id	sid	tid	token	lemma	pos
ejpam-1950	1	1	compile	compile	NOUN
ejpam-1950	1	2	/	/	SYM
ejpam-1950	1	3	output.dvi	output.dvi	NOUN
ejpam-1950	1	4	european	european	ADJ
ejpam-1950	1	5	journal	journal	NOUN
ejpam-1950	1	6	of	of	ADP
ejpam-1950	1	7	pure	pure	ADJ
ejpam-1950	1	8	and	and	CCONJ
ejpam-1950	1	9	applied	apply	VERB
ejpam-1950	1	10	mathematics	mathematic	NOUN
ejpam-1950	1	11	vol	vol	NOUN
ejpam-1950	1	12	.	.	PROPN
ejpam-1950	1	13	8	8	NUM
ejpam-1950	1	14	,	,	PUNCT
ejpam-1950	1	15	no	no	INTJ
ejpam-1950	1	16	.	.	NOUN
ejpam-1950	1	17	3	3	NUM
ejpam-1950	1	18	,	,	PUNCT
ejpam-1950	1	19	2015	2015	NUM
ejpam-1950	1	20	,	,	PUNCT
ejpam-1950	1	21	357	357	NUM
ejpam-1950	1	22	-	-	SYM
ejpam-1950	1	23	367	367	NUM
ejpam-1950	1	24	issn	issn	PROPN
ejpam-1950	1	25	1307	1307	NUM
ejpam-1950	1	26	-	-	SYM
ejpam-1950	1	27	5543	5543	NUM
ejpam-1950	1	28	–	–	PUNCT
ejpam-1950	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-1950	1	30	on	on	ADP
ejpam-1950	1	31	statistical	statistical	ADJ
ejpam-1950	1	32	and	and	CCONJ
ejpam-1950	1	33	ideal	ideal	ADJ
ejpam-1950	1	34	convergence	convergence	NOUN
ejpam-1950	1	35	of	of	ADP
ejpam-1950	1	36	sequences	sequence	NOUN
ejpam-1950	1	37	of	of	ADP
ejpam-1950	1	38	bounded	bound	VERB
ejpam-1950	1	39	linear	linear	PROPN
ejpam-1950	1	40	operators	operators	PROPN
ejpam-1950	1	41	enno	enno	PROPN
ejpam-1950	1	42	kolk	kolk	PROPN
ejpam-1950	1	43	institute	institute	PROPN
ejpam-1950	1	44	of	of	ADP
ejpam-1950	1	45	mathematics	mathematics	PROPN
ejpam-1950	1	46	,	,	PUNCT
ejpam-1950	1	47	university	university	NOUN
ejpam-1950	1	48	of	of	ADP
ejpam-1950	1	49	tartu	tartu	NOUN
ejpam-1950	1	50	,	,	PUNCT
ejpam-1950	1	51	50090	50090	NUM
ejpam-1950	1	52	tartu	tartu	NOUN
ejpam-1950	1	53	,	,	PUNCT
ejpam-1950	1	54	estonia	estonia	PROPN
ejpam-1950	1	55	abstract	abstract	NOUN
ejpam-1950	1	56	.	.	PUNCT
ejpam-1950	2	1	let	let	VERB
ejpam-1950	2	2	(	(	PUNCT
ejpam-1950	2	3	an	an	X
ejpam-1950	2	4	)	)	PUNCT
ejpam-1950	2	5	be	be	AUX
ejpam-1950	2	6	a	a	DET
ejpam-1950	2	7	sequence	sequence	NOUN
ejpam-1950	2	8	of	of	ADP
ejpam-1950	2	9	bounded	bounded	ADJ
ejpam-1950	2	10	linear	linear	PROPN
ejpam-1950	2	11	operators	operator	NOUN
ejpam-1950	2	12	from	from	ADP
ejpam-1950	2	13	a	a	DET
ejpam-1950	2	14	separable	separable	ADJ
ejpam-1950	2	15	banach	banach	NOUN
ejpam-1950	2	16	space	space	NOUN
ejpam-1950	2	17	x	x	PUNCT
ejpam-1950	2	18	into	into	ADP
ejpam-1950	2	19	a	a	DET
ejpam-1950	2	20	banach	banach	NOUN
ejpam-1950	2	21	space	space	NOUN
ejpam-1950	2	22	y	y	PROPN
ejpam-1950	2	23	.	.	PUNCT
ejpam-1950	3	1	suppose	suppose	VERB
ejpam-1950	3	2	that	that	SCONJ
ejpam-1950	3	3	φ	φ	PROPN
ejpam-1950	3	4	is	be	AUX
ejpam-1950	3	5	a	a	DET
ejpam-1950	3	6	countable	countable	ADJ
ejpam-1950	3	7	fundamental	fundamental	ADJ
ejpam-1950	3	8	set	set	NOUN
ejpam-1950	3	9	of	of	ADP
ejpam-1950	3	10	x	x	PUNCT
ejpam-1950	3	11	and	and	CCONJ
ejpam-1950	3	12	the	the	DET
ejpam-1950	3	13	ideal	ideal	NOUN
ejpam-1950	3	14	i	i	PRON
ejpam-1950	3	15	of	of	ADP
ejpam-1950	3	16	subsets	subset	NOUN
ejpam-1950	3	17	of	of	ADP
ejpam-1950	3	18	n	n	PROPN
ejpam-1950	3	19	has	have	VERB
ejpam-1950	3	20	property	property	NOUN
ejpam-1950	3	21	(	(	PUNCT
ejpam-1950	3	22	ap	ap	PROPN
ejpam-1950	3	23	)	)	PUNCT
ejpam-1950	3	24	.	.	PUNCT
ejpam-1950	4	1	the	the	DET
ejpam-1950	4	2	sequence	sequence	NOUN
ejpam-1950	4	3	(	(	PUNCT
ejpam-1950	4	4	an	an	X
ejpam-1950	4	5	)	)	PUNCT
ejpam-1950	4	6	is	be	AUX
ejpam-1950	4	7	said	say	VERB
ejpam-1950	4	8	to	to	PART
ejpam-1950	4	9	be	be	AUX
ejpam-1950	4	10	b∗i	b∗i	ADJ
ejpam-1950	4	11	-convergent	-convergent	ADJ
ejpam-1950	4	12	if	if	SCONJ
ejpam-1950	4	13	it	it	PRON
ejpam-1950	4	14	is	be	AUX
ejpam-1950	4	15	pointwise	pointwise	PROPN
ejpam-1950	4	16	i	i	PRON
ejpam-1950	4	17	-convergent	-convergent	ADJ
ejpam-1950	4	18	and	and	CCONJ
ejpam-1950	4	19	there	there	PRON
ejpam-1950	4	20	exists	exist	VERB
ejpam-1950	4	21	an	an	DET
ejpam-1950	4	22	index	index	NOUN
ejpam-1950	4	23	set	set	VERB
ejpam-1950	4	24	k	k	ADP
ejpam-1950	4	25	such	such	ADJ
ejpam-1950	4	26	that	that	SCONJ
ejpam-1950	4	27	n	n	NOUN
ejpam-1950	4	28	\	\	NOUN
ejpam-1950	4	29	k	k	PROPN
ejpam-1950	4	30	∈	∈	PROPN
ejpam-1950	5	1	i	i	PRON
ejpam-1950	5	2	and	and	CCONJ
ejpam-1950	5	3	(	(	PUNCT
ejpam-1950	5	4	ak	ak	PROPN
ejpam-1950	5	5	x)k∈k	x)k∈k	PROPN
ejpam-1950	5	6	is	be	AUX
ejpam-1950	5	7	bounded	bound	VERB
ejpam-1950	5	8	for	for	ADP
ejpam-1950	5	9	any	any	DET
ejpam-1950	5	10	x	x	SYM
ejpam-1950	5	11	∈	∈	PROPN
ejpam-1950	5	12	x	x	X
ejpam-1950	5	13	.	.	PUNCT
ejpam-1950	6	1	we	we	PRON
ejpam-1950	6	2	prove	prove	VERB
ejpam-1950	6	3	that	that	SCONJ
ejpam-1950	6	4	the	the	DET
ejpam-1950	6	5	sequence	sequence	NOUN
ejpam-1950	6	6	(	(	PUNCT
ejpam-1950	6	7	an	an	NOUN
ejpam-1950	6	8	)	)	PUNCT
ejpam-1950	6	9	is	be	AUX
ejpam-1950	6	10	b∗i	b∗i	ADJ
ejpam-1950	6	11	-convergent	-convergent	ADJ
ejpam-1950	6	12	if	if	SCONJ
ejpam-1950	6	13	and	and	CCONJ
ejpam-1950	6	14	only	only	ADV
ejpam-1950	6	15	if	if	SCONJ
ejpam-1950	6	16	(	(	PUNCT
ejpam-1950	6	17	‖an‖	‖an‖	PROPN
ejpam-1950	6	18	)	)	PUNCT
ejpam-1950	6	19	is	be	AUX
ejpam-1950	6	20	i	i	PRON
ejpam-1950	6	21	-bounded	-bounded	ADJ
ejpam-1950	6	22	and	and	CCONJ
ejpam-1950	6	23	(	(	PUNCT
ejpam-1950	6	24	anφ	anφ	ADJ
ejpam-1950	6	25	)	)	PUNCT
ejpam-1950	6	26	is	be	AUX
ejpam-1950	6	27	i	i	PRON
ejpam-1950	6	28	-convergent	-convergent	ADJ
ejpam-1950	6	29	for	for	ADP
ejpam-1950	6	30	any	any	DET
ejpam-1950	6	31	φ	φ	PROPN
ejpam-1950	6	32	∈	∈	PROPN
ejpam-1950	6	33	φ	φ	PROPN
ejpam-1950	6	34	.	.	PUNCT
ejpam-1950	7	1	applications	application	NOUN
ejpam-1950	7	2	of	of	ADP
ejpam-1950	7	3	this	this	DET
ejpam-1950	7	4	banach	banach	NOUN
ejpam-1950	7	5	–	–	PUNCT
ejpam-1950	7	6	steinhaus	steinhaus	NOUN
ejpam-1950	7	7	type	type	NOUN
ejpam-1950	7	8	theorem	theorem	NOUN
ejpam-1950	7	9	are	be	AUX
ejpam-1950	7	10	related	relate	VERB
ejpam-1950	7	11	to	to	ADP
ejpam-1950	7	12	some	some	DET
ejpam-1950	7	13	sequence	sequence	NOUN
ejpam-1950	7	14	-	-	PUNCT
ejpam-1950	7	15	to	to	ADP
ejpam-1950	7	16	-	-	PUNCT
ejpam-1950	7	17	sequence	sequence	NOUN
ejpam-1950	7	18	matrix	matrix	NOUN
ejpam-1950	7	19	transformations	transformation	NOUN
ejpam-1950	7	20	and	and	CCONJ
ejpam-1950	7	21	to	to	ADP
ejpam-1950	7	22	the	the	DET
ejpam-1950	7	23	weak	weak	ADJ
ejpam-1950	7	24	i	i	INTJ
ejpam-1950	7	25	-convergence	-convergence	NOUN
ejpam-1950	7	26	in	in	ADP
ejpam-1950	7	27	banach	banach	NOUN
ejpam-1950	7	28	spaces	space	NOUN
ejpam-1950	7	29	.	.	PUNCT
ejpam-1950	8	1	2010	2010	NUM
ejpam-1950	8	2	mathematics	mathematic	NOUN
ejpam-1950	8	3	subject	subject	NOUN
ejpam-1950	8	4	classifications	classification	NOUN
ejpam-1950	8	5	:	:	PUNCT
ejpam-1950	8	6	40a35	40a35	NUM
ejpam-1950	8	7	;	;	PUNCT
ejpam-1950	8	8	40c05	40c05	NUM
ejpam-1950	8	9	,	,	PUNCT
ejpam-1950	8	10	40j05	40j05	NUM
ejpam-1950	8	11	,	,	PUNCT
ejpam-1950	8	12	46b15	46b15	NUM
ejpam-1950	8	13	,	,	PUNCT
ejpam-1950	8	14	46b45	46b45	DET
ejpam-1950	8	15	key	key	ADJ
ejpam-1950	8	16	words	word	NOUN
ejpam-1950	8	17	and	and	CCONJ
ejpam-1950	8	18	phrases	phrase	NOUN
ejpam-1950	8	19	:	:	PUNCT
ejpam-1950	8	20	banach	banach	NOUN
ejpam-1950	8	21	space	space	NOUN
ejpam-1950	8	22	,	,	PUNCT
ejpam-1950	8	23	bounded	bound	VERB
ejpam-1950	8	24	linear	linear	ADJ
ejpam-1950	8	25	operator	operator	NOUN
ejpam-1950	8	26	,	,	PUNCT
ejpam-1950	8	27	ideal	ideal	ADJ
ejpam-1950	8	28	,	,	PUNCT
ejpam-1950	8	29	i	i	PRON
ejpam-1950	8	30	-convergence	-convergence	PROPN
ejpam-1950	8	31	,	,	PUNCT
ejpam-1950	8	32	i	i	PRON
ejpam-1950	8	33	-boundedness	-boundedness	VERB
ejpam-1950	8	34	,	,	PUNCT
ejpam-1950	8	35	matrix	matrix	NOUN
ejpam-1950	8	36	method	method	NOUN
ejpam-1950	8	37	of	of	ADP
ejpam-1950	8	38	summability	summability	NOUN
ejpam-1950	8	39	,	,	PUNCT
ejpam-1950	8	40	sequence	sequence	NOUN
ejpam-1950	8	41	space	space	NOUN
ejpam-1950	8	42	,	,	PUNCT
ejpam-1950	8	43	statistical	statistical	ADJ
ejpam-1950	8	44	convergence	convergence	NOUN
ejpam-1950	8	45	,	,	PUNCT
ejpam-1950	8	46	weak	weak	ADJ
ejpam-1950	8	47	i	i	NOUN
ejpam-1950	8	48	-convergence	-convergence	NOUN
ejpam-1950	8	49	,	,	PUNCT
ejpam-1950	8	50	weak	weak	ADJ
ejpam-1950	8	51	statistical	statistical	ADJ
ejpam-1950	8	52	convergence	convergence	NOUN
ejpam-1950	8	53	1	1	NUM
ejpam-1950	8	54	.	.	PUNCT
ejpam-1950	9	1	introduction	introduction	NOUN
ejpam-1950	9	2	and	and	CCONJ
ejpam-1950	9	3	preliminaries	preliminary	NOUN
ejpam-1950	9	4	let	let	VERB
ejpam-1950	9	5	n	n	X
ejpam-1950	9	6	=	=	SYM
ejpam-1950	9	7	{	{	PUNCT
ejpam-1950	9	8	1,2	1,2	NUM
ejpam-1950	9	9	,	,	PUNCT
ejpam-1950	9	10	.	.	PUNCT
ejpam-1950	9	11	.	.	PUNCT
ejpam-1950	9	12	.	.	PUNCT
ejpam-1950	10	1	}	}	PUNCT
ejpam-1950	11	1	and	and	CCONJ
ejpam-1950	11	2	let	let	VERB
ejpam-1950	11	3	x	x	PRON
ejpam-1950	11	4	,	,	PUNCT
ejpam-1950	11	5	y	y	PROPN
ejpam-1950	11	6	be	be	VERB
ejpam-1950	11	7	two	two	NUM
ejpam-1950	11	8	normed	normed	ADJ
ejpam-1950	11	9	spaces	space	NOUN
ejpam-1950	11	10	over	over	ADP
ejpam-1950	11	11	the	the	DET
ejpam-1950	11	12	field	field	NOUN
ejpam-1950	12	1	k	k	PROPN
ejpam-1950	12	2	of	of	ADP
ejpam-1950	12	3	real	real	ADJ
ejpam-1950	12	4	numbers	number	NOUN
ejpam-1950	12	5	r	r	NOUN
ejpam-1950	12	6	or	or	CCONJ
ejpam-1950	12	7	complex	complex	ADJ
ejpam-1950	12	8	numbers	number	NOUN
ejpam-1950	12	9	c.	c.	PROPN
ejpam-1950	12	10	a	a	DET
ejpam-1950	12	11	subset	subset	VERB
ejpam-1950	12	12	φ	φ	PROPN
ejpam-1950	12	13	of	of	ADP
ejpam-1950	12	14	x	x	PROPN
ejpam-1950	12	15	is	be	AUX
ejpam-1950	12	16	called	call	VERB
ejpam-1950	12	17	fundamental	fundamental	ADJ
ejpam-1950	12	18	if	if	SCONJ
ejpam-1950	12	19	the	the	DET
ejpam-1950	12	20	linear	linear	ADJ
ejpam-1950	12	21	span	span	NOUN
ejpam-1950	12	22	of	of	ADP
ejpam-1950	12	23	φ	φ	PROPN
ejpam-1950	12	24	is	be	AUX
ejpam-1950	12	25	dense	dense	ADJ
ejpam-1950	12	26	in	in	ADP
ejpam-1950	12	27	x	x	X
ejpam-1950	12	28	.	.	PUNCT
ejpam-1950	13	1	by	by	ADP
ejpam-1950	13	2	b(x	b(x	PROPN
ejpam-1950	13	3	,	,	PUNCT
ejpam-1950	13	4	y	y	PROPN
ejpam-1950	13	5	)	)	PUNCT
ejpam-1950	13	6	we	we	PRON
ejpam-1950	13	7	denote	denote	VERB
ejpam-1950	13	8	the	the	DET
ejpam-1950	13	9	space	space	NOUN
ejpam-1950	13	10	of	of	ADP
ejpam-1950	13	11	all	all	DET
ejpam-1950	13	12	bounded	bound	VERB
ejpam-1950	13	13	linear	linear	PROPN
ejpam-1950	13	14	operators	operator	NOUN
ejpam-1950	13	15	from	from	ADP
ejpam-1950	13	16	x	x	PUNCT
ejpam-1950	13	17	into	into	ADP
ejpam-1950	13	18	y	y	PROPN
ejpam-1950	13	19	.	.	PUNCT
ejpam-1950	14	1	as	as	ADP
ejpam-1950	14	2	usual	usual	ADJ
ejpam-1950	14	3	,	,	PUNCT
ejpam-1950	14	4	the	the	DET
ejpam-1950	14	5	dual	dual	ADJ
ejpam-1950	14	6	of	of	ADP
ejpam-1950	14	7	x	x	NOUN
ejpam-1950	14	8	is	be	AUX
ejpam-1950	14	9	defined	define	VERB
ejpam-1950	14	10	by	by	ADP
ejpam-1950	14	11	x	x	X
ejpam-1950	14	12	′	′	NOUN
ejpam-1950	14	13	=	=	PUNCT
ejpam-1950	14	14	b(x	b(x	NOUN
ejpam-1950	14	15	,	,	PUNCT
ejpam-1950	14	16	k	k	NOUN
ejpam-1950	14	17	)	)	PUNCT
ejpam-1950	14	18	.	.	PUNCT
ejpam-1950	15	1	byω(x	byω(x	PROPN
ejpam-1950	15	2	)	)	PUNCT
ejpam-1950	15	3	we	we	PRON
ejpam-1950	15	4	denote	denote	VERB
ejpam-1950	15	5	the	the	DET
ejpam-1950	15	6	set	set	NOUN
ejpam-1950	15	7	of	of	ADP
ejpam-1950	15	8	all	all	PRON
ejpam-1950	15	9	x	x	SYM
ejpam-1950	15	10	-valued	-valued	ADJ
ejpam-1950	15	11	sequences	sequence	NOUN
ejpam-1950	15	12	.	.	PUNCT
ejpam-1950	16	1	we	we	PRON
ejpam-1950	16	2	write	write	VERB
ejpam-1950	16	3	supn	supn	NOUN
ejpam-1950	16	4	,	,	PUNCT
ejpam-1950	16	5	limn	limn	NOUN
ejpam-1950	16	6	and	and	CCONJ
ejpam-1950	16	7	∑	∑	PROPN
ejpam-1950	16	8	n	n	PRON
ejpam-1950	16	9	instead	instead	ADV
ejpam-1950	16	10	of	of	ADP
ejpam-1950	16	11	supn∈n	supn∈n	PROPN
ejpam-1950	16	12	,	,	PUNCT
ejpam-1950	16	13	limn→∞	limn→∞	PROPN
ejpam-1950	16	14	and	and	CCONJ
ejpam-1950	16	15	∑∞	∑∞	PROPN
ejpam-1950	16	16	n=1	n=1	PROPN
ejpam-1950	16	17	,	,	PUNCT
ejpam-1950	16	18	respectively	respectively	ADV
ejpam-1950	16	19	.	.	PUNCT
ejpam-1950	17	1	by	by	ADP
ejpam-1950	17	2	an	an	DET
ejpam-1950	17	3	index	index	NOUN
ejpam-1950	17	4	set	set	NOUN
ejpam-1950	17	5	we	we	PRON
ejpam-1950	17	6	mean	mean	VERB
ejpam-1950	17	7	any	any	DET
ejpam-1950	17	8	infinite	infinite	ADJ
ejpam-1950	17	9	set	set	NOUN
ejpam-1950	17	10	{	{	PUNCT
ejpam-1950	17	11	ki	ki	PROPN
ejpam-1950	17	12	}	}	PUNCT
ejpam-1950	17	13	⊂	⊂	PROPN
ejpam-1950	17	14	n	n	CCONJ
ejpam-1950	17	15	with	with	ADP
ejpam-1950	17	16	ki	ki	PROPN
ejpam-1950	17	17	<	<	X
ejpam-1950	17	18	ki+1	ki+1	PROPN
ejpam-1950	17	19	for	for	ADP
ejpam-1950	17	20	each	each	DET
ejpam-1950	17	21	i	i	PRON
ejpam-1950	17	22	∈	∈	PROPN
ejpam-1950	17	23	n.	n.	NOUN
ejpam-1950	17	24	let	let	VERB
ejpam-1950	17	25	an	an	DET
ejpam-1950	17	26	∈	∈	NOUN
ejpam-1950	17	27	b(x	b(x	NOUN
ejpam-1950	17	28	,	,	PUNCT
ejpam-1950	17	29	y	y	PROPN
ejpam-1950	17	30	)	)	PUNCT
ejpam-1950	17	31	(	(	PUNCT
ejpam-1950	17	32	n	n	CCONJ
ejpam-1950	17	33	∈	∈	PROPN
ejpam-1950	17	34	n	n	CCONJ
ejpam-1950	17	35	)	)	PUNCT
ejpam-1950	17	36	.	.	PUNCT
ejpam-1950	18	1	the	the	DET
ejpam-1950	18	2	following	follow	VERB
ejpam-1950	18	3	theorems	theorem	NOUN
ejpam-1950	18	4	of	of	ADP
ejpam-1950	18	5	functional	functional	ADJ
ejpam-1950	18	6	analysis	analysis	NOUN
ejpam-1950	18	7	are	be	AUX
ejpam-1950	18	8	well	well	ADV
ejpam-1950	18	9	known	know	VERB
ejpam-1950	18	10	(	(	PUNCT
ejpam-1950	18	11	see	see	VERB
ejpam-1950	18	12	,	,	PUNCT
ejpam-1950	18	13	for	for	ADP
ejpam-1950	18	14	example	example	NOUN
ejpam-1950	18	15	,	,	PUNCT
ejpam-1950	18	16	[	[	X
ejpam-1950	18	17	11	11	NUM
ejpam-1950	18	18	]	]	PUNCT
ejpam-1950	18	19	or	or	CCONJ
ejpam-1950	18	20	[	[	X
ejpam-1950	18	21	17	17	NUM
ejpam-1950	18	22	]	]	NUM
ejpam-1950	18	23	)	)	PUNCT
ejpam-1950	18	24	.	.	PUNCT
ejpam-1950	19	1	theorem	theorem	ADJ
ejpam-1950	19	2	1	1	NUM
ejpam-1950	19	3	(	(	PUNCT
ejpam-1950	19	4	principle	principle	NOUN
ejpam-1950	19	5	of	of	ADP
ejpam-1950	19	6	uniform	uniform	ADJ
ejpam-1950	19	7	boundedness	boundedness	PROPN
ejpam-1950	19	8	)	)	PUNCT
ejpam-1950	19	9	.	.	PUNCT
ejpam-1950	20	1	let	let	VERB
ejpam-1950	20	2	x	x	PRON
ejpam-1950	20	3	be	be	AUX
ejpam-1950	20	4	a	a	DET
ejpam-1950	20	5	banach	banach	NOUN
ejpam-1950	20	6	space	space	NOUN
ejpam-1950	20	7	.	.	PUNCT
ejpam-1950	21	1	if	if	SCONJ
ejpam-1950	21	2	supn	supn	PROPN
ejpam-1950	21	3	‖an	‖an	PROPN
ejpam-1950	21	4	x‖<∞	x‖<∞	PROPN
ejpam-1950	21	5	for	for	ADP
ejpam-1950	21	6	every	every	DET
ejpam-1950	21	7	x	x	SYM
ejpam-1950	21	8	∈	∈	PROPN
ejpam-1950	21	9	x	x	X
ejpam-1950	21	10	,	,	PUNCT
ejpam-1950	21	11	then	then	ADV
ejpam-1950	21	12	sup	sup	NOUN
ejpam-1950	21	13	n	n	CCONJ
ejpam-1950	21	14	‖an‖<∞.	‖an‖<∞.	NUM
ejpam-1950	21	15	(	(	PUNCT
ejpam-1950	21	16	1	1	X
ejpam-1950	21	17	)	)	PUNCT
ejpam-1950	21	18	email	email	NOUN
ejpam-1950	21	19	address	address	NOUN
ejpam-1950	21	20	:	:	PUNCT
ejpam-1950	21	21	enno.kolk@ut.ee	enno.kolk@ut.ee	NOUN
ejpam-1950	21	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1950	22	1	357	357	NUM
ejpam-1950	22	2	c	c	NOUN
ejpam-1950	22	3	©	©	PROPN
ejpam-1950	22	4	2015	2015	NUM
ejpam-1950	22	5	ejpam	ejpam	NOUN
ejpam-1950	22	6	all	all	DET
ejpam-1950	22	7	rights	right	NOUN
ejpam-1950	22	8	reserved	reserve	VERB
ejpam-1950	22	9	.	.	PUNCT
ejpam-1950	23	1	e.	e.	PROPN
ejpam-1950	23	2	kolk	kolk	PROPN
ejpam-1950	23	3	/	/	SYM
ejpam-1950	23	4	eur	eur	PROPN
ejpam-1950	23	5	.	.	PUNCT
ejpam-1950	24	1	j.	j.	PROPN
ejpam-1950	24	2	pure	pure	PROPN
ejpam-1950	24	3	appl	appl	PROPN
ejpam-1950	24	4	.	.	PROPN
ejpam-1950	24	5	math	math	PROPN
ejpam-1950	24	6	,	,	PUNCT
ejpam-1950	24	7	8	8	NUM
ejpam-1950	24	8	(	(	PUNCT
ejpam-1950	24	9	2015	2015	NUM
ejpam-1950	24	10	)	)	PUNCT
ejpam-1950	24	11	,	,	PUNCT
ejpam-1950	24	12	357	357	NUM
ejpam-1950	24	13	-	-	SYM
ejpam-1950	24	14	367	367	NUM
ejpam-1950	24	15	358	358	NUM
ejpam-1950	24	16	theorem	theorem	VERB
ejpam-1950	24	17	2	2	NUM
ejpam-1950	24	18	(	(	PUNCT
ejpam-1950	24	19	banach	banach	NOUN
ejpam-1950	24	20	–	–	PUNCT
ejpam-1950	24	21	steinhaus	steinhaus	NOUN
ejpam-1950	24	22	)	)	PUNCT
ejpam-1950	24	23	.	.	PUNCT
ejpam-1950	25	1	let	let	VERB
ejpam-1950	25	2	x	x	PRON
ejpam-1950	25	3	,	,	PUNCT
ejpam-1950	25	4	y	y	PROPN
ejpam-1950	25	5	be	be	AUX
ejpam-1950	25	6	two	two	NUM
ejpam-1950	25	7	banach	banach	NOUN
ejpam-1950	25	8	spaces	space	NOUN
ejpam-1950	25	9	and	and	CCONJ
ejpam-1950	25	10	let	let	VERB
ejpam-1950	25	11	φ	φ	PROPN
ejpam-1950	25	12	be	be	AUX
ejpam-1950	25	13	a	a	DET
ejpam-1950	25	14	fundamental	fundamental	ADJ
ejpam-1950	25	15	set	set	NOUN
ejpam-1950	25	16	of	of	ADP
ejpam-1950	25	17	x	x	X
ejpam-1950	25	18	.	.	PUNCT
ejpam-1950	26	1	the	the	DET
ejpam-1950	26	2	limit	limit	NOUN
ejpam-1950	26	3	limn	limn	NOUN
ejpam-1950	26	4	an	an	DET
ejpam-1950	26	5	x	x	PRON
ejpam-1950	26	6	exists	exist	VERB
ejpam-1950	26	7	for	for	ADP
ejpam-1950	26	8	any	any	DET
ejpam-1950	26	9	x	x	SYM
ejpam-1950	26	10	∈	∈	PROPN
ejpam-1950	26	11	x	x	SYM
ejpam-1950	26	12	if	if	SCONJ
ejpam-1950	26	13	and	and	CCONJ
ejpam-1950	26	14	only	only	ADV
ejpam-1950	26	15	if	if	SCONJ
ejpam-1950	26	16	(	(	PUNCT
ejpam-1950	26	17	1	1	X
ejpam-1950	26	18	)	)	PUNCT
ejpam-1950	26	19	holds	hold	NOUN
ejpam-1950	26	20	and	and	CCONJ
ejpam-1950	26	21	limn	limn	ADJ
ejpam-1950	26	22	anφ	anφ	NOUN
ejpam-1950	26	23	exists	exist	VERB
ejpam-1950	26	24	for	for	ADP
ejpam-1950	26	25	every	every	DET
ejpam-1950	26	26	φ	φ	PROPN
ejpam-1950	26	27	∈	∈	PROPN
ejpam-1950	26	28	φ	φ	PROPN
ejpam-1950	26	29	.	.	PUNCT
ejpam-1950	27	1	moreover	moreover	ADV
ejpam-1950	27	2	,	,	PUNCT
ejpam-1950	27	3	the	the	DET
ejpam-1950	27	4	limit	limit	NOUN
ejpam-1950	27	5	operator	operator	NOUN
ejpam-1950	27	6	a0	a0	NOUN
ejpam-1950	27	7	,	,	PUNCT
ejpam-1950	27	8	a0	a0	NOUN
ejpam-1950	27	9	x	x	PUNCT
ejpam-1950	28	1	=	=	SYM
ejpam-1950	28	2	limn	limn	NOUN
ejpam-1950	28	3	an	an	PRON
ejpam-1950	28	4	x	x	PUNCT
ejpam-1950	28	5	is	be	AUX
ejpam-1950	28	6	bounded	bound	VERB
ejpam-1950	28	7	and	and	CCONJ
ejpam-1950	28	8	linear	linear	ADJ
ejpam-1950	28	9	,	,	PUNCT
ejpam-1950	28	10	i.e.	i.e.	X
ejpam-1950	28	11	,	,	PUNCT
ejpam-1950	28	12	a0	a0	PROPN
ejpam-1950	28	13	∈	∈	PROPN
ejpam-1950	28	14	b(x	b(x	PROPN
ejpam-1950	28	15	,	,	PUNCT
ejpam-1950	28	16	y	y	PROPN
ejpam-1950	28	17	)	)	PUNCT
ejpam-1950	28	18	,	,	PUNCT
ejpam-1950	28	19	and	and	CCONJ
ejpam-1950	29	1	‖a0‖	‖a0‖	ADP
ejpam-1950	29	2	≤	≤	NUM
ejpam-1950	29	3	supn	supn	NOUN
ejpam-1950	29	4	‖an‖.	‖an‖.	PROPN
ejpam-1950	29	5	if	if	SCONJ
ejpam-1950	29	6	a	a	DET
ejpam-1950	29	7	∈	∈	PROPN
ejpam-1950	29	8	b(x	b(x	NOUN
ejpam-1950	29	9	,	,	PUNCT
ejpam-1950	29	10	y	y	PROPN
ejpam-1950	29	11	)	)	PUNCT
ejpam-1950	29	12	,	,	PUNCT
ejpam-1950	29	13	then	then	ADV
ejpam-1950	29	14	limn	limn	VERB
ejpam-1950	29	15	an	an	DET
ejpam-1950	29	16	x	x	X
ejpam-1950	29	17	=	=	PRON
ejpam-1950	29	18	ax	ax	NOUN
ejpam-1950	29	19	for	for	ADP
ejpam-1950	29	20	any	any	DET
ejpam-1950	29	21	x	x	SYM
ejpam-1950	29	22	∈	∈	PROPN
ejpam-1950	29	23	x	x	SYM
ejpam-1950	29	24	if	if	SCONJ
ejpam-1950	29	25	and	and	CCONJ
ejpam-1950	29	26	only	only	ADV
ejpam-1950	29	27	if	if	SCONJ
ejpam-1950	29	28	(	(	PUNCT
ejpam-1950	29	29	1	1	X
ejpam-1950	29	30	)	)	PUNCT
ejpam-1950	29	31	holds	hold	NOUN
ejpam-1950	29	32	and	and	CCONJ
ejpam-1950	29	33	limn	limn	ADJ
ejpam-1950	29	34	anφ	anφ	NOUN
ejpam-1950	29	35	=	=	SYM
ejpam-1950	29	36	aφ	aφ	X
ejpam-1950	29	37	(	(	PUNCT
ejpam-1950	29	38	φ	φ	PROPN
ejpam-1950	29	39	∈	∈	PROPN
ejpam-1950	29	40	φ	φ	PROPN
ejpam-1950	29	41	)	)	PUNCT
ejpam-1950	29	42	.	.	PUNCT
ejpam-1950	30	1	the	the	DET
ejpam-1950	30	2	first	first	ADJ
ejpam-1950	30	3	idea	idea	NOUN
ejpam-1950	30	4	of	of	ADP
ejpam-1950	30	5	statistical	statistical	ADJ
ejpam-1950	30	6	convergence	convergence	NOUN
ejpam-1950	30	7	appeared	appear	VERB
ejpam-1950	30	8	,	,	PUNCT
ejpam-1950	30	9	under	under	ADP
ejpam-1950	30	10	the	the	DET
ejpam-1950	30	11	name	name	NOUN
ejpam-1950	30	12	of	of	ADP
ejpam-1950	30	13	almost	almost	ADV
ejpam-1950	30	14	convergence	convergence	NOUN
ejpam-1950	30	15	,	,	PUNCT
ejpam-1950	30	16	in	in	ADP
ejpam-1950	30	17	the	the	DET
ejpam-1950	30	18	first	first	ADJ
ejpam-1950	30	19	edition	edition	NOUN
ejpam-1950	30	20	(	(	PUNCT
ejpam-1950	30	21	warsaw	warsaw	PROPN
ejpam-1950	30	22	,	,	PUNCT
ejpam-1950	30	23	1935	1935	NUM
ejpam-1950	30	24	)	)	PUNCT
ejpam-1950	30	25	of	of	ADP
ejpam-1950	30	26	the	the	DET
ejpam-1950	30	27	monograph	monograph	NOUN
ejpam-1950	31	1	[	[	X
ejpam-1950	31	2	25	25	NUM
ejpam-1950	31	3	]	]	PUNCT
ejpam-1950	31	4	of	of	ADP
ejpam-1950	31	5	zygmund	zygmund	PROPN
ejpam-1950	31	6	.	.	PUNCT
ejpam-1950	32	1	since	since	SCONJ
ejpam-1950	32	2	1951	1951	NUM
ejpam-1950	32	3	when	when	SCONJ
ejpam-1950	32	4	fast	fast	ADJ
ejpam-1950	32	5	[	[	X
ejpam-1950	32	6	7	7	NUM
ejpam-1950	32	7	]	]	PUNCT
ejpam-1950	32	8	(	(	PUNCT
ejpam-1950	32	9	see	see	VERB
ejpam-1950	32	10	also	also	ADV
ejpam-1950	32	11	[	[	X
ejpam-1950	32	12	23	23	NUM
ejpam-1950	32	13	]	]	PUNCT
ejpam-1950	32	14	and	and	CCONJ
ejpam-1950	32	15	[	[	X
ejpam-1950	32	16	22	22	NUM
ejpam-1950	32	17	]	]	PUNCT
ejpam-1950	32	18	)	)	PUNCT
ejpam-1950	32	19	introduced	introduce	VERB
ejpam-1950	32	20	statistical	statistical	ADJ
ejpam-1950	32	21	convergence	convergence	NOUN
ejpam-1950	32	22	of	of	ADP
ejpam-1950	32	23	number	number	NOUN
ejpam-1950	32	24	sequences	sequence	NOUN
ejpam-1950	32	25	in	in	ADP
ejpam-1950	32	26	terms	term	NOUN
ejpam-1950	32	27	of	of	ADP
ejpam-1950	32	28	asymptotic	asymptotic	ADJ
ejpam-1950	32	29	density	density	NOUN
ejpam-1950	32	30	of	of	ADP
ejpam-1950	32	31	subsets	subset	NOUN
ejpam-1950	32	32	of	of	ADP
ejpam-1950	32	33	n	n	CCONJ
ejpam-1950	32	34	,	,	PUNCT
ejpam-1950	32	35	several	several	ADJ
ejpam-1950	32	36	applications	application	NOUN
ejpam-1950	32	37	and	and	CCONJ
ejpam-1950	32	38	generalizations	generalization	NOUN
ejpam-1950	32	39	of	of	ADP
ejpam-1950	32	40	this	this	DET
ejpam-1950	32	41	notion	notion	NOUN
ejpam-1950	32	42	have	have	AUX
ejpam-1950	32	43	been	be	AUX
ejpam-1950	32	44	investigated	investigate	VERB
ejpam-1950	32	45	(	(	PUNCT
ejpam-1950	32	46	for	for	SCONJ
ejpam-1950	32	47	references	reference	NOUN
ejpam-1950	32	48	see	see	VERB
ejpam-1950	32	49	[	[	X
ejpam-1950	32	50	4	4	X
ejpam-1950	32	51	]	]	PUNCT
ejpam-1950	32	52	and	and	CCONJ
ejpam-1950	32	53	[	[	X
ejpam-1950	32	54	6	6	NUM
ejpam-1950	32	55	]	]	PUNCT
ejpam-1950	32	56	)	)	PUNCT
ejpam-1950	32	57	.	.	PUNCT
ejpam-1950	33	1	for	for	ADP
ejpam-1950	33	2	instance	instance	NOUN
ejpam-1950	33	3	,	,	PUNCT
ejpam-1950	33	4	maddox	maddox	PROPN
ejpam-1950	33	5	[	[	X
ejpam-1950	33	6	20	20	NUM
ejpam-1950	33	7	]	]	PUNCT
ejpam-1950	33	8	and	and	CCONJ
ejpam-1950	33	9	kolk	kolk	NOUN
ejpam-1950	34	1	[	[	X
ejpam-1950	34	2	13	13	NUM
ejpam-1950	34	3	]	]	PUNCT
ejpam-1950	34	4	considered	consider	VERB
ejpam-1950	34	5	the	the	DET
ejpam-1950	34	6	statistical	statistical	ADJ
ejpam-1950	34	7	convergence	convergence	NOUN
ejpam-1950	34	8	of	of	ADP
ejpam-1950	34	9	sequences	sequence	NOUN
ejpam-1950	34	10	taking	take	VERB
ejpam-1950	34	11	values	value	NOUN
ejpam-1950	34	12	in	in	ADP
ejpam-1950	34	13	a	a	DET
ejpam-1950	34	14	locally	locally	ADV
ejpam-1950	34	15	convex	convex	ADJ
ejpam-1950	34	16	space	space	NOUN
ejpam-1950	34	17	or	or	CCONJ
ejpam-1950	34	18	a	a	DET
ejpam-1950	34	19	normed	normed	ADJ
ejpam-1950	34	20	space	space	NOUN
ejpam-1950	34	21	,	,	PUNCT
ejpam-1950	34	22	respectively	respectively	ADV
ejpam-1950	34	23	.	.	PUNCT
ejpam-1950	35	1	an	an	DET
ejpam-1950	35	2	another	another	DET
ejpam-1950	35	3	extension	extension	NOUN
ejpam-1950	35	4	of	of	ADP
ejpam-1950	35	5	statistical	statistical	ADJ
ejpam-1950	35	6	convergence	convergence	NOUN
ejpam-1950	35	7	is	be	AUX
ejpam-1950	35	8	related	relate	VERB
ejpam-1950	35	9	to	to	ADP
ejpam-1950	35	10	generalized	generalized	ADJ
ejpam-1950	35	11	densities	density	NOUN
ejpam-1950	35	12	.	.	PUNCT
ejpam-1950	36	1	let	let	AUX
ejpam-1950	36	2	t	t	NOUN
ejpam-1950	36	3	=	=	SYM
ejpam-1950	36	4	(	(	PUNCT
ejpam-1950	36	5	tnk	tnk	PROPN
ejpam-1950	36	6	)	)	PUNCT
ejpam-1950	36	7	be	be	AUX
ejpam-1950	36	8	a	a	DET
ejpam-1950	36	9	non	non	ADJ
ejpam-1950	36	10	-	-	ADJ
ejpam-1950	36	11	negative	negative	ADJ
ejpam-1950	36	12	regular	regular	ADJ
ejpam-1950	36	13	matrix	matrix	NOUN
ejpam-1950	36	14	of	of	ADP
ejpam-1950	36	15	scalars	scalar	NOUN
ejpam-1950	36	16	(	(	PUNCT
ejpam-1950	36	17	i.e.	i.e.	X
ejpam-1950	36	18	,	,	PUNCT
ejpam-1950	36	19	tnk	tnk	PROPN
ejpam-1950	36	20	≥	≥	PROPN
ejpam-1950	36	21	0	0	NUM
ejpam-1950	36	22	(	(	PUNCT
ejpam-1950	36	23	n	n	CCONJ
ejpam-1950	36	24	,	,	PUNCT
ejpam-1950	36	25	k	k	PROPN
ejpam-1950	36	26	∈	∈	PROPN
ejpam-1950	36	27	n	n	CCONJ
ejpam-1950	36	28	)	)	PUNCT
ejpam-1950	36	29	and	and	CCONJ
ejpam-1950	36	30	limn	limn	PROPN
ejpam-1950	36	31	∑	∑	PROPN
ejpam-1950	36	32	k	k	PROPN
