id	sid	tid	token	lemma	pos
ejpam-5750	1	1	european	european	PROPN
ejpam-5750	1	2	journal	journal	PROPN
ejpam-5750	1	3	of	of	ADP
ejpam-5750	1	4	pure	pure	ADJ
ejpam-5750	1	5	and	and	CCONJ
ejpam-5750	1	6	applied	applied	ADJ
ejpam-5750	1	7	mathematics	mathematic	NOUN
ejpam-5750	1	8	2025	2025	NUM
ejpam-5750	1	9	,	,	PUNCT
ejpam-5750	1	10	vol	vol	NOUN
ejpam-5750	1	11	.	.	PROPN
ejpam-5750	1	12	18	18	NUM
ejpam-5750	1	13	,	,	PUNCT
ejpam-5750	1	14	issue	issue	NOUN
ejpam-5750	1	15	2	2	NUM
ejpam-5750	1	16	,	,	PUNCT
ejpam-5750	1	17	article	article	NOUN
ejpam-5750	1	18	number	number	NOUN
ejpam-5750	1	19	5750	5750	NUM
ejpam-5750	1	20	issn	issn	PROPN
ejpam-5750	1	21	1307	1307	NUM
ejpam-5750	1	22	-	-	SYM
ejpam-5750	1	23	5543	5543	NUM
ejpam-5750	1	24	–	–	PUNCT
ejpam-5750	1	25	ejpam.com	ejpam.com	X
ejpam-5750	1	26	published	publish	VERB
ejpam-5750	1	27	by	by	ADP
ejpam-5750	1	28	new	new	PROPN
ejpam-5750	1	29	york	york	PROPN
ejpam-5750	1	30	business	business	PROPN
ejpam-5750	1	31	global	global	PROPN
ejpam-5750	1	32	flux	flux	NOUN
ejpam-5750	1	33	at	at	ADP
ejpam-5750	1	34	infinity	infinity	NOUN
ejpam-5750	1	35	of	of	ADP
ejpam-5750	1	36	subharmonic	subharmonic	ADJ
ejpam-5750	1	37	functions	function	NOUN
ejpam-5750	1	38	on	on	ADP
ejpam-5750	1	39	r2	r2	PROPN
ejpam-5750	1	40	amulya	amulya	PROPN
ejpam-5750	1	41	smyrna	smyrna	PROPN
ejpam-5750	1	42	c.1	c.1	PROPN
ejpam-5750	1	43	,	,	PUNCT
ejpam-5750	1	44	,	,	PUNCT
ejpam-5750	1	45	n.	n.	PROPN
ejpam-5750	1	46	nathiya1∗	nathiya1∗	PROPN
ejpam-5750	1	47	1	1	NUM
ejpam-5750	1	48	department	department	NOUN
ejpam-5750	1	49	of	of	ADP
ejpam-5750	1	50	mathematics	mathematic	NOUN
ejpam-5750	1	51	,	,	PUNCT
ejpam-5750	1	52	school	school	NOUN
ejpam-5750	1	53	of	of	ADP
ejpam-5750	1	54	advanced	advanced	ADJ
ejpam-5750	1	55	sciences	science	NOUN
ejpam-5750	1	56	,	,	PUNCT
ejpam-5750	1	57	vellore	vellore	PROPN
ejpam-5750	1	58	institute	institute	PROPN
ejpam-5750	1	59	of	of	ADP
ejpam-5750	1	60	technology	technology	PROPN
ejpam-5750	1	61	chennai	chennai	PROPN
ejpam-5750	1	62	,	,	PUNCT
ejpam-5750	1	63	tamil	tamil	PROPN
ejpam-5750	1	64	nadu	nadu	PROPN
ejpam-5750	1	65	,	,	PUNCT
ejpam-5750	1	66	india	india	PROPN
ejpam-5750	1	67	abstract	abstract	NOUN
ejpam-5750	1	68	.	.	PUNCT
ejpam-5750	2	1	for	for	ADP
ejpam-5750	2	2	a	a	DET
ejpam-5750	2	3	c2	c2	PROPN
ejpam-5750	2	4	-	-	PUNCT
ejpam-5750	2	5	function	function	NOUN
ejpam-5750	2	6	f(x	f(x	PROPN
ejpam-5750	2	7	)	)	PUNCT
ejpam-5750	2	8	on	on	ADP
ejpam-5750	2	9	a	a	DET
ejpam-5750	2	10	bounded	bounded	ADJ
ejpam-5750	2	11	domain	domain	NOUN
ejpam-5750	2	12	ω	ω	NOUN
ejpam-5750	2	13	in	in	ADP
ejpam-5750	2	14	r2	r2	PROPN
ejpam-5750	2	15	the	the	DET
ejpam-5750	2	16	flux	flux	NOUN
ejpam-5750	2	17	is	be	AUX
ejpam-5750	2	18	defined	define	VERB
ejpam-5750	2	19	by	by	ADP
ejpam-5750	2	20	means	mean	NOUN
ejpam-5750	2	21	of	of	ADP
ejpam-5750	2	22	outer	outer	ADJ
ejpam-5750	2	23	normal	normal	ADJ
ejpam-5750	2	24	derivative	derivative	NOUN
ejpam-5750	2	25	of	of	ADP
ejpam-5750	2	26	f	f	PROPN
ejpam-5750	2	27	.	.	PUNCT
ejpam-5750	3	1	in	in	ADP
ejpam-5750	3	2	this	this	DET
ejpam-5750	3	3	paper	paper	NOUN
ejpam-5750	3	4	,	,	PUNCT
ejpam-5750	3	5	we	we	PRON
ejpam-5750	3	6	introduce	introduce	VERB
ejpam-5750	3	7	the	the	DET
ejpam-5750	3	8	notion	notion	NOUN
ejpam-5750	3	9	of	of	ADP
ejpam-5750	3	10	flux(f	flux(f	PROPN
ejpam-5750	3	11	)	)	PUNCT
ejpam-5750	3	12	for	for	ADP
ejpam-5750	3	13	any	any	DET
ejpam-5750	3	14	real	real	ADV
ejpam-5750	3	15	-	-	PUNCT
ejpam-5750	3	16	valued	value	VERB
ejpam-5750	3	17	function	function	NOUN
ejpam-5750	3	18	on	on	ADP
ejpam-5750	3	19	r2	r2	PROPN
ejpam-5750	3	20	.	.	PUNCT
ejpam-5750	4	1	we	we	PRON
ejpam-5750	4	2	define	define	VERB
ejpam-5750	4	3	flux	flux	NOUN
ejpam-5750	4	4	on	on	ADP
ejpam-5750	4	5	bounded	bounded	ADJ
ejpam-5750	4	6	domain	domain	PROPN
ejpam-5750	4	7	ω	ω	NOUN
ejpam-5750	4	8	and	and	CCONJ
ejpam-5750	4	9	take	take	VERB
ejpam-5750	4	10	limits	limit	NOUN
ejpam-5750	4	11	when	when	SCONJ
ejpam-5750	4	12	ω	ω	PROPN
ejpam-5750	4	13	grows	grow	VERB
ejpam-5750	4	14	into	into	ADP
ejpam-5750	4	15	r2	r2	PROPN
ejpam-5750	4	16	and	and	CCONJ
ejpam-5750	4	17	the	the	DET
ejpam-5750	4	18	limit	limit	NOUN
ejpam-5750	4	19	is	be	AUX
ejpam-5750	4	20	defined	define	VERB
ejpam-5750	4	21	as	as	ADP
ejpam-5750	4	22	”	"	PUNCT
ejpam-5750	4	23	at	at	ADP
ejpam-5750	4	24	infinity	infinity	NOUN
ejpam-5750	4	25	”	"	PUNCT
ejpam-5750	4	26	,	,	PUNCT
ejpam-5750	4	27	the	the	DET
ejpam-5750	4	28	flux(f	flux(f	PROPN
ejpam-5750	4	29	)	)	PUNCT
ejpam-5750	4	30	at	at	ADP
ejpam-5750	4	31	infinity	infinity	NOUN
ejpam-5750	4	32	denoted	denote	VERB
ejpam-5750	4	33	as	as	ADP
ejpam-5750	4	34	flux∞f	flux∞f	PROPN
ejpam-5750	4	35	.	.	PUNCT
ejpam-5750	5	1	this	this	DET
ejpam-5750	5	2	limit	limit	NOUN
ejpam-5750	5	3	flux∞f	flux∞f	PROPN
ejpam-5750	5	4	may	may	AUX
ejpam-5750	5	5	or	or	CCONJ
ejpam-5750	5	6	may	may	AUX
ejpam-5750	5	7	not	not	PART
ejpam-5750	5	8	be	be	AUX
ejpam-5750	5	9	finite	finite	VERB
ejpam-5750	5	10	.	.	PUNCT
ejpam-5750	6	1	the	the	DET
ejpam-5750	6	2	related	related	ADJ
ejpam-5750	6	3	development	development	NOUN
ejpam-5750	6	4	is	be	AUX
ejpam-5750	6	5	carried	carry	VERB
ejpam-5750	6	6	out	out	ADP
ejpam-5750	6	7	by	by	ADP
ejpam-5750	6	8	employing	employ	VERB
ejpam-5750	6	9	the	the	DET
ejpam-5750	6	10	notion	notion	NOUN
ejpam-5750	6	11	of	of	ADP
ejpam-5750	6	12	inversion	inversion	NOUN
ejpam-5750	6	13	on	on	ADP
ejpam-5750	6	14	r2	r2	PROPN
ejpam-5750	6	15	and	and	CCONJ
ejpam-5750	6	16	the	the	DET
ejpam-5750	6	17	fact	fact	NOUN
ejpam-5750	6	18	that	that	SCONJ
ejpam-5750	6	19	a	a	DET
ejpam-5750	6	20	harmonic	harmonic	ADJ
ejpam-5750	6	21	function	function	NOUN
ejpam-5750	6	22	defined	define	VERB
ejpam-5750	6	23	outside	outside	ADP
ejpam-5750	6	24	a	a	DET
ejpam-5750	6	25	compact	compact	ADJ
ejpam-5750	6	26	set	set	NOUN
ejpam-5750	6	27	in	in	ADP
ejpam-5750	6	28	r2	r2	PROPN
ejpam-5750	6	29	is	be	AUX
ejpam-5750	6	30	the	the	DET
ejpam-5750	6	31	difference	difference	NOUN
ejpam-5750	6	32	of	of	ADP
ejpam-5750	6	33	two	two	NUM
ejpam-5750	6	34	subharmonic	subharmonic	ADJ
ejpam-5750	6	35	functions	function	NOUN
ejpam-5750	6	36	on	on	ADP
ejpam-5750	6	37	r2	r2	NOUN
ejpam-5750	6	38	that	that	PRON
ejpam-5750	6	39	are	be	AUX
ejpam-5750	6	40	harmonic	harmonic	ADJ
ejpam-5750	6	41	outside	outside	ADP
ejpam-5750	6	42	a	a	DET
ejpam-5750	6	43	compact	compact	ADJ
ejpam-5750	6	44	set	set	NOUN
ejpam-5750	6	45	.	.	PUNCT
ejpam-5750	7	1	2020	2020	NUM
ejpam-5750	7	2	mathematics	mathematics	PROPN
ejpam-5750	7	3	subject	subject	NOUN
ejpam-5750	7	4	classifications	classification	NOUN
ejpam-5750	7	5	:	:	PUNCT
ejpam-5750	7	6	31a05	31a05	NUM
ejpam-5750	7	7	,	,	PUNCT
ejpam-5750	7	8	31a10	31a10	NUM
ejpam-5750	7	9	key	key	ADJ
ejpam-5750	7	10	words	word	NOUN
ejpam-5750	7	11	and	and	CCONJ
ejpam-5750	7	12	phrases	phrase	NOUN
ejpam-5750	7	13	:	:	PUNCT
ejpam-5750	7	14	subharmonic	subharmonic	ADJ
ejpam-5750	7	15	function	function	NOUN
ejpam-5750	7	16	,	,	PUNCT
ejpam-5750	7	17	harmonic	harmonic	ADJ
ejpam-5750	7	18	function	function	NOUN
ejpam-5750	7	19	,	,	PUNCT
ejpam-5750	7	20	flux	flux	NOUN
ejpam-5750	7	21	1	1	NUM
ejpam-5750	7	22	.	.	PUNCT
ejpam-5750	8	1	introduction	introduction	NOUN
ejpam-5750	8	2	in	in	ADP
ejpam-5750	8	3	the	the	DET
ejpam-5750	8	4	euclidean	euclidean	ADJ
ejpam-5750	8	5	plane	plane	NOUN
ejpam-5750	8	6	r2	r2	NOUN
ejpam-5750	8	7	,	,	PUNCT
ejpam-5750	8	8	let	let	VERB
ejpam-5750	8	9	ω	ω	PRON
ejpam-5750	8	10	be	be	AUX
ejpam-5750	8	11	a	a	DET
ejpam-5750	8	12	bounded	bounded	ADJ
ejpam-5750	8	13	domain	domain	NOUN
ejpam-5750	8	14	with	with	ADP
ejpam-5750	8	15	smooth	smooth	ADJ
ejpam-5750	8	16	boundary	boundary	NOUN
ejpam-5750	8	17	and	and	CCONJ
ejpam-5750	8	18	f(x	f(x	PROPN
ejpam-5750	8	19	)	)	PUNCT
ejpam-5750	8	20	be	be	VERB
ejpam-5750	8	21	a	a	DET
ejpam-5750	8	22	c2−function	c2−function	NOUN
ejpam-5750	8	23	defined	define	VERB
ejpam-5750	8	24	on	on	ADP
ejpam-5750	8	25	a	a	DET
ejpam-5750	8	26	neighbourhood	neighbourhood	NOUN
ejpam-5750	8	27	of	of	ADP
ejpam-5750	8	28	ω	ω	PROPN
ejpam-5750	8	29	.	.	PUNCT
ejpam-5750	9	1	then	then	ADV
ejpam-5750	9	2	the	the	DET
ejpam-5750	9	3	exit	exit	NOUN
ejpam-5750	9	4	flux	flux	NOUN
ejpam-5750	9	5	(	(	PUNCT
ejpam-5750	9	6	the	the	DET
ejpam-5750	9	7	flux	flux	NOUN
ejpam-5750	9	8	acting	acting	NOUN
ejpam-5750	9	9	outwards	outward	NOUN
ejpam-5750	9	10	from	from	ADP
ejpam-5750	9	11	a	a	DET
ejpam-5750	9	12	closed	closed	ADJ
ejpam-5750	9	13	surface	surface	NOUN
ejpam-5750	9	14	)	)	PUNCT
ejpam-5750	9	15	of	of	ADP
ejpam-5750	9	16	f	f	PROPN
ejpam-5750	9	17	from	from	ADP
ejpam-5750	9	18	ω	ω	PROPN
ejpam-5750	9	19	is	be	AUX
ejpam-5750	9	20	defined	define	VERB
ejpam-5750	9	21	as	as	ADP
ejpam-5750	9	22	∫	∫	PROPN
ejpam-5750	9	23	∂ω	∂ω	PROPN
ejpam-5750	9	24	∂f	∂f	PROPN
ejpam-5750	9	25	∂n+ds	∂n+ds	NOUN
ejpam-5750	9	26	where	where	SCONJ
ejpam-5750	9	27	∂	∂	NOUN
ejpam-5750	9	28	∂n+	∂n+	X
ejpam-5750	9	29	is	be	AUX
ejpam-5750	9	30	the	the	DET
ejpam-5750	9	31	outward	outward	ADJ
ejpam-5750	9	32	normal	normal	ADJ
ejpam-5750	9	33	derivative	derivative	NOUN
ejpam-5750	9	34	at	at	ADP
ejpam-5750	9	35	boundary	boundary	ADJ
ejpam-5750	9	36	points	point	NOUN
ejpam-5750	10	1	[	[	X
ejpam-5750	10	2	1	1	NUM
ejpam-5750	10	3	]	]	PUNCT
ejpam-5750	10	4	.	.	PUNCT
ejpam-5750	11	1	by	by	ADP
ejpam-5750	11	2	using	use	VERB
ejpam-5750	11	3	green	green	PROPN
ejpam-5750	11	4	’s	’s	PART
ejpam-5750	11	5	theorem	theorem	PROPN
ejpam-5750	11	6	,	,	PUNCT
ejpam-5750	11	7	the	the	DET
ejpam-5750	11	8	function	function	NOUN
ejpam-5750	11	9	f(x	f(x	PROPN
ejpam-5750	11	10	)	)	PUNCT
ejpam-5750	11	11	is	be	AUX
ejpam-5750	11	12	harmonic	harmonic	ADJ
ejpam-5750	11	13	on	on	ADP
ejpam-5750	11	14	ω	ω	NUM
ejpam-5750	11	15	if	if	SCONJ
ejpam-5750	12	1	and	and	CCONJ
ejpam-5750	12	2	only	only	ADV
ejpam-5750	12	3	if	if	SCONJ
ejpam-5750	12	4	the	the	DET
ejpam-5750	12	5	exit	exit	NOUN
ejpam-5750	12	6	flux	flux	NOUN
ejpam-5750	12	7	of	of	ADP
ejpam-5750	12	8	f	f	PROPN
ejpam-5750	12	9	from	from	ADP
ejpam-5750	12	10	ω	ω	PROPN
ejpam-5750	12	11	is	be	AUX
ejpam-5750	12	12	0	0	NUM
ejpam-5750	12	13	.	.	PUNCT
ejpam-5750	13	1	there	there	PRON
ejpam-5750	13	2	is	be	VERB
ejpam-5750	13	3	also	also	ADV
ejpam-5750	13	4	a	a	DET
ejpam-5750	13	5	theorem	theorem	NOUN
ejpam-5750	13	6	in	in	ADP
ejpam-5750	13	7	(	(	PUNCT
ejpam-5750	13	8	brelot	brelot	NOUN
ejpam-5750	13	9	[	[	X
ejpam-5750	13	10	2	2	NUM
ejpam-5750	13	11	]	]	PUNCT
ejpam-5750	13	12	)	)	PUNCT
ejpam-5750	13	13	,	,	PUNCT
ejpam-5750	13	14	by	by	ADP
ejpam-5750	13	15	using	use	VERB
ejpam-5750	13	16	a	a	DET
ejpam-5750	13	17	series	series	NOUN
ejpam-5750	13	18	representation	representation	NOUN
ejpam-5750	13	19	for	for	ADP
ejpam-5750	13	20	harmonic	harmonic	ADJ
ejpam-5750	13	21	functions	function	NOUN
ejpam-5750	13	22	defined	define	VERB
ejpam-5750	13	23	outside	outside	ADP
ejpam-5750	13	24	a	a	DET
ejpam-5750	13	25	compact	compact	ADJ
ejpam-5750	13	26	set	set	NOUN
ejpam-5750	13	27	in	in	ADP
ejpam-5750	13	28	r2	r2	PROPN
ejpam-5750	13	29	,	,	PUNCT
ejpam-5750	13	30	it	it	PRON
ejpam-5750	13	31	states	state	VERB
ejpam-5750	13	32	that	that	SCONJ
ejpam-5750	13	33	given	give	VERB
ejpam-5750	13	34	a	a	DET
ejpam-5750	13	35	harmonic	harmonic	ADJ
ejpam-5750	13	36	function	function	NOUN
ejpam-5750	13	37	h	h	NOUN
ejpam-5750	13	38	outside	outside	ADP
ejpam-5750	13	39	a	a	DET
ejpam-5750	13	40	compact	compact	ADJ
ejpam-5750	13	41	set	set	NOUN
ejpam-5750	13	42	in	in	ADP
ejpam-5750	13	43	r2	r2	PROPN
ejpam-5750	13	44	,	,	PUNCT
ejpam-5750	13	45	there	there	PRON
ejpam-5750	13	46	exists	exist	VERB
ejpam-5750	13	47	a	a	DET
ejpam-5750	13	48	harmonic	harmonic	ADJ
ejpam-5750	13	49	function	function	NOUN
ejpam-5750	13	50	h	h	NOUN
ejpam-5750	13	51	on	on	ADP
ejpam-5750	13	52	r2	r2	PROPN
ejpam-5750	13	53	such	such	ADJ
ejpam-5750	13	54	that	that	PRON
ejpam-5750	13	55	|h−h|	|h−h|	VERB
ejpam-5750	13	56	is	be	AUX
ejpam-5750	13	57	bounded	bound	VERB
ejpam-5750	13	58	if	if	SCONJ
ejpam-5750	13	59	and	and	CCONJ
ejpam-5750	13	60	only	only	ADV
ejpam-5750	13	61	if	if	SCONJ
ejpam-5750	13	62	the	the	DET
ejpam-5750	13	63	flux	flux	NOUN
ejpam-5750	13	64	at	at	ADP
ejpam-5750	13	65	infinity	infinity	NOUN
ejpam-5750	13	66	of	of	ADP
ejpam-5750	13	67	h	h	NOUN
ejpam-5750	13	68	is	be	AUX
ejpam-5750	13	69	0	0	NUM
ejpam-5750	13	70	.	.	PUNCT
ejpam-5750	14	1	now	now	ADV
ejpam-5750	14	2	,	,	PUNCT
ejpam-5750	14	3	what	what	PRON
ejpam-5750	14	4	is	be	AUX
ejpam-5750	14	5	the	the	DET
ejpam-5750	14	6	relation	relation	NOUN
ejpam-5750	14	7	between	between	ADP
ejpam-5750	14	8	these	these	DET
ejpam-5750	14	9	two	two	NUM
ejpam-5750	14	10	notions	notion	NOUN
ejpam-5750	14	11	of	of	ADP
ejpam-5750	14	12	flux	flux	NOUN
ejpam-5750	14	13	in	in	ADP
ejpam-5750	14	14	r2	r2	PROPN
ejpam-5750	14	15	?	?	PUNCT
ejpam-5750	15	1	in	in	ADP
ejpam-5750	15	2	this	this	DET
ejpam-5750	15	3	article	article	NOUN
ejpam-5750	15	4	,	,	PUNCT
ejpam-5750	15	5	we	we	PRON
ejpam-5750	15	6	find	find	VERB
ejpam-5750	15	7	an	an	DET
ejpam-5750	15	8	answer	answer	NOUN
ejpam-5750	15	9	to	to	ADP
ejpam-5750	15	10	this	this	DET
ejpam-5750	15	11	question	question	NOUN
ejpam-5750	15	12	by	by	ADP
ejpam-5750	15	13	using	use	VERB
ejpam-5750	15	14	more	more	ADV
ejpam-5750	15	15	generally	generally	ADV
ejpam-5750	15	16	,	,	PUNCT
ejpam-5750	15	17	subharmonic	subharmonic	ADJ
ejpam-5750	15	18	function	function	NOUN
ejpam-5750	15	19	on	on	ADP
ejpam-5750	15	20	r2	r2	PROPN
ejpam-5750	15	21	which	which	PRON
ejpam-5750	15	22	is	be	AUX
ejpam-5750	15	23	locally	locally	ADV
ejpam-5750	15	24	lebesgue	lebesgue	ADJ
ejpam-5750	15	25	integrable	integrable	ADJ
ejpam-5750	15	26	functions	function	NOUN
ejpam-5750	15	27	with	with	ADP
ejpam-5750	15	28	a	a	DET
ejpam-5750	15	29	certain	certain	ADJ
ejpam-5750	15	30	mean	mean	NOUN
ejpam-5750	15	31	value	value	NOUN
ejpam-5750	15	32	property	property	NOUN
ejpam-5750	15	33	.	.	PUNCT
ejpam-5750	16	1	first	first	ADV
ejpam-5750	16	2	we	we	PRON
ejpam-5750	16	3	extend	extend	VERB
ejpam-5750	16	4	the	the	DET
ejpam-5750	16	5	definition	definition	NOUN
ejpam-5750	16	6	of	of	ADP
ejpam-5750	16	7	flux	flux	NOUN
ejpam-5750	16	8	to	to	ADP
ejpam-5750	16	9	a	a	DET
ejpam-5750	16	10	subharmonic	subharmonic	ADJ
ejpam-5750	16	11	function	function	NOUN
ejpam-5750	16	12	defined	define	VERB
ejpam-5750	16	13	on	on	ADP
ejpam-5750	16	14	a	a	DET
ejpam-5750	16	15	bounded	bounded	ADJ
ejpam-5750	16	16	domain	domain	NOUN
ejpam-5750	16	17	in	in	ADP
ejpam-5750	16	18	r2	r2	PROPN
ejpam-5750	16	19	by	by	ADP
ejpam-5750	16	20	using	use	VERB
ejpam-5750	16	21	the	the	DET
ejpam-5750	16	22	distributions	distribution	NOUN
ejpam-5750	16	23	.	.	PUNCT
ejpam-5750	17	1	then	then	ADV
ejpam-5750	17	2	we	we	PRON
ejpam-5750	17	3	introduce	introduce	VERB
ejpam-5750	17	4	the	the	DET
ejpam-5750	17	5	notion	notion	NOUN
ejpam-5750	17	6	of	of	ADP
ejpam-5750	17	7	flux	flux	NOUN
ejpam-5750	17	8	at	at	ADP
ejpam-5750	17	9	infinity	infinity	NOUN
ejpam-5750	17	10	for	for	ADP
ejpam-5750	17	11	a	a	DET
ejpam-5750	17	12	subharmonic	subharmonic	ADJ
ejpam-5750	17	13	function	function	NOUN
ejpam-5750	17	14	defined	define	VERB
ejpam-5750	17	15	outside	outside	ADP
ejpam-5750	17	16	a	a	DET
ejpam-5750	17	17	compact	compact	ADJ
ejpam-5750	17	18	set	set	NOUN
ejpam-5750	17	19	in	in	ADP
ejpam-5750	17	20	r2	r2	PROPN
ejpam-5750	17	21	.	.	PUNCT
ejpam-5750	18	1	for	for	ADP
ejpam-5750	18	2	this	this	PRON
ejpam-5750	18	3	we	we	PRON
ejpam-5750	18	4	require	require	VERB
ejpam-5750	18	5	the	the	DET
ejpam-5750	18	6	∗corresponding	∗corresponde	VERB
ejpam-5750	18	7	author	author	NOUN
ejpam-5750	18	8	.	.	PUNCT
ejpam-5750	19	1	doi	doi	NOUN
ejpam-5750	19	2	:	:	PUNCT
ejpam-5750	19	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5750	https://doi.org/10.29020/nybg.ejpam.v18i2.5750	PART
ejpam-5750	19	4	email	email	NOUN
ejpam-5750	19	5	addresses	address	NOUN
ejpam-5750	19	6	:	:	PUNCT
ejpam-5750	19	7	amulyasmyrna.c@gmail.com	amulyasmyrna.c@gmail.com	NUM
ejpam-5750	19	8	(	(	PUNCT
ejpam-5750	19	9	amulya	amulya	PROPN
ejpam-5750	19	10	smyrna	smyrna	PROPN
ejpam-5750	19	11	c.	c.	PROPN
ejpam-5750	19	12	)	)	PUNCT
ejpam-5750	19	13	,	,	PUNCT
ejpam-5750	19	14	nadhiyan@gmail.com	nadhiyan@gmail.com	X
ejpam-5750	19	15	(	(	PUNCT
ejpam-5750	19	16	n.	n.	PROPN
ejpam-5750	19	17	nathiya	nathiya	PROPN
ejpam-5750	19	18	)	)	PUNCT
ejpam-5750	19	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5750	20	1	1	1	NUM
ejpam-5750	20	2	copyright	copyright	NOUN
ejpam-5750	20	3	:	:	PUNCT
ejpam-5750	20	4	©	©	PROPN
ejpam-5750	20	5	2025	2025	NUM
ejpam-5750	20	6	the	the	DET
ejpam-5750	20	7	author(s	author(s	NOUN
ejpam-5750	20	8	)	)	PUNCT
ejpam-5750	20	9	.	.	PUNCT
ejpam-5750	21	1	(	(	PUNCT
ejpam-5750	21	2	cc	cc	NOUN
ejpam-5750	21	3	by	by	ADP
ejpam-5750	21	4	-	-	PUNCT
ejpam-5750	21	5	nc	nc	PROPN
ejpam-5750	21	6	4.0	4.0	NUM
ejpam-5750	21	7	)	)	PUNCT
ejpam-5750	21	8	amulya	amulya	PROPN
ejpam-5750	21	9	smyrna	smyrna	PROPN
ejpam-5750	21	10	c.	c.	PROPN
ejpam-5750	21	11	,	,	PUNCT
ejpam-5750	21	12	n.	n.	PROPN
ejpam-5750	21	13	nathiya	nathiya	PROPN
ejpam-5750	21	14	/	/	SYM
ejpam-5750	21	15	eur	eur	PROPN
ejpam-5750	21	16	.	.	PUNCT
ejpam-5750	22	1	j.	j.	PROPN
ejpam-5750	22	2	pure	pure	PROPN
ejpam-5750	22	3	appl	appl	PROPN
ejpam-5750	22	4	.	.	PROPN
ejpam-5750	22	5	math	math	PROPN
ejpam-5750	22	6	,	,	PUNCT
ejpam-5750	22	7	18	18	NUM
ejpam-5750	22	8	(	(	PUNCT
ejpam-5750	22	9	2	2	NUM
ejpam-5750	22	10	)	)	PUNCT
ejpam-5750	22	11	(	(	PUNCT
ejpam-5750	22	12	2025	2025	NUM
ejpam-5750	22	13	)	)	PUNCT
ejpam-5750	22	14	,	,	PUNCT
ejpam-5750	22	15	5750	5750	NUM
ejpam-5750	22	16	2	2	NUM
ejpam-5750	22	17	of	of	ADP
ejpam-5750	22	18	9	9	NUM
ejpam-5750	22	19	measure	measure	NOUN
ejpam-5750	22	20	associated	associate	VERB
ejpam-5750	22	21	with	with	ADP
ejpam-5750	22	22	a	a	DET
ejpam-5750	22	23	subharmonic	subharmonic	ADJ
ejpam-5750	22	24	function	function	NOUN
ejpam-5750	22	25	in	in	ADP
ejpam-5750	22	26	a	a	DET
ejpam-5750	22	27	local	local	ADJ
ejpam-5750	22	28	riesz	riesz	NOUN
ejpam-5750	22	29	representation	representation	NOUN
ejpam-5750	22	30	as	as	ADP
ejpam-5750	22	31	an	an	DET
ejpam-5750	22	32	integral	integral	ADJ
ejpam-5750	22	33	,	,	PUNCT
ejpam-5750	22	34	(	(	PUNCT
ejpam-5750	22	35	helms	helm	NOUN
ejpam-5750	22	36	[	[	X
ejpam-5750	22	37	3	3	NUM
ejpam-5750	22	38	]	]	PUNCT
ejpam-5750	22	39	,	,	PUNCT
ejpam-5750	22	40	ransford	ransford	NOUN
ejpam-5750	23	1	[	[	X
ejpam-5750	23	2	4	4	NUM
ejpam-5750	23	3	]	]	PUNCT
ejpam-5750	23	4	)	)	PUNCT
ejpam-5750	23	5	.	.	PUNCT
ejpam-5750	24	1	we	we	PRON
ejpam-5750	24	2	prove	prove	VERB
ejpam-5750	24	3	that	that	SCONJ
ejpam-5750	24	4	for	for	ADP
ejpam-5750	24	5	a	a	DET
ejpam-5750	24	6	subharmonic	subharmonic	ADJ
ejpam-5750	24	7	function	function	NOUN
ejpam-5750	24	8	s(x	s(x	PROPN
ejpam-5750	24	9	)	)	PUNCT
ejpam-5750	24	10	defined	define	VERB
ejpam-5750	24	11	on	on	ADP
ejpam-5750	24	12	r2	r2	PROPN
ejpam-5750	24	13	,	,	PUNCT
ejpam-5750	24	14	the	the	DET
ejpam-5750	24	15	flux	flux	NOUN
ejpam-5750	24	16	at	at	ADP
ejpam-5750	24	17	infinity	infinity	NOUN
ejpam-5750	24	18	of	of	ADP
ejpam-5750	24	19	s	s	NOUN
ejpam-5750	24	20	is	be	AUX
ejpam-5750	24	21	finite	finite	ADJ
ejpam-5750	24	22	if	if	SCONJ
ejpam-5750	24	23	and	and	CCONJ
ejpam-5750	24	24	only	only	ADV
ejpam-5750	24	25	if	if	SCONJ
ejpam-5750	24	26	the	the	DET
ejpam-5750	24	27	total	total	ADJ
ejpam-5750	24	28	measure	measure	NOUN
ejpam-5750	24	29	associated	associate	VERB
ejpam-5750	24	30	with	with	ADP
ejpam-5750	24	31	s	s	PROPN
ejpam-5750	24	32	in	in	ADP
ejpam-5750	24	33	r2	r2	PROPN
ejpam-5750	24	34	is	be	AUX
ejpam-5750	24	35	finite	finite	ADJ
ejpam-5750	24	36	or	or	CCONJ
ejpam-5750	24	37	equivalently	equivalently	ADV
ejpam-5750	24	38	if	if	SCONJ
ejpam-5750	24	39	and	and	CCONJ
ejpam-5750	24	40	only	only	ADV
ejpam-5750	24	41	if	if	SCONJ
ejpam-5750	24	42	s(x	s(x	NOUN
ejpam-5750	24	43	)	)	PUNCT
ejpam-5750	24	44	has	have	VERB
ejpam-5750	24	45	a	a	DET
ejpam-5750	24	46	harmonic	harmonic	ADJ
ejpam-5750	24	47	majorant	majorant	NOUN
