradict	VERB
ejpam-7013	184	16	the	the	DET
ejpam-7013	184	17	limit	limit	NOUN
ejpam-7013	184	18	behaviour	behaviour	NOUN
ejpam-7013	184	19	)	)	PUNCT
ejpam-7013	184	20	forces	force	NOUN
ejpam-7013	184	21	dα(k	dα(k	PROPN
ejpam-7013	184	22	,	,	PUNCT
ejpam-7013	184	23	t	t	PROPN
ejpam-7013	184	24	(	(	PUNCT
ejpam-7013	184	25	k	k	NOUN
ejpam-7013	184	26	)	)	PUNCT
ejpam-7013	184	27	)	)	PUNCT
ejpam-7013	185	1	=	=	PUNCT
ejpam-7013	185	2	0	0	X
ejpam-7013	185	3	.	.	X
ejpam-7013	185	4	more	more	ADV
ejpam-7013	185	5	concretely	concretely	ADV
ejpam-7013	185	6	,	,	PUNCT
ejpam-7013	185	7	if	if	SCONJ
ejpam-7013	185	8	dα(k	dα(k	NUM
ejpam-7013	185	9	,	,	PUNCT
ejpam-7013	185	10	t	t	PROPN
ejpam-7013	185	11	(	(	PUNCT
ejpam-7013	185	12	k	k	NOUN
ejpam-7013	185	13	)	)	PUNCT
ejpam-7013	185	14	)	)	PUNCT
ejpam-7013	185	15	=	=	PUNCT
ejpam-7013	185	16	δ	δ	PROPN
ejpam-7013	185	17	>	>	X
ejpam-7013	185	18	0	0	NUM
ejpam-7013	185	19	,	,	PUNCT
ejpam-7013	185	20	repeating	repeat	VERB
ejpam-7013	185	21	the	the	DET
ejpam-7013	185	22	estimates	estimate	NOUN
ejpam-7013	185	23	above	above	ADP
ejpam-7013	185	24	yields	yield	NOUN
ejpam-7013	185	25	a	a	DET
ejpam-7013	185	26	linear	linear	ADJ
ejpam-7013	185	27	inequality	inequality	NOUN
ejpam-7013	185	28	of	of	ADP
ejpam-7013	185	29	the	the	DET
ejpam-7013	185	30	form	form	NOUN
ejpam-7013	185	31	δ	δ	PROPN
ejpam-7013	185	32	≤	≤	PROPN
ejpam-7013	185	33	q	q	PROPN
ejpam-7013	185	34	δ	δ	PROPN
ejpam-7013	185	35	with	with	ADP
ejpam-7013	185	36	q	q	X
ejpam-7013	185	37	<	<	X
ejpam-7013	185	38	1	1	NUM
ejpam-7013	185	39	,	,	PUNCT
ejpam-7013	185	40	which	which	PRON
ejpam-7013	185	41	is	be	AUX
ejpam-7013	185	42	impossible	impossible	ADJ
ejpam-7013	185	43	.	.	PUNCT
ejpam-7013	186	1	therefore	therefore	ADV
ejpam-7013	186	2	dα(k	dα(k	PROPN
ejpam-7013	186	3	,	,	PUNCT
ejpam-7013	186	4	t	t	PROPN
ejpam-7013	186	5	(	(	PUNCT
ejpam-7013	186	6	k	k	NOUN
ejpam-7013	186	7	)	)	PUNCT
ejpam-7013	186	8	)	)	PUNCT
ejpam-7013	187	1	=	=	PUNCT
ejpam-7013	187	2	0	0	X
ejpam-7013	187	3	.	.	PUNCT
ejpam-7013	188	1	since	since	SCONJ
ejpam-7013	188	2	t	t	PROPN
ejpam-7013	188	3	(	(	PUNCT
ejpam-7013	188	4	k	k	NOUN
ejpam-7013	188	5	)	)	PUNCT
ejpam-7013	188	6	is	be	AUX
ejpam-7013	188	7	closed	close	VERB
ejpam-7013	188	8	,	,	PUNCT
ejpam-7013	188	9	this	this	PRON
ejpam-7013	188	10	implies	imply	VERB
ejpam-7013	188	11	k	k	PROPN
ejpam-7013	188	12	∈	∈	PROPN
ejpam-7013	188	13	t	t	PROPN
ejpam-7013	188	14	(	(	PUNCT
ejpam-7013	188	15	k	k	NOUN
ejpam-7013	188	16	)	)	PUNCT
ejpam-7013	188	17	.	.	PUNCT
ejpam-7013	189	1	hence	hence	ADV
ejpam-7013	189	2	{	{	PUNCT
ejpam-7013	189	3	k	k	NOUN
ejpam-7013	189	4	}	}	PUNCT
ejpam-7013	189	5	⊆	⊆	NUM
ejpam-7013	189	6	t	t	NOUN
ejpam-7013	189	7	(	(	PUNCT
ejpam-7013	189	8	k	k	NOUN
ejpam-7013	189	9	)	)	PUNCT
ejpam-7013	189	10	,	,	PUNCT
ejpam-7013	189	11	and	and	CCONJ
ejpam-7013	189	12	the	the	DET
ejpam-7013	189	13	proof	proof	NOUN
ejpam-7013	189	14	is	be	AUX
ejpam-7013	189	15	complete	complete	ADJ
ejpam-7013	189	16	.	.	PUNCT
ejpam-7013	190	1	example	example	NOUN
ejpam-7013	191	1	1	1	NUM
ejpam-7013	191	2	.	.	PUNCT
ejpam-7013	191	3	let	let	VERB
ejpam-7013	191	4	x	x	PUNCT
ejpam-7013	191	5	=	=	PUNCT
ejpam-7013	192	1	[	[	X
ejpam-7013	192	2	0	0	NUM
ejpam-7013	192	3	,	,	PUNCT
ejpam-7013	192	4	1	1	NUM
ejpam-7013	192	5	]	]	PUNCT
ejpam-7013	192	6	equipped	equip	VERB
ejpam-7013	192	7	with	with	ADP
ejpam-7013	192	8	the	the	DET
ejpam-7013	192	9	usual	usual	ADJ
ejpam-7013	192	10	metric	metric	ADJ
ejpam-7013	192	11	d(x	d(x	PROPN
ejpam-7013	192	12	,	,	PUNCT
ejpam-7013	192	13	y	y	NOUN
ejpam-7013	192	14	)	)	PUNCT
ejpam-7013	192	15	=	=	NOUN
ejpam-7013	192	16	|x	|x	NOUN
ejpam-7013	192	17	−	−	NOUN
ejpam-7013	192	18	y|	y|	NOUN
ejpam-7013	193	1	(	(	PUNCT
ejpam-7013	193	2	so	so	ADV
ejpam-7013	193	3	the	the	DET
ejpam-7013	193	4	underlying	underlie	VERB
ejpam-7013	193	5	b	b	X
ejpam-7013	193	6	-	-	ADJ
ejpam-7013	193	7	metric	metric	ADJ
ejpam-7013	193	8	constant	constant	ADJ
ejpam-7013	193	9	is	be	AUX
ejpam-7013	193	10	s	s	NOUN
ejpam-7013	193	11	=	=	NOUN
ejpam-7013	193	12	1	1	NUM
ejpam-7013	193	13	)	)	PUNCT
ejpam-7013	193	14	.	.	PUNCT
ejpam-7013	194	1	define	define	VERB
ejpam-7013	194	2	a	a	DET
ejpam-7013	194	3	continuous	continuous	ADJ
ejpam-7013	194	4	fuzzy	fuzzy	ADJ
ejpam-7013	194	5	metric	metric	ADJ
ejpam-7013	194	6	m	m	NOUN
ejpam-7013	194	7	on	on	ADP
ejpam-7013	194	8	x	x	PUNCT
ejpam-7013	194	9	by	by	ADP
ejpam-7013	194	10	m(x	m(x	PROPN
ejpam-7013	194	11	,	,	PUNCT
ejpam-7013	194	12	y	y	PROPN
ejpam-7013	194	13	,	,	PUNCT
ejpam-7013	194	14	t	t	PROPN
ejpam-7013	194	15	)	)	PUNCT
ejpam-7013	194	16	=	=	SYM
ejpam-7013	194	17	e−|x−y|/t	e−|x−y|/t	X
ejpam-7013	194	18	(	(	PUNCT
ejpam-7013	194	19	x	x	X
ejpam-7013	194	20	,	,	PUNCT
ejpam-7013	194	21	y	y	PROPN
ejpam-7013	194	22	∈	∈	PROPN
ejpam-7013	194	23	x	x	PROPN
ejpam-7013	194	24	,	,	PUNCT
ejpam-7013	194	25	t	t	PROPN
ejpam-7013	194	26	>	>	X
ejpam-7013	194	27	0	0	NUM
ejpam-7013	194	28	)	)	PUNCT
ejpam-7013	194	29	,	,	PUNCT
ejpam-7013	194	30	which	which	PRON
ejpam-7013	194	31	is	be	AUX
ejpam-7013	194	32	the	the	DET
ejpam-7013	194	33	standard	standard	ADJ
ejpam-7013	194	34	kramosil	kramosil	NOUN
ejpam-7013	194	35	–	–	PUNCT
ejpam-7013	194	36	michálek	michálek	NOUN
ejpam-7013	194	37	type	type	NOUN
ejpam-7013	194	38	fuzzy	fuzzy	ADJ
ejpam-7013	194	39	metric	metric	ADJ
ejpam-7013	194	40	and	and	CCONJ
ejpam-7013	194	41	is	be	AUX
ejpam-7013	194	42	compatible	compatible	ADJ
ejpam-7013	194	43	with	with	ADP
ejpam-7013	194	44	d.	d.	PROPN
ejpam-7013	194	45	for	for	ADP
ejpam-7013	194	46	each	each	DET
ejpam-7013	194	47	x	x	SYM
ejpam-7013	194	48	∈	∈	PROPN
ejpam-7013	194	49	x	x	PUNCT
ejpam-7013	194	50	define	define	VERB
ejpam-7013	194	51	the	the	DET
ejpam-7013	194	52	multivalued	multivalue	VERB
ejpam-7013	194	53	mapping	mapping	NOUN
ejpam-7013	194	54	t	t	NOUN
ejpam-7013	194	55	(	(	PUNCT
ejpam-7013	194	56	x	x	NOUN
ejpam-7013	194	57	)	)	PUNCT
ejpam-7013	194	58	:	:	PUNCT
ejpam-7013	194	59	=	=	SYM
ejpam-7013	194	60	{	{	PUNCT
ejpam-7013	194	61	0	0	NUM
ejpam-7013	194	62	}	}	PUNCT
ejpam-7013	194	63	⊆	⊆	NUM
ejpam-7013	194	64	x.	x.	NOUN
ejpam-7013	194	65	d.	d.	PROPN
ejpam-7013	194	66	gerbeti	gerbeti	PROPN
ejpam-7013	194	67	et	et	PROPN
ejpam-7013	194	68	al	al	PROPN
ejpam-7013	194	69	.	.	PUNCT
ejpam-7013	194	70	/	/	SYM
ejpam-7013	194	71	eur	eur	PROPN
ejpam-7013	194	72	.	.	PUNCT
ejpam-7013	195	1	j.	j.	PROPN
ejpam-7013	195	2	pure	pure	PROPN
ejpam-7013	195	3	appl	appl	PROPN
ejpam-7013	195	4	.	.	PROPN
ejpam-7013	195	5	math	math	PROPN
ejpam-7013	195	6	,	,	PUNCT
ejpam-7013	195	7	18	18	NUM
ejpam-7013	195	8	(	(	PUNCT
ejpam-7013	195	9	4	4	NUM
ejpam-7013	195	10	)	)	PUNCT
ejpam-7013	195	11	(	(	PUNCT
ejpam-7013	195	12	2025	2025	NUM
ejpam-7013	195	13	)	)	PUNCT
ejpam-7013	195	14	,	,	PUNCT
ejpam-7013	195	15	7013	7013	NUM
ejpam-7013	195	16	8	8	NUM
ejpam-7013	195	17	of	of	ADP
ejpam-7013	195	18	17	17	NUM
ejpam-7013	195	19	then	then	ADV
ejpam-7013	195	20	t	t	X
ejpam-7013	195	21	:	:	PUNCT
ejpam-7013	195	22	x	x	X
ejpam-7013	195	23	→	→	SYM
ejpam-7013	195	24	w(x	w(x	NOUN
ejpam-7013	195	25	)	)	PUNCT
ejpam-7013	195	26	(	(	PUNCT
ejpam-7013	195	27	nonempty	nonempty	ADV
ejpam-7013	195	28	closed	close	VERB
ejpam-7013	195	29	singletons	singleton	NOUN
ejpam-7013	195	30	)	)	PUNCT
ejpam-7013	195	31	.	.	PUNCT
ejpam-7013	196	1	for	for	ADP
ejpam-7013	196	2	any	any	DET
ejpam-7013	196	3	x	x	NOUN
ejpam-7013	196	4	,	,	PUNCT
ejpam-7013	196	5	y	y	PROPN
ejpam-7013	196	6	∈	∈	PROPN
ejpam-7013	196	7	x	x	INTJ
ejpam-7013	196	8	we	we	PRON
ejpam-7013	196	9	have	have	VERB
ejpam-7013	196	10	h	h	NOUN
ejpam-7013	196	11	(	(	PUNCT
ejpam-7013	196	12	t	t	PROPN
ejpam-7013	196	13	(	(	PUNCT
ejpam-7013	196	14	x	x	NOUN
ejpam-7013	196	15	)	)	PUNCT
ejpam-7013	196	16	,	,	PUNCT
ejpam-7013	196	17	t	t	PROPN
ejpam-7013	196	18	(	(	PUNCT
ejpam-7013	196	19	y	y	NOUN
ejpam-7013	196	20	)	)	PUNCT
ejpam-7013	196	21	)	)	PUNCT
ejpam-7013	197	1	=	=	SYM
ejpam-7013	197	2	h({0	h({0	ADJ
ejpam-7013	197	3	}	}	PUNCT
ejpam-7013	197	4	,	,	PUNCT
ejpam-7013	197	5	{	{	PUNCT
ejpam-7013	197	6	0	0	NUM
ejpam-7013	197	7	}	}	PUNCT
ejpam-7013	197	8	)	)	PUNCT
ejpam-7013	197	9	=	=	SYM
ejpam-7013	197	10	0	0	NUM
ejpam-7013	197	11	,	,	PUNCT
ejpam-7013	197	12	dα(x	dα(x	NOUN
ejpam-7013	197	13	,	,	PUNCT
ejpam-7013	197	14	t	t	PROPN
ejpam-7013	197	15	(	(	PUNCT
ejpam-7013	197	16	y	y	NOUN
ejpam-7013	197	17	)	)	PUNCT
ejpam-7013	197	18	)	)	PUNCT
ejpam-7013	198	1	=	=	SYM
ejpam-7013	198	2	inf	inf	PROPN
ejpam-7013	198	3	z∈t	z∈t	NOUN
ejpam-7013	198	4	(	(	PUNCT
ejpam-7013	198	5	y	y	NOUN
ejpam-7013	198	6	)	)	PUNCT
ejpam-7013	198	7	d(x	d(x	PROPN
ejpam-7013	198	8	,	,	PUNCT
ejpam-7013	198	9	z	z	NOUN
ejpam-7013	198	10	)	)	PUNCT
ejpam-7013	198	11	=	=	SYM
ejpam-7013	198	12	d(x	d(x	PROPN
ejpam-7013	198	13	,	,	PUNCT
ejpam-7013	198	14	0	0	NUM
ejpam-7013	198	15	)	)	PUNCT
ejpam-7013	198	16	=	=	SYM
ejpam-7013	198	17	x	x	NOUN
ejpam-7013	198	18	,	,	PUNCT
ejpam-7013	198	19	and	and	CCONJ
ejpam-7013	198	20	similarly	similarly	ADV
ejpam-7013	198	21	dα(y	dα(y	NOUN
ejpam-7013	198	22	,	,	PUNCT
ejpam-7013	198	23	t	t	PROPN
ejpam-7013	198	24	(	(	PUNCT
ejpam-7013	198	25	x	x	NOUN
ejpam-7013	198	26	)	)	PUNCT
ejpam-7013	198	27	)	)	PUNCT
ejpam-7013	199	1	=	=	SYM
ejpam-7013	199	2	y	y	PROPN
ejpam-7013	199	3	,	,	PUNCT
ejpam-7013	199	4	while	while	SCONJ
ejpam-7013	199	5	dα(x	dα(x	NOUN
ejpam-7013	199	6	,	,	PUNCT
ejpam-7013	199	7	t	t	PROPN
ejpam-7013	199	8	(	(	PUNCT
ejpam-7013	199	9	x	x	NOUN
ejpam-7013	199	10	)	)	PUNCT
ejpam-7013	199	11	)	)	PUNCT
ejpam-7013	200	1	=	=	PUNCT
ejpam-7013	200	2	x.	x.	NOUN
ejpam-7013	200	3	choose	choose	VERB
ejpam-7013	200	4	constants	constant	NOUN
ejpam-7013	200	5	λ1	λ1	PROPN
ejpam-7013	200	6	=	=	SYM
ejpam-7013	200	7	0	0	NUM
ejpam-7013	200	8	,	,	PUNCT
ejpam-7013	200	9	λ2	λ2	NOUN
ejpam-7013	200	10	=	=	SYM
ejpam-7013	200	11	0	0	NUM
ejpam-7013	200	12	,	,	PUNCT
ejpam-7013	200	13	λ3	λ3	PROPN
ejpam-7013	200	14	=	=	NOUN
ejpam-7013	200	15	1	1	NUM
ejpam-7013	200	16	2	2	NUM
ejpam-7013	200	17	.	.	PUNCT
ejpam-7013	201	1	then	then	ADV
ejpam-7013	201	2	the	the	DET
ejpam-7013	201	3	parameter	parameter	NOUN
ejpam-7013	201	4	conditions	condition	NOUN
ejpam-7013	201	5	are	be	AUX
ejpam-7013	201	6	satisfied	satisfied	ADJ
ejpam-7013	201	7	:	:	PUNCT
ejpam-7013	201	8	λ1s	λ1s	X
ejpam-7013	201	9	=	=	SYM
ejpam-7013	201	10	0	0	PUNCT
ejpam-7013	201	11	<	<	X
ejpam-7013	201	12	1	1	NUM
ejpam-7013	201	13	,	,	PUNCT
ejpam-7013	201	14	2λ1s+	2λ1s+	NUM
ejpam-7013	201	15	λ2	λ2	NOUN
ejpam-7013	202	1	+	+	CCONJ
ejpam-7013	202	2	λ3	λ3	PROPN
ejpam-7013	202	3	=	=	SYM
ejpam-7013	202	4	0	0	PUNCT
ejpam-7013	203	1	+	+	CCONJ
ejpam-7013	203	2	0	0	NUM
ejpam-7013	204	1	+	+	CCONJ
ejpam-7013	204	2	1	1	NUM
ejpam-7013	204	3	2	2	NUM
ejpam-7013	204	4	<	<	X
ejpam-7013	204	5	1	1	NUM
ejpam-7013	204	6	.	.	PUNCT
ejpam-7013	205	1	the	the	DET
ejpam-7013	205	2	contractive	contractive	ADJ
ejpam-7013	205	3	inequality	inequality	NOUN
ejpam-7013	205	4	in	in	ADP
ejpam-7013	205	5	the	the	DET
ejpam-7013	205	6	theorem	theorem	NOUN
ejpam-7013	205	7	reduces	reduce	VERB
ejpam-7013	205	8	to	to	ADP
ejpam-7013	205	9	h	h	PROPN
ejpam-7013	205	10	(	(	PUNCT
ejpam-7013	205	11	t	t	PROPN
ejpam-7013	205	12	(	(	PUNCT
ejpam-7013	205	13	x	x	NOUN
ejpam-7013	205	14	)	)	PUNCT
ejpam-7013	205	15	,	,	PUNCT
ejpam-7013	205	16	t	t	PROPN
ejpam-7013	205	17	(	(	PUNCT
ejpam-7013	205	18	y	y	NOUN
ejpam-7013	205	19	)	)	PUNCT
ejpam-7013	205	20	)	)	PUNCT
ejpam-7013	206	1	=	=	SYM
ejpam-7013	206	2	0	0	X
ejpam-7013	206	3	≤	≤	NOUN
ejpam-7013	206	4	λ1	λ1	PROPN
ejpam-7013	206	5	(	(	PUNCT
ejpam-7013	206	6	dα(x	dα(x	NOUN
ejpam-7013	206	7	,	,	PUNCT
ejpam-7013	206	8	t	t	PROPN
ejpam-7013	206	9	(	(	PUNCT
ejpam-7013	206	10	y	y	NOUN
ejpam-7013	206	11	)	)	PUNCT
ejpam-7013	206	12	)	)	PUNCT
ejpam-7013	207	1	+	+	PUNCT
ejpam-7013	207	2	dα(y	dα(y	NOUN
ejpam-7013	207	3	,	,	PUNCT
ejpam-7013	207	4	t	t	PROPN
ejpam-7013	207	5	(	(	PUNCT
ejpam-7013	207	6	x	x	NOUN
ejpam-7013	207	7	)	)	PUNCT
ejpam-7013	207	8	)	)	PUNCT
ejpam-7013	207	9	)	)	PUNCT
ejpam-7013	208	1	+	+	CCONJ
ejpam-7013	208	2	λ2dα(x	λ2dα(x	PROPN
ejpam-7013	208	3	,	,	PUNCT
ejpam-7013	208	4	t	t	PROPN
ejpam-7013	208	5	(	(	PUNCT
ejpam-7013	208	6	x	x	NOUN
ejpam-7013	208	7	)	)	PUNCT
ejpam-7013	208	8	)	)	PUNCT
ejpam-7013	209	1	+	+	CCONJ
ejpam-7013	209	2	λ3d(x	λ3d(x	PROPN
ejpam-7013	209	3	,	,	PUNCT
ejpam-7013	209	4	y	y	NOUN
ejpam-7013	209	5	)	)	PUNCT
ejpam-7013	209	6	,	,	PUNCT
ejpam-7013	209	7	which	which	PRON
ejpam-7013	209	8	becomes	become	VERB
ejpam-7013	209	9	0	0	NUM
ejpam-7013	209	10	≤	≤	NUM
ejpam-7013	209	11	0	0	NUM
ejpam-7013	210	1	+	+	CCONJ
ejpam-7013	210	2	0	0	NUM
ejpam-7013	211	1	+	+	CCONJ
ejpam-7013	211	2	1	1	NUM
ejpam-7013	211	3	2	2	NUM
ejpam-7013	211	4	|x−	|x−	NOUN
ejpam-7013	211	5	y|	y|	NOUN
ejpam-7013	211	6	,	,	PUNCT
ejpam-7013	211	7	and	and	CCONJ
ejpam-7013	211	8	this	this	PRON
ejpam-7013	211	9	holds	hold	VERB
ejpam-7013	211	10	for	for	ADP
ejpam-7013	211	11	all	all	DET
ejpam-7013	211	12	x	x	NOUN
ejpam-7013	211	13	,	,	PUNCT
ejpam-7013	211	14	y	y	PROPN
ejpam-7013	211	15	∈	∈	PROPN
ejpam-7013	212	1	[	[	X
ejpam-7013	212	2	0	0	NUM
ejpam-7013	212	3	,	,	PUNCT
ejpam-7013	212	4	1	1	NUM
ejpam-7013	212	5	]	]	PUNCT
ejpam-7013	212	6	.	.	PUNCT
ejpam-7013	213	1	therefore	therefore	ADV
ejpam-7013	213	2	all	all	DET
ejpam-7013	213	3	hypotheses	hypothesis	NOUN
ejpam-7013	213	4	of	of	ADP
ejpam-7013	213	5	the	the	DET
ejpam-7013	213	6	theorem	theorem	NOUN
ejpam-7013	213	7	are	be	AUX
ejpam-7013	213	8	satisfied	satisfied	ADJ
ejpam-7013	213	9	.	.	PUNCT
ejpam-7013	214	1	the	the	DET
ejpam-7013	214	2	conclusion	conclusion	NOUN
ejpam-7013	214	3	gives	give	VERB
ejpam-7013	214	4	a	a	DET
ejpam-7013	214	5	fuzzy	fuzzy	ADJ
ejpam-7013	214	6	fp	fp	NOUN
ejpam-7013	214	7	.	.	PROPN
ejpam-7013	214	8	indeed	indeed	ADV
ejpam-7013	214	9	,	,	PUNCT
ejpam-7013	214	10	t	t	PROPN
ejpam-7013	214	11	(	(	PUNCT
ejpam-7013	214	12	0	0	NUM
ejpam-7013	214	13	)	)	PUNCT
ejpam-7013	214	14	=	=	PRON
ejpam-7013	214	15	{	{	PUNCT
ejpam-7013	214	16	0	0	NUM
ejpam-7013	214	17	}	}	PUNCT
ejpam-7013	214	18	,	,	PUNCT
ejpam-7013	214	19	so	so	ADV
ejpam-7013	214	20	0	0	NUM
ejpam-7013	214	21	∈	∈	PROPN
ejpam-7013	214	22	t	t	NOUN
ejpam-7013	214	23	(	(	PUNCT
ejpam-7013	214	24	0	0	NUM
ejpam-7013	214	25	)	)	PUNCT
ejpam-7013	214	26	and	and	CCONJ
ejpam-7013	214	27	{	{	PUNCT
ejpam-7013	214	28	0	0	NUM
ejpam-7013	214	29	}	}	SYM
ejpam-7013	214	30	⊆	⊆	NUM
ejpam-7013	214	31	t	t	NOUN
ejpam-7013	214	32	(	(	PUNCT
ejpam-7013	214	33	0	0	NUM
ejpam-7013	214	34	)	)	PUNCT
ejpam-7013	214	35	;	;	PUNCT
ejpam-7013	214	36	hence	hence	ADV
ejpam-7013	214	37	0	0	NUM
ejpam-7013	214	38	is	be	AUX
ejpam-7013	214	39	a	a	DET
ejpam-7013	214	40	fuzzy	fuzzy	ADJ
ejpam-7013	214	41	fp	fp	NOUN
ejpam-7013	214	42	of	of	ADP
ejpam-7013	214	43	t	t	PROPN
ejpam-7013	214	44	.	.	PUNCT
ejpam-7013	215	1	figure	figure	VERB
ejpam-7013	215	2	1	1	NUM
ejpam-7013	215	3	:	:	PUNCT
ejpam-7013	215	4	illustration	illustration	NOUN
ejpam-7013	215	5	of	of	ADP
ejpam-7013	215	6	the	the	DET
ejpam-7013	215	7	mapping	mapping	NOUN
ejpam-7013	215	8	t	t	NOUN
ejpam-7013	215	9	(	(	PUNCT
ejpam-7013	215	10	x	x	X
ejpam-7013	215	11	)	)	PUNCT
ejpam-7013	215	12	=	=	SYM
ejpam-7013	215	13	{	{	PUNCT
ejpam-7013	215	14	0	0	NUM
ejpam-7013	215	15	}	}	PUNCT
ejpam-7013	215	16	on	on	ADP
ejpam-7013	215	17	the	the	DET
ejpam-7013	215	18	interval	interval	NOUN
ejpam-7013	215	19	[	[	X
ejpam-7013	215	20	0	0	NUM
ejpam-7013	215	21	,	,	PUNCT
ejpam-7013	215	22	1	1	NUM
ejpam-7013	215	23	]	]	PUNCT
ejpam-7013	215	24	.	.	PUNCT
ejpam-7013	216	1	every	every	DET
ejpam-7013	216	2	point	point	NOUN
ejpam-7013	216	3	x	x	X
ejpam-7013	216	4	∈	∈	NOUN
ejpam-7013	217	1	[	[	X
ejpam-7013	217	2	0	0	NUM
ejpam-7013	217	3	,	,	PUNCT
ejpam-7013	217	4	1	1	NUM
ejpam-7013	217	5	]	]	PUNCT
ejpam-7013	217	6	is	be	AUX
ejpam-7013	217	7	mapped	map	VERB
ejpam-7013	217	8	to	to	ADP
ejpam-7013	217	9	the	the	DET
ejpam-7013	217	10	singleton	singleton	NOUN
ejpam-7013	217	11	{	{	PUNCT
ejpam-7013	217	12	0	0	NUM
ejpam-7013	217	13	}	}	PUNCT
ejpam-7013	217	14	,	,	PUNCT
ejpam-7013	217	15	showing	show	VERB
ejpam-7013	217	16	that	that	SCONJ
ejpam-7013	217	17	0	0	NUM
ejpam-7013	217	18	is	be	AUX
ejpam-7013	217	19	the	the	DET
ejpam-7013	217	20	fuzzy	fuzzy	ADJ
ejpam-7013	217	21	fixed	fix	VERB
ejpam-7013	217	22	point	point	NOUN
ejpam-7013	217	23	of	of	ADP
ejpam-7013	217	24	t	t	PROPN
ejpam-7013	217	25	.	.	PUNCT
ejpam-7013	218	1	d.	d.	PROPN
ejpam-7013	218	2	gerbeti	gerbeti	PROPN
ejpam-7013	218	3	et	et	PROPN
ejpam-7013	218	4	al	al	PROPN
ejpam-7013	218	5	.	.	PUNCT
ejpam-7013	218	6	/	/	SYM
ejpam-7013	218	7	eur	eur	PROPN
ejpam-7013	218	8	.	.	PUNCT
ejpam-7013	219	1	j.	j.	PROPN
ejpam-7013	219	2	pure	pure	PROPN
ejpam-7013	219	3	appl	appl	PROPN
ejpam-7013	219	4	.	.	PROPN
ejpam-7013	219	5	math	math	PROPN
ejpam-7013	219	6	,	,	PUNCT
ejpam-7013	219	7	18	18	NUM
ejpam-7013	219	8	(	(	PUNCT
ejpam-7013	219	9	4	4	NUM
ejpam-7013	219	10	)	)	PUNCT
ejpam-7013	219	11	(	(	PUNCT
ejpam-7013	219	12	2025	2025	NUM
ejpam-7013	219	13	)	)	PUNCT
ejpam-7013	219	14	,	,	PUNCT
ejpam-7013	219	15	7013	7013	NUM
ejpam-7013	219	16	9	9	NUM
ejpam-7013	219	17	of	of	ADP
ejpam-7013	219	18	17	17	NUM
ejpam-7013	219	19	theorem	theorem	NOUN
ejpam-7013	219	20	3	3	X
ejpam-7013	219	21	.	.	PUNCT
ejpam-7013	220	1	let	let	AUX
ejpam-7013	220	2	(	(	PUNCT
ejpam-7013	220	3	x	x	X
ejpam-7013	220	4	,	,	PUNCT
ejpam-7013	220	5	m	m	PROPN
ejpam-7013	220	6	,	,	PUNCT
ejpam-7013	220	7	∗	∗	NOUN
ejpam-7013	220	8	)	)	PUNCT
ejpam-7013	220	9	be	be	VERB
ejpam-7013	220	10	a	a	DET
ejpam-7013	220	11	complete	complete	ADJ
ejpam-7013	220	12	b	b	NOUN
ejpam-7013	220	13	-	-	PUNCT
ejpam-7013	220	14	fms	fms	PROPN
ejpam-7013	220	15	and	and	CCONJ
ejpam-7013	220	16	let	let	VERB
ejpam-7013	220	17	t	t	NOUN
ejpam-7013	220	18	:	:	PUNCT
ejpam-7013	220	19	x	x	X
ejpam-7013	220	20	→	→	SYM
ejpam-7013	220	21	w(x	w(x	NOUN
ejpam-7013	220	22	)	)	PUNCT
ejpam-7013	220	23	be	be	AUX
ejpam-7013	220	24	a	a	DET
ejpam-7013	220	25	multivalued	multivalued	ADJ
ejpam-7013	220	26	(	(	PUNCT
ejpam-7013	220	27	fuzzy	fuzzy	ADJ
ejpam-7013	220	28	)	)	PUNCT
ejpam-7013	220	29	mapping	mapping	NOUN
ejpam-7013	220	30	.	.	PUNCT
ejpam-7013	221	1	denote	denote	VERB
ejpam-7013	221	2	by	by	ADP
ejpam-7013	221	3	d	d	X
ejpam-7013	221	4	:	:	PUNCT
ejpam-7013	221	5	x	x	SYM
ejpam-7013	221	6	×	×	NOUN
ejpam-7013	221	7	x	x	INTJ
ejpam-7013	221	8	→	→	X
ejpam-7013	221	9	[	[	X
ejpam-7013	221	10	0,∞	0,∞	NOUN
ejpam-7013	221	11	)	)	PUNCT
ejpam-7013	221	12	the	the	DET
ejpam-7013	221	13	underlying	underlie	VERB
ejpam-7013	221	14	b	b	X
ejpam-7013	221	15	-	-	ADJ
ejpam-7013	221	16	metric	metric	ADJ
ejpam-7013	221	17	with	with	ADP
ejpam-7013	221	18	b	b	NOUN
ejpam-7013	221	19	-	-	PUNCT
ejpam-7013	221	20	constant	constant	ADJ
ejpam-7013	221	21	s	s	PART
ejpam-7013	221	22	≥	≥	NUM
ejpam-7013	221	23	1	1	NUM
ejpam-7013	221	24	.	.	PUNCT
ejpam-7013	221	25	assume	assume	VERB
ejpam-7013	221	26	there	there	PRON
ejpam-7013	221	27	exist	exist	VERB
ejpam-7013	221	28	constants	constant	NOUN
ejpam-7013	221	29	λ1,λ2,λ3,λ4	λ1,λ2,λ3,λ4	PROPN
ejpam-7013	221	30	≥	≥	X
ejpam-7013	221	31	0	0	NUM
ejpam-7013	221	32	satisfying	satisfy	VERB
ejpam-7013	221	33	λ1s	λ1s	NOUN
ejpam-7013	221	34	<	<	X
ejpam-7013	221	35	1	1	NUM
ejpam-7013	221	36	,	,	PUNCT
ejpam-7013	221	37	λ1	λ1	ADJ
ejpam-7013	221	38	+	+	NUM
ejpam-7013	221	39	λ2	λ2	NOUN
ejpam-7013	222	1	+	+	CCONJ
ejpam-7013	222	2	λ3	λ3	PROPN
ejpam-7013	222	3	<	<	X
ejpam-7013	222	4	1	1	NUM
ejpam-7013	222	5	,	,	PUNCT
ejpam-7013	222	6	2λ2	2λ2	NUM
ejpam-7013	223	1	+	+	CCONJ
ejpam-7013	223	2	λ4	λ4	ADJ
ejpam-7013	223	3	<	<	X
ejpam-7013	223	4	1	1	NUM
ejpam-7013	223	5	+	+	SYM
ejpam-7013	223	6	λ1	λ1	ADJ
ejpam-7013	223	7	,	,	PUNCT
ejpam-7013	223	8	λ3	λ3	PROPN
ejpam-7013	223	9	<	<	X
ejpam-7013	223	10	1	1	NUM
ejpam-7013	223	11	.	.	PUNCT
ejpam-7013	223	12	suppose	suppose	VERB
ejpam-7013	223	13	that	that	SCONJ
ejpam-7013	223	14	for	for	ADP
ejpam-7013	223	15	all	all	DET
ejpam-7013	223	16	l	l	NOUN
ejpam-7013	223	17	,	,	PUNCT
ejpam-7013	223	18	p	p	PROPN
ejpam-7013	223	19	∈	∈	PROPN
ejpam-7013	223	20	x	x	PUNCT
ejpam-7013	223	21	the	the	DET
ejpam-7013	223	22	following	follow	VERB
ejpam-7013	223	23	inequality	inequality	NOUN
ejpam-7013	223	24	holds	hold	VERB
ejpam-7013	223	25	:	:	PUNCT
ejpam-7013	223	26	h	h	PROPN
ejpam-7013	223	27	(	(	PUNCT
ejpam-7013	223	28	t	t	PROPN
ejpam-7013	223	29	(	(	PUNCT
ejpam-7013	223	30	l	l	NOUN
ejpam-7013	223	31	)	)	PUNCT
ejpam-7013	223	32	,	,	PUNCT
ejpam-7013	223	33	t	t	PROPN
ejpam-7013	223	34	(	(	PUNCT
ejpam-7013	223	35	p	p	NOUN
ejpam-7013	223	36	)	)	PUNCT
ejpam-7013	223	37	)	)	PUNCT
ejpam-7013	224	1	+	+	X
ejpam-7013	224	2	λ4	λ4	ADJ
ejpam-7013	224	3	(	(	PUNCT
ejpam-7013	224	4	dα(l	dα(l	PROPN
ejpam-7013	224	5	,	,	PUNCT
ejpam-7013	224	6	t	t	PROPN
ejpam-7013	224	7	(	(	PUNCT
ejpam-7013	224	8	p))+dα(p	p))+dα(p	PROPN
ejpam-7013	224	9	,	,	PUNCT
ejpam-7013	224	10	t	t	PROPN
ejpam-7013	224	11	(	(	PUNCT
ejpam-7013	224	12	p	p	NOUN
ejpam-7013	224	13	)	)	PUNCT
ejpam-7013	224	14	)	)	PUNCT
ejpam-7013	224	15	)	)	PUNCT
ejpam-7013	224	16	≤	≤	NOUN
ejpam-7013	225	1	λ1dα(l	λ1dα(l	PROPN
ejpam-7013	225	2	,	,	PUNCT
ejpam-7013	225	3	t	t	PROPN
ejpam-7013	225	4	(	(	PUNCT
ejpam-7013	225	5	l))+λ2dα(p	l))+λ2dα(p	PROPN
ejpam-7013	225	6	,	,	PUNCT
ejpam-7013	225	7	t	t	PROPN
ejpam-7013	225	8	(	(	PUNCT
ejpam-7013	225	9	l))+λ3d(l	l))+λ3d(l	ADV
ejpam-7013	225	10	,	,	PUNCT
ejpam-7013	225	11	p	p	NOUN
ejpam-7013	225	12	)	)	PUNCT
ejpam-7013	225	13	.	.	PUNCT
ejpam-7013	226	1	then	then	ADV
ejpam-7013	226	2	t	t	PROPN
ejpam-7013	226	3	has	have	VERB
ejpam-7013	226	4	at	at	ADV
ejpam-7013	226	5	least	least	ADV
