id	sid	tid	token	lemma	pos
ejpam-4612	1	1	european	european	PROPN
ejpam-4612	1	2	journal	journal	PROPN
ejpam-4612	1	3	of	of	ADP
ejpam-4612	1	4	pure	pure	ADJ
ejpam-4612	1	5	and	and	CCONJ
ejpam-4612	1	6	applied	apply	VERB
ejpam-4612	1	7	mathematics	mathematic	NOUN
ejpam-4612	1	8	vol	vol	NOUN
ejpam-4612	1	9	.	.	PUNCT
ejpam-4612	2	1	16	16	NUM
ejpam-4612	2	2	,	,	PUNCT
ejpam-4612	2	3	no	no	INTJ
ejpam-4612	2	4	.	.	NOUN
ejpam-4612	2	5	1	1	NUM
ejpam-4612	2	6	,	,	PUNCT
ejpam-4612	2	7	2023	2023	NUM
ejpam-4612	2	8	,	,	PUNCT
ejpam-4612	2	9	144	144	NUM
ejpam-4612	2	10	-	-	SYM
ejpam-4612	2	11	155	155	NUM
ejpam-4612	2	12	issn	issn	PROPN
ejpam-4612	2	13	1307	1307	NUM
ejpam-4612	2	14	-	-	SYM
ejpam-4612	2	15	5543	5543	NUM
ejpam-4612	2	16	–	–	PUNCT
ejpam-4612	2	17	ejpam.com	ejpam.com	X
ejpam-4612	2	18	published	publish	VERB
ejpam-4612	2	19	by	by	ADP
ejpam-4612	2	20	new	new	PROPN
ejpam-4612	2	21	york	york	PROPN
ejpam-4612	2	22	business	business	PROPN
ejpam-4612	2	23	global	global	ADJ
ejpam-4612	2	24	inner	inner	ADJ
ejpam-4612	2	25	products	product	NOUN
ejpam-4612	2	26	on	on	ADP
ejpam-4612	2	27	discrete	discrete	ADJ
ejpam-4612	2	28	morrey	morrey	NOUN
ejpam-4612	2	29	spaces	space	NOUN
ejpam-4612	2	30	muhammad	muhammad	PROPN
ejpam-4612	2	31	jakfar1,∗	jakfar1,∗	PROPN
ejpam-4612	2	32	,	,	PUNCT
ejpam-4612	2	33	manuharawati1	manuharawati1	PROPN
ejpam-4612	2	34	,	,	PUNCT
ejpam-4612	2	35	agung	agung	PROPN
ejpam-4612	2	36	lukito1	lukito1	PROPN
ejpam-4612	2	37	,	,	PUNCT
ejpam-4612	2	38	shofan	shofan	ADJ
ejpam-4612	2	39	fiangga1	fiangga1	NOUN
ejpam-4612	2	40	1	1	NUM
ejpam-4612	2	41	department	department	NOUN
ejpam-4612	2	42	of	of	ADP
ejpam-4612	2	43	mathematics	mathematic	NOUN
ejpam-4612	2	44	,	,	PUNCT
ejpam-4612	2	45	faculty	faculty	NOUN
ejpam-4612	2	46	of	of	ADP
ejpam-4612	2	47	mathematics	mathematic	NOUN
ejpam-4612	2	48	and	and	CCONJ
ejpam-4612	2	49	science	science	NOUN
ejpam-4612	2	50	,	,	PUNCT
ejpam-4612	2	51	universitas	universita	NOUN
ejpam-4612	2	52	negeri	negeri	PROPN
ejpam-4612	2	53	surabaya	surabaya	PROPN
ejpam-4612	2	54	,	,	PUNCT
ejpam-4612	2	55	surabaya	surabaya	PROPN
ejpam-4612	2	56	,	,	PUNCT
ejpam-4612	2	57	east	east	PROPN
ejpam-4612	2	58	java	java	PROPN
ejpam-4612	2	59	,	,	PUNCT
ejpam-4612	2	60	indonesia	indonesia	PROPN
ejpam-4612	2	61	abstract	abstract	NOUN
ejpam-4612	2	62	.	.	PUNCT
ejpam-4612	3	1	the	the	DET
ejpam-4612	3	2	discrete	discrete	ADJ
ejpam-4612	3	3	morrey	morrey	PROPN
ejpam-4612	3	4	space	space	NOUN
ejpam-4612	3	5	mu	mu	PROPN
ejpam-4612	3	6	,	,	PUNCT
ejpam-4612	3	7	p	p	PROPN
ejpam-4612	3	8	is	be	AUX
ejpam-4612	3	9	a	a	DET
ejpam-4612	3	10	generalization	generalization	NOUN
ejpam-4612	3	11	of	of	ADP
ejpam-4612	3	12	the	the	DET
ejpam-4612	3	13	p	p	ADJ
ejpam-4612	3	14	-	-	PUNCT
ejpam-4612	3	15	summable	summable	ADJ
ejpam-4612	3	16	sequence	sequence	NOUN
ejpam-4612	3	17	space	space	NOUN
ejpam-4612	3	18	ℓp	ℓp	NOUN
ejpam-4612	3	19	.	.	PUNCT
ejpam-4612	4	1	it	it	PRON
ejpam-4612	4	2	is	be	AUX
ejpam-4612	4	3	known	know	VERB
ejpam-4612	4	4	that	that	SCONJ
ejpam-4612	4	5	the	the	DET
ejpam-4612	4	6	discrete	discrete	ADJ
ejpam-4612	4	7	morrey	morrey	NOUN
ejpam-4612	4	8	space	space	NOUN
ejpam-4612	4	9	is	be	AUX
ejpam-4612	4	10	a	a	DET
ejpam-4612	4	11	normed	normed	ADJ
ejpam-4612	4	12	space	space	NOUN
ejpam-4612	4	13	.	.	PUNCT
ejpam-4612	5	1	furthermore	furthermore	ADV
ejpam-4612	5	2	,	,	PUNCT
ejpam-4612	5	3	for	for	ADP
ejpam-4612	5	4	p	p	PROPN
ejpam-4612	5	5	̸=	̸=	PROPN
ejpam-4612	5	6	2	2	NUM
ejpam-4612	5	7	,	,	PUNCT
ejpam-4612	5	8	the	the	DET
ejpam-4612	5	9	space	space	NOUN
ejpam-4612	5	10	mu	mu	NOUN
ejpam-4612	5	11	,	,	PUNCT
ejpam-4612	5	12	p	p	PROPN
ejpam-4612	5	13	equipped	equip	VERB
ejpam-4612	5	14	with	with	ADP
ejpam-4612	5	15	the	the	DET
ejpam-4612	5	16	usual	usual	ADJ
ejpam-4612	5	17	norm	norm	NOUN
ejpam-4612	5	18	is	be	AUX
ejpam-4612	5	19	not	not	PART
ejpam-4612	5	20	an	an	DET
ejpam-4612	5	21	inner	inner	ADJ
ejpam-4612	5	22	product	product	NOUN
ejpam-4612	5	23	space	space	NOUN
ejpam-4612	5	24	.	.	PUNCT
ejpam-4612	6	1	in	in	ADP
ejpam-4612	6	2	this	this	DET
ejpam-4612	6	3	paper	paper	NOUN
ejpam-4612	6	4	,	,	PUNCT
ejpam-4612	6	5	we	we	PRON
ejpam-4612	6	6	shall	shall	AUX
ejpam-4612	6	7	show	show	VERB
ejpam-4612	6	8	that	that	SCONJ
ejpam-4612	6	9	this	this	DET
ejpam-4612	6	10	space	space	NOUN
ejpam-4612	6	11	is	be	AUX
ejpam-4612	6	12	actually	actually	ADV
ejpam-4612	6	13	contained	contain	VERB
ejpam-4612	6	14	in	in	ADP
ejpam-4612	6	15	an	an	DET
ejpam-4612	6	16	inner	inner	ADJ
ejpam-4612	6	17	product	product	NOUN
ejpam-4612	6	18	space	space	NOUN
ejpam-4612	6	19	.	.	PUNCT
ejpam-4612	7	1	that	that	PRON
ejpam-4612	7	2	means	mean	VERB
ejpam-4612	7	3	this	this	DET
ejpam-4612	7	4	space	space	NOUN
ejpam-4612	7	5	equipped	equip	VERB
ejpam-4612	7	6	with	with	ADP
ejpam-4612	7	7	the	the	DET
ejpam-4612	7	8	inner	inner	ADJ
ejpam-4612	7	9	product	product	NOUN
ejpam-4612	7	10	is	be	AUX
ejpam-4612	7	11	an	an	DET
ejpam-4612	7	12	inner	inner	ADJ
ejpam-4612	7	13	product	product	NOUN
ejpam-4612	7	14	space	space	NOUN
ejpam-4612	7	15	.	.	PUNCT
ejpam-4612	8	1	the	the	DET
ejpam-4612	8	2	relationship	relationship	NOUN
ejpam-4612	8	3	between	between	ADP
ejpam-4612	8	4	a	a	DET
ejpam-4612	8	5	standard	standard	ADJ
ejpam-4612	8	6	norm	norm	NOUN
ejpam-4612	8	7	on	on	ADP
ejpam-4612	8	8	mu	mu	PROPN
ejpam-4612	8	9	,	,	PUNCT
ejpam-4612	8	10	p	p	NOUN
ejpam-4612	8	11	and	and	CCONJ
ejpam-4612	8	12	the	the	DET
ejpam-4612	8	13	inner	inner	ADJ
ejpam-4612	8	14	product	product	NOUN
ejpam-4612	8	15	is	be	AUX
ejpam-4612	8	16	studied	study	VERB
ejpam-4612	8	17	.	.	PUNCT
ejpam-4612	9	1	2020	2020	NUM
ejpam-4612	9	2	mathematics	mathematic	NOUN
ejpam-4612	9	3	subject	subject	NOUN
ejpam-4612	9	4	classifications	classification	NOUN
ejpam-4612	9	5	:	:	PUNCT
ejpam-4612	9	6	46a45	46a45	NUM
ejpam-4612	9	7	key	key	ADJ
ejpam-4612	9	8	words	word	NOUN
ejpam-4612	9	9	and	and	CCONJ
ejpam-4612	9	10	phrases	phrase	NOUN
ejpam-4612	9	11	:	:	PUNCT
ejpam-4612	9	12	discrete	discrete	VERB
ejpam-4612	9	13	morrey	morrey	PROPN
ejpam-4612	9	14	space	space	NOUN
ejpam-4612	9	15	,	,	PUNCT
ejpam-4612	9	16	inner	inner	ADJ
ejpam-4612	9	17	product	product	NOUN
ejpam-4612	9	18	,	,	PUNCT
ejpam-4612	9	19	normed	normed	ADJ
ejpam-4612	9	20	space	space	NOUN
ejpam-4612	9	21	,	,	PUNCT
ejpam-4612	9	22	p	p	ADJ
ejpam-4612	9	23	-	-	PUNCT
ejpam-4612	9	24	summable	summable	ADJ
ejpam-4612	9	25	space	space	NOUN
ejpam-4612	9	26	1	1	NUM
ejpam-4612	9	27	.	.	PUNCT
ejpam-4612	9	28	introduction	introduction	NOUN
ejpam-4612	9	29	the	the	DET
ejpam-4612	9	30	discrete	discrete	ADJ
ejpam-4612	9	31	morrey	morrey	NOUN
ejpam-4612	9	32	space	space	NOUN
ejpam-4612	9	33	(	(	PUNCT
ejpam-4612	9	34	mu	mu	NOUN
ejpam-4612	9	35	,	,	PUNCT
ejpam-4612	9	36	p	p	NOUN
ejpam-4612	9	37	)	)	PUNCT
ejpam-4612	9	38	is	be	AUX
ejpam-4612	9	39	defined	define	VERB
ejpam-4612	9	40	as	as	SCONJ
ejpam-4612	9	41	follows	follow	VERB
ejpam-4612	9	42	.	.	PUNCT
ejpam-4612	10	1	let	let	VERB
ejpam-4612	10	2	m	m	PRON
ejpam-4612	10	3	∈	∈	PROPN
ejpam-4612	10	4	z	z	PROPN
ejpam-4612	10	5	,	,	PUNCT
ejpam-4612	10	6	n	n	PROPN
ejpam-4612	10	7	∈	∈	NOUN
ejpam-4612	10	8	ω	ω	NOUN
ejpam-4612	10	9	:	:	PUNCT
ejpam-4612	10	10	=	=	NOUN
ejpam-4612	10	11	n	n	CCONJ
ejpam-4612	10	12	⋃	⋃	NOUN
ejpam-4612	10	13	{	{	PUNCT
ejpam-4612	10	14	0	0	NUM
ejpam-4612	10	15	}	}	PUNCT
ejpam-4612	10	16	,	,	PUNCT
ejpam-4612	10	17	and	and	CCONJ
ejpam-4612	10	18	we	we	PRON
ejpam-4612	10	19	write	write	VERB
ejpam-4612	10	20	sm	sm	PROPN
ejpam-4612	10	21	,	,	PUNCT
ejpam-4612	10	22	n	n	PROPN
ejpam-4612	10	23	;	;	PUNCT
ejpam-4612	10	24	=	=	SYM
ejpam-4612	10	25	{	{	PUNCT
ejpam-4612	10	26	m−n	m−n	PROPN
ejpam-4612	10	27	,	,	PUNCT
ejpam-4612	10	28	.	.	PUNCT
ejpam-4612	10	29	.	.	PUNCT
ejpam-4612	11	1	.	.	PUNCT
ejpam-4612	12	1	,	,	PUNCT
ejpam-4612	12	2	m	m	PROPN
ejpam-4612	12	3	,	,	PUNCT
ejpam-4612	12	4	.	.	PUNCT
ejpam-4612	12	5	.	.	PUNCT
ejpam-4612	13	1	.	.	PUNCT
ejpam-4612	14	1	,	,	PUNCT
ejpam-4612	15	1	m+n	m+n	NUM
ejpam-4612	15	2	}	}	PUNCT
ejpam-4612	15	3	.	.	PUNCT
ejpam-4612	16	1	hence	hence	ADV
ejpam-4612	16	2	,	,	PUNCT
ejpam-4612	16	3	|sm	|sm	ADV
ejpam-4612	16	4	,	,	PUNCT
ejpam-4612	16	5	n	n	CCONJ
ejpam-4612	16	6	|	|	NOUN
ejpam-4612	16	7	=	=	SYM
ejpam-4612	16	8	2n	2n	NUM
ejpam-4612	17	1	+	+	CCONJ
ejpam-4612	17	2	1	1	X
ejpam-4612	17	3	.	.	PUNCT
ejpam-4612	17	4	now	now	ADV
ejpam-4612	17	5	,	,	PUNCT
ejpam-4612	17	6	let	let	VERB
ejpam-4612	17	7	k	k	PRON
ejpam-4612	17	8	be	be	AUX
ejpam-4612	17	9	r	r	NOUN
ejpam-4612	17	10	or	or	CCONJ
ejpam-4612	17	11	c	c	NOUN
ejpam-4612	17	12	and	and	CCONJ
ejpam-4612	17	13	1	1	NUM
ejpam-4612	17	14	≤	≤	NOUN
ejpam-4612	17	15	p	p	ADJ
ejpam-4612	17	16	≤	≤	NUM
ejpam-4612	17	17	u	u	NOUN
ejpam-4612	17	18	≤	≤	PUNCT
ejpam-4612	17	19	∞.	∞.	PROPN
ejpam-4612	17	20	the	the	DET
ejpam-4612	17	21	discrete	discrete	ADJ
ejpam-4612	17	22	morrey	morrey	PROPN
ejpam-4612	17	23	space	space	NOUN
ejpam-4612	17	24	,	,	PUNCT
ejpam-4612	17	25	denoted	denote	VERB
ejpam-4612	17	26	by	by	ADP
ejpam-4612	17	27	mu	mu	NOUN
ejpam-4612	17	28	,	,	PUNCT
ejpam-4612	17	29	p	p	PRON
ejpam-4612	17	30	,	,	PUNCT
ejpam-4612	17	31	is	be	AUX
ejpam-4612	17	32	the	the	DET
ejpam-4612	17	33	set	set	NOUN
ejpam-4612	17	34	of	of	ADP
ejpam-4612	17	35	sequences	sequence	NOUN
ejpam-4612	17	36	λ	λ	NOUN
ejpam-4612	17	37	=	=	SYM
ejpam-4612	17	38	(	(	PUNCT
ejpam-4612	17	39	λk)k∈z	λk)k∈z	NUM
ejpam-4612	17	40	taking	take	VERB
ejpam-4612	17	41	values	value	NOUN
ejpam-4612	17	42	in	in	ADP
ejpam-4612	17	43	k	k	PROPN
ejpam-4612	17	44	such	such	ADJ
ejpam-4612	17	45	that	that	SCONJ
ejpam-4612	17	46	∥λ∥mu	∥λ∥mu	VERB
ejpam-4612	17	47	,	,	PUNCT
ejpam-4612	17	48	p	p	X
ejpam-4612	17	49	:	:	PUNCT
ejpam-4612	17	50	=	=	NUM
ejpam-4612	17	51	sup	sup	NUM
ejpam-4612	17	52	m∈z	m∈z	NOUN
ejpam-4612	17	53	,	,	PUNCT
ejpam-4612	17	54	n∈ω	n∈ω	NOUN
ejpam-4612	17	55	|sm	|sm	ADV
ejpam-4612	17	56	,	,	PUNCT
ejpam-4612	17	57	n	n	CCONJ
ejpam-4612	17	58	|	|	ADV
ejpam-4612	17	59	1	1	NUM
ejpam-4612	17	60	u	u	NOUN
ejpam-4612	17	61	−	−	PROPN
ejpam-4612	17	62	1	1	NUM
ejpam-4612	17	63	p	p	NOUN
ejpam-4612	17	64	(	(	PUNCT
ejpam-4612	17	65	∑	∑	PUNCT
ejpam-4612	17	66	k∈sm	k∈sm	PROPN
ejpam-4612	17	67	,	,	PUNCT
ejpam-4612	17	68	n	n	CCONJ
ejpam-4612	17	69	|λk|p	|λk|p	PUNCT
ejpam-4612	17	70	)	)	PUNCT
ejpam-4612	17	71	1	1	NUM
ejpam-4612	17	72	p	p	NOUN
ejpam-4612	17	73	<	<	X
ejpam-4612	17	74	∞.	∞.	PROPN
ejpam-4612	17	75	clearly	clearly	ADV
ejpam-4612	17	76	mu	mu	PROPN
ejpam-4612	17	77	,	,	PUNCT
ejpam-4612	17	78	p	p	PROPN
ejpam-4612	17	79	is	be	AUX
ejpam-4612	17	80	a	a	DET
ejpam-4612	17	81	vector	vector	NOUN
ejpam-4612	17	82	space	space	NOUN
ejpam-4612	17	83	.	.	PUNCT
ejpam-4612	18	1	we	we	PRON
ejpam-4612	18	2	remark	remark	VERB
ejpam-4612	18	3	that	that	SCONJ
ejpam-4612	18	4	when	when	SCONJ
ejpam-4612	18	5	u	u	PROPN
ejpam-4612	18	6	=	=	SYM
ejpam-4612	18	7	p	p	X
ejpam-4612	18	8	,	,	PUNCT
ejpam-4612	18	9	we	we	PRON
ejpam-4612	18	10	have	have	VERB
ejpam-4612	18	11	mu	mu	NOUN
ejpam-4612	18	12	,	,	PUNCT
ejpam-4612	18	13	p	p	NOUN
ejpam-4612	18	14	=	=	SYM
ejpam-4612	18	15	ℓp	ℓp	NOUN
ejpam-4612	18	16	,	,	PUNCT
ejpam-4612	18	17	the	the	DET
ejpam-4612	18	18	space	space	NOUN
ejpam-4612	18	19	of	of	ADP
ejpam-4612	18	20	p	p	NOUN
ejpam-4612	18	21	-	-	PUNCT
ejpam-4612	18	22	summable	summable	ADJ
ejpam-4612	18	23	sequences	sequence	NOUN
ejpam-4612	18	24	with	with	ADP
ejpam-4612	18	25	integer	integer	NOUN
ejpam-4612	18	26	indices	index	NOUN
ejpam-4612	18	27	.	.	PUNCT
ejpam-4612	19	1	we	we	PRON
ejpam-4612	19	2	also	also	ADV
ejpam-4612	19	3	have	have	VERB
ejpam-4612	19	4	some	some	DET
ejpam-4612	19	5	notes	note	NOUN
ejpam-4612	19	6	among	among	ADP
ejpam-4612	19	7	mu	mu	NOUN
ejpam-4612	19	8	,	,	PUNCT
ejpam-4612	19	9	p	p	NOUN
ejpam-4612	19	10	as	as	SCONJ
ejpam-4612	19	11	follows	follow	VERB
ejpam-4612	19	12	.	.	PUNCT
ejpam-4612	20	1	theorem	theorem	NOUN
ejpam-4612	20	2	1	1	NUM
ejpam-4612	20	3	.	.	PUNCT
ejpam-4612	21	1	[	[	X
ejpam-4612	21	2	5	5	NUM
ejpam-4612	21	3	]	]	PUNCT
ejpam-4612	21	4	for	for	ADP
ejpam-4612	21	5	1	1	NUM
ejpam-4612	21	6	≤	≤	NOUN
ejpam-4612	21	7	p	p	PROPN
ejpam-4612	21	8	≤	≤	NUM
ejpam-4612	21	9	u	u	NOUN
ejpam-4612	21	10	<	<	X
ejpam-4612	21	11	∞	∞	PROPN
ejpam-4612	21	12	,	,	PUNCT
ejpam-4612	21	13	the	the	DET
ejpam-4612	21	14	space	space	NOUN
ejpam-4612	21	15	(	(	PUNCT
ejpam-4612	21	16	mu	mu	NOUN
ejpam-4612	21	17	,	,	PUNCT
ejpam-4612	21	18	p	p	X
ejpam-4612	21	19	,	,	PUNCT
ejpam-4612	21	20	∥	∥	X
ejpam-4612	21	21	·	·	PUNCT
ejpam-4612	21	22	∥mu	∥mu	NOUN
ejpam-4612	21	23	,	,	PUNCT
ejpam-4612	21	24	p	p	NOUN
ejpam-4612	21	25	)	)	PUNCT
ejpam-4612	21	26	is	be	AUX
ejpam-4612	21	27	a	a	DET
ejpam-4612	21	28	normed	normed	ADJ
ejpam-4612	21	29	space	space	NOUN
ejpam-4612	21	30	.	.	PUNCT
ejpam-4612	22	1	moreover	moreover	ADV
ejpam-4612	22	2	,	,	PUNCT
ejpam-4612	22	3	the	the	DET
ejpam-4612	22	4	space	space	NOUN
ejpam-4612	22	5	is	be	AUX
ejpam-4612	22	6	a	a	DET
ejpam-4612	22	7	bannach	bannach	NOUN
ejpam-4612	22	8	space	space	NOUN
ejpam-4612	22	9	.	.	PUNCT
ejpam-4612	23	1	∗corresponding	∗corresponde	VERB
ejpam-4612	23	2	author	author	NOUN
ejpam-4612	23	3	.	.	PUNCT
ejpam-4612	24	1	doi	doi	NOUN
ejpam-4612	24	2	:	:	PUNCT
ejpam-4612	24	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4612	https://doi.org/10.29020/nybg.ejpam.v16i1.4612	ADJ
ejpam-4612	24	4	email	email	NOUN
ejpam-4612	24	5	addresses	address	NOUN
ejpam-4612	24	6	:	:	PUNCT
ejpam-4612	24	7	muhammadjakfar@unesa.ac.id	muhammadjakfar@unesa.ac.id	NOUN
ejpam-4612	24	8	(	(	PUNCT
ejpam-4612	24	9	m.	m.	NOUN
ejpam-4612	24	10	jakfar	jakfar	PROPN
ejpam-4612	24	11	)	)	PUNCT
ejpam-4612	24	12	,	,	PUNCT
ejpam-4612	24	13	manuharawati@unesa.ac.id	manuharawati@unesa.ac.id	NOUN
ejpam-4612	24	14	(	(	PUNCT
ejpam-4612	24	15	manuharawati	manuharawati	NOUN
ejpam-4612	24	16	)	)	PUNCT
ejpam-4612	24	17	,	,	PUNCT
ejpam-4612	24	18	agunglukito@unesa.ac.id	agunglukito@unesa.ac.id	NOUN
ejpam-4612	24	19	(	(	PUNCT
ejpam-4612	24	20	a.	a.	NOUN
ejpam-4612	24	21	lukito	lukito	PROPN
ejpam-4612	24	22	)	)	PUNCT
ejpam-4612	24	23	,	,	PUNCT
ejpam-4612	24	24	shofanfiangga@unesa.ac.id	shofanfiangga@unesa.ac.id	PROPN
ejpam-4612	24	25	(	(	PUNCT
ejpam-4612	24	26	s.	s.	PROPN
ejpam-4612	24	27	fiangga	fiangga	PROPN
ejpam-4612	24	28	)	)	PUNCT
ejpam-4612	24	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4612	25	1	144	144	NUM
ejpam-4612	26	1	©	©	PROPN
ejpam-4612	26	2	2023	2023	NUM
ejpam-4612	26	3	ejpam	ejpam	NOUN
ejpam-4612	26	4	all	all	DET
ejpam-4612	26	5	rights	right	NOUN
ejpam-4612	26	6	reserved	reserve	VERB
ejpam-4612	26	7	.	.	PUNCT
ejpam-4612	27	1	m.	m.	NOUN
ejpam-4612	27	2	jakfar	jakfar	PROPN
ejpam-4612	27	3	et	et	PROPN
ejpam-4612	27	4	al	al	PROPN
ejpam-4612	27	5	.	.	PUNCT
ejpam-4612	27	6	/	/	SYM
ejpam-4612	27	7	eur	eur	PROPN
ejpam-4612	27	8	.	.	PUNCT
ejpam-4612	28	1	j.	j.	PROPN
ejpam-4612	28	2	pure	pure	PROPN
ejpam-4612	28	3	appl	appl	PROPN
ejpam-4612	28	4	.	.	PROPN
ejpam-4612	28	5	math	math	PROPN
ejpam-4612	28	6	,	,	PUNCT
ejpam-4612	28	7	16	16	NUM
ejpam-4612	28	8	(	(	PUNCT
ejpam-4612	28	9	1	1	NUM
ejpam-4612	28	10	)	)	PUNCT
ejpam-4612	28	11	(	(	PUNCT
ejpam-4612	28	12	2023	2023	NUM
ejpam-4612	28	13	)	)	PUNCT
ejpam-4612	28	14	,	,	PUNCT
ejpam-4612	28	15	144	144	NUM
ejpam-4612	28	16	-	-	SYM
ejpam-4612	28	17	155	155	NUM
ejpam-4612	28	18	145	145	NUM
ejpam-4612	28	19	theorem	theorem	NOUN
ejpam-4612	28	20	2	2	NUM
ejpam-4612	28	21	.	.	PUNCT
ejpam-4612	29	1	[	[	X
ejpam-4612	29	2	5	5	NUM
ejpam-4612	29	3	]	]	PUNCT
ejpam-4612	29	4	for	for	ADP
ejpam-4612	29	5	1	1	NUM
ejpam-4612	29	6	≤	≤	NOUN
ejpam-4612	29	7	p	p	PROPN
ejpam-4612	29	8	≤	≤	NUM
ejpam-4612	29	9	u	u	NOUN
ejpam-4612	29	10	<	<	X
ejpam-4612	29	11	∞	∞	PROPN
ejpam-4612	29	12	,	,	PUNCT
ejpam-4612	29	13	we	we	PRON
ejpam-4612	29	14	have	have	VERB
ejpam-4612	29	15	mu	mu	NOUN
ejpam-4612	29	16	,	,	PUNCT
ejpam-4612	29	17	p	p	PROPN
ejpam-4612	29	18	⊂	⊂	X
ejpam-4612	29	19	ℓp	ℓp	ADJ
ejpam-4612	29	20	and	and	CCONJ
ejpam-4612	29	21	∥λ∥mu	∥λ∥mu	PROPN
ejpam-4612	29	22	,	,	PUNCT
ejpam-4612	29	23	p	p	ADJ
ejpam-4612	29	24	≤	≤	NUM
ejpam-4612	29	25	∥λ∥ℓp	∥λ∥ℓp	NOUN
ejpam-4612	29	26	for	for	ADP
ejpam-4612	29	27	every	every	DET
ejpam-4612	29	28	λ	λ	PROPN
ejpam-4612	29	29	∈	∈	PROPN
ejpam-4612	29	30	mu	mu	NOUN
ejpam-4612	29	31	,	,	PUNCT
ejpam-4612	29	32	q.	q.	NOUN
ejpam-4612	29	33	many	many	ADJ
ejpam-4612	29	34	mathematicians	mathematician	NOUN
ejpam-4612	29	35	had	have	AUX
ejpam-4612	29	36	discussed	discuss	VERB
ejpam-4612	29	37	about	about	ADP
ejpam-4612	29	38	the	the	DET
ejpam-4612	29	39	discrete	discrete	ADJ
ejpam-4612	29	40	morrey	morrey	NOUN
ejpam-4612	29	41	space	space	NOUN
ejpam-4612	29	42	(	(	PUNCT
ejpam-4612	29	43	see	see	VERB
ejpam-4612	29	44	[	[	X
ejpam-4612	29	45	1	1	NUM
ejpam-4612	29	46	]	]	PUNCT
ejpam-4612	29	47	,	,	PUNCT
ejpam-4612	30	1	[	[	X
ejpam-4612	30	2	2	2	NUM
ejpam-4612	30	3	]	]	PUNCT
ejpam-4612	30	4	,	,	PUNCT
ejpam-4612	30	5	[	[	X
ejpam-4612	30	6	4	4	NUM
ejpam-4612	30	7	]	]	PUNCT
ejpam-4612	30	8	,	,	PUNCT
ejpam-4612	30	9	[	[	X
ejpam-4612	30	10	5	5	NUM
ejpam-4612	30	11	]	]	PUNCT
ejpam-4612	30	12	,	,	PUNCT
ejpam-4612	30	13	[	[	X
ejpam-4612	30	14	6	6	NUM
ejpam-4612	30	15	]	]	PUNCT
ejpam-4612	30	16	,	,	PUNCT
ejpam-4612	30	17	[	[	X
ejpam-4612	30	18	7	7	NUM
ejpam-4612	30	19	]	]	PUNCT
ejpam-4612	30	20	,	,	PUNCT
ejpam-4612	30	21	[	[	X
ejpam-4612	30	22	8	8	NUM
ejpam-4612	30	23	]	]	PUNCT
ejpam-4612	30	24	,	,	PUNCT
ejpam-4612	30	25	[	[	X
ejpam-4612	30	26	9	9	NUM
ejpam-4612	30	27	]	]	PUNCT
ejpam-4612	30	28	,	,	PUNCT
ejpam-4612	30	29	[	[	X
ejpam-4612	30	30	10	10	NUM
ejpam-4612	30	31	]	]	PUNCT
ejpam-4612	30	32	,	,	PUNCT
ejpam-4612	30	33	[	[	X
ejpam-4612	30	34	11	11	NUM
ejpam-4612	30	35	]	]	PUNCT
ejpam-4612	30	36	,	,	PUNCT
ejpam-4612	30	37	[	[	X
ejpam-4612	30	38	12	12	NUM
ejpam-4612	30	39	]	]	PUNCT
ejpam-4612	30	40	,	,	PUNCT
ejpam-4612	30	41	[	[	X
ejpam-4612	30	42	13	13	NUM
ejpam-4612	30	43	]	]	PUNCT
ejpam-4612	30	44	,	,	PUNCT
ejpam-4612	30	45	[	[	X
ejpam-4612	30	46	14	14	NUM
ejpam-4612	30	47	]	]	PUNCT
ejpam-4612	30	48	,	,	PUNCT
ejpam-4612	30	49	[	[	X
ejpam-4612	30	50	20	20	NUM
ejpam-4612	30	51	]	]	PUNCT
ejpam-4612	30	52	,	,	PUNCT
ejpam-4612	31	1	[	[	X
ejpam-4612	31	2	21	21	NUM
ejpam-4612	31	3	]	]	PUNCT
ejpam-4612	31	4	,	,	PUNCT
ejpam-4612	31	5	and	and	CCONJ
ejpam-4612	31	6	[	[	X
ejpam-4612	31	7	22	22	NUM
ejpam-4612	31	8	]	]	PUNCT
ejpam-4612	31	9	)	)	PUNCT
ejpam-4612	31	10	.	.	PUNCT
ejpam-4612	32	1	we	we	PRON
ejpam-4612	32	2	have	have	AUX
ejpam-4612	32	3	known	know	VERB
ejpam-4612	32	4	that	that	SCONJ
ejpam-4612	32	5	the	the	DET
ejpam-4612	32	6	space	space	NOUN
ejpam-4612	32	7	(	(	PUNCT
ejpam-4612	32	8	mu	mu	NOUN
ejpam-4612	32	9	,	,	PUNCT
ejpam-4612	32	10	p	p	X
ejpam-4612	32	11	,	,	PUNCT
ejpam-4612	32	12	∥	∥	X
ejpam-4612	32	13	·	·	PUNCT
ejpam-4612	32	14	∥mu	∥mu	NOUN
ejpam-4612	32	15	,	,	PUNCT
ejpam-4612	32	16	p	p	NOUN
ejpam-4612	32	17	)	)	PUNCT
ejpam-4612	32	18	is	be	AUX
ejpam-4612	32	19	a	a	DET
ejpam-4612	32	20	normed	normed	ADJ
ejpam-4612	32	21	space	space	NOUN
ejpam-4612	32	22	.	.	PUNCT
ejpam-4612	33	1	however	however	ADV
ejpam-4612	33	2	,	,	PUNCT
ejpam-4612	33	3	for	for	ADP
ejpam-4612	33	4	p	p	PROPN
ejpam-4612	33	5	̸=	̸=	PROPN
ejpam-4612	33	6	2	2	NUM
ejpam-4612	33	7	,	,	PUNCT
ejpam-4612	33	8	the	the	DET
ejpam-4612	33	9	discrete	discrete	ADJ
ejpam-4612	33	10	morrey	morrey	NOUN
ejpam-4612	33	11	space	space	NOUN
ejpam-4612	33	12	is	be	AUX
ejpam-4612	33	13	not	not	PART
ejpam-4612	33	14	an	an	DET
ejpam-4612	33	15	inner	inner	ADJ
ejpam-4612	33	16	product	product	NOUN
ejpam-4612	33	17	space	space	NOUN
ejpam-4612	33	18	,	,	PUNCT
ejpam-4612	33	19	because	because	SCONJ
ejpam-4612	33	20	if	if	SCONJ
ejpam-4612	33	21	we	we	PRON
ejpam-4612	33	22	take	take	VERB
ejpam-4612	33	23	u	u	NOUN
ejpam-4612	33	24	=	=	NOUN
ejpam-4612	33	25	p	p	PROPN
ejpam-4612	33	26	then	then	ADV
ejpam-4612	33	27	the	the	DET
ejpam-4612	33	28	norm	norm	NOUN
ejpam-4612	33	29	∥	∥	X
ejpam-4612	33	30	·	·	PUNCT
ejpam-4612	33	31	∥mu	∥mu	NOUN
ejpam-4612	33	32	,	,	PUNCT
ejpam-4612	33	33	p	p	NOUN
ejpam-4612	33	34	is	be	AUX
ejpam-4612	33	35	equal	equal	ADJ
ejpam-4612	33	36	to	to	ADP
ejpam-4612	33	37	the	the	DET
