id	sid	tid	token	lemma	pos
ejpam-2691	1	1	european	european	PROPN
ejpam-2691	1	2	journal	journal	PROPN
ejpam-2691	1	3	of	of	ADP
ejpam-2691	1	4	pure	pure	ADJ
ejpam-2691	1	5	and	and	CCONJ
ejpam-2691	1	6	applied	apply	VERB
ejpam-2691	1	7	mathematics	mathematic	NOUN
ejpam-2691	1	8	vol	vol	NOUN
ejpam-2691	1	9	.	.	PROPN
ejpam-2691	2	1	10	10	NUM
ejpam-2691	2	2	,	,	PUNCT
ejpam-2691	2	3	no	no	INTJ
ejpam-2691	2	4	.	.	NOUN
ejpam-2691	2	5	2	2	NUM
ejpam-2691	2	6	,	,	PUNCT
ejpam-2691	2	7	2017	2017	NUM
ejpam-2691	2	8	,	,	PUNCT
ejpam-2691	2	9	295	295	NUM
ejpam-2691	2	10	-	-	SYM
ejpam-2691	2	11	311	311	NUM
ejpam-2691	2	12	issn	issn	PROPN
ejpam-2691	2	13	1307	1307	NUM
ejpam-2691	2	14	-	-	SYM
ejpam-2691	2	15	5543	5543	NUM
ejpam-2691	2	16	–	–	PUNCT
ejpam-2691	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2691	2	18	published	publish	VERB
ejpam-2691	2	19	by	by	ADP
ejpam-2691	2	20	new	new	PROPN
ejpam-2691	2	21	york	york	PROPN
ejpam-2691	2	22	business	business	PROPN
ejpam-2691	2	23	global	global	PROPN
ejpam-2691	2	24	n	n	CCONJ
ejpam-2691	2	25	-	-	PUNCT
ejpam-2691	2	26	tupled	tuple	VERB
ejpam-2691	2	27	common	common	ADJ
ejpam-2691	2	28	fixed	fix	VERB
ejpam-2691	2	29	point	point	NOUN
ejpam-2691	2	30	theorems	theorem	NOUN
ejpam-2691	2	31	via	via	ADP
ejpam-2691	2	32	α	α	NOUN
ejpam-2691	2	33	-	-	PUNCT
ejpam-2691	2	34	series	series	NOUN
ejpam-2691	2	35	in	in	ADP
ejpam-2691	2	36	ordered	order	VERB
ejpam-2691	2	37	metric	metric	ADJ
ejpam-2691	2	38	spaces	space	NOUN
ejpam-2691	2	39	manju	manju	PROPN
ejpam-2691	2	40	grewal1	grewal1	PROPN
ejpam-2691	2	41	,	,	PUNCT
ejpam-2691	2	42	ramesh	ramesh	PROPN
ejpam-2691	2	43	kumar	kumar	PROPN
ejpam-2691	2	44	vats2	vats2	PROPN
ejpam-2691	2	45	,	,	PUNCT
ejpam-2691	2	46	amit	amit	PROPN
ejpam-2691	2	47	kumar3,∗	kumar3,∗	PROPN
ejpam-2691	2	48	1,2	1,2	NUM
ejpam-2691	2	49	department	department	NOUN
ejpam-2691	2	50	of	of	ADP
ejpam-2691	2	51	mathematics	mathematics	PROPN
ejpam-2691	2	52	national	national	PROPN
ejpam-2691	2	53	institute	institute	PROPN
ejpam-2691	2	54	of	of	ADP
ejpam-2691	2	55	technology	technology	PROPN
ejpam-2691	2	56	,	,	PUNCT
ejpam-2691	2	57	hamirpur	hamirpur	PROPN
ejpam-2691	2	58	,	,	PUNCT
ejpam-2691	2	59	india	india	PROPN
ejpam-2691	2	60	.	.	PROPN
ejpam-2691	2	61	3	3	NUM
ejpam-2691	2	62	department	department	NOUN
ejpam-2691	2	63	of	of	ADP
ejpam-2691	2	64	mathematics	mathematics	PROPN
ejpam-2691	2	65	&	&	CCONJ
ejpam-2691	2	66	statistic	statistic	PROPN
ejpam-2691	2	67	,	,	PUNCT
ejpam-2691	2	68	banasthali	banasthali	PROPN
ejpam-2691	2	69	university	university	PROPN
ejpam-2691	2	70	,	,	PUNCT
ejpam-2691	2	71	banasthali	banasthali	ADJ
ejpam-2691	2	72	,	,	PUNCT
ejpam-2691	2	73	rajasthan	rajasthan	PROPN
ejpam-2691	2	74	,	,	PUNCT
ejpam-2691	2	75	india	india	PROPN
ejpam-2691	2	76	.	.	PUNCT
ejpam-2691	2	77	abstract	abstract	PROPN
ejpam-2691	2	78	.	.	PUNCT
ejpam-2691	3	1	the	the	DET
ejpam-2691	3	2	aim	aim	NOUN
ejpam-2691	3	3	of	of	ADP
ejpam-2691	3	4	this	this	DET
ejpam-2691	3	5	paper	paper	NOUN
ejpam-2691	3	6	is	be	AUX
ejpam-2691	3	7	to	to	PART
ejpam-2691	3	8	establish	establish	VERB
ejpam-2691	3	9	some	some	DET
ejpam-2691	3	10	results	result	NOUN
ejpam-2691	3	11	about	about	ADP
ejpam-2691	3	12	the	the	DET
ejpam-2691	3	13	existence	existence	NOUN
ejpam-2691	3	14	and	and	CCONJ
ejpam-2691	3	15	uniqueness	uniqueness	NOUN
ejpam-2691	3	16	of	of	ADP
ejpam-2691	3	17	n	n	ADV
ejpam-2691	3	18	-	-	PUNCT
ejpam-2691	3	19	tupled	tuple	VERB
ejpam-2691	3	20	fixed	fix	VERB
ejpam-2691	3	21	point	point	NOUN
ejpam-2691	3	22	that	that	PRON
ejpam-2691	3	23	extend	extend	VERB
ejpam-2691	3	24	the	the	DET
ejpam-2691	3	25	previous	previous	ADJ
ejpam-2691	3	26	results	result	NOUN
ejpam-2691	3	27	,	,	PUNCT
ejpam-2691	3	28	using	use	VERB
ejpam-2691	3	29	the	the	DET
ejpam-2691	3	30	concept	concept	NOUN
ejpam-2691	3	31	of	of	ADP
ejpam-2691	3	32	an	an	DET
ejpam-2691	3	33	α	α	NOUN
ejpam-2691	3	34	-	-	PUNCT
ejpam-2691	3	35	series	series	NOUN
ejpam-2691	3	36	for	for	ADP
ejpam-2691	3	37	sequence	sequence	NOUN
ejpam-2691	3	38	of	of	ADP
ejpam-2691	3	39	mappings	mapping	NOUN
ejpam-2691	3	40	having	have	VERB
ejpam-2691	3	41	mixed	mix	VERB
ejpam-2691	3	42	monotone	monotone	ADJ
ejpam-2691	3	43	property	property	NOUN
ejpam-2691	3	44	in	in	ADP
ejpam-2691	3	45	the	the	DET
ejpam-2691	3	46	framework	framework	NOUN
ejpam-2691	3	47	of	of	ADP
ejpam-2691	3	48	ordered	order	VERB
ejpam-2691	3	49	complete	complete	ADJ
ejpam-2691	3	50	metric	metric	ADJ
ejpam-2691	3	51	spaces	space	NOUN
ejpam-2691	3	52	.	.	PUNCT
ejpam-2691	4	1	the	the	DET
ejpam-2691	4	2	main	main	ADJ
ejpam-2691	4	3	result	result	NOUN
ejpam-2691	4	4	is	be	AUX
ejpam-2691	4	5	supported	support	VERB
ejpam-2691	4	6	with	with	ADP
ejpam-2691	4	7	the	the	DET
ejpam-2691	4	8	aid	aid	NOUN
ejpam-2691	4	9	of	of	ADP
ejpam-2691	4	10	an	an	DET
ejpam-2691	4	11	illustrative	illustrative	ADJ
ejpam-2691	4	12	example	example	NOUN
ejpam-2691	4	13	.	.	PUNCT
ejpam-2691	5	1	2010	2010	NUM
ejpam-2691	5	2	mathematics	mathematic	NOUN
ejpam-2691	5	3	subject	subject	NOUN
ejpam-2691	5	4	classifications	classification	NOUN
ejpam-2691	5	5	:	:	PUNCT
ejpam-2691	5	6	47h10	47h10	NUM
ejpam-2691	5	7	,	,	PUNCT
ejpam-2691	5	8	54h25	54h25	NUM
ejpam-2691	5	9	key	key	ADJ
ejpam-2691	5	10	words	word	NOUN
ejpam-2691	5	11	and	and	CCONJ
ejpam-2691	5	12	phrases	phrase	NOUN
ejpam-2691	5	13	:	:	PUNCT
ejpam-2691	5	14	α	α	X
ejpam-2691	5	15	-	-	PUNCT
ejpam-2691	5	16	series	series	NOUN
ejpam-2691	5	17	,	,	PUNCT
ejpam-2691	5	18	compatible	compatible	ADJ
ejpam-2691	5	19	mappings	mapping	NOUN
ejpam-2691	5	20	,	,	PUNCT
ejpam-2691	5	21	common	common	ADJ
ejpam-2691	5	22	fixed	fix	VERB
ejpam-2691	5	23	point	point	NOUN
ejpam-2691	5	24	,	,	PUNCT
ejpam-2691	5	25	ordered	order	VERB
ejpam-2691	5	26	metric	metric	ADJ
ejpam-2691	5	27	space	space	NOUN
ejpam-2691	5	28	1	1	NUM
ejpam-2691	5	29	.	.	PUNCT
ejpam-2691	5	30	introduction	introduction	NOUN
ejpam-2691	5	31	for	for	ADP
ejpam-2691	5	32	standard	standard	ADJ
ejpam-2691	5	33	terminology	terminology	NOUN
ejpam-2691	5	34	and	and	CCONJ
ejpam-2691	5	35	notations	notation	NOUN
ejpam-2691	5	36	in	in	ADP
ejpam-2691	5	37	fixed	fix	VERB
ejpam-2691	5	38	point	point	NOUN
ejpam-2691	5	39	theory	theory	NOUN
ejpam-2691	5	40	,	,	PUNCT
ejpam-2691	5	41	not	not	PART
ejpam-2691	5	42	specifically	specifically	ADV
ejpam-2691	5	43	mentioned	mention	VERB
ejpam-2691	5	44	or	or	CCONJ
ejpam-2691	5	45	defined	define	VERB
ejpam-2691	5	46	we	we	PRON
ejpam-2691	5	47	refer	refer	VERB
ejpam-2691	5	48	the	the	DET
ejpam-2691	5	49	reader	reader	NOUN
ejpam-2691	5	50	to	to	ADP
ejpam-2691	5	51	the	the	DET
ejpam-2691	5	52	standard	standard	ADJ
ejpam-2691	5	53	textbook	textbook	NOUN
ejpam-2691	5	54	[	[	X
ejpam-2691	5	55	21	21	NUM
ejpam-2691	5	56	]	]	PUNCT
ejpam-2691	5	57	.	.	PUNCT
ejpam-2691	6	1	throughout	throughout	ADP
ejpam-2691	6	2	the	the	DET
ejpam-2691	6	3	paper	paper	NOUN
ejpam-2691	6	4	,	,	PUNCT
ejpam-2691	6	5	for	for	ADP
ejpam-2691	6	6	a	a	DET
ejpam-2691	6	7	nonempty	nonempty	ADJ
ejpam-2691	6	8	set	set	VERB
ejpam-2691	6	9	x	x	NOUN
ejpam-2691	6	10	,	,	PUNCT
ejpam-2691	6	11	∏r	∏r	NOUN
ejpam-2691	6	12	λ=1x	λ=1x	NOUN
ejpam-2691	6	13	λ	λ	PROPN
ejpam-2691	6	14	denote	denote	VERB
ejpam-2691	6	15	the	the	DET
ejpam-2691	6	16	product	product	NOUN
ejpam-2691	6	17	space	space	NOUN
ejpam-2691	6	18	∏r	∏r	NOUN
ejpam-2691	6	19	λ=1x	λ=1x	ADJ
ejpam-2691	6	20	λ	λ	NOUN
ejpam-2691	6	21	=	=	SYM
ejpam-2691	6	22	x×x×x×	x×x×x×	PROPN
ejpam-2691	6	23	·	·	PUNCT
ejpam-2691	6	24	·	·	PUNCT
ejpam-2691	6	25	·	·	PUNCT
ejpam-2691	6	26	×x	×x	X
ejpam-2691	6	27	.	.	PUNCT
ejpam-2691	7	1	the	the	DET
ejpam-2691	7	2	existence	existence	NOUN
ejpam-2691	7	3	of	of	ADP
ejpam-2691	7	4	a	a	DET
ejpam-2691	7	5	fixed	fix	VERB
ejpam-2691	7	6	point	point	NOUN
ejpam-2691	7	7	for	for	ADP
ejpam-2691	7	8	contraction	contraction	NOUN
ejpam-2691	7	9	type	type	NOUN
ejpam-2691	7	10	mappings	mapping	NOUN
ejpam-2691	7	11	in	in	ADP
ejpam-2691	7	12	metric	metric	ADJ
ejpam-2691	7	13	spaces	space	NOUN
ejpam-2691	7	14	along	along	ADP
ejpam-2691	7	15	with	with	ADP
ejpam-2691	7	16	applications	application	NOUN
ejpam-2691	7	17	have	have	AUX
ejpam-2691	7	18	been	be	AUX
ejpam-2691	7	19	taken	take	VERB
ejpam-2691	7	20	a	a	DET
ejpam-2691	7	21	considerable	considerable	ADJ
ejpam-2691	7	22	attention	attention	NOUN
ejpam-2691	7	23	.	.	PUNCT
ejpam-2691	8	1	the	the	DET
ejpam-2691	8	2	banach	banach	NOUN
ejpam-2691	8	3	contraction	contraction	NOUN
ejpam-2691	8	4	principle	principle	NOUN
ejpam-2691	8	5	is	be	AUX
ejpam-2691	8	6	one	one	NUM
ejpam-2691	8	7	of	of	ADP
ejpam-2691	8	8	the	the	DET
ejpam-2691	8	9	earliest	early	ADJ
ejpam-2691	8	10	and	and	CCONJ
ejpam-2691	8	11	the	the	DET
ejpam-2691	8	12	most	most	ADV
ejpam-2691	8	13	important	important	ADJ
ejpam-2691	8	14	results	result	NOUN
ejpam-2691	8	15	in	in	ADP
ejpam-2691	8	16	the	the	DET
ejpam-2691	8	17	area	area	NOUN
ejpam-2691	8	18	of	of	ADP
ejpam-2691	8	19	fixed	fix	VERB
ejpam-2691	8	20	point	point	NOUN
ejpam-2691	8	21	theory	theory	NOUN
ejpam-2691	8	22	.	.	PUNCT
ejpam-2691	9	1	several	several	ADJ
ejpam-2691	9	2	authors	author	NOUN
ejpam-2691	9	3	have	have	AUX
ejpam-2691	9	4	improved	improve	VERB
ejpam-2691	9	5	,	,	PUNCT
ejpam-2691	9	6	generalized	generalize	VERB
ejpam-2691	9	7	,	,	PUNCT
ejpam-2691	9	8	and	and	CCONJ
ejpam-2691	9	9	extended	extend	VERB
ejpam-2691	9	10	this	this	DET
ejpam-2691	9	11	classical	classical	ADJ
ejpam-2691	9	12	result	result	NOUN
ejpam-2691	9	13	in	in	ADP
ejpam-2691	9	14	nonlinear	nonlinear	ADJ
ejpam-2691	9	15	analysis	analysis	NOUN
ejpam-2691	9	16	.	.	PUNCT
ejpam-2691	10	1	the	the	DET
ejpam-2691	10	2	notion	notion	NOUN
ejpam-2691	10	3	of	of	ADP
ejpam-2691	10	4	coupled	couple	VERB
ejpam-2691	10	5	fixed	fix	VERB
ejpam-2691	10	6	point	point	NOUN
ejpam-2691	10	7	is	be	AUX
ejpam-2691	10	8	introduced	introduce	VERB
ejpam-2691	10	9	by	by	ADP
ejpam-2691	10	10	bhaskar	bhaskar	NOUN
ejpam-2691	10	11	and	and	CCONJ
ejpam-2691	10	12	lakshmikantham	lakshmikantham	VERB
ejpam-2691	10	13	[	[	X
ejpam-2691	10	14	7	7	NUM
ejpam-2691	10	15	]	]	PUNCT
ejpam-2691	10	16	.	.	PUNCT
ejpam-2691	11	1	afterwards	afterwards	ADV
ejpam-2691	11	2	lakshmikantham	lakshmikantham	VERB
ejpam-2691	11	3	and	and	CCONJ
ejpam-2691	11	4	ciric	ciric	ADJ
ejpam-2691	11	5	[	[	X
ejpam-2691	11	6	18	18	NUM
ejpam-2691	11	7	]	]	PUNCT
ejpam-2691	11	8	extended	extend	VERB
ejpam-2691	11	9	this	this	DET
ejpam-2691	11	10	notion	notion	NOUN
ejpam-2691	11	11	by	by	ADP
ejpam-2691	11	12	defining	define	VERB
ejpam-2691	11	13	the	the	DET
ejpam-2691	11	14	gmonotone	gmonotone	NOUN
ejpam-2691	11	15	property	property	NOUN
ejpam-2691	11	16	in	in	ADP
ejpam-2691	11	17	partially	partially	ADV
ejpam-2691	11	18	ordered	order	VERB
ejpam-2691	11	19	spaces	space	NOUN
ejpam-2691	11	20	.	.	PUNCT
ejpam-2691	12	1	for	for	ADP
ejpam-2691	12	2	a	a	DET
ejpam-2691	12	3	detailed	detailed	ADJ
ejpam-2691	12	4	study	study	NOUN
ejpam-2691	12	5	on	on	ADP
ejpam-2691	12	6	coupled	couple	VERB
ejpam-2691	12	7	coincidence	coincidence	NOUN
ejpam-2691	12	8	and	and	CCONJ
ejpam-2691	12	9	coupled	couple	VERB
ejpam-2691	12	10	common	common	ADJ
ejpam-2691	12	11	fixed	fix	VERB
ejpam-2691	12	12	point	point	NOUN
ejpam-2691	12	13	results	result	NOUN
ejpam-2691	12	14	,	,	PUNCT
ejpam-2691	12	15	we	we	PRON
ejpam-2691	12	16	refer	refer	VERB
ejpam-2691	12	17	the	the	DET
ejpam-2691	12	18	reader	reader	NOUN
ejpam-2691	12	19	to	to	ADP
ejpam-2691	12	20	[	[	X
ejpam-2691	12	21	5	5	NUM
ejpam-2691	12	22	,	,	PUNCT
ejpam-2691	12	23	11	11	NUM
ejpam-2691	12	24	,	,	PUNCT
ejpam-2691	12	25	12	12	NUM
ejpam-2691	12	26	,	,	PUNCT
ejpam-2691	12	27	13	13	NUM
ejpam-2691	12	28	,	,	PUNCT
ejpam-2691	12	29	18	18	NUM
ejpam-2691	12	30	]	]	PUNCT
ejpam-2691	12	31	.	.	PUNCT
ejpam-2691	13	1	berinde	berinde	NOUN
ejpam-2691	13	2	and	and	CCONJ
ejpam-2691	13	3	borcut	borcut	VERB
ejpam-2691	13	4	[	[	PUNCT
ejpam-2691	13	5	6	6	NUM
ejpam-2691	13	6	]	]	PUNCT
ejpam-2691	13	7	introduced	introduce	VERB
ejpam-2691	13	8	the	the	DET
ejpam-2691	13	9	concept	concept	NOUN
ejpam-2691	13	10	of	of	ADP
ejpam-2691	13	11	tripled	triple	VERB
ejpam-2691	13	12	fixed	fix	VERB
ejpam-2691	13	13	point	point	NOUN
ejpam-2691	13	14	.	.	PUNCT
ejpam-2691	14	1	an	an	DET
ejpam-2691	14	2	enough	enough	ADJ
ejpam-2691	14	3	considerable	considerable	ADJ
ejpam-2691	14	4	work	work	NOUN
ejpam-2691	14	5	have	have	AUX
ejpam-2691	14	6	been	be	AUX
ejpam-2691	14	7	done	do	VERB
ejpam-2691	14	8	in	in	ADP
ejpam-2691	14	9	this	this	DET
ejpam-2691	14	10	area	area	NOUN
ejpam-2691	14	11	by	by	ADP
ejpam-2691	14	12	several	several	ADJ
ejpam-2691	14	13	authors	author	NOUN
ejpam-2691	14	14	(	(	PUNCT
ejpam-2691	14	15	see	see	VERB
ejpam-2691	14	16	,	,	PUNCT
ejpam-2691	14	17	for	for	ADP
ejpam-2691	14	18	instance	instance	NOUN
ejpam-2691	14	19	,	,	PUNCT
ejpam-2691	14	20	[	[	X
ejpam-2691	14	21	1	1	NUM
ejpam-2691	14	22	,	,	PUNCT
ejpam-2691	14	23	2	2	NUM
ejpam-2691	14	24	,	,	PUNCT
ejpam-2691	14	25	3	3	NUM
ejpam-2691	14	26	,	,	PUNCT
ejpam-2691	14	27	4	4	NUM
ejpam-2691	14	28	,	,	PUNCT
ejpam-2691	14	29	16	16	NUM
ejpam-2691	14	30	,	,	PUNCT
ejpam-2691	14	31	17	17	NUM
ejpam-2691	14	32	,	,	PUNCT
ejpam-2691	14	33	23	23	NUM
ejpam-2691	14	34	]	]	PUNCT
ejpam-2691	14	35	)	)	PUNCT
ejpam-2691	14	36	.	.	PUNCT
ejpam-2691	15	1	in	in	ADP
ejpam-2691	15	2	2010	2010	NUM
ejpam-2691	15	3	,	,	PUNCT
ejpam-2691	15	4	samet	samet	NOUN
ejpam-2691	15	5	and	and	CCONJ
ejpam-2691	15	6	vetro	vetro	VERB
ejpam-2691	15	7	[	[	X
ejpam-2691	15	8	20	20	NUM
ejpam-2691	15	9	]	]	PUNCT
ejpam-2691	15	10	extended	extend	VERB
ejpam-2691	15	11	the	the	DET
ejpam-2691	15	12	idea	idea	NOUN
ejpam-2691	15	13	of	of	ADP
ejpam-2691	15	14	coupled	couple	VERB
ejpam-2691	15	15	fixed	fix	VERB
ejpam-2691	15	16	point	point	NOUN
ejpam-2691	15	17	to	to	ADP
ejpam-2691	15	18	higher	high	ADJ
ejpam-2691	15	19	dimensions	dimension	NOUN
ejpam-2691	15	20	by	by	ADP
ejpam-2691	15	21	introducing	introduce	VERB
ejpam-2691	15	22	the	the	DET
ejpam-2691	15	23	notion	notion	NOUN
ejpam-2691	15	24	of	of	ADP
ejpam-2691	15	25	fixed	fix	VERB
ejpam-2691	15	26	point	point	NOUN
ejpam-2691	15	27	of	of	ADP
ejpam-2691	15	28	n	n	CCONJ
ejpam-2691	15	29	-	-	PUNCT
ejpam-2691	15	30	order	order	NOUN
ejpam-2691	15	31	(	(	PUNCT
ejpam-2691	15	32	or	or	CCONJ
ejpam-2691	15	33	n	n	CCONJ
ejpam-2691	15	34	-	-	PUNCT
ejpam-2691	15	35	tupled	tuple	VERB
ejpam-2691	15	36	fixed	fix	VERB
ejpam-2691	15	37	point	point	NOUN
ejpam-2691	15	38	,	,	PUNCT
ejpam-2691	15	39	∗corresponding	∗corresponde	VERB
ejpam-2691	15	40	author	author	NOUN
ejpam-2691	15	41	.	.	PUNCT
ejpam-2691	16	1	email	email	NOUN
ejpam-2691	16	2	addresses	address	NOUN
ejpam-2691	16	3	:	:	PUNCT
ejpam-2691	16	4	amitsu48@gmail.com	amitsu48@gmail.com	X
ejpam-2691	16	5	(	(	PUNCT
ejpam-2691	16	6	amit	amit	PROPN
ejpam-2691	16	7	kumar	kumar	PROPN
ejpam-2691	16	8	)	)	PUNCT
ejpam-2691	16	9	,	,	PUNCT
ejpam-2691	16	10	ramesh−vats@rediffmail.com	ramesh−vats@rediffmail.com	PROPN
ejpam-2691	16	11	(	(	PUNCT
ejpam-2691	16	12	ramesh	ramesh	PROPN
ejpam-2691	16	13	kumar	kumar	PROPN
ejpam-2691	16	14	vats),manjudahiyautku@gmail.com	vats),manjudahiyautku@gmail.com	PROPN
ejpam-2691	16	15	(	(	PUNCT
ejpam-2691	16	16	manju	manju	PROPN
ejpam-2691	16	17	grewal	grewal	PROPN
ejpam-2691	16	18	)	)	PUNCT
ejpam-2691	16	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2691	17	1	295	295	NUM
ejpam-2691	18	1	c	c	X
ejpam-2691	18	2	©	©	PROPN
ejpam-2691	18	3	2017	2017	NUM
ejpam-2691	18	4	ejpam	ejpam	VERB
ejpam-2691	18	5	all	all	DET
ejpam-2691	18	6	rights	right	NOUN
ejpam-2691	18	7	reserved	reserve	VERB
ejpam-2691	18	8	.	.	PUNCT
ejpam-2691	19	1	m.	m.	NOUN
ejpam-2691	19	2	grewal	grewal	PROPN
ejpam-2691	19	3	,	,	PUNCT
ejpam-2691	19	4	r.	r.	PROPN
ejpam-2691	19	5	kumar	kumar	PROPN
ejpam-2691	19	6	,	,	PUNCT
ejpam-2691	19	7	a.	a.	PROPN
ejpam-2691	19	8	kumar	kumar	PROPN
ejpam-2691	19	9	/	/	SYM
ejpam-2691	19	10	eur	eur	PROPN
ejpam-2691	19	11	.	.	PUNCT
ejpam-2691	20	1	j.	j.	PROPN
ejpam-2691	20	2	pure	pure	PROPN
ejpam-2691	20	3	appl	appl	PROPN
ejpam-2691	20	4	.	.	PROPN
ejpam-2691	20	5	math	math	PROPN
ejpam-2691	20	6	,	,	PUNCT
ejpam-2691	20	7	10	10	NUM
ejpam-2691	20	8	(	(	PUNCT
ejpam-2691	20	9	2	2	NUM
ejpam-2691	20	10	)	)	PUNCT
ejpam-2691	20	11	(	(	PUNCT
ejpam-2691	20	12	2017	2017	NUM
ejpam-2691	20	13	)	)	PUNCT
ejpam-2691	20	14	,	,	PUNCT
ejpam-2691	20	15	295	295	NUM
ejpam-2691	20	16	-	-	SYM
ejpam-2691	20	17	311	311	NUM
ejpam-2691	20	18	296	296	NUM
ejpam-2691	20	19	where	where	SCONJ
ejpam-2691	20	20	n	n	AUX
ejpam-2691	20	21	∈	∈	PROPN
ejpam-2691	20	22	n	n	CCONJ
ejpam-2691	20	23	,	,	PUNCT
ejpam-2691	20	24	n	n	PRON
ejpam-2691	20	25	≥	≥	NOUN
ejpam-2691	20	26	2	2	NUM
ejpam-2691	20	27	)	)	PUNCT
ejpam-2691	21	1	and	and	CCONJ
ejpam-2691	21	2	presented	present	VERB
ejpam-2691	21	3	some	some	DET
ejpam-2691	21	4	n	n	ADV
ejpam-2691	21	5	-	-	PUNCT
ejpam-2691	21	6	tupled	tuple	VERB
ejpam-2691	21	7	fixed	fix	VERB
ejpam-2691	21	8	point	point	NOUN
ejpam-2691	21	9	results	result	NOUN
ejpam-2691	21	10	in	in	ADP
ejpam-2691	21	11	complete	complete	ADJ
ejpam-2691	21	12	metric	metric	ADJ
ejpam-2691	21	13	spaces	space	NOUN
ejpam-2691	21	14	.	.	PUNCT
ejpam-2691	22	1	in	in	ADP
ejpam-2691	22	2	2011	2011	NUM
ejpam-2691	22	3	,	,	PUNCT
ejpam-2691	22	4	gordji	gordji	NOUN
ejpam-2691	22	5	and	and	CCONJ
ejpam-2691	22	6	ramezani	ramezani	NOUN
ejpam-2691	22	7	[	[	X
ejpam-2691	22	8	14	14	NUM
ejpam-2691	22	9	]	]	PUNCT
ejpam-2691	22	10	introduced	introduce	VERB
ejpam-2691	22	11	and	and	CCONJ
ejpam-2691	22	12	investigated	investigate	VERB
ejpam-2691	22	13	the	the	DET
ejpam-2691	22	14	concept	concept	NOUN
ejpam-2691	22	15	of	of	ADP
ejpam-2691	22	16	an	an	DET
ejpam-2691	22	17	n	n	ADV
ejpam-2691	22	18	-	-	PUNCT
ejpam-2691	22	19	tupled	tuple	VERB
ejpam-2691	22	20	fixed	fix	VERB
ejpam-2691	22	21	point	point	NOUN
ejpam-2691	22	22	.	.	PUNCT
ejpam-2691	23	1	in	in	ADP
ejpam-2691	23	2	2013	2013	NUM
ejpam-2691	23	3	,	,	PUNCT
ejpam-2691	23	4	imdad	imdad	PROPN
ejpam-2691	23	5	et	et	PROPN
ejpam-2691	23	6	al	al	PROPN
ejpam-2691	23	7	.	.	PUNCT
ejpam-2691	24	1	[	[	X
ejpam-2691	24	2	15	15	NUM
ejpam-2691	24	3	]	]	X
ejpam-2691	24	4	generalized	generalize	VERB
ejpam-2691	24	5	the	the	DET
ejpam-2691	24	6	idea	idea	NOUN
ejpam-2691	24	7	of	of	ADP
ejpam-2691	24	8	n	n	ADV
ejpam-2691	24	9	-	-	PUNCT
ejpam-2691	24	10	tupled	tuple	VERB
ejpam-2691	24	11	fixed	fix	VERB
ejpam-2691	24	12	point	point	NOUN
ejpam-2691	24	13	by	by	ADP
ejpam-2691	24	14	considering	consider	VERB
ejpam-2691	24	15	even	even	ADV
ejpam-2691	24	16	-	-	PUNCT
ejpam-2691	24	17	tupled	tuple	VERB
ejpam-2691	24	18	coincidence	coincidence	NOUN
ejpam-2691	24	19	point	point	NOUN
ejpam-2691	24	20	by	by	ADP
ejpam-2691	24	21	initiating	initiate	VERB
ejpam-2691	24	22	the	the	DET
ejpam-2691	24	23	idea	idea	NOUN
ejpam-2691	24	24	of	of	ADP
ejpam-2691	24	25	mixed	mixed	ADJ
ejpam-2691	24	26	g	g	NOUN
ejpam-2691	24	27	-	-	PUNCT
ejpam-2691	24	28	monotone	monotone	NOUN
ejpam-2691	24	29	property	property	NOUN
ejpam-2691	24	30	on	on	ADP
ejpam-2691	24	31	xn	xn	PROPN
ejpam-2691	24	32	and	and	CCONJ
ejpam-2691	24	33	proved	prove	VERB
ejpam-2691	24	34	an	an	DET
ejpam-2691	24	35	even	even	ADV
ejpam-2691	24	36	-	-	PUNCT
ejpam-2691	24	37	tupled	tuple	VERB
ejpam-2691	24	38	coincidence	coincidence	NOUN
ejpam-2691	24	39	point	point	NOUN
ejpam-2691	24	40	theorem	theorem	VERB
ejpam-2691	24	41	for	for	ADP
ejpam-2691	24	42	nonlinear	nonlinear	ADJ
ejpam-2691	24	43	f	f	PROPN
ejpam-2691	24	44	contraction	contraction	NOUN
ejpam-2691	24	45	mappings	mapping	NOUN
ejpam-2691	24	46	satisfying	satisfy	VERB
ejpam-2691	24	47	mixed	mixed	ADJ
ejpam-2691	24	48	g	g	NOUN
ejpam-2691	24	49	-	-	PUNCT
ejpam-2691	24	50	monotone	monotone	NOUN
ejpam-2691	24	51	property	property	NOUN
ejpam-2691	24	52	.	.	PUNCT
ejpam-2691	25	1	however	however	ADV
ejpam-2691	25	2	,	,	PUNCT
ejpam-2691	25	3	the	the	DET
ejpam-2691	25	4	concept	concept	NOUN
ejpam-2691	25	5	of	of	ADP
ejpam-2691	25	6	n	n	ADV
ejpam-2691	25	7	-	-	PUNCT
ejpam-2691	25	8	tupled	tuple	VERB
ejpam-2691	25	9	fixed	fix	VERB
ejpam-2691	25	10	point	point	NOUN
ejpam-2691	25	11	given	give	VERB
ejpam-2691	25	12	by	by	ADP
ejpam-2691	25	13	imdad	imdad	PROPN
ejpam-2691	25	14	et	et	PROPN
ejpam-2691	25	15	al	al	PROPN
ejpam-2691	25	16	.	.	PUNCT
ejpam-2691	26	1	[	[	X
ejpam-2691	26	2	15	15	NUM
ejpam-2691	26	3	]	]	X
ejpam-2691	26	4	,	,	PUNCT
ejpam-2691	26	5	which	which	PRON
ejpam-2691	26	6	is	be	AUX
ejpam-2691	26	7	quite	quite	ADV
ejpam-2691	26	8	different	different	ADJ
ejpam-2691	26	9	from	from	ADP
ejpam-2691	26	10	the	the	DET
ejpam-2691	26	11	concept	concept	NOUN
ejpam-2691	26	12	of	of	ADP
ejpam-2691	26	13	gordji	gordji	PROPN
ejpam-2691	26	14	and	and	CCONJ
ejpam-2691	26	15	ramezani	ramezani	NOUN
ejpam-2691	27	1	[	[	X
ejpam-2691	27	2	14	14	NUM
ejpam-2691	27	3	]	]	PUNCT
ejpam-2691	27	4	.	.	PUNCT
ejpam-2691	28	1	in	in	ADP
ejpam-2691	28	2	this	this	DET
ejpam-2691	28	3	paper	paper	NOUN
ejpam-2691	28	4	,	,	PUNCT
ejpam-2691	28	5	we	we	PRON
ejpam-2691	28	6	shall	shall	AUX
ejpam-2691	28	7	also	also	ADV
ejpam-2691	28	8	point	point	VERB
ejpam-2691	28	9	out	out	ADP
ejpam-2691	28	10	some	some	DET
ejpam-2691	28	11	useful	useful	ADJ
ejpam-2691	28	12	remarks	remark	NOUN
ejpam-2691	28	13	on	on	ADP
ejpam-2691	28	14	mappings	mapping	NOUN
ejpam-2691	28	15	whenever	whenever	SCONJ
ejpam-2691	28	16	found	find	VERB
ejpam-2691	28	17	prominent	prominent	ADJ
ejpam-2691	28	18	or	or	CCONJ
ejpam-2691	28	19	pertinent	pertinent	ADJ
ejpam-2691	28	20	as	as	SCONJ
ejpam-2691	28	21	we	we	PRON
ejpam-2691	28	22	proceed	proceed	VERB
ejpam-2691	28	23	with	with	ADP
ejpam-2691	28	24	this	this	DET
ejpam-2691	28	25	article	article	NOUN
ejpam-2691	28	26	.	.	PUNCT
ejpam-2691	29	1	our	our	PRON
ejpam-2691	29	2	focus	focus	NOUN
ejpam-2691	29	3	however	however	ADV
ejpam-2691	29	4	will	will	AUX
ejpam-2691	29	5	be	be	AUX
ejpam-2691	29	6	on	on	ADP
ejpam-2691	29	7	results	result	NOUN
ejpam-2691	29	8	that	that	PRON
ejpam-2691	29	9	gives	give	VERB
ejpam-2691	29	10	the	the	DET
ejpam-2691	29	11	guarantee	guarantee	NOUN
ejpam-2691	29	12	about	about	ADP
ejpam-2691	29	13	the	the	DET
ejpam-2691	29	14	existence	existence	NOUN
ejpam-2691	29	15	and	and	CCONJ
ejpam-2691	29	16	uniqueness	uniqueness	NOUN
ejpam-2691	29	17	of	of	ADP
ejpam-2691	29	18	n	n	ADV
ejpam-2691	29	19	-	-	PUNCT
ejpam-2691	29	20	tupled	tuple	VERB
ejpam-2691	29	21	fixed	fix	VERB
ejpam-2691	29	22	point	point	NOUN
ejpam-2691	29	23	that	that	PRON
ejpam-2691	29	24	extend	extend	VERB
ejpam-2691	29	25	the	the	DET
ejpam-2691	29	26	previous	previous	ADJ
ejpam-2691	29	27	results	result	NOUN
ejpam-2691	29	28	in	in	ADP
ejpam-2691	29	29	the	the	DET
ejpam-2691	29	30	framework	framework	NOUN
ejpam-2691	29	31	of	of	ADP
ejpam-2691	29	32	ordered	order	VERB
ejpam-2691	29	33	complete	complete	ADJ
ejpam-2691	29	34	metric	metric	ADJ
ejpam-2691	29	35	spaces	space	NOUN
ejpam-2691	29	36	,	,	PUNCT
ejpam-2691	29	37	using	use	VERB
ejpam-2691	29	38	the	the	DET
ejpam-2691	29	39	concept	concept	NOUN
ejpam-2691	29	40	of	of	ADP
ejpam-2691	29	41	an	an	DET
ejpam-2691	29	42	α	α	NOUN
ejpam-2691	29	43	-	-	PUNCT
ejpam-2691	29	44	series	series	NOUN
ejpam-2691	29	45	for	for	ADP
ejpam-2691	29	46	sequence	sequence	NOUN
ejpam-2691	29	47	of	of	ADP
ejpam-2691	29	48	mappings	mapping	NOUN
ejpam-2691	29	49	having	have	VERB
ejpam-2691	29	50	mixed	mix	VERB
ejpam-2691	29	51	monotone	monotone	ADJ
ejpam-2691	29	52	property	property	NOUN
ejpam-2691	29	53	in	in	ADP
ejpam-2691	29	54	ordered	order	VERB
ejpam-2691	29	55	complete	complete	ADJ
ejpam-2691	29	56	metric	metric	ADJ
ejpam-2691	29	57	spaces	space	NOUN
ejpam-2691	29	58	.	.	PUNCT
ejpam-2691	30	1	in	in	ADP
ejpam-2691	30	2	order	order	NOUN
ejpam-2691	30	3	to	to	PART
ejpam-2691	30	4	do	do	AUX
ejpam-2691	30	5	so	so	ADV
ejpam-2691	30	6	,	,	PUNCT
ejpam-2691	30	7	we	we	PRON
ejpam-2691	30	8	propose	propose	VERB
ejpam-2691	30	9	a	a	DET
ejpam-2691	30	10	notion	notion	NOUN
ejpam-2691	30	11	of	of	ADP
ejpam-2691	30	12	compatible	compatible	ADJ
ejpam-2691	30	13	mapping	mapping	NOUN
ejpam-2691	30	14	for	for	ADP
ejpam-2691	30	15	mapping	map	VERB
ejpam-2691	30	16	f	f	NOUN
ejpam-2691	30	17	:	:	PUNCT
ejpam-2691	30	18	∏r	∏r	X
ejpam-2691	30	19	i=1x	i=1x	NOUN
ejpam-2691	30	20	i	i	X
ejpam-2691	30	21	→	→	SYM
ejpam-2691	30	22	x	x	X
ejpam-2691	30	23	and	and	CCONJ
ejpam-2691	30	24	self	self	NOUN
ejpam-2691	30	25	mapping	mapping	NOUN
ejpam-2691	30	26	g	g	NOUN
ejpam-2691	30	27	akin	akin	ADJ
ejpam-2691	30	28	to	to	ADP
ejpam-2691	30	29	compatible	compatible	ADJ
ejpam-2691	30	30	mapping	mapping	NOUN
ejpam-2691	30	31	as	as	SCONJ
ejpam-2691	30	32	introduced	introduce	VERB
ejpam-2691	30	33	by	by	ADP
ejpam-2691	30	34	choudhary	choudhary	PROPN
ejpam-2691	30	35	and	and	CCONJ
ejpam-2691	30	36	kundu	kundu	NOUN
ejpam-2691	31	1	[	[	X
ejpam-2691	31	2	13	13	NUM
ejpam-2691	31	3	]	]	PUNCT
ejpam-2691	31	4	for	for	ADP
ejpam-2691	31	5	bivariate	bivariate	ADJ
ejpam-2691	31	6	mapping	mapping	NOUN
ejpam-2691	31	7	f	f	NOUN
ejpam-2691	31	8	and	and	CCONJ
ejpam-2691	31	9	self	self	NOUN
ejpam-2691	31	10	mapping	mapping	NOUN
ejpam-2691	31	11	g.	g.	NOUN
ejpam-2691	32	1	the	the	DET
ejpam-2691	32	2	methodology	methodology	NOUN
ejpam-2691	32	3	is	be	AUX
ejpam-2691	32	4	analogous	analogous	ADJ
ejpam-2691	32	5	to	to	ADP
ejpam-2691	32	6	those	those	PRON
ejpam-2691	32	7	used	use	VERB
ejpam-2691	32	8	in	in	ADP
ejpam-2691	32	9	[	[	X
ejpam-2691	32	10	15	15	NUM
ejpam-2691	32	11	]	]	PUNCT
ejpam-2691	32	12	.	.	PUNCT
ejpam-2691	33	1	finally	finally	ADV
ejpam-2691	33	2	,	,	PUNCT
ejpam-2691	33	3	the	the	DET
ejpam-2691	33	4	main	main	ADJ
ejpam-2691	33	5	result	result	NOUN
ejpam-2691	33	6	of	of	ADP
ejpam-2691	33	7	the	the	DET
ejpam-2691	33	8	manuscript	manuscript	NOUN
ejpam-2691	33	9	is	be	AUX
ejpam-2691	33	10	supported	support	VERB
ejpam-2691	33	11	with	with	ADP
ejpam-2691	33	12	the	the	DET
ejpam-2691	33	13	aid	aid	NOUN
ejpam-2691	33	14	of	of	ADP
ejpam-2691	33	15	an	an	DET
ejpam-2691	33	16	illustrative	illustrative	ADJ
ejpam-2691	33	17	example	example	NOUN
ejpam-2691	33	18	.	.	PUNCT
ejpam-2691	34	1	2	2	X
ejpam-2691	34	2	.	.	X
ejpam-2691	34	3	preliminaries	preliminary	NOUN
ejpam-2691	34	4	in	in	ADP
ejpam-2691	34	5	this	this	DET
ejpam-2691	34	6	section	section	NOUN
ejpam-2691	34	7	,	,	PUNCT
ejpam-2691	34	8	we	we	PRON
ejpam-2691	34	9	collect	collect	VERB
ejpam-2691	34	10	some	some	DET
ejpam-2691	34	11	definitions	definition	NOUN
ejpam-2691	34	12	,	,	PUNCT
ejpam-2691	34	13	properties	property	NOUN
ejpam-2691	34	14	and	and	CCONJ
ejpam-2691	34	15	results	result	NOUN
ejpam-2691	34	16	which	which	PRON
ejpam-2691	34	17	will	will	AUX
ejpam-2691	34	18	be	be	AUX
ejpam-2691	34	19	frequently	frequently	ADV
ejpam-2691	34	20	used	use	VERB
ejpam-2691	34	21	in	in	ADP
ejpam-2691	34	22	this	this	DET
ejpam-2691	34	23	paper	paper	NOUN
ejpam-2691	34	24	.	.	PUNCT
ejpam-2691	35	1	as	as	SCONJ
ejpam-2691	35	2	in	in	ADP
ejpam-2691	35	3	[	[	X
ejpam-2691	35	4	19	19	NUM
ejpam-2691	35	5	]	]	X
ejpam-2691	35	6	we	we	PRON
ejpam-2691	35	7	define	define	VERB
ejpam-2691	35	8	a	a	DET
ejpam-2691	35	9	metric	metric	NOUN
ejpam-2691	35	10	on	on	ADP
ejpam-2691	35	11	x	x	X
ejpam-2691	35	12	,	,	PUNCT
ejpam-2691	35	13	a	a	DET
ejpam-2691	35	14	mapping	mapping	NOUN
ejpam-2691	35	15	d	d	NOUN
ejpam-2691	35	16	:	:	PUNCT
ejpam-2691	35	17	x	x	SYM
ejpam-2691	35	18	×	×	NOUN
ejpam-2691	35	19	x	x	INTJ
ejpam-2691	35	20	→	→	PUNCT
ejpam-2691	35	21	r	r	NOUN
ejpam-2691	35	22	such	such	ADJ
ejpam-2691	35	23	that	that	PRON
ejpam-2691	35	24	for	for	ADP
ejpam-2691	35	25	all	all	DET
ejpam-2691	35	26	x	x	NOUN
ejpam-2691	35	27	,	,	PUNCT
ejpam-2691	35	28	y	y	PROPN
ejpam-2691	35	29	,	,	PUNCT
ejpam-2691	35	30	z	z	PROPN
ejpam-2691	35	31	∈	∈	PROPN
ejpam-2691	36	1	x	x	X
ejpam-2691	36	2	:	:	PUNCT
ejpam-2691	36	3	(	(	PUNCT
ejpam-2691	36	4	i	i	NOUN
ejpam-2691	36	5	)	)	PUNCT
ejpam-2691	36	6	d(x	d(x	PROPN
ejpam-2691	36	7	,	,	PUNCT
ejpam-2691	36	8	y	y	NOUN
ejpam-2691	36	9	)	)	PUNCT
ejpam-2691	36	10	=	=	SYM
ejpam-2691	36	11	0	0	PUNCT
ejpam-2691	37	1	if	if	SCONJ
ejpam-2691	37	2	and	and	CCONJ
ejpam-2691	37	3	only	only	ADV
ejpam-2691	37	4	if	if	SCONJ
ejpam-2691	37	5	,	,	PUNCT
ejpam-2691	37	6	x	x	PROPN
ejpam-2691	37	7	=	=	SYM
ejpam-2691	37	8	y	y	PROPN
ejpam-2691	37	9	;	;	PUNCT
ejpam-2691	37	10	(	(	PUNCT
ejpam-2691	37	11	ii	ii	NOUN
ejpam-2691	37	12	)	)	PUNCT
ejpam-2691	37	13	d(x	d(x	PROPN
ejpam-2691	37	14	,	,	PUNCT
ejpam-2691	37	15	y	y	NOUN
ejpam-2691	37	16	)	)	PUNCT
ejpam-2691	37	17	=	=	PUNCT
ejpam-2691	37	18	d(z	d(z	PROPN
ejpam-2691	37	19	,	,	PUNCT
ejpam-2691	37	20	x	x	NOUN
ejpam-2691	37	21	)	)	PUNCT
ejpam-2691	37	22	+	+	CCONJ
ejpam-2691	37	23	d(z	d(z	PROPN
ejpam-2691	37	24	,	,	PUNCT
ejpam-2691	37	25	y	y	NOUN
ejpam-2691	37	26	)	)	PUNCT
ejpam-2691	37	27	.	.	PUNCT
ejpam-2691	38	1	thus	thus	ADV
ejpam-2691	38	2	,	,	PUNCT
ejpam-2691	38	3	in	in	ADP
ejpam-2691	38	4	light	light	NOUN
ejpam-2691	38	5	of	of	ADP
ejpam-2691	38	6	the	the	DET
ejpam-2691	38	7	above	above	ADJ
ejpam-2691	38	8	properties	property	NOUN
ejpam-2691	38	9	one	one	PRON
ejpam-2691	38	10	can	can	AUX
ejpam-2691	38	11	easily	easily	ADV
ejpam-2691	38	12	deduce	deduce	VERB
ejpam-2691	38	13	that	that	SCONJ
ejpam-2691	38	14	d(x	d(x	NOUN
ejpam-2691	38	15	,	,	PUNCT
ejpam-2691	38	16	y	y	PROPN
ejpam-2691	38	17	)	)	PUNCT
ejpam-2691	38	18	≥	≥	NOUN
ejpam-2691	38	19	0	0	NUM
ejpam-2691	38	20	and	and	CCONJ
ejpam-2691	38	21	d(y	d(y	NOUN
ejpam-2691	38	22	,	,	PUNCT
ejpam-2691	38	23	x	x	NOUN
ejpam-2691	38	24	)	)	PUNCT
ejpam-2691	38	25	=	=	SYM
ejpam-2691	38	26	d(x	d(x	PROPN
ejpam-2691	38	27	,	,	PUNCT
ejpam-2691	38	28	y	y	NOUN
ejpam-2691	38	29	)	)	PUNCT
ejpam-2691	38	30	for	for	ADP
ejpam-2691	38	31	all	all	DET
ejpam-2691	38	32	x	x	NOUN
ejpam-2691	38	33	,	,	PUNCT
ejpam-2691	38	34	y	y	PROPN
ejpam-2691	38	35	∈	∈	PROPN
ejpam-2691	38	36	x.	x.	NOUN
ejpam-2691	39	1	the	the	DET
ejpam-2691	39	2	last	last	ADJ
ejpam-2691	39	3	requirement	requirement	NOUN
ejpam-2691	39	4	is	be	AUX
ejpam-2691	39	5	called	call	VERB
ejpam-2691	39	6	the	the	DET
ejpam-2691	39	7	triangle	triangle	NOUN
ejpam-2691	39	8	inequality	inequality	NOUN
ejpam-2691	39	9	.	.	PUNCT
ejpam-2691	40	1	if	if	SCONJ
ejpam-2691	40	2	d	d	PROPN
ejpam-2691	40	3	is	be	AUX
ejpam-2691	40	4	a	a	DET
ejpam-2691	40	5	metric	metric	NOUN
ejpam-2691	40	6	on	on	ADP
ejpam-2691	40	7	x	x	NOUN
ejpam-2691	40	8	,	,	PUNCT
ejpam-2691	40	9	then	then	ADV
ejpam-2691	40	10	we	we	PRON
ejpam-2691	40	11	say	say	VERB
ejpam-2691	40	12	that	that	SCONJ
ejpam-2691	40	13	(	(	PUNCT
ejpam-2691	40	14	x	x	X
ejpam-2691	40	15	,	,	PUNCT
ejpam-2691	40	16	d	d	NOUN
ejpam-2691	40	17	)	)	PUNCT
ejpam-2691	40	18	is	be	AUX
ejpam-2691	40	19	a	a	DET
ejpam-2691	40	20	metric	metric	ADJ
ejpam-2691	40	21	space	space	NOUN
ejpam-2691	40	22	.	.	PUNCT
ejpam-2691	41	1	definition	definition	NOUN
ejpam-2691	41	2	1	1	NUM
ejpam-2691	41	3	.	.	PUNCT
ejpam-2691	42	1	[	[	X
ejpam-2691	42	2	10	10	NUM
ejpam-2691	42	3	]	]	X
ejpam-2691	42	4	a	a	DET
ejpam-2691	42	5	triple	triple	ADJ
ejpam-2691	42	6	(	(	PUNCT
ejpam-2691	42	7	x	x	NOUN
ejpam-2691	42	8	,	,	PUNCT
ejpam-2691	42	9	d	d	PROPN
ejpam-2691	42	10	,	,	PUNCT
ejpam-2691	42	11	�	�	PROPN
ejpam-2691	42	12	)	)	PUNCT
ejpam-2691	42	13	is	be	AUX
ejpam-2691	42	14	called	call	VERB
ejpam-2691	42	15	an	an	DET
ejpam-2691	42	16	ordered	order	VERB
ejpam-2691	42	17	metric	metric	ADJ
ejpam-2691	42	18	space	space	NOUN
ejpam-2691	42	19	if	if	SCONJ
ejpam-2691	42	20	(	(	PUNCT
ejpam-2691	42	21	x	x	NOUN
ejpam-2691	42	22	,	,	PUNCT
ejpam-2691	42	23	d	d	NOUN
ejpam-2691	42	24	)	)	PUNCT
ejpam-2691	42	25	is	be	AUX
ejpam-2691	42	26	a	a	DET
ejpam-2691	42	27	metric	metric	ADJ
ejpam-2691	42	28	space	space	NOUN
ejpam-2691	42	29	and	and	CCONJ
ejpam-2691	42	30	(	(	PUNCT
ejpam-2691	42	31	x	x	NOUN
ejpam-2691	42	32	,	,	PUNCT
ejpam-2691	42	33	�	�	PROPN
ejpam-2691	42	34	)	)	PUNCT
ejpam-2691	42	35	is	be	AUX
ejpam-2691	42	36	a	a	DET
ejpam-2691	42	37	partially	partially	ADV
ejpam-2691	42	38	ordered	order	VERB
ejpam-2691	42	39	set	set	NOUN
ejpam-2691	42	40	.	.	PUNCT
ejpam-2691	43	1	imdad	imdad	PROPN
ejpam-2691	43	2	et	et	PROPN
ejpam-2691	43	3	al	al	PROPN
ejpam-2691	43	4	.	.	PUNCT
ejpam-2691	44	1	[	[	X
ejpam-2691	44	2	15	15	NUM
ejpam-2691	44	3	]	]	PUNCT
ejpam-2691	44	4	introduced	introduce	VERB
ejpam-2691	44	5	the	the	DET
ejpam-2691	44	6	concept	concept	NOUN
ejpam-2691	44	7	of	of	ADP
ejpam-2691	44	8	mixed	mixed	ADJ
ejpam-2691	44	9	monotone	monotone	ADJ
ejpam-2691	44	10	property	property	NOUN
ejpam-2691	44	11	and	and	CCONJ
ejpam-2691	44	12	g	g	NOUN
ejpam-2691	44	13	-	-	PUNCT
ejpam-2691	44	14	mixed	mixed	ADJ
ejpam-2691	44	15	monotone	monotone	ADJ
ejpam-2691	44	16	property	property	NOUN
ejpam-2691	44	17	for	for	ADP
ejpam-2691	44	18	n	n	ADV
ejpam-2691	44	19	-	-	PUNCT
ejpam-2691	44	20	tupled	tuple	VERB
ejpam-2691	44	21	mapping	mapping	NOUN
ejpam-2691	44	22	f	f	NOUN
ejpam-2691	44	23	:	:	PUNCT
ejpam-2691	44	24	∏r	∏r	X
ejpam-2691	44	25	λ=1x	λ=1x	ADJ
ejpam-2691	44	26	λ	λ	X
ejpam-2691	44	27	→	→	SYM
ejpam-2691	44	28	x	x	PROPN
ejpam-2691	44	29	in	in	ADP
ejpam-2691	44	30	the	the	DET
ejpam-2691	44	31	following	following	ADJ
ejpam-2691	44	32	way	way	NOUN
ejpam-2691	44	33	:	:	PUNCT
ejpam-2691	44	34	definition	definition	NOUN
ejpam-2691	44	35	2	2	NUM
ejpam-2691	44	36	.	.	PUNCT
ejpam-2691	45	1	let	let	VERB
ejpam-2691	45	2	(	(	PUNCT
ejpam-2691	45	3	x	x	NOUN
ejpam-2691	45	4	,	,	PUNCT
ejpam-2691	45	5	�	�	PROPN
ejpam-2691	45	6	)	)	PUNCT
ejpam-2691	45	7	be	be	VERB
ejpam-2691	45	8	a	a	DET
ejpam-2691	45	9	partially	partially	ADV
ejpam-2691	45	10	ordered	order	VERB
ejpam-2691	45	11	set	set	NOUN
ejpam-2691	45	12	and	and	CCONJ
ejpam-2691	45	13	f	f	NOUN
ejpam-2691	45	14	:	:	PUNCT
ejpam-2691	45	15	∏r	∏r	X
ejpam-2691	45	16	λ=1x	λ=1x	ADJ
ejpam-2691	45	17	λ	λ	X
ejpam-2691	45	18	→	→	SYM
ejpam-2691	45	19	x	x	PART
ejpam-2691	45	20	be	be	AUX
ejpam-2691	45	21	a	a	DET
ejpam-2691	45	22	mapping	mapping	NOUN
ejpam-2691	45	23	.	.	PUNCT
ejpam-2691	46	1	the	the	DET
ejpam-2691	46	2	mapping	mapping	NOUN
ejpam-2691	46	3	f	f	PROPN
ejpam-2691	46	4	is	be	AUX
ejpam-2691	46	5	said	say	VERB
ejpam-2691	46	6	to	to	PART
ejpam-2691	46	7	have	have	VERB
ejpam-2691	46	8	the	the	DET
ejpam-2691	46	9	mixed	mixed	ADJ
ejpam-2691	46	10	monotone	monotone	ADJ
ejpam-2691	46	11	property	property	NOUN
ejpam-2691	46	12	if	if	SCONJ
ejpam-2691	46	13	f	f	PROPN
ejpam-2691	46	14	is	be	AUX
ejpam-2691	46	15	nondecreasing	nondecrease	VERB
ejpam-2691	46	16	in	in	ADP
ejpam-2691	46	17	its	its	PRON
ejpam-2691	46	18	odd	odd	ADJ
ejpam-2691	46	19	position	position	NOUN
ejpam-2691	46	20	arguments	argument	NOUN
ejpam-2691	46	21	and	and	CCONJ