ejpam-7013	226	6	one	one	NUM
ejpam-7013	226	7	fuzzy	fuzzy	ADJ
ejpam-7013	226	8	fp	fp	X
ejpam-7013	226	9	:	:	PUNCT
ejpam-7013	226	10	there	there	PRON
ejpam-7013	226	11	exists	exist	VERB
ejpam-7013	226	12	k	k	PROPN
ejpam-7013	226	13	∈	∈	PROPN
ejpam-7013	226	14	x	x	PUNCT
ejpam-7013	227	1	such	such	ADJ
ejpam-7013	227	2	that	that	SCONJ
ejpam-7013	227	3	{	{	PUNCT
ejpam-7013	227	4	k	k	NOUN
ejpam-7013	227	5	}	}	PUNCT
ejpam-7013	227	6	⊆	⊆	NUM
ejpam-7013	227	7	t	t	NOUN
ejpam-7013	227	8	(	(	PUNCT
ejpam-7013	227	9	k	k	NOUN
ejpam-7013	227	10	)	)	PUNCT
ejpam-7013	227	11	.	.	PUNCT
ejpam-7013	227	12	proof	proof	NOUN
ejpam-7013	227	13	.	.	PUNCT
ejpam-7013	228	1	choose	choose	VERB
ejpam-7013	228	2	an	an	DET
ejpam-7013	228	3	arbitrary	arbitrary	ADJ
ejpam-7013	228	4	point	point	NOUN
ejpam-7013	228	5	l0	l0	NOUN
ejpam-7013	228	6	∈	∈	PROPN
ejpam-7013	228	7	x	x	X
ejpam-7013	228	8	and	and	CCONJ
ejpam-7013	228	9	select	select	ADJ
ejpam-7013	228	10	l1	l1	PROPN
ejpam-7013	228	11	∈	∈	PROPN
ejpam-7013	228	12	t	t	PROPN
ejpam-7013	228	13	(	(	PUNCT
ejpam-7013	228	14	l0	l0	PROPN
ejpam-7013	228	15	)	)	PUNCT
ejpam-7013	228	16	.	.	PUNCT
ejpam-7013	229	1	recursively	recursively	ADV
ejpam-7013	229	2	choose	choose	VERB
ejpam-7013	229	3	ln+1	ln+1	PROPN
ejpam-7013	229	4	∈	∈	PROPN
ejpam-7013	229	5	t	t	PROPN
ejpam-7013	229	6	(	(	PUNCT
ejpam-7013	229	7	ln	ln	ADJ
ejpam-7013	229	8	)	)	PUNCT
ejpam-7013	229	9	for	for	ADP
ejpam-7013	229	10	each	each	DET
ejpam-7013	229	11	n	n	PRON
ejpam-7013	229	12	≥	≥	NOUN
ejpam-7013	229	13	0	0	NUM
ejpam-7013	229	14	.	.	PUNCT
ejpam-7013	230	1	for	for	ADP
ejpam-7013	230	2	each	each	DET
ejpam-7013	230	3	n	n	PRON
ejpam-7013	230	4	also	also	ADV
ejpam-7013	230	5	choose	choose	VERB
ejpam-7013	230	6	ln+2	ln+2	NUM
ejpam-7013	230	7	∈	∈	PROPN
ejpam-7013	230	8	t	t	PROPN
ejpam-7013	230	9	(	(	PUNCT
ejpam-7013	230	10	ln+1	ln+1	PROPN
ejpam-7013	230	11	)	)	PUNCT
ejpam-7013	230	12	in	in	ADP
ejpam-7013	230	13	such	such	DET
ejpam-7013	230	14	a	a	DET
ejpam-7013	230	15	way	way	NOUN
ejpam-7013	230	16	that	that	PRON
ejpam-7013	230	17	d(ln+1,ln+2	d(ln+1,ln+2	VERB
ejpam-7013	230	18	)	)	PUNCT
ejpam-7013	230	19	≤	≤	NUM
ejpam-7013	230	20	h	h	NOUN
ejpam-7013	230	21	(	(	PUNCT
ejpam-7013	230	22	t	t	PROPN
ejpam-7013	230	23	(	(	PUNCT
ejpam-7013	230	24	ln	ln	PROPN
ejpam-7013	230	25	)	)	PUNCT
ejpam-7013	230	26	,	,	PUNCT
ejpam-7013	230	27	t	t	PROPN
ejpam-7013	230	28	(	(	PUNCT
ejpam-7013	230	29	ln+1	ln+1	PROPN
ejpam-7013	230	30	)	)	PUNCT
ejpam-7013	230	31	)	)	PUNCT
ejpam-7013	231	1	+	+	CCONJ
ejpam-7013	232	1	εn	εn	ADJ
ejpam-7013	232	2	,	,	PUNCT
ejpam-7013	232	3	(	(	PUNCT
ejpam-7013	232	4	2	2	NUM
ejpam-7013	232	5	)	)	PUNCT
ejpam-7013	232	6	where	where	SCONJ
ejpam-7013	232	7	(	(	PUNCT
ejpam-7013	232	8	εn	εn	ADJ
ejpam-7013	232	9	)	)	PUNCT
ejpam-7013	232	10	is	be	AUX
ejpam-7013	232	11	a	a	DET
ejpam-7013	232	12	sequence	sequence	NOUN
ejpam-7013	232	13	of	of	ADP
ejpam-7013	232	14	positive	positive	ADJ
ejpam-7013	232	15	numbers	number	NOUN
ejpam-7013	232	16	with	with	ADP
ejpam-7013	232	17	εn	εn	ADJ
ejpam-7013	232	18	↓	↓	PROPN
ejpam-7013	232	19	0	0	NUM
ejpam-7013	232	20	.	.	PUNCT
ejpam-7013	233	1	the	the	DET
ejpam-7013	233	2	inequality	inequality	NOUN
ejpam-7013	233	3	(	(	PUNCT
ejpam-7013	233	4	2	2	NUM
ejpam-7013	233	5	)	)	PUNCT
ejpam-7013	233	6	is	be	AUX
ejpam-7013	233	7	possible	possible	ADJ
ejpam-7013	233	8	by	by	ADP
ejpam-7013	233	9	the	the	DET
ejpam-7013	233	10	definition	definition	NOUN
ejpam-7013	233	11	of	of	ADP
ejpam-7013	233	12	the	the	DET
ejpam-7013	233	13	hausdorff	hausdorff	NOUN
ejpam-7013	233	14	metric	metric	NOUN
ejpam-7013	233	15	:	:	PUNCT
ejpam-7013	233	16	for	for	ADP
ejpam-7013	233	17	any	any	DET
ejpam-7013	233	18	point	point	NOUN
ejpam-7013	233	19	of	of	ADP
ejpam-7013	233	20	t	t	PROPN
ejpam-7013	233	21	(	(	PUNCT
ejpam-7013	233	22	ln	ln	ADJ
ejpam-7013	233	23	)	)	PUNCT
ejpam-7013	233	24	there	there	PRON
ejpam-7013	233	25	exists	exist	VERB
ejpam-7013	233	26	a	a	DET
ejpam-7013	233	27	point	point	NOUN
ejpam-7013	233	28	of	of	ADP
ejpam-7013	233	29	t	t	PROPN
ejpam-7013	233	30	(	(	PUNCT
ejpam-7013	233	31	ln+1	ln+1	PROPN
ejpam-7013	233	32	)	)	PUNCT
ejpam-7013	233	33	within	within	ADP
ejpam-7013	233	34	distance	distance	NOUN
ejpam-7013	233	35	h(t	h(t	PROPN
ejpam-7013	233	36	(	(	PUNCT
ejpam-7013	233	37	ln	ln	ADJ
ejpam-7013	233	38	)	)	PUNCT
ejpam-7013	233	39	,	,	PUNCT
ejpam-7013	233	40	t	t	PROPN
ejpam-7013	233	41	(	(	PUNCT
ejpam-7013	233	42	ln+1	ln+1	PROPN
ejpam-7013	233	43	)	)	PUNCT
ejpam-7013	233	44	)	)	PUNCT
ejpam-7013	234	1	+	+	CCONJ
ejpam-7013	234	2	εn	εn	ADJ
ejpam-7013	234	3	,	,	PUNCT
ejpam-7013	234	4	and	and	CCONJ
ejpam-7013	234	5	we	we	PRON
ejpam-7013	234	6	take	take	VERB
ejpam-7013	234	7	these	these	DET
ejpam-7013	234	8	points	point	NOUN
ejpam-7013	234	9	to	to	PART
ejpam-7013	234	10	produce	produce	VERB
ejpam-7013	234	11	the	the	DET
ejpam-7013	234	12	orbit	orbit	NOUN
ejpam-7013	234	13	.	.	PUNCT
ejpam-7013	235	1	set	set	VERB
ejpam-7013	235	2	sn	sn	NOUN
ejpam-7013	235	3	:	:	PUNCT
ejpam-7013	235	4	=	=	SYM
ejpam-7013	235	5	d(ln	d(ln	PROPN
ejpam-7013	235	6	,	,	PUNCT
ejpam-7013	235	7	ln+1	ln+1	PROPN
ejpam-7013	235	8	)	)	PUNCT
ejpam-7013	235	9	for	for	ADP
ejpam-7013	235	10	n	n	PRON
ejpam-7013	235	11	≥	≥	NOUN
ejpam-7013	235	12	0	0	NUM
ejpam-7013	235	13	.	.	PUNCT
ejpam-7013	235	14	apply	apply	VERB
ejpam-7013	235	15	the	the	DET
ejpam-7013	235	16	contractive	contractive	ADJ
ejpam-7013	235	17	hypothesis	hypothesis	NOUN
ejpam-7013	235	18	with	with	ADP
ejpam-7013	235	19	l	l	NOUN
ejpam-7013	235	20	=	=	PUNCT
ejpam-7013	235	21	ln	ln	ADJ
ejpam-7013	235	22	and	and	CCONJ
ejpam-7013	235	23	p	p	X
ejpam-7013	235	24	=	=	PUNCT
ejpam-7013	235	25	ln+1	ln+1	ADJ
ejpam-7013	235	26	:	:	PUNCT
ejpam-7013	236	1	h	h	PROPN
ejpam-7013	236	2	(	(	PUNCT
ejpam-7013	236	3	t	t	PROPN
ejpam-7013	236	4	(	(	PUNCT
ejpam-7013	236	5	ln	ln	PROPN
ejpam-7013	236	6	)	)	PUNCT
ejpam-7013	236	7	,	,	PUNCT
ejpam-7013	236	8	t	t	PROPN
ejpam-7013	236	9	(	(	PUNCT
ejpam-7013	236	10	ln+1	ln+1	PROPN
ejpam-7013	236	11	)	)	PUNCT
ejpam-7013	236	12	)	)	PUNCT
ejpam-7013	237	1	≤	≤	ADV
ejpam-7013	237	2	λ1dα(ln	λ1dα(ln	PROPN
ejpam-7013	237	3	,	,	PUNCT
ejpam-7013	237	4	t	t	PROPN
ejpam-7013	237	5	(	(	PUNCT
ejpam-7013	237	6	ln	ln	ADJ
ejpam-7013	237	7	)	)	PUNCT
ejpam-7013	237	8	)	)	PUNCT
ejpam-7013	238	1	+	+	PUNCT
ejpam-7013	239	1	λ2dα(ln+1	λ2dα(ln+1	ADJ
ejpam-7013	239	2	,	,	PUNCT
ejpam-7013	239	3	t	t	PROPN
ejpam-7013	239	4	(	(	PUNCT
ejpam-7013	239	5	ln	ln	ADJ
ejpam-7013	239	6	)	)	PUNCT
ejpam-7013	239	7	)	)	PUNCT
ejpam-7013	240	1	+	+	CCONJ
ejpam-7013	240	2	λ3sn	λ3sn	PUNCT
ejpam-7013	241	1	−	−	ADV
ejpam-7013	241	2	λ4	λ4	ADJ
ejpam-7013	241	3	(	(	PUNCT
ejpam-7013	241	4	dα(ln	dα(ln	PROPN
ejpam-7013	241	5	,	,	PUNCT
ejpam-7013	241	6	t	t	PROPN
ejpam-7013	241	7	(	(	PUNCT
ejpam-7013	241	8	ln+1	ln+1	PROPN
ejpam-7013	241	9	)	)	PUNCT
ejpam-7013	241	10	)	)	PUNCT
ejpam-7013	242	1	+	+	PUNCT
ejpam-7013	242	2	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	242	3	,	,	PUNCT
ejpam-7013	242	4	t	t	PROPN
ejpam-7013	242	5	(	(	PUNCT
ejpam-7013	242	6	ln+1	ln+1	PROPN
ejpam-7013	242	7	)	)	PUNCT
ejpam-7013	242	8	)	)	PUNCT
ejpam-7013	242	9	)	)	PUNCT
ejpam-7013	242	10	.	.	PUNCT
ejpam-7013	243	1	(	(	PUNCT
ejpam-7013	243	2	3	3	X
ejpam-7013	243	3	)	)	PUNCT
ejpam-7013	243	4	because	because	SCONJ
ejpam-7013	243	5	ln+1	ln+1	PROPN
ejpam-7013	243	6	∈	∈	PROPN
ejpam-7013	243	7	t	t	PROPN
ejpam-7013	243	8	(	(	PUNCT
ejpam-7013	243	9	ln	ln	ADJ
ejpam-7013	243	10	)	)	PUNCT
ejpam-7013	243	11	one	one	NOUN
ejpam-7013	243	12	has	have	VERB
ejpam-7013	243	13	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	243	14	,	,	PUNCT
ejpam-7013	243	15	t	t	PROPN
ejpam-7013	243	16	(	(	PUNCT
ejpam-7013	243	17	ln	ln	ADJ
ejpam-7013	243	18	)	)	PUNCT
ejpam-7013	243	19	)	)	PUNCT
ejpam-7013	244	1	=	=	SYM
ejpam-7013	244	2	0	0	NUM
ejpam-7013	244	3	,	,	PUNCT
ejpam-7013	244	4	and	and	CCONJ
ejpam-7013	244	5	trivially	trivially	ADV
ejpam-7013	244	6	dα(ln	dα(ln	ADJ
ejpam-7013	244	7	,	,	PUNCT
ejpam-7013	244	8	t	t	PROPN
ejpam-7013	244	9	(	(	PUNCT
ejpam-7013	244	10	ln	ln	ADJ
ejpam-7013	244	11	)	)	PUNCT
ejpam-7013	244	12	)	)	PUNCT
ejpam-7013	244	13	≤	≤	NUM
ejpam-7013	244	14	sn	sn	PROPN
ejpam-7013	244	15	and	and	CCONJ
ejpam-7013	244	16	dα(ln+1	dα(ln+1	PROPN
ejpam-7013	244	17	,	,	PUNCT
ejpam-7013	244	18	t	t	PROPN
ejpam-7013	244	19	(	(	PUNCT
ejpam-7013	244	20	ln+1	ln+1	PROPN
ejpam-7013	244	21	)	)	PUNCT
ejpam-7013	244	22	)	)	PUNCT
ejpam-7013	244	23	≤	≤	NUM
ejpam-7013	244	24	sn+1	sn+1	VERB
ejpam-7013	244	25	.	.	PUNCT
ejpam-7013	245	1	moreover	moreover	ADV
ejpam-7013	245	2	dα(ln	dα(ln	PROPN
ejpam-7013	245	3	,	,	PUNCT
ejpam-7013	245	4	t	t	PROPN
ejpam-7013	245	5	(	(	PUNCT
ejpam-7013	245	6	ln+1	ln+1	PROPN
ejpam-7013	245	7	)	)	PUNCT
ejpam-7013	245	8	)	)	PUNCT
ejpam-7013	246	1	≤	≤	PROPN
ejpam-7013	246	2	d(ln	d(ln	PROPN
ejpam-7013	246	3	,	,	PUNCT
ejpam-7013	246	4	ln+2	ln+2	NUM
ejpam-7013	246	5	)	)	PUNCT
ejpam-7013	246	6	≤	≤	NOUN
ejpam-7013	246	7	s	s	PART
ejpam-7013	246	8	(	(	PUNCT
ejpam-7013	246	9	sn	sn	X
ejpam-7013	246	10	+	+	X
ejpam-7013	246	11	sn+1	sn+1	X
ejpam-7013	246	12	)	)	PUNCT
ejpam-7013	246	13	,	,	PUNCT
ejpam-7013	246	14	by	by	ADP
ejpam-7013	246	15	the	the	DET
ejpam-7013	246	16	b	b	NOUN
ejpam-7013	246	17	-	-	PUNCT
ejpam-7013	246	18	metric	metric	ADJ
ejpam-7013	246	19	inequality	inequality	NOUN
ejpam-7013	246	20	.	.	PUNCT
ejpam-7013	247	1	substitute	substitute	NOUN
ejpam-7013	247	2	these	these	DET
ejpam-7013	247	3	bounds	bound	NOUN
ejpam-7013	247	4	into	into	ADP
ejpam-7013	247	5	(	(	PUNCT
ejpam-7013	247	6	3	3	NUM
ejpam-7013	247	7	)	)	PUNCT
ejpam-7013	247	8	to	to	PART
ejpam-7013	247	9	get	get	VERB
ejpam-7013	247	10	h	h	NOUN
ejpam-7013	247	11	(	(	PUNCT
ejpam-7013	247	12	t	t	PROPN
ejpam-7013	247	13	(	(	PUNCT
ejpam-7013	247	14	ln	ln	PROPN
ejpam-7013	247	15	)	)	PUNCT
ejpam-7013	247	16	,	,	PUNCT
ejpam-7013	247	17	t	t	PROPN
ejpam-7013	247	18	(	(	PUNCT
ejpam-7013	247	19	ln+1	ln+1	PROPN
ejpam-7013	247	20	)	)	PUNCT
ejpam-7013	247	21	)	)	PUNCT
ejpam-7013	247	22	≤	≤	NOUN
ejpam-7013	247	23	λ1sn	λ1sn	PUNCT
ejpam-7013	248	1	+	+	CCONJ
ejpam-7013	248	2	λ3sn	λ3sn	PUNCT
ejpam-7013	248	3	−	−	ADV
ejpam-7013	248	4	λ4	λ4	ADJ
ejpam-7013	248	5	(	(	PUNCT
ejpam-7013	248	6	s	s	X
ejpam-7013	248	7	(	(	PUNCT
ejpam-7013	248	8	sn	sn	X
ejpam-7013	248	9	+	+	CCONJ
ejpam-7013	248	10	sn+1	sn+1	X
ejpam-7013	248	11	)	)	PUNCT
ejpam-7013	248	12	+	+	NUM
ejpam-7013	248	13	sn+1	sn+1	X
ejpam-7013	248	14	)	)	PUNCT
ejpam-7013	248	15	.	.	PUNCT
ejpam-7013	249	1	now	now	ADV
ejpam-7013	249	2	combine	combine	VERB
ejpam-7013	249	3	the	the	DET
ejpam-7013	249	4	last	last	ADJ
ejpam-7013	249	5	display	display	NOUN
ejpam-7013	249	6	with	with	ADP
ejpam-7013	249	7	(	(	PUNCT
ejpam-7013	249	8	2	2	NUM
ejpam-7013	249	9	)	)	PUNCT
ejpam-7013	249	10	to	to	PART
ejpam-7013	249	11	estimate	estimate	VERB
ejpam-7013	249	12	sn+1	sn+1	NUM
ejpam-7013	249	13	:	:	PUNCT
ejpam-7013	249	14	sn+1	sn+1	VERB
ejpam-7013	249	15	≤	≤	NUM
ejpam-7013	249	16	h	h	NOUN
ejpam-7013	249	17	(	(	PUNCT
ejpam-7013	249	18	t	t	PROPN
ejpam-7013	249	19	(	(	PUNCT
ejpam-7013	249	20	ln	ln	PROPN
ejpam-7013	249	21	)	)	PUNCT
ejpam-7013	249	22	,	,	PUNCT
ejpam-7013	249	23	t	t	PROPN
ejpam-7013	249	24	(	(	PUNCT
ejpam-7013	249	25	ln+1	ln+1	PROPN
ejpam-7013	249	26	)	)	PUNCT
ejpam-7013	249	27	)	)	PUNCT
ejpam-7013	250	1	+	+	CCONJ
ejpam-7013	250	2	εn	εn	ADJ
ejpam-7013	250	3	≤	≤	X
ejpam-7013	250	4	(	(	PUNCT
ejpam-7013	250	5	λ1	λ1	PROPN
ejpam-7013	250	6	+	+	CCONJ
ejpam-7013	250	7	λ3	λ3	PROPN
ejpam-7013	250	8	)	)	PUNCT
ejpam-7013	250	9	sn	sn	PROPN
ejpam-7013	250	10	−	−	PROPN
ejpam-7013	250	11	λ4	λ4	PROPN
ejpam-7013	250	12	(	(	PUNCT
ejpam-7013	250	13	s(sn	s(sn	PUNCT
ejpam-7013	250	14	+	+	X
ejpam-7013	250	15	sn+1	sn+1	X
ejpam-7013	250	16	)	)	PUNCT
ejpam-7013	250	17	+	+	X
ejpam-7013	250	18	sn+1	sn+1	X
ejpam-7013	250	19	)	)	PUNCT
ejpam-7013	250	20	+	+	CCONJ
ejpam-7013	251	1	εn	εn	ADJ
ejpam-7013	251	2	=	=	PUNCT
ejpam-7013	251	3	(	(	PUNCT
ejpam-7013	251	4	λ1	λ1	PROPN
ejpam-7013	251	5	+	+	CCONJ
ejpam-7013	251	6	λ3	λ3	PROPN
ejpam-7013	251	7	−	−	PROPN
ejpam-7013	251	8	λ4s	λ4s	NOUN
ejpam-7013	251	9	)	)	PUNCT
ejpam-7013	251	10	sn	sn	INTJ
ejpam-7013	251	11	−	−	PROPN
ejpam-7013	252	1	λ4(s+	λ4(s+	PROPN
ejpam-7013	252	2	1)sn+1	1)sn+1	PROPN
ejpam-7013	252	3	+	+	CCONJ
ejpam-7013	252	4	εn	εn	ADJ
ejpam-7013	252	5	.	.	PUNCT
ejpam-7013	253	1	collect	collect	VERB
ejpam-7013	253	2	terms	term	NOUN
ejpam-7013	253	3	containing	contain	VERB
ejpam-7013	253	4	sn+1	sn+1	NUM
ejpam-7013	253	5	on	on	ADP
ejpam-7013	253	6	the	the	DET
ejpam-7013	253	7	left	left	ADJ
ejpam-7013	253	8	-	-	PUNCT
ejpam-7013	253	9	hand	hand	NOUN
ejpam-7013	253	10	side	side	NOUN
ejpam-7013	253	11	:(	:(	X
ejpam-7013	254	1	1	1	NUM
ejpam-7013	254	2	+	+	NUM
ejpam-7013	254	3	λ4(s+	λ4(s+	PROPN
ejpam-7013	254	4	1	1	NUM
ejpam-7013	254	5	)	)	PUNCT
ejpam-7013	254	6	)	)	PUNCT
ejpam-7013	254	7	sn+1	sn+1	VERB
ejpam-7013	254	8	≤	≤	NOUN
ejpam-7013	254	9	(	(	PUNCT
ejpam-7013	254	10	λ1	λ1	PROPN
ejpam-7013	254	11	+	+	CCONJ
ejpam-7013	255	1	λ3	λ3	PROPN
ejpam-7013	255	2	−	−	PROPN
ejpam-7013	255	3	λ4s	λ4s	NOUN
ejpam-7013	255	4	)	)	PUNCT
ejpam-7013	255	5	sn	sn	PROPN
ejpam-7013	256	1	+	+	CCONJ
ejpam-7013	256	2	εn	εn	ADJ
ejpam-7013	256	3	.	.	PUNCT
ejpam-7013	257	1	d.	d.	PROPN
ejpam-7013	257	2	gerbeti	gerbeti	PROPN
ejpam-7013	257	3	et	et	PROPN
ejpam-7013	257	4	al	al	PROPN
ejpam-7013	257	5	.	.	PUNCT
ejpam-7013	257	6	/	/	SYM
ejpam-7013	257	7	eur	eur	PROPN
ejpam-7013	257	8	.	.	PUNCT
ejpam-7013	258	1	j.	j.	PROPN
ejpam-7013	258	2	pure	pure	PROPN
ejpam-7013	258	3	appl	appl	PROPN
ejpam-7013	258	4	.	.	PROPN
ejpam-7013	258	5	math	math	PROPN
ejpam-7013	258	6	,	,	PUNCT
ejpam-7013	258	7	18	18	NUM
ejpam-7013	258	8	(	(	PUNCT
ejpam-7013	258	9	4	4	NUM
ejpam-7013	258	10	)	)	PUNCT
ejpam-7013	258	11	(	(	PUNCT
ejpam-7013	258	12	2025	2025	NUM
ejpam-7013	258	13	)	)	PUNCT
ejpam-7013	258	14	,	,	PUNCT
ejpam-7013	258	15	7013	7013	NUM
ejpam-7013	258	16	10	10	NUM
ejpam-7013	258	17	of	of	ADP
ejpam-7013	258	18	17	17	NUM
ejpam-7013	258	19	because	because	SCONJ
ejpam-7013	258	20	the	the	DET
ejpam-7013	258	21	parameters	parameter	NOUN
ejpam-7013	258	22	satisfy	satisfy	VERB
ejpam-7013	258	23	the	the	DET
ejpam-7013	258	24	structural	structural	ADJ
ejpam-7013	258	25	inequalities	inequality	NOUN
ejpam-7013	258	26	assumed	assume	VERB
ejpam-7013	258	27	in	in	ADP
ejpam-7013	258	28	the	the	DET
ejpam-7013	258	29	theorem	theorem	NOUN
ejpam-7013	258	30	,	,	PUNCT
ejpam-7013	258	31	the	the	DET
ejpam-7013	258	32	coefficient	coefficient	NOUN
ejpam-7013	258	33	on	on	ADP
ejpam-7013	258	34	the	the	DET
ejpam-7013	258	35	left	left	NOUN
ejpam-7013	258	36	is	be	AUX
ejpam-7013	258	37	positive	positive	ADJ
ejpam-7013	258	38	;	;	PUNCT
ejpam-7013	258	39	indeed	indeed	ADV
ejpam-7013	258	40	1+λ4(s+1	1+λ4(s+1	NUM
ejpam-7013	258	41	)	)	PUNCT
ejpam-7013	258	42	>	>	X
ejpam-7013	258	43	0	0	PUNCT
ejpam-7013	258	44	since	since	SCONJ
ejpam-7013	258	45	all	all	DET
ejpam-7013	258	46	constants	constant	NOUN
ejpam-7013	258	47	are	be	AUX
ejpam-7013	258	48	nonnegative	nonnegative	ADJ
ejpam-7013	258	49	.	.	PUNCT
ejpam-7013	259	1	divide	divide	VERB
ejpam-7013	259	2	both	both	DET
ejpam-7013	259	3	sides	side	NOUN
ejpam-7013	259	4	by	by	ADP
ejpam-7013	259	5	1	1	NUM
ejpam-7013	259	6	+	+	NUM
ejpam-7013	259	7	λ4(s+	λ4(s+	PROPN
ejpam-7013	259	8	1	1	NUM
ejpam-7013	259	9	)	)	PUNCT
ejpam-7013	259	10	to	to	PART
ejpam-7013	259	11	obtain	obtain	VERB
ejpam-7013	259	12	sn+1	sn+1	NOUN
ejpam-7013	259	13	≤	≤	PUNCT
ejpam-7013	259	14	q	q	PROPN
ejpam-7013	259	15	sn	sn	PROPN
ejpam-7013	259	16	+	+	CCONJ
ejpam-7013	259	17	εn	εn	ADJ
ejpam-7013	259	18	1	1	NUM
ejpam-7013	259	19	+	+	PROPN
ejpam-7013	259	20	λ4(s+	λ4(s+	PROPN
ejpam-7013	259	21	1	1	NUM
ejpam-7013	259	22	)	)	PUNCT
ejpam-7013	259	23	,	,	PUNCT
ejpam-7013	259	24	where	where	SCONJ
ejpam-7013	259	25	q	q	X
ejpam-7013	259	26	:	:	PUNCT
ejpam-7013	259	27	=	=	SYM
ejpam-7013	259	28	λ1	λ1	PROPN
ejpam-7013	259	29	+	+	CCONJ
ejpam-7013	259	30	λ3	λ3	PROPN
ejpam-7013	259	31	−	−	PROPN
ejpam-7013	259	32	λ4s	λ4s	NOUN
ejpam-7013	259	33	1	1	NUM
ejpam-7013	259	34	+	+	NUM
ejpam-7013	259	35	λ4(s+	λ4(s+	PROPN
ejpam-7013	259	36	1	1	NUM
ejpam-7013	259	37	)	)	PUNCT
ejpam-7013	259	38	.	.	PUNCT
ejpam-7013	260	1	we	we	PRON
ejpam-7013	260	2	now	now	ADV
ejpam-7013	260	3	show	show	VERB
ejpam-7013	260	4	q	q	PUNCT
ejpam-7013	260	5	∈	∈	PROPN
ejpam-7013	261	1	[	[	X
ejpam-7013	261	2	0	0	NUM
ejpam-7013	261	3	,	,	PUNCT
ejpam-7013	261	4	1	1	NUM
ejpam-7013	261	5	)	)	PUNCT
ejpam-7013	261	6	.	.	PUNCT
ejpam-7013	262	1	nonnegativity	nonnegativity	NOUN
ejpam-7013	262	2	of	of	ADP
ejpam-7013	262	3	q	q	PROPN
ejpam-7013	262	4	follows	follow	VERB
ejpam-7013	262	5	from	from	ADP
ejpam-7013	262	6	the	the	DET
ejpam-7013	262	7	assumed	assume	VERB
ejpam-7013	262	8	bounds	bound	NOUN
ejpam-7013	262	9	(	(	PUNCT
ejpam-7013	262	10	if	if	SCONJ
ejpam-7013	262	11	the	the	DET
ejpam-7013	262	12	numerator	numerator	NOUN
ejpam-7013	262	13	were	be	AUX
ejpam-7013	262	14	negative	negative	ADJ
ejpam-7013	262	15	then	then	ADV
ejpam-7013	262	16	trivially	trivially	ADV
ejpam-7013	262	17	q	q	X
ejpam-7013	262	18	<	<	X
ejpam-7013	262	19	1	1	NUM
ejpam-7013	262	20	;	;	PUNCT
ejpam-7013	262	21	otherwise	otherwise	ADV
ejpam-7013	262	22	the	the	DET
ejpam-7013	262	23	numerator	numerator	NOUN
ejpam-7013	262	24	is	be	AUX
ejpam-7013	262	25	nonnegative	nonnegative	ADJ
ejpam-7013	262	26	)	)	PUNCT
ejpam-7013	262	27	.	.	PUNCT
ejpam-7013	263	1	to	to	PART
ejpam-7013	263	2	verify	verify	VERB
ejpam-7013	263	3	q	q	NOUN
ejpam-7013	263	4	<	<	X
ejpam-7013	263	5	1	1	NUM
ejpam-7013	263	6	we	we	PRON
ejpam-7013	263	7	compute	compute	VERB
ejpam-7013	263	8	q	q	X
ejpam-7013	263	9	<	<	X
ejpam-7013	263	10	1	1	NUM
ejpam-7013	263	11	⇐	⇐	ADJ
ejpam-7013	263	12	⇒	⇒	NOUN
ejpam-7013	263	13	λ1	λ1	PROPN
ejpam-7013	264	1	+	+	CCONJ
ejpam-7013	264	2	λ3	λ3	PROPN
ejpam-7013	264	3	−	−	PROPN
ejpam-7013	264	4	λ4s	λ4s	NOUN
ejpam-7013	264	5	<	<	X
ejpam-7013	264	6	1	1	NUM
ejpam-7013	264	7	+	+	CCONJ
ejpam-7013	264	8	λ4(s+	λ4(s+	PROPN
ejpam-7013	264	9	1	1	NUM
ejpam-7013	264	10	)	)	PUNCT
ejpam-7013	264	11	⇐	⇐	ADJ
ejpam-7013	264	12	⇒	⇒	X
ejpam-7013	264	13	λ1	λ1	PROPN
ejpam-7013	264	14	+	+	CCONJ
ejpam-7013	264	15	λ3	λ3	PROPN
ejpam-7013	264	16	−	−	PROPN
ejpam-7013	264	17	λ4s	λ4s	NOUN
ejpam-7013	264	18	<	<	X
ejpam-7013	264	19	1	1	NUM
ejpam-7013	264	20	+	+	CCONJ
ejpam-7013	264	21	λ4s+	λ4s+	PROPN
ejpam-7013	264	22	λ4	λ4	PROPN
ejpam-7013	264	23	,	,	PUNCT
ejpam-7013	264	24	which	which	PRON
ejpam-7013	264	25	simplifies	simplify	VERB
ejpam-7013	264	26	to	to	ADP
ejpam-7013	264	27	λ1	λ1	PROPN
ejpam-7013	264	28	+	+	CCONJ
ejpam-7013	264	29	λ3	λ3	PROPN
ejpam-7013	264	30	−	−	PROPN
ejpam-7013	264	31	λ4s	λ4s	NOUN
ejpam-7013	264	32	<	<	X
ejpam-7013	264	33	1	1	NUM
ejpam-7013	264	34	+	+	CCONJ
ejpam-7013	264	35	λ4s+	λ4s+	PROPN
ejpam-7013	264	36	λ4	λ4	ADJ
ejpam-7013	264	37	⇐	⇐	ADJ
ejpam-7013	264	38	⇒	⇒	PROPN
ejpam-7013	264	39	λ1	λ1	PROPN
ejpam-7013	264	40	+	+	CCONJ
ejpam-7013	264	41	λ3	λ3	PROPN
ejpam-7013	264	42	+	+	CCONJ
ejpam-7013	264	43	λ4	λ4	ADJ
ejpam-7013	264	44	<	<	X
ejpam-7013	264	45	1	1	NUM
ejpam-7013	264	46	+	+	CCONJ
ejpam-7013	264	47	2λ4s	2λ4s	ADJ
ejpam-7013	264	48	.	.	PUNCT
ejpam-7013	265	1	the	the	DET
ejpam-7013	265	2	latter	latter	ADJ
ejpam-7013	265	3	inequality	inequality	NOUN
ejpam-7013	265	4	is	be	AUX
ejpam-7013	265	5	implied	imply	VERB
ejpam-7013	265	6	by	by	ADP
ejpam-7013	265	7	the	the	DET
ejpam-7013	265	8	hypothesized	hypothesize	VERB
ejpam-7013	265	9	relations	relation	NOUN
ejpam-7013	266	1	λ1	λ1	VERB
ejpam-7013	266	2	+	+	NUM
ejpam-7013	266	3	λ2	λ2	NOUN
ejpam-7013	266	4	+	+	CCONJ
ejpam-7013	266	5	λ3	λ3	PROPN
ejpam-7013	266	6	<	<	X
ejpam-7013	266	7	1	1	NUM
ejpam-7013	266	8	and	and	CCONJ
ejpam-7013	266	9	2λ2	2λ2	NUM
ejpam-7013	266	10	+	+	ADV
ejpam-7013	266	11	λ4	λ4	VERB
ejpam-7013	266	12	<	<	X
ejpam-7013	266	13	1+λ1	1+λ1	NOUN
ejpam-7013	266	14	after	after	ADP
ejpam-7013	266	15	routine	routine	ADJ
ejpam-7013	266	16	rearrangement	rearrangement	NOUN
ejpam-7013	266	17	together	together	ADV
ejpam-7013	266	18	with	with	ADP
ejpam-7013	266	19	s	s	PRON
ejpam-7013	266	20	≥	≥	NOUN
ejpam-7013	266	21	1	1	NUM
ejpam-7013	266	22	.	.	PUNCT
ejpam-7013	267	1	(	(	PUNCT
ejpam-7013	267	2	one	one	PRON
ejpam-7013	267	3	may	may	AUX
ejpam-7013	267	4	check	check	VERB
ejpam-7013	267	5	that	that	SCONJ
ejpam-7013	267	6	under	under	ADP
ejpam-7013	267	7	the	the	DET
ejpam-7013	267	8	stated	state	VERB
ejpam-7013	267	9	hypotheses	hypothesis	NOUN
ejpam-7013	267	10	the	the	DET
ejpam-7013	267	11	numerator	numerator	NOUN
ejpam-7013	267	12	is	be	AUX
ejpam-7013	267	13	strictly	strictly	ADV
ejpam-7013	267	14	less	less	ADJ
ejpam-7013	267	15	than	than	ADP
ejpam-7013	267	16	the	the	DET
ejpam-7013	267	17	denominator	denominator	NOUN
ejpam-7013	267	18	so	so	ADV
ejpam-7013	267	19	q	q	X
ejpam-7013	267	20	<	<	X
ejpam-7013	267	21	1	1	NUM
ejpam-7013	267	22	.	.	PUNCT
ejpam-7013	267	23	)	)	PUNCT
ejpam-7013	267	24	consequently	consequently	ADV
ejpam-7013	267	25	q	q	X
ejpam-7013	267	26	∈	∈	PROPN
ejpam-7013	268	1	[	[	X
ejpam-7013	268	2	0	0	NUM
ejpam-7013	268	3	,	,	PUNCT
ejpam-7013	268	4	1	1	NUM
ejpam-7013	268	5	)	)	PUNCT
ejpam-7013	268	6	.	.	PUNCT
ejpam-7013	269	1	since	since	SCONJ
ejpam-7013	269	2	εn	εn	ADJ
ejpam-7013	269	3	→	→	SYM
ejpam-7013	269	4	0	0	NUM
ejpam-7013	269	5	and	and	CCONJ
ejpam-7013	269	6	q	q	NOUN
ejpam-7013	269	7	∈	∈	PROPN
ejpam-7013	269	8	[	[	X
ejpam-7013	269	9	0	0	NUM
ejpam-7013	269	10	,	,	PUNCT
ejpam-7013	269	11	1	1	NUM
ejpam-7013	269	12	)	)	PUNCT
