id	sid	tid	token	lemma	pos
iajs-727	1	1	ibn	ibn	PROPN
iajs-727	1	2	alhaitham	alhaitham	NOUN
iajs-727	1	3	j.	j.	PROPN
iajs-727	2	1	fo	fo	ADP
iajs-727	2	2	r	r	NOUN
iajs-727	2	3	pure	pure	ADJ
iajs-727	2	4	&	&	CCONJ
iajs-727	2	5	appl	appl	PROPN
iajs-727	2	6	.	.	PUNCT
iajs-727	3	1	sc	sc	PROPN
iajs-727	3	2	i.	i.	PROPN
iajs-727	3	3	vol.24	vol.24	PROPN
iajs-727	3	4	(	(	PUNCT
iajs-727	3	5	3	3	NUM
iajs-727	3	6	)	)	PUNCT
iajs-727	3	7	2011	2011	NUM
iajs-727	3	8	approximations	approximation	NOUN
iajs-727	3	9	of	of	ADP
iajs-727	3	10	entire	entire	ADJ
iajs-727	3	11	functions	function	NOUN
iajs-727	3	12	in	in	ADP
iajs-727	3	13	locally	locally	ADV
iajs-727	3	14	global	global	ADJ
iajs-727	3	15	norms	norm	NOUN
iajs-727	3	16	s.k.jassim	s.k.jassim	NOUN
iajs-727	3	17	,	,	PUNCT
iajs-727	3	18	n.j.mohamed	n.j.mohamed	ADJ
iajs-727	3	19	department	department	NOUN
iajs-727	3	20	of	of	ADP
iajs-727	3	21	mathematics	mathematic	NOUN
iajs-727	3	22	,	,	PUNCT
iajs-727	3	23	college	college	NOUN
iajs-727	3	24	of	of	ADP
iajs-727	3	25	science	science	NOUN
iajs-727	3	26	,	,	PUNCT
iajs-727	3	27	university	university	PROPN
iajs-727	3	28	of	of	ADP
iajs-727	3	29	al	al	PROPN
iajs-727	3	30	-	-	PUNCT
iajs-727	3	31	mustansirya	mustansirya	PROPN
iajs-727	3	32	department	department	NOUN
iajs-727	3	33	of	of	ADP
iajs-727	3	34	mathematics	mathematics	PROPN
iajs-727	3	35	,	,	PUNCT
iajs-727	3	36	college	college	NOUN
iajs-727	3	37	of	of	ADP
iajs-727	3	38	education	education	PROPN
iajs-727	3	39	ibn	ibn	PROPN
iajs-727	3	40	al	al	PROPN
iajs-727	3	41	-	-	PUNCT
iajs-727	3	42	haitham	haitham	PROPN
iajs-727	3	43	,	,	PUNCT
iajs-727	3	44	university	university	PROPN
iajs-727	3	45	of	of	ADP
iajs-727	3	46	baghdad	baghdad	PROPN
iajs-727	3	47	received	receive	VERB
iajs-727	3	48	in	in	ADP
iajs-727	3	49	:	:	PUNCT
iajs-727	3	50	3	3	NUM
iajs-727	3	51	february	february	NOUN
iajs-727	3	52	2011	2011	NUM
iajs-727	3	53	accepted	accept	VERB
iajs-727	3	54	in	in	ADP
iajs-727	3	55	:	:	PUNCT
iajs-727	3	56	10	10	NUM
iajs-727	3	57	may	may	PROPN
iajs-727	3	58	2011	2011	NUM
iajs-727	3	59	abstract	abstract	ADV
iajs-727	3	60	the	the	DET
iajs-727	3	61	purpose	purpose	NOUN
iajs-727	3	62	of	of	ADP
iajs-727	3	63	this	this	DET
iajs-727	3	64	paper	paper	NOUN
iajs-727	3	65	is	be	AUX
iajs-727	3	66	to	to	PART
iajs-727	3	67	evaluate	evaluate	VERB
iajs-727	3	68	the	the	DET
iajs-727	3	69	error	error	NOUN
iajs-727	3	70	of	of	ADP
iajs-727	3	71	the	the	DET
iajs-727	3	72	approximation	approximation	NOUN
iajs-727	3	73	of	of	ADP
iajs-727	3	74	an	an	DET
iajs-727	3	75	entire	entire	ADJ
iajs-727	3	76	function	function	NOUN
iajs-727	3	77	by	by	ADP
iajs-727	3	78	some	some	DET
iajs-727	3	79	discrete	discrete	ADJ
iajs-727	3	80	operators	operator	NOUN
iajs-727	3	81	in	in	ADP
iajs-727	3	82	locally	locally	ADV
iajs-727	3	83	global	global	ADJ
iajs-727	3	84	quasi	quasi	NOUN
iajs-727	3	85	-	-	NOUN
iajs-727	3	86	norms	norm	NOUN
iajs-727	3	87	(	(	PUNCT
iajs-727	3	88	l,p	l,p	ADJ
iajs-727	3	89	-	-	PUNCT
iajs-727	3	90	space	space	NOUN
iajs-727	3	91	)	)	PUNCT
iajs-727	3	92	,	,	PUNCT
iajs-727	3	93	we	we	PRON
iajs-727	3	94	intend	intend	VERB
iajs-727	3	95	to	to	PART
iajs-727	3	96	establish	establish	VERB
iajs-727	3	97	new	new	ADJ
iajs-727	3	98	theorems	theorem	NOUN
iajs-727	3	99	concerning	concern	VERB
iajs-727	3	100	that	that	PRON
iajs-727	3	101	jackson	jackson	PROPN
iajs-727	3	102	polynomial	polynomial	PROPN
iajs-727	3	103	and	and	CCONJ
iajs-727	3	104	valee	valee	PROPN
iajs-727	3	105	-	-	PUNCT
iajs-727	3	106	poussin	poussin	NOUN
iajs-727	3	107	operator	operator	NOUN
iajs-727	3	108	remain	remain	VERB
iajs-727	3	109	within	within	ADP
iajs-727	3	110	the	the	DET
iajs-727	3	111	same	same	ADJ
iajs-727	3	112	bounds	bound	NOUN
iajs-727	3	113	as	as	ADP
iajs-727	3	114	bounded	bounded	ADJ
iajs-727	3	115	and	and	CCONJ
iajs-727	3	116	periodic	periodic	ADJ
iajs-727	3	117	entire	entire	ADJ
iajs-727	3	118	function	function	NOUN
iajs-727	3	119	in	in	ADP
iajs-727	3	120	locally	locally	ADV
iajs-727	3	121	global	global	ADJ
iajs-727	3	122	norms	norm	NOUN
iajs-727	3	123	(	(	PUNCT
iajs-727	3	124	l,p	l,p	PROPN
iajs-727	3	125	)	)	PUNCT
iajs-727	3	126	,	,	PUNCT
iajs-727	3	127	(	(	PUNCT
iajs-727	3	128	0	0	PUNCT
iajs-727	3	129	<	<	X
iajs-727	3	130	p	p	X
iajs-727	3	131			NUM
iajs-727	3	132	1	1	NUM
iajs-727	3	133	)	)	PUNCT
iajs-727	3	134	.	.	PUNCT
iajs-727	4	1	key	key	ADJ
iajs-727	4	2	words	word	NOUN
iajs-727	4	3	:	:	PUNCT
iajs-727	4	4	entire	entire	ADJ
iajs-727	4	5	functions	function	NOUN
iajs-727	4	6	,	,	PUNCT
iajs-727	4	7	bounded	bound	VERB
iajs-727	4	8	masurable	masurable	ADJ
iajs-727	4	9	functions	function	NOUN
iajs-727	4	10	,	,	PUNCT
iajs-727	4	11	quasi	quasi	ADJ
iajs-727	4	12	-	-	ADJ
iajs-727	4	13	normed	normed	ADJ
iajs-727	4	14	space	space	NOUN
iajs-727	4	15	.	.	PUNCT
iajs-727	5	1	introduction	introduction	NOUN
iajs-727	5	2	and	and	CCONJ
iajs-727	5	3	preliminaries	preliminary	NOUN
iajs-727	5	4	al	al	PROPN
iajs-727	5	5	-	-	PUNCT
iajs-727	5	6	abdulla	abdulla	PROPN
iajs-727	5	7	,	,	PUNCT
iajs-727	5	8	a.	a.	NOUN
iajs-727	6	1	[	[	X
iajs-727	6	2	1	1	NUM
iajs-727	6	3	]	]	PUNCT
iajs-727	6	4	,	,	PUNCT
iajs-727	6	5	al	al	PROPN
iajs-727	6	6	-	-	PUNCT
iajs-727	6	7	saidy	saidy	ADJ
iajs-727	6	8	,	,	PUNCT
iajs-727	6	9	s.k	s.k	NOUN
iajs-727	6	10	.	.	PUNCT
iajs-727	7	1	[	[	X
iajs-727	7	2	2	2	NUM
iajs-727	7	3	]	]	PUNCT
iajs-727	7	4	and	and	CCONJ
iajs-727	7	5	e.s.bhayah	e.s.bhayah	ADJ
iajs-727	7	6	[	[	X
iajs-727	7	7	3	3	NUM
iajs-727	7	8	]	]	PUNCT
iajs-727	7	9	gave	give	VERB
iajs-727	7	10	estimation	estimation	NOUN
iajs-727	7	11	for	for	ADP
iajs-727	7	12	approximation	approximation	NOUN
iajs-727	7	13	of	of	ADP
iajs-727	7	14	bounded	bounded	ADJ
iajs-727	7	15	measurable	measurable	ADJ
iajs-727	7	16	functions	function	NOUN
iajs-727	7	17	with	with	ADP
iajs-727	7	18	some	some	DET
iajs-727	7	19	discrete	discrete	ADJ
iajs-727	7	20	operators	operator	NOUN
iajs-727	7	21	in	in	ADP
iajs-727	7	22	lp	lp	NOUN
iajs-727	7	23	-	-	PUNCT
iajs-727	7	24	norm	norm	NOUN
iajs-727	7	25	(	(	PUNCT
iajs-727	7	26	0	0	PUNCT
iajs-727	7	27	<	<	X
iajs-727	7	28	p	p	X
iajs-727	7	29			NUM
iajs-727	7	30	1	1	NUM
iajs-727	7	31	)	)	PUNCT
iajs-727	7	32	.	.	PUNCT
iajs-727	8	1	here	here	ADV
iajs-727	8	2	,	,	PUNCT
iajs-727	8	3	we	we	PRON
iajs-727	8	4	give	give	VERB
iajs-727	8	5	an	an	DET
iajs-727	8	6	estimation	estimation	NOUN
iajs-727	8	7	for	for	ADP
iajs-727	8	8	approximation	approximation	NOUN
iajs-727	8	9	of	of	ADP
iajs-727	8	10	entire	entire	ADJ
iajs-727	8	11	functions	function	NOUN
iajs-727	8	12	in	in	ADP
iajs-727	8	13	l,p	l,p	ADJ
iajs-727	8	14	-	-	PUNCT
iajs-727	8	15	space	space	NOUN
iajs-727	8	16	.	.	PUNCT
iajs-727	9	1	let	let	VERB
iajs-727	9	2	x	x	PUNCT
iajs-727	10	1	=	=	PUNCT
iajs-727	10	2	[	[	X
iajs-727	10	3	–	–	PUNCT
iajs-727	10	4	,	,	NOUN
iajs-727	10	5	]	]	X
iajs-727	10	6	we	we	PRON
iajs-727	10	7	denote	denote	VERB
iajs-727	10	8	the	the	DET
iajs-727	10	9	set	set	NOUN
iajs-727	10	10	of	of	ADP
iajs-727	10	11	all	all	DET
iajs-727	10	12	2-periodic	2-periodic	NUM
iajs-727	10	13	bounded	bound	VERB
iajs-727	10	14	measurable	measurable	ADJ
iajs-727	10	15	function	function	NOUN
iajs-727	10	16	with	with	ADP
iajs-727	10	17	usual	usual	ADJ
iajs-727	10	18	sup	sup	NOUN
iajs-727	10	19	-	-	PUNCT
iajs-727	10	20	norm	norm	NOUN
iajs-727	10	21	by	by	ADP
iajs-727	10	22	l	l	NOUN
iajs-727	10	23	,	,	PUNCT
iajs-727	10	24	such	such	ADJ
iajs-727	10	25	that	that	DET
iajs-727	10	26	l(x	l(x	NOUN
iajs-727	10	27	)	)	PUNCT
iajs-727	10	28	=	=	PRON
iajs-727	11	1	{	{	PUNCT
iajs-727	11	2	f	f	X
iajs-727	11	3	:	:	PUNCT
iajs-727	11	4	f	f	PROPN
iajs-727	11	5	is	be	AUX
iajs-727	11	6	2-periodic	2-periodic	NUM
iajs-727	11	7	bounded	bounded	ADJ
iajs-727	11	8	measurable	measurable	ADJ
iajs-727	11	9	function	function	NOUN
iajs-727	11	10	}	}	PUNCT
iajs-727	11	11	with	with	ADP
iajs-727	11	12	norm	norm	NOUN
iajs-727	11	13	f	f	PROPN
iajs-727	11	14	sup	sup	PROPN
iajs-727	11	15	{	{	PUNCT
iajs-727	11	16	f	f	PROPN
iajs-727	11	17	(	(	PUNCT
iajs-727	11	18	x	x	X
iajs-727	11	19	)	)	PUNCT
iajs-727	11	20	x	x	SYM
iajs-727	11	21	x	x	X
iajs-727	11	22	}	}	PUNCT
iajs-727	11	23			VERB
iajs-727	11	24			NUM
iajs-727	11	25			ADJ
iajs-727	11	26			NOUN
iajs-727	11	27			PROPN
iajs-727	11	28			VERB
iajs-727	11	29	…	…	PUNCT
iajs-727	11	30	(	(	PUNCT
iajs-727	11	31	1.1	1.1	NUM
iajs-727	11	32	)	)	PUNCT
iajs-727	11	33	and	and	CCONJ
iajs-727	11	34	the	the	DET
iajs-727	11	35	lp	lp	NOUN
iajs-727	11	36	-	-	PUNCT
iajs-727	11	37	norm	norm	NOUN
iajs-727	11	38	(	(	PUNCT
iajs-727	11	39	1	1	NUM
iajs-727	11	40			NOUN
iajs-727	11	41	p	p	NOUN
iajs-727	11	42	<	<	X
iajs-727	11	43			PROPN
iajs-727	11	44	)	)	PUNCT
iajs-727	11	45	of	of	ADP
iajs-727	11	46	f	f	PROPN
iajs-727	11	47			PROPN
iajs-727	11	48	lp	lp	ADP
iajs-727	11	49	by	by	ADP
iajs-727	11	50	lp	lp	PROPN
iajs-727	11	51	f	f	PROPN
iajs-727	11	52	,	,	PUNCT
iajs-727	11	53	such	such	ADJ
iajs-727	11	54	that	that	SCONJ
iajs-727	11	55	p	p	PROPN
iajs-727	11	56	p	p	X
iajs-727	11	57	1	1	NUM
iajs-727	11	58	p	p	NOUN
iajs-727	11	59	p	p	NOUN
iajs-727	11	60	p	p	X
iajs-727	11	61	p	p	PROPN