ejpam-2691	46	22	nonincreasing	nonincrease	VERB
ejpam-2691	46	23	in	in	ADP
ejpam-2691	46	24	its	its	PRON
ejpam-2691	46	25	even	even	ADJ
ejpam-2691	46	26	position	position	NOUN
ejpam-2691	46	27	arguments	argument	NOUN
ejpam-2691	46	28	,	,	PUNCT
ejpam-2691	47	1	that	that	SCONJ
ejpam-2691	47	2	is,	is,	PROPN
ejpam-2691	47	3	∀	∀	X
ejpam-2691	47	4	x11	x11	PROPN
ejpam-2691	47	5	,	,	PUNCT
ejpam-2691	47	6	x12	x12	NUM
ejpam-2691	47	7	∈	∈	PROPN
ejpam-2691	47	8	x	x	NOUN
ejpam-2691	47	9	,	,	PUNCT
ejpam-2691	47	10	x11	x11	PROPN
ejpam-2691	47	11	�	�	PROPN
ejpam-2691	47	12	x12	x12	NUM
ejpam-2691	47	13	⇒	⇒	PROPN
ejpam-2691	47	14	f	f	PROPN
ejpam-2691	47	15	(	(	PUNCT
ejpam-2691	47	16	x11	x11	PROPN
ejpam-2691	47	17	,	,	PUNCT
ejpam-2691	47	18	x	x	PROPN
ejpam-2691	47	19	2	2	NUM
ejpam-2691	47	20	,	,	PUNCT
ejpam-2691	47	21	.	.	PUNCT
ejpam-2691	47	22	.	.	PUNCT
ejpam-2691	48	1	.	.	PUNCT
ejpam-2691	49	1	,	,	PUNCT
ejpam-2691	49	2	xr	xr	PROPN
ejpam-2691	49	3	)	)	PUNCT
ejpam-2691	49	4	�	�	PROPN
ejpam-2691	49	5	f	f	PROPN
ejpam-2691	49	6	(	(	PUNCT
ejpam-2691	49	7	x12	x12	PROPN
ejpam-2691	49	8	,	,	PUNCT
ejpam-2691	49	9	x	x	NOUN
ejpam-2691	49	10	2	2	NUM
ejpam-2691	49	11	,	,	PUNCT
ejpam-2691	49	12	.	.	PUNCT
ejpam-2691	49	13	.	.	PUNCT
ejpam-2691	49	14	.	.	PUNCT
ejpam-2691	49	15	,	,	PUNCT
ejpam-2691	49	16	xr	xr	PROPN
ejpam-2691	49	17	)	)	PUNCT
ejpam-2691	49	18	,	,	PUNCT
ejpam-2691	49	19	∀	∀	X
ejpam-2691	49	20	x21	x21	NUM
ejpam-2691	49	21	,	,	PUNCT
ejpam-2691	49	22	x22	x22	NOUN
ejpam-2691	49	23	∈	∈	PROPN
ejpam-2691	49	24	x	x	PRON
ejpam-2691	49	25	,	,	PUNCT
ejpam-2691	49	26	x21	x21	PROPN
ejpam-2691	49	27	�	�	PROPN
ejpam-2691	49	28	x22	x22	PROPN
ejpam-2691	49	29	⇒	⇒	PROPN
ejpam-2691	49	30	f	f	PROPN
ejpam-2691	50	1	(	(	PUNCT
ejpam-2691	50	2	x1	x1	PROPN
ejpam-2691	50	3	,	,	PUNCT
ejpam-2691	50	4	x21	x21	PROPN
ejpam-2691	50	5	,	,	PUNCT
ejpam-2691	50	6	.	.	PUNCT
ejpam-2691	50	7	.	.	PUNCT
ejpam-2691	51	1	.	.	PUNCT
ejpam-2691	52	1	,	,	PUNCT
ejpam-2691	52	2	x	x	X
ejpam-2691	52	3	r	r	X
ejpam-2691	52	4	)	)	PUNCT
ejpam-2691	52	5	�	�	PROPN
ejpam-2691	52	6	f	f	PROPN
ejpam-2691	52	7	(	(	PUNCT
ejpam-2691	52	8	x1	x1	PROPN
ejpam-2691	52	9	,	,	PUNCT
ejpam-2691	52	10	x22	x22	PROPN
ejpam-2691	52	11	,	,	PUNCT
ejpam-2691	52	12	.	.	PUNCT
ejpam-2691	52	13	.	.	PUNCT
ejpam-2691	52	14	.	.	PUNCT
ejpam-2691	53	1	,	,	PUNCT
ejpam-2691	53	2	x	x	X
ejpam-2691	53	3	r	r	NOUN
ejpam-2691	53	4	)	)	PUNCT
ejpam-2691	53	5	,	,	PUNCT
ejpam-2691	53	6	∀	∀	X
ejpam-2691	53	7	x31	x31	NUM
ejpam-2691	53	8	,	,	PUNCT
ejpam-2691	53	9	x32	x32	PROPN
ejpam-2691	53	10	∈	∈	PROPN
ejpam-2691	53	11	x	x	PRON
ejpam-2691	53	12	,	,	PUNCT
ejpam-2691	53	13	x31	x31	PROPN
ejpam-2691	53	14	�	�	PROPN
ejpam-2691	53	15	x32	x32	PROPN
ejpam-2691	53	16	⇒	⇒	PROPN
ejpam-2691	54	1	f	f	PROPN
ejpam-2691	54	2	(	(	PUNCT
ejpam-2691	54	3	x1	x1	PROPN
ejpam-2691	54	4	,	,	PUNCT
ejpam-2691	54	5	x2	x2	PROPN
ejpam-2691	54	6	,	,	PUNCT
ejpam-2691	54	7	x31	x31	PROPN
ejpam-2691	54	8	,	,	PUNCT
ejpam-2691	54	9	.	.	PUNCT
ejpam-2691	54	10	.	.	PUNCT
ejpam-2691	54	11	.	.	PUNCT
ejpam-2691	55	1	,	,	PUNCT
ejpam-2691	55	2	x	x	X
ejpam-2691	55	3	r	r	X
ejpam-2691	55	4	)	)	PUNCT
ejpam-2691	55	5	�	�	PROPN
ejpam-2691	55	6	f	f	PROPN
ejpam-2691	55	7	(	(	PUNCT
ejpam-2691	55	8	x1	x1	PROPN
ejpam-2691	55	9	,	,	PUNCT
ejpam-2691	55	10	x2	x2	PROPN
ejpam-2691	55	11	,	,	PUNCT
ejpam-2691	55	12	x32	x32	PROPN
ejpam-2691	55	13	,	,	PUNCT
ejpam-2691	55	14	.	.	PUNCT
ejpam-2691	55	15	.	.	PUNCT
ejpam-2691	55	16	.	.	PUNCT
ejpam-2691	56	1	,	,	PUNCT
ejpam-2691	56	2	x	x	X
ejpam-2691	56	3	r	r	NOUN
ejpam-2691	56	4	)	)	PUNCT
ejpam-2691	56	5	,	,	PUNCT
ejpam-2691	56	6	...	...	PUNCT
ejpam-2691	56	7	∀	∀	X
ejpam-2691	56	8	xr1	xr1	NOUN
ejpam-2691	56	9	,	,	PUNCT
ejpam-2691	56	10	xr2	xr2	PROPN
ejpam-2691	56	11	∈	∈	PROPN
ejpam-2691	56	12	x	x	PROPN
ejpam-2691	56	13	,	,	PUNCT
ejpam-2691	56	14	xr1	xr1	PROPN
ejpam-2691	56	15	�	�	PROPN
ejpam-2691	56	16	xr2	xr2	PROPN
ejpam-2691	57	1	⇒	⇒	PROPN
ejpam-2691	57	2	f	f	PROPN
ejpam-2691	57	3	(	(	PUNCT
ejpam-2691	57	4	x1	x1	PROPN
ejpam-2691	57	5	,	,	PUNCT
ejpam-2691	57	6	x2	x2	PROPN
ejpam-2691	57	7	,	,	PUNCT
ejpam-2691	57	8	x3	x3	ADJ
ejpam-2691	57	9	,	,	PUNCT
ejpam-2691	57	10	.	.	PUNCT
ejpam-2691	57	11	.	.	PUNCT
ejpam-2691	57	12	.	.	PUNCT
ejpam-2691	58	1	,	,	PUNCT
ejpam-2691	58	2	xr1	xr1	PROPN
ejpam-2691	58	3	)	)	PUNCT
ejpam-2691	58	4	�	�	PROPN
ejpam-2691	58	5	f	f	PROPN
ejpam-2691	58	6	(	(	PUNCT
ejpam-2691	58	7	x1	x1	PROPN
ejpam-2691	58	8	,	,	PUNCT
ejpam-2691	58	9	x2	x2	PROPN
ejpam-2691	58	10	,	,	PUNCT
ejpam-2691	58	11	x3	x3	ADJ
ejpam-2691	58	12	,	,	PUNCT
ejpam-2691	58	13	.	.	PUNCT
ejpam-2691	58	14	.	.	PUNCT
ejpam-2691	58	15	.	.	PUNCT
ejpam-2691	59	1	,	,	PUNCT
ejpam-2691	59	2	xr2	xr2	PROPN
ejpam-2691	59	3	)	)	PUNCT
ejpam-2691	59	4	.	.	PUNCT
ejpam-2691	60	1	m.	m.	PROPN
ejpam-2691	60	2	grewal	grewal	PROPN
ejpam-2691	60	3	,	,	PUNCT
ejpam-2691	60	4	r.	r.	PROPN
ejpam-2691	60	5	kumar	kumar	PROPN
ejpam-2691	60	6	,	,	PUNCT
ejpam-2691	60	7	a.	a.	PROPN
ejpam-2691	60	8	kumar	kumar	PROPN
ejpam-2691	60	9	/	/	SYM
ejpam-2691	60	10	eur	eur	PROPN
ejpam-2691	60	11	.	.	PUNCT
ejpam-2691	61	1	j.	j.	PROPN
ejpam-2691	61	2	pure	pure	PROPN
ejpam-2691	61	3	appl	appl	PROPN
ejpam-2691	61	4	.	.	PROPN
ejpam-2691	61	5	math	math	PROPN
ejpam-2691	61	6	,	,	PUNCT
ejpam-2691	61	7	10	10	NUM
ejpam-2691	61	8	(	(	PUNCT
ejpam-2691	61	9	2	2	NUM
ejpam-2691	61	10	)	)	PUNCT
ejpam-2691	61	11	(	(	PUNCT
ejpam-2691	61	12	2017	2017	NUM
ejpam-2691	61	13	)	)	PUNCT
ejpam-2691	61	14	,	,	PUNCT
ejpam-2691	61	15	295	295	NUM
ejpam-2691	61	16	-	-	SYM
ejpam-2691	61	17	311	311	NUM
ejpam-2691	61	18	297	297	NUM
ejpam-2691	61	19	definition	definition	NOUN
ejpam-2691	61	20	3	3	NUM
ejpam-2691	61	21	.	.	PUNCT
ejpam-2691	62	1	[	[	X
ejpam-2691	62	2	15	15	NUM
ejpam-2691	62	3	]	]	X
ejpam-2691	62	4	let	let	VERB
ejpam-2691	62	5	(	(	PUNCT
ejpam-2691	62	6	x	x	NOUN
ejpam-2691	62	7	,	,	PUNCT
ejpam-2691	62	8	�	�	PROPN
ejpam-2691	62	9	)	)	PUNCT
ejpam-2691	62	10	be	be	VERB
ejpam-2691	62	11	a	a	DET
ejpam-2691	62	12	partially	partially	ADV
ejpam-2691	62	13	ordered	order	VERB
ejpam-2691	62	14	set	set	NOUN
ejpam-2691	62	15	.	.	PUNCT
ejpam-2691	63	1	let	let	VERB
ejpam-2691	63	2	f	f	NOUN
ejpam-2691	63	3	:	:	PUNCT
ejpam-2691	63	4	∏r	∏r	X
ejpam-2691	63	5	λ=1x	λ=1x	ADJ
ejpam-2691	63	6	λ	λ	X
ejpam-2691	63	7	→	→	SYM
ejpam-2691	63	8	x	x	X
ejpam-2691	63	9	and	and	CCONJ
ejpam-2691	63	10	g	g	NOUN
ejpam-2691	63	11	:	:	PUNCT
ejpam-2691	63	12	x	x	SYM
ejpam-2691	63	13	→	→	PUNCT
ejpam-2691	63	14	x	x	PUNCT
ejpam-2691	63	15	be	be	AUX
ejpam-2691	63	16	two	two	NUM
ejpam-2691	63	17	mappings	mapping	NOUN
ejpam-2691	63	18	.	.	PUNCT
ejpam-2691	64	1	then	then	ADV
ejpam-2691	64	2	the	the	DET
ejpam-2691	64	3	mapping	mapping	NOUN
ejpam-2691	64	4	f	f	NOUN
ejpam-2691	64	5	is	be	AUX
ejpam-2691	64	6	said	say	VERB
ejpam-2691	64	7	to	to	PART
ejpam-2691	64	8	have	have	VERB
ejpam-2691	64	9	the	the	DET
ejpam-2691	64	10	mixed	mixed	ADJ
ejpam-2691	64	11	g	g	NOUN
ejpam-2691	64	12	-	-	PUNCT
ejpam-2691	64	13	monotone	monotone	NOUN
ejpam-2691	64	14	property	property	NOUN
ejpam-2691	64	15	if	if	SCONJ
ejpam-2691	64	16	f	f	PROPN
ejpam-2691	64	17	is	be	AUX
ejpam-2691	64	18	g	g	NOUN
ejpam-2691	64	19	-	-	PUNCT
ejpam-2691	64	20	nondecreasing	nondecrease	VERB
ejpam-2691	64	21	in	in	ADP
ejpam-2691	64	22	its	its	PRON
ejpam-2691	64	23	odd	odd	ADJ
ejpam-2691	64	24	position	position	NOUN
ejpam-2691	64	25	arguments	argument	NOUN
ejpam-2691	64	26	and	and	CCONJ
ejpam-2691	64	27	g	g	NOUN
ejpam-2691	64	28	-	-	PUNCT
ejpam-2691	64	29	nonincreasing	nonincreasing	NOUN
ejpam-2691	64	30	in	in	ADP
ejpam-2691	64	31	its	its	PRON
ejpam-2691	64	32	even	even	ADJ
ejpam-2691	64	33	position	position	NOUN
ejpam-2691	64	34	arguments	argument	NOUN
ejpam-2691	64	35	,	,	PUNCT
ejpam-2691	64	36	that	that	SCONJ
ejpam-2691	64	37	is	is	PROPN
ejpam-2691	64	38	∀	∀	X
ejpam-2691	64	39	x11	x11	NOUN
ejpam-2691	64	40	,	,	PUNCT
ejpam-2691	65	1	x12	x12	NUM
ejpam-2691	65	2	∈	∈	PROPN
ejpam-2691	65	3	x	x	SYM
ejpam-2691	65	4	,	,	PUNCT
ejpam-2691	65	5	g(x11	g(x11	PROPN
ejpam-2691	65	6	)	)	PUNCT
ejpam-2691	65	7	�	�	PROPN
ejpam-2691	66	1	g(x12)⇒	g(x12)⇒	PROPN
ejpam-2691	66	2	f	f	PROPN
ejpam-2691	66	3	(	(	PUNCT
ejpam-2691	66	4	x11	x11	PROPN
ejpam-2691	66	5	,	,	PUNCT
ejpam-2691	66	6	x	x	PROPN
ejpam-2691	66	7	2	2	NUM
ejpam-2691	66	8	,	,	PUNCT
ejpam-2691	66	9	.	.	PUNCT
ejpam-2691	66	10	.	.	PUNCT
ejpam-2691	66	11	.	.	PUNCT
ejpam-2691	67	1	,	,	PUNCT
ejpam-2691	67	2	xr	xr	PROPN
ejpam-2691	67	3	)	)	PUNCT
ejpam-2691	67	4	�	�	PROPN
ejpam-2691	67	5	f	f	PROPN
ejpam-2691	67	6	(	(	PUNCT
ejpam-2691	67	7	x12	x12	PROPN
ejpam-2691	67	8	,	,	PUNCT
ejpam-2691	67	9	x	x	NOUN
ejpam-2691	67	10	2	2	NUM
ejpam-2691	67	11	,	,	PUNCT
ejpam-2691	67	12	.	.	PUNCT
ejpam-2691	67	13	.	.	PUNCT
ejpam-2691	67	14	.	.	PUNCT
ejpam-2691	67	15	,	,	PUNCT
ejpam-2691	67	16	xr	xr	PROPN
ejpam-2691	67	17	)	)	PUNCT
ejpam-2691	67	18	,	,	PUNCT
ejpam-2691	67	19	∀	∀	X
ejpam-2691	67	20	x21	x21	NUM
ejpam-2691	67	21	,	,	PUNCT
ejpam-2691	67	22	x22	x22	NOUN
ejpam-2691	67	23	∈	∈	PROPN
ejpam-2691	67	24	x	x	SYM
ejpam-2691	67	25	,	,	PUNCT
ejpam-2691	67	26	g(x21	g(x21	NOUN
ejpam-2691	67	27	)	)	PUNCT
ejpam-2691	67	28	�	�	PROPN
ejpam-2691	67	29	g(x22)⇒	g(x22)⇒	PUNCT
ejpam-2691	67	30	f	f	PROPN
ejpam-2691	67	31	(	(	PUNCT
ejpam-2691	67	32	x1	x1	PROPN
ejpam-2691	67	33	,	,	PUNCT
ejpam-2691	67	34	x21	x21	PROPN
ejpam-2691	67	35	,	,	PUNCT
ejpam-2691	67	36	.	.	PUNCT
ejpam-2691	67	37	.	.	PUNCT
ejpam-2691	67	38	.	.	PUNCT
ejpam-2691	68	1	,	,	PUNCT
ejpam-2691	68	2	x	x	X
ejpam-2691	68	3	r	r	X
ejpam-2691	68	4	)	)	PUNCT
ejpam-2691	68	5	�	�	PROPN
ejpam-2691	68	6	f	f	PROPN
ejpam-2691	68	7	(	(	PUNCT
ejpam-2691	68	8	x1	x1	PROPN
ejpam-2691	68	9	,	,	PUNCT
ejpam-2691	68	10	x22	x22	PROPN
ejpam-2691	68	11	,	,	PUNCT
ejpam-2691	68	12	.	.	PUNCT
ejpam-2691	68	13	.	.	PUNCT
ejpam-2691	68	14	.	.	PUNCT
ejpam-2691	69	1	,	,	PUNCT
ejpam-2691	69	2	x	x	X
ejpam-2691	69	3	r	r	NOUN
ejpam-2691	69	4	)	)	PUNCT
ejpam-2691	69	5	,	,	PUNCT
ejpam-2691	69	6	∀	∀	X
ejpam-2691	69	7	x31	x31	NUM
ejpam-2691	69	8	,	,	PUNCT
ejpam-2691	69	9	x32	x32	PROPN
ejpam-2691	69	10	∈	∈	PROPN
ejpam-2691	69	11	x	x	NOUN
ejpam-2691	69	12	,	,	PUNCT
ejpam-2691	69	13	g(x31	g(x31	NOUN
ejpam-2691	69	14	)	)	PUNCT
ejpam-2691	69	15	�	�	PROPN
ejpam-2691	70	1	g(x32)⇒	g(x32)⇒	X
ejpam-2691	70	2	f	f	X
ejpam-2691	70	3	(	(	PUNCT
ejpam-2691	70	4	x1	x1	PROPN
ejpam-2691	70	5	,	,	PUNCT
ejpam-2691	70	6	x2	x2	PROPN
ejpam-2691	70	7	,	,	PUNCT
ejpam-2691	70	8	x31	x31	PROPN
ejpam-2691	70	9	,	,	PUNCT
ejpam-2691	70	10	.	.	PUNCT
ejpam-2691	70	11	.	.	PUNCT
ejpam-2691	70	12	.	.	PUNCT
ejpam-2691	71	1	,	,	PUNCT
ejpam-2691	71	2	x	x	X
ejpam-2691	71	3	r	r	X
ejpam-2691	71	4	)	)	PUNCT
ejpam-2691	71	5	�	�	PROPN
ejpam-2691	71	6	f	f	PROPN
ejpam-2691	71	7	(	(	PUNCT
ejpam-2691	71	8	x1	x1	PROPN
ejpam-2691	71	9	,	,	PUNCT
ejpam-2691	71	10	x2	x2	PROPN
ejpam-2691	71	11	,	,	PUNCT
ejpam-2691	71	12	x32	x32	PROPN
ejpam-2691	71	13	,	,	PUNCT
ejpam-2691	71	14	.	.	PUNCT
ejpam-2691	71	15	.	.	PUNCT
ejpam-2691	71	16	.	.	PUNCT
ejpam-2691	72	1	,	,	PUNCT
ejpam-2691	72	2	x	x	X
ejpam-2691	72	3	r	r	NOUN
ejpam-2691	72	4	)	)	PUNCT
ejpam-2691	72	5	,	,	PUNCT
ejpam-2691	72	6	...	...	PUNCT
ejpam-2691	72	7	∀	∀	X
ejpam-2691	72	8	xr1	xr1	NOUN
ejpam-2691	72	9	,	,	PUNCT
ejpam-2691	72	10	xr2	xr2	PROPN
ejpam-2691	72	11	∈	∈	PROPN
ejpam-2691	72	12	x	x	SYM
ejpam-2691	72	13	,	,	PUNCT
ejpam-2691	72	14	g(xr1	g(xr1	PROPN
ejpam-2691	72	15	)	)	PUNCT
ejpam-2691	72	16	�	�	PROPN
ejpam-2691	72	17	g(xr2)⇒	g(xr2)⇒	PROPN
ejpam-2691	73	1	f	f	PROPN
ejpam-2691	74	1	(	(	PUNCT
ejpam-2691	74	2	x1	x1	PROPN
ejpam-2691	74	3	,	,	PUNCT
ejpam-2691	74	4	x2	x2	PROPN
ejpam-2691	74	5	,	,	PUNCT
ejpam-2691	74	6	x3	x3	ADJ
ejpam-2691	74	7	,	,	PUNCT
ejpam-2691	74	8	.	.	PUNCT
ejpam-2691	74	9	.	.	PUNCT
ejpam-2691	74	10	.	.	PUNCT
ejpam-2691	75	1	,	,	PUNCT
ejpam-2691	75	2	xr1	xr1	PROPN
ejpam-2691	75	3	)	)	PUNCT
ejpam-2691	75	4	�	�	PROPN
ejpam-2691	75	5	f	f	PROPN
ejpam-2691	75	6	(	(	PUNCT
ejpam-2691	75	7	x1	x1	PROPN
ejpam-2691	75	8	,	,	PUNCT
ejpam-2691	75	9	x2	x2	PROPN
ejpam-2691	75	10	,	,	PUNCT
ejpam-2691	75	11	x3	x3	ADJ
ejpam-2691	75	12	,	,	PUNCT
ejpam-2691	75	13	.	.	PUNCT
ejpam-2691	75	14	.	.	PUNCT
ejpam-2691	75	15	.	.	PUNCT
ejpam-2691	76	1	,	,	PUNCT
ejpam-2691	76	2	xr2	xr2	PROPN
ejpam-2691	76	3	)	)	PUNCT
ejpam-2691	76	4	.	.	PUNCT
ejpam-2691	77	1	now	now	ADV
ejpam-2691	77	2	,	,	PUNCT
ejpam-2691	77	3	we	we	PRON
ejpam-2691	77	4	introduce	introduce	VERB
ejpam-2691	77	5	the	the	DET
ejpam-2691	77	6	concept	concept	NOUN
ejpam-2691	77	7	of	of	ADP
ejpam-2691	77	8	compatible	compatible	ADJ
ejpam-2691	77	9	mapping	mapping	NOUN
ejpam-2691	77	10	for	for	ADP
ejpam-2691	77	11	mapping	map	VERB
ejpam-2691	77	12	f	f	NOUN
ejpam-2691	77	13	:	:	PUNCT
ejpam-2691	77	14	∏r	∏r	X
ejpam-2691	77	15	λ=1x	λ=1x	ADJ
ejpam-2691	77	16	λ	λ	X
ejpam-2691	77	17	→	→	SYM
ejpam-2691	77	18	x	x	X
ejpam-2691	77	19	and	and	CCONJ
ejpam-2691	77	20	self	self	NOUN
ejpam-2691	77	21	mapping	mapping	NOUN
ejpam-2691	77	22	g	g	NOUN
ejpam-2691	77	23	akin	akin	ADJ
ejpam-2691	77	24	to	to	ADP
ejpam-2691	77	25	compatible	compatible	ADJ
ejpam-2691	77	26	mapping	mapping	NOUN
ejpam-2691	77	27	as	as	SCONJ
ejpam-2691	77	28	introduced	introduce	VERB
ejpam-2691	77	29	by	by	ADP
ejpam-2691	77	30	choudhary	choudhary	PROPN
ejpam-2691	77	31	and	and	CCONJ
ejpam-2691	77	32	kundu	kundu	NOUN
ejpam-2691	78	1	[	[	X
ejpam-2691	78	2	13	13	NUM
ejpam-2691	78	3	]	]	PUNCT
ejpam-2691	78	4	for	for	ADP
ejpam-2691	78	5	mapping	mapping	NOUN
ejpam-2691	78	6	f	f	NOUN
ejpam-2691	78	7	and	and	CCONJ
ejpam-2691	78	8	self	self	NOUN
ejpam-2691	78	9	mapping	mapping	NOUN
ejpam-2691	78	10	g.	g.	NOUN
ejpam-2691	78	11	definition	definition	NOUN
ejpam-2691	78	12	4	4	X
ejpam-2691	78	13	.	.	PUNCT
ejpam-2691	79	1	let	let	VERB
ejpam-2691	79	2	f	f	NOUN
ejpam-2691	79	3	:	:	PUNCT
ejpam-2691	79	4	∏r	∏r	X
ejpam-2691	79	5	λ=1x	λ=1x	ADJ
ejpam-2691	79	6	λ	λ	X
ejpam-2691	79	7	→	→	SYM
ejpam-2691	79	8	x	x	X
ejpam-2691	79	9	and	and	CCONJ
ejpam-2691	79	10	g	g	NOUN
ejpam-2691	79	11	:	:	PUNCT
ejpam-2691	79	12	x	x	SYM
ejpam-2691	79	13	→	→	PUNCT
ejpam-2691	79	14	x	x	PUNCT
ejpam-2691	79	15	be	be	AUX
ejpam-2691	79	16	two	two	NUM
ejpam-2691	79	17	mappings	mapping	NOUN
ejpam-2691	79	18	.	.	PUNCT
ejpam-2691	80	1	then	then	ADV
ejpam-2691	80	2	f	f	PROPN
ejpam-2691	80	3	and	and	CCONJ
ejpam-2691	80	4	g	g	PROPN
ejpam-2691	80	5	are	be	AUX
ejpam-2691	80	6	said	say	VERB
ejpam-2691	80	7	to	to	PART
ejpam-2691	80	8	be	be	AUX
ejpam-2691	80	9	compatible	compatible	ADJ
ejpam-2691	80	10	if	if	PROPN
ejpam-2691	81	1	lim	lim	PROPN
ejpam-2691	81	2	n→+∞	n→+∞	VERB
ejpam-2691	81	3	d(g(f	d(g(f	PROPN
ejpam-2691	81	4	(	(	PUNCT
ejpam-2691	81	5	x1n	x1n	PROPN
ejpam-2691	81	6	,	,	PUNCT
ejpam-2691	81	7	x	x	PROPN
ejpam-2691	81	8	2	2	NUM
ejpam-2691	81	9	n	n	NUM
ejpam-2691	81	10	,	,	PUNCT
ejpam-2691	81	11	.	.	PUNCT
ejpam-2691	81	12	.	.	PUNCT
ejpam-2691	81	13	.	.	PUNCT
ejpam-2691	82	1	,	,	PUNCT
ejpam-2691	82	2	x	x	PUNCT
ejpam-2691	82	3	r	r	NOUN
ejpam-2691	82	4	n	n	NUM
ejpam-2691	82	5	)	)	PUNCT
ejpam-2691	82	6	)	)	PUNCT
ejpam-2691	82	7	,	,	PUNCT
ejpam-2691	82	8	f	f	PROPN
ejpam-2691	82	9	(	(	PUNCT
ejpam-2691	82	10	g(x1n	g(x1n	PROPN
ejpam-2691	82	11	)	)	PUNCT
ejpam-2691	82	12	,	,	PUNCT
ejpam-2691	82	13	g(x2n	g(x2n	PROPN
ejpam-2691	82	14	)	)	PUNCT
ejpam-2691	82	15	,	,	PUNCT
ejpam-2691	82	16	.	.	PUNCT
ejpam-2691	82	17	.	.	PUNCT
ejpam-2691	83	1	.	.	PUNCT
ejpam-2691	84	1	,	,	PUNCT
ejpam-2691	84	2	g(xrn	g(xrn	NOUN
ejpam-2691	84	3	)	)	PUNCT
ejpam-2691	84	4	)	)	PUNCT
ejpam-2691	84	5	)	)	PUNCT
ejpam-2691	85	1	=	=	SYM
ejpam-2691	85	2	0	0	NUM
ejpam-2691	85	3	,	,	PUNCT
ejpam-2691	85	4	lim	lim	PROPN
ejpam-2691	85	5	n→+∞	n→+∞	VERB
ejpam-2691	85	6	d(g(f	d(g(f	PROPN
ejpam-2691	85	7	(	(	PUNCT
ejpam-2691	85	8	x2n	x2n	PROPN
ejpam-2691	85	9	,	,	PUNCT
ejpam-2691	85	10	x	x	PROPN
ejpam-2691	85	11	3	3	NUM
ejpam-2691	85	12	n	n	NUM
ejpam-2691	85	13	,	,	PUNCT
ejpam-2691	85	14	.	.	PUNCT
ejpam-2691	85	15	.	.	PUNCT
ejpam-2691	85	16	.	.	PUNCT
ejpam-2691	86	1	,	,	PUNCT
ejpam-2691	86	2	x	x	PUNCT
ejpam-2691	86	3	r	r	NOUN
ejpam-2691	86	4	n	n	CCONJ
ejpam-2691	86	5	,	,	PUNCT
ejpam-2691	86	6	x	x	PROPN
ejpam-2691	86	7	1	1	NUM
ejpam-2691	86	8	n	n	NUM
ejpam-2691	86	9	)	)	PUNCT
ejpam-2691	86	10	)	)	PUNCT
ejpam-2691	86	11	,	,	PUNCT
ejpam-2691	86	12	f	f	PROPN
ejpam-2691	86	13	(	(	PUNCT
ejpam-2691	86	14	g(x2n	g(x2n	PROPN
ejpam-2691	86	15	)	)	PUNCT
ejpam-2691	86	16	,	,	PUNCT
ejpam-2691	86	17	g(x3n	g(x3n	PROPN
ejpam-2691	86	18	)	)	PUNCT
ejpam-2691	86	19	,	,	PUNCT
ejpam-2691	86	20	.	.	PUNCT
ejpam-2691	86	21	.	.	PUNCT
ejpam-2691	86	22	.	.	PUNCT
ejpam-2691	87	1	,	,	PUNCT
ejpam-2691	87	2	g(xrn	g(xrn	NOUN
ejpam-2691	87	3	)	)	PUNCT
ejpam-2691	87	4	,	,	PUNCT
ejpam-2691	87	5	g(x1n	g(x1n	PROPN
ejpam-2691	87	6	)	)	PUNCT
ejpam-2691	87	7	)	)	PUNCT
ejpam-2691	87	8	)	)	PUNCT
ejpam-2691	88	1	=	=	SYM
ejpam-2691	88	2	0	0	NUM
ejpam-2691	88	3	,	,	PUNCT
ejpam-2691	88	4	lim	lim	PROPN
ejpam-2691	88	5	n→+∞	n→+∞	VERB
ejpam-2691	88	6	d(g(f	d(g(f	PROPN
ejpam-2691	88	7	(	(	PUNCT
ejpam-2691	88	8	x3n	x3n	PROPN
ejpam-2691	88	9	,	,	PUNCT
ejpam-2691	88	10	x	x	PROPN
ejpam-2691	88	11	4	4	NUM
ejpam-2691	88	12	n	n	NUM
ejpam-2691	88	13	,	,	PUNCT
ejpam-2691	88	14	.	.	PUNCT
ejpam-2691	88	15	.	.	PUNCT
ejpam-2691	88	16	.	.	PUNCT
ejpam-2691	89	1	,	,	PUNCT
ejpam-2691	89	2	x	x	X
ejpam-2691	89	3	1	1	NUM
ejpam-2691	89	4	n	n	CCONJ
ejpam-2691	89	5	,	,	PUNCT
ejpam-2691	89	6	x	x	PROPN
ejpam-2691	89	7	2	2	NUM
ejpam-2691	89	8	n	n	NUM
ejpam-2691	89	9	)	)	PUNCT
ejpam-2691	89	10	)	)	PUNCT
ejpam-2691	89	11	,	,	PUNCT
ejpam-2691	89	12	f	f	PROPN
ejpam-2691	89	13	(	(	PUNCT
ejpam-2691	89	14	g(x3n	g(x3n	PROPN
ejpam-2691	89	15	)	)	PUNCT
ejpam-2691	89	16	,	,	PUNCT
ejpam-2691	89	17	g(x4n	g(x4n	NUM
ejpam-2691	89	18	)	)	PUNCT
ejpam-2691	89	19	,	,	PUNCT
ejpam-2691	89	20	.	.	PUNCT
ejpam-2691	89	21	.	.	PUNCT
ejpam-2691	90	1	.	.	PUNCT
ejpam-2691	91	1	,	,	PUNCT
ejpam-2691	91	2	g(x1n	g(x1n	PROPN
ejpam-2691	91	3	)	)	PUNCT
ejpam-2691	91	4	,	,	PUNCT
ejpam-2691	91	5	g(x2n	g(x2n	PROPN
ejpam-2691	91	6	)	)	PUNCT
ejpam-2691	91	7	)	)	PUNCT
ejpam-2691	91	8	)	)	PUNCT
ejpam-2691	92	1	=	=	PUNCT
ejpam-2691	92	2	0	0	NUM
ejpam-2691	92	3	,	,	PUNCT
ejpam-2691	92	4	...	...	PUNCT
ejpam-2691	93	1	lim	lim	PROPN
ejpam-2691	93	2	n→+∞	n→+∞	VERB
ejpam-2691	93	3	d(g(f	d(g(f	PROPN
ejpam-2691	93	4	(	(	PUNCT
ejpam-2691	93	5	xrn	xrn	PROPN
ejpam-2691	93	6	,	,	PUNCT
ejpam-2691	93	7	x	x	PROPN
ejpam-2691	93	8	1	1	NUM
ejpam-2691	93	9	n	n	CCONJ
ejpam-2691	93	10	,	,	PUNCT
ejpam-2691	93	11	.	.	PUNCT
ejpam-2691	93	12	.	.	PUNCT
ejpam-2691	93	13	.	.	PUNCT
ejpam-2691	94	1	,	,	PUNCT
ejpam-2691	94	2	x	x	X
ejpam-2691	94	3	r−1	r−1	PROPN
ejpam-2691	94	4	n	n	NUM
ejpam-2691	94	5	)	)	PUNCT
ejpam-2691	94	6	)	)	PUNCT
ejpam-2691	94	7	,	,	PUNCT
ejpam-2691	94	8	f	f	PROPN
ejpam-2691	94	9	(	(	PUNCT
ejpam-2691	94	10	g(xrn	g(xrn	NOUN
ejpam-2691	94	11	)	)	PUNCT
ejpam-2691	94	12	,	,	PUNCT
ejpam-2691	94	13	g(x1n	g(x1n	PROPN
ejpam-2691	94	14	)	)	PUNCT
ejpam-2691	94	15	,	,	PUNCT
ejpam-2691	94	16	.	.	PUNCT
ejpam-2691	94	17	.	.	PUNCT
ejpam-2691	95	1	.	.	PUNCT
ejpam-2691	96	1	,	,	PUNCT
ejpam-2691	96	2	g(xr−1n	g(xr−1n	NOUN
ejpam-2691	96	3	)	)	PUNCT
ejpam-2691	96	4	)	)	PUNCT
ejpam-2691	96	5	)	)	PUNCT
ejpam-2691	97	1	=	=	PUNCT
ejpam-2691	97	2	0	0	NUM
ejpam-2691	97	3	,	,	PUNCT
ejpam-2691	97	4	whenever	whenever	SCONJ
ejpam-2691	97	5	{	{	PUNCT
ejpam-2691	97	6	x1n	x1n	NOUN
ejpam-2691	97	7	}	}	PUNCT
ejpam-2691	97	8	,	,	PUNCT
ejpam-2691	97	9	{	{	PUNCT
ejpam-2691	97	10	x2n	x2n	NOUN
ejpam-2691	97	11	}	}	PUNCT
ejpam-2691	97	12	,	,	PUNCT
ejpam-2691	97	13	.	.	PUNCT
ejpam-2691	97	14	.	.	PUNCT
ejpam-2691	97	15	.	.	PUNCT
ejpam-2691	98	1	,	,	PUNCT
ejpam-2691	98	2	{	{	PUNCT
ejpam-2691	98	3	xrn	xrn	ADV
ejpam-2691	98	4	}	}	PUNCT
ejpam-2691	98	5	are	be	AUX
ejpam-2691	98	6	sequences	sequence	NOUN
ejpam-2691	98	7	in	in	ADP
ejpam-2691	98	8	x	x	NOUN
ejpam-2691	98	9	,	,	PUNCT
ejpam-2691	98	10	such	such	ADJ
ejpam-2691	98	11	that	that	PROPN
ejpam-2691	98	12	lim	lim	PROPN
ejpam-2691	98	13	n→+∞	n→+∞	PROPN
ejpam-2691	98	14	f	f	PROPN
ejpam-2691	98	15	(	(	PUNCT
ejpam-2691	98	16	x1n	x1n	PROPN
ejpam-2691	98	17	,	,	PUNCT
ejpam-2691	98	18	x	x	PROPN
ejpam-2691	98	19	2	2	NUM
ejpam-2691	98	20	n	n	NUM
ejpam-2691	98	21	,	,	PUNCT
ejpam-2691	98	22	.	.	PUNCT
ejpam-2691	98	23	.	.	PUNCT
ejpam-2691	99	1	.	.	PUNCT
ejpam-2691	100	1	,	,	PUNCT
ejpam-2691	100	2	x	x	PUNCT
ejpam-2691	100	3	r	r	NOUN
ejpam-2691	100	4	n	n	CCONJ
ejpam-2691	100	5	)	)	PUNCT
ejpam-2691	101	1	=	=	VERB
ejpam-2691	101	2	lim	lim	PROPN
ejpam-2691	101	3	n→+∞	n→+∞	VERB
ejpam-2691	101	4	g(x1n	g(x1n	PROPN
ejpam-2691	101	5	)	)	PUNCT
ejpam-2691	101	6	=	=	SYM
ejpam-2691	102	1	x1	x1	PROPN
ejpam-2691	102	2	,	,	PUNCT
ejpam-2691	102	3	lim	lim	PROPN
ejpam-2691	102	4	n→+∞	n→+∞	VERB
ejpam-2691	102	5	f	f	X
ejpam-2691	102	6	(	(	PUNCT
ejpam-2691	102	7	x2n	x2n	ADV
ejpam-2691	102	8	,	,	PUNCT
ejpam-2691	102	9	x	x	PROPN
ejpam-2691	102	10	3	3	NUM
ejpam-2691	102	11	n	n	NUM
ejpam-2691	102	12	,	,	PUNCT
ejpam-2691	102	13	.	.	PUNCT
ejpam-2691	102	14	.	.	PUNCT
ejpam-2691	102	15	.	.	PUNCT
ejpam-2691	103	1	,	,	PUNCT
ejpam-2691	103	2	x	x	PUNCT
ejpam-2691	103	3	r	r	NOUN
ejpam-2691	103	4	n	n	CCONJ
ejpam-2691	103	5	,	,	PUNCT
ejpam-2691	103	6	x	x	PROPN
ejpam-2691	103	7	1	1	NUM
ejpam-2691	103	8	n	n	CCONJ
ejpam-2691	103	9	)	)	PUNCT
ejpam-2691	104	1	=	=	VERB
ejpam-2691	104	2	lim	lim	PROPN
ejpam-2691	104	3	n→+∞	n→+∞	PROPN
ejpam-2691	104	4	g(x2n	g(x2n	PROPN
ejpam-2691	104	5	)	)	PUNCT
ejpam-2691	104	6	=	=	SYM
ejpam-2691	104	7	x2	x2	PROPN
ejpam-2691	104	8	...	...	PUNCT
ejpam-2691	105	1	lim	lim	PROPN
ejpam-2691	105	2	n→+∞	n→+∞	VERB
ejpam-2691	105	3	f	f	X
ejpam-2691	105	4	(	(	PUNCT
ejpam-2691	105	5	xrn	xrn	PROPN
ejpam-2691	105	6	,	,	PUNCT
ejpam-2691	105	7	x	x	PROPN
ejpam-2691	105	8	1	1	NUM
ejpam-2691	105	9	n	n	CCONJ
ejpam-2691	105	10	,	,	PUNCT
ejpam-2691	105	11	.	.	PUNCT
ejpam-2691	105	12	.	.	PUNCT
ejpam-2691	105	13	.	.	PUNCT
ejpam-2691	106	1	,	,	PUNCT
ejpam-2691	106	2	x	x	X
ejpam-2691	106	3	r−1	r−1	PROPN
ejpam-2691	106	4	n	n	ADV
ejpam-2691	106	5	)	)	PUNCT
ejpam-2691	107	1	=	=	SYM
ejpam-2691	107	2	lim	lim	PROPN
ejpam-2691	107	3	n→+∞	n→+∞	PROPN
ejpam-2691	107	4	g(xrn	g(xrn	PROPN
ejpam-2691	107	5	)	)	PUNCT
ejpam-2691	107	6	=	=	SYM
ejpam-2691	107	7	xr	xr	PROPN
ejpam-2691	107	8	,	,	PUNCT
ejpam-2691	107	9	(	(	PUNCT
ejpam-2691	107	10	1	1	X
ejpam-2691	107	11	)	)	PUNCT
ejpam-2691	107	12	for	for	ADP
ejpam-2691	107	13	all	all	DET
ejpam-2691	107	14	x1	x1	PROPN
ejpam-2691	107	15	,	,	PUNCT
ejpam-2691	107	16	x2	x2	PROPN
ejpam-2691	107	17	,	,	PUNCT
ejpam-2691	107	18	.	.	PUNCT
ejpam-2691	107	19	.	.	PUNCT
ejpam-2691	108	1	.	.	PUNCT
ejpam-2691	109	1	,	,	PUNCT
ejpam-2691	109	2	xr	xr	PROPN
ejpam-2691	109	3	∈	∈	PROPN
ejpam-2691	109	4	x.	x.	NOUN
ejpam-2691	110	1	the	the	DET
ejpam-2691	110	2	following	follow	VERB
ejpam-2691	110	3	is	be	AUX
ejpam-2691	110	4	the	the	DET
ejpam-2691	110	5	definition	definition	NOUN
ejpam-2691	110	6	of	of	ADP
ejpam-2691	110	7	reciprocally	reciprocally	NOUN
ejpam-2691	110	8	continuity	continuity	NOUN
ejpam-2691	110	9	and	and	CCONJ
ejpam-2691	110	10	weakly	weakly	ADJ
ejpam-2691	110	11	reciprocally	reciprocally	ADJ
ejpam-2691	110	12	continuity	continuity	NOUN
ejpam-2691	110	13	for	for	ADP
ejpam-2691	110	14	mapping	map	VERB
ejpam-2691	110	15	f	f	NOUN
ejpam-2691	110	16	:	:	PUNCT
ejpam-2691	110	17	∏r	∏r	X
ejpam-2691	110	18	λ=1x	λ=1x	ADJ
ejpam-2691	110	19	λ	λ	X
ejpam-2691	110	20	→	→	SYM
ejpam-2691	110	21	x	x	X
ejpam-2691	110	22	and	and	CCONJ
ejpam-2691	110	23	self	self	NOUN
ejpam-2691	110	24	mapping	mapping	NOUN
ejpam-2691	110	25	g	g	NOUN
ejpam-2691	110	26	:	:	PUNCT
ejpam-2691	110	27	definition	definition	NOUN
ejpam-2691	110	28	5	5	NUM
ejpam-2691	110	29	.	.	PUNCT
ejpam-2691	111	1	let	let	VERB
ejpam-2691	111	2	f	f	NOUN
ejpam-2691	111	3	:	:	PUNCT
ejpam-2691	111	4	∏r	∏r	X
ejpam-2691	111	5	λ=1x	λ=1x	ADJ
ejpam-2691	111	6	λ	λ	X
ejpam-2691	111	7	→	→	SYM
ejpam-2691	111	8	x	x	X
ejpam-2691	111	9	and	and	CCONJ
ejpam-2691	111	10	g	g	NOUN
ejpam-2691	111	11	:	:	PUNCT
ejpam-2691	111	12	x	x	SYM
ejpam-2691	111	13	→	→	PUNCT
ejpam-2691	111	14	x	x	PUNCT
ejpam-2691	111	15	be	be	AUX
ejpam-2691	111	16	two	two	NUM
ejpam-2691	111	17	mappings	mapping	NOUN
ejpam-2691	111	18	.	.	PUNCT
ejpam-2691	112	1	then	then	ADV
ejpam-2691	112	2	f	f	PROPN
ejpam-2691	112	3	and	and	CCONJ
ejpam-2691	112	4	g	g	PROPN
ejpam-2691	112	5	are	be	AUX
ejpam-2691	112	6	said	say	VERB
ejpam-2691	112	7	to	to	PART
ejpam-2691	112	8	be	be	AUX
ejpam-2691	112	9	m.	m.	NOUN
ejpam-2691	112	10	grewal	grewal	PROPN
ejpam-2691	112	11	,	,	PUNCT
ejpam-2691	112	12	r.	r.	PROPN
ejpam-2691	112	13	kumar	kumar	PROPN
ejpam-2691	112	14	,	,	PUNCT
ejpam-2691	112	15	a.	a.	PROPN
ejpam-2691	112	16	kumar	kumar	PROPN
ejpam-2691	112	17	/	/	SYM
ejpam-2691	112	18	eur	eur	PROPN
ejpam-2691	112	19	.	.	PUNCT
ejpam-2691	113	1	j.	j.	PROPN
ejpam-2691	113	2	pure	pure	PROPN
ejpam-2691	113	3	appl	appl	PROPN
ejpam-2691	113	4	.	.	PROPN
ejpam-2691	113	5	math	math	PROPN
ejpam-2691	113	6	,	,	PUNCT
ejpam-2691	113	7	10	10	NUM
ejpam-2691	113	8	(	(	PUNCT
ejpam-2691	113	9	2	2	NUM
ejpam-2691	113	10	)	)	PUNCT
ejpam-2691	113	11	(	(	PUNCT
ejpam-2691	113	12	2017	2017	NUM
ejpam-2691	113	13	)	)	PUNCT
ejpam-2691	113	14	,	,	PUNCT
ejpam-2691	113	15	295	295	NUM
ejpam-2691	113	16	-	-	SYM
ejpam-2691	113	17	311	311	NUM
ejpam-2691	113	18	298	298	NUM
ejpam-2691	113	19	(	(	PUNCT
ejpam-2691	113	20	i	i	NOUN
ejpam-2691	113	21	)	)	PUNCT
ejpam-2691	113	22	reciprocally	reciprocally	ADV
ejpam-2691	113	23	continuous	continuous	ADJ
ejpam-2691	113	24	if	if	PROPN
ejpam-2691	113	25	lim	lim	PROPN
ejpam-2691	113	26	n→+∞	n→+∞	VERB
ejpam-2691	113	27	g(f	g(f	PROPN
ejpam-2691	113	28	(	(	PUNCT
ejpam-2691	113	29	x1n	x1n	PROPN
ejpam-2691	113	30	,	,	PUNCT
ejpam-2691	113	31	x	x	PROPN
ejpam-2691	113	32	2	2	NUM
ejpam-2691	113	33	n	n	NUM
ejpam-2691	113	34	,	,	PUNCT
ejpam-2691	113	35	.	.	PUNCT
ejpam-2691	113	36	.	.	PUNCT
ejpam-2691	113	37	.	.	PUNCT
ejpam-2691	114	1	,	,	PUNCT
ejpam-2691	114	2	x	x	PUNCT
ejpam-2691	114	3	r	r	NOUN
ejpam-2691	114	4	n	n	CCONJ
ejpam-2691	114	5	)	)	PUNCT
ejpam-2691	114	6	=	=	SYM
ejpam-2691	114	7	g(x1	g(x1	NOUN
ejpam-2691	114	8	)	)	PUNCT
ejpam-2691	114	9	and	and	CCONJ
ejpam-2691	114	10	lim	lim	PROPN
ejpam-2691	114	11	n→+∞	n→+∞	VERB
ejpam-2691	114	12	f	f	PROPN
ejpam-2691	114	13	(	(	PUNCT
ejpam-2691	114	14	g(x1n	g(x1n	PROPN
ejpam-2691	114	15	)	)	PUNCT
ejpam-2691	114	16	,	,	PUNCT
ejpam-2691	114	17	g(x2n	g(x2n	PROPN
ejpam-2691	114	18	)	)	PUNCT
ejpam-2691	114	19	,	,	PUNCT
ejpam-2691	114	20	.	.	PUNCT
ejpam-2691	114	21	.	.	PUNCT
ejpam-2691	115	1	.	.	PUNCT
ejpam-2691	116	1	,	,	PUNCT
ejpam-2691	116	2	g(xrn	g(xrn	NOUN
ejpam-2691	116	3	)	)	PUNCT
ejpam-2691	116	4	)	)	PUNCT
ejpam-2691	117	1	=	=	SYM
ejpam-2691	117	2	f	f	X
ejpam-2691	117	3	(	(	PUNCT
ejpam-2691	117	4	x1	x1	PROPN
ejpam-2691	117	5	,	,	PUNCT
ejpam-2691	117	6	x2	x2	PROPN
ejpam-2691	117	7	,	,	PUNCT
ejpam-2691	117	8	.	.	PUNCT
ejpam-2691	117	9	.	.	PUNCT
ejpam-2691	117	10	.	.	PUNCT
ejpam-2691	117	11	,	,	PUNCT
ejpam-2691	117	12	xr	xr	PROPN
ejpam-2691	117	13	)	)	PUNCT
ejpam-2691	117	14	;	;	PUNCT
ejpam-2691	117	15	lim	lim	PROPN
ejpam-2691	117	16	n→+∞	n→+∞	VERB
ejpam-2691	117	17	g(f	g(f	PROPN
ejpam-2691	117	18	(	(	PUNCT
ejpam-2691	117	19	x2n	x2n	ADV
ejpam-2691	117	20	,	,	PUNCT
ejpam-2691	117	21	x	x	PROPN
ejpam-2691	117	22	3	3	NUM
ejpam-2691	117	23	n	n	NUM
ejpam-2691	117	24	,	,	PUNCT
ejpam-2691	117	25	.	.	PUNCT
ejpam-2691	117	26	.	.	PUNCT
ejpam-2691	117	27	.	.	PUNCT
ejpam-2691	118	1	,	,	PUNCT
ejpam-2691	118	2	x	x	PUNCT
ejpam-2691	118	3	r	r	NOUN
ejpam-2691	118	4	n	n	CCONJ
ejpam-2691	118	5	,	,	PUNCT
ejpam-2691	118	6	x	x	PROPN
ejpam-2691	118	7	1	1	NUM
ejpam-2691	118	8	n	n	CCONJ
ejpam-2691	118	9	)	)	PUNCT
ejpam-2691	118	10	=	=	SYM
ejpam-2691	118	11	g(x2	g(x2	NOUN
ejpam-2691	118	12	)	)	PUNCT
ejpam-2691	118	13	and	and	CCONJ
ejpam-2691	118	14	lim	lim	PROPN
ejpam-2691	118	15	n→+∞	n→+∞	VERB
ejpam-2691	118	16	f	f	PROPN
ejpam-2691	118	17	(	(	PUNCT
ejpam-2691	118	18	g(x2n	g(x2n	PROPN
ejpam-2691	118	19	)	)	PUNCT
ejpam-2691	118	20	,	,	PUNCT
ejpam-2691	118	21	g(x3n	g(x3n	PROPN
ejpam-2691	118	22	)	)	PUNCT
ejpam-2691	118	23	,	,	PUNCT
ejpam-2691	118	24	.	.	PUNCT
ejpam-2691	118	25	.	.	PUNCT
ejpam-2691	118	26	.	.	PUNCT
ejpam-2691	119	1	,	,	PUNCT
ejpam-2691	119	2	g(xrn	g(xrn	NOUN
ejpam-2691	119	3	)	)	PUNCT
ejpam-2691	119	4	,	,	PUNCT
ejpam-2691	119	5	g(x1n	g(x1n	NOUN
ejpam-2691	119	6	)	)	PUNCT
ejpam-2691	119	7	)	)	PUNCT
ejpam-2691	120	1	=	=	SYM
ejpam-2691	120	2	f	f	X
ejpam-2691	120	3	(	(	PUNCT
ejpam-2691	120	4	x2	x2	PROPN
ejpam-2691	120	5	,	,	PUNCT
ejpam-2691	120	6	x3	x3	ADJ
ejpam-2691	120	7	,	,	PUNCT
ejpam-2691	120	8	.	.	PUNCT
ejpam-2691	120	9	.	.	PUNCT
ejpam-2691	120	10	.	.	PUNCT
ejpam-2691	120	11	,	,	PUNCT
ejpam-2691	120	12	xr	xr	PROPN
ejpam-2691	120	13	,	,	PUNCT
ejpam-2691	120	14	x1	x1	PROPN
ejpam-2691	120	15	)	)	PUNCT
ejpam-2691	120	16	;	;	PUNCT
ejpam-2691	120	17	...	...	PUNCT
ejpam-2691	121	1	lim	lim	PROPN
ejpam-2691	121	2	n→+∞	n→+∞	VERB
ejpam-2691	121	3	g(f	g(f	PROPN
ejpam-2691	121	4	(	(	PUNCT
ejpam-2691	121	5	xrn	xrn	PROPN
ejpam-2691	121	6	,	,	PUNCT
ejpam-2691	121	7	x	x	PROPN
ejpam-2691	121	8	1	1	NUM
ejpam-2691	121	9	n	n	CCONJ
ejpam-2691	121	10	,	,	PUNCT
ejpam-2691	121	11	.	.	PUNCT
ejpam-2691	121	12	.	.	PUNCT
ejpam-2691	121	13	.	.	PUNCT
ejpam-2691	122	1	,	,	PUNCT
ejpam-2691	122	2	x	x	X
ejpam-2691	122	3	r−1	r−1	PROPN
ejpam-2691	122	4	n	n	ADV
ejpam-2691	122	5	)	)	PUNCT
ejpam-2691	122	6	=	=	SYM
ejpam-2691	122	7	g(xr	g(xr	PROPN
ejpam-2691	122	8	)	)	PUNCT
ejpam-2691	122	9	and	and	CCONJ
ejpam-2691	122	10	lim	lim	PROPN
ejpam-2691	122	11	n→+∞	n→+∞	VERB
ejpam-2691	122	12	f	f	PROPN
ejpam-2691	122	13	(	(	PUNCT
ejpam-2691	122	14	g(xrn	g(xrn	NOUN
ejpam-2691	122	15	)	)	PUNCT
ejpam-2691	122	16	,	,	PUNCT
ejpam-2691	122	17	g(x1n	g(x1n	PROPN
ejpam-2691	122	18	)	)	PUNCT
ejpam-2691	122	19	,	,	PUNCT
ejpam-2691	122	20	.	.	PUNCT
ejpam-2691	122	21	.	.	PUNCT
ejpam-2691	122	22	.	.	PUNCT
ejpam-2691	123	1	,	,	PUNCT
ejpam-2691	123	2	g(xr−1n	g(xr−1n	NOUN
ejpam-2691	123	3	)	)	PUNCT
ejpam-2691	123	4	)	)	PUNCT
ejpam-2691	124	1	=	=	SYM
ejpam-2691	124	2	f	f	PROPN
ejpam-2691	124	3	(	(	PUNCT
ejpam-2691	124	4	xr	xr	PROPN
ejpam-2691	124	5	,	,	PUNCT
ejpam-2691	124	6	x1	x1	PROPN
ejpam-2691	124	7	,	,	PUNCT
ejpam-2691	124	8	.	.	PUNCT
ejpam-2691	124	9	.	.	PUNCT
ejpam-2691	124	10	.	.	PUNCT
ejpam-2691	125	1	,	,	PUNCT
ejpam-2691	125	2	xr−1	xr−1	PROPN
ejpam-2691	125	3	)	)	PUNCT
ejpam-2691	125	4	.	.	PUNCT
ejpam-2691	126	1	whenever	whenever	SCONJ
ejpam-2691	126	2	{	{	PUNCT
ejpam-2691	126	3	x1n	x1n	NOUN
ejpam-2691	126	4	}	}	PUNCT
ejpam-2691	126	5	,	,	PUNCT
ejpam-2691	126	6	{	{	PUNCT
ejpam-2691	126	7	x2n	x2n	NOUN
ejpam-2691	126	8	}	}	PUNCT
ejpam-2691	126	9	,	,	PUNCT
ejpam-2691	126	10	.	.	PUNCT
ejpam-2691	126	11	.	.	PUNCT
ejpam-2691	126	12	.	.	PUNCT
ejpam-2691	127	1	,	,	PUNCT
ejpam-2691	127	2	{	{	PUNCT
ejpam-2691	127	3	xrn	xrn	ADV
ejpam-2691	127	4	}	}	PUNCT
ejpam-2691	127	5	are	be	AUX
ejpam-2691	127	6	sequences	sequence	NOUN
ejpam-2691	127	7	in	in	ADP
ejpam-2691	127	8	x	x	NOUN
ejpam-2691	127	9	,	,	PUNCT
ejpam-2691	127	10	such	such	ADJ
ejpam-2691	127	11	that	that	PROPN
ejpam-2691	127	12	lim	lim	PROPN
ejpam-2691	127	13	n→+∞	n→+∞	PROPN
ejpam-2691	127	14	f	f	PROPN
ejpam-2691	127	15	(	(	PUNCT
ejpam-2691	127	16	x1n	x1n	PROPN
ejpam-2691	127	17	,	,	PUNCT
ejpam-2691	127	18	x	x	PROPN
ejpam-2691	127	19	2	2	NUM
ejpam-2691	127	20	n	n	NUM
ejpam-2691	127	21	,	,	PUNCT
ejpam-2691	127	22	.	.	PUNCT
ejpam-2691	127	23	.	.	PUNCT
ejpam-2691	128	1	.	.	PUNCT
ejpam-2691	129	1	,	,	PUNCT
ejpam-2691	129	2	x	x	PUNCT
ejpam-2691	129	3	r	r	NOUN
ejpam-2691	129	4	n	n	CCONJ
ejpam-2691	129	5	)	)	PUNCT
ejpam-2691	130	1	=	=	VERB
ejpam-2691	130	2	lim	lim	PROPN
ejpam-2691	130	3	n→+∞	n→+∞	VERB
ejpam-2691	130	4	g(x1n	g(x1n	PROPN
ejpam-2691	130	5	)	)	PUNCT
ejpam-2691	130	6	=	=	SYM
ejpam-2691	131	1	x1	x1	PROPN
ejpam-2691	131	2	,	,	PUNCT
ejpam-2691	131	3	lim	lim	PROPN
ejpam-2691	131	4	n→+∞	n→+∞	VERB
ejpam-2691	131	5	f	f	X
ejpam-2691	131	6	(	(	PUNCT
ejpam-2691	131	7	x2n	x2n	ADV
ejpam-2691	131	8	,	,	PUNCT
ejpam-2691	131	9	x	x	PROPN
ejpam-2691	131	10	3	3	NUM
ejpam-2691	131	11	n	n	NUM
ejpam-2691	131	12	,	,	PUNCT
ejpam-2691	131	13	.	.	PUNCT
ejpam-2691	131	14	.	.	PUNCT
ejpam-2691	131	15	.	.	PUNCT
ejpam-2691	132	1	,	,	PUNCT
ejpam-2691	132	2	x	x	PUNCT
ejpam-2691	132	3	r	r	NOUN
ejpam-2691	132	4	n	n	CCONJ
ejpam-2691	132	5	,	,	PUNCT
ejpam-2691	132	6	x	x	PROPN
ejpam-2691	132	7	1	1	NUM
ejpam-2691	132	8	n	n	CCONJ
ejpam-2691	132	9	)	)	PUNCT
ejpam-2691	133	1	=	=	VERB
ejpam-2691	133	2	lim	lim	PROPN
ejpam-2691	133	3	n→+∞	n→+∞	PROPN
ejpam-2691	133	4	g(x2n	g(x2n	PROPN
ejpam-2691	133	5	)	)	PUNCT
ejpam-2691	133	6	=	=	SYM
ejpam-2691	133	7	x2	x2	PROPN
ejpam-2691	133	8	...	...	PUNCT
ejpam-2691	134	1	lim	lim	PROPN
ejpam-2691	134	2	n→+∞	n→+∞	VERB
ejpam-2691	134	3	f	f	X
ejpam-2691	134	4	(	(	PUNCT
ejpam-2691	134	5	xrn	xrn	PROPN
ejpam-2691	134	6	,	,	PUNCT
ejpam-2691	134	7	x	x	PROPN
ejpam-2691	134	8	1	1	NUM
ejpam-2691	134	9	n	n	CCONJ
ejpam-2691	134	10	,	,	PUNCT
ejpam-2691	134	11	.	.	PUNCT
ejpam-2691	134	12	.	.	PUNCT
ejpam-2691	134	13	.	.	PUNCT
ejpam-2691	135	1	,	,	PUNCT
ejpam-2691	135	2	x	x	X
ejpam-2691	135	3	r−1	r−1	PROPN
ejpam-2691	135	4	n	n	ADV
ejpam-2691	135	5	)	)	PUNCT
ejpam-2691	136	1	=	=	SYM
ejpam-2691	136	2	lim	lim	PROPN
ejpam-2691	136	3	n→+∞	n→+∞	PROPN
ejpam-2691	136	4	g(xrn	g(xrn	PROPN
ejpam-2691	136	5	)	)	PUNCT
ejpam-2691	136	6	=	=	SYM
ejpam-2691	136	7	xr	xr	PROPN
ejpam-2691	136	8	,	,	PUNCT
ejpam-2691	136	9	for	for	ADP
ejpam-2691	136	10	some	some	DET
ejpam-2691	136	11	x1	x1	PROPN
ejpam-2691	136	12	,	,	PUNCT
ejpam-2691	136	13	x2	x2	PROPN
ejpam-2691	136	14	,	,	PUNCT
ejpam-2691	136	15	.	.	PUNCT
ejpam-2691	136	16	.	.	PUNCT
ejpam-2691	137	1	.	.	PUNCT
ejpam-2691	138	1	,	,	PUNCT
ejpam-2691	138	2	xr	xr	PROPN
ejpam-2691	138	3	∈	∈	PROPN
ejpam-2691	138	4	x.	x.	NOUN
ejpam-2691	138	5	(	(	PUNCT
ejpam-2691	138	6	ii	ii	NOUN
ejpam-2691	138	7	)	)	PUNCT
ejpam-2691	138	8	weakly	weakly	ADV
ejpam-2691	138	9	reciprocally	reciprocally	ADV
ejpam-2691	138	10	continuous	continuous	ADJ
ejpam-2691	138	11	if	if	PROPN
ejpam-2691	138	12	lim	lim	PROPN
ejpam-2691	138	13	n→+∞	n→+∞	VERB
ejpam-2691	138	14	g(f	g(f	PROPN
ejpam-2691	138	15	(	(	PUNCT
ejpam-2691	138	16	x1n	x1n	PROPN
ejpam-2691	138	17	,	,	PUNCT
ejpam-2691	138	18	x	x	PROPN
ejpam-2691	138	19	2	2	NUM
ejpam-2691	138	20	n	n	NUM
ejpam-2691	138	21	,	,	PUNCT
ejpam-2691	138	22	.	.	PUNCT
ejpam-2691	138	23	.	.	PUNCT
ejpam-2691	138	24	.	.	PUNCT
ejpam-2691	139	1	,	,	PUNCT
