id	sid	tid	token	lemma	pos
ma-20	1	1	2022	2022	NUM
ma-20	1	2	ada	ada	PROPN
ma-20	1	3	academica	academica	PROPN
ma-20	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-20	1	5	.	.	PUNCT
ma-20	2	1	j.	j.	PROPN
ma-20	2	2	math	math	PROPN
ma-20	2	3	.	.	PUNCT
ma-20	3	1	anal	anal	ADJ
ma-20	3	2	.	.	PUNCT
ma-20	3	3	2	2	NUM
ma-20	3	4	(	(	PUNCT
ma-20	3	5	2022	2022	NUM
ma-20	3	6	)	)	PUNCT
ma-20	4	1	2doi	2doi	NUM
ma-20	4	2	:	:	PUNCT
ma-20	4	3	10.28924	10.28924	NUM
ma-20	4	4	/	/	SYM
ma-20	4	5	ada	ada	PROPN
ma-20	4	6	/	/	SYM
ma-20	4	7	ma.2.2	ma.2.2	NOUN
ma-20	4	8	on	on	ADP
ma-20	4	9	geometric	geometric	ADJ
ma-20	4	10	constants	constant	NOUN
ma-20	4	11	for	for	ADP
ma-20	4	12	discrete	discrete	ADJ
ma-20	4	13	morrey	morrey	NOUN
ma-20	4	14	spaces	space	VERB
ma-20	4	15	adam	adam	PROPN
ma-20	4	16	adam	adam	PROPN
ma-20	4	17	,	,	PUNCT
ma-20	4	18	hendra	hendra	PROPN
ma-20	4	19	gunawan∗	gunawan∗	NOUN
ma-20	4	20	analysis	analysis	NOUN
ma-20	4	21	and	and	CCONJ
ma-20	4	22	geometry	geometry	NOUN
ma-20	4	23	group	group	NOUN
ma-20	4	24	,	,	PUNCT
ma-20	4	25	faculty	faculty	NOUN
ma-20	4	26	of	of	ADP
ma-20	4	27	mathematics	mathematic	NOUN
ma-20	4	28	and	and	CCONJ
ma-20	4	29	natural	natural	ADJ
ma-20	4	30	sciences	science	NOUN
ma-20	4	31	,	,	PUNCT
ma-20	4	32	bandung	bandung	PROPN
ma-20	4	33	institute	institute	PROPN
ma-20	4	34	of	of	ADP
ma-20	4	35	technology	technology	PROPN
ma-20	4	36	,	,	PUNCT
ma-20	4	37	bandung	bandung	PROPN
ma-20	4	38	40132	40132	NUM
ma-20	4	39	,	,	PUNCT
ma-20	4	40	indonesia	indonesia	PROPN
ma-20	4	41	adam_adam@students.itb.ac.id	adam_adam@students.itb.ac.id	PROPN
ma-20	4	42	,	,	PUNCT
ma-20	4	43	hgunawan@math.itb.ac.id	hgunawan@math.itb.ac.id	PROPN
ma-20	4	44	∗correspondence	∗correspondence	NOUN
ma-20	4	45	:	:	PUNCT
ma-20	4	46	hgunawan@math.itb.ac.id	hgunawan@math.itb.ac.id	NOUN
ma-20	4	47	abstract	abstract	NOUN
ma-20	4	48	.	.	PUNCT
ma-20	5	1	in	in	ADP
ma-20	5	2	this	this	DET
ma-20	5	3	paper	paper	NOUN
ma-20	5	4	we	we	PRON
ma-20	5	5	prove	prove	VERB
ma-20	5	6	that	that	SCONJ
ma-20	5	7	the	the	DET
ma-20	5	8	n	n	CCONJ
ma-20	5	9	-	-	PUNCT
ma-20	5	10	th	th	X
ma-20	5	11	von	von	PROPN
ma-20	5	12	neumann	neumann	PROPN
ma-20	5	13	-	-	PUNCT
ma-20	5	14	jordan	jordan	PROPN
ma-20	5	15	constant	constant	PROPN
ma-20	5	16	and	and	CCONJ
ma-20	5	17	the	the	DET
ma-20	5	18	n	n	CCONJ
ma-20	5	19	-	-	PUNCT
ma-20	5	20	th	th	VERB
ma-20	5	21	jamesconstant	jamesconstant	NOUN
ma-20	5	22	for	for	ADP
ma-20	5	23	discrete	discrete	ADJ
ma-20	5	24	morrey	morrey	NOUN
ma-20	5	25	spaces	space	NOUN
ma-20	5	26	`	`	PUNCT
ma-20	5	27	pq	pq	INTJ
ma-20	5	28	where	where	SCONJ
ma-20	5	29	1	1	NUM
ma-20	5	30	≤	≤	NOUN
ma-20	5	31	p	p	NOUN
ma-20	5	32	<	<	X
ma-20	5	33	q	q	X
ma-20	5	34	<	<	X
ma-20	5	35	∞	∞	PROPN
ma-20	5	36	are	be	AUX
ma-20	5	37	both	both	ADV
ma-20	5	38	equal	equal	ADJ
ma-20	5	39	to	to	PART
ma-20	5	40	n.	n.	VERB
ma-20	5	41	this	this	PRON
ma-20	5	42	resulttells	resulttell	VERB
ma-20	5	43	us	we	PRON
ma-20	5	44	that	that	SCONJ
ma-20	5	45	the	the	DET
ma-20	5	46	discrete	discrete	ADJ
ma-20	5	47	morrey	morrey	NOUN
ma-20	5	48	spaces	space	NOUN
ma-20	5	49	are	be	AUX
ma-20	5	50	not	not	PART
ma-20	5	51	uniformly	uniformly	ADV
ma-20	5	52	non-`1	non-`1	NOUN
ma-20	5	53	,	,	PUNCT
ma-20	5	54	and	and	CCONJ
ma-20	5	55	hence	hence	ADV
ma-20	5	56	they	they	PRON
ma-20	5	57	are	be	AUX
ma-20	5	58	not	not	PART
ma-20	5	59	uniformly	uniformly	ADV
ma-20	5	60	n	n	CCONJ
ma-20	5	61	-	-	PUNCT
ma-20	5	62	convex	convex	NOUN
ma-20	5	63	.	.	PUNCT
ma-20	6	1	1	1	X
ma-20	6	2	.	.	X
ma-20	6	3	introduction	introduction	NOUN
ma-20	6	4	let	let	VERB
ma-20	6	5	n	n	PRON
ma-20	6	6	≥	≥	X
ma-20	6	7	2	2	NUM
ma-20	6	8	be	be	AUX
ma-20	6	9	a	a	DET
ma-20	6	10	non	non	ADJ
ma-20	6	11	-	-	ADJ
ma-20	6	12	negative	negative	ADJ
ma-20	6	13	integer	integer	NOUN
ma-20	6	14	and	and	CCONJ
ma-20	6	15	(	(	PUNCT
ma-20	6	16	x	x	NOUN
ma-20	6	17	,	,	PUNCT
ma-20	6	18	‖	‖	PROPN
ma-20	6	19	·	·	PUNCT
ma-20	6	20	‖	‖	NUM
ma-20	6	21	)	)	PUNCT
ma-20	6	22	be	be	AUX
ma-20	6	23	a	a	DET
ma-20	6	24	banach	banach	NOUN
ma-20	6	25	space	space	NOUN
ma-20	6	26	.	.	PUNCT
ma-20	7	1	the	the	DET
ma-20	7	2	n	n	ADV
ma-20	7	3	-	-	PUNCT
ma-20	7	4	th	th	X
ma-20	7	5	von	von	PROPN
ma-20	7	6	neumannjordan	neumannjordan	PROPN
ma-20	7	7	constant	constant	PROPN
ma-20	7	8	for	for	ADP
ma-20	7	9	x	x	SYM
ma-20	8	1	[	[	X
ma-20	8	2	6	6	NUM
ma-20	8	3	]	]	PUNCT
ma-20	8	4	is	be	AUX
ma-20	8	5	defined	define	VERB
ma-20	8	6	by	by	ADP
ma-20	8	7	c	c	PROPN
ma-20	8	8	(	(	PUNCT
ma-20	8	9	n	n	CCONJ
ma-20	8	10	)	)	PUNCT
ma-20	8	11	nj	nj	PROPN
ma-20	8	12	(	(	PUNCT
ma-20	8	13	x	x	X
ma-20	8	14	)	)	PUNCT
ma-20	8	15	:	:	PUNCT
ma-20	8	16	=	=	SYM
ma-20	8	17	sup	sup	INTJ
ma-20	8	18	{	{	PUNCT
ma-20	8	19	∑	∑	PROPN
ma-20	8	20	±	±	PROPN
ma-20	8	21	‖u1	‖u1	PROPN
ma-20	8	22	±	±	PROPN
ma-20	8	23	u2	u2	PROPN
ma-20	8	24	±	±	PROPN
ma-20	8	25	·	·	PUNCT
ma-20	8	26	·	·	PUNCT
ma-20	8	27	·	·	PUNCT
ma-20	8	28	±	±	NUM
ma-20	8	29	un‖2x	un‖2x	NOUN
ma-20	8	30	2n−1	2n−1	NUM
ma-20	8	31	∑n	∑n	PROPN
ma-20	8	32	i=1	i=1	PROPN
ma-20	9	1	‖ui‖x	‖ui‖x	PROPN
ma-20	9	2	:	:	PUNCT
ma-20	9	3	ui	ui	PROPN
ma-20	10	1	6=	6=	NUM
ma-20	10	2	0	0	NUM
ma-20	10	3	,	,	PUNCT
ma-20	10	4	i	i	PRON
ma-20	10	5	=	=	NOUN
ma-20	10	6	1	1	NUM
ma-20	10	7	,	,	PUNCT
ma-20	10	8	2	2	NUM
ma-20	10	9	,	,	PUNCT
ma-20	10	10	.	.	PUNCT
ma-20	10	11	.	.	PUNCT
ma-20	11	1	.	.	PUNCT
ma-20	12	1	,	,	PUNCT
ma-20	12	2	n	n	CCONJ
ma-20	12	3	}	}	PUNCT
ma-20	12	4	and	and	CCONJ
ma-20	12	5	the	the	DET
ma-20	12	6	n	n	ADV
ma-20	12	7	-	-	PUNCT
ma-20	12	8	th	th	X
ma-20	12	9	james	james	PROPN
ma-20	12	10	constant	constant	ADJ
ma-20	12	11	for	for	ADP
ma-20	12	12	x	x	SYM
ma-20	13	1	[	[	X
ma-20	13	2	7	7	NUM
ma-20	13	3	]	]	PUNCT
ma-20	13	4	is	be	AUX
ma-20	13	5	defined	define	VERB
ma-20	13	6	by	by	ADP
ma-20	13	7	c	c	PROPN
ma-20	13	8	(	(	PUNCT
ma-20	13	9	n	n	CCONJ
ma-20	13	10	)	)	PUNCT
ma-20	13	11	j	j	PROPN
ma-20	13	12	(	(	PUNCT
ma-20	13	13	x	x	NOUN
ma-20	13	14	)	)	PUNCT
ma-20	13	15	:	:	PUNCT
ma-20	13	16	=	=	PUNCT
ma-20	13	17	sup{min	sup{min	PROPN
ma-20	13	18	‖u1	‖u1	PROPN
ma-20	13	19	±	±	PROPN
ma-20	13	20	u2	u2	PROPN
ma-20	13	21	±	±	PROPN
ma-20	13	22	·	·	PUNCT
ma-20	13	23	·	·	PUNCT
ma-20	13	24	·	·	PUNCT
ma-20	13	25	±	±	NUM
ma-20	14	1	un‖	un‖	NOUN
ma-20	14	2	:	:	PUNCT
ma-20	14	3	ui	ui	PROPN
ma-20	14	4	∈	∈	PROPN
ma-20	14	5	sx	sx	PROPN
ma-20	14	6	,	,	PUNCT
ma-20	14	7	i	i	PRON
ma-20	14	8	=	=	NOUN
ma-20	14	9	1	1	NUM
ma-20	14	10	,	,	PUNCT
ma-20	14	11	2	2	NUM
ma-20	14	12	,	,	PUNCT
ma-20	14	13	.	.	PUNCT
ma-20	14	14	.	.	PUNCT
ma-20	14	15	.	.	PUNCT
ma-20	15	1	,	,	PUNCT
ma-20	15	2	n}.note	n}.note	VERB
ma-20	15	3	that	that	SCONJ
ma-20	15	4	in	in	ADP
ma-20	15	5	the	the	DET
ma-20	15	6	definition	definition	NOUN
ma-20	15	7	of	of	ADP
ma-20	15	8	c(n)nj	c(n)nj	X
ma-20	15	9	(	(	PUNCT
ma-20	15	10	x	x	NOUN
ma-20	15	11	)	)	PUNCT
ma-20	15	12	,	,	PUNCT
ma-20	15	13	the	the	DET
ma-20	15	14	sum	sum	NOUN
ma-20	15	15	∑	∑	PROPN
ma-20	15	16	±	±	NOUN
ma-20	15	17	is	be	AUX
ma-20	15	18	taken	take	VERB
ma-20	15	19	over	over	ADP
ma-20	15	20	all	all	DET
ma-20	15	21	possible	possible	ADJ
ma-20	15	22	combinations	combination	NOUN
ma-20	15	23	of	of	ADP
ma-20	15	24	±signs	±sign	NOUN
ma-20	15	25	.	.	PUNCT
ma-20	16	1	similarly	similarly	ADV
ma-20	16	2	,	,	PUNCT
ma-20	16	3	in	in	ADP
ma-20	16	4	the	the	DET
ma-20	16	5	definition	definition	NOUN
ma-20	16	6	of	of	ADP
ma-20	16	7	c(n)j	c(n)j	PROPN
ma-20	16	8	(	(	PUNCT
ma-20	16	9	x	x	NOUN
ma-20	16	10	)	)	PUNCT
ma-20	16	11	,	,	PUNCT
ma-20	16	12	the	the	DET
ma-20	16	13	minimum	minimum	NOUN
ma-20	16	14	is	be	AUX
ma-20	16	15	taken	take	VERB
ma-20	16	16	over	over	ADP
ma-20	16	17	all	all	DET
ma-20	16	18	possible	possible	ADJ
ma-20	16	19	combinationsof	combinationsof	NOUN
ma-20	16	20	±	±	NOUN
ma-20	16	21	signs	sign	NOUN
ma-20	16	22	,	,	PUNCT
ma-20	16	23	while	while	SCONJ
ma-20	16	24	the	the	DET
ma-20	16	25	supremum	supremum	NOUN
ma-20	16	26	is	be	AUX
ma-20	16	27	taken	take	VERB
ma-20	16	28	over	over	ADP
ma-20	16	29	all	all	DET
ma-20	16	30	ui	ui	PROPN
ma-20	16	31	’s	’s	NOUN
ma-20	16	32	in	in	ADP
ma-20	16	33	the	the	DET
ma-20	16	34	unit	unit	NOUN
ma-20	16	35	sphere	sphere	NOUN
ma-20	16	36	sx	sx	PROPN
ma-20	16	37	:	:	PUNCT
ma-20	16	38	=	=	SYM
ma-20	16	39	{	{	PUNCT
ma-20	16	40	u	u	NOUN
ma-20	16	41	∈	∈	PROPN
ma-20	16	42	x	x	X
ma-20	16	43	:	:	PUNCT
ma-20	17	1	‖u‖	‖u‖	PROPN
ma-20	17	2	=	=	PUNCT
ma-20	17	3	1}.these	1}.these	NUM
ma-20	17	4	constants	constant	NOUN
ma-20	17	5	measure	measure	VERB
ma-20	17	6	some	some	DET
ma-20	17	7	sort	sort	NOUN
ma-20	17	8	of	of	ADP
ma-20	17	9	convexity	convexity	NOUN
ma-20	17	10	of	of	ADP
ma-20	17	11	a	a	DET
ma-20	17	12	banach	banach	NOUN
ma-20	17	13	space.we	space.we	PRON
ma-20	17	14	say	say	VERB
ma-20	17	15	that	that	SCONJ
ma-20	17	16	x	x	PRON
ma-20	17	17	is	be	AUX
ma-20	17	18	uniformly	uniformly	ADV
ma-20	17	19	n	n	CCONJ
ma-20	17	20	-	-	PUNCT
ma-20	17	21	convex	convex	NOUN
ma-20	18	1	[	[	X
ma-20	18	2	2	2	NUM
ma-20	18	3	]	]	X
ma-20	18	4	if	if	SCONJ
ma-20	18	5	for	for	ADP
ma-20	18	6	every	every	DET
ma-20	18	7	ε	ε	PROPN
ma-20	18	8	∈	∈	PROPN
ma-20	18	9	(	(	PUNCT
ma-20	18	10	0	0	NUM
ma-20	18	11	,	,	PUNCT
ma-20	18	12	n	n	CCONJ
ma-20	18	13	]	]	PUNCT
ma-20	18	14	there	there	PRON
ma-20	18	15	exists	exist	VERB
ma-20	18	16	a	a	DET
ma-20	18	17	δ	δ	PROPN
ma-20	18	18	∈	∈	PROPN
ma-20	18	19	(	(	PUNCT
ma-20	18	20	0	0	NUM
ma-20	18	21	,	,	PUNCT
ma-20	18	22	1	1	NUM
ma-20	18	23	)	)	PUNCT
ma-20	18	24	such	such	ADJ
ma-20	18	25	thatfor	thatfor	ADP
ma-20	18	26	every	every	DET
ma-20	18	27	u1	u1	NOUN
ma-20	18	28	,	,	PUNCT
ma-20	18	29	u2	u2	NOUN
ma-20	18	30	,	,	PUNCT
ma-20	18	31	.	.	PUNCT
ma-20	18	32	.	.	PUNCT
ma-20	19	1	.	.	PUNCT
ma-20	20	1	,	,	PUNCT
ma-20	20	2	un	un	PROPN
ma-20	20	3	∈	∈	PROPN
ma-20	20	4	sx	sx	PROPN
ma-20	20	5	with	with	ADP
ma-20	20	6	‖u1	‖u1	PROPN
ma-20	20	7	±	±	PROPN
ma-20	20	8	u2	u2	PROPN
ma-20	20	9	±	±	PROPN
ma-20	20	10	·	·	PUNCT
ma-20	20	11	·	·	PUNCT
ma-20	20	12	·	·	PUNCT
ma-20	21	1	±	±	NUM
ma-20	21	2	un‖	un‖	PROPN
ma-20	21	3	≥	≥	X
ma-20	21	4	ε	ε	VERB
ma-20	21	5	for	for	ADP
ma-20	21	6	all	all	DET
ma-20	21	7	combinations	combination	NOUN
ma-20	21	8	of	of	ADP
ma-20	21	9	±	±	NOUN
ma-20	21	10	signs	sign	NOUN
ma-20	21	11	exceptfor	exceptfor	VERB
ma-20	21	12	‖u1	‖u1	ADV
ma-20	21	13	+	+	CCONJ
ma-20	21	14	u2	u2	PROPN
ma-20	21	15	+	+	CCONJ
ma-20	21	16	·	·	PUNCT
ma-20	21	17	·	·	PUNCT
ma-20	21	18	·	·	PUNCT
ma-20	22	1	+	+	CCONJ
ma-20	22	2	un‖	un‖	NOUN
ma-20	22	3	,	,	PUNCT
ma-20	22	4	we	we	PRON
ma-20	22	5	have	have	VERB
ma-20	22	6	‖u1	‖u1	ADV
ma-20	23	1	+	+	CCONJ
ma-20	23	2	u2	u2	PROPN
ma-20	23	3	+	+	CCONJ
ma-20	23	4	·	·	PUNCT
ma-20	23	5	·	·	PUNCT
ma-20	23	6	·	·	PUNCT
ma-20	23	7	+	+	NUM
ma-20	23	8	un‖	un‖	PROPN
ma-20	23	9	≤	≤	NUM
ma-20	23	10	n(1−	n(1−	PROPN
ma-20	23	11	δ	δ	PROPN
ma-20	23	12	)	)	PUNCT
ma-20	23	13	.	.	PUNCT
ma-20	24	1	received	receive	VERB
ma-20	24	2	:	:	PUNCT
ma-20	24	3	31	31	NUM
ma-20	24	4	aug	aug	PROPN
ma-20	24	5	2021	2021	NUM
ma-20	24	6	.	.	PUNCT
ma-20	25	1	key	key	ADJ
ma-20	25	2	words	word	NOUN
ma-20	25	3	and	and	CCONJ
ma-20	25	4	phrases	phrase	NOUN
ma-20	25	5	.	.	PUNCT
ma-20	26	1	n	n	CCONJ
ma-20	26	2	-	-	PUNCT
ma-20	26	3	th	th	X
ma-20	26	4	von	von	PROPN
ma-20	26	5	neumann	neumann	PROPN
ma-20	26	6	-	-	PUNCT
ma-20	26	7	jordan	jordan	PROPN
ma-20	26	8	constant	constant	PROPN
ma-20	26	9	;	;	PUNCT
ma-20	26	10	n	n	CCONJ
ma-20	26	11	-	-	PUNCT
ma-20	26	12	th	th	X
ma-20	26	13	james	james	PROPN
ma-20	26	14	constant	constant	PROPN
ma-20	26	15	;	;	PUNCT
ma-20	26	16	discrete	discrete	ADJ
ma-20	26	17	morrey	morrey	NOUN
ma-20	26	18	spaces	space	NOUN
ma-20	26	19	;	;	PUNCT
ma-20	26	20	uniformlynon-`1	uniformlynon-`1	NUM
ma-20	26	21	spaces	space	VERB
ma-20	26	22	;	;	PUNCT
ma-20	26	23	uniformly	uniformly	ADV
ma-20	26	24	n	n	CCONJ
ma-20	26	25	-	-	PUNCT
ma-20	26	26	convex	convex	NOUN
ma-20	26	27	spaces	space	NOUN
ma-20	26	28	.	.	PUNCT
ma-20	27	1	1	1	NUM
ma-20	27	2	https://adac.ee	https://adac.ee	PROPN
ma-20	27	3	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	27	4	https://orcid.org/0000-0001-7879-8321	https://orcid.org/0000-0001-7879-8321	PROPN
ma-20	27	5	eur	eur	PROPN
ma-20	27	6	.	.	PUNCT
ma-20	28	1	j.	j.	PROPN
ma-20	28	2	math	math	PROPN
ma-20	28	3	.	.	PUNCT
ma-20	29	1	anal	anal	PROPN
ma-20	29	2	.	.	PUNCT
ma-20	30	1	10.28924	10.28924	NUM
ma-20	30	2	/	/	SYM
ma-20	30	3	ada	ada	PROPN
ma-20	30	4	/	/	SYM
ma-20	30	5	ma.2.2	ma.2.2	NOUN
ma-20	30	6	2meanwhile	2meanwhile	NUM
ma-20	30	7	,	,	PUNCT
ma-20	30	8	we	we	PRON
ma-20	30	9	say	say	VERB
ma-20	30	10	that	that	SCONJ
ma-20	30	11	x	x	PRON
ma-20	30	12	is	be	AUX
ma-20	30	13	uniformly	uniformly	ADV
ma-20	30	14	non-`1n	non-`1n	PROPN
ma-20	31	1	[	[	X
ma-20	31	2	1,5,8	1,5,8	X
ma-20	31	3	]	]	X
ma-20	31	4	if	if	SCONJ
ma-20	31	5	there	there	PRON
ma-20	31	6	exists	exist	VERB
ma-20	31	7	a	a	DET
ma-20	31	8	δ	δ	PROPN
ma-20	31	9	∈	∈	PROPN
ma-20	31	10	(	(	PUNCT
ma-20	31	11	0	0	NUM
ma-20	31	12	,	,	PUNCT
ma-20	31	13	1	1	NUM
ma-20	31	14	)	)	PUNCT
ma-20	31	15	such	such	ADJ
ma-20	31	16	that	that	PRON
ma-20	31	17	for	for	ADP
ma-20	31	18	every	every	DET
ma-20	31	19	u1	u1	NOUN
ma-20	31	20	,	,	PUNCT
ma-20	31	21	u2	u2	NOUN
ma-20	31	22	,	,	PUNCT
ma-20	31	23	.	.	PUNCT
ma-20	31	24	.	.	PUNCT
ma-20	32	1	.	.	PUNCT
ma-20	33	1	,	,	PUNCT
ma-20	33	2	un	un	PROPN
ma-20	33	3	∈	∈	PROPN
ma-20	33	4	sx	sx	PROPN
ma-20	33	5	we	we	PRON
ma-20	33	6	have	have	VERB
ma-20	33	7	min	min	PROPN
ma-20	33	8	‖u1	‖u1	PROPN
ma-20	33	9	±	±	PROPN
ma-20	33	10	u2	u2	PROPN
ma-20	33	11	±	±	PROPN
ma-20	33	12	·	·	PUNCT
ma-20	33	13	·	·	PUNCT
ma-20	33	14	·	·	PUNCT
ma-20	33	15	±	±	NUM
ma-20	34	1	un‖	un‖	NOUN
ma-20	34	2	≤	≤	NUM
ma-20	34	3	n(1−	n(1−	PROPN
ma-20	34	4	δ	δ	PROPN
ma-20	34	5	)	)	PUNCT
ma-20	34	6	.	.	PUNCT
ma-20	35	1	note	note	VERB
ma-20	35	2	that	that	SCONJ
ma-20	35	3	for	for	ADP
ma-20	35	4	n	n	NOUN
ma-20	35	5	=	=	SYM
ma-20	35	6	2	2	NUM
ma-20	35	7	,	,	PUNCT
ma-20	35	8	uniformly	uniformly	ADV
ma-20	35	9	non-`1n	non-`1n	PROPN
ma-20	35	10	spaces	space	NOUN
ma-20	35	11	are	be	AUX
ma-20	35	12	known	know	VERB
ma-20	35	13	as	as	ADP
ma-20	35	14	uniformly	uniformly	ADV
ma-20	35	15	nonsquare	nonsquare	ADJ
ma-20	35	16	spaces	space	NOUN
ma-20	35	17	,	,	PUNCT
ma-20	35	18	while	while	SCONJ
ma-20	35	19	for	for	ADP
ma-20	35	20	n	n	NOUN
ma-20	35	21	=	=	SYM
ma-20	35	22	3	3	NUM
ma-20	35	23	they	they	PRON
ma-20	35	24	are	be	AUX
ma-20	35	25	known	know	VERB
ma-20	35	26	as	as	ADP
ma-20	35	27	uniformly	uniformly	ADV
ma-20	35	28	non	non	ADJ
ma-20	35	29	-	-	ADJ
ma-20	35	30	octahedral	octahedral	ADJ
ma-20	35	31	spaces	space	NOUN
ma-20	35	32	.	.	PUNCT
ma-20	36	1	one	one	PRON
ma-20	36	2	may	may	AUX
ma-20	36	3	verify	verify	VERB
ma-20	36	4	that	that	SCONJ
ma-20	36	5	if	if	SCONJ
ma-20	36	6	x	x	PRON
ma-20	36	7	is	be	AUX
ma-20	36	8	uniformly	uniformly	ADV
ma-20	36	9	n	n	CCONJ
ma-20	36	10	-	-	PUNCT
ma-20	36	11	convex	convex	NOUN
ma-20	36	12	,	,	PUNCT
ma-20	36	13	then	then	ADV
ma-20	36	14	x	x	PUNCT
ma-20	36	15	is	be	AUX
ma-20	36	16	uniformly	uniformly	ADV
ma-20	36	17	non-`1n	non-`1n	PROPN