iajs-727	11	62	l	l	NOUN
iajs-727	11	63	(	(	PUNCT
iajs-727	11	64	x	x	X
iajs-727	11	65	)	)	PUNCT
iajs-727	11	66	x	x	X
iajs-727	11	67	l	l	NOUN
iajs-727	11	68	(	(	PUNCT
iajs-727	11	69	x	x	X
iajs-727	11	70	)	)	PUNCT
iajs-727	11	71	f	f	NOUN
iajs-727	11	72	:	:	PUNCT
iajs-727	11	73	f	f	PROPN
iajs-727	11	74	(	(	PUNCT
iajs-727	11	75	f(x	f(x	PROPN
iajs-727	11	76	)	)	PUNCT
iajs-727	11	77	dx	dx	PROPN
iajs-727	11	78	)	)	PUNCT
iajs-727	11	79	;	;	PUNCT
iajs-727	12	1	f	f	PROPN
iajs-727	12	2	f	f	PROPN
iajs-727	12	3			ADV
iajs-727	12	4			ADJ
iajs-727	12	5			NUM
iajs-727	12	6			NOUN
iajs-727	12	7			PROPN
iajs-727	12	8			PROPN
iajs-727	12	9			VERB
iajs-727	12	10			PROPN
iajs-727	12	11			PROPN
iajs-727	12	12			NUM
iajs-727	12	13			PROPN
iajs-727	12	14			PROPN
iajs-727	12	15			X
iajs-727	12	16	…	…	PUNCT
iajs-727	12	17	(	(	PUNCT
iajs-727	12	18	1.2	1.2	NUM
iajs-727	12	19	)	)	PUNCT
iajs-727	12	20	now	now	ADV
iajs-727	12	21	let	let	VERB
iajs-727	12	22	us	we	PRON
iajs-727	12	23	consider	consider	VERB
iajs-727	12	24	the	the	DET
iajs-727	12	25	dirich	dirich	NOUN
iajs-727	12	26	let	let	VERB
iajs-727	12	27	kernel	kernel	NOUN
iajs-727	12	28	of	of	ADP
iajs-727	12	29	degree	degree	NOUN
iajs-727	12	30	n	n	CCONJ
iajs-727	12	31	,	,	PUNCT
iajs-727	12	32	[	[	X
iajs-727	12	33	4	4	X
iajs-727	12	34	]	]	SYM
iajs-727	12	35	n	n	CCONJ
iajs-727	12	36	n	n	NOUN
iajs-727	12	37	v	v	NOUN
iajs-727	12	38	1	1	NUM
iajs-727	12	39	1	1	NUM
iajs-727	12	40	d	d	PROPN
iajs-727	12	41	(	(	PUNCT
iajs-727	12	42	u	u	NOUN
iajs-727	12	43	)	)	PUNCT
iajs-727	12	44	cos(vu	cos(vu	NOUN
iajs-727	12	45	)	)	PUNCT
iajs-727	12	46	2	2	NUM
iajs-727	12	47			NUM
iajs-727	12	48			PROPN
iajs-727	12	49			NOUN
iajs-727	12	50			PROPN
iajs-727	12	51	ur	ur	PROPN
iajs-727	12	52	,	,	PUNCT
iajs-727	12	53	n=0,1	n=0,1	ADV
iajs-727	12	54	,	,	PUNCT
iajs-727	12	55	…	…	PUNCT
iajs-727	12	56	…	…	PUNCT
iajs-727	12	57	(	(	PUNCT
iajs-727	12	58	1.3	1.3	NUM
iajs-727	12	59	)	)	PUNCT
iajs-727	12	60	let	let	AUX
iajs-727	12	61	be	be	AUX
iajs-727	12	62	the	the	DET
iajs-727	12	63	fejer	fejer	ADJ
iajs-727	12	64	kernel	kernel	NOUN
iajs-727	12	65	of	of	ADP
iajs-727	12	66	degree	degree	NOUN
iajs-727	12	67	not	not	PART
iajs-727	12	68	grater	grater	NOUN
iajs-727	12	69	than	than	ADP
iajs-727	12	70	n.	n.	NOUN
iajs-727	12	71	where	where	SCONJ
iajs-727	12	72	k	k	NOUN
iajs-727	12	73	,	,	PUNCT
iajs-727	12	74	n	n	PRON
iajs-727	12	75	2k	2k	NOUN
iajs-727	12	76	x	x	SYM
iajs-727	12	77	,	,	PUNCT
iajs-727	12	78	(	(	PUNCT
iajs-727	12	79	k	k	NOUN
iajs-727	12	80	0,1	0,1	NUM
iajs-727	12	81	,	,	PUNCT
iajs-727	12	82	2	2	NUM
iajs-727	12	83	,	,	PUNCT
iajs-727	12	84	...	...	PUNCT
iajs-727	12	85	,	,	PUNCT
iajs-727	12	86	n	n	CCONJ
iajs-727	12	87	)	)	PUNCT
iajs-727	12	88	,	,	PUNCT
iajs-727	12	89	n	n	PROPN
iajs-727	13	1	1	1	NUM
iajs-727	13	2			NUM
iajs-727	13	3			PROPN
iajs-727	13	4			PUNCT
iajs-727	13	5			NOUN
iajs-727	13	6	be	be	AUX
iajs-727	13	7	the	the	DET
iajs-727	13	8	so	so	ADV
iajs-727	13	9	called	call	VERB
iajs-727	13	10	jackson	jackson	PROPN
iajs-727	13	11	polynomial	polynomial	PROPN
iajs-727	13	12	of	of	ADP
iajs-727	13	13	function	function	PROPN
iajs-727	13	14	f	f	PROPN
iajs-727	13	15			NOUN
iajs-727	14	1	l.	l.	NOUN
iajs-727	14	2	n	n	CCONJ
iajs-727	14	3	0	0	NUM
iajs-727	14	4	1	1	NUM
iajs-727	14	5	n	n	NUM
iajs-727	14	6	1	1	NUM
iajs-727	14	7	k	k	X
iajs-727	14	8	(	(	PUNCT
iajs-727	14	9	u	u	NOUN
iajs-727	14	10	)	)	PUNCT
iajs-727	15	1	[	[	X
iajs-727	15	2	d	d	X
iajs-727	15	3	(	(	PUNCT
iajs-727	15	4	u	u	NOUN
iajs-727	15	5	)	)	PUNCT
iajs-727	15	6	d	d	NOUN
iajs-727	15	7	(	(	PUNCT
iajs-727	15	8	u	u	NOUN
iajs-727	15	9	)	)	PUNCT
iajs-727	15	10	...	...	PUNCT
iajs-727	16	1	d	d	X
iajs-727	16	2	(	(	PUNCT
iajs-727	16	3	u	u	NOUN
iajs-727	16	4	)	)	PUNCT
iajs-727	16	5	]	]	PUNCT
iajs-727	16	6	n	n	CCONJ
iajs-727	16	7	1	1	NUM
iajs-727	16	8			PROPN
iajs-727	16	9			ADV
iajs-727	16	10			PUNCT
iajs-727	16	11			PUNCT
iajs-727	16	12			PUNCT
iajs-727	16	13	…	…	PUNCT
iajs-727	16	14	(	(	PUNCT
iajs-727	16	15	1.4	1.4	NUM
iajs-727	16	16	)	)	PUNCT
iajs-727	16	17	n	n	CCONJ
iajs-727	16	18	n	n	NOUN
iajs-727	16	19	k	k	NOUN
iajs-727	16	20	,	,	PUNCT
iajs-727	16	21	n	n	PROPN
iajs-727	16	22	n	n	CCONJ
iajs-727	16	23	k	k	NOUN
iajs-727	16	24	,	,	PUNCT
iajs-727	16	25	n	n	PROPN
iajs-727	16	26	k	k	NOUN
iajs-727	16	27	0	0	NUM
iajs-727	16	28	2	2	NUM
iajs-727	16	29	j	j	PROPN
iajs-727	16	30	(	(	PUNCT
iajs-727	16	31	f	f	PROPN
iajs-727	16	32	,	,	PUNCT
iajs-727	16	33	x	x	X
iajs-727	16	34	)	)	PUNCT
iajs-727	16	35	f	f	NOUN
iajs-727	16	36	(	(	PUNCT
iajs-727	16	37	x	x	X
iajs-727	16	38	)	)	PUNCT
iajs-727	16	39	k	k	NOUN
iajs-727	16	40	(	(	PUNCT
iajs-727	16	41	x	x	NOUN
iajs-727	16	42	x	x	X
iajs-727	16	43	)	)	PUNCT
iajs-727	16	44	n	n	CCONJ
iajs-727	16	45	1	1	NUM
iajs-727	16	46			NUM
iajs-727	16	47			PROPN
iajs-727	16	48			PROPN
iajs-727	16	49			VERB
iajs-727	16	50			X
iajs-727	16	51	…	…	PUNCT
iajs-727	16	52	(	(	PUNCT
iajs-727	16	53	1.5	1.5	NUM
iajs-727	16	54	)	)	PUNCT
iajs-727	16	55	ibn	ibn	NOUN
iajs-727	16	56	alhaitham	alhaitham	NOUN
iajs-727	16	57	j.	j.	PROPN
iajs-727	17	1	fo	fo	ADP
iajs-727	17	2	r	r	NOUN
iajs-727	17	3	pure	pure	ADJ
iajs-727	17	4	&	&	CCONJ
iajs-727	17	5	appl	appl	PROPN
iajs-727	17	6	.	.	PUNCT
iajs-727	18	1	sc	sc	PROPN
iajs-727	18	2	i.	i.	PROPN
iajs-727	18	3	vol.24	vol.24	PROPN
iajs-727	18	4	(	(	PUNCT
iajs-727	18	5	3	3	NUM
iajs-727	18	6	)	)	PUNCT
iajs-727	18	7	2011	2011	NUM
iajs-727	18	8	let	let	VERB
iajs-727	18	9	j	j	PROPN
iajs-727	18	10	2	2	NUM
iajs-727	18	11	j	j	NOUN
iajs-727	18	12	x	x	SYM
iajs-727	18	13	3n	3n	NUM
iajs-727	18	14	1	1	NUM
iajs-727	18	15			PROPN
iajs-727	18	16			PROPN
iajs-727	18	17			PROPN
iajs-727	18	18	,	,	PUNCT
iajs-727	18	19	j=0,1,	j=0,1,	PROPN
iajs-727	18	20	…	…	PROPN
iajs-727	18	21	,3n	,3n	PROPN
iajs-727	18	22	.	.	PUNCT
iajs-727	19	1	then	then	ADV
iajs-727	19	2	we	we	PRON
iajs-727	19	3	define	define	VERB
iajs-727	19	4	the	the	DET
iajs-727	19	5	following	follow	VERB
iajs-727	19	6	operator	operator	NOUN
iajs-727	19	7	.	.	PUNCT
iajs-727	20	1	be	be	AUX
iajs-727	20	2	the	the	DET
iajs-727	20	3	valee	valee	PROPN
iajs-727	20	4	-	-	PUNCT
iajs-727	20	5	poussin	poussin	NOUN
iajs-727	20	6	discrete	discrete	ADJ
iajs-727	20	7	operator	operator	NOUN
iajs-727	20	8	of	of	ADP
iajs-727	20	9	2-periodic	2-periodic	NUM
iajs-727	20	10	bounded	bounded	ADJ
iajs-727	20	11	measurable	measurable	ADJ
iajs-727	20	12	function	function	NOUN
iajs-727	20	13	.	.	PUNCT
iajs-727	21	1	the	the	DET
iajs-727	21	2	unique	unique	ADJ
iajs-727	21	3	linear	linear	ADJ
iajs-727	21	4	trigonometric	trigonometric	NOUN
iajs-727	21	5	polynomial	polynomial	NOUN
iajs-727	21	6	which	which	PRON
iajs-727	21	7	is	be	AUX
iajs-727	21	8	interpolating	interpolate	VERB
iajs-727	21	9	a	a	DET
iajs-727	21	10	given	give	VERB
iajs-727	21	11	function	function	NOUN
iajs-727	21	12	f	f	PROPN
iajs-727	21	13	lp(x	lp(x	PROPN
iajs-727	21	14	)	)	PUNCT
iajs-727	21	15	at	at	ADP
iajs-727	21	16	the	the	DET
iajs-727	21	17	point	point	NOUN
iajs-727	21	18	xj	xj	PROPN
iajs-727	21	19	is	be	AUX
iajs-727	21	20	denote	denote	VERB
iajs-727	21	21	by	by	ADP
iajs-727	21	22	in(t	in(t	NOUN
iajs-727	21	23	)	)	PUNCT
iajs-727	21	24	which	which	PRON
iajs-727	21	25	has	have	VERB
iajs-727	21	26	the	the	DET
iajs-727	21	27	representation	representation	NOUN
iajs-727	21	28	:	:	PUNCT
iajs-727	21	29	now	now	ADV
iajs-727	21	30	let	let	VERB
iajs-727	21	31	bn	bn	PART
iajs-727	21	32	be	be	AUX
iajs-727	21	33	the	the	DET
iajs-727	21	34	set	set	NOUN
iajs-727	21	35	of	of	ADP
iajs-727	21	36	all	all	DET
iajs-727	21	37	entire	entire	ADJ
iajs-727	21	38	functions	function	NOUN
iajs-727	21	39	,	,	PUNCT
iajs-727	21	40	since	since	SCONJ
iajs-727	21	41	the	the	DET
iajs-727	21	42	derivative	derivative	NOUN
iajs-727	21	43	of	of	ADP
iajs-727	21	44	polynomial	polynomial	ADJ
iajs-727	21	45	exists	exist	VERB
iajs-727	21	46	every	every	DET
iajs-727	21	47	where	where	SCONJ
iajs-727	21	48	,	,	PUNCT
iajs-727	21	49	then	then	ADV
iajs-727	21	50	we	we	PRON
iajs-727	21	51	get	get	VERB
iajs-727	21	52	that	that	SCONJ
iajs-727	21	53	every	every	DET
iajs-727	21	54	polynomial	polynomial	NOUN
iajs-727	21	55	is	be	AUX
iajs-727	21	56	an	an	DET
iajs-727	21	57	entire	entire	ADJ
iajs-727	21	58	function	function	NOUN
iajs-727	21	59	[	[	X
iajs-727	21	60	5	5	NUM
iajs-727	21	61	]	]	PUNCT
iajs-727	21	62	,	,	PUNCT
iajs-727	21	63	so	so	SCONJ
iajs-727	21	64	we	we	PRON
iajs-727	21	65	consider	consider	VERB
iajs-727	21	66	that	that	SCONJ
iajs-727	21	67	f	f	PROPN
iajs-727	21	68	bn	bn	PROPN
iajs-727	21	69	and	and	CCONJ
iajs-727	21	70	jn(f	jn(f	NUM
iajs-727	21	71	)	)	PUNCT
iajs-727	21	72	bn	bn	NOUN
iajs-727	21	73	,	,	PUNCT
iajs-727	21	74	v2n,3n(f	v2n,3n(f	PROPN
iajs-727	21	75	)	)	PUNCT
iajs-727	21	76	bn	bn	PROPN
iajs-727	21	77	.	.	PUNCT
iajs-727	22	1	let	let	VERB
iajs-727	22	2	n	n	PRON
iajs-727	22	3	,	,	PUNCT
iajs-727	22	4	k	k	X
iajs-727	22	5	be	be	VERB
iajs-727	22	6	positive	positive	ADJ
iajs-727	22	7	integers	integer	NOUN
iajs-727	22	8	,	,	PUNCT
iajs-727	22	9	(	(	PUNCT
iajs-727	22	10	0	0	PUNCT
iajs-727	22	11	<	<	X
iajs-727	22	12	p	p	X