ejpam-2691	139	2	x	x	PUNCT
ejpam-2691	139	3	r	r	NOUN
ejpam-2691	139	4	n	n	CCONJ
ejpam-2691	139	5	)	)	PUNCT
ejpam-2691	139	6	=	=	SYM
ejpam-2691	139	7	g(x1	g(x1	NOUN
ejpam-2691	139	8	)	)	PUNCT
ejpam-2691	139	9	or	or	CCONJ
ejpam-2691	139	10	lim	lim	PROPN
ejpam-2691	139	11	n→+∞	n→+∞	VERB
ejpam-2691	139	12	f	f	PROPN
ejpam-2691	139	13	(	(	PUNCT
ejpam-2691	139	14	g(x1n	g(x1n	PROPN
ejpam-2691	139	15	)	)	PUNCT
ejpam-2691	139	16	,	,	PUNCT
ejpam-2691	139	17	g(x2n	g(x2n	PROPN
ejpam-2691	139	18	)	)	PUNCT
ejpam-2691	139	19	,	,	PUNCT
ejpam-2691	139	20	.	.	PUNCT
ejpam-2691	139	21	.	.	PUNCT
ejpam-2691	139	22	.	.	PUNCT
ejpam-2691	140	1	,	,	PUNCT
ejpam-2691	140	2	g(xrn	g(xrn	NOUN
ejpam-2691	140	3	)	)	PUNCT
ejpam-2691	140	4	)	)	PUNCT
ejpam-2691	141	1	=	=	SYM
ejpam-2691	141	2	f	f	X
ejpam-2691	141	3	(	(	PUNCT
ejpam-2691	141	4	x1	x1	PROPN
ejpam-2691	141	5	,	,	PUNCT
ejpam-2691	141	6	x2	x2	PROPN
ejpam-2691	141	7	,	,	PUNCT
ejpam-2691	141	8	.	.	PUNCT
ejpam-2691	141	9	.	.	PUNCT
ejpam-2691	141	10	.	.	PUNCT
ejpam-2691	141	11	,	,	PUNCT
ejpam-2691	141	12	xr	xr	PROPN
ejpam-2691	141	13	)	)	PUNCT
ejpam-2691	141	14	;	;	PUNCT
ejpam-2691	141	15	lim	lim	PROPN
ejpam-2691	141	16	n→+∞	n→+∞	VERB
ejpam-2691	141	17	g(f	g(f	PROPN
ejpam-2691	141	18	(	(	PUNCT
ejpam-2691	141	19	x2n	x2n	ADV
ejpam-2691	141	20	,	,	PUNCT
ejpam-2691	141	21	x	x	PROPN
ejpam-2691	141	22	3	3	NUM
ejpam-2691	141	23	n	n	NUM
ejpam-2691	141	24	,	,	PUNCT
ejpam-2691	141	25	.	.	PUNCT
ejpam-2691	141	26	.	.	PUNCT
ejpam-2691	141	27	.	.	PUNCT
ejpam-2691	142	1	,	,	PUNCT
ejpam-2691	142	2	x	x	PUNCT
ejpam-2691	142	3	r	r	NOUN
ejpam-2691	142	4	n	n	CCONJ
ejpam-2691	142	5	,	,	PUNCT
ejpam-2691	142	6	x	x	PROPN
ejpam-2691	142	7	1	1	NUM
ejpam-2691	142	8	n	n	CCONJ
ejpam-2691	142	9	)	)	PUNCT
ejpam-2691	142	10	=	=	SYM
ejpam-2691	142	11	g(x2	g(x2	NOUN
ejpam-2691	142	12	)	)	PUNCT
ejpam-2691	142	13	or	or	CCONJ
ejpam-2691	142	14	lim	lim	PROPN
ejpam-2691	142	15	n→+∞	n→+∞	VERB
ejpam-2691	142	16	f	f	PROPN
ejpam-2691	142	17	(	(	PUNCT
ejpam-2691	142	18	g(x2n	g(x2n	PROPN
ejpam-2691	142	19	)	)	PUNCT
ejpam-2691	142	20	,	,	PUNCT
ejpam-2691	142	21	g(x3n	g(x3n	PROPN
ejpam-2691	142	22	)	)	PUNCT
ejpam-2691	142	23	,	,	PUNCT
ejpam-2691	142	24	.	.	PUNCT
ejpam-2691	142	25	.	.	PUNCT
ejpam-2691	142	26	.	.	PUNCT
ejpam-2691	143	1	,	,	PUNCT
ejpam-2691	143	2	g(xrn	g(xrn	NOUN
ejpam-2691	143	3	)	)	PUNCT
ejpam-2691	143	4	,	,	PUNCT
ejpam-2691	143	5	g(x1n	g(x1n	NOUN
ejpam-2691	143	6	)	)	PUNCT
ejpam-2691	143	7	)	)	PUNCT
ejpam-2691	144	1	=	=	SYM
ejpam-2691	144	2	f	f	X
ejpam-2691	144	3	(	(	PUNCT
ejpam-2691	144	4	x2	x2	PROPN
ejpam-2691	144	5	,	,	PUNCT
ejpam-2691	144	6	x3	x3	ADJ
ejpam-2691	144	7	,	,	PUNCT
ejpam-2691	144	8	.	.	PUNCT
ejpam-2691	144	9	.	.	PUNCT
ejpam-2691	144	10	.	.	PUNCT
ejpam-2691	144	11	,	,	PUNCT
ejpam-2691	144	12	xr	xr	PROPN
ejpam-2691	144	13	,	,	PUNCT
ejpam-2691	144	14	x1	x1	PROPN
ejpam-2691	144	15	)	)	PUNCT
ejpam-2691	144	16	;	;	PUNCT
ejpam-2691	144	17	...	...	PUNCT
ejpam-2691	145	1	lim	lim	PROPN
ejpam-2691	145	2	n→+∞	n→+∞	VERB
ejpam-2691	145	3	g(f	g(f	PROPN
ejpam-2691	145	4	(	(	PUNCT
ejpam-2691	145	5	xrn	xrn	PROPN
ejpam-2691	145	6	,	,	PUNCT
ejpam-2691	145	7	x	x	PROPN
ejpam-2691	145	8	1	1	NUM
ejpam-2691	145	9	n	n	CCONJ
ejpam-2691	145	10	,	,	PUNCT
ejpam-2691	145	11	.	.	PUNCT
ejpam-2691	145	12	.	.	PUNCT
ejpam-2691	145	13	.	.	PUNCT
ejpam-2691	146	1	,	,	PUNCT
ejpam-2691	146	2	x	x	X
ejpam-2691	146	3	r−1	r−1	PROPN
ejpam-2691	146	4	n	n	ADV
ejpam-2691	146	5	)	)	PUNCT
ejpam-2691	146	6	=	=	SYM
ejpam-2691	146	7	g(xr	g(xr	PROPN
ejpam-2691	146	8	)	)	PUNCT
ejpam-2691	146	9	or	or	CCONJ
ejpam-2691	146	10	lim	lim	PROPN
ejpam-2691	146	11	n→+∞	n→+∞	VERB
ejpam-2691	146	12	f	f	PROPN
ejpam-2691	146	13	(	(	PUNCT
ejpam-2691	146	14	g(xrn	g(xrn	NOUN
ejpam-2691	146	15	)	)	PUNCT
ejpam-2691	146	16	,	,	PUNCT
ejpam-2691	146	17	g(x1n	g(x1n	PROPN
ejpam-2691	146	18	)	)	PUNCT
ejpam-2691	146	19	,	,	PUNCT
ejpam-2691	146	20	.	.	PUNCT
ejpam-2691	146	21	.	.	PUNCT
ejpam-2691	146	22	.	.	PUNCT
ejpam-2691	147	1	,	,	PUNCT
ejpam-2691	147	2	g(xr−1n	g(xr−1n	NOUN
ejpam-2691	147	3	)	)	PUNCT
ejpam-2691	147	4	)	)	PUNCT
ejpam-2691	148	1	=	=	SYM
ejpam-2691	148	2	f	f	PROPN
ejpam-2691	148	3	(	(	PUNCT
ejpam-2691	148	4	xr	xr	PROPN
ejpam-2691	148	5	,	,	PUNCT
ejpam-2691	148	6	x1	x1	PROPN
ejpam-2691	148	7	,	,	PUNCT
ejpam-2691	148	8	.	.	PUNCT
ejpam-2691	148	9	.	.	PUNCT
ejpam-2691	148	10	.	.	PUNCT
ejpam-2691	149	1	,	,	PUNCT
ejpam-2691	149	2	xr−1	xr−1	PROPN
ejpam-2691	149	3	)	)	PUNCT
ejpam-2691	149	4	.	.	PUNCT
ejpam-2691	150	1	(	(	PUNCT
ejpam-2691	150	2	2	2	X
ejpam-2691	150	3	)	)	PUNCT
ejpam-2691	150	4	whenever	whenever	SCONJ
ejpam-2691	150	5	{	{	PUNCT
ejpam-2691	150	6	x1n	x1n	NOUN
ejpam-2691	150	7	}	}	PUNCT
ejpam-2691	150	8	,	,	PUNCT
ejpam-2691	150	9	{	{	PUNCT
ejpam-2691	150	10	x2n	x2n	NOUN
ejpam-2691	150	11	}	}	PUNCT
ejpam-2691	150	12	,	,	PUNCT
ejpam-2691	150	13	.	.	PUNCT
ejpam-2691	150	14	.	.	PUNCT
ejpam-2691	151	1	.	.	PUNCT
ejpam-2691	152	1	,	,	PUNCT
ejpam-2691	152	2	{	{	PUNCT
ejpam-2691	152	3	xrn	xrn	ADV
ejpam-2691	152	4	}	}	PUNCT
ejpam-2691	152	5	are	be	AUX
ejpam-2691	152	6	sequences	sequence	NOUN
ejpam-2691	152	7	in	in	ADP
ejpam-2691	152	8	x	x	NOUN
ejpam-2691	152	9	,	,	PUNCT
ejpam-2691	152	10	such	such	ADJ
ejpam-2691	152	11	that	that	PROPN
ejpam-2691	152	12	lim	lim	PROPN
ejpam-2691	152	13	n→+∞	n→+∞	PROPN
ejpam-2691	152	14	f	f	PROPN
ejpam-2691	152	15	(	(	PUNCT
ejpam-2691	152	16	x1n	x1n	PROPN
ejpam-2691	152	17	,	,	PUNCT
ejpam-2691	152	18	x	x	PROPN
ejpam-2691	152	19	2	2	NUM
ejpam-2691	152	20	n	n	NUM
ejpam-2691	152	21	,	,	PUNCT
ejpam-2691	152	22	.	.	PUNCT
ejpam-2691	152	23	.	.	PUNCT
ejpam-2691	153	1	.	.	PUNCT
ejpam-2691	154	1	,	,	PUNCT
ejpam-2691	154	2	x	x	PUNCT
ejpam-2691	154	3	r	r	NOUN
ejpam-2691	154	4	n	n	CCONJ
ejpam-2691	154	5	)	)	PUNCT
ejpam-2691	155	1	=	=	VERB
ejpam-2691	155	2	lim	lim	PROPN
ejpam-2691	155	3	n→+∞	n→+∞	VERB
ejpam-2691	155	4	g(x1n	g(x1n	PROPN
ejpam-2691	155	5	)	)	PUNCT
ejpam-2691	155	6	=	=	SYM
ejpam-2691	156	1	x1	x1	PROPN
ejpam-2691	156	2	,	,	PUNCT
ejpam-2691	156	3	lim	lim	PROPN
ejpam-2691	156	4	n→+∞	n→+∞	VERB
ejpam-2691	156	5	f	f	X
ejpam-2691	156	6	(	(	PUNCT
ejpam-2691	156	7	x2n	x2n	ADV
ejpam-2691	156	8	,	,	PUNCT
ejpam-2691	156	9	x	x	PROPN
ejpam-2691	156	10	3	3	NUM
ejpam-2691	156	11	n	n	NUM
ejpam-2691	156	12	,	,	PUNCT
ejpam-2691	156	13	.	.	PUNCT
ejpam-2691	156	14	.	.	PUNCT
ejpam-2691	156	15	.	.	PUNCT
ejpam-2691	157	1	,	,	PUNCT
ejpam-2691	157	2	x	x	PUNCT
ejpam-2691	157	3	r	r	NOUN
ejpam-2691	157	4	n	n	CCONJ
ejpam-2691	157	5	,	,	PUNCT
ejpam-2691	157	6	x	x	PROPN
ejpam-2691	157	7	1	1	NUM
ejpam-2691	157	8	n	n	CCONJ
ejpam-2691	157	9	)	)	PUNCT
ejpam-2691	158	1	=	=	VERB
ejpam-2691	158	2	lim	lim	PROPN
ejpam-2691	158	3	n→+∞	n→+∞	PROPN
ejpam-2691	158	4	g(x2n	g(x2n	PROPN
ejpam-2691	158	5	)	)	PUNCT
ejpam-2691	158	6	=	=	SYM
ejpam-2691	158	7	x2	x2	PROPN
ejpam-2691	158	8	...	...	PUNCT
ejpam-2691	159	1	lim	lim	PROPN
ejpam-2691	159	2	n→+∞	n→+∞	VERB
ejpam-2691	159	3	f	f	X
ejpam-2691	159	4	(	(	PUNCT
ejpam-2691	159	5	xrn	xrn	PROPN
ejpam-2691	159	6	,	,	PUNCT
ejpam-2691	159	7	x	x	PROPN
ejpam-2691	159	8	1	1	NUM
ejpam-2691	159	9	n	n	CCONJ
ejpam-2691	159	10	,	,	PUNCT
ejpam-2691	159	11	.	.	PUNCT
ejpam-2691	159	12	.	.	PUNCT
ejpam-2691	159	13	.	.	PUNCT
ejpam-2691	160	1	,	,	PUNCT
ejpam-2691	160	2	x	x	X
ejpam-2691	160	3	r−1	r−1	PROPN
ejpam-2691	160	4	n	n	ADV
ejpam-2691	160	5	)	)	PUNCT
ejpam-2691	161	1	=	=	SYM
ejpam-2691	161	2	lim	lim	PROPN
ejpam-2691	161	3	n→+∞	n→+∞	PROPN
ejpam-2691	161	4	g(xrn	g(xrn	PROPN
ejpam-2691	161	5	)	)	PUNCT
ejpam-2691	161	6	=	=	SYM
ejpam-2691	161	7	xr	xr	PROPN
ejpam-2691	161	8	,	,	PUNCT
ejpam-2691	161	9	for	for	ADP
ejpam-2691	161	10	some	some	DET
ejpam-2691	161	11	x1	x1	PROPN
ejpam-2691	161	12	,	,	PUNCT
ejpam-2691	161	13	x2	x2	PROPN
ejpam-2691	161	14	,	,	PUNCT
ejpam-2691	161	15	.	.	PUNCT
ejpam-2691	161	16	.	.	PUNCT
ejpam-2691	162	1	.	.	PUNCT
ejpam-2691	163	1	,	,	PUNCT
ejpam-2691	163	2	xr	xr	PROPN
ejpam-2691	163	3	∈	∈	PROPN
ejpam-2691	163	4	x.	x.	PROPN
ejpam-2691	163	5	m.	m.	PROPN
ejpam-2691	163	6	grewal	grewal	PROPN
ejpam-2691	163	7	,	,	PUNCT
ejpam-2691	163	8	r.	r.	PROPN
ejpam-2691	163	9	kumar	kumar	PROPN
ejpam-2691	163	10	,	,	PUNCT
ejpam-2691	163	11	a.	a.	PROPN
ejpam-2691	163	12	kumar	kumar	PROPN
ejpam-2691	163	13	/	/	SYM
ejpam-2691	163	14	eur	eur	PROPN
ejpam-2691	163	15	.	.	PUNCT
ejpam-2691	164	1	j.	j.	PROPN
ejpam-2691	164	2	pure	pure	PROPN
ejpam-2691	164	3	appl	appl	PROPN
ejpam-2691	164	4	.	.	PROPN
ejpam-2691	164	5	math	math	PROPN
ejpam-2691	164	6	,	,	PUNCT
ejpam-2691	164	7	10	10	NUM
ejpam-2691	164	8	(	(	PUNCT
ejpam-2691	164	9	2	2	NUM
ejpam-2691	164	10	)	)	PUNCT
ejpam-2691	164	11	(	(	PUNCT
ejpam-2691	164	12	2017	2017	NUM
ejpam-2691	164	13	)	)	PUNCT
ejpam-2691	164	14	,	,	PUNCT
ejpam-2691	164	15	295	295	NUM
ejpam-2691	164	16	-	-	SYM
ejpam-2691	164	17	311	311	NUM
ejpam-2691	164	18	299	299	NUM
ejpam-2691	164	19	remark	remark	NOUN
ejpam-2691	164	20	1	1	NUM
ejpam-2691	164	21	.	.	PUNCT
ejpam-2691	165	1	every	every	DET
ejpam-2691	165	2	pair	pair	NOUN
ejpam-2691	165	3	of	of	ADP
ejpam-2691	165	4	reciprocally	reciprocally	ADV
ejpam-2691	165	5	continuous	continuous	ADJ
ejpam-2691	165	6	mapping	mapping	NOUN
ejpam-2691	165	7	(	(	PUNCT
ejpam-2691	165	8	f	f	X
ejpam-2691	165	9	,	,	PUNCT
ejpam-2691	165	10	g	g	NOUN
ejpam-2691	165	11	)	)	PUNCT
ejpam-2691	165	12	is	be	AUX
ejpam-2691	165	13	weakly	weakly	ADV
ejpam-2691	165	14	reciprocally	reciprocally	ADV
ejpam-2691	165	15	continuous	continuous	ADJ
ejpam-2691	165	16	but	but	CCONJ
ejpam-2691	165	17	not	not	PART
ejpam-2691	165	18	conversely	conversely	ADV
ejpam-2691	165	19	.	.	PUNCT
ejpam-2691	166	1	definition	definition	NOUN
ejpam-2691	166	2	6	6	NUM
ejpam-2691	166	3	.	.	PUNCT
ejpam-2691	167	1	let	let	AUX
ejpam-2691	167	2	(	(	PUNCT
ejpam-2691	167	3	x	x	NOUN
ejpam-2691	167	4	,	,	PUNCT
ejpam-2691	167	5	d	d	PROPN
ejpam-2691	167	6	,	,	PUNCT
ejpam-2691	167	7	�	�	PROPN
ejpam-2691	167	8	)	)	PUNCT
ejpam-2691	167	9	be	be	VERB
ejpam-2691	167	10	an	an	DET
ejpam-2691	167	11	ordered	ordered	ADJ
ejpam-2691	167	12	metric	metric	ADJ
ejpam-2691	167	13	space	space	NOUN
ejpam-2691	167	14	.	.	PUNCT
ejpam-2691	168	1	we	we	PRON
ejpam-2691	168	2	say	say	VERB
ejpam-2691	168	3	that	that	SCONJ
ejpam-2691	168	4	x	x	PRON
ejpam-2691	168	5	is	be	AUX
ejpam-2691	168	6	regular	regular	ADJ
ejpam-2691	168	7	if	if	SCONJ
ejpam-2691	168	8	the	the	DET
ejpam-2691	168	9	following	follow	VERB
ejpam-2691	168	10	conditions	condition	NOUN
ejpam-2691	168	11	hold	hold	VERB
ejpam-2691	168	12	:	:	PUNCT
ejpam-2691	168	13	(	(	PUNCT
ejpam-2691	168	14	i	i	NOUN
ejpam-2691	168	15	)	)	PUNCT
ejpam-2691	168	16	if	if	SCONJ
ejpam-2691	168	17	a	a	DET
ejpam-2691	168	18	non	non	ADJ
ejpam-2691	168	19	-	-	ADJ
ejpam-2691	168	20	decreasing	decrease	VERB
ejpam-2691	168	21	sequence	sequence	NOUN
ejpam-2691	168	22	{	{	PUNCT
ejpam-2691	168	23	xn	xn	PUNCT
ejpam-2691	168	24	}	}	PUNCT
ejpam-2691	168	25	is	be	AUX
ejpam-2691	168	26	such	such	ADJ
ejpam-2691	168	27	that	that	SCONJ
ejpam-2691	168	28	xn	xn	PUNCT
ejpam-2691	169	1	→	→	SYM
ejpam-2691	169	2	x	x	X
ejpam-2691	169	3	,	,	PUNCT
ejpam-2691	169	4	then	then	ADV
ejpam-2691	169	5	xn	xn	PROPN
ejpam-2691	169	6	�	�	PROPN
ejpam-2691	169	7	x	x	PUNCT
ejpam-2691	169	8	for	for	ADP
ejpam-2691	169	9	all	all	DET
ejpam-2691	169	10	n	n	PRON
ejpam-2691	169	11	≥	≥	NOUN
ejpam-2691	169	12	0	0	NUM
ejpam-2691	169	13	,	,	PUNCT
ejpam-2691	169	14	(	(	PUNCT
ejpam-2691	169	15	ii	ii	NOUN
ejpam-2691	169	16	)	)	PUNCT
ejpam-2691	169	17	if	if	SCONJ
ejpam-2691	169	18	a	a	DET
ejpam-2691	169	19	non	non	ADJ
ejpam-2691	169	20	-	-	ADJ
ejpam-2691	169	21	increasing	increasing	ADJ
ejpam-2691	169	22	sequence	sequence	NOUN
ejpam-2691	169	23	{	{	PUNCT
ejpam-2691	169	24	yn	yn	NOUN
ejpam-2691	169	25	}	}	PUNCT
ejpam-2691	169	26	is	be	AUX
ejpam-2691	169	27	such	such	ADJ
ejpam-2691	169	28	that	that	SCONJ
ejpam-2691	169	29	yn	yn	PROPN
ejpam-2691	169	30	→	→	SYM
ejpam-2691	169	31	y	y	PROPN
ejpam-2691	169	32	,	,	PUNCT
ejpam-2691	169	33	then	then	ADV
ejpam-2691	169	34	yn	yn	PROPN
ejpam-2691	169	35	�	�	PROPN
ejpam-2691	169	36	y	y	PROPN
ejpam-2691	169	37	for	for	ADP
ejpam-2691	169	38	all	all	DET
ejpam-2691	169	39	n	n	PRON
ejpam-2691	169	40	≥	≥	NOUN
ejpam-2691	169	41	0	0	NUM
ejpam-2691	169	42	.	.	PUNCT
ejpam-2691	170	1	definition	definition	NOUN
ejpam-2691	170	2	7	7	NUM
ejpam-2691	170	3	.	.	PUNCT
ejpam-2691	171	1	[	[	X
ejpam-2691	171	2	22	22	NUM
ejpam-2691	171	3	]	]	PUNCT
ejpam-2691	171	4	let	let	AUX
ejpam-2691	171	5	{	{	PUNCT
ejpam-2691	171	6	sn	sn	AUX
ejpam-2691	171	7	}	}	PUNCT
ejpam-2691	171	8	be	be	AUX
ejpam-2691	171	9	a	a	DET
ejpam-2691	171	10	sequence	sequence	NOUN
ejpam-2691	171	11	of	of	ADP
ejpam-2691	171	12	non	non	ADJ
ejpam-2691	171	13	-	-	ADJ
ejpam-2691	171	14	negative	negative	ADJ
ejpam-2691	171	15	real	real	ADJ
ejpam-2691	171	16	numbers	number	NOUN
ejpam-2691	171	17	.	.	PUNCT
ejpam-2691	172	1	we	we	PRON
ejpam-2691	172	2	say	say	VERB
ejpam-2691	172	3	that	that	SCONJ
ejpam-2691	172	4	a	a	DET
ejpam-2691	172	5	series	series	NOUN
ejpam-2691	172	6	∑+∞	∑+∞	PUNCT
ejpam-2691	172	7	n=1	n=1	PROPN
ejpam-2691	172	8	sn	sn	PROPN
ejpam-2691	172	9	is	be	AUX
ejpam-2691	172	10	an	an	DET
ejpam-2691	172	11	α	α	NOUN
ejpam-2691	172	12	-	-	PUNCT
ejpam-2691	172	13	series	series	NOUN
ejpam-2691	172	14	,	,	PUNCT
ejpam-2691	172	15	if	if	SCONJ
ejpam-2691	172	16	there	there	PRON
ejpam-2691	172	17	exist	exist	VERB
ejpam-2691	172	18	0	0	NUM
ejpam-2691	172	19	<	<	X
ejpam-2691	172	20	α	α	X
ejpam-2691	172	21	<	<	X
ejpam-2691	172	22	1	1	NUM
ejpam-2691	172	23	and	and	CCONJ
ejpam-2691	172	24	nα	nα	ADP
ejpam-2691	172	25	∈	∈	NOUN
ejpam-2691	172	26	n	n	NOUN
ejpam-2691	172	27	such	such	ADJ
ejpam-2691	172	28	that	that	SCONJ
ejpam-2691	172	29	∑k	∑k	PROPN
ejpam-2691	172	30	i=1	i=1	X
ejpam-2691	172	31	si	si	NOUN
ejpam-2691	172	32	≤	≤	ADJ
ejpam-2691	172	33	αk	αk	NOUN
ejpam-2691	172	34	for	for	ADP
ejpam-2691	172	35	each	each	DET
ejpam-2691	172	36	k	k	PROPN
ejpam-2691	172	37	≥	≥	PROPN
ejpam-2691	172	38	nα	nα	PROPN
ejpam-2691	172	39	.	.	PROPN
ejpam-2691	172	40	example	example	NOUN
ejpam-2691	173	1	1	1	NUM
ejpam-2691	173	2	.	.	PUNCT
ejpam-2691	174	1	the	the	DET
ejpam-2691	174	2	series	series	NOUN
ejpam-2691	174	3	∑+∞	∑+∞	PUNCT
ejpam-2691	174	4	n=1	n=1	PROPN
ejpam-2691	174	5	1	1	NUM
ejpam-2691	174	6	n2	n2	NOUN
ejpam-2691	174	7	is	be	AUX
ejpam-2691	174	8	an	an	DET
ejpam-2691	174	9	α	α	NOUN
ejpam-2691	174	10	-	-	PUNCT
ejpam-2691	174	11	series	series	NOUN
ejpam-2691	174	12	.	.	PUNCT
ejpam-2691	175	1	remark	remark	PROPN
ejpam-2691	175	2	2	2	NUM
ejpam-2691	175	3	.	.	PUNCT
ejpam-2691	176	1	[	[	X
ejpam-2691	176	2	22	22	NUM
ejpam-2691	176	3	]	]	X
ejpam-2691	176	4	it	it	PRON
ejpam-2691	176	5	is	be	AUX
ejpam-2691	176	6	bring	bring	VERB
ejpam-2691	176	7	here	here	ADV
ejpam-2691	176	8	to	to	PART
ejpam-2691	176	9	notice	notice	VERB
ejpam-2691	176	10	that	that	SCONJ
ejpam-2691	176	11	each	each	DET
ejpam-2691	176	12	convergent	convergent	ADJ
ejpam-2691	176	13	series	series	NOUN
ejpam-2691	176	14	of	of	ADP
ejpam-2691	176	15	non	non	ADJ
ejpam-2691	176	16	-	-	ADJ
ejpam-2691	176	17	negative	negative	ADJ
ejpam-2691	176	18	real	real	ADJ
ejpam-2691	176	19	terms	term	NOUN
ejpam-2691	176	20	is	be	AUX
ejpam-2691	176	21	an	an	DET
ejpam-2691	176	22	α	α	NOUN
ejpam-2691	176	23	-	-	PUNCT
ejpam-2691	176	24	series	series	NOUN
ejpam-2691	176	25	.	.	PUNCT
ejpam-2691	177	1	however	however	ADV
ejpam-2691	177	2	,	,	PUNCT
ejpam-2691	177	3	there	there	PRON
ejpam-2691	177	4	are	be	VERB
ejpam-2691	177	5	also	also	ADV
ejpam-2691	177	6	divergent	divergent	ADJ
ejpam-2691	177	7	series	series	NOUN
ejpam-2691	177	8	that	that	PRON
ejpam-2691	177	9	are	be	AUX
ejpam-2691	177	10	α	α	NOUN
ejpam-2691	177	11	-	-	PUNCT
ejpam-2691	177	12	series	series	NOUN
ejpam-2691	177	13	.	.	PUNCT
ejpam-2691	178	1	as	as	ADP
ejpam-2691	178	2	for	for	ADP
ejpam-2691	178	3	instance	instance	NOUN
ejpam-2691	178	4	;	;	PUNCT
ejpam-2691	178	5	the	the	DET
ejpam-2691	178	6	series	series	NOUN
ejpam-2691	178	7	∑+∞	∑+∞	PUNCT
ejpam-2691	178	8	n=1	n=1	ADP
ejpam-2691	178	9	1	1	NUM
ejpam-2691	178	10	n	n	NOUN
ejpam-2691	178	11	,	,	PUNCT
ejpam-2691	178	12	is	be	AUX
ejpam-2691	178	13	an	an	DET
ejpam-2691	178	14	α	α	NOUN
ejpam-2691	178	15	-	-	PUNCT
ejpam-2691	178	16	series	series	NOUN
ejpam-2691	178	17	.	.	PUNCT
ejpam-2691	179	1	definition	definition	NOUN
ejpam-2691	179	2	8	8	NUM
ejpam-2691	179	3	.	.	PUNCT
ejpam-2691	180	1	let	let	VERB
ejpam-2691	180	2	x	x	PRON
ejpam-2691	180	3	be	be	AUX
ejpam-2691	180	4	a	a	DET
ejpam-2691	180	5	nonempty	nonempty	ADV
ejpam-2691	180	6	set	set	VERB
ejpam-2691	180	7	.	.	PUNCT
ejpam-2691	181	1	an	an	DET
ejpam-2691	181	2	element	element	NOUN
ejpam-2691	181	3	(	(	PUNCT
ejpam-2691	181	4	x1	x1	PROPN
ejpam-2691	181	5	,	,	PUNCT
ejpam-2691	181	6	x2	x2	PROPN
ejpam-2691	181	7	,	,	PUNCT
ejpam-2691	181	8	.	.	PUNCT
ejpam-2691	181	9	.	.	PUNCT
ejpam-2691	181	10	.	.	PUNCT
ejpam-2691	181	11	,	,	PUNCT
ejpam-2691	181	12	xr	xr	PROPN
ejpam-2691	181	13	)	)	PUNCT
ejpam-2691	181	14	∈	∈	PROPN
ejpam-2691	181	15	∏r	∏r	NOUN
ejpam-2691	181	16	λ=1x	λ=1x	NOUN
ejpam-2691	181	17	λ	λ	PROPN
ejpam-2691	181	18	is	be	AUX
ejpam-2691	181	19	called	call	VERB
ejpam-2691	181	20	r	r	NOUN
ejpam-2691	181	21	-	-	PUNCT
ejpam-2691	181	22	tupled	tuple	VERB
ejpam-2691	181	23	fixed	fix	VERB
ejpam-2691	181	24	point	point	NOUN
ejpam-2691	181	25	of	of	ADP
ejpam-2691	181	26	the	the	DET
ejpam-2691	181	27	mapping	mapping	NOUN
ejpam-2691	181	28	f	f	NOUN
ejpam-2691	181	29	:	:	PUNCT
ejpam-2691	181	30	∏r	∏r	X
ejpam-2691	181	31	λ=1x	λ=1x	ADJ
ejpam-2691	181	32	λ	λ	X
ejpam-2691	181	33	→	→	SYM
ejpam-2691	181	34	x	x	PROPN
ejpam-2691	181	35	if	if	PROPN
ejpam-2691	181	36	f	f	X
ejpam-2691	181	37	(	(	PUNCT
ejpam-2691	181	38	x1	x1	PROPN
ejpam-2691	181	39	,	,	PUNCT
ejpam-2691	181	40	x2	x2	PROPN
ejpam-2691	181	41	,	,	PUNCT
ejpam-2691	181	42	.	.	PUNCT
ejpam-2691	181	43	.	.	PUNCT
ejpam-2691	181	44	.	.	PUNCT
ejpam-2691	181	45	,	,	PUNCT
ejpam-2691	181	46	xr	xr	X
ejpam-2691	181	47	)	)	PUNCT
ejpam-2691	181	48	=	=	SYM
ejpam-2691	182	1	x1	x1	PROPN
ejpam-2691	182	2	,	,	PUNCT
ejpam-2691	182	3	f	f	PROPN
ejpam-2691	182	4	(	(	PUNCT
ejpam-2691	182	5	x2	x2	PROPN
ejpam-2691	182	6	,	,	PUNCT
ejpam-2691	182	7	x3	x3	ADJ
ejpam-2691	182	8	,	,	PUNCT
ejpam-2691	182	9	.	.	PUNCT
ejpam-2691	182	10	.	.	PUNCT
ejpam-2691	182	11	.	.	PUNCT
ejpam-2691	183	1	,	,	PUNCT
ejpam-2691	183	2	x1	x1	X
ejpam-2691	183	3	)	)	PUNCT
ejpam-2691	183	4	=	=	SYM
ejpam-2691	183	5	x2	x2	PROPN
ejpam-2691	183	6	,	,	PUNCT
ejpam-2691	183	7	f	f	PROPN
ejpam-2691	183	8	(	(	PUNCT
ejpam-2691	183	9	x3	x3	PROPN
ejpam-2691	183	10	,	,	PUNCT
ejpam-2691	183	11	x4	x4	PROPN
ejpam-2691	183	12	,	,	PUNCT
ejpam-2691	183	13	.	.	PUNCT
ejpam-2691	183	14	.	.	PUNCT
ejpam-2691	183	15	.	.	PUNCT
ejpam-2691	184	1	,	,	PUNCT
ejpam-2691	184	2	x2	x2	X
ejpam-2691	184	3	)	)	PUNCT
ejpam-2691	184	4	=	=	SYM
ejpam-2691	184	5	x3	x3	ADJ
ejpam-2691	184	6	,	,	PUNCT
ejpam-2691	184	7	...	...	PUNCT
ejpam-2691	185	1	f	f	X
ejpam-2691	185	2	(	(	PUNCT
ejpam-2691	185	3	xr	xr	PROPN
ejpam-2691	185	4	,	,	PUNCT
ejpam-2691	185	5	x1	x1	PROPN
ejpam-2691	185	6	,	,	PUNCT
ejpam-2691	185	7	.	.	PUNCT
ejpam-2691	185	8	.	.	PUNCT
ejpam-2691	185	9	.	.	PUNCT
ejpam-2691	186	1	,	,	PUNCT
ejpam-2691	186	2	xr−1	xr−1	PROPN
ejpam-2691	186	3	)	)	PUNCT
ejpam-2691	186	4	=	=	PUNCT
ejpam-2691	187	1	xr	xr	PROPN
ejpam-2691	187	2	.	.	PUNCT
ejpam-2691	188	1	(	(	PUNCT
ejpam-2691	188	2	3	3	X
ejpam-2691	188	3	)	)	PUNCT
ejpam-2691	188	4	example	example	NOUN
ejpam-2691	189	1	2	2	NUM
ejpam-2691	189	2	.	.	X
ejpam-2691	190	1	let	let	AUX
ejpam-2691	190	2	(	(	PUNCT
ejpam-2691	190	3	x	x	NOUN
ejpam-2691	190	4	,	,	PUNCT
ejpam-2691	190	5	d	d	PROPN
ejpam-2691	190	6	,	,	PUNCT
ejpam-2691	190	7	�	�	PROPN
ejpam-2691	190	8	)	)	PUNCT
ejpam-2691	190	9	be	be	VERB
ejpam-2691	190	10	an	an	DET
ejpam-2691	190	11	ordered	ordered	ADJ
ejpam-2691	190	12	metric	metric	ADJ
ejpam-2691	190	13	space	space	NOUN
ejpam-2691	190	14	with	with	ADP
ejpam-2691	190	15	�	�	PROPN
ejpam-2691	190	16	as	as	ADP
ejpam-2691	190	17	natural	natural	ADJ
ejpam-2691	190	18	ordering	ordering	NOUN
ejpam-2691	190	19	and	and	CCONJ
ejpam-2691	190	20	let	let	VERB
ejpam-2691	190	21	f	f	NOUN
ejpam-2691	190	22	:	:	PUNCT
ejpam-2691	190	23	∏r	∏r	X
ejpam-2691	190	24	λ=1x	λ=1x	ADJ
ejpam-2691	190	25	λ	λ	X
ejpam-2691	190	26	→	→	SYM
ejpam-2691	190	27	x	x	PART
ejpam-2691	190	28	be	be	AUX
ejpam-2691	190	29	a	a	DET
ejpam-2691	190	30	mapping	mapping	NOUN
ejpam-2691	190	31	defined	define	VERB
ejpam-2691	190	32	by	by	ADP
ejpam-2691	190	33	f	f	PROPN
ejpam-2691	190	34	(	(	PUNCT
ejpam-2691	190	35	x1	x1	PROPN
ejpam-2691	190	36	,	,	PUNCT
ejpam-2691	190	37	x2	x2	PROPN
ejpam-2691	190	38	,	,	PUNCT
ejpam-2691	190	39	.	.	PUNCT
ejpam-2691	190	40	.	.	PUNCT
ejpam-2691	191	1	.	.	PUNCT
ejpam-2691	192	1	,	,	PUNCT
ejpam-2691	192	2	xr	xr	X
ejpam-2691	192	3	)	)	PUNCT
ejpam-2691	192	4	=	=	PRON
ejpam-2691	192	5	(	(	PUNCT
ejpam-2691	192	6	x1	x1	PROPN
ejpam-2691	192	7	·	·	PUNCT
ejpam-2691	192	8	x2	x2	X
ejpam-2691	192	9	·	·	PUNCT
ejpam-2691	192	10	·	·	PUNCT
ejpam-2691	193	1	·	·	PUNCT
ejpam-2691	193	2	xr)2	xr)2	PROPN
ejpam-2691	193	3	,	,	PUNCT
ejpam-2691	193	4	for	for	ADP
ejpam-2691	193	5	any	any	DET
ejpam-2691	193	6	x1	x1	PROPN
ejpam-2691	193	7	,	,	PUNCT
ejpam-2691	193	8	x2	x2	PROPN
ejpam-2691	193	9	,	,	PUNCT
ejpam-2691	193	10	.	.	PUNCT
ejpam-2691	193	11	.	.	PUNCT
ejpam-2691	194	1	.	.	PUNCT
ejpam-2691	195	1	,	,	PUNCT
ejpam-2691	195	2	xr	xr	PROPN
ejpam-2691	195	3	∈	∈	PROPN
ejpam-2691	195	4	x.	x.	NOUN
ejpam-2691	195	5	then	then	ADV
ejpam-2691	195	6	(	(	PUNCT
ejpam-2691	195	7	0	0	NUM
ejpam-2691	195	8	,	,	PUNCT
ejpam-2691	195	9	0	0	NUM
ejpam-2691	195	10	,	,	PUNCT
ejpam-2691	195	11	.	.	PUNCT
ejpam-2691	195	12	.	.	PUNCT
ejpam-2691	196	1	.	.	PUNCT
ejpam-2691	197	1	,	,	PUNCT
ejpam-2691	197	2	0	0	NUM
ejpam-2691	197	3	)	)	PUNCT
ejpam-2691	197	4	and	and	CCONJ
ejpam-2691	197	5	(	(	PUNCT
ejpam-2691	197	6	1	1	NUM
ejpam-2691	197	7	,	,	PUNCT
ejpam-2691	197	8	1	1	NUM
ejpam-2691	197	9	,	,	PUNCT
ejpam-2691	197	10	.	.	PUNCT
ejpam-2691	197	11	.	.	PUNCT
ejpam-2691	198	1	.	.	PUNCT
ejpam-2691	199	1	,	,	PUNCT
ejpam-2691	199	2	1	1	X
ejpam-2691	199	3	)	)	PUNCT
ejpam-2691	199	4	are	be	AUX
ejpam-2691	199	5	both	both	PRON
ejpam-2691	199	6	r	r	NOUN
ejpam-2691	199	7	-	-	PUNCT
ejpam-2691	199	8	tupled	tuple	VERB
ejpam-2691	199	9	fixed	fix	VERB
ejpam-2691	199	10	points	point	NOUN
ejpam-2691	199	11	of	of	ADP
ejpam-2691	199	12	f	f	PROPN
ejpam-2691	199	13	.	.	PUNCT
ejpam-2691	200	1	definition	definition	NOUN
ejpam-2691	200	2	9	9	NUM
ejpam-2691	200	3	.	.	PUNCT
ejpam-2691	201	1	let	let	VERB
ejpam-2691	201	2	x	x	PRON
ejpam-2691	201	3	be	be	AUX
ejpam-2691	201	4	a	a	DET
ejpam-2691	201	5	nonempty	nonempty	ADV
ejpam-2691	201	6	set	set	VERB
ejpam-2691	201	7	.	.	PUNCT
ejpam-2691	202	1	an	an	DET
ejpam-2691	202	2	element	element	NOUN
ejpam-2691	202	3	(	(	PUNCT
ejpam-2691	202	4	x1	x1	PROPN
ejpam-2691	202	5	,	,	PUNCT
ejpam-2691	202	6	x2	x2	PROPN
ejpam-2691	202	7	,	,	PUNCT
ejpam-2691	202	8	.	.	PUNCT
ejpam-2691	202	9	.	.	PUNCT
ejpam-2691	202	10	.	.	PUNCT
ejpam-2691	202	11	,	,	PUNCT
ejpam-2691	202	12	xr	xr	PROPN
ejpam-2691	202	13	)	)	PUNCT
ejpam-2691	202	14	∈	∈	PROPN
ejpam-2691	202	15	∏r	∏r	NOUN
ejpam-2691	202	16	λ=1x	λ=1x	NOUN
ejpam-2691	202	17	λ	λ	PROPN
ejpam-2691	202	18	is	be	AUX
ejpam-2691	202	19	called	call	VERB
ejpam-2691	202	20	r	r	NOUN
ejpam-2691	202	21	-	-	PUNCT
ejpam-2691	202	22	tupled	tuple	VERB
ejpam-2691	202	23	coincidence	coincidence	NOUN
ejpam-2691	202	24	point	point	NOUN
ejpam-2691	202	25	of	of	ADP
ejpam-2691	202	26	the	the	DET
ejpam-2691	202	27	mappings	mapping	NOUN
ejpam-2691	202	28	f	f	NOUN
ejpam-2691	202	29	:	:	PUNCT
ejpam-2691	202	30	∏r	∏r	X
ejpam-2691	202	31	λ=1x	λ=1x	ADJ
ejpam-2691	202	32	λ	λ	X
ejpam-2691	202	33	→	→	SYM
ejpam-2691	202	34	x	x	X
ejpam-2691	202	35	and	and	CCONJ
ejpam-2691	202	36	g	g	NOUN
ejpam-2691	202	37	:	:	PUNCT
ejpam-2691	202	38	x	x	SYM
ejpam-2691	202	39	→	→	SYM
ejpam-2691	202	40	x	x	PUNCT
ejpam-2691	202	41	if	if	PROPN
ejpam-2691	202	42	f	f	X
ejpam-2691	202	43	(	(	PUNCT
ejpam-2691	202	44	x1	x1	PROPN
ejpam-2691	202	45	,	,	PUNCT
ejpam-2691	202	46	x2	x2	PROPN
ejpam-2691	202	47	,	,	PUNCT
ejpam-2691	202	48	.	.	PUNCT
ejpam-2691	202	49	.	.	PUNCT
ejpam-2691	202	50	.	.	PUNCT
ejpam-2691	202	51	,	,	PUNCT
ejpam-2691	202	52	xr	xr	X
ejpam-2691	202	53	)	)	PUNCT
ejpam-2691	202	54	=	=	SYM
ejpam-2691	202	55	g(x1	g(x1	NOUN
ejpam-2691	202	56	)	)	PUNCT
ejpam-2691	202	57	,	,	PUNCT
ejpam-2691	202	58	f	f	PROPN
ejpam-2691	202	59	(	(	PUNCT
ejpam-2691	202	60	x2	x2	PROPN
ejpam-2691	202	61	,	,	PUNCT
ejpam-2691	202	62	x3	x3	ADJ
ejpam-2691	202	63	,	,	PUNCT
ejpam-2691	202	64	.	.	PUNCT
ejpam-2691	202	65	.	.	PUNCT
ejpam-2691	202	66	.	.	PUNCT
ejpam-2691	202	67	,	,	PUNCT
ejpam-2691	202	68	x1	x1	X
ejpam-2691	202	69	)	)	PUNCT
ejpam-2691	202	70	=	=	SYM
ejpam-2691	202	71	g(x2	g(x2	NOUN
ejpam-2691	202	72	)	)	PUNCT
ejpam-2691	202	73	,	,	PUNCT
ejpam-2691	202	74	f	f	PROPN
ejpam-2691	202	75	(	(	PUNCT
ejpam-2691	202	76	x3	x3	PROPN
ejpam-2691	202	77	,	,	PUNCT
ejpam-2691	202	78	x4	x4	PROPN
ejpam-2691	202	79	,	,	PUNCT
ejpam-2691	202	80	.	.	PUNCT
ejpam-2691	202	81	.	.	PUNCT
ejpam-2691	202	82	.	.	PUNCT
ejpam-2691	202	83	,	,	PUNCT
ejpam-2691	202	84	x2	x2	X
ejpam-2691	202	85	)	)	PUNCT
ejpam-2691	202	86	=	=	SYM
ejpam-2691	202	87	g(x3	g(x3	NOUN
ejpam-2691	202	88	)	)	PUNCT
ejpam-2691	202	89	,	,	PUNCT
ejpam-2691	202	90	...	...	PUNCT
ejpam-2691	203	1	f	f	X
ejpam-2691	203	2	(	(	PUNCT
ejpam-2691	203	3	xr	xr	PROPN
ejpam-2691	203	4	,	,	PUNCT
ejpam-2691	203	5	x1	x1	PROPN
ejpam-2691	203	6	,	,	PUNCT
ejpam-2691	203	7	.	.	PUNCT
ejpam-2691	203	8	.	.	PUNCT
ejpam-2691	203	9	.	.	PUNCT
ejpam-2691	204	1	,	,	PUNCT
ejpam-2691	204	2	xr−1	xr−1	PROPN
ejpam-2691	204	3	)	)	PUNCT
ejpam-2691	204	4	=	=	PUNCT
ejpam-2691	204	5	g(xr	g(xr	PROPN
ejpam-2691	204	6	)	)	PUNCT
ejpam-2691	204	7	.	.	PUNCT
ejpam-2691	205	1	(	(	PUNCT
ejpam-2691	205	2	4	4	X
ejpam-2691	205	3	)	)	PUNCT
ejpam-2691	205	4	example	example	NOUN
ejpam-2691	205	5	3	3	X
ejpam-2691	205	6	.	.	PUNCT
ejpam-2691	206	1	let	let	AUX
ejpam-2691	206	2	(	(	PUNCT
ejpam-2691	206	3	x	x	NOUN
ejpam-2691	206	4	,	,	PUNCT
ejpam-2691	206	5	d	d	PROPN
ejpam-2691	206	6	,	,	PUNCT
ejpam-2691	206	7	�	�	PROPN
ejpam-2691	206	8	)	)	PUNCT
ejpam-2691	206	9	be	be	VERB
ejpam-2691	206	10	an	an	DET
ejpam-2691	206	11	ordered	ordered	ADJ
ejpam-2691	206	12	metric	metric	ADJ
ejpam-2691	206	13	space	space	NOUN
ejpam-2691	206	14	with	with	ADP
ejpam-2691	206	15	�	�	PROPN
ejpam-2691	206	16	as	as	ADP
ejpam-2691	206	17	natural	natural	ADJ
ejpam-2691	206	18	ordering	ordering	NOUN
ejpam-2691	206	19	and	and	CCONJ
ejpam-2691	206	20	let	let	VERB
ejpam-2691	206	21	f	f	NOUN
ejpam-2691	206	22	:	:	PUNCT
ejpam-2691	206	23	∏r	∏r	X
ejpam-2691	206	24	λ=1x	λ=1x	ADJ
ejpam-2691	206	25	λ	λ	X
ejpam-2691	206	26	→	→	SYM
ejpam-2691	206	27	x	x	PART
ejpam-2691	206	28	be	be	AUX
ejpam-2691	206	29	a	a	DET
ejpam-2691	206	30	mapping	mapping	NOUN
ejpam-2691	206	31	defined	define	VERB
ejpam-2691	206	32	by	by	ADP
ejpam-2691	206	33	f	f	PROPN
ejpam-2691	206	34	(	(	PUNCT
ejpam-2691	206	35	x1	x1	PROPN
ejpam-2691	206	36	,	,	PUNCT
ejpam-2691	206	37	x2	x2	PROPN
ejpam-2691	206	38	,	,	PUNCT
ejpam-2691	206	39	.	.	PUNCT
ejpam-2691	206	40	.	.	PUNCT
ejpam-2691	207	1	.	.	PUNCT
ejpam-2691	208	1	,	,	PUNCT
ejpam-2691	208	2	xr	xr	X
ejpam-2691	208	3	)	)	PUNCT
ejpam-2691	208	4	=	=	PUNCT
ejpam-2691	209	1	sin(x1	sin(x1	ADJ
ejpam-2691	209	2	·	·	PUNCT
ejpam-2691	209	3	x2	x2	PROPN
ejpam-2691	209	4	·	·	PUNCT
ejpam-2691	209	5	·	·	PUNCT
ejpam-2691	209	6	·	·	PUNCT
ejpam-2691	209	7	xr	xr	X
ejpam-2691	209	8	)	)	PUNCT
ejpam-2691	209	9	,	,	PUNCT
ejpam-2691	209	10	for	for	ADP
ejpam-2691	209	11	any	any	DET
ejpam-2691	209	12	x1	x1	PROPN
ejpam-2691	209	13	,	,	PUNCT
ejpam-2691	209	14	x2	x2	PROPN
ejpam-2691	209	15	,	,	PUNCT
ejpam-2691	209	16	.	.	PUNCT
ejpam-2691	209	17	.	.	PUNCT
ejpam-2691	209	18	.	.	PUNCT
ejpam-2691	210	1	,	,	PUNCT
ejpam-2691	210	2	xr	xr	PROPN
ejpam-2691	210	3	∈	∈	PROPN
ejpam-2691	210	4	x	x	X
ejpam-2691	210	5	and	and	CCONJ
ejpam-2691	210	6	g	g	NOUN
ejpam-2691	210	7	:	:	PUNCT
ejpam-2691	210	8	x	x	SYM
ejpam-2691	210	9	→	→	PUNCT
ejpam-2691	210	10	x	x	PART
ejpam-2691	210	11	be	be	VERB
ejpam-2691	210	12	mapping	mapping	NOUN
ejpam-2691	210	13	defined	define	VERB
ejpam-2691	210	14	by	by	ADP
ejpam-2691	210	15	g(x	g(x	NOUN
ejpam-2691	210	16	)	)	PUNCT
ejpam-2691	211	1	=	=	SYM
ejpam-2691	211	2	x2	x2	PROPN
ejpam-2691	211	3	.	.	PUNCT
ejpam-2691	212	1	then	then	ADV
ejpam-2691	212	2	(	(	PUNCT
ejpam-2691	212	3	0	0	NUM
ejpam-2691	212	4	,	,	PUNCT
ejpam-2691	212	5	0	0	NUM
ejpam-2691	212	6	,	,	PUNCT
ejpam-2691	212	7	.	.	PUNCT
ejpam-2691	212	8	.	.	PUNCT
ejpam-2691	212	9	.	.	PUNCT
ejpam-2691	213	1	,	,	PUNCT
ejpam-2691	213	2	0	0	X
ejpam-2691	213	3	)	)	PUNCT
ejpam-2691	213	4	is	be	AUX
ejpam-2691	213	5	r	r	NOUN
ejpam-2691	213	6	-	-	PUNCT
ejpam-2691	213	7	tupled	tuple	VERB
ejpam-2691	213	8	coincidence	coincidence	NOUN
ejpam-2691	213	9	point	point	NOUN
ejpam-2691	213	10	of	of	ADP
ejpam-2691	213	11	f	f	PROPN
ejpam-2691	213	12	and	and	CCONJ
ejpam-2691	213	13	g.	g.	PROPN
ejpam-2691	213	14	m.	m.	PROPN
ejpam-2691	213	15	grewal	grewal	PROPN
ejpam-2691	213	16	,	,	PUNCT
ejpam-2691	213	17	r.	r.	PROPN
ejpam-2691	213	18	kumar	kumar	PROPN
ejpam-2691	213	19	,	,	PUNCT
ejpam-2691	213	20	a.	a.	PROPN
ejpam-2691	213	21	kumar	kumar	PROPN
ejpam-2691	213	22	/	/	SYM
ejpam-2691	213	23	eur	eur	PROPN
ejpam-2691	213	24	.	.	PUNCT
ejpam-2691	214	1	j.	j.	PROPN
ejpam-2691	214	2	pure	pure	PROPN
ejpam-2691	214	3	appl	appl	PROPN
ejpam-2691	214	4	.	.	PROPN
ejpam-2691	214	5	math	math	PROPN
ejpam-2691	214	6	,	,	PUNCT
ejpam-2691	214	7	10	10	NUM
ejpam-2691	214	8	(	(	PUNCT
ejpam-2691	214	9	2	2	NUM
ejpam-2691	214	10	)	)	PUNCT
ejpam-2691	214	11	(	(	PUNCT
ejpam-2691	214	12	2017	2017	NUM
ejpam-2691	214	13	)	)	PUNCT
ejpam-2691	214	14	,	,	PUNCT
ejpam-2691	214	15	295	295	NUM
ejpam-2691	214	16	-	-	SYM
ejpam-2691	214	17	311	311	NUM
ejpam-2691	214	18	300	300	NUM
ejpam-2691	214	19	proposition	proposition	NOUN
ejpam-2691	214	20	1	1	NUM
ejpam-2691	214	21	.	.	PUNCT
ejpam-2691	215	1	let	let	AUX
ejpam-2691	215	2	(	(	PUNCT
ejpam-2691	215	3	x	x	NOUN
ejpam-2691	215	4	,	,	PUNCT
ejpam-2691	215	5	d	d	PROPN
ejpam-2691	215	6	,	,	PUNCT
ejpam-2691	215	7	�	�	PROPN
ejpam-2691	215	8	)	)	PUNCT
ejpam-2691	215	9	be	be	VERB
ejpam-2691	215	10	an	an	DET
ejpam-2691	215	11	ordered	ordered	ADJ
ejpam-2691	215	12	metric	metric	ADJ
ejpam-2691	215	13	space	space	NOUN
ejpam-2691	215	14	.	.	PUNCT
ejpam-2691	216	1	let	let	VERB
ejpam-2691	216	2	g	g	PRON
ejpam-2691	216	3	be	be	AUX
ejpam-2691	216	4	a	a	DET
ejpam-2691	216	5	self	self	NOUN
ejpam-2691	216	6	-	-	PUNCT
ejpam-2691	216	7	mapping	mapping	NOUN
ejpam-2691	216	8	on	on	ADP
ejpam-2691	216	9	x	x	PUNCT
ejpam-2691	216	10	and	and	CCONJ
ejpam-2691	216	11	{	{	PUNCT
ejpam-2691	216	12	ti}i∈n	ti}i∈n	ADV
ejpam-2691	216	13	be	be	AUX
ejpam-2691	216	14	a	a	DET
ejpam-2691	216	15	sequence	sequence	NOUN
ejpam-2691	216	16	of	of	ADP
ejpam-2691	216	17	mappings	mapping	NOUN
ejpam-2691	216	18	from	from	ADP
ejpam-2691	216	19	∏r	∏r	NOUN
ejpam-2691	216	20	λ=1x	λ=1x	ADJ
ejpam-2691	216	21	λ	λ	PROPN
ejpam-2691	216	22	→	→	SYM
ejpam-2691	216	23	x.	x.	NOUN
ejpam-2691	216	24	then	then	ADV
ejpam-2691	216	25	the	the	DET
ejpam-2691	216	26	pair	pair	NOUN
ejpam-2691	216	27	of	of	ADP
ejpam-2691	216	28	mappings	mapping	NOUN
ejpam-2691	216	29	(	(	PUNCT
ejpam-2691	216	30	ti	ti	NOUN
ejpam-2691	216	31	,	,	PUNCT
ejpam-2691	216	32	g	g	NOUN
ejpam-2691	216	33	)	)	PUNCT
ejpam-2691	216	34	is	be	AUX
ejpam-2691	216	35	said	say	VERB
ejpam-2691	216	36	to	to	PART
ejpam-2691	216	37	have	have	VERB
ejpam-2691	216	38	property	property	NOUN
ejpam-2691	216	39	(	(	PUNCT
ejpam-2691	216	40	a	a	X
ejpam-2691	216	41	)	)	PUNCT
ejpam-2691	216	42	if	if	SCONJ
ejpam-2691	216	43	for	for	ADP
ejpam-2691	216	44	x1	x1	PROPN
ejpam-2691	216	45	,	,	PUNCT
ejpam-2691	216	46	x2	x2	PROPN
ejpam-2691	216	47	,	,	PUNCT
ejpam-2691	216	48	.	.	PUNCT
ejpam-2691	216	49	.	.	PUNCT
ejpam-2691	217	1	.	.	PUNCT
ejpam-2691	218	1	,	,	PUNCT
ejpam-2691	218	2	xr	xr	PROPN
ejpam-2691	218	3	,	,	PUNCT
ejpam-2691	218	4	y1	y1	PROPN
ejpam-2691	218	5	,	,	PUNCT
ejpam-2691	218	6	y2	y2	PROPN
ejpam-2691	218	7	,	,	PUNCT
ejpam-2691	218	8	.	.	PUNCT
ejpam-2691	218	9	.	.	PUNCT
ejpam-2691	219	1	.	.	PUNCT
ejpam-2691	220	1	,	,	PUNCT
ejpam-2691	220	2	yr	yr	PROPN
ejpam-2691	220	3	∈	∈	PROPN
ejpam-2691	220	4	x	x	X
ejpam-2691	220	5	d(ti(x	d(ti(x	PROPN
ejpam-2691	220	6	1	1	NUM
ejpam-2691	220	7	,	,	PUNCT
ejpam-2691	220	8	x2	x2	PROPN
ejpam-2691	220	9	,	,	PUNCT
ejpam-2691	220	10	.	.	PUNCT
ejpam-2691	220	11	.	.	PUNCT
ejpam-2691	220	12	.	.	PUNCT
ejpam-2691	221	1	,	,	PUNCT
ejpam-2691	221	2	xr	xr	PROPN
ejpam-2691	221	3	)	)	PUNCT
ejpam-2691	221	4	,	,	PUNCT
ejpam-2691	221	5	tj(y	tj(y	VERB
ejpam-2691	221	6	1	1	NUM
ejpam-2691	221	7	,	,	PUNCT
ejpam-2691	221	8	y2	y2	INTJ
ejpam-2691	221	9	,	,	PUNCT
ejpam-2691	221	10	.	.	PUNCT
ejpam-2691	221	11	.	.	PUNCT
ejpam-2691	222	1	.	.	PUNCT
ejpam-2691	223	1	,	,	PUNCT
ejpam-2691	223	2	yr	yr	NOUN
ejpam-2691	223	3	)	)	PUNCT
ejpam-2691	223	4	)	)	PUNCT
ejpam-2691	224	1	≤	≤	NOUN
ejpam-2691	225	1	βi	βi	PROPN
ejpam-2691	225	2	,	,	PUNCT
ejpam-2691	225	3	j	j	PROPN
ejpam-2691	226	1	[	[	X
ejpam-2691	226	2	d(g(x1	d(g(x1	PROPN
ejpam-2691	226	3	)	)	PUNCT
ejpam-2691	226	4	,	,	PUNCT
ejpam-2691	226	5	ti(x	ti(x	NOUN
ejpam-2691	226	6	1	1	NUM
ejpam-2691	226	7	,	,	PUNCT
ejpam-2691	226	8	x2	x2	PROPN
ejpam-2691	226	9	,	,	PUNCT
ejpam-2691	226	10	.	.	PUNCT
ejpam-2691	226	11	.	.	PUNCT
ejpam-2691	227	1	.	.	PUNCT
ejpam-2691	228	1	,	,	PUNCT
ejpam-2691	228	2	xr	xr	PROPN
ejpam-2691	228	3	)	)	PUNCT
ejpam-2691	228	4	)	)	PUNCT
ejpam-2691	229	1	+	+	PUNCT
ejpam-2691	229	2	d(g(y1	d(g(y1	NOUN
ejpam-2691	229	3	)	)	PUNCT
ejpam-2691	229	4	,	,	PUNCT
ejpam-2691	229	5	tj(y	tj(y	VERB
ejpam-2691	229	6	1	1	NUM
ejpam-2691	229	7	,	,	PUNCT
ejpam-2691	229	8	y2	y2	INTJ
ejpam-2691	229	9	,	,	PUNCT
ejpam-2691	229	10	.	.	PUNCT
ejpam-2691	229	11	.	.	PUNCT
ejpam-2691	229	12	.	.	PUNCT
ejpam-2691	230	1	,	,	PUNCT
ejpam-2691	230	2	yr	yr	NOUN
ejpam-2691	230	3	)	)	PUNCT
ejpam-2691	230	4	)	)	PUNCT
ejpam-2691	230	5	]	]	PUNCT
ejpam-2691	231	1	+	+	PUNCT
ejpam-2691	231	2	γi	γi	NOUN
ejpam-2691	231	3	,	,	PUNCT
ejpam-2691	231	4	jd(g(y1	jd(g(y1	PROPN
ejpam-2691	231	5	)	)	PUNCT
ejpam-2691	231	6	,	,	PUNCT
ejpam-2691	231	7	g(x1	g(x1	NOUN
ejpam-2691	231	8	)	)	PUNCT
ejpam-2691	231	9	)	)	PUNCT
ejpam-2691	231	10	(	(	PUNCT
ejpam-2691	231	11	5	5	X
ejpam-2691	231	12	)	)	PUNCT
ejpam-2691	231	13	with	with	ADP
ejpam-2691	231	14	g(x1	g(x1	NOUN