ma-20	37	1	[	[	X
ma-20	37	2	2].now	2].now	NUM
ma-20	37	3	a	a	DET
ma-20	37	4	few	few	ADJ
ma-20	37	5	remarks	remark	NOUN
ma-20	37	6	about	about	ADP
ma-20	37	7	the	the	DET
ma-20	37	8	two	two	NUM
ma-20	37	9	constants	constant	NOUN
ma-20	37	10	,	,	PUNCT
ma-20	37	11	and	and	CCONJ
ma-20	37	12	their	their	PRON
ma-20	37	13	associations	association	NOUN
ma-20	37	14	with	with	ADP
ma-20	37	15	the	the	DET
ma-20	37	16	uniformly	uniformly	ADJ
ma-20	37	17	non-`1nand	non-`1nand	CCONJ
ma-20	37	18	uniformly	uniformly	ADV
ma-20	37	19	n	n	CCONJ
ma-20	37	20	-	-	PUNCT
ma-20	37	21	convex	convex	NOUN
ma-20	37	22	properties	property	NOUN
ma-20	37	23	.	.	PUNCT
ma-20	38	1	•	•	NUM
ma-20	38	2	1	1	NUM
ma-20	38	3	≤	≤	NUM
ma-20	38	4	c(n)nj	c(n)nj	NUM
ma-20	38	5	(	(	PUNCT
ma-20	38	6	x	x	NOUN
ma-20	38	7	)	)	PUNCT
ma-20	38	8	≤	≤	NOUN
ma-20	38	9	n	n	CCONJ
ma-20	38	10	and	and	CCONJ
ma-20	38	11	c(n)nj	c(n)nj	ADJ
ma-20	38	12	(	(	PUNCT
ma-20	38	13	x	x	X
ma-20	38	14	)	)	PUNCT
ma-20	38	15	=	=	SYM
ma-20	38	16	1	1	NUM
ma-20	38	17	if	if	SCONJ
ma-20	38	18	and	and	CCONJ
ma-20	38	19	only	only	ADV
ma-20	38	20	if	if	SCONJ
ma-20	38	21	x	x	PRON
ma-20	38	22	is	be	AUX
ma-20	38	23	a	a	DET
ma-20	38	24	hilbert	hilbert	NOUN
ma-20	38	25	space	space	NOUN
ma-20	39	1	[	[	X
ma-20	39	2	6	6	NUM
ma-20	39	3	]	]	PUNCT
ma-20	39	4	.	.	PUNCT
ma-20	40	1	•	•	NUM
ma-20	40	2	1	1	NUM
ma-20	40	3	≤	≤	NOUN
ma-20	40	4	c(n)j	c(n)j	PROPN
ma-20	40	5	(	(	PUNCT
ma-20	40	6	x	x	NOUN
ma-20	40	7	)	)	PUNCT
ma-20	40	8	≤	≤	NOUN
ma-20	40	9	n.	n.	NOUN
ma-20	40	10	if	if	SCONJ
ma-20	40	11	dim(x	dim(x	PROPN
ma-20	40	12	)	)	PUNCT
ma-20	40	13	=	=	SYM
ma-20	41	1	∞	∞	PROPN
ma-20	41	2	,	,	PUNCT
ma-20	41	3	then	then	ADV
ma-20	41	4	√n	√n	ADJ
ma-20	41	5	≤	≤	ADJ
ma-20	41	6	c(n)j	c(n)j	PROPN
ma-20	41	7	(	(	PUNCT
ma-20	41	8	x	x	NOUN
ma-20	41	9	)	)	PUNCT
ma-20	41	10	≤	≤	NOUN
ma-20	41	11	n.	n.	NOUN
ma-20	41	12	moreover	moreover	ADV
ma-20	41	13	,	,	PUNCT
ma-20	41	14	if	if	SCONJ
ma-20	41	15	x	x	PRON
ma-20	41	16	is	be	AUX
ma-20	41	17	a	a	DET
ma-20	41	18	hilbertspace	hilbertspace	NOUN
ma-20	41	19	,	,	PUNCT
ma-20	41	20	then	then	ADV
ma-20	41	21	c(n)j	c(n)j	PROPN
ma-20	41	22	(	(	PUNCT
ma-20	41	23	x	x	X
ma-20	41	24	)	)	PUNCT
ma-20	41	25	=	=	PUNCT
ma-20	41	26	√n	√n	NOUN
ma-20	42	1	[	[	X
ma-20	42	2	7	7	NUM
ma-20	42	3	]	]	PUNCT
ma-20	42	4	.	.	PUNCT
ma-20	43	1	•	•	NOUN
ma-20	44	1	x	x	X
ma-20	44	2	is	be	AUX
ma-20	44	3	uniformly	uniformly	ADV
ma-20	44	4	non-`1n	non-`1n	PROPN
ma-20	45	1	if	if	SCONJ
ma-20	45	2	and	and	CCONJ
ma-20	45	3	only	only	ADV
ma-20	45	4	if	if	SCONJ
ma-20	45	5	c(n)nj	c(n)nj	X
ma-20	45	6	(	(	PUNCT
ma-20	45	7	x	x	NOUN
ma-20	45	8	)	)	PUNCT
ma-20	45	9	<	<	X
ma-20	45	10	n	n	X
ma-20	45	11	[	[	X
ma-20	45	12	6	6	NUM
ma-20	45	13	]	]	PUNCT
ma-20	45	14	.	.	PUNCT
ma-20	46	1	•	•	NOUN
ma-20	47	1	x	x	X
ma-20	47	2	is	be	AUX
ma-20	47	3	uniformly	uniformly	ADV
ma-20	47	4	non-`1n	non-`1n	PROPN
ma-20	48	1	if	if	SCONJ
ma-20	48	2	and	and	CCONJ
ma-20	48	3	only	only	ADV
ma-20	48	4	if	if	SCONJ
ma-20	48	5	c(n)j	c(n)j	PROPN
ma-20	48	6	(	(	PUNCT
ma-20	48	7	x	x	X
ma-20	48	8	)	)	PUNCT
ma-20	48	9	<	<	X
ma-20	48	10	n	n	X
ma-20	49	1	[	[	X
ma-20	49	2	7	7	NUM
ma-20	49	3	]	]	PUNCT
ma-20	49	4	.	.	PUNCT
ma-20	50	1	the	the	DET
ma-20	50	2	last	last	ADJ
ma-20	50	3	two	two	NUM
ma-20	50	4	statements	statement	NOUN
ma-20	50	5	tell	tell	VERB
ma-20	50	6	us	we	PRON
ma-20	50	7	that	that	SCONJ
ma-20	50	8	if	if	SCONJ
ma-20	50	9	c(n)nj	c(n)nj	X
ma-20	50	10	(	(	PUNCT
ma-20	50	11	x	x	NOUN
ma-20	50	12	)	)	PUNCT
ma-20	50	13	=	=	SYM
ma-20	50	14	n	n	PROPN
ma-20	50	15	or	or	CCONJ
ma-20	50	16	c(n)j	c(n)j	PROPN
ma-20	50	17	(	(	PUNCT
ma-20	50	18	x	x	X
ma-20	50	19	)	)	PUNCT
ma-20	50	20	=	=	SYM
ma-20	50	21	n	n	CCONJ
ma-20	50	22	,	,	PUNCT
ma-20	50	23	then	then	ADV
ma-20	50	24	x	x	PUNCT
ma-20	50	25	is	be	AUX
ma-20	50	26	not	not	PART
ma-20	50	27	uniformly	uniformly	ADJ
ma-20	50	28	non-`1nand	non-`1nand	ADV
ma-20	50	29	hence	hence	ADV
ma-20	50	30	not	not	PART
ma-20	50	31	uniformly	uniformly	ADV
ma-20	50	32	n-convex.in	n-convex.in	VERB
ma-20	50	33	this	this	DET
ma-20	50	34	paper	paper	NOUN
ma-20	50	35	,	,	PUNCT
ma-20	50	36	we	we	PRON
ma-20	50	37	shall	shall	AUX
ma-20	50	38	compute	compute	VERB
ma-20	50	39	the	the	DET
ma-20	50	40	value	value	NOUN
ma-20	50	41	of	of	ADP
ma-20	50	42	the	the	DET
ma-20	50	43	two	two	NUM
ma-20	50	44	constants	constant	NOUN
ma-20	50	45	for	for	ADP
ma-20	50	46	discrete	discrete	ADJ
ma-20	50	47	morrey	morrey	NOUN
ma-20	50	48	spaces	space	NOUN
ma-20	50	49	.	.	PUNCT
ma-20	51	1	let	let	VERB
ma-20	51	2	ω	ω	NOUN
ma-20	51	3	:	:	PUNCT
ma-20	51	4	=	=	SYM
ma-20	51	5	n	n	PRON
ma-20	51	6	∪	∪	X
ma-20	51	7	{	{	PUNCT
ma-20	51	8	0	0	NUM
ma-20	51	9	}	}	PUNCT
ma-20	51	10	and	and	CCONJ
ma-20	51	11	m	m	PROPN
ma-20	51	12	=	=	SYM
ma-20	51	13	(	(	PUNCT
ma-20	51	14	m1	m1	PROPN
ma-20	51	15	,	,	PUNCT
ma-20	51	16	m2	m2	PROPN
ma-20	51	17	,	,	PUNCT
ma-20	51	18	.	.	PUNCT
ma-20	51	19	.	.	PUNCT
ma-20	52	1	.	.	PUNCT
ma-20	53	1	,	,	PUNCT
ma-20	53	2	md	md	PROPN
ma-20	53	3	)	)	PUNCT
ma-20	53	4	∈	∈	PROPN
ma-20	54	1	zd	zd	PROPN
ma-20	54	2	.	.	PUNCT
ma-20	55	1	define	define	VERB
ma-20	55	2	sm	sm	PROPN
ma-20	55	3	,	,	PUNCT
ma-20	55	4	n	n	PROPN
ma-20	55	5	:	:	PUNCT
ma-20	55	6	=	=	SYM
ma-20	55	7	{	{	PUNCT
ma-20	55	8	k	k	PROPN
ma-20	55	9	∈	∈	PROPN
ma-20	55	10	zd	zd	PROPN
ma-20	55	11	:	:	PUNCT
ma-20	55	12	‖k	‖k	VERB
ma-20	55	13	−m‖∞	−m‖∞	NOUN
ma-20	55	14	≤	≤	NOUN
ma-20	55	15	n	n	CCONJ
ma-20	55	16	}	}	PUNCT
ma-20	55	17	where	where	SCONJ
ma-20	55	18	n	n	DET
ma-20	55	19	∈	∈	PROPN
ma-20	55	20	ω	ω	PROPN
ma-20	55	21	and	and	CCONJ
ma-20	56	1	‖m‖∞	‖m‖∞	PROPN
ma-20	56	2	=	=	PUNCT
ma-20	56	3	max{|mi	max{|mi	PROPN
ma-20	57	1	|	|	ADV
ma-20	57	2	:	:	PUNCT
ma-20	57	3	1	1	NUM
ma-20	57	4	≤	≤	NUM
ma-20	57	5	i	i	X
ma-20	57	6	≤	≤	NOUN
ma-20	58	1	d	d	NOUN
ma-20	58	2	}	}	PUNCT
ma-20	58	3	.	.	PUNCT
ma-20	59	1	denote	denote	VERB
ma-20	59	2	by	by	ADP
ma-20	59	3	|sm	|sm	ADP
ma-20	59	4	,	,	PUNCT
ma-20	59	5	n	n	CCONJ
ma-20	59	6	|	|	ADV
ma-20	59	7	the	the	DET
ma-20	59	8	cardinality	cardinality	NOUN
ma-20	59	9	of	of	ADP
ma-20	59	10	sm	sm	PROPN
ma-20	59	11	,	,	PUNCT
ma-20	59	12	n	n	PROPN
ma-20	59	13	for	for	ADP
ma-20	59	14	m	m	PROPN
ma-20	59	15	∈	∈	PROPN
ma-20	59	16	zd	zd	PROPN
ma-20	59	17	and	and	CCONJ
ma-20	59	18	n	n	PRON
ma-20	59	19	∈	∈	PROPN
ma-20	59	20	ω	ω	PROPN
ma-20	59	21	.	.	PUNCT
ma-20	60	1	then	then	ADV
ma-20	60	2	we	we	PRON
ma-20	60	3	have	have	VERB
ma-20	60	4	|sm	|sm	NUM
ma-20	60	5	,	,	PUNCT
ma-20	60	6	n	n	CCONJ
ma-20	61	1	|	|	NOUN
ma-20	61	2	=	=	SYM
ma-20	61	3	(	(	PUNCT
ma-20	61	4	2n	2n	NUM
ma-20	61	5	+	+	CCONJ
ma-20	61	6	1)d	1)d	NUM
ma-20	61	7	.now	.now	PUNCT
ma-20	62	1	let	let	VERB
ma-20	62	2	1	1	NUM
ma-20	62	3	≤	≤	NOUN
ma-20	62	4	p	p	NOUN
ma-20	62	5	≤	≤	ADJ
ma-20	62	6	q	q	NOUN
ma-20	62	7	<	<	X
ma-20	62	8	∞.	∞.	PROPN
ma-20	62	9	define	define	VERB
ma-20	62	10	`	`	PUNCT
ma-20	62	11	pq	pq	INTJ
ma-20	62	12	=	=	PUNCT
ma-20	62	13	`	`	PUNCT
ma-20	62	14	pq(zd	pq(zd	NOUN
ma-20	62	15	)	)	PUNCT
ma-20	62	16	to	to	PART
ma-20	62	17	be	be	AUX
ma-20	62	18	the	the	DET
ma-20	62	19	discrete	discrete	ADJ
ma-20	62	20	morrey	morrey	NOUN
ma-20	62	21	space	space	NOUN
ma-20	62	22	as	as	ADP
ma-20	62	23	introducedin	introducedin	VERB
ma-20	62	24	[	[	X
ma-20	62	25	3	3	NUM
ma-20	62	26	]	]	PUNCT
ma-20	62	27	,	,	PUNCT
ma-20	62	28	which	which	PRON
ma-20	62	29	consists	consist	VERB
ma-20	62	30	of	of	ADP
ma-20	62	31	all	all	DET
ma-20	62	32	sequences	sequence	NOUN
ma-20	62	33	x	x	X
ma-20	62	34	:	:	PUNCT
ma-20	62	35	zd	zd	PROPN
ma-20	62	36	→	→	SYM
ma-20	62	37	r	r	NOUN
ma-20	62	38	with	with	ADP
ma-20	62	39	‖x‖`pq	‖x‖`pq	NUM
ma-20	62	40	:	:	PUNCT
ma-20	62	41	=	=	NUM
ma-20	62	42	sup	sup	NOUN
ma-20	62	43	m∈zd	m∈zd	NOUN
ma-20	62	44	,	,	PUNCT
ma-20	62	45	n∈ω	n∈ω	NOUN
ma-20	62	46	|sm	|sm	NUM
ma-20	62	47	,	,	PUNCT
ma-20	62	48	n	n	CCONJ
ma-20	62	49	|	|	ADV
ma-20	62	50	1	1	NUM
ma-20	62	51	q	q	NOUN
ma-20	62	52	−	−	PROPN
ma-20	62	53	1	1	NUM
ma-20	62	54	p	p	NOUN
ma-20	62	55	(	(	PUNCT
ma-20	62	56	∑	∑	PUNCT
ma-20	62	57	k∈sm	k∈sm	PROPN
ma-20	62	58	,	,	PUNCT
ma-20	62	59	n	n	X
ma-20	62	60	|xk	|xk	X
ma-20	62	61	|p	|p	X
ma-20	62	62	)	)	PUNCT
ma-20	62	63	1	1	NUM
ma-20	63	1	p	p	NOUN
ma-20	63	2	<	<	X
ma-20	63	3	∞	∞	PROPN
ma-20	63	4	,	,	PUNCT
ma-20	63	5	where	where	SCONJ
ma-20	63	6	x	x	X
ma-20	63	7	:	:	PUNCT
ma-20	63	8	=	=	SYM
ma-20	63	9	(	(	PUNCT
ma-20	63	10	xk	xk	NOUN
ma-20	63	11	)	)	PUNCT
ma-20	63	12	with	with	ADP
ma-20	63	13	k	k	PROPN
ma-20	63	14	∈	∈	PROPN
ma-20	63	15	zd	zd	PROPN
ma-20	63	16	.	.	PUNCT
ma-20	64	1	one	one	PRON
ma-20	64	2	may	may	AUX
ma-20	64	3	observe	observe	VERB
ma-20	64	4	that	that	SCONJ
ma-20	64	5	these	these	DET
ma-20	64	6	discrete	discrete	ADJ
ma-20	64	7	morrey	morrey	NOUN
ma-20	64	8	spaces	space	NOUN
ma-20	64	9	are	be	AUX
ma-20	64	10	banachspaces	banachspace	NOUN
ma-20	64	11	[	[	X
ma-20	64	12	3	3	NUM
ma-20	64	13	]	]	PUNCT
ma-20	64	14	.	.	PUNCT
ma-20	65	1	note	note	NOUN
ma-20	65	2	,	,	PUNCT
ma-20	65	3	in	in	ADP
ma-20	65	4	particular	particular	ADJ
ma-20	65	5	,	,	PUNCT
ma-20	65	6	that	that	SCONJ
ma-20	65	7	for	for	ADP
ma-20	65	8	p	p	NOUN
ma-20	65	9	=	=	NOUN
ma-20	65	10	q	q	NOUN
ma-20	65	11	,	,	PUNCT
ma-20	65	12	we	we	PRON
ma-20	65	13	have	have	VERB
ma-20	65	14	`	`	PUNCT
ma-20	65	15	pq	pq	INTJ
ma-20	65	16	=	=	PUNCT
ma-20	66	1	`	`	PUNCT
ma-20	66	2	q	q	X
ma-20	66	3	.from	.from	ADP
ma-20	66	4	[	[	X
ma-20	66	5	4	4	X
ma-20	66	6	]	]	PUNCT
ma-20	66	7	we	we	PRON
ma-20	66	8	already	already	ADV
ma-20	66	9	know	know	VERB
ma-20	66	10	that	that	SCONJ
ma-20	66	11	cnj(`pq	cnj(`pq	X
ma-20	66	12	)	)	PUNCT
ma-20	66	13	=	=	SYM
ma-20	66	14	cj	cj	NOUN
ma-20	66	15	(	(	PUNCT
ma-20	66	16	`	`	PUNCT
ma-20	66	17	p	p	X
ma-20	66	18	q	q	NOUN
ma-20	66	19	)	)	PUNCT
ma-20	66	20	=	=	SYM
ma-20	66	21	2	2	NUM
ma-20	66	22	for	for	ADP
ma-20	66	23	1	1	NUM
ma-20	66	24	≤	≤	NOUN
ma-20	66	25	p	p	NOUN
ma-20	66	26	<	<	X
ma-20	66	27	q	q	X
ma-20	66	28	<	<	X
ma-20	66	29	∞	∞	PROPN
ma-20	66	30	,	,	PUNCT
ma-20	66	31	which	which	PRON
ma-20	66	32	impliesthat	impliesthat	VERB
ma-20	66	33	`	`	PUNCT
ma-20	66	34	pq	pq	INTJ
ma-20	66	35	are	be	AUX
ma-20	66	36	not	not	PART
ma-20	66	37	uniformly	uniformly	ADJ
ma-20	66	38	nonsquares	nonsquare	NOUN
ma-20	66	39	for	for	ADP
ma-20	66	40	those	those	DET
ma-20	66	41	p	p	X
ma-20	66	42	’s	’s	NOUN
ma-20	67	1	and	and	CCONJ
ma-20	67	2	q	q	NOUN
ma-20	67	3	’s	’s	NOUN
ma-20	67	4	.	.	PUNCT
ma-20	68	1	in	in	ADP
ma-20	68	2	this	this	DET
ma-20	68	3	paper	paper	NOUN
ma-20	68	4	,	,	PUNCT
ma-20	68	5	we	we	PRON
ma-20	68	6	shall	shall	AUX
ma-20	68	7	show	show	VERB
ma-20	68	8	that	that	SCONJ
ma-20	68	9	c	c	NOUN
ma-20	68	10	(	(	PUNCT
ma-20	68	11	n	n	CCONJ
ma-20	68	12	)	)	PUNCT
ma-20	68	13	nj	nj	PROPN
ma-20	68	14	(	(	PUNCT
ma-20	68	15	`	`	PUNCT
ma-20	68	16	p	p	X
ma-20	68	17	q	q	NOUN
ma-20	68	18	)	)	PUNCT
ma-20	68	19	=	=	SYM
ma-20	68	20	c	c	X
ma-20	68	21	(	(	PUNCT
ma-20	68	22	n	n	CCONJ
ma-20	68	23	)	)	PUNCT
ma-20	68	24	j	j	NOUN
ma-20	68	25	(	(	PUNCT
ma-20	68	26	`	`	PUNCT
ma-20	68	27	p	p	X
ma-20	68	28	q	q	NOUN
ma-20	68	29	)	)	PUNCT
ma-20	68	30	=	=	SYM
ma-20	68	31	n	n	PROPN
ma-20	68	32	for	for	ADP
ma-20	68	33	1	1	NUM
ma-20	68	34	≤	≤	NOUN
ma-20	68	35	p	p	NOUN
ma-20	68	36	<	<	X
ma-20	68	37	q	q	X
ma-20	68	38	<	<	X
ma-20	68	39	∞	∞	PROPN
ma-20	68	40	,	,	PUNCT
ma-20	68	41	which	which	PRON
ma-20	68	42	leads	lead	VERB
ma-20	68	43	us	we	PRON
ma-20	68	44	to	to	ADP
ma-20	68	45	the	the	DET
ma-20	68	46	conclusion	conclusion	NOUN
ma-20	68	47	that	that	SCONJ
ma-20	68	48	`	`	PUNCT
ma-20	68	49	pq	pq	INTJ
ma-20	68	50	arenot	arenot	ADV
ma-20	68	51	uniformly	uniformly	ADV
ma-20	68	52	non-`1n	non-`1n	PROPN
ma-20	68	53	for	for	ADP
ma-20	68	54	those	those	DET
ma-20	68	55	p	p	X
ma-20	68	56	’s	’s	NOUN
ma-20	69	1	and	and	CCONJ
ma-20	69	2	q	q	NOUN
ma-20	69	3	’s	’s	X
ma-20	69	4	,	,	PUNCT
ma-20	69	5	which	which	PRON
ma-20	69	6	is	be	AUX
ma-20	69	7	sharper	sharp	ADJ
ma-20	69	8	than	than	ADP
ma-20	69	9	the	the	DET
ma-20	69	10	existing	exist	VERB
ma-20	69	11	result	result	NOUN
ma-20	69	12	.	.	PUNCT
ma-20	70	1	(	(	PUNCT
ma-20	70	2	if	if	SCONJ
ma-20	70	3	x	x	PRON
ma-20	70	4	is	be	AUX
ma-20	70	5	notuniformly	notuniformly	ADV
ma-20	70	6	non-`1n	non-`1n	PROPN
ma-20	70	7	,	,	PUNCT
ma-20	70	8	then	then	ADV
ma-20	70	9	x	x	PUNCT
ma-20	70	10	is	be	AUX
ma-20	70	11	not	not	PART
ma-20	70	12	uniformly	uniformly	ADV
ma-20	70	13	non-`1n−1	non-`1n−1	ADJ
ma-20	70	14	,	,	PUNCT
ma-20	70	15	provided	provide	VERB
ma-20	70	16	that	that	SCONJ
ma-20	70	17	n	n	NUM
ma-20	70	18	≥	≥	NOUN
ma-20	70	19	3	3	NUM
ma-20	70	20	.	.	PUNCT
ma-20	70	21	)	)	PUNCT
ma-20	71	1	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	71	2	eur	eur	PROPN
ma-20	71	3	.	.	PUNCT
ma-20	72	1	j.	j.	PROPN
ma-20	72	2	math	math	PROPN
ma-20	72	3	.	.	PUNCT
ma-20	73	1	anal	anal	PROPN
ma-20	73	2	.	.	PUNCT
ma-20	74	1	10.28924	10.28924	NUM
ma-20	74	2	/	/	SYM
ma-20	74	3	ada	ada	PROPN
ma-20	74	4	/	/	SYM
ma-20	74	5	ma.2.2	ma.2.2	PROPN
ma-20	74	6	32	32	NUM
ma-20	74	7	.	.	PUNCT
ma-20	75	1	main	main	ADJ
ma-20	75	2	results	result	NOUN
ma-20	75	3	the	the	DET
ma-20	75	4	value	value	NOUN
ma-20	75	5	of	of	ADP
ma-20	75	6	the	the	DET
ma-20	75	7	n	n	ADV
ma-20	75	8	-	-	PUNCT
ma-20	75	9	th	th	X
ma-20	75	10	von	von	PROPN
ma-20	75	11	neumann	neumann	PROPN
ma-20	75	12	-	-	PUNCT
ma-20	75	13	jordan	jordan	PROPN
ma-20	75	14	constant	constant	PROPN
ma-20	75	15	and	and	CCONJ
ma-20	75	16	the	the	DET
ma-20	75	17	n	n	ADV
ma-20	75	18	-	-	PUNCT
ma-20	75	19	th	th	X
ma-20	75	20	james	james	PROPN
ma-20	75	21	constant	constant	PROPN
ma-20	75	22	for	for	ADP
ma-20	75	23	discretemorrey	discretemorrey	NOUN
ma-20	75	24	spaces	space	NOUN
ma-20	75	25	are	be	AUX
ma-20	75	26	stated	state	VERB
ma-20	75	27	in	in	ADP
ma-20	75	28	the	the	DET
ma-20	75	29	following	follow	VERB
ma-20	75	30	theorems	theorem	NOUN
ma-20	75	31	.	.	PUNCT
ma-20	76	1	to	to	PART
ma-20	76	2	understand	understand	VERB
ma-20	76	3	the	the	DET
ma-20	76	4	idea	idea	NOUN
ma-20	76	5	of	of	ADP
ma-20	76	6	the	the	DET
ma-20	76	7	proof	proof	NOUN
ma-20	76	8	,	,	PUNCT
ma-20	76	9	we	we	PRON
ma-20	76	10	firstpresent	firstpresent	VERB
ma-20	76	11	the	the	DET
ma-20	76	12	result	result	NOUN
ma-20	76	13	for	for	ADP
ma-20	76	14	n	n	NOUN
ma-20	76	15	=	=	SYM
ma-20	76	16	3	3	X
ma-20	76	17	.	.	PUNCT
ma-20	76	18	theorem	theorem	VERB
ma-20	76	19	2.1	2.1	NUM
ma-20	76	20	.	.	PUNCT
ma-20	77	1	for	for	ADP
ma-20	77	2	1	1	NUM
ma-20	77	3	≤	≤	NOUN
ma-20	77	4	p	p	NOUN
ma-20	77	5	<	<	X
ma-20	77	6	q	q	X
ma-20	77	7	<	<	X
ma-20	77	8	∞	∞	PROPN
ma-20	77	9	,	,	PUNCT
ma-20	77	10	we	we	PRON
ma-20	77	11	have	have	AUX
ma-20	77	12	c(3)nj	c(3)nj	VERB
ma-20	77	13	(	(	PUNCT
ma-20	77	14	`	`	PUNCT
ma-20	77	15	p	p	PRON
ma-20	77	16	q(zd	q(zd	NOUN
ma-20	77	17	)	)	PUNCT
ma-20	77	18	)	)	PUNCT
ma-20	78	1	=	=	SYM
ma-20	78	2	c(3)j	c(3)j	PROPN
ma-20	78	3	(	(	PUNCT
ma-20	78	4	`	`	PUNCT
ma-20	78	5	p	p	PRON
ma-20	78	6	q(zd	q(zd	NOUN
ma-20	78	7	)	)	PUNCT
ma-20	78	8	)	)	PUNCT
ma-20	79	1	=	=	SYM
ma-20	79	2	3	3	X
ma-20	79	3	.	.	X
ma-20	79	4	proof	proof	NOUN
ma-20	79	5	.	.	PUNCT