iajs-727	22	13			NUM
iajs-727	22	14	1	1	NUM
iajs-727	22	15	)	)	PUNCT
iajs-727	22	16	and	and	CCONJ
iajs-727	22	17	(	(	PUNCT
iajs-727	22	18			NUM
iajs-727	22	19	>	>	X
iajs-727	22	20	0	0	NUM
iajs-727	22	21	)	)	PUNCT
iajs-727	22	22	are	be	AUX
iajs-727	22	23	fixed	fix	VERB
iajs-727	22	24	numbers	number	NOUN
iajs-727	22	25	which	which	PRON
iajs-727	22	26	will	will	AUX
iajs-727	22	27	be	be	AUX
iajs-727	22	28	used	use	VERB
iajs-727	22	29	for	for	ADP
iajs-727	22	30	the	the	DET
iajs-727	22	31	degree	degree	NOUN
iajs-727	22	32	of	of	ADP
iajs-727	22	33	approximating	approximate	VERB
iajs-727	22	34	polynomial	polynomial	ADJ
iajs-727	22	35	,	,	PUNCT
iajs-727	22	36	for	for	ADP
iajs-727	22	37	the	the	DET
iajs-727	22	38	rate	rate	NOUN
iajs-727	22	39	order	order	NOUN
iajs-727	22	40	of	of	ADP
iajs-727	22	41	modulus	modulus	NOUN
iajs-727	22	42	and	and	CCONJ
iajs-727	22	43	for	for	ADP
iajs-727	22	44	the	the	DET
iajs-727	22	45	space	space	NOUN
iajs-727	22	46	l,p	l,p	PROPN
iajs-727	22	47	respectively	respectively	ADV
iajs-727	22	48	.	.	PUNCT
iajs-727	23	1	we	we	PRON
iajs-727	23	2	consider	consider	VERB
iajs-727	23	3	the	the	DET
iajs-727	23	4	locally	locally	ADV
iajs-727	23	5	global	global	ADJ
iajs-727	23	6	norm	norm	NOUN
iajs-727	23	7	for	for	ADP
iajs-727	23	8	(	(	PUNCT
iajs-727	23	9			NUM
iajs-727	23	10	>	>	X
iajs-727	23	11	0	0	NUM
iajs-727	23	12	)	)	PUNCT
iajs-727	23	13	,	,	PUNCT
iajs-727	23	14	(	(	PUNCT
iajs-727	23	15	0	0	PUNCT
iajs-727	23	16	<	<	X
iajs-727	23	17	p	p	PROPN
iajs-727	23	18			NUM
iajs-727	23	19			NOUN
iajs-727	23	20	)	)	PUNCT
iajs-727	23	21	now	now	ADV
iajs-727	23	22	the	the	DET
iajs-727	23	23	kth	kth	PROPN
iajs-727	23	24	average	average	ADJ
iajs-727	23	25	modulus	modulus	NOUN
iajs-727	23	26	of	of	ADP
iajs-727	23	27	smoothness	smoothness	NOUN
iajs-727	23	28	for	for	ADP
iajs-727	23	29	f	f	PROPN
iajs-727	23	30			PROPN
iajs-727	23	31	l,p	l,p	NOUN
iajs-727	23	32	are	be	AUX
iajs-727	23	33	defined	define	VERB
iajs-727	23	34	by	by	ADP
iajs-727	23	35	the	the	DET
iajs-727	23	36	following	following	NOUN
iajs-727	23	37	respectively	respectively	ADV
iajs-727	23	38	,	,	PUNCT
iajs-727	23	39	[	[	X
iajs-727	23	40	6	6	NUM
iajs-727	23	41	]	]	PUNCT
iajs-727	23	42	,	,	PUNCT
iajs-727	23	43	[	[	X
iajs-727	23	44	7	7	X
iajs-727	23	45	]	]	PUNCT
iajs-727	23	46	where	where	SCONJ
iajs-727	23	47	the	the	DET
iajs-727	23	48	kth	kth	PROPN
iajs-727	23	49	modulus	modulus	NOUN
iajs-727	23	50	of	of	ADP
iajs-727	23	51	smoothness	smoothness	NOUN
iajs-727	23	52	for	for	ADP
iajs-727	23	53	f	f	PROPN
iajs-727	23	54			PROPN
iajs-727	23	55	l,p	l,p	PROPN
iajs-727	23	56	,	,	PUNCT
iajs-727	23	57	k	k	PROPN
iajs-727	23	58			PROPN
iajs-727	23	59	is	be	AUX
iajs-727	23	60	defined	define	VERB
iajs-727	23	61	by	by	ADP
iajs-727	23	62	now	now	ADV
iajs-727	23	63	,	,	PUNCT
iajs-727	23	64	we	we	PRON
iajs-727	23	65	set	set	VERB
iajs-727	24	1	k	k	PROPN
iajs-727	25	1	k	k	PROPN
iajs-727	25	2	m	m	VERB
iajs-727	25	3	k	k	NOUN
iajs-727	25	4	m	m	VERB
iajs-727	25	5	0h	0h	PROPN
iajs-727	25	6	k	k	PROPN
iajs-727	25	7	(	(	PUNCT
iajs-727	25	8	1	1	X
iajs-727	25	9	)	)	PUNCT
iajs-727	25	10	f	f	NOUN
iajs-727	25	11	(	(	PUNCT
iajs-727	25	12	t	t	PROPN
iajs-727	25	13	mh	mh	PROPN
iajs-727	25	14	)	)	PUNCT
iajs-727	26	1	if	if	SCONJ
iajs-727	26	2	t	t	PROPN
iajs-727	26	3	or	or	CCONJ
iajs-727	26	4	t	t	PROPN
iajs-727	26	5	kh	kh	PROPN
iajs-727	26	6	x	x	PROPN
iajs-727	26	7	f	f	PROPN
iajs-727	26	8	(	(	PUNCT
iajs-727	26	9	t	t	PROPN
iajs-727	26	10	)	)	PUNCT
iajs-727	26	11	m	m	VERB
iajs-727	26	12	0	0	NUM
iajs-727	27	1	otherwise	otherwise	ADV
iajs-727	27	2			VERB
iajs-727	27	3			PRON
iajs-727	27	4			ADP
iajs-727	27	5			NOUN
iajs-727	27	6			PROPN
iajs-727	27	7			PROPN
iajs-727	27	8			ADV
iajs-727	27	9			PRON
iajs-727	27	10			PUNCT
iajs-727	27	11			PUNCT
iajs-727	27	12			PROPN
iajs-727	27	13			PROPN
iajs-727	27	14			NUM
iajs-727	27	15			NOUN
iajs-727	27	16			VERB
iajs-727	27	17			NUM
iajs-727	27	18			PRON
iajs-727	27	19			NUM
iajs-727	27	20			PROPN
iajs-727	27	21			X
iajs-727	27	22	.	.	PUNCT
iajs-727	28	1	in	in	ADP
iajs-727	28	2	the	the	DET
iajs-727	28	3	following	following	NOUN
iajs-727	28	4	we	we	PRON
iajs-727	28	5	recall	recall	VERB
iajs-727	28	6	some	some	DET
iajs-727	28	7	theorems	theorem	NOUN
iajs-727	28	8	which	which	PRON
iajs-727	28	9	are	be	AUX
iajs-727	28	10	needed	need	VERB
iajs-727	28	11	:	:	PUNCT
iajs-727	28	12	theorem	theorem	VERB
iajs-727	28	13	1.1	1.1	NUM
iajs-727	28	14	:	:	PUNCT
iajs-727	29	1	[	[	X
iajs-727	29	2	6	6	NUM
iajs-727	29	3	]	]	PUNCT
iajs-727	29	4	if	if	SCONJ
iajs-727	29	5	f	f	PROPN
iajs-727	29	6			PROPN
iajs-727	29	7	bn	bn	PROPN
iajs-727	29	8	,	,	PUNCT
iajs-727	29	9	then	then	ADV
iajs-727	29	10	for	for	ADP
iajs-727	29	11	(	(	PUNCT
iajs-727	29	12	0	0	PUNCT
iajs-727	29	13	<	<	X
iajs-727	29	14	p	p	X
iajs-727	29	15			NUM
iajs-727	29	16	1	1	NUM
iajs-727	29	17	)	)	PUNCT
iajs-727	29	18	and	and	CCONJ
iajs-727	29	19	(	(	PUNCT
iajs-727	29	20			NUM
iajs-727	29	21	>	>	X
iajs-727	29	22	0	0	NUM
iajs-727	29	23	)	)	PUNCT
iajs-727	29	24	,	,	PUNCT
iajs-727	29	25	we	we	PRON
iajs-727	29	26	have	have	VERB
iajs-727	29	27	,	,	PUNCT
iajs-727	29	28	1	1	NUM
iajs-727	29	29	1	1	NUM
iajs-727	29	30	p	p	NOUN
iajs-727	29	31	p	p	NOUN
iajs-727	29	32	,	,	PUNCT
iajs-727	29	33	p	p	X
iajs-727	29	34	p	p	X
iajs-727	29	35	f	f	X
iajs-727	29	36	c(p)[(1	c(p)[(1	PROPN
iajs-727	29	37	n	n	PROPN
iajs-727	29	38	)	)	PUNCT
iajs-727	29	39	(	(	PUNCT
iajs-727	29	40	ns	ns	NUM
iajs-727	29	41	)	)	PUNCT
iajs-727	29	42	]	]	PUNCT
iajs-727	29	43	f	f	PROPN
iajs-727	29	44			VERB
iajs-727	29	45			PROPN
iajs-727	29	46			NUM
iajs-727	29	47	.	.	PUNCT
iajs-727	30	1	2n	2n	NUM
iajs-727	30	2	n	n	CCONJ
iajs-727	30	3	n	n	PROPN
iajs-727	30	4	1	1	NUM
iajs-727	30	5	2n	2n	NUM
iajs-727	30	6	1	1	NUM
iajs-727	30	7	v	v	NOUN
iajs-727	30	8	(	(	PUNCT
iajs-727	30	9	t	t	NOUN
iajs-727	30	10	)	)	PUNCT
iajs-727	31	1	[	[	X
iajs-727	31	2	d	d	X
iajs-727	31	3	(	(	PUNCT
iajs-727	31	4	t	t	PROPN
iajs-727	31	5	)	)	PUNCT
iajs-727	31	6	d	d	PROPN
iajs-727	31	7	(	(	PUNCT
iajs-727	31	8	t	t	NOUN
iajs-727	31	9	)	)	PUNCT
iajs-727	31	10	d	d	PROPN
iajs-727	31	11	(	(	PUNCT
iajs-727	31	12	t	t	PROPN
iajs-727	31	13	)	)	PUNCT
iajs-727	31	14	]	]	PUNCT
iajs-727	32	1	n	n	CCONJ
iajs-727	32	2	1	1	NUM
iajs-727	32	3			ADJ
iajs-727	32	4			NOUN
iajs-727	32	5			PUNCT
iajs-727	32	6			PUNCT
iajs-727	32	7	…	…	PUNCT
iajs-727	32	8	(	(	PUNCT
iajs-727	32	9	1.6	1.6	NUM
iajs-727	32	10	)	)	PUNCT
iajs-727	32	11	3n	3n	NOUN
iajs-727	32	12	2n,3n	2n,3n	NUM
iajs-727	32	13	j	j	PROPN
iajs-727	32	14	2n	2n	NUM
iajs-727	32	15	j	j	PROPN
iajs-727	32	16	j	j	PROPN
iajs-727	32	17	0	0	NUM
iajs-727	32	18	2	2	NUM
iajs-727	32	19	v	v	NOUN
iajs-727	32	20	(	(	PUNCT
iajs-727	32	21	f	f	PROPN
iajs-727	32	22	,	,	PUNCT
iajs-727	32	23	x	x	PROPN
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iajs-727	32	25	f(x	f(x	PROPN
iajs-727	32	26	)	)	PUNCT
iajs-727	32	27	v	v	NOUN
iajs-727	32	28	(	(	PUNCT
iajs-727	32	29	x	x	NOUN
iajs-727	32	30	x	x	X
iajs-727	32	31	)	)	PUNCT
iajs-727	32	32	3n	3n	NUM
iajs-727	32	33	1	1	NUM
iajs-727	32	34			NUM
iajs-727	32	35			PROPN
iajs-727	32	36			PROPN
iajs-727	32	37			VERB
iajs-727	32	38			X
iajs-727	32	39	…	…	PUNCT
iajs-727	32	40	(	(	PUNCT
iajs-727	32	41	1.7	1.7	NUM
iajs-727	32	42	)	)	PUNCT
iajs-727	32	43	2n	2n	NUM
iajs-727	33	1	n	n	CCONJ
iajs-727	33	2	j	j	PROPN
iajs-727	33	3	n	n	ADP
iajs-727	33	4	j	j	PROPN
iajs-727	33	5	j	j	PROPN
iajs-727	33	6	0	0	NUM
iajs-727	33	7	2	2	NUM
iajs-727	33	8	i	i	NOUN
iajs-727	33	9	(	(	PUNCT
iajs-727	33	10	f	f	PROPN
iajs-727	33	11	,	,	PUNCT
iajs-727	33	12	x	x	PROPN
iajs-727	33	13	)	)	PUNCT
iajs-727	33	14	f	f	NOUN
iajs-727	33	15	(	(	PUNCT
iajs-727	33	16	x	x	X
iajs-727	33	17	)	)	PUNCT
iajs-727	33	18	d	d	NOUN
iajs-727	33	19	(	(	PUNCT
iajs-727	33	20	x	x	NOUN
iajs-727	33	21	x	x	SYM
iajs-727	33	22	)	)	PUNCT
iajs-727	33	23	2n	2n	NUM
iajs-727	33	24	1	1	NUM
iajs-727	33	25			NUM
iajs-727	33	26			PROPN
iajs-727	33	27			PROPN
iajs-727	33	28			VERB
iajs-727	33	29			X
iajs-727	33	30	…	…	PUNCT
iajs-727	33	31	(	(	PUNCT
iajs-727	33	32	1.8	1.8	NUM
iajs-727	33	33	)	)	PUNCT
iajs-727	33	34	1	1	NUM
iajs-727	33	35	p	p	NOUN
iajs-727	33	36	p	p	NOUN
iajs-727	33	37	,	,	PUNCT
iajs-727	33	38	p	p	X
iajs-727	33	39	x	x	X
iajs-727	33	40	f	f	NOUN
iajs-727	33	41	sup	sup	NOUN
iajs-727	33	42	f	f	PROPN
iajs-727	33	43	(	(	PUNCT
iajs-727	33	44	y	y	PROPN
iajs-727	33	45	)	)	PUNCT
iajs-727	33	46	,	,	PUNCT
iajs-727	33	47	y	y	PROPN
iajs-727	33	48	x	x	X
iajs-727	33	49	,	,	PUNCT
iajs-727	33	50	x	x	X
iajs-727	33	51	dx	dx	PROPN
iajs-727	33	52	2	2	NUM
iajs-727	33	53	2	2	NUM
iajs-727	33	54			NOUN
iajs-727	33	55			NOUN
iajs-727	33	56			PART
iajs-727	33	57			VERB
iajs-727	33	58			PROPN
iajs-727	33	59			PROPN
iajs-727	33	60			NOUN
iajs-727	33	61			PROPN
iajs-727	33	62			NOUN
iajs-727	33	63			VERB
iajs-727	33	64			NOUN
iajs-727	34	1			PROPN
iajs-727	34	2			PROPN
iajs-727	34	3			PROPN
iajs-727	34	4			VERB
iajs-727	34	5			PRON
iajs-727	35	1			NUM
iajs-727	35	2			NUM
iajs-727	35	3	,	,	PUNCT
iajs-727	35	4	x[–,	x[–,	PROPN
iajs-727	35	5	]	]	X
iajs-727	35	6	.	.	PUNCT
