id	sid	tid	token	lemma	pos
bibechana-9308	1	1	microsoft	microsoft	PROPN
bibechana-9308	1	2	word	word	PROPN
bibechana-9308	1	3	n.	n.	PROPN
bibechana-9308	1	4	pahari	pahari	PROPN
bibechana-9308	1	5	.	.	PUNCT
bibechana-9308	2	1	_	_	NOUN
bibechana-9308	2	2	34	34	NUM
bibechana-9308	2	3	-	-	SYM
bibechana-9308	2	4	44_.doc	44_.doc	NUM
bibechana-9308	2	5	n.p	n.p	PROPN
bibechana-9308	2	6	.	.	PROPN
bibechana-9308	2	7	pahari	pahari	PROPN
bibechana-9308	2	8	/	/	SYM
bibechana-9308	2	9	bibechana	bibechana	NOUN
bibechana-9308	2	10	10	10	NUM
bibechana-9308	2	11	(	(	PUNCT
bibechana-9308	2	12	2014	2014	NUM
bibechana-9308	2	13	)	)	PUNCT
bibechana-9308	2	14	20	20	NUM
bibechana-9308	2	15	-	-	SYM
bibechana-9308	2	16	30	30	NUM
bibechana-9308	2	17	:	:	PUNCT
bibechana-9308	2	18	bmhss	bmhss	PROPN
bibechana-9308	2	19	,	,	PUNCT
bibechana-9308	2	20	p.20	p.20	PUNCT
bibechana-9308	2	21	(	(	PUNCT
bibechana-9308	2	22	online	online	ADJ
bibechana-9308	2	23	publication	publication	NOUN
bibechana-9308	2	24	:	:	PUNCT
bibechana-9308	2	25	dec	dec	PROPN
bibechana-9308	2	26	.	.	PROPN
bibechana-9308	2	27	,	,	PUNCT
bibechana-9308	2	28	2013	2013	NUM
bibechana-9308	2	29	)	)	PUNCT
bibechana-9308	2	30	bibechana	bibechana	NOUN
bibechana-9308	2	31	a	a	DET
bibechana-9308	2	32	multidisciplinary	multidisciplinary	ADJ
bibechana-9308	2	33	journal	journal	NOUN
bibechana-9308	2	34	of	of	ADP
bibechana-9308	2	35	science	science	NOUN
bibechana-9308	2	36	,	,	PUNCT
bibechana-9308	2	37	technology	technology	NOUN
bibechana-9308	2	38	and	and	CCONJ
bibechana-9308	2	39	mathematics	mathematic	NOUN
bibechana-9308	2	40	issn	issn	VERB
bibechana-9308	2	41	2091	2091	NUM
bibechana-9308	2	42	-	-	SYM
bibechana-9308	2	43	0762	0762	NUM
bibechana-9308	2	44	(	(	PUNCT
bibechana-9308	2	45	online	online	ADJ
bibechana-9308	2	46	)	)	PUNCT
bibechana-9308	2	47	journal	journal	NOUN
bibechana-9308	2	48	homepage	homepage	NOUN
bibechana-9308	2	49	:	:	PUNCT
bibechana-9308	2	50	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-9308	2	51	on	on	ADP
bibechana-9308	2	52	2	2	NUM
bibechana-9308	2	53	normed	normed	ADJ
bibechana-9308	2	54	space	space	NOUN
bibechana-9308	2	55	valued	value	VERB
bibechana-9308	2	56	paranormed	paranorme	VERB
bibechana-9308	2	57	null	null	ADJ
bibechana-9308	2	58	sequence	sequence	NOUN
bibechana-9308	2	59	space	space	NOUN
bibechana-9308	2	60	(	(	PUNCT
bibechana-9308	2	61	c0	c0	NOUN
bibechana-9308	2	62	(	(	PUNCT
bibechana-9308	2	63	s	s	PROPN
bibechana-9308	2	64	,	,	PUNCT
bibechana-9308	2	65	αααα	αααα	NOUN
bibechana-9308	2	66	–	–	PUNCT
bibechana-9308	2	67	,	,	PUNCT
bibechana-9308	2	68	u	u	NOUN
bibechana-9308	2	69	–	–	PUNCT
bibechana-9308	2	70	,	,	PUNCT
bibechana-9308	2	71	||	||	PROPN
bibechana-9308	2	72	.	.	PUNCT
bibechana-9308	2	73	,	,	PUNCT
bibechana-9308	2	74	.||	.||	PROPN
bibechana-9308	2	75	)	)	PUNCT
bibechana-9308	2	76	,	,	PUNCT
bibechana-9308	2	77	t	t	PROPN
bibechana-9308	2	78	)	)	PUNCT
bibechana-9308	2	79	narayan	narayan	PROPN
bibechana-9308	2	80	prasad	prasad	PROPN
bibechana-9308	2	81	pahari	pahari	PROPN
bibechana-9308	2	82	central	central	ADJ
bibechana-9308	2	83	department	department	NOUN
bibechana-9308	2	84	of	of	ADP
bibechana-9308	2	85	mathematics	mathematics	PROPN
bibechana-9308	2	86	,	,	PUNCT
bibechana-9308	2	87	tribhuvan	tribhuvan	PROPN
bibechana-9308	2	88	university	university	PROPN
bibechana-9308	2	89	,	,	PUNCT
bibechana-9308	2	90	university	university	NOUN
bibechana-9308	2	91	campus	campus	NOUN
bibechana-9308	2	92	,	,	PUNCT
bibechana-9308	2	93	kirtipur	kirtipur	NOUN
bibechana-9308	2	94	,	,	PUNCT
bibechana-9308	2	95	kathmandu	kathmandu	NOUN
bibechana-9308	2	96	,	,	PUNCT
bibechana-9308	2	97	nepal	nepal	ADJ
bibechana-9308	2	98	email	email	NOUN
bibechana-9308	2	99	:	:	PUNCT
bibechana-9308	2	100	nppahari	nppahari	ADV
bibechana-9308	2	101	@	@	ADP
bibechana-9308	2	102	gmail.com	gmail.com	X
bibechana-9308	2	103	article	article	NOUN
bibechana-9308	2	104	history	history	NOUN
bibechana-9308	2	105	:	:	PUNCT
bibechana-9308	2	106	received	receive	VERB
bibechana-9308	2	107	5	5	NUM
bibechana-9308	2	108	september	september	PROPN
bibechana-9308	2	109	,	,	PUNCT
bibechana-9308	2	110	2013	2013	NUM
bibechana-9308	2	111	;	;	PUNCT
bibechana-9308	2	112	accepted	accept	VERB
bibechana-9308	2	113	23	23	NUM
bibechana-9308	2	114	september	september	PROPN
bibechana-9308	2	115	,	,	PUNCT
bibechana-9308	2	116	2013	2013	NUM
bibechana-9308	2	117	abstract	abstract	NOUN
bibechana-9308	2	118	in	in	ADP
bibechana-9308	2	119	this	this	DET
bibechana-9308	2	120	paper	paper	NOUN
bibechana-9308	2	121	we	we	PRON
bibechana-9308	2	122	introduce	introduce	VERB
bibechana-9308	2	123	and	and	CCONJ
bibechana-9308	2	124	study	study	VERB
bibechana-9308	2	125	a	a	DET
bibechana-9308	2	126	new	new	ADJ
bibechana-9308	2	127	class	class	NOUN
bibechana-9308	2	128	c0	c0	NOUN
bibechana-9308	2	129	(	(	PUNCT
bibechana-9308	2	130	s	s	PROPN
bibechana-9308	2	131	,	,	PUNCT
bibechana-9308	2	132	α	α	PROPN
bibechana-9308	2	133	–	–	PUNCT
bibechana-9308	2	134	,	,	PUNCT
bibechana-9308	2	135	u	u	NOUN
bibechana-9308	2	136	–	–	PUNCT
bibechana-9308	2	137	,	,	PUNCT
bibechana-9308	2	138	||	||	PROPN
bibechana-9308	2	139	.	.	PUNCT
bibechana-9308	2	140	,	,	PUNCT
bibechana-9308	2	141	.||	.||	PROPN
bibechana-9308	2	142	)	)	PUNCT
bibechana-9308	2	143	of	of	ADP
bibechana-9308	2	144	sequences	sequence	NOUN
bibechana-9308	2	145	with	with	ADP
bibechana-9308	2	146	values	value	NOUN
bibechana-9308	2	147	in	in	ADP
bibechana-9308	2	148	2normed	2normed	NUM
bibechana-9308	2	149	space	space	NOUN
bibechana-9308	2	150	as	as	ADP
bibechana-9308	2	151	a	a	DET
bibechana-9308	2	152	generalization	generalization	NOUN
bibechana-9308	2	153	of	of	ADP
bibechana-9308	2	154	basic	basic	ADJ
bibechana-9308	2	155	null	null	ADJ
bibechana-9308	2	156	sequence	sequence	NOUN
bibechana-9308	2	157	space	space	NOUN
bibechana-9308	2	158	c0	c0	NOUN
bibechana-9308	2	159	.	.	PUNCT
bibechana-9308	3	1	we	we	PRON
bibechana-9308	3	2	investigate	investigate	VERB
bibechana-9308	3	3	some	some	DET
bibechana-9308	3	4	conditions	condition	NOUN
bibechana-9308	3	5	pertaining	pertain	VERB
bibechana-9308	3	6	to	to	ADP
bibechana-9308	3	7	the	the	DET
bibechana-9308	3	8	containment	containment	NOUN
bibechana-9308	3	9	relations	relation	NOUN
bibechana-9308	3	10	of	of	ADP
bibechana-9308	3	11	the	the	DET
bibechana-9308	3	12	class	class	NOUN
bibechana-9308	3	13	c0	c0	NOUN
bibechana-9308	3	14	(	(	PUNCT
bibechana-9308	3	15	s	s	PROPN
bibechana-9308	3	16	,	,	PUNCT
bibechana-9308	3	17	α	α	PROPN
bibechana-9308	3	18	–	–	PUNCT
bibechana-9308	3	19	,	,	PUNCT
bibechana-9308	3	20	u	u	NOUN
bibechana-9308	3	21	–	–	PUNCT
bibechana-9308	3	22	,	,	PUNCT
bibechana-9308	3	23	||	||	PROPN
bibechana-9308	3	24	.	.	PUNCT
bibechana-9308	3	25	,	,	PUNCT
bibechana-9308	3	26	.||	.||	PROPN
bibechana-9308	3	27	)	)	PUNCT
bibechana-9308	3	28	in	in	ADP
bibechana-9308	3	29	terms	term	NOUN
bibechana-9308	3	30	of	of	ADP
bibechana-9308	3	31	different	different	ADJ
bibechana-9308	3	32	α	α	NOUN
bibechana-9308	3	33	–	–	PUNCT
bibechana-9308	3	34	and	and	CCONJ
bibechana-9308	3	35	u	u	NOUN
bibechana-9308	3	36	–	–	PUNCT
bibechana-9308	3	37	and	and	CCONJ
bibechana-9308	3	38	explore	explore	VERB
bibechana-9308	3	39	the	the	DET
bibechana-9308	3	40	linear	linear	ADJ
bibechana-9308	3	41	topological	topological	ADJ
bibechana-9308	3	42	structures	structure	NOUN
bibechana-9308	3	43	of	of	ADP
bibechana-9308	3	44	the	the	DET
bibechana-9308	3	45	space	space	NOUN
bibechana-9308	3	46	c0	c0	NOUN
bibechana-9308	3	47	(	(	PUNCT
bibechana-9308	3	48	s	s	PROPN
bibechana-9308	3	49	,	,	PUNCT
bibechana-9308	3	50	α	α	PROPN
bibechana-9308	3	51	–	–	PUNCT
bibechana-9308	3	52	,	,	PUNCT
bibechana-9308	3	53	u	u	NOUN
bibechana-9308	3	54	–	–	PUNCT
bibechana-9308	3	55	,	,	PUNCT
bibechana-9308	3	56	||	||	PROPN
bibechana-9308	3	57	.	.	PUNCT
bibechana-9308	3	58	,	,	PUNCT
bibechana-9308	3	59	.||	.||	PROPN
bibechana-9308	3	60	)	)	PUNCT
bibechana-9308	3	61	by	by	ADP
bibechana-9308	3	62	endowing	endow	VERB
bibechana-9308	3	63	it	it	PRON
bibechana-9308	3	64	with	with	ADP
bibechana-9308	3	65	a	a	DET
bibechana-9308	3	66	suitable	suitable	ADJ
bibechana-9308	3	67	natural	natural	ADJ
bibechana-9308	3	68	paranorm	paranorm	NOUN
bibechana-9308	3	69	.	.	PUNCT
bibechana-9308	4	1	keywords	keyword	NOUN
bibechana-9308	4	2	:	:	PUNCT
bibechana-9308	4	3	2normed	2normed	NUM
bibechana-9308	4	4	space	space	NOUN
bibechana-9308	4	5	,	,	PUNCT
bibechana-9308	4	6	2	2	NUM
bibechana-9308	4	7	–	–	PUNCT
bibechana-9308	4	8	banach	banach	NOUN
bibechana-9308	4	9	space	space	NOUN
bibechana-9308	4	10	,	,	PUNCT
bibechana-9308	4	11	paranormed	paranorme	VERB
bibechana-9308	4	12	space	space	NOUN
bibechana-9308	4	13	,	,	PUNCT
bibechana-9308	4	14	sequence	sequence	NOUN
bibechana-9308	4	15	space	space	NOUN
bibechana-9308	4	16	.	.	PUNCT
bibechana-9308	5	1	1	1	X
bibechana-9308	5	2	.	.	X
bibechana-9308	5	3	introduction	introduction	NOUN
bibechana-9308	5	4	and	and	CCONJ
bibechana-9308	5	5	preliminaries	preliminary	NOUN
bibechana-9308	5	6	before	before	ADP
bibechana-9308	5	7	proceeding	proceed	VERB
bibechana-9308	5	8	with	with	ADP
bibechana-9308	5	9	the	the	DET
bibechana-9308	5	10	main	main	ADJ
bibechana-9308	5	11	results	result	NOUN
bibechana-9308	5	12	,	,	PUNCT
bibechana-9308	5	13	we	we	PRON
bibechana-9308	5	14	recall	recall	VERB
bibechana-9308	5	15	some	some	PRON
bibechana-9308	5	16	of	of	ADP
bibechana-9308	5	17	the	the	DET
bibechana-9308	5	18	basic	basic	ADJ
bibechana-9308	5	19	notations	notation	NOUN
bibechana-9308	5	20	and	and	CCONJ
bibechana-9308	5	21	definitions	definition	NOUN
bibechana-9308	5	22	that	that	PRON
bibechana-9308	5	23	are	be	AUX
bibechana-9308	5	24	used	use	VERB
bibechana-9308	5	25	in	in	ADP
bibechana-9308	5	26	this	this	DET
bibechana-9308	5	27	paper	paper	NOUN
bibechana-9308	5	28	.	.	PUNCT
bibechana-9308	6	1	the	the	DET
bibechana-9308	6	2	notion	notion	NOUN
bibechana-9308	6	3	of	of	ADP
bibechana-9308	6	4	2	2	NUM
bibechana-9308	6	5	–	–	PUNCT
bibechana-9308	6	6	normed	norme	VERB
bibechana-9308	6	7	space	space	NOUN
bibechana-9308	6	8	was	be	AUX
bibechana-9308	6	9	initially	initially	ADV
bibechana-9308	6	10	introduced	introduce	VERB
bibechana-9308	6	11	by	by	ADP
bibechana-9308	6	12	s.	s.	PROPN
bibechana-9308	6	13	gäahler	gäahler	PROPN
bibechana-9308	7	1	[	[	X
bibechana-9308	7	2	1	1	X
bibechana-9308	7	3	]	]	PUNCT
bibechana-9308	7	4	as	as	ADP
bibechana-9308	7	5	an	an	DET
bibechana-9308	7	6	interesting	interesting	ADJ
bibechana-9308	7	7	linear	linear	ADJ
bibechana-9308	7	8	generalization	generalization	NOUN
bibechana-9308	7	9	of	of	ADP
bibechana-9308	7	10	a	a	DET
bibechana-9308	7	11	normed	normed	ADJ
bibechana-9308	7	12	linear	linear	ADJ
bibechana-9308	7	13	space	space	NOUN
bibechana-9308	7	14	,	,	PUNCT
bibechana-9308	7	15	which	which	PRON
bibechana-9308	7	16	was	be	AUX
bibechana-9308	7	17	further	far	ADV
bibechana-9308	7	18	studied	study	VERB
bibechana-9308	7	19	by	by	ADP
bibechana-9308	7	20	j.a	j.a	PROPN
bibechana-9308	7	21	.	.	PROPN
bibechana-9308	7	22	white	white	PROPN
bibechana-9308	7	23	and	and	CCONJ
bibechana-9308	7	24	y.j	y.j	PROPN
bibechana-9308	7	25	.	.	PROPN
bibechana-9308	7	26	cho	cho	PROPN
bibechana-9308	8	1	[	[	X
bibechana-9308	8	2	2	2	NUM
bibechana-9308	8	3	]	]	PUNCT
bibechana-9308	8	4	,	,	PUNCT
bibechana-9308	8	5	k.iseki	k.iseki	PUNCT
bibechana-9308	8	6	[	[	X
bibechana-9308	8	7	3	3	NUM
bibechana-9308	8	8	]	]	PUNCT
bibechana-9308	8	9	,	,	PUNCT
bibechana-9308	8	10	r.	r.	PROPN
bibechana-9308	8	11	freese	freese	PROPN
bibechana-9308	8	12	et	et	PROPN
bibechana-9308	8	13	al	al	PROPN
bibechana-9308	8	14	.	.	PUNCT
bibechana-9308	9	1	[	[	X
bibechana-9308	9	2	4,5	4,5	NUM
bibechana-9308	9	3	]	]	PUNCT
bibechana-9308	9	4	,	,	PUNCT
bibechana-9308	9	5	w.raymond	w.raymond	NOUN
bibechana-9308	9	6	et	et	PROPN
bibechana-9308	9	7	al	al	PROPN
bibechana-9308	9	8	.	.	PUNCT
bibechana-9308	10	1	[	[	X
bibechana-9308	10	2	6	6	NUM
bibechana-9308	10	3	]	]	PUNCT
bibechana-9308	10	4	and	and	CCONJ
bibechana-9308	10	5	many	many	ADJ
bibechana-9308	10	6	others	other	NOUN
bibechana-9308	10	7	.	.	PUNCT
bibechana-9308	11	1	recently	recently	ADV
bibechana-9308	11	2	a	a	DET
bibechana-9308	11	3	lot	lot	NOUN
bibechana-9308	11	4	of	of	ADP
bibechana-9308	11	5	activities	activity	NOUN
bibechana-9308	11	6	have	have	AUX
bibechana-9308	11	7	been	be	AUX
bibechana-9308	11	8	started	start	VERB
bibechana-9308	11	9	by	by	ADP
bibechana-9308	11	10	many	many	ADJ
bibechana-9308	11	11	researchers	researcher	NOUN
bibechana-9308	11	12	to	to	PART
bibechana-9308	11	13	study	study	VERB
bibechana-9308	11	14	this	this	DET
bibechana-9308	11	15	concept	concept	NOUN
bibechana-9308	11	16	in	in	ADP
bibechana-9308	11	17	different	different	ADJ
bibechana-9308	11	18	directions	direction	NOUN
bibechana-9308	11	19	,	,	PUNCT
bibechana-9308	11	20	for	for	ADP
bibechana-9308	11	21	instances	instance	NOUN
bibechana-9308	11	22	e.	e.	PROPN
bibechana-9308	11	23	savas	savas	PROPN
bibechana-9308	12	1	[	[	X
bibechana-9308	12	2	7	7	NUM
bibechana-9308	12	3	]	]	PUNCT
bibechana-9308	12	4	,	,	PUNCT
bibechana-9308	12	5	h.	h.	PROPN
bibechana-9308	12	6	gunawan	gunawan	PROPN
bibechana-9308	12	7	and	and	CCONJ
bibechana-9308	12	8	h.	h.	PROPN
bibechana-9308	12	9	mashadi	mashadi	PROPN
bibechana-9308	12	10	[	[	X
bibechana-9308	12	11	8	8	NUM
bibechana-9308	12	12	]	]	PUNCT
bibechana-9308	12	13	,	,	PUNCT
bibechana-9308	12	14	j.k	j.k	PROPN
bibechana-9308	12	15	.	.	PROPN
bibechana-9308	12	16	srivastava	srivastava	PROPN
bibechana-9308	12	17	and	and	CCONJ
bibechana-9308	12	18	n.p	n.p	PROPN
bibechana-9308	12	19	.	.	PROPN
bibechana-9308	12	20	pahari	pahari	PROPN
bibechana-9308	13	1	[	[	X
bibechana-9308	13	2	9	9	NUM
bibechana-9308	13	3	]	]	PUNCT
bibechana-9308	13	4	,	,	PUNCT
bibechana-9308	13	5	m.	m.	NOUN
bibechana-9308	13	6	açikgöz	açikgöz	PROPN
bibechana-9308	14	1	[	[	X
bibechana-9308	14	2	10	10	NUM
bibechana-9308	14	3	]	]	PUNCT
bibechana-9308	14	4	and	and	CCONJ
bibechana-9308	14	5	others	other	NOUN
bibechana-9308	14	6	.	.	PUNCT
bibechana-9308	15	1	let	let	VERB
bibechana-9308	15	2	s	s	PRON
bibechana-9308	15	3	be	be	AUX
bibechana-9308	15	4	a	a	DET
bibechana-9308	15	5	vector	vector	NOUN
bibechana-9308	15	6	space	space	NOUN
bibechana-9308	15	7	of	of	ADP
bibechana-9308	15	8	dimension	dimension	NOUN
bibechana-9308	16	1	d	d	PROPN
bibechana-9308	16	2	>	>	X
bibechana-9308	16	3	1	1	NUM
bibechana-9308	16	4	over	over	ADP
bibechana-9308	16	5	k	k	PROPN
bibechana-9308	16	6	,	,	PUNCT
bibechana-9308	16	7	the	the	DET
bibechana-9308	16	8	field	field	NOUN
bibechana-9308	16	9	of	of	ADP
bibechana-9308	16	10	real	real	ADJ
bibechana-9308	16	11	or	or	CCONJ
bibechana-9308	16	12	complex	complex	ADJ
bibechana-9308	16	13	numbers	number	NOUN
bibechana-9308	16	14	.	.	PUNCT
bibechana-9308	17	1	a	a	DET
bibechana-9308	17	2	2	2	NUM
bibechana-9308	17	3	norm	norm	NOUN
bibechana-9308	17	4	on	on	ADP
bibechana-9308	17	5	s	s	PROPN
bibechana-9308	17	6	is	be	AUX
bibechana-9308	17	7	a	a	DET
bibechana-9308	17	8	real	real	ADV
bibechana-9308	17	9	valued	value	VERB
bibechana-9308	17	10	function	function	NOUN
bibechana-9308	17	11	||	||	PROPN
bibechana-9308	17	12	.	.	PUNCT
bibechana-9308	18	1	,	,	PUNCT
bibechana-9308	18	2	.||	.||	VERB
bibechana-9308	18	3	on	on	ADP
bibechana-9308	18	4	s	s	PRON
bibechana-9308	18	5	×	×	NOUN
bibechana-9308	18	6	s	s	X
bibechana-9308	18	7	satisfying	satisfy	VERB
bibechana-9308	18	8	the	the	DET
bibechana-9308	18	9	following	following	ADJ
bibechana-9308	18	10	conditions	condition	NOUN
bibechana-9308	18	11	:	:	PUNCT
bibechana-9308	18	12	2n1	2n1	NUM
bibechana-9308	18	13	:	:	PUNCT
bibechana-9308	18	14	||	||	X
bibechana-9308	19	1	ξ	ξ	PROPN
bibechana-9308	19	2	,	,	PUNCT
bibechana-9308	19	3	η	η	PROPN
bibechana-9308	19	4	||	||	PROPN
bibechana-9308	19	5	≥	≥	NUM
bibechana-9308	19	6	0	0	NUM
bibechana-9308	19	7	and	and	CCONJ
bibechana-9308	19	8	||	||	NUM
bibechana-9308	19	9	ξ	ξ	PROPN
bibechana-9308	19	10	,	,	PUNCT
bibechana-9308	19	11	η	η	PROPN
bibechana-9308	19	12	||	||	PROPN
bibechana-9308	20	1	=	=	SYM
bibechana-9308	20	2	0	0	PUNCT
bibechana-9308	21	1	if	if	SCONJ
bibechana-9308	21	2	and	and	CCONJ
bibechana-9308	21	3	only	only	ADV
bibechana-9308	21	4	if	if	SCONJ
bibechana-9308	21	5	ξ	ξ	PROPN
bibechana-9308	21	6	and	and	CCONJ
bibechana-9308	21	7	η	η	PROPN
bibechana-9308	21	8	are	be	AUX
bibechana-9308	21	9	linearly	linearly	ADV
bibechana-9308	21	10	dependent	dependent	ADJ
bibechana-9308	21	11	;	;	PUNCT
bibechana-9308	21	12	2	2	NUM
bibechana-9308	21	13	-	-	PUNCT
bibechana-9308	21	14	n2	n2	NOUN
bibechana-9308	21	15	:	:	PUNCT
bibechana-9308	21	16	||	||	X
bibechana-9308	22	1	ξ	ξ	PROPN
bibechana-9308	22	2	,	,	PUNCT
bibechana-9308	22	3	η	η	PROPN
bibechana-9308	22	4	||	||	PROPN
bibechana-9308	22	5	=	=	SYM
bibechana-9308	22	6	||	||	PROPN
bibechana-9308	23	1	η	η	PROPN
bibechana-9308	23	2	,	,	PUNCT
bibechana-9308	23	3	ξ	ξ	PROPN
bibechana-9308	23	4	||	||	PROPN
bibechana-9308	23	5	,	,	PUNCT
bibechana-9308	23	6	for	for	ADP
bibechana-9308	23	7	all	all	DET
bibechana-9308	23	8	ξ	ξ	PROPN
bibechana-9308	23	9	,	,	PUNCT
bibechana-9308	23	10	η	η	PROPN
bibechana-9308	23	11	∈	∈	PROPN
bibechana-9308	23	12	s	s	PART
bibechana-9308	23	13	;	;	PUNCT
bibechana-9308	23	14	2	2	NUM
bibechana-9308	23	15	-	-	PUNCT
bibechana-9308	23	16	n3	n3	NOUN
bibechana-9308	23	17	:	:	PUNCT
bibechana-9308	23	18	||	||	NOUN
bibechana-9308	23	19	γξ	γξ	ADP
bibechana-9308	23	20	,	,	PUNCT
bibechana-9308	23	21	η	η	PROPN
bibechana-9308	23	22	||	||	PROPN
bibechana-9308	24	1	=	=	PRON
bibechana-9308	24	2	|γ	|γ	ADP
bibechana-9308	24	3	|	|	ADV
bibechana-9308	24	4	||ξ¸	||ξ¸	PUNCT
bibechana-9308	24	5	η	η	PROPN
bibechana-9308	24	6	||	||	PROPN
bibechana-9308	24	7	,	,	PUNCT
bibechana-9308	24	8	where	where	SCONJ
bibechana-9308	24	9	γ∈k	γ∈k	PROPN
bibechana-9308	24	10	and	and	CCONJ
bibechana-9308	24	11	ξ	ξ	PROPN
bibechana-9308	24	12	,	,	PUNCT
bibechana-9308	24	13	η	η	PROPN
bibechana-9308	24	14	∈	∈	PROPN
bibechana-9308	24	15	s;and	s;and	PROPN
bibechana-9308	24	16	2	2	PROPN
bibechana-9308	24	17	-	-	PUNCT
bibechana-9308	24	18	n4	n4	PROPN
bibechana-9308	24	19	:	:	PUNCT
bibechana-9308	24	20	||	||	NUM
bibechana-9308	25	1	ξ1	ξ1	PROPN
bibechana-9308	25	2	+	+	CCONJ
bibechana-9308	25	3	ξ2	ξ2	ADJ
bibechana-9308	25	4	,	,	PUNCT
bibechana-9308	25	5	η	η	PROPN
bibechana-9308	25	6	||	||	PROPN
bibechana-9308	25	7	≤	≤	NUM
bibechana-9308	25	8	||	||	PUNCT
bibechana-9308	25	9	ξ1	ξ1	NOUN
bibechana-9308	25	10	,	,	PUNCT
bibechana-9308	25	11	η	η	PROPN
bibechana-9308	25	12	||	||	PROPN
bibechana-9308	26	1	+	+	CCONJ
bibechana-9308	26	2	||	||	NUM
bibechana-9308	26	3	ξ2	ξ2	NOUN
bibechana-9308	26	4	,	,	PUNCT
bibechana-9308	26	5	η	η	PROPN
bibechana-9308	26	6	||	||	PROPN
bibechana-9308	26	7	,	,	PUNCT
bibechana-9308	26	8	for	for	ADP
bibechana-9308	26	9	all	all	DET
bibechana-9308	26	10	ξ1	ξ1	NOUN
bibechana-9308	26	11	,	,	PUNCT
bibechana-9308	26	12	ξ2	ξ2	NOUN
bibechana-9308	26	13	and	and	CCONJ
bibechana-9308	26	14	η∈	η∈	PROPN
bibechana-9308	26	15	s.	s.	PROPN
bibechana-9308	26	16	the	the	DET
bibechana-9308	26	17	pair	pair	NOUN
bibechana-9308	26	18	(	(	PUNCT
bibechana-9308	26	19	x	x	X
bibechana-9308	26	20	,	,	PUNCT
bibechana-9308	26	21	||	||	PROPN
bibechana-9308	26	22	.	.	PUNCT
bibechana-9308	26	23	,	,	PUNCT
bibechana-9308	27	1	.||	.||	PROPN
bibechana-9308	27	2	)	)	PUNCT
bibechana-9308	27	3	is	be	AUX
bibechana-9308	27	4	called	call	VERB
bibechana-9308	27	5	a	a	DET
bibechana-9308	27	6	2	2	NUM
bibechana-9308	27	7	–	–	PUNCT
bibechana-9308	27	8	normed	normed	ADJ
bibechana-9308	27	9	space	space	NOUN
bibechana-9308	27	10	.	.	PUNCT
bibechana-9308	28	1	thus	thus	ADV
bibechana-9308	28	2	the	the	DET
bibechana-9308	28	3	notion	notion	NOUN
bibechana-9308	28	4	of	of	ADP
bibechana-9308	28	5	2	2	NUM
bibechana-9308	28	6	–	–	PUNCT
bibechana-9308	28	7	normed	norme	VERB
bibechana-9308	28	8	space	space	NOUN
bibechana-9308	28	9	is	be	AUX
bibechana-9308	28	10	just	just	ADV
bibechana-9308	28	11	a	a	DET
bibechana-9308	28	12	two	two	NUM
bibechana-9308	28	13	dimensional	dimensional	ADJ
bibechana-9308	28	14	analogue	analogue	NOUN
bibechana-9308	28	15	of	of	ADP
bibechana-9308	28	16	a	a	DET
bibechana-9308	28	17	normed	normed	ADJ
bibechana-9308	28	18	space	space	NOUN
bibechana-9308	28	19	.	.	PUNCT
bibechana-9308	29	1	recall	recall	VERB
bibechana-9308	29	2	that	that	PRON
bibechana-9308	29	3	(	(	PUNCT
bibechana-9308	29	4	x	x	X
bibechana-9308	29	5	,	,	PUNCT
bibechana-9308	29	6	||	||	PROPN
bibechana-9308	29	7	.	.	PUNCT
bibechana-9308	29	8	,	,	PUNCT
bibechana-9308	29	9	.||	.||	PROPN
bibechana-9308	29	10	)	)	PUNCT
bibechana-9308	29	11	is	be	AUX
bibechana-9308	29	12	a	a	DET
bibechana-9308	29	13	2	2	NUM
bibechana-9308	29	14	-	-	PUNCT
bibechana-9308	29	15	banach	banach	NOUN
bibechana-9308	29	16	space	space	NOUN
bibechana-9308	29	17	if	if	SCONJ
bibechana-9308	29	18	every	every	DET
bibechana-9308	29	19	cauchy	cauchy	ADJ
bibechana-9308	29	20	sequence	sequence	NOUN
bibechana-9308	29	21	in	in	ADP
bibechana-9308	29	22	x	x	PROPN
bibechana-9308	29	23	is	be	AUX
bibechana-9308	29	24	convergent	convergent	ADJ
bibechana-9308	29	25	to	to	ADP
bibechana-9308	29	26	some	some	DET
bibechana-9308	29	27	x0	x0	PROPN
bibechana-9308	29	28	in	in	ADP
bibechana-9308	29	29	x.	x.	PROPN
bibechana-9308	29	30	n.p	n.p	PROPN
bibechana-9308	29	31	.	.	PROPN
bibechana-9308	29	32	pahari	pahari	PROPN
bibechana-9308	29	33	/	/	SYM
bibechana-9308	29	34	bibechana	bibechana	NOUN
bibechana-9308	29	35	10	10	NUM
bibechana-9308	29	36	(	(	PUNCT
bibechana-9308	29	37	2014	2014	NUM
bibechana-9308	29	38	)	)	PUNCT
bibechana-9308	29	39	20	20	NUM
bibechana-9308	29	40	-	-	SYM
bibechana-9308	29	41	30	30	NUM
bibechana-9308	29	42	:	:	PUNCT
bibechana-9308	29	43	bmhss	bmhss	PROPN
bibechana-9308	29	44	,	,	PUNCT
bibechana-9308	29	45	p.21	p.21	NOUN
bibechana-9308	29	46	(	(	PUNCT
bibechana-9308	29	47	online	online	ADJ
bibechana-9308	29	48	publication	publication	NOUN
bibechana-9308	29	49	:	:	PUNCT
bibechana-9308	29	50	dec	dec	PROPN
bibechana-9308	29	51	.	.	PROPN
bibechana-9308	29	52	,	,	PUNCT
bibechana-9308	29	53	2013	2013	NUM
bibechana-9308	29	54	)	)	PUNCT
bibechana-9308	29	55	the	the	DET
bibechana-9308	29	56	pair	pair	NOUN
bibechana-9308	29	57	(	(	PUNCT
bibechana-9308	29	58	s	s	NOUN
bibechana-9308	29	59	,	,	PUNCT
bibechana-9308	29	60	||	||	PROPN
bibechana-9308	29	61	.	.	PUNCT
bibechana-9308	29	62	,	,	PUNCT
bibechana-9308	29	63	.||	.||	PROPN
bibechana-9308	29	64	)	)	PUNCT
bibechana-9308	29	65	is	be	AUX
bibechana-9308	29	66	called	call	VERB
bibechana-9308	29	67	a	a	DET
bibechana-9308	29	68	2	2	NUM
bibechana-9308	29	69	–	–	PUNCT
bibechana-9308	29	70	normed	normed	ADJ
bibechana-9308	29	71	space	space	NOUN
bibechana-9308	29	72	.	.	PUNCT
bibechana-9308	30	1	thus	thus	ADV
bibechana-9308	30	2	the	the	DET
bibechana-9308	30	3	notion	notion	NOUN
bibechana-9308	30	4	of	of	ADP
bibechana-9308	30	5	2	2	NUM
bibechana-9308	30	6	–	–	PUNCT
bibechana-9308	30	7	normed	norme	VERB
bibechana-9308	30	8	space	space	NOUN
bibechana-9308	30	9	is	be	AUX
bibechana-9308	30	10	just	just	ADV
bibechana-9308	30	11	a	a	DET
bibechana-9308	30	12	two	two	NUM
bibechana-9308	30	13	dimensional	dimensional	ADJ
bibechana-9308	30	14	analogue	analogue	NOUN
bibechana-9308	30	15	of	of	ADP
bibechana-9308	30	16	a	a	DET
bibechana-9308	30	17	normed	normed	ADJ
bibechana-9308	30	18	space	space	NOUN
bibechana-9308	30	19	.	.	PUNCT
bibechana-9308	31	1	recall	recall	VERB
bibechana-9308	31	2	that	that	PRON
bibechana-9308	31	3	(	(	PUNCT
bibechana-9308	31	4	s	s	NOUN
bibechana-9308	31	5	,	,	PUNCT
bibechana-9308	31	6	||	||	PROPN
bibechana-9308	31	7	.	.	PUNCT
bibechana-9308	31	8	,	,	PUNCT
bibechana-9308	31	9	.||	.||	PROPN
bibechana-9308	31	10	)	)	PUNCT
bibechana-9308	31	11	is	be	AUX
bibechana-9308	31	12	a	a	DET
bibechana-9308	31	13	2	2	NUM
bibechana-9308	31	14	-	-	PUNCT
bibechana-9308	31	15	banach	banach	NOUN
bibechana-9308	31	16	space	space	NOUN
bibechana-9308	31	17	if	if	SCONJ
bibechana-9308	31	18	every	every	DET
bibechana-9308	31	19	cauchy	cauchy	ADJ
bibechana-9308	31	20	sequence	sequence	NOUN
bibechana-9308	31	21	in	in	ADP
bibechana-9308	31	22	s	s	PROPN
bibechana-9308	31	23	is	be	AUX
bibechana-9308	31	24	convergent	convergent	ADJ
bibechana-9308	31	25	to	to	ADP
bibechana-9308	31	26	some	some	DET
bibechana-9308	31	27	ξ0	ξ0	NOUN
bibechana-9308	31	28	in	in	ADP
bibechana-9308	31	29	s.	s.	PROPN
bibechana-9308	31	30	geometrically	geometrically	PROPN
bibechana-9308	31	31	,	,	PUNCT
bibechana-9308	31	32	a	a	DET
bibechana-9308	31	33	2	2	NUM
bibechana-9308	31	34	-	-	PUNCT
bibechana-9308	31	35	norm	norm	NOUN
bibechana-9308	31	36	function	function	NOUN
bibechana-9308	31	37	generalizes	generalize	VERB
bibechana-9308	31	38	the	the	DET
bibechana-9308	31	39	concept	concept	NOUN
bibechana-9308	31	40	of	of	ADP
bibechana-9308	31	41	area	area	NOUN
bibechana-9308	31	42	function	function	NOUN
bibechana-9308	31	43	of	of	ADP
bibechana-9308	31	44	parallelogram	parallelogram	NOUN
bibechana-9308	31	45	due	due	ADP
bibechana-9308	31	46	to	to	ADP
bibechana-9308	31	47	the	the	DET
bibechana-9308	31	48	fact	fact	NOUN
bibechana-9308	31	49	that	that	SCONJ
bibechana-9308	31	50	,	,	PUNCT
bibechana-9308	31	51	in	in	ADP
bibechana-9308	31	52	the	the	DET
bibechana-9308	31	53	standard	standard	ADJ
bibechana-9308	31	54	case	case	NOUN
bibechana-9308	31	55	,	,	PUNCT
bibechana-9308	31	56	it	it	PRON
bibechana-9308	31	57	represents	represent	VERB
bibechana-9308	31	58	the	the	DET
bibechana-9308	31	59	area	area	NOUN
bibechana-9308	31	60	of	of	ADP
bibechana-9308	31	61	the	the	DET
bibechana-9308	31	62	usual	usual	ADJ
bibechana-9308	31	63	parallelogram	parallelogram	NOUN
bibechana-9308	31	64	spanned	span	VERB
bibechana-9308	31	65	by	by	ADP
bibechana-9308	31	66	the	the	DET
bibechana-9308	31	67	two	two	NUM
bibechana-9308	31	68	associated	associate	VERB
bibechana-9308	31	69	vectors.for	vectors.for	ADP
bibechana-9308	31	70	example	example	NOUN
bibechana-9308	31	71	,	,	PUNCT
bibechana-9308	31	72	consider	consider	VERB
bibechana-9308	31	73	s	s	NOUN
bibechana-9308	31	74	=	=	NOUN
bibechana-9308	31	75	r2	r2	PROPN
bibechana-9308	31	76	,	,	PUNCT
bibechana-9308	31	77	being	be	AUX
bibechana-9308	31	78	equipped	equip	VERB
bibechana-9308	31	79	with	with	ADP
bibechana-9308	31	80	||	||	PROPN
bibechana-9308	31	81	ξ	ξ	PROPN
bibechana-9308	31	82	,	,	PUNCT
bibechana-9308	31	83	η	η	PROPN
bibechana-9308	31	84	||	||	PROPN
bibechana-9308	32	1	=	=	PUNCT
bibechana-9308	33	1	|	|	CCONJ
bibechana-9308	33	2	ξ1η2	ξ1η2	ADP
bibechana-9308	33	3	–	–	PUNCT
bibechana-9308	33	4	ξ2η1|	ξ2η1|	PROPN
bibechana-9308	33	5	,	,	PUNCT
bibechana-9308	33	6	where	where	SCONJ
bibechana-9308	33	7	ξ	ξ	X
bibechana-9308	33	8	=	=	SYM
bibechana-9308	33	9	(	(	PUNCT
bibechana-9308	33	10	ξ1	ξ1	PROPN
bibechana-9308	33	11	,	,	PUNCT
bibechana-9308	33	12	ξ2	ξ2	NOUN
bibechana-9308	33	13	)	)	PUNCT
bibechana-9308	33	14	and	and	CCONJ
bibechana-9308	33	15	η	η	PROPN
bibechana-9308	33	16	=	=	SYM
bibechana-9308	33	17	(	(	PUNCT
bibechana-9308	33	18	η1	η1	NOUN
bibechana-9308	33	19	,	,	PUNCT
bibechana-9308	33	20	η2	η2	PROPN
bibechana-9308	33	21	)	)	PUNCT
bibechana-9308	33	22	.	.	PUNCT
bibechana-9308	34	1	then	then	ADV
bibechana-9308	34	2	(	(	PUNCT
bibechana-9308	34	3	s	s	X
bibechana-9308	34	4	,	,	PUNCT
bibechana-9308	34	5	||	||	PROPN
bibechana-9308	34	6	.	.	PUNCT
bibechana-9308	34	7	,	,	PUNCT
bibechana-9308	34	8	.||	.||	PROPN
bibechana-9308	34	9	)	)	PUNCT
bibechana-9308	34	10	forms	form	VERB
bibechana-9308	34	11	a	a	DET
bibechana-9308	34	12	2	2	NUM
bibechana-9308	34	13	–	–	PUNCT
bibechana-9308	34	14	normed	normed	ADJ
bibechana-9308	34	15	space	space	NOUN
bibechana-9308	34	16	and	and	CCONJ
bibechana-9308	34	17	||	||	NUM
bibechana-9308	34	18	ξ	ξ	PROPN
bibechana-9308	34	19	,	,	PUNCT
bibechana-9308	34	20	η	η	PROPN
bibechana-9308	34	21	||	||	PROPN
bibechana-9308	34	22	represents	represent	VERB
bibechana-9308	34	23	the	the	DET
bibechana-9308	34	24	area	area	NOUN
bibechana-9308	34	25	of	of	ADP
bibechana-9308	34	26	the	the	DET
bibechana-9308	34	27	parallelogram	parallelogram	NOUN
bibechana-9308	34	28	spanned	span	VERB
bibechana-9308	34	29	by	by	ADP
bibechana-9308	34	30	the	the	DET
bibechana-9308	34	31	two	two	NUM
bibechana-9308	34	32	associated	associated	ADJ
bibechana-9308	34	33	vectors	vector	NOUN
bibechana-9308	34	34	ξ	ξ	PROPN
bibechana-9308	34	35	and	and	CCONJ
bibechana-9308	34	36	η	η	PROPN
bibechana-9308	34	37	.	.	PROPN
bibechana-9308	34	38	again	again	ADV
bibechana-9308	34	39	,	,	PUNCT
bibechana-9308	34	40	let	let	VERB
bibechana-9308	34	41	s	s	PRON
bibechana-9308	34	42	=	=	NOUN
bibechana-9308	34	43	r	r	NOUN
bibechana-9308	34	44	3	3	NUM
bibechana-9308	34	45	and	and	CCONJ
bibechana-9308	34	46	define	define	VERB
bibechana-9308	34	47	the	the	DET
bibechana-9308	34	48	function	function	NOUN
bibechana-9308	34	49	||	||	PROPN
bibechana-9308	34	50	.	.	PUNCT
bibechana-9308	35	1	,	,	PUNCT
bibechana-9308	35	2	.||	.||	VERB
bibechana-9308	35	3	on	on	ADP
bibechana-9308	35	4	s	s	PRON
bibechana-9308	35	5	×	×	NOUN
bibechana-9308	35	6	s	s	VERB
bibechana-9308	35	7	by	by	ADP
bibechana-9308	35	8	||	||	PROPN
bibechana-9308	35	9	ξ	ξ	PROPN
bibechana-9308	35	10	,	,	PUNCT
bibechana-9308	35	11	η	η	PROPN
bibechana-9308	35	12	||	||	PROPN
bibechana-9308	35	13	=	=	PUNCT
bibechana-9308	35	14			PROPN
bibechana-9308	35	15			PROPN
bibechana-9308	35	16			PROPN
bibechana-9308	35	17			PROPN
bibechana-9308	35	18			PROPN
bibechana-9308	35	19			PROPN
bibechana-9308	35	20	det	det	PROPN
bibechana-9308	35	21			PROPN
bibechana-9308	35	22			NOUN
bibechana-9308	35	23			NOUN
bibechana-9308	35	24			PUNCT
bibechana-9308	35	25			VERB
bibechana-9308	36	1	i	i	PROPN
bibechana-9308	36	2	j	j	PROPN
bibechana-9308	37	1	k	k	PROPN
bibechana-9308	37	2	ξ1	ξ1	PROPN
bibechana-9308	37	3	ξ2	ξ2	PROPN
bibechana-9308	37	4	ξ3	ξ3	PROPN
bibechana-9308	37	5	η1	η1	NOUN
bibechana-9308	37	6	η2	η2	VERB
bibechana-9308	37	7	η3	η3	NOUN
bibechana-9308	37	8	where	where	SCONJ
bibechana-9308	37	9	ξ	ξ	PROPN
bibechana-9308	37	10	=	=	SYM
bibechana-9308	37	11	(	(	PUNCT
bibechana-9308	37	12	ξ1	ξ1	PROPN
bibechana-9308	37	13	,	,	PUNCT
bibechana-9308	37	14	ξ2	ξ2	ADJ
bibechana-9308	37	15	,	,	PUNCT
bibechana-9308	37	16	ξ3	ξ3	NOUN
bibechana-9308	37	17	)	)	PUNCT
bibechana-9308	37	18	and	and	CCONJ
bibechana-9308	37	19	y	y	PROPN
bibechana-9308	37	20	=	=	SYM
bibechana-9308	37	21	(	(	PUNCT
bibechana-9308	37	22	η1	η1	NOUN
bibechana-9308	37	23	,	,	PUNCT
bibechana-9308	37	24	η2	η2	NOUN
bibechana-9308	37	25	,	,	PUNCT
bibechana-9308	37	26	η3	η3	NOUN
bibechana-9308	37	27	)	)	PUNCT
bibechana-9308	37	28	.	.	PUNCT
bibechana-9308	38	1	obviously	obviously	ADV
bibechana-9308	38	2	(	(	PUNCT
bibechana-9308	38	3	s	s	X
bibechana-9308	38	4	,	,	PUNCT
bibechana-9308	38	5	||	||	PROPN
bibechana-9308	38	6	.	.	PUNCT
bibechana-9308	38	7	,	,	PUNCT
bibechana-9308	38	8	.||	.||	PROPN
bibechana-9308	38	9	)	)	PUNCT
bibechana-9308	38	10	forms	form	VERB
bibechana-9308	38	11	a	a	DET
bibechana-9308	38	12	2	2	NUM
bibechana-9308	38	13	–	–	PUNCT
bibechana-9308	38	14	normed	normed	ADJ
bibechana-9308	38	15	space	space	NOUN
bibechana-9308	38	16	.	.	PUNCT
bibechana-9308	39	1	analogously	analogously	ADV
bibechana-9308	39	2	,	,	PUNCT
bibechana-9308	39	3	if	if	SCONJ
bibechana-9308	39	4	(	(	PUNCT
bibechana-9308	39	5	s	s	NOUN
bibechana-9308	39	6	,	,	PUNCT
bibechana-9308	39	7	<	<	X
bibechana-9308	39	8	.	.	PUNCT
bibechana-9308	39	9	,	,	PUNCT
bibechana-9308	39	10	.	.	PUNCT
bibechana-9308	39	11	>	>	PUNCT
bibechana-9308	39	12	)	)	PUNCT
bibechana-9308	39	13	be	be	AUX
bibechana-9308	39	14	a	a	DET
bibechana-9308	39	15	finite	finite	ADJ
bibechana-9308	39	16	dimensional	dimensional	ADJ
bibechana-9308	39	17	inner	inner	ADJ
bibechana-9308	39	18	product	product	NOUN
bibechana-9308	39	19	space	space	NOUN
bibechana-9308	39	20	and	and	CCONJ
bibechana-9308	39	21	||	||	NOUN
bibechana-9308	39	22	.	.	PUNCT
bibechana-9308	40	1	,	,	PUNCT
bibechana-9308	40	2	.||	.||	PROPN
bibechana-9308	40	3	defined	define	VERB
bibechana-9308	40	4	on	on	ADP
bibechana-9308	40	5	s	s	PRON
bibechana-9308	40	6	×	×	NOUN
bibechana-9308	40	7	s	s	VERB
bibechana-9308	40	8	by	by	ADP
bibechana-9308	40	9	||	||	PROPN
bibechana-9308	40	10	ξ	ξ	PROPN