ejpam-5750	24	48	outside	outside	ADP
ejpam-5750	24	49	a	a	DET
ejpam-5750	24	50	compact	compact	ADJ
ejpam-5750	24	51	set	set	NOUN
ejpam-5750	24	52	.	.	PUNCT
ejpam-5750	25	1	as	as	ADP
ejpam-5750	25	2	an	an	DET
ejpam-5750	25	3	aside	aside	NOUN
ejpam-5750	25	4	,	,	PUNCT
ejpam-5750	25	5	we	we	PRON
ejpam-5750	25	6	have	have	VERB
ejpam-5750	25	7	also	also	ADV
ejpam-5750	25	8	that	that	SCONJ
ejpam-5750	25	9	if	if	SCONJ
ejpam-5750	25	10	s(x	s(x	NOUN
ejpam-5750	25	11	)	)	PUNCT
ejpam-5750	25	12	is	be	AUX
ejpam-5750	25	13	a	a	DET
ejpam-5750	25	14	subharmonic	subharmonic	ADJ
ejpam-5750	25	15	function	function	NOUN
ejpam-5750	25	16	outside	outside	ADP
ejpam-5750	25	17	a	a	DET
ejpam-5750	25	18	compact	compact	ADJ
ejpam-5750	25	19	set	set	NOUN
ejpam-5750	25	20	in	in	ADP
ejpam-5750	25	21	r2	r2	PROPN
ejpam-5750	25	22	,	,	PUNCT
ejpam-5750	25	23	then	then	ADV
ejpam-5750	25	24	s(x	s(x	PROPN
ejpam-5750	25	25	)	)	PUNCT
ejpam-5750	26	1	=	=	SYM
ejpam-5750	27	1	v(x)−	v(x)−	PROPN
ejpam-5750	27	2	αs	αs	INTJ
ejpam-5750	27	3	log	log	VERB
ejpam-5750	27	4	|x|	|x|	PROPN
ejpam-5750	27	5	where	where	SCONJ
ejpam-5750	27	6	v(x	v(x	PROPN
ejpam-5750	27	7	)	)	PUNCT
ejpam-5750	27	8	is	be	AUX
ejpam-5750	27	9	subharmonic	subharmonic	ADJ
ejpam-5750	27	10	on	on	ADP
ejpam-5750	27	11	r2	r2	PROPN
ejpam-5750	27	12	,	,	PUNCT
ejpam-5750	27	13	αs	αs	PRON
ejpam-5750	27	14	≥	≥	NOUN
ejpam-5750	27	15	0	0	PUNCT
ejpam-5750	27	16	a	a	DET
ejpam-5750	27	17	constant	constant	ADJ
ejpam-5750	27	18	.	.	PUNCT
ejpam-5750	28	1	we	we	PRON
ejpam-5750	28	2	define	define	VERB
ejpam-5750	28	3	the	the	DET
ejpam-5750	28	4	flux	flux	NOUN
ejpam-5750	28	5	at	at	ADP
ejpam-5750	28	6	infinity	infinity	NOUN
ejpam-5750	28	7	of	of	ADP
ejpam-5750	28	8	s(x	s(x	NOUN
ejpam-5750	28	9	)	)	PUNCT
ejpam-5750	28	10	as	as	ADP
ejpam-5750	28	11	[	[	X
ejpam-5750	28	12	flux∞s(x	flux∞s(x	NOUN
ejpam-5750	28	13	)	)	PUNCT
ejpam-5750	28	14	]	]	PUNCT
ejpam-5750	29	1	=	=	PUNCT
ejpam-5750	30	1	[	[	X
ejpam-5750	30	2	total	total	ADJ
ejpam-5750	30	3	measure	measure	NOUN
ejpam-5750	30	4	associated	associate	VERB
ejpam-5750	30	5	with	with	ADP
ejpam-5750	30	6	v(x	v(x	PROPN
ejpam-5750	30	7	)	)	PUNCT
ejpam-5750	30	8	on	on	ADP
ejpam-5750	30	9	r2	r2	PROPN
ejpam-5750	30	10	]	]	PUNCT
ejpam-5750	30	11	−	−	PROPN
ejpam-5750	31	1	αs	αs	INTJ
ejpam-5750	31	2	;	;	PUNCT
ejpam-5750	31	3	this	this	PRON
ejpam-5750	31	4	[	[	X
ejpam-5750	31	5	flux∞s(x	flux∞s(x	PROPN
ejpam-5750	31	6	)	)	PUNCT
ejpam-5750	31	7	]	]	PUNCT
ejpam-5750	31	8	is	be	AUX
ejpam-5750	31	9	independent	independent	ADJ
ejpam-5750	31	10	of	of	ADP
ejpam-5750	31	11	the	the	DET
ejpam-5750	31	12	representation	representation	NOUN
ejpam-5750	31	13	of	of	ADP
ejpam-5750	31	14	s(x	s(x	PROPN
ejpam-5750	31	15	)	)	PUNCT
ejpam-5750	31	16	=	=	SYM
ejpam-5750	31	17	v(x	v(x	PROPN
ejpam-5750	31	18	)	)	PUNCT
ejpam-5750	31	19	−	−	PROPN
ejpam-5750	32	1	αs	αs	INTJ
ejpam-5750	32	2	log	log	VERB
ejpam-5750	32	3	|x|	|x|	PROPN
ejpam-5750	32	4	,	,	PUNCT
ejpam-5750	32	5	which	which	PRON
ejpam-5750	32	6	may	may	AUX
ejpam-5750	32	7	or	or	CCONJ
ejpam-5750	32	8	may	may	AUX
ejpam-5750	32	9	not	not	PART
ejpam-5750	32	10	be	be	AUX
ejpam-5750	32	11	finite	finite	ADJ
ejpam-5750	32	12	.	.	PUNCT
ejpam-5750	33	1	we	we	PRON
ejpam-5750	33	2	deduce	deduce	VERB
ejpam-5750	33	3	that	that	SCONJ
ejpam-5750	33	4	if	if	SCONJ
ejpam-5750	33	5	h(x	h(x	PROPN
ejpam-5750	33	6	)	)	PUNCT
ejpam-5750	33	7	is	be	AUX
ejpam-5750	33	8	a	a	DET
ejpam-5750	33	9	function	function	NOUN
ejpam-5750	33	10	harmonic	harmonic	NOUN
ejpam-5750	33	11	outside	outside	ADP
ejpam-5750	33	12	a	a	DET
ejpam-5750	33	13	compact	compact	ADJ
ejpam-5750	33	14	set	set	NOUN
ejpam-5750	33	15	then	then	ADV
ejpam-5750	33	16	h(x	h(x	PROPN
ejpam-5750	33	17	)	)	PUNCT
ejpam-5750	34	1	=	=	SYM
ejpam-5750	34	2	h(x	h(x	PROPN
ejpam-5750	34	3	)	)	PUNCT
ejpam-5750	35	1	+	+	CCONJ
ejpam-5750	35	2	αh	αh	PART
ejpam-5750	35	3	log	log	NOUN
ejpam-5750	35	4	|x|	|x|	PROPN
ejpam-5750	35	5	+	+	CCONJ
ejpam-5750	35	6	b(x	b(x	PROPN
ejpam-5750	35	7	)	)	PUNCT
ejpam-5750	35	8	,	,	PUNCT
ejpam-5750	35	9	where	where	SCONJ
ejpam-5750	35	10	h(x	h(x	PROPN
ejpam-5750	35	11	)	)	PUNCT
ejpam-5750	35	12	is	be	AUX
ejpam-5750	35	13	harmonic	harmonic	ADJ
ejpam-5750	35	14	on	on	ADP
ejpam-5750	35	15	r2	r2	NOUN
ejpam-5750	35	16	,	,	PUNCT
ejpam-5750	35	17	and	and	CCONJ
ejpam-5750	35	18	αh	αh	NOUN
ejpam-5750	35	19	is	be	AUX
ejpam-5750	35	20	uniquely	uniquely	ADV
ejpam-5750	35	21	determined	determined	ADJ
ejpam-5750	35	22	constant	constant	ADJ
ejpam-5750	35	23	and	and	CCONJ
ejpam-5750	35	24	b(x	b(x	ADJ
ejpam-5750	35	25	)	)	PUNCT
ejpam-5750	35	26	is	be	AUX
ejpam-5750	35	27	bounded	bound	VERB
ejpam-5750	35	28	harmonic	harmonic	ADJ
ejpam-5750	35	29	tending	tend	VERB
ejpam-5750	35	30	to	to	ADP
ejpam-5750	35	31	0	0	NUM
ejpam-5750	35	32	at	at	ADP
ejpam-5750	35	33	infinity	infinity	NOUN
ejpam-5750	35	34	.	.	PUNCT
ejpam-5750	36	1	we	we	PRON
ejpam-5750	36	2	conclude	conclude	VERB
ejpam-5750	36	3	with	with	ADP
ejpam-5750	36	4	the	the	DET
ejpam-5750	36	5	result	result	NOUN
ejpam-5750	36	6	that	that	SCONJ
ejpam-5750	36	7	if	if	SCONJ
ejpam-5750	36	8	the	the	DET
ejpam-5750	36	9	subharmonic	subharmonic	ADJ
ejpam-5750	36	10	function	function	NOUN
ejpam-5750	36	11	s(x	s(x	PROPN
ejpam-5750	36	12	)	)	PUNCT
ejpam-5750	36	13	outside	outside	ADP
ejpam-5750	36	14	a	a	DET
ejpam-5750	36	15	compact	compact	ADJ
ejpam-5750	36	16	set	set	NOUN
ejpam-5750	36	17	in	in	ADP
ejpam-5750	36	18	r2	r2	PROPN
ejpam-5750	36	19	has	have	VERB
ejpam-5750	36	20	a	a	DET
ejpam-5750	36	21	harmonic	harmonic	ADJ
ejpam-5750	36	22	majorant	majorant	NOUN
ejpam-5750	36	23	,	,	PUNCT
ejpam-5750	36	24	then	then	ADV
ejpam-5750	36	25	the	the	DET
ejpam-5750	36	26	flux	flux	NOUN
ejpam-5750	36	27	at	at	ADP
ejpam-5750	36	28	infinity	infinity	NOUN
ejpam-5750	36	29	of	of	ADP
ejpam-5750	36	30	s(x	s(x	PROPN
ejpam-5750	36	31	)	)	PUNCT
ejpam-5750	36	32	is	be	AUX
ejpam-5750	36	33	αh	αh	ADP
ejpam-5750	36	34	where	where	SCONJ
ejpam-5750	36	35	h(x	h(x	PROPN
ejpam-5750	36	36	)	)	PUNCT
ejpam-5750	36	37	is	be	AUX
ejpam-5750	36	38	the	the	DET
ejpam-5750	36	39	least	least	ADJ
ejpam-5750	36	40	harmonic	harmonic	ADJ
ejpam-5750	36	41	majorant	majorant	NOUN
ejpam-5750	36	42	of	of	ADP
ejpam-5750	36	43	s(x	s(x	PROPN
ejpam-5750	36	44	)	)	PUNCT
ejpam-5750	36	45	outside	outside	ADP
ejpam-5750	36	46	a	a	DET
ejpam-5750	36	47	compact	compact	ADJ
ejpam-5750	36	48	set	set	NOUN
ejpam-5750	36	49	.	.	PUNCT
ejpam-5750	37	1	in	in	ADP
ejpam-5750	37	2	the	the	DET
ejpam-5750	37	3	brelot	brelot	NOUN
ejpam-5750	37	4	’s	’s	PART
ejpam-5750	37	5	axiomatic	axiomatic	ADJ
ejpam-5750	37	6	potential	potential	ADJ
ejpam-5750	37	7	theory	theory	NOUN
ejpam-5750	37	8	without	without	ADP
ejpam-5750	37	9	positive	positive	ADJ
ejpam-5750	37	10	potentials	potential	NOUN
ejpam-5750	37	11	,	,	PUNCT
ejpam-5750	37	12	a	a	DET
ejpam-5750	37	13	superharmonic	superharmonic	ADJ
ejpam-5750	37	14	function	function	NOUN
ejpam-5750	37	15	s(x	s(x	PROPN
ejpam-5750	37	16	)	)	PUNCT
ejpam-5750	37	17	on	on	ADP
ejpam-5750	37	18	the	the	DET
ejpam-5750	37	19	harmonic	harmonic	ADJ
ejpam-5750	37	20	space	space	NOUN
ejpam-5750	37	21	x	x	PUNCT
ejpam-5750	37	22	is	be	AUX
ejpam-5750	37	23	termed	term	VERB
ejpam-5750	37	24	as	as	ADP
ejpam-5750	37	25	admissible	admissible	ADJ
ejpam-5750	37	26	in	in	ADP
ejpam-5750	37	27	(	(	PUNCT
ejpam-5750	37	28	anandam	anandam	PROPN
ejpam-5750	37	29	[	[	X
ejpam-5750	37	30	5	5	NUM
ejpam-5750	37	31	,	,	PUNCT
ejpam-5750	37	32	6	6	NUM
ejpam-5750	37	33	]	]	NUM
ejpam-5750	37	34	)	)	PUNCT
ejpam-5750	37	35	,	,	PUNCT
ejpam-5750	37	36	if	if	SCONJ
ejpam-5750	37	37	it	it	PRON
ejpam-5750	37	38	has	have	VERB
ejpam-5750	37	39	a	a	DET
ejpam-5750	37	40	harmonic	harmonic	ADJ
ejpam-5750	37	41	minorant	minorant	NOUN
ejpam-5750	37	42	outside	outside	ADP
ejpam-5750	37	43	a	a	DET
ejpam-5750	37	44	compact	compact	ADJ
ejpam-5750	37	45	set	set	NOUN
ejpam-5750	37	46	.	.	PUNCT
ejpam-5750	38	1	therein	therein	ADV
ejpam-5750	38	2	is	be	AUX
ejpam-5750	38	3	a	a	DET
ejpam-5750	38	4	definition	definition	NOUN
ejpam-5750	38	5	of	of	ADP
ejpam-5750	38	6	flux	flux	NOUN
ejpam-5750	38	7	at	at	ADP
ejpam-5750	38	8	infinity	infinity	NOUN
ejpam-5750	38	9	of	of	ADP
ejpam-5750	38	10	a	a	DET
ejpam-5750	38	11	harmonic	harmonic	ADJ
ejpam-5750	38	12	function	function	NOUN
ejpam-5750	38	13	outside	outside	ADP
ejpam-5750	38	14	a	a	DET
ejpam-5750	38	15	compact	compact	ADJ
ejpam-5750	38	16	set	set	NOUN
ejpam-5750	38	17	in	in	ADP
ejpam-5750	38	18	x.	x.	NOUN
ejpam-5750	38	19	but	but	CCONJ
ejpam-5750	38	20	only	only	ADV
ejpam-5750	38	21	with	with	ADP
ejpam-5750	38	22	the	the	DET
ejpam-5750	38	23	three	three	NUM
ejpam-5750	38	24	axioms	axiom	NOUN
ejpam-5750	38	25	of	of	ADP
ejpam-5750	38	26	(	(	PUNCT
ejpam-5750	38	27	brelot	brelot	NOUN
ejpam-5750	38	28	[	[	X
ejpam-5750	38	29	7	7	NUM
ejpam-5750	38	30	]	]	NUM
ejpam-5750	38	31	)	)	PUNCT
ejpam-5750	38	32	,	,	PUNCT
ejpam-5750	38	33	it	it	PRON
ejpam-5750	38	34	is	be	AUX
ejpam-5750	38	35	not	not	PART
ejpam-5750	38	36	possible	possible	ADJ
ejpam-5750	38	37	to	to	PART
ejpam-5750	38	38	introduce	introduce	VERB
ejpam-5750	38	39	a	a	DET
ejpam-5750	38	40	comprehensive	comprehensive	ADJ
ejpam-5750	38	41	comparative	comparative	ADJ
ejpam-5750	38	42	study	study	NOUN
ejpam-5750	38	43	of	of	ADP
ejpam-5750	38	44	the	the	DET
ejpam-5750	38	45	total	total	ADJ
ejpam-5750	38	46	measure	measure	NOUN
ejpam-5750	38	47	of	of	ADP
ejpam-5750	38	48	a	a	DET
ejpam-5750	38	49	superharmonic	superharmonic	ADJ
ejpam-5750	38	50	function	function	NOUN
ejpam-5750	38	51	and	and	CCONJ
ejpam-5750	38	52	its	its	PRON
ejpam-5750	38	53	flux	flux	NOUN
ejpam-5750	38	54	at	at	ADP
ejpam-5750	38	55	infinity	infinity	NOUN
ejpam-5750	38	56	on	on	ADP
ejpam-5750	38	57	a	a	DET
ejpam-5750	38	58	harmonic	harmonic	ADJ
ejpam-5750	38	59	space	space	NOUN
ejpam-5750	38	60	(	(	PUNCT
ejpam-5750	38	61	that	that	PRON
ejpam-5750	38	62	is	be	AUX
ejpam-5750	38	63	locally	locally	ADV
ejpam-5750	38	64	compact	compact	ADJ
ejpam-5750	38	65	)	)	PUNCT
ejpam-5750	38	66	without	without	ADP
ejpam-5750	38	67	positive	positive	ADJ
ejpam-5750	38	68	potentials	potential	NOUN
ejpam-5750	38	69	.	.	PUNCT
ejpam-5750	39	1	see	see	VERB
ejpam-5750	39	2	also	also	ADV
ejpam-5750	39	3	the	the	DET
ejpam-5750	39	4	paper	paper	NOUN
ejpam-5750	39	5	(	(	PUNCT
ejpam-5750	39	6	bajunaid	bajunaid	X
ejpam-5750	39	7	et	et	X
ejpam-5750	39	8	.	.	PUNCT
ejpam-5750	40	1	al	al	PROPN
ejpam-5750	40	2	.	.	PUNCT
ejpam-5750	41	1	[	[	X
ejpam-5750	41	2	8	8	NUM
ejpam-5750	41	3	]	]	PUNCT
ejpam-5750	41	4	)	)	PUNCT
ejpam-5750	41	5	.	.	PUNCT
ejpam-5750	42	1	if	if	SCONJ
ejpam-5750	42	2	f(x	f(x	PROPN
ejpam-5750	42	3	)	)	PUNCT
ejpam-5750	42	4	is	be	AUX
ejpam-5750	42	5	a	a	DET
ejpam-5750	42	6	c2	c2	PROPN
ejpam-5750	42	7	-	-	PUNCT
ejpam-5750	42	8	function	function	NOUN
ejpam-5750	42	9	defined	define	VERB
ejpam-5750	42	10	on	on	ADP
ejpam-5750	42	11	a	a	DET
ejpam-5750	42	12	bounded	bounded	ADJ
ejpam-5750	42	13	domain	domain	NOUN
ejpam-5750	42	14	ω̄	ω̄	NOUN
ejpam-5750	42	15	with	with	ADP
ejpam-5750	42	16	smooth	smooth	ADJ
ejpam-5750	42	17	boundary	boundary	NOUN
ejpam-5750	42	18	,	,	PUNCT
ejpam-5750	42	19	then	then	ADV
ejpam-5750	42	20	the	the	DET
ejpam-5750	42	21	flux(f	flux(f	NOUN
ejpam-5750	42	22	)	)	PUNCT
ejpam-5750	42	23	is	be	AUX
ejpam-5750	42	24	defined	define	VERB
ejpam-5750	42	25	by	by	ADP
ejpam-5750	42	26	means	mean	NOUN
ejpam-5750	42	27	of	of	ADP
ejpam-5750	42	28	the	the	DET
ejpam-5750	42	29	outer	outer	ADJ
ejpam-5750	42	30	normal	normal	ADJ
ejpam-5750	42	31	derivatives	derivative	NOUN
ejpam-5750	42	32	of	of	ADP
ejpam-5750	42	33	f	f	PROPN
ejpam-5750	42	34	.	.	PUNCT
ejpam-5750	43	1	in	in	ADP
ejpam-5750	43	2	this	this	DET
ejpam-5750	43	3	note	note	NOUN
ejpam-5750	43	4	,	,	PUNCT
ejpam-5750	43	5	we	we	PRON
ejpam-5750	43	6	introduce	introduce	VERB
ejpam-5750	43	7	the	the	DET
ejpam-5750	43	8	notion	notion	NOUN
ejpam-5750	43	9	of	of	ADP
ejpam-5750	43	10	the	the	DET
ejpam-5750	43	11	linear	linear	PROPN
ejpam-5750	43	12	function	function	NOUN
ejpam-5750	43	13	flux(f	flux(f	PROPN
ejpam-5750	43	14	)	)	PUNCT
ejpam-5750	43	15	for	for	ADP
ejpam-5750	43	16	any	any	DET
ejpam-5750	43	17	real	real	ADV
ejpam-5750	43	18	-	-	PUNCT
ejpam-5750	43	19	valued	value	VERB
ejpam-5750	43	20	function	function	NOUN
ejpam-5750	43	21	f	f	PROPN
ejpam-5750	43	22	defined	define	VERB
ejpam-5750	43	23	on	on	ADP
ejpam-5750	43	24	r2	r2	PROPN
ejpam-5750	43	25	.	.	PUNCT
ejpam-5750	44	1	since	since	SCONJ
ejpam-5750	44	2	any	any	DET
ejpam-5750	44	3	real	real	ADV
ejpam-5750	44	4	-	-	PUNCT
ejpam-5750	44	5	valued	value	VERB
ejpam-5750	44	6	function	function	NOUN
ejpam-5750	44	7	f	f	PROPN
ejpam-5750	44	8	on	on	ADP
ejpam-5750	44	9	r2	r2	PROPN
ejpam-5750	44	10	is	be	AUX
ejpam-5750	44	11	the	the	DET
ejpam-5750	44	12	difference	difference	NOUN
ejpam-5750	44	13	of	of	ADP
ejpam-5750	44	14	two	two	NUM
ejpam-5750	44	15	subharmonic	subharmonic	ADJ
ejpam-5750	44	16	functions	function	NOUN
ejpam-5750	44	17	,	,	PUNCT
ejpam-5750	44	18	it	it	PRON
ejpam-5750	44	19	is	be	AUX
ejpam-5750	44	20	enough	enough	ADJ
ejpam-5750	44	21	to	to	PART
ejpam-5750	44	22	define	define	VERB
ejpam-5750	44	23	flux(s	flux(s	NOUN
ejpam-5750	44	24	)	)	PUNCT
ejpam-5750	44	25	for	for	ADP
ejpam-5750	44	26	any	any	DET
ejpam-5750	44	27	subharmonic	subharmonic	ADJ
ejpam-5750	44	28	functions	function	NOUN
ejpam-5750	44	29	s	s	PART
ejpam-5750	44	30	on	on	ADP
ejpam-5750	44	31	r2	r2	PROPN
ejpam-5750	44	32	with	with	ADP
ejpam-5750	44	33	associated	associated	ADJ
ejpam-5750	44	34	radon	radon	PROPN
ejpam-5750	44	35	measure	measure	NOUN
ejpam-5750	44	36	µ	µ	X
ejpam-5750	44	37	in	in	ADP
ejpam-5750	44	38	a	a	DET
ejpam-5750	44	39	local	local	ADJ
ejpam-5750	44	40	riesz	riesz	NOUN
ejpam-5750	44	41	representation	representation	NOUN
ejpam-5750	44	42	as	as	ADP
ejpam-5750	44	43	a	a	DET
ejpam-5750	44	44	sum	sum	NOUN
ejpam-5750	44	45	of	of	ADP
ejpam-5750	44	46	an	an	DET
ejpam-5750	44	47	integral	integral	ADJ
ejpam-5750	44	48	with	with	ADP
ejpam-5750	44	49	respect	respect	NOUN
ejpam-5750	44	50	to	to	ADP
ejpam-5750	44	51	µ	µ	NOUN
ejpam-5750	44	52	and	and	CCONJ
ejpam-5750	44	53	a	a	DET
ejpam-5750	44	54	harmonic	harmonic	ADJ
ejpam-5750	44	55	function	function	NOUN
ejpam-5750	44	56	.	.	PUNCT
ejpam-5750	45	1	if	if	SCONJ
ejpam-5750	45	2	u	u	NOUN
ejpam-5750	45	3	is	be	AUX
ejpam-5750	45	4	a	a	DET
ejpam-5750	45	5	c2	c2	PROPN
ejpam-5750	45	6	-	-	PUNCT
ejpam-5750	45	7	function	function	NOUN
ejpam-5750	45	8	on	on	ADP
ejpam-5750	45	9	d	d	PROPN
ejpam-5750	45	10	=	=	PUNCT
ejpam-5750	45	11	{	{	PUNCT
ejpam-5750	45	12	x	x	X
ejpam-5750	45	13	:	:	PUNCT
ejpam-5750	45	14	|x|	|x|	PROPN
ejpam-5750	45	15	≤	≤	NUM
ejpam-5750	45	16	r	r	NOUN
ejpam-5750	45	17	}	}	PUNCT
ejpam-5750	45	18	in	in	ADP
ejpam-5750	45	19	r2	r2	PROPN
ejpam-5750	45	20	,	,	PUNCT
ejpam-5750	45	21	then	then	ADV
ejpam-5750	45	22	∫	∫	PROPN
ejpam-5750	45	23	|x|<r	|x|<r	PROPN
ejpam-5750	45	24	∆u(x)dx	∆u(x)dx	VERB
ejpam-5750	45	25	=	=	PUNCT
ejpam-5750	45	26	∫	∫	PROPN
ejpam-5750	45	27	|z|=r	|z|=r	PROPN
ejpam-5750	45	28	∂u	∂u	PROPN
ejpam-5750	45	29	∂n+	∂n+	X
ejpam-5750	45	30	(	(	PUNCT
ejpam-5750	45	31	z)dσ	z)dσ	VERB
ejpam-5750	45	32	which	which	PRON
ejpam-5750	45	33	is	be	AUX
ejpam-5750	45	34	the	the	DET
ejpam-5750	45	35	flux(u	flux(u	NOUN
ejpam-5750	45	36	)	)	PUNCT
ejpam-5750	45	37	on	on	ADP
ejpam-5750	45	38	d.	d.	PROPN
ejpam-5750	45	39	if	if	SCONJ
ejpam-5750	45	40	s	s	X
ejpam-5750	45	41	is	be	AUX
ejpam-5750	45	42	any	any	DET
ejpam-5750	45	43	subharmonic	subharmonic	ADJ
ejpam-5750	45	44	function	function	NOUN
ejpam-5750	45	45	on	on	ADP
ejpam-5750	45	46	r2	r2	PROPN
ejpam-5750	45	47	,	,	PUNCT
ejpam-5750	45	48	then	then	ADV
ejpam-5750	45	49	there	there	PRON
ejpam-5750	45	50	exists	exist	VERB
ejpam-5750	45	51	an	an	DET
ejpam-5750	45	52	increasing	increase	VERB
ejpam-5750	45	53	sequence	sequence	NOUN
ejpam-5750	45	54	of	of	ADP
ejpam-5750	45	55	c2	c2	PROPN
ejpam-5750	45	56	-	-	PUNCT
ejpam-5750	45	57	subharmonic	subharmonic	ADJ
ejpam-5750	45	58	functions	function	NOUN
ejpam-5750	45	59	tending	tend	VERB
ejpam-5750	45	60	to	to	ADP
ejpam-5750	45	61	s.	s.	PROPN
ejpam-5750	45	62	thus	thus	ADV
ejpam-5750	45	63	,	,	PUNCT
ejpam-5750	45	64	we	we	PRON
ejpam-5750	45	65	can	can	AUX
ejpam-5750	45	66	write∫	write∫	VERB
ejpam-5750	45	67	|x|<r	|x|<r	NOUN
ejpam-5750	45	68	∆s(x)dx	∆s(x)dx	PROPN
ejpam-5750	45	69	=	=	PUNCT
ejpam-5750	45	70	∫	∫	PROPN
ejpam-5750	46	1	|z|=r	|z|=r	PROPN
ejpam-5750	46	2	∂s	∂s	PROPN
ejpam-5750	46	3	∂n+	∂n+	PROPN
ejpam-5750	46	4	(	(	PUNCT
ejpam-5750	46	5	z)dσ	z)dσ	PROPN
ejpam-5750	46	6	.	.	PUNCT
ejpam-5750	46	7	since	since	SCONJ
ejpam-5750	46	8	∆s	∆s	PROPN
ejpam-5750	46	9	≥	≥	NOUN
ejpam-5750	46	10	0	0	NUM
ejpam-5750	46	11	then	then	ADV
ejpam-5750	46	12	∆s	∆s	PROPN
ejpam-5750	46	13	defines	define	VERB
ejpam-5750	46	14	a	a	DET
ejpam-5750	46	15	radon	radon	ADJ
ejpam-5750	46	16	measure	measure	NOUN
ejpam-5750	46	17	µ	µ	X
ejpam-5750	46	18	on	on	ADP
ejpam-5750	46	19	r2	r2	PROPN
ejpam-5750	46	20	and	and	CCONJ
ejpam-5750	46	21	we	we	PRON
ejpam-5750	46	22	define	define	VERB
ejpam-5750	46	23	flux(s	flux(s	NOUN
ejpam-5750	46	24	)	)	PUNCT
ejpam-5750	46	25	=	=	SYM
ejpam-5750	46	26	µ(r2	µ(r2	NOUN
ejpam-5750	46	27	)	)	PUNCT
ejpam-5750	46	28	=	=	SYM
ejpam-5750	46	29	lim	lim	PROPN
ejpam-5750	46	30	r→∞	r→∞	PRON
ejpam-5750	46	31	∫	∫	PROPN
ejpam-5750	46	32	∂s	∂s	PROPN
ejpam-5750	46	33	∂n+dσ	∂n+dσ	PROPN
ejpam-5750	46	34	at	at	ADP
ejpam-5750	46	35	infinity	infinity	NOUN
ejpam-5750	46	36	.	.	PUNCT
ejpam-5750	47	1	thus	thus	ADV
ejpam-5750	47	2	the	the	DET
ejpam-5750	47	3	flux(s	flux(s	NOUN
ejpam-5750	47	4	)	)	PUNCT
ejpam-5750	47	5	at	at	ADP
ejpam-5750	47	6	infinity	infinity	NOUN
ejpam-5750	47	7	may	may	AUX
ejpam-5750	47	8	or	or	CCONJ
ejpam-5750	47	9	may	may	AUX
ejpam-5750	47	10	not	not	PART
ejpam-5750	47	11	be	be	AUX
ejpam-5750	47	12	finite	finite	ADJ
ejpam-5750	47	13	.	.	PUNCT
ejpam-5750	48	1	by	by	ADP
ejpam-5750	48	2	using	use	VERB
ejpam-5750	48	3	inversion	inversion	NOUN
ejpam-5750	48	4	,	,	PUNCT
ejpam-5750	48	5	we	we	PRON
ejpam-5750	48	6	show	show	VERB
ejpam-5750	48	7	that	that	SCONJ
ejpam-5750	48	8	flux(s	flux(s	NOUN
ejpam-5750	48	9	)	)	PUNCT
ejpam-5750	48	10	is	be	AUX
ejpam-5750	48	11	finite	finite	ADJ
ejpam-5750	48	12	if	if	SCONJ
ejpam-5750	48	13	and	and	CCONJ
ejpam-5750	48	14	only	only	ADV
ejpam-5750	48	15	if	if	SCONJ
ejpam-5750	48	16	it	it	PRON
ejpam-5750	48	17	has	have	VERB
ejpam-5750	48	18	a	a	DET
ejpam-5750	48	19	harmonic	harmonic	ADJ
ejpam-5750	48	20	majorant	majorant	NOUN
ejpam-5750	48	21	h	h	NOUN
ejpam-5750	48	22	outside	outside	ADP
ejpam-5750	48	23	a	a	DET
ejpam-5750	48	24	compact	compact	ADJ
ejpam-5750	48	25	set	set	NOUN
ejpam-5750	48	26	.	.	PUNCT
ejpam-5750	49	1	any	any	DET
ejpam-5750	49	2	such	such	ADJ
ejpam-5750	49	3	harmonic	harmonic	ADJ
ejpam-5750	49	4	function	function	NOUN
ejpam-5750	49	5	outside	outside	ADP
ejpam-5750	49	6	a	a	DET
ejpam-5750	49	7	compact	compact	ADJ
ejpam-5750	49	8	set	set	NOUN
ejpam-5750	49	9	has	have	VERB
ejpam-5750	49	10	a	a	DET
ejpam-5750	49	11	unique	unique	ADJ
ejpam-5750	49	12	representation	representation	NOUN
ejpam-5750	49	13	h(x	h(x	PROPN
ejpam-5750	49	14	)	)	PUNCT
ejpam-5750	49	15	=	=	SYM
ejpam-5750	49	16	h(x	h(x	PROPN
ejpam-5750	49	17	)	)	PUNCT
ejpam-5750	50	1	+	+	CCONJ
ejpam-5750	50	2	α	α	PRON
ejpam-5750	50	3	log	log	NOUN
ejpam-5750	50	4	|x|+	|x|+	NOUN
ejpam-5750	50	5	b(x	b(x	NOUN
ejpam-5750	50	6	)	)	PUNCT
ejpam-5750	50	7	where	where	SCONJ
ejpam-5750	50	8	h(x	h(x	PROPN
ejpam-5750	50	9	)	)	PUNCT
ejpam-5750	50	10	is	be	AUX
ejpam-5750	50	11	harmonic	harmonic	ADJ
ejpam-5750	50	12	on	on	ADP
ejpam-5750	50	13	r2	r2	PROPN
ejpam-5750	50	14	,	,	PUNCT
ejpam-5750	50	15	α	α	PROPN
ejpam-5750	50	16	is	be	AUX
ejpam-5750	50	17	a	a	DET
ejpam-5750	50	18	constant	constant	ADJ
ejpam-5750	50	19	and	and	CCONJ
ejpam-5750	50	20	b(x	b(x	ADJ
ejpam-5750	50	21	)	)	PUNCT
ejpam-5750	50	22	→	→	SYM
ejpam-5750	50	23	0	0	NUM
ejpam-5750	50	24	at	at	ADP