ma-20	80	1	to	to	PART
ma-20	80	2	prove	prove	VERB
ma-20	80	3	the	the	DET
ma-20	80	4	theorem	theorem	NOUN
ma-20	80	5	,	,	PUNCT
ma-20	80	6	it	it	PRON
ma-20	80	7	suffices	suffice	VERB
ma-20	80	8	for	for	SCONJ
ma-20	80	9	us	we	PRON
ma-20	80	10	to	to	PART
ma-20	80	11	find	find	VERB
ma-20	80	12	x	x	SYM
ma-20	80	13	(	(	PUNCT
ma-20	80	14	1	1	NUM
ma-20	80	15	)	)	PUNCT
ma-20	80	16	,	,	PUNCT
ma-20	80	17	x	x	X
ma-20	80	18	(	(	PUNCT
ma-20	80	19	2	2	NUM
ma-20	80	20	)	)	PUNCT
ma-20	80	21	,	,	PUNCT
ma-20	80	22	x	x	X
ma-20	80	23	(	(	PUNCT
ma-20	80	24	3	3	X
ma-20	80	25	)	)	PUNCT
ma-20	80	26	∈	∈	NOUN
ma-20	80	27	`	`	PUNCT
ma-20	80	28	pq	pq	INTJ
ma-20	80	29	such	such	ADJ
ma-20	80	30	that∑	that∑	NOUN
ma-20	80	31	±	±	NUM
ma-20	80	32	‖x	‖x	NOUN
ma-20	80	33	(	(	PUNCT
ma-20	80	34	1	1	X
ma-20	80	35	)	)	PUNCT
ma-20	80	36	±	±	NOUN
ma-20	80	37	x	x	SYM
ma-20	80	38	(	(	PUNCT
ma-20	80	39	2	2	NUM
ma-20	80	40	)	)	PUNCT
ma-20	80	41	±	±	NOUN
ma-20	80	42	x	x	SYM
ma-20	80	43	(	(	PUNCT
ma-20	80	44	3)‖2`pq	3)‖2`pq	NUM
ma-20	80	45	22	22	NUM
ma-20	80	46	∑3	∑3	PROPN
ma-20	80	47	i=1	i=1	PROPN
ma-20	80	48	‖x	‖x	PROPN
ma-20	80	49	(	(	PUNCT
ma-20	80	50	i)‖`pq	i)‖`pq	X
ma-20	80	51	=	=	SYM
ma-20	80	52	3	3	NUM
ma-20	80	53	for	for	ADP
ma-20	80	54	the	the	DET
ma-20	80	55	von	von	PROPN
ma-20	80	56	neumann	neumann	PROPN
ma-20	80	57	-	-	PUNCT
ma-20	80	58	jordan	jordan	PROPN
ma-20	80	59	constant	constant	PROPN
ma-20	80	60	,	,	PUNCT
ma-20	80	61	and	and	CCONJ
ma-20	80	62	min	min	NOUN
ma-20	80	63	‖x	‖x	NOUN
ma-20	80	64	(	(	PUNCT
ma-20	80	65	1	1	X
ma-20	80	66	)	)	PUNCT
ma-20	80	67	±	±	NOUN
ma-20	80	68	x	x	SYM
ma-20	80	69	(	(	PUNCT
ma-20	80	70	2	2	NUM
ma-20	80	71	)	)	PUNCT
ma-20	80	72	±	±	NOUN
ma-20	80	73	x	x	SYM
ma-20	80	74	(	(	PUNCT
ma-20	80	75	3)‖`pq	3)‖`pq	NUM
ma-20	80	76	=	=	SYM
ma-20	80	77	3	3	NUM
ma-20	80	78	for	for	ADP
ma-20	80	79	the	the	DET
ma-20	80	80	james	james	PROPN
ma-20	80	81	constant	constant	PROPN
ma-20	80	82	.	.	PUNCT
ma-20	81	1	case	case	NOUN
ma-20	81	2	1	1	NUM
ma-20	81	3	:	:	PUNCT
ma-20	81	4	d	d	NOUN
ma-20	81	5	=	=	SYM
ma-20	81	6	1	1	X
ma-20	81	7	.	.	PUNCT
ma-20	82	1	let	let	VERB
ma-20	82	2	j	j	PROPN
ma-20	82	3	∈	∈	PROPN
ma-20	82	4	z	z	PROPN
ma-20	82	5	be	be	AUX
ma-20	82	6	a	a	DET
ma-20	82	7	nonnegative	nonnegative	ADJ
ma-20	82	8	,	,	PUNCT
ma-20	82	9	even	even	ADV
ma-20	82	10	integer	integer	VERB
ma-20	82	11	such	such	ADJ
ma-20	82	12	that	that	SCONJ
ma-20	82	13	j	j	PROPN
ma-20	82	14	>	>	X
ma-20	82	15	4	4	NUM
ma-20	82	16	q	q	NOUN
ma-20	82	17	q−p	q−p	NOUN
ma-20	82	18	−	−	PROPN
ma-20	82	19	1	1	NUM
ma-20	82	20	,	,	PUNCT
ma-20	82	21	or	or	CCONJ
ma-20	82	22	equivalently	equivalently	ADV
ma-20	82	23	(	(	PUNCT
ma-20	82	24	j	j	PROPN
ma-20	83	1	+	+	CCONJ
ma-20	83	2	1	1	X
ma-20	83	3	)	)	PUNCT
ma-20	83	4	1	1	NUM
ma-20	83	5	q	q	NOUN
ma-20	83	6	−	−	PROPN
ma-20	83	7	1	1	NUM
ma-20	83	8	p	p	NOUN
ma-20	83	9	<	<	X
ma-20	83	10	4−	4−	NUM
ma-20	83	11	1	1	NUM
ma-20	83	12	p	p	NOUN
ma-20	83	13	.	.	PUNCT
ma-20	84	1	construct	construct	VERB
ma-20	84	2	x	x	SYM
ma-20	84	3	(	(	PUNCT
ma-20	84	4	1	1	NUM
ma-20	84	5	)	)	PUNCT
ma-20	84	6	,	,	PUNCT
ma-20	84	7	x	x	X
ma-20	84	8	(	(	PUNCT
ma-20	84	9	2	2	NUM
ma-20	84	10	)	)	PUNCT
ma-20	84	11	,	,	PUNCT
ma-20	84	12	x	x	X
ma-20	84	13	(	(	PUNCT
ma-20	84	14	3	3	X
ma-20	84	15	)	)	PUNCT
ma-20	84	16	∈	∈	NOUN
ma-20	84	17	`	`	PUNCT
ma-20	84	18	pq(z	pq(z	NUM
ma-20	84	19	)	)	PUNCT
ma-20	84	20	as	as	SCONJ
ma-20	84	21	follows	follow	VERB
ma-20	84	22	:	:	PUNCT
ma-20	84	23	•	•	NUM
ma-20	84	24	x	x	SYM
ma-20	84	25	(	(	PUNCT
ma-20	84	26	1	1	NUM
ma-20	84	27	)	)	PUNCT
ma-20	84	28	=	=	SYM
ma-20	84	29	(	(	PUNCT
ma-20	84	30	x	x	X
ma-20	84	31	(	(	PUNCT
ma-20	84	32	1)k	1)k	NUM
ma-20	84	33	)	)	PUNCT
ma-20	84	34	k∈z	k∈z	PROPN
ma-20	84	35	is	be	AUX
ma-20	84	36	defined	define	VERB
ma-20	84	37	by	by	ADP
ma-20	84	38	x	x	SYM
ma-20	84	39	(	(	PUNCT
ma-20	84	40	1	1	NUM
ma-20	84	41	)	)	PUNCT
ma-20	84	42	k	k	NOUN
ma-20	84	43	=	=	PUNCT
ma-20	84	44	1	1	PROPN
ma-20	84	45	,	,	PUNCT
ma-20	84	46	k	k	NOUN
ma-20	84	47	=	=	SYM
ma-20	84	48	0	0	PROPN
ma-20	84	49	,	,	PUNCT
ma-20	84	50	j	j	NOUN
ma-20	84	51	,	,	PUNCT
ma-20	84	52	2j	2j	NUM
ma-20	84	53	,	,	PUNCT
ma-20	84	54	3j	3j	NUM
ma-20	84	55	,	,	PUNCT
ma-20	84	56	0	0	NUM
ma-20	84	57	,	,	PUNCT
ma-20	84	58	otherwise	otherwise	ADV
ma-20	84	59	;	;	PUNCT
ma-20	84	60	•	•	X
ma-20	84	61	x	x	X
ma-20	84	62	(	(	PUNCT
ma-20	84	63	2	2	NUM
ma-20	84	64	)	)	PUNCT
ma-20	84	65	=	=	SYM
ma-20	85	1	(	(	PUNCT
ma-20	85	2	x	x	X
ma-20	85	3	(	(	PUNCT
ma-20	85	4	2)k	2)k	NOUN
ma-20	85	5	)	)	PUNCT
ma-20	85	6	k∈z	k∈z	PROPN
ma-20	85	7	is	be	AUX
ma-20	85	8	defined	define	VERB
ma-20	85	9	by	by	ADP
ma-20	85	10	x	x	SYM
ma-20	85	11	(	(	PUNCT
ma-20	85	12	2	2	NUM
ma-20	85	13	)	)	PUNCT
ma-20	85	14	k	k	NOUN
ma-20	85	15	=	=	PUNCT
ma-20	86	1			PROPN
ma-20	86	2	1	1	NUM
ma-20	86	3	,	,	PUNCT
ma-20	86	4	k	k	NOUN
ma-20	86	5	=	=	SYM
ma-20	86	6	0	0	PROPN
ma-20	86	7	,	,	PUNCT
ma-20	86	8	j	j	NOUN
ma-20	86	9	,	,	PUNCT
ma-20	86	10	−1	−1	PROPN
ma-20	86	11	,	,	PUNCT
ma-20	86	12	k	k	NOUN
ma-20	86	13	=	=	PUNCT
ma-20	86	14	2j	2j	NUM
ma-20	86	15	,	,	PUNCT
ma-20	86	16	3j	3j	NUM
ma-20	86	17	,	,	PUNCT
ma-20	86	18	0	0	NUM
ma-20	86	19	,	,	PUNCT
ma-20	86	20	otherwise	otherwise	ADV
ma-20	86	21	;	;	PUNCT
ma-20	86	22	•	•	X
ma-20	86	23	x	x	X
ma-20	86	24	(	(	PUNCT
ma-20	86	25	3	3	NUM
ma-20	86	26	)	)	PUNCT
ma-20	86	27	=	=	SYM
ma-20	86	28	(	(	PUNCT
ma-20	86	29	x	x	SYM
ma-20	86	30	(	(	PUNCT
ma-20	86	31	3)k	3)k	NUM
ma-20	86	32	)	)	PUNCT
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ma-20	87	3	,	,	PUNCT
ma-20	87	4	k	k	NOUN
ma-20	87	5	=	=	SYM
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ma-20	87	7	,	,	PUNCT
ma-20	87	8	2j	2j	NUM
ma-20	87	9	,	,	PUNCT
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ma-20	87	11	,	,	PUNCT
ma-20	87	12	k	k	PROPN
ma-20	87	13	=	=	SYM
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ma-20	87	17	,	,	PUNCT
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ma-20	87	19	,	,	PUNCT
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ma-20	88	3	.	.	PUNCT
ma-20	89	1	j.	j.	PROPN
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ma-20	89	3	.	.	PUNCT
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ma-20	90	2	.	.	PUNCT
ma-20	91	1	10.28924	10.28924	NUM
ma-20	91	2	/	/	SYM
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ma-20	91	9	are	be	AUX
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ma-20	91	15	`	`	PUNCT
ma-20	91	16	pq(z	pq(z	NUM
ma-20	91	17	)	)	PUNCT
ma-20	91	18	.	.	PUNCT
ma-20	92	1	indeed	indeed	ADV
ma-20	92	2	,	,	PUNCT
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ma-20	92	4	the	the	DET
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ma-20	92	6	sequence	sequence	NOUN
ma-20	92	7	,	,	PUNCT
ma-20	92	8	we	we	PRON
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ma-20	92	11	(	(	PUNCT
ma-20	92	12	1)‖`pq	1)‖`pq	NUM
ma-20	92	13	=	=	SYM
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ma-20	92	16	,	,	PUNCT
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ma-20	92	19	,	,	PUNCT
ma-20	92	20	n	n	CCONJ
ma-20	92	21	|	|	ADV
ma-20	93	1	1	1	NUM
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ma-20	93	4	1	1	NUM
ma-20	93	5	p	p	NOUN
ma-20	93	6	(	(	PUNCT
ma-20	93	7	∑	∑	PUNCT
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ma-20	93	9	,	,	PUNCT
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ma-20	93	13	1)k	1)k	NUM
ma-20	93	14	|	|	CCONJ
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ma-20	93	82	1	1	X
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ma-20	93	87	1	1	NUM
ma-20	93	88	p	p	NOUN
ma-20	93	89	4	4	NUM
ma-20	93	90	1	1	NUM
ma-20	93	91	p	p	NOUN
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ma-20	93	93	.	.	PUNCT
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ma-20	94	2	(	(	PUNCT
ma-20	94	3	3j	3j	NOUN
ma-20	94	4	+	+	CCONJ
ma-20	94	5	1	1	X
ma-20	94	6	)	)	PUNCT
ma-20	94	7	1q−	1q−	NUM
ma-20	94	8	1p	1p	NOUN
ma-20	94	9	<	<	X
ma-20	94	10	(	(	PUNCT
ma-20	94	11	2j	2j	X
ma-20	94	12	+	+	CCONJ
ma-20	94	13	1	1	X
ma-20	94	14	)	)	PUNCT
ma-20	94	15	1q−	1q−	NUM
ma-20	94	16	1p	1p	NOUN
ma-20	94	17	<	<	X
ma-20	94	18	(	(	PUNCT
ma-20	94	19	j	j	NOUN
ma-20	94	20	+	+	CCONJ
ma-20	94	21	1	1	X
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ma-20	94	25	<	<	X
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ma-20	94	27	1p	1p	NUM
ma-20	94	28	,	,	PUNCT
ma-20	94	29	we	we	PRON
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ma-20	94	31	‖x	‖x	NOUN
ma-20	95	1	(	(	PUNCT
ma-20	95	2	1)‖`pq	1)‖`pq	NUM
ma-20	95	3	=	=	SYM
ma-20	95	4	1	1	NUM
ma-20	95	5	.	.	PUNCT
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ma-20	95	7	,	,	PUNCT
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ma-20	95	10	that	that	SCONJ
ma-20	95	11	‖x	‖x	PRON
ma-20	95	12	(	(	PUNCT
ma-20	95	13	2)‖`pq	2)‖`pq	NUM
ma-20	95	14	=	=	SYM
ma-20	95	15	‖x	‖x	NOUN
ma-20	95	16	(	(	PUNCT
ma-20	95	17	3)‖`pq	3)‖`pq	NUM
ma-20	95	18	=	=	SYM
ma-20	95	19	1.next	1.next	NUM
ma-20	95	20	,	,	PUNCT
ma-20	95	21	we	we	PRON
ma-20	95	22	observe	observe	VERB
ma-20	95	23	that	that	SCONJ
ma-20	95	24	x	x	SYM
ma-20	95	25	(	(	PUNCT
ma-20	95	26	1	1	NUM
ma-20	95	27	)	)	PUNCT
ma-20	95	28	k	k	NOUN
ma-20	96	1	+	+	CCONJ
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ma-20	96	3	(	(	PUNCT
ma-20	96	4	2	2	NUM
ma-20	96	5	)	)	PUNCT
ma-20	96	6	k	k	NOUN
ma-20	97	1	+	+	CCONJ
ma-20	97	2	x	x	SYM
ma-20	97	3	(	(	PUNCT
ma-20	97	4	3	3	NUM
ma-20	97	5	)	)	PUNCT
ma-20	97	6	k	k	NOUN
ma-20	97	7	=	=	PUNCT
ma-20	97	8			PROPN
ma-20	97	9	3	3	NUM
ma-20	97	10	,	,	PUNCT
ma-20	97	11	k	k	PROPN
ma-20	97	12	=	=	SYM
ma-20	97	13	0	0	NUM
ma-20	97	14	,	,	PUNCT
ma-20	97	15	1	1	NUM
ma-20	97	16	,	,	PUNCT
ma-20	97	17	k	k	PROPN
ma-20	97	18	=	=	SYM
ma-20	97	19	j	j	PROPN
ma-20	97	20	,	,	PUNCT
ma-20	97	21	2j	2j	NUM
ma-20	97	22	,	,	PUNCT
ma-20	97	23	−1	−1	NOUN
ma-20	97	24	,	,	PUNCT
ma-20	97	25	k	k	PROPN
ma-20	97	26	=	=	SYM
ma-20	97	27	3j	3j	NUM
ma-20	97	28	,	,	PUNCT
ma-20	97	29	0	0	NUM
ma-20	97	30	,	,	PUNCT
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ma-20	97	32	;	;	PUNCT
ma-20	97	33	x	x	X
ma-20	97	34	(	(	PUNCT
ma-20	97	35	1	1	NUM
ma-20	97	36	)	)	PUNCT
ma-20	97	37	k	k	NOUN
ma-20	98	1	+	+	CCONJ
ma-20	98	2	x	x	SYM
ma-20	98	3	(	(	PUNCT
ma-20	98	4	2	2	NUM
ma-20	98	5	)	)	PUNCT
ma-20	98	6	k	k	NOUN
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ma-20	98	8	x	x	SYM
ma-20	98	9	(	(	PUNCT
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ma-20	98	11	)	)	PUNCT
ma-20	98	12	k	k	NOUN
ma-20	98	13	=	=	PUNCT
ma-20	98	14			PROPN
ma-20	98	15	3	3	NUM
ma-20	98	16	,	,	PUNCT
ma-20	98	17	k	k	PROPN
ma-20	98	18	=	=	SYM
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ma-20	98	22	,	,	PUNCT
ma-20	98	23	k	k	NOUN
ma-20	98	24	=	=	SYM
ma-20	98	25	0	0	NUM
ma-20	98	26	,	,	PUNCT
ma-20	98	27	3j	3j	NUM
ma-20	98	28	,	,	PUNCT
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ma-20	98	30	,	,	PUNCT
ma-20	98	31	k	k	NOUN
ma-20	98	32	=	=	PUNCT
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ma-20	98	34	,	,	PUNCT
ma-20	98	35	0	0	NUM
ma-20	98	36	,	,	PUNCT
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ma-20	98	40	(	(	PUNCT
ma-20	98	41	1	1	NUM
ma-20	98	42	)	)	PUNCT
ma-20	99	1	k	k	NOUN
ma-20	99	2	−	−	NOUN
ma-20	99	3	x	x	SYM
ma-20	99	4	(	(	PUNCT
ma-20	99	5	2	2	NUM
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ma-20	100	1	+	+	CCONJ
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ma-20	100	3	(	(	PUNCT
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ma-20	100	5	)	)	PUNCT
ma-20	100	6	k	k	NOUN
ma-20	100	7	=	=	PUNCT
ma-20	100	8			PROPN
ma-20	100	9	3	3	NUM
ma-20	100	10	,	,	PUNCT
ma-20	100	11	k	k	NOUN
ma-20	100	12	=	=	PUNCT
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ma-20	100	14	,	,	PUNCT
ma-20	100	15	1	1	NUM
ma-20	100	16	,	,	PUNCT
ma-20	100	17	k	k	NOUN
ma-20	100	18	=	=	SYM
ma-20	100	19	0	0	NUM
ma-20	100	20	,	,	PUNCT
ma-20	100	21	3j	3j	NUM
ma-20	100	22	,	,	PUNCT
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ma-20	100	24	,	,	PUNCT
ma-20	100	25	k	k	PROPN
ma-20	100	26	=	=	SYM
ma-20	100	27	j	j	PROPN
ma-20	100	28	,	,	PUNCT
ma-20	100	29	0	0	NUM
ma-20	100	30	,	,	PUNCT
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ma-20	100	32	;	;	PUNCT
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ma-20	100	34	(	(	PUNCT
ma-20	100	35	1	1	NUM
ma-20	100	36	)	)	PUNCT
ma-20	100	37	k	k	NOUN
ma-20	101	1	−	−	NOUN
ma-20	101	2	x	x	SYM
ma-20	101	3	(	(	PUNCT
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ma-20	101	5	)	)	PUNCT
ma-20	101	6	k	k	NOUN
ma-20	101	7	−	−	NOUN
ma-20	101	8	x	x	SYM
ma-20	101	9	(	(	PUNCT
ma-20	101	10	3	3	NUM
ma-20	101	11	)	)	PUNCT
ma-20	101	12	k	k	NOUN
ma-20	102	1	=	=	PUNCT
ma-20	102	2			PROPN
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ma-20	102	4	,	,	PUNCT
ma-20	102	5	k	k	PROPN
ma-20	102	6	=	=	SYM
ma-20	102	7	3j	3j	NUM
ma-20	102	8	,	,	PUNCT
ma-20	102	9	1	1	NUM
ma-20	102	10	,	,	PUNCT
ma-20	102	11	k	k	PROPN
ma-20	102	12	=	=	SYM
ma-20	102	13	j	j	PROPN
ma-20	102	14	,	,	PUNCT
ma-20	102	15	2j	2j	NUM
ma-20	102	16	,	,	PUNCT
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ma-20	102	18	,	,	PUNCT
ma-20	102	19	k	k	PROPN
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ma-20	103	3	,	,	PUNCT
ma-20	103	4	0	0	NUM
ma-20	103	5	,	,	PUNCT
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ma-20	103	8	compute	compute	VERB
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ma-20	104	2	‖x	‖x	PRON
ma-20	104	3	(	(	PUNCT
ma-20	104	4	1)+	1)+	NUM
ma-20	104	5	x	x	SYM
ma-20	104	6	(	(	PUNCT
ma-20	104	7	2)+	2)+	NUM
ma-20	104	8	x	x	X
ma-20	104	9	(	(	PUNCT
ma-20	104	10	3)‖`pq	3)‖`pq	NUM
ma-20	104	11	=	=	SYM
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ma-20	104	18	1	1	NUM
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ma-20	104	21	1	1	NUM
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ma-20	104	23	(	(	PUNCT
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ma-20	104	26	1	1	NUM
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ma-20	104	28	,	,	PUNCT
ma-20	104	29	(	(	PUNCT
ma-20	104	30	2j	2j	X
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ma-20	104	45	3j	3j	PROPN
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ma-20	104	48	1	1	NUM
ma-20	104	49	q	q	NOUN
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ma-20	104	51	1	1	NUM
ma-20	104	52	p	p	NOUN
ma-20	104	53	(	(	PUNCT
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ma-20	104	56	1	1	NUM
ma-20	104	57	p	p	NOUN
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ma-20	105	3	•	•	X
ma-20	105	4	(	(	PUNCT
ma-20	105	5	j	j	NOUN
ma-20	105	6	+	+	CCONJ
ma-20	105	7	1	1	X
ma-20	105	8	)	)	PUNCT
ma-20	105	9	1	1	NUM
ma-20	105	10	q	q	NOUN
ma-20	105	11	−	−	PROPN
ma-20	105	12	1	1	NUM
ma-20	105	13	p	p	NOUN
ma-20	105	14	(	(	PUNCT
ma-20	105	15	3p	3p	NUM
ma-20	105	16	+	+	CCONJ
ma-20	105	17	1	1	NUM
ma-20	105	18	)	)	PUNCT
ma-20	105	19	1	1	NUM
ma-20	105	20	p	p	NOUN
ma-20	105	21	<	<	X
ma-20	105	22	(	(	PUNCT
ma-20	105	23	3p+1p	3p+1p	NUM