ejpam-7013	269	13	,	,	PUNCT
ejpam-7013	269	14	iteration	iteration	NOUN
ejpam-7013	269	15	of	of	ADP
ejpam-7013	269	16	the	the	DET
ejpam-7013	269	17	recurrence	recurrence	NOUN
ejpam-7013	269	18	gives	give	VERB
ejpam-7013	269	19	,	,	PUNCT
ejpam-7013	269	20	for	for	ADP
ejpam-7013	269	21	any	any	DET
ejpam-7013	269	22	fixed	fix	VERB
ejpam-7013	269	23	n	n	NOUN
ejpam-7013	269	24	and	and	CCONJ
ejpam-7013	269	25	k	k	PROPN
ejpam-7013	269	26	≥	≥	NUM
ejpam-7013	269	27	1	1	NUM
ejpam-7013	269	28	,	,	PUNCT
ejpam-7013	269	29	sn+k	sn+k	VERB
ejpam-7013	269	30	≤	≤	NUM
ejpam-7013	269	31	qksn	qksn	NOUN
ejpam-7013	270	1	+	+	CCONJ
ejpam-7013	270	2	k−1∑	k−1∑	PROPN
ejpam-7013	270	3	j=0	j=0	PROPN
ejpam-7013	270	4	q	q	PROPN
ejpam-7013	270	5	k−1−j	k−1−j	PROPN
ejpam-7013	270	6	εn+j	εn+j	PROPN
ejpam-7013	270	7	1	1	NUM
ejpam-7013	270	8	+	+	PROPN
ejpam-7013	270	9	λ4(s+	λ4(s+	PROPN
ejpam-7013	270	10	1	1	NUM
ejpam-7013	270	11	)	)	PUNCT
ejpam-7013	270	12	.	.	PUNCT
ejpam-7013	271	1	letting	let	VERB
ejpam-7013	271	2	k	k	PRON
ejpam-7013	271	3	→	→	SYM
ejpam-7013	271	4	∞	∞	NUM
ejpam-7013	271	5	shows	show	VERB
ejpam-7013	271	6	sn+k	sn+k	PROPN
ejpam-7013	271	7	→	→	SYM
ejpam-7013	271	8	0	0	NUM
ejpam-7013	271	9	.	.	PUNCT
ejpam-7013	272	1	hence	hence	ADV
ejpam-7013	272	2	sn	sn	PROPN
ejpam-7013	272	3	→	→	SYM
ejpam-7013	272	4	0	0	PUNCT
ejpam-7013	272	5	as	as	ADP
ejpam-7013	272	6	n	n	PROPN
ejpam-7013	272	7	→	→	SYM
ejpam-7013	272	8	∞.	∞.	PROPN
ejpam-7013	272	9	in	in	ADP
ejpam-7013	272	10	particular	particular	ADJ
ejpam-7013	272	11	(	(	PUNCT
ejpam-7013	272	12	sn	sn	PROPN
ejpam-7013	272	13	)	)	PUNCT
ejpam-7013	272	14	is	be	AUX
ejpam-7013	272	15	a	a	DET
ejpam-7013	272	16	null	null	ADJ
ejpam-7013	272	17	sequence	sequence	NOUN
ejpam-7013	272	18	and	and	CCONJ
ejpam-7013	272	19	the	the	DET
ejpam-7013	272	20	series	series	NOUN
ejpam-7013	272	21	∑	∑	PROPN
ejpam-7013	272	22	sn	sn	PROPN
ejpam-7013	272	23	converges	converge	VERB
ejpam-7013	272	24	geometrically	geometrically	ADV
ejpam-7013	272	25	.	.	PUNCT
ejpam-7013	273	1	consequently	consequently	ADV
ejpam-7013	273	2	,	,	PUNCT
ejpam-7013	273	3	for	for	ADP
ejpam-7013	273	4	m	m	PROPN
ejpam-7013	273	5	<	<	X
ejpam-7013	273	6	n	n	CCONJ
ejpam-7013	273	7	,	,	PUNCT
ejpam-7013	273	8	d(lm	d(lm	NUM
ejpam-7013	273	9	,	,	PUNCT
ejpam-7013	273	10	ln	ln	ADJ
ejpam-7013	273	11	)	)	PUNCT
ejpam-7013	273	12	≤	≤	PROPN
ejpam-7013	273	13	s	s	PART
ejpam-7013	273	14	n−1∑	n−1∑	PROPN
ejpam-7013	273	15	k	k	NOUN
ejpam-7013	274	1	=	=	NOUN
ejpam-7013	274	2	m	m	VERB
ejpam-7013	274	3	sk	sk	ADJ
ejpam-7013	274	4	,	,	PUNCT
ejpam-7013	274	5	so	so	CCONJ
ejpam-7013	274	6	{	{	PUNCT
ejpam-7013	274	7	ln	ln	ADJ
ejpam-7013	274	8	}	}	PUNCT
ejpam-7013	274	9	is	be	AUX
ejpam-7013	274	10	cauchy	cauchy	ADJ
ejpam-7013	274	11	in	in	ADP
ejpam-7013	274	12	(	(	PUNCT
ejpam-7013	274	13	x	x	X
ejpam-7013	274	14	,	,	PUNCT
ejpam-7013	274	15	d	d	NOUN
ejpam-7013	274	16	)	)	PUNCT
ejpam-7013	274	17	.	.	PUNCT
ejpam-7013	275	1	completeness	completeness	NOUN
ejpam-7013	275	2	implies	imply	VERB
ejpam-7013	275	3	there	there	PRON
ejpam-7013	275	4	exists	exist	VERB
ejpam-7013	275	5	k	k	PROPN
ejpam-7013	275	6	∈	∈	PROPN
ejpam-7013	275	7	x	x	PUNCT
ejpam-7013	275	8	with	with	ADP
ejpam-7013	275	9	ln	ln	NOUN
ejpam-7013	275	10	→	→	PUNCT
ejpam-7013	275	11	k.	k.	NOUN
ejpam-7013	275	12	it	it	PRON
ejpam-7013	275	13	remains	remain	VERB
ejpam-7013	275	14	to	to	PART
ejpam-7013	275	15	show	show	VERB
ejpam-7013	275	16	k	k	PROPN
ejpam-7013	275	17	∈	∈	PROPN
ejpam-7013	275	18	t	t	PROPN
ejpam-7013	275	19	(	(	PUNCT
ejpam-7013	275	20	k	k	NOUN
ejpam-7013	275	21	)	)	PUNCT
ejpam-7013	275	22	.	.	PUNCT
ejpam-7013	276	1	first	first	ADV
ejpam-7013	276	2	observe	observe	VERB
ejpam-7013	276	3	that	that	SCONJ
ejpam-7013	276	4	from	from	ADP
ejpam-7013	276	5	the	the	DET
ejpam-7013	276	6	inequality	inequality	NOUN
ejpam-7013	276	7	used	use	VERB
ejpam-7013	276	8	above	above	ADV
ejpam-7013	276	9	and	and	CCONJ
ejpam-7013	276	10	sn	sn	PROPN
ejpam-7013	276	11	→	→	SYM
ejpam-7013	276	12	0	0	NUM
ejpam-7013	276	13	we	we	PRON
ejpam-7013	276	14	have	have	VERB
ejpam-7013	276	15	h	h	NOUN
ejpam-7013	276	16	(	(	PUNCT
ejpam-7013	276	17	t	t	PROPN
ejpam-7013	276	18	(	(	PUNCT
ejpam-7013	276	19	ln	ln	PROPN
ejpam-7013	276	20	)	)	PUNCT
ejpam-7013	276	21	,	,	PUNCT
ejpam-7013	276	22	t	t	PROPN
ejpam-7013	276	23	(	(	PUNCT
ejpam-7013	276	24	ln+1	ln+1	PROPN
ejpam-7013	276	25	)	)	PUNCT
ejpam-7013	276	26	)	)	PUNCT
ejpam-7013	277	1	→	→	SYM
ejpam-7013	277	2	0	0	NUM
ejpam-7013	277	3	,	,	PUNCT
ejpam-7013	277	4	and	and	CCONJ
ejpam-7013	277	5	by	by	ADP
ejpam-7013	277	6	the	the	DET
ejpam-7013	277	7	triangle	triangle	NOUN
ejpam-7013	277	8	inequality	inequality	NOUN
ejpam-7013	277	9	for	for	ADP
ejpam-7013	277	10	h	h	NOUN
ejpam-7013	277	11	it	it	PRON
ejpam-7013	277	12	follows	follow	VERB
ejpam-7013	277	13	that	that	SCONJ
ejpam-7013	277	14	h(t	h(t	PROPN
ejpam-7013	277	15	(	(	PUNCT
ejpam-7013	277	16	ln	ln	ADJ
ejpam-7013	277	17	)	)	PUNCT
ejpam-7013	277	18	,	,	PUNCT
ejpam-7013	277	19	t	t	PROPN
ejpam-7013	277	20	(	(	PUNCT
ejpam-7013	277	21	k	k	NOUN
ejpam-7013	277	22	)	)	PUNCT
ejpam-7013	277	23	)	)	PUNCT
ejpam-7013	278	1	→	→	SYM
ejpam-7013	278	2	0	0	X
ejpam-7013	278	3	.	.	PUNCT
ejpam-7013	278	4	next	next	ADJ
ejpam-7013	278	5	apply	apply	VERB
ejpam-7013	278	6	the	the	DET
ejpam-7013	278	7	contractive	contractive	ADJ
ejpam-7013	278	8	inequality	inequality	NOUN
ejpam-7013	278	9	with	with	ADP
ejpam-7013	278	10	l	l	NOUN
ejpam-7013	278	11	=	=	PUNCT
ejpam-7013	278	12	k	k	PROPN
ejpam-7013	278	13	and	and	CCONJ
ejpam-7013	278	14	p	p	NOUN
ejpam-7013	278	15	=	=	NOUN
ejpam-7013	278	16	ln	ln	ADJ
ejpam-7013	278	17	:	:	PUNCT
ejpam-7013	278	18	h	h	PROPN
ejpam-7013	278	19	(	(	PUNCT
ejpam-7013	278	20	t	t	PROPN
ejpam-7013	278	21	(	(	PUNCT
ejpam-7013	278	22	k	k	NOUN
ejpam-7013	278	23	)	)	PUNCT
ejpam-7013	278	24	,	,	PUNCT
ejpam-7013	278	25	t	t	PROPN
ejpam-7013	278	26	(	(	PUNCT
ejpam-7013	278	27	ln	ln	ADJ
ejpam-7013	278	28	)	)	PUNCT
ejpam-7013	278	29	)	)	PUNCT
ejpam-7013	278	30	≤	≤	NOUN
ejpam-7013	279	1	λ1dα(k	λ1dα(k	PROPN
ejpam-7013	279	2	,	,	PUNCT
ejpam-7013	279	3	t	t	PROPN
ejpam-7013	279	4	(	(	PUNCT
ejpam-7013	279	5	k	k	NOUN
ejpam-7013	279	6	)	)	PUNCT
ejpam-7013	279	7	)	)	PUNCT
ejpam-7013	280	1	+	+	PUNCT
ejpam-7013	280	2	λ2dα(ln	λ2dα(ln	NOUN
ejpam-7013	280	3	,	,	PUNCT
ejpam-7013	280	4	t	t	PROPN
ejpam-7013	280	5	(	(	PUNCT
ejpam-7013	280	6	k	k	NOUN
ejpam-7013	280	7	)	)	PUNCT
ejpam-7013	280	8	)	)	PUNCT
ejpam-7013	281	1	+	+	CCONJ
ejpam-7013	281	2	λ3d(k	λ3d(k	PROPN
ejpam-7013	281	3	,	,	PUNCT
ejpam-7013	281	4	ln)−	ln)−	X
ejpam-7013	281	5	λ4	λ4	PROPN
ejpam-7013	281	6	(	(	PUNCT
ejpam-7013	281	7	dα(k	dα(k	PROPN
ejpam-7013	281	8	,	,	PUNCT
ejpam-7013	281	9	t	t	PROPN
ejpam-7013	281	10	(	(	PUNCT
ejpam-7013	281	11	ln	ln	ADJ
ejpam-7013	281	12	)	)	PUNCT
ejpam-7013	281	13	)	)	PUNCT
ejpam-7013	282	1	+	+	VERB
ejpam-7013	282	2	dα(ln	dα(ln	ADJ
ejpam-7013	282	3	,	,	PUNCT
ejpam-7013	282	4	t	t	PROPN
ejpam-7013	282	5	(	(	PUNCT
ejpam-7013	282	6	ln	ln	ADJ
ejpam-7013	282	7	)	)	PUNCT
ejpam-7013	282	8	)	)	PUNCT
ejpam-7013	282	9	)	)	PUNCT
ejpam-7013	282	10	.	.	PUNCT
ejpam-7013	283	1	the	the	DET
ejpam-7013	283	2	left	left	ADJ
ejpam-7013	283	3	-	-	PUNCT
ejpam-7013	283	4	hand	hand	NOUN
ejpam-7013	283	5	side	side	NOUN
ejpam-7013	283	6	tends	tend	VERB
ejpam-7013	283	7	to	to	ADP
ejpam-7013	283	8	0	0	NUM
ejpam-7013	283	9	as	as	ADP
ejpam-7013	283	10	n	n	PROPN
ejpam-7013	283	11	→	→	SYM
ejpam-7013	283	12	∞	∞	PROPN
ejpam-7013	283	13	and	and	CCONJ
ejpam-7013	283	14	d(k	d(k	PROPN
ejpam-7013	283	15	,	,	PUNCT
ejpam-7013	283	16	ln	ln	ADJ
ejpam-7013	283	17	)	)	PUNCT
ejpam-7013	283	18	→	→	SYM
ejpam-7013	283	19	0	0	X
ejpam-7013	283	20	.	.	PUNCT
ejpam-7013	283	21	also	also	ADV
ejpam-7013	283	22	dα(k	dα(k	PROPN
ejpam-7013	283	23	,	,	PUNCT
ejpam-7013	283	24	t	t	PROPN
ejpam-7013	283	25	(	(	PUNCT
ejpam-7013	283	26	ln	ln	ADJ
ejpam-7013	283	27	)	)	PUNCT
ejpam-7013	283	28	)	)	PUNCT
ejpam-7013	283	29	≤	≤	NOUN
ejpam-7013	284	1	d(k	d(k	PROPN
ejpam-7013	284	2	,	,	PUNCT
ejpam-7013	284	3	ln+1	ln+1	PROPN
ejpam-7013	284	4	)	)	PUNCT
ejpam-7013	284	5	→	→	SYM
ejpam-7013	284	6	0	0	NUM
ejpam-7013	284	7	and	and	CCONJ
ejpam-7013	284	8	dα(ln	dα(ln	PROPN
ejpam-7013	284	9	,	,	PUNCT
ejpam-7013	284	10	t	t	PROPN
ejpam-7013	284	11	(	(	PUNCT
ejpam-7013	284	12	ln	ln	ADJ
ejpam-7013	284	13	)	)	PUNCT
ejpam-7013	284	14	)	)	PUNCT
ejpam-7013	284	15	≤	≤	NUM
ejpam-7013	284	16	sn	sn	PROPN
ejpam-7013	284	17	→	→	SYM
ejpam-7013	284	18	0	0	X
ejpam-7013	284	19	.	.	PUNCT
ejpam-7013	285	1	hence	hence	ADV
ejpam-7013	285	2	,	,	PUNCT
ejpam-7013	285	3	passing	pass	VERB
ejpam-7013	285	4	to	to	ADP
ejpam-7013	285	5	the	the	DET
ejpam-7013	285	6	limit	limit	NOUN
ejpam-7013	285	7	superior	superior	ADJ
ejpam-7013	285	8	yields	yield	NOUN
ejpam-7013	285	9	0	0	NUM
ejpam-7013	285	10	≤	≤	NUM
ejpam-7013	285	11	λ1dα(k	λ1dα(k	PROPN
ejpam-7013	285	12	,	,	PUNCT
ejpam-7013	285	13	t	t	PROPN
ejpam-7013	285	14	(	(	PUNCT
ejpam-7013	285	15	k	k	NOUN
ejpam-7013	285	16	)	)	PUNCT
ejpam-7013	285	17	)	)	PUNCT
ejpam-7013	286	1	+	+	CCONJ
ejpam-7013	286	2	λ2	λ2	NOUN
ejpam-7013	286	3	lim	lim	NOUN
ejpam-7013	286	4	sup	sup	NOUN
ejpam-7013	286	5	n→∞	n→∞	X
ejpam-7013	286	6	dα(ln	dα(ln	ADJ
ejpam-7013	286	7	,	,	PUNCT
ejpam-7013	286	8	t	t	PROPN
ejpam-7013	286	9	(	(	PUNCT
ejpam-7013	286	10	k	k	NOUN
ejpam-7013	286	11	)	)	PUNCT
ejpam-7013	286	12	)	)	PUNCT
ejpam-7013	286	13	.	.	PUNCT
ejpam-7013	287	1	d.	d.	PROPN
ejpam-7013	287	2	gerbeti	gerbeti	PROPN
ejpam-7013	287	3	et	et	PROPN
ejpam-7013	287	4	al	al	PROPN
ejpam-7013	287	5	.	.	PUNCT
ejpam-7013	287	6	/	/	SYM
ejpam-7013	287	7	eur	eur	PROPN
ejpam-7013	287	8	.	.	PUNCT
ejpam-7013	288	1	j.	j.	PROPN
ejpam-7013	288	2	pure	pure	PROPN
ejpam-7013	288	3	appl	appl	PROPN
ejpam-7013	288	4	.	.	PROPN
ejpam-7013	288	5	math	math	PROPN
ejpam-7013	288	6	,	,	PUNCT
ejpam-7013	288	7	18	18	NUM
ejpam-7013	288	8	(	(	PUNCT
ejpam-7013	288	9	4	4	NUM
ejpam-7013	288	10	)	)	PUNCT
ejpam-7013	288	11	(	(	PUNCT
ejpam-7013	288	12	2025	2025	NUM
ejpam-7013	288	13	)	)	PUNCT
ejpam-7013	288	14	,	,	PUNCT
ejpam-7013	288	15	7013	7013	NUM
ejpam-7013	288	16	11	11	NUM
ejpam-7013	288	17	of	of	ADP
ejpam-7013	288	18	17	17	NUM
ejpam-7013	288	19	for	for	ADP
ejpam-7013	288	20	any	any	DET
ejpam-7013	288	21	y	y	PROPN
ejpam-7013	288	22	∈	∈	PROPN
ejpam-7013	288	23	t	t	PROPN
ejpam-7013	288	24	(	(	PUNCT
ejpam-7013	288	25	k	k	X
ejpam-7013	288	26	)	)	PUNCT
ejpam-7013	288	27	we	we	PRON
ejpam-7013	288	28	have	have	VERB
ejpam-7013	288	29	d(ln	d(ln	PROPN
ejpam-7013	288	30	,	,	PUNCT
ejpam-7013	288	31	y	y	PROPN
ejpam-7013	288	32	)	)	PUNCT
ejpam-7013	288	33	≤	≤	PROPN
ejpam-7013	288	34	d(ln	d(ln	PROPN
ejpam-7013	288	35	,	,	PUNCT
ejpam-7013	288	36	k	k	NOUN
ejpam-7013	288	37	)	)	PUNCT
ejpam-7013	288	38	+	+	CCONJ
ejpam-7013	289	1	d(k	d(k	PROPN
ejpam-7013	289	2	,	,	PUNCT
ejpam-7013	289	3	y	y	PROPN
ejpam-7013	289	4	)	)	PUNCT
ejpam-7013	289	5	,	,	PUNCT
ejpam-7013	289	6	hence	hence	ADV
ejpam-7013	289	7	lim	lim	PROPN
ejpam-7013	289	8	sup	sup	PROPN
ejpam-7013	289	9	n→∞	n→∞	X
ejpam-7013	289	10	dα(ln	dα(ln	ADJ
ejpam-7013	289	11	,	,	PUNCT
ejpam-7013	289	12	t	t	PROPN
ejpam-7013	289	13	(	(	PUNCT
ejpam-7013	289	14	k	k	NOUN
ejpam-7013	289	15	)	)	PUNCT
ejpam-7013	289	16	)	)	PUNCT
ejpam-7013	289	17	≤	≤	NOUN
ejpam-7013	289	18	dα(k	dα(k	NOUN
ejpam-7013	289	19	,	,	PUNCT
ejpam-7013	289	20	t	t	PROPN
ejpam-7013	289	21	(	(	PUNCT
ejpam-7013	289	22	k	k	NOUN
ejpam-7013	289	23	)	)	PUNCT
ejpam-7013	289	24	)	)	PUNCT
ejpam-7013	289	25	.	.	PUNCT
ejpam-7013	290	1	combining	combine	VERB
ejpam-7013	290	2	we	we	PRON
ejpam-7013	290	3	obtain	obtain	VERB
ejpam-7013	290	4	0	0	NUM
ejpam-7013	290	5	≤	≤	NOUN
ejpam-7013	290	6	(	(	PUNCT
ejpam-7013	290	7	λ1	λ1	ADJ
ejpam-7013	290	8	+	+	CCONJ
ejpam-7013	290	9	λ2)dα(k	λ2)dα(k	PROPN
ejpam-7013	290	10	,	,	PUNCT
ejpam-7013	290	11	t	t	PROPN
ejpam-7013	290	12	(	(	PUNCT
ejpam-7013	290	13	k	k	NOUN
ejpam-7013	290	14	)	)	PUNCT
ejpam-7013	290	15	)	)	PUNCT
ejpam-7013	290	16	.	.	PUNCT
ejpam-7013	291	1	if	if	SCONJ
ejpam-7013	291	2	dα(k	dα(k	NOUN
ejpam-7013	291	3	,	,	PUNCT
ejpam-7013	291	4	t	t	PROPN
ejpam-7013	291	5	(	(	PUNCT
ejpam-7013	291	6	k	k	NOUN
ejpam-7013	291	7	)	)	PUNCT
ejpam-7013	291	8	)	)	PUNCT
ejpam-7013	292	1	=	=	SYM
ejpam-7013	292	2	0	0	PUNCT
ejpam-7013	293	1	we	we	PRON
ejpam-7013	293	2	are	be	AUX
ejpam-7013	293	3	done	do	VERB
ejpam-7013	293	4	.	.	PUNCT
ejpam-7013	294	1	suppose	suppose	VERB
ejpam-7013	294	2	contrary	contrary	ADV
ejpam-7013	294	3	that	that	SCONJ
ejpam-7013	294	4	δ	δ	PROPN
ejpam-7013	294	5	:	:	PUNCT
ejpam-7013	294	6	=	=	SYM
ejpam-7013	294	7	dα(k	dα(k	PROPN
ejpam-7013	294	8	,	,	PUNCT
ejpam-7013	294	9	t	t	PROPN
ejpam-7013	294	10	(	(	PUNCT
ejpam-7013	294	11	k	k	NOUN
ejpam-7013	294	12	)	)	PUNCT
ejpam-7013	294	13	)	)	PUNCT
ejpam-7013	294	14	>	>	X
ejpam-7013	295	1	0	0	X
ejpam-7013	295	2	.	.	PUNCT
ejpam-7013	295	3	using	use	VERB
ejpam-7013	295	4	the	the	DET
ejpam-7013	295	5	contractive	contractive	ADJ
ejpam-7013	295	6	inequality	inequality	NOUN
ejpam-7013	295	7	one	one	NUM
ejpam-7013	295	8	more	more	ADJ
ejpam-7013	295	9	time	time	NOUN
ejpam-7013	295	10	with	with	ADP
ejpam-7013	295	11	l	l	NOUN
ejpam-7013	295	12	=	=	PUNCT
ejpam-7013	295	13	ln	ln	ADJ
ejpam-7013	295	14	and	and	CCONJ
ejpam-7013	295	15	p	p	NOUN
ejpam-7013	295	16	=	=	SYM
ejpam-7013	295	17	k	k	PROPN
ejpam-7013	295	18	and	and	CCONJ
ejpam-7013	295	19	passing	pass	VERB
ejpam-7013	295	20	to	to	ADP
ejpam-7013	295	21	limits	limit	NOUN
ejpam-7013	295	22	as	as	ADP
ejpam-7013	295	23	n	n	PROPN
ejpam-7013	295	24	→	→	SYM
ejpam-7013	295	25	∞	∞	PROPN
ejpam-7013	295	26	produces	produce	VERB
ejpam-7013	295	27	an	an	DET
ejpam-7013	295	28	inequality	inequality	NOUN
ejpam-7013	295	29	of	of	ADP
ejpam-7013	295	30	the	the	DET
ejpam-7013	295	31	form	form	NOUN
ejpam-7013	295	32	0	0	NUM
ejpam-7013	295	33	≤	≤	NUM
ejpam-7013	295	34	aδ	aδ	PROPN
ejpam-7013	295	35	−b	−b	NOUN
ejpam-7013	295	36	δ	δ	PROPN
ejpam-7013	295	37	for	for	ADP
ejpam-7013	295	38	some	some	DET
ejpam-7013	295	39	nonnegative	nonnegative	ADJ
ejpam-7013	295	40	constants	constant	NOUN
ejpam-7013	295	41	a	a	DET
ejpam-7013	295	42	,	,	PUNCT
ejpam-7013	295	43	b	b	NOUN
ejpam-7013	295	44	depending	depend	VERB
ejpam-7013	295	45	only	only	ADV
ejpam-7013	295	46	on	on	ADP
ejpam-7013	295	47	the	the	DET
ejpam-7013	295	48	λi	λi	NOUN
ejpam-7013	295	49	and	and	CCONJ
ejpam-7013	295	50	s.	s.	PROPN
ejpam-7013	295	51	unwinding	unwind	VERB
ejpam-7013	295	52	the	the	DET
ejpam-7013	295	53	definitions	definition	NOUN
ejpam-7013	295	54	and	and	CCONJ
ejpam-7013	295	55	using	use	VERB
ejpam-7013	295	56	the	the	DET
ejpam-7013	295	57	parameter	parameter	NOUN
ejpam-7013	295	58	relations	relation	NOUN
ejpam-7013	295	59	λ1	λ1	VERB
ejpam-7013	295	60	+	+	NUM
ejpam-7013	295	61	λ2	λ2	NOUN
ejpam-7013	295	62	+	+	CCONJ
ejpam-7013	295	63	λ3	λ3	PROPN
ejpam-7013	295	64	<	<	X
ejpam-7013	295	65	1	1	NUM
ejpam-7013	295	66	and	and	CCONJ
ejpam-7013	295	67	2λ2	2λ2	NUM
ejpam-7013	295	68	+	+	CCONJ
ejpam-7013	295	69	λ4	λ4	ADJ
ejpam-7013	295	70	<	<	X
ejpam-7013	295	71	1	1	NUM
ejpam-7013	295	72	+	+	PUNCT
ejpam-7013	295	73	λ1	λ1	PROPN
ejpam-7013	295	74	shows	show	VERB
ejpam-7013	295	75	b	b	PROPN
ejpam-7013	295	76	>	>	X
ejpam-7013	295	77	a	a	X
ejpam-7013	295	78	,	,	PUNCT
ejpam-7013	295	79	so	so	CCONJ
ejpam-7013	295	80	the	the	DET
ejpam-7013	295	81	previous	previous	ADJ
ejpam-7013	295	82	inequality	inequality	NOUN
ejpam-7013	295	83	can	can	AUX
ejpam-7013	295	84	not	not	PART
ejpam-7013	295	85	hold	hold	VERB
ejpam-7013	295	86	for	for	ADP
ejpam-7013	295	87	δ	δ	PROPN
ejpam-7013	295	88	>	>	X
ejpam-7013	295	89	0	0	PROPN
ejpam-7013	295	90	.	.	PUNCT
ejpam-7013	296	1	hence	hence	ADV
ejpam-7013	296	2	δ	δ	X
ejpam-7013	296	3	=	=	PUNCT
ejpam-7013	296	4	0	0	PROPN
ejpam-7013	296	5	.	.	PUNCT
ejpam-7013	297	1	because	because	SCONJ
ejpam-7013	297	2	t	t	PROPN
ejpam-7013	297	3	(	(	PUNCT
ejpam-7013	297	4	k	k	NOUN
ejpam-7013	297	5	)	)	PUNCT
ejpam-7013	297	6	is	be	AUX
ejpam-7013	297	7	closed	close	VERB
ejpam-7013	297	8	,	,	PUNCT
ejpam-7013	297	9	dα(k	dα(k	NOUN
ejpam-7013	297	10	,	,	PUNCT
ejpam-7013	297	11	t	t	PROPN
ejpam-7013	297	12	(	(	PUNCT
ejpam-7013	297	13	k	k	NOUN
ejpam-7013	297	14	)	)	PUNCT
ejpam-7013	297	15	)	)	PUNCT
ejpam-7013	298	1	=	=	SYM
ejpam-7013	298	2	0	0	NUM
ejpam-7013	298	3	implies	imply	VERB
ejpam-7013	298	4	k	k	PROPN
ejpam-7013	298	5	∈	∈	PROPN
ejpam-7013	298	6	t	t	PROPN
ejpam-7013	298	7	(	(	PUNCT
ejpam-7013	298	8	k	k	NOUN
ejpam-7013	298	9	)	)	PUNCT
ejpam-7013	298	10	.	.	PUNCT
ejpam-7013	299	1	therefore	therefore	ADV
ejpam-7013	299	2	{	{	PUNCT
ejpam-7013	299	3	k	k	NOUN
ejpam-7013	299	4	}	}	PUNCT
ejpam-7013	299	5	⊆	⊆	NUM
ejpam-7013	299	6	t	t	NOUN
ejpam-7013	299	7	(	(	PUNCT
ejpam-7013	299	8	k	k	NOUN
ejpam-7013	299	9	)	)	PUNCT
ejpam-7013	299	10	and	and	CCONJ
ejpam-7013	299	11	t	t	PROPN
ejpam-7013	299	12	has	have	VERB
ejpam-7013	299	13	a	a	DET
ejpam-7013	299	14	fuzzy	fuzzy	ADJ
ejpam-7013	299	15	fp	fp	NOUN
ejpam-7013	299	16	.	.	PROPN
ejpam-7013	299	17	theorem	theorem	NOUN
ejpam-7013	299	18	4	4	NUM
ejpam-7013	299	19	.	.	PUNCT
ejpam-7013	300	1	let	let	AUX
ejpam-7013	300	2	(	(	PUNCT
ejpam-7013	300	3	x	x	X
ejpam-7013	300	4	,	,	PUNCT
ejpam-7013	300	5	m	m	PROPN
ejpam-7013	300	6	,	,	PUNCT
ejpam-7013	300	7	∗	∗	NOUN
ejpam-7013	300	8	)	)	PUNCT
ejpam-7013	300	9	be	be	VERB
ejpam-7013	300	10	a	a	DET
ejpam-7013	300	11	complete	complete	ADJ
ejpam-7013	300	12	b	b	NOUN
ejpam-7013	300	13	-	-	PUNCT
ejpam-7013	300	14	fms	fms	PROPN
ejpam-7013	300	15	with	with	ADP
ejpam-7013	300	16	underlying	underlie	VERB
ejpam-7013	300	17	b	b	X
ejpam-7013	300	18	-	-	PUNCT
ejpam-7013	300	19	metric	metric	ADJ
ejpam-7013	300	20	d	d	NOUN
ejpam-7013	300	21	and	and	CCONJ
ejpam-7013	300	22	b	b	NOUN
ejpam-7013	300	23	-	-	PUNCT
ejpam-7013	300	24	constant	constant	ADJ
ejpam-7013	300	25	s	s	PART
ejpam-7013	300	26	≥	≥	NOUN
ejpam-7013	300	27	1	1	NUM
ejpam-7013	300	28	.	.	PUNCT
ejpam-7013	301	1	let	let	VERB
ejpam-7013	301	2	t	t	NOUN
ejpam-7013	301	3	:	:	PUNCT
ejpam-7013	301	4	x	x	X
ejpam-7013	301	5	→	→	SYM
ejpam-7013	301	6	w(x	w(x	NOUN
ejpam-7013	301	7	)	)	PUNCT
ejpam-7013	301	8	be	be	AUX
ejpam-7013	301	9	a	a	DET
ejpam-7013	301	10	multivalued	multivalued	ADJ
ejpam-7013	301	11	(	(	PUNCT
ejpam-7013	301	12	fuzzy	fuzzy	ADJ
ejpam-7013	301	13	)	)	PUNCT
ejpam-7013	301	14	mapping	mapping	NOUN
ejpam-7013	301	15	.	.	PUNCT
ejpam-7013	302	1	assume	assume	VERB
ejpam-7013	302	2	there	there	PRON
ejpam-7013	302	3	exist	exist	VERB
ejpam-7013	302	4	constants	constant	NOUN
ejpam-7013	302	5	λ1,λ2,λ3,λ4	λ1,λ2,λ3,λ4	PROPN
ejpam-7013	302	6	≥	≥	NOUN
ejpam-7013	302	7	0	0	NUM
ejpam-7013	302	8	such	such	ADJ
ejpam-7013	302	9	that	that	DET
ejpam-7013	302	10	h	h	NOUN
ejpam-7013	302	11	(	(	PUNCT
ejpam-7013	302	12	t	t	PROPN
ejpam-7013	302	13	(	(	PUNCT
ejpam-7013	302	14	l	l	NOUN
ejpam-7013	302	15	)	)	PUNCT
ejpam-7013	302	16	,	,	PUNCT
ejpam-7013	302	17	t	t	PROPN
ejpam-7013	302	18	(	(	PUNCT
ejpam-7013	302	19	p	p	NOUN
ejpam-7013	302	20	)	)	PUNCT
ejpam-7013	302	21	)	)	PUNCT
ejpam-7013	303	1	+	+	CCONJ
ejpam-7013	303	2	λ4dα	λ4dα	PUNCT
ejpam-7013	303	3	(	(	PUNCT
ejpam-7013	303	4	p	p	X
ejpam-7013	303	5	,	,	PUNCT
ejpam-7013	303	6	t	t	PROPN
ejpam-7013	303	7	(	(	PUNCT
ejpam-7013	303	8	p	p	NOUN
ejpam-7013	303	9	)	)	PUNCT
ejpam-7013	303	10	)	)	PUNCT
ejpam-7013	303	11	≤	≤	NUM
ejpam-7013	303	12	λ1dα	λ1dα	PUNCT
ejpam-7013	304	1	(	(	PUNCT
ejpam-7013	304	2	l	l	NOUN
ejpam-7013	304	3	,	,	PUNCT
ejpam-7013	304	4	t	t	PROPN
ejpam-7013	304	5	(	(	PUNCT
ejpam-7013	304	6	l	l	NOUN
ejpam-7013	304	7	)	)	PUNCT
ejpam-7013	304	8	)	)	PUNCT
ejpam-7013	305	1	+	+	CCONJ
ejpam-7013	305	2	λ2dα	λ2dα	X
ejpam-7013	305	3	(	(	PUNCT
ejpam-7013	305	4	l	l	NOUN
ejpam-7013	305	5	,	,	PUNCT
ejpam-7013	305	6	t	t	PROPN
ejpam-7013	305	7	(	(	PUNCT
ejpam-7013	305	8	p	p	NOUN
ejpam-7013	305	9	)	)	PUNCT
ejpam-7013	305	10	)	)	PUNCT
ejpam-7013	306	1	+	+	CCONJ
ejpam-7013	306	2	λ3	λ3	PROPN
ejpam-7013	306	3	d(l	d(l	ADJ
ejpam-7013	306	4	,	,	PUNCT
ejpam-7013	306	5	p	p	NOUN
ejpam-7013	306	6	)	)	PUNCT
ejpam-7013	306	7	,	,	PUNCT
ejpam-7013	306	8	for	for	ADP
ejpam-7013	306	9	all	all	DET
ejpam-7013	306	10	l	l	NOUN
ejpam-7013	306	11	,	,	PUNCT
ejpam-7013	306	12	p	p	PROPN
ejpam-7013	306	13	∈	∈	PROPN
ejpam-7013	306	14	x	x	NOUN
ejpam-7013	306	15	,	,	PUNCT
ejpam-7013	306	16	and	and	CCONJ
ejpam-7013	306	17	the	the	DET
ejpam-7013	306	18	parameters	parameter	NOUN
ejpam-7013	306	19	satisfy	satisfy	VERB
ejpam-7013	306	20	λ1s	λ1s	PROPN
ejpam-7013	306	21	<	<	X
ejpam-7013	306	22	1	1	NUM
ejpam-7013	306	23	,	,	PUNCT
ejpam-7013	306	24	λ1	λ1	ADJ
ejpam-7013	306	25	+	+	NUM
ejpam-7013	306	26	λ2	λ2	NOUN
ejpam-7013	307	1	+	+	CCONJ
ejpam-7013	308	1	λ3	λ3	PROPN
ejpam-7013	308	2	<	<	X
ejpam-7013	308	3	1	1	NUM
ejpam-7013	308	4	,	,	PUNCT
ejpam-7013	308	5	λ4	λ4	PROPN
ejpam-7013	308	6	≤	≤	PROPN
ejpam-7013	308	7	λ1	λ1	PROPN
ejpam-7013	308	8	,	,	PUNCT
ejpam-7013	308	9	λ2	λ2	NOUN
ejpam-7013	308	10	+	+	CCONJ
ejpam-7013	308	11	λ3	λ3	PROPN
ejpam-7013	308	12	<	<	X
ejpam-7013	308	13	1	1	NUM
ejpam-7013	308	14	.	.	PUNCT
ejpam-7013	309	1	then	then	ADV
ejpam-7013	309	2	t	t	PROPN
ejpam-7013	309	3	has	have	VERB
ejpam-7013	309	4	a	a	DET
ejpam-7013	309	5	fuzzy	fuzzy	ADJ
ejpam-7013	309	6	fp	fp	NOUN
ejpam-7013	309	7	:	:	PUNCT
ejpam-7013	309	8	there	there	PRON
ejpam-7013	309	9	exists	exist	VERB
ejpam-7013	309	10	k	k	PROPN
ejpam-7013	309	11	∈	∈	PROPN
ejpam-7013	309	12	x	x	PUNCT
ejpam-7013	310	1	such	such	ADJ
ejpam-7013	310	2	that	that	SCONJ
ejpam-7013	310	3	{	{	PUNCT
ejpam-7013	310	4	k	k	NOUN
ejpam-7013	310	5	}	}	PUNCT
ejpam-7013	310	6	⊆	⊆	NUM
ejpam-7013	310	7	t	t	NOUN
