id	sid	tid	token	lemma	pos
iajs-2140	1	1	26	26	NUM
iajs-2140	1	2	ibn	ibn	PROPN
iajs-2140	1	3	al	al	PROPN
iajs-2140	1	4	-	-	PUNCT
iajs-2140	1	5	haitham	haitham	PROPN
iajs-2140	1	6	jour	jour	X
iajs-2140	1	7	.	.	PROPN
iajs-2140	1	8	for	for	ADP
iajs-2140	1	9	pure	pure	ADJ
iajs-2140	1	10	&	&	CCONJ
iajs-2140	1	11	appl	appl	PROPN
iajs-2140	1	12	.	.	PUNCT
iajs-2140	2	1	sci	sci	PROPN
iajs-2140	2	2	.	.	PROPN
iajs-2140	2	3	32	32	NUM
iajs-2140	2	4	(	(	PUNCT
iajs-2140	2	5	2	2	NUM
iajs-2140	2	6	)	)	PUNCT
iajs-2140	2	7	2019	2019	NUM
iajs-2140	2	8	abstract	abstract	NOUN
iajs-2140	2	9	the	the	DET
iajs-2140	2	10	objective	objective	NOUN
iajs-2140	2	11	of	of	ADP
iajs-2140	2	12	this	this	DET
iajs-2140	2	13	paper	paper	NOUN
iajs-2140	2	14	is	be	AUX
iajs-2140	2	15	,	,	PUNCT
iajs-2140	2	16	first	first	ADV
iajs-2140	2	17	,	,	PUNCT
iajs-2140	2	18	study	study	VERB
iajs-2140	2	19	a	a	DET
iajs-2140	2	20	new	new	ADJ
iajs-2140	2	21	collection	collection	NOUN
iajs-2140	2	22	of	of	ADP
iajs-2140	2	23	sets	set	NOUN
iajs-2140	2	24	such	such	ADJ
iajs-2140	2	25	as	as	ADP
iajs-2140	2	26	–	–	PUNCT
iajs-2140	2	27	field	field	NOUN
iajs-2140	2	28	and	and	CCONJ
iajs-2140	2	29	we	we	PRON
iajs-2140	2	30	discuss	discuss	VERB
iajs-2140	2	31	the	the	DET
iajs-2140	2	32	properties	property	NOUN
iajs-2140	2	33	of	of	ADP
iajs-2140	2	34	this	this	DET
iajs-2140	2	35	collection	collection	NOUN
iajs-2140	2	36	.	.	PUNCT
iajs-2140	3	1	second	second	ADJ
iajs-2140	3	2	,	,	PUNCT
iajs-2140	3	3	introduce	introduce	VERB
iajs-2140	3	4	a	a	DET
iajs-2140	3	5	new	new	ADJ
iajs-2140	3	6	concepts	concept	NOUN
iajs-2140	3	7	related	relate	VERB
iajs-2140	3	8	to	to	ADP
iajs-2140	3	9	the	the	DET
iajs-2140	3	10	–	–	PUNCT
iajs-2140	3	11	field	field	NOUN
iajs-2140	3	12	such	such	ADJ
iajs-2140	3	13	as	as	ADP
iajs-2140	3	14	measure	measure	NOUN
iajs-2140	3	15	on	on	ADP
iajs-2140	3	16	–	–	PUNCT
iajs-2140	3	17	field	field	NOUN
iajs-2140	3	18	,	,	PUNCT
iajs-2140	3	19	outer	outer	ADJ
iajs-2140	3	20	measure	measure	NOUN
iajs-2140	3	21	on	on	ADP
iajs-2140	3	22	–	–	PUNCT
iajs-2140	3	23	field	field	NOUN
iajs-2140	3	24	and	and	CCONJ
iajs-2140	3	25	we	we	PRON
iajs-2140	3	26	obtain	obtain	VERB
iajs-2140	3	27	some	some	DET
iajs-2140	3	28	important	important	ADJ
iajs-2140	3	29	results	result	NOUN
iajs-2140	3	30	deals	deal	NOUN
iajs-2140	3	31	with	with	ADP
iajs-2140	3	32	these	these	DET
iajs-2140	3	33	concepts	concept	NOUN
iajs-2140	3	34	.	.	PUNCT
iajs-2140	4	1	third	third	ADV
iajs-2140	4	2	,	,	PUNCT
iajs-2140	4	3	introduce	introduce	VERB
iajs-2140	4	4	the	the	DET
iajs-2140	4	5	concept	concept	NOUN
iajs-2140	4	6	of	of	ADP
