id	sid	tid	token	lemma	pos
ejpam-2552	1	1	proximity	proximity	NOUN
ejpam-2552	1	2	between	between	ADP
ejpam-2552	1	3	selfadjoint	selfadjoint	NOUN
ejpam-2552	1	4	operators	operator	NOUN
ejpam-2552	1	5	and	and	CCONJ
ejpam-2552	1	6	between	between	ADP
ejpam-2552	1	7	their	their	PRON
ejpam-2552	1	8	associated	associated	ADJ
ejpam-2552	1	9	spectral	spectral	ADJ
ejpam-2552	1	10	measures	measure	NOUN
ejpam-2552	1	11	european	european	ADJ
ejpam-2552	1	12	journal	journal	PROPN
ejpam-2552	1	13	of	of	ADP
ejpam-2552	1	14	pure	pure	ADJ
ejpam-2552	1	15	and	and	CCONJ
ejpam-2552	1	16	applied	apply	VERB
ejpam-2552	1	17	mathematics	mathematic	NOUN
ejpam-2552	1	18	vol	vol	NOUN
ejpam-2552	1	19	.	.	PUNCT
ejpam-2552	2	1	11	11	NUM
ejpam-2552	2	2	,	,	PUNCT
ejpam-2552	2	3	no	no	INTJ
ejpam-2552	2	4	.	.	NOUN
ejpam-2552	2	5	4	4	NUM
ejpam-2552	2	6	,	,	PUNCT
ejpam-2552	2	7	2018	2018	NUM
ejpam-2552	2	8	,	,	PUNCT
ejpam-2552	2	9	893	893	NUM
ejpam-2552	2	10	-	-	SYM
ejpam-2552	2	11	910	910	NUM
ejpam-2552	2	12	issn	issn	PROPN
ejpam-2552	2	13	1307	1307	NUM
ejpam-2552	2	14	-	-	SYM
ejpam-2552	2	15	5543	5543	NUM
ejpam-2552	2	16	–	–	PUNCT
ejpam-2552	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2552	2	18	published	publish	VERB
ejpam-2552	2	19	by	by	ADP
ejpam-2552	2	20	new	new	PROPN
ejpam-2552	2	21	york	york	PROPN
ejpam-2552	2	22	business	business	PROPN
ejpam-2552	2	23	global	global	ADJ
ejpam-2552	2	24	proximity	proximity	NOUN
ejpam-2552	2	25	between	between	ADP
ejpam-2552	2	26	selfadjoint	selfadjoint	NOUN
ejpam-2552	2	27	operators	operator	NOUN
ejpam-2552	2	28	and	and	CCONJ
ejpam-2552	2	29	between	between	ADP
ejpam-2552	2	30	their	their	PRON
ejpam-2552	2	31	associated	associated	ADJ
ejpam-2552	2	32	spectral	spectral	ADJ
ejpam-2552	2	33	measures	measure	NOUN
ejpam-2552	2	34	alain	alain	PROPN
ejpam-2552	2	35	boudou1	boudou1	PROPN
ejpam-2552	2	36	,	,	PUNCT
ejpam-2552	2	37	sylvie	sylvie	ADJ
ejpam-2552	2	38	viguier	viguier	NOUN
ejpam-2552	2	39	-	-	PUNCT
ejpam-2552	2	40	pla2,1,∗	pla2,1,∗	NOUN
ejpam-2552	2	41	1	1	NUM
ejpam-2552	2	42	equipe	equipe	NOUN
ejpam-2552	2	43	de	de	X
ejpam-2552	2	44	stat	stat	PROPN
ejpam-2552	2	45	.	.	PUNCT
ejpam-2552	3	1	et	et	PROPN
ejpam-2552	3	2	proba	proba	PROPN
ejpam-2552	3	3	.	.	PROPN
ejpam-2552	3	4	,	,	PUNCT
ejpam-2552	3	5	institut	institut	PROPN
ejpam-2552	3	6	de	de	PROPN
ejpam-2552	3	7	mathématiques	mathématiques	PROPN
ejpam-2552	3	8	,	,	PUNCT
ejpam-2552	3	9	umr5219	umr5219	ADJ
ejpam-2552	3	10	,	,	PUNCT
ejpam-2552	3	11	université	université	ADJ
ejpam-2552	3	12	paul	paul	PROPN
ejpam-2552	3	13	sabatier	sabatier	PROPN
ejpam-2552	3	14	,	,	PUNCT
ejpam-2552	3	15	118	118	NUM
ejpam-2552	3	16	route	route	PROPN
ejpam-2552	3	17	de	de	PROPN
ejpam-2552	3	18	narbonne	narbonne	PROPN
ejpam-2552	3	19	,	,	PUNCT
ejpam-2552	3	20	f-31062	f-31062	PROPN
ejpam-2552	3	21	toulouse	toulouse	NOUN
ejpam-2552	3	22	cedex	cedex	NOUN
ejpam-2552	3	23	9	9	NUM
ejpam-2552	3	24	,	,	PUNCT
ejpam-2552	3	25	france	france	PROPN
ejpam-2552	3	26	2	2	NUM
ejpam-2552	3	27	lamps	lamp	NOUN
ejpam-2552	3	28	,	,	PUNCT
ejpam-2552	3	29	université	université	NOUN
ejpam-2552	3	30	de	de	X
ejpam-2552	3	31	perpignan	perpignan	PROPN
ejpam-2552	3	32	,	,	PUNCT
ejpam-2552	3	33	56	56	NUM
ejpam-2552	3	34	avenue	avenue	NOUN
ejpam-2552	3	35	paul	paul	PROPN
ejpam-2552	3	36	alduy	alduy	PROPN
ejpam-2552	3	37	,	,	PUNCT
ejpam-2552	3	38	f-66860	f-66860	PROPN
ejpam-2552	3	39	perpignan	perpignan	PROPN
ejpam-2552	3	40	cedex	cedex	PROPN
ejpam-2552	3	41	,	,	PUNCT
ejpam-2552	3	42	france	france	PROPN
ejpam-2552	3	43	abstract	abstract	NOUN
ejpam-2552	3	44	.	.	PUNCT
ejpam-2552	4	1	we	we	PRON
ejpam-2552	4	2	study	study	VERB
ejpam-2552	4	3	how	how	SCONJ
ejpam-2552	4	4	the	the	DET
ejpam-2552	4	5	proximity	proximity	NOUN
ejpam-2552	4	6	between	between	ADP
ejpam-2552	4	7	two	two	NUM
ejpam-2552	4	8	selfadjoint	selfadjoint	NOUN
ejpam-2552	4	9	bounded	bounded	ADJ
ejpam-2552	4	10	operators	operator	NOUN
ejpam-2552	4	11	can	can	AUX
ejpam-2552	4	12	be	be	AUX
ejpam-2552	4	13	expressed	express	VERB
ejpam-2552	4	14	as	as	ADP
ejpam-2552	4	15	a	a	DET
ejpam-2552	4	16	proximity	proximity	NOUN
ejpam-2552	4	17	between	between	ADP
ejpam-2552	4	18	the	the	DET
ejpam-2552	4	19	associated	associated	ADJ
ejpam-2552	4	20	spectral	spectral	ADJ
ejpam-2552	4	21	measures	measure	NOUN
ejpam-2552	4	22	.	.	PUNCT
ejpam-2552	5	1	between	between	ADP
ejpam-2552	5	2	two	two	NUM
ejpam-2552	5	3	operators	operator	NOUN
ejpam-2552	5	4	,	,	PUNCT
ejpam-2552	5	5	we	we	PRON
ejpam-2552	5	6	use	use	VERB
ejpam-2552	5	7	a	a	DET
ejpam-2552	5	8	classical	classical	ADJ
ejpam-2552	5	9	distance	distance	NOUN
ejpam-2552	5	10	.	.	PUNCT
ejpam-2552	6	1	for	for	ADP
ejpam-2552	6	2	projector	projector	NOUN
ejpam-2552	6	3	-	-	PUNCT
ejpam-2552	6	4	valued	value	VERB
ejpam-2552	6	5	spectral	spectral	ADJ
ejpam-2552	6	6	measures	measure	NOUN
ejpam-2552	6	7	,	,	PUNCT
ejpam-2552	6	8	we	we	PRON
ejpam-2552	6	9	introduce	introduce	VERB
ejpam-2552	6	10	the	the	DET
ejpam-2552	6	11	notion	notion	NOUN
ejpam-2552	6	12	of	of	ADP
ejpam-2552	6	13	α−equivalence	α−equivalence	NOUN
ejpam-2552	6	14	,	,	PUNCT
ejpam-2552	6	15	which	which	PRON
ejpam-2552	6	16	is	be	AUX
ejpam-2552	6	17	based	base	VERB
ejpam-2552	6	18	on	on	ADP
ejpam-2552	6	19	a	a	DET
ejpam-2552	6	20	partial	partial	ADJ
ejpam-2552	6	21	order	order	NOUN
ejpam-2552	6	22	relation	relation	NOUN
ejpam-2552	6	23	on	on	ADP
ejpam-2552	6	24	the	the	DET
ejpam-2552	6	25	set	set	NOUN
ejpam-2552	6	26	of	of	ADP
ejpam-2552	6	27	projectors	projector	NOUN
ejpam-2552	6	28	.	.	PUNCT
ejpam-2552	7	1	assuming	assume	VERB
ejpam-2552	7	2	an	an	DET
ejpam-2552	7	3	hypothesis	hypothesis	NOUN
ejpam-2552	7	4	of	of	ADP
ejpam-2552	7	5	commutativity	commutativity	NOUN
ejpam-2552	7	6	,	,	PUNCT
ejpam-2552	7	7	we	we	PRON
ejpam-2552	7	8	show	show	VERB
ejpam-2552	7	9	that	that	SCONJ
ejpam-2552	7	10	the	the	DET
ejpam-2552	7	11	proximity	proximity	NOUN
ejpam-2552	7	12	between	between	ADP
ejpam-2552	7	13	operators	operator	NOUN
ejpam-2552	7	14	is	be	AUX
ejpam-2552	7	15	equivalent	equivalent	ADJ
ejpam-2552	7	16	with	with	ADP
ejpam-2552	7	17	the	the	DET
ejpam-2552	7	18	proximity	proximity	NOUN
ejpam-2552	7	19	between	between	ADP
ejpam-2552	7	20	the	the	DET
ejpam-2552	7	21	associated	associated	ADJ
ejpam-2552	7	22	spectral	spectral	ADJ
ejpam-2552	7	23	measures	measure	NOUN
ejpam-2552	7	24	.	.	PUNCT
ejpam-2552	8	1	we	we	PRON
ejpam-2552	8	2	develop	develop	VERB
ejpam-2552	8	3	the	the	DET
ejpam-2552	8	4	particular	particular	ADJ
ejpam-2552	8	5	case	case	NOUN
ejpam-2552	8	6	where	where	SCONJ
ejpam-2552	8	7	the	the	DET
ejpam-2552	8	8	operators	operator	NOUN
ejpam-2552	8	9	are	be	AUX
ejpam-2552	8	10	compact	compact	ADJ
ejpam-2552	8	11	,	,	PUNCT
ejpam-2552	8	12	and	and	CCONJ
ejpam-2552	8	13	give	give	VERB
ejpam-2552	8	14	some	some	DET
ejpam-2552	8	15	illustrations	illustration	NOUN
ejpam-2552	8	16	.	.	PUNCT
ejpam-2552	9	1	2010	2010	NUM
ejpam-2552	9	2	mathematics	mathematic	NOUN
ejpam-2552	9	3	subject	subject	NOUN
ejpam-2552	9	4	classifications	classification	NOUN
ejpam-2552	9	5	:	:	PUNCT
ejpam-2552	9	6	60g57	60g57	NUM
ejpam-2552	9	7	,	,	PUNCT
ejpam-2552	9	8	60g10	60g10	NOUN
ejpam-2552	9	9	,	,	PUNCT
ejpam-2552	9	10	60b15	60b15	NUM
ejpam-2552	9	11	,	,	PUNCT
ejpam-2552	9	12	60h05	60h05	NUM
ejpam-2552	9	13	key	key	ADJ
ejpam-2552	9	14	words	word	NOUN
ejpam-2552	9	15	and	and	CCONJ
ejpam-2552	9	16	phrases	phrase	NOUN
ejpam-2552	9	17	:	:	PUNCT
ejpam-2552	9	18	random	random	ADJ
ejpam-2552	9	19	measures	measure	NOUN
ejpam-2552	9	20	,	,	PUNCT
ejpam-2552	9	21	stationary	stationary	ADJ
ejpam-2552	9	22	processes	process	NOUN
ejpam-2552	9	23	,	,	PUNCT
ejpam-2552	9	24	convolution	convolution	NOUN
ejpam-2552	9	25	,	,	PUNCT
ejpam-2552	9	26	spectral	spectral	ADJ
ejpam-2552	9	27	measures	measure	NOUN
ejpam-2552	9	28	1	1	NUM
ejpam-2552	9	29	.	.	X
ejpam-2552	9	30	introduction	introduction	NOUN
ejpam-2552	9	31	the	the	DET
ejpam-2552	9	32	question	question	NOUN
ejpam-2552	9	33	of	of	ADP
ejpam-2552	9	34	the	the	DET
ejpam-2552	9	35	association	association	NOUN
ejpam-2552	9	36	of	of	ADP
ejpam-2552	9	37	a	a	DET
ejpam-2552	9	38	spectral	spectral	ADJ
ejpam-2552	9	39	measure	measure	NOUN
ejpam-2552	9	40	(	(	PUNCT
ejpam-2552	9	41	s.m	s.m	PROPN
ejpam-2552	9	42	.	.	PROPN
ejpam-2552	9	43	)	)	PUNCT
ejpam-2552	10	1	with	with	ADP
ejpam-2552	10	2	an	an	DET
ejpam-2552	10	3	operator	operator	NOUN
ejpam-2552	10	4	is	be	AUX
ejpam-2552	10	5	a	a	DET
ejpam-2552	10	6	usefull	usefull	ADJ
ejpam-2552	10	7	technique	technique	NOUN
ejpam-2552	10	8	,	,	PUNCT
ejpam-2552	10	9	and	and	CCONJ
ejpam-2552	10	10	often	often	ADV
ejpam-2552	10	11	considered	consider	VERB
ejpam-2552	10	12	for	for	ADP
ejpam-2552	10	13	the	the	DET
ejpam-2552	10	14	analysis	analysis	NOUN
ejpam-2552	10	15	of	of	ADP
ejpam-2552	10	16	their	their	PRON
ejpam-2552	10	17	properties	property	NOUN
ejpam-2552	10	18	(	(	PUNCT
ejpam-2552	10	19	[	[	X
ejpam-2552	10	20	4	4	NUM
ejpam-2552	10	21	]	]	PUNCT
ejpam-2552	10	22	,	,	PUNCT
ejpam-2552	10	23	[	[	X
ejpam-2552	10	24	3	3	NUM
ejpam-2552	10	25	]	]	NUM
ejpam-2552	10	26	)	)	PUNCT
ejpam-2552	10	27	.	.	PUNCT
ejpam-2552	11	1	therefore	therefore	ADV
ejpam-2552	11	2	,	,	PUNCT
ejpam-2552	11	3	if	if	SCONJ
ejpam-2552	11	4	p	p	NOUN
ejpam-2552	11	5	is	be	AUX
ejpam-2552	11	6	an	an	DET
ejpam-2552	11	7	orthogonal	orthogonal	ADJ
ejpam-2552	11	8	projector	projector	NOUN
ejpam-2552	11	9	,	,	PUNCT
ejpam-2552	11	10	and	and	CCONJ
ejpam-2552	11	11	λ	λ	X
ejpam-2552	11	12	a	a	DET
ejpam-2552	11	13	real	real	NOUN
ejpam-2552	11	14	,	,	PUNCT
ejpam-2552	11	15	then	then	ADV
ejpam-2552	11	16	a	a	PRON
ejpam-2552	11	17	=	=	X
ejpam-2552	11	18	λp	λp	X
ejpam-2552	11	19	is	be	AUX
ejpam-2552	11	20	a	a	DET
ejpam-2552	11	21	selfadjoint	selfadjoint	NOUN
ejpam-2552	11	22	bounded	bound	VERB
ejpam-2552	11	23	operator	operator	NOUN
ejpam-2552	11	24	,	,	PUNCT
ejpam-2552	11	25	which	which	PRON
ejpam-2552	11	26	associated	associate	VERB
ejpam-2552	11	27	s.m	s.m	PROPN
ejpam-2552	11	28	.	.	PROPN
ejpam-2552	11	29	is	be	AUX
ejpam-2552	11	30	e	e	NOUN
ejpam-2552	11	31	=	=	X
ejpam-2552	11	32	δ0p⊥	δ0p⊥	NOUN
ejpam-2552	11	33	+	+	SYM
ejpam-2552	11	34	δλp	δλp	NOUN
ejpam-2552	11	35	.	.	PUNCT
ejpam-2552	12	1	besides	besides	SCONJ
ejpam-2552	12	2	,	,	PUNCT
ejpam-2552	12	3	the	the	DET
ejpam-2552	12	4	null	null	ADJ
ejpam-2552	12	5	operator	operator	NOUN
ejpam-2552	12	6	o	o	NOUN
ejpam-2552	12	7	is	be	AUX
ejpam-2552	12	8	associated	associate	VERB
ejpam-2552	12	9	with	with	ADP
ejpam-2552	12	10	the	the	DET
ejpam-2552	12	11	s.m	s.m	PROPN
ejpam-2552	12	12	.	.	PUNCT
ejpam-2552	13	1	er	er	INTJ
ejpam-2552	13	2	=	=	PUNCT
ejpam-2552	13	3	δ0i	δ0i	PROPN
ejpam-2552	13	4	.	.	PUNCT
ejpam-2552	14	1	as	as	ADP
ejpam-2552	14	2	‖a−o‖	‖a−o‖	PROPN
ejpam-2552	14	3	=	=	SYM
ejpam-2552	14	4	|λ|	|λ|	PROPN
ejpam-2552	14	5	,	,	PUNCT
ejpam-2552	14	6	a	a	PRON
ejpam-2552	14	7	and	and	CCONJ
ejpam-2552	14	8	o	o	NOUN
ejpam-2552	14	9	are	be	AUX
ejpam-2552	14	10	two	two	NUM
ejpam-2552	14	11	selfadjoint	selfadjoint	NOUN
ejpam-2552	14	12	operators	operator	NOUN
ejpam-2552	14	13	as	as	ADV
ejpam-2552	14	14	close	close	ADV
ejpam-2552	14	15	as	as	SCONJ
ejpam-2552	14	16	we	we	PRON
ejpam-2552	14	17	want	want	VERB
ejpam-2552	14	18	,	,	PUNCT
ejpam-2552	14	19	as	as	ADV
ejpam-2552	14	20	far	far	ADV
ejpam-2552	14	21	as	as	SCONJ
ejpam-2552	14	22	we	we	PRON
ejpam-2552	14	23	can	can	AUX
ejpam-2552	14	24	get	get	VERB
ejpam-2552	14	25	|λ|	|λ|	NOUN
ejpam-2552	14	26	as	as	ADV
ejpam-2552	14	27	small	small	ADJ
ejpam-2552	14	28	as	as	SCONJ
ejpam-2552	14	29	we	we	PRON
ejpam-2552	14	30	want	want	VERB
ejpam-2552	14	31	.	.	PUNCT
ejpam-2552	15	1	nevertheless	nevertheless	ADV
ejpam-2552	15	2	,	,	PUNCT
ejpam-2552	15	3	let	let	VERB
ejpam-2552	15	4	us	we	PRON
ejpam-2552	15	5	consider	consider	VERB
ejpam-2552	15	6	the	the	DET
ejpam-2552	15	7	proximity	proximity	NOUN
ejpam-2552	15	8	between	between	ADP
ejpam-2552	15	9	their	their	PRON
ejpam-2552	15	10	associated	associated	ADJ
ejpam-2552	15	11	s.m	s.m	PROPN
ejpam-2552	15	12	.	.	PROPN
ejpam-2552	15	13	’s	’s	PART
ejpam-2552	15	14	.	.	PUNCT
ejpam-2552	16	1	for	for	ADP
ejpam-2552	16	2	any	any	DET
ejpam-2552	16	3	b	b	NOUN
ejpam-2552	16	4	of	of	ADP
ejpam-2552	16	5	a	a	DET
ejpam-2552	16	6	σ−field	σ−field	NOUN
ejpam-2552	16	7	defined	define	VERB
ejpam-2552	16	8	on	on	ADP
ejpam-2552	16	9	r	r	NOUN
ejpam-2552	16	10	,	,	PUNCT
ejpam-2552	16	11	we	we	PRON
ejpam-2552	16	12	have	have	VERB
ejpam-2552	16	13	e(b)−	e(b)−	NOUN
ejpam-2552	16	14	er(b	er(b	NOUN
ejpam-2552	16	15	)	)	PUNCT
ejpam-2552	16	16	=	=	SYM
ejpam-2552	16	17	δ0(b)p⊥	δ0(b)p⊥	PRON
ejpam-2552	17	1	+	+	CCONJ
ejpam-2552	17	2	δλ(b)p	δλ(b)p	NUM
ejpam-2552	17	3	−	−	NOUN
ejpam-2552	17	4	δ0(b)p⊥	δ0(b)p⊥	NOUN
ejpam-2552	17	5	−	−	NOUN
ejpam-2552	17	6	δ0(b)p	δ0(b)p	ADJ
ejpam-2552	17	7	=	=	SYM
ejpam-2552	17	8	δλ(b)p	δλ(b)p	NUM
ejpam-2552	17	9	−	−	NOUN
ejpam-2552	17	10	δ0(b)p	δ0(b)p	ADJ
ejpam-2552	17	11	.	.	PUNCT
ejpam-2552	18	1	so	so	ADV
ejpam-2552	18	2	‖e(b)−	‖e(b)−	PROPN
ejpam-2552	18	3	er(b)‖	er(b)‖	PROPN
ejpam-2552	18	4	=	=	PROPN
ejpam-2552	18	5	|δλ(b)−	|δλ(b)−	PROPN
ejpam-2552	18	6	δ0(b)|	δ0(b)|	PROPN
ejpam-2552	18	7	,	,	PUNCT
ejpam-2552	18	8	which	which	DET
ejpam-2552	18	9	maximum	maximum	NOUN
ejpam-2552	18	10	is	be	AUX
ejpam-2552	18	11	obviously	obviously	ADV
ejpam-2552	18	12	equal	equal	ADJ
ejpam-2552	18	13	to	to	ADP
ejpam-2552	18	14	1	1	NUM
ejpam-2552	18	15	.	.	PUNCT
ejpam-2552	19	1	this	this	PRON
ejpam-2552	19	2	shows	show	VERB
ejpam-2552	19	3	that	that	SCONJ
ejpam-2552	19	4	the	the	DET
ejpam-2552	19	5	proximity	proximity	NOUN
ejpam-2552	19	6	between	between	ADP
ejpam-2552	19	7	two	two	NUM
ejpam-2552	19	8	s.m	s.m	PROPN
ejpam-2552	19	9	.	.	PROPN
ejpam-2552	19	10	’s	’s	PART
ejpam-2552	19	11	,	,	PUNCT
ejpam-2552	19	12	evaluated	evaluate	VERB
ejpam-2552	19	13	by	by	ADP
ejpam-2552	19	14	sup{‖e(b)−er(b)‖;b	sup{‖e(b)−er(b)‖;b	PROPN
ejpam-2552	19	15	∈	∈	PROPN
ejpam-2552	19	16	br	br	PROPN
ejpam-2552	19	17	}	}	PUNCT
ejpam-2552	19	18	,	,	PUNCT
ejpam-2552	19	19	is	be	AUX
ejpam-2552	19	20	not	not	PART
ejpam-2552	19	21	appropriate	appropriate	ADJ
ejpam-2552	19	22	to	to	PART
ejpam-2552	19	23	be	be	AUX
ejpam-2552	19	24	linked	link	VERB
ejpam-2552	19	25	with	with	ADP
ejpam-2552	19	26	the	the	DET
ejpam-2552	19	27	proximity	proximity	NOUN
ejpam-2552	19	28	between	between	ADP
ejpam-2552	19	29	their	their	PRON
ejpam-2552	19	30	associated	associated	ADJ
ejpam-2552	19	31	operators	operator	NOUN
ejpam-2552	19	32	.	.	PUNCT
ejpam-2552	20	1	∗corresponding	∗corresponde	VERB
ejpam-2552	20	2	author	author	NOUN
ejpam-2552	20	3	.	.	PUNCT
ejpam-2552	21	1	doi	doi	NOUN
ejpam-2552	21	2	:	:	PUNCT
ejpam-2552	21	3	https://doi.org/10.29020/nybg.ejpam.v11i4.2552	https://doi.org/10.29020/nybg.ejpam.v11i4.2552	NUM
ejpam-2552	21	4	email	email	NOUN
ejpam-2552	21	5	addresses	address	NOUN
ejpam-2552	21	6	:	:	PUNCT
ejpam-2552	21	7	boudou@math.univ-toulouse.fr	boudou@math.univ-toulouse.fr	PROPN
ejpam-2552	21	8	(	(	PUNCT
ejpam-2552	21	9	a.	a.	NOUN
ejpam-2552	21	10	boudou	boudou	NOUN
ejpam-2552	21	11	)	)	PUNCT
ejpam-2552	21	12	,	,	PUNCT
ejpam-2552	21	13	viguier@univ-perp.fr	viguier@univ-perp.fr	X
ejpam-2552	21	14	(	(	PUNCT
ejpam-2552	21	15	s.	s.	PROPN
ejpam-2552	21	16	viguier	viguier	PROPN
ejpam-2552	21	17	-	-	PUNCT
ejpam-2552	21	18	pla	pla	NOUN
ejpam-2552	21	19	)	)	PUNCT
ejpam-2552	21	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2552	22	1	893	893	NUM
ejpam-2552	22	2	c	c	NOUN
ejpam-2552	22	3	©	©	PROPN
ejpam-2552	22	4	2018	2018	NUM
ejpam-2552	22	5	ejpam	ejpam	VERB
ejpam-2552	22	6	all	all	DET
ejpam-2552	22	7	rights	right	NOUN
ejpam-2552	22	8	reserved	reserve	VERB
ejpam-2552	22	9	.	.	PUNCT
ejpam-2552	23	1	a.	a.	NOUN
ejpam-2552	23	2	boudou	boudou	PROPN
ejpam-2552	23	3	,	,	PUNCT
ejpam-2552	23	4	s.	s.	PROPN
ejpam-2552	23	5	viguier	viguier	PROPN
ejpam-2552	23	6	-	-	PUNCT
ejpam-2552	23	7	pla	pla	PROPN
ejpam-2552	23	8	/	/	PUNCT
ejpam-2552	23	9	eur	eur	PROPN
ejpam-2552	23	10	.	.	PUNCT
ejpam-2552	24	1	j.	j.	PROPN
ejpam-2552	24	2	pure	pure	PROPN
ejpam-2552	24	3	appl	appl	PROPN
ejpam-2552	24	4	.	.	PROPN
ejpam-2552	24	5	math	math	PROPN
ejpam-2552	24	6	,	,	PUNCT
ejpam-2552	24	7	11	11	NUM
ejpam-2552	24	8	(	(	PUNCT
ejpam-2552	24	9	4	4	NUM
ejpam-2552	24	10	)	)	PUNCT
ejpam-2552	24	11	(	(	PUNCT
ejpam-2552	24	12	2018	2018	NUM
ejpam-2552	24	13	)	)	PUNCT
ejpam-2552	24	14	,	,	PUNCT
ejpam-2552	24	15	893	893	NUM
ejpam-2552	24	16	-	-	SYM
ejpam-2552	24	17	910	910	NUM
ejpam-2552	24	18	894	894	NUM
ejpam-2552	24	19	in	in	ADP
ejpam-2552	24	20	[	[	X
ejpam-2552	24	21	2	2	NUM
ejpam-2552	24	22	]	]	PUNCT
ejpam-2552	25	1	,	,	PUNCT
ejpam-2552	25	2	we	we	PRON
ejpam-2552	25	3	have	have	AUX
ejpam-2552	25	4	seen	see	VERB
ejpam-2552	25	5	how	how	SCONJ
ejpam-2552	25	6	the	the	DET
ejpam-2552	25	7	proximity	proximity	NOUN
ejpam-2552	25	8	between	between	ADP
ejpam-2552	25	9	unitary	unitary	ADJ
ejpam-2552	25	10	operators	operator	NOUN
ejpam-2552	25	11	could	could	AUX
ejpam-2552	25	12	be	be	AUX
ejpam-2552	25	13	equivalent	equivalent	ADJ
ejpam-2552	25	14	with	with	ADP
ejpam-2552	25	15	proximity	proximity	NOUN
ejpam-2552	25	16	between	between	ADP
ejpam-2552	25	17	their	their	PRON
ejpam-2552	25	18	associated	associated	ADJ
ejpam-2552	25	19	s.m	s.m	PROPN
ejpam-2552	25	20	.	.	PROPN
ejpam-2552	25	21	’s	’s	PART
ejpam-2552	25	22	.	.	PUNCT
ejpam-2552	26	1	in	in	ADP
ejpam-2552	26	2	this	this	DET
ejpam-2552	26	3	paper	paper	NOUN
ejpam-2552	26	4	,	,	PUNCT
ejpam-2552	26	5	we	we	PRON
ejpam-2552	26	6	develop	develop	VERB
ejpam-2552	26	7	tools	tool	NOUN
ejpam-2552	26	8	for	for	ADP
ejpam-2552	26	9	the	the	DET
ejpam-2552	26	10	study	study	NOUN
ejpam-2552	26	11	of	of	ADP
ejpam-2552	26	12	the	the	DET
ejpam-2552	26	13	association	association	NOUN
ejpam-2552	26	14	between	between	ADP
ejpam-2552	26	15	selfadjoint	selfadjoint	PROPN
ejpam-2552	26	16	bounded	bound	VERB
ejpam-2552	26	17	operators	operator	NOUN
ejpam-2552	26	18	and	and	CCONJ
ejpam-2552	26	19	s.m	s.m	PROPN
ejpam-2552	26	20	.	.	PROPN
ejpam-2552	26	21	’s	’s	PART
ejpam-2552	26	22	.	.	PUNCT
ejpam-2552	27	1	our	our	PRON
ejpam-2552	27	2	study	study	NOUN
ejpam-2552	27	3	of	of	ADP
ejpam-2552	27	4	proximity	proximity	NOUN
ejpam-2552	27	5	is	be	AUX
ejpam-2552	27	6	placed	place	VERB
ejpam-2552	27	7	in	in	ADP
ejpam-2552	27	8	this	this	DET
ejpam-2552	27	9	context	context	NOUN
ejpam-2552	27	10	.	.	PUNCT
ejpam-2552	28	1	in	in	ADP
ejpam-2552	28	2	order	order	NOUN
ejpam-2552	28	3	to	to	PART
ejpam-2552	28	4	fix	fix	VERB
ejpam-2552	28	5	notation	notation	NOUN
ejpam-2552	28	6	,	,	PUNCT
ejpam-2552	28	7	section	section	NOUN
ejpam-2552	28	8	2	2	NUM
ejpam-2552	28	9	is	be	AUX
ejpam-2552	28	10	devoted	devote	VERB
ejpam-2552	28	11	to	to	ADP
ejpam-2552	28	12	the	the	DET
ejpam-2552	28	13	recall	recall	NOUN
ejpam-2552	28	14	of	of	ADP
ejpam-2552	28	15	some	some	DET
ejpam-2552	28	16	notions	notion	NOUN
ejpam-2552	28	17	,	,	PUNCT
ejpam-2552	28	18	as	as	ADP
ejpam-2552	28	19	random	random	ADJ
ejpam-2552	28	20	measure	measure	NOUN
ejpam-2552	28	21	,	,	PUNCT
ejpam-2552	28	22	spectral	spectral	ADJ
ejpam-2552	28	23	measure	measure	NOUN
ejpam-2552	28	24	,	,	PUNCT
ejpam-2552	28	25	space	space	NOUN
ejpam-2552	28	26	of	of	ADP
ejpam-2552	28	27	the	the	DET
ejpam-2552	28	28	measurable	measurable	ADJ
ejpam-2552	28	29	applications	application	NOUN
ejpam-2552	28	30	of	of	ADP
ejpam-2552	28	31	integrable	integrable	ADJ
ejpam-2552	28	32	square	square	NOUN
ejpam-2552	28	33	with	with	ADP
ejpam-2552	28	34	respect	respect	NOUN
ejpam-2552	28	35	to	to	ADP
ejpam-2552	28	36	a	a	DET
ejpam-2552	28	37	random	random	ADJ
ejpam-2552	28	38	measure	measure	NOUN
ejpam-2552	28	39	,	,	PUNCT
ejpam-2552	28	40	and	and	CCONJ
ejpam-2552	28	41	projector	projector	NOUN
ejpam-2552	28	42	-	-	PUNCT
ejpam-2552	28	43	valued	value	VERB
ejpam-2552	28	44	spectral	spectral	ADJ
ejpam-2552	28	45	measure	measure	NOUN
ejpam-2552	28	46	.	.	PUNCT
ejpam-2552	29	1	we	we	PRON
ejpam-2552	29	2	introduce	introduce	VERB
ejpam-2552	29	3	in	in	ADP
ejpam-2552	29	4	a	a	DET
ejpam-2552	29	5	third	third	ADJ
ejpam-2552	29	6	section	section	NOUN
ejpam-2552	29	7	the	the	DET
ejpam-2552	29	8	notion	notion	NOUN
ejpam-2552	29	9	of	of	ADP
ejpam-2552	29	10	α−equivalence	α−equivalence	NOUN
ejpam-2552	29	11	,	,	PUNCT
ejpam-2552	29	12	for	for	ADP
ejpam-2552	29	13	α	α	DET
ejpam-2552	29	14	positive	positive	ADJ
ejpam-2552	29	15	real	real	NOUN
ejpam-2552	29	16	,	,	PUNCT
ejpam-2552	29	17	between	between	ADP
ejpam-2552	29	18	two	two	NUM
ejpam-2552	29	19	s.m	s.m	PROPN
ejpam-2552	29	20	.	.	PROPN
ejpam-2552	29	21	’s	’s	PART
ejpam-2552	29	22	.	.	PUNCT
ejpam-2552	30	1	this	this	DET
ejpam-2552	30	2	concept	concept	NOUN
ejpam-2552	30	3	of	of	ADP
ejpam-2552	30	4	proximity	proximity	NOUN
ejpam-2552	30	5	can	can	AUX
ejpam-2552	30	6	be	be	AUX
ejpam-2552	30	7	translated	translate	VERB
ejpam-2552	30	8	by	by	ADP
ejpam-2552	30	9	proximity	proximity	NOUN
ejpam-2552	30	10	between	between	ADP
ejpam-2552	30	11	two	two	NUM
ejpam-2552	30	12	selfadjoint	selfadjoint	NOUN
ejpam-2552	30	13	bounded	bounded	ADJ
ejpam-2552	30	14	operators	operator	NOUN
ejpam-2552	30	15	,	,	PUNCT
ejpam-2552	30	16	what	what	PRON
ejpam-2552	30	17	we	we	PRON
ejpam-2552	30	18	will	will	AUX
ejpam-2552	30	19	develop	develop	VERB
ejpam-2552	30	20	in	in	ADP
ejpam-2552	30	21	section	section	NOUN
ejpam-2552	30	22	4	4	NUM
ejpam-2552	30	23	.	.	PUNCT
ejpam-2552	31	1	the	the	DET
ejpam-2552	31	2	fift	fift	NOUN
ejpam-2552	31	3	section	section	NOUN
ejpam-2552	31	4	will	will	AUX
ejpam-2552	31	5	be	be	AUX
ejpam-2552	31	6	dedicated	dedicate	VERB
ejpam-2552	31	7	to	to	ADP
ejpam-2552	31	8	the	the	DET
ejpam-2552	31	9	case	case	NOUN
ejpam-2552	31	10	of	of	ADP
ejpam-2552	31	11	the	the	DET
ejpam-2552	31	12	compact	compact	ADJ
ejpam-2552	31	13	operators	operator	NOUN
ejpam-2552	31	14	,	,	PUNCT
ejpam-2552	31	15	which	which	PRON
ejpam-2552	31	16	is	be	AUX
ejpam-2552	31	17	frequently	frequently	ADV
ejpam-2552	31	18	encountered	encounter	VERB
ejpam-2552	31	19	in	in	ADP
ejpam-2552	31	20	numerical	numerical	ADJ
ejpam-2552	31	21	applications	application	NOUN
ejpam-2552	31	22	.	.	PUNCT
ejpam-2552	32	1	a	a	DET
ejpam-2552	32	2	numerical	numerical	ADJ
ejpam-2552	32	3	illustration	illustration	NOUN
ejpam-2552	32	4	is	be	AUX
ejpam-2552	32	5	given	give	VERB
ejpam-2552	32	6	in	in	ADP
ejpam-2552	32	7	the	the	DET
ejpam-2552	32	8	last	last	ADJ
ejpam-2552	32	9	section	section	NOUN
ejpam-2552	32	10	.	.	PUNCT
ejpam-2552	33	1	2	2	X
ejpam-2552	33	2	.	.	NUM
ejpam-2552	33	3	recalls	recall	VERB
ejpam-2552	33	4	2.1	2.1	NUM
ejpam-2552	33	5	.	.	PUNCT
ejpam-2552	33	6	orthogonal	orthogonal	ADJ
ejpam-2552	33	7	families	family	NOUN
ejpam-2552	33	8	of	of	ADP
ejpam-2552	33	9	projectors	projector	NOUN
ejpam-2552	33	10	in	in	ADP
ejpam-2552	33	11	this	this	DET
ejpam-2552	33	12	text	text	NOUN
ejpam-2552	33	13	,	,	PUNCT
ejpam-2552	33	14	h	h	NOUN
ejpam-2552	33	15	,	,	PUNCT
ejpam-2552	33	16	l(h	l(h	PROPN
ejpam-2552	33	17	)	)	PUNCT
ejpam-2552	33	18	and	and	CCONJ
ejpam-2552	33	19	p(h	p(h	NOUN
ejpam-2552	33	20	)	)	PUNCT
ejpam-2552	33	21	are	be	AUX
ejpam-2552	33	22	respectively	respectively	ADV
ejpam-2552	33	23	a	a	DET
ejpam-2552	33	24	c−hilbert	c−hilbert	PROPN
ejpam-2552	33	25	space	space	NOUN
ejpam-2552	33	26	,	,	PUNCT
ejpam-2552	33	27	the	the	DET
ejpam-2552	33	28	set	set	NOUN
ejpam-2552	33	29	of	of	ADP
ejpam-2552	33	30	bounded	bound	VERB
ejpam-2552	33	31	endomorphisms	endomorphism	NOUN
ejpam-2552	33	32	of	of	ADP
ejpam-2552	33	33	h	h	PROPN
ejpam-2552	33	34	(	(	PUNCT
ejpam-2552	33	35	which	which	PRON
ejpam-2552	33	36	is	be	AUX
ejpam-2552	33	37	a	a	DET
ejpam-2552	33	38	banach	banach	NOUN
ejpam-2552	33	39	space	space	NOUN
ejpam-2552	33	40	for	for	ADP
ejpam-2552	33	41	the	the	DET
ejpam-2552	33	42	norm	norm	NOUN
ejpam-2552	33	43	‖a‖l	‖a‖l	PROPN
ejpam-2552	33	44	=	=	SYM
ejpam-2552	33	45	sup{‖ax‖	sup{‖ax‖	ADJ
ejpam-2552	33	46	;	;	PUNCT
ejpam-2552	34	1	‖x‖	‖x‖	X
ejpam-2552	34	2	=	=	SYM
ejpam-2552	34	3	1	1	NUM
ejpam-2552	34	4	}	}	PUNCT
ejpam-2552	34	5	)	)	PUNCT
ejpam-2552	34	6	,	,	PUNCT
ejpam-2552	34	7	and	and	CCONJ
ejpam-2552	34	8	the	the	DET
ejpam-2552	34	9	set	set	NOUN
ejpam-2552	34	10	of	of	ADP
ejpam-2552	34	11	the	the	DET
ejpam-2552	34	12	orthogonal	orthogonal	ADJ
ejpam-2552	34	13	projectors	projector	NOUN
ejpam-2552	34	14	on	on	ADP
ejpam-2552	34	15	h.	h.	PROPN
ejpam-2552	34	16	let	let	VERB
ejpam-2552	34	17	p1	p1	PROPN
ejpam-2552	34	18	and	and	CCONJ
ejpam-2552	34	19	p2	p2	PROPN
ejpam-2552	34	20	be	be	VERB
ejpam-2552	34	21	two	two	NUM
ejpam-2552	34	22	elements	element	NOUN
ejpam-2552	34	23	of	of	ADP
ejpam-2552	34	24	p(h	p(h	NOUN
ejpam-2552	34	25	)	)	PUNCT
ejpam-2552	34	26	,	,	PUNCT
ejpam-2552	34	27	p1	p1	PROPN
ejpam-2552	34	28	is	be	AUX
ejpam-2552	34	29	said	say	VERB
ejpam-2552	34	30	to	to	PART
ejpam-2552	34	31	be	be	AUX
ejpam-2552	34	32	“	"	PUNCT
ejpam-2552	34	33	less	less	ADJ
ejpam-2552	34	34	or	or	CCONJ
ejpam-2552	34	35	equal	equal	ADJ
ejpam-2552	34	36	”	"	PUNCT
ejpam-2552	34	37	to	to	ADP
ejpam-2552	34	38	p2	p2	PROPN
ejpam-2552	34	39	,	,	PUNCT
ejpam-2552	34	40	what	what	PRON
ejpam-2552	34	41	we	we	PRON
ejpam-2552	34	42	denote	denote	VERB
ejpam-2552	34	43	p1	p1	PROPN
ejpam-2552	34	44	�	�	PROPN
ejpam-2552	34	45	p2	p2	NOUN
ejpam-2552	34	46	,	,	PUNCT
ejpam-2552	34	47	if	if	SCONJ
ejpam-2552	34	48	p1p2	p1p2	PROPN
ejpam-2552	34	49	=	=	SYM
ejpam-2552	34	50	p1	p1	PROPN
ejpam-2552	34	51	.	.	PUNCT
ejpam-2552	35	1	this	this	DET
ejpam-2552	35	2	defines	define	NOUN
ejpam-2552	35	3	,	,	PUNCT
ejpam-2552	35	4	on	on	ADP
ejpam-2552	35	5	p(h	p(h	NOUN
ejpam-2552	35	6	)	)	PUNCT
ejpam-2552	35	7	,	,	PUNCT
ejpam-2552	35	8	a	a	DET
ejpam-2552	35	9	partial	partial	ADJ
ejpam-2552	35	10	order	order	NOUN
ejpam-2552	35	11	relation	relation	NOUN
ejpam-2552	35	12	.	.	PUNCT
ejpam-2552	36	1	a	a	DET
ejpam-2552	36	2	family	family	NOUN
ejpam-2552	36	3	{	{	PUNCT
ejpam-2552	36	4	pn;n	pn;n	PROPN
ejpam-2552	36	5	∈	∈	PROPN
ejpam-2552	36	6	n	n	CCONJ
ejpam-2552	36	7	}	}	PUNCT
ejpam-2552	36	8	of	of	ADP
ejpam-2552	36	9	elements	element	NOUN
ejpam-2552	36	10	of	of	ADP
ejpam-2552	36	11	p(h	p(h	NOUN
ejpam-2552	36	12	)	)	PUNCT
ejpam-2552	36	13	is	be	AUX
ejpam-2552	36	14	said	say	VERB
ejpam-2552	36	15	to	to	PART
ejpam-2552	36	16	be	be	AUX
ejpam-2552	36	17	orthogonal	orthogonal	ADJ
ejpam-2552	36	18	when	when	SCONJ
ejpam-2552	36	19	pn	pn	PROPN
ejpam-2552	36	20	◦	◦	VERB
ejpam-2552	36	21	pm	pm	NOUN
ejpam-2552	36	22	=	=	SYM
ejpam-2552	36	23	0	0	NUM
ejpam-2552	36	24	,	,	PUNCT
ejpam-2552	36	25	for	for	ADP
ejpam-2552	36	26	any	any	DET
ejpam-2552	36	27	pair	pair	NOUN
ejpam-2552	36	28	(	(	PUNCT
ejpam-2552	36	29	n	n	CCONJ
ejpam-2552	36	30	,	,	PUNCT
ejpam-2552	36	31	m	m	NOUN
ejpam-2552	36	32	)	)	PUNCT
ejpam-2552	36	33	of	of	ADP
ejpam-2552	36	34	distinct	distinct	ADJ
ejpam-2552	36	35	elements	element	NOUN
ejpam-2552	36	36	of	of	ADP
ejpam-2552	36	37	n.	n.	NOUN
ejpam-2552	36	38	then	then	ADV
ejpam-2552	36	39	we	we	PRON
ejpam-2552	36	40	can	can	AUX
ejpam-2552	36	41	show	show	VERB
ejpam-2552	36	42	that	that	SCONJ
ejpam-2552	36	43	a	a	X
ejpam-2552	36	44	)	)	PUNCT
ejpam-2552	36	45	for	for	ADP
ejpam-2552	36	46	any	any	DET
ejpam-2552	36	47	x	x	NOUN
ejpam-2552	36	48	of	of	ADP
ejpam-2552	36	49	h	h	NOUN
ejpam-2552	36	50	,	,	PUNCT
ejpam-2552	36	51	the	the	DET
ejpam-2552	36	52	family	family	NOUN
ejpam-2552	36	53	{	{	PUNCT
ejpam-2552	36	54	pnx;n	pnx;n	PROPN
ejpam-2552	36	55	∈	∈	PROPN
ejpam-2552	36	56	n	n	CCONJ
ejpam-2552	36	57	}	}	PUNCT
ejpam-2552	36	58	is	be	AUX
ejpam-2552	36	59	summable	summable	ADJ
ejpam-2552	36	60	;	;	PUNCT
ejpam-2552	36	61	b	b	X
ejpam-2552	36	62	)	)	PUNCT
ejpam-2552	36	63	the	the	DET
ejpam-2552	36	64	application	application	NOUN
ejpam-2552	36	65	p	p	X
ejpam-2552	36	66	:	:	PUNCT
ejpam-2552	36	67	x	x	SYM
ejpam-2552	36	68	∈	∈	NOUN
ejpam-2552	36	69	h	h	NOUN
ejpam-2552	36	70	7→	7→	NUM
ejpam-2552	36	71	∑	∑	PUNCT
ejpam-2552	36	72	n∈n	n∈n	PUNCT
ejpam-2552	36	73	pnx	pnx	PROPN
ejpam-2552	36	74	∈	∈	PROPN
ejpam-2552	36	75	h	h	NOUN
ejpam-2552	36	76	is	be	AUX
ejpam-2552	36	77	an	an	DET
ejpam-2552	36	78	element	element	NOUN
ejpam-2552	36	79	of	of	ADP
ejpam-2552	36	80	p(h	p(h	NOUN
ejpam-2552	36	81	)	)	PUNCT
ejpam-2552	36	82	which	which	PRON
ejpam-2552	36	83	we	we	PRON
ejpam-2552	36	84	name	name	VERB
ejpam-2552	36	85	the	the	DET
ejpam-2552	36	86	sum	sum	NOUN
ejpam-2552	36	87	of	of	ADP
ejpam-2552	36	88	the	the	DET
ejpam-2552	36	89	orthogonal	orthogonal	ADJ
ejpam-2552	36	90	family	family	NOUN
ejpam-2552	36	91	of	of	ADP
ejpam-2552	36	92	orthogonal	orthogonal	ADJ
ejpam-2552	36	93	projectors	projector	NOUN
ejpam-2552	36	94	{	{	PUNCT
ejpam-2552	36	95	pn;n	pn;n	NOUN
ejpam-2552	36	96	∈	∈	PROPN
ejpam-2552	36	97	n	n	CCONJ
ejpam-2552	36	98	}	}	PUNCT
ejpam-2552	36	99	and	and	CCONJ
ejpam-2552	36	100	which	which	PRON
ejpam-2552	36	101	we	we	PRON
ejpam-2552	36	102	denote	denote	VERB
ejpam-2552	36	103	∑	∑	PROPN
ejpam-2552	36	104	n∈n	n∈n	PROPN
ejpam-2552	36	105	pn	pn	PROPN
ejpam-2552	36	106	;	;	PUNCT
ejpam-2552	36	107	c	c	X
ejpam-2552	36	108	)	)	PUNCT
ejpam-2552	36	109	for	for	ADP
ejpam-2552	36	110	any	any	DET
ejpam-2552	36	111	n	n	NOUN
ejpam-2552	36	112	of	of	ADP
ejpam-2552	36	113	n	n	CCONJ
ejpam-2552	36	114	,	,	PUNCT
ejpam-2552	36	115	we	we	PRON
ejpam-2552	36	116	have	have	VERB
ejpam-2552	36	117	pn	pn	VERB
ejpam-2552	36	118	◦	◦	VERB
ejpam-2552	37	1	p	p	NOUN
ejpam-2552	37	2	=	=	X
ejpam-2552	37	3	pn	pn	PROPN
ejpam-2552	37	4	.	.	PUNCT
ejpam-2552	38	1	we	we	PRON
ejpam-2552	38	2	emphasize	emphasize	VERB
ejpam-2552	38	3	the	the	DET
ejpam-2552	38	4	fact	fact	NOUN
ejpam-2552	38	5	that	that	SCONJ
ejpam-2552	38	6	an	an	DET
ejpam-2552	38	7	orthogonal	orthogonal	ADJ
ejpam-2552	38	8	family	family	NOUN
ejpam-2552	38	9	of	of	ADP
ejpam-2552	38	10	orthogonal	orthogonal	ADJ
ejpam-2552	38	11	projectors	projector	NOUN
ejpam-2552	38	12	can	can	AUX
ejpam-2552	38	13	be	be	AUX
ejpam-2552	38	14	not	not	PART
ejpam-2552	38	15	summable	summable	ADJ
ejpam-2552	38	16	(	(	PUNCT
ejpam-2552	38	17	as	as	ADP
ejpam-2552	38	18	a	a	DET
ejpam-2552	38	19	family	family	NOUN
ejpam-2552	38	20	of	of	ADP
ejpam-2552	38	21	elements	element	NOUN
ejpam-2552	38	22	of	of	ADP
ejpam-2552	38	23	the	the	DET
ejpam-2552	38	24	banach	banach	NOUN
ejpam-2552	38	25	space	space	NOUN
ejpam-2552	38	26	l(h	l(h	PROPN
ejpam-2552	38	27	)	)	PUNCT
ejpam-2552	38	28	)	)	PUNCT
ejpam-2552	38	29	.	.	PUNCT
ejpam-2552	39	1	the	the	DET
ejpam-2552	39	2	following	follow	VERB
ejpam-2552	39	3	first	first	ADJ
ejpam-2552	39	4	result	result	NOUN
ejpam-2552	39	5	,	,	PUNCT
ejpam-2552	39	6	which	which	PRON
ejpam-2552	39	7	can	can	AUX
ejpam-2552	39	8	be	be	AUX
ejpam-2552	39	9	easily	easily	ADV
ejpam-2552	39	10	proved	prove	VERB
ejpam-2552	39	11	,	,	PUNCT
ejpam-2552	39	12	will	will	AUX
ejpam-2552	39	13	be	be	AUX
ejpam-2552	39	14	used	use	VERB
ejpam-2552	39	15	in	in	ADP
ejpam-2552	39	16	section	section	NOUN
ejpam-2552	39	17	3	3	NUM
ejpam-2552	39	18	.	.	PUNCT
ejpam-2552	40	1	lemma	lemma	PROPN
ejpam-2552	40	2	2.1.1	2.1.1	NUM
ejpam-2552	40	3	.	.	PUNCT
ejpam-2552	41	1	if	if	SCONJ
ejpam-2552	41	2	{	{	PUNCT
ejpam-2552	41	3	dn;n	dn;n	VERB
ejpam-2552	41	4	∈	∈	NOUN
ejpam-2552	41	5	n	n	CCONJ
ejpam-2552	41	6	}	}	PUNCT
ejpam-2552	41	7	and	and	CCONJ
ejpam-2552	41	8	{	{	PUNCT
ejpam-2552	41	9	d′n;n	d′n;n	PROPN
ejpam-2552	41	10	∈	∈	PROPN
ejpam-2552	41	11	n	n	CCONJ
ejpam-2552	41	12	}	}	PUNCT
ejpam-2552	41	13	are	be	AUX
ejpam-2552	41	14	two	two	NUM
ejpam-2552	41	15	orthogonal	orthogonal	ADJ
ejpam-2552	41	16	families	family	NOUN
ejpam-2552	41	17	of	of	ADP
ejpam-2552	41	18	orthogonal	orthogonal	ADJ
ejpam-2552	41	19	projectors	projector	NOUN
ejpam-2552	41	20	of	of	ADP
ejpam-2552	41	21	respective	respective	ADJ
ejpam-2552	41	22	sum	sum	NOUN
ejpam-2552	41	23	d	d	NOUN
ejpam-2552	41	24	and	and	CCONJ
ejpam-2552	41	25	d′	d′	PRON
ejpam-2552	41	26	such	such	ADJ
ejpam-2552	41	27	that	that	SCONJ
ejpam-2552	41	28	dn	dn	PROPN
ejpam-2552	41	29	�	�	PROPN
ejpam-2552	41	30	d′n	d′n	PROPN
ejpam-2552	41	31	,	,	PUNCT
ejpam-2552	41	32	for	for	ADP
ejpam-2552	41	33	any	any	DET
ejpam-2552	41	34	n	n	NOUN
ejpam-2552	41	35	of	of	ADP
ejpam-2552	41	36	n	n	CCONJ
ejpam-2552	41	37	,	,	PUNCT
ejpam-2552	41	38	then	then	ADV
ejpam-2552	41	39	d	d	PROPN
ejpam-2552	41	40	�	�	PROPN
ejpam-2552	41	41	d′.	d′.	VERB
ejpam-2552	41	42	2.2	2.2	NUM
ejpam-2552	41	43	.	.	PUNCT
ejpam-2552	42	1	random	random	ADJ
ejpam-2552	42	2	measure	measure	NOUN
ejpam-2552	42	3	let	let	VERB
ejpam-2552	42	4	ξ	ξ	X
ejpam-2552	42	5	be	be	AUX
ejpam-2552	42	6	a	a	DET
ejpam-2552	42	7	σ−field	σ−field	NOUN
ejpam-2552	42	8	of	of	ADP
ejpam-2552	42	9	subsets	subset	NOUN
ejpam-2552	42	10	of	of	ADP
ejpam-2552	42	11	a	a	DET
ejpam-2552	42	12	set	set	ADJ
ejpam-2552	42	13	e.	e.	NOUN
ejpam-2552	42	14	for	for	ADP
ejpam-2552	42	15	any	any	DET
ejpam-2552	42	16	e	e	NOUN
ejpam-2552	42	17	of	of	ADP
ejpam-2552	42	18	e	e	NOUN
ejpam-2552	42	19	,	,	PUNCT
ejpam-2552	42	20	δe	δe	NOUN
ejpam-2552	42	21	stands	stand	VERB
ejpam-2552	42	22	for	for	ADP
ejpam-2552	42	23	the	the	DET
ejpam-2552	42	24	dirac	dirac	NOUN
ejpam-2552	42	25	measure	measure	NOUN
ejpam-2552	42	26	defined	define	VERB
ejpam-2552	42	27	on	on	ADP
ejpam-2552	42	28	ξ	ξ	PROPN
ejpam-2552	42	29	and	and	CCONJ
ejpam-2552	42	30	concentrated	concentrate	VERB
ejpam-2552	42	31	on	on	ADP
ejpam-2552	42	32	e.	e.	PROPN
ejpam-2552	42	33	a	a	DET
ejpam-2552	42	34	random	random	ADJ
ejpam-2552	42	35	measure	measure	NOUN
ejpam-2552	42	36	(	(	PUNCT
ejpam-2552	42	37	r.m	r.m	PROPN
ejpam-2552	42	38	.	.	PROPN
ejpam-2552	42	39	)	)	PUNCT
ejpam-2552	42	40	defined	define	VERB
ejpam-2552	42	41	on	on	ADP
ejpam-2552	42	42	ξ	ξ	PROPN
ejpam-2552	42	43	,	,	PUNCT
ejpam-2552	42	44	taking	take	VERB
ejpam-2552	42	45	values	value	NOUN
ejpam-2552	42	46	in	in	ADP
ejpam-2552	42	47	h	h	NOUN
ejpam-2552	42	48	,	,	PUNCT
ejpam-2552	42	49	is	be	AUX
ejpam-2552	42	50	an	an	DET
ejpam-2552	42	51	application	application	NOUN
ejpam-2552	42	52	z	z	NOUN
ejpam-2552	42	53	from	from	ADP
ejpam-2552	42	54	ξ	ξ	PROPN
ejpam-2552	42	55	into	into	ADP
ejpam-2552	42	56	h	h	PRON
ejpam-2552	42	57	such	such	ADJ
ejpam-2552	42	58	that	that	PRON
ejpam-2552	42	59	:	:	PUNCT
ejpam-2552	42	60	a.	a.	NOUN
ejpam-2552	42	61	boudou	boudou	NOUN
ejpam-2552	42	62	,	,	PUNCT
ejpam-2552	42	63	s.	s.	PROPN
ejpam-2552	42	64	viguier	viguier	PROPN
ejpam-2552	42	65	-	-	PUNCT
ejpam-2552	42	66	pla	pla	PROPN
ejpam-2552	42	67	/	/	PUNCT
ejpam-2552	42	68	eur	eur	PROPN
ejpam-2552	42	69	.	.	PUNCT
ejpam-2552	43	1	j.	j.	PROPN
ejpam-2552	43	2	pure	pure	PROPN
ejpam-2552	43	3	appl	appl	PROPN
ejpam-2552	43	4	.	.	PROPN
ejpam-2552	43	5	math	math	PROPN
ejpam-2552	43	6	,	,	PUNCT
ejpam-2552	43	7	11	11	NUM
ejpam-2552	43	8	(	(	PUNCT
ejpam-2552	43	9	4	4	NUM
ejpam-2552	43	10	)	)	PUNCT
ejpam-2552	43	11	(	(	PUNCT
ejpam-2552	43	12	2018	2018	NUM
ejpam-2552	43	13	)	)	PUNCT
ejpam-2552	43	14	,	,	PUNCT
ejpam-2552	43	15	893	893	NUM
ejpam-2552	43	16	-	-	SYM
ejpam-2552	43	17	910	910	NUM
ejpam-2552	43	18	895	895	NUM
ejpam-2552	43	19	a	a	PRON
ejpam-2552	43	20	)	)	PUNCT
ejpam-2552	43	21	z(a	z(a	NOUN
ejpam-2552	43	22	∪	∪	ADP
ejpam-2552	43	23	b	b	NOUN
ejpam-2552	43	24	)	)	PUNCT
ejpam-2552	43	25	=	=	SYM
ejpam-2552	43	26	z(a	z(a	PROPN
ejpam-2552	43	27	)	)	PUNCT
ejpam-2552	43	28	+	+	NUM
ejpam-2552	43	29	z(b	z(b	NOUN
ejpam-2552	43	30	)	)	PUNCT
ejpam-2552	43	31	and	and	CCONJ
ejpam-2552	43	32	<	<	X
ejpam-2552	43	33	z(a	z(a	NOUN
ejpam-2552	43	34	)	)	PUNCT
ejpam-2552	43	35	,	,	PUNCT
ejpam-2552	43	36	z(b	z(b	PROPN
ejpam-2552	43	37	)	)	PUNCT
ejpam-2552	43	38	>	>	PUNCT
ejpam-2552	43	39	=	=	PUNCT
ejpam-2552	43	40	0	0	NUM
ejpam-2552	43	41	,	,	PUNCT
ejpam-2552	43	42	for	for	ADP
ejpam-2552	43	43	any	any	DET
ejpam-2552	43	44	pair	pair	NOUN
ejpam-2552	43	45	(	(	PUNCT
ejpam-2552	43	46	a	a	DET
ejpam-2552	43	47	,	,	PUNCT
ejpam-2552	43	48	b	b	NOUN
ejpam-2552	43	49	)	)	PUNCT
ejpam-2552	43	50	of	of	ADP
ejpam-2552	43	51	disjoint	disjoint	ADJ
ejpam-2552	43	52	elements	element	NOUN
ejpam-2552	43	53	of	of	ADP
ejpam-2552	43	54	ξ	ξ	PROPN
ejpam-2552	43	55	;	;	PUNCT
ejpam-2552	43	56	b	b	X
ejpam-2552	43	57	)	)	PUNCT
ejpam-2552	43	58	limn→∞z(an	limn→∞z(an	NOUN
ejpam-2552	43	59	)	)	PUNCT
ejpam-2552	44	1	=	=	SYM
ejpam-2552	44	2	0	0	NUM
ejpam-2552	45	1	for	for	ADP
ejpam-2552	45	2	any	any	DET
ejpam-2552	45	3	sequence	sequence	NOUN
ejpam-2552	45	4	(	(	PUNCT
ejpam-2552	45	5	an)n∈n	an)n∈n	NUM
ejpam-2552	45	6	of	of	ADP
ejpam-2552	45	7	elements	element	NOUN
ejpam-2552	45	8	of	of	ADP
ejpam-2552	45	9	ξ	ξ	PROPN
ejpam-2552	45	10	which	which	PRON
ejpam-2552	45	11	decreasingly	decreasingly	ADV
ejpam-2552	45	12	converges	converge	VERB
ejpam-2552	45	13	to	to	ADP
ejpam-2552	45	14	∅.	∅.	VERB
ejpam-2552	45	15	we	we	PRON
ejpam-2552	45	16	then	then	ADV
ejpam-2552	45	17	have	have	VERB
ejpam-2552	45	18	the	the	DET
ejpam-2552	45	19	following	follow	VERB
ejpam-2552	45	20	properties	property	NOUN
ejpam-2552	45	21	.	.	PUNCT
ejpam-2552	46	1	a	a	X
ejpam-2552	46	2	)	)	PUNCT
ejpam-2552	46	3	the	the	DET
ejpam-2552	46	4	application	application	NOUN
ejpam-2552	46	5	µz	µz	NOUN
ejpam-2552	46	6	:	:	PUNCT
ejpam-2552	46	7	a	a	DET
ejpam-2552	46	8	∈	∈	PROPN
ejpam-2552	46	9	ξ	ξ	SYM
ejpam-2552	46	10	7→	7→	NUM
ejpam-2552	46	11	‖z(a)‖2	‖z(a)‖2	NOUN
ejpam-2552	46	12	∈	∈	NOUN
ejpam-2552	46	13	r+	r+	NOUN
ejpam-2552	46	14	is	be	AUX
ejpam-2552	46	15	a	a	DET
ejpam-2552	46	16	bounded	bounded	ADJ
ejpam-2552	46	17	measure	measure	NOUN
ejpam-2552	46	18	;	;	PUNCT
ejpam-2552	46	19	b	b	X
ejpam-2552	46	20	)	)	PUNCT
ejpam-2552	46	21	there	there	PRON
ejpam-2552	46	22	exists	exist	VERB
ejpam-2552	46	23	one	one	NUM
ejpam-2552	46	24	,	,	PUNCT
ejpam-2552	46	25	and	and	CCONJ
ejpam-2552	46	26	only	only	ADV
ejpam-2552	46	27	one	one	NUM
ejpam-2552	46	28	,	,	PUNCT
ejpam-2552	46	29	isometry	isometry	NOUN
ejpam-2552	46	30	from	from	ADP
ejpam-2552	46	31	l2(e	l2(e	PROPN
ejpam-2552	46	32	,	,	PUNCT
ejpam-2552	46	33	ξ	ξ	PROPN
ejpam-2552	46	34	,	,	PUNCT
ejpam-2552	46	35	µz	µz	NOUN
ejpam-2552	46	36	)	)	PUNCT
ejpam-2552	46	37	onto	onto	ADP
ejpam-2552	46	38	hz	hz	PROPN
ejpam-2552	46	39	=	=	SYM
ejpam-2552	46	40	vect{z(a);a	vect{z(a);a	NUM
ejpam-2552	46	41	∈	∈	PROPN
ejpam-2552	46	42	ξ	ξ	PROPN
ejpam-2552	46	43	}	}	PUNCT
ejpam-2552	46	44	such	such	ADJ
ejpam-2552	46	45	that	that	PRON
ejpam-2552	46	46	for	for	ADP
ejpam-2552	46	47	any	any	DET
ejpam-2552	46	48	a	a	PRON
ejpam-2552	46	49	of	of	ADP
ejpam-2552	46	50	ξ	ξ	PROPN
ejpam-2552	46	51	,	,	PUNCT
ejpam-2552	46	52	za	za	PROPN
ejpam-2552	46	53	is	be	AUX
ejpam-2552	46	54	the	the	DET
ejpam-2552	46	55	image	image	NOUN
ejpam-2552	46	56	of	of	ADP
ejpam-2552	46	57	1a	1a	NUM
ejpam-2552	46	58	.	.	PUNCT
ejpam-2552	47	1	the	the	DET
ejpam-2552	47	2	stochastic	stochastic	ADJ
ejpam-2552	47	3	integral	integral	NOUN
ejpam-2552	47	4	of	of	ADP
ejpam-2552	47	5	an	an	DET
ejpam-2552	47	6	element	element	NOUN
ejpam-2552	47	7	ϕ	ϕ	NOUN
ejpam-2552	47	8	of	of	ADP
ejpam-2552	47	9	l2(e	l2(e	PROPN
ejpam-2552	47	10	,	,	PUNCT
ejpam-2552	47	11	ξ	ξ	PROPN
ejpam-2552	47	12	,	,	PUNCT
ejpam-2552	47	13	µz	µz	NOUN
ejpam-2552	47	14	)	)	PUNCT
ejpam-2552	47	15	with	with	ADP
ejpam-2552	47	16	respect	respect	NOUN
ejpam-2552	47	17	to	to	ADP
ejpam-2552	47	18	the	the	DET
ejpam-2552	47	19	r.m	r.m	PROPN
ejpam-2552	47	20	.	.	PROPN
ejpam-2552	48	1	z	z	X
ejpam-2552	48	2	,	,	PUNCT
ejpam-2552	48	3	is	be	AUX
ejpam-2552	48	4	the	the	DET
ejpam-2552	48	5	image	image	NOUN
ejpam-2552	48	6	of	of	ADP
ejpam-2552	48	7	ϕ	ϕ	NOUN
ejpam-2552	48	8	by	by	ADP
ejpam-2552	48	9	this	this	DET
ejpam-2552	48	10	isometry	isometry	NOUN
ejpam-2552	48	11	,	,	PUNCT
ejpam-2552	48	12	and	and	CCONJ
ejpam-2552	48	13	we	we	PRON
ejpam-2552	48	14	note	note	VERB
ejpam-2552	48	15	it	it	PRON
ejpam-2552	48	16	∫	∫	PROPN
ejpam-2552	48	17	ϕdz	ϕdz	PROPN
ejpam-2552	48	18	.	.	PUNCT
ejpam-2552	49	1	for	for	ADP
ejpam-2552	49	2	example	example	NOUN
ejpam-2552	49	3	,	,	PUNCT
ejpam-2552	49	4	if	if	SCONJ
ejpam-2552	49	5	{	{	PUNCT
ejpam-2552	49	6	zn	zn	NOUN
ejpam-2552	49	7	,	,	PUNCT
ejpam-2552	49	8	n	n	PROPN
ejpam-2552	49	9	∈	∈	PROPN
ejpam-2552	49	10	n	n	CCONJ
ejpam-2552	49	11	}	}	PUNCT
ejpam-2552	49	12	is	be	AUX
ejpam-2552	49	13	a	a	DET
ejpam-2552	49	14	summable	summable	ADJ
ejpam-2552	49	15	orthogonal	orthogonal	ADJ
ejpam-2552	49	16	family	family	NOUN
ejpam-2552	49	17	of	of	ADP
ejpam-2552	49	18	elements	element	NOUN
ejpam-2552	49	19	of	of	ADP
ejpam-2552	49	20	h	h	NOUN
ejpam-2552	49	21	,	,	PUNCT
ejpam-2552	49	22	if	if	SCONJ
ejpam-2552	49	23	(	(	PUNCT
ejpam-2552	49	24	en)n∈n	en)n∈n	PROPN
ejpam-2552	49	25	is	be	AUX
ejpam-2552	49	26	a	a	DET
ejpam-2552	49	27	sequence	sequence	NOUN
ejpam-2552	49	28	of	of	ADP
ejpam-2552	49	29	elements	element	NOUN
ejpam-2552	49	30	of	of	ADP
ejpam-2552	49	31	e	e	PRON
ejpam-2552	49	32	such	such	ADJ
ejpam-2552	49	33	that	that	SCONJ
ejpam-2552	49	34	{	{	PUNCT
ejpam-2552	49	35	en	en	X
ejpam-2552	49	36	}	}	PUNCT
ejpam-2552	49	37	∈	∈	PROPN
ejpam-2552	49	38	ξ	ξ	PROPN
ejpam-2552	49	39	,	,	PUNCT