ejpam-5750	50	25	infinity	infinity	NOUN
ejpam-5750	50	26	.	.	PUNCT
ejpam-5750	51	1	finally	finally	ADV
ejpam-5750	51	2	,	,	PUNCT
ejpam-5750	51	3	we	we	PRON
ejpam-5750	51	4	prove	prove	VERB
ejpam-5750	51	5	that	that	SCONJ
ejpam-5750	51	6	if	if	SCONJ
ejpam-5750	51	7	h(x	h(x	PROPN
ejpam-5750	51	8	)	)	PUNCT
ejpam-5750	51	9	is	be	AUX
ejpam-5750	51	10	the	the	DET
ejpam-5750	51	11	least	least	ADJ
ejpam-5750	51	12	harmonic	harmonic	ADJ
ejpam-5750	51	13	majorant	majorant	NOUN
ejpam-5750	51	14	of	of	ADP
ejpam-5750	51	15	s(x	s(x	PROPN
ejpam-5750	51	16	)	)	PUNCT
ejpam-5750	51	17	outside	outside	ADP
ejpam-5750	51	18	a	a	DET
ejpam-5750	51	19	compact	compact	ADJ
ejpam-5750	51	20	set	set	NOUN
ejpam-5750	51	21	,	,	PUNCT
ejpam-5750	51	22	then	then	ADV
ejpam-5750	51	23	flux(s	flux(s	PROPN
ejpam-5750	51	24	)	)	PUNCT
ejpam-5750	51	25	=	=	SYM
ejpam-5750	51	26	α	α	X
ejpam-5750	51	27	.	.	PUNCT
ejpam-5750	51	28	amulya	amulya	PROPN
ejpam-5750	51	29	smyrna	smyrna	PROPN
ejpam-5750	51	30	c.	c.	PROPN
ejpam-5750	51	31	,	,	PUNCT
ejpam-5750	51	32	n.	n.	PROPN
ejpam-5750	51	33	nathiya	nathiya	PROPN
ejpam-5750	51	34	/	/	SYM
ejpam-5750	51	35	eur	eur	PROPN
ejpam-5750	51	36	.	.	PUNCT
ejpam-5750	52	1	j.	j.	PROPN
ejpam-5750	52	2	pure	pure	PROPN
ejpam-5750	52	3	appl	appl	PROPN
ejpam-5750	52	4	.	.	PROPN
ejpam-5750	52	5	math	math	PROPN
ejpam-5750	52	6	,	,	PUNCT
ejpam-5750	52	7	18	18	NUM
ejpam-5750	52	8	(	(	PUNCT
ejpam-5750	52	9	2	2	NUM
ejpam-5750	52	10	)	)	PUNCT
ejpam-5750	52	11	(	(	PUNCT
ejpam-5750	52	12	2025	2025	NUM
ejpam-5750	52	13	)	)	PUNCT
ejpam-5750	52	14	,	,	PUNCT
ejpam-5750	52	15	5750	5750	NUM
ejpam-5750	52	16	3	3	NUM
ejpam-5750	52	17	of	of	ADP
ejpam-5750	52	18	9	9	NUM
ejpam-5750	52	19	2	2	NUM
ejpam-5750	52	20	.	.	PUNCT
ejpam-5750	52	21	preliminaries	preliminary	NOUN
ejpam-5750	52	22	an	an	DET
ejpam-5750	52	23	upper	upper	ADJ
ejpam-5750	52	24	and	and	CCONJ
ejpam-5750	52	25	semi	semi	ADJ
ejpam-5750	52	26	-	-	ADJ
ejpam-5750	52	27	continuous	continuous	ADJ
ejpam-5750	52	28	function	function	NOUN
ejpam-5750	52	29	u	u	NOUN
ejpam-5750	52	30	,	,	PUNCT
ejpam-5750	52	31	−∞	−∞	VERB
ejpam-5750	52	32	≤	≤	X
ejpam-5750	52	33	u(x	u(x	NOUN
ejpam-5750	52	34	)	)	PUNCT
ejpam-5750	52	35	<	<	X
ejpam-5750	52	36	∞	∞	PROPN
ejpam-5750	52	37	,	,	PUNCT
ejpam-5750	52	38	u	u	NOUN
ejpam-5750	52	39	̸≡	̸≡	NOUN
ejpam-5750	52	40	−∞	−∞	X
ejpam-5750	52	41	on	on	ADP
ejpam-5750	52	42	r2	r2	PROPN
ejpam-5750	52	43	is	be	AUX
ejpam-5750	52	44	said	say	VERB
ejpam-5750	52	45	to	to	PART
ejpam-5750	52	46	be	be	AUX
ejpam-5750	52	47	subharmonic	subharmonic	ADJ
ejpam-5750	52	48	if	if	SCONJ
ejpam-5750	52	49	for	for	ADP
ejpam-5750	52	50	any	any	DET
ejpam-5750	52	51	x	x	SYM
ejpam-5750	52	52	=	=	SYM
ejpam-5750	52	53	reiθ	reiθ	PROPN
ejpam-5750	52	54	,	,	PUNCT
ejpam-5750	52	55	where	where	SCONJ
ejpam-5750	52	56	r	r	NOUN
ejpam-5750	52	57	is	be	AUX
ejpam-5750	52	58	the	the	DET
ejpam-5750	52	59	distance	distance	NOUN
ejpam-5750	52	60	of	of	ADP
ejpam-5750	52	61	∂ω	∂ω	PROPN
ejpam-5750	52	62	from	from	ADP
ejpam-5750	52	63	the	the	DET
ejpam-5750	52	64	origin	origin	NOUN
ejpam-5750	52	65	.	.	PUNCT
ejpam-5750	53	1	u(x	u(x	NOUN
ejpam-5750	53	2	)	)	PUNCT
ejpam-5750	53	3	≤	≤	NUM
ejpam-5750	53	4	1	1	NUM
ejpam-5750	53	5	2π	2π	NUM
ejpam-5750	53	6	2π∫	2π∫	NUM
ejpam-5750	53	7	0	0	NUM
ejpam-5750	53	8	r2	r2	PROPN
ejpam-5750	53	9	−	−	PROPN
ejpam-5750	53	10	r2	r2	PROPN
ejpam-5750	53	11	r2	r2	PROPN
ejpam-5750	53	12	−	−	PROPN
ejpam-5750	53	13	2rr	2rr	NOUN
ejpam-5750	54	1	cos	cos	PROPN
ejpam-5750	54	2	θ	θ	PROPN
ejpam-5750	55	1	−	−	PROPN
ejpam-5750	55	2	ϕ+	ϕ+	PUNCT
ejpam-5750	55	3	r2	r2	PROPN
ejpam-5750	55	4	u(reiθ)dϕ	u(reiθ)dϕ	PROPN
ejpam-5750	55	5	suppose	suppose	VERB
ejpam-5750	55	6	v(x	v(x	PROPN
ejpam-5750	55	7	)	)	PUNCT
ejpam-5750	55	8	is	be	AUX
ejpam-5750	55	9	a	a	DET
ejpam-5750	55	10	locally	locally	ADV
ejpam-5750	55	11	lebesgue	lebesgue	ADJ
ejpam-5750	55	12	integrable	integrable	ADJ
ejpam-5750	55	13	function	function	NOUN
ejpam-5750	55	14	in	in	ADP
ejpam-5750	55	15	r2	r2	PROPN
ejpam-5750	55	16	such	such	ADJ
ejpam-5750	55	17	that	that	SCONJ
ejpam-5750	55	18	∆v	∆v	PROPN
ejpam-5750	55	19	≥	≥	NOUN
ejpam-5750	55	20	0	0	NUM
ejpam-5750	55	21	,	,	PUNCT
ejpam-5750	55	22	in	in	ADP
ejpam-5750	55	23	the	the	DET
ejpam-5750	55	24	sense	sense	NOUN
ejpam-5750	55	25	of	of	ADP
ejpam-5750	55	26	distributions	distribution	NOUN
ejpam-5750	55	27	,	,	PUNCT
ejpam-5750	55	28	then	then	ADV
ejpam-5750	55	29	there	there	PRON
ejpam-5750	55	30	exists	exist	VERB
ejpam-5750	55	31	a	a	DET
ejpam-5750	55	32	unique	unique	ADJ
ejpam-5750	55	33	subharmonic	subharmonic	ADJ
ejpam-5750	55	34	u(x	u(x	NOUN
ejpam-5750	55	35	)	)	PUNCT
ejpam-5750	55	36	such	such	ADJ
ejpam-5750	55	37	that	that	SCONJ
ejpam-5750	55	38	v(x	v(x	PROPN
ejpam-5750	56	1	)	)	PUNCT
ejpam-5750	56	2	=	=	SYM
ejpam-5750	56	3	u(x	u(x	PROPN
ejpam-5750	56	4	)	)	PUNCT
ejpam-5750	56	5	almost	almost	ADV
ejpam-5750	56	6	everywhere	everywhere	ADV
ejpam-5750	56	7	.	.	PUNCT
ejpam-5750	57	1	for	for	ADP
ejpam-5750	57	2	any	any	DET
ejpam-5750	57	3	locally	locally	ADV
ejpam-5750	57	4	integrable	integrable	ADJ
ejpam-5750	57	5	function	function	NOUN
ejpam-5750	57	6	f(x	f(x	PROPN
ejpam-5750	57	7	)	)	PUNCT
ejpam-5750	57	8	,	,	PUNCT
ejpam-5750	57	9	there	there	PRON
ejpam-5750	57	10	exists	exist	VERB
ejpam-5750	57	11	a	a	DET
ejpam-5750	57	12	function	function	NOUN
ejpam-5750	57	13	ϕ(x	ϕ(x	NOUN
ejpam-5750	57	14	)	)	PUNCT
ejpam-5750	57	15	such	such	ADJ
ejpam-5750	57	16	that	that	PRON
ejpam-5750	57	17	∆ϕ(x	∆ϕ(x	X
ejpam-5750	57	18	)	)	PUNCT
ejpam-5750	57	19	=	=	SYM
ejpam-5750	57	20	f(x	f(x	PROPN
ejpam-5750	57	21	)	)	PUNCT
ejpam-5750	57	22	,	,	PUNCT
ejpam-5750	57	23	(	(	PUNCT
ejpam-5750	57	24	brelot	brelot	NOUN
ejpam-5750	57	25	[	[	X
ejpam-5750	57	26	2	2	NUM
ejpam-5750	57	27	]	]	NUM
ejpam-5750	57	28	)	)	PUNCT
ejpam-5750	57	29	;	;	PUNCT
ejpam-5750	57	30	write	write	VERB
ejpam-5750	57	31	∆s1(x	∆s1(x	NOUN
ejpam-5750	57	32	)	)	PUNCT
ejpam-5750	57	33	=	=	SYM
ejpam-5750	57	34	g+(x	g+(x	PROPN
ejpam-5750	57	35	)	)	PUNCT
ejpam-5750	57	36	and	and	CCONJ
ejpam-5750	57	37	∆s2(x	∆s2(x	PROPN
ejpam-5750	57	38	)	)	PUNCT
ejpam-5750	58	1	=	=	SYM
ejpam-5750	58	2	g−(x	g−(x	NOUN
ejpam-5750	58	3	)	)	PUNCT
ejpam-5750	58	4	where	where	SCONJ
ejpam-5750	58	5	g(x	g(x	NOUN
ejpam-5750	58	6	)	)	PUNCT
ejpam-5750	58	7	=	=	SYM
ejpam-5750	58	8	∆f(x	∆f(x	PROPN
ejpam-5750	58	9	)	)	PUNCT
ejpam-5750	58	10	,	,	PUNCT
ejpam-5750	58	11	then	then	ADV
ejpam-5750	58	12	s1(x	s1(x	PROPN
ejpam-5750	58	13	)	)	PUNCT
ejpam-5750	58	14	and	and	CCONJ
ejpam-5750	58	15	s2(x	s2(x	X
ejpam-5750	58	16	)	)	PUNCT
ejpam-5750	58	17	are	be	AUX
ejpam-5750	58	18	subharmonic	subharmonic	ADJ
ejpam-5750	58	19	on	on	ADP
ejpam-5750	58	20	r2	r2	PROPN
ejpam-5750	58	21	and	and	CCONJ
ejpam-5750	58	22	∆[f	∆[f	NOUN
ejpam-5750	58	23	−	−	PROPN
ejpam-5750	58	24	(	(	PUNCT
ejpam-5750	58	25	s1	s1	PROPN
ejpam-5750	58	26	−	−	PROPN
ejpam-5750	58	27	s2	s2	PROPN
ejpam-5750	58	28	)	)	PUNCT
ejpam-5750	58	29	]	]	PUNCT
ejpam-5750	59	1	=	=	PUNCT
ejpam-5750	59	2	0	0	PUNCT
ejpam-5750	60	1	so	so	SCONJ
ejpam-5750	60	2	that	that	SCONJ
ejpam-5750	60	3	f	f	PROPN
ejpam-5750	60	4	−	−	PROPN
ejpam-5750	60	5	(	(	PUNCT
ejpam-5750	60	6	s1−s2	s1−s2	NOUN
ejpam-5750	60	7	)	)	PUNCT
ejpam-5750	60	8	is	be	AUX
ejpam-5750	60	9	a	a	DET
ejpam-5750	60	10	harmonic	harmonic	ADJ
ejpam-5750	60	11	function	function	NOUN
ejpam-5750	60	12	h	h	NOUN
ejpam-5750	60	13	almost	almost	ADV
ejpam-5750	60	14	everywhere	everywhere	ADV
ejpam-5750	60	15	.	.	PUNCT
ejpam-5750	61	1	thus	thus	ADV
ejpam-5750	61	2	any	any	DET
ejpam-5750	61	3	locally	locally	ADV
ejpam-5750	61	4	integrable	integrable	ADJ
ejpam-5750	61	5	function	function	NOUN
ejpam-5750	61	6	is	be	AUX
ejpam-5750	61	7	the	the	DET
ejpam-5750	61	8	difference	difference	NOUN
ejpam-5750	61	9	of	of	ADP
ejpam-5750	61	10	two	two	NUM
ejpam-5750	61	11	subharmonic	subharmonic	ADJ
ejpam-5750	61	12	functions	function	NOUN
ejpam-5750	61	13	almost	almost	ADV
ejpam-5750	61	14	everywhere	everywhere	ADV
ejpam-5750	61	15	.	.	PUNCT
ejpam-5750	62	1	for	for	ADP
ejpam-5750	62	2	a	a	DET
ejpam-5750	62	3	subharmonic	subharmonic	ADJ
ejpam-5750	62	4	function	function	NOUN
ejpam-5750	62	5	u(x	u(x	NOUN
ejpam-5750	62	6	)	)	PUNCT
ejpam-5750	62	7	,	,	PUNCT
ejpam-5750	62	8	∆u	∆u	ADV
ejpam-5750	62	9	≥	≥	NUM
ejpam-5750	62	10	0	0	NUM
ejpam-5750	62	11	in	in	ADP
ejpam-5750	62	12	the	the	DET
ejpam-5750	62	13	sense	sense	NOUN
ejpam-5750	62	14	of	of	ADP
ejpam-5750	62	15	distributions	distribution	NOUN
ejpam-5750	62	16	,	,	PUNCT
ejpam-5750	62	17	therefore∫	therefore∫	ADP
ejpam-5750	62	18	2π	2π	NOUN
ejpam-5750	62	19	dµ(x	dµ(x	PUNCT
ejpam-5750	62	20	)	)	PUNCT
ejpam-5750	62	21	=	=	VERB
ejpam-5750	62	22	∆u(x	∆u(x	ADV
ejpam-5750	62	23	)	)	PUNCT
ejpam-5750	62	24	is	be	AUX
ejpam-5750	62	25	a	a	DET
ejpam-5750	62	26	radon	radon	ADJ
ejpam-5750	62	27	measure	measure	NOUN
ejpam-5750	62	28	µ	µ	X
ejpam-5750	62	29	on	on	ADP
ejpam-5750	62	30	r2	r2	NOUN
ejpam-5750	62	31	;	;	PUNCT
ejpam-5750	62	32	furthermore	furthermore	ADV
ejpam-5750	62	33	,	,	PUNCT
ejpam-5750	62	34	for	for	ADP
ejpam-5750	62	35	any	any	DET
ejpam-5750	62	36	bounded	bounded	ADJ
ejpam-5750	62	37	domain	domain	NOUN
ejpam-5750	62	38	ω	ω	NOUN
ejpam-5750	62	39	,	,	PUNCT
ejpam-5750	62	40	u(x	u(x	X
ejpam-5750	62	41	)	)	PUNCT
ejpam-5750	62	42	=	=	SYM
ejpam-5750	62	43	∫	∫	PROPN
ejpam-5750	62	44	y∈ω	y∈ω	PROPN
ejpam-5750	62	45	log	log	PROPN
ejpam-5750	62	46	|x	|x	NOUN
ejpam-5750	62	47	−	−	PROPN
ejpam-5750	62	48	y|dµ(y	y|dµ(y	PROPN
ejpam-5750	62	49	)	)	PUNCT
ejpam-5750	62	50	+	+	CCONJ
ejpam-5750	62	51	h(x	h(x	PROPN
ejpam-5750	62	52	)	)	PUNCT
ejpam-5750	62	53	where	where	SCONJ
ejpam-5750	62	54	h(x	h(x	PROPN
ejpam-5750	62	55	)	)	PUNCT
ejpam-5750	62	56	is	be	AUX
ejpam-5750	62	57	a	a	DET
ejpam-5750	62	58	harmonic	harmonic	ADJ
ejpam-5750	62	59	function	function	NOUN
ejpam-5750	62	60	on	on	ADP
ejpam-5750	62	61	ω	ω	PROPN
ejpam-5750	62	62	.	.	PUNCT
ejpam-5750	63	1	the	the	DET
ejpam-5750	63	2	total	total	ADJ
ejpam-5750	63	3	measure	measure	NOUN
ejpam-5750	63	4	µ(r2	µ(r2	NOUN
ejpam-5750	63	5	)	)	PUNCT
ejpam-5750	63	6	associated	associate	VERB
ejpam-5750	63	7	with	with	ADP
ejpam-5750	63	8	u	u	PRON
ejpam-5750	63	9	may	may	AUX
ejpam-5750	63	10	or	or	CCONJ
ejpam-5750	63	11	may	may	AUX
ejpam-5750	63	12	not	not	PART
ejpam-5750	63	13	be	be	AUX
ejpam-5750	63	14	finite	finite	ADJ
ejpam-5750	63	15	;	;	PUNCT
ejpam-5750	63	16	µ(r2	µ(r2	NOUN
ejpam-5750	63	17	)	)	PUNCT
ejpam-5750	63	18	=	=	SYM
ejpam-5750	63	19	0	0	PUNCT
ejpam-5750	64	1	if	if	SCONJ
ejpam-5750	64	2	and	and	CCONJ
ejpam-5750	64	3	only	only	ADV
ejpam-5750	64	4	if	if	SCONJ
ejpam-5750	64	5	u(x	u(x	NOUN
ejpam-5750	64	6	)	)	PUNCT
ejpam-5750	64	7	is	be	AUX
ejpam-5750	64	8	a	a	DET
ejpam-5750	64	9	harmonic	harmonic	ADJ
ejpam-5750	64	10	function	function	NOUN
ejpam-5750	64	11	.	.	PUNCT
ejpam-5750	65	1	if	if	SCONJ
ejpam-5750	65	2	f(x	f(x	PROPN
ejpam-5750	65	3	)	)	PUNCT
ejpam-5750	65	4	is	be	AUX
ejpam-5750	65	5	a	a	DET
ejpam-5750	65	6	c2−function	c2−function	NOUN
ejpam-5750	65	7	defined	define	VERB
ejpam-5750	65	8	on	on	ADP
ejpam-5750	65	9	a	a	DET
ejpam-5750	65	10	neighbourhood	neighbourhood	NOUN
ejpam-5750	65	11	of	of	ADP
ejpam-5750	65	12	ω	ω	NUM
ejpam-5750	65	13	where	where	SCONJ
ejpam-5750	65	14	ω	ω	NOUN
ejpam-5750	65	15	is	be	AUX
ejpam-5750	65	16	a	a	DET
ejpam-5750	65	17	bounded	bounded	ADJ
ejpam-5750	65	18	domain	domain	NOUN
ejpam-5750	65	19	with	with	ADP
ejpam-5750	65	20	smooth	smooth	ADJ
ejpam-5750	65	21	boundary	boundary	ADJ
ejpam-5750	65	22	∂ω	∂ω	PROPN
ejpam-5750	65	23	,	,	PUNCT
ejpam-5750	65	24	then	then	ADV
ejpam-5750	65	25	by	by	ADP
ejpam-5750	65	26	green	green	PROPN
ejpam-5750	65	27	’s	’s	PART
ejpam-5750	65	28	theorem	theorem	ADJ
ejpam-5750	65	29	∫	∫	PROPN
ejpam-5750	65	30	ω	ω	PROPN
ejpam-5750	65	31	∆f(x)dx	∆f(x)dx	PROPN
ejpam-5750	65	32	=	=	SYM
ejpam-5750	65	33	∫	∫	PROPN
ejpam-5750	65	34	∂ω	∂ω	ADJ
ejpam-5750	65	35	∂f	∂f	PROPN
ejpam-5750	65	36	∂n+ds	∂n+ds	NOUN
ejpam-5750	65	37	,	,	PUNCT
ejpam-5750	65	38	where	where	SCONJ
ejpam-5750	65	39	∂	∂	NOUN
ejpam-5750	65	40	∂n+	∂n+	X
ejpam-5750	65	41	is	be	AUX
ejpam-5750	65	42	the	the	DET
ejpam-5750	65	43	outward	outward	ADJ
ejpam-5750	65	44	normal	normal	ADJ
ejpam-5750	65	45	derivative	derivative	NOUN
ejpam-5750	65	46	.	.	PUNCT
ejpam-5750	66	1	in	in	ADP
ejpam-5750	66	2	particular	particular	ADJ
ejpam-5750	66	3	,	,	PUNCT
ejpam-5750	66	4	for	for	ADP
ejpam-5750	66	5	a	a	DET
ejpam-5750	66	6	c2−subharmonic	c2−subharmonic	ADJ
ejpam-5750	66	7	function	function	NOUN
ejpam-5750	66	8	u	u	NOUN
ejpam-5750	66	9	in	in	ADP
ejpam-5750	66	10	r2	r2	PROPN
ejpam-5750	66	11	,	,	PUNCT
ejpam-5750	66	12	the	the	DET
ejpam-5750	66	13	total	total	ADJ
ejpam-5750	66	14	measure	measure	NOUN
ejpam-5750	66	15	of	of	ADP
ejpam-5750	66	16	u	u	NOUN
ejpam-5750	66	17	is	be	AUX
ejpam-5750	66	18	lim	lim	PROPN
ejpam-5750	66	19	ω−→r2	ω−→r2	VERB
ejpam-5750	66	20	∫	∫	PROPN
ejpam-5750	66	21	∂ω	∂ω	PROPN
ejpam-5750	66	22	∂u	∂u	PROPN
ejpam-5750	66	23	∂n+ds	∂n+ds	NOUN
ejpam-5750	67	1	=	=	SYM
ejpam-5750	67	2	lim	lim	PROPN
ejpam-5750	67	3	m−→∞	m−→∞	PROPN
ejpam-5750	67	4	∫	∫	PROPN
ejpam-5750	67	5	∂ωm	∂ωm	PROPN
ejpam-5750	67	6	∂u	∂u	PROPN
ejpam-5750	67	7	∂n+ds	∂n+ds	NOUN
ejpam-5750	67	8	.	.	PUNCT
ejpam-5750	68	1	suppose	suppose	VERB
ejpam-5750	68	2	now	now	ADV
ejpam-5750	68	3	that	that	SCONJ
ejpam-5750	68	4	s(x	s(x	NOUN
ejpam-5750	68	5	)	)	PUNCT
ejpam-5750	68	6	is	be	AUX
ejpam-5750	68	7	a	a	DET
ejpam-5750	68	8	subharmonic	subharmonic	ADJ
ejpam-5750	68	9	function	function	NOUN
ejpam-5750	68	10	on	on	ADP
ejpam-5750	68	11	r2	r2	PROPN
ejpam-5750	68	12	.	.	PUNCT
ejpam-5750	69	1	then	then	ADV
ejpam-5750	69	2	(	(	PUNCT
ejpam-5750	69	3	see	see	VERB
ejpam-5750	69	4	brelot	brelot	NOUN
ejpam-5750	69	5	[	[	X
ejpam-5750	69	6	2	2	NUM
ejpam-5750	69	7	]	]	PUNCT
ejpam-5750	69	8	)	)	PUNCT
ejpam-5750	69	9	there	there	PRON
ejpam-5750	69	10	exists	exist	VERB
ejpam-5750	69	11	an	an	DET
ejpam-5750	69	12	increasing	increase	VERB
ejpam-5750	69	13	sequence	sequence	NOUN
ejpam-5750	69	14	{	{	PUNCT
ejpam-5750	69	15	sn	sn	NOUN
ejpam-5750	69	16	}	}	PUNCT
ejpam-5750	69	17	of	of	ADP
ejpam-5750	69	18	c2−functions	c2−function	NOUN
ejpam-5750	69	19	tending	tend	VERB
ejpam-5750	69	20	to	to	ADP
ejpam-5750	69	21	s	s	NOUN
ejpam-5750	69	22	on	on	ADP
ejpam-5750	69	23	r2	r2	PROPN
ejpam-5750	69	24	.	.	PUNCT
ejpam-5750	70	1	then	then	ADV
ejpam-5750	70	2	∆sn	∆sn	VERB
ejpam-5750	70	3	−→	−→	ADJ
ejpam-5750	70	4	∆s	∆s	NOUN
ejpam-5750	70	5	so	so	SCONJ
ejpam-5750	70	6	that	that	SCONJ
ejpam-5750	70	7	the	the	DET
ejpam-5750	70	8	total	total	ADJ
ejpam-5750	70	9	measure	measure	NOUN
ejpam-5750	70	10	associated	associate	VERB
ejpam-5750	70	11	with	with	ADP
ejpam-5750	70	12	s	s	PRON
ejpam-5750	70	13	equals	equal	VERB
ejpam-5750	70	14	to	to	ADP
ejpam-5750	70	15	lim	lim	PROPN
ejpam-5750	70	16	n−→∞	n−→∞	PROPN
ejpam-5750	70	17	total	total	ADJ
ejpam-5750	70	18	measure	measure	NOUN
ejpam-5750	70	19	of	of	ADP
ejpam-5750	70	20	sn	sn	PROPN
ejpam-5750	70	21	.	.	PUNCT
ejpam-5750	70	22	remark	remark	NOUN
ejpam-5750	70	23	that	that	SCONJ
ejpam-5750	70	24	this	this	DET
ejpam-5750	70	25	limit	limit	NOUN
ejpam-5750	70	26	does	do	AUX
ejpam-5750	70	27	not	not	PART
ejpam-5750	70	28	depend	depend	VERB
ejpam-5750	70	29	on	on	ADP
ejpam-5750	70	30	the	the	DET
ejpam-5750	70	31	particular	particular	ADJ
ejpam-5750	70	32	sequence	sequence	NOUN
ejpam-5750	70	33	{	{	PUNCT
ejpam-5750	70	34	sn	sn	NOUN
ejpam-5750	70	35	}	}	PUNCT
ejpam-5750	70	36	of	of	ADP
ejpam-5750	70	37	c2−subharmonic	c2−subharmonic	ADJ
ejpam-5750	70	38	functions	function	NOUN
ejpam-5750	70	39	that	that	PRON
ejpam-5750	70	40	increases	increase	VERB
ejpam-5750	70	41	to	to	ADP
ejpam-5750	70	42	s.	s.	PROPN
ejpam-5750	70	43	3	3	NUM
ejpam-5750	70	44	.	.	PUNCT
ejpam-5750	70	45	inversion	inversion	NOUN
ejpam-5750	70	46	and	and	CCONJ
ejpam-5750	70	47	associated	associated	ADJ
ejpam-5750	70	48	measure	measure	NOUN
ejpam-5750	70	49	of	of	ADP
ejpam-5750	70	50	a	a	DET
ejpam-5750	70	51	subharmonic	subharmonic	ADJ
ejpam-5750	70	52	function	function	NOUN
ejpam-5750	70	53	let	let	VERB
ejpam-5750	70	54	s(x	s(x	PROPN
ejpam-5750	70	55	)	)	PUNCT
ejpam-5750	70	56	be	be	AUX
ejpam-5750	70	57	subharmonic	subharmonic	ADJ
ejpam-5750	70	58	on	on	ADP
ejpam-5750	70	59	r2	r2	PROPN
ejpam-5750	70	60	.	.	PUNCT
ejpam-5750	71	1	then	then	ADV
ejpam-5750	71	2	∆s(x	∆s(x	PROPN
ejpam-5750	71	3	)	)	PUNCT
ejpam-5750	71	4	≥	≥	NOUN
ejpam-5750	71	5	0	0	NUM
ejpam-5750	71	6	in	in	ADP
ejpam-5750	71	7	the	the	DET
ejpam-5750	71	8	sense	sense	NOUN
ejpam-5750	71	9	of	of	ADP
ejpam-5750	71	10	distributions	distribution	NOUN
ejpam-5750	71	11	[	[	X
ejpam-5750	71	12	9	9	NUM
ejpam-5750	71	13	,	,	PUNCT
ejpam-5750	71	14	10	10	NUM
ejpam-5750	71	15	]	]	PUNCT
ejpam-5750	71	16	,	,	PUNCT
ejpam-5750	71	17	and	and	CCONJ
ejpam-5750	71	18	hence	hence	ADV
ejpam-5750	71	19	a	a	DET
ejpam-5750	71	20	radon	radon	ADJ
ejpam-5750	71	21	measure	measure	NOUN
ejpam-5750	71	22	µ(x	µ(x	VERB
ejpam-5750	71	23	)	)	PUNCT
ejpam-5750	71	24	,	,	PUNCT
ejpam-5750	71	25	dµ(x	dµ(x	PUNCT
ejpam-5750	71	26	)	)	PUNCT
ejpam-5750	71	27	=	=	SYM
ejpam-5750	71	28	1	1	NUM
ejpam-5750	71	29	2π∆s(x)dx	2π∆s(x)dx	NOUN
ejpam-5750	71	30	such	such	ADJ
ejpam-5750	71	31	that	that	SCONJ
ejpam-5750	71	32	locally	locally	ADV
ejpam-5750	71	33	(	(	PUNCT
ejpam-5750	71	34	i.e.	i.e.	X
ejpam-5750	71	35	in	in	ADP
ejpam-5750	71	36	a	a	DET
ejpam-5750	71	37	neighbourhood	neighbourhood	NOUN
ejpam-5750	71	38	n	n	NOUN
ejpam-5750	71	39	of	of	ADP
ejpam-5750	71	40	a	a	DET
ejpam-5750	71	41	point	point	NOUN
ejpam-5750	71	42	x	x	NOUN
ejpam-5750	71	43	)	)	PUNCT
ejpam-5750	71	44	s(x	s(x	PROPN
ejpam-5750	71	45	)	)	PUNCT
ejpam-5750	72	1	=	=	SYM
ejpam-5750	72	2	∫	∫	PROPN
ejpam-5750	73	1	n	n	CCONJ
ejpam-5750	73	2	log	log	VERB
ejpam-5750	73	3	|x−	|x−	PROPN
ejpam-5750	73	4	y|dµ(y)+	y|dµ(y)+	PROPN
ejpam-5750	74	1	a	a	DET
ejpam-5750	74	2	harmonic	harmonic	ADJ
ejpam-5750	74	3	function	function	NOUN
ejpam-5750	74	4	on	on	ADP
ejpam-5750	74	5	n	n	PROPN
ejpam-5750	74	6	.	.	PUNCT
ejpam-5750	75	1	definition	definition	NOUN
ejpam-5750	75	2	1	1	NUM
ejpam-5750	75	3	.	.	PUNCT
ejpam-5750	76	1	(	(	PUNCT
ejpam-5750	76	2	inversion	inversion	NOUN
ejpam-5750	76	3	)	)	PUNCT
ejpam-5750	77	1	[	[	X
ejpam-5750	77	2	11	11	NUM
ejpam-5750	77	3	]	]	PUNCT
ejpam-5750	77	4	a	a	DET
ejpam-5750	77	5	map	map	NOUN
ejpam-5750	77	6	x	x	INTJ
ejpam-5750	77	7	→	→	SYM
ejpam-5750	77	8	x∗	x∗	X
ejpam-5750	77	9	=	=	PUNCT
ejpam-5750	78	1	x	x	PUNCT
ejpam-5750	78	2	|x|2	|x|2	VERB
ejpam-5750	78	3	if	if	SCONJ
ejpam-5750	78	4	x	x	PROPN
ejpam-5750	78	5	̸=	̸=	PROPN
ejpam-5750	78	6	0	0	NUM
ejpam-5750	78	7	,	,	PUNCT
ejpam-5750	78	8	∞	∞	PROPN
ejpam-5750	78	9	;	;	PUNCT
ejpam-5750	78	10	0	0	NUM
ejpam-5750	78	11	→	→	SYM
ejpam-5750	78	12	∞	∞	NUM
ejpam-5750	78	13	and	and	CCONJ
ejpam-5750	78	14	∞	∞	NUM
ejpam-5750	78	15	→	→	SYM
ejpam-5750	78	16	0	0	NUM
ejpam-5750	78	17	is	be	AUX
ejpam-5750	78	18	known	know	VERB
ejpam-5750	78	19	as	as	ADP
ejpam-5750	78	20	an	an	DET
ejpam-5750	78	21	inversion	inversion	NOUN
ejpam-5750	78	22	(	(	PUNCT
ejpam-5750	78	23	see	see	VERB
ejpam-5750	78	24	for	for	ADP
ejpam-5750	78	25	example	example	NOUN
ejpam-5750	78	26	:	:	PUNCT
ejpam-5750	78	27	axler	axler	NOUN
ejpam-5750	78	28	et	et	PROPN
ejpam-5750	78	29	al	al	PROPN
ejpam-5750	78	30	.	.	PUNCT
ejpam-5750	79	1	pp	pp	ADP
ejpam-5750	79	2	59–61	59–61	NUM
ejpam-5750	79	3	)	)	PUNCT
ejpam-5750	79	4	.	.	PUNCT
ejpam-5750	80	1	if	if	SCONJ
ejpam-5750	80	2	u(x	u(x	NOUN
ejpam-5750	80	3	)	)	PUNCT
ejpam-5750	80	4	is	be	AUX
ejpam-5750	80	5	a	a	DET
ejpam-5750	80	6	subharmonic	subharmonic	ADJ
ejpam-5750	80	7	(	(	PUNCT
ejpam-5750	80	8	respectively	respectively	ADV
ejpam-5750	80	9	harmonic	harmonic	ADJ
ejpam-5750	80	10	)	)	PUNCT
ejpam-5750	80	11	function	function	NOUN
ejpam-5750	80	12	defined	define	VERB
ejpam-5750	80	13	outside	outside	ADP
ejpam-5750	80	14	a	a	DET
ejpam-5750	80	15	compact	compact	ADJ
ejpam-5750	80	16	set	set	VERB
ejpam-5750	80	17	amulya	amulya	PROPN