ma-20	105	24	4	4	NUM
ma-20	105	25	)	)	PUNCT
ma-20	105	26	1	1	NUM
ma-20	106	1	p	p	NOUN
ma-20	106	2	<	<	X
ma-20	106	3	(	(	PUNCT
ma-20	106	4	3p	3p	NUM
ma-20	106	5	)	)	PUNCT
ma-20	106	6	1	1	NUM
ma-20	106	7	p	p	NOUN
ma-20	106	8	=	=	NOUN
ma-20	106	9	3	3	NUM
ma-20	106	10	.	.	NOUN
ma-20	106	11	•	•	NUM
ma-20	106	12	(	(	PUNCT
ma-20	106	13	2j	2j	NUM
ma-20	106	14	+	+	CCONJ
ma-20	106	15	1	1	X
ma-20	106	16	)	)	PUNCT
ma-20	106	17	1	1	NUM
ma-20	106	18	q	q	NOUN
ma-20	106	19	−	−	PROPN
ma-20	106	20	1	1	NUM
ma-20	106	21	p	p	NOUN
ma-20	106	22	(	(	PUNCT
ma-20	106	23	3p	3p	NUM
ma-20	106	24	+	+	CCONJ
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ma-20	106	27	1	1	NUM
ma-20	106	28	p	p	NOUN
ma-20	106	29	<	<	X
ma-20	106	30	(	(	PUNCT
ma-20	106	31	j	j	PROPN
ma-20	106	32	+	+	CCONJ
ma-20	106	33	1	1	X
ma-20	106	34	)	)	PUNCT
ma-20	106	35	1	1	NUM
ma-20	106	36	q	q	NOUN
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ma-20	106	38	1	1	NUM
ma-20	106	39	p	p	NOUN
ma-20	106	40	(	(	PUNCT
ma-20	106	41	3p	3p	NUM
ma-20	106	42	+	+	CCONJ
ma-20	106	43	2	2	NUM
ma-20	106	44	)	)	PUNCT
ma-20	106	45	1	1	NUM
ma-20	106	46	p	p	NOUN
ma-20	106	47	<	<	X
ma-20	106	48	(	(	PUNCT
ma-20	106	49	3p+2	3p+2	ADJ
ma-20	106	50	4	4	NUM
ma-20	106	51	)	)	PUNCT
ma-20	106	52	1	1	NUM
ma-20	106	53	p	p	NOUN
ma-20	106	54	<	<	X
ma-20	106	55	3	3	NUM
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ma-20	107	3	.	.	PUNCT
ma-20	108	1	j.	j.	PROPN
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ma-20	108	3	.	.	PUNCT
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ma-20	109	2	.	.	PUNCT
ma-20	110	1	10.28924	10.28924	NUM
ma-20	110	2	/	/	SYM
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ma-20	110	4	/	/	SYM
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ma-20	110	6	5	5	NUM
ma-20	110	7	•	•	NOUN
ma-20	110	8	(	(	PUNCT
ma-20	110	9	3j	3j	NOUN
ma-20	110	10	+	+	CCONJ
ma-20	110	11	1	1	X
ma-20	110	12	)	)	PUNCT
ma-20	110	13	1	1	NUM
ma-20	110	14	q	q	NOUN
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ma-20	110	16	1	1	NUM
ma-20	110	17	p	p	NOUN
ma-20	110	18	(	(	PUNCT
ma-20	110	19	3p	3p	NUM
ma-20	110	20	+	+	CCONJ
ma-20	110	21	3	3	NUM
ma-20	110	22	)	)	PUNCT
ma-20	110	23	1	1	NUM
ma-20	110	24	p	p	NOUN
ma-20	110	25	<	<	X
ma-20	110	26	(	(	PUNCT
ma-20	110	27	j	j	PROPN
ma-20	110	28	+	+	CCONJ
ma-20	110	29	1	1	X
ma-20	110	30	)	)	PUNCT
ma-20	110	31	1	1	NUM
ma-20	110	32	q	q	NOUN
ma-20	110	33	−	−	PROPN
ma-20	110	34	1	1	NUM
ma-20	110	35	p	p	NOUN
ma-20	110	36	(	(	PUNCT
ma-20	110	37	3p	3p	NUM
ma-20	110	38	+	+	CCONJ
ma-20	110	39	3	3	NUM
ma-20	110	40	)	)	PUNCT
ma-20	110	41	1	1	NUM
ma-20	110	42	p	p	NOUN
ma-20	110	43	<	<	X
ma-20	110	44	(	(	PUNCT
ma-20	110	45	3p+3	3p+3	PROPN
ma-20	110	46	4	4	NUM
ma-20	110	47	)	)	PUNCT
ma-20	110	48	1	1	NUM
ma-20	110	49	p	p	NOUN
ma-20	110	50	<	<	X
ma-20	110	51	3.hence	3.hence	NUM
ma-20	110	52	,	,	PUNCT
ma-20	110	53	we	we	PRON
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ma-20	110	55	‖x	‖x	NOUN
ma-20	110	56	(	(	PUNCT
ma-20	110	57	1	1	NUM
ma-20	110	58	)	)	PUNCT
ma-20	110	59	+	+	NOUN
ma-20	110	60	x	x	SYM
ma-20	110	61	(	(	PUNCT
ma-20	110	62	2	2	NUM
ma-20	110	63	)	)	PUNCT
ma-20	110	64	+	+	NOUN
ma-20	110	65	x	x	SYM
ma-20	110	66	(	(	PUNCT
ma-20	110	67	3)‖`pq	3)‖`pq	NUM
ma-20	110	68	=	=	SYM
ma-20	110	69	3.similarly	3.similarly	NUM
ma-20	110	70	,	,	PUNCT
ma-20	110	71	we	we	PRON
ma-20	110	72	have	have	AUX
ma-20	110	73	‖x	‖x	NOUN
ma-20	110	74	(	(	PUNCT
ma-20	110	75	1	1	X
ma-20	110	76	)	)	PUNCT
ma-20	110	77	±	±	NOUN
ma-20	110	78	x	x	SYM
ma-20	110	79	(	(	PUNCT
ma-20	110	80	2	2	NUM
ma-20	110	81	)	)	PUNCT
ma-20	110	82	±	±	NOUN
ma-20	110	83	x	x	SYM
ma-20	110	84	(	(	PUNCT
ma-20	110	85	3)‖`pq	3)‖`pq	NUM
ma-20	110	86	=	=	SYM
ma-20	110	87	sup	sup	NOUN
ma-20	110	88	m∈z∩[0,3j	m∈z∩[0,3j	NOUN
ma-20	110	89	]	]	X
ma-20	110	90	,	,	PUNCT
ma-20	110	91	n∈z∩[0,3j/2	n∈z∩[0,3j/2	CCONJ
ma-20	110	92	]	]	PUNCT
ma-20	110	93	|sm	|sm	NUM
ma-20	110	94	,	,	PUNCT
ma-20	110	95	n	n	CCONJ
ma-20	110	96	|	|	ADV
ma-20	110	97	1	1	NUM
ma-20	110	98	q	q	NOUN
ma-20	110	99	−	−	PROPN
ma-20	110	100	1	1	NUM
ma-20	110	101	p	p	NOUN
ma-20	110	102	(	(	PUNCT
ma-20	110	103	∑	∑	PUNCT
ma-20	110	104	k∈sm	k∈sm	PROPN
ma-20	110	105	,	,	PUNCT
ma-20	110	106	n	n	PRON
ma-20	110	107	|x	|x	NOUN
ma-20	110	108	(	(	PUNCT
ma-20	110	109	1)k	1)k	NUM
ma-20	110	110	±	±	NUM
ma-20	110	111	x	x	SYM
ma-20	110	112	(	(	PUNCT
ma-20	110	113	2	2	NUM
ma-20	110	114	)	)	PUNCT
ma-20	110	115	k	k	NOUN
ma-20	110	116	±	±	NUM
ma-20	110	117	x	x	SYM
ma-20	110	118	(	(	PUNCT
ma-20	110	119	3	3	NUM
ma-20	110	120	)	)	PUNCT
ma-20	110	121	k	k	NOUN
ma-20	111	1	|	|	ADV
ma-20	111	2	p	p	NOUN
ma-20	111	3	)	)	PUNCT
ma-20	111	4	1	1	NUM
ma-20	111	5	p	p	NOUN
ma-20	111	6	=	=	NOUN
ma-20	111	7	3	3	NUM
ma-20	111	8	for	for	ADP
ma-20	111	9	every	every	DET
ma-20	111	10	combination	combination	NOUN
ma-20	111	11	of	of	ADP
ma-20	111	12	±	±	NUM
ma-20	111	13	signs.consequently	signs.consequently	ADV
ma-20	111	14	,	,	PUNCT
ma-20	111	15	∑±	∑±	PUNCT
ma-20	111	16	‖x(1)±x(2)±x(3)‖2`pq	‖x(1)±x(2)±x(3)‖2`pq	NUM
ma-20	111	17	22	22	NUM
ma-20	112	1	∑3	∑3	PROPN
ma-20	112	2	i=1	i=1	PRON
ma-20	112	3	‖x(i)‖`pq	‖x(i)‖`pq	PUNCT
ma-20	113	1	=	=	SYM
ma-20	113	2	3	3	NUM
ma-20	113	3	and	and	CCONJ
ma-20	113	4	min	min	NOUN
ma-20	113	5	‖x	‖x	NOUN
ma-20	113	6	(	(	PUNCT
ma-20	113	7	1	1	X
ma-20	113	8	)	)	PUNCT
ma-20	113	9	±	±	NOUN
ma-20	113	10	x	x	SYM
ma-20	113	11	(	(	PUNCT
ma-20	113	12	2	2	NUM
ma-20	113	13	)	)	PUNCT
ma-20	113	14	±	±	NOUN
ma-20	113	15	x	x	SYM
ma-20	113	16	(	(	PUNCT
ma-20	113	17	3)‖`pq	3)‖`pq	NUM
ma-20	113	18	=	=	SYM
ma-20	113	19	3	3	NUM
ma-20	113	20	,	,	PUNCT
ma-20	113	21	so	so	SCONJ
ma-20	113	22	we	we	PRON
ma-20	113	23	come	come	VERB
ma-20	113	24	to	to	ADP
ma-20	113	25	theconclusion	theconclusion	NOUN
ma-20	113	26	that	that	SCONJ
ma-20	114	1	c	c	NOUN
ma-20	114	2	(	(	PUNCT
ma-20	114	3	3	3	NUM
ma-20	114	4	)	)	PUNCT
ma-20	114	5	nj	nj	NOUN
ma-20	114	6	(	(	PUNCT
ma-20	114	7	`	`	PUNCT
ma-20	114	8	p	p	X
ma-20	114	9	q(z	q(z	PROPN
ma-20	114	10	)	)	PUNCT
ma-20	114	11	)	)	PUNCT
ma-20	115	1	=	=	PUNCT
ma-20	115	2	c	c	X
ma-20	115	3	(	(	PUNCT
ma-20	115	4	3	3	NUM
ma-20	115	5	)	)	PUNCT
ma-20	115	6	j	j	NOUN
ma-20	115	7	(	(	PUNCT
ma-20	115	8	`	`	PUNCT
ma-20	115	9	p	p	X
ma-20	115	10	q(z	q(z	PROPN
ma-20	115	11	)	)	PUNCT
ma-20	115	12	)	)	PUNCT
ma-20	116	1	=	=	SYM
ma-20	116	2	3	3	X
ma-20	116	3	.	.	X
ma-20	116	4	case	case	NOUN
ma-20	116	5	2	2	NUM
ma-20	116	6	:	:	PUNCT
ma-20	116	7	d	d	X
ma-20	116	8	>	>	X
ma-20	116	9	1	1	X
ma-20	116	10	.	.	PUNCT
ma-20	117	1	let	let	VERB
ma-20	117	2	j	j	PROPN
ma-20	117	3	∈	∈	PROPN
ma-20	117	4	z	z	PROPN
ma-20	117	5	be	be	AUX
ma-20	117	6	a	a	DET
ma-20	117	7	nonnegative	nonnegative	ADJ
ma-20	117	8	,	,	PUNCT
ma-20	117	9	even	even	ADV
ma-20	117	10	integer	integer	VERB
ma-20	117	11	such	such	ADJ
ma-20	117	12	that	that	SCONJ
ma-20	117	13	j	j	PROPN
ma-20	117	14	>	>	X
ma-20	117	15	4	4	NUM
ma-20	117	16	q	q	NOUN
ma-20	117	17	d(q−p	d(q−p	PROPN
ma-20	117	18	)	)	PUNCT
ma-20	117	19	−	−	PROPN
ma-20	117	20	1	1	NUM
ma-20	117	21	,	,	PUNCT
ma-20	117	22	which	which	PRON
ma-20	117	23	isequivalent	isequivalent	NOUN
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ma-20	117	25	(	(	PUNCT
ma-20	117	26	j	j	PROPN
ma-20	117	27	+	+	NUM
ma-20	117	28	1)d	1)d	NUM
ma-20	117	29	(	(	PUNCT
ma-20	117	30	1	1	NUM
ma-20	117	31	q	q	NOUN
ma-20	117	32	−	−	PROPN
ma-20	117	33	1	1	NUM
ma-20	117	34	p	p	NOUN
ma-20	117	35	)	)	PUNCT
ma-20	117	36	<	<	X
ma-20	117	37	4−	4−	NUM
ma-20	117	38	1	1	NUM
ma-20	117	39	p	p	NOUN
ma-20	117	40	.	.	PUNCT
ma-20	118	1	we	we	PRON
ma-20	118	2	then	then	ADV
ma-20	118	3	construct	construct	VERB
ma-20	118	4	x	x	SYM
ma-20	118	5	(	(	PUNCT
ma-20	118	6	1	1	NUM
ma-20	118	7	)	)	PUNCT
ma-20	118	8	,	,	PUNCT
ma-20	118	9	x	x	X
ma-20	118	10	(	(	PUNCT
ma-20	118	11	2	2	NUM
ma-20	118	12	)	)	PUNCT
ma-20	118	13	,	,	PUNCT
ma-20	118	14	x	x	X
ma-20	118	15	(	(	PUNCT
ma-20	118	16	3	3	X
ma-20	118	17	)	)	PUNCT
ma-20	118	18	∈	∈	NOUN
ma-20	118	19	`	`	PUNCT
ma-20	118	20	pq(zd	pq(zd	NOUN
ma-20	118	21	)	)	PUNCT
ma-20	118	22	as	as	SCONJ
ma-20	118	23	follows	follow	VERB
ma-20	118	24	:	:	PUNCT
ma-20	118	25	•	•	NUM
ma-20	118	26	x	x	SYM
ma-20	118	27	(	(	PUNCT
ma-20	118	28	1	1	NUM
ma-20	118	29	)	)	PUNCT
ma-20	118	30	=	=	SYM
ma-20	118	31	(	(	PUNCT
ma-20	118	32	x	x	X
ma-20	118	33	(	(	PUNCT
ma-20	118	34	1)k	1)k	NUM
ma-20	118	35	)	)	PUNCT
ma-20	118	36	k∈zd	k∈zd	NOUN
ma-20	118	37	is	be	AUX
ma-20	118	38	defined	define	VERB
ma-20	118	39	by	by	ADP
ma-20	118	40	x	x	SYM
ma-20	118	41	(	(	PUNCT
ma-20	118	42	1	1	NUM
ma-20	118	43	)	)	PUNCT
ma-20	118	44	k	k	NOUN
ma-20	119	1	=	=	PUNCT
ma-20	119	2	1	1	PROPN
ma-20	119	3	,	,	PUNCT
ma-20	119	4	k	k	X
ma-20	119	5	=	=	PUNCT
ma-20	119	6	(	(	PUNCT
ma-20	119	7	0	0	NUM
ma-20	119	8	,	,	PUNCT
ma-20	119	9	0	0	NUM
ma-20	119	10	,	,	PUNCT
ma-20	119	11	.	.	PUNCT
ma-20	119	12	.	.	PUNCT
ma-20	119	13	.	.	PUNCT
ma-20	120	1	,	,	PUNCT
ma-20	120	2	0	0	NUM
ma-20	120	3	)	)	PUNCT
ma-20	120	4	,	,	PUNCT
ma-20	120	5	(	(	PUNCT
ma-20	120	6	j	j	NOUN
ma-20	120	7	,	,	PUNCT
ma-20	120	8	0	0	NUM
ma-20	120	9	,	,	PUNCT
ma-20	120	10	.	.	PUNCT
ma-20	120	11	.	.	PUNCT
ma-20	121	1	.	.	PUNCT
ma-20	122	1	,	,	PUNCT
ma-20	122	2	0	0	NUM
ma-20	122	3	)	)	PUNCT
ma-20	122	4	,	,	PUNCT
ma-20	122	5	(	(	PUNCT
ma-20	122	6	2j	2j	NOUN
ma-20	122	7	,	,	PUNCT
ma-20	122	8	0	0	NUM
ma-20	122	9	,	,	PUNCT
ma-20	122	10	.	.	PUNCT
ma-20	122	11	.	.	PUNCT
ma-20	123	1	.	.	PUNCT
ma-20	124	1	,	,	PUNCT
ma-20	124	2	0	0	NUM
ma-20	124	3	)	)	PUNCT
ma-20	124	4	,	,	PUNCT
ma-20	124	5	(	(	PUNCT
ma-20	124	6	3j	3j	NOUN
ma-20	124	7	,	,	PUNCT
ma-20	124	8	0	0	NUM
ma-20	124	9	,	,	PUNCT
ma-20	124	10	.	.	PUNCT
ma-20	124	11	.	.	PUNCT
ma-20	125	1	.	.	PUNCT
ma-20	126	1	,	,	PUNCT
ma-20	126	2	0	0	NUM
ma-20	126	3	)	)	PUNCT
ma-20	126	4	,	,	PUNCT
ma-20	126	5	0	0	NUM
ma-20	126	6	,	,	PUNCT
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ma-20	126	8	;	;	PUNCT
ma-20	126	9	•	•	X
ma-20	126	10	x	x	X
ma-20	126	11	(	(	PUNCT
ma-20	126	12	2	2	NUM
ma-20	126	13	)	)	PUNCT
ma-20	126	14	=	=	SYM
ma-20	126	15	(	(	PUNCT
ma-20	126	16	x	x	X
ma-20	126	17	(	(	PUNCT
ma-20	126	18	2)k	2)k	NOUN
ma-20	126	19	)	)	PUNCT
ma-20	126	20	k∈zd	k∈zd	NOUN
ma-20	126	21	is	be	AUX
ma-20	126	22	defined	define	VERB
ma-20	126	23	by	by	ADP
ma-20	126	24	x	x	SYM
ma-20	126	25	(	(	PUNCT
ma-20	126	26	2	2	NUM
ma-20	126	27	)	)	PUNCT
ma-20	126	28	k	k	NOUN
ma-20	127	1	=	=	PUNCT
ma-20	127	2			PROPN
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ma-20	127	4	,	,	PUNCT
ma-20	127	5	k	k	NOUN
ma-20	127	6	=	=	PUNCT
ma-20	127	7	(	(	PUNCT
ma-20	127	8	0	0	NUM
ma-20	127	9	,	,	PUNCT
ma-20	127	10	0	0	NUM
ma-20	127	11	,	,	PUNCT
ma-20	127	12	.	.	PUNCT
ma-20	127	13	.	.	PUNCT
ma-20	128	1	.	.	PUNCT
ma-20	129	1	,	,	PUNCT
ma-20	129	2	0	0	NUM
ma-20	129	3	)	)	PUNCT
ma-20	129	4	,	,	PUNCT
ma-20	129	5	(	(	PUNCT
ma-20	129	6	j	j	NOUN
ma-20	129	7	,	,	PUNCT
ma-20	129	8	0	0	NUM
ma-20	129	9	,	,	PUNCT
ma-20	129	10	.	.	PUNCT
ma-20	129	11	.	.	PUNCT
ma-20	130	1	.	.	PUNCT
ma-20	131	1	,	,	PUNCT
ma-20	131	2	0	0	NUM
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ma-20	131	4	,	,	PUNCT
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ma-20	131	6	,	,	PUNCT
ma-20	131	7	k	k	X
ma-20	132	1	=	=	X
ma-20	132	2	(	(	PUNCT
ma-20	132	3	2j	2j	NUM
ma-20	132	4	,	,	PUNCT
ma-20	132	5	0	0	NUM
ma-20	132	6	,	,	PUNCT
ma-20	132	7	.	.	PUNCT
ma-20	132	8	.	.	PUNCT
ma-20	132	9	.	.	PUNCT
ma-20	133	1	,	,	PUNCT
ma-20	133	2	0	0	NUM
ma-20	133	3	)	)	PUNCT
ma-20	133	4	,	,	PUNCT
ma-20	133	5	(	(	PUNCT
ma-20	133	6	3j	3j	NOUN
ma-20	133	7	,	,	PUNCT
ma-20	133	8	0	0	NUM
ma-20	133	9	,	,	PUNCT
ma-20	133	10	.	.	PUNCT
ma-20	133	11	.	.	PUNCT
ma-20	134	1	.	.	PUNCT
ma-20	135	1	,	,	PUNCT
ma-20	135	2	0	0	NUM
ma-20	135	3	)	)	PUNCT
ma-20	135	4	,	,	PUNCT
ma-20	135	5	0	0	NUM
ma-20	135	6	,	,	PUNCT
ma-20	135	7	otherwise	otherwise	ADV
ma-20	135	8	;	;	PUNCT
ma-20	135	9	•	•	X
ma-20	135	10	x	x	X
ma-20	135	11	(	(	PUNCT
ma-20	135	12	3	3	NUM
ma-20	135	13	)	)	PUNCT
ma-20	135	14	=	=	SYM
ma-20	136	1	(	(	PUNCT
ma-20	136	2	x	x	SYM
ma-20	136	3	(	(	PUNCT
ma-20	136	4	3)k	3)k	NUM
ma-20	136	5	)	)	PUNCT
ma-20	136	6	k∈zd	k∈zd	NOUN
ma-20	136	7	is	be	AUX
ma-20	136	8	defined	define	VERB
ma-20	136	9	by	by	ADP
ma-20	136	10	x	x	SYM
ma-20	136	11	(	(	PUNCT
ma-20	136	12	3	3	NUM
ma-20	136	13	)	)	PUNCT
ma-20	136	14	k	k	NOUN
ma-20	136	15	=	=	PUNCT
ma-20	137	1			PROPN
ma-20	137	2	1	1	NUM
ma-20	137	3	,	,	PUNCT
ma-20	137	4	k	k	NOUN
ma-20	137	5	=	=	PUNCT
ma-20	137	6	(	(	PUNCT
ma-20	137	7	0	0	NUM
ma-20	137	8	,	,	PUNCT
ma-20	137	9	0	0	NUM
ma-20	137	10	,	,	PUNCT
ma-20	137	11	.	.	PUNCT
ma-20	137	12	.	.	PUNCT
ma-20	138	1	.	.	PUNCT
ma-20	139	1	,	,	PUNCT
ma-20	139	2	0	0	NUM
ma-20	139	3	)	)	PUNCT
ma-20	139	4	,	,	PUNCT
ma-20	139	5	(	(	PUNCT
ma-20	139	6	2j	2j	NOUN
ma-20	139	7	,	,	PUNCT
ma-20	139	8	0	0	NUM
ma-20	139	9	,	,	PUNCT
ma-20	139	10	.	.	PUNCT
ma-20	139	11	.	.	PUNCT
ma-20	140	1	.	.	PUNCT
ma-20	141	1	,	,	PUNCT
ma-20	141	2	0	0	NUM
ma-20	141	3	)	)	PUNCT
ma-20	141	4	,	,	PUNCT
ma-20	141	5	−1	−1	NOUN
ma-20	141	6	,	,	PUNCT
ma-20	141	7	k	k	PROPN
ma-20	142	1	=	=	PRON
ma-20	142	2	(	(	PUNCT
ma-20	142	3	j	j	PROPN
ma-20	142	4	,	,	PUNCT
ma-20	142	5	0	0	NUM
ma-20	142	6	,	,	PUNCT
ma-20	142	7	.	.	PUNCT
ma-20	142	8	.	.	PUNCT
ma-20	142	9	.	.	PUNCT
ma-20	143	1	,	,	PUNCT
ma-20	143	2	0	0	NUM
ma-20	143	3	)	)	PUNCT
ma-20	143	4	,	,	PUNCT
ma-20	143	5	(	(	PUNCT
ma-20	143	6	3j	3j	NOUN
ma-20	143	7	,	,	PUNCT
ma-20	143	8	0	0	NUM
ma-20	143	9	,	,	PUNCT
ma-20	143	10	.	.	PUNCT
ma-20	143	11	.	.	PUNCT
ma-20	144	1	.	.	PUNCT
ma-20	145	1	,	,	PUNCT
ma-20	145	2	0	0	NUM
ma-20	145	3	)	)	PUNCT
ma-20	145	4	,	,	PUNCT
ma-20	145	5	0	0	NUM
ma-20	145	6	,	,	PUNCT
ma-20	145	7	otherwise	otherwise	ADV
ma-20	145	8	.	.	PUNCT
ma-20	146	1	as	as	SCONJ
ma-20	146	2	in	in	ADP
ma-20	146	3	the	the	DET
ma-20	146	4	case	case	NOUN
ma-20	146	5	where	where	SCONJ
ma-20	146	6	d	d	NOUN
ma-20	146	7	=	=	SYM
ma-20	146	8	1	1	NUM
ma-20	146	9	,	,	PUNCT
ma-20	146	10	one	one	PRON
ma-20	146	11	may	may	AUX
ma-20	146	12	observe	observe	VERB
ma-20	146	13	that	that	SCONJ
ma-20	146	14	‖x	‖x	PROPN
ma-20	146	15	(	(	PUNCT
ma-20	146	16	1)‖`pq	1)‖`pq	NUM
ma-20	146	17	=	=	SYM
ma-20	146	18	sup	sup	NOUN
ma-20	146	19	m∈zd	m∈zd	NOUN
ma-20	146	20	,	,	PUNCT
ma-20	146	21	n∈ω	n∈ω	NOUN
ma-20	146	22	|sm	|sm	NUM
ma-20	146	23	,	,	PUNCT
ma-20	146	24	n	n	CCONJ
ma-20	146	25	|	|	ADV
ma-20	146	26	1	1	NUM
ma-20	146	27	q	q	NOUN
ma-20	146	28	−	−	PROPN
ma-20	146	29	1	1	NUM
ma-20	146	30	p	p	NOUN
ma-20	146	31	(	(	PUNCT
ma-20	146	32	∑	∑	PUNCT
ma-20	146	33	k∈sm	k∈sm	PROPN
ma-20	146	34	,	,	PUNCT
ma-20	146	35	n	n	PRON
ma-20	146	36	|x	|x	NOUN
ma-20	146	37	(	(	PUNCT
ma-20	146	38	1)k	1)k	NUM
ma-20	146	39	|	|	CCONJ
ma-20	146	40	p	p	NOUN
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ma-20	146	42	1	1	NUM
ma-20	146	43	p	p	NOUN
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ma-20	146	46	,	,	PUNCT
ma-20	146	47	(	(	PUNCT
ma-20	146	48	j	j	PROPN
ma-20	146	49	+	+	NOUN
ma-20	146	50	1)d	1)d	NUM
ma-20	146	51	(	(	PUNCT
ma-20	146	52	1	1	NUM
ma-20	146	53	q	q	NOUN