ejpam-2552	49	40	then	then	ADV
ejpam-2552	49	41	,	,	PUNCT
ejpam-2552	49	42	for	for	ADP
ejpam-2552	49	43	any	any	DET
ejpam-2552	49	44	b	b	PROPN
ejpam-2552	49	45	of	of	ADP
ejpam-2552	49	46	ξ	ξ	PROPN
ejpam-2552	49	47	,	,	PUNCT
ejpam-2552	49	48	the	the	DET
ejpam-2552	49	49	family	family	NOUN
ejpam-2552	49	50	{	{	PUNCT
ejpam-2552	49	51	δen(b)zn	δen(b)zn	PROPN
ejpam-2552	49	52	,	,	PUNCT
ejpam-2552	49	53	n	n	PRON
ejpam-2552	49	54	∈	∈	PROPN
ejpam-2552	49	55	n	n	CCONJ
ejpam-2552	49	56	}	}	PUNCT
ejpam-2552	49	57	,	,	PUNCT
ejpam-2552	49	58	of	of	ADP
ejpam-2552	49	59	elements	element	NOUN
ejpam-2552	49	60	of	of	ADP
ejpam-2552	49	61	h	h	NOUN
ejpam-2552	49	62	,	,	PUNCT
ejpam-2552	49	63	is	be	AUX
ejpam-2552	49	64	summable	summable	ADJ
ejpam-2552	49	65	.	.	PUNCT
ejpam-2552	50	1	the	the	DET
ejpam-2552	50	2	application	application	NOUN
ejpam-2552	50	3	z	z	NOUN
ejpam-2552	50	4	:	:	PUNCT
ejpam-2552	50	5	b	b	X
ejpam-2552	50	6	∈	∈	PROPN
ejpam-2552	50	7	ξ	ξ	X
ejpam-2552	50	8	7→∑	7→∑	NOUN
ejpam-2552	50	9	n∈n	n∈n	NOUN
ejpam-2552	50	10	δen(b)zn	δen(b)zn	NUM
ejpam-2552	50	11	∈	∈	NOUN
ejpam-2552	50	12	h	h	NOUN
ejpam-2552	50	13	is	be	AUX
ejpam-2552	50	14	a	a	DET
ejpam-2552	50	15	r.m	r.m	PROPN
ejpam-2552	50	16	..	..	PUNCT
ejpam-2552	50	17	if	if	SCONJ
ejpam-2552	50	18	f	f	PROPN
ejpam-2552	50	19	is	be	AUX
ejpam-2552	50	20	an	an	DET
ejpam-2552	50	21	element	element	NOUN
ejpam-2552	50	22	of	of	ADP
ejpam-2552	50	23	l2(µz	l2(µz	PROPN
ejpam-2552	50	24	)	)	PUNCT
ejpam-2552	50	25	,	,	PUNCT
ejpam-2552	50	26	then	then	ADV
ejpam-2552	50	27	{	{	PUNCT
ejpam-2552	50	28	f(en)zn	f(en)zn	NOUN
ejpam-2552	50	29	,	,	PUNCT
ejpam-2552	50	30	n	n	PROPN
ejpam-2552	50	31	∈	∈	PROPN
ejpam-2552	50	32	n	n	CCONJ
ejpam-2552	50	33	}	}	PUNCT
ejpam-2552	50	34	is	be	AUX
ejpam-2552	50	35	a	a	DET
ejpam-2552	50	36	summable	summable	ADJ
ejpam-2552	50	37	family	family	NOUN
ejpam-2552	50	38	of	of	ADP
ejpam-2552	50	39	elements	element	NOUN
ejpam-2552	50	40	of	of	ADP
ejpam-2552	50	41	h	h	NOUN
ejpam-2552	50	42	,	,	PUNCT
ejpam-2552	50	43	of	of	ADP
ejpam-2552	50	44	sum	sum	PROPN
ejpam-2552	50	45	∫	∫	PROPN
ejpam-2552	50	46	fdz	fdz	PROPN
ejpam-2552	50	47	.	.	PROPN
ejpam-2552	51	1	in	in	ADP
ejpam-2552	51	2	the	the	DET
ejpam-2552	51	3	all	all	DET
ejpam-2552	51	4	text	text	NOUN
ejpam-2552	51	5	,	,	PUNCT
ejpam-2552	51	6	(	(	PUNCT
ejpam-2552	51	7	e′	e′	PROPN
ejpam-2552	51	8	,	,	PUNCT
ejpam-2552	51	9	ξ′	ξ′	ADJ
ejpam-2552	51	10	)	)	PUNCT
ejpam-2552	51	11	denotes	denote	VERB
ejpam-2552	51	12	a	a	DET
ejpam-2552	51	13	second	second	ADJ
ejpam-2552	51	14	measurable	measurable	ADJ
ejpam-2552	51	15	space	space	NOUN
ejpam-2552	51	16	.	.	PUNCT
ejpam-2552	52	1	let	let	VERB
ejpam-2552	52	2	f	f	PRON
ejpam-2552	52	3	be	be	AUX
ejpam-2552	52	4	a	a	DET
ejpam-2552	52	5	measurable	measurable	ADJ
ejpam-2552	52	6	application	application	NOUN
ejpam-2552	52	7	from	from	ADP
ejpam-2552	52	8	e	e	NOUN
ejpam-2552	52	9	into	into	ADP
ejpam-2552	52	10	e′.	e′.	NOUN
ejpam-2552	52	11	we	we	PRON
ejpam-2552	52	12	can	can	AUX
ejpam-2552	52	13	affirm	affirm	VERB
ejpam-2552	52	14	the	the	DET
ejpam-2552	52	15	following	following	NOUN
ejpam-2552	52	16	.	.	PUNCT
ejpam-2552	53	1	a	a	X
ejpam-2552	53	2	)	)	PUNCT
ejpam-2552	53	3	the	the	DET
ejpam-2552	53	4	application	application	NOUN
ejpam-2552	53	5	f(z	f(z	PROPN
ejpam-2552	53	6	)	)	PUNCT
ejpam-2552	53	7	:	:	PUNCT
ejpam-2552	54	1	a′	a′	PROPN
ejpam-2552	54	2	∈	∈	PROPN
ejpam-2552	54	3	ξ′	ξ′	PROPN
ejpam-2552	54	4	7→	7→	NUM
ejpam-2552	54	5	z(f−1a′	z(f−1a′	NOUN
ejpam-2552	54	6	)	)	PUNCT
ejpam-2552	55	1	∈	∈	PROPN
ejpam-2552	55	2	h	h	NOUN
ejpam-2552	55	3	is	be	AUX
ejpam-2552	55	4	a	a	DET
ejpam-2552	55	5	r.m	r.m	PROPN
ejpam-2552	55	6	.	.	PROPN
ejpam-2552	55	7	,	,	PUNCT
ejpam-2552	55	8	named	name	VERB
ejpam-2552	55	9	r.m	r.m	PROPN
ejpam-2552	55	10	.	.	PROPN
ejpam-2552	55	11	image	image	NOUN
ejpam-2552	55	12	of	of	ADP
ejpam-2552	55	13	z	z	NOUN
ejpam-2552	55	14	by	by	ADP
ejpam-2552	55	15	f	f	PROPN
ejpam-2552	55	16	;	;	PUNCT
ejpam-2552	55	17	b	b	X
ejpam-2552	55	18	)	)	PUNCT
ejpam-2552	55	19	f(µz	f(µz	PROPN
ejpam-2552	55	20	)	)	PUNCT
ejpam-2552	55	21	=	=	NUM
ejpam-2552	55	22	µf(z	µf(z	NOUN
ejpam-2552	55	23	)	)	PUNCT
ejpam-2552	55	24	;	;	PUNCT
ejpam-2552	55	25	c	c	X
ejpam-2552	55	26	)	)	PUNCT
ejpam-2552	55	27	if	if	SCONJ
ejpam-2552	55	28	ϕ′	ϕ′	PRON
ejpam-2552	55	29	is	be	AUX
ejpam-2552	55	30	a	a	DET
ejpam-2552	55	31	element	element	NOUN
ejpam-2552	55	32	of	of	ADP
ejpam-2552	55	33	l2(e′	l2(e′	ADJ
ejpam-2552	55	34	,	,	PUNCT
ejpam-2552	55	35	ξ′	ξ′	NOUN
ejpam-2552	55	36	,	,	PUNCT
ejpam-2552	55	37	µf(z	µf(z	NUM
ejpam-2552	55	38	)	)	PUNCT
ejpam-2552	55	39	)	)	PUNCT
ejpam-2552	55	40	,	,	PUNCT
ejpam-2552	55	41	then	then	ADV
ejpam-2552	55	42	ϕ′	ϕ′	X
ejpam-2552	55	43	◦	◦	NOUN
ejpam-2552	55	44	f	f	VERB
ejpam-2552	55	45	belongs	belong	VERB
ejpam-2552	55	46	to	to	ADP
ejpam-2552	55	47	l2(e	l2(e	PROPN
ejpam-2552	55	48	,	,	PUNCT
ejpam-2552	55	49	ξ	ξ	PROPN
ejpam-2552	55	50	,	,	PUNCT
ejpam-2552	55	51	µz	µz	NOUN
ejpam-2552	55	52	)	)	PUNCT
ejpam-2552	55	53	and	and	CCONJ
ejpam-2552	55	54	∫	∫	PROPN
ejpam-2552	55	55	ϕ′df(z	ϕ′df(z	PROPN
ejpam-2552	55	56	)	)	PUNCT
ejpam-2552	56	1	=	=	NUM
ejpam-2552	56	2	∫	∫	PROPN
ejpam-2552	56	3	ϕ′	ϕ′	PROPN
ejpam-2552	56	4	◦	◦	PROPN
ejpam-2552	56	5	fdz	fdz	PROPN
ejpam-2552	56	6	.	.	PUNCT
ejpam-2552	57	1	a	a	DET
ejpam-2552	57	2	stationary	stationary	ADJ
ejpam-2552	57	3	continuous	continuous	ADJ
ejpam-2552	57	4	random	random	ADJ
ejpam-2552	57	5	function	function	NOUN
ejpam-2552	57	6	(	(	PUNCT
ejpam-2552	57	7	c.r.f	c.r.f	NOUN
ejpam-2552	57	8	.	.	PUNCT
ejpam-2552	57	9	)	)	PUNCT
ejpam-2552	58	1	(	(	PUNCT
ejpam-2552	58	2	xt)t∈r	xt)t∈r	PROPN
ejpam-2552	58	3	is	be	AUX
ejpam-2552	58	4	a	a	DET
ejpam-2552	58	5	family	family	NOUN
ejpam-2552	58	6	of	of	ADP
ejpam-2552	58	7	elements	element	NOUN
ejpam-2552	58	8	of	of	ADP
ejpam-2552	58	9	h	h	NOUN
ejpam-2552	58	10	such	such	ADJ
ejpam-2552	58	11	that	that	SCONJ
ejpam-2552	58	12	the	the	DET
ejpam-2552	58	13	application	application	NOUN
ejpam-2552	58	14	t	t	NOUN
ejpam-2552	58	15	∈	∈	PROPN
ejpam-2552	58	16	r	r	NOUN
ejpam-2552	58	17	7→	7→	NUM
ejpam-2552	58	18	xt	xt	ADP
ejpam-2552	59	1	∈	∈	NOUN
ejpam-2552	59	2	h	h	NOUN
ejpam-2552	59	3	is	be	AUX
ejpam-2552	59	4	continuous	continuous	ADJ
ejpam-2552	59	5	and	and	CCONJ
ejpam-2552	59	6	such	such	ADJ
ejpam-2552	60	1	that	that	SCONJ
ejpam-2552	60	2	<	<	X
ejpam-2552	60	3	xt	xt	PROPN
ejpam-2552	60	4	,	,	PUNCT
ejpam-2552	60	5	xt′	xt′	PROPN
ejpam-2552	60	6	>	>	PUNCT
ejpam-2552	60	7	=	=	X
ejpam-2552	60	8	<	<	X
ejpam-2552	60	9	xt−t′	xt−t′	PROPN
ejpam-2552	60	10	,	,	PUNCT
ejpam-2552	60	11	x0	x0	PROPN
ejpam-2552	60	12	>	>	X
ejpam-2552	60	13	for	for	ADP
ejpam-2552	60	14	any	any	DET
ejpam-2552	60	15	pair	pair	NOUN
ejpam-2552	60	16	(	(	PUNCT
ejpam-2552	60	17	t	t	PROPN
ejpam-2552	60	18	,	,	PUNCT
ejpam-2552	60	19	t′	t′	NUM
ejpam-2552	60	20	)	)	PUNCT
ejpam-2552	60	21	of	of	ADP
ejpam-2552	60	22	elements	element	NOUN
ejpam-2552	60	23	of	of	ADP
ejpam-2552	60	24	r.	r.	PROPN
ejpam-2552	60	25	there	there	PRON
ejpam-2552	60	26	exists	exist	VERB
ejpam-2552	60	27	one	one	NUM
ejpam-2552	60	28	,	,	PUNCT
ejpam-2552	60	29	and	and	CCONJ
ejpam-2552	60	30	only	only	ADV
ejpam-2552	60	31	one	one	NUM
ejpam-2552	60	32	r.m	r.m	PROPN
ejpam-2552	60	33	.	.	PROPN
ejpam-2552	61	1	z	z	PROPN
ejpam-2552	61	2	,	,	PUNCT
ejpam-2552	61	3	named	name	VERB
ejpam-2552	61	4	r.m	r.m	PROPN
ejpam-2552	61	5	.	.	PROPN
ejpam-2552	61	6	associated	associate	VERB
ejpam-2552	61	7	with	with	ADP
ejpam-2552	61	8	the	the	DET
ejpam-2552	61	9	stationary	stationary	ADJ
ejpam-2552	61	10	c.r.f	c.r.f	NOUN
ejpam-2552	61	11	.	.	PUNCT
ejpam-2552	62	1	(	(	PUNCT
ejpam-2552	62	2	xt)t∈r	xt)t∈r	PROPN
ejpam-2552	62	3	,	,	PUNCT
ejpam-2552	62	4	defined	define	VERB
ejpam-2552	62	5	on	on	ADP
ejpam-2552	62	6	br	br	PROPN
ejpam-2552	62	7	,	,	PUNCT
ejpam-2552	62	8	such	such	ADJ
ejpam-2552	62	9	that	that	PRON
ejpam-2552	62	10	xt	xt	PUNCT
ejpam-2552	63	1	=	=	SYM
ejpam-2552	63	2	∫	∫	PROPN
ejpam-2552	63	3	ei.tdz	ei.tdz	PROPN
ejpam-2552	63	4	,	,	PUNCT
ejpam-2552	63	5	for	for	ADP
ejpam-2552	63	6	any	any	DET
ejpam-2552	63	7	t	t	NOUN
ejpam-2552	63	8	of	of	ADP
ejpam-2552	63	9	r.	r.	PROPN
ejpam-2552	63	10	then	then	ADV
ejpam-2552	63	11	we	we	PRON
ejpam-2552	63	12	will	will	AUX
ejpam-2552	63	13	say	say	VERB
ejpam-2552	63	14	that	that	SCONJ
ejpam-2552	63	15	two	two	NUM
ejpam-2552	63	16	c.r.f	c.r.f	NOUN
ejpam-2552	63	17	.	.	PUNCT
ejpam-2552	63	18	’s	’s	PART
ejpam-2552	64	1	(	(	PUNCT
ejpam-2552	64	2	xt)t∈r	xt)t∈r	NUM
ejpam-2552	64	3	and	and	CCONJ
ejpam-2552	64	4	(	(	PUNCT
ejpam-2552	64	5	x	x	X
ejpam-2552	64	6	′t)t∈r	′t)t∈r	NOUN
ejpam-2552	64	7	are	be	AUX
ejpam-2552	64	8	stationarily	stationarily	ADV
ejpam-2552	64	9	correlated	correlate	VERB
ejpam-2552	64	10	when	when	SCONJ
ejpam-2552	64	11	<	<	X
ejpam-2552	64	12	xt	xt	X
ejpam-2552	64	13	,	,	PUNCT
ejpam-2552	64	14	x	x	NOUN
ejpam-2552	64	15	′	′	NUM
ejpam-2552	64	16	t′	t′	NUM
ejpam-2552	64	17	>	>	PUNCT
ejpam-2552	65	1	=	=	X
ejpam-2552	65	2	<	<	X
ejpam-2552	65	3	xt−t′	xt−t′	PROPN
ejpam-2552	65	4	,	,	PUNCT
ejpam-2552	65	5	x	x	X
ejpam-2552	65	6	′	′	NOUN
ejpam-2552	65	7	0	0	NUM
ejpam-2552	65	8	>	>	PUNCT
ejpam-2552	65	9	,	,	PUNCT
ejpam-2552	65	10	for	for	ADP
ejpam-2552	65	11	any	any	DET
ejpam-2552	65	12	pair	pair	NOUN
ejpam-2552	65	13	(	(	PUNCT
ejpam-2552	65	14	t	t	PROPN
ejpam-2552	65	15	,	,	PUNCT
ejpam-2552	65	16	t′	t′	NUM
ejpam-2552	65	17	)	)	PUNCT
ejpam-2552	65	18	of	of	ADP
ejpam-2552	65	19	elements	element	NOUN
ejpam-2552	65	20	of	of	ADP
ejpam-2552	65	21	r.	r.	NOUN
ejpam-2552	65	22	this	this	DET
ejpam-2552	65	23	property	property	NOUN
ejpam-2552	65	24	can	can	AUX
ejpam-2552	65	25	be	be	AUX
ejpam-2552	65	26	expressed	express	VERB
ejpam-2552	65	27	in	in	ADP
ejpam-2552	65	28	terms	term	NOUN
ejpam-2552	65	29	of	of	ADP
ejpam-2552	65	30	associated	associated	PROPN
ejpam-2552	65	31	r.m	r.m	PROPN
ejpam-2552	65	32	.	.	PROPN
ejpam-2552	65	33	’s	’s	PART
ejpam-2552	65	34	:	:	PUNCT
ejpam-2552	65	35	if	if	SCONJ
ejpam-2552	65	36	z	z	PROPN
ejpam-2552	65	37	and	and	CCONJ
ejpam-2552	65	38	z	z	NOUN
ejpam-2552	65	39	′	′	NUM
ejpam-2552	65	40	are	be	AUX
ejpam-2552	65	41	two	two	NUM
ejpam-2552	65	42	r.m	r.m	AUX
ejpam-2552	65	43	.	.	PROPN
ejpam-2552	65	44	’s	’	VERB
ejpam-2552	65	45	associated	associate	VERB
ejpam-2552	65	46	with	with	ADP
ejpam-2552	65	47	two	two	NUM
ejpam-2552	65	48	stationary	stationary	ADJ
ejpam-2552	65	49	c.r.f	c.r.f	NOUN
ejpam-2552	65	50	.	.	PUNCT
ejpam-2552	66	1	’s	’s	PART
ejpam-2552	66	2	,	,	PUNCT
ejpam-2552	66	3	stationarily	stationarily	ADV
ejpam-2552	66	4	correlated	correlate	VERB
ejpam-2552	66	5	,	,	PUNCT
ejpam-2552	66	6	then	then	ADV
ejpam-2552	66	7	,	,	PUNCT
ejpam-2552	66	8	for	for	ADP
ejpam-2552	66	9	any	any	DET
ejpam-2552	66	10	pair	pair	NOUN
ejpam-2552	66	11	(	(	PUNCT
ejpam-2552	66	12	a	a	PRON
ejpam-2552	66	13	,	,	PUNCT
ejpam-2552	66	14	a′	a′	PROPN
ejpam-2552	66	15	)	)	PUNCT
ejpam-2552	66	16	of	of	ADP
ejpam-2552	66	17	disjoint	disjoint	ADJ
ejpam-2552	66	18	elements	element	NOUN
ejpam-2552	66	19	of	of	ADP
ejpam-2552	66	20	br	br	PROPN
ejpam-2552	66	21	,	,	PUNCT
ejpam-2552	66	22	we	we	PRON
ejpam-2552	66	23	have	have	VERB
ejpam-2552	66	24	<	<	X
ejpam-2552	66	25	z(a	z(a	NOUN
ejpam-2552	66	26	)	)	PUNCT
ejpam-2552	66	27	,	,	PUNCT
ejpam-2552	67	1	z	z	NOUN
ejpam-2552	67	2	′(a′	′(a′	NOUN
ejpam-2552	67	3	)	)	PUNCT
ejpam-2552	67	4	>	>	PUNCT
ejpam-2552	67	5	=	=	PUNCT
ejpam-2552	68	1	0	0	NUM
ejpam-2552	68	2	.	.	PROPN
ejpam-2552	69	1	2.3	2.3	NUM
ejpam-2552	69	2	.	.	PUNCT
ejpam-2552	70	1	spectral	spectral	ADJ
ejpam-2552	70	2	measure	measure	NOUN
ejpam-2552	70	3	a	a	DET
ejpam-2552	70	4	spectral	spectral	ADJ
ejpam-2552	70	5	measure	measure	NOUN
ejpam-2552	70	6	(	(	PUNCT
ejpam-2552	70	7	s.m	s.m	PROPN
ejpam-2552	70	8	.	.	PUNCT
ejpam-2552	70	9	)	)	PUNCT
ejpam-2552	71	1	e	e	NOUN
ejpam-2552	71	2	on	on	ADP
ejpam-2552	71	3	ξ	ξ	PROPN
ejpam-2552	71	4	for	for	ADP
ejpam-2552	71	5	h	h	NOUN
ejpam-2552	71	6	is	be	AUX
ejpam-2552	71	7	an	an	DET
ejpam-2552	71	8	application	application	NOUN
ejpam-2552	71	9	from	from	ADP
ejpam-2552	71	10	ξ	ξ	PROPN
ejpam-2552	71	11	into	into	ADP
ejpam-2552	71	12	p(h	p(h	NOUN
ejpam-2552	71	13	)	)	PUNCT
ejpam-2552	71	14	such	such	ADJ
ejpam-2552	71	15	that	that	SCONJ
ejpam-2552	71	16	a	a	DET
ejpam-2552	71	17	)	)	PUNCT
ejpam-2552	71	18	e(e	e(e	NOUN
ejpam-2552	71	19	)	)	PUNCT
ejpam-2552	71	20	=	=	SYM
ejpam-2552	71	21	ih	ih	X
ejpam-2552	71	22	;	;	PUNCT
ejpam-2552	71	23	b	b	X
ejpam-2552	71	24	)	)	PUNCT
ejpam-2552	71	25	e(a	e(a	NOUN
ejpam-2552	71	26	∪b	∪b	NOUN
ejpam-2552	71	27	)	)	PUNCT
ejpam-2552	71	28	=	=	SYM
ejpam-2552	71	29	e(a	e(a	X
ejpam-2552	71	30	)	)	PUNCT
ejpam-2552	71	31	+	+	CCONJ
ejpam-2552	71	32	e(b	e(b	NOUN
ejpam-2552	71	33	)	)	PUNCT
ejpam-2552	71	34	,	,	PUNCT
ejpam-2552	71	35	for	for	ADP
ejpam-2552	71	36	any	any	DET
ejpam-2552	71	37	pair	pair	NOUN
ejpam-2552	71	38	(	(	PUNCT
ejpam-2552	71	39	a	a	DET
ejpam-2552	71	40	,	,	PUNCT
ejpam-2552	71	41	b	b	NOUN
ejpam-2552	71	42	)	)	PUNCT
ejpam-2552	71	43	of	of	ADP
ejpam-2552	71	44	disjoint	disjoint	ADJ
ejpam-2552	71	45	elements	element	NOUN
ejpam-2552	71	46	of	of	ADP
ejpam-2552	71	47	ξ	ξ	NOUN
ejpam-2552	71	48	;	;	PUNCT
ejpam-2552	71	49	c	c	X
ejpam-2552	71	50	)	)	PUNCT
ejpam-2552	71	51	limn→∞e(an)x	limn→∞e(an)x	NOUN
ejpam-2552	71	52	=	=	SYM
ejpam-2552	71	53	0	0	NUM
ejpam-2552	71	54	,	,	PUNCT
ejpam-2552	71	55	for	for	ADP
ejpam-2552	71	56	any	any	DET
ejpam-2552	71	57	x	x	NOUN
ejpam-2552	71	58	of	of	ADP
ejpam-2552	71	59	h	h	NOUN
ejpam-2552	71	60	and	and	CCONJ
ejpam-2552	71	61	for	for	ADP
ejpam-2552	71	62	any	any	DET
ejpam-2552	71	63	sequence	sequence	NOUN
ejpam-2552	71	64	(	(	PUNCT
ejpam-2552	71	65	an)n∈n	an)n∈n	NUM
ejpam-2552	71	66	of	of	ADP
ejpam-2552	71	67	elements	element	NOUN
ejpam-2552	71	68	of	of	ADP
ejpam-2552	71	69	ξ	ξ	PROPN
ejpam-2552	71	70	which	which	PRON
ejpam-2552	71	71	decreasingly	decreasingly	ADV
ejpam-2552	71	72	converges	converge	VERB
ejpam-2552	71	73	to	to	ADP
ejpam-2552	71	74	∅.	∅.	VERB
ejpam-2552	71	75	then	then	ADV
ejpam-2552	71	76	we	we	PRON
ejpam-2552	71	77	easily	easily	ADV
ejpam-2552	71	78	check	check	VERB
ejpam-2552	71	79	the	the	DET
ejpam-2552	71	80	following	follow	VERB
ejpam-2552	71	81	properties	property	NOUN
ejpam-2552	71	82	.	.	PUNCT
ejpam-2552	72	1	a.	a.	NOUN
ejpam-2552	72	2	boudou	boudou	NOUN
ejpam-2552	72	3	,	,	PUNCT
ejpam-2552	72	4	s.	s.	PROPN
ejpam-2552	72	5	viguier	viguier	PROPN
ejpam-2552	72	6	-	-	PUNCT
ejpam-2552	72	7	pla	pla	PROPN
ejpam-2552	72	8	/	/	PUNCT
ejpam-2552	72	9	eur	eur	PROPN
ejpam-2552	72	10	.	.	PUNCT
ejpam-2552	73	1	j.	j.	PROPN
ejpam-2552	73	2	pure	pure	PROPN
ejpam-2552	73	3	appl	appl	PROPN
ejpam-2552	73	4	.	.	PROPN
ejpam-2552	73	5	math	math	PROPN
ejpam-2552	73	6	,	,	PUNCT
ejpam-2552	73	7	11	11	NUM
ejpam-2552	73	8	(	(	PUNCT
ejpam-2552	73	9	4	4	NUM
ejpam-2552	73	10	)	)	PUNCT
ejpam-2552	73	11	(	(	PUNCT
ejpam-2552	73	12	2018	2018	NUM
ejpam-2552	73	13	)	)	PUNCT
ejpam-2552	73	14	,	,	PUNCT
ejpam-2552	73	15	893	893	NUM
ejpam-2552	73	16	-	-	SYM
ejpam-2552	73	17	910	910	NUM
ejpam-2552	73	18	896	896	NUM
ejpam-2552	73	19	a	a	NOUN
ejpam-2552	73	20	)	)	PUNCT
ejpam-2552	73	21	for	for	ADP
ejpam-2552	73	22	any	any	DET
ejpam-2552	73	23	x	x	NOUN
ejpam-2552	73	24	of	of	ADP
ejpam-2552	73	25	h	h	NOUN
ejpam-2552	73	26	,	,	PUNCT
ejpam-2552	73	27	the	the	DET
ejpam-2552	73	28	application	application	NOUN
ejpam-2552	73	29	zxe	zxe	PROPN
ejpam-2552	73	30	:	:	PUNCT
ejpam-2552	73	31	a	a	DET
ejpam-2552	73	32	∈	∈	PROPN
ejpam-2552	73	33	ξ	ξ	PROPN
ejpam-2552	73	34	7→	7→	PROPN
ejpam-2552	73	35	e(a)x	e(a)x	PROPN
ejpam-2552	73	36	∈	∈	PROPN
ejpam-2552	73	37	h	h	NOUN
ejpam-2552	73	38	is	be	AUX
ejpam-2552	73	39	a	a	DET
ejpam-2552	73	40	r.m	r.m	PROPN
ejpam-2552	73	41	..	..	PROPN
ejpam-2552	73	42	b	b	X
ejpam-2552	73	43	)	)	PUNCT
ejpam-2552	73	44	if	if	SCONJ
ejpam-2552	73	45	f	f	PROPN
ejpam-2552	73	46	is	be	AUX
ejpam-2552	73	47	a	a	DET
ejpam-2552	73	48	measurable	measurable	ADJ
ejpam-2552	73	49	application	application	NOUN
ejpam-2552	73	50	from	from	ADP
ejpam-2552	73	51	e	e	NOUN
ejpam-2552	73	52	into	into	ADP
ejpam-2552	73	53	e′	e′	PROPN
ejpam-2552	73	54	,	,	PUNCT
ejpam-2552	73	55	the	the	DET
ejpam-2552	73	56	application	application	NOUN
ejpam-2552	73	57	f(e	f(e	NOUN
ejpam-2552	73	58	)	)	PUNCT
ejpam-2552	73	59	:	:	PUNCT
ejpam-2552	74	1	a′	a′	PROPN
ejpam-2552	74	2	∈	∈	PROPN
ejpam-2552	74	3	ξ′	ξ′	PROPN
ejpam-2552	74	4	7→	7→	NUM
ejpam-2552	74	5	e(f−1a′	e(f−1a′	NUM
ejpam-2552	74	6	)	)	PUNCT
ejpam-2552	74	7	∈	∈	PROPN
ejpam-2552	74	8	p(h	p(h	NOUN
ejpam-2552	74	9	)	)	PUNCT
ejpam-2552	74	10	is	be	AUX
ejpam-2552	74	11	a	a	DET
ejpam-2552	74	12	r.m	r.m	PROPN
ejpam-2552	74	13	.	.	PROPN
ejpam-2552	75	1	on	on	ADP
ejpam-2552	75	2	ξ′	ξ′	NOUN
ejpam-2552	75	3	for	for	ADP
ejpam-2552	75	4	h	h	PROPN
ejpam-2552	75	5	named	name	VERB
ejpam-2552	75	6	s.m	s.m	PROPN
ejpam-2552	75	7	.	.	PROPN
ejpam-2552	75	8	image	image	NOUN
ejpam-2552	75	9	of	of	ADP
ejpam-2552	75	10	e	e	NOUN
ejpam-2552	75	11	by	by	ADP
ejpam-2552	75	12	f	f	PROPN
ejpam-2552	75	13	.	.	PUNCT
ejpam-2552	76	1	for	for	ADP
ejpam-2552	76	2	any	any	DET
ejpam-2552	76	3	x	x	NOUN
ejpam-2552	76	4	of	of	ADP
ejpam-2552	76	5	h	h	NOUN
ejpam-2552	76	6	,	,	PUNCT
ejpam-2552	76	7	we	we	PRON
ejpam-2552	76	8	have	have	VERB
ejpam-2552	76	9	f(zxe	f(zxe	NOUN
ejpam-2552	76	10	)	)	PUNCT
ejpam-2552	77	1	=	=	PUNCT
ejpam-2552	77	2	zxf(e	zxf(e	PROPN
ejpam-2552	77	3	)	)	PUNCT
ejpam-2552	77	4	.	.	PUNCT
ejpam-2552	78	1	let	let	VERB
ejpam-2552	78	2	us	we	PRON
ejpam-2552	78	3	now	now	ADV
ejpam-2552	78	4	examine	examine	VERB
ejpam-2552	78	5	more	more	ADV
ejpam-2552	78	6	particularly	particularly	ADV
ejpam-2552	78	7	the	the	DET
ejpam-2552	78	8	s.m	s.m	PROPN
ejpam-2552	78	9	.	.	PROPN
ejpam-2552	78	10	’s	’s	X
ejpam-2552	78	11	on	on	ADP
ejpam-2552	78	12	br	br	PROPN
ejpam-2552	78	13	,	,	PUNCT
ejpam-2552	78	14	the	the	DET
ejpam-2552	78	15	borel	borel	PROPN
ejpam-2552	78	16	σ−field	σ−field	X
ejpam-2552	78	17	of	of	ADP
ejpam-2552	78	18	r	r	PROPN
ejpam-2552	78	19	,	,	PUNCT
ejpam-2552	78	20	for	for	ADP
ejpam-2552	78	21	h.	h.	PROPN
ejpam-2552	78	22	two	two	NUM
ejpam-2552	78	23	s.m	s.m	PROPN
ejpam-2552	78	24	.	.	PROPN
ejpam-2552	78	25	’s	’s	PROPN
ejpam-2552	78	26	e1	e1	PROPN
ejpam-2552	78	27	and	and	CCONJ
ejpam-2552	78	28	e2	e2	PROPN
ejpam-2552	78	29	,	,	PUNCT
ejpam-2552	78	30	on	on	ADP
ejpam-2552	78	31	br	br	NOUN
ejpam-2552	78	32	for	for	ADP
ejpam-2552	78	33	h	h	NOUN
ejpam-2552	78	34	,	,	PUNCT
ejpam-2552	78	35	commute	commute	VERB
ejpam-2552	78	36	when	when	SCONJ
ejpam-2552	78	37	,	,	PUNCT
ejpam-2552	78	38	for	for	ADP
ejpam-2552	78	39	any	any	DET
ejpam-2552	78	40	pair	pair	NOUN
ejpam-2552	78	41	(	(	PUNCT
ejpam-2552	78	42	a1	a1	NOUN
ejpam-2552	78	43	,	,	PUNCT
ejpam-2552	78	44	a2	a2	PROPN
ejpam-2552	78	45	)	)	PUNCT
ejpam-2552	78	46	of	of	ADP
ejpam-2552	78	47	elements	element	NOUN
ejpam-2552	78	48	of	of	ADP
ejpam-2552	78	49	br	br	NOUN
ejpam-2552	78	50	,	,	PUNCT
ejpam-2552	78	51	e1(a1	e1(a1	NUM
ejpam-2552	78	52	)	)	PUNCT
ejpam-2552	78	53	and	and	CCONJ
ejpam-2552	78	54	e2(a2	e2(a2	ADJ
ejpam-2552	78	55	)	)	PUNCT
ejpam-2552	78	56	commute	commute	NOUN
ejpam-2552	78	57	.	.	PUNCT
ejpam-2552	79	1	if	if	SCONJ
ejpam-2552	79	2	e1	e1	PROPN
ejpam-2552	79	3	and	and	CCONJ
ejpam-2552	79	4	e2	e2	PROPN
ejpam-2552	79	5	are	be	AUX
ejpam-2552	79	6	two	two	NUM
ejpam-2552	79	7	s.m	s.m	PROPN
ejpam-2552	79	8	.	.	PROPN
ejpam-2552	79	9	’s	’s	X
ejpam-2552	79	10	on	on	ADP
ejpam-2552	79	11	br	br	PROPN
ejpam-2552	79	12	for	for	ADP
ejpam-2552	79	13	h	h	NOUN
ejpam-2552	79	14	,	,	PUNCT
ejpam-2552	79	15	which	which	DET
ejpam-2552	79	16	commute	commute	NOUN
ejpam-2552	79	17	,	,	PUNCT
ejpam-2552	79	18	then	then	ADV
ejpam-2552	79	19	there	there	PRON
ejpam-2552	79	20	exists	exist	VERB
ejpam-2552	79	21	one	one	NUM
ejpam-2552	79	22	s.m	s.m	PROPN
ejpam-2552	79	23	.	.	PROPN
ejpam-2552	79	24	,	,	PUNCT
ejpam-2552	79	25	and	and	CCONJ
ejpam-2552	79	26	only	only	ADV
ejpam-2552	79	27	one	one	NUM
ejpam-2552	79	28	,	,	PUNCT
ejpam-2552	79	29	on	on	ADP
ejpam-2552	79	30	br⊗br	br⊗br	PROPN
ejpam-2552	79	31	for	for	ADP
ejpam-2552	79	32	h	h	NOUN
ejpam-2552	79	33	,	,	PUNCT
ejpam-2552	79	34	denoted	denote	VERB
ejpam-2552	79	35	e1⊗e2	e1⊗e2	NOUN
ejpam-2552	79	36	,	,	PUNCT
ejpam-2552	79	37	such	such	ADJ
ejpam-2552	79	38	that	that	SCONJ
ejpam-2552	79	39	e1⊗e2(a1×a2	e1⊗e2(a1×a2	NOUN
ejpam-2552	79	40	)	)	PUNCT
ejpam-2552	79	41	=	=	PUNCT
ejpam-2552	79	42	e1(a1)	e1(a1)	ADJ
ejpam-2552	79	43	◦	◦	NOUN
ejpam-2552	79	44	e2(a2	e2(a2	NOUN
ejpam-2552	79	45	)	)	PUNCT
ejpam-2552	79	46	,	,	PUNCT
ejpam-2552	79	47	for	for	ADP
ejpam-2552	79	48	any	any	DET
ejpam-2552	79	49	(	(	PUNCT
ejpam-2552	79	50	a1	a1	NOUN
ejpam-2552	79	51	,	,	PUNCT
ejpam-2552	79	52	a2	a2	PROPN
ejpam-2552	79	53	)	)	PUNCT
ejpam-2552	79	54	of	of	ADP
ejpam-2552	79	55	br	br	NUM
ejpam-2552	79	56	×	×	PROPN
ejpam-2552	79	57	br	br	NOUN
ejpam-2552	79	58	.	.	PUNCT
ejpam-2552	80	1	we	we	PRON
ejpam-2552	80	2	then	then	ADV
ejpam-2552	80	3	name	name	VERB
ejpam-2552	80	4	convolution	convolution	NOUN
ejpam-2552	80	5	product	product	NOUN
ejpam-2552	80	6	(	(	PUNCT
ejpam-2552	80	7	or	or	CCONJ
ejpam-2552	80	8	shortly	shortly	ADV
ejpam-2552	80	9	convolution	convolution	NOUN
ejpam-2552	80	10	)	)	PUNCT
ejpam-2552	80	11	of	of	ADP
ejpam-2552	80	12	e1	e1	PROPN
ejpam-2552	80	13	and	and	CCONJ
ejpam-2552	80	14	e2	e2	PROPN
ejpam-2552	80	15	,	,	PUNCT
ejpam-2552	80	16	and	and	CCONJ
ejpam-2552	80	17	we	we	PRON
ejpam-2552	80	18	denote	denote	VERB
ejpam-2552	80	19	it	it	PRON
ejpam-2552	80	20	e1	e1	VERB
ejpam-2552	80	21	∗	∗	NOUN
ejpam-2552	80	22	e2	e2	PROPN
ejpam-2552	80	23	,	,	PUNCT
ejpam-2552	80	24	the	the	DET
ejpam-2552	80	25	s.m	s.m	PROPN
ejpam-2552	80	26	.	.	PROPN
ejpam-2552	80	27	image	image	NOUN
ejpam-2552	80	28	of	of	ADP
ejpam-2552	80	29	e1⊗e2	e1⊗e2	NOUN
ejpam-2552	80	30	by	by	ADP
ejpam-2552	80	31	the	the	DET
ejpam-2552	80	32	measurable	measurable	ADJ
ejpam-2552	80	33	application	application	NOUN
ejpam-2552	80	34	s	s	VERB
ejpam-2552	80	35	:	:	PUNCT
ejpam-2552	80	36	(	(	PUNCT
ejpam-2552	80	37	λ1	λ1	ADJ
ejpam-2552	80	38	,	,	PUNCT
ejpam-2552	80	39	λ2	λ2	NOUN
ejpam-2552	80	40	)	)	PUNCT
ejpam-2552	80	41	∈	∈	PROPN
ejpam-2552	80	42	r×r	r×r	PROPN
ejpam-2552	80	43	7→	7→	PROPN
ejpam-2552	81	1	λ1	λ1	ADJ
ejpam-2552	81	2	+	+	CCONJ
ejpam-2552	81	3	λ2	λ2	NOUN
ejpam-2552	81	4	∈	∈	NOUN
ejpam-2552	81	5	r	r	NOUN
ejpam-2552	81	6	(	(	PUNCT
ejpam-2552	81	7	cf	cf	NOUN
ejpam-2552	81	8	.	.	PUNCT
ejpam-2552	82	1	[	[	X
ejpam-2552	82	2	1	1	NUM
ejpam-2552	82	3	]	]	PUNCT
ejpam-2552	82	4	)	)	PUNCT
ejpam-2552	82	5	.	.	PUNCT
ejpam-2552	83	1	this	this	DET
ejpam-2552	83	2	convolution	convolution	NOUN
ejpam-2552	83	3	has	have	AUX
ejpam-2552	83	4	got	get	VERB
ejpam-2552	83	5	an	an	DET
ejpam-2552	83	6	identity	identity	NOUN
ejpam-2552	83	7	element	element	NOUN
ejpam-2552	83	8	.	.	PUNCT
ejpam-2552	84	1	more	more	ADV
ejpam-2552	84	2	precisely	precisely	ADV
ejpam-2552	84	3	,	,	PUNCT
ejpam-2552	84	4	the	the	DET
ejpam-2552	84	5	application	application	NOUN
ejpam-2552	84	6	er	er	INTJ
ejpam-2552	84	7	:	:	PUNCT
ejpam-2552	84	8	a	a	DET
ejpam-2552	84	9	∈	∈	PROPN
ejpam-2552	84	10	br	br	X
ejpam-2552	84	11	7→	7→	NUM
ejpam-2552	84	12	δ0(a)ih	δ0(a)ih	VERB
ejpam-2552	84	13	∈	∈	PROPN
ejpam-2552	84	14	p(h	p(h	NOUN
ejpam-2552	84	15	)	)	PUNCT
ejpam-2552	84	16	is	be	AUX
ejpam-2552	84	17	a	a	DET
ejpam-2552	84	18	s.m	s.m	PROPN
ejpam-2552	84	19	.	.	PROPN
ejpam-2552	84	20	which	which	PRON
ejpam-2552	84	21	commutes	commute	VERB
ejpam-2552	84	22	with	with	ADP
ejpam-2552	84	23	any	any	DET
ejpam-2552	84	24	s.m	s.m	PROPN
ejpam-2552	84	25	.	.	PUNCT
ejpam-2552	84	26	e	e	PROPN
ejpam-2552	84	27	,	,	PUNCT
ejpam-2552	84	28	on	on	ADP
ejpam-2552	84	29	br	br	NOUN
ejpam-2552	84	30	for	for	ADP
ejpam-2552	84	31	h.	h.	PROPN
ejpam-2552	84	32	moreover	moreover	ADV
ejpam-2552	84	33	,	,	PUNCT
ejpam-2552	84	34	e	e	NOUN
ejpam-2552	84	35	∗	∗	NOUN
ejpam-2552	84	36	er	er	INTJ
ejpam-2552	84	37	=	=	SYM
ejpam-2552	84	38	e	e	PROPN
ejpam-2552	84	39	.	.	PUNCT
ejpam-2552	85	1	when	when	SCONJ
ejpam-2552	85	2	one	one	NUM
ejpam-2552	85	3	of	of	ADP
ejpam-2552	85	4	the	the	DET
ejpam-2552	85	5	elements	element	NOUN
ejpam-2552	85	6	of	of	ADP
ejpam-2552	85	7	the	the	DET
ejpam-2552	85	8	product	product	NOUN
ejpam-2552	85	9	e1	e1	PROPN
ejpam-2552	85	10	∗	∗	NOUN
ejpam-2552	85	11	e2	e2	PROPN
ejpam-2552	85	12	is	be	AUX
ejpam-2552	85	13	concentrated	concentrate	VERB
ejpam-2552	85	14	on	on	ADP
ejpam-2552	85	15	a	a	DET
ejpam-2552	85	16	countable	countable	ADJ
ejpam-2552	85	17	family	family	NOUN
ejpam-2552	85	18	of	of	ADP
ejpam-2552	85	19	reals	real	NOUN
ejpam-2552	85	20	λ	λ	PROPN
ejpam-2552	85	21	=	=	PRON
ejpam-2552	85	22	{	{	PUNCT
ejpam-2552	85	23	λj	λj	X
ejpam-2552	85	24	;	;	PUNCT
ejpam-2552	85	25	j	j	PROPN
ejpam-2552	85	26	∈	∈	PROPN
ejpam-2552	85	27	n	n	CCONJ
ejpam-2552	85	28	}	}	PUNCT
ejpam-2552	85	29	,	,	PUNCT
ejpam-2552	85	30	we	we	PRON
ejpam-2552	85	31	get	get	VERB
ejpam-2552	85	32	a	a	DET
ejpam-2552	85	33	result	result	NOUN
ejpam-2552	85	34	which	which	PRON
ejpam-2552	85	35	seems	seem	VERB
ejpam-2552	85	36	natural	natural	ADJ
ejpam-2552	85	37	for	for	ADP
ejpam-2552	85	38	a	a	DET
ejpam-2552	85	39	convolution	convolution	NOUN
ejpam-2552	85	40	.	.	PUNCT
ejpam-2552	86	1	if	if	SCONJ
ejpam-2552	86	2	e1	e1	NOUN
ejpam-2552	86	3	is	be	AUX
ejpam-2552	86	4	a	a	DET
ejpam-2552	86	5	s.m	s.m	PROPN
ejpam-2552	86	6	.	.	PROPN
ejpam-2552	86	7	,	,	PUNCT
ejpam-2552	86	8	on	on	ADP
ejpam-2552	86	9	br	br	NOUN
ejpam-2552	86	10	for	for	ADP
ejpam-2552	86	11	h	h	NOUN
ejpam-2552	86	12	,	,	PUNCT
ejpam-2552	86	13	such	such	ADJ
ejpam-2552	86	14	that	that	PRON
ejpam-2552	86	15	e1(λ	e1(λ	PROPN
ejpam-2552	86	16	)	)	PUNCT
ejpam-2552	86	17	=	=	SYM
ejpam-2552	86	18	ih	ih	NOUN
ejpam-2552	86	19	,	,	PUNCT
ejpam-2552	86	20	and	and	CCONJ
ejpam-2552	86	21	which	which	PRON
ejpam-2552	86	22	commutes	commute	VERB
ejpam-2552	86	23	with	with	ADP
ejpam-2552	86	24	a	a	DET
ejpam-2552	86	25	second	second	ADJ
ejpam-2552	86	26	s.m	s.m	PROPN
ejpam-2552	86	27	.	.	PUNCT
ejpam-2552	86	28	e2	e2	PROPN
ejpam-2552	86	29	,	,	PUNCT
ejpam-2552	86	30	on	on	ADP
ejpam-2552	86	31	br	br	NOUN
ejpam-2552	86	32	for	for	ADP
ejpam-2552	86	33	h	h	NOUN
ejpam-2552	86	34	,	,	PUNCT
ejpam-2552	86	35	then	then	ADV
ejpam-2552	86	36	,	,	PUNCT
ejpam-2552	86	37	for	for	ADP
ejpam-2552	86	38	any	any	DET
ejpam-2552	86	39	a	a	PRON
ejpam-2552	86	40	of	of	ADP
ejpam-2552	86	41	br	br	NOUN
ejpam-2552	86	42	,	,	PUNCT
ejpam-2552	86	43	the	the	DET
ejpam-2552	86	44	set	set	NOUN
ejpam-2552	86	45	{	{	PUNCT
ejpam-2552	86	46	e1({λj	e1({λj	NOUN
ejpam-2552	86	47	}	}	PUNCT
ejpam-2552	86	48	)	)	PUNCT
ejpam-2552	87	1	◦	◦	NOUN
ejpam-2552	87	2	e2(a−	e2(a−	NUM
ejpam-2552	87	3	λj	λj	PROPN
ejpam-2552	87	4	)	)	PUNCT
ejpam-2552	87	5	;	;	PUNCT
ejpam-2552	87	6	j	j	PROPN
ejpam-2552	87	7	∈	∈	PROPN
ejpam-2552	87	8	n	n	CCONJ
ejpam-2552	87	9	}	}	PUNCT
ejpam-2552	87	10	,	,	PUNCT
ejpam-2552	87	11	is	be	AUX
ejpam-2552	87	12	an	an	DET
ejpam-2552	87	13	orthogonal	orthogonal	ADJ
ejpam-2552	87	14	family	family	NOUN
ejpam-2552	87	15	of	of	ADP
ejpam-2552	87	16	projectors	projector	NOUN
ejpam-2552	87	17	which	which	DET
ejpam-2552	87	18	sum	sum	NOUN
ejpam-2552	87	19	equals	equal	VERB
ejpam-2552	87	20	(	(	PUNCT
ejpam-2552	87	21	e1	e1	NOUN
ejpam-2552	87	22	∗	∗	NOUN
ejpam-2552	87	23	e2)(a	e2)(a	NUM
ejpam-2552	87	24	)	)	PUNCT
ejpam-2552	87	25	.	.	PUNCT
ejpam-2552	88	1	let	let	VERB
ejpam-2552	88	2	us	we	PRON
ejpam-2552	88	3	end	end	VERB
ejpam-2552	88	4	these	these	PRON
ejpam-2552	88	5	recalls	recall	VERB
ejpam-2552	88	6	with	with	ADP
ejpam-2552	88	7	algebraic	algebraic	ADJ
ejpam-2552	88	8	properties	property	NOUN
ejpam-2552	88	9	of	of	ADP
ejpam-2552	88	10	the	the	DET
ejpam-2552	88	11	convolution	convolution	NOUN
ejpam-2552	88	12	.	.	PUNCT
ejpam-2552	89	1	if	if	SCONJ
ejpam-2552	89	2	e	e	PROPN
ejpam-2552	89	3	is	be	AUX
ejpam-2552	89	4	a	a	DET
ejpam-2552	89	5	s.m	s.m	PROPN
ejpam-2552	89	6	.	.	PROPN
ejpam-2552	90	1	on	on	ADP
ejpam-2552	90	2	br	br	PROPN
ejpam-2552	90	3	for	for	ADP
ejpam-2552	90	4	h	h	NOUN
ejpam-2552	90	5	,	,	PUNCT
ejpam-2552	90	6	if	if	SCONJ
ejpam-2552	90	7	f1	f1	PROPN
ejpam-2552	90	8	and	and	CCONJ
ejpam-2552	90	9	f2	f2	PROPN
ejpam-2552	90	10	are	be	AUX
ejpam-2552	90	11	two	two	NUM
ejpam-2552	90	12	measurable	measurable	ADJ
ejpam-2552	90	13	applications	application	NOUN
ejpam-2552	90	14	from	from	ADP
ejpam-2552	90	15	r	r	NOUN
ejpam-2552	90	16	into	into	ADP
ejpam-2552	90	17	itself	itself	PRON
ejpam-2552	90	18	,	,	PUNCT
ejpam-2552	90	19	then	then	ADV
ejpam-2552	90	20	the	the	DET
ejpam-2552	90	21	s.m	s.m	PROPN
ejpam-2552	90	22	.	.	PROPN
ejpam-2552	90	23	’s	’s	PART
ejpam-2552	90	24	f1(e	f1(e	NOUN
ejpam-2552	90	25	)	)	PUNCT
ejpam-2552	90	26	and	and	CCONJ
ejpam-2552	90	27	f2(e	f2(e	NOUN
ejpam-2552	90	28	)	)	PUNCT
ejpam-2552	90	29	commute	commute	NOUN
ejpam-2552	90	30	and	and	CCONJ
ejpam-2552	90	31	(	(	PUNCT
ejpam-2552	90	32	f1	f1	PROPN
ejpam-2552	90	33	+	+	CCONJ
ejpam-2552	90	34	f2)(e	f2)(e	PROPN
ejpam-2552	90	35	)	)	PUNCT
ejpam-2552	90	36	=	=	PUNCT
ejpam-2552	90	37	(	(	PUNCT
ejpam-2552	90	38	f1(e	f1(e	ADJ
ejpam-2552	90	39	)	)	PUNCT
ejpam-2552	90	40	)	)	PUNCT
ejpam-2552	90	41	∗	∗	NOUN
ejpam-2552	90	42	(	(	PUNCT
ejpam-2552	90	43	f2(e	f2(e	NOUN
ejpam-2552	90	44	)	)	PUNCT
ejpam-2552	90	45	)	)	PUNCT
ejpam-2552	90	46	.	.	PUNCT
ejpam-2552	91	1	if	if	SCONJ
ejpam-2552	91	2	we	we	PRON
ejpam-2552	91	3	denote	denote	VERB
ejpam-2552	91	4	by	by	ADP
ejpam-2552	91	5	w	w	PROPN
ejpam-2552	91	6	the	the	DET
ejpam-2552	91	7	measurable	measurable	ADJ
ejpam-2552	91	8	application	application	NOUN
ejpam-2552	91	9	x	x	PUNCT
ejpam-2552	91	10	∈	∈	NOUN
ejpam-2552	91	11	r	r	NOUN
ejpam-2552	91	12	7→	7→	NUM
ejpam-2552	91	13	−x	−x	NOUN
ejpam-2552	91	14	∈	∈	NOUN
ejpam-2552	91	15	r	r	NOUN
ejpam-2552	91	16	,	,	PUNCT
ejpam-2552	91	17	then	then	ADV
ejpam-2552	91	18	,	,	PUNCT
ejpam-2552	91	19	taking	take	VERB
ejpam-2552	91	20	into	into	ADP
ejpam-2552	91	21	account	account	NOUN
ejpam-2552	91	22	the	the	DET
ejpam-2552	91	23	previous	previous	ADJ
ejpam-2552	91	24	results	result	NOUN
ejpam-2552	91	25	,	,	PUNCT
ejpam-2552	91	26	for	for	ADP
ejpam-2552	91	27	any	any	DET
ejpam-2552	91	28	s.m	s.m	PROPN
ejpam-2552	91	29	.	.	PUNCT
ejpam-2552	92	1	e	e	X
ejpam-2552	92	2	on	on	ADP
ejpam-2552	92	3	br	br	PROPN
ejpam-2552	92	4	for	for	ADP
ejpam-2552	92	5	h	h	NOUN
ejpam-2552	92	6	,	,	PUNCT
ejpam-2552	92	7	we	we	PRON
ejpam-2552	92	8	can	can	AUX
ejpam-2552	92	9	write	write	VERB
ejpam-2552	92	10	e	e	NOUN
ejpam-2552	92	11	∗	∗	NOUN
ejpam-2552	92	12	(	(	PUNCT
ejpam-2552	92	13	w(e	w(e	PROPN
ejpam-2552	92	14	)	)	PUNCT
ejpam-2552	92	15	)	)	PUNCT
ejpam-2552	93	1	=	=	PRON
ejpam-2552	93	2	(	(	PUNCT
ejpam-2552	93	3	ir	ir	X
ejpam-2552	93	4	+	+	CCONJ
ejpam-2552	93	5	w)(e	w)(e	NOUN
ejpam-2552	93	6	)	)	PUNCT
ejpam-2552	94	1	=	=	SYM
ejpam-2552	94	2	o	o	X
ejpam-2552	94	3	(	(	PUNCT
ejpam-2552	94	4	e	e	NOUN
ejpam-2552	94	5	)	)	PUNCT
ejpam-2552	94	6	=	=	SYM
ejpam-2552	95	1	er	er	INTJ
ejpam-2552	95	2	.	.	PUNCT
ejpam-2552	96	1	this	this	PRON
ejpam-2552	96	2	means	mean	VERB
ejpam-2552	96	3	that	that	SCONJ
ejpam-2552	96	4	any	any	DET
ejpam-2552	96	5	s.m	s.m	PROPN
ejpam-2552	96	6	.	.	PUNCT
ejpam-2552	96	7	e	e	PROPN
ejpam-2552	96	8	has	have	AUX
ejpam-2552	96	9	got	get	VERB
ejpam-2552	96	10	its	its	PRON
ejpam-2552	96	11	symmetric	symmetric	NOUN
ejpam-2552	96	12	,	,	PUNCT
ejpam-2552	96	13	the	the	DET
ejpam-2552	96	14	s.m	s.m	PROPN
ejpam-2552	96	15	.	.	PROPN
ejpam-2552	96	16	w(e	w(e	PROPN
ejpam-2552	96	17	)	)	PUNCT
ejpam-2552	96	18	,	,	PUNCT
ejpam-2552	96	19	for	for	ADP
ejpam-2552	96	20	the	the	DET
ejpam-2552	96	21	convolution	convolution	NOUN
ejpam-2552	96	22	.	.	PUNCT
ejpam-2552	97	1	when	when	SCONJ
ejpam-2552	97	2	it	it	PRON
ejpam-2552	97	3	exists	exist	VERB
ejpam-2552	97	4	,	,	PUNCT
ejpam-2552	97	5	the	the	DET
ejpam-2552	97	6	convolution	convolution	NOUN
ejpam-2552	97	7	is	be	AUX
ejpam-2552	97	8	associative	associative	ADJ
ejpam-2552	97	9	.	.	PUNCT
ejpam-2552	98	1	finally	finally	ADV
ejpam-2552	98	2	,	,	PUNCT
ejpam-2552	98	3	if	if	SCONJ
ejpam-2552	98	4	e1	e1	PROPN
ejpam-2552	98	5	and	and	CCONJ
ejpam-2552	98	6	e2	e2	PROPN
ejpam-2552	98	7	commute	commute	NOUN
ejpam-2552	98	8	,	,	PUNCT
ejpam-2552	98	9	then	then	ADV
ejpam-2552	98	10	the	the	DET
ejpam-2552	98	11	s.m	s.m	PROPN
ejpam-2552	98	12	.	.	PROPN
ejpam-2552	98	13	’s	’s	PROPN
ejpam-2552	98	14	e1	e1	PROPN
ejpam-2552	98	15	and	and	CCONJ
ejpam-2552	98	16	e1	e1	PROPN
ejpam-2552	98	17	∗	∗	PROPN
ejpam-2552	98	18	e2	e2	PROPN
ejpam-2552	98	19	also	also	ADV
ejpam-2552	98	20	commute	commute	VERB
ejpam-2552	98	21	.	.	PUNCT
ejpam-2552	99	1	2.4	2.4	NUM
ejpam-2552	99	2	.	.	PUNCT
ejpam-2552	100	1	the	the	DET
ejpam-2552	100	2	space	space	NOUN
ejpam-2552	100	3	m(e	m(e	PROPN
ejpam-2552	100	4	,	,	PUNCT
ejpam-2552	100	5	e	e	NOUN
ejpam-2552	100	6	)	)	PUNCT
ejpam-2552	100	7	let	let	VERB
ejpam-2552	100	8	e	e	PRON
ejpam-2552	100	9	be	be	AUX
ejpam-2552	100	10	a	a	DET
ejpam-2552	100	11	s.m	s.m	PROPN
ejpam-2552	100	12	.	.	PROPN
ejpam-2552	101	1	on	on	ADP
ejpam-2552	101	2	ξ	ξ	PROPN
ejpam-2552	101	3	,	,	PUNCT
ejpam-2552	101	4	σ−field	σ−field	X
ejpam-2552	101	5	of	of	ADP
ejpam-2552	101	6	subsets	subset	NOUN
ejpam-2552	101	7	of	of	ADP
ejpam-2552	101	8	a	a	DET
ejpam-2552	101	9	set	set	NOUN
ejpam-2552	101	10	e	e	NOUN
ejpam-2552	101	11	,	,	PUNCT
ejpam-2552	101	12	for	for	SCONJ
ejpam-2552	101	13	h.	h.	PROPN
ejpam-2552	101	14	m(e	m(e	PROPN
ejpam-2552	101	15	,	,	PUNCT
ejpam-2552	101	16	e	e	NOUN
ejpam-2552	101	17	)	)	PUNCT
ejpam-2552	101	18	is	be	AUX
ejpam-2552	101	19	the	the	DET
ejpam-2552	101	20	set	set	NOUN
ejpam-2552	101	21	of	of	ADP
ejpam-2552	101	22	the	the	DET
ejpam-2552	101	23	measurable	measurable	ADJ
ejpam-2552	101	24	applications	application	NOUN
ejpam-2552	101	25	ϕ	ϕ	PROPN
ejpam-2552	101	26	,	,	PUNCT
ejpam-2552	101	27	from	from	ADP
ejpam-2552	101	28	e	e	NOUN
ejpam-2552	101	29	into	into	ADP
ejpam-2552	101	30	c	c	PROPN
ejpam-2552	101	31	,	,	PUNCT
ejpam-2552	102	1	such	such	ADJ
ejpam-2552	102	2	that	that	SCONJ
ejpam-2552	102	3	a	a	X
ejpam-2552	102	4	)	)	PUNCT
ejpam-2552	102	5	∫	∫	PROPN
ejpam-2552	103	1	|ϕ|2dµzxe	|ϕ|2dµzxe	PROPN
ejpam-2552	103	2	<	<	X
ejpam-2552	104	1	+	+	PROPN
ejpam-2552	104	2	∞	∞	PROPN
ejpam-2552	104	3	,	,	PUNCT
ejpam-2552	104	4	for	for	ADP
ejpam-2552	104	5	any	any	DET
ejpam-2552	104	6	x	x	NOUN
ejpam-2552	104	7	of	of	ADP
ejpam-2552	104	8	h	h	NOUN
ejpam-2552	104	9	;	;	PUNCT
ejpam-2552	104	10	b	b	X
ejpam-2552	104	11	)	)	PUNCT
ejpam-2552	104	12	the	the	DET
ejpam-2552	104	13	set	set	NOUN
ejpam-2552	104	14	of	of	ADP
ejpam-2552	104	15	the	the	DET
ejpam-2552	104	16	reals	real	NOUN
ejpam-2552	104	17	{	{	PUNCT
ejpam-2552	104	18	∫	∫	PROPN
ejpam-2552	104	19	|ϕ|2dµzxe	|ϕ|2dµzxe	PROPN
ejpam-2552	104	20	;	;	PUNCT
ejpam-2552	104	21	‖x‖	‖x‖	PROPN
ejpam-2552	104	22	=	=	SYM
ejpam-2552	104	23	1	1	X
ejpam-2552	104	24	}	}	PUNCT
ejpam-2552	104	25	is	be	AUX
ejpam-2552	104	26	bounded	bound	VERB
ejpam-2552	104	27	.	.	PUNCT
ejpam-2552	105	1	then	then	ADV
ejpam-2552	105	2	,	,	PUNCT
ejpam-2552	105	3	when	when	SCONJ
ejpam-2552	105	4	ϕ	ϕ	NOUN
ejpam-2552	105	5	is	be	AUX
ejpam-2552	105	6	an	an	DET
ejpam-2552	105	7	element	element	NOUN
ejpam-2552	105	8	of	of	ADP
ejpam-2552	105	9	m(e	m(e	PROPN
ejpam-2552	105	10	,	,	PUNCT
ejpam-2552	105	11	e	e	NOUN
ejpam-2552	105	12	)	)	PUNCT
ejpam-2552	105	13	,	,	PUNCT
ejpam-2552	105	14	we	we	PRON
ejpam-2552	105	15	can	can	AUX
ejpam-2552	105	16	consider	consider	VERB
ejpam-2552	105	17	the	the	DET
ejpam-2552	105	18	application	application	NOUN
ejpam-2552	105	19	eϕ	eϕ	PRON
ejpam-2552	105	20	:	:	PUNCT
ejpam-2552	105	21	x	x	PUNCT
ejpam-2552	105	22	∈	∈	NOUN
ejpam-2552	105	23	h	h	NOUN
ejpam-2552	105	24	7→	7→	NUM
ejpam-2552	105	25	∫	∫	NOUN
ejpam-2552	105	26	ϕdzxe	ϕdzxe	PROPN
ejpam-2552	105	27	∈	∈	PROPN
ejpam-2552	105	28	h	h	NOUN
ejpam-2552	105	29	,	,	PUNCT
ejpam-2552	105	30	and	and	CCONJ
ejpam-2552	105	31	we	we	PRON
ejpam-2552	105	32	have	have	VERB
ejpam-2552	105	33	the	the	DET
ejpam-2552	105	34	following	follow	VERB
ejpam-2552	105	35	property	property	NOUN
ejpam-2552	105	36	.	.	PUNCT
ejpam-2552	106	1	proposition	proposition	NOUN
ejpam-2552	106	2	2.4.1	2.4.1	NUM
ejpam-2552	106	3	.	.	PUNCT
ejpam-2552	107	1	for	for	ADP
ejpam-2552	107	2	any	any	DET
ejpam-2552	107	3	ϕ	ϕ	NOUN
ejpam-2552	107	4	ofm(e	ofm(e	NOUN
ejpam-2552	107	5	,	,	PUNCT
ejpam-2552	107	6	e	e	NOUN
ejpam-2552	107	7	)	)	PUNCT
ejpam-2552	107	8	,	,	PUNCT
ejpam-2552	107	9	the	the	DET
ejpam-2552	107	10	application	application	NOUN
ejpam-2552	107	11	eϕ	eϕ	PROPN
ejpam-2552	107	12	is	be	AUX
ejpam-2552	107	13	linear	linear	ADJ
ejpam-2552	107	14	and	and	CCONJ
ejpam-2552	107	15	bounded	bound	VERB
ejpam-2552	107	16	.	.	PUNCT
ejpam-2552	107	17	a.	a.	PROPN
ejpam-2552	107	18	boudou	boudou	PROPN
ejpam-2552	107	19	,	,	PUNCT
ejpam-2552	107	20	s.	s.	PROPN
ejpam-2552	107	21	viguier	viguier	PROPN
ejpam-2552	107	22	-	-	PUNCT
ejpam-2552	107	23	pla	pla	PROPN
ejpam-2552	107	24	/	/	PUNCT
ejpam-2552	107	25	eur	eur	PROPN
ejpam-2552	107	26	.	.	PUNCT
ejpam-2552	108	1	j.	j.	PROPN
ejpam-2552	108	2	pure	pure	PROPN
ejpam-2552	108	3	appl	appl	PROPN
ejpam-2552	108	4	.	.	PROPN
ejpam-2552	108	5	math	math	PROPN
ejpam-2552	108	6	,	,	PUNCT
ejpam-2552	108	7	11	11	NUM
ejpam-2552	108	8	(	(	PUNCT
ejpam-2552	108	9	4	4	NUM
ejpam-2552	108	10	)	)	PUNCT
ejpam-2552	108	11	(	(	PUNCT
ejpam-2552	108	12	2018	2018	NUM
ejpam-2552	108	13	)	)	PUNCT
ejpam-2552	108	14	,	,	PUNCT
ejpam-2552	108	15	893	893	NUM
ejpam-2552	108	16	-	-	SYM
ejpam-2552	108	17	910	910	NUM
ejpam-2552	108	18	897	897	NUM
ejpam-2552	108	19	proof	proof	NOUN
ejpam-2552	108	20	.	.	PUNCT
ejpam-2552	109	1	if	if	SCONJ
ejpam-2552	109	2	ϕ	ϕ	NOUN
ejpam-2552	109	3	is	be	AUX
ejpam-2552	109	4	an	an	DET
ejpam-2552	109	5	element	element	NOUN
ejpam-2552	109	6	of	of	ADP
ejpam-2552	109	7	m(e	m(e	PROPN
ejpam-2552	109	8	,	,	PUNCT
ejpam-2552	109	9	e	e	NOUN
ejpam-2552	109	10	)	)	PUNCT
ejpam-2552	109	11	,	,	PUNCT
ejpam-2552	109	12	then	then	ADV
ejpam-2552	109	13	,	,	PUNCT
ejpam-2552	109	14	for	for	ADP
ejpam-2552	109	15	any	any	DET
ejpam-2552	109	16	(	(	PUNCT
ejpam-2552	109	17	λ	λ	PROPN
ejpam-2552	109	18	,	,	PUNCT
ejpam-2552	109	19	λ′	λ′	PROPN
ejpam-2552	109	20	,	,	PUNCT
ejpam-2552	109	21	x	x	X
ejpam-2552	109	22	,	,	PUNCT
ejpam-2552	109	23	x	x	NOUN
ejpam-2552	109	24	′	′	NUM
ejpam-2552	109	25	)	)	PUNCT
ejpam-2552	109	26	of	of	ADP
ejpam-2552	109	27	c×	c×	PROPN
ejpam-2552	109	28	c×h	c×h	PROPN
ejpam-2552	109	29	×h	×h	PROPN
ejpam-2552	109	30	,	,	PUNCT
ejpam-2552	109	31	it	it	PRON
ejpam-2552	109	32	belongs	belong	VERB
ejpam-2552	109	33	to	to	ADP
ejpam-2552	109	34	l2(µ	l2(µ	PROPN
ejpam-2552	109	35	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	109	36	e	e	PROPN
ejpam-2552	109	37	+	+	CCONJ
ejpam-2552	109	38	µzxe	µzxe	PROPN
ejpam-2552	109	39	+	+	CCONJ
ejpam-2552	109	40	µ	µ	X
ejpam-2552	109	41	zx	zx	NOUN
ejpam-2552	109	42	′	′	NUM
ejpam-2552	109	43	e	e	NOUN
ejpam-2552	109	44	)	)	PUNCT
ejpam-2552	109	45	(	(	PUNCT
ejpam-2552	109	46	because	because	SCONJ
ejpam-2552	109	47	∫	∫	PROPN
ejpam-2552	109	48	|ϕ|2d(µ	|ϕ|2d(µ	PROPN
ejpam-2552	109	49	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	109	50	e	e	PROPN
ejpam-2552	109	51	+	+	CCONJ
ejpam-2552	109	52	µzxe	µzxe	PROPN
ejpam-2552	109	53	+	+	CCONJ
ejpam-2552	109	54	µ	µ	X
ejpam-2552	109	55	zx	zx	NOUN
ejpam-2552	109	56	′	′	NUM
ejpam-2552	109	57	e	e	NOUN
ejpam-2552	109	58	)	)	PUNCT
ejpam-2552	110	1	=	=	NOUN
ejpam-2552	110	2	∫	∫	PROPN
ejpam-2552	110	3	|ϕ|2dµ	|ϕ|2dµ	PROPN
ejpam-2552	110	4	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	110	5	e	e	PROPN
ejpam-2552	111	1	+	+	CCONJ
ejpam-2552	111	2	∫	∫	PROPN
ejpam-2552	111	3	|ϕ|2dµzxe	|ϕ|2dµzxe	PROPN
ejpam-2552	111	4	+	+	CCONJ
ejpam-2552	111	5	∫	∫	PROPN
ejpam-2552	111	6	|ϕ|2dµ	|ϕ|2dµ	NOUN
ejpam-2552	111	7	zx	zx	PROPN
ejpam-2552	111	8	′	′	NUM
ejpam-2552	111	9	e	e	NOUN
ejpam-2552	111	10	)	)	PUNCT
ejpam-2552	111	11	.	.	PUNCT
ejpam-2552	112	1	taking	take	VERB
ejpam-2552	112	2	into	into	ADP
ejpam-2552	112	3	account	account	NOUN
ejpam-2552	112	4	the	the	DET
ejpam-2552	112	5	properties	property	NOUN
ejpam-2552	112	6	of	of	ADP
ejpam-2552	112	7	density	density	NOUN
ejpam-2552	112	8	of	of	ADP
ejpam-2552	112	9	the	the	DET
ejpam-2552	112	10	indicator	indicator	NOUN
ejpam-2552	112	11	functions	function	NOUN
ejpam-2552	112	12	,	,	PUNCT
ejpam-2552	112	13	ϕ	ϕ	PROPN
ejpam-2552	112	14	can	can	AUX
ejpam-2552	112	15	be	be	AUX
ejpam-2552	112	16	writen	writen	VERB
ejpam-2552	112	17	as	as	SCONJ
ejpam-2552	112	18	follows	follow	VERB
ejpam-2552	112	19	.	.	PUNCT
ejpam-2552	113	1	ϕ	ϕ	X
ejpam-2552	113	2	=	=	SYM
ejpam-2552	113	3	limn→∞	limn→∞	X
ejpam-2552	113	4	∑	∑	PUNCT
ejpam-2552	113	5	j∈jn	j∈jn	PROPN
ejpam-2552	113	6	αn	αn	VERB
ejpam-2552	113	7	,	,	PUNCT
ejpam-2552	113	8	j1bn	j1bn	PROPN
ejpam-2552	113	9	,	,	PUNCT
ejpam-2552	113	10	j	j	PROPN
ejpam-2552	113	11	,	,	PUNCT