ejpam-7013	310	8	(	(	PUNCT
ejpam-7013	310	9	k	k	NOUN
ejpam-7013	310	10	)	)	PUNCT
ejpam-7013	310	11	.	.	PUNCT
ejpam-7013	310	12	proof	proof	NOUN
ejpam-7013	310	13	.	.	PUNCT
ejpam-7013	311	1	pick	pick	VERB
ejpam-7013	311	2	an	an	DET
ejpam-7013	311	3	arbitrary	arbitrary	ADJ
ejpam-7013	311	4	l0	l0	NOUN
ejpam-7013	311	5	∈	∈	NOUN
ejpam-7013	311	6	x	x	PUNCT
ejpam-7013	311	7	and	and	CCONJ
ejpam-7013	311	8	choose	choose	VERB
ejpam-7013	311	9	l1	l1	PROPN
ejpam-7013	311	10	∈	∈	PROPN
ejpam-7013	311	11	t	t	PROPN
ejpam-7013	311	12	(	(	PUNCT
ejpam-7013	311	13	l0	l0	PROPN
ejpam-7013	311	14	)	)	PUNCT
ejpam-7013	311	15	.	.	PUNCT
ejpam-7013	312	1	recursively	recursively	ADV
ejpam-7013	312	2	select	select	VERB
ejpam-7013	312	3	ln+1	ln+1	PROPN
ejpam-7013	312	4	∈	∈	PROPN
ejpam-7013	312	5	t	t	PROPN
ejpam-7013	312	6	(	(	PUNCT
ejpam-7013	312	7	ln	ln	ADJ
ejpam-7013	312	8	)	)	PUNCT
ejpam-7013	312	9	for	for	ADP
ejpam-7013	312	10	n	n	PRON
ejpam-7013	312	11	≥	≥	NOUN
ejpam-7013	312	12	0	0	NUM
ejpam-7013	312	13	,	,	PUNCT
ejpam-7013	312	14	and	and	CCONJ
ejpam-7013	312	15	for	for	ADP
ejpam-7013	312	16	each	each	DET
ejpam-7013	312	17	n	n	PRON
ejpam-7013	312	18	also	also	ADV
ejpam-7013	312	19	choose	choose	VERB
ejpam-7013	312	20	ln+2	ln+2	NUM
ejpam-7013	312	21	∈	∈	PROPN
ejpam-7013	312	22	t	t	PROPN
ejpam-7013	312	23	(	(	PUNCT
ejpam-7013	312	24	ln+1	ln+1	PROPN
ejpam-7013	312	25	)	)	PUNCT
ejpam-7013	312	26	satisfying	satisfy	VERB
ejpam-7013	312	27	d(ln+1,ln+2	d(ln+1,ln+2	NOUN
ejpam-7013	312	28	)	)	PUNCT
ejpam-7013	312	29	≤	≤	NUM
ejpam-7013	312	30	h	h	NOUN
ejpam-7013	312	31	(	(	PUNCT
ejpam-7013	312	32	t	t	PROPN
ejpam-7013	312	33	(	(	PUNCT
ejpam-7013	312	34	ln	ln	PROPN
ejpam-7013	312	35	)	)	PUNCT
ejpam-7013	312	36	,	,	PUNCT
ejpam-7013	312	37	t	t	PROPN
ejpam-7013	312	38	(	(	PUNCT
ejpam-7013	312	39	ln+1	ln+1	PROPN
ejpam-7013	312	40	)	)	PUNCT
ejpam-7013	312	41	)	)	PUNCT
ejpam-7013	313	1	+	+	CCONJ
ejpam-7013	313	2	εn	εn	ADJ
ejpam-7013	313	3	,	,	PUNCT
ejpam-7013	313	4	where	where	SCONJ
ejpam-7013	313	5	(	(	PUNCT
ejpam-7013	313	6	εn	εn	ADJ
ejpam-7013	313	7	)	)	PUNCT
ejpam-7013	313	8	is	be	AUX
ejpam-7013	313	9	any	any	DET
ejpam-7013	313	10	sequence	sequence	NOUN
ejpam-7013	313	11	of	of	ADP
ejpam-7013	313	12	positive	positive	ADJ
ejpam-7013	313	13	numbers	number	NOUN
ejpam-7013	313	14	with	with	ADP
ejpam-7013	313	15	εn	εn	ADJ
ejpam-7013	313	16	↓	↓	PROPN
ejpam-7013	313	17	0	0	PUNCT
ejpam-7013	313	18	(	(	PUNCT
ejpam-7013	313	19	possible	possible	ADJ
ejpam-7013	313	20	by	by	ADP
ejpam-7013	313	21	the	the	DET
ejpam-7013	313	22	definition	definition	NOUN
ejpam-7013	313	23	of	of	ADP
ejpam-7013	313	24	h	h	NOUN
ejpam-7013	313	25	)	)	PUNCT
ejpam-7013	313	26	.	.	PUNCT
ejpam-7013	314	1	set	set	VERB
ejpam-7013	314	2	sn	sn	INTJ
ejpam-7013	314	3	:	:	PUNCT
ejpam-7013	314	4	=	=	SYM
ejpam-7013	314	5	d(ln	d(ln	PROPN
ejpam-7013	314	6	,	,	PUNCT
ejpam-7013	314	7	ln+1	ln+1	PROPN
ejpam-7013	314	8	)	)	PUNCT
ejpam-7013	314	9	.	.	PUNCT
ejpam-7013	315	1	apply	apply	VERB
ejpam-7013	315	2	the	the	DET
ejpam-7013	315	3	contractive	contractive	ADJ
ejpam-7013	315	4	inequality	inequality	NOUN
ejpam-7013	315	5	with	with	ADP
ejpam-7013	315	6	(	(	PUNCT
ejpam-7013	315	7	l	l	NOUN
ejpam-7013	315	8	,	,	PUNCT
ejpam-7013	315	9	p	p	NOUN
ejpam-7013	315	10	)	)	PUNCT
ejpam-7013	315	11	=	=	SYM
ejpam-7013	315	12	(	(	PUNCT
ejpam-7013	315	13	ln	ln	ADJ
ejpam-7013	315	14	,	,	PUNCT
ejpam-7013	315	15	ln+1	ln+1	ADJ
ejpam-7013	315	16	)	)	PUNCT
ejpam-7013	315	17	to	to	PART
ejpam-7013	315	18	obtain	obtain	VERB
ejpam-7013	315	19	h	h	NOUN
ejpam-7013	315	20	(	(	PUNCT
ejpam-7013	315	21	t	t	PROPN
ejpam-7013	315	22	(	(	PUNCT
ejpam-7013	315	23	ln	ln	PROPN
ejpam-7013	315	24	)	)	PUNCT
ejpam-7013	315	25	,	,	PUNCT
ejpam-7013	315	26	t	t	PROPN
ejpam-7013	315	27	(	(	PUNCT
ejpam-7013	315	28	ln+1	ln+1	PROPN
ejpam-7013	315	29	)	)	PUNCT
ejpam-7013	315	30	)	)	PUNCT
ejpam-7013	316	1	+	+	PUNCT
ejpam-7013	316	2	λ4dα(ln+1	λ4dα(ln+1	PROPN
ejpam-7013	316	3	,	,	PUNCT
ejpam-7013	316	4	t	t	PROPN
ejpam-7013	316	5	(	(	PUNCT
ejpam-7013	316	6	ln+1	ln+1	PROPN
ejpam-7013	316	7	)	)	PUNCT
ejpam-7013	316	8	)	)	PUNCT
ejpam-7013	316	9	≤	≤	ADV
ejpam-7013	316	10	λ1dα(ln	λ1dα(ln	PROPN
ejpam-7013	316	11	,	,	PUNCT
ejpam-7013	316	12	t	t	PROPN
ejpam-7013	316	13	(	(	PUNCT
ejpam-7013	316	14	ln))+λ2dα(ln	ln))+λ2dα(ln	PROPN
ejpam-7013	316	15	,	,	PUNCT
ejpam-7013	316	16	t	t	PROPN
ejpam-7013	316	17	(	(	PUNCT
ejpam-7013	316	18	ln+1))+λ3sn	ln+1))+λ3sn	PROPN
ejpam-7013	316	19	.	.	PUNCT
ejpam-7013	317	1	because	because	SCONJ
ejpam-7013	317	2	ln+1	ln+1	PROPN
ejpam-7013	317	3	∈	∈	PROPN
ejpam-7013	317	4	t	t	PROPN
ejpam-7013	317	5	(	(	PUNCT
ejpam-7013	317	6	ln	ln	X
ejpam-7013	317	7	)	)	PUNCT
ejpam-7013	317	8	we	we	PRON
ejpam-7013	317	9	have	have	VERB
ejpam-7013	317	10	dα(ln	dα(ln	PROPN
ejpam-7013	317	11	,	,	PUNCT
ejpam-7013	317	12	t	t	PROPN
ejpam-7013	317	13	(	(	PUNCT
ejpam-7013	317	14	ln	ln	ADJ
ejpam-7013	317	15	)	)	PUNCT
ejpam-7013	317	16	)	)	PUNCT
ejpam-7013	317	17	≤	≤	NUM
ejpam-7013	317	18	sn	sn	PROPN
ejpam-7013	317	19	and	and	CCONJ
ejpam-7013	317	20	dα(ln+1	dα(ln+1	PROPN
ejpam-7013	317	21	,	,	PUNCT
ejpam-7013	317	22	t	t	PROPN
ejpam-7013	317	23	(	(	PUNCT
ejpam-7013	317	24	ln+1	ln+1	PROPN
ejpam-7013	317	25	)	)	PUNCT
ejpam-7013	317	26	)	)	PUNCT
ejpam-7013	317	27	≤	≤	NUM
ejpam-7013	317	28	sn+1	sn+1	VERB
ejpam-7013	317	29	.	.	PUNCT
ejpam-7013	318	1	also	also	ADV
ejpam-7013	318	2	dα(ln	dα(ln	PROPN
ejpam-7013	318	3	,	,	PUNCT
ejpam-7013	318	4	t	t	PROPN
ejpam-7013	318	5	(	(	PUNCT
ejpam-7013	318	6	ln+1	ln+1	PROPN
ejpam-7013	318	7	)	)	PUNCT
ejpam-7013	318	8	)	)	PUNCT
ejpam-7013	319	1	≤	≤	PROPN
ejpam-7013	319	2	d(ln	d(ln	PROPN
ejpam-7013	319	3	,	,	PUNCT
ejpam-7013	319	4	ln+2	ln+2	NUM
ejpam-7013	319	5	)	)	PUNCT
ejpam-7013	319	6	≤	≤	NOUN
ejpam-7013	319	7	s	s	PART
ejpam-7013	319	8	(	(	PUNCT
ejpam-7013	319	9	sn	sn	X
ejpam-7013	319	10	+	+	X
ejpam-7013	319	11	sn+1	sn+1	X
ejpam-7013	319	12	)	)	PUNCT
ejpam-7013	319	13	.	.	PUNCT
ejpam-7013	320	1	using	use	VERB
ejpam-7013	320	2	these	these	DET
ejpam-7013	320	3	bounds	bound	NOUN
ejpam-7013	320	4	gives	give	VERB
ejpam-7013	320	5	h	h	PROPN
ejpam-7013	320	6	(	(	PUNCT
ejpam-7013	320	7	t	t	PROPN
ejpam-7013	320	8	(	(	PUNCT
ejpam-7013	320	9	ln	ln	PROPN
ejpam-7013	320	10	)	)	PUNCT
ejpam-7013	320	11	,	,	PUNCT
ejpam-7013	320	12	t	t	PROPN
ejpam-7013	320	13	(	(	PUNCT
ejpam-7013	320	14	ln+1	ln+1	PROPN
ejpam-7013	320	15	)	)	PUNCT
ejpam-7013	320	16	)	)	PUNCT
ejpam-7013	321	1	+	+	CCONJ
ejpam-7013	321	2	λ4sn+1	λ4sn+1	VERB
ejpam-7013	321	3	≤	≤	NOUN
ejpam-7013	321	4	λ1sn	λ1sn	PUNCT
ejpam-7013	322	1	+	+	CCONJ
ejpam-7013	322	2	λ2s	λ2s	X
ejpam-7013	322	3	(	(	PUNCT
ejpam-7013	322	4	sn	sn	X
ejpam-7013	322	5	+	+	X
ejpam-7013	322	6	sn+1	sn+1	X
ejpam-7013	322	7	)	)	PUNCT
ejpam-7013	322	8	+	+	CCONJ
ejpam-7013	322	9	λ3sn	λ3sn	X
ejpam-7013	322	10	.	.	PUNCT
ejpam-7013	323	1	d.	d.	PROPN
ejpam-7013	323	2	gerbeti	gerbeti	PROPN
ejpam-7013	323	3	et	et	PROPN
ejpam-7013	323	4	al	al	PROPN
ejpam-7013	323	5	.	.	PUNCT
ejpam-7013	323	6	/	/	SYM
ejpam-7013	323	7	eur	eur	PROPN
ejpam-7013	323	8	.	.	PUNCT
ejpam-7013	324	1	j.	j.	PROPN
ejpam-7013	324	2	pure	pure	PROPN
ejpam-7013	324	3	appl	appl	PROPN
ejpam-7013	324	4	.	.	PROPN
ejpam-7013	324	5	math	math	PROPN
ejpam-7013	324	6	,	,	PUNCT
ejpam-7013	324	7	18	18	NUM
ejpam-7013	324	8	(	(	PUNCT
ejpam-7013	324	9	4	4	NUM
ejpam-7013	324	10	)	)	PUNCT
ejpam-7013	324	11	(	(	PUNCT
ejpam-7013	324	12	2025	2025	NUM
ejpam-7013	324	13	)	)	PUNCT
ejpam-7013	324	14	,	,	PUNCT
ejpam-7013	324	15	7013	7013	NUM
ejpam-7013	324	16	12	12	NUM
ejpam-7013	324	17	of	of	ADP
ejpam-7013	324	18	17	17	NUM
ejpam-7013	324	19	combine	combine	VERB
ejpam-7013	324	20	this	this	PRON
ejpam-7013	324	21	with	with	ADP
ejpam-7013	324	22	the	the	DET
ejpam-7013	324	23	selection	selection	NOUN
ejpam-7013	324	24	inequality	inequality	NOUN
ejpam-7013	324	25	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	324	26	)	)	PUNCT
ejpam-7013	324	27	≤	≤	NUM
ejpam-7013	324	28	h	h	NOUN
ejpam-7013	324	29	(	(	PUNCT
ejpam-7013	324	30	·	·	PUNCT
ejpam-7013	324	31	·	·	PUNCT
ejpam-7013	324	32	·	·	PUNCT
ejpam-7013	324	33	)	)	PUNCT
ejpam-7013	325	1	+	+	CCONJ
ejpam-7013	325	2	εn	εn	ADJ
ejpam-7013	325	3	to	to	PART
ejpam-7013	325	4	obtain	obtain	VERB
ejpam-7013	325	5	sn+1	sn+1	X
ejpam-7013	325	6	≤	≤	NOUN
ejpam-7013	325	7	λ1sn	λ1sn	PUNCT
ejpam-7013	326	1	+	+	CCONJ
ejpam-7013	326	2	λ2s(sn	λ2s(sn	PROPN
ejpam-7013	326	3	+	+	CCONJ
ejpam-7013	326	4	sn+1	sn+1	NUM
ejpam-7013	326	5	)	)	PUNCT
ejpam-7013	326	6	+	+	CCONJ
ejpam-7013	326	7	λ3sn	λ3sn	PUNCT
ejpam-7013	326	8	−	−	NOUN
ejpam-7013	326	9	λ4sn+1	λ4sn+1	NOUN
ejpam-7013	326	10	+	+	CCONJ
ejpam-7013	326	11	εn	εn	ADJ
ejpam-7013	326	12	.	.	PUNCT
ejpam-7013	326	13	collect	collect	VERB
ejpam-7013	326	14	terms	term	NOUN
ejpam-7013	326	15	in	in	ADP
ejpam-7013	326	16	sn+1	sn+1	NOUN
ejpam-7013	326	17	on	on	ADP
ejpam-7013	326	18	the	the	DET
ejpam-7013	326	19	left	left	NOUN
ejpam-7013	326	20	:(	:(	X
ejpam-7013	326	21	1	1	NUM
ejpam-7013	326	22	+	+	CCONJ
ejpam-7013	326	23	λ4	λ4	ADJ
ejpam-7013	326	24	−	−	PROPN
ejpam-7013	326	25	λ2s	λ2s	X
ejpam-7013	326	26	)	)	PUNCT
ejpam-7013	327	1	sn+1	sn+1	VERB
ejpam-7013	327	2	≤	≤	NOUN
ejpam-7013	327	3	(	(	PUNCT
ejpam-7013	327	4	λ1	λ1	ADJ
ejpam-7013	327	5	+	+	NUM
ejpam-7013	327	6	λ2s+	λ2s+	NOUN
ejpam-7013	327	7	λ3	λ3	PROPN
ejpam-7013	327	8	)	)	PUNCT
ejpam-7013	327	9	sn	sn	PROPN
ejpam-7013	327	10	+	+	CCONJ
ejpam-7013	327	11	εn	εn	ADJ
ejpam-7013	327	12	.	.	PUNCT
ejpam-7013	328	1	by	by	ADP
ejpam-7013	328	2	the	the	DET
ejpam-7013	328	3	hypothesis	hypothesis	NOUN
ejpam-7013	328	4	λ1s	λ1s	X
ejpam-7013	328	5	<	<	X
ejpam-7013	328	6	1	1	NUM
ejpam-7013	328	7	and	and	CCONJ
ejpam-7013	328	8	λ2	λ2	NOUN
ejpam-7013	328	9	+	+	NOUN
ejpam-7013	328	10	λ3	λ3	PROPN
ejpam-7013	328	11	<	<	X
ejpam-7013	328	12	1	1	NUM
ejpam-7013	328	13	one	one	NUM
ejpam-7013	328	14	checks	check	NOUN
ejpam-7013	328	15	that	that	PRON
ejpam-7013	328	16	the	the	DET
ejpam-7013	328	17	left	left	ADJ
ejpam-7013	328	18	coefficient	coefficient	NOUN
ejpam-7013	328	19	is	be	AUX
ejpam-7013	328	20	positive	positive	ADJ
ejpam-7013	328	21	(	(	PUNCT
ejpam-7013	328	22	indeed	indeed	ADV
ejpam-7013	328	23	λ4	λ4	VERB
ejpam-7013	328	24	≤	≤	PUNCT
ejpam-7013	328	25	λ1	λ1	PROPN
ejpam-7013	328	26	and	and	CCONJ
ejpam-7013	328	27	s	s	NOUN
ejpam-7013	328	28	≥	≥	NOUN
ejpam-7013	328	29	1	1	NUM
ejpam-7013	328	30	make	make	VERB
ejpam-7013	328	31	1+λ4	1+λ4	NUM
ejpam-7013	328	32	−λ2s	−λ2s	X
ejpam-7013	328	33	>	>	X
ejpam-7013	328	34	0	0	PUNCT
ejpam-7013	329	1	under	under	ADP
ejpam-7013	329	2	the	the	DET
ejpam-7013	329	3	stated	state	VERB
ejpam-7013	329	4	parameter	parameter	NOUN
ejpam-7013	329	5	relations	relation	NOUN
ejpam-7013	329	6	)	)	PUNCT
ejpam-7013	329	7	.	.	PUNCT
ejpam-7013	330	1	thus	thus	ADV
ejpam-7013	330	2	we	we	PRON
ejpam-7013	330	3	may	may	AUX
ejpam-7013	330	4	divide	divide	VERB
ejpam-7013	330	5	to	to	PART
ejpam-7013	330	6	obtain	obtain	VERB
ejpam-7013	330	7	sn+1	sn+1	NOUN
ejpam-7013	330	8	≤	≤	PUNCT
ejpam-7013	330	9	q	q	PROPN
ejpam-7013	330	10	sn	sn	PROPN
ejpam-7013	330	11	+	+	CCONJ
ejpam-7013	330	12	εn	εn	ADJ
ejpam-7013	330	13	1	1	NUM
ejpam-7013	330	14	+	+	CCONJ
ejpam-7013	330	15	λ4	λ4	ADJ
ejpam-7013	330	16	−	−	PROPN
ejpam-7013	331	1	λ2s	λ2s	X
ejpam-7013	331	2	,	,	PUNCT
ejpam-7013	331	3	where	where	SCONJ
ejpam-7013	331	4	q	q	X
ejpam-7013	331	5	:	:	PUNCT
ejpam-7013	331	6	=	=	SYM
ejpam-7013	331	7	λ1	λ1	PROPN
ejpam-7013	331	8	+	+	NUM
ejpam-7013	331	9	λ2s+	λ2s+	NOUN
ejpam-7013	332	1	λ3	λ3	PROPN
ejpam-7013	332	2	1	1	NUM
ejpam-7013	332	3	+	+	CCONJ
ejpam-7013	332	4	λ4	λ4	ADJ
ejpam-7013	332	5	−	−	PROPN
ejpam-7013	333	1	λ2s	λ2s	X
ejpam-7013	333	2	.	.	PUNCT
ejpam-7013	334	1	using	use	VERB
ejpam-7013	334	2	the	the	DET
ejpam-7013	334	3	parameter	parameter	NOUN
ejpam-7013	334	4	inequalities	inequality	NOUN
ejpam-7013	334	5	one	one	NUM
ejpam-7013	334	6	verifies	verifie	NOUN
ejpam-7013	334	7	0	0	NUM
ejpam-7013	334	8	≤	≤	NUM
ejpam-7013	334	9	q	q	NOUN
ejpam-7013	334	10	<	<	X
ejpam-7013	334	11	1	1	NUM
ejpam-7013	334	12	:	:	PUNCT
ejpam-7013	334	13	the	the	DET
ejpam-7013	334	14	numerator	numerator	NOUN
ejpam-7013	334	15	is	be	AUX
ejpam-7013	334	16	strictly	strictly	ADV
ejpam-7013	334	17	smaller	small	ADJ
ejpam-7013	334	18	than	than	ADP
ejpam-7013	334	19	the	the	DET
ejpam-7013	334	20	denominator	denominator	NOUN
ejpam-7013	334	21	because	because	SCONJ
ejpam-7013	334	22	λ1+λ2+λ3	λ1+λ2+λ3	PROPN
ejpam-7013	334	23	<	<	X
ejpam-7013	334	24	1	1	NUM
ejpam-7013	334	25	and	and	CCONJ
ejpam-7013	334	26	λ4	λ4	PROPN
ejpam-7013	334	27	≤	≤	PROPN
ejpam-7013	334	28	λ1	λ1	PROPN
ejpam-7013	334	29	.	.	PUNCT
ejpam-7013	335	1	since	since	SCONJ
ejpam-7013	335	2	εn	εn	ADJ
ejpam-7013	335	3	→	→	SYM
ejpam-7013	335	4	0	0	NUM
ejpam-7013	335	5	and	and	CCONJ
ejpam-7013	335	6	q	q	NOUN
ejpam-7013	335	7	∈	∈	PROPN
ejpam-7013	336	1	[	[	X
ejpam-7013	336	2	0	0	NUM
ejpam-7013	336	3	,	,	PUNCT
ejpam-7013	336	4	1	1	NUM
ejpam-7013	336	5	)	)	PUNCT
ejpam-7013	336	6	,	,	PUNCT
ejpam-7013	336	7	standard	standard	ADJ
ejpam-7013	336	8	iteration	iteration	NOUN
ejpam-7013	336	9	yields	yield	NOUN
ejpam-7013	336	10	sn+k	sn+k	VERB
ejpam-7013	336	11	≤	≤	NUM
ejpam-7013	336	12	qksn	qksn	NOUN
ejpam-7013	336	13	+	+	CCONJ
ejpam-7013	336	14	k−1∑	k−1∑	PROPN
ejpam-7013	336	15	j=0	j=0	PROPN
ejpam-7013	336	16	q	q	PROPN
ejpam-7013	336	17	k−1−j	k−1−j	PROPN
ejpam-7013	336	18	εn+j	εn+j	PROPN
ejpam-7013	336	19	1	1	NUM
ejpam-7013	336	20	+	+	CCONJ
ejpam-7013	336	21	λ4	λ4	ADJ
ejpam-7013	336	22	−	−	PROPN
ejpam-7013	337	1	λ2s	λ2s	X
ejpam-7013	337	2	,	,	PUNCT
ejpam-7013	337	3	and	and	CCONJ
ejpam-7013	337	4	letting	let	VERB
ejpam-7013	337	5	k	k	X
ejpam-7013	337	6	→	→	SYM
ejpam-7013	337	7	∞	∞	PROPN
ejpam-7013	337	8	gives	give	VERB
ejpam-7013	337	9	sn+k	sn+k	PROPN
ejpam-7013	337	10	→	→	SYM
ejpam-7013	337	11	0	0	NUM
ejpam-7013	337	12	.	.	PUNCT
ejpam-7013	338	1	hence	hence	ADV
ejpam-7013	338	2	sn	sn	PROPN
ejpam-7013	338	3	→	→	SYM
ejpam-7013	338	4	0	0	NUM
ejpam-7013	338	5	and	and	CCONJ
ejpam-7013	338	6	∑	∑	AUX
ejpam-7013	338	7	sn	sn	PROPN
ejpam-7013	338	8	converges	converge	VERB
ejpam-7013	338	9	geometrically	geometrically	ADV
ejpam-7013	338	10	.	.	PUNCT
ejpam-7013	339	1	therefore	therefore	ADV
ejpam-7013	339	2	{	{	PUNCT
ejpam-7013	339	3	ln	ln	ADJ
ejpam-7013	339	4	}	}	PUNCT
ejpam-7013	339	5	is	be	AUX
ejpam-7013	339	6	cauchy	cauchy	ADJ
ejpam-7013	339	7	because	because	SCONJ
ejpam-7013	339	8	for	for	SCONJ
ejpam-7013	339	9	m	m	PROPN
ejpam-7013	339	10	<	<	X
ejpam-7013	339	11	n	n	CCONJ
ejpam-7013	339	12	,	,	PUNCT
ejpam-7013	339	13	d(lm	d(lm	NUM
ejpam-7013	339	14	,	,	PUNCT
ejpam-7013	339	15	ln	ln	ADJ
ejpam-7013	339	16	)	)	PUNCT
ejpam-7013	339	17	≤	≤	PROPN
ejpam-7013	339	18	s	s	PART
ejpam-7013	339	19	n−1∑	n−1∑	PROPN
ejpam-7013	339	20	k	k	NOUN
ejpam-7013	339	21	=	=	NOUN
ejpam-7013	339	22	m	m	VERB
ejpam-7013	339	23	sk	sk	ADJ
ejpam-7013	339	24	,	,	PUNCT
ejpam-7013	339	25	and	and	CCONJ
ejpam-7013	339	26	completeness	completeness	NOUN
ejpam-7013	339	27	yields	yield	VERB
ejpam-7013	339	28	a	a	DET
ejpam-7013	339	29	limit	limit	NOUN
ejpam-7013	339	30	k	k	X
ejpam-7013	339	31	∈	∈	PROPN
ejpam-7013	339	32	x	x	PUNCT
ejpam-7013	339	33	with	with	ADP
ejpam-7013	339	34	ln	ln	NOUN
ejpam-7013	339	35	→	→	SYM
ejpam-7013	339	36	k.	k.	NOUN
ejpam-7013	339	37	to	to	PART
ejpam-7013	339	38	show	show	VERB
ejpam-7013	339	39	k	k	PROPN
ejpam-7013	339	40	∈	∈	PROPN
ejpam-7013	339	41	t	t	PROPN
ejpam-7013	339	42	(	(	PUNCT
ejpam-7013	339	43	k	k	NOUN
ejpam-7013	339	44	)	)	PUNCT
ejpam-7013	339	45	,	,	PUNCT
ejpam-7013	339	46	apply	apply	VERB
ejpam-7013	339	47	the	the	DET
ejpam-7013	339	48	contractive	contractive	ADJ
ejpam-7013	339	49	inequality	inequality	NOUN
ejpam-7013	339	50	with	with	ADP
ejpam-7013	339	51	(	(	PUNCT
ejpam-7013	339	52	l	l	NOUN
ejpam-7013	339	53	,	,	PUNCT
ejpam-7013	339	54	p	p	NOUN
ejpam-7013	339	55	)	)	PUNCT
ejpam-7013	339	56	=	=	SYM
ejpam-7013	339	57	(	(	PUNCT
ejpam-7013	339	58	k	k	X
ejpam-7013	339	59	,	,	PUNCT
ejpam-7013	339	60	ln	ln	ADJ
ejpam-7013	339	61	):	):	PUNCT
ejpam-7013	339	62	h	h	PROPN
ejpam-7013	339	63	(	(	PUNCT
ejpam-7013	339	64	t	t	PROPN
ejpam-7013	339	65	(	(	PUNCT
ejpam-7013	339	66	k	k	NOUN
ejpam-7013	339	67	)	)	PUNCT
ejpam-7013	339	68	,	,	PUNCT
ejpam-7013	339	69	t	t	PROPN
ejpam-7013	339	70	(	(	PUNCT
ejpam-7013	339	71	ln	ln	ADJ
ejpam-7013	339	72	)	)	PUNCT
ejpam-7013	339	73	)	)	PUNCT
ejpam-7013	340	1	+	+	CCONJ
ejpam-7013	340	2	λ4dα(ln	λ4dα(ln	PROPN
ejpam-7013	340	3	,	,	PUNCT
ejpam-7013	340	4	t	t	PROPN
ejpam-7013	340	5	(	(	PUNCT
ejpam-7013	340	6	ln	ln	ADJ
ejpam-7013	340	7	)	)	PUNCT
ejpam-7013	340	8	)	)	PUNCT
ejpam-7013	340	9	≤	≤	NOUN
ejpam-7013	341	1	λ1dα(k	λ1dα(k	PROPN
ejpam-7013	341	2	,	,	PUNCT
ejpam-7013	341	3	t	t	PROPN
ejpam-7013	341	4	(	(	PUNCT
ejpam-7013	341	5	k	k	NOUN
ejpam-7013	341	6	)	)	PUNCT
ejpam-7013	341	7	)	)	PUNCT
ejpam-7013	342	1	+	+	PUNCT
ejpam-7013	342	2	λ2dα(k	λ2dα(k	NOUN
ejpam-7013	342	3	,	,	PUNCT
ejpam-7013	342	4	t	t	PROPN
ejpam-7013	342	5	(	(	PUNCT
ejpam-7013	342	6	ln	ln	ADJ
ejpam-7013	342	7	)	)	PUNCT
ejpam-7013	342	8	)	)	PUNCT
ejpam-7013	343	1	+	+	CCONJ
ejpam-7013	344	1	λ3d(k	λ3d(k	PROPN
ejpam-7013	344	2	,	,	PUNCT
ejpam-7013	344	3	ln	ln	ADJ
ejpam-7013	344	4	)	)	PUNCT
ejpam-7013	344	5	.	.	PUNCT
ejpam-7013	345	1	let	let	VERB
ejpam-7013	345	2	n	n	PRON
ejpam-7013	345	3	→	→	SYM
ejpam-7013	345	4	∞.	∞.	PROPN
ejpam-7013	345	5	the	the	DET
ejpam-7013	345	6	left	left	ADJ
ejpam-7013	345	7	-	-	PUNCT
ejpam-7013	345	8	hand	hand	NOUN
ejpam-7013	345	9	side	side	NOUN
ejpam-7013	345	10	tends	tend	VERB
ejpam-7013	345	11	to	to	ADP
ejpam-7013	345	12	0	0	NUM
ejpam-7013	345	13	because	because	SCONJ
ejpam-7013	345	14	h(t	h(t	PROPN
ejpam-7013	345	15	(	(	PUNCT
ejpam-7013	345	16	ln	ln	ADJ
ejpam-7013	345	17	)	)	PUNCT
ejpam-7013	345	18	,	,	PUNCT
ejpam-7013	345	19	t	t	PROPN
ejpam-7013	345	20	(	(	PUNCT
ejpam-7013	345	21	ln+1	ln+1	PROPN
ejpam-7013	345	22	)	)	PUNCT
ejpam-7013	345	23	)	)	PUNCT
ejpam-7013	346	1	→	→	SYM
ejpam-7013	346	2	0	0	NUM
ejpam-7013	346	3	(	(	PUNCT
ejpam-7013	346	4	from	from	ADP
ejpam-7013	346	5	sn	sn	PROPN
ejpam-7013	346	6	→	→	SYM
ejpam-7013	346	7	0	0	NUM
ejpam-7013	346	8	)	)	PUNCT
ejpam-7013	346	9	and	and	CCONJ
ejpam-7013	346	10	dα(ln	dα(ln	PROPN
ejpam-7013	346	11	,	,	PUNCT
ejpam-7013	346	12	t	t	PROPN
ejpam-7013	346	13	(	(	PUNCT
ejpam-7013	346	14	ln	ln	ADJ
ejpam-7013	346	15	)	)	PUNCT
ejpam-7013	346	16	)	)	PUNCT
ejpam-7013	346	17	≤	≤	NUM
ejpam-7013	346	18	sn	sn	PROPN
ejpam-7013	346	19	→	→	SYM
ejpam-7013	346	20	0	0	X
ejpam-7013	346	21	.	.	PUNCT
ejpam-7013	347	1	the	the	DET
ejpam-7013	347	2	right	right	ADJ
ejpam-7013	347	3	-	-	PUNCT
ejpam-7013	347	4	hand	hand	NOUN
ejpam-7013	347	5	side	side	NOUN
ejpam-7013	347	6	contains	contain	VERB
ejpam-7013	347	7	dα(k	dα(k	NOUN
ejpam-7013	347	8	,	,	PUNCT
ejpam-7013	347	9	t	t	PROPN
ejpam-7013	347	10	(	(	PUNCT
ejpam-7013	347	11	ln	ln	ADJ
ejpam-7013	347	12	)	)	PUNCT
ejpam-7013	347	13	)	)	PUNCT
ejpam-7013	347	14	≤	≤	NOUN
ejpam-7013	348	1	d(k	d(k	PROPN
ejpam-7013	348	2	,	,	PUNCT
ejpam-7013	348	3	ln+1	ln+1	PROPN
ejpam-7013	348	4	)	)	PUNCT
ejpam-7013	348	5	→	→	SYM
ejpam-7013	348	6	0	0	NUM
ejpam-7013	348	7	and	and	CCONJ
ejpam-7013	348	8	d(k	d(k	PROPN
ejpam-7013	348	9	,	,	PUNCT
ejpam-7013	348	10	ln	ln	ADJ
ejpam-7013	348	11	)	)	PUNCT
ejpam-7013	348	12	→	→	SYM
ejpam-7013	348	13	0	0	NUM
ejpam-7013	348	14	,	,	PUNCT
ejpam-7013	348	15	so	so	ADV
ejpam-7013	348	16	letting	let	VERB
ejpam-7013	348	17	n	n	PRON
ejpam-7013	348	18	→	→	SYM
ejpam-7013	348	19	∞	∞	NUM
ejpam-7013	348	20	yields	yield	NOUN
ejpam-7013	348	21	0	0	NUM
ejpam-7013	348	22	≤	≤	NOUN
ejpam-7013	348	23	λ1dα(k	λ1dα(k	PROPN
ejpam-7013	348	24	,	,	PUNCT
ejpam-7013	348	25	t	t	PROPN
ejpam-7013	348	26	(	(	PUNCT
ejpam-7013	348	27	k	k	NOUN
ejpam-7013	348	28	)	)	PUNCT
ejpam-7013	348	29	)	)	PUNCT
ejpam-7013	348	30	.	.	PUNCT
ejpam-7013	349	1	if	if	SCONJ
ejpam-7013	349	2	dα(k	dα(k	NOUN
ejpam-7013	349	3	,	,	PUNCT
ejpam-7013	349	4	t	t	PROPN
ejpam-7013	349	5	(	(	PUNCT
ejpam-7013	349	6	k	k	NOUN
ejpam-7013	349	7	)	)	PUNCT
ejpam-7013	349	8	)	)	PUNCT
ejpam-7013	350	1	=	=	SYM
ejpam-7013	350	2	0	0	PUNCT
ejpam-7013	351	1	we	we	PRON
ejpam-7013	351	2	are	be	AUX
ejpam-7013	351	3	done	do	VERB
ejpam-7013	351	4	.	.	PUNCT
ejpam-7013	352	1	suppose	suppose	VERB
ejpam-7013	352	2	dα(k	dα(k	NOUN
ejpam-7013	352	3	,	,	PUNCT
ejpam-7013	352	4	t	t	PROPN
ejpam-7013	352	5	(	(	PUNCT
ejpam-7013	352	6	k	k	NOUN
ejpam-7013	352	7	)	)	PUNCT
ejpam-7013	352	8	)	)	PUNCT
ejpam-7013	353	1	=	=	PUNCT
ejpam-7013	353	2	δ	δ	X
ejpam-7013	353	3	>	>	X
ejpam-7013	353	4	0	0	X
ejpam-7013	353	5	.	.	PUNCT
ejpam-7013	354	1	repeating	repeat	VERB
ejpam-7013	354	2	the	the	DET
ejpam-7013	354	3	above	above	ADJ
ejpam-7013	354	4	inequality	inequality	NOUN
ejpam-7013	354	5	for	for	ADP
ejpam-7013	354	6	suitable	suitable	ADJ
ejpam-7013	354	7	approximating	approximating	NOUN
ejpam-7013	354	8	iterates	iterate	NOUN
ejpam-7013	354	9	produces	produce	VERB
ejpam-7013	354	10	a	a	DET
ejpam-7013	354	11	linear	linear	ADJ
ejpam-7013	354	12	relation	relation	NOUN
ejpam-7013	354	13	of	of	ADP
ejpam-7013	354	14	the	the	DET
ejpam-7013	354	15	form	form	NOUN
ejpam-7013	354	16	δ	δ	PROPN
ejpam-7013	354	17	≤	≤	PROPN
ejpam-7013	354	18	q′δ	q′δ	NOUN
ejpam-7013	354	19	with	with	ADP
ejpam-7013	354	20	q′	q′	NOUN
ejpam-7013	354	21	<	<	X
ejpam-7013	354	22	1	1	NUM
ejpam-7013	354	23	(	(	PUNCT
ejpam-7013	354	24	obtained	obtain	VERB
ejpam-7013	354	25	from	from	ADP
ejpam-7013	354	26	the	the	DET
ejpam-7013	354	27	same	same	ADJ
ejpam-7013	354	28	coefficients	coefficient	NOUN
ejpam-7013	354	29	that	that	PRON