bibechana-9308	40	11	,	,	PUNCT
bibechana-9308	40	12	η	η	PROPN
bibechana-9308	40	13	||	||	PROPN
bibechana-9308	40	14	=	=	PUNCT
bibechana-9308	40	15			PROPN
bibechana-9308	40	16			PROPN
bibechana-9308	40	17			PROPN
bibechana-9308	40	18			PROPN
bibechana-9308	40	19			PROPN
bibechana-9308	40	20	<ξ‚ξ	<ξ‚ξ	ADP
bibechana-9308	40	21	>	>	X
bibechana-9308	40	22	<	<	X
bibechana-9308	40	23	ξ	ξ	X
bibechana-9308	40	24	‚	‚	X
bibechana-9308	40	25	η	η	X
bibechana-9308	40	26	>	>	X
bibechana-9308	40	27	<	<	X
bibechana-9308	40	28	η	η	X
bibechana-9308	40	29	‚	‚	X
bibechana-9308	40	30	ξ	ξ	X
bibechana-9308	40	31	>	>	X
bibechana-9308	40	32	<	<	X
bibechana-9308	40	33	η	η	X
bibechana-9308	40	34	‚	‚	PROPN
bibechana-9308	40	35	η	η	PROPN
bibechana-9308	40	36	>	>	X
bibechana-9308	40	37	,	,	PUNCT
bibechana-9308	40	38	then	then	ADV
bibechana-9308	40	39	we	we	PRON
bibechana-9308	40	40	can	can	AUX
bibechana-9308	40	41	see	see	VERB
bibechana-9308	40	42	that	that	PRON
bibechana-9308	40	43	(	(	PUNCT
bibechana-9308	40	44	s	s	NOUN
bibechana-9308	40	45	,	,	PUNCT
bibechana-9308	40	46	||	||	PROPN
bibechana-9308	40	47	.	.	PUNCT
bibechana-9308	40	48	,	,	PUNCT
bibechana-9308	40	49	.||	.||	PROPN
bibechana-9308	40	50	)	)	PUNCT
bibechana-9308	40	51	satisfies	satisfy	VERB
bibechana-9308	40	52	all	all	DET
bibechana-9308	40	53	the	the	DET
bibechana-9308	40	54	conditions	condition	NOUN
bibechana-9308	40	55	of	of	ADP
bibechana-9308	40	56	2	2	NUM
bibechana-9308	40	57	–	–	PUNCT
bibechana-9308	40	58	normed	normed	ADJ
bibechana-9308	40	59	space	space	NOUN
bibechana-9308	40	60	.	.	PUNCT
bibechana-9308	41	1	the	the	DET
bibechana-9308	41	2	notion	notion	NOUN
bibechana-9308	41	3	of	of	ADP
bibechana-9308	41	4	convergence	convergence	NOUN
bibechana-9308	41	5	has	have	AUX
bibechana-9308	41	6	introduced	introduce	VERB
bibechana-9308	41	7	by	by	ADP
bibechana-9308	41	8	white	white	ADJ
bibechana-9308	41	9	and	and	CCONJ
bibechana-9308	41	10	cho	cho	VERB
bibechana-9308	42	1	[	[	X
bibechana-9308	42	2	2	2	NUM
bibechana-9308	42	3	]	]	PUNCT
bibechana-9308	42	4	.	.	PUNCT
bibechana-9308	43	1	a	a	DET
bibechana-9308	43	2	sequence	sequence	NOUN
bibechana-9308	43	3	(	(	PUNCT
bibechana-9308	43	4	ξn	ξn	NOUN
bibechana-9308	43	5	)	)	PUNCT
bibechana-9308	43	6	in	in	ADP
bibechana-9308	43	7	a	a	DET
bibechana-9308	43	8	linear	linear	ADJ
bibechana-9308	43	9	2	2	NUM
bibechana-9308	43	10	–	–	PUNCT
bibechana-9308	43	11	normed	norme	VERB
bibechana-9308	43	12	space	space	NOUN
bibechana-9308	43	13	s	s	PART
bibechana-9308	43	14	is	be	AUX
bibechana-9308	43	15	convergent	convergent	ADJ
bibechana-9308	43	16	if	if	SCONJ
bibechana-9308	43	17	there	there	PRON
bibechana-9308	43	18	is	be	VERB
bibechana-9308	43	19	an	an	DET
bibechana-9308	43	20	ξ	ξ	PROPN
bibechana-9308	43	21	∈	∈	NOUN
bibechana-9308	43	22	s	s	VERB
bibechana-9308	43	23	such	such	ADJ
bibechana-9308	43	24	that	that	SCONJ
bibechana-9308	43	25	lim	lim	PROPN
bibechana-9308	43	26	n→∞	n→∞	PROPN
bibechana-9308	43	27	||	||	PROPN
bibechana-9308	43	28	ξn	ξn	PROPN
bibechana-9308	43	29	–	–	PUNCT
bibechana-9308	43	30	ξ	ξ	PROPN
bibechana-9308	43	31	,	,	PUNCT
bibechana-9308	43	32	η	η	PROPN
bibechana-9308	43	33	||	||	PROPN
bibechana-9308	44	1	=	=	SYM
bibechana-9308	44	2	0	0	NUM
bibechana-9308	44	3	,	,	PUNCT
bibechana-9308	44	4	for	for	ADP
bibechana-9308	44	5	each	each	DET
bibechana-9308	44	6	η	η	PROPN
bibechana-9308	44	7	∈	∈	PROPN
bibechana-9308	44	8	s	s	PART
bibechana-9308	44	9	.it	.it	PUNCT
bibechana-9308	44	10	is	be	AUX
bibechana-9308	44	11	said	say	VERB
bibechana-9308	44	12	to	to	PART
bibechana-9308	44	13	be	be	AUX
bibechana-9308	44	14	a	a	DET
bibechana-9308	44	15	cauchy	cauchy	NOUN
bibechana-9308	44	16	if	if	SCONJ
bibechana-9308	44	17	there	there	PRON
bibechana-9308	44	18	are	be	VERB
bibechana-9308	44	19	η	η	PROPN
bibechana-9308	44	20	and	and	CCONJ
bibechana-9308	44	21	ν	ν	NOUN
bibechana-9308	44	22	in	in	ADP
bibechana-9308	44	23	s	s	PRON
bibechana-9308	44	24	such	such	ADJ
bibechana-9308	44	25	that	that	SCONJ
bibechana-9308	44	26	η	η	PROPN
bibechana-9308	44	27	and	and	CCONJ
bibechana-9308	44	28	ν	ν	NOUN
bibechana-9308	44	29	are	be	AUX
bibechana-9308	44	30	linearly	linearly	ADV
bibechana-9308	44	31	independent	independent	ADJ
bibechana-9308	44	32	and	and	CCONJ
bibechana-9308	44	33	lim	lim	PROPN
bibechana-9308	44	34	m‚n→∞	m‚n→∞	ADJ
bibechana-9308	44	35	||ξm	||ξm	NOUN
bibechana-9308	44	36	–	–	PUNCT
bibechana-9308	44	37	ξn	ξn	VERB
bibechana-9308	44	38	‚	‚	NUM
bibechana-9308	44	39	η||	η||	NOUN
bibechana-9308	44	40	=	=	SYM
bibechana-9308	44	41	0	0	NUM
bibechana-9308	44	42	and	and	CCONJ
bibechana-9308	44	43	lim	lim	PROPN
bibechana-9308	44	44	m‚n→∞	m‚n→∞	ADJ
bibechana-9308	44	45	||ξm	||ξm	NOUN
bibechana-9308	44	46	–	–	PUNCT
bibechana-9308	44	47	ξn	ξn	VERB
bibechana-9308	44	48	‚	‚	NUM
bibechana-9308	44	49	ν||	ν||	NOUN
bibechana-9308	44	50	=	=	SYM
bibechana-9308	44	51	0	0	NUM
bibechana-9308	44	52	.	.	PUNCT
bibechana-9308	45	1	a	a	DET
bibechana-9308	45	2	linear	linear	ADJ
bibechana-9308	45	3	2	2	NUM
bibechana-9308	45	4	–	–	PUNCT
bibechana-9308	45	5	normed	normed	ADJ
bibechana-9308	45	6	space	space	NOUN
bibechana-9308	45	7	(	(	PUNCT
bibechana-9308	45	8	s	s	X
bibechana-9308	45	9	,	,	PUNCT
bibechana-9308	45	10	||.,.||	||.,.||	PRON
bibechana-9308	45	11	)	)	PUNCT
bibechana-9308	45	12	is	be	AUX
bibechana-9308	45	13	called	call	VERB
bibechana-9308	45	14	2	2	NUM
bibechana-9308	45	15	–	–	PUNCT
bibechana-9308	45	16	banach	banach	NOUN
bibechana-9308	45	17	space	space	NOUN
bibechana-9308	45	18	if	if	SCONJ
bibechana-9308	45	19	every	every	DET
bibechana-9308	45	20	cauchy	cauchy	ADJ
bibechana-9308	45	21	sequence	sequence	NOUN
bibechana-9308	45	22	in	in	ADP
bibechana-9308	45	23	s	s	PROPN
bibechana-9308	45	24	is	be	AUX
bibechana-9308	45	25	convergent	convergent	ADJ
bibechana-9308	45	26	to	to	ADP
bibechana-9308	45	27	some	some	DET
bibechana-9308	45	28	ξ	ξ	PROPN
bibechana-9308	45	29	∈	∈	PROPN
bibechana-9308	45	30	s.	s.	PROPN
bibechana-9308	45	31	the	the	DET
bibechana-9308	45	32	notion	notion	NOUN
bibechana-9308	45	33	of	of	ADP
bibechana-9308	45	34	paranormed	paranormed	ADJ
bibechana-9308	45	35	space	space	NOUN
bibechana-9308	45	36	is	be	AUX
bibechana-9308	45	37	closely	closely	ADV
bibechana-9308	45	38	related	relate	VERB
bibechana-9308	45	39	to	to	AUX
bibechana-9308	45	40	linear	linear	VERB
bibechana-9308	45	41	metric	metric	ADJ
bibechana-9308	45	42	space	space	NOUN
bibechana-9308	45	43	,	,	PUNCT
bibechana-9308	45	44	see	see	VERB
bibechana-9308	45	45	a.	a.	NOUN
bibechana-9308	45	46	wilansky	wilansky	PROPN
bibechana-9308	46	1	[	[	X
bibechana-9308	46	2	11	11	NUM
bibechana-9308	46	3	]	]	PUNCT
bibechana-9308	46	4	.	.	PUNCT
bibechana-9308	47	1	a	a	DET
bibechana-9308	47	2	paranormed	paranorme	VERB
bibechana-9308	47	3	space	space	NOUN
bibechana-9308	47	4	(	(	PUNCT
bibechana-9308	47	5	s	s	X
bibechana-9308	47	6	,	,	PUNCT
bibechana-9308	47	7	t	t	PROPN
bibechana-9308	47	8	)	)	PUNCT
bibechana-9308	47	9	is	be	AUX
bibechana-9308	47	10	a	a	DET
bibechana-9308	47	11	linear	linear	ADJ
bibechana-9308	47	12	space	space	NOUN
bibechana-9308	47	13	s	s	NOUN
bibechana-9308	47	14	with	with	ADP
bibechana-9308	47	15	zero	zero	NUM
bibechana-9308	47	16	element	element	NOUN
bibechana-9308	47	17	θ	θ	PROPN
bibechana-9308	47	18	together	together	ADV
bibechana-9308	47	19	with	with	ADP
bibechana-9308	47	20	a	a	DET
bibechana-9308	47	21	function	function	NOUN
bibechana-9308	47	22	t	t	NOUN
bibechana-9308	47	23	:	:	PUNCT
bibechana-9308	47	24	s	s	X
bibechana-9308	47	25	→	→	SYM
bibechana-9308	47	26	r+	r+	X
bibechana-9308	47	27	(	(	PUNCT
bibechana-9308	47	28	called	call	VERB
bibechana-9308	47	29	a	a	DET
bibechana-9308	47	30	paranorm	paranorm	NOUN
bibechana-9308	47	31	on	on	ADP
bibechana-9308	47	32	s	s	NOUN
bibechana-9308	47	33	)	)	PUNCT
bibechana-9308	47	34	which	which	PRON
bibechana-9308	47	35	satisfies	satisfy	VERB
bibechana-9308	47	36	the	the	DET
bibechana-9308	47	37	following	follow	VERB
bibechana-9308	47	38	axioms	axiom	NOUN
bibechana-9308	47	39	:	:	PUNCT
bibechana-9308	47	40	pn1	pn1	NOUN
bibechana-9308	47	41	:	:	PUNCT
bibechana-9308	47	42	t	t	PROPN
bibechana-9308	47	43	(	(	PUNCT
bibechana-9308	47	44	θ	θ	NOUN
bibechana-9308	47	45	)	)	PUNCT
bibechana-9308	47	46	=	=	SYM
bibechana-9308	47	47	0	0	NUM
bibechana-9308	47	48	;	;	PUNCT
bibechana-9308	47	49	pn2	pn2	NOUN
bibechana-9308	47	50	:	:	PUNCT
bibechana-9308	47	51	t	t	PROPN
bibechana-9308	47	52	(	(	PUNCT
bibechana-9308	47	53	ξ	ξ	X
bibechana-9308	47	54	)	)	PUNCT
bibechana-9308	47	55	=	=	SYM
bibechana-9308	47	56	t	t	PROPN
bibechana-9308	47	57	(	(	PUNCT
bibechana-9308	47	58	–	–	PUNCT
bibechana-9308	47	59	ξ	ξ	NOUN
bibechana-9308	47	60	)	)	PUNCT
bibechana-9308	47	61	,	,	PUNCT
bibechana-9308	47	62	for	for	ADP
bibechana-9308	47	63	all	all	DET
bibechana-9308	47	64	ξ	ξ	PROPN
bibechana-9308	47	65	∈	∈	PROPN
bibechana-9308	47	66	s	s	NOUN
bibechana-9308	47	67	;	;	PUNCT
bibechana-9308	47	68	pn3	pn3	NOUN
bibechana-9308	47	69	:	:	PUNCT
bibechana-9308	47	70	t	t	PROPN
bibechana-9308	47	71	(	(	PUNCT
bibechana-9308	47	72	ξ	ξ	PROPN
bibechana-9308	47	73	+	+	X
bibechana-9308	47	74	η	η	NOUN
bibechana-9308	47	75	)	)	PUNCT
bibechana-9308	47	76	≤	≤	PROPN
bibechana-9308	47	77	t	t	PROPN
bibechana-9308	47	78	(	(	PUNCT
bibechana-9308	47	79	ξ	ξ	NOUN
bibechana-9308	47	80	)	)	PUNCT
bibechana-9308	48	1	+	+	NUM
bibechana-9308	48	2	t	t	PROPN
bibechana-9308	48	3	(	(	PUNCT
bibechana-9308	48	4	η	η	PROPN
bibechana-9308	48	5	)	)	PUNCT
bibechana-9308	48	6	,	,	PUNCT
bibechana-9308	48	7	for	for	ADP
bibechana-9308	48	8	all	all	DET
bibechana-9308	48	9	ξ	ξ	PROPN
bibechana-9308	48	10	,	,	PUNCT
bibechana-9308	48	11	η	η	PROPN
bibechana-9308	48	12	∈	∈	PROPN
bibechana-9308	48	13	s	s	PART
bibechana-9308	48	14	;	;	PUNCT
bibechana-9308	48	15	and	and	CCONJ
bibechana-9308	48	16	pn4	pn4	VERB
bibechana-9308	48	17	:	:	PUNCT
bibechana-9308	48	18	scalar	scalar	ADJ
bibechana-9308	48	19	multiplication	multiplication	NOUN
bibechana-9308	48	20	is	be	AUX
bibechana-9308	48	21	continuous	continuous	ADJ
bibechana-9308	48	22	i.e.	i.e.	X
bibechana-9308	48	23	,	,	PUNCT
bibechana-9308	48	24	if	if	SCONJ
bibechana-9308	48	25	(	(	PUNCT
bibechana-9308	48	26	γn	γn	NOUN
bibechana-9308	48	27	)	)	PUNCT
bibechana-9308	48	28	is	be	AUX
bibechana-9308	48	29	a	a	DET
bibechana-9308	48	30	sequence	sequence	NOUN
bibechana-9308	48	31	of	of	ADP
bibechana-9308	48	32	scalars	scalar	NOUN
bibechana-9308	48	33	with	with	ADP
bibechana-9308	48	34	γn	γn	NOUN
bibechana-9308	48	35	→	→	SYM
bibechana-9308	48	36	γ	γ	X
bibechana-9308	48	37	as	as	ADP
bibechana-9308	48	38	n	n	PROPN
bibechana-9308	48	39	→	→	SYM
bibechana-9308	48	40	∞	∞	PROPN
bibechana-9308	48	41	and	and	CCONJ
bibechana-9308	48	42	(	(	PUNCT
bibechana-9308	48	43	ξn	ξn	NOUN
bibechana-9308	48	44	)	)	PUNCT
bibechana-9308	48	45	is	be	AUX
bibechana-9308	48	46	a	a	DET
bibechana-9308	48	47	sequence	sequence	NOUN
bibechana-9308	48	48	of	of	ADP
bibechana-9308	48	49	vectors	vector	NOUN
bibechana-9308	48	50	with	with	ADP
bibechana-9308	48	51	t	t	PROPN
bibechana-9308	48	52	(	(	PUNCT
bibechana-9308	48	53	ξn	ξn	PROPN
bibechana-9308	48	54	−	−	PROPN
bibechana-9308	48	55	ξ	ξ	NOUN
bibechana-9308	48	56	)	)	PUNCT
bibechana-9308	49	1	→	→	SYM
bibechana-9308	49	2	0	0	NUM
bibechana-9308	49	3	as	as	ADP
bibechana-9308	49	4	n	n	NUM
bibechana-9308	49	5	→	→	SYM
bibechana-9308	49	6	∞	∞	PROPN
bibechana-9308	49	7	then	then	ADV
bibechana-9308	49	8	t	t	PROPN
bibechana-9308	49	9	(	(	PUNCT
bibechana-9308	49	10	γn	γn	NOUN
bibechana-9308	49	11	ξn	ξn	PROPN
bibechana-9308	49	12	−	−	PROPN
bibechana-9308	49	13	γξ	γξ	ADP
bibechana-9308	49	14	)	)	PUNCT
bibechana-9308	49	15	→	→	SYM
bibechana-9308	49	16	0	0	NUM
bibechana-9308	49	17	as	as	ADP
bibechana-9308	49	18	n	n	PROPN
bibechana-9308	49	19	→	→	SYM
bibechana-9308	49	20	∞.	∞.	PROPN
bibechana-9308	49	21	note	note	VERB
bibechana-9308	49	22	that	that	SCONJ
bibechana-9308	49	23	the	the	DET
bibechana-9308	49	24	continuity	continuity	NOUN
bibechana-9308	49	25	of	of	ADP
bibechana-9308	49	26	scalar	scalar	ADJ
bibechana-9308	49	27	multiplication	multiplication	NOUN
bibechana-9308	49	28	is	be	AUX
bibechana-9308	49	29	equivalent	equivalent	ADJ
bibechana-9308	49	30	to	to	ADP
bibechana-9308	49	31	(	(	PUNCT
bibechana-9308	49	32	i	i	NOUN
bibechana-9308	49	33	)	)	PUNCT
bibechana-9308	49	34	if	if	SCONJ
bibechana-9308	49	35	t	t	PROPN
bibechana-9308	49	36	(	(	PUNCT
bibechana-9308	49	37	ξn	ξn	PROPN
bibechana-9308	49	38	)	)	PUNCT
bibechana-9308	49	39	→	→	SYM
bibechana-9308	49	40	0	0	NUM
bibechana-9308	49	41	and	and	CCONJ
bibechana-9308	49	42	γn	γn	NOUN
bibechana-9308	49	43	→	→	PUNCT
bibechana-9308	49	44	γ	γ	X
bibechana-9308	49	45	as	as	ADP
bibechana-9308	49	46	n	n	PROPN
bibechana-9308	49	47	→	→	SYM
bibechana-9308	49	48	∞	∞	PROPN
bibechana-9308	49	49	,	,	PUNCT
bibechana-9308	49	50	then	then	ADV
bibechana-9308	49	51	t(γn	t(γn	PROPN
bibechana-9308	49	52	ξn	ξn	PROPN
bibechana-9308	49	53	)	)	PUNCT
bibechana-9308	49	54	→	→	SYM
bibechana-9308	49	55	0	0	NUM
bibechana-9308	49	56	as	as	ADP
bibechana-9308	49	57	n	n	NUM
bibechana-9308	49	58	→	→	SYM
bibechana-9308	49	59	∞	∞	PROPN
bibechana-9308	49	60	and	and	CCONJ
bibechana-9308	49	61	n.p	n.p	PROPN
bibechana-9308	49	62	.	.	PROPN
bibechana-9308	49	63	pahari	pahari	PROPN
bibechana-9308	49	64	/	/	SYM
bibechana-9308	49	65	bibechana	bibechana	NOUN
bibechana-9308	49	66	10	10	NUM
bibechana-9308	49	67	(	(	PUNCT
bibechana-9308	49	68	2014	2014	NUM
bibechana-9308	49	69	)	)	PUNCT
bibechana-9308	49	70	20	20	NUM
bibechana-9308	49	71	-	-	SYM
bibechana-9308	49	72	30	30	NUM
bibechana-9308	49	73	:	:	PUNCT
bibechana-9308	49	74	bmhss	bmhss	PROPN
bibechana-9308	49	75	,	,	PUNCT
bibechana-9308	49	76	p.22	p.22	X
bibechana-9308	49	77	(	(	PUNCT
bibechana-9308	49	78	online	online	ADJ
bibechana-9308	49	79	publication	publication	NOUN
bibechana-9308	49	80	:	:	PUNCT
bibechana-9308	49	81	dec	dec	PROPN
bibechana-9308	49	82	.	.	PROPN
bibechana-9308	49	83	,	,	PUNCT
bibechana-9308	49	84	2013	2013	NUM
bibechana-9308	49	85	)	)	PUNCT
bibechana-9308	49	86	(	(	PUNCT
bibechana-9308	49	87	ii	ii	NOUN
bibechana-9308	49	88	)	)	PUNCT
bibechana-9308	49	89	if	if	SCONJ
bibechana-9308	49	90	γn	γn	ADP
bibechana-9308	49	91	→	→	SYM
bibechana-9308	49	92	0	0	NUM
bibechana-9308	49	93	as	as	ADP
bibechana-9308	49	94	n	n	NUM
bibechana-9308	49	95	→	→	SYM
bibechana-9308	49	96	∞	∞	PROPN
bibechana-9308	49	97	and	and	CCONJ
bibechana-9308	49	98	ξ	ξ	PROPN
bibechana-9308	49	99	be	be	VERB
bibechana-9308	49	100	any	any	DET
bibechana-9308	49	101	element	element	NOUN
bibechana-9308	49	102	in	in	ADP
bibechana-9308	49	103	s	s	PROPN
bibechana-9308	49	104	,	,	PUNCT
bibechana-9308	49	105	then	then	ADV
bibechana-9308	49	106	t	t	PROPN
bibechana-9308	49	107	(	(	PUNCT
bibechana-9308	49	108	γn	γn	ADP
bibechana-9308	49	109	ξ	ξ	NOUN
bibechana-9308	49	110	)	)	PUNCT
bibechana-9308	49	111	→	→	SYM
bibechana-9308	49	112	0	0	NUM
bibechana-9308	49	113	,	,	PUNCT
bibechana-9308	49	114	see	see	VERB
bibechana-9308	49	115	wilansky	wilansky	ADJ
bibechana-9308	49	116	[	[	X
bibechana-9308	49	117	11	11	NUM
bibechana-9308	49	118	]	]	PUNCT
bibechana-9308	49	119	.	.	PUNCT
bibechana-9308	50	1	a	a	DET
bibechana-9308	50	2	paranorm	paranorm	NOUN
bibechana-9308	50	3	is	be	AUX
bibechana-9308	50	4	called	call	VERB
bibechana-9308	50	5	total	total	NOUN
bibechana-9308	50	6	if	if	SCONJ
bibechana-9308	50	7	t	t	PROPN
bibechana-9308	50	8	(	(	PUNCT
bibechana-9308	50	9	ξ	ξ	X
bibechana-9308	50	10	)	)	PUNCT
bibechana-9308	50	11	=	=	SYM
bibechana-9308	50	12	0	0	NUM
bibechana-9308	50	13	implies	imply	VERB
bibechana-9308	50	14	ξ	ξ	PROPN
bibechana-9308	50	15	=	=	SYM
bibechana-9308	50	16	θ	θ	PROPN
bibechana-9308	50	17	,	,	PUNCT
bibechana-9308	50	18	see	see	VERB
bibechana-9308	50	19	a.	a.	NOUN
bibechana-9308	50	20	wilansky	wilansky	PROPN
bibechana-9308	51	1	[	[	X
bibechana-9308	51	2	11	11	NUM
bibechana-9308	51	3	]	]	PUNCT
bibechana-9308	51	4	.	.	PUNCT
bibechana-9308	52	1	the	the	DET
bibechana-9308	52	2	studies	study	NOUN
bibechana-9308	52	3	of	of	ADP
bibechana-9308	52	4	paranorm	paranorm	NOUN
bibechana-9308	52	5	on	on	ADP
bibechana-9308	52	6	sequence	sequence	NOUN
bibechana-9308	52	7	spaces	space	NOUN
bibechana-9308	52	8	were	be	AUX
bibechana-9308	52	9	initiated	initiate	VERB
bibechana-9308	52	10	by	by	ADP
bibechana-9308	52	11	maddox	maddox	PROPN
bibechana-9308	52	12	[	[	X
bibechana-9308	52	13	12	12	NUM
bibechana-9308	52	14	]	]	PUNCT
bibechana-9308	52	15	and	and	CCONJ
bibechana-9308	52	16	many	many	ADJ
bibechana-9308	52	17	others	other	NOUN
bibechana-9308	52	18	.	.	PUNCT
bibechana-9308	53	1	srivastava	srivastava	PROPN
bibechana-9308	53	2	and	and	CCONJ
bibechana-9308	53	3	et	et	PROPN
bibechana-9308	53	4	al	al	PROPN
bibechana-9308	53	5	.	.	PUNCT
bibechana-9308	54	1	[	[	X
bibechana-9308	54	2	13	13	NUM
bibechana-9308	54	3	-	-	SYM
bibechana-9308	54	4	15	15	NUM
bibechana-9308	54	5	]	]	PUNCT
bibechana-9308	54	6	,	,	PUNCT
bibechana-9308	54	7	pahari	pahari	X
bibechana-9308	54	8	[	[	X
bibechana-9308	54	9	16	16	NUM
bibechana-9308	54	10	]	]	PUNCT
bibechana-9308	54	11	,	,	PUNCT
bibechana-9308	54	12	parashar	parashar	PROPN
bibechana-9308	54	13	and	and	CCONJ
bibechana-9308	54	14	choudhary	choudhary	PROPN
bibechana-9308	55	1	[	[	X
bibechana-9308	55	2	17	17	NUM
bibechana-9308	55	3	]	]	PUNCT
bibechana-9308	55	4	,	,	PUNCT
bibechana-9308	55	5	bhardwaj	bhardwaj	PROPN
bibechana-9308	55	6	and	and	CCONJ
bibechana-9308	55	7	bala	bala	PROPN
bibechana-9308	56	1	[	[	X
bibechana-9308	56	2	18	18	NUM
bibechana-9308	56	3	]	]	PUNCT
bibechana-9308	56	4	and	and	CCONJ
bibechana-9308	56	5	many	many	ADJ
bibechana-9308	56	6	others	other	NOUN
bibechana-9308	56	7	further	far	ADV
bibechana-9308	56	8	studied	study	VERB
bibechana-9308	56	9	various	various	ADJ
bibechana-9308	56	10	types	type	NOUN
bibechana-9308	56	11	of	of	ADP
bibechana-9308	56	12	paranormed	paranorme	VERB
bibechana-9308	56	13	sequence	sequence	NOUN
bibechana-9308	56	14	spaces	space	NOUN
bibechana-9308	56	15	and	and	CCONJ
bibechana-9308	56	16	function	function	NOUN
bibechana-9308	56	17	spaces	space	NOUN
bibechana-9308	56	18	.	.	PUNCT
bibechana-9308	57	1	a	a	DET
bibechana-9308	57	2	sequence	sequence	NOUN
bibechana-9308	57	3	space	space	NOUN
bibechana-9308	57	4	s	s	NOUN
bibechana-9308	57	5	is	be	AUX
bibechana-9308	57	6	said	say	VERB
bibechana-9308	57	7	to	to	PART
bibechana-9308	57	8	be	be	AUX
bibechana-9308	57	9	normal	normal	ADJ
bibechana-9308	57	10	if	if	SCONJ
bibechana-9308	57	11	ξ	ξ	X
bibechana-9308	57	12	–	–	PUNCT
bibechana-9308	57	13	=	=	SYM
bibechana-9308	57	14	(	(	PUNCT
bibechana-9308	57	15	ξk	ξk	NOUN
bibechana-9308	57	16	)	)	PUNCT
bibechana-9308	57	17	∈	∈	PROPN
bibechana-9308	57	18	s	s	PART
bibechana-9308	57	19	and	and	CCONJ
bibechana-9308	57	20	α	α	NOUN
bibechana-9308	57	21	–	–	PUNCT
bibechana-9308	57	22	=	=	NOUN
bibechana-9308	57	23	(	(	PUNCT
bibechana-9308	57	24	αk	αk	NOUN
bibechana-9308	57	25	)	)	PUNCT
bibechana-9308	57	26	a	a	DET
bibechana-9308	57	27	sequence	sequence	NOUN
bibechana-9308	57	28	of	of	ADP
bibechana-9308	57	29	scalars	scalar	NOUN
bibechana-9308	57	30	with	with	ADP
bibechana-9308	57	31	|αk|	|αk|	PROPN
bibechana-9308	57	32	≤	≤	NUM
bibechana-9308	57	33	1	1	NUM
bibechana-9308	57	34	,	,	PUNCT
bibechana-9308	57	35	for	for	ADP
bibechana-9308	57	36	all	all	DET
bibechana-9308	57	37	k	k	PROPN
bibechana-9308	57	38	≥	≥	NUM
bibechana-9308	57	39	1	1	NUM
bibechana-9308	57	40	,	,	PUNCT
bibechana-9308	57	41	then	then	ADV
bibechana-9308	57	42	α	α	PROPN
bibechana-9308	57	43	–	–	PUNCT
bibechana-9308	57	44	ξ	ξ	X
bibechana-9308	57	45	–	–	PUNCT
bibechana-9308	57	46	=	=	SYM
bibechana-9308	57	47	(	(	PUNCT
bibechana-9308	57	48	αk	αk	INTJ
bibechana-9308	57	49	ξk	ξk	NOUN
bibechana-9308	57	50	)	)	PUNCT
bibechana-9308	57	51	∈s	∈s	NOUN
bibechana-9308	57	52	.	.	PUNCT
bibechana-9308	58	1	2	2	X
bibechana-9308	58	2	.	.	X
bibechana-9308	58	3	the	the	DET
bibechana-9308	58	4	class	class	NOUN
bibechana-9308	58	5	c0	c0	NOUN
bibechana-9308	58	6	(	(	PUNCT
bibechana-9308	58	7	x	x	NOUN
bibechana-9308	58	8	,	,	PUNCT
bibechana-9308	58	9	λλλλ	λλλλ	X
bibechana-9308	58	10	–	–	PUNCT
bibechana-9308	58	11	,	,	PUNCT
bibechana-9308	58	12	u	u	INTJ
bibechana-9308	58	13	–	–	PUNCT
bibechana-9308	58	14	,	,	PUNCT
bibechana-9308	58	15	||	||	PROPN
bibechana-9308	58	16	.	.	PUNCT
bibechana-9308	58	17	,	,	PUNCT
bibechana-9308	58	18	.||	.||	PROPN
bibechana-9308	58	19	)	)	PUNCT
bibechana-9308	58	20	of	of	ADP
bibechana-9308	58	21	2	2	NUM
bibechana-9308	58	22	-	-	PUNCT
bibechana-9308	58	23	normed	norme	VERB
bibechana-9308	58	24	space	space	NOUN
bibechana-9308	58	25	valued	value	VERB
bibechana-9308	58	26	vector	vector	NOUN
bibechana-9308	58	27	sequences	sequence	NOUN
bibechana-9308	58	28	let	let	VERB
bibechana-9308	58	29	u	u	PRON
bibechana-9308	58	30	–	–	PUNCT
bibechana-9308	58	31	=	=	SYM
bibechana-9308	58	32	(	(	PUNCT
bibechana-9308	58	33	uk	uk	PROPN
bibechana-9308	58	34	)	)	PUNCT
bibechana-9308	58	35	and	and	CCONJ
bibechana-9308	58	36	v	v	NOUN
bibechana-9308	58	37	–	–	PUNCT
bibechana-9308	58	38	=	=	SYM
bibechana-9308	58	39	(	(	PUNCT
bibechana-9308	58	40	vk	vk	NOUN
bibechana-9308	58	41	)	)	PUNCT
bibechana-9308	58	42	be	be	AUX
bibechana-9308	58	43	any	any	DET
bibechana-9308	58	44	sequences	sequence	NOUN
bibechana-9308	58	45	of	of	ADP
bibechana-9308	58	46	strictly	strictly	ADV
bibechana-9308	58	47	positive	positive	ADJ
bibechana-9308	58	48	real	real	ADJ
bibechana-9308	58	49	numbers	number	NOUN
bibechana-9308	58	50	and	and	CCONJ
bibechana-9308	58	51	λ	λ	NOUN
bibechana-9308	58	52	–	–	PUNCT
bibechana-9308	58	53	=	=	SYM
bibechana-9308	58	54	(	(	PUNCT
bibechana-9308	58	55	λk	λk	NOUN
bibechana-9308	58	56	)	)	PUNCT
bibechana-9308	58	57	and	and	CCONJ
bibechana-9308	58	58	µ–=	µ–=	NOUN
bibechana-9308	58	59	(	(	PUNCT
bibechana-9308	58	60	µk	µk	INTJ
bibechana-9308	58	61	)	)	PUNCT
bibechana-9308	58	62	be	be	AUX
bibechana-9308	58	63	the	the	DET
bibechana-9308	58	64	sequences	sequence	NOUN
bibechana-9308	58	65	of	of	ADP
bibechana-9308	58	66	non	non	ADJ
bibechana-9308	58	67	zero	zero	NUM
bibechana-9308	58	68	complex	complex	ADJ
bibechana-9308	58	69	numbers	number	NOUN
bibechana-9308	58	70	.	.	PUNCT
bibechana-9308	59	1	let	let	VERB
bibechana-9308	59	2	(	(	PUNCT
bibechana-9308	59	3	x	x	X
bibechana-9308	59	4	,	,	PUNCT
bibechana-9308	59	5	||	||	PROPN
bibechana-9308	59	6	.	.	PUNCT
bibechana-9308	59	7	,	,	PUNCT
bibechana-9308	60	1	.||	.||	PROPN
bibechana-9308	60	2	)	)	PUNCT
bibechana-9308	60	3	be	be	AUX
bibechana-9308	60	4	the	the	DET
bibechana-9308	60	5	2	2	NUM
bibechana-9308	60	6	normed	normed	ADJ
bibechana-9308	60	7	space	space	NOUN
bibechana-9308	60	8	over	over	ADP
bibechana-9308	60	9	the	the	DET
bibechana-9308	60	10	field	field	NOUN
bibechana-9308	60	11	c	c	NOUN
bibechana-9308	60	12	of	of	ADP
bibechana-9308	60	13	complex	complex	ADJ
bibechana-9308	60	14	numbers	number	NOUN
bibechana-9308	60	15	and	and	CCONJ
bibechana-9308	60	16	θ	θ	PROPN
bibechana-9308	60	17	denotes	denote	VERB
bibechana-9308	60	18	the	the	DET
bibechana-9308	60	19	zero	zero	NUM
bibechana-9308	60	20	element	element	NOUN
bibechana-9308	60	21	of	of	ADP
bibechana-9308	60	22	x.	x.	NOUN
bibechana-9308	60	23	let	let	VERB
bibechana-9308	60	24	ω(x	ω(x	NOUN
bibechana-9308	60	25	)	)	PUNCT
bibechana-9308	60	26	denotes	denote	VERB
bibechana-9308	60	27	the	the	DET
bibechana-9308	60	28	linear	linear	ADJ
bibechana-9308	60	29	space	space	NOUN
bibechana-9308	60	30	of	of	ADP
bibechana-9308	60	31	all	all	DET
bibechana-9308	60	32	sequences	sequence	NOUN
bibechana-9308	61	1	x	x	SYM
bibechana-9308	61	2	–	–	PUNCT
bibechana-9308	61	3	=	=	SYM
bibechana-9308	61	4	(	(	PUNCT
bibechana-9308	61	5	ξk	ξk	NOUN
bibechana-9308	61	6	)	)	PUNCT
bibechana-9308	61	7	and	and	CCONJ
bibechana-9308	61	8	y	y	X
bibechana-9308	61	9	–	–	PUNCT
bibechana-9308	61	10	=	=	SYM
bibechana-9308	61	11	(	(	PUNCT
bibechana-9308	61	12	ηk	ηk	PROPN
bibechana-9308	61	13	)	)	PUNCT
bibechana-9308	61	14	with	with	ADP
bibechana-9308	61	15	ξk	ξk	ADP
bibechana-9308	61	16	,	,	PUNCT
bibechana-9308	61	17	ηk	ηk	PROPN
bibechana-9308	61	18	∈	∈	PROPN
bibechana-9308	61	19	x	x	X
bibechana-9308	61	20	,	,	PUNCT
bibechana-9308	61	21	k	k	X
bibechana-9308	61	22	≥	≥	NUM
bibechana-9308	61	23	1	1	NUM
bibechana-9308	61	24	with	with	ADP
bibechana-9308	61	25	usual	usual	ADJ
bibechana-9308	61	26	coordinate	coordinate	NOUN
bibechana-9308	61	27	wise	wise	ADJ
bibechana-9308	61	28	operations	operation	NOUN
bibechana-9308	61	29	i.e.	i.e.	ADV
bibechana-9308	61	30	,	,	PUNCT
bibechana-9308	61	31	x	x	X
bibechana-9308	61	32	–	–	PUNCT
bibechana-9308	61	33	+	+	NUM
bibechana-9308	61	34	y	y	X
bibechana-9308	61	35	–	–	PUNCT
bibechana-9308	61	36	=	=	SYM
bibechana-9308	61	37	(	(	PUNCT
bibechana-9308	61	38	ξk	ξk	ADP
bibechana-9308	61	39	+	+	NOUN
bibechana-9308	61	40	ηk	ηk	X
bibechana-9308	61	41	)	)	PUNCT
bibechana-9308	61	42	and	and	CCONJ
bibechana-9308	61	43	α	α	NOUN
bibechana-9308	61	44	x	x	X
bibechana-9308	61	45	–	–	PUNCT
bibechana-9308	61	46	=	=	SYM
bibechana-9308	61	47	(	(	PUNCT
bibechana-9308	61	48	αξk	αξk	NOUN
bibechana-9308	61	49	)	)	PUNCT
bibechana-9308	61	50	,	,	PUNCT
bibechana-9308	61	51	for	for	ADP
bibechana-9308	61	52	each	each	PRON
bibechana-9308	61	53	x	x	PROPN
bibechana-9308	61	54	–	–	PUNCT
bibechana-9308	61	55	,	,	PUNCT
bibechana-9308	61	56	y	y	PROPN
bibechana-9308	61	57	–	–	PUNCT
bibechana-9308	61	58	∈	∈	PROPN
bibechana-9308	61	59	ω	ω	X
bibechana-9308	61	60	(	(	PUNCT
bibechana-9308	61	61	x	x	NOUN
bibechana-9308	61	62	)	)	PUNCT
bibechana-9308	61	63	and	and	CCONJ
bibechana-9308	61	64	α∈	α∈	PROPN
bibechana-9308	61	65	c.	c.	NOUN
bibechana-9308	61	66	we	we	PRON
bibechana-9308	61	67	shall	shall	AUX
bibechana-9308	61	68	denote	denote	VERB
bibechana-9308	61	69	ω	ω	PROPN
bibechana-9308	61	70	(	(	PUNCT
bibechana-9308	61	71	c	c	NOUN
bibechana-9308	61	72	)	)	PUNCT
bibechana-9308	61	73	by	by	ADP
bibechana-9308	61	74	ω	ω	PROPN
bibechana-9308	61	75	.	.	PUNCT
bibechana-9308	62	1	further	far	ADV
bibechana-9308	62	2	,	,	PUNCT
bibechana-9308	62	3	λ	λ	INTJ
bibechana-9308	62	4	–	–	PUNCT
bibechana-9308	62	5	=	=	SYM
bibechana-9308	62	6	(	(	PUNCT
bibechana-9308	62	7	λk	λk	NOUN
bibechana-9308	62	8	)	)	PUNCT
bibechana-9308	62	9	∈	∈	PROPN
bibechana-9308	62	10	ω	ω	PROPN
bibechana-9308	62	11	and	and	CCONJ
bibechana-9308	62	12	x	x	X
bibechana-9308	62	13	–	–	PUNCT
bibechana-9308	62	14	∈	∈	PROPN
bibechana-9308	62	15	ω	ω	X
bibechana-9308	62	16	(	(	PUNCT
bibechana-9308	62	17	x	x	X
bibechana-9308	62	18	)	)	PUNCT
bibechana-9308	62	19	we	we	PRON
bibechana-9308	62	20	shall	shall	AUX
bibechana-9308	62	21	write	write	VERB
bibechana-9308	62	22	λ	λ	PROPN
bibechana-9308	62	23	–	–	PUNCT
bibechana-9308	62	24	x	x	X
bibechana-9308	62	25	–	–	PUNCT
bibechana-9308	62	26	=	=	SYM
bibechana-9308	62	27	(	(	PUNCT
bibechana-9308	62	28	λk	λk	NOUN
bibechana-9308	62	29	ξk	ξk	ADP
bibechana-9308	62	30	)	)	PUNCT
bibechana-9308	62	31	.	.	PUNCT
bibechana-9308	63	1	we	we	PRON
bibechana-9308	63	2	now	now	ADV
bibechana-9308	63	3	introduce	introduce	VERB
bibechana-9308	63	4	the	the	DET
bibechana-9308	63	5	following	follow	VERB
bibechana-9308	63	6	classes	class	NOUN
bibechana-9308	63	7	of	of	ADP
bibechana-9308	63	8	2	2	NUM
bibechana-9308	63	9	-	-	PUNCT
bibechana-9308	63	10	normed	norme	VERB
bibechana-9308	63	11	space	space	NOUN
bibechana-9308	63	12	x	x	NOUN
bibechana-9308	63	13	–	–	PUNCT
bibechana-9308	63	14	valued	value	VERB
bibechana-9308	63	15	sequences	sequence	NOUN
bibechana-9308	63	16	c0	c0	NOUN
bibechana-9308	63	17	(	(	PUNCT
bibechana-9308	63	18	x	x	X
bibechana-9308	63	19	,	,	PUNCT
bibechana-9308	63	20	λ	λ	PROPN
bibechana-9308	63	21	–	–	PUNCT
bibechana-9308	63	22	,	,	PUNCT
bibechana-9308	63	23	u	u	NOUN
bibechana-9308	63	24	–	–	PUNCT
bibechana-9308	63	25	,	,	PUNCT
bibechana-9308	63	26	||	||	PROPN
bibechana-9308	63	27	.	.	PUNCT
bibechana-9308	63	28	,	,	PUNCT
bibechana-9308	63	29	.||	.||	PROPN
bibechana-9308	63	30	)	)	PUNCT
bibechana-9308	64	1	=	=	PRON
bibechana-9308	64	2	{	{	PUNCT
bibechana-9308	64	3	x	x	X
bibechana-9308	64	4	–	–	PUNCT
bibechana-9308	64	5	=	=	SYM
bibechana-9308	64	6	(	(	PUNCT
bibechana-9308	64	7	xk	xk	ADJ
bibechana-9308	64	8	)	)	PUNCT
bibechana-9308	64	9	∈	∈	PROPN
bibechana-9308	64	10	ω(x	ω(x	PROPN
bibechana-9308	64	11	)	)	PUNCT
bibechana-9308	64	12	,	,	PUNCT
bibechana-9308	64	13	xk	xk	PROPN
bibechana-9308	64	14	∈	∈	PROPN
bibechana-9308	65	1	x	x	PROPN
bibechana-9308	65	2	,	,	PUNCT
bibechana-9308	65	3	k	k	PROPN
bibechana-9308	65	4	≥	≥	NUM
bibechana-9308	65	5	1	1	NUM
bibechana-9308	65	6	satisfying	satisfying	NOUN
bibechana-9308	65	7	||	||	PROPN
bibechana-9308	66	1	λk	λk	ADP
bibechana-9308	66	2	xk	xk	PROPN
bibechana-9308	66	3	‚	‚	PROPN
bibechana-9308	66	4	y||	y||	PROPN
bibechana-9308	66	5	uk	uk	PROPN
bibechana-9308	66	6	→	→	SYM
bibechana-9308	66	7	0	0	PROPN
bibechana-9308	66	8	as	as	ADP
bibechana-9308	66	9	k→	k→	PROPN
bibechana-9308	66	10	∞	∞	PROPN
bibechana-9308	66	11	,	,	PUNCT
bibechana-9308	66	12	for	for	ADP
bibechana-9308	66	13	each	each	DET
bibechana-9308	66	14	y	y	PROPN
bibechana-9308	66	15	∈	∈	PROPN
bibechana-9308	66	16	x	x	PUNCT
bibechana-9308	66	17	}	}	PUNCT
bibechana-9308	66	18	.	.	PUNCT
bibechana-9308	67	1	in	in	ADP
bibechana-9308	67	2	fact	fact	NOUN
bibechana-9308	67	3	,	,	PUNCT
bibechana-9308	67	4	this	this	DET
bibechana-9308	67	5	class	class	NOUN
bibechana-9308	67	6	is	be	AUX
bibechana-9308	67	7	a	a	DET
bibechana-9308	67	8	generalization	generalization	NOUN
bibechana-9308	67	9	of	of	ADP
bibechana-9308	67	10	the	the	DET
bibechana-9308	67	11	familiar	familiar	ADJ
bibechana-9308	67	12	sequence	sequence	NOUN
bibechana-9308	67	13	spaces	space	NOUN
bibechana-9308	67	14	,	,	PUNCT
bibechana-9308	67	15	studied	study	VERB
bibechana-9308	67	16	in	in	ADP
bibechana-9308	67	17	srivastava	srivastava	PROPN
bibechana-9308	67	18	et	et	PROPN
bibechana-9308	67	19	al	al	PROPN
bibechana-9308	67	20	.	.	PROPN
bibechana-9308	68	1	(	(	PUNCT
bibechana-9308	68	2	1996	1996	NUM
bibechana-9308	68	3	)	)	PUNCT
bibechana-9308	69	1	[	[	X
bibechana-9308	69	2	12	12	NUM
bibechana-9308	69	3	]	]	PUNCT
bibechana-9308	69	4	,	,	PUNCT
bibechana-9308	69	5	srivastava	srivastava	PROPN
bibechana-9308	69	6	(	(	PUNCT
bibechana-9308	69	7	1996	1996	NUM
bibechana-9308	69	8	)	)	PUNCT
bibechana-9308	69	9	,	,	PUNCT
bibechana-9308	69	10	pahari	pahari	X
bibechana-9308	69	11	(	(	PUNCT
bibechana-9308	69	12	2011	2011	NUM
bibechana-9308	69	13	)	)	PUNCT
bibechana-9308	70	1	[	[	X
bibechana-9308	70	2	16	16	NUM
bibechana-9308	70	3	]	]	X
bibechana-9308	70	4	,	,	PUNCT
bibechana-9308	70	5	pahari	pahari	ADJ
bibechana-9308	70	6	and	and	CCONJ
bibechana-9308	70	7	et	et	PROPN
bibechana-9308	70	8	al	al	PROPN
bibechana-9308	70	9	(	(	PUNCT
bibechana-9308	70	10	2011	2011	NUM
bibechana-9308	70	11	)	)	PUNCT
bibechana-9308	71	1	[	[	X
bibechana-9308	71	2	11	11	NUM
bibechana-9308	71	3	]	]	PUNCT
bibechana-9308	71	4	,	,	PUNCT
bibechana-9308	71	5	using	use	VERB
bibechana-9308	71	6	2	2	NUM
bibechana-9308	71	7	-	-	PUNCT
bibechana-9308	71	8	norm	norm	NOUN
bibechana-9308	71	9	.	.	PUNCT
bibechana-9308	72	1	further	far	ADV
bibechana-9308	72	2	,	,	PUNCT
bibechana-9308	72	3	when	when	SCONJ
bibechana-9308	72	4	λk	λk	ADP
bibechana-9308	72	5	=	=	SYM
bibechana-9308	72	6	1	1	NUM
bibechana-9308	72	7	for	for	ADP
bibechana-9308	72	8	all	all	DET
bibechana-9308	72	9	k	k	PROPN
bibechana-9308	72	10	,	,	PUNCT
bibechana-9308	72	11	then	then	ADV
bibechana-9308	72	12	c0	c0	PROPN
bibechana-9308	72	13	(	(	PUNCT
bibechana-9308	72	14	x	x	X
bibechana-9308	72	15	,	,	PUNCT
bibechana-9308	72	16	λ	λ	PROPN
bibechana-9308	72	17	–	–	PUNCT
bibechana-9308	72	18	,	,	PUNCT
bibechana-9308	72	19	u	u	NOUN
bibechana-9308	72	20	–	–	PUNCT
bibechana-9308	72	21	,	,	PUNCT
bibechana-9308	72	22	||	||	PROPN
bibechana-9308	72	23	.	.	PUNCT
bibechana-9308	72	24	,	,	PUNCT
bibechana-9308	72	25	.||	.||	PROPN
bibechana-9308	72	26	)	)	PUNCT
bibechana-9308	72	27	will	will	AUX
bibechana-9308	72	28	be	be	AUX
bibechana-9308	72	29	denoted	denote	VERB
bibechana-9308	72	30	by	by	ADP
bibechana-9308	72	31	c0	c0	PROPN
bibechana-9308	72	32	(	(	PUNCT
bibechana-9308	72	33	x	x	X
bibechana-9308	72	34	,	,	PUNCT
bibechana-9308	72	35	u	u	NOUN
bibechana-9308	72	36	–	–	PUNCT