ejpam-2552	113	12	|jn|	|jn|	PROPN
ejpam-2552	113	13	<	<	X
ejpam-2552	113	14	+	+	NOUN
ejpam-2552	113	15	∞	∞	PROPN
ejpam-2552	113	16	,	,	PUNCT
ejpam-2552	113	17	bn	bn	NOUN
ejpam-2552	113	18	,	,	PUNCT
ejpam-2552	113	19	j	j	PROPN
ejpam-2552	113	20	∈	∈	PROPN
ejpam-2552	113	21	br	br	PROPN
ejpam-2552	113	22	,	,	PUNCT
ejpam-2552	113	23	in	in	ADP
ejpam-2552	113	24	l2(µ	l2(µ	PROPN
ejpam-2552	113	25	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	113	26	e	e	PROPN
ejpam-2552	113	27	+	+	CCONJ
ejpam-2552	113	28	µzxe	µzxe	PROPN
ejpam-2552	113	29	+	+	CCONJ
ejpam-2552	113	30	µ	µ	X
ejpam-2552	113	31	zx	zx	NOUN
ejpam-2552	113	32	′	′	NUM
ejpam-2552	113	33	e	e	NOUN
ejpam-2552	113	34	)	)	PUNCT
ejpam-2552	113	35	.	.	PUNCT
ejpam-2552	114	1	(	(	PUNCT
ejpam-2552	114	2	2.4.1	2.4.1	NUM
ejpam-2552	114	3	)	)	PUNCT
ejpam-2552	114	4	as	as	ADP
ejpam-2552	114	5	‖.‖2l2(µ	‖.‖2l2(µ	PUNCT
ejpam-2552	114	6	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	114	7	e	e	PROPN
ejpam-2552	114	8	+	+	PROPN
ejpam-2552	114	9	µ	µ	X
ejpam-2552	114	10	zxe	zxe	X
ejpam-2552	114	11	+	+	PROPN
ejpam-2552	114	12	µ	µ	X
ejpam-2552	114	13	zx	zx	NOUN
ejpam-2552	114	14	′	′	NUM
ejpam-2552	114	15	e	e	NOUN
ejpam-2552	114	16	)	)	PUNCT
ejpam-2552	114	17	=	=	SYM
ejpam-2552	114	18	‖.‖2l2(µ	‖.‖2l2(µ	PUNCT
ejpam-2552	114	19	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	114	20	e	e	X
ejpam-2552	114	21	)	)	PUNCT
ejpam-2552	115	1	+	+	PROPN
ejpam-2552	115	2	‖.‖2l2(µ	‖.‖2l2(µ	SYM
ejpam-2552	115	3	zxe	zxe	NOUN
ejpam-2552	115	4	)	)	PUNCT
ejpam-2552	116	1	+	+	PUNCT
ejpam-2552	116	2	‖.‖2l2(µ	‖.‖2l2(µ	SYM
ejpam-2552	116	3	zx	zx	NUM
ejpam-2552	116	4	′	′	NUM
ejpam-2552	116	5	e	e	NOUN
ejpam-2552	116	6	)	)	PUNCT
ejpam-2552	116	7	,	,	PUNCT
ejpam-2552	116	8	the	the	DET
ejpam-2552	116	9	equality	equality	NOUN
ejpam-2552	116	10	(	(	PUNCT
ejpam-2552	116	11	2.4.1	2.4.1	NUM
ejpam-2552	116	12	)	)	PUNCT
ejpam-2552	116	13	is	be	AUX
ejpam-2552	116	14	exact	exact	ADJ
ejpam-2552	116	15	in	in	ADP
ejpam-2552	116	16	l2(µ	l2(µ	PROPN
ejpam-2552	116	17	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	116	18	e	e	PROPN
ejpam-2552	116	19	)	)	PUNCT
ejpam-2552	116	20	,	,	PUNCT
ejpam-2552	116	21	l2(µzxe	l2(µzxe	PROPN
ejpam-2552	116	22	)	)	PUNCT
ejpam-2552	116	23	,	,	PUNCT
ejpam-2552	116	24	and	and	CCONJ
ejpam-2552	116	25	l2(µ	l2(µ	ADP
ejpam-2552	116	26	zx	zx	NUM
ejpam-2552	116	27	′	′	NUM
ejpam-2552	116	28	e	e	NOUN
ejpam-2552	116	29	)	)	PUNCT
ejpam-2552	116	30	.	.	PUNCT
ejpam-2552	117	1	integrating	integrate	VERB
ejpam-2552	117	2	it	it	PRON
ejpam-2552	117	3	successively	successively	ADV
ejpam-2552	117	4	with	with	ADP
ejpam-2552	117	5	respect	respect	NOUN
ejpam-2552	117	6	to	to	ADP
ejpam-2552	117	7	the	the	DET
ejpam-2552	117	8	r.m	r.m	PROPN
ejpam-2552	117	9	.	.	PROPN
ejpam-2552	117	10	’s	’s	PROPN
ejpam-2552	117	11	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	117	12	e	e	PROPN
ejpam-2552	117	13	,	,	PUNCT
ejpam-2552	117	14	zxe	zxe	PROPN
ejpam-2552	117	15	and	and	CCONJ
ejpam-2552	117	16	zx	zx	NUM
ejpam-2552	117	17	′	′	NUM
ejpam-2552	118	1	e	e	NOUN
ejpam-2552	118	2	,	,	PUNCT
ejpam-2552	118	3	we	we	PRON
ejpam-2552	118	4	have	have	AUX
ejpam-2552	118	5	:	:	PUNCT
ejpam-2552	118	6	eϕ(λx	eϕ(λx	NOUN
ejpam-2552	118	7	+	+	CCONJ
ejpam-2552	118	8	λ′x	λ′x	PROPN
ejpam-2552	118	9	′	′	NUM
ejpam-2552	118	10	)	)	PUNCT
ejpam-2552	119	1	=	=	SYM
ejpam-2552	119	2	limn→∞	limn→∞	ADJ
ejpam-2552	119	3	∑	∑	PUNCT
ejpam-2552	119	4	j∈jn	j∈jn	PROPN
ejpam-2552	119	5	αn	αn	NUM
ejpam-2552	119	6	,	,	PUNCT
ejpam-2552	119	7	jz	jz	PROPN
ejpam-2552	119	8	λx+λ′x′	λx+λ′x′	PROPN
ejpam-2552	119	9	e	e	X
ejpam-2552	119	10	(	(	PUNCT
ejpam-2552	119	11	bn	bn	PROPN
ejpam-2552	119	12	,	,	PUNCT
ejpam-2552	119	13	j	j	PROPN
ejpam-2552	119	14	)	)	PUNCT
ejpam-2552	119	15	,	,	PUNCT
ejpam-2552	119	16	eϕx	eϕx	NOUN
ejpam-2552	119	17	=	=	SYM
ejpam-2552	119	18	limn→∞	limn→∞	X
ejpam-2552	119	19	∑	∑	PUNCT
ejpam-2552	119	20	j∈jn	j∈jn	PROPN
ejpam-2552	119	21	αn	αn	NUM
ejpam-2552	119	22	,	,	PUNCT
ejpam-2552	119	23	jz	jz	PROPN
ejpam-2552	119	24	x	x	SYM
ejpam-2552	119	25	e	e	X
ejpam-2552	119	26	(	(	PUNCT
ejpam-2552	119	27	bn	bn	PROPN
ejpam-2552	119	28	,	,	PUNCT
ejpam-2552	119	29	j	j	PROPN
ejpam-2552	119	30	)	)	PUNCT
ejpam-2552	119	31	,	,	PUNCT
ejpam-2552	119	32	eϕx	eϕx	NOUN
ejpam-2552	119	33	′	′	NOUN
ejpam-2552	119	34	=	=	PUNCT
ejpam-2552	119	35	limn→∞	limn→∞	X
ejpam-2552	119	36	∑	∑	PUNCT
ejpam-2552	119	37	j∈jn	j∈jn	PROPN
ejpam-2552	119	38	αn	αn	NUM
ejpam-2552	119	39	,	,	PUNCT
ejpam-2552	119	40	jz	jz	PROPN
ejpam-2552	119	41	x′	x′	PROPN
ejpam-2552	119	42	e	e	X
ejpam-2552	119	43	(	(	PUNCT
ejpam-2552	119	44	bn	bn	PROPN
ejpam-2552	119	45	,	,	PUNCT
ejpam-2552	119	46	j	j	PROPN
ejpam-2552	119	47	)	)	PUNCT
ejpam-2552	119	48	.	.	PUNCT
ejpam-2552	120	1	then	then	ADV
ejpam-2552	120	2	the	the	DET
ejpam-2552	120	3	linearity	linearity	NOUN
ejpam-2552	120	4	comes	come	VERB
ejpam-2552	120	5	from	from	ADP
ejpam-2552	120	6	the	the	DET
ejpam-2552	120	7	fact	fact	NOUN
ejpam-2552	120	8	that	that	SCONJ
ejpam-2552	120	9	:	:	PUNCT
ejpam-2552	120	10	zλx+λ′x′	zλx+λ′x′	PROPN
ejpam-2552	120	11	e	e	X
ejpam-2552	120	12	(	(	PUNCT
ejpam-2552	120	13	bn	bn	PROPN
ejpam-2552	120	14	,	,	PUNCT
ejpam-2552	120	15	j	j	NOUN
ejpam-2552	120	16	)	)	PUNCT
ejpam-2552	120	17	=	=	SYM
ejpam-2552	120	18	e(bn	e(bn	NOUN
ejpam-2552	120	19	,	,	PUNCT
ejpam-2552	120	20	j)(λx	j)(λx	VERB
ejpam-2552	120	21	+	+	CCONJ
ejpam-2552	120	22	λ′x	λ′x	PROPN
ejpam-2552	120	23	′	′	NUM
ejpam-2552	120	24	)	)	PUNCT
ejpam-2552	121	1	=	=	PUNCT
ejpam-2552	121	2	λe(bn	λe(bn	PROPN
ejpam-2552	121	3	,	,	PUNCT
ejpam-2552	121	4	j)x	j)x	NOUN
ejpam-2552	122	1	+	+	CCONJ
ejpam-2552	122	2	λ′e(bn	λ′e(bn	PROPN
ejpam-2552	122	3	,	,	PUNCT
ejpam-2552	122	4	j)x	j)x	NOUN
ejpam-2552	122	5	′	′	NUM
ejpam-2552	123	1	=	=	PUNCT
ejpam-2552	123	2	λzxe	λzxe	NOUN
ejpam-2552	123	3	(	(	PUNCT
ejpam-2552	123	4	bn	bn	PROPN
ejpam-2552	123	5	,	,	PUNCT
ejpam-2552	123	6	j	j	NOUN
ejpam-2552	123	7	)	)	PUNCT
ejpam-2552	123	8	+	+	NUM
ejpam-2552	123	9	λ′zx	λ′zx	NOUN
ejpam-2552	123	10	′	′	NUM
ejpam-2552	124	1	e	e	NOUN
ejpam-2552	124	2	(	(	PUNCT
ejpam-2552	124	3	bn	bn	PROPN
ejpam-2552	124	4	,	,	PUNCT
ejpam-2552	124	5	j	j	PROPN
ejpam-2552	124	6	)	)	PUNCT
ejpam-2552	124	7	.	.	PUNCT
ejpam-2552	125	1	finally	finally	ADV
ejpam-2552	125	2	,	,	PUNCT
ejpam-2552	125	3	the	the	DET
ejpam-2552	125	4	continuity	continuity	NOUN
ejpam-2552	125	5	comes	come	VERB
ejpam-2552	125	6	from	from	ADP
ejpam-2552	125	7	the	the	DET
ejpam-2552	125	8	fact	fact	NOUN
ejpam-2552	125	9	that	that	SCONJ
ejpam-2552	125	10	,	,	PUNCT
ejpam-2552	125	11	for	for	ADP
ejpam-2552	125	12	any	any	DET
ejpam-2552	125	13	normed	normed	ADJ
ejpam-2552	125	14	element	element	NOUN
ejpam-2552	125	15	x	x	PUNCT
ejpam-2552	125	16	of	of	ADP
ejpam-2552	125	17	h	h	NOUN
ejpam-2552	125	18	:	:	PUNCT
ejpam-2552	125	19	‖eϕx‖2	‖eϕx‖2	PROPN
ejpam-2552	125	20	=	=	SYM
ejpam-2552	125	21	‖	‖	PROPN
ejpam-2552	125	22	∫	∫	PROPN
ejpam-2552	125	23	ϕdzxe	ϕdzxe	PROPN
ejpam-2552	125	24	‖2	‖2	NOUN
ejpam-2552	126	1	=	=	SYM
ejpam-2552	126	2	∫	∫	PROPN
ejpam-2552	126	3	|ϕ|2dµzxe	|ϕ|2dµzxe	PROPN
ejpam-2552	126	4	6	6	NUM
ejpam-2552	126	5	sup	sup	NOUN
ejpam-2552	126	6	{	{	PUNCT
ejpam-2552	126	7	∫	∫	PROPN
ejpam-2552	126	8	|ϕ|2dµzxe	|ϕ|2dµzxe	PROPN
ejpam-2552	126	9	;	;	PUNCT
ejpam-2552	126	10	‖x‖	‖x‖	PROPN
ejpam-2552	126	11	=	=	SYM
ejpam-2552	126	12	1	1	NUM
ejpam-2552	126	13	}	}	PUNCT
ejpam-2552	126	14	.	.	PUNCT
ejpam-2552	127	1	�	�	PROPN
ejpam-2552	127	2	now	now	ADV
ejpam-2552	127	3	it	it	PRON
ejpam-2552	127	4	is	be	AUX
ejpam-2552	127	5	clear	clear	ADJ
ejpam-2552	127	6	that	that	SCONJ
ejpam-2552	127	7	m(e	m(e	PROPN
ejpam-2552	127	8	,	,	PUNCT
ejpam-2552	127	9	e	e	NOUN
ejpam-2552	127	10	)	)	PUNCT
ejpam-2552	127	11	has	have	AUX
ejpam-2552	127	12	got	get	VERB
ejpam-2552	127	13	a	a	DET
ejpam-2552	127	14	vector	vector	NOUN
ejpam-2552	127	15	space	space	NOUN
ejpam-2552	127	16	structure	structure	NOUN
ejpam-2552	127	17	,	,	PUNCT
ejpam-2552	127	18	as	as	ADP
ejpam-2552	127	19	a	a	DET
ejpam-2552	127	20	subspace	subspace	NOUN
ejpam-2552	127	21	of	of	ADP
ejpam-2552	127	22	the	the	DET
ejpam-2552	127	23	vector	vector	NOUN
ejpam-2552	127	24	space	space	NOUN
ejpam-2552	127	25	of	of	ADP
ejpam-2552	127	26	the	the	DET
ejpam-2552	127	27	measurable	measurable	ADJ
ejpam-2552	127	28	applications	application	NOUN
ejpam-2552	127	29	from	from	ADP
ejpam-2552	127	30	e	e	NOUN
ejpam-2552	127	31	into	into	ADP
ejpam-2552	127	32	c.	c.	NOUN
ejpam-2552	127	33	from	from	ADP
ejpam-2552	127	34	the	the	DET
ejpam-2552	127	35	linearity	linearity	NOUN
ejpam-2552	127	36	of	of	ADP
ejpam-2552	127	37	the	the	DET
ejpam-2552	127	38	stochastic	stochastic	ADJ
ejpam-2552	127	39	integral	integral	ADJ
ejpam-2552	127	40	,	,	PUNCT
ejpam-2552	127	41	we	we	PRON
ejpam-2552	127	42	deduce	deduce	VERB
ejpam-2552	127	43	the	the	DET
ejpam-2552	127	44	following	follow	VERB
ejpam-2552	127	45	proposition	proposition	NOUN
ejpam-2552	127	46	.	.	PUNCT
ejpam-2552	128	1	proposition	proposition	NOUN
ejpam-2552	128	2	2.4.2	2.4.2	NUM
ejpam-2552	128	3	.	.	PUNCT
ejpam-2552	129	1	the	the	DET
ejpam-2552	129	2	application	application	NOUN
ejpam-2552	129	3	ϕ	ϕ	PROPN
ejpam-2552	129	4	∈m(e	∈m(e	PROPN
ejpam-2552	129	5	,	,	PUNCT
ejpam-2552	129	6	e	e	NOUN
ejpam-2552	129	7	)	)	PUNCT
ejpam-2552	129	8	7→	7→	NUM
ejpam-2552	129	9	eϕ	eϕ	NOUN
ejpam-2552	129	10	∈	∈	PROPN
ejpam-2552	129	11	l(h	l(h	PROPN
ejpam-2552	129	12	)	)	PUNCT
ejpam-2552	129	13	is	be	AUX
ejpam-2552	129	14	linear	linear	ADJ
ejpam-2552	129	15	.	.	PUNCT
ejpam-2552	130	1	let	let	VERB
ejpam-2552	130	2	us	we	PRON
ejpam-2552	130	3	now	now	ADV
ejpam-2552	130	4	approach	approach	VERB
ejpam-2552	130	5	a	a	DET
ejpam-2552	130	6	result	result	NOUN
ejpam-2552	130	7	close	close	ADV
ejpam-2552	130	8	to	to	ADP
ejpam-2552	130	9	the	the	DET
ejpam-2552	130	10	transfert	transfert	PROPN
ejpam-2552	130	11	theorem	theorem	PROPN
ejpam-2552	130	12	.	.	PUNCT
ejpam-2552	131	1	proposition	proposition	NOUN
ejpam-2552	131	2	2.4.3	2.4.3	NUM
ejpam-2552	131	3	.	.	PUNCT
ejpam-2552	132	1	when	when	SCONJ
ejpam-2552	132	2	e	e	NOUN
ejpam-2552	132	3	is	be	AUX
ejpam-2552	132	4	a	a	DET
ejpam-2552	132	5	s.m	s.m	PROPN
ejpam-2552	132	6	.	.	PUNCT
ejpam-2552	133	1	on	on	ADP
ejpam-2552	133	2	ξ	ξ	PROPN
ejpam-2552	133	3	,	,	PUNCT
ejpam-2552	133	4	σ−field	σ−field	X
ejpam-2552	133	5	of	of	ADP
ejpam-2552	133	6	subsets	subset	NOUN
ejpam-2552	133	7	of	of	ADP
ejpam-2552	133	8	a	a	DET
ejpam-2552	133	9	set	set	ADJ
ejpam-2552	133	10	e	e	NOUN
ejpam-2552	133	11	for	for	ADP
ejpam-2552	133	12	h	h	NOUN
ejpam-2552	133	13	,	,	PUNCT
ejpam-2552	133	14	and	and	CCONJ
ejpam-2552	133	15	when	when	SCONJ
ejpam-2552	133	16	f	f	PROPN
ejpam-2552	133	17	is	be	AUX
ejpam-2552	133	18	a	a	DET
ejpam-2552	133	19	measurable	measurable	ADJ
ejpam-2552	133	20	application	application	NOUN
ejpam-2552	133	21	from	from	ADP
ejpam-2552	133	22	e	e	NOUN
ejpam-2552	133	23	into	into	ADP
ejpam-2552	133	24	e′	e′	PROPN
ejpam-2552	133	25	,	,	PUNCT
ejpam-2552	133	26	then	then	ADV
ejpam-2552	133	27	,	,	PUNCT
ejpam-2552	133	28	for	for	ADP
ejpam-2552	133	29	any	any	DET
ejpam-2552	133	30	ϕ	ϕ	NOUN
ejpam-2552	133	31	of	of	ADP
ejpam-2552	133	32	m(e′	m(e′	PROPN
ejpam-2552	133	33	,	,	PUNCT
ejpam-2552	133	34	f(e	f(e	NOUN
ejpam-2552	133	35	)	)	PUNCT
ejpam-2552	133	36	)	)	PUNCT
ejpam-2552	133	37	,	,	PUNCT
ejpam-2552	133	38	we	we	PRON
ejpam-2552	133	39	can	can	AUX
ejpam-2552	133	40	affirm	affirm	VERB
ejpam-2552	133	41	that	that	SCONJ
ejpam-2552	133	42	ϕ	ϕ	PROPN
ejpam-2552	133	43	◦	◦	NOUN
ejpam-2552	133	44	f	f	PROPN
ejpam-2552	133	45	belongs	belong	VERB
ejpam-2552	133	46	to	to	ADP
ejpam-2552	133	47	m(e	m(e	PROPN
ejpam-2552	133	48	,	,	PUNCT
ejpam-2552	133	49	e	e	NOUN
ejpam-2552	133	50	)	)	PUNCT
ejpam-2552	133	51	.	.	PUNCT
ejpam-2552	134	1	moreover	moreover	ADV
ejpam-2552	134	2	,	,	PUNCT
ejpam-2552	134	3	we	we	PRON
ejpam-2552	134	4	have	have	VERB
ejpam-2552	134	5	(	(	PUNCT
ejpam-2552	134	6	f(e))ϕ	f(e))ϕ	X
ejpam-2552	134	7	=	=	SYM
ejpam-2552	134	8	eϕ	eϕ	PROPN
ejpam-2552	134	9	◦	◦	NOUN
ejpam-2552	134	10	f	f	PROPN
ejpam-2552	134	11	.	.	PUNCT
ejpam-2552	135	1	proof	proof	NOUN
ejpam-2552	135	2	.	.	PUNCT
ejpam-2552	136	1	the	the	DET
ejpam-2552	136	2	properties	property	NOUN
ejpam-2552	136	3	of	of	ADP
ejpam-2552	136	4	a	a	DET
ejpam-2552	136	5	r.m	r.m	PROPN
ejpam-2552	136	6	.	.	PROPN
ejpam-2552	136	7	image	image	PROPN
ejpam-2552	136	8	allow	allow	VERB
ejpam-2552	136	9	us	we	PRON
ejpam-2552	136	10	,	,	PUNCT
ejpam-2552	136	11	for	for	ADP
ejpam-2552	136	12	any	any	DET
ejpam-2552	136	13	x	x	NOUN
ejpam-2552	136	14	of	of	ADP
ejpam-2552	136	15	h	h	NOUN
ejpam-2552	136	16	,	,	PUNCT
ejpam-2552	136	17	to	to	AUX
ejpam-2552	136	18	obtain:∫	obtain:∫	ADJ
ejpam-2552	136	19	|ϕ	|ϕ	NUM
ejpam-2552	136	20	◦	◦	NOUN
ejpam-2552	136	21	f	f	PROPN
ejpam-2552	136	22	|2dµzxe	|2dµzxe	PROPN
ejpam-2552	136	23	=	=	SYM
ejpam-2552	136	24	∫	∫	PROPN
ejpam-2552	136	25	|ϕ|2	|ϕ|2	PROPN
ejpam-2552	136	26	◦	◦	NOUN
ejpam-2552	136	27	fdµzxe	fdµzxe	NOUN
ejpam-2552	136	28	=	=	SYM
ejpam-2552	136	29	∫	∫	PROPN
ejpam-2552	136	30	|ϕ|2df(µzxe	|ϕ|2df(µzxe	PROPN
ejpam-2552	136	31	)	)	PUNCT
ejpam-2552	137	1	=	=	SYM
ejpam-2552	137	2	∫	∫	PROPN
ejpam-2552	137	3	|ϕ|2dµzx	|ϕ|2dµzx	PROPN
ejpam-2552	137	4	f(e	f(e	PROPN
ejpam-2552	137	5	)	)	PUNCT
ejpam-2552	137	6	,	,	PUNCT
ejpam-2552	137	7	so	so	SCONJ
ejpam-2552	137	8	ϕ	ϕ	PROPN
ejpam-2552	137	9	◦	◦	NOUN
ejpam-2552	137	10	f	f	PROPN
ejpam-2552	137	11	belongs	belong	VERB
ejpam-2552	137	12	to	to	ADP
ejpam-2552	137	13	m(e	m(e	PROPN
ejpam-2552	137	14	,	,	PUNCT
ejpam-2552	137	15	e	e	NOUN
ejpam-2552	137	16	)	)	PUNCT
ejpam-2552	137	17	,	,	PUNCT
ejpam-2552	137	18	because	because	SCONJ
ejpam-2552	137	19	ϕ	ϕ	NOUN
ejpam-2552	137	20	is	be	AUX
ejpam-2552	137	21	an	an	DET
ejpam-2552	137	22	element	element	NOUN
ejpam-2552	137	23	of	of	ADP
ejpam-2552	137	24	m(e′	m(e′	NOUN
ejpam-2552	137	25	,	,	PUNCT
ejpam-2552	137	26	f(e	f(e	NOUN
ejpam-2552	137	27	)	)	PUNCT
ejpam-2552	137	28	)	)	PUNCT
ejpam-2552	137	29	.	.	PUNCT
ejpam-2552	138	1	moreover	moreover	ADV
ejpam-2552	138	2	,	,	PUNCT
ejpam-2552	138	3	(	(	PUNCT
ejpam-2552	138	4	f(e))ϕx	f(e))ϕx	PROPN
ejpam-2552	138	5	=	=	SYM
ejpam-2552	138	6	∫	∫	PROPN
ejpam-2552	138	7	ϕdzxf(e	ϕdzxf(e	NOUN
ejpam-2552	138	8	)	)	PUNCT
ejpam-2552	138	9	=	=	SYM
ejpam-2552	139	1	∫	∫	PROPN
ejpam-2552	139	2	ϕdf(zxe	ϕdf(zxe	PROPN
ejpam-2552	139	3	)	)	PUNCT
ejpam-2552	140	1	=	=	PUNCT
ejpam-2552	141	1	∫	∫	PROPN
ejpam-2552	141	2	ϕ	ϕ	PROPN
ejpam-2552	141	3	◦	◦	NOUN
ejpam-2552	141	4	fdzxe	fdzxe	NOUN
ejpam-2552	141	5	=	=	SYM
ejpam-2552	141	6	(	(	PUNCT
ejpam-2552	141	7	eϕ	eϕ	PROPN
ejpam-2552	141	8	◦	◦	NOUN
ejpam-2552	141	9	f	f	NOUN
ejpam-2552	141	10	)	)	PUNCT
ejpam-2552	141	11	(	(	PUNCT
ejpam-2552	141	12	x	x	NOUN
ejpam-2552	141	13	)	)	PUNCT
ejpam-2552	141	14	,	,	PUNCT
ejpam-2552	141	15	for	for	ADP
ejpam-2552	141	16	any	any	DET
ejpam-2552	141	17	x	x	NOUN
ejpam-2552	141	18	of	of	ADP
ejpam-2552	141	19	h	h	NOUN
ejpam-2552	141	20	,	,	PUNCT
ejpam-2552	141	21	what	what	PRON
ejpam-2552	141	22	ends	end	VERB
ejpam-2552	141	23	the	the	DET
ejpam-2552	141	24	proof	proof	NOUN
ejpam-2552	141	25	.	.	PUNCT
ejpam-2552	142	1	�	�	PROPN
ejpam-2552	142	2	let	let	VERB
ejpam-2552	142	3	us	we	PRON
ejpam-2552	142	4	now	now	ADV
ejpam-2552	142	5	introduce	introduce	VERB
ejpam-2552	142	6	a	a	DET
ejpam-2552	142	7	new	new	ADJ
ejpam-2552	142	8	notion	notion	NOUN
ejpam-2552	142	9	.	.	PUNCT
ejpam-2552	143	1	definition	definition	NOUN
ejpam-2552	143	2	2.4.1	2.4.1	NUM
ejpam-2552	143	3	.	.	PUNCT
ejpam-2552	144	1	we	we	PRON
ejpam-2552	144	2	say	say	VERB
ejpam-2552	144	3	that	that	SCONJ
ejpam-2552	144	4	a	a	DET
ejpam-2552	144	5	s.m	s.m	PROPN
ejpam-2552	144	6	.	.	PROPN
ejpam-2552	145	1	e	e	X
ejpam-2552	145	2	,	,	PUNCT
ejpam-2552	145	3	on	on	ADP
ejpam-2552	145	4	br	br	NOUN
ejpam-2552	145	5	for	for	ADP
ejpam-2552	145	6	h	h	NOUN
ejpam-2552	145	7	,	,	PUNCT
ejpam-2552	145	8	is	be	AUX
ejpam-2552	145	9	bounded	bound	VERB
ejpam-2552	145	10	when	when	SCONJ
ejpam-2552	145	11	there	there	PRON
ejpam-2552	145	12	exists	exist	VERB
ejpam-2552	145	13	a	a	DET
ejpam-2552	145	14	real	real	NOUN
ejpam-2552	145	15	a	a	DET
ejpam-2552	145	16	>	>	X
ejpam-2552	145	17	0	0	NUM
ejpam-2552	146	1	such	such	ADJ
ejpam-2552	146	2	that	that	SCONJ
ejpam-2552	146	3	e([−a	e([−a	PROPN
ejpam-2552	146	4	,	,	PUNCT
ejpam-2552	146	5	a	a	DET
ejpam-2552	146	6	[	[	X
ejpam-2552	146	7	)	)	PUNCT
ejpam-2552	146	8	=	=	NOUN
ejpam-2552	146	9	ih	ih	NOUN
ejpam-2552	146	10	.	.	PUNCT
ejpam-2552	147	1	this	this	DET
ejpam-2552	147	2	characteristic	characteristic	NOUN
ejpam-2552	147	3	is	be	AUX
ejpam-2552	147	4	stable	stable	ADJ
ejpam-2552	147	5	by	by	ADP
ejpam-2552	147	6	convolution	convolution	NOUN
ejpam-2552	147	7	as	as	SCONJ
ejpam-2552	147	8	follows	follow	VERB
ejpam-2552	147	9	.	.	PUNCT
ejpam-2552	148	1	lemma	lemma	PROPN
ejpam-2552	148	2	2.4.1	2.4.1	NUM
ejpam-2552	148	3	.	.	PUNCT
ejpam-2552	149	1	if	if	SCONJ
ejpam-2552	149	2	e1	e1	PROPN
ejpam-2552	149	3	and	and	CCONJ
ejpam-2552	149	4	e2	e2	PROPN
ejpam-2552	149	5	are	be	AUX
ejpam-2552	149	6	two	two	NUM
ejpam-2552	149	7	bounded	bounded	ADJ
ejpam-2552	149	8	r.m	r.m	PROPN
ejpam-2552	149	9	.	.	PROPN
ejpam-2552	149	10	’s	’s	PROPN
ejpam-2552	149	11	,	,	PUNCT
ejpam-2552	149	12	on	on	ADP
ejpam-2552	149	13	br	br	NOUN
ejpam-2552	149	14	for	for	ADP
ejpam-2552	149	15	h	h	NOUN
ejpam-2552	149	16	,	,	PUNCT
ejpam-2552	149	17	which	which	DET
ejpam-2552	149	18	commute	commute	NOUN
ejpam-2552	149	19	,	,	PUNCT
ejpam-2552	149	20	then	then	ADV
ejpam-2552	149	21	e1	e1	PROPN
ejpam-2552	149	22	∗	∗	NOUN
ejpam-2552	149	23	e2	e2	PROPN
ejpam-2552	149	24	is	be	AUX
ejpam-2552	149	25	also	also	ADV
ejpam-2552	149	26	bounded	bound	VERB
ejpam-2552	149	27	.	.	PUNCT
ejpam-2552	150	1	a.	a.	NOUN
ejpam-2552	150	2	boudou	boudou	PROPN
ejpam-2552	150	3	,	,	PUNCT
ejpam-2552	150	4	s.	s.	PROPN
ejpam-2552	150	5	viguier	viguier	PROPN
ejpam-2552	150	6	-	-	PUNCT
ejpam-2552	150	7	pla	pla	PROPN
ejpam-2552	150	8	/	/	PUNCT
ejpam-2552	150	9	eur	eur	PROPN
ejpam-2552	150	10	.	.	PUNCT
ejpam-2552	151	1	j.	j.	PROPN
ejpam-2552	151	2	pure	pure	PROPN
ejpam-2552	151	3	appl	appl	PROPN
ejpam-2552	151	4	.	.	PROPN
ejpam-2552	151	5	math	math	PROPN
ejpam-2552	151	6	,	,	PUNCT
ejpam-2552	151	7	11	11	NUM
ejpam-2552	151	8	(	(	PUNCT
ejpam-2552	151	9	4	4	NUM
ejpam-2552	151	10	)	)	PUNCT
ejpam-2552	151	11	(	(	PUNCT
ejpam-2552	151	12	2018	2018	NUM
ejpam-2552	151	13	)	)	PUNCT
ejpam-2552	151	14	,	,	PUNCT
ejpam-2552	151	15	893	893	NUM
ejpam-2552	151	16	-	-	SYM
ejpam-2552	151	17	910	910	NUM
ejpam-2552	151	18	898	898	NUM
ejpam-2552	151	19	proof	proof	NOUN
ejpam-2552	151	20	.	.	PUNCT
ejpam-2552	152	1	because	because	SCONJ
ejpam-2552	152	2	e1	e1	PROPN
ejpam-2552	152	3	and	and	CCONJ
ejpam-2552	152	4	e2	e2	PROPN
ejpam-2552	152	5	are	be	AUX
ejpam-2552	152	6	bounded	bound	VERB
ejpam-2552	152	7	,	,	PUNCT
ejpam-2552	152	8	there	there	PRON
ejpam-2552	152	9	exists	exist	VERB
ejpam-2552	152	10	two	two	NUM
ejpam-2552	152	11	strictly	strictly	ADV
ejpam-2552	152	12	positive	positive	ADJ
ejpam-2552	152	13	reals	real	NOUN
ejpam-2552	152	14	a1	a1	NOUN
ejpam-2552	152	15	and	and	CCONJ
ejpam-2552	152	16	a2	a2	NOUN
ejpam-2552	152	17	such	such	ADJ
ejpam-2552	152	18	that	that	SCONJ
ejpam-2552	152	19	ih	ih	NOUN
ejpam-2552	152	20	=	=	SYM
ejpam-2552	152	21	e1([−a1	e1([−a1	NOUN
ejpam-2552	152	22	,	,	PUNCT
ejpam-2552	152	23	a1	a1	NOUN
ejpam-2552	152	24	[	[	X
ejpam-2552	152	25	)	)	PUNCT
ejpam-2552	152	26	=	=	PUNCT
ejpam-2552	152	27	e2([−a2	e2([−a2	PROPN
ejpam-2552	152	28	,	,	PUNCT
ejpam-2552	152	29	a2	a2	PROPN
ejpam-2552	152	30	[	[	NOUN
ejpam-2552	152	31	)	)	PUNCT
ejpam-2552	152	32	.	.	PUNCT
ejpam-2552	153	1	if	if	SCONJ
ejpam-2552	153	2	we	we	PRON
ejpam-2552	153	3	denote	denote	VERB
ejpam-2552	153	4	a	a	DET
ejpam-2552	153	5	=	=	NOUN
ejpam-2552	153	6	a1	a1	NOUN
ejpam-2552	153	7	+	+	CCONJ
ejpam-2552	153	8	a2	a2	NOUN
ejpam-2552	153	9	,	,	PUNCT
ejpam-2552	153	10	as	as	ADP
ejpam-2552	153	11	[	[	X
ejpam-2552	153	12	−a1	−a1	ADJ
ejpam-2552	153	13	,	,	PUNCT
ejpam-2552	153	14	a1[×[−a2	a1[×[−a2	NOUN
ejpam-2552	153	15	,	,	PUNCT
ejpam-2552	153	16	a2[⊂	a2[⊂	PUNCT
ejpam-2552	153	17	s−1[−a	s−1[−a	PROPN
ejpam-2552	153	18	,	,	PUNCT
ejpam-2552	153	19	a	a	PRON
ejpam-2552	153	20	[	[	X
ejpam-2552	153	21	,	,	PUNCT
ejpam-2552	153	22	we	we	PRON
ejpam-2552	153	23	can	can	AUX
ejpam-2552	153	24	write	write	VERB
ejpam-2552	153	25	ih	ih	NOUN
ejpam-2552	153	26	=	=	PUNCT
ejpam-2552	153	27	e1	e1	PROPN
ejpam-2552	153	28	⊗	⊗	PROPN
ejpam-2552	153	29	e2([−a1	e2([−a1	PROPN
ejpam-2552	153	30	,	,	PUNCT
ejpam-2552	153	31	a1[×[−a2	a1[×[−a2	NOUN
ejpam-2552	153	32	,	,	PUNCT
ejpam-2552	153	33	a2	a2	PROPN
ejpam-2552	153	34	[	[	NOUN
ejpam-2552	153	35	)	)	PUNCT
ejpam-2552	153	36	�	�	PROPN
ejpam-2552	153	37	e1	e1	PROPN
ejpam-2552	153	38	⊗	⊗	PROPN
ejpam-2552	153	39	e2(s−1[−a	e2(s−1[−a	PROPN
ejpam-2552	153	40	,	,	PUNCT
ejpam-2552	153	41	a	a	DET
ejpam-2552	153	42	[	[	X
ejpam-2552	153	43	)	)	PUNCT
ejpam-2552	153	44	=	=	SYM
ejpam-2552	153	45	e1	e1	NOUN
ejpam-2552	153	46	∗	∗	NOUN
ejpam-2552	153	47	e2([−a	e2([−a	PROPN
ejpam-2552	153	48	,	,	PUNCT
ejpam-2552	153	49	a	a	DET
ejpam-2552	153	50	[	[	X
ejpam-2552	153	51	)	)	PUNCT
ejpam-2552	153	52	6	6	NUM
ejpam-2552	153	53	ih	ih	NOUN
ejpam-2552	153	54	,	,	PUNCT
ejpam-2552	153	55	then	then	ADV
ejpam-2552	153	56	ih	ih	NOUN
ejpam-2552	153	57	=	=	PUNCT
ejpam-2552	153	58	e1	e1	VERB
ejpam-2552	153	59	∗	∗	NOUN
ejpam-2552	153	60	e2([−a	e2([−a	PROPN
ejpam-2552	153	61	,	,	PUNCT
ejpam-2552	153	62	a	a	DET
ejpam-2552	153	63	[	[	X
ejpam-2552	153	64	)	)	PUNCT
ejpam-2552	153	65	,	,	PUNCT
ejpam-2552	153	66	what	what	PRON
ejpam-2552	153	67	ends	end	VERB
ejpam-2552	153	68	the	the	DET
ejpam-2552	153	69	proof	proof	NOUN
ejpam-2552	153	70	.	.	PUNCT
ejpam-2552	154	1	�	�	PROPN
ejpam-2552	154	2	let	let	VERB
ejpam-2552	154	3	us	we	PRON
ejpam-2552	154	4	end	end	VERB
ejpam-2552	154	5	this	this	DET
ejpam-2552	154	6	section	section	NOUN
ejpam-2552	154	7	by	by	ADP
ejpam-2552	154	8	results	result	NOUN
ejpam-2552	154	9	which	which	PRON
ejpam-2552	154	10	we	we	PRON
ejpam-2552	154	11	will	will	AUX
ejpam-2552	154	12	use	use	VERB
ejpam-2552	154	13	later	later	ADV
ejpam-2552	154	14	.	.	PUNCT
ejpam-2552	155	1	for	for	ADP
ejpam-2552	155	2	any	any	DET
ejpam-2552	155	3	n	n	NOUN
ejpam-2552	155	4	of	of	ADP
ejpam-2552	155	5	n	n	CCONJ
ejpam-2552	155	6	,	,	PUNCT
ejpam-2552	155	7	it	it	PRON
ejpam-2552	155	8	is	be	AUX
ejpam-2552	155	9	clear	clear	ADJ
ejpam-2552	155	10	that	that	SCONJ
ejpam-2552	155	11	the	the	DET
ejpam-2552	155	12	application	application	NOUN
ejpam-2552	155	13	jn	jn	NOUN
ejpam-2552	155	14	:	:	PUNCT
ejpam-2552	155	15	λ	λ	X
ejpam-2552	155	16	∈	∈	NOUN
ejpam-2552	155	17	r	r	NOUN
ejpam-2552	155	18	7→	7→	NUM
ejpam-2552	155	19	λn	λn	NOUN
ejpam-2552	155	20	∈	∈	PROPN
ejpam-2552	155	21	c	c	NOUN
ejpam-2552	155	22	is	be	AUX
ejpam-2552	155	23	measurable	measurable	ADJ
ejpam-2552	155	24	and	and	CCONJ
ejpam-2552	155	25	,	,	PUNCT
ejpam-2552	155	26	when	when	SCONJ
ejpam-2552	155	27	µ	µ	X
ejpam-2552	155	28	is	be	AUX
ejpam-2552	155	29	a	a	DET
ejpam-2552	155	30	bounded	bounded	ADJ
ejpam-2552	155	31	measure	measure	NOUN
ejpam-2552	155	32	defined	define	VERB
ejpam-2552	155	33	on	on	ADP
ejpam-2552	155	34	br	br	NOUN
ejpam-2552	155	35	having	have	VERB
ejpam-2552	155	36	a	a	DET
ejpam-2552	155	37	compact	compact	ADJ
ejpam-2552	155	38	support	support	NOUN
ejpam-2552	155	39	,	,	PUNCT
ejpam-2552	155	40	then	then	ADV
ejpam-2552	155	41	vect{jn	vect{jn	NUM
ejpam-2552	155	42	,	,	PUNCT
ejpam-2552	155	43	n	n	PROPN
ejpam-2552	155	44	∈	∈	PROPN
ejpam-2552	155	45	n	n	CCONJ
ejpam-2552	155	46	}	}	PUNCT
ejpam-2552	155	47	is	be	AUX
ejpam-2552	155	48	dense	dense	ADJ
ejpam-2552	155	49	in	in	ADP
ejpam-2552	155	50	l2(r	l2(r	PROPN
ejpam-2552	155	51	,	,	PUNCT
ejpam-2552	155	52	br	br	PROPN
ejpam-2552	155	53	,	,	PUNCT
ejpam-2552	155	54	µ	µ	NOUN
ejpam-2552	155	55	)	)	PUNCT
ejpam-2552	155	56	.	.	PUNCT
ejpam-2552	156	1	so	so	ADV
ejpam-2552	156	2	,	,	PUNCT
ejpam-2552	156	3	when	when	SCONJ
ejpam-2552	156	4	e	e	PROPN
ejpam-2552	156	5	is	be	AUX
ejpam-2552	156	6	a	a	DET
ejpam-2552	156	7	bounded	bounded	ADJ
ejpam-2552	156	8	s.m	s.m	PROPN
ejpam-2552	156	9	.	.	PROPN
ejpam-2552	157	1	on	on	ADP
ejpam-2552	157	2	br	br	PROPN
ejpam-2552	157	3	for	for	ADP
ejpam-2552	157	4	h	h	NOUN
ejpam-2552	157	5	,	,	PUNCT
ejpam-2552	157	6	then	then	ADV
ejpam-2552	157	7	vect{jn	vect{jn	NUM
ejpam-2552	157	8	,	,	PUNCT
ejpam-2552	157	9	n	n	PROPN
ejpam-2552	157	10	∈	∈	PROPN
ejpam-2552	157	11	n	n	CCONJ
ejpam-2552	157	12	}	}	PUNCT
ejpam-2552	157	13	=	=	SYM
ejpam-2552	157	14	l2(r	l2(r	PROPN
ejpam-2552	157	15	,	,	PUNCT
ejpam-2552	157	16	br	br	PROPN
ejpam-2552	157	17	,	,	PUNCT
ejpam-2552	157	18	µzxe	µzxe	PROPN
ejpam-2552	157	19	)	)	PUNCT
ejpam-2552	157	20	,	,	PUNCT
ejpam-2552	157	21	this	this	PRON
ejpam-2552	157	22	for	for	ADP
ejpam-2552	157	23	any	any	DET
ejpam-2552	157	24	x	x	PROPN
ejpam-2552	157	25	of	of	ADP
ejpam-2552	157	26	h.	h.	PROPN
ejpam-2552	157	27	moreover	moreover	ADV
ejpam-2552	157	28	,	,	PUNCT
ejpam-2552	157	29	jn	jn	PROPN
ejpam-2552	157	30	belongs	belong	VERB
ejpam-2552	157	31	to	to	ADP
ejpam-2552	157	32	m(r	m(r	PROPN
ejpam-2552	157	33	,	,	PUNCT
ejpam-2552	157	34	e	e	NOUN
ejpam-2552	157	35	)	)	PUNCT
ejpam-2552	157	36	,	,	PUNCT
ejpam-2552	157	37	so	so	SCONJ
ejpam-2552	157	38	we	we	PRON
ejpam-2552	157	39	can	can	AUX
ejpam-2552	157	40	consider	consider	VERB
ejpam-2552	157	41	the	the	DET
ejpam-2552	157	42	applications	application	NOUN
ejpam-2552	157	43	ejn	ejn	ADV
ejpam-2552	157	44	.	.	PUNCT
ejpam-2552	158	1	lemma	lemma	PROPN
ejpam-2552	158	2	2.4.2	2.4.2	NUM
ejpam-2552	158	3	.	.	PUNCT
ejpam-2552	159	1	if	if	SCONJ
ejpam-2552	159	2	{	{	PUNCT
ejpam-2552	159	3	dp	dp	NOUN
ejpam-2552	159	4	;	;	PUNCT
ejpam-2552	159	5	p	p	PROPN
ejpam-2552	159	6	∈	∈	PROPN
ejpam-2552	159	7	n	n	CCONJ
ejpam-2552	159	8	}	}	PUNCT
ejpam-2552	159	9	is	be	AUX
ejpam-2552	159	10	an	an	DET
ejpam-2552	159	11	orthogonal	orthogonal	ADJ
ejpam-2552	159	12	family	family	NOUN
ejpam-2552	159	13	of	of	ADP
ejpam-2552	159	14	projectors	projector	NOUN
ejpam-2552	159	15	of	of	ADP
ejpam-2552	159	16	sum	sum	NOUN
ejpam-2552	160	1	i	i	PRON
ejpam-2552	160	2	,	,	PUNCT
ejpam-2552	160	3	if	if	SCONJ
ejpam-2552	160	4	(	(	PUNCT
ejpam-2552	160	5	µp)p∈n∗	µp)p∈n∗	NOUN
ejpam-2552	160	6	is	be	AUX
ejpam-2552	160	7	a	a	DET
ejpam-2552	160	8	real	real	ADJ
ejpam-2552	160	9	sequence	sequence	NOUN
ejpam-2552	160	10	which	which	PRON
ejpam-2552	160	11	decreasingly	decreasingly	ADV
ejpam-2552	160	12	strictly	strictly	ADV
ejpam-2552	160	13	converges	converge	VERB
ejpam-2552	160	14	to	to	ADP
ejpam-2552	160	15	0	0	NUM
ejpam-2552	161	1	and	and	CCONJ
ejpam-2552	161	2	if	if	SCONJ
ejpam-2552	161	3	we	we	PRON
ejpam-2552	161	4	set	set	VERB
ejpam-2552	161	5	µ0	µ0	NOUN
ejpam-2552	161	6	=	=	SYM
ejpam-2552	161	7	0	0	NUM
ejpam-2552	161	8	,	,	PUNCT
ejpam-2552	161	9	then	then	ADV
ejpam-2552	161	10	we	we	PRON
ejpam-2552	161	11	can	can	AUX
ejpam-2552	161	12	affirm	affirm	VERB
ejpam-2552	161	13	that	that	SCONJ
ejpam-2552	161	14	a	a	X
ejpam-2552	161	15	)	)	PUNCT
ejpam-2552	161	16	for	for	ADP
ejpam-2552	161	17	any	any	DET
ejpam-2552	161	18	b	b	PROPN
ejpam-2552	161	19	of	of	ADP
ejpam-2552	161	20	br	br	PROPN
ejpam-2552	161	21	,	,	PUNCT
ejpam-2552	161	22	{	{	PUNCT
ejpam-2552	161	23	δµp(b)dp	δµp(b)dp	ADP
ejpam-2552	161	24	;	;	PUNCT
ejpam-2552	161	25	p	p	PROPN
ejpam-2552	161	26	∈	∈	PROPN
ejpam-2552	161	27	n	n	CCONJ
ejpam-2552	161	28	}	}	PUNCT
ejpam-2552	161	29	is	be	AUX
ejpam-2552	161	30	an	an	DET
ejpam-2552	161	31	orthogonal	orthogonal	ADJ
ejpam-2552	161	32	family	family	NOUN
ejpam-2552	161	33	of	of	ADP
ejpam-2552	161	34	projectors	projector	NOUN
ejpam-2552	161	35	;	;	PUNCT
ejpam-2552	161	36	b	b	X
ejpam-2552	161	37	)	)	PUNCT
ejpam-2552	161	38	the	the	DET
ejpam-2552	161	39	application	application	NOUN
ejpam-2552	161	40	e	e	NOUN
ejpam-2552	161	41	:	:	PUNCT
ejpam-2552	161	42	b	b	X
ejpam-2552	161	43	∈	∈	PROPN
ejpam-2552	161	44	br	br	NOUN
ejpam-2552	161	45	7→	7→	NUM
ejpam-2552	161	46	∑	∑	PUNCT
ejpam-2552	161	47	p∈n	p∈n	VERB
ejpam-2552	161	48	δµp(b)dp	δµp(b)dp	NOUN
ejpam-2552	161	49	∈	∈	NOUN
ejpam-2552	161	50	p(h	p(h	NOUN
ejpam-2552	161	51	)	)	PUNCT
ejpam-2552	161	52	is	be	AUX
ejpam-2552	161	53	a	a	DET
ejpam-2552	161	54	bounded	bounded	ADJ
ejpam-2552	161	55	s.m	s.m	PROPN
ejpam-2552	161	56	.	.	PROPN
ejpam-2552	161	57	;	;	PUNCT
ejpam-2552	162	1	c	c	X
ejpam-2552	162	2	)	)	PUNCT
ejpam-2552	162	3	{	{	PUNCT
ejpam-2552	162	4	µpdp	µpdp	NOUN
ejpam-2552	162	5	;	;	PUNCT
ejpam-2552	162	6	p	p	PROPN
ejpam-2552	162	7	∈	∈	PROPN
ejpam-2552	162	8	n	n	CCONJ
ejpam-2552	162	9	}	}	PUNCT
ejpam-2552	162	10	is	be	AUX
ejpam-2552	162	11	a	a	DET
ejpam-2552	162	12	family	family	NOUN
ejpam-2552	162	13	of	of	ADP
ejpam-2552	162	14	elements	element	NOUN
ejpam-2552	162	15	of	of	ADP
ejpam-2552	162	16	l(h	l(h	PROPN
ejpam-2552	162	17	)	)	PUNCT
ejpam-2552	162	18	,	,	PUNCT
ejpam-2552	162	19	summable	summable	ADJ
ejpam-2552	162	20	of	of	ADP
ejpam-2552	162	21	sum	sum	NOUN
ejpam-2552	162	22	ej	ej	PROPN
ejpam-2552	162	23	.	.	PUNCT
ejpam-2552	162	24	proof	proof	NOUN
ejpam-2552	162	25	.	.	PUNCT
ejpam-2552	163	1	for	for	ADP
ejpam-2552	163	2	any	any	DET
ejpam-2552	163	3	b	b	PROPN
ejpam-2552	163	4	of	of	ADP
ejpam-2552	163	5	br	br	PROPN
ejpam-2552	163	6	,	,	PUNCT
ejpam-2552	163	7	it	it	PRON
ejpam-2552	163	8	is	be	AUX
ejpam-2552	163	9	clear	clear	ADJ
ejpam-2552	163	10	that	that	SCONJ
ejpam-2552	163	11	{	{	PUNCT
ejpam-2552	163	12	δµp(b)dp	δµp(b)dp	ADP
ejpam-2552	163	13	;	;	PUNCT
ejpam-2552	163	14	p	p	PROPN
ejpam-2552	163	15	∈	∈	PROPN
ejpam-2552	163	16	n	n	CCONJ
ejpam-2552	163	17	}	}	PUNCT
ejpam-2552	163	18	is	be	AUX
ejpam-2552	163	19	an	an	DET
ejpam-2552	163	20	orthogonal	orthogonal	ADJ
ejpam-2552	163	21	family	family	NOUN
ejpam-2552	163	22	of	of	ADP
ejpam-2552	163	23	projectors	projector	NOUN
ejpam-2552	163	24	.	.	PUNCT
ejpam-2552	164	1	if	if	SCONJ
ejpam-2552	164	2	we	we	PRON
ejpam-2552	164	3	denote	denote	VERB
ejpam-2552	164	4	by	by	ADP
ejpam-2552	164	5	e(b	e(b	NOUN
ejpam-2552	164	6	)	)	PUNCT
ejpam-2552	164	7	its	its	PRON
ejpam-2552	164	8	sum	sum	NOUN
ejpam-2552	164	9	,	,	PUNCT
ejpam-2552	164	10	for	for	ADP
ejpam-2552	164	11	any	any	DET
ejpam-2552	164	12	x	x	NOUN
ejpam-2552	164	13	of	of	ADP
ejpam-2552	164	14	h	h	NOUN
ejpam-2552	164	15	,	,	PUNCT
ejpam-2552	164	16	{	{	PUNCT
ejpam-2552	164	17	δµp(b)dpx	δµp(b)dpx	VERB
ejpam-2552	164	18	;	;	PUNCT
ejpam-2552	164	19	p	p	PROPN
ejpam-2552	164	20	∈	∈	PROPN
ejpam-2552	164	21	n	n	CCONJ
ejpam-2552	164	22	}	}	PUNCT
ejpam-2552	164	23	is	be	AUX
ejpam-2552	164	24	a	a	DET
ejpam-2552	164	25	summable	summable	ADJ
ejpam-2552	164	26	family	family	NOUN
ejpam-2552	164	27	of	of	ADP
ejpam-2552	164	28	sum	sum	NOUN
ejpam-2552	164	29	(	(	PUNCT
ejpam-2552	164	30	e(b))x	e(b))x	PROPN
ejpam-2552	164	31	.	.	PUNCT
ejpam-2552	165	1	as	as	SCONJ
ejpam-2552	165	2	the	the	DET
ejpam-2552	165	3	set	set	NOUN
ejpam-2552	165	4	of	of	ADP
ejpam-2552	165	5	the	the	DET
ejpam-2552	165	6	indexes	index	NOUN
ejpam-2552	165	7	is	be	AUX
ejpam-2552	165	8	n	n	PRON
ejpam-2552	165	9	,	,	PUNCT
ejpam-2552	165	10	we	we	PRON
ejpam-2552	165	11	can	can	AUX
ejpam-2552	165	12	write	write	VERB
ejpam-2552	165	13	(	(	PUNCT
ejpam-2552	165	14	e(b))x	e(b))x	NOUN
ejpam-2552	165	15	=	=	SYM
ejpam-2552	165	16	limn	limn	ADJ
ejpam-2552	165	17	∑n	∑n	PROPN
ejpam-2552	165	18	p=0	p=0	PROPN
ejpam-2552	165	19	δµp(b)dpx	δµp(b)dpx	NOUN
ejpam-2552	165	20	,	,	PUNCT
ejpam-2552	165	21	and	and	CCONJ
ejpam-2552	165	22	then	then	ADV
ejpam-2552	165	23	‖(e(b))x‖2	‖(e(b))x‖2	ADJ
ejpam-2552	165	24	=	=	PUNCT
ejpam-2552	166	1	limn‖	limn‖	PRON
ejpam-2552	166	2	∑n	∑n	PROPN
ejpam-2552	166	3	p=0	p=0	PROPN
ejpam-2552	166	4	δµp(b)dpx‖2	δµp(b)dpx‖2	NOUN
ejpam-2552	166	5	=	=	PUNCT
ejpam-2552	166	6	limn	limn	ADJ
ejpam-2552	166	7	∑n	∑n	PROPN
ejpam-2552	166	8	p=0	p=0	PROPN
ejpam-2552	166	9	δµp(b)‖dpx‖2	δµp(b)‖dpx‖2	VERB
ejpam-2552	166	10	=	=	PUNCT
ejpam-2552	166	11	∑	∑	PUNCT
ejpam-2552	166	12	p∈n	p∈n	NOUN
ejpam-2552	166	13	δµp(b)‖dpx‖2	δµp(b)‖dpx‖2	NOUN
ejpam-2552	166	14	.	.	PUNCT
ejpam-2552	167	1	(	(	PUNCT
ejpam-2552	167	2	2.4.2	2.4.2	NUM
ejpam-2552	167	3	)	)	PUNCT
ejpam-2552	167	4	of	of	ADP
ejpam-2552	167	5	course	course	NOUN
ejpam-2552	167	6	,	,	PUNCT
ejpam-2552	167	7	e(r	e(r	NUM
ejpam-2552	167	8	)	)	PUNCT
ejpam-2552	168	1	=	=	SYM
ejpam-2552	168	2	i	i	INTJ
ejpam-2552	168	3	(	(	PUNCT
ejpam-2552	168	4	because	because	SCONJ
ejpam-2552	168	5	∑	∑	ADV
ejpam-2552	168	6	p∈ndp	p∈ndp	PROPN
ejpam-2552	168	7	=	=	SYM
ejpam-2552	168	8	i	i	PROPN
ejpam-2552	168	9	)	)	PUNCT
ejpam-2552	168	10	.	.	PUNCT
ejpam-2552	169	1	moreover	moreover	ADV
ejpam-2552	169	2	,	,	PUNCT
ejpam-2552	169	3	if	if	SCONJ
ejpam-2552	169	4	(	(	PUNCT
ejpam-2552	169	5	b1	b1	NOUN
ejpam-2552	169	6	,	,	PUNCT
ejpam-2552	169	7	b2	b2	NOUN
ejpam-2552	169	8	)	)	PUNCT
ejpam-2552	169	9	is	be	AUX
ejpam-2552	169	10	a	a	DET
ejpam-2552	169	11	pair	pair	NOUN
ejpam-2552	169	12	of	of	ADP
ejpam-2552	169	13	disjoint	disjoint	ADJ
ejpam-2552	169	14	elements	element	NOUN
ejpam-2552	169	15	of	of	ADP
ejpam-2552	169	16	br	br	PROPN
ejpam-2552	169	17	,	,	PUNCT
ejpam-2552	169	18	we	we	PRON
ejpam-2552	169	19	have	have	AUX
ejpam-2552	169	20	e(b1	e(b1	VERB
ejpam-2552	169	21	∪b2	∪b2	ADJ
ejpam-2552	169	22	)	)	PUNCT
ejpam-2552	169	23	=	=	SYM
ejpam-2552	169	24	e(b1	e(b1	NOUN
ejpam-2552	169	25	)	)	PUNCT
ejpam-2552	170	1	+	+	CCONJ
ejpam-2552	170	2	e(b2	e(b2	NOUN
ejpam-2552	170	3	)	)	PUNCT
ejpam-2552	170	4	,	,	PUNCT
ejpam-2552	170	5	because	because	SCONJ
ejpam-2552	170	6	for	for	ADP
ejpam-2552	170	7	any	any	DET
ejpam-2552	170	8	p	p	NOUN
ejpam-2552	170	9	of	of	ADP
ejpam-2552	170	10	n	n	PRON
ejpam-2552	170	11	we	we	PRON
ejpam-2552	170	12	have	have	AUX
ejpam-2552	170	13	:	:	PUNCT
ejpam-2552	170	14	δµp(b1	δµp(b1	VERB
ejpam-2552	170	15	∪b2)dpx	∪b2)dpx	NOUN
ejpam-2552	171	1	=	=	PUNCT
ejpam-2552	172	1	δµp(b1)dpx	δµp(b1)dpx	NOUN
ejpam-2552	172	2	+	+	NUM
ejpam-2552	172	3	δµp(b2)dpx	δµp(b2)dpx	ADJ
ejpam-2552	172	4	.	.	NOUN
ejpam-2552	173	1	let	let	ADJ
ejpam-2552	173	2	(	(	PUNCT
ejpam-2552	173	3	bn)n∈n	bn)n∈n	NOUN
ejpam-2552	173	4	be	be	AUX
ejpam-2552	173	5	a	a	DET
ejpam-2552	173	6	sequence	sequence	NOUN
ejpam-2552	173	7	of	of	ADP
ejpam-2552	173	8	elements	element	NOUN
ejpam-2552	173	9	of	of	ADP
ejpam-2552	173	10	br	br	NOUN
ejpam-2552	173	11	which	which	PRON
ejpam-2552	173	12	decreasingly	decreasingly	ADV
ejpam-2552	173	13	converges	converge	VERB
ejpam-2552	173	14	to	to	ADP
ejpam-2552	173	15	∅	∅	NOUN
ejpam-2552	173	16	and	and	CCONJ
ejpam-2552	173	17	x	x	SYM
ejpam-2552	173	18	an	an	DET
ejpam-2552	173	19	element	element	NOUN
ejpam-2552	173	20	of	of	ADP
ejpam-2552	173	21	h.	h.	NOUN
ejpam-2552	173	22	in	in	ADP
ejpam-2552	173	23	order	order	NOUN
ejpam-2552	173	24	to	to	PART
ejpam-2552	173	25	prove	prove	VERB
ejpam-2552	173	26	that	that	SCONJ
ejpam-2552	173	27	e	e	NOUN
ejpam-2552	173	28	is	be	AUX
ejpam-2552	173	29	a	a	DET
ejpam-2552	173	30	s.m	s.m	PROPN
ejpam-2552	173	31	.	.	PROPN
ejpam-2552	173	32	,	,	PUNCT
ejpam-2552	173	33	it	it	PRON
ejpam-2552	173	34	remains	remain	VERB
ejpam-2552	173	35	to	to	PART
ejpam-2552	173	36	be	be	AUX
ejpam-2552	173	37	proved	prove	VERB
ejpam-2552	173	38	that	that	DET
ejpam-2552	173	39	limn(e(bn))x	limn(e(bn))x	NOUN
ejpam-2552	174	1	=	=	NOUN
ejpam-2552	174	2	0	0	PROPN
ejpam-2552	174	3	.	.	PUNCT
ejpam-2552	175	1	for	for	ADP
ejpam-2552	175	2	this	this	PRON
ejpam-2552	175	3	,	,	PUNCT
ejpam-2552	175	4	let	let	VERB
ejpam-2552	175	5	us	we	PRON
ejpam-2552	175	6	first	first	ADV
ejpam-2552	175	7	recall	recall	VERB
ejpam-2552	175	8	that	that	SCONJ
ejpam-2552	175	9	,	,	PUNCT
ejpam-2552	175	10	if	if	SCONJ
ejpam-2552	175	11	(	(	PUNCT
ejpam-2552	175	12	ap)p∈n	ap)p∈n	X
ejpam-2552	175	13	is	be	AUX
ejpam-2552	175	14	a	a	DET
ejpam-2552	175	15	sequence	sequence	NOUN
ejpam-2552	175	16	of	of	ADP
ejpam-2552	175	17	elements	element	NOUN
ejpam-2552	175	18	of	of	ADP
ejpam-2552	175	19	r+	r+	NOUN
ejpam-2552	175	20	such	such	ADJ
ejpam-2552	175	21	that∑	that∑	NOUN
ejpam-2552	175	22	p∈n	p∈n	NOUN
ejpam-2552	175	23	ap	ap	NOUN
ejpam-2552	175	24	<	<	X
ejpam-2552	175	25	+	+	PROPN
ejpam-2552	175	26	∞	∞	PROPN
ejpam-2552	175	27	,	,	PUNCT
ejpam-2552	175	28	if	if	SCONJ
ejpam-2552	175	29	{	{	PUNCT
ejpam-2552	175	30	fn	fn	NOUN
ejpam-2552	175	31	,	,	PUNCT
ejpam-2552	175	32	p	p	X
ejpam-2552	175	33	;	;	PUNCT
ejpam-2552	175	34	(	(	PUNCT
ejpam-2552	175	35	n	n	X
ejpam-2552	175	36	,	,	PUNCT
ejpam-2552	175	37	p	p	X
ejpam-2552	175	38	)	)	PUNCT
ejpam-2552	175	39	∈	∈	PROPN
ejpam-2552	175	40	n	n	CCONJ
ejpam-2552	175	41	×	×	NOUN
ejpam-2552	175	42	n	n	CCONJ
ejpam-2552	175	43	}	}	PUNCT
ejpam-2552	175	44	is	be	AUX
ejpam-2552	175	45	a	a	DET
ejpam-2552	175	46	family	family	NOUN
ejpam-2552	175	47	of	of	ADP
ejpam-2552	175	48	positive	positive	ADJ
ejpam-2552	175	49	reals	real	NOUN
ejpam-2552	175	50	such	such	ADJ
ejpam-2552	175	51	that	that	SCONJ
ejpam-2552	175	52	,	,	PUNCT
ejpam-2552	175	53	for	for	ADP
ejpam-2552	175	54	any	any	DET
ejpam-2552	175	55	p	p	NOUN
ejpam-2552	175	56	of	of	ADP
ejpam-2552	175	57	n	n	CCONJ
ejpam-2552	175	58	,	,	PUNCT
ejpam-2552	175	59	limnfn	limnfn	PROPN
ejpam-2552	175	60	,	,	PUNCT
ejpam-2552	175	61	p	p	NOUN
ejpam-2552	175	62	=	=	NOUN
ejpam-2552	175	63	0	0	NUM
ejpam-2552	175	64	,	,	PUNCT
ejpam-2552	175	65	and	and	CCONJ
ejpam-2552	175	66	if	if	SCONJ
ejpam-2552	175	67	fn	fn	NOUN
ejpam-2552	175	68	,	,	PUNCT
ejpam-2552	175	69	p	p	X
ejpam-2552	175	70	<	<	X
ejpam-2552	175	71	ap	ap	PROPN
ejpam-2552	175	72	for	for	ADP
ejpam-2552	175	73	any	any	DET
ejpam-2552	175	74	(	(	PUNCT
ejpam-2552	175	75	n	n	X
ejpam-2552	175	76	,	,	PUNCT
ejpam-2552	175	77	p	p	NOUN
ejpam-2552	175	78	)	)	PUNCT
ejpam-2552	175	79	of	of	ADP
ejpam-2552	175	80	n×	n×	PROPN
ejpam-2552	175	81	n	n	CCONJ
ejpam-2552	175	82	,	,	PUNCT
ejpam-2552	175	83	then	then	ADV
ejpam-2552	175	84	on	on	ADP
ejpam-2552	175	85	one	one	NUM
ejpam-2552	175	86	side	side	NOUN
ejpam-2552	175	87	,	,	PUNCT
ejpam-2552	175	88	for	for	ADP
ejpam-2552	175	89	any	any	DET
ejpam-2552	175	90	n	n	NOUN
ejpam-2552	175	91	of	of	ADP
ejpam-2552	175	92	n	n	CCONJ
ejpam-2552	175	93	,	,	PUNCT
ejpam-2552	175	94	the	the	DET
ejpam-2552	175	95	family	family	NOUN
ejpam-2552	175	96	{	{	PUNCT
ejpam-2552	175	97	fn	fn	NOUN
ejpam-2552	175	98	,	,	PUNCT
ejpam-2552	175	99	p	p	X
ejpam-2552	175	100	;	;	PUNCT
ejpam-2552	175	101	p	p	PROPN
ejpam-2552	175	102	∈	∈	PROPN
ejpam-2552	175	103	n	n	CCONJ
ejpam-2552	175	104	}	}	PUNCT
ejpam-2552	175	105	is	be	AUX
ejpam-2552	175	106	summable	summable	ADJ
ejpam-2552	175	107	,	,	PUNCT
ejpam-2552	175	108	and	and	CCONJ
ejpam-2552	175	109	on	on	ADP
ejpam-2552	175	110	another	another	DET
ejpam-2552	175	111	side	side	NOUN
ejpam-2552	175	112	,	,	PUNCT
ejpam-2552	175	113	limn	limn	ADV
ejpam-2552	175	114	∑	∑	ADV
ejpam-2552	175	115	p∈n	p∈n	PROPN
ejpam-2552	175	116	fn	fn	NOUN
ejpam-2552	175	117	,	,	PUNCT
ejpam-2552	175	118	p	p	NOUN
ejpam-2552	175	119	=	=	NOUN
ejpam-2552	175	120	0	0	X
ejpam-2552	175	121	.	.	PUNCT
ejpam-2552	176	1	now	now	ADV
ejpam-2552	176	2	let	let	VERB
ejpam-2552	176	3	us	we	PRON
ejpam-2552	176	4	apply	apply	VERB
ejpam-2552	176	5	this	this	DET
ejpam-2552	176	6	result	result	NOUN
ejpam-2552	176	7	to	to	ADP
ejpam-2552	176	8	ap	ap	PROPN
ejpam-2552	176	9	=	=	PUNCT
ejpam-2552	177	1	‖dpx‖2	‖dpx‖2	ADJ
ejpam-2552	177	2	and	and	CCONJ
ejpam-2552	177	3	fn	fn	NOUN
ejpam-2552	177	4	,	,	PUNCT
ejpam-2552	177	5	p	p	NOUN
ejpam-2552	177	6	=	=	PUNCT
ejpam-2552	177	7	δµp(bn)‖dpx‖2	δµp(bn)‖dpx‖2	X
ejpam-2552	177	8	,	,	PUNCT
ejpam-2552	177	9	for	for	ADP
ejpam-2552	177	10	any	any	DET
ejpam-2552	177	11	(	(	PUNCT
ejpam-2552	177	12	n	n	X
ejpam-2552	177	13	,	,	PUNCT
ejpam-2552	177	14	p	p	NOUN
ejpam-2552	177	15	)	)	PUNCT
ejpam-2552	177	16	of	of	ADP
ejpam-2552	177	17	n×	n×	PROPN
ejpam-2552	177	18	n.	n.	PROPN
ejpam-2552	177	19	it	it	PRON
ejpam-2552	177	20	comes	come	VERB
ejpam-2552	177	21	limn	limn	ADV
ejpam-2552	177	22	∑	∑	ADV
ejpam-2552	177	23	p∈n	p∈n	VERB
ejpam-2552	177	24	δµp(bn)‖dpx‖2	δµp(bn)‖dpx‖2	PUNCT
ejpam-2552	177	25	=	=	SYM
ejpam-2552	177	26	0	0	NUM
ejpam-2552	177	27	,	,	PUNCT
ejpam-2552	177	28	or	or	CCONJ
ejpam-2552	177	29	,	,	PUNCT
ejpam-2552	177	30	taking	take	VERB
ejpam-2552	177	31	into	into	ADP
ejpam-2552	177	32	account	account	NOUN
ejpam-2552	177	33	the	the	DET
ejpam-2552	177	34	result	result	NOUN
ejpam-2552	177	35	of	of	ADP
ejpam-2552	177	36	(	(	PUNCT
ejpam-2552	177	37	2.4.2	2.4.2	NUM
ejpam-2552	177	38	)	)	PUNCT
ejpam-2552	177	39	,	,	PUNCT
ejpam-2552	177	40	limn‖(e(bn))x‖2	limn‖(e(bn))x‖2	ADJ
ejpam-2552	177	41	=	=	SYM
ejpam-2552	178	1	0	0	NUM
ejpam-2552	178	2	,	,	PUNCT
ejpam-2552	178	3	so	so	ADV
ejpam-2552	178	4	a.	a.	NOUN
ejpam-2552	178	5	boudou	boudou	NOUN
ejpam-2552	178	6	,	,	PUNCT
ejpam-2552	178	7	s.	s.	PROPN
ejpam-2552	178	8	viguier	viguier	PROPN
ejpam-2552	178	9	-	-	PUNCT
ejpam-2552	178	10	pla	pla	PROPN
ejpam-2552	178	11	/	/	PUNCT