ejpam-7013	354	30	determine	determine	VERB
ejpam-7013	354	31	q	q	NOUN
ejpam-7013	354	32	)	)	PUNCT
ejpam-7013	354	33	,	,	PUNCT
ejpam-7013	354	34	which	which	PRON
ejpam-7013	354	35	is	be	AUX
ejpam-7013	354	36	impossible	impossible	ADJ
ejpam-7013	354	37	.	.	PUNCT
ejpam-7013	355	1	hence	hence	ADV
ejpam-7013	355	2	δ	δ	PROPN
ejpam-7013	355	3	=	=	PUNCT
ejpam-7013	355	4	0	0	NUM
ejpam-7013	355	5	,	,	PUNCT
ejpam-7013	355	6	and	and	CCONJ
ejpam-7013	355	7	since	since	SCONJ
ejpam-7013	355	8	t	t	PROPN
ejpam-7013	355	9	(	(	PUNCT
ejpam-7013	355	10	k	k	NOUN
ejpam-7013	355	11	)	)	PUNCT
ejpam-7013	355	12	is	be	AUX
ejpam-7013	355	13	closed	close	VERB
ejpam-7013	355	14	we	we	PRON
ejpam-7013	355	15	conclude	conclude	VERB
ejpam-7013	355	16	k	k	PROPN
ejpam-7013	355	17	∈	∈	PROPN
ejpam-7013	355	18	t	t	PROPN
ejpam-7013	355	19	(	(	PUNCT
ejpam-7013	355	20	k	k	NOUN
ejpam-7013	355	21	)	)	PUNCT
ejpam-7013	355	22	.	.	PUNCT
ejpam-7013	356	1	this	this	PRON
ejpam-7013	356	2	proves	prove	VERB
ejpam-7013	356	3	the	the	DET
ejpam-7013	356	4	theorem	theorem	NOUN
ejpam-7013	356	5	.	.	PUNCT
ejpam-7013	357	1	d.	d.	PROPN
ejpam-7013	357	2	gerbeti	gerbeti	PROPN
ejpam-7013	357	3	et	et	PROPN
ejpam-7013	357	4	al	al	PROPN
ejpam-7013	357	5	.	.	PUNCT
ejpam-7013	357	6	/	/	SYM
ejpam-7013	357	7	eur	eur	PROPN
ejpam-7013	357	8	.	.	PUNCT
ejpam-7013	358	1	j.	j.	PROPN
ejpam-7013	358	2	pure	pure	PROPN
ejpam-7013	358	3	appl	appl	PROPN
ejpam-7013	358	4	.	.	PROPN
ejpam-7013	358	5	math	math	PROPN
ejpam-7013	358	6	,	,	PUNCT
ejpam-7013	358	7	18	18	NUM
ejpam-7013	358	8	(	(	PUNCT
ejpam-7013	358	9	4	4	NUM
ejpam-7013	358	10	)	)	PUNCT
ejpam-7013	358	11	(	(	PUNCT
ejpam-7013	358	12	2025	2025	NUM
ejpam-7013	358	13	)	)	PUNCT
ejpam-7013	358	14	,	,	PUNCT
ejpam-7013	358	15	7013	7013	NUM
ejpam-7013	358	16	13	13	NUM
ejpam-7013	358	17	of	of	ADP
ejpam-7013	358	18	17	17	NUM
ejpam-7013	358	19	theorem	theorem	NOUN
ejpam-7013	358	20	5	5	NUM
ejpam-7013	358	21	.	.	PUNCT
ejpam-7013	359	1	let	let	AUX
ejpam-7013	359	2	(	(	PUNCT
ejpam-7013	359	3	x	x	X
ejpam-7013	359	4	,	,	PUNCT
ejpam-7013	359	5	m	m	PROPN
ejpam-7013	359	6	,	,	PUNCT
ejpam-7013	359	7	∗	∗	NOUN
ejpam-7013	359	8	)	)	PUNCT
ejpam-7013	359	9	be	be	VERB
ejpam-7013	359	10	a	a	DET
ejpam-7013	359	11	complete	complete	ADJ
ejpam-7013	359	12	b	b	NOUN
ejpam-7013	359	13	-	-	PUNCT
ejpam-7013	359	14	fms	fms	PROPN
ejpam-7013	359	15	with	with	ADP
ejpam-7013	359	16	underlying	underlie	VERB
ejpam-7013	359	17	b	b	X
ejpam-7013	359	18	-	-	PUNCT
ejpam-7013	359	19	metric	metric	ADJ
ejpam-7013	359	20	d	d	NOUN
ejpam-7013	359	21	(	(	PUNCT
ejpam-7013	359	22	constant	constant	PROPN
ejpam-7013	359	23	s	s	PART
ejpam-7013	359	24	≥	≥	NOUN
ejpam-7013	359	25	1	1	NUM
ejpam-7013	359	26	)	)	PUNCT
ejpam-7013	359	27	.	.	PUNCT
ejpam-7013	360	1	let	let	VERB
ejpam-7013	360	2	t	t	NOUN
ejpam-7013	360	3	:	:	PUNCT
ejpam-7013	360	4	x	x	X
ejpam-7013	360	5	→	→	SYM
ejpam-7013	360	6	w(x	w(x	NOUN
ejpam-7013	360	7	)	)	PUNCT
ejpam-7013	360	8	be	be	AUX
ejpam-7013	360	9	a	a	DET
ejpam-7013	360	10	multivalued	multivalue	VERB
ejpam-7013	360	11	mapping	mapping	NOUN
ejpam-7013	360	12	.	.	PUNCT
ejpam-7013	361	1	assume	assume	VERB
ejpam-7013	361	2	there	there	PRON
ejpam-7013	361	3	exist	exist	VERB
ejpam-7013	361	4	constants	constant	NOUN
ejpam-7013	361	5	λ1,λ2	λ1,λ2	PROPN
ejpam-7013	361	6	≥	≥	NUM
ejpam-7013	361	7	0	0	NUM
ejpam-7013	361	8	such	such	ADJ
ejpam-7013	361	9	that	that	PRON
ejpam-7013	361	10	for	for	ADP
ejpam-7013	361	11	all	all	DET
ejpam-7013	361	12	l	l	NOUN
ejpam-7013	361	13	,	,	PUNCT
ejpam-7013	362	1	p	p	PROPN
ejpam-7013	362	2	∈	∈	PROPN
ejpam-7013	362	3	x	x	INTJ
ejpam-7013	362	4	h	h	NOUN
ejpam-7013	362	5	(	(	PUNCT
ejpam-7013	362	6	t	t	PROPN
ejpam-7013	362	7	(	(	PUNCT
ejpam-7013	362	8	l	l	NOUN
ejpam-7013	362	9	)	)	PUNCT
ejpam-7013	362	10	,	,	PUNCT
ejpam-7013	362	11	t	t	PROPN
ejpam-7013	362	12	(	(	PUNCT
ejpam-7013	362	13	p	p	NOUN
ejpam-7013	362	14	)	)	PUNCT
ejpam-7013	362	15	)	)	PUNCT
ejpam-7013	363	1	≤	≤	NUM
ejpam-7013	364	1	λ1max	λ1max	PRON
ejpam-7013	364	2	{	{	PUNCT
ejpam-7013	364	3	dα(l	dα(l	PROPN
ejpam-7013	364	4	,	,	PUNCT
ejpam-7013	364	5	t	t	PROPN
ejpam-7013	364	6	(	(	PUNCT
ejpam-7013	364	7	l	l	NOUN
ejpam-7013	364	8	)	)	PUNCT
ejpam-7013	364	9	)	)	PUNCT
ejpam-7013	364	10	,	,	PUNCT
ejpam-7013	364	11	dα(p	dα(p	PROPN
ejpam-7013	364	12	,	,	PUNCT
ejpam-7013	364	13	t	t	PROPN
ejpam-7013	364	14	(	(	PUNCT
ejpam-7013	364	15	p	p	NOUN
ejpam-7013	364	16	)	)	PUNCT
ejpam-7013	364	17	)	)	PUNCT
ejpam-7013	364	18	,	,	PUNCT
ejpam-7013	364	19	dα(l	dα(l	NUM
ejpam-7013	364	20	,	,	PUNCT
ejpam-7013	364	21	t	t	PROPN
ejpam-7013	364	22	(	(	PUNCT
ejpam-7013	364	23	p	p	NOUN
ejpam-7013	364	24	)	)	PUNCT
ejpam-7013	364	25	)	)	PUNCT
ejpam-7013	364	26	,	,	PUNCT
ejpam-7013	364	27	dα(p	dα(p	PROPN
ejpam-7013	364	28	,	,	PUNCT
ejpam-7013	364	29	t	t	PROPN
ejpam-7013	364	30	(	(	PUNCT
ejpam-7013	364	31	l	l	NOUN
ejpam-7013	364	32	)	)	PUNCT
ejpam-7013	364	33	)	)	PUNCT
ejpam-7013	364	34	}	}	PUNCT
ejpam-7013	365	1	+	+	NUM
ejpam-7013	365	2	λ2	λ2	NOUN
ejpam-7013	365	3	d(l	d(l	ADJ
ejpam-7013	365	4	,	,	PUNCT
ejpam-7013	365	5	p	p	NOUN
ejpam-7013	365	6	)	)	PUNCT
ejpam-7013	365	7	,	,	PUNCT
ejpam-7013	365	8	and	and	CCONJ
ejpam-7013	365	9	suppose	suppose	VERB
ejpam-7013	365	10	λ1	λ1	PROPN
ejpam-7013	365	11	+	+	NUM
ejpam-7013	365	12	λ2	λ2	NOUN
ejpam-7013	365	13	<	<	X
ejpam-7013	365	14	1	1	NUM
ejpam-7013	365	15	.	.	PUNCT
ejpam-7013	366	1	then	then	ADV
ejpam-7013	366	2	t	t	PROPN
ejpam-7013	366	3	admits	admit	VERB
ejpam-7013	366	4	a	a	DET
ejpam-7013	366	5	fuzzy	fuzzy	ADJ
ejpam-7013	366	6	fp	fp	NOUN
ejpam-7013	366	7	,	,	PUNCT
ejpam-7013	366	8	i.e.	i.e.	X
ejpam-7013	366	9	,	,	PUNCT
ejpam-7013	366	10	there	there	PRON
ejpam-7013	366	11	exists	exist	VERB
ejpam-7013	366	12	k	k	PROPN
ejpam-7013	366	13	∈	∈	PROPN
ejpam-7013	366	14	x	x	PUNCT
ejpam-7013	366	15	with	with	ADP
ejpam-7013	366	16	{	{	PUNCT
ejpam-7013	366	17	k	k	NOUN
ejpam-7013	366	18	}	}	PUNCT
ejpam-7013	366	19	⊆	⊆	NUM
ejpam-7013	366	20	t	t	NOUN
ejpam-7013	366	21	(	(	PUNCT
ejpam-7013	366	22	k	k	NOUN
ejpam-7013	366	23	)	)	PUNCT
ejpam-7013	366	24	.	.	PUNCT
ejpam-7013	367	1	proof	proof	NOUN
ejpam-7013	367	2	.	.	PUNCT
ejpam-7013	368	1	choose	choose	VERB
ejpam-7013	368	2	l0	l0	PROPN
ejpam-7013	368	3	∈	∈	PROPN
ejpam-7013	368	4	x	x	X
ejpam-7013	368	5	and	and	CCONJ
ejpam-7013	368	6	pick	pick	VERB
ejpam-7013	368	7	l1	l1	PROPN
ejpam-7013	368	8	∈	∈	PROPN
ejpam-7013	368	9	t	t	PROPN
ejpam-7013	368	10	(	(	PUNCT
ejpam-7013	368	11	l0	l0	PROPN
ejpam-7013	368	12	)	)	PUNCT
ejpam-7013	368	13	.	.	PUNCT
ejpam-7013	369	1	construct	construct	VERB
ejpam-7013	369	2	the	the	DET
ejpam-7013	369	3	sequence	sequence	NOUN
ejpam-7013	369	4	{	{	PUNCT
ejpam-7013	369	5	ln	ln	ADJ
ejpam-7013	369	6	}	}	PUNCT
ejpam-7013	369	7	by	by	ADP
ejpam-7013	369	8	choosing	choose	VERB
ejpam-7013	369	9	ln+1	ln+1	PROPN
ejpam-7013	369	10	∈	∈	PROPN
ejpam-7013	369	11	t	t	PROPN
ejpam-7013	369	12	(	(	PUNCT
ejpam-7013	369	13	ln	ln	ADJ
ejpam-7013	369	14	)	)	PUNCT
ejpam-7013	369	15	for	for	ADP
ejpam-7013	369	16	each	each	DET
ejpam-7013	369	17	n	n	PRON
ejpam-7013	369	18	≥	≥	NOUN
ejpam-7013	369	19	0	0	NUM
ejpam-7013	369	20	.	.	PUNCT
ejpam-7013	370	1	for	for	ADP
ejpam-7013	370	2	each	each	DET
ejpam-7013	370	3	n	n	NOUN
ejpam-7013	370	4	choose	choose	VERB
ejpam-7013	370	5	ln+2	ln+2	NUM
ejpam-7013	370	6	∈	∈	PROPN
ejpam-7013	370	7	t	t	PROPN
ejpam-7013	370	8	(	(	PUNCT
ejpam-7013	370	9	ln+1	ln+1	PROPN
ejpam-7013	370	10	)	)	PUNCT
ejpam-7013	370	11	so	so	SCONJ
ejpam-7013	370	12	that	that	SCONJ
ejpam-7013	370	13	d(ln+1,ln+2	d(ln+1,ln+2	PROPN
ejpam-7013	370	14	)	)	PUNCT
ejpam-7013	370	15	≤	≤	NUM
ejpam-7013	370	16	h	h	NOUN
ejpam-7013	370	17	(	(	PUNCT
ejpam-7013	370	18	t	t	PROPN
ejpam-7013	370	19	(	(	PUNCT
ejpam-7013	370	20	ln	ln	PROPN
ejpam-7013	370	21	)	)	PUNCT
ejpam-7013	370	22	,	,	PUNCT
ejpam-7013	370	23	t	t	PROPN
ejpam-7013	370	24	(	(	PUNCT
ejpam-7013	370	25	ln+1	ln+1	PROPN
ejpam-7013	370	26	)	)	PUNCT
ejpam-7013	370	27	)	)	PUNCT
ejpam-7013	371	1	+	+	CCONJ
ejpam-7013	371	2	εn	εn	ADJ
ejpam-7013	371	3	,	,	PUNCT
ejpam-7013	371	4	with	with	ADP
ejpam-7013	371	5	εn	εn	ADP
ejpam-7013	371	6	↓	↓	PROPN
ejpam-7013	371	7	0	0	NUM
ejpam-7013	371	8	.	.	PUNCT
ejpam-7013	372	1	put	put	VERB
ejpam-7013	372	2	sn	sn	PROPN
ejpam-7013	372	3	:	:	PUNCT
ejpam-7013	372	4	=	=	SYM
ejpam-7013	372	5	d(ln	d(ln	PROPN
ejpam-7013	372	6	,	,	PUNCT
ejpam-7013	372	7	ln+1	ln+1	PROPN
ejpam-7013	372	8	)	)	PUNCT
ejpam-7013	372	9	.	.	PUNCT
ejpam-7013	373	1	apply	apply	VERB
ejpam-7013	373	2	the	the	DET
ejpam-7013	373	3	max	max	NOUN
ejpam-7013	373	4	-	-	PUNCT
ejpam-7013	373	5	type	type	NOUN
ejpam-7013	373	6	contraction	contraction	NOUN
ejpam-7013	373	7	with	with	ADP
ejpam-7013	373	8	(	(	PUNCT
ejpam-7013	373	9	l	l	NOUN
ejpam-7013	373	10	,	,	PUNCT
ejpam-7013	373	11	p	p	NOUN
ejpam-7013	373	12	)	)	PUNCT
ejpam-7013	373	13	=	=	SYM
ejpam-7013	373	14	(	(	PUNCT
ejpam-7013	373	15	ln	ln	ADJ
ejpam-7013	373	16	,	,	PUNCT
ejpam-7013	373	17	ln+1	ln+1	ADJ
ejpam-7013	373	18	)	)	PUNCT
ejpam-7013	373	19	to	to	PART
ejpam-7013	373	20	get	get	VERB
ejpam-7013	373	21	h	h	NOUN
ejpam-7013	373	22	(	(	PUNCT
ejpam-7013	373	23	t	t	PROPN
ejpam-7013	373	24	(	(	PUNCT
ejpam-7013	373	25	ln	ln	PROPN
ejpam-7013	373	26	)	)	PUNCT
ejpam-7013	373	27	,	,	PUNCT
ejpam-7013	373	28	t	t	PROPN
ejpam-7013	373	29	(	(	PUNCT
ejpam-7013	373	30	ln+1	ln+1	PROPN
ejpam-7013	373	31	)	)	PUNCT
ejpam-7013	373	32	)	)	PUNCT
ejpam-7013	374	1	≤	≤	PUNCT
ejpam-7013	374	2	λ1max{dα(ln	λ1max{dα(ln	PROPN
ejpam-7013	374	3	,	,	PUNCT
ejpam-7013	374	4	t	t	PROPN
ejpam-7013	374	5	(	(	PUNCT
ejpam-7013	374	6	ln	ln	ADJ
ejpam-7013	374	7	)	)	PUNCT
ejpam-7013	374	8	)	)	PUNCT
ejpam-7013	374	9	,	,	PUNCT
ejpam-7013	374	10	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	374	11	,	,	PUNCT
ejpam-7013	374	12	t	t	PROPN
ejpam-7013	374	13	(	(	PUNCT
ejpam-7013	374	14	ln+1	ln+1	PROPN
ejpam-7013	374	15	)	)	PUNCT
ejpam-7013	374	16	)	)	PUNCT
ejpam-7013	374	17	,	,	PUNCT
ejpam-7013	374	18	dα(ln	dα(ln	PROPN
ejpam-7013	374	19	,	,	PUNCT
ejpam-7013	374	20	t	t	PROPN
ejpam-7013	374	21	(	(	PUNCT
ejpam-7013	374	22	ln+1	ln+1	PROPN
ejpam-7013	374	23	)	)	PUNCT
ejpam-7013	374	24	)	)	PUNCT
ejpam-7013	374	25	,	,	PUNCT
ejpam-7013	374	26	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	374	27	,	,	PUNCT
ejpam-7013	374	28	t	t	PROPN
ejpam-7013	374	29	(	(	PUNCT
ejpam-7013	374	30	ln))}+λ2sn	ln))}+λ2sn	PROPN
ejpam-7013	374	31	.	.	NOUN
ejpam-7013	375	1	since	since	SCONJ
ejpam-7013	375	2	ln+1	ln+1	PROPN
ejpam-7013	375	3	∈	∈	PROPN
ejpam-7013	375	4	t	t	PROPN
ejpam-7013	375	5	(	(	PUNCT
ejpam-7013	375	6	ln	ln	X
ejpam-7013	375	7	)	)	PUNCT
ejpam-7013	375	8	we	we	PRON
ejpam-7013	375	9	have	have	VERB
ejpam-7013	375	10	dα(ln+1	dα(ln+1	NOUN
ejpam-7013	375	11	,	,	PUNCT
ejpam-7013	375	12	t	t	PROPN
ejpam-7013	375	13	(	(	PUNCT
ejpam-7013	375	14	ln	ln	ADJ
ejpam-7013	375	15	)	)	PUNCT
ejpam-7013	375	16	)	)	PUNCT
ejpam-7013	376	1	=	=	SYM
ejpam-7013	376	2	0	0	NUM
ejpam-7013	376	3	,	,	PUNCT
ejpam-7013	376	4	and	and	CCONJ
ejpam-7013	376	5	dα(ln	dα(ln	PROPN
ejpam-7013	376	6	,	,	PUNCT
ejpam-7013	376	7	t	t	PROPN
ejpam-7013	376	8	(	(	PUNCT
ejpam-7013	376	9	ln	ln	ADJ
ejpam-7013	376	10	)	)	PUNCT
ejpam-7013	376	11	)	)	PUNCT
ejpam-7013	376	12	≤	≤	NUM
ejpam-7013	376	13	sn	sn	PROPN
ejpam-7013	376	14	,	,	PUNCT
ejpam-7013	376	15	dα(ln+1	dα(ln+1	PROPN
ejpam-7013	376	16	,	,	PUNCT
ejpam-7013	376	17	t	t	PROPN
ejpam-7013	376	18	(	(	PUNCT
ejpam-7013	376	19	ln+1	ln+1	PROPN
ejpam-7013	376	20	)	)	PUNCT
ejpam-7013	376	21	)	)	PUNCT
ejpam-7013	376	22	≤	≤	NUM
ejpam-7013	376	23	sn+1	sn+1	PROPN
ejpam-7013	376	24	,	,	PUNCT
ejpam-7013	376	25	dα(ln	dα(ln	PROPN
ejpam-7013	376	26	,	,	PUNCT
ejpam-7013	376	27	t	t	PROPN
ejpam-7013	376	28	(	(	PUNCT
ejpam-7013	376	29	ln+1	ln+1	PROPN
ejpam-7013	376	30	)	)	PUNCT
ejpam-7013	376	31	)	)	PUNCT
ejpam-7013	377	1	≤	≤	PROPN
ejpam-7013	377	2	d(ln	d(ln	PROPN
ejpam-7013	377	3	,	,	PUNCT
ejpam-7013	377	4	ln+2	ln+2	NUM
ejpam-7013	377	5	)	)	PUNCT
ejpam-7013	377	6	≤	≤	NUM
ejpam-7013	377	7	s(sn+sn+1	s(sn+sn+1	PROPN
ejpam-7013	377	8	)	)	PUNCT
ejpam-7013	377	9	.	.	PUNCT
ejpam-7013	378	1	thus	thus	ADV
ejpam-7013	378	2	h	h	PROPN
ejpam-7013	378	3	(	(	PUNCT
ejpam-7013	378	4	t	t	PROPN
ejpam-7013	378	5	(	(	PUNCT
ejpam-7013	378	6	ln	ln	PROPN
ejpam-7013	378	7	)	)	PUNCT
ejpam-7013	378	8	,	,	PUNCT
ejpam-7013	378	9	t	t	PROPN
ejpam-7013	378	10	(	(	PUNCT
ejpam-7013	378	11	ln+1	ln+1	PROPN
ejpam-7013	378	12	)	)	PUNCT
ejpam-7013	378	13	)	)	PUNCT
ejpam-7013	378	14	≤	≤	NUM
ejpam-7013	378	15	λ1max{sn	λ1max{sn	PROPN
ejpam-7013	378	16	,	,	PUNCT
ejpam-7013	378	17	sn+1	sn+1	PROPN
ejpam-7013	378	18	,	,	PUNCT
ejpam-7013	378	19	s(sn	s(sn	ADJ
ejpam-7013	378	20	+	+	X
ejpam-7013	378	21	sn+1	sn+1	NUM
ejpam-7013	378	22	)	)	PUNCT
ejpam-7013	378	23	,	,	PUNCT
ejpam-7013	378	24	0}+	0}+	PROPN
ejpam-7013	378	25	λ2sn	λ2sn	PUNCT
ejpam-7013	378	26	.	.	PUNCT
ejpam-7013	379	1	there	there	PRON
ejpam-7013	379	2	are	be	VERB
ejpam-7013	379	3	two	two	NUM
ejpam-7013	379	4	cases	case	NOUN
ejpam-7013	379	5	to	to	PART
ejpam-7013	379	6	estimate	estimate	VERB
ejpam-7013	379	7	the	the	DET
ejpam-7013	379	8	maximum	maximum	NOUN
ejpam-7013	379	9	.	.	PUNCT
ejpam-7013	380	1	if	if	SCONJ
ejpam-7013	380	2	the	the	DET
ejpam-7013	380	3	maximum	maximum	NOUN
ejpam-7013	380	4	equals	equal	VERB
ejpam-7013	380	5	sn+1	sn+1	NOUN
ejpam-7013	380	6	or	or	CCONJ
ejpam-7013	380	7	s(sn+sn+1	s(sn+sn+1	NUM
ejpam-7013	380	8	)	)	PUNCT
ejpam-7013	380	9	,	,	PUNCT
ejpam-7013	380	10	we	we	PRON
ejpam-7013	380	11	still	still	ADV
ejpam-7013	380	12	bound	bind	VERB
ejpam-7013	380	13	it	it	PRON
ejpam-7013	380	14	by	by	ADP
ejpam-7013	380	15	c(sn	c(sn	PROPN
ejpam-7013	380	16	+	+	CCONJ
ejpam-7013	380	17	sn+1	sn+1	X
ejpam-7013	380	18	)	)	PUNCT
ejpam-7013	380	19	for	for	ADP
ejpam-7013	380	20	some	some	DET
ejpam-7013	380	21	constant	constant	ADJ
ejpam-7013	380	22	c	c	NOUN
ejpam-7013	380	23	depending	depend	VERB
ejpam-7013	380	24	only	only	ADV
ejpam-7013	380	25	on	on	ADP
ejpam-7013	380	26	s	s	PRON
ejpam-7013	380	27	and	and	CCONJ
ejpam-7013	380	28	λ1	λ1	ADJ
ejpam-7013	380	29	.	.	PUNCT
ejpam-7013	381	1	to	to	PART
ejpam-7013	381	2	simplify	simplify	VERB
ejpam-7013	381	3	,	,	PUNCT
ejpam-7013	381	4	note	note	VERB
ejpam-7013	381	5	that	that	SCONJ
ejpam-7013	381	6	max{sn	max{sn	PROPN
ejpam-7013	381	7	,	,	PUNCT
ejpam-7013	381	8	sn+1	sn+1	PROPN
ejpam-7013	381	9	,	,	PUNCT
ejpam-7013	381	10	s(sn	s(sn	ADJ
ejpam-7013	381	11	+	+	X
ejpam-7013	381	12	sn+1	sn+1	X
ejpam-7013	381	13	)	)	PUNCT
ejpam-7013	381	14	}	}	PUNCT
ejpam-7013	381	15	≤	≤	NOUN
ejpam-7013	381	16	(	(	PUNCT
ejpam-7013	381	17	1	1	NUM
ejpam-7013	381	18	+	+	NUM
ejpam-7013	381	19	s	s	X
ejpam-7013	381	20	)	)	PUNCT
ejpam-7013	381	21	(	(	PUNCT
ejpam-7013	381	22	sn	sn	PROPN
ejpam-7013	381	23	+	+	CCONJ
ejpam-7013	381	24	sn+1	sn+1	NUM
ejpam-7013	381	25	)	)	PUNCT
ejpam-7013	381	26	.	.	PUNCT
ejpam-7013	382	1	hence	hence	ADV
ejpam-7013	382	2	h	h	PROPN
ejpam-7013	382	3	(	(	PUNCT
ejpam-7013	382	4	t	t	PROPN
ejpam-7013	382	5	(	(	PUNCT
ejpam-7013	382	6	ln	ln	PROPN
ejpam-7013	382	7	)	)	PUNCT
ejpam-7013	382	8	,	,	PUNCT
ejpam-7013	382	9	t	t	PROPN
ejpam-7013	382	10	(	(	PUNCT
ejpam-7013	382	11	ln+1	ln+1	PROPN
ejpam-7013	382	12	)	)	PUNCT
ejpam-7013	382	13	)	)	PUNCT
ejpam-7013	383	1	≤	≤	NOUN
ejpam-7013	383	2	λ1(1	λ1(1	ADJ
ejpam-7013	383	3	+	+	CCONJ
ejpam-7013	383	4	s)(sn	s)(sn	ADJ
ejpam-7013	383	5	+	+	CCONJ
ejpam-7013	383	6	sn+1	sn+1	X
ejpam-7013	383	7	)	)	PUNCT
ejpam-7013	383	8	+	+	CCONJ
ejpam-7013	383	9	λ2sn	λ2sn	PUNCT
ejpam-7013	383	10	.	.	PUNCT
ejpam-7013	384	1	combine	combine	VERB
ejpam-7013	384	2	with	with	ADP
ejpam-7013	384	3	the	the	DET
ejpam-7013	384	4	selection	selection	NOUN
ejpam-7013	384	5	inequality	inequality	NOUN
ejpam-7013	384	6	to	to	PART
ejpam-7013	384	7	obtain	obtain	VERB
ejpam-7013	384	8	sn+1	sn+1	NOUN
ejpam-7013	384	9	≤	≤	NUM
ejpam-7013	384	10	λ1(1	λ1(1	ADJ
ejpam-7013	384	11	+	+	CCONJ
ejpam-7013	384	12	s)(sn	s)(sn	ADJ
ejpam-7013	384	13	+	+	CCONJ
ejpam-7013	384	14	sn+1	sn+1	X
ejpam-7013	384	15	)	)	PUNCT
ejpam-7013	384	16	+	+	CCONJ
ejpam-7013	384	17	λ2sn	λ2sn	X
ejpam-7013	384	18	+	+	CCONJ
ejpam-7013	384	19	εn	εn	ADJ
ejpam-7013	384	20	.	.	PUNCT
ejpam-7013	384	21	collect	collect	VERB
ejpam-7013	384	22	sn+1	sn+1	PROPN
ejpam-7013	384	23	terms	term	NOUN
ejpam-7013	384	24	to	to	ADP
ejpam-7013	384	25	the	the	DET
ejpam-7013	384	26	left	left	NOUN
ejpam-7013	384	27	:(	:(	X
ejpam-7013	384	28	1−	1−	NUM
ejpam-7013	384	29	λ1(1	λ1(1	ADJ
ejpam-7013	384	30	+	+	NUM
ejpam-7013	384	31	s	s	NOUN
ejpam-7013	384	32	)	)	PUNCT
ejpam-7013	384	33	)	)	PUNCT
ejpam-7013	385	1	sn+1	sn+1	VERB
ejpam-7013	385	2	≤	≤	NUM
ejpam-7013	385	3	(	(	PUNCT
ejpam-7013	385	4	λ1(1	λ1(1	ADJ
ejpam-7013	385	5	+	+	NUM
ejpam-7013	385	6	s	s	NOUN
ejpam-7013	385	7	)	)	PUNCT
ejpam-7013	385	8	+	+	NUM
ejpam-7013	385	9	λ2	λ2	NOUN
ejpam-7013	385	10	)	)	PUNCT
ejpam-7013	385	11	sn	sn	PROPN
ejpam-7013	386	1	+	+	CCONJ
ejpam-7013	386	2	εn	εn	ADJ
ejpam-7013	386	3	.	.	PUNCT
ejpam-7013	387	1	now	now	ADV
ejpam-7013	387	2	impose	impose	VERB
ejpam-7013	387	3	a	a	DET
ejpam-7013	387	4	slightly	slightly	ADV
ejpam-7013	387	5	stronger	strong	ADJ
ejpam-7013	387	6	parameter	parameter	NOUN
ejpam-7013	387	7	condition	condition	NOUN
ejpam-7013	387	8	to	to	PART
ejpam-7013	387	9	ensure	ensure	VERB
ejpam-7013	387	10	the	the	DET
ejpam-7013	387	11	left	left	ADJ
ejpam-7013	387	12	coefficient	coefficient	NOUN
ejpam-7013	387	13	is	be	AUX
ejpam-7013	387	14	positive	positive	ADJ
ejpam-7013	387	15	.	.	PUNCT
ejpam-7013	388	1	because	because	SCONJ
ejpam-7013	388	2	the	the	DET
ejpam-7013	388	3	original	original	ADJ
ejpam-7013	388	4	hypothesis	hypothesis	NOUN
ejpam-7013	388	5	λ1+λ2	λ1+λ2	PROPN
ejpam-7013	388	6	<	<	X
ejpam-7013	388	7	1	1	NUM
ejpam-7013	388	8	holds	hold	NOUN
ejpam-7013	388	9	and	and	CCONJ
ejpam-7013	388	10	s	s	X
ejpam-7013	388	11	≥	≥	NOUN
ejpam-7013	388	12	1	1	NUM
ejpam-7013	388	13	,	,	PUNCT
ejpam-7013	388	14	one	one	PRON
ejpam-7013	388	15	may	may	AUX
ejpam-7013	388	16	verify	verify	VERB
ejpam-7013	388	17	(	(	PUNCT
ejpam-7013	388	18	by	by	ADP
ejpam-7013	388	19	reducing	reduce	VERB
ejpam-7013	388	20	λ1	λ1	NOUN
ejpam-7013	388	21	slightly	slightly	ADV
ejpam-7013	388	22	if	if	SCONJ
ejpam-7013	388	23	necessary	necessary	ADJ
ejpam-7013	388	24	)	)	PUNCT
ejpam-7013	388	25	that	that	SCONJ
ejpam-7013	388	26	1−	1−	NUM
ejpam-7013	388	27	λ1(1	λ1(1	ADJ
ejpam-7013	388	28	+	+	X
ejpam-7013	388	29	s	s	NOUN
ejpam-7013	388	30	)	)	PUNCT
ejpam-7013	388	31	>	>	X
ejpam-7013	388	32	0	0	X
ejpam-7013	388	33	.	.	PUNCT
ejpam-7013	389	1	under	under	ADP
ejpam-7013	389	2	this	this	DET
ejpam-7013	389	3	positivity	positivity	NOUN
ejpam-7013	389	4	we	we	PRON
ejpam-7013	389	5	get	get	VERB
ejpam-7013	389	6	sn+1	sn+1	ADJ
ejpam-7013	389	7	≤	≤	PUNCT
ejpam-7013	389	8	q	q	PROPN
ejpam-7013	389	9	sn	sn	PROPN
ejpam-7013	390	1	+	+	CCONJ
ejpam-7013	390	2	εn	εn	ADJ
ejpam-7013	390	3	1−	1−	NUM
ejpam-7013	390	4	λ1(1	λ1(1	ADJ
ejpam-7013	390	5	+	+	CCONJ
ejpam-7013	390	6	s	s	NOUN
ejpam-7013	390	7	)	)	PUNCT
ejpam-7013	390	8	,	,	PUNCT
ejpam-7013	390	9	q	q	NOUN
ejpam-7013	390	10	:	:	PUNCT
ejpam-7013	390	11	=	=	SYM
ejpam-7013	390	12	λ1(1	λ1(1	PROPN
ejpam-7013	390	13	+	+	CCONJ
ejpam-7013	390	14	s	s	NOUN
ejpam-7013	390	15	)	)	PUNCT
ejpam-7013	390	16	+	+	CCONJ
ejpam-7013	390	17	λ2	λ2	NOUN
ejpam-7013	390	18	1−	1−	NUM
ejpam-7013	390	19	λ1(1	λ1(1	ADJ
ejpam-7013	390	20	+	+	X
ejpam-7013	390	21	s	s	NOUN
ejpam-7013	390	22	)	)	PUNCT
ejpam-7013	390	23	.	.	PUNCT
ejpam-7013	391	1	d.	d.	PROPN
ejpam-7013	391	2	gerbeti	gerbeti	PROPN
ejpam-7013	391	3	et	et	PROPN
ejpam-7013	391	4	al	al	PROPN
ejpam-7013	391	5	.	.	PUNCT
ejpam-7013	391	6	/	/	SYM
ejpam-7013	391	7	eur	eur	PROPN
ejpam-7013	391	8	.	.	PUNCT
ejpam-7013	392	1	j.	j.	PROPN
ejpam-7013	392	2	pure	pure	PROPN
ejpam-7013	392	3	appl	appl	PROPN
ejpam-7013	392	4	.	.	PROPN
ejpam-7013	392	5	math	math	PROPN
ejpam-7013	392	6	,	,	PUNCT
ejpam-7013	392	7	18	18	NUM
ejpam-7013	392	8	(	(	PUNCT
ejpam-7013	392	9	4	4	NUM
ejpam-7013	392	10	)	)	PUNCT
ejpam-7013	392	11	(	(	PUNCT
ejpam-7013	392	12	2025	2025	NUM
ejpam-7013	392	13	)	)	PUNCT
ejpam-7013	392	14	,	,	PUNCT
ejpam-7013	392	15	7013	7013	NUM
ejpam-7013	392	16	14	14	NUM
ejpam-7013	392	17	of	of	ADP
ejpam-7013	392	18	17	17	NUM
ejpam-7013	392	19	from	from	ADP
ejpam-7013	392	20	λ1	λ1	PROPN
ejpam-7013	393	1	+	+	PROPN
ejpam-7013	393	2	λ2	λ2	NOUN
ejpam-7013	393	3	<	<	X
ejpam-7013	393	4	1	1	NUM
ejpam-7013	393	5	and	and	CCONJ
ejpam-7013	393	6	small	small	ADJ
ejpam-7013	393	7	algebra	algebra	NOUN
ejpam-7013	393	8	one	one	NUM
ejpam-7013	393	9	checks	check	NOUN
ejpam-7013	393	10	q	q	X
ejpam-7013	393	11	∈	∈	PROPN
ejpam-7013	394	1	[	[	X
ejpam-7013	394	2	0	0	NUM
ejpam-7013	394	3	,	,	PUNCT
ejpam-7013	394	4	1	1	NUM
ejpam-7013	394	5	)	)	PUNCT
ejpam-7013	394	6	(	(	PUNCT
ejpam-7013	394	7	one	one	PRON
ejpam-7013	394	8	can	can	AUX
ejpam-7013	394	9	always	always	ADV
ejpam-7013	394	10	replace	replace	VERB
ejpam-7013	394	11	λ1	λ1	VERB
ejpam-7013	394	12	by	by	ADP
ejpam-7013	394	13	a	a	DET
ejpam-7013	394	14	slightly	slightly	ADV
ejpam-7013	394	15	smaller	small	ADJ
ejpam-7013	394	16	number	number	NOUN
ejpam-7013	394	17	if	if	SCONJ
ejpam-7013	394	18	the	the	DET
ejpam-7013	394	19	strict	strict	ADJ
ejpam-7013	394	20	inequality	inequality	NOUN
ejpam-7013	394	21	needs	need	VERB
ejpam-7013	394	22	to	to	PART
ejpam-7013	394	23	be	be	AUX
ejpam-7013	394	24	enforced	enforce	VERB
ejpam-7013	394	25	in	in	ADP
ejpam-7013	394	26	presence	presence	NOUN
ejpam-7013	394	27	of	of	ADP
ejpam-7013	394	28	s	s	NOUN
ejpam-7013	394	29	)	)	PUNCT
ejpam-7013	394	30	.	.	PUNCT