ejpam-1950	36	33	tnkuk	tnkuk	NOUN
ejpam-1950	36	34	=	=	PUNCT
ejpam-1950	36	35	limk	limk	PROPN
ejpam-1950	36	36	uk	uk	PROPN
ejpam-1950	36	37	for	for	ADP
ejpam-1950	36	38	any	any	DET
ejpam-1950	36	39	convergent	convergent	NOUN
ejpam-1950	36	40	scalar	scalar	ADJ
ejpam-1950	36	41	sequence	sequence	NOUN
ejpam-1950	36	42	(	(	PUNCT
ejpam-1950	36	43	uk	uk	PROPN
ejpam-1950	36	44	)	)	PUNCT
ejpam-1950	36	45	)	)	PUNCT
ejpam-1950	36	46	.	.	PUNCT
ejpam-1950	37	1	a	a	DET
ejpam-1950	37	2	set	set	NOUN
ejpam-1950	37	3	k	k	PROPN
ejpam-1950	37	4	⊂	⊂	PROPN
ejpam-1950	37	5	n	n	AUX
ejpam-1950	37	6	is	be	AUX
ejpam-1950	37	7	said	say	VERB
ejpam-1950	37	8	to	to	PART
ejpam-1950	37	9	have	have	VERB
ejpam-1950	37	10	t	t	PROPN
ejpam-1950	37	11	-	-	PUNCT
ejpam-1950	37	12	density	density	NOUN
ejpam-1950	37	13	δt	δt	X
ejpam-1950	37	14	(	(	PUNCT
ejpam-1950	37	15	k	k	X
ejpam-1950	37	16	)	)	PUNCT
ejpam-1950	37	17	if	if	SCONJ
ejpam-1950	37	18	the	the	DET
ejpam-1950	37	19	limit	limit	NOUN
ejpam-1950	37	20	δt	δt	X
ejpam-1950	37	21	(	(	PUNCT
ejpam-1950	37	22	k	k	NOUN
ejpam-1950	37	23	)	)	PUNCT
ejpam-1950	38	1	=	=	SYM
ejpam-1950	38	2	lim	lim	PROPN
ejpam-1950	38	3	n	n	CCONJ
ejpam-1950	38	4	∑	∑	PROPN
ejpam-1950	38	5	k∈k	k∈k	PROPN
ejpam-1950	38	6	tnk	tnk	PROPN
ejpam-1950	38	7	exists	exist	VERB
ejpam-1950	38	8	(	(	PUNCT
ejpam-1950	38	9	cf	cf	NOUN
ejpam-1950	38	10	.	.	PUNCT
ejpam-1950	39	1	[	[	X
ejpam-1950	39	2	9	9	NUM
ejpam-1950	39	3	]	]	SYM
ejpam-1950	39	4	)	)	PUNCT
ejpam-1950	39	5	.	.	PUNCT
ejpam-1950	40	1	a	a	DET
ejpam-1950	40	2	sequence	sequence	NOUN
ejpam-1950	40	3	x	x	PUNCT
ejpam-1950	40	4	=	=	SYM
ejpam-1950	40	5	(	(	PUNCT
ejpam-1950	40	6	xk	xk	ADJ
ejpam-1950	40	7	)	)	PUNCT
ejpam-1950	40	8	∈	∈	PROPN
ejpam-1950	40	9	ω(x	ω(x	PROPN
ejpam-1950	40	10	)	)	PUNCT
ejpam-1950	40	11	is	be	AUX
ejpam-1950	40	12	called	call	VERB
ejpam-1950	40	13	t	t	PROPN
ejpam-1950	40	14	-	-	PUNCT
ejpam-1950	40	15	statistically	statistically	ADV
ejpam-1950	40	16	convergent	convergent	NOUN
ejpam-1950	40	17	to	to	ADP
ejpam-1950	40	18	a	a	DET
ejpam-1950	40	19	point	point	NOUN
ejpam-1950	40	20	l	l	NOUN
ejpam-1950	40	21	∈	∈	PROPN
ejpam-1950	40	22	x	x	X
ejpam-1950	40	23	,	,	PUNCT
ejpam-1950	40	24	briefly	briefly	ADV
ejpam-1950	40	25	stt	stt	PROPN
ejpam-1950	40	26	-lim	-lim	PUNCT
ejpam-1950	40	27	xk	xk	PROPN
ejpam-1950	41	1	=	=	PUNCT
ejpam-1950	41	2	l	l	PROPN
ejpam-1950	41	3	,	,	PUNCT
ejpam-1950	41	4	if	if	SCONJ
ejpam-1950	41	5	δt	δt	X
ejpam-1950	41	6	(	(	PUNCT
ejpam-1950	41	7	{	{	PUNCT
ejpam-1950	41	8	k	k	X
ejpam-1950	41	9	:	:	PUNCT
ejpam-1950	41	10	‖xk	‖xk	NUM
ejpam-1950	41	11	−	−	PROPN
ejpam-1950	41	12	l‖	l‖	PROPN
ejpam-1950	41	13	≥	≥	NOUN
ejpam-1950	41	14	ǫ	ǫ	NOUN
ejpam-1950	41	15	}	}	PUNCT
ejpam-1950	41	16	)	)	PUNCT
ejpam-1950	42	1	=	=	SYM
ejpam-1950	42	2	0	0	NUM
ejpam-1950	43	1	for	for	ADP
ejpam-1950	43	2	every	every	DET
ejpam-1950	43	3	ǫ	ǫ	NOUN
ejpam-1950	43	4	>	>	X
ejpam-1950	43	5	0	0	PUNCT
ejpam-1950	44	1	(	(	PUNCT
ejpam-1950	44	2	see	see	VERB
ejpam-1950	44	3	[	[	X
ejpam-1950	44	4	3	3	NUM
ejpam-1950	44	5	,	,	PUNCT
ejpam-1950	44	6	definition	definition	NOUN
ejpam-1950	44	7	7	7	NUM
ejpam-1950	44	8	]	]	PUNCT
ejpam-1950	44	9	and	and	CCONJ
ejpam-1950	44	10	[	[	X
ejpam-1950	44	11	14	14	NUM
ejpam-1950	44	12	,	,	PUNCT
ejpam-1950	44	13	p.	p.	NOUN
ejpam-1950	44	14	44	44	NUM
ejpam-1950	44	15	]	]	PUNCT
ejpam-1950	44	16	)	)	PUNCT
ejpam-1950	44	17	.	.	PUNCT
ejpam-1950	45	1	if	if	SCONJ
ejpam-1950	45	2	t	t	PROPN
ejpam-1950	45	3	is	be	AUX
ejpam-1950	45	4	the	the	DET
ejpam-1950	45	5	identity	identity	NOUN
ejpam-1950	45	6	matrix	matrix	NOUN
ejpam-1950	45	7	i	i	PRON
ejpam-1950	45	8	,	,	PUNCT
ejpam-1950	45	9	then	then	ADV
ejpam-1950	45	10	t	t	PROPN
ejpam-1950	45	11	-statistical	-statistical	ADJ
ejpam-1950	45	12	convergence	convergence	NOUN
ejpam-1950	45	13	is	be	AUX
ejpam-1950	45	14	just	just	ADV
ejpam-1950	45	15	the	the	DET
ejpam-1950	45	16	ordinary	ordinary	ADJ
ejpam-1950	45	17	convergence	convergence	NOUN
ejpam-1950	45	18	in	in	ADP
ejpam-1950	45	19	x	x	PUNCT
ejpam-1950	46	1	and	and	CCONJ
ejpam-1950	46	2	if	if	SCONJ
ejpam-1950	46	3	t	t	PROPN
ejpam-1950	46	4	is	be	AUX
ejpam-1950	46	5	the	the	DET
ejpam-1950	46	6	cesàro	cesàro	PROPN
ejpam-1950	46	7	matrix	matrix	NOUN
ejpam-1950	46	8	c1	c1	PROPN
ejpam-1950	46	9	,	,	PUNCT
ejpam-1950	46	10	then	then	ADV
ejpam-1950	46	11	t	t	PROPN
ejpam-1950	46	12	-statistical	-statistical	ADJ
ejpam-1950	46	13	convergence	convergence	NOUN
ejpam-1950	46	14	is	be	AUX
ejpam-1950	46	15	statistical	statistical	ADJ
ejpam-1950	46	16	convergence	convergence	NOUN
ejpam-1950	46	17	as	as	SCONJ
ejpam-1950	46	18	defined	define	VERB
ejpam-1950	46	19	by	by	ADP
ejpam-1950	46	20	fast	fast	ADJ
ejpam-1950	46	21	[	[	X
ejpam-1950	46	22	7	7	NUM
ejpam-1950	46	23	]	]	PUNCT
ejpam-1950	46	24	.	.	PUNCT
ejpam-1950	47	1	a	a	DET
ejpam-1950	47	2	further	further	ADJ
ejpam-1950	47	3	extension	extension	NOUN
ejpam-1950	47	4	of	of	ADP
ejpam-1950	47	5	statistical	statistical	ADJ
ejpam-1950	47	6	convergence	convergence	NOUN
ejpam-1950	47	7	was	be	AUX
ejpam-1950	47	8	given	give	VERB
ejpam-1950	47	9	in	in	ADP
ejpam-1950	47	10	[	[	X
ejpam-1950	47	11	16	16	NUM
ejpam-1950	47	12	]	]	PUNCT
ejpam-1950	47	13	by	by	ADP
ejpam-1950	47	14	means	mean	NOUN
ejpam-1950	47	15	of	of	ADP
ejpam-1950	47	16	ideals	ideal	NOUN
ejpam-1950	47	17	.	.	PUNCT
ejpam-1950	48	1	recall	recall	VERB
ejpam-1950	48	2	that	that	SCONJ
ejpam-1950	48	3	a	a	DET
ejpam-1950	48	4	subfamily	subfamily	ADV
ejpam-1950	48	5	i	i	PRON
ejpam-1950	48	6	of	of	ADP
ejpam-1950	48	7	the	the	DET
ejpam-1950	48	8	family	family	NOUN
ejpam-1950	48	9	2n	2n	NUM
ejpam-1950	48	10	of	of	ADP
ejpam-1950	48	11	all	all	DET
ejpam-1950	48	12	subsets	subset	NOUN
ejpam-1950	48	13	of	of	ADP
ejpam-1950	48	14	n	n	PROPN
ejpam-1950	48	15	is	be	AUX
ejpam-1950	48	16	called	call	VERB
ejpam-1950	48	17	an	an	DET
ejpam-1950	48	18	ideal	ideal	NOUN
ejpam-1950	48	19	if	if	SCONJ
ejpam-1950	48	20	for	for	ADP
ejpam-1950	48	21	each	each	DET
ejpam-1950	48	22	k	k	PROPN
ejpam-1950	48	23	,	,	PUNCT
ejpam-1950	49	1	l	l	PROPN
ejpam-1950	49	2	∈	∈	PROPN
ejpam-1950	50	1	i	i	PRON
ejpam-1950	50	2	we	we	PRON
ejpam-1950	50	3	have	have	VERB
ejpam-1950	50	4	k	k	PRON
ejpam-1950	50	5	⋃	⋃	NOUN
ejpam-1950	50	6	l	l	NOUN
ejpam-1950	50	7	∈	∈	NOUN
ejpam-1950	51	1	i	i	PRON
ejpam-1950	51	2	and	and	CCONJ
ejpam-1950	51	3	for	for	ADP
ejpam-1950	51	4	each	each	DET
ejpam-1950	51	5	k	k	PROPN
ejpam-1950	51	6	∈	∈	PROPN
ejpam-1950	52	1	i	i	PRON
ejpam-1950	52	2	and	and	CCONJ
ejpam-1950	52	3	each	each	DET
ejpam-1950	52	4	l	l	NOUN
ejpam-1950	53	1	⊂	⊂	PROPN
ejpam-1950	54	1	k	k	X
ejpam-1950	54	2	we	we	PRON
ejpam-1950	54	3	have	have	VERB
ejpam-1950	54	4	l	l	NOUN
ejpam-1950	54	5	∈	∈	PROPN
ejpam-1950	55	1	i	i	PRON
ejpam-1950	55	2	.	.	PUNCT
ejpam-1950	56	1	an	an	DET
ejpam-1950	56	2	ideal	ideal	NOUN
ejpam-1950	56	3	i	i	PRON
ejpam-1950	56	4	is	be	AUX
ejpam-1950	56	5	called	call	VERB
ejpam-1950	56	6	non	non	ADJ
ejpam-1950	56	7	-	-	ADJ
ejpam-1950	56	8	trivial	trivial	ADJ
ejpam-1950	56	9	if	if	SCONJ
ejpam-1950	56	10	i	i	PRON
ejpam-1950	56	11	6=	6=	NUM
ejpam-1950	56	12	;	;	PUNCT
ejpam-1950	56	13	and	and	CCONJ
ejpam-1950	56	14	n	n	CCONJ
ejpam-1950	56	15	/∈	/∈	PUNCT
ejpam-1950	57	1	i	i	INTJ
ejpam-1950	57	2	.	.	PUNCT
ejpam-1950	58	1	a	a	DET
ejpam-1950	58	2	non	non	ADJ
ejpam-1950	58	3	-	-	ADJ
ejpam-1950	58	4	trivial	trivial	ADJ
ejpam-1950	58	5	ideal	ideal	NOUN
ejpam-1950	58	6	i	i	PRON
ejpam-1950	58	7	is	be	AUX
ejpam-1950	58	8	called	call	VERB
ejpam-1950	58	9	admissible	admissible	ADJ
ejpam-1950	58	10	if	if	SCONJ
ejpam-1950	58	11	i	i	PRON
ejpam-1950	58	12	contains	contain	VERB
ejpam-1950	58	13	all	all	DET
ejpam-1950	58	14	finite	finite	ADJ
ejpam-1950	58	15	subsets	subset	NOUN
ejpam-1950	58	16	of	of	ADP
ejpam-1950	58	17	n.	n.	PROPN
ejpam-1950	58	18	any	any	DET
ejpam-1950	58	19	non	non	ADJ
ejpam-1950	58	20	-	-	ADJ
ejpam-1950	58	21	trivial	trivial	ADJ
ejpam-1950	58	22	ideal	ideal	NOUN
ejpam-1950	58	23	i	i	PRON
ejpam-1950	58	24	defines	define	VERB
ejpam-1950	58	25	a	a	DET
ejpam-1950	58	26	filter	filter	NOUN
ejpam-1950	58	27	f	f	NOUN
ejpam-1950	58	28	(	(	PUNCT
ejpam-1950	58	29	i	i	NOUN
ejpam-1950	58	30	)	)	PUNCT
ejpam-1950	58	31	=	=	PRON
ejpam-1950	59	1	{	{	PUNCT
ejpam-1950	59	2	k	k	X
ejpam-1950	59	3	⊂	⊂	PROPN
ejpam-1950	59	4	n	n	X
ejpam-1950	59	5	:	:	PUNCT
ejpam-1950	59	6	n	n	CCONJ
ejpam-1950	59	7	\	\	NOUN
ejpam-1950	59	8	k	k	PROPN
ejpam-1950	59	9	∈	∈	PROPN
ejpam-1950	60	1	i	i	PRON
ejpam-1950	60	2	}	}	PUNCT
ejpam-1950	60	3	.	.	PUNCT
ejpam-1950	61	1	for	for	ADP
ejpam-1950	61	2	example	example	NOUN
ejpam-1950	61	3	,	,	PUNCT
ejpam-1950	61	4	it	it	PRON
ejpam-1950	61	5	=	=	PRON
ejpam-1950	61	6	{	{	PUNCT
ejpam-1950	61	7	k	k	X
ejpam-1950	61	8	⊂	⊂	PROPN
ejpam-1950	61	9	n	n	X
ejpam-1950	61	10	:	:	PUNCT
ejpam-1950	61	11	δt	δt	X
ejpam-1950	61	12	(	(	PUNCT
ejpam-1950	61	13	k	k	NOUN
ejpam-1950	61	14	)	)	PUNCT
ejpam-1950	61	15	=	=	SYM
ejpam-1950	61	16	0	0	X
ejpam-1950	61	17	}	}	PUNCT
ejpam-1950	61	18	is	be	AUX
ejpam-1950	61	19	an	an	DET
ejpam-1950	61	20	admissible	admissible	ADJ
ejpam-1950	61	21	ideal	ideal	NOUN
ejpam-1950	61	22	and	and	CCONJ
ejpam-1950	61	23	the	the	DET
ejpam-1950	61	24	it	it	PRON
ejpam-1950	61	25	-convergence	-convergence	PROPN
ejpam-1950	61	26	coincides	coincide	VERB
ejpam-1950	61	27	with	with	ADP
ejpam-1950	61	28	the	the	DET
ejpam-1950	61	29	t	t	PROPN
ejpam-1950	61	30	-statistical	-statistical	ADJ
ejpam-1950	61	31	convergence	convergence	NOUN
ejpam-1950	61	32	.	.	PUNCT
ejpam-1950	62	1	an	an	DET
ejpam-1950	62	2	admissible	admissible	ADJ
ejpam-1950	62	3	ideal	ideal	NOUN
ejpam-1950	62	4	i	i	PRON
ejpam-1950	62	5	⊂	⊂	PROPN
ejpam-1950	62	6	2n	2n	NUM
ejpam-1950	62	7	is	be	AUX
ejpam-1950	62	8	said	say	VERB
ejpam-1950	62	9	to	to	PART
ejpam-1950	62	10	have	have	VERB
ejpam-1950	62	11	property	property	NOUN
ejpam-1950	62	12	(	(	PUNCT
ejpam-1950	62	13	ap	ap	PROPN
ejpam-1950	62	14	)	)	PUNCT
ejpam-1950	62	15	if	if	SCONJ
ejpam-1950	62	16	for	for	ADP
ejpam-1950	62	17	every	every	DET
ejpam-1950	62	18	countable	countable	ADJ
ejpam-1950	62	19	family	family	NOUN
ejpam-1950	62	20	of	of	ADP
ejpam-1950	62	21	mutually	mutually	ADV
ejpam-1950	62	22	disjoint	disjoint	NOUN
ejpam-1950	62	23	sets	set	NOUN
ejpam-1950	62	24	k1	k1	NOUN
ejpam-1950	62	25	,	,	PUNCT
ejpam-1950	62	26	k2	k2	NOUN
ejpam-1950	62	27	,	,	PUNCT
ejpam-1950	62	28	.	.	PUNCT
ejpam-1950	62	29	.	.	PUNCT
ejpam-1950	63	1	.	.	PUNCT
ejpam-1950	64	1	from	from	ADP
ejpam-1950	64	2	i	i	PRON
ejpam-1950	64	3	there	there	PRON
ejpam-1950	64	4	exist	exist	VERB
ejpam-1950	64	5	sets	set	NOUN
ejpam-1950	64	6	l1	l1	PROPN
ejpam-1950	64	7	,	,	PUNCT
ejpam-1950	64	8	l2	l2	NOUN
ejpam-1950	64	9	,	,	PUNCT
ejpam-1950	64	10	.	.	PUNCT
ejpam-1950	64	11	.	.	PUNCT
ejpam-1950	65	1	.	.	PUNCT
ejpam-1950	66	1	from	from	ADP
ejpam-1950	66	2	2n	2n	NUM
ejpam-1950	66	3	such	such	ADJ
ejpam-1950	66	4	that	that	SCONJ
ejpam-1950	66	5	the	the	DET
ejpam-1950	66	6	symmetric	symmetric	ADJ
ejpam-1950	66	7	differences	difference	NOUN
ejpam-1950	66	8	ki∆li	ki∆li	PUNCT
ejpam-1950	66	9	(	(	PUNCT
ejpam-1950	66	10	i	i	NOUN
ejpam-1950	66	11	∈	∈	PROPN
ejpam-1950	66	12	n	n	CCONJ
ejpam-1950	66	13	)	)	PUNCT
ejpam-1950	66	14	are	be	AUX
ejpam-1950	66	15	finite	finite	ADJ
ejpam-1950	66	16	and	and	CCONJ
ejpam-1950	66	17	l	l	NOUN
ejpam-1950	66	18	=	=	PUNCT
ejpam-1950	66	19	⋃	⋃	PROPN
ejpam-1950	66	20	i	i	PRON
ejpam-1950	66	21	li	li	PROPN
ejpam-1950	66	22	∈	∈	PROPN
ejpam-1950	66	23	i	i	PRON
ejpam-1950	66	24	.	.	PUNCT
ejpam-1950	67	1	e.	e.	PROPN
ejpam-1950	67	2	kolk	kolk	PROPN
ejpam-1950	67	3	/	/	SYM
ejpam-1950	67	4	eur	eur	PROPN
ejpam-1950	67	5	.	.	PUNCT
ejpam-1950	68	1	j.	j.	PROPN
ejpam-1950	68	2	pure	pure	PROPN
ejpam-1950	68	3	appl	appl	PROPN
ejpam-1950	68	4	.	.	PROPN
ejpam-1950	68	5	math	math	PROPN
ejpam-1950	68	6	,	,	PUNCT
ejpam-1950	68	7	8	8	NUM
ejpam-1950	68	8	(	(	PUNCT
ejpam-1950	68	9	2015	2015	NUM
ejpam-1950	68	10	)	)	PUNCT
ejpam-1950	68	11	,	,	PUNCT
ejpam-1950	68	12	357	357	NUM
ejpam-1950	68	13	-	-	SYM
ejpam-1950	68	14	367	367	NUM
ejpam-1950	68	15	359	359	NUM
ejpam-1950	68	16	remark	remark	NOUN
ejpam-1950	68	17	1	1	NUM
ejpam-1950	68	18	(	(	PUNCT
ejpam-1950	68	19	[	[	X
ejpam-1950	68	20	1	1	NUM
ejpam-1950	68	21	]	]	PUNCT
ejpam-1950	68	22	,	,	PUNCT
ejpam-1950	68	23	proposition	proposition	NOUN
ejpam-1950	68	24	1	1	NUM
ejpam-1950	68	25	)	)	PUNCT
ejpam-1950	68	26	.	.	PUNCT
ejpam-1950	69	1	the	the	DET
ejpam-1950	69	2	property	property	NOUN
ejpam-1950	69	3	(	(	PUNCT
ejpam-1950	69	4	ap	ap	PROPN
ejpam-1950	69	5	)	)	PUNCT
ejpam-1950	69	6	is	be	AUX
ejpam-1950	69	7	equivalent	equivalent	ADJ
ejpam-1950	69	8	to	to	ADP
ejpam-1950	69	9	the	the	DET
ejpam-1950	69	10	property	property	NOUN
ejpam-1950	69	11	(	(	PUNCT
ejpam-1950	69	12	p	p	NOUN
ejpam-1950	69	13	):	):	PUNCT
ejpam-1950	69	14	for	for	ADP
ejpam-1950	69	15	every	every	DET
ejpam-1950	69	16	countable	countable	ADJ
ejpam-1950	69	17	family	family	NOUN
ejpam-1950	69	18	of	of	ADP
ejpam-1950	69	19	sets	set	NOUN
ejpam-1950	69	20	k1	k1	NOUN
ejpam-1950	69	21	,	,	PUNCT
ejpam-1950	69	22	k2	k2	NOUN
ejpam-1950	69	23	,	,	PUNCT
ejpam-1950	69	24	.	.	PUNCT
ejpam-1950	69	25	.	.	PUNCT
ejpam-1950	70	1	.	.	PUNCT
ejpam-1950	71	1	from	from	ADP
ejpam-1950	71	2	i	i	PRON
ejpam-1950	71	3	there	there	PRON
ejpam-1950	71	4	exist	exist	VERB
ejpam-1950	71	5	a	a	DET
ejpam-1950	71	6	set	set	NOUN
ejpam-1950	71	7	k	k	PROPN
ejpam-1950	71	8	∈	∈	PROPN
ejpam-1950	72	1	i	i	PRON
ejpam-1950	72	2	such	such	ADJ
ejpam-1950	72	3	that	that	SCONJ
ejpam-1950	72	4	the	the	DET
ejpam-1950	72	5	differences	difference	NOUN
ejpam-1950	72	6	ki	ki	PROPN
ejpam-1950	72	7	\k	\k	PROPN
ejpam-1950	72	8	(	(	PUNCT
ejpam-1950	72	9	i	i	PROPN
ejpam-1950	72	10	∈	∈	PROPN
ejpam-1950	72	11	n	n	CCONJ
ejpam-1950	72	12	)	)	PUNCT
ejpam-1950	72	13	are	be	AUX
ejpam-1950	72	14	finite	finite	ADJ
ejpam-1950	72	15	.	.	PUNCT
ejpam-1950	73	1	a	a	DET
ejpam-1950	73	2	sequence	sequence	NOUN
ejpam-1950	73	3	x	x	PUNCT
ejpam-1950	73	4	=	=	SYM
ejpam-1950	73	5	(	(	PUNCT
ejpam-1950	73	6	xk	xk	ADJ
ejpam-1950	73	7	)	)	PUNCT
ejpam-1950	73	8	∈	∈	PROPN
ejpam-1950	73	9	ω(x	ω(x	PROPN
ejpam-1950	73	10	)	)	PUNCT
ejpam-1950	73	11	is	be	AUX
ejpam-1950	73	12	said	say	VERB
ejpam-1950	73	13	to	to	PART
ejpam-1950	73	14	be	be	AUX
ejpam-1950	73	15	i	i	PRON
ejpam-1950	73	16	-convergent	-convergent	ADJ
ejpam-1950	73	17	to	to	ADP
ejpam-1950	73	18	l	l	NOUN
ejpam-1950	73	19	∈	∈	PROPN
ejpam-1950	74	1	x	x	X
ejpam-1950	74	2	,	,	PUNCT
ejpam-1950	74	3	briefly	briefly	INTJ
ejpam-1950	74	4	i	i	PRON
ejpam-1950	74	5	-limk	-limk	VERB
ejpam-1950	74	6	xk	xk	PROPN
ejpam-1950	75	1	=	=	SYM
ejpam-1950	75	2	l	l	PROPN
ejpam-1950	75	3	,	,	PUNCT
ejpam-1950	75	4	if	if	SCONJ
ejpam-1950	75	5	for	for	ADP
ejpam-1950	75	6	each	each	DET
ejpam-1950	75	7	ǫ	ǫ	PRON
ejpam-1950	75	8	>	>	X
ejpam-1950	75	9	0	0	PUNCT
ejpam-1950	76	1	the	the	DET
ejpam-1950	76	2	set	set	NOUN
ejpam-1950	76	3	{	{	PUNCT
ejpam-1950	76	4	k	k	PROPN
ejpam-1950	76	5	∈	∈	PROPN
ejpam-1950	76	6	n	n	CCONJ
ejpam-1950	76	7	:	:	PUNCT
ejpam-1950	76	8	‖xk	‖xk	NUM
ejpam-1950	76	9	−	−	PROPN
ejpam-1950	76	10	l‖	l‖	PROPN
ejpam-1950	76	11	≥	≥	NOUN
ejpam-1950	76	12	ǫ	ǫ	NOUN
ejpam-1950	76	13	}	}	PUNCT
ejpam-1950	76	14	belongs	belong	VERB
ejpam-1950	76	15	to	to	ADP
ejpam-1950	76	16	i	i	PRON
ejpam-1950	76	17	[	[	X
ejpam-1950	76	18	16	16	NUM
ejpam-1950	76	19	,	,	PUNCT
ejpam-1950	76	20	definition	definition	NOUN
ejpam-1950	76	21	3.1	3.1	NUM
ejpam-1950	76	22	]	]	PUNCT
ejpam-1950	76	23	.	.	PUNCT
ejpam-1950	77	1	with	with	ADP
ejpam-1950	77	2	the	the	DET
ejpam-1950	77	3	i	i	PROPN
ejpam-1950	77	4	-convergence	-convergence	PROPN
ejpam-1950	77	5	are	be	AUX
ejpam-1950	77	6	closely	closely	ADV
ejpam-1950	77	7	related	relate	VERB
ejpam-1950	77	8	the	the	DET
ejpam-1950	77	9	following	follow	VERB
ejpam-1950	77	10	two	two	NUM
ejpam-1950	77	11	notions	notion	NOUN
ejpam-1950	77	12	.	.	PUNCT
ejpam-1950	78	1	a	a	DET
ejpam-1950	78	2	sequence	sequence	NOUN
ejpam-1950	78	3	x	x	PUNCT
ejpam-1950	78	4	=	=	SYM
ejpam-1950	78	5	(	(	PUNCT
ejpam-1950	78	6	xk	xk	ADJ
ejpam-1950	78	7	)	)	PUNCT
ejpam-1950	78	8	∈	∈	PROPN
ejpam-1950	78	9	ω(x	ω(x	PROPN
ejpam-1950	78	10	)	)	PUNCT
ejpam-1950	78	11	is	be	AUX
ejpam-1950	78	12	said	say	VERB
ejpam-1950	78	13	to	to	PART
ejpam-1950	78	14	be	be	AUX
ejpam-1950	78	15	i	i	PRON
ejpam-1950	78	16	∗-convergent	∗-convergent	NOUN
ejpam-1950	78	17	to	to	ADP
ejpam-1950	78	18	l	l	NOUN
ejpam-1950	78	19	∈	∈	PROPN
ejpam-1950	79	1	x	x	X
ejpam-1950	79	2	,	,	PUNCT
ejpam-1950	79	3	briefly	briefly	ADV
ejpam-1950	79	4	i	i	PRON
ejpam-1950	79	5	∗-lim	∗-lim	PROPN
ejpam-1950	79	6	xk	xk	PROPN
ejpam-1950	79	7	=	=	PUNCT
ejpam-1950	79	8	l	l	PROPN
ejpam-1950	79	9	,	,	PUNCT
ejpam-1950	79	10	if	if	SCONJ
ejpam-1950	79	11	there	there	PRON
ejpam-1950	79	12	exists	exist	VERB
ejpam-1950	79	13	an	an	DET
ejpam-1950	79	14	index	index	NOUN
ejpam-1950	79	15	set	set	VERB
ejpam-1950	79	16	k	k	PROPN
ejpam-1950	79	17	=	=	PRON
ejpam-1950	79	18	(	(	PUNCT
ejpam-1950	79	19	ki	ki	INTJ
ejpam-1950	79	20	)	)	PUNCT
ejpam-1950	79	21	such	such	ADJ
ejpam-1950	79	22	that	that	SCONJ
ejpam-1950	79	23	k	k	PROPN
ejpam-1950	79	24	∈	∈	PROPN
ejpam-1950	79	25	f	f	X
ejpam-1950	79	26	(	(	PUNCT
ejpam-1950	79	27	i	i	NOUN
ejpam-1950	79	28	)	)	PUNCT
ejpam-1950	79	29	and	and	CCONJ
ejpam-1950	79	30	limi	limi	VERB
ejpam-1950	79	31	xki	xki	PROPN
ejpam-1950	79	32	=	=	PUNCT
ejpam-1950	79	33	l	l	NOUN
ejpam-1950	79	34	in	in	ADP
ejpam-1950	79	35	x	x	PROPN
ejpam-1950	80	1	[	[	X
ejpam-1950	80	2	16	16	NUM
ejpam-1950	80	3	,	,	PUNCT
ejpam-1950	80	4	definition	definition	NOUN
ejpam-1950	80	5	3.2	3.2	NUM
ejpam-1950	80	6	]	]	PUNCT
ejpam-1950	80	7	)	)	PUNCT
ejpam-1950	80	8	.	.	PUNCT
ejpam-1950	81	1	a	a	DET
ejpam-1950	81	2	sequence	sequence	NOUN
ejpam-1950	81	3	x	x	PUNCT
ejpam-1950	81	4	=	=	SYM
ejpam-1950	81	5	(	(	PUNCT
ejpam-1950	81	6	xk	xk	ADJ
ejpam-1950	81	7	)	)	PUNCT
ejpam-1950	81	8	∈	∈	PROPN
ejpam-1950	81	9	ω(x	ω(x	PROPN
ejpam-1950	81	10	)	)	PUNCT
ejpam-1950	81	11	is	be	AUX
ejpam-1950	81	12	said	say	VERB
ejpam-1950	81	13	to	to	PART
ejpam-1950	81	14	be	be	AUX
ejpam-1950	81	15	i	i	PRON
ejpam-1950	81	16	-bounded	-bounded	ADJ
ejpam-1950	81	17	,	,	PUNCT
ejpam-1950	81	18	briefly	briefly	ADV
ejpam-1950	81	19	xk	xk	X
ejpam-1950	82	1	=	=	PRON
ejpam-1950	82	2	oi	oi	X
ejpam-1950	82	3	(	(	PUNCT
ejpam-1950	82	4	1	1	NUM
ejpam-1950	82	5	)	)	PUNCT
ejpam-1950	82	6	,	,	PUNCT
ejpam-1950	82	7	if	if	SCONJ
ejpam-1950	82	8	there	there	PRON
ejpam-1950	82	9	exists	exist	VERB
ejpam-1950	82	10	an	an	DET
ejpam-1950	82	11	index	index	NOUN
ejpam-1950	82	12	set	set	VERB
ejpam-1950	82	13	k	k	PROPN
ejpam-1950	82	14	=	=	PRON
ejpam-1950	82	15	(	(	PUNCT
ejpam-1950	82	16	ki	ki	INTJ
ejpam-1950	82	17	)	)	PUNCT
ejpam-1950	82	18	such	such	ADJ
ejpam-1950	82	19	that	that	SCONJ
ejpam-1950	82	20	k	k	PROPN
ejpam-1950	82	21	∈	∈	PROPN
ejpam-1950	82	22	f	f	X
ejpam-1950	82	23	(	(	PUNCT
ejpam-1950	82	24	i	i	NOUN
ejpam-1950	82	25	)	)	PUNCT
ejpam-1950	82	26	and	and	CCONJ
ejpam-1950	82	27	the	the	DET
ejpam-1950	82	28	sequence	sequence	NOUN
ejpam-1950	82	29	(	(	PUNCT
ejpam-1950	82	30	ki	ki	PROPN
ejpam-1950	82	31	)	)	PUNCT
ejpam-1950	82	32	is	be	AUX
ejpam-1950	82	33	bounded	bound	VERB
ejpam-1950	82	34	in	in	ADP
ejpam-1950	82	35	x	x	PROPN
ejpam-1950	82	36	(	(	PUNCT
ejpam-1950	82	37	cf	cf	NOUN
ejpam-1950	82	38	.	.	PUNCT
ejpam-1950	83	1	[	[	X
ejpam-1950	83	2	10	10	NUM
ejpam-1950	83	3	]	]	NUM
ejpam-1950	83	4	)	)	PUNCT
ejpam-1950	83	5	.	.	PUNCT
ejpam-1950	84	1	in	in	ADP
ejpam-1950	84	2	the	the	DET
ejpam-1950	84	3	special	special	ADJ
ejpam-1950	84	4	case	case	NOUN
ejpam-1950	85	1	i	i	PRON
ejpam-1950	85	2	=	=	PRON
ejpam-1950	86	1	it	it	PRON
ejpam-1950	86	2	we	we	PRON
ejpam-1950	86	3	write	write	VERB
ejpam-1950	86	4	ostt	ostt	ADJ
ejpam-1950	86	5	(	(	PUNCT
ejpam-1950	86	6	1	1	NUM
ejpam-1950	86	7	)	)	PUNCT
ejpam-1950	86	8	instead	instead	ADV
ejpam-1950	86	9	of	of	ADP
ejpam-1950	86	10	oi	oi	INTJ
ejpam-1950	86	11	(	(	PUNCT
ejpam-1950	86	12	1	1	NUM
ejpam-1950	86	13	)	)	PUNCT
ejpam-1950	86	14	.	.	PUNCT
ejpam-1950	87	1	we	we	PRON
ejpam-1950	87	2	remark	remark	VERB
ejpam-1950	87	3	that	that	SCONJ
ejpam-1950	87	4	thei	thei	PROPN
ejpam-1950	87	5	∗-convergence	∗-convergence	ADJ
ejpam-1950	87	6	of	of	ADP
ejpam-1950	87	7	number	number	NOUN
ejpam-1950	87	8	sequences	sequence	NOUN
ejpam-1950	87	9	was	be	AUX
ejpam-1950	87	10	introduced	introduce	VERB
ejpam-1950	87	11	already	already	ADV
ejpam-1950	87	12	by	by	ADP
ejpam-1950	87	13	freedman	freedman	PROPN
ejpam-1950	88	1	[	[	X
ejpam-1950	88	2	8	8	NUM
ejpam-1950	88	3	]	]	PUNCT
ejpam-1950	88	4	as	as	SCONJ
ejpam-1950	88	5	i	i	PRON
ejpam-1950	88	6	-near	-near	VERB
ejpam-1950	88	7	convergence	convergence	NOUN
ejpam-1950	88	8	.	.	PUNCT
ejpam-1950	89	1	it	it	PRON
ejpam-1950	89	2	is	be	AUX
ejpam-1950	89	3	easy	easy	ADJ
ejpam-1950	89	4	to	to	PART
ejpam-1950	89	5	see	see	VERB
ejpam-1950	89	6	that	that	SCONJ
ejpam-1950	89	7	i	i	PRON
ejpam-1950	89	8	∗-convergence	∗-convergence	VERB
ejpam-1950	89	9	implies	imply	VERB
ejpam-1950	89	10	i	i	PRON
ejpam-1950	89	11	-convergence	-convergence	PROPN
ejpam-1950	90	1	and	and	CCONJ
ejpam-1950	90	2	every	every	DET
ejpam-1950	90	3	i	i	NOUN
ejpam-1950	90	4	∗-convergent	∗-convergent	NOUN
ejpam-1950	90	5	sequence	sequence	NOUN
ejpam-1950	90	6	is	be	AUX
ejpam-1950	90	7	i	i	PRON
ejpam-1950	90	8	-bounded	-bounded	ADJ
ejpam-1950	90	9	.	.	PUNCT
ejpam-1950	91	1	the	the	DET
ejpam-1950	91	2	following	follow	VERB
ejpam-1950	91	3	characterization	characterization	NOUN
ejpam-1950	91	4	of	of	ADP
ejpam-1950	91	5	i	i	PRON
ejpam-1950	91	6	-convergence	-convergence	PROPN
ejpam-1950	91	7	is	be	AUX
ejpam-1950	91	8	important	important	ADJ
ejpam-1950	91	9	for	for	ADP
ejpam-1950	91	10	us	we	PRON
ejpam-1950	91	11	.	.	PUNCT
ejpam-1950	92	1	proposition	proposition	NOUN
ejpam-1950	92	2	1	1	NUM
ejpam-1950	92	3	(	(	PUNCT
ejpam-1950	92	4	[	[	X
ejpam-1950	92	5	16	16	NUM
ejpam-1950	92	6	,	,	PUNCT
ejpam-1950	92	7	theorem	theorem	VERB
ejpam-1950	92	8	3.2	3.2	NUM
ejpam-1950	92	9	]	]	PUNCT
ejpam-1950	92	10	)	)	PUNCT
ejpam-1950	92	11	.	.	PUNCT
ejpam-1950	93	1	if	if	SCONJ
ejpam-1950	93	2	the	the	DET
ejpam-1950	93	3	ideal	ideal	NOUN
ejpam-1950	93	4	i	i	PRON
ejpam-1950	93	5	has	have	VERB
ejpam-1950	93	6	property	property	NOUN
ejpam-1950	93	7	(	(	PUNCT
ejpam-1950	93	8	ap	ap	PROPN
ejpam-1950	93	9	)	)	PUNCT
ejpam-1950	93	10	,	,	PUNCT
ejpam-1950	93	11	then	then	ADV
ejpam-1950	93	12	i	i	PRON
ejpam-1950	93	13	-lim	-lim	PUNCT
ejpam-1950	93	14	xk	xk	X
ejpam-1950	93	15	=	=	PUNCT
ejpam-1950	93	16	l	l	PROPN
ejpam-1950	93	17	in	in	ADP
ejpam-1950	93	18	a	a	DET
ejpam-1950	93	19	banach	banach	NOUN
ejpam-1950	93	20	space	space	NOUN
ejpam-1950	93	21	x	x	INTJ
ejpam-1950	93	22	if	if	SCONJ
ejpam-1950	94	1	and	and	CCONJ
ejpam-1950	94	2	only	only	ADV
ejpam-1950	94	3	if	if	SCONJ
ejpam-1950	94	4	i	i	PRON
ejpam-1950	94	5	∗-lim	∗-lim	VERB
ejpam-1950	94	6	xk	xk	X
ejpam-1950	94	7	=	=	PUNCT
ejpam-1950	94	8	l.	l.	PROPN
ejpam-1950	94	9	by	by	ADP
ejpam-1950	94	10	ci	ci	PROPN
ejpam-1950	94	11	(	(	PUNCT
ejpam-1950	94	12	x	x	X
ejpam-1950	94	13	)	)	PUNCT
ejpam-1950	94	14	we	we	PRON
ejpam-1950	94	15	denote	denote	VERB
ejpam-1950	94	16	the	the	DET
ejpam-1950	94	17	set	set	NOUN
ejpam-1950	94	18	of	of	ADP
ejpam-1950	94	19	all	all	PRON
ejpam-1950	94	20	i	i	PRON
ejpam-1950	94	21	-convergent	-convergent	ADJ
ejpam-1950	94	22	x	x	SYM
ejpam-1950	94	23	-valued	-valued	ADJ
ejpam-1950	94	24	sequences	sequence	NOUN
ejpam-1950	94	25	.	.	PUNCT
ejpam-1950	95	1	let	let	VERB
ejpam-1950	95	2	ℓ∞(x	ℓ∞(x	NOUN
ejpam-1950	95	3	)	)	PUNCT
ejpam-1950	95	4	,	,	PUNCT
ejpam-1950	95	5	c(x	c(x	NOUN
ejpam-1950	95	6	)	)	PUNCT
ejpam-1950	95	7	and	and	CCONJ
ejpam-1950	95	8	c0(x	c0(x	SCONJ
ejpam-1950	95	9	)	)	PUNCT
ejpam-1950	95	10	be	be	AUX
ejpam-1950	95	11	the	the	DET
ejpam-1950	95	12	sets	set	NOUN
ejpam-1950	95	13	of	of	ADP
ejpam-1950	95	14	all	all	PRON
ejpam-1950	95	15	bounded	bounded	ADJ
ejpam-1950	95	16	,	,	PUNCT
ejpam-1950	95	17	convergent	convergent	NOUN
ejpam-1950	95	18	and	and	CCONJ
ejpam-1950	95	19	convergent	convergent	NOUN
ejpam-1950	95	20	to	to	ADP
ejpam-1950	95	21	zero	zero	NUM
ejpam-1950	95	22	x	x	SYM
ejpam-1950	95	23	-valued	-value	VERB
ejpam-1950	95	24	sequences	sequence	NOUN
ejpam-1950	95	25	,	,	PUNCT
ejpam-1950	95	26	respectively	respectively	ADV
ejpam-1950	95	27	.	.	PUNCT
ejpam-1950	96	1	for	for	ADP
ejpam-1950	96	2	1	1	NUM
ejpam-1950	96	3	≤	≤	NOUN
ejpam-1950	96	4	p	p	NOUN
ejpam-1950	96	5	<	<	X
ejpam-1950	96	6	∞	∞	NUM
ejpam-1950	96	7	let	let	VERB
ejpam-1950	96	8	ℓp(x	ℓp(x	X
ejpam-1950	96	9	)	)	PUNCT
ejpam-1950	96	10	be	be	AUX
ejpam-1950	96	11	the	the	DET
ejpam-1950	96	12	set	set	NOUN
ejpam-1950	96	13	of	of	ADP