ejpam-2691	231	15	)	)	PUNCT
ejpam-2691	231	16	�	�	PROPN
ejpam-2691	231	17	g(y1	g(y1	PROPN
ejpam-2691	231	18	)	)	PUNCT
ejpam-2691	231	19	,	,	PUNCT
ejpam-2691	231	20	g(x2	g(x2	NOUN
ejpam-2691	231	21	)	)	PUNCT
ejpam-2691	231	22	�	�	PROPN
ejpam-2691	231	23	g(y2	g(y2	PROPN
ejpam-2691	231	24	)	)	PUNCT
ejpam-2691	231	25	,	,	PUNCT
ejpam-2691	231	26	g(x3	g(x3	NUM
ejpam-2691	231	27	)	)	PUNCT
ejpam-2691	231	28	�	�	PROPN
ejpam-2691	231	29	g(y3	g(y3	NOUN
ejpam-2691	231	30	)	)	PUNCT
ejpam-2691	231	31	,	,	PUNCT
ejpam-2691	231	32	...	...	PUNCT
ejpam-2691	231	33	g(xr	g(xr	X
ejpam-2691	231	34	)	)	PUNCT
ejpam-2691	231	35	�	�	PROPN
ejpam-2691	231	36	g(yr	g(yr	NUM
ejpam-2691	231	37	)	)	PUNCT
ejpam-2691	231	38	,	,	PUNCT
ejpam-2691	231	39	where	where	SCONJ
ejpam-2691	231	40	0	0	NUM
ejpam-2691	231	41	≤	≤	NOUN
ejpam-2691	231	42	βi	βi	PROPN
ejpam-2691	231	43	,	,	PUNCT
ejpam-2691	231	44	j	j	PROPN
ejpam-2691	231	45	,	,	PUNCT
ejpam-2691	231	46	γi	γi	PROPN
ejpam-2691	231	47	,	,	PUNCT
ejpam-2691	231	48	j	j	PROPN
ejpam-2691	231	49	<	<	X
ejpam-2691	231	50	1	1	NUM
ejpam-2691	231	51	for	for	ADP
ejpam-2691	231	52	i	i	PRON
ejpam-2691	231	53	,	,	PUNCT
ejpam-2691	231	54	j	j	PROPN
ejpam-2691	231	55	∈	∈	PROPN
ejpam-2691	231	56	n	n	PROPN
ejpam-2691	231	57	and	and	CCONJ
ejpam-2691	231	58	lim	lim	PROPN
ejpam-2691	231	59	n→+∞	n→+∞	VERB
ejpam-2691	231	60	supβi	supβi	PROPN
ejpam-2691	231	61	,	,	PUNCT
ejpam-2691	231	62	n	n	CCONJ
ejpam-2691	231	63	<	<	X
ejpam-2691	231	64	1	1	NUM
ejpam-2691	231	65	.	.	PUNCT
ejpam-2691	231	66	proposition	proposition	NOUN
ejpam-2691	231	67	2	2	NUM
ejpam-2691	231	68	.	.	PUNCT
ejpam-2691	232	1	let	let	VERB
ejpam-2691	232	2	(	(	PUNCT
ejpam-2691	232	3	x	x	NOUN
ejpam-2691	232	4	,	,	PUNCT
ejpam-2691	232	5	�	�	PROPN
ejpam-2691	232	6	)	)	PUNCT
ejpam-2691	232	7	be	be	VERB
ejpam-2691	232	8	a	a	DET
ejpam-2691	232	9	partially	partially	ADV
ejpam-2691	232	10	ordered	order	VERB
ejpam-2691	232	11	set	set	NOUN
ejpam-2691	232	12	and	and	CCONJ
ejpam-2691	232	13	{	{	PUNCT
ejpam-2691	232	14	ti}i∈n	ti}i∈n	ADV
ejpam-2691	232	15	be	be	AUX
ejpam-2691	232	16	a	a	DET
ejpam-2691	232	17	sequence	sequence	NOUN
ejpam-2691	232	18	of	of	ADP
ejpam-2691	232	19	mappings	mapping	NOUN
ejpam-2691	232	20	from	from	ADP
ejpam-2691	232	21	∏r	∏r	NOUN
ejpam-2691	232	22	λ=1x	λ=1x	ADJ
ejpam-2691	232	23	λ	λ	PROPN
ejpam-2691	232	24	→	→	SYM
ejpam-2691	232	25	x.	x.	NOUN
ejpam-2691	232	26	then	then	ADV
ejpam-2691	232	27	{	{	PUNCT
ejpam-2691	232	28	ti}i∈n	ti}i∈n	ADV
ejpam-2691	232	29	is	be	AUX
ejpam-2691	232	30	said	say	VERB
ejpam-2691	232	31	to	to	PART
ejpam-2691	232	32	have	have	VERB
ejpam-2691	232	33	property	property	NOUN
ejpam-2691	232	34	(	(	PUNCT
ejpam-2691	232	35	b	b	NOUN
ejpam-2691	232	36	)	)	PUNCT
ejpam-2691	232	37	if	if	SCONJ
ejpam-2691	232	38	for	for	ADP
ejpam-2691	232	39	x1	x1	PROPN
ejpam-2691	232	40	,	,	PUNCT
ejpam-2691	232	41	x2	x2	PROPN
ejpam-2691	232	42	,	,	PUNCT
ejpam-2691	232	43	.	.	PUNCT
ejpam-2691	232	44	.	.	PUNCT
ejpam-2691	233	1	.	.	PUNCT
ejpam-2691	234	1	,	,	PUNCT
ejpam-2691	234	2	xr	xr	PROPN
ejpam-2691	234	3	,	,	PUNCT
ejpam-2691	234	4	y1	y1	PROPN
ejpam-2691	234	5	,	,	PUNCT
ejpam-2691	234	6	y2	y2	PROPN
ejpam-2691	234	7	,	,	PUNCT
ejpam-2691	234	8	.	.	PUNCT
ejpam-2691	234	9	.	.	PUNCT
ejpam-2691	235	1	.	.	PUNCT
ejpam-2691	236	1	,	,	PUNCT
ejpam-2691	236	2	yr	yr	PROPN
ejpam-2691	236	3	∈	∈	PROPN
ejpam-2691	236	4	x	x	X
ejpam-2691	236	5	ti(x	ti(x	X
ejpam-2691	236	6	1	1	NUM
ejpam-2691	236	7	,	,	PUNCT
ejpam-2691	236	8	x2	x2	PROPN
ejpam-2691	236	9	,	,	PUNCT
ejpam-2691	236	10	.	.	PUNCT
ejpam-2691	236	11	.	.	PUNCT
ejpam-2691	237	1	.	.	PUNCT
ejpam-2691	238	1	,	,	PUNCT
ejpam-2691	238	2	xr	xr	PROPN
ejpam-2691	238	3	)	)	PUNCT
ejpam-2691	238	4	�	�	PROPN
ejpam-2691	238	5	ti+1(y	ti+1(y	PROPN
ejpam-2691	238	6	1	1	NUM
ejpam-2691	238	7	,	,	PUNCT
ejpam-2691	238	8	y2	y2	INTJ
ejpam-2691	238	9	,	,	PUNCT
ejpam-2691	238	10	.	.	PUNCT
ejpam-2691	238	11	.	.	PUNCT
ejpam-2691	239	1	.	.	PUNCT
ejpam-2691	240	1	,	,	PUNCT
ejpam-2691	240	2	yr	yr	NOUN
ejpam-2691	240	3	)	)	PUNCT
ejpam-2691	240	4	,	,	PUNCT
ejpam-2691	240	5	ti+1(y	ti+1(y	PROPN
ejpam-2691	240	6	2	2	NUM
ejpam-2691	240	7	,	,	PUNCT
ejpam-2691	240	8	y3	y3	NOUN
ejpam-2691	240	9	,	,	PUNCT
ejpam-2691	240	10	.	.	PUNCT
ejpam-2691	240	11	.	.	PUNCT
ejpam-2691	240	12	.	.	PUNCT
ejpam-2691	241	1	,	,	PUNCT
ejpam-2691	241	2	yr	yr	NOUN
ejpam-2691	241	3	,	,	PUNCT
ejpam-2691	241	4	y1	y1	ADJ
ejpam-2691	241	5	)	)	PUNCT
ejpam-2691	241	6	�	�	PROPN
ejpam-2691	241	7	ti(x2	ti(x2	PROPN
ejpam-2691	241	8	,	,	PUNCT
ejpam-2691	241	9	x3	x3	ADJ
ejpam-2691	241	10	,	,	PUNCT
ejpam-2691	241	11	.	.	PUNCT
ejpam-2691	241	12	.	.	PUNCT
ejpam-2691	241	13	.	.	PUNCT
ejpam-2691	242	1	,	,	PUNCT
ejpam-2691	242	2	xr	xr	PROPN
ejpam-2691	242	3	,	,	PUNCT
ejpam-2691	242	4	x1	x1	PROPN
ejpam-2691	242	5	)	)	PUNCT
ejpam-2691	242	6	,	,	PUNCT
ejpam-2691	242	7	...	...	PUNCT
ejpam-2691	243	1	ti+1(x	ti+1(x	NOUN
ejpam-2691	243	2	r	r	NOUN
ejpam-2691	243	3	,	,	PUNCT
ejpam-2691	243	4	x1	x1	PROPN
ejpam-2691	243	5	,	,	PUNCT
ejpam-2691	243	6	x2	x2	PROPN
ejpam-2691	243	7	·	·	PUNCT
ejpam-2691	243	8	·	·	PUNCT
ejpam-2691	243	9	·	·	PUNCT
ejpam-2691	243	10	,	,	PUNCT
ejpam-2691	243	11	xr−1	xr−1	PROPN
ejpam-2691	243	12	)	)	PUNCT
ejpam-2691	243	13	�	�	PROPN
ejpam-2691	244	1	ti(yr	ti(yr	PROPN
ejpam-2691	244	2	,	,	PUNCT
ejpam-2691	244	3	y1	y1	NOUN
ejpam-2691	244	4	,	,	PUNCT
ejpam-2691	244	5	y2	y2	PROPN
ejpam-2691	244	6	,	,	PUNCT
ejpam-2691	244	7	.	.	PUNCT
ejpam-2691	244	8	.	.	PUNCT
ejpam-2691	244	9	.	.	PUNCT
ejpam-2691	245	1	,	,	PUNCT
ejpam-2691	245	2	yr−1	yr−1	PROPN
ejpam-2691	245	3	)	)	PUNCT
ejpam-2691	245	4	.	.	PUNCT
ejpam-2691	246	1	(	(	PUNCT
ejpam-2691	246	2	6	6	NUM
ejpam-2691	246	3	)	)	SYM
ejpam-2691	246	4	3	3	NUM
ejpam-2691	246	5	.	.	X
ejpam-2691	246	6	main	main	ADJ
ejpam-2691	246	7	results	result	NOUN
ejpam-2691	246	8	theorem	theorem	VERB
ejpam-2691	246	9	1	1	NUM
ejpam-2691	246	10	.	.	PUNCT
ejpam-2691	247	1	let	let	AUX
ejpam-2691	247	2	(	(	PUNCT
ejpam-2691	247	3	x	x	NOUN
ejpam-2691	247	4	,	,	PUNCT
ejpam-2691	247	5	d	d	PROPN
ejpam-2691	247	6	,	,	PUNCT
ejpam-2691	247	7	�	�	PROPN
ejpam-2691	247	8	)	)	PUNCT
ejpam-2691	247	9	be	be	VERB
ejpam-2691	247	10	an	an	DET
ejpam-2691	247	11	ordered	ordered	ADJ
ejpam-2691	247	12	metric	metric	ADJ
ejpam-2691	247	13	space	space	NOUN
ejpam-2691	247	14	.	.	PUNCT
ejpam-2691	248	1	let	let	VERB
ejpam-2691	248	2	g	g	PRON
ejpam-2691	248	3	be	be	AUX
ejpam-2691	248	4	a	a	DET
ejpam-2691	248	5	continious	continious	ADJ
ejpam-2691	248	6	self	self	NOUN
ejpam-2691	248	7	-	-	PUNCT
ejpam-2691	248	8	mapping	mapping	NOUN
ejpam-2691	248	9	on	on	ADP
ejpam-2691	248	10	x	x	PUNCT
ejpam-2691	248	11	and	and	CCONJ
ejpam-2691	248	12	{	{	PUNCT
ejpam-2691	248	13	ti}i∈n	ti}i∈n	ADV
ejpam-2691	248	14	be	be	AUX
ejpam-2691	248	15	a	a	DET
ejpam-2691	248	16	sequence	sequence	NOUN
ejpam-2691	248	17	of	of	ADP
ejpam-2691	248	18	mappings	mapping	NOUN
ejpam-2691	248	19	from	from	ADP
ejpam-2691	248	20	∏r	∏r	NOUN
ejpam-2691	248	21	λ=1x	λ=1x	ADJ
ejpam-2691	248	22	λ	λ	PROPN
ejpam-2691	248	23	→	→	SYM
ejpam-2691	248	24	x	x	SYM
ejpam-2691	248	25	such	such	ADJ
ejpam-2691	248	26	that	that	SCONJ
ejpam-2691	248	27	i	i	NOUN
ejpam-2691	248	28	)	)	PUNCT
ejpam-2691	248	29	ti	ti	PROPN
ejpam-2691	248	30	(	(	PUNCT
ejpam-2691	248	31	∏r	∏r	NOUN
ejpam-2691	248	32	λ=1x	λ=1x	ADJ
ejpam-2691	248	33	λ	λ	PROPN
ejpam-2691	248	34	)	)	PUNCT
ejpam-2691	248	35	⊆	⊆	NUM
ejpam-2691	248	36	g(x	g(x	NOUN
ejpam-2691	248	37	)	)	PUNCT
ejpam-2691	248	38	,	,	PUNCT
ejpam-2691	248	39	g(x	g(x	NOUN
ejpam-2691	248	40	)	)	PUNCT
ejpam-2691	248	41	is	be	AUX
ejpam-2691	248	42	regular	regular	ADJ
ejpam-2691	248	43	and	and	CCONJ
ejpam-2691	248	44	complete	complete	ADJ
ejpam-2691	248	45	subset	subset	NOUN
ejpam-2691	248	46	of	of	ADP
ejpam-2691	248	47	x	x	PROPN
ejpam-2691	248	48	;	;	PUNCT
ejpam-2691	248	49	ii	ii	NUM
ejpam-2691	248	50	)	)	PUNCT
ejpam-2691	248	51	{	{	PUNCT
ejpam-2691	248	52	ti}i∈n	ti}i∈n	ADV
ejpam-2691	248	53	have	have	VERB
ejpam-2691	248	54	g	g	NOUN
ejpam-2691	248	55	-	-	PUNCT
ejpam-2691	248	56	mixed	mix	VERB
ejpam-2691	248	57	monotone	monotone	ADJ
ejpam-2691	248	58	property	property	NOUN
ejpam-2691	248	59	,	,	PUNCT
ejpam-2691	248	60	the	the	DET
ejpam-2691	248	61	pair	pair	NOUN
ejpam-2691	248	62	{	{	PUNCT
ejpam-2691	248	63	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	248	64	and	and	CCONJ
ejpam-2691	248	65	g	g	NOUN
ejpam-2691	248	66	are	be	AUX
ejpam-2691	248	67	compatible	compatible	ADJ
ejpam-2691	248	68	,	,	PUNCT
ejpam-2691	248	69	weakly	weakly	ADV
ejpam-2691	248	70	reciprocally	reciprocally	ADV
ejpam-2691	248	71	continuous	continuous	ADJ
ejpam-2691	248	72	and	and	CCONJ
ejpam-2691	248	73	satisfy	satisfy	VERB
ejpam-2691	248	74	property	property	NOUN
ejpam-2691	248	75	(	(	PUNCT
ejpam-2691	248	76	a	a	NOUN
ejpam-2691	248	77	)	)	PUNCT
ejpam-2691	248	78	and	and	CCONJ
ejpam-2691	248	79	(	(	PUNCT
ejpam-2691	248	80	b	b	NOUN
ejpam-2691	248	81	)	)	PUNCT
ejpam-2691	248	82	.	.	PUNCT
ejpam-2691	249	1	iii	iii	X
ejpam-2691	249	2	)	)	PUNCT
ejpam-2691	249	3	there	there	PRON
ejpam-2691	249	4	exists	exist	VERB
ejpam-2691	249	5	x10	x10	NOUN
ejpam-2691	249	6	,	,	PUNCT
ejpam-2691	249	7	x	x	NOUN
ejpam-2691	249	8	2	2	NUM
ejpam-2691	249	9	0	0	NUM
ejpam-2691	249	10	,	,	PUNCT
ejpam-2691	249	11	.	.	PUNCT
ejpam-2691	249	12	.	.	PUNCT
ejpam-2691	250	1	.	.	PUNCT
ejpam-2691	251	1	,	,	PUNCT
ejpam-2691	251	2	x	x	PUNCT
ejpam-2691	251	3	r	r	NOUN
ejpam-2691	251	4	0	0	NUM
ejpam-2691	251	5	∈	∈	NOUN
ejpam-2691	251	6	x	x	X
ejpam-2691	251	7	such	such	ADJ
ejpam-2691	251	8	that	that	PROPN
ejpam-2691	251	9	g(x10	g(x10	NOUN
ejpam-2691	251	10	)	)	PUNCT
ejpam-2691	251	11	�	�	PROPN
ejpam-2691	251	12	t0(x10	t0(x10	PROPN
ejpam-2691	251	13	,	,	PUNCT
ejpam-2691	251	14	x20	x20	NOUN
ejpam-2691	251	15	,	,	PUNCT
ejpam-2691	251	16	.	.	PUNCT
ejpam-2691	251	17	.	.	PUNCT
ejpam-2691	251	18	.	.	PUNCT
ejpam-2691	252	1	,	,	PUNCT
ejpam-2691	252	2	xr0	xr0	PROPN
ejpam-2691	252	3	)	)	PUNCT
ejpam-2691	252	4	;	;	PUNCT
ejpam-2691	252	5	g(x20	g(x20	X
ejpam-2691	252	6	)	)	PUNCT
ejpam-2691	252	7	�	�	PROPN
ejpam-2691	252	8	t0(x20	t0(x20	PROPN
ejpam-2691	252	9	,	,	PUNCT
ejpam-2691	252	10	x30	x30	PROPN
ejpam-2691	252	11	,	,	PUNCT
ejpam-2691	252	12	.	.	PUNCT
ejpam-2691	252	13	.	.	PUNCT
ejpam-2691	253	1	.	.	PUNCT
ejpam-2691	254	1	,	,	PUNCT
ejpam-2691	254	2	xr0	xr0	PROPN
ejpam-2691	254	3	,	,	PUNCT
ejpam-2691	254	4	x10	x10	NOUN
ejpam-2691	254	5	)	)	PUNCT
ejpam-2691	254	6	;	;	PUNCT
ejpam-2691	254	7	g(x30	g(x30	X
ejpam-2691	254	8	)	)	PUNCT
ejpam-2691	254	9	�	�	PROPN
ejpam-2691	254	10	t0(x30	t0(x30	PROPN
ejpam-2691	254	11	,	,	PUNCT
ejpam-2691	254	12	x40	x40	PROPN
ejpam-2691	254	13	,	,	PUNCT
ejpam-2691	254	14	.	.	PUNCT
ejpam-2691	254	15	.	.	PUNCT
ejpam-2691	254	16	.	.	PUNCT
ejpam-2691	255	1	,	,	PUNCT
ejpam-2691	255	2	x10	x10	NOUN
ejpam-2691	255	3	,	,	PUNCT
ejpam-2691	255	4	x20	x20	NUM
ejpam-2691	255	5	)	)	PUNCT
ejpam-2691	255	6	;	;	PUNCT
ejpam-2691	255	7	...	...	PUNCT
ejpam-2691	255	8	g(xr0	g(xr0	NOUN
ejpam-2691	255	9	)	)	PUNCT
ejpam-2691	255	10	�	�	PROPN
ejpam-2691	255	11	t0(xr0	t0(xr0	PROPN
ejpam-2691	255	12	,	,	PUNCT
ejpam-2691	255	13	x10	x10	NOUN
ejpam-2691	255	14	,	,	PUNCT
ejpam-2691	255	15	.	.	PUNCT
ejpam-2691	255	16	.	.	PUNCT
ejpam-2691	255	17	.	.	PUNCT
ejpam-2691	256	1	,	,	PUNCT
ejpam-2691	256	2	x	x	X
ejpam-2691	256	3	r−1	r−1	PROPN
ejpam-2691	256	4	0	0	NUM
ejpam-2691	256	5	)	)	PUNCT
ejpam-2691	256	6	.	.	PUNCT
ejpam-2691	257	1	(	(	PUNCT
ejpam-2691	257	2	7	7	NUM
ejpam-2691	257	3	)	)	PUNCT
ejpam-2691	257	4	.	.	PUNCT
ejpam-2691	258	1	m.	m.	PROPN
ejpam-2691	258	2	grewal	grewal	PROPN
ejpam-2691	258	3	,	,	PUNCT
ejpam-2691	258	4	r.	r.	PROPN
ejpam-2691	258	5	kumar	kumar	PROPN
ejpam-2691	258	6	,	,	PUNCT
ejpam-2691	258	7	a.	a.	PROPN
ejpam-2691	258	8	kumar	kumar	PROPN
ejpam-2691	258	9	/	/	SYM
ejpam-2691	258	10	eur	eur	PROPN
ejpam-2691	258	11	.	.	PUNCT
ejpam-2691	259	1	j.	j.	PROPN
ejpam-2691	259	2	pure	pure	PROPN
ejpam-2691	259	3	appl	appl	PROPN
ejpam-2691	259	4	.	.	PROPN
ejpam-2691	259	5	math	math	PROPN
ejpam-2691	259	6	,	,	PUNCT
ejpam-2691	259	7	10	10	NUM
ejpam-2691	259	8	(	(	PUNCT
ejpam-2691	259	9	2	2	NUM
ejpam-2691	259	10	)	)	PUNCT
ejpam-2691	259	11	(	(	PUNCT
ejpam-2691	259	12	2017	2017	NUM
ejpam-2691	259	13	)	)	PUNCT
ejpam-2691	259	14	,	,	PUNCT
ejpam-2691	259	15	295	295	NUM
ejpam-2691	259	16	-	-	SYM
ejpam-2691	259	17	311	311	NUM
ejpam-2691	259	18	301	301	NUM
ejpam-2691	259	19	if	if	SCONJ
ejpam-2691	259	20	∑+∞	∑+∞	VERB
ejpam-2691	259	21	i=1	i=1	PROPN
ejpam-2691	259	22	(	(	PUNCT
ejpam-2691	259	23	βi	βi	PROPN
ejpam-2691	259	24	,	,	PUNCT
ejpam-2691	259	25	i+1+γi	i+1+γi	NOUN
ejpam-2691	259	26	,	,	PUNCT
ejpam-2691	259	27	i+1	i+1	NOUN
ejpam-2691	259	28	1−βi	1−βi	NUM
ejpam-2691	259	29	,	,	PUNCT
ejpam-2691	259	30	i+1	i+1	NUM
ejpam-2691	259	31	)	)	PUNCT
ejpam-2691	259	32	is	be	AUX
ejpam-2691	259	33	an	an	DET
ejpam-2691	259	34	α	α	NOUN
ejpam-2691	259	35	-	-	PUNCT
ejpam-2691	259	36	series	series	NOUN
ejpam-2691	259	37	,	,	PUNCT
ejpam-2691	259	38	then	then	ADV
ejpam-2691	259	39	{	{	PUNCT
ejpam-2691	259	40	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	259	41	and	and	CCONJ
ejpam-2691	259	42	g	g	PROPN
ejpam-2691	259	43	have	have	AUX
ejpam-2691	259	44	a	a	DET
ejpam-2691	259	45	r	r	NOUN
ejpam-2691	259	46	-	-	PUNCT
ejpam-2691	259	47	tupled	tuple	VERB
ejpam-2691	259	48	coincidence	coincidence	NOUN
ejpam-2691	259	49	point	point	NOUN
ejpam-2691	259	50	.	.	PUNCT
ejpam-2691	260	1	proof	proof	NOUN
ejpam-2691	260	2	.	.	PUNCT
ejpam-2691	261	1	let	let	VERB
ejpam-2691	261	2	(	(	PUNCT
ejpam-2691	261	3	x	x	NOUN
ejpam-2691	261	4	,	,	PUNCT
ejpam-2691	261	5	�	�	PROPN
ejpam-2691	261	6	)	)	PUNCT
ejpam-2691	261	7	be	be	VERB
ejpam-2691	261	8	a	a	DET
ejpam-2691	261	9	partially	partially	ADV
ejpam-2691	261	10	ordered	order	VERB
ejpam-2691	261	11	set	set	NOUN
ejpam-2691	261	12	,	,	PUNCT
ejpam-2691	261	13	g	g	PROPN
ejpam-2691	261	14	be	be	AUX
ejpam-2691	261	15	a	a	DET
ejpam-2691	261	16	self	self	NOUN
ejpam-2691	261	17	-	-	PUNCT
ejpam-2691	261	18	mapping	mapping	NOUN
ejpam-2691	261	19	on	on	ADP
ejpam-2691	261	20	x	x	PUNCT
ejpam-2691	261	21	and	and	CCONJ
ejpam-2691	261	22	{	{	PUNCT
ejpam-2691	261	23	ti}i∈n	ti}i∈n	ADV
ejpam-2691	261	24	be	be	AUX
ejpam-2691	261	25	a	a	DET
ejpam-2691	261	26	sequence	sequence	NOUN
ejpam-2691	261	27	of	of	ADP
ejpam-2691	261	28	mappings	mapping	NOUN
ejpam-2691	261	29	from	from	ADP
ejpam-2691	261	30	∏r	∏r	NOUN
ejpam-2691	261	31	λ=1x	λ=1x	ADJ
ejpam-2691	261	32	λ	λ	PROPN
ejpam-2691	261	33	→	→	SYM
ejpam-2691	261	34	x.	x.	NOUN
ejpam-2691	261	35	since	since	SCONJ
ejpam-2691	261	36	ti	ti	X
ejpam-2691	261	37	(	(	PUNCT
ejpam-2691	261	38	∏r	∏r	NOUN
ejpam-2691	261	39	λ=1x	λ=1x	ADJ
ejpam-2691	261	40	λ	λ	PROPN
ejpam-2691	261	41	)	)	PUNCT
ejpam-2691	261	42	⊆	⊆	NUM
ejpam-2691	261	43	g(x	g(x	NOUN
ejpam-2691	261	44	)	)	PUNCT
ejpam-2691	261	45	,	,	PUNCT
ejpam-2691	261	46	one	one	PRON
ejpam-2691	261	47	can	can	AUX
ejpam-2691	261	48	always	always	ADV
ejpam-2691	261	49	have	have	VERB
ejpam-2691	261	50	x11	x11	PROPN
ejpam-2691	261	51	,	,	PUNCT
ejpam-2691	261	52	x	x	NOUN
ejpam-2691	261	53	2	2	NUM
ejpam-2691	261	54	1	1	NUM
ejpam-2691	261	55	,	,	PUNCT
ejpam-2691	261	56	.	.	PUNCT
ejpam-2691	261	57	.	.	PUNCT
ejpam-2691	262	1	.	.	PUNCT
ejpam-2691	263	1	,	,	PUNCT
ejpam-2691	263	2	x	x	X
ejpam-2691	263	3	r	r	NOUN
ejpam-2691	263	4	1	1	NUM
ejpam-2691	263	5	∈	∈	NOUN
ejpam-2691	263	6	x	x	PUNCT
ejpam-2691	263	7	such	such	ADJ
ejpam-2691	263	8	that	that	PROPN
ejpam-2691	263	9	g(x11	g(x11	NOUN
ejpam-2691	263	10	)	)	PUNCT
ejpam-2691	263	11	=	=	PUNCT
ejpam-2691	264	1	t1(x	t1(x	NUM
ejpam-2691	264	2	1	1	NUM
ejpam-2691	264	3	0	0	NUM
ejpam-2691	264	4	,	,	PUNCT
ejpam-2691	264	5	x	x	NOUN
ejpam-2691	264	6	2	2	NUM
ejpam-2691	264	7	0	0	NUM
ejpam-2691	264	8	,	,	PUNCT
ejpam-2691	264	9	.	.	PUNCT
ejpam-2691	264	10	.	.	PUNCT
ejpam-2691	264	11	.	.	PUNCT
ejpam-2691	265	1	,	,	PUNCT
ejpam-2691	265	2	x	x	PUNCT
ejpam-2691	265	3	r	r	NOUN
ejpam-2691	265	4	0	0	NUM
ejpam-2691	265	5	)	)	PUNCT
ejpam-2691	265	6	,	,	PUNCT
ejpam-2691	265	7	g(x21	g(x21	NOUN
ejpam-2691	265	8	)	)	PUNCT
ejpam-2691	266	1	=	=	PUNCT
ejpam-2691	267	1	t1(x	t1(x	NUM
ejpam-2691	267	2	2	2	NUM
ejpam-2691	267	3	0	0	NUM
ejpam-2691	267	4	,	,	PUNCT
ejpam-2691	267	5	x	x	X
ejpam-2691	267	6	3	3	NUM
ejpam-2691	267	7	0	0	NUM
ejpam-2691	267	8	,	,	PUNCT
ejpam-2691	267	9	.	.	PUNCT
ejpam-2691	267	10	.	.	PUNCT
ejpam-2691	267	11	.	.	PUNCT
ejpam-2691	268	1	,	,	PUNCT
ejpam-2691	268	2	x	x	PUNCT
ejpam-2691	268	3	r	r	NOUN
ejpam-2691	268	4	0	0	NUM
ejpam-2691	268	5	,	,	PUNCT
ejpam-2691	268	6	x	x	NOUN
ejpam-2691	268	7	1	1	NUM
ejpam-2691	268	8	0	0	NUM
ejpam-2691	268	9	)	)	PUNCT
ejpam-2691	268	10	,	,	PUNCT
ejpam-2691	268	11	...	...	PUNCT
ejpam-2691	269	1	g(xr1	g(xr1	NOUN
ejpam-2691	269	2	)	)	PUNCT
ejpam-2691	270	1	=	=	PUNCT
ejpam-2691	271	1	t1(x	t1(x	PUNCT
ejpam-2691	271	2	r	r	NOUN
ejpam-2691	271	3	0	0	NUM
ejpam-2691	271	4	,	,	PUNCT
ejpam-2691	271	5	x	x	NOUN
ejpam-2691	271	6	1	1	NUM
ejpam-2691	271	7	0	0	NUM
ejpam-2691	271	8	,	,	PUNCT
ejpam-2691	271	9	.	.	PUNCT
ejpam-2691	271	10	.	.	PUNCT
ejpam-2691	272	1	.	.	PUNCT
ejpam-2691	273	1	,	,	PUNCT
ejpam-2691	273	2	x	x	X
ejpam-2691	273	3	r−1	r−1	PROPN
ejpam-2691	273	4	0	0	NUM
ejpam-2691	273	5	)	)	PUNCT
ejpam-2691	273	6	.	.	PUNCT
ejpam-2691	274	1	again	again	ADV
ejpam-2691	274	2	we	we	PRON
ejpam-2691	274	3	can	can	AUX
ejpam-2691	274	4	choose	choose	VERB
ejpam-2691	274	5	x12	x12	NUM
ejpam-2691	274	6	,	,	PUNCT
ejpam-2691	274	7	x	x	NOUN
ejpam-2691	274	8	2	2	NUM
ejpam-2691	274	9	2	2	NUM
ejpam-2691	274	10	,	,	PUNCT
ejpam-2691	274	11	.	.	PUNCT
ejpam-2691	274	12	.	.	PUNCT
ejpam-2691	274	13	.	.	PUNCT
ejpam-2691	275	1	,	,	PUNCT
ejpam-2691	275	2	x	x	X
ejpam-2691	275	3	r	r	NOUN
ejpam-2691	275	4	2	2	NUM
ejpam-2691	275	5	∈	∈	NOUN
ejpam-2691	275	6	x	x	PUNCT
ejpam-2691	275	7	such	such	ADJ
ejpam-2691	275	8	that	that	PROPN
ejpam-2691	275	9	g(x12	g(x12	NUM
ejpam-2691	275	10	)	)	PUNCT
ejpam-2691	276	1	=	=	PUNCT
ejpam-2691	277	1	t2(x	t2(x	NUM
ejpam-2691	277	2	1	1	NUM
ejpam-2691	277	3	1	1	NUM
ejpam-2691	277	4	,	,	PUNCT
ejpam-2691	277	5	x	x	NOUN
ejpam-2691	277	6	2	2	NUM
ejpam-2691	277	7	1	1	NUM
ejpam-2691	277	8	,	,	PUNCT
ejpam-2691	277	9	.	.	PUNCT
ejpam-2691	277	10	.	.	PUNCT
ejpam-2691	278	1	.	.	PUNCT
ejpam-2691	279	1	,	,	PUNCT
ejpam-2691	279	2	x	x	PUNCT
ejpam-2691	279	3	r	r	NOUN
ejpam-2691	279	4	1	1	NUM
ejpam-2691	279	5	)	)	PUNCT
ejpam-2691	279	6	,	,	PUNCT
ejpam-2691	279	7	g(x22	g(x22	ADJ
ejpam-2691	279	8	)	)	PUNCT
ejpam-2691	279	9	=	=	PUNCT
ejpam-2691	280	1	t2(x	t2(x	NUM
ejpam-2691	280	2	2	2	NUM
ejpam-2691	280	3	1	1	NUM
ejpam-2691	280	4	,	,	PUNCT
ejpam-2691	280	5	x	x	NOUN
ejpam-2691	280	6	3	3	NUM
ejpam-2691	280	7	1	1	NUM
ejpam-2691	280	8	,	,	PUNCT
ejpam-2691	280	9	.	.	PUNCT
ejpam-2691	280	10	.	.	PUNCT
ejpam-2691	281	1	.	.	PUNCT
ejpam-2691	282	1	,	,	PUNCT
ejpam-2691	282	2	x	x	PUNCT
ejpam-2691	282	3	r	r	NOUN
ejpam-2691	282	4	1	1	NUM
ejpam-2691	282	5	,	,	PUNCT
ejpam-2691	282	6	x	x	NOUN
ejpam-2691	282	7	1	1	NUM
ejpam-2691	282	8	1	1	NUM
ejpam-2691	282	9	)	)	PUNCT
ejpam-2691	282	10	,	,	PUNCT
ejpam-2691	282	11	...	...	PUNCT
ejpam-2691	283	1	g(xr2	g(xr2	X
ejpam-2691	283	2	)	)	PUNCT
ejpam-2691	283	3	=	=	PUNCT
ejpam-2691	284	1	t2(x	t2(x	PUNCT
ejpam-2691	284	2	r	r	NOUN
ejpam-2691	284	3	1	1	NUM
ejpam-2691	284	4	,	,	PUNCT
ejpam-2691	284	5	x	x	NOUN
ejpam-2691	284	6	1	1	NUM
ejpam-2691	284	7	1	1	NUM
ejpam-2691	284	8	,	,	PUNCT
ejpam-2691	284	9	·	·	PUNCT
ejpam-2691	284	10	·	·	PUNCT
ejpam-2691	284	11	·	·	PUNCT
ejpam-2691	284	12	,	,	PUNCT
ejpam-2691	284	13	x	x	PUNCT
ejpam-2691	284	14	r−1	r−1	PROPN
ejpam-2691	284	15	1	1	NUM
ejpam-2691	284	16	)	)	PUNCT
ejpam-2691	284	17	.	.	PUNCT
ejpam-2691	285	1	continuing	continue	VERB
ejpam-2691	285	2	in	in	ADP
ejpam-2691	285	3	this	this	DET
ejpam-2691	285	4	way	way	NOUN
ejpam-2691	285	5	,	,	PUNCT
ejpam-2691	285	6	we	we	PRON
ejpam-2691	285	7	can	can	AUX
ejpam-2691	285	8	construct	construct	VERB
ejpam-2691	285	9	the	the	DET
ejpam-2691	285	10	{	{	PUNCT
ejpam-2691	285	11	x1	x1	PROPN
ejpam-2691	285	12	m	m	PROPN
ejpam-2691	285	13	}	}	PUNCT
ejpam-2691	285	14	,	,	PUNCT
ejpam-2691	285	15	{	{	PUNCT
ejpam-2691	285	16	x2	x2	NOUN
ejpam-2691	285	17	m	m	PROPN
ejpam-2691	285	18	}	}	PUNCT
ejpam-2691	285	19	,	,	PUNCT
ejpam-2691	285	20	.	.	PUNCT
ejpam-2691	285	21	.	.	PUNCT
ejpam-2691	286	1	.	.	PUNCT
ejpam-2691	287	1	,	,	PUNCT
ejpam-2691	287	2	{	{	PUNCT
ejpam-2691	287	3	xrm	xrm	NOUN
ejpam-2691	287	4	}	}	PUNCT
ejpam-2691	287	5	sequences	sequence	NOUN
ejpam-2691	287	6	as	as	SCONJ
ejpam-2691	287	7	follows	follow	VERB
ejpam-2691	287	8	:	:	PUNCT
ejpam-2691	287	9			PROPN
ejpam-2691	287	10	g(x1m+1	g(x1m+1	X
ejpam-2691	287	11	)	)	PUNCT
ejpam-2691	288	1	=	=	PUNCT
ejpam-2691	288	2	tn(x1	tn(x1	NUM
ejpam-2691	288	3	m	m	PROPN
ejpam-2691	288	4	,	,	PUNCT
ejpam-2691	288	5	x	x	PROPN
ejpam-2691	288	6	2	2	NUM
ejpam-2691	288	7	m	m	NOUN
ejpam-2691	288	8	,	,	PUNCT
ejpam-2691	288	9	.	.	PUNCT
ejpam-2691	288	10	.	.	PUNCT
ejpam-2691	288	11	.	.	PUNCT
ejpam-2691	289	1	,	,	PUNCT
ejpam-2691	289	2	x	x	PUNCT
ejpam-2691	289	3	r	r	NOUN
ejpam-2691	289	4	m	m	PROPN
ejpam-2691	289	5	)	)	PUNCT
ejpam-2691	289	6	,	,	PUNCT
ejpam-2691	289	7	g(x2m+1	g(x2m+1	X
ejpam-2691	289	8	)	)	PUNCT
ejpam-2691	289	9	=	=	SYM
ejpam-2691	289	10	tn(x2	tn(x2	NOUN
ejpam-2691	289	11	m	m	PROPN
ejpam-2691	289	12	,	,	PUNCT
ejpam-2691	289	13	x	x	PROPN
ejpam-2691	289	14	3	3	NUM
ejpam-2691	289	15	m	m	NOUN
ejpam-2691	289	16	,	,	PUNCT
ejpam-2691	289	17	.	.	PUNCT
ejpam-2691	289	18	.	.	PUNCT
ejpam-2691	289	19	.	.	PUNCT
ejpam-2691	290	1	,	,	PUNCT
ejpam-2691	290	2	x	x	PUNCT
ejpam-2691	290	3	r	r	NOUN
ejpam-2691	290	4	m	m	PROPN
ejpam-2691	290	5	,	,	PUNCT
ejpam-2691	290	6	x	x	PROPN
ejpam-2691	290	7	1	1	NUM
ejpam-2691	290	8	m	m	NOUN
ejpam-2691	290	9	)	)	PUNCT
ejpam-2691	290	10	,	,	PUNCT
ejpam-2691	290	11	...	...	PUNCT
ejpam-2691	291	1	g(xrm+1	g(xrm+1	X
ejpam-2691	291	2	)	)	PUNCT
ejpam-2691	291	3	=	=	SYM
ejpam-2691	292	1	tn(xrm	tn(xrm	PROPN
ejpam-2691	292	2	,	,	PUNCT
ejpam-2691	292	3	x	x	PROPN
ejpam-2691	292	4	1	1	NUM
ejpam-2691	292	5	m	m	NOUN
ejpam-2691	292	6	,	,	PUNCT
ejpam-2691	292	7	.	.	PUNCT
ejpam-2691	292	8	.	.	PUNCT
ejpam-2691	292	9	.	.	PUNCT
ejpam-2691	293	1	,	,	PUNCT
ejpam-2691	294	1	x	x	X
ejpam-2691	294	2	r−1	r−1	PROPN
ejpam-2691	294	3	m	m	PROPN
ejpam-2691	294	4	)	)	PUNCT
ejpam-2691	294	5	.	.	PUNCT
ejpam-2691	295	1	(	(	PUNCT
ejpam-2691	295	2	8)	8)	NUM
ejpam-2691	295	3	now	now	ADV
ejpam-2691	295	4	our	our	PRON
ejpam-2691	295	5	claim	claim	NOUN
ejpam-2691	295	6	is	be	AUX
ejpam-2691	295	7	that	that	SCONJ
ejpam-2691	295	8	for	for	ADP
ejpam-2691	295	9	all	all	DET
ejpam-2691	295	10	m	m	PROPN
ejpam-2691	295	11	≥	≥	NOUN
ejpam-2691	295	12	0	0	NUM
ejpam-2691	295	13	.	.	PUNCT
ejpam-2691	296	1	g(x1	g(x1	NOUN
ejpam-2691	296	2	m	m	NOUN
ejpam-2691	296	3	)	)	PUNCT
ejpam-2691	296	4	�	�	PROPN
ejpam-2691	296	5	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	296	6	)	)	PUNCT
ejpam-2691	297	1	,	,	PUNCT
ejpam-2691	297	2	g(x2	g(x2	NOUN
ejpam-2691	297	3	m	m	NOUN
ejpam-2691	297	4	)	)	PUNCT
ejpam-2691	297	5	�	�	PROPN
ejpam-2691	297	6	g(x2m+1	g(x2m+1	NOUN
ejpam-2691	297	7	)	)	PUNCT
ejpam-2691	297	8	,	,	PUNCT
ejpam-2691	297	9	.	.	PUNCT
ejpam-2691	298	1	.	.	PUNCT
ejpam-2691	299	1	.	.	PUNCT
ejpam-2691	300	1	,	,	PUNCT
ejpam-2691	300	2	g(xrm	g(xrm	PROPN
ejpam-2691	300	3	)	)	PUNCT
ejpam-2691	300	4	�	�	PROPN
ejpam-2691	300	5	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	300	6	)	)	PUNCT
ejpam-2691	300	7	.	.	PUNCT
ejpam-2691	301	1	(	(	PUNCT
ejpam-2691	301	2	9	9	X
ejpam-2691	301	3	)	)	PUNCT
ejpam-2691	301	4	we	we	PRON
ejpam-2691	301	5	shall	shall	AUX
ejpam-2691	301	6	our	our	PRON
ejpam-2691	301	7	claim	claim	NOUN
ejpam-2691	301	8	by	by	ADP
ejpam-2691	301	9	the	the	DET
ejpam-2691	301	10	principle	principle	NOUN
ejpam-2691	301	11	of	of	ADP
ejpam-2691	301	12	mathematical	mathematical	ADJ
ejpam-2691	301	13	induction	induction	NOUN
ejpam-2691	301	14	.	.	PUNCT
ejpam-2691	302	1	since	since	SCONJ
ejpam-2691	302	2			NUM
ejpam-2691	302	3	g(x10	g(x10	NOUN
ejpam-2691	302	4	)	)	PUNCT
ejpam-2691	302	5	�	�	PROPN
ejpam-2691	302	6	t0(x10	t0(x10	PROPN
ejpam-2691	302	7	,	,	PUNCT
ejpam-2691	302	8	x20	x20	NOUN
ejpam-2691	302	9	,	,	PUNCT
ejpam-2691	302	10	.	.	PUNCT
ejpam-2691	302	11	.	.	PUNCT
ejpam-2691	303	1	.	.	PUNCT
ejpam-2691	304	1	,	,	PUNCT
ejpam-2691	304	2	xr0	xr0	PROPN
ejpam-2691	304	3	)	)	PUNCT
ejpam-2691	304	4	=	=	SYM
ejpam-2691	304	5	x11	x11	NOUN
ejpam-2691	304	6	,	,	PUNCT
ejpam-2691	304	7	g(x20	g(x20	NOUN
ejpam-2691	304	8	)	)	PUNCT
ejpam-2691	304	9	�	�	PROPN
ejpam-2691	304	10	t0(x20	t0(x20	PROPN
ejpam-2691	304	11	,	,	PUNCT
ejpam-2691	304	12	x30	x30	PROPN
ejpam-2691	304	13	,	,	PUNCT
ejpam-2691	304	14	.	.	PUNCT
ejpam-2691	304	15	.	.	PUNCT
ejpam-2691	305	1	.	.	PUNCT
ejpam-2691	306	1	,	,	PUNCT
ejpam-2691	306	2	xr0	xr0	PROPN
ejpam-2691	306	3	,	,	PUNCT
ejpam-2691	306	4	x10	x10	NOUN
ejpam-2691	306	5	)	)	PUNCT
ejpam-2691	306	6	=	=	SYM
ejpam-2691	306	7	x21	x21	PROPN
ejpam-2691	306	8	,	,	PUNCT
ejpam-2691	306	9	g(x30	g(x30	PROPN
ejpam-2691	306	10	)	)	PUNCT
ejpam-2691	306	11	�	�	PROPN
ejpam-2691	306	12	t0(x30	t0(x30	PROPN
ejpam-2691	306	13	,	,	PUNCT
ejpam-2691	306	14	x40	x40	PROPN
ejpam-2691	306	15	,	,	PUNCT
ejpam-2691	306	16	.	.	PUNCT
ejpam-2691	306	17	.	.	PUNCT
ejpam-2691	306	18	.	.	PUNCT
ejpam-2691	307	1	,	,	PUNCT
ejpam-2691	307	2	x10	x10	NOUN
ejpam-2691	307	3	,	,	PUNCT
ejpam-2691	307	4	x20	x20	NUM
ejpam-2691	307	5	)	)	PUNCT
ejpam-2691	307	6	=	=	SYM
ejpam-2691	307	7	x31	x31	PROPN
ejpam-2691	307	8	,	,	PUNCT
ejpam-2691	307	9	...	...	PUNCT
ejpam-2691	307	10	g(xr0	g(xr0	PROPN
ejpam-2691	307	11	)	)	PUNCT
ejpam-2691	307	12	�	�	PROPN
ejpam-2691	307	13	t0(xr0	t0(xr0	PROPN
ejpam-2691	307	14	,	,	PUNCT
ejpam-2691	307	15	x10	x10	NOUN
ejpam-2691	307	16	,	,	PUNCT
ejpam-2691	307	17	.	.	PUNCT
ejpam-2691	307	18	.	.	PUNCT
ejpam-2691	307	19	.	.	PUNCT
ejpam-2691	308	1	,	,	PUNCT
ejpam-2691	308	2	x	x	X
ejpam-2691	308	3	r−1	r−1	NOUN
ejpam-2691	308	4	0	0	NUM
ejpam-2691	308	5	)	)	PUNCT
ejpam-2691	309	1	=	=	SYM
ejpam-2691	309	2	xr1	xr1	PROPN
ejpam-2691	309	3	.	.	PUNCT
ejpam-2691	310	1	and	and	CCONJ
ejpam-2691	310	2			PROPN
ejpam-2691	310	3	g(x11	g(x11	NOUN
ejpam-2691	310	4	)	)	PUNCT
ejpam-2691	311	1	=	=	PUNCT
ejpam-2691	311	2	t0(x	t0(x	PUNCT
ejpam-2691	311	3	1	1	NUM
ejpam-2691	311	4	0	0	NUM
ejpam-2691	311	5	,	,	PUNCT
ejpam-2691	311	6	x	x	NOUN
ejpam-2691	311	7	2	2	NUM
ejpam-2691	311	8	0	0	NUM
ejpam-2691	311	9	,	,	PUNCT
ejpam-2691	311	10	.	.	PUNCT
ejpam-2691	311	11	.	.	PUNCT
ejpam-2691	312	1	.	.	PUNCT
ejpam-2691	313	1	,	,	PUNCT
ejpam-2691	313	2	x	x	PUNCT
ejpam-2691	313	3	r	r	NOUN
ejpam-2691	313	4	0	0	NUM
ejpam-2691	313	5	)	)	PUNCT
ejpam-2691	313	6	,	,	PUNCT
ejpam-2691	313	7	g(x21	g(x21	NOUN
ejpam-2691	313	8	)	)	PUNCT
ejpam-2691	314	1	=	=	PUNCT
ejpam-2691	314	2	t0(x	t0(x	PUNCT
ejpam-2691	314	3	2	2	NUM
ejpam-2691	314	4	0	0	NUM
ejpam-2691	314	5	,	,	PUNCT
ejpam-2691	314	6	x	x	X
ejpam-2691	314	7	3	3	NUM
ejpam-2691	314	8	0	0	NUM
ejpam-2691	314	9	,	,	PUNCT
ejpam-2691	314	10	.	.	PUNCT
ejpam-2691	314	11	.	.	PUNCT
ejpam-2691	315	1	.	.	PUNCT
ejpam-2691	316	1	,	,	PUNCT
ejpam-2691	316	2	x	x	PUNCT
ejpam-2691	316	3	r	r	NOUN
ejpam-2691	316	4	0	0	NUM
ejpam-2691	316	5	,	,	PUNCT
ejpam-2691	316	6	x	x	NOUN
ejpam-2691	316	7	1	1	NUM
ejpam-2691	316	8	0	0	NUM
ejpam-2691	316	9	)	)	PUNCT
ejpam-2691	316	10	,	,	PUNCT
ejpam-2691	316	11	...	...	PUNCT
ejpam-2691	317	1	g(xr1	g(xr1	NOUN
ejpam-2691	317	2	)	)	PUNCT
ejpam-2691	318	1	=	=	SYM
ejpam-2691	318	2	t0(x	t0(x	NOUN
ejpam-2691	318	3	r	r	NOUN
ejpam-2691	318	4	0	0	NUM
ejpam-2691	318	5	,	,	PUNCT
ejpam-2691	318	6	x	x	NOUN
ejpam-2691	318	7	1	1	NUM
ejpam-2691	318	8	0	0	NUM
ejpam-2691	318	9	,	,	PUNCT
ejpam-2691	318	10	.	.	PUNCT
ejpam-2691	318	11	.	.	PUNCT
ejpam-2691	319	1	.	.	PUNCT
ejpam-2691	320	1	,	,	PUNCT
ejpam-2691	320	2	x	x	X
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ejpam-2691	320	4	0	0	NUM
ejpam-2691	320	5	)	)	PUNCT
ejpam-2691	320	6	.	.	PUNCT
ejpam-2691	321	1	m.	m.	PROPN
ejpam-2691	321	2	grewal	grewal	PROPN
ejpam-2691	321	3	,	,	PUNCT
ejpam-2691	321	4	r.	r.	PROPN
ejpam-2691	321	5	kumar	kumar	PROPN
ejpam-2691	321	6	,	,	PUNCT
ejpam-2691	321	7	a.	a.	PROPN
ejpam-2691	321	8	kumar	kumar	PROPN
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ejpam-2691	321	10	eur	eur	PROPN
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ejpam-2691	322	2	pure	pure	PROPN
ejpam-2691	322	3	appl	appl	PROPN
ejpam-2691	322	4	.	.	PROPN
ejpam-2691	322	5	math	math	PROPN
ejpam-2691	322	6	,	,	PUNCT
ejpam-2691	322	7	10	10	NUM
ejpam-2691	322	8	(	(	PUNCT
ejpam-2691	322	9	2	2	NUM
ejpam-2691	322	10	)	)	PUNCT
ejpam-2691	322	11	(	(	PUNCT
ejpam-2691	322	12	2017	2017	NUM
ejpam-2691	322	13	)	)	PUNCT
ejpam-2691	322	14	,	,	PUNCT
ejpam-2691	322	15	295	295	NUM
ejpam-2691	322	16	-	-	SYM
ejpam-2691	322	17	311	311	NUM
ejpam-2691	322	18	302	302	NUM
ejpam-2691	322	19	thus	thus	ADV
ejpam-2691	322	20	we	we	PRON
ejpam-2691	322	21	get	get	VERB
ejpam-2691	322	22			NUM
ejpam-2691	322	23	g(x10	g(x10	NOUN
ejpam-2691	322	24	)	)	PUNCT
ejpam-2691	322	25	�	�	PROPN
ejpam-2691	322	26	g(x11	g(x11	NUM
ejpam-2691	322	27	)	)	PUNCT
ejpam-2691	322	28	,	,	PUNCT
ejpam-2691	322	29	g(x20	g(x20	NOUN
ejpam-2691	322	30	)	)	PUNCT
ejpam-2691	322	31	�	�	PROPN
ejpam-2691	322	32	g(x21	g(x21	NOUN
ejpam-2691	322	33	)	)	PUNCT
ejpam-2691	322	34	,	,	PUNCT
ejpam-2691	322	35	g(x30	g(x30	PROPN
ejpam-2691	322	36	)	)	PUNCT
ejpam-2691	322	37	�	�	PROPN
ejpam-2691	322	38	g(x31	g(x31	NOUN
ejpam-2691	322	39	)	)	PUNCT
ejpam-2691	322	40	,	,	PUNCT
ejpam-2691	322	41	...	...	PUNCT
ejpam-2691	322	42	g(xr0	g(xr0	NOUN
ejpam-2691	322	43	)	)	PUNCT
ejpam-2691	322	44	�	�	PROPN
ejpam-2691	322	45	g(xr1	g(xr1	PROPN
ejpam-2691	322	46	)	)	PUNCT
ejpam-2691	322	47	.	.	PUNCT
ejpam-2691	323	1	which	which	PRON
ejpam-2691	323	2	shows	show	VERB
ejpam-2691	323	3	that	that	SCONJ
ejpam-2691	323	4	(	(	PUNCT
ejpam-2691	323	5	9	9	X
ejpam-2691	323	6	)	)	PUNCT
ejpam-2691	323	7	holds	hold	VERB
ejpam-2691	323	8	for	for	ADP
ejpam-2691	323	9	m	m	PROPN
ejpam-2691	323	10	=	=	SYM
ejpam-2691	323	11	0	0	PROPN
ejpam-2691	323	12	.	.	PUNCT
ejpam-2691	324	1	now	now	ADV
ejpam-2691	324	2	assume	assume	VERB
ejpam-2691	324	3	that	that	SCONJ
ejpam-2691	324	4	(	(	PUNCT
ejpam-2691	324	5	9	9	X
ejpam-2691	324	6	)	)	PUNCT
ejpam-2691	324	7	holds	hold	VERB
ejpam-2691	324	8	for	for	ADP
ejpam-2691	324	9	some	some	DET
ejpam-2691	324	10	m	m	NOUN
ejpam-2691	324	11	>	>	X
ejpam-2691	324	12	0	0	NUM
ejpam-2691	324	13	.	.	PUNCT
ejpam-2691	325	1	from	from	ADP
ejpam-2691	325	2	(	(	PUNCT
ejpam-2691	325	3	8)	8)	NUM
ejpam-2691	325	4	and	and	CCONJ
ejpam-2691	325	5	(	(	PUNCT
ejpam-2691	325	6	9	9	NUM
ejpam-2691	325	7	)	)	PUNCT
ejpam-2691	325	8	,	,	PUNCT
ejpam-2691	325	9	one	one	PRON
ejpam-2691	325	10	can	can	AUX
ejpam-2691	325	11	deduce	deduce	VERB
ejpam-2691	325	12	that	that	DET
ejpam-2691	325	13	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	325	14	)	)	PUNCT
ejpam-2691	326	1	=	=	SYM
ejpam-2691	326	2	tm(x1	tm(x1	PROPN
ejpam-2691	326	3	m	m	PROPN
ejpam-2691	326	4	,	,	PUNCT
ejpam-2691	326	5	x	x	PROPN
ejpam-2691	326	6	2	2	NUM
ejpam-2691	326	7	m	m	NOUN
ejpam-2691	326	8	,	,	PUNCT
ejpam-2691	326	9	.	.	PUNCT
ejpam-2691	326	10	.	.	PUNCT
ejpam-2691	327	1	.	.	PUNCT
ejpam-2691	328	1	,	,	PUNCT
ejpam-2691	328	2	x	x	PUNCT
ejpam-2691	328	3	r	r	NOUN
ejpam-2691	328	4	m	m	NOUN
ejpam-2691	328	5	)	)	PUNCT
ejpam-2691	328	6	�	�	PROPN
ejpam-2691	328	7	tm+1(x	tm+1(x	PROPN
ejpam-2691	328	8	1	1	NUM
ejpam-2691	328	9	m+1	m+1	NOUN
ejpam-2691	328	10	,	,	PUNCT
ejpam-2691	328	11	x	x	PROPN
ejpam-2691	328	12	2	2	NUM
ejpam-2691	328	13	m	m	NOUN
ejpam-2691	328	14	,	,	PUNCT
ejpam-2691	328	15	.	.	PUNCT
ejpam-2691	328	16	.	.	PUNCT
ejpam-2691	329	1	.	.	PUNCT
ejpam-2691	330	1	,	,	PUNCT
ejpam-2691	330	2	x	x	PUNCT
ejpam-2691	330	3	r	r	NOUN
ejpam-2691	330	4	m	m	NOUN
ejpam-2691	330	5	)	)	PUNCT
ejpam-2691	330	6	�	�	PROPN
ejpam-2691	330	7	tm+1(x	tm+1(x	PROPN
ejpam-2691	330	8	1	1	NUM
ejpam-2691	330	9	m+1	m+1	NOUN
ejpam-2691	330	10	,	,	PUNCT
ejpam-2691	330	11	x	x	X
ejpam-2691	330	12	2	2	NUM
ejpam-2691	330	13	m+1	m+1	NUM
ejpam-2691	330	14	,	,	PUNCT
ejpam-2691	330	15	.	.	PUNCT
ejpam-2691	330	16	.	.	PUNCT
ejpam-2691	331	1	.	.	PUNCT
ejpam-2691	332	1	,	,	PUNCT
ejpam-2691	332	2	x	x	PUNCT
ejpam-2691	332	3	r	r	NOUN
ejpam-2691	332	4	m	m	PROPN
ejpam-2691	332	5	)	)	PUNCT
ejpam-2691	332	6	...	...	PUNCT
ejpam-2691	333	1	�	�	PROPN
ejpam-2691	333	2	tm+1(x	tm+1(x	PROPN
ejpam-2691	333	3	1	1	NUM
ejpam-2691	333	4	m+1	m+1	NOUN
ejpam-2691	333	5	,	,	PUNCT
ejpam-2691	333	6	x	x	X
ejpam-2691	333	7	2	2	NUM
ejpam-2691	333	8	m+1	m+1	NUM
ejpam-2691	333	9	,	,	PUNCT
ejpam-2691	333	10	.	.	PUNCT
ejpam-2691	333	11	.	.	PUNCT
ejpam-2691	333	12	.	.	PUNCT
ejpam-2691	334	1	,	,	PUNCT
ejpam-2691	334	2	x	x	PUNCT
ejpam-2691	334	3	r	r	NOUN
ejpam-2691	334	4	m+1	m+1	NUM
ejpam-2691	334	5	)	)	PUNCT
ejpam-2691	334	6	=	=	SYM
ejpam-2691	334	7	g(x1m+2	g(x1m+2	NOUN
ejpam-2691	334	8	)	)	PUNCT
ejpam-2691	334	9	.	.	PUNCT
ejpam-2691	335	1	g(x2m+1	g(x2m+1	X
ejpam-2691	335	2	)	)	PUNCT
ejpam-2691	336	1	=	=	PUNCT
ejpam-2691	336	2	tm+1(x	tm+1(x	PROPN
ejpam-2691	336	3	2	2	NUM
ejpam-2691	336	4	m	m	NOUN
ejpam-2691	336	5	,	,	PUNCT
ejpam-2691	336	6	x	x	PROPN
ejpam-2691	336	7	3	3	NUM
ejpam-2691	336	8	m	m	NOUN
ejpam-2691	336	9	,	,	PUNCT
ejpam-2691	336	10	.	.	PUNCT
ejpam-2691	336	11	.	.	PUNCT
ejpam-2691	336	12	.	.	PUNCT
ejpam-2691	337	1	,	,	PUNCT
ejpam-2691	337	2	x	x	PUNCT
ejpam-2691	337	3	r	r	NOUN
ejpam-2691	337	4	m	m	PROPN
ejpam-2691	337	5	,	,	PUNCT
ejpam-2691	337	6	x	x	PROPN
ejpam-2691	337	7	1	1	NUM
ejpam-2691	337	8	m	m	NOUN
ejpam-2691	337	9	)	)	PUNCT
ejpam-2691	337	10	�	�	PROPN
ejpam-2691	337	11	tm+1(x	tm+1(x	PROPN
ejpam-2691	337	12	2	2	NUM
ejpam-2691	337	13	m+1	m+1	NOUN
ejpam-2691	337	14	,	,	PUNCT
ejpam-2691	337	15	x	x	X
ejpam-2691	337	16	3	3	NUM
ejpam-2691	337	17	m	m	NOUN
ejpam-2691	337	18	,	,	PUNCT
ejpam-2691	337	19	.	.	PUNCT
ejpam-2691	337	20	.	.	PUNCT
ejpam-2691	337	21	.	.	PUNCT
ejpam-2691	338	1	,	,	PUNCT
ejpam-2691	338	2	x	x	PUNCT
ejpam-2691	338	3	r	r	NOUN
ejpam-2691	338	4	m	m	PROPN
ejpam-2691	338	5	)	)	PUNCT
ejpam-2691	338	6	,	,	PUNCT
ejpam-2691	338	7	x1	x1	PROPN
ejpam-2691	338	8	m	m	PROPN
ejpam-2691	338	9	�	�	PROPN
ejpam-2691	338	10	tm+1(x	tm+1(x	PROPN
ejpam-2691	338	11	2	2	NUM
ejpam-2691	338	12	m+1	m+1	NOUN
ejpam-2691	338	13	,	,	PUNCT
ejpam-2691	338	14	x	x	X
ejpam-2691	338	15	3	3	NUM
ejpam-2691	338	16	m+1	m+1	NUM
ejpam-2691	338	17	,	,	PUNCT
ejpam-2691	338	18	.	.	PUNCT
ejpam-2691	338	19	.	.	PUNCT
ejpam-2691	338	20	.	.	PUNCT