ejpam-5750	80	18	smyrna	smyrna	PROPN
ejpam-5750	80	19	c.	c.	PROPN
ejpam-5750	80	20	,	,	PUNCT
ejpam-5750	80	21	n.	n.	PROPN
ejpam-5750	80	22	nathiya	nathiya	PROPN
ejpam-5750	80	23	/	/	SYM
ejpam-5750	80	24	eur	eur	PROPN
ejpam-5750	80	25	.	.	PUNCT
ejpam-5750	81	1	j.	j.	PROPN
ejpam-5750	81	2	pure	pure	PROPN
ejpam-5750	81	3	appl	appl	PROPN
ejpam-5750	81	4	.	.	PROPN
ejpam-5750	81	5	math	math	PROPN
ejpam-5750	81	6	,	,	PUNCT
ejpam-5750	81	7	18	18	NUM
ejpam-5750	81	8	(	(	PUNCT
ejpam-5750	81	9	2	2	NUM
ejpam-5750	81	10	)	)	PUNCT
ejpam-5750	81	11	(	(	PUNCT
ejpam-5750	81	12	2025	2025	NUM
ejpam-5750	81	13	)	)	PUNCT
ejpam-5750	81	14	,	,	PUNCT
ejpam-5750	81	15	5750	5750	NUM
ejpam-5750	81	16	4	4	NUM
ejpam-5750	81	17	of	of	ADP
ejpam-5750	81	18	9	9	NUM
ejpam-5750	81	19	then	then	ADV
ejpam-5750	81	20	u(x∗	u(x∗	X
ejpam-5750	81	21	)	)	PUNCT
ejpam-5750	82	1	=	=	SYM
ejpam-5750	82	2	u	u	NOUN
ejpam-5750	82	3	(	(	PUNCT
ejpam-5750	82	4	x	x	PART
ejpam-5750	82	5	|x|2	|x|2	PROPN
ejpam-5750	82	6	)	)	PUNCT
ejpam-5750	82	7	is	be	AUX
ejpam-5750	82	8	a	a	DET
ejpam-5750	82	9	subharmonic	subharmonic	ADJ
ejpam-5750	82	10	(	(	PUNCT
ejpam-5750	82	11	respectively	respectively	ADV
ejpam-5750	82	12	harmonic	harmonic	ADJ
ejpam-5750	82	13	)	)	PUNCT
ejpam-5750	82	14	function	function	NOUN
ejpam-5750	82	15	in	in	ADP
ejpam-5750	82	16	a	a	DET
ejpam-5750	82	17	neighbourhood	neighbourhood	NOUN
ejpam-5750	82	18	of	of	ADP
ejpam-5750	82	19	0	0	NUM
ejpam-5750	82	20	,	,	PUNCT
ejpam-5750	82	21	excluding	exclude	VERB
ejpam-5750	82	22	0	0	NUM
ejpam-5750	82	23	.	.	PUNCT
ejpam-5750	83	1	for	for	ADP
ejpam-5750	83	2	a	a	DET
ejpam-5750	83	3	set	set	ADJ
ejpam-5750	83	4	e	e	NOUN
ejpam-5750	83	5	in	in	ADP
ejpam-5750	83	6	r2	r2	PROPN
ejpam-5750	83	7	write	write	VERB
ejpam-5750	83	8	e∗	e∗	PROPN
ejpam-5750	83	9	=	=	SYM
ejpam-5750	83	10	{	{	PUNCT
ejpam-5750	83	11	x∗	x∗	PROPN
ejpam-5750	83	12	:	:	PUNCT
ejpam-5750	83	13	x	x	PUNCT
ejpam-5750	83	14	∈	∈	NOUN
ejpam-5750	83	15	e	e	NOUN
ejpam-5750	83	16	}	}	PUNCT
ejpam-5750	83	17	.	.	PUNCT
ejpam-5750	84	1	theorem	theorem	NOUN
ejpam-5750	84	2	1	1	NUM
ejpam-5750	84	3	.	.	PUNCT
ejpam-5750	85	1	let	let	AUX
ejpam-5750	85	2	u(x	u(x	NOUN
ejpam-5750	85	3	)	)	PUNCT
ejpam-5750	85	4	be	be	AUX
ejpam-5750	85	5	a	a	DET
ejpam-5750	85	6	subharmonic	subharmonic	ADJ
ejpam-5750	85	7	function	function	NOUN
ejpam-5750	85	8	defined	define	VERB
ejpam-5750	85	9	outside	outside	ADP
ejpam-5750	85	10	a	a	DET
ejpam-5750	85	11	compact	compact	ADJ
ejpam-5750	85	12	set	set	NOUN
ejpam-5750	85	13	k	k	PROPN
ejpam-5750	85	14	with	with	ADP
ejpam-5750	85	15	associated	associated	ADJ
ejpam-5750	85	16	measure	measure	NOUN
ejpam-5750	85	17	λ	λ	PROPN
ejpam-5750	85	18	.	.	PROPN
ejpam-5750	85	19	then	then	ADV
ejpam-5750	85	20	u(x	u(x	VERB
ejpam-5750	85	21	)	)	PUNCT
ejpam-5750	86	1	has	have	VERB
ejpam-5750	86	2	a	a	DET
ejpam-5750	86	3	harmonic	harmonic	ADJ
ejpam-5750	86	4	majorant	majorant	NOUN
ejpam-5750	86	5	h(x	h(x	PROPN
ejpam-5750	86	6	)	)	PUNCT
ejpam-5750	86	7	outside	outside	ADP
ejpam-5750	86	8	a	a	DET
ejpam-5750	86	9	compact	compact	ADJ
ejpam-5750	86	10	set	set	NOUN
ejpam-5750	86	11	k	k	NOUN
ejpam-5750	87	1	if	if	SCONJ
ejpam-5750	88	1	and	and	CCONJ
ejpam-5750	88	2	only	only	ADV
ejpam-5750	88	3	if	if	SCONJ
ejpam-5750	88	4	∫	∫	PROPN
ejpam-5750	88	5	r2\k	r2\k	VERB
ejpam-5750	88	6	dλ(x	dλ(x	PUNCT
ejpam-5750	88	7	)	)	PUNCT
ejpam-5750	88	8	<	<	X
ejpam-5750	88	9	∞.	∞.	PROPN
ejpam-5750	88	10	proof	proof	NOUN
ejpam-5750	88	11	.	.	PUNCT
ejpam-5750	89	1	write	write	VERB
ejpam-5750	89	2	z	z	NOUN
ejpam-5750	89	3	=	=	SYM
ejpam-5750	89	4	x∗.	x∗.	PROPN
ejpam-5750	89	5	then	then	ADV
ejpam-5750	89	6	v(z	v(z	NOUN
ejpam-5750	89	7	)	)	PUNCT
ejpam-5750	89	8	=	=	SYM
ejpam-5750	89	9	u(z	u(z	NOUN
ejpam-5750	89	10	)	)	PUNCT
ejpam-5750	89	11	−	−	PROPN
ejpam-5750	90	1	h(z	h(z	NOUN
ejpam-5750	90	2	)	)	PUNCT
ejpam-5750	90	3	is	be	AUX
ejpam-5750	90	4	an	an	DET
ejpam-5750	90	5	upper	upper	ADJ
ejpam-5750	90	6	bounded	bounded	ADJ
ejpam-5750	90	7	subharmonic	subharmonic	ADJ
ejpam-5750	90	8	function	function	NOUN
ejpam-5750	90	9	on	on	ADP
ejpam-5750	90	10	0	0	NUM
ejpam-5750	90	11	<	<	X
ejpam-5750	90	12	|z|	|z|	NOUN
ejpam-5750	90	13	<	<	X
ejpam-5750	90	14	ϵ	ϵ	NOUN
ejpam-5750	90	15	;	;	PUNCT
ejpam-5750	90	16	hence	hence	ADV
ejpam-5750	90	17	extends	extend	VERB
ejpam-5750	90	18	as	as	ADP
ejpam-5750	90	19	a	a	DET
ejpam-5750	90	20	subharmonic	subharmonic	ADJ
ejpam-5750	90	21	function	function	NOUN
ejpam-5750	90	22	v(z	v(z	NOUN
ejpam-5750	90	23	)	)	PUNCT
ejpam-5750	90	24	on	on	ADP
ejpam-5750	90	25	|z|	|z|	NOUN
ejpam-5750	90	26	<	<	X
ejpam-5750	90	27	ϵ	ϵ	X
ejpam-5750	90	28	whose	whose	DET
ejpam-5750	90	29	associated	associated	ADJ
ejpam-5750	90	30	measure	measure	NOUN
ejpam-5750	90	31	is	be	AUX
ejpam-5750	90	32	denoted	denote	VERB
ejpam-5750	90	33	by	by	ADP
ejpam-5750	90	34	σ(x	σ(x	NOUN
ejpam-5750	90	35	)	)	PUNCT
ejpam-5750	90	36	so	so	SCONJ
ejpam-5750	90	37	that	that	SCONJ
ejpam-5750	90	38	v(z	v(z	NOUN
ejpam-5750	90	39	)	)	PUNCT
ejpam-5750	91	1	=	=	SYM
ejpam-5750	91	2	∫	∫	PROPN
ejpam-5750	92	1	|y|<ϵ	|y|<ϵ	PROPN
ejpam-5750	92	2	log	log	VERB
ejpam-5750	92	3	|z	|z	PROPN
ejpam-5750	93	1	−	−	PROPN
ejpam-5750	93	2	y|dσ(y)+	y|dσ(y)+	PROPN
ejpam-5750	93	3	a	a	DET
ejpam-5750	93	4	harmonic	harmonic	ADJ
ejpam-5750	93	5	function	function	NOUN
ejpam-5750	93	6	on	on	ADP
ejpam-5750	93	7	|z|	|z|	NOUN
ejpam-5750	93	8	<	<	X
ejpam-5750	93	9	ϵ.	ϵ.	NOUN
ejpam-5750	93	10	note	note	NOUN
ejpam-5750	93	11	that	that	SCONJ
ejpam-5750	93	12	∫	∫	PROPN
ejpam-5750	93	13	|y|≤	|y|≤	NUM
ejpam-5750	93	14	ϵ	ϵ	X
ejpam-5750	93	15	2	2	NUM
ejpam-5750	93	16	dσ(y	dσ(y	NOUN
ejpam-5750	93	17	)	)	PUNCT
ejpam-5750	93	18	is	be	AUX
ejpam-5750	93	19	finite	finite	ADJ
ejpam-5750	93	20	and	and	CCONJ
ejpam-5750	94	1	σ	σ	NOUN
ejpam-5750	94	2	=	=	SYM
ejpam-5750	94	3	λ	λ	PROPN
ejpam-5750	94	4	on	on	ADP
ejpam-5750	94	5	any	any	DET
ejpam-5750	94	6	compact	compact	ADJ
ejpam-5750	94	7	set	set	NOUN
ejpam-5750	94	8	in	in	ADP
ejpam-5750	94	9	0	0	NUM
ejpam-5750	94	10	<	<	X
ejpam-5750	94	11	|z|	|z|	NOUN
ejpam-5750	94	12	<	<	X
ejpam-5750	94	13	ϵ	ϵ	X
ejpam-5750	94	14	2	2	NUM
ejpam-5750	94	15	.	.	PUNCT
ejpam-5750	95	1	hence	hence	ADV
ejpam-5750	95	2	λ(e	λ(e	VERB
ejpam-5750	95	3	)	)	PUNCT
ejpam-5750	95	4	where	where	SCONJ
ejpam-5750	95	5	e	e	NOUN
ejpam-5750	95	6	=	=	SYM
ejpam-5750	95	7	(	(	PUNCT
ejpam-5750	95	8	z	z	NOUN
ejpam-5750	95	9	:	:	PUNCT
ejpam-5750	95	10	0	0	NUM
ejpam-5750	95	11	<	<	X
ejpam-5750	95	12	|z|	|z|	PROPN
ejpam-5750	95	13	<	<	X
ejpam-5750	95	14	ϵ	ϵ	PROPN
ejpam-5750	95	15	2	2	NUM
ejpam-5750	95	16	)	)	PUNCT
ejpam-5750	95	17	is	be	AUX
ejpam-5750	95	18	finite	finite	ADJ
ejpam-5750	95	19	.	.	PUNCT
ejpam-5750	96	1	take	take	VERB
ejpam-5750	96	2	an	an	DET
ejpam-5750	96	3	inversion	inversion	NOUN
ejpam-5750	96	4	to	to	PART
ejpam-5750	96	5	conclude	conclude	VERB
ejpam-5750	96	6	that	that	PRON
ejpam-5750	96	7	λ(e∗	λ(e∗	CCONJ
ejpam-5750	96	8	)	)	PUNCT
ejpam-5750	96	9	is	be	AUX
ejpam-5750	96	10	finite	finite	ADJ
ejpam-5750	96	11	leading	lead	VERB
ejpam-5750	96	12	to	to	ADP
ejpam-5750	96	13	the	the	DET
ejpam-5750	96	14	conclusion	conclusion	NOUN
ejpam-5750	96	15	λ(r2\k	λ(r2\k	NUM
ejpam-5750	96	16	)	)	PUNCT
ejpam-5750	96	17	is	be	AUX
ejpam-5750	96	18	finite	finite	PROPN
ejpam-5750	96	19	.	.	PUNCT
ejpam-5750	97	1	note	note	VERB
ejpam-5750	97	2	that	that	PRON
ejpam-5750	97	3	e∗	e∗	PROPN
ejpam-5750	97	4	is	be	AUX
ejpam-5750	97	5	a	a	DET
ejpam-5750	97	6	neighbourhood	neighbourhood	NOUN
ejpam-5750	97	7	of	of	ADP
ejpam-5750	97	8	the	the	DET
ejpam-5750	97	9	point	point	NOUN
ejpam-5750	97	10	at	at	ADP
ejpam-5750	97	11	infiniy	infiniy	NOUN
ejpam-5750	97	12	.	.	PUNCT
ejpam-5750	98	1	converse	converse	NOUN
ejpam-5750	98	2	:	:	PUNCT
ejpam-5750	98	3	if	if	SCONJ
ejpam-5750	98	4	∫	∫	PROPN
ejpam-5750	98	5	r2\k	r2\k	VERB
ejpam-5750	98	6	dλ(x	dλ(x	PUNCT
ejpam-5750	98	7	)	)	PUNCT
ejpam-5750	98	8	<	<	X
ejpam-5750	98	9	∞	∞	PROPN
ejpam-5750	98	10	,	,	PUNCT
ejpam-5750	98	11	define	define	VERB
ejpam-5750	98	12	a	a	DET
ejpam-5750	98	13	radon	radon	ADJ
ejpam-5750	98	14	measure	measure	NOUN
ejpam-5750	98	15	ν	ν	NOUN
ejpam-5750	98	16	on	on	ADP
ejpam-5750	98	17	n	n	NOUN
ejpam-5750	98	18	=	=	PUNCT
ejpam-5750	98	19	{	{	PUNCT
ejpam-5750	98	20	z	z	NOUN
ejpam-5750	98	21	:	:	PUNCT
ejpam-5750	98	22	|z|	|z|	NOUN
ejpam-5750	98	23	<	<	X
ejpam-5750	98	24	ϵ	ϵ	X
ejpam-5750	98	25	}	}	PUNCT
ejpam-5750	98	26	by	by	ADP
ejpam-5750	98	27	taking	take	VERB
ejpam-5750	98	28	for	for	ADP
ejpam-5750	98	29	any	any	DET
ejpam-5750	98	30	compact	compact	ADJ
ejpam-5750	98	31	set	set	VERB
ejpam-5750	98	32	a	a	DET
ejpam-5750	98	33	∈	∈	NOUN
ejpam-5750	98	34	r2	r2	NOUN
ejpam-5750	98	35	,	,	PUNCT
ejpam-5750	98	36	ν(a	ν(a	PROPN
ejpam-5750	98	37	)	)	PUNCT
ejpam-5750	99	1	=	=	SYM
ejpam-5750	99	2	λ[(a	λ[(a	X
ejpam-5750	99	3	∩	∩	X
ejpam-5750	99	4	n)∗	n)∗	PROPN
ejpam-5750	99	5	]	]	PUNCT
ejpam-5750	99	6	where	where	SCONJ
ejpam-5750	99	7	(	(	PUNCT
ejpam-5750	99	8	a	a	DET
ejpam-5750	99	9	∩	∩	NOUN
ejpam-5750	99	10	n)∗	n)∗	PROPN
ejpam-5750	99	11	is	be	AUX
ejpam-5750	99	12	the	the	DET
ejpam-5750	99	13	inversion	inversion	NOUN
ejpam-5750	99	14	set	set	NOUN
ejpam-5750	99	15	of	of	ADP
ejpam-5750	99	16	(	(	PUNCT
ejpam-5750	99	17	a	a	DET
ejpam-5750	99	18	∩	∩	NOUN
ejpam-5750	99	19	n	n	CCONJ
ejpam-5750	99	20	)	)	PUNCT
ejpam-5750	99	21	.	.	PUNCT
ejpam-5750	100	1	note	note	VERB
ejpam-5750	100	2	ν	ν	PROPN
ejpam-5750	100	3	is	be	AUX
ejpam-5750	100	4	a	a	DET
ejpam-5750	100	5	radon	radon	ADJ
ejpam-5750	100	6	measure	measure	NOUN
ejpam-5750	100	7	on	on	ADP
ejpam-5750	100	8	r2	r2	PROPN
ejpam-5750	100	9	with	with	ADP
ejpam-5750	100	10	compact	compact	ADJ
ejpam-5750	100	11	harmonic	harmonic	ADJ
ejpam-5750	100	12	support	support	NOUN
ejpam-5750	100	13	taking	take	VERB
ejpam-5750	100	14	ν({0	ν({0	PRON
ejpam-5750	100	15	}	}	PUNCT
ejpam-5750	100	16	)	)	PUNCT
ejpam-5750	101	1	=	=	SYM
ejpam-5750	101	2	0	0	X
ejpam-5750	101	3	.	.	PUNCT
ejpam-5750	101	4	write	write	VERB
ejpam-5750	101	5	z	z	NOUN
ejpam-5750	101	6	=	=	SYM
ejpam-5750	101	7	x∗	x∗	PROPN
ejpam-5750	101	8	,	,	PUNCT
ejpam-5750	101	9	x	x	PUNCT
ejpam-5750	101	10	in	in	ADP
ejpam-5750	101	11	a	a	DET
ejpam-5750	101	12	neighbourhood	neighbourhood	NOUN
ejpam-5750	101	13	of	of	ADP
ejpam-5750	101	14	infinity	infinity	NOUN
ejpam-5750	101	15	.	.	PUNCT
ejpam-5750	102	1	then	then	ADV
ejpam-5750	102	2	s(x	s(x	PROPN
ejpam-5750	102	3	)	)	PUNCT
ejpam-5750	103	1	=	=	SYM
ejpam-5750	103	2	∫	∫	PROPN
ejpam-5750	103	3	r2	r2	PROPN
ejpam-5750	103	4	log	log	PROPN
ejpam-5750	103	5	|x	|x	PROPN
ejpam-5750	103	6	−	−	PROPN
ejpam-5750	103	7	y|dν(y	y|dν(y	NOUN
ejpam-5750	103	8	)	)	PUNCT
ejpam-5750	103	9	is	be	AUX
ejpam-5750	103	10	subharmonic	subharmonic	ADJ
ejpam-5750	103	11	on	on	ADP
ejpam-5750	103	12	r2	r2	PROPN
ejpam-5750	103	13	.	.	PUNCT
ejpam-5750	104	1	hence	hence	ADV
ejpam-5750	104	2	∃	∃	PROPN
ejpam-5750	104	3	a	a	DET
ejpam-5750	104	4	harmonic	harmonic	ADJ
ejpam-5750	104	5	function	function	NOUN
ejpam-5750	104	6	h(x	h(x	PROPN
ejpam-5750	104	7	)	)	PUNCT
ejpam-5750	104	8	≥	≥	NOUN
ejpam-5750	104	9	s(x	s(x	PROPN
ejpam-5750	104	10	)	)	PUNCT
ejpam-5750	104	11	on	on	ADP
ejpam-5750	104	12	n	n	PROPN
ejpam-5750	104	13	.	.	PUNCT
ejpam-5750	105	1	note	note	VERB
ejpam-5750	105	2	that	that	SCONJ
ejpam-5750	105	3	s(z	s(z	PROPN
ejpam-5750	105	4	)	)	PUNCT
ejpam-5750	105	5	on	on	ADP
ejpam-5750	105	6	n\{0	n\{0	ADV
ejpam-5750	105	7	}	}	PUNCT
ejpam-5750	105	8	is	be	AUX
ejpam-5750	105	9	the	the	DET
ejpam-5750	105	10	same	same	ADJ
ejpam-5750	105	11	as	as	ADP
ejpam-5750	105	12	u(x∗	u(x∗	NOUN
ejpam-5750	105	13	)	)	PUNCT
ejpam-5750	106	1	=	=	SYM
ejpam-5750	106	2	u(z	u(z	NOUN
ejpam-5750	106	3	)	)	PUNCT
ejpam-5750	106	4	up	up	ADP
ejpam-5750	106	5	to	to	ADP
ejpam-5750	106	6	an	an	DET
ejpam-5750	106	7	additive	additive	ADJ
ejpam-5750	106	8	harmonic	harmonic	ADJ
ejpam-5750	106	9	function	function	NOUN
ejpam-5750	106	10	v(z	v(z	NOUN
ejpam-5750	106	11	)	)	PUNCT
ejpam-5750	106	12	.	.	PUNCT
ejpam-5750	107	1	also	also	ADV
ejpam-5750	107	2	note	note	VERB
ejpam-5750	107	3	that	that	SCONJ
ejpam-5750	107	4	on	on	ADP
ejpam-5750	107	5	n\{0	n\{0	NOUN
ejpam-5750	107	6	}	}	PUNCT
ejpam-5750	107	7	,	,	PUNCT
ejpam-5750	107	8	the	the	DET
ejpam-5750	107	9	harmonic	harmonic	ADJ
ejpam-5750	107	10	functions	function	NOUN
ejpam-5750	107	11	h(z	h(z	NOUN
ejpam-5750	107	12	)	)	PUNCT
ejpam-5750	107	13	and	and	CCONJ
ejpam-5750	107	14	v(z	v(z	NOUN
ejpam-5750	107	15	)	)	PUNCT
ejpam-5750	107	16	can	can	AUX
ejpam-5750	107	17	also	also	ADV
ejpam-5750	107	18	be	be	AUX
ejpam-5750	107	19	written	write	VERB
ejpam-5750	107	20	as	as	ADP
ejpam-5750	107	21	h(x∗	h(x∗	NOUN
ejpam-5750	107	22	)	)	PUNCT
ejpam-5750	107	23	and	and	CCONJ
ejpam-5750	107	24	v(x∗	v(x∗	NOUN
ejpam-5750	107	25	)	)	PUNCT
ejpam-5750	107	26	so	so	SCONJ
ejpam-5750	107	27	that	that	SCONJ
ejpam-5750	107	28	we	we	PRON
ejpam-5750	107	29	have	have	VERB
ejpam-5750	107	30	h(x∗	h(x∗	NOUN
ejpam-5750	107	31	)	)	PUNCT
ejpam-5750	107	32	≥	≥	NOUN
ejpam-5750	107	33	u(x∗	u(x∗	X
ejpam-5750	107	34	)	)	PUNCT
ejpam-5750	107	35	+	+	NUM
ejpam-5750	107	36	v(x∗	v(x∗	NOUN
ejpam-5750	107	37	)	)	PUNCT
ejpam-5750	107	38	on	on	ADP
ejpam-5750	107	39	n\{0	n\{0	ADJ
ejpam-5750	107	40	}	}	PUNCT
ejpam-5750	107	41	.	.	PUNCT
ejpam-5750	108	1	an	an	DET
ejpam-5750	108	2	inversion	inversion	NOUN
ejpam-5750	108	3	shows	show	VERB
ejpam-5750	108	4	that	that	SCONJ
ejpam-5750	108	5	h(x	h(x	PROPN
ejpam-5750	108	6	)	)	PUNCT
ejpam-5750	108	7	≥	≥	NOUN
ejpam-5750	108	8	u(x	u(x	PROPN
ejpam-5750	108	9	)	)	PUNCT
ejpam-5750	108	10	+	+	CCONJ
ejpam-5750	108	11	v(x	v(x	NOUN
ejpam-5750	108	12	)	)	PUNCT
ejpam-5750	108	13	.	.	PUNCT
ejpam-5750	109	1	thus	thus	ADV
ejpam-5750	109	2	u(x	u(x	NOUN
ejpam-5750	109	3	)	)	PUNCT
ejpam-5750	109	4	≤	≤	NUM
ejpam-5750	109	5	h(x	h(x	PROPN
ejpam-5750	109	6	)	)	PUNCT
ejpam-5750	109	7	−	−	PROPN
ejpam-5750	110	1	v(x	v(x	NOUN
ejpam-5750	110	2	)	)	PUNCT
ejpam-5750	110	3	near	near	ADP
ejpam-5750	110	4	infinity	infinity	NOUN
ejpam-5750	110	5	.	.	PUNCT
ejpam-5750	111	1	that	that	PRON
ejpam-5750	111	2	is	be	AUX
ejpam-5750	111	3	u(x	u(x	NOUN
ejpam-5750	111	4	)	)	PUNCT
ejpam-5750	111	5	is	be	AUX
ejpam-5750	111	6	majorised	majorise	VERB
ejpam-5750	111	7	by	by	ADP
ejpam-5750	111	8	a	a	DET
ejpam-5750	111	9	harmonic	harmonic	ADJ
ejpam-5750	111	10	function	function	NOUN
ejpam-5750	111	11	near	near	ADP
ejpam-5750	111	12	infinity	infinity	NOUN
ejpam-5750	111	13	if	if	SCONJ
ejpam-5750	111	14	the	the	DET
ejpam-5750	111	15	associated	associated	ADJ
ejpam-5750	111	16	measure	measure	NOUN
ejpam-5750	111	17	λ	λ	PROPN
ejpam-5750	111	18	of	of	ADP
ejpam-5750	111	19	u	u	NOUN
ejpam-5750	111	20	is	be	AUX
ejpam-5750	111	21	such	such	ADJ
ejpam-5750	111	22	that	that	SCONJ
ejpam-5750	111	23	∫	∫	PROPN
ejpam-5750	111	24	r2\k	r2\k	X
ejpam-5750	111	25	dλ(x	dλ(x	PUNCT
ejpam-5750	111	26	)	)	PUNCT
ejpam-5750	112	1	<	<	X
ejpam-5750	112	2	∞.	∞.	PROPN
ejpam-5750	112	3	corollary	corollary	NOUN
ejpam-5750	112	4	1	1	NUM
ejpam-5750	112	5	.	.	PUNCT
ejpam-5750	113	1	let	let	AUX
ejpam-5750	113	2	s(x	s(x	PROPN
ejpam-5750	113	3	)	)	PUNCT
ejpam-5750	113	4	be	be	AUX
ejpam-5750	113	5	a	a	DET
ejpam-5750	113	6	subharmonic	subharmonic	ADJ
ejpam-5750	113	7	function	function	NOUN
ejpam-5750	113	8	on	on	ADP
ejpam-5750	113	9	r2	r2	PROPN
ejpam-5750	113	10	with	with	ADP
ejpam-5750	113	11	associated	associated	ADJ
ejpam-5750	113	12	measure	measure	NOUN
ejpam-5750	113	13	µ(x	µ(x	VERB
ejpam-5750	113	14	)	)	PUNCT
ejpam-5750	113	15	.	.	PUNCT
ejpam-5750	114	1	then	then	ADV
ejpam-5750	114	2	s(x	s(x	PROPN
ejpam-5750	114	3	)	)	PUNCT
ejpam-5750	114	4	has	have	VERB
ejpam-5750	114	5	a	a	DET
ejpam-5750	114	6	harmonic	harmonic	ADJ
ejpam-5750	114	7	majorant	majorant	NOUN
ejpam-5750	114	8	outside	outside	ADP
ejpam-5750	114	9	a	a	DET
ejpam-5750	114	10	compact	compact	ADJ
ejpam-5750	114	11	set	set	NOUN
ejpam-5750	114	12	if	if	SCONJ
ejpam-5750	114	13	and	and	CCONJ
ejpam-5750	114	14	only	only	ADV
ejpam-5750	114	15	if	if	SCONJ
ejpam-5750	114	16	∫	∫	PROPN
ejpam-5750	114	17	x	x	X
ejpam-5750	114	18	dµ(x	dµ(x	PUNCT
ejpam-5750	114	19	)	)	PUNCT
ejpam-5750	114	20	<	<	X
ejpam-5750	114	21	∞.	∞.	PROPN
ejpam-5750	114	22	proof	proof	NOUN
ejpam-5750	114	23	.	.	PUNCT
ejpam-5750	115	1	follows	follow	VERB
ejpam-5750	115	2	from	from	ADP
ejpam-5750	115	3	the	the	DET
ejpam-5750	115	4	theorem	theorem	ADJ
ejpam-5750	115	5	1	1	NUM
ejpam-5750	115	6	4	4	NUM
ejpam-5750	115	7	.	.	PUNCT
ejpam-5750	115	8	flux	flux	NOUN
ejpam-5750	115	9	at	at	ADP
ejpam-5750	115	10	infinity	infinity	NOUN
ejpam-5750	115	11	suppose	suppose	VERB
ejpam-5750	115	12	u(x	u(x	NOUN
ejpam-5750	115	13	)	)	PUNCT
ejpam-5750	115	14	is	be	AUX
ejpam-5750	115	15	a	a	DET
ejpam-5750	115	16	subharmonic	subharmonic	ADJ
ejpam-5750	115	17	function	function	NOUN
ejpam-5750	115	18	defined	define	VERB
ejpam-5750	115	19	outside	outside	ADP
ejpam-5750	115	20	a	a	DET
ejpam-5750	115	21	compact	compact	ADJ
ejpam-5750	115	22	set	set	NOUN
ejpam-5750	115	23	.	.	PUNCT
ejpam-5750	116	1	then	then	ADV
ejpam-5750	116	2	there	there	PRON
ejpam-5750	116	3	exists	exist	VERB
ejpam-5750	116	4	a	a	DET
ejpam-5750	116	5	subharmonic	subharmonic	ADJ
ejpam-5750	116	6	function	function	NOUN
ejpam-5750	116	7	s(x	s(x	PROPN
ejpam-5750	116	8	)	)	PUNCT
ejpam-5750	116	9	that	that	PRON
ejpam-5750	116	10	is	be	AUX
ejpam-5750	116	11	harmonic	harmonic	ADJ
ejpam-5750	116	12	on	on	ADP
ejpam-5750	116	13	a	a	DET
ejpam-5750	116	14	neighbourhood	neighbourhood	NOUN
ejpam-5750	116	15	of	of	ADP
ejpam-5750	116	16	0	0	NUM
ejpam-5750	116	17	and	and	CCONJ
ejpam-5750	116	18	a	a	DET
ejpam-5750	116	19	constant	constant	ADJ
ejpam-5750	116	20	α	α	PRON
ejpam-5750	116	21	≥	≥	NOUN
ejpam-5750	116	22	0	0	NUM
ejpam-5750	116	23	such	such	ADJ
ejpam-5750	116	24	that	that	SCONJ
ejpam-5750	116	25	u(x	u(x	NOUN
ejpam-5750	116	26	)	)	PUNCT
ejpam-5750	116	27	=	=	PUNCT
ejpam-5750	117	1	s(x)−	s(x)−	PROPN
ejpam-5750	117	2	α	α	PROPN
ejpam-5750	117	3	log	log	NOUN
ejpam-5750	117	4	|x|	|x|	PROPN
ejpam-5750	117	5	outside	outside	ADP
ejpam-5750	117	6	a	a	DET
ejpam-5750	117	7	disc	disc	NOUN
ejpam-5750	117	8	(	(	PUNCT
ejpam-5750	117	9	anandam	anandam	PROPN
ejpam-5750	117	10	[	[	X
ejpam-5750	117	11	12	12	NUM
ejpam-5750	117	12	]	]	PUNCT
ejpam-5750	117	13	)	)	PUNCT
ejpam-5750	117	14	.	.	PUNCT
ejpam-5750	118	1	amulya	amulya	PROPN
ejpam-5750	118	2	smyrna	smyrna	PROPN
ejpam-5750	118	3	c.	c.	PROPN
ejpam-5750	118	4	,	,	PUNCT
ejpam-5750	118	5	n.	n.	PROPN
ejpam-5750	118	6	nathiya	nathiya	PROPN
ejpam-5750	118	7	/	/	SYM
ejpam-5750	118	8	eur	eur	PROPN
ejpam-5750	118	9	.	.	PUNCT
ejpam-5750	119	1	j.	j.	PROPN
ejpam-5750	119	2	pure	pure	PROPN
ejpam-5750	119	3	appl	appl	PROPN
ejpam-5750	119	4	.	.	PROPN
ejpam-5750	119	5	math	math	PROPN
ejpam-5750	119	6	,	,	PUNCT
ejpam-5750	119	7	18	18	NUM
ejpam-5750	119	8	(	(	PUNCT
ejpam-5750	119	9	2	2	NUM
ejpam-5750	119	10	)	)	PUNCT
ejpam-5750	119	11	(	(	PUNCT
ejpam-5750	119	12	2025	2025	NUM
ejpam-5750	119	13	)	)	PUNCT
ejpam-5750	119	14	,	,	PUNCT
ejpam-5750	119	15	5750	5750	NUM
ejpam-5750	119	16	5	5	NUM
ejpam-5750	119	17	of	of	ADP
ejpam-5750	119	18	9	9	NUM
ejpam-5750	119	19	definition	definition	NOUN
ejpam-5750	119	20	2	2	NUM
ejpam-5750	119	21	.	.	PUNCT
ejpam-5750	120	1	let	let	AUX
ejpam-5750	120	2	u(x	u(x	NOUN
ejpam-5750	120	3	)	)	PUNCT
ejpam-5750	120	4	be	be	AUX
ejpam-5750	120	5	a	a	DET
ejpam-5750	120	6	subharmonic	subharmonic	ADJ
ejpam-5750	120	7	function	function	NOUN
ejpam-5750	120	8	defined	define	VERB
ejpam-5750	120	9	outside	outside	ADP
ejpam-5750	120	10	of	of	ADP
ejpam-5750	120	11	a	a	DET
ejpam-5750	120	12	compact	compact	ADJ
ejpam-5750	120	13	set	set	NOUN
ejpam-5750	120	14	.	.	PUNCT
ejpam-5750	121	1	let	let	VERB
ejpam-5750	121	2	u(x	u(x	NOUN
ejpam-5750	121	3	)	)	PUNCT
ejpam-5750	121	4	=	=	SYM
ejpam-5750	121	5	s(x)−α	s(x)−α	NOUN
ejpam-5750	121	6	log	log	VERB
ejpam-5750	121	7	|x|	|x|	PROPN
ejpam-5750	121	8	.	.	PUNCT
ejpam-5750	122	1	then	then	ADV
ejpam-5750	122	2	define	define	VERB
ejpam-5750	122	3	the	the	DET