ejpam-2552	178	12	eur	eur	PROPN
ejpam-2552	178	13	.	.	PUNCT
ejpam-2552	179	1	j.	j.	PROPN
ejpam-2552	179	2	pure	pure	PROPN
ejpam-2552	179	3	appl	appl	PROPN
ejpam-2552	179	4	.	.	PROPN
ejpam-2552	179	5	math	math	PROPN
ejpam-2552	179	6	,	,	PUNCT
ejpam-2552	179	7	11	11	NUM
ejpam-2552	179	8	(	(	PUNCT
ejpam-2552	179	9	4	4	NUM
ejpam-2552	179	10	)	)	PUNCT
ejpam-2552	179	11	(	(	PUNCT
ejpam-2552	179	12	2018	2018	NUM
ejpam-2552	179	13	)	)	PUNCT
ejpam-2552	179	14	,	,	PUNCT
ejpam-2552	179	15	893	893	NUM
ejpam-2552	179	16	-	-	SYM
ejpam-2552	179	17	910	910	NUM
ejpam-2552	179	18	899	899	NUM
ejpam-2552	179	19	limn(e(bn))x	limn(e(bn))x	NOUN
ejpam-2552	179	20	=	=	NOUN
ejpam-2552	179	21	0	0	X
ejpam-2552	179	22	.	.	PUNCT
ejpam-2552	180	1	so	so	ADV
ejpam-2552	180	2	e	e	PROPN
ejpam-2552	180	3	is	be	AUX
ejpam-2552	180	4	a	a	DET
ejpam-2552	180	5	s.m	s.m	PROPN
ejpam-2552	180	6	.	.	PROPN
ejpam-2552	180	7	,	,	PUNCT
ejpam-2552	180	8	and	and	CCONJ
ejpam-2552	180	9	is	be	AUX
ejpam-2552	180	10	clearly	clearly	ADV
ejpam-2552	180	11	bounded	bound	VERB
ejpam-2552	180	12	(	(	PUNCT
ejpam-2552	180	13	because	because	SCONJ
ejpam-2552	180	14	,	,	PUNCT
ejpam-2552	180	15	if	if	SCONJ
ejpam-2552	180	16	we	we	PRON
ejpam-2552	180	17	choose	choose	VERB
ejpam-2552	180	18	a	a	DET
ejpam-2552	180	19	such	such	ADJ
ejpam-2552	180	20	that	that	SCONJ
ejpam-2552	180	21	{	{	PUNCT
ejpam-2552	180	22	µp	µp	NOUN
ejpam-2552	180	23	;	;	PUNCT
ejpam-2552	180	24	p	p	PROPN
ejpam-2552	180	25	∈	∈	PROPN
ejpam-2552	180	26	n	n	CCONJ
ejpam-2552	180	27	}	}	PUNCT
ejpam-2552	180	28	⊂	⊂	PROPN
ejpam-2552	181	1	[	[	X
ejpam-2552	181	2	−a	−a	X
ejpam-2552	181	3	,	,	PUNCT
ejpam-2552	181	4	a	a	DET
ejpam-2552	181	5	[	[	X
ejpam-2552	181	6	,	,	PUNCT
ejpam-2552	181	7	then	then	ADV
ejpam-2552	181	8	e({[−a	e({[−a	NOUN
ejpam-2552	181	9	,	,	PUNCT
ejpam-2552	181	10	a	a	PRON
ejpam-2552	181	11	[	[	X
ejpam-2552	181	12	)	)	PUNCT
ejpam-2552	181	13	=	=	SYM
ejpam-2552	181	14	0	0	NUM
ejpam-2552	181	15	)	)	PUNCT
ejpam-2552	181	16	.	.	PUNCT
ejpam-2552	182	1	when	when	SCONJ
ejpam-2552	182	2	x	x	PRON
ejpam-2552	182	3	is	be	AUX
ejpam-2552	182	4	an	an	DET
ejpam-2552	182	5	element	element	NOUN
ejpam-2552	182	6	of	of	ADP
ejpam-2552	182	7	h	h	NOUN
ejpam-2552	182	8	,	,	PUNCT
ejpam-2552	182	9	from	from	ADP
ejpam-2552	182	10	recalls	recall	NOUN
ejpam-2552	182	11	of	of	ADP
ejpam-2552	182	12	section	section	NOUN
ejpam-2552	182	13	2.2	2.2	NUM
ejpam-2552	182	14	,	,	PUNCT
ejpam-2552	182	15	as	as	ADP
ejpam-2552	182	16	{	{	PUNCT
ejpam-2552	182	17	dpx	dpx	NOUN
ejpam-2552	182	18	;	;	PUNCT
ejpam-2552	182	19	p	p	PROPN
ejpam-2552	182	20	∈	∈	PROPN
ejpam-2552	182	21	n	n	CCONJ
ejpam-2552	182	22	}	}	PUNCT
ejpam-2552	182	23	is	be	AUX
ejpam-2552	182	24	a	a	DET
ejpam-2552	182	25	summable	summable	ADJ
ejpam-2552	182	26	orthogonal	orthogonal	ADJ
ejpam-2552	182	27	family	family	NOUN
ejpam-2552	182	28	of	of	ADP
ejpam-2552	182	29	elements	element	NOUN
ejpam-2552	182	30	of	of	ADP
ejpam-2552	182	31	h	h	NOUN
ejpam-2552	182	32	,	,	PUNCT
ejpam-2552	182	33	the	the	DET
ejpam-2552	182	34	family	family	NOUN
ejpam-2552	182	35	{	{	PUNCT
ejpam-2552	182	36	j(µp)dpx	j(µp)dpx	PROPN
ejpam-2552	182	37	;	;	PUNCT
ejpam-2552	182	38	p	p	PROPN
ejpam-2552	182	39	∈	∈	PROPN
ejpam-2552	182	40	n	n	CCONJ
ejpam-2552	182	41	}	}	PUNCT
ejpam-2552	182	42	,	,	PUNCT
ejpam-2552	182	43	and	and	CCONJ
ejpam-2552	182	44	then	then	ADV
ejpam-2552	182	45	the	the	DET
ejpam-2552	182	46	family	family	NOUN
ejpam-2552	182	47	{	{	PUNCT
ejpam-2552	182	48	µpdpx	µpdpx	NOUN
ejpam-2552	182	49	;	;	PUNCT
ejpam-2552	182	50	p	p	PROPN
ejpam-2552	182	51	∈	∈	PROPN
ejpam-2552	182	52	n	n	CCONJ
ejpam-2552	182	53	}	}	PUNCT
ejpam-2552	182	54	,	,	PUNCT
ejpam-2552	182	55	is	be	AUX
ejpam-2552	182	56	summable	summable	ADJ
ejpam-2552	182	57	of	of	ADP
ejpam-2552	182	58	sum	sum	NOUN
ejpam-2552	182	59	∫	∫	PROPN
ejpam-2552	182	60	jdzxe	jdzxe	PROPN
ejpam-2552	182	61	,	,	PUNCT
ejpam-2552	182	62	and	and	CCONJ
ejpam-2552	182	63	hence	hence	ADV
ejpam-2552	182	64	of	of	ADP
ejpam-2552	182	65	sum	sum	NOUN
ejpam-2552	182	66	ej(x	ej(x	PUNCT
ejpam-2552	182	67	)	)	PUNCT
ejpam-2552	182	68	.	.	PUNCT
ejpam-2552	183	1	as	as	SCONJ
ejpam-2552	183	2	the	the	DET
ejpam-2552	183	3	set	set	NOUN
ejpam-2552	183	4	of	of	ADP
ejpam-2552	183	5	indices	index	NOUN
ejpam-2552	183	6	is	be	AUX
ejpam-2552	183	7	n	n	PRON
ejpam-2552	183	8	,	,	PUNCT
ejpam-2552	183	9	we	we	PRON
ejpam-2552	183	10	can	can	AUX
ejpam-2552	183	11	write	write	VERB
ejpam-2552	183	12	ej(x	ej(x	NOUN
ejpam-2552	183	13	)	)	PUNCT
ejpam-2552	184	1	=	=	PRON
ejpam-2552	184	2	limp→+∞	limp→+∞	PROPN
ejpam-2552	184	3	∑p	∑p	PROPN
ejpam-2552	184	4	k=0	k=0	PROPN
ejpam-2552	184	5	µkdkx	µkdkx	PROPN
ejpam-2552	184	6	.	.	PUNCT
ejpam-2552	185	1	let	let	VERB
ejpam-2552	185	2	us	we	PRON
ejpam-2552	185	3	consider	consider	VERB
ejpam-2552	185	4	ε	ε	PROPN
ejpam-2552	185	5	an	an	DET
ejpam-2552	185	6	element	element	NOUN
ejpam-2552	185	7	of	of	ADP
ejpam-2552	185	8	r∗+	r∗+	PROPN
ejpam-2552	185	9	.	.	PUNCT
ejpam-2552	186	1	there	there	PRON
ejpam-2552	186	2	exists	exist	VERB
ejpam-2552	186	3	an	an	DET
ejpam-2552	186	4	integer	integer	NOUN
ejpam-2552	186	5	nε	nε	NOUN
ejpam-2552	186	6	such	such	ADJ
ejpam-2552	186	7	that	that	PRON
ejpam-2552	186	8	µnε	µnε	PROPN
ejpam-2552	186	9	6	6	NUM
ejpam-2552	186	10	ε	ε	PROPN
ejpam-2552	186	11	(	(	PUNCT
ejpam-2552	186	12	because	because	SCONJ
ejpam-2552	186	13	limnµn	limnµn	ADJ
ejpam-2552	186	14	=	=	NOUN
ejpam-2552	186	15	0	0	NUM
ejpam-2552	186	16	)	)	PUNCT
ejpam-2552	186	17	.	.	PUNCT
ejpam-2552	187	1	for	for	ADP
ejpam-2552	187	2	any	any	DET
ejpam-2552	187	3	finite	finite	ADJ
ejpam-2552	187	4	part	part	NOUN
ejpam-2552	187	5	j	j	PROPN
ejpam-2552	187	6	of	of	ADP
ejpam-2552	187	7	n	n	CCONJ
ejpam-2552	187	8	,	,	PUNCT
ejpam-2552	187	9	disjoint	disjoint	NOUN
ejpam-2552	187	10	of	of	ADP
ejpam-2552	187	11	{	{	PUNCT
ejpam-2552	187	12	0	0	NUM
ejpam-2552	187	13	,	,	PUNCT
ejpam-2552	187	14	1	1	NUM
ejpam-2552	187	15	,	,	PUNCT
ejpam-2552	187	16	.	.	PUNCT
ejpam-2552	187	17	.	.	PUNCT
ejpam-2552	187	18	.	.	PUNCT
ejpam-2552	188	1	,	,	PUNCT
ejpam-2552	188	2	nε−	nε−	PROPN
ejpam-2552	188	3	1	1	NUM
ejpam-2552	188	4	,	,	PUNCT
ejpam-2552	188	5	nε	nε	ADJ
ejpam-2552	188	6	}	}	PUNCT
ejpam-2552	188	7	,	,	PUNCT
ejpam-2552	188	8	we	we	PRON
ejpam-2552	188	9	can	can	AUX
ejpam-2552	188	10	write	write	VERB
ejpam-2552	188	11	‖	‖	PROPN
ejpam-2552	188	12	∑	∑	ADV
ejpam-2552	188	13	p∈j	p∈j	NOUN
ejpam-2552	188	14	µpdp‖	µpdp‖	ADP
ejpam-2552	188	15	6	6	NUM
ejpam-2552	188	16	max{µp	max{µp	NOUN
ejpam-2552	188	17	;	;	PUNCT
ejpam-2552	188	18	p	p	PROPN
ejpam-2552	188	19	∈	∈	PROPN
ejpam-2552	188	20	j	j	PROPN
ejpam-2552	188	21	}	}	PUNCT
ejpam-2552	188	22	<	<	X
ejpam-2552	188	23	µnε	µnε	PROPN
ejpam-2552	188	24	6	6	NUM
ejpam-2552	188	25	ε	ε	PROPN
ejpam-2552	188	26	.	.	PUNCT
ejpam-2552	189	1	this	this	PRON
ejpam-2552	189	2	allows	allow	VERB
ejpam-2552	189	3	us	we	PRON
ejpam-2552	189	4	to	to	PART
ejpam-2552	189	5	affirm	affirm	VERB
ejpam-2552	189	6	that	that	SCONJ
ejpam-2552	189	7	{	{	PUNCT
ejpam-2552	189	8	µpdp	µpdp	NOUN
ejpam-2552	189	9	;	;	PUNCT
ejpam-2552	189	10	p	p	PROPN
ejpam-2552	189	11	∈	∈	PROPN
ejpam-2552	189	12	n	n	CCONJ
ejpam-2552	189	13	}	}	PUNCT
ejpam-2552	189	14	is	be	AUX
ejpam-2552	189	15	a	a	DET
ejpam-2552	189	16	summable	summable	ADJ
ejpam-2552	189	17	family	family	NOUN
ejpam-2552	189	18	of	of	ADP
ejpam-2552	189	19	elements	element	NOUN
ejpam-2552	189	20	of	of	ADP
ejpam-2552	189	21	l(h	l(h	PROPN
ejpam-2552	189	22	)	)	PUNCT
ejpam-2552	189	23	.	.	PUNCT
ejpam-2552	190	1	as	as	SCONJ
ejpam-2552	190	2	the	the	DET
ejpam-2552	190	3	set	set	NOUN
ejpam-2552	190	4	of	of	ADP
ejpam-2552	190	5	indices	index	NOUN
ejpam-2552	190	6	of	of	ADP
ejpam-2552	190	7	this	this	DET
ejpam-2552	190	8	summable	summable	ADJ
ejpam-2552	190	9	family	family	NOUN
ejpam-2552	190	10	is	be	AUX
ejpam-2552	190	11	n	n	PRON
ejpam-2552	190	12	,	,	PUNCT
ejpam-2552	190	13	it	it	PRON
ejpam-2552	190	14	comes	come	VERB
ejpam-2552	190	15	(	(	PUNCT
ejpam-2552	190	16	∑	∑	PUNCT
ejpam-2552	190	17	p∈n	p∈n	VERB
ejpam-2552	190	18	µpdp)x	µpdp)x	PROPN
ejpam-2552	190	19	=	=	SYM
ejpam-2552	190	20	(	(	PUNCT
ejpam-2552	190	21	limp	limp	ADJ
ejpam-2552	190	22	∑p	∑p	PUNCT
ejpam-2552	190	23	k=0	k=0	PROPN
ejpam-2552	190	24	µpdp)x	µpdp)x	PUNCT
ejpam-2552	190	25	=	=	NOUN
ejpam-2552	190	26	limp	limp	ADJ
ejpam-2552	190	27	∑p	∑p	ADJ
ejpam-2552	190	28	k=0	k=0	PROPN
ejpam-2552	190	29	µpdpx	µpdpx	NOUN
ejpam-2552	190	30	=	=	SYM
ejpam-2552	190	31	ej(x	ej(x	X
ejpam-2552	190	32	)	)	PUNCT
ejpam-2552	190	33	,	,	PUNCT
ejpam-2552	190	34	taking	take	VERB
ejpam-2552	190	35	into	into	ADP
ejpam-2552	190	36	account	account	NOUN
ejpam-2552	190	37	what	what	PRON
ejpam-2552	190	38	precedes	precede	VERB
ejpam-2552	190	39	.	.	PUNCT
ejpam-2552	191	1	this	this	PRON
ejpam-2552	191	2	ends	end	VERB
ejpam-2552	191	3	the	the	DET
ejpam-2552	191	4	proof	proof	NOUN
ejpam-2552	191	5	of	of	ADP
ejpam-2552	191	6	point	point	NOUN
ejpam-2552	191	7	c	c	NOUN
ejpam-2552	191	8	)	)	PUNCT
ejpam-2552	191	9	.	.	PUNCT
ejpam-2552	192	1	�	�	PROPN
ejpam-2552	192	2	2.5	2.5	NUM
ejpam-2552	192	3	.	.	PUNCT
ejpam-2552	193	1	spectral	spectral	ADJ
ejpam-2552	193	2	measure	measure	NOUN
ejpam-2552	193	3	associated	associate	VERB
ejpam-2552	193	4	with	with	ADP
ejpam-2552	193	5	an	an	DET
ejpam-2552	193	6	operator	operator	NOUN
ejpam-2552	193	7	many	many	ADJ
ejpam-2552	193	8	monographs	monograph	NOUN
ejpam-2552	193	9	(	(	PUNCT
ejpam-2552	193	10	see	see	VERB
ejpam-2552	193	11	,	,	PUNCT
ejpam-2552	193	12	for	for	ADP
ejpam-2552	193	13	instance	instance	NOUN
ejpam-2552	193	14	,	,	PUNCT
ejpam-2552	193	15	dunford	dunford	PROPN
ejpam-2552	193	16	and	and	CCONJ
ejpam-2552	193	17	schwartz	schwartz	PROPN
ejpam-2552	193	18	,	,	PUNCT
ejpam-2552	193	19	1963	1963	NUM
ejpam-2552	193	20	,	,	PUNCT
ejpam-2552	193	21	riesz	riesz	NOUN
ejpam-2552	193	22	and	and	CCONJ
ejpam-2552	193	23	nagy	nagy	NOUN
ejpam-2552	193	24	,	,	PUNCT
ejpam-2552	193	25	1991	1991	NUM
ejpam-2552	193	26	)	)	PUNCT
ejpam-2552	193	27	evoque	evoque	VERB
ejpam-2552	193	28	an	an	DET
ejpam-2552	193	29	association	association	NOUN
ejpam-2552	193	30	between	between	ADP
ejpam-2552	193	31	a	a	DET
ejpam-2552	193	32	s.m	s.m	PROPN
ejpam-2552	193	33	.	.	PUNCT
ejpam-2552	193	34	e	e	PROPN
ejpam-2552	193	35	and	and	CCONJ
ejpam-2552	193	36	a	a	DET
ejpam-2552	193	37	selfadjoint	selfadjoint	NOUN
ejpam-2552	193	38	operator	operator	NOUN
ejpam-2552	193	39	a	a	PRON
ejpam-2552	193	40	which	which	PRON
ejpam-2552	193	41	allows	allow	VERB
ejpam-2552	193	42	to	to	PART
ejpam-2552	193	43	express	express	VERB
ejpam-2552	193	44	this	this	DET
ejpam-2552	193	45	last	last	ADJ
ejpam-2552	193	46	one	one	NOUN
ejpam-2552	193	47	as	as	ADP
ejpam-2552	193	48	an	an	DET
ejpam-2552	193	49	integral	integral	ADJ
ejpam-2552	193	50	:	:	PUNCT
ejpam-2552	193	51	a	a	DET
ejpam-2552	193	52	=	=	X
ejpam-2552	193	53	∫	∫	PROPN
ejpam-2552	193	54	λde(λ	λde(λ	PROPN
ejpam-2552	193	55	)	)	PUNCT
ejpam-2552	193	56	.	.	PUNCT
ejpam-2552	194	1	more	more	ADV
ejpam-2552	194	2	precisely	precisely	ADV
ejpam-2552	194	3	,	,	PUNCT
ejpam-2552	194	4	we	we	PRON
ejpam-2552	194	5	check	check	VERB
ejpam-2552	194	6	the	the	DET
ejpam-2552	194	7	following	following	NOUN
ejpam-2552	194	8	.	.	PUNCT
ejpam-2552	195	1	let	let	VERB
ejpam-2552	195	2	a	a	PRON
ejpam-2552	195	3	be	be	AUX
ejpam-2552	195	4	a	a	DET
ejpam-2552	195	5	bounded	bounded	ADJ
ejpam-2552	195	6	selfadjoint	selfadjoint	NOUN
ejpam-2552	195	7	operator	operator	NOUN
ejpam-2552	195	8	.	.	PUNCT
ejpam-2552	196	1	there	there	PRON
ejpam-2552	196	2	exists	exist	VERB
ejpam-2552	196	3	one	one	NUM
ejpam-2552	196	4	,	,	PUNCT
ejpam-2552	196	5	and	and	CCONJ
ejpam-2552	196	6	only	only	ADV
ejpam-2552	196	7	one	one	NUM
ejpam-2552	196	8	,	,	PUNCT
ejpam-2552	196	9	bounded	bound	VERB
ejpam-2552	196	10	s.m	s.m	PROPN
ejpam-2552	196	11	.	.	PROPN
ejpam-2552	196	12	e	e	PROPN
ejpam-2552	196	13	,	,	PUNCT
ejpam-2552	196	14	named	name	VERB
ejpam-2552	196	15	s.m	s.m	PROPN
ejpam-2552	196	16	.	.	PROPN
ejpam-2552	196	17	associated	associate	VERB
ejpam-2552	196	18	with	with	ADP
ejpam-2552	196	19	a	a	PRON
ejpam-2552	196	20	,	,	PUNCT
ejpam-2552	196	21	such	such	ADJ
ejpam-2552	196	22	that	that	SCONJ
ejpam-2552	196	23	,	,	PUNCT
ejpam-2552	196	24	for	for	ADP
ejpam-2552	196	25	any	any	DET
ejpam-2552	196	26	x	x	NOUN
ejpam-2552	196	27	of	of	ADP
ejpam-2552	196	28	h	h	NOUN
ejpam-2552	196	29	,	,	PUNCT
ejpam-2552	196	30	ax	ax	NOUN
ejpam-2552	196	31	=	=	SYM
ejpam-2552	196	32	∫	∫	PROPN
ejpam-2552	196	33	jdzxe	jdzxe	PROPN
ejpam-2552	196	34	.	.	PUNCT
ejpam-2552	197	1	this	this	DET
ejpam-2552	197	2	s.m	s.m	PROPN
ejpam-2552	197	3	.	.	PROPN
ejpam-2552	197	4	is	be	AUX
ejpam-2552	197	5	such	such	ADJ
ejpam-2552	197	6	that	that	SCONJ
ejpam-2552	197	7	‖a‖	‖a‖	PROPN
ejpam-2552	197	8	=	=	PUNCT
ejpam-2552	197	9	inf{a	inf{a	PROPN
ejpam-2552	197	10	∈	∈	PROPN
ejpam-2552	197	11	r+	r+	NOUN
ejpam-2552	197	12	;	;	PUNCT
ejpam-2552	197	13	e([−a	e([−a	PROPN
ejpam-2552	197	14	,	,	PUNCT
ejpam-2552	197	15	a	a	DET
ejpam-2552	197	16	]	]	X
ejpam-2552	197	17	)	)	PUNCT
ejpam-2552	197	18	=	=	PUNCT
ejpam-2552	197	19	ih	ih	NOUN
ejpam-2552	197	20	}	}	PUNCT
ejpam-2552	197	21	.	.	PUNCT
ejpam-2552	198	1	without	without	ADP
ejpam-2552	198	2	pretention	pretention	NOUN
ejpam-2552	198	3	of	of	ADP
ejpam-2552	198	4	giving	give	VERB
ejpam-2552	198	5	exhaustive	exhaustive	ADJ
ejpam-2552	198	6	explanations	explanation	NOUN
ejpam-2552	198	7	,	,	PUNCT
ejpam-2552	198	8	we	we	PRON
ejpam-2552	198	9	will	will	AUX
ejpam-2552	198	10	give	give	VERB
ejpam-2552	198	11	some	some	DET
ejpam-2552	198	12	indications	indication	NOUN
ejpam-2552	198	13	on	on	ADP
ejpam-2552	198	14	the	the	DET
ejpam-2552	198	15	way	way	NOUN
ejpam-2552	198	16	the	the	DET
ejpam-2552	198	17	s.m	s.m	PROPN
ejpam-2552	198	18	.	.	PUNCT
ejpam-2552	199	1	e	e	PROPN
ejpam-2552	199	2	is	be	AUX
ejpam-2552	199	3	defined	define	VERB
ejpam-2552	199	4	.	.	PUNCT
ejpam-2552	200	1	if	if	SCONJ
ejpam-2552	200	2	a	a	PRON
ejpam-2552	200	3	is	be	AUX
ejpam-2552	200	4	a	a	DET
ejpam-2552	200	5	bounded	bounded	ADJ
ejpam-2552	200	6	selfadjoint	selfadjoint	NOUN
ejpam-2552	200	7	operator	operator	NOUN
ejpam-2552	200	8	,	,	PUNCT
ejpam-2552	200	9	it	it	PRON
ejpam-2552	200	10	is	be	AUX
ejpam-2552	200	11	easy	easy	ADJ
ejpam-2552	200	12	to	to	PART
ejpam-2552	200	13	verify	verify	VERB
ejpam-2552	200	14	that	that	SCONJ
ejpam-2552	200	15	(	(	PUNCT
ejpam-2552	200	16	eita(x))t∈r	eita(x))t∈r	NOUN
ejpam-2552	200	17	is	be	AUX
ejpam-2552	200	18	a	a	DET
ejpam-2552	200	19	stationary	stationary	ADJ
ejpam-2552	200	20	c.r.f	c.r.f	NOUN
ejpam-2552	200	21	.	.	PUNCT
ejpam-2552	200	22	,	,	PUNCT
ejpam-2552	200	23	and	and	CCONJ
ejpam-2552	200	24	we	we	PRON
ejpam-2552	200	25	denote	denote	VERB
ejpam-2552	200	26	by	by	ADP
ejpam-2552	200	27	zx	zx	PROPN
ejpam-2552	200	28	its	its	PRON
ejpam-2552	200	29	associated	associated	PROPN
ejpam-2552	200	30	r.m	r.m	PROPN
ejpam-2552	200	31	..	..	PROPN
ejpam-2552	201	1	so	so	ADV
ejpam-2552	201	2	we	we	PRON
ejpam-2552	201	3	obtain	obtain	VERB
ejpam-2552	201	4	a	a	DET
ejpam-2552	201	5	family	family	NOUN
ejpam-2552	201	6	of	of	ADP
ejpam-2552	201	7	stationary	stationary	ADJ
ejpam-2552	201	8	c.r.f	c.r.f	NOUN
ejpam-2552	201	9	.	.	PUNCT
ejpam-2552	201	10	’s	’s	PROPN
ejpam-2552	201	11	,	,	PUNCT
ejpam-2552	201	12	which	which	PRON
ejpam-2552	201	13	are	be	AUX
ejpam-2552	201	14	pairwise	pairwise	NOUN
ejpam-2552	201	15	stationarily	stationarily	ADV
ejpam-2552	201	16	correlated	correlate	VERB
ejpam-2552	201	17	.	.	PUNCT
ejpam-2552	202	1	from	from	ADP
ejpam-2552	202	2	this	this	DET
ejpam-2552	202	3	fact	fact	NOUN
ejpam-2552	202	4	,	,	PUNCT
ejpam-2552	202	5	we	we	PRON
ejpam-2552	202	6	deduce	deduce	VERB
ejpam-2552	202	7	,	,	PUNCT
ejpam-2552	202	8	on	on	ADP
ejpam-2552	202	9	one	one	NUM
ejpam-2552	202	10	hand	hand	NOUN
ejpam-2552	202	11	,	,	PUNCT
ejpam-2552	202	12	that	that	SCONJ
ejpam-2552	202	13	for	for	ADP
ejpam-2552	202	14	any	any	DET
ejpam-2552	202	15	b	b	PROPN
ejpam-2552	202	16	of	of	ADP
ejpam-2552	202	17	br	br	PROPN
ejpam-2552	202	18	,	,	PUNCT
ejpam-2552	202	19	the	the	DET
ejpam-2552	202	20	application	application	NOUN
ejpam-2552	202	21	e(b	e(b	VERB
ejpam-2552	202	22	)	)	PUNCT
ejpam-2552	202	23	:	:	PUNCT
ejpam-2552	203	1	x	x	X
ejpam-2552	203	2	∈	∈	NOUN
ejpam-2552	203	3	h	h	NOUN
ejpam-2552	203	4	7→	7→	NUM
ejpam-2552	203	5	zx(b	zx(b	NUM
ejpam-2552	203	6	)	)	PUNCT
ejpam-2552	203	7	∈	∈	PROPN
ejpam-2552	203	8	h	h	NOUN
ejpam-2552	203	9	is	be	AUX
ejpam-2552	203	10	a	a	DET
ejpam-2552	203	11	projector	projector	NOUN
ejpam-2552	203	12	,	,	PUNCT
ejpam-2552	203	13	and	and	CCONJ
ejpam-2552	203	14	on	on	ADP
ejpam-2552	203	15	another	another	DET
ejpam-2552	203	16	hand	hand	NOUN
ejpam-2552	203	17	,	,	PUNCT
ejpam-2552	203	18	that	that	SCONJ
ejpam-2552	203	19	the	the	DET
ejpam-2552	203	20	application	application	NOUN
ejpam-2552	203	21	e	e	NOUN
ejpam-2552	203	22	:	:	PUNCT
ejpam-2552	203	23	b	b	X
ejpam-2552	203	24	∈	∈	PROPN
ejpam-2552	203	25	br	br	NOUN
ejpam-2552	203	26	7→	7→	NUM
ejpam-2552	203	27	e(b	e(b	NOUN
ejpam-2552	203	28	)	)	PUNCT
ejpam-2552	203	29	∈	∈	PROPN
ejpam-2552	203	30	p(h	p(h	NOUN
ejpam-2552	203	31	)	)	PUNCT
ejpam-2552	203	32	is	be	AUX
ejpam-2552	203	33	a	a	DET
ejpam-2552	203	34	bounded	bounded	ADJ
ejpam-2552	203	35	s.m	s.m	PROPN
ejpam-2552	203	36	.	.	PROPN
ejpam-2552	204	1	such	such	ADJ
ejpam-2552	204	2	that	that	SCONJ
ejpam-2552	204	3	a	a	DET
ejpam-2552	204	4	=	=	SYM
ejpam-2552	204	5	ej	ej	X
ejpam-2552	204	6	,	,	PUNCT
ejpam-2552	204	7	or	or	CCONJ
ejpam-2552	204	8	,	,	PUNCT
ejpam-2552	204	9	in	in	ADP
ejpam-2552	204	10	other	other	ADJ
ejpam-2552	204	11	words	word	NOUN
ejpam-2552	204	12	,	,	PUNCT
ejpam-2552	204	13	such	such	ADJ
ejpam-2552	204	14	that	that	DET
ejpam-2552	204	15	ax	ax	NOUN
ejpam-2552	204	16	=	=	SYM
ejpam-2552	204	17	∫	∫	PROPN
ejpam-2552	204	18	jdzxe	jdzxe	PROPN
ejpam-2552	204	19	,	,	PUNCT
ejpam-2552	204	20	for	for	ADP
ejpam-2552	204	21	any	any	DET
ejpam-2552	204	22	x	x	PROPN
ejpam-2552	204	23	of	of	ADP
ejpam-2552	204	24	h.	h.	NOUN
ejpam-2552	204	25	for	for	ADP
ejpam-2552	204	26	any	any	DET
ejpam-2552	204	27	a	a	DET
ejpam-2552	204	28	>	>	X
ejpam-2552	204	29	‖a‖	‖a‖	PROPN
ejpam-2552	204	30	,	,	PUNCT
ejpam-2552	204	31	we	we	PRON
ejpam-2552	204	32	can	can	AUX
ejpam-2552	204	33	write	write	VERB
ejpam-2552	205	1	a	a	DET
ejpam-2552	205	2	=	=	X
ejpam-2552	205	3	limm→∞	limm→∞	PROPN
ejpam-2552	205	4	∑k	∑k	PROPN
ejpam-2552	205	5	=	=	PROPN
ejpam-2552	205	6	m−1	m−1	PROPN
ejpam-2552	205	7	k=0	k=0	PROPN
ejpam-2552	205	8	(	(	PUNCT
ejpam-2552	205	9	−a+	−a+	X
ejpam-2552	205	10	k	k	PROPN
ejpam-2552	205	11	2a	2a	PROPN
ejpam-2552	205	12	m	m	VERB
ejpam-2552	205	13	)	)	PUNCT
ejpam-2552	205	14	e([−a+	e([−a+	PROPN
ejpam-2552	205	15	k	k	PROPN
ejpam-2552	205	16	2a	2a	PROPN
ejpam-2552	205	17	m	m	VERB
ejpam-2552	205	18	,	,	PUNCT
ejpam-2552	205	19	−a+	−a+	X
ejpam-2552	205	20	(	(	PUNCT
ejpam-2552	205	21	k	k	NOUN
ejpam-2552	206	1	+	+	NUM
ejpam-2552	206	2	1)2am	1)2am	NUM
ejpam-2552	206	3	[	[	X
ejpam-2552	206	4	)	)	PUNCT
ejpam-2552	206	5	,	,	PUNCT
ejpam-2552	206	6	in	in	ADP
ejpam-2552	206	7	l(h	l(h	PROPN
ejpam-2552	206	8	)	)	PUNCT
ejpam-2552	206	9	,	,	PUNCT
ejpam-2552	206	10	expression	expression	NOUN
ejpam-2552	206	11	which	which	PRON
ejpam-2552	206	12	evoques	evoque	VERB
ejpam-2552	206	13	a	a	DET
ejpam-2552	206	14	riemann	riemann	PROPN
ejpam-2552	206	15	sum	sum	NOUN
ejpam-2552	206	16	associated	associate	VERB
ejpam-2552	206	17	with	with	ADP
ejpam-2552	206	18	an	an	DET
ejpam-2552	206	19	integral	integral	NOUN
ejpam-2552	206	20	of	of	ADP
ejpam-2552	206	21	the	the	DET
ejpam-2552	206	22	type	type	NOUN
ejpam-2552	206	23	∫	∫	PROPN
ejpam-2552	206	24	λde(λ	λde(λ	PROPN
ejpam-2552	206	25	)	)	PUNCT
ejpam-2552	206	26	.	.	PUNCT
ejpam-2552	207	1	let	let	VERB
ejpam-2552	207	2	us	we	PRON
ejpam-2552	207	3	now	now	ADV
ejpam-2552	207	4	examine	examine	VERB
ejpam-2552	207	5	the	the	DET
ejpam-2552	207	6	following	following	ADJ
ejpam-2552	207	7	preliminary	preliminary	ADJ
ejpam-2552	207	8	result	result	NOUN
ejpam-2552	207	9	.	.	PUNCT
ejpam-2552	208	1	lemma	lemma	PROPN
ejpam-2552	208	2	2.5.1	2.5.1	NUM
ejpam-2552	208	3	.	.	PUNCT
ejpam-2552	209	1	if	if	SCONJ
ejpam-2552	209	2	e	e	PROPN
ejpam-2552	209	3	is	be	AUX
ejpam-2552	209	4	the	the	DET
ejpam-2552	209	5	s.m	s.m	PROPN
ejpam-2552	209	6	.	.	PROPN
ejpam-2552	209	7	associated	associate	VERB
ejpam-2552	209	8	with	with	ADP
ejpam-2552	209	9	the	the	DET
ejpam-2552	209	10	bounded	bounded	ADJ
ejpam-2552	209	11	selfadjoint	selfadjoint	NOUN
ejpam-2552	209	12	operator	operator	NOUN
ejpam-2552	209	13	a	a	PRON
ejpam-2552	209	14	,	,	PUNCT
ejpam-2552	209	15	then	then	ADV
ejpam-2552	209	16	,	,	PUNCT
ejpam-2552	209	17	for	for	ADP
ejpam-2552	209	18	any	any	DET
ejpam-2552	209	19	n	n	NOUN
ejpam-2552	209	20	of	of	ADP
ejpam-2552	209	21	n	n	CCONJ
ejpam-2552	209	22	,	,	PUNCT
ejpam-2552	209	23	we	we	PRON
ejpam-2552	209	24	have	have	VERB
ejpam-2552	209	25	an	an	DET
ejpam-2552	209	26	=	=	NOUN
ejpam-2552	209	27	ejn	ejn	NOUN
ejpam-2552	209	28	.	.	PUNCT
ejpam-2552	210	1	proof	proof	NOUN
ejpam-2552	210	2	.	.	PUNCT
ejpam-2552	211	1	the	the	DET
ejpam-2552	211	2	proof	proof	NOUN
ejpam-2552	211	3	is	be	AUX
ejpam-2552	211	4	obtained	obtain	VERB
ejpam-2552	211	5	by	by	ADP
ejpam-2552	211	6	induction	induction	NOUN
ejpam-2552	211	7	.	.	PUNCT
ejpam-2552	212	1	in	in	ADP
ejpam-2552	212	2	fact	fact	NOUN
ejpam-2552	212	3	,	,	PUNCT
ejpam-2552	212	4	if	if	SCONJ
ejpam-2552	212	5	n	n	PRON
ejpam-2552	212	6	is	be	AUX
ejpam-2552	212	7	an	an	DET
ejpam-2552	212	8	integer	integer	NOUN
ejpam-2552	212	9	such	such	DET
ejpam-2552	212	10	that	that	SCONJ
ejpam-2552	212	11	an	an	DET
ejpam-2552	212	12	=	=	NOUN
ejpam-2552	212	13	ejn	ejn	NOUN
ejpam-2552	212	14	,	,	PUNCT
ejpam-2552	212	15	then	then	ADV
ejpam-2552	212	16	,	,	PUNCT
ejpam-2552	212	17	for	for	ADP
ejpam-2552	212	18	any	any	DET
ejpam-2552	212	19	x	x	NOUN
ejpam-2552	212	20	of	of	ADP
ejpam-2552	212	21	h	h	NOUN
ejpam-2552	212	22	,	,	PUNCT
ejpam-2552	212	23	we	we	PRON
ejpam-2552	212	24	have	have	VERB
ejpam-2552	212	25	:	:	PUNCT
ejpam-2552	212	26	<	<	X
ejpam-2552	212	27	an+1x	an+1x	PROPN
ejpam-2552	212	28	,	,	PUNCT
ejpam-2552	212	29	x	x	X
ejpam-2552	212	30	>	>	PUNCT
ejpam-2552	212	31	=	=	X
ejpam-2552	212	32	<	<	X
ejpam-2552	212	33	anx	anx	ADJ
ejpam-2552	212	34	,	,	PUNCT
ejpam-2552	212	35	ax	ax	NOUN
ejpam-2552	212	36	>	>	PUNCT
ejpam-2552	212	37	=	=	X
ejpam-2552	212	38	<	<	X
ejpam-2552	212	39	ejn(x	ejn(x	PROPN
ejpam-2552	212	40	)	)	PUNCT
ejpam-2552	212	41	,	,	PUNCT
ejpam-2552	212	42	ej(x	ej(x	X
ejpam-2552	212	43	)	)	PUNCT
ejpam-2552	212	44	>	>	PUNCT
ejpam-2552	213	1	=	=	PUNCT
ejpam-2552	213	2	<	<	X
ejpam-2552	213	3	∫	∫	PROPN
ejpam-2552	213	4	jndzxe	jndzxe	PROPN
ejpam-2552	213	5	,	,	PUNCT
ejpam-2552	213	6	∫	∫	PROPN
ejpam-2552	213	7	jdzxe	jdzxe	PROPN
ejpam-2552	213	8	>	>	X
ejpam-2552	214	1	=	=	X
ejpam-2552	214	2	<	<	X
ejpam-2552	214	3	jn	jn	PROPN
ejpam-2552	214	4	,	,	PUNCT
ejpam-2552	214	5	j	j	PROPN
ejpam-2552	214	6	>	>	PUNCT
ejpam-2552	214	7	l2(µ	l2(µ	PROPN
ejpam-2552	214	8	zxe	zxe	PROPN
ejpam-2552	214	9	)	)	PUNCT
ejpam-2552	214	10	=	=	SYM
ejpam-2552	215	1	∫	∫	PROPN
ejpam-2552	215	2	jn+1dµzxe	jn+1dµzxe	PROPN
ejpam-2552	216	1	=	=	X
ejpam-2552	216	2	<	<	X
ejpam-2552	216	3	∫	∫	PROPN
ejpam-2552	216	4	jn+1dzxe	jn+1dzxe	PROPN
ejpam-2552	216	5	,	,	PUNCT
ejpam-2552	216	6	∫	∫	PROPN
ejpam-2552	216	7	r	r	NOUN
ejpam-2552	216	8	dzxe	dzxe	NOUN
ejpam-2552	216	9	>	>	PUNCT
ejpam-2552	217	1	=	=	X
ejpam-2552	217	2	<	<	X
ejpam-2552	217	3	ejn+1x	ejn+1x	PROPN
ejpam-2552	217	4	,	,	PUNCT
ejpam-2552	217	5	x	x	X
ejpam-2552	217	6	>	>	PUNCT
ejpam-2552	217	7	.	.	PUNCT
ejpam-2552	217	8	a.	a.	NOUN
ejpam-2552	217	9	boudou	boudou	NOUN
ejpam-2552	217	10	,	,	PUNCT
ejpam-2552	217	11	s.	s.	PROPN
ejpam-2552	217	12	viguier	viguier	PROPN
ejpam-2552	217	13	-	-	PUNCT
ejpam-2552	217	14	pla	pla	PROPN
ejpam-2552	217	15	/	/	PUNCT
ejpam-2552	217	16	eur	eur	PROPN
ejpam-2552	217	17	.	.	PUNCT
ejpam-2552	218	1	j.	j.	PROPN
ejpam-2552	218	2	pure	pure	PROPN
ejpam-2552	218	3	appl	appl	PROPN
ejpam-2552	218	4	.	.	PROPN
ejpam-2552	218	5	math	math	PROPN
ejpam-2552	218	6	,	,	PUNCT
ejpam-2552	218	7	11	11	NUM
ejpam-2552	218	8	(	(	PUNCT
ejpam-2552	218	9	4	4	NUM
ejpam-2552	218	10	)	)	PUNCT
ejpam-2552	218	11	(	(	PUNCT
ejpam-2552	218	12	2018	2018	NUM
ejpam-2552	218	13	)	)	PUNCT
ejpam-2552	218	14	,	,	PUNCT
ejpam-2552	218	15	893	893	NUM
ejpam-2552	218	16	-	-	SYM
ejpam-2552	218	17	910	910	NUM
ejpam-2552	218	18	900	900	NUM
ejpam-2552	218	19	then	then	ADV
ejpam-2552	218	20	an+1	an+1	VERB
ejpam-2552	218	21	=	=	SYM
ejpam-2552	218	22	ejn+1	ejn+1	X
ejpam-2552	218	23	,	,	PUNCT
ejpam-2552	218	24	what	what	PRON
ejpam-2552	218	25	means	mean	VERB
ejpam-2552	218	26	that	that	SCONJ
ejpam-2552	218	27	the	the	DET
ejpam-2552	218	28	property	property	NOUN
ejpam-2552	218	29	is	be	AUX
ejpam-2552	218	30	true	true	ADJ
ejpam-2552	218	31	for	for	ADP
ejpam-2552	218	32	n+	n+	PRON
ejpam-2552	218	33	1	1	X
ejpam-2552	218	34	.	.	X
ejpam-2552	218	35	�	�	PROPN
ejpam-2552	218	36	so	so	SCONJ
ejpam-2552	218	37	the	the	DET
ejpam-2552	218	38	proposition	proposition	NOUN
ejpam-2552	218	39	follows	follow	VERB
ejpam-2552	218	40	.	.	PUNCT
ejpam-2552	219	1	proposition	proposition	NOUN
ejpam-2552	219	2	2.5.1	2.5.1	NUM
ejpam-2552	219	3	.	.	PUNCT
ejpam-2552	220	1	if	if	SCONJ
ejpam-2552	220	2	a	a	PRON
ejpam-2552	220	3	is	be	AUX
ejpam-2552	220	4	a	a	DET
ejpam-2552	220	5	bounded	bounded	ADJ
ejpam-2552	220	6	selfadjoint	selfadjoint	NOUN
ejpam-2552	220	7	operator	operator	NOUN
ejpam-2552	220	8	of	of	ADP
ejpam-2552	220	9	associated	associated	ADJ
ejpam-2552	220	10	s.m	s.m	PROPN
ejpam-2552	220	11	.	.	PUNCT
ejpam-2552	221	1	e	e	X
ejpam-2552	221	2	,	,	PUNCT
ejpam-2552	221	3	if	if	SCONJ
ejpam-2552	221	4	t	t	PROPN
ejpam-2552	221	5	is	be	AUX
ejpam-2552	221	6	an	an	DET
ejpam-2552	221	7	element	element	NOUN
ejpam-2552	221	8	of	of	ADP
ejpam-2552	221	9	l(h	l(h	PROPN
ejpam-2552	221	10	)	)	PUNCT
ejpam-2552	221	11	such	such	ADJ
ejpam-2552	221	12	that	that	SCONJ
ejpam-2552	221	13	t	t	PROPN
ejpam-2552	221	14	◦	◦	NOUN
ejpam-2552	221	15	a	a	DET
ejpam-2552	221	16	=	=	NOUN
ejpam-2552	221	17	a	a	DET
ejpam-2552	221	18	◦	◦	NOUN
ejpam-2552	221	19	t	t	NOUN
ejpam-2552	221	20	,	,	PUNCT
ejpam-2552	221	21	then	then	ADV
ejpam-2552	221	22	,	,	PUNCT
ejpam-2552	221	23	for	for	ADP
ejpam-2552	221	24	any	any	DET
ejpam-2552	221	25	b	b	PROPN
ejpam-2552	221	26	of	of	ADP
ejpam-2552	221	27	br	br	PROPN
ejpam-2552	221	28	,	,	PUNCT
ejpam-2552	221	29	t	t	PROPN
ejpam-2552	221	30	and	and	CCONJ
ejpam-2552	221	31	e(b	e(b	PROPN
ejpam-2552	221	32	)	)	PUNCT
ejpam-2552	221	33	commute	commute	NOUN
ejpam-2552	221	34	.	.	PUNCT
ejpam-2552	222	1	proof	proof	NOUN
ejpam-2552	222	2	.	.	PUNCT
ejpam-2552	223	1	as	as	SCONJ
ejpam-2552	223	2	µztxe	µztxe	NOUN
ejpam-2552	223	3	+	+	CCONJ
ejpam-2552	223	4	µzxe	µzxe	NOUN
ejpam-2552	223	5	has	have	VERB
ejpam-2552	223	6	a	a	DET
ejpam-2552	223	7	compact	compact	ADJ
ejpam-2552	223	8	support	support	NOUN
ejpam-2552	223	9	,	,	PUNCT
ejpam-2552	223	10	for	for	ADP
ejpam-2552	223	11	any	any	DET
ejpam-2552	223	12	b	b	PROPN
ejpam-2552	223	13	of	of	ADP
ejpam-2552	223	14	br	br	PROPN
ejpam-2552	223	15	,	,	PUNCT
ejpam-2552	223	16	1b	1b	PROPN
ejpam-2552	223	17	can	can	AUX
ejpam-2552	223	18	be	be	AUX
ejpam-2552	223	19	writen	writen	VERB
ejpam-2552	223	20	as	as	ADP
ejpam-2552	223	21	1b	1b	NUM
ejpam-2552	223	22	=	=	SYM
ejpam-2552	223	23	limm→∞	limm→∞	PROPN
ejpam-2552	223	24	∑	∑	ADV
ejpam-2552	223	25	j∈jm	j∈jm	PROPN
ejpam-2552	223	26	αj	αj	PROPN
ejpam-2552	223	27	,	,	PUNCT
ejpam-2552	223	28	mj	mj	PROPN
ejpam-2552	223	29	nj	nj	PROPN
ejpam-2552	223	30	,	,	PUNCT
ejpam-2552	223	31	m	m	PROPN
ejpam-2552	223	32	,	,	PUNCT
ejpam-2552	223	33	|jm|	|jm|	X
ejpam-2552	223	34	<	<	X
ejpam-2552	223	35	+	+	PROPN
ejpam-2552	223	36	∞	∞	PROPN
ejpam-2552	223	37	,	,	PUNCT
ejpam-2552	223	38	in	in	ADP
ejpam-2552	223	39	l2(µztxe	l2(µztxe	ADJ
ejpam-2552	223	40	+	+	CCONJ
ejpam-2552	223	41	µzxe	µzxe	NOUN
ejpam-2552	223	42	)	)	PUNCT
ejpam-2552	223	43	.	.	PUNCT
ejpam-2552	224	1	(	(	PUNCT
ejpam-2552	224	2	2.5.1	2.5.1	X
ejpam-2552	224	3	)	)	PUNCT
ejpam-2552	224	4	equality	equality	NOUN
ejpam-2552	224	5	(	(	PUNCT
ejpam-2552	224	6	2.5.1	2.5.1	NUM
ejpam-2552	224	7	)	)	PUNCT
ejpam-2552	224	8	is	be	AUX
ejpam-2552	224	9	exact	exact	ADJ
ejpam-2552	224	10	in	in	ADP
ejpam-2552	224	11	l2(µztxe	l2(µztxe	ADJ
ejpam-2552	224	12	)	)	PUNCT
ejpam-2552	224	13	and	and	CCONJ
ejpam-2552	224	14	in	in	ADP
ejpam-2552	224	15	l2(µzxe	l2(µzxe	PROPN
ejpam-2552	224	16	)	)	PUNCT
ejpam-2552	224	17	,	,	PUNCT
ejpam-2552	224	18	its	its	PRON
ejpam-2552	224	19	integrations	integration	NOUN
ejpam-2552	224	20	successively	successively	ADV
ejpam-2552	224	21	with	with	ADP
ejpam-2552	224	22	respect	respect	NOUN
ejpam-2552	224	23	to	to	ADP
ejpam-2552	224	24	the	the	DET
ejpam-2552	224	25	r.m	r.m	PROPN
ejpam-2552	224	26	.	.	PROPN
ejpam-2552	224	27	’s	’s	PROPN
ejpam-2552	224	28	ztxe	ztxe	PROPN
ejpam-2552	224	29	and	and	CCONJ
ejpam-2552	224	30	zxe	zxe	PROPN
ejpam-2552	224	31	give	give	VERB
ejpam-2552	224	32	:	:	PUNCT
ejpam-2552	224	33	(	(	PUNCT
ejpam-2552	224	34	e(b))tx	e(b))tx	ADV
ejpam-2552	224	35	=	=	SYM
ejpam-2552	224	36	limm→∞	limm→∞	PROPN
ejpam-2552	224	37	∑	∑	ADV
ejpam-2552	224	38	j∈jm	j∈jm	PROPN
ejpam-2552	224	39	αj	αj	PROPN
ejpam-2552	224	40	,	,	PUNCT
ejpam-2552	224	41	ma	ma	PROPN
ejpam-2552	224	42	nj	nj	PROPN
ejpam-2552	224	43	,	,	PUNCT
ejpam-2552	224	44	mtx	mtx	PROPN
ejpam-2552	224	45	,	,	PUNCT
ejpam-2552	224	46	(	(	PUNCT
ejpam-2552	224	47	2.5.2	2.5.2	NUM
ejpam-2552	224	48	)	)	PUNCT
ejpam-2552	224	49	and	and	CCONJ
ejpam-2552	224	50	(	(	PUNCT
ejpam-2552	224	51	e(b))x	e(b))x	NOUN
ejpam-2552	224	52	=	=	SYM
ejpam-2552	224	53	limm→∞	limm→∞	PROPN
ejpam-2552	224	54	∑	∑	ADV
ejpam-2552	224	55	j∈jm	j∈jm	PROPN
ejpam-2552	224	56	αj	αj	PROPN
ejpam-2552	224	57	,	,	PUNCT
ejpam-2552	224	58	ma	ma	PROPN
ejpam-2552	224	59	nj	nj	PROPN
ejpam-2552	224	60	,	,	PUNCT
ejpam-2552	224	61	mx	mx	PROPN
ejpam-2552	224	62	,	,	PUNCT
ejpam-2552	224	63	hence	hence	ADV
ejpam-2552	224	64	t	t	PROPN
ejpam-2552	224	65	(	(	PUNCT
ejpam-2552	224	66	e(b))x	e(b))x	NOUN
ejpam-2552	224	67	=	=	SYM
ejpam-2552	224	68	limm→∞	limm→∞	PROPN
ejpam-2552	224	69	∑	∑	ADV
ejpam-2552	224	70	j∈jm	j∈jm	PROPN
ejpam-2552	224	71	αj	αj	PROPN
ejpam-2552	224	72	,	,	PUNCT
ejpam-2552	224	73	mta	mta	PROPN
ejpam-2552	224	74	nj	nj	PROPN
ejpam-2552	224	75	,	,	PUNCT
ejpam-2552	224	76	mx	mx	PROPN
ejpam-2552	224	77	,	,	PUNCT
ejpam-2552	224	78	what	what	PRON
ejpam-2552	224	79	,	,	PUNCT
ejpam-2552	224	80	taking	take	VERB
ejpam-2552	224	81	into	into	ADP
ejpam-2552	224	82	account	account	NOUN
ejpam-2552	224	83	result	result	NOUN
ejpam-2552	224	84	(	(	PUNCT
ejpam-2552	224	85	2.5.2	2.5.2	NUM
ejpam-2552	224	86	)	)	PUNCT
ejpam-2552	224	87	,	,	PUNCT
ejpam-2552	224	88	and	and	CCONJ
ejpam-2552	224	89	as	as	SCONJ
ejpam-2552	224	90	anj	anj	PROPN
ejpam-2552	224	91	,	,	PUNCT
ejpam-2552	224	92	m	m	VERB
ejpam-2552	224	93	◦	◦	NOUN
ejpam-2552	224	94	t	t	PROPN
ejpam-2552	224	95	=	=	SYM
ejpam-2552	224	96	t	t	PROPN
ejpam-2552	224	97	◦	◦	PROPN
ejpam-2552	224	98	anj	anj	PROPN
ejpam-2552	224	99	,	,	PUNCT
ejpam-2552	224	100	m	m	VERB
ejpam-2552	224	101	,	,	PUNCT
ejpam-2552	224	102	allows	allow	VERB
ejpam-2552	224	103	us	we	PRON
ejpam-2552	224	104	to	to	PART
ejpam-2552	224	105	write	write	VERB
ejpam-2552	224	106	e(b	e(b	PROPN
ejpam-2552	224	107	)	)	PUNCT
ejpam-2552	224	108	◦	◦	NOUN
ejpam-2552	224	109	t	t	NOUN
ejpam-2552	224	110	=	=	SYM
ejpam-2552	224	111	t	t	PROPN
ejpam-2552	224	112	◦	◦	NOUN
ejpam-2552	224	113	e(b	e(b	X
ejpam-2552	224	114	)	)	PUNCT
ejpam-2552	224	115	.	.	PUNCT
ejpam-2552	225	1	�	�	PROPN
ejpam-2552	225	2	this	this	DET
ejpam-2552	225	3	property	property	NOUN
ejpam-2552	225	4	has	have	AUX
ejpam-2552	225	5	got	get	VERB
ejpam-2552	225	6	its	its	PRON
ejpam-2552	225	7	converse	converse	NOUN
ejpam-2552	225	8	.	.	PUNCT
ejpam-2552	226	1	proposition	proposition	NOUN
ejpam-2552	226	2	2.5.2	2.5.2	NUM
ejpam-2552	226	3	.	.	PUNCT
ejpam-2552	227	1	if	if	SCONJ
ejpam-2552	227	2	a	a	PRON
ejpam-2552	227	3	is	be	AUX
ejpam-2552	227	4	a	a	DET
ejpam-2552	227	5	bounded	bounded	ADJ
ejpam-2552	227	6	selfadjoint	selfadjoint	NOUN
ejpam-2552	227	7	operator	operator	NOUN
ejpam-2552	227	8	of	of	ADP
ejpam-2552	227	9	associated	associated	ADJ
ejpam-2552	227	10	s.m	s.m	PROPN
ejpam-2552	227	11	.	.	PUNCT
ejpam-2552	228	1	e	e	X
ejpam-2552	228	2	,	,	PUNCT
ejpam-2552	228	3	if	if	SCONJ
ejpam-2552	228	4	t	t	PROPN
ejpam-2552	228	5	is	be	AUX
ejpam-2552	228	6	an	an	DET
ejpam-2552	228	7	element	element	NOUN
ejpam-2552	228	8	of	of	ADP
ejpam-2552	228	9	l(h	l(h	PROPN
ejpam-2552	228	10	)	)	PUNCT
ejpam-2552	228	11	such	such	ADJ
ejpam-2552	228	12	that	that	SCONJ
ejpam-2552	228	13	t	t	PROPN
ejpam-2552	228	14	◦	◦	NOUN
ejpam-2552	228	15	e(b	e(b	X
ejpam-2552	228	16	)	)	PUNCT
ejpam-2552	229	1	=	=	PRON
ejpam-2552	229	2	e(b	e(b	X
ejpam-2552	229	3	)	)	PUNCT
ejpam-2552	229	4	◦	◦	NOUN
ejpam-2552	229	5	t	t	NOUN
ejpam-2552	229	6	,	,	PUNCT
ejpam-2552	229	7	then	then	ADV
ejpam-2552	229	8	,	,	PUNCT
ejpam-2552	229	9	for	for	ADP
ejpam-2552	229	10	any	any	DET
ejpam-2552	229	11	b	b	PROPN
ejpam-2552	229	12	of	of	ADP
ejpam-2552	229	13	br	br	PROPN
ejpam-2552	229	14	,	,	PUNCT
ejpam-2552	229	15	t	t	PROPN
ejpam-2552	229	16	and	and	CCONJ
ejpam-2552	229	17	a	a	DET
ejpam-2552	229	18	commute	commute	NOUN
ejpam-2552	229	19	.	.	PUNCT
ejpam-2552	230	1	proof	proof	NOUN
ejpam-2552	230	2	.	.	PUNCT
ejpam-2552	231	1	taking	take	VERB
ejpam-2552	231	2	into	into	ADP
ejpam-2552	231	3	account	account	NOUN
ejpam-2552	231	4	the	the	DET
ejpam-2552	231	5	property	property	NOUN
ejpam-2552	231	6	of	of	ADP
ejpam-2552	231	7	density	density	NOUN
ejpam-2552	231	8	of	of	ADP
ejpam-2552	231	9	the	the	DET
ejpam-2552	231	10	indicator	indicator	NOUN
ejpam-2552	231	11	functions	function	NOUN
ejpam-2552	231	12	,	,	PUNCT
ejpam-2552	231	13	the	the	DET
ejpam-2552	231	14	element	element	NOUN
ejpam-2552	231	15	j	j	PROPN
ejpam-2552	231	16	of	of	ADP
ejpam-2552	231	17	l2(µztxe	l2(µztxe	PROPN
ejpam-2552	231	18	+	+	CCONJ
ejpam-2552	231	19	µzxe	µzxe	NOUN
ejpam-2552	231	20	)	)	PUNCT
ejpam-2552	231	21	can	can	AUX
ejpam-2552	231	22	be	be	AUX
ejpam-2552	231	23	writen	writen	VERB
ejpam-2552	231	24	as	as	ADP
ejpam-2552	231	25	:	:	PUNCT
ejpam-2552	231	26	j	j	PROPN
ejpam-2552	231	27	=	=	SYM
ejpam-2552	231	28	limm→∞	limm→∞	PROPN
ejpam-2552	231	29	∑	∑	ADV
ejpam-2552	231	30	j∈jm	j∈jm	PROPN
ejpam-2552	231	31	αj	αj	PROPN
ejpam-2552	231	32	,	,	PUNCT
ejpam-2552	231	33	m1bj	m1bj	X
ejpam-2552	231	34	,	,	PUNCT
ejpam-2552	231	35	m	m	PRON
ejpam-2552	231	36	,	,	PUNCT
ejpam-2552	231	37	bj	bj	VERB
ejpam-2552	231	38	,	,	PUNCT
ejpam-2552	231	39	m	m	VERB
ejpam-2552	231	40	∈	∈	ADJ
ejpam-2552	231	41	br	br	NOUN
ejpam-2552	231	42	,	,	PUNCT
ejpam-2552	231	43	|jm|	|jm|	X
ejpam-2552	231	44	<	<	X
ejpam-2552	231	45	+	+	PROPN
ejpam-2552	231	46	∞	∞	PROPN
ejpam-2552	231	47	,	,	PUNCT
ejpam-2552	231	48	in	in	ADP
ejpam-2552	231	49	l2(µztxe	l2(µztxe	ADJ
ejpam-2552	231	50	+	+	CCONJ
ejpam-2552	231	51	µzxe	µzxe	NOUN
ejpam-2552	231	52	)	)	PUNCT
ejpam-2552	231	53	.	.	PUNCT
ejpam-2552	232	1	(	(	PUNCT
ejpam-2552	232	2	2.5.3	2.5.3	NUM
ejpam-2552	232	3	)	)	PUNCT
ejpam-2552	232	4	the	the	DET
ejpam-2552	232	5	equality	equality	NOUN
ejpam-2552	232	6	(	(	PUNCT
ejpam-2552	232	7	2.5.3	2.5.3	NUM
ejpam-2552	232	8	)	)	PUNCT
ejpam-2552	232	9	is	be	AUX
ejpam-2552	232	10	true	true	ADJ
ejpam-2552	232	11	in	in	ADP
ejpam-2552	232	12	l2(µztxe	l2(µztxe	ADJ
ejpam-2552	232	13	)	)	PUNCT
ejpam-2552	232	14	and	and	CCONJ
ejpam-2552	232	15	in	in	ADP
ejpam-2552	232	16	l2(µzxe	l2(µzxe	PROPN
ejpam-2552	232	17	)	)	PUNCT
ejpam-2552	232	18	,	,	PUNCT
ejpam-2552	232	19	by	by	ADP
ejpam-2552	232	20	integration	integration	NOUN
ejpam-2552	232	21	with	with	ADP
ejpam-2552	232	22	respect	respect	NOUN
ejpam-2552	232	23	to	to	ADP
ejpam-2552	232	24	the	the	DET
ejpam-2552	232	25	r.m	r.m	PROPN
ejpam-2552	232	26	.	.	PROPN
ejpam-2552	232	27	’s	’s	PROPN
ejpam-2552	232	28	ztxe	ztxe	PROPN
ejpam-2552	232	29	and	and	CCONJ
ejpam-2552	232	30	zxe	zxe	PROPN
ejpam-2552	232	31	,	,	PUNCT
ejpam-2552	232	32	we	we	PRON
ejpam-2552	232	33	have	have	VERB
ejpam-2552	232	34	:	:	PUNCT
ejpam-2552	232	35	atx	atx	PROPN
ejpam-2552	232	36	=	=	SYM
ejpam-2552	232	37	limm→∞	limm→∞	PROPN
ejpam-2552	232	38	∑	∑	ADV
ejpam-2552	232	39	j∈jm	j∈jm	PROPN
ejpam-2552	232	40	αj	αj	PROPN
ejpam-2552	232	41	,	,	PUNCT
ejpam-2552	232	42	m(e(bj	m(e(bj	NOUN
ejpam-2552	232	43	,	,	PUNCT
ejpam-2552	232	44	m))tx	m))tx	PROPN
ejpam-2552	232	45	,	,	PUNCT
ejpam-2552	232	46	(	(	PUNCT
ejpam-2552	232	47	2.5.4	2.5.4	NUM
ejpam-2552	232	48	)	)	PUNCT
ejpam-2552	232	49	and	and	CCONJ
ejpam-2552	232	50	ax	ax	NOUN
ejpam-2552	232	51	=	=	PUNCT
ejpam-2552	232	52	limm→∞	limm→∞	PROPN
ejpam-2552	232	53	∑	∑	ADV
ejpam-2552	232	54	j∈jm	j∈jm	PROPN
ejpam-2552	232	55	αj	αj	PROPN
ejpam-2552	232	56	,	,	PUNCT
ejpam-2552	232	57	m(e(bj	m(e(bj	NOUN
ejpam-2552	232	58	,	,	PUNCT
ejpam-2552	232	59	m))x	m))x	NOUN
ejpam-2552	232	60	,	,	PUNCT
ejpam-2552	232	61	hence	hence	ADV
ejpam-2552	232	62	tax	tax	NOUN
ejpam-2552	232	63	=	=	SYM
ejpam-2552	232	64	limm→∞	limm→∞	PROPN
ejpam-2552	232	65	∑	∑	ADV
ejpam-2552	232	66	j∈jm	j∈jm	PROPN
ejpam-2552	232	67	αj	αj	PROPN
ejpam-2552	232	68	,	,	PUNCT
ejpam-2552	232	69	mt	mt	PROPN
ejpam-2552	232	70	(	(	PUNCT
ejpam-2552	232	71	e(bj	e(bj	PROPN
ejpam-2552	232	72	,	,	PUNCT
ejpam-2552	232	73	m))x	m))x	NOUN
ejpam-2552	232	74	,	,	PUNCT
ejpam-2552	232	75	what	what	PRON
ejpam-2552	232	76	allows	allow	VERB
ejpam-2552	232	77	,	,	PUNCT
ejpam-2552	232	78	thanks	thank	NOUN
ejpam-2552	232	79	to	to	ADP
ejpam-2552	232	80	(	(	PUNCT
ejpam-2552	232	81	2.5.4	2.5.4	NUM
ejpam-2552	232	82	)	)	PUNCT
ejpam-2552	232	83	and	and	CCONJ
ejpam-2552	232	84	to	to	ADP
ejpam-2552	232	85	the	the	DET
ejpam-2552	232	86	fact	fact	NOUN
ejpam-2552	233	1	that	that	SCONJ
ejpam-2552	233	2	t	t	PROPN
ejpam-2552	233	3	◦	◦	NOUN
ejpam-2552	233	4	e(bj	e(bj	NOUN
ejpam-2552	233	5	,	,	PUNCT
ejpam-2552	233	6	m	m	NOUN
ejpam-2552	233	7	)	)	PUNCT
ejpam-2552	233	8	=	=	SYM
ejpam-2552	233	9	e(bj	e(bj	NOUN
ejpam-2552	233	10	,	,	PUNCT
ejpam-2552	233	11	m)	m)	NOUN
ejpam-2552	233	12	◦	◦	NOUN
ejpam-2552	233	13	t	t	NOUN
ejpam-2552	233	14	,	,	PUNCT
ejpam-2552	233	15	to	to	PART
ejpam-2552	233	16	write	write	VERB
ejpam-2552	233	17	:	:	PUNCT
ejpam-2552	233	18	a	a	DET
ejpam-2552	233	19	◦	◦	NOUN
ejpam-2552	233	20	t	t	X
ejpam-2552	233	21	=	=	SYM
ejpam-2552	233	22	t	t	PROPN
ejpam-2552	233	23	◦	◦	PROPN
ejpam-2552	233	24	a.	a.	NOUN
ejpam-2552	233	25	�	�	PROPN
ejpam-2552	233	26	the	the	DET
ejpam-2552	233	27	following	follow	VERB
ejpam-2552	233	28	property	property	NOUN
ejpam-2552	233	29	is	be	AUX
ejpam-2552	233	30	obtained	obtain	VERB
ejpam-2552	233	31	combining	combine	VERB
ejpam-2552	233	32	these	these	DET
ejpam-2552	233	33	two	two	NUM
ejpam-2552	233	34	last	last	ADJ
ejpam-2552	233	35	results	result	NOUN
ejpam-2552	233	36	.	.	PUNCT
ejpam-2552	234	1	proposition	proposition	NOUN
ejpam-2552	234	2	2.5.3	2.5.3	NUM
ejpam-2552	234	3	.	.	PROPN
ejpam-2552	235	1	two	two	NUM
ejpam-2552	235	2	bounded	bounded	ADJ
ejpam-2552	235	3	selfadjoint	selfadjoint	NOUN
ejpam-2552	235	4	operators	operator	NOUN
ejpam-2552	235	5	a	a	DET
ejpam-2552	235	6	and	and	CCONJ
ejpam-2552	235	7	a′	a′	PROPN
ejpam-2552	235	8	commute	commute	NOUN
ejpam-2552	235	9	if	if	SCONJ
ejpam-2552	235	10	,	,	PUNCT
ejpam-2552	235	11	and	and	CCONJ
ejpam-2552	235	12	only	only	ADV
ejpam-2552	235	13	if	if	SCONJ
ejpam-2552	235	14	,	,	PUNCT
ejpam-2552	235	15	their	their	PRON
ejpam-2552	235	16	associated	associate	VERB
ejpam-2552	235	17	bounded	bounded	PROPN
ejpam-2552	235	18	s.m	s.m	PROPN
ejpam-2552	235	19	.	.	PROPN
ejpam-2552	235	20	’s	’s	PART
ejpam-2552	235	21	commute	commute	NOUN
ejpam-2552	235	22	.	.	PUNCT
ejpam-2552	236	1	we	we	PRON
ejpam-2552	236	2	are	be	AUX
ejpam-2552	236	3	now	now	ADV
ejpam-2552	236	4	able	able	ADJ
ejpam-2552	236	5	to	to	PART
ejpam-2552	236	6	examine	examine	VERB
ejpam-2552	236	7	the	the	DET
ejpam-2552	236	8	main	main	ADJ
ejpam-2552	236	9	result	result	NOUN
ejpam-2552	236	10	of	of	ADP
ejpam-2552	236	11	this	this	DET
ejpam-2552	236	12	section	section	NOUN
ejpam-2552	236	13	.	.	PUNCT
ejpam-2552	237	1	proposition	proposition	NOUN
ejpam-2552	237	2	2.5.4	2.5.4	NUM
ejpam-2552	237	3	.	.	PUNCT
ejpam-2552	238	1	if	if	SCONJ
ejpam-2552	238	2	a	a	PRON
ejpam-2552	238	3	and	and	CCONJ
ejpam-2552	238	4	a′	a′	NOUN
ejpam-2552	238	5	are	be	AUX
ejpam-2552	238	6	two	two	NUM
ejpam-2552	238	7	bounded	bounded	ADJ
ejpam-2552	238	8	selfadjoint	selfadjoint	NOUN
ejpam-2552	238	9	operators	operator	NOUN
ejpam-2552	238	10	which	which	PRON
ejpam-2552	238	11	commute	commute	VERB
ejpam-2552	238	12	,	,	PUNCT
ejpam-2552	238	13	of	of	ADP
ejpam-2552	238	14	respective	respective	ADJ
ejpam-2552	238	15	associated	associate	VERB
ejpam-2552	238	16	s.m	s.m	PROPN