ejpam-2691	339	1	,	,	PUNCT
ejpam-2691	339	2	x	x	PUNCT
ejpam-2691	339	3	r	r	NOUN
ejpam-2691	339	4	m	m	PROPN
ejpam-2691	339	5	,	,	PUNCT
ejpam-2691	339	6	x	x	PROPN
ejpam-2691	339	7	1	1	NUM
ejpam-2691	339	8	m	m	NOUN
ejpam-2691	339	9	)	)	PUNCT
ejpam-2691	339	10	...	...	PUNCT
ejpam-2691	340	1	�	�	PROPN
ejpam-2691	340	2	tm(x2m+1	tm(x2m+1	PROPN
ejpam-2691	340	3	,	,	PUNCT
ejpam-2691	340	4	x	x	X
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ejpam-2691	340	6	m+1	m+1	NUM
ejpam-2691	340	7	,	,	PUNCT
ejpam-2691	340	8	.	.	PUNCT
ejpam-2691	340	9	.	.	PUNCT
ejpam-2691	340	10	.	.	PUNCT
ejpam-2691	341	1	,	,	PUNCT
ejpam-2691	341	2	x	x	PUNCT
ejpam-2691	341	3	r	r	NOUN
ejpam-2691	341	4	m+1	m+1	PROPN
ejpam-2691	341	5	,	,	PUNCT
ejpam-2691	341	6	x	x	X
ejpam-2691	341	7	1	1	NUM
ejpam-2691	341	8	m+1	m+1	NUM
ejpam-2691	341	9	)	)	PUNCT
ejpam-2691	341	10	=	=	SYM
ejpam-2691	341	11	g(x2m+2	g(x2m+2	NOUN
ejpam-2691	341	12	)	)	PUNCT
ejpam-2691	341	13	.	.	PUNCT
ejpam-2691	342	1	g(x3m+1	g(x3m+1	PUNCT
ejpam-2691	342	2	)	)	PUNCT
ejpam-2691	342	3	=	=	PUNCT
ejpam-2691	342	4	tm(x3	tm(x3	NOUN
ejpam-2691	342	5	m	m	PROPN
ejpam-2691	342	6	,	,	PUNCT
ejpam-2691	342	7	x	x	PROPN
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ejpam-2691	342	10	,	,	PUNCT
ejpam-2691	342	11	.	.	PUNCT
ejpam-2691	342	12	.	.	PUNCT
ejpam-2691	342	13	.	.	PUNCT
ejpam-2691	343	1	,	,	PUNCT
ejpam-2691	343	2	x	x	PUNCT
ejpam-2691	343	3	r	r	NOUN
ejpam-2691	343	4	m	m	PROPN
ejpam-2691	343	5	,	,	PUNCT
ejpam-2691	343	6	x	x	PROPN
ejpam-2691	343	7	1	1	NUM
ejpam-2691	343	8	m	m	NOUN
ejpam-2691	343	9	,	,	PUNCT
ejpam-2691	343	10	x	x	PROPN
ejpam-2691	343	11	2	2	NUM
ejpam-2691	343	12	m	m	NOUN
ejpam-2691	343	13	)	)	PUNCT
ejpam-2691	343	14	�	�	PROPN
ejpam-2691	343	15	tm+1(x	tm+1(x	PROPN
ejpam-2691	343	16	3	3	NUM
ejpam-2691	343	17	m+1	m+1	NOUN
ejpam-2691	343	18	,	,	PUNCT
ejpam-2691	343	19	x	x	X
ejpam-2691	343	20	4	4	NUM
ejpam-2691	343	21	m	m	NOUN
ejpam-2691	343	22	,	,	PUNCT
ejpam-2691	343	23	.	.	PUNCT
ejpam-2691	343	24	.	.	PUNCT
ejpam-2691	344	1	.	.	PUNCT
ejpam-2691	345	1	,	,	PUNCT
ejpam-2691	345	2	x	x	PUNCT
ejpam-2691	345	3	r	r	NOUN
ejpam-2691	345	4	m	m	PROPN
ejpam-2691	345	5	,	,	PUNCT
ejpam-2691	345	6	x	x	PROPN
ejpam-2691	345	7	1	1	NUM
ejpam-2691	345	8	m	m	NOUN
ejpam-2691	345	9	,	,	PUNCT
ejpam-2691	345	10	x	x	PROPN
ejpam-2691	345	11	2	2	NUM
ejpam-2691	345	12	m	m	NOUN
ejpam-2691	345	13	)	)	PUNCT
ejpam-2691	345	14	...	...	PUNCT
ejpam-2691	346	1	�	�	PROPN
ejpam-2691	346	2	tm+1(x	tm+1(x	PROPN
ejpam-2691	346	3	3	3	NUM
ejpam-2691	346	4	m+1	m+1	NOUN
ejpam-2691	346	5	,	,	PUNCT
ejpam-2691	346	6	x	x	X
ejpam-2691	346	7	4	4	NUM
ejpam-2691	346	8	m+1	m+1	NUM
ejpam-2691	346	9	,	,	PUNCT
ejpam-2691	346	10	.	.	PUNCT
ejpam-2691	346	11	.	.	PUNCT
ejpam-2691	346	12	.	.	PUNCT
ejpam-2691	347	1	,	,	PUNCT
ejpam-2691	347	2	x	x	PUNCT
ejpam-2691	347	3	r	r	NOUN
ejpam-2691	347	4	m+1	m+1	PROPN
ejpam-2691	347	5	,	,	PUNCT
ejpam-2691	347	6	x	x	X
ejpam-2691	347	7	1	1	NUM
ejpam-2691	347	8	m+1	m+1	NUM
ejpam-2691	347	9	,	,	PUNCT
ejpam-2691	347	10	x	x	X
ejpam-2691	347	11	2	2	NUM
ejpam-2691	347	12	m+1	m+1	NUM
ejpam-2691	347	13	)	)	PUNCT
ejpam-2691	347	14	=	=	SYM
ejpam-2691	347	15	g(x3m+2	g(x3m+2	PROPN
ejpam-2691	347	16	)	)	PUNCT
ejpam-2691	347	17	.	.	PUNCT
ejpam-2691	348	1	continuing	continue	VERB
ejpam-2691	348	2	in	in	ADP
ejpam-2691	348	3	this	this	DET
ejpam-2691	348	4	way	way	NOUN
ejpam-2691	348	5	g(xrm+1	g(xrm+1	X
ejpam-2691	348	6	)	)	PUNCT
ejpam-2691	348	7	=	=	SYM
ejpam-2691	348	8	tm(xrm	tm(xrm	NOUN
ejpam-2691	348	9	,	,	PUNCT
ejpam-2691	348	10	x	x	PROPN
ejpam-2691	348	11	1	1	NUM
ejpam-2691	348	12	m	m	NOUN
ejpam-2691	348	13	,	,	PUNCT
ejpam-2691	348	14	x	x	PROPN
ejpam-2691	348	15	2	2	NUM
ejpam-2691	348	16	m	m	NOUN
ejpam-2691	348	17	,	,	PUNCT
ejpam-2691	348	18	.	.	PUNCT
ejpam-2691	348	19	.	.	PUNCT
ejpam-2691	348	20	.	.	PUNCT
ejpam-2691	349	1	,	,	PUNCT
ejpam-2691	349	2	x	x	X
ejpam-2691	349	3	r−1	r−1	PROPN
ejpam-2691	349	4	m	m	NOUN
ejpam-2691	349	5	)	)	PUNCT
ejpam-2691	349	6	�	�	PROPN
ejpam-2691	349	7	tm+1(x	tm+1(x	PROPN
ejpam-2691	349	8	r	r	NOUN
ejpam-2691	349	9	m+1	m+1	PROPN
ejpam-2691	349	10	,	,	PUNCT
ejpam-2691	349	11	x	x	PROPN
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ejpam-2691	349	14	,	,	PUNCT
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ejpam-2691	349	18	,	,	PUNCT
ejpam-2691	349	19	.	.	PUNCT
ejpam-2691	349	20	.	.	PUNCT
ejpam-2691	350	1	.	.	PUNCT
ejpam-2691	351	1	,	,	PUNCT
ejpam-2691	351	2	x	x	X
ejpam-2691	351	3	r−1	r−1	PROPN
ejpam-2691	351	4	m	m	NOUN
ejpam-2691	351	5	)	)	PUNCT
ejpam-2691	351	6	�	�	PROPN
ejpam-2691	351	7	tm+1(x	tm+1(x	PROPN
ejpam-2691	351	8	r	r	NOUN
ejpam-2691	351	9	m+1	m+1	PROPN
ejpam-2691	351	10	,	,	PUNCT
ejpam-2691	351	11	x	x	X
ejpam-2691	351	12	1	1	NUM
ejpam-2691	351	13	m+1	m+1	NUM
ejpam-2691	351	14	,	,	PUNCT
ejpam-2691	351	15	x	x	PROPN
ejpam-2691	351	16	2	2	NUM
ejpam-2691	351	17	m	m	NOUN
ejpam-2691	351	18	,	,	PUNCT
ejpam-2691	351	19	.	.	PUNCT
ejpam-2691	351	20	.	.	PUNCT
ejpam-2691	352	1	.	.	PUNCT
ejpam-2691	353	1	,	,	PUNCT
ejpam-2691	353	2	x	x	X
ejpam-2691	353	3	r−1	r−1	PROPN
ejpam-2691	353	4	m	m	NOUN
ejpam-2691	353	5	)	)	PUNCT
ejpam-2691	353	6	m.	m.	NOUN
ejpam-2691	353	7	grewal	grewal	PROPN
ejpam-2691	353	8	,	,	PUNCT
ejpam-2691	353	9	r.	r.	PROPN
ejpam-2691	353	10	kumar	kumar	PROPN
ejpam-2691	353	11	,	,	PUNCT
ejpam-2691	353	12	a.	a.	PROPN
ejpam-2691	353	13	kumar	kumar	PROPN
ejpam-2691	353	14	/	/	SYM
ejpam-2691	353	15	eur	eur	PROPN
ejpam-2691	353	16	.	.	PUNCT
ejpam-2691	354	1	j.	j.	PROPN
ejpam-2691	354	2	pure	pure	PROPN
ejpam-2691	354	3	appl	appl	PROPN
ejpam-2691	354	4	.	.	PROPN
ejpam-2691	354	5	math	math	PROPN
ejpam-2691	354	6	,	,	PUNCT
ejpam-2691	354	7	10	10	NUM
ejpam-2691	354	8	(	(	PUNCT
ejpam-2691	354	9	2	2	NUM
ejpam-2691	354	10	)	)	PUNCT
ejpam-2691	354	11	(	(	PUNCT
ejpam-2691	354	12	2017	2017	NUM
ejpam-2691	354	13	)	)	PUNCT
ejpam-2691	354	14	,	,	PUNCT
ejpam-2691	354	15	295	295	NUM
ejpam-2691	354	16	-	-	SYM
ejpam-2691	354	17	311	311	NUM
ejpam-2691	354	18	303	303	NUM
ejpam-2691	354	19	...	...	PUNCT
ejpam-2691	354	20	�	�	PROPN
ejpam-2691	354	21	tm+1(x	tm+1(x	PROPN
ejpam-2691	354	22	r	r	NOUN
ejpam-2691	354	23	m+1	m+1	PROPN
ejpam-2691	354	24	,	,	PUNCT
ejpam-2691	354	25	x	x	X
ejpam-2691	354	26	1	1	NUM
ejpam-2691	354	27	m+1	m+1	NUM
ejpam-2691	354	28	,	,	PUNCT
ejpam-2691	354	29	x	x	X
ejpam-2691	354	30	2	2	NUM
ejpam-2691	354	31	m+1	m+1	NUM
ejpam-2691	354	32	,	,	PUNCT
ejpam-2691	354	33	·	·	PUNCT
ejpam-2691	354	34	·	·	PUNCT
ejpam-2691	354	35	·	·	PUNCT
ejpam-2691	354	36	,	,	PUNCT
ejpam-2691	354	37	xr−1m+1	xr−1m+1	NUM
ejpam-2691	354	38	)	)	PUNCT
ejpam-2691	354	39	=	=	SYM
ejpam-2691	354	40	g(xrm+2	g(xrm+2	PROPN
ejpam-2691	354	41	)	)	PUNCT
ejpam-2691	354	42	.	.	PUNCT
ejpam-2691	355	1	thus	thus	ADV
ejpam-2691	355	2	by	by	ADP
ejpam-2691	355	3	the	the	DET
ejpam-2691	355	4	principle	principle	NOUN
ejpam-2691	355	5	of	of	ADP
ejpam-2691	355	6	mathematical	mathematical	ADJ
ejpam-2691	355	7	induction	induction	NOUN
ejpam-2691	355	8	,	,	PUNCT
ejpam-2691	355	9	we	we	PRON
ejpam-2691	355	10	conclude	conclude	VERB
ejpam-2691	355	11	that	that	SCONJ
ejpam-2691	355	12	(	(	PUNCT
ejpam-2691	355	13	9	9	X
ejpam-2691	355	14	)	)	PUNCT
ejpam-2691	355	15	holds	hold	VERB
ejpam-2691	355	16	for	for	ADP
ejpam-2691	355	17	all	all	DET
ejpam-2691	355	18	n	n	PRON
ejpam-2691	355	19	≥	≥	NOUN
ejpam-2691	355	20	0	0	NUM
ejpam-2691	355	21	.	.	PUNCT
ejpam-2691	356	1	therefore	therefore	ADV
ejpam-2691	356	2	,	,	PUNCT
ejpam-2691	356	3	g(x1	g(x1	NOUN
ejpam-2691	356	4	m	m	NOUN
ejpam-2691	356	5	)	)	PUNCT
ejpam-2691	356	6	�	�	PROPN
ejpam-2691	356	7	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	356	8	)	)	PUNCT
ejpam-2691	356	9	g(x2	g(x2	NOUN
ejpam-2691	356	10	m	m	NOUN
ejpam-2691	356	11	)	)	PUNCT
ejpam-2691	356	12	�	�	PROPN
ejpam-2691	356	13	g(x2m+1	g(x2m+1	PROPN
ejpam-2691	356	14	)	)	PUNCT
ejpam-2691	356	15	g(x3	g(x3	NOUN
ejpam-2691	356	16	m	m	NOUN
ejpam-2691	356	17	)	)	PUNCT
ejpam-2691	356	18	�	�	PROPN
ejpam-2691	356	19	g(x3m+1	g(x3m+1	X
ejpam-2691	356	20	)	)	PUNCT
ejpam-2691	356	21	...	...	PUNCT
ejpam-2691	356	22	g(xrm	g(xrm	PROPN
ejpam-2691	356	23	)	)	PUNCT
ejpam-2691	356	24	�	�	PROPN
ejpam-2691	356	25	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	356	26	)	)	PUNCT
ejpam-2691	356	27	.	.	PUNCT
ejpam-2691	357	1	we	we	PRON
ejpam-2691	357	2	consider	consider	VERB
ejpam-2691	357	3	the	the	DET
ejpam-2691	357	4	sequences	sequence	NOUN
ejpam-2691	357	5	{	{	PUNCT
ejpam-2691	357	6	x1	x1	PROPN
ejpam-2691	357	7	m	m	PROPN
ejpam-2691	357	8	}	}	PUNCT
ejpam-2691	357	9	,	,	PUNCT
ejpam-2691	357	10	{	{	PUNCT
ejpam-2691	357	11	x2	x2	NOUN
ejpam-2691	357	12	m	m	PROPN
ejpam-2691	357	13	}	}	PUNCT
ejpam-2691	357	14	,	,	PUNCT
ejpam-2691	357	15	.	.	PUNCT
ejpam-2691	357	16	.	.	PUNCT
ejpam-2691	358	1	.	.	PUNCT
ejpam-2691	359	1	,	,	PUNCT
ejpam-2691	359	2	{	{	PUNCT
ejpam-2691	359	3	xrm	xrm	NOUN
ejpam-2691	359	4	}	}	PUNCT
ejpam-2691	359	5	in	in	ADP
ejpam-2691	359	6	x	x	PUNCT
ejpam-2691	359	7	constructed	construct	VERB
ejpam-2691	359	8	in	in	ADP
ejpam-2691	359	9	(	(	PUNCT
ejpam-2691	359	10	8)	8)	NUM
ejpam-2691	359	11	and	and	CCONJ
ejpam-2691	359	12	represent	represent	VERB
ejpam-2691	359	13	them	they	PRON
ejpam-2691	359	14	by	by	ADP
ejpam-2691	359	15	δm	δm	ADP
ejpam-2691	359	16	such	such	ADJ
ejpam-2691	359	17	that	that	SCONJ
ejpam-2691	359	18	δm	δm	ADV
ejpam-2691	359	19	=	=	PUNCT
ejpam-2691	359	20	d(g(x1	d(g(x1	PROPN
ejpam-2691	359	21	m	m	PROPN
ejpam-2691	359	22	)	)	PUNCT
ejpam-2691	359	23	,	,	PUNCT
ejpam-2691	359	24	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	359	25	)	)	PUNCT
ejpam-2691	359	26	)	)	PUNCT
ejpam-2691	360	1	+	+	CCONJ
ejpam-2691	360	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	360	3	m	m	NOUN
ejpam-2691	360	4	)	)	PUNCT
ejpam-2691	360	5	,	,	PUNCT
ejpam-2691	360	6	g(x2m+1)),+	g(x2m+1)),+	NOUN
ejpam-2691	360	7	.	.	PUNCT
ejpam-2691	360	8	.	.	PUNCT
ejpam-2691	361	1	.	.	PUNCT
ejpam-2691	362	1	,	,	PUNCT
ejpam-2691	363	1	+	+	NOUN
ejpam-2691	363	2	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	363	3	)	)	PUNCT
ejpam-2691	363	4	,	,	PUNCT
ejpam-2691	363	5	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	363	6	)	)	PUNCT
ejpam-2691	363	7	)	)	PUNCT
ejpam-2691	363	8	.	.	PUNCT
ejpam-2691	364	1	now	now	ADV
ejpam-2691	364	2	from	from	ADP
ejpam-2691	364	3	the	the	DET
ejpam-2691	364	4	property	property	NOUN
ejpam-2691	364	5	(	(	PUNCT
ejpam-2691	364	6	a	a	NOUN
ejpam-2691	364	7	)	)	PUNCT
ejpam-2691	364	8	of	of	ADP
ejpam-2691	364	9	{	{	PUNCT
ejpam-2691	364	10	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	364	11	and	and	CCONJ
ejpam-2691	364	12	g	g	NOUN
ejpam-2691	364	13	in	in	ADP
ejpam-2691	364	14	(	(	PUNCT
ejpam-2691	364	15	5	5	X
ejpam-2691	364	16	)	)	PUNCT
ejpam-2691	364	17	we	we	PRON
ejpam-2691	364	18	get	get	VERB
ejpam-2691	364	19	d(g(x11	d(g(x11	PROPN
ejpam-2691	364	20	)	)	PUNCT
ejpam-2691	364	21	,	,	PUNCT
ejpam-2691	364	22	g(x12	g(x12	NUM
ejpam-2691	364	23	)	)	PUNCT
ejpam-2691	364	24	)	)	PUNCT
ejpam-2691	365	1	=	=	PUNCT
ejpam-2691	365	2	d(t0(x	d(t0(x	PROPN
ejpam-2691	365	3	1	1	NUM
ejpam-2691	365	4	0	0	NUM
ejpam-2691	365	5	,	,	PUNCT
ejpam-2691	365	6	x	x	NOUN
ejpam-2691	365	7	2	2	NUM
ejpam-2691	365	8	0	0	NUM
ejpam-2691	365	9	,	,	PUNCT
ejpam-2691	365	10	.	.	PUNCT
ejpam-2691	365	11	.	.	PUNCT
ejpam-2691	365	12	.	.	PUNCT
ejpam-2691	366	1	x	x	PUNCT
ejpam-2691	366	2	r	r	NOUN
ejpam-2691	366	3	0	0	NUM
ejpam-2691	366	4	)	)	PUNCT
ejpam-2691	366	5	)	)	PUNCT
ejpam-2691	366	6	,	,	PUNCT
ejpam-2691	366	7	t1(x	t1(x	PROPN
ejpam-2691	366	8	1	1	NUM
ejpam-2691	366	9	1	1	NUM
ejpam-2691	366	10	,	,	PUNCT
ejpam-2691	366	11	x	x	NOUN
ejpam-2691	366	12	2	2	NUM
ejpam-2691	366	13	1	1	NUM
ejpam-2691	366	14	,	,	PUNCT
ejpam-2691	366	15	.	.	PUNCT
ejpam-2691	366	16	.	.	PUNCT
ejpam-2691	366	17	.	.	PUNCT
ejpam-2691	367	1	x	x	PUNCT
ejpam-2691	367	2	r	r	NOUN
ejpam-2691	367	3	1	1	NUM
ejpam-2691	367	4	)	)	PUNCT
ejpam-2691	367	5	≤	≤	NOUN
ejpam-2691	367	6	β0,1[d(g(x10	β0,1[d(g(x10	NOUN
ejpam-2691	367	7	)	)	PUNCT
ejpam-2691	367	8	,	,	PUNCT
ejpam-2691	367	9	t0(x	t0(x	NOUN
ejpam-2691	367	10	1	1	NUM
ejpam-2691	367	11	0	0	NUM
ejpam-2691	367	12	,	,	PUNCT
ejpam-2691	367	13	x	x	NOUN
ejpam-2691	367	14	2	2	NUM
ejpam-2691	367	15	0	0	NUM
ejpam-2691	367	16	,	,	PUNCT
ejpam-2691	367	17	.	.	PUNCT
ejpam-2691	367	18	.	.	PUNCT
ejpam-2691	367	19	.	.	PUNCT
ejpam-2691	368	1	x	x	PUNCT
ejpam-2691	368	2	r	r	NOUN
ejpam-2691	368	3	0	0	NUM
ejpam-2691	368	4	)	)	PUNCT
ejpam-2691	368	5	)	)	PUNCT
ejpam-2691	369	1	+	+	CCONJ
ejpam-2691	369	2	d(g(x11	d(g(x11	PROPN
ejpam-2691	369	3	)	)	PUNCT
ejpam-2691	369	4	,	,	PUNCT
ejpam-2691	369	5	t1(x	t1(x	PROPN
ejpam-2691	369	6	1	1	NUM
ejpam-2691	369	7	1	1	NUM
ejpam-2691	369	8	,	,	PUNCT
ejpam-2691	369	9	x	x	NOUN
ejpam-2691	369	10	2	2	NUM
ejpam-2691	369	11	1	1	NUM
ejpam-2691	369	12	,	,	PUNCT
ejpam-2691	369	13	.	.	PUNCT
ejpam-2691	369	14	.	.	PUNCT
ejpam-2691	369	15	.	.	PUNCT
ejpam-2691	370	1	x	x	PUNCT
ejpam-2691	370	2	r	r	NOUN
ejpam-2691	370	3	1	1	NUM
ejpam-2691	370	4	)	)	PUNCT
ejpam-2691	370	5	)	)	PUNCT
ejpam-2691	370	6	]	]	PUNCT
ejpam-2691	371	1	+	+	X
ejpam-2691	371	2	γ0,1[d(g(x10	γ0,1[d(g(x10	NOUN
ejpam-2691	371	3	)	)	PUNCT
ejpam-2691	371	4	,	,	PUNCT
ejpam-2691	371	5	g(x11	g(x11	NOUN
ejpam-2691	371	6	)	)	PUNCT
ejpam-2691	371	7	)	)	PUNCT
ejpam-2691	371	8	]	]	PUNCT
ejpam-2691	372	1	=	=	SYM
ejpam-2691	372	2	β0,1[d(g(x10	β0,1[d(g(x10	X
ejpam-2691	372	3	)	)	PUNCT
ejpam-2691	372	4	,	,	PUNCT
ejpam-2691	372	5	g(x11	g(x11	NOUN
ejpam-2691	372	6	)	)	PUNCT
ejpam-2691	372	7	)	)	PUNCT
ejpam-2691	373	1	+	+	CCONJ
ejpam-2691	373	2	d(g(x11	d(g(x11	PROPN
ejpam-2691	373	3	)	)	PUNCT
ejpam-2691	373	4	,	,	PUNCT
ejpam-2691	373	5	g(x12	g(x12	NUM
ejpam-2691	373	6	)	)	PUNCT
ejpam-2691	373	7	)	)	PUNCT
ejpam-2691	373	8	]	]	PUNCT
ejpam-2691	374	1	+	+	X
ejpam-2691	374	2	γ0,1[d(g(x10	γ0,1[d(g(x10	NOUN
ejpam-2691	374	3	)	)	PUNCT
ejpam-2691	374	4	,	,	PUNCT
ejpam-2691	374	5	g(x11	g(x11	NOUN
ejpam-2691	374	6	)	)	PUNCT
ejpam-2691	374	7	)	)	PUNCT
ejpam-2691	374	8	]	]	PUNCT
ejpam-2691	374	9	.	.	PUNCT
ejpam-2691	375	1	consequently	consequently	ADV
ejpam-2691	375	2	,	,	PUNCT
ejpam-2691	375	3	(	(	PUNCT
ejpam-2691	375	4	1−	1−	NUM
ejpam-2691	375	5	β0,1)d(g(x11	β0,1)d(g(x11	NOUN
ejpam-2691	375	6	)	)	PUNCT
ejpam-2691	375	7	,	,	PUNCT
ejpam-2691	375	8	g(x12	g(x12	NUM
ejpam-2691	375	9	)	)	PUNCT
ejpam-2691	375	10	)	)	PUNCT
ejpam-2691	376	1	≤	≤	NOUN
ejpam-2691	376	2	(	(	PUNCT
ejpam-2691	376	3	β0,1	β0,1	NOUN
ejpam-2691	376	4	+	+	NUM
ejpam-2691	376	5	γ0,1)d(g(x10	γ0,1)d(g(x10	NOUN
ejpam-2691	376	6	)	)	PUNCT
ejpam-2691	376	7	,	,	PUNCT
ejpam-2691	376	8	g(x11	g(x11	NOUN
ejpam-2691	376	9	)	)	PUNCT
ejpam-2691	376	10	)	)	PUNCT
ejpam-2691	376	11	,	,	PUNCT
ejpam-2691	376	12	or	or	CCONJ
ejpam-2691	376	13	equivalently	equivalently	ADV
ejpam-2691	376	14	,	,	PUNCT
ejpam-2691	376	15	d(g(x11	d(g(x11	PROPN
ejpam-2691	376	16	)	)	PUNCT
ejpam-2691	376	17	,	,	PUNCT
ejpam-2691	376	18	g(x12	g(x12	NUM
ejpam-2691	376	19	)	)	PUNCT
ejpam-2691	376	20	)	)	PUNCT
ejpam-2691	377	1	≤	≤	NOUN
ejpam-2691	377	2	(	(	PUNCT
ejpam-2691	377	3	β0,1+γ0,1	β0,1+γ0,1	ADV
ejpam-2691	377	4	1−β0,1	1−β0,1	NUM
ejpam-2691	377	5	)	)	PUNCT
ejpam-2691	378	1	d(g(x10	d(g(x10	PROPN
ejpam-2691	378	2	)	)	PUNCT
ejpam-2691	378	3	,	,	PUNCT
ejpam-2691	378	4	g(x11	g(x11	NOUN
ejpam-2691	378	5	)	)	PUNCT
ejpam-2691	378	6	)	)	PUNCT
ejpam-2691	378	7	.	.	PUNCT
ejpam-2691	379	1	now	now	ADV
ejpam-2691	379	2	d(g(x12	d(g(x12	PROPN
ejpam-2691	379	3	)	)	PUNCT
ejpam-2691	379	4	,	,	PUNCT
ejpam-2691	379	5	g(x13	g(x13	NOUN
ejpam-2691	379	6	)	)	PUNCT
ejpam-2691	379	7	)	)	PUNCT
ejpam-2691	380	1	=	=	PUNCT
ejpam-2691	380	2	d(t1(x	d(t1(x	NOUN
ejpam-2691	380	3	1	1	NUM
ejpam-2691	380	4	1	1	NUM
ejpam-2691	380	5	,	,	PUNCT
ejpam-2691	380	6	x	x	NOUN
ejpam-2691	380	7	2	2	NUM
ejpam-2691	380	8	1	1	NUM
ejpam-2691	380	9	,	,	PUNCT
ejpam-2691	380	10	.	.	PUNCT
ejpam-2691	380	11	.	.	PUNCT
ejpam-2691	380	12	.	.	PUNCT
ejpam-2691	381	1	x	x	PUNCT
ejpam-2691	381	2	r	r	NOUN
ejpam-2691	381	3	1	1	NUM
ejpam-2691	381	4	)	)	PUNCT
ejpam-2691	381	5	,	,	PUNCT
ejpam-2691	381	6	t2(x	t2(x	NOUN
ejpam-2691	381	7	1	1	NUM
ejpam-2691	381	8	2	2	NUM
ejpam-2691	381	9	,	,	PUNCT
ejpam-2691	381	10	x	x	NOUN
ejpam-2691	381	11	2	2	NUM
ejpam-2691	381	12	2	2	NUM
ejpam-2691	381	13	,	,	PUNCT
ejpam-2691	381	14	.	.	PUNCT
ejpam-2691	381	15	.	.	PUNCT
ejpam-2691	381	16	.	.	PUNCT
ejpam-2691	382	1	x	x	PUNCT
ejpam-2691	382	2	r	r	NOUN
ejpam-2691	382	3	2	2	NUM
ejpam-2691	382	4	)	)	PUNCT
ejpam-2691	382	5	)	)	PUNCT
ejpam-2691	382	6	≤	≤	NOUN
ejpam-2691	382	7	(	(	PUNCT
ejpam-2691	382	8	β1,2	β1,2	NUM
ejpam-2691	382	9	+	+	NUM
ejpam-2691	382	10	γ1,2	γ1,2	ADJ
ejpam-2691	382	11	1−	1−	NUM
ejpam-2691	382	12	β1,2	β1,2	NUM
ejpam-2691	382	13	)	)	PUNCT
ejpam-2691	382	14	d(g(x11	d(g(x11	PROPN
ejpam-2691	382	15	)	)	PUNCT
ejpam-2691	382	16	,	,	PUNCT
ejpam-2691	382	17	g(x12	g(x12	NUM
ejpam-2691	382	18	)	)	PUNCT
ejpam-2691	382	19	)	)	PUNCT
ejpam-2691	382	20	≤	≤	NOUN
ejpam-2691	382	21	(	(	PUNCT
ejpam-2691	382	22	β1,2	β1,2	NUM
ejpam-2691	382	23	+	+	NUM
ejpam-2691	382	24	γ1,2	γ1,2	ADJ
ejpam-2691	382	25	1−	1−	NUM
ejpam-2691	382	26	β1,2	β1,2	NUM
ejpam-2691	382	27	)	)	PUNCT
ejpam-2691	382	28	(	(	PUNCT
ejpam-2691	382	29	β0,1	β0,1	NOUN
ejpam-2691	382	30	+	+	CCONJ
ejpam-2691	382	31	γ0,1	γ0,1	PROPN
ejpam-2691	382	32	1−	1−	NUM
ejpam-2691	382	33	β0,1	β0,1	NOUN
ejpam-2691	382	34	)	)	PUNCT
ejpam-2691	383	1	d(g(x10	d(g(x10	PROPN
ejpam-2691	383	2	)	)	PUNCT
ejpam-2691	383	3	,	,	PUNCT
ejpam-2691	383	4	g(x11	g(x11	NOUN
ejpam-2691	383	5	)	)	PUNCT
ejpam-2691	383	6	)	)	PUNCT
ejpam-2691	383	7	.	.	PUNCT
ejpam-2691	384	1	continuing	continue	VERB
ejpam-2691	384	2	in	in	ADP
ejpam-2691	384	3	this	this	DET
ejpam-2691	384	4	way	way	NOUN
ejpam-2691	384	5	,	,	PUNCT
ejpam-2691	384	6	we	we	PRON
ejpam-2691	384	7	get	get	VERB
ejpam-2691	384	8	d(g(x1	d(g(x1	ADJ
ejpam-2691	384	9	m	m	NOUN
ejpam-2691	384	10	)	)	PUNCT
ejpam-2691	384	11	,	,	PUNCT
ejpam-2691	384	12	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	384	13	)	)	PUNCT
ejpam-2691	384	14	)	)	PUNCT
ejpam-2691	385	1	≤	≤	NUM
ejpam-2691	385	2	d(tm−1(x	d(tm−1(x	NOUN
ejpam-2691	385	3	1	1	NUM
ejpam-2691	385	4	m−1	m−1	PROPN
ejpam-2691	385	5	,	,	PUNCT
ejpam-2691	385	6	x	x	PROPN
ejpam-2691	385	7	2	2	NUM
ejpam-2691	385	8	m−1	m−1	PROPN
ejpam-2691	385	9	,	,	PUNCT
ejpam-2691	385	10	.	.	PUNCT
ejpam-2691	385	11	.	.	PUNCT
ejpam-2691	385	12	.	.	PUNCT
ejpam-2691	386	1	x	x	PUNCT
ejpam-2691	386	2	r	r	NOUN
ejpam-2691	386	3	m−1	m−1	PROPN
ejpam-2691	386	4	)	)	PUNCT
ejpam-2691	386	5	,	,	PUNCT
ejpam-2691	386	6	tm(x1	tm(x1	PROPN
ejpam-2691	386	7	m	m	PROPN
ejpam-2691	386	8	,	,	PUNCT
ejpam-2691	386	9	x	x	PROPN
ejpam-2691	386	10	2	2	NUM
ejpam-2691	386	11	m	m	NOUN
ejpam-2691	386	12	,	,	PUNCT
ejpam-2691	386	13	.	.	PUNCT
ejpam-2691	386	14	.	.	PUNCT
ejpam-2691	386	15	.	.	PUNCT
ejpam-2691	387	1	x	x	PUNCT
ejpam-2691	387	2	r	r	NOUN
ejpam-2691	387	3	m	m	NOUN
ejpam-2691	387	4	)	)	PUNCT
ejpam-2691	387	5	)	)	PUNCT
ejpam-2691	387	6	m.	m.	NOUN
ejpam-2691	387	7	grewal	grewal	PROPN
ejpam-2691	387	8	,	,	PUNCT
ejpam-2691	387	9	r.	r.	PROPN
ejpam-2691	387	10	kumar	kumar	PROPN
ejpam-2691	387	11	,	,	PUNCT
ejpam-2691	387	12	a.	a.	PROPN
ejpam-2691	387	13	kumar	kumar	PROPN
ejpam-2691	387	14	/	/	SYM
ejpam-2691	387	15	eur	eur	PROPN
ejpam-2691	387	16	.	.	PUNCT
ejpam-2691	388	1	j.	j.	PROPN
ejpam-2691	388	2	pure	pure	PROPN
ejpam-2691	388	3	appl	appl	PROPN
ejpam-2691	388	4	.	.	PROPN
ejpam-2691	388	5	math	math	PROPN
ejpam-2691	388	6	,	,	PUNCT
ejpam-2691	388	7	10	10	NUM
ejpam-2691	388	8	(	(	PUNCT
ejpam-2691	388	9	2	2	NUM
ejpam-2691	388	10	)	)	PUNCT
ejpam-2691	388	11	(	(	PUNCT
ejpam-2691	388	12	2017	2017	NUM
ejpam-2691	388	13	)	)	PUNCT
ejpam-2691	388	14	,	,	PUNCT
ejpam-2691	388	15	295	295	NUM
ejpam-2691	388	16	-	-	SYM
ejpam-2691	388	17	311	311	NUM
ejpam-2691	388	18	304	304	NUM
ejpam-2691	388	19	≤	≤	NOUN
ejpam-2691	388	20	m−1∏	m−1∏	PROPN
ejpam-2691	388	21	i=0	i=0	PROPN
ejpam-2691	388	22	(	(	PUNCT
ejpam-2691	388	23	βi	βi	PROPN
ejpam-2691	388	24	,	,	PUNCT
ejpam-2691	388	25	i+1	i+1	NOUN
ejpam-2691	388	26	+	+	NUM
ejpam-2691	388	27	γi	γi	NOUN
ejpam-2691	388	28	,	,	PUNCT
ejpam-2691	388	29	i+1	i+1	NOUN
ejpam-2691	388	30	1−	1−	NUM
ejpam-2691	388	31	βi	βi	NOUN
ejpam-2691	388	32	,	,	PUNCT
ejpam-2691	388	33	i+1	i+1	NUM
ejpam-2691	388	34	)	)	PUNCT
ejpam-2691	388	35	d(g(x10	d(g(x10	PROPN
ejpam-2691	388	36	)	)	PUNCT
ejpam-2691	388	37	,	,	PUNCT
ejpam-2691	388	38	g(x11	g(x11	NOUN
ejpam-2691	388	39	)	)	PUNCT
ejpam-2691	388	40	)	)	PUNCT
ejpam-2691	388	41	.	.	PUNCT
ejpam-2691	389	1	(	(	PUNCT
ejpam-2691	389	2	10	10	NUM
ejpam-2691	389	3	)	)	PUNCT
ejpam-2691	389	4	d(g(x2	d(g(x2	NOUN
ejpam-2691	389	5	m	m	NOUN
ejpam-2691	389	6	)	)	PUNCT
ejpam-2691	389	7	,	,	PUNCT
ejpam-2691	389	8	g(x2m+1	g(x2m+1	X
ejpam-2691	389	9	)	)	PUNCT
ejpam-2691	389	10	)	)	PUNCT
ejpam-2691	390	1	≤	≤	NUM
ejpam-2691	390	2	d(tm−1(x	d(tm−1(x	NOUN
ejpam-2691	390	3	2	2	NUM
ejpam-2691	390	4	m−1	m−1	PROPN
ejpam-2691	390	5	,	,	PUNCT
ejpam-2691	390	6	x	x	PROPN
ejpam-2691	390	7	3	3	NUM
ejpam-2691	390	8	m−1	m−1	PROPN
ejpam-2691	390	9	,	,	PUNCT
ejpam-2691	390	10	.	.	PUNCT
ejpam-2691	390	11	.	.	PUNCT
ejpam-2691	390	12	.	.	PUNCT
ejpam-2691	391	1	,	,	PUNCT
ejpam-2691	391	2	x	x	PUNCT
ejpam-2691	391	3	r	r	NOUN
ejpam-2691	391	4	m−1	m−1	PROPN
ejpam-2691	391	5	,	,	PUNCT
ejpam-2691	391	6	x	x	PROPN
ejpam-2691	391	7	1	1	NUM
ejpam-2691	391	8	m−1	m−1	PROPN
ejpam-2691	391	9	)	)	PUNCT
ejpam-2691	391	10	,	,	PUNCT
ejpam-2691	391	11	tm(x2	tm(x2	NOUN
ejpam-2691	391	12	m	m	PROPN
ejpam-2691	391	13	,	,	PUNCT
ejpam-2691	391	14	x	x	PROPN
ejpam-2691	391	15	3	3	NUM
ejpam-2691	391	16	m	m	NOUN
ejpam-2691	391	17	,	,	PUNCT
ejpam-2691	391	18	.	.	PUNCT
ejpam-2691	391	19	.	.	PUNCT
ejpam-2691	391	20	.	.	PUNCT
ejpam-2691	392	1	x	x	PUNCT
ejpam-2691	392	2	r	r	NOUN
ejpam-2691	392	3	m	m	PROPN
ejpam-2691	392	4	,	,	PUNCT
ejpam-2691	392	5	x	x	PROPN
ejpam-2691	392	6	1	1	NUM
ejpam-2691	392	7	m	m	NOUN
ejpam-2691	392	8	)	)	PUNCT
ejpam-2691	392	9	)	)	PUNCT
ejpam-2691	392	10	≤	≤	PUNCT
ejpam-2691	392	11	m−1∏	m−1∏	PROPN
ejpam-2691	392	12	i=0	i=0	PROPN
ejpam-2691	392	13	(	(	PUNCT
ejpam-2691	392	14	βi	βi	PROPN
ejpam-2691	392	15	,	,	PUNCT
ejpam-2691	392	16	i+1	i+1	NOUN
ejpam-2691	392	17	+	+	NUM
ejpam-2691	392	18	γi	γi	NOUN
ejpam-2691	392	19	,	,	PUNCT
ejpam-2691	392	20	i+1	i+1	NOUN
ejpam-2691	392	21	1−	1−	NUM
ejpam-2691	392	22	βi	βi	NOUN
ejpam-2691	392	23	,	,	PUNCT
ejpam-2691	392	24	i+1	i+1	NUM
ejpam-2691	392	25	)	)	PUNCT
ejpam-2691	392	26	d(g(x20	d(g(x20	PROPN
ejpam-2691	392	27	)	)	PUNCT
ejpam-2691	392	28	,	,	PUNCT
ejpam-2691	392	29	g(x21	g(x21	NOUN
ejpam-2691	392	30	)	)	PUNCT
ejpam-2691	392	31	)	)	PUNCT
ejpam-2691	392	32	.	.	PUNCT
ejpam-2691	393	1	similarly	similarly	ADV
ejpam-2691	393	2	,	,	PUNCT
ejpam-2691	393	3	one	one	PRON
ejpam-2691	393	4	can	can	AUX
ejpam-2691	393	5	inductively	inductively	ADV
ejpam-2691	393	6	write	write	PROPN
ejpam-2691	393	7	d(g(x2	d(g(x2	NOUN
ejpam-2691	393	8	m	m	PROPN
ejpam-2691	393	9	)	)	PUNCT
ejpam-2691	393	10	,	,	PUNCT
ejpam-2691	393	11	g(x2m+1	g(x2m+1	X
ejpam-2691	393	12	)	)	PUNCT
ejpam-2691	393	13	)	)	PUNCT
ejpam-2691	393	14	≤	≤	NUM
ejpam-2691	394	1	∏m−1	∏m−1	PROPN
ejpam-2691	394	2	i=0	i=0	PROPN
ejpam-2691	394	3	(	(	PUNCT
ejpam-2691	394	4	βi	βi	PROPN
ejpam-2691	394	5	,	,	PUNCT
ejpam-2691	394	6	i+1+γi	i+1+γi	NOUN
ejpam-2691	394	7	,	,	PUNCT
ejpam-2691	394	8	i+1	i+1	NOUN
ejpam-2691	394	9	1−βi	1−βi	NUM
ejpam-2691	394	10	,	,	PUNCT
ejpam-2691	394	11	i+1	i+1	NUM
ejpam-2691	394	12	)	)	PUNCT
ejpam-2691	394	13	d(g(x20	d(g(x20	PROPN
ejpam-2691	394	14	)	)	PUNCT
ejpam-2691	394	15	,	,	PUNCT
ejpam-2691	394	16	g(x21	g(x21	NOUN
ejpam-2691	394	17	)	)	PUNCT
ejpam-2691	394	18	)	)	PUNCT
ejpam-2691	394	19	.	.	PUNCT
ejpam-2691	395	1	d(g(x3	d(g(x3	NOUN
ejpam-2691	395	2	m	m	NOUN
ejpam-2691	395	3	)	)	PUNCT
ejpam-2691	395	4	,	,	PUNCT
ejpam-2691	395	5	g(x3m+1	g(x3m+1	NUM
ejpam-2691	395	6	)	)	PUNCT
ejpam-2691	395	7	)	)	PUNCT
ejpam-2691	395	8	≤	≤	NUM
ejpam-2691	396	1	∏m−1	∏m−1	PROPN
ejpam-2691	396	2	i=0	i=0	PROPN
ejpam-2691	396	3	(	(	PUNCT
ejpam-2691	396	4	βi	βi	PROPN
ejpam-2691	396	5	,	,	PUNCT
ejpam-2691	396	6	i+1+γi	i+1+γi	NOUN
ejpam-2691	396	7	,	,	PUNCT
ejpam-2691	396	8	i+1	i+1	NOUN
ejpam-2691	396	9	1−βi	1−βi	NUM
ejpam-2691	396	10	,	,	PUNCT
ejpam-2691	396	11	i+1	i+1	NUM
ejpam-2691	396	12	)	)	PUNCT
ejpam-2691	396	13	d(g(x30	d(g(x30	PROPN
ejpam-2691	396	14	)	)	PUNCT
ejpam-2691	396	15	,	,	PUNCT
ejpam-2691	396	16	g(x31	g(x31	NOUN
ejpam-2691	396	17	)	)	PUNCT
ejpam-2691	396	18	)	)	PUNCT
ejpam-2691	396	19	.	.	PUNCT
ejpam-2691	396	20	...	...	PUNCT
ejpam-2691	397	1	d(g(xrm	d(g(xrm	NUM
ejpam-2691	397	2	)	)	PUNCT
ejpam-2691	397	3	,	,	PUNCT
ejpam-2691	397	4	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	397	5	)	)	PUNCT
ejpam-2691	397	6	)	)	PUNCT
ejpam-2691	397	7	≤	≤	NUM
ejpam-2691	398	1	∏m−1	∏m−1	PROPN
ejpam-2691	398	2	i=0	i=0	PROPN
ejpam-2691	398	3	(	(	PUNCT
ejpam-2691	398	4	βi	βi	PROPN
ejpam-2691	398	5	,	,	PUNCT
ejpam-2691	398	6	i+1+γi	i+1+γi	NOUN
ejpam-2691	398	7	,	,	PUNCT
ejpam-2691	398	8	i+1	i+1	NOUN
ejpam-2691	398	9	1−βi	1−βi	NUM
ejpam-2691	398	10	,	,	PUNCT
ejpam-2691	398	11	i+1	i+1	NUM
ejpam-2691	398	12	)	)	PUNCT
ejpam-2691	398	13	d(g(xr0	d(g(xr0	PROPN
ejpam-2691	398	14	)	)	PUNCT
ejpam-2691	398	15	,	,	PUNCT
ejpam-2691	398	16	g(xr1	g(xr1	NOUN
ejpam-2691	398	17	)	)	PUNCT
ejpam-2691	398	18	)	)	PUNCT
ejpam-2691	398	19	.	.	PUNCT
ejpam-2691	399	1	(	(	PUNCT
ejpam-2691	399	2	11	11	X
ejpam-2691	399	3	)	)	PUNCT
ejpam-2691	399	4	adding	add	VERB
ejpam-2691	399	5	(	(	PUNCT
ejpam-2691	399	6	10	10	NUM
ejpam-2691	399	7	)	)	PUNCT
ejpam-2691	399	8	and	and	CCONJ
ejpam-2691	399	9	(	(	PUNCT
ejpam-2691	399	10	11	11	NUM
ejpam-2691	399	11	)	)	PUNCT
ejpam-2691	399	12	,	,	PUNCT
ejpam-2691	399	13	we	we	PRON
ejpam-2691	399	14	have	have	VERB
ejpam-2691	399	15	δm	δm	PROPN
ejpam-2691	399	16	=	=	PUNCT
ejpam-2691	399	17	d(g(x1	d(g(x1	PROPN
ejpam-2691	399	18	m	m	PROPN
ejpam-2691	399	19	)	)	PUNCT
ejpam-2691	399	20	,	,	PUNCT
ejpam-2691	399	21	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	399	22	)	)	PUNCT
ejpam-2691	399	23	)	)	PUNCT
ejpam-2691	400	1	+	+	CCONJ
ejpam-2691	400	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	400	3	m	m	NOUN
ejpam-2691	400	4	)	)	PUNCT
ejpam-2691	400	5	,	,	PUNCT
ejpam-2691	400	6	g(x2m+1	g(x2m+1	X
ejpam-2691	400	7	)	)	PUNCT
ejpam-2691	400	8	+	+	CCONJ
ejpam-2691	400	9	·	·	PUNCT
ejpam-2691	400	10	·	·	PUNCT
ejpam-2691	400	11	·	·	PUNCT
ejpam-2691	400	12	+	+	NUM
ejpam-2691	400	13	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	400	14	)	)	PUNCT
ejpam-2691	400	15	,	,	PUNCT
ejpam-2691	400	16	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	400	17	)	)	PUNCT
ejpam-2691	400	18	≤	≤	NOUN
ejpam-2691	400	19	m−1∏	m−1∏	PROPN
ejpam-2691	400	20	i=0	i=0	PROPN
ejpam-2691	400	21	(	(	PUNCT
ejpam-2691	400	22	βi	βi	PROPN
ejpam-2691	400	23	,	,	PUNCT
ejpam-2691	400	24	i+1	i+1	NOUN
ejpam-2691	400	25	+	+	NUM
ejpam-2691	400	26	γi	γi	NOUN
ejpam-2691	400	27	,	,	PUNCT
ejpam-2691	400	28	i+1	i+1	NOUN
ejpam-2691	400	29	1−	1−	NUM
ejpam-2691	400	30	βi	βi	NOUN
ejpam-2691	400	31	,	,	PUNCT
ejpam-2691	400	32	i+1	i+1	NUM
ejpam-2691	400	33	)	)	PUNCT
ejpam-2691	401	1	[	[	X
ejpam-2691	401	2	d(g(x10	d(g(x10	PROPN
ejpam-2691	401	3	)	)	PUNCT
ejpam-2691	401	4	,	,	PUNCT
ejpam-2691	401	5	g(x11	g(x11	NOUN
ejpam-2691	401	6	)	)	PUNCT
ejpam-2691	401	7	)	)	PUNCT
ejpam-2691	401	8	+	+	CCONJ
ejpam-2691	402	1	d(g(x20	d(g(x20	PROPN
ejpam-2691	402	2	)	)	PUNCT
ejpam-2691	402	3	,	,	PUNCT
ejpam-2691	402	4	g(x21	g(x21	NOUN
ejpam-2691	402	5	)	)	PUNCT
ejpam-2691	402	6	)	)	PUNCT
ejpam-2691	403	1	+	+	CCONJ
ejpam-2691	403	2	·	·	PUNCT
ejpam-2691	403	3	·	·	PUNCT
ejpam-2691	403	4	·	·	PUNCT
ejpam-2691	403	5	+	+	NUM
ejpam-2691	403	6	d(g(xr0	d(g(xr0	NOUN
ejpam-2691	403	7	)	)	PUNCT
ejpam-2691	403	8	,	,	PUNCT
ejpam-2691	403	9	g(xr1	g(xr1	NOUN
ejpam-2691	403	10	)	)	PUNCT
ejpam-2691	403	11	)	)	PUNCT
ejpam-2691	403	12	]	]	PUNCT
ejpam-2691	404	1	=	=	PUNCT
ejpam-2691	404	2	m−1∏	m−1∏	PROPN
ejpam-2691	404	3	i=0	i=0	PROPN
ejpam-2691	404	4	(	(	PUNCT
ejpam-2691	404	5	βi	βi	PROPN
ejpam-2691	404	6	,	,	PUNCT
ejpam-2691	404	7	i+1	i+1	NOUN
ejpam-2691	404	8	+	+	NUM
ejpam-2691	404	9	γi	γi	NOUN
ejpam-2691	404	10	,	,	PUNCT
ejpam-2691	404	11	i+1	i+1	NOUN
ejpam-2691	404	12	1−	1−	NUM
ejpam-2691	404	13	βi	βi	NOUN
ejpam-2691	404	14	,	,	PUNCT
ejpam-2691	404	15	i+1	i+1	NUM
ejpam-2691	404	16	)	)	PUNCT
ejpam-2691	404	17	δ0	δ0	NOUN
ejpam-2691	404	18	.	.	PUNCT
ejpam-2691	405	1	moreover	moreover	ADV
ejpam-2691	405	2	,	,	PUNCT
ejpam-2691	405	3	for	for	ADP
ejpam-2691	405	4	p	p	NOUN
ejpam-2691	405	5	>	>	X
ejpam-2691	405	6	0	0	PUNCT
ejpam-2691	405	7	and	and	CCONJ
ejpam-2691	405	8	by	by	ADP
ejpam-2691	405	9	repeated	repeat	VERB
ejpam-2691	405	10	use	use	NOUN
ejpam-2691	405	11	of	of	ADP
ejpam-2691	405	12	the	the	DET
ejpam-2691	405	13	triangle	triangle	NOUN
ejpam-2691	405	14	inequality	inequality	NOUN
ejpam-2691	405	15	,	,	PUNCT
ejpam-2691	405	16	ones	one	NOUN
ejpam-2691	405	17	obtain	obtain	VERB
ejpam-2691	405	18	d(g(x1	d(g(x1	ADJ
ejpam-2691	405	19	m	m	NOUN
ejpam-2691	405	20	)	)	PUNCT
ejpam-2691	405	21	,	,	PUNCT
ejpam-2691	405	22	g(x1m+p	g(x1m+p	NOUN
ejpam-2691	405	23	)	)	PUNCT
ejpam-2691	405	24	)	)	PUNCT
ejpam-2691	406	1	+	+	CCONJ
ejpam-2691	406	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	406	3	m	m	NOUN
ejpam-2691	406	4	)	)	PUNCT
ejpam-2691	406	5	,	,	PUNCT
ejpam-2691	406	6	g(x2m+p	g(x2m+p	NOUN
ejpam-2691	406	7	)	)	PUNCT
ejpam-2691	406	8	)	)	PUNCT
ejpam-2691	407	1	+	+	CCONJ
ejpam-2691	407	2	·	·	PUNCT
ejpam-2691	407	3	·	·	PUNCT
ejpam-2691	407	4	·	·	PUNCT
ejpam-2691	407	5	+	+	NUM
ejpam-2691	407	6	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	407	7	)	)	PUNCT
ejpam-2691	407	8	,	,	PUNCT
ejpam-2691	407	9	g(xrm+p	g(xrm+p	NOUN
ejpam-2691	407	10	)	)	PUNCT
ejpam-2691	407	11	)	)	PUNCT
ejpam-2691	407	12	≤	≤	NOUN
ejpam-2691	408	1	[	[	X
ejpam-2691	408	2	(	(	PUNCT
ejpam-2691	408	3	d(g(x1	d(g(x1	PROPN
ejpam-2691	408	4	m	m	NOUN
ejpam-2691	408	5	)	)	PUNCT
ejpam-2691	408	6	,	,	PUNCT
ejpam-2691	408	7	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	408	8	)	)	PUNCT
ejpam-2691	408	9	)	)	PUNCT
ejpam-2691	409	1	+	+	CCONJ
ejpam-2691	409	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	409	3	m	m	NOUN
ejpam-2691	409	4	)	)	PUNCT
ejpam-2691	409	5	,	,	PUNCT
ejpam-2691	409	6	g(x2m+1	g(x2m+1	NOUN
ejpam-2691	409	7	)	)	PUNCT
ejpam-2691	409	8	)	)	PUNCT
ejpam-2691	410	1	+	+	CCONJ
ejpam-2691	410	2	·	·	PUNCT
ejpam-2691	410	3	·	·	PUNCT
ejpam-2691	410	4	·	·	PUNCT
ejpam-2691	410	5	+	+	NUM
ejpam-2691	410	6	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	410	7	)	)	PUNCT
ejpam-2691	410	8	,	,	PUNCT
ejpam-2691	410	9	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	410	10	)	)	PUNCT
ejpam-2691	410	11	)	)	PUNCT
ejpam-2691	410	12	)	)	PUNCT
ejpam-2691	411	1	+	+	ADJ
ejpam-2691	411	2	(	(	PUNCT
ejpam-2691	411	3	d(g(x1	d(g(x1	PROPN
ejpam-2691	411	4	m	m	NOUN
ejpam-2691	411	5	)	)	PUNCT
ejpam-2691	411	6	,	,	PUNCT
ejpam-2691	411	7	g(x1m+2	g(x1m+2	NOUN
ejpam-2691	411	8	)	)	PUNCT
ejpam-2691	411	9	)	)	PUNCT
ejpam-2691	412	1	+	+	CCONJ
ejpam-2691	412	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	412	3	m	m	NOUN
ejpam-2691	412	4	)	)	PUNCT
ejpam-2691	412	5	,	,	PUNCT
ejpam-2691	412	6	g(x2m+2	g(x2m+2	NOUN
ejpam-2691	412	7	)	)	PUNCT
ejpam-2691	412	8	)	)	PUNCT
ejpam-2691	413	1	+	+	CCONJ
ejpam-2691	413	2	·	·	PUNCT
ejpam-2691	413	3	·	·	PUNCT
ejpam-2691	413	4	·	·	PUNCT
ejpam-2691	413	5	+	+	NUM
ejpam-2691	413	6	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	413	7	)	)	PUNCT
ejpam-2691	413	8	,	,	PUNCT
ejpam-2691	413	9	g(xrm+2	g(xrm+2	PROPN
ejpam-2691	413	10	)	)	PUNCT
ejpam-2691	413	11	)	)	PUNCT
ejpam-2691	413	12	)	)	PUNCT
ejpam-2691	413	13	·	·	PUNCT
ejpam-2691	414	1	·	·	PUNCT
ejpam-2691	414	2	·	·	PUNCT
ejpam-2691	414	3	+	+	NUM
ejpam-2691	414	4	(	(	PUNCT
ejpam-2691	414	5	d(g(x1m+p−1	d(g(x1m+p−1	NOUN
ejpam-2691	414	6	)	)	PUNCT
ejpam-2691	414	7	,	,	PUNCT
ejpam-2691	414	8	g(x1m+p	g(x1m+p	NOUN
ejpam-2691	414	9	)	)	PUNCT
ejpam-2691	414	10	)	)	PUNCT
ejpam-2691	415	1	+	+	CCONJ
ejpam-2691	415	2	d(g(x2m+p−1	d(g(x2m+p−1	ADJ
ejpam-2691	415	3	)	)	PUNCT
ejpam-2691	415	4	,	,	PUNCT
ejpam-2691	415	5	g(x2m+p	g(x2m+p	NOUN
ejpam-2691	415	6	)	)	PUNCT
ejpam-2691	415	7	)	)	PUNCT
ejpam-2691	416	1	+	+	CCONJ
ejpam-2691	416	2	·	·	PUNCT
ejpam-2691	416	3	·	·	PUNCT
ejpam-2691	416	4	·	·	PUNCT
ejpam-2691	416	5	+	+	NUM
ejpam-2691	416	6	d(g(xrm+p−1	d(g(xrm+p−1	NOUN
ejpam-2691	416	7	)	)	PUNCT
ejpam-2691	416	8	,	,	PUNCT
ejpam-2691	416	9	g(xrm+p	g(xrm+p	NOUN
ejpam-2691	416	10	)	)	PUNCT
ejpam-2691	416	11	)	)	PUNCT
ejpam-2691	416	12	)	)	PUNCT
ejpam-2691	416	13	]	]	PUNCT
ejpam-2691	417	1	≤	≤	PROPN
ejpam-2691	417	2	m−1∏	m−1∏	PROPN
ejpam-2691	417	3	i=0	i=0	PROPN
ejpam-2691	417	4	(	(	PUNCT
ejpam-2691	417	5	βi	βi	PROPN
ejpam-2691	417	6	,	,	PUNCT
ejpam-2691	417	7	i+1	i+1	NOUN
ejpam-2691	417	8	+	+	NUM
ejpam-2691	417	9	γi	γi	NOUN
ejpam-2691	417	10	,	,	PUNCT
ejpam-2691	417	11	i+1	i+1	NOUN
ejpam-2691	417	12	1−	1−	NUM
ejpam-2691	417	13	βi	βi	NOUN
ejpam-2691	417	14	,	,	PUNCT
ejpam-2691	417	15	i+1	i+1	X
ejpam-2691	417	16	)	)	PUNCT
ejpam-2691	417	17	δ0	δ0	NOUN
ejpam-2691	417	18	+	+	CCONJ
ejpam-2691	417	19	m∏	m∏	PROPN
ejpam-2691	417	20	i=0	i=0	PROPN
ejpam-2691	417	21	(	(	PUNCT
ejpam-2691	417	22	βi	βi	PROPN
ejpam-2691	417	23	,	,	PUNCT
ejpam-2691	417	24	i+1	i+1	NOUN
ejpam-2691	417	25	+	+	NUM
ejpam-2691	417	26	γi	γi	NOUN
ejpam-2691	417	27	,	,	PUNCT
ejpam-2691	417	28	i+1	i+1	NOUN
ejpam-2691	417	29	1−	1−	NUM
ejpam-2691	417	30	βi	βi	NOUN
ejpam-2691	417	31	,	,	PUNCT
ejpam-2691	417	32	i+1	i+1	X
ejpam-2691	417	33	)	)	PUNCT
ejpam-2691	417	34	δ0	δ0	NOUN
ejpam-2691	417	35	+	+	NOUN
ejpam-2691	417	36	·	·	PUNCT
ejpam-2691	417	37	·	·	PUNCT
ejpam-2691	417	38	·	·	PUNCT
ejpam-2691	418	1	+	+	NUM
ejpam-2691	418	2	m+p−2∏	m+p−2∏	X
ejpam-2691	418	3	i=0	i=0	PROPN
ejpam-2691	418	4	(	(	PUNCT
ejpam-2691	418	5	βi	βi	PROPN
ejpam-2691	418	6	,	,	PUNCT
ejpam-2691	418	7	i+1	i+1	NOUN
ejpam-2691	418	8	+	+	NUM
ejpam-2691	418	9	γi	γi	NOUN
ejpam-2691	418	10	,	,	PUNCT
ejpam-2691	418	11	i+1	i+1	NOUN
ejpam-2691	418	12	1−	1−	NUM
ejpam-2691	418	13	βi	βi	NOUN
ejpam-2691	418	14	,	,	PUNCT
ejpam-2691	418	15	i+1	i+1	X
ejpam-2691	418	16	)	)	PUNCT
ejpam-2691	418	17	δ0	δ0	NOUN
ejpam-2691	418	18	=	=	SYM
ejpam-2691	418	19	p−1∑	p−1∑	NOUN
ejpam-2691	418	20	k=0	k=0	PROPN
ejpam-2691	418	21	m+k−1∏	m+k−1∏	PROPN
ejpam-2691	418	22	i=0	i=0	PROPN
ejpam-2691	418	23	(	(	PUNCT
ejpam-2691	418	24	βi	βi	PROPN
ejpam-2691	418	25	,	,	PUNCT
ejpam-2691	418	26	i+1	i+1	NOUN
ejpam-2691	418	27	+	+	NUM