ejpam-7013	395	1	as	as	ADP
ejpam-7013	395	2	before	before	ADV
ejpam-7013	395	3	,	,	PUNCT
ejpam-7013	395	4	iteration	iteration	NOUN
ejpam-7013	395	5	gives	give	VERB
ejpam-7013	395	6	sn	sn	PROPN
ejpam-7013	395	7	→	→	SYM
ejpam-7013	395	8	0	0	NUM
ejpam-7013	395	9	,	,	PUNCT
ejpam-7013	395	10	hence	hence	ADV
ejpam-7013	395	11	{	{	PUNCT
ejpam-7013	395	12	ln	ln	ADJ
ejpam-7013	395	13	}	}	PUNCT
ejpam-7013	395	14	is	be	AUX
ejpam-7013	395	15	cauchy	cauchy	ADJ
ejpam-7013	395	16	and	and	CCONJ
ejpam-7013	395	17	converges	converge	VERB
ejpam-7013	395	18	to	to	ADP
ejpam-7013	395	19	some	some	DET
ejpam-7013	395	20	k	k	PROPN
ejpam-7013	395	21	∈	∈	PROPN
ejpam-7013	395	22	x.	x.	NOUN
ejpam-7013	395	23	finally	finally	ADV
ejpam-7013	395	24	,	,	PUNCT
ejpam-7013	395	25	the	the	DET
ejpam-7013	395	26	argument	argument	NOUN
ejpam-7013	395	27	that	that	SCONJ
ejpam-7013	395	28	k	k	PROPN
ejpam-7013	395	29	∈	∈	PROPN
ejpam-7013	395	30	t	t	PROPN
ejpam-7013	395	31	(	(	PUNCT
ejpam-7013	395	32	k	k	NOUN
ejpam-7013	395	33	)	)	PUNCT
ejpam-7013	395	34	follows	follow	VERB
ejpam-7013	395	35	from	from	ADP
ejpam-7013	395	36	passing	pass	VERB
ejpam-7013	395	37	limits	limit	NOUN
ejpam-7013	395	38	in	in	ADP
ejpam-7013	395	39	the	the	DET
ejpam-7013	395	40	contractive	contractive	ADJ
ejpam-7013	395	41	inequality	inequality	NOUN
ejpam-7013	395	42	:	:	PUNCT
ejpam-7013	395	43	h(t	h(t	PROPN
ejpam-7013	395	44	(	(	PUNCT
ejpam-7013	395	45	ln	ln	ADJ
ejpam-7013	395	46	)	)	PUNCT
ejpam-7013	395	47	,	,	PUNCT
ejpam-7013	395	48	t	t	PROPN
ejpam-7013	395	49	(	(	PUNCT
ejpam-7013	395	50	k	k	NOUN
ejpam-7013	395	51	)	)	PUNCT
ejpam-7013	395	52	)	)	PUNCT
ejpam-7013	396	1	→	→	SYM
ejpam-7013	396	2	0	0	NUM
ejpam-7013	396	3	,	,	PUNCT
ejpam-7013	396	4	dα(ln	dα(ln	PROPN
ejpam-7013	396	5	,	,	PUNCT
ejpam-7013	396	6	t	t	PROPN
ejpam-7013	396	7	(	(	PUNCT
ejpam-7013	396	8	ln	ln	ADJ
ejpam-7013	396	9	)	)	PUNCT
ejpam-7013	396	10	)	)	PUNCT
ejpam-7013	396	11	≤	≤	NUM
ejpam-7013	396	12	sn	sn	PROPN
ejpam-7013	396	13	→	→	SYM
ejpam-7013	396	14	0	0	NUM
ejpam-7013	396	15	,	,	PUNCT
ejpam-7013	396	16	and	and	CCONJ
ejpam-7013	396	17	dα(k	dα(k	NOUN
ejpam-7013	396	18	,	,	PUNCT
ejpam-7013	396	19	t	t	PROPN
ejpam-7013	396	20	(	(	PUNCT
ejpam-7013	396	21	ln	ln	ADJ
ejpam-7013	396	22	)	)	PUNCT
ejpam-7013	396	23	)	)	PUNCT
ejpam-7013	397	1	≤	≤	NOUN
ejpam-7013	397	2	d(k	d(k	PROPN
ejpam-7013	397	3	,	,	PUNCT
ejpam-7013	397	4	ln+1	ln+1	PROPN
ejpam-7013	397	5	)	)	PUNCT
ejpam-7013	397	6	→	→	SYM
ejpam-7013	397	7	0	0	X
ejpam-7013	397	8	.	.	X
ejpam-7013	397	9	taking	take	VERB
ejpam-7013	397	10	limits	limit	NOUN
ejpam-7013	397	11	yields	yield	NOUN
ejpam-7013	397	12	a	a	DET
ejpam-7013	397	13	contradiction	contradiction	NOUN
ejpam-7013	397	14	if	if	SCONJ
ejpam-7013	397	15	dα(k	dα(k	NOUN
ejpam-7013	397	16	,	,	PUNCT
ejpam-7013	397	17	t	t	PROPN
ejpam-7013	397	18	(	(	PUNCT
ejpam-7013	397	19	k	k	NOUN
ejpam-7013	397	20	)	)	PUNCT
ejpam-7013	397	21	)	)	PUNCT
ejpam-7013	397	22	>	>	X
ejpam-7013	398	1	0	0	NUM
ejpam-7013	398	2	,	,	PUNCT
ejpam-7013	398	3	so	so	ADV
ejpam-7013	398	4	dα(k	dα(k	NOUN
ejpam-7013	398	5	,	,	PUNCT
ejpam-7013	398	6	t	t	PROPN
ejpam-7013	398	7	(	(	PUNCT
ejpam-7013	398	8	k	k	NOUN
ejpam-7013	398	9	)	)	PUNCT
ejpam-7013	398	10	)	)	PUNCT
ejpam-7013	399	1	=	=	PUNCT
ejpam-7013	399	2	0	0	NUM
ejpam-7013	399	3	,	,	PUNCT
ejpam-7013	399	4	and	and	CCONJ
ejpam-7013	399	5	since	since	SCONJ
ejpam-7013	399	6	t	t	PROPN
ejpam-7013	399	7	(	(	PUNCT
ejpam-7013	399	8	k	k	NOUN
ejpam-7013	399	9	)	)	PUNCT
ejpam-7013	399	10	is	be	AUX
ejpam-7013	399	11	closed	close	VERB
ejpam-7013	399	12	we	we	PRON
ejpam-7013	399	13	get	get	VERB
ejpam-7013	399	14	k	k	PROPN
ejpam-7013	399	15	∈	∈	PROPN
ejpam-7013	399	16	t	t	PROPN
ejpam-7013	399	17	(	(	PUNCT
ejpam-7013	399	18	k	k	NOUN
ejpam-7013	399	19	)	)	PUNCT
ejpam-7013	399	20	.	.	PUNCT
ejpam-7013	400	1	thus	thus	ADV
ejpam-7013	400	2	t	t	PROPN
ejpam-7013	400	3	admits	admit	VERB
ejpam-7013	400	4	a	a	DET
ejpam-7013	400	5	fuzzy	fuzzy	ADJ
ejpam-7013	400	6	fp	fp	NOUN
ejpam-7013	400	7	.	.	PROPN
ejpam-7013	400	8	4	4	NUM
ejpam-7013	400	9	.	.	X
ejpam-7013	400	10	application	application	NOUN
ejpam-7013	400	11	:	:	PUNCT
ejpam-7013	400	12	a	a	DET
ejpam-7013	400	13	nonlinear	nonlinear	ADJ
ejpam-7013	400	14	volterra	volterra	NOUN
ejpam-7013	400	15	–	–	PUNCT
ejpam-7013	400	16	fredholm	fredholm	ADJ
ejpam-7013	400	17	integral	integral	ADJ
ejpam-7013	400	18	equation	equation	NOUN
ejpam-7013	400	19	in	in	ADP
ejpam-7013	400	20	this	this	DET
ejpam-7013	400	21	section	section	NOUN
ejpam-7013	400	22	we	we	PRON
ejpam-7013	400	23	apply	apply	VERB
ejpam-7013	400	24	theorem	theorem	VERB
ejpam-7013	400	25	3	3	NUM
ejpam-7013	400	26	to	to	PART
ejpam-7013	400	27	prove	prove	VERB
ejpam-7013	400	28	existence	existence	NOUN
ejpam-7013	400	29	(	(	PUNCT
ejpam-7013	400	30	and	and	CCONJ
ejpam-7013	400	31	uniqueness	uniqueness	NOUN
ejpam-7013	400	32	)	)	PUNCT
ejpam-7013	400	33	of	of	ADP
ejpam-7013	400	34	a	a	DET
ejpam-7013	400	35	solution	solution	NOUN
ejpam-7013	400	36	for	for	ADP
ejpam-7013	400	37	a	a	DET
ejpam-7013	400	38	nonlinear	nonlinear	ADJ
ejpam-7013	400	39	volterra	volterra	NOUN
ejpam-7013	400	40	–	–	PUNCT
ejpam-7013	400	41	fredholm	fredholm	ADJ
ejpam-7013	400	42	integral	integral	ADJ
ejpam-7013	400	43	equation	equation	NOUN
ejpam-7013	400	44	in	in	ADP
ejpam-7013	400	45	a	a	DET
ejpam-7013	400	46	b	b	NOUN
ejpam-7013	400	47	-	-	PUNCT
ejpam-7013	400	48	fuzzy	fuzzy	ADJ
ejpam-7013	400	49	metric	metric	ADJ
ejpam-7013	400	50	setting	setting	NOUN
ejpam-7013	400	51	.	.	PUNCT
ejpam-7013	401	1	let	let	VERB
ejpam-7013	401	2	x	x	SYM
ejpam-7013	401	3	=	=	SYM
ejpam-7013	401	4	c([0	c([0	NOUN
ejpam-7013	401	5	,	,	PUNCT
ejpam-7013	401	6	1],r	1],r	NUM
ejpam-7013	401	7	)	)	PUNCT
ejpam-7013	401	8	be	be	VERB
ejpam-7013	401	9	the	the	DET
ejpam-7013	401	10	banach	banach	NOUN
ejpam-7013	401	11	space	space	NOUN
ejpam-7013	401	12	of	of	ADP
ejpam-7013	401	13	continuous	continuous	ADJ
ejpam-7013	401	14	real	real	ADV
ejpam-7013	401	15	-	-	PUNCT
ejpam-7013	401	16	valued	value	VERB
ejpam-7013	401	17	functions	function	NOUN
ejpam-7013	401	18	on	on	ADP
ejpam-7013	401	19	[	[	X
ejpam-7013	401	20	0	0	NUM
ejpam-7013	401	21	,	,	PUNCT
ejpam-7013	401	22	1	1	NUM
ejpam-7013	401	23	]	]	PUNCT
ejpam-7013	401	24	equipped	equip	VERB
ejpam-7013	401	25	with	with	ADP
ejpam-7013	401	26	the	the	DET
ejpam-7013	401	27	supremum	supremum	ADJ
ejpam-7013	401	28	norm	norm	NOUN
ejpam-7013	402	1	‖u‖∞	‖u‖∞	NUM
ejpam-7013	402	2	:	:	PUNCT
ejpam-7013	403	1	=	=	SYM
ejpam-7013	403	2	sup	sup	NOUN
ejpam-7013	403	3	t∈[0,1	t∈[0,1	NOUN
ejpam-7013	403	4	]	]	PUNCT
ejpam-7013	403	5	|u(t)|	|u(t)|	NOUN
ejpam-7013	403	6	.	.	NOUN
ejpam-7013	404	1	we	we	PRON
ejpam-7013	404	2	regard	regard	VERB
ejpam-7013	404	3	x	x	PUNCT
ejpam-7013	404	4	as	as	ADP
ejpam-7013	404	5	a	a	DET
ejpam-7013	404	6	b	b	NOUN
ejpam-7013	404	7	-	-	PUNCT
ejpam-7013	404	8	fms	fms	PROPN
ejpam-7013	404	9	with	with	ADP
ejpam-7013	404	10	underlying	underlie	VERB
ejpam-7013	404	11	b	b	X
ejpam-7013	404	12	-	-	PUNCT
ejpam-7013	404	13	metric	metric	ADJ
ejpam-7013	404	14	d(u	d(u	PROPN
ejpam-7013	404	15	,	,	PUNCT
ejpam-7013	404	16	v	v	NOUN
ejpam-7013	404	17	)	)	PUNCT
ejpam-7013	404	18	=	=	SYM
ejpam-7013	404	19	‖u	‖u	PROPN
ejpam-7013	404	20	−	−	PUNCT
ejpam-7013	404	21	v‖∞	v‖∞	NOUN
ejpam-7013	404	22	and	and	CCONJ
ejpam-7013	404	23	b	b	X
ejpam-7013	404	24	-	-	PUNCT
ejpam-7013	404	25	constant	constant	ADJ
ejpam-7013	404	26	s	s	X
ejpam-7013	404	27	=	=	SYM
ejpam-7013	404	28	1	1	X
ejpam-7013	404	29	.	.	PUNCT
ejpam-7013	404	30	denote	denote	VERB
ejpam-7013	404	31	by	by	ADP
ejpam-7013	404	32	f(r	f(r	NOUN
ejpam-7013	404	33	)	)	PUNCT
ejpam-7013	404	34	the	the	DET
ejpam-7013	404	35	class	class	NOUN
ejpam-7013	404	36	of	of	ADP
ejpam-7013	404	37	fuzzy	fuzzy	ADJ
ejpam-7013	404	38	numbers	number	NOUN
ejpam-7013	404	39	;	;	PUNCT
ejpam-7013	404	40	for	for	ADP
ejpam-7013	404	41	simplicity	simplicity	NOUN
ejpam-7013	404	42	(	(	PUNCT
ejpam-7013	404	43	and	and	CCONJ
ejpam-7013	404	44	as	as	ADP
ejpam-7013	404	45	a	a	DET
ejpam-7013	404	46	standard	standard	ADJ
ejpam-7013	404	47	reduction	reduction	NOUN
ejpam-7013	404	48	used	use	VERB
ejpam-7013	404	49	in	in	ADP
ejpam-7013	404	50	many	many	ADJ
ejpam-7013	404	51	fixed	fix	VERB
ejpam-7013	404	52	-	-	PUNCT
ejpam-7013	404	53	point	point	NOUN
ejpam-7013	404	54	applications	application	NOUN
ejpam-7013	404	55	)	)	PUNCT
ejpam-7013	404	56	we	we	PRON
ejpam-7013	404	57	work	work	VERB
ejpam-7013	404	58	with	with	ADP
ejpam-7013	404	59	crisp	crisp	ADJ
ejpam-7013	404	60	singleton	singleton	NOUN
ejpam-7013	404	61	values	value	NOUN
ejpam-7013	404	62	and	and	CCONJ
ejpam-7013	404	63	interpret	interpret	VERB
ejpam-7013	404	64	fuzzy	fuzzy	ADJ
ejpam-7013	404	65	images	image	NOUN
ejpam-7013	404	66	as	as	ADP
ejpam-7013	404	67	singletons	singleton	NOUN
ejpam-7013	404	68	(	(	PUNCT
ejpam-7013	404	69	this	this	PRON
ejpam-7013	404	70	is	be	AUX
ejpam-7013	404	71	a	a	DET
ejpam-7013	404	72	harmless	harmless	ADJ
ejpam-7013	404	73	specialization	specialization	NOUN
ejpam-7013	404	74	:	:	PUNCT
ejpam-7013	404	75	the	the	DET
ejpam-7013	404	76	multivalued	multivalue	VERB
ejpam-7013	404	77	maps	map	NOUN
ejpam-7013	404	78	in	in	ADP
ejpam-7013	404	79	our	our	PRON
ejpam-7013	404	80	theorems	theorem	NOUN
ejpam-7013	404	81	accept	accept	VERB
ejpam-7013	404	82	singletons	singleton	NOUN
ejpam-7013	404	83	as	as	ADP
ejpam-7013	404	84	valid	valid	ADJ
ejpam-7013	404	85	images	image	NOUN
ejpam-7013	404	86	)	)	PUNCT
ejpam-7013	404	87	.	.	PUNCT
ejpam-7013	405	1	thus	thus	ADV
ejpam-7013	405	2	we	we	PRON
ejpam-7013	405	3	identify	identify	VERB
ejpam-7013	405	4	t	t	PROPN
ejpam-7013	405	5	(	(	PUNCT
ejpam-7013	405	6	u	u	NOUN
ejpam-7013	405	7	)	)	PUNCT
ejpam-7013	405	8	=	=	SYM
ejpam-7013	405	9	{	{	PUNCT
ejpam-7013	405	10	f	f	PROPN
ejpam-7013	405	11	(	(	PUNCT
ejpam-7013	405	12	u	u	NOUN
ejpam-7013	405	13	)	)	PUNCT
ejpam-7013	405	14	}	}	PUNCT
ejpam-7013	405	15	where	where	SCONJ
ejpam-7013	405	16	f	f	X
ejpam-7013	405	17	:	:	PUNCT
ejpam-7013	405	18	x	x	X
ejpam-7013	405	19	→	→	PUNCT
ejpam-7013	405	20	x	x	X
ejpam-7013	405	21	is	be	AUX
ejpam-7013	405	22	an	an	DET
ejpam-7013	405	23	operator	operator	NOUN
ejpam-7013	405	24	.	.	PUNCT
ejpam-7013	406	1	consider	consider	VERB
ejpam-7013	406	2	the	the	DET
ejpam-7013	406	3	nonlinear	nonlinear	PROPN
ejpam-7013	406	4	volterra	volterra	PROPN
ejpam-7013	406	5	–	–	PUNCT
ejpam-7013	406	6	fredholm	fredholm	ADJ
ejpam-7013	406	7	integral	integral	ADJ
ejpam-7013	406	8	equation	equation	NOUN
ejpam-7013	406	9	u(t	u(t	NOUN
ejpam-7013	406	10	)	)	PUNCT
ejpam-7013	406	11	=	=	SYM
ejpam-7013	406	12	g(t	g(t	PROPN
ejpam-7013	406	13	)	)	PUNCT
ejpam-7013	407	1	+	+	CCONJ
ejpam-7013	407	2	∫	∫	PROPN
ejpam-7013	407	3	t	t	PROPN
ejpam-7013	407	4	0	0	NUM
ejpam-7013	407	5	k1(t	k1(t	PROPN
ejpam-7013	407	6	,	,	PUNCT
ejpam-7013	407	7	s	s	X
ejpam-7013	407	8	,	,	PUNCT
ejpam-7013	407	9	u(s	u(s	ADJ
ejpam-7013	407	10	)	)	PUNCT
ejpam-7013	407	11	)	)	PUNCT
ejpam-7013	408	1	ds	ds	PROPN
ejpam-7013	409	1	+	+	CCONJ
ejpam-7013	409	2	∫	∫	PROPN
ejpam-7013	409	3	1	1	NUM
ejpam-7013	409	4	0	0	NUM
ejpam-7013	409	5	k2(t	k2(t	PROPN
ejpam-7013	409	6	,	,	PUNCT
ejpam-7013	409	7	s	s	X
ejpam-7013	409	8	,	,	PUNCT
ejpam-7013	409	9	u(s	u(s	ADJ
ejpam-7013	409	10	)	)	PUNCT
ejpam-7013	409	11	)	)	PUNCT
ejpam-7013	409	12	ds	ds	PROPN
ejpam-7013	409	13	,	,	PUNCT
ejpam-7013	409	14	t	t	PROPN
ejpam-7013	409	15	∈	∈	PROPN
ejpam-7013	410	1	[	[	X
ejpam-7013	410	2	0	0	NUM
ejpam-7013	410	3	,	,	PUNCT
ejpam-7013	410	4	1	1	NUM
ejpam-7013	410	5	]	]	PUNCT
ejpam-7013	410	6	,	,	PUNCT
ejpam-7013	410	7	(	(	PUNCT
ejpam-7013	410	8	4	4	X
ejpam-7013	410	9	)	)	PUNCT
ejpam-7013	410	10	where	where	SCONJ
ejpam-7013	410	11	g	g	PROPN
ejpam-7013	410	12	∈	∈	PROPN
ejpam-7013	410	13	x	x	PUNCT
ejpam-7013	410	14	is	be	AUX
ejpam-7013	410	15	given	give	VERB
ejpam-7013	410	16	and	and	CCONJ
ejpam-7013	410	17	the	the	DET
ejpam-7013	410	18	kernels	kernel	NOUN
ejpam-7013	410	19	k1,k2	k1,k2	PROPN
ejpam-7013	410	20	:	:	PUNCT
ejpam-7013	411	1	[	[	X
ejpam-7013	411	2	0	0	NUM
ejpam-7013	411	3	,	,	PUNCT
ejpam-7013	411	4	1]×	1]×	NUM
ejpam-7013	411	5	[	[	X
ejpam-7013	411	6	0	0	NUM
ejpam-7013	411	7	,	,	PUNCT
ejpam-7013	411	8	1]×	1]×	NUM
ejpam-7013	411	9	r	r	NOUN
ejpam-7013	411	10	→	→	SYM
ejpam-7013	411	11	r	r	NOUN
ejpam-7013	411	12	are	be	AUX
ejpam-7013	411	13	continuous	continuous	ADJ
ejpam-7013	411	14	in	in	ADP
ejpam-7013	411	15	all	all	DET
ejpam-7013	411	16	arguments	argument	NOUN
ejpam-7013	411	17	.	.	PUNCT
ejpam-7013	412	1	define	define	VERB
ejpam-7013	412	2	the	the	DET
ejpam-7013	412	3	operator	operator	NOUN
ejpam-7013	412	4	f	f	NOUN
ejpam-7013	412	5	:	:	PUNCT
ejpam-7013	412	6	x	x	X
ejpam-7013	412	7	→	→	SYM
ejpam-7013	412	8	x	x	SYM
ejpam-7013	412	9	by	by	ADP
ejpam-7013	412	10	(	(	PUNCT
ejpam-7013	412	11	fu)(t	fu)(t	PROPN
ejpam-7013	412	12	)	)	PUNCT
ejpam-7013	412	13	:	:	PUNCT
ejpam-7013	412	14	=	=	SYM
ejpam-7013	412	15	g(t	g(t	PROPN
ejpam-7013	412	16	)	)	PUNCT
ejpam-7013	413	1	+	+	CCONJ
ejpam-7013	413	2	∫	∫	PROPN
ejpam-7013	413	3	t	t	PROPN
ejpam-7013	413	4	0	0	NUM
ejpam-7013	413	5	k1(t	k1(t	PROPN
ejpam-7013	413	6	,	,	PUNCT
ejpam-7013	413	7	s	s	X
ejpam-7013	413	8	,	,	PUNCT
ejpam-7013	413	9	u(s	u(s	ADJ
ejpam-7013	413	10	)	)	PUNCT
ejpam-7013	413	11	)	)	PUNCT
ejpam-7013	413	12	ds+	ds+	PROPN
ejpam-7013	413	13	∫	∫	PROPN
ejpam-7013	414	1	1	1	NUM
ejpam-7013	414	2	0	0	NUM
ejpam-7013	414	3	k2(t	k2(t	PROPN
ejpam-7013	414	4	,	,	PUNCT
ejpam-7013	414	5	s	s	X
ejpam-7013	414	6	,	,	PUNCT
ejpam-7013	414	7	u(s	u(s	ADJ
ejpam-7013	414	8	)	)	PUNCT
ejpam-7013	414	9	)	)	PUNCT
ejpam-7013	414	10	ds	ds	NOUN
ejpam-7013	414	11	,	,	PUNCT
ejpam-7013	414	12	and	and	CCONJ
ejpam-7013	414	13	consider	consider	VERB
ejpam-7013	414	14	the	the	DET
ejpam-7013	414	15	multimap	multimap	NOUN
ejpam-7013	414	16	t	t	NOUN
ejpam-7013	414	17	:	:	PUNCT
ejpam-7013	414	18	x	x	X
ejpam-7013	414	19	→	→	SYM
ejpam-7013	414	20	w(x	w(x	NOUN
ejpam-7013	414	21	)	)	PUNCT
ejpam-7013	414	22	given	give	VERB
ejpam-7013	414	23	by	by	ADP
ejpam-7013	414	24	t	t	PROPN
ejpam-7013	414	25	(	(	PUNCT
ejpam-7013	414	26	u	u	NOUN
ejpam-7013	414	27	)	)	PUNCT
ejpam-7013	414	28	=	=	SYM
ejpam-7013	414	29	{	{	PUNCT
ejpam-7013	414	30	fu	fu	NOUN
ejpam-7013	414	31	}	}	PUNCT
ejpam-7013	414	32	.	.	PUNCT
ejpam-7013	415	1	a	a	PRON
ejpam-7013	415	2	fp	fp	PROPN
ejpam-7013	415	3	{	{	PUNCT
ejpam-7013	415	4	u	u	NOUN
ejpam-7013	415	5	}	}	PUNCT
ejpam-7013	415	6	⊆	⊆	NUM
ejpam-7013	415	7	t	t	NOUN
ejpam-7013	415	8	(	(	PUNCT
ejpam-7013	415	9	u	u	NOUN
ejpam-7013	415	10	)	)	PUNCT
ejpam-7013	415	11	is	be	AUX
ejpam-7013	415	12	equivalent	equivalent	ADJ
ejpam-7013	415	13	to	to	ADP
ejpam-7013	415	14	a	a	DET
ejpam-7013	415	15	solution	solution	NOUN
ejpam-7013	415	16	u	u	NOUN
ejpam-7013	415	17	∈	∈	PROPN
ejpam-7013	415	18	x	x	SYM
ejpam-7013	415	19	of	of	ADP
ejpam-7013	415	20	(	(	PUNCT
ejpam-7013	415	21	4	4	NUM
ejpam-7013	415	22	)	)	PUNCT
ejpam-7013	415	23	.	.	PUNCT
ejpam-7013	416	1	assume	assume	VERB
ejpam-7013	416	2	there	there	PRON
ejpam-7013	416	3	exist	exist	VERB
ejpam-7013	416	4	nonnegative	nonnegative	ADJ
ejpam-7013	416	5	functions	function	NOUN
ejpam-7013	416	6	l1	l1	PROPN
ejpam-7013	416	7	,	,	PUNCT
ejpam-7013	416	8	l2	l2	NOUN
ejpam-7013	416	9	on	on	ADP
ejpam-7013	416	10	[	[	X
ejpam-7013	416	11	0	0	NUM
ejpam-7013	416	12	,	,	PUNCT
ejpam-7013	416	13	1]2	1]2	NUM
ejpam-7013	416	14	such	such	ADJ
ejpam-7013	416	15	that	that	PRON
ejpam-7013	416	16	for	for	ADP
ejpam-7013	416	17	all	all	DET
ejpam-7013	416	18	t	t	PROPN
ejpam-7013	416	19	,	,	PUNCT
ejpam-7013	416	20	s	s	PART
ejpam-7013	416	21	∈	∈	PROPN
ejpam-7013	417	1	[	[	X
ejpam-7013	417	2	0	0	NUM
ejpam-7013	417	3	,	,	PUNCT
ejpam-7013	417	4	1	1	NUM
ejpam-7013	417	5	]	]	PUNCT
ejpam-7013	417	6	and	and	CCONJ
ejpam-7013	417	7	all	all	DET
ejpam-7013	417	8	x	x	NOUN
ejpam-7013	417	9	,	,	PUNCT
ejpam-7013	417	10	y	y	PROPN
ejpam-7013	417	11	∈	∈	PROPN
ejpam-7013	417	12	r	r	PROPN
ejpam-7013	417	13	,	,	PUNCT
ejpam-7013	417	14	|k1(t	|k1(t	PROPN
ejpam-7013	417	15	,	,	PUNCT
ejpam-7013	417	16	s	s	X
ejpam-7013	417	17	,	,	PUNCT
ejpam-7013	417	18	x)−k1(t	x)−k1(t	NOUN
ejpam-7013	417	19	,	,	PUNCT
ejpam-7013	417	20	s	s	AUX
ejpam-7013	417	21	,	,	PUNCT
ejpam-7013	417	22	y)|	y)|	PROPN
ejpam-7013	417	23	≤	≤	PUNCT
ejpam-7013	417	24	`	`	PUNCT
ejpam-7013	417	25	1(s	1(s	NUM
ejpam-7013	417	26	)	)	PUNCT
ejpam-7013	417	27	|x−	|x−	PROPN
ejpam-7013	418	1	y|	y|	NOUN
ejpam-7013	418	2	,	,	PUNCT
ejpam-7013	418	3	|k2(t	|k2(t	PROPN
ejpam-7013	418	4	,	,	PUNCT
ejpam-7013	418	5	s	s	X
ejpam-7013	418	6	,	,	PUNCT
ejpam-7013	418	7	x)−k2(t	x)−k2(t	ADJ
ejpam-7013	418	8	,	,	PUNCT
ejpam-7013	418	9	s	s	PROPN
ejpam-7013	418	10	,	,	PUNCT
ejpam-7013	418	11	y)|	y)|	PROPN
ejpam-7013	418	12	≤	≤	NOUN
ejpam-7013	418	13	`	`	PUNCT
ejpam-7013	418	14	2(s	2(s	NUM
ejpam-7013	418	15	)	)	PUNCT
ejpam-7013	418	16	|x−	|x−	PROPN
ejpam-7013	418	17	y|	y|	NOUN
ejpam-7013	418	18	,	,	PUNCT
ejpam-7013	418	19	d.	d.	PROPN
ejpam-7013	418	20	gerbeti	gerbeti	PROPN
ejpam-7013	418	21	et	et	PROPN
ejpam-7013	418	22	al	al	PROPN
ejpam-7013	418	23	.	.	PUNCT
ejpam-7013	418	24	/	/	SYM
ejpam-7013	418	25	eur	eur	PROPN
ejpam-7013	418	26	.	.	PUNCT
ejpam-7013	419	1	j.	j.	PROPN
ejpam-7013	419	2	pure	pure	PROPN
ejpam-7013	419	3	appl	appl	PROPN
ejpam-7013	419	4	.	.	PROPN
ejpam-7013	419	5	math	math	PROPN
ejpam-7013	419	6	,	,	PUNCT
ejpam-7013	419	7	18	18	NUM
ejpam-7013	419	8	(	(	PUNCT
ejpam-7013	419	9	4	4	NUM
ejpam-7013	419	10	)	)	PUNCT
ejpam-7013	419	11	(	(	PUNCT
ejpam-7013	419	12	2025	2025	NUM
ejpam-7013	419	13	)	)	PUNCT
ejpam-7013	419	14	,	,	PUNCT
ejpam-7013	419	15	7013	7013	NUM
ejpam-7013	419	16	15	15	NUM
ejpam-7013	419	17	of	of	ADP
ejpam-7013	419	18	17	17	NUM
ejpam-7013	419	19	with	with	ADP
ejpam-7013	419	20	`	`	PUNCT
ejpam-7013	419	21	1	1	NUM
ejpam-7013	419	22	,	,	PUNCT
ejpam-7013	419	23	`	`	PUNCT
ejpam-7013	419	24	2	2	NUM
ejpam-7013	419	25	∈	∈	NOUN
ejpam-7013	419	26	l1([0	l1([0	NOUN
ejpam-7013	419	27	,	,	PUNCT
ejpam-7013	419	28	1	1	NUM
ejpam-7013	419	29	]	]	NUM
ejpam-7013	419	30	)	)	PUNCT
ejpam-7013	419	31	.	.	PUNCT
ejpam-7013	420	1	set	set	VERB
ejpam-7013	420	2	l	l	NOUN
ejpam-7013	420	3	:	:	PUNCT
ejpam-7013	421	1	=	=	SYM
ejpam-7013	421	2	∫	∫	PROPN
ejpam-7013	421	3	1	1	NUM
ejpam-7013	421	4	0	0	NUM
ejpam-7013	421	5	(	(	PUNCT
ejpam-7013	421	6	`	`	PUNCT
ejpam-7013	421	7	1(s	1(s	NUM
ejpam-7013	421	8	)	)	PUNCT
ejpam-7013	421	9	+	+	CCONJ
ejpam-7013	421	10	`	`	PUNCT
ejpam-7013	421	11	2(s	2(s	NUM
ejpam-7013	421	12	)	)	PUNCT
ejpam-7013	421	13	)	)	PUNCT
ejpam-7013	421	14	ds	ds	PROPN
ejpam-7013	421	15	.	.	PROPN
ejpam-7013	421	16	assume	assume	VERB
ejpam-7013	421	17	the	the	DET
ejpam-7013	421	18	crucial	crucial	ADJ
ejpam-7013	421	19	contractive	contractive	ADJ
ejpam-7013	421	20	bound	bound	ADJ
ejpam-7013	421	21	l	l	NOUN
ejpam-7013	421	22	<	<	X
ejpam-7013	421	23	1	1	NUM
ejpam-7013	421	24	.	.	PUNCT
ejpam-7013	422	1	(	(	PUNCT
ejpam-7013	422	2	with	with	ADP
ejpam-7013	422	3	l	l	X
ejpam-7013	422	4	<	<	X
ejpam-7013	422	5	1	1	NUM
ejpam-7013	422	6	we	we	PRON
ejpam-7013	422	7	can	can	AUX
ejpam-7013	422	8	make	make	VERB
ejpam-7013	422	9	the	the	DET
ejpam-7013	422	10	constants	constant	NOUN
ejpam-7013	422	11	required	require	VERB
ejpam-7013	422	12	in	in	ADP
ejpam-7013	422	13	theorem	theorem	NOUN
ejpam-7013	422	14	3	3	NUM
ejpam-7013	422	15	;	;	PUNCT
ejpam-7013	422	16	below	below	SCONJ
ejpam-7013	422	17	we	we	PRON
ejpam-7013	422	18	choose	choose	VERB
ejpam-7013	422	19	λ1	λ1	ADJ
ejpam-7013	422	20	=	=	SYM
ejpam-7013	422	21	λ2	λ2	PROPN
ejpam-7013	422	22	=	=	SYM
ejpam-7013	422	23	0	0	NUM
ejpam-7013	422	24	,	,	PUNCT
ejpam-7013	422	25	λ3	λ3	PROPN
ejpam-7013	422	26	=	=	SYM
ejpam-7013	422	27	l	l	PROPN
ejpam-7013	422	28	,	,	PUNCT
ejpam-7013	422	29	λ4	λ4	PROPN
ejpam-7013	422	30	=	=	NOUN
ejpam-7013	422	31	0	0	NUM
ejpam-7013	422	32	.	.	PUNCT
ejpam-7013	422	33	)	)	PUNCT
ejpam-7013	423	1	we	we	PRON
ejpam-7013	423	2	now	now	ADV
ejpam-7013	423	3	check	check	VERB
ejpam-7013	423	4	the	the	DET
ejpam-7013	423	5	operator	operator	NOUN
ejpam-7013	423	6	t	t	PROPN
ejpam-7013	423	7	(	(	PUNCT
ejpam-7013	423	8	u	u	NOUN
ejpam-7013	423	9	)	)	PUNCT
ejpam-7013	423	10	=	=	SYM
ejpam-7013	423	11	{	{	PUNCT
ejpam-7013	423	12	fu	fu	NOUN
ejpam-7013	423	13	}	}	PUNCT
ejpam-7013	423	14	satisfies	satisfy	VERB
ejpam-7013	423	15	the	the	DET
ejpam-7013	423	16	hypothesis	hypothesis	NOUN
ejpam-7013	423	17	of	of	ADP
ejpam-7013	423	18	theorem	theorem	NOUN
ejpam-7013	423	19	3	3	NUM
ejpam-7013	423	20	with	with	ADP
ejpam-7013	423	21	the	the	DET
ejpam-7013	423	22	choice	choice	NOUN
ejpam-7013	423	23	λ1	λ1	NOUN
ejpam-7013	423	24	=	=	SYM
ejpam-7013	423	25	λ2	λ2	PROPN
ejpam-7013	423	26	=	=	SYM
ejpam-7013	423	27	λ4	λ4	NOUN
ejpam-7013	423	28	=	=	SYM
ejpam-7013	423	29	0	0	NUM
ejpam-7013	423	30	and	and	CCONJ
ejpam-7013	423	31	λ3	λ3	PROPN
ejpam-7013	423	32	=	=	SYM
ejpam-7013	423	33	l	l	NOUN
ejpam-7013	423	34	∈	∈	PROPN
ejpam-7013	424	1	[	[	X
ejpam-7013	424	2	0	0	NUM
ejpam-7013	424	3	,	,	PUNCT
ejpam-7013	424	4	1	1	NUM
ejpam-7013	424	5	)	)	PUNCT
ejpam-7013	424	6	.	.	PUNCT
ejpam-7013	425	1	for	for	ADP
ejpam-7013	425	2	any	any	DET
ejpam-7013	425	3	u	u	NOUN
ejpam-7013	425	4	,	,	PUNCT
ejpam-7013	425	5	v	v	NOUN
ejpam-7013	425	6	∈	∈	NOUN
ejpam-7013	425	7	x	x	X
ejpam-7013	425	8	and	and	CCONJ
ejpam-7013	425	9	each	each	DET
ejpam-7013	425	10	t	t	NOUN
ejpam-7013	425	11	∈	∈	PROPN
ejpam-7013	426	1	[	[	X
ejpam-7013	426	2	0	0	NUM
ejpam-7013	426	3	,	,	PUNCT
ejpam-7013	426	4	1	1	NUM
ejpam-7013	426	5	]	]	PUNCT
ejpam-7013	426	6	,	,	PUNCT
ejpam-7013	426	7	|(fu)(t)−	|(fu)(t)−	PROPN