iajs-727	36	1	…	…	PUNCT
iajs-727	36	2	(	(	PUNCT
iajs-727	36	3	1.9	1.9	NUM
iajs-727	36	4	)	)	PUNCT
iajs-727	36	5	k	k	NOUN
iajs-727	37	1	p	p	X
iajs-727	37	2	k	k	PROPN
iajs-727	37	3	p	p	X
iajs-727	37	4	k	k	PROPN
iajs-727	37	5	,	,	PUNCT
iajs-727	37	6	p	p	PROPN
iajs-727	37	7	k	k	PROPN
iajs-727	37	8	,	,	PUNCT
iajs-727	37	9	p	p	PROPN
iajs-727	37	10	1	1	NUM
iajs-727	37	11	1	1	NUM
iajs-727	37	12	(	(	PUNCT
iajs-727	37	13	f	f	PROPN
iajs-727	37	14	,	,	PUNCT
iajs-727	37	15	)	)	PUNCT
iajs-727	37	16	w	w	X
iajs-727	37	17	(	(	PUNCT
iajs-727	37	18	f	f	PROPN
iajs-727	37	19	,	,	PUNCT
iajs-727	37	20	.	.	PUNCT
iajs-727	37	21	,	,	PUNCT
iajs-727	37	22	)	)	PUNCT
iajs-727	37	23	,	,	PUNCT
iajs-727	37	24	n	n	CCONJ
iajs-727	37	25	n	n	CCONJ
iajs-727	37	26	1	1	NUM
iajs-727	37	27	1	1	NUM
iajs-727	37	28	(	(	PUNCT
iajs-727	37	29	f	f	PROPN
iajs-727	37	30	,	,	PUNCT
iajs-727	37	31	)	)	PUNCT
iajs-727	37	32	w	w	X
iajs-727	37	33	(	(	PUNCT
iajs-727	37	34	f	f	PROPN
iajs-727	37	35	,	,	PUNCT
iajs-727	37	36	.	.	PUNCT
iajs-727	37	37	,	,	PUNCT
iajs-727	37	38	)	)	PUNCT
iajs-727	38	1	n	n	CCONJ
iajs-727	38	2	n	n	ADV
iajs-727	38	3			NOUN
iajs-727	39	1			PROPN
iajs-727	39	2			NOUN
iajs-727	39	3			NUM
iajs-727	39	4			NUM
iajs-727	39	5			NUM
iajs-727	39	6			NUM
iajs-727	39	7			NOUN
iajs-727	39	8			NUM
iajs-727	39	9			PROPN
iajs-727	39	10			NUM
iajs-727	39	11			PROPN
iajs-727	39	12			PROPN
iajs-727	40	1			PROPN
iajs-727	40	2			ADJ
iajs-727	40	3			NOUN
iajs-727	40	4			NOUN
iajs-727	40	5	…	…	PUNCT
iajs-727	40	6	(	(	PUNCT
iajs-727	40	7	1.10	1.10	NUM
iajs-727	40	8	)	)	PUNCT
iajs-727	40	9	k	k	NOUN
iajs-727	41	1	k	k	PROPN
iajs-727	41	2	h	h	NOUN
iajs-727	42	1	1	1	NUM
iajs-727	42	2	k	k	X
iajs-727	43	1	k	k	PROPN
iajs-727	43	2	w	w	PROPN
iajs-727	43	3	(	(	PUNCT
iajs-727	43	4	f	f	PROPN
iajs-727	43	5	,	,	PUNCT
iajs-727	43	6	x	x	NOUN
iajs-727	43	7	,	,	PUNCT
iajs-727	43	8	)	)	PUNCT
iajs-727	43	9	sup	sup	NOUN
iajs-727	43	10	f(t	f(t	NOUN
iajs-727	43	11	)	)	PUNCT
iajs-727	43	12	:	:	PUNCT
iajs-727	44	1	t	t	PROPN
iajs-727	44	2	,	,	PUNCT
iajs-727	44	3	t	t	PROPN
iajs-727	44	4	kh	kh	PROPN
iajs-727	44	5	x	x	X
iajs-727	44	6	,	,	PUNCT
iajs-727	44	7	x	x	PUNCT
iajs-727	44	8	x	x	SYM
iajs-727	44	9	n	n	CCONJ
iajs-727	44	10	2	2	NUM
iajs-727	44	11	2	2	NUM
iajs-727	44	12			NOUN
iajs-727	44	13			VERB
iajs-727	44	14			NOUN
iajs-727	44	15			NOUN
iajs-727	44	16			NOUN
iajs-727	44	17			VERB
iajs-727	44	18			PROPN
iajs-727	44	19			PROPN
iajs-727	44	20			PUNCT
iajs-727	44	21			PROPN
iajs-727	44	22			VERB
iajs-727	44	23			DET
iajs-727	44	24			PROPN
iajs-727	45	1			PROPN
iajs-727	46	1			NUM
iajs-727	46	2			NUM
iajs-727	46	3	…	…	SYM
iajs-727	46	4	(	(	PUNCT
iajs-727	46	5	1.11	1.11	NUM
iajs-727	46	6	)	)	PUNCT
iajs-727	46	7	ibn	ibn	NOUN
iajs-727	46	8	alhaitham	alhaitham	NOUN
iajs-727	46	9	j.	j.	PROPN
iajs-727	47	1	fo	fo	ADP
iajs-727	47	2	r	r	NOUN
iajs-727	47	3	pure	pure	ADJ
iajs-727	47	4	&	&	CCONJ
iajs-727	47	5	appl	appl	PROPN
iajs-727	47	6	.	.	PUNCT
iajs-727	48	1	sc	sc	PROPN
iajs-727	48	2	i.	i.	PROPN
iajs-727	48	3	vol.24	vol.24	PROPN
iajs-727	48	4	(	(	PUNCT
iajs-727	48	5	3	3	NUM
iajs-727	48	6	)	)	PUNCT
iajs-727	48	7	2011	2011	NUM
iajs-727	48	8	theorem	theorem	VERB
iajs-727	48	9	1.2	1.2	NUM
iajs-727	48	10	:	:	PUNCT
iajs-727	49	1	[	[	X
iajs-727	49	2	3	3	X
iajs-727	49	3	]	]	PUNCT
iajs-727	49	4	if	if	SCONJ
iajs-727	49	5	f	f	PROPN
iajs-727	49	6			PROPN
iajs-727	49	7	2-periodic	2-periodic	NUM
iajs-727	49	8	bounded	bound	VERB
iajs-727	49	9	measurable	measurable	ADJ
iajs-727	49	10	functions	function	NOUN
iajs-727	49	11	,	,	PUNCT
iajs-727	49	12	then	then	ADV
iajs-727	49	13	for	for	ADP
iajs-727	49	14	(	(	PUNCT
iajs-727	49	15	0	0	PUNCT
iajs-727	49	16	<	<	X
iajs-727	49	17	p	p	X
iajs-727	49	18			NUM
iajs-727	49	19	1	1	NUM
iajs-727	49	20	)	)	PUNCT
iajs-727	49	21	n	n	DET
iajs-727	49	22	1	1	NUM
iajs-727	49	23	pp	pp	ADP
iajs-727	49	24	1	1	NUM
iajs-727	49	25	f	f	PROPN
iajs-727	49	26	j	j	PROPN
iajs-727	49	27	(	(	PUNCT
iajs-727	49	28	f	f	PROPN
iajs-727	49	29	)	)	PUNCT
iajs-727	49	30	c(p	c(p	NOUN
iajs-727	49	31	)	)	PUNCT
iajs-727	49	32	(	(	PUNCT
iajs-727	49	33	f	f	X
iajs-727	49	34	,	,	PUNCT
iajs-727	49	35	)	)	PUNCT
iajs-727	49	36	n	n	CCONJ
iajs-727	49	37			PROPN
iajs-727	49	38			PROPN
iajs-727	49	39			NOUN
iajs-727	49	40			NOUN
iajs-727	49	41	.	.	PUNCT
iajs-727	50	1	theorem	theorem	VERB
iajs-727	50	2	1.3	1.3	NUM
iajs-727	50	3	:	:	PUNCT
iajs-727	51	1	[	[	X
iajs-727	51	2	3	3	X
iajs-727	51	3	]	]	PUNCT
iajs-727	51	4	if	if	SCONJ
iajs-727	51	5	f	f	PROPN
iajs-727	51	6			PROPN
iajs-727	51	7	2-periodic	2-periodic	NUM
iajs-727	51	8	bounded	bound	VERB
iajs-727	51	9	measurable	measurable	ADJ
iajs-727	51	10	function	function	NOUN
iajs-727	51	11	,	,	PUNCT
iajs-727	51	12	then	then	ADV
iajs-727	51	13	for	for	ADP
iajs-727	51	14	(	(	PUNCT
iajs-727	51	15	0	0	PUNCT
iajs-727	51	16	<	<	X
iajs-727	51	17	p	p	X
iajs-727	51	18			NUM
iajs-727	51	19	1	1	NUM
iajs-727	51	20	)	)	PUNCT
iajs-727	51	21	2n,3n	2n,3n	NUM
iajs-727	52	1	k	k	NOUN
iajs-727	53	1	pp	pp	ADV
iajs-727	53	2	1	1	NUM
iajs-727	53	3	f	f	NOUN
iajs-727	53	4	v	v	NOUN
iajs-727	53	5	(	(	PUNCT
iajs-727	53	6	f	f	PROPN
iajs-727	53	7	)	)	PUNCT
iajs-727	53	8	c(p	c(p	PROPN
iajs-727	53	9	,	,	PUNCT
iajs-727	53	10	k	k	NOUN
iajs-727	53	11	,	,	PUNCT
iajs-727	53	12	)	)	PUNCT
iajs-727	53	13	(	(	PUNCT
iajs-727	53	14	f	f	NOUN
iajs-727	53	15	,	,	PUNCT
iajs-727	53	16	)	)	PUNCT
iajs-727	53	17	2n	2n	NUM
iajs-727	53	18			PROPN
iajs-727	53	19			PROPN
iajs-727	53	20			ADJ
iajs-727	53	21			NOUN
iajs-727	53	22	,	,	PUNCT
iajs-727	53	23	where	where	SCONJ
iajs-727	53	24	n=1,2	n=1,2	ADJ
iajs-727	53	25	,	,	PUNCT
iajs-727	53	26	…	…	PUNCT
iajs-727	53	27	and	and	CCONJ
iajs-727	53	28	(	(	PUNCT
iajs-727	53	29	p	p	X
iajs-727	53	30	,	,	PUNCT
iajs-727	53	31	k,ℓ	k,ℓ	NOUN
iajs-727	53	32	)	)	PUNCT
iajs-727	53	33	is	be	AUX
iajs-727	53	34	a	a	DET
iajs-727	53	35	constant	constant	ADJ
iajs-727	53	36	depends	depend	VERB
iajs-727	53	37	on	on	ADP
iajs-727	53	38	p	p	X
iajs-727	53	39	,	,	PUNCT
iajs-727	53	40	k	k	PROPN
iajs-727	53	41	and	and	CCONJ
iajs-727	53	42	ℓ.	ℓ.	NOUN
iajs-727	53	43	theorem	theorem	VERB
iajs-727	53	44	1.4	1.4	NUM
iajs-727	53	45	:	:	PUNCT
iajs-727	54	1	[	[	X
iajs-727	54	2	3	3	X
iajs-727	54	3	]	]	PUNCT
iajs-727	54	4	let	let	VERB
iajs-727	54	5	f	f	PRON
iajs-727	54	6	be	be	AUX
iajs-727	54	7	2-periodic	2-periodic	NUM
iajs-727	54	8	bounded	bounded	ADJ
iajs-727	54	9	measurable	measurable	ADJ
iajs-727	54	10	function	function	NOUN
iajs-727	54	11	,	,	PUNCT
iajs-727	54	12	then	then	ADV
iajs-727	54	13	for	for	ADP
iajs-727	54	14	(	(	PUNCT
iajs-727	54	15	0	0	PUNCT
iajs-727	54	16	<	<	X
iajs-727	54	17	p	p	X
iajs-727	54	18			NUM
iajs-727	54	19	1	1	NUM
iajs-727	54	20	)	)	PUNCT
iajs-727	54	21	,	,	PUNCT
iajs-727	54	22	we	we	PRON
iajs-727	54	23	have	have	VERB
iajs-727	54	24	n	n	ADV
iajs-727	55	1	k	k	NOUN
iajs-727	56	1	pp	pp	ADV
iajs-727	57	1	1	1	NUM
iajs-727	58	1	f	f	NOUN
iajs-727	59	1	i	i	PRON
iajs-727	59	2	(	(	PUNCT
iajs-727	59	3	f	f	PROPN
iajs-727	59	4	)	)	PUNCT
iajs-727	59	5	c(p	c(p	PROPN
iajs-727	59	6	,	,	PUNCT
iajs-727	59	7	k	k	NOUN
iajs-727	59	8	,	,	PUNCT
iajs-727	59	9	)	)	PUNCT
iajs-727	59	10	(	(	PUNCT
iajs-727	59	11	f	f	NOUN
iajs-727	59	12	,	,	PUNCT
iajs-727	59	13	)	)	PUNCT
iajs-727	59	14	n	n	CCONJ
iajs-727	59	15			PROPN
iajs-727	59	16			NOUN
iajs-727	59	17			ADJ
iajs-727	59	18			NOUN
iajs-727	59	19	,	,	PUNCT
iajs-727	59	20	where	where	SCONJ
iajs-727	59	21	p	p	X
iajs-727	59	22	,	,	PUNCT
iajs-727	59	23	k,ℓ	k,ℓ	NOUN
iajs-727	59	24	is	be	AUX
iajs-727	59	25	a	a	DET
iajs-727	59	26	constant	constant	ADJ
iajs-727	59	27	depends	depend	VERB
iajs-727	59	28	on	on	ADP
iajs-727	59	29	p	p	X
iajs-727	59	30	,	,	PUNCT
iajs-727	59	31	k	k	PROPN
iajs-727	59	32	and	and	CCONJ
iajs-727	59	33	ℓ.	ℓ.	ADJ
iajs-727	59	34	main	main	ADJ
iajs-727	59	35	results	result	NOUN
iajs-727	59	36	we	we	PRON
iajs-727	59	37	shall	shall	AUX
iajs-727	59	38	prove	prove	VERB
iajs-727	59	39	direct	direct	ADJ
iajs-727	59	40	inequality	inequality	NOUN
iajs-727	59	41	to	to	PART
iajs-727	59	42	find	find	VERB
iajs-727	59	43	the	the	DET
iajs-727	59	44	degree	degree	NOUN
iajs-727	59	45	of	of	ADP
iajs-727	59	46	approximation	approximation	NOUN
iajs-727	59	47	of	of	ADP
iajs-727	59	48	2-periodic	2-periodic	NUM
iajs-727	59	49	entire	entire	ADJ
iajs-727	59	50	function	function	NOUN
iajs-727	59	51	by	by	ADP
iajs-727	59	52	some	some	DET
iajs-727	59	53	discrete	discrete	ADJ
iajs-727	59	54	operators	operator	NOUN
iajs-727	59	55	in	in	ADP
iajs-727	59	56	(	(	PUNCT
iajs-727	59	57	l,p	l,p	ADJ
iajs-727	59	58	)	)	PUNCT
iajs-727	59	59	spaces	space	NOUN
iajs-727	59	60	,	,	PUNCT
iajs-727	59	61	(	(	PUNCT
iajs-727	59	62	0	0	PUNCT
iajs-727	59	63	<	<	X
iajs-727	59	64	p	p	X
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iajs-727	60	1	lemma	lemma	PROPN
iajs-727	60	2	2.1	2.1	NUM
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iajs-727	60	4	let	let	VERB
iajs-727	60	5	f	f	PRON
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iajs-727	60	14	0	0	PUNCT
iajs-727	60	15	<	<	X
iajs-727	60	16	p	p	X
iajs-727	60	17			NUM
iajs-727	60	18	1	1	NUM