ma-20	146	54	−	−	PROPN
ma-20	146	55	1	1	NUM
ma-20	146	56	p	p	NOUN
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ma-20	146	59	1	1	NUM
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ma-20	146	61	,	,	PUNCT
ma-20	146	62	(	(	PUNCT
ma-20	146	63	2j	2j	X
ma-20	146	64	+	+	CCONJ
ma-20	146	65	1)d	1)d	NUM
ma-20	146	66	(	(	PUNCT
ma-20	146	67	1	1	NUM
ma-20	146	68	q	q	NOUN
ma-20	146	69	−	−	PROPN
ma-20	146	70	1	1	NUM
ma-20	146	71	p	p	NOUN
ma-20	146	72	)	)	PUNCT
ma-20	146	73	3	3	NUM
ma-20	146	74	1	1	NUM
ma-20	146	75	p	p	NOUN
ma-20	146	76	,	,	PUNCT
ma-20	146	77	(	(	PUNCT
ma-20	146	78	3j	3j	NOUN
ma-20	146	79	+	+	CCONJ
ma-20	146	80	1)d	1)d	NUM
ma-20	146	81	(	(	PUNCT
ma-20	146	82	1	1	NUM
ma-20	146	83	q	q	NOUN
ma-20	146	84	−	−	PROPN
ma-20	146	85	1	1	NUM
ma-20	146	86	p	p	NOUN
ma-20	146	87	)	)	PUNCT
ma-20	146	88	4	4	NUM
ma-20	146	89	1	1	NUM
ma-20	146	90	p	p	NOUN
ma-20	146	91	}	}	PUNCT
ma-20	146	92	=	=	SYM
ma-20	146	93	1	1	X
ma-20	146	94	.	.	X
ma-20	147	1	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	147	2	eur	eur	PROPN
ma-20	147	3	.	.	PUNCT
ma-20	148	1	j.	j.	PROPN
ma-20	148	2	math	math	PROPN
ma-20	148	3	.	.	PUNCT
ma-20	149	1	anal	anal	PROPN
ma-20	149	2	.	.	PUNCT
ma-20	150	1	10.28924	10.28924	NUM
ma-20	150	2	/	/	SYM
ma-20	150	3	ada	ada	PROPN
ma-20	150	4	/	/	SYM
ma-20	150	5	ma.2.2	ma.2.2	PROPN
ma-20	150	6	6we	6we	NOUN
ma-20	150	7	also	also	ADV
ma-20	150	8	get	get	VERB
ma-20	150	9	‖x	‖x	NOUN
ma-20	150	10	(	(	PUNCT
ma-20	150	11	2)‖`pq	2)‖`pq	NUM
ma-20	150	12	=	=	SYM
ma-20	150	13	‖x	‖x	NOUN
ma-20	150	14	(	(	PUNCT
ma-20	150	15	3)‖`pq	3)‖`pq	NUM
ma-20	150	16	=	=	SYM
ma-20	150	17	1	1	NUM
ma-20	150	18	.	.	PUNCT
ma-20	151	1	moreover	moreover	ADV
ma-20	151	2	,	,	PUNCT
ma-20	151	3	through	through	ADP
ma-20	151	4	similar	similar	ADJ
ma-20	151	5	observation	observation	NOUN
ma-20	151	6	as	as	ADP
ma-20	151	7	in	in	ADP
ma-20	151	8	the	the	DET
ma-20	151	9	1	1	NUM
ma-20	151	10	-	-	PUNCT
ma-20	151	11	dimensionalcase	dimensionalcase	NOUN
ma-20	151	12	,	,	PUNCT
ma-20	151	13	we	we	PRON
ma-20	151	14	have	have	VERB
ma-20	151	15	‖x	‖x	NOUN
ma-20	151	16	(	(	PUNCT
ma-20	151	17	1	1	X
ma-20	151	18	)	)	PUNCT
ma-20	151	19	±	±	NOUN
ma-20	151	20	x	x	SYM
ma-20	151	21	(	(	PUNCT
ma-20	151	22	2	2	NUM
ma-20	151	23	)	)	PUNCT
ma-20	151	24	±	±	NOUN
ma-20	151	25	x	x	SYM
ma-20	151	26	(	(	PUNCT
ma-20	152	1	3)‖`pq	3)‖`pq	NUM
ma-20	152	2	=	=	SYM
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ma-20	152	4	every	every	DET
ma-20	152	5	possible	possible	ADJ
ma-20	152	6	combinations	combination	NOUN
ma-20	152	7	of	of	ADP
ma-20	152	8	±	±	NOUN
ma-20	152	9	signs	sign	NOUN
ma-20	152	10	.	.	PUNCT
ma-20	153	1	it	it	PRON
ma-20	153	2	thus	thus	ADV
ma-20	153	3	follows	follow	VERB
ma-20	153	4	that	that	SCONJ
ma-20	153	5	c	c	PROPN
ma-20	153	6	(	(	PUNCT
ma-20	153	7	3	3	NUM
ma-20	153	8	)	)	PUNCT
ma-20	153	9	j	j	NOUN
ma-20	153	10	(	(	PUNCT
ma-20	153	11	`	`	PUNCT
ma-20	153	12	p	p	PRON
ma-20	153	13	q(zd	q(zd	NOUN
ma-20	153	14	)	)	PUNCT
ma-20	153	15	)	)	PUNCT
ma-20	154	1	=	=	PUNCT
ma-20	154	2	sup{min	sup{min	PROPN
ma-20	154	3	‖x1	‖x1	NOUN
ma-20	154	4	±	±	NUM
ma-20	154	5	x2	x2	PROPN
ma-20	154	6	±	±	PROPN
ma-20	154	7	x3‖`pq	x3‖`pq	NUM
ma-20	154	8	:	:	PUNCT
ma-20	155	1	x1	x1	X
ma-20	155	2	,	,	PUNCT
ma-20	155	3	x2	x2	PROPN
ma-20	155	4	,	,	PUNCT
ma-20	155	5	x3	x3	PROPN
ma-20	155	6	∈	∈	PROPN
ma-20	155	7	s`pq	s`pq	PROPN
ma-20	155	8	}	}	PUNCT
ma-20	155	9	=	=	SYM
ma-20	155	10	3	3	NUM
ma-20	155	11	and	and	CCONJ
ma-20	155	12	c	c	PROPN
ma-20	155	13	(	(	PUNCT
ma-20	155	14	3	3	NUM
ma-20	155	15	)	)	PUNCT
ma-20	155	16	nj	nj	NOUN
ma-20	155	17	(	(	PUNCT
ma-20	155	18	`	`	PUNCT
ma-20	155	19	p	p	PRON
ma-20	155	20	q(zd	q(zd	NOUN
ma-20	155	21	)	)	PUNCT
ma-20	155	22	)	)	PUNCT
ma-20	156	1	=	=	PUNCT
ma-20	156	2	sup	sup	NOUN
ma-20	156	3	{	{	PUNCT
ma-20	156	4	∑	∑	PROPN
ma-20	156	5	±	±	NUM
ma-20	156	6	‖x1	‖x1	NOUN
ma-20	156	7	±	±	NUM
ma-20	156	8	x2	x2	PROPN
ma-20	156	9	±	±	PROPN
ma-20	156	10	x3‖2`pq	x3‖2`pq	PROPN
ma-20	156	11	22	22	NUM
ma-20	156	12	∑3	∑3	PROPN
ma-20	156	13	i=1	i=1	PROPN
ma-20	156	14	‖xi‖`pq	‖xi‖`pq	NOUN
ma-20	156	15	:	:	PUNCT
ma-20	156	16	xi	xi	PROPN
ma-20	156	17	6=	6=	NUM
ma-20	156	18	0	0	NUM
ma-20	156	19	,	,	PUNCT
ma-20	156	20	i	i	PRON
ma-20	156	21	=	=	NOUN
ma-20	156	22	1	1	NUM
ma-20	156	23	,	,	PUNCT
ma-20	156	24	2	2	NUM
ma-20	156	25	,	,	PUNCT
ma-20	156	26	3	3	NUM
ma-20	156	27	}	}	PUNCT
ma-20	156	28	=	=	SYM
ma-20	156	29	3	3	X
ma-20	156	30	.	.	X
ma-20	156	31	�	�	PROPN
ma-20	156	32	we	we	PRON
ma-20	156	33	now	now	ADV
ma-20	156	34	state	state	VERB
ma-20	156	35	the	the	DET
ma-20	156	36	general	general	ADJ
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ma-20	156	38	for	for	ADP
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ma-20	156	41	3	3	NUM
ma-20	156	42	.	.	PUNCT
ma-20	157	1	(	(	PUNCT
ma-20	157	2	the	the	DET
ma-20	157	3	proof	proof	NOUN
ma-20	157	4	is	be	AUX
ma-20	157	5	also	also	ADV
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ma-20	157	7	for	for	ADP
ma-20	157	8	n	n	NOUN
ma-20	157	9	=	=	SYM
ma-20	157	10	2	2	NUM
ma-20	157	11	,	,	PUNCT
ma-20	157	12	which	which	PRON
ma-20	157	13	amounts	amount	VERB
ma-20	157	14	tothe	tothe	ADJ
ma-20	157	15	work	work	NOUN
ma-20	157	16	of	of	ADP
ma-20	157	17	[	[	X
ma-20	157	18	3	3	NUM
ma-20	157	19	]	]	PUNCT
ma-20	157	20	.	.	PUNCT
ma-20	157	21	)	)	PUNCT
ma-20	158	1	theorem	theorem	VERB
ma-20	158	2	2.2	2.2	NUM
ma-20	158	3	.	.	PUNCT
ma-20	159	1	for	for	ADP
ma-20	159	2	1	1	NUM
ma-20	159	3	≤	≤	NOUN
ma-20	159	4	p	p	NOUN
ma-20	159	5	<	<	X
ma-20	159	6	q	q	X
ma-20	159	7	<	<	X
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ma-20	159	9	,	,	PUNCT
ma-20	159	10	we	we	PRON
ma-20	159	11	have	have	VERB
ma-20	159	12	c(n)nj	c(n)nj	NUM
ma-20	159	13	(	(	PUNCT
ma-20	159	14	`	`	PUNCT
ma-20	159	15	p	p	PRON
ma-20	159	16	q(zd	q(zd	NOUN
ma-20	159	17	)	)	PUNCT
ma-20	159	18	)	)	PUNCT
ma-20	160	1	=	=	SYM
ma-20	160	2	c(n)j	c(n)j	PROPN
ma-20	160	3	(	(	PUNCT
ma-20	160	4	`	`	PUNCT
ma-20	160	5	p	p	PRON
ma-20	160	6	q(zd	q(zd	NOUN
ma-20	160	7	)	)	PUNCT
ma-20	160	8	)	)	PUNCT
ma-20	161	1	=	=	PUNCT
ma-20	161	2	n.	n.	NOUN
ma-20	161	3	proof	proof	NOUN
ma-20	161	4	.	.	PUNCT
ma-20	162	1	as	as	ADP
ma-20	162	2	for	for	ADP
ma-20	162	3	n	n	NOUN
ma-20	162	4	=	=	SYM
ma-20	162	5	3	3	NUM
ma-20	162	6	,	,	PUNCT
ma-20	162	7	we	we	PRON
ma-20	162	8	shall	shall	AUX
ma-20	162	9	consider	consider	VERB
ma-20	162	10	the	the	DET
ma-20	162	11	case	case	NOUN
ma-20	162	12	where	where	SCONJ
ma-20	162	13	d	d	NOUN
ma-20	162	14	=	=	SYM
ma-20	162	15	1	1	NUM
ma-20	162	16	first	first	ADV
ma-20	162	17	,	,	PUNCT
ma-20	162	18	and	and	CCONJ
ma-20	162	19	then	then	ADV
ma-20	162	20	the	the	DET
ma-20	162	21	case	case	NOUN
ma-20	162	22	where	where	SCONJ
ma-20	162	23	d	d	X
ma-20	162	24	>	>	X
ma-20	162	25	1later	1later	NUM
ma-20	162	26	.	.	PUNCT
ma-20	162	27	case	case	NOUN
ma-20	162	28	1	1	NUM
ma-20	162	29	:	:	PUNCT
ma-20	162	30	d	d	NOUN
ma-20	162	31	=	=	SYM
ma-20	162	32	1	1	X
ma-20	162	33	.	.	PUNCT
ma-20	162	34	let	let	VERB
ma-20	162	35	j	j	PROPN
ma-20	162	36	∈	∈	PROPN
ma-20	162	37	z	z	PROPN
ma-20	162	38	be	be	AUX
ma-20	162	39	a	a	DET
ma-20	162	40	nonnegative	nonnegative	ADJ
ma-20	162	41	,	,	PUNCT
ma-20	162	42	even	even	ADV
ma-20	162	43	integer	integer	VERB
ma-20	162	44	such	such	ADJ
ma-20	162	45	that	that	SCONJ
ma-20	162	46	j	j	PROPN
ma-20	162	47	>	>	X
ma-20	162	48	2(n−1	2(n−1	PROPN
ma-20	162	49	)	)	PUNCT
ma-20	162	50	(	(	PUNCT
ma-20	162	51	qq−p	qq−p	PROPN
ma-20	162	52	)	)	PUNCT
ma-20	163	1	−	−	PROPN
ma-20	163	2	1	1	NUM
ma-20	163	3	,	,	PUNCT
ma-20	163	4	which	which	PRON
ma-20	163	5	isequivalent	isequivalent	NOUN
ma-20	163	6	to	to	ADP
ma-20	163	7	(	(	PUNCT
ma-20	163	8	j	j	PROPN
ma-20	163	9	+	+	CCONJ
ma-20	163	10	1	1	X
ma-20	163	11	)	)	PUNCT
ma-20	163	12	1	1	NUM
ma-20	163	13	q	q	NOUN
ma-20	163	14	−	−	PROPN
ma-20	163	15	1	1	NUM
ma-20	163	16	p	p	X
ma-20	163	17	<	<	X
ma-20	163	18	2−	2−	NUM
ma-20	163	19	(	(	PUNCT
ma-20	163	20	n−1	n−1	PROPN
ma-20	163	21	)	)	PUNCT
ma-20	163	22	p	p	NOUN
ma-20	163	23	.	.	PUNCT
ma-20	164	1	we	we	PRON
ma-20	164	2	construct	construct	VERB
ma-20	164	3	x	x	PUNCT
ma-20	164	4	(	(	PUNCT
ma-20	164	5	i	i	NOUN
ma-20	164	6	)	)	PUNCT
ma-20	164	7	∈	∈	PROPN
ma-20	164	8	`	`	PUNCT
ma-20	164	9	pq	pq	NOUN
ma-20	164	10	∈	∈	PROPN
ma-20	164	11	z	z	PROPN
ma-20	164	12	for	for	ADP
ma-20	164	13	i	i	PRON
ma-20	164	14	=	=	NOUN
ma-20	164	15	1	1	NUM
ma-20	164	16	,	,	PUNCT
ma-20	164	17	2	2	NUM
ma-20	164	18	,	,	PUNCT
ma-20	164	19	.	.	PUNCT
ma-20	164	20	.	.	PUNCT
ma-20	165	1	.	.	PUNCT
ma-20	166	1	,	,	PUNCT
ma-20	166	2	n	n	CCONJ
ma-20	166	3	as	as	SCONJ
ma-20	166	4	follows	follow	VERB
ma-20	166	5	:	:	PUNCT
ma-20	166	6	•	•	NUM
ma-20	166	7	x	x	SYM
ma-20	166	8	(	(	PUNCT
ma-20	166	9	1	1	NUM
ma-20	166	10	)	)	PUNCT
ma-20	166	11	=	=	SYM
ma-20	166	12	(	(	PUNCT
ma-20	166	13	x	x	X
ma-20	166	14	(	(	PUNCT
ma-20	166	15	1)k	1)k	NUM
ma-20	166	16	)	)	PUNCT
ma-20	166	17	k∈z	k∈z	PROPN
ma-20	166	18	is	be	AUX
ma-20	166	19	defined	define	VERB
ma-20	166	20	by	by	ADP
ma-20	166	21	x	x	SYM
ma-20	166	22	(	(	PUNCT
ma-20	166	23	1	1	NUM
ma-20	166	24	)	)	PUNCT
ma-20	166	25	k	k	NOUN
ma-20	166	26	=	=	PUNCT
ma-20	166	27	1	1	PROPN
ma-20	166	28	,	,	PUNCT
ma-20	166	29	k	k	PROPN
ma-20	166	30	∈	∈	PROPN
ma-20	166	31	s(1)1	s(1)1	PROPN
ma-20	166	32	,	,	PUNCT
ma-20	166	33	0	0	NUM
ma-20	166	34	,	,	PUNCT
ma-20	166	35	otherwise	otherwise	ADV
ma-20	166	36	,	,	PUNCT
ma-20	166	37	where	where	SCONJ
ma-20	166	38	s	s	X
ma-20	166	39	(	(	PUNCT
ma-20	166	40	1	1	NUM
ma-20	166	41	)	)	SYM
ma-20	166	42	1	1	NUM
ma-20	166	43	=	=	SYM
ma-20	166	44	{	{	PUNCT
ma-20	166	45	0	0	NUM
ma-20	166	46	,	,	PUNCT
ma-20	166	47	j	j	NOUN
ma-20	166	48	,	,	PUNCT
ma-20	166	49	2j	2j	NUM
ma-20	166	50	,	,	PUNCT
ma-20	166	51	3j	3j	NUM
ma-20	166	52	,	,	PUNCT
ma-20	166	53	.	.	PUNCT
ma-20	166	54	.	.	PUNCT
ma-20	167	1	.	.	PUNCT
ma-20	168	1	,	,	PUNCT
ma-20	168	2	(	(	PUNCT
ma-20	168	3	2	2	NUM
ma-20	168	4	n−1	n−1	PROPN
ma-20	168	5	−	−	PROPN
ma-20	168	6	1)j	1)j	NUM
ma-20	168	7	}	}	PUNCT
ma-20	168	8	;	;	PUNCT
ma-20	168	9	•	•	NOUN
ma-20	168	10	x	x	X
ma-20	168	11	(	(	PUNCT
ma-20	168	12	i	i	NOUN
ma-20	168	13	)	)	PUNCT
ma-20	168	14	=	=	SYM
ma-20	169	1	(	(	PUNCT
ma-20	169	2	x	x	X
ma-20	169	3	(	(	PUNCT
ma-20	169	4	i)k	i)k	NOUN
ma-20	169	5	)	)	PUNCT
ma-20	169	6	k∈z	k∈z	VERB
ma-20	169	7	for	for	ADP
ma-20	169	8	2	2	NUM
ma-20	169	9	≤	≤	NUM
ma-20	169	10	i	i	PRON
ma-20	169	11	≤	≤	NOUN
ma-20	169	12	n	n	CCONJ
ma-20	169	13	is	be	AUX
ma-20	169	14	defined	define	VERB
ma-20	169	15	by	by	ADP
ma-20	169	16	x	x	SYM
ma-20	169	17	(	(	PUNCT
ma-20	169	18	i	i	NOUN
ma-20	169	19	)	)	PUNCT
ma-20	169	20	k	k	X
ma-20	170	1	=	=	PUNCT
ma-20	170	2			PROPN
ma-20	170	3	1	1	NUM
ma-20	170	4	,	,	PUNCT
ma-20	170	5	k	k	PROPN
ma-20	170	6	∈	∈	PROPN
ma-20	170	7	s(i)1	s(i)1	PROPN
ma-20	170	8	,	,	PUNCT
ma-20	170	9	−1	−1	ADP
ma-20	170	10	,	,	PUNCT
ma-20	170	11	k	k	PROPN
ma-20	170	12	∈	∈	PROPN
ma-20	170	13	s(i)−1	s(i)−1	PROPN
ma-20	170	14	,	,	PUNCT
ma-20	170	15	0	0	NUM
ma-20	170	16	,	,	PUNCT
ma-20	170	17	otherwise	otherwise	ADV
ma-20	170	18	,	,	PUNCT
ma-20	170	19	with	with	ADP
ma-20	170	20	the	the	DET
ma-20	170	21	following	follow	VERB
ma-20	170	22	rules	rule	NOUN
ma-20	170	23	:	:	PUNCT
ma-20	170	24	write	write	VERB
ma-20	170	25	p	p	NOUN
ma-20	170	26	=	=	PUNCT
ma-20	170	27	{	{	PUNCT
ma-20	170	28	0	0	NUM
ma-20	170	29	,	,	PUNCT
ma-20	170	30	j	j	NOUN
ma-20	170	31	,	,	PUNCT
ma-20	170	32	2j	2j	NUM
ma-20	170	33	,	,	PUNCT
ma-20	170	34	.	.	PUNCT
ma-20	170	35	.	.	PUNCT
ma-20	170	36	.	.	PUNCT
ma-20	171	1	,	,	PUNCT
ma-20	171	2	(	(	PUNCT
ma-20	171	3	2n−1	2n−1	NUM
ma-20	171	4	−	−	PROPN
ma-20	171	5	1)j	1)j	NUM
ma-20	171	6	}	}	PUNCT
ma-20	171	7	as	as	ADP
ma-20	171	8	p	p	NOUN
ma-20	171	9	=	=	NOUN
ma-20	171	10	p	p	X
ma-20	171	11	(	(	PUNCT
ma-20	171	12	i	i	NOUN
ma-20	171	13	)	)	PUNCT
ma-20	171	14	1	1	NUM
ma-20	171	15	∪	∪	ADP
ma-20	171	16	p	p	PROPN
ma-20	171	17	(	(	PUNCT
ma-20	171	18	i	i	NOUN
ma-20	171	19	)	)	PUNCT
ma-20	171	20	2	2	NUM
ma-20	171	21	∪	∪	X
ma-20	171	22	·	·	PUNCT
ma-20	171	23	·	·	PUNCT
ma-20	171	24	·	·	PUNCT
ma-20	171	25	∪	∪	ADP
ma-20	171	26	p	p	X
ma-20	171	27	(	(	PUNCT
ma-20	171	28	i	i	NOUN
ma-20	171	29	)	)	PUNCT
ma-20	171	30	2i−1	2i−1	PROPN
ma-20	171	31	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	171	32	eur	eur	PROPN
ma-20	171	33	.	.	PUNCT
ma-20	172	1	j.	j.	PROPN
ma-20	172	2	math	math	PROPN
ma-20	172	3	.	.	PUNCT
ma-20	173	1	anal	anal	PROPN
ma-20	173	2	.	.	PUNCT
ma-20	174	1	10.28924	10.28924	NUM
ma-20	174	2	/	/	SYM
ma-20	174	3	ada	ada	PROPN
ma-20	174	4	/	/	SYM
ma-20	174	5	ma.2.2	ma.2.2	NOUN
ma-20	174	6	7	7	NUM
ma-20	174	7	where	where	SCONJ
ma-20	174	8	p	p	NOUN
ma-20	174	9	(	(	PUNCT
ma-20	174	10	i)1	i)1	NOUN
ma-20	174	11	consists	consist	VERB
ma-20	174	12	of	of	ADP
ma-20	174	13	the	the	DET
ma-20	174	14	first	first	ADJ
ma-20	174	15	2n−1	2n−1	NUM
ma-20	174	16	2i−1	2i−1	NUM
ma-20	174	17	terms	term	NOUN
ma-20	174	18	of	of	ADP
ma-20	174	19	p	p	NOUN
ma-20	174	20	,	,	PUNCT
ma-20	174	21	p	p	X
ma-20	174	22	(	(	PUNCT
ma-20	174	23	i)2	i)2	ADJ
ma-20	174	24	consists	consist	VERB
ma-20	174	25	of	of	ADP
ma-20	174	26	the	the	DET
ma-20	174	27	next	next	ADJ
ma-20	174	28	2n−1	2n−1	NUM
ma-20	174	29	2i−1	2i−1	NUM
ma-20	174	30	terms	term	NOUN
ma-20	174	31	of	of	ADP
ma-20	174	32	p	p	NOUN
ma-20	174	33	,	,	PUNCT
ma-20	174	34	and	and	CCONJ
ma-20	174	35	so	so	ADV
ma-20	174	36	on	on	ADV
ma-20	174	37	.	.	PUNCT
ma-20	175	1	then	then	ADV
ma-20	175	2	s(i)1	s(i)1	NOUN
ma-20	175	3	and	and	CCONJ
ma-20	175	4	s(i)−1	s(i)−1	NOUN
ma-20	175	5	are	be	AUX
ma-20	175	6	given	give	VERB
ma-20	175	7	by	by	ADP
ma-20	175	8	s	s	PROPN
ma-20	175	9	(	(	PUNCT
ma-20	175	10	i	i	NOUN
ma-20	175	11	)	)	PUNCT
ma-20	175	12	1	1	NUM
ma-20	175	13	=	=	SYM
ma-20	175	14	p	p	X
ma-20	175	15	(	(	PUNCT
ma-20	175	16	i	i	NOUN
ma-20	175	17	)	)	PUNCT
ma-20	175	18	1	1	NUM
ma-20	175	19	∪	∪	ADP
ma-20	175	20	p	p	PROPN
ma-20	175	21	(	(	PUNCT
ma-20	175	22	i	i	NOUN
ma-20	175	23	)	)	PUNCT
ma-20	175	24	3	3	NUM
ma-20	175	25	∪	∪	X
ma-20	175	26	·	·	PUNCT
ma-20	175	27	·	·	PUNCT
ma-20	175	28	·	·	PUNCT
ma-20	175	29	∪	∪	ADP
ma-20	175	30	p	p	X
ma-20	175	31	(	(	PUNCT
ma-20	175	32	i	i	NOUN
ma-20	175	33	)	)	PUNCT
ma-20	175	34	2i−1−1	2i−1−1	NUM
ma-20	175	35	,	,	PUNCT
ma-20	175	36	s	s	PART
ma-20	175	37	(	(	PUNCT
ma-20	175	38	i	i	NOUN
ma-20	175	39	)	)	PUNCT
ma-20	175	40	−1	−1	NOUN
ma-20	176	1	=	=	SYM
ma-20	176	2	p	p	X
ma-20	176	3	(	(	PUNCT
ma-20	176	4	i	i	NOUN
ma-20	176	5	)	)	PUNCT
ma-20	176	6	2	2	NUM
ma-20	176	7	∪	∪	ADP
ma-20	176	8	p	p	PROPN
ma-20	176	9	(	(	PUNCT
ma-20	176	10	i	i	NOUN
ma-20	176	11	)	)	PUNCT
ma-20	176	12	4	4	NUM
ma-20	176	13	∪	∪	X
ma-20	176	14	·	·	PUNCT
ma-20	176	15	·	·	PUNCT
ma-20	176	16	·	·	PUNCT
ma-20	176	17	∪	∪	ADP
ma-20	176	18	p	p	X
ma-20	176	19	(	(	PUNCT
ma-20	176	20	i	i	NOUN
ma-20	176	21	)	)	PUNCT
ma-20	176	22	2i−1	2i−1	NUM
ma-20	176	23	.	.	PUNCT
ma-20	177	1	for	for	ADP
ma-20	177	2	example	example	NOUN
ma-20	177	3	,	,	PUNCT
ma-20	177	4	for	for	ADP
ma-20	177	5	i	i	PROPN
ma-20	177	6	=	=	SYM