ejpam-1950	96	14	sequences	sequence	NOUN
ejpam-1950	96	15	(	(	PUNCT
ejpam-1950	96	16	xk	xk	ADJ
ejpam-1950	96	17	)	)	PUNCT
ejpam-1950	96	18	∈	∈	PROPN
ejpam-1950	96	19	ω(x	ω(x	PROPN
ejpam-1950	96	20	)	)	PUNCT
ejpam-1950	96	21	such	such	ADJ
ejpam-1950	96	22	that	that	SCONJ
ejpam-1950	96	23	∑	∑	PROPN
ejpam-1950	97	1	k	k	PROPN
ejpam-1950	97	2	‖xk‖	‖xk‖	PROPN
ejpam-1950	97	3	p	p	X
ejpam-1950	97	4	<	<	AUX
ejpam-1950	97	5	∞.	∞.	PROPN
ejpam-1950	97	6	using	use	VERB
ejpam-1950	97	7	proposition	proposition	NOUN
ejpam-1950	97	8	1	1	NUM
ejpam-1950	97	9	and	and	CCONJ
ejpam-1950	97	10	theorem	theorem	VERB
ejpam-1950	97	11	2	2	NUM
ejpam-1950	97	12	,	,	PUNCT
ejpam-1950	97	13	we	we	PRON
ejpam-1950	97	14	proved	prove	VERB
ejpam-1950	97	15	in	in	ADP
ejpam-1950	97	16	[	[	X
ejpam-1950	97	17	15	15	NUM
ejpam-1950	97	18	]	]	X
ejpam-1950	97	19	the	the	DET
ejpam-1950	97	20	following	follow	VERB
ejpam-1950	97	21	banach	banach	NOUN
ejpam-1950	97	22	–	–	PUNCT
ejpam-1950	97	23	steinhaus	steinhaus	NOUN
ejpam-1950	97	24	type	type	NOUN
ejpam-1950	97	25	theorem	theorem	NOUN
ejpam-1950	97	26	for	for	ADP
ejpam-1950	97	27	i	i	PROPN
ejpam-1950	97	28	-convergence	-convergence	PROPN
ejpam-1950	97	29	.	.	PUNCT
ejpam-1950	98	1	theorem	theorem	VERB
ejpam-1950	98	2	3	3	NUM
ejpam-1950	98	3	(	(	PUNCT
ejpam-1950	98	4	[	[	X
ejpam-1950	98	5	15	15	NUM
ejpam-1950	98	6	,	,	PUNCT
ejpam-1950	98	7	theorem	theorem	VERB
ejpam-1950	98	8	3	3	NUM
ejpam-1950	98	9	]	]	PUNCT
ejpam-1950	98	10	)	)	PUNCT
ejpam-1950	98	11	.	.	PUNCT
ejpam-1950	99	1	let	let	VERB
ejpam-1950	99	2	x	x	PRON
ejpam-1950	99	3	and	and	CCONJ
ejpam-1950	99	4	y	y	PROPN
ejpam-1950	99	5	be	be	AUX
ejpam-1950	99	6	two	two	NUM
ejpam-1950	99	7	banach	banach	NOUN
ejpam-1950	99	8	spaces	space	NOUN
ejpam-1950	99	9	,	,	PUNCT
ejpam-1950	99	10	where	where	SCONJ
ejpam-1950	99	11	x	x	PRON
ejpam-1950	99	12	has	have	VERB
ejpam-1950	99	13	a	a	DET
ejpam-1950	99	14	countable	countable	ADJ
ejpam-1950	99	15	fundamental	fundamental	ADJ
ejpam-1950	99	16	set	set	NOUN
ejpam-1950	99	17	φ	φ	NOUN
ejpam-1950	99	18	.	.	PUNCT
ejpam-1950	100	1	if	if	SCONJ
ejpam-1950	100	2	the	the	DET
ejpam-1950	100	3	ideal	ideal	NOUN
ejpam-1950	100	4	i	i	PRON
ejpam-1950	100	5	has	have	VERB
ejpam-1950	100	6	property	property	NOUN
ejpam-1950	100	7	(	(	PUNCT
ejpam-1950	100	8	ap	ap	PROPN
ejpam-1950	100	9	)	)	PUNCT
ejpam-1950	100	10	,	,	PUNCT
ejpam-1950	100	11	then	then	ADV
ejpam-1950	100	12	the	the	DET
ejpam-1950	100	13	sequence	sequence	NOUN
ejpam-1950	100	14	(	(	PUNCT
ejpam-1950	100	15	an	an	X
ejpam-1950	100	16	)	)	PUNCT
ejpam-1950	100	17	is	be	AUX
ejpam-1950	100	18	bi	bi	ADJ
ejpam-1950	100	19	-convergent	-convergent	PROPN
ejpam-1950	100	20	(	(	PUNCT
ejpam-1950	100	21	i.e.	i.e.	X
ejpam-1950	100	22	,	,	PUNCT
ejpam-1950	100	23	(	(	PUNCT
ejpam-1950	100	24	an	an	DET
ejpam-1950	100	25	x	x	NOUN
ejpam-1950	100	26	)	)	PUNCT
ejpam-1950	100	27	∈	∈	PROPN
ejpam-1950	100	28	ci	ci	NOUN
ejpam-1950	100	29	(	(	PUNCT
ejpam-1950	100	30	y	y	NOUN
ejpam-1950	100	31	)	)	PUNCT
ejpam-1950	100	32	∩	∩	ADJ
ejpam-1950	100	33	ℓ∞(y	ℓ∞(y	X
ejpam-1950	100	34	)	)	PUNCT
ejpam-1950	100	35	for	for	ADP
ejpam-1950	100	36	any	any	DET
ejpam-1950	100	37	x	x	SYM
ejpam-1950	100	38	∈	∈	PROPN
ejpam-1950	100	39	x	x	X
ejpam-1950	100	40	)	)	PUNCT
ejpam-1950	100	41	if	if	SCONJ
ejpam-1950	100	42	and	and	CCONJ
ejpam-1950	100	43	only	only	ADV
ejpam-1950	100	44	if	if	SCONJ
ejpam-1950	100	45	(	(	PUNCT
ejpam-1950	100	46	1	1	X
ejpam-1950	100	47	)	)	PUNCT
ejpam-1950	100	48	holds	hold	VERB
ejpam-1950	100	49	and	and	CCONJ
ejpam-1950	100	50	(	(	PUNCT
ejpam-1950	100	51	anφ	anφ	ADJ
ejpam-1950	100	52	)	)	PUNCT
ejpam-1950	100	53	is	be	AUX
ejpam-1950	100	54	i	i	PRON
ejpam-1950	100	55	-convergent	-convergent	ADJ
ejpam-1950	100	56	for	for	ADP
ejpam-1950	100	57	every	every	DET
ejpam-1950	100	58	φ	φ	PROPN
ejpam-1950	100	59	∈	∈	PROPN
ejpam-1950	100	60	φ	φ	PROPN
ejpam-1950	100	61	.	.	PUNCT
ejpam-1950	101	1	thereby	thereby	ADV
ejpam-1950	101	2	,	,	PUNCT
ejpam-1950	101	3	the	the	DET
ejpam-1950	101	4	limit	limit	NOUN
ejpam-1950	101	5	operator	operator	NOUN
ejpam-1950	101	6	a	a	PRON
ejpam-1950	101	7	,	,	PUNCT
ejpam-1950	101	8	ax	ax	NOUN
ejpam-1950	101	9	=	=	PUNCT
ejpam-1950	101	10	i	i	PRON
ejpam-1950	101	11	-lim	-lim	PUNCT
ejpam-1950	101	12	an	an	DET
ejpam-1950	101	13	x	x	NOUN
ejpam-1950	101	14	,	,	PUNCT
ejpam-1950	101	15	is	be	AUX
ejpam-1950	101	16	bounded	bound	VERB
ejpam-1950	101	17	and	and	CCONJ
ejpam-1950	101	18	linear	linear	ADJ
ejpam-1950	101	19	,	,	PUNCT
ejpam-1950	101	20	and	and	CCONJ
ejpam-1950	101	21	‖a‖	‖a‖	PROPN
ejpam-1950	101	22	≤	≤	NUM
ejpam-1950	101	23	supn	supn	NOUN
ejpam-1950	101	24	‖an‖.	‖an‖.	NOUN
ejpam-1950	101	25	in	in	ADP
ejpam-1950	101	26	this	this	DET
ejpam-1950	101	27	paper	paper	NOUN
ejpam-1950	101	28	we	we	PRON
ejpam-1950	101	29	introduce	introduce	VERB
ejpam-1950	101	30	the	the	DET
ejpam-1950	101	31	notion	notion	NOUN
ejpam-1950	101	32	of	of	ADP
ejpam-1950	101	33	b∗i	b∗i	PUNCT
ejpam-1950	101	34	-convergence	-convergence	NOUN
ejpam-1950	101	35	of	of	ADP
ejpam-1950	101	36	sequences	sequence	NOUN
ejpam-1950	101	37	of	of	ADP
ejpam-1950	101	38	bounded	bounded	ADJ
ejpam-1950	101	39	linear	linear	PROPN
ejpam-1950	101	40	operators	operator	NOUN
ejpam-1950	101	41	(	(	PUNCT
ejpam-1950	101	42	an	an	X
ejpam-1950	101	43	)	)	PUNCT
ejpam-1950	101	44	and	and	CCONJ
ejpam-1950	101	45	give	give	VERB
ejpam-1950	101	46	an	an	DET
ejpam-1950	101	47	analogue	analogue	NOUN
ejpam-1950	101	48	of	of	ADP
ejpam-1950	101	49	theorem	theorem	NOUN
ejpam-1950	101	50	3	3	NUM
ejpam-1950	101	51	by	by	ADP
ejpam-1950	101	52	finding	find	VERB
ejpam-1950	101	53	necessary	necessary	ADJ
ejpam-1950	101	54	and	and	CCONJ
ejpam-1950	101	55	sufficient	sufficient	ADJ
ejpam-1950	101	56	conditions	condition	NOUN
ejpam-1950	101	57	for	for	ADP
ejpam-1950	101	58	b∗i	b∗i	PUNCT
ejpam-1950	101	59	-convergence	-convergence	NOUN
ejpam-1950	101	60	of	of	ADP
ejpam-1950	101	61	such	such	ADJ
ejpam-1950	101	62	sequences	sequence	NOUN
ejpam-1950	101	63	(	(	PUNCT
ejpam-1950	101	64	an	an	NOUN
ejpam-1950	101	65	)	)	PUNCT
ejpam-1950	101	66	.	.	PUNCT
ejpam-1950	102	1	as	as	ADP
ejpam-1950	102	2	applications	application	NOUN
ejpam-1950	102	3	of	of	ADP
ejpam-1950	102	4	this	this	DET
ejpam-1950	102	5	result	result	NOUN
ejpam-1950	102	6	we	we	PRON
ejpam-1950	102	7	characterize	characterize	VERB
ejpam-1950	102	8	infinite	infinite	ADJ
ejpam-1950	102	9	summability	summability	NOUN
ejpam-1950	102	10	matrices	matrice	VERB
ejpam-1950	102	11	a	a	DET
ejpam-1950	102	12	=	=	SYM
ejpam-1950	102	13	(	(	PUNCT
ejpam-1950	102	14	ank	ank	PROPN
ejpam-1950	102	15	)	)	PUNCT
ejpam-1950	102	16	of	of	ADP
ejpam-1950	102	17	type	type	NOUN
ejpam-1950	102	18	a	a	DET
ejpam-1950	102	19	:	:	PUNCT
ejpam-1950	102	20	λ(x	λ(x	X
ejpam-1950	102	21	)	)	PUNCT
ejpam-1950	102	22	b∗i	b∗i	PUNCT
ejpam-1950	102	23	−→	−→	ADJ
ejpam-1950	102	24	c(y	c(y	PROPN
ejpam-1950	102	25	)	)	PUNCT
ejpam-1950	102	26	with	with	ADP
ejpam-1950	102	27	ank	ank	PROPN
ejpam-1950	102	28	∈	∈	PROPN
ejpam-1950	102	29	b(x	b(x	PROPN
ejpam-1950	102	30	,	,	PUNCT
ejpam-1950	102	31	y	y	PROPN
ejpam-1950	102	32	)	)	PUNCT
ejpam-1950	102	33	(	(	PUNCT
ejpam-1950	102	34	n	n	X
ejpam-1950	102	35	,	,	PUNCT
ejpam-1950	102	36	k	k	PROPN
ejpam-1950	102	37	∈	∈	PROPN
ejpam-1950	102	38	n	n	CCONJ
ejpam-1950	102	39	)	)	PUNCT
ejpam-1950	102	40	and	and	CCONJ
ejpam-1950	102	41	λ	λ	X
ejpam-1950	102	42	∈	∈	PROPN
ejpam-1950	102	43	{	{	PUNCT
ejpam-1950	102	44	c	c	NOUN
ejpam-1950	102	45	,	,	PUNCT
ejpam-1950	102	46	c0	c0	NOUN
ejpam-1950	102	47	,	,	PUNCT
ejpam-1950	102	48	ℓ1	ℓ1	PROPN
ejpam-1950	102	49	}	}	PUNCT
ejpam-1950	102	50	,	,	PUNCT
ejpam-1950	102	51	also	also	ADV
ejpam-1950	102	52	consider	consider	VERB
ejpam-1950	102	53	the	the	DET
ejpam-1950	102	54	weak	weak	ADJ
ejpam-1950	102	55	b∗i	b∗i	ADJ
ejpam-1950	102	56	-convergence	-convergence	NOUN
ejpam-1950	102	57	in	in	ADP
ejpam-1950	102	58	banach	banach	NOUN
ejpam-1950	102	59	spaces	space	NOUN
ejpam-1950	102	60	.	.	PUNCT
ejpam-1950	103	1	2	2	X
ejpam-1950	103	2	.	.	X
ejpam-1950	103	3	main	main	ADJ
ejpam-1950	103	4	theorems	theorem	NOUN
ejpam-1950	103	5	in	in	ADP
ejpam-1950	103	6	the	the	DET
ejpam-1950	103	7	following	following	NOUN
ejpam-1950	103	8	let	let	VERB
ejpam-1950	103	9	x	x	PRON
ejpam-1950	103	10	,	,	PUNCT
ejpam-1950	103	11	y	y	PROPN
ejpam-1950	103	12	be	be	AUX
ejpam-1950	103	13	two	two	NUM
ejpam-1950	103	14	banach	banach	NOUN
ejpam-1950	103	15	spaces	space	NOUN
ejpam-1950	103	16	,	,	PUNCT
ejpam-1950	103	17	an	an	DET
ejpam-1950	103	18	∈	∈	NOUN
ejpam-1950	103	19	b(x	b(x	NOUN
ejpam-1950	103	20	,	,	PUNCT
ejpam-1950	103	21	y	y	PROPN
ejpam-1950	103	22	)	)	PUNCT
ejpam-1950	103	23	(	(	PUNCT
ejpam-1950	103	24	n	n	CCONJ
ejpam-1950	103	25	∈	∈	PROPN
ejpam-1950	103	26	n	n	CCONJ
ejpam-1950	103	27	)	)	PUNCT
ejpam-1950	103	28	and	and	CCONJ
ejpam-1950	103	29	let	let	VERB
ejpam-1950	103	30	i	i	PRON
ejpam-1950	103	31	⊂	⊂	PROPN
ejpam-1950	103	32	2n	2n	NUM
ejpam-1950	103	33	be	be	VERB
ejpam-1950	103	34	a	a	DET
ejpam-1950	103	35	non	non	ADJ
ejpam-1950	103	36	-	-	ADJ
ejpam-1950	103	37	trivial	trivial	ADJ
ejpam-1950	103	38	admissible	admissible	ADJ
ejpam-1950	103	39	ideal	ideal	NOUN
ejpam-1950	103	40	.	.	PUNCT
ejpam-1950	104	1	e.	e.	PROPN
ejpam-1950	104	2	kolk	kolk	PROPN
ejpam-1950	104	3	/	/	SYM
ejpam-1950	104	4	eur	eur	PROPN
ejpam-1950	104	5	.	.	PUNCT
ejpam-1950	105	1	j.	j.	PROPN
ejpam-1950	105	2	pure	pure	PROPN
ejpam-1950	105	3	appl	appl	PROPN
ejpam-1950	105	4	.	.	PROPN
ejpam-1950	105	5	math	math	PROPN
ejpam-1950	105	6	,	,	PUNCT
ejpam-1950	105	7	8	8	NUM
ejpam-1950	105	8	(	(	PUNCT
ejpam-1950	105	9	2015	2015	NUM
ejpam-1950	105	10	)	)	PUNCT
ejpam-1950	105	11	,	,	PUNCT
ejpam-1950	105	12	357	357	NUM
ejpam-1950	105	13	-	-	SYM
ejpam-1950	105	14	367	367	NUM
ejpam-1950	105	15	360	360	NUM
ejpam-1950	105	16	recall	recall	NOUN
ejpam-1950	105	17	that	that	SCONJ
ejpam-1950	105	18	a	a	DET
ejpam-1950	105	19	sequence	sequence	NOUN
ejpam-1950	105	20	(	(	PUNCT
ejpam-1950	105	21	xn	xn	PROPN
ejpam-1950	105	22	)	)	PUNCT
ejpam-1950	105	23	∈ω(x	∈ω(x	PROPN
ejpam-1950	105	24	)	)	PUNCT
ejpam-1950	105	25	is	be	AUX
ejpam-1950	105	26	said	say	VERB
ejpam-1950	105	27	to	to	PART
ejpam-1950	105	28	be	be	AUX
ejpam-1950	105	29	weakly	weakly	ADJ
ejpam-1950	105	30	i	i	PRON
ejpam-1950	105	31	-convergent	-convergent	ADJ
ejpam-1950	105	32	(	(	PUNCT
ejpam-1950	105	33	weakly	weakly	ADJ
ejpam-1950	105	34	t	t	PROPN
ejpam-1950	105	35	-	-	PUNCT
ejpam-1950	105	36	statistically	statistically	ADV
ejpam-1950	105	37	convergent	convergent	NOUN
ejpam-1950	105	38	)	)	PUNCT
ejpam-1950	105	39	to	to	ADP
ejpam-1950	105	40	a	a	DET
ejpam-1950	105	41	point	point	NOUN
ejpam-1950	105	42	l	l	NOUN
ejpam-1950	105	43	∈	∈	PROPN
ejpam-1950	105	44	x	x	INTJ
ejpam-1950	105	45	if	if	SCONJ
ejpam-1950	105	46	i	i	PRON
ejpam-1950	105	47	-lim	-lim	PUNCT
ejpam-1950	105	48	x	x	SYM
ejpam-1950	105	49	′(xn	′(xn	NOUN
ejpam-1950	105	50	)	)	PUNCT
ejpam-1950	105	51	=	=	PUNCT
ejpam-1950	105	52	x	x	SYM
ejpam-1950	105	53	′(l	′(l	ADV
ejpam-1950	105	54	)	)	PUNCT
ejpam-1950	105	55	(	(	PUNCT
ejpam-1950	105	56	stt	stt	PROPN
ejpam-1950	105	57	-lim	-lim	NUM
ejpam-1950	105	58	x	x	SYM
ejpam-1950	105	59	′(xn	′(xn	NOUN
ejpam-1950	105	60	)	)	PUNCT
ejpam-1950	105	61	=	=	PUNCT
ejpam-1950	105	62	x	x	SYM
ejpam-1950	105	63	′(l	′(l	ADV
ejpam-1950	105	64	)	)	PUNCT
ejpam-1950	105	65	)	)	PUNCT
ejpam-1950	106	1	for	for	ADP
ejpam-1950	106	2	any	any	DET
ejpam-1950	106	3	x	x	SYM
ejpam-1950	106	4	′	′	NUM
ejpam-1950	106	5	∈	∈	NOUN
ejpam-1950	106	6	x	x	PUNCT
ejpam-1950	107	1	′	′	NUM
ejpam-1950	108	1	[	[	X
ejpam-1950	108	2	2	2	NUM
ejpam-1950	108	3	,	,	PUNCT
ejpam-1950	108	4	21	21	NUM
ejpam-1950	108	5	]	]	PUNCT
ejpam-1950	108	6	.	.	PUNCT
ejpam-1950	109	1	we	we	PRON
ejpam-1950	109	2	know	know	VERB
ejpam-1950	109	3	that	that	SCONJ
ejpam-1950	109	4	every	every	DET
ejpam-1950	109	5	weakly	weakly	ADJ
ejpam-1950	109	6	convergent	convergent	ADJ
ejpam-1950	109	7	sequence	sequence	NOUN
ejpam-1950	109	8	in	in	ADP
ejpam-1950	109	9	a	a	DET
ejpam-1950	109	10	banach	banach	NOUN
ejpam-1950	109	11	space	space	NOUN
ejpam-1950	109	12	x	x	VERB
ejpam-1950	109	13	is	be	AUX
ejpam-1950	109	14	bounded	bound	VERB
ejpam-1950	109	15	.	.	PUNCT
ejpam-1950	110	1	but	but	CCONJ
ejpam-1950	110	2	a	a	DET
ejpam-1950	110	3	weakly	weakly	ADJ
ejpam-1950	110	4	i	i	PRON
ejpam-1950	110	5	-convergent	-convergent	ADJ
ejpam-1950	110	6	sequence	sequence	NOUN
ejpam-1950	110	7	is	be	AUX
ejpam-1950	110	8	not	not	PART
ejpam-1950	110	9	necessary	necessary	ADJ
ejpam-1950	110	10	i	i	PRON
ejpam-1950	110	11	-bounded	-bounded	ADJ
ejpam-1950	110	12	(	(	PUNCT
ejpam-1950	110	13	cf	cf	NOUN
ejpam-1950	110	14	.	.	PUNCT
ejpam-1950	111	1	[	[	X
ejpam-1950	111	2	5	5	NUM
ejpam-1950	111	3	,	,	PUNCT
ejpam-1950	111	4	theorem	theorem	VERB
ejpam-1950	111	5	1	1	NUM
ejpam-1950	111	6	]	]	PUNCT
ejpam-1950	111	7	)	)	PUNCT
ejpam-1950	111	8	.	.	PUNCT
ejpam-1950	112	1	example	example	NOUN
ejpam-1950	112	2	2	2	NUM
ejpam-1950	112	3	from	from	ADP
ejpam-1950	112	4	[	[	X
ejpam-1950	112	5	5	5	NUM
ejpam-1950	112	6	]	]	PUNCT
ejpam-1950	112	7	shows	show	VERB
ejpam-1950	112	8	that	that	SCONJ
ejpam-1950	112	9	the	the	DET
ejpam-1950	112	10	banach	banach	NOUN
ejpam-1950	112	11	sequence	sequence	NOUN
ejpam-1950	112	12	space	space	NOUN
ejpam-1950	112	13	ℓ2	ℓ2	NOUN
ejpam-1950	112	14	contains	contain	VERB
ejpam-1950	112	15	a	a	DET
ejpam-1950	112	16	weakly	weakly	ADJ
ejpam-1950	112	17	statistically	statistically	ADV
ejpam-1950	112	18	null	null	ADJ
ejpam-1950	112	19	sequence	sequence	NOUN
ejpam-1950	112	20	(	(	PUNCT
ejpam-1950	112	21	zk	zk	PROPN
ejpam-1950	112	22	)	)	PUNCT
ejpam-1950	112	23	with	with	ADP
ejpam-1950	112	24	no	no	DET
ejpam-1950	112	25	bounded	bounded	ADJ
ejpam-1950	112	26	subsequences	subsequence	NOUN
ejpam-1950	112	27	.	.	PUNCT
ejpam-1950	113	1	thus	thus	ADV
ejpam-1950	113	2	some	some	DET
ejpam-1950	113	3	results	result	NOUN
ejpam-1950	113	4	of	of	ADP
ejpam-1950	113	5	bhardwaj	bhardwaj	PROPN
ejpam-1950	113	6	and	and	CCONJ
ejpam-1950	113	7	bala	bala	PROPN
ejpam-1950	114	1	[	[	X
ejpam-1950	114	2	2	2	NUM
ejpam-1950	114	3	,	,	PUNCT
ejpam-1950	114	4	theorem	theorem	VERB
ejpam-1950	114	5	3.1	3.1	NUM
ejpam-1950	114	6	and	and	CCONJ
ejpam-1950	114	7	lemma	lemma	PROPN
ejpam-1950	114	8	3.2	3.2	NUM
ejpam-1950	114	9	]	]	PUNCT
ejpam-1950	114	10	are	be	AUX
ejpam-1950	114	11	incorrect	incorrect	ADJ
ejpam-1950	114	12	.	.	PUNCT
ejpam-1950	115	1	at	at	ADP
ejpam-1950	115	2	it	it	PRON
ejpam-1950	115	3	,	,	PUNCT
ejpam-1950	115	4	defining	define	VERB
ejpam-1950	115	5	fn	fn	NOUN
ejpam-1950	115	6	x	x	NOUN
ejpam-1950	115	7	′	′	NUM
ejpam-1950	115	8	=	=	SYM
ejpam-1950	115	9	x	x	SYM
ejpam-1950	115	10	′(zn	′(zn	NOUN
ejpam-1950	115	11	)	)	PUNCT
ejpam-1950	115	12	(	(	PUNCT
ejpam-1950	115	13	x	x	X
ejpam-1950	115	14	′	′	NUM
ejpam-1950	115	15	∈	∈	PROPN
ejpam-1950	115	16	ℓ′2	ℓ′2	NOUN
ejpam-1950	115	17	,	,	PUNCT
ejpam-1950	115	18	n	n	PROPN
ejpam-1950	115	19	∈	∈	PROPN
ejpam-1950	115	20	n	n	CCONJ
ejpam-1950	115	21	)	)	PUNCT
ejpam-1950	115	22	,	,	PUNCT
ejpam-1950	115	23	we	we	PRON
ejpam-1950	115	24	get	get	VERB
ejpam-1950	115	25	the	the	DET
ejpam-1950	115	26	sequence	sequence	NOUN
ejpam-1950	115	27	(	(	PUNCT
ejpam-1950	115	28	fn	fn	NOUN
ejpam-1950	115	29	)	)	PUNCT
ejpam-1950	115	30	of	of	ADP
ejpam-1950	115	31	bounded	bound	VERB
ejpam-1950	115	32	linear	linear	PROPN
ejpam-1950	115	33	functionals	functional	NOUN
ejpam-1950	116	1	fn	fn	INTJ
ejpam-1950	116	2	:	:	PUNCT
ejpam-1950	116	3	ℓ′2	ℓ′2	PROPN
ejpam-1950	116	4	→	→	X
ejpam-1950	116	5	r.	r.	PROPN
ejpam-1950	116	6	since	since	SCONJ
ejpam-1950	116	7	‖fn‖	‖fn‖	PROPN
ejpam-1950	116	8	=	=	SYM
ejpam-1950	116	9	‖zn‖	‖zn‖	PROPN
ejpam-1950	116	10	by	by	ADP
ejpam-1950	116	11	the	the	DET
ejpam-1950	116	12	classical	classical	ADJ
ejpam-1950	116	13	hahn	hahn	PROPN
ejpam-1950	116	14	–	–	PUNCT
ejpam-1950	116	15	banach	banach	NOUN
ejpam-1950	116	16	theorem	theorem	VERB
ejpam-1950	116	17	,	,	PUNCT
ejpam-1950	116	18	the	the	DET
ejpam-1950	116	19	sequence	sequence	NOUN
ejpam-1950	116	20	of	of	ADP
ejpam-1950	116	21	functionals	functional	NOUN
ejpam-1950	116	22	(	(	PUNCT
ejpam-1950	116	23	fn	fn	NOUN
ejpam-1950	116	24	)	)	PUNCT
ejpam-1950	116	25	converges	converge	VERB
ejpam-1950	116	26	statistically	statistically	ADV
ejpam-1950	116	27	to	to	ADP
ejpam-1950	116	28	zero	zero	NUM
ejpam-1950	116	29	for	for	ADP
ejpam-1950	116	30	any	any	DET
ejpam-1950	116	31	x	x	SYM
ejpam-1950	116	32	′	′	NUM
ejpam-1950	116	33	∈	∈	PROPN
ejpam-1950	116	34	ℓ′2	ℓ′2	NOUN
ejpam-1950	116	35	,	,	PUNCT
ejpam-1950	116	36	but	but	CCONJ
ejpam-1950	116	37	the	the	DET
ejpam-1950	116	38	sequence	sequence	NOUN
ejpam-1950	116	39	of	of	ADP
ejpam-1950	116	40	norms	norm	NOUN
ejpam-1950	116	41	(	(	PUNCT
ejpam-1950	116	42	‖fn‖	‖fn‖	NOUN
ejpam-1950	116	43	)	)	PUNCT
ejpam-1950	116	44	contains	contain	VERB
ejpam-1950	116	45	no	no	DET
ejpam-1950	116	46	bounded	bounded	ADJ
ejpam-1950	116	47	subsequences	subsequence	NOUN
ejpam-1950	116	48	.	.	PUNCT
ejpam-1950	117	1	this	this	DET
ejpam-1950	117	2	example	example	NOUN
ejpam-1950	117	3	justifies	justify	VERB
ejpam-1950	117	4	the	the	DET
ejpam-1950	117	5	following	follow	VERB
ejpam-1950	117	6	definition	definition	NOUN
ejpam-1950	117	7	.	.	PUNCT
ejpam-1950	118	1	definition	definition	NOUN
ejpam-1950	118	2	1	1	NUM
ejpam-1950	118	3	.	.	PUNCT
ejpam-1950	119	1	a	a	DET
ejpam-1950	119	2	sequence	sequence	NOUN
ejpam-1950	119	3	(	(	PUNCT
ejpam-1950	119	4	an	an	NOUN
ejpam-1950	119	5	)	)	PUNCT
ejpam-1950	119	6	of	of	ADP
ejpam-1950	119	7	operators	operator	NOUN
ejpam-1950	119	8	an	an	DET
ejpam-1950	119	9	∈	∈	NOUN
ejpam-1950	119	10	b(x	b(x	NOUN
ejpam-1950	119	11	,	,	PUNCT
ejpam-1950	119	12	y	y	PROPN
ejpam-1950	119	13	)	)	PUNCT
ejpam-1950	119	14	(	(	PUNCT
ejpam-1950	119	15	n	n	CCONJ
ejpam-1950	119	16	∈	∈	PROPN
ejpam-1950	119	17	n	n	CCONJ
ejpam-1950	119	18	)	)	PUNCT
ejpam-1950	119	19	is	be	AUX
ejpam-1950	119	20	said	say	VERB
ejpam-1950	119	21	to	to	PART
ejpam-1950	119	22	be	be	AUX
ejpam-1950	119	23	b∗i	b∗i	ADJ
ejpam-1950	119	24	-convergent	-convergent	ADJ
ejpam-1950	119	25	(	(	PUNCT
ejpam-1950	119	26	to	to	ADP
ejpam-1950	119	27	a∈	a∈	PROPN
ejpam-1950	119	28	b(x	b(x	PROPN
ejpam-1950	119	29	,	,	PUNCT
ejpam-1950	119	30	y	y	PROPN
ejpam-1950	119	31	)	)	PUNCT
ejpam-1950	119	32	)	)	PUNCT
ejpam-1950	120	1	if	if	SCONJ
ejpam-1950	120	2	i	i	PRON
ejpam-1950	120	3	limn	limn	VERB
ejpam-1950	120	4	an	an	DET
ejpam-1950	120	5	x	x	PRON
ejpam-1950	120	6	exists	exist	VERB
ejpam-1950	120	7	(	(	PUNCT
ejpam-1950	120	8	i	i	PRON
ejpam-1950	120	9	lim	lim	PROPN
ejpam-1950	120	10	an	an	DET
ejpam-1950	120	11	x	x	NOUN
ejpam-1950	120	12	=	=	SYM
ejpam-1950	120	13	ax	ax	NOUN
ejpam-1950	120	14	)	)	PUNCT
ejpam-1950	120	15	for	for	ADP
ejpam-1950	120	16	any	any	DET
ejpam-1950	120	17	x	x	SYM
ejpam-1950	120	18	∈	∈	PROPN
ejpam-1950	120	19	x	x	X
ejpam-1950	120	20	and	and	CCONJ
ejpam-1950	120	21	there	there	PRON
ejpam-1950	120	22	is	be	VERB
ejpam-1950	120	23	a	a	DET
ejpam-1950	120	24	set	set	NOUN
ejpam-1950	120	25	k	k	PROPN
ejpam-1950	120	26	∈	∈	PROPN
ejpam-1950	120	27	f	f	X
ejpam-1950	120	28	(	(	PUNCT
ejpam-1950	120	29	i	i	NOUN
ejpam-1950	120	30	)	)	PUNCT
ejpam-1950	120	31	such	such	ADJ
ejpam-1950	120	32	that	that	SCONJ
ejpam-1950	120	33	(	(	PUNCT
ejpam-1950	120	34	ak	ak	PROPN
ejpam-1950	120	35	x)k∈k	x)k∈k	PROPN
ejpam-1950	120	36	is	be	AUX
ejpam-1950	120	37	bounded	bound	VERB
ejpam-1950	120	38	for	for	ADP
ejpam-1950	120	39	every	every	DET
ejpam-1950	120	40	x	x	SYM
ejpam-1950	120	41	∈	∈	PROPN
ejpam-1950	120	42	x	x	X
ejpam-1950	120	43	.	.	PUNCT
ejpam-1950	121	1	in	in	ADP
ejpam-1950	121	2	the	the	DET
ejpam-1950	121	3	special	special	ADJ
ejpam-1950	121	4	case	case	NOUN
ejpam-1950	122	1	i	i	PRON
ejpam-1950	122	2	=	=	PRON
ejpam-1950	123	1	it	it	PRON
ejpam-1950	123	2	we	we	PRON
ejpam-1950	123	3	get	get	VERB
ejpam-1950	123	4	the	the	DET
ejpam-1950	123	5	notion	notion	NOUN
ejpam-1950	123	6	of	of	ADP
ejpam-1950	123	7	b∗t	b∗t	ADJ
ejpam-1950	123	8	-	-	PUNCT
ejpam-1950	123	9	statistical	statistical	ADJ
ejpam-1950	123	10	convergence	convergence	NOUN
ejpam-1950	123	11	.	.	PUNCT
ejpam-1950	124	1	the	the	DET
ejpam-1950	124	2	b∗i	b∗i	ADJ
ejpam-1950	124	3	-limit	-limit	NOUN
ejpam-1950	124	4	and	and	CCONJ
ejpam-1950	124	5	the	the	DET
ejpam-1950	124	6	b∗t	b∗t	NUM
ejpam-1950	124	7	-	-	PUNCT
ejpam-1950	124	8	statistical	statistical	ADJ
ejpam-1950	124	9	limit	limit	NOUN
ejpam-1950	124	10	of	of	ADP
ejpam-1950	124	11	(	(	PUNCT
ejpam-1950	124	12	an	an	X
ejpam-1950	124	13	)	)	PUNCT
ejpam-1950	124	14	are	be	AUX
ejpam-1950	124	15	denoted	denote	VERB
ejpam-1950	124	16	,	,	PUNCT
ejpam-1950	124	17	respectively	respectively	ADV
ejpam-1950	124	18	,	,	PUNCT
ejpam-1950	124	19	by	by	ADP
ejpam-1950	124	20	b∗i	b∗i	PUNCT
ejpam-1950	124	21	limn	limn	NOUN
ejpam-1950	124	22	an	an	PRON
ejpam-1950	124	23	and	and	CCONJ
ejpam-1950	124	24	b∗stt	b∗stt	PROPN
ejpam-1950	124	25	limn	limn	NOUN
ejpam-1950	124	26	an	an	PROPN
ejpam-1950	124	27	.	.	PUNCT
ejpam-1950	125	1	in	in	ADP
ejpam-1950	125	2	view	view	NOUN
ejpam-1950	125	3	of	of	ADP
ejpam-1950	125	4	theorem	theorem	NOUN
ejpam-1950	125	5	1	1	NUM
ejpam-1950	125	6	we	we	PRON
ejpam-1950	125	7	can	can	AUX
ejpam-1950	125	8	say	say	VERB
ejpam-1950	125	9	that	that	SCONJ
ejpam-1950	125	10	a	a	DET
ejpam-1950	125	11	sequence	sequence	NOUN
ejpam-1950	125	12	(	(	PUNCT
ejpam-1950	125	13	an	an	NOUN
ejpam-1950	125	14	)	)	PUNCT
ejpam-1950	125	15	is	be	AUX
ejpam-1950	125	16	b∗i	b∗i	ADJ
ejpam-1950	125	17	-convergent	-convergent	ADJ
ejpam-1950	125	18	if	if	SCONJ
ejpam-1950	125	19	and	and	CCONJ
ejpam-1950	126	1	only	only	ADV
ejpam-1950	126	2	if	if	SCONJ
ejpam-1950	126	3	i	i	PRON
ejpam-1950	126	4	-lim	-lim	X
ejpam-1950	126	5	an	an	DET
ejpam-1950	126	6	x	x	VERB
ejpam-1950	126	7	exists	exist	VERB
ejpam-1950	126	8	for	for	ADP
ejpam-1950	126	9	any	any	DET
ejpam-1950	126	10	x	x	SYM
ejpam-1950	126	11	∈	∈	PROPN
ejpam-1950	126	12	x	x	X
ejpam-1950	126	13	and	and	CCONJ
ejpam-1950	126	14	sup	sup	NOUN
ejpam-1950	126	15	k∈k	k∈k	NOUN
ejpam-1950	126	16	‖ak‖)<∞	‖ak‖)<∞	NOUN
ejpam-1950	126	17	for	for	ADP
ejpam-1950	126	18	some	some	DET
ejpam-1950	126	19	k	k	PROPN
ejpam-1950	126	20	∈	∈	PROPN
ejpam-1950	126	21	f	f	X
ejpam-1950	126	22	(	(	PUNCT
ejpam-1950	126	23	i	i	NOUN
ejpam-1950	126	24	)	)	PUNCT
ejpam-1950	126	25	.	.	PUNCT
ejpam-1950	127	1	(	(	PUNCT
ejpam-1950	127	2	2	2	X
ejpam-1950	127	3	)	)	PUNCT
ejpam-1950	127	4	theorem	theorem	NOUN
ejpam-1950	127	5	3	3	NUM
ejpam-1950	127	6	shows	show	VERB
ejpam-1950	127	7	that	that	SCONJ
ejpam-1950	127	8	bi	bi	PROPN
ejpam-1950	127	9	-convergence	-convergence	PROPN
ejpam-1950	127	10	implies	imply	VERB
ejpam-1950	127	11	b∗i	b∗i	ADJ
ejpam-1950	127	12	-convergence	-convergence	NOUN
ejpam-1950	127	13	by	by	ADP
ejpam-1950	127	14	the	the	DET
ejpam-1950	127	15	suppositions	supposition	NOUN
ejpam-1950	127	16	that	that	SCONJ
ejpam-1950	127	17	x	x	PRON
ejpam-1950	127	18	is	be	AUX
ejpam-1950	127	19	separable	separable	ADJ
ejpam-1950	127	20	and	and	CCONJ
ejpam-1950	127	21	i	i	PRON
ejpam-1950	127	22	satisfies	satisfy	VERB
ejpam-1950	127	23	the	the	DET
ejpam-1950	127	24	condition	condition	NOUN
ejpam-1950	127	25	(	(	PUNCT
ejpam-1950	127	26	ap	ap	PROPN
ejpam-1950	127	27	)	)	PUNCT
ejpam-1950	127	28	.	.	PUNCT
ejpam-1950	128	1	to	to	PART
ejpam-1950	128	2	prove	prove	VERB
ejpam-1950	128	3	our	our	PRON
ejpam-1950	128	4	main	main	ADJ
ejpam-1950	128	5	theorem	theorem	NOUN
ejpam-1950	128	6	we	we	PRON
ejpam-1950	128	7	need	need	VERB
ejpam-1950	128	8	the	the	DET
ejpam-1950	128	9	following	follow	VERB
ejpam-1950	128	10	lemma	lemma	PROPN
ejpam-1950	128	11	.	.	PUNCT
ejpam-1950	129	1	lemma	lemma	PROPN
ejpam-1950	129	2	1	1	NUM
ejpam-1950	129	3	.	.	PUNCT
ejpam-1950	129	4	suppose	suppose	VERB
ejpam-1950	129	5	that	that	SCONJ
ejpam-1950	129	6	the	the	DET
ejpam-1950	129	7	ideal	ideal	NOUN
ejpam-1950	129	8	i	i	PRON
ejpam-1950	129	9	has	have	VERB
ejpam-1950	129	10	property	property	NOUN
ejpam-1950	129	11	(	(	PUNCT
ejpam-1950	129	12	ap	ap	PROPN
ejpam-1950	129	13	)	)	PUNCT
ejpam-1950	129	14	and	and	CCONJ
ejpam-1950	129	15	let	let	VERB
ejpam-1950	129	16	zk	zk	PROPN
ejpam-1950	129	17	j	j	PROPN
ejpam-1950	129	18	∈	∈	PROPN
ejpam-1950	129	19	x	x	X
ejpam-1950	129	20	(	(	PUNCT
ejpam-1950	129	21	k	k	NOUN
ejpam-1950	129	22	,	,	PUNCT
ejpam-1950	129	23	j	j	PROPN
ejpam-1950	129	24	∈	∈	PROPN
ejpam-1950	129	25	n	n	CCONJ
ejpam-1950	129	26	)	)	PUNCT
ejpam-1950	129	27	.	.	PUNCT
ejpam-1950	130	1	if	if	SCONJ
ejpam-1950	130	2	i	i	PRON
ejpam-1950	130	3	-limk	-limk	VERB
ejpam-1950	130	4	zk	zk	PROPN
ejpam-1950	130	5	j	j	PROPN
ejpam-1950	130	6	=	=	PROPN