iajs-727	60	19	)	)	PUNCT
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iajs-727	60	23	k	k	PROPN
iajs-727	60	24	p	p	PROPN
iajs-727	60	25	k	k	PROPN
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iajs-727	60	27	p	p	PROPN
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iajs-727	60	29	1	1	NUM
iajs-727	60	30	(	(	PUNCT
iajs-727	60	31	f	f	NOUN
iajs-727	60	32	,	,	PUNCT
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iajs-727	60	34	(	(	PUNCT
iajs-727	60	35	f	f	NOUN
iajs-727	60	36	,	,	PUNCT
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iajs-727	61	3			NUM
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iajs-727	61	5			NOUN
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iajs-727	61	7	:	:	PUNCT
iajs-727	62	1	k	k	PROPN
iajs-727	62	2	p	p	X
iajs-727	63	1	k	k	PROPN
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iajs-727	63	3	k	k	PROPN
iajs-727	63	4	h	h	NOUN
iajs-727	63	5	p	p	PROPN
iajs-727	64	1	k	k	PROPN
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iajs-727	65	2	k	k	NOUN
iajs-727	66	1	i	i	VERB
iajs-727	66	2	0	0	PUNCT
iajs-727	67	1	p	p	X
iajs-727	67	2	p	p	X
iajs-727	67	3	k	k	PROPN
iajs-727	68	1	i	i	PRON
iajs-727	68	2	k	k	NOUN
iajs-727	69	1	i	i	VERB
iajs-727	69	2	0	0	NUM
iajs-727	69	3	1	1	NUM
iajs-727	69	4	1	1	NUM
iajs-727	69	5	(	(	PUNCT
iajs-727	69	6	f	f	PROPN
iajs-727	69	7	,	,	PUNCT
iajs-727	69	8	)	)	PUNCT
iajs-727	69	9	w	w	X
iajs-727	69	10	(	(	PUNCT
iajs-727	69	11	f	f	PROPN
iajs-727	69	12	,	,	PUNCT
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iajs-727	70	1	n	n	CCONJ
iajs-727	71	1	n	n	NOUN
iajs-727	71	2	k	k	NOUN
iajs-727	72	1	k	k	PROPN
iajs-727	72	2	sup	sup	PROPN
iajs-727	72	3	f	f	PROPN
iajs-727	72	4	(	(	PUNCT
iajs-727	72	5	t	t	PROPN
iajs-727	72	6	)	)	PUNCT
iajs-727	72	7	;	;	PUNCT
iajs-727	72	8	t	t	PROPN
iajs-727	72	9	,	,	PUNCT
iajs-727	72	10	t	t	PROPN
iajs-727	72	11	kh	kh	PROPN
iajs-727	72	12	x	x	X
iajs-727	72	13	,	,	PUNCT
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iajs-727	72	15	x	x	SYM
iajs-727	72	16	2n	2n	NUM
iajs-727	72	17	2n	2n	NUM
iajs-727	73	1	k	k	X
iajs-727	73	2	k	k	PROPN
iajs-727	73	3	k	k	PROPN
iajs-727	73	4	sup	sup	PROPN
iajs-727	73	5	(	(	PUNCT
iajs-727	73	6	1	1	NUM
iajs-727	73	7	)	)	PUNCT
iajs-727	73	8	f	f	NOUN
iajs-727	73	9	(	(	PUNCT
iajs-727	73	10	t	t	PROPN
iajs-727	73	11	ih	ih	PROPN
iajs-727	73	12	)	)	PUNCT
iajs-727	73	13	;	;	PUNCT
iajs-727	74	1	t	t	PROPN
iajs-727	74	2	,	,	PUNCT
iajs-727	74	3	t	t	PROPN
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iajs-727	74	5	x	x	X
iajs-727	74	6	,	,	PUNCT
iajs-727	74	7	x	x	PUNCT
iajs-727	74	8	x	x	PUNCT
iajs-727	74	9	i	i	PRON
iajs-727	74	10	2n	2n	NUM
iajs-727	74	11	2n	2n	NUM
iajs-727	75	1	k	k	X
iajs-727	75	2	k	k	PROPN
iajs-727	75	3	k	k	PROPN
iajs-727	75	4	sup	sup	PROPN
iajs-727	75	5	(	(	PUNCT
iajs-727	75	6	1	1	NUM
iajs-727	75	7	)	)	PUNCT
iajs-727	75	8	f	f	NOUN
iajs-727	75	9	(	(	PUNCT
iajs-727	75	10	t	t	PROPN
iajs-727	75	11	ih	ih	PROPN
iajs-727	75	12	)	)	PUNCT
iajs-727	75	13	;	;	PUNCT
iajs-727	76	1	t	t	PROPN
iajs-727	76	2	,	,	PUNCT
iajs-727	76	3	t	t	PROPN
iajs-727	76	4	kh	kh	PROPN
iajs-727	76	5	x	x	X
iajs-727	76	6	,	,	PUNCT
iajs-727	76	7	x	x	PUNCT
iajs-727	76	8	x	x	PUNCT
iajs-727	76	9	i	i	PRON
iajs-727	76	10	2n	2n	NUM
iajs-727	76	11	2n	2n	NUM
iajs-727	76	12			ADV
iajs-727	76	13			PROPN
iajs-727	76	14			VERB
iajs-727	76	15			ADV
iajs-727	76	16			NOUN
iajs-727	76	17			ADP
iajs-727	76	18			VERB
iajs-727	76	19			VERB
iajs-727	76	20			NOUN
iajs-727	76	21			NOUN
iajs-727	76	22			VERB
iajs-727	76	23			PROPN
iajs-727	76	24			PROPN
iajs-727	76	25			PUNCT
iajs-727	76	26			PROPN
iajs-727	76	27			VERB
iajs-727	77	1			DET
iajs-727	77	2			ADJ
iajs-727	78	1			PROPN
iajs-727	78	2			ADP
iajs-727	78	3			PROPN
iajs-727	78	4			VERB
iajs-727	78	5			ADJ
iajs-727	78	6			PRON
iajs-727	78	7			PROPN
iajs-727	78	8			PROPN
iajs-727	78	9			ADV
iajs-727	78	10			PUNCT
iajs-727	78	11			PROPN
iajs-727	78	12			PROPN
iajs-727	78	13			PUNCT
iajs-727	78	14			PROPN
iajs-727	78	15			PROPN
iajs-727	78	16			ADJ
iajs-727	78	17			NOUN
iajs-727	78	18			NOUN
iajs-727	78	19			NOUN
iajs-727	78	20			PUNCT
iajs-727	78	21			VERB
iajs-727	78	22			NOUN
iajs-727	78	23			PROPN
iajs-727	78	24			ADP
iajs-727	78	25			NOUN
iajs-727	78	26			PROPN
iajs-727	78	27			PART
iajs-727	78	28			VERB
iajs-727	78	29			PROPN
iajs-727	78	30			PROPN
iajs-727	78	31			ADV
iajs-727	78	32			PUNCT
iajs-727	78	33			PROPN
iajs-727	78	34			PROPN
iajs-727	78	35			PUNCT
iajs-727	78	36			PROPN
iajs-727	78	37			PROPN
iajs-727	78	38			PROPN
iajs-727	78	39			NOUN
iajs-727	78	40			PROPN
iajs-727	78	41			PROPN
iajs-727	78	42			PROPN
iajs-727	78	43			PROPN
iajs-727	78	44			X
iajs-727	78	45			X
iajs-727	78	46			PROPN
iajs-727	78	47	1	1	NUM
iajs-727	78	48	p	p	NOUN
iajs-727	78	49	x	x	SYM
iajs-727	78	50	1	1	NUM
iajs-727	78	51	p	p	NOUN
iajs-727	78	52	ppk	ppk	NOUN
iajs-727	79	1	i	i	NOUN
iajs-727	79	2	k	k	NOUN
iajs-727	80	1	i	i	PRON
iajs-727	80	2	0x	0x	VERB
iajs-727	80	3	k	k	PROPN
iajs-727	80	4	h	h	PROPN
iajs-727	80	5	,	,	PUNCT
iajs-727	80	6	p	p	PROPN
iajs-727	80	7	k	k	PROPN
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iajs-727	80	9	p	p	PROPN
iajs-727	80	10	k	k	PROPN
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iajs-727	80	12	p	p	PROPN
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iajs-727	81	1	k	k	PROPN
iajs-727	81	2	k	k	PROPN
iajs-727	82	1	k	k	PROPN
iajs-727	82	2	k	k	PROPN
iajs-727	82	3	k	k	PROPN
iajs-727	82	4	sup	sup	NOUN
iajs-727	82	5	sup	sup	NOUN
iajs-727	82	6	(	(	PUNCT
iajs-727	82	7	1	1	NUM
iajs-727	82	8	)	)	PUNCT
iajs-727	82	9	f	f	NOUN
iajs-727	82	10	(	(	PUNCT
iajs-727	82	11	t	t	PROPN
iajs-727	82	12	ih	ih	PROPN
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iajs-727	82	14	;	;	PUNCT
iajs-727	83	1	t	t	PROPN
iajs-727	83	2	,	,	PUNCT
iajs-727	83	3	t	t	PROPN
iajs-727	83	4	kh	kh	PROPN
iajs-727	83	5	y	y	PROPN
iajs-727	83	6	,	,	PUNCT
iajs-727	83	7	y	y	PROPN
iajs-727	83	8	x	x	SYM
iajs-727	83	9	y	y	NOUN
iajs-727	83	10	x	x	INTJ
iajs-727	83	11	,	,	PUNCT
iajs-727	83	12	x	x	X
iajs-727	83	13	dx	dx	PROPN
iajs-727	83	14	i	i	PROPN
iajs-727	83	15	2n	2n	NUM
iajs-727	83	16	2n	2n	NUM
iajs-727	83	17	2n	2n	NUM
iajs-727	83	18	2n	2n	NUM
iajs-727	83	19	k	k	X
iajs-727	84	1	k	k	PROPN
iajs-727	84	2	sup	sup	PROPN
iajs-727	84	3	f	f	PROPN
iajs-727	84	4	(	(	PUNCT
iajs-727	84	5	t	t	PROPN
iajs-727	84	6	)	)	PUNCT
iajs-727	84	7	;	;	PUNCT
iajs-727	84	8	t	t	PROPN
iajs-727	84	9	,	,	PUNCT
iajs-727	84	10	t	t	PROPN
iajs-727	84	11	kh	kh	PROPN
iajs-727	84	12	x	x	X
iajs-727	84	13	,	,	PUNCT
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iajs-727	84	15	x	x	SYM
iajs-727	84	16	2n	2n	NUM
iajs-727	84	17	2n	2n	NUM
iajs-727	84	18	1	1	NUM
iajs-727	84	19	w	w	NOUN
iajs-727	84	20	(	(	PUNCT
iajs-727	84	21	f	f	PROPN
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iajs-727	84	25	)	)	PUNCT
iajs-727	85	1	n	n	ADV
iajs-727	85	2	1	1	NUM
iajs-727	85	3	(	(	PUNCT
iajs-727	85	4	f	f	PROPN
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iajs-727	85	6	)	)	PUNCT
iajs-727	86	1	n	n	CCONJ
iajs-727	86	2			ADP
iajs-727	87	1			NUM
iajs-727	87	2			NOUN
iajs-727	87	3			NOUN
iajs-727	87	4			PROPN
iajs-727	88	1			PROPN
iajs-727	89	1			PROPN
iajs-727	89	2			PROPN
iajs-727	90	1			PROPN
iajs-727	90	2			PROPN
iajs-727	90	3			NOUN
iajs-727	90	4			PROPN
iajs-727	90	5			NOUN
iajs-727	90	6			PROPN
iajs-727	90	7			PROPN
iajs-727	90	8			X
iajs-727	90	9			PROPN
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iajs-727	90	11			ADJ
iajs-727	90	12			PROPN
iajs-727	90	13			PUNCT
iajs-727	90	14			PUNCT
iajs-727	90	15			PROPN
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iajs-727	90	17			VERB
iajs-727	90	18			PUNCT
iajs-727	90	19			NOUN
iajs-727	90	20			NOUN
iajs-727	90	21			VERB
iajs-727	90	22			NOUN
iajs-727	90	23			PRON
iajs-727	90	24			NOUN
iajs-727	90	25			NOUN
iajs-727	90	26			NOUN
iajs-727	90	27			NOUN
iajs-727	90	28			PROPN
iajs-727	90	29			PROPN
iajs-727	90	30			VERB
iajs-727	90	31			PROPN
iajs-727	90	32			PROPN
iajs-727	90	33			PROPN
iajs-727	90	34			NOUN
iajs-727	90	35			VERB
iajs-727	90	36			VERB
iajs-727	91	1			NOUN
iajs-727	91	2			NOUN
iajs-727	91	3			NOUN
iajs-727	91	4			VERB
iajs-727	91	5			PROPN
iajs-727	91	6			PROPN
iajs-727	91	7			PUNCT
iajs-727	91	8			PROPN
iajs-727	91	9			VERB
iajs-727	91	10			NOUN
iajs-727	91	11			VERB
iajs-727	92	1			NOUN
iajs-727	93	1			NOUN
iajs-727	94	1			NOUN
iajs-727	94	2			NOUN
iajs-727	94	3			SYM
iajs-727	94	4			PROPN
iajs-727	95	1			NUM
iajs-727	95	2			PROPN
iajs-727	95	3			PROPN
iajs-727	95	4	theorem	theorem	NOUN
iajs-727	95	5	2.2	2.2	NUM
iajs-727	95	6	:	:	PUNCT
iajs-727	95	7	let	let	VERB
iajs-727	95	8	f	f	PRON
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iajs-727	95	11	bounded	bounded	ADJ
iajs-727	95	12	measurable	measurable	ADJ
iajs-727	95	13	entire	entire	ADJ
iajs-727	95	14	function	function	NOUN
iajs-727	95	15	,	,	PUNCT
iajs-727	95	16	(	(	PUNCT
iajs-727	95	17	f	f	PROPN
iajs-727	95	18			PROPN
iajs-727	95	19	l,p	l,p	PROPN
iajs-727	95	20	)	)	PUNCT
iajs-727	95	21	,	,	PUNCT
iajs-727	95	22	(	(	PUNCT