ejpam-5750	122	4	flux∞u	flux∞u	NOUN
ejpam-5750	122	5	=	=	SYM
ejpam-5750	122	6	flux	flux	NOUN
ejpam-5750	122	7	at	at	ADP
ejpam-5750	122	8	infinity	infinity	NOUN
ejpam-5750	122	9	of	of	ADP
ejpam-5750	122	10	u(x	u(x	NOUN
ejpam-5750	122	11	)	)	PUNCT
ejpam-5750	122	12	=	=	PUNCT
ejpam-5750	123	1	[	[	X
ejpam-5750	123	2	total	total	ADJ
ejpam-5750	123	3	measure	measure	NOUN
ejpam-5750	123	4	of	of	ADP
ejpam-5750	123	5	s(x)]−α	s(x)]−α	PROPN
ejpam-5750	123	6	.	.	PUNCT
ejpam-5750	123	7	remark	remark	PROPN
ejpam-5750	123	8	1	1	NUM
ejpam-5750	123	9	.	.	PUNCT
ejpam-5750	124	1	if	if	SCONJ
ejpam-5750	124	2	u(x	u(x	NOUN
ejpam-5750	124	3	)	)	PUNCT
ejpam-5750	124	4	=	=	SYM
ejpam-5750	124	5	s1(x	s1(x	NOUN
ejpam-5750	124	6	)	)	PUNCT
ejpam-5750	124	7	−	−	PROPN
ejpam-5750	125	1	α1	α1	PROPN
ejpam-5750	125	2	log	log	NOUN
ejpam-5750	125	3	|x|	|x|	PROPN
ejpam-5750	125	4	is	be	AUX
ejpam-5750	125	5	another	another	DET
ejpam-5750	125	6	such	such	ADJ
ejpam-5750	125	7	decomposition	decomposition	NOUN
ejpam-5750	125	8	outside	outside	ADP
ejpam-5750	125	9	a	a	DET
ejpam-5750	125	10	compact	compact	ADJ
ejpam-5750	125	11	set	set	NOUN
ejpam-5750	125	12	,	,	PUNCT
ejpam-5750	125	13	then	then	ADV
ejpam-5750	125	14	s(x	s(x	PROPN
ejpam-5750	125	15	)	)	PUNCT
ejpam-5750	125	16	−	−	PROPN
ejpam-5750	126	1	α	α	PRON
ejpam-5750	126	2	log	log	NOUN
ejpam-5750	126	3	|x|	|x|	PROPN
ejpam-5750	126	4	=	=	SYM
ejpam-5750	126	5	s1(x	s1(x	PROPN
ejpam-5750	126	6	)	)	PUNCT
ejpam-5750	126	7	−	−	PROPN
ejpam-5750	127	1	α1	α1	PROPN
ejpam-5750	127	2	log	log	VERB
ejpam-5750	127	3	|x|	|x|	PROPN
ejpam-5750	127	4	outside	outside	ADP
ejpam-5750	127	5	a	a	DET
ejpam-5750	127	6	compact	compact	ADJ
ejpam-5750	127	7	set	set	NOUN
ejpam-5750	127	8	.	.	PUNCT
ejpam-5750	128	1	since	since	SCONJ
ejpam-5750	128	2	v(x	v(x	NUM
ejpam-5750	128	3	)	)	PUNCT
ejpam-5750	128	4	=	=	NOUN
ejpam-5750	128	5	s(x)+α1	s(x)+α1	NOUN
ejpam-5750	128	6	log	log	VERB
ejpam-5750	128	7	|x|	|x|	PROPN
ejpam-5750	128	8	=	=	PUNCT
ejpam-5750	129	1	s1(x)+α	s1(x)+α	AUX
ejpam-5750	129	2	log	log	VERB
ejpam-5750	129	3	|x|	|x|	PROPN
ejpam-5750	129	4	outside	outside	ADP
ejpam-5750	129	5	a	a	DET
ejpam-5750	129	6	compact	compact	ADJ
ejpam-5750	129	7	set	set	NOUN
ejpam-5750	129	8	represents	represent	VERB
ejpam-5750	129	9	two	two	NUM
ejpam-5750	129	10	forms	form	NOUN
ejpam-5750	129	11	of	of	ADP
ejpam-5750	129	12	the	the	DET
ejpam-5750	129	13	same	same	ADJ
ejpam-5750	129	14	subharmonic	subharmonic	ADJ
ejpam-5750	129	15	function	function	NOUN
ejpam-5750	129	16	v(x	v(x	PROPN
ejpam-5750	129	17	)	)	PUNCT
ejpam-5750	129	18	,	,	PUNCT
ejpam-5750	130	1	[	[	X
ejpam-5750	130	2	total	total	ADJ
ejpam-5750	130	3	measure	measure	NOUN
ejpam-5750	130	4	of	of	ADP
ejpam-5750	130	5	v(x	v(x	PROPN
ejpam-5750	130	6	)	)	PUNCT
ejpam-5750	130	7	]	]	PUNCT
ejpam-5750	130	8	can	can	AUX
ejpam-5750	130	9	be	be	AUX
ejpam-5750	130	10	calculated	calculate	VERB
ejpam-5750	130	11	by	by	ADP
ejpam-5750	130	12	using	use	VERB
ejpam-5750	130	13	the	the	DET
ejpam-5750	130	14	normal	normal	ADJ
ejpam-5750	130	15	derivative	derivative	ADJ
ejpam-5750	130	16	form	form	NOUN
ejpam-5750	130	17	in	in	ADP
ejpam-5750	130	18	the	the	DET
ejpam-5750	130	19	green	green	PROPN
ejpam-5750	130	20	’s	’s	PART
ejpam-5750	130	21	theorem	theorem	PROPN
ejpam-5750	130	22	.	.	PUNCT
ejpam-5750	131	1	hence	hence	ADV
ejpam-5750	131	2	,	,	PUNCT
ejpam-5750	131	3	total	total	ADJ
ejpam-5750	131	4	measure	measure	NOUN
ejpam-5750	131	5	of	of	ADP
ejpam-5750	131	6	s1	s1	NOUN
ejpam-5750	131	7	+	+	CCONJ
ejpam-5750	131	8	α2	α2	ADJ
ejpam-5750	131	9	=	=	SYM
ejpam-5750	131	10	total	total	ADJ
ejpam-5750	131	11	measure	measure	NOUN
ejpam-5750	131	12	of	of	ADP
ejpam-5750	131	13	s2	s2	NOUN
ejpam-5750	131	14	+	+	CCONJ
ejpam-5750	131	15	α1	α1	NOUN
ejpam-5750	131	16	,	,	PUNCT
ejpam-5750	131	17	so	so	SCONJ
ejpam-5750	131	18	that	that	SCONJ
ejpam-5750	131	19	total	total	ADJ
ejpam-5750	131	20	measure	measure	NOUN
ejpam-5750	131	21	of	of	ADP
ejpam-5750	131	22	s1	s1	PROPN
ejpam-5750	131	23	−	−	PROPN
ejpam-5750	131	24	α1	α1	PROPN
ejpam-5750	131	25	=	=	SYM
ejpam-5750	131	26	total	total	ADJ
ejpam-5750	131	27	measure	measure	NOUN
ejpam-5750	131	28	of	of	ADP
ejpam-5750	131	29	s2	s2	PROPN
ejpam-5750	131	30	−	−	ADV
ejpam-5750	131	31	α2	α2	ADJ
ejpam-5750	131	32	remark	remark	NOUN
ejpam-5750	131	33	2	2	NUM
ejpam-5750	131	34	.	.	PUNCT
ejpam-5750	132	1	if	if	SCONJ
ejpam-5750	132	2	s(x	s(x	NOUN
ejpam-5750	132	3	)	)	PUNCT
ejpam-5750	132	4	is	be	AUX
ejpam-5750	132	5	a	a	DET
ejpam-5750	132	6	subharmonic	subharmonic	ADJ
ejpam-5750	132	7	function	function	NOUN
ejpam-5750	132	8	on	on	ADP
ejpam-5750	132	9	r2	r2	PROPN
ejpam-5750	132	10	,	,	PUNCT
ejpam-5750	132	11	then	then	ADV
ejpam-5750	132	12	total	total	ADJ
ejpam-5750	132	13	measure	measure	NOUN
ejpam-5750	132	14	of	of	ADP
ejpam-5750	132	15	s(x	s(x	PROPN
ejpam-5750	132	16	)	)	PUNCT
ejpam-5750	132	17	=	=	SYM
ejpam-5750	132	18	flux∞s(x	flux∞s(x	PROPN
ejpam-5750	132	19	)	)	PUNCT
ejpam-5750	132	20	theorem	theorem	NOUN
ejpam-5750	132	21	2	2	NUM
ejpam-5750	132	22	.	.	PUNCT
ejpam-5750	133	1	let	let	VERB
ejpam-5750	133	2	h(x	h(x	PROPN
ejpam-5750	133	3	)	)	PUNCT
ejpam-5750	133	4	be	be	AUX
ejpam-5750	133	5	a	a	DET
ejpam-5750	133	6	harmonic	harmonic	ADJ
ejpam-5750	133	7	function	function	NOUN
ejpam-5750	133	8	defined	define	VERB
ejpam-5750	133	9	outside	outside	ADP
ejpam-5750	133	10	a	a	DET
ejpam-5750	133	11	compact	compact	ADJ
ejpam-5750	133	12	set	set	NOUN
ejpam-5750	133	13	in	in	ADP
ejpam-5750	133	14	r2	r2	PROPN
ejpam-5750	133	15	.	.	PUNCT
ejpam-5750	134	1	then	then	ADV
ejpam-5750	134	2	h(x	h(x	PROPN
ejpam-5750	134	3	)	)	PUNCT
ejpam-5750	135	1	=	=	SYM
ejpam-5750	135	2	h(x	h(x	PROPN
ejpam-5750	135	3	)	)	PUNCT
ejpam-5750	136	1	+	+	CCONJ
ejpam-5750	136	2	α	α	PRON
ejpam-5750	136	3	log	log	NOUN
ejpam-5750	136	4	|x|	|x|	PROPN
ejpam-5750	136	5	+	+	CCONJ
ejpam-5750	136	6	b(x	b(x	PROPN
ejpam-5750	136	7	)	)	PUNCT
ejpam-5750	136	8	where	where	SCONJ
ejpam-5750	136	9	h(x	h(x	PROPN
ejpam-5750	136	10	)	)	PUNCT
ejpam-5750	136	11	is	be	AUX
ejpam-5750	136	12	harmonic	harmonic	ADJ
ejpam-5750	136	13	on	on	ADP
ejpam-5750	136	14	r2	r2	PROPN
ejpam-5750	136	15	,	,	PUNCT
ejpam-5750	136	16	α	α	X
ejpam-5750	137	1	a	a	PRON
ejpam-5750	137	2	constant	constant	ADJ
ejpam-5750	137	3	,	,	PUNCT
ejpam-5750	137	4	and	and	CCONJ
ejpam-5750	137	5	b(x	b(x	NOUN
ejpam-5750	137	6	)	)	PUNCT
ejpam-5750	137	7	bounded	bound	VERB
ejpam-5750	137	8	harmonic	harmonic	ADJ
ejpam-5750	137	9	tending	tend	VERB
ejpam-5750	137	10	to	to	ADP
ejpam-5750	137	11	0	0	NUM
ejpam-5750	137	12	at	at	ADP
ejpam-5750	137	13	infinity	infinity	NOUN
ejpam-5750	137	14	.	.	PUNCT
ejpam-5750	138	1	this	this	DET
ejpam-5750	138	2	representation	representation	NOUN
ejpam-5750	138	3	is	be	AUX
ejpam-5750	138	4	unique	unique	ADJ
ejpam-5750	138	5	and	and	CCONJ
ejpam-5750	138	6	[	[	X
ejpam-5750	138	7	flux∞h(x	flux∞h(x	PROPN
ejpam-5750	138	8	)	)	PUNCT
ejpam-5750	138	9	]	]	PUNCT
ejpam-5750	139	1	=	=	SYM
ejpam-5750	139	2	α	α	X
ejpam-5750	139	3	.	.	PUNCT
ejpam-5750	139	4	proof	proof	NOUN
ejpam-5750	139	5	.	.	PUNCT
ejpam-5750	140	1	write	write	VERB
ejpam-5750	140	2	h(x	h(x	PROPN
ejpam-5750	140	3	)	)	PUNCT
ejpam-5750	141	1	=	=	PUNCT
ejpam-5750	142	1	s(x)−β	s(x)−β	ADP
ejpam-5750	142	2	log	log	NOUN
ejpam-5750	142	3	|x|	|x|	PROPN
ejpam-5750	142	4	,	,	PUNCT
ejpam-5750	142	5	β	β	X
ejpam-5750	142	6	≥	≥	NOUN
ejpam-5750	142	7	0	0	NUM
ejpam-5750	142	8	and	and	CCONJ
ejpam-5750	142	9	s(x	s(x	NOUN
ejpam-5750	142	10	)	)	PUNCT
ejpam-5750	142	11	subharmonic	subharmonic	NOUN
ejpam-5750	142	12	on	on	ADP
ejpam-5750	142	13	r2	r2	PROPN
ejpam-5750	142	14	.	.	PUNCT
ejpam-5750	143	1	the	the	DET
ejpam-5750	143	2	function	function	NOUN
ejpam-5750	143	3	s(x	s(x	PROPN
ejpam-5750	143	4	)	)	PUNCT
ejpam-5750	143	5	should	should	AUX
ejpam-5750	143	6	be	be	AUX
ejpam-5750	143	7	harmonic	harmonic	ADJ
ejpam-5750	143	8	outside	outside	ADP
ejpam-5750	143	9	a	a	DET
ejpam-5750	143	10	compact	compact	ADJ
ejpam-5750	143	11	set	set	VERB
ejpam-5750	143	12	k.	k.	PROPN
ejpam-5750	143	13	hence	hence	ADV
ejpam-5750	143	14	s(x	s(x	PROPN
ejpam-5750	143	15	)	)	PUNCT
ejpam-5750	144	1	=	=	SYM
ejpam-5750	144	2	∫	∫	PROPN
ejpam-5750	145	1	k	k	PROPN
ejpam-5750	145	2	log	log	PROPN
ejpam-5750	145	3	|x	|x	PROPN
ejpam-5750	145	4	−	−	PROPN
ejpam-5750	145	5	y|dµ(y	y|dµ(y	PROPN
ejpam-5750	145	6	)	)	PUNCT
ejpam-5750	146	1	+	+	CCONJ
ejpam-5750	146	2	a	a	DET
ejpam-5750	146	3	harmonic	harmonic	ADJ
ejpam-5750	146	4	function	function	NOUN
ejpam-5750	146	5	h(x	h(x	PROPN
ejpam-5750	146	6	)	)	PUNCT
ejpam-5750	146	7	on	on	ADP
ejpam-5750	146	8	r2	r2	PROPN
ejpam-5750	146	9	.	.	PUNCT
ejpam-5750	147	1	since	since	SCONJ
ejpam-5750	147	2	the	the	DET
ejpam-5750	147	3	integral	integral	ADJ
ejpam-5750	147	4	equals	equal	VERB
ejpam-5750	147	5	µ(k	µ(k	NOUN
ejpam-5750	147	6	)	)	PUNCT
ejpam-5750	147	7	log	log	VERB
ejpam-5750	147	8	|x|+	|x|+	NOUN
ejpam-5750	147	9	b(x	b(x	NOUN
ejpam-5750	147	10	)	)	PUNCT
ejpam-5750	147	11	outside	outside	ADP
ejpam-5750	147	12	a	a	DET
ejpam-5750	147	13	compact	compact	ADJ
ejpam-5750	147	14	set	set	NOUN
ejpam-5750	147	15	where	where	SCONJ
ejpam-5750	147	16	b(x	b(x	NOUN
ejpam-5750	147	17	)	)	PUNCT
ejpam-5750	147	18	−→	−→	NOUN
ejpam-5750	147	19	0	0	NUM
ejpam-5750	147	20	at	at	ADP
ejpam-5750	147	21	infinity	infinity	NOUN
ejpam-5750	147	22	,	,	PUNCT
ejpam-5750	147	23	we	we	PRON
ejpam-5750	147	24	have	have	VERB
ejpam-5750	147	25	h(x	h(x	PROPN
ejpam-5750	147	26	)	)	PUNCT
ejpam-5750	148	1	=	=	SYM
ejpam-5750	148	2	h(x	h(x	PROPN
ejpam-5750	148	3	)	)	PUNCT
ejpam-5750	149	1	+	+	CCONJ
ejpam-5750	150	1	[	[	X
ejpam-5750	150	2	µ(k)−	µ(k)−	NUM
ejpam-5750	150	3	β	β	X
ejpam-5750	150	4	]	]	X
ejpam-5750	150	5	log	log	NOUN
ejpam-5750	150	6	|x|+	|x|+	NOUN
ejpam-5750	150	7	b(x	b(x	NOUN
ejpam-5750	150	8	)	)	PUNCT
ejpam-5750	150	9	=	=	SYM
ejpam-5750	150	10	h(x	h(x	PROPN
ejpam-5750	150	11	)	)	PUNCT
ejpam-5750	151	1	+	+	CCONJ
ejpam-5750	151	2	α	α	PRON
ejpam-5750	151	3	log	log	NOUN
ejpam-5750	151	4	|x|+	|x|+	NOUN
ejpam-5750	151	5	b(x),writing	b(x),write	VERB
ejpam-5750	152	1	α	α	NOUN
ejpam-5750	152	2	=	=	SYM
ejpam-5750	152	3	µ(k)−	µ(k)−	PROPN
ejpam-5750	152	4	β	β	NOUN
ejpam-5750	152	5	uniqueness	uniqueness	NOUN
ejpam-5750	152	6	of	of	ADP
ejpam-5750	152	7	the	the	DET
ejpam-5750	152	8	representation	representation	NOUN
ejpam-5750	152	9	:	:	PUNCT
ejpam-5750	152	10	suppose	suppose	VERB
ejpam-5750	152	11	h(x	h(x	PROPN
ejpam-5750	152	12	)	)	PUNCT
ejpam-5750	153	1	=	=	PUNCT
ejpam-5750	153	2	h1(x)+α1	h1(x)+α1	NOUN
ejpam-5750	153	3	log	log	NOUN
ejpam-5750	153	4	|x|+	|x|+	PROPN
ejpam-5750	153	5	b1(x	b1(x	NOUN
ejpam-5750	153	6	)	)	PUNCT
ejpam-5750	153	7	,	,	PUNCT
ejpam-5750	153	8	then	then	ADV
ejpam-5750	153	9	h(x)+	h(x)+	VERB
ejpam-5750	153	10	α	α	PRON
ejpam-5750	153	11	log	log	VERB
ejpam-5750	153	12	|x|+	|x|+	NOUN
ejpam-5750	153	13	b(x	b(x	NOUN
ejpam-5750	153	14	)	)	PUNCT
ejpam-5750	153	15	=	=	SYM
ejpam-5750	153	16	h1(x	h1(x	NOUN
ejpam-5750	153	17	)	)	PUNCT
ejpam-5750	153	18	+	+	CCONJ
ejpam-5750	153	19	α1	α1	PROPN
ejpam-5750	153	20	log	log	NOUN
ejpam-5750	153	21	|x|+	|x|+	NOUN
ejpam-5750	153	22	b1(x	b1(x	NOUN
ejpam-5750	153	23	)	)	PUNCT
ejpam-5750	153	24	outside	outside	ADP
ejpam-5750	153	25	a	a	DET
ejpam-5750	153	26	compact	compact	ADJ
ejpam-5750	153	27	set	set	NOUN
ejpam-5750	153	28	.	.	PUNCT
ejpam-5750	154	1	now	now	ADV
ejpam-5750	154	2	for	for	ADP
ejpam-5750	154	3	large	large	ADJ
ejpam-5750	154	4	r	r	NOUN
ejpam-5750	154	5	,	,	PUNCT
ejpam-5750	154	6	take	take	VERB
ejpam-5750	154	7	the	the	DET
ejpam-5750	154	8	integral	integral	ADJ
ejpam-5750	154	9	1	1	NUM
ejpam-5750	154	10	2πr	2πr	NOUN
ejpam-5750	154	11	2π∫	2π∫	NOUN
ejpam-5750	154	12	0	0	NUM
ejpam-5750	155	1	on	on	ADP
ejpam-5750	155	2	|x|	|x|	PROPN
ejpam-5750	155	3	=	=	SYM
ejpam-5750	155	4	r	r	NOUN
ejpam-5750	155	5	,	,	PUNCT
ejpam-5750	155	6	to	to	PART
ejpam-5750	155	7	see	see	VERB
ejpam-5750	155	8	h(0)−h1(0	h(0)−h1(0	PRON
ejpam-5750	155	9	)	)	PUNCT
ejpam-5750	155	10	=	=	SYM
ejpam-5750	155	11	(	(	PUNCT
ejpam-5750	155	12	α1	α1	PROPN
ejpam-5750	155	13	−	−	PROPN
ejpam-5750	155	14	α	α	NOUN
ejpam-5750	155	15	)	)	PUNCT
ejpam-5750	155	16	logr+	logr+	X
ejpam-5750	156	1	[	[	X
ejpam-5750	156	2	a	a	DET
ejpam-5750	156	3	bounded	bounded	ADJ
ejpam-5750	156	4	function	function	NOUN
ejpam-5750	156	5	]	]	PUNCT
ejpam-5750	156	6	.	.	PUNCT
ejpam-5750	157	1	this	this	PRON
ejpam-5750	157	2	is	be	AUX
ejpam-5750	157	3	possible	possible	ADJ
ejpam-5750	157	4	for	for	SCONJ
ejpam-5750	157	5	all	all	DET
ejpam-5750	157	6	large	large	ADJ
ejpam-5750	157	7	r	r	NOUN
ejpam-5750	157	8	if	if	SCONJ
ejpam-5750	157	9	and	and	CCONJ
ejpam-5750	157	10	only	only	ADV
ejpam-5750	157	11	if	if	SCONJ
ejpam-5750	157	12	α1	α1	PROPN
ejpam-5750	157	13	=	=	PUNCT
ejpam-5750	157	14	α	α	NOUN
ejpam-5750	157	15	in	in	ADP
ejpam-5750	157	16	which	which	DET
ejpam-5750	157	17	case	case	NOUN
ejpam-5750	157	18	h(x	h(x	PROPN
ejpam-5750	157	19	)	)	PUNCT
ejpam-5750	157	20	−	−	ADP
ejpam-5750	158	1	h1(x	h1(x	NOUN
ejpam-5750	158	2	)	)	PUNCT
ejpam-5750	158	3	is	be	AUX
ejpam-5750	158	4	bounded	bound	VERB
ejpam-5750	158	5	,	,	PUNCT
ejpam-5750	158	6	hence	hence	ADV
ejpam-5750	158	7	a	a	DET
ejpam-5750	158	8	constant	constant	ADJ
ejpam-5750	158	9	tending	tending	NOUN
ejpam-5750	158	10	to	to	ADP
ejpam-5750	158	11	0	0	NUM
ejpam-5750	158	12	.	.	PUNCT
ejpam-5750	159	1	therefore	therefore	ADV
ejpam-5750	159	2	h1	h1	PROPN
ejpam-5750	159	3	=	=	SYM
ejpam-5750	159	4	h	h	NOUN
ejpam-5750	159	5	,	,	PUNCT
ejpam-5750	159	6	proving	prove	VERB
ejpam-5750	159	7	the	the	DET
ejpam-5750	159	8	uniqueness	uniqueness	NOUN
ejpam-5750	159	9	of	of	ADP
ejpam-5750	159	10	the	the	DET
ejpam-5750	159	11	representation	representation	NOUN
ejpam-5750	159	12	.	.	PUNCT
ejpam-5750	160	1	flux	flux	NOUN
ejpam-5750	160	2	at	at	ADP
ejpam-5750	160	3	infinity	infinity	NOUN
ejpam-5750	160	4	of	of	ADP
ejpam-5750	160	5	h	h	NOUN
ejpam-5750	160	6	:	:	PUNCT
ejpam-5750	160	7	since	since	SCONJ
ejpam-5750	160	8	h(x	h(x	PROPN
ejpam-5750	160	9	)	)	PUNCT
ejpam-5750	161	1	=	=	PUNCT
ejpam-5750	162	1	s(x)−β	s(x)−β	ADP
ejpam-5750	162	2	log	log	NOUN
ejpam-5750	162	3	|x|	|x|	PROPN
ejpam-5750	162	4	,	,	PUNCT
ejpam-5750	162	5	then	then	ADV
ejpam-5750	162	6	flux∞h	flux∞h	PROPN
ejpam-5750	163	1	=	=	PUNCT
ejpam-5750	164	1	[	[	X
ejpam-5750	164	2	total	total	ADJ
ejpam-5750	164	3	measure	measure	NOUN
ejpam-5750	164	4	of	of	ADP
ejpam-5750	164	5	s]−β	s]−β	NOUN
ejpam-5750	164	6	=	=	SYM
ejpam-5750	164	7	∥µ∥	∥µ∥	NOUN
ejpam-5750	164	8	−	−	NOUN
ejpam-5750	164	9	β	β	NOUN
ejpam-5750	164	10	=	=	SYM
ejpam-5750	164	11	α	α	NUM
ejpam-5750	164	12	corollary	corollary	NOUN
ejpam-5750	164	13	2	2	X
ejpam-5750	164	14	.	.	PUNCT
ejpam-5750	165	1	let	let	VERB
ejpam-5750	165	2	h	h	PRON
ejpam-5750	165	3	be	be	AUX
ejpam-5750	165	4	harmonic	harmonic	ADJ
ejpam-5750	165	5	outside	outside	ADP
ejpam-5750	165	6	a	a	DET
ejpam-5750	165	7	compact	compact	ADJ
ejpam-5750	165	8	set	set	NOUN
ejpam-5750	165	9	.	.	PUNCT
ejpam-5750	166	1	then	then	ADV
ejpam-5750	166	2	there	there	PRON
ejpam-5750	166	3	exists	exist	VERB
ejpam-5750	166	4	a	a	DET
ejpam-5750	166	5	harmonic	harmonic	ADJ
ejpam-5750	166	6	function	function	NOUN
ejpam-5750	166	7	h	h	NOUN
ejpam-5750	166	8	on	on	ADP
ejpam-5750	166	9	r2	r2	PROPN
ejpam-5750	166	10	such	such	ADJ
ejpam-5750	166	11	that	that	PRON
ejpam-5750	166	12	|h−h|	|h−h|	PUNCT
ejpam-5750	166	13	is	be	AUX
ejpam-5750	166	14	bounded	bound	VERB
ejpam-5750	166	15	near	near	ADP
ejpam-5750	166	16	infinity	infinity	NOUN
ejpam-5750	166	17	if	if	SCONJ
ejpam-5750	166	18	and	and	CCONJ
ejpam-5750	166	19	only	only	ADV
ejpam-5750	166	20	if	if	SCONJ
ejpam-5750	166	21	[	[	X
ejpam-5750	166	22	flux∞h	flux∞h	X
ejpam-5750	166	23	]	]	X
ejpam-5750	166	24	=	=	SYM
ejpam-5750	166	25	0	0	X
ejpam-5750	166	26	.	.	PUNCT
ejpam-5750	166	27	amulya	amulya	PROPN
ejpam-5750	166	28	smyrna	smyrna	PROPN
ejpam-5750	166	29	c.	c.	PROPN
ejpam-5750	166	30	,	,	PUNCT
ejpam-5750	166	31	n.	n.	PROPN
ejpam-5750	166	32	nathiya	nathiya	PROPN
ejpam-5750	166	33	/	/	SYM
ejpam-5750	166	34	eur	eur	PROPN
ejpam-5750	166	35	.	.	PUNCT
ejpam-5750	167	1	j.	j.	PROPN
ejpam-5750	167	2	pure	pure	PROPN
ejpam-5750	167	3	appl	appl	PROPN
ejpam-5750	167	4	.	.	PROPN
ejpam-5750	167	5	math	math	PROPN
ejpam-5750	167	6	,	,	PUNCT
ejpam-5750	167	7	18	18	NUM
ejpam-5750	167	8	(	(	PUNCT
ejpam-5750	167	9	2	2	NUM
ejpam-5750	167	10	)	)	PUNCT
ejpam-5750	167	11	(	(	PUNCT
ejpam-5750	167	12	2025	2025	NUM
ejpam-5750	167	13	)	)	PUNCT
ejpam-5750	167	14	,	,	PUNCT
ejpam-5750	167	15	5750	5750	NUM
ejpam-5750	167	16	6	6	NUM
ejpam-5750	167	17	of	of	ADP
ejpam-5750	167	18	9	9	NUM
ejpam-5750	167	19	proof	proof	NOUN
ejpam-5750	167	20	.	.	PUNCT
ejpam-5750	168	1	from	from	ADP
ejpam-5750	168	2	the	the	DET
ejpam-5750	168	3	above	above	ADJ
ejpam-5750	168	4	theorem	theorem	ADJ
ejpam-5750	168	5	h(x	h(x	PROPN
ejpam-5750	168	6	)	)	PUNCT
ejpam-5750	168	7	is	be	AUX
ejpam-5750	168	8	represented	represent	VERB
ejpam-5750	168	9	as	as	ADP
ejpam-5750	168	10	h(x	h(x	PROPN
ejpam-5750	168	11	)	)	PUNCT
ejpam-5750	169	1	=	=	SYM
ejpam-5750	169	2	h(x	h(x	PROPN
ejpam-5750	169	3	)	)	PUNCT
ejpam-5750	170	1	+	+	CCONJ
ejpam-5750	170	2	α	α	PRON
ejpam-5750	170	3	log	log	NOUN
ejpam-5750	170	4	|x|+	|x|+	NOUN
ejpam-5750	170	5	b(x	b(x	NOUN
ejpam-5750	170	6	)	)	PUNCT
ejpam-5750	170	7	,	,	PUNCT
ejpam-5750	170	8	(	(	PUNCT
ejpam-5750	170	9	1	1	X
ejpam-5750	170	10	)	)	PUNCT
ejpam-5750	170	11	where	where	SCONJ
ejpam-5750	170	12	h(x	h(x	PROPN
ejpam-5750	170	13	)	)	PUNCT
ejpam-5750	170	14	is	be	AUX
ejpam-5750	170	15	harmonic	harmonic	ADJ
ejpam-5750	170	16	on	on	ADP
ejpam-5750	170	17	r2	r2	NOUN
ejpam-5750	170	18	,	,	PUNCT
ejpam-5750	170	19	b(x	b(x	NOUN
ejpam-5750	170	20	)	)	PUNCT
ejpam-5750	170	21	is	be	AUX
ejpam-5750	170	22	bounded	bound	VERB
ejpam-5750	170	23	harmonic	harmonic	ADJ
ejpam-5750	170	24	tending	tend	VERB
ejpam-5750	170	25	to	to	ADP
ejpam-5750	170	26	0	0	NUM
ejpam-5750	170	27	at	at	ADP
ejpam-5750	170	28	infinity	infinity	NOUN
ejpam-5750	170	29	and	and	CCONJ
ejpam-5750	170	30	α	α	PRON
ejpam-5750	170	31	is	be	AUX
ejpam-5750	170	32	a	a	DET
ejpam-5750	170	33	constant	constant	ADJ
ejpam-5750	170	34	.	.	PUNCT
ejpam-5750	171	1	let	let	VERB
ejpam-5750	171	2	flux∞h	flux∞h	PROPN
ejpam-5750	172	1	=	=	NOUN
ejpam-5750	172	2	0	0	X
ejpam-5750	172	3	.	.	PUNCT
ejpam-5750	173	1	by	by	ADP
ejpam-5750	173	2	(	(	PUNCT
ejpam-5750	173	3	1	1	X
ejpam-5750	173	4	)	)	PUNCT
ejpam-5750	173	5	we	we	PRON
ejpam-5750	173	6	get	get	VERB
ejpam-5750	173	7	|h	|h	NOUN
ejpam-5750	173	8	−	−	X
ejpam-5750	173	9	h|	h|	PROPN
ejpam-5750	173	10	=	=	SYM
ejpam-5750	173	11	b(x	b(x	NOUN
ejpam-5750	173	12	)	)	PUNCT
ejpam-5750	173	13	at	at	ADP
ejpam-5750	173	14	infinity	infinity	NOUN
ejpam-5750	173	15	.	.	PUNCT
ejpam-5750	174	1	this	this	PRON
ejpam-5750	174	2	shows	show	VERB
ejpam-5750	174	3	that	that	SCONJ
ejpam-5750	174	4	|h	|h	NOUN
ejpam-5750	174	5	−	−	PROPN
ejpam-5750	175	1	h|	h|	PROPN
ejpam-5750	175	2	is	be	AUX
ejpam-5750	175	3	bounded	bound	VERB
ejpam-5750	175	4	at	at	ADP
ejpam-5750	175	5	infinity	infinity	NOUN
ejpam-5750	175	6	.	.	PUNCT
ejpam-5750	176	1	conversely	conversely	ADV
ejpam-5750	176	2	,	,	PUNCT
ejpam-5750	176	3	if	if	SCONJ
ejpam-5750	176	4	|h	|h	PRON
ejpam-5750	176	5	−	−	PROPN
ejpam-5750	176	6	h|	h|	PROPN
ejpam-5750	176	7	is	be	AUX
ejpam-5750	176	8	bounded	bound	VERB
ejpam-5750	176	9	at	at	ADP
ejpam-5750	176	10	infinity	infinity	NOUN
ejpam-5750	176	11	then	then	ADV
ejpam-5750	176	12	flux∞h	flux∞h	PROPN
ejpam-5750	177	1	=	=	PUNCT
ejpam-5750	177	2	0	0	X
ejpam-5750	177	3	.	.	PUNCT
ejpam-5750	177	4	proposition	proposition	NOUN
ejpam-5750	177	5	1	1	NUM
ejpam-5750	177	6	.	.	PUNCT
ejpam-5750	178	1	if	if	SCONJ
ejpam-5750	178	2	b(x	b(x	VERB
ejpam-5750	178	3	)	)	PUNCT
ejpam-5750	178	4	is	be	AUX
ejpam-5750	178	5	a	a	DET
ejpam-5750	178	6	bounded	bounded	ADJ
ejpam-5750	178	7	harmonic	harmonic	ADJ
ejpam-5750	178	8	function	function	NOUN
ejpam-5750	178	9	outside	outside	ADP