ejpam-4612	33	38	norm	norm	NOUN
ejpam-4612	33	39	∥	∥	X
ejpam-4612	33	40	·	·	PUNCT
ejpam-4612	33	41	∥ℓp	∥ℓp	X
ejpam-4612	33	42	which	which	PRON
ejpam-4612	33	43	do	do	AUX
ejpam-4612	33	44	not	not	PART
ejpam-4612	33	45	satisfy	satisfy	VERB
ejpam-4612	33	46	the	the	DET
ejpam-4612	33	47	parallelogram	parallelogram	NOUN
ejpam-4612	33	48	’s	’s	PART
ejpam-4612	33	49	law	law	NOUN
ejpam-4612	33	50	(	(	PUNCT
ejpam-4612	33	51	see	see	VERB
ejpam-4612	33	52	[	[	X
ejpam-4612	33	53	15	15	NUM
ejpam-4612	33	54	]	]	PUNCT
ejpam-4612	33	55	)	)	PUNCT
ejpam-4612	33	56	.	.	PUNCT
ejpam-4612	34	1	in	in	ADP
ejpam-4612	34	2	this	this	DET
ejpam-4612	34	3	paper	paper	NOUN
ejpam-4612	34	4	,	,	PUNCT
ejpam-4612	34	5	we	we	PRON
ejpam-4612	34	6	will	will	AUX
ejpam-4612	34	7	show	show	VERB
ejpam-4612	34	8	that	that	SCONJ
ejpam-4612	34	9	we	we	PRON
ejpam-4612	34	10	can	can	AUX
ejpam-4612	34	11	define	define	VERB
ejpam-4612	34	12	an	an	DET
ejpam-4612	34	13	inner	inner	ADJ
ejpam-4612	34	14	product	product	NOUN
ejpam-4612	34	15	on	on	ADP
ejpam-4612	34	16	the	the	DET
ejpam-4612	34	17	discrete	discrete	ADJ
ejpam-4612	34	18	morrey	morrey	NOUN
ejpam-4612	34	19	space	space	NOUN
ejpam-4612	34	20	.	.	PUNCT
ejpam-4612	35	1	so	so	ADV
ejpam-4612	35	2	,	,	PUNCT
ejpam-4612	35	3	this	this	PRON
ejpam-4612	35	4	is	be	AUX
ejpam-4612	35	5	the	the	DET
ejpam-4612	35	6	first	first	ADJ
ejpam-4612	35	7	time	time	NOUN
ejpam-4612	35	8	to	to	PART
ejpam-4612	35	9	say	say	VERB
ejpam-4612	35	10	that	that	SCONJ
ejpam-4612	35	11	the	the	DET
ejpam-4612	35	12	discrete	discrete	ADJ
ejpam-4612	35	13	morrey	morrey	NOUN
ejpam-4612	35	14	space	space	NOUN
ejpam-4612	35	15	is	be	AUX
ejpam-4612	35	16	an	an	DET
ejpam-4612	35	17	inner	inner	ADJ
ejpam-4612	35	18	product	product	NOUN
ejpam-4612	35	19	space	space	NOUN
ejpam-4612	35	20	.	.	PUNCT
ejpam-4612	36	1	we	we	PRON
ejpam-4612	36	2	also	also	ADV
ejpam-4612	36	3	discuss	discuss	VERB
ejpam-4612	36	4	the	the	DET
ejpam-4612	36	5	relationship	relationship	NOUN
ejpam-4612	36	6	between	between	ADP
ejpam-4612	36	7	a	a	DET
ejpam-4612	36	8	standard	standard	ADJ
ejpam-4612	36	9	norm	norm	NOUN
ejpam-4612	36	10	and	and	CCONJ
ejpam-4612	36	11	the	the	DET
ejpam-4612	36	12	inner	inner	ADJ
ejpam-4612	36	13	product	product	NOUN
ejpam-4612	36	14	on	on	ADP
ejpam-4612	36	15	the	the	DET
ejpam-4612	36	16	space	space	NOUN
ejpam-4612	36	17	.	.	PUNCT
ejpam-4612	37	1	to	to	PART
ejpam-4612	37	2	define	define	VERB
ejpam-4612	37	3	an	an	DET
ejpam-4612	37	4	inner	inner	ADJ
ejpam-4612	37	5	product	product	NOUN
ejpam-4612	37	6	on	on	ADP
ejpam-4612	37	7	mu	mu	PROPN
ejpam-4612	37	8	,	,	PUNCT
ejpam-4612	37	9	p	p	X
ejpam-4612	37	10	,	,	PUNCT
ejpam-4612	37	11	the	the	DET
ejpam-4612	37	12	first	first	ADJ
ejpam-4612	37	13	,	,	PUNCT
ejpam-4612	37	14	we	we	PRON
ejpam-4612	37	15	will	will	AUX
ejpam-4612	37	16	show	show	VERB
ejpam-4612	37	17	for	for	ADP
ejpam-4612	37	18	p	p	NOUN
ejpam-4612	37	19	=	=	SYM
ejpam-4612	37	20	2	2	NUM
ejpam-4612	37	21	,	,	PUNCT
ejpam-4612	37	22	the	the	DET
ejpam-4612	37	23	space	space	NOUN
ejpam-4612	37	24	mu	mu	NOUN
ejpam-4612	37	25	,	,	PUNCT
ejpam-4612	37	26	p	p	PROPN
ejpam-4612	37	27	or	or	CCONJ
ejpam-4612	37	28	mu,2	mu,2	PROPN
ejpam-4612	37	29	is	be	AUX
ejpam-4612	37	30	an	an	DET
ejpam-4612	37	31	inner	inner	ADJ
ejpam-4612	37	32	product	product	NOUN
ejpam-4612	37	33	space	space	NOUN
ejpam-4612	37	34	.	.	PUNCT
ejpam-4612	38	1	then	then	ADV
ejpam-4612	38	2	we	we	PRON
ejpam-4612	38	3	begin	begin	VERB
ejpam-4612	38	4	try	try	VERB
ejpam-4612	38	5	to	to	PART
ejpam-4612	38	6	define	define	VERB
ejpam-4612	38	7	an	an	DET
ejpam-4612	38	8	inner	inner	ADJ
ejpam-4612	38	9	product	product	NOUN
ejpam-4612	38	10	on	on	ADP
ejpam-4612	38	11	mu	mu	PROPN
ejpam-4612	38	12	,	,	PUNCT
ejpam-4612	38	13	p	p	NOUN
ejpam-4612	38	14	for	for	ADP
ejpam-4612	38	15	p	p	PROPN
ejpam-4612	39	1	>	>	X
ejpam-4612	39	2	2	2	NUM
ejpam-4612	39	3	.	.	PUNCT
ejpam-4612	40	1	the	the	DET
ejpam-4612	40	2	next	next	ADJ
ejpam-4612	40	3	,	,	PUNCT
ejpam-4612	40	4	we	we	PRON
ejpam-4612	40	5	construct	construct	VERB
ejpam-4612	40	6	an	an	DET
ejpam-4612	40	7	inner	inner	ADJ
ejpam-4612	40	8	product	product	NOUN
ejpam-4612	40	9	on	on	ADP
ejpam-4612	40	10	mu	mu	PROPN
ejpam-4612	40	11	,	,	PUNCT
ejpam-4612	40	12	p	p	NOUN
ejpam-4612	40	13	for	for	ADP
ejpam-4612	40	14	p	p	X
ejpam-4612	40	15	<	<	X
ejpam-4612	40	16	2	2	NUM
ejpam-4612	40	17	.	.	PUNCT
ejpam-4612	41	1	throughout	throughout	ADP
ejpam-4612	41	2	the	the	DET
ejpam-4612	41	3	paper	paper	NOUN
ejpam-4612	41	4	,	,	PUNCT
ejpam-4612	41	5	we	we	PRON
ejpam-4612	41	6	assume	assume	VERB
ejpam-4612	41	7	that	that	SCONJ
ejpam-4612	41	8	x	x	PRON
ejpam-4612	41	9	is	be	AUX
ejpam-4612	41	10	a	a	DET
ejpam-4612	41	11	real	real	ADJ
ejpam-4612	41	12	vector	vector	NOUN
ejpam-4612	41	13	space	space	NOUN
ejpam-4612	41	14	,	,	PUNCT
ejpam-4612	41	15	as	as	ADP
ejpam-4612	41	16	in	in	ADP
ejpam-4612	41	17	[	[	X
ejpam-4612	41	18	16	16	NUM
ejpam-4612	41	19	]	]	PUNCT
ejpam-4612	41	20	,	,	PUNCT
ejpam-4612	41	21	the	the	DET
ejpam-4612	41	22	norm	norm	NOUN
ejpam-4612	41	23	on	on	ADP
ejpam-4612	41	24	x	x	X
ejpam-4612	41	25	is	be	AUX
ejpam-4612	41	26	a	a	DET
ejpam-4612	41	27	mapping	mapping	NOUN
ejpam-4612	41	28	∥	∥	X
ejpam-4612	41	29	·	·	PUNCT
ejpam-4612	41	30	∥	∥	X
ejpam-4612	41	31	:	:	PUNCT
ejpam-4612	41	32	x	x	X
ejpam-4612	42	1	→	→	X
ejpam-4612	42	2	r+	r+	NOUN
ejpam-4612	42	3	such	such	ADJ
ejpam-4612	42	4	that	that	PRON
ejpam-4612	42	5	for	for	ADP
ejpam-4612	42	6	all	all	DET
ejpam-4612	42	7	vector	vector	NOUN
ejpam-4612	42	8	x	x	NOUN
ejpam-4612	42	9	,	,	PUNCT
ejpam-4612	42	10	y	y	PROPN
ejpam-4612	42	11	∈	∈	PROPN
ejpam-4612	42	12	x	x	X
ejpam-4612	42	13	and	and	CCONJ
ejpam-4612	42	14	a	a	DET
ejpam-4612	42	15	scalar	scalar	NOUN
ejpam-4612	42	16	a	a	DET
ejpam-4612	42	17	∈	∈	NOUN
ejpam-4612	42	18	r	r	NOUN
ejpam-4612	42	19	we	we	PRON
ejpam-4612	42	20	have	have	VERB
ejpam-4612	42	21	:	:	PUNCT
ejpam-4612	42	22	(	(	PUNCT
ejpam-4612	42	23	i	i	NOUN
ejpam-4612	42	24	)	)	PUNCT
ejpam-4612	42	25	∥x∥	∥x∥	PROPN
ejpam-4612	42	26	≥	≥	NOUN
ejpam-4612	42	27	0	0	NUM
ejpam-4612	42	28	and	and	CCONJ
ejpam-4612	42	29	∥x∥	∥x∥	NOUN
ejpam-4612	42	30	=	=	SYM
ejpam-4612	42	31	0	0	PUNCT
ejpam-4612	42	32	if	if	SCONJ
ejpam-4612	42	33	and	and	CCONJ
ejpam-4612	42	34	only	only	ADV
ejpam-4612	42	35	if	if	SCONJ
ejpam-4612	42	36	x	x	SYM
ejpam-4612	42	37	=	=	SYM
ejpam-4612	42	38	0	0	NUM
ejpam-4612	42	39	(	(	PUNCT
ejpam-4612	42	40	ii	ii	NOUN
ejpam-4612	42	41	)	)	PUNCT
ejpam-4612	42	42	∥ax∥	∥ax∥	PUNCT
ejpam-4612	43	1	=	=	PROPN
ejpam-4612	43	2	|a|∥x∥	|a|∥x∥	PROPN
ejpam-4612	43	3	(	(	PUNCT
ejpam-4612	43	4	iii	iii	PROPN
ejpam-4612	43	5	)	)	PUNCT
ejpam-4612	43	6	∥x+	∥x+	NOUN
ejpam-4612	43	7	y∥	y∥	VERB
ejpam-4612	43	8	≤	≤	NUM
ejpam-4612	43	9	∥x∥+	∥x∥+	ADP
ejpam-4612	43	10	∥y∥	∥y∥	PRON
ejpam-4612	43	11	the	the	DET
ejpam-4612	43	12	inner	inner	ADJ
ejpam-4612	43	13	product	product	NOUN
ejpam-4612	43	14	onx	onx	PROPN
ejpam-4612	43	15	is	be	AUX
ejpam-4612	43	16	a	a	DET
ejpam-4612	43	17	mapping	mapping	NOUN
ejpam-4612	43	18	⟨	⟨	NOUN
ejpam-4612	43	19	·	·	PUNCT
ejpam-4612	43	20	,	,	PUNCT
ejpam-4612	43	21	·	·	PUNCT
ejpam-4612	43	22	⟩	⟩	NOUN
ejpam-4612	43	23	:	:	PUNCT
ejpam-4612	43	24	x×x	x×x	PROPN
ejpam-4612	43	25	→	→	PUNCT
ejpam-4612	43	26	r	r	NOUN
ejpam-4612	43	27	such	such	ADJ
ejpam-4612	43	28	that	that	PRON
ejpam-4612	43	29	for	for	ADP
ejpam-4612	43	30	all	all	DET
ejpam-4612	43	31	vectors	vector	NOUN
ejpam-4612	43	32	x	x	SYM
ejpam-4612	43	33	,	,	PUNCT
ejpam-4612	43	34	y	y	PROPN
ejpam-4612	43	35	,	,	PUNCT
ejpam-4612	43	36	z	z	NOUN
ejpam-4612	43	37	∈	∈	PROPN
ejpam-4612	43	38	x	x	X
ejpam-4612	43	39	and	and	CCONJ
ejpam-4612	43	40	a	a	DET
ejpam-4612	43	41	scalar	scalar	NOUN
ejpam-4612	43	42	a	a	DET
ejpam-4612	43	43	∈	∈	NOUN
ejpam-4612	44	1	r	r	NOUN
ejpam-4612	44	2	we	we	PRON
ejpam-4612	44	3	have	have	VERB
ejpam-4612	44	4	:	:	PUNCT
ejpam-4612	44	5	(	(	PUNCT
ejpam-4612	44	6	i	i	NOUN
ejpam-4612	44	7	)	)	PUNCT
ejpam-4612	44	8	⟨x	⟨x	VERB
ejpam-4612	44	9	,	,	PUNCT
ejpam-4612	44	10	x⟩	x⟩	PUNCT
ejpam-4612	44	11	≥	≥	X
ejpam-4612	44	12	0	0	NUM
ejpam-4612	44	13	and	and	CCONJ
ejpam-4612	44	14	⟨x	⟨x	NUM
ejpam-4612	44	15	,	,	PUNCT
ejpam-4612	44	16	x⟩	x⟩	PUNCT
ejpam-4612	45	1	=	=	SYM
ejpam-4612	45	2	0	0	PUNCT
ejpam-4612	46	1	if	if	SCONJ
ejpam-4612	46	2	and	and	CCONJ
ejpam-4612	46	3	only	only	ADV
ejpam-4612	46	4	if	if	SCONJ
ejpam-4612	46	5	x	x	SYM
ejpam-4612	46	6	=	=	SYM
ejpam-4612	46	7	0	0	NUM
ejpam-4612	46	8	(	(	PUNCT
ejpam-4612	46	9	ii	ii	NOUN
ejpam-4612	46	10	)	)	PUNCT
ejpam-4612	46	11	⟨x	⟨x	VERB
ejpam-4612	46	12	,	,	PUNCT
ejpam-4612	46	13	y⟩	y⟩	NOUN
ejpam-4612	46	14	=	=	PUNCT
ejpam-4612	46	15	⟨y	⟨y	NOUN
ejpam-4612	46	16	,	,	PUNCT
ejpam-4612	46	17	x⟩	x⟩	PUNCT
ejpam-4612	46	18	(	(	PUNCT
ejpam-4612	46	19	iii	iii	NOUN
ejpam-4612	46	20	)	)	PUNCT
ejpam-4612	46	21	⟨ax	⟨ax	VERB
ejpam-4612	46	22	,	,	PUNCT
ejpam-4612	46	23	y⟩	y⟩	NOUN
ejpam-4612	46	24	=	=	SYM
ejpam-4612	46	25	a⟨x	a⟨x	PROPN
ejpam-4612	46	26	,	,	PUNCT
ejpam-4612	46	27	y⟩	y⟩	NOUN
ejpam-4612	46	28	(	(	PUNCT
ejpam-4612	46	29	iv	iv	X
ejpam-4612	46	30	)	)	PUNCT
ejpam-4612	46	31	⟨x+	⟨x+	PART
ejpam-4612	46	32	y	y	PROPN
ejpam-4612	46	33	,	,	PUNCT
ejpam-4612	46	34	z⟩	z⟩	NOUN
ejpam-4612	46	35	≤	≤	NUM
ejpam-4612	46	36	⟨x	⟨x	VERB
ejpam-4612	46	37	,	,	PUNCT
ejpam-4612	46	38	z⟩+	z⟩+	PROPN
ejpam-4612	46	39	⟨y	⟨y	NUM
ejpam-4612	46	40	,	,	PUNCT
ejpam-4612	46	41	z⟩	z⟩	NOUN
ejpam-4612	46	42	note	note	VERB
ejpam-4612	46	43	:	:	PUNCT
ejpam-4612	46	44	the	the	DET
ejpam-4612	46	45	space	space	NOUN
ejpam-4612	46	46	x	x	PUNCT
ejpam-4612	46	47	which	which	PRON
ejpam-4612	46	48	is	be	AUX
ejpam-4612	46	49	equipped	equip	VERB
ejpam-4612	46	50	by	by	ADP
ejpam-4612	46	51	a	a	DET
ejpam-4612	46	52	norm	norm	NOUN
ejpam-4612	46	53	∥	∥	X
ejpam-4612	46	54	·	·	PUNCT
ejpam-4612	46	55	∥	∥	NUM
ejpam-4612	46	56	,	,	PUNCT
ejpam-4612	46	57	(	(	PUNCT
ejpam-4612	46	58	x	x	X
ejpam-4612	46	59	,	,	PUNCT
ejpam-4612	46	60	∥	∥	X
ejpam-4612	46	61	·	·	PUNCT
ejpam-4612	46	62	∥	∥	NUM
ejpam-4612	46	63	)	)	PUNCT
ejpam-4612	46	64	,	,	PUNCT
ejpam-4612	46	65	is	be	AUX
ejpam-4612	46	66	called	call	VERB
ejpam-4612	46	67	a	a	DET
ejpam-4612	46	68	normed	normed	ADJ
ejpam-4612	46	69	space	space	NOUN
ejpam-4612	46	70	.	.	PUNCT
ejpam-4612	47	1	the	the	DET
ejpam-4612	47	2	space	space	NOUN
ejpam-4612	47	3	x	x	PUNCT
ejpam-4612	47	4	which	which	PRON
ejpam-4612	47	5	is	be	AUX
ejpam-4612	47	6	equipped	equip	VERB
ejpam-4612	47	7	by	by	ADP
ejpam-4612	47	8	an	an	DET
ejpam-4612	47	9	inner	inner	ADJ
ejpam-4612	47	10	product	product	NOUN
ejpam-4612	47	11	⟨	⟨	VERB
ejpam-4612	47	12	·	·	PUNCT
ejpam-4612	47	13	,	,	PUNCT
ejpam-4612	47	14	·	·	PUNCT
ejpam-4612	47	15	⟩	⟩	NOUN
ejpam-4612	47	16	,	,	PUNCT
ejpam-4612	47	17	(	(	PUNCT
ejpam-4612	47	18	x	x	NOUN
ejpam-4612	47	19	,	,	PUNCT
ejpam-4612	47	20	⟨	⟨	NOUN
ejpam-4612	47	21	·	·	SYM
ejpam-4612	47	22	,	,	PUNCT
ejpam-4612	47	23	·	·	PUNCT
ejpam-4612	47	24	⟩	⟩	NOUN
ejpam-4612	47	25	)	)	PUNCT
ejpam-4612	47	26	,	,	PUNCT
ejpam-4612	47	27	is	be	AUX
ejpam-4612	47	28	called	call	VERB
ejpam-4612	47	29	an	an	DET
ejpam-4612	47	30	inner	inner	ADJ
ejpam-4612	47	31	product	product	NOUN
ejpam-4612	47	32	space	space	NOUN
ejpam-4612	47	33	.	.	PUNCT
ejpam-4612	48	1	2	2	X
ejpam-4612	48	2	.	.	X
ejpam-4612	48	3	result	result	VERB
ejpam-4612	48	4	2.1	2.1	NUM
ejpam-4612	48	5	.	.	PUNCT
ejpam-4612	49	1	inner	inner	ADJ
ejpam-4612	49	2	product	product	NOUN
ejpam-4612	49	3	on	on	ADP
ejpam-4612	49	4	mu	mu	PROPN
ejpam-4612	49	5	,	,	PUNCT
ejpam-4612	49	6	p	p	NOUN
ejpam-4612	49	7	for	for	ADP
ejpam-4612	49	8	p	p	NOUN
ejpam-4612	49	9	=	=	SYM
ejpam-4612	49	10	2	2	NUM
ejpam-4612	49	11	in	in	ADP
ejpam-4612	49	12	mu,2	mu,2	PROPN
ejpam-4612	49	13	,	,	PUNCT
ejpam-4612	49	14	the	the	DET
ejpam-4612	49	15	norm	norm	NOUN
ejpam-4612	49	16	of	of	ADP
ejpam-4612	49	17	λ	λ	X
ejpam-4612	49	18	=	=	SYM
ejpam-4612	49	19	(	(	PUNCT
ejpam-4612	49	20	λk)k∈z	λk)k∈z	NUM
ejpam-4612	49	21	∈	∈	PROPN
ejpam-4612	49	22	mu,2	mu,2	PROPN
ejpam-4612	49	23	is	be	AUX
ejpam-4612	49	24	defined	define	VERB
ejpam-4612	49	25	as	as	ADP
ejpam-4612	49	26	∥λ∥mu,2	∥λ∥mu,2	PRON
ejpam-4612	49	27	:	:	PUNCT
ejpam-4612	49	28	=	=	NUM
ejpam-4612	49	29	sup	sup	NUM
ejpam-4612	49	30	m∈z	m∈z	NOUN
ejpam-4612	49	31	,	,	PUNCT
ejpam-4612	49	32	n∈ω	n∈ω	NOUN
ejpam-4612	49	33	|sm	|sm	ADV
ejpam-4612	49	34	,	,	PUNCT
ejpam-4612	49	35	n	n	CCONJ
ejpam-4612	49	36	|	|	ADV
ejpam-4612	49	37	1	1	NUM
ejpam-4612	49	38	u	u	NOUN
ejpam-4612	49	39	−	−	PROPN
ejpam-4612	49	40	1	1	NUM
ejpam-4612	49	41	2	2	NUM
ejpam-4612	49	42	(	(	PUNCT
ejpam-4612	49	43	∑	∑	ADV
ejpam-4612	49	44	k∈sm	k∈sm	NOUN
ejpam-4612	49	45	,	,	PUNCT
ejpam-4612	49	46	n	n	NOUN
ejpam-4612	49	47	|λk|2	|λk|2	PUNCT
ejpam-4612	49	48	)	)	PUNCT
ejpam-4612	49	49	1	1	NUM
ejpam-4612	49	50	2	2	NUM
ejpam-4612	49	51	.	.	PUNCT
ejpam-4612	50	1	m.	m.	NOUN
ejpam-4612	50	2	jakfar	jakfar	PROPN
ejpam-4612	50	3	et	et	PROPN
ejpam-4612	50	4	al	al	PROPN
ejpam-4612	50	5	.	.	PUNCT
ejpam-4612	50	6	/	/	SYM
ejpam-4612	50	7	eur	eur	PROPN
ejpam-4612	50	8	.	.	PUNCT
ejpam-4612	51	1	j.	j.	PROPN
ejpam-4612	51	2	pure	pure	PROPN
ejpam-4612	51	3	appl	appl	PROPN
ejpam-4612	51	4	.	.	PROPN
ejpam-4612	51	5	math	math	PROPN
ejpam-4612	51	6	,	,	PUNCT
ejpam-4612	51	7	16	16	NUM
ejpam-4612	51	8	(	(	PUNCT
ejpam-4612	51	9	1	1	NUM
ejpam-4612	51	10	)	)	PUNCT
ejpam-4612	51	11	(	(	PUNCT
ejpam-4612	51	12	2023	2023	NUM
ejpam-4612	51	13	)	)	PUNCT
ejpam-4612	51	14	,	,	PUNCT
ejpam-4612	51	15	144	144	NUM
ejpam-4612	51	16	-	-	SYM
ejpam-4612	51	17	155	155	NUM
ejpam-4612	51	18	146	146	NUM
ejpam-4612	51	19	we	we	PRON
ejpam-4612	51	20	can	can	AUX
ejpam-4612	51	21	observe	observe	VERB
ejpam-4612	51	22	that	that	SCONJ
ejpam-4612	51	23	the	the	DET
ejpam-4612	51	24	norm	norm	NOUN
ejpam-4612	51	25	satisfies	satisfy	VERB
ejpam-4612	51	26	the	the	DET
ejpam-4612	51	27	parallelogram	parallelogram	NOUN
ejpam-4612	51	28	’s	’s	PART
ejpam-4612	51	29	law	law	NOUN
ejpam-4612	51	30	∥λ+	∥λ+	PROPN
ejpam-4612	51	31	µ∥2mu,2	µ∥2mu,2	NOUN
ejpam-4612	51	32	+	+	CCONJ
ejpam-4612	51	33	∥λ−	∥λ−	NUM
ejpam-4612	51	34	µ∥2mu,2	µ∥2mu,2	NOUN
ejpam-4612	51	35	=	=	PUNCT
ejpam-4612	51	36	∥λ∥2mu,2	∥λ∥2mu,2	NOUN
ejpam-4612	51	37	+	+	CCONJ
ejpam-4612	51	38	∥µ∥2mu,2	∥µ∥2mu,2	NOUN
ejpam-4612	51	39	for	for	ADP
ejpam-4612	51	40	every	every	DET
ejpam-4612	51	41	λ	λ	NOUN
ejpam-4612	51	42	=	=	SYM
ejpam-4612	51	43	(	(	PUNCT
ejpam-4612	51	44	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	51	45	,	,	PUNCT
ejpam-4612	51	46	µ	µ	X
ejpam-4612	51	47	=	=	PUNCT
ejpam-4612	51	48	(	(	PUNCT
ejpam-4612	51	49	µk)k∈z	µk)k∈z	NUM
ejpam-4612	51	50	∈	∈	PROPN
ejpam-4612	51	51	mu,2	mu,2	PROPN
ejpam-4612	51	52	.	.	PUNCT
ejpam-4612	52	1	that	that	PRON
ejpam-4612	52	2	means	mean	VERB
ejpam-4612	52	3	,	,	PUNCT
ejpam-4612	52	4	the	the	DET
ejpam-4612	52	5	norm	norm	NOUN
ejpam-4612	52	6	is	be	AUX
ejpam-4612	52	7	formed	form	VERB
ejpam-4612	52	8	from	from	ADP
ejpam-4612	52	9	an	an	DET
ejpam-4612	52	10	inner	inner	ADJ
ejpam-4612	52	11	product	product	NOUN
ejpam-4612	52	12	.	.	PUNCT
ejpam-4612	53	1	so	so	ADV
ejpam-4612	53	2	,	,	PUNCT
ejpam-4612	53	3	we	we	PRON
ejpam-4612	53	4	know	know	VERB
ejpam-4612	53	5	that	that	SCONJ
ejpam-4612	53	6	mu,2	mu,2	PROPN
ejpam-4612	53	7	is	be	AUX
ejpam-4612	53	8	an	an	DET
ejpam-4612	53	9	inner	inner	ADJ
ejpam-4612	53	10	product	product	NOUN
ejpam-4612	53	11	space	space	NOUN
ejpam-4612	53	12	,	,	PUNCT
ejpam-4612	53	13	equipped	equip	VERB
ejpam-4612	53	14	with	with	ADP
ejpam-4612	53	15	the	the	DET
ejpam-4612	53	16	inner	inner	ADJ
ejpam-4612	53	17	product	product	NOUN
ejpam-4612	53	18	⟨λ	⟨λ	NUM
ejpam-4612	53	19	,	,	PUNCT
ejpam-4612	53	20	µ⟩mu,2	µ⟩mu,2	PUNCT
ejpam-4612	53	21	:	:	PUNCT
ejpam-4612	53	22	=	=	NUM
ejpam-4612	53	23	sup	sup	NUM
ejpam-4612	53	24	m∈z	m∈z	NOUN
ejpam-4612	53	25	,	,	PUNCT
ejpam-4612	53	26	n∈ω	n∈ω	NOUN
ejpam-4612	53	27	|sm	|sm	NUM
ejpam-4612	53	28	,	,	PUNCT
ejpam-4612	53	29	n	n	X
ejpam-4612	53	30	|2	|2	NUM
ejpam-4612	53	31	(	(	PUNCT
ejpam-4612	53	32	1	1	NUM
ejpam-4612	53	33	u	u	NOUN
ejpam-4612	53	34	−	−	PROPN
ejpam-4612	53	35	1	1	NUM
ejpam-4612	53	36	2	2	NUM
ejpam-4612	53	37	)	)	PUNCT
ejpam-4612	53	38	(	(	PUNCT
ejpam-4612	53	39	∑	∑	ADV
ejpam-4612	53	40	k∈sm	k∈sm	PROPN
ejpam-4612	53	41	,	,	PUNCT
ejpam-4612	53	42	n	n	NOUN
ejpam-4612	53	43	λkµk	λkµk	NUM
ejpam-4612	53	44	)	)	PUNCT
ejpam-4612	53	45	.	.	PUNCT
ejpam-4612	54	1	then	then	ADV
ejpam-4612	54	2	∥λ∥2mu,2	∥λ∥2mu,2	NOUN
ejpam-4612	54	3	=	=	SYM
ejpam-4612	54	4	⟨λ	⟨λ	NUM
ejpam-4612	54	5	,	,	PUNCT
ejpam-4612	54	6	λ⟩mu,2	λ⟩mu,2	X
ejpam-4612	54	7	.	.	PUNCT
ejpam-4612	55	1	proposition	proposition	NOUN
ejpam-4612	55	2	1	1	NUM
ejpam-4612	55	3	.	.	PUNCT
ejpam-4612	56	1	in	in	ADP
ejpam-4612	56	2	the	the	DET
ejpam-4612	56	3	space	space	NOUN
ejpam-4612	56	4	mu,2	mu,2	PROPN
ejpam-4612	56	5	,	,	PUNCT
ejpam-4612	56	6	the	the	DET
ejpam-4612	56	7	mapping	mapping	NOUN
ejpam-4612	56	8	⟨	⟨	VERB
ejpam-4612	56	9	·	·	PUNCT
ejpam-4612	56	10	,	,	PUNCT
ejpam-4612	56	11	·	·	PUNCT
ejpam-4612	56	12	⟩mu,2	⟩mu,2	VERB
ejpam-4612	56	13	defines	define	VERB
ejpam-4612	56	14	an	an	DET
ejpam-4612	56	15	inner	inner	ADJ
ejpam-4612	56	16	product	product	NOUN
ejpam-4612	56	17	on	on	ADP
ejpam-4612	56	18	mu,2	mu,2	PROPN
ejpam-4612	56	19	.	.	PUNCT
ejpam-4612	57	1	proof	proof	NOUN
ejpam-4612	57	2	.	.	PUNCT
ejpam-4612	58	1	we	we	PRON
ejpam-4612	58	2	will	will	AUX
ejpam-4612	58	3	show	show	VERB
ejpam-4612	58	4	that	that	SCONJ
ejpam-4612	58	5	the	the	DET
ejpam-4612	58	6	mapping	mapping	NOUN
ejpam-4612	58	7	⟨	⟨	VERB
ejpam-4612	58	8	·	·	PUNCT
ejpam-4612	58	9	,	,	PUNCT
ejpam-4612	58	10	·	·	PUNCT
ejpam-4612	58	11	⟩mu,2	⟩mu,2	VERB
ejpam-4612	58	12	satisfy	satisfy	VERB
ejpam-4612	58	13	all	all	DET
ejpam-4612	58	14	conditions	condition	NOUN
ejpam-4612	58	15	of	of	ADP
ejpam-4612	58	16	an	an	DET
ejpam-4612	58	17	inner	inner	ADJ
ejpam-4612	58	18	product	product	NOUN
ejpam-4612	58	19	on	on	ADP
ejpam-4612	58	20	mu,2	mu,2	PROPN
ejpam-4612	58	21	.	.	PUNCT
ejpam-4612	59	1	(	(	PUNCT
ejpam-4612	59	2	i	i	NOUN
ejpam-4612	59	3	)	)	PUNCT
ejpam-4612	59	4	clear	clear	ADJ
ejpam-4612	59	5	,	,	PUNCT
ejpam-4612	59	6	for	for	ADP
ejpam-4612	59	7	every	every	DET
ejpam-4612	59	8	λ	λ	NOUN
ejpam-4612	59	9	=	=	PRON
ejpam-4612	59	10	(	(	PUNCT
ejpam-4612	59	11	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	59	12	∈	∈	PROPN
ejpam-4612	59	13	mu,2	mu,2	PROPN
ejpam-4612	59	14	,	,	PUNCT
ejpam-4612	59	15	we	we	PRON
ejpam-4612	59	16	get	get	VERB
ejpam-4612	59	17	⟨λ	⟨λ	NOUN
ejpam-4612	59	18	,	,	PUNCT
ejpam-4612	59	19	λ⟩mu,2	λ⟩mu,2	CCONJ
ejpam-4612	59	20	=	=	PUNCT
ejpam-4612	59	21	∥λ∥2mu,2	∥λ∥2mu,2	NOUN
ejpam-4612	59	22	≥	≥	NOUN
ejpam-4612	59	23	0	0	NUM
ejpam-4612	59	24	.	.	PUNCT
ejpam-4612	60	1	if	if	SCONJ
ejpam-4612	60	2	λ	λ	X
ejpam-4612	60	3	=	=	SYM
ejpam-4612	60	4	0	0	NUM
ejpam-4612	60	5	then	then	ADV
ejpam-4612	60	6	⟨λ	⟨λ	NUM
ejpam-4612	60	7	,	,	PUNCT
ejpam-4612	60	8	λ⟩mu,2	λ⟩mu,2	CCONJ
ejpam-4612	60	9	=	=	SYM
ejpam-4612	60	10	0	0	NUM
ejpam-4612	60	11	.	.	PUNCT
ejpam-4612	61	1	and	and	CCONJ
ejpam-4612	61	2	,	,	PUNCT
ejpam-4612	61	3	if	if	SCONJ
ejpam-4612	61	4	⟨λ	⟨λ	NUM
ejpam-4612	61	5	,	,	PUNCT
ejpam-4612	61	6	λ⟩mu,2	λ⟩mu,2	ADV
ejpam-4612	61	7	=	=	SYM
ejpam-4612	61	8	0	0	PUNCT
ejpam-4612	61	9	then	then	ADV
ejpam-4612	61	10	∥λ∥2mu,2	∥λ∥2mu,2	NOUN
ejpam-4612	61	11	=	=	SYM
ejpam-4612	61	12	0	0	NUM
ejpam-4612	61	13	,	,	PUNCT
ejpam-4612	61	14	so	so	ADV
ejpam-4612	61	15	,	,	PUNCT
ejpam-4612	61	16	it	it	PRON
ejpam-4612	61	17	must	must	AUX
ejpam-4612	61	18	be	be	AUX
ejpam-4612	61	19	λ	λ	NOUN
ejpam-4612	61	20	=	=	NOUN
ejpam-4612	61	21	0	0	NUM
ejpam-4612	61	22	.	.	PUNCT
ejpam-4612	62	1	(	(	PUNCT
ejpam-4612	62	2	ii	ii	NOUN
ejpam-4612	62	3	)	)	PUNCT
ejpam-4612	62	4	given	give	VERB
ejpam-4612	62	5	λ	λ	PROPN
ejpam-4612	62	6	=	=	SYM
ejpam-4612	62	7	(	(	PUNCT
ejpam-4612	62	8	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	62	9	,	,	PUNCT
ejpam-4612	62	10	µ	µ	X
ejpam-4612	62	11	=	=	PUNCT
ejpam-4612	62	12	(	(	PUNCT
ejpam-4612	62	13	µk)k∈z	µk)k∈z	NUM
ejpam-4612	62	14	∈	∈	PROPN
ejpam-4612	62	15	mu,2	mu,2	PROPN
ejpam-4612	62	16	.	.	PUNCT
ejpam-4612	63	1	then	then	ADV
ejpam-4612	63	2	we	we	PRON
ejpam-4612	63	3	have	have	VERB