bibechana-9308	72	37	,	,	PUNCT
bibechana-9308	72	38	||	||	PROPN
bibechana-9308	72	39	.	.	PUNCT
bibechana-9308	72	40	,	,	PUNCT
bibechana-9308	73	1	.||	.||	PROPN
bibechana-9308	73	2	)	)	PUNCT
bibechana-9308	74	1	and	and	CCONJ
bibechana-9308	74	2	when	when	SCONJ
bibechana-9308	74	3	uk	uk	PROPN
bibechana-9308	74	4	=	=	PROPN
bibechana-9308	74	5	1	1	NUM
bibechana-9308	74	6	for	for	ADP
bibechana-9308	74	7	all	all	DET
bibechana-9308	74	8	k	k	PROPN
bibechana-9308	74	9	,	,	PUNCT
bibechana-9308	74	10	then	then	ADV
bibechana-9308	74	11	c0	c0	PROPN
bibechana-9308	74	12	(	(	PUNCT
bibechana-9308	74	13	x	x	X
bibechana-9308	74	14	,	,	PUNCT
bibechana-9308	74	15	λ	λ	PROPN
bibechana-9308	74	16	–	–	PUNCT
bibechana-9308	74	17	,	,	PUNCT
bibechana-9308	74	18	u	u	NOUN
bibechana-9308	74	19	–	–	PUNCT
bibechana-9308	74	20	,	,	PUNCT
bibechana-9308	74	21	||	||	PROPN
bibechana-9308	74	22	.	.	PUNCT
bibechana-9308	74	23	,	,	PUNCT
bibechana-9308	74	24	.||	.||	PROPN
bibechana-9308	74	25	)	)	PUNCT
bibechana-9308	74	26	will	will	AUX
bibechana-9308	74	27	be	be	AUX
bibechana-9308	74	28	denoted	denote	VERB
bibechana-9308	74	29	by	by	ADP
bibechana-9308	74	30	c0	c0	PROPN
bibechana-9308	74	31	(	(	PUNCT
bibechana-9308	74	32	x	x	X
bibechana-9308	74	33	,	,	PUNCT
bibechana-9308	74	34	λ	λ	PROPN
bibechana-9308	74	35	–	–	PUNCT
bibechana-9308	74	36	,	,	PUNCT
bibechana-9308	74	37	||	||	PROPN
bibechana-9308	74	38	.	.	PUNCT
bibechana-9308	74	39	,	,	PUNCT
bibechana-9308	74	40	.||	.||	PROPN
bibechana-9308	74	41	)	)	PUNCT
bibechana-9308	74	42	.	.	PUNCT
bibechana-9308	75	1	if	if	SCONJ
bibechana-9308	75	2	uk	uk	PROPN
bibechana-9308	75	3	=	=	PUNCT
bibechana-9308	75	4	λk	λk	PROPN
bibechana-9308	75	5	=	=	SYM
bibechana-9308	75	6	1	1	NUM
bibechana-9308	75	7	for	for	ADP
bibechana-9308	75	8	all	all	DET
bibechana-9308	75	9	k	k	PROPN
bibechana-9308	75	10	,	,	PUNCT
bibechana-9308	75	11	then	then	ADV
bibechana-9308	75	12	the	the	DET
bibechana-9308	75	13	class	class	NOUN
bibechana-9308	75	14	c0	c0	NOUN
bibechana-9308	75	15	(	(	PUNCT
bibechana-9308	75	16	x	x	X
bibechana-9308	75	17	,	,	PUNCT
bibechana-9308	75	18	λ	λ	PROPN
bibechana-9308	75	19	–	–	PUNCT
bibechana-9308	75	20	,	,	PUNCT
bibechana-9308	75	21	u	u	NOUN
bibechana-9308	75	22	–	–	PUNCT
bibechana-9308	75	23	,	,	PUNCT
bibechana-9308	75	24	||	||	PROPN
bibechana-9308	75	25	.	.	PUNCT
bibechana-9308	75	26	,	,	PUNCT
bibechana-9308	75	27	.||	.||	PROPN
bibechana-9308	75	28	)	)	PUNCT
bibechana-9308	75	29	will	will	AUX
bibechana-9308	75	30	be	be	AUX
bibechana-9308	75	31	denoted	denote	VERB
bibechana-9308	75	32	by	by	ADP
bibechana-9308	75	33	c0	c0	PROPN
bibechana-9308	75	34	(	(	PUNCT
bibechana-9308	75	35	x	x	X
bibechana-9308	75	36	,	,	PUNCT
bibechana-9308	75	37	||	||	PROPN
bibechana-9308	75	38	.	.	PUNCT
bibechana-9308	76	1	,	,	PUNCT
bibechana-9308	76	2	.||	.||	PROPN
bibechana-9308	76	3	)	)	PUNCT
bibechana-9308	76	4	.	.	PUNCT
bibechana-9308	77	1	further	far	ADV
bibechana-9308	77	2	,	,	PUNCT
bibechana-9308	77	3	when	when	SCONJ
bibechana-9308	77	4	x	x	X
bibechana-9308	77	5	=	=	PUNCT
bibechana-9308	77	6	c	c	X
bibechana-9308	77	7	we	we	PRON
bibechana-9308	77	8	simply	simply	ADV
bibechana-9308	77	9	write	write	VERB
bibechana-9308	77	10	c0	c0	NOUN
bibechana-9308	77	11	(	(	PUNCT
bibechana-9308	77	12	x	x	X
bibechana-9308	77	13	,	,	PUNCT
bibechana-9308	77	14	λ	λ	PROPN
bibechana-9308	77	15	–	–	PUNCT
bibechana-9308	77	16	,	,	PUNCT
bibechana-9308	77	17	u	u	NOUN
bibechana-9308	77	18	–	–	PUNCT
bibechana-9308	77	19	,	,	PUNCT
bibechana-9308	77	20	||	||	PROPN
bibechana-9308	77	21	.	.	PUNCT
bibechana-9308	77	22	,	,	PUNCT
bibechana-9308	77	23	.||	.||	PROPN
bibechana-9308	77	24	)	)	PUNCT
bibechana-9308	77	25	as	as	ADP
bibechana-9308	77	26	c0	c0	PROPN
bibechana-9308	77	27	(	(	PUNCT
bibechana-9308	77	28	λ	λ	PROPN
bibechana-9308	77	29	–	–	PUNCT
bibechana-9308	77	30	,	,	PUNCT
bibechana-9308	77	31	u	u	NOUN
bibechana-9308	77	32	–	–	PUNCT
bibechana-9308	77	33	,	,	PUNCT
bibechana-9308	77	34	||	||	PROPN
bibechana-9308	77	35	.	.	PUNCT
bibechana-9308	77	36	,	,	PUNCT
bibechana-9308	77	37	.||	.||	PROPN
bibechana-9308	77	38	)	)	PUNCT
bibechana-9308	77	39	.	.	PUNCT
bibechana-9308	78	1	3	3	X
bibechana-9308	78	2	.	.	X
bibechana-9308	78	3	containment	containment	NOUN
bibechana-9308	78	4	relations	relation	NOUN
bibechana-9308	78	5	in	in	ADP
bibechana-9308	78	6	this	this	DET
bibechana-9308	78	7	section	section	NOUN
bibechana-9308	78	8	,	,	PUNCT
bibechana-9308	78	9	we	we	PRON
bibechana-9308	78	10	investigate	investigate	VERB
bibechana-9308	78	11	some	some	DET
bibechana-9308	78	12	inclusion	inclusion	NOUN
bibechana-9308	78	13	relations	relation	NOUN
bibechana-9308	78	14	of	of	ADP
bibechana-9308	78	15	the	the	DET
bibechana-9308	78	16	class	class	NOUN
bibechana-9308	78	17	c0	c0	X
bibechana-9308	78	18	(	(	PUNCT
bibechana-9308	78	19	s	s	PROPN
bibechana-9308	78	20	,	,	PUNCT
bibechana-9308	78	21	||	||	PROPN
bibechana-9308	78	22	.	.	PUNCT
bibechana-9308	78	23	,	,	PUNCT
bibechana-9308	79	1	.||	.||	PROPN
bibechana-9308	79	2	,	,	PUNCT
bibechana-9308	79	3	α	α	PROPN
bibechana-9308	79	4	–	–	PUNCT
bibechana-9308	79	5	,	,	PUNCT
bibechana-9308	79	6	u	u	NOUN
bibechana-9308	79	7	–	–	PUNCT
bibechana-9308	79	8	)	)	PUNCT
bibechana-9308	79	9	arising	arise	VERB
bibechana-9308	79	10	in	in	ADP
bibechana-9308	79	11	terms	term	NOUN
bibechana-9308	79	12	of	of	ADP
bibechana-9308	79	13	different	different	ADJ
bibechana-9308	79	14	u	u	NOUN
bibechana-9308	79	15	–	–	PUNCT
bibechana-9308	79	16	and	and	CCONJ
bibechana-9308	79	17	α	α	PRON
bibechana-9308	79	18	–	–	PUNCT
bibechana-9308	79	19	.	.	PUNCT
bibechana-9308	80	1	throughout	throughout	ADP
bibechana-9308	80	2	,	,	PUNCT
bibechana-9308	80	3	we	we	PRON
bibechana-9308	80	4	denote	denote	VERB
bibechana-9308	80	5	sup	sup	NOUN
bibechana-9308	80	6	uk	uk	PROPN
bibechana-9308	80	7	=	=	NOUN
bibechana-9308	80	8	l	l	PROPN
bibechana-9308	80	9	for	for	ADP
bibechana-9308	80	10	each	each	DET
bibechana-9308	80	11	k	k	PROPN
bibechana-9308	80	12	and	and	CCONJ
bibechana-9308	80	13	for	for	ADP
bibechana-9308	80	14	scalar	scalar	ADJ
bibechana-9308	80	15	α	α	NOUN
bibechana-9308	80	16	,	,	PUNCT
bibechana-9308	80	17	a	a	DET
bibechana-9308	80	18	[	[	X
bibechana-9308	80	19	α	α	X
bibechana-9308	80	20	]	]	X
bibechana-9308	80	21	=	=	X
bibechana-9308	80	22	max	max	X
bibechana-9308	80	23	(	(	PUNCT
bibechana-9308	80	24	1	1	NUM
bibechana-9308	80	25	,	,	PUNCT
bibechana-9308	80	26	|α|	|α|	PROPN
bibechana-9308	80	27	)	)	PUNCT
bibechana-9308	80	28	.	.	PUNCT
bibechana-9308	81	1	but	but	CCONJ
bibechana-9308	81	2	when	when	SCONJ
bibechana-9308	81	3	the	the	DET
bibechana-9308	81	4	sequences	sequence	NOUN
bibechana-9308	81	5	uk	uk	PROPN
bibechana-9308	81	6	and	and	CCONJ
bibechana-9308	81	7	vk	vk	NOUN
bibechana-9308	81	8	occur	occur	VERB
bibechana-9308	81	9	,	,	PUNCT
bibechana-9308	81	10	then	then	ADV
bibechana-9308	81	11	to	to	PART
bibechana-9308	81	12	distinguish	distinguish	VERB
bibechana-9308	81	13	l	l	NOUN
bibechana-9308	81	14	we	we	PRON
bibechana-9308	81	15	use	use	VERB
bibechana-9308	81	16	the	the	DET
bibechana-9308	81	17	notations	notation	NOUN
bibechana-9308	81	18	l(u	l(u	PROPN
bibechana-9308	81	19	)	)	PUNCT
bibechana-9308	81	20	and	and	CCONJ
bibechana-9308	81	21	l(v	l(v	NOUN
bibechana-9308	81	22	)	)	PUNCT
bibechana-9308	81	23	respectively	respectively	ADV
bibechana-9308	81	24	.	.	PUNCT
bibechana-9308	82	1	theorem	theorem	VERB
bibechana-9308	82	2	3.1	3.1	NUM
bibechana-9308	82	3	:	:	PUNCT
bibechana-9308	82	4	for	for	ADP
bibechana-9308	82	5	any	any	DET
bibechana-9308	82	6	u	u	NOUN
bibechana-9308	82	7	–	–	PUNCT
bibechana-9308	82	8	=	=	SYM
bibechana-9308	82	9	(	(	PUNCT
bibechana-9308	82	10	uk	uk	PROPN
bibechana-9308	82	11	)	)	PUNCT
bibechana-9308	82	12	,	,	PUNCT
bibechana-9308	82	13	c0	c0	X
bibechana-9308	82	14	(	(	PUNCT
bibechana-9308	82	15	s	s	PROPN
bibechana-9308	82	16	,	,	PUNCT
bibechana-9308	82	17	α	α	PROPN
bibechana-9308	82	18	–	–	PUNCT
bibechana-9308	82	19	,	,	PUNCT
bibechana-9308	82	20	u	u	INTJ
bibechana-9308	82	21	–	–	PUNCT
bibechana-9308	82	22	,	,	PUNCT
bibechana-9308	82	23	||	||	PROPN
bibechana-9308	82	24	.	.	PUNCT
bibechana-9308	82	25	,	,	PUNCT
bibechana-9308	82	26	.||	.||	PROPN
bibechana-9308	82	27	)	)	PUNCT
bibechana-9308	83	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	83	2	c0	c0	NOUN
bibechana-9308	83	3	(	(	PUNCT
bibechana-9308	83	4	s	s	PROPN
bibechana-9308	83	5	,	,	PUNCT
bibechana-9308	83	6	β	β	X
bibechana-9308	83	7	–	–	PUNCT
bibechana-9308	83	8	,	,	PUNCT
bibechana-9308	83	9	u	u	INTJ
bibechana-9308	83	10	–	–	PUNCT
bibechana-9308	83	11	,	,	PUNCT
bibechana-9308	83	12	||	||	PROPN
bibechana-9308	83	13	.	.	PUNCT
bibechana-9308	83	14	,	,	PUNCT
bibechana-9308	83	15	.||	.||	PROPN
bibechana-9308	83	16	)	)	PUNCT
bibechana-9308	84	1	if	if	SCONJ
bibechana-9308	84	2	and	and	CCONJ
bibechana-9308	84	3	only	only	ADV
bibechana-9308	84	4	if	if	SCONJ
bibechana-9308	84	5	lim	lim	PROPN
bibechana-9308	84	6	inf	inf	PROPN
bibechana-9308	84	7	k	k	PROPN
bibechana-9308	84	8			PROPN
bibechana-9308	84	9			PROPN
bibechana-9308	84	10			PROPN
bibechana-9308	84	11	αk	αk	ADP
bibechana-9308	84	12	βk	βk	ADP
bibechana-9308	84	13	uk	uk	PROPN
bibechana-9308	84	14	>	>	X
bibechana-9308	84	15	0	0	X
bibechana-9308	84	16	.	.	PUNCT
bibechana-9308	85	1	proof	proof	NOUN
bibechana-9308	85	2	:	:	PUNCT
bibechana-9308	85	3	n.p	n.p	PROPN
bibechana-9308	85	4	.	.	PROPN
bibechana-9308	85	5	pahari	pahari	PROPN
bibechana-9308	85	6	/	/	SYM
bibechana-9308	85	7	bibechana	bibechana	NOUN
bibechana-9308	85	8	10	10	NUM
bibechana-9308	85	9	(	(	PUNCT
bibechana-9308	85	10	2014	2014	NUM
bibechana-9308	85	11	)	)	PUNCT
bibechana-9308	85	12	20	20	NUM
bibechana-9308	85	13	-	-	SYM
bibechana-9308	85	14	30	30	NUM
bibechana-9308	85	15	:	:	PUNCT
bibechana-9308	85	16	bmhss	bmhss	PROPN
bibechana-9308	85	17	,	,	PUNCT
bibechana-9308	85	18	p.23	p.23	PROPN
bibechana-9308	85	19	(	(	PUNCT
bibechana-9308	85	20	online	online	ADJ
bibechana-9308	85	21	publication	publication	NOUN
bibechana-9308	85	22	:	:	PUNCT
bibechana-9308	85	23	dec	dec	PROPN
bibechana-9308	85	24	.	.	PROPN
bibechana-9308	85	25	,	,	PUNCT
bibechana-9308	85	26	2013	2013	NUM
bibechana-9308	85	27	)	)	PUNCT
bibechana-9308	85	28	for	for	ADP
bibechana-9308	85	29	the	the	DET
bibechana-9308	85	30	necessity	necessity	NOUN
bibechana-9308	85	31	,	,	PUNCT
bibechana-9308	85	32	assume	assume	VERB
bibechana-9308	85	33	that	that	SCONJ
bibechana-9308	85	34	c0	c0	PROPN
bibechana-9308	85	35	(	(	PUNCT
bibechana-9308	85	36	s	s	PROPN
bibechana-9308	85	37	,	,	PUNCT
bibechana-9308	85	38	α	α	PROPN
bibechana-9308	85	39	–	–	PUNCT
bibechana-9308	85	40	,	,	PUNCT
bibechana-9308	85	41	u	u	NOUN
bibechana-9308	85	42	–	–	PUNCT
bibechana-9308	85	43	,	,	PUNCT
bibechana-9308	85	44	||	||	PROPN
bibechana-9308	85	45	.	.	PUNCT
bibechana-9308	85	46	,	,	PUNCT
bibechana-9308	85	47	.||	.||	PROPN
bibechana-9308	85	48	)	)	PUNCT
bibechana-9308	86	1	⊂	⊂	PROPN
bibechana-9308	86	2	c0	c0	PROPN
bibechana-9308	86	3	(	(	PUNCT
bibechana-9308	86	4	s	s	PROPN
bibechana-9308	86	5	,	,	PUNCT
bibechana-9308	86	6	β	β	X
bibechana-9308	86	7	–	–	PUNCT
bibechana-9308	86	8	,	,	PUNCT
bibechana-9308	86	9	u	u	NOUN
bibechana-9308	86	10	–	–	PUNCT
bibechana-9308	86	11	,	,	PUNCT
bibechana-9308	86	12	||	||	PROPN
bibechana-9308	86	13	.	.	PUNCT
bibechana-9308	86	14	,	,	PUNCT
bibechana-9308	86	15	.||	.||	PROPN
bibechana-9308	86	16	)	)	PUNCT
bibechana-9308	86	17	but	but	CCONJ
bibechana-9308	86	18	lim	lim	PROPN
bibechana-9308	86	19	infk	infk	PROPN
bibechana-9308	86	20			PROPN
bibechana-9308	86	21			PROPN
bibechana-9308	86	22			PROPN
bibechana-9308	86	23	αk	αk	ADP
bibechana-9308	86	24	βk	βk	ADP
bibechana-9308	86	25	uk	uk	PROPN
bibechana-9308	86	26	=	=	SYM
bibechana-9308	86	27	0	0	PROPN
bibechana-9308	86	28	.	.	PUNCT
bibechana-9308	87	1	then	then	ADV
bibechana-9308	87	2	we	we	PRON
bibechana-9308	87	3	can	can	AUX
bibechana-9308	87	4	find	find	VERB
bibechana-9308	87	5	a	a	DET
bibechana-9308	87	6	sequence	sequence	NOUN
bibechana-9308	87	7	(	(	PUNCT
bibechana-9308	87	8	k(n	k(n	PROPN
bibechana-9308	87	9	)	)	PUNCT
bibechana-9308	87	10	)	)	PUNCT
bibechana-9308	87	11	of	of	ADP
bibechana-9308	87	12	integers	integer	NOUN
bibechana-9308	87	13	such	such	ADJ
bibechana-9308	87	14	that	that	SCONJ
bibechana-9308	87	15	1	1	NUM
bibechana-9308	87	16	≤	≤	NUM
bibechana-9308	87	17	k(n	k(n	X
bibechana-9308	87	18	)	)	PUNCT
bibechana-9308	87	19	<	<	X
bibechana-9308	87	20	k(n	k(n	PROPN
bibechana-9308	87	21	+1	+1	PROPN
bibechana-9308	87	22	)	)	PUNCT
bibechana-9308	87	23	,	,	PUNCT
bibechana-9308	87	24	n	n	X
bibechana-9308	87	25	≥	≥	NOUN
bibechana-9308	87	26	1	1	NUM
bibechana-9308	87	27	for	for	ADP
bibechana-9308	87	28	which	which	PRON
bibechana-9308	87	29	n	n	NOUN
bibechana-9308	87	30	2	2	NUM
bibechana-9308	87	31	|αk(n	|αk(n	NOUN
bibechana-9308	87	32	)	)	PUNCT
bibechana-9308	87	33	|	|	ADV
bibechana-9308	87	34	uk(n	uk(n	PRON
bibechana-9308	87	35	)	)	PUNCT
bibechana-9308	87	36	<	<	X
bibechana-9308	87	37	|βk(n)|	|βk(n)|	PROPN
bibechana-9308	87	38	uk(n	uk(n	X
bibechana-9308	87	39	)	)	PUNCT
bibechana-9308	87	40	,	,	PUNCT
bibechana-9308	87	41	for	for	ADP
bibechana-9308	87	42	all	all	DET
bibechana-9308	87	43	n	n	DET
bibechana-9308	87	44	≥	≥	NOUN
bibechana-9308	87	45	1	1	NUM
bibechana-9308	87	46	.	.	PUNCT
bibechana-9308	87	47	...	...	PUNCT
bibechana-9308	88	1	(	(	PUNCT
bibechana-9308	88	2	3.1	3.1	NUM
bibechana-9308	88	3	)	)	PUNCT
bibechana-9308	88	4	now	now	ADV
bibechana-9308	88	5	,	,	PUNCT
bibechana-9308	88	6	corresponding	correspond	VERB
bibechana-9308	88	7	to	to	ADP
bibechana-9308	88	8	ρ	ρ	PROPN
bibechana-9308	88	9	∈	∈	PROPN
bibechana-9308	88	10	s	s	PART
bibechana-9308	88	11	and	and	CCONJ
bibechana-9308	88	12	ρ	ρ	NOUN
bibechana-9308	88	13	≠	≠	PROPN
bibechana-9308	88	14	θ	θ	PROPN
bibechana-9308	88	15	,	,	PUNCT
bibechana-9308	88	16	we	we	PRON
bibechana-9308	88	17	define	define	VERB
bibechana-9308	88	18	the	the	DET
bibechana-9308	88	19	sequence	sequence	NOUN
bibechana-9308	88	20	ξ	ξ	PROPN
bibechana-9308	88	21	–	–	PUNCT
bibechana-9308	88	22	=	=	SYM
bibechana-9308	88	23	(	(	PUNCT
bibechana-9308	88	24	ξk	ξk	ADP
bibechana-9308	88	25	)	)	PUNCT
bibechana-9308	88	26	by	by	ADP
bibechana-9308	88	27	ξk	ξk	ADV
bibechana-9308	88	28	=	=	ADJ
bibechana-9308	88	29			NOUN
bibechana-9308	88	30			ADJ
bibechana-9308	88	31	αk(n	αk(n	NOUN
bibechana-9308	88	32	)	)	PUNCT
bibechana-9308	88	33	-1	-1	PUNCT
bibechana-9308	88	34	n-2	n-2	PROPN
bibechana-9308	88	35	/	/	SYM
bibechana-9308	88	36	uk(n	uk(n	NUM
bibechana-9308	88	37	)	)	PUNCT
bibechana-9308	89	1	ρ	ρ	X
bibechana-9308	89	2	‚	‚	NOUN
bibechana-9308	89	3	if	if	SCONJ
bibechana-9308	89	4	k	k	PROPN
bibechana-9308	89	5	=	=	SYM
bibechana-9308	89	6	k(n	k(n	X
bibechana-9308	89	7	)	)	PUNCT
bibechana-9308	89	8	‚	‚	NOUN
bibechana-9308	89	9	n	n	PRON
bibechana-9308	89	10	≥1	≥1	NUM
bibechana-9308	89	11	and	and	CCONJ
bibechana-9308	89	12	θ	θ	NOUN
bibechana-9308	89	13	‚	‚	NOUN
bibechana-9308	89	14	otherwise	otherwise	ADV
bibechana-9308	89	15	.	.	PUNCT
bibechana-9308	90	1	...	...	PUNCT
bibechana-9308	90	2	(	(	PUNCT
bibechana-9308	90	3	3.2	3.2	NUM
bibechana-9308	90	4	)	)	PUNCT
bibechana-9308	90	5	then	then	ADV
bibechana-9308	90	6	for	for	ADP
bibechana-9308	90	7	k	k	PROPN
bibechana-9308	90	8	=	=	SYM
bibechana-9308	90	9	k(n	k(n	PROPN
bibechana-9308	90	10	)	)	PUNCT
bibechana-9308	90	11	,	,	PUNCT
bibechana-9308	90	12	n	n	PRON
bibechana-9308	90	13	≥	≥	NOUN
bibechana-9308	90	14	1	1	NUM
bibechana-9308	90	15	,	,	PUNCT
bibechana-9308	90	16	we	we	PRON
bibechana-9308	90	17	have	have	VERB
bibechana-9308	90	18	||	||	NOUN
bibechana-9308	91	1	αk	αk	ADP
bibechana-9308	91	2	ξk	ξk	ADP
bibechana-9308	91	3	‚	‚	NUM
bibechana-9308	91	4	η||	η||	NOUN
bibechana-9308	91	5	uk	uk	NOUN
bibechana-9308	91	6	=	=	SYM
bibechana-9308	91	7	||n-2	||n-2	NOUN
bibechana-9308	91	8	/	/	SYM
bibechana-9308	91	9	uk(n	uk(n	NUM
bibechana-9308	91	10	)	)	PUNCT
bibechana-9308	91	11	ρ	ρ	PROPN
bibechana-9308	91	12	‚	‚	PROPN
bibechana-9308	91	13	η	η	PROPN
bibechana-9308	91	14	||	||	PROPN
bibechana-9308	91	15	uk(n	uk(n	NUM
bibechana-9308	91	16	)	)	PUNCT
bibechana-9308	91	17	≤	≤	NUM
bibechana-9308	91	18	1	1	NUM
bibechana-9308	91	19	n2	n2	NOUN
bibechana-9308	91	20	||ρ	||ρ	PROPN
bibechana-9308	91	21	‚	‚	PROPN
bibechana-9308	91	22	η	η	PROPN
bibechana-9308	91	23	||	||	PROPN
bibechana-9308	91	24	uk(n	uk(n	NUM
bibechana-9308	91	25	)	)	PUNCT
bibechana-9308	91	26	≤	≤	NUM
bibechana-9308	91	27	1	1	NUM
bibechana-9308	91	28	n2	n2	NOUN
bibechana-9308	91	29	a	a	DET
bibechana-9308	91	30	[	[	PUNCT
bibechana-9308	91	31	||ρ	||ρ	NOUN
bibechana-9308	91	32	‚	‚	NUM
bibechana-9308	91	33	η||	η||	X
bibechana-9308	91	34	l(u	l(u	NOUN
bibechana-9308	91	35	)	)	PUNCT
bibechana-9308	91	36	]	]	PUNCT
bibechana-9308	92	1	→	→	SYM
bibechana-9308	92	2	0	0	NUM
bibechana-9308	92	3	as	as	ADP
bibechana-9308	92	4	n→	n→	ADV
bibechana-9308	92	5	∞	∞	PROPN
bibechana-9308	92	6	,	,	PUNCT
bibechana-9308	92	7	where	where	SCONJ
bibechana-9308	92	8	||ρ	||ρ	NOUN
bibechana-9308	92	9	,	,	PUNCT
bibechana-9308	92	10	η||	η||	NOUN
bibechana-9308	92	11	uk(n	uk(n	X
bibechana-9308	92	12	)	)	PUNCT
bibechana-9308	92	13	≤	≤	NOUN
bibechana-9308	92	14	a	a	DET
bibechana-9308	92	15	[	[	PUNCT
bibechana-9308	92	16	||	||	NOUN
bibechana-9308	92	17	ρ	ρ	PROPN
bibechana-9308	92	18	,	,	PUNCT
bibechana-9308	92	19	η||	η||	X
bibechana-9308	92	20	l(u	l(u	PROPN
bibechana-9308	92	21	)	)	PUNCT
bibechana-9308	92	22	]	]	PUNCT
bibechana-9308	92	23	for	for	SCONJ
bibechana-9308	92	24	each	each	DET
bibechana-9308	92	25	n	n	PRON
bibechana-9308	92	26	≥	≥	NOUN
bibechana-9308	92	27	1	1	NUM
bibechana-9308	92	28	is	be	AUX
bibechana-9308	92	29	used	use	VERB
bibechana-9308	92	30	and	and	CCONJ
bibechana-9308	92	31	||	||	NOUN
bibechana-9308	93	1	αk	αk	CCONJ
bibechana-9308	93	2	ξk	ξk	ADP
bibechana-9308	93	3	‚	‚	NUM
bibechana-9308	93	4	η||	η||	X
bibechana-9308	93	5	u	u	NOUN
bibechana-9308	93	6	k	k	NOUN
bibechana-9308	93	7	=	=	SYM
bibechana-9308	93	8	0	0	NUM
bibechana-9308	93	9	,	,	PUNCT
bibechana-9308	93	10	for	for	ADP
bibechana-9308	93	11	k	k	PROPN
bibechana-9308	93	12	≠	≠	PROPN
bibechana-9308	93	13	k(n	k(n	PROPN
bibechana-9308	93	14	)	)	PUNCT
bibechana-9308	93	15	,	,	PUNCT
bibechana-9308	93	16	n	n	X
bibechana-9308	93	17	≥	≥	NOUN
bibechana-9308	93	18	1	1	NUM
bibechana-9308	93	19	.	.	PUNCT
bibechana-9308	94	1	this	this	PRON
bibechana-9308	94	2	shows	show	VERB
bibechana-9308	94	3	that	that	SCONJ
bibechana-9308	94	4	ξ	ξ	X
bibechana-9308	94	5	–	–	PUNCT
bibechana-9308	94	6	∈	∈	PROPN
bibechana-9308	94	7	c0	c0	NOUN
bibechana-9308	94	8	(	(	PUNCT
bibechana-9308	94	9	s	s	PROPN
bibechana-9308	94	10	,	,	PUNCT
bibechana-9308	94	11	α	α	PROPN
bibechana-9308	94	12	–	–	PUNCT
bibechana-9308	94	13	,	,	PUNCT
bibechana-9308	94	14	u	u	NOUN
bibechana-9308	94	15	–	–	PUNCT
bibechana-9308	94	16	,	,	PUNCT
bibechana-9308	94	17	||	||	PROPN
bibechana-9308	94	18	.	.	PUNCT
bibechana-9308	94	19	,	,	PUNCT
bibechana-9308	94	20	.||	.||	PROPN
bibechana-9308	94	21	)	)	PUNCT
bibechana-9308	94	22	.	.	PUNCT
bibechana-9308	95	1	on	on	ADP
bibechana-9308	95	2	the	the	DET
bibechana-9308	95	3	other	other	ADJ
bibechana-9308	95	4	hand	hand	NOUN
bibechana-9308	95	5	,	,	PUNCT
bibechana-9308	95	6	let	let	VERB
bibechana-9308	95	7	us	we	PRON
bibechana-9308	95	8	choose	choose	VERB
bibechana-9308	95	9	η	η	PROPN
bibechana-9308	95	10	∈	∈	PROPN
bibechana-9308	95	11	s	s	VERB
bibechana-9308	96	1	such	such	ADJ
bibechana-9308	96	2	that	that	DET
bibechana-9308	96	3	||	||	PROPN
bibechana-9308	96	4	w	w	PROPN
bibechana-9308	96	5	,	,	PUNCT
bibechana-9308	96	6	η	η	PROPN
bibechana-9308	96	7	||	||	PROPN
bibechana-9308	97	1	=	=	SYM
bibechana-9308	98	1	1	1	X
bibechana-9308	98	2	.	.	PUNCT
bibechana-9308	98	3	then	then	ADV
bibechana-9308	98	4	for	for	ADP
bibechana-9308	98	5	k	k	PROPN
bibechana-9308	98	6	=	=	SYM
bibechana-9308	98	7	k(n	k(n	PROPN
bibechana-9308	98	8	)	)	PUNCT
bibechana-9308	98	9	,	,	PUNCT
bibechana-9308	98	10	n	n	PRON
bibechana-9308	98	11	≥	≥	NOUN
bibechana-9308	98	12	1	1	NUM
bibechana-9308	98	13	,	,	PUNCT
bibechana-9308	98	14	and	and	CCONJ
bibechana-9308	98	15	in	in	ADP
bibechana-9308	98	16	view	view	NOUN
bibechana-9308	98	17	of	of	ADP
bibechana-9308	98	18	(	(	PUNCT
bibechana-9308	98	19	3.1	3.1	NUM
bibechana-9308	98	20	)	)	PUNCT
bibechana-9308	98	21	and	and	CCONJ
bibechana-9308	98	22	(	(	PUNCT
bibechana-9308	98	23	3.2	3.2	NUM
bibechana-9308	98	24	)	)	PUNCT
bibechana-9308	98	25	,	,	PUNCT
bibechana-9308	98	26	we	we	PRON
bibechana-9308	98	27	have	have	VERB
bibechana-9308	98	28	||	||	NOUN
bibechana-9308	98	29	βk	βk	ADP
bibechana-9308	98	30	ξk	ξk	ADP
bibechana-9308	98	31	‚	‚	NOUN
bibechana-9308	98	32	η||	η||	NOUN
bibechana-9308	98	33	uk	uk	NOUN
bibechana-9308	98	34	=	=	PUNCT
bibechana-9308	98	35	||	||	PROPN
bibechana-9308	98	36	β	β	X
bibechana-9308	98	37	k(n	k(n	X
bibechana-9308	98	38	)	)	PUNCT
bibechana-9308	98	39	ξ	ξ	X
bibechana-9308	98	40	k(n	k(n	PROPN
bibechana-9308	98	41	)	)	PUNCT
bibechana-9308	98	42	‚	‚	X
bibechana-9308	98	43	η	η	PROPN
bibechana-9308	98	44	||	||	PROPN
bibechana-9308	98	45	u	u	PROPN
bibechana-9308	98	46	k(n	k(n	X
bibechana-9308	98	47	)	)	PUNCT
bibechana-9308	98	48	=	=	SYM
bibechana-9308	98	49	1	1	NUM
bibechana-9308	98	50	n	n	NUM
bibechana-9308	98	51	2	2	NUM
bibechana-9308	98	52	||	||	NOUN
bibechana-9308	98	53	w	w	PROPN
bibechana-9308	98	54	‚	‚	PROPN
bibechana-9308	98	55	η||uk(n	η||uk(n	NOUN
bibechana-9308	98	56	)	)	PUNCT
bibechana-9308	98	57			PROPN
bibechana-9308	98	58			PROPN
bibechana-9308	98	59			PROPN
bibechana-9308	98	60	αk(n	αk(n	X
bibechana-9308	98	61	)	)	PUNCT
bibechana-9308	98	62	βk	βk	ADP
bibechana-9308	98	63	(	(	PUNCT
bibechana-9308	98	64	n	n	CCONJ
bibechana-9308	98	65	)	)	PUNCT
bibechana-9308	98	66	uk(n	uk(n	NUM
bibechana-9308	98	67	)	)	PUNCT
bibechana-9308	98	68	≥	≥	NOUN
bibechana-9308	99	1	1	1	NUM
bibechana-9308	99	2	.	.	PUNCT
bibechana-9308	100	1	this	this	PRON
bibechana-9308	100	2	shows	show	VERB
bibechana-9308	100	3	that	that	SCONJ
bibechana-9308	100	4	ξ	ξ	X
bibechana-9308	100	5	–	–	PUNCT
bibechana-9308	100	6	∉	∉	PROPN
bibechana-9308	100	7	c0	c0	X
bibechana-9308	100	8	(	(	PUNCT
bibechana-9308	100	9	s	s	PROPN
bibechana-9308	100	10	,	,	PUNCT
bibechana-9308	100	11	β	β	X
bibechana-9308	100	12	–	–	PUNCT
bibechana-9308	100	13	,	,	PUNCT
bibechana-9308	100	14	u–,||	u–,||	PROPN
bibechana-9308	100	15	.	.	PUNCT
bibechana-9308	100	16	,	,	PUNCT
bibechana-9308	100	17	.||	.||	PROPN
bibechana-9308	100	18	)	)	PUNCT
bibechana-9308	100	19	,	,	PUNCT
bibechana-9308	100	20	a	a	DET
bibechana-9308	100	21	contradiction	contradiction	NOUN
bibechana-9308	100	22	.	.	PUNCT
bibechana-9308	101	1	for	for	ADP
bibechana-9308	101	2	the	the	DET
bibechana-9308	101	3	sufficiency	sufficiency	NOUN
bibechana-9308	101	4	,	,	PUNCT
bibechana-9308	101	5	assume	assume	VERB
bibechana-9308	101	6	that	that	SCONJ
bibechana-9308	101	7	lim	lim	PROPN
bibechana-9308	101	8	infk	infk	PROPN
bibechana-9308	101	9			PROPN
bibechana-9308	101	10			PROPN
bibechana-9308	101	11			PROPN
bibechana-9308	101	12	αk	αk	ADP
bibechana-9308	101	13	βk	βk	ADP
bibechana-9308	101	14	uk	uk	PROPN
bibechana-9308	101	15	>	>	X
bibechana-9308	101	16	0.then	0.then	PUNCT
bibechana-9308	101	17	there	there	PRON
bibechana-9308	101	18	exists	exist	VERB
bibechana-9308	101	19	m	m	VERB
bibechana-9308	101	20	>	>	X
bibechana-9308	101	21	0	0	NUM
bibechana-9308	101	22	such	such	ADJ
bibechana-9308	101	23	that	that	SCONJ
bibechana-9308	101	24	m	m	VERB
bibechana-9308	101	25	|βk|	|βk|	PROPN
bibechana-9308	101	26	uk	uk	PROPN
bibechana-9308	101	27	<	<	X
bibechana-9308	101	28	|αk	|αk	ADP
bibechana-9308	101	29	|	|	ADV
bibechana-9308	101	30	uk	uk	PROPN
bibechana-9308	101	31	for	for	ADP
bibechana-9308	101	32	all	all	DET
bibechana-9308	101	33	sufficiently	sufficiently	ADV
bibechana-9308	101	34	large	large	ADJ
bibechana-9308	101	35	values	value	NOUN
bibechana-9308	101	36	of	of	ADP
bibechana-9308	101	37	k.	k.	PROPN
bibechana-9308	101	38	let	let	VERB
bibechana-9308	101	39	ξ	ξ	X
bibechana-9308	101	40	–	–	PUNCT
bibechana-9308	101	41	=	=	SYM
bibechana-9308	101	42	(	(	PUNCT
bibechana-9308	101	43	ξk	ξk	NOUN
bibechana-9308	101	44	)	)	PUNCT
bibechana-9308	101	45	∈	∈	PROPN
bibechana-9308	101	46	c0	c0	NOUN
bibechana-9308	101	47	(	(	PUNCT
bibechana-9308	101	48	x	x	X
bibechana-9308	101	49	,	,	PUNCT
bibechana-9308	101	50	α	α	PROPN
bibechana-9308	101	51	–	–	PUNCT
bibechana-9308	101	52	,	,	PUNCT
bibechana-9308	101	53	u	u	NOUN
bibechana-9308	101	54	–	–	PUNCT
bibechana-9308	101	55	,	,	PUNCT
bibechana-9308	101	56	||	||	PROPN
bibechana-9308	101	57	.	.	PUNCT
bibechana-9308	101	58	,	,	PUNCT
bibechana-9308	101	59	.||	.||	PROPN
bibechana-9308	101	60	)	)	PUNCT
bibechana-9308	101	61	.	.	PUNCT
bibechana-9308	102	1	then	then	ADV
bibechana-9308	102	2	for	for	ADP
bibechana-9308	102	3	each	each	DET
bibechana-9308	102	4	η	η	PROPN
bibechana-9308	102	5	∈s	∈s	PROPN
bibechana-9308	102	6	,	,	PUNCT
bibechana-9308	102	7	||	||	NOUN
bibechana-9308	102	8	αk	αk	CCONJ
bibechana-9308	103	1	ξk	ξk	ADP
bibechana-9308	103	2	‚	‚	NUM
bibechana-9308	103	3	η||	η||	X
bibechana-9308	103	4	u	u	NOUN
bibechana-9308	103	5	k	k	PROPN
bibechana-9308	103	6	→	→	SYM
bibechana-9308	103	7	0	0	PUNCT
bibechana-9308	103	8	as	as	ADP
bibechana-9308	103	9	k→	k→	PROPN
bibechana-9308	103	10	∞	∞	PROPN
bibechana-9308	103	11	.	.	PUNCT
bibechana-9308	104	1	now	now	ADV
bibechana-9308	104	2	for	for	SCONJ
bibechana-9308	104	3	each	each	DET
bibechana-9308	104	4	η	η	PROPN
bibechana-9308	104	5	∈	∈	PROPN
bibechana-9308	104	6	s	s	PROPN
bibechana-9308	104	7	,	,	PUNCT
bibechana-9308	104	8	||βk	||βk	NOUN
bibechana-9308	104	9	ξk	ξk	ADP
bibechana-9308	104	10	‚	‚	NUM
bibechana-9308	104	11	η||	η||	NOUN
bibechana-9308	104	12	uk	uk	PROPN
bibechana-9308	104	13	≤	≤	NUM
bibechana-9308	104	14	|αk|	|αk|	PROPN
bibechana-9308	104	15	uk	uk	PROPN
bibechana-9308	104	16	m	m	PROPN
bibechana-9308	104	17	||ξk	||ξk	NOUN
bibechana-9308	104	18	‚	‚	NOUN
bibechana-9308	104	19	η||	η||	NOUN
bibechana-9308	104	20	uk	uk	PROPN
bibechana-9308	104	21	≤	≤	NOUN
bibechana-9308	104	22	1	1	NUM
bibechana-9308	104	23	m	m	NOUN
bibechana-9308	104	24	||	||	NOUN
bibechana-9308	105	1	αk	αk	ADP
bibechana-9308	106	1	ξk	ξk	ADP
bibechana-9308	106	2	‚	‚	NUM
bibechana-9308	106	3	η||	η||	X
bibechana-9308	106	4	uk	uk	PROPN
bibechana-9308	106	5	→	→	SYM
bibechana-9308	106	6	0	0	PROPN
bibechana-9308	106	7	as	as	SCONJ
bibechana-9308	106	8	k	k	PROPN
bibechana-9308	106	9	→	→	SYM
bibechana-9308	106	10	∞.	∞.	PROPN
bibechana-9308	106	11	this	this	PRON
bibechana-9308	106	12	clearly	clearly	ADV
bibechana-9308	106	13	implies	imply	VERB
bibechana-9308	106	14	that	that	SCONJ
bibechana-9308	106	15	ξ	ξ	X
bibechana-9308	106	16	–	–	PUNCT
bibechana-9308	106	17	∈	∈	PROPN
bibechana-9308	106	18	c0	c0	NOUN
bibechana-9308	106	19	(	(	PUNCT
bibechana-9308	106	20	s	s	PROPN
bibechana-9308	106	21	,	,	PUNCT
bibechana-9308	106	22	β	β	X
bibechana-9308	106	23	–	–	PUNCT
bibechana-9308	106	24	,	,	PUNCT
bibechana-9308	106	25	u	u	NOUN
bibechana-9308	106	26	–	–	PUNCT
bibechana-9308	106	27	,	,	PUNCT
bibechana-9308	106	28	||	||	PROPN
bibechana-9308	106	29	.	.	PUNCT
bibechana-9308	106	30	,	,	PUNCT
bibechana-9308	106	31	.||	.||	PROPN
bibechana-9308	106	32	)	)	PUNCT
bibechana-9308	106	33	and	and	CCONJ
bibechana-9308	106	34	hence	hence	ADV
bibechana-9308	106	35	c0	c0	PROPN
bibechana-9308	106	36	(	(	PUNCT
bibechana-9308	106	37	s	s	PROPN
bibechana-9308	106	38	,	,	PUNCT
bibechana-9308	106	39	α	α	PROPN
bibechana-9308	106	40	–	–	PUNCT
bibechana-9308	106	41	,	,	PUNCT
bibechana-9308	106	42	u	u	NOUN
bibechana-9308	106	43	–	–	PUNCT
bibechana-9308	106	44	,	,	PUNCT
bibechana-9308	106	45	||	||	PROPN
bibechana-9308	106	46	.	.	PUNCT
bibechana-9308	106	47	,	,	PUNCT
bibechana-9308	107	1	.||	.||	PROPN
bibechana-9308	107	2	)	)	PUNCT
bibechana-9308	108	1	⊂	⊂	PROPN
bibechana-9308	108	2	c0	c0	PROPN
bibechana-9308	108	3	(	(	PUNCT
bibechana-9308	108	4	s	s	PROPN
bibechana-9308	108	5	,	,	PUNCT
bibechana-9308	108	6	β	β	X
bibechana-9308	108	7	–	–	PUNCT
bibechana-9308	108	8	,	,	PUNCT
bibechana-9308	108	9	u	u	NOUN
bibechana-9308	108	10	–	–	PUNCT
bibechana-9308	108	11	,	,	PUNCT
bibechana-9308	108	12	||	||	PROPN
bibechana-9308	108	13	.	.	PUNCT
bibechana-9308	108	14	,	,	PUNCT
bibechana-9308	108	15	.||	.||	PROPN
bibechana-9308	108	16	)	)	PUNCT
bibechana-9308	108	17	.	.	PUNCT
bibechana-9308	109	1	this	this	PRON
bibechana-9308	109	2	completes	complete	VERB
bibechana-9308	109	3	the	the	DET
bibechana-9308	109	4	proof	proof	NOUN
bibechana-9308	109	5	.	.	PUNCT
bibechana-9308	110	1	theorem	theorem	VERB
bibechana-9308	110	2	3.2	3.2	NUM
bibechana-9308	110	3	:	:	PUNCT
bibechana-9308	110	4	for	for	ADP
bibechana-9308	110	5	any	any	DET
bibechana-9308	110	6	u	u	NOUN
bibechana-9308	110	7	–	–	PUNCT
bibechana-9308	110	8	=	=	SYM
bibechana-9308	110	9	(	(	PUNCT
bibechana-9308	110	10	uk	uk	PROPN
bibechana-9308	110	11	)	)	PUNCT
bibechana-9308	110	12	,	,	PUNCT
bibechana-9308	110	13	c0	c0	X
bibechana-9308	110	14	(	(	PUNCT
bibechana-9308	110	15	s	s	PROPN
bibechana-9308	110	16	,	,	PUNCT
bibechana-9308	110	17	β	β	X
bibechana-9308	110	18	–	–	PUNCT
bibechana-9308	110	19	,	,	PUNCT
bibechana-9308	110	20	u	u	INTJ
bibechana-9308	110	21	–	–	PUNCT
bibechana-9308	110	22	,	,	PUNCT
bibechana-9308	110	23	||	||	PROPN
bibechana-9308	110	24	.	.	PUNCT
bibechana-9308	110	25	,	,	PUNCT
bibechana-9308	110	26	.||	.||	PROPN
bibechana-9308	110	27	)	)	PUNCT
bibechana-9308	111	1	⊂	⊂	PROPN
bibechana-9308	111	2	⊂	⊂	PROPN
bibechana-9308	112	1	⊂	⊂	PROPN
bibechana-9308	112	2	⊂	⊂	PROPN
bibechana-9308	112	3	c0	c0	PROPN
bibechana-9308	112	4	(	(	PUNCT
bibechana-9308	112	5	s	s	PROPN
bibechana-9308	112	6	,	,	PUNCT
bibechana-9308	112	7	α	α	PROPN
bibechana-9308	112	8	–	–	PUNCT
bibechana-9308	112	9	,	,	PUNCT
bibechana-9308	112	10	u	u	NOUN
bibechana-9308	112	11	–	–	PUNCT
bibechana-9308	112	12	,	,	PUNCT
bibechana-9308	112	13	||	||	PROPN
bibechana-9308	112	14	.	.	PUNCT
bibechana-9308	112	15	,	,	PUNCT
bibechana-9308	112	16	.||	.||	PROPN
bibechana-9308	112	17	)	)	PUNCT
bibechana-9308	113	1	if	if	SCONJ
bibechana-9308	113	2	and	and	CCONJ
bibechana-9308	113	3	only	only	ADV
bibechana-9308	113	4	if	if	SCONJ
bibechana-9308	113	5	lim	lim	PROPN
bibechana-9308	113	6	supk	supk	PROPN
bibechana-9308	113	7			PROPN
bibechana-9308	113	8			PROPN
bibechana-9308	113	9			PROPN
bibechana-9308	113	10	αk	αk	ADP
bibechana-9308	113	11	βk	βk	ADP
bibechana-9308	113	12	uk	uk	PROPN
bibechana-9308	113	13	<	<	X
bibechana-9308	113	14	∞∞∞∞.	∞∞∞∞.	PROPN
bibechana-9308	113	15	n.p	n.p	PROPN
bibechana-9308	113	16	.	.	PROPN
bibechana-9308	113	17	pahari	pahari	PROPN
bibechana-9308	113	18	/	/	SYM
bibechana-9308	113	19	bibechana	bibechana	NOUN
bibechana-9308	113	20	10	10	NUM
bibechana-9308	113	21	(	(	PUNCT
bibechana-9308	113	22	2014	2014	NUM
bibechana-9308	113	23	)	)	PUNCT
bibechana-9308	113	24	20	20	NUM
bibechana-9308	113	25	-	-	SYM
bibechana-9308	113	26	30	30	NUM
bibechana-9308	113	27	:	:	PUNCT
bibechana-9308	113	28	bmhss	bmhss	PROPN
bibechana-9308	113	29	,	,	PUNCT
bibechana-9308	113	30	p.24	p.24	PROPN
bibechana-9308	113	31	(	(	PUNCT
bibechana-9308	113	32	online	online	ADJ
bibechana-9308	113	33	publication	publication	NOUN
bibechana-9308	113	34	:	:	PUNCT
bibechana-9308	114	1	dec	dec	PROPN
bibechana-9308	114	2	.	.	PROPN
bibechana-9308	114	3	,	,	PUNCT
bibechana-9308	114	4	2013	2013	NUM
bibechana-9308	114	5	)	)	PUNCT
bibechana-9308	114	6	proof	proof	NOUN
bibechana-9308	114	7	:	:	PUNCT
bibechana-9308	114	8	for	for	ADP
bibechana-9308	114	9	the	the	DET
bibechana-9308	114	10	necessity	necessity	NOUN
bibechana-9308	114	11	,	,	PUNCT
bibechana-9308	114	12	suppose	suppose	VERB
bibechana-9308	114	13	that	that	SCONJ
bibechana-9308	114	14	c0	c0	PROPN
bibechana-9308	114	15	(	(	PUNCT
bibechana-9308	114	16	s	s	PROPN
bibechana-9308	114	17	,	,	PUNCT
bibechana-9308	114	18	β	β	X
bibechana-9308	114	19	–	–	PUNCT
bibechana-9308	114	20	,	,	PUNCT
bibechana-9308	114	21	u–,||	u–,||	PROPN
bibechana-9308	114	22	.	.	PUNCT
bibechana-9308	114	23	,	,	PUNCT
bibechana-9308	114	24	.||	.||	PROPN
bibechana-9308	114	25	)	)	PUNCT
bibechana-9308	114	26	⊂	⊂	PROPN
bibechana-9308	114	27	c0	c0	PROPN
bibechana-9308	114	28	(	(	PUNCT