ejpam-5750	178	10	a	a	DET
ejpam-5750	178	11	compact	compact	ADJ
ejpam-5750	178	12	set	set	NOUN
ejpam-5750	178	13	then	then	ADV
ejpam-5750	178	14	[	[	X
ejpam-5750	178	15	flux∞b(x	flux∞b(x	NOUN
ejpam-5750	178	16	)	)	PUNCT
ejpam-5750	178	17	]	]	PUNCT
ejpam-5750	179	1	=	=	PUNCT
ejpam-5750	179	2	0	0	X
ejpam-5750	179	3	.	.	PUNCT
ejpam-5750	180	1	proof	proof	NOUN
ejpam-5750	180	2	.	.	PUNCT
ejpam-5750	181	1	write	write	VERB
ejpam-5750	181	2	b(x	b(x	NOUN
ejpam-5750	181	3	)	)	PUNCT
ejpam-5750	181	4	=	=	SYM
ejpam-5750	181	5	s(x	s(x	PROPN
ejpam-5750	181	6	)	)	PUNCT
ejpam-5750	181	7	−	−	PROPN
ejpam-5750	182	1	α	α	PRON
ejpam-5750	182	2	log	log	NOUN
ejpam-5750	182	3	|x|	|x|	PROPN
ejpam-5750	182	4	.	.	PUNCT
ejpam-5750	183	1	then	then	ADV
ejpam-5750	183	2	s(x	s(x	PROPN
ejpam-5750	183	3	)	)	PUNCT
ejpam-5750	183	4	is	be	AUX
ejpam-5750	183	5	harmonic	harmonic	ADJ
ejpam-5750	183	6	near	near	ADP
ejpam-5750	183	7	infinity	infinity	NOUN
ejpam-5750	183	8	so	so	SCONJ
ejpam-5750	183	9	that	that	SCONJ
ejpam-5750	183	10	s(x	s(x	NOUN
ejpam-5750	183	11	)	)	PUNCT
ejpam-5750	183	12	=	=	SYM
ejpam-5750	183	13	∫	∫	PROPN
ejpam-5750	183	14	log	log	PROPN
ejpam-5750	183	15	|x−	|x−	PROPN
ejpam-5750	183	16	y|dµ|y|+h(x	y|dµ|y|+h(x	PROPN
ejpam-5750	183	17	)	)	PUNCT
ejpam-5750	183	18	,	,	PUNCT
ejpam-5750	183	19	where	where	SCONJ
ejpam-5750	183	20	h(x	h(x	PROPN
ejpam-5750	183	21	)	)	PUNCT
ejpam-5750	183	22	is	be	AUX
ejpam-5750	183	23	harmonic	harmonic	ADJ
ejpam-5750	183	24	on	on	ADP
ejpam-5750	183	25	r2	r2	PROPN
ejpam-5750	183	26	.	.	PUNCT
ejpam-5750	184	1	now	now	ADV
ejpam-5750	184	2	∫	∫	PROPN
ejpam-5750	184	3	log	log	PROPN
ejpam-5750	184	4	|x−	|x−	PROPN
ejpam-5750	184	5	y|dµ(y)−∥µ∥	y|dµ(y)−∥µ∥	PROPN
ejpam-5750	184	6	log	log	VERB
ejpam-5750	184	7	|x|	|x|	PROPN
ejpam-5750	184	8	=	=	SYM
ejpam-5750	184	9	b1(x	b1(x	PROPN
ejpam-5750	184	10	)	)	PUNCT
ejpam-5750	184	11	which	which	PRON
ejpam-5750	184	12	is	be	AUX
ejpam-5750	184	13	harmonic	harmonic	ADJ
ejpam-5750	184	14	tending	tend	VERB
ejpam-5750	184	15	to	to	ADP
ejpam-5750	184	16	0	0	NUM
ejpam-5750	184	17	at	at	ADP
ejpam-5750	184	18	infinity	infinity	NOUN
ejpam-5750	184	19	.	.	PUNCT
ejpam-5750	185	1	then	then	ADV
ejpam-5750	185	2	b(x	b(x	NOUN
ejpam-5750	185	3	)	)	PUNCT
ejpam-5750	185	4	=	=	SYM
ejpam-5750	185	5	(	(	PUNCT
ejpam-5750	185	6	∥µ∥	∥µ∥	NOUN
ejpam-5750	185	7	−	−	NOUN
ejpam-5750	185	8	α	α	NOUN
ejpam-5750	185	9	)	)	PUNCT
ejpam-5750	185	10	log	log	NOUN
ejpam-5750	185	11	|x|+h(x	|x|+h(x	NOUN
ejpam-5750	185	12	)	)	PUNCT
ejpam-5750	186	1	+	+	PUNCT
ejpam-5750	186	2	b1(x	b1(x	NOUN
ejpam-5750	186	3	)	)	PUNCT
ejpam-5750	186	4	near	near	ADP
ejpam-5750	186	5	infinity	infinity	NOUN
ejpam-5750	186	6	.	.	PUNCT
ejpam-5750	187	1	since	since	SCONJ
ejpam-5750	187	2	(	(	PUNCT
ejpam-5750	187	3	b	b	X
ejpam-5750	187	4	−	−	PROPN
ejpam-5750	187	5	b1	b1	NOUN
ejpam-5750	187	6	)	)	PUNCT
ejpam-5750	187	7	is	be	AUX
ejpam-5750	187	8	bounded	bound	VERB
ejpam-5750	187	9	,	,	PUNCT
ejpam-5750	187	10	if	if	SCONJ
ejpam-5750	187	11	∥µ∥	∥µ∥	NUM
ejpam-5750	188	1	−	−	PROPN
ejpam-5750	188	2	α	α	NOUN
ejpam-5750	188	3	=	=	SYM
ejpam-5750	188	4	β	β	X
ejpam-5750	188	5	̸=	̸=	PROPN
ejpam-5750	188	6	0	0	NUM
ejpam-5750	188	7	then	then	ADV
ejpam-5750	188	8	h(x	h(x	PROPN
ejpam-5750	188	9	)	)	PUNCT
ejpam-5750	188	10	is	be	AUX
ejpam-5750	188	11	bounded	bound	VERB
ejpam-5750	188	12	on	on	ADP
ejpam-5750	188	13	one	one	NUM
ejpam-5750	188	14	side	side	NOUN
ejpam-5750	188	15	and	and	CCONJ
ejpam-5750	188	16	hence	hence	ADV
ejpam-5750	188	17	a	a	DET
ejpam-5750	188	18	constant	constant	ADJ
ejpam-5750	188	19	so	so	SCONJ
ejpam-5750	188	20	that	that	SCONJ
ejpam-5750	188	21	β	β	NOUN
ejpam-5750	188	22	log	log	VERB
ejpam-5750	188	23	|x|	|x|	PROPN
ejpam-5750	188	24	should	should	AUX
ejpam-5750	188	25	be	be	AUX
ejpam-5750	188	26	bounded	bound	VERB
ejpam-5750	188	27	near	near	ADP
ejpam-5750	188	28	infinity	infinity	NOUN
ejpam-5750	188	29	,	,	PUNCT
ejpam-5750	188	30	not	not	PART
ejpam-5750	188	31	possible	possible	ADJ
ejpam-5750	188	32	.	.	PUNCT
ejpam-5750	189	1	hence	hence	ADV
ejpam-5750	189	2	∥µ∥	∥µ∥	VERB
ejpam-5750	190	1	−	−	PROPN
ejpam-5750	190	2	α	α	NOUN
ejpam-5750	190	3	=	=	SYM
ejpam-5750	190	4	0	0	NUM
ejpam-5750	190	5	,	,	PUNCT
ejpam-5750	190	6	so	so	SCONJ
ejpam-5750	190	7	that	that	SCONJ
ejpam-5750	190	8	flux∞b(x	flux∞b(x	NOUN
ejpam-5750	190	9	)	)	PUNCT
ejpam-5750	190	10	]	]	PUNCT
ejpam-5750	191	1	=	=	SYM
ejpam-5750	191	2	∥µ∥	∥µ∥	VERB
ejpam-5750	192	1	−	−	NOUN
ejpam-5750	192	2	α	α	NOUN
ejpam-5750	192	3	=	=	SYM
ejpam-5750	192	4	0	0	NUM
ejpam-5750	192	5	proposition	proposition	NOUN
ejpam-5750	192	6	2	2	NUM
ejpam-5750	192	7	.	.	PUNCT
ejpam-5750	193	1	let	let	VERB
ejpam-5750	193	2	f(x	f(x	PROPN
ejpam-5750	193	3	)	)	PUNCT
ejpam-5750	193	4	be	be	AUX
ejpam-5750	193	5	a	a	DET
ejpam-5750	193	6	real	real	ADV
ejpam-5750	193	7	-	-	PUNCT
ejpam-5750	193	8	valued	value	VERB
ejpam-5750	193	9	function	function	NOUN
ejpam-5750	193	10	is	be	AUX
ejpam-5750	193	11	on	on	ADP
ejpam-5750	193	12	r2	r2	PROPN
ejpam-5750	193	13	,	,	PUNCT
ejpam-5750	193	14	such	such	ADJ
ejpam-5750	193	15	that	that	DET
ejpam-5750	193	16	∫	∫	PROPN
ejpam-5750	193	17	|f(x)|dx	|f(x)|dx	NOUN
ejpam-5750	193	18	<	<	X
ejpam-5750	193	19	∞.	∞.	PROPN
ejpam-5750	193	20	there	there	PRON
ejpam-5750	193	21	exists	exist	VERB
ejpam-5750	193	22	two	two	NUM
ejpam-5750	193	23	admissible	admissible	ADJ
ejpam-5750	193	24	subharmonic	subharmonic	ADJ
ejpam-5750	193	25	functions	function	NOUN
ejpam-5750	193	26	s1	s1	NOUN
ejpam-5750	193	27	and	and	CCONJ
ejpam-5750	193	28	s2	s2	NOUN
ejpam-5750	193	29	on	on	ADP
ejpam-5750	193	30	r2	r2	PROPN
ejpam-5750	193	31	such	such	ADJ
ejpam-5750	193	32	that	that	SCONJ
ejpam-5750	193	33	,	,	PUNCT
ejpam-5750	193	34	if	if	SCONJ
ejpam-5750	193	35	s	s	PART
ejpam-5750	193	36	=	=	NOUN
ejpam-5750	193	37	s1−s2	s1−s2	NOUN
ejpam-5750	193	38	,	,	PUNCT
ejpam-5750	193	39	then	then	ADV
ejpam-5750	193	40	∆s(x	∆s(x	PROPN
ejpam-5750	193	41	)	)	PUNCT
ejpam-5750	193	42	=	=	SYM
ejpam-5750	193	43	f(x	f(x	PROPN
ejpam-5750	193	44	)	)	PUNCT
ejpam-5750	193	45	in	in	ADP
ejpam-5750	193	46	the	the	DET
ejpam-5750	193	47	sense	sense	NOUN
ejpam-5750	193	48	of	of	ADP
ejpam-5750	193	49	distributions	distribution	NOUN
ejpam-5750	193	50	.	.	PUNCT
ejpam-5750	194	1	proof	proof	NOUN
ejpam-5750	194	2	.	.	PUNCT
ejpam-5750	195	1	let	let	VERB
ejpam-5750	195	2	∆s1	∆s1	PROPN
ejpam-5750	195	3	=	=	SYM
ejpam-5750	195	4	f+	f+	NOUN
ejpam-5750	195	5	and	and	CCONJ
ejpam-5750	195	6	∆s2	∆s2	PROPN
ejpam-5750	195	7	=	=	PUNCT
ejpam-5750	195	8	f−.	f−.	VERB
ejpam-5750	195	9	then	then	ADV
ejpam-5750	195	10	s1	s1	PROPN
ejpam-5750	195	11	and	and	CCONJ
ejpam-5750	195	12	s2	s2	NOUN
ejpam-5750	195	13	are	be	AUX
ejpam-5750	195	14	subharmonic	subharmonic	ADJ
ejpam-5750	195	15	on	on	ADP
ejpam-5750	195	16	r2	r2	PROPN
ejpam-5750	195	17	.	.	PUNCT
ejpam-5750	195	18	since∫	since∫	VERB
ejpam-5750	195	19	f+(x)dx	f+(x)dx	PUNCT
ejpam-5750	195	20	<	<	X
ejpam-5750	195	21	∞	∞	PROPN
ejpam-5750	195	22	and	and	CCONJ
ejpam-5750	195	23	∫	∫	PROPN
ejpam-5750	196	1	f−(x)dx	f−(x)dx	ADJ
ejpam-5750	196	2	<	<	X
ejpam-5750	196	3	∞	∞	PROPN
ejpam-5750	196	4	,	,	PUNCT
ejpam-5750	196	5	then	then	ADV
ejpam-5750	196	6	s1	s1	PROPN
ejpam-5750	196	7	and	and	CCONJ
ejpam-5750	196	8	s2	s2	NOUN
ejpam-5750	196	9	are	be	AUX
ejpam-5750	196	10	admissible	admissible	ADJ
ejpam-5750	196	11	.	.	PUNCT
ejpam-5750	197	1	hence	hence	ADV
ejpam-5750	197	2	the	the	DET
ejpam-5750	197	3	proposition	proposition	NOUN
ejpam-5750	197	4	is	be	AUX
ejpam-5750	197	5	proved	prove	VERB
ejpam-5750	197	6	.	.	PUNCT
ejpam-5750	198	1	theorem	theorem	ADJ
ejpam-5750	198	2	3	3	X
ejpam-5750	198	3	.	.	PUNCT
ejpam-5750	198	4	suppose	suppose	VERB
ejpam-5750	198	5	s(x	s(x	NOUN
ejpam-5750	198	6	)	)	PUNCT
ejpam-5750	198	7	is	be	AUX
ejpam-5750	198	8	a	a	DET
ejpam-5750	198	9	subharmonic	subharmonic	ADJ
ejpam-5750	198	10	function	function	NOUN
ejpam-5750	198	11	on	on	ADP
ejpam-5750	198	12	r2	r2	PROPN
ejpam-5750	198	13	,	,	PUNCT
ejpam-5750	198	14	having	have	VERB
ejpam-5750	198	15	a	a	DET
ejpam-5750	198	16	harmonic	harmonic	ADJ
ejpam-5750	198	17	majorant	majorant	NOUN
ejpam-5750	198	18	outside	outside	ADP
ejpam-5750	198	19	a	a	DET
ejpam-5750	198	20	compact	compact	ADJ
ejpam-5750	198	21	set	set	NOUN
ejpam-5750	199	1	k.	k.	PROPN
ejpam-5750	199	2	then	then	ADV
ejpam-5750	199	3	the	the	DET
ejpam-5750	199	4	flux	flux	NOUN
ejpam-5750	199	5	of	of	ADP
ejpam-5750	199	6	s	s	PRON
ejpam-5750	199	7	at	at	ADP
ejpam-5750	199	8	infinity	infinity	NOUN
ejpam-5750	199	9	=	=	NOUN
ejpam-5750	199	10	flux	flux	NOUN
ejpam-5750	199	11	at	at	ADP
ejpam-5750	199	12	infinity	infinity	NOUN
ejpam-5750	199	13	of	of	ADP
ejpam-5750	199	14	the	the	DET
ejpam-5750	199	15	least	least	ADJ
ejpam-5750	199	16	harmonic	harmonic	ADJ
ejpam-5750	199	17	majorant	majorant	NOUN
ejpam-5750	199	18	of	of	ADP
ejpam-5750	199	19	s	s	PRON
ejpam-5750	199	20	outside	outside	ADV
ejpam-5750	199	21	k.	k.	PROPN
ejpam-5750	199	22	proof	proof	PROPN
ejpam-5750	199	23	.	.	PUNCT
ejpam-5750	200	1	suppose	suppose	VERB
ejpam-5750	200	2	s(x	s(x	NOUN
ejpam-5750	200	3	)	)	PUNCT
ejpam-5750	200	4	has	have	VERB
ejpam-5750	200	5	a	a	DET
ejpam-5750	200	6	harmonic	harmonic	ADJ
ejpam-5750	200	7	majorant	majorant	NOUN
ejpam-5750	200	8	on	on	ADP
ejpam-5750	200	9	|x|	|x|	PROPN
ejpam-5750	200	10	>	>	X
ejpam-5750	200	11	r.	r.	PROPN
ejpam-5750	200	12	take	take	VERB
ejpam-5750	200	13	an	an	DET
ejpam-5750	200	14	increasing	increase	VERB
ejpam-5750	200	15	sequence	sequence	NOUN
ejpam-5750	200	16	of	of	ADP
ejpam-5750	200	17	numbers	number	NOUN
ejpam-5750	200	18	rn	rn	ADV
ejpam-5750	200	19	such	such	ADJ
ejpam-5750	200	20	that	that	SCONJ
ejpam-5750	200	21	r	r	NOUN
ejpam-5750	200	22	<	<	X
ejpam-5750	200	23	rn	rn	NOUN
ejpam-5750	200	24	for	for	ADP
ejpam-5750	200	25	all	all	DET
ejpam-5750	200	26	n	n	NOUN
ejpam-5750	200	27	and	and	CCONJ
ejpam-5750	200	28	rn	rn	PROPN
ejpam-5750	200	29	−→	−→	PROPN
ejpam-5750	200	30	∞.	∞.	PROPN
ejpam-5750	200	31	let	let	VERB
ejpam-5750	200	32	sn	sn	PROPN
ejpam-5750	200	33	be	be	AUX
ejpam-5750	200	34	the	the	DET
ejpam-5750	200	35	function	function	NOUN
ejpam-5750	200	36	on	on	ADP
ejpam-5750	200	37	|x|	|x|	PROPN
ejpam-5750	200	38	>	>	X
ejpam-5750	200	39	r	r	NOUN
ejpam-5750	200	40	which	which	PRON
ejpam-5750	200	41	is	be	AUX
ejpam-5750	200	42	the	the	DET
ejpam-5750	200	43	dirichlet	dirichlet	NOUN
ejpam-5750	200	44	solution	solution	NOUN
ejpam-5750	200	45	on	on	ADP
ejpam-5750	200	46	r	r	NOUN
ejpam-5750	200	47	<	<	X
ejpam-5750	200	48	|x|	|x|	PROPN
ejpam-5750	200	49	<	<	X
ejpam-5750	200	50	rn	rn	PROPN
ejpam-5750	200	51	with	with	ADP
ejpam-5750	200	52	boundary	boundary	ADJ
ejpam-5750	200	53	values	value	NOUN
ejpam-5750	200	54	s(x	s(x	PROPN
ejpam-5750	200	55	)	)	PUNCT
ejpam-5750	200	56	and	and	CCONJ
ejpam-5750	200	57	extended	extend	VERB
ejpam-5750	200	58	by	by	ADP
ejpam-5750	200	59	s(x	s(x	NOUN
ejpam-5750	200	60	)	)	PUNCT
ejpam-5750	200	61	on	on	ADP
ejpam-5750	200	62	|x|	|x|	PROPN
ejpam-5750	200	63	>	>	X
ejpam-5750	200	64	rn	rn	PROPN
ejpam-5750	200	65	.	.	PUNCT
ejpam-5750	200	66	then	then	ADV
ejpam-5750	200	67	note	note	VERB
ejpam-5750	200	68	:	:	PUNCT
ejpam-5750	200	69	(	(	PUNCT
ejpam-5750	200	70	a	a	X
ejpam-5750	200	71	)	)	PUNCT
ejpam-5750	200	72	sn	sn	PROPN
ejpam-5750	200	73	tends	tend	VERB
ejpam-5750	200	74	to	to	ADP
ejpam-5750	200	75	the	the	DET
ejpam-5750	200	76	least	least	ADJ
ejpam-5750	200	77	harmonic	harmonic	ADJ
ejpam-5750	200	78	majorant	majorant	NOUN
ejpam-5750	200	79	h	h	NOUN
ejpam-5750	200	80	of	of	ADP
ejpam-5750	200	81	s	s	PRON
ejpam-5750	200	82	on	on	ADP
ejpam-5750	200	83	|x|	|x|	PROPN
ejpam-5750	200	84	>	>	X
ejpam-5750	200	85	r	r	NOUN
ejpam-5750	200	86	;	;	PUNCT
ejpam-5750	200	87	(	(	PUNCT
ejpam-5750	200	88	b	b	X
ejpam-5750	200	89	)	)	PUNCT
ejpam-5750	200	90	for	for	ADP
ejpam-5750	200	91	every	every	DET
ejpam-5750	200	92	n	n	NOUN
ejpam-5750	200	93	,	,	PUNCT
ejpam-5750	200	94	flux	flux	NOUN
ejpam-5750	200	95	of	of	ADP
ejpam-5750	200	96	sn	sn	PROPN
ejpam-5750	200	97	at	at	ADP
ejpam-5750	200	98	infinity	infinity	NOUN
ejpam-5750	200	99	=	=	SYM
ejpam-5750	200	100	flux	flux	NOUN
ejpam-5750	200	101	of	of	ADP
ejpam-5750	200	102	s	s	PRON
ejpam-5750	200	103	at	at	ADP
ejpam-5750	200	104	infinity	infinity	NOUN
ejpam-5750	200	105	;	;	PUNCT
ejpam-5750	200	106	(	(	PUNCT
ejpam-5750	200	107	c	c	X
ejpam-5750	200	108	)	)	PUNCT
ejpam-5750	200	109	flux	flux	NOUN
ejpam-5750	200	110	of	of	ADP
ejpam-5750	200	111	h(x	h(x	PROPN
ejpam-5750	200	112	)	)	PUNCT
ejpam-5750	200	113	at	at	ADP
ejpam-5750	200	114	infinity	infinity	NOUN
ejpam-5750	200	115	=	=	PROPN
ejpam-5750	200	116	lim	lim	PROPN
ejpam-5750	200	117	n−→∞	n−→∞	PROPN
ejpam-5750	200	118	flux	flux	PROPN
ejpam-5750	200	119	at	at	ADP
ejpam-5750	200	120	infinity	infinity	NOUN
ejpam-5750	200	121	of	of	ADP
ejpam-5750	200	122	sn(x	sn(x	NOUN
ejpam-5750	200	123	)	)	PUNCT
ejpam-5750	200	124	.	.	PUNCT
ejpam-5750	201	1	consequently	consequently	ADV
ejpam-5750	201	2	,	,	PUNCT
ejpam-5750	201	3	the	the	DET
ejpam-5750	201	4	flux	flux	NOUN
ejpam-5750	201	5	of	of	ADP
ejpam-5750	201	6	s(x	s(x	PROPN
ejpam-5750	201	7	)	)	PUNCT
ejpam-5750	201	8	at	at	ADP
ejpam-5750	201	9	infinity	infinity	NOUN
ejpam-5750	201	10	=	=	SYM
ejpam-5750	201	11	flux	flux	NOUN
ejpam-5750	201	12	of	of	ADP
ejpam-5750	201	13	the	the	DET
ejpam-5750	201	14	least	least	ADJ
ejpam-5750	201	15	harmonic	harmonic	ADJ
ejpam-5750	201	16	majorant	majorant	NOUN
ejpam-5750	201	17	h(x	h(x	PROPN
ejpam-5750	201	18	)	)	PUNCT
ejpam-5750	201	19	of	of	ADP
ejpam-5750	201	20	s(x	s(x	PROPN
ejpam-5750	201	21	)	)	PUNCT
ejpam-5750	201	22	.	.	PUNCT
ejpam-5750	202	1	amulya	amulya	PROPN
ejpam-5750	202	2	smyrna	smyrna	PROPN
ejpam-5750	202	3	c.	c.	PROPN
ejpam-5750	202	4	,	,	PUNCT
ejpam-5750	202	5	n.	n.	PROPN
ejpam-5750	202	6	nathiya	nathiya	PROPN
ejpam-5750	202	7	/	/	SYM
ejpam-5750	202	8	eur	eur	PROPN
ejpam-5750	202	9	.	.	PUNCT
ejpam-5750	203	1	j.	j.	PROPN
ejpam-5750	203	2	pure	pure	PROPN
ejpam-5750	203	3	appl	appl	PROPN
ejpam-5750	203	4	.	.	PROPN
ejpam-5750	203	5	math	math	PROPN
ejpam-5750	203	6	,	,	PUNCT
ejpam-5750	203	7	18	18	NUM
ejpam-5750	203	8	(	(	PUNCT
ejpam-5750	203	9	2	2	NUM
ejpam-5750	203	10	)	)	PUNCT
ejpam-5750	203	11	(	(	PUNCT
ejpam-5750	203	12	2025	2025	NUM
ejpam-5750	203	13	)	)	PUNCT
ejpam-5750	203	14	,	,	PUNCT
ejpam-5750	203	15	5750	5750	NUM
ejpam-5750	203	16	7	7	NUM
ejpam-5750	203	17	of	of	ADP
ejpam-5750	203	18	9	9	NUM
ejpam-5750	203	19	5	5	NUM
ejpam-5750	203	20	.	.	PUNCT
ejpam-5750	203	21	total	total	ADJ
ejpam-5750	203	22	measures	measure	NOUN
ejpam-5750	203	23	of	of	ADP
ejpam-5750	203	24	subharmonic	subharmonic	ADJ
ejpam-5750	203	25	functions	function	NOUN
ejpam-5750	203	26	and	and	CCONJ
ejpam-5750	203	27	least	least	ADJ
ejpam-5750	203	28	harmonic	harmonic	ADJ
ejpam-5750	203	29	majorants	majorant	NOUN
ejpam-5750	203	30	proposition	proposition	NOUN
ejpam-5750	203	31	3	3	X
ejpam-5750	203	32	.	.	PUNCT
ejpam-5750	204	1	if	if	SCONJ
ejpam-5750	204	2	h1	h1	PROPN
ejpam-5750	204	3	,	,	PUNCT
ejpam-5750	204	4	h2	h2	PROPN
ejpam-5750	204	5	are	be	AUX
ejpam-5750	204	6	two	two	NUM
ejpam-5750	204	7	harmonic	harmonic	ADJ
ejpam-5750	204	8	functions	function	NOUN
ejpam-5750	204	9	outside	outside	ADP
ejpam-5750	204	10	of	of	ADP
ejpam-5750	204	11	a	a	DET
ejpam-5750	204	12	compact	compact	ADJ
ejpam-5750	204	13	set	set	NOUN
ejpam-5750	204	14	in	in	ADP
ejpam-5750	204	15	r2	r2	PROPN
ejpam-5750	204	16	,	,	PUNCT
ejpam-5750	204	17	such	such	ADJ
ejpam-5750	204	18	that	that	SCONJ
ejpam-5750	204	19	h1	h1	PROPN
ejpam-5750	204	20	≥	≥	PROPN
ejpam-5750	204	21	h2	h2	PROPN
ejpam-5750	204	22	.	.	PUNCT
ejpam-5750	205	1	let	let	VERB
ejpam-5750	205	2	hi	hi	INTJ
ejpam-5750	205	3	=	=	VERB
ejpam-5750	205	4	hi+αi	hi+αi	VERB
ejpam-5750	205	5	log	log	NOUN
ejpam-5750	205	6	|x|+bi(x	|x|+bi(x	NOUN
ejpam-5750	205	7	)	)	PUNCT
ejpam-5750	205	8	,	,	PUNCT
ejpam-5750	205	9	for	for	ADP
ejpam-5750	205	10	i	i	PROPN
ejpam-5750	205	11	=	=	SYM
ejpam-5750	205	12	1	1	NUM
ejpam-5750	205	13	,	,	PUNCT
ejpam-5750	205	14	2	2	NUM
ejpam-5750	205	15	,	,	PUNCT
ejpam-5750	205	16	·	·	PUNCT
ejpam-5750	205	17	·	·	PUNCT
ejpam-5750	205	18	·	·	PUNCT
ejpam-5750	205	19	,	,	PUNCT
ejpam-5750	205	20	be	be	AUX
ejpam-5750	205	21	the	the	DET
ejpam-5750	205	22	unique	unique	ADJ
ejpam-5750	205	23	representations	representation	NOUN
ejpam-5750	205	24	as	as	ADP
ejpam-5750	205	25	above	above	ADV
ejpam-5750	205	26	.	.	PUNCT
ejpam-5750	206	1	then	then	ADV
ejpam-5750	206	2	α1	α1	PROPN
ejpam-5750	206	3	≥	≥	NUM
ejpam-5750	206	4	α2	α2	ADJ
ejpam-5750	206	5	.	.	PUNCT
ejpam-5750	207	1	proof	proof	NOUN
ejpam-5750	207	2	.	.	PUNCT
ejpam-5750	208	1	for	for	ADP
ejpam-5750	208	2	h1(x	h1(x	NOUN
ejpam-5750	208	3	)	)	PUNCT
ejpam-5750	208	4	+	+	CCONJ
ejpam-5750	208	5	α1	α1	PROPN
ejpam-5750	208	6	log	log	VERB
ejpam-5750	208	7	|x|	|x|	PROPN
ejpam-5750	208	8	+	+	CCONJ
ejpam-5750	208	9	b1(x	b1(x	NOUN
ejpam-5750	208	10	)	)	PUNCT
ejpam-5750	208	11	≥	≥	NOUN
ejpam-5750	208	12	h2(x	h2(x	X
ejpam-5750	208	13	)	)	PUNCT
ejpam-5750	209	1	+	+	CCONJ
ejpam-5750	209	2	α2	α2	ADJ
ejpam-5750	209	3	log	log	VERB
ejpam-5750	209	4	|x|	|x|	PROPN
ejpam-5750	209	5	+	+	CCONJ
ejpam-5750	209	6	b2(x	b2(x	NOUN
ejpam-5750	209	7	)	)	PUNCT
ejpam-5750	209	8	near	near	ADP
ejpam-5750	209	9	infinity	infinity	NOUN
ejpam-5750	209	10	.	.	PUNCT
ejpam-5750	210	1	then	then	ADV
ejpam-5750	210	2	for	for	ADP
ejpam-5750	210	3	large	large	ADJ
ejpam-5750	210	4	r	r	NOUN
ejpam-5750	210	5	,	,	PUNCT
ejpam-5750	210	6	∫	∫	PROPN
ejpam-5750	210	7	|x|=r	|x|=r	PROPN
ejpam-5750	210	8	h1(x	h1(x	PROPN
ejpam-5750	210	9	)	)	PUNCT
ejpam-5750	210	10	+	+	CCONJ
ejpam-5750	210	11	α1	α1	PROPN
ejpam-5750	210	12	log	log	NOUN
ejpam-5750	210	13	|x|+	|x|+	NOUN
ejpam-5750	210	14	b1(x)dx	b1(x)dx	ADJ
ejpam-5750	210	15	≥	≥	X
ejpam-5750	210	16	∫	∫	PROPN
ejpam-5750	210	17	|x|=r	|x|=r	PROPN
ejpam-5750	210	18	h2(x	h2(x	PROPN
ejpam-5750	210	19	)	)	PUNCT
ejpam-5750	211	1	+	+	CCONJ
ejpam-5750	211	2	α2	α2	ADJ
ejpam-5750	211	3	log	log	VERB
ejpam-5750	211	4	|x|+	|x|+	NOUN
ejpam-5750	211	5	b2(x)dx	b2(x)dx	NOUN
ejpam-5750	211	6	.	.	PUNCT
ejpam-5750	212	1	then	then	ADV
ejpam-5750	212	2	rh1(0)+	rh1(0)+	PROPN
ejpam-5750	212	3	2πrα1	2πrα1	PROPN
ejpam-5750	212	4	log	log	VERB
ejpam-5750	212	5	r+	r+	PUNCT
ejpam-5750	212	6	∫	∫	PROPN
ejpam-5750	212	7	|x|=r	|x|=r	PROPN
ejpam-5750	212	8	b1(x)dx	b1(x)dx	PART
ejpam-5750	212	9	≥	≥	NOUN
ejpam-5750	213	1	rh2(0)+	rh2(0)+	NOUN
ejpam-5750	213	2	2πrα2	2πrα2	NUM
ejpam-5750	213	3	log	log	NOUN
ejpam-5750	213	4	r+	r+	PUNCT
ejpam-5750	213	5	∫	∫	PROPN
ejpam-5750	213	6	|x|=r	|x|=r	PROPN
ejpam-5750	213	7	b2(x)dx	b2(x)dx	VERB
ejpam-5750	213	8	.	.	PUNCT
ejpam-5750	214	1	now	now	ADV
ejpam-5750	214	2	,	,	PUNCT
ejpam-5750	214	3	if	if	SCONJ
ejpam-5750	214	4	|bi(x)|	|bi(x)|	NOUN
ejpam-5750	214	5	≤	≤	NUM
ejpam-5750	214	6	mi	mi	NOUN
ejpam-5750	214	7	,	,	PUNCT
ejpam-5750	214	8	then	then	ADV
ejpam-5750	214	9	|	|	ADV
ejpam-5750	214	10	∫	∫	PROPN
ejpam-5750	215	1	|x|=r	|x|=r	PROPN
ejpam-5750	215	2	bi(x)dx	bi(x)dx	PROPN
ejpam-5750	215	3	≤	≤	NUM
ejpam-5750	215	4	mir2π	mir2π	PROPN
ejpam-5750	215	5	.	.	PUNCT
ejpam-5750	216	1	hence	hence	ADV
ejpam-5750	216	2	,	,	PUNCT
ejpam-5750	216	3	from	from	ADP
ejpam-5750	216	4	the	the	DET
ejpam-5750	216	5	above	above	NOUN
ejpam-5750	216	6	,	,	PUNCT
ejpam-5750	216	7	after	after	ADP
ejpam-5750	216	8	dividing	divide	VERB
ejpam-5750	216	9	by	by	ADP
ejpam-5750	216	10	r	r	NOUN
ejpam-5750	216	11	,	,	PUNCT
ejpam-5750	216	12	we	we	PRON
ejpam-5750	216	13	get	get	VERB
ejpam-5750	216	14	the	the	DET
ejpam-5750	216	15	inequality	inequality	NOUN
ejpam-5750	216	16	2πα1	2πα1	NUM
ejpam-5750	216	17	≥	≥	NOUN
ejpam-5750	216	18	2πα2	2πα2	NUM
ejpam-5750	216	19	log	log	NOUN
ejpam-5750	216	20	r	r	NOUN
ejpam-5750	217	1	+	+	CCONJ
ejpam-5750	217	2	(	(	PUNCT
ejpam-5750	217	3	a	a	DET
ejpam-5750	217	4	bounded	bounded	ADJ
ejpam-5750	217	5	function	function	NOUN
ejpam-5750	217	6	in	in	ADP
ejpam-5750	217	7	r	r	NOUN
ejpam-5750	217	8	)	)	PUNCT
ejpam-5750	217	9	.	.	PUNCT