ejpam-4612	63	4	⟨λ	⟨λ	NUM
ejpam-4612	63	5	,	,	PUNCT
ejpam-4612	63	6	µ⟩mu,2	µ⟩mu,2	NOUN
ejpam-4612	63	7	=	=	SYM
ejpam-4612	63	8	sup	sup	NUM
ejpam-4612	63	9	m∈z	m∈z	NOUN
ejpam-4612	63	10	,	,	PUNCT
ejpam-4612	63	11	n∈ω	n∈ω	NOUN
ejpam-4612	63	12	|sm	|sm	NUM
ejpam-4612	63	13	,	,	PUNCT
ejpam-4612	63	14	n	n	X
ejpam-4612	63	15	|2	|2	NUM
ejpam-4612	63	16	(	(	PUNCT
ejpam-4612	63	17	1	1	NUM
ejpam-4612	63	18	u	u	NOUN
ejpam-4612	63	19	−	−	PROPN
ejpam-4612	63	20	1	1	NUM
ejpam-4612	63	21	2	2	NUM
ejpam-4612	63	22	)	)	PUNCT
ejpam-4612	63	23	(	(	PUNCT
ejpam-4612	63	24	∑	∑	ADV
ejpam-4612	63	25	k∈sm	k∈sm	PROPN
ejpam-4612	63	26	,	,	PUNCT
ejpam-4612	63	27	n	n	NOUN
ejpam-4612	63	28	λkµk	λkµk	NOUN
ejpam-4612	63	29	)	)	PUNCT
ejpam-4612	64	1	=	=	NOUN
ejpam-4612	64	2	sup	sup	NUM
ejpam-4612	64	3	m∈z	m∈z	NOUN
ejpam-4612	64	4	,	,	PUNCT
ejpam-4612	64	5	n∈ω	n∈ω	NOUN
ejpam-4612	64	6	|sm	|sm	NUM
ejpam-4612	64	7	,	,	PUNCT
ejpam-4612	64	8	n	n	X
ejpam-4612	64	9	|2	|2	NUM
ejpam-4612	64	10	(	(	PUNCT
ejpam-4612	64	11	1	1	NUM
ejpam-4612	64	12	u	u	NOUN
ejpam-4612	64	13	−	−	PROPN
ejpam-4612	64	14	1	1	NUM
ejpam-4612	64	15	2	2	NUM
ejpam-4612	64	16	)	)	PUNCT
ejpam-4612	64	17	(	(	PUNCT
ejpam-4612	64	18	∑	∑	ADV
ejpam-4612	64	19	k∈sm	k∈sm	PROPN
ejpam-4612	64	20	,	,	PUNCT
ejpam-4612	64	21	n	n	PRON
ejpam-4612	64	22	µkλk	µkλk	ADV
ejpam-4612	64	23	)	)	PUNCT
ejpam-4612	64	24	=	=	SYM
ejpam-4612	65	1	⟨µ	⟨µ	NOUN
ejpam-4612	65	2	,	,	PUNCT
ejpam-4612	65	3	λ⟩mu,2	λ⟩mu,2	X
ejpam-4612	65	4	(	(	PUNCT
ejpam-4612	65	5	iii	iii	NOUN
ejpam-4612	65	6	)	)	PUNCT
ejpam-4612	65	7	given	give	VERB
ejpam-4612	65	8	a	a	DET
ejpam-4612	65	9	∈	∈	NOUN
ejpam-4612	65	10	r	r	NOUN
ejpam-4612	65	11	and	and	CCONJ
ejpam-4612	65	12	λ	λ	PROPN
ejpam-4612	65	13	=	=	SYM
ejpam-4612	65	14	(	(	PUNCT
ejpam-4612	65	15	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	65	16	,	,	PUNCT
ejpam-4612	65	17	µ	µ	X
ejpam-4612	65	18	=	=	PUNCT
ejpam-4612	65	19	(	(	PUNCT
ejpam-4612	65	20	µk)k∈z	µk)k∈z	NUM
ejpam-4612	65	21	∈	∈	PROPN
ejpam-4612	65	22	mu,2	mu,2	PROPN
ejpam-4612	65	23	.	.	PUNCT
ejpam-4612	66	1	we	we	PRON
ejpam-4612	66	2	get	get	VERB
ejpam-4612	66	3	a⟨λ	a⟨λ	PUNCT
ejpam-4612	66	4	,	,	PUNCT
ejpam-4612	66	5	µ⟩mu,2	µ⟩mu,2	NOUN
ejpam-4612	66	6	=	=	SYM
ejpam-4612	66	7	sup	sup	NUM
ejpam-4612	66	8	m∈z	m∈z	NOUN
ejpam-4612	66	9	,	,	PUNCT
ejpam-4612	66	10	n∈ω	n∈ω	NOUN
ejpam-4612	66	11	|sm	|sm	NUM
ejpam-4612	66	12	,	,	PUNCT
ejpam-4612	66	13	n	n	X
ejpam-4612	66	14	|2	|2	NUM
ejpam-4612	66	15	(	(	PUNCT
ejpam-4612	66	16	1	1	NUM
ejpam-4612	66	17	u	u	NOUN
ejpam-4612	66	18	−	−	PROPN
ejpam-4612	66	19	1	1	NUM
ejpam-4612	66	20	2	2	NUM
ejpam-4612	66	21	)	)	PUNCT
ejpam-4612	66	22	(	(	PUNCT
ejpam-4612	66	23	∑	∑	ADV
ejpam-4612	66	24	k∈sm	k∈sm	PROPN
ejpam-4612	66	25	,	,	PUNCT
ejpam-4612	66	26	n	n	PRON
ejpam-4612	66	27	aλkµk	aλkµk	NOUN
ejpam-4612	66	28	)	)	PUNCT
ejpam-4612	67	1	=	=	PUNCT
ejpam-4612	67	2	a	a	DET
ejpam-4612	67	3	sup	sup	NOUN
ejpam-4612	67	4	m∈z	m∈z	NOUN
ejpam-4612	67	5	,	,	PUNCT
ejpam-4612	67	6	n∈ω	n∈ω	NOUN
ejpam-4612	67	7	|sm	|sm	NUM
ejpam-4612	67	8	,	,	PUNCT
ejpam-4612	67	9	n	n	X
ejpam-4612	67	10	|2	|2	NUM
ejpam-4612	67	11	(	(	PUNCT
ejpam-4612	67	12	1	1	NUM
ejpam-4612	67	13	u	u	NOUN
ejpam-4612	67	14	−	−	PROPN
ejpam-4612	67	15	1	1	NUM
ejpam-4612	67	16	2	2	NUM
ejpam-4612	67	17	)	)	PUNCT
ejpam-4612	67	18	(	(	PUNCT
ejpam-4612	67	19	∑	∑	ADV
ejpam-4612	67	20	k∈sm	k∈sm	PROPN
ejpam-4612	67	21	,	,	PUNCT
ejpam-4612	67	22	n	n	NOUN
ejpam-4612	67	23	λkµk	λkµk	NOUN
ejpam-4612	67	24	)	)	PUNCT
ejpam-4612	68	1	=	=	SYM
ejpam-4612	68	2	a⟨λ	a⟨λ	PROPN
ejpam-4612	68	3	,	,	PUNCT
ejpam-4612	68	4	µ⟩mu,2	µ⟩mu,2	ADJ
ejpam-4612	68	5	(	(	PUNCT
ejpam-4612	68	6	iv	iv	X
ejpam-4612	68	7	)	)	PUNCT
ejpam-4612	68	8	give	give	VERB
ejpam-4612	68	9	λ	λ	X
ejpam-4612	68	10	=	=	SYM
ejpam-4612	68	11	(	(	PUNCT
ejpam-4612	68	12	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	68	13	,	,	PUNCT
ejpam-4612	68	14	γ	γ	X
ejpam-4612	68	15	=	=	X
ejpam-4612	68	16	(	(	PUNCT
ejpam-4612	68	17	γk)k∈z	γk)k∈z	NUM
ejpam-4612	68	18	,	,	PUNCT
ejpam-4612	68	19	µ	µ	X
ejpam-4612	68	20	=	=	PUNCT
ejpam-4612	68	21	(	(	PUNCT
ejpam-4612	68	22	µk)k∈z	µk)k∈z	NUM
ejpam-4612	68	23	∈	∈	PROPN
ejpam-4612	68	24	mu,2	mu,2	PROPN
ejpam-4612	68	25	.	.	PUNCT
ejpam-4612	69	1	thus	thus	ADV
ejpam-4612	69	2	⟨λ+	⟨λ+	X
ejpam-4612	69	3	γ	γ	X
ejpam-4612	69	4	,	,	PUNCT
ejpam-4612	69	5	µ⟩mu,2	µ⟩mu,2	ADJ
ejpam-4612	69	6	=	=	SYM
ejpam-4612	69	7	sup	sup	NUM
ejpam-4612	69	8	m∈z	m∈z	NOUN
ejpam-4612	69	9	,	,	PUNCT
ejpam-4612	69	10	n∈ω	n∈ω	NOUN
ejpam-4612	69	11	|sm	|sm	NUM
ejpam-4612	69	12	,	,	PUNCT
ejpam-4612	69	13	n	n	X
ejpam-4612	69	14	|2	|2	NUM
ejpam-4612	69	15	(	(	PUNCT
ejpam-4612	69	16	1	1	NUM
ejpam-4612	69	17	u	u	NOUN
ejpam-4612	69	18	−	−	PROPN
ejpam-4612	69	19	1	1	NUM
ejpam-4612	69	20	2	2	NUM
ejpam-4612	69	21	)	)	PUNCT
ejpam-4612	69	22	(	(	PUNCT
ejpam-4612	69	23	∑	∑	ADV
ejpam-4612	69	24	k∈sm	k∈sm	PROPN
ejpam-4612	69	25	,	,	PUNCT
ejpam-4612	69	26	n	n	X
ejpam-4612	69	27	(	(	PUNCT
ejpam-4612	69	28	λk	λk	X
ejpam-4612	69	29	+	+	NUM
ejpam-4612	69	30	γk)µk	γk)µk	NOUN
ejpam-4612	69	31	)	)	PUNCT
ejpam-4612	69	32	=	=	NOUN
ejpam-4612	69	33	sup	sup	NUM
ejpam-4612	69	34	m∈z	m∈z	NOUN
ejpam-4612	69	35	,	,	PUNCT
ejpam-4612	69	36	n∈ω	n∈ω	NOUN
ejpam-4612	69	37	|sm	|sm	NUM
ejpam-4612	69	38	,	,	PUNCT
ejpam-4612	69	39	n	n	X
ejpam-4612	69	40	|2	|2	NUM
ejpam-4612	69	41	(	(	PUNCT
ejpam-4612	69	42	1	1	NUM
ejpam-4612	69	43	u	u	NOUN
ejpam-4612	69	44	−	−	PROPN
ejpam-4612	69	45	1	1	NUM
ejpam-4612	69	46	2	2	NUM
ejpam-4612	69	47	)	)	PUNCT
ejpam-4612	69	48	(	(	PUNCT
ejpam-4612	69	49	∑	∑	ADV
ejpam-4612	69	50	k∈sm	k∈sm	PROPN
ejpam-4612	69	51	,	,	PUNCT
ejpam-4612	69	52	n	n	NOUN
ejpam-4612	69	53	λkµk	λkµk	NOUN
ejpam-4612	69	54	+	+	CCONJ
ejpam-4612	69	55	∑	∑	ADV
ejpam-4612	69	56	k∈sm	k∈sm	PROPN
ejpam-4612	69	57	,	,	PUNCT
ejpam-4612	69	58	n	n	PRON
ejpam-4612	69	59	γkµk	γkµk	VERB
ejpam-4612	69	60	)	)	PUNCT
ejpam-4612	70	1	=	=	SYM
ejpam-4612	70	2	sup	sup	NUM
ejpam-4612	70	3	m∈z	m∈z	NOUN
ejpam-4612	70	4	,	,	PUNCT
ejpam-4612	70	5	n∈ω	n∈ω	NOUN
ejpam-4612	70	6	|sm	|sm	NUM
ejpam-4612	70	7	,	,	PUNCT
ejpam-4612	70	8	n	n	X
ejpam-4612	70	9	|2	|2	NUM
ejpam-4612	70	10	(	(	PUNCT
ejpam-4612	70	11	1	1	NUM
ejpam-4612	70	12	u	u	NOUN
ejpam-4612	70	13	−	−	PROPN
ejpam-4612	70	14	1	1	NUM
ejpam-4612	70	15	2	2	NUM
ejpam-4612	70	16	)	)	PUNCT
ejpam-4612	70	17	(	(	PUNCT
ejpam-4612	70	18	∑	∑	ADV
ejpam-4612	70	19	k∈sm	k∈sm	PROPN
ejpam-4612	70	20	,	,	PUNCT
ejpam-4612	70	21	n	n	PROPN
ejpam-4612	70	22	λkµk	λkµk	NOUN
ejpam-4612	70	23	)	)	PUNCT
ejpam-4612	71	1	m.	m.	NOUN
ejpam-4612	71	2	jakfar	jakfar	INTJ
ejpam-4612	71	3	et	et	PROPN
ejpam-4612	71	4	al	al	PROPN
ejpam-4612	71	5	.	.	PUNCT
ejpam-4612	71	6	/	/	SYM
ejpam-4612	71	7	eur	eur	PROPN
ejpam-4612	71	8	.	.	PUNCT
ejpam-4612	72	1	j.	j.	PROPN
ejpam-4612	72	2	pure	pure	PROPN
ejpam-4612	72	3	appl	appl	PROPN
ejpam-4612	72	4	.	.	PROPN
ejpam-4612	72	5	math	math	PROPN
ejpam-4612	72	6	,	,	PUNCT
ejpam-4612	72	7	16	16	NUM
ejpam-4612	72	8	(	(	PUNCT
ejpam-4612	72	9	1	1	NUM
ejpam-4612	72	10	)	)	PUNCT
ejpam-4612	72	11	(	(	PUNCT
ejpam-4612	72	12	2023	2023	NUM
ejpam-4612	72	13	)	)	PUNCT
ejpam-4612	72	14	,	,	PUNCT
ejpam-4612	72	15	144	144	NUM
ejpam-4612	72	16	-	-	SYM
ejpam-4612	72	17	155	155	NUM
ejpam-4612	72	18	147	147	NUM
ejpam-4612	72	19	+	+	CCONJ
ejpam-4612	72	20	sup	sup	PROPN
ejpam-4612	72	21	m∈z	m∈z	NOUN
ejpam-4612	72	22	,	,	PUNCT
ejpam-4612	72	23	n∈ω	n∈ω	NOUN
ejpam-4612	72	24	|sm	|sm	NUM
ejpam-4612	72	25	,	,	PUNCT
ejpam-4612	72	26	n	n	X
ejpam-4612	72	27	|2	|2	NUM
ejpam-4612	72	28	(	(	PUNCT
ejpam-4612	72	29	1	1	NUM
ejpam-4612	72	30	u	u	NOUN
ejpam-4612	72	31	−	−	PROPN
ejpam-4612	72	32	1	1	NUM
ejpam-4612	72	33	2	2	NUM
ejpam-4612	72	34	)	)	PUNCT
ejpam-4612	72	35	(	(	PUNCT
ejpam-4612	72	36	∑	∑	ADV
ejpam-4612	72	37	k∈sm	k∈sm	PROPN
ejpam-4612	72	38	,	,	PUNCT
ejpam-4612	72	39	n	n	PRON
ejpam-4612	72	40	γkµk	γkµk	VERB
ejpam-4612	72	41	)	)	PUNCT
ejpam-4612	72	42	=	=	SYM
ejpam-4612	73	1	⟨λ	⟨λ	X
ejpam-4612	73	2	,	,	PUNCT
ejpam-4612	73	3	µ⟩mu,2	µ⟩mu,2	X
ejpam-4612	73	4	+	+	CCONJ
ejpam-4612	73	5	⟨γ	⟨γ	ADJ
ejpam-4612	73	6	,	,	PUNCT
ejpam-4612	73	7	µ⟩mu,2	µ⟩mu,2	PART
ejpam-4612	73	8	■	■	PUNCT
ejpam-4612	73	9	remark	remark	NOUN
ejpam-4612	73	10	1	1	NUM
ejpam-4612	73	11	.	.	PUNCT
ejpam-4612	74	1	the	the	DET
ejpam-4612	74	2	space	space	NOUN
ejpam-4612	74	3	(	(	PUNCT
ejpam-4612	74	4	mu,2	mu,2	PROPN
ejpam-4612	74	5	,	,	PUNCT
ejpam-4612	74	6	∥	∥	X
ejpam-4612	74	7	·	·	PUNCT
ejpam-4612	74	8	∥mu,2	∥mu,2	X
ejpam-4612	74	9	)	)	PUNCT
ejpam-4612	74	10	is	be	AUX
ejpam-4612	74	11	an	an	DET
ejpam-4612	74	12	inner	inner	ADJ
ejpam-4612	74	13	product	product	NOUN
ejpam-4612	74	14	space	space	NOUN
ejpam-4612	74	15	.	.	PUNCT
ejpam-4612	75	1	moreover	moreover	ADV
ejpam-4612	75	2	,	,	PUNCT
ejpam-4612	75	3	by	by	ADP
ejpam-4612	75	4	theorem	theorem	NOUN
ejpam-4612	75	5	1	1	NUM
ejpam-4612	75	6	,	,	PUNCT
ejpam-4612	75	7	the	the	DET
ejpam-4612	75	8	space	space	NOUN
ejpam-4612	75	9	is	be	AUX
ejpam-4612	75	10	a	a	DET
ejpam-4612	75	11	complete	complete	ADJ
ejpam-4612	75	12	.	.	PUNCT
ejpam-4612	76	1	accordingly	accordingly	ADV
ejpam-4612	76	2	,	,	PUNCT
ejpam-4612	76	3	(	(	PUNCT
ejpam-4612	76	4	mu,2	mu,2	PROPN
ejpam-4612	76	5	,	,	PUNCT
ejpam-4612	76	6	⟨	⟨	NOUN
ejpam-4612	76	7	·	·	PUNCT
ejpam-4612	76	8	,	,	PUNCT
ejpam-4612	76	9	·	·	PUNCT
ejpam-4612	76	10	⟩mu,2	⟩mu,2	X
ejpam-4612	76	11	)	)	PUNCT
ejpam-4612	76	12	is	be	AUX
ejpam-4612	76	13	a	a	DET
ejpam-4612	76	14	hilbert	hilbert	NOUN
ejpam-4612	76	15	space	space	NOUN
ejpam-4612	76	16	.	.	PUNCT
ejpam-4612	77	1	for	for	ADP
ejpam-4612	77	2	p	p	PROPN
ejpam-4612	77	3	̸=	̸=	PROPN
ejpam-4612	77	4	2	2	NUM
ejpam-4612	77	5	,	,	PUNCT
ejpam-4612	77	6	the	the	DET
ejpam-4612	77	7	space	space	NOUN
ejpam-4612	77	8	mu	mu	NOUN
ejpam-4612	77	9	,	,	PUNCT
ejpam-4612	77	10	p	p	NOUN
ejpam-4612	77	11	is	be	AUX
ejpam-4612	77	12	not	not	PART
ejpam-4612	77	13	an	an	DET
ejpam-4612	77	14	inner	inner	ADJ
ejpam-4612	77	15	product	product	NOUN
ejpam-4612	77	16	space	space	NOUN
ejpam-4612	77	17	.	.	PUNCT
ejpam-4612	78	1	because	because	SCONJ
ejpam-4612	78	2	the	the	DET
ejpam-4612	78	3	norm	norm	NOUN
ejpam-4612	78	4	is	be	AUX
ejpam-4612	78	5	not	not	PART
ejpam-4612	78	6	satisfy	satisfy	VERB
ejpam-4612	78	7	the	the	DET
ejpam-4612	78	8	parallelogram	parallelogram	NOUN
ejpam-4612	78	9	’s	’s	PART
ejpam-4612	78	10	law	law	NOUN
ejpam-4612	78	11	.	.	PUNCT
ejpam-4612	79	1	so	so	ADV
ejpam-4612	79	2	,	,	PUNCT
ejpam-4612	79	3	in	in	ADP
ejpam-4612	79	4	the	the	DET
ejpam-4612	79	5	next	next	ADJ
ejpam-4612	79	6	section	section	NOUN
ejpam-4612	79	7	,	,	PUNCT
ejpam-4612	79	8	we	we	PRON
ejpam-4612	79	9	will	will	AUX
ejpam-4612	79	10	try	try	VERB
ejpam-4612	79	11	to	to	PART
ejpam-4612	79	12	define	define	VERB
ejpam-4612	79	13	an	an	DET
ejpam-4612	79	14	inner	inner	ADJ
ejpam-4612	79	15	product	product	NOUN
ejpam-4612	79	16	on	on	ADP
ejpam-4612	79	17	mu	mu	PROPN
ejpam-4612	79	18	,	,	PUNCT
ejpam-4612	79	19	p	p	NOUN
ejpam-4612	79	20	for	for	ADP
ejpam-4612	79	21	p	p	PROPN
ejpam-4612	79	22	̸=	̸=	PROPN
ejpam-4612	79	23	2	2	NUM
ejpam-4612	79	24	.	.	PUNCT
ejpam-4612	79	25	2.2	2.2	NUM
ejpam-4612	79	26	.	.	PUNCT
ejpam-4612	80	1	inner	inner	ADJ
ejpam-4612	80	2	product	product	NOUN
ejpam-4612	80	3	on	on	ADP
ejpam-4612	80	4	mu	mu	PROPN
ejpam-4612	80	5	,	,	PUNCT
ejpam-4612	80	6	p	p	NOUN
ejpam-4612	80	7	for	for	ADP
ejpam-4612	80	8	2	2	NUM
ejpam-4612	80	9	<	<	X
ejpam-4612	80	10	p	p	X
ejpam-4612	80	11	<	<	X
ejpam-4612	80	12	∞	∞	PROPN
ejpam-4612	80	13	in	in	ADP
ejpam-4612	80	14	this	this	DET
ejpam-4612	80	15	section	section	NOUN
ejpam-4612	80	16	,	,	PUNCT
ejpam-4612	80	17	we	we	PRON
ejpam-4612	80	18	let	let	VERB
ejpam-4612	80	19	2	2	NUM
ejpam-4612	80	20	<	<	X
ejpam-4612	80	21	p	p	X
ejpam-4612	80	22	≤	≤	NUM
ejpam-4612	80	23	u	u	NOUN
ejpam-4612	80	24	<	<	X
ejpam-4612	80	25	∞	∞	PROPN
ejpam-4612	80	26	,	,	PUNCT
ejpam-4612	80	27	unless	unless	SCONJ
ejpam-4612	80	28	otherwise	otherwise	ADV
ejpam-4612	80	29	stated	state	VERB
ejpam-4612	80	30	.	.	PUNCT
ejpam-4612	81	1	we	we	PRON
ejpam-4612	81	2	will	will	AUX
ejpam-4612	81	3	define	define	VERB
ejpam-4612	81	4	an	an	DET
ejpam-4612	81	5	inner	inner	ADJ
ejpam-4612	81	6	product	product	NOUN
ejpam-4612	81	7	on	on	ADP
ejpam-4612	81	8	the	the	DET
ejpam-4612	81	9	space	space	NOUN
ejpam-4612	81	10	mu	mu	NOUN
ejpam-4612	81	11	,	,	PUNCT
ejpam-4612	81	12	p.	p.	PROPN
ejpam-4612	81	13	first	first	ADV
ejpam-4612	81	14	,	,	PUNCT
ejpam-4612	81	15	before	before	SCONJ
ejpam-4612	81	16	we	we	PRON
ejpam-4612	81	17	define	define	VERB
ejpam-4612	81	18	an	an	DET
ejpam-4612	81	19	inner	inner	ADJ
ejpam-4612	81	20	product	product	NOUN
ejpam-4612	81	21	on	on	ADP
ejpam-4612	81	22	the	the	DET
ejpam-4612	81	23	space	space	NOUN
ejpam-4612	81	24	mu	mu	NOUN
ejpam-4612	81	25	,	,	PUNCT
ejpam-4612	81	26	p	p	PRON
ejpam-4612	81	27	,	,	PUNCT
ejpam-4612	81	28	we	we	PRON
ejpam-4612	81	29	observe	observe	VERB
ejpam-4612	81	30	that	that	SCONJ
ejpam-4612	81	31	mu	mu	NOUN
ejpam-4612	81	32	,	,	PUNCT
ejpam-4612	81	33	p	p	PROPN
ejpam-4612	81	34	⊂	⊂	PROPN
ejpam-4612	81	35	mu,2	mu,2	PROPN
ejpam-4612	81	36	(	(	PUNCT
ejpam-4612	81	37	as	as	ADP
ejpam-4612	81	38	set	set	NOUN
ejpam-4612	81	39	)	)	PUNCT
ejpam-4612	81	40	.	.	PUNCT
ejpam-4612	82	1	indeed	indeed	ADV
ejpam-4612	82	2	,	,	PUNCT
ejpam-4612	82	3	if	if	SCONJ
ejpam-4612	82	4	λ	λ	X
ejpam-4612	82	5	=	=	SYM
ejpam-4612	82	6	(	(	PUNCT
ejpam-4612	82	7	λk)k∈z	λk)k∈z	NUM
ejpam-4612	82	8	is	be	AUX
ejpam-4612	82	9	a	a	DET
ejpam-4612	82	10	sequence	sequence	NOUN
ejpam-4612	82	11	in	in	ADP
ejpam-4612	82	12	mu	mu	PROPN
ejpam-4612	82	13	,	,	PUNCT
ejpam-4612	82	14	p	p	NOUN
ejpam-4612	82	15	,	,	PUNCT
ejpam-4612	82	16	then	then	ADV
ejpam-4612	82	17	by	by	ADP
ejpam-4612	82	18	holder	holder	NOUN
ejpam-4612	82	19	’s	’s	PART
ejpam-4612	82	20	inequality	inequality	NOUN
ejpam-4612	82	21	,	,	PUNCT
ejpam-4612	82	22	we	we	PRON
ejpam-4612	82	23	have∑	have∑	VERB
ejpam-4612	82	24	k∈sm	k∈sm	PROPN
ejpam-4612	82	25	,	,	PUNCT
ejpam-4612	82	26	n	n	NOUN
ejpam-4612	82	27	|λk|2	|λk|2	PUNCT
ejpam-4612	82	28	≤	≤	NUM
ejpam-4612	82	29	(	(	PUNCT
ejpam-4612	82	30	∑	∑	ADV
ejpam-4612	82	31	k∈sm	k∈sm	PROPN
ejpam-4612	82	32	,	,	PUNCT
ejpam-4612	82	33	n	n	CCONJ
ejpam-4612	82	34	|λk|p	|λk|p	PROPN
ejpam-4612	82	35	)	)	PUNCT
ejpam-4612	82	36	2	2	NUM
ejpam-4612	82	37	p	p	NOUN
ejpam-4612	82	38	(	(	PUNCT
ejpam-4612	82	39	∑	∑	PUNCT
ejpam-4612	82	40	k∈sm	k∈sm	PROPN
ejpam-4612	82	41	,	,	PUNCT
ejpam-4612	82	42	n	n	PRON
ejpam-4612	82	43	1	1	NUM
ejpam-4612	82	44	)	)	PUNCT
ejpam-4612	82	45	1−	1−	NUM
ejpam-4612	82	46	2	2	NUM
ejpam-4612	82	47	p	p	NOUN
ejpam-4612	82	48	=	=	NOUN
ejpam-4612	82	49	|sm	|sm	NUM
ejpam-4612	82	50	,	,	PUNCT
ejpam-4612	82	51	n	n	X
ejpam-4612	82	52	|1−	|1−	VERB
ejpam-4612	82	53	2	2	NUM
ejpam-4612	82	54	p	p	NOUN
ejpam-4612	82	55	(	(	PUNCT
ejpam-4612	82	56	∑	∑	PUNCT
ejpam-4612	82	57	k∈sm	k∈sm	PROPN
ejpam-4612	82	58	,	,	PUNCT
ejpam-4612	82	59	n	n	CCONJ
ejpam-4612	82	60	|λk|p	|λk|p	PUNCT
ejpam-4612	82	61	)	)	PUNCT
ejpam-4612	82	62	2	2	NUM
ejpam-4612	82	63	p	p	NOUN
ejpam-4612	82	64	=	=	SYM
ejpam-4612	82	65	∣∣sm	∣∣sm	PROPN
ejpam-4612	82	66	,	,	PUNCT
ejpam-4612	82	67	n	n	X
ejpam-4612	82	68	∣∣	∣∣	X
ejpam-4612	82	69	(	(	PUNCT
ejpam-4612	82	70	1∣∣sm	1∣∣sm	NUM
ejpam-4612	82	71	,	,	PUNCT
ejpam-4612	82	72	n	n	X
ejpam-4612	82	73	∣∣	∣∣	NUM
ejpam-4612	82	74	∑	∑	ADV
ejpam-4612	82	75	k∈sm	k∈sm	PROPN
ejpam-4612	82	76	,	,	PUNCT
ejpam-4612	82	77	n	n	CCONJ
ejpam-4612	82	78	|λk|p	|λk|p	PROPN
ejpam-4612	82	79	)	)	PUNCT
ejpam-4612	82	80	2	2	NUM
ejpam-4612	82	81	p	p	NOUN
ejpam-4612	82	82	.	.	PUNCT
ejpam-4612	83	1	thus	thus	ADV
ejpam-4612	83	2	1∣∣sm	1∣∣sm	NUM
ejpam-4612	83	3	,	,	PUNCT
ejpam-4612	83	4	n	n	X
ejpam-4612	83	5	∣∣	∣∣	NUM
ejpam-4612	83	6	∑	∑	ADV
ejpam-4612	83	7	k∈sm	k∈sm	PROPN
ejpam-4612	83	8	,	,	PUNCT
ejpam-4612	83	9	n	n	NOUN
ejpam-4612	83	10	|λk|2	|λk|2	PUNCT
ejpam-4612	83	11	≤	≤	NUM
ejpam-4612	83	12	(	(	PUNCT
ejpam-4612	83	13	1∣∣sm	1∣∣sm	NUM
ejpam-4612	83	14	,	,	PUNCT
ejpam-4612	83	15	n	n	X
ejpam-4612	83	16	∣∣	∣∣	NUM
ejpam-4612	83	17	∑	∑	ADV
ejpam-4612	83	18	k∈sm	k∈sm	PROPN
ejpam-4612	83	19	,	,	PUNCT
ejpam-4612	83	20	n	n	CCONJ
ejpam-4612	83	21	|λk|p	|λk|p	PROPN
ejpam-4612	83	22	)	)	PUNCT
ejpam-4612	83	23	2	2	NUM
ejpam-4612	83	24	p	p	NOUN
ejpam-4612	83	25	.	.	PUNCT
ejpam-4612	84	1	so	so	ADV
ejpam-4612	84	2	,	,	PUNCT
ejpam-4612	84	3	taking	take	VERB
ejpam-4612	84	4	the	the	DET
ejpam-4612	84	5	square	square	ADJ
ejpam-4612	84	6	roots	root	NOUN
ejpam-4612	84	7	of	of	ADP
ejpam-4612	84	8	both	both	DET
ejpam-4612	84	9	sides	side	NOUN
ejpam-4612	84	10	,	,	PUNCT
ejpam-4612	84	11	we	we	PRON
ejpam-4612	84	12	get	get	VERB
ejpam-4612	84	13	(	(	PUNCT
ejpam-4612	84	14	1∣∣sm	1∣∣sm	NUM
ejpam-4612	84	15	,	,	PUNCT
ejpam-4612	84	16	n	n	X
ejpam-4612	84	17	∣∣	∣∣	NUM
ejpam-4612	84	18	∑	∑	ADV
ejpam-4612	84	19	k∈sm	k∈sm	PROPN
ejpam-4612	84	20	,	,	PUNCT
ejpam-4612	84	21	n	n	NOUN
ejpam-4612	84	22	|λk|2	|λk|2	PUNCT
ejpam-4612	84	23	)	)	PUNCT
ejpam-4612	84	24	1	1	NUM
ejpam-4612	84	25	2	2	NUM
ejpam-4612	84	26	≤	≤	NOUN
ejpam-4612	84	27	(	(	PUNCT
ejpam-4612	84	28	1∣∣sm	1∣∣sm	NUM
ejpam-4612	84	29	,	,	PUNCT
ejpam-4612	84	30	n	n	X
ejpam-4612	84	31	∣∣	∣∣	NUM
ejpam-4612	84	32	∑	∑	ADV
ejpam-4612	84	33	k∈sm	k∈sm	PROPN
ejpam-4612	84	34	,	,	PUNCT
ejpam-4612	84	35	n	n	CCONJ
ejpam-4612	84	36	|λk|p	|λk|p	PUNCT
ejpam-4612	84	37	)	)	PUNCT
ejpam-4612	84	38	1	1	NUM
ejpam-4612	84	39	p	p	NOUN
ejpam-4612	84	40	or	or	CCONJ
ejpam-4612	84	41	∣∣sm	∣∣sm	PROPN
ejpam-4612	84	42	,	,	PUNCT
ejpam-4612	84	43	n	n	PRON
ejpam-4612	84	44	∣∣−	∣∣−	VERB
ejpam-4612	84	45	1	1	NUM
ejpam-4612	84	46	2	2	NUM
ejpam-4612	84	47	(	(	PUNCT
ejpam-4612	84	48	∑	∑	ADV
ejpam-4612	84	49	k∈sm	k∈sm	NOUN
ejpam-4612	84	50	,	,	PUNCT
ejpam-4612	84	51	n	n	NOUN
ejpam-4612	84	52	|λk|2	|λk|2	PUNCT
ejpam-4612	84	53	)	)	PUNCT
ejpam-4612	84	54	1	1	NUM
ejpam-4612	84	55	2	2	NUM
ejpam-4612	84	56	≤	≤	NUM
ejpam-4612	84	57	∣∣sm	∣∣sm	PROPN
ejpam-4612	84	58	,	,	PUNCT
ejpam-4612	84	59	n	n	PRON
ejpam-4612	84	60	∣∣−	∣∣−	VERB
ejpam-4612	84	61	1	1	NUM
ejpam-4612	84	62	p	p	NOUN
ejpam-4612	84	63	(	(	PUNCT
ejpam-4612	84	64	∑	∑	PUNCT
ejpam-4612	84	65	k∈sm	k∈sm	PROPN
ejpam-4612	84	66	,	,	PUNCT
ejpam-4612	84	67	n	n	CCONJ
ejpam-4612	84	68	|λk|p	|λk|p	PROPN
ejpam-4612	84	69	)	)	PUNCT
ejpam-4612	84	70	1	1	NUM
ejpam-4612	84	71	p	p	NOUN
ejpam-4612	84	72	.	.	PUNCT
ejpam-4612	85	1	then	then	ADV
ejpam-4612	85	2	sup	sup	PROPN
ejpam-4612	85	3	m∈z	m∈z	NOUN
ejpam-4612	85	4	,	,	PUNCT
ejpam-4612	85	5	n∈ω	n∈ω	ADP
ejpam-4612	85	6	∣∣sm	∣∣sm	PROPN
ejpam-4612	85	7	,	,	PUNCT
ejpam-4612	85	8	n	n	NUM
ejpam-4612	85	9	∣∣	∣∣	NUM
ejpam-4612	85	10	1	1	NUM
ejpam-4612	85	11	u	u	NOUN
ejpam-4612	85	12	−	−	PROPN
ejpam-4612	85	13	1	1	NUM
ejpam-4612	85	14	2	2	NUM
ejpam-4612	85	15	(	(	PUNCT
ejpam-4612	85	16	∑	∑	ADV
ejpam-4612	85	17	k∈sm	k∈sm	NOUN
ejpam-4612	85	18	,	,	PUNCT
ejpam-4612	85	19	n	n	NOUN
ejpam-4612	85	20	|λk|2	|λk|2	PUNCT
ejpam-4612	85	21	)	)	PUNCT
ejpam-4612	85	22	1	1	NUM
ejpam-4612	85	23	2	2	NUM
ejpam-4612	85	24	≤	≤	NUM
ejpam-4612	85	25	sup	sup	NOUN
ejpam-4612	85	26	m∈z	m∈z	NOUN
ejpam-4612	85	27	,	,	PUNCT
ejpam-4612	85	28	n∈ω	n∈ω	ADP
ejpam-4612	85	29	∣∣sm	∣∣sm	PROPN
ejpam-4612	85	30	,	,	PUNCT
ejpam-4612	85	31	n	n	NUM
ejpam-4612	85	32	∣∣	∣∣	NUM
ejpam-4612	85	33	1	1	NUM
ejpam-4612	85	34	u	u	NOUN
ejpam-4612	85	35	−	−	PROPN
ejpam-4612	85	36	1	1	NUM
ejpam-4612	85	37	p	p	NOUN
ejpam-4612	85	38	(	(	PUNCT
ejpam-4612	85	39	∑	∑	PUNCT
ejpam-4612	85	40	k∈sm	k∈sm	PROPN
ejpam-4612	85	41	,	,	PUNCT
ejpam-4612	85	42	n	n	CCONJ
ejpam-4612	85	43	|λk|p	|λk|p	PROPN
ejpam-4612	85	44	)	)	PUNCT
ejpam-4612	85	45	1	1	NUM
ejpam-4612	85	46	p	p	NOUN
ejpam-4612	85	47	.	.	PUNCT
ejpam-4612	86	1	m.	m.	NOUN
ejpam-4612	86	2	jakfar	jakfar	PROPN
ejpam-4612	86	3	et	et	PROPN
ejpam-4612	86	4	al	al	PROPN
ejpam-4612	86	5	.	.	PUNCT
ejpam-4612	86	6	/	/	SYM
ejpam-4612	86	7	eur	eur	PROPN
ejpam-4612	86	8	.	.	PUNCT
ejpam-4612	87	1	j.	j.	PROPN
ejpam-4612	87	2	pure	pure	PROPN
ejpam-4612	87	3	appl	appl	PROPN
ejpam-4612	87	4	.	.	PROPN
ejpam-4612	87	5	math	math	PROPN
ejpam-4612	87	6	,	,	PUNCT
ejpam-4612	87	7	16	16	NUM
ejpam-4612	87	8	(	(	PUNCT
ejpam-4612	87	9	1	1	NUM
ejpam-4612	87	10	)	)	PUNCT