iajs-2140	4	7	null	null	NOUN
iajs-2140	4	8	-	-	PUNCT
iajs-2140	4	9	additive	additive	NOUN
iajs-2140	4	10	on	on	ADP
iajs-2140	4	11	–	–	PUNCT
iajs-2140	4	12	field	field	NOUN
iajs-2140	4	13	as	as	ADP
iajs-2140	4	14	a	a	DET
iajs-2140	4	15	generalization	generalization	NOUN
iajs-2140	4	16	of	of	ADP
iajs-2140	4	17	the	the	DET
iajs-2140	4	18	concept	concept	NOUN
iajs-2140	4	19	of	of	ADP
iajs-2140	4	20	measure	measure	NOUN
iajs-2140	4	21	on	on	ADP
iajs-2140	4	22	–	–	PUNCT
iajs-2140	4	23	field	field	NOUN
iajs-2140	4	24	.	.	PUNCT
iajs-2140	5	1	furthermore	furthermore	ADV
iajs-2140	5	2	,	,	PUNCT
iajs-2140	5	3	we	we	PRON
iajs-2140	5	4	establish	establish	VERB
iajs-2140	5	5	new	new	ADJ
iajs-2140	5	6	concept	concept	NOUN
iajs-2140	5	7	related	relate	VERB
iajs-2140	5	8	to	to	ADP
iajs-2140	5	9	field	field	NOUN
iajs-2140	5	10	noted	note	VERB
iajs-2140	5	11	by	by	ADP
iajs-2140	5	12	weakly	weakly	ADJ
iajs-2140	5	13	null	null	NOUN
iajs-2140	5	14	-	-	PUNCT
iajs-2140	5	15	additive	additive	NOUN
iajs-2140	5	16	on	on	ADP
iajs-2140	5	17	–	–	PUNCT
iajs-2140	5	18	field	field	NOUN
iajs-2140	5	19	as	as	ADP
iajs-2140	5	20	a	a	DET
iajs-2140	5	21	generalizations	generalization	NOUN
iajs-2140	5	22	of	of	ADP
iajs-2140	5	23	the	the	DET
iajs-2140	5	24	concepts	concept	NOUN
iajs-2140	5	25	of	of	ADP
iajs-2140	5	26	measure	measure	NOUN
iajs-2140	5	27	on	on	ADP
iajs-2140	5	28	and	and	CCONJ
iajs-2140	5	29	null	null	NOUN
iajs-2140	5	30	-	-	PUNCT
iajs-2140	5	31	additive	additive	NOUN
iajs-2140	5	32	.	.	PUNCT
iajs-2140	6	1	finally	finally	ADV
iajs-2140	6	2	,	,	PUNCT
iajs-2140	6	3	we	we	PRON
iajs-2140	6	4	introduce	introduce	VERB
iajs-2140	6	5	the	the	DET
iajs-2140	6	6	restriction	restriction	NOUN
iajs-2140	6	7	of	of	ADP
iajs-2140	6	8	a	a	DET
iajs-2140	6	9	set	set	ADJ
iajs-2140	6	10	function	function	NOUN
iajs-2140	6	11	on	on	ADP
iajs-2140	6	12	–	–	PUNCT
iajs-2140	6	13	field	field	NOUN
iajs-2140	6	14	and	and	CCONJ
iajs-2140	6	15	many	many	ADJ
iajs-2140	6	16	of	of	ADP
iajs-2140	6	17	its	its	PRON
iajs-2140	6	18	properties	property	NOUN
iajs-2140	6	19	and	and	CCONJ
iajs-2140	6	20	characterizations	characterization	NOUN
iajs-2140	6	21	are	be	AUX
iajs-2140	6	22	given	give	VERB
iajs-2140	6	23	.	.	PUNCT
iajs-2140	7	1	keywords	keyword	NOUN
iajs-2140	7	2	:	:	PUNCT
iajs-2140	7	3	–	–	PUNCT
iajs-2140	7	4	field	field	NOUN
iajs-2140	7	5	,	,	PUNCT
iajs-2140	7	6	measure	measure	NOUN
iajs-2140	7	7	on	on	ADP
iajs-2140	7	8	–	–	PUNCT
iajs-2140	7	9	field	field	NOUN
iajs-2140	7	10	,	,	PUNCT
iajs-2140	7	11	monotone	monotone	ADJ
iajs-2140	7	12	measure	measure	NOUN
iajs-2140	7	13	,	,	PUNCT
iajs-2140	7	14	null	null	NOUN