ejpam-1950	130	7	z	z	PROPN
ejpam-1950	130	8	j	j	PROPN
ejpam-1950	130	9	for	for	ADP
ejpam-1950	130	10	any	any	DET
ejpam-1950	130	11	j	j	PROPN
ejpam-1950	130	12	∈	∈	PROPN
ejpam-1950	130	13	n	n	CCONJ
ejpam-1950	130	14	,	,	PUNCT
ejpam-1950	130	15	then	then	ADV
ejpam-1950	130	16	there	there	PRON
ejpam-1950	130	17	exists	exist	VERB
ejpam-1950	130	18	an	an	DET
ejpam-1950	130	19	index	index	NOUN
ejpam-1950	130	20	set	set	VERB
ejpam-1950	130	21	n	n	NOUN
ejpam-1950	130	22	=	=	SYM
ejpam-1950	130	23	(	(	PUNCT
ejpam-1950	130	24	ni	ni	PROPN
ejpam-1950	130	25	)	)	PUNCT
ejpam-1950	130	26	such	such	ADJ
ejpam-1950	130	27	that	that	SCONJ
ejpam-1950	130	28	n	n	NUM
ejpam-1950	130	29	∈	∈	PROPN
ejpam-1950	130	30	f	f	X
ejpam-1950	130	31	(	(	PUNCT
ejpam-1950	130	32	i	i	NOUN
ejpam-1950	130	33	)	)	PUNCT
ejpam-1950	130	34	and	and	CCONJ
ejpam-1950	130	35	limi	limi	VERB
ejpam-1950	130	36	zni	zni	PROPN
ejpam-1950	130	37	,	,	PUNCT
ejpam-1950	130	38	j	j	PROPN
ejpam-1950	130	39	=	=	SYM
ejpam-1950	130	40	z	z	PROPN
ejpam-1950	130	41	j	j	PROPN
ejpam-1950	130	42	for	for	ADP
ejpam-1950	130	43	any	any	DET
ejpam-1950	130	44	j	j	PROPN
ejpam-1950	130	45	∈	∈	PROPN
ejpam-1950	130	46	n.	n.	NOUN
ejpam-1950	130	47	proof	proof	NOUN
ejpam-1950	130	48	.	.	PUNCT
ejpam-1950	131	1	assume	assume	VERB
ejpam-1950	131	2	that	that	SCONJ
ejpam-1950	131	3	i	i	PRON
ejpam-1950	131	4	-limk	-limk	VERB
ejpam-1950	131	5	zk	zk	PROPN
ejpam-1950	131	6	j	j	PROPN
ejpam-1950	132	1	=	=	SYM
ejpam-1950	132	2	z	z	PROPN
ejpam-1950	132	3	j	j	PROPN
ejpam-1950	132	4	(	(	PUNCT
ejpam-1950	132	5	j	j	PROPN
ejpam-1950	132	6	∈	∈	PROPN
ejpam-1950	132	7	n	n	CCONJ
ejpam-1950	132	8	)	)	PUNCT
ejpam-1950	132	9	.	.	PUNCT
ejpam-1950	133	1	since	since	SCONJ
ejpam-1950	133	2	i	i	PRON
ejpam-1950	133	3	has	have	VERB
ejpam-1950	133	4	property	property	NOUN
ejpam-1950	133	5	(	(	PUNCT
ejpam-1950	133	6	ap	ap	PROPN
ejpam-1950	133	7	)	)	PUNCT
ejpam-1950	133	8	,	,	PUNCT
ejpam-1950	133	9	by	by	ADP
ejpam-1950	133	10	proposition	proposition	NOUN
ejpam-1950	133	11	1	1	NUM
ejpam-1950	133	12	there	there	PRON
ejpam-1950	133	13	exist	exist	VERB
ejpam-1950	133	14	index	index	NOUN
ejpam-1950	133	15	sets	set	VERB
ejpam-1950	134	1	k	k	PROPN
ejpam-1950	134	2	j	j	PROPN
ejpam-1950	135	1	=	=	PRON
ejpam-1950	135	2	{	{	PUNCT
ejpam-1950	135	3	ki	ki	PROPN
ejpam-1950	135	4	(	(	PUNCT
ejpam-1950	135	5	j	j	NOUN
ejpam-1950	135	6	)	)	PUNCT
ejpam-1950	135	7	}	}	PUNCT
ejpam-1950	135	8	(	(	PUNCT
ejpam-1950	135	9	j	j	PROPN
ejpam-1950	135	10	∈	∈	PROPN
ejpam-1950	135	11	n	n	CCONJ
ejpam-1950	135	12	)	)	PUNCT
ejpam-1950	135	13	such	such	ADJ
ejpam-1950	135	14	that	that	SCONJ
ejpam-1950	135	15	lim	lim	PROPN
ejpam-1950	135	16	i	i	PRON
ejpam-1950	135	17	zki	zki	VERB
ejpam-1950	135	18	(	(	PUNCT
ejpam-1950	135	19	j	j	PROPN
ejpam-1950	135	20	)	)	PUNCT
ejpam-1950	135	21	,	,	PUNCT
ejpam-1950	135	22	j	j	X
ejpam-1950	135	23	=	=	SYM
ejpam-1950	135	24	z	z	PROPN
ejpam-1950	135	25	j	j	PROPN
ejpam-1950	135	26	(	(	PUNCT
ejpam-1950	135	27	j	j	PROPN
ejpam-1950	135	28	∈	∈	PROPN
ejpam-1950	135	29	n	n	CCONJ
ejpam-1950	135	30	)	)	PUNCT
ejpam-1950	135	31	(	(	PUNCT
ejpam-1950	135	32	3	3	X
ejpam-1950	135	33	)	)	PUNCT
ejpam-1950	135	34	and	and	CCONJ
ejpam-1950	135	35	k	k	PROPN
ejpam-1950	136	1	′	′	NUM
ejpam-1950	136	2	j	j	PROPN
ejpam-1950	136	3	=	=	PUNCT
ejpam-1950	136	4	n	n	PROPN
ejpam-1950	136	5	\	\	NOUN
ejpam-1950	136	6	k	k	PROPN
ejpam-1950	136	7	j	j	PROPN
ejpam-1950	136	8	∈	∈	PROPN
ejpam-1950	137	1	i	i	PRON
ejpam-1950	137	2	for	for	ADP
ejpam-1950	137	3	any	any	DET
ejpam-1950	137	4	j	j	PROPN
ejpam-1950	137	5	∈	∈	PROPN
ejpam-1950	137	6	n.	n.	NOUN
ejpam-1950	137	7	because	because	SCONJ
ejpam-1950	137	8	of	of	ADP
ejpam-1950	137	9	remark	remark	NOUN
ejpam-1950	137	10	1	1	NUM
ejpam-1950	137	11	we	we	PRON
ejpam-1950	137	12	can	can	AUX
ejpam-1950	137	13	find	find	VERB
ejpam-1950	137	14	the	the	DET
ejpam-1950	137	15	set	set	NOUN
ejpam-1950	137	16	n	n	NOUN
ejpam-1950	137	17	′	′	NUM
ejpam-1950	137	18	∈	∈	NOUN
ejpam-1950	138	1	i	i	PRON
ejpam-1950	138	2	such	such	ADJ
ejpam-1950	138	3	that	that	SCONJ
ejpam-1950	138	4	the	the	DET
ejpam-1950	138	5	differences	difference	NOUN
ejpam-1950	138	6	k	k	NOUN
ejpam-1950	138	7	′	′	NUM
ejpam-1950	138	8	j	j	NOUN
ejpam-1950	138	9	\	\	PROPN
ejpam-1950	139	1	n	n	CCONJ
ejpam-1950	139	2	′	′	NUM
ejpam-1950	139	3	(	(	PUNCT
ejpam-1950	139	4	j	j	PROPN
ejpam-1950	139	5	∈	∈	PROPN
ejpam-1950	139	6	n	n	CCONJ
ejpam-1950	139	7	)	)	PUNCT
ejpam-1950	139	8	are	be	AUX
ejpam-1950	139	9	finite	finite	ADJ
ejpam-1950	139	10	.	.	PUNCT
ejpam-1950	140	1	now	now	ADV
ejpam-1950	140	2	,	,	PUNCT
ejpam-1950	140	3	for	for	ADP
ejpam-1950	140	4	n	n	NOUN
ejpam-1950	140	5	=	=	SYM
ejpam-1950	140	6	n	n	CCONJ
ejpam-1950	140	7	\	\	NOUN
ejpam-1950	140	8	n	n	CCONJ
ejpam-1950	140	9	′	′	NOUN
ejpam-1950	140	10	we	we	PRON
ejpam-1950	140	11	have	have	VERB
ejpam-1950	140	12	that	that	PRON
ejpam-1950	140	13	n	n	PROPN
ejpam-1950	140	14	∈	∈	PROPN
ejpam-1950	140	15	f	f	X
ejpam-1950	140	16	(	(	PUNCT
ejpam-1950	140	17	i	i	NOUN
ejpam-1950	140	18	)	)	PUNCT
ejpam-1950	140	19	and	and	CCONJ
ejpam-1950	140	20	the	the	DET
ejpam-1950	140	21	differences	difference	NOUN
ejpam-1950	140	22	n	n	PRON
ejpam-1950	140	23	\k	\k	NOUN
ejpam-1950	140	24	j	j	PROPN
ejpam-1950	140	25	are	be	AUX
ejpam-1950	140	26	finite	finite	ADJ
ejpam-1950	140	27	.	.	PUNCT
ejpam-1950	141	1	consequently	consequently	ADV
ejpam-1950	141	2	,	,	PUNCT
ejpam-1950	141	3	denoting	denote	VERB
ejpam-1950	141	4	n	n	X
ejpam-1950	141	5	=	=	SYM
ejpam-1950	141	6	(	(	PUNCT
ejpam-1950	141	7	ni	ni	NOUN
ejpam-1950	141	8	)	)	PUNCT
ejpam-1950	141	9	,	,	PUNCT
ejpam-1950	141	10	from	from	ADP
ejpam-1950	141	11	(	(	PUNCT
ejpam-1950	141	12	3	3	X
ejpam-1950	141	13	)	)	PUNCT
ejpam-1950	141	14	it	it	PRON
ejpam-1950	141	15	follows	follow	VERB
ejpam-1950	141	16	that	that	SCONJ
ejpam-1950	141	17	limi	limi	NOUN
ejpam-1950	141	18	zni	zni	PROPN
ejpam-1950	141	19	,	,	PUNCT
ejpam-1950	141	20	j	j	PROPN
ejpam-1950	141	21	=	=	SYM
ejpam-1950	141	22	z	z	PROPN
ejpam-1950	141	23	j	j	PROPN
ejpam-1950	141	24	for	for	ADP
ejpam-1950	141	25	any	any	DET
ejpam-1950	141	26	j	j	PROPN
ejpam-1950	141	27	∈	∈	PROPN
ejpam-1950	141	28	n.	n.	PROPN
ejpam-1950	141	29	theorem	theorem	VERB
ejpam-1950	141	30	4	4	NUM
ejpam-1950	141	31	.	.	PUNCT
ejpam-1950	142	1	let	let	VERB
ejpam-1950	142	2	x	x	PRON
ejpam-1950	142	3	and	and	CCONJ
ejpam-1950	142	4	y	y	PROPN
ejpam-1950	142	5	be	be	AUX
ejpam-1950	142	6	two	two	NUM
ejpam-1950	142	7	banach	banach	NOUN
ejpam-1950	142	8	spaces	space	NOUN
ejpam-1950	142	9	,	,	PUNCT
ejpam-1950	142	10	where	where	SCONJ
ejpam-1950	142	11	x	x	PRON
ejpam-1950	142	12	has	have	VERB
ejpam-1950	142	13	a	a	DET
ejpam-1950	142	14	countable	countable	ADJ
ejpam-1950	142	15	fundamental	fundamental	ADJ
ejpam-1950	142	16	set	set	NOUN
ejpam-1950	142	17	φ	φ	NOUN
ejpam-1950	142	18	.	.	PUNCT
ejpam-1950	143	1	if	if	SCONJ
ejpam-1950	143	2	the	the	DET
ejpam-1950	143	3	ideal	ideal	NOUN
ejpam-1950	143	4	i	i	PRON
ejpam-1950	143	5	has	have	VERB
ejpam-1950	143	6	property	property	NOUN
ejpam-1950	143	7	(	(	PUNCT
ejpam-1950	143	8	ap	ap	PROPN
ejpam-1950	143	9	)	)	PUNCT
ejpam-1950	143	10	.	.	PUNCT
ejpam-1950	144	1	a	a	DET
ejpam-1950	144	2	sequence	sequence	NOUN
ejpam-1950	144	3	(	(	PUNCT
ejpam-1950	144	4	an	an	NOUN
ejpam-1950	144	5	)	)	PUNCT
ejpam-1950	144	6	of	of	ADP
ejpam-1950	144	7	operators	operator	NOUN
ejpam-1950	144	8	an	an	DET
ejpam-1950	144	9	∈	∈	NOUN
ejpam-1950	144	10	b(x	b(x	NOUN
ejpam-1950	144	11	,	,	PUNCT
ejpam-1950	144	12	y	y	PROPN
ejpam-1950	144	13	)	)	PUNCT
ejpam-1950	144	14	is	be	AUX
ejpam-1950	144	15	b∗i	b∗i	ADJ
ejpam-1950	144	16	-convergent	-convergent	ADJ
ejpam-1950	144	17	if	if	SCONJ
ejpam-1950	144	18	and	and	CCONJ
ejpam-1950	144	19	only	only	ADV
ejpam-1950	144	20	if	if	SCONJ
ejpam-1950	144	21	(	(	PUNCT
ejpam-1950	144	22	‖an‖	‖an‖	PROPN
ejpam-1950	144	23	)	)	PUNCT
ejpam-1950	144	24	is	be	AUX
ejpam-1950	144	25	i	i	PRON
ejpam-1950	144	26	-bounded	-bounded	ADJ
ejpam-1950	144	27	,	,	PUNCT
ejpam-1950	144	28	i.e.	i.e.	X
ejpam-1950	144	29	,	,	PUNCT
ejpam-1950	144	30	(	(	PUNCT
ejpam-1950	144	31	2	2	X
ejpam-1950	144	32	)	)	PUNCT
ejpam-1950	144	33	holds	hold	NOUN
ejpam-1950	144	34	,	,	PUNCT
ejpam-1950	144	35	and	and	CCONJ
ejpam-1950	144	36	(	(	PUNCT
ejpam-1950	144	37	anφ	anφ	ADJ
ejpam-1950	144	38	)	)	PUNCT
ejpam-1950	144	39	is	be	AUX
ejpam-1950	144	40	i	i	PRON
ejpam-1950	144	41	-convergent	-convergent	ADJ
ejpam-1950	144	42	for	for	ADP
ejpam-1950	144	43	every	every	DET
ejpam-1950	144	44	φ	φ	PROPN
ejpam-1950	144	45	∈	∈	PROPN
ejpam-1950	144	46	φ	φ	PROPN
ejpam-1950	144	47	.	.	PUNCT
ejpam-1950	145	1	thereby	thereby	ADV
ejpam-1950	145	2	,	,	PUNCT
ejpam-1950	145	3	the	the	DET
ejpam-1950	145	4	limit	limit	NOUN
ejpam-1950	145	5	operator	operator	NOUN
ejpam-1950	145	6	a0	a0	NOUN
ejpam-1950	145	7	,	,	PUNCT
ejpam-1950	145	8	a0	a0	NOUN
ejpam-1950	145	9	x	x	PUNCT
ejpam-1950	146	1	=	=	PUNCT
ejpam-1950	146	2	i	i	PRON
ejpam-1950	146	3	-lim	-lim	PUNCT
ejpam-1950	146	4	an	an	DET
ejpam-1950	146	5	x	x	NOUN
ejpam-1950	146	6	,	,	PUNCT
ejpam-1950	146	7	is	be	AUX
ejpam-1950	146	8	bounded	bound	VERB
ejpam-1950	146	9	and	and	CCONJ
ejpam-1950	146	10	linear	linear	ADJ
ejpam-1950	146	11	,	,	PUNCT
ejpam-1950	146	12	and	and	CCONJ
ejpam-1950	146	13	‖a0‖	‖a0‖	SCONJ
ejpam-1950	146	14	≤	≤	ADJ
ejpam-1950	146	15	supk∈k	supk∈k	NOUN
ejpam-1950	146	16	‖ak‖.	‖ak‖.	NOUN
ejpam-1950	146	17	if	if	SCONJ
ejpam-1950	146	18	a	a	DET
ejpam-1950	146	19	∈	∈	PROPN
ejpam-1950	146	20	b(x	b(x	NOUN
ejpam-1950	146	21	,	,	PUNCT
ejpam-1950	146	22	y	y	PROPN
ejpam-1950	146	23	)	)	PUNCT
ejpam-1950	146	24	,	,	PUNCT
ejpam-1950	147	1	then	then	ADV
ejpam-1950	147	2	b∗i	b∗i	VERB
ejpam-1950	147	3	limn	limn	NOUN
ejpam-1950	147	4	an	an	DET
ejpam-1950	147	5	=	=	X
ejpam-1950	147	6	a	a	DET
ejpam-1950	147	7	if	if	NOUN
ejpam-1950	147	8	and	and	CCONJ
ejpam-1950	147	9	only	only	ADV
ejpam-1950	147	10	if	if	SCONJ
ejpam-1950	147	11	(	(	PUNCT
ejpam-1950	147	12	‖an‖	‖an‖	PROPN
ejpam-1950	147	13	)	)	PUNCT
ejpam-1950	147	14	is	be	AUX
ejpam-1950	147	15	i	i	PRON
ejpam-1950	147	16	-bounded	-bounded	ADJ
ejpam-1950	148	1	and	and	CCONJ
ejpam-1950	148	2	i	i	PRON
ejpam-1950	148	3	limn	limn	NOUN
ejpam-1950	148	4	anφ	anφ	PROPN
ejpam-1950	148	5	=	=	SYM
ejpam-1950	148	6	aφ	aφ	X
ejpam-1950	148	7	(	(	PUNCT
ejpam-1950	148	8	φ	φ	PROPN
ejpam-1950	148	9	∈	∈	PROPN
ejpam-1950	148	10	φ	φ	PROPN
ejpam-1950	148	11	)	)	PUNCT
ejpam-1950	148	12	.	.	PUNCT
ejpam-1950	149	1	e.	e.	PROPN
ejpam-1950	149	2	kolk	kolk	PROPN
ejpam-1950	149	3	/	/	SYM
ejpam-1950	149	4	eur	eur	PROPN
ejpam-1950	149	5	.	.	PUNCT
ejpam-1950	150	1	j.	j.	PROPN
ejpam-1950	150	2	pure	pure	PROPN
ejpam-1950	150	3	appl	appl	PROPN
ejpam-1950	150	4	.	.	PROPN
ejpam-1950	150	5	math	math	PROPN
ejpam-1950	150	6	,	,	PUNCT
ejpam-1950	150	7	8	8	NUM
ejpam-1950	150	8	(	(	PUNCT
ejpam-1950	150	9	2015	2015	NUM
ejpam-1950	150	10	)	)	PUNCT
ejpam-1950	150	11	,	,	PUNCT
ejpam-1950	150	12	357	357	NUM
ejpam-1950	150	13	-	-	SYM
ejpam-1950	150	14	367	367	NUM
ejpam-1950	150	15	361	361	NUM
ejpam-1950	150	16	proof	proof	NOUN
ejpam-1950	150	17	.	.	PUNCT
ejpam-1950	151	1	if	if	SCONJ
ejpam-1950	151	2	(	(	PUNCT
ejpam-1950	151	3	an	an	X
ejpam-1950	151	4	)	)	PUNCT
ejpam-1950	151	5	is	be	AUX
ejpam-1950	151	6	b∗i	b∗i	ADJ
ejpam-1950	151	7	-convergent	-convergent	ADJ
ejpam-1950	151	8	(	(	PUNCT
ejpam-1950	151	9	b∗i	b∗i	X
ejpam-1950	151	10	limn	limn	NOUN
ejpam-1950	151	11	an	an	DET
ejpam-1950	151	12	=	=	PUNCT
ejpam-1950	151	13	a	a	NOUN
ejpam-1950	151	14	)	)	PUNCT
ejpam-1950	151	15	,	,	PUNCT
ejpam-1950	151	16	then	then	ADV
ejpam-1950	151	17	(	(	PUNCT
ejpam-1950	151	18	2	2	X
ejpam-1950	151	19	)	)	PUNCT
ejpam-1950	151	20	is	be	AUX
ejpam-1950	151	21	satisfied	satisfied	ADJ
ejpam-1950	151	22	and	and	CCONJ
ejpam-1950	151	23	i	i	PRON
ejpam-1950	151	24	-lim	-lim	AUX
ejpam-1950	151	25	anφ	anφ	VERB
ejpam-1950	151	26	exists	exist	VERB
ejpam-1950	151	27	(	(	PUNCT
ejpam-1950	151	28	i	i	NOUN
ejpam-1950	151	29	-lim	-lim	NOUN
ejpam-1950	151	30	anφ	anφ	NOUN
ejpam-1950	151	31	=	=	SYM
ejpam-1950	151	32	aφ	aφ	NOUN
ejpam-1950	151	33	)	)	PUNCT
ejpam-1950	151	34	for	for	ADP
ejpam-1950	151	35	every	every	DET
ejpam-1950	151	36	φ	φ	PROPN
ejpam-1950	151	37	∈	∈	PROPN
ejpam-1950	151	38	φ	φ	NOUN
ejpam-1950	151	39	.	.	PUNCT
ejpam-1950	152	1	conversely	conversely	ADV
ejpam-1950	152	2	,	,	PUNCT
ejpam-1950	152	3	assume	assume	VERB
ejpam-1950	152	4	that	that	SCONJ
ejpam-1950	152	5	(	(	PUNCT
ejpam-1950	152	6	2	2	X
ejpam-1950	152	7	)	)	PUNCT
ejpam-1950	152	8	holds	hold	VERB
ejpam-1950	152	9	and	and	CCONJ
ejpam-1950	152	10	i	i	PRON
ejpam-1950	152	11	-lim	-lim	AUX
ejpam-1950	152	12	anφ	anφ	PRON
ejpam-1950	152	13	j	j	PROPN
ejpam-1950	152	14	exists	exist	VERB
ejpam-1950	152	15	(	(	PUNCT
ejpam-1950	152	16	or	or	CCONJ
ejpam-1950	152	17	i	i	PRON
ejpam-1950	152	18	-lim	-lim	AUX
ejpam-1950	152	19	anφ	anφ	PROPN
ejpam-1950	153	1	j	j	PROPN
ejpam-1950	153	2	=	=	SYM
ejpam-1950	153	3	aφ	aφ	PROPN
ejpam-1950	153	4	j	j	PROPN
ejpam-1950	153	5	)	)	PUNCT
ejpam-1950	153	6	for	for	ADP
ejpam-1950	153	7	every	every	DET
ejpam-1950	153	8	j	j	PROPN
ejpam-1950	153	9	∈	∈	PROPN
ejpam-1950	153	10	n	n	CCONJ
ejpam-1950	153	11	,	,	PUNCT
ejpam-1950	153	12	where	where	SCONJ
ejpam-1950	153	13	φ	φ	PROPN
ejpam-1950	153	14	=	=	SYM
ejpam-1950	153	15	{	{	PUNCT
ejpam-1950	153	16	φ	φ	PROPN
ejpam-1950	153	17	j	j	PROPN
ejpam-1950	153	18	}	}	PUNCT
ejpam-1950	153	19	.	.	PUNCT
ejpam-1950	154	1	applying	apply	VERB
ejpam-1950	154	2	lemma	lemma	PROPN
ejpam-1950	154	3	1	1	NUM
ejpam-1950	154	4	to	to	ADP
ejpam-1950	154	5	zn	zn	PROPN
ejpam-1950	154	6	j	j	PROPN
ejpam-1950	154	7	=	=	SYM
ejpam-1950	154	8	anφ	anφ	PROPN
ejpam-1950	154	9	j	j	PROPN
ejpam-1950	154	10	(	(	PUNCT
ejpam-1950	154	11	and	and	CCONJ
ejpam-1950	154	12	z	z	NOUN
ejpam-1950	154	13	j	j	PROPN
ejpam-1950	154	14	=	=	SYM
ejpam-1950	154	15	aφ	aφ	PROPN
ejpam-1950	154	16	j	j	PROPN
ejpam-1950	154	17	)	)	PUNCT
ejpam-1950	154	18	,	,	PUNCT
ejpam-1950	154	19	we	we	PRON
ejpam-1950	154	20	fix	fix	VERB
ejpam-1950	154	21	an	an	DET
ejpam-1950	154	22	index	index	NOUN
ejpam-1950	154	23	set	set	VERB
ejpam-1950	154	24	n	n	NOUN
ejpam-1950	155	1	=	=	SYM
ejpam-1950	155	2	(	(	PUNCT
ejpam-1950	155	3	ni	ni	PROPN
ejpam-1950	155	4	)	)	PUNCT
ejpam-1950	155	5	∈	∈	PROPN
ejpam-1950	155	6	f	f	X
ejpam-1950	155	7	(	(	PUNCT
ejpam-1950	155	8	i	i	NOUN
ejpam-1950	155	9	)	)	PUNCT
ejpam-1950	155	10	such	such	ADJ
ejpam-1950	155	11	that	that	DET
ejpam-1950	155	12	limi	limi	PROPN
ejpam-1950	155	13	ani	ani	PROPN
ejpam-1950	155	14	φ	φ	PROPN
ejpam-1950	155	15	j	j	PROPN
ejpam-1950	155	16	exists	exist	VERB
ejpam-1950	155	17	(	(	PUNCT
ejpam-1950	155	18	limi	limi	PROPN
ejpam-1950	155	19	ani	ani	X
ejpam-1950	155	20	φ	φ	PROPN
ejpam-1950	155	21	j	j	PROPN
ejpam-1950	155	22	=	=	PUNCT
ejpam-1950	155	23	aφ	aφ	PROPN
ejpam-1950	155	24	j	j	PROPN
ejpam-1950	155	25	)	)	PUNCT
ejpam-1950	155	26	for	for	ADP
ejpam-1950	155	27	any	any	DET
ejpam-1950	155	28	j	j	PROPN
ejpam-1950	155	29	∈	∈	PROPN
ejpam-1950	155	30	n.	n.	NOUN
ejpam-1950	155	31	since	since	SCONJ
ejpam-1950	155	32	the	the	DET
ejpam-1950	155	33	set	set	NOUN
ejpam-1950	155	34	m	m	PROPN
ejpam-1950	155	35	=	=	SYM
ejpam-1950	155	36	n	n	PROPN
ejpam-1950	155	37	∩	∩	NOUN
ejpam-1950	155	38	k	k	PROPN
ejpam-1950	155	39	also	also	ADV
ejpam-1950	155	40	belongs	belong	VERB
ejpam-1950	155	41	to	to	ADP
ejpam-1950	155	42	f	f	PROPN
ejpam-1950	155	43	(	(	PUNCT
ejpam-1950	155	44	i	i	NOUN
ejpam-1950	155	45	)	)	PUNCT
ejpam-1950	155	46	,	,	PUNCT
ejpam-1950	155	47	denoting	denote	VERB
ejpam-1950	155	48	m	m	PROPN
ejpam-1950	155	49	=	=	SYM
ejpam-1950	155	50	(	(	PUNCT
ejpam-1950	155	51	mi	mi	PROPN
ejpam-1950	155	52	)	)	PUNCT
ejpam-1950	155	53	,	,	PUNCT
ejpam-1950	155	54	we	we	PRON
ejpam-1950	155	55	have	have	VERB
ejpam-1950	155	56	that	that	DET
ejpam-1950	155	57	limi	limi	PROPN
ejpam-1950	155	58	ami	ami	PROPN
ejpam-1950	155	59	φ	φ	PROPN
ejpam-1950	155	60	j	j	PROPN
ejpam-1950	155	61	exists	exist	VERB
ejpam-1950	155	62	(	(	PUNCT
ejpam-1950	155	63	limi	limi	PROPN
ejpam-1950	155	64	ami	ami	PROPN
ejpam-1950	155	65	φ	φ	PROPN
ejpam-1950	155	66	j	j	PROPN
ejpam-1950	156	1	=	=	PUNCT
ejpam-1950	156	2	aφ	aφ	PROPN
ejpam-1950	156	3	j	j	PROPN
ejpam-1950	156	4	)	)	PUNCT
ejpam-1950	157	1	for	for	ADP
ejpam-1950	157	2	any	any	DET
ejpam-1950	157	3	j	j	PROPN
ejpam-1950	157	4	∈	∈	PROPN
ejpam-1950	157	5	n	n	ADV
ejpam-1950	157	6	and	and	CCONJ
ejpam-1950	157	7	supi	supi	NOUN
ejpam-1950	157	8	‖ami	‖ami	PROPN
ejpam-1950	158	1	‖<∞.	‖<∞.	ADP
ejpam-1950	158	2	so	so	ADV
ejpam-1950	158	3	,	,	PUNCT
ejpam-1950	158	4	by	by	ADP
ejpam-1950	158	5	theorem	theorem	NOUN
ejpam-1950	158	6	2	2	NUM
ejpam-1950	158	7	,	,	PUNCT
ejpam-1950	158	8	the	the	DET
ejpam-1950	158	9	limit	limit	NOUN
ejpam-1950	158	10	a0	a0	NOUN
ejpam-1950	158	11	x	x	PUNCT
ejpam-1950	158	12	=	=	SYM
ejpam-1950	158	13	limi	limi	NOUN
ejpam-1950	158	14	ami	ami	NOUN
ejpam-1950	158	15	x	x	AUX
ejpam-1950	158	16	exists	exist	VERB
ejpam-1950	158	17	(	(	PUNCT
ejpam-1950	158	18	limi	limi	NOUN
ejpam-1950	158	19	ami	ami	NOUN
ejpam-1950	158	20	x	x	PUNCT
ejpam-1950	158	21	=	=	SYM
ejpam-1950	158	22	ax	ax	NOUN
ejpam-1950	158	23	)	)	PUNCT
ejpam-1950	158	24	for	for	ADP
ejpam-1950	158	25	any	any	DET
ejpam-1950	158	26	x	x	SYM
ejpam-1950	158	27	∈	∈	PROPN
ejpam-1950	158	28	x	x	X
ejpam-1950	158	29	,	,	PUNCT
ejpam-1950	158	30	a0	a0	PROPN
ejpam-1950	158	31	∈	∈	PROPN
ejpam-1950	158	32	b(x	b(x	PROPN
ejpam-1950	158	33	,	,	PUNCT
ejpam-1950	158	34	y	y	PROPN
ejpam-1950	158	35	)	)	PUNCT
ejpam-1950	158	36	and	and	CCONJ
ejpam-1950	158	37	‖a0‖	‖a0‖	SCONJ
ejpam-1950	158	38	≤	≤	NUM
ejpam-1950	158	39	supi	supi	NOUN
ejpam-1950	158	40	‖ami	‖ami	PROPN
ejpam-1950	158	41	‖.	‖.	PROPN
ejpam-1950	158	42	the	the	DET
ejpam-1950	158	43	proof	proof	NOUN
ejpam-1950	158	44	is	be	AUX
ejpam-1950	158	45	completed	complete	VERB
ejpam-1950	158	46	if	if	SCONJ
ejpam-1950	158	47	we	we	PRON
ejpam-1950	158	48	remark	remark	VERB
ejpam-1950	158	49	that	that	SCONJ
ejpam-1950	158	50	limi	limi	NOUN
ejpam-1950	158	51	ami	ami	NOUN
ejpam-1950	158	52	x	x	PUNCT
ejpam-1950	159	1	=	=	VERB
ejpam-1950	159	2	i	i	PRON
ejpam-1950	159	3	lim	lim	PROPN
ejpam-1950	159	4	an	an	X
ejpam-1950	159	5	x	x	PUNCT
ejpam-1950	159	6	by	by	ADP
ejpam-1950	159	7	proposition	proposition	NOUN
ejpam-1950	159	8	1	1	NUM
ejpam-1950	159	9	.	.	PUNCT
ejpam-1950	160	1	it	it	PRON
ejpam-1950	160	2	is	be	AUX
ejpam-1950	160	3	known	know	VERB
ejpam-1950	160	4	that	that	SCONJ
ejpam-1950	160	5	the	the	DET
ejpam-1950	160	6	ideal	ideal	NOUN
ejpam-1950	160	7	it	it	PRON
ejpam-1950	160	8	=	=	PUNCT
ejpam-1950	160	9	{	{	PUNCT
ejpam-1950	160	10	k	k	X
ejpam-1950	160	11	⊂	⊂	PROPN
ejpam-1950	160	12	n	n	X
ejpam-1950	160	13	:	:	PUNCT
ejpam-1950	160	14	δt	δt	X
ejpam-1950	160	15	(	(	PUNCT
ejpam-1950	160	16	k	k	NOUN
ejpam-1950	160	17	)	)	PUNCT
ejpam-1950	160	18	=	=	SYM
ejpam-1950	160	19	0	0	X
ejpam-1950	160	20	}	}	PUNCT
ejpam-1950	160	21	defined	define	VERB
ejpam-1950	160	22	by	by	ADP
ejpam-1950	160	23	a	a	DET
ejpam-1950	160	24	non	non	ADJ
ejpam-1950	160	25	-	-	ADJ
ejpam-1950	160	26	negative	negative	ADJ
ejpam-1950	160	27	regular	regular	ADJ
ejpam-1950	160	28	matrix	matrix	NOUN
ejpam-1950	160	29	t	t	NOUN
ejpam-1950	160	30	has	have	VERB
ejpam-1950	160	31	the	the	DET
ejpam-1950	160	32	property	property	NOUN
ejpam-1950	160	33	(	(	PUNCT
ejpam-1950	160	34	ap	ap	PROPN
ejpam-1950	160	35	)	)	PUNCT
ejpam-1950	160	36	(	(	PUNCT
ejpam-1950	160	37	see	see	VERB
ejpam-1950	160	38	[	[	X
ejpam-1950	160	39	9	9	NUM
ejpam-1950	160	40	,	,	PUNCT
ejpam-1950	160	41	proposition	proposition	NOUN
ejpam-1950	160	42	3.2	3.2	NUM
ejpam-1950	160	43	]	]	PUNCT
ejpam-1950	160	44	)	)	PUNCT
ejpam-1950	160	45	.	.	PUNCT
ejpam-1950	161	1	since	since	SCONJ
ejpam-1950	161	2	it	it	PRON
ejpam-1950	161	3	-convergence	-convergence	PROPN
ejpam-1950	161	4	coincides	coincide	VERB
ejpam-1950	161	5	with	with	ADP
ejpam-1950	161	6	t	t	PROPN
ejpam-1950	161	7	-statistical	-statistical	ADJ
ejpam-1950	161	8	convergence	convergence	NOUN
ejpam-1950	161	9	,	,	PUNCT
ejpam-1950	161	10	from	from	ADP
ejpam-1950	161	11	theorem	theorem	NOUN
ejpam-1950	161	12	4	4	NUM
ejpam-1950	161	13	we	we	PRON
ejpam-1950	161	14	immediately	immediately	ADV
ejpam-1950	161	15	get	get	VERB
ejpam-1950	161	16	the	the	DET
ejpam-1950	161	17	following	follow	VERB
ejpam-1950	161	18	banach	banach	NOUN
ejpam-1950	161	19	–	–	PUNCT
ejpam-1950	161	20	steinhaus	steinhaus	NOUN
ejpam-1950	161	21	type	type	NOUN
ejpam-1950	161	22	theorem	theorem	NOUN
ejpam-1950	161	23	for	for	ADP
ejpam-1950	161	24	b∗t	b∗t	NUM
ejpam-1950	161	25	-statistical	-statistical	ADJ
ejpam-1950	161	26	convergence	convergence	NOUN
ejpam-1950	161	27	.	.	PUNCT
ejpam-1950	162	1	theorem	theorem	NOUN
ejpam-1950	162	2	5	5	NUM
ejpam-1950	162	3	.	.	PUNCT
ejpam-1950	162	4	suppose	suppose	VERB
ejpam-1950	162	5	that	that	SCONJ
ejpam-1950	162	6	t	t	PROPN
ejpam-1950	162	7	is	be	AUX
ejpam-1950	162	8	a	a	DET
ejpam-1950	162	9	non	non	ADJ
ejpam-1950	162	10	-	-	ADJ
ejpam-1950	162	11	negative	negative	ADJ
ejpam-1950	162	12	regular	regular	ADJ
ejpam-1950	162	13	matrix	matrix	NOUN
ejpam-1950	162	14	and	and	CCONJ
ejpam-1950	162	15	x	x	PRON
ejpam-1950	162	16	has	have	VERB
ejpam-1950	162	17	a	a	DET
ejpam-1950	162	18	countable	countable	ADJ
ejpam-1950	162	19	fundamental	fundamental	ADJ
ejpam-1950	162	20	set	set	NOUN
ejpam-1950	162	21	φ	φ	PROPN
ejpam-1950	162	22	.	.	PUNCT
ejpam-1950	163	1	a	a	DET
ejpam-1950	163	2	sequence	sequence	NOUN
ejpam-1950	163	3	(	(	PUNCT
ejpam-1950	163	4	an	an	NOUN
ejpam-1950	163	5	)	)	PUNCT
ejpam-1950	163	6	of	of	ADP
ejpam-1950	163	7	operators	operator	NOUN
ejpam-1950	163	8	an	an	DET
ejpam-1950	163	9	∈	∈	NOUN
ejpam-1950	163	10	b(x	b(x	NOUN
ejpam-1950	163	11	,	,	PUNCT
ejpam-1950	163	12	y	y	PROPN
ejpam-1950	163	13	)	)	PUNCT
ejpam-1950	163	14	is	be	AUX
ejpam-1950	163	15	b∗t	b∗t	NUM
ejpam-1950	163	16	-	-	PUNCT
ejpam-1950	163	17	statistically	statistically	ADV
ejpam-1950	163	18	convergent	convergent	NOUN
ejpam-1950	163	19	if	if	SCONJ
ejpam-1950	163	20	and	and	CCONJ
ejpam-1950	163	21	only	only	ADV
ejpam-1950	163	22	if	if	SCONJ
ejpam-1950	163	23	(	(	PUNCT
ejpam-1950	163	24	2	2	X
ejpam-1950	163	25	)	)	PUNCT
ejpam-1950	163	26	holds	hold	NOUN
ejpam-1950	163	27	and	and	CCONJ
ejpam-1950	163	28	stt	stt	PROPN
ejpam-1950	163	29	-lim	-lim	PUNCT
ejpam-1950	163	30	anφ	anφ	PROPN
ejpam-1950	163	31	exists	exist	VERB
ejpam-1950	163	32	for	for	ADP
ejpam-1950	163	33	any	any	DET
ejpam-1950	163	34	φ	φ	PROPN
ejpam-1950	163	35	∈	∈	PROPN
ejpam-1950	163	36	φ	φ	NOUN
ejpam-1950	163	37	.	.	PUNCT
ejpam-1950	164	1	in	in	ADP
ejpam-1950	164	2	this	this	DET
ejpam-1950	164	3	case	case	NOUN
ejpam-1950	164	4	the	the	DET
ejpam-1950	164	5	limit	limit	NOUN
ejpam-1950	164	6	operator	operator	NOUN
ejpam-1950	164	7	a0	a0	NOUN
ejpam-1950	164	8	,	,	PUNCT
ejpam-1950	164	9	a0	a0	NOUN
ejpam-1950	164	10	x	x	PUNCT
ejpam-1950	165	1	=	=	PUNCT
ejpam-1950	165	2	stt	stt	PROPN
ejpam-1950	165	3	-lim	-lim	X
ejpam-1950	165	4	an	an	X
ejpam-1950	165	5	x	x	X
ejpam-1950	165	6	(	(	PUNCT
ejpam-1950	165	7	x	x	SYM
ejpam-1950	165	8	∈	∈	NOUN
ejpam-1950	165	9	x	x	X
ejpam-1950	165	10	)	)	PUNCT
ejpam-1950	165	11	,	,	PUNCT
ejpam-1950	165	12	belongs	belong	VERB
ejpam-1950	165	13	to	to	ADP
ejpam-1950	165	14	b(x	b(x	PROPN
ejpam-1950	165	15	,	,	PUNCT
ejpam-1950	165	16	y	y	PROPN
ejpam-1950	165	17	)	)	PUNCT
ejpam-1950	165	18	and	and	CCONJ
ejpam-1950	165	19	‖a0‖	‖a0‖	SCONJ
ejpam-1950	165	20	≤	≤	NUM
ejpam-1950	165	21	supk∈k	supk∈k	NOUN
ejpam-1950	165	22	‖ak‖.	‖ak‖.	NOUN
ejpam-1950	165	23	if	if	SCONJ
ejpam-1950	165	24	a	a	DET
ejpam-1950	165	25	∈	∈	PROPN
ejpam-1950	165	26	b(x	b(x	NOUN
ejpam-1950	165	27	,	,	PUNCT
ejpam-1950	165	28	y	y	PROPN
ejpam-1950	165	29	)	)	PUNCT
ejpam-1950	165	30	,	,	PUNCT
ejpam-1950	165	31	then	then	ADV
ejpam-1950	165	32	b∗stt	b∗stt	PROPN
ejpam-1950	165	33	limn	limn	NOUN
ejpam-1950	166	1	an	an	X
ejpam-1950	166	2	=	=	PUNCT
ejpam-1950	166	3	a	a	DET
ejpam-1950	166	4	if	if	NOUN
ejpam-1950	166	5	and	and	CCONJ
ejpam-1950	166	6	only	only	ADV
ejpam-1950	166	7	if	if	SCONJ
ejpam-1950	166	8	(	(	PUNCT
ejpam-1950	166	9	‖an‖	‖an‖	PROPN
ejpam-1950	166	10	)	)	PUNCT
ejpam-1950	166	11	is	be	AUX
ejpam-1950	166	12	i	i	PRON
ejpam-1950	166	13	-bounded	-bounded	ADJ
ejpam-1950	166	14	and	and	CCONJ
ejpam-1950	166	15	stt	stt	PROPN
ejpam-1950	166	16	limn	limn	PROPN
ejpam-1950	166	17	anφ	anφ	PROPN
ejpam-1950	167	1	=	=	SYM
ejpam-1950	167	2	aφ	aφ	X
ejpam-1950	167	3	(	(	PUNCT
ejpam-1950	167	4	φ	φ	PROPN
ejpam-1950	167	5	∈	∈	PROPN
ejpam-1950	167	6	φ	φ	PROPN
ejpam-1950	167	7	)	)	PUNCT
ejpam-1950	167	8	.	.	PUNCT
ejpam-1950	168	1	3	3	X
ejpam-1950	168	2	.	.	X
ejpam-1950	169	1	some	some	DET