ejpam-2552	238	17	.	.	PROPN
ejpam-2552	238	18	’s	’s	PART
ejpam-2552	238	19	e	e	PROPN
ejpam-2552	238	20	and	and	CCONJ
ejpam-2552	238	21	e	e	PROPN
ejpam-2552	238	22	′	′	NOUN
ejpam-2552	238	23	,	,	PUNCT
ejpam-2552	238	24	then	then	ADV
ejpam-2552	238	25	e	e	NOUN
ejpam-2552	238	26	∗	∗	NOUN
ejpam-2552	238	27	e	e	X
ejpam-2552	238	28	′	′	NOUN
ejpam-2552	238	29	is	be	AUX
ejpam-2552	238	30	the	the	DET
ejpam-2552	238	31	s.m	s.m	PROPN
ejpam-2552	238	32	.	.	PROPN
ejpam-2552	238	33	associated	associate	VERB
ejpam-2552	238	34	with	with	ADP
ejpam-2552	238	35	the	the	DET
ejpam-2552	238	36	operator	operator	NOUN
ejpam-2552	238	37	a+a′.	a+a′.	NOUN
ejpam-2552	238	38	a.	a.	NOUN
ejpam-2552	238	39	boudou	boudou	NOUN
ejpam-2552	238	40	,	,	PUNCT
ejpam-2552	238	41	s.	s.	PROPN
ejpam-2552	238	42	viguier	viguier	PROPN
ejpam-2552	238	43	-	-	PUNCT
ejpam-2552	238	44	pla	pla	PROPN
ejpam-2552	238	45	/	/	PUNCT
ejpam-2552	238	46	eur	eur	PROPN
ejpam-2552	238	47	.	.	PUNCT
ejpam-2552	239	1	j.	j.	PROPN
ejpam-2552	239	2	pure	pure	PROPN
ejpam-2552	239	3	appl	appl	PROPN
ejpam-2552	239	4	.	.	PROPN
ejpam-2552	239	5	math	math	PROPN
ejpam-2552	239	6	,	,	PUNCT
ejpam-2552	239	7	11	11	NUM
ejpam-2552	239	8	(	(	PUNCT
ejpam-2552	239	9	4	4	NUM
ejpam-2552	239	10	)	)	PUNCT
ejpam-2552	239	11	(	(	PUNCT
ejpam-2552	239	12	2018	2018	NUM
ejpam-2552	239	13	)	)	PUNCT
ejpam-2552	239	14	,	,	PUNCT
ejpam-2552	239	15	893	893	NUM
ejpam-2552	239	16	-	-	SYM
ejpam-2552	239	17	910	910	NUM
ejpam-2552	239	18	901	901	NUM
ejpam-2552	239	19	proof	proof	NOUN
ejpam-2552	239	20	.	.	PUNCT
ejpam-2552	240	1	let	let	VERB
ejpam-2552	240	2	us	we	PRON
ejpam-2552	240	3	first	first	ADV
ejpam-2552	240	4	notice	notice	VERB
ejpam-2552	240	5	that	that	SCONJ
ejpam-2552	240	6	,	,	PUNCT
ejpam-2552	240	7	because	because	SCONJ
ejpam-2552	240	8	a	a	DET
ejpam-2552	240	9	and	and	CCONJ
ejpam-2552	240	10	a′	a′	PROPN
ejpam-2552	240	11	commute	commute	NOUN
ejpam-2552	240	12	,	,	PUNCT
ejpam-2552	240	13	the	the	DET
ejpam-2552	240	14	bounded	bounded	ADJ
ejpam-2552	240	15	s.m	s.m	PROPN
ejpam-2552	240	16	.	.	PROPN
ejpam-2552	240	17	’s	’s	PART
ejpam-2552	240	18	e	e	PROPN
ejpam-2552	240	19	and	and	CCONJ
ejpam-2552	240	20	e	e	NOUN
ejpam-2552	240	21	′	′	NOUN
ejpam-2552	240	22	also	also	ADV
ejpam-2552	240	23	commute	commute	VERB
ejpam-2552	240	24	.	.	PUNCT
ejpam-2552	241	1	so	so	ADV
ejpam-2552	241	2	we	we	PRON
ejpam-2552	241	3	can	can	AUX
ejpam-2552	241	4	consider	consider	VERB
ejpam-2552	241	5	the	the	DET
ejpam-2552	241	6	s.m	s.m	PROPN
ejpam-2552	241	7	.	.	PROPN
ejpam-2552	241	8	’s	’s	PART
ejpam-2552	241	9	e	e	PROPN
ejpam-2552	241	10	⊗	⊗	PROPN
ejpam-2552	241	11	e	e	PROPN
ejpam-2552	241	12	′	′	NOUN
ejpam-2552	241	13	and	and	CCONJ
ejpam-2552	241	14	e	e	NOUN
ejpam-2552	241	15	∗	∗	NOUN
ejpam-2552	241	16	e	e	NOUN
ejpam-2552	241	17	′	′	NOUN
ejpam-2552	241	18	,	,	PUNCT
ejpam-2552	241	19	this	this	DET
ejpam-2552	241	20	last	last	ADJ
ejpam-2552	241	21	one	one	NOUN
ejpam-2552	241	22	being	be	AUX
ejpam-2552	241	23	bounded	bound	VERB
ejpam-2552	241	24	.	.	PUNCT
ejpam-2552	242	1	let	let	VERB
ejpam-2552	242	2	us	we	PRON
ejpam-2552	242	3	denote	denote	VERB
ejpam-2552	242	4	by	by	ADP
ejpam-2552	242	5	p	p	PROPN
ejpam-2552	242	6	(	(	PUNCT
ejpam-2552	242	7	resp	resp	NOUN
ejpam-2552	242	8	.	.	PUNCT
ejpam-2552	243	1	p	p	NOUN
ejpam-2552	243	2	′	′	NOUN
ejpam-2552	243	3	)	)	PUNCT
ejpam-2552	244	1	the	the	DET
ejpam-2552	244	2	measurable	measurable	ADJ
ejpam-2552	244	3	application	application	NOUN
ejpam-2552	244	4	(	(	PUNCT
ejpam-2552	244	5	λ	λ	NOUN
ejpam-2552	244	6	,	,	PUNCT
ejpam-2552	244	7	λ′	λ′	NUM
ejpam-2552	244	8	)	)	PUNCT
ejpam-2552	244	9	∈	∈	PROPN
ejpam-2552	244	10	r2	r2	PROPN
ejpam-2552	244	11	7→	7→	PROPN
ejpam-2552	244	12	λ	λ	NOUN
ejpam-2552	244	13	∈	∈	NOUN
ejpam-2552	244	14	r	r	NOUN
ejpam-2552	244	15	(	(	PUNCT
ejpam-2552	244	16	resp	resp	NOUN
ejpam-2552	244	17	.	.	PUNCT
ejpam-2552	245	1	(	(	PUNCT
ejpam-2552	245	2	λ	λ	X
ejpam-2552	245	3	,	,	PUNCT
ejpam-2552	245	4	λ′	λ′	NUM
ejpam-2552	245	5	)	)	PUNCT
ejpam-2552	245	6	∈	∈	PROPN
ejpam-2552	245	7	r2	r2	PROPN
ejpam-2552	245	8	7→	7→	PROPN
ejpam-2552	245	9	λ′	λ′	X
ejpam-2552	245	10	∈	∈	PROPN
ejpam-2552	245	11	r	r	NOUN
ejpam-2552	245	12	)	)	PUNCT
ejpam-2552	245	13	.	.	PUNCT
ejpam-2552	246	1	we	we	PRON
ejpam-2552	246	2	easily	easily	ADV
ejpam-2552	246	3	verify	verify	VERB
ejpam-2552	246	4	that	that	SCONJ
ejpam-2552	247	1	p	p	X
ejpam-2552	247	2	(	(	PUNCT
ejpam-2552	247	3	e	e	PROPN
ejpam-2552	247	4	⊗	⊗	PROPN
ejpam-2552	247	5	e	e	NOUN
ejpam-2552	247	6	′	′	NOUN
ejpam-2552	247	7	)	)	PUNCT
ejpam-2552	247	8	=	=	SYM
ejpam-2552	247	9	e	e	X
ejpam-2552	247	10	(	(	PUNCT
ejpam-2552	247	11	resp	resp	NOUN
ejpam-2552	247	12	.	.	PUNCT
ejpam-2552	248	1	p	p	PROPN
ejpam-2552	248	2	′(e	′(e	PROPN
ejpam-2552	248	3	⊗	⊗	PROPN
ejpam-2552	248	4	e	e	PROPN
ejpam-2552	248	5	′	′	NOUN
ejpam-2552	248	6	)	)	PUNCT
ejpam-2552	249	1	=	=	SYM
ejpam-2552	249	2	e	e	NOUN
ejpam-2552	249	3	′	′	NUM
ejpam-2552	249	4	)	)	PUNCT
ejpam-2552	249	5	.	.	PUNCT
ejpam-2552	250	1	as	as	SCONJ
ejpam-2552	250	2	e	e	PROPN
ejpam-2552	250	3	is	be	AUX
ejpam-2552	250	4	a	a	DET
ejpam-2552	250	5	bounded	bounded	ADJ
ejpam-2552	250	6	s.m	s.m	PROPN
ejpam-2552	250	7	.	.	PROPN
ejpam-2552	250	8	,	,	PUNCT
ejpam-2552	250	9	j	j	PROPN
ejpam-2552	250	10	belongs	belong	VERB
ejpam-2552	250	11	tom(r	tom(r	PROPN
ejpam-2552	250	12	,	,	PUNCT
ejpam-2552	250	13	e	e	NOUN
ejpam-2552	250	14	)	)	PUNCT
ejpam-2552	250	15	,	,	PUNCT
ejpam-2552	250	16	so	so	SCONJ
ejpam-2552	250	17	tom(r	tom(r	PROPN
ejpam-2552	250	18	,	,	PUNCT
ejpam-2552	250	19	p	p	X
ejpam-2552	250	20	(	(	PUNCT
ejpam-2552	250	21	e⊗e	e⊗e	PROPN
ejpam-2552	250	22	′	′	NUM
ejpam-2552	250	23	)	)	PUNCT
ejpam-2552	250	24	)	)	PUNCT
ejpam-2552	250	25	.	.	PUNCT
ejpam-2552	251	1	proposition	proposition	NOUN
ejpam-2552	251	2	2.4.3	2.4.3	NUM
ejpam-2552	251	3	allows	allow	VERB
ejpam-2552	251	4	us	we	PRON
ejpam-2552	251	5	to	to	PART
ejpam-2552	251	6	affirm	affirm	VERB
ejpam-2552	251	7	that	that	SCONJ
ejpam-2552	251	8	j	j	PROPN
ejpam-2552	251	9	◦	◦	PROPN
ejpam-2552	251	10	p	p	PROPN
ejpam-2552	251	11	belongs	belong	VERB
ejpam-2552	251	12	tom(r×r	tom(r×r	VERB
ejpam-2552	251	13	,	,	PUNCT
ejpam-2552	251	14	e	e	NOUN
ejpam-2552	251	15	⊗e	⊗e	NOUN
ejpam-2552	251	16	′	′	NUM
ejpam-2552	251	17	)	)	PUNCT
ejpam-2552	251	18	and	and	CCONJ
ejpam-2552	251	19	that	that	SCONJ
ejpam-2552	251	20	ej	ej	AUX
ejpam-2552	251	21	=	=	PRON
ejpam-2552	252	1	(	(	PUNCT
ejpam-2552	252	2	e	e	NOUN
ejpam-2552	252	3	⊗e	⊗e	ADJ
ejpam-2552	252	4	′)j	′)j	NUM
ejpam-2552	252	5	◦	◦	NOUN
ejpam-2552	252	6	p	p	NOUN
ejpam-2552	252	7	.	.	PUNCT
ejpam-2552	253	1	in	in	ADP
ejpam-2552	253	2	a	a	DET
ejpam-2552	253	3	same	same	ADJ
ejpam-2552	253	4	way	way	NOUN
ejpam-2552	253	5	,	,	PUNCT
ejpam-2552	253	6	we	we	PRON
ejpam-2552	253	7	get	get	VERB
ejpam-2552	253	8	e	e	NOUN
ejpam-2552	253	9	′j	′j	NOUN
ejpam-2552	253	10	=	=	SYM
ejpam-2552	253	11	(	(	PUNCT
ejpam-2552	253	12	e⊗e	e⊗e	NOUN
ejpam-2552	253	13	′)j	′)j	NOUN
ejpam-2552	253	14	◦	◦	NOUN
ejpam-2552	253	15	p	p	NOUN
ejpam-2552	253	16	′	′	NOUN
ejpam-2552	253	17	.	.	PUNCT
ejpam-2552	254	1	the	the	DET
ejpam-2552	254	2	linearity	linearity	NOUN
ejpam-2552	254	3	of	of	ADP
ejpam-2552	254	4	the	the	DET
ejpam-2552	254	5	application	application	NOUN
ejpam-2552	254	6	f	f	PROPN
ejpam-2552	254	7	∈m(r×r	∈m(r×r	NOUN
ejpam-2552	254	8	,	,	PUNCT
ejpam-2552	254	9	e⊗e	e⊗e	PROPN
ejpam-2552	254	10	′	′	NOUN
ejpam-2552	254	11	)	)	PUNCT
ejpam-2552	254	12	7→	7→	PROPN
ejpam-2552	254	13	(	(	PUNCT
ejpam-2552	254	14	e	e	PROPN
ejpam-2552	254	15	⊗	⊗	PROPN
ejpam-2552	254	16	e	e	PROPN
ejpam-2552	254	17	′)f	′)f	PROPN
ejpam-2552	254	18	∈	∈	PROPN
ejpam-2552	254	19	l(h	l(h	PROPN
ejpam-2552	254	20	)	)	PUNCT
ejpam-2552	254	21	allows	allow	VERB
ejpam-2552	254	22	us	we	PRON
ejpam-2552	254	23	to	to	PART
ejpam-2552	254	24	write	write	VERB
ejpam-2552	254	25	:	:	PUNCT
ejpam-2552	254	26	ej	ej	PROPN
ejpam-2552	255	1	+	+	CCONJ
ejpam-2552	255	2	e	e	X
ejpam-2552	255	3	′j	′j	NOUN
ejpam-2552	255	4	=	=	PUNCT
ejpam-2552	255	5	(	(	PUNCT
ejpam-2552	255	6	e	e	PROPN
ejpam-2552	255	7	⊗	⊗	PROPN
ejpam-2552	255	8	e	e	PROPN
ejpam-2552	255	9	′)j	′)j	NOUN
ejpam-2552	255	10	◦	◦	NOUN
ejpam-2552	255	11	p	p	NOUN
ejpam-2552	255	12	+	+	X
ejpam-2552	255	13	(	(	PUNCT
ejpam-2552	255	14	e	e	PROPN
ejpam-2552	255	15	⊗	⊗	PROPN
ejpam-2552	255	16	e	e	PROPN
ejpam-2552	255	17	′)j	′)j	NOUN
ejpam-2552	255	18	◦	◦	NOUN
ejpam-2552	255	19	p	p	NOUN
ejpam-2552	255	20	′	′	NOUN
ejpam-2552	255	21	=	=	SYM
ejpam-2552	255	22	(	(	PUNCT
ejpam-2552	255	23	e	e	PROPN
ejpam-2552	255	24	⊗	⊗	PROPN
ejpam-2552	255	25	e	e	PROPN
ejpam-2552	255	26	′)j	′)j	NOUN
ejpam-2552	255	27	◦	◦	NOUN
ejpam-2552	255	28	p+j	p+j	NOUN
ejpam-2552	255	29	◦	◦	NOUN
ejpam-2552	255	30	p	p	NOUN
ejpam-2552	255	31	′	′	NOUN
ejpam-2552	255	32	=	=	SYM
ejpam-2552	255	33	(	(	PUNCT
ejpam-2552	255	34	e	e	PROPN
ejpam-2552	255	35	⊗	⊗	PROPN
ejpam-2552	255	36	e	e	PROPN
ejpam-2552	255	37	′)j	′)j	NOUN
ejpam-2552	255	38	◦	◦	NOUN
ejpam-2552	255	39	s	s	X
ejpam-2552	255	40	(	(	PUNCT
ejpam-2552	255	41	2.5.5	2.5.5	NUM
ejpam-2552	255	42	)	)	PUNCT
ejpam-2552	255	43	besides	besides	SCONJ
ejpam-2552	255	44	,	,	PUNCT
ejpam-2552	255	45	as	as	SCONJ
ejpam-2552	255	46	j	j	PROPN
ejpam-2552	255	47	is	be	AUX
ejpam-2552	255	48	an	an	DET
ejpam-2552	255	49	element	element	NOUN
ejpam-2552	255	50	ofm(r	ofm(r	NOUN
ejpam-2552	255	51	,	,	PUNCT
ejpam-2552	255	52	e∗e	e∗e	NUM
ejpam-2552	255	53	′	′	NUM
ejpam-2552	255	54	)	)	PUNCT
ejpam-2552	255	55	,	,	PUNCT
ejpam-2552	255	56	so	so	ADV
ejpam-2552	255	57	ofm(r	ofm(r	NOUN
ejpam-2552	255	58	,	,	PUNCT
ejpam-2552	255	59	s(e⊗e	s(e⊗e	NOUN
ejpam-2552	255	60	′	′	NUM
ejpam-2552	255	61	)	)	PUNCT
ejpam-2552	255	62	)	)	PUNCT
ejpam-2552	255	63	,	,	PUNCT
ejpam-2552	255	64	from	from	ADP
ejpam-2552	255	65	proposition	proposition	NOUN
ejpam-2552	255	66	2.4.3	2.4.3	NUM
ejpam-2552	255	67	,	,	PUNCT
ejpam-2552	255	68	j	j	PROPN
ejpam-2552	255	69	◦	◦	NOUN
ejpam-2552	255	70	s	s	VERB
ejpam-2552	255	71	belongs	belong	VERB
ejpam-2552	255	72	to	to	ADP
ejpam-2552	255	73	m(r×	m(r×	DET
ejpam-2552	255	74	r	r	NOUN
ejpam-2552	255	75	,	,	PUNCT
ejpam-2552	255	76	e	e	PROPN
ejpam-2552	255	77	⊗	⊗	PROPN
ejpam-2552	255	78	e	e	PROPN
ejpam-2552	255	79	′	′	NOUN
ejpam-2552	255	80	)	)	PUNCT
ejpam-2552	255	81	and	and	CCONJ
ejpam-2552	255	82	(	(	PUNCT
ejpam-2552	255	83	s(e	s(e	PROPN
ejpam-2552	255	84	⊗	⊗	PROPN
ejpam-2552	255	85	e	e	NOUN
ejpam-2552	255	86	′))j	′))j	NOUN
ejpam-2552	255	87	=	=	SYM
ejpam-2552	255	88	(	(	PUNCT
ejpam-2552	255	89	e	e	PROPN
ejpam-2552	255	90	⊗	⊗	PROPN
ejpam-2552	255	91	e	e	PROPN
ejpam-2552	255	92	′)j	′)j	NOUN
ejpam-2552	255	93	◦	◦	NOUN
ejpam-2552	255	94	s	s	PART
ejpam-2552	255	95	.	.	PUNCT
ejpam-2552	256	1	so	so	ADV
ejpam-2552	256	2	,	,	PUNCT
ejpam-2552	256	3	taking	take	VERB
ejpam-2552	256	4	into	into	ADP
ejpam-2552	256	5	account	account	NOUN
ejpam-2552	256	6	(	(	PUNCT
ejpam-2552	256	7	2.5.5	2.5.5	NUM
ejpam-2552	256	8	)	)	PUNCT
ejpam-2552	256	9	,	,	PUNCT
ejpam-2552	256	10	we	we	PRON
ejpam-2552	256	11	have	have	VERB
ejpam-2552	256	12	ej	ej	X
ejpam-2552	257	1	+	+	CCONJ
ejpam-2552	257	2	e	e	X
ejpam-2552	257	3	′j	′j	NOUN
ejpam-2552	257	4	=	=	PUNCT
ejpam-2552	257	5	(	(	PUNCT
ejpam-2552	257	6	s(e	s(e	PROPN
ejpam-2552	257	7	⊗	⊗	PROPN
ejpam-2552	257	8	e	e	NOUN
ejpam-2552	257	9	′))j	′))j	NOUN
ejpam-2552	257	10	=	=	SYM
ejpam-2552	257	11	(	(	PUNCT
ejpam-2552	257	12	e	e	NOUN
ejpam-2552	257	13	∗	∗	X
ejpam-2552	257	14	e	e	X
ejpam-2552	257	15	′)j	′)j	NOUN
ejpam-2552	257	16	,	,	PUNCT
ejpam-2552	257	17	or	or	CCONJ
ejpam-2552	257	18	also	also	ADV
ejpam-2552	257	19	a+a′	a+a′	ADJ
ejpam-2552	257	20	=	=	SYM
ejpam-2552	257	21	(	(	PUNCT
ejpam-2552	257	22	e	e	NOUN
ejpam-2552	257	23	∗	∗	X
ejpam-2552	257	24	e	e	NOUN
ejpam-2552	257	25	′)j	′)j	PROPN
ejpam-2552	257	26	,	,	PUNCT
ejpam-2552	257	27	what	what	PRON
ejpam-2552	257	28	ends	end	VERB
ejpam-2552	257	29	the	the	DET
ejpam-2552	257	30	proof	proof	NOUN
ejpam-2552	257	31	.	.	PUNCT
ejpam-2552	258	1	�	�	PROPN
ejpam-2552	258	2	3	3	NUM
ejpam-2552	258	3	.	.	PUNCT
ejpam-2552	259	1	the	the	DET
ejpam-2552	259	2	α−equivalence	α−equivalence	NOUN
ejpam-2552	259	3	in	in	ADP
ejpam-2552	259	4	this	this	DET
ejpam-2552	259	5	section	section	NOUN
ejpam-2552	259	6	,	,	PUNCT
ejpam-2552	259	7	we	we	PRON
ejpam-2552	259	8	will	will	AUX
ejpam-2552	259	9	examine	examine	VERB
ejpam-2552	259	10	a	a	DET
ejpam-2552	259	11	proximity	proximity	NOUN
ejpam-2552	259	12	relation	relation	NOUN
ejpam-2552	259	13	between	between	ADP
ejpam-2552	259	14	s.m	s.m	PROPN
ejpam-2552	259	15	.	.	PROPN
ejpam-2552	259	16	’s	’s	X
ejpam-2552	259	17	on	on	ADP
ejpam-2552	259	18	br	br	PROPN
ejpam-2552	259	19	for	for	ADP
ejpam-2552	259	20	h.	h.	NOUN
ejpam-2552	259	21	we	we	PRON
ejpam-2552	259	22	will	will	AUX
ejpam-2552	259	23	frequently	frequently	ADV
ejpam-2552	259	24	use	use	VERB
ejpam-2552	259	25	the	the	DET
ejpam-2552	259	26	fact	fact	NOUN
ejpam-2552	259	27	that	that	SCONJ
ejpam-2552	259	28	,	,	PUNCT
ejpam-2552	259	29	if	if	SCONJ
ejpam-2552	259	30	b	b	PROPN
ejpam-2552	259	31	is	be	AUX
ejpam-2552	259	32	a	a	DET
ejpam-2552	259	33	compact	compact	ADJ
ejpam-2552	259	34	subset	subset	NOUN
ejpam-2552	259	35	of	of	ADP
ejpam-2552	259	36	r	r	NOUN
ejpam-2552	259	37	and	and	CCONJ
ejpam-2552	259	38	α	α	NOUN
ejpam-2552	259	39	an	an	DET
ejpam-2552	259	40	element	element	NOUN
ejpam-2552	259	41	of	of	ADP
ejpam-2552	259	42	r∗+	r∗+	PROPN
ejpam-2552	259	43	,	,	PUNCT
ejpam-2552	259	44	then	then	ADV
ejpam-2552	259	45	b	b	X
ejpam-2552	259	46	+	+	PROPN
ejpam-2552	260	1	[	[	X
ejpam-2552	260	2	−α	−α	NOUN
ejpam-2552	260	3	,	,	PUNCT
ejpam-2552	260	4	α	α	NOUN
ejpam-2552	260	5	]	]	X
ejpam-2552	260	6	is	be	AUX
ejpam-2552	260	7	compact	compact	ADJ
ejpam-2552	260	8	.	.	PUNCT
ejpam-2552	261	1	definition	definition	NOUN
ejpam-2552	261	2	3.1	3.1	NUM
ejpam-2552	261	3	.	.	PUNCT
ejpam-2552	262	1	let	let	VERB
ejpam-2552	262	2	α	α	PRON
ejpam-2552	262	3	be	be	AUX
ejpam-2552	262	4	an	an	DET
ejpam-2552	262	5	element	element	NOUN
ejpam-2552	262	6	of	of	ADP
ejpam-2552	262	7	r∗+	r∗+	PROPN
ejpam-2552	262	8	,	,	PUNCT
ejpam-2552	262	9	we	we	PRON
ejpam-2552	262	10	say	say	VERB
ejpam-2552	262	11	that	that	SCONJ
ejpam-2552	262	12	two	two	NUM
ejpam-2552	262	13	s.m	s.m	PROPN
ejpam-2552	262	14	.	.	PROPN
ejpam-2552	262	15	’s	’s	PROPN
ejpam-2552	262	16	e1	e1	PROPN
ejpam-2552	262	17	and	and	CCONJ
ejpam-2552	262	18	e2	e2	PROPN
ejpam-2552	262	19	are	be	AUX
ejpam-2552	262	20	α−equivalent	α−equivalent	NOUN
ejpam-2552	262	21	,	,	PUNCT
ejpam-2552	262	22	what	what	PRON
ejpam-2552	262	23	we	we	PRON
ejpam-2552	262	24	denote	denote	VERB
ejpam-2552	262	25	e1	e1	PROPN
ejpam-2552	262	26	α∼	α∼	PROPN
ejpam-2552	262	27	e2	e2	NOUN
ejpam-2552	262	28	,	,	PUNCT
ejpam-2552	262	29	when	when	SCONJ
ejpam-2552	262	30	,	,	PUNCT
ejpam-2552	262	31	for	for	ADP
ejpam-2552	262	32	any	any	DET
ejpam-2552	262	33	compact	compact	ADJ
ejpam-2552	262	34	b	b	NOUN
ejpam-2552	262	35	,	,	PUNCT
ejpam-2552	262	36	we	we	PRON
ejpam-2552	262	37	have	have	VERB
ejpam-2552	262	38	i	i	PRON
ejpam-2552	262	39	)	)	PUNCT
ejpam-2552	262	40	e1(b	e1(b	X
ejpam-2552	262	41	)	)	PUNCT
ejpam-2552	262	42	�	�	PROPN
ejpam-2552	262	43	e2(b	e2(b	PROPN
ejpam-2552	262	44	+	+	PROPN
ejpam-2552	263	1	[	[	X
ejpam-2552	263	2	−α	−α	NOUN
ejpam-2552	263	3	,	,	PUNCT
ejpam-2552	263	4	α	α	NOUN
ejpam-2552	263	5	]	]	X
ejpam-2552	263	6	)	)	PUNCT
ejpam-2552	263	7	;	;	PUNCT
ejpam-2552	263	8	ii	ii	X
ejpam-2552	263	9	)	)	PUNCT
ejpam-2552	263	10	e2(b	e2(b	NOUN
ejpam-2552	263	11	)	)	PUNCT
ejpam-2552	263	12	�	�	PROPN
ejpam-2552	263	13	e1(b	e1(b	PART
ejpam-2552	263	14	+	+	PROPN
ejpam-2552	263	15	[	[	X
ejpam-2552	263	16	−α	−α	NOUN
ejpam-2552	263	17	,	,	PUNCT
ejpam-2552	263	18	α	α	NOUN
ejpam-2552	263	19	]	]	X
ejpam-2552	263	20	)	)	PUNCT
ejpam-2552	263	21	.	.	PUNCT
ejpam-2552	264	1	remark	remark	PROPN
ejpam-2552	264	2	.	.	PUNCT
ejpam-2552	265	1	when	when	SCONJ
ejpam-2552	265	2	two	two	NUM
ejpam-2552	265	3	s.m	s.m	PROPN
ejpam-2552	265	4	.	.	PROPN
ejpam-2552	265	5	’s	’s	PART
ejpam-2552	265	6	are	be	AUX
ejpam-2552	265	7	α−equivalent	α−equivalent	PROPN
ejpam-2552	265	8	,	,	PUNCT
ejpam-2552	265	9	for	for	ADP
ejpam-2552	265	10	any	any	DET
ejpam-2552	265	11	compact	compact	ADJ
ejpam-2552	265	12	b	b	NOUN
ejpam-2552	265	13	,	,	PUNCT
ejpam-2552	265	14	we	we	PRON
ejpam-2552	265	15	have	have	VERB
ejpam-2552	265	16	:	:	PUNCT
ejpam-2552	265	17	e1(b	e1(b	X
ejpam-2552	265	18	)	)	PUNCT
ejpam-2552	265	19	�	�	PROPN
ejpam-2552	265	20	e2(b	e2(b	NOUN
ejpam-2552	266	1	+	+	PROPN
ejpam-2552	267	1	[	[	X
ejpam-2552	267	2	−α	−α	NOUN
ejpam-2552	267	3	,	,	PUNCT
ejpam-2552	267	4	α	α	NOUN
ejpam-2552	267	5	]	]	X
ejpam-2552	267	6	)	)	PUNCT
ejpam-2552	267	7	�	�	PROPN
ejpam-2552	267	8	e1(b	e1(b	X
ejpam-2552	267	9	+	+	PROPN
ejpam-2552	268	1	[	[	X
ejpam-2552	268	2	−2α	−2α	PROPN
ejpam-2552	268	3	,	,	PUNCT
ejpam-2552	268	4	2α	2α	NOUN
ejpam-2552	268	5	]	]	PUNCT
ejpam-2552	268	6	)	)	PUNCT
ejpam-2552	268	7	.	.	PUNCT
ejpam-2552	269	1	as	as	ADV
ejpam-2552	269	2	far	far	ADV
ejpam-2552	269	3	as	as	SCONJ
ejpam-2552	269	4	α	α	PROPN
ejpam-2552	269	5	is	be	AUX
ejpam-2552	269	6	small	small	ADJ
ejpam-2552	269	7	,	,	PUNCT
ejpam-2552	269	8	the	the	DET
ejpam-2552	269	9	compact	compact	ADJ
ejpam-2552	269	10	sets	set	NOUN
ejpam-2552	269	11	b	b	PROPN
ejpam-2552	269	12	,	,	PUNCT
ejpam-2552	269	13	b	b	PROPN
ejpam-2552	270	1	+	+	CCONJ
ejpam-2552	270	2	[	[	X
ejpam-2552	270	3	−α	−α	NOUN
ejpam-2552	270	4	,	,	PUNCT
ejpam-2552	270	5	α	α	NOUN
ejpam-2552	270	6	]	]	X
ejpam-2552	270	7	and	and	CCONJ
ejpam-2552	270	8	b	b	NOUN
ejpam-2552	271	1	+	+	CCONJ
ejpam-2552	272	1	[	[	X
ejpam-2552	272	2	−2α	−2α	PROPN
ejpam-2552	272	3	,	,	PUNCT
ejpam-2552	272	4	2α	2α	NOUN
ejpam-2552	272	5	]	]	PUNCT
ejpam-2552	272	6	are	be	AUX
ejpam-2552	272	7	close	close	ADJ
ejpam-2552	272	8	together	together	ADV
ejpam-2552	272	9	.	.	PUNCT
ejpam-2552	273	1	it	it	PRON
ejpam-2552	273	2	is	be	AUX
ejpam-2552	273	3	also	also	ADV
ejpam-2552	273	4	the	the	DET
ejpam-2552	273	5	case	case	NOUN
ejpam-2552	273	6	for	for	ADP
ejpam-2552	273	7	the	the	DET
ejpam-2552	273	8	projectors	projector	NOUN
ejpam-2552	273	9	e1(b	e1(b	NOUN
ejpam-2552	273	10	)	)	PUNCT
ejpam-2552	273	11	and	and	CCONJ
ejpam-2552	273	12	e1(b	e1(b	X
ejpam-2552	274	1	+	+	CCONJ
ejpam-2552	275	1	[	[	X
ejpam-2552	275	2	−2α	−2α	PROPN
ejpam-2552	275	3	,	,	PUNCT
ejpam-2552	275	4	2α	2α	NOUN
ejpam-2552	275	5	]	]	PUNCT
ejpam-2552	275	6	)	)	PUNCT
ejpam-2552	275	7	.	.	PUNCT
ejpam-2552	276	1	so	so	ADV
ejpam-2552	276	2	the	the	DET
ejpam-2552	276	3	projector	projector	NOUN
ejpam-2552	276	4	e2(b	e2(b	PROPN
ejpam-2552	276	5	+	+	SYM
ejpam-2552	277	1	[	[	X
ejpam-2552	277	2	−α	−α	NOUN
ejpam-2552	277	3	,	,	PUNCT
ejpam-2552	277	4	α	α	NOUN
ejpam-2552	277	5	]	]	X
ejpam-2552	277	6	)	)	PUNCT
ejpam-2552	277	7	,	,	PUNCT
ejpam-2552	277	8	which	which	PRON
ejpam-2552	277	9	is	be	AUX
ejpam-2552	277	10	between	between	ADP
ejpam-2552	277	11	e1(b	e1(b	PROPN
ejpam-2552	277	12	)	)	PUNCT
ejpam-2552	277	13	and	and	CCONJ
ejpam-2552	277	14	e1(b	e1(b	X
ejpam-2552	277	15	+	+	CCONJ
ejpam-2552	278	1	[	[	X
ejpam-2552	278	2	−2α	−2α	PROPN
ejpam-2552	278	3	,	,	PUNCT
ejpam-2552	278	4	2α	2α	NOUN
ejpam-2552	278	5	]	]	PUNCT
ejpam-2552	278	6	)	)	PUNCT
ejpam-2552	278	7	,	,	PUNCT
ejpam-2552	278	8	is	be	AUX
ejpam-2552	278	9	close	close	ADJ
ejpam-2552	278	10	to	to	ADP
ejpam-2552	278	11	e1(b	e1(b	NOUN
ejpam-2552	278	12	)	)	PUNCT
ejpam-2552	278	13	.	.	PUNCT
ejpam-2552	279	1	this	this	PRON
ejpam-2552	279	2	induces	induce	VERB
ejpam-2552	279	3	the	the	DET
ejpam-2552	279	4	proximity	proximity	NOUN
ejpam-2552	279	5	between	between	ADP
ejpam-2552	279	6	e1(b	e1(b	PROPN
ejpam-2552	279	7	)	)	PUNCT
ejpam-2552	279	8	and	and	CCONJ
ejpam-2552	279	9	e2(b	e2(b	PROPN
ejpam-2552	279	10	)	)	PUNCT
ejpam-2552	279	11	.	.	PUNCT
ejpam-2552	280	1	apparently	apparently	ADV
ejpam-2552	280	2	,	,	PUNCT
ejpam-2552	280	3	the	the	DET
ejpam-2552	280	4	relation	relation	NOUN
ejpam-2552	280	5	of	of	ADP
ejpam-2552	280	6	α−equivalence	α−equivalence	NOUN
ejpam-2552	280	7	is	be	AUX
ejpam-2552	280	8	symmetric	symmetric	ADJ
ejpam-2552	280	9	,	,	PUNCT
ejpam-2552	280	10	so	so	ADV
ejpam-2552	280	11	the	the	DET
ejpam-2552	280	12	following	follow	VERB
ejpam-2552	280	13	property	property	NOUN
ejpam-2552	280	14	is	be	AUX
ejpam-2552	280	15	close	close	ADJ
ejpam-2552	280	16	to	to	ADP
ejpam-2552	280	17	a	a	DET
ejpam-2552	280	18	property	property	NOUN
ejpam-2552	280	19	of	of	ADP
ejpam-2552	280	20	transitivity	transitivity	NOUN
ejpam-2552	280	21	.	.	PUNCT
ejpam-2552	281	1	proposition	proposition	NOUN
ejpam-2552	281	2	3.1	3.1	NUM
ejpam-2552	281	3	.	.	PUNCT
ejpam-2552	282	1	if	if	SCONJ
ejpam-2552	282	2	three	three	NUM
ejpam-2552	282	3	s.m	s.m	PROPN
ejpam-2552	282	4	.	.	PROPN
ejpam-2552	282	5	’s	’s	PROPN
ejpam-2552	282	6	e1	e1	PROPN
ejpam-2552	282	7	,	,	PUNCT
ejpam-2552	282	8	e2	e2	PROPN
ejpam-2552	282	9	and	and	CCONJ
ejpam-2552	282	10	e3	e3	NOUN
ejpam-2552	282	11	are	be	AUX
ejpam-2552	282	12	such	such	ADJ
ejpam-2552	282	13	that	that	SCONJ
ejpam-2552	282	14	e1	e1	VERB
ejpam-2552	282	15	α∼	α∼	PROPN
ejpam-2552	282	16	e2	e2	PROPN
ejpam-2552	282	17	and	and	CCONJ
ejpam-2552	282	18	e2	e2	PROPN
ejpam-2552	282	19	α′∼	α′∼	PROPN
ejpam-2552	282	20	e3	e3	NOUN
ejpam-2552	282	21	,	,	PUNCT
ejpam-2552	282	22	where	where	SCONJ
ejpam-2552	282	23	α	α	NOUN
ejpam-2552	282	24	and	and	CCONJ
ejpam-2552	282	25	α′	α′	PROPN
ejpam-2552	282	26	are	be	AUX
ejpam-2552	282	27	elements	element	NOUN
ejpam-2552	282	28	of	of	ADP
ejpam-2552	282	29	r∗+	r∗+	PROPN
ejpam-2552	282	30	,	,	PUNCT
ejpam-2552	282	31	then	then	ADV
ejpam-2552	282	32	e1	e1	VERB
ejpam-2552	282	33	α+α′∼	α+α′∼	ADJ
ejpam-2552	282	34	e3	e3	NOUN
ejpam-2552	282	35	.	.	PUNCT
ejpam-2552	283	1	proof	proof	NOUN
ejpam-2552	283	2	.	.	PUNCT
ejpam-2552	284	1	it	it	PRON
ejpam-2552	284	2	is	be	AUX
ejpam-2552	284	3	the	the	DET
ejpam-2552	284	4	result	result	NOUN
ejpam-2552	284	5	of	of	ADP
ejpam-2552	284	6	the	the	DET
ejpam-2552	284	7	relations	relation	NOUN
ejpam-2552	284	8	:	:	PUNCT
ejpam-2552	284	9	e1(b	e1(b	X
ejpam-2552	284	10	)	)	PUNCT
ejpam-2552	284	11	�	�	PROPN
ejpam-2552	284	12	e2(b	e2(b	PROPN
ejpam-2552	285	1	+	+	PROPN
ejpam-2552	286	1	[	[	X
ejpam-2552	286	2	−α	−α	NOUN
ejpam-2552	286	3	,	,	PUNCT
ejpam-2552	286	4	α	α	NOUN
ejpam-2552	286	5	]	]	X
ejpam-2552	286	6	)	)	PUNCT
ejpam-2552	286	7	�	�	PROPN
ejpam-2552	286	8	e3((b	e3((b	VERB
ejpam-2552	286	9	+	+	CCONJ
ejpam-2552	287	1	[	[	X
ejpam-2552	287	2	−α	−α	NOUN
ejpam-2552	287	3	,	,	PUNCT
ejpam-2552	287	4	α	α	NOUN
ejpam-2552	287	5	]	]	X
ejpam-2552	287	6	)	)	PUNCT
ejpam-2552	288	1	+	+	CCONJ
ejpam-2552	289	1	[	[	X
ejpam-2552	289	2	−α′	−α′	NOUN
ejpam-2552	289	3	,	,	PUNCT
ejpam-2552	289	4	α′	α′	NUM
ejpam-2552	289	5	]	]	PUNCT
ejpam-2552	289	6	)	)	PUNCT
ejpam-2552	290	1	=	=	PUNCT
ejpam-2552	291	1	e3(b	e3(b	PROPN
ejpam-2552	292	1	+	+	X
ejpam-2552	292	2	[	[	X
ejpam-2552	292	3	−(α+	−(α+	NUM
ejpam-2552	292	4	α′	α′	NUM
ejpam-2552	292	5	)	)	PUNCT
ejpam-2552	292	6	,	,	PUNCT
ejpam-2552	292	7	α+	α+	X
ejpam-2552	292	8	α′	α′	NUM
ejpam-2552	292	9	]	]	PUNCT
ejpam-2552	292	10	)	)	PUNCT
ejpam-2552	292	11	,	,	PUNCT
ejpam-2552	292	12	a.	a.	NOUN
ejpam-2552	292	13	boudou	boudou	NOUN
ejpam-2552	292	14	,	,	PUNCT
ejpam-2552	292	15	s.	s.	PROPN
ejpam-2552	292	16	viguier	viguier	PROPN
ejpam-2552	292	17	-	-	PUNCT
ejpam-2552	292	18	pla	pla	PROPN
ejpam-2552	292	19	/	/	PUNCT
ejpam-2552	292	20	eur	eur	PROPN
ejpam-2552	292	21	.	.	PUNCT
ejpam-2552	293	1	j.	j.	PROPN
ejpam-2552	293	2	pure	pure	PROPN
ejpam-2552	293	3	appl	appl	PROPN
ejpam-2552	293	4	.	.	PROPN
ejpam-2552	293	5	math	math	PROPN
ejpam-2552	293	6	,	,	PUNCT
ejpam-2552	293	7	11	11	NUM
ejpam-2552	293	8	(	(	PUNCT
ejpam-2552	293	9	4	4	NUM
ejpam-2552	293	10	)	)	PUNCT
ejpam-2552	293	11	(	(	PUNCT
ejpam-2552	293	12	2018	2018	NUM
ejpam-2552	293	13	)	)	PUNCT
ejpam-2552	293	14	,	,	PUNCT
ejpam-2552	293	15	893	893	NUM
ejpam-2552	293	16	-	-	SYM
ejpam-2552	293	17	910	910	NUM
ejpam-2552	293	18	902	902	NUM
ejpam-2552	293	19	and	and	CCONJ
ejpam-2552	293	20	,	,	PUNCT
ejpam-2552	293	21	in	in	ADP
ejpam-2552	293	22	a	a	DET
ejpam-2552	293	23	symmetric	symmetric	ADJ
ejpam-2552	293	24	way	way	NOUN
ejpam-2552	293	25	:	:	PUNCT
ejpam-2552	293	26	e3(b	e3(b	ADJ
ejpam-2552	293	27	)	)	PUNCT
ejpam-2552	293	28	�	�	PROPN
ejpam-2552	293	29	e2(b	e2(b	PROPN
ejpam-2552	293	30	+	+	PROPN
ejpam-2552	294	1	[	[	X
ejpam-2552	294	2	−α′	−α′	NOUN
ejpam-2552	294	3	,	,	PUNCT
ejpam-2552	294	4	α′	α′	NUM
ejpam-2552	294	5	]	]	PUNCT
ejpam-2552	294	6	)	)	PUNCT
ejpam-2552	294	7	�	�	PROPN
ejpam-2552	294	8	e1((b	e1((b	VERB
ejpam-2552	294	9	+	+	CCONJ
ejpam-2552	295	1	[	[	X
ejpam-2552	295	2	−α′	−α′	NOUN
ejpam-2552	295	3	,	,	PUNCT
ejpam-2552	295	4	α′	α′	NUM
ejpam-2552	295	5	]	]	PUNCT
ejpam-2552	295	6	)	)	PUNCT
ejpam-2552	296	1	+	+	CCONJ
ejpam-2552	297	1	[	[	X
ejpam-2552	297	2	−α	−α	NOUN
ejpam-2552	297	3	,	,	PUNCT
ejpam-2552	297	4	α	α	NOUN
ejpam-2552	297	5	]	]	X
ejpam-2552	297	6	)	)	PUNCT
ejpam-2552	297	7	=	=	PUNCT
ejpam-2552	297	8	e1(b	e1(b	PROPN
ejpam-2552	298	1	+	+	CCONJ
ejpam-2552	298	2	[	[	X
ejpam-2552	298	3	−(α+	−(α+	NUM
ejpam-2552	298	4	α′	α′	NUM
ejpam-2552	298	5	)	)	PUNCT
ejpam-2552	298	6	,	,	PUNCT
ejpam-2552	298	7	α+	α+	X
ejpam-2552	298	8	α′	α′	NUM
ejpam-2552	298	9	]	]	PUNCT
ejpam-2552	298	10	)	)	PUNCT
ejpam-2552	298	11	,	,	PUNCT
ejpam-2552	298	12	for	for	ADP
ejpam-2552	298	13	any	any	DET
ejpam-2552	298	14	compact	compact	ADJ
ejpam-2552	298	15	b.	b.	PROPN
ejpam-2552	298	16	�	�	PROPN
ejpam-2552	298	17	the	the	DET
ejpam-2552	298	18	α−equivalence	α−equivalence	NOUN
ejpam-2552	298	19	provides	provide	VERB
ejpam-2552	298	20	a	a	DET
ejpam-2552	298	21	kind	kind	NOUN
ejpam-2552	298	22	of	of	ADP
ejpam-2552	298	23	continuity	continuity	NOUN
ejpam-2552	298	24	as	as	SCONJ
ejpam-2552	298	25	follows	follow	VERB
ejpam-2552	298	26	.	.	PUNCT
ejpam-2552	299	1	proposition	proposition	NOUN
ejpam-2552	299	2	3.2	3.2	NUM
ejpam-2552	299	3	.	.	PUNCT
ejpam-2552	300	1	if	if	SCONJ
ejpam-2552	300	2	(	(	PUNCT
ejpam-2552	300	3	αn)n∈n	αn)n∈n	NUM
ejpam-2552	300	4	is	be	AUX
ejpam-2552	300	5	a	a	DET
ejpam-2552	300	6	sequence	sequence	NOUN
ejpam-2552	300	7	of	of	ADP
ejpam-2552	300	8	elements	element	NOUN
ejpam-2552	300	9	of	of	ADP
ejpam-2552	300	10	r∗+	r∗+	PROPN
ejpam-2552	300	11	which	which	PRON
ejpam-2552	300	12	decreasingly	decreasingly	ADV
ejpam-2552	300	13	converges	converge	VERB
ejpam-2552	300	14	to	to	ADP
ejpam-2552	300	15	α	α	PRON
ejpam-2552	300	16	,	,	PUNCT
ejpam-2552	300	17	element	element	NOUN
ejpam-2552	300	18	of	of	ADP
ejpam-2552	300	19	r∗+	r∗+	PROPN
ejpam-2552	300	20	,	,	PUNCT
ejpam-2552	300	21	if	if	SCONJ
ejpam-2552	300	22	e1	e1	PROPN
ejpam-2552	300	23	and	and	CCONJ
ejpam-2552	300	24	e2	e2	PROPN
ejpam-2552	300	25	are	be	AUX
ejpam-2552	300	26	two	two	NUM
ejpam-2552	300	27	s.m	s.m	PROPN
ejpam-2552	300	28	.	.	PROPN
ejpam-2552	300	29	’s	’s	PART
ejpam-2552	300	30	such	such	ADJ
ejpam-2552	300	31	that	that	SCONJ
ejpam-2552	300	32	e1	e1	PROPN
ejpam-2552	300	33	αn∼	αn∼	PROPN
ejpam-2552	300	34	e2	e2	PROPN
ejpam-2552	300	35	,	,	PUNCT
ejpam-2552	300	36	for	for	ADP
ejpam-2552	300	37	any	any	DET
ejpam-2552	300	38	n	n	NOUN
ejpam-2552	300	39	of	of	ADP
ejpam-2552	300	40	n	n	CCONJ
ejpam-2552	300	41	,	,	PUNCT
ejpam-2552	300	42	then	then	ADV
ejpam-2552	300	43	e1	e1	VERB
ejpam-2552	300	44	α∼	α∼	PROPN
ejpam-2552	300	45	e2	e2	NOUN
ejpam-2552	300	46	.	.	PUNCT
ejpam-2552	301	1	proof	proof	NOUN
ejpam-2552	301	2	.	.	PUNCT
ejpam-2552	302	1	let	let	VERB
ejpam-2552	302	2	b	b	X
ejpam-2552	302	3	be	be	AUX
ejpam-2552	302	4	a	a	DET
ejpam-2552	302	5	compact	compact	NOUN
ejpam-2552	302	6	.	.	PUNCT
ejpam-2552	303	1	it	it	PRON
ejpam-2552	303	2	is	be	AUX
ejpam-2552	303	3	known	know	VERB
ejpam-2552	303	4	that	that	SCONJ
ejpam-2552	303	5	b	b	X
ejpam-2552	304	1	+	+	CCONJ
ejpam-2552	305	1	[	[	X
ejpam-2552	305	2	−α	−α	NOUN
ejpam-2552	305	3	,	,	PUNCT
ejpam-2552	305	4	α	α	NOUN
ejpam-2552	305	5	]	]	X
ejpam-2552	305	6	=	=	SYM
ejpam-2552	305	7	∩n∈n(b	∩n∈n(b	NOUN
ejpam-2552	305	8	+	+	X
ejpam-2552	306	1	[	[	X
ejpam-2552	306	2	−αn	−αn	X
ejpam-2552	306	3	,	,	PUNCT
ejpam-2552	306	4	αn	αn	NOUN
ejpam-2552	306	5	]	]	PUNCT
ejpam-2552	306	6	)	)	PUNCT
ejpam-2552	306	7	.	.	PUNCT
ejpam-2552	307	1	as	as	ADP
ejpam-2552	307	2	(	(	PUNCT
ejpam-2552	307	3	b+	b+	X
ejpam-2552	307	4	[	[	X
ejpam-2552	307	5	−αn	−αn	X
ejpam-2552	307	6	,	,	PUNCT
ejpam-2552	307	7	αn])n∈n	αn])n∈n	PROPN
ejpam-2552	307	8	is	be	AUX
ejpam-2552	307	9	a	a	DET
ejpam-2552	307	10	decreasing	decrease	VERB
ejpam-2552	307	11	sequence	sequence	NOUN
ejpam-2552	307	12	of	of	ADP
ejpam-2552	307	13	elements	element	NOUN
ejpam-2552	307	14	of	of	ADP
ejpam-2552	307	15	br	br	NOUN
ejpam-2552	307	16	,	,	PUNCT
ejpam-2552	307	17	for	for	ADP
ejpam-2552	307	18	any	any	DET
ejpam-2552	307	19	x	x	NOUN
ejpam-2552	307	20	of	of	ADP
ejpam-2552	307	21	h	h	NOUN
ejpam-2552	307	22	,	,	PUNCT
ejpam-2552	307	23	the	the	DET
ejpam-2552	307	24	properties	property	NOUN
ejpam-2552	307	25	of	of	ADP
ejpam-2552	307	26	continuity	continuity	NOUN
ejpam-2552	307	27	of	of	ADP
ejpam-2552	307	28	the	the	DET
ejpam-2552	307	29	r.m	r.m	PROPN
ejpam-2552	307	30	.	.	PROPN
ejpam-2552	307	31	’s	’s	PART
ejpam-2552	307	32	allow	allow	VERB
ejpam-2552	307	33	us	we	PRON
ejpam-2552	307	34	to	to	PART
ejpam-2552	307	35	write	write	VERB
ejpam-2552	307	36	:	:	PUNCT
ejpam-2552	307	37	limn→∞e1(b	limn→∞e1(b	VERB
ejpam-2552	308	1	+	+	CCONJ
ejpam-2552	308	2	[	[	X
ejpam-2552	308	3	−αn	−αn	X
ejpam-2552	308	4	,	,	PUNCT
ejpam-2552	308	5	αn])x	αn])x	NOUN
ejpam-2552	308	6	=	=	SYM
ejpam-2552	308	7	limn→∞z	limn→∞z	NOUN
ejpam-2552	308	8	x	x	X
ejpam-2552	308	9	e1(b	e1(b	PROPN
ejpam-2552	309	1	+	+	CCONJ
ejpam-2552	309	2	[	[	X
ejpam-2552	309	3	−αn	−αn	X
ejpam-2552	309	4	,	,	PUNCT
ejpam-2552	309	5	αn	αn	NOUN
ejpam-2552	309	6	]	]	X
ejpam-2552	309	7	)	)	PUNCT
ejpam-2552	310	1	=	=	SYM
ejpam-2552	310	2	zxe1(∩n∈n(b	zxe1(∩n∈n(b	X
ejpam-2552	311	1	+	+	PUNCT
ejpam-2552	311	2	[	[	X
ejpam-2552	311	3	−αn	−αn	X
ejpam-2552	311	4	,	,	PUNCT
ejpam-2552	311	5	αn	αn	NOUN
ejpam-2552	311	6	]	]	PUNCT
ejpam-2552	311	7	)	)	PUNCT
ejpam-2552	311	8	)	)	PUNCT
ejpam-2552	312	1	=	=	SYM
ejpam-2552	312	2	zxe1(b	zxe1(b	PUNCT
ejpam-2552	312	3	+	+	SYM
ejpam-2552	313	1	[	[	X
ejpam-2552	313	2	−α	−α	NOUN
ejpam-2552	313	3	,	,	PUNCT
ejpam-2552	313	4	α	α	NOUN
ejpam-2552	313	5	]	]	X
ejpam-2552	313	6	)	)	PUNCT
ejpam-2552	313	7	=	=	PUNCT
ejpam-2552	313	8	e1(b	e1(b	PROPN
ejpam-2552	314	1	+	+	CCONJ
ejpam-2552	315	1	[	[	X
ejpam-2552	315	2	−α	−α	NOUN
ejpam-2552	315	3	,	,	PUNCT
ejpam-2552	315	4	α])x	α])x	PROPN
ejpam-2552	315	5	,	,	PUNCT
ejpam-2552	315	6	then	then	ADV
ejpam-2552	315	7	limn→∞(e2(b))(e1(b	limn→∞(e2(b))(e1(b	PROPN
ejpam-2552	315	8	+	+	PROPN
ejpam-2552	316	1	[	[	X
ejpam-2552	316	2	−αn	−αn	X
ejpam-2552	316	3	,	,	PUNCT
ejpam-2552	316	4	αn]))x	αn]))x	NOUN
ejpam-2552	316	5	=	=	SYM
ejpam-2552	316	6	(	(	PUNCT
ejpam-2552	316	7	e2(b))(e1(b	e2(b))(e1(b	PROPN
ejpam-2552	316	8	+	+	PROPN
ejpam-2552	317	1	[	[	X
ejpam-2552	317	2	−α	−α	NOUN
ejpam-2552	317	3	,	,	PUNCT
ejpam-2552	317	4	α]))x	α]))x	NOUN
ejpam-2552	317	5	.	.	PUNCT
ejpam-2552	318	1	as	as	ADP
ejpam-2552	318	2	(	(	PUNCT
ejpam-2552	318	3	e2(b))(e1(b	e2(b))(e1(b	PROPN
ejpam-2552	318	4	+	+	PROPN
ejpam-2552	318	5	[	[	X
ejpam-2552	318	6	−αn	−αn	X
ejpam-2552	318	7	,	,	PUNCT
ejpam-2552	318	8	αn]))x	αn]))x	NOUN
ejpam-2552	318	9	=	=	SYM
ejpam-2552	318	10	e2(b	e2(b	NOUN
ejpam-2552	318	11	)	)	PUNCT
ejpam-2552	318	12	,	,	PUNCT
ejpam-2552	318	13	because	because	SCONJ
ejpam-2552	318	14	e2(b	e2(b	ADJ
ejpam-2552	318	15	)	)	PUNCT
ejpam-2552	318	16	�	�	PROPN
ejpam-2552	318	17	e1(b	e1(b	PROPN
ejpam-2552	318	18	+	+	CCONJ
ejpam-2552	318	19	[	[	X
ejpam-2552	318	20	−αn	−αn	X
ejpam-2552	318	21	,	,	PUNCT
ejpam-2552	318	22	αn	αn	NOUN
ejpam-2552	318	23	]	]	PUNCT
ejpam-2552	318	24	)	)	PUNCT
ejpam-2552	318	25	,	,	PUNCT
ejpam-2552	318	26	what	what	PRON
ejpam-2552	318	27	precedes	precede	VERB
ejpam-2552	318	28	lets	let	VERB
ejpam-2552	318	29	us	we	PRON
ejpam-2552	318	30	write	write	VERB
ejpam-2552	318	31	(	(	PUNCT
ejpam-2552	318	32	e2(b))x	e2(b))x	NOUN
ejpam-2552	318	33	=	=	SYM
ejpam-2552	318	34	(	(	PUNCT
ejpam-2552	318	35	e2(b))(e1(b	e2(b))(e1(b	PROPN
ejpam-2552	318	36	+	+	PROPN
ejpam-2552	319	1	[	[	X
ejpam-2552	319	2	−α	−α	NOUN
ejpam-2552	319	3	,	,	PUNCT
ejpam-2552	319	4	α]))x	α]))x	NOUN
ejpam-2552	319	5	.	.	PUNCT
ejpam-2552	320	1	it	it	PRON
ejpam-2552	320	2	is	be	AUX
ejpam-2552	320	3	then	then	ADV
ejpam-2552	320	4	clear	clear	ADJ
ejpam-2552	320	5	that	that	SCONJ
ejpam-2552	320	6	e2(b	e2(b	NOUN
ejpam-2552	320	7	)	)	PUNCT
ejpam-2552	320	8	�	�	PROPN
ejpam-2552	320	9	e1(b	e1(b	PART
ejpam-2552	320	10	+	+	PROPN
ejpam-2552	321	1	[	[	X
ejpam-2552	321	2	−α	−α	NOUN
ejpam-2552	321	3	,	,	PUNCT
ejpam-2552	321	4	α	α	NOUN
ejpam-2552	321	5	]	]	X
ejpam-2552	321	6	)	)	PUNCT
ejpam-2552	321	7	.	.	PUNCT
ejpam-2552	322	1	the	the	DET
ejpam-2552	322	2	relation	relation	NOUN
ejpam-2552	322	3	e2(b	e2(b	NOUN
ejpam-2552	322	4	)	)	PUNCT
ejpam-2552	322	5	�	�	PROPN
ejpam-2552	322	6	e1(b	e1(b	PART
ejpam-2552	322	7	+	+	PROPN
ejpam-2552	323	1	[	[	X
ejpam-2552	323	2	−α	−α	NOUN
ejpam-2552	323	3	,	,	PUNCT
ejpam-2552	323	4	α	α	NOUN
ejpam-2552	323	5	]	]	X
ejpam-2552	323	6	)	)	PUNCT
ejpam-2552	323	7	can	can	AUX
ejpam-2552	323	8	be	be	AUX
ejpam-2552	323	9	proved	prove	VERB
ejpam-2552	323	10	in	in	ADP
ejpam-2552	323	11	a	a	DET
ejpam-2552	323	12	similar	similar	ADJ
ejpam-2552	323	13	way	way	NOUN
ejpam-2552	323	14	,	,	PUNCT
ejpam-2552	323	15	what	what	PRON
ejpam-2552	323	16	ends	end	VERB
ejpam-2552	323	17	the	the	DET
ejpam-2552	323	18	proof	proof	NOUN
ejpam-2552	323	19	.	.	PUNCT
ejpam-2552	324	1	�	�	PROPN
ejpam-2552	324	2	when	when	SCONJ
ejpam-2552	324	3	a	a	DET
ejpam-2552	324	4	s.m	s.m	PROPN
ejpam-2552	324	5	.	.	PROPN
ejpam-2552	324	6	is	be	AUX
ejpam-2552	324	7	concentrated	concentrate	VERB
ejpam-2552	324	8	on	on	ADP
ejpam-2552	324	9	the	the	DET
ejpam-2552	324	10	neigbourhood	neigbourhood	NOUN
ejpam-2552	324	11	of	of	ADP
ejpam-2552	324	12	0	0	NUM
ejpam-2552	324	13	,	,	PUNCT
ejpam-2552	324	14	it	it	PRON
ejpam-2552	324	15	is	be	AUX
ejpam-2552	324	16	close	close	ADJ
ejpam-2552	324	17	to	to	ADP
ejpam-2552	324	18	er	er	INTJ
ejpam-2552	324	19	,	,	PUNCT
ejpam-2552	324	20	this	this	PRON
ejpam-2552	324	21	is	be	AUX
ejpam-2552	324	22	what	what	PRON
ejpam-2552	324	23	is	be	AUX
ejpam-2552	324	24	expressed	express	VERB
ejpam-2552	324	25	in	in	ADP
ejpam-2552	324	26	the	the	DET
ejpam-2552	324	27	following	follow	VERB
ejpam-2552	324	28	result	result	NOUN
ejpam-2552	324	29	.	.	PUNCT
ejpam-2552	325	1	proposition	proposition	NOUN
ejpam-2552	325	2	3.3	3.3	NUM
ejpam-2552	325	3	.	.	PUNCT
ejpam-2552	326	1	a	a	DET
ejpam-2552	326	2	s.m	s.m	PROPN
ejpam-2552	326	3	.	.	PUNCT
ejpam-2552	327	1	e	e	PROPN
ejpam-2552	327	2	is	be	AUX
ejpam-2552	327	3	α−equivalent	α−equivalent	NUM
ejpam-2552	327	4	to	to	PART
ejpam-2552	327	5	er	er	INTJ
ejpam-2552	327	6	if	if	SCONJ
ejpam-2552	328	1	and	and	CCONJ
ejpam-2552	328	2	only	only	ADV
ejpam-2552	328	3	if	if	SCONJ
ejpam-2552	328	4	e([−α	e([−α	PROPN
ejpam-2552	328	5	,	,	PUNCT
ejpam-2552	328	6	α	α	NOUN
ejpam-2552	328	7	]	]	X
ejpam-2552	328	8	)	)	PUNCT
ejpam-2552	328	9	=	=	SYM
ejpam-2552	328	10	ih	ih	X
ejpam-2552	328	11	.	.	PUNCT
ejpam-2552	329	1	proof	proof	NOUN
ejpam-2552	329	2	.	.	PUNCT
ejpam-2552	330	1	let	let	VERB
ejpam-2552	330	2	e	e	PRON
ejpam-2552	330	3	be	be	AUX
ejpam-2552	330	4	a	a	DET
ejpam-2552	330	5	s.m	s.m	PROPN
ejpam-2552	330	6	.	.	PUNCT
ejpam-2552	331	1	such	such	ADJ
ejpam-2552	331	2	that	that	SCONJ
ejpam-2552	331	3	e([−α	e([−α	PROPN
ejpam-2552	331	4	,	,	PUNCT
ejpam-2552	331	5	α	α	NOUN
ejpam-2552	331	6	]	]	X
ejpam-2552	331	7	)	)	PUNCT
ejpam-2552	331	8	=	=	SYM
ejpam-2552	331	9	ih	ih	X
ejpam-2552	331	10	.	.	PUNCT
ejpam-2552	332	1	let	let	VERB
ejpam-2552	332	2	us	we	PRON
ejpam-2552	332	3	consider	consider	VERB
ejpam-2552	332	4	a	a	DET
ejpam-2552	332	5	compact	compact	ADJ
ejpam-2552	332	6	b.	b.	NOUN
ejpam-2552	333	1	if	if	SCONJ
ejpam-2552	333	2	0	0	NUM
ejpam-2552	333	3	∈	∈	PROPN
ejpam-2552	333	4	b+[−α	b+[−α	PROPN
ejpam-2552	333	5	,	,	PUNCT
ejpam-2552	333	6	α	α	NOUN
ejpam-2552	333	7	]	]	X
ejpam-2552	333	8	,	,	PUNCT
ejpam-2552	333	9	then	then	ADV
ejpam-2552	333	10	e(b	e(b	PROPN
ejpam-2552	333	11	)	)	PUNCT
ejpam-2552	333	12	�	�	PROPN
ejpam-2552	333	13	ih	ih	NOUN
ejpam-2552	333	14	=	=	SYM
ejpam-2552	333	15	er(b+[−α	er(b+[−α	PROPN
ejpam-2552	333	16	,	,	PUNCT
ejpam-2552	333	17	α	α	NOUN
ejpam-2552	333	18	]	]	X
ejpam-2552	333	19	)	)	PUNCT
ejpam-2552	333	20	.	.	PUNCT
ejpam-2552	334	1	if	if	SCONJ
ejpam-2552	334	2	0	0	NUM
ejpam-2552	334	3	6∈	6∈	PROPN
ejpam-2552	334	4	b+[−α	b+[−α	PROPN
ejpam-2552	334	5	,	,	PUNCT
ejpam-2552	334	6	α	α	PROPN
ejpam-2552	334	7	]	]	X
ejpam-2552	334	8	,	,	PUNCT
ejpam-2552	334	9	thenb∩[−α	thenb∩[−α	NOUN
ejpam-2552	334	10	,	,	PUNCT
ejpam-2552	334	11	α	α	NOUN
ejpam-2552	334	12	]	]	X
ejpam-2552	334	13	=	=	SYM
ejpam-2552	334	14	∅	∅	NOUN
ejpam-2552	334	15	and	and	CCONJ
ejpam-2552	334	16	then	then	ADV
ejpam-2552	334	17	0	0	X
ejpam-2552	334	18	=	=	SYM
ejpam-2552	334	19	e(b	e(b	X
ejpam-2552	334	20	∩	∩	NOUN
ejpam-2552	334	21	[	[	X
ejpam-2552	334	22	−α	−α	NOUN
ejpam-2552	334	23	,	,	PUNCT
ejpam-2552	334	24	α	α	NOUN
ejpam-2552	334	25	]	]	X
ejpam-2552	334	26	)	)	PUNCT
ejpam-2552	334	27	=	=	SYM
ejpam-2552	335	1	(	(	PUNCT
ejpam-2552	335	2	e(b))(e([−α	e(b))(e([−α	NOUN
ejpam-2552	335	3	,	,	PUNCT
ejpam-2552	335	4	α	α	NOUN
ejpam-2552	335	5	]	]	X
ejpam-2552	335	6	)	)	PUNCT
ejpam-2552	335	7	)	)	PUNCT
ejpam-2552	335	8	=	=	SYM
ejpam-2552	335	9	e(b	e(b	X
ejpam-2552	335	10	)	)	PUNCT
ejpam-2552	335	11	�	�	PROPN
ejpam-2552	335	12	er(b	er(b	X
ejpam-2552	335	13	+	+	CCONJ
ejpam-2552	336	1	[	[	X
ejpam-2552	336	2	−α	−α	NOUN
ejpam-2552	336	3	,	,	PUNCT
ejpam-2552	336	4	α	α	NOUN
ejpam-2552	336	5	]	]	X
ejpam-2552	336	6	)	)	PUNCT
ejpam-2552	336	7	.	.	PUNCT
ejpam-2552	337	1	in	in	ADP
ejpam-2552	337	2	both	both	DET
ejpam-2552	337	3	cases	case	NOUN
ejpam-2552	337	4	we	we	PRON
ejpam-2552	337	5	have	have	AUX
ejpam-2552	337	6	e(b	e(b	VERB
ejpam-2552	337	7	)	)	PUNCT
ejpam-2552	337	8	�	�	PROPN
ejpam-2552	337	9	er(b	er(b	X
ejpam-2552	337	10	+	+	CCONJ
ejpam-2552	338	1	[	[	X
ejpam-2552	338	2	−α	−α	NOUN
ejpam-2552	338	3	,	,	PUNCT
ejpam-2552	338	4	α	α	NOUN
ejpam-2552	338	5	]	]	X
ejpam-2552	338	6	)	)	PUNCT
ejpam-2552	338	7	.	.	PUNCT
ejpam-2552	339	1	in	in	ADP
ejpam-2552	339	2	order	order	NOUN
ejpam-2552	339	3	to	to	PART
ejpam-2552	339	4	prove	prove	VERB
ejpam-2552	339	5	that	that	SCONJ
ejpam-2552	339	6	er(b	er(b	NOUN
ejpam-2552	339	7	)	)	PUNCT
ejpam-2552	339	8	�	�	PROPN
ejpam-2552	339	9	e(b	e(b	PROPN
ejpam-2552	339	10	+	+	CCONJ
ejpam-2552	339	11	[	[	X
ejpam-2552	339	12	−α	−α	NOUN
ejpam-2552	339	13	,	,	PUNCT
ejpam-2552	339	14	α	α	NOUN
ejpam-2552	339	15	]	]	X
ejpam-2552	339	16	)	)	PUNCT
ejpam-2552	339	17	,	,	PUNCT
ejpam-2552	339	18	we	we	PRON
ejpam-2552	339	19	also	also	ADV
ejpam-2552	339	20	have	have	VERB
ejpam-2552	339	21	two	two	NUM
ejpam-2552	339	22	possibilities	possibility	NOUN
ejpam-2552	339	23	.	.	PUNCT
ejpam-2552	340	1	either	either	CCONJ
ejpam-2552	340	2	er(b	er(b	PUNCT
ejpam-2552	340	3	)	)	PUNCT
ejpam-2552	341	1	=	=	SYM
ejpam-2552	341	2	ih	ih	X
ejpam-2552	341	3	,	,	PUNCT
ejpam-2552	341	4	either	either	CCONJ
ejpam-2552	341	5	er(b	er(b	PUNCT
ejpam-2552	341	6	)	)	PUNCT
ejpam-2552	341	7	=	=	SYM
ejpam-2552	341	8	0	0	X
ejpam-2552	341	9	.	.	PUNCT
ejpam-2552	342	1	in	in	ADP
ejpam-2552	342	2	the	the	DET
ejpam-2552	342	3	first	first	ADJ
ejpam-2552	342	4	case	case	NOUN
ejpam-2552	342	5	,	,	PUNCT
ejpam-2552	342	6	0	0	NUM
ejpam-2552	342	7	∈	∈	PROPN
ejpam-2552	342	8	b	b	NOUN
ejpam-2552	342	9	and	and	CCONJ
ejpam-2552	342	10	then	then	ADV
ejpam-2552	343	1	[	[	X
ejpam-2552	343	2	−α	−α	NOUN
ejpam-2552	343	3	,	,	PUNCT
ejpam-2552	343	4	α	α	NOUN
ejpam-2552	343	5	]	]	X
ejpam-2552	343	6	⊂	⊂	PROPN
ejpam-2552	343	7	b+[−α	b+[−α	PROPN
ejpam-2552	343	8	,	,	PUNCT
ejpam-2552	343	9	α	α	NOUN
ejpam-2552	343	10	]	]	X
ejpam-2552	343	11	,	,	PUNCT
ejpam-2552	343	12	so	so	ADV
ejpam-2552	343	13	er(b	er(b	PUNCT
ejpam-2552	343	14	)	)	PUNCT
ejpam-2552	343	15	=	=	SYM
ejpam-2552	344	1	ih	ih	X
ejpam-2552	344	2	=	=	SYM
ejpam-2552	344	3	e([−α	e([−α	PROPN
ejpam-2552	344	4	,	,	PUNCT
ejpam-2552	344	5	α	α	NOUN
ejpam-2552	344	6	]	]	X
ejpam-2552	344	7	)	)	PUNCT
ejpam-2552	344	8	�	�	PROPN
ejpam-2552	344	9	e(b	e(b	PROPN
ejpam-2552	344	10	+	+	CCONJ
ejpam-2552	345	1	[	[	X
ejpam-2552	345	2	−α	−α	NOUN
ejpam-2552	345	3	,	,	PUNCT
ejpam-2552	345	4	α	α	NOUN
ejpam-2552	345	5	]	]	X
ejpam-2552	345	6	)	)	PUNCT
ejpam-2552	345	7	.	.	PUNCT
ejpam-2552	346	1	in	in	ADP
ejpam-2552	346	2	the	the	DET
ejpam-2552	346	3	second	second	ADJ
ejpam-2552	346	4	case	case	NOUN
ejpam-2552	346	5	,	,	PUNCT
ejpam-2552	346	6	er(b	er(b	NOUN
ejpam-2552	346	7	)	)	PUNCT
ejpam-2552	346	8	=	=	SYM
ejpam-2552	346	9	0	0	NUM
ejpam-2552	346	10	�	�	PROPN
ejpam-2552	346	11	e(b	e(b	VERB