iajs-2140	7	15	-	-	PUNCT
iajs-2140	7	16	additive	additive	NOUN
iajs-2140	7	17	.	.	PUNCT
iajs-2140	8	1	1	1	X
iajs-2140	8	2	.	.	X
iajs-2140	8	3	introduction	introduction	NOUN
iajs-2140	8	4	the	the	DET
iajs-2140	8	5	theory	theory	NOUN
iajs-2140	8	6	of	of	ADP
iajs-2140	8	7	measure	measure	NOUN
iajs-2140	8	8	is	be	AUX
iajs-2140	8	9	an	an	DET
iajs-2140	8	10	important	important	ADJ
iajs-2140	8	11	subject	subject	NOUN
iajs-2140	8	12	in	in	ADP
iajs-2140	8	13	mathematics	mathematic	NOUN
iajs-2140	8	14	.	.	PUNCT
iajs-2140	9	1	in	in	ADP
iajs-2140	9	2	1972	1972	NUM
iajs-2140	9	3	,	,	PUNCT
iajs-2140	9	4	robret	robret	NOUN
iajs-2140	10	1	[	[	X
iajs-2140	10	2	1	1	NUM
iajs-2140	10	3	]	]	PUNCT
iajs-2140	10	4	,	,	PUNCT
iajs-2140	10	5	discusses	discuss	VERB
iajs-2140	10	6	many	many	ADJ
iajs-2140	10	7	details	detail	NOUN
iajs-2140	10	8	about	about	ADP
iajs-2140	10	9	measure	measure	NOUN
iajs-2140	10	10	and	and	CCONJ
iajs-2140	10	11	proves	prove	VERB
iajs-2140	10	12	some	some	DET
iajs-2140	10	13	important	important	ADJ
iajs-2140	10	14	results	result	NOUN
iajs-2140	10	15	in	in	ADP
iajs-2140	10	16	measure	measure	NOUN
iajs-2140	10	17	theory	theory	NOUN
iajs-2140	10	18	.	.	PUNCT
iajs-2140	11	1	the	the	DET
iajs-2140	11	2	notion	notion	NOUN
iajs-2140	11	3	of	of	ADP
iajs-2140	11	4	–	–	PUNCT
iajs-2140	11	5	field	field	NOUN
iajs-2140	11	6	was	be	AUX
iajs-2140	11	7	studied	study	VERB
iajs-2140	11	8	by	by	ADP
iajs-2140	11	9	robret	robret	NOUN
iajs-2140	11	10	and	and	CCONJ
iajs-2140	11	11	dietmar	dietmar	PROPN
iajs-2140	11	12	,	,	PUNCT
iajs-2140	11	13	where	where	SCONJ
iajs-2140	11	14	be	be	AUX
iajs-2140	11	15	a	a	DET
iajs-2140	11	16	nonempty	nonempty	ADV
iajs-2140	11	17	set	set	VERB
iajs-2140	11	18	.	.	PUNCT
iajs-2140	12	1	a	a	DET
iajs-2140	12	2	collection	collection	NOUN
iajs-2140	12	3	is	be	AUX
iajs-2140	12	4	said	say	VERB
iajs-2140	12	5	to	to	ADP
iajs-2140	12	6	–	–	PUNCT
iajs-2140	12	7	field	field	NOUN
iajs-2140	12	8	iff	iff	NOUN
iajs-2140	12	9	and	and	CCONJ
iajs-2140	12	10	is	be	AUX
iajs-2140	12	11	closed	close	VERB
iajs-2140	12	12	under	under	ADP
iajs-2140	12	13	complementation	complementation	NOUN
iajs-2140	12	14	and	and	CCONJ
iajs-2140	12	15	countable	countable	ADJ
iajs-2140	12	16	union	union	NOUN
iajs-2140	13	1	[	[	X
iajs-2140	13	2	1	1	NUM
iajs-2140	13	3	,	,	PUNCT
iajs-2140	13	4	2	2	NUM
iajs-2140	13	5	]	]	PUNCT
iajs-2140	13	6	.	.	PUNCT
iajs-2140	14	1	zhenyuan	zhenyuan	PROPN
iajs-2140	14	2	and	and	CCONJ
iajs-2140	14	3	george	george	PROPN
iajs-2140	14	4	in	in	ADP
iajs-2140	14	5	2009	2009	NUM
iajs-2140	14	6	and	and	CCONJ
iajs-2140	14	7	junhi	junhi	NOUN