ejpam-4612	87	11	(	(	PUNCT
ejpam-4612	87	12	2023	2023	NUM
ejpam-4612	87	13	)	)	PUNCT
ejpam-4612	87	14	,	,	PUNCT
ejpam-4612	87	15	144	144	NUM
ejpam-4612	87	16	-	-	SYM
ejpam-4612	87	17	155	155	NUM
ejpam-4612	87	18	148	148	NUM
ejpam-4612	88	1	so	so	ADV
ejpam-4612	88	2	,	,	PUNCT
ejpam-4612	88	3	we	we	PRON
ejpam-4612	88	4	have	have	VERB
ejpam-4612	88	5	∥λ∥mu,2	∥λ∥mu,2	NOUN
ejpam-4612	88	6	≤	≤	NUM
ejpam-4612	88	7	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	88	8	,	,	PUNCT
ejpam-4612	88	9	p	p	NOUN
ejpam-4612	88	10	which	which	PRON
ejpam-4612	88	11	means	mean	VERB
ejpam-4612	88	12	that	that	SCONJ
ejpam-4612	88	13	λ	λ	NOUN
ejpam-4612	88	14	is	be	AUX
ejpam-4612	88	15	in	in	ADP
ejpam-4612	88	16	mu,2	mu,2	PROPN
ejpam-4612	88	17	.	.	PUNCT
ejpam-4612	89	1	thus	thus	ADV
ejpam-4612	89	2	,	,	PUNCT
ejpam-4612	89	3	we	we	PRON
ejpam-4612	89	4	realize	realize	VERB
ejpam-4612	89	5	that	that	SCONJ
ejpam-4612	89	6	mu	mu	NOUN
ejpam-4612	89	7	,	,	PUNCT
ejpam-4612	89	8	p	p	PROPN
ejpam-4612	89	9	can	can	AUX
ejpam-4612	89	10	actually	actually	ADV
ejpam-4612	89	11	be	be	AUX
ejpam-4612	89	12	considered	consider	VERB
ejpam-4612	89	13	as	as	ADP
ejpam-4612	89	14	a	a	DET
ejpam-4612	89	15	subspace	subspace	NOUN
ejpam-4612	89	16	of	of	ADP
ejpam-4612	89	17	mu,2	mu,2	PROPN
ejpam-4612	89	18	,	,	PUNCT
ejpam-4612	89	19	equipped	equip	VERB
ejpam-4612	89	20	with	with	ADP
ejpam-4612	89	21	the	the	DET
ejpam-4612	89	22	inner	inner	ADJ
ejpam-4612	89	23	product	product	NOUN
ejpam-4612	89	24	⟨λ	⟨λ	NUM
ejpam-4612	89	25	,	,	PUNCT
ejpam-4612	89	26	µ⟩mu,2	µ⟩mu,2	PUNCT
ejpam-4612	89	27	:	:	PUNCT
ejpam-4612	89	28	=	=	NUM
ejpam-4612	89	29	sup	sup	NUM
ejpam-4612	89	30	m∈z	m∈z	NOUN
ejpam-4612	89	31	,	,	PUNCT
ejpam-4612	89	32	n∈ω	n∈ω	NOUN
ejpam-4612	89	33	|sm	|sm	NUM
ejpam-4612	89	34	,	,	PUNCT
ejpam-4612	89	35	n	n	X
ejpam-4612	89	36	|2	|2	NUM
ejpam-4612	89	37	(	(	PUNCT
ejpam-4612	89	38	1	1	NUM
ejpam-4612	89	39	u	u	NOUN
ejpam-4612	89	40	−	−	PROPN
ejpam-4612	89	41	1	1	NUM
ejpam-4612	89	42	2	2	NUM
ejpam-4612	89	43	)	)	PUNCT
ejpam-4612	89	44	(	(	PUNCT
ejpam-4612	89	45	∑	∑	ADV
ejpam-4612	89	46	k∈sm	k∈sm	PROPN
ejpam-4612	89	47	,	,	PUNCT
ejpam-4612	89	48	n	n	NOUN
ejpam-4612	89	49	λkµk	λkµk	NOUN
ejpam-4612	89	50	)	)	PUNCT
ejpam-4612	89	51	and	and	CCONJ
ejpam-4612	89	52	the	the	DET
ejpam-4612	89	53	norm	norm	NOUN
ejpam-4612	89	54	∥λ∥mu,2	∥λ∥mu,2	NOUN
ejpam-4612	89	55	:	:	PUNCT
ejpam-4612	89	56	=	=	NUM
ejpam-4612	89	57	sup	sup	NUM
ejpam-4612	89	58	m∈z	m∈z	NOUN
ejpam-4612	89	59	,	,	PUNCT
ejpam-4612	89	60	n∈ω	n∈ω	NOUN
ejpam-4612	89	61	|sm	|sm	ADV
ejpam-4612	89	62	,	,	PUNCT
ejpam-4612	89	63	n	n	CCONJ
ejpam-4612	89	64	|	|	ADV
ejpam-4612	89	65	1	1	NUM
ejpam-4612	89	66	u	u	NOUN
ejpam-4612	89	67	−	−	PROPN
ejpam-4612	89	68	1	1	NUM
ejpam-4612	89	69	2	2	NUM
ejpam-4612	89	70	(	(	PUNCT
ejpam-4612	89	71	∑	∑	ADV
ejpam-4612	89	72	k∈sm	k∈sm	NOUN
ejpam-4612	89	73	,	,	PUNCT
ejpam-4612	89	74	n	n	NOUN
ejpam-4612	89	75	|λk|2	|λk|2	PUNCT
ejpam-4612	89	76	)	)	PUNCT
ejpam-4612	89	77	1	1	NUM
ejpam-4612	89	78	2	2	NUM
ejpam-4612	89	79	for	for	ADP
ejpam-4612	89	80	every	every	DET
ejpam-4612	89	81	λ	λ	PROPN
ejpam-4612	89	82	,	,	PUNCT
ejpam-4612	89	83	µ	µ	PROPN
ejpam-4612	89	84	∈	∈	NOUN
ejpam-4612	89	85	mu	mu	NOUN
ejpam-4612	89	86	,	,	PUNCT
ejpam-4612	89	87	p.	p.	NOUN
ejpam-4612	89	88	a	a	DET
ejpam-4612	89	89	more	more	ADV
ejpam-4612	89	90	general	general	ADJ
ejpam-4612	89	91	result	result	NOUN
ejpam-4612	89	92	is	be	AUX
ejpam-4612	89	93	formulated	formulate	VERB
ejpam-4612	89	94	in	in	ADP
ejpam-4612	89	95	the	the	DET
ejpam-4612	89	96	following	follow	VERB
ejpam-4612	89	97	proposition	proposition	NOUN
ejpam-4612	89	98	.	.	PUNCT
ejpam-4612	90	1	proposition	proposition	NOUN
ejpam-4612	90	2	2	2	NUM
ejpam-4612	90	3	.	.	PUNCT
ejpam-4612	90	4	for	for	ADP
ejpam-4612	90	5	1	1	NUM
ejpam-4612	90	6	≤	≤	NUM
ejpam-4612	90	7	q	q	PROPN
ejpam-4612	90	8	≤	≤	PROPN
ejpam-4612	90	9	p	p	NOUN
ejpam-4612	90	10	≤	≤	NUM
ejpam-4612	90	11	u	u	NOUN
ejpam-4612	90	12	<	<	X
ejpam-4612	90	13	∞	∞	PROPN
ejpam-4612	91	1	then	then	ADV
ejpam-4612	91	2	mu	mu	PROPN
ejpam-4612	91	3	,	,	PUNCT
ejpam-4612	91	4	p	p	PROPN
ejpam-4612	91	5	⊂	⊂	PROPN
ejpam-4612	91	6	mu	mu	PROPN
ejpam-4612	91	7	,	,	PUNCT
ejpam-4612	91	8	q	q	NOUN
ejpam-4612	91	9	and	and	CCONJ
ejpam-4612	91	10	∥λ∥mu	∥λ∥mu	PROPN
ejpam-4612	91	11	,	,	PUNCT
ejpam-4612	91	12	q	q	PROPN
ejpam-4612	91	13	≤	≤	NUM
ejpam-4612	91	14	∥λ∥mu	∥λ∥mu	ADP
ejpam-4612	91	15	,	,	PUNCT
ejpam-4612	91	16	p	p	NOUN
ejpam-4612	91	17	for	for	ADP
ejpam-4612	91	18	every	every	DET
ejpam-4612	91	19	λ	λ	PROPN
ejpam-4612	91	20	∈	∈	PROPN
ejpam-4612	91	21	mu	mu	NOUN
ejpam-4612	91	22	,	,	PUNCT
ejpam-4612	91	23	p.	p.	NOUN
ejpam-4612	91	24	proof	proof	NOUN
ejpam-4612	91	25	.	.	PUNCT
ejpam-4612	92	1	let	let	VERB
ejpam-4612	92	2	1	1	NUM
ejpam-4612	92	3	≤	≤	NOUN
ejpam-4612	92	4	q	q	ADJ
ejpam-4612	92	5	≤	≤	NUM
ejpam-4612	92	6	p	p	NOUN
ejpam-4612	92	7	≤	≤	NUM
ejpam-4612	92	8	u	u	NOUN
ejpam-4612	92	9	<	<	X
ejpam-4612	92	10	∞.	∞.	PROPN
ejpam-4612	92	11	for	for	ADP
ejpam-4612	92	12	every	every	DET
ejpam-4612	92	13	λ	λ	PROPN
ejpam-4612	92	14	=	=	PRON
ejpam-4612	92	15	(	(	PUNCT
ejpam-4612	92	16	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	92	17	∈	∈	PROPN
ejpam-4612	92	18	mu	mu	NOUN
ejpam-4612	92	19	,	,	PUNCT
ejpam-4612	92	20	p	p	PRON
ejpam-4612	92	21	,	,	PUNCT
ejpam-4612	92	22	we	we	PRON
ejpam-4612	92	23	have	have	VERB
ejpam-4612	92	24	∑	∑	ADV
ejpam-4612	92	25	k∈sm	k∈sm	PROPN
ejpam-4612	92	26	,	,	PUNCT
ejpam-4612	92	27	n	n	CCONJ
ejpam-4612	92	28	|λk|q	|λk|q	PROPN
ejpam-4612	92	29	≤	≤	X
ejpam-4612	92	30	(	(	PUNCT
ejpam-4612	92	31	∑	∑	ADV
ejpam-4612	92	32	k∈sm	k∈sm	PROPN
ejpam-4612	92	33	,	,	PUNCT
ejpam-4612	92	34	n	n	CCONJ
ejpam-4612	92	35	|λk|p	|λk|p	PUNCT
ejpam-4612	92	36	)	)	PUNCT
ejpam-4612	93	1	q	q	NOUN
ejpam-4612	93	2	p	p	X
ejpam-4612	93	3	(	(	PUNCT
ejpam-4612	93	4	∑	∑	ADV
ejpam-4612	93	5	k∈sm	k∈sm	PROPN
ejpam-4612	93	6	,	,	PUNCT
ejpam-4612	93	7	n	n	PRON
ejpam-4612	93	8	1	1	NUM
ejpam-4612	93	9	)	)	PUNCT
ejpam-4612	93	10	1−	1−	NUM
ejpam-4612	93	11	q	q	NOUN
ejpam-4612	94	1	p	p	X
ejpam-4612	94	2	=	=	NOUN
ejpam-4612	94	3	|sm	|sm	NUM
ejpam-4612	94	4	,	,	PUNCT
ejpam-4612	94	5	n	n	X
ejpam-4612	94	6	|1−	|1−	VERB
ejpam-4612	94	7	q	q	PROPN
ejpam-4612	94	8	p	p	X
ejpam-4612	94	9	(	(	PUNCT
ejpam-4612	94	10	∑	∑	ADV
ejpam-4612	94	11	k∈sm	k∈sm	PROPN
ejpam-4612	94	12	,	,	PUNCT
ejpam-4612	94	13	n	n	CCONJ
ejpam-4612	94	14	|λk|p	|λk|p	PUNCT
ejpam-4612	94	15	)	)	PUNCT
ejpam-4612	94	16	q	q	X
ejpam-4612	95	1	p	p	X
ejpam-4612	95	2	=	=	PROPN
ejpam-4612	95	3	∣∣sm	∣∣sm	PROPN
ejpam-4612	95	4	,	,	PUNCT
ejpam-4612	95	5	n	n	X
ejpam-4612	95	6	∣∣	∣∣	X
ejpam-4612	95	7	(	(	PUNCT
ejpam-4612	95	8	1∣∣sm	1∣∣sm	NUM
ejpam-4612	95	9	,	,	PUNCT
ejpam-4612	95	10	n	n	X
ejpam-4612	95	11	∣∣	∣∣	NUM
ejpam-4612	95	12	∑	∑	ADV
ejpam-4612	95	13	k∈sm	k∈sm	PROPN
ejpam-4612	95	14	,	,	PUNCT
ejpam-4612	95	15	n	n	CCONJ
ejpam-4612	95	16	|λk|p	|λk|p	PUNCT
ejpam-4612	95	17	)	)	PUNCT
ejpam-4612	96	1	q	q	PROPN
ejpam-4612	96	2	p	p	NOUN
ejpam-4612	96	3	.	.	PUNCT
ejpam-4612	97	1	taking	take	VERB
ejpam-4612	97	2	the	the	DET
ejpam-4612	97	3	q	q	NOUN
ejpam-4612	97	4	-	-	PUNCT
ejpam-4612	97	5	roots	root	NOUN
ejpam-4612	97	6	of	of	ADP
ejpam-4612	97	7	both	both	DET
ejpam-4612	97	8	sides	side	NOUN
ejpam-4612	97	9	,	,	PUNCT
ejpam-4612	97	10	multiplying	multiply	VERB
ejpam-4612	97	11	by	by	ADP
ejpam-4612	97	12	|sm	|sm	PROPN
ejpam-4612	97	13	,	,	PUNCT
ejpam-4612	97	14	n	n	CCONJ
ejpam-4612	97	15	|	|	ADV
ejpam-4612	97	16	1	1	NUM
ejpam-4612	97	17	u	u	NOUN
ejpam-4612	97	18	of	of	ADP
ejpam-4612	97	19	both	both	DET
ejpam-4612	97	20	sides	side	NOUN
ejpam-4612	97	21	,	,	PUNCT
ejpam-4612	97	22	and	and	CCONJ
ejpam-4612	97	23	taking	take	VERB
ejpam-4612	97	24	supremum	supremum	ADV
ejpam-4612	97	25	of	of	ADP
ejpam-4612	97	26	both	both	DET
ejpam-4612	97	27	sides	side	NOUN
ejpam-4612	97	28	we	we	PRON
ejpam-4612	97	29	get	get	VERB
ejpam-4612	97	30	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	97	31	,	,	PUNCT
ejpam-4612	97	32	q	q	PROPN
ejpam-4612	97	33	≤	≤	NUM
ejpam-4612	97	34	∥λ∥mu	∥λ∥mu	ADP
ejpam-4612	97	35	,	,	PUNCT
ejpam-4612	97	36	p	p	X
ejpam-4612	97	37	,	,	PUNCT
ejpam-4612	97	38	which	which	PRON
ejpam-4612	97	39	tell	tell	VERB
ejpam-4612	97	40	us	we	PRON
ejpam-4612	97	41	mu	mu	NOUN
ejpam-4612	97	42	,	,	PUNCT
ejpam-4612	97	43	p	p	PROPN
ejpam-4612	97	44	⊂	⊂	PROPN
ejpam-4612	97	45	mu	mu	PROPN
ejpam-4612	97	46	,	,	PUNCT
ejpam-4612	97	47	q.	q.	PROPN
ejpam-4612	97	48	■	■	PUNCT
ejpam-4612	97	49	corollary	corollary	ADJ
ejpam-4612	97	50	1	1	NUM
ejpam-4612	97	51	.	.	PUNCT
ejpam-4612	98	1	for	for	ADP
ejpam-4612	98	2	2	2	NUM
ejpam-4612	98	3	≤	≤	NOUN
ejpam-4612	98	4	p	p	NOUN
ejpam-4612	98	5	≤	≤	NUM
ejpam-4612	98	6	u	u	NOUN
ejpam-4612	98	7	<	<	X
ejpam-4612	98	8	∞	∞	PROPN
ejpam-4612	98	9	then	then	ADV
ejpam-4612	98	10	mu	mu	PROPN
ejpam-4612	98	11	,	,	PUNCT
ejpam-4612	98	12	p	p	PROPN
ejpam-4612	98	13	⊂	⊂	PROPN
ejpam-4612	98	14	mu,2	mu,2	PROPN
ejpam-4612	98	15	and	and	CCONJ
ejpam-4612	98	16	∥λ∥mu,2	∥λ∥mu,2	PRON
ejpam-4612	98	17	≤	≤	NUM
ejpam-4612	98	18	∥λ∥mu	∥λ∥mu	ADP
ejpam-4612	98	19	,	,	PUNCT
ejpam-4612	98	20	p	p	NOUN
ejpam-4612	98	21	for	for	ADP
ejpam-4612	98	22	every	every	DET
ejpam-4612	98	23	λ	λ	PROPN
ejpam-4612	98	24	∈	∈	PROPN
ejpam-4612	98	25	mu	mu	NOUN
ejpam-4612	98	26	,	,	PUNCT
ejpam-4612	98	27	p.	p.	NOUN
ejpam-4612	98	28	proof	proof	NOUN
ejpam-4612	98	29	.	.	PUNCT
ejpam-4612	99	1	applying	apply	VERB
ejpam-4612	99	2	proposition	proposition	NOUN
ejpam-4612	99	3	2	2	NUM
ejpam-4612	99	4	,	,	PUNCT
ejpam-4612	99	5	take	take	VERB
ejpam-4612	99	6	q	q	NOUN
ejpam-4612	99	7	=	=	NUM
ejpam-4612	99	8	2	2	NUM
ejpam-4612	99	9	,	,	PUNCT
ejpam-4612	99	10	then	then	ADV
ejpam-4612	99	11	the	the	DET
ejpam-4612	99	12	corollary	corollary	NOUN
ejpam-4612	99	13	is	be	AUX
ejpam-4612	99	14	proved	prove	VERB
ejpam-4612	99	15	.	.	PUNCT
ejpam-4612	100	1	■	■	PUNCT
ejpam-4612	100	2	remark	remark	NOUN
ejpam-4612	100	3	2	2	NUM
ejpam-4612	100	4	.	.	PUNCT
ejpam-4612	101	1	for	for	ADP
ejpam-4612	101	2	2	2	NUM
ejpam-4612	101	3	<	<	X
ejpam-4612	101	4	p	p	X
ejpam-4612	101	5	≤	≤	NUM
ejpam-4612	101	6	u	u	NOUN
ejpam-4612	101	7	<	<	X
ejpam-4612	101	8	∞	∞	PROPN
ejpam-4612	101	9	,	,	PUNCT
ejpam-4612	101	10	the	the	DET
ejpam-4612	101	11	space	space	NOUN
ejpam-4612	101	12	(	(	PUNCT
ejpam-4612	101	13	mu	mu	NOUN
ejpam-4612	101	14	,	,	PUNCT
ejpam-4612	101	15	p	p	X
ejpam-4612	101	16	,	,	PUNCT
ejpam-4612	101	17	∥	∥	PROPN
ejpam-4612	101	18	·	·	PUNCT
ejpam-4612	101	19	∥mu,2	∥mu,2	NOUN
ejpam-4612	101	20	)	)	PUNCT
ejpam-4612	101	21	is	be	AUX
ejpam-4612	101	22	an	an	DET
ejpam-4612	101	23	inner	inner	ADJ
ejpam-4612	101	24	product	product	NOUN
ejpam-4612	101	25	space	space	NOUN
ejpam-4612	101	26	.	.	PUNCT
ejpam-4612	102	1	for	for	ADP
ejpam-4612	102	2	2	2	NUM
ejpam-4612	102	3	<	<	X
ejpam-4612	102	4	p	p	X
ejpam-4612	102	5	<	<	X
ejpam-4612	102	6	∞	∞	PROPN
ejpam-4612	102	7	,	,	PUNCT
ejpam-4612	102	8	we	we	PRON
ejpam-4612	102	9	finish	finish	VERB
ejpam-4612	102	10	to	to	PART
ejpam-4612	102	11	define	define	VERB
ejpam-4612	102	12	an	an	DET
ejpam-4612	102	13	inner	inner	ADJ
ejpam-4612	102	14	product	product	NOUN
ejpam-4612	102	15	on	on	ADP
ejpam-4612	102	16	mu	mu	PROPN
ejpam-4612	102	17	,	,	PUNCT
ejpam-4612	102	18	p	p	X
ejpam-4612	102	19	,	,	PUNCT
ejpam-4612	102	20	in	in	ADP
ejpam-4612	102	21	the	the	DET
ejpam-4612	102	22	next	next	ADJ
ejpam-4612	102	23	section	section	NOUN
ejpam-4612	102	24	,	,	PUNCT
ejpam-4612	102	25	we	we	PRON
ejpam-4612	102	26	will	will	AUX
ejpam-4612	102	27	try	try	VERB
ejpam-4612	102	28	to	to	PART
ejpam-4612	102	29	define	define	VERB
ejpam-4612	102	30	an	an	DET
ejpam-4612	102	31	inner	inner	ADJ
ejpam-4612	102	32	product	product	NOUN
ejpam-4612	102	33	on	on	ADP
ejpam-4612	102	34	mu	mu	PROPN
ejpam-4612	102	35	,	,	PUNCT
ejpam-4612	102	36	p	p	NOUN
ejpam-4612	102	37	for	for	ADP
ejpam-4612	102	38	1	1	NUM
ejpam-4612	102	39	≤	≤	NOUN
ejpam-4612	103	1	p	p	NOUN
ejpam-4612	103	2	<	<	X
ejpam-4612	103	3	2	2	NUM
ejpam-4612	103	4	.	.	PUNCT
ejpam-4612	103	5	m.	m.	NOUN
ejpam-4612	103	6	jakfar	jakfar	PROPN
ejpam-4612	103	7	et	et	PROPN
ejpam-4612	103	8	al	al	PROPN
ejpam-4612	103	9	.	.	PUNCT
ejpam-4612	103	10	/	/	SYM
ejpam-4612	103	11	eur	eur	PROPN
ejpam-4612	103	12	.	.	PUNCT
ejpam-4612	104	1	j.	j.	PROPN
ejpam-4612	104	2	pure	pure	PROPN
ejpam-4612	104	3	appl	appl	PROPN
ejpam-4612	104	4	.	.	PROPN
ejpam-4612	104	5	math	math	PROPN
ejpam-4612	104	6	,	,	PUNCT
ejpam-4612	104	7	16	16	NUM
ejpam-4612	104	8	(	(	PUNCT
ejpam-4612	104	9	1	1	NUM
ejpam-4612	104	10	)	)	PUNCT
ejpam-4612	104	11	(	(	PUNCT
ejpam-4612	104	12	2023	2023	NUM
ejpam-4612	104	13	)	)	PUNCT
ejpam-4612	104	14	,	,	PUNCT
ejpam-4612	104	15	144	144	NUM
ejpam-4612	104	16	-	-	SYM
ejpam-4612	104	17	155	155	NUM
ejpam-4612	104	18	149	149	NUM
ejpam-4612	104	19	2.3	2.3	NUM
ejpam-4612	104	20	.	.	PUNCT
ejpam-4612	105	1	inner	inner	ADJ
ejpam-4612	105	2	product	product	NOUN
ejpam-4612	105	3	on	on	ADP
ejpam-4612	105	4	mu	mu	PROPN
ejpam-4612	105	5	,	,	PUNCT
ejpam-4612	105	6	p	p	NOUN
ejpam-4612	105	7	for	for	ADP
ejpam-4612	105	8	1	1	NUM
ejpam-4612	105	9	≤	≤	NOUN
ejpam-4612	105	10	p	p	NOUN
ejpam-4612	105	11	<	<	X
ejpam-4612	105	12	2	2	NUM
ejpam-4612	105	13	in	in	ADP
ejpam-4612	105	14	this	this	DET
ejpam-4612	105	15	section	section	NOUN
ejpam-4612	105	16	,	,	PUNCT
ejpam-4612	105	17	we	we	PRON
ejpam-4612	105	18	let	let	VERB
ejpam-4612	105	19	1	1	NUM
ejpam-4612	105	20	≤	≤	NOUN
ejpam-4612	106	1	p	p	X
ejpam-4612	106	2	<	<	X
ejpam-4612	106	3	2	2	NUM
ejpam-4612	106	4	.	.	PUNCT
ejpam-4612	106	5	first	first	ADV
ejpam-4612	106	6	for	for	ADP
ejpam-4612	106	7	all	all	PRON
ejpam-4612	106	8	,	,	PUNCT
ejpam-4612	106	9	we	we	PRON
ejpam-4612	106	10	begin	begin	VERB
ejpam-4612	106	11	to	to	PART
ejpam-4612	106	12	discuss	discuss	VERB
ejpam-4612	106	13	the	the	DET
ejpam-4612	106	14	following	follow	VERB
ejpam-4612	106	15	proposition	proposition	NOUN
ejpam-4612	106	16	.	.	PUNCT
ejpam-4612	107	1	proposition	proposition	NOUN
ejpam-4612	107	2	3	3	NUM
ejpam-4612	107	3	.	.	PUNCT
ejpam-4612	108	1	for	for	ADP
ejpam-4612	108	2	1	1	NUM
ejpam-4612	108	3	≤	≤	NOUN
ejpam-4612	108	4	p	p	PROPN
ejpam-4612	108	5	≤	≤	NUM
ejpam-4612	108	6	u	u	NOUN
ejpam-4612	108	7	<	<	X
ejpam-4612	108	8	2	2	NUM
ejpam-4612	108	9	and	and	CCONJ
ejpam-4612	108	10	v	v	NOUN
ejpam-4612	108	11	=	=	SYM
ejpam-4612	108	12	2up	2up	ADJ
ejpam-4612	108	13	2p−2u+up	2p−2u+up	PROPN
ejpam-4612	108	14	,	,	PUNCT
ejpam-4612	108	15	then	then	ADV
ejpam-4612	108	16	mu	mu	PROPN
ejpam-4612	108	17	,	,	PUNCT
ejpam-4612	108	18	p	p	PROPN
ejpam-4612	108	19	⊂	⊂	PROPN
ejpam-4612	108	20	mv,2	mv,2	PROPN
ejpam-4612	108	21	and	and	CCONJ
ejpam-4612	108	22	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	108	23	≤	≤	NUM
ejpam-4612	108	24	∥λ∥mu	∥λ∥mu	ADP
ejpam-4612	108	25	,	,	PUNCT
ejpam-4612	108	26	p	p	NOUN
ejpam-4612	108	27	for	for	ADP
ejpam-4612	108	28	every	every	DET
ejpam-4612	108	29	λ	λ	PROPN
ejpam-4612	108	30	∈	∈	PROPN
ejpam-4612	108	31	mu	mu	NOUN
ejpam-4612	108	32	,	,	PUNCT
ejpam-4612	108	33	p.	p.	NOUN
ejpam-4612	108	34	proof	proof	NOUN
ejpam-4612	108	35	.	.	PUNCT
ejpam-4612	109	1	let	let	VERB
ejpam-4612	109	2	λ	λ	X
ejpam-4612	109	3	=	=	PRON
ejpam-4612	109	4	(	(	PUNCT
ejpam-4612	109	5	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	109	6	∈	∈	PROPN
ejpam-4612	109	7	mu	mu	NOUN
ejpam-4612	109	8	,	,	PUNCT
ejpam-4612	109	9	p.	p.	NOUN
ejpam-4612	109	10	then	then	ADV
ejpam-4612	109	11	∥λ∥2mv,2	∥λ∥2mv,2	NOUN
ejpam-4612	109	12	=	=	SYM
ejpam-4612	109	13	sup	sup	NOUN
ejpam-4612	109	14	m∈z	m∈z	NOUN
ejpam-4612	109	15	,	,	PUNCT
ejpam-4612	109	16	n∈ω	n∈ω	NOUN
ejpam-4612	109	17	|sm	|sm	NUM
ejpam-4612	109	18	,	,	PUNCT
ejpam-4612	109	19	n	n	X
ejpam-4612	109	20	|2	|2	NUM
ejpam-4612	109	21	(	(	PUNCT
ejpam-4612	109	22	1	1	NUM
ejpam-4612	109	23	v	v	NOUN
ejpam-4612	109	24	−	−	NUM
ejpam-4612	109	25	1	1	NUM
ejpam-4612	109	26	2	2	NUM
ejpam-4612	109	27	)	)	PUNCT
ejpam-4612	109	28	(	(	PUNCT
ejpam-4612	109	29	∑	∑	ADV
ejpam-4612	109	30	k∈sm	k∈sm	PROPN
ejpam-4612	109	31	,	,	PUNCT
ejpam-4612	109	32	n	n	NOUN
ejpam-4612	109	33	|λk|2	|λk|2	PUNCT
ejpam-4612	109	34	)	)	PUNCT
ejpam-4612	110	1	=	=	SYM
ejpam-4612	110	2	sup	sup	NUM
ejpam-4612	110	3	m∈z	m∈z	NOUN
ejpam-4612	110	4	,	,	PUNCT
ejpam-4612	110	5	n∈ω	n∈ω	NOUN
ejpam-4612	110	6	|sm	|sm	NUM
ejpam-4612	110	7	,	,	PUNCT
ejpam-4612	110	8	n	n	X
ejpam-4612	110	9	|2	|2	NUM
ejpam-4612	110	10	(	(	PUNCT
ejpam-4612	110	11	1	1	NUM
ejpam-4612	110	12	v	v	NOUN
ejpam-4612	110	13	−	−	NUM
ejpam-4612	110	14	1	1	NUM
ejpam-4612	110	15	2	2	NUM
ejpam-4612	110	16	)	)	PUNCT
ejpam-4612	110	17	(	(	PUNCT
ejpam-4612	110	18	∑	∑	ADV
ejpam-4612	110	19	k∈sm	k∈sm	PROPN
ejpam-4612	110	20	,	,	PUNCT
ejpam-4612	110	21	n	n	CCONJ
ejpam-4612	110	22	|λk|2−p|λk|p	|λk|2−p|λk|p	PROPN
ejpam-4612	110	23	)	)	PUNCT
ejpam-4612	110	24	≤	≤	NUM
ejpam-4612	110	25	sup	sup	NOUN
ejpam-4612	110	26	m∈z	m∈z	NOUN
ejpam-4612	110	27	,	,	PUNCT
ejpam-4612	110	28	n∈ω	n∈ω	NOUN
ejpam-4612	110	29	|sm	|sm	NUM
ejpam-4612	110	30	,	,	PUNCT
ejpam-4612	110	31	n	n	X
ejpam-4612	110	32	|2	|2	NUM
ejpam-4612	110	33	(	(	PUNCT
ejpam-4612	110	34	1	1	NUM
ejpam-4612	110	35	v	v	NOUN
ejpam-4612	110	36	−	−	NUM
ejpam-4612	110	37	1	1	NUM
ejpam-4612	110	38	2	2	NUM
ejpam-4612	110	39	)	)	PUNCT
ejpam-4612	110	40	(	(	PUNCT
ejpam-4612	110	41	sup	sup	NOUN
ejpam-4612	110	42	k∈sm	k∈sm	NOUN
ejpam-4612	110	43	,	,	PUNCT
ejpam-4612	110	44	n	n	CCONJ
ejpam-4612	110	45	|λk|2−p	|λk|2−p	NOUN
ejpam-4612	110	46	∑	∑	ADV
ejpam-4612	110	47	k∈sm	k∈sm	PROPN
ejpam-4612	110	48	,	,	PUNCT
ejpam-4612	110	49	n	n	CCONJ
ejpam-4612	110	50	|λk|p	|λk|p	PRON
ejpam-4612	110	51	)	)	PUNCT
ejpam-4612	110	52	≤	≤	NUM
ejpam-4612	110	53	sup	sup	NOUN
ejpam-4612	110	54	m∈z	m∈z	NOUN
ejpam-4612	110	55	,	,	PUNCT
ejpam-4612	110	56	n∈ω	n∈ω	NOUN
ejpam-4612	110	57	|sm	|sm	NUM
ejpam-4612	110	58	,	,	PUNCT
ejpam-4612	110	59	n	n	X
ejpam-4612	110	60	|2	|2	NUM
ejpam-4612	110	61	(	(	PUNCT
ejpam-4612	110	62	1	1	NUM
ejpam-4612	110	63	v	v	NOUN
ejpam-4612	110	64	−	−	NUM
ejpam-4612	110	65	1	1	NUM
ejpam-4612	110	66	2	2	NUM
ejpam-4612	110	67	)	)	PUNCT
ejpam-4612	110	68	(	(	PUNCT
ejpam-4612	110	69	∑	∑	ADV
ejpam-4612	110	70	k∈sm	k∈sm	PROPN
ejpam-4612	110	71	,	,	PUNCT
ejpam-4612	110	72	n	n	CCONJ
ejpam-4612	110	73	|λk|p	|λk|p	PUNCT
ejpam-4612	110	74	)	)	PUNCT
ejpam-4612	110	75	2−p	2−p	NUM
ejpam-4612	111	1	p	p	NOUN
ejpam-4612	111	2	(	(	PUNCT
ejpam-4612	111	3	∑	∑	PUNCT
ejpam-4612	111	4	k∈sm	k∈sm	PROPN
ejpam-4612	111	5	,	,	PUNCT
ejpam-4612	111	6	n	n	CCONJ
ejpam-4612	111	7	|λk|p	|λk|p	PUNCT
ejpam-4612	111	8	)	)	PUNCT
ejpam-4612	111	9	=	=	SYM
ejpam-4612	111	10	sup	sup	NUM
ejpam-4612	111	11	m∈z	m∈z	NOUN
ejpam-4612	111	12	,	,	PUNCT
ejpam-4612	111	13	n∈ω	n∈ω	NOUN
ejpam-4612	111	14	|sm	|sm	NUM
ejpam-4612	111	15	,	,	PUNCT
ejpam-4612	111	16	n	n	X
ejpam-4612	111	17	|2	|2	NUM
ejpam-4612	111	18	(	(	PUNCT
ejpam-4612	111	19	1	1	NUM
ejpam-4612	111	20	v	v	NOUN
ejpam-4612	111	21	−	−	NUM
ejpam-4612	111	22	1	1	NUM
ejpam-4612	111	23	2	2	NUM
ejpam-4612	111	24	)	)	PUNCT
ejpam-4612	111	25	(	(	PUNCT
ejpam-4612	111	26	∑	∑	ADV
ejpam-4612	111	27	k∈sm	k∈sm	PROPN
ejpam-4612	111	28	,	,	PUNCT
ejpam-4612	111	29	n	n	CCONJ
ejpam-4612	111	30	|λk|p	|λk|p	PUNCT
ejpam-4612	111	31	)	)	PUNCT
ejpam-4612	111	32	2	2	NUM
ejpam-4612	111	33	p	p	NOUN
ejpam-4612	111	34	take	take	VERB
ejpam-4612	111	35	the	the	DET
ejpam-4612	111	36	square	square	ADJ
ejpam-4612	111	37	roots	root	NOUN
ejpam-4612	111	38	of	of	ADP
ejpam-4612	111	39	both	both	DET
ejpam-4612	111	40	sides	side	NOUN
ejpam-4612	111	41	,	,	PUNCT
ejpam-4612	111	42	we	we	PRON
ejpam-4612	111	43	get	get	VERB
ejpam-4612	111	44	∥λ∥mv,2	∥λ∥mv,2	ADJ
ejpam-4612	111	45	≤	≤	NUM
ejpam-4612	111	46	sup	sup	NOUN
ejpam-4612	111	47	m∈z	m∈z	NOUN
ejpam-4612	111	48	,	,	PUNCT
ejpam-4612	111	49	n∈ω	n∈ω	NOUN
ejpam-4612	111	50	|sm	|sm	ADV
ejpam-4612	111	51	,	,	PUNCT
ejpam-4612	111	52	n	n	CCONJ
ejpam-4612	111	53	|	|	ADV
ejpam-4612	111	54	1	1	NUM
ejpam-4612	111	55	v	v	NOUN
ejpam-4612	111	56	−	−	NUM
ejpam-4612	111	57	1	1	NUM
ejpam-4612	111	58	2	2	NUM
ejpam-4612	111	59	(	(	PUNCT
ejpam-4612	111	60	∑	∑	ADV
ejpam-4612	111	61	k∈sm	k∈sm	PROPN