bibechana-9308	114	29	s	s	PROPN
bibechana-9308	114	30	,	,	PUNCT
bibechana-9308	114	31	α	α	PROPN
bibechana-9308	114	32	–	–	PUNCT
bibechana-9308	114	33	,	,	PUNCT
bibechana-9308	114	34	u	u	NOUN
bibechana-9308	114	35	–	–	PUNCT
bibechana-9308	114	36	,	,	PUNCT
bibechana-9308	114	37	||	||	PROPN
bibechana-9308	114	38	.	.	PUNCT
bibechana-9308	114	39	,	,	PUNCT
bibechana-9308	114	40	.||	.||	PROPN
bibechana-9308	114	41	)	)	PUNCT
bibechana-9308	115	1	but	but	CCONJ
bibechana-9308	115	2	lim	lim	PROPN
bibechana-9308	115	3	supk	supk	PROPN
bibechana-9308	115	4			PROPN
bibechana-9308	115	5			PROPN
bibechana-9308	115	6			PROPN
bibechana-9308	115	7	αk	αk	ADP
bibechana-9308	115	8	βk	βk	ADP
bibechana-9308	115	9	uk	uk	PROPN
bibechana-9308	115	10	=	=	SYM
bibechana-9308	115	11	∞.	∞.	PROPN
bibechana-9308	115	12	then	then	ADV
bibechana-9308	115	13	there	there	PRON
bibechana-9308	115	14	exists	exist	VERB
bibechana-9308	115	15	a	a	DET
bibechana-9308	115	16	sequence	sequence	NOUN
bibechana-9308	115	17	(	(	PUNCT
bibechana-9308	115	18	k(n	k(n	PROPN
bibechana-9308	115	19	)	)	PUNCT
bibechana-9308	115	20	)	)	PUNCT
bibechana-9308	115	21	of	of	ADP
bibechana-9308	115	22	positive	positive	ADJ
bibechana-9308	115	23	integers	integer	NOUN
bibechana-9308	115	24	with	with	ADP
bibechana-9308	115	25	1	1	NUM
bibechana-9308	115	26	≤	≤	NUM
bibechana-9308	115	27	k(n	k(n	X
bibechana-9308	115	28	)	)	PUNCT
bibechana-9308	115	29	<	<	X
bibechana-9308	115	30	k(n	k(n	PROPN
bibechana-9308	115	31	+	+	CCONJ
bibechana-9308	115	32	1	1	NUM
bibechana-9308	115	33	)	)	PUNCT
bibechana-9308	115	34	,	,	PUNCT
bibechana-9308	116	1	n	n	X
bibechana-9308	116	2	≥	≥	NOUN
bibechana-9308	116	3	1	1	NUM
bibechana-9308	116	4	satisfying	satisfy	VERB
bibechana-9308	116	5	|αk(n)|	|αk(n)|	PROPN
bibechana-9308	116	6	uk(n	uk(n	X
bibechana-9308	116	7	)	)	PUNCT
bibechana-9308	116	8	>	>	PUNCT
bibechana-9308	116	9	n2	n2	ADJ
bibechana-9308	116	10	|βk(n)|	|βk(n)|	PROPN
bibechana-9308	116	11	uk(n	uk(n	X
bibechana-9308	116	12	)	)	PUNCT
bibechana-9308	116	13	,	,	PUNCT
bibechana-9308	116	14	for	for	ADP
bibechana-9308	116	15	each	each	DET
bibechana-9308	116	16	n	n	PRON
bibechana-9308	116	17	≥	≥	NOUN
bibechana-9308	116	18	1	1	NUM
bibechana-9308	116	19	.	.	PUNCT
bibechana-9308	116	20	...	...	PUNCT
bibechana-9308	117	1	(	(	PUNCT
bibechana-9308	117	2	3.3	3.3	NUM
bibechana-9308	117	3	)	)	PUNCT
bibechana-9308	117	4	corresponding	correspond	VERB
bibechana-9308	117	5	to	to	ADP
bibechana-9308	117	6	ρ	ρ	PROPN
bibechana-9308	117	7	∈	∈	PROPN
bibechana-9308	117	8	s	s	PART
bibechana-9308	117	9	and	and	CCONJ
bibechana-9308	117	10	ρ	ρ	NOUN
bibechana-9308	117	11	≠	≠	PROPN
bibechana-9308	117	12	θ	θ	PROPN
bibechana-9308	117	13	,	,	PUNCT
bibechana-9308	117	14	we	we	PRON
bibechana-9308	117	15	define	define	VERB
bibechana-9308	117	16	a	a	DET
bibechana-9308	117	17	sequence	sequence	NOUN
bibechana-9308	117	18	ξ	ξ	NOUN
bibechana-9308	117	19	–	–	PUNCT
bibechana-9308	117	20	=	=	SYM
bibechana-9308	117	21	(	(	PUNCT
bibechana-9308	117	22	ξk	ξk	NOUN
bibechana-9308	117	23	)	)	PUNCT
bibechana-9308	117	24	by	by	ADP
bibechana-9308	117	25	ξk	ξk	ADV
bibechana-9308	117	26	=	=	ADJ
bibechana-9308	117	27			NOUN
bibechana-9308	117	28			ADJ
bibechana-9308	117	29	βk(n	βk(n	NOUN
bibechana-9308	117	30	)	)	PUNCT
bibechana-9308	117	31	-1	-1	PUNCT
bibechana-9308	117	32	n-2	n-2	PROPN
bibechana-9308	117	33	/	/	SYM
bibechana-9308	117	34	uk(n	uk(n	NUM
bibechana-9308	117	35	)	)	PUNCT
bibechana-9308	118	1	ρ	ρ	X
bibechana-9308	118	2	‚	‚	NOUN
bibechana-9308	118	3	if	if	SCONJ
bibechana-9308	118	4	k	k	PROPN
bibechana-9308	118	5	=	=	SYM
bibechana-9308	118	6	k(n	k(n	X
bibechana-9308	118	7	)	)	PUNCT
bibechana-9308	118	8	‚	‚	NOUN
bibechana-9308	118	9	n	n	CCONJ
bibechana-9308	118	10	≥1	≥1	NUM
bibechana-9308	118	11	and	and	CCONJ
bibechana-9308	118	12	θ	θ	NOUN
bibechana-9308	118	13	‚	‚	NOUN
bibechana-9308	118	14	otherwise	otherwise	ADV
bibechana-9308	118	15	.	.	PUNCT
bibechana-9308	119	1	...	...	PUNCT
bibechana-9308	119	2	(	(	PUNCT
bibechana-9308	119	3	3.4	3.4	NUM
bibechana-9308	119	4	)	)	PUNCT
bibechana-9308	119	5	then	then	ADV
bibechana-9308	119	6	for	for	ADP
bibechana-9308	119	7	k	k	PROPN
bibechana-9308	119	8	=	=	SYM
bibechana-9308	119	9	k(n	k(n	PROPN
bibechana-9308	119	10	)	)	PUNCT
bibechana-9308	119	11	,	,	PUNCT
bibechana-9308	119	12	n	n	PRON
bibechana-9308	119	13	≥	≥	NOUN
bibechana-9308	119	14	1	1	NUM
bibechana-9308	119	15	,	,	PUNCT
bibechana-9308	119	16	we	we	PRON
bibechana-9308	119	17	have	have	VERB
bibechana-9308	119	18	||	||	NOUN
bibechana-9308	119	19	βk	βk	ADP
bibechana-9308	119	20	ξk	ξk	ADP
bibechana-9308	119	21	‚	‚	NOUN
bibechana-9308	119	22	η||	η||	NOUN
bibechana-9308	119	23	uk	uk	NOUN
bibechana-9308	119	24	=	=	PUNCT
bibechana-9308	120	1	||	||	PROPN
bibechana-9308	120	2	β	β	X
bibechana-9308	120	3	k(n	k(n	X
bibechana-9308	120	4	)	)	PUNCT
bibechana-9308	121	1	ξ	ξ	X
bibechana-9308	121	2	k(n	k(n	PROPN
bibechana-9308	121	3	)	)	PUNCT
bibechana-9308	121	4	‚	‚	X
bibechana-9308	121	5	η	η	PROPN
bibechana-9308	121	6	||	||	PROPN
bibechana-9308	121	7	u	u	PROPN
bibechana-9308	121	8	k(n	k(n	X
bibechana-9308	121	9	)	)	PUNCT
bibechana-9308	121	10	=	=	PUNCT
bibechana-9308	121	11	||n-2	||n-2	X
bibechana-9308	121	12	/	/	SYM
bibechana-9308	121	13	uk(n	uk(n	NUM
bibechana-9308	121	14	)	)	PUNCT
bibechana-9308	121	15	ρ	ρ	PROPN
bibechana-9308	121	16	‚	‚	PROPN
bibechana-9308	121	17	η	η	PROPN
bibechana-9308	121	18	||	||	PROPN
bibechana-9308	121	19	uk(n	uk(n	NUM
bibechana-9308	121	20	)	)	PUNCT
bibechana-9308	121	21	≤	≤	NUM
bibechana-9308	121	22	1	1	NUM
bibechana-9308	121	23	n2	n2	NOUN
bibechana-9308	121	24	||ρ	||ρ	PROPN
bibechana-9308	121	25	‚	‚	PROPN
bibechana-9308	121	26	η	η	PROPN
bibechana-9308	121	27	||	||	PROPN
bibechana-9308	121	28	uk(n	uk(n	NUM
bibechana-9308	121	29	)	)	PUNCT
bibechana-9308	121	30	≤	≤	NUM
bibechana-9308	121	31	1	1	NUM
bibechana-9308	121	32	n2	n2	NOUN
bibechana-9308	121	33	a	a	DET
bibechana-9308	121	34	[	[	PUNCT
bibechana-9308	121	35	||ρ	||ρ	NOUN
bibechana-9308	121	36	‚	‚	NUM
bibechana-9308	121	37	η	η	PROPN
bibechana-9308	121	38	||	||	PROPN
bibechana-9308	121	39	l(u	l(u	PROPN
bibechana-9308	121	40	)	)	PUNCT
bibechana-9308	121	41	]	]	PUNCT
bibechana-9308	122	1	→	→	SYM
bibechana-9308	122	2	0	0	NUM
bibechana-9308	122	3	as	as	ADP
bibechana-9308	122	4	n→	n→	ADV
bibechana-9308	122	5	∞	∞	PROPN
bibechana-9308	122	6	and	and	CCONJ
bibechana-9308	122	7	||βk	||βk	NOUN
bibechana-9308	122	8	ξk	ξk	ADP
bibechana-9308	122	9	‚	‚	NUM
bibechana-9308	122	10	η||	η||	NOUN
bibechana-9308	122	11	uk	uk	NOUN
bibechana-9308	122	12	=	=	SYM
bibechana-9308	122	13	0	0	NUM
bibechana-9308	122	14	,	,	PUNCT
bibechana-9308	122	15	for	for	ADP
bibechana-9308	122	16	k	k	PROPN
bibechana-9308	122	17	≠	≠	PROPN
bibechana-9308	122	18	k(n	k(n	PROPN
bibechana-9308	122	19	)	)	PUNCT
bibechana-9308	122	20	,	,	PUNCT
bibechana-9308	122	21	n	n	X
bibechana-9308	122	22	≥	≥	NOUN
bibechana-9308	122	23	1	1	NUM
bibechana-9308	122	24	.	.	PUNCT
bibechana-9308	123	1	this	this	PRON
bibechana-9308	123	2	shows	show	VERB
bibechana-9308	123	3	that	that	SCONJ
bibechana-9308	123	4	ξ	ξ	X
bibechana-9308	123	5	–	–	PUNCT
bibechana-9308	123	6	∈	∈	PROPN
bibechana-9308	123	7	c0	c0	NOUN
bibechana-9308	123	8	(	(	PUNCT
bibechana-9308	123	9	s	s	PROPN
bibechana-9308	123	10	,	,	PUNCT
bibechana-9308	123	11	β	β	X
bibechana-9308	123	12	–	–	PUNCT
bibechana-9308	123	13	,	,	PUNCT
bibechana-9308	123	14	u–,||	u–,||	PROPN
bibechana-9308	123	15	.	.	PUNCT
bibechana-9308	123	16	,	,	PUNCT
bibechana-9308	123	17	.||	.||	PROPN
bibechana-9308	123	18	)	)	PUNCT
bibechana-9308	123	19	.	.	PUNCT
bibechana-9308	124	1	on	on	ADP
bibechana-9308	124	2	the	the	DET
bibechana-9308	124	3	other	other	ADJ
bibechana-9308	124	4	hand	hand	NOUN
bibechana-9308	124	5	,	,	PUNCT
bibechana-9308	124	6	let	let	VERB
bibechana-9308	124	7	us	we	PRON
bibechana-9308	124	8	choose	choose	VERB
bibechana-9308	124	9	η	η	PROPN
bibechana-9308	124	10	∈	∈	PROPN
bibechana-9308	124	11	s	s	VERB
bibechana-9308	124	12	such	such	ADJ
bibechana-9308	124	13	that	that	DET
bibechana-9308	124	14	||ρ	||ρ	NOUN
bibechana-9308	124	15	,	,	PUNCT
bibechana-9308	124	16	η||	η||	NOUN
bibechana-9308	124	17	=	=	SYM
bibechana-9308	124	18	1	1	X
bibechana-9308	124	19	.	.	PUNCT
bibechana-9308	124	20	then	then	ADV
bibechana-9308	124	21	for	for	ADP
bibechana-9308	124	22	k	k	PROPN
bibechana-9308	124	23	=	=	SYM
bibechana-9308	124	24	k(n	k(n	PROPN
bibechana-9308	124	25	)	)	PUNCT
bibechana-9308	124	26	,	,	PUNCT
bibechana-9308	124	27	n	n	PRON
bibechana-9308	124	28	≥	≥	NOUN
bibechana-9308	124	29	1	1	NUM
bibechana-9308	124	30	,	,	PUNCT
bibechana-9308	124	31	in	in	ADP
bibechana-9308	124	32	view	view	NOUN
bibechana-9308	124	33	of	of	ADP
bibechana-9308	124	34	(	(	PUNCT
bibechana-9308	124	35	3.3	3.3	NUM
bibechana-9308	124	36	)	)	PUNCT
bibechana-9308	124	37	and	and	CCONJ
bibechana-9308	124	38	(	(	PUNCT
bibechana-9308	124	39	3.4	3.4	NUM
bibechana-9308	124	40	)	)	PUNCT
bibechana-9308	124	41	,	,	PUNCT
bibechana-9308	124	42	we	we	PRON
bibechana-9308	124	43	have	have	VERB
bibechana-9308	124	44	||	||	NOUN
bibechana-9308	125	1	αk	αk	ADP
bibechana-9308	125	2	ξk	ξk	ADP
bibechana-9308	125	3	‚	‚	NOUN
bibechana-9308	125	4	η||	η||	NOUN
bibechana-9308	125	5	uk	uk	PROPN
bibechana-9308	125	6	=	=	SYM
bibechana-9308	125	7			PROPN
bibechana-9308	125	8			PROPN
bibechana-9308	125	9			PROPN
bibechana-9308	125	10	αk(n	αk(n	X
bibechana-9308	125	11	)	)	PUNCT
bibechana-9308	125	12	βk	βk	ADP
bibechana-9308	125	13	(	(	PUNCT
bibechana-9308	125	14	n	n	CCONJ
bibechana-9308	125	15	)	)	PUNCT
bibechana-9308	125	16	uk(n	uk(n	NUM
bibechana-9308	125	17	)	)	PUNCT
bibechana-9308	125	18	.	.	PUNCT
bibechana-9308	126	1	1	1	NUM
bibechana-9308	126	2	n	n	SYM
bibechana-9308	126	3	2	2	NUM
bibechana-9308	126	4	||ρ	||ρ	NOUN
bibechana-9308	126	5	‚	‚	NUM
bibechana-9308	126	6	η||uk(n	η||uk(n	NOUN
bibechana-9308	126	7	)	)	PUNCT
bibechana-9308	126	8	≥	≥	NOUN
bibechana-9308	126	9	1	1	NUM
bibechana-9308	126	10	and	and	CCONJ
bibechana-9308	126	11	so	so	ADV
bibechana-9308	126	12	ξ	ξ	PROPN
bibechana-9308	126	13	–	–	PUNCT
bibechana-9308	126	14	∉	∉	PROPN
bibechana-9308	126	15	c0	c0	X
bibechana-9308	126	16	(	(	PUNCT
bibechana-9308	126	17	s	s	PROPN
bibechana-9308	126	18	,	,	PUNCT
bibechana-9308	126	19	α	α	PROPN
bibechana-9308	126	20	–	–	PUNCT
bibechana-9308	126	21	,	,	PUNCT
bibechana-9308	126	22	u	u	NOUN
bibechana-9308	126	23	–	–	PUNCT
bibechana-9308	126	24	,	,	PUNCT
bibechana-9308	126	25	||	||	PROPN
bibechana-9308	126	26	.	.	PUNCT
bibechana-9308	126	27	,	,	PUNCT
bibechana-9308	126	28	.||	.||	PROPN
bibechana-9308	126	29	)	)	PUNCT
bibechana-9308	126	30	,	,	PUNCT
bibechana-9308	126	31	a	a	DET
bibechana-9308	126	32	contradiction	contradiction	NOUN
bibechana-9308	126	33	.	.	PUNCT
bibechana-9308	127	1	for	for	ADP
bibechana-9308	127	2	the	the	DET
bibechana-9308	127	3	sufficiency	sufficiency	NOUN
bibechana-9308	127	4	,	,	PUNCT
bibechana-9308	127	5	assume	assume	VERB
bibechana-9308	127	6	that	that	SCONJ
bibechana-9308	127	7	lim	lim	PROPN
bibechana-9308	127	8	supk	supk	PROPN
bibechana-9308	127	9			PROPN
bibechana-9308	127	10			PROPN
bibechana-9308	127	11			PROPN
bibechana-9308	127	12	αk	αk	ADP
bibechana-9308	127	13	βk	βk	ADP
bibechana-9308	127	14	uk	uk	PROPN
bibechana-9308	127	15	<	<	X
bibechana-9308	127	16	∞.	∞.	PROPN
bibechana-9308	127	17	then	then	ADV
bibechana-9308	127	18	we	we	PRON
bibechana-9308	127	19	can	can	AUX
bibechana-9308	127	20	find	find	VERB
bibechana-9308	127	21	a	a	DET
bibechana-9308	127	22	positive	positive	ADJ
bibechana-9308	127	23	constant	constant	ADJ
bibechana-9308	127	24	d	d	NOUN
bibechana-9308	127	25	such	such	ADJ
bibechana-9308	127	26	that	that	SCONJ
bibechana-9308	127	27	d	d	PROPN
bibechana-9308	127	28	|βk|	|βk|	PROPN
bibechana-9308	127	29	uk	uk	PROPN
bibechana-9308	127	30	>	>	X
bibechana-9308	127	31	|αk|	|αk|	PROPN
bibechana-9308	127	32	uk	uk	PROPN
bibechana-9308	127	33	for	for	ADP
bibechana-9308	127	34	all	all	DET
bibechana-9308	127	35	sufficiently	sufficiently	ADV
bibechana-9308	127	36	large	large	ADJ
bibechana-9308	127	37	values	value	NOUN
bibechana-9308	127	38	of	of	ADP
bibechana-9308	127	39	k.	k.	PROPN
bibechana-9308	127	40	let	let	VERB
bibechana-9308	127	41	ξ	ξ	X
bibechana-9308	127	42	–	–	PUNCT
bibechana-9308	127	43	=	=	SYM
bibechana-9308	127	44	(	(	PUNCT
bibechana-9308	127	45	ξk	ξk	NOUN
bibechana-9308	127	46	)	)	PUNCT
bibechana-9308	127	47	∈	∈	PROPN
bibechana-9308	127	48	c0	c0	NOUN
bibechana-9308	127	49	(	(	PUNCT
bibechana-9308	127	50	s	s	PROPN
bibechana-9308	127	51	,	,	PUNCT
bibechana-9308	127	52	β	β	X
bibechana-9308	127	53	–	–	PUNCT
bibechana-9308	127	54	,	,	PUNCT
bibechana-9308	127	55	u–,||	u–,||	PROPN
bibechana-9308	127	56	.	.	PUNCT
bibechana-9308	127	57	,	,	PUNCT
bibechana-9308	127	58	.||	.||	PROPN
bibechana-9308	127	59	)	)	PUNCT
bibechana-9308	127	60	.	.	PUNCT
bibechana-9308	128	1	then	then	ADV
bibechana-9308	128	2	we	we	PRON
bibechana-9308	128	3	have	have	VERB
bibechana-9308	128	4	||βk	||βk	NOUN
bibechana-9308	128	5	ξk	ξk	ADP
bibechana-9308	128	6	‚	‚	NUM
bibechana-9308	128	7	η||	η||	NOUN
bibechana-9308	128	8	uk	uk	PROPN
bibechana-9308	128	9	→	→	SYM
bibechana-9308	128	10	0	0	PUNCT
bibechana-9308	128	11	as	as	ADP
bibechana-9308	128	12	k→	k→	PROPN
bibechana-9308	128	13	∞	∞	PROPN
bibechana-9308	128	14	,	,	PUNCT
bibechana-9308	128	15	for	for	ADP
bibechana-9308	128	16	each	each	DET
bibechana-9308	128	17	η	η	PROPN
bibechana-9308	128	18	∈s	∈s	PROPN
bibechana-9308	128	19	.	.	PUNCT
bibechana-9308	129	1	now	now	ADV
bibechana-9308	129	2	we	we	PRON
bibechana-9308	129	3	have	have	VERB
bibechana-9308	129	4	||αk	||αk	NOUN
bibechana-9308	129	5	ξk	ξk	ADP
bibechana-9308	129	6	‚	‚	PROPN
bibechana-9308	129	7	η	η	PROPN
bibechana-9308	129	8	||	||	PROPN
bibechana-9308	129	9	uk	uk	PROPN
bibechana-9308	129	10	≤	≤	PROPN
bibechana-9308	129	11	d|βk|	d|βk|	PROPN
bibechana-9308	129	12	uk	uk	PROPN
bibechana-9308	129	13	||	||	NOUN
bibechana-9308	130	1	ξk	ξk	ADP
bibechana-9308	130	2	‚	‚	NUM
bibechana-9308	130	3	η||	η||	NOUN
bibechana-9308	130	4	uk	uk	PROPN
bibechana-9308	130	5	≤	≤	NOUN
bibechana-9308	130	6	||βk	||βk	NOUN
bibechana-9308	130	7	ξk	ξk	ADP
bibechana-9308	130	8	‚	‚	NUM
bibechana-9308	130	9	η||	η||	X
bibechana-9308	130	10	uk	uk	PROPN
bibechana-9308	130	11	→	→	SYM
bibechana-9308	130	12	0	0	PUNCT
bibechana-9308	130	13	as	as	ADP
bibechana-9308	130	14	k→	k→	PROPN
bibechana-9308	130	15	∞	∞	PROPN
bibechana-9308	130	16	,	,	PUNCT
bibechana-9308	130	17	for	for	ADP
bibechana-9308	130	18	each	each	DET
bibechana-9308	130	19	η	η	PROPN
bibechana-9308	130	20	∈s	∈s	PROPN
bibechana-9308	130	21	.	.	PUNCT
bibechana-9308	131	1	this	this	PRON
bibechana-9308	131	2	clearly	clearly	ADV
bibechana-9308	131	3	implies	imply	VERB
bibechana-9308	131	4	that	that	SCONJ
bibechana-9308	131	5	ξ	ξ	X
bibechana-9308	131	6	–	–	PUNCT
bibechana-9308	131	7	∈	∈	PROPN
bibechana-9308	131	8	c0	c0	NOUN
bibechana-9308	131	9	(	(	PUNCT
bibechana-9308	131	10	s	s	PROPN
bibechana-9308	131	11	,	,	PUNCT
bibechana-9308	131	12	α	α	PROPN
bibechana-9308	131	13	–	–	PUNCT
bibechana-9308	131	14	,	,	PUNCT
bibechana-9308	131	15	u	u	NOUN
bibechana-9308	131	16	–	–	PUNCT
bibechana-9308	131	17	,	,	PUNCT
bibechana-9308	131	18	||	||	PROPN
bibechana-9308	131	19	.	.	PUNCT
bibechana-9308	131	20	,	,	PUNCT
bibechana-9308	131	21	.||	.||	PROPN
bibechana-9308	131	22	)	)	PUNCT
bibechana-9308	131	23	and	and	CCONJ
bibechana-9308	131	24	hence	hence	ADV
bibechana-9308	131	25	c0	c0	PROPN
bibechana-9308	131	26	(	(	PUNCT
bibechana-9308	131	27	s	s	PROPN
bibechana-9308	131	28	,	,	PUNCT
bibechana-9308	131	29	β	β	X
bibechana-9308	131	30	–	–	PUNCT
bibechana-9308	131	31	,	,	PUNCT
bibechana-9308	131	32	u–,||	u–,||	PROPN
bibechana-9308	131	33	.	.	PUNCT
bibechana-9308	131	34	,	,	PUNCT
bibechana-9308	131	35	.||	.||	PROPN
bibechana-9308	131	36	)	)	PUNCT
bibechana-9308	132	1	⊂	⊂	PROPN
bibechana-9308	132	2	c0	c0	PROPN
bibechana-9308	132	3	(	(	PUNCT
bibechana-9308	132	4	s	s	PROPN
bibechana-9308	132	5	,	,	PUNCT
bibechana-9308	132	6	α	α	PROPN
bibechana-9308	132	7	–	–	PUNCT
bibechana-9308	132	8	,	,	PUNCT
bibechana-9308	132	9	u	u	NOUN
bibechana-9308	132	10	–	–	PUNCT
bibechana-9308	132	11	,	,	PUNCT
bibechana-9308	132	12	||	||	PROPN
bibechana-9308	132	13	.	.	PUNCT
bibechana-9308	132	14	,	,	PUNCT
bibechana-9308	132	15	.||	.||	PROPN
bibechana-9308	132	16	)	)	PUNCT
bibechana-9308	132	17	.	.	PUNCT
bibechana-9308	133	1	the	the	DET
bibechana-9308	133	2	proof	proof	NOUN
bibechana-9308	133	3	is	be	AUX
bibechana-9308	133	4	now	now	ADV
bibechana-9308	133	5	complete	complete	ADJ
bibechana-9308	133	6	.	.	PUNCT
bibechana-9308	134	1	on	on	ADP
bibechana-9308	134	2	combining	combine	VERB
bibechana-9308	134	3	the	the	DET
bibechana-9308	134	4	theorems	theorem	NOUN
bibechana-9308	134	5	3.1	3.1	NUM
bibechana-9308	134	6	and	and	CCONJ
bibechana-9308	134	7	3.2	3.2	NUM
bibechana-9308	134	8	,	,	PUNCT
bibechana-9308	134	9	we	we	PRON
bibechana-9308	134	10	get	get	AUX
bibechana-9308	134	11	:	:	PUNCT
bibechana-9308	134	12	theorem	theorem	VERB
bibechana-9308	134	13	3.3	3.3	NUM
bibechana-9308	134	14	:	:	PUNCT
bibechana-9308	134	15	for	for	ADP
bibechana-9308	134	16	any	any	DET
bibechana-9308	134	17	u	u	NOUN
bibechana-9308	134	18	–	–	PUNCT
bibechana-9308	134	19	=	=	SYM
bibechana-9308	134	20	(	(	PUNCT
bibechana-9308	134	21	uk	uk	PROPN
bibechana-9308	134	22	)	)	PUNCT
bibechana-9308	134	23	,	,	PUNCT
bibechana-9308	134	24	c0	c0	X
bibechana-9308	134	25	(	(	PUNCT
bibechana-9308	134	26	s	s	PROPN
bibechana-9308	134	27	,	,	PUNCT
bibechana-9308	134	28	α	α	PROPN
bibechana-9308	134	29	–	–	PUNCT
bibechana-9308	134	30	,	,	PUNCT
bibechana-9308	134	31	u	u	INTJ
bibechana-9308	134	32	–	–	PUNCT
bibechana-9308	134	33	,	,	PUNCT
bibechana-9308	134	34	||	||	PROPN
bibechana-9308	134	35	.	.	PUNCT
bibechana-9308	134	36	,	,	PUNCT
bibechana-9308	134	37	.||	.||	PROPN
bibechana-9308	134	38	)	)	PUNCT
bibechana-9308	135	1	=	=	SYM
bibechana-9308	135	2	c0	c0	X
bibechana-9308	135	3	(	(	PUNCT
bibechana-9308	135	4	s	s	PROPN
bibechana-9308	135	5	,	,	PUNCT
bibechana-9308	135	6	β	β	X
bibechana-9308	135	7	–	–	PUNCT
bibechana-9308	135	8	,	,	PUNCT
bibechana-9308	135	9	u	u	INTJ
bibechana-9308	135	10	–	–	PUNCT
bibechana-9308	135	11	,	,	PUNCT
bibechana-9308	135	12	||	||	PROPN
bibechana-9308	135	13	.	.	PUNCT
bibechana-9308	135	14	,	,	PUNCT
bibechana-9308	135	15	.||	.||	PROPN
bibechana-9308	135	16	)	)	PUNCT
bibechana-9308	136	1	if	if	SCONJ
bibechana-9308	136	2	and	and	CCONJ
bibechana-9308	136	3	only	only	ADV
bibechana-9308	136	4	if	if	SCONJ
bibechana-9308	136	5	0	0	NUM
bibechana-9308	136	6	<	<	X
bibechana-9308	136	7	lim	lim	PROPN
bibechana-9308	136	8	infk	infk	PROPN
bibechana-9308	136	9			PROPN
bibechana-9308	136	10			PROPN
bibechana-9308	136	11			PROPN
bibechana-9308	136	12	αk	αk	ADP
bibechana-9308	136	13	βk	βk	ADP
bibechana-9308	136	14	uk	uk	PROPN
bibechana-9308	136	15	≤	≤	NOUN
bibechana-9308	136	16	≤	≤	NUM
bibechana-9308	136	17	≤	≤	NOUN
bibechana-9308	136	18	≤	≤	NUM
bibechana-9308	136	19	lim	lim	PROPN
bibechana-9308	136	20	supk	supk	PROPN
bibechana-9308	136	21			PROPN
bibechana-9308	136	22			PROPN
bibechana-9308	136	23			PROPN
bibechana-9308	136	24	αk	αk	ADP
bibechana-9308	136	25	βk	βk	ADP
bibechana-9308	136	26	uk	uk	PROPN
bibechana-9308	136	27	<	<	X
bibechana-9308	136	28	∞.∞.∞.∞.	∞.∞.∞.∞.	PROPN
bibechana-9308	136	29	corollary	corollary	ADJ
bibechana-9308	136	30	3.4	3.4	NUM
bibechana-9308	136	31	:	:	PUNCT
bibechana-9308	136	32	for	for	ADP
bibechana-9308	136	33	any	any	DET
bibechana-9308	136	34	u	u	NOUN
bibechana-9308	136	35	–	–	PUNCT
bibechana-9308	136	36	=	=	SYM
bibechana-9308	136	37	(	(	PUNCT
bibechana-9308	136	38	uk	uk	PROPN
bibechana-9308	136	39	)	)	PUNCT
bibechana-9308	136	40	,	,	PUNCT
bibechana-9308	136	41	n.p	n.p	PROPN
bibechana-9308	136	42	.	.	PROPN
bibechana-9308	136	43	pahari	pahari	PROPN
bibechana-9308	136	44	/	/	SYM
bibechana-9308	136	45	bibechana	bibechana	NOUN
bibechana-9308	136	46	10	10	NUM
bibechana-9308	136	47	(	(	PUNCT
bibechana-9308	136	48	2014	2014	NUM
bibechana-9308	136	49	)	)	PUNCT
bibechana-9308	136	50	20	20	NUM
bibechana-9308	136	51	-	-	SYM
bibechana-9308	136	52	30	30	NUM
bibechana-9308	136	53	:	:	PUNCT
bibechana-9308	136	54	bmhss	bmhss	PROPN
bibechana-9308	136	55	,	,	PUNCT
bibechana-9308	136	56	p.25	p.25	PROPN
bibechana-9308	136	57	(	(	PUNCT
bibechana-9308	136	58	online	online	ADJ
bibechana-9308	136	59	publication	publication	NOUN
bibechana-9308	136	60	:	:	PUNCT
bibechana-9308	136	61	dec	dec	PROPN
bibechana-9308	136	62	.	.	PROPN
bibechana-9308	136	63	,	,	PUNCT
bibechana-9308	136	64	2013	2013	NUM
bibechana-9308	136	65	)	)	PUNCT
bibechana-9308	136	66	(	(	PUNCT
bibechana-9308	136	67	i	i	NOUN
bibechana-9308	136	68	)	)	PUNCT
bibechana-9308	136	69	c0	c0	PROPN
bibechana-9308	136	70	(	(	PUNCT
bibechana-9308	136	71	s	s	PROPN
bibechana-9308	136	72	,	,	PUNCT
bibechana-9308	136	73	α	α	PROPN
bibechana-9308	136	74	–	–	PUNCT
bibechana-9308	136	75	,	,	PUNCT
bibechana-9308	136	76	u	u	INTJ
bibechana-9308	136	77	–	–	PUNCT
bibechana-9308	136	78	,	,	PUNCT
bibechana-9308	136	79	||	||	PROPN
bibechana-9308	136	80	.	.	PUNCT
bibechana-9308	136	81	,	,	PUNCT
bibechana-9308	136	82	.||	.||	PROPN
bibechana-9308	136	83	)	)	PUNCT
bibechana-9308	137	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	137	2	c0	c0	NOUN
bibechana-9308	137	3	(	(	PUNCT
bibechana-9308	137	4	s	s	PROPN
bibechana-9308	137	5	,	,	PUNCT
bibechana-9308	137	6	u	u	NOUN
bibechana-9308	137	7	–	–	PUNCT
bibechana-9308	137	8	,	,	PUNCT
bibechana-9308	137	9	||	||	PROPN
bibechana-9308	137	10	.	.	PUNCT
bibechana-9308	137	11	,	,	PUNCT
bibechana-9308	137	12	.||	.||	PROPN
bibechana-9308	137	13	)	)	PUNCT
bibechana-9308	138	1	if	if	SCONJ
bibechana-9308	138	2	and	and	CCONJ
bibechana-9308	138	3	only	only	ADV
bibechana-9308	138	4	if	if	SCONJ
bibechana-9308	138	5	lim	lim	PROPN
bibechana-9308	138	6	infk	infk	VERB
bibechana-9308	138	7	|ααααk|	|ααααk|	PROPN
bibechana-9308	138	8	uk	uk	PROPN
bibechana-9308	138	9	>	>	X
bibechana-9308	138	10	0	0	NUM
bibechana-9308	138	11	;	;	PUNCT
bibechana-9308	138	12	(	(	PUNCT
bibechana-9308	138	13	ii	ii	NOUN
bibechana-9308	138	14	)	)	PUNCT
bibechana-9308	138	15	c0	c0	NOUN
bibechana-9308	138	16	(	(	PUNCT
bibechana-9308	138	17	s	s	PROPN
bibechana-9308	138	18	,	,	PUNCT
bibechana-9308	138	19	u	u	NOUN
bibechana-9308	138	20	–	–	PUNCT
bibechana-9308	138	21	,	,	PUNCT
bibechana-9308	138	22	||	||	PROPN
bibechana-9308	138	23	.	.	PUNCT
bibechana-9308	138	24	,	,	PUNCT
bibechana-9308	138	25	.||	.||	PROPN
bibechana-9308	138	26	)	)	PUNCT
bibechana-9308	139	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	139	2	c0	c0	NOUN
bibechana-9308	139	3	(	(	PUNCT
bibechana-9308	139	4	s	s	PROPN
bibechana-9308	139	5	,	,	PUNCT
bibechana-9308	139	6	α	α	PROPN
bibechana-9308	139	7	–	–	PUNCT
bibechana-9308	139	8	,	,	PUNCT
bibechana-9308	139	9	u	u	INTJ
bibechana-9308	139	10	–	–	PUNCT
bibechana-9308	139	11	,	,	PUNCT
bibechana-9308	139	12	||	||	PROPN
bibechana-9308	139	13	.	.	PUNCT
bibechana-9308	139	14	,	,	PUNCT
bibechana-9308	139	15	.||	.||	PROPN
bibechana-9308	139	16	)	)	PUNCT
bibechana-9308	140	1	if	if	SCONJ
bibechana-9308	140	2	and	and	CCONJ
bibechana-9308	140	3	only	only	ADV
bibechana-9308	140	4	if	if	SCONJ
bibechana-9308	140	5	lim	lim	PROPN
bibechana-9308	140	6	supk	supk	PROPN
bibechana-9308	140	7	|ααααk|	|ααααk|	PROPN
bibechana-9308	140	8	uk	uk	PROPN
bibechana-9308	140	9	<	<	X
bibechana-9308	140	10	∞∞∞∞;and	∞∞∞∞;and	NUM
bibechana-9308	140	11	(	(	PUNCT
bibechana-9308	140	12	iii	iii	NOUN
bibechana-9308	140	13	)	)	PUNCT
bibechana-9308	140	14	c0	c0	NOUN
bibechana-9308	140	15	(	(	PUNCT
bibechana-9308	140	16	s	s	PROPN
bibechana-9308	140	17	,	,	PUNCT
bibechana-9308	140	18	α	α	PROPN
bibechana-9308	140	19	–	–	PUNCT
bibechana-9308	140	20	,	,	PUNCT
bibechana-9308	140	21	u	u	INTJ
bibechana-9308	140	22	–	–	PUNCT
bibechana-9308	140	23	,	,	PUNCT
bibechana-9308	140	24	||	||	PROPN
bibechana-9308	140	25	.	.	PUNCT
bibechana-9308	140	26	,	,	PUNCT
bibechana-9308	140	27	.||	.||	PROPN
bibechana-9308	140	28	)	)	PUNCT
bibechana-9308	141	1	=	=	SYM
bibechana-9308	141	2	c0	c0	X
bibechana-9308	141	3	(	(	PUNCT
bibechana-9308	141	4	s	s	PROPN
bibechana-9308	141	5	,	,	PUNCT
bibechana-9308	141	6	u	u	NOUN
bibechana-9308	141	7	–	–	PUNCT
bibechana-9308	141	8	,	,	PUNCT
bibechana-9308	141	9	||	||	PROPN
bibechana-9308	141	10	.	.	PUNCT
bibechana-9308	141	11	,	,	PUNCT
bibechana-9308	141	12	.||	.||	PROPN
bibechana-9308	141	13	)	)	PUNCT
bibechana-9308	142	1	if	if	SCONJ
bibechana-9308	142	2	and	and	CCONJ
bibechana-9308	142	3	only	only	ADV
bibechana-9308	142	4	if	if	SCONJ
bibechana-9308	142	5	0	0	NUM
bibechana-9308	142	6	<	<	X
bibechana-9308	142	7	lim	lim	PROPN
bibechana-9308	142	8	infk	infk	PROPN
bibechana-9308	142	9	|ααααk|	|ααααk|	PROPN
bibechana-9308	142	10	uk	uk	PROPN
bibechana-9308	142	11	≤	≤	PROPN
bibechana-9308	142	12	≤	≤	NUM
bibechana-9308	142	13	≤	≤	NOUN
bibechana-9308	142	14	≤	≤	NUM
bibechana-9308	142	15	lim	lim	PROPN
bibechana-9308	142	16	supk	supk	PROPN
bibechana-9308	142	17	|ααααk|	|ααααk|	PROPN
bibechana-9308	142	18	uk	uk	PROPN
bibechana-9308	142	19	<	<	X
bibechana-9308	142	20	∞∞∞∞.	∞∞∞∞.	PROPN
bibechana-9308	142	21	proof	proof	NOUN
bibechana-9308	142	22	:	:	PUNCT
bibechana-9308	142	23	the	the	DET
bibechana-9308	142	24	proof	proof	NOUN
bibechana-9308	142	25	follows	follow	VERB
bibechana-9308	142	26	by	by	ADP
bibechana-9308	142	27	putting	put	VERB
bibechana-9308	142	28	βk	βk	ADV
bibechana-9308	142	29	=	=	NOUN
bibechana-9308	142	30	1	1	NUM
bibechana-9308	142	31	for	for	ADP
bibechana-9308	142	32	all	all	DET
bibechana-9308	142	33	k	k	PROPN
bibechana-9308	142	34	in	in	ADP
bibechana-9308	142	35	theorems	theorem	NOUN
bibechana-9308	142	36	3.1	3.1	NUM
bibechana-9308	142	37	,	,	PUNCT
bibechana-9308	142	38	3.2	3.2	NUM
bibechana-9308	142	39	and	and	CCONJ
bibechana-9308	142	40	3.3	3.3	NUM
bibechana-9308	142	41	.	.	PUNCT
bibechana-9308	143	1	theorem	theorem	VERB
bibechana-9308	143	2	3.5	3.5	NUM
bibechana-9308	143	3	:	:	PUNCT
bibechana-9308	143	4	for	for	ADP
bibechana-9308	143	5	any	any	DET
bibechana-9308	143	6	α	α	NOUN
bibechana-9308	143	7	–	–	PUNCT
bibechana-9308	143	8	=	=	NOUN
bibechana-9308	143	9	(	(	PUNCT
bibechana-9308	143	10	ααααk	ααααk	NOUN
bibechana-9308	143	11	)	)	PUNCT
bibechana-9308	143	12	,	,	PUNCT
bibechana-9308	143	13	c0	c0	NOUN
bibechana-9308	143	14	(	(	PUNCT
bibechana-9308	143	15	s	s	PROPN
bibechana-9308	143	16	,	,	PUNCT
bibechana-9308	143	17	α	α	PROPN
bibechana-9308	143	18	–	–	PUNCT
bibechana-9308	143	19	,	,	PUNCT
bibechana-9308	143	20	u	u	INTJ
bibechana-9308	143	21	–	–	PUNCT
bibechana-9308	143	22	,	,	PUNCT
bibechana-9308	143	23	||	||	PROPN
bibechana-9308	143	24	.	.	PUNCT
bibechana-9308	143	25	,	,	PUNCT
bibechana-9308	143	26	.||	.||	PROPN
bibechana-9308	143	27	)	)	PUNCT
bibechana-9308	144	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	144	2	c0	c0	NOUN
bibechana-9308	144	3	(	(	PUNCT
bibechana-9308	144	4	s	s	PROPN
bibechana-9308	144	5	,	,	PUNCT
bibechana-9308	144	6	α	α	PROPN
bibechana-9308	144	7	–	–	PUNCT
bibechana-9308	144	8	,	,	PUNCT
bibechana-9308	144	9	v	v	INTJ
bibechana-9308	144	10	–	–	PUNCT
bibechana-9308	144	11	,	,	PUNCT
bibechana-9308	144	12	||	||	PROPN
bibechana-9308	144	13	.	.	PUNCT
bibechana-9308	144	14	,	,	PUNCT
bibechana-9308	144	15	.||	.||	PROPN
bibechana-9308	144	16	)	)	PUNCT
bibechana-9308	145	1	if	if	SCONJ
bibechana-9308	145	2	and	and	CCONJ
bibechana-9308	145	3	only	only	ADV
bibechana-9308	145	4	if	if	SCONJ
bibechana-9308	145	5	lim	lim	PROPN
bibechana-9308	145	6	infk	infk	PROPN
bibechana-9308	145	7	vk	vk	PROPN
bibechana-9308	145	8	uk	uk	PROPN
bibechana-9308	145	9	>	>	X
bibechana-9308	145	10	0	0	X
bibechana-9308	145	11	.	.	PUNCT
bibechana-9308	146	1	proof	proof	NOUN
bibechana-9308	146	2	:	:	PUNCT
bibechana-9308	146	3	for	for	ADP
bibechana-9308	146	4	the	the	DET
bibechana-9308	146	5	necessity	necessity	NOUN
bibechana-9308	146	6	,	,	PUNCT
bibechana-9308	146	7	suppose	suppose	VERB
bibechana-9308	146	8	that	that	SCONJ
bibechana-9308	146	9	the	the	DET
bibechana-9308	146	10	inclusion	inclusion	NOUN
bibechana-9308	146	11	holds	hold	VERB
bibechana-9308	146	12	but	but	CCONJ
bibechana-9308	146	13	lim	lim	PROPN
bibechana-9308	146	14	infk	infk	PROPN
bibechana-9308	146	15	vk	vk	PROPN
bibechana-9308	146	16	uk	uk	PROPN
bibechana-9308	146	17	=	=	X
bibechana-9308	146	18	0	0	PROPN
bibechana-9308	146	19	.	.	PUNCT
bibechana-9308	147	1	then	then	ADV
bibechana-9308	147	2	there	there	PRON
bibechana-9308	147	3	exists	exist	VERB
bibechana-9308	147	4	a	a	DET
bibechana-9308	147	5	sequence	sequence	NOUN
bibechana-9308	147	6	(	(	PUNCT
bibechana-9308	147	7	k(n	k(n	PROPN
bibechana-9308	147	8	)	)	PUNCT
bibechana-9308	147	9	)	)	PUNCT
bibechana-9308	147	10	of	of	ADP
bibechana-9308	147	11	positive	positive	ADJ
bibechana-9308	147	12	integers	integer	NOUN
bibechana-9308	147	13	such	such	ADJ
bibechana-9308	147	14	that	that	SCONJ
bibechana-9308	147	15	1	1	NUM
bibechana-9308	147	16	≤	≤	NUM
bibechana-9308	147	17	k(n	k(n	X
bibechana-9308	147	18	)	)	PUNCT
bibechana-9308	147	19	<	<	X
bibechana-9308	147	20	k(n	k(n	PROPN
bibechana-9308	147	21	+	+	CCONJ
bibechana-9308	147	22	1	1	NUM
bibechana-9308	147	23	)	)	PUNCT
bibechana-9308	147	24	,	,	PUNCT
bibechana-9308	148	1	n	n	X
bibechana-9308	148	2	≥	≥	NOUN
bibechana-9308	148	3	1	1	NUM
bibechana-9308	148	4	for	for	ADP
bibechana-9308	148	5	which	which	PRON
bibechana-9308	148	6	n	n	PRON
bibechana-9308	148	7	vk(n	vk(n	X
bibechana-9308	148	8	)	)	PUNCT
bibechana-9308	148	9	<	<	X
bibechana-9308	148	10	uk(n	uk(n	X
bibechana-9308	148	11	)	)	PUNCT
bibechana-9308	148	12	,	,	PUNCT
bibechana-9308	148	13	for	for	ADP
bibechana-9308	148	14	each	each	DET
bibechana-9308	148	15	n	n	PRON
bibechana-9308	148	16	≥	≥	NOUN
bibechana-9308	148	17	1	1	NUM
bibechana-9308	148	18	.	.	PUNCT
bibechana-9308	148	19	…	…	PUNCT
bibechana-9308	148	20	(	(	PUNCT
bibechana-9308	148	21	3.5	3.5	NUM
bibechana-9308	148	22	)	)	PUNCT
bibechana-9308	148	23	let	let	VERB
bibechana-9308	148	24	ρ	ρ	PROPN
bibechana-9308	148	25	∈	∈	PROPN
bibechana-9308	148	26	s	s	X
bibechana-9308	148	27	and	and	CCONJ
bibechana-9308	148	28	ρ	ρ	NOUN
bibechana-9308	148	29	≠	≠	PROPN
bibechana-9308	148	30	θ	θ	PROPN
bibechana-9308	148	31	.	.	PUNCT
bibechana-9308	149	1	we	we	PRON
bibechana-9308	149	2	define	define	VERB
bibechana-9308	149	3	a	a	DET
bibechana-9308	149	4	sequence	sequence	NOUN
bibechana-9308	149	5	ξ	ξ	NOUN
bibechana-9308	149	6	–	–	PUNCT
bibechana-9308	149	7	=	=	SYM
bibechana-9308	149	8	(	(	PUNCT
bibechana-9308	149	9	ξk	ξk	NOUN
bibechana-9308	149	10	)	)	PUNCT
bibechana-9308	149	11	by	by	ADP
bibechana-9308	149	12	ξk	ξk	ADV
bibechana-9308	149	13	=	=	ADJ
bibechana-9308	149	14			NOUN
bibechana-9308	149	15			ADJ
bibechana-9308	149	16	αk(n	αk(n	NOUN
bibechana-9308	149	17	)	)	PUNCT
bibechana-9308	149	18	-1	-1	ADP
bibechana-9308	149	19	n	n	CCONJ
bibechana-9308	149	20	-1	-1	ADJ
bibechana-9308	149	21	/	/	SYM
bibechana-9308	149	22	uk(n	uk(n	NUM
bibechana-9308	149	23	)	)	PUNCT
bibechana-9308	150	1	ρ	ρ	X
bibechana-9308	150	2	‚	‚	NOUN
bibechana-9308	150	3	for	for	ADP
bibechana-9308	150	4	k	k	PROPN
bibechana-9308	150	5	=	=	SYM
bibechana-9308	150	6	k(n	k(n	PROPN
bibechana-9308	150	7	)	)	PUNCT
bibechana-9308	150	8	‚	‚	NOUN
bibechana-9308	151	1	n	n	DET
bibechana-9308	151	2	≥1	≥1	NUM
bibechana-9308	151	3	and	and	CCONJ
bibechana-9308	151	4	θ	θ	NOUN
bibechana-9308	151	5	‚	‚	NOUN
bibechana-9308	151	6	otherwise	otherwise	ADV
bibechana-9308	151	7	.	.	PUNCT
bibechana-9308	152	1	...	...	PUNCT
bibechana-9308	152	2	(	(	PUNCT
bibechana-9308	152	3	3.6	3.6	NUM
bibechana-9308	152	4	)	)	PUNCT
bibechana-9308	152	5	then	then	ADV
bibechana-9308	152	6	for	for	ADP
bibechana-9308	152	7	each	each	DET
bibechana-9308	152	8	η	η	PROPN
bibechana-9308	152	9	∈	∈	PROPN
bibechana-9308	152	10	s	s	PROPN
bibechana-9308	152	11	,	,	PUNCT
bibechana-9308	152	12	k	k	X
bibechana-9308	152	13	=	=	SYM
bibechana-9308	152	14	k(n	k(n	X
bibechana-9308	152	15	)	)	PUNCT
bibechana-9308	152	16	,	,	PUNCT
bibechana-9308	152	17	n	n	PRON
bibechana-9308	152	18	≥	≥	NOUN
bibechana-9308	152	19	1	1	NUM
bibechana-9308	152	20	,	,	PUNCT
bibechana-9308	152	21	we	we	PRON