ma-20	177	7	2	2	NUM
ma-20	177	8	,	,	PUNCT
ma-20	177	9	x	x	X
ma-20	177	10	(	(	PUNCT
ma-20	177	11	2	2	NUM
ma-20	177	12	)	)	PUNCT
ma-20	177	13	=	=	SYM
ma-20	177	14	(	(	PUNCT
ma-20	177	15	x	x	X
ma-20	177	16	(	(	PUNCT
ma-20	177	17	2)k	2)k	NOUN
ma-20	177	18	)	)	PUNCT
ma-20	177	19	k∈z	k∈z	PROPN
ma-20	177	20	is	be	AUX
ma-20	177	21	defined	define	VERB
ma-20	177	22	by	by	ADP
ma-20	177	23	x	x	SYM
ma-20	177	24	(	(	PUNCT
ma-20	177	25	2	2	NUM
ma-20	177	26	)	)	PUNCT
ma-20	177	27	k	k	NOUN
ma-20	178	1	=	=	PUNCT
ma-20	178	2			PROPN
ma-20	178	3	1	1	NUM
ma-20	178	4	,	,	PUNCT
ma-20	178	5	k	k	PROPN
ma-20	178	6	∈	∈	PROPN
ma-20	178	7	s(2)1	s(2)1	PROPN
ma-20	178	8	,	,	PUNCT
ma-20	178	9	−1	−1	NOUN
ma-20	178	10	,	,	PUNCT
ma-20	178	11	k	k	PROPN
ma-20	178	12	∈	∈	PROPN
ma-20	178	13	s(2)−1	s(2)−1	NOUN
ma-20	178	14	,	,	PUNCT
ma-20	178	15	0	0	NUM
ma-20	178	16	,	,	PUNCT
ma-20	178	17	otherwise	otherwise	ADV
ma-20	178	18	,	,	PUNCT
ma-20	178	19	where	where	SCONJ
ma-20	178	20	s	s	X
ma-20	178	21	(	(	PUNCT
ma-20	178	22	2	2	NUM
ma-20	178	23	)	)	PUNCT
ma-20	178	24	1	1	NUM
ma-20	178	25	=	=	SYM
ma-20	178	26	{	{	PUNCT
ma-20	178	27	0	0	NUM
ma-20	178	28	,	,	PUNCT
ma-20	178	29	j	j	NOUN
ma-20	178	30	,	,	PUNCT
ma-20	178	31	2j	2j	NUM
ma-20	178	32	,	,	PUNCT
ma-20	178	33	3j	3j	NUM
ma-20	178	34	,	,	PUNCT
ma-20	178	35	.	.	PUNCT
ma-20	178	36	.	.	PUNCT
ma-20	178	37	.	.	PUNCT
ma-20	179	1	,	,	PUNCT
ma-20	179	2	(	(	PUNCT
ma-20	179	3	2n−1	2n−1	NUM
ma-20	179	4	2	2	NUM
ma-20	179	5	−	−	NOUN
ma-20	179	6	1	1	NUM
ma-20	179	7	)	)	PUNCT
ma-20	179	8	j	j	PROPN
ma-20	179	9	}	}	PUNCT
ma-20	179	10	s	s	PROPN
ma-20	179	11	(	(	PUNCT
ma-20	179	12	2	2	NUM
ma-20	179	13	)	)	PUNCT
ma-20	179	14	−1	−1	NOUN
ma-20	179	15	=	=	SYM
ma-20	179	16	{	{	PUNCT
ma-20	179	17	(	(	PUNCT
ma-20	179	18	2n−1	2n−1	NUM
ma-20	179	19	2	2	NUM
ma-20	179	20	)	)	PUNCT
ma-20	179	21	j	j	NOUN
ma-20	179	22	,	,	PUNCT
ma-20	179	23	(	(	PUNCT
ma-20	179	24	2n−1	2n−1	NUM
ma-20	179	25	2	2	NUM
ma-20	179	26	+	+	CCONJ
ma-20	179	27	1	1	NUM
ma-20	179	28	)	)	PUNCT
ma-20	179	29	j	j	NOUN
ma-20	179	30	,	,	PUNCT
ma-20	179	31	.	.	PUNCT
ma-20	179	32	.	.	PUNCT
ma-20	179	33	.	.	PUNCT
ma-20	180	1	,	,	PUNCT
ma-20	180	2	(	(	PUNCT
ma-20	180	3	2n−1	2n−1	NUM
ma-20	180	4	−	−	PROPN
ma-20	180	5	1)j	1)j	PROPN
ma-20	180	6	}	}	PUNCT
ma-20	180	7	;	;	PUNCT
ma-20	180	8	note	note	VERB
ma-20	180	9	that	that	SCONJ
ma-20	180	10	the	the	DET
ma-20	180	11	largest	large	ADJ
ma-20	180	12	absolute	absolute	ADJ
ma-20	180	13	value	value	NOUN
ma-20	180	14	of	of	ADP
ma-20	180	15	the	the	DET
ma-20	180	16	terms	term	NOUN
ma-20	180	17	of	of	ADP
ma-20	180	18	x	x	X
ma-20	180	19	(	(	PUNCT
ma-20	180	20	i	i	NOUN
ma-20	180	21	)	)	PUNCT
ma-20	180	22	in	in	ADP
ma-20	180	23	the	the	DET
ma-20	180	24	above	above	ADJ
ma-20	180	25	construction	construction	NOUN
ma-20	180	26	will	will	AUX
ma-20	180	27	beequal	beequal	ADJ
ma-20	180	28	to	to	ADP
ma-20	180	29	1	1	NUM
ma-20	180	30	for	for	ADP
ma-20	180	31	each	each	DET
ma-20	180	32	i	i	NOUN
ma-20	180	33	=	=	NOUN
ma-20	180	34	1	1	NUM
ma-20	180	35	,	,	PUNCT
ma-20	180	36	.	.	PUNCT
ma-20	180	37	.	.	PUNCT
ma-20	180	38	.	.	PUNCT
ma-20	181	1	,	,	PUNCT
ma-20	181	2	n.	n.	PROPN
ma-20	181	3	next	next	ADV
ma-20	181	4	,	,	PUNCT
ma-20	181	5	since	since	SCONJ
ma-20	181	6	the	the	DET
ma-20	181	7	number	number	NOUN
ma-20	181	8	of	of	ADP
ma-20	181	9	possible	possible	ADJ
ma-20	181	10	combinations	combination	NOUN
ma-20	181	11	of	of	ADP
ma-20	181	12	±	±	NOUN
ma-20	181	13	signs	sign	NOUN
ma-20	181	14	in	in	ADP
ma-20	181	15	x	x	SYM
ma-20	181	16	(	(	PUNCT
ma-20	181	17	1	1	X
ma-20	181	18	)	)	PUNCT
ma-20	181	19	±	±	NOUN
ma-20	181	20	x	x	SYM
ma-20	181	21	(	(	PUNCT
ma-20	181	22	2	2	X
ma-20	181	23	)	)	PUNCT
ma-20	181	24	±	±	NOUN
ma-20	181	25	·	·	PUNCT
ma-20	181	26	·	·	PUNCT
ma-20	181	27	·	·	PUNCT
ma-20	181	28	±	±	NUM
ma-20	181	29	x	x	SYM
ma-20	181	30	(	(	PUNCT
ma-20	181	31	n	n	CCONJ
ma-20	181	32	)	)	PUNCT
ma-20	181	33	is	be	AUX
ma-20	181	34	2n−1	2n−1	NUM
ma-20	181	35	,	,	PUNCT
ma-20	181	36	the	the	DET
ma-20	181	37	above	above	ADJ
ma-20	181	38	construction	construction	NOUN
ma-20	181	39	will	will	AUX
ma-20	181	40	give	give	VERB
ma-20	181	41	us	we	PRON
ma-20	181	42	1	1	NUM
ma-20	181	43	+	+	CCONJ
ma-20	181	44	1	1	NUM
ma-20	181	45	+	+	NUM
ma-20	181	46	·	·	PUNCT
ma-20	181	47	·	·	PUNCT
ma-20	181	48	·	·	PUNCT
ma-20	182	1	+	+	PUNCT
ma-20	182	2	1	1	NUM
ma-20	182	3	=	=	SYM
ma-20	182	4	n	n	PRON
ma-20	182	5	as	as	ADV
ma-20	182	6	thelargest	thelarg	ADJ
ma-20	182	7	absolute	absolute	ADJ
ma-20	182	8	value	value	NOUN
ma-20	182	9	of	of	ADP
ma-20	182	10	x	x	X
ma-20	182	11	(	(	PUNCT
ma-20	182	12	1)±	1)±	NUM
ma-20	182	13	x	x	SYM
ma-20	182	14	(	(	PUNCT
ma-20	182	15	2)±	2)±	NUM
ma-20	182	16	·	·	PUNCT
ma-20	182	17	·	·	PUNCT
ma-20	182	18	·	·	PUNCT
ma-20	182	19	±	±	NUM
ma-20	182	20	x	x	SYM
ma-20	182	21	(	(	PUNCT
ma-20	182	22	n	n	CCONJ
ma-20	182	23	)	)	PUNCT
ma-20	182	24	for	for	ADP
ma-20	182	25	every	every	DET
ma-20	182	26	combination	combination	NOUN
ma-20	182	27	of	of	ADP
ma-20	182	28	±	±	NUM
ma-20	182	29	signs	sign	NOUN
ma-20	182	30	.	.	PUNCT
ma-20	183	1	this	this	PRON
ma-20	183	2	means	mean	VERB
ma-20	183	3	that	that	SCONJ
ma-20	183	4	,	,	PUNCT
ma-20	183	5	if	if	SCONJ
ma-20	183	6	x	x	X
ma-20	183	7	(	(	PUNCT
ma-20	183	8	1	1	X
ma-20	183	9	)	)	PUNCT
ma-20	183	10	±	±	NOUN
ma-20	183	11	x	x	SYM
ma-20	183	12	(	(	PUNCT
ma-20	183	13	2	2	X
ma-20	183	14	)	)	PUNCT
ma-20	183	15	±	±	NOUN
ma-20	183	16	·	·	PUNCT
ma-20	183	17	·	·	PUNCT
ma-20	183	18	·	·	PUNCT
ma-20	183	19	±	±	NUM
ma-20	183	20	x	x	SYM
ma-20	183	21	(	(	PUNCT
ma-20	183	22	n	n	CCONJ
ma-20	183	23	)	)	PUNCT
ma-20	183	24	=	=	SYM
ma-20	183	25	(	(	PUNCT
ma-20	183	26	xk)k∈z	xk)k∈z	NUM
ma-20	183	27	,	,	PUNCT
ma-20	183	28	then	then	ADV
ma-20	183	29	max	max	PROPN
ma-20	183	30	k∈z	k∈z	PROPN
ma-20	183	31	|xk	|xk	X
ma-20	183	32	|	|	ADV
ma-20	184	1	=	=	SYM
ma-20	185	1	n.let	n.let	NOUN
ma-20	185	2	us	we	PRON
ma-20	185	3	now	now	ADV
ma-20	185	4	compute	compute	VERB
ma-20	185	5	the	the	DET
ma-20	185	6	norms	norm	NOUN
ma-20	185	7	.	.	PUNCT
ma-20	186	1	for	for	ADP
ma-20	186	2	x	x	SYM
ma-20	186	3	(	(	PUNCT
ma-20	186	4	1	1	NUM
ma-20	186	5	)	)	PUNCT
ma-20	186	6	,	,	PUNCT
ma-20	186	7	we	we	PRON
ma-20	186	8	have	have	VERB
ma-20	186	9	‖x	‖x	NOUN
ma-20	186	10	(	(	PUNCT
ma-20	186	11	1)‖`pq	1)‖`pq	NUM
ma-20	186	12	=	=	SYM
ma-20	186	13	sup	sup	NOUN
ma-20	186	14	m∈z	m∈z	NOUN
ma-20	186	15	,	,	PUNCT
ma-20	186	16	n∈ω	n∈ω	NOUN
ma-20	186	17	|sm	|sm	ADV
ma-20	186	18	,	,	PUNCT
ma-20	186	19	n	n	CCONJ
ma-20	186	20	|	|	ADV
ma-20	187	1	1	1	NUM
ma-20	187	2	q	q	NOUN
ma-20	187	3	−	−	PROPN
ma-20	187	4	1	1	NUM
ma-20	187	5	p	p	NOUN
ma-20	187	6	(	(	PUNCT
ma-20	187	7	∑	∑	PUNCT
ma-20	187	8	k∈sm	k∈sm	PROPN
ma-20	187	9	,	,	PUNCT
ma-20	187	10	n	n	PRON
ma-20	187	11	|x	|x	NOUN
ma-20	187	12	(	(	PUNCT
ma-20	187	13	1)k	1)k	NUM
ma-20	187	14	|	|	CCONJ
ma-20	187	15	p	p	NOUN
ma-20	187	16	)	)	PUNCT
ma-20	187	17	1	1	NUM
ma-20	187	18	p	p	NOUN
ma-20	187	19	=	=	NOUN
ma-20	187	20	sup	sup	NOUN
ma-20	187	21	m∈z∩[0,(2n−1−1)j	m∈z∩[0,(2n−1−1)j	NOUN
ma-20	187	22	]	]	X
ma-20	187	23	,	,	PUNCT
ma-20	187	24	n∈z∩[0,(2n−1−1)j/2	n∈z∩[0,(2n−1−1)j/2	X
ma-20	187	25	]	]	X
ma-20	187	26	|sm	|sm	NUM
ma-20	187	27	,	,	PUNCT
ma-20	187	28	n	n	CCONJ
ma-20	187	29	|	|	ADV
ma-20	187	30	1	1	NUM
ma-20	187	31	q	q	NOUN
ma-20	187	32	−	−	PROPN
ma-20	187	33	1	1	NUM
ma-20	187	34	p	p	NOUN
ma-20	187	35	(	(	PUNCT
ma-20	187	36	∑	∑	PUNCT
ma-20	187	37	k∈sm	k∈sm	PROPN
ma-20	187	38	,	,	PUNCT
ma-20	187	39	n	n	PRON
ma-20	187	40	|x	|x	NOUN
ma-20	187	41	(	(	PUNCT
ma-20	187	42	1)k	1)k	NUM
ma-20	187	43	|	|	CCONJ
ma-20	187	44	p	p	NOUN
ma-20	187	45	)	)	PUNCT
ma-20	187	46	1	1	NUM
ma-20	187	47	p	p	NOUN
ma-20	187	48	=	=	NOUN
ma-20	187	49	max{1	max{1	NOUN
ma-20	187	50	,	,	PUNCT
ma-20	187	51	(	(	PUNCT
ma-20	187	52	j	j	NOUN
ma-20	187	53	+	+	CCONJ
ma-20	187	54	1	1	X
ma-20	187	55	)	)	PUNCT
ma-20	187	56	1	1	NUM
ma-20	187	57	q	q	NOUN
ma-20	187	58	−	−	PROPN
ma-20	187	59	1	1	NUM
ma-20	187	60	p	p	NOUN
ma-20	187	61	2	2	NUM
ma-20	187	62	1	1	NUM
ma-20	187	63	p	p	NOUN
ma-20	187	64	,	,	PUNCT
ma-20	187	65	(	(	PUNCT
ma-20	187	66	2j	2j	X
ma-20	187	67	+	+	CCONJ
ma-20	187	68	1	1	X
ma-20	187	69	)	)	PUNCT
ma-20	187	70	1	1	NUM
ma-20	187	71	q	q	NOUN
ma-20	187	72	−	−	PROPN
ma-20	187	73	1	1	NUM
ma-20	187	74	p	p	NOUN
ma-20	187	75	3	3	NUM
ma-20	187	76	1	1	NUM
ma-20	187	77	p	p	NOUN
ma-20	187	78	,	,	PUNCT
ma-20	187	79	.	.	PUNCT
ma-20	187	80	.	.	PUNCT
ma-20	188	1	.	.	PUNCT
ma-20	189	1	,	,	PUNCT
ma-20	189	2	(	(	PUNCT
ma-20	189	3	(	(	PUNCT
ma-20	189	4	2n−1	2n−1	NUM
ma-20	189	5	−	−	NOUN
ma-20	189	6	1)j	1)j	NUM
ma-20	189	7	+	+	CCONJ
ma-20	189	8	1	1	X
ma-20	189	9	)	)	PUNCT
ma-20	189	10	1	1	NUM
ma-20	189	11	q	q	NOUN
ma-20	189	12	−	−	PROPN
ma-20	189	13	1	1	NUM
ma-20	189	14	p	p	NOUN
ma-20	189	15	2	2	NUM
ma-20	189	16	n−1	n−1	PROPN
ma-20	189	17	p	p	NOUN
ma-20	189	18	}	}	PUNCT
ma-20	189	19	.	.	PUNCT
ma-20	190	1	for	for	ADP
ma-20	190	2	each	each	DET
ma-20	190	3	r	r	NOUN
ma-20	190	4	=	=	SYM
ma-20	190	5	1	1	NUM
ma-20	190	6	,	,	PUNCT
ma-20	190	7	2	2	NUM
ma-20	190	8	,	,	PUNCT
ma-20	190	9	.	.	PUNCT
ma-20	190	10	.	.	PUNCT
ma-20	190	11	.	.	PUNCT
ma-20	191	1	,	,	PUNCT
ma-20	191	2	2n−1	2n−1	NUM
ma-20	191	3	−	−	NOUN
ma-20	191	4	1	1	NUM
ma-20	191	5	,	,	PUNCT
ma-20	191	6	we	we	PRON
ma-20	191	7	have	have	VERB
ma-20	191	8	(	(	PUNCT
ma-20	191	9	r	r	NOUN
ma-20	191	10	j	j	PROPN
ma-20	191	11	+	+	CCONJ
ma-20	191	12	1	1	X
ma-20	191	13	)	)	PUNCT
ma-20	191	14	1q−	1q−	NUM
ma-20	191	15	1p	1p	NUM
ma-20	191	16	≤	≤	NOUN
ma-20	191	17	(	(	PUNCT
ma-20	191	18	j	j	NOUN
ma-20	191	19	+	+	CCONJ
ma-20	192	1	1	1	X
ma-20	192	2	)	)	PUNCT
ma-20	192	3	1q−	1q−	NUM
ma-20	192	4	1p	1p	NUM
ma-20	192	5	and	and	CCONJ
ma-20	192	6	(	(	PUNCT
ma-20	192	7	r	r	NOUN
ma-20	192	8	+	+	NOUN
ma-20	192	9	1	1	NUM
ma-20	192	10	)	)	PUNCT
ma-20	192	11	1p	1p	ADJ
ma-20	192	12	≤	≤	NUM
ma-20	192	13	2	2	NUM
ma-20	192	14	n−1p	n−1p	NOUN
ma-20	192	15	,	,	PUNCT
ma-20	192	16	so	so	SCONJ
ma-20	192	17	that	that	SCONJ
ma-20	192	18	(	(	PUNCT
ma-20	192	19	r	r	NOUN
ma-20	192	20	j	j	PROPN
ma-20	192	21	+	+	CCONJ
ma-20	192	22	1	1	X
ma-20	192	23	)	)	PUNCT
ma-20	192	24	1	1	NUM
ma-20	192	25	q	q	NOUN
ma-20	192	26	−	−	PROPN
ma-20	192	27	1	1	NUM
ma-20	192	28	p	p	NOUN
ma-20	192	29	(	(	PUNCT
ma-20	192	30	r	r	NOUN
ma-20	192	31	+	+	NOUN
ma-20	192	32	1	1	NUM
ma-20	192	33	)	)	PUNCT
ma-20	192	34	1	1	NUM
ma-20	192	35	p	p	NOUN
ma-20	192	36	≤	≤	NOUN
ma-20	192	37	(	(	PUNCT
ma-20	192	38	j	j	NOUN
ma-20	192	39	+	+	CCONJ
ma-20	192	40	1	1	X
ma-20	192	41	)	)	PUNCT
ma-20	192	42	1	1	NUM
ma-20	192	43	q	q	NOUN
ma-20	192	44	−	−	PROPN
ma-20	192	45	1	1	NUM
ma-20	192	46	p	p	NOUN
ma-20	192	47	2	2	NUM
ma-20	192	48	n−1	n−1	PROPN
ma-20	192	49	p	p	NOUN
ma-20	192	50	<	<	X
ma-20	192	51	2−	2−	NUM
ma-20	192	52	n−1	n−1	PROPN
ma-20	192	53	p	p	NOUN
ma-20	192	54	2	2	NUM
ma-20	192	55	n−1	n−1	PROPN
ma-20	192	56	p	p	NOUN
ma-20	192	57	=	=	NOUN
ma-20	192	58	1	1	X
ma-20	192	59	.	.	PUNCT
ma-20	193	1	hence	hence	ADV
ma-20	193	2	we	we	PRON
ma-20	193	3	obtain	obtain	VERB
ma-20	193	4	‖x	‖x	NOUN
ma-20	194	1	(	(	PUNCT
ma-20	194	2	1)‖`pq	1)‖`pq	NUM
ma-20	194	3	=	=	SYM
ma-20	194	4	1	1	NUM
ma-20	194	5	.	.	PUNCT
ma-20	194	6	similarly	similarly	ADV
ma-20	194	7	,	,	PUNCT
ma-20	194	8	one	one	PRON
ma-20	194	9	may	may	AUX
ma-20	194	10	verify	verify	VERB
ma-20	194	11	that	that	SCONJ
ma-20	194	12	‖x	‖x	NOUN
ma-20	194	13	(	(	PUNCT
ma-20	194	14	2)‖`pq	2)‖`pq	NUM
ma-20	194	15	=	=	SYM
ma-20	194	16	‖x	‖x	NOUN
ma-20	194	17	(	(	PUNCT
ma-20	194	18	3)‖`pq	3)‖`pq	NUM
ma-20	194	19	=	=	SYM
ma-20	194	20	·	·	PUNCT
ma-20	194	21	·	·	PUNCT
ma-20	194	22	·	·	PUNCT
ma-20	195	1	=	=	PUNCT
ma-20	195	2	‖x	‖x	NOUN
ma-20	195	3	(	(	PUNCT
ma-20	195	4	n)‖`pq	n)‖`pq	NOUN
ma-20	195	5	=	=	SYM
ma-20	195	6	1	1	X
ma-20	195	7	.	.	PUNCT
ma-20	196	1	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	196	2	eur	eur	PROPN
ma-20	196	3	.	.	PUNCT
ma-20	197	1	j.	j.	PROPN
ma-20	197	2	math	math	PROPN
ma-20	197	3	.	.	PUNCT
ma-20	198	1	anal	anal	PROPN
ma-20	198	2	.	.	PUNCT
ma-20	199	1	10.28924	10.28924	NUM
ma-20	199	2	/	/	SYM
ma-20	199	3	ada	ada	PROPN
ma-20	199	4	/	/	SYM
ma-20	199	5	ma.2.2	ma.2.2	PROPN
ma-20	199	6	8next	8next	NUM
ma-20	199	7	,	,	PUNCT
ma-20	199	8	we	we	PRON
ma-20	199	9	shall	shall	AUX
ma-20	199	10	compute	compute	VERB
ma-20	199	11	the	the	DET
ma-20	199	12	norms	norm	NOUN
ma-20	199	13	of	of	ADP
ma-20	199	14	x	x	SYM
ma-20	199	15	(	(	PUNCT
ma-20	199	16	1)±x	1)±x	NUM
ma-20	199	17	(	(	PUNCT
ma-20	199	18	2)±	2)±	NUM
ma-20	199	19	·	·	PUNCT
ma-20	199	20	·	·	PUNCT
ma-20	200	1	·	·	PUNCT
ma-20	200	2	±x	±x	PROPN
ma-20	200	3	(	(	PUNCT
ma-20	200	4	n	n	CCONJ
ma-20	200	5	)	)	PUNCT
ma-20	200	6	.	.	PUNCT
ma-20	201	1	write	write	VERB
ma-20	201	2	x	x	SYM
ma-20	201	3	(	(	PUNCT
ma-20	201	4	1)+x	1)+x	NUM
ma-20	201	5	(	(	PUNCT
ma-20	201	6	2)+	2)+	NUM
ma-20	201	7	·	·	PUNCT
ma-20	201	8	·	·	PUNCT
ma-20	201	9	·	·	PUNCT
ma-20	202	1	+	+	ADJ
ma-20	202	2	x	x	X
ma-20	202	3	(	(	PUNCT
ma-20	202	4	n	n	CCONJ
ma-20	202	5	)	)	PUNCT
ma-20	202	6	=	=	SYM
ma-20	203	1	(	(	PUNCT
ma-20	203	2	xk)k∈zwhere	xk)k∈zwhere	NUM
ma-20	203	3	xk	xk	PROPN
ma-20	203	4	:	:	PUNCT
ma-20	203	5	=	=	NOUN
ma-20	203	6			NUM
ma-20	203	7	a1	a1	PROPN
ma-20	203	8	,	,	PUNCT
ma-20	203	9	k	k	NOUN
ma-20	203	10	=	=	SYM
ma-20	203	11	0	0	NUM
ma-20	203	12	,	,	PUNCT
ma-20	203	13	a2	a2	PROPN
ma-20	203	14	,	,	PUNCT
ma-20	203	15	k	k	PROPN
ma-20	203	16	=	=	SYM
ma-20	203	17	j	j	PROPN
ma-20	203	18	,	,	PUNCT
ma-20	203	19	a3	a3	NOUN
ma-20	203	20	,	,	PUNCT
ma-20	203	21	k	k	PROPN
ma-20	203	22	=	=	PUNCT
ma-20	203	23	2j	2j	NUM
ma-20	203	24	,	,	PUNCT
ma-20	203	25	...	...	PUNCT
ma-20	204	1	a2n−1	a2n−1	ADJ
ma-20	204	2	,	,	PUNCT
ma-20	204	3	k	k	X
ma-20	204	4	=	=	PUNCT
ma-20	204	5	(	(	PUNCT
ma-20	204	6	2n−1	2n−1	NUM
ma-20	204	7	−	−	PROPN
ma-20	204	8	1)j	1)j	NUM
ma-20	204	9	,	,	PUNCT
ma-20	204	10	0	0	NUM
ma-20	204	11	,	,	PUNCT
ma-20	204	12	otherwise	otherwise	ADV
ma-20	204	13	,	,	PUNCT
ma-20	204	14	with	with	ADP
ma-20	204	15	a1	a1	NOUN
ma-20	204	16	=	=	PUNCT
ma-20	204	17	n	n	NOUN
ma-20	204	18	and	and	CCONJ
ma-20	204	19	|ai	|ai	NUM
ma-20	204	20	|	|	CCONJ
ma-20	204	21	<	<	X
ma-20	204	22	n	n	X
ma-20	204	23	for	for	ADP
ma-20	204	24	i	i	PRON
ma-20	204	25	=	=	SYM
ma-20	204	26	2	2	NUM
ma-20	204	27	,	,	PUNCT
ma-20	204	28	3	3	NUM
ma-20	204	29	,	,	PUNCT
ma-20	204	30	.	.	PUNCT
ma-20	204	31	.	.	PUNCT
ma-20	204	32	.	.	PUNCT
ma-20	205	1	,	,	PUNCT
ma-20	205	2	(	(	PUNCT
ma-20	205	3	2n−1)j	2n−1)j	NUM
ma-20	205	4	.	.	PUNCT
ma-20	206	1	accordingly	accordingly	ADV
ma-20	206	2	,	,	PUNCT
ma-20	206	3	we	we	PRON
ma-20	206	4	have	have	VERB
ma-20	206	5	‖x	‖x	NOUN
ma-20	206	6	(	(	PUNCT
ma-20	206	7	1	1	NUM
ma-20	206	8	)	)	PUNCT
ma-20	207	1	+	+	NOUN
ma-20	207	2	x	x	SYM
ma-20	207	3	(	(	PUNCT
ma-20	207	4	2	2	NUM
ma-20	207	5	)	)	PUNCT
ma-20	207	6	+	+	NUM
ma-20	207	7	·	·	PUNCT
ma-20	207	8	·	·	PUNCT
ma-20	207	9	·	·	PUNCT
ma-20	207	10	+	+	CCONJ
ma-20	207	11	x	x	SYM
ma-20	207	12	(	(	PUNCT
ma-20	207	13	n)‖`pq	n)‖`pq	NOUN
ma-20	207	14	=	=	SYM
ma-20	207	15	sup	sup	NOUN
ma-20	207	16	m∈z	m∈z	NOUN