iajs-2140	14	8	,	,	PUNCT
iajs-2140	14	9	radko	radko	PROPN
iajs-2140	14	10	and	and	CCONJ
iajs-2140	14	11	endre	endre	PROPN
iajs-2140	14	12	in	in	ADP
iajs-2140	14	13	2014	2014	NUM
iajs-2140	14	14	are	be	AUX
iajs-2140	14	15	used	use	VERB
iajs-2140	14	16	the	the	DET
iajs-2140	14	17	concept	concept	NOUN
iajs-2140	14	18	of	of	ADP
iajs-2140	14	19	null	null	NOUN
iajs-2140	14	20	-	-	PUNCT
iajs-2140	14	21	additive	additive	NOUN
iajs-2140	14	22	on	on	ADP
iajs-2140	14	23	–	–	PUNCT
iajs-2140	14	24	field	field	NOUN
iajs-2140	14	25	,	,	PUNCT
iajs-2140	14	26	where	where	SCONJ
iajs-2140	14	27	be	be	AUX
iajs-2140	14	28	a	a	DET
iajs-2140	14	29	–	–	PUNCT
iajs-2140	14	30	field	field	NOUN
iajs-2140	14	31	,	,	PUNCT
iajs-2140	14	32	then	then	ADV
iajs-2140	14	33	a	a	DET
iajs-2140	14	34	set	set	NOUN
iajs-2140	14	35	function	function	NOUN
iajs-2140	14	36	,	,	PUNCT
iajs-2140	14	37	is	be	AUX
iajs-2140	14	38	called	call	VERB
iajs-2140	14	39	null	null	NOUN
iajs-2140	14	40	-	-	PUNCT
iajs-2140	14	41	additive	additive	NOUN
iajs-2140	14	42	on	on	ADP
iajs-2140	14	43	if	if	SCONJ
iajs-2140	14	44	are	be	AUX
iajs-2140	14	45	disjoint	disjoint	NOUN
iajs-2140	14	46	sets	set	NOUN
iajs-2140	14	47	in	in	ADP
iajs-2140	14	48	and	and	CCONJ
iajs-2140	14	49	(	(	PUNCT
iajs-2140	14	50	)	)	PUNCT
iajs-2140	14	51	,	,	PUNCT
iajs-2140	14	52	then	then	ADV
iajs-2140	14	53	(	(	PUNCT
iajs-2140	14	54	)	)	PUNCT
iajs-2140	14	55	(	(	PUNCT
iajs-2140	14	56	)	)	PUNCT
iajs-2140	15	1	[	[	X
iajs-2140	15	2	3,4	3,4	NUM
iajs-2140	15	3	]	]	PUNCT
iajs-2140	15	4	.	.	PUNCT
iajs-2140	16	1	in	in	ADP
iajs-2140	16	2	2016	2016	NUM
iajs-2140	16	3	,	,	PUNCT
iajs-2140	16	4	juha	juha	PROPN
iajs-2140	16	5	used	use	VERB
iajs-2140	16	6	the	the	DET
iajs-2140	16	7	concept	concept	NOUN
iajs-2140	16	8	of	of	ADP
iajs-2140	16	9	–	–	PUNCT
iajs-2140	16	10	field	field	NOUN
iajs-2140	16	11	to	to	PART
iajs-2140	16	12	define	define	VERB
iajs-2140	16	13	measure	measure	NOUN
iajs-2140	16	14	,	,	PUNCT
iajs-2140	16	15	where	where	SCONJ
iajs-2140	16	16	be	be	AUX
iajs-2140	16	17	a	a	DET
iajs-2140	16	18	–	–	PUNCT
iajs-2140	16	19	field	field	NOUN
iajs-2140	16	20	,	,	PUNCT
iajs-2140	16	21	then	then	ADV
iajs-2140	16	22	a	a	DET
iajs-2140	16	23	measure	measure	NOUN
iajs-2140	16	24	on	on	ADP
iajs-2140	16	25	is	be	AUX
iajs-2140	16	26	a	a	DET
iajs-2140	16	27	set	set	NOUN
iajs-2140	16	28	function	function	NOUN
iajs-2140	16	29	,	,	PUNCT
iajs-2140	16	30	such	such	ADJ
iajs-2140	16	31	that	that	SCONJ
iajs-2140	16	32	(	(	PUNCT
iajs-2140	16	33	)	)	PUNCT
iajs-2140	16	34	and	and	CCONJ
iajs-2140	16	35	if	if	SCONJ
iajs-2140	16	36	form	form	VERB
iajs-2140	16	37	a	a	DET