bibechana-9308	152	22	have	have	VERB
bibechana-9308	152	23	||αk	||αk	NOUN
bibechana-9308	152	24	ξk	ξk	ADP
bibechana-9308	152	25	‚	‚	NUM
bibechana-9308	152	26	η||	η||	X
bibechana-9308	152	27	u	u	NOUN
bibechana-9308	152	28	k	k	NOUN
bibechana-9308	152	29	=	=	PUNCT
bibechana-9308	152	30	||n	||n	NOUN
bibechana-9308	152	31	-1	-1	ADJ
bibechana-9308	152	32	/	/	SYM
bibechana-9308	152	33	u	u	NOUN
bibechana-9308	152	34	k(n	k(n	X
bibechana-9308	152	35	)	)	PUNCT
bibechana-9308	152	36	ρ	ρ	NOUN
bibechana-9308	152	37	‚	‚	NOUN
bibechana-9308	152	38	η||	η||	NOUN
bibechana-9308	152	39	uk(n	uk(n	X
bibechana-9308	152	40	)	)	PUNCT
bibechana-9308	152	41	=	=	SYM
bibechana-9308	153	1	1	1	NUM
bibechana-9308	153	2	n	n	NUM
bibechana-9308	153	3	||	||	NOUN
bibechana-9308	153	4	ρ	ρ	NUM
bibechana-9308	153	5	‚	‚	PROPN
bibechana-9308	153	6	η||uk(n	η||uk(n	NOUN
bibechana-9308	153	7	)	)	PUNCT
bibechana-9308	153	8	≤	≤	NUM
bibechana-9308	153	9	1	1	NUM
bibechana-9308	153	10	n	n	ADP
bibechana-9308	153	11	a	a	DET
bibechana-9308	153	12	[	[	PUNCT
bibechana-9308	153	13	||ρ	||ρ	PROPN
bibechana-9308	153	14	‚	‚	NUM
bibechana-9308	153	15	η	η	PROPN
bibechana-9308	153	16	||	||	PROPN
bibechana-9308	153	17	l(u	l(u	PROPN
bibechana-9308	153	18	)	)	PUNCT
bibechana-9308	153	19	]	]	PUNCT
bibechana-9308	154	1	→	→	SYM
bibechana-9308	154	2	0	0	PUNCT
bibechana-9308	154	3	as	as	ADP
bibechana-9308	154	4	n	n	X
bibechana-9308	154	5	→∞	→∞	NOUN
bibechana-9308	154	6	and	and	CCONJ
bibechana-9308	154	7	||αk	||αk	ADV
bibechana-9308	154	8	ξk	ξk	ADP
bibechana-9308	154	9	‚	‚	NUM
bibechana-9308	154	10	η||	η||	NOUN
bibechana-9308	154	11	uk	uk	NOUN
bibechana-9308	154	12	=	=	SYM
bibechana-9308	154	13	0	0	NUM
bibechana-9308	154	14	,	,	PUNCT
bibechana-9308	154	15	for	for	ADP
bibechana-9308	154	16	k	k	PROPN
bibechana-9308	154	17	≠	≠	PROPN
bibechana-9308	154	18	k(n	k(n	PROPN
bibechana-9308	154	19	)	)	PUNCT
bibechana-9308	154	20	,	,	PUNCT
bibechana-9308	154	21	n	n	X
bibechana-9308	154	22	≥	≥	NOUN
bibechana-9308	154	23	1	1	NUM
bibechana-9308	154	24	.	.	PUNCT
bibechana-9308	155	1	this	this	PRON
bibechana-9308	155	2	shows	show	VERB
bibechana-9308	155	3	that	that	SCONJ
bibechana-9308	155	4	ξ	ξ	X
bibechana-9308	155	5	–	–	PUNCT
bibechana-9308	155	6	∈	∈	PROPN
bibechana-9308	155	7	c0	c0	NOUN
bibechana-9308	155	8	(	(	PUNCT
bibechana-9308	155	9	s	s	PROPN
bibechana-9308	155	10	,	,	PUNCT
bibechana-9308	155	11	α	α	PROPN
bibechana-9308	155	12	–	–	PUNCT
bibechana-9308	155	13	,	,	PUNCT
bibechana-9308	155	14	u	u	NOUN
bibechana-9308	155	15	–	–	PUNCT
bibechana-9308	155	16	,	,	PUNCT
bibechana-9308	155	17	||	||	PROPN
bibechana-9308	155	18	.	.	PUNCT
bibechana-9308	155	19	,	,	PUNCT
bibechana-9308	155	20	.||	.||	PROPN
bibechana-9308	155	21	)	)	PUNCT
bibechana-9308	155	22	.	.	PUNCT
bibechana-9308	156	1	but	but	CCONJ
bibechana-9308	156	2	on	on	ADP
bibechana-9308	156	3	the	the	DET
bibechana-9308	156	4	other	other	ADJ
bibechana-9308	156	5	hand	hand	NOUN
bibechana-9308	156	6	,	,	PUNCT
bibechana-9308	156	7	let	let	VERB
bibechana-9308	156	8	us	we	PRON
bibechana-9308	156	9	choose	choose	VERB
bibechana-9308	156	10	η	η	PROPN
bibechana-9308	156	11	∈	∈	PROPN
bibechana-9308	156	12	s	s	VERB
bibechana-9308	156	13	such	such	ADJ
bibechana-9308	156	14	that	that	DET
bibechana-9308	156	15	||ρ	||ρ	NOUN
bibechana-9308	156	16	,	,	PUNCT
bibechana-9308	156	17	η||	η||	NOUN
bibechana-9308	156	18	=	=	SYM
bibechana-9308	156	19	1	1	X
bibechana-9308	156	20	.	.	PUNCT
bibechana-9308	156	21	then	then	ADV
bibechana-9308	156	22	for	for	ADP
bibechana-9308	156	23	k	k	PROPN
bibechana-9308	156	24	=	=	SYM
bibechana-9308	156	25	k(n	k(n	PROPN
bibechana-9308	156	26	)	)	PUNCT
bibechana-9308	156	27	,	,	PUNCT
bibechana-9308	156	28	n	n	PRON
bibechana-9308	156	29	≥	≥	NOUN
bibechana-9308	156	30	1	1	NUM
bibechana-9308	156	31	,	,	PUNCT
bibechana-9308	156	32	in	in	ADP
bibechana-9308	156	33	view	view	NOUN
bibechana-9308	156	34	of	of	ADP
bibechana-9308	156	35	(	(	PUNCT
bibechana-9308	156	36	3.5	3.5	NUM
bibechana-9308	156	37	)	)	PUNCT
bibechana-9308	156	38	and	and	CCONJ
bibechana-9308	156	39	(	(	PUNCT
bibechana-9308	156	40	3.6	3.6	NUM
bibechana-9308	156	41	)	)	PUNCT
bibechana-9308	156	42	,	,	PUNCT
bibechana-9308	156	43	we	we	PRON
bibechana-9308	156	44	have	have	VERB
bibechana-9308	156	45	||αk	||αk	NOUN
bibechana-9308	156	46	ξk	ξk	ADP
bibechana-9308	156	47	‚	‚	NUM
bibechana-9308	156	48	η||	η||	NOUN
bibechana-9308	156	49	v	v	NOUN
bibechana-9308	156	50	k	k	NOUN
bibechana-9308	156	51	=	=	PUNCT
bibechana-9308	156	52	||α	||α	NOUN
bibechana-9308	156	53	k(n	k(n	X
bibechana-9308	156	54	)	)	PUNCT
bibechana-9308	157	1	ξ	ξ	X
bibechana-9308	157	2	k(n	k(n	X
bibechana-9308	157	3	)	)	PUNCT
bibechana-9308	157	4	‚	‚	NOUN
bibechana-9308	157	5	η||	η||	NOUN
bibechana-9308	157	6	vk(n	vk(n	X
bibechana-9308	157	7	)	)	PUNCT
bibechana-9308	158	1	=	=	PUNCT
bibechana-9308	158	2	||	||	NOUN
bibechana-9308	158	3	n-1	n-1	PROPN
bibechana-9308	158	4	/	/	SYM
bibechana-9308	158	5	uk(n	uk(n	NUM
bibechana-9308	158	6	)	)	PUNCT
bibechana-9308	159	1	ρ	ρ	X
bibechana-9308	159	2	‚	‚	NOUN
bibechana-9308	159	3	η||	η||	NOUN
bibechana-9308	159	4	vk(n	vk(n	X
bibechana-9308	159	5	)	)	PUNCT
bibechana-9308	159	6	≥	≥	NOUN
bibechana-9308	160	1	1	1	NUM
bibechana-9308	160	2	n	n	NUM
bibechana-9308	160	3	1	1	NUM
bibechana-9308	160	4	/	/	SYM
bibechana-9308	160	5	n	n	NOUN
bibechana-9308	160	6	||	||	NOUN
bibechana-9308	160	7	ρ	ρ	NUM
bibechana-9308	160	8	‚	‚	NOUN
bibechana-9308	160	9	η||	η||	NOUN
bibechana-9308	160	10	vk(n	vk(n	X
bibechana-9308	160	11	)	)	PUNCT
bibechana-9308	160	12	≥	≥	NOUN
bibechana-9308	160	13	1	1	NUM
bibechana-9308	160	14	n	n	NUM
bibechana-9308	160	15	1/2	1/2	NUM
bibechana-9308	160	16	this	this	PRON
bibechana-9308	160	17	shows	show	VERB
bibechana-9308	160	18	that	that	SCONJ
bibechana-9308	160	19	ξ	ξ	X
bibechana-9308	160	20	–	–	PUNCT
bibechana-9308	160	21	∉	∉	PROPN
bibechana-9308	160	22	c0	c0	X
bibechana-9308	160	23	(	(	PUNCT
bibechana-9308	160	24	s	s	PROPN
bibechana-9308	160	25	,	,	PUNCT
bibechana-9308	160	26	α	α	NOUN
bibechana-9308	160	27	–	–	PUNCT
bibechana-9308	160	28	,	,	PUNCT
bibechana-9308	160	29	v–,||	v–,||	NUM
bibechana-9308	160	30	.	.	PUNCT
bibechana-9308	160	31	,	,	PUNCT
bibechana-9308	160	32	.||	.||	PROPN
bibechana-9308	160	33	)	)	PUNCT
bibechana-9308	160	34	,	,	PUNCT
bibechana-9308	160	35	which	which	PRON
bibechana-9308	160	36	contradicts	contradict	VERB
bibechana-9308	160	37	our	our	PRON
bibechana-9308	160	38	assumption	assumption	NOUN
bibechana-9308	160	39	.	.	PUNCT
bibechana-9308	161	1	for	for	ADP
bibechana-9308	161	2	the	the	DET
bibechana-9308	161	3	sufficiency	sufficiency	NOUN
bibechana-9308	161	4	of	of	ADP
bibechana-9308	161	5	the	the	DET
bibechana-9308	161	6	condition	condition	NOUN
bibechana-9308	161	7	,	,	PUNCT
bibechana-9308	161	8	suppose	suppose	VERB
bibechana-9308	161	9	that	that	SCONJ
bibechana-9308	161	10	lim	lim	PROPN
bibechana-9308	161	11	infk	infk	PROPN
bibechana-9308	161	12	vk	vk	PROPN
bibechana-9308	161	13	uk	uk	PROPN
bibechana-9308	161	14	>	>	X
bibechana-9308	161	15	0	0	PROPN
bibechana-9308	161	16	.	.	PUNCT
bibechana-9308	162	1	then	then	ADV
bibechana-9308	162	2	there	there	PRON
bibechana-9308	162	3	exists	exist	VERB
bibechana-9308	162	4	a	a	DET
bibechana-9308	162	5	m	m	NOUN
bibechana-9308	162	6	>	>	X
bibechana-9308	162	7	0	0	NUM
bibechana-9308	162	8	such	such	ADJ
bibechana-9308	162	9	that	that	PRON
bibechana-9308	162	10	vk	vk	PROPN
bibechana-9308	162	11	>	>	X
bibechana-9308	162	12	m	m	VERB
bibechana-9308	162	13	uk	uk	PROPN
bibechana-9308	162	14	for	for	ADP
bibechana-9308	162	15	all	all	DET
bibechana-9308	162	16	sufficiently	sufficiently	ADV
bibechana-9308	162	17	large	large	ADJ
bibechana-9308	162	18	values	value	NOUN
bibechana-9308	162	19	of	of	ADP
bibechana-9308	162	20	k.	k.	PROPN
bibechana-9308	162	21	let	let	VERB
bibechana-9308	162	22	ξ	ξ	X
bibechana-9308	162	23	–	–	PUNCT
bibechana-9308	162	24	=	=	SYM
bibechana-9308	162	25	(	(	PUNCT
bibechana-9308	162	26	ξk	ξk	NOUN
bibechana-9308	162	27	)	)	PUNCT
bibechana-9308	162	28	∈	∈	PROPN
bibechana-9308	162	29	c0	c0	NOUN
bibechana-9308	162	30	(	(	PUNCT
bibechana-9308	162	31	s	s	PROPN
bibechana-9308	162	32	,	,	PUNCT
bibechana-9308	162	33	α	α	PROPN
bibechana-9308	162	34	–	–	PUNCT
bibechana-9308	162	35	,	,	PUNCT
bibechana-9308	162	36	u	u	NOUN
bibechana-9308	162	37	–	–	PUNCT
bibechana-9308	162	38	,	,	PUNCT
bibechana-9308	162	39	||	||	PROPN
bibechana-9308	162	40	.	.	PUNCT
bibechana-9308	162	41	,	,	PUNCT
bibechana-9308	162	42	.||	.||	PROPN
bibechana-9308	162	43	)	)	PUNCT
bibechana-9308	162	44	.	.	PUNCT
bibechana-9308	163	1	then	then	ADV
bibechana-9308	163	2	for	for	ADP
bibechana-9308	163	3	each	each	DET
bibechana-9308	163	4	η	η	PROPN
bibechana-9308	163	5	∈	∈	PROPN
bibechana-9308	163	6	s	s	PART
bibechana-9308	163	7	||αk	||αk	NOUN
bibechana-9308	163	8	ξk	ξk	ADP
bibechana-9308	163	9	‚	‚	NUM
bibechana-9308	163	10	η||	η||	X
bibechana-9308	163	11	uk	uk	PROPN
bibechana-9308	163	12	→	→	SYM
bibechana-9308	163	13	0	0	PROPN
bibechana-9308	163	14	as	as	ADP
bibechana-9308	163	15	k	k	PROPN
bibechana-9308	163	16	→	→	SYM
bibechana-9308	163	17	∞.	∞.	PROPN
bibechana-9308	163	18	hence	hence	ADV
bibechana-9308	163	19	for	for	ADP
bibechana-9308	163	20	a	a	DET
bibechana-9308	163	21	given	give	VERB
bibechana-9308	163	22	ε	ε	PROPN
bibechana-9308	163	23	>	>	X
bibechana-9308	163	24	0	0	PROPN
bibechana-9308	163	25	,	,	PUNCT
bibechana-9308	163	26	if	if	SCONJ
bibechana-9308	163	27	we	we	PRON
bibechana-9308	163	28	choose	choose	VERB
bibechana-9308	163	29	0	0	PUNCT
bibechana-9308	163	30	<	<	X
bibechana-9308	163	31	δ	δ	X
bibechana-9308	163	32	<	<	X
bibechana-9308	163	33	1	1	NUM
bibechana-9308	163	34	satisfying	satisfy	VERB
bibechana-9308	163	35	δ	δ	PROPN
bibechana-9308	163	36	m	m	VERB
bibechana-9308	163	37	<	<	X
bibechana-9308	163	38	ε	ε	X
bibechana-9308	163	39	satisfying	satisfy	VERB
bibechana-9308	163	40	n.p	n.p	PROPN
bibechana-9308	163	41	.	.	PROPN
bibechana-9308	163	42	pahari	pahari	PROPN
bibechana-9308	163	43	/	/	SYM
bibechana-9308	163	44	bibechana	bibechana	NOUN
bibechana-9308	163	45	10	10	NUM
bibechana-9308	163	46	(	(	PUNCT
bibechana-9308	163	47	2014	2014	NUM
bibechana-9308	163	48	)	)	PUNCT
bibechana-9308	163	49	20	20	NUM
bibechana-9308	163	50	-	-	SYM
bibechana-9308	163	51	30	30	NUM
bibechana-9308	163	52	:	:	PUNCT
bibechana-9308	163	53	bmhss	bmhss	PROPN
bibechana-9308	163	54	,	,	PUNCT
bibechana-9308	163	55	p.26	p.26	PROPN
bibechana-9308	163	56	(	(	PUNCT
bibechana-9308	163	57	online	online	ADJ
bibechana-9308	163	58	publication	publication	NOUN
bibechana-9308	163	59	:	:	PUNCT
bibechana-9308	163	60	dec	dec	PROPN
bibechana-9308	163	61	.	.	PROPN
bibechana-9308	163	62	,	,	PUNCT
bibechana-9308	163	63	2013	2013	NUM
bibechana-9308	163	64	)	)	PUNCT
bibechana-9308	163	65	||αk	||αk	NOUN
bibechana-9308	163	66	ξk	ξk	ADP
bibechana-9308	163	67	,	,	PUNCT
bibechana-9308	163	68	η	η	PROPN
bibechana-9308	163	69	||	||	PROPN
bibechana-9308	163	70	uk	uk	PROPN
bibechana-9308	163	71	<	<	X
bibechana-9308	163	72	δ	δ	PROPN
bibechana-9308	163	73	<	<	X
bibechana-9308	163	74	1	1	NUM
bibechana-9308	163	75	for	for	ADP
bibechana-9308	163	76	each	each	DET
bibechana-9308	163	77	η	η	PROPN
bibechana-9308	163	78	∈	∈	PROPN
bibechana-9308	163	79	s	s	X
bibechana-9308	163	80	and	and	CCONJ
bibechana-9308	163	81	for	for	ADP
bibechana-9308	163	82	all	all	DET
bibechana-9308	163	83	sufficiently	sufficiently	ADV
bibechana-9308	163	84	large	large	ADJ
bibechana-9308	163	85	values	value	NOUN
bibechana-9308	163	86	of	of	ADP
bibechana-9308	163	87	k.thus	k.thus	NOUN
bibechana-9308	163	88	||αk	||αk	NOUN
bibechana-9308	163	89	ξk	ξk	ADP
bibechana-9308	163	90	,	,	PUNCT
bibechana-9308	163	91	η	η	PROPN
bibechana-9308	163	92	||	||	PROPN
bibechana-9308	163	93	vk	vk	PROPN
bibechana-9308	163	94	≤	≤	NOUN
bibechana-9308	164	1	[	[	PUNCT
bibechana-9308	164	2	||αk	||αk	NOUN
bibechana-9308	164	3	ξk	ξk	ADP
bibechana-9308	164	4	‚	‚	PROPN
bibechana-9308	164	5	η	η	PROPN
bibechana-9308	164	6	||	||	PROPN
bibechana-9308	164	7	uk	uk	PROPN
bibechana-9308	164	8	]	]	SYM
bibechana-9308	164	9	m	m	VERB
bibechana-9308	164	10	≤	≤	NOUN
bibechana-9308	164	11	δ	δ	X
bibechana-9308	164	12	m	m	NOUN
bibechana-9308	164	13	<	<	X
bibechana-9308	164	14	ε	ε	PROPN
bibechana-9308	164	15	,	,	PUNCT
bibechana-9308	164	16	for	for	ADP
bibechana-9308	164	17	each	each	DET
bibechana-9308	164	18	η	η	PROPN
bibechana-9308	164	19	∈	∈	PROPN
bibechana-9308	164	20	s	s	X
bibechana-9308	164	21	and	and	CCONJ
bibechana-9308	164	22	for	for	ADP
bibechana-9308	164	23	all	all	DET
bibechana-9308	164	24	sufficiently	sufficiently	ADV
bibechana-9308	164	25	large	large	ADJ
bibechana-9308	164	26	values	value	NOUN
bibechana-9308	164	27	of	of	ADP
bibechana-9308	164	28	k	k	PROPN
bibechana-9308	164	29	and	and	CCONJ
bibechana-9308	164	30	consequently	consequently	ADV
bibechana-9308	164	31	ξ	ξ	X
bibechana-9308	164	32	–	–	PUNCT
bibechana-9308	164	33	∈	∈	PROPN
bibechana-9308	164	34	c0	c0	NOUN
bibechana-9308	164	35	(	(	PUNCT
bibechana-9308	164	36	s	s	PROPN
bibechana-9308	164	37	,	,	PUNCT
bibechana-9308	164	38	α	α	NOUN
bibechana-9308	164	39	–	–	PUNCT
bibechana-9308	164	40	,	,	PUNCT
bibechana-9308	164	41	v–,||	v–,||	NUM
bibechana-9308	164	42	.	.	PUNCT
bibechana-9308	164	43	,	,	PUNCT
bibechana-9308	164	44	.||	.||	PROPN
bibechana-9308	164	45	)	)	PUNCT
bibechana-9308	164	46	.	.	PUNCT
bibechana-9308	165	1	hence	hence	ADV
bibechana-9308	165	2	c0	c0	PROPN
bibechana-9308	165	3	(	(	PUNCT
bibechana-9308	165	4	s	s	PROPN
bibechana-9308	165	5	,	,	PUNCT
bibechana-9308	165	6	α	α	PROPN
bibechana-9308	165	7	–	–	PUNCT
bibechana-9308	165	8	,	,	PUNCT
bibechana-9308	165	9	u	u	NOUN
bibechana-9308	165	10	–	–	PUNCT
bibechana-9308	165	11	,	,	PUNCT
bibechana-9308	165	12	||	||	PROPN
bibechana-9308	165	13	.	.	PUNCT
bibechana-9308	165	14	,	,	PUNCT
bibechana-9308	165	15	.||	.||	PROPN
bibechana-9308	165	16	)	)	PUNCT
bibechana-9308	166	1	⊂	⊂	PROPN
bibechana-9308	166	2	c0	c0	PROPN
bibechana-9308	166	3	(	(	PUNCT
bibechana-9308	166	4	s	s	PROPN
bibechana-9308	166	5	,	,	PUNCT
bibechana-9308	166	6	α	α	NOUN
bibechana-9308	166	7	–	–	PUNCT
bibechana-9308	166	8	,	,	PUNCT
bibechana-9308	166	9	v–,||	v–,||	NUM
bibechana-9308	166	10	.	.	PUNCT
bibechana-9308	166	11	,	,	PUNCT
bibechana-9308	166	12	.||	.||	PROPN
bibechana-9308	166	13	)	)	PUNCT
bibechana-9308	166	14	.	.	PUNCT
bibechana-9308	167	1	this	this	PRON
bibechana-9308	167	2	completes	complete	VERB
bibechana-9308	167	3	the	the	DET
bibechana-9308	167	4	proof	proof	NOUN
bibechana-9308	167	5	of	of	ADP
bibechana-9308	167	6	the	the	DET
bibechana-9308	167	7	theorem	theorem	PROPN
bibechana-9308	167	8	.	.	PUNCT
bibechana-9308	167	9	theorem	theorem	VERB
bibechana-9308	167	10	3.6	3.6	NUM
bibechana-9308	167	11	:	:	PUNCT
bibechana-9308	167	12	for	for	ADP
bibechana-9308	167	13	any	any	DET
bibechana-9308	167	14	α	α	NOUN
bibechana-9308	167	15	–	–	PUNCT
bibechana-9308	167	16	=	=	NOUN
bibechana-9308	167	17	(	(	PUNCT
bibechana-9308	167	18	ααααk	ααααk	NOUN
bibechana-9308	167	19	)	)	PUNCT
bibechana-9308	167	20	,	,	PUNCT
bibechana-9308	167	21	c0	c0	NOUN
bibechana-9308	167	22	(	(	PUNCT
bibechana-9308	167	23	s	s	PROPN
bibechana-9308	167	24	,	,	PUNCT
bibechana-9308	167	25	α	α	PROPN
bibechana-9308	167	26	–	–	PUNCT
bibechana-9308	167	27	,	,	PUNCT
bibechana-9308	167	28	v	v	INTJ
bibechana-9308	167	29	–	–	PUNCT
bibechana-9308	167	30	,	,	PUNCT
bibechana-9308	167	31	||	||	PROPN
bibechana-9308	167	32	.	.	PUNCT
bibechana-9308	167	33	,	,	PUNCT
bibechana-9308	167	34	.||	.||	PROPN
bibechana-9308	167	35	)	)	PUNCT
bibechana-9308	168	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	168	2	c0	c0	NOUN
bibechana-9308	168	3	(	(	PUNCT
bibechana-9308	168	4	s	s	PROPN
bibechana-9308	168	5	,	,	PUNCT
bibechana-9308	168	6	α	α	PROPN
bibechana-9308	168	7	–	–	PUNCT
bibechana-9308	168	8	,	,	PUNCT
bibechana-9308	168	9	u	u	INTJ
bibechana-9308	168	10	–	–	PUNCT
bibechana-9308	168	11	,	,	PUNCT
bibechana-9308	168	12	||	||	PROPN
bibechana-9308	168	13	.	.	PUNCT
bibechana-9308	168	14	,	,	PUNCT
bibechana-9308	168	15	.||	.||	PROPN
bibechana-9308	168	16	)	)	PUNCT
bibechana-9308	169	1	if	if	SCONJ
bibechana-9308	169	2	and	and	CCONJ
bibechana-9308	169	3	only	only	ADV
bibechana-9308	169	4	if	if	SCONJ
bibechana-9308	169	5	lim	lim	PROPN
bibechana-9308	169	6	supk	supk	PROPN
bibechana-9308	169	7	vk	vk	PROPN
bibechana-9308	169	8	uk	uk	PROPN
bibechana-9308	169	9	<	<	X
bibechana-9308	169	10	∞∞∞∞.	∞∞∞∞.	PROPN
bibechana-9308	169	11	proof	proof	NOUN
bibechana-9308	169	12	:	:	PUNCT
bibechana-9308	169	13	for	for	ADP
bibechana-9308	169	14	the	the	DET
bibechana-9308	169	15	necessity	necessity	NOUN
bibechana-9308	169	16	,	,	PUNCT
bibechana-9308	169	17	suppose	suppose	VERB
bibechana-9308	169	18	that	that	SCONJ
bibechana-9308	169	19	the	the	DET
bibechana-9308	169	20	inclusion	inclusion	NOUN
bibechana-9308	169	21	holds	hold	VERB
bibechana-9308	169	22	but	but	CCONJ
bibechana-9308	169	23	lim	lim	PROPN
bibechana-9308	169	24	supk	supk	PROPN
bibechana-9308	169	25	vk	vk	PROPN
bibechana-9308	169	26	uk	uk	PROPN
bibechana-9308	169	27	=	=	SYM
bibechana-9308	169	28	∞	∞	PROPN
bibechana-9308	169	29	.	.	PUNCT
bibechana-9308	170	1	then	then	ADV
bibechana-9308	170	2	there	there	PRON
bibechana-9308	170	3	exists	exist	VERB
bibechana-9308	170	4	a	a	DET
bibechana-9308	170	5	sequence	sequence	NOUN
bibechana-9308	170	6	(	(	PUNCT
bibechana-9308	170	7	k(n	k(n	PROPN
bibechana-9308	170	8	)	)	PUNCT
bibechana-9308	170	9	)	)	PUNCT
bibechana-9308	170	10	of	of	ADP
bibechana-9308	170	11	positive	positive	ADJ
bibechana-9308	170	12	integers	integer	NOUN
bibechana-9308	170	13	such	such	ADJ
bibechana-9308	170	14	that	that	SCONJ
bibechana-9308	170	15	1	1	NUM
bibechana-9308	170	16	≤	≤	NUM
bibechana-9308	170	17	k(n	k(n	X
bibechana-9308	170	18	)	)	PUNCT
bibechana-9308	170	19	<	<	X
bibechana-9308	170	20	k(n+	k(n+	PROPN
bibechana-9308	170	21	1	1	NUM
bibechana-9308	170	22	)	)	PUNCT
bibechana-9308	170	23	,	,	PUNCT
bibechana-9308	171	1	n	n	X
bibechana-9308	171	2	≥	≥	NOUN
bibechana-9308	171	3	1	1	NUM
bibechana-9308	171	4	for	for	ADP
bibechana-9308	171	5	which	which	PRON
bibechana-9308	171	6	vk(n	vk(n	X
bibechana-9308	171	7	)	)	PUNCT
bibechana-9308	171	8	>	>	X
bibechana-9308	172	1	n	n	CCONJ
bibechana-9308	172	2	uk(n	uk(n	NUM
bibechana-9308	172	3	)	)	PUNCT
bibechana-9308	172	4	,	,	PUNCT
bibechana-9308	172	5	for	for	ADP
bibechana-9308	172	6	all	all	DET
bibechana-9308	172	7	n	n	PRON
bibechana-9308	172	8	≥	≥	NOUN
bibechana-9308	172	9	1	1	NUM
bibechana-9308	172	10	.	.	PUNCT
bibechana-9308	172	11	...	...	PUNCT
bibechana-9308	173	1	(	(	PUNCT
bibechana-9308	173	2	3.7	3.7	NUM
bibechana-9308	173	3	)	)	PUNCT
bibechana-9308	173	4	corresponding	correspond	VERB
bibechana-9308	173	5	to	to	ADP
bibechana-9308	173	6	ρ	ρ	PROPN
bibechana-9308	173	7	∈	∈	PROPN
bibechana-9308	173	8	s	s	PART
bibechana-9308	173	9	and	and	CCONJ
bibechana-9308	173	10	ρ	ρ	NOUN
bibechana-9308	173	11	≠	≠	PROPN
bibechana-9308	173	12	θ	θ	PROPN
bibechana-9308	173	13	,	,	PUNCT
bibechana-9308	173	14	we	we	PRON
bibechana-9308	173	15	define	define	VERB
bibechana-9308	173	16	a	a	DET
bibechana-9308	173	17	sequence	sequence	NOUN
bibechana-9308	173	18	ξ	ξ	NOUN
bibechana-9308	173	19	–	–	PUNCT
bibechana-9308	173	20	=	=	SYM
bibechana-9308	173	21	(	(	PUNCT
bibechana-9308	173	22	ξk	ξk	NOUN
bibechana-9308	173	23	)	)	PUNCT
bibechana-9308	173	24	by	by	ADP
bibechana-9308	173	25	ξk	ξk	ADV
bibechana-9308	173	26	=	=	ADJ
bibechana-9308	173	27			NOUN
bibechana-9308	173	28			ADJ
bibechana-9308	173	29	αk(n	αk(n	NOUN
bibechana-9308	173	30	)	)	PUNCT
bibechana-9308	173	31	-1	-1	ADP
bibechana-9308	173	32	n	n	CCONJ
bibechana-9308	173	33	-1	-1	ADJ
bibechana-9308	173	34	/	/	SYM
bibechana-9308	173	35	vk(n	vk(n	NUM
bibechana-9308	173	36	)	)	PUNCT
bibechana-9308	174	1	ρ	ρ	X
bibechana-9308	174	2	‚	‚	NOUN
bibechana-9308	174	3	for	for	ADP
bibechana-9308	174	4	k	k	PROPN
bibechana-9308	174	5	=	=	SYM
bibechana-9308	174	6	k(n	k(n	PROPN
bibechana-9308	174	7	)	)	PUNCT
bibechana-9308	174	8	‚	‚	NOUN
bibechana-9308	175	1	n	n	DET
bibechana-9308	175	2	≥1	≥1	NUM
bibechana-9308	175	3	and	and	CCONJ
bibechana-9308	175	4	θ	θ	NOUN
bibechana-9308	175	5	‚	‚	NOUN
bibechana-9308	175	6	otherwise	otherwise	ADV
bibechana-9308	175	7	.	.	PUNCT
bibechana-9308	176	1	...	...	PUNCT
bibechana-9308	176	2	(	(	PUNCT
bibechana-9308	176	3	3.8	3.8	NUM
bibechana-9308	176	4	)	)	PUNCT
bibechana-9308	176	5	then	then	ADV
bibechana-9308	176	6	for	for	ADP
bibechana-9308	176	7	each	each	DET
bibechana-9308	176	8	η	η	PROPN
bibechana-9308	176	9	∈	∈	PROPN
bibechana-9308	176	10	s	s	PROPN
bibechana-9308	176	11	,	,	PUNCT
bibechana-9308	176	12	k	k	X
bibechana-9308	176	13	=	=	SYM
bibechana-9308	176	14	k(n	k(n	X
bibechana-9308	176	15	)	)	PUNCT
bibechana-9308	176	16	,	,	PUNCT
bibechana-9308	176	17	n	n	PRON
bibechana-9308	176	18	≥	≥	NOUN
bibechana-9308	176	19	1	1	NUM
bibechana-9308	176	20	,	,	PUNCT
bibechana-9308	176	21	we	we	PRON
bibechana-9308	176	22	have	have	VERB
bibechana-9308	176	23	||αk	||αk	NOUN
bibechana-9308	176	24	ξk	ξk	ADP
bibechana-9308	176	25	‚	‚	NOUN
bibechana-9308	176	26	η	η	PROPN
bibechana-9308	176	27	||	||	PROPN
bibechana-9308	177	1	vk	vk	PROPN
bibechana-9308	177	2	=	=	SYM
bibechana-9308	177	3	||n-1	||n-1	NOUN
bibechana-9308	177	4	/	/	SYM
bibechana-9308	177	5	vk(n	vk(n	NUM
bibechana-9308	177	6	)	)	PUNCT
bibechana-9308	177	7	ρ‚η||	ρ‚η||	NOUN
bibechana-9308	177	8	vk(n	vk(n	X
bibechana-9308	177	9	)	)	PUNCT
bibechana-9308	177	10	=	=	SYM
bibechana-9308	178	1	1	1	NUM
bibechana-9308	178	2	n	n	NUM
bibechana-9308	178	3	||	||	NOUN
bibechana-9308	178	4	ρ	ρ	NUM
bibechana-9308	178	5	‚	‚	NUM
bibechana-9308	178	6	η||vk(n	η||vk(n	NOUN
bibechana-9308	178	7	)	)	PUNCT
bibechana-9308	178	8	≤	≤	NOUN
bibechana-9308	178	9	1	1	NUM
bibechana-9308	178	10	n	n	ADP
bibechana-9308	178	11	a	a	DET
bibechana-9308	178	12	[	[	PUNCT
bibechana-9308	178	13	||ρ	||ρ	PROPN
bibechana-9308	178	14	‚	‚	NUM
bibechana-9308	178	15	η	η	PROPN
bibechana-9308	178	16	||	||	PROPN
bibechana-9308	178	17	l(v	l(v	PROPN
bibechana-9308	178	18	)	)	PUNCT
bibechana-9308	178	19	]	]	PUNCT
bibechana-9308	179	1	→	→	SYM
bibechana-9308	179	2	0	0	PUNCT
bibechana-9308	179	3	as	as	ADP
bibechana-9308	179	4	n	n	X
bibechana-9308	179	5	→∞	→∞	NOUN
bibechana-9308	179	6	and	and	CCONJ
bibechana-9308	179	7	||αk	||αk	ADV
bibechana-9308	179	8	ξk	ξk	ADP
bibechana-9308	179	9	‚	‚	NUM
bibechana-9308	179	10	η||	η||	NOUN
bibechana-9308	179	11	v	v	NOUN
bibechana-9308	179	12	k	k	NOUN
bibechana-9308	179	13	=	=	SYM
bibechana-9308	179	14	0	0	NUM
bibechana-9308	179	15	,	,	PUNCT
bibechana-9308	179	16	for	for	ADP
bibechana-9308	179	17	k	k	PROPN
bibechana-9308	179	18	≠	≠	PROPN
bibechana-9308	179	19	k(n	k(n	PROPN
bibechana-9308	179	20	)	)	PUNCT
bibechana-9308	179	21	,	,	PUNCT
bibechana-9308	179	22	n	n	X
bibechana-9308	179	23	≥	≥	NOUN
bibechana-9308	179	24	1	1	NUM
bibechana-9308	179	25	.	.	PUNCT
bibechana-9308	180	1	this	this	PRON
bibechana-9308	180	2	shows	show	VERB
bibechana-9308	180	3	that	that	SCONJ
bibechana-9308	180	4	ξ	ξ	X
bibechana-9308	180	5	–	–	PUNCT
bibechana-9308	180	6	∈	∈	PROPN
bibechana-9308	180	7	c0	c0	NOUN
bibechana-9308	180	8	(	(	PUNCT
bibechana-9308	180	9	s	s	PROPN
bibechana-9308	180	10	,	,	PUNCT
bibechana-9308	180	11	α	α	NOUN
bibechana-9308	180	12	–	–	PUNCT
bibechana-9308	180	13	,	,	PUNCT
bibechana-9308	180	14	v–,||	v–,||	NUM
bibechana-9308	180	15	.	.	PUNCT
bibechana-9308	180	16	,	,	PUNCT
bibechana-9308	180	17	.||	.||	PROPN
bibechana-9308	180	18	)	)	PUNCT
bibechana-9308	180	19	.	.	PUNCT
bibechana-9308	181	1	but	but	CCONJ
bibechana-9308	181	2	on	on	ADP
bibechana-9308	181	3	the	the	DET
bibechana-9308	181	4	other	other	ADJ
bibechana-9308	181	5	hand	hand	NOUN
bibechana-9308	181	6	,	,	PUNCT
bibechana-9308	181	7	let	let	VERB
bibechana-9308	181	8	us	we	PRON
bibechana-9308	181	9	choose	choose	VERB
bibechana-9308	181	10	η	η	PROPN
bibechana-9308	181	11	∈	∈	PROPN
bibechana-9308	181	12	s	s	VERB
bibechana-9308	181	13	such	such	ADJ
bibechana-9308	181	14	that	that	DET
bibechana-9308	181	15	||	||	PROPN
bibechana-9308	181	16	ρ	ρ	NOUN
bibechana-9308	181	17	,	,	PUNCT
bibechana-9308	181	18	η||	η||	NOUN
bibechana-9308	181	19	=	=	SYM
bibechana-9308	182	1	1	1	X
bibechana-9308	182	2	.	.	PUNCT
bibechana-9308	182	3	then	then	ADV
bibechana-9308	182	4	for	for	ADP
bibechana-9308	182	5	k	k	PROPN
bibechana-9308	182	6	=	=	SYM
bibechana-9308	182	7	k(n	k(n	PROPN
bibechana-9308	182	8	)	)	PUNCT
bibechana-9308	182	9	,	,	PUNCT
bibechana-9308	182	10	n	n	PRON
bibechana-9308	182	11	≥	≥	NOUN
bibechana-9308	182	12	1	1	NUM
bibechana-9308	182	13	,	,	PUNCT
bibechana-9308	182	14	in	in	ADP
bibechana-9308	182	15	view	view	NOUN
bibechana-9308	182	16	of	of	ADP
bibechana-9308	182	17	(	(	PUNCT
bibechana-9308	182	18	3.7	3.7	NUM
bibechana-9308	182	19	)	)	PUNCT
bibechana-9308	182	20	and	and	CCONJ
bibechana-9308	182	21	(	(	PUNCT
bibechana-9308	182	22	3.8	3.8	NUM
bibechana-9308	182	23	)	)	PUNCT
bibechana-9308	182	24	,	,	PUNCT
bibechana-9308	182	25	we	we	PRON
bibechana-9308	182	26	have	have	VERB
bibechana-9308	182	27	||αk	||αk	NOUN
bibechana-9308	182	28	ξk	ξk	ADP
bibechana-9308	182	29	‚	‚	NUM
bibechana-9308	182	30	η||	η||	X
bibechana-9308	182	31	u	u	NOUN
bibechana-9308	182	32	k	k	NOUN
bibechana-9308	182	33	=	=	PUNCT
bibechana-9308	182	34	||	||	NOUN
bibechana-9308	182	35	n-1	n-1	NUM
bibechana-9308	182	36	/	/	SYM
bibechana-9308	182	37	vk(n	vk(n	NUM
bibechana-9308	182	38	)	)	PUNCT
bibechana-9308	183	1	ρ	ρ	X
bibechana-9308	183	2	‚	‚	NOUN
bibechana-9308	183	3	η||	η||	NOUN
bibechana-9308	183	4	uk(n	uk(n	X
bibechana-9308	183	5	)	)	PUNCT
bibechana-9308	183	6	≥	≥	NOUN
bibechana-9308	184	1	1	1	NUM
bibechana-9308	184	2	n	n	NUM
bibechana-9308	184	3	1	1	NUM
bibechana-9308	184	4	/	/	SYM
bibechana-9308	184	5	n	n	NOUN
bibechana-9308	184	6	||	||	NOUN
bibechana-9308	184	7	ρ	ρ	NUM
bibechana-9308	184	8	‚	‚	NOUN
bibechana-9308	184	9	η||	η||	NOUN
bibechana-9308	184	10	uk(n	uk(n	X
bibechana-9308	184	11	)	)	PUNCT
bibechana-9308	184	12	≥	≥	NOUN
bibechana-9308	184	13	1	1	NUM
bibechana-9308	184	14	n	n	NUM
bibechana-9308	184	15	1/2	1/2	NUM
bibechana-9308	184	16	this	this	PRON
bibechana-9308	184	17	shows	show	VERB
bibechana-9308	184	18	that	that	SCONJ
bibechana-9308	184	19	ξ	ξ	X
bibechana-9308	184	20	–	–	PUNCT
bibechana-9308	184	21	∉	∉	PROPN
bibechana-9308	184	22	c0	c0	X
bibechana-9308	184	23	(	(	PUNCT
bibechana-9308	184	24	s	s	PROPN
bibechana-9308	184	25	,	,	PUNCT
bibechana-9308	184	26	α	α	PROPN
bibechana-9308	184	27	–	–	PUNCT
bibechana-9308	184	28	,	,	PUNCT
bibechana-9308	184	29	u	u	NOUN
bibechana-9308	184	30	–	–	PUNCT
bibechana-9308	184	31	,	,	PUNCT
bibechana-9308	184	32	||	||	PROPN
bibechana-9308	184	33	.	.	PUNCT
bibechana-9308	184	34	,	,	PUNCT
bibechana-9308	184	35	.||	.||	PROPN
bibechana-9308	184	36	)	)	PUNCT
bibechana-9308	184	37	,	,	PUNCT
bibechana-9308	184	38	a	a	DET
bibechana-9308	184	39	contradiction	contradiction	NOUN
bibechana-9308	184	40	.	.	PUNCT
bibechana-9308	185	1	for	for	ADP
bibechana-9308	185	2	the	the	DET
bibechana-9308	185	3	sufficiency	sufficiency	NOUN
bibechana-9308	185	4	of	of	ADP
bibechana-9308	185	5	the	the	DET
bibechana-9308	185	6	condition	condition	NOUN
bibechana-9308	185	7	,	,	PUNCT
bibechana-9308	185	8	assume	assume	VERB
bibechana-9308	185	9	that	that	SCONJ
bibechana-9308	185	10	lim	lim	PROPN
bibechana-9308	185	11	supk	supk	PROPN
bibechana-9308	185	12	vk	vk	PROPN
bibechana-9308	185	13	uk	uk	PROPN
bibechana-9308	185	14	<	<	X
bibechana-9308	185	15	∞.	∞.	PROPN
bibechana-9308	185	16	hence	hence	ADV
bibechana-9308	185	17	there	there	PRON
bibechana-9308	185	18	exists	exist	VERB
bibechana-9308	185	19	d	d	X
bibechana-9308	185	20	>	>	X
bibechana-9308	185	21	0	0	NUM
bibechana-9308	185	22	such	such	ADJ
bibechana-9308	185	23	that	that	PRON
bibechana-9308	185	24	vk	vk	NOUN
bibechana-9308	185	25	<	<	X
bibechana-9308	185	26	d	d	X
bibechana-9308	185	27	uk	uk	PROPN
bibechana-9308	185	28	for	for	ADP
bibechana-9308	185	29	all	all	DET
bibechana-9308	185	30	sufficiently	sufficiently	ADV
bibechana-9308	185	31	large	large	ADJ
bibechana-9308	185	32	values	value	NOUN
bibechana-9308	185	33	of	of	ADP
bibechana-9308	185	34	k.	k.	PROPN
bibechana-9308	185	35	let	let	VERB
bibechana-9308	185	36	ξ	ξ	X
bibechana-9308	185	37	–	–	PUNCT
bibechana-9308	185	38	=	=	SYM
bibechana-9308	185	39	(	(	PUNCT
bibechana-9308	185	40	ξk	ξk	NOUN
bibechana-9308	185	41	)	)	PUNCT
bibechana-9308	185	42	∈	∈	PROPN
bibechana-9308	185	43	c0	c0	NOUN
bibechana-9308	185	44	(	(	PUNCT
bibechana-9308	185	45	s	s	PROPN
bibechana-9308	185	46	,	,	PUNCT
bibechana-9308	185	47	α	α	NOUN
bibechana-9308	185	48	–	–	PUNCT
bibechana-9308	185	49	,	,	PUNCT
bibechana-9308	185	50	v–,||	v–,||	NUM
bibechana-9308	185	51	.	.	PUNCT
bibechana-9308	185	52	,	,	PUNCT
bibechana-9308	185	53	.||	.||	PROPN
bibechana-9308	185	54	)	)	PUNCT
bibechana-9308	185	55	.	.	PUNCT
bibechana-9308	186	1	then	then	ADV
bibechana-9308	186	2	for	for	SCONJ
bibechana-9308	186	3	each	each	DET
bibechana-9308	186	4	η	η	PROPN
bibechana-9308	186	5	∈	∈	PROPN
bibechana-9308	186	6	s	s	PART
bibechana-9308	186	7	||αk	||αk	NOUN
bibechana-9308	186	8	ξk	ξk	ADP
bibechana-9308	186	9	‚	‚	NUM
bibechana-9308	186	10	η||	η||	NOUN
bibechana-9308	186	11	v	v	ADP
bibechana-9308	186	12	k	k	PROPN
bibechana-9308	186	13	→	→	SYM
bibechana-9308	186	14	0	0	PUNCT
bibechana-9308	186	15	as	as	ADP
bibechana-9308	186	16	k	k	PROPN
bibechana-9308	186	17	→	→	SYM
bibechana-9308	186	18	∞.	∞.	PROPN
bibechana-9308	186	19	hence	hence	ADV
bibechana-9308	186	20	for	for	ADP
bibechana-9308	186	21	a	a	DET
bibechana-9308	186	22	given	give	VERB
bibechana-9308	186	23	ε	ε	PROPN
bibechana-9308	186	24	>	>	X
bibechana-9308	186	25	0	0	PROPN
bibechana-9308	186	26	,	,	PUNCT
bibechana-9308	186	27	if	if	SCONJ
bibechana-9308	186	28	we	we	PRON
bibechana-9308	186	29	choose	choose	VERB
bibechana-9308	186	30	0	0	PUNCT
bibechana-9308	186	31	<	<	X
bibechana-9308	186	32	δ	δ	X
bibechana-9308	186	33	<	<	X
bibechana-9308	186	34	1	1	NUM
bibechana-9308	186	35	satisfying	satisfy	VERB
bibechana-9308	186	36	δ	δ	NOUN
bibechana-9308	186	37	1	1	NUM
bibechana-9308	186	38	/	/	SYM
bibechana-9308	186	39	d	d	NOUN
bibechana-9308	186	40	<	<	X
bibechana-9308	186	41	ε	ε	X
bibechana-9308	186	42	satisfying	satisfy	VERB
bibechana-9308	186	43	||αk	||αk	NOUN
bibechana-9308	186	44	ξk	ξk	ADP
bibechana-9308	186	45	,	,	PUNCT
bibechana-9308	186	46	η	η	PROPN
bibechana-9308	186	47	||	||	PROPN
bibechana-9308	186	48	vk	vk	ADP
bibechana-9308	186	49	<	<	X
bibechana-9308	186	50	δ	δ	X
bibechana-9308	186	51	<	<	X
bibechana-9308	186	52	1	1	NUM
bibechana-9308	186	53	for	for	ADP
bibechana-9308	186	54	each	each	DET
bibechana-9308	186	55	η	η	PROPN
bibechana-9308	186	56	∈	∈	PROPN
bibechana-9308	186	57	s	s	X
bibechana-9308	186	58	and	and	CCONJ
bibechana-9308	186	59	for	for	ADP
bibechana-9308	186	60	all	all	DET
bibechana-9308	186	61	sufficiently	sufficiently	ADV
bibechana-9308	186	62	large	large	ADJ
bibechana-9308	186	63	values	value	NOUN
bibechana-9308	186	64	of	of	ADP
bibechana-9308	186	65	k.thus	k.thus	NOUN
bibechana-9308	186	66	||αk	||αk	NOUN
bibechana-9308	186	67	ξk	ξk	ADP
bibechana-9308	186	68	,	,	PUNCT
bibechana-9308	186	69	η	η	PROPN
bibechana-9308	186	70	||	||	PROPN
bibechana-9308	186	71	uk	uk	PROPN
bibechana-9308	186	72	≤	≤	PROPN
bibechana-9308	187	1	[	[	X
bibechana-9308	187	2	||αk	||αk	NOUN
bibechana-9308	187	3	ξk	ξk	ADP
bibechana-9308	187	4	‚	‚	NUM
bibechana-9308	187	5	η||	η||	NOUN
bibechana-9308	187	6	v	v	NOUN
bibechana-9308	187	7	k	k	X
bibechana-9308	187	8	]	]	X
bibechana-9308	187	9	1	1	NUM
bibechana-9308	187	10	/	/	SYM
bibechana-9308	187	11	d	d	X
bibechana-9308	187	12	n.p	n.p	PROPN
bibechana-9308	187	13	.	.	PROPN
bibechana-9308	187	14	pahari	pahari	PROPN
bibechana-9308	187	15	/	/	SYM
bibechana-9308	187	16	bibechana	bibechana	NOUN
bibechana-9308	187	17	10	10	NUM
bibechana-9308	187	18	(	(	PUNCT
bibechana-9308	187	19	2014	2014	NUM
bibechana-9308	187	20	)	)	PUNCT
bibechana-9308	187	21	20	20	NUM
bibechana-9308	187	22	-	-	SYM
bibechana-9308	187	23	30	30	NUM
bibechana-9308	187	24	:	:	PUNCT
bibechana-9308	187	25	bmhss	bmhss	PROPN
bibechana-9308	187	26	,	,	PUNCT
bibechana-9308	187	27	p.27	p.27	X
bibechana-9308	187	28	(	(	PUNCT