ejpam-5750	218	1	allow	allow	VERB
ejpam-5750	218	2	r	r	NOUN
ejpam-5750	218	3	−→	−→	NOUN
ejpam-5750	218	4	∞	∞	PROPN
ejpam-5750	218	5	to	to	PART
ejpam-5750	218	6	conclude	conclude	VERB
ejpam-5750	218	7	that	that	SCONJ
ejpam-5750	218	8	α1	α1	PROPN
ejpam-5750	218	9	≥	≥	NUM
ejpam-5750	218	10	α2	α2	ADJ
ejpam-5750	218	11	.	.	PUNCT
ejpam-5750	219	1	if	if	SCONJ
ejpam-5750	219	2	u	u	NOUN
ejpam-5750	219	3	is	be	AUX
ejpam-5750	219	4	a	a	DET
ejpam-5750	219	5	c2	c2	PROPN
ejpam-5750	219	6	-	-	PUNCT
ejpam-5750	219	7	function	function	NOUN
ejpam-5750	219	8	and	and	CCONJ
ejpam-5750	219	9	ω	ω	PROPN
ejpam-5750	219	10	is	be	AUX
ejpam-5750	219	11	a	a	DET
ejpam-5750	219	12	bounded	bounded	ADJ
ejpam-5750	219	13	domain	domain	NOUN
ejpam-5750	219	14	in	in	ADP
ejpam-5750	219	15	r2	r2	PROPN
ejpam-5750	219	16	∫	∫	PROPN
ejpam-5750	220	1	ω	ω	PROPN
ejpam-5750	220	2	∆u(x)d(x	∆u(x)d(x	PROPN
ejpam-5750	220	3	)	)	PUNCT
ejpam-5750	220	4	=	=	SYM
ejpam-5750	220	5	∫	∫	PROPN
ejpam-5750	220	6	∂ω	∂ω	PROPN
ejpam-5750	220	7	∂u	∂u	PROPN
ejpam-5750	220	8	∂n+ds	∂n+ds	NOUN
ejpam-5750	220	9	,	,	PUNCT
ejpam-5750	220	10	in	in	ADP
ejpam-5750	220	11	the	the	DET
ejpam-5750	220	12	classical	classical	ADJ
ejpam-5750	220	13	sense	sense	NOUN
ejpam-5750	220	14	.	.	PUNCT
ejpam-5750	221	1	when	when	SCONJ
ejpam-5750	221	2	v	v	NOUN
ejpam-5750	221	3	is	be	AUX
ejpam-5750	221	4	a	a	DET
ejpam-5750	221	5	subharmonic	subharmonic	ADJ
ejpam-5750	221	6	function	function	NOUN
ejpam-5750	221	7	on	on	ADP
ejpam-5750	221	8	r2	r2	PROPN
ejpam-5750	221	9	,	,	PUNCT
ejpam-5750	221	10	there	there	PRON
ejpam-5750	221	11	exists	exist	VERB
ejpam-5750	221	12	an	an	DET
ejpam-5750	221	13	increasing	increase	VERB
ejpam-5750	221	14	sequence	sequence	NOUN
ejpam-5750	221	15	of	of	ADP
ejpam-5750	221	16	c2	c2	PROPN
ejpam-5750	221	17	-	-	PUNCT
ejpam-5750	221	18	subharmonic	subharmonic	ADJ
ejpam-5750	221	19	functions	function	NOUN
ejpam-5750	221	20	tending	tend	VERB
ejpam-5750	221	21	to	to	ADP
ejpam-5750	221	22	v	v	NOUN
ejpam-5750	221	23	[	[	X
ejpam-5750	221	24	2	2	NUM
ejpam-5750	221	25	]	]	PUNCT
ejpam-5750	221	26	.	.	PUNCT
ejpam-5750	222	1	in	in	ADP
ejpam-5750	222	2	classical	classical	ADJ
ejpam-5750	222	3	sense	sense	NOUN
ejpam-5750	222	4	,	,	PUNCT
ejpam-5750	222	5	where	where	SCONJ
ejpam-5750	222	6	limits	limit	NOUN
ejpam-5750	222	7	are	be	AUX
ejpam-5750	222	8	not	not	PART
ejpam-5750	222	9	permissible	permissible	ADJ
ejpam-5750	222	10	,	,	PUNCT
ejpam-5750	222	11	the	the	DET
ejpam-5750	222	12	continuity	continuity	NOUN
ejpam-5750	222	13	of	of	ADP
ejpam-5750	222	14	subharmonic	subharmonic	ADJ
ejpam-5750	222	15	function	function	NOUN
ejpam-5750	222	16	(	(	PUNCT
ejpam-5750	222	17	upper	upper	ADJ
ejpam-5750	222	18	continuous	continuous	ADJ
ejpam-5750	222	19	function	function	NOUN
ejpam-5750	222	20	)	)	PUNCT
ejpam-5750	222	21	is	be	AUX
ejpam-5750	222	22	not	not	PART
ejpam-5750	222	23	always	always	ADV
ejpam-5750	222	24	true	true	ADJ
ejpam-5750	222	25	,	,	PUNCT
ejpam-5750	222	26	therefore	therefore	ADV
ejpam-5750	222	27	the	the	DET
ejpam-5750	222	28	distribution	distribution	NOUN
ejpam-5750	222	29	sense	sense	NOUN
ejpam-5750	222	30	is	be	AUX
ejpam-5750	222	31	adopted	adopt	VERB
ejpam-5750	222	32	to	to	PART
ejpam-5750	222	33	show	show	VERB
ejpam-5750	222	34	the	the	DET
ejpam-5750	222	35	continuity	continuity	NOUN
ejpam-5750	222	36	of	of	ADP
ejpam-5750	222	37	the	the	DET
ejpam-5750	222	38	function	function	NOUN
ejpam-5750	222	39	,	,	PUNCT
ejpam-5750	222	40	as	as	SCONJ
ejpam-5750	222	41	limits	limit	NOUN
ejpam-5750	222	42	exists	exist	VERB
ejpam-5750	222	43	in	in	ADP
ejpam-5750	222	44	distribution	distribution	NOUN
ejpam-5750	222	45	case	case	NOUN
ejpam-5750	223	1	[	[	X
ejpam-5750	223	2	9	9	NUM
ejpam-5750	223	3	]	]	PUNCT
ejpam-5750	223	4	.	.	PUNCT
ejpam-5750	224	1	consequently	consequently	ADV
ejpam-5750	224	2	in	in	ADP
ejpam-5750	224	3	the	the	DET
ejpam-5750	224	4	sense	sense	NOUN
ejpam-5750	224	5	of	of	ADP
ejpam-5750	224	6	distributions∫	distributions∫	PROPN
ejpam-5750	224	7	ω	ω	PROPN
ejpam-5750	224	8	∆v(x)d(x	∆v(x)d(x	PROPN
ejpam-5750	224	9	)	)	PUNCT
ejpam-5750	224	10	=	=	SYM
ejpam-5750	224	11	∫	∫	PROPN
ejpam-5750	224	12	∂ω	∂ω	PROPN
ejpam-5750	224	13	∂v	∂v	PROPN
ejpam-5750	224	14	∂n+	∂n+	PART
ejpam-5750	224	15	ds	ds	PROPN
ejpam-5750	224	16	.	.	PROPN
ejpam-5750	224	17	theorem	theorem	PROPN
ejpam-5750	224	18	4	4	NUM
ejpam-5750	224	19	.	.	PUNCT
ejpam-5750	225	1	let	let	AUX
ejpam-5750	225	2	v(x	v(x	PROPN
ejpam-5750	225	3	)	)	PUNCT
ejpam-5750	225	4	be	be	AUX
ejpam-5750	225	5	a	a	DET
ejpam-5750	225	6	subharmonic	subharmonic	ADJ
ejpam-5750	225	7	function	function	NOUN
ejpam-5750	225	8	on	on	ADP
ejpam-5750	225	9	r2	r2	PROPN
ejpam-5750	225	10	having	have	VERB
ejpam-5750	225	11	a	a	DET
ejpam-5750	225	12	harmonic	harmonic	ADJ
ejpam-5750	225	13	majorant	majorant	NOUN
ejpam-5750	225	14	near	near	ADP
ejpam-5750	225	15	infinity	infinity	NOUN
ejpam-5750	225	16	.	.	PUNCT
ejpam-5750	226	1	let	let	VERB
ejpam-5750	226	2	h(x	h(x	PROPN
ejpam-5750	226	3	)	)	PUNCT
ejpam-5750	227	1	=	=	PUNCT
ejpam-5750	228	1	α	α	PRON
ejpam-5750	228	2	log	log	NOUN
ejpam-5750	228	3	|x|+	|x|+	PROPN
ejpam-5750	228	4	b(x)+	b(x)+	NOUN
ejpam-5750	228	5	(	(	PUNCT
ejpam-5750	228	6	a	a	DET
ejpam-5750	228	7	harmonic	harmonic	ADJ
ejpam-5750	228	8	function	function	NOUN
ejpam-5750	228	9	r2	r2	NOUN
ejpam-5750	228	10	)	)	PUNCT
ejpam-5750	228	11	be	be	VERB
ejpam-5750	228	12	the	the	DET
ejpam-5750	228	13	least	least	ADJ
ejpam-5750	228	14	harmonic	harmonic	ADJ
ejpam-5750	228	15	majorant	majorant	NOUN
ejpam-5750	228	16	of	of	ADP
ejpam-5750	228	17	v(x	v(x	PROPN
ejpam-5750	228	18	)	)	PUNCT
ejpam-5750	228	19	outside	outside	ADP
ejpam-5750	228	20	a	a	DET
ejpam-5750	228	21	compact	compact	ADJ
ejpam-5750	228	22	set	set	NOUN
ejpam-5750	228	23	.	.	PUNCT
ejpam-5750	229	1	then	then	ADV
ejpam-5750	229	2	the	the	DET
ejpam-5750	229	3	total	total	ADJ
ejpam-5750	229	4	measure	measure	NOUN
ejpam-5750	229	5	associated	associate	VERB
ejpam-5750	229	6	with	with	ADP
ejpam-5750	229	7	v(x	v(x	PROPN
ejpam-5750	229	8	)	)	PUNCT
ejpam-5750	229	9	equals	equal	VERB
ejpam-5750	229	10	α	α	PRON
ejpam-5750	229	11	.	.	PUNCT
ejpam-5750	229	12	proof	proof	NOUN
ejpam-5750	229	13	.	.	PUNCT
ejpam-5750	230	1	suppose	suppose	VERB
ejpam-5750	230	2	v	v	NOUN
ejpam-5750	230	3	has	have	VERB
ejpam-5750	230	4	a	a	DET
ejpam-5750	230	5	harmonic	harmonic	ADJ
ejpam-5750	230	6	majorant	majorant	NOUN
ejpam-5750	230	7	h	h	NOUN
ejpam-5750	230	8	outside	outside	ADP
ejpam-5750	230	9	a	a	DET
ejpam-5750	230	10	compact	compact	ADJ
ejpam-5750	230	11	set	set	NOUN
ejpam-5750	230	12	.	.	PUNCT
ejpam-5750	231	1	v(x	v(x	NOUN
ejpam-5750	231	2	)	)	PUNCT
ejpam-5750	231	3	≤	≤	NUM
ejpam-5750	231	4	h(x	h(x	PROPN
ejpam-5750	231	5	)	)	PUNCT
ejpam-5750	231	6	if	if	SCONJ
ejpam-5750	231	7	|x|	|x|	PROPN
ejpam-5750	231	8	≥	≥	X
ejpam-5750	231	9	m.	m.	NOUN
ejpam-5750	231	10	then	then	ADV
ejpam-5750	231	11	for	for	ADP
ejpam-5750	231	12	large	large	ADJ
ejpam-5750	231	13	r	r	NOUN
ejpam-5750	231	14	>	>	X
ejpam-5750	231	15	m	m	VERB
ejpam-5750	231	16	let	let	VERB
ejpam-5750	231	17	hr	hr	NOUN
ejpam-5750	231	18	be	be	AUX
ejpam-5750	231	19	the	the	DET
ejpam-5750	231	20	dirichlet	dirichlet	NOUN
ejpam-5750	231	21	solution	solution	NOUN
ejpam-5750	231	22	in	in	ADP
ejpam-5750	231	23	r	r	NOUN
ejpam-5750	231	24	<	<	X
ejpam-5750	231	25	|x|	|x|	X
ejpam-5750	231	26	<	<	X
ejpam-5750	231	27	r	r	NOUN
ejpam-5750	231	28	+	+	NOUN
ejpam-5750	231	29	1	1	NUM
ejpam-5750	231	30	with	with	ADP
ejpam-5750	231	31	boundary	boundary	ADJ
ejpam-5750	231	32	values	value	NOUN
ejpam-5750	231	33	v(x	v(x	PROPN
ejpam-5750	231	34	)	)	PUNCT
ejpam-5750	231	35	.	.	PUNCT
ejpam-5750	232	1	write	write	VERB
ejpam-5750	232	2	vr(x	vr(x	PUNCT
ejpam-5750	232	3	)	)	PUNCT
ejpam-5750	233	1	=	=	PRON
ejpam-5750	233	2	{	{	PUNCT
ejpam-5750	233	3	hr(x	hr(x	NOUN
ejpam-5750	233	4	)	)	PUNCT
ejpam-5750	233	5	,	,	PUNCT
ejpam-5750	233	6	in	in	ADP
ejpam-5750	233	7	r	r	NOUN
ejpam-5750	233	8	<	<	X
ejpam-5750	233	9	|x|	|x|	X
ejpam-5750	233	10	<	<	X
ejpam-5750	233	11	r	r	NOUN
ejpam-5750	233	12	+	+	NUM
ejpam-5750	233	13	1	1	NUM
ejpam-5750	233	14	v(x	v(x	NOUN
ejpam-5750	233	15	)	)	PUNCT
ejpam-5750	233	16	,	,	PUNCT
ejpam-5750	233	17	otherwise	otherwise	ADV
ejpam-5750	233	18	in	in	ADP
ejpam-5750	233	19	r2	r2	PROPN
ejpam-5750	233	20	then	then	ADV
ejpam-5750	233	21	vr(x	vr(x	PUNCT
ejpam-5750	233	22	)	)	PUNCT
ejpam-5750	233	23	is	be	AUX
ejpam-5750	233	24	a	a	DET
ejpam-5750	233	25	subharmonic	subharmonic	ADJ
ejpam-5750	233	26	function	function	NOUN
ejpam-5750	233	27	on	on	ADP
ejpam-5750	233	28	r2	r2	PROPN
ejpam-5750	233	29	and∫	and∫	PROPN
ejpam-5750	233	30	|x|<r+2	|x|<r+2	PROPN
ejpam-5750	233	31	∆vr(x)dx	∆vr(x)dx	PROPN
ejpam-5750	233	32	=	=	SYM
ejpam-5750	233	33	∫	∫	NUM
ejpam-5750	233	34	|x|=r+2	|x|=r+2	PROPN
ejpam-5750	233	35	∂vr(x	∂vr(x	NOUN
ejpam-5750	233	36	)	)	PUNCT
ejpam-5750	233	37	∂n+	∂n+	VERB
ejpam-5750	233	38	ds	ds	PROPN
ejpam-5750	233	39	=	=	SYM
ejpam-5750	233	40	∫	∫	PROPN
ejpam-5750	233	41	|x|=r+2	|x|=r+2	NOUN
ejpam-5750	233	42	∂v(x	∂v(x	PROPN
ejpam-5750	233	43	)	)	PUNCT
ejpam-5750	234	1	∂n+	∂n+	VERB
ejpam-5750	235	1	ds	ds	PROPN
ejpam-5750	235	2	=	=	SYM
ejpam-5750	235	3	∫	∫	PROPN
ejpam-5750	235	4	|x|<r+2	|x|<r+2	PROPN
ejpam-5750	235	5	∆v(x)dx	∆v(x)dx	VERB
ejpam-5750	235	6	amulya	amulya	PROPN
ejpam-5750	235	7	smyrna	smyrna	PROPN
ejpam-5750	235	8	c.	c.	PROPN
ejpam-5750	235	9	,	,	PUNCT
ejpam-5750	235	10	n.	n.	PROPN
ejpam-5750	235	11	nathiya	nathiya	PROPN
ejpam-5750	235	12	/	/	SYM
ejpam-5750	235	13	eur	eur	PROPN
ejpam-5750	235	14	.	.	PUNCT
ejpam-5750	236	1	j.	j.	PROPN
ejpam-5750	236	2	pure	pure	PROPN
ejpam-5750	236	3	appl	appl	PROPN
ejpam-5750	236	4	.	.	PROPN
ejpam-5750	236	5	math	math	PROPN
ejpam-5750	236	6	,	,	PUNCT
ejpam-5750	236	7	18	18	NUM
ejpam-5750	236	8	(	(	PUNCT
ejpam-5750	236	9	2	2	NUM
ejpam-5750	236	10	)	)	PUNCT
ejpam-5750	236	11	(	(	PUNCT
ejpam-5750	236	12	2025	2025	NUM
ejpam-5750	236	13	)	)	PUNCT
ejpam-5750	236	14	,	,	PUNCT
ejpam-5750	236	15	5750	5750	NUM
ejpam-5750	236	16	8	8	NUM
ejpam-5750	236	17	of	of	ADP
ejpam-5750	236	18	9	9	NUM
ejpam-5750	236	19	that	that	PRON
ejpam-5750	236	20	is	be	AUX
ejpam-5750	236	21	,	,	PUNCT
ejpam-5750	236	22	the	the	DET
ejpam-5750	236	23	total	total	ADJ
ejpam-5750	236	24	measure	measure	NOUN
ejpam-5750	236	25	associated	associate	VERB
ejpam-5750	236	26	with	with	ADP
ejpam-5750	236	27	vr	vr	PROPN
ejpam-5750	236	28	is	be	AUX
ejpam-5750	236	29	the	the	DET
ejpam-5750	236	30	same	same	ADJ
ejpam-5750	236	31	as	as	SCONJ
ejpam-5750	236	32	the	the	DET
ejpam-5750	236	33	total	total	ADJ
ejpam-5750	236	34	measure	measure	NOUN
ejpam-5750	236	35	associated	associate	VERB
ejpam-5750	236	36	with	with	ADP
ejpam-5750	236	37	v.	v.	ADP
ejpam-5750	236	38	note	note	VERB
ejpam-5750	236	39	that	that	PRON
ejpam-5750	236	40	vr(x	vr(x	PUNCT
ejpam-5750	236	41	)	)	PUNCT
ejpam-5750	236	42	is	be	AUX
ejpam-5750	236	43	a	a	DET
ejpam-5750	236	44	subharmonic	subharmonic	ADJ
ejpam-5750	236	45	function	function	NOUN
ejpam-5750	236	46	on	on	ADP
ejpam-5750	236	47	r2	r2	NOUN
ejpam-5750	236	48	increasing	increase	VERB
ejpam-5750	236	49	with	with	ADP
ejpam-5750	236	50	r	r	NOUN
ejpam-5750	236	51	and	and	CCONJ
ejpam-5750	236	52	f(x	f(x	PROPN
ejpam-5750	236	53	)	)	PUNCT
ejpam-5750	237	1	=	=	SYM
ejpam-5750	237	2	lim	lim	PROPN
ejpam-5750	237	3	r→∞	r→∞	NUM
ejpam-5750	237	4	vr(x	vr(x	X
ejpam-5750	237	5	)	)	PUNCT
ejpam-5750	237	6	is	be	AUX
ejpam-5750	237	7	subharmonic	subharmonic	ADJ
ejpam-5750	237	8	on	on	ADP
ejpam-5750	237	9	r2	r2	PROPN
ejpam-5750	237	10	and	and	CCONJ
ejpam-5750	237	11	is	be	AUX
ejpam-5750	237	12	a	a	DET
ejpam-5750	237	13	harmonic	harmonic	ADJ
ejpam-5750	237	14	function	function	NOUN
ejpam-5750	237	15	h(x	h(x	PROPN
ejpam-5750	237	16	)	)	PUNCT
ejpam-5750	237	17	when	when	SCONJ
ejpam-5750	237	18	|x|	|x|	PROPN
ejpam-5750	237	19	>	>	X
ejpam-5750	237	20	r	r	NOUN
ejpam-5750	237	21	;	;	PUNCT
ejpam-5750	237	22	also	also	ADV
ejpam-5750	237	23	h(x	h(x	PROPN
ejpam-5750	237	24	)	)	PUNCT
ejpam-5750	237	25	is	be	AUX
ejpam-5750	237	26	the	the	DET
ejpam-5750	237	27	least	least	ADJ
ejpam-5750	237	28	harmonic	harmonic	ADJ
ejpam-5750	237	29	majorant	majorant	NOUN
ejpam-5750	237	30	of	of	ADP
ejpam-5750	237	31	v(x	v(x	PROPN
ejpam-5750	237	32	)	)	PUNCT
ejpam-5750	237	33	on	on	ADP
ejpam-5750	237	34	|x|	|x|	PROPN
ejpam-5750	237	35	>	>	X
ejpam-5750	237	36	r.	r.	PROPN
ejpam-5750	237	37	thus	thus	ADV
ejpam-5750	237	38	f(x	f(x	PROPN
ejpam-5750	237	39	)	)	PUNCT
ejpam-5750	238	1	=	=	PRON
ejpam-5750	238	2	{	{	PUNCT
ejpam-5750	238	3	v(x	v(x	PROPN
ejpam-5750	238	4	)	)	PUNCT
ejpam-5750	238	5	,	,	PUNCT
ejpam-5750	238	6	if	if	SCONJ
ejpam-5750	238	7	|x|	|x|	PROPN
ejpam-5750	238	8	≤	≤	NUM
ejpam-5750	238	9	r	r	NOUN
ejpam-5750	238	10	is	be	AUX
ejpam-5750	238	11	subharmonic	subharmonic	ADJ
ejpam-5750	238	12	on	on	ADP
ejpam-5750	238	13	r2	r2	PROPN
ejpam-5750	238	14	h(x	h(x	PROPN
ejpam-5750	238	15	)	)	PUNCT
ejpam-5750	238	16	,	,	PUNCT
ejpam-5750	238	17	if	if	SCONJ
ejpam-5750	238	18	|x|	|x|	PROPN
ejpam-5750	238	19	>	>	X
ejpam-5750	238	20	r	r	NOUN
ejpam-5750	238	21	since	since	SCONJ
ejpam-5750	238	22	∆f(x	∆f(x	PROPN
ejpam-5750	238	23	)	)	PUNCT
ejpam-5750	239	1	=	=	SYM
ejpam-5750	239	2	lim	lim	PROPN
ejpam-5750	239	3	r→∞	r→∞	PROPN
ejpam-5750	239	4	∆vr(x	∆vr(x	PROPN
ejpam-5750	239	5	)	)	PUNCT
ejpam-5750	239	6	in	in	ADP
ejpam-5750	239	7	the	the	DET
ejpam-5750	239	8	sense	sense	NOUN
ejpam-5750	239	9	of	of	ADP
ejpam-5750	239	10	distributions	distribution	NOUN
ejpam-5750	239	11	,	,	PUNCT
ejpam-5750	239	12	the	the	DET
ejpam-5750	239	13	total	total	ADJ
ejpam-5750	239	14	measure	measure	NOUN
ejpam-5750	239	15	associated	associate	VERB
ejpam-5750	239	16	with	with	ADP
ejpam-5750	239	17	f(x	f(x	PROPN
ejpam-5750	239	18	)	)	PUNCT
ejpam-5750	239	19	is	be	AUX
ejpam-5750	239	20	the	the	DET
ejpam-5750	239	21	total	total	ADJ
ejpam-5750	239	22	measure	measure	NOUN
ejpam-5750	239	23	associated	associate	VERB
ejpam-5750	239	24	with	with	ADP
ejpam-5750	239	25	v(x	v(x	PROPN
ejpam-5750	239	26	)	)	PUNCT
ejpam-5750	239	27	.	.	PUNCT
ejpam-5750	240	1	since	since	SCONJ
ejpam-5750	240	2	near	near	ADP
ejpam-5750	240	3	infinity	infinity	NOUN
ejpam-5750	240	4	f(x	f(x	PROPN
ejpam-5750	240	5	)	)	PUNCT
ejpam-5750	240	6	=	=	SYM
ejpam-5750	240	7	h(x	h(x	PROPN
ejpam-5750	240	8	)	)	PUNCT
ejpam-5750	241	1	=	=	PUNCT
ejpam-5750	242	1	α	α	PRON
ejpam-5750	242	2	log	log	VERB
ejpam-5750	242	3	|x|	|x|	PROPN
ejpam-5750	242	4	+	+	CCONJ
ejpam-5750	242	5	b(x	b(x	NOUN
ejpam-5750	242	6	)	)	PUNCT
ejpam-5750	243	1	+	+	CCONJ
ejpam-5750	243	2	(	(	PUNCT
ejpam-5750	243	3	a	a	DET
ejpam-5750	243	4	harmonic	harmonic	ADJ
ejpam-5750	243	5	function	function	NOUN
ejpam-5750	243	6	on	on	ADP
ejpam-5750	243	7	)	)	PUNCT
ejpam-5750	243	8	r2	r2	PROPN
ejpam-5750	243	9	total	total	ADJ
ejpam-5750	243	10	measure	measure	NOUN
ejpam-5750	243	11	associated	associate	VERB
ejpam-5750	243	12	with	with	ADP
ejpam-5750	243	13	f(x	f(x	PROPN
ejpam-5750	243	14	)	)	PUNCT
ejpam-5750	243	15	is	be	AUX
ejpam-5750	243	16	α	α	X
ejpam-5750	243	17	.	.	PUNCT
ejpam-5750	244	1	consequently	consequently	ADV
ejpam-5750	244	2	,	,	PUNCT
ejpam-5750	244	3	total	total	ADJ
ejpam-5750	244	4	measure	measure	NOUN
ejpam-5750	244	5	associated	associate	VERB
ejpam-5750	244	6	with	with	ADP
ejpam-5750	244	7	v(x	v(x	PROPN
ejpam-5750	244	8	)	)	PUNCT
ejpam-5750	244	9	equals	equal	VERB
ejpam-5750	244	10	the	the	DET
ejpam-5750	244	11	constant	constant	ADJ
ejpam-5750	244	12	α	α	NOUN
ejpam-5750	244	13	in	in	ADP
ejpam-5750	244	14	the	the	DET
ejpam-5750	244	15	expression	expression	NOUN
ejpam-5750	244	16	of	of	ADP
ejpam-5750	244	17	h(x	h(x	PROPN
ejpam-5750	244	18	)	)	PUNCT
ejpam-5750	244	19	which	which	PRON
ejpam-5750	244	20	is	be	AUX
ejpam-5750	244	21	the	the	DET
ejpam-5750	244	22	least	least	ADJ
ejpam-5750	244	23	harmonic	harmonic	ADJ
ejpam-5750	244	24	majorant	majorant	NOUN
ejpam-5750	244	25	of	of	ADP
ejpam-5750	244	26	v(x	v(x	PROPN
ejpam-5750	244	27	)	)	PUNCT
ejpam-5750	244	28	near	near	ADP
ejpam-5750	244	29	infinity	infinity	NOUN
ejpam-5750	244	30	.	.	PUNCT
ejpam-5750	245	1	corollary	corollary	ADJ
ejpam-5750	245	2	3	3	NUM
ejpam-5750	245	3	.	.	PUNCT
ejpam-5750	246	1	let	let	VERB
ejpam-5750	246	2	s1	s1	NOUN
ejpam-5750	246	3	and	and	CCONJ
ejpam-5750	246	4	s2	s2	NOUN
ejpam-5750	246	5	be	be	AUX
ejpam-5750	246	6	two	two	NUM
ejpam-5750	246	7	subharmonic	subharmonic	ADJ
ejpam-5750	246	8	functions	function	NOUN
ejpam-5750	246	9	on	on	ADP
ejpam-5750	246	10	r2	r2	NOUN
ejpam-5750	246	11	,	,	PUNCT
ejpam-5750	246	12	s1	s1	PROPN
ejpam-5750	246	13	≤	≤	NUM
ejpam-5750	246	14	s2	s2	PROPN
ejpam-5750	246	15	.	.	PUNCT
ejpam-5750	247	1	then	then	ADV
ejpam-5750	247	2	the	the	DET
ejpam-5750	247	3	(	(	PUNCT
ejpam-5750	247	4	total	total	ADJ
ejpam-5750	247	5	measure	measure	NOUN
ejpam-5750	247	6	associated	associate	VERB
ejpam-5750	247	7	with	with	ADP
ejpam-5750	247	8	s1	s1	NOUN
ejpam-5750	247	9	)	)	PUNCT
ejpam-5750	247	10	≤(total	≤(total	ADJ
ejpam-5750	247	11	measure	measure	NOUN
ejpam-5750	247	12	associated	associate	VERB
ejpam-5750	247	13	with	with	ADP
ejpam-5750	247	14	s2	s2	PROPN
ejpam-5750	247	15	)	)	PUNCT
ejpam-5750	247	16	.	.	PUNCT
ejpam-5750	248	1	proof	proof	NOUN
ejpam-5750	248	2	.	.	PUNCT
ejpam-5750	249	1	if	if	SCONJ
ejpam-5750	249	2	(	(	PUNCT
ejpam-5750	249	3	total	total	ADJ
ejpam-5750	249	4	measure	measure	NOUN
ejpam-5750	249	5	associated	associate	VERB
ejpam-5750	249	6	with	with	ADP
ejpam-5750	249	7	s1	s1	NOUN
ejpam-5750	249	8	)	)	PUNCT
ejpam-5750	249	9	=	=	SYM
ejpam-5750	249	10	∞	∞	PROPN
ejpam-5750	249	11	,	,	PUNCT
ejpam-5750	249	12	then	then	ADV
ejpam-5750	249	13	s1	s1	NOUN
ejpam-5750	249	14	does	do	AUX
ejpam-5750	249	15	not	not	PART
ejpam-5750	249	16	have	have	VERB
ejpam-5750	249	17	a	a	DET
ejpam-5750	249	18	harmonic	harmonic	ADJ
ejpam-5750	249	19	majorant	majorant	NOUN
ejpam-5750	249	20	near	near	ADP
ejpam-5750	249	21	infinity	infinity	NOUN
ejpam-5750	249	22	consequently	consequently	ADV
ejpam-5750	249	23	,	,	PUNCT
ejpam-5750	249	24	s2	s2	PROPN
ejpam-5750	249	25	can	can	AUX
ejpam-5750	249	26	not	not	PART
ejpam-5750	249	27	have	have	VERB
ejpam-5750	249	28	a	a	DET
ejpam-5750	249	29	harmonic	harmonic	ADJ
ejpam-5750	249	30	majorant	majorant	NOUN
ejpam-5750	249	31	near	near	ADP
ejpam-5750	249	32	infinity	infinity	NOUN
ejpam-5750	249	33	,	,	PUNCT
ejpam-5750	249	34	so	so	SCONJ
ejpam-5750	249	35	that	that	SCONJ
ejpam-5750	249	36	(	(	PUNCT
ejpam-5750	249	37	total	total	ADJ
ejpam-5750	249	38	measure	measure	NOUN
ejpam-5750	249	39	associated	associate	VERB
ejpam-5750	249	40	with	with	ADP
ejpam-5750	249	41	s2	s2	PROPN
ejpam-5750	249	42	)	)	PUNCT
ejpam-5750	249	43	.	.	PUNCT
ejpam-5750	250	1	hence	hence	ADV
ejpam-5750	250	2	let	let	VERB
ejpam-5750	250	3	us	we	PRON
ejpam-5750	250	4	assume	assume	VERB
ejpam-5750	250	5	that	that	SCONJ
ejpam-5750	250	6	the	the	DET
ejpam-5750	250	7	total	total	ADJ
ejpam-5750	250	8	measure	measure	NOUN
ejpam-5750	250	9	of	of	ADP
ejpam-5750	250	10	s1	s1	NOUN
ejpam-5750	250	11	is	be	AUX
ejpam-5750	250	12	finite	finite	ADJ
ejpam-5750	250	13	.	.	PUNCT
ejpam-5750	251	1	in	in	ADP
ejpam-5750	251	2	this	this	DET
ejpam-5750	251	3	case	case	NOUN
ejpam-5750	251	4	,	,	PUNCT
ejpam-5750	251	5	if	if	SCONJ
ejpam-5750	251	6	total	total	ADJ
ejpam-5750	251	7	measure	measure	NOUN
ejpam-5750	251	8	of	of	ADP
ejpam-5750	251	9	s2	s2	PROPN
ejpam-5750	251	10	is	be	AUX
ejpam-5750	251	11	infinite	infinite	ADJ
ejpam-5750	251	12	,	,	PUNCT
ejpam-5750	251	13	nothing	nothing	PRON
ejpam-5750	251	14	to	to	PART
ejpam-5750	251	15	prove	prove	VERB
ejpam-5750	251	16	.	.	PUNCT
ejpam-5750	252	1	so	so	ADV
ejpam-5750	252	2	we	we	PRON
ejpam-5750	252	3	have	have	VERB
ejpam-5750	252	4	to	to	PART
ejpam-5750	252	5	consider	consider	VERB
ejpam-5750	252	6	only	only	ADV
ejpam-5750	252	7	the	the	DET
ejpam-5750	252	8	case	case	NOUN
ejpam-5750	252	9	when	when	SCONJ
ejpam-5750	252	10	the	the	DET
ejpam-5750	252	11	total	total	ADJ