ejpam-4612	111	62	,	,	PUNCT
ejpam-4612	111	63	n	n	CCONJ
ejpam-4612	111	64	|λk|p	|λk|p	PUNCT
ejpam-4612	111	65	)	)	PUNCT
ejpam-4612	111	66	1	1	NUM
ejpam-4612	111	67	p	p	NOUN
ejpam-4612	111	68	because	because	SCONJ
ejpam-4612	111	69	v	v	NOUN
ejpam-4612	111	70	=	=	SYM
ejpam-4612	111	71	2up	2up	ADJ
ejpam-4612	112	1	2p−2u+up	2p−2u+up	NUM
ejpam-4612	112	2	then	then	ADV
ejpam-4612	112	3	we	we	PRON
ejpam-4612	112	4	find	find	VERB
ejpam-4612	112	5	1	1	NUM
ejpam-4612	112	6	v	v	ADP
ejpam-4612	112	7	−	−	NUM
ejpam-4612	112	8	1	1	NUM
ejpam-4612	112	9	2	2	NUM
ejpam-4612	112	10	=	=	SYM
ejpam-4612	112	11	1	1	NUM
ejpam-4612	112	12	(	(	PUNCT
ejpam-4612	112	13	2up	2up	ADJ
ejpam-4612	112	14	2p−2u+up	2p−2u+up	NUM
ejpam-4612	112	15	)	)	PUNCT
ejpam-4612	112	16	−	−	NOUN
ejpam-4612	113	1	1	1	NUM
ejpam-4612	113	2	2	2	NUM
ejpam-4612	113	3	=	=	SYM
ejpam-4612	113	4	2p−	2p−	NUM
ejpam-4612	113	5	2u+	2u+	NUM
ejpam-4612	113	6	up	up	ADP
ejpam-4612	113	7	2up	2up	ADV
ejpam-4612	113	8	−	−	NOUN
ejpam-4612	113	9	1	1	NUM
ejpam-4612	113	10	2	2	NUM
ejpam-4612	113	11	=	=	SYM
ejpam-4612	114	1	2p−	2p−	NUM
ejpam-4612	114	2	2u+	2u+	NUM
ejpam-4612	114	3	up	up	ADP
ejpam-4612	114	4	2up	2up	ADJ
ejpam-4612	114	5	−	−	NOUN
ejpam-4612	114	6	up	up	ADP
ejpam-4612	114	7	2up	2up	PROPN
ejpam-4612	114	8	=	=	PUNCT
ejpam-4612	115	1	2p−	2p−	NUM
ejpam-4612	115	2	2u	2u	NOUN
ejpam-4612	115	3	2up	2up	NOUN
ejpam-4612	115	4	=	=	PUNCT
ejpam-4612	116	1	p−	p−	X
ejpam-4612	116	2	u	u	NOUN
ejpam-4612	116	3	up	up	ADV
ejpam-4612	116	4	=	=	SYM
ejpam-4612	116	5	1	1	NUM
ejpam-4612	116	6	u	u	NOUN
ejpam-4612	116	7	−	−	PROPN
ejpam-4612	116	8	1	1	NUM
ejpam-4612	116	9	p	p	NOUN
ejpam-4612	116	10	m.	m.	NOUN
ejpam-4612	116	11	jakfar	jakfar	NOUN
ejpam-4612	116	12	et	et	PROPN
ejpam-4612	116	13	al	al	PROPN
ejpam-4612	116	14	.	.	PUNCT
ejpam-4612	116	15	/	/	SYM
ejpam-4612	116	16	eur	eur	PROPN
ejpam-4612	116	17	.	.	PUNCT
ejpam-4612	117	1	j.	j.	PROPN
ejpam-4612	117	2	pure	pure	PROPN
ejpam-4612	117	3	appl	appl	PROPN
ejpam-4612	117	4	.	.	PROPN
ejpam-4612	117	5	math	math	PROPN
ejpam-4612	117	6	,	,	PUNCT
ejpam-4612	117	7	16	16	NUM
ejpam-4612	117	8	(	(	PUNCT
ejpam-4612	117	9	1	1	NUM
ejpam-4612	117	10	)	)	PUNCT
ejpam-4612	117	11	(	(	PUNCT
ejpam-4612	117	12	2023	2023	NUM
ejpam-4612	117	13	)	)	PUNCT
ejpam-4612	117	14	,	,	PUNCT
ejpam-4612	117	15	144	144	NUM
ejpam-4612	117	16	-	-	SYM
ejpam-4612	117	17	155	155	NUM
ejpam-4612	117	18	150	150	NUM
ejpam-4612	117	19	because	because	SCONJ
ejpam-4612	117	20	1	1	NUM
ejpam-4612	117	21	≤	≤	NOUN
ejpam-4612	117	22	p	p	X
ejpam-4612	117	23	≤	≤	NUM
ejpam-4612	117	24	u	u	NOUN
ejpam-4612	117	25	<	<	X
ejpam-4612	117	26	2	2	NUM
ejpam-4612	117	27	,	,	PUNCT
ejpam-4612	117	28	then	then	ADV
ejpam-4612	117	29	2	2	NUM
ejpam-4612	117	30	≤	≤	NOUN
ejpam-4612	117	31	v	v	NOUN
ejpam-4612	117	32	and	and	CCONJ
ejpam-4612	117	33	0	0	NUM
ejpam-4612	117	34	<	<	X
ejpam-4612	117	35	1	1	NUM
ejpam-4612	117	36	v	v	NUM
ejpam-4612	117	37	≤	≤	NUM
ejpam-4612	117	38	1	1	NUM
ejpam-4612	117	39	2	2	NUM
ejpam-4612	117	40	.	.	PUNCT
ejpam-4612	118	1	and	and	CCONJ
ejpam-4612	118	2	also	also	ADV
ejpam-4612	118	3	,	,	PUNCT
ejpam-4612	118	4	we	we	PRON
ejpam-4612	118	5	get	get	VERB
ejpam-4612	118	6	∥λ∥mv,2	∥λ∥mv,2	ADJ
ejpam-4612	118	7	≤	≤	NUM
ejpam-4612	118	8	sup	sup	NOUN
ejpam-4612	118	9	m∈z	m∈z	NOUN
ejpam-4612	118	10	,	,	PUNCT
ejpam-4612	118	11	n∈ω	n∈ω	NOUN
ejpam-4612	118	12	|sm	|sm	ADV
ejpam-4612	118	13	,	,	PUNCT
ejpam-4612	118	14	n	n	CCONJ
ejpam-4612	118	15	|	|	ADV
ejpam-4612	118	16	1	1	NUM
ejpam-4612	118	17	u	u	NOUN
ejpam-4612	118	18	−	−	PROPN
ejpam-4612	118	19	1	1	NUM
ejpam-4612	118	20	p	p	NOUN
ejpam-4612	118	21	(	(	PUNCT
ejpam-4612	118	22	∑	∑	PUNCT
ejpam-4612	118	23	k∈sm	k∈sm	PROPN
ejpam-4612	118	24	,	,	PUNCT
ejpam-4612	118	25	n	n	CCONJ
ejpam-4612	118	26	|λk|p	|λk|p	PUNCT
ejpam-4612	118	27	)	)	PUNCT
ejpam-4612	118	28	1	1	NUM
ejpam-4612	119	1	p	p	NOUN
ejpam-4612	119	2	=	=	SYM
ejpam-4612	119	3	∥λ∥mu	∥λ∥mu	PROPN
ejpam-4612	119	4	,	,	PUNCT
ejpam-4612	119	5	p	p	PRON
ejpam-4612	119	6	consequently	consequently	ADV
ejpam-4612	119	7	,	,	PUNCT
ejpam-4612	119	8	we	we	PRON
ejpam-4612	119	9	have	have	AUX
ejpam-4612	119	10	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	119	11	≤	≤	NUM
ejpam-4612	119	12	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	119	13	,	,	PUNCT
ejpam-4612	119	14	p	p	NOUN
ejpam-4612	119	15	since	since	SCONJ
ejpam-4612	119	16	λ	λ	PROPN
ejpam-4612	119	17	∈	∈	PROPN
ejpam-4612	119	18	mu	mu	NOUN
ejpam-4612	119	19	,	,	PUNCT
ejpam-4612	119	20	p	p	PROPN
ejpam-4612	119	21	is	be	AUX
ejpam-4612	119	22	arbitrary	arbitrary	ADJ
ejpam-4612	119	23	,	,	PUNCT
ejpam-4612	119	24	then	then	ADV
ejpam-4612	119	25	from	from	ADP
ejpam-4612	119	26	the	the	DET
ejpam-4612	119	27	inequality	inequality	NOUN
ejpam-4612	119	28	,	,	PUNCT
ejpam-4612	119	29	every	every	DET
ejpam-4612	119	30	element	element	NOUN
ejpam-4612	119	31	of	of	ADP
ejpam-4612	119	32	mu	mu	PROPN
ejpam-4612	119	33	,	,	PUNCT
ejpam-4612	119	34	p	p	NOUN
ejpam-4612	119	35	is	be	AUX
ejpam-4612	119	36	also	also	ADV
ejpam-4612	119	37	in	in	ADP
ejpam-4612	119	38	mv,2	mv,2	PROPN
ejpam-4612	119	39	.	.	PUNCT
ejpam-4612	120	1	it	it	PRON
ejpam-4612	120	2	means	mean	VERB
ejpam-4612	120	3	mu	mu	NOUN
ejpam-4612	120	4	,	,	PUNCT
ejpam-4612	120	5	p	p	PROPN
ejpam-4612	120	6	⊂	⊂	PROPN
ejpam-4612	120	7	mv,2	mv,2	PROPN
ejpam-4612	120	8	.	.	PUNCT
ejpam-4612	121	1	■	■	PUNCT
ejpam-4612	121	2	remark	remark	NOUN
ejpam-4612	121	3	3	3	NUM
ejpam-4612	121	4	.	.	PUNCT
ejpam-4612	122	1	for	for	ADP
ejpam-4612	122	2	1	1	NUM
ejpam-4612	122	3	≤	≤	NOUN
ejpam-4612	122	4	p	p	PROPN
ejpam-4612	122	5	≤	≤	NUM
ejpam-4612	122	6	u	u	NOUN
ejpam-4612	122	7	<	<	X
ejpam-4612	122	8	2	2	NUM
ejpam-4612	122	9	and	and	CCONJ
ejpam-4612	122	10	v	v	NOUN
ejpam-4612	122	11	=	=	SYM
ejpam-4612	122	12	2up	2up	ADJ
ejpam-4612	122	13	2p−2u+up	2p−2u+up	NUM
ejpam-4612	122	14	,	,	PUNCT
ejpam-4612	122	15	the	the	DET
ejpam-4612	122	16	space	space	NOUN
ejpam-4612	122	17	(	(	PUNCT
ejpam-4612	122	18	mu	mu	NOUN
ejpam-4612	122	19	,	,	PUNCT
ejpam-4612	122	20	p	p	X
ejpam-4612	122	21	,	,	PUNCT
ejpam-4612	122	22	∥	∥	X
ejpam-4612	122	23	·	·	PUNCT
ejpam-4612	122	24	∥mv,2	∥mv,2	NUM
ejpam-4612	122	25	)	)	PUNCT
ejpam-4612	122	26	is	be	AUX
ejpam-4612	122	27	an	an	DET
ejpam-4612	122	28	inner	inner	ADJ
ejpam-4612	122	29	product	product	NOUN
ejpam-4612	122	30	space	space	NOUN
ejpam-4612	122	31	.	.	PUNCT
ejpam-4612	123	1	a	a	DET
ejpam-4612	123	2	more	more	ADV
ejpam-4612	123	3	general	general	ADJ
ejpam-4612	123	4	result	result	NOUN
ejpam-4612	123	5	of	of	ADP
ejpam-4612	123	6	proposition	proposition	NOUN
ejpam-4612	123	7	3	3	NUM
ejpam-4612	123	8	is	be	AUX
ejpam-4612	123	9	formulated	formulate	VERB
ejpam-4612	123	10	in	in	ADP
ejpam-4612	123	11	the	the	DET
ejpam-4612	123	12	following	following	NOUN
ejpam-4612	123	13	theorem	theorem	VERB
ejpam-4612	123	14	.	.	PUNCT
ejpam-4612	124	1	but	but	CCONJ
ejpam-4612	124	2	,	,	PUNCT
ejpam-4612	124	3	before	before	ADP
ejpam-4612	124	4	discussing	discuss	VERB
ejpam-4612	124	5	the	the	DET
ejpam-4612	124	6	theorem	theorem	NOUN
ejpam-4612	124	7	,	,	PUNCT
ejpam-4612	124	8	we	we	PRON
ejpam-4612	124	9	need	need	VERB
ejpam-4612	124	10	to	to	PART
ejpam-4612	124	11	introduce	introduce	VERB
ejpam-4612	124	12	the	the	DET
ejpam-4612	124	13	following	follow	VERB
ejpam-4612	124	14	proposition	proposition	NOUN
ejpam-4612	124	15	.	.	PUNCT
ejpam-4612	125	1	proposition	proposition	NOUN
ejpam-4612	125	2	4	4	NUM
ejpam-4612	125	3	.	.	PUNCT
ejpam-4612	126	1	if	if	SCONJ
ejpam-4612	126	2	1	1	NUM
ejpam-4612	126	3	≤	≤	NOUN
ejpam-4612	126	4	p	p	ADJ
ejpam-4612	126	5	≤	≤	NUM
ejpam-4612	126	6	u	u	NOUN
ejpam-4612	126	7	≤	≤	X
ejpam-4612	126	8	q	q	NOUN
ejpam-4612	126	9	<	<	X
ejpam-4612	126	10	∞	∞	NUM
ejpam-4612	126	11	such	such	ADJ
ejpam-4612	126	12	that	that	SCONJ
ejpam-4612	126	13	1	1	NUM
ejpam-4612	126	14	p	p	NOUN
ejpam-4612	126	15	−	−	PROPN
ejpam-4612	126	16	1	1	NUM
ejpam-4612	126	17	u	u	NOUN
ejpam-4612	126	18	<	<	X
ejpam-4612	126	19	1	1	NUM
ejpam-4612	126	20	q	q	NOUN
ejpam-4612	126	21	,	,	PUNCT
ejpam-4612	126	22	then	then	ADV
ejpam-4612	126	23	there	there	PRON
ejpam-4612	126	24	is	be	VERB
ejpam-4612	126	25	v	v	ADP
ejpam-4612	126	26	>	>	X
ejpam-4612	126	27	0	0	NUM
ejpam-4612	126	28	such	such	ADJ
ejpam-4612	126	29	that	that	DET
ejpam-4612	126	30	q	q	PROPN
ejpam-4612	126	31	≤	≤	X
ejpam-4612	126	32	v	v	NOUN
ejpam-4612	126	33	and	and	CCONJ
ejpam-4612	126	34	1	1	NUM
ejpam-4612	126	35	v	v	NOUN
ejpam-4612	126	36	−	−	PROPN
ejpam-4612	126	37	1	1	NUM
ejpam-4612	126	38	q	q	NOUN
ejpam-4612	126	39	=	=	SYM
ejpam-4612	126	40	1	1	NUM
ejpam-4612	126	41	u	u	NOUN
ejpam-4612	126	42	−	−	PROPN
ejpam-4612	126	43	1	1	NUM
ejpam-4612	126	44	p	p	NOUN
ejpam-4612	126	45	.	.	PUNCT
ejpam-4612	127	1	that	that	PRON
ejpam-4612	127	2	is	be	AUX
ejpam-4612	127	3	,	,	PUNCT
ejpam-4612	127	4	v	v	NOUN
ejpam-4612	127	5	=	=	PUNCT
ejpam-4612	127	6	upq	upq	NOUN
ejpam-4612	127	7	pq−uq+up	pq−uq+up	PROPN
ejpam-4612	127	8	.	.	PUNCT
ejpam-4612	128	1	proof	proof	NOUN
ejpam-4612	128	2	.	.	PUNCT
ejpam-4612	129	1	let	let	VERB
ejpam-4612	129	2	1	1	NUM
ejpam-4612	129	3	≤	≤	NOUN
ejpam-4612	129	4	p	p	NOUN
ejpam-4612	129	5	≤	≤	NUM
ejpam-4612	129	6	u	u	NOUN
ejpam-4612	129	7	≤	≤	X
ejpam-4612	129	8	q	q	NOUN
ejpam-4612	129	9	<	<	X
ejpam-4612	129	10	∞	∞	PROPN
ejpam-4612	129	11	and	and	CCONJ
ejpam-4612	129	12	∣∣	∣∣	NUM
ejpam-4612	129	13	1	1	NUM
ejpam-4612	129	14	u	u	NOUN
ejpam-4612	129	15	−	−	PROPN
ejpam-4612	129	16	1	1	NUM
ejpam-4612	129	17	p	p	X
ejpam-4612	129	18	∣∣	∣∣	X
ejpam-4612	129	19	<	<	X
ejpam-4612	129	20	1	1	NUM
ejpam-4612	129	21	q	q	NOUN
ejpam-4612	129	22	.	.	PUNCT
ejpam-4612	130	1	take	take	VERB
ejpam-4612	130	2	v	v	NOUN
ejpam-4612	130	3	=	=	PUNCT
ejpam-4612	130	4	upq	upq	NOUN
ejpam-4612	130	5	pq−uq+up	pq−uq+up	PROPN
ejpam-4612	130	6	.	.	PUNCT
ejpam-4612	131	1	then	then	ADV
ejpam-4612	131	2	1	1	NUM
ejpam-4612	131	3	v	v	NOUN
ejpam-4612	131	4	−	−	PROPN
ejpam-4612	131	5	1	1	NUM
ejpam-4612	131	6	q	q	NOUN
ejpam-4612	131	7	=	=	SYM
ejpam-4612	131	8	1	1	NUM
ejpam-4612	131	9	(	(	PUNCT
ejpam-4612	131	10	upq	upq	ADV
ejpam-4612	131	11	pq−uq+up	pq−uq+up	PROPN
ejpam-4612	131	12	)	)	PUNCT
ejpam-4612	131	13	−	−	PROPN
ejpam-4612	131	14	1	1	NUM
ejpam-4612	131	15	q	q	NOUN
ejpam-4612	131	16	=	=	PUNCT
ejpam-4612	131	17	pq	pq	NOUN
ejpam-4612	131	18	−	−	PROPN
ejpam-4612	132	1	uq	uq	NOUN
ejpam-4612	133	1	+	+	X
ejpam-4612	133	2	up	up	ADV
ejpam-4612	133	3	upq	upq	ADV
ejpam-4612	133	4	−	−	PROPN
ejpam-4612	133	5	1	1	NUM
ejpam-4612	133	6	q	q	NOUN
ejpam-4612	133	7	=	=	PUNCT
ejpam-4612	133	8	pq	pq	NOUN
ejpam-4612	133	9	−	−	PROPN
ejpam-4612	134	1	uq	uq	NOUN
ejpam-4612	134	2	upq	upq	NOUN
ejpam-4612	134	3	=	=	SYM
ejpam-4612	134	4	1	1	NUM
ejpam-4612	134	5	u	u	NOUN
ejpam-4612	134	6	−	−	PROPN
ejpam-4612	134	7	1	1	NUM
ejpam-4612	134	8	p	p	NOUN
ejpam-4612	134	9	.	.	PUNCT
ejpam-4612	135	1	because	because	SCONJ
ejpam-4612	135	2	p	p	ADJ
ejpam-4612	135	3	≤	≤	NUM
ejpam-4612	135	4	u	u	NOUN
ejpam-4612	135	5	then	then	ADV
ejpam-4612	135	6	1	1	NUM
ejpam-4612	135	7	u	u	NOUN
ejpam-4612	135	8	≤	≤	NUM
ejpam-4612	135	9	1	1	NUM
ejpam-4612	135	10	p	p	NOUN
ejpam-4612	135	11	.	.	PUNCT
ejpam-4612	136	1	hence	hence	ADV
ejpam-4612	136	2	,	,	PUNCT
ejpam-4612	136	3	1	1	NUM
ejpam-4612	136	4	v	v	NOUN
ejpam-4612	136	5	≤	≤	NUM
ejpam-4612	136	6	1	1	NUM
ejpam-4612	136	7	q	q	NOUN
ejpam-4612	136	8	and	and	CCONJ
ejpam-4612	136	9	q	q	PROPN
ejpam-4612	136	10	≤	≤	PROPN
ejpam-4612	136	11	v.	v.	CCONJ
ejpam-4612	136	12	since	since	SCONJ
ejpam-4612	136	13	1	1	NUM
ejpam-4612	136	14	p	p	NOUN
ejpam-4612	136	15	−	−	PROPN
ejpam-4612	136	16	1	1	NUM
ejpam-4612	136	17	u	u	NOUN
ejpam-4612	136	18	<	<	X
ejpam-4612	136	19	1	1	NUM
ejpam-4612	136	20	q	q	NOUN
ejpam-4612	136	21	then	then	ADV
ejpam-4612	136	22	1	1	NUM
ejpam-4612	136	23	q	q	NOUN
ejpam-4612	136	24	−	−	PROPN
ejpam-4612	136	25	1	1	NUM
ejpam-4612	136	26	v	v	NOUN
ejpam-4612	136	27	<	<	X
ejpam-4612	136	28	1	1	NUM
ejpam-4612	136	29	q	q	NOUN
ejpam-4612	136	30	.	.	PUNCT
ejpam-4612	137	1	so	so	ADV
ejpam-4612	137	2	,	,	PUNCT
ejpam-4612	137	3	1	1	NUM
ejpam-4612	137	4	v	v	NOUN
ejpam-4612	137	5	>	>	X
ejpam-4612	137	6	0	0	PUNCT
ejpam-4612	137	7	and	and	CCONJ
ejpam-4612	137	8	v	v	ADP
ejpam-4612	137	9	≤	≤	NUM
ejpam-4612	137	10	0	0	NUM
ejpam-4612	137	11	.	.	PUNCT
ejpam-4612	138	1	■	■	PUNCT
ejpam-4612	138	2	theorem	theorem	ADJ
ejpam-4612	138	3	3	3	NUM
ejpam-4612	138	4	.	.	PUNCT
ejpam-4612	138	5	for	for	ADP
ejpam-4612	138	6	1	1	NUM
ejpam-4612	138	7	≤	≤	NOUN
ejpam-4612	138	8	p	p	NOUN
ejpam-4612	138	9	≤	≤	NUM
ejpam-4612	138	10	u	u	NOUN
ejpam-4612	138	11	≤	≤	X
ejpam-4612	138	12	q	q	NOUN
ejpam-4612	138	13	<	<	X
ejpam-4612	138	14	∞	∞	PROPN
ejpam-4612	138	15	and	and	CCONJ
ejpam-4612	138	16	v	v	NOUN
ejpam-4612	138	17	=	=	PUNCT
ejpam-4612	138	18	upq	upq	NOUN
ejpam-4612	138	19	pq−uq+up	pq−uq+up	PROPN
ejpam-4612	138	20	,	,	PUNCT
ejpam-4612	138	21	then	then	ADV
ejpam-4612	138	22	mu	mu	PROPN
ejpam-4612	138	23	,	,	PUNCT
ejpam-4612	138	24	p	p	PROPN
ejpam-4612	138	25	⊂	⊂	PROPN
ejpam-4612	138	26	mv	mv	PROPN
ejpam-4612	138	27	,	,	PUNCT
ejpam-4612	138	28	q	q	X
ejpam-4612	138	29	and	and	CCONJ
ejpam-4612	138	30	∥λ∥mv	∥λ∥mv	VERB
ejpam-4612	138	31	,	,	PUNCT
ejpam-4612	138	32	q	q	PROPN
ejpam-4612	138	33	≤	≤	NUM
ejpam-4612	138	34	∥λ∥mu	∥λ∥mu	ADP
ejpam-4612	138	35	,	,	PUNCT
ejpam-4612	138	36	p	p	NOUN
ejpam-4612	138	37	for	for	ADP
ejpam-4612	138	38	every	every	DET
ejpam-4612	138	39	λ	λ	PROPN
ejpam-4612	138	40	∈	∈	PROPN
ejpam-4612	138	41	mu	mu	NOUN
ejpam-4612	138	42	,	,	PUNCT
ejpam-4612	138	43	p.	p.	NOUN
ejpam-4612	138	44	proof	proof	NOUN
ejpam-4612	138	45	.	.	PUNCT
ejpam-4612	139	1	let	let	VERB
ejpam-4612	139	2	λ	λ	X
ejpam-4612	139	3	=	=	PRON
ejpam-4612	139	4	(	(	PUNCT
ejpam-4612	139	5	λk)k∈z	λk)k∈z	PROPN
ejpam-4612	139	6	∈	∈	PROPN
ejpam-4612	139	7	mu	mu	NOUN
ejpam-4612	139	8	,	,	PUNCT
ejpam-4612	139	9	p.	p.	NOUN
ejpam-4612	139	10	then	then	ADV
ejpam-4612	139	11	∥λ∥qmv	∥λ∥qmv	NOUN
ejpam-4612	139	12	,	,	PUNCT
ejpam-4612	139	13	q	q	NOUN
ejpam-4612	139	14	=	=	NOUN
ejpam-4612	139	15	sup	sup	NOUN
ejpam-4612	139	16	m∈z	m∈z	NOUN
ejpam-4612	139	17	,	,	PUNCT
ejpam-4612	139	18	n∈ω	n∈ω	NOUN
ejpam-4612	139	19	|sm	|sm	NUM
ejpam-4612	139	20	,	,	PUNCT
ejpam-4612	139	21	n	n	X
ejpam-4612	139	22	|q	|q	NOUN
ejpam-4612	139	23	(	(	PUNCT
ejpam-4612	139	24	1	1	NUM
ejpam-4612	139	25	v	v	PART
ejpam-4612	139	26	−	−	PROPN
ejpam-4612	139	27	1	1	NUM
ejpam-4612	139	28	q	q	NOUN
ejpam-4612	139	29	)	)	PUNCT
ejpam-4612	139	30	(	(	PUNCT
ejpam-4612	139	31	∑	∑	ADV
ejpam-4612	139	32	k∈sm	k∈sm	PROPN
ejpam-4612	139	33	,	,	PUNCT
ejpam-4612	139	34	n	n	X
ejpam-4612	139	35	|λk|q	|λk|q	X
ejpam-4612	139	36	)	)	PUNCT
ejpam-4612	140	1	=	=	SYM
ejpam-4612	140	2	sup	sup	NUM
ejpam-4612	140	3	m∈z	m∈z	NOUN
ejpam-4612	140	4	,	,	PUNCT
ejpam-4612	140	5	n∈ω	n∈ω	NOUN
ejpam-4612	140	6	|sm	|sm	NUM
ejpam-4612	140	7	,	,	PUNCT
ejpam-4612	140	8	n	n	X
ejpam-4612	140	9	|q	|q	NOUN
ejpam-4612	140	10	(	(	PUNCT
ejpam-4612	140	11	1	1	NUM
ejpam-4612	140	12	v	v	PART
ejpam-4612	140	13	−	−	PROPN
ejpam-4612	140	14	1	1	NUM
ejpam-4612	140	15	q	q	NOUN
ejpam-4612	140	16	)	)	PUNCT
ejpam-4612	140	17	(	(	PUNCT
ejpam-4612	140	18	∑	∑	ADV
ejpam-4612	140	19	k∈sm	k∈sm	PROPN
ejpam-4612	140	20	,	,	PUNCT
ejpam-4612	140	21	n	n	PRON
ejpam-4612	140	22	|λk|q−p|λk|p	|λk|q−p|λk|p	X
ejpam-4612	140	23	)	)	PUNCT
ejpam-4612	140	24	≤	≤	NUM
ejpam-4612	140	25	sup	sup	NOUN
ejpam-4612	140	26	m∈z	m∈z	NOUN
ejpam-4612	140	27	,	,	PUNCT
ejpam-4612	140	28	n∈ω	n∈ω	NOUN
ejpam-4612	140	29	|sm	|sm	NUM
ejpam-4612	140	30	,	,	PUNCT
ejpam-4612	140	31	n	n	X
ejpam-4612	140	32	|q	|q	NOUN
ejpam-4612	140	33	(	(	PUNCT
ejpam-4612	140	34	1	1	NUM
ejpam-4612	140	35	v	v	PART
ejpam-4612	140	36	−	−	PROPN
ejpam-4612	140	37	1	1	NUM
ejpam-4612	140	38	q	q	NOUN
ejpam-4612	140	39	)	)	PUNCT
ejpam-4612	140	40	(	(	PUNCT
ejpam-4612	140	41	sup	sup	NOUN
ejpam-4612	140	42	k∈sm	k∈sm	NOUN
ejpam-4612	140	43	,	,	PUNCT
ejpam-4612	140	44	n	n	PRON
ejpam-4612	140	45	|λk|q−p	|λk|q−p	NOUN
ejpam-4612	140	46	∑	∑	ADV
ejpam-4612	140	47	k∈sm	k∈sm	PROPN
ejpam-4612	140	48	,	,	PUNCT
ejpam-4612	140	49	n	n	CCONJ
ejpam-4612	140	50	|λk|p	|λk|p	PRON
ejpam-4612	140	51	)	)	PUNCT
ejpam-4612	140	52	≤	≤	NUM
ejpam-4612	140	53	sup	sup	NOUN
ejpam-4612	140	54	m∈z	m∈z	NOUN
ejpam-4612	140	55	,	,	PUNCT
ejpam-4612	140	56	n∈ω	n∈ω	NOUN
ejpam-4612	140	57	|sm	|sm	NUM
ejpam-4612	140	58	,	,	PUNCT
ejpam-4612	140	59	n	n	X
ejpam-4612	140	60	|q	|q	NOUN
ejpam-4612	140	61	(	(	PUNCT
ejpam-4612	140	62	1	1	NUM
ejpam-4612	140	63	v	v	PART
ejpam-4612	140	64	−	−	PROPN
ejpam-4612	140	65	1	1	NUM
ejpam-4612	140	66	q	q	NOUN
ejpam-4612	140	67	)	)	PUNCT
ejpam-4612	140	68	(	(	PUNCT
ejpam-4612	140	69	∑	∑	ADV
ejpam-4612	140	70	k∈sm	k∈sm	PROPN
ejpam-4612	140	71	,	,	PUNCT
ejpam-4612	140	72	n	n	CCONJ
ejpam-4612	140	73	|λk|p	|λk|p	PUNCT
ejpam-4612	140	74	)	)	PUNCT
ejpam-4612	140	75	q−p	q−p	PROPN
ejpam-4612	140	76	p	p	X
ejpam-4612	140	77	(	(	PUNCT
ejpam-4612	140	78	∑	∑	PUNCT
ejpam-4612	140	79	k∈sm	k∈sm	PROPN
ejpam-4612	140	80	,	,	PUNCT
ejpam-4612	140	81	n	n	CCONJ
ejpam-4612	140	82	|λk|p	|λk|p	PRON
ejpam-4612	140	83	)	)	PUNCT
ejpam-4612	141	1	m.	m.	NOUN
ejpam-4612	141	2	jakfar	jakfar	INTJ
ejpam-4612	141	3	et	et	PROPN
ejpam-4612	141	4	al	al	PROPN
ejpam-4612	141	5	.	.	PUNCT
ejpam-4612	141	6	/	/	SYM
ejpam-4612	141	7	eur	eur	PROPN
ejpam-4612	141	8	.	.	PUNCT
ejpam-4612	142	1	j.	j.	PROPN
ejpam-4612	142	2	pure	pure	PROPN
ejpam-4612	142	3	appl	appl	PROPN
ejpam-4612	142	4	.	.	PROPN
ejpam-4612	142	5	math	math	PROPN
ejpam-4612	142	6	,	,	PUNCT
ejpam-4612	142	7	16	16	NUM
ejpam-4612	142	8	(	(	PUNCT
ejpam-4612	142	9	1	1	NUM
ejpam-4612	142	10	)	)	PUNCT
ejpam-4612	142	11	(	(	PUNCT
ejpam-4612	142	12	2023	2023	NUM
ejpam-4612	142	13	)	)	PUNCT
ejpam-4612	142	14	,	,	PUNCT
ejpam-4612	142	15	144	144	NUM
ejpam-4612	142	16	-	-	SYM
ejpam-4612	142	17	155	155	NUM
ejpam-4612	142	18	151	151	NUM
ejpam-4612	142	19	=	=	NOUN
ejpam-4612	142	20	sup	sup	NOUN
ejpam-4612	142	21	m∈z	m∈z	NOUN
ejpam-4612	142	22	,	,	PUNCT
ejpam-4612	142	23	n∈ω	n∈ω	NOUN
ejpam-4612	142	24	|sm	|sm	NUM
ejpam-4612	142	25	,	,	PUNCT
ejpam-4612	142	26	n	n	X
ejpam-4612	142	27	|q	|q	NOUN
ejpam-4612	142	28	(	(	PUNCT
ejpam-4612	142	29	1	1	NUM
ejpam-4612	142	30	v	v	PART
ejpam-4612	142	31	−	−	PROPN
ejpam-4612	142	32	1	1	NUM
ejpam-4612	142	33	q	q	NOUN
ejpam-4612	142	34	)	)	PUNCT
ejpam-4612	142	35	(	(	PUNCT
ejpam-4612	142	36	∑	∑	ADV
ejpam-4612	142	37	k∈sm	k∈sm	PROPN
ejpam-4612	142	38	,	,	PUNCT
ejpam-4612	142	39	n	n	CCONJ
ejpam-4612	142	40	|λk|p	|λk|p	PUNCT
ejpam-4612	142	41	)	)	PUNCT
ejpam-4612	142	42	q	q	NOUN
ejpam-4612	143	1	p	p	NOUN
ejpam-4612	143	2	take	take	VERB
ejpam-4612	143	3	the	the	DET
ejpam-4612	143	4	q	q	NOUN
ejpam-4612	143	5	-	-	PUNCT
ejpam-4612	143	6	roots	root	NOUN
ejpam-4612	143	7	of	of	ADP
ejpam-4612	143	8	both	both	DET
ejpam-4612	143	9	sides	side	NOUN
ejpam-4612	143	10	and	and	CCONJ
ejpam-4612	143	11	apply	apply	VERB
ejpam-4612	143	12	proposition	proposition	NOUN
ejpam-4612	143	13	5	5	NUM
ejpam-4612	143	14	,	,	PUNCT
ejpam-4612	143	15	we	we	PRON
ejpam-4612	143	16	get	get	AUX
ejpam-4612	143	17	∥λ∥mv	∥λ∥mv	VERB
ejpam-4612	143	18	,	,	PUNCT
ejpam-4612	143	19	q	q	PROPN
ejpam-4612	143	20	≤	≤	NUM
ejpam-4612	143	21	sup	sup	NOUN
ejpam-4612	143	22	m∈z	m∈z	NOUN
ejpam-4612	143	23	,	,	PUNCT
ejpam-4612	143	24	n∈ω	n∈ω	NOUN
ejpam-4612	143	25	|sm	|sm	ADV
ejpam-4612	143	26	,	,	PUNCT
ejpam-4612	143	27	n	n	CCONJ
ejpam-4612	143	28	|	|	ADV
ejpam-4612	143	29	1	1	NUM
ejpam-4612	143	30	v	v	NOUN
ejpam-4612	143	31	−	−	PROPN
ejpam-4612	143	32	1	1	NUM
ejpam-4612	143	33	q	q	NOUN
ejpam-4612	143	34	(	(	PUNCT
ejpam-4612	143	35	∑	∑	ADV
ejpam-4612	143	36	k∈sm	k∈sm	PROPN
ejpam-4612	143	37	,	,	PUNCT
ejpam-4612	143	38	n	n	CCONJ
ejpam-4612	143	39	|λk|p	|λk|p	PUNCT
ejpam-4612	143	40	)	)	PUNCT
ejpam-4612	143	41	1	1	NUM
ejpam-4612	144	1	p	p	NOUN
ejpam-4612	144	2	=	=	SYM
ejpam-4612	144	3	∥λ∥mu	∥λ∥mu	PROPN
ejpam-4612	144	4	,	,	PUNCT
ejpam-4612	144	5	p	p	NOUN
ejpam-4612	144	6	since	since	SCONJ
ejpam-4612	144	7	λ	λ	PROPN
ejpam-4612	144	8	∈	∈	PROPN
ejpam-4612	144	9	mu	mu	NOUN
ejpam-4612	144	10	,	,	PUNCT
ejpam-4612	144	11	p	p	PROPN
ejpam-4612	144	12	is	be	AUX
ejpam-4612	144	13	arbitrary	arbitrary	ADJ