ejpam-1950	169	2	applications	application	NOUN
ejpam-1950	169	3	let	let	VERB
ejpam-1950	169	4	λ(x	λ(x	PROPN
ejpam-1950	169	5	)	)	PUNCT
ejpam-1950	169	6	be	be	AUX
ejpam-1950	169	7	a	a	DET
ejpam-1950	169	8	subspace	subspace	NOUN
ejpam-1950	169	9	of	of	ADP
ejpam-1950	169	10	ω(x	ω(x	NUM
ejpam-1950	169	11	)	)	PUNCT
ejpam-1950	169	12	,	,	PUNCT
ejpam-1950	169	13	µ(y	µ(y	PROPN
ejpam-1950	169	14	)	)	PUNCT
ejpam-1950	169	15	a	a	DET
ejpam-1950	169	16	subspaces	subspace	NOUN
ejpam-1950	169	17	of	of	ADP
ejpam-1950	169	18	ω(y	ω(y	PROPN
ejpam-1950	169	19	)	)	PUNCT
ejpam-1950	169	20	and	and	CCONJ
ejpam-1950	169	21	a	a	DET
ejpam-1950	169	22	=	=	SYM
ejpam-1950	169	23	(	(	PUNCT
ejpam-1950	169	24	ank	ank	PROPN
ejpam-1950	169	25	)	)	PUNCT
ejpam-1950	169	26	an	an	DET
ejpam-1950	169	27	infinite	infinite	ADJ
ejpam-1950	169	28	matrix	matrix	NOUN
ejpam-1950	169	29	of	of	ADP
ejpam-1950	169	30	operators	operator	NOUN
ejpam-1950	169	31	ank	ank	PROPN
ejpam-1950	169	32	∈	∈	PROPN
ejpam-1950	169	33	b(x	b(x	PROPN
ejpam-1950	169	34	,	,	PUNCT
ejpam-1950	169	35	y	y	PROPN
ejpam-1950	169	36	)	)	PUNCT
ejpam-1950	169	37	(	(	PUNCT
ejpam-1950	169	38	n	n	X
ejpam-1950	169	39	,	,	PUNCT
ejpam-1950	169	40	k	k	PROPN
ejpam-1950	169	41	∈	∈	PROPN
ejpam-1950	169	42	n	n	CCONJ
ejpam-1950	169	43	)	)	PUNCT
ejpam-1950	169	44	.	.	PUNCT
ejpam-1950	170	1	we	we	PRON
ejpam-1950	170	2	say	say	VERB
ejpam-1950	170	3	that	that	SCONJ
ejpam-1950	170	4	a	a	DET
ejpam-1950	170	5	maps	map	NOUN
ejpam-1950	170	6	λ(x	λ(x	X
ejpam-1950	170	7	)	)	PUNCT
ejpam-1950	170	8	into	into	ADP
ejpam-1950	170	9	µ(y	µ(y	PROPN
ejpam-1950	170	10	)	)	PUNCT
ejpam-1950	170	11	,	,	PUNCT
ejpam-1950	170	12	and	and	CCONJ
ejpam-1950	170	13	write	write	VERB
ejpam-1950	170	14	a	a	DET
ejpam-1950	170	15	:	:	PUNCT
ejpam-1950	170	16	λ(x	λ(x	X
ejpam-1950	170	17	)	)	PUNCT
ejpam-1950	170	18	→µ(y	→µ(y	PROPN
ejpam-1950	170	19	)	)	PUNCT
ejpam-1950	170	20	,	,	PUNCT
ejpam-1950	170	21	if	if	SCONJ
ejpam-1950	170	22	for	for	ADP
ejpam-1950	170	23	all	all	PRON
ejpam-1950	170	24	x	x	X
ejpam-1950	170	25	=	=	SYM
ejpam-1950	170	26	(	(	PUNCT
ejpam-1950	170	27	xk	xk	ADJ
ejpam-1950	170	28	)	)	PUNCT
ejpam-1950	170	29	∈	∈	PROPN
ejpam-1950	170	30	λ(x	λ(x	PROPN
ejpam-1950	170	31	)	)	PUNCT
ejpam-1950	170	32	the	the	DET
ejpam-1950	170	33	series	series	NOUN
ejpam-1950	170	34	anx	anx	PROPN
ejpam-1950	170	35	=	=	PUNCT
ejpam-1950	170	36	∑	∑	PUNCT
ejpam-1950	170	37	k	k	PROPN
ejpam-1950	170	38	ank	ank	PROPN
ejpam-1950	170	39	xk	xk	PROPN
ejpam-1950	170	40	(	(	PUNCT
ejpam-1950	170	41	n	n	CCONJ
ejpam-1950	170	42	∈	∈	PROPN
ejpam-1950	170	43	n	n	CCONJ
ejpam-1950	170	44	)	)	PUNCT
ejpam-1950	170	45	converge	converge	VERB
ejpam-1950	170	46	and	and	CCONJ
ejpam-1950	170	47	the	the	DET
ejpam-1950	170	48	sequence	sequence	NOUN
ejpam-1950	170	49	ax=	ax=	NOUN
ejpam-1950	170	50	(	(	PUNCT
ejpam-1950	170	51	anx	anx	PROPN
ejpam-1950	170	52	)	)	PUNCT
ejpam-1950	170	53	belongs	belong	VERB
ejpam-1950	170	54	to	to	ADP
ejpam-1950	170	55	µ(y	µ(y	PROPN
ejpam-1950	170	56	)	)	PUNCT
ejpam-1950	170	57	.	.	PUNCT
ejpam-1950	171	1	it	it	PRON
ejpam-1950	171	2	is	be	AUX
ejpam-1950	171	3	well	well	ADV
ejpam-1950	171	4	known	know	VERB
ejpam-1950	171	5	that	that	SCONJ
ejpam-1950	171	6	c(x	c(x	NOUN
ejpam-1950	171	7	)	)	PUNCT
ejpam-1950	171	8	,	,	PUNCT
ejpam-1950	171	9	c0(x	c0(x	ADP
ejpam-1950	171	10	)	)	PUNCT
ejpam-1950	171	11	and	and	CCONJ
ejpam-1950	171	12	ℓ∞(x	ℓ∞(x	NOUN
ejpam-1950	171	13	)	)	PUNCT
ejpam-1950	171	14	are	be	AUX
ejpam-1950	171	15	banach	banach	NOUN
ejpam-1950	171	16	spaces	space	NOUN
ejpam-1950	171	17	with	with	ADP
ejpam-1950	171	18	the	the	DET
ejpam-1950	171	19	norm	norm	NOUN
ejpam-1950	171	20	‖x‖∞	‖x‖∞	PROPN
ejpam-1950	171	21	=	=	PUNCT
ejpam-1950	171	22	supk	supk	DET
ejpam-1950	171	23	‖xk‖	‖xk‖	PROPN
ejpam-1950	171	24	,	,	PUNCT
ejpam-1950	171	25	and	and	CCONJ
ejpam-1950	171	26	ℓp(x	ℓp(x	X
ejpam-1950	171	27	)	)	PUNCT
ejpam-1950	171	28	is	be	AUX
ejpam-1950	171	29	banach	banach	NOUN
ejpam-1950	171	30	space	space	NOUN
ejpam-1950	171	31	with	with	ADP
ejpam-1950	171	32	the	the	DET
ejpam-1950	171	33	norm	norm	NOUN
ejpam-1950	171	34	‖x‖p	‖x‖p	X
ejpam-1950	171	35	=	=	SYM
ejpam-1950	171	36	�	�	PROPN
ejpam-1950	171	37	∑	∑	PROPN
ejpam-1950	171	38	k	k	PROPN
ejpam-1950	171	39	‖xk‖	‖xk‖	PROPN
ejpam-1950	171	40	p	p	PROPN
ejpam-1950	171	41	�	�	PROPN
ejpam-1950	171	42	1	1	NUM
ejpam-1950	171	43	/	/	SYM
ejpam-1950	171	44	p	p	NOUN
ejpam-1950	171	45	if	if	SCONJ
ejpam-1950	171	46	1≤	1≤	NUM
ejpam-1950	171	47	p	p	X
ejpam-1950	171	48	<	<	X
ejpam-1950	171	49	∞.	∞.	PROPN
ejpam-1950	171	50	for	for	ADP
ejpam-1950	171	51	x	x	SYM
ejpam-1950	171	52	∈	∈	PROPN
ejpam-1950	171	53	x	x	X
ejpam-1950	171	54	and	and	CCONJ
ejpam-1950	171	55	n	n	PRON
ejpam-1950	171	56	∈	∈	PROPN
ejpam-1950	171	57	n	n	ADV
ejpam-1950	171	58	let	let	VERB
ejpam-1950	171	59	e(x	e(x	NUM
ejpam-1950	171	60	)	)	PUNCT
ejpam-1950	171	61	=	=	SYM
ejpam-1950	171	62	(	(	PUNCT
ejpam-1950	171	63	x	x	X
ejpam-1950	171	64	,	,	PUNCT
ejpam-1950	171	65	x	x	INTJ
ejpam-1950	171	66	,	,	PUNCT
ejpam-1950	171	67	.	.	PUNCT
ejpam-1950	171	68	.	.	PUNCT
ejpam-1950	171	69	.	.	PUNCT
ejpam-1950	171	70	)	)	PUNCT
ejpam-1950	172	1	be	be	AUX
ejpam-1950	172	2	constant	constant	ADJ
ejpam-1950	172	3	sequence	sequence	NOUN
ejpam-1950	172	4	and	and	CCONJ
ejpam-1950	172	5	ek(x	ek(x	NOUN
ejpam-1950	172	6	)	)	PUNCT
ejpam-1950	173	1	=	=	PRON
ejpam-1950	173	2	(	(	PUNCT
ejpam-1950	173	3	ek	ek	PROPN
ejpam-1950	173	4	j	j	PROPN
ejpam-1950	173	5	(	(	PUNCT
ejpam-1950	173	6	x	x	NOUN
ejpam-1950	173	7	)	)	PUNCT
ejpam-1950	173	8	)	)	PUNCT
ejpam-1950	173	9	the	the	DET
ejpam-1950	173	10	sequence	sequence	NOUN
ejpam-1950	173	11	with	with	ADP
ejpam-1950	173	12	ek	ek	PROPN
ejpam-1950	173	13	j	j	PROPN
ejpam-1950	173	14	(	(	PUNCT
ejpam-1950	173	15	x	x	X
ejpam-1950	173	16	)	)	PUNCT
ejpam-1950	173	17	=	=	PUNCT
ejpam-1950	174	1	x	x	X
ejpam-1950	174	2	if	if	SCONJ
ejpam-1950	174	3	j	j	PROPN
ejpam-1950	174	4	=	=	SYM
ejpam-1950	174	5	k	k	PROPN
ejpam-1950	174	6	and	and	CCONJ
ejpam-1950	174	7	ek	ek	PROPN
ejpam-1950	174	8	j	j	PROPN
ejpam-1950	174	9	(	(	PUNCT
ejpam-1950	174	10	x	x	X
ejpam-1950	174	11	)	)	PUNCT
ejpam-1950	174	12	=	=	SYM
ejpam-1950	174	13	0	0	PUNCT
ejpam-1950	175	1	otherwise	otherwise	ADV
ejpam-1950	175	2	.	.	PUNCT
ejpam-1950	176	1	it	it	PRON
ejpam-1950	176	2	is	be	AUX
ejpam-1950	176	3	not	not	PART
ejpam-1950	176	4	difficult	difficult	ADJ
ejpam-1950	176	5	to	to	PART
ejpam-1950	176	6	see	see	VERB
ejpam-1950	176	7	that	that	SCONJ
ejpam-1950	176	8	if	if	SCONJ
ejpam-1950	176	9	φ	φ	PROPN
ejpam-1950	176	10	is	be	AUX
ejpam-1950	176	11	a	a	DET
ejpam-1950	176	12	(	(	PUNCT
ejpam-1950	176	13	countable	countable	ADJ
ejpam-1950	176	14	)	)	PUNCT
ejpam-1950	176	15	fundamental	fundamental	ADJ
ejpam-1950	176	16	set	set	NOUN
ejpam-1950	176	17	in	in	ADP
ejpam-1950	176	18	x	x	PROPN
ejpam-1950	176	19	,	,	PUNCT
ejpam-1950	176	20	then	then	ADV
ejpam-1950	176	21	e0(φ	e0(φ	NUM
ejpam-1950	176	22	)	)	PUNCT
ejpam-1950	176	23	=	=	SYM
ejpam-1950	176	24	{	{	PUNCT
ejpam-1950	176	25	e	e	X
ejpam-1950	176	26	k(φ	k(φ	PROPN
ejpam-1950	176	27	)	)	PUNCT
ejpam-1950	176	28	:	:	PUNCT
ejpam-1950	177	1	k	k	PROPN
ejpam-1950	177	2	∈	∈	PROPN
ejpam-1950	177	3	n	n	CCONJ
ejpam-1950	177	4	,	,	PUNCT
ejpam-1950	177	5	φ	φ	PROPN
ejpam-1950	177	6	∈	∈	PROPN
ejpam-1950	177	7	φ	φ	PROPN
ejpam-1950	177	8	}	}	PUNCT
ejpam-1950	177	9	is	be	AUX
ejpam-1950	177	10	a	a	DET
ejpam-1950	177	11	(	(	PUNCT
ejpam-1950	177	12	countable	countable	ADJ
ejpam-1950	177	13	)	)	PUNCT
ejpam-1950	177	14	fundamental	fundamental	ADJ
ejpam-1950	177	15	set	set	NOUN
ejpam-1950	177	16	in	in	ADP
ejpam-1950	177	17	banach	banach	NOUN
ejpam-1950	177	18	spaces	space	NOUN
ejpam-1950	177	19	c0(x	c0(x	X
ejpam-1950	177	20	)	)	PUNCT
ejpam-1950	177	21	and	and	CCONJ
ejpam-1950	177	22	ℓp(x	ℓp(x	NUM
ejpam-1950	177	23	)	)	PUNCT
ejpam-1950	177	24	,	,	PUNCT
ejpam-1950	177	25	and	and	CCONJ
ejpam-1950	177	26	e0(φ	e0(φ	ADP
ejpam-1950	177	27	)	)	PUNCT
ejpam-1950	177	28	⋃	⋃	NOUN
ejpam-1950	177	29	e1(φ	e1(φ	NOUN
ejpam-1950	177	30	)	)	PUNCT
ejpam-1950	177	31	with	with	ADP
ejpam-1950	177	32	e1(φ	e1(φ	PROPN
ejpam-1950	177	33	)	)	PUNCT
ejpam-1950	177	34	=	=	PRON
ejpam-1950	177	35	{	{	PUNCT
ejpam-1950	177	36	e(φ	e(φ	PROPN
ejpam-1950	177	37	)	)	PUNCT
ejpam-1950	177	38	:	:	PUNCT
ejpam-1950	177	39	φ	φ	PROPN
ejpam-1950	177	40	∈	∈	PROPN
ejpam-1950	177	41	φ	φ	PROPN
ejpam-1950	177	42	}	}	PUNCT
ejpam-1950	177	43	is	be	AUX
ejpam-1950	177	44	a	a	DET
ejpam-1950	177	45	(	(	PUNCT
ejpam-1950	177	46	countable	countable	ADJ
ejpam-1950	177	47	)	)	PUNCT
ejpam-1950	177	48	fundamental	fundamental	ADJ
ejpam-1950	177	49	set	set	NOUN
ejpam-1950	177	50	in	in	ADP
ejpam-1950	177	51	banach	banach	NOUN
ejpam-1950	177	52	space	space	NOUN
ejpam-1950	177	53	c(x	c(x	NOUN
ejpam-1950	177	54	)	)	PUNCT
ejpam-1950	177	55	.	.	PUNCT
ejpam-1950	178	1	using	use	VERB
ejpam-1950	178	2	theorem	theorem	NOUN
ejpam-1950	178	3	2	2	NUM
ejpam-1950	178	4	,	,	PUNCT
ejpam-1950	178	5	zeller	zeller	NOUN
ejpam-1950	179	1	[	[	X
ejpam-1950	179	2	24	24	NUM
ejpam-1950	179	3	]	]	PUNCT
ejpam-1950	179	4	(	(	PUNCT
ejpam-1950	179	5	see	see	VERB
ejpam-1950	179	6	also	also	ADV
ejpam-1950	179	7	[	[	X
ejpam-1950	179	8	19	19	NUM
ejpam-1950	179	9	]	]	PUNCT
ejpam-1950	179	10	)	)	PUNCT
ejpam-1950	180	1	and	and	CCONJ
ejpam-1950	180	2	kangro	kangro	VERB
ejpam-1950	181	1	[	[	X
ejpam-1950	181	2	12	12	NUM
ejpam-1950	181	3	]	]	PUNCT
ejpam-1950	181	4	characterized	characterize	VERB
ejpam-1950	181	5	the	the	DET
ejpam-1950	181	6	matrices	matrix	NOUN
ejpam-1950	181	7	a	a	DET
ejpam-1950	181	8	:	:	PUNCT
ejpam-1950	181	9	c(x	c(x	NOUN
ejpam-1950	181	10	)	)	PUNCT
ejpam-1950	181	11	→	→	SYM
ejpam-1950	181	12	c(y	c(y	PROPN
ejpam-1950	181	13	)	)	PUNCT
ejpam-1950	181	14	,	,	PUNCT
ejpam-1950	181	15	a	a	DET
ejpam-1950	181	16	:	:	PUNCT
ejpam-1950	181	17	c0(x	c0(x	NOUN
ejpam-1950	181	18	)	)	PUNCT
ejpam-1950	181	19	→	→	SYM
ejpam-1950	181	20	c(y	c(y	PROPN
ejpam-1950	181	21	)	)	PUNCT
ejpam-1950	181	22	and	and	CCONJ
ejpam-1950	181	23	a	a	DET
ejpam-1950	181	24	:	:	PUNCT
ejpam-1950	181	25	ℓ1(x	ℓ1(x	NOUN
ejpam-1950	181	26	)	)	PUNCT
ejpam-1950	181	27	→	→	SYM
ejpam-1950	181	28	c(y	c(y	PROPN
ejpam-1950	181	29	)	)	PUNCT
ejpam-1950	181	30	as	as	SCONJ
ejpam-1950	181	31	follows	follow	VERB
ejpam-1950	181	32	.	.	PUNCT
ejpam-1950	182	1	theorem	theorem	ADJ
ejpam-1950	182	2	6	6	NUM
ejpam-1950	182	3	.	.	PUNCT
ejpam-1950	183	1	let	let	AUX
ejpam-1950	183	2	a=	a=	ADV
ejpam-1950	183	3	(	(	PUNCT
ejpam-1950	183	4	ank	ank	PROPN
ejpam-1950	183	5	)	)	PUNCT
ejpam-1950	183	6	be	be	AUX
ejpam-1950	183	7	an	an	DET
ejpam-1950	183	8	infinite	infinite	ADJ
ejpam-1950	183	9	matrix	matrix	NOUN
ejpam-1950	183	10	with	with	ADP
ejpam-1950	183	11	ank	ank	PROPN
ejpam-1950	183	12	∈	∈	PROPN
ejpam-1950	183	13	b(x	b(x	PROPN
ejpam-1950	183	14	,	,	PUNCT
ejpam-1950	183	15	y	y	PROPN
ejpam-1950	183	16	)	)	PUNCT
ejpam-1950	183	17	.	.	PUNCT
ejpam-1950	184	1	then	then	ADV
ejpam-1950	184	2	:	:	PUNCT
ejpam-1950	184	3	(	(	PUNCT
ejpam-1950	184	4	i	i	NOUN
ejpam-1950	184	5	)	)	PUNCT
ejpam-1950	184	6	a	a	DET
ejpam-1950	184	7	:	:	PUNCT
ejpam-1950	184	8	c(x	c(x	NOUN
ejpam-1950	184	9	)	)	PUNCT
ejpam-1950	184	10	→	→	SYM
ejpam-1950	184	11	c(y	c(y	PROPN
ejpam-1950	184	12	)	)	PUNCT
ejpam-1950	184	13	if	if	SCONJ
ejpam-1950	184	14	and	and	CCONJ
ejpam-1950	184	15	only	only	ADV
ejpam-1950	184	16	if	if	SCONJ
ejpam-1950	184	17	gn	gn	PROPN
ejpam-1950	184	18	=	=	NOUN
ejpam-1950	184	19	sup	sup	NOUN
ejpam-1950	184	20	r	r	NOUN
ejpam-1950	184	21	sup	sup	NOUN
ejpam-1950	184	22	‖xk‖≤1	‖xk‖≤1	PUNCT
ejpam-1950	184	23	r	r	NOUN
ejpam-1950	184	24	∑	∑	PUNCT
ejpam-1950	184	25	k=1	k=1	PROPN
ejpam-1950	184	26	ank	ank	PROPN
ejpam-1950	184	27	xk	xk	PROPN
ejpam-1950	185	1	<	<	X
ejpam-1950	185	2	∞	∞	PROPN
ejpam-1950	185	3	(	(	PUNCT
ejpam-1950	185	4	n	n	NOUN
ejpam-1950	185	5	∈	∈	PROPN
ejpam-1950	185	6	n	n	CCONJ
ejpam-1950	185	7	)	)	PUNCT
ejpam-1950	185	8	,	,	PUNCT
ejpam-1950	185	9	(	(	PUNCT
ejpam-1950	185	10	4	4	X
ejpam-1950	185	11	)	)	PUNCT
ejpam-1950	185	12	e.	e.	PROPN
ejpam-1950	185	13	kolk	kolk	PROPN
ejpam-1950	185	14	/	/	SYM
ejpam-1950	185	15	eur	eur	PROPN
ejpam-1950	185	16	.	.	PUNCT
ejpam-1950	186	1	j.	j.	PROPN
ejpam-1950	186	2	pure	pure	PROPN
ejpam-1950	186	3	appl	appl	PROPN
ejpam-1950	186	4	.	.	PROPN
ejpam-1950	186	5	math	math	PROPN
ejpam-1950	186	6	,	,	PUNCT
ejpam-1950	186	7	8	8	NUM
ejpam-1950	186	8	(	(	PUNCT
ejpam-1950	186	9	2015	2015	NUM
ejpam-1950	186	10	)	)	PUNCT
ejpam-1950	186	11	,	,	PUNCT
ejpam-1950	186	12	357	357	NUM
ejpam-1950	186	13	-	-	SYM
ejpam-1950	186	14	367	367	NUM
ejpam-1950	186	15	362	362	NUM
ejpam-1950	186	16	sup	sup	NOUN
ejpam-1950	186	17	n	n	NOUN
ejpam-1950	186	18	gn	gn	X
ejpam-1950	186	19	<	<	X
ejpam-1950	186	20	∞	∞	PROPN
ejpam-1950	186	21	,	,	PUNCT
ejpam-1950	186	22	(	(	PUNCT
ejpam-1950	186	23	5	5	X
ejpam-1950	186	24	)	)	PUNCT
ejpam-1950	186	25	∃	∃	PROPN
ejpam-1950	186	26	lim	lim	PROPN
ejpam-1950	186	27	n	n	PROPN
ejpam-1950	186	28	ank	ank	PROPN
ejpam-1950	186	29	x	x	X
ejpam-1950	186	30	(	(	PUNCT
ejpam-1950	186	31	k	k	PROPN
ejpam-1950	186	32	∈	∈	PROPN
ejpam-1950	186	33	n	n	CCONJ
ejpam-1950	186	34	,	,	PUNCT
ejpam-1950	186	35	x	x	X
ejpam-1950	186	36	∈	∈	NOUN
ejpam-1950	186	37	x	x	X
ejpam-1950	186	38	)	)	PUNCT
ejpam-1950	186	39	,	,	PUNCT
ejpam-1950	186	40	(	(	PUNCT
ejpam-1950	186	41	6	6	X
ejpam-1950	186	42	)	)	PUNCT
ejpam-1950	186	43	∃	∃	PROPN
ejpam-1950	186	44	lim	lim	PROPN
ejpam-1950	186	45	m	m	VERB
ejpam-1950	186	46	m	m	VERB
ejpam-1950	186	47	∑	∑	PROPN
ejpam-1950	186	48	k=1	k=1	PROPN
ejpam-1950	186	49	ank	ank	PROPN
ejpam-1950	186	50	x	x	PROPN
ejpam-1950	186	51	(	(	PUNCT
ejpam-1950	186	52	n	n	X
ejpam-1950	186	53	∈	∈	PROPN
ejpam-1950	186	54	n	n	CCONJ
ejpam-1950	186	55	,	,	PUNCT
ejpam-1950	186	56	x	x	X
ejpam-1950	186	57	∈	∈	NOUN
ejpam-1950	186	58	x	x	X
ejpam-1950	186	59	)	)	PUNCT
ejpam-1950	186	60	,	,	PUNCT
ejpam-1950	186	61	(	(	PUNCT
ejpam-1950	186	62	7	7	X
ejpam-1950	186	63	)	)	PUNCT
ejpam-1950	186	64	∃	∃	PROPN
ejpam-1950	186	65	lim	lim	PROPN
ejpam-1950	186	66	n	n	PROPN
ejpam-1950	186	67	∑	∑	PROPN
ejpam-1950	186	68	k	k	PROPN
ejpam-1950	186	69	ank	ank	PROPN
ejpam-1950	186	70	x	x	X
ejpam-1950	186	71	(	(	PUNCT
ejpam-1950	186	72	x	x	SYM
ejpam-1950	186	73	∈	∈	NOUN
ejpam-1950	186	74	x	x	X
ejpam-1950	186	75	)	)	PUNCT
ejpam-1950	186	76	;	;	PUNCT
ejpam-1950	186	77	(	(	PUNCT
ejpam-1950	186	78	8)	8)	NUM
ejpam-1950	186	79	(	(	PUNCT
ejpam-1950	186	80	ii	ii	NOUN
ejpam-1950	186	81	)	)	PUNCT
ejpam-1950	186	82	a	a	DET
ejpam-1950	186	83	:	:	PUNCT
ejpam-1950	186	84	c0(x	c0(x	NOUN
ejpam-1950	186	85	)	)	PUNCT
ejpam-1950	186	86	→	→	SYM
ejpam-1950	186	87	c(y	c(y	PROPN
ejpam-1950	186	88	)	)	PUNCT
ejpam-1950	186	89	if	if	SCONJ
ejpam-1950	186	90	and	and	CCONJ
ejpam-1950	186	91	only	only	ADV
ejpam-1950	186	92	if	if	SCONJ
ejpam-1950	186	93	(	(	PUNCT
ejpam-1950	186	94	4)–(6	4)–(6	X
ejpam-1950	186	95	)	)	PUNCT
ejpam-1950	186	96	hold	hold	VERB
ejpam-1950	186	97	;	;	PUNCT
ejpam-1950	186	98	(	(	PUNCT
ejpam-1950	186	99	iii	iii	X
ejpam-1950	186	100	)	)	PUNCT
ejpam-1950	186	101	a	a	PRON
ejpam-1950	186	102	:	:	PUNCT
ejpam-1950	186	103	ℓ1(x	ℓ1(x	NOUN
ejpam-1950	186	104	)	)	PUNCT
ejpam-1950	186	105	→	→	SYM
ejpam-1950	186	106	c(y	c(y	PROPN
ejpam-1950	186	107	)	)	PUNCT
ejpam-1950	187	1	if	if	SCONJ
ejpam-1950	187	2	and	and	CCONJ
ejpam-1950	187	3	only	only	ADV
ejpam-1950	187	4	if	if	SCONJ
ejpam-1950	187	5	(	(	PUNCT
ejpam-1950	187	6	6	6	NUM
ejpam-1950	187	7	)	)	PUNCT
ejpam-1950	187	8	is	be	AUX
ejpam-1950	187	9	satisfied	satisfied	ADJ
ejpam-1950	187	10	and	and	CCONJ
ejpam-1950	187	11	hn	hn	PROPN
ejpam-1950	187	12	=	=	NOUN
ejpam-1950	187	13	sup	sup	PROPN
ejpam-1950	187	14	k	k	PROPN
ejpam-1950	187	15	ank	ank	PROPN
ejpam-1950	187	16	<	<	X
ejpam-1950	187	17	∞	∞	PROPN
ejpam-1950	187	18	(	(	PUNCT
ejpam-1950	187	19	n	n	X
ejpam-1950	187	20	∈	∈	PROPN
ejpam-1950	187	21	n	n	CCONJ
ejpam-1950	187	22	)	)	PUNCT
ejpam-1950	187	23	,	,	PUNCT
ejpam-1950	187	24	(	(	PUNCT
ejpam-1950	187	25	9	9	X
ejpam-1950	187	26	)	)	PUNCT
ejpam-1950	187	27	sup	sup	NOUN
ejpam-1950	187	28	n	n	INTJ
ejpam-1950	187	29	hn	hn	PROPN
ejpam-1950	187	30	<	<	X
ejpam-1950	187	31	∞	∞	PROPN
ejpam-1950	187	32	,	,	PUNCT
ejpam-1950	187	33	remark	remark	NOUN
ejpam-1950	187	34	2	2	NUM
ejpam-1950	187	35	.	.	PUNCT
ejpam-1950	188	1	it	it	PRON
ejpam-1950	188	2	is	be	AUX
ejpam-1950	188	3	not	not	PART
ejpam-1950	188	4	difficult	difficult	ADJ
ejpam-1950	188	5	to	to	PART
ejpam-1950	188	6	see	see	VERB
ejpam-1950	188	7	,	,	PUNCT
ejpam-1950	188	8	using	use	VERB
ejpam-1950	188	9	theorem	theorem	NOUN
ejpam-1950	188	10	2	2	NUM
ejpam-1950	188	11	,	,	PUNCT
ejpam-1950	188	12	that	that	SCONJ
ejpam-1950	188	13	in	in	ADP
ejpam-1950	188	14	theorem	theorem	NOUN
ejpam-1950	188	15	6	6	NUM
ejpam-1950	188	16	it	it	PRON
ejpam-1950	188	17	suffices	suffice	VERB
ejpam-1950	188	18	to	to	PART
ejpam-1950	188	19	require	require	VERB
ejpam-1950	188	20	the	the	DET
ejpam-1950	188	21	fulfillment	fulfillment	NOUN
ejpam-1950	188	22	of	of	ADP
ejpam-1950	188	23	conditions	condition	NOUN
ejpam-1950	188	24	(	(	PUNCT
ejpam-1950	188	25	6)–(8	6)–(8	NUM
ejpam-1950	188	26	)	)	PUNCT
ejpam-1950	188	27	for	for	ADP
ejpam-1950	188	28	all	all	DET
ejpam-1950	188	29	elements	element	NOUN
ejpam-1950	188	30	φ	φ	NOUN
ejpam-1950	188	31	from	from	ADP
ejpam-1950	188	32	a	a	DET
ejpam-1950	188	33	fundamental	fundamental	ADJ
ejpam-1950	188	34	set	set	NOUN
ejpam-1950	188	35	φ	φ	PROPN
ejpam-1950	188	36	of	of	ADP
ejpam-1950	188	37	x	x	PROPN
ejpam-1950	188	38	.	.	PUNCT
ejpam-1950	189	1	the	the	DET
ejpam-1950	189	2	notion	notion	NOUN
ejpam-1950	189	3	of	of	ADP
ejpam-1950	189	4	b∗i	b∗i	PUNCT
ejpam-1950	189	5	-convergence	-convergence	NOUN
ejpam-1950	189	6	of	of	ADP
ejpam-1950	189	7	sequences	sequence	NOUN
ejpam-1950	189	8	of	of	ADP
ejpam-1950	189	9	bounded	bound	VERB
ejpam-1950	189	10	linear	linear	PROPN
ejpam-1950	189	11	operators	operator	NOUN
ejpam-1950	189	12	leads	lead	VERB
ejpam-1950	189	13	us	we	PRON
ejpam-1950	189	14	to	to	ADP
ejpam-1950	189	15	the	the	DET
ejpam-1950	189	16	definition	definition	NOUN
ejpam-1950	189	17	of	of	ADP
ejpam-1950	189	18	new	new	ADJ
ejpam-1950	189	19	type	type	NOUN
ejpam-1950	189	20	summability	summability	NOUN
ejpam-1950	189	21	maps	map	NOUN
ejpam-1950	189	22	.	.	PUNCT
ejpam-1950	190	1	definition	definition	NOUN
ejpam-1950	190	2	2	2	NUM
ejpam-1950	190	3	.	.	PUNCT
ejpam-1950	190	4	let	let	VERB
ejpam-1950	190	5	λ(x	λ(x	PROPN
ejpam-1950	190	6	)	)	PUNCT
ejpam-1950	190	7	and	and	CCONJ
ejpam-1950	190	8	µ(y	µ(y	PROPN
ejpam-1950	190	9	)	)	PUNCT
ejpam-1950	190	10	be	be	AUX
ejpam-1950	190	11	two	two	NUM
ejpam-1950	190	12	linear	linear	ADJ
ejpam-1950	190	13	subspaces	subspace	NOUN
ejpam-1950	190	14	of	of	ADP
ejpam-1950	190	15	ω(x	ω(x	NUM
ejpam-1950	190	16	)	)	PUNCT
ejpam-1950	190	17	and	and	CCONJ
ejpam-1950	190	18	ω(y	ω(y	NUM
ejpam-1950	190	19	)	)	PUNCT
ejpam-1950	190	20	,	,	PUNCT
ejpam-1950	190	21	respectively	respectively	ADV
ejpam-1950	190	22	,	,	PUNCT
ejpam-1950	190	23	and	and	CCONJ
ejpam-1950	190	24	let	let	VERB
ejpam-1950	190	25	i	i	PRON
ejpam-1950	190	26	⊂	⊂	PROPN
ejpam-1950	190	27	2n	2n	NUM
ejpam-1950	190	28	be	be	VERB
ejpam-1950	190	29	a	a	DET
ejpam-1950	190	30	non	non	ADJ
ejpam-1950	190	31	-	-	ADJ
ejpam-1950	190	32	trivial	trivial	ADJ
ejpam-1950	190	33	admissible	admissible	ADJ
ejpam-1950	190	34	ideal	ideal	NOUN
ejpam-1950	190	35	.	.	PUNCT
ejpam-1950	191	1	we	we	PRON
ejpam-1950	191	2	say	say	VERB
ejpam-1950	191	3	that	that	SCONJ
ejpam-1950	191	4	a	a	DET
ejpam-1950	191	5	matrix	matrix	NOUN
ejpam-1950	191	6	a	a	DET
ejpam-1950	191	7	maps	map	NOUN
ejpam-1950	191	8	λ(x	λ(x	PROPN
ejpam-1950	191	9	)	)	PUNCT
ejpam-1950	191	10	in	in	ADP
ejpam-1950	191	11	the	the	DET
ejpam-1950	191	12	sense	sense	NOUN
ejpam-1950	191	13	of	of	ADP
ejpam-1950	191	14	b∗i	b∗i	PUNCT
ejpam-1950	191	15	-convergence	-convergence	NOUN
ejpam-1950	191	16	into	into	ADP
ejpam-1950	191	17	µ(y	µ(y	PROPN
ejpam-1950	191	18	)	)	PUNCT
ejpam-1950	191	19	,	,	PUNCT
ejpam-1950	191	20	and	and	CCONJ
ejpam-1950	191	21	write	write	VERB
ejpam-1950	191	22	a	a	DET
ejpam-1950	191	23	:	:	PUNCT
ejpam-1950	191	24	λ(x	λ(x	X
ejpam-1950	191	25	)	)	PUNCT
ejpam-1950	191	26	b∗i	b∗i	PROPN
ejpam-1950	191	27	−→µ(y	−→µ(y	PROPN
ejpam-1950	191	28	)	)	PUNCT
ejpam-1950	191	29	,	,	PUNCT
ejpam-1950	191	30	if	if	SCONJ
ejpam-1950	191	31	i	i	PRON
ejpam-1950	191	32	limanx	limanx	NOUN
ejpam-1950	191	33	exists	exist	VERB
ejpam-1950	191	34	for	for	ADP
ejpam-1950	191	35	any	any	DET
ejpam-1950	191	36	x	x	SYM
ejpam-1950	191	37	∈	∈	PROPN
ejpam-1950	191	38	λ(x	λ(x	PROPN
ejpam-1950	191	39	)	)	PUNCT
ejpam-1950	191	40	and	and	CCONJ
ejpam-1950	191	41	there	there	PRON
ejpam-1950	191	42	is	be	VERB
ejpam-1950	191	43	an	an	DET
ejpam-1950	191	44	index	index	NOUN
ejpam-1950	191	45	set	set	VERB
ejpam-1950	191	46	n	n	NOUN
ejpam-1950	191	47	=	=	SYM
ejpam-1950	191	48	(	(	PUNCT
ejpam-1950	191	49	ni	ni	PROPN
ejpam-1950	191	50	)	)	PUNCT
ejpam-1950	191	51	from	from	ADP
ejpam-1950	191	52	f	f	PROPN
ejpam-1950	191	53	(	(	PUNCT
ejpam-1950	191	54	i	i	NOUN
ejpam-1950	191	55	)	)	PUNCT
ejpam-1950	191	56	such	such	ADJ
ejpam-1950	191	57	that	that	SCONJ
ejpam-1950	191	58	the	the	DET
ejpam-1950	191	59	submatrix	submatrix	NOUN
ejpam-1950	191	60	a(n	a(n	NOUN
ejpam-1950	191	61	)	)	PUNCT
ejpam-1950	191	62	=	=	SYM
ejpam-1950	191	63	(	(	PUNCT
ejpam-1950	191	64	ani	ani	X
ejpam-1950	191	65	,	,	PUNCT
ejpam-1950	191	66	k	k	NOUN
ejpam-1950	191	67	)	)	PUNCT
ejpam-1950	191	68	maps	map	VERB
ejpam-1950	191	69	λ(x	λ(x	PROPN
ejpam-1950	191	70	)	)	PUNCT
ejpam-1950	191	71	into	into	ADP
ejpam-1950	191	72	ℓ∞(y	ℓ∞(y	NOUN
ejpam-1950	191	73	)	)	PUNCT
ejpam-1950	191	74	.	.	PUNCT
ejpam-1950	192	1	in	in	ADP
ejpam-1950	192	2	the	the	DET
ejpam-1950	192	3	case	case	NOUN
ejpam-1950	192	4	of	of	ADP
ejpam-1950	192	5	i	i	PRON
ejpam-1950	192	6	=	=	PRON
ejpam-1950	192	7	it	it	PRON
ejpam-1950	192	8	we	we	PRON
ejpam-1950	192	9	get	get	VERB
ejpam-1950	192	10	the	the	DET
ejpam-1950	192	11	matrices	matrix	NOUN
ejpam-1950	192	12	of	of	ADP
ejpam-1950	192	13	type	type	NOUN
ejpam-1950	192	14	a	a	DET
ejpam-1950	192	15	:	:	PUNCT
ejpam-1950	192	16	λ(x	λ(x	X
ejpam-1950	192	17	)	)	PUNCT
ejpam-1950	192	18	b∗stt	b∗stt	PROPN
ejpam-1950	192	19	−→µ(y	−→µ(y	PROPN
ejpam-1950	192	20	)	)	PUNCT
ejpam-1950	192	21	.	.	PUNCT
ejpam-1950	193	1	based	base	VERB
ejpam-1950	193	2	on	on	ADP
ejpam-1950	193	3	theorems	theorem	NOUN
ejpam-1950	193	4	4	4	NUM
ejpam-1950	193	5	and	and	CCONJ
ejpam-1950	193	6	5	5	NUM
ejpam-1950	193	7	,	,	PUNCT
ejpam-1950	193	8	we	we	PRON
ejpam-1950	193	9	describe	describe	VERB
ejpam-1950	193	10	the	the	DET
ejpam-1950	193	11	matrices	matrix	NOUN
ejpam-1950	193	12	a	a	DET
ejpam-1950	193	13	:	:	PUNCT
ejpam-1950	193	14	λ(x	λ(x	X
ejpam-1950	193	15	)	)	PUNCT
ejpam-1950	193	16	b∗i	b∗i	PUNCT
ejpam-1950	193	17	−→	−→	ADJ
ejpam-1950	193	18	c(y	c(y	PROPN
ejpam-1950	193	19	)	)	PUNCT
ejpam-1950	193	20	and	and	CCONJ
ejpam-1950	193	21	a	a	DET
ejpam-1950	193	22	:	:	PUNCT
ejpam-1950	193	23	λ(x	λ(x	X
ejpam-1950	193	24	)	)	PUNCT
ejpam-1950	193	25	b∗stt	b∗stt	PROPN
ejpam-1950	193	26	−→	−→	PROPN
ejpam-1950	193	27	c(y	c(y	PROPN
ejpam-1950	193	28	)	)	PUNCT
ejpam-1950	193	29	,	,	PUNCT
ejpam-1950	193	30	where	where	SCONJ
ejpam-1950	193	31	λ	λ	PROPN
ejpam-1950	193	32	∈	∈	PROPN
ejpam-1950	193	33	{	{	PUNCT
ejpam-1950	193	34	c	c	NOUN
ejpam-1950	193	35	,	,	PUNCT
ejpam-1950	193	36	c0	c0	NOUN
ejpam-1950	193	37	,	,	PUNCT
ejpam-1950	193	38	ℓp	ℓp	ADJ
ejpam-1950	193	39	}	}	PUNCT
ejpam-1950	193	40	.	.	PUNCT
ejpam-1950	194	1	proposition	proposition	NOUN
ejpam-1950	194	2	2	2	NUM
ejpam-1950	194	3	.	.	PUNCT
ejpam-1950	194	4	let	let	VERB
ejpam-1950	194	5	a	a	DET
ejpam-1950	194	6	=	=	SYM
ejpam-1950	194	7	(	(	PUNCT
ejpam-1950	194	8	ank	ank	PROPN
ejpam-1950	194	9	)	)	PUNCT
ejpam-1950	194	10	be	be	VERB
ejpam-1950	194	11	an	an	DET
ejpam-1950	194	12	infinite	infinite	ADJ
ejpam-1950	194	13	matrix	matrix	NOUN
ejpam-1950	194	14	with	with	ADP
ejpam-1950	194	15	ank	ank	PROPN
ejpam-1950	194	16	∈	∈	PROPN
ejpam-1950	194	17	b(x	b(x	PROPN
ejpam-1950	194	18	,	,	PUNCT
ejpam-1950	194	19	y	y	PROPN
ejpam-1950	194	20	)	)	PUNCT
ejpam-1950	194	21	.	.	PUNCT
ejpam-1950	195	1	suppose	suppose	VERB
ejpam-1950	195	2	that	that	SCONJ
ejpam-1950	195	3	x	x	PRON
ejpam-1950	195	4	has	have	VERB
ejpam-1950	195	5	a	a	DET
ejpam-1950	195	6	countable	countable	ADJ
ejpam-1950	195	7	fundamental	fundamental	ADJ
ejpam-1950	195	8	set	set	NOUN
ejpam-1950	195	9	φ	φ	PROPN
ejpam-1950	195	10	and	and	CCONJ
ejpam-1950	195	11	the	the	DET
ejpam-1950	195	12	ideal	ideal	NOUN
ejpam-1950	195	13	i	i	PRON
ejpam-1950	195	14	has	have	VERB
ejpam-1950	195	15	property	property	NOUN