ejpam-2691	418	28	γi	γi	NOUN
ejpam-2691	418	29	,	,	PUNCT
ejpam-2691	418	30	i+1	i+1	NOUN
ejpam-2691	418	31	1−	1−	NUM
ejpam-2691	418	32	βi	βi	NOUN
ejpam-2691	418	33	,	,	PUNCT
ejpam-2691	418	34	i+1	i+1	X
ejpam-2691	418	35	)	)	PUNCT
ejpam-2691	418	36	δ0	δ0	NOUN
ejpam-2691	418	37	=	=	PUNCT
ejpam-2691	418	38	m+p−1∑	m+p−1∑	NOUN
ejpam-2691	418	39	k	k	PROPN
ejpam-2691	418	40	=	=	NOUN
ejpam-2691	418	41	m	m	PROPN
ejpam-2691	418	42	k−1∏	k−1∏	PROPN
ejpam-2691	418	43	i=0	i=0	PROPN
ejpam-2691	418	44	(	(	PUNCT
ejpam-2691	418	45	βi	βi	PROPN
ejpam-2691	418	46	,	,	PUNCT
ejpam-2691	418	47	i+1	i+1	NOUN
ejpam-2691	418	48	+	+	NUM
ejpam-2691	418	49	γi	γi	NOUN
ejpam-2691	418	50	,	,	PUNCT
ejpam-2691	418	51	i+1	i+1	NOUN
ejpam-2691	418	52	1−	1−	NUM
ejpam-2691	418	53	βi	βi	NOUN
ejpam-2691	418	54	,	,	PUNCT
ejpam-2691	418	55	i+1	i+1	NUM
ejpam-2691	418	56	)	)	PUNCT
ejpam-2691	418	57	δ0	δ0	NOUN
ejpam-2691	418	58	.	.	PUNCT
ejpam-2691	419	1	m.	m.	PROPN
ejpam-2691	419	2	grewal	grewal	PROPN
ejpam-2691	419	3	,	,	PUNCT
ejpam-2691	419	4	r.	r.	PROPN
ejpam-2691	419	5	kumar	kumar	PROPN
ejpam-2691	419	6	,	,	PUNCT
ejpam-2691	419	7	a.	a.	PROPN
ejpam-2691	419	8	kumar	kumar	PROPN
ejpam-2691	419	9	/	/	SYM
ejpam-2691	419	10	eur	eur	PROPN
ejpam-2691	419	11	.	.	PUNCT
ejpam-2691	420	1	j.	j.	PROPN
ejpam-2691	420	2	pure	pure	PROPN
ejpam-2691	420	3	appl	appl	PROPN
ejpam-2691	420	4	.	.	PROPN
ejpam-2691	420	5	math	math	PROPN
ejpam-2691	420	6	,	,	PUNCT
ejpam-2691	420	7	10	10	NUM
ejpam-2691	420	8	(	(	PUNCT
ejpam-2691	420	9	2	2	NUM
ejpam-2691	420	10	)	)	PUNCT
ejpam-2691	420	11	(	(	PUNCT
ejpam-2691	420	12	2017	2017	NUM
ejpam-2691	420	13	)	)	PUNCT
ejpam-2691	420	14	,	,	PUNCT
ejpam-2691	420	15	295	295	NUM
ejpam-2691	420	16	-	-	SYM
ejpam-2691	420	17	311	311	NUM
ejpam-2691	420	18	305	305	NUM
ejpam-2691	420	19	now	now	ADV
ejpam-2691	420	20	using	use	VERB
ejpam-2691	420	21	the	the	DET
ejpam-2691	420	22	fact	fact	NOUN
ejpam-2691	420	23	that	that	SCONJ
ejpam-2691	420	24	the	the	DET
ejpam-2691	420	25	geometric	geometric	ADJ
ejpam-2691	420	26	mean	mean	NOUN
ejpam-2691	420	27	of	of	ADP
ejpam-2691	420	28	non	non	ADJ
ejpam-2691	420	29	-	-	ADJ
ejpam-2691	420	30	negative	negative	ADJ
ejpam-2691	420	31	numbers	number	NOUN
ejpam-2691	420	32	is	be	AUX
ejpam-2691	420	33	always	always	ADV
ejpam-2691	420	34	less	less	ADV
ejpam-2691	420	35	or	or	CCONJ
ejpam-2691	420	36	equal	equal	ADJ
ejpam-2691	420	37	to	to	ADP
ejpam-2691	420	38	the	the	DET
ejpam-2691	420	39	arithmetic	arithmetic	ADJ
ejpam-2691	420	40	mean	mean	NOUN
ejpam-2691	420	41	,	,	PUNCT
ejpam-2691	420	42	one	one	PRON
ejpam-2691	420	43	have	have	VERB
ejpam-2691	420	44	d(g(x1	d(g(x1	PROPN
ejpam-2691	420	45	m	m	NOUN
ejpam-2691	420	46	)	)	PUNCT
ejpam-2691	420	47	,	,	PUNCT
ejpam-2691	420	48	g(x1m+p	g(x1m+p	NOUN
ejpam-2691	420	49	)	)	PUNCT
ejpam-2691	420	50	)	)	PUNCT
ejpam-2691	421	1	+	+	CCONJ
ejpam-2691	421	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	421	3	m	m	NOUN
ejpam-2691	421	4	)	)	PUNCT
ejpam-2691	421	5	,	,	PUNCT
ejpam-2691	421	6	g(x2m+p	g(x2m+p	NOUN
ejpam-2691	421	7	)	)	PUNCT
ejpam-2691	421	8	)	)	PUNCT
ejpam-2691	422	1	+	+	CCONJ
ejpam-2691	422	2	·	·	PUNCT
ejpam-2691	422	3	·	·	PUNCT
ejpam-2691	422	4	·	·	PUNCT
ejpam-2691	422	5	+	+	NUM
ejpam-2691	422	6	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	422	7	)	)	PUNCT
ejpam-2691	422	8	,	,	PUNCT
ejpam-2691	422	9	g(xrm+p	g(xrm+p	NOUN
ejpam-2691	422	10	)	)	PUNCT
ejpam-2691	422	11	)	)	PUNCT
ejpam-2691	422	12	≤	≤	PUNCT
ejpam-2691	423	1	m+p−1∑	m+p−1∑	ADP
ejpam-2691	423	2	k	k	PROPN
ejpam-2691	423	3	=	=	NOUN
ejpam-2691	423	4	m	m	X
ejpam-2691	423	5	[	[	PUNCT
ejpam-2691	423	6	1	1	NUM
ejpam-2691	423	7	k	k	X
ejpam-2691	423	8	k−1∏	k−1∏	PROPN
ejpam-2691	423	9	i=0	i=0	PROPN
ejpam-2691	423	10	(	(	PUNCT
ejpam-2691	423	11	βi	βi	PROPN
ejpam-2691	423	12	,	,	PUNCT
ejpam-2691	423	13	i+1	i+1	NOUN
ejpam-2691	423	14	+	+	NUM
ejpam-2691	423	15	γi	γi	NOUN
ejpam-2691	423	16	,	,	PUNCT
ejpam-2691	423	17	i+1	i+1	NOUN
ejpam-2691	423	18	1−	1−	NUM
ejpam-2691	423	19	βi	βi	NOUN
ejpam-2691	423	20	,	,	PUNCT
ejpam-2691	423	21	i+1	i+1	NUM
ejpam-2691	423	22	)	)	PUNCT
ejpam-2691	423	23	]	]	PUNCT
ejpam-2691	423	24	kδ0	kδ0	NOUN
ejpam-2691	423	25	.	.	PUNCT
ejpam-2691	423	26	≤	≤	NUM
ejpam-2691	423	27	(	(	PUNCT
ejpam-2691	423	28	m+p−1∑	m+p−1∑	NOUN
ejpam-2691	423	29	k	k	NOUN
ejpam-2691	423	30	=	=	NOUN
ejpam-2691	423	31	m	m	AUX
ejpam-2691	423	32	αk)δ0	αk)δ0	VERB
ejpam-2691	423	33	.	.	PUNCT
ejpam-2691	424	1	≤	≤	NUM
ejpam-2691	424	2	αm	αm	ADP
ejpam-2691	424	3	1−	1−	NUM
ejpam-2691	424	4	α	α	NUM
ejpam-2691	424	5	δ0	δ0	NOUN
ejpam-2691	424	6	now	now	ADV
ejpam-2691	424	7	,	,	PUNCT
ejpam-2691	424	8	proceeding	proceed	VERB
ejpam-2691	424	9	the	the	DET
ejpam-2691	424	10	limit	limit	NOUN
ejpam-2691	424	11	as	as	ADP
ejpam-2691	424	12	m→	m→	PROPN
ejpam-2691	424	13	+	+	PROPN
ejpam-2691	424	14	∞	∞	PROPN
ejpam-2691	424	15	,	,	PUNCT
ejpam-2691	424	16	ones	one	NOUN
ejpam-2691	424	17	deduce	deduce	VERB
ejpam-2691	424	18	that	that	SCONJ
ejpam-2691	424	19	lim	lim	PROPN
ejpam-2691	424	20	m→+∞	m→+∞	PROPN
ejpam-2691	424	21	δm	δm	PROPN
ejpam-2691	424	22	=	=	PROPN
ejpam-2691	424	23	lim	lim	PROPN
ejpam-2691	424	24	m→+∞	m→+∞	PROPN
ejpam-2691	424	25	αm	αm	NOUN
ejpam-2691	424	26	1−	1−	NUM
ejpam-2691	424	27	α	α	NOUN
ejpam-2691	424	28	δ0	δ0	NOUN
ejpam-2691	424	29	=	=	SYM
ejpam-2691	424	30	0	0	PUNCT
ejpam-2691	424	31	as	as	ADP
ejpam-2691	424	32	α	α	PRON
ejpam-2691	424	33	<	<	X
ejpam-2691	424	34	1	1	NUM
ejpam-2691	424	35	.	.	PUNCT
ejpam-2691	425	1	i.e.	i.e.	X
ejpam-2691	425	2	,	,	PUNCT
ejpam-2691	425	3	lim	lim	PROPN
ejpam-2691	425	4	m→+∞	m→+∞	PROPN
ejpam-2691	426	1	[	[	X
ejpam-2691	426	2	d(g(x1	d(g(x1	PROPN
ejpam-2691	426	3	m	m	NOUN
ejpam-2691	426	4	)	)	PUNCT
ejpam-2691	426	5	,	,	PUNCT
ejpam-2691	426	6	g(x1m+p	g(x1m+p	NOUN
ejpam-2691	426	7	)	)	PUNCT
ejpam-2691	426	8	)	)	PUNCT
ejpam-2691	427	1	+	+	CCONJ
ejpam-2691	427	2	d(g(x2	d(g(x2	PROPN
ejpam-2691	427	3	m	m	NOUN
ejpam-2691	427	4	)	)	PUNCT
ejpam-2691	427	5	,	,	PUNCT
ejpam-2691	427	6	g(x2m+p	g(x2m+p	NOUN
ejpam-2691	427	7	)	)	PUNCT
ejpam-2691	427	8	)	)	PUNCT
ejpam-2691	428	1	+	+	CCONJ
ejpam-2691	428	2	·	·	PUNCT
ejpam-2691	428	3	·	·	PUNCT
ejpam-2691	428	4	·	·	PUNCT
ejpam-2691	428	5	+	+	NUM
ejpam-2691	428	6	d(g(xrm	d(g(xrm	NOUN
ejpam-2691	428	7	)	)	PUNCT
ejpam-2691	428	8	,	,	PUNCT
ejpam-2691	428	9	g(xrm+p	g(xrm+p	NOUN
ejpam-2691	428	10	)	)	PUNCT
ejpam-2691	428	11	)	)	PUNCT
ejpam-2691	428	12	]	]	PUNCT
ejpam-2691	429	1	=	=	PUNCT
ejpam-2691	429	2	0	0	X
ejpam-2691	429	3	.	.	NOUN
ejpam-2691	429	4	which	which	PRON
ejpam-2691	429	5	further	far	ADV
ejpam-2691	429	6	implies	imply	VERB
ejpam-2691	429	7	that	that	SCONJ
ejpam-2691	429	8	lim	lim	PROPN
ejpam-2691	429	9	m→+∞	m→+∞	PROPN
ejpam-2691	429	10	d(g(x1	d(g(x1	PROPN
ejpam-2691	429	11	m	m	NOUN
ejpam-2691	429	12	)	)	PUNCT
ejpam-2691	429	13	,	,	PUNCT
ejpam-2691	429	14	g(x1m+p	g(x1m+p	NOUN
ejpam-2691	429	15	)	)	PUNCT
ejpam-2691	429	16	)	)	PUNCT
ejpam-2691	430	1	=	=	VERB
ejpam-2691	430	2	lim	lim	PROPN
ejpam-2691	430	3	n→+∞	n→+∞	VERB
ejpam-2691	430	4	d(g(x2	d(g(x2	PROPN
ejpam-2691	430	5	m	m	NOUN
ejpam-2691	430	6	)	)	PUNCT
ejpam-2691	430	7	,	,	PUNCT
ejpam-2691	430	8	g(x2m+p	g(x2m+p	NOUN
ejpam-2691	430	9	)	)	PUNCT
ejpam-2691	430	10	)	)	PUNCT
ejpam-2691	431	1	=	=	SYM
ejpam-2691	431	2	·	·	PUNCT
ejpam-2691	431	3	·	·	PUNCT
ejpam-2691	431	4	·	·	PUNCT
ejpam-2691	432	1	=	=	SYM
ejpam-2691	432	2	lim	lim	PROPN
ejpam-2691	432	3	n→+∞	n→+∞	PROPN
ejpam-2691	432	4	d(g(xrm	d(g(xrm	PROPN
ejpam-2691	432	5	)	)	PUNCT
ejpam-2691	432	6	,	,	PUNCT
ejpam-2691	432	7	g(xrm+p	g(xrm+p	NOUN
ejpam-2691	432	8	)	)	PUNCT
ejpam-2691	432	9	)	)	PUNCT
ejpam-2691	433	1	=	=	PUNCT
ejpam-2691	433	2	0	0	X
ejpam-2691	433	3	.	.	PUNCT
ejpam-2691	433	4	{	{	PUNCT
ejpam-2691	433	5	g(x1	g(x1	NOUN
ejpam-2691	433	6	m	m	NOUN
ejpam-2691	433	7	)	)	PUNCT
ejpam-2691	433	8	}	}	PUNCT
ejpam-2691	433	9	,	,	PUNCT
ejpam-2691	433	10	{	{	PUNCT
ejpam-2691	433	11	g(x2	g(x2	NOUN
ejpam-2691	433	12	m	m	PROPN
ejpam-2691	433	13	)	)	PUNCT
ejpam-2691	433	14	}	}	PUNCT
ejpam-2691	433	15	,	,	PUNCT
ejpam-2691	433	16	.	.	PUNCT
ejpam-2691	433	17	.	.	PUNCT
ejpam-2691	433	18	.	.	PUNCT
ejpam-2691	434	1	,	,	PUNCT
ejpam-2691	434	2	{	{	PUNCT
ejpam-2691	434	3	g(x1	g(x1	NOUN
ejpam-2691	434	4	m	m	NOUN
ejpam-2691	434	5	)	)	PUNCT
ejpam-2691	434	6	}	}	PUNCT
ejpam-2691	434	7	are	be	AUX
ejpam-2691	434	8	all	all	PRON
ejpam-2691	434	9	cauchy	cauchy	ADJ
ejpam-2691	434	10	sequences	sequence	NOUN
ejpam-2691	434	11	in	in	ADP
ejpam-2691	434	12	(	(	PUNCT
ejpam-2691	434	13	x	x	NOUN
ejpam-2691	434	14	,	,	PUNCT
ejpam-2691	434	15	d	d	PROPN
ejpam-2691	434	16	,	,	PUNCT
ejpam-2691	434	17	�	�	PROPN
ejpam-2691	434	18	)	)	PUNCT
ejpam-2691	434	19	.	.	PUNCT
ejpam-2691	435	1	since	since	SCONJ
ejpam-2691	435	2	g(x	g(x	NOUN
ejpam-2691	435	3	)	)	PUNCT
ejpam-2691	435	4	is	be	AUX
ejpam-2691	435	5	complete	complete	ADJ
ejpam-2691	435	6	subspace	subspace	NOUN
ejpam-2691	435	7	ofx	ofx	NOUN
ejpam-2691	435	8	,	,	PUNCT
ejpam-2691	435	9	and	and	CCONJ
ejpam-2691	435	10	hence	hence	ADV
ejpam-2691	435	11	there	there	PRON
ejpam-2691	435	12	exists	exist	VERB
ejpam-2691	435	13	(	(	PUNCT
ejpam-2691	435	14	x10	x10	NOUN
ejpam-2691	435	15	,	,	PUNCT
ejpam-2691	435	16	x	x	NOUN
ejpam-2691	435	17	2	2	NUM
ejpam-2691	435	18	0	0	NUM
ejpam-2691	435	19	,	,	PUNCT
ejpam-2691	435	20	.	.	PUNCT
ejpam-2691	435	21	.	.	PUNCT
ejpam-2691	435	22	.	.	PUNCT
ejpam-2691	436	1	,	,	PUNCT
ejpam-2691	436	2	x	x	PUNCT
ejpam-2691	436	3	r	r	NOUN
ejpam-2691	436	4	0	0	NUM
ejpam-2691	436	5	)	)	PUNCT
ejpam-2691	436	6	∈	∈	PROPN
ejpam-2691	436	7	∏r	∏r	NOUN
ejpam-2691	436	8	λ=1x	λ=1x	NOUN
ejpam-2691	436	9	λ	λ	NOUN
ejpam-2691	436	10	such	such	ADJ
ejpam-2691	436	11	that	that	SCONJ
ejpam-2691	436	12			PROPN
ejpam-2691	436	13	g(x10	g(x10	NOUN
ejpam-2691	436	14	)	)	PUNCT
ejpam-2691	437	1	=	=	SYM
ejpam-2691	437	2	x1	x1	ADJ
ejpam-2691	437	3	,	,	PUNCT
ejpam-2691	437	4	g(x20	g(x20	NOUN
ejpam-2691	437	5	)	)	PUNCT
ejpam-2691	437	6	=	=	SYM
ejpam-2691	437	7	x2	x2	PROPN
ejpam-2691	437	8	,	,	PUNCT
ejpam-2691	437	9	...	...	PUNCT
ejpam-2691	437	10	g(xr0	g(xr0	NOUN
ejpam-2691	437	11	)	)	PUNCT
ejpam-2691	437	12	=	=	PUNCT
ejpam-2691	437	13	xr	xr	PROPN
ejpam-2691	437	14	.	.	PUNCT
ejpam-2691	438	1	(	(	PUNCT
ejpam-2691	438	2	12	12	NUM
ejpam-2691	438	3	)	)	PUNCT
ejpam-2691	438	4	by	by	ADP
ejpam-2691	438	5	the	the	DET
ejpam-2691	438	6	continuity	continuity	NOUN
ejpam-2691	438	7	of	of	ADP
ejpam-2691	438	8	g	g	PROPN
ejpam-2691	438	9	and	and	CCONJ
ejpam-2691	438	10	(	(	PUNCT
ejpam-2691	438	11	12	12	NUM
ejpam-2691	438	12	)	)	PUNCT
ejpam-2691	438	13	,	,	PUNCT
ejpam-2691	438	14	we	we	PRON
ejpam-2691	438	15	have	have	VERB
ejpam-2691	438	16	g(g(x10	g(g(x10	PROPN
ejpam-2691	438	17	)	)	PUNCT
ejpam-2691	438	18	)	)	PUNCT
ejpam-2691	439	1	=	=	SYM
ejpam-2691	439	2	g(x1	g(x1	NOUN
ejpam-2691	439	3	)	)	PUNCT
ejpam-2691	439	4	,	,	PUNCT
ejpam-2691	439	5	g(g(x20	g(g(x20	PROPN
ejpam-2691	439	6	)	)	PUNCT
ejpam-2691	439	7	)	)	PUNCT
ejpam-2691	439	8	=	=	SYM
ejpam-2691	439	9	g(x2	g(x2	NOUN
ejpam-2691	439	10	)	)	PUNCT
ejpam-2691	439	11	,	,	PUNCT
ejpam-2691	439	12	...	...	PUNCT
ejpam-2691	439	13	g(g(xr0	g(g(xr0	NOUN
ejpam-2691	439	14	)	)	PUNCT
ejpam-2691	439	15	)	)	PUNCT
ejpam-2691	440	1	=	=	PUNCT
ejpam-2691	440	2	g(xr	g(xr	PROPN
ejpam-2691	440	3	)	)	PUNCT
ejpam-2691	440	4	.	.	PUNCT
ejpam-2691	441	1	(	(	PUNCT
ejpam-2691	441	2	13	13	NUM
ejpam-2691	441	3	)	)	PUNCT
ejpam-2691	441	4	now	now	ADV
ejpam-2691	441	5	using	use	VERB
ejpam-2691	441	6	the	the	DET
ejpam-2691	441	7	above	above	ADJ
ejpam-2691	441	8	equations	equation	NOUN
ejpam-2691	441	9	we	we	PRON
ejpam-2691	441	10	have	have	PROPN
ejpam-2691	441	11	lim	lim	PROPN
ejpam-2691	441	12	m→+∞	m→+∞	PROPN
ejpam-2691	441	13	g(x1m+1	g(x1m+1	NOUN
ejpam-2691	441	14	)	)	PUNCT
ejpam-2691	442	1	=	=	SYM
ejpam-2691	442	2	lim	lim	PROPN
ejpam-2691	442	3	m→+∞	m→+∞	PROPN
ejpam-2691	442	4	tm(x1	tm(x1	PROPN
ejpam-2691	442	5	m	m	PROPN
ejpam-2691	442	6	,	,	PUNCT
ejpam-2691	442	7	x	x	PROPN
ejpam-2691	442	8	2	2	NUM
ejpam-2691	442	9	m	m	NOUN
ejpam-2691	442	10	,	,	PUNCT
ejpam-2691	442	11	.	.	PUNCT
ejpam-2691	442	12	.	.	PUNCT
ejpam-2691	443	1	.	.	PUNCT
ejpam-2691	444	1	,	,	PUNCT
ejpam-2691	444	2	x	x	PUNCT
ejpam-2691	444	3	r	r	NOUN
ejpam-2691	444	4	m	m	PROPN
ejpam-2691	444	5	)	)	PUNCT
ejpam-2691	445	1	=	=	SYM
ejpam-2691	445	2	x1	x1	PROPN
ejpam-2691	445	3	,	,	PUNCT
ejpam-2691	445	4	lim	lim	PROPN
ejpam-2691	445	5	m→+∞	m→+∞	PROPN
ejpam-2691	445	6	g(x2m+1	g(x2m+1	PROPN
ejpam-2691	445	7	)	)	PUNCT
ejpam-2691	446	1	=	=	SYM
ejpam-2691	446	2	lim	lim	PROPN
ejpam-2691	446	3	m→+∞	m→+∞	PROPN
ejpam-2691	446	4	tm(x2	tm(x2	NOUN
ejpam-2691	446	5	m	m	PROPN
ejpam-2691	446	6	,	,	PUNCT
ejpam-2691	446	7	x	x	PROPN
ejpam-2691	446	8	3	3	NUM
ejpam-2691	446	9	m	m	NOUN
ejpam-2691	446	10	,	,	PUNCT
ejpam-2691	446	11	.	.	PUNCT
ejpam-2691	446	12	.	.	PUNCT
ejpam-2691	447	1	.	.	PUNCT
ejpam-2691	448	1	,	,	PUNCT
ejpam-2691	448	2	x	x	PUNCT
ejpam-2691	448	3	r	r	NOUN
ejpam-2691	448	4	m	m	PROPN
ejpam-2691	448	5	,	,	PUNCT
ejpam-2691	448	6	x	x	PROPN
ejpam-2691	448	7	1	1	NUM
ejpam-2691	448	8	m	m	NOUN
ejpam-2691	448	9	)	)	PUNCT
ejpam-2691	448	10	=	=	SYM
ejpam-2691	448	11	x2	x2	PROPN
ejpam-2691	448	12	,	,	PUNCT
ejpam-2691	448	13	...	...	PUNCT
ejpam-2691	448	14	and	and	CCONJ
ejpam-2691	448	15	lim	lim	PROPN
ejpam-2691	448	16	m→+∞	m→+∞	PROPN
ejpam-2691	448	17	g(xrm+1	g(xrm+1	PROPN
ejpam-2691	448	18	)	)	PUNCT
ejpam-2691	449	1	=	=	PROPN
ejpam-2691	449	2	lim	lim	PROPN
ejpam-2691	449	3	m→+∞	m→+∞	PROPN
ejpam-2691	449	4	tm(xrm	tm(xrm	PROPN
ejpam-2691	449	5	,	,	PUNCT
ejpam-2691	449	6	x	x	PROPN
ejpam-2691	449	7	1	1	NUM
ejpam-2691	449	8	m	m	NOUN
ejpam-2691	449	9	,	,	PUNCT
ejpam-2691	449	10	.	.	PUNCT
ejpam-2691	449	11	.	.	PUNCT
ejpam-2691	449	12	.	.	PUNCT
ejpam-2691	450	1	,	,	PUNCT
ejpam-2691	451	1	x	x	X
ejpam-2691	451	2	r−1	r−1	NOUN
ejpam-2691	451	3	m	m	ADV
ejpam-2691	451	4	)	)	PUNCT
ejpam-2691	452	1	=	=	PUNCT
ejpam-2691	452	2	xr	xr	PROPN
ejpam-2691	452	3	.	.	PUNCT
ejpam-2691	452	4	m.	m.	PROPN
ejpam-2691	452	5	grewal	grewal	PROPN
ejpam-2691	452	6	,	,	PUNCT
ejpam-2691	452	7	r.	r.	PROPN
ejpam-2691	452	8	kumar	kumar	PROPN
ejpam-2691	452	9	,	,	PUNCT
ejpam-2691	452	10	a.	a.	PROPN
ejpam-2691	452	11	kumar	kumar	PROPN
ejpam-2691	452	12	/	/	SYM
ejpam-2691	452	13	eur	eur	PROPN
ejpam-2691	452	14	.	.	PUNCT
ejpam-2691	453	1	j.	j.	PROPN
ejpam-2691	453	2	pure	pure	PROPN
ejpam-2691	453	3	appl	appl	PROPN
ejpam-2691	453	4	.	.	PROPN
ejpam-2691	453	5	math	math	PROPN
ejpam-2691	453	6	,	,	PUNCT
ejpam-2691	453	7	10	10	NUM
ejpam-2691	453	8	(	(	PUNCT
ejpam-2691	453	9	2	2	NUM
ejpam-2691	453	10	)	)	PUNCT
ejpam-2691	453	11	(	(	PUNCT
ejpam-2691	453	12	2017	2017	NUM
ejpam-2691	453	13	)	)	PUNCT
ejpam-2691	453	14	,	,	PUNCT
ejpam-2691	453	15	295	295	NUM
ejpam-2691	453	16	-	-	SYM
ejpam-2691	453	17	311	311	NUM
ejpam-2691	453	18	306	306	NUM
ejpam-2691	453	19	since	since	SCONJ
ejpam-2691	453	20	{	{	PUNCT
ejpam-2691	453	21	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	453	22	and	and	CCONJ
ejpam-2691	453	23	g	g	NOUN
ejpam-2691	453	24	are	be	AUX
ejpam-2691	453	25	weakly	weakly	ADV
ejpam-2691	453	26	reciprocally	reciprocally	ADV
ejpam-2691	453	27	continuous	continuous	ADJ
ejpam-2691	453	28	,	,	PUNCT
ejpam-2691	453	29	thus	thus	PROPN
ejpam-2691	453	30	lim	lim	PROPN
ejpam-2691	453	31	m→+∞	m→+∞	PROPN
ejpam-2691	453	32	g(tm(x1	g(tm(x1	ADJ
ejpam-2691	453	33	m	m	NOUN
ejpam-2691	453	34	,	,	PUNCT
ejpam-2691	453	35	x	x	PROPN
ejpam-2691	453	36	2	2	NUM
ejpam-2691	453	37	m	m	NOUN
ejpam-2691	453	38	,	,	PUNCT
ejpam-2691	453	39	.	.	PUNCT
ejpam-2691	453	40	.	.	PUNCT
ejpam-2691	453	41	.	.	PUNCT
ejpam-2691	454	1	,	,	PUNCT
ejpam-2691	454	2	x	x	PUNCT
ejpam-2691	454	3	r	r	NOUN
ejpam-2691	454	4	m	m	PROPN
ejpam-2691	454	5	)	)	PUNCT
ejpam-2691	454	6	)	)	PUNCT
ejpam-2691	455	1	=	=	SYM
ejpam-2691	455	2	g(x1	g(x1	NOUN
ejpam-2691	455	3	)	)	PUNCT
ejpam-2691	455	4	,	,	PUNCT
ejpam-2691	455	5	lim	lim	PROPN
ejpam-2691	455	6	m→+∞	m→+∞	PROPN
ejpam-2691	455	7	g(tm(x2	g(tm(x2	NOUN
ejpam-2691	455	8	m	m	NOUN
ejpam-2691	455	9	,	,	PUNCT
ejpam-2691	455	10	x	x	PROPN
ejpam-2691	455	11	3	3	NUM
ejpam-2691	455	12	m	m	NOUN
ejpam-2691	455	13	,	,	PUNCT
ejpam-2691	455	14	.	.	PUNCT
ejpam-2691	455	15	.	.	PUNCT
ejpam-2691	455	16	.	.	PUNCT
ejpam-2691	456	1	,	,	PUNCT
ejpam-2691	456	2	x	x	PUNCT
ejpam-2691	456	3	r	r	NOUN
ejpam-2691	456	4	m	m	PROPN
ejpam-2691	456	5	,	,	PUNCT
ejpam-2691	456	6	x	x	PROPN
ejpam-2691	456	7	1	1	NUM
ejpam-2691	456	8	m	m	NOUN
ejpam-2691	456	9	)	)	PUNCT
ejpam-2691	456	10	=	=	SYM
ejpam-2691	456	11	g(x2	g(x2	NOUN
ejpam-2691	456	12	)	)	PUNCT
ejpam-2691	456	13	,	,	PUNCT
ejpam-2691	456	14	...	...	PUNCT
ejpam-2691	456	15	and	and	CCONJ
ejpam-2691	456	16	lim	lim	PROPN
ejpam-2691	456	17	m→+∞	m→+∞	PROPN
ejpam-2691	456	18	g(tm(xrm	g(tm(xrm	PROPN
ejpam-2691	456	19	,	,	PUNCT
ejpam-2691	456	20	x	x	PROPN
ejpam-2691	456	21	1	1	NUM
ejpam-2691	456	22	m	m	NOUN
ejpam-2691	456	23	,	,	PUNCT
ejpam-2691	456	24	.	.	PUNCT
ejpam-2691	456	25	.	.	PUNCT
ejpam-2691	456	26	.	.	PUNCT
ejpam-2691	457	1	,	,	PUNCT
ejpam-2691	457	2	x	x	X
ejpam-2691	457	3	r−1	r−1	NOUN
ejpam-2691	457	4	m	m	PROPN
ejpam-2691	457	5	)	)	PUNCT
ejpam-2691	457	6	)	)	PUNCT
ejpam-2691	458	1	=	=	PUNCT
ejpam-2691	458	2	g(xr	g(xr	NOUN
ejpam-2691	458	3	)	)	PUNCT
ejpam-2691	458	4	.	.	PUNCT
ejpam-2691	459	1	on	on	ADP
ejpam-2691	459	2	the	the	DET
ejpam-2691	459	3	other	other	ADJ
ejpam-2691	459	4	hand	hand	NOUN
ejpam-2691	459	5	,	,	PUNCT
ejpam-2691	459	6	the	the	DET
ejpam-2691	459	7	compatibility	compatibility	NOUN
ejpam-2691	459	8	of	of	ADP
ejpam-2691	459	9	{	{	PUNCT
ejpam-2691	459	10	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	459	11	and	and	CCONJ
ejpam-2691	459	12	g	g	NOUN
ejpam-2691	459	13	yields	yield	NOUN
ejpam-2691	459	14	.	.	PUNCT
ejpam-2691	460	1			NUM
ejpam-2691	460	2	lim	lim	PROPN
ejpam-2691	460	3	m→+∞	m→+∞	PROPN
ejpam-2691	460	4	d(g(tm(x1	d(g(tm(x1	PROPN
ejpam-2691	460	5	m	m	NOUN
ejpam-2691	460	6	,	,	PUNCT
ejpam-2691	460	7	x	x	PROPN
ejpam-2691	460	8	2	2	NUM
ejpam-2691	460	9	m	m	NOUN
ejpam-2691	460	10	,	,	PUNCT
ejpam-2691	460	11	.	.	PUNCT
ejpam-2691	460	12	.	.	PUNCT
ejpam-2691	460	13	.	.	PUNCT
ejpam-2691	461	1	,	,	PUNCT
ejpam-2691	461	2	x	x	PUNCT
ejpam-2691	461	3	r	r	NOUN
ejpam-2691	461	4	m	m	PROPN
ejpam-2691	461	5	)	)	PUNCT
ejpam-2691	461	6	)	)	PUNCT
ejpam-2691	461	7	,	,	PUNCT
ejpam-2691	461	8	tm(g(x1	tm(g(x1	PROPN
ejpam-2691	461	9	m	m	NOUN
ejpam-2691	461	10	)	)	PUNCT
ejpam-2691	461	11	,	,	PUNCT
ejpam-2691	461	12	g(x2	g(x2	NOUN
ejpam-2691	461	13	m	m	PROPN
ejpam-2691	461	14	)	)	PUNCT
ejpam-2691	461	15	,	,	PUNCT
ejpam-2691	461	16	.	.	PUNCT
ejpam-2691	461	17	.	.	PUNCT
ejpam-2691	461	18	.	.	PUNCT
ejpam-2691	462	1	,	,	PUNCT
ejpam-2691	462	2	g(xrm	g(xrm	NOUN
ejpam-2691	462	3	)	)	PUNCT
ejpam-2691	462	4	)	)	PUNCT
ejpam-2691	462	5	)	)	PUNCT
ejpam-2691	463	1	=	=	SYM
ejpam-2691	463	2	0	0	NUM
ejpam-2691	463	3	,	,	PUNCT
ejpam-2691	463	4	lim	lim	PROPN
ejpam-2691	463	5	m→+∞	m→+∞	PROPN
ejpam-2691	463	6	d(g(tm(x2	d(g(tm(x2	PROPN
ejpam-2691	463	7	m	m	PROPN
ejpam-2691	463	8	,	,	PUNCT
ejpam-2691	463	9	x	x	PROPN
ejpam-2691	463	10	3	3	NUM
ejpam-2691	463	11	m	m	NOUN
ejpam-2691	463	12	,	,	PUNCT
ejpam-2691	463	13	.	.	PUNCT
ejpam-2691	463	14	.	.	PUNCT
ejpam-2691	463	15	.	.	PUNCT
ejpam-2691	464	1	,	,	PUNCT
ejpam-2691	464	2	x	x	PUNCT
ejpam-2691	464	3	r	r	NOUN
ejpam-2691	464	4	m	m	PROPN
ejpam-2691	464	5	,	,	PUNCT
ejpam-2691	464	6	x	x	PROPN
ejpam-2691	464	7	1	1	NUM
ejpam-2691	464	8	m	m	NOUN
ejpam-2691	464	9	)	)	PUNCT
ejpam-2691	464	10	)	)	PUNCT
ejpam-2691	464	11	,	,	PUNCT
ejpam-2691	464	12	tm(g(x2	tm(g(x2	PROPN
ejpam-2691	464	13	m	m	NOUN
ejpam-2691	464	14	)	)	PUNCT
ejpam-2691	464	15	,	,	PUNCT
ejpam-2691	464	16	g(x3	g(x3	NOUN
ejpam-2691	464	17	m	m	NOUN
ejpam-2691	464	18	)	)	PUNCT
ejpam-2691	464	19	,	,	PUNCT
ejpam-2691	464	20	.	.	PUNCT
ejpam-2691	464	21	.	.	PUNCT
ejpam-2691	465	1	.	.	PUNCT
ejpam-2691	466	1	,	,	PUNCT
ejpam-2691	466	2	g(xrm	g(xrm	NOUN
ejpam-2691	466	3	)	)	PUNCT
ejpam-2691	466	4	,	,	PUNCT
ejpam-2691	466	5	g(x1	g(x1	NOUN
ejpam-2691	466	6	m	m	NOUN
ejpam-2691	466	7	)	)	PUNCT
ejpam-2691	466	8	)	)	PUNCT
ejpam-2691	466	9	)	)	PUNCT
ejpam-2691	467	1	=	=	PUNCT
ejpam-2691	467	2	0	0	NUM
ejpam-2691	467	3	,	,	PUNCT
ejpam-2691	467	4	...	...	PUNCT
ejpam-2691	467	5	and	and	CCONJ
ejpam-2691	467	6	lim	lim	PROPN
ejpam-2691	467	7	m→+∞	m→+∞	PROPN
ejpam-2691	467	8	d(g(tm(xrm	d(g(tm(xrm	PROPN
ejpam-2691	467	9	,	,	PUNCT
ejpam-2691	467	10	x	x	PROPN
ejpam-2691	467	11	1	1	NUM
ejpam-2691	467	12	m	m	NOUN
ejpam-2691	467	13	,	,	PUNCT
ejpam-2691	467	14	.	.	PUNCT
ejpam-2691	467	15	.	.	PUNCT
ejpam-2691	467	16	.	.	PUNCT
ejpam-2691	468	1	,	,	PUNCT
ejpam-2691	469	1	x	x	X
ejpam-2691	469	2	r−1	r−1	PROPN
ejpam-2691	469	3	m	m	PROPN
ejpam-2691	469	4	)	)	PUNCT
ejpam-2691	469	5	)	)	PUNCT
ejpam-2691	469	6	,	,	PUNCT
ejpam-2691	469	7	tm(g(xrm	tm(g(xrm	ADJ
ejpam-2691	469	8	)	)	PUNCT
ejpam-2691	469	9	,	,	PUNCT
ejpam-2691	469	10	g(x1	g(x1	NOUN
ejpam-2691	469	11	m	m	NOUN
ejpam-2691	469	12	)	)	PUNCT
ejpam-2691	469	13	,	,	PUNCT
ejpam-2691	469	14	.	.	PUNCT
ejpam-2691	469	15	.	.	PUNCT
ejpam-2691	470	1	.	.	PUNCT
ejpam-2691	471	1	,	,	PUNCT
ejpam-2691	471	2	g(xr−1	g(xr−1	PROPN
ejpam-2691	471	3	m	m	NOUN
ejpam-2691	471	4	)	)	PUNCT
ejpam-2691	471	5	)	)	PUNCT
ejpam-2691	471	6	)	)	PUNCT
ejpam-2691	472	1	=	=	PUNCT
ejpam-2691	472	2	0	0	X
ejpam-2691	472	3	.	.	PUNCT
ejpam-2691	473	1	thus	thus	ADV
ejpam-2691	473	2	the	the	DET
ejpam-2691	473	3	above	above	ADJ
ejpam-2691	473	4	expression	expression	NOUN
ejpam-2691	473	5	turns	turn	VERB
ejpam-2691	473	6	out	out	ADP
ejpam-2691	473	7	to	to	ADP
ejpam-2691	473	8	be	be	PROPN
ejpam-2691	473	9	lim	lim	PROPN
ejpam-2691	473	10	m→+∞	m→+∞	PROPN
ejpam-2691	473	11	tm(g(x1	tm(g(x1	PROPN
ejpam-2691	473	12	m	m	NOUN
ejpam-2691	473	13	)	)	PUNCT
ejpam-2691	473	14	,	,	PUNCT
ejpam-2691	473	15	g(x2	g(x2	NOUN
ejpam-2691	473	16	m	m	PROPN
ejpam-2691	473	17	)	)	PUNCT
ejpam-2691	473	18	,	,	PUNCT
ejpam-2691	473	19	.	.	PUNCT
ejpam-2691	473	20	.	.	PUNCT
ejpam-2691	474	1	.	.	PUNCT
ejpam-2691	475	1	,	,	PUNCT
ejpam-2691	475	2	g(xrm	g(xrm	NOUN
ejpam-2691	475	3	)	)	PUNCT
ejpam-2691	475	4	)	)	PUNCT
ejpam-2691	476	1	=	=	SYM
ejpam-2691	476	2	g(x1	g(x1	NOUN
ejpam-2691	476	3	)	)	PUNCT
ejpam-2691	476	4	lim	lim	PROPN
ejpam-2691	476	5	m→+∞	m→+∞	PROPN
ejpam-2691	476	6	tm(g(x2	tm(g(x2	PROPN
ejpam-2691	476	7	m	m	PROPN
ejpam-2691	476	8	)	)	PUNCT
ejpam-2691	476	9	,	,	PUNCT
ejpam-2691	476	10	g(x3	g(x3	NOUN
ejpam-2691	476	11	m	m	NOUN
ejpam-2691	476	12	)	)	PUNCT
ejpam-2691	476	13	,	,	PUNCT
ejpam-2691	476	14	.	.	PUNCT
ejpam-2691	476	15	.	.	PUNCT
ejpam-2691	476	16	.	.	PUNCT
ejpam-2691	477	1	,	,	PUNCT
ejpam-2691	477	2	g(xrm	g(xrm	NOUN
ejpam-2691	477	3	,	,	PUNCT
ejpam-2691	477	4	x	x	PROPN
ejpam-2691	477	5	1	1	NUM
ejpam-2691	477	6	m	m	NOUN
ejpam-2691	477	7	)	)	PUNCT
ejpam-2691	477	8	)	)	PUNCT
ejpam-2691	478	1	=	=	SYM
ejpam-2691	478	2	g(x2	g(x2	NOUN
ejpam-2691	478	3	)	)	PUNCT
ejpam-2691	478	4	...	...	PUNCT
ejpam-2691	478	5	and	and	CCONJ
ejpam-2691	478	6	lim	lim	PROPN
ejpam-2691	478	7	m→+∞	m→+∞	PROPN
ejpam-2691	478	8	tm(g(xrm	tm(g(xrm	PROPN
ejpam-2691	478	9	)	)	PUNCT
ejpam-2691	478	10	,	,	PUNCT
ejpam-2691	478	11	g(x1	g(x1	NOUN
ejpam-2691	478	12	m	m	NOUN
ejpam-2691	478	13	)	)	PUNCT
ejpam-2691	478	14	,	,	PUNCT
ejpam-2691	478	15	.	.	PUNCT
ejpam-2691	478	16	.	.	PUNCT
ejpam-2691	478	17	.	.	PUNCT
ejpam-2691	479	1	,	,	PUNCT
ejpam-2691	479	2	g(xr−1	g(xr−1	PROPN
ejpam-2691	479	3	m	m	NOUN
ejpam-2691	479	4	)	)	PUNCT
ejpam-2691	479	5	)	)	PUNCT
ejpam-2691	480	1	=	=	PUNCT
ejpam-2691	480	2	g(xr	g(xr	NOUN
ejpam-2691	480	3	)	)	PUNCT
ejpam-2691	480	4	.	.	PUNCT
ejpam-2691	481	1	since	since	SCONJ
ejpam-2691	481	2	{	{	PUNCT
ejpam-2691	481	3	g(xim	g(xim	NOUN
ejpam-2691	481	4	)	)	PUNCT
ejpam-2691	481	5	}	}	PUNCT
ejpam-2691	481	6	are	be	AUX
ejpam-2691	481	7	non	non	ADJ
ejpam-2691	481	8	-	-	ADJ
ejpam-2691	481	9	decreasing	decrease	VERB
ejpam-2691	481	10	or	or	CCONJ
ejpam-2691	481	11	non	non	ADJ
ejpam-2691	481	12	-	-	ADJ
ejpam-2691	481	13	increasing	increase	VERB
ejpam-2691	481	14	according	accord	VERB
ejpam-2691	481	15	as	as	SCONJ
ejpam-2691	481	16	i	i	PRON
ejpam-2691	481	17	is	be	AUX
ejpam-2691	481	18	odd	odd	ADJ
ejpam-2691	481	19	or	or	CCONJ
ejpam-2691	481	20	even	even	ADV
ejpam-2691	481	21	,	,	PUNCT
ejpam-2691	481	22	respectively	respectively	ADV
ejpam-2691	481	23	.	.	PUNCT
ejpam-2691	482	1	using	use	VERB
ejpam-2691	482	2	the	the	DET
ejpam-2691	482	3	regularity	regularity	NOUN
ejpam-2691	482	4	of	of	ADP
ejpam-2691	482	5	g(x	g(x	NOUN
ejpam-2691	482	6	)	)	PUNCT
ejpam-2691	482	7	,	,	PUNCT
ejpam-2691	482	8	we	we	PRON
ejpam-2691	482	9	have	have	VERB
ejpam-2691	482	10	g(xim	g(xim	NOUN
ejpam-2691	482	11	)	)	PUNCT
ejpam-2691	482	12	�	�	PROPN
ejpam-2691	482	13	xi	xi	ADP
ejpam-2691	482	14	,	,	PUNCT
ejpam-2691	482	15	when	when	SCONJ
ejpam-2691	482	16	i	i	PRON
ejpam-2691	482	17	is	be	AUX
ejpam-2691	482	18	odd	odd	ADJ
ejpam-2691	482	19	;	;	PUNCT
ejpam-2691	482	20	and	and	CCONJ
ejpam-2691	482	21	g(xim	g(xim	NOUN
ejpam-2691	482	22	)	)	PUNCT
ejpam-2691	482	23	�	�	PROPN
ejpam-2691	483	1	xi	xi	ADP
ejpam-2691	483	2	,	,	PUNCT
ejpam-2691	483	3	when	when	SCONJ
ejpam-2691	483	4	i	i	PRON
ejpam-2691	483	5	is	be	AUX
ejpam-2691	483	6	even	even	ADV
ejpam-2691	483	7	.	.	PUNCT
ejpam-2691	484	1	therefore	therefore	ADV
ejpam-2691	484	2	g(g(xim	g(g(xim	VERB
ejpam-2691	484	3	)	)	PUNCT
ejpam-2691	484	4	)	)	PUNCT
ejpam-2691	485	1	�	�	PROPN
ejpam-2691	486	1	g(xi),when	g(xi),when	PROPN
ejpam-2691	486	2	i	i	PRON
ejpam-2691	486	3	is	be	AUX
ejpam-2691	486	4	odd	odd	ADJ
ejpam-2691	486	5	;	;	PUNCT
ejpam-2691	486	6	and	and	CCONJ
ejpam-2691	486	7	g(g(xim	g(g(xim	NOUN
ejpam-2691	486	8	)	)	PUNCT
ejpam-2691	486	9	)	)	PUNCT
ejpam-2691	487	1	�	�	PROPN
ejpam-2691	488	1	g(xi),when	g(xi),when	PROPN
ejpam-2691	488	2	i	i	PRON
ejpam-2691	488	3	is	be	AUX
ejpam-2691	488	4	even	even	ADV
ejpam-2691	488	5	.	.	PUNCT
ejpam-2691	489	1	then	then	ADV
ejpam-2691	489	2	by	by	ADP
ejpam-2691	489	3	(	(	PUNCT
ejpam-2691	489	4	5	5	NUM
ejpam-2691	489	5	)	)	PUNCT
ejpam-2691	489	6	,	,	PUNCT
ejpam-2691	489	7	ones	one	NOUN
ejpam-2691	489	8	obtain	obtain	VERB
ejpam-2691	489	9	d(ti(x	d(ti(x	PROPN
ejpam-2691	489	10	1	1	NUM
ejpam-2691	489	11	,	,	PUNCT
ejpam-2691	489	12	x2	x2	PROPN
ejpam-2691	489	13	,	,	PUNCT
ejpam-2691	489	14	.	.	PUNCT
ejpam-2691	489	15	.	.	PUNCT
ejpam-2691	490	1	.	.	PUNCT
ejpam-2691	491	1	,	,	PUNCT
ejpam-2691	491	2	xr	xr	PROPN
ejpam-2691	491	3	)	)	PUNCT
ejpam-2691	491	4	,	,	PUNCT
ejpam-2691	491	5	tm(g(x1	tm(g(x1	PROPN
ejpam-2691	491	6	m	m	NOUN
ejpam-2691	491	7	)	)	PUNCT
ejpam-2691	491	8	,	,	PUNCT
ejpam-2691	491	9	g(x2	g(x2	NOUN
ejpam-2691	491	10	m	m	PROPN
ejpam-2691	491	11	)	)	PUNCT
ejpam-2691	491	12	,	,	PUNCT
ejpam-2691	491	13	.	.	PUNCT
ejpam-2691	491	14	.	.	PUNCT
ejpam-2691	492	1	.	.	PUNCT
ejpam-2691	493	1	,	,	PUNCT
ejpam-2691	493	2	g(xrm	g(xrm	NOUN
ejpam-2691	493	3	)	)	PUNCT
ejpam-2691	493	4	)	)	PUNCT
ejpam-2691	493	5	)	)	PUNCT
ejpam-2691	494	1	≤	≤	NUM
ejpam-2691	495	1	βi	βi	PROPN
ejpam-2691	495	2	,	,	PUNCT
ejpam-2691	495	3	m[d(g(x1	m[d(g(x1	PROPN
ejpam-2691	495	4	)	)	PUNCT
ejpam-2691	495	5	,	,	PUNCT
ejpam-2691	495	6	ti(x	ti(x	NOUN
ejpam-2691	495	7	1	1	NUM
ejpam-2691	495	8	,	,	PUNCT
ejpam-2691	495	9	x2	x2	PROPN
ejpam-2691	495	10	,	,	PUNCT
ejpam-2691	495	11	.	.	PUNCT
ejpam-2691	495	12	.	.	PUNCT
ejpam-2691	495	13	.	.	PUNCT
ejpam-2691	495	14	,	,	PUNCT
ejpam-2691	495	15	xr	xr	X
ejpam-2691	495	16	)	)	PUNCT
ejpam-2691	495	17	+	+	NOUN
ejpam-2691	495	18	d(g(g(x1	d(g(g(x1	PROPN
ejpam-2691	495	19	m	m	NOUN
ejpam-2691	495	20	)	)	PUNCT
ejpam-2691	495	21	)	)	PUNCT
ejpam-2691	495	22	,	,	PUNCT
ejpam-2691	495	23	tm(g(x1	tm(g(x1	PROPN
ejpam-2691	495	24	m	m	NOUN
ejpam-2691	495	25	)	)	PUNCT
ejpam-2691	495	26	,	,	PUNCT
ejpam-2691	495	27	g(x2	g(x2	NOUN
ejpam-2691	495	28	m	m	PROPN
ejpam-2691	495	29	)	)	PUNCT
ejpam-2691	495	30	,	,	PUNCT
ejpam-2691	495	31	.	.	PUNCT
ejpam-2691	495	32	.	.	PUNCT
ejpam-2691	495	33	.	.	PUNCT
ejpam-2691	496	1	,	,	PUNCT
ejpam-2691	496	2	g(xrm	g(xrm	NOUN
ejpam-2691	496	3	)	)	PUNCT
ejpam-2691	496	4	]	]	PUNCT
ejpam-2691	497	1	+	+	PUNCT
ejpam-2691	497	2	γi	γi	NOUN
ejpam-2691	497	3	,	,	PUNCT
ejpam-2691	497	4	m[d(g(g(x1	m[d(g(g(x1	PROPN
ejpam-2691	497	5	m	m	NOUN
ejpam-2691	497	6	)	)	PUNCT
ejpam-2691	497	7	)	)	PUNCT
ejpam-2691	497	8	,	,	PUNCT
ejpam-2691	497	9	g(x1	g(x1	NOUN
ejpam-2691	497	10	)	)	PUNCT
ejpam-2691	497	11	)	)	PUNCT
ejpam-2691	497	12	]	]	PUNCT
ejpam-2691	497	13	.	.	PUNCT
ejpam-2691	498	1	proceeding	proceeding	NOUN
ejpam-2691	498	2	limit	limit	NOUN
ejpam-2691	498	3	as	as	ADP
ejpam-2691	498	4	m	m	PROPN
ejpam-2691	498	5	→	→	SYM
ejpam-2691	498	6	+	+	ADJ
ejpam-2691	498	7	∞	∞	PROPN
ejpam-2691	498	8	in	in	ADP
ejpam-2691	498	9	the	the	DET
ejpam-2691	498	10	above	above	ADJ
ejpam-2691	498	11	inequality	inequality	NOUN
ejpam-2691	498	12	,	,	PUNCT
ejpam-2691	498	13	using	use	VERB
ejpam-2691	498	14	(	(	PUNCT
ejpam-2691	498	15	13	13	NUM
ejpam-2691	498	16	)	)	PUNCT
ejpam-2691	498	17	with	with	ADP
ejpam-2691	498	18	the	the	DET
ejpam-2691	498	19	fact	fact	NOUN
ejpam-2691	498	20	that	that	SCONJ
ejpam-2691	498	21	βi	βi	PRON
ejpam-2691	498	22	,	,	PUNCT
ejpam-2691	498	23	m	m	VERB
ejpam-2691	498	24	<	<	X
ejpam-2691	498	25	1	1	NUM
ejpam-2691	498	26	,	,	PUNCT
ejpam-2691	498	27	we	we	PRON
ejpam-2691	498	28	get	get	VERB
ejpam-2691	498	29	ti(x	ti(x	NOUN
ejpam-2691	498	30	1	1	NUM
ejpam-2691	498	31	,	,	PUNCT
ejpam-2691	498	32	x2	x2	PROPN
ejpam-2691	498	33	,	,	PUNCT
ejpam-2691	498	34	.	.	PUNCT
ejpam-2691	498	35	.	.	PUNCT
ejpam-2691	499	1	.	.	PUNCT
ejpam-2691	500	1	,	,	PUNCT
ejpam-2691	500	2	xr	xr	PROPN
ejpam-2691	500	3	=	=	SYM
ejpam-2691	500	4	g(x1	g(x1	PROPN
ejpam-2691	500	5	)	)	PUNCT
ejpam-2691	500	6	.	.	PUNCT
ejpam-2691	501	1	similarly	similarly	ADV
ejpam-2691	501	2	,	,	PUNCT
ejpam-2691	501	3	it	it	PRON
ejpam-2691	501	4	can	can	AUX
ejpam-2691	501	5	also	also	ADV
ejpam-2691	501	6	be	be	AUX
ejpam-2691	501	7	shown	show	VERB
ejpam-2691	501	8	that	that	DET
ejpam-2691	501	9	g(x2	g(x2	NOUN
ejpam-2691	501	10	)	)	PUNCT
ejpam-2691	502	1	=	=	SYM
ejpam-2691	502	2	ti(x	ti(x	NUM
ejpam-2691	503	1	2	2	NUM
ejpam-2691	503	2	,	,	PUNCT
ejpam-2691	503	3	x3	x3	ADJ
ejpam-2691	503	4	,	,	PUNCT
ejpam-2691	503	5	.	.	PUNCT
ejpam-2691	503	6	.	.	PUNCT
ejpam-2691	504	1	.	.	PUNCT
ejpam-2691	505	1	,	,	PUNCT
ejpam-2691	505	2	xr	xr	PROPN
ejpam-2691	505	3	,	,	PUNCT
ejpam-2691	505	4	x1	x1	PROPN
ejpam-2691	505	5	)	)	PUNCT
ejpam-2691	505	6	m.	m.	NOUN
ejpam-2691	505	7	grewal	grewal	PROPN
ejpam-2691	505	8	,	,	PUNCT
ejpam-2691	505	9	r.	r.	PROPN
ejpam-2691	505	10	kumar	kumar	PROPN
ejpam-2691	505	11	,	,	PUNCT
ejpam-2691	505	12	a.	a.	PROPN
ejpam-2691	505	13	kumar	kumar	PROPN
ejpam-2691	505	14	/	/	SYM
ejpam-2691	505	15	eur	eur	PROPN
ejpam-2691	505	16	.	.	PUNCT
ejpam-2691	506	1	j.	j.	PROPN
ejpam-2691	506	2	pure	pure	PROPN
ejpam-2691	506	3	appl	appl	PROPN
ejpam-2691	506	4	.	.	PROPN
ejpam-2691	506	5	math	math	PROPN
ejpam-2691	506	6	,	,	PUNCT
ejpam-2691	506	7	10	10	NUM
ejpam-2691	506	8	(	(	PUNCT
ejpam-2691	506	9	2	2	NUM
ejpam-2691	506	10	)	)	PUNCT
ejpam-2691	506	11	(	(	PUNCT
ejpam-2691	506	12	2017	2017	NUM
ejpam-2691	506	13	)	)	PUNCT
ejpam-2691	506	14	,	,	PUNCT
ejpam-2691	506	15	295	295	NUM
ejpam-2691	506	16	-	-	SYM
ejpam-2691	506	17	311	311	NUM
ejpam-2691	506	18	307	307	NUM
ejpam-2691	506	19	g(x3	g(x3	NUM
ejpam-2691	506	20	)	)	PUNCT
ejpam-2691	507	1	=	=	SYM
ejpam-2691	507	2	ti(x	ti(x	NUM
ejpam-2691	507	3	3	3	NUM
ejpam-2691	507	4	,	,	PUNCT
ejpam-2691	507	5	x4	x4	PROPN
ejpam-2691	507	6	,	,	PUNCT
ejpam-2691	507	7	.	.	PUNCT
ejpam-2691	507	8	.	.	PUNCT
ejpam-2691	508	1	.	.	PUNCT
ejpam-2691	509	1	,	,	PUNCT
ejpam-2691	509	2	xr	xr	PROPN
ejpam-2691	509	3	,	,	PUNCT
ejpam-2691	509	4	x1	x1	PROPN
ejpam-2691	509	5	,	,	PUNCT
ejpam-2691	509	6	x2	x2	PROPN
ejpam-2691	509	7	)	)	PUNCT
ejpam-2691	509	8	...	...	PUNCT
ejpam-2691	509	9	g(xr	g(xr	X
ejpam-2691	509	10	)	)	PUNCT
ejpam-2691	509	11	=	=	SYM
ejpam-2691	509	12	ti(x	ti(x	X
ejpam-2691	510	1	r	r	NOUN
ejpam-2691	510	2	,	,	PUNCT
ejpam-2691	510	3	x1	x1	PROPN
ejpam-2691	510	4	,	,	PUNCT
ejpam-2691	510	5	.	.	PUNCT
ejpam-2691	510	6	.	.	PUNCT
ejpam-2691	510	7	.	.	PUNCT
ejpam-2691	511	1	,	,	PUNCT
ejpam-2691	511	2	xr−1	xr−1	PROPN
ejpam-2691	511	3	)	)	PUNCT
ejpam-2691	511	4	.	.	PUNCT
ejpam-2691	512	1	this	this	PRON
ejpam-2691	512	2	shows	show	VERB
ejpam-2691	512	3	that	that	SCONJ
ejpam-2691	512	4	(	(	PUNCT
ejpam-2691	512	5	x1	x1	ADJ
ejpam-2691	512	6	,	,	PUNCT
ejpam-2691	512	7	x2	x2	PROPN
ejpam-2691	512	8	,	,	PUNCT
ejpam-2691	512	9	.	.	PUNCT
ejpam-2691	512	10	.	.	PUNCT
ejpam-2691	513	1	.	.	PUNCT
ejpam-2691	514	1	,	,	PUNCT
ejpam-2691	514	2	xr	xr	PROPN
ejpam-2691	514	3	)	)	PUNCT
ejpam-2691	514	4	∈	∈	PROPN
ejpam-2691	514	5	∏r	∏r	NOUN
ejpam-2691	514	6	λ=1x	λ=1x	NOUN
ejpam-2691	514	7	λ	λ	PROPN
ejpam-2691	514	8	is	be	AUX
ejpam-2691	514	9	a	a	DET
ejpam-2691	514	10	r	r	NOUN
ejpam-2691	514	11	-	-	PUNCT
ejpam-2691	514	12	tupled	tuple	VERB
ejpam-2691	514	13	coincidence	coincidence	NOUN
ejpam-2691	514	14	point	point	NOUN
ejpam-2691	514	15	of	of	ADP
ejpam-2691	514	16	{	{	PUNCT
ejpam-2691	514	17	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	514	18	and	and	CCONJ
ejpam-2691	514	19	g.	g.	PROPN
ejpam-2691	514	20	�	�	PROPN
ejpam-2691	514	21	theorem	theorem	VERB
ejpam-2691	514	22	2	2	NUM
ejpam-2691	514	23	.	.	PUNCT
ejpam-2691	515	1	let	let	VERB
ejpam-2691	515	2	x	x	PRON
ejpam-2691	515	3	be	be	AUX
ejpam-2691	515	4	regular	regular	ADJ
ejpam-2691	515	5	and	and	CCONJ
ejpam-2691	515	6	(	(	PUNCT
ejpam-2691	515	7	x	x	NOUN
ejpam-2691	515	8	,	,	PUNCT
ejpam-2691	515	9	d	d	PROPN
ejpam-2691	515	10	,	,	PUNCT
ejpam-2691	515	11	�	�	PROPN
ejpam-2691	515	12	)	)	PUNCT
ejpam-2691	515	13	be	be	VERB
ejpam-2691	515	14	a	a	DET
ejpam-2691	515	15	complete	complete	ADJ
ejpam-2691	515	16	ordered	order	VERB
ejpam-2691	515	17	metric	metric	ADJ
ejpam-2691	515	18	space	space	NOUN
ejpam-2691	515	19	.	.	PUNCT
ejpam-2691	516	1	let	let	VERB
ejpam-2691	516	2	{	{	PUNCT
ejpam-2691	516	3	ti}i∈n	ti}i∈n	ADV
ejpam-2691	516	4	be	be	AUX
ejpam-2691	516	5	a	a	DET
ejpam-2691	516	6	sequence	sequence	NOUN
ejpam-2691	516	7	of	of	ADP
ejpam-2691	516	8	mappings	mapping	NOUN
ejpam-2691	516	9	from	from	ADP
ejpam-2691	516	10	∏r	∏r	NOUN
ejpam-2691	516	11	λ=1x	λ=1x	ADJ
ejpam-2691	516	12	λ	λ	PROPN
ejpam-2691	516	13	→	→	SYM
ejpam-2691	516	14	x	x	X
ejpam-2691	516	15	such	such	ADJ
ejpam-2691	516	16	that	that	PRON
ejpam-2691	516	17	for	for	ADP
ejpam-2691	516	18	all	all	DET
ejpam-2691	516	19	x1	x1	PROPN
ejpam-2691	516	20	,	,	PUNCT
ejpam-2691	516	21	x2	x2	PROPN