iajs-727	95	23	0	0	PUNCT
iajs-727	95	24	<	<	X
iajs-727	95	25	p	p	X
iajs-727	95	26			NUM
iajs-727	95	27	1	1	NUM
iajs-727	95	28	)	)	PUNCT
iajs-727	95	29	,	,	PUNCT
iajs-727	95	30	we	we	PRON
iajs-727	95	31	have	have	VERB
iajs-727	95	32	ibn	ibn	PROPN
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iajs-727	95	34	j.	j.	PROPN
iajs-727	96	1	fo	fo	ADP
iajs-727	96	2	r	r	NOUN
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iajs-727	96	4	&	&	CCONJ
iajs-727	96	5	appl	appl	PROPN
iajs-727	96	6	.	.	PUNCT
iajs-727	97	1	sc	sc	PROPN
iajs-727	97	2	i.	i.	PROPN
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iajs-727	97	5	3	3	NUM
iajs-727	97	6	)	)	PUNCT
iajs-727	97	7	2011	2011	NUM
iajs-727	97	8	n	n	SYM
iajs-727	97	9	1	1	NUM
iajs-727	97	10	,	,	PUNCT
iajs-727	97	11	p	p	X
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iajs-727	97	13	p	p	PROPN
iajs-727	97	14	1	1	NUM
iajs-727	97	15	f	f	PROPN
iajs-727	97	16	j	j	PROPN
iajs-727	97	17	(	(	PUNCT
iajs-727	97	18	f	f	PROPN
iajs-727	97	19	)	)	PUNCT
iajs-727	97	20	c(p	c(p	NOUN
iajs-727	97	21	)	)	PUNCT
iajs-727	97	22	(	(	PUNCT
iajs-727	97	23	f	f	X
iajs-727	97	24	,	,	PUNCT
iajs-727	97	25	)	)	PUNCT
iajs-727	97	26	,	,	PUNCT
iajs-727	97	27	n	n	CCONJ
iajs-727	97	28			VERB
iajs-727	97	29			NOUN
iajs-727	97	30			ADV
iajs-727	97	31			NOUN
iajs-727	97	32	where	where	SCONJ
iajs-727	97	33	c(p	c(p	NOUN
iajs-727	97	34	)	)	PUNCT
iajs-727	97	35	is	be	AUX
iajs-727	97	36	a	a	DET
iajs-727	97	37	constant	constant	ADJ
iajs-727	97	38	depends	depend	VERB
iajs-727	97	39	only	only	ADV
iajs-727	97	40	on	on	ADP
iajs-727	97	41	p.	p.	NOUN
iajs-727	97	42	proof	proof	NOUN
iajs-727	97	43	:	:	PUNCT
iajs-727	97	44	by	by	ADP
iajs-727	97	45	theorem	theorem	NOUN
iajs-727	97	46	(	(	PUNCT
iajs-727	97	47	1.1	1.1	NUM
iajs-727	97	48	)	)	PUNCT
iajs-727	97	49	,	,	PUNCT
iajs-727	97	50	we	we	PRON
iajs-727	97	51	get	get	VERB
iajs-727	97	52	1	1	NUM
iajs-727	97	53	1	1	NUM
iajs-727	97	54	p	p	NOUN
iajs-727	97	55	p	p	PROPN
iajs-727	97	56	p	p	PROPN
iajs-727	97	57	n	n	CCONJ
iajs-727	97	58	n	n	CCONJ
iajs-727	97	59	,	,	PUNCT
iajs-727	97	60	p	p	X
iajs-727	97	61	p	p	X
iajs-727	97	62	f	f	PROPN
iajs-727	97	63	j	j	PROPN
iajs-727	97	64	(	(	PUNCT
iajs-727	97	65	f	f	PROPN
iajs-727	97	66	)	)	PUNCT
iajs-727	97	67	c(p)[1	c(p)[1	NOUN
iajs-727	97	68	(	(	PUNCT
iajs-727	97	69	1	1	NUM
iajs-727	97	70	_	_	NUM
iajs-727	97	71	n	n	NUM
iajs-727	97	72	)	)	PUNCT
iajs-727	97	73	(	(	PUNCT
iajs-727	97	74	n	n	X
iajs-727	97	75	)	)	PUNCT
iajs-727	97	76	]	]	PUNCT
iajs-727	98	1	f	f	X
iajs-727	98	2	j	j	PROPN
iajs-727	98	3	(	(	PUNCT
iajs-727	98	4	f	f	PROPN
iajs-727	98	5	)	)	PUNCT
iajs-727	98	6	.	.	PUNCT
iajs-727	99	1			NOUN
iajs-727	99	2			VERB
iajs-727	99	3			PROPN
iajs-727	99	4			NUM
iajs-727	99	5			NUM
iajs-727	99	6			NUM
iajs-727	99	7	now	now	ADV
iajs-727	99	8	since	since	SCONJ
iajs-727	99	9	(	(	PUNCT
iajs-727	99	10			NUM
iajs-727	99	11	>	>	X
iajs-727	99	12	0	0	NUM
iajs-727	99	13	)	)	PUNCT
iajs-727	99	14	,	,	PUNCT
iajs-727	99	15	then	then	ADV
iajs-727	99	16	n	n	PROPN
iajs-727	99	17	1	1	NUM
iajs-727	99	18	n	n	CCONJ
iajs-727	99	19	,	,	PUNCT
iajs-727	99	20	p	p	X
iajs-727	99	21	p	p	X
iajs-727	99	22	f	f	PROPN
iajs-727	99	23	j	j	PROPN
iajs-727	99	24	(	(	PUNCT
iajs-727	99	25	f	f	PROPN
iajs-727	99	26	)	)	PUNCT
iajs-727	99	27	c	c	NOUN
iajs-727	99	28	(	(	PUNCT
iajs-727	99	29	p	p	NOUN
iajs-727	99	30	)	)	PUNCT
iajs-727	100	1	f	f	PROPN
iajs-727	100	2	j	j	PROPN
iajs-727	100	3	(	(	PUNCT
iajs-727	100	4	f	f	PROPN
iajs-727	100	5	)	)	PUNCT
iajs-727	100	6	.	.	PUNCT
iajs-727	101	1			NOUN
iajs-727	101	2			VERB
iajs-727	101	3			VERB
iajs-727	101	4	then	then	ADV
iajs-727	101	5	by	by	ADP
iajs-727	101	6	using	use	VERB
iajs-727	101	7	theorem	theorem	NOUN
iajs-727	101	8	(	(	PUNCT
iajs-727	101	9	1.2	1.2	NUM
iajs-727	101	10	)	)	PUNCT
iajs-727	101	11	and	and	CCONJ
iajs-727	101	12	lemma	lemma	PROPN
iajs-727	101	13	(	(	PUNCT
iajs-727	101	14	2.1	2.1	NUM
iajs-727	101	15	)	)	PUNCT
iajs-727	101	16	,	,	PUNCT
iajs-727	101	17	we	we	PRON
iajs-727	101	18	get	get	VERB
iajs-727	101	19	that	that	PRON
iajs-727	101	20	n	n	PROPN
iajs-727	101	21	2	2	NUM
iajs-727	101	22	1	1	NUM
iajs-727	101	23	p	p	NOUN
iajs-727	101	24	,	,	PUNCT
iajs-727	101	25	p	p	NOUN
iajs-727	101	26	1	1	NUM
iajs-727	101	27	,	,	PUNCT
iajs-727	102	1	p	p	NOUN
iajs-727	102	2	1	1	NUM
iajs-727	102	3	f	f	PROPN
iajs-727	102	4	j	j	PROPN
iajs-727	102	5	(	(	PUNCT
iajs-727	102	6	f	f	PROPN
iajs-727	102	7	)	)	PUNCT
iajs-727	102	8	c	c	NOUN
iajs-727	102	9	(	(	PUNCT
iajs-727	102	10	p	p	NOUN
iajs-727	102	11	)	)	PUNCT
iajs-727	102	12	(	(	PUNCT
iajs-727	102	13	f	f	PROPN
iajs-727	102	14	,	,	PUNCT
iajs-727	102	15	)	)	PUNCT
iajs-727	102	16	n	n	CCONJ
iajs-727	102	17	1	1	NUM
iajs-727	102	18	c(p	c(p	NOUN
iajs-727	102	19	)	)	PUNCT
iajs-727	102	20	(	(	PUNCT
iajs-727	102	21	f	f	X
iajs-727	102	22	,	,	PUNCT
iajs-727	102	23	)	)	PUNCT
iajs-727	102	24	n	n	CCONJ
iajs-727	102	25			VERB
iajs-727	102	26			NOUN
iajs-727	102	27			NOUN
iajs-727	102	28			NUM
iajs-727	102	29			ADJ
iajs-727	102	30			NOUN
iajs-727	102	31			NOUN
iajs-727	102	32	theorem	theorem	VERB
iajs-727	102	33	2.3	2.3	NUM
iajs-727	102	34	:	:	PUNCT
iajs-727	102	35	let	let	VERB
iajs-727	102	36	f	f	PRON
iajs-727	102	37	be	be	AUX
iajs-727	102	38	2-periodic	2-periodic	NUM
iajs-727	102	39	bounded	bounded	ADJ
iajs-727	102	40	measurable	measurable	ADJ
iajs-727	102	41	entire	entire	ADJ
iajs-727	102	42	function	function	NOUN
iajs-727	102	43	,	,	PUNCT
iajs-727	102	44	(	(	PUNCT
iajs-727	102	45	f	f	PROPN
iajs-727	102	46			PROPN
iajs-727	102	47	l,p	l,p	PROPN
iajs-727	102	48	)	)	PUNCT
iajs-727	102	49	,	,	PUNCT
iajs-727	102	50	(	(	PUNCT
iajs-727	102	51	0	0	PUNCT
iajs-727	102	52	<	<	X
iajs-727	102	53	p	p	X
iajs-727	102	54			NUM
iajs-727	102	55	1	1	NUM
iajs-727	102	56	)	)	PUNCT
iajs-727	102	57	,	,	PUNCT
iajs-727	102	58	we	we	PRON
iajs-727	102	59	have	have	VERB
iajs-727	102	60	2n,3n	2n,3n	NUM
iajs-727	102	61	k	k	PROPN
iajs-727	102	62	,	,	PUNCT
iajs-727	102	63	p	p	X
iajs-727	102	64	,	,	PUNCT
iajs-727	102	65	p	p	PROPN
iajs-727	102	66	1	1	NUM
iajs-727	102	67	f	f	NOUN
iajs-727	102	68	v	v	NOUN
iajs-727	102	69	(	(	PUNCT
iajs-727	102	70	f	f	PROPN
iajs-727	102	71	)	)	PUNCT
iajs-727	102	72	c(p	c(p	PROPN
iajs-727	102	73	,	,	PUNCT
iajs-727	102	74	k	k	NOUN
iajs-727	102	75	,	,	PUNCT
iajs-727	102	76	)	)	PUNCT
iajs-727	102	77	(	(	PUNCT
iajs-727	102	78	f	f	X
iajs-727	102	79	,	,	PUNCT
iajs-727	102	80	)	)	PUNCT
iajs-727	102	81	,	,	PUNCT
iajs-727	102	82	2n	2n	NUM
iajs-727	102	83			PROPN
iajs-727	102	84			NOUN
iajs-727	102	85			VERB
iajs-727	102	86			PRON
iajs-727	102	87			NOUN
iajs-727	102	88	where	where	SCONJ
iajs-727	102	89	p	p	X
iajs-727	102	90	,	,	PUNCT
iajs-727	102	91	k,ℓ	k,ℓ	NOUN
iajs-727	102	92	is	be	AUX
iajs-727	102	93	a	a	DET
iajs-727	102	94	constant	constant	ADJ
iajs-727	102	95	depends	depend	VERB
iajs-727	102	96	on	on	ADP
iajs-727	102	97	p	p	X
iajs-727	102	98	,	,	PUNCT
iajs-727	102	99	k	k	PROPN
iajs-727	102	100	and	and	CCONJ
iajs-727	102	101	ℓ.	ℓ.	NOUN
iajs-727	102	102	proof	proof	NOUN
iajs-727	102	103	:	:	PUNCT
iajs-727	102	104	by	by	ADP
iajs-727	102	105	using	use	VERB
iajs-727	102	106	theorem	theorem	NOUN
iajs-727	102	107	(	(	PUNCT
iajs-727	102	108	1.1	1.1	NUM
iajs-727	102	109	)	)	PUNCT
iajs-727	102	110	,	,	PUNCT
iajs-727	102	111	we	we	PRON
iajs-727	102	112	get	get	VERB
iajs-727	102	113	1	1	NUM
iajs-727	102	114	1	1	NUM
iajs-727	102	115	p	p	NOUN
iajs-727	102	116	p	p	X
iajs-727	102	117	p	p	X
iajs-727	102	118	2n,3n	2n,3n	NUM
iajs-727	102	119	1	1	NUM
iajs-727	102	120	2n,3n	2n,3n	NUM
iajs-727	102	121	,	,	PUNCT
iajs-727	102	122	p	p	X
iajs-727	103	1	p	p	X
iajs-727	103	2	f	f	X
iajs-727	103	3	v	v	X
iajs-727	103	4	(	(	PUNCT
iajs-727	103	5	f	f	PROPN
iajs-727	103	6	)	)	PUNCT
iajs-727	103	7	c	c	NOUN
iajs-727	103	8	(	(	PUNCT
iajs-727	103	9	p)[1	p)[1	PROPN
iajs-727	103	10	(	(	PUNCT
iajs-727	103	11	1	1	NUM
iajs-727	103	12	n	n	NOUN
iajs-727	103	13	)	)	PUNCT
iajs-727	103	14	(	(	PUNCT
iajs-727	103	15	n	n	X
iajs-727	103	16	)	)	PUNCT
iajs-727	103	17	]	]	PUNCT
iajs-727	104	1	f	f	X
iajs-727	104	2	v	v	X
iajs-727	104	3	(	(	PUNCT
iajs-727	104	4	f	f	NOUN
iajs-727	104	5	)	)	PUNCT
iajs-727	104	6			PROPN
iajs-727	104	7			PROPN
iajs-727	104	8			ADV
iajs-727	104	9			VERB
iajs-727	104	10			PROPN
iajs-727	104	11			NUM
iajs-727	104	12			PROPN
iajs-727	104	13			NUM
iajs-727	104	14	.	.	PUNCT
iajs-727	105	1	since	since	SCONJ
iajs-727	105	2	1	1	NUM
iajs-727	105	3	n	n	DET
iajs-727	105	4			NUM
iajs-727	105	5			NOUN
iajs-727	105	6	,	,	PUNCT
iajs-727	105	7	then	then	ADV
iajs-727	105	8	2n,3n	2n,3n	NUM
iajs-727	105	9	2	2	NUM
iajs-727	105	10	2n,3n	2n,3n	NUM
iajs-727	105	11	,	,	PUNCT
iajs-727	105	12	p	p	X
iajs-727	105	13	p	p	X
iajs-727	105	14	f	f	X
iajs-727	105	15	v	v	X
iajs-727	105	16	(	(	PUNCT
iajs-727	105	17	f	f	PROPN
iajs-727	105	18	)	)	PUNCT
iajs-727	105	19	c	c	NOUN
iajs-727	105	20	(	(	PUNCT
iajs-727	105	21	p	p	NOUN
iajs-727	105	22	)	)	PUNCT
iajs-727	105	23	f	f	PROPN
iajs-727	105	24	v	v	X
iajs-727	105	25	(	(	PUNCT
iajs-727	105	26	f	f	NOUN
iajs-727	105	27	)	)	PUNCT
iajs-727	105	28	.	.	NOUN
iajs-727	106	1			NOUN