ejpam-1950	195	16	(	(	PUNCT
ejpam-1950	195	17	ap	ap	PROPN
ejpam-1950	195	18	)	)	PUNCT
ejpam-1950	195	19	.	.	PUNCT
ejpam-1950	196	1	then	then	ADV
ejpam-1950	196	2	:	:	PUNCT
ejpam-1950	196	3	(	(	PUNCT
ejpam-1950	196	4	i	i	NOUN
ejpam-1950	196	5	)	)	PUNCT
ejpam-1950	196	6	a	a	DET
ejpam-1950	196	7	:	:	PUNCT
ejpam-1950	196	8	c(x	c(x	NOUN
ejpam-1950	196	9	)	)	PUNCT
ejpam-1950	196	10	b∗i	b∗i	PUNCT
ejpam-1950	196	11	−→	−→	NOUN
ejpam-1950	196	12	c(y	c(y	PROPN
ejpam-1950	196	13	)	)	PUNCT
ejpam-1950	197	1	if	if	SCONJ
ejpam-1950	197	2	and	and	CCONJ
ejpam-1950	197	3	only	only	ADV
ejpam-1950	197	4	if	if	SCONJ
ejpam-1950	197	5	(	(	PUNCT
ejpam-1950	197	6	4	4	NUM
ejpam-1950	197	7	)	)	PUNCT
ejpam-1950	197	8	and	and	CCONJ
ejpam-1950	197	9	(	(	PUNCT
ejpam-1950	197	10	7	7	X
ejpam-1950	197	11	)	)	PUNCT
ejpam-1950	197	12	hold	hold	NOUN
ejpam-1950	197	13	,	,	PUNCT
ejpam-1950	197	14	gn	gn	PROPN
ejpam-1950	198	1	=	=	PRON
ejpam-1950	198	2	oi	oi	X
ejpam-1950	198	3	(	(	PUNCT
ejpam-1950	198	4	1	1	NUM
ejpam-1950	198	5	)	)	PUNCT
ejpam-1950	198	6	,	,	PUNCT
ejpam-1950	198	7	(	(	PUNCT
ejpam-1950	198	8	10	10	NUM
ejpam-1950	198	9	)	)	PUNCT
ejpam-1950	198	10	∃i	∃i	PROPN
ejpam-1950	198	11	lim	lim	PROPN
ejpam-1950	198	12	n	n	PRON
ejpam-1950	198	13	ankφ	ankφ	NOUN
ejpam-1950	198	14	(	(	PUNCT
ejpam-1950	198	15	k	k	PROPN
ejpam-1950	198	16	∈	∈	PROPN
ejpam-1950	198	17	n	n	CCONJ
ejpam-1950	198	18	,	,	PUNCT
ejpam-1950	198	19	φ	φ	PROPN
ejpam-1950	198	20	∈	∈	PROPN
ejpam-1950	198	21	φ	φ	PROPN
ejpam-1950	198	22	)	)	PUNCT
ejpam-1950	198	23	,	,	PUNCT
ejpam-1950	198	24	(	(	PUNCT
ejpam-1950	198	25	11	11	NUM
ejpam-1950	198	26	)	)	PUNCT
ejpam-1950	198	27	∃i	∃i	PROPN
ejpam-1950	198	28	lim	lim	PROPN
ejpam-1950	198	29	n	n	PROPN
ejpam-1950	198	30	∑	∑	PROPN
ejpam-1950	198	31	k	k	PROPN
ejpam-1950	198	32	ankφ	ankφ	PROPN
ejpam-1950	198	33	(	(	PUNCT
ejpam-1950	198	34	φ	φ	PROPN
ejpam-1950	198	35	∈	∈	PROPN
ejpam-1950	198	36	φ	φ	PROPN
ejpam-1950	198	37	)	)	PUNCT
ejpam-1950	198	38	;	;	PUNCT
ejpam-1950	198	39	(	(	PUNCT
ejpam-1950	198	40	12	12	NUM
ejpam-1950	198	41	)	)	PUNCT
ejpam-1950	198	42	(	(	PUNCT
ejpam-1950	198	43	ii	ii	NOUN
ejpam-1950	198	44	)	)	PUNCT
ejpam-1950	198	45	a	a	PRON
ejpam-1950	198	46	:	:	PUNCT
ejpam-1950	198	47	c0(x	c0(x	NOUN
ejpam-1950	198	48	)	)	PUNCT
ejpam-1950	198	49	b∗i	b∗i	PUNCT
ejpam-1950	198	50	−→	−→	NOUN
ejpam-1950	198	51	c(y	c(y	PROPN
ejpam-1950	198	52	)	)	PUNCT
ejpam-1950	199	1	if	if	SCONJ
ejpam-1950	199	2	and	and	CCONJ
ejpam-1950	199	3	only	only	ADV
ejpam-1950	199	4	if	if	SCONJ
ejpam-1950	199	5	(	(	PUNCT
ejpam-1950	199	6	4	4	NUM
ejpam-1950	199	7	)	)	PUNCT
ejpam-1950	199	8	,	,	PUNCT
ejpam-1950	199	9	(	(	PUNCT
ejpam-1950	199	10	10	10	NUM
ejpam-1950	199	11	)	)	PUNCT
ejpam-1950	199	12	and	and	CCONJ
ejpam-1950	199	13	(	(	PUNCT
ejpam-1950	199	14	11	11	X
ejpam-1950	199	15	)	)	PUNCT
ejpam-1950	199	16	hold	hold	NOUN
ejpam-1950	199	17	;	;	PUNCT
ejpam-1950	199	18	e.	e.	PROPN
ejpam-1950	199	19	kolk	kolk	PROPN
ejpam-1950	199	20	/	/	SYM
ejpam-1950	199	21	eur	eur	PROPN
ejpam-1950	199	22	.	.	PUNCT
ejpam-1950	200	1	j.	j.	PROPN
ejpam-1950	200	2	pure	pure	PROPN
ejpam-1950	200	3	appl	appl	PROPN
ejpam-1950	200	4	.	.	PROPN
ejpam-1950	200	5	math	math	PROPN
ejpam-1950	200	6	,	,	PUNCT
ejpam-1950	200	7	8	8	NUM
ejpam-1950	200	8	(	(	PUNCT
ejpam-1950	200	9	2015	2015	NUM
ejpam-1950	200	10	)	)	PUNCT
ejpam-1950	200	11	,	,	PUNCT
ejpam-1950	200	12	357	357	NUM
ejpam-1950	200	13	-	-	SYM
ejpam-1950	200	14	367	367	NUM
ejpam-1950	200	15	363	363	NUM
ejpam-1950	200	16	(	(	PUNCT
ejpam-1950	200	17	iii	iii	NOUN
ejpam-1950	200	18	)	)	PUNCT
ejpam-1950	200	19	a	a	PRON
ejpam-1950	200	20	:	:	PUNCT
ejpam-1950	200	21	ℓ1(x	ℓ1(x	NOUN
ejpam-1950	200	22	)	)	PUNCT
ejpam-1950	200	23	b∗i	b∗i	PUNCT
ejpam-1950	200	24	−→	−→	NOUN
ejpam-1950	200	25	c(y	c(y	PROPN
ejpam-1950	200	26	)	)	PUNCT
ejpam-1950	201	1	if	if	SCONJ
ejpam-1950	201	2	and	and	CCONJ
ejpam-1950	201	3	only	only	ADV
ejpam-1950	201	4	if	if	SCONJ
ejpam-1950	201	5	(	(	PUNCT
ejpam-1950	201	6	9	9	X
ejpam-1950	201	7	)	)	PUNCT
ejpam-1950	201	8	is	be	AUX
ejpam-1950	201	9	satisfied	satisfied	ADJ
ejpam-1950	201	10	and	and	CCONJ
ejpam-1950	201	11	(	(	PUNCT
ejpam-1950	201	12	hn	hn	NOUN
ejpam-1950	201	13	)	)	PUNCT
ejpam-1950	201	14	is	be	AUX
ejpam-1950	201	15	i	i	PRON
ejpam-1950	201	16	-bounded	-bounded	ADJ
ejpam-1950	201	17	.	.	PUNCT
ejpam-1950	202	1	proof	proof	NOUN
ejpam-1950	202	2	.	.	PUNCT
ejpam-1950	203	1	the	the	DET
ejpam-1950	203	2	equality	equality	NOUN
ejpam-1950	203	3	a(r)n	a(r)n	PROPN
ejpam-1950	203	4	x	x	PUNCT
ejpam-1950	204	1	=	=	PUNCT
ejpam-1950	204	2	∑r	∑r	PROPN
ejpam-1950	204	3	k=1	k=1	PROPN
ejpam-1950	204	4	ank	ank	PROPN
ejpam-1950	204	5	xk	xk	PROPN
ejpam-1950	204	6	defines	define	VERB
ejpam-1950	204	7	a	a	DET
ejpam-1950	204	8	linear	linear	ADJ
ejpam-1950	204	9	operator	operator	NOUN
ejpam-1950	204	10	a(r)n	a(r)n	PROPN
ejpam-1950	204	11	on	on	ADP
ejpam-1950	204	12	c(x	c(x	NOUN
ejpam-1950	204	13	)	)	PUNCT
ejpam-1950	204	14	and	and	CCONJ
ejpam-1950	204	15	c0(x	c0(x	ADP
ejpam-1950	204	16	)	)	PUNCT
ejpam-1950	204	17	for	for	ADP
ejpam-1950	204	18	any	any	DET
ejpam-1950	204	19	n	n	NOUN
ejpam-1950	204	20	,	,	PUNCT
ejpam-1950	204	21	r	r	NOUN
ejpam-1950	204	22	∈	∈	PROPN
ejpam-1950	204	23	n.	n.	NOUN
ejpam-1950	204	24	since	since	SCONJ
ejpam-1950	204	25	‖a(r)n	‖a(r)n	NUM
ejpam-1950	204	26	‖=	‖=	NUM
ejpam-1950	204	27	r	r	NOUN
ejpam-1950	204	28	∑	∑	PROPN
ejpam-1950	204	29	k=1	k=1	PROPN
ejpam-1950	204	30	ank	ank	PROPN
ejpam-1950	204	31	xk	xk	PROPN
ejpam-1950	204	32	,	,	PUNCT
ejpam-1950	204	33	by	by	ADP
ejpam-1950	204	34	theorem	theorem	NOUN
ejpam-1950	204	35	2	2	NUM
ejpam-1950	204	36	we	we	PRON
ejpam-1950	204	37	get	get	VERB
ejpam-1950	204	38	that	that	SCONJ
ejpam-1950	204	39	the	the	DET
ejpam-1950	204	40	series	series	NOUN
ejpam-1950	204	41	anx	anx	PROPN
ejpam-1950	204	42	(	(	PUNCT
ejpam-1950	204	43	n	n	NOUN
ejpam-1950	204	44	∈	∈	PROPN
ejpam-1950	204	45	n	n	CCONJ
ejpam-1950	204	46	)	)	PUNCT
ejpam-1950	204	47	converge	converge	VERB
ejpam-1950	204	48	for	for	ADP
ejpam-1950	204	49	all	all	DET
ejpam-1950	204	50	x	x	SYM
ejpam-1950	204	51	∈	∈	PROPN
ejpam-1950	204	52	c(x	c(x	NOUN
ejpam-1950	204	53	)	)	PUNCT
ejpam-1950	204	54	and	and	CCONJ
ejpam-1950	204	55	an	an	DET
ejpam-1950	204	56	∈	∈	PROPN
ejpam-1950	204	57	b(c(x	b(c(x	PROPN
ejpam-1950	204	58	)	)	PUNCT
ejpam-1950	204	59	,	,	PUNCT
ejpam-1950	204	60	y	y	PROPN
ejpam-1950	204	61	)	)	PUNCT
ejpam-1950	204	62	if	if	SCONJ
ejpam-1950	204	63	and	and	CCONJ
ejpam-1950	204	64	only	only	ADV
ejpam-1950	204	65	if	if	SCONJ
ejpam-1950	204	66	(	(	PUNCT
ejpam-1950	204	67	4	4	NUM
ejpam-1950	204	68	)	)	PUNCT
ejpam-1950	204	69	,	,	PUNCT
ejpam-1950	204	70	(	(	PUNCT
ejpam-1950	204	71	7	7	X
ejpam-1950	204	72	)	)	PUNCT
ejpam-1950	204	73	are	be	AUX
ejpam-1950	204	74	satisfied	satisfied	ADJ
ejpam-1950	204	75	.	.	PUNCT
ejpam-1950	205	1	similarly	similarly	ADV
ejpam-1950	205	2	,	,	PUNCT
ejpam-1950	205	3	an	an	DET
ejpam-1950	205	4	∈	∈	PROPN
ejpam-1950	205	5	b(c0(x	b(c0(x	PROPN
ejpam-1950	205	6	)	)	PUNCT
ejpam-1950	205	7	,	,	PUNCT
ejpam-1950	205	8	y	y	PROPN
ejpam-1950	205	9	)	)	PUNCT
ejpam-1950	205	10	if	if	SCONJ
ejpam-1950	205	11	and	and	CCONJ
ejpam-1950	205	12	only	only	ADV
ejpam-1950	205	13	if	if	SCONJ
ejpam-1950	205	14	(	(	PUNCT
ejpam-1950	205	15	4	4	X
ejpam-1950	205	16	)	)	PUNCT
ejpam-1950	205	17	holds	hold	VERB
ejpam-1950	205	18	.	.	PUNCT
ejpam-1950	206	1	now	now	ADV
ejpam-1950	206	2	,	,	PUNCT
ejpam-1950	206	3	applying	apply	VERB
ejpam-1950	206	4	theorem	theorem	NOUN
ejpam-1950	206	5	4	4	NUM
ejpam-1950	206	6	to	to	ADP
ejpam-1950	206	7	the	the	DET
ejpam-1950	206	8	operators	operator	NOUN
ejpam-1950	206	9	an	an	PRON
ejpam-1950	206	10	,	,	PUNCT
ejpam-1950	206	11	we	we	PRON
ejpam-1950	206	12	have	have	VERB
ejpam-1950	206	13	that	that	DET
ejpam-1950	206	14	a	a	DET
ejpam-1950	206	15	:	:	PUNCT
ejpam-1950	206	16	c(x	c(x	NOUN
ejpam-1950	206	17	)	)	PUNCT
ejpam-1950	206	18	b∗i	b∗i	PUNCT
ejpam-1950	206	19	−→	−→	NOUN
ejpam-1950	206	20	c(y	c(y	PROPN
ejpam-1950	206	21	)	)	PUNCT
ejpam-1950	206	22	(	(	PUNCT
ejpam-1950	206	23	or	or	CCONJ
ejpam-1950	206	24	a	a	DET
ejpam-1950	206	25	:	:	PUNCT
ejpam-1950	206	26	c0(x	c0(x	NOUN
ejpam-1950	206	27	)	)	PUNCT
ejpam-1950	206	28	b∗i	b∗i	PUNCT
ejpam-1950	206	29	−→	−→	ADJ
ejpam-1950	206	30	c(y	c(y	PROPN
ejpam-1950	206	31	)	)	PUNCT
ejpam-1950	206	32	)	)	PUNCT
ejpam-1950	207	1	if	if	SCONJ
ejpam-1950	207	2	and	and	CCONJ
ejpam-1950	207	3	only	only	ADV
ejpam-1950	207	4	if	if	SCONJ
ejpam-1950	207	5	(	(	PUNCT
ejpam-1950	207	6	10	10	NUM
ejpam-1950	207	7	)	)	PUNCT
ejpam-1950	207	8	holds	hold	VERB
ejpam-1950	207	9	and	and	CCONJ
ejpam-1950	207	10	(	(	PUNCT
ejpam-1950	207	11	any	any	PRON
ejpam-1950	207	12	)	)	PUNCT
ejpam-1950	207	13	is	be	AUX
ejpam-1950	207	14	i	i	PRON
ejpam-1950	207	15	-convergent	-convergent	ADJ
ejpam-1950	207	16	for	for	ADP
ejpam-1950	207	17	any	any	DET
ejpam-1950	207	18	y	y	PROPN
ejpam-1950	207	19	∈	∈	PROPN
ejpam-1950	207	20	e1(φ	e1(φ	PROPN
ejpam-1950	207	21	)	)	PUNCT
ejpam-1950	207	22	(	(	PUNCT
ejpam-1950	207	23	respectively	respectively	ADV
ejpam-1950	207	24	,	,	PUNCT
ejpam-1950	207	25	y	y	PROPN
ejpam-1950	207	26	∈	∈	PROPN
ejpam-1950	207	27	e0(φ	e0(φ	PROPN
ejpam-1950	207	28	)	)	PUNCT
ejpam-1950	207	29	)	)	PUNCT
ejpam-1950	207	30	.	.	PUNCT
ejpam-1950	208	1	but	but	CCONJ
ejpam-1950	208	2	this	this	PRON
ejpam-1950	208	3	reduces	reduce	VERB
ejpam-1950	208	4	to	to	ADP
ejpam-1950	208	5	(	(	PUNCT
ejpam-1950	208	6	11	11	NUM
ejpam-1950	208	7	)	)	PUNCT
ejpam-1950	208	8	and	and	CCONJ
ejpam-1950	208	9	(	(	PUNCT
ejpam-1950	208	10	12	12	NUM
ejpam-1950	208	11	)	)	PUNCT
ejpam-1950	208	12	because	because	SCONJ
ejpam-1950	208	13	anek(φ	anek(φ	PROPN
ejpam-1950	208	14	)	)	PUNCT
ejpam-1950	209	1	=	=	NOUN
ejpam-1950	209	2	ankφ	ankφ	NOUN
ejpam-1950	209	3	and	and	CCONJ
ejpam-1950	209	4	ane(φ	ane(φ	PROPN
ejpam-1950	209	5	)	)	PUNCT
ejpam-1950	210	1	=	=	PUNCT
ejpam-1950	210	2	∑	∑	PUNCT
ejpam-1950	210	3	k	k	PROPN
ejpam-1950	210	4	ankφ	ankφ	PROPN
ejpam-1950	210	5	.	.	PUNCT
ejpam-1950	211	1	since	since	SCONJ
ejpam-1950	211	2	an	an	DET
ejpam-1950	211	3	∈	∈	PROPN
ejpam-1950	211	4	b(ℓ1(x	b(ℓ1(x	PROPN
ejpam-1950	211	5	)	)	PUNCT
ejpam-1950	211	6	,	,	PUNCT
ejpam-1950	211	7	y	y	PROPN
ejpam-1950	211	8	)	)	PUNCT
ejpam-1950	211	9	if	if	SCONJ
ejpam-1950	211	10	and	and	CCONJ
ejpam-1950	211	11	only	only	ADV
ejpam-1950	211	12	if	if	SCONJ
ejpam-1950	211	13	(	(	PUNCT
ejpam-1950	211	14	9	9	X
ejpam-1950	211	15	)	)	PUNCT
ejpam-1950	211	16	holds	hold	VERB
ejpam-1950	211	17	,	,	PUNCT
ejpam-1950	211	18	the	the	DET
ejpam-1950	211	19	statement	statement	NOUN
ejpam-1950	211	20	(	(	PUNCT
ejpam-1950	211	21	iii	iii	NOUN
ejpam-1950	211	22	)	)	PUNCT
ejpam-1950	211	23	also	also	ADV
ejpam-1950	211	24	follows	follow	VERB
ejpam-1950	211	25	by	by	ADP
ejpam-1950	211	26	theorem	theorem	NOUN
ejpam-1950	211	27	4	4	NUM
ejpam-1950	211	28	.	.	PUNCT
ejpam-1950	212	1	the	the	DET
ejpam-1950	212	2	matrix	matrix	NOUN
ejpam-1950	212	3	map	map	NOUN
ejpam-1950	212	4	a	a	PRON
ejpam-1950	212	5	:	:	PUNCT
ejpam-1950	212	6	ℓp(x	ℓp(x	NUM
ejpam-1950	212	7	)	)	PUNCT
ejpam-1950	212	8	b∗i	b∗i	PUNCT
ejpam-1950	212	9	−→	−→	ADJ
ejpam-1950	212	10	c(y	c(y	PROPN
ejpam-1950	212	11	)	)	PUNCT
ejpam-1950	212	12	we	we	PRON
ejpam-1950	212	13	consider	consider	VERB
ejpam-1950	212	14	in	in	ADP
ejpam-1950	212	15	the	the	DET
ejpam-1950	212	16	special	special	ADJ
ejpam-1950	212	17	cases	case	NOUN
ejpam-1950	212	18	y	y	NOUN
ejpam-1950	212	19	=	=	SYM
ejpam-1950	212	20	k	k	PROPN
ejpam-1950	212	21	and	and	CCONJ
ejpam-1950	212	22	1	1	NUM
ejpam-1950	212	23	<	<	X
ejpam-1950	212	24	p	p	X
ejpam-1950	212	25	<	<	X
ejpam-1950	212	26	∞.	∞.	PROPN
ejpam-1950	212	27	then	then	ADV
ejpam-1950	212	28	b(x	b(x	PROPN
ejpam-1950	212	29	,	,	PUNCT
ejpam-1950	212	30	y	y	PROPN
ejpam-1950	212	31	)	)	PUNCT
ejpam-1950	212	32	=	=	PUNCT
ejpam-1950	213	1	x	x	PUNCT
ejpam-1950	213	2	′	′	NOUN
ejpam-1950	214	1	and	and	CCONJ
ejpam-1950	214	2	so	so	ADV
ejpam-1950	214	3	,	,	PUNCT
ejpam-1950	214	4	ank	ank	PROPN
ejpam-1950	214	5	∈	∈	PROPN
ejpam-1950	214	6	x	x	SYM
ejpam-1950	215	1	′	′	NUM
ejpam-1950	215	2	(	(	PUNCT
ejpam-1950	215	3	n	n	X
ejpam-1950	215	4	,	,	PUNCT
ejpam-1950	215	5	k	k	PROPN
ejpam-1950	215	6	∈	∈	PROPN
ejpam-1950	215	7	n	n	CCONJ
ejpam-1950	215	8	)	)	PUNCT
ejpam-1950	215	9	.	.	PUNCT
ejpam-1950	216	1	in	in	ADP
ejpam-1950	216	2	this	this	DET
ejpam-1950	216	3	case	case	NOUN
ejpam-1950	216	4	an	an	DET
ejpam-1950	216	5	∈	∈	NOUN
ejpam-1950	216	6	(	(	PUNCT
ejpam-1950	216	7	ℓp(x	ℓp(x	X
ejpam-1950	216	8	)	)	PUNCT
ejpam-1950	216	9	)	)	PUNCT
ejpam-1950	217	1	′	′	VERB
ejpam-1950	218	1	if	if	SCONJ
ejpam-1950	218	2	and	and	CCONJ
ejpam-1950	218	3	only	only	ADV
ejpam-1950	218	4	if	if	SCONJ
ejpam-1950	218	5	(	(	PUNCT
ejpam-1950	218	6	ank)k∈n	ank)k∈n	PROPN
ejpam-1950	218	7	∈	∈	NOUN
ejpam-1950	218	8	ℓq(x	ℓq(x	PUNCT
ejpam-1950	218	9	′	′	NOUN
ejpam-1950	218	10	)	)	PUNCT
ejpam-1950	218	11	,	,	PUNCT
ejpam-1950	218	12	i.e.	i.e.	X
ejpam-1950	218	13	,	,	PUNCT
ejpam-1950	218	14	∑	∑	PUNCT
ejpam-1950	218	15	k	k	X
ejpam-1950	218	16	‖ank‖	‖ank‖	PROPN
ejpam-1950	218	17	q	q	X
ejpam-1950	218	18	<	<	X
ejpam-1950	218	19	∞	∞	PROPN
ejpam-1950	218	20	,	,	PUNCT
ejpam-1950	218	21	where	where	SCONJ
ejpam-1950	218	22	1	1	NUM
ejpam-1950	218	23	/	/	SYM
ejpam-1950	218	24	p	p	NOUN
ejpam-1950	218	25	+	+	NOUN
ejpam-1950	218	26	1	1	NUM
ejpam-1950	218	27	/	/	SYM
ejpam-1950	218	28	q	q	NOUN
ejpam-1950	218	29	=	=	ADJ
ejpam-1950	218	30	1	1	X
ejpam-1950	218	31	.	.	PUNCT
ejpam-1950	218	32	therefore	therefore	ADV
ejpam-1950	218	33	,	,	PUNCT
ejpam-1950	218	34	denoting	denote	VERB
ejpam-1950	218	35	c	c	NOUN
ejpam-1950	218	36	=	=	SYM
ejpam-1950	218	37	c(k	c(k	NOUN
ejpam-1950	218	38	)	)	PUNCT
ejpam-1950	218	39	and	and	CCONJ
ejpam-1950	218	40	using	use	VERB
ejpam-1950	218	41	the	the	DET
ejpam-1950	218	42	same	same	ADJ
ejpam-1950	218	43	arguments	argument	NOUN
ejpam-1950	218	44	as	as	ADP
ejpam-1950	218	45	in	in	ADP
ejpam-1950	218	46	the	the	DET
ejpam-1950	218	47	proof	proof	NOUN
ejpam-1950	218	48	of	of	ADP
ejpam-1950	218	49	proposition	proposition	NOUN
ejpam-1950	218	50	2	2	NUM
ejpam-1950	218	51	,	,	PUNCT
ejpam-1950	218	52	we	we	PRON
ejpam-1950	218	53	get	get	VERB
ejpam-1950	218	54	the	the	DET
ejpam-1950	218	55	following	follow	VERB
ejpam-1950	218	56	result	result	NOUN
ejpam-1950	218	57	.	.	PUNCT
ejpam-1950	219	1	proposition	proposition	NOUN
ejpam-1950	219	2	3	3	X
ejpam-1950	219	3	.	.	PUNCT
ejpam-1950	220	1	let	let	VERB
ejpam-1950	220	2	a	a	DET
ejpam-1950	220	3	=	=	SYM
ejpam-1950	220	4	(	(	PUNCT
ejpam-1950	220	5	ank	ank	PROPN
ejpam-1950	220	6	)	)	PUNCT
ejpam-1950	220	7	be	be	VERB
ejpam-1950	220	8	an	an	DET
ejpam-1950	220	9	infinite	infinite	ADJ
ejpam-1950	220	10	matrix	matrix	NOUN
ejpam-1950	220	11	with	with	ADP
ejpam-1950	220	12	ank	ank	PROPN
ejpam-1950	220	13	∈	∈	PROPN
ejpam-1950	220	14	x	x	SYM
ejpam-1950	220	15	′.	′.	PROPN
ejpam-1950	220	16	suppose	suppose	VERB
ejpam-1950	220	17	that	that	SCONJ
ejpam-1950	220	18	x	x	PRON
ejpam-1950	220	19	has	have	VERB
ejpam-1950	220	20	a	a	DET
ejpam-1950	220	21	countable	countable	ADJ
ejpam-1950	220	22	fundamental	fundamental	ADJ
ejpam-1950	220	23	set	set	NOUN
ejpam-1950	220	24	φ	φ	PROPN
ejpam-1950	220	25	,	,	PUNCT
ejpam-1950	220	26	the	the	DET
ejpam-1950	220	27	ideal	ideal	NOUN
ejpam-1950	220	28	i	i	PRON
ejpam-1950	220	29	has	have	VERB
ejpam-1950	220	30	property	property	NOUN
ejpam-1950	220	31	(	(	PUNCT
ejpam-1950	220	32	ap	ap	PROPN
ejpam-1950	220	33	)	)	PUNCT
ejpam-1950	220	34	and	and	CCONJ
ejpam-1950	220	35	1	1	NUM
ejpam-1950	220	36	<	<	X
ejpam-1950	220	37	p	p	X
ejpam-1950	220	38	<	<	X
ejpam-1950	220	39	∞	∞	PROPN
ejpam-1950	220	40	,	,	PUNCT
ejpam-1950	220	41	1	1	NUM
ejpam-1950	220	42	/	/	SYM
ejpam-1950	220	43	p	p	NOUN
ejpam-1950	220	44	+	+	NOUN
ejpam-1950	220	45	1	1	NUM
ejpam-1950	220	46	/	/	SYM
ejpam-1950	220	47	q	q	NOUN
ejpam-1950	220	48	=	=	ADJ
ejpam-1950	220	49	1	1	X
ejpam-1950	220	50	.	.	PUNCT
ejpam-1950	220	51	then	then	ADV
ejpam-1950	220	52	a	a	DET
ejpam-1950	220	53	:	:	PUNCT
ejpam-1950	220	54	ℓp(x	ℓp(x	X
ejpam-1950	220	55	)	)	PUNCT
ejpam-1950	220	56	b∗i	b∗i	PUNCT
ejpam-1950	220	57	−→	−→	NOUN
ejpam-1950	220	58	c	c	NOUN
ejpam-1950	220	59	if	if	SCONJ
ejpam-1950	220	60	and	and	CCONJ
ejpam-1950	220	61	only	only	ADV
ejpam-1950	220	62	if	if	SCONJ
ejpam-1950	220	63	(	(	PUNCT
ejpam-1950	220	64	11	11	NUM
ejpam-1950	220	65	)	)	PUNCT
ejpam-1950	220	66	holds	hold	VERB
ejpam-1950	220	67	and	and	CCONJ
ejpam-1950	220	68	∑	∑	PUNCT
ejpam-1950	220	69	k	k	PROPN
ejpam-1950	220	70	‖ank‖	‖ank‖	PUNCT
ejpam-1950	220	71	q	q	PROPN
ejpam-1950	220	72	=	=	PRON
ejpam-1950	220	73	oi	oi	X
ejpam-1950	220	74	(	(	PUNCT
ejpam-1950	220	75	1	1	NUM
ejpam-1950	220	76	)	)	PUNCT
ejpam-1950	220	77	.	.	PUNCT
ejpam-1950	221	1	if	if	SCONJ
ejpam-1950	221	2	x	x	X
ejpam-1950	221	3	=	=	PUNCT
ejpam-1950	221	4	y	y	PROPN
ejpam-1950	221	5	=	=	SYM
ejpam-1950	221	6	k	k	PROPN
ejpam-1950	221	7	,	,	PUNCT
ejpam-1950	221	8	then	then	ADV
ejpam-1950	221	9	the	the	DET
ejpam-1950	221	10	matrix	matrix	NOUN
ejpam-1950	221	11	map	map	NOUN
ejpam-1950	221	12	a	a	DET
ejpam-1950	221	13	reduces	reduce	NOUN
ejpam-1950	221	14	to	to	ADP
ejpam-1950	221	15	the	the	DET
ejpam-1950	221	16	transformation	transformation	NOUN
ejpam-1950	221	17	a	a	DET
ejpam-1950	221	18	:	:	PUNCT
ejpam-1950	221	19	λ→	λ→	PROPN
ejpam-1950	221	20	µ	µ	PRON
ejpam-1950	221	21	defined	define	VERB
ejpam-1950	221	22	by	by	ADP
ejpam-1950	221	23	an	an	DET
ejpam-1950	221	24	infinite	infinite	ADJ
ejpam-1950	221	25	scalar	scalar	ADJ
ejpam-1950	221	26	matrix	matrix	NOUN
ejpam-1950	221	27	a=	a=	X
ejpam-1950	221	28	(	(	PUNCT
ejpam-1950	221	29	ank	ank	PROPN
ejpam-1950	221	30	)	)	PUNCT
ejpam-1950	221	31	.	.	PUNCT
ejpam-1950	222	1	using	use	VERB
ejpam-1950	222	2	the	the	DET
ejpam-1950	222	3	fact	fact	NOUN
ejpam-1950	222	4	that	that	SCONJ
ejpam-1950	222	5	for	for	ADP
ejpam-1950	222	6	y	y	PROPN
ejpam-1950	222	7	=	=	PUNCT
ejpam-1950	222	8	k	k	PROPN
ejpam-1950	222	9	we	we	PRON
ejpam-1950	222	10	have	have	AUX
ejpam-1950	222	11	(	(	PUNCT
ejpam-1950	222	12	see	see	VERB
ejpam-1950	222	13	[	[	X
ejpam-1950	222	14	12	12	NUM
ejpam-1950	222	15	,	,	PUNCT
ejpam-1950	222	16	p.	p.	NOUN
ejpam-1950	222	17	114	114	NUM
ejpam-1950	222	18	]	]	SYM
ejpam-1950	222	19	)	)	PUNCT
ejpam-1950	222	20	sup	sup	NOUN
ejpam-1950	223	1	‖xk‖≤1	‖xk‖≤1	PUNCT
ejpam-1950	223	2	r	r	NOUN
ejpam-1950	223	3	∑	∑	PUNCT
ejpam-1950	224	1	k=1	k=1	PROPN
ejpam-1950	224	2	ank	ank	PROPN
ejpam-1950	224	3	xk	xk	PROPN
ejpam-1950	224	4	=	=	PUNCT
ejpam-1950	224	5	r	r	PROPN
ejpam-1950	224	6	∑	∑	PUNCT
ejpam-1950	224	7	k=1	k=1	PROPN
ejpam-1950	224	8	‖ank‖	‖ank‖	PROPN
ejpam-1950	224	9	,	,	PUNCT
ejpam-1950	224	10	from	from	ADP
ejpam-1950	224	11	propositions	proposition	NOUN
ejpam-1950	224	12	2	2	NUM
ejpam-1950	224	13	and	and	CCONJ
ejpam-1950	224	14	3	3	NUM
ejpam-1950	224	15	we	we	PRON
ejpam-1950	224	16	obtain	obtain	VERB
ejpam-1950	224	17	the	the	DET
ejpam-1950	224	18	following	follow	VERB
ejpam-1950	224	19	corollary	corollary	NOUN
ejpam-1950	224	20	.	.	PUNCT
ejpam-1950	225	1	corollary	corollary	ADJ
ejpam-1950	225	2	1	1	NUM
ejpam-1950	225	3	.	.	PUNCT
ejpam-1950	226	1	let	let	AUX
ejpam-1950	226	2	a=	a=	ADV
ejpam-1950	226	3	(	(	PUNCT
ejpam-1950	226	4	ank	ank	PROPN
ejpam-1950	226	5	)	)	PUNCT
ejpam-1950	226	6	be	be	AUX
ejpam-1950	226	7	an	an	DET
ejpam-1950	226	8	infinite	infinite	ADJ
ejpam-1950	226	9	matrix	matrix	NOUN
ejpam-1950	226	10	of	of	ADP
ejpam-1950	226	11	scalars	scalar	NOUN
ejpam-1950	226	12	,	,	PUNCT
ejpam-1950	226	13	1	1	NUM
ejpam-1950	226	14	<	<	X
ejpam-1950	226	15	p	p	X
ejpam-1950	226	16	<	<	X
ejpam-1950	226	17	∞	∞	NUM
ejpam-1950	226	18	and	and	CCONJ
ejpam-1950	226	19	1	1	NUM
ejpam-1950	226	20	/	/	SYM
ejpam-1950	226	21	p	p	NOUN
ejpam-1950	227	1	+	+	NOUN
ejpam-1950	227	2	1	1	NUM
ejpam-1950	227	3	/	/	SYM
ejpam-1950	227	4	q	q	NOUN
ejpam-1950	227	5	=	=	NOUN
ejpam-1950	227	6	1	1	X
ejpam-1950	227	7	.	.	PUNCT
ejpam-1950	228	1	if	if	SCONJ
ejpam-1950	228	2	the	the	DET
ejpam-1950	228	3	ideal	ideal	NOUN
ejpam-1950	228	4	i	i	PRON
ejpam-1950	228	5	has	have	VERB
ejpam-1950	228	6	property	property	NOUN
ejpam-1950	228	7	(	(	PUNCT
ejpam-1950	228	8	ap	ap	PROPN
ejpam-1950	228	9	)	)	PUNCT
ejpam-1950	228	10	,	,	PUNCT
ejpam-1950	228	11	then	then	ADV
ejpam-1950	228	12	:	:	PUNCT
ejpam-1950	228	13	(	(	PUNCT
ejpam-1950	228	14	i	i	NOUN
ejpam-1950	228	15	)	)	PUNCT
ejpam-1950	228	16	a	a	X
ejpam-1950	228	17	:	:	PUNCT
ejpam-1950	228	18	c	c	NOUN
ejpam-1950	228	19	b∗i	b∗i	PUNCT
ejpam-1950	228	20	−→	−→	NOUN
ejpam-1950	228	21	c	c	NOUN
ejpam-1950	228	22	if	if	SCONJ
ejpam-1950	228	23	and	and	CCONJ
ejpam-1950	228	24	only	only	ADV
ejpam-1950	228	25	if	if	SCONJ
ejpam-1950	228	26	∑	∑	PROPN
ejpam-1950	228	27	k	k	PROPN
ejpam-1950	228	28	|ank|=	|ank|=	PROPN
ejpam-1950	228	29	oi	oi	X
ejpam-1950	228	30	(	(	PUNCT
ejpam-1950	228	31	1	1	NUM
ejpam-1950	228	32	)	)	PUNCT
ejpam-1950	228	33	,	,	PUNCT
ejpam-1950	228	34	(	(	PUNCT
ejpam-1950	228	35	13	13	X
ejpam-1950	228	36	)	)	PUNCT
ejpam-1950	228	37	∃i	∃i	PROPN
ejpam-1950	228	38	lim	lim	PROPN
ejpam-1950	228	39	n	n	PROPN
ejpam-1950	228	40	ank	ank	PROPN
ejpam-1950	228	41	(	(	PUNCT
ejpam-1950	228	42	k	k	PROPN
ejpam-1950	228	43	∈	∈	PROPN
ejpam-1950	228	44	n	n	CCONJ
ejpam-1950	228	45	)	)	PUNCT
ejpam-1950	228	46	,	,	PUNCT
ejpam-1950	228	47	(	(	PUNCT
ejpam-1950	228	48	14	14	NUM
ejpam-1950	228	49	)	)	PUNCT
ejpam-1950	228	50	∃i	∃i	PROPN
ejpam-1950	228	51	lim	lim	PROPN
ejpam-1950	228	52	n	n	PROPN
ejpam-1950	228	53	∑	∑	PROPN
ejpam-1950	228	54	k	k	PROPN
ejpam-1950	228	55	ank	ank	PROPN
ejpam-1950	228	56	;	;	PUNCT
ejpam-1950	228	57	e.	e.	PROPN
ejpam-1950	228	58	kolk	kolk	PROPN
ejpam-1950	228	59	/	/	SYM
ejpam-1950	228	60	eur	eur	PROPN
ejpam-1950	228	61	.	.	PUNCT
ejpam-1950	229	1	j.	j.	PROPN
ejpam-1950	229	2	pure	pure	PROPN
ejpam-1950	229	3	appl	appl	PROPN
ejpam-1950	229	4	.	.	PROPN
ejpam-1950	229	5	math	math	PROPN
ejpam-1950	229	6	,	,	PUNCT
ejpam-1950	229	7	8	8	NUM
ejpam-1950	229	8	(	(	PUNCT
ejpam-1950	229	9	2015	2015	NUM
ejpam-1950	229	10	)	)	PUNCT
ejpam-1950	229	11	,	,	PUNCT
ejpam-1950	229	12	357	357	NUM
ejpam-1950	229	13	-	-	SYM
ejpam-1950	229	14	367	367	NUM
ejpam-1950	229	15	364	364	NUM
ejpam-1950	229	16	(	(	PUNCT
ejpam-1950	229	17	ii	ii	NOUN
ejpam-1950	229	18	)	)	PUNCT
ejpam-1950	229	19	a	a	PRON
ejpam-1950	229	20	:	:	PUNCT
ejpam-1950	229	21	c0	c0	PROPN
ejpam-1950	229	22	b∗i	b∗i	PUNCT
ejpam-1950	229	23	−→	−→	ADV
ejpam-1950	229	24	c	c	NOUN
ejpam-1950	229	25	if	if	SCONJ
ejpam-1950	230	1	and	and	CCONJ
ejpam-1950	230	2	only	only	ADV
ejpam-1950	230	3	if	if	SCONJ
ejpam-1950	230	4	(	(	PUNCT
ejpam-1950	230	5	13	13	NUM
ejpam-1950	230	6	)	)	PUNCT
ejpam-1950	230	7	and	and	CCONJ
ejpam-1950	230	8	(	(	PUNCT
ejpam-1950	230	9	14	14	NUM
ejpam-1950	230	10	)	)	PUNCT
ejpam-1950	230	11	hold	hold	VERB
ejpam-1950	230	12	;	;	PUNCT
ejpam-1950	230	13	(	(	PUNCT
ejpam-1950	230	14	iii	iii	X
ejpam-1950	230	15	)	)	PUNCT
ejpam-1950	230	16	a	a	DET
ejpam-1950	230	17	:	:	PUNCT
ejpam-1950	230	18	ℓ1	ℓ1	ADJ
ejpam-1950	230	19	b∗i	b∗i	PUNCT
ejpam-1950	230	20	−→	−→	NOUN
ejpam-1950	230	21	c	c	NOUN
ejpam-1950	230	22	if	if	SCONJ
ejpam-1950	230	23	and	and	CCONJ
ejpam-1950	230	24	only	only	ADV
ejpam-1950	230	25	if	if	SCONJ
ejpam-1950	230	26	(	(	PUNCT
ejpam-1950	230	27	14	14	NUM
ejpam-1950	230	28	)	)	PUNCT
ejpam-1950	230	29	is	be	AUX
ejpam-1950	230	30	satisfied	satisfied	ADJ
ejpam-1950	230	31	,	,	PUNCT
ejpam-1950	230	32	hn	hn	PROPN
ejpam-1950	230	33	=	=	NOUN
ejpam-1950	231	1	supk	supk	PRON
ejpam-1950	231	2	|ank|	|ank|	ADJ
ejpam-1950	231	3	<	<	X
ejpam-1950	231	4	∞	∞	PROPN
ejpam-1950	231	5	(	(	PUNCT
ejpam-1950	231	6	n	n	NOUN
ejpam-1950	231	7	∈	∈	PROPN
ejpam-1950	231	8	n	n	CCONJ
ejpam-1950	231	9	)	)	PUNCT
ejpam-1950	231	10	and	and	CCONJ
ejpam-1950	231	11	(	(	PUNCT
ejpam-1950	231	12	hn	hn	NOUN
ejpam-1950	231	13	)	)	PUNCT
ejpam-1950	231	14	is	be	AUX
ejpam-1950	231	15	i	i	PRON
ejpam-1950	231	16	-bounded	-bounded	ADJ
ejpam-1950	231	17	;	;	PUNCT
ejpam-1950	231	18	(	(	PUNCT
ejpam-1950	231	19	iv	iv	X
ejpam-1950	231	20	)	)	PUNCT
ejpam-1950	231	21	a	a	PRON
ejpam-1950	231	22	:	:	PUNCT
ejpam-1950	231	23	ℓp	ℓp	ADJ
ejpam-1950	231	24	b∗i	b∗i	PUNCT
ejpam-1950	231	25	−→	−→	NOUN
ejpam-1950	231	26	c	c	NOUN
ejpam-1950	231	27	if	if	SCONJ
ejpam-1950	231	28	and	and	CCONJ
ejpam-1950	231	29	only	only	ADV
ejpam-1950	231	30	if	if	SCONJ
ejpam-1950	231	31	(	(	PUNCT
ejpam-1950	231	32	14	14	NUM
ejpam-1950	231	33	)	)	PUNCT
ejpam-1950	231	34	is	be	AUX
ejpam-1950	231	35	satisfied	satisfied	ADJ
ejpam-1950	231	36	and	and	CCONJ
ejpam-1950	232	1	∑	∑	ADP
ejpam-1950	232	2	k	k	PROPN
ejpam-1950	232	3	|ank|	|ank|	PROPN