ejpam-2691	516	22	,	,	PUNCT
ejpam-2691	516	23	.	.	PUNCT
ejpam-2691	516	24	.	.	PUNCT
ejpam-2691	517	1	.	.	PUNCT
ejpam-2691	518	1	,	,	PUNCT
ejpam-2691	518	2	xr	xr	PROPN
ejpam-2691	518	3	,	,	PUNCT
ejpam-2691	518	4	y1	y1	PROPN
ejpam-2691	518	5	,	,	PUNCT
ejpam-2691	518	6	y2	y2	PROPN
ejpam-2691	518	7	,	,	PUNCT
ejpam-2691	518	8	.	.	PUNCT
ejpam-2691	518	9	.	.	PUNCT
ejpam-2691	519	1	.	.	PUNCT
ejpam-2691	520	1	,	,	PUNCT
ejpam-2691	520	2	yr	yr	PROPN
ejpam-2691	520	3	∈	∈	PROPN
ejpam-2691	520	4	x	x	PUNCT
ejpam-2691	520	5	with	with	ADP
ejpam-2691	520	6	x1	x1	PROPN
ejpam-2691	520	7	�	�	PROPN
ejpam-2691	520	8	y1	y1	PROPN
ejpam-2691	520	9	,	,	PUNCT
ejpam-2691	520	10	x2	x2	PROPN
ejpam-2691	520	11	�	�	PROPN
ejpam-2691	520	12	y2	y2	PROPN
ejpam-2691	520	13	,	,	PUNCT
ejpam-2691	520	14	x3	x3	PROPN
ejpam-2691	520	15	�	�	PROPN
ejpam-2691	520	16	y3	y3	PROPN
ejpam-2691	520	17	,	,	PUNCT
ejpam-2691	520	18	.	.	PUNCT
ejpam-2691	520	19	.	.	PUNCT
ejpam-2691	520	20	.	.	PUNCT
ejpam-2691	521	1	,	,	PUNCT
ejpam-2691	521	2	xr	xr	PROPN
ejpam-2691	521	3	�	�	PROPN
ejpam-2691	521	4	yr	yr	PROPN
ejpam-2691	521	5	,	,	PUNCT
ejpam-2691	521	6	{	{	PUNCT
ejpam-2691	521	7	ti}i∈n	ti}i∈n	ADV
ejpam-2691	521	8	satisfy	satisfy	VERB
ejpam-2691	521	9	the	the	DET
ejpam-2691	521	10	following	follow	VERB
ejpam-2691	521	11	conditions	condition	NOUN
ejpam-2691	521	12	:	:	PUNCT
ejpam-2691	521	13	i	i	NOUN
ejpam-2691	521	14	)	)	PUNCT
ejpam-2691	521	15	tm(x1	tm(x1	PROPN
ejpam-2691	521	16	,	,	PUNCT
ejpam-2691	521	17	x2	x2	PROPN
ejpam-2691	521	18	,	,	PUNCT
ejpam-2691	521	19	.	.	PUNCT
ejpam-2691	521	20	.	.	PUNCT
ejpam-2691	522	1	.	.	PUNCT
ejpam-2691	523	1	,	,	PUNCT
ejpam-2691	523	2	xr	xr	PROPN
ejpam-2691	523	3	)	)	PUNCT
ejpam-2691	523	4	�	�	PROPN
ejpam-2691	523	5	tm+1(y	tm+1(y	PROPN
ejpam-2691	523	6	1	1	NUM
ejpam-2691	523	7	,	,	PUNCT
ejpam-2691	523	8	y2	y2	INTJ
ejpam-2691	523	9	,	,	PUNCT
ejpam-2691	523	10	.	.	PUNCT
ejpam-2691	523	11	.	.	PUNCT
ejpam-2691	524	1	.	.	PUNCT
ejpam-2691	525	1	,	,	PUNCT
ejpam-2691	525	2	yr	yr	PROPN
ejpam-2691	525	3	)	)	PUNCT
ejpam-2691	525	4	;	;	PUNCT
ejpam-2691	525	5	ii	ii	X
ejpam-2691	525	6	)	)	PUNCT
ejpam-2691	525	7	d(ti(x	d(ti(x	PROPN
ejpam-2691	525	8	1	1	NUM
ejpam-2691	525	9	,	,	PUNCT
ejpam-2691	525	10	x2	x2	PROPN
ejpam-2691	525	11	,	,	PUNCT
ejpam-2691	525	12	.	.	PUNCT
ejpam-2691	525	13	.	.	PUNCT
ejpam-2691	525	14	.	.	PUNCT
ejpam-2691	526	1	,	,	PUNCT
ejpam-2691	526	2	xr	xr	PROPN
ejpam-2691	526	3	)	)	PUNCT
ejpam-2691	526	4	,	,	PUNCT
ejpam-2691	526	5	tj(y	tj(y	VERB
ejpam-2691	526	6	1	1	NUM
ejpam-2691	526	7	,	,	PUNCT
ejpam-2691	526	8	y2	y2	INTJ
ejpam-2691	526	9	,	,	PUNCT
ejpam-2691	526	10	.	.	PUNCT
ejpam-2691	526	11	.	.	PUNCT
ejpam-2691	527	1	.	.	PUNCT
ejpam-2691	528	1	,	,	PUNCT
ejpam-2691	528	2	yr	yr	NOUN
ejpam-2691	528	3	)	)	PUNCT
ejpam-2691	528	4	)	)	PUNCT
ejpam-2691	529	1	≤	≤	NOUN
ejpam-2691	530	1	βi	βi	PROPN
ejpam-2691	530	2	,	,	PUNCT
ejpam-2691	530	3	j	j	PROPN
ejpam-2691	531	1	[	[	X
ejpam-2691	531	2	d(x	d(x	PROPN
ejpam-2691	531	3	,	,	PUNCT
ejpam-2691	531	4	ti(x	ti(x	X
ejpam-2691	531	5	1	1	NUM
ejpam-2691	531	6	,	,	PUNCT
ejpam-2691	531	7	x2	x2	PROPN
ejpam-2691	531	8	,	,	PUNCT
ejpam-2691	531	9	.	.	PUNCT
ejpam-2691	531	10	.	.	PUNCT
ejpam-2691	532	1	.	.	PUNCT
ejpam-2691	533	1	,	,	PUNCT
ejpam-2691	533	2	xr	xr	PROPN
ejpam-2691	533	3	)	)	PUNCT
ejpam-2691	533	4	)	)	PUNCT
ejpam-2691	534	1	+	+	CCONJ
ejpam-2691	534	2	d(y1	d(y1	NOUN
ejpam-2691	534	3	,	,	PUNCT
ejpam-2691	534	4	tj(y	tj(y	NOUN
ejpam-2691	534	5	1	1	NUM
ejpam-2691	534	6	,	,	PUNCT
ejpam-2691	534	7	y2	y2	INTJ
ejpam-2691	534	8	,	,	PUNCT
ejpam-2691	534	9	.	.	PUNCT
ejpam-2691	534	10	.	.	PUNCT
ejpam-2691	534	11	.	.	PUNCT
ejpam-2691	535	1	,	,	PUNCT
ejpam-2691	535	2	yr	yr	NOUN
ejpam-2691	535	3	)	)	PUNCT
ejpam-2691	535	4	)	)	PUNCT
ejpam-2691	535	5	]	]	PUNCT
ejpam-2691	536	1	+	+	CCONJ
ejpam-2691	536	2	γi	γi	NOUN
ejpam-2691	536	3	,	,	PUNCT
ejpam-2691	536	4	jd(y1	jd(y1	NOUN
ejpam-2691	536	5	,	,	PUNCT
ejpam-2691	536	6	x1	x1	PROPN
ejpam-2691	536	7	)	)	PUNCT
ejpam-2691	536	8	.	.	PUNCT
ejpam-2691	537	1	where	where	SCONJ
ejpam-2691	537	2	0	0	NUM
ejpam-2691	537	3	≤	≤	NOUN
ejpam-2691	537	4	βi	βi	PROPN
ejpam-2691	537	5	,	,	PUNCT
ejpam-2691	537	6	j	j	PROPN
ejpam-2691	537	7	,	,	PUNCT
ejpam-2691	537	8	γi	γi	PROPN
ejpam-2691	537	9	,	,	PUNCT
ejpam-2691	537	10	j	j	PROPN
ejpam-2691	537	11	<	<	X
ejpam-2691	537	12	1	1	NUM
ejpam-2691	537	13	∀	∀	NOUN
ejpam-2691	538	1	i	i	NOUN
ejpam-2691	538	2	,	,	PUNCT
ejpam-2691	538	3	j	j	PROPN
ejpam-2691	538	4	∈	∈	PROPN
ejpam-2691	538	5	n	n	PRON
ejpam-2691	538	6	iii	iii	X
ejpam-2691	538	7	)	)	PUNCT
ejpam-2691	538	8	there	there	PRON
ejpam-2691	538	9	exists	exist	VERB
ejpam-2691	538	10	(	(	PUNCT
ejpam-2691	538	11	x10	x10	NOUN
ejpam-2691	538	12	,	,	PUNCT
ejpam-2691	538	13	x	x	NOUN
ejpam-2691	538	14	2	2	NUM
ejpam-2691	538	15	0	0	NUM
ejpam-2691	538	16	,	,	PUNCT
ejpam-2691	538	17	.	.	PUNCT
ejpam-2691	538	18	.	.	PUNCT
ejpam-2691	538	19	.	.	PUNCT
ejpam-2691	539	1	,	,	PUNCT
ejpam-2691	539	2	x	x	PUNCT
ejpam-2691	539	3	r	r	NOUN
ejpam-2691	539	4	0	0	NUM
ejpam-2691	539	5	)	)	PUNCT
ejpam-2691	539	6	∈	∈	PROPN
ejpam-2691	539	7	∏r	∏r	NOUN
ejpam-2691	539	8	λ=1x	λ=1x	NOUN
ejpam-2691	539	9	λ	λ	PROPN
ejpam-2691	539	10	such	such	ADJ
ejpam-2691	539	11	that	that	PROPN
ejpam-2691	539	12	x10	x10	PROPN
ejpam-2691	539	13	�	�	PROPN
ejpam-2691	539	14	t0(x10	t0(x10	PROPN
ejpam-2691	539	15	,	,	PUNCT
ejpam-2691	539	16	x20	x20	PROPN
ejpam-2691	539	17	,	,	PUNCT
ejpam-2691	539	18	.	.	PUNCT
ejpam-2691	539	19	.	.	PUNCT
ejpam-2691	540	1	.	.	PUNCT
ejpam-2691	541	1	,	,	PUNCT
ejpam-2691	541	2	xr0	xr0	PROPN
ejpam-2691	541	3	)	)	PUNCT
ejpam-2691	541	4	,	,	PUNCT
ejpam-2691	541	5	x20	x20	PROPN
ejpam-2691	541	6	�	�	PROPN
ejpam-2691	541	7	t0(x20	t0(x20	PROPN
ejpam-2691	541	8	,	,	PUNCT
ejpam-2691	541	9	x30	x30	PROPN
ejpam-2691	541	10	,	,	PUNCT
ejpam-2691	541	11	.	.	PUNCT
ejpam-2691	541	12	.	.	PUNCT
ejpam-2691	542	1	.	.	PUNCT
ejpam-2691	543	1	,	,	PUNCT
ejpam-2691	543	2	xr0	xr0	PROPN
ejpam-2691	543	3	,	,	PUNCT
ejpam-2691	543	4	x10	x10	NOUN
ejpam-2691	543	5	)	)	PUNCT
ejpam-2691	543	6	,	,	PUNCT
ejpam-2691	543	7	x30	x30	PROPN
ejpam-2691	543	8	�	�	PROPN
ejpam-2691	543	9	t0(x30	t0(x30	PROPN
ejpam-2691	543	10	,	,	PUNCT
ejpam-2691	543	11	x40	x40	PROPN
ejpam-2691	543	12	,	,	PUNCT
ejpam-2691	543	13	.	.	PUNCT
ejpam-2691	543	14	.	.	PUNCT
ejpam-2691	543	15	.	.	PUNCT
ejpam-2691	544	1	,	,	PUNCT
ejpam-2691	544	2	x10	x10	NOUN
ejpam-2691	544	3	,	,	PUNCT
ejpam-2691	544	4	x20	x20	NUM
ejpam-2691	544	5	)	)	PUNCT
ejpam-2691	544	6	,	,	PUNCT
ejpam-2691	544	7	...	...	PUNCT
ejpam-2691	545	1	xr0	xr0	PROPN
ejpam-2691	545	2	�	�	PROPN
ejpam-2691	545	3	t0(xr0	t0(xr0	PROPN
ejpam-2691	545	4	,	,	PUNCT
ejpam-2691	545	5	x10	x10	NOUN
ejpam-2691	545	6	,	,	PUNCT
ejpam-2691	545	7	.	.	PUNCT
ejpam-2691	545	8	.	.	PUNCT
ejpam-2691	545	9	.	.	PUNCT
ejpam-2691	546	1	,	,	PUNCT
ejpam-2691	546	2	x	x	X
ejpam-2691	546	3	r−1	r−1	PROPN
ejpam-2691	546	4	0	0	NUM
ejpam-2691	546	5	)	)	PUNCT
ejpam-2691	546	6	.	.	PUNCT
ejpam-2691	547	1	if	if	SCONJ
ejpam-2691	547	2	∑+∞	∑+∞	VERB
ejpam-2691	547	3	i=1	i=1	PROPN
ejpam-2691	547	4	(	(	PUNCT
ejpam-2691	547	5	βi	βi	PROPN
ejpam-2691	547	6	,	,	PUNCT
ejpam-2691	547	7	i+1+γi	i+1+γi	NOUN
ejpam-2691	547	8	,	,	PUNCT
ejpam-2691	547	9	i+1	i+1	NOUN
ejpam-2691	547	10	1−βi	1−βi	NUM
ejpam-2691	547	11	,	,	PUNCT
ejpam-2691	547	12	i+1	i+1	NUM
ejpam-2691	547	13	)	)	PUNCT
ejpam-2691	547	14	is	be	AUX
ejpam-2691	547	15	an	an	DET
ejpam-2691	547	16	α	α	NOUN
ejpam-2691	547	17	-	-	PUNCT
ejpam-2691	547	18	series	series	NOUN
ejpam-2691	547	19	,	,	PUNCT
ejpam-2691	547	20	then	then	ADV
ejpam-2691	547	21	{	{	PUNCT
ejpam-2691	547	22	ti}i∈n	ti}i∈n	ADV
ejpam-2691	547	23	has	have	VERB
ejpam-2691	547	24	r	r	NOUN
ejpam-2691	547	25	-	-	PUNCT
ejpam-2691	547	26	tupled	tuple	VERB
ejpam-2691	547	27	fixed	fix	VERB
ejpam-2691	547	28	point	point	NOUN
ejpam-2691	547	29	.	.	PUNCT
ejpam-2691	548	1	proof	proof	NOUN
ejpam-2691	548	2	.	.	PUNCT
ejpam-2691	549	1	the	the	DET
ejpam-2691	549	2	proof	proof	NOUN
ejpam-2691	549	3	easily	easily	ADV
ejpam-2691	549	4	follows	follow	VERB
ejpam-2691	549	5	from	from	ADP
ejpam-2691	549	6	the	the	DET
ejpam-2691	549	7	proof	proof	NOUN
ejpam-2691	549	8	of	of	ADP
ejpam-2691	549	9	theorem	theorem	NOUN
ejpam-2691	549	10	1	1	NUM
ejpam-2691	549	11	by	by	ADP
ejpam-2691	549	12	taking	take	VERB
ejpam-2691	549	13	g	g	NOUN
ejpam-2691	549	14	to	to	PART
ejpam-2691	549	15	be	be	AUX
ejpam-2691	549	16	an	an	DET
ejpam-2691	549	17	identity	identity	NOUN
ejpam-2691	549	18	mapping	mapping	NOUN
ejpam-2691	549	19	.	.	PUNCT
ejpam-2691	550	1	�	�	PROPN
ejpam-2691	550	2	now	now	ADV
ejpam-2691	550	3	,	,	PUNCT
ejpam-2691	550	4	we	we	PRON
ejpam-2691	550	5	give	give	VERB
ejpam-2691	550	6	useful	useful	ADJ
ejpam-2691	550	7	conditions	condition	NOUN
ejpam-2691	550	8	for	for	ADP
ejpam-2691	550	9	existence	existence	NOUN
ejpam-2691	550	10	and	and	CCONJ
ejpam-2691	550	11	uniqueness	uniqueness	NOUN
ejpam-2691	550	12	of	of	ADP
ejpam-2691	550	13	a	a	DET
ejpam-2691	550	14	n	n	ADV
ejpam-2691	550	15	-	-	PUNCT
ejpam-2691	550	16	tupled	tuple	VERB
ejpam-2691	550	17	common	common	ADJ
ejpam-2691	550	18	fixed	fix	VERB
ejpam-2691	550	19	point	point	NOUN
ejpam-2691	550	20	.	.	PUNCT
ejpam-2691	551	1	theorem	theorem	NOUN
ejpam-2691	551	2	3	3	NUM
ejpam-2691	551	3	.	.	PUNCT
ejpam-2691	552	1	in	in	ADP
ejpam-2691	552	2	addition	addition	NOUN
ejpam-2691	552	3	to	to	ADP
ejpam-2691	552	4	the	the	DET
ejpam-2691	552	5	hypotheses	hypothesis	NOUN
ejpam-2691	552	6	of	of	ADP
ejpam-2691	552	7	theorem	theorem	NOUN
ejpam-2691	552	8	1	1	NUM
ejpam-2691	552	9	,	,	PUNCT
ejpam-2691	552	10	suppose	suppose	VERB
ejpam-2691	552	11	that	that	SCONJ
ejpam-2691	552	12	the	the	DET
ejpam-2691	552	13	set	set	NOUN
ejpam-2691	552	14	of	of	ADP
ejpam-2691	552	15	coincidence	coincidence	NOUN
ejpam-2691	552	16	points	point	NOUN
ejpam-2691	552	17	is	be	AUX
ejpam-2691	552	18	comparable	comparable	ADJ
ejpam-2691	552	19	with	with	ADP
ejpam-2691	552	20	respect	respect	NOUN
ejpam-2691	552	21	to	to	ADP
ejpam-2691	552	22	g	g	NOUN
ejpam-2691	552	23	,	,	PUNCT
ejpam-2691	552	24	then	then	ADV
ejpam-2691	552	25	{	{	PUNCT
ejpam-2691	552	26	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	552	27	and	and	CCONJ
ejpam-2691	552	28	g	g	PROPN
ejpam-2691	552	29	have	have	VERB
ejpam-2691	552	30	a	a	DET
ejpam-2691	552	31	unique	unique	ADJ
ejpam-2691	552	32	r	r	NOUN
ejpam-2691	552	33	-	-	PUNCT
ejpam-2691	552	34	tupled	tuple	VERB
ejpam-2691	552	35	common	common	ADJ
ejpam-2691	552	36	fixed	fix	VERB
ejpam-2691	552	37	point	point	NOUN
ejpam-2691	552	38	.	.	PUNCT
ejpam-2691	553	1	proof	proof	NOUN
ejpam-2691	553	2	.	.	PUNCT
ejpam-2691	554	1	it	it	PRON
ejpam-2691	554	2	is	be	AUX
ejpam-2691	554	3	clear	clear	ADJ
ejpam-2691	554	4	from	from	ADP
ejpam-2691	554	5	theorem	theorem	ADJ
ejpam-2691	554	6	1	1	NUM
ejpam-2691	554	7	that	that	SCONJ
ejpam-2691	554	8	the	the	DET
ejpam-2691	554	9	set	set	NOUN
ejpam-2691	554	10	of	of	ADP
ejpam-2691	554	11	r	r	NOUN
ejpam-2691	554	12	-	-	PUNCT
ejpam-2691	554	13	tupled	tuple	VERB
ejpam-2691	554	14	coincidence	coincidence	NOUN
ejpam-2691	554	15	points	point	NOUN
ejpam-2691	554	16	is	be	AUX
ejpam-2691	554	17	nonempty	nonempty	ADJ
ejpam-2691	554	18	.	.	PUNCT
ejpam-2691	555	1	let	let	VERB
ejpam-2691	555	2	(	(	PUNCT
ejpam-2691	555	3	x1	x1	ADJ
ejpam-2691	555	4	,	,	PUNCT
ejpam-2691	555	5	x2	x2	PROPN
ejpam-2691	555	6	,	,	PUNCT
ejpam-2691	555	7	.	.	PUNCT
ejpam-2691	555	8	.	.	PUNCT
ejpam-2691	555	9	.	.	PUNCT
ejpam-2691	556	1	,	,	PUNCT
ejpam-2691	556	2	xr	xr	PROPN
ejpam-2691	556	3	)	)	PUNCT
ejpam-2691	556	4	and	and	CCONJ
ejpam-2691	556	5	(	(	PUNCT
ejpam-2691	556	6	y1	y1	INTJ
ejpam-2691	556	7	,	,	PUNCT
ejpam-2691	556	8	y2	y2	PROPN
ejpam-2691	556	9	,	,	PUNCT
ejpam-2691	556	10	.	.	PUNCT
ejpam-2691	556	11	.	.	PUNCT
ejpam-2691	556	12	.	.	PUNCT
ejpam-2691	557	1	,	,	PUNCT
ejpam-2691	557	2	yr	yr	X
ejpam-2691	557	3	)	)	PUNCT
ejpam-2691	557	4	∈	∈	PROPN
ejpam-2691	557	5	∏r	∏r	NOUN
ejpam-2691	557	6	λ=1x	λ=1x	NOUN
ejpam-2691	557	7	λ	λ	X
ejpam-2691	557	8	be	be	VERB
ejpam-2691	557	9	two	two	NUM
ejpam-2691	557	10	r	r	NOUN
ejpam-2691	557	11	-	-	PUNCT
ejpam-2691	557	12	tupled	tuple	VERB
ejpam-2691	557	13	coincidence	coincidence	NOUN
ejpam-2691	557	14	points	point	NOUN
ejpam-2691	557	15	of	of	ADP
ejpam-2691	557	16	{	{	PUNCT
ejpam-2691	557	17	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	557	18	and	and	CCONJ
ejpam-2691	557	19	g.	g.	PROPN
ejpam-2691	557	20	then	then	ADV
ejpam-2691	557	21	g(x1	g(x1	NOUN
ejpam-2691	557	22	)	)	PUNCT
ejpam-2691	558	1	=	=	SYM
ejpam-2691	558	2	ti(x	ti(x	NUM
ejpam-2691	559	1	1	1	NUM
ejpam-2691	559	2	,	,	PUNCT
ejpam-2691	559	3	x2	x2	PROPN
ejpam-2691	559	4	,	,	PUNCT
ejpam-2691	559	5	.	.	PUNCT
ejpam-2691	559	6	.	.	PUNCT
ejpam-2691	560	1	.	.	PUNCT
ejpam-2691	561	1	,	,	PUNCT
ejpam-2691	561	2	xr	xr	PROPN
ejpam-2691	561	3	)	)	PUNCT
ejpam-2691	561	4	g(x2	g(x2	NOUN
ejpam-2691	561	5	)	)	PUNCT
ejpam-2691	562	1	=	=	SYM
ejpam-2691	562	2	ti(x	ti(x	NUM
ejpam-2691	563	1	2	2	NUM
ejpam-2691	563	2	,	,	PUNCT
ejpam-2691	563	3	x3	x3	ADJ
ejpam-2691	563	4	,	,	PUNCT
ejpam-2691	563	5	.	.	PUNCT
ejpam-2691	563	6	.	.	PUNCT
ejpam-2691	564	1	.	.	PUNCT
ejpam-2691	565	1	,	,	PUNCT
ejpam-2691	565	2	xr	xr	PROPN
ejpam-2691	565	3	,	,	PUNCT
ejpam-2691	565	4	x1	x1	PROPN
ejpam-2691	565	5	)	)	PUNCT
ejpam-2691	565	6	m.	m.	NOUN
ejpam-2691	565	7	grewal	grewal	PROPN
ejpam-2691	565	8	,	,	PUNCT
ejpam-2691	565	9	r.	r.	PROPN
ejpam-2691	565	10	kumar	kumar	PROPN
ejpam-2691	565	11	,	,	PUNCT
ejpam-2691	565	12	a.	a.	PROPN
ejpam-2691	565	13	kumar	kumar	PROPN
ejpam-2691	565	14	/	/	SYM
ejpam-2691	565	15	eur	eur	PROPN
ejpam-2691	565	16	.	.	PUNCT
ejpam-2691	566	1	j.	j.	PROPN
ejpam-2691	566	2	pure	pure	PROPN
ejpam-2691	566	3	appl	appl	PROPN
ejpam-2691	566	4	.	.	PROPN
ejpam-2691	566	5	math	math	PROPN
ejpam-2691	566	6	,	,	PUNCT
ejpam-2691	566	7	10	10	NUM
ejpam-2691	566	8	(	(	PUNCT
ejpam-2691	566	9	2	2	NUM
ejpam-2691	566	10	)	)	PUNCT
ejpam-2691	566	11	(	(	PUNCT
ejpam-2691	566	12	2017	2017	NUM
ejpam-2691	566	13	)	)	PUNCT
ejpam-2691	566	14	,	,	PUNCT
ejpam-2691	566	15	295	295	NUM
ejpam-2691	566	16	-	-	SYM
ejpam-2691	566	17	311	311	NUM
ejpam-2691	566	18	308	308	NUM
ejpam-2691	566	19	...	...	PUNCT
ejpam-2691	566	20	g(xr	g(xr	X
ejpam-2691	566	21	)	)	PUNCT
ejpam-2691	566	22	=	=	SYM
ejpam-2691	566	23	ti(x	ti(x	X
ejpam-2691	567	1	r	r	NOUN
ejpam-2691	567	2	,	,	PUNCT
ejpam-2691	567	3	x1	x1	PROPN
ejpam-2691	567	4	,	,	PUNCT
ejpam-2691	567	5	.	.	PUNCT
ejpam-2691	567	6	.	.	PUNCT
ejpam-2691	567	7	.	.	PUNCT
ejpam-2691	568	1	,	,	PUNCT
ejpam-2691	568	2	xr−1	xr−1	PROPN
ejpam-2691	568	3	)	)	PUNCT
ejpam-2691	568	4	.	.	PUNCT
ejpam-2691	569	1	and	and	CCONJ
ejpam-2691	569	2	g(y1	g(y1	NOUN
ejpam-2691	569	3	)	)	PUNCT
ejpam-2691	569	4	=	=	NOUN
ejpam-2691	569	5	ti(y	ti(y	NUM
ejpam-2691	569	6	1	1	NUM
ejpam-2691	569	7	,	,	PUNCT
ejpam-2691	569	8	y2	y2	INTJ
ejpam-2691	569	9	,	,	PUNCT
ejpam-2691	569	10	.	.	PUNCT
ejpam-2691	569	11	.	.	PUNCT
ejpam-2691	569	12	.	.	PUNCT
ejpam-2691	570	1	,	,	PUNCT
ejpam-2691	570	2	yr	yr	NOUN
ejpam-2691	570	3	)	)	PUNCT
ejpam-2691	570	4	g(y2	g(y2	NOUN
ejpam-2691	570	5	)	)	PUNCT
ejpam-2691	570	6	=	=	NOUN
ejpam-2691	570	7	ti(y	ti(y	NUM
ejpam-2691	570	8	2	2	NUM
ejpam-2691	570	9	,	,	PUNCT
ejpam-2691	570	10	y3	y3	NOUN
ejpam-2691	570	11	,	,	PUNCT
ejpam-2691	570	12	.	.	PUNCT
ejpam-2691	570	13	.	.	PUNCT
ejpam-2691	570	14	.	.	PUNCT
ejpam-2691	571	1	,	,	PUNCT
ejpam-2691	571	2	yr	yr	NOUN
ejpam-2691	571	3	,	,	PUNCT
ejpam-2691	571	4	x1	x1	PROPN
ejpam-2691	571	5	)	)	PUNCT
ejpam-2691	571	6	...	...	PUNCT
ejpam-2691	572	1	g(yr	g(yr	NUM
ejpam-2691	572	2	)	)	PUNCT
ejpam-2691	572	3	=	=	PRON
ejpam-2691	572	4	ti(y	ti(y	NUM
ejpam-2691	572	5	r	r	NOUN
ejpam-2691	572	6	,	,	PUNCT
ejpam-2691	572	7	y1	y1	NOUN
ejpam-2691	572	8	,	,	PUNCT
ejpam-2691	572	9	.	.	PUNCT
ejpam-2691	572	10	.	.	PUNCT
ejpam-2691	573	1	.	.	PUNCT
ejpam-2691	574	1	,	,	PUNCT
ejpam-2691	574	2	yr−1	yr−1	PROPN
ejpam-2691	574	3	)	)	PUNCT
ejpam-2691	574	4	.	.	PUNCT
ejpam-2691	575	1	now	now	ADV
ejpam-2691	575	2	our	our	PRON
ejpam-2691	575	3	aim	aim	NOUN
ejpam-2691	575	4	is	be	AUX
ejpam-2691	575	5	to	to	PART
ejpam-2691	575	6	show	show	VERB
ejpam-2691	575	7	that	that	SCONJ
ejpam-2691	575	8	g(x1	g(x1	NOUN
ejpam-2691	575	9	)	)	PUNCT
ejpam-2691	575	10	=	=	SYM
ejpam-2691	575	11	g(y1	g(y1	NOUN
ejpam-2691	575	12	)	)	PUNCT
ejpam-2691	575	13	g(x2	g(x2	NOUN
ejpam-2691	575	14	)	)	PUNCT
ejpam-2691	575	15	=	=	SYM
ejpam-2691	575	16	g(y2	g(y2	NOUN
ejpam-2691	575	17	)	)	PUNCT
ejpam-2691	575	18	...	...	PUNCT
ejpam-2691	576	1	g(xr	g(xr	X
ejpam-2691	576	2	)	)	PUNCT
ejpam-2691	576	3	=	=	SYM
ejpam-2691	576	4	g(yr	g(yr	NUM
ejpam-2691	576	5	)	)	PUNCT
ejpam-2691	576	6	.	.	PUNCT
ejpam-2691	577	1	since	since	SCONJ
ejpam-2691	577	2	the	the	DET
ejpam-2691	577	3	set	set	NOUN
ejpam-2691	577	4	of	of	ADP
ejpam-2691	577	5	coincidence	coincidence	NOUN
ejpam-2691	577	6	points	point	NOUN
ejpam-2691	577	7	is	be	AUX
ejpam-2691	577	8	comparable	comparable	ADJ
ejpam-2691	577	9	,	,	PUNCT
ejpam-2691	577	10	using	use	VERB
ejpam-2691	577	11	property	property	NOUN
ejpam-2691	577	12	(	(	PUNCT
ejpam-2691	577	13	a	a	NOUN
ejpam-2691	577	14	)	)	PUNCT
ejpam-2691	577	15	to	to	ADP
ejpam-2691	577	16	these	these	DET
ejpam-2691	577	17	points	point	NOUN
ejpam-2691	577	18	we	we	PRON
ejpam-2691	577	19	obtain	obtain	VERB
ejpam-2691	577	20	,	,	PUNCT
ejpam-2691	577	21	d(g(x1	d(g(x1	ADJ
ejpam-2691	577	22	)	)	PUNCT
ejpam-2691	577	23	,	,	PUNCT
ejpam-2691	577	24	g(y1	g(y1	NOUN
ejpam-2691	577	25	)	)	PUNCT
ejpam-2691	577	26	)	)	PUNCT
ejpam-2691	578	1	=	=	PUNCT
ejpam-2691	578	2	d(ti(x	d(ti(x	PROPN
ejpam-2691	578	3	1	1	NUM
ejpam-2691	578	4	,	,	PUNCT
ejpam-2691	578	5	x2	x2	PROPN
ejpam-2691	578	6	,	,	PUNCT
ejpam-2691	578	7	.	.	PUNCT
ejpam-2691	578	8	.	.	PUNCT
ejpam-2691	578	9	.	.	PUNCT
ejpam-2691	579	1	xr	xr	PROPN
ejpam-2691	579	2	)	)	PUNCT
ejpam-2691	579	3	)	)	PUNCT
ejpam-2691	580	1	,	,	PUNCT
ejpam-2691	580	2	tj(y	tj(y	VERB
ejpam-2691	580	3	1	1	NUM
ejpam-2691	580	4	,	,	PUNCT
ejpam-2691	580	5	y2	y2	INTJ
ejpam-2691	580	6	,	,	PUNCT
ejpam-2691	580	7	.	.	PUNCT
ejpam-2691	580	8	.	.	PUNCT
ejpam-2691	580	9	.	.	PUNCT
ejpam-2691	581	1	yr	yr	X
ejpam-2691	581	2	)	)	PUNCT
ejpam-2691	581	3	≤	≤	NOUN
ejpam-2691	582	1	βi	βi	PROPN
ejpam-2691	582	2	,	,	PUNCT
ejpam-2691	582	3	j	j	PROPN
ejpam-2691	583	1	[	[	X
ejpam-2691	583	2	d(g(x1	d(g(x1	PROPN
ejpam-2691	583	3	)	)	PUNCT
ejpam-2691	583	4	,	,	PUNCT
ejpam-2691	583	5	ti(x	ti(x	NOUN
ejpam-2691	583	6	1	1	NUM
ejpam-2691	583	7	,	,	PUNCT
ejpam-2691	583	8	x2	x2	PROPN
ejpam-2691	583	9	,	,	PUNCT
ejpam-2691	583	10	.	.	PUNCT
ejpam-2691	583	11	.	.	PUNCT
ejpam-2691	583	12	.	.	PUNCT
ejpam-2691	584	1	xr	xr	X
ejpam-2691	584	2	)	)	PUNCT
ejpam-2691	584	3	)	)	PUNCT
ejpam-2691	585	1	+	+	PUNCT
ejpam-2691	585	2	d(g(y1	d(g(y1	NOUN
ejpam-2691	585	3	)	)	PUNCT
ejpam-2691	585	4	,	,	PUNCT
ejpam-2691	585	5	tj(y	tj(y	VERB
ejpam-2691	585	6	1	1	NUM
ejpam-2691	585	7	,	,	PUNCT
ejpam-2691	585	8	y2	y2	INTJ
ejpam-2691	585	9	,	,	PUNCT
ejpam-2691	585	10	.	.	PUNCT
ejpam-2691	585	11	.	.	PUNCT
ejpam-2691	585	12	.	.	PUNCT
ejpam-2691	586	1	yr	yr	X
ejpam-2691	586	2	)	)	PUNCT
ejpam-2691	586	3	)	)	PUNCT
ejpam-2691	586	4	]	]	PUNCT
ejpam-2691	587	1	+	+	PUNCT
ejpam-2691	587	2	γi	γi	NOUN
ejpam-2691	587	3	,	,	PUNCT
ejpam-2691	587	4	j	j	PROPN
ejpam-2691	587	5	[	[	X
ejpam-2691	587	6	d(g(y1	d(g(y1	PROPN
ejpam-2691	587	7	)	)	PUNCT
ejpam-2691	587	8	,	,	PUNCT
ejpam-2691	587	9	g(x1	g(x1	NOUN
ejpam-2691	587	10	)	)	PUNCT
ejpam-2691	587	11	)	)	PUNCT
ejpam-2691	587	12	]	]	PUNCT
ejpam-2691	587	13	i.e.	i.e.	X
ejpam-2691	587	14	,	,	PUNCT
ejpam-2691	587	15	(	(	PUNCT
ejpam-2691	587	16	1−	1−	NUM
ejpam-2691	587	17	γi	γi	NOUN
ejpam-2691	587	18	,	,	PUNCT
ejpam-2691	587	19	j)d(g(x1	j)d(g(x1	NUM
ejpam-2691	587	20	)	)	PUNCT
ejpam-2691	587	21	,	,	PUNCT
ejpam-2691	587	22	g(y1	g(y1	NOUN
ejpam-2691	587	23	)	)	PUNCT
ejpam-2691	587	24	)	)	PUNCT
ejpam-2691	587	25	≤	≤	NUM
ejpam-2691	588	1	βi	βi	PROPN
ejpam-2691	588	2	,	,	PUNCT
ejpam-2691	588	3	j	j	PROPN
ejpam-2691	589	1	[	[	X
ejpam-2691	589	2	d(g(x1	d(g(x1	PROPN
ejpam-2691	589	3	)	)	PUNCT
ejpam-2691	589	4	,	,	PUNCT
ejpam-2691	589	5	ti(x	ti(x	NOUN
ejpam-2691	589	6	1	1	NUM
ejpam-2691	589	7	,	,	PUNCT
ejpam-2691	589	8	x2	x2	PROPN
ejpam-2691	589	9	,	,	PUNCT
ejpam-2691	589	10	.	.	PUNCT
ejpam-2691	589	11	.	.	PUNCT
ejpam-2691	589	12	.	.	PUNCT
ejpam-2691	590	1	xr	xr	X
ejpam-2691	590	2	)	)	PUNCT
ejpam-2691	590	3	)	)	PUNCT
ejpam-2691	591	1	+	+	PUNCT
ejpam-2691	591	2	d(g(y1	d(g(y1	NOUN
ejpam-2691	591	3	)	)	PUNCT
ejpam-2691	591	4	,	,	PUNCT
ejpam-2691	591	5	tj(y	tj(y	VERB
ejpam-2691	591	6	1	1	NUM
ejpam-2691	591	7	,	,	PUNCT
ejpam-2691	591	8	y2	y2	INTJ
ejpam-2691	591	9	,	,	PUNCT
ejpam-2691	591	10	.	.	PUNCT
ejpam-2691	591	11	.	.	PUNCT
ejpam-2691	591	12	.	.	PUNCT
ejpam-2691	592	1	yr	yr	NOUN
ejpam-2691	592	2	)	)	PUNCT
ejpam-2691	592	3	)	)	PUNCT
ejpam-2691	593	1	]	]	PUNCT
ejpam-2691	593	2	⇒	⇒	X
ejpam-2691	593	3	d(g(x1	d(g(x1	PROPN
ejpam-2691	593	4	)	)	PUNCT
ejpam-2691	593	5	,	,	PUNCT
ejpam-2691	593	6	g(y1	g(y1	NOUN
ejpam-2691	593	7	)	)	PUNCT
ejpam-2691	593	8	)	)	PUNCT
ejpam-2691	593	9	≤	≤	NUM
ejpam-2691	593	10	βi	βi	PROPN
ejpam-2691	593	11	,	,	PUNCT
ejpam-2691	593	12	j	j	PROPN
ejpam-2691	593	13	(	(	PUNCT
ejpam-2691	593	14	1−	1−	NUM
ejpam-2691	593	15	γi	γi	PROPN
ejpam-2691	593	16	,	,	PUNCT
ejpam-2691	593	17	j	j	NOUN
ejpam-2691	593	18	)	)	PUNCT
ejpam-2691	594	1	[	[	X
ejpam-2691	594	2	d(g(x1	d(g(x1	ADJ
ejpam-2691	594	3	)	)	PUNCT
ejpam-2691	594	4	,	,	PUNCT
ejpam-2691	594	5	ti(x	ti(x	NOUN
ejpam-2691	594	6	1	1	NUM
ejpam-2691	594	7	,	,	PUNCT
ejpam-2691	594	8	x2	x2	PROPN
ejpam-2691	594	9	,	,	PUNCT
ejpam-2691	594	10	.	.	PUNCT
ejpam-2691	594	11	.	.	PUNCT
ejpam-2691	594	12	.	.	PUNCT
ejpam-2691	595	1	xr	xr	X
ejpam-2691	595	2	)	)	PUNCT
ejpam-2691	595	3	)	)	PUNCT
ejpam-2691	596	1	+	+	PUNCT
ejpam-2691	596	2	d(g(y1	d(g(y1	NOUN
ejpam-2691	596	3	)	)	PUNCT
ejpam-2691	596	4	,	,	PUNCT
ejpam-2691	596	5	tj(y	tj(y	VERB
ejpam-2691	596	6	1	1	NUM
ejpam-2691	596	7	,	,	PUNCT
ejpam-2691	596	8	y2	y2	INTJ
ejpam-2691	596	9	,	,	PUNCT
ejpam-2691	596	10	.	.	PUNCT
ejpam-2691	596	11	.	.	PUNCT
ejpam-2691	596	12	.	.	PUNCT
ejpam-2691	597	1	yr	yr	NOUN
ejpam-2691	597	2	)	)	PUNCT
ejpam-2691	597	3	)	)	PUNCT
ejpam-2691	598	1	]	]	PUNCT
ejpam-2691	598	2	.	.	PUNCT
ejpam-2691	599	1	also	also	ADV
ejpam-2691	599	2	γi	γi	PROPN
ejpam-2691	599	3	,	,	PUNCT
ejpam-2691	599	4	j	j	PROPN
ejpam-2691	599	5	<	<	X
ejpam-2691	599	6	1	1	NUM
ejpam-2691	599	7	and	and	CCONJ
ejpam-2691	599	8	the	the	DET
ejpam-2691	599	9	elements	element	NOUN
ejpam-2691	599	10	of	of	ADP
ejpam-2691	599	11	coincidence	coincidence	NOUN
ejpam-2691	599	12	point	point	NOUN
ejpam-2691	599	13	are	be	AUX
ejpam-2691	599	14	comparable	comparable	ADJ
ejpam-2691	599	15	,	,	PUNCT
ejpam-2691	599	16	thus	thus	ADV
ejpam-2691	599	17	d(g(x1	d(g(x1	ADJ
ejpam-2691	599	18	)	)	PUNCT
ejpam-2691	599	19	,	,	PUNCT
ejpam-2691	599	20	g(y1	g(y1	NOUN
ejpam-2691	599	21	)	)	PUNCT
ejpam-2691	599	22	)	)	PUNCT
ejpam-2691	600	1	=	=	SYM
ejpam-2691	600	2	0	0	NUM
ejpam-2691	600	3	⇒	⇒	PROPN
ejpam-2691	600	4	g(x1	g(x1	NOUN
ejpam-2691	600	5	)	)	PUNCT
ejpam-2691	600	6	=	=	SYM
ejpam-2691	600	7	g(y1	g(y1	NOUN
ejpam-2691	600	8	)	)	PUNCT
ejpam-2691	600	9	.	.	PUNCT
ejpam-2691	601	1	using	use	VERB
ejpam-2691	601	2	the	the	DET
ejpam-2691	601	3	argument	argument	NOUN
ejpam-2691	601	4	analogous	analogous	ADJ
ejpam-2691	601	5	to	to	ADP
ejpam-2691	601	6	those	those	PRON
ejpam-2691	601	7	used	use	VERB
ejpam-2691	601	8	above	above	ADV
ejpam-2691	601	9	,	,	PUNCT
ejpam-2691	601	10	one	one	PRON
ejpam-2691	601	11	can	can	AUX
ejpam-2691	601	12	show	show	VERB
ejpam-2691	601	13	that	that	DET
ejpam-2691	601	14	g(x2	g(x2	NOUN
ejpam-2691	601	15	)	)	PUNCT
ejpam-2691	601	16	=	=	SYM
ejpam-2691	601	17	g(y2	g(y2	NOUN
ejpam-2691	601	18	)	)	PUNCT
ejpam-2691	601	19	g(x3	g(x3	NOUN
ejpam-2691	601	20	)	)	PUNCT
ejpam-2691	601	21	=	=	SYM
ejpam-2691	601	22	g(y3	g(y3	NOUN
ejpam-2691	601	23	)	)	PUNCT
ejpam-2691	601	24	...	...	PUNCT
ejpam-2691	602	1	g(xr	g(xr	X
ejpam-2691	602	2	)	)	PUNCT
ejpam-2691	602	3	=	=	SYM
ejpam-2691	602	4	g(yr	g(yr	NUM
ejpam-2691	602	5	)	)	PUNCT
ejpam-2691	602	6	.	.	PUNCT
ejpam-2691	603	1	hence	hence	ADV
ejpam-2691	603	2	{	{	PUNCT
ejpam-2691	603	3	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	603	4	and	and	CCONJ
ejpam-2691	603	5	g	g	PROPN
ejpam-2691	603	6	have	have	VERB
ejpam-2691	603	7	a	a	DET
ejpam-2691	603	8	unique	unique	ADJ
ejpam-2691	603	9	r	r	NOUN
ejpam-2691	603	10	-	-	PUNCT
ejpam-2691	603	11	tupled	tuple	VERB
ejpam-2691	603	12	coincidence	coincidence	NOUN
ejpam-2691	603	13	point	point	NOUN
ejpam-2691	603	14	.	.	PUNCT
ejpam-2691	604	1	it	it	PRON
ejpam-2691	604	2	is	be	AUX
ejpam-2691	604	3	well	well	ADV
ejpam-2691	604	4	-	-	PUNCT
ejpam-2691	604	5	known	know	VERB
ejpam-2691	604	6	that	that	SCONJ
ejpam-2691	604	7	two	two	NUM
ejpam-2691	604	8	compatible	compatible	ADJ
ejpam-2691	604	9	mappings	mapping	NOUN
ejpam-2691	604	10	are	be	AUX
ejpam-2691	604	11	also	also	ADV
ejpam-2691	604	12	weakly	weakly	ADV
ejpam-2691	604	13	compatible	compatible	ADJ
ejpam-2691	604	14	,	,	PUNCT
ejpam-2691	604	15	(	(	PUNCT
ejpam-2691	604	16	i.e.	i.e.	X
ejpam-2691	604	17	,	,	PUNCT
ejpam-2691	604	18	they	they	PRON
ejpam-2691	604	19	commute	commute	VERB
ejpam-2691	604	20	at	at	ADP
ejpam-2691	604	21	their	their	PRON
ejpam-2691	604	22	coincidence	coincidence	NOUN
ejpam-2691	604	23	references	reference	NOUN
ejpam-2691	604	24	309	309	NUM
ejpam-2691	604	25	points	point	NOUN
ejpam-2691	604	26	)	)	PUNCT
ejpam-2691	604	27	.	.	PUNCT
ejpam-2691	605	1	thus	thus	ADV
ejpam-2691	605	2	,	,	PUNCT
ejpam-2691	605	3	{	{	PUNCT
ejpam-2691	605	4	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	605	5	and	and	CCONJ
ejpam-2691	605	6	g	g	PROPN
ejpam-2691	605	7	have	have	VERB
ejpam-2691	605	8	a	a	DET
ejpam-2691	605	9	unique	unique	ADJ
ejpam-2691	605	10	r	r	NOUN
ejpam-2691	605	11	-	-	PUNCT
ejpam-2691	605	12	tupled	tuple	VERB
ejpam-2691	605	13	common	common	ADJ
ejpam-2691	605	14	fixed	fix	VERB
ejpam-2691	605	15	point	point	NOUN
ejpam-2691	605	16	.	.	PUNCT
ejpam-2691	606	1	hence	hence	ADV
ejpam-2691	606	2	the	the	DET
ejpam-2691	606	3	result	result	NOUN
ejpam-2691	606	4	.	.	PUNCT
ejpam-2691	607	1	�	�	PROPN
ejpam-2691	607	2	example	example	NOUN
ejpam-2691	607	3	4	4	X
ejpam-2691	607	4	.	.	X
ejpam-2691	608	1	take	take	VERB
ejpam-2691	608	2	x	x	PUNCT
ejpam-2691	608	3	=	=	PUNCT
ejpam-2691	609	1	[	[	X
ejpam-2691	609	2	0	0	NUM
ejpam-2691	609	3	,	,	PUNCT
ejpam-2691	609	4	1	1	NUM
ejpam-2691	609	5	]	]	PUNCT
ejpam-2691	609	6	endowed	endow	VERB
ejpam-2691	609	7	with	with	ADP
ejpam-2691	609	8	usual	usual	ADJ
ejpam-2691	609	9	metric	metric	ADJ
ejpam-2691	609	10	d	d	NOUN
ejpam-2691	609	11	=	=	NOUN
ejpam-2691	609	12	|x−y|	|x−y|	PUNCT
ejpam-2691	609	13	for	for	ADP
ejpam-2691	609	14	all	all	DET
ejpam-2691	609	15	x	x	NOUN
ejpam-2691	609	16	,	,	PUNCT
ejpam-2691	609	17	y	y	PROPN
ejpam-2691	609	18	∈	∈	PROPN
ejpam-2691	609	19	x	x	X
ejpam-2691	609	20	and	and	CCONJ
ejpam-2691	609	21	�	�	PROPN
ejpam-2691	609	22	be	be	AUX
ejpam-2691	609	23	defined	define	VERB
ejpam-2691	609	24	as	as	ADP
ejpam-2691	609	25	“	"	PUNCT
ejpam-2691	609	26	greater	great	ADJ
ejpam-2691	609	27	equal	equal	ADJ
ejpam-2691	609	28	”	"	PUNCT
ejpam-2691	609	29	the	the	DET
ejpam-2691	609	30	(	(	PUNCT
ejpam-2691	609	31	x	x	NOUN
ejpam-2691	609	32	,	,	PUNCT
ejpam-2691	609	33	d	d	PROPN
ejpam-2691	609	34	,	,	PUNCT
ejpam-2691	609	35	�	�	PROPN
ejpam-2691	609	36	)	)	PUNCT
ejpam-2691	609	37	be	be	AUX
ejpam-2691	609	38	ordered	order	VERB
ejpam-2691	609	39	metric	metric	ADJ
ejpam-2691	609	40	space	space	NOUN
ejpam-2691	609	41	.	.	PUNCT
ejpam-2691	610	1	let	let	VERB
ejpam-2691	610	2	ti	ti	NOUN
ejpam-2691	610	3	:	:	PUNCT
ejpam-2691	610	4	∏r	∏r	X
ejpam-2691	610	5	λ=1x	λ=1x	ADJ
ejpam-2691	610	6	λ	λ	X
ejpam-2691	610	7	→	→	SYM
ejpam-2691	610	8	x	x	VERB
ejpam-2691	610	9	be	be	AUX
ejpam-2691	610	10	mapping	mapping	NOUN
ejpam-2691	610	11	defined	define	VERB
ejpam-2691	610	12	as	as	ADP
ejpam-2691	610	13	ti(x	ti(x	NOUN
ejpam-2691	610	14	1	1	NUM
ejpam-2691	610	15	,	,	PUNCT
ejpam-2691	610	16	x2	x2	PROPN
ejpam-2691	610	17	,	,	PUNCT
ejpam-2691	610	18	.	.	PUNCT
ejpam-2691	610	19	.	.	PUNCT
ejpam-2691	611	1	.	.	PUNCT
ejpam-2691	612	1	,	,	PUNCT
ejpam-2691	612	2	xr	xr	X
ejpam-2691	612	3	)	)	PUNCT
ejpam-2691	612	4	=	=	SYM
ejpam-2691	612	5	1	1	NUM
ejpam-2691	612	6	r	r	NOUN
ejpam-2691	612	7	[	[	PUNCT
ejpam-2691	612	8	x1	x1	PROPN
ejpam-2691	613	1	+	+	CCONJ
ejpam-2691	613	2	x2	x2	PROPN
ejpam-2691	614	1	+	+	CCONJ
ejpam-2691	614	2	.	.	PUNCT
ejpam-2691	614	3	.	.	PUNCT
ejpam-2691	615	1	.+	.+	NOUN
ejpam-2691	615	2	xr	xr	PROPN
ejpam-2691	616	1	i	i	PRON
ejpam-2691	616	2	]	]	X
ejpam-2691	616	3	;	;	PUNCT
ejpam-2691	616	4	i	i	PRON
ejpam-2691	616	5	∈	∈	PROPN
ejpam-2691	616	6	n	n	ADV
ejpam-2691	616	7	and	and	CCONJ
ejpam-2691	616	8	g	g	PROPN
ejpam-2691	616	9	is	be	AUX
ejpam-2691	616	10	a	a	DET
ejpam-2691	616	11	self	self	NOUN
ejpam-2691	616	12	mapping	mapping	NOUN
ejpam-2691	616	13	defined	define	VERB
ejpam-2691	616	14	as	as	ADP
ejpam-2691	616	15	g(x	g(x	NOUN
ejpam-2691	616	16	)	)	PUNCT
ejpam-2691	617	1	=	=	SYM
ejpam-2691	617	2	x2	x2	PROPN
ejpam-2691	617	3	.	.	PUNCT
ejpam-2691	618	1	by	by	ADP
ejpam-2691	618	2	choosing	choose	VERB
ejpam-2691	618	3	the	the	DET
ejpam-2691	618	4	sequences	sequence	NOUN
ejpam-2691	618	5	{	{	PUNCT
ejpam-2691	618	6	x1	x1	PROPN
ejpam-2691	618	7	m	m	PROPN
ejpam-2691	618	8	}	}	PUNCT
ejpam-2691	618	9	=	=	SYM
ejpam-2691	618	10	1	1	NUM
ejpam-2691	618	11	m	m	NOUN
ejpam-2691	618	12	{	{	PUNCT
ejpam-2691	618	13	x2	x2	PROPN
ejpam-2691	618	14	m	m	PROPN
ejpam-2691	618	15	}	}	PUNCT
ejpam-2691	618	16	=	=	SYM
ejpam-2691	618	17	1	1	NUM
ejpam-2691	618	18	m+	m+	NUM
ejpam-2691	618	19	1	1	NUM
ejpam-2691	618	20	...	...	PUNCT
ejpam-2691	618	21	{	{	PUNCT
ejpam-2691	618	22	x2	x2	NOUN
ejpam-2691	618	23	m	m	PROPN
ejpam-2691	618	24	}	}	PUNCT
ejpam-2691	618	25	=	=	SYM
ejpam-2691	618	26	1	1	NUM
ejpam-2691	618	27	m+	m+	NUM
ejpam-2691	618	28	r	r	NOUN
ejpam-2691	618	29	−	−	PROPN
ejpam-2691	618	30	1	1	NUM
ejpam-2691	618	31	.	.	PUNCT
ejpam-2691	619	1	one	one	PRON
ejpam-2691	619	2	can	can	AUX
ejpam-2691	619	3	easily	easily	ADV
ejpam-2691	619	4	observe	observe	VERB
ejpam-2691	619	5	that	that	SCONJ
ejpam-2691	619	6	(	(	PUNCT
ejpam-2691	619	7	1	1	X
ejpam-2691	619	8	)	)	PUNCT
ejpam-2691	619	9	{	{	PUNCT
ejpam-2691	619	10	ti}i∈n	ti}i∈n	ADV
ejpam-2691	619	11	have	have	VERB
ejpam-2691	619	12	g	g	NOUN
ejpam-2691	619	13	-	-	PUNCT
ejpam-2691	619	14	mixed	mix	VERB
ejpam-2691	619	15	monotone	monotone	ADJ
ejpam-2691	619	16	property	property	NOUN
ejpam-2691	619	17	;	;	PUNCT
ejpam-2691	619	18	(	(	PUNCT
ejpam-2691	619	19	2	2	X
ejpam-2691	619	20	)	)	PUNCT
ejpam-2691	619	21	{	{	PUNCT
ejpam-2691	619	22	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	619	23	and	and	CCONJ
ejpam-2691	619	24	g	g	NOUN
ejpam-2691	619	25	are	be	AUX
ejpam-2691	619	26	compatible	compatible	ADJ
ejpam-2691	619	27	,	,	PUNCT
ejpam-2691	619	28	weakly	weakly	ADV
ejpam-2691	619	29	reciprocally	reciprocally	ADV
ejpam-2691	619	30	continuous	continuous	ADJ
ejpam-2691	619	31	(	(	PUNCT
ejpam-2691	619	32	3	3	NUM
ejpam-2691	619	33	)	)	PUNCT
ejpam-2691	619	34	g	g	NOUN
ejpam-2691	619	35	is	be	AUX
ejpam-2691	619	36	continuous	continuous	ADJ
ejpam-2691	619	37	.	.	PUNCT
ejpam-2691	620	1	by	by	ADP
ejpam-2691	620	2	taking	take	VERB
ejpam-2691	620	3	0	0	NUM
ejpam-2691	620	4	<	<	X
ejpam-2691	620	5	βi	βi	PROPN
ejpam-2691	620	6	,	,	PUNCT
ejpam-2691	620	7	j	j	PROPN
ejpam-2691	620	8	<	<	X
ejpam-2691	620	9	1	1	NUM
ejpam-2691	620	10	and	and	CCONJ
ejpam-2691	620	11	0	0	NUM
ejpam-2691	620	12	≤	≤	NUM
ejpam-2691	620	13	γi	γi	NOUN
ejpam-2691	620	14	,	,	PUNCT
ejpam-2691	620	15	j	j	PROPN
ejpam-2691	620	16	<	<	X
ejpam-2691	620	17	1	1	NUM
ejpam-2691	620	18	it	it	PRON
ejpam-2691	620	19	is	be	AUX
ejpam-2691	620	20	easy	easy	ADJ
ejpam-2691	620	21	to	to	PART
ejpam-2691	620	22	verify	verify	VERB
ejpam-2691	620	23	property	property	NOUN
ejpam-2691	620	24	(	(	PUNCT
ejpam-2691	620	25	a	a	NOUN
ejpam-2691	620	26	)	)	PUNCT
ejpam-2691	620	27	and	and	CCONJ
ejpam-2691	620	28	(	(	PUNCT
ejpam-2691	620	29	b	b	NOUN
ejpam-2691	620	30	)	)	PUNCT
ejpam-2691	620	31	.	.	PUNCT
ejpam-2691	621	1	thus	thus	ADV
ejpam-2691	621	2	all	all	DET
ejpam-2691	621	3	the	the	DET
ejpam-2691	621	4	hypotheses	hypothesis	NOUN
ejpam-2691	621	5	of	of	ADP
ejpam-2691	621	6	theorem	theorem	NOUN
ejpam-2691	621	7	1	1	NUM
ejpam-2691	621	8	are	be	AUX
ejpam-2691	621	9	satisfied	satisfied	ADJ
ejpam-2691	621	10	and	and	CCONJ
ejpam-2691	621	11	(	(	PUNCT
ejpam-2691	621	12	0	0	NUM
ejpam-2691	621	13	,	,	PUNCT
ejpam-2691	621	14	0	0	NUM
ejpam-2691	621	15	,	,	PUNCT
ejpam-2691	621	16	0	0	NUM
ejpam-2691	621	17	,	,	PUNCT
ejpam-2691	621	18	.	.	PUNCT
ejpam-2691	621	19	.	.	PUNCT
ejpam-2691	622	1	.	.	PUNCT
ejpam-2691	623	1	,	,	PUNCT
ejpam-2691	623	2	0	0	X
ejpam-2691	623	3	)	)	PUNCT
ejpam-2691	623	4	is	be	AUX
ejpam-2691	623	5	the	the	DET
ejpam-2691	623	6	only	only	ADJ
ejpam-2691	623	7	r	r	NOUN
ejpam-2691	623	8	-	-	PUNCT
ejpam-2691	623	9	tupled	tuple	VERB
ejpam-2691	623	10	coincident	coincident	ADJ
ejpam-2691	623	11	point	point	NOUN
ejpam-2691	623	12	of	of	ADP
ejpam-2691	623	13	g	g	NOUN
ejpam-2691	623	14	and	and	CCONJ
ejpam-2691	623	15	ti	ti	NOUN
ejpam-2691	623	16	for	for	ADP
ejpam-2691	623	17	all	all	DET
ejpam-2691	623	18	i	i	PRON
ejpam-2691	623	19	,	,	PUNCT
ejpam-2691	623	20	i	i	PRON
ejpam-2691	623	21	∈	∈	PROPN
ejpam-2691	623	22	n.	n.	NOUN
ejpam-2691	623	23	the	the	DET
ejpam-2691	623	24	following	follow	VERB
ejpam-2691	623	25	remarks	remark	NOUN
ejpam-2691	623	26	depicts	depict	VERB
ejpam-2691	623	27	that	that	SCONJ
ejpam-2691	623	28	if	if	SCONJ
ejpam-2691	623	29	we	we	PRON
ejpam-2691	623	30	take	take	VERB
ejpam-2691	623	31	ti	ti	NOUN
ejpam-2691	623	32	to	to	PART
ejpam-2691	623	33	be	be	AUX
ejpam-2691	623	34	a	a	DET
ejpam-2691	623	35	single	single	ADJ
ejpam-2691	623	36	mapping	mapping	NOUN
ejpam-2691	623	37	rather	rather	ADV
ejpam-2691	623	38	than	than	ADP
ejpam-2691	623	39	the	the	DET
ejpam-2691	623	40	sequence	sequence	NOUN
ejpam-2691	623	41	of	of	ADP
ejpam-2691	623	42	mappings	mapping	NOUN
ejpam-2691	623	43	{	{	PUNCT
ejpam-2691	623	44	ti}i∈n	ti}i∈n	NOUN
ejpam-2691	623	45	,	,	PUNCT
ejpam-2691	623	46	then	then	ADV
ejpam-2691	623	47	the	the	DET
ejpam-2691	623	48	pair	pair	NOUN
ejpam-2691	623	49	ti	ti	NOUN
ejpam-2691	623	50	and	and	CCONJ
ejpam-2691	623	51	g	g	PROPN
ejpam-2691	623	52	may	may	AUX
ejpam-2691	623	53	have	have	VERB
ejpam-2691	623	54	more	more	ADJ