ejpam-2552	346	12	+	+	CCONJ
ejpam-2552	347	1	[	[	X
ejpam-2552	347	2	−α	−α	NOUN
ejpam-2552	347	3	,	,	PUNCT
ejpam-2552	347	4	α	α	NOUN
ejpam-2552	347	5	]	]	X
ejpam-2552	347	6	)	)	PUNCT
ejpam-2552	347	7	.	.	PUNCT
ejpam-2552	348	1	so	so	ADV
ejpam-2552	348	2	we	we	PRON
ejpam-2552	348	3	can	can	AUX
ejpam-2552	348	4	conclude	conclude	VERB
ejpam-2552	348	5	to	to	ADP
ejpam-2552	348	6	the	the	DET
ejpam-2552	348	7	α−equivalence	α−equivalence	NOUN
ejpam-2552	348	8	between	between	ADP
ejpam-2552	348	9	the	the	DET
ejpam-2552	348	10	s.m	s.m	PROPN
ejpam-2552	348	11	.	.	PROPN
ejpam-2552	348	12	’s	’s	PROPN
ejpam-2552	348	13	e	e	PROPN
ejpam-2552	348	14	and	and	CCONJ
ejpam-2552	348	15	er	er	INTJ
ejpam-2552	348	16	.	.	PUNCT
ejpam-2552	349	1	as	as	ADP
ejpam-2552	349	2	for	for	ADP
ejpam-2552	349	3	the	the	DET
ejpam-2552	349	4	converse	converse	NOUN
ejpam-2552	349	5	,	,	PUNCT
ejpam-2552	349	6	it	it	PRON
ejpam-2552	349	7	comes	come	VERB
ejpam-2552	349	8	from	from	ADP
ejpam-2552	349	9	the	the	DET
ejpam-2552	349	10	relations	relation	NOUN
ejpam-2552	349	11	ih	ih	NOUN
ejpam-2552	349	12	=	=	PUNCT
ejpam-2552	349	13	er({0	er({0	X
ejpam-2552	349	14	}	}	PUNCT
ejpam-2552	349	15	)	)	PUNCT
ejpam-2552	349	16	�	�	PROPN
ejpam-2552	349	17	e({0}+	e({0}+	PROPN
ejpam-2552	350	1	[	[	X
ejpam-2552	350	2	−α	−α	PROPN
ejpam-2552	350	3	,	,	PUNCT
ejpam-2552	350	4	α	α	NOUN
ejpam-2552	350	5	]	]	X
ejpam-2552	350	6	)	)	PUNCT
ejpam-2552	350	7	=	=	SYM
ejpam-2552	350	8	e([−α	e([−α	PROPN
ejpam-2552	350	9	,	,	PUNCT
ejpam-2552	350	10	α	α	NOUN
ejpam-2552	350	11	]	]	X
ejpam-2552	350	12	)	)	PUNCT
ejpam-2552	350	13	=	=	SYM
ejpam-2552	350	14	ih	ih	X
ejpam-2552	350	15	.	.	PUNCT
ejpam-2552	351	1	�	�	PROPN
ejpam-2552	351	2	let	let	VERB
ejpam-2552	351	3	us	we	PRON
ejpam-2552	351	4	now	now	ADV
ejpam-2552	351	5	start	start	VERB
ejpam-2552	351	6	the	the	DET
ejpam-2552	351	7	study	study	NOUN
ejpam-2552	351	8	of	of	ADP
ejpam-2552	351	9	the	the	DET
ejpam-2552	351	10	transmission	transmission	NOUN
ejpam-2552	351	11	of	of	ADP
ejpam-2552	351	12	the	the	DET
ejpam-2552	351	13	α−equivalence	α−equivalence	NOUN
ejpam-2552	351	14	through	through	ADP
ejpam-2552	351	15	convolution	convolution	NOUN
ejpam-2552	351	16	.	.	PUNCT
ejpam-2552	352	1	first	first	ADV
ejpam-2552	352	2	of	of	ADP
ejpam-2552	352	3	all	all	PRON
ejpam-2552	352	4	,	,	PUNCT
ejpam-2552	352	5	let	let	VERB
ejpam-2552	352	6	us	we	PRON
ejpam-2552	352	7	introduce	introduce	VERB
ejpam-2552	352	8	a	a	DET
ejpam-2552	352	9	preliminary	preliminary	ADJ
ejpam-2552	352	10	result	result	NOUN
ejpam-2552	352	11	.	.	PUNCT
ejpam-2552	353	1	lemma	lemma	PROPN
ejpam-2552	353	2	3.1	3.1	NUM
ejpam-2552	353	3	.	.	PUNCT
ejpam-2552	354	1	let	let	VERB
ejpam-2552	354	2	e	e	NOUN
ejpam-2552	354	3	and	and	CCONJ
ejpam-2552	354	4	e	e	NOUN
ejpam-2552	354	5	′	′	NOUN
ejpam-2552	354	6	be	be	AUX
ejpam-2552	354	7	two	two	NUM
ejpam-2552	354	8	s.m	s.m	PROPN
ejpam-2552	354	9	.	.	PROPN
ejpam-2552	354	10	’s	’s	PART
ejpam-2552	354	11	which	which	DET
ejpam-2552	354	12	commute	commute	NOUN
ejpam-2552	354	13	.	.	PUNCT
ejpam-2552	355	1	if	if	SCONJ
ejpam-2552	355	2	e	e	NOUN
ejpam-2552	355	3	is	be	AUX
ejpam-2552	355	4	α−equivalent	α−equivalent	NOUN
ejpam-2552	355	5	with	with	ADP
ejpam-2552	355	6	er	er	INTJ
ejpam-2552	355	7	,	,	PUNCT
ejpam-2552	355	8	then	then	ADV
ejpam-2552	355	9	e	e	NOUN
ejpam-2552	355	10	′	′	NOUN
ejpam-2552	355	11	∗	∗	NOUN
ejpam-2552	355	12	e	e	X
ejpam-2552	355	13	α∼	α∼	NUM
ejpam-2552	355	14	e	e	NOUN
ejpam-2552	355	15	′.	′.	NOUN
ejpam-2552	355	16	proof	proof	NOUN
ejpam-2552	355	17	.	.	PUNCT
ejpam-2552	356	1	for	for	ADP
ejpam-2552	356	2	any	any	DET
ejpam-2552	356	3	compact	compact	ADJ
ejpam-2552	356	4	b	b	PROPN
ejpam-2552	356	5	of	of	ADP
ejpam-2552	356	6	r	r	NOUN
ejpam-2552	356	7	,	,	PUNCT
ejpam-2552	356	8	a.	a.	NOUN
ejpam-2552	356	9	boudou	boudou	NOUN
ejpam-2552	356	10	,	,	PUNCT
ejpam-2552	356	11	s.	s.	PROPN
ejpam-2552	356	12	viguier	viguier	PROPN
ejpam-2552	356	13	-	-	PUNCT
ejpam-2552	356	14	pla	pla	PROPN
ejpam-2552	356	15	/	/	PUNCT
ejpam-2552	356	16	eur	eur	PROPN
ejpam-2552	356	17	.	.	PUNCT
ejpam-2552	357	1	j.	j.	PROPN
ejpam-2552	357	2	pure	pure	PROPN
ejpam-2552	357	3	appl	appl	PROPN
ejpam-2552	357	4	.	.	PROPN
ejpam-2552	357	5	math	math	PROPN
ejpam-2552	357	6	,	,	PUNCT
ejpam-2552	357	7	11	11	NUM
ejpam-2552	357	8	(	(	PUNCT
ejpam-2552	357	9	4	4	NUM
ejpam-2552	357	10	)	)	PUNCT
ejpam-2552	357	11	(	(	PUNCT
ejpam-2552	357	12	2018	2018	NUM
ejpam-2552	357	13	)	)	PUNCT
ejpam-2552	357	14	,	,	PUNCT
ejpam-2552	357	15	893	893	NUM
ejpam-2552	357	16	-	-	SYM
ejpam-2552	357	17	910	910	NUM
ejpam-2552	357	18	903	903	NUM
ejpam-2552	357	19	(	(	PUNCT
ejpam-2552	357	20	r×	r×	NOUN
ejpam-2552	358	1	[	[	X
ejpam-2552	358	2	−α	−α	NOUN
ejpam-2552	358	3	,	,	PUNCT
ejpam-2552	358	4	α	α	NOUN
ejpam-2552	358	5	]	]	X
ejpam-2552	358	6	)	)	PUNCT
ejpam-2552	358	7	∩	∩	NOUN
ejpam-2552	358	8	s−1b	s−1b	X
ejpam-2552	358	9	⊂	⊂	X
ejpam-2552	358	10	(	(	PUNCT
ejpam-2552	358	11	b	b	X
ejpam-2552	358	12	+	+	CCONJ
ejpam-2552	358	13	[	[	X
ejpam-2552	358	14	−α	−α	NOUN
ejpam-2552	358	15	,	,	PUNCT
ejpam-2552	358	16	α])×	α])×	PROPN
ejpam-2552	359	1	[	[	X
ejpam-2552	359	2	−α	−α	NOUN
ejpam-2552	359	3	,	,	PUNCT
ejpam-2552	359	4	α	α	NOUN
ejpam-2552	359	5	]	]	X
ejpam-2552	359	6	,	,	PUNCT
ejpam-2552	359	7	and	and	CCONJ
ejpam-2552	359	8	we	we	PRON
ejpam-2552	359	9	can	can	AUX
ejpam-2552	359	10	write	write	VERB
ejpam-2552	359	11	,	,	PUNCT
ejpam-2552	359	12	from	from	ADP
ejpam-2552	359	13	the	the	DET
ejpam-2552	359	14	fact	fact	NOUN
ejpam-2552	359	15	that	that	SCONJ
ejpam-2552	359	16	e([−α	e([−α	PROPN
ejpam-2552	359	17	,	,	PUNCT
ejpam-2552	359	18	α	α	NOUN
ejpam-2552	359	19	]	]	X
ejpam-2552	359	20	)	)	PUNCT
ejpam-2552	359	21	=	=	SYM
ejpam-2552	359	22	ih	ih	INTJ
ejpam-2552	359	23	:	:	PUNCT
ejpam-2552	359	24	(	(	PUNCT
ejpam-2552	359	25	e	e	NOUN
ejpam-2552	359	26	′	′	NOUN
ejpam-2552	359	27	∗	∗	NOUN
ejpam-2552	359	28	e)(b	e)(b	PROPN
ejpam-2552	359	29	)	)	PUNCT
ejpam-2552	359	30	=	=	PUNCT
ejpam-2552	359	31	(	(	PUNCT
ejpam-2552	359	32	e	e	NOUN
ejpam-2552	359	33	′	′	NOUN
ejpam-2552	359	34	⊗	⊗	NUM
ejpam-2552	359	35	e)(s−1b	e)(s−1b	PROPN
ejpam-2552	359	36	)	)	PUNCT
ejpam-2552	359	37	=	=	PRON
ejpam-2552	360	1	(	(	PUNCT
ejpam-2552	360	2	e	e	NOUN
ejpam-2552	360	3	′	′	NUM
ejpam-2552	360	4	⊗	⊗	PROPN
ejpam-2552	360	5	e)(r×	e)(r×	PROPN
ejpam-2552	361	1	[	[	X
ejpam-2552	361	2	−α	−α	NOUN
ejpam-2552	361	3	,	,	PUNCT
ejpam-2552	361	4	α])(e	α])(e	NUM
ejpam-2552	361	5	′	′	NUM
ejpam-2552	361	6	⊗	⊗	NUM
ejpam-2552	361	7	e)(s−1b	e)(s−1b	PROPN
ejpam-2552	361	8	)	)	PUNCT
ejpam-2552	361	9	=	=	PRON
ejpam-2552	362	1	(	(	PUNCT
ejpam-2552	362	2	e	e	NOUN
ejpam-2552	362	3	′	′	NOUN
ejpam-2552	362	4	⊗	⊗	PROPN
ejpam-2552	362	5	e)((r×	e)((r×	PROPN
ejpam-2552	363	1	[	[	X
ejpam-2552	363	2	−α	−α	NOUN
ejpam-2552	363	3	,	,	PUNCT
ejpam-2552	363	4	α	α	NOUN
ejpam-2552	363	5	]	]	X
ejpam-2552	363	6	)	)	PUNCT
ejpam-2552	363	7	∩	∩	ADJ
ejpam-2552	363	8	s−1b	s−1b	X
ejpam-2552	363	9	)	)	PUNCT
ejpam-2552	363	10	�	�	PROPN
ejpam-2552	363	11	(	(	PUNCT
ejpam-2552	363	12	e	e	NOUN
ejpam-2552	363	13	′	′	NOUN
ejpam-2552	363	14	⊗	⊗	PROPN
ejpam-2552	363	15	e)((b	e)((b	X
ejpam-2552	364	1	+	+	CCONJ
ejpam-2552	364	2	[	[	X
ejpam-2552	364	3	−α	−α	NOUN
ejpam-2552	364	4	,	,	PUNCT
ejpam-2552	364	5	α])×	α])×	PROPN
ejpam-2552	365	1	[	[	X
ejpam-2552	365	2	−α	−α	NOUN
ejpam-2552	365	3	,	,	PUNCT
ejpam-2552	365	4	α	α	NOUN
ejpam-2552	365	5	]	]	X
ejpam-2552	365	6	)	)	PUNCT
ejpam-2552	365	7	=	=	SYM
ejpam-2552	365	8	e	e	NOUN
ejpam-2552	365	9	′(b	′(b	VERB
ejpam-2552	366	1	+	+	CCONJ
ejpam-2552	367	1	[	[	X
ejpam-2552	367	2	−α	−α	NOUN
ejpam-2552	367	3	,	,	PUNCT
ejpam-2552	367	4	α	α	NOUN
ejpam-2552	367	5	]	]	X
ejpam-2552	367	6	)	)	PUNCT
ejpam-2552	367	7	.	.	PUNCT
ejpam-2552	368	1	moreover	moreover	ADV
ejpam-2552	368	2	,	,	PUNCT
ejpam-2552	368	3	as	as	ADP
ejpam-2552	368	4	b	b	X
ejpam-2552	368	5	×	×	NOUN
ejpam-2552	369	1	[	[	X
ejpam-2552	369	2	−α	−α	NOUN
ejpam-2552	369	3	,	,	PUNCT
ejpam-2552	369	4	α	α	NOUN
ejpam-2552	369	5	]	]	X
ejpam-2552	369	6	⊂	⊂	PROPN
ejpam-2552	369	7	s−1(b	s−1(b	PROPN
ejpam-2552	370	1	+	+	CCONJ
ejpam-2552	371	1	[	[	X
ejpam-2552	371	2	−α	−α	NOUN
ejpam-2552	371	3	,	,	PUNCT
ejpam-2552	371	4	α	α	NOUN
ejpam-2552	371	5	]	]	X
ejpam-2552	371	6	)	)	PUNCT
ejpam-2552	371	7	,	,	PUNCT
ejpam-2552	371	8	we	we	PRON
ejpam-2552	371	9	also	also	ADV
ejpam-2552	371	10	have	have	VERB
ejpam-2552	371	11	e	e	NOUN
ejpam-2552	371	12	′(b	′(b	NOUN
ejpam-2552	371	13	)	)	PUNCT
ejpam-2552	371	14	=	=	PUNCT
ejpam-2552	372	1	e	e	X
ejpam-2552	372	2	′	′	PROPN
ejpam-2552	372	3	⊗	⊗	PROPN
ejpam-2552	372	4	e(b	e(b	PROPN
ejpam-2552	372	5	×	×	PROPN
ejpam-2552	373	1	[	[	X
ejpam-2552	373	2	−α	−α	NOUN
ejpam-2552	373	3	,	,	PUNCT
ejpam-2552	373	4	α	α	NOUN
ejpam-2552	373	5	]	]	X
ejpam-2552	373	6	)	)	PUNCT
ejpam-2552	373	7	�	�	PROPN
ejpam-2552	373	8	e	e	X
ejpam-2552	373	9	′	′	NOUN
ejpam-2552	373	10	⊗	⊗	PROPN
ejpam-2552	374	1	e(s−1(b	e(s−1(b	PROPN
ejpam-2552	374	2	+	+	PROPN
ejpam-2552	375	1	[	[	X
ejpam-2552	375	2	−α	−α	NOUN
ejpam-2552	375	3	,	,	PUNCT
ejpam-2552	375	4	α	α	NOUN
ejpam-2552	375	5	]	]	NOUN
ejpam-2552	375	6	)	)	PUNCT
ejpam-2552	375	7	)	)	PUNCT
ejpam-2552	375	8	=	=	PUNCT
ejpam-2552	375	9	e	e	NOUN
ejpam-2552	375	10	′	′	NOUN
ejpam-2552	375	11	∗	∗	NOUN
ejpam-2552	375	12	e(b	e(b	X
ejpam-2552	375	13	+	+	CCONJ
ejpam-2552	376	1	[	[	X
ejpam-2552	376	2	−α	−α	NOUN
ejpam-2552	376	3	,	,	PUNCT
ejpam-2552	376	4	α	α	NOUN
ejpam-2552	376	5	]	]	X
ejpam-2552	376	6	)	)	PUNCT
ejpam-2552	376	7	,	,	PUNCT
ejpam-2552	376	8	what	what	PRON
ejpam-2552	376	9	allows	allow	VERB
ejpam-2552	376	10	to	to	PART
ejpam-2552	376	11	conclude	conclude	VERB
ejpam-2552	376	12	.	.	PUNCT
ejpam-2552	377	1	�	�	PROPN
ejpam-2552	377	2	let	let	VERB
ejpam-2552	377	3	us	we	PRON
ejpam-2552	377	4	now	now	ADV
ejpam-2552	377	5	examine	examine	VERB
ejpam-2552	377	6	the	the	DET
ejpam-2552	377	7	case	case	NOUN
ejpam-2552	377	8	where	where	SCONJ
ejpam-2552	377	9	a	a	DET
ejpam-2552	377	10	s.m	s.m	PROPN
ejpam-2552	377	11	.	.	PROPN
ejpam-2552	377	12	is	be	AUX
ejpam-2552	377	13	concentrated	concentrate	VERB
ejpam-2552	377	14	on	on	ADP
ejpam-2552	377	15	a	a	DET
ejpam-2552	377	16	countable	countable	ADJ
ejpam-2552	377	17	family	family	NOUN
ejpam-2552	377	18	.	.	PUNCT
ejpam-2552	378	1	lemma	lemma	PROPN
ejpam-2552	378	2	3.2	3.2	NUM
ejpam-2552	378	3	.	.	PUNCT
ejpam-2552	379	1	let	let	VERB
ejpam-2552	379	2	λ	λ	INTJ
ejpam-2552	379	3	=	=	PRON
ejpam-2552	379	4	{	{	PUNCT
ejpam-2552	379	5	λn;n	λn;n	X
ejpam-2552	379	6	∈	∈	PROPN
ejpam-2552	379	7	n	n	CCONJ
ejpam-2552	379	8	}	}	PUNCT
ejpam-2552	379	9	be	be	AUX
ejpam-2552	379	10	a	a	DET
ejpam-2552	379	11	countable	countable	ADJ
ejpam-2552	379	12	family	family	NOUN
ejpam-2552	379	13	of	of	ADP
ejpam-2552	379	14	reals	real	NOUN
ejpam-2552	379	15	,	,	PUNCT
ejpam-2552	379	16	and	and	CCONJ
ejpam-2552	379	17	e	e	NOUN
ejpam-2552	379	18	be	be	AUX
ejpam-2552	379	19	a	a	DET
ejpam-2552	379	20	s.m	s.m	PROPN
ejpam-2552	379	21	.	.	PUNCT
ejpam-2552	380	1	such	such	ADJ
ejpam-2552	380	2	that	that	DET
ejpam-2552	380	3	e(λ	e(λ	NOUN
ejpam-2552	380	4	)	)	PUNCT
ejpam-2552	381	1	=	=	NOUN
ejpam-2552	381	2	ih	ih	NOUN
ejpam-2552	381	3	.	.	PUNCT
ejpam-2552	382	1	if	if	SCONJ
ejpam-2552	382	2	e1	e1	PROPN
ejpam-2552	382	3	and	and	CCONJ
ejpam-2552	382	4	e2	e2	PROPN
ejpam-2552	382	5	are	be	AUX
ejpam-2552	382	6	two	two	NUM
ejpam-2552	382	7	α−equivalent	α−equivalent	NUM
ejpam-2552	382	8	s.m	s.m	PROPN
ejpam-2552	382	9	.	.	PROPN
ejpam-2552	382	10	’s	’	VERB
ejpam-2552	382	11	which	which	PRON
ejpam-2552	382	12	commute	commute	VERB
ejpam-2552	382	13	with	with	ADP
ejpam-2552	382	14	e	e	NOUN
ejpam-2552	382	15	,	,	PUNCT
ejpam-2552	382	16	then	then	ADV
ejpam-2552	382	17	e	e	NOUN
ejpam-2552	382	18	∗	∗	NOUN
ejpam-2552	382	19	e1	e1	VERB
ejpam-2552	382	20	α∼	α∼	NUM
ejpam-2552	382	21	e	e	PROPN
ejpam-2552	382	22	∗	∗	NOUN
ejpam-2552	382	23	e2	e2	PROPN
ejpam-2552	382	24	.	.	PUNCT
ejpam-2552	383	1	proof	proof	NOUN
ejpam-2552	383	2	.	.	PUNCT
ejpam-2552	384	1	let	let	VERB
ejpam-2552	384	2	b	b	X
ejpam-2552	384	3	be	be	AUX
ejpam-2552	384	4	a	a	DET
ejpam-2552	384	5	compact	compact	NOUN
ejpam-2552	384	6	of	of	ADP
ejpam-2552	384	7	r.	r.	PROPN
ejpam-2552	384	8	from	from	ADP
ejpam-2552	384	9	section	section	NOUN
ejpam-2552	384	10	2.3	2.3	NUM
ejpam-2552	384	11	,	,	PUNCT
ejpam-2552	384	12	we	we	PRON
ejpam-2552	384	13	can	can	AUX
ejpam-2552	384	14	affirm	affirm	VERB
ejpam-2552	384	15	that	that	SCONJ
ejpam-2552	384	16	i	i	PRON
ejpam-2552	384	17	)	)	PUNCT
ejpam-2552	384	18	{	{	PUNCT
ejpam-2552	384	19	e({λn})e1(b	e({λn})e1(b	ADV
ejpam-2552	384	20	−	−	NOUN
ejpam-2552	384	21	λn);n	λn);n	PROPN
ejpam-2552	384	22	∈	∈	PROPN
ejpam-2552	384	23	n	n	CCONJ
ejpam-2552	384	24	}	}	PUNCT
ejpam-2552	384	25	is	be	AUX
ejpam-2552	384	26	an	an	DET
ejpam-2552	384	27	orthogonal	orthogonal	ADJ
ejpam-2552	384	28	family	family	NOUN
ejpam-2552	384	29	of	of	ADP
ejpam-2552	384	30	projectors	projector	NOUN
ejpam-2552	384	31	which	which	DET
ejpam-2552	384	32	sum	sum	NOUN
ejpam-2552	384	33	is	be	AUX
ejpam-2552	384	34	e	e	NOUN
ejpam-2552	384	35	∗	∗	NOUN
ejpam-2552	384	36	e1b	e1b	NOUN
ejpam-2552	384	37	;	;	PUNCT
ejpam-2552	384	38	ii	ii	X
ejpam-2552	384	39	)	)	PUNCT
ejpam-2552	384	40	{	{	PUNCT
ejpam-2552	384	41	e({λn})e2(b	e({λn})e2(b	PROPN
ejpam-2552	384	42	+	+	PROPN
ejpam-2552	385	1	[	[	X
ejpam-2552	385	2	−α	−α	NOUN
ejpam-2552	385	3	,	,	PUNCT
ejpam-2552	385	4	α	α	NOUN
ejpam-2552	385	5	]	]	X
ejpam-2552	385	6	−	−	ADP
ejpam-2552	385	7	λn);n	λn);n	PROPN
ejpam-2552	385	8	∈	∈	PROPN
ejpam-2552	385	9	n	n	CCONJ
ejpam-2552	385	10	}	}	PUNCT
ejpam-2552	385	11	is	be	AUX
ejpam-2552	385	12	an	an	DET
ejpam-2552	385	13	orthogonal	orthogonal	ADJ
ejpam-2552	385	14	family	family	NOUN
ejpam-2552	385	15	of	of	ADP
ejpam-2552	385	16	projectors	projector	NOUN
ejpam-2552	385	17	which	which	DET
ejpam-2552	385	18	sum	sum	NOUN
ejpam-2552	385	19	is	be	AUX
ejpam-2552	385	20	e	e	NOUN
ejpam-2552	385	21	∗	∗	NOUN
ejpam-2552	385	22	e2(b	e2(b	NOUN
ejpam-2552	385	23	+	+	SYM
ejpam-2552	386	1	[	[	X
ejpam-2552	386	2	−α	−α	NOUN
ejpam-2552	386	3	,	,	PUNCT
ejpam-2552	386	4	α	α	NOUN
ejpam-2552	386	5	]	]	X
ejpam-2552	386	6	)	)	PUNCT
ejpam-2552	386	7	.	.	PUNCT
ejpam-2552	387	1	as	as	ADP
ejpam-2552	387	2	the	the	DET
ejpam-2552	387	3	s.m	s.m	PROPN
ejpam-2552	387	4	.	.	PROPN
ejpam-2552	387	5	’s	’s	PART
ejpam-2552	387	6	e	e	PROPN
ejpam-2552	387	7	and	and	CCONJ
ejpam-2552	387	8	e1	e1	PROPN
ejpam-2552	387	9	commute	commute	NOUN
ejpam-2552	387	10	and	and	CCONJ
ejpam-2552	387	11	from	from	ADP
ejpam-2552	387	12	e1(b	e1(b	PRON
ejpam-2552	387	13	−	−	PROPN
ejpam-2552	387	14	λn	λn	NOUN
ejpam-2552	387	15	)	)	PUNCT
ejpam-2552	387	16	◦	◦	NOUN
ejpam-2552	387	17	e2(b	e2(b	NOUN
ejpam-2552	388	1	+	+	SYM
ejpam-2552	388	2	[	[	X
ejpam-2552	388	3	−α	−α	NOUN
ejpam-2552	388	4	,	,	PUNCT
ejpam-2552	388	5	α]−	α]−	PRON
ejpam-2552	388	6	λn	λn	NOUN
ejpam-2552	388	7	)	)	PUNCT
ejpam-2552	388	8	=	=	PUNCT
ejpam-2552	389	1	e1(b	e1(b	PRON
ejpam-2552	389	2	−	−	PROPN
ejpam-2552	389	3	λn	λn	NOUN
ejpam-2552	389	4	)	)	PUNCT
ejpam-2552	389	5	,	,	PUNCT
ejpam-2552	389	6	(	(	PUNCT
ejpam-2552	389	7	because	because	SCONJ
ejpam-2552	389	8	e1	e1	PROPN
ejpam-2552	389	9	α∼	α∼	PROPN
ejpam-2552	389	10	e2	e2	NOUN
ejpam-2552	389	11	)	)	PUNCT
ejpam-2552	389	12	we	we	PRON
ejpam-2552	389	13	can	can	AUX
ejpam-2552	389	14	write	write	VERB
ejpam-2552	389	15	e({λn})e1(b	e({λn})e1(b	ADV
ejpam-2552	389	16	−	−	PROPN
ejpam-2552	390	1	λn)e({λn})e2(b	λn)e({λn})e2(b	PROPN
ejpam-2552	391	1	+	+	PUNCT
ejpam-2552	391	2	[	[	X
ejpam-2552	391	3	−α	−α	NOUN
ejpam-2552	391	4	,	,	PUNCT
ejpam-2552	391	5	α]−	α]−	PRON
ejpam-2552	391	6	λn	λn	NOUN
ejpam-2552	391	7	)	)	PUNCT
ejpam-2552	391	8	=	=	PUNCT
ejpam-2552	391	9	e({λn})e1(b	e({λn})e1(b	PROPN
ejpam-2552	392	1	−	−	PROPN
ejpam-2552	392	2	λn)e2(b	λn)e2(b	PROPN
ejpam-2552	392	3	+	+	PROPN
ejpam-2552	393	1	[	[	X
ejpam-2552	393	2	−α	−α	NOUN
ejpam-2552	393	3	,	,	PUNCT
ejpam-2552	393	4	α]−	α]−	PRON
ejpam-2552	393	5	λn	λn	NOUN
ejpam-2552	393	6	)	)	PUNCT
ejpam-2552	393	7	=	=	PUNCT
ejpam-2552	393	8	e({λn})e1(b	e({λn})e1(b	PROPN
ejpam-2552	393	9	−	−	PROPN
ejpam-2552	393	10	λn	λn	NOUN
ejpam-2552	393	11	)	)	PUNCT
ejpam-2552	393	12	,	,	PUNCT
ejpam-2552	393	13	and	and	CCONJ
ejpam-2552	393	14	so	so	ADV
ejpam-2552	393	15	e({λn})e1(b	e({λn})e1(b	ADJ
ejpam-2552	393	16	−	−	PROPN
ejpam-2552	393	17	λn	λn	NOUN
ejpam-2552	393	18	)	)	PUNCT
ejpam-2552	393	19	�	�	PROPN
ejpam-2552	393	20	e({λn})e2(b	e({λn})e2(b	PROPN
ejpam-2552	393	21	+	+	PROPN
ejpam-2552	394	1	[	[	X
ejpam-2552	394	2	−α	−α	NOUN
ejpam-2552	394	3	,	,	PUNCT
ejpam-2552	394	4	α]−	α]−	PRON
ejpam-2552	394	5	λn	λn	NOUN
ejpam-2552	394	6	)	)	PUNCT
ejpam-2552	394	7	,	,	PUNCT
ejpam-2552	394	8	this	this	PRON
ejpam-2552	394	9	for	for	ADP
ejpam-2552	394	10	any	any	DET
ejpam-2552	394	11	n	n	PRON
ejpam-2552	394	12	∈	∈	PROPN
ejpam-2552	394	13	n.	n.	NOUN
ejpam-2552	394	14	from	from	ADP
ejpam-2552	394	15	the	the	DET
ejpam-2552	394	16	recalls	recall	NOUN
ejpam-2552	394	17	of	of	ADP
ejpam-2552	394	18	section	section	NOUN
ejpam-2552	394	19	2.1	2.1	NUM
ejpam-2552	394	20	,	,	PUNCT
ejpam-2552	394	21	we	we	PRON
ejpam-2552	394	22	can	can	AUX
ejpam-2552	394	23	affirm	affirm	VERB
ejpam-2552	394	24	that	that	SCONJ
ejpam-2552	394	25	e	e	PROPN
ejpam-2552	394	26	∗	∗	NOUN
ejpam-2552	394	27	e1(b	e1(b	NOUN
ejpam-2552	394	28	)	)	PUNCT
ejpam-2552	394	29	�	�	PROPN
ejpam-2552	394	30	e	e	PROPN
ejpam-2552	394	31	∗	∗	VERB
ejpam-2552	394	32	e2(b	e2(b	NOUN
ejpam-2552	394	33	+	+	SYM
ejpam-2552	395	1	[	[	X
ejpam-2552	395	2	−α	−α	NOUN
ejpam-2552	395	3	,	,	PUNCT
ejpam-2552	395	4	α	α	NOUN
ejpam-2552	395	5	]	]	X
ejpam-2552	395	6	)	)	PUNCT
ejpam-2552	395	7	.	.	PUNCT
ejpam-2552	396	1	conversely	conversely	ADV
ejpam-2552	396	2	,	,	PUNCT
ejpam-2552	396	3	we	we	PRON
ejpam-2552	396	4	could	could	AUX
ejpam-2552	396	5	prove	prove	VERB
ejpam-2552	396	6	that	that	SCONJ
ejpam-2552	396	7	e	e	PROPN
ejpam-2552	396	8	∗	∗	NOUN
ejpam-2552	396	9	e2(b	e2(b	NOUN
ejpam-2552	396	10	)	)	PUNCT
ejpam-2552	396	11	�	�	PROPN
ejpam-2552	396	12	e	e	PROPN
ejpam-2552	396	13	∗	∗	VERB
ejpam-2552	396	14	e1(b	e1(b	PROPN
ejpam-2552	396	15	+	+	CCONJ
ejpam-2552	396	16	[	[	X
ejpam-2552	396	17	−α	−α	NOUN
ejpam-2552	396	18	,	,	PUNCT
ejpam-2552	396	19	α	α	NOUN
ejpam-2552	396	20	]	]	X
ejpam-2552	396	21	)	)	PUNCT
ejpam-2552	396	22	,	,	PUNCT
ejpam-2552	396	23	what	what	PRON
ejpam-2552	396	24	allows	allow	VERB
ejpam-2552	396	25	to	to	PART
ejpam-2552	396	26	conclude	conclude	VERB
ejpam-2552	396	27	.	.	PUNCT
ejpam-2552	397	1	�	�	PROPN
ejpam-2552	397	2	a	a	DET
ejpam-2552	397	3	discretization	discretization	NOUN
ejpam-2552	397	4	of	of	ADP
ejpam-2552	397	5	r	r	NOUN
ejpam-2552	397	6	allows	allow	VERB
ejpam-2552	397	7	to	to	PART
ejpam-2552	397	8	approximate	approximate	VERB
ejpam-2552	397	9	any	any	DET
ejpam-2552	397	10	s.m	s.m	PROPN
ejpam-2552	397	11	.	.	PROPN
ejpam-2552	397	12	by	by	ADP
ejpam-2552	397	13	a	a	DET
ejpam-2552	397	14	s.m	s.m	PROPN
ejpam-2552	397	15	.	.	PROPN
ejpam-2552	397	16	concentrated	concentrate	VERB
ejpam-2552	397	17	on	on	ADP
ejpam-2552	397	18	a	a	DET
ejpam-2552	397	19	countable	countable	ADJ
ejpam-2552	397	20	family	family	NOUN
ejpam-2552	397	21	.	.	PUNCT
ejpam-2552	398	1	for	for	ADP
ejpam-2552	398	2	this	this	PRON
ejpam-2552	398	3	,	,	PUNCT
ejpam-2552	398	4	let	let	VERB
ejpam-2552	398	5	us	we	PRON
ejpam-2552	398	6	denote	denote	VERB
ejpam-2552	398	7	by	by	ADP
ejpam-2552	398	8	ln	ln	DET
ejpam-2552	398	9	the	the	DET
ejpam-2552	398	10	measurable	measurable	ADJ
ejpam-2552	398	11	application	application	NOUN
ejpam-2552	399	1	x	x	PUNCT
ejpam-2552	399	2	∈	∈	NOUN
ejpam-2552	399	3	r	r	NOUN
ejpam-2552	399	4	7→	7→	NUM
ejpam-2552	399	5	[	[	X
ejpam-2552	399	6	nx	nx	X
ejpam-2552	399	7	]	]	PUNCT
ejpam-2552	399	8	n	n	PRON
ejpam-2552	399	9	∈	∈	PROPN
ejpam-2552	399	10	r	r	NOUN
ejpam-2552	399	11	,	,	PUNCT
ejpam-2552	399	12	where	where	SCONJ
ejpam-2552	399	13	n	n	PRON
ejpam-2552	399	14	is	be	AUX
ejpam-2552	399	15	an	an	DET
ejpam-2552	399	16	element	element	NOUN
ejpam-2552	399	17	of	of	ADP
ejpam-2552	399	18	n∗	n∗	PROPN
ejpam-2552	399	19	and	and	CCONJ
ejpam-2552	399	20	[	[	X
ejpam-2552	399	21	nx	nx	X
ejpam-2552	399	22	]	]	X
ejpam-2552	399	23	the	the	DET
ejpam-2552	399	24	integer	integer	ADJ
ejpam-2552	399	25	part	part	NOUN
ejpam-2552	399	26	of	of	ADP
ejpam-2552	399	27	nx	nx	PROPN
ejpam-2552	399	28	.	.	PUNCT
ejpam-2552	400	1	then	then	ADV
ejpam-2552	400	2	the	the	DET
ejpam-2552	400	3	proposition	proposition	NOUN
ejpam-2552	400	4	follows	follow	VERB
ejpam-2552	400	5	.	.	PUNCT
ejpam-2552	401	1	proposition	proposition	NOUN
ejpam-2552	401	2	3.4	3.4	NUM
ejpam-2552	401	3	.	.	PUNCT
ejpam-2552	402	1	for	for	ADP
ejpam-2552	402	2	any	any	DET
ejpam-2552	402	3	n	n	NOUN
ejpam-2552	402	4	of	of	ADP
ejpam-2552	402	5	n∗	n∗	PROPN
ejpam-2552	402	6	and	and	CCONJ
ejpam-2552	402	7	for	for	ADP
ejpam-2552	402	8	any	any	DET
ejpam-2552	402	9	s.m	s.m	PROPN
ejpam-2552	402	10	.	.	PUNCT
ejpam-2552	402	11	e	e	X
ejpam-2552	402	12	,	,	PUNCT
ejpam-2552	402	13	we	we	PRON
ejpam-2552	402	14	can	can	AUX
ejpam-2552	402	15	affirm	affirm	VERB
ejpam-2552	402	16	that	that	SCONJ
ejpam-2552	402	17	a	a	X
ejpam-2552	402	18	)	)	PUNCT
ejpam-2552	402	19	lne	lne	NOUN
ejpam-2552	402	20	∗	∗	NOUN
ejpam-2552	402	21	we	we	PRON
ejpam-2552	402	22	1	1	X
ejpam-2552	402	23	n∼	n∼	PROPN
ejpam-2552	402	24	er	er	INTJ
ejpam-2552	402	25	;	;	PUNCT
ejpam-2552	402	26	b	b	X
ejpam-2552	402	27	)	)	PUNCT
ejpam-2552	402	28	lne	lne	VERB
ejpam-2552	402	29	1	1	NUM
ejpam-2552	402	30	n∼	n∼	PROPN
ejpam-2552	402	31	e.	e.	PROPN
ejpam-2552	402	32	proof	proof	PROPN
ejpam-2552	402	33	.	.	PUNCT
ejpam-2552	403	1	it	it	PRON
ejpam-2552	403	2	is	be	AUX
ejpam-2552	403	3	easy	easy	ADJ
ejpam-2552	403	4	to	to	PART
ejpam-2552	403	5	verify	verify	VERB
ejpam-2552	403	6	that	that	SCONJ
ejpam-2552	403	7	,	,	PUNCT
ejpam-2552	403	8	for	for	ADP
ejpam-2552	403	9	any	any	DET
ejpam-2552	403	10	x	x	PUNCT
ejpam-2552	403	11	of	of	ADP
ejpam-2552	403	12	r	r	NOUN
ejpam-2552	403	13	,	,	PUNCT
ejpam-2552	403	14	−	−	PROPN
ejpam-2552	403	15	1	1	NUM
ejpam-2552	403	16	n	n	NOUN
ejpam-2552	403	17	<	<	X
ejpam-2552	403	18	(	(	PUNCT
ejpam-2552	403	19	ln	ln	PROPN
ejpam-2552	403	20	+	+	X
ejpam-2552	403	21	w)(x	w)(x	PROPN
ejpam-2552	403	22	)	)	PUNCT
ejpam-2552	403	23	6	6	NUM
ejpam-2552	403	24	0	0	NUM
ejpam-2552	403	25	,	,	PUNCT
ejpam-2552	403	26	a.	a.	NOUN
ejpam-2552	403	27	boudou	boudou	NOUN
ejpam-2552	403	28	,	,	PUNCT
ejpam-2552	403	29	s.	s.	PROPN
ejpam-2552	403	30	viguier	viguier	PROPN
ejpam-2552	403	31	-	-	PUNCT
ejpam-2552	403	32	pla	pla	PROPN
ejpam-2552	403	33	/	/	PUNCT
ejpam-2552	403	34	eur	eur	PROPN
ejpam-2552	403	35	.	.	PUNCT
ejpam-2552	404	1	j.	j.	PROPN
ejpam-2552	404	2	pure	pure	PROPN
ejpam-2552	404	3	appl	appl	PROPN
ejpam-2552	404	4	.	.	PROPN
ejpam-2552	404	5	math	math	PROPN
ejpam-2552	404	6	,	,	PUNCT
ejpam-2552	404	7	11	11	NUM
ejpam-2552	404	8	(	(	PUNCT
ejpam-2552	404	9	4	4	NUM
ejpam-2552	404	10	)	)	PUNCT
ejpam-2552	404	11	(	(	PUNCT
ejpam-2552	404	12	2018	2018	NUM
ejpam-2552	404	13	)	)	PUNCT
ejpam-2552	404	14	,	,	PUNCT
ejpam-2552	404	15	893	893	NUM
ejpam-2552	404	16	-	-	SYM
ejpam-2552	404	17	910	910	NUM
ejpam-2552	404	18	904	904	NUM
ejpam-2552	404	19	we	we	PRON
ejpam-2552	404	20	deduce	deduce	VERB
ejpam-2552	404	21	from	from	ADP
ejpam-2552	404	22	this	this	PRON
ejpam-2552	405	1	that	that	SCONJ
ejpam-2552	405	2	(	(	PUNCT
ejpam-2552	405	3	ln	ln	NOUN
ejpam-2552	405	4	+	+	NUM
ejpam-2552	405	5	w)−1[−	w)−1[−	NOUN
ejpam-2552	405	6	1	1	NUM
ejpam-2552	405	7	n	n	NOUN
ejpam-2552	405	8	,	,	PUNCT
ejpam-2552	405	9	1	1	NUM
ejpam-2552	405	10	n	n	NOUN
ejpam-2552	405	11	]	]	PUNCT
ejpam-2552	405	12	=	=	PUNCT
ejpam-2552	405	13	r.	r.	PROPN
ejpam-2552	405	14	so	so	ADV
ejpam-2552	405	15	it	it	PRON
ejpam-2552	405	16	comes	come	VERB
ejpam-2552	405	17	(	(	PUNCT
ejpam-2552	405	18	ln	ln	ADJ
ejpam-2552	406	1	+	+	CCONJ
ejpam-2552	406	2	w)e([−	w)e([−	PRON
ejpam-2552	406	3	1	1	NUM
ejpam-2552	406	4	n	n	NOUN
ejpam-2552	406	5	,	,	PUNCT
ejpam-2552	406	6	1	1	NUM
ejpam-2552	406	7	n	n	NOUN
ejpam-2552	406	8	]	]	PUNCT
ejpam-2552	406	9	)	)	PUNCT
ejpam-2552	407	1	=	=	SYM
ejpam-2552	407	2	e((ln	e((ln	X
ejpam-2552	408	1	+	+	NUM
ejpam-2552	408	2	w)−1[−	w)−1[−	NOUN
ejpam-2552	408	3	1	1	NUM
ejpam-2552	408	4	n	n	NOUN
ejpam-2552	408	5	,	,	PUNCT
ejpam-2552	408	6	1	1	NUM
ejpam-2552	408	7	n	n	NOUN
ejpam-2552	408	8	]	]	PUNCT
ejpam-2552	408	9	)	)	PUNCT
ejpam-2552	408	10	=	=	SYM
ejpam-2552	408	11	e(r	e(r	X
ejpam-2552	408	12	)	)	PUNCT
ejpam-2552	409	1	=	=	SYM
ejpam-2552	409	2	ih	ih	NOUN
ejpam-2552	409	3	.	.	PUNCT
ejpam-2552	410	1	then	then	ADV
ejpam-2552	410	2	,	,	PUNCT
ejpam-2552	410	3	from	from	ADP
ejpam-2552	410	4	proposition	proposition	NOUN
ejpam-2552	410	5	3.3	3.3	NUM
ejpam-2552	410	6	,	,	PUNCT
ejpam-2552	410	7	(	(	PUNCT
ejpam-2552	410	8	ln	ln	ADJ
ejpam-2552	410	9	+	+	CCONJ
ejpam-2552	410	10	w)e	w)e	ADJ
ejpam-2552	410	11	1	1	X
ejpam-2552	410	12	n∼	n∼	PROPN
ejpam-2552	410	13	er	er	INTJ
ejpam-2552	410	14	,	,	PUNCT
ejpam-2552	410	15	or	or	CCONJ
ejpam-2552	410	16	in	in	ADP
ejpam-2552	410	17	other	other	ADJ
ejpam-2552	410	18	words	word	NOUN
ejpam-2552	410	19	(	(	PUNCT
ejpam-2552	410	20	lne	lne	PROPN
ejpam-2552	410	21	)	)	PUNCT
ejpam-2552	410	22	∗	∗	NOUN
ejpam-2552	410	23	(	(	PUNCT
ejpam-2552	410	24	we	we	PRON
ejpam-2552	410	25	)	)	PUNCT
ejpam-2552	410	26	1	1	NUM
ejpam-2552	410	27	n∼	n∼	PROPN
ejpam-2552	410	28	er	er	INTJ
ejpam-2552	410	29	,	,	PUNCT
ejpam-2552	410	30	and	and	CCONJ
ejpam-2552	410	31	point	point	VERB
ejpam-2552	410	32	a	a	PRON
ejpam-2552	410	33	)	)	PUNCT
ejpam-2552	410	34	is	be	AUX
ejpam-2552	410	35	proved	prove	VERB
ejpam-2552	410	36	.	.	PUNCT
ejpam-2552	411	1	as	as	ADP
ejpam-2552	411	2	for	for	ADP
ejpam-2552	411	3	point	point	NOUN
ejpam-2552	411	4	b	b	NOUN
ejpam-2552	411	5	)	)	PUNCT
ejpam-2552	411	6	,	,	PUNCT
ejpam-2552	411	7	it	it	PRON
ejpam-2552	411	8	is	be	AUX
ejpam-2552	411	9	a	a	DET
ejpam-2552	411	10	consequence	consequence	NOUN
ejpam-2552	411	11	of	of	ADP
ejpam-2552	411	12	point	point	NOUN
ejpam-2552	411	13	a	a	NOUN
ejpam-2552	411	14	)	)	PUNCT
ejpam-2552	411	15	and	and	CCONJ
ejpam-2552	411	16	of	of	ADP
ejpam-2552	411	17	lemma	lemma	PROPN
ejpam-2552	411	18	3.1	3.1	NUM
ejpam-2552	411	19	.	.	PUNCT
ejpam-2552	411	20	�	�	PROPN
ejpam-2552	411	21	this	this	DET
ejpam-2552	411	22	last	last	ADJ
ejpam-2552	411	23	property	property	NOUN
ejpam-2552	411	24	lets	let	VERB
ejpam-2552	411	25	us	we	PRON
ejpam-2552	411	26	generalize	generalize	VERB
ejpam-2552	411	27	both	both	CCONJ
ejpam-2552	411	28	lemma	lemma	PROPN
ejpam-2552	411	29	3.1	3.1	NUM
ejpam-2552	411	30	and	and	CCONJ
ejpam-2552	411	31	lemma	lemma	PROPN
ejpam-2552	411	32	3.2	3.2	NUM
ejpam-2552	411	33	.	.	PUNCT
ejpam-2552	412	1	proposition	proposition	NOUN
ejpam-2552	412	2	3.5	3.5	NUM
ejpam-2552	412	3	.	.	PUNCT
ejpam-2552	413	1	if	if	SCONJ
ejpam-2552	413	2	e1	e1	PROPN
ejpam-2552	413	3	and	and	CCONJ
ejpam-2552	413	4	e2	e2	PROPN
ejpam-2552	413	5	are	be	AUX
ejpam-2552	413	6	two	two	NUM
ejpam-2552	413	7	α−equivalent	α−equivalent	NUM
ejpam-2552	413	8	s.m	s.m	PROPN
ejpam-2552	413	9	.	.	PROPN
ejpam-2552	413	10	’s	’s	PART
ejpam-2552	413	11	,	,	PUNCT
ejpam-2552	413	12	which	which	PRON
ejpam-2552	413	13	commute	commute	VERB
ejpam-2552	413	14	with	with	ADP
ejpam-2552	413	15	a	a	DET
ejpam-2552	413	16	third	third	ADJ
ejpam-2552	413	17	s.m	s.m	PROPN
ejpam-2552	413	18	.	.	PUNCT
ejpam-2552	414	1	e	e	X
ejpam-2552	414	2	,	,	PUNCT
ejpam-2552	414	3	then	then	ADV
ejpam-2552	414	4	we	we	PRON
ejpam-2552	414	5	have	have	VERB
ejpam-2552	414	6	e	e	NOUN
ejpam-2552	414	7	∗	∗	NOUN
ejpam-2552	414	8	e1	e1	PROPN
ejpam-2552	414	9	α∼	α∼	NUM
ejpam-2552	414	10	e	e	PROPN
ejpam-2552	414	11	∗	∗	NOUN
ejpam-2552	414	12	e2	e2	PROPN
ejpam-2552	414	13	.	.	PUNCT
ejpam-2552	415	1	proof	proof	NOUN
ejpam-2552	415	2	.	.	PUNCT
ejpam-2552	416	1	for	for	ADP
ejpam-2552	416	2	any	any	DET
ejpam-2552	416	3	n	n	NOUN
ejpam-2552	416	4	of	of	ADP
ejpam-2552	416	5	n∗	n∗	PROPN
ejpam-2552	416	6	,	,	PUNCT
ejpam-2552	416	7	we	we	PRON
ejpam-2552	416	8	can	can	AUX
ejpam-2552	416	9	affirm	affirm	VERB
ejpam-2552	416	10	that	that	SCONJ
ejpam-2552	416	11	lne	lne	PROPN
ejpam-2552	416	12	∗	∗	NOUN
ejpam-2552	416	13	we	we	PRON
ejpam-2552	416	14	1	1	X
ejpam-2552	416	15	n∼	n∼	PROPN
ejpam-2552	416	16	er	er	INTJ
ejpam-2552	416	17	.	.	PUNCT
ejpam-2552	417	1	as	as	ADP
ejpam-2552	417	2	the	the	DET
ejpam-2552	417	3	s.m	s.m	PROPN
ejpam-2552	417	4	.	.	PROPN
ejpam-2552	417	5	’s	’s	PROPN
ejpam-2552	417	6	lne	lne	PROPN
ejpam-2552	417	7	∗	∗	NOUN
ejpam-2552	417	8	we	we	PRON
ejpam-2552	417	9	and	and	CCONJ
ejpam-2552	417	10	e	e	PROPN
ejpam-2552	417	11	∗	∗	PROPN
ejpam-2552	417	12	e1	e1	PROPN
ejpam-2552	417	13	commute	commute	NOUN
ejpam-2552	417	14	,	,	PUNCT
ejpam-2552	417	15	lemma	lemma	PROPN
ejpam-2552	417	16	3.1	3.1	NUM
ejpam-2552	417	17	allows	allow	VERB
ejpam-2552	417	18	us	we	PRON
ejpam-2552	417	19	to	to	PART
ejpam-2552	417	20	write	write	VERB
ejpam-2552	417	21	(	(	PUNCT
ejpam-2552	417	22	lne	lne	PROPN
ejpam-2552	417	23	∗	∗	NOUN
ejpam-2552	417	24	we	we	PRON
ejpam-2552	417	25	)	)	PUNCT
ejpam-2552	417	26	∗	∗	NOUN
ejpam-2552	417	27	(	(	PUNCT
ejpam-2552	417	28	e	e	NOUN
ejpam-2552	417	29	∗	∗	NOUN
ejpam-2552	417	30	e1	e1	PROPN
ejpam-2552	417	31	)	)	PUNCT
ejpam-2552	417	32	1	1	NUM
ejpam-2552	417	33	n∼	n∼	PROPN
ejpam-2552	417	34	e	e	PROPN
ejpam-2552	417	35	∗	∗	NOUN
ejpam-2552	417	36	e1	e1	PROPN
ejpam-2552	417	37	,	,	PUNCT
ejpam-2552	417	38	or	or	CCONJ
ejpam-2552	417	39	,	,	PUNCT
ejpam-2552	417	40	taking	take	VERB
ejpam-2552	417	41	into	into	ADP
ejpam-2552	417	42	account	account	NOUN
ejpam-2552	417	43	the	the	DET
ejpam-2552	417	44	associativity	associativity	NOUN
ejpam-2552	417	45	of	of	ADP
ejpam-2552	417	46	the	the	DET
ejpam-2552	417	47	convolution	convolution	NOUN
ejpam-2552	417	48	,	,	PUNCT
ejpam-2552	417	49	lne	lne	PROPN
ejpam-2552	417	50	∗	∗	NOUN
ejpam-2552	417	51	e1	e1	PROPN
ejpam-2552	417	52	1	1	NUM
ejpam-2552	417	53	n∼	n∼	PROPN
ejpam-2552	417	54	e	e	PROPN
ejpam-2552	417	55	∗	∗	NOUN
ejpam-2552	417	56	e1	e1	PROPN
ejpam-2552	417	57	.	.	PUNCT
ejpam-2552	418	1	(	(	PUNCT
ejpam-2552	418	2	3.1	3.1	NUM
ejpam-2552	418	3	)	)	PUNCT
ejpam-2552	418	4	in	in	ADP
ejpam-2552	418	5	a	a	DET
ejpam-2552	418	6	similar	similar	ADJ
ejpam-2552	418	7	way	way	NOUN
ejpam-2552	418	8	,	,	PUNCT
ejpam-2552	418	9	we	we	PRON
ejpam-2552	418	10	can	can	AUX
ejpam-2552	418	11	prove	prove	VERB
ejpam-2552	418	12	that	that	SCONJ
ejpam-2552	418	13	lne	lne	PROPN
ejpam-2552	418	14	∗	∗	PROPN
ejpam-2552	418	15	e2	e2	PROPN
ejpam-2552	418	16	1	1	NUM
ejpam-2552	418	17	n∼	n∼	PROPN
ejpam-2552	418	18	e	e	PROPN
ejpam-2552	418	19	∗	∗	PROPN
ejpam-2552	418	20	e2	e2	PROPN
ejpam-2552	418	21	.	.	PUNCT
ejpam-2552	419	1	(	(	PUNCT
ejpam-2552	419	2	3.2	3.2	NUM
ejpam-2552	419	3	)	)	PUNCT
ejpam-2552	419	4	as	as	SCONJ
ejpam-2552	419	5	lne	lne	PROPN
ejpam-2552	419	6	is	be	AUX
ejpam-2552	419	7	a	a	DET
ejpam-2552	419	8	s.m	s.m	PROPN
ejpam-2552	419	9	.	.	PROPN
ejpam-2552	419	10	concentrated	concentrate	VERB
ejpam-2552	419	11	on	on	ADP
ejpam-2552	419	12	a	a	DET
ejpam-2552	419	13	countable	countable	ADJ
ejpam-2552	419	14	family	family	NOUN
ejpam-2552	419	15	,	,	PUNCT
ejpam-2552	419	16	and	and	CCONJ
ejpam-2552	419	17	as	as	ADP
ejpam-2552	419	18	e1	e1	PROPN
ejpam-2552	419	19	α∼	α∼	PROPN
ejpam-2552	419	20	e2	e2	PROPN
ejpam-2552	419	21	,	,	PUNCT
ejpam-2552	419	22	lemma	lemma	PROPN
ejpam-2552	419	23	3.2	3.2	NUM
ejpam-2552	419	24	lets	let	VERB
ejpam-2552	419	25	us	we	PRON
ejpam-2552	419	26	write	write	VERB
ejpam-2552	419	27	:	:	PUNCT
ejpam-2552	419	28	lne	lne	PROPN
ejpam-2552	419	29	∗	∗	PROPN
ejpam-2552	419	30	e1	e1	PROPN
ejpam-2552	419	31	α∼	α∼	PROPN
ejpam-2552	419	32	lne	lne	PROPN
ejpam-2552	419	33	∗	∗	NOUN
ejpam-2552	419	34	e2	e2	PROPN
ejpam-2552	419	35	.	.	PUNCT
ejpam-2552	420	1	(	(	PUNCT
ejpam-2552	420	2	3.3	3.3	NUM
ejpam-2552	420	3	)	)	PUNCT
ejpam-2552	420	4	from	from	ADP
ejpam-2552	420	5	relations	relation	NOUN
ejpam-2552	420	6	(	(	PUNCT
ejpam-2552	420	7	3.1	3.1	NUM
ejpam-2552	420	8	)	)	PUNCT
ejpam-2552	420	9	,	,	PUNCT
ejpam-2552	420	10	(	(	PUNCT
ejpam-2552	420	11	3.2	3.2	NUM
ejpam-2552	420	12	)	)	PUNCT
ejpam-2552	420	13	and	and	CCONJ
ejpam-2552	420	14	(	(	PUNCT
ejpam-2552	420	15	3.3	3.3	NUM
ejpam-2552	420	16	)	)	PUNCT
ejpam-2552	420	17	,	,	PUNCT
ejpam-2552	420	18	we	we	PRON
ejpam-2552	420	19	deduce	deduce	VERB
ejpam-2552	420	20	e	e	NOUN
ejpam-2552	420	21	∗	∗	NOUN
ejpam-2552	420	22	e1	e1	VERB
ejpam-2552	420	23	α+	α+	PUNCT
ejpam-2552	420	24	2	2	NUM
ejpam-2552	420	25	n∼	n∼	PROPN
ejpam-2552	420	26	e	e	PROPN
ejpam-2552	420	27	∗	∗	PROPN
ejpam-2552	420	28	e2	e2	PROPN
ejpam-2552	420	29	.	.	PUNCT
ejpam-2552	421	1	as	as	SCONJ
ejpam-2552	421	2	the	the	DET
ejpam-2552	421	3	sequence	sequence	NOUN
ejpam-2552	421	4	(	(	PUNCT
ejpam-2552	421	5	α+	α+	PROPN
ejpam-2552	421	6	2	2	NUM
ejpam-2552	421	7	n)n∈n∗	n)n∈n∗	NOUN
ejpam-2552	421	8	decreasingly	decreasingly	ADV
ejpam-2552	421	9	converges	converge	VERB
ejpam-2552	421	10	to	to	ADP
ejpam-2552	421	11	α	α	PRON
ejpam-2552	421	12	,	,	PUNCT
ejpam-2552	421	13	proposition	proposition	NOUN
ejpam-2552	421	14	3.2	3.2	NUM
ejpam-2552	421	15	allows	allow	VERB
ejpam-2552	421	16	us	we	PRON
ejpam-2552	421	17	to	to	PART
ejpam-2552	421	18	conclude	conclude	VERB
ejpam-2552	421	19	.	.	PUNCT
ejpam-2552	422	1	�	�	PROPN
ejpam-2552	422	2	4	4	NUM
ejpam-2552	422	3	.	.	X
ejpam-2552	422	4	proximity	proximity	NOUN
ejpam-2552	422	5	between	between	ADP
ejpam-2552	422	6	operators	operator	NOUN
ejpam-2552	422	7	and	and	CCONJ
ejpam-2552	422	8	α−equivalence	α−equivalence	NOUN
ejpam-2552	422	9	if	if	SCONJ
ejpam-2552	422	10	e	e	NOUN
ejpam-2552	422	11	is	be	AUX
ejpam-2552	422	12	the	the	DET
ejpam-2552	422	13	s.m	s.m	PROPN
ejpam-2552	422	14	.	.	PROPN
ejpam-2552	422	15	associated	associate	VERB
ejpam-2552	422	16	with	with	ADP
ejpam-2552	422	17	a	a	DET
ejpam-2552	422	18	bounded	bound	VERB
ejpam-2552	422	19	selfadjoint	selfadjoint	NOUN
ejpam-2552	422	20	operatora	operatora	PROPN
ejpam-2552	422	21	,	,	PUNCT
ejpam-2552	422	22	then	then	ADV
ejpam-2552	422	23	e([−‖a‖	e([−‖a‖	NOUN
ejpam-2552	422	24	,	,	PUNCT
ejpam-2552	422	25	‖a‖	‖a‖	PROPN
ejpam-2552	422	26	]	]	PUNCT
ejpam-2552	422	27	)	)	PUNCT
ejpam-2552	422	28	=	=	SYM
ejpam-2552	422	29	ih	ih	NOUN
ejpam-2552	422	30	,	,	PUNCT
ejpam-2552	422	31	and	and	CCONJ
ejpam-2552	422	32	proposition	proposition	NOUN
ejpam-2552	422	33	3.3	3.3	NUM
ejpam-2552	422	34	induces	induce	VERB
ejpam-2552	422	35	the	the	DET
ejpam-2552	422	36	following	follow	VERB
ejpam-2552	422	37	result	result	NOUN
ejpam-2552	422	38	.	.	PUNCT
ejpam-2552	423	1	proposition	proposition	NOUN
ejpam-2552	423	2	4.1	4.1	NUM
ejpam-2552	423	3	.	.	PUNCT
ejpam-2552	424	1	if	if	SCONJ
ejpam-2552	424	2	e	e	PROPN
ejpam-2552	424	3	is	be	AUX
ejpam-2552	424	4	the	the	DET
ejpam-2552	424	5	s.m	s.m	PROPN
ejpam-2552	424	6	.	.	PROPN
ejpam-2552	424	7	associated	associate	VERB
ejpam-2552	424	8	with	with	ADP
ejpam-2552	424	9	a	a	DET
ejpam-2552	424	10	bounded	bounded	ADJ
ejpam-2552	424	11	selfadjoint	selfadjoint	NOUN
ejpam-2552	424	12	operator	operator	NOUN
ejpam-2552	424	13	a	a	PRON
ejpam-2552	424	14	,	,	PUNCT
ejpam-2552	424	15	then	then	ADV
ejpam-2552	424	16	e	e	PROPN
ejpam-2552	424	17	‖a‖∼	‖a‖∼	PROPN
ejpam-2552	425	1	er	er	INTJ
ejpam-2552	425	2	.	.	PUNCT
ejpam-2552	426	1	this	this	PRON
ejpam-2552	426	2	means	mean	VERB
ejpam-2552	426	3	that	that	SCONJ
ejpam-2552	426	4	if	if	SCONJ
ejpam-2552	426	5	a	a	PRON
ejpam-2552	426	6	is	be	AUX
ejpam-2552	426	7	close	close	ADJ
ejpam-2552	426	8	to	to	ADP
ejpam-2552	426	9	the	the	DET
ejpam-2552	426	10	null	null	ADJ
ejpam-2552	426	11	operator	operator	NOUN
ejpam-2552	426	12	o	o	NOUN
ejpam-2552	426	13	,	,	PUNCT
ejpam-2552	426	14	then	then	ADV
ejpam-2552	426	15	the	the	DET
ejpam-2552	426	16	s.m	s.m	PROPN
ejpam-2552	426	17	.	.	PUNCT
ejpam-2552	427	1	e	e	PROPN
ejpam-2552	427	2	is	be	AUX
ejpam-2552	427	3	close	close	ADJ
ejpam-2552	427	4	to	to	ADP
ejpam-2552	427	5	er	er	INTJ
ejpam-2552	427	6	,	,	PUNCT
ejpam-2552	427	7	the	the	DET
ejpam-2552	427	8	s.m	s.m	PROPN
ejpam-2552	427	9	.	.	PROPN
ejpam-2552	427	10	associated	associate	VERB
ejpam-2552	427	11	with	with	ADP
ejpam-2552	427	12	o.	o.	PROPN
ejpam-2552	427	13	indeed	indeed	ADV
ejpam-2552	427	14	,	,	PUNCT
ejpam-2552	427	15	as	as	ADP
ejpam-2552	427	16	zxer	zxer	NOUN
ejpam-2552	427	17	=	=	PUNCT
ejpam-2552	427	18	δ0(.)x	δ0(.)x	ADV
ejpam-2552	427	19	,	,	PUNCT
ejpam-2552	427	20	it	it	PRON
ejpam-2552	427	21	comes	come	VERB
ejpam-2552	427	22	(	(	PUNCT
ejpam-2552	427	23	er)jx	er)jx	PROPN
ejpam-2552	427	24	=	=	SYM
ejpam-2552	427	25	∫	∫	PROPN
ejpam-2552	427	26	jdδ0(.)x	jdδ0(.)x	PROPN
ejpam-2552	428	1	=	=	NOUN
ejpam-2552	428	2	j(0)x	j(0)x	X
ejpam-2552	428	3	=	=	SYM
ejpam-2552	428	4	0	0	NUM
ejpam-2552	428	5	,	,	PUNCT
ejpam-2552	428	6	for	for	ADP
ejpam-2552	428	7	any	any	DET
ejpam-2552	428	8	x	x	PROPN
ejpam-2552	428	9	of	of	ADP
ejpam-2552	428	10	h.	h.	NOUN
ejpam-2552	428	11	so	so	SCONJ
ejpam-2552	428	12	it	it	PRON
ejpam-2552	428	13	seams	seam	VERB
ejpam-2552	428	14	that	that	SCONJ
ejpam-2552	428	15	the	the	DET
ejpam-2552	428	16	proximity	proximity	NOUN
ejpam-2552	428	17	between	between	ADP
ejpam-2552	428	18	operators	operator	NOUN
ejpam-2552	428	19	can	can	AUX
ejpam-2552	428	20	be	be	AUX
ejpam-2552	428	21	transposed	transpose	VERB
ejpam-2552	428	22	to	to	ADP
ejpam-2552	428	23	s.m	s.m	PROPN
ejpam-2552	428	24	.	.	PROPN
ejpam-2552	428	25	’s	’s	PART
ejpam-2552	428	26	.	.	PUNCT
ejpam-2552	429	1	the	the	DET
ejpam-2552	429	2	following	following	ADJ
ejpam-2552	429	3	result	result	NOUN
ejpam-2552	429	4	lets	let	VERB
ejpam-2552	429	5	us	we	PRON
ejpam-2552	429	6	approach	approach	VERB
ejpam-2552	429	7	this	this	DET
ejpam-2552	429	8	aspect	aspect	NOUN
ejpam-2552	429	9	.	.	PUNCT
ejpam-2552	430	1	lemma	lemma	PROPN
ejpam-2552	430	2	4.1	4.1	NUM
ejpam-2552	430	3	.	.	PUNCT
ejpam-2552	431	1	if	if	SCONJ
ejpam-2552	431	2	a	a	PRON
ejpam-2552	431	3	and	and	CCONJ
ejpam-2552	431	4	a′	a′	NOUN
ejpam-2552	431	5	are	be	AUX
ejpam-2552	431	6	two	two	NUM
ejpam-2552	431	7	bounded	bounded	ADJ
ejpam-2552	431	8	selfadjoint	selfadjoint	NOUN
ejpam-2552	431	9	operators	operator	NOUN
ejpam-2552	431	10	which	which	PRON
ejpam-2552	431	11	commute	commute	VERB
ejpam-2552	431	12	,	,	PUNCT
ejpam-2552	431	13	of	of	ADP
ejpam-2552	431	14	respective	respective	ADJ
ejpam-2552	431	15	associated	associate	VERB
ejpam-2552	431	16	s.m	s.m	PROPN
ejpam-2552	431	17	.	.	PROPN
ejpam-2552	431	18	’s	’s	PART
ejpam-2552	431	19	e	e	PROPN
ejpam-2552	431	20	and	and	CCONJ
ejpam-2552	431	21	e	e	PROPN
ejpam-2552	431	22	′	′	NOUN
ejpam-2552	431	23	,	,	PUNCT
ejpam-2552	431	24	then	then	ADV
ejpam-2552	431	25	e	e	X
ejpam-2552	431	26	∗(we	∗(we	PROPN
ejpam-2552	431	27	′	′	NOUN
ejpam-2552	431	28	)	)	PUNCT
ejpam-2552	431	29	is	be	AUX
ejpam-2552	431	30	the	the	DET
ejpam-2552	431	31	s.m	s.m	PROPN
ejpam-2552	431	32	.	.	PROPN
ejpam-2552	431	33	associated	associate	VERB
ejpam-2552	431	34	with	with	ADP
ejpam-2552	431	35	the	the	DET
ejpam-2552	431	36	bounded	bounded	ADJ
ejpam-2552	431	37	selfadjoint	selfadjoint	NOUN
ejpam-2552	431	38	operator	operator	NOUN
ejpam-2552	431	39	a−a′.	a−a′.	PROPN
ejpam-2552	431	40	a.	a.	NOUN
ejpam-2552	431	41	boudou	boudou	NOUN
ejpam-2552	431	42	,	,	PUNCT
ejpam-2552	431	43	s.	s.	PROPN
ejpam-2552	431	44	viguier	viguier	PROPN
ejpam-2552	431	45	-	-	PUNCT
ejpam-2552	431	46	pla	pla	PROPN
ejpam-2552	431	47	/	/	PUNCT
ejpam-2552	431	48	eur	eur	PROPN
ejpam-2552	431	49	.	.	PUNCT
ejpam-2552	432	1	j.	j.	PROPN
ejpam-2552	432	2	pure	pure	PROPN
ejpam-2552	432	3	appl	appl	PROPN
ejpam-2552	432	4	.	.	PROPN
ejpam-2552	432	5	math	math	PROPN
ejpam-2552	432	6	,	,	PUNCT
ejpam-2552	432	7	11	11	NUM
ejpam-2552	432	8	(	(	PUNCT
ejpam-2552	432	9	4	4	NUM
ejpam-2552	432	10	)	)	PUNCT
ejpam-2552	432	11	(	(	PUNCT
ejpam-2552	432	12	2018	2018	NUM
ejpam-2552	432	13	)	)	PUNCT
ejpam-2552	432	14	,	,	PUNCT
ejpam-2552	432	15	893	893	NUM
ejpam-2552	432	16	-	-	SYM
ejpam-2552	432	17	910	910	NUM
ejpam-2552	432	18	905	905	NUM
ejpam-2552	432	19	proof	proof	NOUN
ejpam-2552	432	20	.	.	PUNCT
ejpam-2552	433	1	it	it	PRON
ejpam-2552	433	2	is	be	AUX
ejpam-2552	433	3	clear	clear	ADJ
ejpam-2552	433	4	that	that	SCONJ
ejpam-2552	433	5	if	if	SCONJ
ejpam-2552	433	6	e	e	NOUN
ejpam-2552	433	7	′	′	NOUN
ejpam-2552	433	8	is	be	AUX
ejpam-2552	433	9	the	the	DET
ejpam-2552	433	10	s.m	s.m	PROPN
ejpam-2552	433	11	.	.	PROPN
ejpam-2552	433	12	associated	associate	VERB
ejpam-2552	433	13	with	with	ADP
ejpam-2552	433	14	a′	a′	PROPN
ejpam-2552	433	15	,	,	PUNCT
ejpam-2552	433	16	then	then	ADV
ejpam-2552	433	17	we	we	PRON
ejpam-2552	433	18	′	′	VERB
ejpam-2552	433	19	is	be	AUX
ejpam-2552	433	20	the	the	DET
ejpam-2552	433	21	s.m	s.m	PROPN
ejpam-2552	433	22	.	.	PROPN
ejpam-2552	433	23	associated	associate	VERB
ejpam-2552	433	24	with	with	ADP
ejpam-2552	433	25	−a′.	−a′.	NOUN
ejpam-2552	433	26	indeed	indeed	ADV