ejpam-1950	232	4	q	q	X
ejpam-1950	232	5	=	=	SYM
ejpam-1950	232	6	oi	oi	X
ejpam-1950	232	7	(	(	PUNCT
ejpam-1950	232	8	1	1	NUM
ejpam-1950	232	9	)	)	PUNCT
ejpam-1950	232	10	.	.	PUNCT
ejpam-1950	233	1	letting	let	VERB
ejpam-1950	233	2	i	i	PRON
ejpam-1950	233	3	=	=	PUNCT
ejpam-1950	233	4	it	it	PRON
ejpam-1950	233	5	in	in	ADP
ejpam-1950	233	6	propositions	proposition	NOUN
ejpam-1950	233	7	2	2	NUM
ejpam-1950	233	8	,	,	PUNCT
ejpam-1950	233	9	3	3	NUM
ejpam-1950	233	10	and	and	CCONJ
ejpam-1950	233	11	corollary	corollary	ADJ
ejpam-1950	233	12	1	1	NUM
ejpam-1950	233	13	,	,	PUNCT
ejpam-1950	233	14	we	we	PRON
ejpam-1950	233	15	get	get	VERB
ejpam-1950	233	16	the	the	DET
ejpam-1950	233	17	characterizations	characterization	NOUN
ejpam-1950	233	18	of	of	ADP
ejpam-1950	233	19	analogical	analogical	ADJ
ejpam-1950	233	20	matrix	matrix	NOUN
ejpam-1950	233	21	maps	map	NOUN
ejpam-1950	233	22	in	in	ADP
ejpam-1950	233	23	the	the	DET
ejpam-1950	233	24	sense	sense	NOUN
ejpam-1950	233	25	of	of	ADP
ejpam-1950	233	26	b∗t	b∗t	PUNCT
ejpam-1950	233	27	-statistical	-statistical	ADJ
ejpam-1950	233	28	convergence	convergence	NOUN
ejpam-1950	233	29	.	.	PUNCT
ejpam-1950	234	1	we	we	PRON
ejpam-1950	234	2	also	also	ADV
ejpam-1950	234	3	remark	remark	VERB
ejpam-1950	234	4	that	that	SCONJ
ejpam-1950	234	5	the	the	DET
ejpam-1950	234	6	matrix	matrix	NOUN
ejpam-1950	234	7	maps	map	NOUN
ejpam-1950	234	8	in	in	ADP
ejpam-1950	234	9	the	the	DET
ejpam-1950	234	10	sense	sense	NOUN
ejpam-1950	234	11	of	of	ADP
ejpam-1950	234	12	bi	bi	NOUN
ejpam-1950	234	13	and	and	CCONJ
ejpam-1950	234	14	bstt	bstt	NOUN
ejpam-1950	234	15	-convergence	-convergence	PROPN
ejpam-1950	234	16	were	be	AUX
ejpam-1950	234	17	studied	study	VERB
ejpam-1950	234	18	in	in	ADP
ejpam-1950	234	19	[	[	X
ejpam-1950	234	20	15	15	NUM
ejpam-1950	234	21	]	]	PUNCT
ejpam-1950	234	22	.	.	PUNCT
ejpam-1950	235	1	at	at	ADP
ejpam-1950	235	2	the	the	DET
ejpam-1950	235	3	beginning	beginning	NOUN
ejpam-1950	235	4	of	of	ADP
ejpam-1950	235	5	section	section	NOUN
ejpam-1950	235	6	2	2	NUM
ejpam-1950	235	7	we	we	PRON
ejpam-1950	235	8	remarked	remark	VERB
ejpam-1950	235	9	that	that	SCONJ
ejpam-1950	235	10	a	a	DET
ejpam-1950	235	11	weakly	weakly	ADJ
ejpam-1950	235	12	i	i	PRON
ejpam-1950	235	13	-convergent	-convergent	ADJ
ejpam-1950	235	14	sequence	sequence	NOUN
ejpam-1950	235	15	is	be	AUX
ejpam-1950	235	16	not	not	PART
ejpam-1950	235	17	necessary	necessary	ADJ
ejpam-1950	235	18	i	i	PRON
ejpam-1950	235	19	-bounded	-bounded	ADJ
ejpam-1950	235	20	.	.	PUNCT
ejpam-1950	236	1	this	this	DET
ejpam-1950	236	2	fact	fact	NOUN
ejpam-1950	236	3	leads	lead	VERB
ejpam-1950	236	4	us	we	PRON
ejpam-1950	236	5	to	to	ADP
ejpam-1950	236	6	a	a	DET
ejpam-1950	236	7	new	new	ADJ
ejpam-1950	236	8	variant	variant	NOUN
ejpam-1950	236	9	of	of	ADP
ejpam-1950	236	10	weak	weak	ADJ
ejpam-1950	236	11	i	i	PROPN
ejpam-1950	236	12	-convergence	-convergence	PROPN
ejpam-1950	236	13	.	.	PUNCT
ejpam-1950	237	1	definition	definition	NOUN
ejpam-1950	237	2	3	3	NUM
ejpam-1950	237	3	.	.	PUNCT
ejpam-1950	238	1	a	a	DET
ejpam-1950	238	2	sequence	sequence	NOUN
ejpam-1950	238	3	x	x	NOUN
ejpam-1950	238	4	=	=	SYM
ejpam-1950	238	5	(	(	PUNCT
ejpam-1950	238	6	xn	xn	X
ejpam-1950	238	7	)	)	PUNCT
ejpam-1950	238	8	∈	∈	PROPN
ejpam-1950	238	9	ω(x	ω(x	PROPN
ejpam-1950	238	10	)	)	PUNCT
ejpam-1950	238	11	is	be	AUX
ejpam-1950	238	12	said	say	VERB
ejpam-1950	238	13	to	to	PART
ejpam-1950	238	14	be	be	AUX
ejpam-1950	238	15	weakly	weakly	ADJ
ejpam-1950	238	16	b∗i	b∗i	ADJ
ejpam-1950	238	17	-convergent	-convergent	ADJ
ejpam-1950	238	18	to	to	ADP
ejpam-1950	238	19	l	l	NOUN
ejpam-1950	238	20	∈	∈	PROPN
ejpam-1950	238	21	x	x	X
ejpam-1950	238	22	,	,	PUNCT
ejpam-1950	238	23	briefly	briefly	ADV
ejpam-1950	238	24	wb∗i	wb∗i	VERB
ejpam-1950	238	25	limn	limn	NOUN
ejpam-1950	238	26	xn	xn	PUNCT
ejpam-1950	239	1	=	=	SYM
ejpam-1950	239	2	l	l	NOUN
ejpam-1950	239	3	,	,	PUNCT
ejpam-1950	239	4	if	if	SCONJ
ejpam-1950	239	5	x	x	PRON
ejpam-1950	239	6	is	be	AUX
ejpam-1950	239	7	weakly	weakly	ADJ
ejpam-1950	239	8	i	i	PRON
ejpam-1950	239	9	-convergent	-convergent	ADJ
ejpam-1950	239	10	to	to	ADP
ejpam-1950	239	11	l	l	NOUN
ejpam-1950	239	12	and	and	CCONJ
ejpam-1950	239	13	there	there	PRON
ejpam-1950	239	14	is	be	VERB
ejpam-1950	239	15	a	a	DET
ejpam-1950	239	16	set	set	NOUN
ejpam-1950	239	17	k	k	PROPN
ejpam-1950	239	18	∈	∈	PROPN
ejpam-1950	239	19	f	f	X
ejpam-1950	239	20	(	(	PUNCT
ejpam-1950	239	21	i	i	NOUN
ejpam-1950	239	22	)	)	PUNCT
ejpam-1950	239	23	such	such	ADJ
ejpam-1950	239	24	that	that	SCONJ
ejpam-1950	239	25	the	the	DET
ejpam-1950	239	26	sequence	sequence	NOUN
ejpam-1950	239	27	(	(	PUNCT
ejpam-1950	239	28	x	x	SYM
ejpam-1950	239	29	′(xk))k∈k	′(xk))k∈k	NOUN
ejpam-1950	239	30	is	be	AUX
ejpam-1950	239	31	bounded	bound	VERB
ejpam-1950	239	32	for	for	ADP
ejpam-1950	239	33	every	every	DET
ejpam-1950	239	34	x	x	SYM
ejpam-1950	239	35	′	′	NUM
ejpam-1950	239	36	∈	∈	NOUN
ejpam-1950	239	37	x	x	NOUN
ejpam-1950	239	38	′.	′.	NOUN
ejpam-1950	239	39	for	for	ADP
ejpam-1950	239	40	i	i	PRON
ejpam-1950	240	1	=	=	PRON
ejpam-1950	240	2	it	it	PRON
ejpam-1950	240	3	we	we	PRON
ejpam-1950	240	4	get	get	VERB
ejpam-1950	240	5	the	the	DET
ejpam-1950	240	6	notion	notion	NOUN
ejpam-1950	240	7	of	of	ADP
ejpam-1950	240	8	weak	weak	ADJ
ejpam-1950	240	9	b∗t	b∗t	ADJ
ejpam-1950	240	10	-	-	PUNCT
ejpam-1950	240	11	statistical	statistical	ADJ
ejpam-1950	240	12	convergence	convergence	NOUN
ejpam-1950	240	13	,	,	PUNCT
ejpam-1950	240	14	in	in	ADP
ejpam-1950	240	15	this	this	DET
ejpam-1950	240	16	case	case	NOUN
ejpam-1950	240	17	we	we	PRON
ejpam-1950	240	18	write	write	VERB
ejpam-1950	240	19	wb∗stt	wb∗stt	PROPN
ejpam-1950	240	20	limn	limn	PROPN
ejpam-1950	240	21	xn	xn	PUNCT
ejpam-1950	241	1	=	=	PUNCT
ejpam-1950	241	2	l.	l.	PROPN
ejpam-1950	241	3	using	use	VERB
ejpam-1950	241	4	bounded	bound	VERB
ejpam-1950	241	5	linear	linear	PROPN
ejpam-1950	241	6	functionals	functional	NOUN
ejpam-1950	241	7	fz	fz	VERB
ejpam-1950	241	8	:	:	PUNCT
ejpam-1950	241	9	x	x	X
ejpam-1950	241	10	′	′	NUM
ejpam-1950	241	11	→	→	SYM
ejpam-1950	241	12	r	r	NOUN
ejpam-1950	241	13	,	,	PUNCT
ejpam-1950	241	14	fz	fz	NOUN
ejpam-1950	241	15	x	x	PUNCT
ejpam-1950	241	16	′	′	NUM
ejpam-1950	241	17	=	=	NOUN
ejpam-1950	241	18	x	x	NOUN
ejpam-1950	241	19	′(z	′(z	NOUN
ejpam-1950	241	20	)	)	PUNCT
ejpam-1950	241	21	(	(	PUNCT
ejpam-1950	241	22	x	x	X
ejpam-1950	241	23	′	′	NUM
ejpam-1950	241	24	∈	∈	NOUN
ejpam-1950	241	25	x	x	PUNCT
ejpam-1950	241	26	′	′	NOUN
ejpam-1950	241	27	,	,	PUNCT
ejpam-1950	241	28	z	z	NOUN
ejpam-1950	241	29	∈	∈	PROPN
ejpam-1950	241	30	x	x	X
ejpam-1950	241	31	)	)	PUNCT
ejpam-1950	241	32	,	,	PUNCT
ejpam-1950	241	33	we	we	PRON
ejpam-1950	241	34	can	can	AUX
ejpam-1950	241	35	say	say	VERB
ejpam-1950	241	36	that	that	SCONJ
ejpam-1950	241	37	wb∗i	wb∗i	VERB
ejpam-1950	241	38	limn	limn	NOUN
ejpam-1950	241	39	xn	xn	PUNCT
ejpam-1950	242	1	=	=	PUNCT
ejpam-1950	242	2	l	l	PROPN
ejpam-1950	242	3	(	(	PUNCT
ejpam-1950	242	4	wb∗stt	wb∗stt	PROPN
ejpam-1950	242	5	limn	limn	PROPN
ejpam-1950	242	6	xn	xn	PUNCT
ejpam-1950	243	1	=	=	PUNCT
ejpam-1950	243	2	l	l	NOUN
ejpam-1950	243	3	)	)	PUNCT
ejpam-1950	243	4	if	if	SCONJ
ejpam-1950	243	5	and	and	CCONJ
ejpam-1950	243	6	only	only	ADV
ejpam-1950	243	7	if	if	SCONJ
ejpam-1950	243	8	the	the	DET
ejpam-1950	243	9	sequence	sequence	NOUN
ejpam-1950	243	10	(	(	PUNCT
ejpam-1950	243	11	fxn	fxn	NOUN
ejpam-1950	243	12	)	)	PUNCT
ejpam-1950	243	13	is	be	AUX
ejpam-1950	243	14	b∗i	b∗i	ADJ
ejpam-1950	243	15	-convergent	-convergent	ADJ
ejpam-1950	243	16	(	(	PUNCT
ejpam-1950	243	17	b∗t	b∗t	NUM
ejpam-1950	243	18	-statistically	-statistically	ADV
ejpam-1950	243	19	convergent	convergent	NOUN
ejpam-1950	243	20	)	)	PUNCT
ejpam-1950	243	21	to	to	ADP
ejpam-1950	243	22	fl	fl	PROPN
ejpam-1950	243	23	.	.	PUNCT
ejpam-1950	244	1	thus	thus	ADV
ejpam-1950	244	2	,	,	PUNCT
ejpam-1950	244	3	since	since	SCONJ
ejpam-1950	244	4	‖fz‖	‖fz‖	PROPN
ejpam-1950	244	5	=	=	SYM
ejpam-1950	244	6	‖z‖	‖z‖	PROPN
ejpam-1950	244	7	,	,	PUNCT
ejpam-1950	244	8	by	by	ADP
ejpam-1950	244	9	theorems	theorem	NOUN
ejpam-1950	244	10	4	4	NUM
ejpam-1950	244	11	and	and	CCONJ
ejpam-1950	244	12	5	5	NUM
ejpam-1950	244	13	we	we	PRON
ejpam-1950	244	14	get	get	VERB
ejpam-1950	244	15	the	the	DET
ejpam-1950	244	16	following	follow	VERB
ejpam-1950	244	17	characterizations	characterization	NOUN
ejpam-1950	244	18	of	of	ADP
ejpam-1950	244	19	these	these	DET
ejpam-1950	244	20	new	new	ADJ
ejpam-1950	244	21	types	type	NOUN
ejpam-1950	244	22	of	of	ADP
ejpam-1950	244	23	weak	weak	ADJ
ejpam-1950	244	24	convergence	convergence	NOUN
ejpam-1950	244	25	.	.	PUNCT
ejpam-1950	245	1	proposition	proposition	NOUN
ejpam-1950	245	2	4	4	NUM
ejpam-1950	245	3	.	.	PUNCT
ejpam-1950	246	1	let	let	VERB
ejpam-1950	246	2	x	x	PUNCT
ejpam-1950	246	3	=	=	SYM
ejpam-1950	246	4	(	(	PUNCT
ejpam-1950	246	5	xn	xn	X
ejpam-1950	246	6	)	)	PUNCT
ejpam-1950	246	7	∈	∈	PROPN
ejpam-1950	246	8	ω(x	ω(x	PROPN
ejpam-1950	246	9	)	)	PUNCT
ejpam-1950	246	10	and	and	CCONJ
ejpam-1950	246	11	l	l	NOUN
ejpam-1950	246	12	∈	∈	PROPN
ejpam-1950	246	13	x	x	X
ejpam-1950	246	14	.	.	PUNCT
ejpam-1950	247	1	assume	assume	VERB
ejpam-1950	247	2	that	that	SCONJ
ejpam-1950	247	3	x	x	SYM
ejpam-1950	247	4	′	′	NOUN
ejpam-1950	247	5	has	have	VERB
ejpam-1950	247	6	a	a	DET
ejpam-1950	247	7	countable	countable	ADJ
ejpam-1950	247	8	fundamental	fundamental	ADJ
ejpam-1950	247	9	set	set	NOUN
ejpam-1950	247	10	φ′.	φ′.	INTJ
ejpam-1950	247	11	(	(	PUNCT
ejpam-1950	247	12	i	i	NOUN
ejpam-1950	247	13	)	)	PUNCT
ejpam-1950	247	14	if	if	SCONJ
ejpam-1950	247	15	i	i	PRON
ejpam-1950	247	16	is	be	AUX
ejpam-1950	247	17	an	an	DET
ejpam-1950	247	18	ideal	ideal	NOUN
ejpam-1950	247	19	with	with	ADP
ejpam-1950	247	20	the	the	DET
ejpam-1950	247	21	property	property	NOUN
ejpam-1950	247	22	(	(	PUNCT
ejpam-1950	247	23	ap	ap	PROPN
ejpam-1950	247	24	)	)	PUNCT
ejpam-1950	247	25	,	,	PUNCT
ejpam-1950	247	26	then	then	ADV
ejpam-1950	247	27	wb∗i	wb∗i	VERB
ejpam-1950	247	28	limn	limn	NOUN
ejpam-1950	247	29	xn	xn	PUNCT
ejpam-1950	248	1	=	=	PUNCT
ejpam-1950	248	2	l	l	NOUN
ejpam-1950	248	3	if	if	SCONJ
ejpam-1950	248	4	and	and	CCONJ
ejpam-1950	248	5	only	only	ADV
ejpam-1950	248	6	if	if	SCONJ
ejpam-1950	248	7	‖xn‖=oi	‖xn‖=oi	NOUN
ejpam-1950	248	8	(	(	PUNCT
ejpam-1950	248	9	1	1	NUM
ejpam-1950	248	10	)	)	PUNCT
ejpam-1950	248	11	,	,	PUNCT
ejpam-1950	248	12	(	(	PUNCT
ejpam-1950	248	13	15	15	X
ejpam-1950	248	14	)	)	PUNCT
ejpam-1950	248	15	i	i	PRON
ejpam-1950	248	16	lim	lim	PROPN
ejpam-1950	248	17	n	n	PRON
ejpam-1950	248	18	φ′(xn	φ′(xn	PROPN
ejpam-1950	248	19	)	)	PUNCT
ejpam-1950	248	20	=	=	PROPN
ejpam-1950	248	21	φ	φ	PROPN
ejpam-1950	248	22	′(l	′(l	ADV
ejpam-1950	248	23	)	)	PUNCT
ejpam-1950	248	24	(	(	PUNCT
ejpam-1950	248	25	φ′	φ′	NUM
ejpam-1950	248	26	∈	∈	PROPN
ejpam-1950	248	27	φ′	φ′	NUM
ejpam-1950	248	28	)	)	PUNCT
ejpam-1950	248	29	.	.	PUNCT
ejpam-1950	249	1	(	(	PUNCT
ejpam-1950	249	2	16	16	NUM
ejpam-1950	249	3	)	)	PUNCT
ejpam-1950	249	4	(	(	PUNCT
ejpam-1950	249	5	ii	ii	NOUN
ejpam-1950	249	6	)	)	PUNCT
ejpam-1950	249	7	if	if	SCONJ
ejpam-1950	249	8	t	t	PROPN
ejpam-1950	249	9	is	be	AUX
ejpam-1950	249	10	a	a	DET
ejpam-1950	249	11	regular	regular	ADJ
ejpam-1950	249	12	matrix	matrix	NOUN
ejpam-1950	249	13	,	,	PUNCT
ejpam-1950	249	14	then	then	ADV
ejpam-1950	249	15	wb∗stt	wb∗stt	PROPN
ejpam-1950	249	16	limn	limn	PROPN
ejpam-1950	249	17	xn	xn	PUNCT
ejpam-1950	250	1	=	=	PUNCT
ejpam-1950	250	2	l	l	NOUN
ejpam-1950	250	3	if	if	SCONJ
ejpam-1950	250	4	and	and	CCONJ
ejpam-1950	250	5	only	only	ADV
ejpam-1950	250	6	if	if	SCONJ
ejpam-1950	250	7	(	(	PUNCT
ejpam-1950	250	8	15	15	NUM
ejpam-1950	250	9	)	)	PUNCT
ejpam-1950	250	10	and	and	CCONJ
ejpam-1950	250	11	(	(	PUNCT
ejpam-1950	250	12	16	16	NUM
ejpam-1950	250	13	)	)	PUNCT
ejpam-1950	250	14	are	be	AUX
ejpam-1950	250	15	satisfied	satisfied	ADJ
ejpam-1950	250	16	with	with	ADP
ejpam-1950	250	17	stt	stt	PROPN
ejpam-1950	250	18	instead	instead	ADV
ejpam-1950	250	19	of	of	ADP
ejpam-1950	250	20	i	i	PRON
ejpam-1950	250	21	.	.	PUNCT
ejpam-1950	251	1	finally	finally	ADV
ejpam-1950	251	2	we	we	PRON
ejpam-1950	251	3	apply	apply	VERB
ejpam-1950	251	4	proposition	proposition	NOUN
ejpam-1950	251	5	4	4	NUM
ejpam-1950	251	6	to	to	PART
ejpam-1950	251	7	banach	banach	NOUN
ejpam-1950	251	8	sequence	sequence	NOUN
ejpam-1950	251	9	spaces	space	VERB
ejpam-1950	251	10	c0(x	c0(x	X
ejpam-1950	251	11	)	)	PUNCT
ejpam-1950	251	12	and	and	CCONJ
ejpam-1950	251	13	ℓp(x	ℓp(x	NUM
ejpam-1950	251	14	)	)	PUNCT
ejpam-1950	251	15	with	with	ADP
ejpam-1950	251	16	1	1	NUM
ejpam-1950	251	17	<	<	X
ejpam-1950	251	18	p	p	X
ejpam-1950	251	19	<	<	X
ejpam-1950	251	20	∞.	∞.	PROPN
ejpam-1950	251	21	it	it	PRON
ejpam-1950	251	22	is	be	AUX
ejpam-1950	251	23	known	know	VERB
ejpam-1950	251	24	that	that	SCONJ
ejpam-1950	251	25	the	the	DET
ejpam-1950	251	26	dual	dual	ADJ
ejpam-1950	251	27	spaces	space	NOUN
ejpam-1950	251	28	c0(x	c0(x	X
ejpam-1950	251	29	)	)	PUNCT
ejpam-1950	251	30	′	′	NOUN
ejpam-1950	251	31	and	and	CCONJ
ejpam-1950	251	32	ℓp(x	ℓp(x	PUNCT
ejpam-1950	251	33	)	)	PUNCT
ejpam-1950	251	34	′	′	NUM
ejpam-1950	251	35	are	be	AUX
ejpam-1950	251	36	isometrically	isometrically	PROPN
ejpam-1950	251	37	isomorphic	isomorphic	ADJ
ejpam-1950	251	38	,	,	PUNCT
ejpam-1950	251	39	respectively	respectively	ADV
ejpam-1950	251	40	,	,	PUNCT
ejpam-1950	251	41	to	to	ADP
ejpam-1950	251	42	ℓ1(x	ℓ1(x	NOUN
ejpam-1950	251	43	′	′	NUM
ejpam-1950	251	44	)	)	PUNCT
ejpam-1950	251	45	and	and	CCONJ
ejpam-1950	251	46	ℓq(x	ℓq(x	PUNCT
ejpam-1950	251	47	′	′	NOUN
ejpam-1950	251	48	)	)	PUNCT
ejpam-1950	251	49	,	,	PUNCT
ejpam-1950	251	50	where	where	SCONJ
ejpam-1950	251	51	1	1	X
ejpam-1950	251	52	/	/	SYM
ejpam-1950	251	53	p	p	NOUN
ejpam-1950	252	1	+	+	NOUN
ejpam-1950	252	2	1	1	NUM
ejpam-1950	252	3	/	/	SYM
ejpam-1950	252	4	q	q	NOUN
ejpam-1950	252	5	=	=	SYM
ejpam-1950	252	6	1	1	NUM
ejpam-1950	252	7	(	(	PUNCT
ejpam-1950	252	8	see	see	VERB
ejpam-1950	252	9	,	,	PUNCT
ejpam-1950	252	10	for	for	ADP
ejpam-1950	252	11	example	example	NOUN
ejpam-1950	252	12	,	,	PUNCT
ejpam-1950	252	13	[	[	X
ejpam-1950	252	14	18	18	NUM
ejpam-1950	252	15	]	]	PUNCT
ejpam-1950	252	16	)	)	PUNCT
ejpam-1950	252	17	.	.	PUNCT
ejpam-1950	253	1	if	if	SCONJ
ejpam-1950	253	2	φ′	φ′	NUM
ejpam-1950	253	3	is	be	AUX
ejpam-1950	253	4	a	a	DET
ejpam-1950	253	5	fundamental	fundamental	ADJ
ejpam-1950	253	6	set	set	NOUN
ejpam-1950	253	7	of	of	ADP
ejpam-1950	253	8	x	x	PROPN
ejpam-1950	253	9	′	′	NUM
ejpam-1950	253	10	,	,	PUNCT
ejpam-1950	253	11	then	then	ADV
ejpam-1950	253	12	e0(φ	e0(φ	PROPN
ejpam-1950	253	13	′	′	NOUN
ejpam-1950	253	14	)	)	PUNCT
ejpam-1950	253	15	is	be	AUX
ejpam-1950	253	16	the	the	DET
ejpam-1950	253	17	fundamental	fundamental	ADJ
ejpam-1950	253	18	set	set	NOUN
ejpam-1950	253	19	of	of	ADP
ejpam-1950	253	20	ℓ1(x	ℓ1(x	NOUN
ejpam-1950	253	21	′	′	NOUN
ejpam-1950	253	22	)	)	PUNCT
ejpam-1950	253	23	and	and	CCONJ
ejpam-1950	253	24	ℓq(x	ℓq(x	PUNCT
ejpam-1950	253	25	′	′	NOUN
ejpam-1950	253	26	)	)	PUNCT
ejpam-1950	253	27	.	.	PUNCT
ejpam-1950	254	1	thus	thus	ADV
ejpam-1950	254	2	from	from	ADP
ejpam-1950	254	3	proposition	proposition	NOUN
ejpam-1950	254	4	4	4	NUM
ejpam-1950	254	5	we	we	PRON
ejpam-1950	254	6	get	get	VERB
ejpam-1950	254	7	the	the	DET
ejpam-1950	254	8	following	follow	VERB
ejpam-1950	254	9	two	two	NUM
ejpam-1950	254	10	corollaries	corollary	NOUN
ejpam-1950	254	11	.	.	PUNCT
ejpam-1950	255	1	corollary	corollary	ADJ
ejpam-1950	255	2	2	2	NUM
ejpam-1950	255	3	.	.	PUNCT
ejpam-1950	256	1	let	let	VERB
ejpam-1950	256	2	xn	xn	PUNCT
ejpam-1950	257	1	=	=	SYM
ejpam-1950	257	2	(	(	PUNCT
ejpam-1950	257	3	xni	xni	PROPN
ejpam-1950	257	4	)	)	PUNCT
ejpam-1950	257	5	(	(	PUNCT
ejpam-1950	257	6	n	n	CCONJ
ejpam-1950	257	7	∈	∈	PROPN
ejpam-1950	257	8	n	n	CCONJ
ejpam-1950	257	9	)	)	PUNCT
ejpam-1950	257	10	and	and	CCONJ
ejpam-1950	257	11	x0	x0	NUM
ejpam-1950	257	12	=	=	PRON
ejpam-1950	258	1	(	(	PUNCT
ejpam-1950	258	2	x	x	SYM
ejpam-1950	258	3	i	i	NOUN
ejpam-1950	258	4	)	)	PUNCT
ejpam-1950	258	5	be	be	VERB
ejpam-1950	258	6	the	the	DET
ejpam-1950	258	7	elements	element	NOUN
ejpam-1950	258	8	of	of	ADP
ejpam-1950	258	9	c0(x	c0(x	X
ejpam-1950	258	10	)	)	PUNCT
ejpam-1950	258	11	.	.	PUNCT
ejpam-1950	259	1	assume	assume	VERB
ejpam-1950	259	2	that	that	SCONJ
ejpam-1950	259	3	the	the	DET
ejpam-1950	259	4	dual	dual	ADJ
ejpam-1950	259	5	x	x	SYM
ejpam-1950	259	6	′	′	NOUN
ejpam-1950	259	7	has	have	VERB
ejpam-1950	259	8	a	a	DET
ejpam-1950	259	9	countable	countable	ADJ
ejpam-1950	259	10	fundamental	fundamental	ADJ
ejpam-1950	259	11	set	set	NOUN
ejpam-1950	259	12	φ′.	φ′.	PROPN
ejpam-1950	259	13	references	reference	NOUN
ejpam-1950	259	14	365	365	NUM
ejpam-1950	259	15	(	(	PUNCT
ejpam-1950	259	16	i	i	NOUN
ejpam-1950	259	17	)	)	PUNCT
ejpam-1950	259	18	if	if	SCONJ
ejpam-1950	259	19	i	i	PRON
ejpam-1950	259	20	is	be	AUX
ejpam-1950	259	21	an	an	DET
ejpam-1950	259	22	ideal	ideal	NOUN
ejpam-1950	259	23	with	with	ADP
ejpam-1950	259	24	the	the	DET
ejpam-1950	259	25	property	property	NOUN
ejpam-1950	259	26	(	(	PUNCT
ejpam-1950	259	27	ap	ap	PROPN
ejpam-1950	259	28	)	)	PUNCT
ejpam-1950	259	29	,	,	PUNCT
ejpam-1950	259	30	then	then	ADV
ejpam-1950	259	31	wb∗i	wb∗i	VERB
ejpam-1950	259	32	limn	limn	NOUN
ejpam-1950	259	33	xn	xn	PUNCT
ejpam-1950	260	1	=	=	PUNCT
ejpam-1950	260	2	x0	x0	PROPN
ejpam-1950	260	3	if	if	SCONJ
ejpam-1950	260	4	and	and	CCONJ
ejpam-1950	260	5	only	only	ADV
ejpam-1950	260	6	if	if	SCONJ
ejpam-1950	260	7	‖xn‖∞	‖xn‖∞	PROPN
ejpam-1950	260	8	=	=	SYM
ejpam-1950	260	9	oi	oi	X
ejpam-1950	260	10	(	(	PUNCT
ejpam-1950	260	11	1	1	NUM
ejpam-1950	260	12	)	)	PUNCT
ejpam-1950	260	13	,	,	PUNCT
ejpam-1950	260	14	(	(	PUNCT
ejpam-1950	260	15	17	17	NUM
ejpam-1950	260	16	)	)	PUNCT
ejpam-1950	261	1	i	i	PRON
ejpam-1950	261	2	lim	lim	PROPN
ejpam-1950	261	3	i	i	PRON
ejpam-1950	261	4	φ′(xni	φ′(xni	NUM
ejpam-1950	261	5	)	)	PUNCT
ejpam-1950	262	1	=	=	NOUN
ejpam-1950	262	2	φ	φ	NOUN
ejpam-1950	262	3	′(x	′(x	NOUN
ejpam-1950	262	4	i	i	NOUN
ejpam-1950	262	5	)	)	PUNCT
ejpam-1950	262	6	(	(	PUNCT
ejpam-1950	262	7	φ	φ	PROPN
ejpam-1950	262	8	′	′	NUM
ejpam-1950	262	9	∈	∈	PROPN
ejpam-1950	262	10	φ′	φ′	PROPN
ejpam-1950	262	11	,	,	PUNCT
ejpam-1950	262	12	n	n	PROPN
ejpam-1950	262	13	∈	∈	PROPN
ejpam-1950	262	14	n	n	CCONJ
ejpam-1950	262	15	)	)	PUNCT
ejpam-1950	262	16	.	.	PUNCT
ejpam-1950	263	1	(	(	PUNCT
ejpam-1950	263	2	18	18	NUM
ejpam-1950	263	3	)	)	PUNCT
ejpam-1950	263	4	(	(	PUNCT
ejpam-1950	263	5	ii	ii	NOUN
ejpam-1950	263	6	)	)	PUNCT
ejpam-1950	263	7	if	if	SCONJ
ejpam-1950	263	8	t	t	PROPN
ejpam-1950	263	9	is	be	AUX
ejpam-1950	263	10	a	a	DET
ejpam-1950	263	11	non	non	ADJ
ejpam-1950	263	12	-	-	ADJ
ejpam-1950	263	13	negative	negative	ADJ
ejpam-1950	263	14	regular	regular	ADJ
ejpam-1950	263	15	matrix	matrix	NOUN
ejpam-1950	263	16	,	,	PUNCT
ejpam-1950	263	17	then	then	ADV
ejpam-1950	263	18	wb∗stt	wb∗stt	PROPN
ejpam-1950	263	19	limn	limn	PROPN
ejpam-1950	263	20	xn	xn	PUNCT
ejpam-1950	264	1	=	=	PUNCT
ejpam-1950	264	2	x0	x0	PROPN
ejpam-1950	264	3	if	if	SCONJ
ejpam-1950	264	4	and	and	CCONJ
ejpam-1950	264	5	only	only	ADV
ejpam-1950	264	6	(	(	PUNCT
ejpam-1950	264	7	17	17	NUM
ejpam-1950	264	8	)	)	PUNCT
ejpam-1950	264	9	and	and	CCONJ
ejpam-1950	264	10	(	(	PUNCT
ejpam-1950	264	11	18	18	NUM
ejpam-1950	264	12	)	)	PUNCT
ejpam-1950	264	13	hold	hold	VERB
ejpam-1950	264	14	with	with	ADP
ejpam-1950	264	15	stt	stt	PROPN
ejpam-1950	264	16	instead	instead	ADV
ejpam-1950	264	17	of	of	ADP
ejpam-1950	264	18	i	i	PRON
ejpam-1950	264	19	.	.	PUNCT
ejpam-1950	265	1	corollary	corollary	ADJ
ejpam-1950	265	2	3	3	X
ejpam-1950	265	3	.	.	PUNCT
ejpam-1950	266	1	let	let	VERB
ejpam-1950	266	2	xn	xn	PUNCT
ejpam-1950	267	1	=	=	SYM
ejpam-1950	267	2	(	(	PUNCT
ejpam-1950	267	3	xni	xni	PROPN
ejpam-1950	267	4	)	)	PUNCT
ejpam-1950	267	5	(	(	PUNCT
ejpam-1950	267	6	n	n	CCONJ
ejpam-1950	267	7	∈	∈	PROPN
ejpam-1950	267	8	n	n	CCONJ
ejpam-1950	267	9	)	)	PUNCT
ejpam-1950	267	10	and	and	CCONJ
ejpam-1950	267	11	x0	x0	NUM
ejpam-1950	267	12	=	=	PRON
ejpam-1950	268	1	(	(	PUNCT
ejpam-1950	268	2	x	x	SYM
ejpam-1950	268	3	i	i	NOUN
ejpam-1950	268	4	)	)	PUNCT
ejpam-1950	268	5	be	be	VERB
ejpam-1950	268	6	the	the	DET
ejpam-1950	268	7	elements	element	NOUN
ejpam-1950	268	8	of	of	ADP
ejpam-1950	268	9	ℓp(x	ℓp(x	NUM
ejpam-1950	268	10	)	)	PUNCT
ejpam-1950	268	11	(	(	PUNCT
ejpam-1950	268	12	1	1	NUM
ejpam-1950	268	13	<	<	X
ejpam-1950	268	14	p	p	X
ejpam-1950	268	15	<	<	X
ejpam-1950	268	16	∞	∞	NUM
ejpam-1950	268	17	)	)	PUNCT
ejpam-1950	268	18	.	.	PUNCT
ejpam-1950	269	1	assume	assume	VERB
ejpam-1950	269	2	that	that	SCONJ
ejpam-1950	269	3	x	x	SYM
ejpam-1950	269	4	′	′	NOUN
ejpam-1950	269	5	has	have	VERB
ejpam-1950	269	6	a	a	DET
ejpam-1950	269	7	countable	countable	ADJ
ejpam-1950	269	8	fundamental	fundamental	ADJ
ejpam-1950	269	9	set	set	NOUN
ejpam-1950	269	10	φ′.	φ′.	INTJ
ejpam-1950	269	11	(	(	PUNCT
ejpam-1950	269	12	i	i	NOUN
ejpam-1950	269	13	)	)	PUNCT
ejpam-1950	269	14	if	if	SCONJ
ejpam-1950	269	15	i	i	PRON
ejpam-1950	269	16	is	be	AUX
ejpam-1950	269	17	an	an	DET
ejpam-1950	269	18	ideal	ideal	NOUN
ejpam-1950	269	19	with	with	ADP
ejpam-1950	269	20	the	the	DET
ejpam-1950	269	21	property	property	NOUN
ejpam-1950	269	22	(	(	PUNCT
ejpam-1950	269	23	ap	ap	PROPN
ejpam-1950	269	24	)	)	PUNCT
ejpam-1950	269	25	,	,	PUNCT
ejpam-1950	269	26	then	then	ADV
ejpam-1950	269	27	wb∗i	wb∗i	VERB
ejpam-1950	269	28	limn	limn	NOUN
ejpam-1950	269	29	xn	xn	PUNCT
ejpam-1950	270	1	=	=	PUNCT
ejpam-1950	270	2	x0	x0	PROPN
ejpam-1950	270	3	if	if	SCONJ
ejpam-1950	270	4	and	and	CCONJ
ejpam-1950	270	5	only	only	ADV
ejpam-1950	270	6	if	if	SCONJ
ejpam-1950	270	7	(	(	PUNCT
ejpam-1950	270	8	18	18	NUM
ejpam-1950	270	9	)	)	PUNCT
ejpam-1950	270	10	is	be	AUX
ejpam-1950	270	11	true	true	ADJ
ejpam-1950	270	12	and	and	CCONJ
ejpam-1950	270	13	‖xn‖p	‖xn‖p	PROPN
ejpam-1950	270	14	=	=	SYM
ejpam-1950	270	15	oi	oi	X
ejpam-1950	270	16	(	(	PUNCT
ejpam-1950	270	17	1	1	NUM
ejpam-1950	270	18	)	)	PUNCT
ejpam-1950	270	19	.	.	PUNCT
ejpam-1950	271	1	(	(	PUNCT
ejpam-1950	271	2	19	19	NUM
ejpam-1950	271	3	)	)	PUNCT
ejpam-1950	271	4	(	(	PUNCT
ejpam-1950	271	5	ii	ii	NOUN
ejpam-1950	271	6	)	)	PUNCT
ejpam-1950	271	7	if	if	SCONJ
ejpam-1950	271	8	t	t	PROPN
ejpam-1950	271	9	is	be	AUX
ejpam-1950	271	10	a	a	DET
ejpam-1950	271	11	non	non	ADJ
ejpam-1950	271	12	-	-	ADJ
ejpam-1950	271	13	negative	negative	ADJ
ejpam-1950	271	14	regular	regular	ADJ
ejpam-1950	271	15	matrix	matrix	NOUN
ejpam-1950	271	16	,	,	PUNCT
ejpam-1950	271	17	then	then	ADV
ejpam-1950	271	18	wb∗stt	wb∗stt	PROPN
ejpam-1950	271	19	limn	limn	PROPN
ejpam-1950	271	20	xn	xn	PUNCT
ejpam-1950	272	1	=	=	PUNCT
ejpam-1950	272	2	x0	x0	PROPN
ejpam-1950	272	3	if	if	SCONJ
ejpam-1950	272	4	and	and	CCONJ
ejpam-1950	272	5	only	only	ADV
ejpam-1950	272	6	(	(	PUNCT
ejpam-1950	272	7	18	18	NUM
ejpam-1950	272	8	)	)	PUNCT
ejpam-1950	272	9	and	and	CCONJ
ejpam-1950	272	10	(	(	PUNCT
ejpam-1950	272	11	19	19	NUM
ejpam-1950	272	12	)	)	PUNCT
ejpam-1950	272	13	hold	hold	VERB
ejpam-1950	272	14	with	with	ADP
ejpam-1950	272	15	stt	stt	PROPN
ejpam-1950	272	16	instead	instead	ADV
ejpam-1950	272	17	of	of	ADP
ejpam-1950	272	18	i	i	PRON
ejpam-1950	272	19	.	.	PUNCT
ejpam-1950	273	1	proposition	proposition	NOUN
ejpam-1950	273	2	4(ii	4(ii	NUM
ejpam-1950	273	3	)	)	PUNCT
ejpam-1950	273	4	and	and	CCONJ
ejpam-1950	273	5	corollary	corollary	ADJ
ejpam-1950	273	6	3(ii	3(ii	NUM
ejpam-1950	273	7	)	)	PUNCT
ejpam-1950	273	8	,	,	PUNCT
ejpam-1950	273	9	for	for	ADP
ejpam-1950	273	10	t	t	PROPN
ejpam-1950	273	11	=	=	SYM
ejpam-1950	273	12	c1	c1	PROPN
ejpam-1950	273	13	,	,	PUNCT
ejpam-1950	273	14	may	may	AUX
ejpam-1950	273	15	be	be	AUX
ejpam-1950	273	16	considered	consider	VERB
ejpam-1950	273	17	as	as	ADP
ejpam-1950	273	18	some	some	DET
ejpam-1950	273	19	corrected	correct	VERB
ejpam-1950	273	20	versions	version	NOUN
ejpam-1950	273	21	,	,	PUNCT
ejpam-1950	273	22	respectively	respectively	ADV
ejpam-1950	273	23	,	,	PUNCT
ejpam-1950	273	24	of	of	ADP
ejpam-1950	273	25	theorem	theorem	ADJ
ejpam-1950	273	26	3.1	3.1	NUM
ejpam-1950	273	27	and	and	CCONJ
ejpam-1950	273	28	lemma	lemma	PROPN
ejpam-1950	273	29	3.2	3.2	NUM
ejpam-1950	273	30	from	from	ADP
ejpam-1950	273	31	[	[	X
ejpam-1950	273	32	2	2	NUM
ejpam-1950	273	33	]	]	PUNCT
ejpam-1950	273	34	.	.	PUNCT
ejpam-1950	274	1	acknowledgements	acknowledgement	NOUN
ejpam-1950	274	2	the	the	DET
ejpam-1950	274	3	author	author	NOUN
ejpam-1950	274	4	is	be	AUX
ejpam-1950	274	5	thankful	thankful	ADJ
ejpam-1950	274	6	for	for	ADP
ejpam-1950	274	7	the	the	DET
ejpam-1950	274	8	support	support	NOUN
ejpam-1950	274	9	by	by	ADP