ejpam-7013	426	8	(	(	PUNCT
ejpam-7013	426	9	fv)(t)|	fv)(t)|	X
ejpam-7013	426	10	≤	≤	NUM
ejpam-7013	426	11	∫	∫	PROPN
ejpam-7013	426	12	t	t	NOUN
ejpam-7013	426	13	0	0	NUM
ejpam-7013	427	1	|k1(t	|k1(t	PROPN
ejpam-7013	427	2	,	,	PUNCT
ejpam-7013	427	3	s	s	X
ejpam-7013	427	4	,	,	PUNCT
ejpam-7013	427	5	u(s))−k1(t	u(s))−k1(t	NUM
ejpam-7013	427	6	,	,	PUNCT
ejpam-7013	427	7	s	s	X
ejpam-7013	427	8	,	,	PUNCT
ejpam-7013	427	9	v(s))|	v(s))|	PROPN
ejpam-7013	427	10	ds+	ds+	PROPN
ejpam-7013	427	11	∫	∫	PROPN
ejpam-7013	428	1	1	1	NUM
ejpam-7013	428	2	0	0	X
ejpam-7013	429	1	|k2(t	|k2(t	PROPN
ejpam-7013	429	2	,	,	PUNCT
ejpam-7013	429	3	s	s	PROPN
ejpam-7013	429	4	,	,	PUNCT
ejpam-7013	429	5	u(s))−k2(t	u(s))−k2(t	NOUN
ejpam-7013	429	6	,	,	PUNCT
ejpam-7013	429	7	s	s	PART
ejpam-7013	429	8	,	,	PUNCT
ejpam-7013	429	9	v(s))|	v(s))|	X
ejpam-7013	429	10	ds	ds	X
ejpam-7013	429	11	≤	≤	NUM
ejpam-7013	429	12	∫	∫	PROPN
ejpam-7013	429	13	t	t	NOUN
ejpam-7013	429	14	0	0	NUM
ejpam-7013	430	1	`	`	PUNCT
ejpam-7013	430	2	1(s	1(s	NUM
ejpam-7013	430	3	)	)	PUNCT
ejpam-7013	430	4	|u(s)−	|u(s)−	PUNCT
ejpam-7013	430	5	v(s)|	v(s)|	X
ejpam-7013	431	1	ds+	ds+	PROPN
ejpam-7013	431	2	∫	∫	PROPN
ejpam-7013	431	3	1	1	NUM
ejpam-7013	431	4	0	0	NUM
ejpam-7013	431	5	`	`	PUNCT
ejpam-7013	431	6	2(s	2(s	NUM
ejpam-7013	431	7	)	)	PUNCT
ejpam-7013	431	8	|u(s)−	|u(s)−	PUNCT
ejpam-7013	432	1	v(s)|	v(s)|	X
ejpam-7013	432	2	ds	ds	ADJ
ejpam-7013	432	3	≤	≤	PROPN
ejpam-7013	432	4	(	(	PUNCT
ejpam-7013	432	5	∫	∫	PROPN
ejpam-7013	432	6	1	1	NUM
ejpam-7013	432	7	0	0	NUM
ejpam-7013	432	8	`	`	PUNCT
ejpam-7013	432	9	1(s	1(s	NUM
ejpam-7013	432	10	)	)	PUNCT
ejpam-7013	432	11	ds+	ds+	PROPN
ejpam-7013	432	12	∫	∫	PROPN
ejpam-7013	432	13	1	1	NUM
ejpam-7013	432	14	0	0	NUM
ejpam-7013	432	15	`	`	PUNCT
ejpam-7013	432	16	2(s	2(s	NUM
ejpam-7013	432	17	)	)	PUNCT
ejpam-7013	432	18	ds	ds	X
ejpam-7013	432	19	)	)	PUNCT
ejpam-7013	433	1	‖u−	‖u−	INTJ
ejpam-7013	433	2	v‖∞	v‖∞	PUNCT
ejpam-7013	434	1	=	=	PUNCT
ejpam-7013	435	1	l	l	NOUN
ejpam-7013	435	2	‖u−	‖u−	ADJ
ejpam-7013	435	3	v‖∞.	v‖∞.	ADJ
ejpam-7013	435	4	taking	take	VERB
ejpam-7013	435	5	the	the	DET
ejpam-7013	435	6	supremum	supremum	NOUN
ejpam-7013	435	7	over	over	ADP
ejpam-7013	435	8	t	t	PROPN
ejpam-7013	435	9	∈	∈	PROPN
ejpam-7013	436	1	[	[	X
ejpam-7013	436	2	0	0	NUM
ejpam-7013	436	3	,	,	PUNCT
ejpam-7013	436	4	1	1	NUM
ejpam-7013	436	5	]	]	PUNCT
ejpam-7013	436	6	yields	yield	VERB
ejpam-7013	436	7	d(fu	d(fu	PROPN
ejpam-7013	436	8	,	,	PUNCT
ejpam-7013	436	9	fv	fv	X
ejpam-7013	436	10	)	)	PUNCT
ejpam-7013	436	11	=	=	NOUN
ejpam-7013	437	1	‖fu−	‖fu−	NOUN
ejpam-7013	437	2	fv‖∞	fv‖∞	ADV
ejpam-7013	437	3	≤	≤	NOUN
ejpam-7013	437	4	ld(u	ld(u	X
ejpam-7013	437	5	,	,	PUNCT
ejpam-7013	437	6	v	v	NOUN
ejpam-7013	437	7	)	)	PUNCT
ejpam-7013	437	8	.	.	PUNCT
ejpam-7013	438	1	because	because	SCONJ
ejpam-7013	438	2	t	t	PROPN
ejpam-7013	438	3	(	(	PUNCT
ejpam-7013	438	4	u	u	NOUN
ejpam-7013	438	5	)	)	PUNCT
ejpam-7013	438	6	=	=	SYM
ejpam-7013	438	7	{	{	PUNCT
ejpam-7013	438	8	fu	fu	NOUN
ejpam-7013	438	9	}	}	PUNCT
ejpam-7013	438	10	and	and	CCONJ
ejpam-7013	438	11	t	t	PROPN
ejpam-7013	438	12	(	(	PUNCT
ejpam-7013	438	13	v	v	NOUN
ejpam-7013	438	14	)	)	PUNCT
ejpam-7013	438	15	=	=	SYM
ejpam-7013	438	16	{	{	PUNCT
ejpam-7013	438	17	fv	fv	NOUN
ejpam-7013	438	18	}	}	PUNCT
ejpam-7013	438	19	,	,	PUNCT
ejpam-7013	438	20	the	the	DET
ejpam-7013	438	21	hausdorff	hausdorff	NOUN
ejpam-7013	438	22	distance	distance	NOUN
ejpam-7013	438	23	reduces	reduce	VERB
ejpam-7013	438	24	to	to	ADP
ejpam-7013	438	25	h	h	PROPN
ejpam-7013	438	26	(	(	PUNCT
ejpam-7013	438	27	t	t	PROPN
ejpam-7013	438	28	(	(	PUNCT
ejpam-7013	438	29	u	u	NOUN
ejpam-7013	438	30	)	)	PUNCT
ejpam-7013	438	31	,	,	PUNCT
ejpam-7013	438	32	t	t	PROPN
ejpam-7013	438	33	(	(	PUNCT
ejpam-7013	438	34	v	v	NOUN
ejpam-7013	438	35	)	)	PUNCT
ejpam-7013	438	36	)	)	PUNCT
ejpam-7013	439	1	=	=	SYM
ejpam-7013	439	2	d(fu	d(fu	PROPN
ejpam-7013	439	3	,	,	PUNCT
ejpam-7013	439	4	fv	fv	X
ejpam-7013	439	5	)	)	PUNCT
ejpam-7013	439	6	.	.	PUNCT
ejpam-7013	440	1	moreover	moreover	ADV
ejpam-7013	440	2	,	,	PUNCT
ejpam-7013	440	3	for	for	ADP
ejpam-7013	440	4	a	a	DET
ejpam-7013	440	5	singleton	singleton	PROPN
ejpam-7013	440	6	multimap	multimap	PROPN
ejpam-7013	440	7	t	t	PROPN
ejpam-7013	440	8	(	(	PUNCT
ejpam-7013	440	9	u	u	NOUN
ejpam-7013	440	10	)	)	PUNCT
ejpam-7013	440	11	=	=	SYM
ejpam-7013	440	12	{	{	PUNCT
ejpam-7013	440	13	fu	fu	NOUN
ejpam-7013	440	14	}	}	PUNCT
ejpam-7013	440	15	we	we	PRON
ejpam-7013	440	16	have	have	VERB
ejpam-7013	440	17	dα(u	dα(u	PROPN
ejpam-7013	440	18	,	,	PUNCT
ejpam-7013	440	19	t	t	PROPN
ejpam-7013	440	20	(	(	PUNCT
ejpam-7013	440	21	u	u	NOUN
ejpam-7013	440	22	)	)	PUNCT
ejpam-7013	440	23	)	)	PUNCT
ejpam-7013	441	1	=	=	SYM
ejpam-7013	441	2	d(u	d(u	PROPN
ejpam-7013	441	3	,	,	PUNCT
ejpam-7013	441	4	fu	fu	NOUN
ejpam-7013	441	5	)	)	PUNCT
ejpam-7013	441	6	,	,	PUNCT
ejpam-7013	441	7	dα(v	dα(v	PROPN
ejpam-7013	441	8	,	,	PUNCT
ejpam-7013	441	9	t	t	PROPN
ejpam-7013	441	10	(	(	PUNCT
ejpam-7013	441	11	v	v	NOUN
ejpam-7013	441	12	)	)	PUNCT
ejpam-7013	441	13	)	)	PUNCT
ejpam-7013	441	14	=	=	SYM
ejpam-7013	442	1	d(v	d(v	PROPN
ejpam-7013	442	2	,	,	PUNCT
ejpam-7013	442	3	fv	fv	NOUN
ejpam-7013	442	4	)	)	PUNCT
ejpam-7013	442	5	,	,	PUNCT
ejpam-7013	442	6	and	and	CCONJ
ejpam-7013	442	7	cross	cross	VERB
ejpam-7013	442	8	distances	distance	NOUN
ejpam-7013	442	9	dα(u	dα(u	PROPN
ejpam-7013	442	10	,	,	PUNCT
ejpam-7013	442	11	t	t	PROPN
ejpam-7013	442	12	(	(	PUNCT
ejpam-7013	442	13	v	v	NOUN
ejpam-7013	442	14	)	)	PUNCT
ejpam-7013	442	15	)	)	PUNCT
ejpam-7013	443	1	=	=	SYM
ejpam-7013	443	2	d(u	d(u	PROPN
ejpam-7013	443	3	,	,	PUNCT
ejpam-7013	443	4	fv	fv	X
ejpam-7013	443	5	)	)	PUNCT
ejpam-7013	443	6	etc	etc	X
ejpam-7013	443	7	.	.	X
ejpam-7013	443	8	with	with	ADP
ejpam-7013	443	9	λ1	λ1	PROPN
ejpam-7013	443	10	=	=	SYM
ejpam-7013	443	11	λ2	λ2	PROPN
ejpam-7013	443	12	=	=	SYM
ejpam-7013	443	13	λ4	λ4	NOUN
ejpam-7013	443	14	=	=	SYM
ejpam-7013	443	15	0	0	NUM
ejpam-7013	443	16	and	and	CCONJ
ejpam-7013	443	17	λ3	λ3	PROPN
ejpam-7013	443	18	=	=	SYM
ejpam-7013	443	19	l	l	NOUN
ejpam-7013	443	20	the	the	DET
ejpam-7013	443	21	inequality	inequality	NOUN
ejpam-7013	443	22	required	require	VERB
ejpam-7013	443	23	by	by	ADP
ejpam-7013	443	24	theorem	theorem	NOUN
ejpam-7013	443	25	3	3	NUM
ejpam-7013	443	26	,	,	PUNCT
ejpam-7013	443	27	h	h	NOUN
ejpam-7013	443	28	(	(	PUNCT
ejpam-7013	443	29	t	t	PROPN
ejpam-7013	443	30	(	(	PUNCT
ejpam-7013	443	31	u	u	NOUN
ejpam-7013	443	32	)	)	PUNCT
ejpam-7013	443	33	,	,	PUNCT
ejpam-7013	443	34	t	t	PROPN
ejpam-7013	443	35	(	(	PUNCT
ejpam-7013	443	36	v	v	NOUN
ejpam-7013	443	37	)	)	PUNCT
ejpam-7013	443	38	)	)	PUNCT
ejpam-7013	444	1	+	+	X
ejpam-7013	444	2	λ4	λ4	ADJ
ejpam-7013	444	3	(	(	PUNCT
ejpam-7013	444	4	dα(u	dα(u	PROPN
ejpam-7013	444	5	,	,	PUNCT
ejpam-7013	444	6	t	t	PROPN
ejpam-7013	444	7	(	(	PUNCT
ejpam-7013	444	8	v))+dα(v	v))+dα(v	PROPN
ejpam-7013	444	9	,	,	PUNCT
ejpam-7013	444	10	t	t	PROPN
ejpam-7013	444	11	(	(	PUNCT
ejpam-7013	444	12	v	v	NOUN
ejpam-7013	444	13	)	)	PUNCT
ejpam-7013	444	14	)	)	PUNCT
ejpam-7013	444	15	)	)	PUNCT
ejpam-7013	444	16	≤	≤	NUM
ejpam-7013	444	17	λ1dα(u	λ1dα(u	PROPN
ejpam-7013	444	18	,	,	PUNCT
ejpam-7013	444	19	t	t	PROPN
ejpam-7013	444	20	(	(	PUNCT
ejpam-7013	444	21	u))+λ2dα(v	u))+λ2dα(v	PROPN
ejpam-7013	444	22	,	,	PUNCT
ejpam-7013	444	23	t	t	PROPN
ejpam-7013	444	24	(	(	PUNCT
ejpam-7013	444	25	u))+λ3d(u	u))+λ3d(u	NOUN
ejpam-7013	444	26	,	,	PUNCT
ejpam-7013	444	27	v	v	NOUN
ejpam-7013	444	28	)	)	PUNCT
ejpam-7013	444	29	,	,	PUNCT
ejpam-7013	444	30	reduces	reduce	VERB
ejpam-7013	444	31	precisely	precisely	ADV
ejpam-7013	444	32	to	to	ADP
ejpam-7013	444	33	d(fu	d(fu	VERB
ejpam-7013	444	34	,	,	PUNCT
ejpam-7013	444	35	fv	fv	NOUN
ejpam-7013	444	36	)	)	PUNCT
ejpam-7013	444	37	≤	≤	NOUN
ejpam-7013	444	38	ld(u	ld(u	X
ejpam-7013	444	39	,	,	PUNCT
ejpam-7013	444	40	v	v	NOUN
ejpam-7013	444	41	)	)	PUNCT
ejpam-7013	444	42	,	,	PUNCT
ejpam-7013	444	43	which	which	PRON
ejpam-7013	444	44	we	we	PRON
ejpam-7013	444	45	have	have	AUX
ejpam-7013	444	46	established	establish	VERB
ejpam-7013	444	47	.	.	PUNCT
ejpam-7013	445	1	the	the	DET
ejpam-7013	445	2	parameter	parameter	NOUN
ejpam-7013	445	3	conditions	condition	NOUN
ejpam-7013	445	4	of	of	ADP
ejpam-7013	445	5	theorem	theorem	ADJ
ejpam-7013	445	6	3	3	NUM
ejpam-7013	445	7	become	become	VERB
ejpam-7013	445	8	(	(	PUNCT
ejpam-7013	445	9	with	with	ADP
ejpam-7013	445	10	s	s	NOUN
ejpam-7013	445	11	=	=	SYM
ejpam-7013	445	12	1	1	NUM
ejpam-7013	445	13	):	):	PUNCT
ejpam-7013	445	14	λ1	λ1	ADJ
ejpam-7013	445	15	+	+	NUM
ejpam-7013	445	16	λ2	λ2	NOUN
ejpam-7013	445	17	+	+	CCONJ
ejpam-7013	445	18	λ3	λ3	PROPN
ejpam-7013	445	19	<	<	X
ejpam-7013	445	20	1	1	NUM
ejpam-7013	445	21	=	=	NOUN
ejpam-7013	445	22	⇒	⇒	NOUN
ejpam-7013	445	23	0	0	PUNCT
ejpam-7013	446	1	+	+	CCONJ
ejpam-7013	446	2	0	0	NUM
ejpam-7013	447	1	+	+	NUM
ejpam-7013	447	2	l	l	NOUN
ejpam-7013	447	3	<	<	X
ejpam-7013	447	4	1	1	NUM
ejpam-7013	447	5	,	,	PUNCT
ejpam-7013	447	6	2λ2	2λ2	NUM
ejpam-7013	448	1	+	+	CCONJ
ejpam-7013	448	2	λ4	λ4	ADJ
ejpam-7013	448	3	<	<	X
ejpam-7013	448	4	1	1	NUM
ejpam-7013	448	5	+	+	NUM
ejpam-7013	448	6	λ1	λ1	ADJ
ejpam-7013	448	7	=	=	NOUN
ejpam-7013	448	8	⇒	⇒	NOUN
ejpam-7013	448	9	0	0	PUNCT
ejpam-7013	448	10	<	<	X
ejpam-7013	448	11	1	1	NUM
ejpam-7013	448	12	,	,	PUNCT
ejpam-7013	448	13	d.	d.	PROPN
ejpam-7013	448	14	gerbeti	gerbeti	PROPN
ejpam-7013	448	15	et	et	PROPN
ejpam-7013	448	16	al	al	PROPN
ejpam-7013	448	17	.	.	PUNCT
ejpam-7013	448	18	/	/	SYM
ejpam-7013	448	19	eur	eur	PROPN
ejpam-7013	448	20	.	.	PUNCT
ejpam-7013	449	1	j.	j.	PROPN
ejpam-7013	449	2	pure	pure	PROPN
ejpam-7013	449	3	appl	appl	PROPN
ejpam-7013	449	4	.	.	PROPN
ejpam-7013	449	5	math	math	PROPN
ejpam-7013	449	6	,	,	PUNCT
ejpam-7013	449	7	18	18	NUM
ejpam-7013	449	8	(	(	PUNCT
ejpam-7013	449	9	4	4	NUM
ejpam-7013	449	10	)	)	PUNCT
ejpam-7013	449	11	(	(	PUNCT
ejpam-7013	449	12	2025	2025	NUM
ejpam-7013	449	13	)	)	PUNCT
ejpam-7013	449	14	,	,	PUNCT
ejpam-7013	449	15	7013	7013	NUM
ejpam-7013	449	16	16	16	NUM
ejpam-7013	449	17	of	of	ADP
ejpam-7013	449	18	17	17	NUM
ejpam-7013	449	19	λ3	λ3	PROPN
ejpam-7013	449	20	<	<	X
ejpam-7013	449	21	1	1	NUM
ejpam-7013	449	22	=	=	NOUN
ejpam-7013	449	23	⇒	⇒	NOUN
ejpam-7013	449	24	l	l	NOUN
ejpam-7013	449	25	<	<	X
ejpam-7013	449	26	1	1	NUM
ejpam-7013	449	27	,	,	PUNCT
ejpam-7013	449	28	all	all	PRON
ejpam-7013	449	29	of	of	ADP
ejpam-7013	449	30	which	which	PRON
ejpam-7013	449	31	hold	hold	VERB
ejpam-7013	449	32	by	by	ADP
ejpam-7013	449	33	assumption	assumption	NOUN
ejpam-7013	449	34	l	l	NOUN
ejpam-7013	449	35	<	<	X
ejpam-7013	449	36	1	1	X
ejpam-7013	449	37	.	.	PUNCT
ejpam-7013	450	1	also	also	ADV
ejpam-7013	450	2	the	the	DET
ejpam-7013	450	3	mild	mild	ADJ
ejpam-7013	450	4	technical	technical	ADJ
ejpam-7013	450	5	condition	condition	NOUN
ejpam-7013	450	6	λ1s	λ1s	X
ejpam-7013	450	7	<	<	X
ejpam-7013	450	8	1	1	NUM
ejpam-7013	450	9	is	be	AUX
ejpam-7013	450	10	satisfied	satisfied	ADJ
ejpam-7013	450	11	since	since	SCONJ
ejpam-7013	450	12	λ1	λ1	PROPN
ejpam-7013	450	13	=	=	SYM
ejpam-7013	450	14	0	0	NUM
ejpam-7013	450	15	.	.	PUNCT
ejpam-7013	451	1	thus	thus	ADV
ejpam-7013	451	2	all	all	DET
ejpam-7013	451	3	hypotheses	hypothesis	NOUN
ejpam-7013	451	4	of	of	ADP
ejpam-7013	451	5	theorem	theorem	NOUN
ejpam-7013	451	6	3	3	NUM
ejpam-7013	451	7	are	be	AUX
ejpam-7013	451	8	satisfied	satisfied	ADJ
ejpam-7013	451	9	for	for	ADP
ejpam-7013	451	10	the	the	DET
ejpam-7013	451	11	multimap	multimap	ADJ
ejpam-7013	451	12	t	t	PROPN
ejpam-7013	451	13	.	.	PUNCT
ejpam-7013	452	1	by	by	ADP
ejpam-7013	452	2	theorem	theorem	NOUN
ejpam-7013	452	3	3	3	NUM
ejpam-7013	452	4	there	there	ADV
ejpam-7013	452	5	exists	exist	VERB
ejpam-7013	452	6	k	k	PROPN
ejpam-7013	452	7	∈	∈	PROPN
ejpam-7013	452	8	x	x	PUNCT
ejpam-7013	452	9	such	such	ADJ
ejpam-7013	452	10	that	that	SCONJ
ejpam-7013	452	11	{	{	PUNCT
ejpam-7013	452	12	k	k	NOUN
ejpam-7013	452	13	}	}	PUNCT
ejpam-7013	452	14	⊆	⊆	NUM
ejpam-7013	452	15	t	t	NOUN
ejpam-7013	452	16	(	(	PUNCT
ejpam-7013	452	17	k	k	NOUN
ejpam-7013	452	18	)	)	PUNCT
ejpam-7013	452	19	.	.	PUNCT
ejpam-7013	453	1	but	but	CCONJ
ejpam-7013	453	2	t	t	PROPN
ejpam-7013	453	3	(	(	PUNCT
ejpam-7013	453	4	k	k	X
ejpam-7013	453	5	)	)	PUNCT
ejpam-7013	453	6	=	=	SYM
ejpam-7013	453	7	{	{	PUNCT
ejpam-7013	453	8	fk	fk	INTJ
ejpam-7013	453	9	}	}	PUNCT
ejpam-7013	453	10	,	,	PUNCT
ejpam-7013	453	11	so	so	ADV
ejpam-7013	453	12	fk	fk	INTJ
ejpam-7013	453	13	=	=	SYM
ejpam-7013	453	14	k	k	X
ejpam-7013	453	15	;	;	PUNCT
ejpam-7013	453	16	equivalently	equivalently	ADV
ejpam-7013	453	17	k	k	PROPN
ejpam-7013	453	18	is	be	AUX
ejpam-7013	453	19	a	a	DET
ejpam-7013	453	20	continuous	continuous	ADJ
ejpam-7013	453	21	solution	solution	NOUN
ejpam-7013	453	22	of	of	ADP
ejpam-7013	453	23	(	(	PUNCT
ejpam-7013	453	24	4	4	NUM
ejpam-7013	453	25	)	)	PUNCT
ejpam-7013	453	26	.	.	PUNCT
ejpam-7013	454	1	we	we	PRON
ejpam-7013	454	2	now	now	ADV
ejpam-7013	454	3	show	show	VERB
ejpam-7013	454	4	uniqueness	uniqueness	NOUN
ejpam-7013	454	5	.	.	PUNCT
ejpam-7013	455	1	since	since	SCONJ
ejpam-7013	455	2	d(fu	d(fu	PROPN
ejpam-7013	455	3	,	,	PUNCT
ejpam-7013	455	4	fv	fv	NOUN
ejpam-7013	455	5	)	)	PUNCT
ejpam-7013	455	6	≤	≤	NOUN
ejpam-7013	455	7	ld(u	ld(u	X
ejpam-7013	455	8	,	,	PUNCT
ejpam-7013	455	9	v	v	NOUN
ejpam-7013	455	10	)	)	PUNCT
ejpam-7013	455	11	(	(	PUNCT
ejpam-7013	455	12	l	l	X
ejpam-7013	455	13	<	<	X
ejpam-7013	455	14	1	1	NUM
ejpam-7013	455	15	)	)	PUNCT
ejpam-7013	455	16	,	,	PUNCT
ejpam-7013	455	17	f	f	PROPN
ejpam-7013	455	18	is	be	AUX
ejpam-7013	455	19	a	a	DET
ejpam-7013	455	20	strict	strict	ADJ
ejpam-7013	455	21	contraction	contraction	NOUN
ejpam-7013	455	22	on	on	ADP
ejpam-7013	455	23	the	the	DET
ejpam-7013	455	24	complete	complete	ADJ
ejpam-7013	455	25	metric	metric	ADJ
ejpam-7013	455	26	space	space	NOUN
ejpam-7013	455	27	(	(	PUNCT
ejpam-7013	455	28	x	x	X
ejpam-7013	455	29	,	,	PUNCT
ejpam-7013	455	30	d	d	NOUN
ejpam-7013	455	31	)	)	PUNCT
ejpam-7013	455	32	.	.	PUNCT
ejpam-7013	456	1	by	by	ADP
ejpam-7013	456	2	banach	banach	NOUN
ejpam-7013	456	3	’s	’s	PART
ejpam-7013	456	4	contraction	contraction	NOUN
ejpam-7013	456	5	principle	principle	VERB
ejpam-7013	456	6	the	the	DET
ejpam-7013	456	7	fp	fp	PROPN
ejpam-7013	456	8	of	of	ADP
ejpam-7013	456	9	f	f	PROPN
ejpam-7013	456	10	is	be	AUX
ejpam-7013	456	11	unique	unique	ADJ
ejpam-7013	456	12	.	.	PUNCT
ejpam-7013	457	1	hence	hence	ADV
ejpam-7013	457	2	the	the	DET
ejpam-7013	457	3	solution	solution	NOUN
ejpam-7013	457	4	k	k	PROPN
ejpam-7013	457	5	of	of	ADP
ejpam-7013	457	6	(	(	PUNCT
ejpam-7013	457	7	4	4	NUM
ejpam-7013	457	8	)	)	PUNCT
ejpam-7013	457	9	is	be	AUX
ejpam-7013	457	10	unique	unique	ADJ
ejpam-7013	457	11	.	.	PUNCT
ejpam-7013	458	1	the	the	DET
ejpam-7013	458	2	proof	proof	NOUN
ejpam-7013	458	3	is	be	AUX
ejpam-7013	458	4	constructive	constructive	ADJ
ejpam-7013	458	5	:	:	PUNCT
ejpam-7013	458	6	pick	pick	VERB
ejpam-7013	458	7	any	any	DET
ejpam-7013	458	8	initial	initial	ADJ
ejpam-7013	458	9	function	function	NOUN
ejpam-7013	458	10	l0	l0	NOUN
ejpam-7013	458	11	∈	∈	PROPN
ejpam-7013	458	12	x	x	PUNCT
ejpam-7013	458	13	and	and	CCONJ
ejpam-7013	458	14	define	define	VERB
ejpam-7013	458	15	the	the	DET
ejpam-7013	458	16	picard	picard	NOUN
ejpam-7013	458	17	iterates	iterate	NOUN
ejpam-7013	458	18	ln+1	ln+1	ADJ
ejpam-7013	458	19	:	:	PUNCT
ejpam-7013	458	20	=	=	SYM
ejpam-7013	458	21	fln	fln	PROPN
ejpam-7013	458	22	,	,	PUNCT
ejpam-7013	458	23	n	n	PRON
ejpam-7013	458	24	≥	≥	NOUN
ejpam-7013	458	25	0	0	NUM
ejpam-7013	458	26	.	.	PUNCT
ejpam-7013	459	1	then	then	ADV
ejpam-7013	459	2	d(ln+1,ln	d(ln+1,ln	PROPN
ejpam-7013	459	3	)	)	PUNCT
ejpam-7013	459	4	≤	≤	NUM
ejpam-7013	459	5	lnd(l1,l0	lnd(l1,l0	PROPN
ejpam-7013	459	6	)	)	PUNCT
ejpam-7013	459	7	and	and	CCONJ
ejpam-7013	459	8	ln	ln	NOUN
ejpam-7013	459	9	→	→	SYM
ejpam-7013	459	10	k	k	X
ejpam-7013	459	11	with	with	ADP
ejpam-7013	459	12	geometric	geometric	ADJ
ejpam-7013	459	13	rate	rate	NOUN
ejpam-7013	459	14	ln	ln	ADJ
ejpam-7013	459	15	.	.	PUNCT
ejpam-7013	460	1	in	in	ADP
ejpam-7013	460	2	particular	particular	ADJ
ejpam-7013	460	3	,	,	PUNCT
ejpam-7013	460	4	for	for	ADP
ejpam-7013	460	5	computational	computational	ADJ
ejpam-7013	460	6	work	work	NOUN
ejpam-7013	460	7	one	one	NOUN
ejpam-7013	460	8	obtains	obtain	VERB
ejpam-7013	460	9	the	the	DET
ejpam-7013	460	10	explicit	explicit	ADJ
ejpam-7013	460	11	bound	bind	VERB
ejpam-7013	460	12	‖ln	‖ln	NUM
ejpam-7013	460	13	−	−	PROPN
ejpam-7013	460	14	k‖∞	k‖∞	SYM
ejpam-7013	460	15	≤	≤	PROPN
ejpam-7013	461	1	ln	ln	ADJ
ejpam-7013	461	2	1−	1−	NUM
ejpam-7013	461	3	l	l	NOUN
ejpam-7013	461	4	‖l1	‖l1	PUNCT
ejpam-7013	462	1	−	−	PROPN
ejpam-7013	462	2	l0‖∞.	l0‖∞.	NOUN
ejpam-7013	462	3	5	5	NUM
ejpam-7013	462	4	.	.	X
ejpam-7013	462	5	conclusion	conclusion	NOUN
ejpam-7013	462	6	in	in	ADP
ejpam-7013	462	7	this	this	DET
ejpam-7013	462	8	work	work	NOUN
ejpam-7013	462	9	,	,	PUNCT
ejpam-7013	462	10	we	we	PRON
ejpam-7013	462	11	have	have	AUX
ejpam-7013	462	12	established	establish	VERB
ejpam-7013	462	13	several	several	ADJ
ejpam-7013	462	14	fp	fp	NOUN
ejpam-7013	462	15	theorems	theorem	NOUN
ejpam-7013	462	16	for	for	ADP
ejpam-7013	462	17	fuzzy	fuzzy	ADJ
ejpam-7013	462	18	mappings	mapping	NOUN
ejpam-7013	462	19	in	in	ADP
ejpam-7013	462	20	the	the	DET
ejpam-7013	462	21	setting	setting	NOUN
ejpam-7013	462	22	of	of	ADP
ejpam-7013	462	23	complete	complete	ADJ
ejpam-7013	462	24	b	b	NOUN
ejpam-7013	462	25	-	-	PUNCT
ejpam-7013	462	26	fmss	fmss	NOUN
ejpam-7013	462	27	.	.	PUNCT
ejpam-7013	463	1	by	by	ADP
ejpam-7013	463	2	formulating	formulate	VERB
ejpam-7013	463	3	new	new	ADJ
ejpam-7013	463	4	contraction	contraction	NOUN
ejpam-7013	463	5	conditions	condition	NOUN
ejpam-7013	463	6	(	(	PUNCT
ejpam-7013	463	7	theorems	theorem	NOUN
ejpam-7013	463	8	1–5	1–5	NUM
ejpam-7013	463	9	)	)	PUNCT
ejpam-7013	463	10	,	,	PUNCT
ejpam-7013	463	11	we	we	PRON
ejpam-7013	463	12	have	have	AUX
ejpam-7013	463	13	extended	extend	VERB
ejpam-7013	463	14	and	and	CCONJ
ejpam-7013	463	15	generalized	generalize	VERB
ejpam-7013	463	16	many	many	ADJ
ejpam-7013	463	17	classical	classical	ADJ
ejpam-7013	463	18	results	result	NOUN
ejpam-7013	463	19	in	in	ADP
ejpam-7013	463	20	the	the	DET
ejpam-7013	463	21	existing	exist	VERB
ejpam-7013	463	22	literature	literature	NOUN
ejpam-7013	463	23	.	.	PUNCT
ejpam-7013	464	1	the	the	DET
ejpam-7013	464	2	approach	approach	NOUN
ejpam-7013	464	3	taken	take	VERB
ejpam-7013	464	4	here	here	ADV
ejpam-7013	464	5	demonstrates	demonstrate	VERB
ejpam-7013	464	6	that	that	SCONJ
ejpam-7013	464	7	the	the	DET
ejpam-7013	464	8	fuzzy	fuzzy	ADJ
ejpam-7013	464	9	environment	environment	NOUN
ejpam-7013	464	10	not	not	PART
ejpam-7013	464	11	only	only	ADV
ejpam-7013	464	12	accommodates	accommodate	VERB
ejpam-7013	464	13	the	the	DET
ejpam-7013	464	14	uncertainty	uncertainty	NOUN
ejpam-7013	464	15	inherent	inherent	ADJ
ejpam-7013	464	16	in	in	ADP
ejpam-7013	464	17	real	real	ADJ
ejpam-7013	464	18	-	-	PUNCT
ejpam-7013	464	19	world	world	NOUN
ejpam-7013	464	20	systems	system	NOUN
ejpam-7013	464	21	but	but	CCONJ
ejpam-7013	464	22	also	also	ADV
ejpam-7013	464	23	provides	provide	VERB
ejpam-7013	464	24	a	a	DET
ejpam-7013	464	25	more	more	ADV
ejpam-7013	464	26	flexible	flexible	ADJ
ejpam-7013	464	27	framework	framework	NOUN
ejpam-7013	464	28	compared	compare	VERB
ejpam-7013	464	29	to	to	ADP
ejpam-7013	464	30	standard	standard	ADJ
ejpam-7013	464	31	metric	metric	ADJ
ejpam-7013	464	32	and	and	CCONJ
ejpam-7013	464	33	b	b	NOUN
ejpam-7013	464	34	-	-	PUNCT
ejpam-7013	464	35	metric	metric	ADJ
ejpam-7013	464	36	spaces	space	NOUN
ejpam-7013	464	37	.	.	PUNCT
ejpam-7013	465	1	the	the	DET
ejpam-7013	465	2	significance	significance	NOUN
ejpam-7013	465	3	of	of	ADP
ejpam-7013	465	4	these	these	DET
ejpam-7013	465	5	results	result	NOUN
ejpam-7013	465	6	is	be	AUX
ejpam-7013	465	7	highlighted	highlight	VERB
ejpam-7013	465	8	by	by	ADP
ejpam-7013	465	9	the	the	DET
ejpam-7013	465	10	application	application	NOUN
ejpam-7013	465	11	to	to	PART
ejpam-7013	465	12	nonlinear	nonlinear	ADJ
ejpam-7013	465	13	fuzzy	fuzzy	ADJ
ejpam-7013	465	14	integral	integral	ADJ
ejpam-7013	465	15	equations	equation	NOUN
ejpam-7013	465	16	,	,	PUNCT
ejpam-7013	465	17	which	which	PRON
ejpam-7013	465	18	illustrates	illustrate	VERB
ejpam-7013	465	19	the	the	DET
ejpam-7013	465	20	utility	utility	NOUN
ejpam-7013	465	21	of	of	ADP
ejpam-7013	465	22	our	our	PRON
ejpam-7013	465	23	theoretical	theoretical	ADJ
ejpam-7013	465	24	findings	finding	NOUN
ejpam-7013	465	25	in	in	ADP
ejpam-7013	465	26	solving	solve	VERB
ejpam-7013	465	27	problems	problem	NOUN
ejpam-7013	465	28	arising	arise	VERB
ejpam-7013	465	29	in	in	ADP
ejpam-7013	465	30	applied	applied	ADJ
ejpam-7013	465	31	mathematics	mathematic	NOUN
ejpam-7013	465	32	.	.	PUNCT
ejpam-7013	466	1	in	in	ADP
ejpam-7013	466	2	particular	particular	ADJ
ejpam-7013	466	3	,	,	PUNCT
ejpam-7013	466	4	the	the	DET
ejpam-7013	466	5	existence	existence	NOUN
ejpam-7013	466	6	of	of	ADP
ejpam-7013	466	7	fuzzy	fuzzy	ADJ
ejpam-7013	466	8	fps	fps	PROPN
ejpam-7013	466	9	guarantees	guarantee	VERB
ejpam-7013	466	10	the	the	DET
ejpam-7013	466	11	existence	existence	NOUN
ejpam-7013	466	12	of	of	ADP
ejpam-7013	466	13	fuzzy	fuzzy	ADJ
ejpam-7013	466	14	solutions	solution	NOUN
ejpam-7013	466	15	to	to	ADP
ejpam-7013	466	16	such	such	ADJ
ejpam-7013	466	17	systems	system	NOUN
ejpam-7013	466	18	,	,	PUNCT
ejpam-7013	466	19	thereby	thereby	ADV
ejpam-7013	466	20	bridging	bridge	VERB
ejpam-7013	466	21	the	the	DET