ejpam-2552	433	27	,	,	PUNCT
ejpam-2552	433	28	from	from	ADP
ejpam-2552	433	29	one	one	NUM
ejpam-2552	433	30	side	side	NOUN
ejpam-2552	433	31	,	,	PUNCT
ejpam-2552	433	32	we	we	PRON
ejpam-2552	433	33	′	′	VERB
ejpam-2552	433	34	is	be	AUX
ejpam-2552	433	35	bounded	bound	VERB
ejpam-2552	433	36	,	,	PUNCT
ejpam-2552	433	37	and	and	CCONJ
ejpam-2552	433	38	from	from	ADP
ejpam-2552	433	39	another	another	DET
ejpam-2552	433	40	side	side	NOUN
ejpam-2552	433	41	,	,	PUNCT
ejpam-2552	433	42	we	we	PRON
ejpam-2552	433	43	have	have	VERB
ejpam-2552	433	44	(	(	PUNCT
ejpam-2552	433	45	we	we	PRON
ejpam-2552	433	46	′)jx	′)jx	VERB
ejpam-2552	433	47	=	=	SYM
ejpam-2552	433	48	∫	∫	PROPN
ejpam-2552	433	49	jdzxwe	jdzxwe	PROPN
ejpam-2552	433	50	′	′	NUM
ejpam-2552	434	1	=	=	SYM
ejpam-2552	434	2	∫	∫	PROPN
ejpam-2552	434	3	jdw(zxe	jdw(zxe	PROPN
ejpam-2552	434	4	′	′	NUM
ejpam-2552	434	5	)	)	PUNCT
ejpam-2552	435	1	=	=	SYM
ejpam-2552	436	1	∫	∫	PROPN
ejpam-2552	436	2	j	j	PROPN
ejpam-2552	436	3	◦	◦	NOUN
ejpam-2552	436	4	wdzxe	wdzxe	VERB
ejpam-2552	436	5	′	′	NUM
ejpam-2552	437	1	=	=	SYM
ejpam-2552	437	2	∫	∫	PROPN
ejpam-2552	437	3	−jdzxe	−jdzxe	NOUN
ejpam-2552	437	4	′	′	NUM
ejpam-2552	438	1	=	=	PUNCT
ejpam-2552	438	2	−a′x	−a′x	ADV
ejpam-2552	438	3	,	,	PUNCT
ejpam-2552	438	4	for	for	ADP
ejpam-2552	438	5	any	any	DET
ejpam-2552	438	6	x	x	PROPN
ejpam-2552	438	7	of	of	ADP
ejpam-2552	438	8	h.	h.	PROPN
ejpam-2552	438	9	so	so	ADV
ejpam-2552	438	10	,	,	PUNCT
ejpam-2552	438	11	from	from	ADP
ejpam-2552	438	12	proposition	proposition	NOUN
ejpam-2552	438	13	2.5.4	2.5.4	NUM
ejpam-2552	438	14	,	,	PUNCT
ejpam-2552	438	15	the	the	DET
ejpam-2552	438	16	s.m	s.m	PROPN
ejpam-2552	438	17	.	.	PROPN
ejpam-2552	438	18	associated	associate	VERB
ejpam-2552	438	19	with	with	ADP
ejpam-2552	438	20	a−a′	a−a′	PROPN
ejpam-2552	438	21	is	be	AUX
ejpam-2552	438	22	e	e	NOUN
ejpam-2552	438	23	∗	∗	NOUN
ejpam-2552	438	24	(	(	PUNCT
ejpam-2552	438	25	we	we	PRON
ejpam-2552	438	26	′	′	NUM
ejpam-2552	438	27	)	)	PUNCT
ejpam-2552	438	28	.	.	PUNCT
ejpam-2552	439	1	�	�	PROPN
ejpam-2552	439	2	we	we	PRON
ejpam-2552	439	3	are	be	AUX
ejpam-2552	439	4	now	now	ADV
ejpam-2552	439	5	able	able	ADJ
ejpam-2552	439	6	to	to	PART
ejpam-2552	439	7	enunciate	enunciate	VERB
ejpam-2552	439	8	a	a	DET
ejpam-2552	439	9	property	property	NOUN
ejpam-2552	439	10	which	which	PRON
ejpam-2552	439	11	generalizes	generalize	VERB
ejpam-2552	439	12	the	the	DET
ejpam-2552	439	13	previous	previous	ADJ
ejpam-2552	439	14	result	result	NOUN
ejpam-2552	439	15	.	.	PUNCT
ejpam-2552	440	1	proposition	proposition	NOUN
ejpam-2552	440	2	4.2	4.2	NUM
ejpam-2552	440	3	.	.	PUNCT
ejpam-2552	441	1	if	if	SCONJ
ejpam-2552	441	2	a	a	PRON
ejpam-2552	441	3	and	and	CCONJ
ejpam-2552	441	4	a′	a′	NOUN
ejpam-2552	441	5	are	be	AUX
ejpam-2552	441	6	two	two	NUM
ejpam-2552	441	7	bounded	bounded	ADJ
ejpam-2552	441	8	selfadjoint	selfadjoint	NOUN
ejpam-2552	441	9	operators	operator	NOUN
ejpam-2552	441	10	which	which	PRON
ejpam-2552	441	11	commute	commute	VERB
ejpam-2552	441	12	,	,	PUNCT
ejpam-2552	441	13	of	of	ADP
ejpam-2552	441	14	respective	respective	ADJ
ejpam-2552	441	15	associated	associate	VERB
ejpam-2552	441	16	s.m	s.m	PROPN
ejpam-2552	441	17	.	.	PROPN
ejpam-2552	441	18	’s	’s	PART
ejpam-2552	441	19	e	e	PROPN
ejpam-2552	441	20	and	and	CCONJ
ejpam-2552	441	21	e	e	PROPN
ejpam-2552	441	22	′	′	NOUN
ejpam-2552	441	23	,	,	PUNCT
ejpam-2552	441	24	then	then	ADV
ejpam-2552	441	25	e	e	PROPN
ejpam-2552	441	26	‖a−a	‖a−a	PROPN
ejpam-2552	441	27	′‖∼	′‖∼	PROPN
ejpam-2552	441	28	e	e	PROPN
ejpam-2552	441	29	′.	′.	NOUN
ejpam-2552	441	30	proof	proof	NOUN
ejpam-2552	441	31	.	.	PUNCT
ejpam-2552	442	1	as	as	SCONJ
ejpam-2552	442	2	e	e	NOUN
ejpam-2552	442	3	∗we	∗we	NOUN
ejpam-2552	442	4	′	′	NUM
ejpam-2552	442	5	is	be	AUX
ejpam-2552	442	6	the	the	DET
ejpam-2552	442	7	s.m	s.m	PROPN
ejpam-2552	442	8	.	.	PROPN
ejpam-2552	442	9	associated	associate	VERB
ejpam-2552	442	10	with	with	ADP
ejpam-2552	442	11	the	the	DET
ejpam-2552	442	12	bounded	bounded	ADJ
ejpam-2552	442	13	selfadjoint	selfadjoint	NOUN
ejpam-2552	442	14	operator	operator	NOUN
ejpam-2552	442	15	a−a′	a−a′	PART
ejpam-2552	442	16	,	,	PUNCT
ejpam-2552	442	17	proposition	proposition	NOUN
ejpam-2552	442	18	4.1	4.1	NUM
ejpam-2552	442	19	allows	allow	VERB
ejpam-2552	442	20	us	we	PRON
ejpam-2552	442	21	to	to	PART
ejpam-2552	442	22	write	write	VERB
ejpam-2552	442	23	e	e	NOUN
ejpam-2552	442	24	∗	∗	NOUN
ejpam-2552	442	25	we	we	PRON
ejpam-2552	442	26	′	′	VERB
ejpam-2552	442	27	‖a−a	‖a−a	PUNCT
ejpam-2552	443	1	′‖∼	′‖∼	PROPN
ejpam-2552	443	2	er	er	INTJ
ejpam-2552	443	3	.	.	PUNCT
ejpam-2552	444	1	as	as	SCONJ
ejpam-2552	444	2	e	e	X
ejpam-2552	444	3	′	′	NUM
ejpam-2552	444	4	commute	commute	NOUN
ejpam-2552	444	5	with	with	ADP
ejpam-2552	444	6	e	e	NOUN
ejpam-2552	444	7	∗	∗	NOUN
ejpam-2552	444	8	we	we	PRON
ejpam-2552	444	9	′	′	VERB
ejpam-2552	444	10	,	,	PUNCT
ejpam-2552	444	11	lemma	lemma	PROPN
ejpam-2552	444	12	3.1	3.1	NUM
ejpam-2552	444	13	allows	allow	VERB
ejpam-2552	444	14	us	we	PRON
ejpam-2552	444	15	to	to	PART
ejpam-2552	444	16	affirm	affirm	VERB
ejpam-2552	444	17	that	that	SCONJ
ejpam-2552	444	18	e	e	NOUN
ejpam-2552	444	19	′	′	NUM
ejpam-2552	444	20	∗	∗	NOUN
ejpam-2552	444	21	(	(	PUNCT
ejpam-2552	444	22	e	e	NOUN
ejpam-2552	444	23	∗	∗	NOUN
ejpam-2552	444	24	we	we	PRON
ejpam-2552	444	25	′	′	VERB
ejpam-2552	444	26	)	)	PUNCT
ejpam-2552	444	27	‖a−a	‖a−a	PUNCT
ejpam-2552	445	1	′‖∼	′‖∼	PROPN
ejpam-2552	445	2	e	e	PROPN
ejpam-2552	445	3	′	′	NOUN
ejpam-2552	445	4	,	,	PUNCT
ejpam-2552	445	5	so	so	SCONJ
ejpam-2552	445	6	that	that	SCONJ
ejpam-2552	445	7	e	e	X
ejpam-2552	445	8	‖a−a	‖a−a	PROPN
ejpam-2552	445	9	′‖∼	′‖∼	PROPN
ejpam-2552	445	10	e	e	PROPN
ejpam-2552	445	11	′	′	NOUN
ejpam-2552	445	12	,	,	PUNCT
ejpam-2552	445	13	and	and	CCONJ
ejpam-2552	445	14	the	the	DET
ejpam-2552	445	15	property	property	NOUN
ejpam-2552	445	16	is	be	AUX
ejpam-2552	445	17	proved	prove	VERB
ejpam-2552	445	18	.	.	PUNCT
ejpam-2552	446	1	�	�	PROPN
ejpam-2552	446	2	the	the	DET
ejpam-2552	446	3	following	follow	VERB
ejpam-2552	446	4	property	property	NOUN
ejpam-2552	446	5	is	be	AUX
ejpam-2552	446	6	,	,	PUNCT
ejpam-2552	446	7	in	in	ADP
ejpam-2552	446	8	some	some	DET
ejpam-2552	446	9	way	way	NOUN
ejpam-2552	446	10	,	,	PUNCT
ejpam-2552	446	11	the	the	DET
ejpam-2552	446	12	converse	converse	NOUN
ejpam-2552	446	13	of	of	ADP
ejpam-2552	446	14	the	the	DET
ejpam-2552	446	15	previous	previous	ADJ
ejpam-2552	446	16	one	one	NUM
ejpam-2552	446	17	.	.	PUNCT
ejpam-2552	447	1	proposition	proposition	NOUN
ejpam-2552	447	2	4.3	4.3	NUM
ejpam-2552	447	3	.	.	PUNCT
ejpam-2552	448	1	let	let	VERB
ejpam-2552	448	2	e	e	NOUN
ejpam-2552	448	3	and	and	CCONJ
ejpam-2552	448	4	e	e	X
ejpam-2552	448	5	′	′	NOUN
ejpam-2552	448	6	be	be	AUX
ejpam-2552	448	7	respectively	respectively	ADV
ejpam-2552	448	8	the	the	DET
ejpam-2552	448	9	s.m	s.m	PROPN
ejpam-2552	448	10	.	.	PROPN
ejpam-2552	448	11	’s	’s	AUX
ejpam-2552	448	12	associated	associate	VERB
ejpam-2552	448	13	with	with	ADP
ejpam-2552	448	14	the	the	DET
ejpam-2552	448	15	bounded	bounded	ADJ
ejpam-2552	448	16	selfadjoint	selfadjoint	NOUN
ejpam-2552	448	17	operators	operator	NOUN
ejpam-2552	448	18	a	a	PRON
ejpam-2552	448	19	and	and	CCONJ
ejpam-2552	448	20	a′	a′	PROPN
ejpam-2552	448	21	,	,	PUNCT
ejpam-2552	448	22	which	which	PRON
ejpam-2552	448	23	commute	commute	NOUN
ejpam-2552	448	24	.	.	PUNCT
ejpam-2552	449	1	if	if	SCONJ
ejpam-2552	449	2	e	e	NOUN
ejpam-2552	449	3	and	and	CCONJ
ejpam-2552	449	4	e	e	NOUN
ejpam-2552	449	5	′	′	NOUN
ejpam-2552	449	6	are	be	AUX
ejpam-2552	449	7	α−equivalent	α−equivalent	NOUN
ejpam-2552	449	8	,	,	PUNCT
ejpam-2552	449	9	then	then	ADV
ejpam-2552	449	10	‖a−	‖a−	VERB
ejpam-2552	449	11	a′‖	a′‖	SYM
ejpam-2552	449	12	6	6	NUM
ejpam-2552	449	13	α	α	NOUN
ejpam-2552	449	14	.	.	PUNCT
ejpam-2552	450	1	proof	proof	NOUN
ejpam-2552	450	2	.	.	PUNCT
ejpam-2552	451	1	the	the	DET
ejpam-2552	451	2	hypothesis	hypothesis	NOUN
ejpam-2552	451	3	of	of	ADP
ejpam-2552	451	4	the	the	DET
ejpam-2552	451	5	proposition	proposition	NOUN
ejpam-2552	451	6	can	can	AUX
ejpam-2552	451	7	be	be	AUX
ejpam-2552	451	8	writen	writen	VERB
ejpam-2552	451	9	e	e	X
ejpam-2552	451	10	α∼	α∼	PROPN
ejpam-2552	451	11	e	e	NOUN
ejpam-2552	451	12	′.	′.	NOUN
ejpam-2552	451	13	as	as	SCONJ
ejpam-2552	451	14	we	we	PRON
ejpam-2552	451	15	′	′	VERB
ejpam-2552	451	16	commutes	commute	NOUN
ejpam-2552	451	17	with	with	ADP
ejpam-2552	451	18	e	e	X
ejpam-2552	451	19	(	(	PUNCT
ejpam-2552	451	20	because	because	SCONJ
ejpam-2552	451	21	e	e	NOUN
ejpam-2552	451	22	commutes	commute	NOUN
ejpam-2552	451	23	with	with	ADP
ejpam-2552	451	24	e	e	NOUN
ejpam-2552	451	25	′	′	NUM
ejpam-2552	451	26	)	)	PUNCT
ejpam-2552	451	27	,	,	PUNCT
ejpam-2552	451	28	proposition	proposition	NOUN
ejpam-2552	451	29	3.5	3.5	NUM
ejpam-2552	451	30	allows	allow	VERB
ejpam-2552	451	31	us	we	PRON
ejpam-2552	451	32	to	to	PART
ejpam-2552	451	33	write	write	VERB
ejpam-2552	451	34	we	we	PRON
ejpam-2552	451	35	′	′	NOUN
ejpam-2552	451	36	∗	∗	NOUN
ejpam-2552	451	37	e	e	X
ejpam-2552	451	38	α∼	α∼	NOUN
ejpam-2552	451	39	we	we	PRON
ejpam-2552	451	40	′	′	VERB
ejpam-2552	451	41	∗	∗	NOUN
ejpam-2552	451	42	e	e	NOUN
ejpam-2552	451	43	′	′	NOUN
ejpam-2552	451	44	,	,	PUNCT
ejpam-2552	451	45	that	that	PRON
ejpam-2552	451	46	is	is	ADV
ejpam-2552	451	47	e	e	NOUN
ejpam-2552	451	48	∗	∗	NOUN
ejpam-2552	451	49	we	we	PRON
ejpam-2552	451	50	′	′	VERB
ejpam-2552	451	51	α∼	α∼	NUM
ejpam-2552	451	52	er	er	INTJ
ejpam-2552	451	53	.	.	PUNCT
ejpam-2552	452	1	from	from	ADP
ejpam-2552	452	2	proposition	proposition	NOUN
ejpam-2552	452	3	3.3	3.3	NUM
ejpam-2552	452	4	,	,	PUNCT
ejpam-2552	452	5	we	we	PRON
ejpam-2552	452	6	have	have	VERB
ejpam-2552	452	7	then	then	ADV
ejpam-2552	452	8	e	e	NOUN
ejpam-2552	452	9	∗	∗	NOUN
ejpam-2552	452	10	we	we	PRON
ejpam-2552	452	11	′([−α	′([−α	PROPN
ejpam-2552	452	12	,	,	PUNCT
ejpam-2552	452	13	α	α	NOUN
ejpam-2552	452	14	]	]	X
ejpam-2552	452	15	)	)	PUNCT
ejpam-2552	453	1	=	=	SYM
ejpam-2552	453	2	ih	ih	X
ejpam-2552	453	3	.	.	PUNCT
ejpam-2552	454	1	but	but	CCONJ
ejpam-2552	454	2	,	,	PUNCT
ejpam-2552	454	3	as	as	ADP
ejpam-2552	454	4	‖a	‖a	NOUN
ejpam-2552	454	5	−	−	PROPN
ejpam-2552	454	6	a′‖	a′‖	DET
ejpam-2552	454	7	=	=	PUNCT
ejpam-2552	454	8	inf{a	inf{a	PROPN
ejpam-2552	454	9	∈	∈	PROPN
ejpam-2552	454	10	r∗+	r∗+	PROPN
ejpam-2552	454	11	,	,	PUNCT
ejpam-2552	454	12	e	e	X
ejpam-2552	454	13	∗	∗	NOUN
ejpam-2552	454	14	we	we	PRON
ejpam-2552	454	15	′([−a	′([−a	PROPN
ejpam-2552	454	16	,	,	PUNCT
ejpam-2552	454	17	a	a	DET
ejpam-2552	454	18	]	]	X
ejpam-2552	454	19	)	)	PUNCT
ejpam-2552	454	20	=	=	SYM
ejpam-2552	454	21	ih	ih	NOUN
ejpam-2552	454	22	}	}	PUNCT
ejpam-2552	454	23	,	,	PUNCT
ejpam-2552	454	24	because	because	SCONJ
ejpam-2552	454	25	e	e	NOUN
ejpam-2552	454	26	∗	∗	NOUN
ejpam-2552	454	27	we	we	PRON
ejpam-2552	454	28	′	′	VERB
ejpam-2552	454	29	is	be	AUX
ejpam-2552	454	30	the	the	DET
ejpam-2552	454	31	s.m	s.m	PROPN
ejpam-2552	454	32	.	.	PROPN
ejpam-2552	454	33	associated	associate	VERB
ejpam-2552	454	34	with	with	ADP
ejpam-2552	454	35	a−a′.	a−a′.	PROPN
ejpam-2552	454	36	we	we	PRON
ejpam-2552	454	37	have	have	VERB
ejpam-2552	454	38	then	then	ADV
ejpam-2552	454	39	‖a−a′‖	‖a−a′‖	PUNCT
ejpam-2552	454	40	6	6	NUM
ejpam-2552	454	41	α	α	NOUN
ejpam-2552	454	42	,	,	PUNCT
ejpam-2552	454	43	what	what	PRON
ejpam-2552	454	44	allows	allow	VERB
ejpam-2552	454	45	to	to	PART
ejpam-2552	454	46	conclude	conclude	VERB
ejpam-2552	454	47	.	.	PUNCT
ejpam-2552	455	1	�	�	PROPN
ejpam-2552	455	2	the	the	DET
ejpam-2552	455	3	notion	notion	NOUN
ejpam-2552	455	4	of	of	ADP
ejpam-2552	455	5	α−equivalence	α−equivalence	NOUN
ejpam-2552	455	6	is	be	AUX
ejpam-2552	455	7	a	a	DET
ejpam-2552	455	8	good	good	ADJ
ejpam-2552	455	9	translation	translation	NOUN
ejpam-2552	455	10	of	of	ADP
ejpam-2552	455	11	the	the	DET
ejpam-2552	455	12	proximity	proximity	NOUN
ejpam-2552	455	13	of	of	ADP
ejpam-2552	455	14	s.m	s.m	PROPN
ejpam-2552	455	15	.	.	PROPN
ejpam-2552	455	16	’s	’s	AUX
ejpam-2552	455	17	associated	associate	VERB
ejpam-2552	455	18	with	with	ADP
ejpam-2552	455	19	two	two	NUM
ejpam-2552	455	20	operators	operator	NOUN
ejpam-2552	455	21	,	,	PUNCT
ejpam-2552	455	22	because	because	SCONJ
ejpam-2552	455	23	of	of	ADP
ejpam-2552	455	24	the	the	DET
ejpam-2552	455	25	equivalence	equivalence	NOUN
ejpam-2552	455	26	with	with	ADP
ejpam-2552	455	27	the	the	DET
ejpam-2552	455	28	closeness	closeness	NOUN
ejpam-2552	455	29	of	of	ADP
ejpam-2552	455	30	the	the	DET
ejpam-2552	455	31	associated	associated	ADJ
ejpam-2552	455	32	operators	operator	NOUN
ejpam-2552	455	33	.	.	PUNCT
ejpam-2552	456	1	remark	remark	PROPN
ejpam-2552	456	2	.	.	PUNCT
ejpam-2552	457	1	from	from	ADP
ejpam-2552	457	2	proposition	proposition	NOUN
ejpam-2552	457	3	4.2	4.2	NUM
ejpam-2552	457	4	,	,	PUNCT
ejpam-2552	457	5	when	when	SCONJ
ejpam-2552	457	6	two	two	NUM
ejpam-2552	457	7	self	self	NOUN
ejpam-2552	457	8	-	-	PUNCT
ejpam-2552	457	9	adjoint	adjoint	NOUN
ejpam-2552	457	10	bounded	bound	VERB
ejpam-2552	457	11	operators	operator	NOUN
ejpam-2552	457	12	which	which	DET
ejpam-2552	457	13	commute	commute	NOUN
ejpam-2552	457	14	are	be	AUX
ejpam-2552	457	15	close	close	ADV
ejpam-2552	457	16	together	together	ADV
ejpam-2552	457	17	,	,	PUNCT
ejpam-2552	457	18	the	the	DET
ejpam-2552	457	19	same	same	ADJ
ejpam-2552	457	20	happens	happen	VERB
ejpam-2552	457	21	for	for	ADP
ejpam-2552	457	22	their	their	PRON
ejpam-2552	457	23	respectively	respectively	ADV
ejpam-2552	457	24	associated	associate	VERB
ejpam-2552	457	25	s.m	s.m	PROPN
ejpam-2552	457	26	.	.	PROPN
ejpam-2552	457	27	’s	’s	PART
ejpam-2552	457	28	,	,	PUNCT
ejpam-2552	457	29	according	accord	VERB
ejpam-2552	457	30	to	to	ADP
ejpam-2552	457	31	the	the	DET
ejpam-2552	457	32	α−equivalence	α−equivalence	NOUN
ejpam-2552	457	33	.	.	PUNCT
ejpam-2552	458	1	we	we	PRON
ejpam-2552	458	2	examine	examine	VERB
ejpam-2552	458	3	here	here	ADV
ejpam-2552	458	4	an	an	DET
ejpam-2552	458	5	example	example	NOUN
ejpam-2552	458	6	where	where	SCONJ
ejpam-2552	458	7	,	,	PUNCT
ejpam-2552	458	8	when	when	SCONJ
ejpam-2552	458	9	the	the	DET
ejpam-2552	458	10	commutativity	commutativity	NOUN
ejpam-2552	458	11	is	be	AUX
ejpam-2552	458	12	not	not	PART
ejpam-2552	458	13	satisfied	satisfied	ADJ
ejpam-2552	458	14	,	,	PUNCT
ejpam-2552	458	15	the	the	DET
ejpam-2552	458	16	proximity	proximity	NOUN
ejpam-2552	458	17	of	of	ADP
ejpam-2552	458	18	the	the	DET
ejpam-2552	458	19	operators	operator	NOUN
ejpam-2552	458	20	does	do	AUX
ejpam-2552	458	21	not	not	PART
ejpam-2552	458	22	imply	imply	VERB
ejpam-2552	458	23	the	the	DET
ejpam-2552	458	24	proximity	proximity	NOUN
ejpam-2552	458	25	of	of	ADP
ejpam-2552	458	26	the	the	DET
ejpam-2552	458	27	associated	associated	ADJ
ejpam-2552	458	28	s.m	s.m	PROPN
ejpam-2552	458	29	.	.	PROPN
ejpam-2552	458	30	’s	’s	PART
ejpam-2552	458	31	.	.	PUNCT
ejpam-2552	459	1	it	it	PRON
ejpam-2552	459	2	illustrates	illustrate	VERB
ejpam-2552	459	3	the	the	DET
ejpam-2552	459	4	necessity	necessity	NOUN
ejpam-2552	459	5	of	of	ADP
ejpam-2552	459	6	this	this	DET
ejpam-2552	459	7	hypothesis	hypothesis	NOUN
ejpam-2552	459	8	for	for	ADP
ejpam-2552	459	9	this	this	DET
ejpam-2552	459	10	proposition	proposition	NOUN
ejpam-2552	459	11	.	.	PUNCT
ejpam-2552	460	1	let	let	VERB
ejpam-2552	460	2	us	we	PRON
ejpam-2552	460	3	consider	consider	VERB
ejpam-2552	460	4	two	two	NUM
ejpam-2552	460	5	elements	element	NOUN
ejpam-2552	460	6	y	y	PROPN
ejpam-2552	460	7	and	and	CCONJ
ejpam-2552	460	8	h	h	PROPN
ejpam-2552	460	9	of	of	ADP
ejpam-2552	460	10	h	h	NOUN
ejpam-2552	460	11	such	such	ADJ
ejpam-2552	460	12	that	that	SCONJ
ejpam-2552	460	13	<	<	X
ejpam-2552	460	14	y	y	PROPN
ejpam-2552	460	15	,	,	PUNCT
ejpam-2552	460	16	h	h	NOUN
ejpam-2552	460	17	>	>	X
ejpam-2552	460	18	=	=	PUNCT
ejpam-2552	460	19	0	0	NUM
ejpam-2552	460	20	,	,	PUNCT
ejpam-2552	460	21	‖y‖2	‖y‖2	PROPN
ejpam-2552	461	1	+	+	NUM
ejpam-2552	461	2	‖h‖2	‖h‖2	NOUN
ejpam-2552	461	3	=	=	SYM
ejpam-2552	461	4	1	1	NUM
ejpam-2552	461	5	,	,	PUNCT
ejpam-2552	461	6	‖y‖.‖h‖	‖y‖.‖h‖	PROPN
ejpam-2552	461	7	6=	6=	ADP
ejpam-2552	461	8	0	0	NUM
ejpam-2552	461	9	,	,	PUNCT
ejpam-2552	461	10	and	and	CCONJ
ejpam-2552	461	11	‖h‖	‖h‖	ADP
ejpam-2552	461	12	<	<	X
ejpam-2552	461	13	1	1	NUM
ejpam-2552	461	14	4	4	NUM
ejpam-2552	461	15	.	.	PUNCT
ejpam-2552	462	1	let	let	VERB
ejpam-2552	462	2	x	x	PUNCT
ejpam-2552	462	3	=	=	PUNCT
ejpam-2552	462	4	y	y	PROPN
ejpam-2552	462	5	+	+	CCONJ
ejpam-2552	462	6	h	h	PROPN
ejpam-2552	462	7	and	and	CCONJ
ejpam-2552	462	8	x′	x′	PROPN
ejpam-2552	463	1	=	=	SYM
ejpam-2552	463	2	y	y	PROPN
ejpam-2552	463	3	−	−	PROPN
ejpam-2552	463	4	h.	h.	PROPN
ejpam-2552	463	5	a.	a.	NOUN
ejpam-2552	463	6	boudou	boudou	NOUN
ejpam-2552	463	7	,	,	PUNCT
ejpam-2552	463	8	s.	s.	PROPN
ejpam-2552	463	9	viguier	viguier	PROPN
ejpam-2552	463	10	-	-	PUNCT
ejpam-2552	463	11	pla	pla	PROPN
ejpam-2552	463	12	/	/	PUNCT
ejpam-2552	463	13	eur	eur	PROPN
ejpam-2552	463	14	.	.	PUNCT
ejpam-2552	464	1	j.	j.	PROPN
ejpam-2552	464	2	pure	pure	PROPN
ejpam-2552	464	3	appl	appl	PROPN
ejpam-2552	464	4	.	.	PROPN
ejpam-2552	464	5	math	math	PROPN
ejpam-2552	464	6	,	,	PUNCT
ejpam-2552	464	7	11	11	NUM
ejpam-2552	464	8	(	(	PUNCT
ejpam-2552	464	9	4	4	NUM
ejpam-2552	464	10	)	)	PUNCT
ejpam-2552	464	11	(	(	PUNCT
ejpam-2552	464	12	2018	2018	NUM
ejpam-2552	464	13	)	)	PUNCT
ejpam-2552	464	14	,	,	PUNCT
ejpam-2552	464	15	893	893	NUM
ejpam-2552	464	16	-	-	SYM
ejpam-2552	464	17	910	910	NUM
ejpam-2552	464	18	906	906	NUM
ejpam-2552	464	19	it	it	PRON
ejpam-2552	464	20	is	be	AUX
ejpam-2552	464	21	clear	clear	ADJ
ejpam-2552	464	22	that	that	SCONJ
ejpam-2552	464	23	p	p	X
ejpam-2552	464	24	=	=	X
ejpam-2552	464	25	x	x	SYM
ejpam-2552	464	26	⊗	⊗	PROPN
ejpam-2552	464	27	x	x	X
ejpam-2552	464	28	and	and	CCONJ
ejpam-2552	464	29	p	p	NOUN
ejpam-2552	465	1	′	′	NUM
ejpam-2552	465	2	=	=	PUNCT
ejpam-2552	465	3	x′	x′	PROPN
ejpam-2552	466	1	⊗	⊗	PROPN
ejpam-2552	466	2	x′	x′	PROPN
ejpam-2552	466	3	are	be	AUX
ejpam-2552	466	4	orthogonal	orthogonal	ADJ
ejpam-2552	466	5	projectors	projector	NOUN
ejpam-2552	466	6	such	such	ADJ
ejpam-2552	466	7	that	that	DET
ejpam-2552	466	8	‖p	‖p	PROPN
ejpam-2552	467	1	−	−	PROPN
ejpam-2552	467	2	p	p	NOUN
ejpam-2552	467	3	′‖	′‖	PUNCT
ejpam-2552	467	4	6	6	NUM
ejpam-2552	467	5	2‖h‖	2‖h‖	NOUN
ejpam-2552	467	6	<	<	X
ejpam-2552	467	7	1	1	NUM
ejpam-2552	467	8	2	2	NUM
ejpam-2552	467	9	.	.	PUNCT
ejpam-2552	468	1	we	we	PRON
ejpam-2552	468	2	can	can	AUX
ejpam-2552	468	3	easily	easily	ADV
ejpam-2552	468	4	verify	verify	VERB
ejpam-2552	468	5	that	that	SCONJ
ejpam-2552	468	6	<	<	X
ejpam-2552	468	7	x	x	X
ejpam-2552	468	8	,	,	PUNCT
ejpam-2552	468	9	x′	x′	PROPN
ejpam-2552	468	10	>	>	PUNCT
ejpam-2552	468	11	6=	6=	NUM
ejpam-2552	468	12	0	0	NUM
ejpam-2552	469	1	and	and	CCONJ
ejpam-2552	469	2	that	that	SCONJ
ejpam-2552	469	3	{	{	PUNCT
ejpam-2552	469	4	x	x	X
ejpam-2552	469	5	,	,	PUNCT
ejpam-2552	469	6	x′	x′	NUM
ejpam-2552	469	7	}	}	PUNCT
ejpam-2552	469	8	is	be	AUX
ejpam-2552	469	9	a	a	DET
ejpam-2552	469	10	free	free	ADJ
ejpam-2552	469	11	family	family	NOUN
ejpam-2552	469	12	.	.	PUNCT
ejpam-2552	470	1	from	from	ADP
ejpam-2552	470	2	these	these	DET
ejpam-2552	470	3	last	last	ADJ
ejpam-2552	470	4	two	two	NUM
ejpam-2552	470	5	points	point	NOUN
ejpam-2552	470	6	we	we	PRON
ejpam-2552	470	7	can	can	AUX
ejpam-2552	470	8	deduce	deduce	VERB
ejpam-2552	470	9	that	that	PRON
ejpam-2552	470	10	p	p	PROPN
ejpam-2552	470	11	and	and	CCONJ
ejpam-2552	470	12	p	p	NOUN
ejpam-2552	470	13	′	′	NOUN
ejpam-2552	470	14	do	do	AUX
ejpam-2552	470	15	not	not	PART
ejpam-2552	470	16	commute	commute	VERB
ejpam-2552	470	17	.	.	PUNCT
ejpam-2552	471	1	so	so	ADV
ejpam-2552	471	2	the	the	DET
ejpam-2552	471	3	selfadjoint	selfadjoint	NOUN
ejpam-2552	471	4	bounded	bound	VERB
ejpam-2552	471	5	operators	operator	NOUN
ejpam-2552	471	6	a	a	DET
ejpam-2552	471	7	=	=	X
ejpam-2552	471	8	λp	λp	PROPN
ejpam-2552	471	9	and	and	CCONJ
ejpam-2552	471	10	a′	a′	PROPN
ejpam-2552	471	11	=	=	SYM
ejpam-2552	471	12	λp	λp	PROPN
ejpam-2552	471	13	′	′	NOUN
ejpam-2552	471	14	,	,	PUNCT
ejpam-2552	471	15	λ	λ	NOUN
ejpam-2552	471	16	being	be	AUX
ejpam-2552	471	17	an	an	DET
ejpam-2552	471	18	element	element	NOUN
ejpam-2552	471	19	of	of	ADP
ejpam-2552	471	20	r∗	r∗	PROPN
ejpam-2552	471	21	,	,	PUNCT
ejpam-2552	471	22	also	also	ADV
ejpam-2552	471	23	do	do	AUX
ejpam-2552	471	24	not	not	PART
ejpam-2552	471	25	commute	commute	VERB
ejpam-2552	471	26	.	.	PUNCT
ejpam-2552	472	1	the	the	DET
ejpam-2552	472	2	s.m	s.m	PROPN
ejpam-2552	472	3	.	.	PROPN
ejpam-2552	472	4	’s	’s	PART
ejpam-2552	472	5	respectively	respectively	ADV
ejpam-2552	472	6	associated	associate	VERB
ejpam-2552	472	7	with	with	ADP
ejpam-2552	472	8	a	a	PRON
ejpam-2552	472	9	and	and	CCONJ
ejpam-2552	472	10	a′	a′	NOUN
ejpam-2552	472	11	are	be	AUX
ejpam-2552	472	12	,	,	PUNCT
ejpam-2552	472	13	with	with	ADP
ejpam-2552	472	14	obvious	obvious	ADJ
ejpam-2552	472	15	notation	notation	NOUN
ejpam-2552	472	16	:	:	PUNCT
ejpam-2552	472	17	e	e	X
ejpam-2552	472	18	=	=	SYM
ejpam-2552	472	19	δ0(.)p⊥	δ0(.)p⊥	PROPN
ejpam-2552	472	20	+	+	CCONJ
ejpam-2552	472	21	δλ(.)p	δλ(.)p	NOUN
ejpam-2552	472	22	and	and	CCONJ
ejpam-2552	472	23	e	e	NOUN
ejpam-2552	472	24	′	′	NOUN
ejpam-2552	472	25	=	=	SYM
ejpam-2552	472	26	δ0(.)p	δ0(.)p	NOUN
ejpam-2552	473	1	′	′	NUM
ejpam-2552	473	2	⊥	⊥	NOUN
ejpam-2552	473	3	+	+	CCONJ
ejpam-2552	473	4	δλ(.)p	δλ(.)p	X
ejpam-2552	473	5	′.	′.	NOUN
ejpam-2552	473	6	if	if	SCONJ
ejpam-2552	473	7	we	we	PRON
ejpam-2552	473	8	assume	assume	VERB
ejpam-2552	473	9	that	that	SCONJ
ejpam-2552	473	10	e	e	NOUN
ejpam-2552	473	11	′	′	NOUN
ejpam-2552	473	12	‖a−a	‖a−a	PUNCT
ejpam-2552	473	13	′‖∼	′‖∼	PROPN
ejpam-2552	473	14	e	e	PROPN
ejpam-2552	473	15	,	,	PUNCT
ejpam-2552	473	16	then	then	ADV
ejpam-2552	473	17	we	we	PRON
ejpam-2552	473	18	have	have	VERB
ejpam-2552	473	19	:	:	PUNCT
ejpam-2552	473	20	p	p	X
ejpam-2552	473	21	′⊥	′⊥	PROPN
ejpam-2552	473	22	=	=	PUNCT
ejpam-2552	473	23	e	e	X
ejpam-2552	473	24	′{0	′{0	PROPN
ejpam-2552	473	25	}	}	PUNCT
ejpam-2552	473	26	�	�	PROPN
ejpam-2552	473	27	e({0	e({0	PUNCT
ejpam-2552	473	28	}	}	PUNCT
ejpam-2552	474	1	+	+	PUNCT
ejpam-2552	475	1	[	[	X
ejpam-2552	475	2	−‖a	−‖a	PROPN
ejpam-2552	475	3	−	−	PROPN
ejpam-2552	475	4	a′‖	a′‖	NOUN
ejpam-2552	475	5	,	,	PUNCT
ejpam-2552	475	6	‖a	‖a	NOUN
ejpam-2552	475	7	−	−	NOUN
ejpam-2552	475	8	a′‖	a′‖	NOUN
ejpam-2552	475	9	]	]	PUNCT
ejpam-2552	475	10	)	)	PUNCT
ejpam-2552	475	11	=	=	SYM
ejpam-2552	475	12	e([−‖a	e([−‖a	NOUN
ejpam-2552	475	13	−	−	NOUN
ejpam-2552	475	14	a′‖	a′‖	NOUN
ejpam-2552	475	15	,	,	PUNCT
ejpam-2552	475	16	‖a	‖a	NOUN
ejpam-2552	475	17	−	−	NOUN
ejpam-2552	475	18	a′‖	a′‖	NOUN
ejpam-2552	475	19	]	]	PUNCT
ejpam-2552	475	20	)	)	PUNCT
ejpam-2552	476	1	=	=	SYM
ejpam-2552	476	2	p⊥	p⊥	NOUN
ejpam-2552	476	3	+	+	CCONJ
ejpam-2552	476	4	δλ([−‖a−a′‖	δλ([−‖a−a′‖	NOUN
ejpam-2552	476	5	,	,	PUNCT
ejpam-2552	476	6	‖a−a′‖])p	‖a−a′‖])p	NOUN
ejpam-2552	476	7	=	=	PUNCT
ejpam-2552	476	8	p⊥	p⊥	NOUN
ejpam-2552	476	9	(	(	PUNCT
ejpam-2552	476	10	because	because	SCONJ
ejpam-2552	476	11	λ	λ	PROPN
ejpam-2552	476	12	6∈	6∈	NOUN
ejpam-2552	477	1	[	[	X
ejpam-2552	477	2	−‖a−a′‖	−‖a−a′‖	NOUN
ejpam-2552	477	3	,	,	PUNCT
ejpam-2552	477	4	‖a−a′‖	‖a−a′‖	PRON
ejpam-2552	477	5	]	]	PUNCT
ejpam-2552	477	6	)	)	PUNCT
ejpam-2552	477	7	.	.	PUNCT
ejpam-2552	478	1	so	so	ADV
ejpam-2552	478	2	p	p	X
ejpam-2552	478	3	�	�	PROPN
ejpam-2552	478	4	p	p	NOUN
ejpam-2552	479	1	′	′	NOUN
ejpam-2552	480	1	and	and	CCONJ
ejpam-2552	480	2	then	then	ADV
ejpam-2552	480	3	pp	pp	ADV
ejpam-2552	480	4	′	′	NOUN
ejpam-2552	481	1	=	=	PUNCT
ejpam-2552	482	1	p	p	PRON
ejpam-2552	482	2	′p	′p	NUM
ejpam-2552	482	3	=	=	PUNCT
ejpam-2552	482	4	p	p	X
ejpam-2552	482	5	,	,	PUNCT
ejpam-2552	482	6	what	what	PRON
ejpam-2552	482	7	is	be	AUX
ejpam-2552	482	8	the	the	DET
ejpam-2552	482	9	opposite	opposite	NOUN
ejpam-2552	482	10	of	of	ADP
ejpam-2552	482	11	the	the	DET
ejpam-2552	482	12	hypothesis	hypothesis	NOUN
ejpam-2552	482	13	made	make	VERB
ejpam-2552	482	14	at	at	ADP
ejpam-2552	482	15	the	the	DET
ejpam-2552	482	16	beginning	beginning	NOUN
ejpam-2552	482	17	.	.	PUNCT
ejpam-2552	483	1	so	so	ADV
ejpam-2552	483	2	the	the	DET
ejpam-2552	483	3	relation	relation	NOUN
ejpam-2552	483	4	e	e	NOUN
ejpam-2552	483	5	′	′	NOUN
ejpam-2552	483	6	‖a−a	‖a−a	PUNCT
ejpam-2552	483	7	′‖∼	′‖∼	PROPN
ejpam-2552	483	8	e	e	PROPN
ejpam-2552	483	9	is	be	AUX
ejpam-2552	483	10	false	false	ADJ
ejpam-2552	483	11	.	.	PUNCT
ejpam-2552	484	1	5	5	X
ejpam-2552	484	2	.	.	PUNCT
ejpam-2552	484	3	the	the	DET
ejpam-2552	484	4	case	case	NOUN
ejpam-2552	484	5	of	of	ADP
ejpam-2552	484	6	compact	compact	ADJ
ejpam-2552	484	7	operators	operator	NOUN
ejpam-2552	484	8	in	in	ADP
ejpam-2552	484	9	this	this	DET
ejpam-2552	484	10	section	section	NOUN
ejpam-2552	484	11	we	we	PRON
ejpam-2552	484	12	will	will	AUX
ejpam-2552	484	13	examine	examine	VERB
ejpam-2552	484	14	the	the	DET
ejpam-2552	484	15	particular	particular	ADJ
ejpam-2552	484	16	case	case	NOUN
ejpam-2552	484	17	of	of	ADP
ejpam-2552	484	18	the	the	DET
ejpam-2552	484	19	compact	compact	ADJ
ejpam-2552	484	20	selfadjoint	selfadjoint	VERB
ejpam-2552	484	21	positive	positive	ADJ
ejpam-2552	484	22	operators	operator	NOUN
ejpam-2552	484	23	.	.	PUNCT
ejpam-2552	485	1	this	this	DET
ejpam-2552	485	2	particular	particular	ADJ
ejpam-2552	485	3	case	case	NOUN
ejpam-2552	485	4	plays	play	VERB
ejpam-2552	485	5	an	an	DET
ejpam-2552	485	6	important	important	ADJ
ejpam-2552	485	7	role	role	NOUN
ejpam-2552	485	8	in	in	ADP
ejpam-2552	485	9	various	various	ADJ
ejpam-2552	485	10	fields	field	NOUN
ejpam-2552	485	11	of	of	ADP
ejpam-2552	485	12	mathematics	mathematic	NOUN
ejpam-2552	485	13	,	,	PUNCT
ejpam-2552	485	14	and	and	CCONJ
ejpam-2552	485	15	in	in	ADP
ejpam-2552	485	16	particular	particular	ADJ
ejpam-2552	485	17	,	,	PUNCT
ejpam-2552	485	18	in	in	ADP
ejpam-2552	485	19	statistics	statistic	NOUN
ejpam-2552	485	20	,	,	PUNCT
ejpam-2552	485	21	the	the	DET
ejpam-2552	485	22	covariance	covariance	NOUN
ejpam-2552	485	23	operators	operator	NOUN
ejpam-2552	485	24	belong	belong	VERB
ejpam-2552	485	25	to	to	ADP
ejpam-2552	485	26	this	this	DET
ejpam-2552	485	27	family	family	NOUN
ejpam-2552	485	28	.	.	PUNCT
ejpam-2552	486	1	it	it	PRON
ejpam-2552	486	2	is	be	AUX
ejpam-2552	486	3	well	well	ADV
ejpam-2552	486	4	known	know	VERB
ejpam-2552	486	5	that	that	SCONJ
ejpam-2552	486	6	any	any	DET
ejpam-2552	486	7	compact	compact	ADJ
ejpam-2552	486	8	operator	operator	NOUN
ejpam-2552	486	9	is	be	AUX
ejpam-2552	486	10	the	the	DET
ejpam-2552	486	11	limit	limit	NOUN
ejpam-2552	486	12	,	,	PUNCT
ejpam-2552	486	13	in	in	ADP
ejpam-2552	486	14	l(h	l(h	PROPN
ejpam-2552	486	15	)	)	PUNCT
ejpam-2552	486	16	,	,	PUNCT
ejpam-2552	486	17	of	of	ADP
ejpam-2552	486	18	a	a	DET
ejpam-2552	486	19	sequence	sequence	NOUN
ejpam-2552	486	20	of	of	ADP
ejpam-2552	486	21	finite	finite	PROPN
ejpam-2552	486	22	rank	rank	PROPN
ejpam-2552	486	23	operators	operator	NOUN
ejpam-2552	486	24	(	(	PUNCT
ejpam-2552	486	25	an)n∈n	an)n∈n	PROPN
ejpam-2552	486	26	.	.	PUNCT
ejpam-2552	487	1	moreover	moreover	ADV
ejpam-2552	487	2	,	,	PUNCT
ejpam-2552	487	3	when	when	SCONJ
ejpam-2552	487	4	a	a	PRON
ejpam-2552	487	5	is	be	AUX
ejpam-2552	487	6	positive	positive	ADJ
ejpam-2552	487	7	and	and	CCONJ
ejpam-2552	487	8	selfadjoint	selfadjoint	NOUN
ejpam-2552	487	9	,	,	PUNCT
ejpam-2552	487	10	the	the	DET
ejpam-2552	487	11	operators	operator	NOUN
ejpam-2552	487	12	an	an	PRON
ejpam-2552	487	13	are	be	AUX
ejpam-2552	487	14	linear	linear	ADJ
ejpam-2552	487	15	combinations	combination	NOUN
ejpam-2552	487	16	of	of	ADP
ejpam-2552	487	17	projectors	projector	NOUN
ejpam-2552	487	18	.	.	PUNCT
ejpam-2552	488	1	more	more	ADV
ejpam-2552	488	2	precisely	precisely	ADV
ejpam-2552	488	3	,	,	PUNCT
ejpam-2552	488	4	we	we	PRON
ejpam-2552	488	5	have	have	VERB
ejpam-2552	488	6	the	the	DET
ejpam-2552	488	7	following	following	NOUN
ejpam-2552	488	8	.	.	PUNCT
ejpam-2552	489	1	if	if	SCONJ
ejpam-2552	489	2	a	a	PRON
ejpam-2552	489	3	is	be	AUX
ejpam-2552	489	4	a	a	DET
ejpam-2552	489	5	positive	positive	ADJ
ejpam-2552	489	6	selfadjoint	selfadjoint	NOUN
ejpam-2552	489	7	compact	compact	ADJ
ejpam-2552	489	8	operator	operator	NOUN
ejpam-2552	489	9	,	,	PUNCT
ejpam-2552	489	10	which	which	DET
ejpam-2552	489	11	image	image	NOUN
ejpam-2552	489	12	is	be	AUX
ejpam-2552	489	13	of	of	ADP
ejpam-2552	489	14	infinite	infinite	ADJ
ejpam-2552	489	15	dimension	dimension	NOUN
ejpam-2552	489	16	,	,	PUNCT
ejpam-2552	489	17	we	we	PRON
ejpam-2552	489	18	can	can	AUX
ejpam-2552	489	19	say	say	VERB
ejpam-2552	489	20	that	that	SCONJ
ejpam-2552	489	21	−	−	PROPN
ejpam-2552	489	22	there	there	PRON
ejpam-2552	489	23	exists	exist	VERB
ejpam-2552	489	24	a	a	DET
ejpam-2552	489	25	real	real	ADJ
ejpam-2552	489	26	sequence	sequence	NOUN
ejpam-2552	489	27	(	(	PUNCT
ejpam-2552	489	28	λp)p∈n	λp)p∈n	PROPN
ejpam-2552	489	29	which	which	PRON
ejpam-2552	489	30	strictly	strictly	ADV
ejpam-2552	489	31	decreasingly	decreasingly	ADV
ejpam-2552	489	32	converges	converge	VERB
ejpam-2552	489	33	to	to	ADP
ejpam-2552	489	34	0	0	NUM
ejpam-2552	489	35	,	,	PUNCT
ejpam-2552	489	36	−	−	PUNCT
ejpam-2552	489	37	there	there	PRON
ejpam-2552	489	38	exists	exist	VERB
ejpam-2552	489	39	a	a	DET
ejpam-2552	489	40	family	family	NOUN
ejpam-2552	489	41	{	{	PUNCT
ejpam-2552	489	42	pp	pp	ADV
ejpam-2552	489	43	;	;	PUNCT
ejpam-2552	489	44	p	p	PROPN
ejpam-2552	489	45	∈	∈	PROPN
ejpam-2552	489	46	n	n	CCONJ
ejpam-2552	489	47	}	}	PUNCT
ejpam-2552	489	48	of	of	ADP
ejpam-2552	489	49	orthogonal	orthogonal	ADJ
ejpam-2552	489	50	projectors	projector	NOUN
ejpam-2552	489	51	such	such	ADJ
ejpam-2552	489	52	that	that	PRON
ejpam-2552	489	53	,	,	PUNCT
ejpam-2552	489	54	for	for	ADP
ejpam-2552	489	55	any	any	DET
ejpam-2552	489	56	p	p	NOUN
ejpam-2552	489	57	of	of	ADP
ejpam-2552	489	58	n	n	CCONJ
ejpam-2552	489	59	,	,	PUNCT
ejpam-2552	489	60	pp	pp	PROPN
ejpam-2552	489	61	6=	6=	NOUN
ejpam-2552	489	62	o	o	NOUN
ejpam-2552	489	63	and	and	CCONJ
ejpam-2552	489	64	dim	dim	ADJ
ejpam-2552	489	65	impp	impp	NOUN
ejpam-2552	489	66	<	<	X
ejpam-2552	490	1	+	+	NOUN
ejpam-2552	490	2	∞.	∞.	PROPN
ejpam-2552	490	3	this	this	DET
ejpam-2552	490	4	real	real	ADJ
ejpam-2552	490	5	sequence	sequence	NOUN
ejpam-2552	490	6	and	and	CCONJ
ejpam-2552	490	7	this	this	DET
ejpam-2552	490	8	family	family	NOUN
ejpam-2552	490	9	of	of	ADP
ejpam-2552	490	10	projectors	projector	NOUN
ejpam-2552	490	11	are	be	AUX
ejpam-2552	490	12	such	such	ADJ
ejpam-2552	490	13	that	that	SCONJ
ejpam-2552	490	14	a	a	X
ejpam-2552	490	15	)	)	PUNCT
ejpam-2552	490	16	the	the	DET
ejpam-2552	490	17	family	family	NOUN
ejpam-2552	490	18	{	{	PUNCT
ejpam-2552	490	19	λppp	λppp	NOUN
ejpam-2552	490	20	;	;	PUNCT
ejpam-2552	490	21	p	p	PROPN
ejpam-2552	490	22	∈	∈	PROPN
ejpam-2552	490	23	n	n	CCONJ
ejpam-2552	490	24	}	}	PUNCT
ejpam-2552	490	25	of	of	ADP
ejpam-2552	490	26	elements	element	NOUN
ejpam-2552	490	27	of	of	ADP
ejpam-2552	490	28	l(h	l(h	PROPN
ejpam-2552	490	29	)	)	PUNCT
ejpam-2552	490	30	,	,	PUNCT
ejpam-2552	490	31	is	be	AUX
ejpam-2552	490	32	summable	summable	ADJ
ejpam-2552	490	33	of	of	ADP
ejpam-2552	490	34	sum	sum	NOUN
ejpam-2552	490	35	a	a	PRON
ejpam-2552	490	36	;	;	PUNCT
ejpam-2552	490	37	b	b	X
ejpam-2552	490	38	)	)	PUNCT
ejpam-2552	490	39	{	{	PUNCT
ejpam-2552	490	40	λp	λp	X
ejpam-2552	490	41	;	;	PUNCT
ejpam-2552	490	42	p	p	PROPN
ejpam-2552	490	43	∈	∈	PROPN
ejpam-2552	490	44	n	n	CCONJ
ejpam-2552	490	45	}	}	PUNCT
ejpam-2552	490	46	is	be	AUX
ejpam-2552	490	47	the	the	DET
ejpam-2552	490	48	family	family	NOUN
ejpam-2552	490	49	of	of	ADP
ejpam-2552	490	50	the	the	DET
ejpam-2552	490	51	eigenvalues	eigenvalue	NOUN
ejpam-2552	490	52	of	of	ADP
ejpam-2552	490	53	a	a	PRON
ejpam-2552	490	54	,	,	PUNCT
ejpam-2552	490	55	different	different	ADJ
ejpam-2552	490	56	from	from	ADP
ejpam-2552	490	57	0	0	NUM
ejpam-2552	490	58	;	;	PUNCT
ejpam-2552	490	59	c	c	X
ejpam-2552	490	60	)	)	PUNCT
ejpam-2552	490	61	for	for	ADP
ejpam-2552	490	62	any	any	DET
ejpam-2552	490	63	p	p	NOUN
ejpam-2552	490	64	of	of	ADP
ejpam-2552	490	65	n	n	CCONJ
ejpam-2552	490	66	,	,	PUNCT
ejpam-2552	490	67	impp	impp	NOUN
ejpam-2552	490	68	is	be	AUX
ejpam-2552	490	69	the	the	DET
ejpam-2552	490	70	eigenspace	eigenspace	NOUN
ejpam-2552	490	71	of	of	ADP
ejpam-2552	490	72	a	a	DET
ejpam-2552	490	73	associated	associate	VERB
ejpam-2552	490	74	with	with	ADP
ejpam-2552	490	75	the	the	DET
ejpam-2552	490	76	eigenvalue	eigenvalue	PROPN
ejpam-2552	490	77	λp	λp	PROPN
ejpam-2552	490	78	;	;	PUNCT
ejpam-2552	490	79	d	d	X
ejpam-2552	490	80	)	)	PUNCT
ejpam-2552	490	81	if	if	SCONJ
ejpam-2552	490	82	we	we	PRON
ejpam-2552	490	83	denote	denote	VERB
ejpam-2552	490	84	by	by	ADP
ejpam-2552	490	85	d	d	PROPN
ejpam-2552	490	86	the	the	DET
ejpam-2552	490	87	projector	projector	NOUN
ejpam-2552	490	88	,	,	PUNCT
ejpam-2552	490	89	sum	sum	NOUN
ejpam-2552	490	90	of	of	ADP
ejpam-2552	490	91	the	the	DET
ejpam-2552	490	92	orthogonal	orthogonal	ADJ
ejpam-2552	490	93	family	family	NOUN
ejpam-2552	490	94	of	of	ADP
ejpam-2552	490	95	projectors	projector	NOUN
ejpam-2552	490	96	{	{	PUNCT
ejpam-2552	490	97	pp	pp	ADV
ejpam-2552	490	98	;	;	PUNCT
ejpam-2552	490	99	p	p	PROPN
ejpam-2552	490	100	∈	∈	PROPN
ejpam-2552	490	101	n	n	CCONJ
ejpam-2552	490	102	}	}	PUNCT
ejpam-2552	490	103	,	,	PUNCT
ejpam-2552	490	104	then	then	ADV
ejpam-2552	490	105	kera	kera	PROPN
ejpam-2552	490	106	=	=	SYM
ejpam-2552	490	107	im(i	im(i	ADV
ejpam-2552	490	108	−d	−d	ADJ
ejpam-2552	490	109	)	)	PUNCT
ejpam-2552	490	110	.	.	PUNCT
ejpam-2552	491	1	let	let	VERB
ejpam-2552	491	2	us	we	PRON
ejpam-2552	491	3	set	set	VERB
ejpam-2552	491	4	µ0	µ0	NOUN
ejpam-2552	491	5	=	=	SYM
ejpam-2552	491	6	0	0	NUM
ejpam-2552	491	7	,	,	PUNCT
ejpam-2552	491	8	d0	d0	NOUN
ejpam-2552	491	9	=	=	PUNCT
ejpam-2552	492	1	i	i	PRON
ejpam-2552	492	2	−d	−d	VERB
ejpam-2552	492	3	and	and	CCONJ
ejpam-2552	492	4	,	,	PUNCT
ejpam-2552	492	5	for	for	ADP
ejpam-2552	492	6	any	any	DET
ejpam-2552	492	7	p	p	NOUN
ejpam-2552	492	8	of	of	ADP
ejpam-2552	492	9	n∗	n∗	PROPN
ejpam-2552	492	10	,	,	PUNCT
ejpam-2552	492	11	µp	µp	NOUN
ejpam-2552	492	12	=	=	PUNCT
ejpam-2552	492	13	λp−1	λp−1	ADJ
ejpam-2552	492	14	and	and	CCONJ
ejpam-2552	492	15	dp	dp	NOUN
ejpam-2552	492	16	=	=	NOUN
ejpam-2552	492	17	pp−1	pp−1	NOUN
ejpam-2552	492	18	.	.	PUNCT
ejpam-2552	493	1	then	then	ADV
ejpam-2552	493	2	we	we	PRON
ejpam-2552	493	3	can	can	AUX
ejpam-2552	493	4	affirm	affirm	VERB
ejpam-2552	493	5	that	that	SCONJ
ejpam-2552	493	6	a	a	X
ejpam-2552	493	7	)	)	PUNCT
ejpam-2552	493	8	for	for	ADP
ejpam-2552	493	9	any	any	DET
ejpam-2552	493	10	p	p	NOUN
ejpam-2552	493	11	of	of	ADP
ejpam-2552	493	12	n∗	n∗	PROPN
ejpam-2552	493	13	,	,	PUNCT
ejpam-2552	493	14	µp	µp	PROPN
ejpam-2552	493	15	is	be	AUX
ejpam-2552	493	16	the	the	DET
ejpam-2552	493	17	pth	pth	NOUN
ejpam-2552	493	18	largest	large	ADJ
ejpam-2552	493	19	eigenvalue	eigenvalue	NOUN
ejpam-2552	493	20	of	of	ADP
ejpam-2552	493	21	a	a	DET
ejpam-2552	493	22	;	;	PUNCT
ejpam-2552	493	23	b	b	X
ejpam-2552	493	24	)	)	PUNCT
ejpam-2552	493	25	imdp	imdp	NOUN
ejpam-2552	493	26	is	be	AUX
ejpam-2552	493	27	the	the	DET
ejpam-2552	493	28	eigenspace	eigenspace	NOUN
ejpam-2552	493	29	associated	associate	VERB
ejpam-2552	493	30	with	with	ADP
ejpam-2552	493	31	the	the	DET
ejpam-2552	493	32	eigenvalue	eigenvalue	PROPN
ejpam-2552	493	33	µp	µp	NOUN
ejpam-2552	493	34	;	;	PUNCT
ejpam-2552	493	35	c	c	X
ejpam-2552	493	36	)	)	PUNCT
ejpam-2552	493	37	the	the	DET
ejpam-2552	493	38	family	family	NOUN
ejpam-2552	493	39	{	{	PUNCT
ejpam-2552	493	40	µpdp	µpdp	NOUN
ejpam-2552	493	41	;	;	PUNCT
ejpam-2552	493	42	p	p	PROPN
ejpam-2552	493	43	∈	∈	PROPN
ejpam-2552	493	44	n∗	n∗	PROPN
ejpam-2552	493	45	}	}	PUNCT
ejpam-2552	493	46	,	,	PUNCT
ejpam-2552	493	47	of	of	ADP
ejpam-2552	493	48	elements	element	NOUN
ejpam-2552	493	49	of	of	ADP
ejpam-2552	493	50	l(h	l(h	PROPN
ejpam-2552	493	51	)	)	PUNCT
ejpam-2552	493	52	,	,	PUNCT
ejpam-2552	493	53	is	be	AUX
ejpam-2552	493	54	summable	summable	ADJ
ejpam-2552	493	55	of	of	ADP
ejpam-2552	493	56	sum	sum	NOUN
ejpam-2552	493	57	a	a	PRON
ejpam-2552	493	58	;	;	PUNCT
ejpam-2552	493	59	d	d	X
ejpam-2552	493	60	)	)	PUNCT
ejpam-2552	493	61	imd0	imd0	NOUN
ejpam-2552	493	62	=	=	SYM
ejpam-2552	493	63	kera	kera	PROPN
ejpam-2552	493	64	;	;	PUNCT
ejpam-2552	493	65	e	e	X
ejpam-2552	493	66	)	)	PUNCT
ejpam-2552	493	67	{	{	PUNCT
ejpam-2552	493	68	dp	dp	NOUN
ejpam-2552	493	69	;	;	PUNCT
ejpam-2552	493	70	p	p	PROPN
ejpam-2552	493	71	∈	∈	PROPN
ejpam-2552	493	72	n	n	CCONJ
ejpam-2552	493	73	}	}	PUNCT
ejpam-2552	493	74	is	be	AUX
ejpam-2552	493	75	an	an	DET
ejpam-2552	493	76	orthogonal	orthogonal	ADJ
ejpam-2552	493	77	family	family	NOUN
ejpam-2552	493	78	of	of	ADP
ejpam-2552	493	79	projectors	projector	NOUN
ejpam-2552	493	80	of	of	ADP
ejpam-2552	493	81	sum	sum	NOUN
ejpam-2552	493	82	i.	i.	NOUN
ejpam-2552	493	83	with	with	ADP
ejpam-2552	493	84	these	these	DET
ejpam-2552	493	85	notation	notation	NOUN
ejpam-2552	493	86	,	,	PUNCT
ejpam-2552	493	87	we	we	PRON
ejpam-2552	493	88	can	can	AUX
ejpam-2552	493	89	write	write	VERB
ejpam-2552	493	90	the	the	DET
ejpam-2552	493	91	following	follow	VERB
ejpam-2552	493	92	result	result	NOUN
ejpam-2552	493	93	.	.	PUNCT
ejpam-2552	494	1	proposition	proposition	NOUN
ejpam-2552	494	2	5.1	5.1	NUM
ejpam-2552	494	3	.	.	PUNCT
ejpam-2552	495	1	if	if	SCONJ
ejpam-2552	495	2	,	,	PUNCT
ejpam-2552	495	3	for	for	ADP
ejpam-2552	495	4	any	any	DET
ejpam-2552	495	5	p	p	NOUN
ejpam-2552	495	6	of	of	ADP
ejpam-2552	495	7	n∗	n∗	PROPN
ejpam-2552	495	8	,	,	PUNCT
ejpam-2552	495	9	we	we	PRON
ejpam-2552	495	10	denote	denote	VERB
ejpam-2552	495	11	by	by	ADP
ejpam-2552	495	12	µp	µp	NOUN
ejpam-2552	495	13	and	and	CCONJ
ejpam-2552	495	14	dp	dp	NOUN
ejpam-2552	495	15	respectively	respectively	ADV
ejpam-2552	495	16	the	the	DET
ejpam-2552	495	17	p−th	p−th	PROPN
ejpam-2552	495	18	greatest	greatest	ADV
ejpam-2552	495	19	eigenvalue	eigenvalue	PROPN
ejpam-2552	495	20	and	and	CCONJ
ejpam-2552	495	21	the	the	DET
ejpam-2552	495	22	associated	associated	ADJ
ejpam-2552	495	23	eigenprojector	eigenprojector	NOUN
ejpam-2552	495	24	of	of	ADP
ejpam-2552	495	25	a	a	DET
ejpam-2552	495	26	,	,	PUNCT
ejpam-2552	495	27	positive	positive	ADJ
ejpam-2552	495	28	selfadjoint	selfadjoint	NOUN
ejpam-2552	495	29	operator	operator	NOUN
ejpam-2552	495	30	,	,	PUNCT
ejpam-2552	495	31	if	if	SCONJ
ejpam-2552	495	32	a.	a.	NOUN
ejpam-2552	495	33	boudou	boudou	NOUN
ejpam-2552	495	34	,	,	PUNCT
ejpam-2552	495	35	s.	s.	PROPN
ejpam-2552	495	36	viguier	viguier	PROPN
ejpam-2552	495	37	-	-	PUNCT
ejpam-2552	495	38	pla	pla	PROPN
ejpam-2552	495	39	/	/	PUNCT
ejpam-2552	495	40	eur	eur	PROPN
ejpam-2552	495	41	.	.	PUNCT
ejpam-2552	496	1	j.	j.	PROPN
ejpam-2552	496	2	pure	pure	PROPN
ejpam-2552	496	3	appl	appl	PROPN
ejpam-2552	496	4	.	.	PROPN
ejpam-2552	496	5	math	math	PROPN
ejpam-2552	496	6	,	,	PUNCT
ejpam-2552	496	7	11	11	NUM
ejpam-2552	496	8	(	(	PUNCT
ejpam-2552	496	9	4	4	NUM
ejpam-2552	496	10	)	)	PUNCT
ejpam-2552	496	11	(	(	PUNCT
ejpam-2552	496	12	2018	2018	NUM
ejpam-2552	496	13	)	)	PUNCT
ejpam-2552	496	14	,	,	PUNCT
ejpam-2552	496	15	893	893	NUM
ejpam-2552	496	16	-	-	SYM
ejpam-2552	496	17	910	910	NUM
ejpam-2552	496	18	907	907	NUM
ejpam-2552	496	19	we	we	PRON
ejpam-2552	496	20	set	set	VERB
ejpam-2552	496	21	µ0	µ0	NOUN
ejpam-2552	496	22	=	=	SYM
ejpam-2552	496	23	0	0	NUM
ejpam-2552	496	24	and	and	CCONJ
ejpam-2552	496	25	d0	d0	NOUN
ejpam-2552	496	26	=	=	PUNCT
ejpam-2552	497	1	i	i	PRON
ejpam-2552	497	2	−	−	VERB
ejpam-2552	497	3	∑	∑	INTJ
ejpam-2552	497	4	p∈n∗	p∈n∗	ADP
ejpam-2552	497	5	dp	dp	PROPN
ejpam-2552	497	6	,	,	PUNCT
ejpam-2552	497	7	then	then	ADV
ejpam-2552	497	8	,	,	PUNCT
ejpam-2552	497	9	i	i	NOUN
ejpam-2552	497	10	)	)	PUNCT
ejpam-2552	497	11	for	for	ADP
ejpam-2552	497	12	any	any	DET
ejpam-2552	497	13	b	b	PROPN
ejpam-2552	497	14	of	of	ADP
ejpam-2552	497	15	br	br	PROPN
ejpam-2552	497	16	,	,	PUNCT
ejpam-2552	497	17	{	{	PUNCT
ejpam-2552	497	18	δµp(b)dp	δµp(b)dp	ADP
ejpam-2552	497	19	;	;	PUNCT
ejpam-2552	497	20	p	p	PROPN
ejpam-2552	497	21	∈	∈	PROPN
ejpam-2552	497	22	n	n	CCONJ
ejpam-2552	497	23	}	}	PUNCT
ejpam-2552	497	24	is	be	AUX
ejpam-2552	497	25	an	an	DET
ejpam-2552	497	26	orthogonal	orthogonal	ADJ
ejpam-2552	497	27	family	family	NOUN
ejpam-2552	497	28	of	of	ADP
ejpam-2552	497	29	projectors	projector	NOUN
ejpam-2552	497	30	;	;	PUNCT
ejpam-2552	497	31	ii	ii	X
ejpam-2552	497	32	)	)	PUNCT
ejpam-2552	497	33	the	the	DET
ejpam-2552	497	34	application	application	NOUN
ejpam-2552	497	35	e	e	NOUN
ejpam-2552	497	36	:	:	PUNCT
ejpam-2552	497	37	b	b	X
ejpam-2552	497	38	∈	∈	PROPN
ejpam-2552	497	39	br	br	NOUN
ejpam-2552	497	40	7→	7→	NUM
ejpam-2552	497	41	∑	∑	PUNCT
ejpam-2552	497	42	p∈n	p∈n	VERB
ejpam-2552	497	43	δµp(b)dp	δµp(b)dp	NOUN
ejpam-2552	497	44	∈	∈	NOUN
ejpam-2552	497	45	p(h	p(h	NOUN
ejpam-2552	497	46	)	)	PUNCT