ma-20	207	17	,	,	PUNCT
ma-20	207	18	n∈ω	n∈ω	NOUN
ma-20	207	19	|sm	|sm	ADV
ma-20	207	20	,	,	PUNCT
ma-20	207	21	n	n	CCONJ
ma-20	207	22	|	|	ADV
ma-20	207	23	1	1	NUM
ma-20	207	24	q	q	NOUN
ma-20	207	25	−	−	PROPN
ma-20	207	26	1	1	NUM
ma-20	207	27	p	p	NOUN
ma-20	207	28	(	(	PUNCT
ma-20	207	29	∑	∑	PUNCT
ma-20	207	30	k∈sm	k∈sm	PROPN
ma-20	207	31	,	,	PUNCT
ma-20	207	32	n	n	X
ma-20	207	33	|xk	|xk	X
ma-20	207	34	|p	|p	X
ma-20	207	35	)	)	PUNCT
ma-20	207	36	1	1	NUM
ma-20	207	37	p	p	NOUN
ma-20	207	38	=	=	NOUN
ma-20	207	39	sup	sup	NOUN
ma-20	207	40	m∈z∩[0,(2n−1−1)j	m∈z∩[0,(2n−1−1)j	NOUN
ma-20	207	41	]	]	X
ma-20	207	42	,	,	PUNCT
ma-20	207	43	n∈z∩[0,(2n−1−1)j/2	n∈z∩[0,(2n−1−1)j/2	X
ma-20	207	44	]	]	X
ma-20	207	45	|sm	|sm	NUM
ma-20	207	46	,	,	PUNCT
ma-20	207	47	n	n	CCONJ
ma-20	207	48	|	|	ADV
ma-20	207	49	1	1	NUM
ma-20	207	50	q	q	NOUN
ma-20	207	51	−	−	PROPN
ma-20	207	52	1	1	NUM
ma-20	207	53	p	p	NOUN
ma-20	207	54	(	(	PUNCT
ma-20	207	55	∑	∑	PUNCT
ma-20	207	56	k∈sm	k∈sm	PROPN
ma-20	207	57	,	,	PUNCT
ma-20	207	58	n	n	X
ma-20	207	59	|xk	|xk	X
ma-20	207	60	|p	|p	X
ma-20	207	61	)	)	PUNCT
ma-20	207	62	1	1	NUM
ma-20	207	63	p	p	NOUN
ma-20	207	64	=	=	PRON
ma-20	207	65	max	max	X
ma-20	207	66	{	{	PUNCT
ma-20	207	67	n	n	CCONJ
ma-20	207	68	,	,	PUNCT
ma-20	207	69	(	(	PUNCT
ma-20	207	70	j	j	PROPN
ma-20	207	71	+	+	CCONJ
ma-20	207	72	1	1	X
ma-20	207	73	)	)	PUNCT
ma-20	207	74	1	1	NUM
ma-20	207	75	q	q	NOUN
ma-20	207	76	−	−	PROPN
ma-20	207	77	1	1	NUM
ma-20	207	78	p	p	NOUN
ma-20	207	79	(	(	PUNCT
ma-20	207	80	np	np	INTJ
ma-20	207	81	+	+	CCONJ
ma-20	207	82	ap2	ap2	PROPN
ma-20	207	83	)	)	PUNCT
ma-20	207	84	1	1	NUM
ma-20	207	85	p	p	NOUN
ma-20	207	86	,	,	PUNCT
ma-20	207	87	(	(	PUNCT
ma-20	207	88	2j	2j	X
ma-20	207	89	+	+	CCONJ
ma-20	207	90	1	1	X
ma-20	207	91	)	)	PUNCT
ma-20	207	92	1	1	NUM
ma-20	207	93	q	q	NOUN
ma-20	207	94	−	−	PROPN
ma-20	207	95	1	1	NUM
ma-20	207	96	p	p	NOUN
ma-20	207	97	(	(	PUNCT
ma-20	207	98	np	np	INTJ
ma-20	207	99	+	+	CCONJ
ma-20	207	100	ap2	ap2	PROPN
ma-20	207	101	+	+	CCONJ
ma-20	207	102	a	a	DET
ma-20	207	103	p	p	NOUN
ma-20	207	104	3	3	NUM
ma-20	207	105	)	)	PUNCT
ma-20	207	106	1	1	NUM
ma-20	207	107	p	p	NOUN
ma-20	207	108	,	,	PUNCT
ma-20	207	109	.	.	PUNCT
ma-20	207	110	.	.	PUNCT
ma-20	207	111	.	.	PUNCT
ma-20	208	1	,	,	PUNCT
ma-20	208	2	(	(	PUNCT
ma-20	208	3	(	(	PUNCT
ma-20	208	4	2n−1	2n−1	NUM
ma-20	208	5	−	−	NOUN
ma-20	208	6	1)j	1)j	NUM
ma-20	208	7	+	+	CCONJ
ma-20	208	8	1	1	X
ma-20	208	9	)	)	PUNCT
ma-20	208	10	1	1	NUM
ma-20	208	11	q	q	NOUN
ma-20	208	12	−	−	PROPN
ma-20	208	13	1	1	NUM
ma-20	208	14	p	p	NOUN
ma-20	208	15	(	(	PUNCT
ma-20	208	16	np	np	INTJ
ma-20	209	1	+	+	NUM
ma-20	209	2	2n−1∑	2n−1∑	ADJ
ma-20	209	3	i=2	i=2	PROPN
ma-20	209	4	api	api	NOUN
ma-20	209	5	)	)	PUNCT
ma-20	209	6	1	1	NUM
ma-20	209	7	p	p	NOUN
ma-20	209	8	}	}	PUNCT
ma-20	209	9	.	.	PUNCT
ma-20	210	1	since	since	SCONJ
ma-20	210	2	(	(	PUNCT
ma-20	210	3	r	r	NOUN
ma-20	210	4	j	j	PROPN
ma-20	210	5	+	+	CCONJ
ma-20	210	6	1	1	X
ma-20	210	7	)	)	PUNCT
ma-20	210	8	1q−	1q−	NUM
ma-20	210	9	1p	1p	NUM
ma-20	210	10	≤	≤	NOUN
ma-20	210	11	(	(	PUNCT
ma-20	210	12	j	j	NOUN
ma-20	210	13	+	+	CCONJ
ma-20	210	14	1	1	X
ma-20	210	15	)	)	PUNCT
ma-20	210	16	1q−	1q−	NUM
ma-20	210	17	1p	1p	NUM
ma-20	210	18	for	for	ADP
ma-20	210	19	each	each	DET
ma-20	210	20	r	r	NOUN
ma-20	210	21	=	=	SYM
ma-20	210	22	1	1	NUM
ma-20	210	23	,	,	PUNCT
ma-20	210	24	2	2	NUM
ma-20	210	25	,	,	PUNCT
ma-20	210	26	.	.	PUNCT
ma-20	210	27	.	.	PUNCT
ma-20	210	28	.	.	PUNCT
ma-20	211	1	,	,	PUNCT
ma-20	211	2	2n−1	2n−1	NUM
ma-20	211	3	−	−	NOUN
ma-20	211	4	1	1	NUM
ma-20	211	5	,	,	PUNCT
ma-20	211	6	we	we	PRON
ma-20	211	7	obtain	obtain	VERB
ma-20	211	8	(	(	PUNCT
ma-20	211	9	r	r	NOUN
ma-20	211	10	j	j	PROPN
ma-20	212	1	+	+	CCONJ
ma-20	212	2	1	1	X
ma-20	212	3	)	)	PUNCT
ma-20	212	4	1	1	NUM
ma-20	212	5	q	q	NOUN
ma-20	212	6	−	−	PROPN
ma-20	212	7	1	1	NUM
ma-20	212	8	p	p	NOUN
ma-20	212	9	(	(	PUNCT
ma-20	212	10	np	np	INTJ
ma-20	212	11	+	+	CCONJ
ma-20	212	12	r+1∑	r+1∑	PROPN
ma-20	212	13	i=2	i=2	PROPN
ma-20	212	14	api	api	NOUN
ma-20	212	15	)	)	PUNCT
ma-20	212	16	1	1	NUM
ma-20	212	17	p	p	NOUN
ma-20	212	18	≤	≤	NOUN
ma-20	212	19	(	(	PUNCT
ma-20	212	20	j	j	NOUN
ma-20	212	21	+	+	CCONJ
ma-20	212	22	1	1	X
ma-20	212	23	)	)	PUNCT
ma-20	212	24	1	1	NUM
ma-20	212	25	q	q	NOUN
ma-20	212	26	−	−	PROPN
ma-20	212	27	1	1	NUM
ma-20	212	28	p	p	NOUN
ma-20	212	29	(	(	PUNCT
ma-20	212	30	np	np	INTJ
ma-20	212	31	+	+	CCONJ
ma-20	212	32	r+1∑	r+1∑	PROPN
ma-20	212	33	i=2	i=2	PROPN
ma-20	212	34	api	api	NOUN
ma-20	212	35	)	)	PUNCT
ma-20	212	36	1	1	NUM
ma-20	212	37	p	p	NOUN
ma-20	212	38	<	<	X
ma-20	212	39	2−	2−	NUM
ma-20	212	40	(	(	PUNCT
ma-20	212	41	n−1	n−1	PROPN
ma-20	212	42	)	)	PUNCT
ma-20	212	43	p	p	NOUN
ma-20	212	44	(	(	PUNCT
ma-20	212	45	np	np	INTJ
ma-20	212	46	+	+	CCONJ
ma-20	212	47	r+1∑	r+1∑	PROPN
ma-20	212	48	i=2	i=2	PROPN
ma-20	212	49	api	api	NOUN
ma-20	212	50	)	)	PUNCT
ma-20	212	51	1	1	NUM
ma-20	212	52	p	p	NOUN
ma-20	212	53	<	<	X
ma-20	212	54	2−	2−	NUM
ma-20	212	55	(	(	PUNCT
ma-20	212	56	n−1	n−1	PROPN
ma-20	212	57	)	)	PUNCT
ma-20	212	58	p	p	NOUN
ma-20	212	59	(	(	PUNCT
ma-20	212	60	np	np	INTJ
ma-20	212	61	+	+	CCONJ
ma-20	212	62	np	np	PROPN
ma-20	212	63	+	+	NUM
ma-20	212	64	·	·	PUNCT
ma-20	212	65	·	·	PUNCT
ma-20	212	66	·	·	PUNCT
ma-20	212	67	+	+	NUM
ma-20	212	68	np︸	np︸	PROPN
ma-20	212	69	︷︷	︷︷	PROPN
ma-20	212	70	︸	︸	ADP
ma-20	212	71	r	r	NOUN
ma-20	212	72	+	+	NUM
ma-20	212	73	1	1	NUM
ma-20	212	74	times	time	NOUN
ma-20	212	75	)	)	PUNCT
ma-20	212	76	1	1	NUM
ma-20	212	77	p	p	NOUN
ma-20	212	78	=	=	SYM
ma-20	212	79	2−	2−	NUM
ma-20	212	80	(	(	PUNCT
ma-20	212	81	n−1	n−1	PROPN
ma-20	212	82	)	)	PUNCT
ma-20	212	83	p	p	NOUN
ma-20	212	84	(	(	PUNCT
ma-20	212	85	r	r	NOUN
ma-20	212	86	+	+	NOUN
ma-20	212	87	1	1	NUM
ma-20	212	88	)	)	PUNCT
ma-20	212	89	1	1	NUM
ma-20	212	90	p	p	NOUN
ma-20	212	91	(	(	PUNCT
ma-20	212	92	np	np	INTJ
ma-20	212	93	)	)	PUNCT
ma-20	212	94	1	1	NUM
ma-20	212	95	p	p	NOUN
ma-20	212	96	≤	≤	NUM
ma-20	212	97	2−	2−	NUM
ma-20	212	98	(	(	PUNCT
ma-20	212	99	n−1	n−1	PROPN
ma-20	212	100	)	)	PUNCT
ma-20	212	101	p	p	NOUN
ma-20	212	102	2	2	NUM
ma-20	212	103	(	(	PUNCT
ma-20	212	104	n−1	n−1	PROPN
ma-20	212	105	)	)	PUNCT
ma-20	212	106	p	p	NOUN
ma-20	212	107	n	n	NOUN
ma-20	212	108	=	=	SYM
ma-20	212	109	n.	n.	NOUN
ma-20	212	110	it	it	PRON
ma-20	212	111	thus	thus	ADV
ma-20	212	112	follows	follow	VERB
ma-20	212	113	that	that	SCONJ
ma-20	212	114	‖x	‖x	PROPN
ma-20	212	115	(	(	PUNCT
ma-20	212	116	1	1	X
ma-20	212	117	)	)	PUNCT
ma-20	213	1	+	+	NOUN
ma-20	213	2	x	x	SYM
ma-20	213	3	(	(	PUNCT
ma-20	213	4	2	2	NUM
ma-20	213	5	)	)	PUNCT
ma-20	213	6	+	+	NUM
ma-20	213	7	·	·	PUNCT
ma-20	213	8	·	·	PUNCT
ma-20	213	9	·	·	PUNCT
ma-20	213	10	+	+	CCONJ
ma-20	213	11	x	x	SYM
ma-20	213	12	(	(	PUNCT
ma-20	213	13	n)‖`pq	n)‖`pq	NOUN
ma-20	213	14	=	=	SYM
ma-20	213	15	n.as	n.as	NOUN
ma-20	213	16	we	we	PRON
ma-20	213	17	have	have	AUX
ma-20	213	18	remarked	remark	VERB
ma-20	213	19	earlier	early	ADV
ma-20	213	20	,	,	PUNCT
ma-20	213	21	the	the	DET
ma-20	213	22	largest	large	ADJ
ma-20	213	23	absolute	absolute	ADJ
ma-20	213	24	value	value	NOUN
ma-20	213	25	of	of	ADP
ma-20	213	26	x	x	X
ma-20	213	27	(	(	PUNCT
ma-20	213	28	1	1	X
ma-20	213	29	)	)	PUNCT
ma-20	213	30	±	±	NOUN
ma-20	213	31	x	x	SYM
ma-20	213	32	(	(	PUNCT
ma-20	213	33	2	2	X
ma-20	213	34	)	)	PUNCT
ma-20	213	35	±	±	NOUN
ma-20	213	36	·	·	PUNCT
ma-20	213	37	·	·	PUNCT
ma-20	213	38	·	·	PUNCT
ma-20	213	39	±	±	NUM
ma-20	213	40	x	x	SYM
ma-20	213	41	(	(	PUNCT
ma-20	213	42	n	n	CCONJ
ma-20	213	43	)	)	PUNCT
ma-20	213	44	is	be	AUX
ma-20	213	45	equal	equal	ADJ
ma-20	213	46	to	to	ADP
ma-20	213	47	n	n	NOUN
ma-20	213	48	for	for	ADP
ma-20	213	49	every	every	DET
ma-20	213	50	combination	combination	NOUN
ma-20	213	51	of	of	ADP
ma-20	213	52	±	±	NUM
ma-20	213	53	signs	sign	NOUN
ma-20	213	54	.	.	PUNCT
ma-20	214	1	moreover	moreover	ADV
ma-20	214	2	,	,	PUNCT
ma-20	214	3	it	it	PRON
ma-20	214	4	is	be	AUX
ma-20	214	5	clear	clear	ADJ
ma-20	214	6	that	that	SCONJ
ma-20	214	7	for	for	ADP
ma-20	214	8	k	k	PROPN
ma-20	214	9	/∈	/∈	PUNCT
ma-20	214	10	{	{	PUNCT
ma-20	214	11	0	0	NUM
ma-20	214	12	,	,	PUNCT
ma-20	214	13	2j	2j	NUM
ma-20	214	14	,	,	PUNCT
ma-20	214	15	.	.	PUNCT
ma-20	214	16	.	.	PUNCT
ma-20	214	17	.	.	PUNCT
ma-20	215	1	,	,	PUNCT
ma-20	215	2	(	(	PUNCT
ma-20	215	3	2n−1	2n−1	NUM
ma-20	215	4	−	−	PROPN
ma-20	215	5	1)j	1)j	NUM
ma-20	215	6	}	}	PUNCT
ma-20	215	7	,	,	PUNCT
ma-20	215	8	the	the	DET
ma-20	215	9	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	215	10	eur	eur	PROPN
ma-20	215	11	.	.	PUNCT
ma-20	216	1	j.	j.	PROPN
ma-20	216	2	math	math	PROPN
ma-20	216	3	.	.	PUNCT
ma-20	217	1	anal	anal	PROPN
ma-20	217	2	.	.	PUNCT
ma-20	218	1	10.28924	10.28924	NUM
ma-20	218	2	/	/	SYM
ma-20	218	3	ada	ada	PROPN
ma-20	218	4	/	/	SYM
ma-20	218	5	ma.2.2	ma.2.2	NOUN
ma-20	218	6	9	9	NUM
ma-20	218	7	k	k	NOUN
ma-20	218	8	-	-	PUNCT
ma-20	218	9	th	th	VERB
ma-20	218	10	term	term	NOUN
ma-20	218	11	of	of	ADP
ma-20	218	12	x	x	X
ma-20	218	13	(	(	PUNCT
ma-20	218	14	1	1	X
ma-20	218	15	)	)	PUNCT
ma-20	218	16	±	±	NOUN
ma-20	218	17	x	x	SYM
ma-20	218	18	(	(	PUNCT
ma-20	218	19	2	2	X
ma-20	218	20	)	)	PUNCT
ma-20	218	21	±	±	NOUN
ma-20	218	22	·	·	PUNCT
ma-20	218	23	·	·	PUNCT
ma-20	218	24	·	·	PUNCT
ma-20	219	1	±	±	NUM
ma-20	219	2	x	x	SYM
ma-20	219	3	(	(	PUNCT
ma-20	219	4	n	n	CCONJ
ma-20	219	5	)	)	PUNCT
ma-20	219	6	is	be	AUX
ma-20	219	7	equal	equal	ADJ
ma-20	219	8	to	to	ADP
ma-20	219	9	0	0	NUM
ma-20	219	10	.	.	PUNCT
ma-20	220	1	hence	hence	ADV
ma-20	220	2	,	,	PUNCT
ma-20	220	3	we	we	PRON
ma-20	220	4	obtain	obtain	VERB
ma-20	220	5	‖x	‖x	NOUN
ma-20	220	6	(	(	PUNCT
ma-20	220	7	1	1	X
ma-20	220	8	)	)	PUNCT
ma-20	220	9	±	±	NOUN
ma-20	220	10	x	x	SYM
ma-20	220	11	(	(	PUNCT
ma-20	220	12	2	2	X
ma-20	220	13	)	)	PUNCT
ma-20	220	14	±	±	NOUN
ma-20	220	15	·	·	PUNCT
ma-20	220	16	·	·	PUNCT
ma-20	220	17	·	·	PUNCT
ma-20	221	1	±	±	NUM
ma-20	221	2	x	x	SYM
ma-20	221	3	(	(	PUNCT
ma-20	221	4	n)‖`pq	n)‖`pq	NOUN
ma-20	221	5	=	=	SYM
ma-20	221	6	sup	sup	NOUN
ma-20	221	7	m∈z	m∈z	NOUN
ma-20	221	8	,	,	PUNCT
ma-20	221	9	n∈ω	n∈ω	NOUN
ma-20	221	10	|sm	|sm	ADV
ma-20	221	11	,	,	PUNCT
ma-20	221	12	n	n	CCONJ
ma-20	221	13	|	|	ADV
ma-20	221	14	1	1	NUM
ma-20	221	15	q	q	NOUN
ma-20	221	16	−	−	PROPN
ma-20	221	17	1	1	NUM
ma-20	221	18	p	p	NOUN
ma-20	221	19	(	(	PUNCT
ma-20	221	20	∑	∑	PUNCT
ma-20	221	21	k∈sm	k∈sm	PROPN
ma-20	221	22	,	,	PUNCT
ma-20	221	23	n	n	PRON
ma-20	221	24	|x	|x	NOUN
ma-20	221	25	(	(	PUNCT
ma-20	221	26	1)k	1)k	NUM
ma-20	221	27	±	±	NUM
ma-20	221	28	x	x	SYM
ma-20	221	29	(	(	PUNCT
ma-20	221	30	2	2	NUM
ma-20	221	31	)	)	PUNCT
ma-20	221	32	k	k	PROPN
ma-20	221	33	±	±	PROPN
ma-20	221	34	·	·	PUNCT
ma-20	221	35	·	·	PUNCT
ma-20	221	36	·	·	PUNCT
ma-20	221	37	±	±	NUM
ma-20	221	38	x	x	SYM
ma-20	221	39	(	(	PUNCT
ma-20	221	40	n	n	CCONJ
ma-20	221	41	)	)	PUNCT
ma-20	221	42	k	k	NOUN
ma-20	222	1	|	|	ADV
ma-20	222	2	p	p	NOUN
ma-20	222	3	)	)	PUNCT
ma-20	223	1	1	1	NUM
ma-20	223	2	p	p	NOUN
ma-20	223	3	=	=	NOUN
ma-20	223	4	sup	sup	NOUN
ma-20	223	5	m∈z∩[0,(2n−1−1)j	m∈z∩[0,(2n−1−1)j	NOUN
ma-20	223	6	]	]	X
ma-20	223	7	,	,	PUNCT
ma-20	223	8	n∈z∩[0,(2n−1−1)j/2	n∈z∩[0,(2n−1−1)j/2	X
ma-20	223	9	]	]	X
ma-20	223	10	|sm	|sm	NUM
ma-20	223	11	,	,	PUNCT
ma-20	223	12	n	n	CCONJ
ma-20	223	13	|	|	ADV
ma-20	223	14	1	1	NUM
ma-20	223	15	q	q	NOUN
ma-20	223	16	−	−	PROPN
ma-20	223	17	1	1	NUM
ma-20	223	18	p	p	NOUN
ma-20	223	19	(	(	PUNCT
ma-20	223	20	∑	∑	PUNCT
ma-20	223	21	k∈sm	k∈sm	PROPN
ma-20	223	22	,	,	PUNCT
ma-20	223	23	n	n	PRON
ma-20	223	24	|x	|x	NOUN
ma-20	223	25	(	(	PUNCT
ma-20	223	26	1)k	1)k	NUM
ma-20	223	27	±	±	NUM
ma-20	223	28	x	x	SYM
ma-20	223	29	(	(	PUNCT
ma-20	223	30	2	2	NUM
ma-20	223	31	)	)	PUNCT
ma-20	223	32	k	k	PROPN
ma-20	223	33	±	±	PROPN
ma-20	223	34	·	·	PUNCT
ma-20	223	35	·	·	PUNCT
ma-20	223	36	·	·	PUNCT
ma-20	223	37	±	±	NUM
ma-20	223	38	x	x	SYM
ma-20	223	39	(	(	PUNCT
ma-20	223	40	n	n	CCONJ
ma-20	223	41	)	)	PUNCT
ma-20	223	42	k	k	NOUN
ma-20	224	1	|	|	ADV
ma-20	224	2	p	p	NOUN
ma-20	224	3	)	)	PUNCT
ma-20	224	4	1	1	NUM
ma-20	224	5	p	p	NOUN
ma-20	224	6	=	=	NOUN
ma-20	224	7	n.	n.	NOUN
ma-20	224	8	consequently	consequently	ADV
ma-20	224	9	,	,	PUNCT
ma-20	224	10	we	we	PRON
ma-20	224	11	get	get	VERB
ma-20	224	12	∑	∑	PUNCT
ma-20	224	13	±	±	NUM
ma-20	224	14	‖x	‖x	NOUN
ma-20	225	1	(	(	PUNCT
ma-20	225	2	1	1	X
ma-20	225	3	)	)	PUNCT
ma-20	225	4	±	±	NOUN
ma-20	225	5	x	x	SYM
ma-20	225	6	(	(	PUNCT
ma-20	225	7	2	2	X
ma-20	225	8	)	)	PUNCT
ma-20	225	9	±	±	NOUN
ma-20	225	10	·	·	PUNCT
ma-20	225	11	·	·	PUNCT
ma-20	225	12	·	·	PUNCT
ma-20	226	1	±	±	NUM
ma-20	226	2	x	x	SYM
ma-20	226	3	(	(	PUNCT
ma-20	226	4	n)‖2`pq	n)‖2`pq	NOUN
ma-20	226	5	2n−1	2n−1	NUM
ma-20	226	6	∑n	∑n	PROPN
ma-20	226	7	i=1	i=1	PROPN
ma-20	226	8	‖xi‖`pq	‖xi‖`pq	NOUN
ma-20	226	9	=	=	SYM
ma-20	226	10	2n−1n2	2n−1n2	NUM
ma-20	226	11	2n−1n	2n−1n	NUM
ma-20	226	12	=	=	SYM
ma-20	226	13	n	n	NOUN
ma-20	226	14	and	and	CCONJ
ma-20	226	15	min	min	NOUN
ma-20	226	16	‖x	‖x	NOUN
ma-20	226	17	(	(	PUNCT
ma-20	226	18	1	1	X
ma-20	226	19	)	)	PUNCT
ma-20	226	20	±	±	NOUN
ma-20	226	21	x	x	SYM
ma-20	226	22	(	(	PUNCT
ma-20	226	23	2	2	X
ma-20	226	24	)	)	PUNCT
ma-20	226	25	±	±	NOUN
ma-20	226	26	·	·	PUNCT
ma-20	226	27	·	·	PUNCT
ma-20	226	28	·	·	PUNCT
ma-20	227	1	±	±	NUM
ma-20	227	2	x	x	SYM
ma-20	227	3	(	(	PUNCT
ma-20	227	4	n)‖`pq	n)‖`pq	NOUN
ma-20	227	5	=	=	SYM
ma-20	227	6	n	n	CCONJ
ma-20	227	7	,	,	PUNCT
ma-20	227	8	whence	whence	NOUN
ma-20	227	9	c	c	PROPN
ma-20	227	10	(	(	PUNCT
ma-20	227	11	n	n	CCONJ
ma-20	227	12	)	)	PUNCT
ma-20	227	13	nj	nj	PROPN
ma-20	227	14	(	(	PUNCT
ma-20	227	15	`	`	PUNCT
ma-20	227	16	p	p	X
ma-20	227	17	q(z	q(z	PROPN
ma-20	227	18	)	)	PUNCT
ma-20	227	19	)	)	PUNCT
ma-20	228	1	=	=	SYM
ma-20	228	2	c	c	X
ma-20	228	3	(	(	PUNCT
ma-20	228	4	n	n	CCONJ
ma-20	228	5	)	)	PUNCT
ma-20	228	6	j	j	NOUN
ma-20	228	7	(	(	PUNCT
ma-20	228	8	`	`	PUNCT
ma-20	228	9	p	p	X
ma-20	228	10	q(z	q(z	PROPN
ma-20	228	11	)	)	PUNCT
ma-20	228	12	)	)	PUNCT
ma-20	229	1	=	=	PUNCT
ma-20	229	2	n.	n.	NOUN
ma-20	229	3	case	case	NOUN
ma-20	229	4	2	2	NUM
ma-20	229	5	:	:	PUNCT
ma-20	229	6	d	d	X
ma-20	229	7	>	>	X
ma-20	229	8	1	1	NUM
ma-20	229	9	.	.	PUNCT
ma-20	230	1	here	here	ADV
ma-20	230	2	we	we	PRON
ma-20	230	3	choose	choose	VERB
ma-20	230	4	j	j	PROPN
ma-20	230	5	∈	∈	PROPN
ma-20	230	6	z	z	PROPN
ma-20	230	7	to	to	PART
ma-20	230	8	be	be	AUX
ma-20	230	9	a	a	DET
ma-20	230	10	nonnegative	nonnegative	ADJ
ma-20	230	11	,	,	PUNCT
ma-20	230	12	even	even	ADV
ma-20	230	13	integer	integer	VERB
ma-20	230	14	such	such	ADJ
ma-20	230	15	that	that	SCONJ
ma-20	230	16	j	j	PROPN
ma-20	230	17	>	>	X
ma-20	230	18	2	2	NUM
ma-20	230	19	(	(	PUNCT
ma-20	230	20	n−1	n−1	PROPN
ma-20	230	21	d	d	PROPN
ma-20	230	22	)	)	PUNCT
ma-20	230	23	(	(	PUNCT
ma-20	230	24	q	q	PROPN
ma-20	230	25	q−p	q−p	PROPN
ma-20	230	26	)	)	PUNCT
ma-20	231	1	−	−	PROPN
ma-20	231	2	1	1	NUM
ma-20	231	3	or	or	CCONJ
ma-20	231	4	,	,	PUNCT
ma-20	231	5	equivalently	equivalently	ADV
ma-20	231	6	,	,	PUNCT
ma-20	231	7	(	(	PUNCT
ma-20	231	8	j	j	PROPN