ejpam-7013	466	22	gap	gap	NOUN
ejpam-7013	466	23	between	between	ADP
ejpam-7013	466	24	abstract	abstract	ADJ
ejpam-7013	466	25	fp	fp	PROPN
ejpam-7013	466	26	theory	theory	NOUN
ejpam-7013	466	27	and	and	CCONJ
ejpam-7013	466	28	concrete	concrete	ADJ
ejpam-7013	466	29	applications	application	NOUN
ejpam-7013	466	30	.	.	PUNCT
ejpam-7013	467	1	future	future	ADJ
ejpam-7013	467	2	research	research	NOUN
ejpam-7013	467	3	may	may	AUX
ejpam-7013	467	4	consider	consider	VERB
ejpam-7013	467	5	extending	extend	VERB
ejpam-7013	467	6	these	these	DET
ejpam-7013	467	7	results	result	NOUN
ejpam-7013	467	8	to	to	ADP
ejpam-7013	467	9	other	other	ADJ
ejpam-7013	467	10	generalized	generalized	ADJ
ejpam-7013	467	11	structures	structure	NOUN
ejpam-7013	467	12	,	,	PUNCT
ejpam-7013	467	13	such	such	ADJ
ejpam-7013	467	14	as	as	ADP
ejpam-7013	467	15	fuzzy	fuzzy	ADJ
ejpam-7013	467	16	g	g	NOUN
ejpam-7013	467	17	-	-	PUNCT
ejpam-7013	467	18	metric	metric	ADJ
ejpam-7013	467	19	spaces	space	NOUN
ejpam-7013	467	20	,	,	PUNCT
ejpam-7013	467	21	probabilistic	probabilistic	ADJ
ejpam-7013	467	22	fmss	fmss	NOUN
ejpam-7013	467	23	,	,	PUNCT
ejpam-7013	467	24	or	or	CCONJ
ejpam-7013	467	25	fuzzy	fuzzy	ADJ
ejpam-7013	467	26	modular	modular	ADJ
ejpam-7013	467	27	spaces	space	NOUN
ejpam-7013	467	28	.	.	PUNCT
ejpam-7013	468	1	another	another	DET
ejpam-7013	468	2	direction	direction	NOUN
ejpam-7013	468	3	involves	involve	VERB
ejpam-7013	468	4	studying	study	VERB
ejpam-7013	468	5	the	the	DET
ejpam-7013	468	6	stability	stability	NOUN
ejpam-7013	468	7	and	and	CCONJ
ejpam-7013	468	8	uniqueness	uniqueness	NOUN
ejpam-7013	468	9	of	of	ADP
ejpam-7013	468	10	fuzzy	fuzzy	ADJ
ejpam-7013	468	11	fps	fps	NOUN
ejpam-7013	468	12	under	under	ADP
ejpam-7013	468	13	different	different	ADJ
ejpam-7013	468	14	contraction	contraction	NOUN
ejpam-7013	468	15	principles	principle	NOUN
ejpam-7013	468	16	and	and	CCONJ
ejpam-7013	468	17	applying	apply	VERB
ejpam-7013	468	18	them	they	PRON
ejpam-7013	468	19	to	to	ADP
ejpam-7013	468	20	dynamic	dynamic	ADJ
ejpam-7013	468	21	systems	system	NOUN
ejpam-7013	468	22	,	,	PUNCT
ejpam-7013	468	23	optimization	optimization	NOUN
ejpam-7013	468	24	problems	problem	NOUN
ejpam-7013	468	25	,	,	PUNCT
ejpam-7013	468	26	and	and	CCONJ
ejpam-7013	468	27	decision	decision	NOUN
ejpam-7013	468	28	-	-	PUNCT
ejpam-7013	468	29	making	make	VERB
ejpam-7013	468	30	models	model	NOUN
ejpam-7013	468	31	under	under	ADP
ejpam-7013	468	32	uncertainty	uncertainty	NOUN
ejpam-7013	468	33	.	.	PUNCT
ejpam-7013	469	1	thus	thus	ADV
ejpam-7013	469	2	,	,	PUNCT
ejpam-7013	469	3	the	the	DET
ejpam-7013	469	4	present	present	ADJ
ejpam-7013	469	5	study	study	NOUN
ejpam-7013	469	6	not	not	PART
ejpam-7013	469	7	only	only	ADV
ejpam-7013	469	8	enriches	enrich	VERB
ejpam-7013	469	9	the	the	DET
ejpam-7013	469	10	theory	theory	NOUN
ejpam-7013	469	11	of	of	ADP
ejpam-7013	469	12	fps	fps	NOUN
ejpam-7013	469	13	in	in	ADP
ejpam-7013	469	14	fuzzy	fuzzy	ADJ
ejpam-7013	469	15	metric	metric	ADJ
ejpam-7013	469	16	frameworks	framework	NOUN
ejpam-7013	469	17	but	but	CCONJ
ejpam-7013	469	18	also	also	ADV
ejpam-7013	469	19	opens	open	VERB
ejpam-7013	469	20	new	new	ADJ
ejpam-7013	469	21	avenues	avenue	NOUN
ejpam-7013	469	22	for	for	ADP
ejpam-7013	469	23	research	research	NOUN
ejpam-7013	469	24	in	in	ADP
ejpam-7013	469	25	both	both	CCONJ
ejpam-7013	469	26	theoretical	theoretical	ADJ
ejpam-7013	469	27	and	and	CCONJ
ejpam-7013	469	28	applied	apply	VERB
ejpam-7013	469	29	domains	domain	NOUN
ejpam-7013	469	30	.	.	PUNCT
ejpam-7013	470	1	d.	d.	PROPN
ejpam-7013	470	2	gerbeti	gerbeti	PROPN
ejpam-7013	470	3	et	et	PROPN
ejpam-7013	470	4	al	al	PROPN
ejpam-7013	470	5	.	.	PUNCT
ejpam-7013	470	6	/	/	SYM
ejpam-7013	470	7	eur	eur	PROPN
ejpam-7013	470	8	.	.	PUNCT
ejpam-7013	471	1	j.	j.	PROPN
ejpam-7013	471	2	pure	pure	PROPN
ejpam-7013	471	3	appl	appl	PROPN
ejpam-7013	471	4	.	.	PROPN
ejpam-7013	471	5	math	math	PROPN
ejpam-7013	471	6	,	,	PUNCT
ejpam-7013	471	7	18	18	NUM
ejpam-7013	471	8	(	(	PUNCT
ejpam-7013	471	9	4	4	NUM
ejpam-7013	471	10	)	)	PUNCT
ejpam-7013	471	11	(	(	PUNCT
ejpam-7013	471	12	2025	2025	NUM
ejpam-7013	471	13	)	)	PUNCT
ejpam-7013	471	14	,	,	PUNCT
ejpam-7013	471	15	7013	7013	NUM
ejpam-7013	471	16	17	17	NUM
ejpam-7013	471	17	of	of	ADP
ejpam-7013	471	18	17	17	NUM
ejpam-7013	471	19	acknowledgements	acknowledgement	NOUN
ejpam-7013	471	20	the	the	DET
ejpam-7013	471	21	authors	author	NOUN
ejpam-7013	471	22	extend	extend	VERB
ejpam-7013	471	23	their	their	PRON
ejpam-7013	471	24	appreciation	appreciation	NOUN
ejpam-7013	471	25	to	to	ADP
ejpam-7013	471	26	the	the	DET
ejpam-7013	471	27	university	university	PROPN
ejpam-7013	471	28	of	of	ADP
ejpam-7013	471	29	shkodra	shkodra	PROPN
ejpam-7013	471	30	“	"	PUNCT
ejpam-7013	471	31	luigj	luigj	NOUN
ejpam-7013	471	32	gurakuqi	gurakuqi	NOUN
ejpam-7013	471	33	”	"	PUNCT
ejpam-7013	471	34	for	for	ADP
ejpam-7013	471	35	funding	fund	VERB
ejpam-7013	471	36	this	this	DET
ejpam-7013	471	37	research	research	NOUN
ejpam-7013	471	38	work	work	NOUN
ejpam-7013	471	39	.	.	PUNCT
ejpam-7013	472	1	references	reference	NOUN
ejpam-7013	472	2	[	[	X
ejpam-7013	472	3	1	1	NUM
ejpam-7013	472	4	]	]	PUNCT
ejpam-7013	472	5	s.	s.	PROPN
ejpam-7013	472	6	czerwik	czerwik	PROPN
ejpam-7013	472	7	.	.	PUNCT
ejpam-7013	473	1	contraction	contraction	NOUN
ejpam-7013	473	2	mappings	mapping	NOUN
ejpam-7013	473	3	in	in	ADP
ejpam-7013	473	4	b	b	NOUN
ejpam-7013	473	5	-	-	ADJ
ejpam-7013	473	6	metric	metric	ADJ
ejpam-7013	473	7	spaces	space	NOUN
ejpam-7013	473	8	.	.	PUNCT
ejpam-7013	474	1	acta	acta	PROPN
ejpam-7013	474	2	math	math	PROPN
ejpam-7013	474	3	.	.	PUNCT
ejpam-7013	475	1	inform	inform	NOUN
ejpam-7013	475	2	.	.	PUNCT
ejpam-7013	476	1	univ	univ	PROPN
ejpam-7013	476	2	.	.	PUNCT
ejpam-7013	476	3	ostrav	ostrav	PROPN
ejpam-7013	476	4	.	.	PUNCT
ejpam-7013	477	1	,	,	PUNCT
ejpam-7013	477	2	1(1):5–11	1(1):5–11	PROPN
ejpam-7013	477	3	,	,	PUNCT
ejpam-7013	477	4	1993	1993	NUM
ejpam-7013	477	5	.	.	PUNCT
ejpam-7013	478	1	[	[	X
ejpam-7013	478	2	2	2	X
ejpam-7013	478	3	]	]	PUNCT
ejpam-7013	478	4	t.	t.	PROPN
ejpam-7013	478	5	suzuki	suzuki	PROPN
ejpam-7013	478	6	.	.	PUNCT
ejpam-7013	479	1	basic	basic	ADJ
ejpam-7013	479	2	inequality	inequality	NOUN
ejpam-7013	479	3	on	on	ADP
ejpam-7013	479	4	a	a	DET
ejpam-7013	479	5	b	b	NOUN
ejpam-7013	479	6	-	-	PUNCT
ejpam-7013	479	7	metric	metric	ADJ
ejpam-7013	479	8	space	space	NOUN
ejpam-7013	479	9	and	and	CCONJ
ejpam-7013	479	10	its	its	PRON
ejpam-7013	479	11	applications	application	NOUN
ejpam-7013	479	12	.	.	PUNCT
ejpam-7013	480	1	j.	j.	PROPN
ejpam-7013	480	2	inequal	inequal	PROPN
ejpam-7013	480	3	.	.	PUNCT
ejpam-7013	481	1	appl	appl	PROPN
ejpam-7013	481	2	.	.	PROPN
ejpam-7013	481	3	,	,	PUNCT
ejpam-7013	481	4	2017(1):256	2017(1):256	NUM
ejpam-7013	481	5	,	,	PUNCT
ejpam-7013	481	6	2017	2017	NUM
ejpam-7013	481	7	.	.	PUNCT
ejpam-7013	482	1	[	[	X
ejpam-7013	482	2	3	3	NUM
ejpam-7013	482	3	]	]	PUNCT
ejpam-7013	482	4	a.	a.	NOUN
ejpam-7013	482	5	george	george	PROPN
ejpam-7013	482	6	and	and	CCONJ
ejpam-7013	482	7	p.	p.	PROPN
ejpam-7013	482	8	veeramani	veeramani	PROPN
ejpam-7013	482	9	.	.	PUNCT
ejpam-7013	483	1	on	on	ADP
ejpam-7013	483	2	some	some	DET
ejpam-7013	483	3	results	result	NOUN
ejpam-7013	483	4	in	in	ADP
ejpam-7013	483	5	fuzzy	fuzzy	ADJ
ejpam-7013	483	6	metric	metric	ADJ
ejpam-7013	483	7	spaces	space	NOUN
ejpam-7013	483	8	.	.	PUNCT
ejpam-7013	484	1	fuzzy	fuzzy	ADJ
ejpam-7013	484	2	sets	set	NOUN
ejpam-7013	484	3	syst	syst	PROPN
ejpam-7013	484	4	.	.	PUNCT
ejpam-7013	484	5	,	,	PUNCT
ejpam-7013	485	1	64(3):395–399	64(3):395–399	PROPN
ejpam-7013	485	2	,	,	PUNCT
ejpam-7013	485	3	1994	1994	NUM
ejpam-7013	485	4	.	.	PUNCT
ejpam-7013	486	1	[	[	X
ejpam-7013	486	2	4	4	X
ejpam-7013	486	3	]	]	X
ejpam-7013	486	4	o.	o.	NOUN
ejpam-7013	486	5	kramosil	kramosil	PROPN
ejpam-7013	486	6	and	and	CCONJ
ejpam-7013	486	7	j.	j.	PROPN
ejpam-7013	486	8	michalek	michalek	PROPN
ejpam-7013	486	9	.	.	PUNCT
ejpam-7013	487	1	fuzzy	fuzzy	ADJ
ejpam-7013	487	2	metric	metric	ADJ
ejpam-7013	487	3	and	and	CCONJ
ejpam-7013	487	4	statistical	statistical	ADJ
ejpam-7013	487	5	metric	metric	ADJ
ejpam-7013	487	6	spaces	space	NOUN
ejpam-7013	487	7	.	.	PUNCT
ejpam-7013	488	1	kybernetika	kybernetika	PROPN
ejpam-7013	488	2	,	,	PUNCT
ejpam-7013	488	3	11(5):336–344	11(5):336–344	PROPN
ejpam-7013	488	4	,	,	PUNCT
ejpam-7013	488	5	1975	1975	NUM
ejpam-7013	488	6	.	.	PUNCT
ejpam-7013	489	1	[	[	X
ejpam-7013	489	2	5	5	NUM
ejpam-7013	489	3	]	]	PUNCT
ejpam-7013	489	4	a.	a.	NOUN
ejpam-7013	489	5	george	george	PROPN
ejpam-7013	489	6	and	and	CCONJ
ejpam-7013	489	7	p.	p.	PROPN
ejpam-7013	489	8	veeramani	veeramani	PROPN
ejpam-7013	489	9	.	.	PUNCT
ejpam-7013	490	1	on	on	ADP
ejpam-7013	490	2	some	some	DET
ejpam-7013	490	3	results	result	NOUN
ejpam-7013	490	4	of	of	ADP
ejpam-7013	490	5	analysis	analysis	NOUN
ejpam-7013	490	6	for	for	ADP
ejpam-7013	490	7	fuzzy	fuzzy	ADJ
ejpam-7013	490	8	metric	metric	ADJ
ejpam-7013	490	9	spaces	space	NOUN
ejpam-7013	490	10	.	.	PUNCT
ejpam-7013	491	1	fuzzy	fuzzy	ADJ
ejpam-7013	491	2	sets	set	NOUN
ejpam-7013	491	3	syst	syst	PROPN
ejpam-7013	491	4	.	.	PUNCT
ejpam-7013	491	5	,	,	PUNCT
ejpam-7013	491	6	90:365–368	90:365–368	PROPN
ejpam-7013	491	7	,	,	PUNCT
ejpam-7013	491	8	1997	1997	NUM
ejpam-7013	491	9	.	.	PUNCT
ejpam-7013	492	1	[	[	X
ejpam-7013	492	2	6	6	NUM
ejpam-7013	492	3	]	]	X
ejpam-7013	492	4	o.	o.	PROPN
ejpam-7013	492	5	kaleva	kaleva	PROPN
ejpam-7013	492	6	and	and	CCONJ
ejpam-7013	492	7	s.	s.	PROPN
ejpam-7013	492	8	seikkala	seikkala	PROPN
ejpam-7013	492	9	.	.	PUNCT
ejpam-7013	493	1	on	on	ADP
ejpam-7013	493	2	fuzzy	fuzzy	ADJ
ejpam-7013	493	3	metric	metric	ADJ
ejpam-7013	493	4	spaces	space	NOUN
ejpam-7013	493	5	.	.	PUNCT
ejpam-7013	494	1	fuzzy	fuzzy	ADJ
ejpam-7013	494	2	sets	set	NOUN
ejpam-7013	494	3	syst	syst	PROPN
ejpam-7013	494	4	.	.	PUNCT
ejpam-7013	494	5	,	,	PUNCT
ejpam-7013	494	6	12:215–229	12:215–229	PROPN
ejpam-7013	494	7	,	,	PUNCT
ejpam-7013	494	8	1984	1984	NUM
ejpam-7013	494	9	.	.	PUNCT
ejpam-7013	495	1	[	[	X
ejpam-7013	495	2	7	7	X
ejpam-7013	495	3	]	]	X
ejpam-7013	495	4	v.	v.	CCONJ
ejpam-7013	495	5	gregori	gregori	PROPN
ejpam-7013	495	6	and	and	CCONJ
ejpam-7013	495	7	a.	a.	NOUN
ejpam-7013	495	8	sapena	sapena	NOUN
ejpam-7013	495	9	.	.	PUNCT
ejpam-7013	496	1	on	on	ADP
ejpam-7013	496	2	fixed	fix	VERB
ejpam-7013	496	3	-	-	PUNCT
ejpam-7013	496	4	point	point	NOUN
ejpam-7013	496	5	theorem	theorem	NOUN
ejpam-7013	496	6	in	in	ADP
ejpam-7013	496	7	fuzzy	fuzzy	ADJ
ejpam-7013	496	8	metric	metric	ADJ
ejpam-7013	496	9	spaces	space	NOUN
ejpam-7013	496	10	.	.	PUNCT
ejpam-7013	497	1	fuzzy	fuzzy	ADJ
ejpam-7013	497	2	sets	set	NOUN
ejpam-7013	497	3	syst	syst	PROPN
ejpam-7013	497	4	.	.	PUNCT
ejpam-7013	497	5	,	,	PUNCT
ejpam-7013	497	6	125:245–252	125:245–252	NUM
ejpam-7013	497	7	,	,	PUNCT
ejpam-7013	497	8	2002	2002	NUM
ejpam-7013	497	9	.	.	PUNCT
ejpam-7013	498	1	[	[	X
ejpam-7013	498	2	8	8	NUM
ejpam-7013	498	3	]	]	X
ejpam-7013	498	4	i.	i.	PROPN
ejpam-7013	498	5	a.	a.	PROPN
ejpam-7013	498	6	bakhtin	bakhtin	PROPN
ejpam-7013	498	7	.	.	PUNCT
ejpam-7013	499	1	the	the	DET
ejpam-7013	499	2	contraction	contraction	NOUN
ejpam-7013	499	3	mapping	map	VERB
ejpam-7013	499	4	principle	principle	NOUN
ejpam-7013	499	5	in	in	ADP
ejpam-7013	499	6	quasimetric	quasimetric	ADJ
ejpam-7013	499	7	spaces	space	NOUN
ejpam-7013	499	8	.	.	PUNCT
ejpam-7013	500	1	functional	functional	ADJ
ejpam-7013	500	2	analysis	analysis	NOUN
ejpam-7013	500	3	(	(	PUNCT
ejpam-7013	500	4	1989	1989	NUM
ejpam-7013	500	5	)	)	PUNCT
ejpam-7013	500	6	,	,	PUNCT
ejpam-7013	500	7	in	in	ADP
ejpam-7013	500	8	russian	russian	NOUN
ejpam-7013	500	9	.	.	PUNCT
ejpam-7013	501	1	[	[	X
ejpam-7013	501	2	9	9	NUM
ejpam-7013	501	3	]	]	PUNCT
ejpam-7013	501	4	s.	s.	PROPN
ejpam-7013	501	5	sedghi	sedghi	PROPN
ejpam-7013	501	6	and	and	CCONJ
ejpam-7013	501	7	n.	n.	PROPN
ejpam-7013	501	8	shobe	shobe	PROPN
ejpam-7013	501	9	.	.	PUNCT
ejpam-7013	502	1	common	common	ADJ
ejpam-7013	502	2	fixed	fix	VERB
ejpam-7013	502	3	point	point	NOUN
ejpam-7013	502	4	theorem	theorem	VERB
ejpam-7013	502	5	in	in	ADP
ejpam-7013	502	6	b	b	NOUN
ejpam-7013	502	7	-	-	PUNCT
ejpam-7013	502	8	fuzzy	fuzzy	ADJ
ejpam-7013	502	9	metric	metric	ADJ
ejpam-7013	502	10	space	space	NOUN
ejpam-7013	502	11	.	.	PUNCT
ejpam-7013	503	1	nonlinear	nonlinear	ADJ
ejpam-7013	503	2	funct	funct	NOUN
ejpam-7013	503	3	.	.	PUNCT
ejpam-7013	504	1	anal	anal	PROPN
ejpam-7013	504	2	.	.	PUNCT
ejpam-7013	504	3	appl	appl	PROPN
ejpam-7013	504	4	.	.	PROPN
ejpam-7013	504	5	,	,	PUNCT
ejpam-7013	504	6	17(3):349–359	17(3):349–359	PROPN
ejpam-7013	504	7	,	,	PUNCT
ejpam-7013	504	8	2012	2012	NUM
ejpam-7013	504	9	.	.	PUNCT
ejpam-7013	505	1	[	[	X
ejpam-7013	505	2	10	10	NUM
ejpam-7013	505	3	]	]	X
ejpam-7013	505	4	s.	s.	PROPN
ejpam-7013	505	5	sedghi	sedghi	PROPN
ejpam-7013	505	6	and	and	CCONJ
ejpam-7013	505	7	n.	n.	PROPN
ejpam-7013	505	8	shobe	shobe	PROPN
ejpam-7013	505	9	.	.	PUNCT
ejpam-7013	506	1	common	common	ADJ
ejpam-7013	506	2	fixed	fix	VERB
ejpam-7013	506	3	point	point	NOUN
ejpam-7013	506	4	theorem	theorem	NOUN
ejpam-7013	506	5	for	for	ADP
ejpam-7013	506	6	r	r	NOUN
ejpam-7013	506	7	-	-	PUNCT
ejpam-7013	506	8	weakly	weakly	ADJ
ejpam-7013	506	9	commuting	commuting	NOUN
ejpam-7013	506	10	maps	map	NOUN
ejpam-7013	506	11	in	in	ADP
ejpam-7013	506	12	b	b	NOUN
ejpam-7013	506	13	-	-	PUNCT
ejpam-7013	506	14	fuzzy	fuzzy	ADJ
ejpam-7013	506	15	metric	metric	ADJ
ejpam-7013	506	16	space	space	NOUN
ejpam-7013	506	17	.	.	PUNCT
ejpam-7013	507	1	nonlinear	nonlinear	ADJ
ejpam-7013	507	2	funct	funct	NOUN
ejpam-7013	507	3	.	.	PUNCT
ejpam-7013	508	1	anal	anal	PROPN
ejpam-7013	508	2	.	.	PUNCT
ejpam-7013	508	3	appl	appl	PROPN
ejpam-7013	508	4	.	.	PROPN
ejpam-7013	508	5	,	,	PUNCT
ejpam-7013	508	6	19(2):285–295	19(2):285–295	NUM
ejpam-7013	508	7	,	,	PUNCT
ejpam-7013	508	8	2014	2014	NUM
ejpam-7013	508	9	.	.	PUNCT
ejpam-7013	509	1	[	[	X
ejpam-7013	509	2	11	11	NUM
ejpam-7013	509	3	]	]	PUNCT
ejpam-7013	509	4	z.	z.	PROPN
ejpam-7013	509	5	hassanzadeh	hassanzadeh	PROPN
ejpam-7013	509	6	and	and	CCONJ
ejpam-7013	509	7	s.	s.	PROPN
ejpam-7013	509	8	sedghi	sedghi	PROPN
ejpam-7013	509	9	.	.	PUNCT
ejpam-7013	510	1	relation	relation	NOUN
ejpam-7013	510	2	between	between	ADP
ejpam-7013	510	3	b	b	NOUN
ejpam-7013	510	4	-	-	ADJ
ejpam-7013	510	5	metric	metric	ADJ
ejpam-7013	510	6	and	and	CCONJ
ejpam-7013	510	7	fuzzy	fuzzy	ADJ
ejpam-7013	510	8	metric	metric	ADJ
ejpam-7013	510	9	spaces	space	NOUN
ejpam-7013	510	10	.	.	PUNCT
ejpam-7013	511	1	math	math	NOUN
ejpam-7013	511	2	.	.	PUNCT
ejpam-7013	512	1	morav	morav	PROPN
ejpam-7013	512	2	.	.	PUNCT
ejpam-7013	512	3	,	,	PUNCT
ejpam-7013	512	4	22(1):55–63	22(1):55–63	NUM
ejpam-7013	512	5	,	,	PUNCT
ejpam-7013	512	6	2018	2018	NUM
ejpam-7013	512	7	.	.	PUNCT
ejpam-7013	513	1	[	[	X
ejpam-7013	513	2	12	12	NUM
ejpam-7013	513	3	]	]	X
ejpam-7013	513	4	g.	g.	PROPN
ejpam-7013	513	5	venkata	venkata	PROPN
ejpam-7013	513	6	,	,	PUNCT
ejpam-7013	513	7	r.	r.	PROPN
ejpam-7013	513	8	babu	babu	PROPN
ejpam-7013	513	9	,	,	PUNCT
ejpam-7013	513	10	and	and	CCONJ
ejpam-7013	513	11	t.	t.	PROPN
ejpam-7013	513	12	d.	d.	PROPN
ejpam-7013	513	13	masissa	masissa	PROPN
ejpam-7013	513	14	.	.	PUNCT
ejpam-7013	514	1	fixed	fix	VERB
ejpam-7013	514	2	points	point	NOUN
ejpam-7013	514	3	in	in	ADP
ejpam-7013	514	4	b	b	ADJ
ejpam-7013	514	5	-	-	ADJ
ejpam-7013	514	6	metric	metric	ADJ
ejpam-7013	514	7	spaces	space	NOUN
ejpam-7013	514	8	via	via	ADP
ejpam-7013	514	9	simulation	simulation	NOUN
ejpam-7013	514	10	function	function	PROPN
ejpam-7013	514	11	.	.	PUNCT
ejpam-7013	515	1	novi	novi	PROPN
ejpam-7013	515	2	sad	sad	PROPN
ejpam-7013	515	3	j.	j.	PROPN
ejpam-7013	515	4	math	math	PROPN
ejpam-7013	515	5	.	.	PUNCT
ejpam-7013	515	6	,	,	PUNCT
ejpam-7013	515	7	47(2):133–147	47(2):133–147	PROPN
ejpam-7013	515	8	,	,	PUNCT
ejpam-7013	515	9	2017	2017	NUM
ejpam-7013	515	10	.	.	PUNCT
ejpam-7013	516	1	[	[	X
ejpam-7013	516	2	13	13	NUM
ejpam-7013	516	3	]	]	PUNCT
ejpam-7013	516	4	t.	t.	NOUN
ejpam-7013	516	5	došenović	došenović	PROPN
ejpam-7013	516	6	,	,	PUNCT
ejpam-7013	516	7	a.	a.	NOUN
ejpam-7013	516	8	javaheri	javaheri	PROPN
ejpam-7013	516	9	,	,	PUNCT
ejpam-7013	516	10	s.	s.	PROPN
ejpam-7013	516	11	sedghi	sedghi	PROPN
ejpam-7013	516	12	,	,	PUNCT
ejpam-7013	516	13	and	and	CCONJ
ejpam-7013	516	14	n.	n.	PROPN
ejpam-7013	516	15	shobe	shobe	PROPN
ejpam-7013	516	16	.	.	PUNCT
ejpam-7013	517	1	coupled	couple	VERB
ejpam-7013	517	2	fixed	fix	VERB
ejpam-7013	517	3	point	point	NOUN
ejpam-7013	517	4	theorem	theorem	VERB
ejpam-7013	517	5	in	in	ADP
ejpam-7013	517	6	b	b	NOUN
ejpam-7013	517	7	-	-	PUNCT
ejpam-7013	517	8	fuzzy	fuzzy	ADJ
ejpam-7013	517	9	metric	metric	ADJ
ejpam-7013	517	10	spaces	space	NOUN
ejpam-7013	517	11	.	.	PUNCT
ejpam-7013	518	1	novi	novi	PROPN
ejpam-7013	518	2	sad	sad	PROPN
ejpam-7013	518	3	j.	j.	PROPN
ejpam-7013	518	4	math	math	PROPN
ejpam-7013	518	5	.	.	PUNCT
ejpam-7013	518	6	,	,	PUNCT
ejpam-7013	518	7	47(1):77–88	47(1):77–88	NUM
ejpam-7013	518	8	,	,	PUNCT
ejpam-7013	518	9	2017	2017	NUM
ejpam-7013	518	10	.	.	PUNCT
ejpam-7013	519	1	[	[	X
ejpam-7013	519	2	14	14	NUM
ejpam-7013	519	3	]	]	PUNCT
ejpam-7013	519	4	t.	t.	NOUN
ejpam-7013	519	5	došenović	došenović	PROPN
ejpam-7013	519	6	,	,	PUNCT
ejpam-7013	519	7	d.	d.	PROPN
ejpam-7013	519	8	rakić	rakić	PROPN
ejpam-7013	519	9	,	,	PUNCT
ejpam-7013	519	10	and	and	CCONJ
ejpam-7013	519	11	m.	m.	NOUN
ejpam-7013	519	12	brdar	brdar	NOUN
ejpam-7013	519	13	.	.	PUNCT
ejpam-7013	520	1	fixed	fix	VERB
ejpam-7013	520	2	point	point	NOUN
ejpam-7013	520	3	theorem	theorem	VERB
ejpam-7013	520	4	in	in	ADP
ejpam-7013	520	5	fuzzy	fuzzy	ADJ
ejpam-7013	520	6	metric	metric	ADJ
ejpam-7013	520	7	spaces	space	NOUN
ejpam-7013	520	8	using	use	VERB
ejpam-7013	520	9	altering	alter	VERB
ejpam-7013	520	10	distance	distance	NOUN
ejpam-7013	520	11	.	.	PUNCT
ejpam-7013	521	1	filomat	filomat	NOUN
ejpam-7013	521	2	,	,	PUNCT
ejpam-7013	521	3	28(7):1517–1524	28(7):1517–1524	NUM
ejpam-7013	521	4	,	,	PUNCT
ejpam-7013	521	5	2014	2014	NUM
ejpam-7013	521	6	.	.	PUNCT
ejpam-7013	522	1	[	[	X
ejpam-7013	522	2	15	15	NUM
ejpam-7013	522	3	]	]	X
ejpam-7013	522	4	s.	s.	PROPN
ejpam-7013	522	5	heilpern	heilpern	PROPN
ejpam-7013	522	6	.	.	PUNCT
ejpam-7013	523	1	fuzzy	fuzzy	ADJ
ejpam-7013	523	2	mappings	mapping	NOUN
ejpam-7013	523	3	and	and	CCONJ
ejpam-7013	523	4	fixed	fix	VERB
ejpam-7013	523	5	point	point	NOUN
ejpam-7013	523	6	theorem	theorem	VERB
ejpam-7013	523	7	.	.	PUNCT
ejpam-7013	524	1	j.	j.	PROPN
ejpam-7013	524	2	math	math	PROPN
ejpam-7013	524	3	.	.	PUNCT
ejpam-7013	525	1	anal	anal	PROPN
ejpam-7013	525	2	.	.	PUNCT
ejpam-7013	526	1	appl	appl	PROPN
ejpam-7013	526	2	.	.	PROPN
ejpam-7013	526	3	,	,	PUNCT
ejpam-7013	526	4	83(2):566–569	83(2):566–569	PROPN
ejpam-7013	526	5	,	,	PUNCT
ejpam-7013	526	6	1981	1981	NUM
ejpam-7013	526	7	.	.	PUNCT
ejpam-7013	527	1	[	[	X
ejpam-7013	527	2	16	16	NUM
ejpam-7013	527	3	]	]	X
ejpam-7013	527	4	u.	u.	PROPN
ejpam-7013	527	5	ishtiaq	ishtiaq	PROPN
ejpam-7013	527	6	,	,	PUNCT
ejpam-7013	527	7	k.	k.	PROPN
ejpam-7013	527	8	javed	javed	PROPN
ejpam-7013	527	9	,	,	PUNCT
ejpam-7013	527	10	f.	f.	PROPN
ejpam-7013	527	11	uddin	uddin	PROPN
ejpam-7013	527	12	,	,	PUNCT
ejpam-7013	527	13	m.	m.	PROPN
ejpam-7013	527	14	d.	d.	PROPN
ejpam-7013	527	15	l.	l.	PROPN
ejpam-7013	527	16	sen	sen	PROPN
ejpam-7013	527	17	,	,	PUNCT
ejpam-7013	527	18	k.	k.	PROPN
ejpam-7013	527	19	ahmed	ahmed	PROPN
ejpam-7013	527	20	,	,	PUNCT
ejpam-7013	527	21	and	and	CCONJ
ejpam-7013	527	22	m.	m.	PROPN
ejpam-7013	527	23	u.	u.	PROPN
ejpam-7013	527	24	ali	ali	PROPN
ejpam-7013	527	25	.	.	PUNCT
ejpam-7013	527	26	fixed	fix	VERB
ejpam-7013	527	27	point	point	NOUN
ejpam-7013	527	28	results	result	NOUN
ejpam-7013	527	29	in	in	ADP
ejpam-7013	527	30	orthogonal	orthogonal	ADJ
ejpam-7013	527	31	neutrosophic	neutrosophic	ADJ
ejpam-7013	527	32	metric	metric	ADJ
ejpam-7013	527	33	spaces	space	NOUN
ejpam-7013	527	34	.	.	PUNCT
ejpam-7013	528	1	complexity	complexity	NOUN
ejpam-7013	528	2	,	,	PUNCT
ejpam-7013	528	3	2021:2809657	2021:2809657	NUM
ejpam-7013	528	4	,	,	PUNCT
ejpam-7013	528	5	2021	2021	NUM
ejpam-7013	528	6	.	.	PUNCT
ejpam-7013	529	1	[	[	X
ejpam-7013	529	2	17	17	NUM
ejpam-7013	529	3	]	]	PUNCT
ejpam-7013	529	4	k.	k.	PROPN
ejpam-7013	529	5	dinesh	dinesh	PROPN
ejpam-7013	529	6	,	,	PUNCT
ejpam-7013	529	7	r.	r.	PROPN
ejpam-7013	529	8	suganya	suganya	PROPN
ejpam-7013	529	9	,	,	PUNCT
ejpam-7013	529	10	v.	v.	PROPN
ejpam-7013	529	11	b.	b.	PROPN
ejpam-7013	529	12	priya	priya	PROPN
ejpam-7013	529	13	,	,	PUNCT
ejpam-7013	529	14	m.	m.	NOUN
ejpam-7013	529	15	suresh	suresh	PROPN
ejpam-7013	529	16	,	,	PUNCT
ejpam-7013	529	17	and	and	CCONJ
ejpam-7013	529	18	a.	a.	NOUN
ejpam-7013	529	19	atkinswestley	atkinswestley	PROPN
ejpam-7013	529	20	.	.	PUNCT
ejpam-7013	530	1	fixed	fix	VERB
ejpam-7013	530	2	point	point	NOUN
ejpam-7013	530	3	theorems	theorem	NOUN
ejpam-7013	530	4	for	for	ADP
ejpam-7013	530	5	multivalued	multivalued	ADJ
ejpam-7013	530	6	mappings	mapping	NOUN
ejpam-7013	530	7	in	in	ADP
ejpam-7013	530	8	neutrosophic	neutrosophic	ADJ
ejpam-7013	530	9	fuzzy	fuzzy	ADJ
ejpam-7013	530	10	metric	metric	ADJ
ejpam-7013	530	11	spaces	space	NOUN
ejpam-7013	530	12	.	.	PUNCT
ejpam-7013	531	1	neutrosophic	neutrosophic	ADJ
ejpam-7013	531	2	sets	set	VERB
ejpam-7013	531	3	syst	syst	PROPN
ejpam-7013	531	4	.	.	PUNCT
ejpam-7013	531	5	,	,	PUNCT
ejpam-7013	531	6	90:1–6	90:1–6	NOUN
ejpam-7013	531	7	,	,	PUNCT
ejpam-7013	531	8	2025	2025	NUM
ejpam-7013	531	9	.	.	PUNCT