ejpam-2691	623	55	than	than	ADP
ejpam-2691	623	56	one	one	NUM
ejpam-2691	623	57	r	r	NOUN
ejpam-2691	623	58	-	-	PUNCT
ejpam-2691	623	59	tupled	tuple	VERB
ejpam-2691	623	60	coincident	coincident	ADJ
ejpam-2691	623	61	points	point	NOUN
ejpam-2691	623	62	which	which	PRON
ejpam-2691	623	63	depends	depend	VERB
ejpam-2691	623	64	upon	upon	SCONJ
ejpam-2691	623	65	the	the	DET
ejpam-2691	623	66	value	value	NOUN
ejpam-2691	623	67	of	of	ADP
ejpam-2691	623	68	i.	i.	PROPN
ejpam-2691	623	69	remark	remark	PROPN
ejpam-2691	623	70	3	3	NUM
ejpam-2691	623	71	.	.	PUNCT
ejpam-2691	624	1	one	one	PRON
ejpam-2691	624	2	can	can	AUX
ejpam-2691	624	3	notice	notice	VERB
ejpam-2691	624	4	that	that	SCONJ
ejpam-2691	624	5	if	if	SCONJ
ejpam-2691	624	6	we	we	PRON
ejpam-2691	624	7	consider	consider	VERB
ejpam-2691	624	8	x	x	PRON
ejpam-2691	624	9	,	,	PUNCT
ejpam-2691	624	10	d	d	PROPN
ejpam-2691	624	11	,	,	PUNCT
ejpam-2691	624	12	�	�	PROPN
ejpam-2691	624	13	,	,	PUNCT
ejpam-2691	624	14	ti	ti	NOUN
ejpam-2691	624	15	and	and	CCONJ
ejpam-2691	624	16	g	g	NOUN
ejpam-2691	624	17	as	as	SCONJ
ejpam-2691	624	18	taken	take	VERB
ejpam-2691	624	19	in	in	ADP
ejpam-2691	624	20	the	the	DET
ejpam-2691	624	21	above	above	ADJ
ejpam-2691	624	22	example	example	NOUN
ejpam-2691	624	23	,	,	PUNCT
ejpam-2691	624	24	then	then	ADV
ejpam-2691	624	25	(	(	PUNCT
ejpam-2691	624	26	1	1	NUM
ejpam-2691	624	27	,	,	PUNCT
ejpam-2691	624	28	1	1	NUM
ejpam-2691	624	29	,	,	PUNCT
ejpam-2691	624	30	1	1	NUM
ejpam-2691	624	31	,	,	PUNCT
ejpam-2691	624	32	.	.	PUNCT
ejpam-2691	624	33	.	.	PUNCT
ejpam-2691	624	34	.	.	PUNCT
ejpam-2691	625	1	,	,	PUNCT
ejpam-2691	625	2	1	1	X
ejpam-2691	625	3	)	)	PUNCT
ejpam-2691	625	4	is	be	AUX
ejpam-2691	625	5	an	an	DET
ejpam-2691	625	6	r	r	NOUN
ejpam-2691	625	7	-	-	PUNCT
ejpam-2691	625	8	tupled	tuple	VERB
ejpam-2691	625	9	coincident	coincident	ADJ
ejpam-2691	625	10	point	point	NOUN
ejpam-2691	625	11	of	of	ADP
ejpam-2691	625	12	g	g	PROPN
ejpam-2691	625	13	and	and	CCONJ
ejpam-2691	625	14	t1	t1	NOUN
ejpam-2691	625	15	.	.	PUNCT
ejpam-2691	626	1	also	also	ADV
ejpam-2691	626	2	(	(	PUNCT
ejpam-2691	626	3	12	12	NUM
ejpam-2691	626	4	,	,	PUNCT
ejpam-2691	626	5	1	1	NUM
ejpam-2691	626	6	2	2	NUM
ejpam-2691	626	7	,	,	PUNCT
ejpam-2691	626	8	1	1	NUM
ejpam-2691	626	9	2	2	NUM
ejpam-2691	626	10	,	,	PUNCT
ejpam-2691	626	11	.	.	PUNCT
ejpam-2691	626	12	.	.	PUNCT
ejpam-2691	627	1	.	.	PUNCT
ejpam-2691	628	1	,	,	PUNCT
ejpam-2691	628	2	1	1	NUM
ejpam-2691	628	3	2	2	NUM
ejpam-2691	628	4	)	)	PUNCT
ejpam-2691	628	5	is	be	AUX
ejpam-2691	628	6	an	an	DET
ejpam-2691	628	7	r	r	NOUN
ejpam-2691	628	8	-	-	PUNCT
ejpam-2691	628	9	tupled	tuple	VERB
ejpam-2691	628	10	coincident	coincident	ADJ
ejpam-2691	628	11	point	point	NOUN
ejpam-2691	628	12	of	of	ADP
ejpam-2691	628	13	g	g	NOUN
ejpam-2691	628	14	and	and	CCONJ
ejpam-2691	628	15	t2	t2	PROPN
ejpam-2691	628	16	.	.	PUNCT
ejpam-2691	629	1	similarly	similarly	ADV
ejpam-2691	629	2	,	,	PUNCT
ejpam-2691	629	3	(	(	PUNCT
ejpam-2691	629	4	1k	1k	NUM
ejpam-2691	629	5	,	,	PUNCT
ejpam-2691	629	6	1	1	NUM
ejpam-2691	629	7	k	k	NOUN
ejpam-2691	629	8	,	,	PUNCT
ejpam-2691	629	9	1	1	NUM
ejpam-2691	629	10	k	k	NOUN
ejpam-2691	629	11	,	,	PUNCT
ejpam-2691	629	12	.	.	PUNCT
ejpam-2691	629	13	.	.	PUNCT
ejpam-2691	630	1	.	.	PUNCT
ejpam-2691	631	1	,	,	PUNCT
ejpam-2691	631	2	1	1	X
ejpam-2691	631	3	k	k	X
ejpam-2691	631	4	)	)	PUNCT
ejpam-2691	631	5	is	be	AUX
ejpam-2691	631	6	r	r	NOUN
ejpam-2691	631	7	-	-	PUNCT
ejpam-2691	631	8	tupled	tuple	VERB
ejpam-2691	631	9	coincident	coincident	ADJ
ejpam-2691	631	10	point	point	NOUN
ejpam-2691	631	11	of	of	ADP
ejpam-2691	631	12	g	g	PROPN
ejpam-2691	631	13	and	and	CCONJ
ejpam-2691	631	14	tk	tk	PROPN
ejpam-2691	631	15	for	for	ADP
ejpam-2691	631	16	a	a	DET
ejpam-2691	631	17	fixed	fixed	ADJ
ejpam-2691	631	18	k	k	NOUN
ejpam-2691	631	19	,	,	PUNCT
ejpam-2691	631	20	k	k	PROPN
ejpam-2691	631	21	∈	∈	PROPN
ejpam-2691	631	22	n.	n.	NOUN
ejpam-2691	631	23	remark	remark	NOUN
ejpam-2691	631	24	4	4	NUM
ejpam-2691	631	25	.	.	PUNCT
ejpam-2691	632	1	one	one	PRON
ejpam-2691	632	2	can	can	AUX
ejpam-2691	632	3	also	also	ADV
ejpam-2691	632	4	notice	notice	VERB
ejpam-2691	632	5	that	that	SCONJ
ejpam-2691	632	6	if	if	SCONJ
ejpam-2691	632	7	we	we	PRON
ejpam-2691	632	8	consider	consider	VERB
ejpam-2691	632	9	x	x	PRON
ejpam-2691	632	10	,	,	PUNCT
ejpam-2691	632	11	d	d	PROPN
ejpam-2691	632	12	,	,	PUNCT
ejpam-2691	632	13	�	�	PROPN
ejpam-2691	632	14	,	,	PUNCT
ejpam-2691	632	15	ti	ti	NOUN
ejpam-2691	632	16	as	as	SCONJ
ejpam-2691	632	17	taken	take	VERB
ejpam-2691	632	18	in	in	ADP
ejpam-2691	632	19	the	the	DET
ejpam-2691	632	20	above	above	ADJ
ejpam-2691	632	21	example	example	NOUN
ejpam-2691	632	22	and	and	CCONJ
ejpam-2691	632	23	g(x	g(x	NOUN
ejpam-2691	632	24	)	)	PUNCT
ejpam-2691	633	1	=	=	SYM
ejpam-2691	633	2	x	x	X
ejpam-2691	633	3	,	,	PUNCT
ejpam-2691	633	4	then	then	ADV
ejpam-2691	633	5	(	(	PUNCT
ejpam-2691	633	6	0	0	NUM
ejpam-2691	633	7	,	,	PUNCT
ejpam-2691	633	8	0	0	NUM
ejpam-2691	633	9	,	,	PUNCT
ejpam-2691	633	10	0	0	NUM
ejpam-2691	633	11	,	,	PUNCT
ejpam-2691	633	12	.	.	PUNCT
ejpam-2691	633	13	.	.	PUNCT
ejpam-2691	633	14	.	.	PUNCT
ejpam-2691	634	1	,	,	PUNCT
ejpam-2691	634	2	0	0	X
ejpam-2691	634	3	)	)	PUNCT
ejpam-2691	634	4	is	be	AUX
ejpam-2691	634	5	only	only	ADV
ejpam-2691	634	6	r	r	NOUN
ejpam-2691	634	7	-	-	PUNCT
ejpam-2691	634	8	tupled	tuple	VERB
ejpam-2691	634	9	coincident	coincident	ADJ
ejpam-2691	634	10	point	point	NOUN
ejpam-2691	634	11	of	of	ADP
ejpam-2691	634	12	g	g	NOUN
ejpam-2691	634	13	and	and	CCONJ
ejpam-2691	634	14	ti	ti	NOUN
ejpam-2691	634	15	,	,	PUNCT
ejpam-2691	634	16	∀	∀	VERB
ejpam-2691	635	1	i	i	NOUN
ejpam-2691	635	2	∈	∈	PROPN
ejpam-2691	635	3	n.	n.	NOUN
ejpam-2691	635	4	however	however	ADV
ejpam-2691	635	5	(	(	PUNCT
ejpam-2691	635	6	0	0	NUM
ejpam-2691	635	7	,	,	PUNCT
ejpam-2691	635	8	0	0	NUM
ejpam-2691	635	9	,	,	PUNCT
ejpam-2691	635	10	0	0	NUM
ejpam-2691	635	11	,	,	PUNCT
ejpam-2691	635	12	.	.	PUNCT
ejpam-2691	635	13	.	.	PUNCT
ejpam-2691	636	1	.	.	PUNCT
ejpam-2691	637	1	,	,	PUNCT
ejpam-2691	637	2	0	0	NUM
ejpam-2691	637	3	)	)	PUNCT
ejpam-2691	637	4	and	and	CCONJ
ejpam-2691	637	5	(	(	PUNCT
ejpam-2691	637	6	1	1	NUM
ejpam-2691	637	7	,	,	PUNCT
ejpam-2691	637	8	1	1	NUM
ejpam-2691	637	9	,	,	PUNCT
ejpam-2691	637	10	1	1	NUM
ejpam-2691	637	11	,	,	PUNCT
ejpam-2691	637	12	.	.	PUNCT
ejpam-2691	637	13	.	.	PUNCT
ejpam-2691	638	1	.	.	PUNCT
ejpam-2691	639	1	,	,	PUNCT
ejpam-2691	639	2	1	1	X
ejpam-2691	639	3	)	)	PUNCT
ejpam-2691	639	4	are	be	AUX
ejpam-2691	639	5	only	only	ADV
ejpam-2691	639	6	r	r	NOUN
ejpam-2691	639	7	-	-	PUNCT
ejpam-2691	639	8	tupled	tuple	VERB
ejpam-2691	639	9	coincident	coincident	ADJ
ejpam-2691	639	10	point	point	NOUN
ejpam-2691	639	11	of	of	ADP
ejpam-2691	639	12	g	g	NOUN
ejpam-2691	639	13	and	and	CCONJ
ejpam-2691	639	14	ti	ti	NOUN
ejpam-2691	639	15	only	only	ADV
ejpam-2691	639	16	for	for	ADP
ejpam-2691	639	17	i	i	PRON
ejpam-2691	639	18	=	=	NOUN
ejpam-2691	639	19	1	1	X
ejpam-2691	639	20	.	.	PUNCT
ejpam-2691	639	21	references	reference	NOUN
ejpam-2691	640	1	[	[	X
ejpam-2691	640	2	1	1	NUM
ejpam-2691	640	3	]	]	X
ejpam-2691	640	4	h.	h.	PROPN
ejpam-2691	640	5	aydi	aydi	PROPN
ejpam-2691	640	6	,	,	PUNCT
ejpam-2691	640	7	erdal	erdal	PROPN
ejpam-2691	640	8	karapinarb	karapinarb	PROPN
ejpam-2691	640	9	and	and	CCONJ
ejpam-2691	640	10	calogero	calogero	PROPN
ejpam-2691	640	11	vetroc	vetroc	PROPN
ejpam-2691	640	12	,	,	PUNCT
ejpam-2691	640	13	meir	meir	PROPN
ejpam-2691	640	14	-	-	PUNCT
ejpam-2691	640	15	keeler	keeler	PROPN
ejpam-2691	640	16	type	type	NOUN
ejpam-2691	640	17	contractions	contraction	NOUN
ejpam-2691	640	18	for	for	ADP
ejpam-2691	640	19	tripled	triple	VERB
ejpam-2691	640	20	fixed	fix	VERB
ejpam-2691	640	21	points	point	NOUN
ejpam-2691	640	22	,	,	PUNCT
ejpam-2691	640	23	acta	acta	PROPN
ejpam-2691	640	24	mathematica	mathematica	PROPN
ejpam-2691	640	25	scientia	scientia	PROPN
ejpam-2691	640	26	,	,	PUNCT
ejpam-2691	640	27	32(6	32(6	NUM
ejpam-2691	640	28	)	)	PUNCT
ejpam-2691	640	29	(	(	PUNCT
ejpam-2691	640	30	2012	2012	NUM
ejpam-2691	640	31	)	)	PUNCT
ejpam-2691	640	32	,	,	PUNCT
ejpam-2691	640	33	2119–2130	2119–2130	NUM
ejpam-2691	640	34	.	.	PUNCT
ejpam-2691	641	1	references	reference	NOUN
ejpam-2691	641	2	310	310	NUM
ejpam-2691	641	3	[	[	X
ejpam-2691	641	4	2	2	NUM
ejpam-2691	641	5	]	]	X
ejpam-2691	641	6	h.	h.	PROPN
ejpam-2691	641	7	aydi	aydi	PROPN
ejpam-2691	641	8	,	,	PUNCT
ejpam-2691	641	9	erdal	erdal	PROPN
ejpam-2691	641	10	karapinar	karapinar	PROPN
ejpam-2691	641	11	and	and	CCONJ
ejpam-2691	641	12	stojan	stojan	ADP
ejpam-2691	641	13	radenovic	radenovic	PROPN
ejpam-2691	641	14	,	,	PUNCT
ejpam-2691	641	15	tripled	triple	VERB
ejpam-2691	641	16	coincidence	coincidence	NOUN
ejpam-2691	641	17	fixed	fix	VERB
ejpam-2691	641	18	point	point	NOUN
ejpam-2691	641	19	results	result	NOUN
ejpam-2691	641	20	for	for	ADP
ejpam-2691	641	21	boyd	boyd	PROPN
ejpam-2691	641	22	-	-	PUNCT
ejpam-2691	641	23	wong	wong	PROPN
ejpam-2691	641	24	and	and	CCONJ
ejpam-2691	641	25	matkowski	matkowski	PROPN
ejpam-2691	641	26	type	type	NOUN
ejpam-2691	641	27	contractions	contraction	NOUN
ejpam-2691	641	28	,	,	PUNCT
ejpam-2691	641	29	racsam	racsam	PROPN
ejpam-2691	641	30	revista	revista	PROPN
ejpam-2691	641	31	de	de	X
ejpam-2691	641	32	la	la	PROPN
ejpam-2691	641	33	real	real	PROPN
ejpam-2691	641	34	academia	academia	PROPN
ejpam-2691	641	35	de	de	PROPN
ejpam-2691	641	36	ciencias	ciencias	PROPN
ejpam-2691	641	37	exactas	exacta	NOUN
ejpam-2691	641	38	,	,	PUNCT
ejpam-2691	641	39	fsicas	fsicas	PROPN
ejpam-2691	641	40	y	y	PROPN
ejpam-2691	641	41	naturales	naturales	PROPN
ejpam-2691	641	42	.	.	PUNCT
ejpam-2691	642	1	serie	serie	PROPN
ejpam-2691	642	2	a.	a.	PROPN
ejpam-2691	642	3	matemticas	matemticas	PROPN
ejpam-2691	642	4	september	september	PROPN
ejpam-2691	642	5	,	,	PUNCT
ejpam-2691	642	6	107(2	107(2	NUM
ejpam-2691	642	7	)	)	PUNCT
ejpam-2691	642	8	(	(	PUNCT
ejpam-2691	642	9	2013	2013	NUM
ejpam-2691	642	10	)	)	PUNCT
ejpam-2691	642	11	,	,	PUNCT
ejpam-2691	642	12	339–353	339–353	NUM
ejpam-2691	642	13	.	.	PUNCT
ejpam-2691	643	1	[	[	X
ejpam-2691	643	2	3	3	X
ejpam-2691	643	3	]	]	X
ejpam-2691	643	4	h.	h.	PROPN
ejpam-2691	643	5	aydi	aydi	PROPN
ejpam-2691	643	6	,	,	PUNCT
ejpam-2691	643	7	erdal	erdal	PROPN
ejpam-2691	643	8	karapinar	karapinar	PROPN
ejpam-2691	643	9	and	and	CCONJ
ejpam-2691	643	10	wasfi	wasfi	ADV
ejpam-2691	643	11	shatanawi	shatanawi	PROPN
ejpam-2691	643	12	,	,	PUNCT
ejpam-2691	643	13	tripled	triple	VERB
ejpam-2691	643	14	common	common	ADJ
ejpam-2691	643	15	fixed	fix	VERB
ejpam-2691	643	16	point	point	NOUN
ejpam-2691	643	17	results	result	NOUN
ejpam-2691	643	18	for	for	ADP
ejpam-2691	643	19	generalized	generalized	ADJ
ejpam-2691	643	20	contractions	contraction	NOUN
ejpam-2691	643	21	in	in	ADP
ejpam-2691	643	22	ordered	order	VERB
ejpam-2691	643	23	generalized	generalized	ADJ
ejpam-2691	643	24	metric	metric	ADJ
ejpam-2691	643	25	spaces	space	NOUN
ejpam-2691	643	26	,	,	PUNCT
ejpam-2691	643	27	fixed	fix	VERB
ejpam-2691	643	28	point	point	NOUN
ejpam-2691	643	29	theory	theory	NOUN
ejpam-2691	643	30	appl	appl	PROPN
ejpam-2691	643	31	.	.	PUNCT
ejpam-2691	643	32	,(2012	,(2012	PROPN
ejpam-2691	643	33	)	)	PUNCT
ejpam-2691	643	34	,	,	PUNCT
ejpam-2691	644	1	2012:101	2012:101	NUM
ejpam-2691	644	2	[	[	X
ejpam-2691	644	3	4	4	NUM
ejpam-2691	644	4	]	]	X
ejpam-2691	644	5	h.	h.	PROPN
ejpam-2691	644	6	aydi	aydi	PROPN
ejpam-2691	644	7	,	,	PUNCT
ejpam-2691	644	8	erdal	erdal	PROPN
ejpam-2691	644	9	karapinar	karapinar	PROPN
ejpam-2691	644	10	and	and	CCONJ
ejpam-2691	644	11	wasfi	wasfi	ADV
ejpam-2691	644	12	shatanawi	shatanawi	PROPN
ejpam-2691	644	13	,	,	PUNCT
ejpam-2691	644	14	tripled	triple	VERB
ejpam-2691	644	15	fixed	fix	VERB
ejpam-2691	644	16	point	point	NOUN
ejpam-2691	644	17	results	result	NOUN
ejpam-2691	644	18	in	in	ADP
ejpam-2691	644	19	generalized	generalized	ADJ
ejpam-2691	644	20	metric	metric	ADJ
ejpam-2691	644	21	spaces	space	NOUN
ejpam-2691	644	22	,	,	PUNCT
ejpam-2691	644	23	j.	j.	PROPN
ejpam-2691	644	24	appl	appl	PROPN
ejpam-2691	644	25	.	.	PROPN
ejpam-2691	644	26	math	math	PROPN
ejpam-2691	644	27	.	.	PUNCT
ejpam-2691	645	1	,	,	PUNCT
ejpam-2691	645	2	2012	2012	NUM
ejpam-2691	645	3	(	(	PUNCT
ejpam-2691	645	4	2012	2012	NUM
ejpam-2691	645	5	)	)	PUNCT
ejpam-2691	645	6	article	article	NOUN
ejpam-2691	645	7	i	i	PROPN
ejpam-2691	645	8	d	d	PROPN
ejpam-2691	645	9	:	:	PUNCT
ejpam-2691	645	10	314279	314279	NUM
ejpam-2691	645	11	.	.	PUNCT
ejpam-2691	646	1	[	[	X
ejpam-2691	646	2	5	5	NUM
ejpam-2691	646	3	]	]	PUNCT
ejpam-2691	646	4	v.	v.	CCONJ
ejpam-2691	646	5	berinde	berinde	NOUN
ejpam-2691	646	6	,	,	PUNCT
ejpam-2691	646	7	generalized	generalize	VERB
ejpam-2691	646	8	coupled	couple	VERB
ejpam-2691	646	9	fixed	fix	VERB
ejpam-2691	646	10	point	point	NOUN
ejpam-2691	646	11	theorems	theorem	NOUN
ejpam-2691	646	12	for	for	ADP
ejpam-2691	646	13	mixed	mixed	ADJ
ejpam-2691	646	14	monotone	monotone	ADJ
ejpam-2691	646	15	mappings	mapping	NOUN
ejpam-2691	646	16	in	in	ADP
ejpam-2691	646	17	partially	partially	ADV
ejpam-2691	646	18	ordered	order	VERB
ejpam-2691	646	19	metric	metric	ADJ
ejpam-2691	646	20	spaces	space	NOUN
ejpam-2691	646	21	,	,	PUNCT
ejpam-2691	646	22	nonlinear	nonlinear	ADJ
ejpam-2691	646	23	anal	anal	NOUN
ejpam-2691	646	24	.	.	PUNCT
ejpam-2691	646	25	,	,	PUNCT
ejpam-2691	646	26	74(2010	74(2010	NUM
ejpam-2691	646	27	)	)	PUNCT
ejpam-2691	646	28	,	,	PUNCT
ejpam-2691	646	29	7347–7355	7347–7355	NUM
ejpam-2691	646	30	.	.	PUNCT
ejpam-2691	647	1	[	[	X
ejpam-2691	647	2	6	6	NUM
ejpam-2691	647	3	]	]	PUNCT
ejpam-2691	647	4	v.	v.	ADP
ejpam-2691	647	5	berinde	berinde	NOUN
ejpam-2691	647	6	and	and	CCONJ
ejpam-2691	647	7	m.	m.	NOUN
ejpam-2691	647	8	borcut	borcut	VERB
ejpam-2691	647	9	,	,	PUNCT
ejpam-2691	647	10	tripled	triple	VERB
ejpam-2691	647	11	fixed	fix	VERB
ejpam-2691	647	12	point	point	NOUN
ejpam-2691	647	13	theorems	theorem	NOUN
ejpam-2691	647	14	for	for	ADP
ejpam-2691	647	15	contractive	contractive	ADJ
ejpam-2691	647	16	type	type	NOUN
ejpam-2691	647	17	mappings	mapping	NOUN
ejpam-2691	647	18	in	in	ADP
ejpam-2691	647	19	partially	partially	ADV
ejpam-2691	647	20	ordered	order	VERB
ejpam-2691	647	21	metric	metric	ADJ
ejpam-2691	647	22	spaces	space	NOUN
ejpam-2691	647	23	,	,	PUNCT
ejpam-2691	647	24	nonlinear	nonlinear	ADJ
ejpam-2691	647	25	anal	anal	NOUN
ejpam-2691	647	26	.	.	PUNCT
ejpam-2691	647	27	,	,	PUNCT
ejpam-2691	647	28	74(15	74(15	NUM
ejpam-2691	647	29	)	)	PUNCT
ejpam-2691	647	30	(	(	PUNCT
ejpam-2691	647	31	2011	2011	NUM
ejpam-2691	647	32	)	)	PUNCT
ejpam-2691	647	33	,	,	PUNCT
ejpam-2691	647	34	4889–4897	4889–4897	NUM
ejpam-2691	647	35	.	.	PUNCT
ejpam-2691	648	1	[	[	X
ejpam-2691	648	2	7	7	X
ejpam-2691	648	3	]	]	PUNCT
ejpam-2691	648	4	t.	t.	NOUN
ejpam-2691	648	5	g.	g.	PROPN
ejpam-2691	648	6	bhaskar	bhaskar	PROPN
ejpam-2691	648	7	and	and	CCONJ
ejpam-2691	648	8	v.	v.	ADP
ejpam-2691	648	9	lakshmikantham	lakshmikantham	ADJ
ejpam-2691	648	10	,	,	PUNCT
ejpam-2691	648	11	fixed	fix	VERB
ejpam-2691	648	12	point	point	NOUN
ejpam-2691	648	13	theorems	theorem	NOUN
ejpam-2691	648	14	in	in	ADP
ejpam-2691	648	15	partially	partially	ADV
ejpam-2691	648	16	ordered	order	VERB
ejpam-2691	648	17	metric	metric	ADJ
ejpam-2691	648	18	space	space	NOUN
ejpam-2691	648	19	and	and	CCONJ
ejpam-2691	648	20	applications	application	NOUN
ejpam-2691	648	21	,	,	PUNCT
ejpam-2691	648	22	nonlinear	nonlinear	ADJ
ejpam-2691	648	23	anal	anal	NOUN
ejpam-2691	648	24	.	.	PUNCT
ejpam-2691	648	25	,	,	PUNCT
ejpam-2691	648	26	65	65	NUM
ejpam-2691	648	27	(	(	PUNCT
ejpam-2691	648	28	2006	2006	NUM
ejpam-2691	648	29	)	)	PUNCT
ejpam-2691	648	30	,	,	PUNCT
ejpam-2691	648	31	1379–1393	1379–1393	NUM
ejpam-2691	648	32	.	.	PUNCT
ejpam-2691	649	1	[	[	X
ejpam-2691	649	2	8	8	NUM
ejpam-2691	649	3	]	]	X
ejpam-2691	649	4	m.	m.	NOUN
ejpam-2691	649	5	borcut	borcut	VERB
ejpam-2691	649	6	,	,	PUNCT
ejpam-2691	649	7	tripled	triple	VERB
ejpam-2691	649	8	coincidence	coincidence	NOUN
ejpam-2691	649	9	theorems	theorem	NOUN
ejpam-2691	649	10	for	for	ADP
ejpam-2691	649	11	contractive	contractive	ADJ
ejpam-2691	649	12	type	type	NOUN
ejpam-2691	649	13	mappings	mapping	NOUN
ejpam-2691	649	14	in	in	ADP
ejpam-2691	649	15	partially	partially	ADV
ejpam-2691	649	16	ordered	order	VERB
ejpam-2691	649	17	metric	metric	ADJ
ejpam-2691	649	18	spaces	space	NOUN
ejpam-2691	649	19	,	,	PUNCT
ejpam-2691	649	20	applied	apply	VERB
ejpam-2691	649	21	mathematics	mathematic	NOUN
ejpam-2691	649	22	and	and	CCONJ
ejpam-2691	649	23	computation	computation	NOUN
ejpam-2691	649	24	,	,	PUNCT
ejpam-2691	649	25	218(14	218(14	NUM
ejpam-2691	649	26	)	)	PUNCT
ejpam-2691	649	27	(	(	PUNCT
ejpam-2691	649	28	2012	2012	NUM
ejpam-2691	649	29	)	)	PUNCT
ejpam-2691	649	30	,	,	PUNCT
ejpam-2691	649	31	7339	7339	NUM
ejpam-2691	649	32	–	–	PUNCT
ejpam-2691	649	33	7346	7346	NUM
ejpam-2691	649	34	.	.	PUNCT
ejpam-2691	650	1	[	[	X
ejpam-2691	650	2	9	9	NUM
ejpam-2691	650	3	]	]	PUNCT
ejpam-2691	650	4	m.	m.	NOUN
ejpam-2691	650	5	borcut	borcut	VERB
ejpam-2691	650	6	and	and	CCONJ
ejpam-2691	650	7	v.	v.	ADP
ejpam-2691	650	8	berinde	berinde	NOUN
ejpam-2691	650	9	,	,	PUNCT
ejpam-2691	650	10	tripled	triple	VERB
ejpam-2691	650	11	coincidence	coincidence	NOUN
ejpam-2691	650	12	theorems	theorem	NOUN
ejpam-2691	650	13	for	for	ADP
ejpam-2691	650	14	contractive	contractive	ADJ
ejpam-2691	650	15	type	type	NOUN
ejpam-2691	650	16	mappings	mapping	NOUN
ejpam-2691	650	17	in	in	ADP
ejpam-2691	650	18	partially	partially	ADV
ejpam-2691	650	19	ordered	order	VERB
ejpam-2691	650	20	metric	metric	ADJ
ejpam-2691	650	21	spaces	space	NOUN
ejpam-2691	650	22	,	,	PUNCT
ejpam-2691	650	23	applied	apply	VERB
ejpam-2691	650	24	mathematics	mathematic	NOUN
ejpam-2691	650	25	and	and	CCONJ
ejpam-2691	650	26	computation	computation	NOUN
ejpam-2691	650	27	,	,	PUNCT
ejpam-2691	650	28	218(10	218(10	NUM
ejpam-2691	650	29	)	)	PUNCT
ejpam-2691	650	30	(	(	PUNCT
ejpam-2691	650	31	2012	2012	NUM
ejpam-2691	650	32	)	)	PUNCT
ejpam-2691	650	33	,	,	PUNCT
ejpam-2691	650	34	5929–5936	5929–5936	NUM
ejpam-2691	650	35	.	.	PUNCT
ejpam-2691	651	1	[	[	X
ejpam-2691	651	2	10	10	NUM
ejpam-2691	651	3	]	]	X
ejpam-2691	651	4	l.	l.	PROPN
ejpam-2691	651	5	ćirić	ćirić	PROPN
ejpam-2691	651	6	,	,	PUNCT
ejpam-2691	651	7	m.	m.	NOUN
ejpam-2691	651	8	abbas	abbas	PROPN
ejpam-2691	651	9	,	,	PUNCT
ejpam-2691	651	10	b.	b.	PROPN
ejpam-2691	651	11	damjanovic	damjanovic	PROPN
ejpam-2691	651	12	and	and	CCONJ
ejpam-2691	651	13	r.	r.	PROPN
ejpam-2691	651	14	saadati	saadati	PROPN
ejpam-2691	651	15	,	,	PUNCT
ejpam-2691	651	16	common	common	ADJ
ejpam-2691	651	17	fuzzy	fuzzy	ADJ
ejpam-2691	651	18	fixed	fix	VERB
ejpam-2691	651	19	point	point	NOUN
ejpam-2691	651	20	theorems	theorem	NOUN
ejpam-2691	651	21	in	in	ADP
ejpam-2691	651	22	ordered	order	VERB
ejpam-2691	651	23	metric	metric	ADJ
ejpam-2691	651	24	spaces	space	NOUN
ejpam-2691	651	25	,	,	PUNCT
ejpam-2691	651	26	math	math	NOUN
ejpam-2691	651	27	.	.	PUNCT
ejpam-2691	652	1	comput	comput	NOUN
ejpam-2691	652	2	.	.	PUNCT
ejpam-2691	653	1	modelling	modelling	NOUN
ejpam-2691	653	2	,	,	PUNCT
ejpam-2691	653	3	53	53	NUM
ejpam-2691	653	4	(	(	PUNCT
ejpam-2691	653	5	2011	2011	NUM
ejpam-2691	653	6	)	)	PUNCT
ejpam-2691	653	7	,	,	PUNCT
ejpam-2691	653	8	1737–1741	1737–1741	NUM
ejpam-2691	653	9	.	.	PUNCT
ejpam-2691	654	1	[	[	X
ejpam-2691	654	2	11	11	NUM
ejpam-2691	654	3	]	]	PUNCT
ejpam-2691	654	4	l.	l.	PROPN
ejpam-2691	654	5	ćirić	ćirić	PROPN
ejpam-2691	654	6	and	and	CCONJ
ejpam-2691	654	7	v.	v.	ADP
ejpam-2691	654	8	lakshmikantham	lakshmikantham	ADV
ejpam-2691	654	9	,	,	PUNCT
ejpam-2691	654	10	coupled	couple	VERB
ejpam-2691	654	11	random	random	ADJ
ejpam-2691	654	12	fixed	fix	VERB
ejpam-2691	654	13	point	point	NOUN
ejpam-2691	654	14	theorems	theorem	NOUN
ejpam-2691	654	15	for	for	ADP
ejpam-2691	654	16	nonlinear	nonlinear	ADJ
ejpam-2691	654	17	contractions	contraction	NOUN
ejpam-2691	654	18	in	in	ADP
ejpam-2691	654	19	partially	partially	ADV
ejpam-2691	654	20	ordered	order	VERB
ejpam-2691	654	21	metric	metric	ADJ
ejpam-2691	654	22	spaces	space	NOUN
ejpam-2691	654	23	,	,	PUNCT
ejpam-2691	654	24	stoch	stoch	NOUN
ejpam-2691	654	25	.	.	PUNCT
ejpam-2691	655	1	anal	anal	PROPN
ejpam-2691	655	2	.	.	PROPN
ejpam-2691	655	3	,	,	PUNCT
ejpam-2691	655	4	27(6	27(6	NUM
ejpam-2691	655	5	)	)	PUNCT
ejpam-2691	655	6	(	(	PUNCT
ejpam-2691	655	7	2009	2009	NUM
ejpam-2691	655	8	)	)	PUNCT
ejpam-2691	655	9	,	,	PUNCT
ejpam-2691	655	10	1246–1259	1246–1259	NUM
ejpam-2691	655	11	.	.	PUNCT
ejpam-2691	656	1	[	[	X
ejpam-2691	656	2	12	12	NUM
ejpam-2691	656	3	]	]	PUNCT
ejpam-2691	656	4	s.	s.	PROPN
ejpam-2691	656	5	s.	s.	PROPN
ejpam-2691	656	6	chang	chang	PROPN
ejpam-2691	656	7	and	and	CCONJ
ejpam-2691	656	8	y.h	y.h	PROPN
ejpam-2691	656	9	.	.	PROPN
ejpam-2691	656	10	ma	ma	PROPN
ejpam-2691	656	11	,	,	PUNCT
ejpam-2691	656	12	coupled	couple	VERB
ejpam-2691	656	13	fixed	fix	VERB
ejpam-2691	656	14	point	point	NOUN
ejpam-2691	656	15	for	for	ADP
ejpam-2691	656	16	mixed	mixed	ADJ
ejpam-2691	656	17	monotone	monotone	ADJ
ejpam-2691	656	18	condensing	condense	VERB
ejpam-2691	656	19	operators	operator	NOUN
ejpam-2691	656	20	and	and	CCONJ
ejpam-2691	656	21	an	an	DET
ejpam-2691	656	22	existence	existence	NOUN
ejpam-2691	656	23	theorem	theorem	NOUN
ejpam-2691	656	24	of	of	ADP
ejpam-2691	656	25	the	the	DET
ejpam-2691	656	26	solutions	solution	NOUN
ejpam-2691	656	27	for	for	ADP
ejpam-2691	656	28	a	a	DET
ejpam-2691	656	29	class	class	NOUN
ejpam-2691	656	30	of	of	ADP
ejpam-2691	656	31	functional	functional	ADJ
ejpam-2691	656	32	equations	equation	NOUN
ejpam-2691	656	33	arising	arise	VERB
ejpam-2691	656	34	in	in	ADP
ejpam-2691	656	35	dynamic	dynamic	ADJ
ejpam-2691	656	36	programming	programming	NOUN
ejpam-2691	656	37	,	,	PUNCT
ejpam-2691	656	38	j.	j.	PROPN
ejpam-2691	656	39	math	math	PROPN
ejpam-2691	656	40	.	.	PUNCT
ejpam-2691	657	1	anal	anal	PROPN
ejpam-2691	657	2	.	.	PUNCT
ejpam-2691	658	1	appl	appl	PROPN
ejpam-2691	658	2	.	.	PROPN
ejpam-2691	659	1	,	,	PUNCT
ejpam-2691	659	2	160	160	NUM
ejpam-2691	659	3	(	(	PUNCT
ejpam-2691	659	4	1991	1991	NUM
ejpam-2691	659	5	)	)	PUNCT
ejpam-2691	659	6	,	,	PUNCT
ejpam-2691	659	7	468–479	468–479	NUM
ejpam-2691	659	8	.	.	PUNCT
ejpam-2691	660	1	[	[	X
ejpam-2691	660	2	13	13	NUM
ejpam-2691	660	3	]	]	X
ejpam-2691	660	4	b.	b.	PROPN
ejpam-2691	660	5	s.	s.	PROPN
ejpam-2691	660	6	choudhary	choudhary	PROPN
ejpam-2691	660	7	and	and	CCONJ
ejpam-2691	660	8	a.	a.	NOUN
ejpam-2691	660	9	kundu	kundu	NOUN
ejpam-2691	660	10	,	,	PUNCT
ejpam-2691	660	11	a	a	DET
ejpam-2691	660	12	coupled	couple	VERB
ejpam-2691	660	13	coincidence	coincidence	NOUN
ejpam-2691	660	14	point	point	NOUN
ejpam-2691	660	15	result	result	NOUN
ejpam-2691	660	16	in	in	ADP
ejpam-2691	660	17	partially	partially	ADV
ejpam-2691	660	18	ordered	order	VERB
ejpam-2691	660	19	metric	metric	ADJ
ejpam-2691	660	20	spaces	space	NOUN
ejpam-2691	660	21	for	for	ADP
ejpam-2691	660	22	compatible	compatible	ADJ
ejpam-2691	660	23	mappings	mapping	NOUN
ejpam-2691	660	24	,	,	PUNCT
ejpam-2691	660	25	nonlinear	nonlinear	ADJ
ejpam-2691	660	26	anal	anal	NOUN
ejpam-2691	660	27	.	.	PUNCT
ejpam-2691	660	28	,	,	PUNCT
ejpam-2691	660	29	73	73	NUM
ejpam-2691	660	30	(	(	PUNCT
ejpam-2691	660	31	2010	2010	NUM
ejpam-2691	660	32	)	)	PUNCT
ejpam-2691	660	33	,	,	PUNCT
ejpam-2691	660	34	2524	2524	NUM
ejpam-2691	660	35	–	–	PUNCT
ejpam-2691	660	36	2531	2531	NUM
ejpam-2691	660	37	.	.	PUNCT
ejpam-2691	661	1	[	[	X
ejpam-2691	661	2	14	14	NUM
ejpam-2691	661	3	]	]	PUNCT
ejpam-2691	661	4	m.	m.	PROPN
ejpam-2691	661	5	e.	e.	PROPN
ejpam-2691	661	6	gordji	gordji	PROPN
ejpam-2691	661	7	and	and	CCONJ
ejpam-2691	661	8	m.	m.	NOUN
ejpam-2691	661	9	ramezani	ramezani	PROPN
ejpam-2691	661	10	,	,	PUNCT
ejpam-2691	661	11	n	n	X
ejpam-2691	661	12	-fixed	-fixe	VERB
ejpam-2691	661	13	point	point	NOUN
ejpam-2691	661	14	theorems	theorem	NOUN
ejpam-2691	661	15	in	in	ADP
ejpam-2691	661	16	partially	partially	ADV
ejpam-2691	661	17	ordered	order	VERB
ejpam-2691	661	18	metric	metric	ADJ
ejpam-2691	661	19	spaces	space	NOUN
ejpam-2691	661	20	,	,	PUNCT
ejpam-2691	661	21	nonlinear	nonlinear	ADJ
ejpam-2691	661	22	anal	anal	NOUN
ejpam-2691	661	23	.	.	PUNCT
ejpam-2691	661	24	,	,	PUNCT
ejpam-2691	661	25	74(13	74(13	NUM
ejpam-2691	661	26	)	)	PUNCT
ejpam-2691	661	27	(	(	PUNCT
ejpam-2691	661	28	2011	2011	NUM
ejpam-2691	661	29	)	)	PUNCT
ejpam-2691	661	30	,	,	PUNCT
ejpam-2691	661	31	4544–4549	4544–4549	NOUN
ejpam-2691	661	32	.	.	PUNCT
ejpam-2691	662	1	references	reference	NOUN
ejpam-2691	662	2	311	311	NUM
ejpam-2691	662	3	[	[	X
ejpam-2691	662	4	15	15	NUM
ejpam-2691	662	5	]	]	PUNCT
ejpam-2691	662	6	m.	m.	NOUN
ejpam-2691	662	7	imdad	imdad	PROPN
ejpam-2691	662	8	,	,	PUNCT
ejpam-2691	662	9	a.	a.	PROPN
ejpam-2691	662	10	h.	h.	PROPN
ejpam-2691	662	11	soliman	soliman	PROPN
ejpam-2691	662	12	,	,	PUNCT
ejpam-2691	662	13	b.s	b.s	PROPN
ejpam-2691	662	14	.	.	PROPN
ejpam-2691	662	15	choudhury	choudhury	PROPN
ejpam-2691	662	16	and	and	CCONJ
ejpam-2691	662	17	p.	p.	PROPN
ejpam-2691	662	18	das	das	PROPN
ejpam-2691	662	19	,	,	PUNCT
ejpam-2691	662	20	on	on	ADP
ejpam-2691	662	21	n	n	CCONJ
ejpam-2691	662	22	-	-	PUNCT
ejpam-2691	662	23	tupled	tuple	VERB
ejpam-2691	662	24	coincidence	coincidence	NOUN
ejpam-2691	662	25	and	and	CCONJ
ejpam-2691	662	26	common	common	ADJ
ejpam-2691	662	27	fixed	fix	VERB
ejpam-2691	662	28	points	point	NOUN
ejpam-2691	662	29	results	result	NOUN
ejpam-2691	662	30	in	in	ADP
ejpam-2691	662	31	metric	metric	ADJ
ejpam-2691	662	32	spaces	space	NOUN
ejpam-2691	662	33	.	.	PUNCT
ejpam-2691	663	1	journal	journal	NOUN
ejpam-2691	663	2	of	of	ADP
ejpam-2691	663	3	operator	operator	NOUN
ejpam-2691	663	4	,	,	PUNCT
ejpam-2691	663	5	2013	2013	NUM
ejpam-2691	663	6	,	,	PUNCT
ejpam-2691	663	7	article	article	NOUN
ejpam-2691	663	8	i	i	PROPN
ejpam-2691	663	9	d	d	PROPN
ejpam-2691	663	10	:	:	PUNCT
ejpam-2691	663	11	532867	532867	NUM
ejpam-2691	663	12	(	(	PUNCT
ejpam-2691	663	13	2013	2013	NUM
ejpam-2691	663	14	)	)	PUNCT
ejpam-2691	663	15	.	.	PUNCT
ejpam-2691	664	1	[	[	X
ejpam-2691	664	2	16	16	NUM
ejpam-2691	664	3	]	]	X
ejpam-2691	664	4	e.	e.	PROPN
ejpam-2691	664	5	karapinar	karapinar	PROPN
ejpam-2691	664	6	,	,	PUNCT
ejpam-2691	664	7	h.	h.	PROPN
ejpam-2691	664	8	aydi	aydi	PROPN
ejpam-2691	664	9	,	,	PUNCT
ejpam-2691	664	10	z.	z.	PROPN
ejpam-2691	664	11	mustafa	mustafa	PROPN
ejpam-2691	664	12	,	,	PUNCT
ejpam-2691	664	13	some	some	PRON
ejpam-2691	664	14	tripled	triple	VERB
ejpam-2691	664	15	coincidence	coincidence	NOUN
ejpam-2691	664	16	point	point	NOUN
ejpam-2691	664	17	theorems	theorem	NOUN
ejpam-2691	664	18	for	for	ADP
ejpam-2691	664	19	almos	almos	NOUN
ejpam-2691	664	20	generalized	generalize	VERB
ejpam-2691	664	21	contractions	contraction	NOUN
ejpam-2691	664	22	in	in	ADP
ejpam-2691	664	23	ordered	order	VERB
ejpam-2691	664	24	metric	metric	ADJ
ejpam-2691	664	25	spaces	space	NOUN
ejpam-2691	664	26	.	.	PUNCT
ejpam-2691	665	1	tamkang	tamkang	PROPN
ejpam-2691	665	2	j.	j.	PROPN
ejpam-2691	665	3	math	math	PROPN
ejpam-2691	665	4	.	.	PUNCT
ejpam-2691	665	5	,	,	PUNCT
ejpam-2691	665	6	44(3	44(3	NUM
ejpam-2691	665	7	)	)	PUNCT
ejpam-2691	665	8	(	(	PUNCT
ejpam-2691	665	9	2013	2013	NUM
ejpam-2691	665	10	)	)	PUNCT
ejpam-2691	665	11	,	,	PUNCT
ejpam-2691	665	12	233–251	233–251	NUM
ejpam-2691	665	13	.	.	PUNCT
ejpam-2691	666	1	[	[	X
ejpam-2691	666	2	17	17	NUM
ejpam-2691	666	3	]	]	X
ejpam-2691	666	4	amit	amit	PROPN
ejpam-2691	666	5	kumar	kumar	PROPN
ejpam-2691	666	6	,	,	PUNCT
ejpam-2691	666	7	fixed	fix	VERB
ejpam-2691	666	8	point	point	NOUN
ejpam-2691	666	9	theorems	theorem	NOUN
ejpam-2691	666	10	for	for	ADP
ejpam-2691	666	11	set	set	ADJ
ejpam-2691	666	12	valued	value	VERB
ejpam-2691	666	13	mappings	mapping	NOUN
ejpam-2691	666	14	in	in	ADP
ejpam-2691	666	15	partially	partially	ADV
ejpam-2691	666	16	ordered	order	VERB
ejpam-2691	666	17	gmetric	gmetric	ADJ
ejpam-2691	666	18	space	space	NOUN
ejpam-2691	666	19	,	,	PUNCT
ejpam-2691	666	20	tbilisi	tbilisi	PROPN
ejpam-2691	666	21	mathematical	mathematical	PROPN
ejpam-2691	666	22	journal	journal	PROPN
ejpam-2691	666	23	,	,	PUNCT
ejpam-2691	666	24	7(1	7(1	NUM
ejpam-2691	666	25	)	)	PUNCT
ejpam-2691	666	26	(	(	PUNCT
ejpam-2691	666	27	2014	2014	NUM
ejpam-2691	666	28	)	)	PUNCT
ejpam-2691	666	29	,	,	PUNCT
ejpam-2691	666	30	45–54	45–54	NUM
ejpam-2691	666	31	.	.	PUNCT
ejpam-2691	667	1	[	[	X
ejpam-2691	667	2	18	18	NUM
ejpam-2691	667	3	]	]	PUNCT
ejpam-2691	667	4	v.	v.	CCONJ
ejpam-2691	667	5	lakshmikantham	lakshmikantham	NOUN
ejpam-2691	667	6	and	and	CCONJ
ejpam-2691	667	7	l.	l.	PROPN
ejpam-2691	667	8	ciric	ciric	PROPN
ejpam-2691	667	9	,	,	PUNCT
ejpam-2691	667	10	coupled	couple	VERB
ejpam-2691	667	11	fixed	fix	VERB
ejpam-2691	667	12	point	point	NOUN
ejpam-2691	667	13	theorems	theorem	NOUN
ejpam-2691	667	14	for	for	ADP
ejpam-2691	667	15	nonlinear	nonlinear	ADJ
ejpam-2691	667	16	contractions	contraction	NOUN
ejpam-2691	667	17	in	in	ADP
ejpam-2691	667	18	partially	partially	ADV
ejpam-2691	667	19	ordered	order	VERB
ejpam-2691	667	20	metric	metric	ADJ
ejpam-2691	667	21	spaces	space	NOUN
ejpam-2691	667	22	,	,	PUNCT
ejpam-2691	667	23	nonlinear	nonlinear	ADJ
ejpam-2691	667	24	anal	anal	NOUN
ejpam-2691	667	25	.	.	PUNCT
ejpam-2691	667	26	,	,	PUNCT
ejpam-2691	667	27	70	70	NUM
ejpam-2691	667	28	(	(	PUNCT
ejpam-2691	667	29	2009	2009	NUM
ejpam-2691	667	30	)	)	PUNCT
ejpam-2691	667	31	,	,	PUNCT
ejpam-2691	667	32	4341–4349	4341–4349	NUM
ejpam-2691	667	33	.	.	PUNCT
ejpam-2691	668	1	[	[	X
ejpam-2691	668	2	19	19	NUM
ejpam-2691	668	3	]	]	PUNCT
ejpam-2691	668	4	maurice	maurice	PROPN
ejpam-2691	668	5	fréchet	fréchet	PROPN
ejpam-2691	668	6	,	,	PUNCT
ejpam-2691	668	7	sur	sur	PROPN
ejpam-2691	668	8	quelques	quelques	PROPN
ejpam-2691	668	9	points	point	NOUN
ejpam-2691	668	10	du	du	PROPN
ejpam-2691	668	11	calcul	calcul	PROPN
ejpam-2691	668	12	fonctionnel	fonctionnel	PROPN
ejpam-2691	668	13	,	,	PUNCT
ejpam-2691	668	14	rendic	rendic	ADJ
ejpam-2691	668	15	.	.	PUNCT
ejpam-2691	669	1	circ	circ	PROPN
ejpam-2691	669	2	.	.	PUNCT
ejpam-2691	670	1	mat	mat	NOUN
ejpam-2691	670	2	.	.	PUNCT
ejpam-2691	670	3	palermo	palermo	NOUN
ejpam-2691	670	4	,	,	PUNCT
ejpam-2691	670	5	22	22	NUM
ejpam-2691	670	6	(	(	PUNCT
ejpam-2691	670	7	1906	1906	NUM
ejpam-2691	670	8	)	)	PUNCT
ejpam-2691	670	9	,	,	PUNCT
ejpam-2691	670	10	1–74	1–74	NUM
ejpam-2691	670	11	.	.	PUNCT
ejpam-2691	671	1	[	[	X
ejpam-2691	671	2	20	20	NUM
ejpam-2691	671	3	]	]	PUNCT
ejpam-2691	671	4	b.	b.	PROPN
ejpam-2691	671	5	samet	samet	PROPN
ejpam-2691	671	6	and	and	CCONJ
ejpam-2691	671	7	c.	c.	PROPN
ejpam-2691	671	8	vetro	vetro	PROPN
ejpam-2691	671	9	,	,	PUNCT
ejpam-2691	671	10	coupled	couple	VERB
ejpam-2691	671	11	fixed	fix	VERB
ejpam-2691	671	12	point	point	NOUN
ejpam-2691	671	13	,	,	PUNCT
ejpam-2691	671	14	f	f	PROPN
ejpam-2691	671	15	-invariant	-invariant	NOUN
ejpam-2691	671	16	set	set	VERB
ejpam-2691	671	17	and	and	CCONJ
ejpam-2691	671	18	fixed	fix	VERB
ejpam-2691	671	19	point	point	NOUN
ejpam-2691	671	20	of	of	ADP
ejpam-2691	671	21	n	n	DET
ejpam-2691	671	22	order	order	NOUN
ejpam-2691	671	23	.	.	PUNCT
ejpam-2691	672	1	ann	ann	PROPN
ejpam-2691	672	2	.	.	PUNCT
ejpam-2691	672	3	funct	funct	PROPN
ejpam-2691	672	4	.	.	PUNCT
ejpam-2691	673	1	anal	anal	PROPN
ejpam-2691	673	2	.	.	PUNCT
ejpam-2691	674	1	1(2	1(2	NUM
ejpam-2691	674	2	)	)	PUNCT
ejpam-2691	674	3	(	(	PUNCT
ejpam-2691	674	4	2010	2010	NUM
ejpam-2691	674	5	)	)	PUNCT
ejpam-2691	674	6	,	,	PUNCT
ejpam-2691	674	7	4656–4662	4656–4662	NUM
ejpam-2691	674	8	.	.	PUNCT
ejpam-2691	675	1	[	[	X
ejpam-2691	675	2	21	21	NUM
ejpam-2691	675	3	]	]	PUNCT
ejpam-2691	675	4	m.	m.	NOUN
ejpam-2691	675	5	.	.	PUNCT
ejpam-2691	676	1	searćid	searćid	NOUN
ejpam-2691	676	2	,	,	PUNCT
ejpam-2691	676	3	metric	metric	ADJ
ejpam-2691	676	4	spaces	space	NOUN
ejpam-2691	676	5	,	,	PUNCT
ejpam-2691	676	6	springer	springer	NOUN
ejpam-2691	676	7	-	-	PUNCT
ejpam-2691	676	8	verlag	verlag	PROPN
ejpam-2691	676	9	london	london	PROPN
ejpam-2691	676	10	limited	limit	VERB
ejpam-2691	676	11	2007	2007	NUM
ejpam-2691	676	12	.	.	PUNCT
ejpam-2691	677	1	[	[	X
ejpam-2691	677	2	22	22	NUM
ejpam-2691	677	3	]	]	PUNCT
ejpam-2691	677	4	v.	v.	ADP
ejpam-2691	677	5	sihag	sihag	PROPN
ejpam-2691	677	6	,	,	PUNCT
ejpam-2691	677	7	c.	c.	PROPN
ejpam-2691	677	8	vetro	vetro	PROPN
ejpam-2691	677	9	and	and	CCONJ
ejpam-2691	677	10	r.	r.	PROPN
ejpam-2691	677	11	k.	k.	PROPN
ejpam-2691	677	12	vats	vat	NOUN
ejpam-2691	677	13	,	,	PUNCT
ejpam-2691	677	14	a	a	DET
ejpam-2691	677	15	fixed	fix	VERB
ejpam-2691	677	16	point	point	NOUN
ejpam-2691	677	17	theorem	theorem	VERB
ejpam-2691	677	18	in	in	ADP
ejpam-2691	677	19	g	g	NOUN
ejpam-2691	677	20	-	-	PUNCT
ejpam-2691	677	21	metric	metric	ADJ
ejpam-2691	677	22	spaces	space	NOUN
ejpam-2691	677	23	via	via	ADP
ejpam-2691	677	24	α	α	NOUN
ejpam-2691	677	25	-	-	PUNCT
ejpam-2691	677	26	series	series	NOUN
ejpam-2691	677	27	,	,	PUNCT
ejpam-2691	677	28	quaestiones	quaestione	NOUN
ejpam-2691	677	29	mathematicae	mathematicae	PROPN
ejpam-2691	677	30	,	,	PUNCT
ejpam-2691	677	31	37	37	NUM
ejpam-2691	677	32	(	(	PUNCT
ejpam-2691	677	33	2014	2014	NUM
ejpam-2691	677	34	)	)	PUNCT
ejpam-2691	677	35	,	,	PUNCT
ejpam-2691	677	36	1–6	1–6	X
ejpam-2691	677	37	.	.	PUNCT
ejpam-2691	678	1	[	[	X
ejpam-2691	678	2	23	23	NUM
ejpam-2691	678	3	]	]	PUNCT
ejpam-2691	678	4	r.	r.	PROPN
ejpam-2691	678	5	k.	k.	PROPN
ejpam-2691	678	6	vats	vats	PROPN
ejpam-2691	678	7	,	,	PUNCT
ejpam-2691	678	8	kenan	kenan	PROPN
ejpam-2691	678	9	tas	tas	PROPN
ejpam-2691	678	10	,	,	PUNCT
ejpam-2691	678	11	vizender	vizender	NOUN
ejpam-2691	678	12	sihag	sihag	PROPN
ejpam-2691	678	13	and	and	CCONJ
ejpam-2691	678	14	amit	amit	PROPN
ejpam-2691	678	15	kumar	kumar	PROPN
ejpam-2691	678	16	,	,	PUNCT
ejpam-2691	678	17	tripled	triple	VERB
ejpam-2691	678	18	fixed	fix	VERB
ejpam-2691	678	19	point	point	NOUN
ejpam-2691	678	20	theorems	theorem	NOUN
ejpam-2691	678	21	via	via	ADP
ejpam-2691	678	22	α	α	NOUN
ejpam-2691	678	23	-	-	PUNCT
ejpam-2691	678	24	series	series	NOUN
ejpam-2691	678	25	in	in	ADP
ejpam-2691	678	26	partially	partially	ADV
ejpam-2691	678	27	ordered	order	VERB
ejpam-2691	678	28	metric	metric	ADJ
ejpam-2691	678	29	spaces	space	NOUN
ejpam-2691	678	30	,	,	PUNCT
ejpam-2691	678	31	journal	journal	NOUN
ejpam-2691	678	32	of	of	ADP
ejpam-2691	678	33	inequalities	inequality	NOUN
ejpam-2691	678	34	and	and	CCONJ
ejpam-2691	678	35	applications	application	NOUN
ejpam-2691	678	36	,	,	PUNCT
ejpam-2691	678	37	2014:176	2014:176	NOUN
ejpam-2691	678	38	.	.	PUNCT