ejpam-5750	252	12	measures	measure	NOUN
ejpam-5750	252	13	of	of	ADP
ejpam-5750	252	14	s1	s1	NOUN
ejpam-5750	252	15	and	and	CCONJ
ejpam-5750	252	16	s2	s2	PROPN
ejpam-5750	252	17	are	be	AUX
ejpam-5750	252	18	finite	finite	ADJ
ejpam-5750	252	19	.	.	PUNCT
ejpam-5750	253	1	then	then	ADV
ejpam-5750	253	2	outside	outside	ADP
ejpam-5750	253	3	a	a	DET
ejpam-5750	253	4	compact	compact	ADJ
ejpam-5750	253	5	set	set	NOUN
ejpam-5750	253	6	if	if	SCONJ
ejpam-5750	253	7	h1	h1	PROPN
ejpam-5750	253	8	,	,	PUNCT
ejpam-5750	253	9	h2	h2	PROPN
ejpam-5750	253	10	are	be	AUX
ejpam-5750	253	11	the	the	DET
ejpam-5750	253	12	least	least	ADJ
ejpam-5750	253	13	harmonic	harmonic	ADJ
ejpam-5750	253	14	majorants	majorant	NOUN
ejpam-5750	253	15	of	of	ADP
ejpam-5750	253	16	s1	s1	NOUN
ejpam-5750	253	17	,	,	PUNCT
ejpam-5750	253	18	s2	s2	PROPN
ejpam-5750	253	19	,	,	PUNCT
ejpam-5750	253	20	then	then	ADV
ejpam-5750	253	21	h1	h1	VERB
ejpam-5750	253	22	≤	≤	NUM
ejpam-5750	253	23	h2	h2	NOUN
ejpam-5750	253	24	so	so	SCONJ
ejpam-5750	253	25	that	that	SCONJ
ejpam-5750	253	26	if	if	SCONJ
ejpam-5750	253	27	we	we	PRON
ejpam-5750	253	28	write	write	VERB
ejpam-5750	253	29	hi	hi	INTJ
ejpam-5750	253	30	=	=	X
ejpam-5750	253	31	hi	hi	INTJ
ejpam-5750	254	1	+	+	CCONJ
ejpam-5750	254	2	αi	αi	NOUN
ejpam-5750	254	3	log	log	VERB
ejpam-5750	254	4	|x|	|x|	PROPN
ejpam-5750	254	5	+	+	NUM
ejpam-5750	254	6	bi(x	bi(x	NUM
ejpam-5750	254	7	)	)	PUNCT
ejpam-5750	254	8	,	,	PUNCT
ejpam-5750	254	9	then	then	ADV
ejpam-5750	254	10	α1	α1	PROPN
ejpam-5750	254	11	≤	≤	PROPN
ejpam-5750	254	12	α2	α2	PROPN
ejpam-5750	254	13	.	.	PUNCT
ejpam-5750	255	1	then	then	ADV
ejpam-5750	255	2	by	by	ADP
ejpam-5750	255	3	the	the	DET
ejpam-5750	255	4	above	above	ADJ
ejpam-5750	255	5	theorem	theorem	NOUN
ejpam-5750	255	6	(	(	PUNCT
ejpam-5750	255	7	total	total	ADJ
ejpam-5750	255	8	measure	measure	NOUN
ejpam-5750	255	9	associated	associate	VERB
ejpam-5750	255	10	with	with	ADP
ejpam-5750	255	11	s1	s1	NOUN
ejpam-5750	255	12	)	)	PUNCT
ejpam-5750	255	13	≤(total	≤(total	ADJ
ejpam-5750	255	14	measure	measure	NOUN
ejpam-5750	255	15	associated	associate	VERB
ejpam-5750	255	16	with	with	ADP
ejpam-5750	255	17	s2	s2	PROPN
ejpam-5750	255	18	)	)	PUNCT
ejpam-5750	255	19	.	.	PUNCT
ejpam-5750	256	1	conclusion	conclusion	NOUN
ejpam-5750	256	2	in	in	ADP
ejpam-5750	256	3	complex	complex	ADJ
ejpam-5750	256	4	analysis	analysis	NOUN
ejpam-5750	256	5	,	,	PUNCT
ejpam-5750	256	6	the	the	DET
ejpam-5750	256	7	relation	relation	NOUN
ejpam-5750	256	8	between	between	ADP
ejpam-5750	256	9	the	the	DET
ejpam-5750	256	10	zeros	zero	NOUN
ejpam-5750	256	11	of	of	ADP
ejpam-5750	256	12	an	an	DET
ejpam-5750	256	13	analytic	analytic	ADJ
ejpam-5750	256	14	function	function	NOUN
ejpam-5750	256	15	f(z	f(z	PROPN
ejpam-5750	256	16	)	)	PUNCT
ejpam-5750	256	17	and	and	CCONJ
ejpam-5750	256	18	the	the	DET
ejpam-5750	256	19	measure	measure	NOUN
ejpam-5750	256	20	representing	represent	VERB
ejpam-5750	256	21	the	the	DET
ejpam-5750	256	22	subharmonic	subharmonic	ADJ
ejpam-5750	256	23	function	function	NOUN
ejpam-5750	256	24	log	log	NOUN
ejpam-5750	256	25	|f(z)|	|f(z)|	PROPN
ejpam-5750	256	26	as	as	ADP
ejpam-5750	256	27	an	an	DET
ejpam-5750	256	28	integral	integral	ADJ
ejpam-5750	256	29	is	be	AUX
ejpam-5750	256	30	intriguingly	intriguingly	ADV
ejpam-5750	256	31	fascinating	fascinating	ADJ
ejpam-5750	256	32	.	.	PUNCT
ejpam-5750	257	1	in	in	ADP
ejpam-5750	257	2	this	this	DET
ejpam-5750	257	3	article	article	NOUN
ejpam-5750	257	4	,	,	PUNCT
ejpam-5750	257	5	we	we	PRON
ejpam-5750	257	6	have	have	AUX
ejpam-5750	257	7	attempted	attempt	VERB
ejpam-5750	257	8	to	to	PART
ejpam-5750	257	9	answer	answer	VERB
ejpam-5750	257	10	the	the	DET
ejpam-5750	257	11	question	question	NOUN
ejpam-5750	257	12	:	:	PUNCT
ejpam-5750	257	13	if	if	SCONJ
ejpam-5750	257	14	s(x	s(x	NOUN
ejpam-5750	257	15	)	)	PUNCT
ejpam-5750	257	16	is	be	AUX
ejpam-5750	257	17	a	a	DET
ejpam-5750	257	18	subharmonic	subharmonic	ADJ
ejpam-5750	257	19	function	function	NOUN
ejpam-5750	257	20	on	on	ADP
ejpam-5750	257	21	the	the	DET
ejpam-5750	257	22	complex	complex	ADJ
ejpam-5750	257	23	plane	plane	NOUN
ejpam-5750	257	24	with	with	ADP
ejpam-5750	257	25	the	the	DET
ejpam-5750	257	26	associated	associated	ADJ
ejpam-5750	257	27	radon	radon	PROPN
ejpam-5750	257	28	measure	measure	NOUN
ejpam-5750	258	1	µ	µ	PRON
ejpam-5750	258	2	representing	represent	VERB
ejpam-5750	258	3	s(x	s(x	NOUN
ejpam-5750	258	4	)	)	PUNCT
ejpam-5750	258	5	as	as	ADP
ejpam-5750	258	6	an	an	DET
ejpam-5750	258	7	integral	integral	ADJ
ejpam-5750	258	8	in	in	ADP
ejpam-5750	258	9	a	a	DET
ejpam-5750	258	10	local	local	ADJ
ejpam-5750	258	11	representation	representation	NOUN
ejpam-5750	258	12	,	,	PUNCT
ejpam-5750	258	13	when	when	SCONJ
ejpam-5750	258	14	will	will	AUX
ejpam-5750	258	15	the	the	DET
ejpam-5750	258	16	total	total	ADJ
ejpam-5750	258	17	measure	measure	NOUN
ejpam-5750	258	18	∥µ∥	∥µ∥	NOUN
ejpam-5750	258	19	be	be	AUX
ejpam-5750	258	20	finite	finite	ADJ
ejpam-5750	258	21	?	?	PUNCT
ejpam-5750	259	1	by	by	ADP
ejpam-5750	259	2	introducing	introduce	VERB
ejpam-5750	259	3	the	the	DET
ejpam-5750	259	4	notion	notion	NOUN
ejpam-5750	259	5	of	of	ADP
ejpam-5750	259	6	flux	flux	NOUN
ejpam-5750	259	7	at	at	ADP
ejpam-5750	259	8	infinity	infinity	NOUN
ejpam-5750	259	9	of	of	ADP
ejpam-5750	259	10	a	a	DET
ejpam-5750	259	11	subharmonic	subharmonic	ADJ
ejpam-5750	259	12	function	function	NOUN
ejpam-5750	259	13	defined	define	VERB
ejpam-5750	259	14	outside	outside	ADP
ejpam-5750	259	15	a	a	DET
ejpam-5750	259	16	compact	compact	ADJ
ejpam-5750	259	17	set	set	NOUN
ejpam-5750	259	18	,	,	PUNCT
ejpam-5750	259	19	we	we	PRON
ejpam-5750	259	20	characterise	characterise	VERB
ejpam-5750	259	21	the	the	DET
ejpam-5750	259	22	case	case	NOUN
ejpam-5750	259	23	where	where	SCONJ
ejpam-5750	259	24	∥µ∥	∥µ∥	NOUN
ejpam-5750	259	25	is	be	AUX
ejpam-5750	259	26	finite	finite	ADJ
ejpam-5750	259	27	.	.	PUNCT
ejpam-5750	260	1	we	we	PRON
ejpam-5750	260	2	have	have	AUX
ejpam-5750	260	3	also	also	ADV
ejpam-5750	260	4	mentioned	mention	VERB
ejpam-5750	260	5	some	some	DET
ejpam-5750	260	6	related	related	ADJ
ejpam-5750	260	7	researchers	researcher	NOUN
ejpam-5750	260	8	on	on	ADP
ejpam-5750	260	9	subharmonic	subharmonic	ADJ
ejpam-5750	260	10	functions	function	NOUN
ejpam-5750	260	11	on	on	ADP
ejpam-5750	260	12	locally	locally	ADV
ejpam-5750	260	13	compact	compact	ADJ
ejpam-5750	260	14	harmonic	harmonic	ADJ
ejpam-5750	260	15	spaces	space	NOUN
ejpam-5750	260	16	in	in	ADP
ejpam-5750	260	17	the	the	DET
ejpam-5750	260	18	brelot	brelot	NOUN
ejpam-5750	260	19	axiomatic	axiomatic	ADJ
ejpam-5750	260	20	potential	potential	NOUN
ejpam-5750	260	21	without	without	ADP
ejpam-5750	260	22	positive	positive	ADJ
ejpam-5750	260	23	potentials	potential	NOUN
ejpam-5750	260	24	.	.	PUNCT
ejpam-5750	261	1	declarations	declaration	NOUN
ejpam-5750	261	2	(	(	PUNCT
ejpam-5750	261	3	i	i	NOUN
ejpam-5750	261	4	)	)	PUNCT
ejpam-5750	261	5	author	author	NOUN
ejpam-5750	261	6	contribution	contribution	NOUN
ejpam-5750	261	7	both	both	CCONJ
ejpam-5750	261	8	the	the	DET
ejpam-5750	261	9	authors	author	NOUN
ejpam-5750	261	10	contributed	contribute	VERB
ejpam-5750	261	11	equally	equally	ADV
ejpam-5750	261	12	.	.	PUNCT
ejpam-5750	262	1	amulya	amulya	PROPN
ejpam-5750	262	2	smyrna	smyrna	PROPN
ejpam-5750	262	3	c.	c.	PROPN
ejpam-5750	262	4	,	,	PUNCT
ejpam-5750	262	5	n.	n.	PROPN
ejpam-5750	262	6	nathiya	nathiya	PROPN
ejpam-5750	262	7	/	/	SYM
ejpam-5750	262	8	eur	eur	PROPN
ejpam-5750	262	9	.	.	PUNCT
ejpam-5750	263	1	j.	j.	PROPN
ejpam-5750	263	2	pure	pure	PROPN
ejpam-5750	263	3	appl	appl	PROPN
ejpam-5750	263	4	.	.	PROPN
ejpam-5750	263	5	math	math	PROPN
ejpam-5750	263	6	,	,	PUNCT
ejpam-5750	263	7	18	18	NUM
ejpam-5750	263	8	(	(	PUNCT
ejpam-5750	263	9	2	2	NUM
ejpam-5750	263	10	)	)	PUNCT
ejpam-5750	263	11	(	(	PUNCT
ejpam-5750	263	12	2025	2025	NUM
ejpam-5750	263	13	)	)	PUNCT
ejpam-5750	263	14	,	,	PUNCT
ejpam-5750	263	15	5750	5750	NUM
ejpam-5750	263	16	9	9	NUM
ejpam-5750	263	17	of	of	ADP
ejpam-5750	263	18	9	9	NUM
ejpam-5750	263	19	the	the	DET
ejpam-5750	263	20	authors	author	NOUN
ejpam-5750	263	21	(	(	PUNCT
ejpam-5750	263	22	amulya	amulya	PROPN
ejpam-5750	263	23	smyrna	smyrna	PROPN
ejpam-5750	263	24	c.	c.	PROPN
ejpam-5750	263	25	and	and	CCONJ
ejpam-5750	263	26	n.	n.	PROPN
ejpam-5750	263	27	nathiya	nathiya	PROPN
ejpam-5750	263	28	)	)	PUNCT
ejpam-5750	263	29	of	of	ADP
ejpam-5750	263	30	this	this	DET
ejpam-5750	263	31	manuscript	manuscript	NOUN
ejpam-5750	263	32	titled	title	VERB
ejpam-5750	263	33	”	"	PUNCT
ejpam-5750	263	34	flux	flux	NOUN
ejpam-5750	263	35	at	at	ADP
ejpam-5750	263	36	infinity	infinity	NOUN
ejpam-5750	263	37	of	of	ADP
ejpam-5750	263	38	subharmonic	subharmonic	ADJ
ejpam-5750	263	39	functions	function	NOUN
ejpam-5750	263	40	on	on	ADP
ejpam-5750	263	41	r2	r2	NOUN
ejpam-5750	263	42	”	"	PUNCT
ejpam-5750	263	43	have	have	VERB
ejpam-5750	263	44	no	no	DET
ejpam-5750	263	45	competing	compete	VERB
ejpam-5750	263	46	interests	interest	NOUN
ejpam-5750	263	47	to	to	PART
ejpam-5750	263	48	declare	declare	VERB
ejpam-5750	263	49	that	that	PRON
ejpam-5750	263	50	are	be	AUX
ejpam-5750	263	51	relevant	relevant	ADJ
ejpam-5750	263	52	to	to	ADP
ejpam-5750	263	53	the	the	DET
ejpam-5750	263	54	content	content	NOUN
ejpam-5750	263	55	of	of	ADP
ejpam-5750	263	56	this	this	DET
ejpam-5750	263	57	article	article	NOUN
ejpam-5750	263	58	.	.	PUNCT
ejpam-5750	264	1	references	reference	NOUN
ejpam-5750	264	2	[	[	X
ejpam-5750	264	3	1	1	X
ejpam-5750	264	4	]	]	PUNCT
ejpam-5750	264	5	david	david	PROPN
ejpam-5750	264	6	h	h	PROPN
ejpam-5750	264	7	armitage	armitage	PROPN
ejpam-5750	264	8	and	and	CCONJ
ejpam-5750	264	9	stephen	stephen	PROPN
ejpam-5750	264	10	j	j	PROPN
ejpam-5750	264	11	gardiner	gardiner	PROPN
ejpam-5750	264	12	.	.	PUNCT
ejpam-5750	265	1	classical	classical	ADJ
ejpam-5750	265	2	potential	potential	ADJ
ejpam-5750	265	3	theory	theory	NOUN
ejpam-5750	265	4	.	.	PUNCT
ejpam-5750	266	1	springer	springer	NOUN
ejpam-5750	266	2	science	science	PROPN
ejpam-5750	266	3	&	&	CCONJ
ejpam-5750	266	4	business	business	NOUN
ejpam-5750	266	5	media	medium	NOUN
ejpam-5750	266	6	,	,	PUNCT
ejpam-5750	266	7	2012	2012	NUM
ejpam-5750	266	8	.	.	PUNCT
ejpam-5750	267	1	[	[	X
ejpam-5750	267	2	2	2	NUM
ejpam-5750	267	3	]	]	X
ejpam-5750	267	4	marcel	marcel	PROPN
ejpam-5750	267	5	brelot	brelot	PROPN
ejpam-5750	267	6	.	.	PUNCT
ejpam-5750	268	1	éléments	éléments	PROPN
ejpam-5750	268	2	de	de	X
ejpam-5750	268	3	la	la	X
ejpam-5750	268	4	théorie	théorie	PROPN
ejpam-5750	268	5	classique	classique	X
ejpam-5750	268	6	du	du	X
ejpam-5750	268	7	potentiel	potentiel	PROPN
ejpam-5750	268	8	.	.	PUNCT
ejpam-5750	269	1	(	(	PUNCT
ejpam-5750	269	2	no	no	DET
ejpam-5750	269	3	title	title	NOUN
ejpam-5750	269	4	)	)	PUNCT
ejpam-5750	269	5	,	,	PUNCT
ejpam-5750	269	6	1959	1959	NUM
ejpam-5750	269	7	.	.	PUNCT
ejpam-5750	270	1	[	[	X
ejpam-5750	270	2	3	3	X
ejpam-5750	270	3	]	]	X
ejpam-5750	270	4	lester	lester	PROPN
ejpam-5750	270	5	la	la	PROPN
ejpam-5750	270	6	verne	verne	PROPN
ejpam-5750	270	7	helms	helm	NOUN
ejpam-5750	270	8	et	et	PROPN
ejpam-5750	271	1	al	al	PROPN
ejpam-5750	271	2	.	.	PROPN
ejpam-5750	271	3	potential	potential	ADJ
ejpam-5750	271	4	theory	theory	NOUN
ejpam-5750	271	5	.	.	PUNCT
ejpam-5750	272	1	springer	springer	NOUN
ejpam-5750	272	2	,	,	PUNCT
ejpam-5750	272	3	2009	2009	NUM
ejpam-5750	272	4	.	.	PUNCT
ejpam-5750	273	1	[	[	X
ejpam-5750	273	2	4	4	NUM
ejpam-5750	273	3	]	]	PUNCT
ejpam-5750	273	4	thomas	thomas	PROPN
ejpam-5750	273	5	ransford	ransford	PROPN
ejpam-5750	273	6	.	.	PUNCT
ejpam-5750	274	1	potential	potential	ADJ
ejpam-5750	274	2	theory	theory	NOUN
ejpam-5750	274	3	in	in	ADP
ejpam-5750	274	4	the	the	DET
ejpam-5750	274	5	complex	complex	ADJ
ejpam-5750	274	6	plane	plane	NOUN
ejpam-5750	274	7	.	.	PUNCT
ejpam-5750	275	1	number	number	NOUN
ejpam-5750	275	2	28	28	NUM
ejpam-5750	275	3	.	.	PUNCT
ejpam-5750	276	1	cambridge	cambridge	PROPN
ejpam-5750	276	2	university	university	PROPN
ejpam-5750	276	3	press	press	NOUN
ejpam-5750	276	4	,	,	PUNCT
ejpam-5750	276	5	1995	1995	NUM
ejpam-5750	276	6	.	.	PUNCT
ejpam-5750	277	1	[	[	X
ejpam-5750	277	2	5	5	NUM
ejpam-5750	277	3	]	]	X
ejpam-5750	277	4	victor	victor	PROPN
ejpam-5750	277	5	anandam	anandam	PROPN
ejpam-5750	277	6	.	.	PUNCT
ejpam-5750	278	1	espaces	espace	VERB
ejpam-5750	278	2	harmoniques	harmonique	NOUN
ejpam-5750	278	3	sans	sans	PROPN
ejpam-5750	278	4	potentiel	potentiel	PROPN
ejpam-5750	278	5	positif	positif	PROPN
ejpam-5750	278	6	.	.	PUNCT
ejpam-5750	279	1	in	in	ADP
ejpam-5750	279	2	annales	annales	PROPN
ejpam-5750	279	3	de	de	X
ejpam-5750	279	4	l’institut	l’institut	X
ejpam-5750	279	5	fourier	fourier	NOUN
ejpam-5750	279	6	,	,	PUNCT
ejpam-5750	279	7	volume	volume	NOUN
ejpam-5750	279	8	22	22	NUM
ejpam-5750	279	9	,	,	PUNCT
ejpam-5750	279	10	pages	page	NOUN
ejpam-5750	279	11	97–160	97–160	PROPN
ejpam-5750	279	12	,	,	PUNCT
ejpam-5750	279	13	1972	1972	NUM
ejpam-5750	279	14	.	.	PUNCT
ejpam-5750	280	1	[	[	X
ejpam-5750	280	2	6	6	NUM
ejpam-5750	280	3	]	]	X
ejpam-5750	280	4	victor	victor	NOUN
ejpam-5750	280	5	anandam	anandam	PROPN
ejpam-5750	280	6	.	.	PUNCT
ejpam-5750	280	7	admissible	admissible	ADJ
ejpam-5750	280	8	superharmonic	superharmonic	ADJ
ejpam-5750	280	9	functions	function	NOUN
ejpam-5750	280	10	and	and	CCONJ
ejpam-5750	280	11	associated	associated	ADJ
ejpam-5750	280	12	measures	measure	NOUN
ejpam-5750	280	13	.	.	PUNCT
ejpam-5750	281	1	journal	journal	NOUN
ejpam-5750	281	2	of	of	ADP
ejpam-5750	281	3	the	the	DET
ejpam-5750	281	4	london	london	PROPN
ejpam-5750	281	5	mathematical	mathematical	ADJ
ejpam-5750	281	6	society	society	NOUN
ejpam-5750	281	7	,	,	PUNCT
ejpam-5750	281	8	2(1):65–78	2(1):65–78	NUM
ejpam-5750	281	9	,	,	PUNCT
ejpam-5750	281	10	1979	1979	NUM
ejpam-5750	281	11	.	.	PUNCT
ejpam-5750	282	1	[	[	X
ejpam-5750	282	2	7	7	NUM
ejpam-5750	282	3	]	]	X
ejpam-5750	282	4	marcel	marcel	PROPN
ejpam-5750	282	5	brelot	brelot	PROPN
ejpam-5750	282	6	.	.	PUNCT
ejpam-5750	283	1	axiomatique	axiomatique	PROPN
ejpam-5750	283	2	des	des	PROPN
ejpam-5750	283	3	fonctions	fonctions	PROPN
ejpam-5750	283	4	harmoniques	harmonique	NOUN
ejpam-5750	283	5	.	.	PUNCT
ejpam-5750	284	1	(	(	PUNCT
ejpam-5750	284	2	no	no	DET
ejpam-5750	284	3	title	title	NOUN
ejpam-5750	284	4	)	)	PUNCT
ejpam-5750	284	5	,	,	PUNCT
ejpam-5750	284	6	1966	1966	NUM
ejpam-5750	284	7	.	.	PUNCT
ejpam-5750	285	1	[	[	X
ejpam-5750	285	2	8	8	NUM
ejpam-5750	285	3	]	]	X
ejpam-5750	285	4	ibtesam	ibtesam	PROPN
ejpam-5750	285	5	bajunaid	bajunaid	PROPN
ejpam-5750	285	6	,	,	PUNCT
ejpam-5750	285	7	joel	joel	PROPN
ejpam-5750	285	8	m	m	PROPN
ejpam-5750	285	9	cohen	cohen	PROPN
ejpam-5750	285	10	,	,	PUNCT
ejpam-5750	285	11	flavia	flavia	PROPN
ejpam-5750	285	12	colonna	colonna	PROPN
ejpam-5750	285	13	,	,	PUNCT
ejpam-5750	285	14	and	and	CCONJ
ejpam-5750	285	15	david	david	PROPN
ejpam-5750	285	16	singman	singman	PROPN
ejpam-5750	285	17	.	.	PUNCT
ejpam-5750	286	1	a	a	DET
ejpam-5750	286	2	riesz	riesz	NOUN
ejpam-5750	286	3	decomposition	decomposition	NOUN
ejpam-5750	286	4	theorem	theorem	VERB
ejpam-5750	286	5	on	on	ADP
ejpam-5750	286	6	harmonic	harmonic	ADJ
ejpam-5750	286	7	spaces	space	NOUN
ejpam-5750	286	8	without	without	ADP
ejpam-5750	286	9	positive	positive	ADJ
ejpam-5750	286	10	potentials	potential	NOUN
ejpam-5750	286	11	.	.	PUNCT
ejpam-5750	287	1	hiroshima	hiroshima	PROPN
ejpam-5750	287	2	mathematical	mathematical	PROPN
ejpam-5750	287	3	journal	journal	PROPN
ejpam-5750	287	4	,	,	PUNCT
ejpam-5750	287	5	38(1):37–50	38(1):37–50	NUM
ejpam-5750	287	6	,	,	PUNCT
ejpam-5750	287	7	2008	2008	NUM
ejpam-5750	287	8	.	.	PUNCT
ejpam-5750	288	1	[	[	X
ejpam-5750	288	2	9	9	NUM
ejpam-5750	288	3	]	]	X
ejpam-5750	288	4	walter	walter	PROPN
ejpam-5750	288	5	rudin	rudin	PROPN
ejpam-5750	288	6	.	.	PUNCT
ejpam-5750	289	1	the	the	DET
ejpam-5750	289	2	lemma	lemma	PROPN
ejpam-5750	289	3	of	of	ADP
ejpam-5750	289	4	the	the	DET
ejpam-5750	289	5	logarithmic	logarithmic	ADJ
ejpam-5750	289	6	derivative	derivative	NOUN
ejpam-5750	289	7	for	for	ADP
ejpam-5750	289	8	subharmonic	subharmonic	ADJ
ejpam-5750	289	9	functions	function	NOUN
ejpam-5750	289	10	.	.	PUNCT
ejpam-5750	290	1	in	in	ADP
ejpam-5750	290	2	mathematical	mathematical	ADJ
ejpam-5750	290	3	proceedings	proceeding	NOUN
ejpam-5750	290	4	of	of	ADP
ejpam-5750	290	5	the	the	DET
ejpam-5750	290	6	cambridge	cambridge	PROPN
ejpam-5750	290	7	philosophical	philosophical	ADJ
ejpam-5750	290	8	society	society	NOUN
ejpam-5750	290	9	,	,	PUNCT
ejpam-5750	290	10	volume	volume	NOUN
ejpam-5750	290	11	120	120	NUM
ejpam-5750	290	12	,	,	PUNCT
ejpam-5750	290	13	pages	page	NOUN
ejpam-5750	290	14	347–354	347–354	NUM
ejpam-5750	290	15	.	.	PUNCT
ejpam-5750	291	1	cambridge	cambridge	PROPN
ejpam-5750	291	2	university	university	PROPN
ejpam-5750	291	3	press	press	NOUN
ejpam-5750	291	4	,	,	PUNCT
ejpam-5750	291	5	1996	1996	NUM
ejpam-5750	291	6	.	.	PUNCT
ejpam-5750	292	1	[	[	X
ejpam-5750	292	2	10	10	NUM
ejpam-5750	292	3	]	]	X
ejpam-5750	292	4	walter	walter	PROPN
ejpam-5750	292	5	kurt	kurt	PROPN
ejpam-5750	292	6	hayman	hayman	PROPN
ejpam-5750	292	7	and	and	CCONJ
ejpam-5750	292	8	patrick	patrick	PROPN
ejpam-5750	292	9	brendan	brendan	PROPN
ejpam-5750	292	10	kennedy	kennedy	PROPN
ejpam-5750	292	11	.	.	PROPN
ejpam-5750	292	12	subharmonic	subharmonic	ADJ
ejpam-5750	292	13	functions	function	NOUN
ejpam-5750	292	14	/	/	SYM
ejpam-5750	292	15	w.	w.	PROPN
ejpam-5750	292	16	k.	k.	PROPN
ejpam-5750	292	17	hayman	hayman	PROPN
ejpam-5750	292	18	and	and	CCONJ
ejpam-5750	292	19	p.	p.	PROPN
ejpam-5750	293	1	b.	b.	PROPN
ejpam-5750	293	2	kennedy	kennedy	PROPN
ejpam-5750	293	3	.	.	PUNCT
ejpam-5750	294	1	l.m.s	l.m.s	PROPN
ejpam-5750	294	2	.	.	PUNCT
ejpam-5750	295	1	monographs	monograph	NOUN
ejpam-5750	295	2	;	;	PUNCT
ejpam-5750	295	3	9	9	NUM
ejpam-5750	295	4	,	,	PUNCT
ejpam-5750	295	5	20	20	NUM
ejpam-5750	295	6	.	.	PUNCT
ejpam-5750	296	1	academic	academic	ADJ
ejpam-5750	296	2	press	press	PROPN
ejpam-5750	296	3	,	,	PUNCT
ejpam-5750	296	4	london	london	PROPN
ejpam-5750	296	5	;	;	PUNCT
ejpam-5750	296	6	,	,	PUNCT
ejpam-5750	296	7	1976	1976	NUM
ejpam-5750	296	8	.	.	PUNCT
ejpam-5750	297	1	[	[	X
ejpam-5750	297	2	11	11	NUM
ejpam-5750	297	3	]	]	X
ejpam-5750	297	4	sheldon	sheldon	PROPN
ejpam-5750	297	5	axler	axler	NOUN
ejpam-5750	297	6	,	,	PUNCT
ejpam-5750	297	7	paul	paul	PROPN
ejpam-5750	297	8	bourdon	bourdon	PROPN
ejpam-5750	297	9	,	,	PUNCT
ejpam-5750	297	10	and	and	CCONJ
ejpam-5750	297	11	ramey	ramey	PROPN
ejpam-5750	297	12	wade	wade	PROPN
ejpam-5750	297	13	.	.	PUNCT
ejpam-5750	298	1	harmonic	harmonic	PROPN
ejpam-5750	298	2	function	function	NOUN
ejpam-5750	298	3	theory	theory	NOUN
ejpam-5750	298	4	,	,	PUNCT
ejpam-5750	298	5	volume	volume	NOUN
ejpam-5750	298	6	137	137	NUM
ejpam-5750	298	7	.	.	PUNCT
ejpam-5750	299	1	springer	springer	NOUN
ejpam-5750	299	2	science	science	PROPN
ejpam-5750	299	3	&	&	CCONJ
ejpam-5750	299	4	business	business	NOUN
ejpam-5750	299	5	media	medium	NOUN
ejpam-5750	299	6	,	,	PUNCT
ejpam-5750	299	7	2013	2013	NUM
ejpam-5750	299	8	.	.	PUNCT
ejpam-5750	300	1	[	[	X
ejpam-5750	300	2	12	12	NUM
ejpam-5750	300	3	]	]	X
ejpam-5750	300	4	victor	victor	PROPN
ejpam-5750	300	5	anandam	anandam	PROPN
ejpam-5750	300	6	.	.	PUNCT
ejpam-5750	300	7	subharmonic	subharmonic	ADJ
ejpam-5750	300	8	functions	function	NOUN
ejpam-5750	300	9	outside	outside	ADP
ejpam-5750	300	10	a	a	DET
ejpam-5750	300	11	compact	compact	ADJ
ejpam-5750	300	12	set	set	NOUN
ejpam-5750	300	13	in	in	ADP
ejpam-5750	300	14	rn	rn	PROPN
ejpam-5750	300	15	.	.	PUNCT
ejpam-5750	300	16	proceedings	proceeding	NOUN
ejpam-5750	300	17	of	of	ADP
ejpam-5750	300	18	the	the	DET
ejpam-5750	300	19	american	american	PROPN
ejpam-5750	300	20	mathematical	mathematical	PROPN
ejpam-5750	300	21	society	society	NOUN
ejpam-5750	300	22	,	,	PUNCT
ejpam-5750	300	23	84(1):52–54	84(1):52–54	NUM
ejpam-5750	300	24	,	,	PUNCT
ejpam-5750	300	25	1982	1982	NUM
ejpam-5750	300	26	.	.	PUNCT