iajs-727	106	2			VERB
iajs-727	106	3			NUM
iajs-727	106	4	now	now	ADV
iajs-727	106	5	by	by	ADP
iajs-727	106	6	using	use	VERB
iajs-727	106	7	theorem	theorem	NOUN
iajs-727	106	8	(	(	PUNCT
iajs-727	106	9	1.3	1.3	NUM
iajs-727	106	10	)	)	PUNCT
iajs-727	106	11	and	and	CCONJ
iajs-727	106	12	lemma	lemma	PROPN
iajs-727	106	13	(	(	PUNCT
iajs-727	106	14	2.1	2.1	NUM
iajs-727	106	15	)	)	PUNCT
iajs-727	106	16	,	,	PUNCT
iajs-727	106	17	we	we	PRON
iajs-727	106	18	have	have	VERB
iajs-727	106	19	2n,3n	2n,3n	NUM
iajs-727	107	1	k	k	NOUN
iajs-727	108	1	p	p	X
iajs-727	108	2	,	,	PUNCT
iajs-727	108	3	p	p	PROPN
iajs-727	108	4	k	k	PROPN
iajs-727	108	5	,	,	PUNCT
iajs-727	108	6	p	p	PROPN
iajs-727	108	7	1	1	NUM
iajs-727	108	8	f	f	NOUN
iajs-727	108	9	v	v	NOUN
iajs-727	108	10	(	(	PUNCT
iajs-727	108	11	f	f	PROPN
iajs-727	108	12	)	)	PUNCT
iajs-727	108	13	c(p	c(p	PROPN
iajs-727	108	14	,	,	PUNCT
iajs-727	108	15	k	k	NOUN
iajs-727	108	16	,	,	PUNCT
iajs-727	108	17	)	)	PUNCT
iajs-727	108	18	(	(	PUNCT
iajs-727	108	19	f	f	X
iajs-727	108	20	,	,	PUNCT
iajs-727	108	21	)	)	PUNCT
iajs-727	108	22	2n	2n	NUM
iajs-727	108	23	1	1	NUM
iajs-727	108	24	c(p	c(p	NOUN
iajs-727	108	25	,	,	PUNCT
iajs-727	108	26	k	k	NOUN
iajs-727	108	27	,	,	PUNCT
iajs-727	108	28	)	)	PUNCT
iajs-727	108	29	(	(	PUNCT
iajs-727	108	30	f	f	X
iajs-727	108	31	,	,	PUNCT
iajs-727	108	32	)	)	PUNCT
iajs-727	108	33	.	.	PUNCT
iajs-727	109	1	2n	2n	NUM
iajs-727	109	2			PROPN
iajs-727	109	3			PROPN
iajs-727	109	4			NOUN
iajs-727	109	5			X
iajs-727	109	6			ADJ
iajs-727	109	7			PROPN
iajs-727	109	8			ADJ
iajs-727	109	9			NOUN
iajs-727	109	10			NOUN
iajs-727	109	11	theorem	theorem	VERB
iajs-727	109	12	2.4	2.4	NUM
iajs-727	109	13	:	:	PUNCT
iajs-727	109	14	let	let	VERB
iajs-727	109	15	f	f	PRON
iajs-727	109	16	be	be	AUX
iajs-727	109	17	2-periodic	2-periodic	NUM
iajs-727	109	18	bounded	bounded	ADJ
iajs-727	109	19	measurable	measurable	ADJ
iajs-727	109	20	entire	entire	ADJ
iajs-727	109	21	function	function	NOUN
iajs-727	109	22	,	,	PUNCT
iajs-727	109	23	(	(	PUNCT
iajs-727	109	24	f	f	PROPN
iajs-727	109	25			PROPN
iajs-727	109	26	l,p	l,p	PROPN
iajs-727	109	27	)	)	PUNCT
iajs-727	109	28	,	,	PUNCT
iajs-727	109	29	(	(	PUNCT
iajs-727	109	30	0	0	PUNCT
iajs-727	109	31	<	<	X
iajs-727	109	32	p	p	X
iajs-727	109	33			NUM
iajs-727	109	34	1	1	NUM
iajs-727	109	35	)	)	PUNCT
iajs-727	109	36	,	,	PUNCT
iajs-727	109	37	we	we	PRON
iajs-727	109	38	have	have	VERB
iajs-727	109	39	n	n	PROPN
iajs-727	109	40	k	k	NOUN
iajs-727	109	41	,	,	PUNCT
iajs-727	109	42	p	p	X
iajs-727	109	43	,	,	PUNCT
iajs-727	109	44	p	p	PROPN
iajs-727	110	1	1	1	NUM
iajs-727	110	2	f	f	X
iajs-727	111	1	i	i	PRON
iajs-727	111	2	(	(	PUNCT
iajs-727	111	3	f	f	PROPN
iajs-727	111	4	)	)	PUNCT
iajs-727	111	5	c(p	c(p	PROPN
iajs-727	111	6	,	,	PUNCT
iajs-727	111	7	k	k	NOUN
iajs-727	111	8	,	,	PUNCT
iajs-727	111	9	)	)	PUNCT
iajs-727	111	10	(	(	PUNCT
iajs-727	111	11	f	f	NOUN
iajs-727	111	12	,	,	PUNCT
iajs-727	111	13	)	)	PUNCT
iajs-727	111	14	2n	2n	NUM
iajs-727	111	15			X
iajs-727	111	16			NUM
iajs-727	111	17			NOUN
iajs-727	111	18			NOUN
iajs-727	111	19	,	,	PUNCT
iajs-727	111	20	where	where	SCONJ
iajs-727	111	21	p	p	X
iajs-727	111	22	,	,	PUNCT
iajs-727	111	23	k,ℓ	k,ℓ	NOUN
iajs-727	111	24	is	be	AUX
iajs-727	111	25	a	a	DET
iajs-727	111	26	constant	constant	ADJ
iajs-727	111	27	depends	depend	VERB
iajs-727	111	28	on	on	ADP
iajs-727	111	29	p	p	X
iajs-727	111	30	,	,	PUNCT
iajs-727	111	31	k	k	PROPN
iajs-727	111	32	and	and	CCONJ
iajs-727	111	33	ℓ.	ℓ.	NOUN
iajs-727	111	34	proof	proof	NOUN
iajs-727	111	35	:	:	PUNCT
iajs-727	111	36	by	by	ADP
iajs-727	111	37	using	use	VERB
iajs-727	111	38	theorem	theorem	NOUN
iajs-727	111	39	(	(	PUNCT
iajs-727	111	40	1.1	1.1	NUM
iajs-727	111	41	)	)	PUNCT
iajs-727	111	42	,	,	PUNCT
iajs-727	111	43	we	we	PRON
iajs-727	111	44	get	get	VERB
iajs-727	111	45	1	1	NUM
iajs-727	111	46	p	p	NOUN
iajs-727	111	47	p	p	NOUN
iajs-727	111	48	n	n	PRON
iajs-727	111	49	1	1	NUM
iajs-727	111	50	p	p	NOUN
iajs-727	111	51	n	n	NOUN
iajs-727	111	52	,	,	PUNCT
iajs-727	111	53	p	p	X
iajs-727	112	1	p	p	X
iajs-727	113	1	f	f	X
iajs-727	114	1	i	i	PRON
iajs-727	114	2	(	(	PUNCT
iajs-727	114	3	f	f	PROPN
iajs-727	114	4	)	)	PUNCT
iajs-727	114	5	c	c	NOUN
iajs-727	114	6	(	(	PUNCT
iajs-727	114	7	p)[1	p)[1	PROPN
iajs-727	114	8	(	(	PUNCT
iajs-727	114	9	1	1	NUM
iajs-727	114	10	n	n	NOUN
iajs-727	114	11	)	)	PUNCT
iajs-727	114	12	(	(	PUNCT
iajs-727	114	13	n	n	X
iajs-727	114	14	)	)	PUNCT
iajs-727	114	15	y	y	PROPN
iajs-727	114	16	]	]	PUNCT
iajs-727	115	1	f	f	X
iajs-727	116	1	i	i	PRON
iajs-727	116	2	(	(	PUNCT
iajs-727	116	3	f)	f)	PROPN
iajs-727	116	4			PROPN
iajs-727	116	5			ADV
iajs-727	116	6			VERB
iajs-727	116	7			PROPN
iajs-727	116	8			NUM
iajs-727	116	9			PROPN
iajs-727	116	10			NUM
iajs-727	116	11	.	.	PUNCT
iajs-727	117	1	since	since	SCONJ
iajs-727	117	2	1	1	NUM
iajs-727	117	3	n	n	DET
iajs-727	117	4			NUM
iajs-727	117	5			NOUN
iajs-727	117	6	,	,	PUNCT
iajs-727	117	7	then	then	ADV
iajs-727	117	8	n	n	PROPN
iajs-727	117	9	2	2	NUM
iajs-727	117	10	n	n	CCONJ
iajs-727	117	11	,	,	PUNCT
iajs-727	117	12	p	p	X
iajs-727	117	13	p	p	X
iajs-727	117	14	f	f	X
iajs-727	117	15	i	i	PRON
iajs-727	117	16	(	(	PUNCT
iajs-727	117	17	f	f	PROPN
iajs-727	117	18	)	)	PUNCT
iajs-727	117	19	c	c	NOUN
iajs-727	117	20	(	(	PUNCT
iajs-727	117	21	p	p	X
iajs-727	117	22	)	)	PUNCT
iajs-727	117	23	f	f	NOUN
iajs-727	118	1	i	i	PRON
iajs-727	118	2	(	(	PUNCT
iajs-727	118	3	f	f	PROPN
iajs-727	118	4	)	)	PUNCT
iajs-727	118	5	.	.	PUNCT
iajs-727	119	1			NOUN
iajs-727	119	2			VERB
iajs-727	119	3			VERB
iajs-727	119	4	then	then	ADV
iajs-727	119	5	by	by	ADP
iajs-727	119	6	using	use	VERB
iajs-727	119	7	theorem	theorem	NOUN
iajs-727	119	8	(	(	PUNCT
iajs-727	119	9	1.4	1.4	NUM
iajs-727	119	10	)	)	PUNCT
iajs-727	119	11	and	and	CCONJ
iajs-727	119	12	lemma	lemma	PROPN
iajs-727	119	13	(	(	PUNCT
iajs-727	119	14	2.1	2.1	NUM
iajs-727	119	15	)	)	PUNCT
iajs-727	119	16	,	,	PUNCT
iajs-727	119	17	we	we	PRON
iajs-727	119	18	get	get	VERB
iajs-727	119	19	ibn	ibn	PROPN
iajs-727	119	20	alhaitham	alhaitham	NOUN
iajs-727	119	21	j.	j.	PROPN
iajs-727	120	1	fo	fo	ADP
iajs-727	120	2	r	r	NOUN
iajs-727	120	3	pure	pure	ADJ
iajs-727	120	4	&	&	CCONJ
iajs-727	120	5	appl	appl	PROPN
iajs-727	120	6	.	.	PUNCT
iajs-727	121	1	sc	sc	PROPN
iajs-727	121	2	i.	i.	PROPN
iajs-727	121	3	vol.24	vol.24	PROPN
iajs-727	121	4	(	(	PUNCT
iajs-727	121	5	3	3	NUM
iajs-727	121	6	)	)	PUNCT
iajs-727	121	7	2011	2011	NUM
iajs-727	121	8	n	n	NOUN
iajs-727	121	9	k	k	PROPN
iajs-727	121	10	p	p	X
iajs-727	121	11	,	,	PUNCT
iajs-727	121	12	p	p	PROPN
iajs-727	121	13	k	k	PROPN
iajs-727	121	14	,	,	PUNCT
iajs-727	121	15	p	p	PROPN
iajs-727	121	16	1	1	NUM
iajs-727	121	17	f	f	X
iajs-727	121	18	i	i	PRON
iajs-727	121	19	(	(	PUNCT
iajs-727	121	20	f	f	PROPN
iajs-727	121	21	)	)	PUNCT
iajs-727	121	22	c(p	c(p	PROPN
iajs-727	121	23	,	,	PUNCT
iajs-727	121	24	k	k	NOUN
iajs-727	121	25	,	,	PUNCT
iajs-727	121	26	)	)	PUNCT
iajs-727	121	27	(	(	PUNCT
iajs-727	121	28	f	f	X
iajs-727	121	29	,	,	PUNCT
iajs-727	121	30	)	)	PUNCT
iajs-727	121	31	n	n	CCONJ
iajs-727	121	32	1	1	NUM
iajs-727	121	33	c(p	c(p	NOUN
iajs-727	121	34	,	,	PUNCT
iajs-727	121	35	k	k	NOUN
iajs-727	121	36	,	,	PUNCT
iajs-727	121	37	)	)	PUNCT
iajs-727	121	38	(	(	PUNCT
iajs-727	121	39	f	f	X
iajs-727	121	40	,	,	PUNCT
iajs-727	121	41	)	)	PUNCT
iajs-727	121	42	.	.	PUNCT
iajs-727	122	1	n	n	CCONJ
iajs-727	122	2			VERB
iajs-727	122	3			PROPN
iajs-727	122	4			NOUN
iajs-727	122	5			X
iajs-727	122	6			ADJ
iajs-727	122	7			PROPN
iajs-727	122	8			ADJ
iajs-727	122	9			NOUN
iajs-727	122	10			NOUN
iajs-727	122	11	conclusion	conclusion	NOUN
iajs-727	122	12	we	we	PRON
iajs-727	122	13	found	find	VERB
iajs-727	122	14	the	the	DET
iajs-727	122	15	degree	degree	NOUN
iajs-727	122	16	of	of	ADP
iajs-727	122	17	approximation	approximation	NOUN
iajs-727	122	18	of	of	ADP
iajs-727	122	19	entire	entire	ADJ
iajs-727	122	20	functions	function	NOUN
iajs-727	122	21	by	by	ADP
iajs-727	122	22	using	use	VERB
iajs-727	122	23	jackson	jackson	PROPN
iajs-727	122	24	,	,	PUNCT
iajs-727	122	25	vallee	vallee	PROPN
iajs-727	122	26	pouson	pouson	PROPN
iajs-727	122	27	and	and	CCONJ
iajs-727	122	28	interpolation	interpolation	NOUN
iajs-727	122	29	polynomials	polynomial	NOUN
iajs-727	122	30	in	in	ADP
iajs-727	122	31	locally	locally	ADV
iajs-727	122	32	quasi	quasi	ADJ
iajs-727	122	33	-	-	ADJ
iajs-727	122	34	norms	norms	ADJ
iajs-727	122	35	l,p	l,p	PROPN
iajs-727	122	36	(	(	PUNCT
iajs-727	122	37	0	0	X
iajs-727	122	38	<	<	X
iajs-727	122	39	p	p	X
iajs-727	122	40	<	<	X
iajs-727	122	41	1	1	NUM
iajs-727	122	42	)	)	PUNCT
iajs-727	122	43	.	.	PUNCT
iajs-727	123	1	references	reference	NOUN
iajs-727	123	2	1	1	NUM
iajs-727	123	3	.	.	PUNCT
iajs-727	124	1	al	al	PROPN
iajs-727	124	2	-	-	PUNCT
iajs-727	124	3	abdullah	abdullah	PROPN
iajs-727	124	4	,	,	PUNCT
iajs-727	124	5	a.	a.	NOUN
iajs-727	124	6	(	(	PUNCT
iajs-727	124	7	2005	2005	NUM
iajs-727	124	8	)	)	PUNCT
iajs-727	124	9	,	,	PUNCT
iajs-727	124	10	on	on	ADP
iajs-727	124	11	equi	equi	NOUN
iajs-727	124	12	-	-	PUNCT