bibechana-9308	187	29	online	online	ADJ
bibechana-9308	187	30	publication	publication	NOUN
bibechana-9308	187	31	:	:	PUNCT
bibechana-9308	187	32	dec	dec	PROPN
bibechana-9308	187	33	.	.	PROPN
bibechana-9308	187	34	,	,	PUNCT
bibechana-9308	187	35	2013	2013	NUM
bibechana-9308	187	36	)	)	PUNCT
bibechana-9308	187	37	≤	≤	NUM
bibechana-9308	187	38	δ	δ	X
bibechana-9308	187	39	1	1	NUM
bibechana-9308	187	40	/	/	SYM
bibechana-9308	187	41	d	d	X
bibechana-9308	187	42	<	<	X
bibechana-9308	187	43	ε	ε	PROPN
bibechana-9308	187	44	,	,	PUNCT
bibechana-9308	187	45	for	for	ADP
bibechana-9308	187	46	each	each	DET
bibechana-9308	187	47	η	η	PROPN
bibechana-9308	187	48	∈	∈	PROPN
bibechana-9308	187	49	s	s	X
bibechana-9308	187	50	and	and	CCONJ
bibechana-9308	187	51	for	for	ADP
bibechana-9308	187	52	all	all	DET
bibechana-9308	187	53	sufficiently	sufficiently	ADV
bibechana-9308	187	54	large	large	ADJ
bibechana-9308	187	55	values	value	NOUN
bibechana-9308	187	56	of	of	ADP
bibechana-9308	187	57	k	k	PROPN
bibechana-9308	187	58	and	and	CCONJ
bibechana-9308	187	59	consequently	consequently	ADV
bibechana-9308	187	60	ξ	ξ	X
bibechana-9308	187	61	–	–	PUNCT
bibechana-9308	187	62	∈	∈	PROPN
bibechana-9308	187	63	c0	c0	NOUN
bibechana-9308	187	64	(	(	PUNCT
bibechana-9308	187	65	s	s	PROPN
bibechana-9308	187	66	,	,	PUNCT
bibechana-9308	187	67	α	α	NOUN
bibechana-9308	187	68	–	–	PUNCT
bibechana-9308	187	69	,	,	PUNCT
bibechana-9308	187	70	u–,||	u–,||	PROPN
bibechana-9308	187	71	.	.	PUNCT
bibechana-9308	187	72	,	,	PUNCT
bibechana-9308	187	73	.||	.||	PROPN
bibechana-9308	187	74	)	)	PUNCT
bibechana-9308	187	75	.	.	PUNCT
bibechana-9308	188	1	hence	hence	ADV
bibechana-9308	188	2	c0	c0	PROPN
bibechana-9308	188	3	(	(	PUNCT
bibechana-9308	188	4	s	s	PROPN
bibechana-9308	188	5	,	,	PUNCT
bibechana-9308	188	6	α	α	NOUN
bibechana-9308	188	7	–	–	PUNCT
bibechana-9308	188	8	,	,	PUNCT
bibechana-9308	188	9	v–,||	v–,||	NUM
bibechana-9308	188	10	.	.	PUNCT
bibechana-9308	188	11	,	,	PUNCT
bibechana-9308	188	12	.||	.||	PROPN
bibechana-9308	188	13	)	)	PUNCT
bibechana-9308	189	1	⊂	⊂	PROPN
bibechana-9308	189	2	c0	c0	PROPN
bibechana-9308	189	3	(	(	PUNCT
bibechana-9308	189	4	s	s	PROPN
bibechana-9308	189	5	,	,	PUNCT
bibechana-9308	189	6	α	α	PROPN
bibechana-9308	189	7	–	–	PUNCT
bibechana-9308	189	8	,	,	PUNCT
bibechana-9308	189	9	u	u	NOUN
bibechana-9308	189	10	–	–	PUNCT
bibechana-9308	189	11	,	,	PUNCT
bibechana-9308	189	12	||	||	PROPN
bibechana-9308	189	13	.	.	PUNCT
bibechana-9308	189	14	,	,	PUNCT
bibechana-9308	189	15	.||	.||	PROPN
bibechana-9308	189	16	)	)	PUNCT
bibechana-9308	189	17	.	.	PUNCT
bibechana-9308	190	1	this	this	PRON
bibechana-9308	190	2	completes	complete	VERB
bibechana-9308	190	3	the	the	DET
bibechana-9308	190	4	proof	proof	NOUN
bibechana-9308	190	5	.	.	PUNCT
bibechana-9308	191	1	on	on	ADP
bibechana-9308	191	2	combining	combine	VERB
bibechana-9308	191	3	the	the	DET
bibechana-9308	191	4	theorems	theorem	NOUN
bibechana-9308	191	5	3.5	3.5	NUM
bibechana-9308	191	6	and	and	CCONJ
bibechana-9308	191	7	3.6	3.6	NUM
bibechana-9308	191	8	,	,	PUNCT
bibechana-9308	191	9	one	one	NUM
bibechana-9308	191	10	obtain	obtain	NOUN
bibechana-9308	191	11	theorem	theorem	VERB
bibechana-9308	191	12	3.7	3.7	NUM
bibechana-9308	191	13	:	:	PUNCT
bibechana-9308	191	14	for	for	ADP
bibechana-9308	191	15	any	any	DET
bibechana-9308	191	16	α	α	NOUN
bibechana-9308	191	17	–	–	PUNCT
bibechana-9308	191	18	=	=	SYM
bibechana-9308	191	19	(	(	PUNCT
bibechana-9308	191	20	ααααk),c0	ααααk),c0	NOUN
bibechana-9308	191	21	(	(	PUNCT
bibechana-9308	191	22	s	s	PROPN
bibechana-9308	191	23	,	,	PUNCT
bibechana-9308	191	24	α	α	PROPN
bibechana-9308	191	25	–	–	PUNCT
bibechana-9308	191	26	,	,	PUNCT
bibechana-9308	191	27	u	u	INTJ
bibechana-9308	191	28	–	–	PUNCT
bibechana-9308	191	29	,	,	PUNCT
bibechana-9308	191	30	||	||	PROPN
bibechana-9308	191	31	.	.	PUNCT
bibechana-9308	191	32	,	,	PUNCT
bibechana-9308	191	33	.||	.||	PROPN
bibechana-9308	191	34	)	)	PUNCT
bibechana-9308	192	1	=	=	SYM
bibechana-9308	192	2	c0	c0	X
bibechana-9308	192	3	(	(	PUNCT
bibechana-9308	192	4	s	s	PROPN
bibechana-9308	192	5	,	,	PUNCT
bibechana-9308	192	6	α	α	PROPN
bibechana-9308	192	7	–	–	PUNCT
bibechana-9308	192	8	,	,	PUNCT
bibechana-9308	192	9	v	v	INTJ
bibechana-9308	192	10	–	–	PUNCT
bibechana-9308	192	11	,	,	PUNCT
bibechana-9308	192	12	||	||	PROPN
bibechana-9308	192	13	.	.	PUNCT
bibechana-9308	192	14	,	,	PUNCT
bibechana-9308	192	15	.||	.||	PROPN
bibechana-9308	192	16	)	)	PUNCT
bibechana-9308	193	1	if	if	SCONJ
bibechana-9308	193	2	and	and	CCONJ
bibechana-9308	193	3	only	only	ADV
bibechana-9308	193	4	if	if	SCONJ
bibechana-9308	193	5	0	0	NUM
bibechana-9308	193	6	<	<	X
bibechana-9308	193	7	lim	lim	PROPN
bibechana-9308	193	8	infk	infk	PROPN
bibechana-9308	193	9	vk	vk	PROPN
bibechana-9308	193	10	uk	uk	PROPN
bibechana-9308	193	11	≤≤≤≤	≤≤≤≤	PROPN
bibechana-9308	193	12	lim	lim	PROPN
bibechana-9308	193	13	supk	supk	PROPN
bibechana-9308	193	14	vk	vk	PROPN
bibechana-9308	193	15	uk	uk	PROPN
bibechana-9308	193	16	<	<	X
bibechana-9308	193	17	∞.∞.∞.∞.	∞.∞.∞.∞.	PROPN
bibechana-9308	193	18	corollary	corollary	ADJ
bibechana-9308	193	19	3.8	3.8	NUM
bibechana-9308	193	20	:	:	PUNCT
bibechana-9308	193	21	for	for	ADP
bibechana-9308	193	22	any	any	DET
bibechana-9308	193	23	α	α	NOUN
bibechana-9308	193	24	–	–	PUNCT
bibechana-9308	193	25	=	=	NOUN
bibechana-9308	193	26	(	(	PUNCT
bibechana-9308	193	27	ααααk	ααααk	NOUN
bibechana-9308	193	28	)	)	PUNCT
bibechana-9308	193	29	,	,	PUNCT
bibechana-9308	193	30	(	(	PUNCT
bibechana-9308	193	31	i	i	NOUN
bibechana-9308	193	32	)	)	PUNCT
bibechana-9308	193	33	c0	c0	PROPN
bibechana-9308	193	34	(	(	PUNCT
bibechana-9308	193	35	s	s	PROPN
bibechana-9308	193	36	,	,	PUNCT
bibechana-9308	193	37	α	α	PROPN
bibechana-9308	193	38	–	–	PUNCT
bibechana-9308	193	39	,	,	PUNCT
bibechana-9308	193	40	||	||	X
bibechana-9308	193	41	.	.	PUNCT
bibechana-9308	193	42	,	,	PUNCT
bibechana-9308	193	43	.||	.||	PROPN
bibechana-9308	193	44	)	)	PUNCT
bibechana-9308	194	1	⊂	⊂	PROPN
bibechana-9308	194	2	⊂	⊂	PROPN
bibechana-9308	195	1	⊂	⊂	PROPN
bibechana-9308	195	2	⊂	⊂	PROPN
bibechana-9308	195	3	c0	c0	PROPN
bibechana-9308	195	4	(	(	PUNCT
bibechana-9308	195	5	s	s	PROPN
bibechana-9308	195	6	,	,	PUNCT
bibechana-9308	195	7	α	α	PROPN
bibechana-9308	195	8	–	–	PUNCT
bibechana-9308	195	9	,	,	PUNCT
bibechana-9308	195	10	u	u	INTJ
bibechana-9308	195	11	–	–	PUNCT
bibechana-9308	195	12	,	,	PUNCT
bibechana-9308	195	13	||	||	PROPN
bibechana-9308	195	14	.	.	PUNCT
bibechana-9308	195	15	,	,	PUNCT
bibechana-9308	195	16	.||	.||	PROPN
bibechana-9308	195	17	)	)	PUNCT
bibechana-9308	196	1	if	if	SCONJ
bibechana-9308	196	2	and	and	CCONJ
bibechana-9308	196	3	only	only	ADV
bibechana-9308	196	4	if	if	SCONJ
bibechana-9308	196	5	lim	lim	PROPN
bibechana-9308	196	6	inf	inf	PROPN
bibechana-9308	196	7	k	k	PROPN
bibechana-9308	196	8	uk	uk	PROPN
bibechana-9308	196	9	>	>	X
bibechana-9308	196	10	0	0	NUM
bibechana-9308	196	11	;	;	PUNCT
bibechana-9308	196	12	(	(	PUNCT
bibechana-9308	196	13	ii	ii	NOUN
bibechana-9308	196	14	)	)	PUNCT
bibechana-9308	196	15	c0	c0	NOUN
bibechana-9308	196	16	(	(	PUNCT
bibechana-9308	196	17	s	s	PROPN
bibechana-9308	196	18	,	,	PUNCT
bibechana-9308	196	19	α	α	PROPN
bibechana-9308	196	20	–	–	PUNCT
bibechana-9308	196	21	,	,	PUNCT
bibechana-9308	196	22	u	u	INTJ
bibechana-9308	196	23	–	–	PUNCT
bibechana-9308	196	24	,	,	PUNCT
bibechana-9308	196	25	||	||	PROPN
bibechana-9308	196	26	.	.	PUNCT
bibechana-9308	196	27	,	,	PUNCT
bibechana-9308	196	28	.||	.||	PROPN
bibechana-9308	196	29	)	)	PUNCT
bibechana-9308	197	1	⊂⊂⊂⊂	⊂⊂⊂⊂	NUM
bibechana-9308	197	2	c0	c0	NOUN
bibechana-9308	197	3	(	(	PUNCT
bibechana-9308	197	4	s	s	PROPN
bibechana-9308	197	5	,	,	PUNCT
bibechana-9308	197	6	α	α	PROPN
bibechana-9308	197	7	–	–	PUNCT
bibechana-9308	197	8	,	,	PUNCT
bibechana-9308	197	9	||	||	X
bibechana-9308	197	10	.	.	PUNCT
bibechana-9308	197	11	,	,	PUNCT
bibechana-9308	197	12	.||	.||	PROPN
bibechana-9308	197	13	)	)	PUNCT
bibechana-9308	198	1	if	if	SCONJ
bibechana-9308	198	2	and	and	CCONJ
bibechana-9308	198	3	only	only	ADV
bibechana-9308	198	4	if	if	SCONJ
bibechana-9308	198	5	lim	lim	PROPN
bibechana-9308	198	6	sup	sup	PROPN
bibechana-9308	198	7	k	k	PROPN
bibechana-9308	198	8	uk	uk	PROPN
bibechana-9308	198	9	<	<	X
bibechana-9308	198	10	∞∞∞∞	∞∞∞∞	PROPN
bibechana-9308	198	11	;	;	PUNCT
bibechana-9308	198	12	and	and	CCONJ
bibechana-9308	198	13	(	(	PUNCT
bibechana-9308	198	14	iii	iii	X
bibechana-9308	198	15	)	)	PUNCT
bibechana-9308	198	16	c0	c0	NOUN
bibechana-9308	198	17	(	(	PUNCT
bibechana-9308	198	18	s	s	PROPN
bibechana-9308	198	19	,	,	PUNCT
bibechana-9308	198	20	α	α	PROPN
bibechana-9308	198	21	–	–	PUNCT
bibechana-9308	198	22	,	,	PUNCT
bibechana-9308	198	23	u	u	INTJ
bibechana-9308	198	24	–	–	PUNCT
bibechana-9308	198	25	,	,	PUNCT
bibechana-9308	198	26	||	||	PROPN
bibechana-9308	198	27	.	.	PUNCT
bibechana-9308	198	28	,	,	PUNCT
bibechana-9308	198	29	.||	.||	PROPN
bibechana-9308	198	30	)	)	PUNCT
bibechana-9308	199	1	=	=	SYM
bibechana-9308	199	2	c0	c0	X
bibechana-9308	199	3	(	(	PUNCT
bibechana-9308	199	4	s	s	PROPN
bibechana-9308	199	5	,	,	PUNCT
bibechana-9308	199	6	α	α	PROPN
bibechana-9308	199	7	–	–	PUNCT
bibechana-9308	199	8	,	,	PUNCT
bibechana-9308	199	9	||	||	X
bibechana-9308	199	10	.	.	PUNCT
bibechana-9308	199	11	,	,	PUNCT
bibechana-9308	199	12	.||	.||	PROPN
bibechana-9308	199	13	)	)	PUNCT
bibechana-9308	200	1	if	if	SCONJ
bibechana-9308	200	2	and	and	CCONJ
bibechana-9308	200	3	only	only	ADV
bibechana-9308	200	4	if	if	SCONJ
bibechana-9308	200	5	0	0	NUM
bibechana-9308	200	6	<	<	X
bibechana-9308	200	7	lim	lim	PROPN
bibechana-9308	200	8	infk	infk	PROPN
bibechana-9308	200	9	uk	uk	PROPN
bibechana-9308	200	10	≤≤≤≤	≤≤≤≤	PROPN
bibechana-9308	200	11	lim	lim	PROPN
bibechana-9308	200	12	supk	supk	PROPN
bibechana-9308	200	13	uk	uk	PROPN
bibechana-9308	200	14	<	<	X
bibechana-9308	200	15	∞∞∞∞.	∞∞∞∞.	PROPN
bibechana-9308	200	16	proof	proof	NOUN
bibechana-9308	200	17	:	:	PUNCT
bibechana-9308	200	18	proof	proof	NOUN
bibechana-9308	200	19	follows	follow	VERB
bibechana-9308	200	20	by	by	ADP
bibechana-9308	200	21	taking	take	VERB
bibechana-9308	200	22	uk	uk	PROPN
bibechana-9308	200	23	=	=	X
bibechana-9308	200	24	1	1	NUM
bibechana-9308	200	25	for	for	ADP
bibechana-9308	200	26	all	all	DET
bibechana-9308	200	27	k	k	PROPN
bibechana-9308	200	28	and	and	CCONJ
bibechana-9308	200	29	replacing	replace	VERB
bibechana-9308	200	30	v	v	NOUN
bibechana-9308	200	31	–	–	PUNCT
bibechana-9308	200	32	by	by	ADP
bibechana-9308	200	33	u	u	NOUN
bibechana-9308	200	34	–	–	PUNCT
bibechana-9308	200	35	in	in	ADP
bibechana-9308	200	36	theorems	theorem	NOUN
bibechana-9308	200	37	3.5	3.5	NUM
bibechana-9308	200	38	,	,	PUNCT
bibechana-9308	200	39	3.6	3.6	NUM
bibechana-9308	200	40	and	and	CCONJ
bibechana-9308	200	41	3.7	3.7	NUM
bibechana-9308	200	42	.	.	PUNCT
bibechana-9308	201	1	theorem	theorem	VERB
bibechana-9308	201	2	3.9	3.9	NUM
bibechana-9308	201	3	:	:	PUNCT
bibechana-9308	201	4	for	for	ADP
bibechana-9308	201	5	any	any	DET
bibechana-9308	201	6	α	α	NOUN
bibechana-9308	201	7	–	–	PUNCT
bibechana-9308	201	8	=	=	NOUN
bibechana-9308	201	9	(	(	PUNCT
bibechana-9308	201	10	ααααk	ααααk	NOUN
bibechana-9308	201	11	)	)	PUNCT
bibechana-9308	201	12	,	,	PUNCT
bibechana-9308	201	13	β	β	X
bibechana-9308	201	14	–	–	PUNCT
bibechana-9308	201	15	=	=	SYM
bibechana-9308	201	16	(	(	PUNCT
bibechana-9308	201	17	ββββk	ββββk	NOUN
bibechana-9308	201	18	)	)	PUNCT
bibechana-9308	201	19	,	,	PUNCT
bibechana-9308	201	20	u	u	NOUN
bibechana-9308	201	21	–	–	PUNCT
bibechana-9308	201	22	=	=	SYM
bibechana-9308	201	23	(	(	PUNCT
bibechana-9308	201	24	uk	uk	PROPN
bibechana-9308	201	25	)	)	PUNCT
bibechana-9308	201	26	and	and	CCONJ
bibechana-9308	201	27	v	v	NOUN
bibechana-9308	201	28	–	–	PUNCT
bibechana-9308	201	29	=	=	SYM
bibechana-9308	201	30	(	(	PUNCT
bibechana-9308	201	31	vk	vk	PROPN
bibechana-9308	201	32	)	)	PUNCT
bibechana-9308	201	33	,	,	PUNCT
bibechana-9308	201	34	c0	c0	X
bibechana-9308	201	35	(	(	PUNCT
bibechana-9308	201	36	s	s	PROPN
bibechana-9308	201	37	,	,	PUNCT
bibechana-9308	201	38	α	α	PROPN
bibechana-9308	201	39	–	–	PUNCT
bibechana-9308	201	40	,	,	PUNCT
bibechana-9308	201	41	u	u	INTJ
bibechana-9308	201	42	–	–	PUNCT
bibechana-9308	201	43	,	,	PUNCT
bibechana-9308	201	44	||	||	PROPN
bibechana-9308	201	45	.	.	PUNCT
bibechana-9308	201	46	,	,	PUNCT
bibechana-9308	201	47	.||	.||	PROPN
bibechana-9308	201	48	)	)	PUNCT
bibechana-9308	202	1	⊂	⊂	PROPN
bibechana-9308	202	2	⊂	⊂	PROPN
bibechana-9308	203	1	⊂	⊂	PROPN
bibechana-9308	204	1	⊂	⊂	PROPN
bibechana-9308	205	1	c0	c0	PROPN
bibechana-9308	205	2	(	(	PUNCT
bibechana-9308	205	3	s	s	PROPN
bibechana-9308	205	4	,	,	PUNCT
bibechana-9308	205	5	β	β	X
bibechana-9308	205	6	–	–	PUNCT
bibechana-9308	205	7	,	,	PUNCT
bibechana-9308	205	8	v	v	INTJ
bibechana-9308	205	9	–	–	PUNCT
bibechana-9308	205	10	,	,	PUNCT
bibechana-9308	205	11	||	||	X
bibechana-9308	205	12	.	.	PUNCT
bibechana-9308	205	13	,	,	PUNCT
bibechana-9308	205	14	.||	.||	PROPN
bibechana-9308	205	15	)	)	PUNCT
bibechana-9308	206	1	if	if	SCONJ
bibechana-9308	206	2	and	and	CCONJ
bibechana-9308	206	3	only	only	ADV
bibechana-9308	206	4	if	if	SCONJ
bibechana-9308	206	5	(	(	PUNCT
bibechana-9308	206	6	i	i	NOUN
bibechana-9308	206	7	)	)	PUNCT
bibechana-9308	206	8	lim	lim	PROPN
bibechana-9308	206	9	infk	infk	PROPN
bibechana-9308	206	10			PROPN
bibechana-9308	206	11			PROPN
bibechana-9308	206	12			PROPN
bibechana-9308	206	13	αk	αk	ADP
bibechana-9308	206	14	βk	βk	ADP
bibechana-9308	206	15	uk	uk	PROPN
bibechana-9308	206	16	>	>	X
bibechana-9308	206	17	0	0	NUM
bibechana-9308	206	18	;	;	PUNCT
bibechana-9308	206	19	and	and	CCONJ
bibechana-9308	206	20	(	(	PUNCT
bibechana-9308	206	21	ii	ii	NOUN
bibechana-9308	206	22	)	)	PUNCT
bibechana-9308	206	23	lim	lim	PROPN
bibechana-9308	206	24	infk	infk	PROPN
bibechana-9308	206	25	vk	vk	PROPN
bibechana-9308	206	26	uk	uk	PROPN
bibechana-9308	206	27	>	>	X
bibechana-9308	206	28	0	0	X
bibechana-9308	206	29	.	.	PUNCT
bibechana-9308	206	30	proof	proof	NOUN
bibechana-9308	206	31	:	:	PUNCT
bibechana-9308	206	32	proof	proof	NOUN
bibechana-9308	206	33	of	of	ADP
bibechana-9308	206	34	the	the	DET
bibechana-9308	206	35	theorem	theorem	NOUN
bibechana-9308	206	36	follows	follow	VERB
bibechana-9308	206	37	immediately	immediately	ADV
bibechana-9308	206	38	from	from	ADP
bibechana-9308	206	39	the	the	DET
bibechana-9308	206	40	theorems	theorem	NOUN
bibechana-9308	206	41	3.1	3.1	NUM
bibechana-9308	206	42	and	and	CCONJ
bibechana-9308	206	43	3.5	3.5	NUM
bibechana-9308	206	44	.	.	PUNCT
bibechana-9308	207	1	in	in	ADP
bibechana-9308	207	2	the	the	DET
bibechana-9308	207	3	following	follow	VERB
bibechana-9308	207	4	example	example	NOUN
bibechana-9308	207	5	,	,	PUNCT
bibechana-9308	207	6	c0	c0	PROPN
bibechana-9308	207	7	(	(	PUNCT
bibechana-9308	207	8	s	s	PROPN
bibechana-9308	207	9	,	,	PUNCT
bibechana-9308	207	10	α	α	PROPN
bibechana-9308	207	11	–	–	PUNCT
bibechana-9308	207	12	,	,	PUNCT
bibechana-9308	207	13	u	u	NOUN
bibechana-9308	207	14	–	–	PUNCT
bibechana-9308	207	15	,	,	PUNCT
bibechana-9308	207	16	||	||	PROPN
bibechana-9308	207	17	.	.	PUNCT
bibechana-9308	207	18	,	,	PUNCT
bibechana-9308	207	19	.||	.||	PROPN
bibechana-9308	207	20	)	)	PUNCT
bibechana-9308	207	21	may	may	AUX
bibechana-9308	207	22	strictly	strictly	ADV
bibechana-9308	207	23	be	be	AUX
bibechana-9308	207	24	contained	contain	VERB
bibechana-9308	207	25	in	in	ADP
bibechana-9308	207	26	c0	c0	PROPN
bibechana-9308	207	27	(	(	PUNCT
bibechana-9308	207	28	s	s	PROPN
bibechana-9308	207	29	,	,	PUNCT
bibechana-9308	207	30	β	β	X
bibechana-9308	207	31	–	–	PUNCT
bibechana-9308	207	32	,	,	PUNCT
bibechana-9308	207	33	v	v	NOUN
bibechana-9308	207	34	–	–	PUNCT
bibechana-9308	207	35	,	,	PUNCT
bibechana-9308	207	36	||	||	PROPN
bibechana-9308	207	37	.	.	PUNCT
bibechana-9308	207	38	,	,	PUNCT
bibechana-9308	208	1	.||	.||	PROPN
bibechana-9308	208	2	)	)	PUNCT
bibechana-9308	209	1	in	in	ADP
bibechana-9308	209	2	spite	spite	NOUN
bibechana-9308	209	3	of	of	ADP
bibechana-9308	209	4	the	the	DET
bibechana-9308	209	5	satisfaction	satisfaction	NOUN
bibechana-9308	209	6	of	of	ADP
bibechana-9308	209	7	the	the	DET
bibechana-9308	209	8	conditions	condition	NOUN
bibechana-9308	209	9	(	(	PUNCT
bibechana-9308	209	10	i	i	NOUN
bibechana-9308	209	11	)	)	PUNCT
bibechana-9308	209	12	and	and	CCONJ
bibechana-9308	209	13	(	(	PUNCT
bibechana-9308	209	14	ii	ii	NOUN
bibechana-9308	209	15	)	)	PUNCT
bibechana-9308	209	16	of	of	ADP
bibechana-9308	209	17	theorem	theorem	ADJ
bibechana-9308	209	18	3.9	3.9	NUM
bibechana-9308	209	19	.	.	PUNCT
bibechana-9308	209	20	example	example	NOUN
bibechana-9308	209	21	3.10	3.10	NUM
bibechana-9308	209	22	:	:	PUNCT
bibechana-9308	209	23	let	let	VERB
bibechana-9308	209	24	(	(	PUNCT
bibechana-9308	209	25	s	s	NOUN
bibechana-9308	209	26	,	,	PUNCT
bibechana-9308	209	27	||	||	PROPN
bibechana-9308	209	28	.	.	PUNCT
bibechana-9308	209	29	,	,	PUNCT
bibechana-9308	209	30	.||	.||	PROPN
bibechana-9308	209	31	)	)	PUNCT
bibechana-9308	209	32	be	be	AUX
bibechana-9308	209	33	a	a	DET
bibechana-9308	209	34	2normed	2normed	NUM
bibechana-9308	209	35	space	space	NOUN
bibechana-9308	209	36	and	and	CCONJ
bibechana-9308	209	37	consider	consider	VERB
bibechana-9308	209	38	a	a	DET
bibechana-9308	209	39	sequence	sequence	NOUN
bibechana-9308	209	40	ξ	ξ	NOUN
bibechana-9308	209	41	–	–	PUNCT
bibechana-9308	209	42	=	=	SYM
bibechana-9308	209	43	(	(	PUNCT
bibechana-9308	209	44	ξk	ξk	NOUN
bibechana-9308	209	45	)	)	PUNCT
bibechana-9308	209	46	defined	define	VERB
bibechana-9308	209	47	by	by	ADP
bibechana-9308	209	48	ξk	ξk	ADP
bibechana-9308	209	49	=	=	SYM
bibechana-9308	209	50	k	k	PROPN
bibechana-9308	209	51	–	–	PUNCT
bibechana-9308	209	52	k	k	PROPN
bibechana-9308	209	53	ρ	ρ	PROPN
bibechana-9308	209	54	,	,	PUNCT
bibechana-9308	209	55	if	if	SCONJ
bibechana-9308	209	56	k	k	PROPN
bibechana-9308	209	57	=	=	SYM
bibechana-9308	209	58	1	1	NUM
bibechana-9308	209	59	,	,	PUNCT
bibechana-9308	209	60	2	2	NUM
bibechana-9308	209	61	,	,	PUNCT
bibechana-9308	209	62	3	3	NUM
bibechana-9308	209	63	,	,	PUNCT
bibechana-9308	209	64	…	…	PUNCT
bibechana-9308	209	65	,	,	PUNCT
bibechana-9308	209	66	where	where	SCONJ
bibechana-9308	209	67	ρ	ρ	PROPN
bibechana-9308	209	68	∈	∈	PROPN
bibechana-9308	209	69	s	s	X
bibechana-9308	209	70	and	and	CCONJ
bibechana-9308	209	71	ρ	ρ	NOUN
bibechana-9308	209	72	≠	≠	PROPN
bibechana-9308	209	73	θ	θ	PROPN
bibechana-9308	209	74	.	.	PUNCT
bibechana-9308	209	75	further	far	ADV
bibechana-9308	209	76	,	,	PUNCT
bibechana-9308	209	77	let	let	VERB
bibechana-9308	209	78	uk	uk	PROPN
bibechana-9308	209	79	=	=	PROPN
bibechana-9308	209	80	k	k	PROPN
bibechana-9308	209	81	–	–	PUNCT
bibechana-9308	209	82	1	1	NUM
bibechana-9308	209	83	,	,	PUNCT
bibechana-9308	209	84	if	if	SCONJ
bibechana-9308	209	85	k	k	PROPN
bibechana-9308	209	86	is	be	AUX
bibechana-9308	209	87	odd	odd	ADJ
bibechana-9308	209	88	integer	integer	NOUN
bibechana-9308	209	89	,	,	PUNCT
bibechana-9308	209	90	uk	uk	PROPN
bibechana-9308	209	91	=	=	SYM
bibechana-9308	209	92	k	k	PROPN
bibechana-9308	209	93	–	–	PUNCT
bibechana-9308	209	94	2	2	NUM
bibechana-9308	209	95	,	,	PUNCT
bibechana-9308	209	96	if	if	SCONJ
bibechana-9308	209	97	k	k	PROPN
bibechana-9308	209	98	is	be	AUX
bibechana-9308	209	99	even	even	ADV
bibechana-9308	209	100	integer	integer	ADJ
bibechana-9308	209	101	,	,	PUNCT
bibechana-9308	209	102	vk	vk	ADP
bibechana-9308	209	103	=	=	SYM
bibechana-9308	209	104	k	k	X
bibechana-9308	209	105	–	–	PUNCT
bibechana-9308	209	106	1	1	NUM
bibechana-9308	209	107	for	for	ADP
bibechana-9308	209	108	all	all	DET
bibechana-9308	209	109	values	value	NOUN
bibechana-9308	209	110	of	of	ADP
bibechana-9308	209	111	k	k	NOUN
bibechana-9308	209	112	,	,	PUNCT
bibechana-9308	209	113	αk	αk	ADP
bibechana-9308	209	114	=	=	SYM
bibechana-9308	209	115	3k	3k	NUM
bibechana-9308	209	116	,	,	PUNCT
bibechana-9308	209	117	βk	βk	ADP
bibechana-9308	209	118	=	=	NOUN
bibechana-9308	209	119	2k	2k	NUM
bibechana-9308	209	120	for	for	ADP
bibechana-9308	209	121	all	all	DET
bibechana-9308	209	122	values	value	NOUN
bibechana-9308	209	123	of	of	ADP
bibechana-9308	209	124	k.	k.	PROPN
bibechana-9308	209	125	then	then	ADV
bibechana-9308	209	126			PROPN
bibechana-9308	209	127			PROPN
bibechana-9308	209	128			PROPN
bibechana-9308	209	129	αk	αk	ADP
bibechana-9308	209	130	βk	βk	ADP
bibechana-9308	209	131	uk	uk	PROPN
bibechana-9308	209	132	=	=	NOUN
bibechana-9308	209	133	3	3	NUM
bibechana-9308	209	134	2	2	NUM
bibechana-9308	209	135	or	or	CCONJ
bibechana-9308	209	136			NOUN
bibechana-9308	209	137			NOUN
bibechana-9308	209	138			PUNCT
bibechana-9308	210	1			PROPN
bibechana-9308	210	2	3	3	NUM
bibechana-9308	210	3	2	2	NUM
bibechana-9308	210	4	1	1	NUM
bibechana-9308	210	5	/	/	SYM
bibechana-9308	210	6	k	k	NOUN
bibechana-9308	210	7	according	accord	VERB
bibechana-9308	210	8	as	as	SCONJ
bibechana-9308	210	9	k	k	PROPN
bibechana-9308	210	10	is	be	AUX
bibechana-9308	210	11	odd	odd	ADJ
bibechana-9308	210	12	or	or	CCONJ
bibechana-9308	210	13	even	even	ADV
bibechana-9308	210	14	integer	integer	NOUN
bibechana-9308	210	15	and	and	CCONJ
bibechana-9308	210	16	hence	hence	ADV
bibechana-9308	210	17	lim	lim	PROPN
bibechana-9308	210	18	infk	infk	PROPN
bibechana-9308	210	19			PROPN
bibechana-9308	210	20			PROPN
bibechana-9308	210	21			PROPN
bibechana-9308	210	22	αk	αk	ADP
bibechana-9308	210	23	βk	βk	ADP
bibechana-9308	210	24	uk	uk	PROPN
bibechana-9308	210	25	>	>	X
bibechana-9308	210	26	0	0	X
bibechana-9308	210	27	.	.	PUNCT
bibechana-9308	211	1	further	far	ADV
bibechana-9308	211	2	,	,	PUNCT
bibechana-9308	211	3	vk	vk	ADP
bibechana-9308	211	4	uk	uk	NOUN
bibechana-9308	211	5	=	=	SYM
bibechana-9308	211	6	1	1	NUM
bibechana-9308	211	7	,	,	PUNCT
bibechana-9308	211	8	if	if	SCONJ
bibechana-9308	211	9	k	k	PROPN
bibechana-9308	211	10	is	be	AUX
bibechana-9308	211	11	odd	odd	ADJ
bibechana-9308	211	12	integer	integer	NOUN
bibechana-9308	211	13	,	,	PUNCT
bibechana-9308	211	14	vk	vk	ADP
bibechana-9308	211	15	uk	uk	NOUN
bibechana-9308	211	16	=	=	SYM
bibechana-9308	211	17	k	k	PROPN
bibechana-9308	211	18	,	,	PUNCT
bibechana-9308	211	19	if	if	SCONJ
bibechana-9308	211	20	k	k	PROPN
bibechana-9308	211	21	is	be	AUX
bibechana-9308	211	22	even	even	ADV
bibechana-9308	211	23	integer	integer	ADJ
bibechana-9308	211	24	.	.	PUNCT
bibechana-9308	212	1	therefore	therefore	ADV
bibechana-9308	212	2	lim	lim	PROPN
bibechana-9308	212	3	infk	infk	PROPN
bibechana-9308	212	4	vk	vk	PROPN
bibechana-9308	212	5	uk	uk	PROPN
bibechana-9308	212	6	>	>	X
bibechana-9308	212	7	0	0	X
bibechana-9308	212	8	.	.	PUNCT
bibechana-9308	213	1	hence	hence	ADV
bibechana-9308	213	2	the	the	DET
bibechana-9308	213	3	conditions	condition	NOUN
bibechana-9308	213	4	(	(	PUNCT
bibechana-9308	213	5	i	i	NOUN
bibechana-9308	213	6	)	)	PUNCT
bibechana-9308	213	7	and	and	CCONJ
bibechana-9308	213	8	(	(	PUNCT
bibechana-9308	213	9	ii	ii	NOUN
bibechana-9308	213	10	)	)	PUNCT
bibechana-9308	213	11	of	of	ADP
bibechana-9308	213	12	theorem	theorem	ADJ
bibechana-9308	213	13	3.9	3.9	NUM
bibechana-9308	213	14	are	be	AUX
bibechana-9308	213	15	satisfied	satisfied	ADJ
bibechana-9308	213	16	.	.	PUNCT
bibechana-9308	214	1	now	now	ADV
bibechana-9308	214	2	for	for	ADP
bibechana-9308	214	3	each	each	DET
bibechana-9308	214	4	η	η	PROPN
bibechana-9308	214	5	∈	∈	PROPN
bibechana-9308	214	6	s	s	PART
bibechana-9308	214	7	,	,	PUNCT
bibechana-9308	214	8	we	we	PRON
bibechana-9308	214	9	have	have	VERB
bibechana-9308	214	10	n.p	n.p	PROPN
bibechana-9308	214	11	.	.	PROPN
bibechana-9308	214	12	pahari	pahari	PROPN
bibechana-9308	214	13	/	/	SYM
bibechana-9308	214	14	bibechana	bibechana	NOUN
bibechana-9308	214	15	10	10	NUM
bibechana-9308	214	16	(	(	PUNCT
bibechana-9308	214	17	2014	2014	NUM
bibechana-9308	214	18	)	)	PUNCT
bibechana-9308	214	19	20	20	NUM
bibechana-9308	214	20	-	-	SYM
bibechana-9308	214	21	30	30	NUM
bibechana-9308	214	22	:	:	PUNCT
bibechana-9308	214	23	bmhss	bmhss	PROPN
bibechana-9308	214	24	,	,	PUNCT
bibechana-9308	214	25	p.28	p.28	PROPN
bibechana-9308	214	26	(	(	PUNCT
bibechana-9308	214	27	online	online	ADJ
bibechana-9308	214	28	publication	publication	NOUN
bibechana-9308	214	29	:	:	PUNCT
bibechana-9308	215	1	dec	dec	PROPN
bibechana-9308	215	2	.	.	PROPN
bibechana-9308	215	3	,	,	PUNCT
bibechana-9308	215	4	2013	2013	NUM
bibechana-9308	215	5	)	)	PUNCT
bibechana-9308	215	6	||βk	||βk	NOUN
bibechana-9308	215	7	ξk	ξk	ADP
bibechana-9308	215	8	‚	‚	NUM
bibechana-9308	215	9	η||	η||	NOUN
bibechana-9308	215	10	v	v	NOUN
bibechana-9308	215	11	k	k	NOUN
bibechana-9308	215	12	=	=	PUNCT
bibechana-9308	215	13	||2k	||2k	PUNCT
bibechana-9308	216	1	k	k	X
bibechana-9308	216	2	–	–	PUNCT
bibechana-9308	216	3	k	k	PROPN
bibechana-9308	216	4	ρ	ρ	NUM
bibechana-9308	216	5	‚	‚	X
bibechana-9308	216	6	η||	η||	X
bibechana-9308	216	7	1	1	NUM
bibechana-9308	216	8	/	/	SYM
bibechana-9308	216	9	k	k	NOUN
bibechana-9308	216	10	≤	≤	NUM
bibechana-9308	216	11	1	1	NUM
bibechana-9308	216	12	k	k	SYM
bibechana-9308	216	13	2	2	NUM
bibechana-9308	216	14	||	||	NUM
bibechana-9308	216	15	ρ	ρ	NUM
bibechana-9308	216	16	‚	‚	NOUN
bibechana-9308	216	17	η||	η||	X
bibechana-9308	216	18	1	1	NUM
bibechana-9308	216	19	/	/	SYM
bibechana-9308	216	20	k	k	NOUN
bibechana-9308	216	21	≤	≤	NUM
bibechana-9308	216	22	1	1	NUM
bibechana-9308	216	23	k	k	PROPN
bibechana-9308	216	24	2a	2a	NUM
bibechana-9308	216	25	[	[	PUNCT
bibechana-9308	216	26	||	||	NOUN
bibechana-9308	216	27	ρ	ρ	NUM
bibechana-9308	216	28	‚	‚	PROPN
bibechana-9308	216	29	η	η	PROPN
bibechana-9308	216	30	||	||	PROPN
bibechana-9308	216	31	]	]	PUNCT
bibechana-9308	217	1	→	→	SYM
bibechana-9308	217	2	0	0	PUNCT
bibechana-9308	217	3	as	as	ADP
bibechana-9308	217	4	k	k	PROPN
bibechana-9308	217	5	→	→	SYM
bibechana-9308	217	6	∞	∞	PROPN
bibechana-9308	217	7	,	,	PUNCT
bibechana-9308	217	8	and	and	CCONJ
bibechana-9308	217	9	it	it	PRON
bibechana-9308	217	10	shows	show	VERB
bibechana-9308	217	11	that	that	SCONJ
bibechana-9308	217	12	ξ	ξ	X
bibechana-9308	217	13	–	–	PUNCT
bibechana-9308	217	14	∈	∈	PROPN
bibechana-9308	217	15	c0	c0	NOUN
bibechana-9308	217	16	(	(	PUNCT
bibechana-9308	217	17	s	s	PROPN
bibechana-9308	217	18	,	,	PUNCT
bibechana-9308	217	19	β	β	X
bibechana-9308	217	20	–	–	PUNCT
bibechana-9308	217	21	,	,	PUNCT
bibechana-9308	217	22	v	v	NOUN
bibechana-9308	217	23	–	–	PUNCT
bibechana-9308	217	24	,	,	PUNCT
bibechana-9308	217	25	||	||	PROPN
bibechana-9308	217	26	.	.	PUNCT
bibechana-9308	217	27	,	,	PUNCT
bibechana-9308	217	28	.||	.||	PROPN
bibechana-9308	217	29	)	)	PUNCT
bibechana-9308	217	30	.	.	PUNCT
bibechana-9308	218	1	but	but	CCONJ
bibechana-9308	218	2	on	on	ADP
bibechana-9308	218	3	the	the	DET
bibechana-9308	218	4	other	other	ADJ
bibechana-9308	218	5	hand	hand	NOUN
bibechana-9308	218	6	,	,	PUNCT
bibechana-9308	218	7	let	let	VERB
bibechana-9308	218	8	us	we	PRON
bibechana-9308	218	9	choose	choose	VERB
bibechana-9308	218	10	η	η	PROPN
bibechana-9308	218	11	∈	∈	PROPN
bibechana-9308	218	12	s	s	VERB
bibechana-9308	218	13	such	such	ADJ
bibechana-9308	218	14	that	that	DET
bibechana-9308	218	15	||	||	PROPN
bibechana-9308	218	16	ρ	ρ	PROPN
bibechana-9308	218	17	,	,	PUNCT
bibechana-9308	218	18	η	η	PROPN
bibechana-9308	218	19	||	||	PROPN
bibechana-9308	219	1	=	=	SYM
bibechana-9308	219	2	1	1	X
bibechana-9308	219	3	.	.	PUNCT
bibechana-9308	219	4	then	then	ADV
bibechana-9308	219	5	for	for	ADP
bibechana-9308	219	6	each	each	DET
bibechana-9308	219	7	even	even	ADV
bibechana-9308	219	8	integer	integer	PROPN
bibechana-9308	219	9	k	k	PROPN
bibechana-9308	219	10	,	,	PUNCT
bibechana-9308	219	11	we	we	PRON
bibechana-9308	219	12	have	have	VERB
bibechana-9308	219	13	||	||	NOUN
bibechana-9308	220	1	αk	αk	ADP
bibechana-9308	220	2	ξk	ξk	ADP
bibechana-9308	220	3	‚	‚	NUM
bibechana-9308	220	4	η||	η||	NOUN
bibechana-9308	220	5	uk	uk	NOUN
bibechana-9308	220	6	=	=	PRON
bibechana-9308	220	7	||3k	||3k	PROPN
bibechana-9308	220	8	k	k	PROPN
bibechana-9308	220	9	–	–	PUNCT
bibechana-9308	220	10	k	k	PROPN
bibechana-9308	220	11	ρ	ρ	NUM
bibechana-9308	220	12	‚	‚	X
bibechana-9308	220	13	η||	η||	X
bibechana-9308	220	14	1	1	NUM
bibechana-9308	220	15	/	/	SYM
bibechana-9308	220	16	k	k	NOUN
bibechana-9308	220	17	2	2	NUM
bibechana-9308	220	18	=	=	SYM
bibechana-9308	220	19	(	(	PUNCT
bibechana-9308	220	20	3	3	NUM
bibechana-9308	220	21	/	/	SYM
bibechana-9308	220	22	k)1/	k)1/	NOUN
bibechana-9308	220	23	k	k	X
bibechana-9308	220	24	||	||	PROPN
bibechana-9308	221	1	ρ	ρ	NUM
bibechana-9308	221	2	‚	‚	X
bibechana-9308	221	3	η||	η||	X
bibechana-9308	221	4	1	1	NUM
bibechana-9308	221	5	/	/	SYM
bibechana-9308	221	6	k	k	NOUN
bibechana-9308	221	7	2	2	NUM
bibechana-9308	221	8	>	>	SYM
bibechana-9308	221	9	1	1	NUM
bibechana-9308	221	10	2	2	NUM
bibechana-9308	221	11	.	.	PUNCT
bibechana-9308	222	1	this	this	PRON
bibechana-9308	222	2	implies	imply	VERB
bibechana-9308	222	3	that	that	SCONJ
bibechana-9308	222	4	ξ	ξ	PROPN
bibechana-9308	222	5	–	–	PUNCT
bibechana-9308	222	6	∉	∉	PROPN
bibechana-9308	222	7	c0	c0	X
bibechana-9308	222	8	(	(	PUNCT
bibechana-9308	222	9	s	s	PROPN
bibechana-9308	222	10	,	,	PUNCT
bibechana-9308	222	11	α	α	PROPN
bibechana-9308	222	12	–	–	PUNCT
bibechana-9308	222	13	,	,	PUNCT
bibechana-9308	222	14	u	u	NOUN
bibechana-9308	222	15	–	–	PUNCT
bibechana-9308	222	16	,	,	PUNCT
bibechana-9308	222	17	||	||	PROPN
bibechana-9308	222	18	.	.	PUNCT
bibechana-9308	222	19	,	,	PUNCT
bibechana-9308	222	20	.||	.||	PROPN
bibechana-9308	222	21	)	)	PUNCT
bibechana-9308	222	22	.thus	.thus	CCONJ
bibechana-9308	222	23	the	the	DET
bibechana-9308	222	24	containment	containment	NOUN
bibechana-9308	222	25	of	of	ADP
bibechana-9308	222	26	c0	c0	PROPN
bibechana-9308	222	27	(	(	PUNCT
bibechana-9308	222	28	s	s	PROPN
bibechana-9308	222	29	,	,	PUNCT
bibechana-9308	222	30	α	α	PROPN
bibechana-9308	222	31	–	–	PUNCT
bibechana-9308	222	32	,	,	PUNCT
bibechana-9308	222	33	u	u	NOUN
bibechana-9308	222	34	–	–	PUNCT
bibechana-9308	222	35	,	,	PUNCT
bibechana-9308	222	36	||	||	PROPN
bibechana-9308	222	37	.	.	PUNCT
bibechana-9308	222	38	,	,	PUNCT
bibechana-9308	222	39	.||	.||	PROPN
bibechana-9308	222	40	)	)	PUNCT
bibechana-9308	222	41	in	in	ADP
bibechana-9308	222	42	c0	c0	PROPN
bibechana-9308	222	43	(	(	PUNCT
bibechana-9308	222	44	s	s	PROPN
bibechana-9308	222	45	,	,	PUNCT
bibechana-9308	222	46	β	β	X
bibechana-9308	222	47	–	–	PUNCT
bibechana-9308	222	48	,	,	PUNCT
bibechana-9308	222	49	v	v	NOUN
bibechana-9308	222	50	–	–	PUNCT
bibechana-9308	222	51	,	,	PUNCT
bibechana-9308	222	52	||	||	PROPN
bibechana-9308	222	53	.	.	PUNCT
bibechana-9308	222	54	,	,	PUNCT
bibechana-9308	222	55	.||	.||	PROPN
bibechana-9308	222	56	)	)	PUNCT
bibechana-9308	222	57	is	be	AUX
bibechana-9308	222	58	strict	strict	ADJ
bibechana-9308	222	59	inspite	inspite	ADJ
bibechana-9308	222	60	of	of	ADP
bibechana-9308	222	61	the	the	DET
bibechana-9308	222	62	satisfaction	satisfaction	NOUN
bibechana-9308	222	63	of	of	ADP
bibechana-9308	222	64	the	the	DET
bibechana-9308	222	65	conditions	condition	NOUN
bibechana-9308	222	66	(	(	PUNCT
bibechana-9308	222	67	i	i	NOUN
bibechana-9308	222	68	)	)	PUNCT
bibechana-9308	222	69	and	and	CCONJ
bibechana-9308	222	70	(	(	PUNCT
bibechana-9308	222	71	ii	ii	NOUN
bibechana-9308	222	72	)	)	PUNCT
bibechana-9308	222	73	of	of	ADP
bibechana-9308	222	74	the	the	DET
bibechana-9308	222	75	theorem	theorem	NOUN
bibechana-9308	222	76	3.9	3.9	NUM
bibechana-9308	222	77	.	.	NOUN
bibechana-9308	223	1	4	4	NUM
bibechana-9308	223	2	.	.	X
bibechana-9308	224	1	linear	linear	ADJ
bibechana-9308	224	2	topological	topological	ADJ
bibechana-9308	224	3	structures	structure	NOUN
bibechana-9308	224	4	of	of	ADP
bibechana-9308	224	5	c0	c0	PROPN
bibechana-9308	224	6	(	(	PUNCT
bibechana-9308	224	7	s	s	PROPN
bibechana-9308	224	8	,	,	PUNCT
bibechana-9308	224	9	α	α	PROPN
bibechana-9308	224	10	–	–	PUNCT
bibechana-9308	224	11	,	,	PUNCT
bibechana-9308	224	12	u	u	INTJ
bibechana-9308	224	13	–	–	PUNCT
bibechana-9308	224	14	,	,	PUNCT
bibechana-9308	224	15	||	||	PROPN
bibechana-9308	224	16	.	.	PUNCT
bibechana-9308	224	17	,	,	PUNCT
bibechana-9308	224	18	.||	.||	PROPN
bibechana-9308	224	19	)	)	PUNCT
bibechana-9308	224	20	in	in	ADP