ejpam-2552	497	47	is	be	AUX
ejpam-2552	497	48	the	the	DET
ejpam-2552	497	49	bounded	bounded	ADJ
ejpam-2552	497	50	s.m	s.m	PROPN
ejpam-2552	497	51	.	.	PROPN
ejpam-2552	497	52	associated	associate	VERB
ejpam-2552	497	53	with	with	ADP
ejpam-2552	497	54	a.	a.	NOUN
ejpam-2552	497	55	proof	proof	NOUN
ejpam-2552	497	56	.	.	PUNCT
ejpam-2552	498	1	it	it	PRON
ejpam-2552	498	2	is	be	AUX
ejpam-2552	498	3	clear	clear	ADJ
ejpam-2552	498	4	that	that	SCONJ
ejpam-2552	498	5	{	{	PUNCT
ejpam-2552	498	6	dp	dp	NOUN
ejpam-2552	498	7	;	;	PUNCT
ejpam-2552	498	8	p	p	PROPN
ejpam-2552	498	9	∈	∈	PROPN
ejpam-2552	498	10	n	n	CCONJ
ejpam-2552	498	11	}	}	PUNCT
ejpam-2552	498	12	is	be	AUX
ejpam-2552	498	13	a	a	DET
ejpam-2552	498	14	family	family	NOUN
ejpam-2552	498	15	of	of	ADP
ejpam-2552	498	16	orthogonal	orthogonal	ADJ
ejpam-2552	498	17	projectors	projector	NOUN
ejpam-2552	498	18	of	of	ADP
ejpam-2552	498	19	sum	sum	NOUN
ejpam-2552	498	20	d0	d0	NOUN
ejpam-2552	498	21	+	+	PROPN
ejpam-2552	498	22	∑	∑	PROPN
ejpam-2552	498	23	p≥1dp	p≥1dp	PROPN
ejpam-2552	498	24	=	=	PUNCT
ejpam-2552	499	1	i	i	PRON
ejpam-2552	499	2	−d	−d	VERB
ejpam-2552	499	3	+	+	CCONJ
ejpam-2552	499	4	∑	∑	PROPN
ejpam-2552	499	5	n∈n	n∈n	ADJ
ejpam-2552	499	6	pn	pn	PROPN
ejpam-2552	499	7	=	=	PROPN
ejpam-2552	499	8	i.	i.	PROPN
ejpam-2552	499	9	as	as	SCONJ
ejpam-2552	499	10	(	(	PUNCT
ejpam-2552	499	11	µp)p∈n∗	µp)p∈n∗	PROPN
ejpam-2552	499	12	is	be	AUX
ejpam-2552	499	13	a	a	DET
ejpam-2552	499	14	real	real	ADJ
ejpam-2552	499	15	sequence	sequence	NOUN
ejpam-2552	499	16	which	which	PRON
ejpam-2552	499	17	strictly	strictly	ADV
ejpam-2552	499	18	converges	converge	VERB
ejpam-2552	499	19	,	,	PUNCT
ejpam-2552	499	20	lemma	lemma	PROPN
ejpam-2552	499	21	2.4.2	2.4.2	NUM
ejpam-2552	499	22	lets	let	VERB
ejpam-2552	499	23	us	we	PRON
ejpam-2552	499	24	affirm	affirm	VERB
ejpam-2552	499	25	that	that	SCONJ
ejpam-2552	499	26	a	a	X
ejpam-2552	499	27	)	)	PUNCT
ejpam-2552	499	28	for	for	ADP
ejpam-2552	499	29	any	any	DET
ejpam-2552	499	30	b	b	PROPN
ejpam-2552	499	31	of	of	ADP
ejpam-2552	499	32	br	br	PROPN
ejpam-2552	499	33	,	,	PUNCT
ejpam-2552	499	34	{	{	PUNCT
ejpam-2552	499	35	δµp(b)dp	δµp(b)dp	ADP
ejpam-2552	499	36	;	;	PUNCT
ejpam-2552	499	37	p	p	PROPN
ejpam-2552	499	38	∈	∈	PROPN
ejpam-2552	499	39	n	n	CCONJ
ejpam-2552	499	40	}	}	PUNCT
ejpam-2552	499	41	is	be	AUX
ejpam-2552	499	42	an	an	DET
ejpam-2552	499	43	orthogonal	orthogonal	ADJ
ejpam-2552	499	44	family	family	NOUN
ejpam-2552	499	45	of	of	ADP
ejpam-2552	499	46	projectors	projector	NOUN
ejpam-2552	499	47	;	;	PUNCT
ejpam-2552	499	48	b	b	X
ejpam-2552	499	49	)	)	PUNCT
ejpam-2552	499	50	the	the	DET
ejpam-2552	499	51	application	application	NOUN
ejpam-2552	499	52	e	e	NOUN
ejpam-2552	499	53	:	:	PUNCT
ejpam-2552	499	54	b	b	X
ejpam-2552	499	55	∈	∈	PROPN
ejpam-2552	499	56	br	br	NOUN
ejpam-2552	499	57	7→	7→	NUM
ejpam-2552	499	58	∑	∑	PUNCT
ejpam-2552	499	59	p∈n	p∈n	VERB
ejpam-2552	499	60	δµp(b)dp	δµp(b)dp	NOUN
ejpam-2552	499	61	∈	∈	NOUN
ejpam-2552	499	62	p(h	p(h	NOUN
ejpam-2552	499	63	)	)	PUNCT
ejpam-2552	499	64	is	be	AUX
ejpam-2552	499	65	a	a	DET
ejpam-2552	499	66	bounded	bounded	ADJ
ejpam-2552	499	67	s.m	s.m	PROPN
ejpam-2552	499	68	.	.	PROPN
ejpam-2552	499	69	;	;	PUNCT
ejpam-2552	500	1	c	c	X
ejpam-2552	500	2	)	)	PUNCT
ejpam-2552	500	3	{	{	PUNCT
ejpam-2552	500	4	µpdp	µpdp	NOUN
ejpam-2552	500	5	;	;	PUNCT
ejpam-2552	500	6	p	p	PROPN
ejpam-2552	500	7	∈	∈	PROPN
ejpam-2552	500	8	n	n	CCONJ
ejpam-2552	500	9	}	}	PUNCT
ejpam-2552	500	10	is	be	AUX
ejpam-2552	500	11	a	a	DET
ejpam-2552	500	12	family	family	NOUN
ejpam-2552	500	13	of	of	ADP
ejpam-2552	500	14	elements	element	NOUN
ejpam-2552	500	15	of	of	ADP
ejpam-2552	500	16	l(h	l(h	PROPN
ejpam-2552	500	17	)	)	PUNCT
ejpam-2552	500	18	,	,	PUNCT
ejpam-2552	500	19	of	of	ADP
ejpam-2552	500	20	sum	sum	NOUN
ejpam-2552	500	21	ej	ej	INTJ
ejpam-2552	500	22	.	.	PUNCT
ejpam-2552	501	1	to	to	PART
ejpam-2552	501	2	complete	complete	VERB
ejpam-2552	501	3	the	the	DET
ejpam-2552	501	4	proof	proof	NOUN
ejpam-2552	501	5	,	,	PUNCT
ejpam-2552	501	6	we	we	PRON
ejpam-2552	501	7	need	need	VERB
ejpam-2552	501	8	to	to	PART
ejpam-2552	501	9	verify	verify	VERB
ejpam-2552	501	10	that	that	PRON
ejpam-2552	501	11	ej	ej	PROPN
ejpam-2552	501	12	=	=	PUNCT
ejpam-2552	501	13	a	a	PROPN
ejpam-2552	501	14	,	,	PUNCT
ejpam-2552	501	15	that	that	PRON
ejpam-2552	501	16	is	be	AUX
ejpam-2552	501	17	that	that	SCONJ
ejpam-2552	501	18	the	the	DET
ejpam-2552	501	19	summable	summable	ADJ
ejpam-2552	501	20	families	family	NOUN
ejpam-2552	501	21	{	{	PUNCT
ejpam-2552	501	22	λppp	λppp	NOUN
ejpam-2552	501	23	;	;	PUNCT
ejpam-2552	501	24	p	p	PROPN
ejpam-2552	501	25	∈	∈	PROPN
ejpam-2552	501	26	n	n	CCONJ
ejpam-2552	501	27	}	}	PUNCT
ejpam-2552	501	28	and	and	CCONJ
ejpam-2552	501	29	{	{	PUNCT
ejpam-2552	501	30	µpdp	µpdp	NOUN
ejpam-2552	501	31	;	;	PUNCT
ejpam-2552	501	32	p	p	PROPN
ejpam-2552	501	33	∈	∈	PROPN
ejpam-2552	501	34	n	n	CCONJ
ejpam-2552	501	35	}	}	PUNCT
ejpam-2552	501	36	are	be	AUX
ejpam-2552	501	37	of	of	ADP
ejpam-2552	501	38	same	same	ADJ
ejpam-2552	501	39	sum	sum	NOUN
ejpam-2552	501	40	.	.	PUNCT
ejpam-2552	502	1	therefore	therefore	ADV
ejpam-2552	502	2	,	,	PUNCT
ejpam-2552	502	3	as	as	SCONJ
ejpam-2552	502	4	the	the	DET
ejpam-2552	502	5	set	set	NOUN
ejpam-2552	502	6	of	of	ADP
ejpam-2552	502	7	indices	index	NOUN
ejpam-2552	502	8	of	of	ADP
ejpam-2552	502	9	these	these	DET
ejpam-2552	502	10	families	family	NOUN
ejpam-2552	502	11	is	be	AUX
ejpam-2552	502	12	n	n	PRON
ejpam-2552	502	13	,	,	PUNCT
ejpam-2552	502	14	we	we	PRON
ejpam-2552	502	15	can	can	AUX
ejpam-2552	502	16	write	write	VERB
ejpam-2552	502	17	ej	ej	PROPN
ejpam-2552	502	18	=	=	NOUN
ejpam-2552	502	19	limn	limn	PROPN
ejpam-2552	503	1	∑n	∑n	PROPN
ejpam-2552	503	2	p=0	p=0	PROPN
ejpam-2552	503	3	µpdp	µpdp	NOUN
ejpam-2552	503	4	=	=	PUNCT
ejpam-2552	503	5	µ0d0	µ0d0	PROPN
ejpam-2552	503	6	+	+	NUM
ejpam-2552	503	7	limn	limn	ADJ
ejpam-2552	503	8	∑n	∑n	PROPN
ejpam-2552	503	9	p=1	p=1	PROPN
ejpam-2552	503	10	µpdp	µpdp	NOUN
ejpam-2552	503	11	=	=	SYM
ejpam-2552	503	12	limn	limn	PROPN
ejpam-2552	503	13	∑n	∑n	PROPN
ejpam-2552	503	14	p=1	p=1	PROPN
ejpam-2552	503	15	λn−1pn−1	λn−1pn−1	PROPN
ejpam-2552	503	16	=	=	SYM
ejpam-2552	503	17	limn	limn	ADJ
ejpam-2552	503	18	∑n−1	∑n−1	X
ejpam-2552	503	19	k=0	k=0	PROPN
ejpam-2552	503	20	λkpk	λkpk	PROPN
ejpam-2552	503	21	=	=	PUNCT
ejpam-2552	504	1	limn	limn	ADJ
ejpam-2552	504	2	∑n	∑n	PROPN
ejpam-2552	504	3	k=0	k=0	PROPN
ejpam-2552	504	4	λkpk	λkpk	VERB
ejpam-2552	504	5	=	=	SYM
ejpam-2552	504	6	a	a	NOUN
ejpam-2552	504	7	,	,	PUNCT
ejpam-2552	504	8	what	what	PRON
ejpam-2552	504	9	ends	end	VERB
ejpam-2552	504	10	the	the	DET
ejpam-2552	504	11	proof	proof	NOUN
ejpam-2552	504	12	.	.	PUNCT
ejpam-2552	505	1	�	�	PROPN
ejpam-2552	505	2	remark	remark	PROPN
ejpam-2552	505	3	.	.	PUNCT
ejpam-2552	506	1	from	from	ADP
ejpam-2552	506	2	properties	property	NOUN
ejpam-2552	506	3	of	of	ADP
ejpam-2552	506	4	a	a	DET
ejpam-2552	506	5	partition	partition	NOUN
ejpam-2552	506	6	of	of	ADP
ejpam-2552	506	7	the	the	DET
ejpam-2552	506	8	set	set	NOUN
ejpam-2552	506	9	of	of	ADP
ejpam-2552	506	10	the	the	DET
ejpam-2552	506	11	indexes	index	NOUN
ejpam-2552	506	12	of	of	ADP
ejpam-2552	506	13	a	a	DET
ejpam-2552	506	14	summable	summable	ADJ
ejpam-2552	506	15	family	family	NOUN
ejpam-2552	506	16	,	,	PUNCT
ejpam-2552	506	17	we	we	PRON
ejpam-2552	506	18	can	can	AUX
ejpam-2552	506	19	affirm	affirm	VERB
ejpam-2552	506	20	that	that	SCONJ
ejpam-2552	506	21	,	,	PUNCT
ejpam-2552	506	22	for	for	ADP
ejpam-2552	506	23	any	any	DET
ejpam-2552	506	24	b	b	PROPN
ejpam-2552	506	25	of	of	ADP
ejpam-2552	506	26	br	br	PROPN
ejpam-2552	506	27	,	,	PUNCT
ejpam-2552	506	28	the	the	DET
ejpam-2552	506	29	family	family	NOUN
ejpam-2552	506	30	{	{	PUNCT
ejpam-2552	506	31	dn;n	dn;n	VERB
ejpam-2552	506	32	∈	∈	NOUN
ejpam-2552	506	33	n	n	CCONJ
ejpam-2552	506	34	such	such	ADJ
ejpam-2552	506	35	that	that	SCONJ
ejpam-2552	506	36	µn	µn	PROPN
ejpam-2552	506	37	∈	∈	PROPN
ejpam-2552	506	38	b	b	AUX
ejpam-2552	506	39	}	}	PUNCT
ejpam-2552	506	40	is	be	AUX
ejpam-2552	506	41	summable	summable	ADJ
ejpam-2552	506	42	of	of	ADP
ejpam-2552	506	43	sum	sum	NOUN
ejpam-2552	506	44	e(b	e(b	ADJ
ejpam-2552	506	45	)	)	PUNCT
ejpam-2552	506	46	.	.	PUNCT
ejpam-2552	507	1	let	let	VERB
ejpam-2552	507	2	us	we	PRON
ejpam-2552	507	3	now	now	ADV
ejpam-2552	507	4	examine	examine	VERB
ejpam-2552	507	5	how	how	SCONJ
ejpam-2552	507	6	the	the	DET
ejpam-2552	507	7	results	result	NOUN
ejpam-2552	507	8	of	of	ADP
ejpam-2552	507	9	the	the	DET
ejpam-2552	507	10	previous	previous	ADJ
ejpam-2552	507	11	section	section	NOUN
ejpam-2552	507	12	will	will	AUX
ejpam-2552	507	13	express	express	VERB
ejpam-2552	507	14	in	in	ADP
ejpam-2552	507	15	terms	term	NOUN
ejpam-2552	507	16	of	of	ADP
ejpam-2552	507	17	eigenspaces	eigenspace	NOUN
ejpam-2552	507	18	of	of	ADP
ejpam-2552	507	19	two	two	NUM
ejpam-2552	507	20	compact	compact	ADJ
ejpam-2552	507	21	operators	operator	NOUN
ejpam-2552	507	22	.	.	PUNCT
ejpam-2552	508	1	proposition	proposition	NOUN
ejpam-2552	508	2	5.2	5.2	NUM
ejpam-2552	508	3	.	.	PUNCT
ejpam-2552	509	1	let	let	VERB
ejpam-2552	509	2	a1	a1	NOUN
ejpam-2552	509	3	and	and	CCONJ
ejpam-2552	509	4	a2	a2	PROPN
ejpam-2552	509	5	be	be	VERB
ejpam-2552	509	6	two	two	NUM
ejpam-2552	509	7	selfadjoint	selfadjoint	NOUN
ejpam-2552	509	8	compact	compact	ADJ
ejpam-2552	509	9	operators	operator	NOUN
ejpam-2552	509	10	which	which	PRON
ejpam-2552	509	11	commute	commute	VERB
ejpam-2552	509	12	.	.	PUNCT
ejpam-2552	510	1	for	for	ADP
ejpam-2552	510	2	any	any	PRON
ejpam-2552	510	3	(	(	PUNCT
ejpam-2552	510	4	i	i	NOUN
ejpam-2552	510	5	,	,	PUNCT
ejpam-2552	510	6	p	p	NOUN
ejpam-2552	510	7	)	)	PUNCT
ejpam-2552	510	8	of	of	ADP
ejpam-2552	510	9	{	{	PUNCT
ejpam-2552	510	10	1	1	NUM
ejpam-2552	510	11	,	,	PUNCT
ejpam-2552	510	12	2	2	NUM
ejpam-2552	510	13	}	}	PUNCT
ejpam-2552	510	14	×	×	NOUN
ejpam-2552	510	15	n∗	n∗	NOUN
ejpam-2552	510	16	,	,	PUNCT
ejpam-2552	510	17	let	let	VERB
ejpam-2552	510	18	us	we	PRON
ejpam-2552	510	19	denote	denote	VERB
ejpam-2552	510	20	respectively	respectively	ADV
ejpam-2552	510	21	by	by	ADP
ejpam-2552	510	22	µip	µip	NOUN
ejpam-2552	510	23	and	and	CCONJ
ejpam-2552	510	24	di	di	NOUN
ejpam-2552	510	25	p	p	PROPN
ejpam-2552	510	26	the	the	DET
ejpam-2552	510	27	p−th	p−th	PROPN
ejpam-2552	510	28	largest	large	ADJ
ejpam-2552	510	29	eigenvalue	eigenvalue	NOUN
ejpam-2552	510	30	of	of	ADP
ejpam-2552	510	31	ai	ai	NOUN
ejpam-2552	510	32	and	and	CCONJ
ejpam-2552	510	33	the	the	DET
ejpam-2552	510	34	associated	associated	ADJ
ejpam-2552	510	35	eigenprojector	eigenprojector	NOUN
ejpam-2552	510	36	.	.	PUNCT
ejpam-2552	511	1	then	then	ADV
ejpam-2552	511	2	for	for	ADP
ejpam-2552	511	3	any	any	DET
ejpam-2552	511	4	p	p	NOUN
ejpam-2552	511	5	of	of	ADP
ejpam-2552	511	6	n∗	n∗	PROPN
ejpam-2552	511	7	,	,	PUNCT
ejpam-2552	511	8	we	we	PRON
ejpam-2552	511	9	have	have	VERB
ejpam-2552	511	10	d1	d1	PROPN
ejpam-2552	511	11	p	p	PROPN
ejpam-2552	511	12	�	�	PROPN
ejpam-2552	511	13	∑	∑	PROPN
ejpam-2552	511	14	k:µ1p−α6µ2k6µ1p+α	k:µ1p−α6µ2k6µ1p+α	PROPN
ejpam-2552	511	15	d2	d2	PROPN
ejpam-2552	511	16	k	k	PROPN
ejpam-2552	511	17	�	�	PROPN
ejpam-2552	511	18	∑	∑	PUNCT
ejpam-2552	511	19	k:µ1p−2α6µ1k6µ1p+2α	k:µ1p−2α6µ1k6µ1p+2α	VERB
ejpam-2552	511	20	d1	d1	PROPN
ejpam-2552	511	21	k	k	PROPN
ejpam-2552	511	22	,	,	PUNCT
ejpam-2552	511	23	with	with	ADP
ejpam-2552	511	24	α	α	NOUN
ejpam-2552	511	25	=	=	SYM
ejpam-2552	511	26	‖a1	‖a1	NOUN
ejpam-2552	511	27	−a2‖.	−a2‖.	NOUN
ejpam-2552	511	28	proof	proof	NOUN
ejpam-2552	511	29	.	.	PUNCT
ejpam-2552	512	1	this	this	DET
ejpam-2552	512	2	proposition	proposition	NOUN
ejpam-2552	512	3	is	be	AUX
ejpam-2552	512	4	a	a	DET
ejpam-2552	512	5	direct	direct	ADJ
ejpam-2552	512	6	consequence	consequence	NOUN
ejpam-2552	512	7	of	of	ADP
ejpam-2552	512	8	proposition	proposition	NOUN
ejpam-2552	512	9	4.2	4.2	NUM
ejpam-2552	512	10	.	.	PUNCT
ejpam-2552	513	1	indeed	indeed	ADV
ejpam-2552	513	2	,	,	PUNCT
ejpam-2552	513	3	let	let	VERB
ejpam-2552	513	4	us	we	PRON
ejpam-2552	513	5	denote	denote	VERB
ejpam-2552	513	6	by	by	ADP
ejpam-2552	513	7	e1	e1	PROPN
ejpam-2552	513	8	and	and	CCONJ
ejpam-2552	513	9	e2	e2	VERB
ejpam-2552	513	10	the	the	DET
ejpam-2552	513	11	respective	respective	ADJ
ejpam-2552	513	12	bounded	bounded	ADJ
ejpam-2552	513	13	s.m	s.m	PROPN
ejpam-2552	513	14	.	.	PROPN
ejpam-2552	513	15	’s	’s	AUX
ejpam-2552	513	16	associated	associate	VERB
ejpam-2552	513	17	with	with	ADP
ejpam-2552	513	18	the	the	DET
ejpam-2552	513	19	operators	operator	NOUN
ejpam-2552	513	20	a1	a1	NOUN
ejpam-2552	513	21	and	and	CCONJ
ejpam-2552	513	22	a2	a2	PROPN
ejpam-2552	513	23	.	.	PUNCT
ejpam-2552	514	1	as	as	ADP
ejpam-2552	514	2	‖a1	‖a1	NOUN
ejpam-2552	514	3	−	−	PROPN
ejpam-2552	514	4	a2‖	a2‖	PROPN
ejpam-2552	514	5	6	6	NUM
ejpam-2552	514	6	α	α	NOUN
ejpam-2552	514	7	,	,	PUNCT
ejpam-2552	514	8	and	and	CCONJ
ejpam-2552	514	9	as	as	ADP
ejpam-2552	514	10	a1	a1	NOUN
ejpam-2552	514	11	and	and	CCONJ
ejpam-2552	514	12	a2	a2	PROPN
ejpam-2552	514	13	commute	commute	NOUN
ejpam-2552	514	14	,	,	PUNCT
ejpam-2552	514	15	we	we	PRON
ejpam-2552	514	16	have	have	AUX
ejpam-2552	514	17	e1	e1	VERB
ejpam-2552	514	18	α∼	α∼	NUM
ejpam-2552	514	19	e2	e2	NOUN
ejpam-2552	514	20	.	.	PUNCT
ejpam-2552	515	1	then	then	ADV
ejpam-2552	515	2	,	,	PUNCT
ejpam-2552	515	3	for	for	ADP
ejpam-2552	515	4	any	any	DET
ejpam-2552	515	5	p	p	NOUN
ejpam-2552	515	6	of	of	ADP
ejpam-2552	515	7	n∗	n∗	PROPN
ejpam-2552	515	8	,	,	PUNCT
ejpam-2552	515	9	e1({µ1p	e1({µ1p	ADJ
ejpam-2552	515	10	}	}	PUNCT
ejpam-2552	515	11	)	)	PUNCT
ejpam-2552	515	12	�	�	PROPN
ejpam-2552	515	13	e2([µ1p	e2([µ1p	PUNCT
ejpam-2552	515	14	−	−	NOUN
ejpam-2552	515	15	α;µ1p	α;µ1p	NOUN
ejpam-2552	515	16	+	+	CCONJ
ejpam-2552	515	17	α	α	X
ejpam-2552	515	18	]	]	X
ejpam-2552	515	19	)	)	PUNCT
ejpam-2552	515	20	�	�	PROPN
ejpam-2552	515	21	e1([µ1p	e1([µ1p	PUNCT
ejpam-2552	515	22	−	−	PROPN
ejpam-2552	515	23	2α;µ1p	2α;µ1p	NUM
ejpam-2552	515	24	+	+	SYM
ejpam-2552	515	25	2α	2α	NOUN
ejpam-2552	515	26	]	]	PUNCT
ejpam-2552	515	27	)	)	PUNCT
ejpam-2552	515	28	.	.	PUNCT
ejpam-2552	516	1	in	in	ADP
ejpam-2552	516	2	other	other	ADJ
ejpam-2552	516	3	terms	term	NOUN
ejpam-2552	516	4	,	,	PUNCT
ejpam-2552	516	5	taking	take	VERB
ejpam-2552	516	6	into	into	ADP
ejpam-2552	516	7	account	account	NOUN
ejpam-2552	516	8	the	the	DET
ejpam-2552	516	9	previous	previous	ADJ
ejpam-2552	516	10	remark	remark	NOUN
ejpam-2552	516	11	:	:	PUNCT
ejpam-2552	516	12	d1	d1	PROPN
ejpam-2552	516	13	p	p	PROPN
ejpam-2552	516	14	�	�	PROPN
ejpam-2552	516	15	∑	∑	PROPN
ejpam-2552	516	16	k:µ1p−α6µ2k6µ1p+α	k:µ1p−α6µ2k6µ1p+α	PROPN
ejpam-2552	516	17	d2	d2	PROPN
ejpam-2552	516	18	k	k	PROPN
ejpam-2552	516	19	�	�	PROPN
ejpam-2552	516	20	∑	∑	PROPN
ejpam-2552	516	21	k:µ1p−2α6µ1k6µ1p+2αd	k:µ1p−2α6µ1k6µ1p+2αd	PROPN
ejpam-2552	516	22	1	1	NUM
ejpam-2552	516	23	k.	k.	PROPN
ejpam-2552	516	24	�	�	PROPN
ejpam-2552	516	25	of	of	ADP
ejpam-2552	516	26	course	course	NOUN
ejpam-2552	516	27	,	,	PUNCT
ejpam-2552	516	28	if	if	SCONJ
ejpam-2552	516	29	a1	a1	NOUN
ejpam-2552	516	30	and	and	CCONJ
ejpam-2552	516	31	a2	a2	PROPN
ejpam-2552	516	32	are	be	AUX
ejpam-2552	516	33	close	close	ADJ
ejpam-2552	516	34	enough	enough	ADJ
ejpam-2552	516	35	such	such	ADJ
ejpam-2552	516	36	that	that	SCONJ
ejpam-2552	516	37	in	in	ADP
ejpam-2552	516	38	the	the	DET
ejpam-2552	516	39	interval	interval	NOUN
ejpam-2552	516	40	[	[	X
ejpam-2552	516	41	µ1p	µ1p	SYM
ejpam-2552	516	42	−	−	PROPN
ejpam-2552	516	43	2α;µ1p	2α;µ1p	NUM
ejpam-2552	516	44	+	+	NOUN
ejpam-2552	516	45	2α	2α	NOUN
ejpam-2552	516	46	]	]	PUNCT
ejpam-2552	516	47	there	there	PRON
ejpam-2552	516	48	is	be	VERB
ejpam-2552	516	49	no	no	DET
ejpam-2552	516	50	other	other	ADJ
ejpam-2552	516	51	eigenvalue	eigenvalue	NOUN
ejpam-2552	516	52	of	of	ADP
ejpam-2552	516	53	a1	a1	NOUN
ejpam-2552	516	54	than	than	ADP
ejpam-2552	516	55	µ1p	µ1p	PROPN
ejpam-2552	516	56	,	,	PUNCT
ejpam-2552	516	57	then	then	ADV
ejpam-2552	516	58	we	we	PRON
ejpam-2552	516	59	have	have	VERB
ejpam-2552	516	60	the	the	DET
ejpam-2552	516	61	following	following	NOUN
ejpam-2552	516	62	.	.	PUNCT
ejpam-2552	517	1	corollary	corollary	ADJ
ejpam-2552	517	2	5.1	5.1	NUM
ejpam-2552	517	3	.	.	PUNCT
ejpam-2552	518	1	let	let	VERB
ejpam-2552	518	2	a1	a1	NOUN
ejpam-2552	518	3	and	and	CCONJ
ejpam-2552	518	4	a2	a2	PROPN
ejpam-2552	518	5	be	be	VERB
ejpam-2552	518	6	two	two	NUM
ejpam-2552	518	7	selfadjoint	selfadjoint	NOUN
ejpam-2552	518	8	compact	compact	ADJ
ejpam-2552	518	9	operators	operator	NOUN
ejpam-2552	518	10	which	which	PRON
ejpam-2552	518	11	commute	commute	VERB
ejpam-2552	518	12	.	.	PUNCT
ejpam-2552	519	1	let	let	VERB
ejpam-2552	519	2	α	α	NOUN
ejpam-2552	519	3	=	=	PUNCT
ejpam-2552	519	4	‖a1	‖a1	NOUN
ejpam-2552	519	5	−a2‖	−a2‖	PROPN
ejpam-2552	519	6	and	and	CCONJ
ejpam-2552	519	7	,	,	PUNCT
ejpam-2552	519	8	for	for	ADP
ejpam-2552	519	9	any	any	PRON
ejpam-2552	519	10	(	(	PUNCT
ejpam-2552	519	11	i	i	NOUN
ejpam-2552	519	12	,	,	PUNCT
ejpam-2552	519	13	p	p	NOUN
ejpam-2552	519	14	)	)	PUNCT
ejpam-2552	519	15	of	of	ADP
ejpam-2552	519	16	{	{	PUNCT
ejpam-2552	519	17	1	1	NUM
ejpam-2552	519	18	,	,	PUNCT
ejpam-2552	519	19	2	2	NUM
ejpam-2552	519	20	}	}	PUNCT
ejpam-2552	519	21	×	×	NOUN
ejpam-2552	519	22	n∗	n∗	NOUN
ejpam-2552	519	23	,	,	PUNCT
ejpam-2552	519	24	let	let	VERB
ejpam-2552	519	25	us	we	PRON
ejpam-2552	519	26	denote	denote	VERB
ejpam-2552	519	27	respectively	respectively	ADV
ejpam-2552	519	28	by	by	ADP
ejpam-2552	519	29	µip	µip	NOUN
ejpam-2552	519	30	and	and	CCONJ
ejpam-2552	519	31	di	di	NOUN
ejpam-2552	519	32	p	p	PROPN
ejpam-2552	519	33	the	the	DET
ejpam-2552	519	34	p−th	p−th	PROPN
ejpam-2552	519	35	largest	large	ADJ
ejpam-2552	519	36	eigenvalue	eigenvalue	NOUN
ejpam-2552	519	37	of	of	ADP
ejpam-2552	519	38	ai	ai	NOUN
ejpam-2552	519	39	and	and	CCONJ
ejpam-2552	519	40	the	the	DET
ejpam-2552	519	41	associated	associated	ADJ
ejpam-2552	519	42	eigenprojector	eigenprojector	NOUN
ejpam-2552	519	43	.	.	PUNCT
ejpam-2552	520	1	we	we	PRON
ejpam-2552	520	2	can	can	AUX
ejpam-2552	520	3	affirm	affirm	VERB
ejpam-2552	520	4	a.	a.	NOUN
ejpam-2552	520	5	boudou	boudou	NOUN
ejpam-2552	520	6	,	,	PUNCT
ejpam-2552	520	7	s.	s.	PROPN
ejpam-2552	520	8	viguier	viguier	PROPN
ejpam-2552	520	9	-	-	PUNCT
ejpam-2552	520	10	pla	pla	PROPN
ejpam-2552	520	11	/	/	PUNCT
ejpam-2552	520	12	eur	eur	PROPN
ejpam-2552	520	13	.	.	PUNCT
ejpam-2552	521	1	j.	j.	PROPN
ejpam-2552	521	2	pure	pure	PROPN
ejpam-2552	521	3	appl	appl	PROPN
ejpam-2552	521	4	.	.	PROPN
ejpam-2552	521	5	math	math	PROPN
ejpam-2552	521	6	,	,	PUNCT
ejpam-2552	521	7	11	11	NUM
ejpam-2552	521	8	(	(	PUNCT
ejpam-2552	521	9	4	4	NUM
ejpam-2552	521	10	)	)	PUNCT
ejpam-2552	521	11	(	(	PUNCT
ejpam-2552	521	12	2018	2018	NUM
ejpam-2552	521	13	)	)	PUNCT
ejpam-2552	521	14	,	,	PUNCT
ejpam-2552	521	15	893	893	NUM
ejpam-2552	521	16	-	-	SYM
ejpam-2552	521	17	910	910	NUM
ejpam-2552	521	18	908	908	NUM
ejpam-2552	522	1	that	that	SCONJ
ejpam-2552	522	2	if	if	SCONJ
ejpam-2552	522	3	µ11	µ11	NOUN
ejpam-2552	522	4	−	−	PROPN
ejpam-2552	522	5	µ12	µ12	PROPN
ejpam-2552	522	6	>	>	X
ejpam-2552	522	7	2α	2α	NOUN
ejpam-2552	522	8	,	,	PUNCT
ejpam-2552	522	9	then	then	ADV
ejpam-2552	522	10	d1	d1	PROPN
ejpam-2552	522	11	1	1	NUM
ejpam-2552	522	12	=	=	SYM
ejpam-2552	522	13	∑	∑	PUNCT
ejpam-2552	522	14	k:µ1p−α6µ2k6µ1p+α	k:µ1p−α6µ2k6µ1p+α	PROPN
ejpam-2552	522	15	d2	d2	PROPN
ejpam-2552	522	16	k.	k.	PROPN
ejpam-2552	522	17	moreover	moreover	ADV
ejpam-2552	522	18	,	,	PUNCT
ejpam-2552	522	19	for	for	ADP
ejpam-2552	522	20	any	any	DET
ejpam-2552	522	21	integer	integer	NOUN
ejpam-2552	522	22	p	p	X
ejpam-2552	522	23	≥	≥	NUM
ejpam-2552	522	24	2	2	NUM
ejpam-2552	522	25	,	,	PUNCT
ejpam-2552	522	26	if	if	SCONJ
ejpam-2552	522	27	µ1p−1	µ1p−1	ADJ
ejpam-2552	522	28	−	−	NOUN
ejpam-2552	522	29	µ1p	µ1p	PUNCT
ejpam-2552	522	30	>	>	X
ejpam-2552	522	31	2α	2α	NOUN
ejpam-2552	522	32	and	and	CCONJ
ejpam-2552	522	33	if	if	SCONJ
ejpam-2552	522	34	µ1p	µ1p	PUNCT
ejpam-2552	522	35	−	−	PUNCT
ejpam-2552	522	36	µ1p+1	µ1p+1	NOUN
ejpam-2552	522	37	>	>	X
ejpam-2552	522	38	2α	2α	NOUN
ejpam-2552	522	39	,	,	PUNCT
ejpam-2552	522	40	we	we	PRON
ejpam-2552	522	41	have	have	VERB
ejpam-2552	522	42	d1	d1	PROPN
ejpam-2552	522	43	p	p	NOUN
ejpam-2552	522	44	=	=	PUNCT
ejpam-2552	522	45	∑	∑	PROPN
ejpam-2552	522	46	k:µ1p−α6µ2k<µ1p6α	k:µ1p−α6µ2k<µ1p6α	PROPN
ejpam-2552	522	47	d2	d2	PROPN
ejpam-2552	522	48	k.	k.	PROPN
ejpam-2552	522	49	proof	proof	PROPN
ejpam-2552	522	50	.	.	PUNCT
ejpam-2552	523	1	it	it	PRON
ejpam-2552	523	2	is	be	AUX
ejpam-2552	523	3	enough	enough	ADJ
ejpam-2552	523	4	to	to	PART
ejpam-2552	523	5	notice	notice	VERB
ejpam-2552	523	6	that	that	SCONJ
ejpam-2552	523	7	if	if	SCONJ
ejpam-2552	523	8	µ11	µ11	NOUN
ejpam-2552	523	9	−	−	PROPN
ejpam-2552	523	10	µ12	µ12	PROPN
ejpam-2552	523	11	>	>	X
ejpam-2552	523	12	2α	2α	NOUN
ejpam-2552	523	13	,	,	PUNCT
ejpam-2552	523	14	then	then	ADV
ejpam-2552	523	15	{	{	PUNCT
ejpam-2552	523	16	k	k	PROPN
ejpam-2552	523	17	∈	∈	PROPN
ejpam-2552	523	18	n;µ11	n;µ11	PUNCT
ejpam-2552	524	1	−	−	NOUN
ejpam-2552	524	2	2α	2α	NOUN
ejpam-2552	524	3	6	6	NUM
ejpam-2552	524	4	µ1k	µ1k	SYM
ejpam-2552	524	5	6	6	NUM
ejpam-2552	524	6	µ11	µ11	NOUN
ejpam-2552	524	7	+	+	CCONJ
ejpam-2552	524	8	2α	2α	NOUN
ejpam-2552	524	9	}	}	PUNCT
ejpam-2552	524	10	=	=	PUNCT
ejpam-2552	524	11	{	{	PUNCT
ejpam-2552	524	12	1	1	NUM
ejpam-2552	524	13	}	}	PUNCT
ejpam-2552	524	14	and	and	CCONJ
ejpam-2552	524	15	then	then	ADV
ejpam-2552	524	16	∑	∑	PUNCT
ejpam-2552	524	17	k:µ1p−α6µ1k<µ1p6α	k:µ1p−α6µ1k<µ1p6α	PROPN
ejpam-2552	524	18	d1	d1	PROPN
ejpam-2552	524	19	k	k	PROPN
ejpam-2552	525	1	=	=	PUNCT
ejpam-2552	525	2	d1	d1	PROPN
ejpam-2552	525	3	1	1	NUM
ejpam-2552	525	4	,	,	PUNCT
ejpam-2552	525	5	so	so	CCONJ
ejpam-2552	525	6	the	the	DET
ejpam-2552	525	7	first	first	ADJ
ejpam-2552	525	8	point	point	NOUN
ejpam-2552	525	9	is	be	AUX
ejpam-2552	525	10	proved	prove	VERB
ejpam-2552	525	11	,	,	PUNCT
ejpam-2552	525	12	thanks	thank	NOUN
ejpam-2552	525	13	to	to	PART
ejpam-2552	525	14	proposition	proposition	VERB
ejpam-2552	525	15	5.2	5.2	NUM
ejpam-2552	525	16	.	.	PUNCT
ejpam-2552	526	1	the	the	DET
ejpam-2552	526	2	proof	proof	NOUN
ejpam-2552	526	3	of	of	ADP
ejpam-2552	526	4	the	the	DET
ejpam-2552	526	5	second	second	ADJ
ejpam-2552	526	6	point	point	NOUN
ejpam-2552	526	7	is	be	AUX
ejpam-2552	526	8	analog	analog	ADJ
ejpam-2552	526	9	if	if	SCONJ
ejpam-2552	526	10	we	we	PRON
ejpam-2552	526	11	remark	remark	VERB
ejpam-2552	526	12	that	that	SCONJ
ejpam-2552	526	13	,	,	PUNCT
ejpam-2552	526	14	from	from	ADP
ejpam-2552	526	15	hypotheses	hypothesis	NOUN
ejpam-2552	526	16	,	,	PUNCT
ejpam-2552	526	17	we	we	PRON
ejpam-2552	526	18	have	have	VERB
ejpam-2552	526	19	{	{	PUNCT
ejpam-2552	526	20	k	k	PROPN
ejpam-2552	526	21	∈	∈	PROPN
ejpam-2552	526	22	n;µ1p	n;µ1p	PROPN
ejpam-2552	526	23	−	−	PROPN
ejpam-2552	526	24	2α	2α	PROPN
ejpam-2552	526	25	6	6	NUM
ejpam-2552	526	26	µ1k	µ1k	SYM
ejpam-2552	526	27	6	6	NUM
ejpam-2552	526	28	µ	µ	DET
ejpam-2552	526	29	1	1	NUM
ejpam-2552	526	30	p	p	NOUN
ejpam-2552	526	31	+	+	NOUN
ejpam-2552	526	32	2α	2α	NOUN
ejpam-2552	526	33	}	}	PUNCT
ejpam-2552	526	34	=	=	PUNCT
ejpam-2552	526	35	{	{	PUNCT
ejpam-2552	526	36	p	p	X
ejpam-2552	526	37	}	}	PUNCT
ejpam-2552	526	38	.	.	PUNCT
ejpam-2552	527	1	�	�	PROPN
ejpam-2552	527	2	remark	remark	PROPN
ejpam-2552	527	3	.	.	PUNCT
ejpam-2552	528	1	there	there	PRON
ejpam-2552	528	2	exists	exist	VERB
ejpam-2552	528	3	at	at	ADP
ejpam-2552	528	4	least	least	ADV
ejpam-2552	528	5	one	one	NUM
ejpam-2552	528	6	eigenvalue	eigenvalue	NOUN
ejpam-2552	528	7	,	,	PUNCT
ejpam-2552	528	8	of	of	ADP
ejpam-2552	528	9	a2	a2	PROPN
ejpam-2552	528	10	,	,	PUNCT
ejpam-2552	528	11	which	which	PRON
ejpam-2552	528	12	belongs	belong	VERB
ejpam-2552	528	13	to	to	ADP
ejpam-2552	528	14	[	[	X
ejpam-2552	528	15	µ1p−α	µ1p−α	PROPN
ejpam-2552	528	16	,	,	PUNCT
ejpam-2552	528	17	µ1p	µ1p	X
ejpam-2552	528	18	+	+	NOUN
ejpam-2552	528	19	α	α	NOUN
ejpam-2552	528	20	]	]	X
ejpam-2552	528	21	.	.	PUNCT
ejpam-2552	529	1	6	6	NUM
ejpam-2552	529	2	.	.	X
ejpam-2552	529	3	numerical	numerical	ADJ
ejpam-2552	529	4	illustration	illustration	NOUN
ejpam-2552	529	5	let	let	VERB
ejpam-2552	529	6	{	{	PUNCT
ejpam-2552	529	7	pj	pj	PROPN
ejpam-2552	529	8	,	,	PUNCT
ejpam-2552	529	9	j	j	PROPN
ejpam-2552	529	10	=	=	NOUN
ejpam-2552	529	11	1	1	NUM
ejpam-2552	529	12	,	,	PUNCT
ejpam-2552	529	13	.	.	PUNCT
ejpam-2552	529	14	.	.	PUNCT
ejpam-2552	529	15	.	.	PUNCT
ejpam-2552	530	1	,	,	PUNCT
ejpam-2552	530	2	k	k	X
ejpam-2552	530	3	}	}	PUNCT
ejpam-2552	530	4	be	be	AUX
ejpam-2552	530	5	a	a	DET
ejpam-2552	530	6	set	set	NOUN
ejpam-2552	530	7	of	of	ADP
ejpam-2552	530	8	orthogonal	orthogonal	ADJ
ejpam-2552	530	9	projectors	projector	NOUN
ejpam-2552	530	10	from	from	ADP
ejpam-2552	530	11	rp	rp	NOUN
ejpam-2552	530	12	into	into	ADP
ejpam-2552	530	13	rp	rp	NOUN
ejpam-2552	530	14	,	,	PUNCT
ejpam-2552	530	15	{	{	PUNCT
ejpam-2552	530	16	λj	λj	PROPN
ejpam-2552	530	17	,	,	PUNCT
ejpam-2552	530	18	j	j	PROPN
ejpam-2552	531	1	=	=	SYM
ejpam-2552	531	2	1	1	NUM
ejpam-2552	531	3	,	,	PUNCT
ejpam-2552	531	4	.	.	PUNCT
ejpam-2552	531	5	.	.	PUNCT
ejpam-2552	532	1	.	.	PUNCT
ejpam-2552	533	1	,	,	PUNCT
ejpam-2552	533	2	k	k	X
ejpam-2552	533	3	}	}	PUNCT
ejpam-2552	533	4	be	be	AUX
ejpam-2552	533	5	a	a	DET
ejpam-2552	533	6	set	set	NOUN
ejpam-2552	533	7	of	of	ADP
ejpam-2552	533	8	real	real	ADJ
ejpam-2552	533	9	values	value	NOUN
ejpam-2552	533	10	,	,	PUNCT
ejpam-2552	533	11	and	and	CCONJ
ejpam-2552	533	12	,	,	PUNCT
ejpam-2552	533	13	for	for	ADP
ejpam-2552	533	14	any	any	DET
ejpam-2552	533	15	j	j	PROPN
ejpam-2552	533	16	of	of	ADP
ejpam-2552	533	17	{	{	PUNCT
ejpam-2552	533	18	1	1	NUM
ejpam-2552	533	19	,	,	PUNCT
ejpam-2552	533	20	.	.	PUNCT
ejpam-2552	533	21	.	.	PUNCT
ejpam-2552	534	1	.	.	PUNCT
ejpam-2552	535	1	,	,	PUNCT
ejpam-2552	535	2	k	k	X
ejpam-2552	535	3	}	}	PUNCT
ejpam-2552	535	4	,	,	PUNCT
ejpam-2552	535	5	(	(	PUNCT
ejpam-2552	535	6	λjn)n∈n	λjn)n∈n	PART
ejpam-2552	535	7	be	be	AUX
ejpam-2552	535	8	a	a	DET
ejpam-2552	535	9	sequence	sequence	NOUN
ejpam-2552	535	10	of	of	ADP
ejpam-2552	535	11	real	real	ADJ
ejpam-2552	535	12	values	value	NOUN
ejpam-2552	535	13	converging	converge	VERB
ejpam-2552	535	14	to	to	ADP
ejpam-2552	535	15	λj	λj	PROPN
ejpam-2552	535	16	.	.	PUNCT
ejpam-2552	536	1	then	then	ADV
ejpam-2552	536	2	,	,	PUNCT
ejpam-2552	536	3	the	the	DET
ejpam-2552	536	4	sequence	sequence	NOUN
ejpam-2552	536	5	of	of	ADP
ejpam-2552	536	6	the	the	DET
ejpam-2552	536	7	selfadjoint	selfadjoint	NOUN
ejpam-2552	536	8	operators	operator	NOUN
ejpam-2552	536	9	(	(	PUNCT
ejpam-2552	536	10	an)n∈n	an)n∈n	PROPN
ejpam-2552	536	11	,	,	PUNCT
ejpam-2552	536	12	where	where	SCONJ
ejpam-2552	536	13	an	an	DET
ejpam-2552	536	14	=	=	SYM
ejpam-2552	536	15	∑k	∑k	PROPN
ejpam-2552	536	16	j=1	j=1	PROPN
ejpam-2552	536	17	λ	λ	X
ejpam-2552	536	18	j	j	PROPN
ejpam-2552	536	19	npj	npj	PROPN
ejpam-2552	536	20	,	,	PUNCT
ejpam-2552	536	21	converges	converge	VERB
ejpam-2552	536	22	to	to	ADP
ejpam-2552	536	23	the	the	DET
ejpam-2552	536	24	selfadjoint	selfadjoint	NOUN
ejpam-2552	536	25	operator	operator	NOUN
ejpam-2552	536	26	a	a	DET
ejpam-2552	536	27	=	=	PUNCT
ejpam-2552	536	28	∑k	∑k	PROPN
ejpam-2552	536	29	j=1	j=1	PROPN
ejpam-2552	536	30	λjpj	λjpj	NOUN
ejpam-2552	536	31	.	.	PUNCT
ejpam-2552	537	1	each	each	PRON
ejpam-2552	537	2	an	an	DET
ejpam-2552	537	3	obviously	obviously	ADV
ejpam-2552	537	4	commutes	commute	NOUN
ejpam-2552	537	5	with	with	ADP
ejpam-2552	537	6	a.	a.	NOUN
ejpam-2552	538	1	so	so	ADV
ejpam-2552	538	2	(	(	PUNCT
ejpam-2552	538	3	(	(	PUNCT
ejpam-2552	538	4	eitan)t∈r	eitan)t∈r	NOUN
ejpam-2552	538	5	)	)	PUNCT
ejpam-2552	538	6	n∈n	n∈n	NOUN
ejpam-2552	538	7	is	be	AUX
ejpam-2552	538	8	a	a	DET
ejpam-2552	538	9	sequence	sequence	NOUN
ejpam-2552	538	10	of	of	ADP
ejpam-2552	538	11	sets	set	NOUN
ejpam-2552	538	12	of	of	ADP
ejpam-2552	538	13	unitary	unitary	ADJ
ejpam-2552	538	14	operators	operator	NOUN
ejpam-2552	538	15	which	which	PRON
ejpam-2552	538	16	converges	converge	VERB
ejpam-2552	538	17	to	to	ADP
ejpam-2552	538	18	(	(	PUNCT
ejpam-2552	538	19	eita)t∈r	eita)t∈r	NOUN
ejpam-2552	538	20	.	.	PUNCT
ejpam-2552	539	1	if	if	SCONJ
ejpam-2552	539	2	x	x	PRON
ejpam-2552	539	3	is	be	AUX
ejpam-2552	539	4	a	a	DET
ejpam-2552	539	5	random	random	ADJ
ejpam-2552	539	6	vector	vector	NOUN
ejpam-2552	539	7	which	which	PRON
ejpam-2552	539	8	takes	take	VERB
ejpam-2552	539	9	values	value	NOUN
ejpam-2552	539	10	in	in	ADP
ejpam-2552	539	11	rp	rp	NOUN
ejpam-2552	539	12	,	,	PUNCT
ejpam-2552	539	13	yn	yn	PROPN
ejpam-2552	539	14	=	=	PUNCT
ejpam-2552	539	15	re	re	PROPN
ejpam-2552	539	16	(	(	PUNCT
ejpam-2552	539	17	(	(	PUNCT
ejpam-2552	539	18	(	(	PUNCT
ejpam-2552	539	19	eitan)x	eitan)x	ADJ
ejpam-2552	539	20	)	)	PUNCT
ejpam-2552	539	21	t∈r	t∈r	NOUN
ejpam-2552	539	22	)	)	PUNCT
ejpam-2552	539	23	,	,	PUNCT
ejpam-2552	539	24	where	where	SCONJ
ejpam-2552	539	25	re	re	NOUN
ejpam-2552	539	26	stands	stand	VERB
ejpam-2552	539	27	for	for	ADP
ejpam-2552	539	28	the	the	DET
ejpam-2552	539	29	real	real	ADJ
ejpam-2552	539	30	part	part	NOUN
ejpam-2552	539	31	,	,	PUNCT
ejpam-2552	539	32	is	be	AUX
ejpam-2552	539	33	a	a	DET
ejpam-2552	539	34	continuous	continuous	ADJ
ejpam-2552	539	35	random	random	ADJ
ejpam-2552	539	36	function	function	NOUN
ejpam-2552	539	37	,	,	PUNCT
ejpam-2552	539	38	and	and	CCONJ
ejpam-2552	539	39	the	the	DET
ejpam-2552	539	40	sequence	sequence	NOUN
ejpam-2552	539	41	(	(	PUNCT
ejpam-2552	539	42	yn)n∈n	yn)n∈n	NUM
ejpam-2552	539	43	converges	converge	VERB
ejpam-2552	539	44	to	to	ADP
ejpam-2552	539	45	the	the	DET
ejpam-2552	539	46	continuous	continuous	ADJ
ejpam-2552	539	47	random	random	ADJ
ejpam-2552	539	48	function	function	NOUN
ejpam-2552	540	1	y	y	PROPN
ejpam-2552	540	2	=	=	SYM
ejpam-2552	540	3	re	re	PROPN
ejpam-2552	540	4	(	(	PUNCT
ejpam-2552	540	5	(	(	PUNCT
ejpam-2552	540	6	(	(	PUNCT
ejpam-2552	540	7	eita)x	eita)x	PROPN
ejpam-2552	540	8	)	)	PUNCT
ejpam-2552	540	9	t∈r	t∈r	NOUN
ejpam-2552	540	10	)	)	PUNCT
ejpam-2552	540	11	.	.	PUNCT
ejpam-2552	541	1	the	the	DET
ejpam-2552	541	2	associated	associated	PROPN
ejpam-2552	541	3	s.m	s.m	PROPN
ejpam-2552	541	4	.	.	PROPN
ejpam-2552	541	5	of	of	ADP
ejpam-2552	541	6	this	this	DET
ejpam-2552	541	7	last	last	ADJ
ejpam-2552	541	8	c.r.f	c.r.f	NOUN
ejpam-2552	541	9	.	.	PUNCT
ejpam-2552	541	10	is	be	AUX
ejpam-2552	541	11	e	e	PROPN
ejpam-2552	541	12	=	=	SYM
ejpam-2552	541	13	∑k	∑k	PROPN
ejpam-2552	541	14	j=1	j=1	PROPN
ejpam-2552	541	15	δλj	δλj	VERB
ejpam-2552	541	16	(	(	PUNCT
ejpam-2552	541	17	.)pjx	.)pjx	NOUN
ejpam-2552	541	18	,	,	PUNCT
ejpam-2552	541	19	and	and	CCONJ
ejpam-2552	541	20	the	the	DET
ejpam-2552	541	21	r.m	r.m	PROPN
ejpam-2552	541	22	.	.	PROPN
ejpam-2552	541	23	is	be	AUX
ejpam-2552	541	24	µzx	µzx	ADJ
ejpam-2552	541	25	=	=	SYM
ejpam-2552	541	26	∑k	∑k	PROPN
ejpam-2552	541	27	j=1	j=1	NOUN
ejpam-2552	541	28	δλj	δλj	VERB
ejpam-2552	541	29	(	(	PUNCT
ejpam-2552	541	30	.)‖pjx‖2	.)‖pjx‖2	ADJ
ejpam-2552	541	31	.	.	PUNCT
ejpam-2552	542	1	in	in	ADP
ejpam-2552	542	2	order	order	NOUN
ejpam-2552	542	3	to	to	PART
ejpam-2552	542	4	give	give	VERB
ejpam-2552	542	5	a	a	DET
ejpam-2552	542	6	simple	simple	ADJ
ejpam-2552	542	7	graph	graph	NOUN
ejpam-2552	542	8	illustration	illustration	NOUN
ejpam-2552	542	9	,	,	PUNCT
ejpam-2552	542	10	we	we	PRON
ejpam-2552	542	11	consider	consider	VERB
ejpam-2552	542	12	here	here	ADV
ejpam-2552	542	13	the	the	DET
ejpam-2552	542	14	case	case	NOUN
ejpam-2552	542	15	where	where	SCONJ
ejpam-2552	542	16	p	p	NOUN
ejpam-2552	542	17	=	=	NOUN
ejpam-2552	542	18	2	2	NUM
ejpam-2552	542	19	,	,	PUNCT
ejpam-2552	542	20	and	and	CCONJ
ejpam-2552	542	21	compute	compute	VERB
ejpam-2552	542	22	simulated	simulate	VERB
ejpam-2552	542	23	sequences	sequence	NOUN
ejpam-2552	542	24	of	of	ADP
ejpam-2552	542	25	yn	yn	PROPN
ejpam-2552	542	26	,	,	PUNCT
ejpam-2552	542	27	with	with	ADP
ejpam-2552	542	28	x	x	PRON
ejpam-2552	542	29	randomized	randomize	VERB
ejpam-2552	542	30	from	from	ADP
ejpam-2552	542	31	the	the	DET
ejpam-2552	542	32	normalized	normalize	VERB
ejpam-2552	542	33	gaussian	gaussian	ADJ
ejpam-2552	542	34	distribution	distribution	NOUN
ejpam-2552	542	35	,	,	PUNCT
ejpam-2552	542	36	(	(	PUNCT
ejpam-2552	542	37	λ1	λ1	ADJ
ejpam-2552	542	38	,	,	PUNCT
ejpam-2552	542	39	λ2	λ2	NOUN
ejpam-2552	542	40	)	)	PUNCT
ejpam-2552	542	41	=	=	SYM
ejpam-2552	542	42	(	(	PUNCT
ejpam-2552	542	43	0.4	0.4	NUM
ejpam-2552	542	44	,	,	PUNCT
ejpam-2552	542	45	2	2	NUM
ejpam-2552	542	46	)	)	PUNCT
ejpam-2552	542	47	,	,	PUNCT
ejpam-2552	542	48	and	and	CCONJ
ejpam-2552	542	49	(	(	PUNCT
ejpam-2552	542	50	λ1n	λ1n	PROPN
ejpam-2552	542	51	,	,	PUNCT
ejpam-2552	542	52	λ	λ	PROPN
ejpam-2552	542	53	2	2	NUM
ejpam-2552	542	54	n	n	CCONJ
ejpam-2552	542	55	)	)	PUNCT
ejpam-2552	542	56	=	=	PUNCT
ejpam-2552	542	57	(	(	PUNCT
ejpam-2552	542	58	0.4	0.4	NUM
ejpam-2552	542	59	+	+	CCONJ
ejpam-2552	542	60	1/2n	1/2n	NUM
ejpam-2552	542	61	,	,	PUNCT
ejpam-2552	542	62	2−	2−	NUM
ejpam-2552	542	63	1	1	NUM
ejpam-2552	542	64	/	/	SYM
ejpam-2552	542	65	n	n	CCONJ
ejpam-2552	542	66	)	)	PUNCT
ejpam-2552	542	67	.	.	PUNCT
ejpam-2552	543	1	references	reference	NOUN
ejpam-2552	543	2	909	909	NUM
ejpam-2552	543	3	figure	figure	NOUN
ejpam-2552	543	4	1	1	NUM
ejpam-2552	543	5	:	:	PUNCT
ejpam-2552	543	6	variations	variation	NOUN
ejpam-2552	543	7	of	of	ADP
ejpam-2552	543	8	yn(t	yn(t	PROPN
ejpam-2552	543	9	)	)	PUNCT
ejpam-2552	543	10	for	for	ADP
ejpam-2552	543	11	three	three	NUM
ejpam-2552	543	12	values	value	NOUN
ejpam-2552	543	13	of	of	ADP
ejpam-2552	543	14	n	n	CCONJ
ejpam-2552	543	15	,	,	PUNCT
ejpam-2552	543	16	t	t	NOUN
ejpam-2552	543	17	varying	varying	NOUN
ejpam-2552	543	18	,	,	PUNCT
ejpam-2552	543	19	in	in	ADP
ejpam-2552	543	20	regard	regard	NOUN
ejpam-2552	543	21	with	with	ADP
ejpam-2552	543	22	the	the	DET
ejpam-2552	543	23	limit	limit	NOUN
ejpam-2552	543	24	process	process	NOUN
ejpam-2552	543	25	y	y	PROPN
ejpam-2552	543	26	(	(	PUNCT
ejpam-2552	543	27	t	t	PROPN
ejpam-2552	543	28	)	)	PUNCT
ejpam-2552	543	29	figure	figure	NOUN
ejpam-2552	543	30	2	2	NUM
ejpam-2552	543	31	:	:	PUNCT
ejpam-2552	543	32	variations	variation	NOUN
ejpam-2552	543	33	of	of	ADP
ejpam-2552	543	34	yn(t	yn(t	PROPN
ejpam-2552	543	35	)	)	PUNCT
ejpam-2552	543	36	for	for	ADP
ejpam-2552	543	37	two	two	NUM
ejpam-2552	543	38	values	value	NOUN
ejpam-2552	543	39	of	of	ADP
ejpam-2552	543	40	t	t	PROPN
ejpam-2552	543	41	,	,	PUNCT
ejpam-2552	543	42	n	n	DET
ejpam-2552	543	43	varying	vary	VERB
ejpam-2552	543	44	,	,	PUNCT
ejpam-2552	543	45	in	in	ADP
ejpam-2552	543	46	regard	regard	NOUN
ejpam-2552	543	47	with	with	ADP
ejpam-2552	543	48	the	the	DET
ejpam-2552	543	49	limit	limit	NOUN
ejpam-2552	543	50	value	value	NOUN
ejpam-2552	543	51	y	y	PROPN
ejpam-2552	543	52	(	(	PUNCT
ejpam-2552	543	53	t	t	PROPN
ejpam-2552	543	54	)	)	PUNCT
ejpam-2552	543	55	in	in	ADP
ejpam-2552	543	56	figure	figure	NOUN
ejpam-2552	543	57	1	1	NUM
ejpam-2552	543	58	,	,	PUNCT
ejpam-2552	543	59	we	we	PRON
ejpam-2552	543	60	see	see	VERB
ejpam-2552	543	61	that	that	SCONJ
ejpam-2552	543	62	the	the	DET
ejpam-2552	543	63	most	most	ADJ
ejpam-2552	543	64	n	n	PRON
ejpam-2552	543	65	is	be	AUX
ejpam-2552	543	66	high	high	ADJ
ejpam-2552	543	67	,	,	PUNCT
ejpam-2552	543	68	the	the	DET
ejpam-2552	543	69	nearest	near	ADJ
ejpam-2552	543	70	the	the	DET
ejpam-2552	543	71	curve	curve	NOUN
ejpam-2552	543	72	yn	yn	PROPN
ejpam-2552	543	73	is	be	AUX
ejpam-2552	543	74	close	close	ADJ
ejpam-2552	543	75	to	to	ADP
ejpam-2552	543	76	the	the	DET
ejpam-2552	543	77	curve	curve	NOUN
ejpam-2552	543	78	y	y	PROPN
ejpam-2552	543	79	.	.	PUNCT
ejpam-2552	544	1	as	as	ADP
ejpam-2552	544	2	for	for	ADP
ejpam-2552	544	3	figure	figure	NOUN
ejpam-2552	544	4	2	2	NUM
ejpam-2552	544	5	,	,	PUNCT
ejpam-2552	544	6	it	it	PRON
ejpam-2552	544	7	shows	show	VERB
ejpam-2552	544	8	how	how	SCONJ
ejpam-2552	544	9	,	,	PUNCT
ejpam-2552	544	10	for	for	ADP
ejpam-2552	544	11	t	t	PROPN
ejpam-2552	544	12	small	small	ADJ
ejpam-2552	544	13	(	(	PUNCT
ejpam-2552	544	14	equal	equal	ADJ
ejpam-2552	544	15	to	to	ADP
ejpam-2552	544	16	1	1	NUM
ejpam-2552	544	17	)	)	PUNCT
ejpam-2552	544	18	and	and	CCONJ
ejpam-2552	544	19	then	then	ADV
ejpam-2552	544	20	t	t	X
ejpam-2552	544	21	higher	higher	ADV
ejpam-2552	544	22	(	(	PUNCT
ejpam-2552	544	23	equal	equal	ADJ
ejpam-2552	544	24	to	to	ADP
ejpam-2552	544	25	10	10	NUM
ejpam-2552	544	26	)	)	PUNCT
ejpam-2552	544	27	,	,	PUNCT
ejpam-2552	544	28	convergence	convergence	NOUN
ejpam-2552	544	29	is	be	AUX
ejpam-2552	544	30	reached	reach	VERB
ejpam-2552	544	31	.	.	PUNCT
ejpam-2552	545	1	we	we	PRON
ejpam-2552	545	2	can	can	AUX
ejpam-2552	545	3	notice	notice	VERB
ejpam-2552	545	4	that	that	SCONJ
ejpam-2552	545	5	the	the	DET
ejpam-2552	545	6	more	more	ADJ
ejpam-2552	545	7	t	t	NOUN
ejpam-2552	545	8	is	be	AUX
ejpam-2552	545	9	high	high	ADJ
ejpam-2552	545	10	,	,	PUNCT
ejpam-2552	545	11	the	the	DET
ejpam-2552	545	12	fastest	fast	ADJ
ejpam-2552	545	13	convergence	convergence	NOUN
ejpam-2552	545	14	is	be	AUX
ejpam-2552	545	15	reached	reach	VERB
ejpam-2552	545	16	.	.	PUNCT
ejpam-2552	546	1	references	reference	NOUN
ejpam-2552	546	2	[	[	X
ejpam-2552	546	3	1	1	NUM
ejpam-2552	546	4	]	]	PUNCT
ejpam-2552	546	5	a.	a.	NOUN
ejpam-2552	546	6	boudou	boudou	NOUN
ejpam-2552	546	7	and	and	CCONJ
ejpam-2552	546	8	y.	y.	PROPN
ejpam-2552	546	9	romain	romain	PROPN
ejpam-2552	546	10	.	.	PUNCT
ejpam-2552	547	1	on	on	ADP
ejpam-2552	547	2	product	product	NOUN
ejpam-2552	547	3	measures	measure	NOUN
ejpam-2552	547	4	associated	associate	VERB
ejpam-2552	547	5	with	with	ADP
ejpam-2552	547	6	stationary	stationary	ADJ
ejpam-2552	547	7	processes	process	NOUN
ejpam-2552	547	8	.	.	PUNCT
ejpam-2552	548	1	in	in	ADP
ejpam-2552	548	2	oxford	oxford	PROPN
ejpam-2552	548	3	univ	univ	PROPN
ejpam-2552	548	4	.	.	PUNCT
ejpam-2552	549	1	press	press	PROPN
ejpam-2552	549	2	,	,	PUNCT
ejpam-2552	549	3	editor	editor	NOUN
ejpam-2552	549	4	,	,	PUNCT
ejpam-2552	549	5	the	the	DET
ejpam-2552	549	6	oxford	oxford	PROPN
ejpam-2552	549	7	handbook	handbook	NOUN
ejpam-2552	549	8	of	of	ADP
ejpam-2552	549	9	functional	functional	ADJ
ejpam-2552	549	10	data	datum	NOUN
ejpam-2552	549	11	analysis	analysis	NOUN
ejpam-2552	549	12	.	.	PUNCT
ejpam-2552	549	13	,	,	PUNCT
ejpam-2552	549	14	pages	page	NOUN
ejpam-2552	549	15	references	reference	VERB
ejpam-2552	549	16	910	910	NUM
ejpam-2552	549	17	423–451	423–451	NUM
ejpam-2552	549	18	,	,	PUNCT
ejpam-2552	549	19	oxford	oxford	NOUN
ejpam-2552	549	20	,	,	PUNCT
ejpam-2552	549	21	2011	2011	NUM
ejpam-2552	549	22	.	.	PUNCT
ejpam-2552	550	1	[	[	X
ejpam-2552	550	2	2	2	NUM
ejpam-2552	550	3	]	]	PUNCT
ejpam-2552	550	4	a.	a.	NOUN
ejpam-2552	550	5	boudou	boudou	NOUN
ejpam-2552	550	6	and	and	CCONJ
ejpam-2552	550	7	s.	s.	PROPN
ejpam-2552	550	8	viguier	viguier	PROPN
ejpam-2552	550	9	-	-	PUNCT
ejpam-2552	550	10	pla	pla	NOUN
ejpam-2552	550	11	.	.	PUNCT
ejpam-2552	550	12	relation	relation	NOUN
ejpam-2552	550	13	between	between	ADP
ejpam-2552	550	14	unit	unit	NOUN
ejpam-2552	550	15	operators	operator	NOUN
ejpam-2552	550	16	proximity	proximity	NOUN
ejpam-2552	550	17	and	and	CCONJ
ejpam-2552	550	18	their	their	PRON
ejpam-2552	550	19	associated	associated	ADJ
ejpam-2552	550	20	spectral	spectral	ADJ
ejpam-2552	550	21	measures	measure	NOUN
ejpam-2552	550	22	.	.	PUNCT
ejpam-2552	551	1	statist	statist	NOUN
ejpam-2552	551	2	.	.	PUNCT
ejpam-2552	552	1	proba	proba	NOUN
ejpam-2552	552	2	.	.	PUNCT
ejpam-2552	553	1	letters	letter	NOUN
ejpam-2552	553	2	,	,	PUNCT
ejpam-2552	553	3	80:1724–1732	80:1724–1732	NUM
ejpam-2552	553	4	,	,	PUNCT
ejpam-2552	553	5	2010	2010	NUM
ejpam-2552	553	6	.	.	PUNCT
ejpam-2552	554	1	[	[	X
ejpam-2552	554	2	3	3	NUM
ejpam-2552	554	3	]	]	X
ejpam-2552	554	4	n.	n.	PROPN
ejpam-2552	554	5	dunford	dunford	PROPN
ejpam-2552	554	6	and	and	CCONJ
ejpam-2552	554	7	j.	j.	PROPN
ejpam-2552	554	8	schwartz	schwartz	PROPN
ejpam-2552	554	9	.	.	PUNCT
ejpam-2552	555	1	linear	linear	PROPN
ejpam-2552	555	2	operators	operator	NOUN
ejpam-2552	555	3	.	.	PUNCT
ejpam-2552	556	1	interscience	interscience	NOUN
ejpam-2552	556	2	publishers	publisher	NOUN
ejpam-2552	556	3	,	,	PUNCT
ejpam-2552	556	4	new	new	ADJ
ejpam-2552	556	5	-	-	PUNCT
ejpam-2552	556	6	york	york	NOUN
ejpam-2552	556	7	,	,	PUNCT
ejpam-2552	556	8	1963	1963	NUM
ejpam-2552	556	9	.	.	PUNCT
ejpam-2552	557	1	[	[	X
ejpam-2552	557	2	4	4	X
ejpam-2552	557	3	]	]	X
ejpam-2552	557	4	f.	f.	PROPN
ejpam-2552	557	5	riesz	riesz	PROPN
ejpam-2552	557	6	and	and	CCONJ
ejpam-2552	557	7	b.	b.	PROPN
ejpam-2552	557	8	nagy	nagy	PROPN
ejpam-2552	557	9	.	.	PUNCT
ejpam-2552	558	1	functional	functional	ADJ
ejpam-2552	558	2	analysis	analysis	NOUN
ejpam-2552	558	3	.	.	PUNCT
ejpam-2552	559	1	dover	dover	PROPN
ejpam-2552	559	2	publications	publication	NOUN
ejpam-2552	559	3	,	,	PUNCT
ejpam-2552	559	4	1991	1991	NUM
ejpam-2552	559	5	.	.	PUNCT