iajs-727	124	13	approximation	approximation	NOUN
iajs-727	124	14	of	of	ADP
iajs-727	124	15	bounded	bounded	ADJ
iajs-727	124	16	-measurable	-measurable	ADJ
iajs-727	124	17	functions	function	NOUN
iajs-727	124	18	in	in	ADP
iajs-727	124	19	lp()-space	lp()-space	NOUN
iajs-727	124	20	,	,	PUNCT
iajs-727	124	21	thesis	thesis	NOUN
iajs-727	124	22	,	,	PUNCT
iajs-727	124	23	university	university	NOUN
iajs-727	124	24	of	of	ADP
iajs-727	124	25	baghdad	baghdad	PROPN
iajs-727	124	26	.	.	PUNCT
iajs-727	125	1	2	2	X
iajs-727	125	2	.	.	X
iajs-727	125	3	al	al	PROPN
iajs-727	125	4	-	-	PUNCT
iajs-727	125	5	saidy	saidy	ADJ
iajs-727	125	6	,	,	PUNCT
iajs-727	125	7	s.k	s.k	PROPN
iajs-727	125	8	.	.	PROPN
iajs-727	125	9	(	(	PUNCT
iajs-727	125	10	2002	2002	NUM
iajs-727	125	11	)	)	PUNCT
iajs-727	125	12	,	,	PUNCT
iajs-727	125	13	best	good	ADJ
iajs-727	125	14	one	one	NUM
iajs-727	125	15	-	-	PUNCT
iajs-727	125	16	sided	sided	ADJ
iajs-727	125	17	approximation	approximation	NOUN
iajs-727	125	18	with	with	ADP
iajs-727	125	19	algebraic	algebraic	ADJ
iajs-727	125	20	polynomials	polynomial	NOUN
iajs-727	125	21	in	in	ADP
iajs-727	125	22	lpspaces	lpspace	NOUN
iajs-727	125	23	,	,	PUNCT
iajs-727	125	24	ibn	ibn	PROPN
iajs-727	125	25	al	al	PROPN
iajs-727	125	26	-	-	PUNCT
iajs-727	125	27	haitham	haitham	PROPN
iajs-727	125	28	j.	j.	PROPN
iajs-727	125	29	for	for	ADP
iajs-727	125	30	pure	pure	ADJ
iajs-727	125	31	and	and	CCONJ
iajs-727	125	32	applied	applied	ADJ
iajs-727	125	33	science	science	NOUN
iajs-727	125	34	.	.	PUNCT
iajs-727	126	1	,	,	PUNCT
iajs-727	126	2	15	15	NUM
iajs-727	126	3	:(	:(	NOUN
iajs-727	126	4	3	3	NUM
iajs-727	126	5	)	)	PUNCT
iajs-727	126	6	.	.	PUNCT
iajs-727	127	1	3	3	X
iajs-727	127	2	.	.	X
iajs-727	127	3	bhayah	bhayah	PROPN
iajs-727	127	4	,	,	PUNCT
iajs-727	127	5	e.s	e.s	PROPN
iajs-727	127	6	.	.	PROPN
iajs-727	127	7	(	(	PUNCT
iajs-727	127	8	1999	1999	NUM
iajs-727	127	9	)	)	PUNCT
iajs-727	127	10	,	,	PUNCT
iajs-727	127	11	a	a	DET
iajs-727	127	12	study	study	NOUN
iajs-727	127	13	on	on	ADP
iajs-727	127	14	approximation	approximation	NOUN
iajs-727	127	15	of	of	ADP
iajs-727	127	16	bounded	bounded	ADJ
iajs-727	127	17	measurable	measurable	ADJ
iajs-727	127	18	functions	function	NOUN
iajs-727	127	19	with	with	ADP
iajs-727	127	20	some	some	DET
iajs-727	127	21	discrete	discrete	ADJ
iajs-727	127	22	series	series	NOUN
iajs-727	127	23	in	in	ADP
iajs-727	127	24	lp	lp	NOUN
iajs-727	127	25	-	-	PUNCT
iajs-727	127	26	spaces	space	NOUN
iajs-727	127	27	(	(	PUNCT
iajs-727	127	28	0	0	PUNCT
iajs-727	127	29	<	<	X
iajs-727	127	30	p	p	X
iajs-727	127	31			NUM
iajs-727	127	32	1	1	NUM
iajs-727	127	33	)	)	PUNCT
iajs-727	127	34	,	,	PUNCT
iajs-727	127	35	thesis	thesis	NOUN
iajs-727	127	36	.	.	PUNCT
iajs-727	128	1	4	4	X
iajs-727	128	2	.	.	X
iajs-727	128	3	zygmund	zygmund	NOUN
iajs-727	128	4	,	,	PUNCT
iajs-727	128	5	a.	a.	NOUN
iajs-727	128	6	(	(	PUNCT
iajs-727	128	7	1958	1958	NUM
iajs-727	128	8	)	)	PUNCT
iajs-727	128	9	,	,	PUNCT
iajs-727	128	10	trigonometric	trigonometric	ADJ
iajs-727	128	11	series	series	NOUN
iajs-727	128	12	,	,	PUNCT
iajs-727	128	13	i	i	PRON
iajs-727	128	14	:	:	SYM
iajs-727	128	15	ii	ii	PROPN
iajs-727	128	16	,	,	PUNCT
iajs-727	128	17	cambridge	cambridge	PROPN
iajs-727	128	18	.	.	PROPN
iajs-727	129	1	5	5	X
iajs-727	129	2	.	.	X
iajs-727	129	3	verhey	verhey	PROPN
iajs-727	129	4	,	,	PUNCT
iajs-727	129	5	c.b	c.b	PROPN
iajs-727	129	6	.	.	PROPN
iajs-727	129	7	,	,	PUNCT
iajs-727	129	8	complex	complex	ADJ
iajs-727	129	9	variables	variable	NOUN
iajs-727	129	10	and	and	CCONJ
iajs-727	129	11	application	application	NOUN
iajs-727	129	12	,	,	PUNCT
iajs-727	129	13	third	third	ADJ
iajs-727	129	14	edition	edition	NOUN
iajs-727	129	15	,	,	PUNCT
iajs-727	129	16	tokyo	tokyo	PROPN
iajs-727	129	17	,	,	PUNCT
iajs-727	129	18	japan	japan	PROPN
iajs-727	129	19	.	.	PUNCT
iajs-727	130	1	6	6	NUM
iajs-727	130	2	.	.	X
iajs-727	130	3	dryanov	dryanov	NOUN
iajs-727	130	4	,	,	PUNCT
iajs-727	130	5	d.	d.	PROPN
iajs-727	130	6	(	(	PUNCT
iajs-727	130	7	1991	1991	NUM
iajs-727	130	8	)	)	PUNCT
iajs-727	130	9	,	,	PUNCT
iajs-727	130	10	equi	equi	NOUN
iajs-727	130	11	convergence	convergence	NOUN
iajs-727	130	12	and	and	CCONJ
iajs-727	130	13	equi	equi	NOUN
iajs-727	130	14	approximation	approximation	NOUN
iajs-727	130	15	for	for	ADP
iajs-727	130	16	entire	entire	ADJ
iajs-727	130	17	functions	function	NOUN
iajs-727	130	18	.	.	PUNCT
iajs-727	131	1	constructive	constructive	ADJ
iajs-727	131	2	theory	theory	NOUN
iajs-727	131	3	of	of	ADP
iajs-727	131	4	functions	function	NOUN
iajs-727	131	5	'	'	PART
iajs-727	131	6	91	91	NUM
iajs-727	131	7	,	,	PUNCT
iajs-727	131	8	international	international	ADJ
iajs-727	131	9	conference	conference	NOUN
iajs-727	131	10	,	,	PUNCT
iajs-727	131	11	varna	varna	NOUN
iajs-727	131	12	,	,	PUNCT
iajs-727	131	13	may	may	AUX
iajs-727	131	14	28	28	NUM
iajs-727	131	15	-	-	SYM
iajs-727	131	16	june	june	PROPN
iajs-727	131	17	3	3	NUM
iajs-727	131	18	.	.	NOUN
iajs-727	131	19	7	7	NUM
iajs-727	131	20	.	.	X
iajs-727	131	21	sendov	sendov	PROPN
iajs-727	131	22	,	,	PUNCT
iajs-727	131	23	b.	b.	PROPN
iajs-727	131	24	and	and	CCONJ
iajs-727	131	25	popov	popov	PROPN
iajs-727	131	26	,	,	PUNCT
iajs-727	131	27	v.a	v.a	PROPN
iajs-727	131	28	.	.	PROPN
iajs-727	131	29	,	,	PUNCT
iajs-727	131	30	(	(	PUNCT
iajs-727	131	31	1983	1983	NUM
iajs-727	131	32	)	)	PUNCT
iajs-727	131	33	,	,	PUNCT
iajs-727	131	34	average	average	ADJ
iajs-727	131	35	modulus	modulus	NOUN
iajs-727	131	36	of	of	ADP
iajs-727	131	37	smoothness	smoothness	NOUN
iajs-727	131	38	,	,	PUNCT
iajs-727	131	39	sofia	sofia	PROPN
iajs-727	131	40	.	.	PROPN
iajs-727	132	1	2011	2011	NUM
iajs-727	132	2	)	)	PUNCT
iajs-727	133	1	3	3	NUM
iajs-727	133	2	(	(	PUNCT
iajs-727	133	3	24للعلوم	24للعلوم	NUM
iajs-727	133	4	الصرفة	الصرفة	NOUN
iajs-727	133	5	والتطبیقیة	والتطبیقیة	PROPN
iajs-727	133	6	المجلد	المجلد	PROPN
iajs-727	133	7	مجلة	مجلة	PROPN
iajs-727	134	1	ابن	ابن	PROPN
iajs-727	134	2	الهیثم	الهیثم	PROPN
iajs-727	134	3	طة	طة	VERB
iajs-727	134	4	المتعددات	المتعددات	ADJ
iajs-727	134	5	المتقطعة	المتقطعة	NOUN
iajs-727	134	6	في	في	ADP
iajs-727	134	7	الفضاءات	الفضاءات	PROPN
iajs-727	134	8	المحلیةاتقریب	المحلیةاتقریب	NOUN
iajs-727	134	9	الدوال	الدوال	NOUN
iajs-727	134	10	الداخلیة	الداخلیة	PROPN
iajs-727	134	11	بواس	بواس	PROPN
iajs-727	134	12	صاحب	صاحب	NOUN
iajs-727	134	13	كحیط	كحیط	VERB
iajs-727	134	14	جاسم	جاسم	PROPN
iajs-727	134	15	،	،	NOUN
iajs-727	134	16	نادیة	نادیة	PROPN
iajs-727	134	17	جاسم	جاسم	NOUN
iajs-727	134	18	محمد	محمد	PROPN
iajs-727	134	19	الجامعة	الجامعة	NOUN
iajs-727	134	20	المستنصریة	المستنصریة	PROPN
iajs-727	134	21	،	،	PROPN
iajs-727	134	22	كلیة	كلیة	PROPN
iajs-727	134	23	العلوم	العلوم	PROPN
iajs-727	134	24	،	،	PROPN
iajs-727	134	25	قسم	قسم	PROPN
iajs-727	134	26	الریاضیات	الریاضیات	VERB
iajs-727	134	27	د	د	PROPN
iajs-727	134	28	،	،	X
iajs-727	134	29	ابن	ابن	X
iajs-727	134	30	الهیثم	الهیثم	PROPN
iajs-727	134	31	-كلیة	-كلیة	PROPN
iajs-727	134	32	التربیة	التربیة	NOUN
iajs-727	134	33	،	،	NOUN
iajs-727	134	34	قسم	قسم	PROPN
iajs-727	134	35	الریاضیات	الریاضیات	PROPN
iajs-727	134	36	جامعة	جامعة	PROPN
iajs-727	134	37	بغدا	بغدا	PROPN
iajs-727	134	38	2011	2011	NUM
iajs-727	134	39	شباط	شباط	ADV
iajs-727	134	40	3	3	NUM
iajs-727	134	41	:	:	PUNCT
iajs-727	134	42	في	في	ADP
iajs-727	134	43	استلم	استلم	PROPN
iajs-727	134	44	البحث	البحث	PROPN
iajs-727	134	45	2011	2011	NUM
iajs-727	134	46	ایار	ایار	ADJ
iajs-727	134	47	10	10	NUM
iajs-727	134	48	:	:	PUNCT
iajs-727	134	49	قبل	قبل	NOUN
iajs-727	134	50	البحث	البحث	VERB
iajs-727	134	51	في	في	DET
iajs-727	134	52	خالصةال	خالصةال	PROPN
iajs-727	135	1	ن	ن	PROPN
iajs-727	135	2	دار	دار	PROPN
iajs-727	135	3	الخطــأ	الخطــأ	PROPN
iajs-727	135	4	ھـو	ھـو	ADP
iajs-727	135	5	حســاب	حســاب	NOUN
iajs-727	135	6	ھــذا	ھــذا	PROPN
iajs-727	135	7	البحـث	البحـث	NOUN
iajs-727	135	8	الغـرض	الغـرض	NOUN
iajs-727	135	9	ـم	ـم	PROPN
iajs-727	135	10	دوال	دوال	PROPN
iajs-727	135	11	مـق	مـق	AUX
iajs-727	135	12	ــة	ــة	PROPN
iajs-727	135	13	لتقریـب	لتقریـب	PROPN
iajs-727	135	14	اـل	اـل	PROPN
iajs-727	135	15	المتقطعـة	المتقطعـة	PROPN
iajs-727	135	16	فــي	فــي	PROPN
iajs-727	135	17	المــؤثرات	المــؤثرات	NOUN
iajs-727	135	18	طة	طة	VERB
iajs-727	135	19	بعـضابواسـ	بعـضابواسـ	ADJ
iajs-727	135	20	الداخلی	الداخلی	PROPN
iajs-727	135	21	k	k	PROPN
iajs-727	135	22	الوسیط	الوسیط	NOUN
iajs-727	135	23	لاباستعم	لاباستعم	PROPN
iajs-727	135	24	المحلیة	المحلیة	PROPN
iajs-727	135	25	شبھ	شبھ	PROPN
iajs-727	135	26	الفضاءات	الفضاءات	NOUN
iajs-727	135	27	p	p	NOUN
iajs-727	135	28	1	1	NUM
iajs-727	135	29	τ	τ	PROPN
iajs-727	135	30	,	,	PUNCT
iajs-727	135	31	)	)	PUNCT
iajs-727	135	32	n	n	PROPN
iajs-727	135	33	.	.	PROPN
iajs-727	135	34	.المعیاريالدوال	.المعیاريالدوال	CCONJ
iajs-727	136	1	الداخلیة	الداخلیة	PROPN
iajs-727	136	2	،	،	PROPN
iajs-727	136	3	الدوال	الدوال	PROPN
iajs-727	136	4	محدودة	محدودة	NOUN
iajs-727	136	5	القیاس	القیاس	PROPN
iajs-727	136	6	،	،	PROPN
iajs-727	136	7	الفضاء	الفضاء	PROPN
iajs-727	136	8	شبھ	شبھ	PROPN
iajs-727	136	9	:	:	PUNCT
iajs-727	136	10	الكلمات	الكلمات	VERB
iajs-727	136	11	المفتاحیة	المفتاحیة	ADV