ejpam-4612	144	14	,	,	PUNCT
ejpam-4612	144	15	then	then	ADV
ejpam-4612	144	16	from	from	ADP
ejpam-4612	144	17	the	the	DET
ejpam-4612	144	18	inequality	inequality	NOUN
ejpam-4612	144	19	,	,	PUNCT
ejpam-4612	144	20	we	we	PRON
ejpam-4612	144	21	get	get	VERB
ejpam-4612	144	22	mu	mu	NOUN
ejpam-4612	144	23	,	,	PUNCT
ejpam-4612	144	24	p	p	PROPN
ejpam-4612	144	25	⊂	⊂	PROPN
ejpam-4612	144	26	mv	mv	PROPN
ejpam-4612	144	27	,	,	PUNCT
ejpam-4612	144	28	q.	q.	PROPN
ejpam-4612	144	29	■	■	PUNCT
ejpam-4612	144	30	3	3	X
ejpam-4612	144	31	.	.	PUNCT
ejpam-4612	145	1	furthermore	furthermore	ADV
ejpam-4612	145	2	results	result	NOUN
ejpam-4612	145	3	now	now	ADV
ejpam-4612	145	4	,	,	PUNCT
ejpam-4612	145	5	we	we	PRON
ejpam-4612	145	6	can	can	AUX
ejpam-4612	145	7	define	define	VERB
ejpam-4612	145	8	two	two	NUM
ejpam-4612	145	9	norms	norm	NOUN
ejpam-4612	145	10	in	in	ADP
ejpam-4612	145	11	mu	mu	NOUN
ejpam-4612	145	12	,	,	PUNCT
ejpam-4612	145	13	p	p	X
ejpam-4612	145	14	,	,	PUNCT
ejpam-4612	145	15	the	the	DET
ejpam-4612	145	16	usual	usual	ADJ
ejpam-4612	145	17	norm	norm	NOUN
ejpam-4612	145	18	∥	∥	X
ejpam-4612	145	19	·	·	PUNCT
ejpam-4612	145	20	∥mu	∥mu	PROPN
ejpam-4612	145	21	,	,	PUNCT
ejpam-4612	145	22	p	p	NOUN
ejpam-4612	145	23	and	and	CCONJ
ejpam-4612	145	24	another	another	DET
ejpam-4612	145	25	new	new	ADJ
ejpam-4612	145	26	norm	norm	NOUN
ejpam-4612	145	27	(	(	PUNCT
ejpam-4612	145	28	∥	∥	X
ejpam-4612	145	29	·	·	PUNCT
ejpam-4612	145	30	∥mu,2	∥mu,2	NOUN
ejpam-4612	145	31	if	if	SCONJ
ejpam-4612	145	32	2	2	NUM
ejpam-4612	145	33	<	<	X
ejpam-4612	145	34	p	p	X
ejpam-4612	145	35	≤	≤	NUM
ejpam-4612	145	36	u	u	NOUN
ejpam-4612	145	37	<	<	X
ejpam-4612	145	38	∞	∞	PROPN
ejpam-4612	145	39	,	,	PUNCT
ejpam-4612	145	40	or	or	CCONJ
ejpam-4612	145	41	∥	∥	X
ejpam-4612	145	42	·	·	PUNCT
ejpam-4612	145	43	∥mv,2	∥mv,2	ADJ
ejpam-4612	145	44	if	if	SCONJ
ejpam-4612	145	45	1	1	NUM
ejpam-4612	145	46	≤	≤	NOUN
ejpam-4612	145	47	p	p	X
ejpam-4612	145	48	≤	≤	NUM
ejpam-4612	145	49	u	u	NOUN
ejpam-4612	145	50	<	<	X
ejpam-4612	145	51	2	2	NUM
ejpam-4612	145	52	with	with	ADP
ejpam-4612	145	53	v	v	NOUN
ejpam-4612	145	54	=	=	SYM
ejpam-4612	145	55	2up	2up	ADJ
ejpam-4612	145	56	2p−2u+up	2p−2u+up	NUM
ejpam-4612	145	57	)	)	PUNCT
ejpam-4612	145	58	.	.	PUNCT
ejpam-4612	146	1	one	one	PRON
ejpam-4612	146	2	might	might	AUX
ejpam-4612	146	3	ask	ask	VERB
ejpam-4612	146	4	whether	whether	SCONJ
ejpam-4612	146	5	∥	∥	NOUN
ejpam-4612	146	6	·	·	PUNCT
ejpam-4612	146	7	∥mv,2	∥mv,2	NUM
ejpam-4612	146	8	is	be	AUX
ejpam-4612	146	9	equivalent	equivalent	ADJ
ejpam-4612	146	10	to	to	ADP
ejpam-4612	146	11	∥	∥	PROPN
ejpam-4612	146	12	·	·	PUNCT
ejpam-4612	147	1	∥mu	∥mu	PROPN
ejpam-4612	147	2	,	,	PUNCT
ejpam-4612	147	3	p	p	NOUN
ejpam-4612	147	4	.	.	PUNCT
ejpam-4612	148	1	the	the	DET
ejpam-4612	148	2	answer	answer	NOUN
ejpam-4612	148	3	is	be	AUX
ejpam-4612	148	4	negative	negative	ADJ
ejpam-4612	148	5	.	.	PUNCT
ejpam-4612	149	1	we	we	PRON
ejpam-4612	149	2	already	already	ADV
ejpam-4612	149	3	have	have	AUX
ejpam-4612	149	4	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	149	5	≤	≤	NUM
ejpam-4612	149	6	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	149	7	,	,	PUNCT
ejpam-4612	149	8	p	p	NOUN
ejpam-4612	149	9	for	for	ADP
ejpam-4612	149	10	every	every	DET
ejpam-4612	149	11	λ	λ	PROPN
ejpam-4612	149	12	∈	∈	PROPN
ejpam-4612	149	13	mu	mu	NOUN
ejpam-4612	149	14	,	,	PUNCT
ejpam-4612	149	15	p.	p.	NOUN
ejpam-4612	150	1	the	the	DET
ejpam-4612	150	2	following	follow	VERB
ejpam-4612	150	3	proposition	proposition	NOUN
ejpam-4612	150	4	say	say	VERB
ejpam-4612	150	5	that	that	SCONJ
ejpam-4612	150	6	we	we	PRON
ejpam-4612	150	7	can	can	AUX
ejpam-4612	150	8	not	not	PART
ejpam-4612	150	9	control	control	VERB
ejpam-4612	150	10	∥λ∥mv,2	∥λ∥mv,2	NOUN
ejpam-4612	150	11	and	and	CCONJ
ejpam-4612	150	12	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	150	13	,	,	PUNCT
ejpam-4612	150	14	p	p	NOUN
ejpam-4612	150	15	for	for	ADP
ejpam-4612	150	16	every	every	DET
ejpam-4612	150	17	λ	λ	PROPN
ejpam-4612	150	18	∈	∈	PROPN
ejpam-4612	150	19	mu	mu	NOUN
ejpam-4612	150	20	,	,	PUNCT
ejpam-4612	150	21	p	p	NOUN
ejpam-4612	150	22	such	such	ADJ
ejpam-4612	150	23	that	that	SCONJ
ejpam-4612	150	24	the	the	DET
ejpam-4612	150	25	norm	norm	NOUN
ejpam-4612	150	26	∥	∥	X
ejpam-4612	150	27	·	·	PUNCT
ejpam-4612	150	28	∥mv,2	∥mv,2	NUM
ejpam-4612	150	29	is	be	AUX
ejpam-4612	150	30	not	not	PART
ejpam-4612	150	31	equivalent	equivalent	ADJ
ejpam-4612	150	32	to	to	ADP
ejpam-4612	150	33	the	the	DET
ejpam-4612	150	34	norm	norm	NOUN
ejpam-4612	151	1	∥	∥	X
ejpam-4612	151	2	·	·	PUNCT
ejpam-4612	151	3	∥mu	∥mu	PROPN
ejpam-4612	151	4	,	,	PUNCT
ejpam-4612	151	5	p	p	NOUN
ejpam-4612	151	6	.	.	PUNCT
ejpam-4612	152	1	proposition	proposition	NOUN
ejpam-4612	152	2	5	5	NUM
ejpam-4612	152	3	.	.	PUNCT
ejpam-4612	153	1	let	let	VERB
ejpam-4612	153	2	1	1	NUM
ejpam-4612	153	3	≤	≤	NOUN
ejpam-4612	153	4	p	p	NOUN
ejpam-4612	153	5	≤	≤	NUM
ejpam-4612	153	6	u	u	NOUN
ejpam-4612	153	7	<	<	X
ejpam-4612	153	8	2	2	NUM
ejpam-4612	153	9	and	and	CCONJ
ejpam-4612	153	10	v	v	NOUN
ejpam-4612	153	11	=	=	SYM
ejpam-4612	153	12	2up	2up	ADJ
ejpam-4612	153	13	2p−2u+up	2p−2u+up	PROPN
ejpam-4612	153	14	.	.	PUNCT
ejpam-4612	154	1	there	there	PRON
ejpam-4612	154	2	is	be	VERB
ejpam-4612	154	3	no	no	DET
ejpam-4612	154	4	constant	constant	ADJ
ejpam-4612	154	5	c	c	NOUN
ejpam-4612	154	6	>	>	X
ejpam-4612	154	7	0	0	NUM
ejpam-4612	155	1	such	such	ADJ
ejpam-4612	155	2	that	that	SCONJ
ejpam-4612	155	3	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	155	4	≥	≥	NOUN
ejpam-4612	155	5	c∥λ∥mu	c∥λ∥mu	PROPN
ejpam-4612	155	6	,	,	PUNCT
ejpam-4612	155	7	p	p	NOUN
ejpam-4612	155	8	for	for	ADP
ejpam-4612	155	9	every	every	DET
ejpam-4612	155	10	λ	λ	PROPN
ejpam-4612	155	11	∈	∈	PROPN
ejpam-4612	155	12	mu	mu	NOUN
ejpam-4612	155	13	,	,	PUNCT
ejpam-4612	155	14	p.	p.	NOUN
ejpam-4612	155	15	proof	proof	NOUN
ejpam-4612	155	16	.	.	PUNCT
ejpam-4612	156	1	for	for	ADP
ejpam-4612	156	2	each	each	DET
ejpam-4612	156	3	n	n	PRON
ejpam-4612	156	4	∈	∈	PROPN
ejpam-4612	156	5	n	n	CCONJ
ejpam-4612	156	6	,	,	PUNCT
ejpam-4612	156	7	take	take	VERB
ejpam-4612	156	8	u	u	NOUN
ejpam-4612	156	9	=	=	NOUN
ejpam-4612	156	10	p	p	NOUN
ejpam-4612	156	11	and	and	CCONJ
ejpam-4612	156	12	λ(n	λ(n	PRON
ejpam-4612	156	13	)	)	PUNCT
ejpam-4612	157	1	=	=	PUNCT
ejpam-4612	157	2	(	(	PUNCT
ejpam-4612	157	3	1	1	NUM
ejpam-4612	157	4	k	k	PROPN
ejpam-4612	157	5	1	1	NUM
ejpam-4612	157	6	p+	p+	NOUN
ejpam-4612	157	7	1	1	NUM
ejpam-4612	157	8	n	n	NOUN
ejpam-4612	157	9	)	)	PUNCT
ejpam-4612	157	10	with	with	ADP
ejpam-4612	157	11	λk(n	λk(n	NOUN
ejpam-4612	157	12	)	)	PUNCT
ejpam-4612	157	13	=	=	SYM
ejpam-4612	157	14	{	{	PUNCT
ejpam-4612	157	15	1	1	NUM
ejpam-4612	157	16	k	k	PROPN
ejpam-4612	157	17	1	1	NUM
ejpam-4612	157	18	p+	p+	NOUN
ejpam-4612	157	19	1	1	NUM
ejpam-4612	157	20	n	n	NOUN
ejpam-4612	157	21	,	,	PUNCT
ejpam-4612	157	22	if	if	SCONJ
ejpam-4612	157	23	k	k	PROPN
ejpam-4612	157	24	∈	∈	PROPN
ejpam-4612	157	25	n	n	PROPN
ejpam-4612	157	26	0	0	NUM
ejpam-4612	157	27	,	,	PUNCT
ejpam-4612	157	28	if	if	SCONJ
ejpam-4612	157	29	k	k	PROPN
ejpam-4612	157	30	/∈	/∈	PUNCT
ejpam-4612	158	1	n	n	INTJ
ejpam-4612	158	2	.	.	PUNCT
ejpam-4612	159	1	then	then	ADV
ejpam-4612	159	2	v	v	X
ejpam-4612	159	3	=	=	SYM
ejpam-4612	159	4	2	2	NUM
ejpam-4612	160	1	and	and	CCONJ
ejpam-4612	160	2	we	we	PRON
ejpam-4612	160	3	have	have	VERB
ejpam-4612	160	4	∥λ(n)∥2mv,2	∥λ(n)∥2mv,2	ADJ
ejpam-4612	160	5	=	=	PUNCT
ejpam-4612	160	6	∥λ(n)∥2ℓ2	∥λ(n)∥2ℓ2	PROPN
ejpam-4612	161	1	=	=	PUNCT
ejpam-4612	161	2	∑	∑	PUNCT
ejpam-4612	161	3	k∈n	k∈n	PROPN
ejpam-4612	161	4	1	1	NUM
ejpam-4612	162	1	k	k	PROPN
ejpam-4612	162	2	2	2	NUM
ejpam-4612	162	3	p	p	NOUN
ejpam-4612	162	4	+	+	CCONJ
ejpam-4612	162	5	2	2	NUM
ejpam-4612	162	6	n	n	PRON
ejpam-4612	162	7	≤	≤	NOUN
ejpam-4612	162	8	∑	∑	PUNCT
ejpam-4612	162	9	k∈n	k∈n	PROPN
ejpam-4612	162	10	1	1	NUM
ejpam-4612	162	11	k	k	PROPN
ejpam-4612	162	12	1	1	NUM
ejpam-4612	162	13	p	p	X
ejpam-4612	162	14	<	<	X
ejpam-4612	162	15	∞	∞	NUM
ejpam-4612	162	16	while	while	SCONJ
ejpam-4612	162	17	∥λ(n)∥pmu	∥λ(n)∥pmu	PROPN
ejpam-4612	162	18	,	,	PUNCT
ejpam-4612	162	19	p	p	NOUN
ejpam-4612	162	20	=	=	NOUN
ejpam-4612	162	21	∥λ(n)∥	∥λ(n)∥	NOUN
ejpam-4612	162	22	p	p	NOUN
ejpam-4612	162	23	ℓp	ℓp	NOUN
ejpam-4612	162	24	=	=	PUNCT
ejpam-4612	162	25	∑	∑	NOUN
ejpam-4612	162	26	k∈n	k∈n	PROPN
ejpam-4612	162	27	1	1	NUM
ejpam-4612	162	28	k1	k1	PROPN
ejpam-4612	162	29	+	+	X
ejpam-4612	162	30	p	p	NOUN
ejpam-4612	162	31	n	n	X
ejpam-4612	162	32	<	<	X
ejpam-4612	162	33	∞	∞	NOUN
ejpam-4612	162	34	we	we	PRON
ejpam-4612	162	35	can	can	AUX
ejpam-4612	162	36	see	see	VERB
ejpam-4612	162	37	that	that	SCONJ
ejpam-4612	162	38	∥λ(n)∥mv,2	∥λ(n)∥mv,2	NOUN
ejpam-4612	162	39	is	be	AUX
ejpam-4612	162	40	bounded	bound	VERB
ejpam-4612	162	41	by	by	ADP
ejpam-4612	162	42	a	a	DET
ejpam-4612	162	43	fix	fix	NOUN
ejpam-4612	162	44	number	number	NOUN
ejpam-4612	162	45	independent	independent	ADJ
ejpam-4612	162	46	of	of	ADP
ejpam-4612	162	47	n	n	CCONJ
ejpam-4612	162	48	,	,	PUNCT
ejpam-4612	162	49	while	while	SCONJ
ejpam-4612	162	50	∥λ(n)∥mu	∥λ(n)∥mu	PROPN
ejpam-4612	162	51	,	,	PUNCT
ejpam-4612	162	52	p	p	NOUN
ejpam-4612	162	53	is	be	AUX
ejpam-4612	162	54	dependent	dependent	ADJ
ejpam-4612	162	55	on	on	ADP
ejpam-4612	162	56	n	n	PRON
ejpam-4612	162	57	and	and	CCONJ
ejpam-4612	162	58	tends	tend	VERB
ejpam-4612	162	59	to	to	ADP
ejpam-4612	162	60	∞	∞	PROPN
ejpam-4612	162	61	as	as	ADP
ejpam-4612	162	62	n	n	PROPN
ejpam-4612	162	63	→	→	SYM
ejpam-4612	162	64	∞.	∞.	PROPN
ejpam-4612	162	65	hence	hence	ADV
ejpam-4612	162	66	∥λ(n)∥mv,2	∥λ(n)∥mv,2	ADJ
ejpam-4612	162	67	∥λ(n)∥mu	∥λ(n)∥mu	PROPN
ejpam-4612	162	68	,	,	PUNCT
ejpam-4612	162	69	p	p	X
ejpam-4612	162	70	→	→	SYM
ejpam-4612	162	71	0	0	NUM
ejpam-4612	162	72	as	as	ADP
ejpam-4612	162	73	n	n	NOUN
ejpam-4612	162	74	→	→	SYM
ejpam-4612	162	75	∞.	∞.	PROPN
ejpam-4612	162	76	so	so	ADV
ejpam-4612	162	77	,	,	PUNCT
ejpam-4612	162	78	there	there	PRON
ejpam-4612	162	79	is	be	VERB
ejpam-4612	162	80	no	no	DET
ejpam-4612	162	81	constant	constant	ADJ
ejpam-4612	162	82	c	c	NOUN
ejpam-4612	162	83	>	>	X
ejpam-4612	162	84	0	0	NUM
ejpam-4612	163	1	such	such	ADJ
ejpam-4612	163	2	that	that	SCONJ
ejpam-4612	163	3	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	163	4	≥	≥	NOUN
ejpam-4612	163	5	c∥λ∥mu	c∥λ∥mu	PROPN
ejpam-4612	163	6	,	,	PUNCT
ejpam-4612	163	7	p	p	NOUN
ejpam-4612	163	8	for	for	ADP
ejpam-4612	163	9	every	every	DET
ejpam-4612	163	10	λ	λ	PROPN
ejpam-4612	163	11	∈	∈	PROPN
ejpam-4612	163	12	mu	mu	NOUN
ejpam-4612	163	13	,	,	PUNCT
ejpam-4612	163	14	p.	p.	NOUN
ejpam-4612	163	15	■	■	PUNCT
ejpam-4612	163	16	m.	m.	NOUN
ejpam-4612	163	17	jakfar	jakfar	NOUN
ejpam-4612	163	18	et	et	PROPN
ejpam-4612	163	19	al	al	PROPN
ejpam-4612	163	20	.	.	PUNCT
ejpam-4612	163	21	/	/	SYM
ejpam-4612	163	22	eur	eur	PROPN
ejpam-4612	163	23	.	.	PUNCT
ejpam-4612	164	1	j.	j.	PROPN
ejpam-4612	164	2	pure	pure	PROPN
ejpam-4612	164	3	appl	appl	PROPN
ejpam-4612	164	4	.	.	PROPN
ejpam-4612	164	5	math	math	PROPN
ejpam-4612	164	6	,	,	PUNCT
ejpam-4612	164	7	16	16	NUM
ejpam-4612	164	8	(	(	PUNCT
ejpam-4612	164	9	1	1	NUM
ejpam-4612	164	10	)	)	PUNCT
ejpam-4612	164	11	(	(	PUNCT
ejpam-4612	164	12	2023	2023	NUM
ejpam-4612	164	13	)	)	PUNCT
ejpam-4612	164	14	,	,	PUNCT
ejpam-4612	164	15	144	144	NUM
ejpam-4612	164	16	-	-	SYM
ejpam-4612	164	17	155	155	NUM
ejpam-4612	164	18	152	152	NUM
ejpam-4612	164	19	proposition	proposition	NOUN
ejpam-4612	164	20	6	6	NUM
ejpam-4612	164	21	.	.	PUNCT
ejpam-4612	165	1	let	let	VERB
ejpam-4612	165	2	2	2	NUM
ejpam-4612	165	3	<	<	X
ejpam-4612	165	4	p	p	X
ejpam-4612	165	5	≤	≤	NUM
ejpam-4612	165	6	u	u	NOUN
ejpam-4612	165	7	<	<	X
ejpam-4612	165	8	∞.	∞.	PROPN
ejpam-4612	165	9	there	there	PRON
ejpam-4612	165	10	is	be	VERB
ejpam-4612	165	11	no	no	DET
ejpam-4612	165	12	constant	constant	ADJ
ejpam-4612	165	13	c	c	NOUN
ejpam-4612	165	14	>	>	X
ejpam-4612	165	15	0	0	NUM
ejpam-4612	166	1	such	such	ADJ
ejpam-4612	166	2	that	that	SCONJ
ejpam-4612	166	3	∥λ∥mu	∥λ∥mu	PROPN
ejpam-4612	166	4	,	,	PUNCT
ejpam-4612	166	5	p	p	ADJ
ejpam-4612	166	6	≤	≤	NUM
ejpam-4612	166	7	c∥λ∥mu,2	c∥λ∥mu,2	NOUN
ejpam-4612	166	8	for	for	ADP
ejpam-4612	166	9	every	every	DET
ejpam-4612	166	10	λ	λ	PROPN
ejpam-4612	166	11	∈	∈	PROPN
ejpam-4612	166	12	mu	mu	NOUN
ejpam-4612	166	13	,	,	PUNCT
ejpam-4612	166	14	p.	p.	NOUN
ejpam-4612	166	15	proof	proof	NOUN
ejpam-4612	166	16	.	.	PUNCT
ejpam-4612	167	1	let	let	VERB
ejpam-4612	167	2	2	2	NUM
ejpam-4612	167	3	<	<	X
ejpam-4612	167	4	p	p	X
ejpam-4612	167	5	≤	≤	NUM
ejpam-4612	167	6	u	u	NOUN
ejpam-4612	167	7	<	<	X
ejpam-4612	167	8	∞.	∞.	PROPN
ejpam-4612	167	9	take	take	VERB
ejpam-4612	167	10	u	u	NOUN
ejpam-4612	167	11	=	=	PROPN
ejpam-4612	167	12	p.	p.	NOUN
ejpam-4612	167	13	suppose	suppose	VERB
ejpam-4612	167	14	that	that	SCONJ
ejpam-4612	167	15	a	a	DET
ejpam-4612	167	16	constant	constant	ADJ
ejpam-4612	167	17	exists	exist	NOUN
ejpam-4612	167	18	.	.	PUNCT
ejpam-4612	168	1	then	then	ADV
ejpam-4612	168	2	,	,	PUNCT
ejpam-4612	168	3	for	for	ADP
ejpam-4612	168	4	λ(n	λ(n	PRON
ejpam-4612	168	5	)	)	PUNCT
ejpam-4612	168	6	=	=	SYM
ejpam-4612	168	7	(	(	PUNCT
ejpam-4612	168	8	.	.	PUNCT
ejpam-4612	168	9	.	.	PUNCT
ejpam-4612	168	10	.	.	PUNCT
ejpam-4612	169	1	,	,	PUNCT
ejpam-4612	169	2	0	0	NUM
ejpam-4612	169	3	,	,	PUNCT
ejpam-4612	169	4	0	0	NUM
ejpam-4612	169	5	,	,	PUNCT
ejpam-4612	169	6	1	1	NUM
ejpam-4612	169	7	,	,	PUNCT
ejpam-4612	169	8	0	0	NUM
ejpam-4612	169	9	,	,	PUNCT
ejpam-4612	169	10	0	0	NUM
ejpam-4612	169	11	,	,	PUNCT
ejpam-4612	169	12	.	.	PUNCT
ejpam-4612	169	13	.	.	PUNCT
ejpam-4612	170	1	.	.	PUNCT
ejpam-4612	171	1	,	,	PUNCT
ejpam-4612	171	2	0	0	NUM
ejpam-4612	171	3	,	,	PUNCT
ejpam-4612	171	4	1	1	NUM
ejpam-4612	171	5	,	,	PUNCT
ejpam-4612	171	6	0	0	NUM
ejpam-4612	171	7	,	,	PUNCT
ejpam-4612	171	8	.	.	PUNCT
ejpam-4612	171	9	.	.	PUNCT
ejpam-4612	172	1	.	.	PUNCT
ejpam-4612	172	2	)	)	PUNCT
ejpam-4612	172	3	,	,	PUNCT
ejpam-4612	172	4	where	where	SCONJ
ejpam-4612	172	5	the	the	DET
ejpam-4612	172	6	first	first	ADJ
ejpam-4612	172	7	1	1	NUM
ejpam-4612	172	8	is	be	AUX
ejpam-4612	172	9	at	at	ADP
ejpam-4612	172	10	k	k	PROPN
ejpam-4612	172	11	=	=	SYM
ejpam-4612	172	12	1	1	NUM
ejpam-4612	172	13	and	and	CCONJ
ejpam-4612	172	14	the	the	DET
ejpam-4612	172	15	second	second	ADJ
ejpam-4612	172	16	1	1	NUM
ejpam-4612	172	17	is	be	AUX
ejpam-4612	172	18	the	the	DET
ejpam-4612	172	19	(	(	PUNCT
ejpam-4612	172	20	n+	n+	X
ejpam-4612	172	21	1)th	1)th	NOUN
ejpam-4612	172	22	-	-	PUNCT
ejpam-4612	172	23	term	term	NOUN
ejpam-4612	172	24	,	,	PUNCT
ejpam-4612	172	25	we	we	PRON
ejpam-4612	172	26	have	have	VERB
ejpam-4612	172	27	2	2	NUM
ejpam-4612	172	28	1	1	NUM
ejpam-4612	172	29	p	p	NOUN
ejpam-4612	172	30	≤	≤	NUM
ejpam-4612	172	31	c	c	NOUN
ejpam-4612	172	32	1	1	NUM
ejpam-4612	172	33	(	(	PUNCT
ejpam-4612	172	34	2n+	2n+	NUM
ejpam-4612	172	35	1	1	NUM
ejpam-4612	172	36	)	)	PUNCT
ejpam-4612	172	37	(	(	PUNCT
ejpam-4612	172	38	1	1	NUM
ejpam-4612	172	39	2	2	NUM
ejpam-4612	172	40	−	−	NOUN
ejpam-4612	172	41	1	1	NUM
ejpam-4612	172	42	p	p	NOUN
ejpam-4612	172	43	)	)	PUNCT
ejpam-4612	173	1	√	√	ADP
ejpam-4612	173	2	2	2	NUM
ejpam-4612	173	3	.	.	PUNCT
ejpam-4612	174	1	but	but	CCONJ
ejpam-4612	174	2	this	this	PRON
ejpam-4612	174	3	can	can	AUX
ejpam-4612	174	4	not	not	PART
ejpam-4612	174	5	be	be	AUX
ejpam-4612	174	6	true	true	ADJ
ejpam-4612	174	7	,	,	PUNCT
ejpam-4612	174	8	since	since	SCONJ
ejpam-4612	174	9	1	1	NUM
ejpam-4612	174	10	(	(	PUNCT
ejpam-4612	174	11	2n+1	2n+1	NOUN
ejpam-4612	174	12	)	)	PUNCT
ejpam-4612	174	13	(	(	PUNCT
ejpam-4612	174	14	1	1	NUM
ejpam-4612	174	15	2	2	NUM
ejpam-4612	174	16	−	−	NOUN
ejpam-4612	174	17	1	1	NUM
ejpam-4612	174	18	p	p	NOUN
ejpam-4612	174	19	)	)	PUNCT
ejpam-4612	174	20	→	→	SYM
ejpam-4612	174	21	0	0	NUM
ejpam-4612	174	22	as	as	SCONJ
ejpam-4612	174	23	n	n	PROPN
ejpam-4612	174	24	→	→	SYM
ejpam-4612	174	25	∞.	∞.	PROPN
ejpam-4612	174	26	■	■	PUNCT
ejpam-4612	174	27	remark	remark	VERB
ejpam-4612	174	28	4	4	NUM
ejpam-4612	174	29	.	.	PUNCT
ejpam-4612	174	30	proposition	proposition	NOUN
ejpam-4612	174	31	5	5	NUM
ejpam-4612	174	32	and	and	CCONJ
ejpam-4612	174	33	6	6	NUM
ejpam-4612	174	34	say	say	VERB
ejpam-4612	174	35	that	that	SCONJ
ejpam-4612	174	36	in	in	ADP
ejpam-4612	174	37	the	the	DET
ejpam-4612	174	38	discrete	discrete	ADJ
ejpam-4612	174	39	morrey	morrey	PROPN
ejpam-4612	174	40	space	space	NOUN
ejpam-4612	174	41	,	,	PUNCT
ejpam-4612	174	42	the	the	DET
ejpam-4612	174	43	usual	usual	ADJ
ejpam-4612	174	44	norm	norm	NOUN
ejpam-4612	174	45	and	and	CCONJ
ejpam-4612	174	46	the	the	DET
ejpam-4612	174	47	second	second	ADJ
ejpam-4612	174	48	norm	norm	NOUN
ejpam-4612	174	49	are	be	AUX
ejpam-4612	174	50	not	not	PART
ejpam-4612	174	51	equivalent	equivalent	ADJ
ejpam-4612	174	52	.	.	PUNCT
ejpam-4612	175	1	let	let	VERB
ejpam-4612	175	2	1	1	NUM
ejpam-4612	175	3	≤	≤	NOUN
ejpam-4612	175	4	p	p	NOUN
ejpam-4612	175	5	≤	≤	NUM
ejpam-4612	175	6	u	u	NOUN
ejpam-4612	175	7	<	<	X
ejpam-4612	175	8	2	2	NUM
ejpam-4612	175	9	and	and	CCONJ
ejpam-4612	175	10	v	v	NOUN
ejpam-4612	175	11	=	=	SYM
ejpam-4612	175	12	2up	2up	ADJ
ejpam-4612	175	13	2p−2u+up	2p−2u+up	PROPN
ejpam-4612	175	14	.	.	PUNCT
ejpam-4612	176	1	as	as	SCONJ
ejpam-4612	176	2	we	we	PRON
ejpam-4612	176	3	have	have	AUX
ejpam-4612	176	4	seen	see	VERB
ejpam-4612	176	5	in	in	ADP
ejpam-4612	176	6	the	the	DET
ejpam-4612	176	7	previous	previous	ADJ
ejpam-4612	176	8	section	section	NOUN
ejpam-4612	176	9	,	,	PUNCT
ejpam-4612	176	10	every	every	DET
ejpam-4612	176	11	sequence	sequence	NOUN
ejpam-4612	176	12	λ	λ	X
ejpam-4612	176	13	∈	∈	NOUN
ejpam-4612	176	14	mu	mu	NOUN
ejpam-4612	176	15	,	,	PUNCT
ejpam-4612	176	16	p	p	PROPN
ejpam-4612	176	17	has	have	VERB
ejpam-4612	176	18	∥λ∥v,2	∥λ∥v,2	NOUN
ejpam-4612	176	19	<	<	X
ejpam-4612	176	20	∞.	∞.	PROPN
ejpam-4612	176	21	this	this	PRON
ejpam-4612	176	22	suggests	suggest	VERB
ejpam-4612	176	23	that	that	SCONJ
ejpam-4612	176	24	mu	mu	NOUN
ejpam-4612	176	25	,	,	PUNCT
ejpam-4612	176	26	p	p	PROPN
ejpam-4612	176	27	⊂	⊂	PROPN
ejpam-4612	176	28	mv,2	mv,2	PROPN
ejpam-4612	176	29	.	.	PUNCT
ejpam-4612	177	1	we	we	PRON
ejpam-4612	177	2	shall	shall	AUX
ejpam-4612	177	3	now	now	ADV
ejpam-4612	177	4	discuss	discuss	VERB
ejpam-4612	177	5	some	some	DET
ejpam-4612	177	6	properties	property	NOUN
ejpam-4612	177	7	of	of	ADP
ejpam-4612	177	8	this	this	DET
ejpam-4612	177	9	space	space	NOUN
ejpam-4612	177	10	.	.	PUNCT
ejpam-4612	178	1	first	first	ADV
ejpam-4612	178	2	,	,	PUNCT
ejpam-4612	178	3	we	we	PRON
ejpam-4612	178	4	have	have	VERB
ejpam-4612	178	5	the	the	DET
ejpam-4612	178	6	following	follow	VERB
ejpam-4612	178	7	proposition	proposition	NOUN
ejpam-4612	178	8	,	,	PUNCT
ejpam-4612	178	9	which	which	PRON
ejpam-4612	178	10	describes	describe	VERB
ejpam-4612	178	11	the	the	DET
ejpam-4612	178	12	relationship	relationship	NOUN
ejpam-4612	178	13	between	between	ADP
ejpam-4612	178	14	mu	mu	PROPN
ejpam-4612	178	15	,	,	PUNCT
ejpam-4612	178	16	p	p	NOUN
ejpam-4612	178	17	and	and	CCONJ
ejpam-4612	178	18	mv,2	mv,2	PROPN
ejpam-4612	178	19	.	.	PUNCT
ejpam-4612	179	1	proposition	proposition	NOUN
ejpam-4612	179	2	7	7	NUM
ejpam-4612	179	3	.	.	PUNCT
ejpam-4612	179	4	as	as	ADP
ejpam-4612	179	5	a	a	DET
ejpam-4612	179	6	set	set	NOUN
ejpam-4612	179	7	,	,	PUNCT
ejpam-4612	179	8	we	we	PRON
ejpam-4612	179	9	have	have	VERB
ejpam-4612	179	10	mu	mu	NOUN
ejpam-4612	179	11	,	,	PUNCT
ejpam-4612	179	12	p	p	PROPN
ejpam-4612	179	13	⊂	⊂	PROPN
ejpam-4612	179	14	mv,2	mv,2	PROPN
ejpam-4612	179	15	and	and	CCONJ
ejpam-4612	179	16	the	the	DET
ejpam-4612	179	17	inclusion	inclusion	NOUN
ejpam-4612	179	18	is	be	AUX
ejpam-4612	179	19	strict	strict	ADJ
ejpam-4612	179	20	.	.	PUNCT
ejpam-4612	180	1	proof	proof	NOUN
ejpam-4612	180	2	.	.	PUNCT
ejpam-4612	181	1	let	let	VERB
ejpam-4612	181	2	1	1	NUM
ejpam-4612	181	3	≤	≤	NOUN
ejpam-4612	181	4	p	p	NOUN
ejpam-4612	181	5	≤	≤	NUM
ejpam-4612	181	6	u	u	NOUN
ejpam-4612	181	7	<	<	X
ejpam-4612	181	8	2	2	NUM
ejpam-4612	181	9	,	,	PUNCT
ejpam-4612	181	10	v	v	NOUN
ejpam-4612	181	11	=	=	SYM
ejpam-4612	181	12	2up	2up	ADJ
ejpam-4612	181	13	2p−2u+up	2p−2u+up	NUM