bibechana-9308	224	21	this	this	DET
bibechana-9308	224	22	section	section	NOUN
bibechana-9308	224	23	,	,	PUNCT
bibechana-9308	224	24	we	we	PRON
bibechana-9308	224	25	shall	shall	AUX
bibechana-9308	224	26	investigate	investigate	VERB
bibechana-9308	224	27	some	some	DET
bibechana-9308	224	28	results	result	NOUN
bibechana-9308	224	29	that	that	PRON
bibechana-9308	224	30	characterize	characterize	VERB
bibechana-9308	224	31	the	the	DET
bibechana-9308	224	32	linear	linear	ADJ
bibechana-9308	224	33	topological	topological	ADJ
bibechana-9308	224	34	structure	structure	NOUN
bibechana-9308	224	35	of	of	ADP
bibechana-9308	224	36	the	the	DET
bibechana-9308	224	37	class	class	NOUN
bibechana-9308	224	38	c0	c0	NOUN
bibechana-9308	224	39	(	(	PUNCT
bibechana-9308	224	40	s	s	PROPN
bibechana-9308	224	41	,	,	PUNCT
bibechana-9308	224	42	α	α	PROPN
bibechana-9308	224	43	–	–	PUNCT
bibechana-9308	224	44	,	,	PUNCT
bibechana-9308	224	45	u	u	NOUN
bibechana-9308	224	46	–	–	PUNCT
bibechana-9308	224	47	,	,	PUNCT
bibechana-9308	224	48	||	||	PROPN
bibechana-9308	224	49	.	.	PUNCT
bibechana-9308	224	50	,	,	PUNCT
bibechana-9308	224	51	.||	.||	PROPN
bibechana-9308	224	52	)	)	PUNCT
bibechana-9308	224	53	by	by	ADP
bibechana-9308	224	54	endowing	endow	VERB
bibechana-9308	224	55	it	it	PRON
bibechana-9308	224	56	with	with	ADP
bibechana-9308	224	57	suitable	suitable	ADJ
bibechana-9308	224	58	natural	natural	ADJ
bibechana-9308	224	59	paranorm	paranorm	NOUN
bibechana-9308	224	60	.	.	PUNCT
bibechana-9308	225	1	throughout	throughout	SCONJ
bibechana-9308	225	2	we	we	PRON
bibechana-9308	225	3	take	take	VERB
bibechana-9308	225	4	coordinatewise	coordinatewise	ADJ
bibechana-9308	225	5	operations	operation	NOUN
bibechana-9308	225	6	of	of	ADP
bibechana-9308	225	7	sequences	sequence	NOUN
bibechana-9308	225	8	over	over	ADP
bibechana-9308	225	9	the	the	DET
bibechana-9308	225	10	field	field	NOUN
bibechana-9308	225	11	c	c	NOUN
bibechana-9308	225	12	of	of	ADP
bibechana-9308	225	13	complex	complex	ADJ
bibechana-9308	225	14	numbers	number	NOUN
bibechana-9308	225	15	i.e.	i.e.	X
bibechana-9308	225	16	,for	,for	PUNCT
bibechana-9308	225	17	ξ	ξ	X
bibechana-9308	225	18	–	–	PUNCT
bibechana-9308	225	19	=	=	SYM
bibechana-9308	225	20	(	(	PUNCT
bibechana-9308	225	21	ξk	ξk	NOUN
bibechana-9308	225	22	)	)	PUNCT
bibechana-9308	225	23	and	and	CCONJ
bibechana-9308	225	24	η	η	PROPN
bibechana-9308	225	25	–	–	PUNCT
bibechana-9308	225	26	=	=	SYM
bibechana-9308	225	27	(	(	PUNCT
bibechana-9308	225	28	ηk	ηk	X
bibechana-9308	225	29	)	)	PUNCT
bibechana-9308	225	30	and	and	CCONJ
bibechana-9308	225	31	scalar	scalar	ADJ
bibechana-9308	225	32	γ	γ	PROPN
bibechana-9308	225	33	,	,	PUNCT
bibechana-9308	225	34	ξ	ξ	PROPN
bibechana-9308	225	35	–	–	PUNCT
bibechana-9308	225	36	+	+	NUM
bibechana-9308	225	37	η	η	PROPN
bibechana-9308	225	38	–	–	PUNCT
bibechana-9308	225	39	=	=	SYM
bibechana-9308	225	40	(	(	PUNCT
bibechana-9308	225	41	ξk	ξk	ADP
bibechana-9308	225	42	+	+	ADV
bibechana-9308	225	43	ηk	ηk	X
bibechana-9308	225	44	)	)	PUNCT
bibechana-9308	225	45	and	and	CCONJ
bibechana-9308	225	46	γ	γ	X
bibechana-9308	225	47	ξ	ξ	PROPN
bibechana-9308	225	48	–	–	PUNCT
bibechana-9308	225	49	=	=	SYM
bibechana-9308	225	50	(	(	PUNCT
bibechana-9308	225	51	γ	γ	X
bibechana-9308	225	52	ξk	ξk	ADV
bibechana-9308	225	53	)	)	PUNCT
bibechana-9308	225	54	and	and	CCONJ
bibechana-9308	225	55	we	we	PRON
bibechana-9308	225	56	see	see	VERB
bibechana-9308	225	57	below	below	ADV
bibechana-9308	225	58	that	that	PRON
bibechana-9308	225	59	each	each	PRON
bibechana-9308	225	60	of	of	ADP
bibechana-9308	225	61	these	these	DET
bibechana-9308	225	62	classes	class	NOUN
bibechana-9308	225	63	forms	form	VERB
bibechana-9308	225	64	a	a	DET
bibechana-9308	225	65	complete	complete	ADJ
bibechana-9308	225	66	paranormed	paranorme	VERB
bibechana-9308	225	67	linear	linear	ADJ
bibechana-9308	225	68	space	space	NOUN
bibechana-9308	225	69	over	over	ADP
bibechana-9308	225	70	c.	c.	PROPN
bibechana-9308	225	71	moreover	moreover	ADV
bibechana-9308	225	72	,	,	PUNCT
bibechana-9308	225	73	we	we	PRON
bibechana-9308	225	74	use	use	VERB
bibechana-9308	225	75	frequently	frequently	ADV
bibechana-9308	225	76	|	|	ADV
bibechana-9308	225	77	ξ	ξ	X
bibechana-9308	226	1	+	+	SYM
bibechana-9308	226	2	η	η	PROPN
bibechana-9308	226	3	|	|	ADP
bibechana-9308	226	4	uk	uk	PROPN
bibechana-9308	226	5	≤	≤	PROPN
bibechana-9308	226	6	s	s	PART
bibechana-9308	226	7	{	{	PUNCT
bibechana-9308	226	8	|ξ|	|ξ|	PROPN
bibechana-9308	226	9	uk	uk	PROPN
bibechana-9308	226	10	+	+	CCONJ
bibechana-9308	226	11	|η|	|η|	PROPN
bibechana-9308	226	12	uk	uk	PROPN
bibechana-9308	226	13	}	}	PUNCT
bibechana-9308	226	14	,	,	PUNCT
bibechana-9308	226	15	where	where	SCONJ
bibechana-9308	226	16	ξ	ξ	X
bibechana-9308	226	17	,	,	PUNCT
bibechana-9308	226	18	η	η	PROPN
bibechana-9308	226	19	∈	∈	PROPN
bibechana-9308	226	20	c	c	PROPN
bibechana-9308	226	21	,	,	PUNCT
bibechana-9308	226	22	0	0	PUNCT
bibechana-9308	226	23	<	<	X
bibechana-9308	226	24	uk	uk	PROPN
bibechana-9308	226	25	≤	≤	PUNCT
bibechana-9308	226	26	supk	supk	PROPN
bibechana-9308	226	27	uk	uk	PROPN
bibechana-9308	226	28	=	=	SYM
bibechana-9308	226	29	l	l	PROPN
bibechana-9308	226	30	<	<	X
bibechana-9308	226	31	∞	∞	PROPN
bibechana-9308	226	32	and	and	CCONJ
bibechana-9308	226	33	a(α	a(α	NOUN
bibechana-9308	226	34	)	)	PUNCT
bibechana-9308	226	35	=	=	SYM
bibechana-9308	226	36	max	max	X
bibechana-9308	226	37	(	(	PUNCT
bibechana-9308	226	38	1	1	NUM
bibechana-9308	226	39	,	,	PUNCT
bibechana-9308	226	40	|α|	|α|	PROPN
bibechana-9308	226	41	)	)	PUNCT
bibechana-9308	226	42	.	.	PUNCT
bibechana-9308	227	1	theorem	theorem	VERB
bibechana-9308	227	2	4.1	4.1	NUM
bibechana-9308	227	3	:	:	PUNCT
bibechana-9308	227	4	the	the	DET
bibechana-9308	227	5	space	space	NOUN
bibechana-9308	227	6	c0	c0	NOUN
bibechana-9308	227	7	(	(	PUNCT
bibechana-9308	227	8	s	s	PROPN
bibechana-9308	227	9	,	,	PUNCT
bibechana-9308	227	10	α	α	PROPN
bibechana-9308	227	11	–	–	PUNCT
bibechana-9308	227	12	,	,	PUNCT
bibechana-9308	227	13	u	u	INTJ
bibechana-9308	227	14	–	–	PUNCT
bibechana-9308	227	15	,	,	PUNCT
bibechana-9308	227	16	||	||	PROPN
bibechana-9308	227	17	.	.	PUNCT
bibechana-9308	227	18	,	,	PUNCT
bibechana-9308	227	19	.||	.||	PROPN
bibechana-9308	227	20	)	)	PUNCT
bibechana-9308	227	21	forms	form	VERB
bibechana-9308	227	22	a	a	DET
bibechana-9308	227	23	linear	linear	ADJ
bibechana-9308	227	24	space	space	NOUN
bibechana-9308	227	25	over	over	ADP
bibechana-9308	227	26	c	c	PROPN
bibechana-9308	228	1	if	if	SCONJ
bibechana-9308	228	2	and	and	CCONJ
bibechana-9308	228	3	only	only	ADV
bibechana-9308	228	4	if	if	SCONJ
bibechana-9308	228	5	supk	supk	PRON
bibechana-9308	228	6	uk	uk	PROPN
bibechana-9308	228	7	is	be	AUX
bibechana-9308	228	8	bounded	bound	VERB
bibechana-9308	228	9	above	above	ADV
bibechana-9308	228	10	.	.	PUNCT
bibechana-9308	229	1	proof	proof	NOUN
bibechana-9308	229	2	:	:	PUNCT
bibechana-9308	229	3	for	for	ADP
bibechana-9308	229	4	the	the	DET
bibechana-9308	229	5	necessity	necessity	NOUN
bibechana-9308	229	6	of	of	ADP
bibechana-9308	229	7	the	the	DET
bibechana-9308	229	8	conditions	condition	NOUN
bibechana-9308	229	9	,	,	PUNCT
bibechana-9308	229	10	suppose	suppose	VERB
bibechana-9308	229	11	that	that	SCONJ
bibechana-9308	229	12	c0	c0	PROPN
bibechana-9308	229	13	(	(	PUNCT
bibechana-9308	229	14	s	s	PROPN
bibechana-9308	229	15	,	,	PUNCT
bibechana-9308	229	16	α	α	PROPN
bibechana-9308	229	17	–	–	PUNCT
bibechana-9308	229	18	,	,	PUNCT
bibechana-9308	229	19	u	u	NOUN
bibechana-9308	229	20	–	–	PUNCT
bibechana-9308	229	21	,	,	PUNCT
bibechana-9308	229	22	||	||	PROPN
bibechana-9308	229	23	.	.	PUNCT
bibechana-9308	229	24	,	,	PUNCT
bibechana-9308	229	25	.||	.||	PROPN
bibechana-9308	229	26	)	)	PUNCT
bibechana-9308	229	27	is	be	AUX
bibechana-9308	229	28	a	a	DET
bibechana-9308	229	29	linear	linear	ADJ
bibechana-9308	229	30	space	space	NOUN
bibechana-9308	229	31	over	over	ADP
bibechana-9308	229	32	c	c	PROPN
bibechana-9308	229	33	but	but	CCONJ
bibechana-9308	229	34	supk	supk	PRON
bibechana-9308	229	35	uk	uk	PROPN
bibechana-9308	229	36	=	=	SYM
bibechana-9308	229	37	∞.	∞.	PROPN
bibechana-9308	229	38	then	then	ADV
bibechana-9308	229	39	there	there	PRON
bibechana-9308	229	40	exists	exist	VERB
bibechana-9308	229	41	a	a	DET
bibechana-9308	229	42	sequence	sequence	NOUN
bibechana-9308	229	43	(	(	PUNCT
bibechana-9308	229	44	k(n	k(n	PROPN
bibechana-9308	229	45	)	)	PUNCT
bibechana-9308	229	46	)	)	PUNCT
bibechana-9308	229	47	of	of	ADP
bibechana-9308	229	48	positive	positive	ADJ
bibechana-9308	229	49	integers	integer	NOUN
bibechana-9308	229	50	satisfying	satisfy	VERB
bibechana-9308	229	51	1	1	NUM
bibechana-9308	229	52	≤	≤	NUM
bibechana-9308	229	53	k(n	k(n	X
bibechana-9308	229	54	)	)	PUNCT
bibechana-9308	229	55	<	<	X
bibechana-9308	229	56	k(n	k(n	PROPN
bibechana-9308	229	57	+	+	CCONJ
bibechana-9308	229	58	1	1	NUM
bibechana-9308	229	59	)	)	PUNCT
bibechana-9308	229	60	,	,	PUNCT
bibechana-9308	229	61	n	n	X
bibechana-9308	229	62	≥	≥	NOUN
bibechana-9308	229	63	1	1	NUM
bibechana-9308	229	64	for	for	ADP
bibechana-9308	229	65	which	which	PRON
bibechana-9308	229	66	uk(n	uk(n	ADP
bibechana-9308	229	67	)	)	PUNCT
bibechana-9308	229	68	>	>	X
bibechana-9308	230	1	n	n	X
bibechana-9308	230	2	,	,	PUNCT
bibechana-9308	230	3	for	for	ADP
bibechana-9308	230	4	each	each	DET
bibechana-9308	230	5	n	n	PRON
bibechana-9308	230	6	≥	≥	NOUN
bibechana-9308	230	7	1	1	NUM
bibechana-9308	230	8	…	…	PUNCT
bibechana-9308	230	9	.(4.1	.(4.1	NUM
bibechana-9308	230	10	)	)	PUNCT
bibechana-9308	230	11	now	now	ADV
bibechana-9308	230	12	,	,	PUNCT
bibechana-9308	230	13	corresponding	correspond	VERB
bibechana-9308	230	14	to	to	ADP
bibechana-9308	230	15	ρ	ρ	PROPN
bibechana-9308	230	16	∈	∈	PROPN
bibechana-9308	230	17	s	s	PART
bibechana-9308	230	18	and	and	CCONJ
bibechana-9308	230	19	ρ	ρ	NOUN
bibechana-9308	230	20	≠	≠	PROPN
bibechana-9308	230	21	θ	θ	PROPN
bibechana-9308	230	22	,	,	PUNCT
bibechana-9308	230	23	we	we	PRON
bibechana-9308	230	24	define	define	VERB
bibechana-9308	230	25	the	the	DET
bibechana-9308	230	26	sequence	sequence	NOUN
bibechana-9308	230	27	ξ	ξ	PROPN
bibechana-9308	230	28	–	–	PUNCT
bibechana-9308	230	29	=	=	SYM
bibechana-9308	230	30	(	(	PUNCT
bibechana-9308	230	31	ξk	ξk	NOUN
bibechana-9308	230	32	)	)	PUNCT
bibechana-9308	230	33	by	by	ADP
bibechana-9308	230	34	ξk	ξk	ADV
bibechana-9308	230	35	=	=	PUNCT
bibechana-9308	230	36			PROPN
bibechana-9308	230	37			ADP
bibechana-9308	230	38	αk(n	αk(n	PROPN
bibechana-9308	230	39	)	)	PUNCT
bibechana-9308	230	40	-1	-1	PUNCT
bibechana-9308	230	41	n-2	n-2	PROPN
bibechana-9308	230	42	/	/	SYM
bibechana-9308	230	43	uk(n	uk(n	NUM
bibechana-9308	230	44	)	)	PUNCT
bibechana-9308	231	1	ρ	ρ	X
bibechana-9308	231	2	‚	‚	NOUN
bibechana-9308	231	3	if	if	SCONJ
bibechana-9308	231	4	k	k	PROPN
bibechana-9308	231	5	=	=	SYM
bibechana-9308	231	6	k(n	k(n	X
bibechana-9308	231	7	)	)	PUNCT
bibechana-9308	231	8	‚	‚	NOUN
bibechana-9308	231	9	n	n	PRON
bibechana-9308	231	10	≥1	≥1	NUM
bibechana-9308	231	11	and	and	CCONJ
bibechana-9308	231	12	θ	θ	NOUN
bibechana-9308	231	13	‚	‚	NOUN
bibechana-9308	231	14	otherwise	otherwise	ADV
bibechana-9308	231	15	.	.	PUNCT
bibechana-9308	232	1	…	…	PUNCT
bibechana-9308	232	2	.(4.2	.(4.2	NUM
bibechana-9308	232	3	)	)	PUNCT
bibechana-9308	232	4	then	then	ADV
bibechana-9308	232	5	for	for	ADP
bibechana-9308	232	6	k	k	PROPN
bibechana-9308	232	7	=	=	SYM
bibechana-9308	232	8	k(n	k(n	PROPN
bibechana-9308	232	9	)	)	PUNCT
bibechana-9308	232	10	,	,	PUNCT
bibechana-9308	232	11	n	n	PRON
bibechana-9308	232	12	≥	≥	NOUN
bibechana-9308	232	13	1	1	NUM
bibechana-9308	232	14	,	,	PUNCT
bibechana-9308	232	15	we	we	PRON
bibechana-9308	232	16	have	have	VERB
bibechana-9308	232	17	||αk	||αk	NOUN
bibechana-9308	232	18	ξk	ξk	ADP
bibechana-9308	232	19	‚	‚	NUM
bibechana-9308	232	20	η||	η||	NOUN
bibechana-9308	232	21	uk	uk	NOUN
bibechana-9308	232	22	=	=	SYM
bibechana-9308	232	23	||n-2	||n-2	NOUN
bibechana-9308	232	24	/	/	SYM
bibechana-9308	232	25	uk(n	uk(n	NUM
bibechana-9308	232	26	)	)	PUNCT
bibechana-9308	232	27	ρ	ρ	PROPN
bibechana-9308	232	28	‚	‚	PROPN
bibechana-9308	232	29	η	η	PROPN
bibechana-9308	232	30	||	||	PROPN
bibechana-9308	232	31	uk(n	uk(n	NUM
bibechana-9308	232	32	)	)	PUNCT
bibechana-9308	232	33	)	)	PUNCT
bibechana-9308	233	1	≤	≤	NUM
bibechana-9308	233	2	||ρ	||ρ	PROPN
bibechana-9308	233	3	‚	‚	NUM
bibechana-9308	233	4	η	η	PROPN
bibechana-9308	233	5	||	||	PROPN
bibechana-9308	233	6	uk(n	uk(n	NUM
bibechana-9308	233	7	)	)	PUNCT
bibechana-9308	233	8	n2	n2	NOUN
bibechana-9308	233	9	→	→	X
bibechana-9308	233	10	0	0	NUM
bibechana-9308	233	11	as	as	ADP
bibechana-9308	233	12	n→	n→	PROPN
bibechana-9308	233	13	∞	∞	PROPN
bibechana-9308	233	14	,	,	PUNCT
bibechana-9308	233	15	n.p	n.p	PROPN
bibechana-9308	233	16	.	.	PROPN
bibechana-9308	233	17	pahari	pahari	PROPN
bibechana-9308	233	18	/	/	SYM
bibechana-9308	233	19	bibechana	bibechana	NOUN
bibechana-9308	233	20	10	10	NUM
bibechana-9308	233	21	(	(	PUNCT
bibechana-9308	233	22	2014	2014	NUM
bibechana-9308	233	23	)	)	PUNCT
bibechana-9308	233	24	20	20	NUM
bibechana-9308	233	25	-	-	SYM
bibechana-9308	233	26	30	30	NUM
bibechana-9308	233	27	:	:	PUNCT
bibechana-9308	233	28	bmhss	bmhss	PROPN
bibechana-9308	233	29	,	,	PUNCT
bibechana-9308	233	30	p.29	p.29	NOUN
bibechana-9308	233	31	(	(	PUNCT
bibechana-9308	233	32	online	online	ADJ
bibechana-9308	233	33	publication	publication	NOUN
bibechana-9308	233	34	:	:	PUNCT
bibechana-9308	233	35	dec	dec	PROPN
bibechana-9308	233	36	.	.	PROPN
bibechana-9308	233	37	,	,	PUNCT
bibechana-9308	233	38	2013	2013	NUM
bibechana-9308	233	39	)	)	PUNCT
bibechana-9308	233	40	and	and	CCONJ
bibechana-9308	233	41	||αk	||αk	ADV
bibechana-9308	233	42	ξk	ξk	ADP
bibechana-9308	233	43	‚	‚	NUM
bibechana-9308	233	44	η||	η||	NOUN
bibechana-9308	233	45	uk	uk	NOUN
bibechana-9308	233	46	=	=	SYM
bibechana-9308	233	47	0	0	NUM
bibechana-9308	233	48	,	,	PUNCT
bibechana-9308	233	49	for	for	ADP
bibechana-9308	233	50	k	k	PROPN
bibechana-9308	233	51	≠	≠	PROPN
bibechana-9308	233	52	k(n	k(n	PROPN
bibechana-9308	233	53	)	)	PUNCT
bibechana-9308	233	54	,	,	PUNCT
bibechana-9308	233	55	n	n	X
bibechana-9308	233	56	≥	≥	NOUN
bibechana-9308	233	57	1	1	NUM
bibechana-9308	233	58	showing	show	VERB
bibechana-9308	233	59	that	that	SCONJ
bibechana-9308	233	60	ξ	ξ	PROPN
bibechana-9308	233	61	–	–	PUNCT
bibechana-9308	233	62	∈	∈	PROPN
bibechana-9308	233	63	c0	c0	NOUN
bibechana-9308	233	64	(	(	PUNCT
bibechana-9308	233	65	s	s	PROPN
bibechana-9308	233	66	,	,	PUNCT
bibechana-9308	233	67	α	α	PROPN
bibechana-9308	233	68	–	–	PUNCT
bibechana-9308	233	69	,	,	PUNCT
bibechana-9308	233	70	u	u	NOUN
bibechana-9308	233	71	–	–	PUNCT
bibechana-9308	233	72	,	,	PUNCT
bibechana-9308	233	73	||	||	PROPN
bibechana-9308	233	74	.	.	PUNCT
bibechana-9308	233	75	,	,	PUNCT
bibechana-9308	233	76	.||	.||	PROPN
bibechana-9308	233	77	)	)	PUNCT
bibechana-9308	233	78	.	.	PUNCT
bibechana-9308	234	1	but	but	CCONJ
bibechana-9308	234	2	on	on	ADP
bibechana-9308	234	3	the	the	DET
bibechana-9308	234	4	other	other	ADJ
bibechana-9308	234	5	hand	hand	NOUN
bibechana-9308	234	6	,	,	PUNCT
bibechana-9308	234	7	let	let	VERB
bibechana-9308	234	8	us	we	PRON
bibechana-9308	234	9	choose	choose	VERB
bibechana-9308	234	10	η	η	PROPN
bibechana-9308	234	11	∈	∈	PROPN
bibechana-9308	234	12	s	s	VERB
bibechana-9308	234	13	such	such	ADJ
bibechana-9308	234	14	that	that	DET
bibechana-9308	234	15	||ρ	||ρ	NOUN
bibechana-9308	234	16	,	,	PUNCT
bibechana-9308	234	17	η||	η||	NOUN
bibechana-9308	234	18	=	=	SYM
bibechana-9308	234	19	1	1	X
bibechana-9308	234	20	.	.	PUNCT
bibechana-9308	234	21	then	then	ADV
bibechana-9308	234	22	for	for	ADP
bibechana-9308	234	23	such	such	ADJ
bibechana-9308	234	24	η	η	PROPN
bibechana-9308	234	25	and	and	CCONJ
bibechana-9308	234	26	scalar	scalar	ADJ
bibechana-9308	234	27	γ	γ	X
bibechana-9308	234	28	=	=	SYM
bibechana-9308	234	29	4	4	NUM
bibechana-9308	234	30	,	,	PUNCT
bibechana-9308	234	31	for	for	ADP
bibechana-9308	234	32	k	k	PROPN
bibechana-9308	234	33	=	=	SYM
bibechana-9308	234	34	k(n	k(n	PROPN
bibechana-9308	234	35	)	)	PUNCT
bibechana-9308	234	36	,	,	PUNCT
bibechana-9308	234	37	n	n	PRON
bibechana-9308	234	38	≥	≥	NOUN
bibechana-9308	234	39	1	1	NUM
bibechana-9308	234	40	,	,	PUNCT
bibechana-9308	234	41	in	in	ADP
bibechana-9308	234	42	view	view	NOUN
bibechana-9308	234	43	of	of	ADP
bibechana-9308	234	44	(	(	PUNCT
bibechana-9308	234	45	4.1	4.1	NUM
bibechana-9308	234	46	)	)	PUNCT
bibechana-9308	234	47	and	and	CCONJ
bibechana-9308	234	48	(	(	PUNCT
bibechana-9308	234	49	4.2	4.2	NUM
bibechana-9308	234	50	)	)	PUNCT
bibechana-9308	234	51	,	,	PUNCT
bibechana-9308	234	52	we	we	PRON
bibechana-9308	234	53	have	have	VERB
bibechana-9308	234	54	||	||	NOUN
bibechana-9308	234	55	γ	γ	X
bibechana-9308	234	56	αk	αk	ADP
bibechana-9308	234	57	ξk	ξk	ADP
bibechana-9308	234	58	‚	‚	PROPN
bibechana-9308	234	59	η	η	PROPN
bibechana-9308	234	60	||	||	PROPN
bibechana-9308	234	61	uk	uk	PROPN
bibechana-9308	234	62	=	=	PRON
bibechana-9308	234	63	||	||	PROPN
bibechana-9308	234	64	αk(n	αk(n	NUM
bibechana-9308	234	65	)	)	PUNCT
bibechana-9308	234	66	γ	γ	X
bibechana-9308	234	67	ξk(n	ξk(n	NUM
bibechana-9308	234	68	)	)	PUNCT
bibechana-9308	235	1	‚	‚	PROPN
bibechana-9308	235	2	η	η	PROPN
bibechana-9308	235	3	||	||	PROPN
bibechana-9308	235	4	uk(n	uk(n	NUM
bibechana-9308	235	5	)	)	PUNCT
bibechana-9308	236	1	=	=	PUNCT
bibechana-9308	236	2	||	||	NOUN
bibechana-9308	236	3	4	4	NUM
bibechana-9308	236	4	n–2/	n–2/	PROPN
bibechana-9308	236	5	uk(n	uk(n	X
bibechana-9308	236	6	)	)	PUNCT
bibechana-9308	237	1	ρ	ρ	PROPN
bibechana-9308	237	2	‚	‚	NUM
bibechana-9308	237	3	η	η	PROPN
bibechana-9308	237	4	||	||	NOUN
bibechana-9308	237	5	uk(n	uk(n	NUM
bibechana-9308	237	6	)	)	PUNCT
bibechana-9308	237	7	=	=	SYM
bibechana-9308	237	8	4	4	NUM
bibechana-9308	237	9	uk(n	uk(n	NUM
bibechana-9308	237	10	)	)	PUNCT
bibechana-9308	237	11	n2	n2	ADJ
bibechana-9308	237	12	≥	≥	NUM
bibechana-9308	237	13	sup	sup	NOUN
bibechana-9308	237	14	n	n	ADP
bibechana-9308	237	15	4	4	NUM
bibechana-9308	237	16	n	n	NUM
bibechana-9308	237	17	n	n	NUM
bibechana-9308	237	18	2	2	NUM
bibechana-9308	237	19	≥	≥	NOUN
bibechana-9308	237	20	1	1	NUM
bibechana-9308	237	21	.	.	PUNCT
bibechana-9308	238	1	this	this	PRON
bibechana-9308	238	2	shows	show	VERB
bibechana-9308	238	3	that	that	SCONJ
bibechana-9308	238	4	γ	γ	PROPN
bibechana-9308	238	5	ξ	ξ	PROPN
bibechana-9308	238	6	–	–	PUNCT
bibechana-9308	238	7	∉	∉	PROPN
bibechana-9308	238	8	c0	c0	X
bibechana-9308	238	9	(	(	PUNCT
bibechana-9308	238	10	s	s	PROPN
bibechana-9308	238	11	,	,	PUNCT
bibechana-9308	238	12	α	α	PROPN
bibechana-9308	238	13	–	–	PUNCT
bibechana-9308	238	14	,	,	PUNCT
bibechana-9308	238	15	u	u	NOUN
bibechana-9308	238	16	–	–	PUNCT
bibechana-9308	238	17	,	,	PUNCT
bibechana-9308	238	18	||	||	PROPN
bibechana-9308	238	19	.	.	PUNCT
bibechana-9308	238	20	,	,	PUNCT
bibechana-9308	238	21	.||	.||	PROPN
bibechana-9308	238	22	)	)	PUNCT
bibechana-9308	238	23	,	,	PUNCT
bibechana-9308	238	24	a	a	DET
bibechana-9308	238	25	contradiction	contradiction	NOUN
bibechana-9308	238	26	.	.	PUNCT
bibechana-9308	239	1	for	for	ADP
bibechana-9308	239	2	the	the	DET
bibechana-9308	239	3	sufficiency	sufficiency	NOUN
bibechana-9308	239	4	of	of	ADP
bibechana-9308	239	5	the	the	DET
bibechana-9308	239	6	condition	condition	NOUN
bibechana-9308	239	7	,	,	PUNCT
bibechana-9308	239	8	assume	assume	VERB
bibechana-9308	239	9	that	that	SCONJ
bibechana-9308	239	10	supk	supk	PROPN
bibechana-9308	239	11	uk	uk	PROPN
bibechana-9308	239	12	<	<	X
bibechana-9308	239	13	∞.	∞.	PROPN
bibechana-9308	239	14	let	let	VERB
bibechana-9308	239	15	ξ	ξ	PROPN
bibechana-9308	239	16	–	–	PUNCT
bibechana-9308	239	17	,	,	PUNCT
bibechana-9308	239	18	η	η	PROPN
bibechana-9308	239	19	–	–	PUNCT
bibechana-9308	239	20	∈	∈	PROPN
bibechana-9308	239	21	c0	c0	NOUN
bibechana-9308	239	22	(	(	PUNCT
bibechana-9308	239	23	s	s	PROPN
bibechana-9308	239	24	,	,	PUNCT
bibechana-9308	239	25	α	α	PROPN
bibechana-9308	239	26	–	–	PUNCT
bibechana-9308	239	27	,	,	PUNCT
bibechana-9308	239	28	u	u	NOUN
bibechana-9308	239	29	–	–	PUNCT
bibechana-9308	239	30	,	,	PUNCT
bibechana-9308	239	31	||	||	PROPN
bibechana-9308	239	32	.	.	PUNCT
bibechana-9308	239	33	,	,	PUNCT
bibechana-9308	239	34	.||	.||	PROPN
bibechana-9308	239	35	)	)	PUNCT
bibechana-9308	239	36	and	and	CCONJ
bibechana-9308	239	37	γ	γ	PROPN
bibechana-9308	239	38	,	,	PUNCT
bibechana-9308	239	39	ρ	ρ	PROPN
bibechana-9308	239	40	∈	∈	PROPN
bibechana-9308	239	41	c.	c.	NOUN
bibechana-9308	239	42	then	then	ADV
bibechana-9308	239	43	for	for	ADP
bibechana-9308	239	44	each	each	DET
bibechana-9308	239	45	η	η	PROPN
bibechana-9308	239	46	∈	∈	PROPN
bibechana-9308	239	47	s	s	PART
bibechana-9308	239	48	,	,	PUNCT
bibechana-9308	239	49	we	we	PRON
bibechana-9308	239	50	have	have	VERB
bibechana-9308	239	51	||αk	||αk	NOUN
bibechana-9308	239	52	ξk	ξk	ADP
bibechana-9308	239	53	‚	‚	NUM
bibechana-9308	239	54	η||	η||	X
bibechana-9308	239	55	uk	uk	PROPN
bibechana-9308	239	56	→	→	SYM
bibechana-9308	239	57	0	0	NUM
bibechana-9308	239	58	and	and	CCONJ
bibechana-9308	239	59	||αk	||αk	NUM
bibechana-9308	239	60	ηk	ηk	VERB
bibechana-9308	239	61	‚	‚	X
bibechana-9308	239	62	η||	η||	NOUN
bibechana-9308	239	63	uk	uk	PROPN
bibechana-9308	239	64	→0	→0	NOUN
bibechana-9308	239	65	,	,	PUNCT
bibechana-9308	239	66	as	as	ADP
bibechana-9308	239	67	k	k	PROPN
bibechana-9308	239	68	→	→	SYM
bibechana-9308	239	69	∞.	∞.	PROPN
bibechana-9308	239	70	we	we	PRON
bibechana-9308	239	71	now	now	ADV
bibechana-9308	239	72	setting	set	VERB
bibechana-9308	239	73	s	s	PART
bibechana-9308	239	74	=	=	X
bibechana-9308	239	75	max	max	X
bibechana-9308	239	76	(	(	PUNCT
bibechana-9308	239	77	1,2l-1	1,2l-1	PROPN
bibechana-9308	239	78	)	)	PUNCT
bibechana-9308	239	79	,	,	PUNCT
bibechana-9308	239	80	then	then	ADV
bibechana-9308	239	81	we	we	PRON
bibechana-9308	239	82	have	have	VERB
bibechana-9308	239	83	||αk	||αk	ADJ
bibechana-9308	239	84	(	(	PUNCT
bibechana-9308	239	85	γξk	γξk	NOUN
bibechana-9308	240	1	+	+	CCONJ
bibechana-9308	240	2	ρηk	ρηk	PROPN
bibechana-9308	240	3	)	)	PUNCT
bibechana-9308	240	4	‚	‚	PROPN
bibechana-9308	240	5	η	η	PROPN
bibechana-9308	240	6	||	||	PROPN
bibechana-9308	240	7	uk	uk	PROPN
bibechana-9308	240	8	=	=	SYM
bibechana-9308	240	9	(	(	PUNCT
bibechana-9308	240	10	||	||	ADP
bibechana-9308	240	11	γαk	γαk	NOUN
bibechana-9308	240	12	ξk	ξk	ADP
bibechana-9308	240	13	‚	‚	PROPN
bibechana-9308	240	14	η	η	PROPN
bibechana-9308	240	15	||	||	PROPN
bibechana-9308	241	1	+	+	CCONJ
bibechana-9308	241	2	||	||	NUM
bibechana-9308	242	1	ρ	ρ	NUM
bibechana-9308	242	2	αk	αk	NOUN
bibechana-9308	242	3	ηk	ηk	PROPN
bibechana-9308	242	4	‚	‚	PROPN
bibechana-9308	242	5	η	η	PROPN
bibechana-9308	242	6	||	||	NUM
bibechana-9308	242	7	)	)	PUNCT
bibechana-9308	243	1	uk	uk	PROPN
bibechana-9308	243	2	≤	≤	PROPN
bibechana-9308	243	3	(	(	PUNCT
bibechana-9308	243	4	s	s	AUX
bibechana-9308	243	5	||	||	NOUN
bibechana-9308	243	6	γ	γ	X
bibechana-9308	243	7	αk	αk	ADP
bibechana-9308	243	8	ξk	ξk	ADP
bibechana-9308	243	9	‚	‚	PROPN
bibechana-9308	243	10	η	η	PROPN
bibechana-9308	243	11	||	||	PROPN
bibechana-9308	243	12	uk	uk	PROPN
bibechana-9308	243	13	+	+	CCONJ
bibechana-9308	243	14	s	s	PART
bibechana-9308	243	15	||	||	NOUN
bibechana-9308	243	16	ρ	ρ	PRON
bibechana-9308	243	17	αk	αk	NOUN
bibechana-9308	243	18	ηk	ηk	PROPN
bibechana-9308	243	19	‚	‚	PROPN
bibechana-9308	243	20	η	η	PROPN
bibechana-9308	243	21	||	||	PROPN
bibechana-9308	243	22	uk	uk	PROPN
bibechana-9308	243	23	)	)	PUNCT
bibechana-9308	244	1	=	=	PRON
bibechana-9308	244	2	s	s	VERB
bibechana-9308	244	3	|γ|	|γ|	PROPN
bibechana-9308	244	4	uk	uk	PROPN
bibechana-9308	244	5	||	||	NOUN
bibechana-9308	245	1	αk	αk	CCONJ
bibechana-9308	246	1	ξk	ξk	ADP
bibechana-9308	246	2	‚	‚	PROPN
bibechana-9308	246	3	η	η	PROPN
bibechana-9308	246	4	||	||	PROPN
bibechana-9308	246	5	uk	uk	PROPN
bibechana-9308	247	1	+	+	CCONJ
bibechana-9308	247	2	s	s	PART
bibechana-9308	247	3	|ρ|	|ρ|	NOUN
bibechana-9308	247	4	uk	uk	NOUN
bibechana-9308	247	5	||	||	NOUN
bibechana-9308	247	6	αk	αk	X
bibechana-9308	247	7	ηk	ηk	PROPN
bibechana-9308	247	8	‚	‚	PROPN
bibechana-9308	247	9	η	η	PROPN
bibechana-9308	247	10	||	||	PROPN
bibechana-9308	247	11	uk	uk	PROPN
bibechana-9308	247	12	which	which	PRON
bibechana-9308	247	13	tends	tend	VERB
bibechana-9308	247	14	to	to	ADP
bibechana-9308	247	15	0	0	NUM
bibechana-9308	247	16	as	as	ADP
bibechana-9308	247	17	k	k	PROPN
bibechana-9308	247	18	→	→	SYM
bibechana-9308	247	19	∞	∞	PROPN
bibechana-9308	247	20	,	,	PUNCT
bibechana-9308	247	21	for	for	ADP
bibechana-9308	247	22	each	each	DET
bibechana-9308	247	23	η	η	PROPN
bibechana-9308	247	24	∈	∈	PROPN
bibechana-9308	247	25	s	s	X
bibechana-9308	247	26	and	and	CCONJ
bibechana-9308	247	27	hence	hence	ADV
bibechana-9308	247	28	αξ	αξ	NOUN
bibechana-9308	247	29	–	–	PUNCT
bibechana-9308	247	30	+	+	NUM
bibechana-9308	247	31	ρ	ρ	PROPN
bibechana-9308	247	32	η	η	PROPN
bibechana-9308	247	33	–	–	PUNCT
bibechana-9308	247	34	∈	∈	PROPN
bibechana-9308	247	35	c0	c0	NOUN
bibechana-9308	247	36	(	(	PUNCT
bibechana-9308	247	37	s	s	PROPN
bibechana-9308	247	38	,	,	PUNCT
bibechana-9308	247	39	α	α	PROPN
bibechana-9308	247	40	–	–	PUNCT
bibechana-9308	247	41	,	,	PUNCT
bibechana-9308	247	42	u	u	NOUN
bibechana-9308	247	43	–	–	PUNCT
bibechana-9308	247	44	,	,	PUNCT
bibechana-9308	247	45	||	||	PROPN
bibechana-9308	247	46	.	.	PUNCT
bibechana-9308	247	47	,	,	PUNCT
bibechana-9308	247	48	.||	.||	PROPN
bibechana-9308	247	49	)	)	PUNCT
bibechana-9308	247	50	.	.	PUNCT
bibechana-9308	248	1	this	this	PRON
bibechana-9308	248	2	implies	imply	VERB
bibechana-9308	248	3	that	that	SCONJ
bibechana-9308	248	4	c0	c0	PROPN
bibechana-9308	248	5	(	(	PUNCT
bibechana-9308	248	6	s	s	PROPN
bibechana-9308	248	7	,	,	PUNCT
bibechana-9308	248	8	α	α	PROPN
bibechana-9308	248	9	–	–	PUNCT
bibechana-9308	248	10	,	,	PUNCT
bibechana-9308	248	11	u	u	NOUN
bibechana-9308	248	12	–	–	PUNCT
bibechana-9308	248	13	,	,	PUNCT
bibechana-9308	248	14	||	||	PROPN
bibechana-9308	248	15	.	.	PUNCT
bibechana-9308	248	16	,	,	PUNCT
bibechana-9308	248	17	.||	.||	PROPN
bibechana-9308	248	18	)	)	PUNCT
bibechana-9308	248	19	forms	form	VERB
bibechana-9308	248	20	a	a	DET
bibechana-9308	248	21	linear	linear	ADJ
bibechana-9308	248	22	space	space	NOUN
bibechana-9308	248	23	over	over	ADP
bibechana-9308	248	24	c.	c.	PROPN
bibechana-9308	248	25	this	this	PRON
bibechana-9308	248	26	completes	complete	VERB
bibechana-9308	248	27	the	the	DET
bibechana-9308	248	28	proof	proof	NOUN
bibechana-9308	248	29	.	.	PUNCT
bibechana-9308	249	1	let	let	VERB
bibechana-9308	249	2	u	u	PRON
bibechana-9308	249	3	–	–	PUNCT
bibechana-9308	249	4	∈	∈	PROPN
bibechana-9308	249	5	ℓ∞	ℓ∞	NOUN
bibechana-9308	249	6	i.e.	i.e.	X
bibechana-9308	249	7	,	,	PUNCT
bibechana-9308	249	8	supk	supk	PROPN
bibechana-9308	249	9	uk	uk	PROPN
bibechana-9308	249	10	<	<	X
bibechana-9308	249	11	∞	∞	PROPN
bibechana-9308	249	12	,	,	PUNCT
bibechana-9308	249	13	m	m	PROPN
bibechana-9308	249	14	=	=	ADJ
bibechana-9308	249	15	max	max	X
bibechana-9308	249	16	(	(	PUNCT
bibechana-9308	249	17	1	1	NUM
bibechana-9308	249	18	,	,	PUNCT
bibechana-9308	249	19	supk	supk	ADJ
bibechana-9308	249	20	uk	uk	PROPN
bibechana-9308	249	21	)	)	PUNCT
bibechana-9308	249	22	and	and	CCONJ
bibechana-9308	249	23	consider	consider	VERB
bibechana-9308	249	24	a	a	DET
bibechana-9308	249	25	real	real	ADV
bibechana-9308	249	26	valued	value	VERB
bibechana-9308	249	27	function	function	NOUN
bibechana-9308	249	28	t	t	NOUN
bibechana-9308	249	29	on	on	ADP
bibechana-9308	249	30	c0	c0	PROPN
bibechana-9308	249	31	(	(	PUNCT
bibechana-9308	249	32	s	s	PROPN
bibechana-9308	249	33	,	,	PUNCT
bibechana-9308	249	34	α	α	PROPN
bibechana-9308	249	35	–	–	PUNCT
bibechana-9308	249	36	,	,	PUNCT
bibechana-9308	249	37	u	u	NOUN
bibechana-9308	249	38	–	–	PUNCT
bibechana-9308	249	39	,	,	PUNCT
bibechana-9308	249	40	||	||	PROPN
bibechana-9308	249	41	.	.	PUNCT
bibechana-9308	249	42	,	,	PUNCT
bibechana-9308	249	43	.||	.||	PROPN
bibechana-9308	249	44	)	)	PUNCT
bibechana-9308	249	45	defined	define	VERB
bibechana-9308	249	46	by	by	ADP
bibechana-9308	249	47	t	t	PROPN
bibechana-9308	249	48	(	(	PUNCT
bibechana-9308	249	49	x	x	NOUN
bibechana-9308	249	50	–	–	PUNCT
bibechana-9308	249	51	)	)	PUNCT
bibechana-9308	250	1	=	=	NOUN
bibechana-9308	250	2	{	{	PUNCT
bibechana-9308	250	3	sup	sup	NOUN
bibechana-9308	250	4	k	k	PROPN
bibechana-9308	250	5	||	||	NOUN
bibechana-9308	251	1	αk	αk	INTJ
bibechana-9308	251	2	ξk	ξk	ADP
bibechana-9308	251	3	‚	‚	PROPN
bibechana-9308	251	4	η	η	PROPN
bibechana-9308	251	5	||	||	PROPN
bibechana-9308	251	6	u	u	PROPN
bibechana-9308	252	1	k	k	PROPN
bibechana-9308	252	2	/m	/m	X
bibechana-9308	252	3	,	,	PUNCT
bibechana-9308	252	4	for	for	ADP
bibechana-9308	252	5	each	each	DET
bibechana-9308	252	6	η	η	PROPN
bibechana-9308	252	7	∈	∈	PROPN
bibechana-9308	252	8	s	s	PART
bibechana-9308	252	9	}	}	PUNCT
bibechana-9308	252	10	,	,	PUNCT
bibechana-9308	252	11	for	for	ADP
bibechana-9308	252	12	ξ	ξ	PROPN
bibechana-9308	252	13	–	–	PUNCT
bibechana-9308	252	14	∈	∈	PROPN
bibechana-9308	252	15	ℓ∞	ℓ∞	PROPN
bibechana-9308	252	16	(	(	PUNCT
bibechana-9308	252	17	s	s	PROPN
bibechana-9308	252	18	,	,	PUNCT
bibechana-9308	252	19	α	α	PROPN
bibechana-9308	252	20	–	–	PUNCT
bibechana-9308	252	21	,	,	PUNCT
bibechana-9308	252	22	u	u	NOUN
bibechana-9308	252	23	–	–	PUNCT
bibechana-9308	252	24	,	,	PUNCT
bibechana-9308	252	25	||	||	PROPN
bibechana-9308	252	26	.	.	PUNCT
bibechana-9308	252	27	,	,	PUNCT
bibechana-9308	252	28	.||	.||	PROPN
bibechana-9308	252	29	)	)	PUNCT
bibechana-9308	252	30	.	.	PUNCT
bibechana-9308	253	1	…	…	PUNCT
bibechana-9308	253	2	(	(	PUNCT
bibechana-9308	253	3	4.3	4.3	NUM
bibechana-9308	253	4	)	)	PUNCT
bibechana-9308	253	5	we	we	PRON
bibechana-9308	253	6	prove	prove	VERB
bibechana-9308	253	7	below	below	ADP
bibechana-9308	253	8	that	that	DET
bibechana-9308	253	9	c0	c0	NOUN
bibechana-9308	253	10	(	(	PUNCT
bibechana-9308	253	11	s	s	PROPN
bibechana-9308	253	12	,	,	PUNCT
bibechana-9308	253	13	α	α	PROPN
bibechana-9308	253	14	–	–	PUNCT
bibechana-9308	253	15	,	,	PUNCT
bibechana-9308	253	16	u	u	NOUN
bibechana-9308	253	17	–	–	PUNCT
bibechana-9308	253	18	,	,	PUNCT
bibechana-9308	253	19	||	||	PROPN
bibechana-9308	253	20	.	.	PUNCT
bibechana-9308	253	21	,	,	PUNCT
bibechana-9308	253	22	.||	.||	PROPN
bibechana-9308	253	23	)	)	PUNCT
bibechana-9308	253	24	with	with	ADP
bibechana-9308	253	25	respect	respect	NOUN
bibechana-9308	253	26	to	to	ADP
bibechana-9308	253	27	t	t	PROPN
bibechana-9308	253	28	forms	form	NOUN
bibechana-9308	253	29	a	a	DET
bibechana-9308	253	30	paranormed	paranorme	VERB
bibechana-9308	253	31	space	space	NOUN
bibechana-9308	253	32	.	.	PUNCT
bibechana-9308	254	1	theorem	theorem	VERB
bibechana-9308	254	2	:	:	PUNCT
bibechana-9308	254	3	4.2	4.2	NUM
bibechana-9308	254	4	(	(	PUNCT
bibechana-9308	254	5	c0	c0	X
bibechana-9308	254	6	(	(	PUNCT
bibechana-9308	254	7	s	s	PROPN
bibechana-9308	254	8	,	,	PUNCT
bibechana-9308	254	9	α	α	PROPN
bibechana-9308	254	10	–	–	PUNCT
bibechana-9308	254	11	,	,	PUNCT
bibechana-9308	254	12	u	u	INTJ
bibechana-9308	254	13	–	–	PUNCT
bibechana-9308	254	14	,	,	PUNCT
bibechana-9308	254	15	||	||	PROPN
bibechana-9308	254	16	.	.	PUNCT
bibechana-9308	254	17	,	,	PUNCT
bibechana-9308	255	1	.||	.||	PROPN
bibechana-9308	255	2	)	)	PUNCT
bibechana-9308	255	3	,	,	PUNCT
bibechana-9308	255	4	t	t	NOUN
bibechana-9308	255	5	)	)	PUNCT
bibechana-9308	255	6	forms	form	VERB
bibechana-9308	255	7	a	a	DET
bibechana-9308	255	8	total	total	ADJ
bibechana-9308	255	9	paranormed	paranormed	ADJ
bibechana-9308	255	10	space	space	NOUN
bibechana-9308	255	11	.	.	PUNCT
bibechana-9308	256	1	proof	proof	NOUN
bibechana-9308	256	2	:	:	PUNCT
bibechana-9308	256	3	since	since	SCONJ
bibechana-9308	256	4	t(ξ	t(ξ	PROPN
bibechana-9308	256	5	–	–	PUNCT
bibechana-9308	256	6	)	)	PUNCT
bibechana-9308	256	7	≥	≥	NOUN
bibechana-9308	256	8	0	0	NUM
bibechana-9308	256	9	;	;	PUNCT
bibechana-9308	256	10	t(ξ	t(ξ	PROPN
bibechana-9308	256	11	–	–	PUNCT
bibechana-9308	256	12	)	)	PUNCT
bibechana-9308	257	1	=	=	SYM
bibechana-9308	257	2	0	0	PUNCT
bibechana-9308	258	1	if	if	SCONJ
bibechana-9308	258	2	and	and	CCONJ