ma-20	231	9	+	+	NOUN
ma-20	231	10	1)d	1)d	NUM
ma-20	231	11	(	(	PUNCT
ma-20	231	12	1	1	NUM
ma-20	231	13	q	q	NOUN
ma-20	231	14	−	−	PROPN
ma-20	231	15	1	1	NUM
ma-20	231	16	p	p	NOUN
ma-20	231	17	)	)	PUNCT
ma-20	231	18	<	<	X
ma-20	231	19	2−	2−	NUM
ma-20	231	20	(	(	PUNCT
ma-20	231	21	n−1	n−1	PROPN
ma-20	231	22	)	)	PUNCT
ma-20	231	23	p	p	NOUN
ma-20	231	24	.	.	PUNCT
ma-20	232	1	then	then	ADV
ma-20	232	2	,	,	PUNCT
ma-20	232	3	using	use	VERB
ma-20	232	4	the	the	DET
ma-20	232	5	sequences	sequence	NOUN
ma-20	232	6	x	x	SYM
ma-20	232	7	(	(	PUNCT
ma-20	232	8	i	i	NOUN
ma-20	232	9	)	)	PUNCT
ma-20	232	10	=	=	PUNCT
ma-20	233	1	(	(	PUNCT
ma-20	233	2	x	x	X
ma-20	233	3	(	(	PUNCT
ma-20	233	4	i	i	NOUN
ma-20	233	5	)	)	PUNCT
ma-20	233	6	k1	k1	NOUN
ma-20	233	7	)	)	PUNCT
ma-20	233	8	k1∈z	k1∈z	PROPN
ma-20	233	9	∈	∈	PROPN
ma-20	233	10	`	`	PUNCT
ma-20	233	11	p	p	PROPN
ma-20	233	12	q(z	q(z	PROPN
ma-20	233	13	)	)	PUNCT
ma-20	233	14	,	,	PUNCT
ma-20	233	15	i	i	PRON
ma-20	233	16	=	=	NOUN
ma-20	233	17	1	1	NUM
ma-20	233	18	,	,	PUNCT
ma-20	233	19	.	.	PUNCT
ma-20	233	20	.	.	PUNCT
ma-20	233	21	.	.	PUNCT
ma-20	234	1	,	,	PUNCT
ma-20	234	2	n	n	CCONJ
ma-20	234	3	,	,	PUNCT
ma-20	234	4	in	in	ADP
ma-20	234	5	the	the	DET
ma-20	234	6	case	case	NOUN
ma-20	234	7	where	where	SCONJ
ma-20	234	8	d	d	NOUN
ma-20	234	9	=	=	SYM
ma-20	234	10	1	1	NUM
ma-20	234	11	,	,	PUNCT
ma-20	234	12	we	we	PRON
ma-20	234	13	now	now	ADV
ma-20	234	14	define	define	VERB
ma-20	234	15	x	x	PUNCT
ma-20	234	16	(	(	PUNCT
ma-20	234	17	i	i	NOUN
ma-20	234	18	)	)	PUNCT
ma-20	235	1	:	:	PUNCT
ma-20	235	2	=	=	SYM
ma-20	235	3	(	(	PUNCT
ma-20	235	4	x	x	X
ma-20	235	5	(	(	PUNCT
ma-20	235	6	i)k	i)k	NOUN
ma-20	235	7	)	)	PUNCT
ma-20	235	8	k∈zd	k∈zd	PROPN
ma-20	235	9	∈	∈	PROPN
ma-20	235	10	`	`	PUNCT
ma-20	235	11	pq(zd	pq(zd	NOUN
ma-20	235	12	)	)	PUNCT
ma-20	235	13	for	for	ADP
ma-20	235	14	i	i	PROPN
ma-20	235	15	=	=	NOUN
ma-20	235	16	1	1	NUM
ma-20	235	17	,	,	PUNCT
ma-20	235	18	.	.	PUNCT
ma-20	235	19	.	.	PUNCT
ma-20	236	1	.	.	PUNCT
ma-20	237	1	,	,	PUNCT
ma-20	238	1	n	n	CCONJ
ma-20	238	2	,	,	PUNCT
ma-20	238	3	where	where	SCONJ
ma-20	238	4	x	x	X
ma-20	238	5	(	(	PUNCT
ma-20	238	6	i	i	NOUN
ma-20	238	7	)	)	PUNCT
ma-20	238	8	k	k	PROPN
ma-20	238	9	=	=	PUNCT
ma-20	239	1	x	x	PROPN
ma-20	239	2	(	(	PUNCT
ma-20	239	3	i)k1	i)k1	PROPN
ma-20	239	4	,	,	PUNCT
ma-20	239	5	k	k	PROPN
ma-20	239	6	=	=	PRON
ma-20	239	7	(	(	PUNCT
ma-20	239	8	k1	k1	PROPN
ma-20	239	9	,	,	PUNCT
ma-20	239	10	0	0	NUM
ma-20	239	11	,	,	PUNCT
ma-20	239	12	0	0	NUM
ma-20	239	13	,	,	PUNCT
ma-20	239	14	.	.	PUNCT
ma-20	239	15	.	.	PUNCT
ma-20	239	16	.	.	PUNCT
ma-20	240	1	,	,	PUNCT
ma-20	240	2	0	0	NUM
ma-20	240	3	)	)	PUNCT
ma-20	240	4	,	,	PUNCT
ma-20	240	5	0	0	NUM
ma-20	240	6	,	,	PUNCT
ma-20	240	7	otherwise	otherwise	ADV
ma-20	240	8	.	.	PUNCT
ma-20	241	1	we	we	PRON
ma-20	241	2	shall	shall	AUX
ma-20	241	3	then	then	ADV
ma-20	241	4	obtain	obtain	VERB
ma-20	241	5	c	c	NOUN
ma-20	241	6	(	(	PUNCT
ma-20	241	7	n	n	CCONJ
ma-20	241	8	)	)	PUNCT
ma-20	241	9	nj	nj	PROPN
ma-20	241	10	(	(	PUNCT
ma-20	241	11	`	`	PUNCT
ma-20	241	12	p	p	PRON
ma-20	241	13	q(zd	q(zd	NOUN
ma-20	241	14	)	)	PUNCT
ma-20	241	15	)	)	PUNCT
ma-20	242	1	=	=	PUNCT
ma-20	242	2	c	c	X
ma-20	242	3	(	(	PUNCT
ma-20	242	4	n	n	CCONJ
ma-20	242	5	)	)	PUNCT
ma-20	242	6	j	j	NOUN
ma-20	242	7	(	(	PUNCT
ma-20	242	8	`	`	PUNCT
ma-20	242	9	p	p	PRON
ma-20	242	10	q(zd	q(zd	NOUN
ma-20	242	11	)	)	PUNCT
ma-20	242	12	)	)	PUNCT
ma-20	243	1	=	=	SYM
ma-20	244	1	n	n	CCONJ
ma-20	244	2	,	,	PUNCT
ma-20	244	3	as	as	SCONJ
ma-20	244	4	desired	desire	VERB
ma-20	244	5	.	.	PUNCT
ma-20	245	1	�	�	PROPN
ma-20	245	2	corollary	corollary	ADJ
ma-20	245	3	2.2.1	2.2.1	NUM
ma-20	245	4	.	.	PUNCT
ma-20	246	1	for	for	ADP
ma-20	246	2	1	1	NUM
ma-20	246	3	≤	≤	NOUN
ma-20	246	4	p	p	NOUN
ma-20	246	5	<	<	X
ma-20	246	6	q	q	X
ma-20	246	7	<	<	X
ma-20	246	8	∞	∞	PROPN
ma-20	246	9	,	,	PUNCT
ma-20	246	10	the	the	DET
ma-20	246	11	space	space	NOUN
ma-20	246	12	`	`	PUNCT
ma-20	246	13	pq	pq	NOUN
ma-20	246	14	is	be	AUX
ma-20	246	15	not	not	PART
ma-20	246	16	uniformly	uniformly	ADV
ma-20	246	17	non-`1n	non-`1n	PROPN
ma-20	246	18	.	.	PUNCT
ma-20	247	1	corollary	corollary	NOUN
ma-20	247	2	2.2.2	2.2.2	NUM
ma-20	247	3	.	.	PUNCT
ma-20	248	1	for	for	ADP
ma-20	248	2	1	1	NUM
ma-20	248	3	≤	≤	NOUN
ma-20	248	4	p	p	NOUN
ma-20	248	5	<	<	X
ma-20	248	6	q	q	X
ma-20	248	7	<	<	X
ma-20	248	8	∞	∞	PROPN
ma-20	248	9	,	,	PUNCT
ma-20	248	10	the	the	DET
ma-20	248	11	space	space	NOUN
ma-20	248	12	`	`	PUNCT
ma-20	248	13	pq	pq	NOUN
ma-20	248	14	is	be	AUX
ma-20	248	15	not	not	PART
ma-20	248	16	uniformly	uniformly	ADV
ma-20	248	17	n	n	CCONJ
ma-20	248	18	-	-	PUNCT
ma-20	248	19	convex	convex	NOUN
ma-20	248	20	.	.	PUNCT
ma-20	249	1	acknowledgement	acknowledgement	NOUN
ma-20	249	2	.	.	PUNCT
ma-20	250	1	the	the	DET
ma-20	250	2	work	work	NOUN
ma-20	250	3	is	be	AUX
ma-20	250	4	part	part	NOUN
ma-20	250	5	of	of	ADP
ma-20	250	6	the	the	DET
ma-20	250	7	first	first	ADJ
ma-20	250	8	author	author	NOUN
ma-20	250	9	’s	’s	PART
ma-20	250	10	thesis	thesis	NOUN
ma-20	250	11	.	.	PUNCT
ma-20	251	1	both	both	DET
ma-20	251	2	authors	author	NOUN
ma-20	251	3	are	be	AUX
ma-20	251	4	supported	support	VERB
ma-20	251	5	byp2mi	byp2mi	PROPN
ma-20	251	6	2021	2021	NUM
ma-20	251	7	program	program	NOUN
ma-20	251	8	of	of	ADP
ma-20	251	9	bandung	bandung	PROPN
ma-20	251	10	institute	institute	PROPN
ma-20	251	11	of	of	ADP
ma-20	251	12	technology	technology	PROPN
ma-20	251	13	.	.	PUNCT
ma-20	252	1	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PROPN
ma-20	252	2	eur	eur	PROPN
ma-20	252	3	.	.	PUNCT
ma-20	253	1	j.	j.	PROPN
ma-20	253	2	math	math	PROPN
ma-20	253	3	.	.	PUNCT
ma-20	254	1	anal	anal	PROPN
ma-20	254	2	.	.	PUNCT
ma-20	255	1	10.28924	10.28924	NUM
ma-20	255	2	/	/	SYM
ma-20	255	3	ada	ada	PROPN
ma-20	255	4	/	/	SYM
ma-20	255	5	ma.2.2	ma.2.2	NOUN
ma-20	255	6	10references	10references	PUNCT
ma-20	256	1	[	[	X
ma-20	256	2	1	1	NUM
ma-20	256	3	]	]	X
ma-20	256	4	b.	b.	PROPN
ma-20	256	5	beauzamy	beauzamy	PROPN
ma-20	256	6	,	,	PUNCT
ma-20	256	7	introduction	introduction	NOUN
ma-20	256	8	to	to	PART
ma-20	256	9	banach	banach	NOUN
ma-20	256	10	spaces	space	NOUN
ma-20	256	11	and	and	CCONJ
ma-20	256	12	their	their	PRON
ma-20	256	13	geometry	geometry	NOUN
ma-20	256	14	,	,	PUNCT
ma-20	256	15	2nd	2nd	PROPN
ma-20	256	16	ed	ed	NOUN
ma-20	256	17	.	.	PROPN
ma-20	256	18	,	,	PUNCT
ma-20	256	19	north	north	PROPN
ma-20	256	20	holland	holland	PROPN
ma-20	256	21	,	,	PUNCT
ma-20	256	22	amsterdamnewyork	amsterdamnewyork	NOUN
ma-20	256	23	-	-	PUNCT
ma-20	256	24	oxford	oxford	PROPN
ma-20	256	25	,	,	PUNCT
ma-20	256	26	1985	1985	NUM
ma-20	256	27	.	.	PUNCT
ma-20	257	1	https://pascal-francis.inist.fr/vibad/index.php?action=getrecorddetail&idt=	https://pascal-francis.inist.fr/vibad/index.php?action=getrecorddetail&idt=	PROPN
ma-20	257	2	pascal82x0319279.[2	pascal82x0319279.[2	PROPN
ma-20	257	3	]	]	X
ma-20	257	4	h.	h.	PROPN
ma-20	257	5	gunawan	gunawan	PROPN
ma-20	257	6	,	,	PUNCT
ma-20	257	7	d.i	d.i	PROPN
ma-20	257	8	.	.	PROPN
ma-20	257	9	hakim	hakim	PROPN
ma-20	257	10	,	,	PUNCT
ma-20	257	11	a.s	a.s	PROPN
ma-20	257	12	.	.	PROPN
ma-20	257	13	putri	putri	PROPN
ma-20	257	14	,	,	PUNCT
ma-20	257	15	on	on	ADP
ma-20	257	16	geometric	geometric	ADJ
ma-20	257	17	properties	property	NOUN
ma-20	257	18	of	of	ADP
ma-20	257	19	morrey	morrey	PROPN
ma-20	257	20	spaces	space	NOUN
ma-20	257	21	,	,	PUNCT
ma-20	257	22	ufimsk	ufimsk	PROPN
ma-20	257	23	.	.	PUNCT
ma-20	258	1	mat	mat	PROPN
ma-20	258	2	.	.	PUNCT
ma-20	259	1	zh	zh	PROPN
ma-20	259	2	.	.	PROPN
ma-20	259	3	13	13	NUM
ma-20	259	4	(	(	PUNCT
ma-20	259	5	2021	2021	NUM
ma-20	259	6	)	)	PUNCT
ma-20	259	7	131–136	131–136	NUM
ma-20	259	8	.	.	PUNCT
ma-20	260	1	https://doi.org/10.13108/2021-13-1-131.[3	https://doi.org/10.13108/2021-13-1-131.[3	PROPN
ma-20	260	2	]	]	X
ma-20	260	3	h.	h.	PROPN
ma-20	260	4	gunawan	gunawan	PROPN
ma-20	260	5	,	,	PUNCT
ma-20	260	6	e.	e.	PROPN
ma-20	260	7	kikianty	kikianty	PROPN
ma-20	260	8	,	,	PUNCT
ma-20	260	9	c.	c.	PROPN
ma-20	260	10	schwanke	schwanke	PROPN
ma-20	260	11	,	,	PUNCT
ma-20	260	12	discrete	discrete	ADJ
ma-20	260	13	morrey	morrey	NOUN
ma-20	260	14	spaces	space	NOUN
ma-20	260	15	and	and	CCONJ
ma-20	260	16	their	their	PRON
ma-20	260	17	inclusion	inclusion	NOUN
ma-20	260	18	properties	property	NOUN
ma-20	260	19	,	,	PUNCT
ma-20	260	20	math	math	NOUN
ma-20	260	21	.	.	PUNCT
ma-20	261	1	nachr	nachr	PROPN
ma-20	261	2	.	.	PUNCT
ma-20	262	1	291(2018	291(2018	NUM
ma-20	262	2	)	)	PUNCT
ma-20	262	3	1283–1296	1283–1296	NUM
ma-20	262	4	.	.	PUNCT
ma-20	263	1	https://doi.org/10.1002/mana.201700054.[4	https://doi.org/10.1002/mana.201700054.[4	PROPN
ma-20	263	2	]	]	X
ma-20	263	3	h.	h.	PROPN
ma-20	263	4	gunawan	gunawan	PROPN
ma-20	263	5	,	,	PUNCT
ma-20	263	6	e.	e.	PROPN
ma-20	263	7	kikianty	kikianty	PROPN
ma-20	263	8	,	,	PUNCT
ma-20	263	9	y.	y.	PROPN
ma-20	263	10	sawano	sawano	PROPN
ma-20	263	11	,	,	PUNCT
ma-20	263	12	and	and	CCONJ
ma-20	263	13	c.	c.	PROPN
ma-20	263	14	schwanke	schwanke	PROPN
ma-20	263	15	,	,	PUNCT
ma-20	263	16	three	three	NUM
ma-20	263	17	geometric	geometric	ADJ
ma-20	263	18	constants	constant	NOUN
ma-20	263	19	for	for	ADP
ma-20	263	20	morrey	morrey	PROPN
ma-20	263	21	spaces	space	NOUN
ma-20	263	22	,	,	PUNCT
ma-20	263	23	bull	bull	NOUN
ma-20	263	24	.	.	PUNCT
ma-20	264	1	korean.math	korean.math	NOUN
ma-20	264	2	.	.	PUNCT
ma-20	264	3	soc	soc	PROPN
ma-20	264	4	.	.	PUNCT
ma-20	265	1	56	56	NUM
ma-20	265	2	(	(	PUNCT
ma-20	265	3	2019	2019	NUM
ma-20	265	4	)	)	PUNCT
ma-20	265	5	1569	1569	NUM
ma-20	265	6	-	-	SYM
ma-20	265	7	1575	1575	NUM
ma-20	265	8	.	.	PUNCT
ma-20	266	1	https://doi.org/10.4134/bkms.b190010.[5	https://doi.org/10.4134/bkms.b190010.[5	PROPN
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ma-20	266	3	r.c	r.c	PROPN
ma-20	266	4	.	.	PROPN
ma-20	266	5	james	james	PROPN
ma-20	266	6	,	,	PUNCT
ma-20	266	7	uniformly	uniformly	ADV
ma-20	266	8	non	non	ADJ
ma-20	266	9	-	-	ADJ
ma-20	266	10	square	square	ADJ
ma-20	266	11	banach	banach	NOUN
ma-20	266	12	spaces	space	NOUN
ma-20	266	13	,	,	PUNCT
ma-20	266	14	ann	ann	PROPN
ma-20	266	15	.	.	PROPN
ma-20	266	16	math	math	PROPN
ma-20	266	17	.	.	PUNCT
ma-20	267	1	80	80	NUM
ma-20	267	2	(	(	PUNCT
ma-20	267	3	1964	1964	NUM
ma-20	267	4	)	)	PUNCT
ma-20	267	5	542	542	NUM
ma-20	267	6	-	-	SYM
ma-20	267	7	550	550	NUM
ma-20	267	8	.	.	PUNCT
ma-20	268	1	https://doi.org/10.2307/	https://doi.org/10.2307/	PROPN
ma-20	268	2	1970663.[6	1970663.[6	NUM
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ma-20	268	4	m.	m.	NOUN
ma-20	268	5	kato	kato	PROPN
ma-20	268	6	,	,	PUNCT
ma-20	268	7	y.	y.	PROPN
ma-20	268	8	takahashi	takahashi	PROPN
ma-20	268	9	,	,	PUNCT
ma-20	268	10	and	and	CCONJ
ma-20	268	11	k.	k.	PROPN
ma-20	268	12	hashimoto	hashimoto	NOUN
ma-20	268	13	,	,	PUNCT
ma-20	268	14	on	on	ADP
ma-20	268	15	n	n	CCONJ
ma-20	268	16	-	-	PUNCT
ma-20	268	17	th	th	X
ma-20	268	18	von	von	PROPN
ma-20	268	19	neumann	neumann	PROPN
ma-20	268	20	-	-	PUNCT
ma-20	268	21	jordan	jordan	PROPN
ma-20	268	22	constants	constant	NOUN
ma-20	268	23	for	for	ADP
ma-20	268	24	banach	banach	NOUN
ma-20	268	25	spaces	space	NOUN
ma-20	268	26	,	,	PUNCT
ma-20	268	27	bull	bull	NOUN
ma-20	268	28	.	.	PUNCT
ma-20	269	1	kyushuinst	kyushuinst	PROPN
ma-20	269	2	.	.	PUNCT
ma-20	270	1	tech	tech	NOUN
ma-20	270	2	.	.	PUNCT
ma-20	271	1	45	45	NUM
ma-20	271	2	(	(	PUNCT
ma-20	271	3	1998	1998	NUM
ma-20	271	4	)	)	PUNCT
ma-20	271	5	,	,	PUNCT
ma-20	271	6	25	25	NUM
ma-20	271	7	-	-	SYM
ma-20	271	8	33	33	NUM
ma-20	271	9	.	.	PUNCT
ma-20	272	1	https://ci.nii.ac.jp/naid/110000079659.[7	https://ci.nii.ac.jp/naid/110000079659.[7	PROPN
ma-20	272	2	]	]	X
ma-20	272	3	l.	l.	PROPN
ma-20	272	4	maligranda	maligranda	PROPN
ma-20	272	5	,	,	PUNCT
ma-20	272	6	l.	l.	PROPN
ma-20	272	7	nikolova	nikolova	PROPN
ma-20	272	8	,	,	PUNCT
ma-20	272	9	l.-e	l.-e	NOUN
ma-20	272	10	.	.	PUNCT
ma-20	273	1	persson	persson	PROPN
ma-20	273	2	,	,	PUNCT
ma-20	273	3	t.	t.	PROPN
ma-20	273	4	zachariades	zachariades	PROPN
ma-20	273	5	,	,	PUNCT
ma-20	273	6	on	on	ADP
ma-20	273	7	n	n	CCONJ
ma-20	273	8	-	-	PUNCT
ma-20	273	9	th	th	X
ma-20	273	10	james	james	PROPN
ma-20	273	11	and	and	CCONJ
ma-20	273	12	khintchine	khintchine	VERB
ma-20	273	13	constants	constant	NOUN
ma-20	273	14	of	of	ADP
ma-20	273	15	banachspaces	banachspace	NOUN
ma-20	273	16	,	,	PUNCT
ma-20	273	17	math	math	NOUN
ma-20	273	18	.	.	PUNCT
ma-20	274	1	inequal	inequal	PROPN
ma-20	274	2	.	.	PUNCT
ma-20	275	1	appl	appl	PROPN
ma-20	275	2	.	.	PROPN
ma-20	276	1	1	1	NUM
ma-20	276	2	(	(	PUNCT
ma-20	276	3	2007	2007	NUM
ma-20	276	4	)	)	PUNCT
ma-20	276	5	1–22	1–22	NOUN
ma-20	276	6	.	.	PUNCT
ma-20	277	1	https://doi.org/10.7153/mia-11-01.[8	https://doi.org/10.7153/mia-11-01.[8	PROPN
ma-20	277	2	]	]	X
ma-20	277	3	w.a	w.a	PROPN
ma-20	277	4	.	.	PROPN
ma-20	277	5	wojczynski	wojczynski	PROPN
ma-20	277	6	,	,	PUNCT
ma-20	277	7	geometry	geometry	NOUN
ma-20	277	8	and	and	CCONJ
ma-20	277	9	martingales	martingale	NOUN
ma-20	277	10	in	in	ADP
ma-20	277	11	banach	banach	NOUN
ma-20	277	12	spaces	space	NOUN
ma-20	277	13	,	,	PUNCT
ma-20	277	14	part	part	PROPN
ma-20	277	15	ii	ii	NOUN
ma-20	277	16	,	,	PUNCT
ma-20	277	17	in	in	ADP
ma-20	277	18	:	:	PUNCT
ma-20	277	19	probability	probability	NOUN
ma-20	277	20	in	in	ADP
ma-20	277	21	banach	banach	NOUN
ma-20	277	22	spaces	space	NOUN
ma-20	277	23	iv	iv	NUM
ma-20	277	24	,	,	PUNCT
ma-20	277	25	j.kuelbs	j.kuelb	NOUN
ma-20	277	26	,	,	PUNCT
ma-20	277	27	ed	ed	NOUN
ma-20	277	28	.	.	PROPN
ma-20	277	29	,	,	PUNCT
ma-20	277	30	marcel	marcel	PROPN
ma-20	277	31	-	-	PUNCT
ma-20	277	32	dekker	dekker	PROPN
ma-20	277	33	,	,	PUNCT
ma-20	277	34	1978	1978	NUM
ma-20	277	35	,	,	PUNCT
ma-20	277	36	267–517	267–517	NUM
ma-20	277	37	.	.	PUNCT
ma-20	277	38	https://doi.org/10.1201/9780429462153	https://doi.org/10.1201/9780429462153	PROPN
ma-20	277	39	.	.	PUNCT
ma-20	278	1	https://doi.org/10.28924/ada/ma.2.2	https://doi.org/10.28924/ada/ma.2.2	PRON
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ma-20	278	4	https://doi.org/10.13108/2021-13-1-131	https://doi.org/10.13108/2021-13-1-131	X
ma-20	278	5	https://doi.org/10.1002/mana.201700054	https://doi.org/10.1002/mana.201700054	NOUN
ma-20	278	6	https://doi.org/10.4134/bkms.b190010	https://doi.org/10.4134/bkms.b190010	PROPN
ma-20	278	7	https://doi.org/10.2307/1970663	https://doi.org/10.2307/1970663	X
ma-20	278	8	https://doi.org/10.2307/1970663	https://doi.org/10.2307/1970663	X
ma-20	278	9	https://ci.nii.ac.jp/naid/110000079659	https://ci.nii.ac.jp/naid/110000079659	X
ma-20	278	10	https://doi.org/10.7153/mia-11-01	https://doi.org/10.7153/mia-11-01	X
ma-20	278	11	https://doi.org/10.1201/9780429462153	https://doi.org/10.1201/9780429462153	VERB
ma-20	278	12	1	1	NUM
ma-20	278	13	.	.	PUNCT
ma-20	278	14	introduction	introduction	NOUN
ma-20	278	15	2	2	NUM
ma-20	278	16	.	.	PUNCT
ma-20	278	17	main	main	ADJ
ma-20	278	18	results	result	NOUN
ma-20	278	19	references	reference	NOUN