ejpam-4612	181	14	,	,	PUNCT
ejpam-4612	181	15	and	and	CCONJ
ejpam-4612	181	16	λ	λ	PROPN
ejpam-4612	181	17	∈	∈	PROPN
ejpam-4612	181	18	mv,2	mv,2	PROPN
ejpam-4612	181	19	.	.	PUNCT
ejpam-4612	182	1	it	it	PRON
ejpam-4612	182	2	follows	follow	VERB
ejpam-4612	182	3	from	from	ADP
ejpam-4612	182	4	corollary	corollary	ADJ
ejpam-4612	182	5	3	3	NUM
ejpam-4612	182	6	that	that	PRON
ejpam-4612	182	7	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	182	8	≤	≤	NUM
ejpam-4612	182	9	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	182	10	,	,	PUNCT
ejpam-4612	182	11	p	p	NOUN
ejpam-4612	182	12	which	which	PRON
ejpam-4612	182	13	means	mean	VERB
ejpam-4612	182	14	that	that	SCONJ
ejpam-4612	182	15	λ	λ	PROPN
ejpam-4612	182	16	∈	∈	PROPN
ejpam-4612	182	17	mv,2	mv,2	PROPN
ejpam-4612	182	18	.	.	PUNCT
ejpam-4612	183	1	to	to	PART
ejpam-4612	183	2	show	show	VERB
ejpam-4612	183	3	that	that	SCONJ
ejpam-4612	183	4	the	the	DET
ejpam-4612	183	5	inclusion	inclusion	NOUN
ejpam-4612	183	6	is	be	AUX
ejpam-4612	183	7	strict	strict	ADJ
ejpam-4612	183	8	,	,	PUNCT
ejpam-4612	183	9	we	we	PRON
ejpam-4612	183	10	need	need	VERB
ejpam-4612	183	11	to	to	PART
ejpam-4612	183	12	find	find	VERB
ejpam-4612	183	13	λ	λ	X
ejpam-4612	183	14	=	=	PRON
ejpam-4612	183	15	(	(	PUNCT
ejpam-4612	183	16	λk)k∈z	λk)k∈z	NUM
ejpam-4612	183	17	such	such	ADJ
ejpam-4612	183	18	that	that	SCONJ
ejpam-4612	183	19	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	183	20	<	<	X
ejpam-4612	183	21	∞	∞	PROPN
ejpam-4612	183	22	but	but	CCONJ
ejpam-4612	183	23	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	183	24	,	,	PUNCT
ejpam-4612	183	25	p	p	NOUN
ejpam-4612	183	26	=	=	SYM
ejpam-4612	183	27	∞.	∞.	PROPN
ejpam-4612	183	28	choose	choose	VERB
ejpam-4612	183	29	u	u	NOUN
ejpam-4612	183	30	=	=	PROPN
ejpam-4612	183	31	p	p	PROPN
ejpam-4612	183	32	and	and	CCONJ
ejpam-4612	183	33	λ	λ	X
ejpam-4612	183	34	=	=	SYM
ejpam-4612	183	35	(	(	PUNCT
ejpam-4612	183	36	λk)k∈z	λk)k∈z	X
ejpam-4612	183	37	with	with	ADP
ejpam-4612	183	38	λk	λk	PROPN
ejpam-4612	183	39	=	=	PUNCT
ejpam-4612	183	40	{	{	PUNCT
ejpam-4612	183	41	(	(	PUNCT
ejpam-4612	183	42	1	1	NUM
ejpam-4612	183	43	k	k	NOUN
ejpam-4612	183	44	)	)	PUNCT
ejpam-4612	183	45	1	1	NUM
ejpam-4612	183	46	p	p	NOUN
ejpam-4612	183	47	,	,	PUNCT
ejpam-4612	183	48	if	if	SCONJ
ejpam-4612	183	49	k	k	PROPN
ejpam-4612	183	50	̸=	̸=	PROPN
ejpam-4612	183	51	0	0	NUM
ejpam-4612	183	52	0	0	NUM
ejpam-4612	183	53	,	,	PUNCT
ejpam-4612	183	54	if	if	SCONJ
ejpam-4612	183	55	k	k	PROPN
ejpam-4612	183	56	=	=	NOUN
ejpam-4612	183	57	0	0	PROPN
ejpam-4612	183	58	.	.	PUNCT
ejpam-4612	184	1	hence	hence	ADV
ejpam-4612	184	2	∥λ∥mv,2	∥λ∥mv,2	VERB
ejpam-4612	184	3	=	=	PUNCT
ejpam-4612	184	4	∥λ∥m2,2	∥λ∥m2,2	PROPN
ejpam-4612	184	5	=	=	SYM
ejpam-4612	184	6	(	(	PUNCT
ejpam-4612	184	7	∑	∑	ADV
ejpam-4612	184	8	k∈sm	k∈sm	PROPN
ejpam-4612	184	9	,	,	PUNCT
ejpam-4612	184	10	n	n	PRON
ejpam-4612	184	11	∣∣(1	∣∣(1	PROPN
ejpam-4612	184	12	k	k	PROPN
ejpam-4612	184	13	)	)	PUNCT
ejpam-4612	184	14	1	1	NUM
ejpam-4612	184	15	p	p	NOUN
ejpam-4612	184	16	∣∣2	∣∣2	PROPN
ejpam-4612	184	17	)	)	PUNCT
ejpam-4612	184	18	1	1	NUM
ejpam-4612	184	19	2	2	NUM
ejpam-4612	184	20	=	=	SYM
ejpam-4612	184	21	(	(	PUNCT
ejpam-4612	184	22	2	2	NUM
ejpam-4612	184	23	∑	∑	PROPN
ejpam-4612	184	24	k∈n	k∈n	PROPN
ejpam-4612	184	25	(	(	PUNCT
ejpam-4612	184	26	1	1	NUM
ejpam-4612	184	27	k	k	NOUN
ejpam-4612	184	28	)	)	PUNCT
ejpam-4612	184	29	2	2	NUM
ejpam-4612	184	30	p	p	NOUN
ejpam-4612	184	31	)	)	PUNCT
ejpam-4612	184	32	1	1	NUM
ejpam-4612	184	33	2	2	NUM
ejpam-4612	184	34	<	<	X
ejpam-4612	184	35	∞	∞	NUM
ejpam-4612	184	36	while	while	SCONJ
ejpam-4612	184	37	∥λ∥mu	∥λ∥mu	NOUN
ejpam-4612	184	38	,	,	PUNCT
ejpam-4612	184	39	p	p	NOUN
ejpam-4612	184	40	=	=	SYM
ejpam-4612	184	41	∥λ∥mp	∥λ∥mp	PROPN
ejpam-4612	184	42	,	,	PUNCT
ejpam-4612	184	43	p	p	NOUN
ejpam-4612	184	44	=	=	SYM
ejpam-4612	184	45	(	(	PUNCT
ejpam-4612	184	46	∑	∑	ADV
ejpam-4612	184	47	k∈sm	k∈sm	PROPN
ejpam-4612	184	48	,	,	PUNCT
ejpam-4612	184	49	n	n	PRON
ejpam-4612	184	50	∣∣(1	∣∣(1	PROPN
ejpam-4612	184	51	k	k	PROPN
ejpam-4612	184	52	)	)	PUNCT
ejpam-4612	184	53	1	1	NUM
ejpam-4612	184	54	p	p	NOUN
ejpam-4612	184	55	∣∣p	∣∣p	PROPN
ejpam-4612	184	56	)	)	PUNCT
ejpam-4612	184	57	1	1	NUM
ejpam-4612	184	58	p	p	NOUN
ejpam-4612	184	59	=	=	PUNCT
ejpam-4612	184	60	(	(	PUNCT
ejpam-4612	184	61	2	2	NUM
ejpam-4612	184	62	∑	∑	PROPN
ejpam-4612	184	63	k∈n	k∈n	PROPN
ejpam-4612	184	64	(	(	PUNCT
ejpam-4612	184	65	1	1	NUM
ejpam-4612	184	66	k	k	NOUN
ejpam-4612	184	67	)	)	PUNCT
ejpam-4612	184	68	)	)	PUNCT
ejpam-4612	184	69	1	1	NUM
ejpam-4612	185	1	p	p	NOUN
ejpam-4612	185	2	=	=	SYM
ejpam-4612	185	3	∞.	∞.	PROPN
ejpam-4612	185	4	this	this	PRON
ejpam-4612	185	5	means	mean	VERB
ejpam-4612	185	6	that	that	SCONJ
ejpam-4612	185	7	λ	λ	NOUN
ejpam-4612	185	8	is	be	AUX
ejpam-4612	185	9	in	in	ADP
ejpam-4612	185	10	mv,2	mv,2	NOUN
ejpam-4612	185	11	but	but	CCONJ
ejpam-4612	185	12	not	not	PART
ejpam-4612	185	13	in	in	ADP
ejpam-4612	185	14	mu	mu	NOUN
ejpam-4612	185	15	,	,	PUNCT
ejpam-4612	185	16	p.	p.	NOUN
ejpam-4612	185	17	■	■	PUNCT
ejpam-4612	185	18	proposition	proposition	NOUN
ejpam-4612	185	19	8	8	NUM
ejpam-4612	185	20	.	.	PUNCT
ejpam-4612	186	1	the	the	DET
ejpam-4612	186	2	space	space	NOUN
ejpam-4612	186	3	(	(	PUNCT
ejpam-4612	186	4	mv,2	mv,2	NOUN
ejpam-4612	186	5	,	,	PUNCT
ejpam-4612	186	6	∥	∥	X
ejpam-4612	186	7	·	·	PUNCT
ejpam-4612	186	8	∥mv,2	∥mv,2	NUM
ejpam-4612	186	9	)	)	PUNCT
ejpam-4612	186	10	is	be	AUX
ejpam-4612	186	11	complete	complete	ADJ
ejpam-4612	186	12	.	.	PUNCT
ejpam-4612	187	1	accordingly	accordingly	ADV
ejpam-4612	187	2	,	,	PUNCT
ejpam-4612	187	3	(	(	PUNCT
ejpam-4612	187	4	mv,2	mv,2	NOUN
ejpam-4612	187	5	,	,	PUNCT
ejpam-4612	187	6	⟨	⟨	NOUN
ejpam-4612	187	7	·	·	PUNCT
ejpam-4612	187	8	,	,	PUNCT
ejpam-4612	187	9	·	·	PUNCT
ejpam-4612	187	10	⟩mv,2	⟩mv,2	X
ejpam-4612	187	11	)	)	PUNCT
ejpam-4612	187	12	is	be	AUX
ejpam-4612	187	13	a	a	DET
ejpam-4612	187	14	hilbert	hilbert	NOUN
ejpam-4612	187	15	space	space	NOUN
ejpam-4612	187	16	.	.	PUNCT
ejpam-4612	188	1	references	reference	NOUN
ejpam-4612	188	2	153	153	NUM
ejpam-4612	188	3	proof	proof	NOUN
ejpam-4612	188	4	.	.	PUNCT
ejpam-4612	189	1	based	base	VERB
ejpam-4612	189	2	on	on	ADP
ejpam-4612	189	3	proposition	proposition	NOUN
ejpam-4612	189	4	1	1	NUM
ejpam-4612	189	5	and	and	CCONJ
ejpam-4612	189	6	theorem	theorem	VERB
ejpam-4612	189	7	1	1	NUM
ejpam-4612	189	8	,	,	PUNCT
ejpam-4612	189	9	the	the	DET
ejpam-4612	189	10	space	space	NOUN
ejpam-4612	189	11	mv,2	mv,2	PROPN
ejpam-4612	189	12	is	be	AUX
ejpam-4612	189	13	a	a	DET
ejpam-4612	189	14	complete	complete	ADJ
ejpam-4612	189	15	.	.	PUNCT
ejpam-4612	190	1	so	so	ADV
ejpam-4612	190	2	,	,	PUNCT
ejpam-4612	190	3	(	(	PUNCT
ejpam-4612	190	4	mv,2	mv,2	NOUN
ejpam-4612	190	5	,	,	PUNCT
ejpam-4612	190	6	⟨	⟨	NOUN
ejpam-4612	190	7	·	·	PUNCT
ejpam-4612	190	8	,	,	PUNCT
ejpam-4612	190	9	·	·	PUNCT
ejpam-4612	190	10	⟩mv,2	⟩mv,2	X
ejpam-4612	190	11	)	)	PUNCT
ejpam-4612	190	12	is	be	AUX
ejpam-4612	190	13	a	a	DET
ejpam-4612	190	14	hilbert	hilbert	NOUN
ejpam-4612	190	15	space	space	NOUN
ejpam-4612	190	16	.	.	PUNCT
ejpam-4612	191	1	■	■	PUNCT
ejpam-4612	191	2	4	4	X
ejpam-4612	191	3	.	.	X
ejpam-4612	191	4	concluding	conclude	VERB
ejpam-4612	191	5	remarks	remark	NOUN
ejpam-4612	191	6	we	we	PRON
ejpam-4612	191	7	have	have	AUX
ejpam-4612	191	8	shown	show	VERB
ejpam-4612	191	9	the	the	DET
ejpam-4612	191	10	space	space	NOUN
ejpam-4612	191	11	mu	mu	NOUN
ejpam-4612	191	12	,	,	PUNCT
ejpam-4612	191	13	p	p	PROPN
ejpam-4612	191	14	can	can	AUX
ejpam-4612	191	15	be	be	AUX
ejpam-4612	191	16	equipped	equip	VERB
ejpam-4612	191	17	with	with	ADP
ejpam-4612	191	18	an	an	DET
ejpam-4612	191	19	inner	inner	ADJ
ejpam-4612	191	20	product	product	NOUN
ejpam-4612	191	21	and	and	CCONJ
ejpam-4612	191	22	its	its	PRON
ejpam-4612	191	23	induced	induced	ADJ
ejpam-4612	191	24	norm	norm	NOUN
ejpam-4612	191	25	.	.	PUNCT
ejpam-4612	192	1	so	so	ADV
ejpam-4612	192	2	,	,	PUNCT
ejpam-4612	192	3	we	we	PRON
ejpam-4612	192	4	can	can	AUX
ejpam-4612	192	5	define	define	VERB
ejpam-4612	192	6	two	two	NUM
ejpam-4612	192	7	norms	norm	NOUN
ejpam-4612	192	8	in	in	ADP
ejpam-4612	192	9	mu	mu	NOUN
ejpam-4612	192	10	,	,	PUNCT
ejpam-4612	192	11	p	p	X
ejpam-4612	192	12	,	,	PUNCT
ejpam-4612	192	13	the	the	DET
ejpam-4612	192	14	standard	standard	ADJ
ejpam-4612	192	15	norm	norm	NOUN
ejpam-4612	192	16	∥	∥	X
ejpam-4612	192	17	·	·	PUNCT
ejpam-4612	192	18	∥mu	∥mu	PROPN
ejpam-4612	192	19	,	,	PUNCT
ejpam-4612	192	20	p	p	NOUN
ejpam-4612	192	21	and	and	CCONJ
ejpam-4612	192	22	another	another	DET
ejpam-4612	192	23	new	new	ADJ
ejpam-4612	192	24	norm	norm	NOUN
ejpam-4612	192	25	(	(	PUNCT
ejpam-4612	192	26	∥	∥	X
ejpam-4612	192	27	·	·	PUNCT
ejpam-4612	192	28	∥mu,2	∥mu,2	NOUN
ejpam-4612	192	29	if	if	SCONJ
ejpam-4612	192	30	2	2	NUM
ejpam-4612	192	31	<	<	X
ejpam-4612	192	32	p	p	X
ejpam-4612	192	33	≤	≤	NUM
ejpam-4612	192	34	u	u	NOUN
ejpam-4612	192	35	<	<	X
ejpam-4612	192	36	∞	∞	PROPN
ejpam-4612	192	37	,	,	PUNCT
ejpam-4612	192	38	or	or	CCONJ
ejpam-4612	192	39	∥	∥	X
ejpam-4612	192	40	·	·	PUNCT
ejpam-4612	192	41	∥mv,2	∥mv,2	ADJ
ejpam-4612	192	42	if	if	SCONJ
ejpam-4612	192	43	1	1	NUM
ejpam-4612	192	44	≤	≤	NOUN
ejpam-4612	192	45	p	p	X
ejpam-4612	192	46	≤	≤	NUM
ejpam-4612	192	47	u	u	NOUN
ejpam-4612	192	48	<	<	X
ejpam-4612	192	49	2	2	NUM
ejpam-4612	192	50	with	with	ADP
ejpam-4612	192	51	v	v	NOUN
ejpam-4612	192	52	=	=	SYM
ejpam-4612	192	53	2up	2up	ADJ
ejpam-4612	192	54	2p−2u+up	2p−2u+up	NUM
ejpam-4612	192	55	)	)	PUNCT
ejpam-4612	192	56	.	.	PUNCT
ejpam-4612	193	1	but	but	CCONJ
ejpam-4612	193	2	,	,	PUNCT
ejpam-4612	193	3	we	we	PRON
ejpam-4612	193	4	have	have	VERB
ejpam-4612	193	5	to	to	PART
ejpam-4612	193	6	know	know	VERB
ejpam-4612	193	7	that	that	SCONJ
ejpam-4612	193	8	the	the	DET
ejpam-4612	193	9	two	two	NUM
ejpam-4612	193	10	norms	norm	NOUN
ejpam-4612	193	11	are	be	AUX
ejpam-4612	193	12	not	not	PART
ejpam-4612	193	13	equivalent	equivalent	ADJ
ejpam-4612	193	14	.	.	PUNCT
ejpam-4612	194	1	using	use	VERB
ejpam-4612	194	2	the	the	DET
ejpam-4612	194	3	inner	inner	ADJ
ejpam-4612	194	4	product	product	NOUN
ejpam-4612	194	5	,	,	PUNCT
ejpam-4612	194	6	one	one	PRON
ejpam-4612	194	7	may	may	AUX
ejpam-4612	194	8	define	define	VERB
ejpam-4612	194	9	angles	angle	NOUN
ejpam-4612	194	10	on	on	ADP
ejpam-4612	194	11	mu	mu	PROPN
ejpam-4612	194	12	,	,	PUNCT
ejpam-4612	194	13	p	p	X
ejpam-4612	194	14	,	,	PUNCT
ejpam-4612	194	15	define	define	VERB
ejpam-4612	194	16	orthogonality	orthogonality	NOUN
ejpam-4612	194	17	on	on	ADP
ejpam-4612	194	18	mu	mu	PROPN
ejpam-4612	194	19	,	,	PUNCT
ejpam-4612	194	20	p	p	PRON
ejpam-4612	194	21	,	,	PUNCT
ejpam-4612	194	22	carry	carry	VERB
ejpam-4612	194	23	out	out	ADP
ejpam-4612	194	24	the	the	DET
ejpam-4612	194	25	gram	gram	NOUN
ejpam-4612	194	26	-	-	PUNCT
ejpam-4612	194	27	schmidt	schmidt	NOUN
ejpam-4612	194	28	process	process	NOUN
ejpam-4612	194	29	to	to	PART
ejpam-4612	194	30	get	get	VERB
ejpam-4612	194	31	an	an	DET
ejpam-4612	194	32	orthogonal	orthogonal	ADJ
ejpam-4612	194	33	set	set	NOUN
ejpam-4612	194	34	(	(	PUNCT
ejpam-4612	194	35	see	see	VERB
ejpam-4612	194	36	[	[	X
ejpam-4612	194	37	3	3	NUM
ejpam-4612	194	38	]	]	NUM
ejpam-4612	194	39	)	)	PUNCT
ejpam-4612	194	40	,	,	PUNCT
ejpam-4612	194	41	define	define	VERB
ejpam-4612	194	42	the	the	DET
ejpam-4612	194	43	volume	volume	NOUN
ejpam-4612	194	44	of	of	ADP
ejpam-4612	194	45	an	an	DET
ejpam-4612	194	46	n	n	ADV
ejpam-4612	194	47	-	-	PUNCT
ejpam-4612	194	48	dimensional	dimensional	ADJ
ejpam-4612	194	49	parallelepiped	parallelepipe	VERB
ejpam-4612	194	50	on	on	ADP
ejpam-4612	194	51	mu	mu	PROPN
ejpam-4612	194	52	,	,	PUNCT
ejpam-4612	194	53	p	p	X
ejpam-4612	194	54	,	,	PUNCT
ejpam-4612	194	55	define	define	VERB
ejpam-4612	194	56	an	an	DET
ejpam-4612	194	57	n	n	CCONJ
ejpam-4612	194	58	-	-	PUNCT
ejpam-4612	194	59	inner	inner	ADJ
ejpam-4612	194	60	product	product	NOUN
ejpam-4612	194	61	on	on	ADP
ejpam-4612	194	62	mu	mu	PROPN
ejpam-4612	194	63	,	,	PUNCT
ejpam-4612	194	64	p	p	PRON
ejpam-4612	194	65	,	,	PUNCT
ejpam-4612	194	66	discuss	discuss	VERB
ejpam-4612	194	67	the	the	DET
ejpam-4612	194	68	concept	concept	NOUN
ejpam-4612	194	69	of	of	ADP
ejpam-4612	194	70	convergence	convergence	NOUN
ejpam-4612	194	71	for	for	ADP
ejpam-4612	194	72	n	n	CCONJ
ejpam-4612	194	73	-	-	PUNCT
ejpam-4612	194	74	dimensional	dimensional	ADJ
ejpam-4612	194	75	subspace	subspace	NOUN
ejpam-4612	194	76	of	of	ADP
ejpam-4612	194	77	mu	mu	PROPN
ejpam-4612	194	78	,	,	PUNCT
ejpam-4612	194	79	p	p	X
ejpam-4612	194	80	(	(	PUNCT
ejpam-4612	194	81	see	see	VERB
ejpam-4612	194	82	[	[	X
ejpam-4612	194	83	19	19	NUM
ejpam-4612	194	84	]	]	PUNCT
ejpam-4612	194	85	,	,	PUNCT
ejpam-4612	194	86	[	[	X
ejpam-4612	194	87	18	18	NUM
ejpam-4612	194	88	]	]	PUNCT
ejpam-4612	194	89	,	,	PUNCT
ejpam-4612	194	90	and	and	CCONJ
ejpam-4612	194	91	[	[	X
ejpam-4612	194	92	17	17	NUM
ejpam-4612	194	93	]	]	NUM
ejpam-4612	194	94	)	)	PUNCT
ejpam-4612	194	95	,	,	PUNCT
ejpam-4612	194	96	and	and	CCONJ
ejpam-4612	194	97	so	so	ADV
ejpam-4612	194	98	on	on	ADV
ejpam-4612	194	99	.	.	PUNCT
ejpam-4612	195	1	conflict	conflict	NOUN
ejpam-4612	195	2	of	of	ADP
ejpam-4612	195	3	interest	interest	NOUN
ejpam-4612	195	4	the	the	DET
ejpam-4612	195	5	authors	author	NOUN
ejpam-4612	195	6	confirm	confirm	VERB
ejpam-4612	195	7	that	that	SCONJ
ejpam-4612	195	8	there	there	PRON
ejpam-4612	195	9	is	be	VERB
ejpam-4612	195	10	no	no	DET
ejpam-4612	195	11	conflict	conflict	NOUN
ejpam-4612	195	12	of	of	ADP
ejpam-4612	195	13	interest	interest	NOUN
ejpam-4612	195	14	to	to	PART
ejpam-4612	195	15	declare	declare	VERB
ejpam-4612	195	16	for	for	ADP
ejpam-4612	195	17	this	this	DET
ejpam-4612	195	18	publication	publication	NOUN
ejpam-4612	195	19	acknowledgements	acknowledgement	NOUN
ejpam-4612	195	20	this	this	DET
ejpam-4612	195	21	research	research	NOUN
ejpam-4612	195	22	received	receive	VERB
ejpam-4612	195	23	a	a	DET
ejpam-4612	195	24	grant	grant	NOUN
ejpam-4612	195	25	from	from	ADP
ejpam-4612	195	26	faculty	faculty	NOUN
ejpam-4612	195	27	of	of	ADP
ejpam-4612	195	28	mathematics	mathematic	NOUN
ejpam-4612	195	29	and	and	CCONJ
ejpam-4612	195	30	science	science	NOUN
ejpam-4612	195	31	,	,	PUNCT
ejpam-4612	195	32	universitas	universita	NOUN
ejpam-4612	195	33	negeri	negeri	PROPN
ejpam-4612	195	34	surabaya	surabaya	PROPN
ejpam-4612	195	35	.	.	PUNCT
ejpam-4612	196	1	the	the	DET
ejpam-4612	196	2	authors	author	NOUN
ejpam-4612	196	3	would	would	AUX
ejpam-4612	196	4	like	like	VERB
ejpam-4612	196	5	to	to	PART
ejpam-4612	196	6	thank	thank	VERB
ejpam-4612	196	7	the	the	DET
ejpam-4612	196	8	editor	editor	NOUN
ejpam-4612	196	9	and	and	CCONJ
ejpam-4612	196	10	anonymous	anonymous	ADJ
ejpam-4612	196	11	reviewers	reviewer	NOUN
ejpam-4612	196	12	for	for	ADP
ejpam-4612	196	13	their	their	PRON
ejpam-4612	196	14	comments	comment	NOUN
ejpam-4612	196	15	that	that	PRON
ejpam-4612	196	16	help	help	VERB
ejpam-4612	196	17	improve	improve	VERB
ejpam-4612	196	18	the	the	DET
ejpam-4612	196	19	quality	quality	NOUN
ejpam-4612	196	20	of	of	ADP
ejpam-4612	196	21	this	this	DET
ejpam-4612	196	22	work	work	NOUN
ejpam-4612	196	23	references	reference	NOUN
ejpam-4612	196	24	[	[	X
ejpam-4612	196	25	1	1	NUM
ejpam-4612	196	26	]	]	PUNCT
ejpam-4612	196	27	a.	a.	NOUN
ejpam-4612	196	28	adam	adam	PROPN
ejpam-4612	196	29	and	and	CCONJ
ejpam-4612	196	30	h.	h.	PROPN
ejpam-4612	196	31	gunawan	gunawan	PROPN
ejpam-4612	196	32	.	.	PUNCT
ejpam-4612	197	1	on	on	ADP
ejpam-4612	197	2	geometric	geometric	ADJ
ejpam-4612	197	3	constants	constant	NOUN
ejpam-4612	197	4	for	for	ADP
ejpam-4612	197	5	discrete	discrete	ADJ
ejpam-4612	197	6	morrey	morrey	NOUN
ejpam-4612	197	7	spaces	space	NOUN
ejpam-4612	197	8	.	.	PUNCT
ejpam-4612	198	1	european	european	PROPN
ejpam-4612	198	2	journal	journal	PROPN
ejpam-4612	198	3	of	of	ADP
ejpam-4612	198	4	mathematical	mathematical	ADJ
ejpam-4612	198	5	analysis	analysis	NOUN
ejpam-4612	198	6	,	,	PUNCT
ejpam-4612	198	7	2(2):1–10	2(2):1–10	NUM
ejpam-4612	198	8	,	,	PUNCT
ejpam-4612	198	9	2022	2022	NUM
ejpam-4612	198	10	.	.	PUNCT
ejpam-4612	199	1	[	[	X
ejpam-4612	199	2	2	2	NUM
ejpam-4612	199	3	]	]	X
ejpam-4612	199	4	r.a	r.a	PROPN
ejpam-4612	199	5	.	.	PROPN
ejpam-4612	199	6	adam	adam	PROPN
ejpam-4612	199	7	and	and	CCONJ
ejpam-4612	199	8	a.n	a.n	PROPN
ejpam-4612	199	9	.	.	PROPN
ejpam-4612	199	10	ahmadova	ahmadova	PROPN
ejpam-4612	199	11	.	.	PUNCT
ejpam-4612	200	1	boundedness	boundedness	PROPN
ejpam-4612	200	2	of	of	ADP
ejpam-4612	200	3	discrete	discrete	ADJ
ejpam-4612	200	4	hilbert	hilbert	NOUN
ejpam-4612	200	5	transform	transform	NOUN
ejpam-4612	200	6	on	on	ADP
ejpam-4612	200	7	discrete	discrete	ADJ
ejpam-4612	200	8	morrey	morrey	NOUN
ejpam-4612	200	9	spaces	space	NOUN
ejpam-4612	200	10	.	.	PUNCT
ejpam-4612	201	1	ufa	ufa	PROPN
ejpam-4612	201	2	mathematical	mathematical	PROPN
ejpam-4612	201	3	journal	journal	PROPN
ejpam-4612	201	4	,	,	PUNCT
ejpam-4612	201	5	13(1):99–109	13(1):99–109	NUM
ejpam-4612	201	6	,	,	PUNCT
ejpam-4612	201	7	2021	2021	NUM
ejpam-4612	201	8	.	.	PUNCT
ejpam-4612	202	1	[	[	X
ejpam-4612	202	2	3	3	X
ejpam-4612	202	3	]	]	X
ejpam-4612	202	4	f.a	f.a	PROPN
ejpam-4612	202	5	.	.	PROPN
ejpam-4612	202	6	akgun	akgun	PROPN
ejpam-4612	202	7	and	and	CCONJ
ejpam-4612	202	8	b.e	b.e	PROPN
ejpam-4612	202	9	.	.	PROPN
ejpam-4612	202	10	rhoades	rhoades	PROPN
ejpam-4612	202	11	.	.	PUNCT
ejpam-4612	203	1	e	e	X
ejpam-4612	203	2	-	-	PROPN
ejpam-4612	203	3	j	j	PROPN
ejpam-4612	203	4	summability	summability	NOUN
ejpam-4612	203	5	of	of	ADP
ejpam-4612	203	6	orthogonal	orthogonal	ADJ
ejpam-4612	203	7	series	series	NOUN
ejpam-4612	203	8	.	.	PUNCT
ejpam-4612	204	1	european	european	PROPN
ejpam-4612	204	2	journal	journal	PROPN
ejpam-4612	204	3	of	of	ADP
ejpam-4612	204	4	pure	pure	ADJ
ejpam-4612	204	5	and	and	CCONJ
ejpam-4612	204	6	applied	applied	ADJ
ejpam-4612	204	7	mathematics	mathematic	NOUN
ejpam-4612	204	8	,	,	PUNCT
ejpam-4612	204	9	13(3):390–402	13(3):390–402	PROPN
ejpam-4612	204	10	,	,	PUNCT
ejpam-4612	204	11	2020	2020	NUM
ejpam-4612	204	12	.	.	PUNCT
ejpam-4612	205	1	[	[	X
ejpam-4612	205	2	4	4	NUM
ejpam-4612	205	3	]	]	X
ejpam-4612	205	4	r.a	r.a	PROPN
ejpam-4612	205	5	.	.	PROPN
ejpam-4612	205	6	aliev	aliev	PROPN
ejpam-4612	205	7	,	,	PUNCT
ejpam-4612	205	8	a.n	a.n	PROPN
ejpam-4612	205	9	.	.	PROPN
ejpam-4612	205	10	ahmadova	ahmadova	PROPN
ejpam-4612	205	11	,	,	PUNCT
ejpam-4612	205	12	and	and	CCONJ
ejpam-4612	205	13	a.f	a.f	PROPN
ejpam-4612	205	14	.	.	PROPN
ejpam-4612	205	15	huseynli	huseynli	PROPN
ejpam-4612	205	16	.	.	PUNCT
ejpam-4612	206	1	boundedness	boundedness	NOUN
ejpam-4612	206	2	of	of	ADP
ejpam-4612	206	3	the	the	DET
ejpam-4612	206	4	discrete	discrete	ADJ
ejpam-4612	206	5	ahlforsbeurling	ahlforsbeurling	NOUN
ejpam-4612	206	6	transform	transform	NOUN
ejpam-4612	206	7	on	on	ADP
ejpam-4612	206	8	discrete	discrete	ADJ
ejpam-4612	206	9	morrey	morrey	NOUN
ejpam-4612	206	10	spaces	space	NOUN
ejpam-4612	206	11	.	.	PUNCT
ejpam-4612	207	1	proceedings	proceeding	NOUN
ejpam-4612	207	2	of	of	ADP
ejpam-4612	207	3	the	the	DET
ejpam-4612	207	4	institute	institute	NOUN
ejpam-4612	207	5	of	of	ADP
ejpam-4612	207	6	mathematics	mathematics	PROPN
ejpam-4612	207	7	and	and	CCONJ
ejpam-4612	207	8	mechanics	mechanic	NOUN
ejpam-4612	207	9	,	,	PUNCT
ejpam-4612	207	10	48(1):123–131	48(1):123–131	PROPN
ejpam-4612	207	11	,	,	PUNCT
ejpam-4612	207	12	2022	2022	NUM
ejpam-4612	207	13	.	.	PUNCT
ejpam-4612	208	1	[	[	X
ejpam-4612	208	2	5	5	NUM
ejpam-4612	208	3	]	]	X
ejpam-4612	208	4	e.i	e.i	PROPN
ejpam-4612	208	5	.	.	PROPN
ejpam-4612	208	6	berezhnoi	berezhnoi	PROPN
ejpam-4612	208	7	.	.	PUNCT
ejpam-4612	209	1	a	a	DET
ejpam-4612	209	2	discrete	discrete	ADJ
ejpam-4612	209	3	version	version	NOUN
ejpam-4612	209	4	of	of	ADP
ejpam-4612	209	5	local	local	ADJ
ejpam-4612	209	6	morrey	morrey	NOUN
ejpam-4612	209	7	spaces	space	NOUN
ejpam-4612	209	8	.	.	PUNCT
ejpam-4612	210	1	izvestiya	izvestiya	NOUN
ejpam-4612	210	2	:	:	PUNCT
ejpam-4612	211	1	mathematics	mathematic	NOUN
ejpam-4612	211	2	,	,	PUNCT
ejpam-4612	211	3	81(1):1	81(1):1	PROPN
ejpam-4612	211	4	,	,	PUNCT