ejpam-1950	274	10	institutional	institutional	ADJ
ejpam-1950	274	11	research	research	NOUN
ejpam-1950	274	12	funding	funding	NOUN
ejpam-1950	274	13	iut20	iut20	PROPN
ejpam-1950	274	14	-	-	PUNCT
ejpam-1950	274	15	57	57	NUM
ejpam-1950	274	16	of	of	ADP
ejpam-1950	274	17	the	the	DET
ejpam-1950	274	18	estonian	estonian	ADJ
ejpam-1950	274	19	ministry	ministry	PROPN
ejpam-1950	274	20	of	of	ADP
ejpam-1950	274	21	education	education	NOUN
ejpam-1950	274	22	and	and	CCONJ
ejpam-1950	274	23	research	research	NOUN
ejpam-1950	274	24	.	.	PUNCT
ejpam-1950	275	1	references	reference	NOUN
ejpam-1950	275	2	[	[	X
ejpam-1950	275	3	1	1	NUM
ejpam-1950	275	4	]	]	PUNCT
ejpam-1950	275	5	m.	m.	NOUN
ejpam-1950	275	6	balcerzak	balcerzak	NOUN
ejpam-1950	275	7	,	,	PUNCT
ejpam-1950	275	8	k.	k.	PROPN
ejpam-1950	275	9	dems	dems	PROPN
ejpam-1950	275	10	,	,	PUNCT
ejpam-1950	275	11	and	and	CCONJ
ejpam-1950	275	12	a.	a.	NOUN
ejpam-1950	275	13	komisarski	komisarski	PROPN
ejpam-1950	275	14	.	.	PUNCT
ejpam-1950	276	1	statistical	statistical	ADJ
ejpam-1950	276	2	convergence	convergence	NOUN
ejpam-1950	276	3	and	and	CCONJ
ejpam-1950	276	4	ideal	ideal	ADJ
ejpam-1950	276	5	convergence	convergence	NOUN
ejpam-1950	276	6	for	for	ADP
ejpam-1950	276	7	sequences	sequence	NOUN
ejpam-1950	276	8	of	of	ADP
ejpam-1950	276	9	functions	function	NOUN
ejpam-1950	276	10	,	,	PUNCT
ejpam-1950	276	11	journal	journal	NOUN
ejpam-1950	276	12	of	of	ADP
ejpam-1950	276	13	mathematical	mathematical	ADJ
ejpam-1950	276	14	analysis	analysis	NOUN
ejpam-1950	276	15	and	and	CCONJ
ejpam-1950	276	16	applications	application	NOUN
ejpam-1950	276	17	,	,	PUNCT
ejpam-1950	276	18	328	328	NUM
ejpam-1950	276	19	,	,	PUNCT
ejpam-1950	276	20	715	715	NUM
ejpam-1950	276	21	–	–	PUNCT
ejpam-1950	276	22	729	729	NUM
ejpam-1950	276	23	.	.	PUNCT
ejpam-1950	276	24	2007	2007	NUM
ejpam-1950	276	25	.	.	PUNCT
ejpam-1950	277	1	[	[	X
ejpam-1950	277	2	2	2	NUM
ejpam-1950	277	3	]	]	X
ejpam-1950	277	4	v.k	v.k	PROPN
ejpam-1950	277	5	.	.	PROPN
ejpam-1950	277	6	bhardwaj	bhardwaj	PROPN
ejpam-1950	277	7	and	and	CCONJ
ejpam-1950	277	8	i.	i.	PROPN
ejpam-1950	277	9	bala	bala	PROPN
ejpam-1950	277	10	.	.	PUNCT
ejpam-1950	278	1	on	on	ADP
ejpam-1950	278	2	weak	weak	ADJ
ejpam-1950	278	3	statistical	statistical	ADJ
ejpam-1950	278	4	convergence	convergence	NOUN
ejpam-1950	278	5	,	,	PUNCT
ejpam-1950	278	6	international	international	ADJ
ejpam-1950	278	7	journal	journal	NOUN
ejpam-1950	278	8	of	of	ADP
ejpam-1950	278	9	mathematics	mathematics	PROPN
ejpam-1950	278	10	and	and	CCONJ
ejpam-1950	278	11	mathematical	mathematical	ADJ
ejpam-1950	278	12	sciences	science	NOUN
ejpam-1950	278	13	,	,	PUNCT
ejpam-1950	278	14	art	art	NOUN
ejpam-1950	278	15	.	.	PUNCT
ejpam-1950	279	1	i	i	PROPN
ejpam-1950	279	2	d	d	PROPN
ejpam-1950	279	3	38530	38530	NUM
ejpam-1950	279	4	,	,	PUNCT
ejpam-1950	279	5	9	9	NUM
ejpam-1950	279	6	,	,	PUNCT
ejpam-1950	279	7	2007	2007	NUM
ejpam-1950	279	8	[	[	X
ejpam-1950	279	9	3	3	X
ejpam-1950	279	10	]	]	PUNCT
ejpam-1950	279	11	j.	j.	PROPN
ejpam-1950	279	12	connor	connor	PROPN
ejpam-1950	279	13	.	.	PUNCT
ejpam-1950	280	1	on	on	ADP
ejpam-1950	280	2	strong	strong	ADJ
ejpam-1950	280	3	matrix	matrix	NOUN
ejpam-1950	280	4	summability	summability	NOUN
ejpam-1950	280	5	with	with	ADP
ejpam-1950	280	6	respect	respect	NOUN
ejpam-1950	280	7	to	to	ADP
ejpam-1950	280	8	a	a	DET
ejpam-1950	280	9	modulus	modulus	ADJ
ejpam-1950	280	10	and	and	CCONJ
ejpam-1950	280	11	statistical	statistical	ADJ
ejpam-1950	280	12	convergence	convergence	NOUN
ejpam-1950	280	13	,	,	PUNCT
ejpam-1950	280	14	canadian	canadian	ADJ
ejpam-1950	280	15	mathematical	mathematical	ADJ
ejpam-1950	280	16	bulletin	bulletin	NOUN
ejpam-1950	280	17	,	,	PUNCT
ejpam-1950	280	18	32	32	NUM
ejpam-1950	280	19	,	,	PUNCT
ejpam-1950	280	20	194–198	194–198	NUM
ejpam-1950	280	21	.	.	NOUN
ejpam-1950	280	22	1989	1989	NUM
ejpam-1950	280	23	.	.	PUNCT
ejpam-1950	281	1	[	[	X
ejpam-1950	281	2	4	4	X
ejpam-1950	281	3	]	]	PUNCT
ejpam-1950	281	4	j.	j.	PROPN
ejpam-1950	281	5	connor	connor	PROPN
ejpam-1950	281	6	.	.	PUNCT
ejpam-1950	282	1	a	a	DET
ejpam-1950	282	2	topological	topological	ADJ
ejpam-1950	282	3	and	and	CCONJ
ejpam-1950	282	4	functional	functional	ADJ
ejpam-1950	282	5	analytic	analytic	ADJ
ejpam-1950	282	6	approach	approach	NOUN
ejpam-1950	282	7	to	to	ADP
ejpam-1950	282	8	statistical	statistical	ADJ
ejpam-1950	282	9	convergence	convergence	NOUN
ejpam-1950	282	10	,	,	PUNCT
ejpam-1950	282	11	applied	apply	VERB
ejpam-1950	282	12	and	and	CCONJ
ejpam-1950	282	13	numerical	numerical	ADJ
ejpam-1950	282	14	harmonic	harmonic	ADJ
ejpam-1950	282	15	analysis	analysis	NOUN
ejpam-1950	282	16	,	,	PUNCT
ejpam-1950	282	17	birkhäuser	birkhäuser	PROPN
ejpam-1950	282	18	boston	boston	PROPN
ejpam-1950	282	19	,	,	PUNCT
ejpam-1950	282	20	boston	boston	PROPN
ejpam-1950	282	21	,	,	PUNCT
ejpam-1950	282	22	ma	ma	PROPN
ejpam-1950	282	23	,	,	PUNCT
ejpam-1950	282	24	pp	pp	X
ejpam-1950	282	25	.	.	PUNCT
ejpam-1950	283	1	403–413	403–413	NUM
ejpam-1950	283	2	.	.	PUNCT
ejpam-1950	284	1	[	[	X
ejpam-1950	284	2	5	5	X
ejpam-1950	284	3	]	]	PUNCT
ejpam-1950	284	4	j.	j.	PROPN
ejpam-1950	284	5	connor	connor	PROPN
ejpam-1950	284	6	,	,	PUNCT
ejpam-1950	284	7	m.	m.	NOUN
ejpam-1950	284	8	ganichev	ganichev	PROPN
ejpam-1950	284	9	,	,	PUNCT
ejpam-1950	284	10	and	and	CCONJ
ejpam-1950	284	11	v.	v.	ADP
ejpam-1950	284	12	kadets	kadet	NOUN
ejpam-1950	284	13	.	.	PUNCT
ejpam-1950	285	1	a	a	DET
ejpam-1950	285	2	characterization	characterization	NOUN
ejpam-1950	285	3	of	of	ADP
ejpam-1950	285	4	banach	banach	NOUN
ejpam-1950	285	5	spces	spce	NOUN
ejpam-1950	285	6	with	with	ADP
ejpam-1950	285	7	separable	separable	ADJ
ejpam-1950	285	8	duals	dual	NOUN
ejpam-1950	285	9	via	via	ADP
ejpam-1950	285	10	weak	weak	ADJ
ejpam-1950	285	11	statistical	statistical	ADJ
ejpam-1950	285	12	convergence	convergence	NOUN
ejpam-1950	285	13	,	,	PUNCT
ejpam-1950	285	14	journal	journal	NOUN
ejpam-1950	285	15	of	of	ADP
ejpam-1950	285	16	mathematical	mathematical	ADJ
ejpam-1950	285	17	analysis	analysis	NOUN
ejpam-1950	285	18	and	and	CCONJ
ejpam-1950	285	19	applications	application	NOUN
ejpam-1950	285	20	,	,	PUNCT
ejpam-1950	285	21	244	244	NUM
ejpam-1950	285	22	,	,	PUNCT
ejpam-1950	285	23	251–261	251–261	NUM
ejpam-1950	285	24	.	.	NOUN
ejpam-1950	285	25	2000	2000	NUM
ejpam-1950	285	26	.	.	PUNCT
ejpam-1950	286	1	[	[	X
ejpam-1950	286	2	6	6	NUM
ejpam-1950	286	3	]	]	X
ejpam-1950	286	4	g.	g.	PROPN
ejpam-1950	286	5	di	di	PROPN
ejpam-1950	286	6	.	.	PROPN
ejpam-1950	286	7	maio	maio	PROPN
ejpam-1950	286	8	and	and	CCONJ
ejpam-1950	286	9	lj	lj	PROPN
ejpam-1950	286	10	.	.	PUNCT
ejpam-1950	286	11	d.	d.	PROPN
ejpam-1950	286	12	r.	r.	PROPN
ejpam-1950	286	13	koc̆inac	koc̆inac	PROPN
ejpam-1950	286	14	.	.	PUNCT
ejpam-1950	287	1	statistical	statistical	ADJ
ejpam-1950	287	2	convergence	convergence	NOUN
ejpam-1950	287	3	in	in	ADP
ejpam-1950	287	4	topology	topology	NOUN
ejpam-1950	287	5	,	,	PUNCT
ejpam-1950	287	6	topology	topology	NOUN
ejpam-1950	287	7	and	and	CCONJ
ejpam-1950	287	8	its	its	PRON
ejpam-1950	287	9	applications	application	NOUN
ejpam-1950	287	10	,	,	PUNCT
ejpam-1950	287	11	156	156	NUM
ejpam-1950	287	12	,	,	PUNCT
ejpam-1950	287	13	28–45	28–45	NUM
ejpam-1950	287	14	.	.	PUNCT
ejpam-1950	287	15	2008	2008	NUM
ejpam-1950	287	16	.	.	PUNCT
ejpam-1950	288	1	references	reference	NOUN
ejpam-1950	288	2	366	366	NUM
ejpam-1950	288	3	[	[	X
ejpam-1950	288	4	7	7	NUM
ejpam-1950	288	5	]	]	X
ejpam-1950	288	6	j.	j.	PROPN
ejpam-1950	288	7	fast	fast	PROPN
ejpam-1950	288	8	.	.	PUNCT
ejpam-1950	289	1	sur	sur	PROPN
ejpam-1950	289	2	la	la	PROPN
ejpam-1950	289	3	convergence	convergence	NOUN
ejpam-1950	289	4	statistique	statistique	NOUN
ejpam-1950	289	5	,	,	PUNCT
ejpam-1950	289	6	colloquium	colloquium	NOUN
ejpam-1950	289	7	mathematicum	mathematicum	NOUN
ejpam-1950	289	8	,	,	PUNCT
ejpam-1950	289	9	2	2	NUM
ejpam-1950	289	10	,	,	PUNCT
ejpam-1950	289	11	241–244	241–244	NUM
ejpam-1950	289	12	.	.	PUNCT
ejpam-1950	289	13	1951	1951	NUM
ejpam-1950	289	14	.	.	PUNCT
ejpam-1950	290	1	[	[	X
ejpam-1950	290	2	8	8	NUM
ejpam-1950	290	3	]	]	PUNCT
ejpam-1950	290	4	a.	a.	PROPN
ejpam-1950	290	5	r.	r.	PROPN
ejpam-1950	290	6	freedman	freedman	PROPN
ejpam-1950	290	7	.	.	PUNCT
ejpam-1950	291	1	generalized	generalize	VERB
ejpam-1950	291	2	limits	limit	NOUN
ejpam-1950	291	3	and	and	CCONJ
ejpam-1950	291	4	sequence	sequence	NOUN
ejpam-1950	291	5	spaces	space	NOUN
ejpam-1950	291	6	,	,	PUNCT
ejpam-1950	291	7	bulletin	bulletin	NOUN
ejpam-1950	291	8	of	of	ADP
ejpam-1950	291	9	the	the	DET
ejpam-1950	291	10	london	london	PROPN
ejpam-1950	291	11	mathematical	mathematical	ADJ
ejpam-1950	291	12	society	society	NOUN
ejpam-1950	291	13	,	,	PUNCT
ejpam-1950	291	14	13	13	NUM
ejpam-1950	291	15	,	,	PUNCT
ejpam-1950	291	16	224–228	224–228	NUM
ejpam-1950	291	17	.	.	NOUN
ejpam-1950	291	18	1981	1981	NUM
ejpam-1950	291	19	.	.	PUNCT
ejpam-1950	292	1	[	[	X
ejpam-1950	292	2	9	9	NUM
ejpam-1950	292	3	]	]	PUNCT
ejpam-1950	292	4	a.	a.	PROPN
ejpam-1950	292	5	r.	r.	PROPN
ejpam-1950	292	6	freedman	freedman	PROPN
ejpam-1950	292	7	and	and	CCONJ
ejpam-1950	292	8	j.	j.	PROPN
ejpam-1950	292	9	j.	j.	PROPN
ejpam-1950	292	10	sember	sember	PROPN
ejpam-1950	292	11	.	.	PUNCT
ejpam-1950	292	12	densities	density	NOUN
ejpam-1950	292	13	and	and	CCONJ
ejpam-1950	292	14	summability	summability	NOUN
ejpam-1950	292	15	,	,	PUNCT
ejpam-1950	292	16	pacific	pacific	ADJ
ejpam-1950	292	17	journal	journal	NOUN
ejpam-1950	292	18	of	of	ADP
ejpam-1950	292	19	mathematics	mathematic	NOUN
ejpam-1950	292	20	,	,	PUNCT
ejpam-1950	292	21	95	95	NUM
ejpam-1950	292	22	,	,	PUNCT
ejpam-1950	292	23	293–305	293–305	NUM
ejpam-1950	292	24	.	.	PUNCT
ejpam-1950	292	25	1981	1981	NUM
ejpam-1950	292	26	.	.	PUNCT
ejpam-1950	293	1	[	[	X
ejpam-1950	293	2	10	10	NUM
ejpam-1950	293	3	]	]	PUNCT
ejpam-1950	293	4	j.	j.	PROPN
ejpam-1950	293	5	a.	a.	PROPN
ejpam-1950	293	6	fridy	fridy	PROPN
ejpam-1950	293	7	and	and	CCONJ
ejpam-1950	293	8	c.	c.	PROPN
ejpam-1950	293	9	orhan	orhan	PROPN
ejpam-1950	293	10	.	.	PUNCT
ejpam-1950	294	1	statistical	statistical	ADJ
ejpam-1950	294	2	limit	limit	NOUN
ejpam-1950	294	3	superior	superior	ADJ
ejpam-1950	294	4	and	and	CCONJ
ejpam-1950	294	5	limit	limit	VERB
ejpam-1950	294	6	inferior	inferior	ADJ
ejpam-1950	294	7	,	,	PUNCT
ejpam-1950	294	8	proceedings	proceeding	NOUN
ejpam-1950	294	9	of	of	ADP
ejpam-1950	294	10	the	the	DET
ejpam-1950	294	11	american	american	PROPN
ejpam-1950	294	12	mathematical	mathematical	PROPN
ejpam-1950	294	13	society	society	NOUN
ejpam-1950	294	14	,	,	PUNCT
ejpam-1950	294	15	125	125	NUM
ejpam-1950	294	16	,	,	PUNCT
ejpam-1950	294	17	3625–3631	3625–3631	NUM
ejpam-1950	294	18	.	.	PUNCT
ejpam-1950	294	19	1997	1997	NUM
ejpam-1950	294	20	.	.	PUNCT
ejpam-1950	295	1	[	[	X
ejpam-1950	295	2	11	11	NUM
ejpam-1950	295	3	]	]	X
ejpam-1950	295	4	h.	h.	PROPN
ejpam-1950	295	5	heuser	heuser	PROPN
ejpam-1950	295	6	.	.	PUNCT
ejpam-1950	295	7	funktionalanalysis	funktionalanalysis	NOUN
ejpam-1950	295	8	,	,	PUNCT
ejpam-1950	295	9	b.	b.	PROPN
ejpam-1950	295	10	g.	g.	PROPN
ejpam-1950	295	11	teubner	teubner	PROPN
ejpam-1950	295	12	,	,	PUNCT
ejpam-1950	295	13	stuttgart	stuttgart	PROPN
ejpam-1950	295	14	,	,	PUNCT
ejpam-1950	295	15	1986	1986	NUM
ejpam-1950	295	16	.	.	PUNCT
ejpam-1950	296	1	[	[	X
ejpam-1950	296	2	12	12	NUM
ejpam-1950	296	3	]	]	X
ejpam-1950	296	4	g.	g.	NOUN
ejpam-1950	296	5	kangro	kangro	PROPN
ejpam-1950	296	6	.	.	PUNCT
ejpam-1950	297	1	on	on	ADP
ejpam-1950	297	2	matrix	matrix	NOUN
ejpam-1950	297	3	transformations	transformation	NOUN
ejpam-1950	297	4	of	of	ADP
ejpam-1950	297	5	sequences	sequence	NOUN
ejpam-1950	297	6	in	in	ADP
ejpam-1950	297	7	banach	banach	NOUN
ejpam-1950	297	8	spaces	space	NOUN
ejpam-1950	297	9	,	,	PUNCT
ejpam-1950	297	10	izvestiya	izvestiya	PROPN
ejpam-1950	297	11	akademii	akademii	PROPN
ejpam-1950	297	12	nauk	nauk	PROPN
ejpam-1950	297	13	éstonskoi	éstonskoi	PROPN
ejpam-1950	297	14	ssr	ssr	PROPN
ejpam-1950	297	15	.	.	PUNCT
ejpam-1950	298	1	seriya	seriya	NOUN
ejpam-1950	298	2	tehnicheskikh	tehnicheskikh	NOUN
ejpam-1950	298	3	i	i	PRON
ejpam-1950	298	4	fiziko	fiziko	NOUN
ejpam-1950	298	5	-	-	PUNCT
ejpam-1950	298	6	matematicheskikh	matematicheskikh	NOUN
ejpam-1950	298	7	nauk	nauk	NOUN
ejpam-1950	298	8	,	,	PUNCT
ejpam-1950	298	9	5	5	NUM
ejpam-1950	298	10	,	,	PUNCT
ejpam-1950	298	11	108–128	108–128	NUM
ejpam-1950	298	12	.	.	NOUN
ejpam-1950	298	13	1956	1956	NUM
ejpam-1950	298	14	.	.	PUNCT
ejpam-1950	299	1	(	(	PUNCT
ejpam-1950	299	2	in	in	ADP
ejpam-1950	299	3	russian	russian	NOUN
ejpam-1950	299	4	)	)	PUNCT
ejpam-1950	300	1	[	[	X
ejpam-1950	300	2	13	13	NUM
ejpam-1950	300	3	]	]	PUNCT
ejpam-1950	300	4	e.	e.	PROPN
ejpam-1950	300	5	kolk	kolk	PROPN
ejpam-1950	300	6	.	.	PUNCT
ejpam-1950	301	1	statistically	statistically	ADV
ejpam-1950	301	2	convergent	convergent	ADJ
ejpam-1950	301	3	sequences	sequence	NOUN
ejpam-1950	301	4	in	in	ADP
ejpam-1950	301	5	normed	normed	ADJ
ejpam-1950	301	6	spaces	space	NOUN
ejpam-1950	301	7	,	,	PUNCT
ejpam-1950	301	8	reports	report	NOUN
ejpam-1950	301	9	of	of	ADP
ejpam-1950	301	10	conference	conference	NOUN
ejpam-1950	301	11	"	"	PUNCT
ejpam-1950	301	12	methods	method	NOUN
ejpam-1950	301	13	of	of	ADP
ejpam-1950	301	14	algebra	algebra	NOUN
ejpam-1950	301	15	and	and	CCONJ
ejpam-1950	301	16	analysis	analysis	NOUN
ejpam-1950	301	17	"	"	PUNCT
ejpam-1950	301	18	(	(	PUNCT
ejpam-1950	301	19	september	september	PROPN
ejpam-1950	301	20	21–23	21–23	NUM
ejpam-1950	301	21	,	,	PUNCT
ejpam-1950	301	22	1988	1988	NUM
ejpam-1950	301	23	,	,	PUNCT
ejpam-1950	301	24	tartu	tartu	NOUN
ejpam-1950	301	25	,	,	PUNCT
ejpam-1950	301	26	estonia	estonia	PROPN
ejpam-1950	301	27	)	)	PUNCT
ejpam-1950	301	28	,	,	PUNCT
ejpam-1950	301	29	63–66	63–66	NOUN
ejpam-1950	301	30	.	.	PUNCT
ejpam-1950	301	31	1988	1988	NUM
ejpam-1950	301	32	.	.	PUNCT
ejpam-1950	302	1	(	(	PUNCT
ejpam-1950	302	2	in	in	ADP
ejpam-1950	302	3	russian	russian	NOUN
ejpam-1950	302	4	)	)	PUNCT
ejpam-1950	303	1	[	[	X
ejpam-1950	303	2	14	14	NUM
ejpam-1950	303	3	]	]	X
ejpam-1950	303	4	e.	e.	PROPN
ejpam-1950	303	5	kolk	kolk	PROPN
ejpam-1950	303	6	.	.	PUNCT
ejpam-1950	304	1	the	the	DET
ejpam-1950	304	2	statistical	statistical	ADJ
ejpam-1950	304	3	convergence	convergence	NOUN
ejpam-1950	304	4	in	in	ADP
ejpam-1950	304	5	banach	banach	NOUN
ejpam-1950	304	6	spaces	space	NOUN
ejpam-1950	304	7	,	,	PUNCT
ejpam-1950	304	8	tartu	tartu	PROPN
ejpam-1950	304	9	ül	ül	NOUN
ejpam-1950	304	10	.	.	PROPN
ejpam-1950	304	11	toimetised	toimetise	VERB
ejpam-1950	304	12	,	,	PUNCT
ejpam-1950	304	13	928:41–52	928:41–52	NUM
ejpam-1950	304	14	1991	1991	NUM
ejpam-1950	304	15	.	.	PUNCT
ejpam-1950	305	1	[	[	X
ejpam-1950	305	2	15	15	NUM
ejpam-1950	305	3	]	]	X
ejpam-1950	305	4	e.	e.	PROPN
ejpam-1950	305	5	kolk	kolk	PROPN
ejpam-1950	305	6	.	.	PUNCT
ejpam-1950	306	1	banach	banach	NOUN
ejpam-1950	306	2	-	-	PUNCT
ejpam-1950	306	3	steinhaus	steinhaus	NOUN
ejpam-1950	306	4	type	type	NOUN
ejpam-1950	306	5	theorems	theorem	NOUN
ejpam-1950	306	6	for	for	ADP
ejpam-1950	306	7	statistical	statistical	ADJ
ejpam-1950	306	8	andi	andi	PROPN
ejpam-1950	306	9	-convergence	-convergence	PROPN
ejpam-1950	306	10	with	with	ADP
ejpam-1950	306	11	applications	application	NOUN
ejpam-1950	306	12	to	to	PART
ejpam-1950	306	13	matrix	matrix	VERB
ejpam-1950	306	14	maps	map	NOUN
ejpam-1950	306	15	,	,	PUNCT
ejpam-1950	306	16	the	the	DET
ejpam-1950	306	17	rocky	rocky	ADJ
ejpam-1950	306	18	mountain	mountain	NOUN
ejpam-1950	306	19	journal	journal	NOUN
ejpam-1950	306	20	of	of	ADP
ejpam-1950	306	21	mathematics	mathematic	NOUN
ejpam-1950	306	22	,	,	PUNCT
ejpam-1950	306	23	40	40	NUM
ejpam-1950	306	24	,	,	PUNCT
ejpam-1950	306	25	279–289	279–289	NUM
ejpam-1950	306	26	.	.	PUNCT
ejpam-1950	307	1	2010	2010	NUM
ejpam-1950	307	2	.	.	PUNCT
ejpam-1950	308	1	[	[	X
ejpam-1950	308	2	16	16	NUM
ejpam-1950	308	3	]	]	PUNCT
ejpam-1950	308	4	p.	p.	PROPN
ejpam-1950	308	5	kostyrko	kostyrko	PROPN
ejpam-1950	308	6	,	,	PUNCT
ejpam-1950	308	7	t.	t.	PROPN
ejpam-1950	308	8	s̆alát	s̆alát	PROPN
ejpam-1950	308	9	,	,	PUNCT
ejpam-1950	308	10	and	and	CCONJ
ejpam-1950	308	11	w.	w.	PROPN
ejpam-1950	308	12	wilczyński	wilczyński	PROPN
ejpam-1950	308	13	.	.	PUNCT
ejpam-1950	309	1	i	i	PRON
ejpam-1950	309	2	-convergence	-convergence	PROPN
ejpam-1950	309	3	,	,	PUNCT
ejpam-1950	309	4	real	real	ADJ
ejpam-1950	309	5	analysis	analysis	NOUN
ejpam-1950	309	6	exchange	exchange	NOUN
ejpam-1950	309	7	,	,	PUNCT
ejpam-1950	309	8	26	26	NUM
ejpam-1950	309	9	,	,	PUNCT
ejpam-1950	309	10	669–686	669–686	NUM
ejpam-1950	309	11	.	.	PUNCT
ejpam-1950	310	1	2000/2001	2000/2001	NUM
ejpam-1950	310	2	.	.	PUNCT
ejpam-1950	311	1	[	[	X
ejpam-1950	311	2	17	17	NUM
ejpam-1950	311	3	]	]	X
ejpam-1950	311	4	g.	g.	PROPN
ejpam-1950	311	5	köthe	köthe	PROPN
ejpam-1950	311	6	.	.	PUNCT
ejpam-1950	311	7	topologische	topologische	PROPN
ejpam-1950	311	8	lineare	lineare	PROPN
ejpam-1950	311	9	räume	räume	PROPN
ejpam-1950	311	10	.	.	PUNCT
ejpam-1950	312	1	i	i	PRON
ejpam-1950	312	2	,	,	PUNCT
ejpam-1950	312	3	die	die	VERB
ejpam-1950	312	4	grundlehren	grundlehren	PROPN
ejpam-1950	312	5	der	der	PROPN
ejpam-1950	312	6	mathematischen	mathematischen	PROPN
ejpam-1950	312	7	wissenschaften	wissenschaften	VERB
ejpam-1950	312	8	,	,	PUNCT
ejpam-1950	312	9	band	band	NOUN
ejpam-1950	312	10	107	107	NUM
ejpam-1950	312	11	,	,	PUNCT
ejpam-1950	312	12	springer	springer	NOUN
ejpam-1950	312	13	-	-	PUNCT
ejpam-1950	312	14	verlag	verlag	PROPN
ejpam-1950	312	15	,	,	PUNCT
ejpam-1950	312	16	berlin	berlin	PROPN
ejpam-1950	312	17	–	–	PUNCT
ejpam-1950	312	18	heidelberg	heidelberg	PROPN
ejpam-1950	312	19	–	–	PUNCT
ejpam-1950	312	20	new	new	PROPN
ejpam-1950	312	21	york	york	PROPN
ejpam-1950	312	22	,	,	PUNCT
ejpam-1950	312	23	1966	1966	NUM
ejpam-1950	312	24	.	.	PUNCT
ejpam-1950	313	1	[	[	X
ejpam-1950	313	2	18	18	NUM
ejpam-1950	313	3	]	]	X
ejpam-1950	313	4	i.	i.	PROPN
ejpam-1950	313	5	e.	e.	PROPN
ejpam-1950	313	6	leonard	leonard	PROPN
ejpam-1950	313	7	.	.	PUNCT
ejpam-1950	314	1	banach	banach	NOUN
ejpam-1950	314	2	sequence	sequence	NOUN
ejpam-1950	314	3	spaces	space	NOUN
ejpam-1950	314	4	,	,	PUNCT
ejpam-1950	314	5	journal	journal	NOUN
ejpam-1950	314	6	of	of	ADP
ejpam-1950	314	7	mathematical	mathematical	ADJ
ejpam-1950	314	8	analysis	analysis	NOUN
ejpam-1950	314	9	and	and	CCONJ
ejpam-1950	314	10	applications	application	NOUN
ejpam-1950	314	11	,	,	PUNCT
ejpam-1950	314	12	54	54	NUM
ejpam-1950	314	13	,	,	PUNCT
ejpam-1950	314	14	245–265	245–265	NUM
ejpam-1950	314	15	.	.	NOUN
ejpam-1950	314	16	1976	1976	NUM
ejpam-1950	314	17	.	.	PUNCT
ejpam-1950	315	1	[	[	X
ejpam-1950	315	2	19	19	NUM
ejpam-1950	315	3	]	]	X
ejpam-1950	315	4	i.j	i.j	PROPN
ejpam-1950	315	5	.	.	PROPN
ejpam-1950	315	6	maddox	maddox	PROPN
ejpam-1950	315	7	.	.	PUNCT
ejpam-1950	316	1	infinite	infinite	ADJ
ejpam-1950	316	2	matrices	matrix	NOUN
ejpam-1950	316	3	of	of	ADP
ejpam-1950	316	4	operators	operator	NOUN
ejpam-1950	316	5	,	,	PUNCT
ejpam-1950	316	6	lecture	lecture	NOUN
ejpam-1950	316	7	notes	note	NOUN
ejpam-1950	316	8	in	in	ADP
ejpam-1950	316	9	mathematics	mathematics	PROPN
ejpam-1950	316	10	786	786	NUM
ejpam-1950	316	11	,	,	PUNCT
ejpam-1950	316	12	springerverlag	springerverlag	NOUN
ejpam-1950	316	13	,	,	PUNCT
ejpam-1950	316	14	berlin	berlin	PROPN
ejpam-1950	316	15	–	–	PUNCT
ejpam-1950	316	16	heidelberg	heidelberg	PROPN
ejpam-1950	316	17	–	–	PUNCT
ejpam-1950	316	18	new	new	PROPN
ejpam-1950	316	19	york	york	PROPN
ejpam-1950	316	20	,	,	PUNCT
ejpam-1950	316	21	1980	1980	NUM
ejpam-1950	316	22	.	.	PUNCT
ejpam-1950	317	1	[	[	X
ejpam-1950	317	2	20	20	NUM
ejpam-1950	317	3	]	]	X
ejpam-1950	317	4	i.	i.	PROPN
ejpam-1950	317	5	j.	j.	PROPN
ejpam-1950	317	6	maddox	maddox	PROPN
ejpam-1950	317	7	.	.	PUNCT
ejpam-1950	318	1	statistical	statistical	ADJ
ejpam-1950	318	2	convergence	convergence	NOUN
ejpam-1950	318	3	in	in	ADP
ejpam-1950	318	4	a	a	DET
ejpam-1950	318	5	locally	locally	ADV
ejpam-1950	318	6	convex	convex	ADJ
ejpam-1950	318	7	space	space	NOUN
ejpam-1950	318	8	,	,	PUNCT
ejpam-1950	318	9	mathematical	mathematical	ADJ
ejpam-1950	318	10	proceedings	proceeding	NOUN
ejpam-1950	318	11	of	of	ADP
ejpam-1950	318	12	the	the	DET
ejpam-1950	318	13	cambridge	cambridge	PROPN
ejpam-1950	318	14	philosophical	philosophical	ADJ
ejpam-1950	318	15	society	society	NOUN
ejpam-1950	318	16	,	,	PUNCT
ejpam-1950	318	17	104	104	NUM
ejpam-1950	318	18	,	,	PUNCT
ejpam-1950	318	19	141–145	141–145	NUM
ejpam-1950	318	20	.	.	PUNCT
ejpam-1950	318	21	1988	1988	NUM
ejpam-1950	318	22	.	.	PUNCT
ejpam-1950	319	1	[	[	X
ejpam-1950	319	2	21	21	NUM
ejpam-1950	319	3	]	]	X
ejpam-1950	319	4	s.	s.	PROPN
ejpam-1950	319	5	pehlivan	pehlivan	PROPN
ejpam-1950	319	6	,	,	PUNCT
ejpam-1950	319	7	c.	c.	PROPN
ejpam-1950	319	8	şençimen	şençimen	PROPN
ejpam-1950	319	9	and	and	CCONJ
ejpam-1950	319	10	z.	z.	PROPN
ejpam-1950	319	11	h.	h.	PROPN
ejpam-1950	319	12	yaman	yaman	PROPN
ejpam-1950	319	13	.	.	PUNCT
ejpam-1950	320	1	on	on	ADP
ejpam-1950	320	2	weak	weak	ADJ
ejpam-1950	320	3	ideal	ideal	ADJ
ejpam-1950	320	4	convergence	convergence	NOUN
ejpam-1950	320	5	in	in	ADP
ejpam-1950	320	6	normed	normed	ADJ
ejpam-1950	320	7	spaces	space	NOUN
ejpam-1950	320	8	,	,	PUNCT
ejpam-1950	320	9	journal	journal	NOUN
ejpam-1950	320	10	of	of	ADP
ejpam-1950	320	11	interdisciplinary	interdisciplinary	ADJ
ejpam-1950	320	12	mathematics	mathematic	NOUN
ejpam-1950	320	13	,	,	PUNCT
ejpam-1950	320	14	13	13	NUM
ejpam-1950	320	15	,	,	PUNCT
ejpam-1950	320	16	153–162	153–162	NUM
ejpam-1950	320	17	.	.	PUNCT
ejpam-1950	320	18	2010	2010	NUM
ejpam-1950	320	19	.	.	PUNCT
ejpam-1950	321	1	[	[	X
ejpam-1950	321	2	22	22	NUM
ejpam-1950	321	3	]	]	X
ejpam-1950	321	4	i.	i.	PROPN
ejpam-1950	321	5	j.	j.	PROPN
ejpam-1950	321	6	schoenberg	schoenberg	PROPN
ejpam-1950	321	7	.	.	PUNCT
ejpam-1950	322	1	the	the	DET
ejpam-1950	322	2	integrability	integrability	NOUN
ejpam-1950	322	3	of	of	ADP
ejpam-1950	322	4	certain	certain	ADJ
ejpam-1950	322	5	functions	function	NOUN
ejpam-1950	322	6	and	and	CCONJ
ejpam-1950	322	7	related	relate	VERB
ejpam-1950	322	8	summability	summability	NOUN
ejpam-1950	322	9	methods	method	NOUN
ejpam-1950	322	10	,	,	PUNCT
ejpam-1950	322	11	the	the	DET
ejpam-1950	322	12	american	american	PROPN
ejpam-1950	322	13	mathematical	mathematical	PROPN
ejpam-1950	322	14	monthly	monthly	ADV
ejpam-1950	322	15	,	,	PUNCT
ejpam-1950	322	16	66	66	NUM
ejpam-1950	322	17	,	,	PUNCT
ejpam-1950	322	18	361–375	361–375	NUM
ejpam-1950	322	19	.	.	PUNCT
ejpam-1950	322	20	1959	1959	NUM
ejpam-1950	322	21	.	.	PUNCT
ejpam-1950	323	1	references	reference	NOUN
ejpam-1950	323	2	367	367	NUM
ejpam-1950	324	1	[	[	X
ejpam-1950	324	2	23	23	NUM
ejpam-1950	324	3	]	]	X
ejpam-1950	324	4	h.	h.	PROPN
ejpam-1950	324	5	steinhaus	steinhaus	PROPN
ejpam-1950	324	6	.	.	PUNCT
ejpam-1950	325	1	sur	sur	PROPN
ejpam-1950	325	2	la	la	PROPN
ejpam-1950	325	3	convergence	convergence	PROPN
ejpam-1950	325	4	ordinarie	ordinarie	PROPN
ejpam-1950	325	5	et	et	NOUN
ejpam-1950	325	6	la	la	PROPN
ejpam-1950	325	7	convergence	convergence	NOUN
ejpam-1950	325	8	asymptotique	asymptotique	NOUN
ejpam-1950	325	9	,	,	PUNCT
ejpam-1950	325	10	colloquium	colloquium	NOUN
ejpam-1950	325	11	mathematicum	mathematicum	NOUN
ejpam-1950	325	12	,	,	PUNCT
ejpam-1950	325	13	2	2	NUM
ejpam-1950	325	14	,	,	PUNCT
ejpam-1950	325	15	73–74	73–74	NUM
ejpam-1950	325	16	.	.	NOUN
ejpam-1950	325	17	1951	1951	NUM
ejpam-1950	325	18	.	.	PUNCT
ejpam-1950	326	1	[	[	X
ejpam-1950	326	2	24	24	NUM
ejpam-1950	326	3	]	]	PUNCT
ejpam-1950	326	4	k.	k.	PROPN
ejpam-1950	326	5	zeller	zeller	PROPN
ejpam-1950	326	6	.	.	PUNCT
ejpam-1950	327	1	verallgemeinerte	verallgemeinerte	PROPN
ejpam-1950	327	2	matrixtransformationen	matrixtransformationen	PROPN
ejpam-1950	327	3	,	,	PUNCT
ejpam-1950	327	4	mathematische	mathematische	NOUN
ejpam-1950	327	5	zeitschrift	zeitschrift	NOUN
ejpam-1950	327	6	,	,	PUNCT
ejpam-1950	327	7	56	56	NUM
ejpam-1950	327	8	,	,	PUNCT
ejpam-1950	327	9	18–20	18–20	NUM
ejpam-1950	327	10	.	.	NOUN
ejpam-1950	327	11	1952	1952	NUM
ejpam-1950	327	12	.	.	PUNCT
ejpam-1950	328	1	[	[	X
ejpam-1950	328	2	25	25	NUM
ejpam-1950	328	3	]	]	PUNCT
ejpam-1950	328	4	a.	a.	NOUN
ejpam-1950	328	5	zygmund	zygmund	PROPN
ejpam-1950	328	6	.	.	PUNCT
ejpam-1950	329	1	trigonometric	trigonometric	PROPN
ejpam-1950	329	2	series	series	PROPN
ejpam-1950	329	3	,	,	PUNCT
ejpam-1950	329	4	cambridge	cambridge	PROPN
ejpam-1950	329	5	university	university	PROPN
ejpam-1950	329	6	press	press	PROPN
ejpam-1950	329	7	,	,	PUNCT
ejpam-1950	329	8	cambridge	cambridge	PROPN
ejpam-1950	329	9	,	,	PUNCT
ejpam-1950	329	10	1979	1979	NUM
ejpam-1950	329	11	.	.	PUNCT