bibechana-9308	258	3	only	only	ADV
bibechana-9308	258	4	if	if	SCONJ
bibechana-9308	258	5	ξ	ξ	X
bibechana-9308	258	6	–	–	PUNCT
bibechana-9308	258	7	=	=	SYM
bibechana-9308	258	8	θ	θ	NOUN
bibechana-9308	258	9	–	–	PUNCT
bibechana-9308	258	10	;	;	PUNCT
bibechana-9308	258	11	t	t	PROPN
bibechana-9308	258	12	(	(	PUNCT
bibechana-9308	258	13	–	–	PUNCT
bibechana-9308	258	14	ξ	ξ	X
bibechana-9308	258	15	–	–	PUNCT
bibechana-9308	258	16	)	)	PUNCT
bibechana-9308	258	17	=	=	SYM
bibechana-9308	258	18	t	t	PROPN
bibechana-9308	258	19	(	(	PUNCT
bibechana-9308	258	20	ξ	ξ	PROPN
bibechana-9308	258	21	–	–	PUNCT
bibechana-9308	258	22	)	)	PUNCT
bibechana-9308	258	23	;	;	PUNCT
bibechana-9308	258	24	and	and	CCONJ
bibechana-9308	258	25	t	t	PROPN
bibechana-9308	258	26	(	(	PUNCT
bibechana-9308	258	27	ξ	ξ	PROPN
bibechana-9308	258	28	–	–	PUNCT
bibechana-9308	258	29	+	+	NUM
bibechana-9308	258	30	η	η	PROPN
bibechana-9308	258	31	–	–	PUNCT
bibechana-9308	258	32	)	)	PUNCT
bibechana-9308	258	33	≤	≤	NOUN
bibechana-9308	258	34	t	t	NOUN
bibechana-9308	258	35	(	(	PUNCT
bibechana-9308	258	36	ξ	ξ	PROPN
bibechana-9308	258	37	–	–	PUNCT
bibechana-9308	258	38	)	)	PUNCT
bibechana-9308	259	1	+	+	CCONJ
bibechana-9308	259	2	t	t	PROPN
bibechana-9308	259	3	(	(	PUNCT
bibechana-9308	259	4	η	η	PROPN
bibechana-9308	259	5	–	–	PUNCT
bibechana-9308	259	6	)	)	PUNCT
bibechana-9308	259	7	easily	easily	ADV
bibechana-9308	259	8	follow	follow	VERB
bibechana-9308	259	9	.	.	PUNCT
bibechana-9308	260	1	so	so	ADV
bibechana-9308	260	2	pn1	pn1	ADV
bibechana-9308	260	3	,	,	PUNCT
bibechana-9308	260	4	pn2	pn2	NOUN
bibechana-9308	260	5	and	and	CCONJ
bibechana-9308	260	6	pn3	pn3	NOUN
bibechana-9308	260	7	are	be	AUX
bibechana-9308	260	8	obvious	obvious	ADJ
bibechana-9308	260	9	.	.	PUNCT
bibechana-9308	261	1	for	for	ADP
bibechana-9308	261	2	pn4	pn4	NOUN
bibechana-9308	261	3	i.e.	i.e.	X
bibechana-9308	261	4	,	,	PUNCT
bibechana-9308	261	5	the	the	DET
bibechana-9308	261	6	continuity	continuity	NOUN
bibechana-9308	261	7	of	of	ADP
bibechana-9308	261	8	scalar	scalar	ADJ
bibechana-9308	261	9	multiplication	multiplication	NOUN
bibechana-9308	261	10	,	,	PUNCT
bibechana-9308	261	11	it	it	PRON
bibechana-9308	261	12	suffices	suffice	VERB
bibechana-9308	261	13	to	to	PART
bibechana-9308	261	14	show	show	VERB
bibechana-9308	261	15	that	that	SCONJ
bibechana-9308	261	16	(	(	PUNCT
bibechana-9308	261	17	a	a	X
bibechana-9308	261	18	)	)	PUNCT
bibechana-9308	261	19	if	if	SCONJ
bibechana-9308	261	20	ξ	ξ	X
bibechana-9308	261	21	–	–	PUNCT
bibechana-9308	261	22	(	(	PUNCT
bibechana-9308	261	23	n	n	CCONJ
bibechana-9308	261	24	)	)	PUNCT
bibechana-9308	261	25	→	→	SYM
bibechana-9308	261	26	θ	θ	X
bibechana-9308	261	27	–	–	PUNCT
bibechana-9308	261	28	in	in	ADP
bibechana-9308	261	29	t	t	PROPN
bibechana-9308	261	30	and	and	CCONJ
bibechana-9308	261	31	γn	γn	X
bibechana-9308	261	32	→	→	PUNCT
bibechana-9308	261	33	γ	γ	X
bibechana-9308	261	34	as	as	ADP
bibechana-9308	261	35	n	n	PROPN
bibechana-9308	261	36	→	→	SYM
bibechana-9308	261	37	∞,then	∞,then	X
bibechana-9308	261	38	γn	γn	ADP
bibechana-9308	261	39	ξ	ξ	PROPN
bibechana-9308	261	40	–	–	PUNCT
bibechana-9308	261	41	(	(	PUNCT
bibechana-9308	261	42	n	n	CCONJ
bibechana-9308	261	43	)	)	PUNCT
bibechana-9308	261	44	→	→	SYM
bibechana-9308	261	45	θ	θ	X
bibechana-9308	261	46	–	–	PUNCT
bibechana-9308	261	47	in	in	ADP
bibechana-9308	261	48	t	t	PROPN
bibechana-9308	261	49	;	;	PUNCT
bibechana-9308	261	50	and	and	CCONJ
bibechana-9308	261	51	(	(	PUNCT
bibechana-9308	261	52	b	b	X
bibechana-9308	261	53	)	)	PUNCT
bibechana-9308	261	54	if	if	SCONJ
bibechana-9308	261	55	γn	γn	ADP
bibechana-9308	261	56	→	→	SYM
bibechana-9308	261	57	0	0	NUM
bibechana-9308	261	58	and	and	CCONJ
bibechana-9308	261	59	ξ	ξ	PROPN
bibechana-9308	261	60	–	–	PUNCT
bibechana-9308	261	61	∈	∈	PROPN
bibechana-9308	261	62	c0	c0	NOUN
bibechana-9308	261	63	(	(	PUNCT
bibechana-9308	261	64	s	s	PROPN
bibechana-9308	261	65	,	,	PUNCT
bibechana-9308	261	66	α	α	PROPN
bibechana-9308	261	67	–	–	PUNCT
bibechana-9308	261	68	,	,	PUNCT
bibechana-9308	261	69	u	u	NOUN
bibechana-9308	261	70	–	–	PUNCT
bibechana-9308	261	71	,	,	PUNCT
bibechana-9308	261	72	||	||	PROPN
bibechana-9308	261	73	.	.	PUNCT
bibechana-9308	261	74	,	,	PUNCT
bibechana-9308	261	75	.||	.||	PROPN
bibechana-9308	261	76	)	)	PUNCT
bibechana-9308	261	77	,	,	PUNCT
bibechana-9308	261	78	then	then	ADV
bibechana-9308	261	79	γn	γn	ADP
bibechana-9308	261	80	ξ	ξ	PROPN
bibechana-9308	261	81	–	–	PUNCT
bibechana-9308	261	82	→	→	SYM
bibechana-9308	261	83	θ	θ	X
bibechana-9308	261	84	–	–	PUNCT
bibechana-9308	261	85	in	in	ADP
bibechana-9308	261	86	t	t	PROPN
bibechana-9308	261	87	.	.	PUNCT
bibechana-9308	262	1	now	now	ADV
bibechana-9308	262	2	(	(	PUNCT
bibechana-9308	262	3	a	a	X
bibechana-9308	262	4	)	)	PUNCT
bibechana-9308	262	5	is	be	AUX
bibechana-9308	262	6	easily	easily	ADV
bibechana-9308	262	7	proved	prove	VERB
bibechana-9308	262	8	if	if	SCONJ
bibechana-9308	262	9	we	we	PRON
bibechana-9308	262	10	suppose	suppose	VERB
bibechana-9308	262	11	|γn|	|γn|	NUM
bibechana-9308	262	12	≤	≤	ADJ
bibechana-9308	262	13	l	l	NOUN
bibechana-9308	262	14	for	for	ADP
bibechana-9308	262	15	all	all	DET
bibechana-9308	262	16	n	n	PRON
bibechana-9308	262	17	≥	≥	NOUN
bibechana-9308	262	18	1	1	NUM
bibechana-9308	262	19	and	and	CCONJ
bibechana-9308	262	20	in	in	ADP
bibechana-9308	262	21	view	view	NOUN
bibechana-9308	262	22	of	of	ADP
bibechana-9308	262	23	(	(	PUNCT
bibechana-9308	262	24	4.3	4.3	NUM
bibechana-9308	262	25	)	)	PUNCT
bibechana-9308	262	26	,	,	PUNCT
bibechana-9308	262	27	we	we	PRON
bibechana-9308	262	28	have	have	VERB
bibechana-9308	262	29	t	t	NOUN
bibechana-9308	262	30	(	(	PUNCT
bibechana-9308	262	31	γn	γn	ADP
bibechana-9308	262	32	ξ	ξ	PROPN
bibechana-9308	262	33	–	–	PUNCT
bibechana-9308	262	34	(	(	PUNCT
bibechana-9308	262	35	n	n	CCONJ
bibechana-9308	262	36	)	)	PUNCT
bibechana-9308	262	37	)	)	PUNCT
bibechana-9308	263	1	=	=	PRON
bibechana-9308	263	2	{	{	PUNCT
bibechana-9308	263	3	sup	sup	NOUN
bibechana-9308	263	4	k	k	NOUN
bibechana-9308	263	5	||	||	NOUN
bibechana-9308	264	1	γn	γn	INTJ
bibechana-9308	264	2	αk	αk	INTJ
bibechana-9308	264	3	ξk	ξk	ADP
bibechana-9308	264	4	(	(	PUNCT
bibechana-9308	264	5	n	n	CCONJ
bibechana-9308	264	6	)	)	PUNCT
bibechana-9308	264	7	‚	‚	PROPN
bibechana-9308	264	8	η	η	PROPN
bibechana-9308	264	9	||	||	PROPN
bibechana-9308	264	10	u	u	PROPN
bibechana-9308	264	11	k	k	PROPN
bibechana-9308	265	1	/m	/m	X
bibechana-9308	265	2	,	,	PUNCT
bibechana-9308	265	3	for	for	ADP
bibechana-9308	265	4	each	each	DET
bibechana-9308	265	5	η	η	PROPN
bibechana-9308	265	6	∈	∈	PROPN
bibechana-9308	265	7	s	s	PART
bibechana-9308	265	8	}	}	PUNCT
bibechana-9308	265	9	≤	≤	NOUN
bibechana-9308	265	10	{	{	PUNCT
bibechana-9308	265	11	sup	sup	NOUN
bibechana-9308	265	12	k	k	PROPN
bibechana-9308	265	13	|γn|	|γn|	PROPN
bibechana-9308	266	1	u	u	PROPN
bibechana-9308	266	2	k	k	PROPN
bibechana-9308	266	3	/m	/m	PUNCT
bibechana-9308	266	4	sup	sup	PROPN
bibechana-9308	266	5	k	k	NOUN
bibechana-9308	266	6	||	||	NOUN
bibechana-9308	267	1	αk	αk	INTJ
bibechana-9308	267	2	ξk	ξk	ADP
bibechana-9308	267	3	(	(	PUNCT
bibechana-9308	267	4	n	n	CCONJ
bibechana-9308	267	5	)	)	PUNCT
bibechana-9308	267	6	‚	‚	PROPN
bibechana-9308	268	1	η	η	PROPN
bibechana-9308	268	2	||	||	PROPN
bibechana-9308	268	3	u	u	PROPN
bibechana-9308	268	4	k	k	PROPN
bibechana-9308	269	1	/m	/m	X
bibechana-9308	269	2	,	,	PUNCT
bibechana-9308	269	3	for	for	ADP
bibechana-9308	269	4	each	each	DET
bibechana-9308	269	5	η	η	PROPN
bibechana-9308	269	6	∈	∈	PROPN
bibechana-9308	269	7	s	s	PART
bibechana-9308	269	8	}	}	PUNCT
bibechana-9308	269	9	n.p	n.p	PROPN
bibechana-9308	269	10	.	.	PROPN
bibechana-9308	269	11	pahari	pahari	PROPN
bibechana-9308	269	12	/	/	SYM
bibechana-9308	269	13	bibechana	bibechana	NOUN
bibechana-9308	269	14	10	10	NUM
bibechana-9308	269	15	(	(	PUNCT
bibechana-9308	269	16	2014	2014	NUM
bibechana-9308	269	17	)	)	PUNCT
bibechana-9308	269	18	20	20	NUM
bibechana-9308	269	19	-	-	SYM
bibechana-9308	269	20	30	30	NUM
bibechana-9308	269	21	:	:	PUNCT
bibechana-9308	269	22	bmhss	bmhss	PROPN
bibechana-9308	269	23	,	,	PUNCT
bibechana-9308	269	24	p.30	p.30	PROPN
bibechana-9308	269	25	(	(	PUNCT
bibechana-9308	269	26	online	online	ADJ
bibechana-9308	269	27	publication	publication	NOUN
bibechana-9308	269	28	:	:	PUNCT
bibechana-9308	269	29	dec	dec	PROPN
bibechana-9308	269	30	.	.	PROPN
bibechana-9308	269	31	,	,	PUNCT
bibechana-9308	269	32	2013	2013	NUM
bibechana-9308	269	33	)	)	PUNCT
bibechana-9308	269	34	=	=	PUNCT
bibechana-9308	269	35	a(l	a(l	PROPN
bibechana-9308	269	36	)	)	PUNCT
bibechana-9308	269	37	{	{	PUNCT
bibechana-9308	270	1	sup	sup	NOUN
bibechana-9308	270	2	k	k	NOUN
bibechana-9308	270	3	||	||	NOUN
bibechana-9308	271	1	αk	αk	INTJ
bibechana-9308	271	2	ξk	ξk	ADP
bibechana-9308	271	3	(	(	PUNCT
bibechana-9308	271	4	n	n	CCONJ
bibechana-9308	271	5	)	)	PUNCT
bibechana-9308	271	6	‚	‚	PROPN
bibechana-9308	272	1	η	η	PROPN
bibechana-9308	272	2	||	||	PROPN
bibechana-9308	272	3	u	u	PROPN
bibechana-9308	272	4	k	k	PROPN
bibechana-9308	273	1	/m	/m	X
bibechana-9308	273	2	,	,	PUNCT
bibechana-9308	273	3	for	for	ADP
bibechana-9308	273	4	each	each	DET
bibechana-9308	273	5	η	η	PROPN
bibechana-9308	273	6	∈	∈	PROPN
bibechana-9308	273	7	s	s	PART
bibechana-9308	273	8	}	}	PUNCT
bibechana-9308	273	9	≤	≤	NUM
bibechana-9308	273	10	a(l	a(l	PROPN
bibechana-9308	273	11	)	)	PUNCT
bibechana-9308	273	12	t	t	NOUN
bibechana-9308	273	13	(	(	PUNCT
bibechana-9308	273	14	ξ	ξ	PROPN
bibechana-9308	273	15	–	–	PUNCT
bibechana-9308	273	16	(	(	PUNCT
bibechana-9308	273	17	n	n	CCONJ
bibechana-9308	273	18	)	)	PUNCT
bibechana-9308	273	19	)	)	PUNCT
bibechana-9308	273	20	,	,	PUNCT
bibechana-9308	273	21	implies	imply	VERB
bibechana-9308	273	22	that	that	SCONJ
bibechana-9308	273	23	t	t	PROPN
bibechana-9308	273	24	(	(	PUNCT
bibechana-9308	273	25	γn	γn	ADP
bibechana-9308	273	26	ξ	ξ	PROPN
bibechana-9308	273	27	–	–	PUNCT
bibechana-9308	273	28	(	(	PUNCT
bibechana-9308	273	29	n	n	CCONJ
bibechana-9308	273	30	)	)	PUNCT
bibechana-9308	273	31	)	)	PUNCT
bibechana-9308	274	1	→	→	SYM
bibechana-9308	274	2	0	0	NUM
bibechana-9308	274	3	,	,	PUNCT
bibechana-9308	274	4	as	as	ADP
bibechana-9308	274	5	t	t	PROPN
bibechana-9308	274	6	(	(	PUNCT
bibechana-9308	274	7	ξ	ξ	X
bibechana-9308	274	8	–	–	PUNCT
bibechana-9308	274	9	(	(	PUNCT
bibechana-9308	274	10	n	n	CCONJ
bibechana-9308	274	11	)	)	PUNCT
bibechana-9308	274	12	)	)	PUNCT
bibechana-9308	275	1	→	→	SYM
bibechana-9308	275	2	0	0	NUM
bibechana-9308	275	3	as	as	SCONJ
bibechana-9308	275	4	n	n	NOUN
bibechana-9308	275	5	→	→	PUNCT
bibechana-9308	275	6	∞.	∞.	PROPN
bibechana-9308	275	7	to	to	PART
bibechana-9308	275	8	prove	prove	VERB
bibechana-9308	275	9	(	(	PUNCT
bibechana-9308	275	10	b	b	NOUN
bibechana-9308	275	11	)	)	PUNCT
bibechana-9308	275	12	,	,	PUNCT
bibechana-9308	275	13	let	let	VERB
bibechana-9308	275	14	ξ	ξ	X
bibechana-9308	275	15	–	–	PUNCT
bibechana-9308	275	16	∈	∈	PROPN
bibechana-9308	275	17	c0	c0	NOUN
bibechana-9308	275	18	(	(	PUNCT
bibechana-9308	275	19	s	s	PROPN
bibechana-9308	275	20	,	,	PUNCT
bibechana-9308	275	21	α	α	PROPN
bibechana-9308	275	22	–	–	PUNCT
bibechana-9308	275	23	,	,	PUNCT
bibechana-9308	275	24	u	u	NOUN
bibechana-9308	275	25	–	–	PUNCT
bibechana-9308	275	26	,	,	PUNCT
bibechana-9308	275	27	||	||	PROPN
bibechana-9308	275	28	.	.	PUNCT
bibechana-9308	275	29	,	,	PUNCT
bibechana-9308	275	30	.||	.||	PROPN
bibechana-9308	275	31	)	)	PUNCT
bibechana-9308	275	32	,	,	PUNCT
bibechana-9308	275	33	|γn|	|γn|	PROPN
bibechana-9308	275	34	<	<	X
bibechana-9308	275	35	1	1	NUM
bibechana-9308	275	36	for	for	ADP
bibechana-9308	275	37	all	all	DET
bibechana-9308	275	38	n	n	PRON
bibechana-9308	275	39	≥	≥	NOUN
bibechana-9308	275	40	n1	n1	PROPN
bibechana-9308	275	41	and	and	CCONJ
bibechana-9308	275	42	ε	ε	PROPN
bibechana-9308	275	43	>	>	X
bibechana-9308	275	44	0	0	PROPN
bibechana-9308	275	45	.	.	PUNCT
bibechana-9308	276	1	then	then	ADV
bibechana-9308	276	2	there	there	PRON
bibechana-9308	276	3	exists	exist	VERB
bibechana-9308	276	4	a	a	DET
bibechana-9308	276	5	positive	positive	ADJ
bibechana-9308	276	6	integer	integer	NOUN
bibechana-9308	276	7	k	k	PROPN
bibechana-9308	276	8	such	such	ADJ
bibechana-9308	276	9	that	that	DET
bibechana-9308	276	10	||αk	||αk	NOUN
bibechana-9308	276	11	ξk	ξk	ADP
bibechana-9308	276	12	‚	‚	PROPN
bibechana-9308	276	13	η	η	PROPN
bibechana-9308	276	14	||	||	PROPN
bibechana-9308	276	15	u	u	NOUN
bibechana-9308	276	16	k	k	X
bibechana-9308	276	17	<	<	X
bibechana-9308	276	18	ε	ε	PROPN
bibechana-9308	276	19	m	m	VERB
bibechana-9308	276	20	for	for	ADP
bibechana-9308	276	21	all	all	PRON
bibechana-9308	276	22	k	k	PROPN
bibechana-9308	276	23	≥	≥	PROPN
bibechana-9308	276	24	k	k	NOUN
bibechana-9308	276	25	and	and	CCONJ
bibechana-9308	276	26	for	for	ADP
bibechana-9308	276	27	each	each	DET
bibechana-9308	276	28	η	η	PROPN
bibechana-9308	276	29	∈	∈	PROPN
bibechana-9308	276	30	s	s	X
bibechana-9308	276	31	and	and	CCONJ
bibechana-9308	276	32	hence	hence	ADV
bibechana-9308	276	33	for	for	ADP
bibechana-9308	276	34	all	all	PRON
bibechana-9308	276	35	k	k	PROPN
bibechana-9308	276	36	≥	≥	PROPN
bibechana-9308	276	37	k	k	NOUN
bibechana-9308	276	38	and	and	CCONJ
bibechana-9308	276	39	n	n	PRON
bibechana-9308	276	40	≥	≥	NOUN
bibechana-9308	276	41	n1	n1	NOUN
bibechana-9308	276	42	,	,	PUNCT
bibechana-9308	276	43	we	we	PRON
bibechana-9308	276	44	have	have	VERB
bibechana-9308	276	45	||	||	NOUN
bibechana-9308	276	46	γn	γn	INTJ
bibechana-9308	276	47	αk	αk	INTJ
bibechana-9308	276	48	ξk	ξk	ADP
bibechana-9308	276	49	‚	‚	PROPN
bibechana-9308	276	50	η	η	PROPN
bibechana-9308	276	51	||	||	PROPN
bibechana-9308	277	1	u	u	NOUN
bibechana-9308	277	2	k	k	PROPN
bibechana-9308	277	3	=	=	SYM
bibechana-9308	277	4	|γn|	|γn|	PROPN
bibechana-9308	278	1	u	u	NOUN
bibechana-9308	279	1	k	k	PROPN
bibechana-9308	279	2	||	||	INTJ
bibechana-9308	280	1	αk	αk	INTJ
bibechana-9308	280	2	ξk	ξk	ADP
bibechana-9308	280	3	‚	‚	PROPN
bibechana-9308	280	4	η	η	PROPN
bibechana-9308	280	5	||	||	PROPN
bibechana-9308	280	6	u	u	NOUN
bibechana-9308	280	7	k	k	X
bibechana-9308	280	8	<	<	X
bibechana-9308	280	9	εm	εm	PROPN
bibechana-9308	280	10	,	,	PUNCT
bibechana-9308	280	11	for	for	ADP
bibechana-9308	280	12	each	each	DET
bibechana-9308	280	13	η	η	PROPN
bibechana-9308	280	14	∈	∈	PROPN
bibechana-9308	280	15	s.	s.	PROPN
bibechana-9308	280	16	now	now	ADV
bibechana-9308	280	17	choose	choose	VERB
bibechana-9308	280	18	n2	n2	ADJ
bibechana-9308	280	19	such	such	ADJ
bibechana-9308	280	20	that	that	PRON
bibechana-9308	280	21	for	for	ADP
bibechana-9308	280	22	all	all	PRON
bibechana-9308	280	23	k	k	NOUN
bibechana-9308	280	24	=	=	SYM
bibechana-9308	280	25	1	1	NUM
bibechana-9308	280	26	,	,	PUNCT
bibechana-9308	280	27	2	2	NUM
bibechana-9308	280	28	,	,	PUNCT
bibechana-9308	280	29	…	…	PUNCT
bibechana-9308	280	30	,	,	PUNCT
bibechana-9308	280	31	k	k	X
bibechana-9308	280	32	–	–	PUNCT
bibechana-9308	280	33	1	1	NUM
bibechana-9308	280	34	and	and	CCONJ
bibechana-9308	280	35	n	n	PRON
bibechana-9308	280	36	≥	≥	NOUN
bibechana-9308	280	37	n2	n2	NOUN
bibechana-9308	280	38	,	,	PUNCT
bibechana-9308	280	39	||	||	NOUN
bibechana-9308	280	40	γn	γn	INTJ
bibechana-9308	280	41	αk	αk	INTJ
bibechana-9308	280	42	ξk	ξk	ADP
bibechana-9308	280	43	‚	‚	PROPN
bibechana-9308	280	44	η	η	PROPN
bibechana-9308	280	45	||	||	PROPN
bibechana-9308	281	1	u	u	NOUN
bibechana-9308	281	2	k	k	PROPN
bibechana-9308	281	3	=	=	SYM
bibechana-9308	281	4	|γn|	|γn|	PROPN
bibechana-9308	282	1	u	u	NOUN
bibechana-9308	283	1	k	k	PROPN
bibechana-9308	283	2	||	||	INTJ
bibechana-9308	284	1	αk	αk	INTJ
bibechana-9308	284	2	ξk	ξk	ADP
bibechana-9308	284	3	‚	‚	PROPN
bibechana-9308	284	4	η	η	PROPN
bibechana-9308	284	5	||	||	PROPN
bibechana-9308	284	6	u	u	NOUN
bibechana-9308	285	1	k	k	X
bibechana-9308	285	2	<	<	X
bibechana-9308	285	3	ε	ε	PROPN
bibechana-9308	285	4	m	m	PROPN
bibechana-9308	285	5	,	,	PUNCT
bibechana-9308	285	6	for	for	ADP
bibechana-9308	285	7	each	each	DET
bibechana-9308	285	8	η	η	PROPN
bibechana-9308	285	9	∈	∈	PROPN
bibechana-9308	285	10	s.	s.	PROPN
bibechana-9308	285	11	thus	thus	ADV
bibechana-9308	285	12	,	,	PUNCT
bibechana-9308	285	13	t	t	PROPN
bibechana-9308	285	14	(	(	PUNCT
bibechana-9308	285	15	γn	γn	ADP
bibechana-9308	285	16	ξ	ξ	PROPN
bibechana-9308	285	17	–	–	PUNCT
bibechana-9308	285	18	)	)	PUNCT
bibechana-9308	285	19	≤	≤	NUM
bibechana-9308	285	20	ε	ε	PROPN
bibechana-9308	285	21	,	,	PUNCT
bibechana-9308	285	22	for	for	ADP
bibechana-9308	285	23	n	n	NUM
bibechana-9308	285	24	≥	≥	NOUN
bibechana-9308	285	25	n	n	PROPN
bibechana-9308	285	26	=	=	SYM
bibechana-9308	285	27	max	max	PROPN
bibechana-9308	285	28	(	(	PUNCT
bibechana-9308	285	29	n1	n1	NOUN
bibechana-9308	285	30	,	,	PUNCT
bibechana-9308	285	31	n2	n2	NOUN
bibechana-9308	285	32	)	)	PUNCT
bibechana-9308	285	33	,	,	PUNCT
bibechana-9308	285	34	which	which	PRON
bibechana-9308	285	35	proves	prove	VERB
bibechana-9308	285	36	(	(	PUNCT
bibechana-9308	285	37	b).the	b).the	ADJ
bibechana-9308	285	38	totality	totality	NOUN
bibechana-9308	285	39	of	of	ADP
bibechana-9308	285	40	t	t	PROPN
bibechana-9308	285	41	is	be	AUX
bibechana-9308	285	42	obvious	obvious	ADJ
bibechana-9308	285	43	.	.	PUNCT
bibechana-9308	286	1	references	reference	NOUN
bibechana-9308	286	2	1	1	NUM
bibechana-9308	286	3	.	.	PUNCT
bibechana-9308	286	4	s.	s.	PROPN
bibechana-9308	286	5	gäahler	gäahler	PROPN
bibechana-9308	286	6	,	,	PUNCT
bibechana-9308	286	7	math	math	NOUN
bibechana-9308	286	8	.	.	PUNCT
bibechana-9308	287	1	nachr	nachr	PROPN
bibechana-9308	287	2	.	.	PROPN
bibechana-9308	287	3	,	,	PUNCT
bibechana-9308	287	4	6	6	NUM
bibechana-9308	287	5	(	(	PUNCT
bibechana-9308	287	6	1963	1963	NUM
bibechana-9308	287	7	)	)	PUNCT
bibechana-9308	287	8	115	115	NUM
bibechana-9308	287	9	-	-	SYM
bibechana-9308	287	10	148	148	NUM
bibechana-9308	287	11	.	.	PUNCT
bibechana-9308	288	1	2	2	X
bibechana-9308	288	2	.	.	X
bibechana-9308	288	3	j.a	j.a	PROPN
bibechana-9308	288	4	.	.	PROPN
bibechana-9308	288	5	white	white	PROPN
bibechana-9308	288	6	and	and	CCONJ
bibechana-9308	288	7	y.j	y.j	PROPN
bibechana-9308	288	8	.	.	PUNCT
bibechana-9308	288	9	cho	cho	PROPN
bibechana-9308	288	10	,	,	PUNCT
bibechana-9308	288	11	bull	bull	NOUN
bibechana-9308	288	12	.	.	PUNCT
bibechana-9308	289	1	korean	korean	ADJ
bibechana-9308	289	2	math	math	PROPN
bibechana-9308	289	3	.	.	PUNCT
bibechana-9308	290	1	soc	soc	PROPN
bibechana-9308	290	2	.	.	PROPN
bibechana-9308	290	3	,	,	PUNCT
bibechana-9308	290	4	21(1	21(1	NUM
bibechana-9308	290	5	)	)	PUNCT
bibechana-9308	290	6	(	(	PUNCT
bibechana-9308	290	7	1984	1984	NUM
bibechana-9308	290	8	)	)	PUNCT
bibechana-9308	290	9	1–6	1–6	NUM
bibechana-9308	290	10	.	.	PUNCT
bibechana-9308	291	1	3	3	X
bibechana-9308	291	2	.	.	PUNCT
bibechana-9308	291	3	k.	k.	PROPN
bibechana-9308	291	4	iseki	iseki	PROPN
bibechana-9308	291	5	,	,	PUNCT
bibechana-9308	291	6	bull	bull	PROPN
bibechana-9308	291	7	.	.	PUNCT
bibechana-9308	292	1	korean	korean	ADJ
bibechana-9308	292	2	,	,	PUNCT
bibechana-9308	292	3	math	math	NOUN
bibechana-9308	292	4	.	.	PUNCT
bibechana-9308	293	1	soc	soc	PROPN
bibechana-9308	293	2	.	.	PUNCT
bibechana-9308	293	3	,	,	PUNCT
bibechana-9308	293	4	13(2	13(2	PROPN
bibechana-9308	293	5	)	)	PUNCT
bibechana-9308	293	6	(	(	PUNCT
bibechana-9308	293	7	1976	1976	NUM
bibechana-9308	293	8	)	)	PUNCT
bibechana-9308	293	9	.	.	PUNCT
bibechana-9308	294	1	4	4	X
bibechana-9308	294	2	.	.	X
bibechana-9308	294	3	r.	r.	PROPN
bibechana-9308	294	4	freese	freese	PROPN
bibechana-9308	294	5	and	and	CCONJ
bibechana-9308	294	6	y.	y.	PROPN
bibechana-9308	294	7	cho	cho	PROPN
bibechana-9308	294	8	,	,	PUNCT
bibechana-9308	294	9	nova	nova	PROPN
bibechana-9308	294	10	science	science	NOUN
bibechana-9308	294	11	publishers	publisher	NOUN
bibechana-9308	294	12	,	,	PUNCT
bibechana-9308	294	13	inc	inc	PROPN
bibechana-9308	294	14	.	.	PROPN
bibechana-9308	294	15	new	new	PROPN
bibechana-9308	294	16	york	york	PROPN
bibechana-9308	294	17	,	,	PUNCT
bibechana-9308	294	18	2001	2001	NUM
bibechana-9308	294	19	.	.	PUNCT
bibechana-9308	295	1	5	5	X
bibechana-9308	295	2	.	.	X
bibechana-9308	295	3	r.w	r.w	PROPN
bibechana-9308	295	4	.	.	PROPN
bibechana-9308	295	5	freese	freese	PROPN
bibechana-9308	295	6	,	,	PUNCT
bibechana-9308	295	7	y.	y.	PROPN
bibechana-9308	295	8	j.	j.	PROPN
bibechana-9308	295	9	cho	cho	PROPN
bibechana-9308	295	10	and	and	CCONJ
bibechana-9308	295	11	s.s	s.s	PROPN
bibechana-9308	295	12	.	.	PROPN
bibechana-9308	295	13	kim	kim	PROPN
bibechana-9308	295	14	,	,	PUNCT
bibechana-9308	295	15	j.	j.	PROPN
bibechana-9308	295	16	korean	korean	PROPN
bibechana-9308	295	17	math	math	PROPN
bibechana-9308	295	18	.	.	PUNCT
bibechana-9308	296	1	soc	soc	PROPN
bibechana-9308	296	2	.	.	PUNCT
bibechana-9308	296	3	,	,	PUNCT
bibechana-9308	296	4	29	29	NUM
bibechana-9308	296	5	(	(	PUNCT
bibechana-9308	296	6	2	2	NUM
bibechana-9308	296	7	)	)	PUNCT
bibechana-9308	296	8	(	(	PUNCT
bibechana-9308	296	9	1992	1992	NUM
bibechana-9308	296	10	)	)	PUNCT
bibechana-9308	296	11	391	391	NUM
bibechana-9308	296	12	–	–	PUNCT
bibechana-9308	296	13	400	400	NUM
bibechana-9308	296	14	.	.	NOUN
bibechana-9308	296	15	6	6	NUM
bibechana-9308	296	16	.	.	PUNCT
bibechana-9308	296	17	w.	w.	PROPN
bibechana-9308	296	18	raymond	raymond	PROPN
bibechana-9308	296	19	,	,	PUNCT
bibechana-9308	296	20	y.	y.	PROPN
bibechana-9308	296	21	freese	freese	PROPN
bibechana-9308	296	22	and	and	CCONJ
bibechana-9308	296	23	j.	j.	PROPN
bibechana-9308	296	24	cho	cho	PROPN
bibechana-9308	296	25	,	,	PUNCT
bibechana-9308	296	26	geometry	geometry	NOUN
bibechana-9308	296	27	of	of	ADP
bibechana-9308	296	28	linear	linear	PROPN
bibechana-9308	296	29	2	2	NUM
bibechana-9308	296	30	-	-	PUNCT
bibechana-9308	296	31	normed	norme	VERB
bibechana-9308	296	32	spaces	space	NOUN
bibechana-9308	296	33	,	,	PUNCT
bibechana-9308	296	34	n.	n.	PROPN
bibechana-9308	296	35	y.	y.	PROPN
bibechana-9308	296	36	nova	nova	PROPN
bibechana-9308	296	37	science	science	NOUN
bibechana-9308	296	38	publishers	publisher	NOUN
bibechana-9308	296	39	,	,	PUNCT
bibechana-9308	296	40	huntington	huntington	PROPN
bibechana-9308	296	41	,	,	PUNCT
bibechana-9308	296	42	2001	2001	NUM
bibechana-9308	296	43	.	.	PUNCT
bibechana-9308	297	1	7	7	X
bibechana-9308	297	2	.	.	X
bibechana-9308	297	3	e.	e.	PROPN
bibechana-9308	297	4	savas	savas	PROPN
bibechana-9308	297	5	,	,	PUNCT
bibechana-9308	297	6	abstract	abstract	ADJ
bibechana-9308	297	7	and	and	CCONJ
bibechana-9308	297	8	applied	apply	VERB
bibechana-9308	297	9	analysis	analysis	NOUN
bibechana-9308	297	10	,	,	PUNCT
bibechana-9308	297	11	2011	2011	NUM
bibechana-9308	297	12	(	(	PUNCT
bibechana-9308	297	13	2010	2010	NUM
bibechana-9308	297	14	)	)	PUNCT
bibechana-9308	297	15	10.1155	10.1155	NUM
bibechana-9308	297	16	.	.	NOUN
bibechana-9308	297	17	8	8	NUM
bibechana-9308	297	18	.	.	PUNCT
bibechana-9308	297	19	h.	h.	PROPN
bibechana-9308	297	20	gunawan	gunawan	PROPN
bibechana-9308	297	21	and	and	CCONJ
bibechana-9308	297	22	h.	h.	PROPN
bibechana-9308	297	23	mashadi	mashadi	PROPN
bibechana-9308	297	24	,	,	PUNCT
bibechana-9308	297	25	soochow	soochow	PROPN
bibechana-9308	297	26	j.math	j.math	NOUN
bibechana-9308	297	27	.	.	PROPN
bibechana-9308	297	28	,	,	PUNCT
bibechana-9308	297	29	27(2001	27(2001	NUM
bibechana-9308	297	30	)	)	PUNCT
bibechana-9308	298	1	321–329	321–329	NUM
bibechana-9308	298	2	.	.	PUNCT
bibechana-9308	299	1	9	9	NUM
bibechana-9308	299	2	.	.	PUNCT
bibechana-9308	299	3	j.	j.	PROPN
bibechana-9308	299	4	k.	k.	PROPN
bibechana-9308	299	5	srivastava	srivastava	PROPN
bibechana-9308	299	6	and	and	CCONJ
bibechana-9308	299	7	n.p	n.p	PROPN
bibechana-9308	299	8	.	.	PROPN
bibechana-9308	299	9	pahari	pahari	PROPN
bibechana-9308	299	10	,	,	PUNCT
bibechana-9308	299	11	south	south	PROPN
bibechana-9308	299	12	east	east	PROPN
bibechana-9308	299	13	asian	asian	PROPN
bibechana-9308	299	14	j.math	j.math	PROPN
bibechana-9308	299	15	.	.	PROPN
bibechana-9308	299	16	&	&	CCONJ
bibechana-9308	299	17	math.sc	math.sc	PROPN
bibechana-9308	299	18	.	.	PUNCT
bibechana-9308	299	19	,	,	PUNCT
bibechana-9308	299	20	10(1	10(1	NUM
bibechana-9308	299	21	)	)	PUNCT
bibechana-9308	299	22	,	,	PUNCT
bibechana-9308	299	23	(	(	PUNCT
bibechana-9308	299	24	2011	2011	NUM
bibechana-9308	299	25	)	)	PUNCT
bibechana-9308	299	26	39	39	NUM
bibechana-9308	299	27	-	-	SYM
bibechana-9308	299	28	49	49	NUM
bibechana-9308	299	29	.	.	PUNCT
bibechana-9308	300	1	10	10	NUM
bibechana-9308	300	2	.	.	PUNCT
bibechana-9308	300	3	m.	m.	NOUN
bibechana-9308	300	4	açikgöz	açikgöz	PROPN
bibechana-9308	300	5	,	,	PUNCT
bibechana-9308	300	6	int	int	PROPN
bibechana-9308	300	7	.	.	PUNCT
bibechana-9308	301	1	journal	journal	PROPN
bibechana-9308	301	2	of	of	ADP
bibechana-9308	301	3	math	math	NOUN
bibechana-9308	301	4	.	.	PUNCT
bibechana-9308	302	1	analysis	analysis	NOUN
bibechana-9308	302	2	,	,	PUNCT
bibechana-9308	302	3	1(4	1(4	NUM
bibechana-9308	302	4	)	)	PUNCT
bibechana-9308	302	5	(	(	PUNCT
bibechana-9308	302	6	2007	2007	NUM
bibechana-9308	302	7	)	)	PUNCT
bibechana-9308	302	8	187	187	NUM
bibechana-9308	302	9	-	-	SYM
bibechana-9308	302	10	191	191	NUM
bibechana-9308	302	11	.	.	PUNCT
bibechana-9308	302	12	11	11	NUM
bibechana-9308	302	13	.	.	PUNCT
bibechana-9308	302	14	a.	a.	PROPN
bibechana-9308	302	15	wilansky	wilansky	PROPN
bibechana-9308	302	16	,	,	PUNCT
bibechana-9308	302	17	modern	modern	ADJ
bibechana-9308	302	18	methods	method	NOUN
bibechana-9308	302	19	in	in	ADP
bibechana-9308	302	20	topological	topological	ADJ
bibechana-9308	302	21	vector	vector	NOUN
bibechana-9308	302	22	spaces	space	NOUN
bibechana-9308	302	23	,	,	PUNCT
bibechana-9308	302	24	mc	mc	PROPN
bibechana-9308	302	25	graw_hill	graw_hill	PROPN
bibechana-9308	302	26	book	book	NOUN
bibechana-9308	302	27	co.inc.new	co.inc.new	PROPN
bibechana-9308	302	28	york	york	PROPN
bibechana-9308	302	29	,	,	PUNCT
bibechana-9308	302	30	1978	1978	NUM
bibechana-9308	302	31	.	.	PUNCT
bibechana-9308	303	1	12	12	NUM
bibechana-9308	303	2	.	.	PUNCT
bibechana-9308	303	3	i.	i.	PROPN
bibechana-9308	303	4	j.	j.	PROPN
bibechana-9308	303	5	maddox	maddox	PROPN
bibechana-9308	303	6	,	,	PUNCT
bibechana-9308	303	7	j.	j.	PROPN
bibechana-9308	303	8	math	math	PROPN
bibechana-9308	303	9	.	.	PUNCT
bibechana-9308	304	1	soc	soc	PROPN
bibechana-9308	304	2	.	.	PUNCT
bibechana-9308	305	1	,	,	PUNCT
bibechana-9308	305	2	2(1	2(1	NUM
bibechana-9308	305	3	)	)	PUNCT
bibechana-9308	305	4	(	(	PUNCT
bibechana-9308	305	5	1969	1969	NUM
bibechana-9308	305	6	)	)	PUNCT
bibechana-9308	305	7	316	316	NUM
bibechana-9308	305	8	-	-	SYM
bibechana-9308	305	9	322	322	NUM
bibechana-9308	305	10	.	.	NOUN
bibechana-9308	305	11	13	13	NUM
bibechana-9308	305	12	.	.	PUNCT
bibechana-9308	306	1	j.	j.	PROPN
bibechana-9308	306	2	k.	k.	PROPN
bibechana-9308	306	3	srivastava	srivastava	PROPN
bibechana-9308	306	4	and	and	CCONJ
bibechana-9308	306	5	b.	b.	PROPN
bibechana-9308	306	6	k.	k.	PROPN
bibechana-9308	306	7	srivastava	srivastava	PROPN
bibechana-9308	306	8	,	,	PUNCT
bibechana-9308	306	9	indian	indian	PROPN
bibechana-9308	306	10	j.	j.	PROPN
bibechana-9308	306	11	pure	pure	PROPN
bibechana-9308	306	12	and	and	CCONJ
bibechana-9308	306	13	appl	appl	PROPN
bibechana-9308	306	14	.	.	PROPN
bibechana-9308	306	15	math	math	PROPN
bibechana-9308	306	16	.	.	PUNCT
bibechana-9308	306	17	,	,	PUNCT
bibechana-9308	306	18	27	27	NUM
bibechana-9308	306	19	(	(	PUNCT
bibechana-9308	306	20	1	1	NUM
bibechana-9308	306	21	)	)	PUNCT
bibechana-9308	306	22	(	(	PUNCT
bibechana-9308	306	23	1996	1996	NUM
bibechana-9308	306	24	)	)	PUNCT
bibechana-9308	306	25	73	73	NUM
bibechana-9308	306	26	-	-	SYM
bibechana-9308	306	27	84	84	NUM
bibechana-9308	306	28	.	.	PUNCT
bibechana-9308	307	1	14	14	NUM
bibechana-9308	307	2	.	.	PUNCT
bibechana-9308	308	1	j.k	j.k	PROPN
bibechana-9308	308	2	.	.	PROPN
bibechana-9308	308	3	srivastava	srivastava	PROPN
bibechana-9308	308	4	and	and	CCONJ
bibechana-9308	308	5	n.p.pahari	n.p.pahari	PROPN
bibechana-9308	308	6	,	,	PUNCT
bibechana-9308	308	7	jour	jour	PROPN
bibechana-9308	308	8	.	.	PROPN
bibechana-9308	308	9	of	of	ADP
bibechana-9308	308	10	rajasthan	rajasthan	PROPN
bibechana-9308	308	11	academy	academy	PROPN
bibechana-9308	308	12	of	of	ADP
bibechana-9308	308	13	physical	physical	PROPN
bibechana-9308	308	14	sciences	sciences	PROPN
bibechana-9308	308	15	,	,	PUNCT
bibechana-9308	308	16	11(2	11(2	NUM
bibechana-9308	308	17	)	)	PUNCT
bibechana-9308	308	18	(	(	PUNCT
bibechana-9308	308	19	2011	2011	NUM
bibechana-9308	308	20	)	)	PUNCT
bibechana-9308	308	21	103	103	NUM
bibechana-9308	308	22	-	-	SYM
bibechana-9308	308	23	116	116	NUM
bibechana-9308	308	24	.	.	PUNCT
bibechana-9308	308	25	15	15	NUM
bibechana-9308	308	26	.	.	PUNCT
bibechana-9308	309	1	j.k	j.k	PROPN
bibechana-9308	309	2	.	.	PROPN
bibechana-9308	309	3	srivastava	srivastava	PROPN
bibechana-9308	309	4	and	and	CCONJ
bibechana-9308	309	5	n.p.pahari	n.p.pahari	ADJ
bibechana-9308	309	6	,	,	PUNCT
bibechana-9308	309	7	proc	proc	NOUN
bibechana-9308	309	8	.	.	PROPN
bibechana-9308	309	9	of	of	ADP
bibechana-9308	309	10	indian	indian	ADJ
bibechana-9308	309	11	soc	soc	PROPN
bibechana-9308	309	12	.	.	PUNCT
bibechana-9308	310	1	of	of	ADP
bibechana-9308	310	2	math	math	NOUN
bibechana-9308	310	3	.	.	PUNCT
bibechana-9308	311	1	and	and	CCONJ
bibechana-9308	311	2	mathematical	mathematical	ADJ
bibechana-9308	311	3	sciences	science	NOUN
bibechana-9308	311	4	,	,	PUNCT
bibechana-9308	311	5	6	6	NUM
bibechana-9308	311	6	(	(	PUNCT
bibechana-9308	311	7	2011	2011	NUM
bibechana-9308	311	8	)	)	PUNCT
bibechana-9308	311	9	243	243	NUM
bibechana-9308	311	10	-	-	SYM
bibechana-9308	311	11	251	251	NUM
bibechana-9308	311	12	.	.	PUNCT
bibechana-9308	312	1	16	16	NUM
bibechana-9308	312	2	.	.	PUNCT
bibechana-9308	313	1	n.p	n.p	PROPN
bibechana-9308	313	2	.	.	PROPN
bibechana-9308	313	3	pahari	pahari	PROPN
bibechana-9308	313	4	,	,	PUNCT
bibechana-9308	313	5	nepal	nepal	ADJ
bibechana-9308	313	6	jour	jour	PROPN
bibechana-9308	313	7	.	.	PROPN
bibechana-9308	313	8	of	of	ADP
bibechana-9308	313	9	science	science	NOUN
bibechana-9308	313	10	and	and	CCONJ
bibechana-9308	313	11	tech	tech	NOUN
bibechana-9308	313	12	.	.	PUNCT
bibechana-9308	313	13	,	,	PUNCT
bibechana-9308	313	14	12	12	NUM
bibechana-9308	313	15	(	(	PUNCT
bibechana-9308	313	16	2011	2011	NUM
bibechana-9308	313	17	)	)	PUNCT
bibechana-9308	313	18	252	252	NUM
bibechana-9308	313	19	-	-	SYM
bibechana-9308	313	20	259	259	NUM
bibechana-9308	313	21	.	.	PUNCT
bibechana-9308	313	22	17	17	NUM
bibechana-9308	313	23	.	.	PUNCT
bibechana-9308	314	1	s.	s.	PROPN
bibechana-9308	314	2	d.	d.	PROPN
bibechana-9308	314	3	parashar	parashar	PROPN
bibechana-9308	314	4	and	and	CCONJ
bibechana-9308	314	5	b.	b.	PROPN
bibechana-9308	314	6	choudhary	choudhary	PROPN
bibechana-9308	314	7	,	,	PUNCT
bibechana-9308	314	8	indian	indian	PROPN
bibechana-9308	314	9	j.	j.	PROPN
bibechana-9308	314	10	pure	pure	PROPN
bibechana-9308	314	11	appl	appl	PROPN
bibechana-9308	314	12	.	.	PUNCT
bibechana-9308	315	1	maths	maths	PROPN
bibechana-9308	315	2	.	.	PUNCT
bibechana-9308	315	3	,	,	PUNCT
bibechana-9308	315	4	25(4	25(4	NOUN
bibechana-9308	315	5	)	)	PUNCT
bibechana-9308	315	6	(	(	PUNCT
bibechana-9308	315	7	1994	1994	NUM
bibechana-9308	315	8	)	)	PUNCT
bibechana-9308	316	1	419–428	419–428	NUM
bibechana-9308	316	2	.	.	PUNCT
bibechana-9308	317	1	18	18	NUM
bibechana-9308	317	2	.	.	PUNCT
bibechana-9308	318	1	v.n	v.n	PROPN
bibechana-9308	318	2	.	.	PROPN
bibechana-9308	318	3	bhardwaj	bhardwaj	PROPN
bibechana-9308	318	4	and	and	CCONJ
bibechana-9308	318	5	i.	i.	PROPN
bibechana-9308	318	6	bala	bala	PROPN
bibechana-9308	318	7	,	,	PUNCT
bibechana-9308	318	8	j.	j.	PROPN
bibechana-9308	318	9	of	of	ADP
bibechana-9308	318	10	pure	pure	ADJ
bibechana-9308	318	11	and	and	CCONJ
bibechana-9308	318	12	appl	appl	ADJ
bibechana-9308	318	13	.	.	PUNCT
bibechana-9308	319	1	maths	maths	PROPN
bibechana-9308	319	2	.	.	PUNCT
bibechana-9308	319	3	,	,	PUNCT
bibechana-9308	319	4	41(5	41(5	NUM
bibechana-9308	319	5	)	)	PUNCT
bibechana-9308	319	6	(	(	PUNCT
bibechana-9308	319	7	2007	2007	NUM
bibechana-9308	319	8	)	)	PUNCT
bibechana-9308	319	9	617–626	617–626	NUM
bibechana-9308	319	10	.	.	PUNCT