ejpam-4612	211	5	2017	2017	NUM
ejpam-4612	211	6	.	.	PUNCT
ejpam-4612	212	1	references	reference	NOUN
ejpam-4612	212	2	154	154	NUM
ejpam-4612	212	3	[	[	X
ejpam-4612	212	4	6	6	NUM
ejpam-4612	212	5	]	]	X
ejpam-4612	212	6	e.i	e.i	PROPN
ejpam-4612	212	7	.	.	PROPN
ejpam-4612	212	8	berezhnoi	berezhnoi	PROPN
ejpam-4612	212	9	.	.	PUNCT
ejpam-4612	213	1	analogs	analog	NOUN
ejpam-4612	213	2	of	of	ADP
ejpam-4612	213	3	the	the	DET
ejpam-4612	213	4	khintchin	khintchin	ADJ
ejpam-4612	213	5	—	—	PUNCT
ejpam-4612	213	6	kolmogorov	kolmogorov	ADJ
ejpam-4612	213	7	inequalities	inequality	NOUN
ejpam-4612	213	8	in	in	ADP
ejpam-4612	213	9	discrete	discrete	ADJ
ejpam-4612	213	10	morrey	morrey	NOUN
ejpam-4612	213	11	spaces	space	NOUN
ejpam-4612	213	12	.	.	PUNCT
ejpam-4612	214	1	in	in	ADP
ejpam-4612	214	2	alexey	alexey	PROPN
ejpam-4612	214	3	karapetyants	karapetyants	PROPN
ejpam-4612	214	4	,	,	PUNCT
ejpam-4612	214	5	vladislav	vladislav	ADJ
ejpam-4612	214	6	kravchenko	kravchenko	PROPN
ejpam-4612	214	7	,	,	PUNCT
ejpam-4612	214	8	and	and	CCONJ
ejpam-4612	214	9	elijah	elijah	PROPN
ejpam-4612	214	10	liflyand	liflyand	PROPN
ejpam-4612	214	11	,	,	PUNCT
ejpam-4612	214	12	editors	editor	NOUN
ejpam-4612	214	13	,	,	PUNCT
ejpam-4612	214	14	modern	modern	ADJ
ejpam-4612	214	15	methods	method	NOUN
ejpam-4612	214	16	in	in	ADP
ejpam-4612	214	17	operator	operator	NOUN
ejpam-4612	214	18	theory	theory	NOUN
ejpam-4612	214	19	and	and	CCONJ
ejpam-4612	214	20	harmonic	harmonic	ADJ
ejpam-4612	214	21	analysis	analysis	NOUN
ejpam-4612	214	22	.	.	PUNCT
ejpam-4612	214	23	,	,	PUNCT
ejpam-4612	214	24	pages	page	NOUN
ejpam-4612	214	25	137–151	137–151	NUM
ejpam-4612	214	26	,	,	PUNCT
ejpam-4612	214	27	cham	cham	NOUN
ejpam-4612	214	28	,	,	PUNCT
ejpam-4612	214	29	2019	2019	NUM
ejpam-4612	214	30	.	.	PUNCT
ejpam-4612	215	1	european	european	ADJ
ejpam-4612	215	2	alliance	alliance	PROPN
ejpam-4612	215	3	for	for	ADP
ejpam-4612	215	4	innovation	innovation	NOUN
ejpam-4612	215	5	,	,	PUNCT
ejpam-4612	215	6	springer	springer	NOUN
ejpam-4612	215	7	international	international	ADJ
ejpam-4612	215	8	publishing	publishing	NOUN
ejpam-4612	215	9	.	.	PUNCT
ejpam-4612	216	1	[	[	X
ejpam-4612	216	2	7	7	X
ejpam-4612	216	3	]	]	X
ejpam-4612	216	4	e.i	e.i	PROPN
ejpam-4612	216	5	.	.	PROPN
ejpam-4612	216	6	berezhnoi	berezhnoi	PROPN
ejpam-4612	216	7	.	.	PUNCT
ejpam-4612	217	1	on	on	ADP
ejpam-4612	217	2	interpolation	interpolation	NOUN
ejpam-4612	217	3	and	and	CCONJ
ejpam-4612	217	4	k	k	NOUN
ejpam-4612	217	5	-	-	NOUN
ejpam-4612	217	6	monotonicity	monotonicity	NOUN
ejpam-4612	217	7	for	for	ADP
ejpam-4612	217	8	discrete	discrete	ADJ
ejpam-4612	217	9	local	local	ADJ
ejpam-4612	217	10	morrey	morrey	NOUN
ejpam-4612	217	11	spaces	space	NOUN
ejpam-4612	217	12	.	.	PUNCT
ejpam-4612	218	1	st	st	PROPN
ejpam-4612	218	2	.	.	PROPN
ejpam-4612	218	3	petersburg	petersburg	PROPN
ejpam-4612	218	4	math	math	PROPN
ejpam-4612	218	5	.	.	PUNCT
ejpam-4612	219	1	j.	j.	PROPN
ejpam-4612	219	2	,	,	PUNCT
ejpam-4612	219	3	33(1):427–447	33(1):427–447	NOUN
ejpam-4612	219	4	,	,	PUNCT
ejpam-4612	219	5	2021	2021	NUM
ejpam-4612	219	6	.	.	PUNCT
ejpam-4612	220	1	[	[	X
ejpam-4612	220	2	8	8	NUM
ejpam-4612	220	3	]	]	X
ejpam-4612	220	4	h.	h.	PROPN
ejpam-4612	220	5	gunawan	gunawan	PROPN
ejpam-4612	220	6	,	,	PUNCT
ejpam-4612	220	7	d.i	d.i	PROPN
ejpam-4612	220	8	.	.	PROPN
ejpam-4612	220	9	hakim	hakim	PROPN
ejpam-4612	220	10	,	,	PUNCT
ejpam-4612	220	11	and	and	CCONJ
ejpam-4612	220	12	m.	m.	PROPN
ejpam-4612	220	13	idris	idris	PROPN
ejpam-4612	220	14	.	.	PUNCT
ejpam-4612	221	1	on	on	ADP
ejpam-4612	221	2	inclusion	inclusion	NOUN
ejpam-4612	221	3	properties	property	NOUN
ejpam-4612	221	4	of	of	ADP
ejpam-4612	221	5	discrete	discrete	ADJ
ejpam-4612	221	6	morrey	morrey	NOUN
ejpam-4612	221	7	spaces	space	NOUN
ejpam-4612	221	8	.	.	PUNCT
ejpam-4612	222	1	georgian	georgian	PROPN
ejpam-4612	222	2	mathematical	mathematical	PROPN
ejpam-4612	222	3	journal	journal	NOUN
ejpam-4612	222	4	,	,	PUNCT
ejpam-4612	222	5	29(1):37–44	29(1):37–44	NUM
ejpam-4612	222	6	,	,	PUNCT
ejpam-4612	222	7	2022	2022	NUM
ejpam-4612	222	8	.	.	PUNCT
ejpam-4612	223	1	[	[	X
ejpam-4612	223	2	9	9	NUM
ejpam-4612	223	3	]	]	X
ejpam-4612	223	4	h.	h.	PROPN
ejpam-4612	223	5	gunawan	gunawan	PROPN
ejpam-4612	223	6	,	,	PUNCT
ejpam-4612	223	7	e.	e.	PROPN
ejpam-4612	223	8	kikianty	kikianty	PROPN
ejpam-4612	223	9	,	,	PUNCT
ejpam-4612	223	10	and	and	CCONJ
ejpam-4612	223	11	y.	y.	PROPN
ejpam-4612	223	12	sawano	sawano	PROPN
ejpam-4612	223	13	.	.	PUNCT
ejpam-4612	224	1	three	three	NUM
ejpam-4612	224	2	geometric	geometric	ADJ
ejpam-4612	224	3	constants	constant	NOUN
ejpam-4612	224	4	for	for	ADP
ejpam-4612	224	5	morrey	morrey	NOUN
ejpam-4612	224	6	spaces	space	NOUN
ejpam-4612	224	7	.	.	PUNCT
ejpam-4612	225	1	bull	bull	NOUN
ejpam-4612	225	2	.	.	PUNCT
ejpam-4612	226	1	korean	korean	ADJ
ejpam-4612	226	2	math	math	PROPN
ejpam-4612	226	3	.	.	PUNCT
ejpam-4612	227	1	soc	soc	PROPN
ejpam-4612	227	2	.	.	PUNCT
ejpam-4612	227	3	,	,	PUNCT
ejpam-4612	228	1	56(6):1569–1575	56(6):1569–1575	NUM
ejpam-4612	228	2	,	,	PUNCT
ejpam-4612	228	3	2019	2019	NUM
ejpam-4612	228	4	.	.	PUNCT
ejpam-4612	229	1	[	[	X
ejpam-4612	229	2	10	10	NUM
ejpam-4612	229	3	]	]	X
ejpam-4612	229	4	h.	h.	PROPN
ejpam-4612	229	5	gunawan	gunawan	PROPN
ejpam-4612	229	6	,	,	PUNCT
ejpam-4612	229	7	e.	e.	PROPN
ejpam-4612	229	8	kikianty	kikianty	PROPN
ejpam-4612	229	9	,	,	PUNCT
ejpam-4612	229	10	and	and	CCONJ
ejpam-4612	229	11	c.	c.	PROPN
ejpam-4612	229	12	schwanke	schwanke	PROPN
ejpam-4612	229	13	.	.	PUNCT
ejpam-4612	230	1	discrete	discrete	ADJ
ejpam-4612	230	2	morrey	morrey	NOUN
ejpam-4612	230	3	spaces	space	NOUN
ejpam-4612	230	4	and	and	CCONJ
ejpam-4612	230	5	their	their	PRON
ejpam-4612	230	6	inclusion	inclusion	NOUN
ejpam-4612	230	7	properties	property	NOUN
ejpam-4612	230	8	.	.	PUNCT
ejpam-4612	231	1	mathematische	mathematische	PROPN
ejpam-4612	231	2	nachrichten	nachrichten	PROPN
ejpam-4612	231	3	,	,	PUNCT
ejpam-4612	231	4	291(8	291(8	NUM
ejpam-4612	231	5	-	-	SYM
ejpam-4612	231	6	9):1283–1296	9):1283–1296	NUM
ejpam-4612	231	7	,	,	PUNCT
ejpam-4612	231	8	2018	2018	NUM
ejpam-4612	231	9	.	.	PUNCT
ejpam-4612	232	1	[	[	X
ejpam-4612	232	2	11	11	NUM
ejpam-4612	232	3	]	]	X
ejpam-4612	232	4	h.	h.	PROPN
ejpam-4612	232	5	gunawan	gunawan	PROPN
ejpam-4612	232	6	and	and	CCONJ
ejpam-4612	232	7	c.	c.	PROPN
ejpam-4612	232	8	schwanke	schwanke	PROPN
ejpam-4612	232	9	.	.	PUNCT
ejpam-4612	233	1	the	the	DET
ejpam-4612	233	2	hardy	hardy	ADJ
ejpam-4612	233	3	–	–	PUNCT
ejpam-4612	233	4	littlewood	littlewood	NOUN
ejpam-4612	233	5	maximal	maximal	ADJ
ejpam-4612	233	6	operator	operator	NOUN
ejpam-4612	233	7	on	on	ADP
ejpam-4612	233	8	discrete	discrete	ADJ
ejpam-4612	233	9	morrey	morrey	NOUN
ejpam-4612	233	10	spaces	space	NOUN
ejpam-4612	233	11	.	.	PUNCT
ejpam-4612	234	1	mediterranean	mediterranean	PROPN
ejpam-4612	234	2	journal	journal	PROPN
ejpam-4612	234	3	of	of	ADP
ejpam-4612	234	4	mathematics	mathematic	NOUN
ejpam-4612	234	5	,	,	PUNCT
ejpam-4612	234	6	16(1):1–12	16(1):1–12	NUM
ejpam-4612	234	7	,	,	PUNCT
ejpam-4612	234	8	2019	2019	NUM
ejpam-4612	234	9	.	.	PUNCT
ejpam-4612	235	1	[	[	X
ejpam-4612	235	2	12	12	NUM
ejpam-4612	235	3	]	]	PUNCT
ejpam-4612	235	4	m.	m.	NOUN
ejpam-4612	235	5	guzman	guzman	PROPN
ejpam-4612	235	6	-	-	PUNCT
ejpam-4612	235	7	partida	partida	PROPN
ejpam-4612	235	8	.	.	PUNCT
ejpam-4612	236	1	boundedness	boundedness	PROPN
ejpam-4612	236	2	and	and	CCONJ
ejpam-4612	236	3	compactness	compactness	NOUN
ejpam-4612	236	4	of	of	ADP
ejpam-4612	236	5	some	some	DET
ejpam-4612	236	6	operators	operator	NOUN
ejpam-4612	236	7	on	on	ADP
ejpam-4612	236	8	discrete	discrete	ADJ
ejpam-4612	236	9	morrey	morrey	NOUN
ejpam-4612	236	10	spaces	space	NOUN
ejpam-4612	236	11	.	.	PUNCT
ejpam-4612	237	1	commentationes	commentatione	NOUN
ejpam-4612	237	2	mathematicae	mathematicae	VERB
ejpam-4612	237	3	universitatis	universitatis	PROPN
ejpam-4612	237	4	carolinae	carolinae	PROPN
ejpam-4612	237	5	,	,	PUNCT
ejpam-4612	237	6	62(2):151	62(2):151	NOUN
ejpam-4612	237	7	–	–	PUNCT
ejpam-4612	237	8	158	158	NUM
ejpam-4612	237	9	,	,	PUNCT
ejpam-4612	237	10	2021	2021	NUM
ejpam-4612	237	11	.	.	PUNCT
ejpam-4612	238	1	[	[	X
ejpam-4612	238	2	13	13	NUM
ejpam-4612	238	3	]	]	X
ejpam-4612	238	4	d.d	d.d	PROPN
ejpam-4612	238	5	.	.	PROPN
ejpam-4612	238	6	haroske	haroske	PROPN
ejpam-4612	238	7	and	and	CCONJ
ejpam-4612	238	8	l.	l.	PROPN
ejpam-4612	238	9	skrzypczak	skrzypczak	PROPN
ejpam-4612	238	10	.	.	PUNCT
ejpam-4612	239	1	morrey	morrey	PROPN
ejpam-4612	239	2	sequence	sequence	NOUN
ejpam-4612	239	3	spaces	space	VERB
ejpam-4612	239	4	:	:	PUNCT
ejpam-4612	239	5	pitt	pitt	PROPN
ejpam-4612	239	6	’s	’s	PART
ejpam-4612	239	7	theorem	theorem	ADJ
ejpam-4612	239	8	and	and	CCONJ
ejpam-4612	239	9	compact	compact	ADJ
ejpam-4612	239	10	embeddings	embedding	NOUN
ejpam-4612	239	11	.	.	PUNCT
ejpam-4612	240	1	constructive	constructive	ADJ
ejpam-4612	240	2	approximation	approximation	NOUN
ejpam-4612	240	3	,	,	PUNCT
ejpam-4612	240	4	51(3):505–535	51(3):505–535	PROPN
ejpam-4612	240	5	,	,	PUNCT
ejpam-4612	240	6	2020	2020	NUM
ejpam-4612	240	7	.	.	PUNCT
ejpam-4612	241	1	[	[	X
ejpam-4612	241	2	14	14	NUM
ejpam-4612	241	3	]	]	X
ejpam-4612	241	4	e.	e.	PROPN
ejpam-4612	241	5	kikianty	kikianty	PROPN
ejpam-4612	241	6	and	and	CCONJ
ejpam-4612	241	7	c.	c.	PROPN
ejpam-4612	241	8	schwanke	schwanke	PROPN
ejpam-4612	241	9	.	.	PUNCT
ejpam-4612	242	1	discrete	discrete	ADJ
ejpam-4612	242	2	morrey	morrey	NOUN
ejpam-4612	242	3	spaces	space	NOUN
ejpam-4612	242	4	are	be	AUX
ejpam-4612	242	5	closed	closed	ADJ
ejpam-4612	242	6	subspaces	subspace	NOUN
ejpam-4612	242	7	of	of	ADP
ejpam-4612	242	8	their	their	PRON
ejpam-4612	242	9	continuous	continuous	ADJ
ejpam-4612	242	10	counterparts	counterpart	NOUN
ejpam-4612	242	11	.	.	PUNCT
ejpam-4612	243	1	banach	banach	NOUN
ejpam-4612	243	2	center	center	NOUN
ejpam-4612	243	3	publications	publication	NOUN
ejpam-4612	243	4	,	,	PUNCT
ejpam-4612	243	5	119(1):223–231	119(1):223–231	NUM
ejpam-4612	243	6	,	,	PUNCT
ejpam-4612	243	7	2019	2019	NUM
ejpam-4612	243	8	.	.	PUNCT
ejpam-4612	244	1	[	[	X
ejpam-4612	244	2	15	15	NUM
ejpam-4612	244	3	]	]	X
ejpam-4612	244	4	s.	s.	PROPN
ejpam-4612	244	5	konca	konca	PROPN
ejpam-4612	244	6	,	,	PUNCT
ejpam-4612	244	7	m.	m.	PROPN
ejpam-4612	244	8	idris	idris	PROPN
ejpam-4612	244	9	,	,	PUNCT
ejpam-4612	244	10	and	and	CCONJ
ejpam-4612	244	11	h.	h.	PROPN
ejpam-4612	244	12	gunawan	gunawan	PROPN
ejpam-4612	244	13	.	.	PUNCT
ejpam-4612	245	1	p	p	X
ejpam-4612	245	2	-	-	PUNCT
ejpam-4612	245	3	summable	summable	ADJ
ejpam-4612	245	4	sequences	sequence	NOUN
ejpam-4612	245	5	with	with	ADP
ejpam-4612	245	6	inner	inner	ADJ
ejpam-4612	245	7	products	product	NOUN
ejpam-4612	245	8	.	.	PUNCT
ejpam-4612	246	1	bitlis	bitlis	PROPN
ejpam-4612	246	2	eren	eren	PROPN
ejpam-4612	246	3	univ	univ	PROPN
ejpam-4612	247	1	j	j	PROPN
ejpam-4612	247	2	sci	sci	PROPN
ejpam-4612	247	3	technol	technol	NOUN
ejpam-4612	247	4	,	,	PUNCT
ejpam-4612	247	5	5(1):37–41	5(1):37–41	NUM
ejpam-4612	247	6	,	,	PUNCT
ejpam-4612	247	7	2015	2015	NUM
ejpam-4612	247	8	.	.	PUNCT
ejpam-4612	248	1	[	[	X
ejpam-4612	248	2	16	16	NUM
ejpam-4612	248	3	]	]	X
ejpam-4612	248	4	e.	e.	PROPN
ejpam-4612	248	5	kreyzig	kreyzig	PROPN
ejpam-4612	248	6	.	.	PUNCT
ejpam-4612	249	1	introductory	introductory	ADJ
ejpam-4612	249	2	functional	functional	ADJ
ejpam-4612	249	3	analysis	analysis	NOUN
ejpam-4612	249	4	with	with	ADP
ejpam-4612	249	5	applications	application	NOUN
ejpam-4612	249	6	.	.	PUNCT
ejpam-4612	250	1	john	john	PROPN
ejpam-4612	250	2	wiley	wiley	PROPN
ejpam-4612	250	3	and	and	CCONJ
ejpam-4612	250	4	sons	son	NOUN
ejpam-4612	250	5	,	,	PUNCT
ejpam-4612	250	6	new	new	PROPN
ejpam-4612	250	7	york	york	PROPN
ejpam-4612	250	8	,	,	PUNCT
ejpam-4612	250	9	1978	1978	NUM
ejpam-4612	250	10	.	.	PUNCT
ejpam-4612	251	1	[	[	X
ejpam-4612	251	2	17	17	NUM
ejpam-4612	251	3	]	]	PUNCT
ejpam-4612	251	4	manuharawati	manuharawati	NOUN
ejpam-4612	251	5	,	,	PUNCT
ejpam-4612	251	6	d.n	d.n	PROPN
ejpam-4612	251	7	.	.	PROPN
ejpam-4612	251	8	yunianti	yunianti	PROPN
ejpam-4612	251	9	,	,	PUNCT
ejpam-4612	251	10	and	and	CCONJ
ejpam-4612	251	11	m.	m.	NOUN
ejpam-4612	251	12	jakfar	jakfar	PROPN
ejpam-4612	251	13	.	.	PUNCT
ejpam-4612	252	1	a	a	DET
ejpam-4612	252	2	sequence	sequence	NOUN
ejpam-4612	252	3	convergence	convergence	NOUN
ejpam-4612	252	4	of	of	ADP
ejpam-4612	252	5	1	1	NUM
ejpam-4612	252	6	dimensional	dimensional	ADJ
ejpam-4612	252	7	subspace	subspace	NOUN
ejpam-4612	252	8	in	in	ADP
ejpam-4612	252	9	a	a	DET
ejpam-4612	252	10	normed	normed	ADJ
ejpam-4612	252	11	space	space	NOUN
ejpam-4612	252	12	.	.	PUNCT
ejpam-4612	253	1	journal	journal	PROPN
ejpam-4612	253	2	of	of	ADP
ejpam-4612	253	3	physics	physics	PROPN
ejpam-4612	253	4	:	:	PUNCT
ejpam-4612	253	5	conference	conference	NOUN
ejpam-4612	253	6	series	series	NOUN
ejpam-4612	253	7	,	,	PUNCT
ejpam-4612	253	8	1108(1):012085	1108(1):012085	NUM
ejpam-4612	253	9	,	,	PUNCT
ejpam-4612	253	10	2018	2018	NUM
ejpam-4612	253	11	.	.	PUNCT
ejpam-4612	254	1	[	[	X
ejpam-4612	254	2	18	18	NUM
ejpam-4612	254	3	]	]	PUNCT
ejpam-4612	254	4	manuharawati	manuharawati	NOUN
ejpam-4612	254	5	,	,	PUNCT
ejpam-4612	254	6	d.n	d.n	PROPN
ejpam-4612	254	7	.	.	PROPN
ejpam-4612	254	8	yunianti	yunianti	PROPN
ejpam-4612	254	9	,	,	PUNCT
ejpam-4612	254	10	and	and	CCONJ
ejpam-4612	254	11	m.	m.	NOUN
ejpam-4612	254	12	jakfar	jakfar	PROPN
ejpam-4612	254	13	.	.	PUNCT
ejpam-4612	255	1	the	the	DET
ejpam-4612	255	2	concept	concept	NOUN
ejpam-4612	255	3	of	of	ADP
ejpam-4612	255	4	convergence	convergence	NOUN
ejpam-4612	255	5	for	for	ADP
ejpam-4612	255	6	2dimensional	2dimensional	ADJ
ejpam-4612	255	7	subspaces	subspace	NOUN
ejpam-4612	255	8	sequence	sequence	NOUN
ejpam-4612	255	9	in	in	ADP
ejpam-4612	255	10	normed	normed	ADJ
ejpam-4612	255	11	spaces	space	NOUN
ejpam-4612	255	12	.	.	PUNCT
ejpam-4612	256	1	australian	australian	ADJ
ejpam-4612	256	2	journal	journal	NOUN
ejpam-4612	256	3	of	of	ADP
ejpam-4612	256	4	mathematical	mathematical	ADJ
ejpam-4612	256	5	analysis	analysis	NOUN
ejpam-4612	256	6	and	and	CCONJ
ejpam-4612	256	7	applications	application	NOUN
ejpam-4612	256	8	,	,	PUNCT
ejpam-4612	256	9	16(2):1–11	16(2):1–11	NUM
ejpam-4612	256	10	,	,	PUNCT
ejpam-4612	256	11	2019	2019	NUM
ejpam-4612	256	12	.	.	PUNCT
ejpam-4612	257	1	[	[	X
ejpam-4612	257	2	19	19	NUM
ejpam-4612	257	3	]	]	PUNCT
ejpam-4612	257	4	manuharawati	manuharawati	NOUN
ejpam-4612	257	5	,	,	PUNCT
ejpam-4612	257	6	d.n	d.n	PROPN
ejpam-4612	257	7	.	.	PROPN
ejpam-4612	257	8	yunianti	yunianti	PROPN
ejpam-4612	257	9	,	,	PUNCT
ejpam-4612	257	10	and	and	CCONJ
ejpam-4612	257	11	m.	m.	NOUN
ejpam-4612	257	12	jakfar	jakfar	PROPN
ejpam-4612	257	13	.	.	PUNCT
ejpam-4612	258	1	the	the	DET
ejpam-4612	258	2	new	new	ADJ
ejpam-4612	258	3	convergence	convergence	NOUN
ejpam-4612	258	4	definition	definition	NOUN
ejpam-4612	258	5	for	for	ADP
ejpam-4612	258	6	sequence	sequence	NOUN
ejpam-4612	258	7	of	of	ADP
ejpam-4612	258	8	k	k	ADJ
ejpam-4612	258	9	-	-	ADJ
ejpam-4612	258	10	dimensional	dimensional	ADJ
ejpam-4612	258	11	subspaces	subspace	NOUN
ejpam-4612	258	12	of	of	ADP
ejpam-4612	258	13	an	an	DET
ejpam-4612	258	14	inner	inner	ADJ
ejpam-4612	258	15	product	product	NOUN
ejpam-4612	258	16	space	space	NOUN
ejpam-4612	258	17	.	.	PUNCT
ejpam-4612	259	1	journal	journal	PROPN
ejpam-4612	259	2	of	of	ADP
ejpam-4612	259	3	physics	physics	PROPN
ejpam-4612	259	4	:	:	PUNCT
ejpam-4612	259	5	conference	conference	NOUN
ejpam-4612	259	6	series	series	NOUN
ejpam-4612	259	7	,	,	PUNCT
ejpam-4612	259	8	1417(1):012020	1417(1):012020	NUM
ejpam-4612	259	9	,	,	PUNCT
ejpam-4612	259	10	2019	2019	NUM
ejpam-4612	259	11	.	.	PUNCT
ejpam-4612	260	1	references	reference	NOUN
ejpam-4612	260	2	155	155	NUM
ejpam-4612	260	3	[	[	SYM
ejpam-4612	260	4	20	20	NUM
ejpam-4612	260	5	]	]	SYM
ejpam-4612	260	6	a.a	a.a	PROPN
ejpam-4612	260	7	.	.	PROPN
ejpam-4612	260	8	mazta	mazta	PROPN
ejpam-4612	260	9	,	,	PUNCT
ejpam-4612	260	10	m.	m.	NOUN
ejpam-4612	260	11	taqiyudin	taqiyudin	NOUN
ejpam-4612	260	12	,	,	PUNCT
ejpam-4612	260	13	and	and	CCONJ
ejpam-4612	260	14	s.	s.	PROPN
ejpam-4612	260	15	fatimah	fatimah	PROPN
ejpam-4612	260	16	.	.	PUNCT
ejpam-4612	261	1	holder	holder	PROPN
ejpam-4612	261	2	’s	’s	PART
ejpam-4612	261	3	inequality	inequality	NOUN
ejpam-4612	261	4	in	in	ADP
ejpam-4612	261	5	discrete	discrete	ADJ
ejpam-4612	261	6	morrey	morrey	NOUN
ejpam-4612	261	7	spaces	space	NOUN
ejpam-4612	261	8	.	.	PUNCT
ejpam-4612	262	1	in	in	ADP
ejpam-4612	262	2	b.n	b.n	PROPN
ejpam-4612	262	3	.	.	PROPN
ejpam-4612	262	4	petrox	petrox	PROPN
ejpam-4612	262	5	and	and	CCONJ
ejpam-4612	262	6	f.	f.	PROPN
ejpam-4612	262	7	csaki	csaki	PROPN
ejpam-4612	262	8	,	,	PUNCT
ejpam-4612	262	9	editors	editor	NOUN
ejpam-4612	262	10	,	,	PUNCT
ejpam-4612	262	11	proceedings	proceeding	NOUN
ejpam-4612	262	12	of	of	ADP
ejpam-4612	262	13	the	the	DET
ejpam-4612	262	14	7th	7th	ADJ
ejpam-4612	262	15	mathematics	mathematic	NOUN
ejpam-4612	262	16	,	,	PUNCT
ejpam-4612	262	17	science	science	NOUN
ejpam-4612	262	18	,	,	PUNCT
ejpam-4612	262	19	and	and	CCONJ
ejpam-4612	262	20	computer	computer	NOUN
ejpam-4612	262	21	science	science	NOUN
ejpam-4612	262	22	education	education	PROPN
ejpam-4612	262	23	international	international	ADJ
ejpam-4612	262	24	seminar	seminar	NOUN
ejpam-4612	262	25	,	,	PUNCT
ejpam-4612	262	26	msceis	msceis	NOUN
ejpam-4612	262	27	2019	2019	NUM
ejpam-4612	262	28	.	.	PUNCT
ejpam-4612	262	29	,	,	PUNCT
ejpam-4612	262	30	page	page	NOUN
ejpam-4612	262	31	303	303	NUM
ejpam-4612	262	32	,	,	PUNCT
ejpam-4612	262	33	bandung	bandung	PROPN
ejpam-4612	262	34	,	,	PUNCT
ejpam-4612	262	35	west	west	PROPN
ejpam-4612	262	36	java	java	PROPN
ejpam-4612	262	37	,	,	PUNCT
ejpam-4612	262	38	indonesia	indonesia	PROPN
ejpam-4612	262	39	,	,	PUNCT
ejpam-4612	262	40	2020	2020	NUM
ejpam-4612	262	41	.	.	PUNCT
ejpam-4612	263	1	european	european	ADJ
ejpam-4612	263	2	alliance	alliance	PROPN
ejpam-4612	263	3	for	for	ADP
ejpam-4612	263	4	innovation	innovation	NOUN
ejpam-4612	263	5	.	.	PUNCT
ejpam-4612	264	1	[	[	X
ejpam-4612	264	2	21	21	NUM
ejpam-4612	264	3	]	]	X
ejpam-4612	264	4	p.a	p.a	PROPN
ejpam-4612	264	5	.	.	PROPN
ejpam-4612	264	6	puadi	puadi	PROPN
ejpam-4612	264	7	,	,	PUNCT
ejpam-4612	264	8	eridani	eridani	X
ejpam-4612	264	9	,	,	PUNCT
ejpam-4612	264	10	and	and	CCONJ
ejpam-4612	264	11	a.	a.	NOUN
ejpam-4612	264	12	jaelani	jaelani	PROPN
ejpam-4612	264	13	.	.	PUNCT
ejpam-4612	265	1	relation	relation	NOUN
ejpam-4612	265	2	of	of	ADP
ejpam-4612	265	3	morrey	morrey	PROPN
ejpam-4612	265	4	sequence	sequence	NOUN
ejpam-4612	265	5	spaces	space	NOUN
ejpam-4612	265	6	,	,	PUNCT
ejpam-4612	265	7	weak	weak	ADJ
ejpam-4612	265	8	type	type	NOUN
ejpam-4612	265	9	morrey	morrey	NOUN
ejpam-4612	265	10	sequence	sequence	NOUN
ejpam-4612	265	11	spaces	space	VERB
ejpam-4612	265	12	,	,	PUNCT
ejpam-4612	265	13	and	and	CCONJ
ejpam-4612	265	14	sequence	sequence	NOUN
ejpam-4612	265	15	spaces	space	NOUN
ejpam-4612	265	16	.	.	PUNCT
ejpam-4612	266	1	jurnal	jurnal	ADJ
ejpam-4612	266	2	matematika	matematika	PROPN
ejpam-4612	266	3	mantik	mantik	PROPN
ejpam-4612	266	4	,	,	PUNCT
ejpam-4612	266	5	8(1):36–44	8(1):36–44	NUM
ejpam-4612	266	6	,	,	PUNCT
ejpam-4612	266	7	2022	2022	NUM
ejpam-4612	266	8	.	.	PUNCT
ejpam-4612	267	1	[	[	X
ejpam-4612	267	2	22	22	NUM
ejpam-4612	267	3	]	]	X
ejpam-4612	267	4	h.	h.	PROPN
ejpam-4612	267	5	rahman	rahman	PROPN
ejpam-4612	267	6	and	and	CCONJ
ejpam-4612	267	7	h.	h.	PROPN
ejpam-4612	267	8	gunawan	gunawan	PROPN
ejpam-4612	267	9	.	.	PUNCT
ejpam-4612	268	1	some	some	DET
ejpam-4612	268	2	generalized	generalize	VERB
ejpam-4612	268	3	geometric	geometric	ADJ
ejpam-4612	268	4	constants	constant	NOUN
ejpam-4612	268	5	for	for	ADP
ejpam-4612	268	6	discrete	discrete	ADJ
ejpam-4612	268	7	morrey	morrey	NOUN
ejpam-4612	268	8	spaces	space	NOUN
ejpam-4612	268	9	.	.	PUNCT
ejpam-4612	269	1	arxiv	arxiv	PROPN
ejpam-4612	269	2	preprint	preprint	VERB
ejpam-4612	269	3	arxiv:2104.12983	arxiv:2104.12983	NOUN
ejpam-4612	269	4	.	.	PUNCT
ejpam-4612	270	1	,	,	PUNCT
ejpam-4612	271	1	2021	2021	NUM
ejpam-4612	271	2	.	.	PUNCT