iajs-2140	16	38	finite	finite	NOUN
iajs-2140	16	39	or	or	CCONJ
iajs-2140	16	40	countably	countably	ADV
iajs-2140	16	41	infinite	infinite	ADJ
iajs-2140	16	42	collection	collection	NOUN
iajs-2140	16	43	of	of	ADP
iajs-2140	16	44	disjoint	disjoint	NOUN
iajs-2140	16	45	sets	set	NOUN
iajs-2140	16	46	in	in	ADP
iajs-2140	16	47	,	,	PUNCT
iajs-2140	16	48	then	then	ADV
iajs-2140	16	49	(	(	PUNCT
iajs-2140	16	50	)	)	PUNCT
iajs-2140	16	51	∑	∑	PROPN
iajs-2140	16	52	(	(	PUNCT
iajs-2140	16	53	)	)	PUNCT
iajs-2140	17	1	[	[	X
iajs-2140	17	2	5	5	NUM
iajs-2140	17	3	]	]	PUNCT
iajs-2140	17	4	.	.	PUNCT
iajs-2140	18	1	and	and	CCONJ
iajs-2140	18	2	also	also	ADV
iajs-2140	18	3	used	use	VERB
iajs-2140	18	4	power	power	NOUN
iajs-2140	18	5	set	set	VERB
iajs-2140	18	6	to	to	PART
iajs-2140	18	7	define	define	VERB
iajs-2140	18	8	outer	outer	ADJ
iajs-2140	18	9	measure	measure	NOUN
iajs-2140	18	10	,	,	PUNCT
iajs-2140	18	11	where	where	SCONJ
iajs-2140	18	12	be	be	AUX
iajs-2140	18	13	a	a	DET
iajs-2140	18	14	non	non	ADJ
iajs-2140	18	15	-	-	ADJ
iajs-2140	18	16	empty	empty	ADJ
iajs-2140	18	17	set	set	NOUN
iajs-2140	18	18	,	,	PUNCT
iajs-2140	18	19	then	then	ADV
iajs-2140	18	20	a	a	DET
iajs-2140	18	21	set	set	NOUN
iajs-2140	18	22	function	function	NOUN
iajs-2140	18	23	(	(	PUNCT
iajs-2140	18	24	)	)	PUNCT
iajs-2140	18	25	,	,	PUNCT
iajs-2140	18	26	is	be	AUX
iajs-2140	18	27	called	call	VERB
iajs-2140	18	28	outer	outer	ADJ
iajs-2140	18	29	measure	measure	NOUN
iajs-2140	18	30	,	,	PUNCT
iajs-2140	18	31	if	if	SCONJ
iajs-2140	18	32	(	(	PUNCT
iajs-2140	18	33	)	)	PUNCT
iajs-2140	18	34	and	and	CCONJ
iajs-2140	18	35	if	if	SCONJ
iajs-2140	18	36	such	such	ADJ
iajs-2140	18	37	that	that	PRON
iajs-2140	18	38	,	,	PUNCT
iajs-2140	18	39	then	then	ADV
iajs-2140	18	40	(	(	PUNCT
iajs-2140	18	41	)	)	PUNCT
iajs-2140	18	42	(	(	PUNCT
iajs-2140	18	43	)	)	PUNCT
iajs-2140	18	44	and	and	CCONJ
iajs-2140	18	45	if	if	SCONJ
iajs-2140	18	46	are	be	AUX
iajs-2140	18	47	subsets	subset	NOUN
iajs-2140	18	48	of	of	ADP
iajs-2140	18	49	,	,	PUNCT
iajs-2140	18	50	then	then	ADV
iajs-2140	18	51	(	(	PUNCT
iajs-2140	18	52	)	)	PUNCT
iajs-2140	18	53	∑	∑	PROPN
iajs-2140	18	54	(	(	PUNCT
iajs-2140	18	55	)	)	PUNCT
iajs-2140	19	1	[	[	X
iajs-2140	19	2	5	5	NUM
iajs-2140	19	3	]	]	PUNCT
iajs-2140	19	4	.	.	PUNCT
iajs-2140	20	1	the	the	DET
iajs-2140	20	2	concept	concept	NOUN
iajs-2140	20	3	of	of	ADP
iajs-2140	20	4	monotone	monotone	ADJ
iajs-2140	20	5	measure	measure	NOUN
iajs-2140	20	6	was	be	AUX
iajs-2140	20	7	studied	study	VERB
iajs-2140	20	8	by	by	ADP
iajs-2140	20	9	peipe	peipe	NOUN
iajs-2140	20	10	,	,	PUNCT
iajs-2140	20	11	minhao	minhao	PROPN
iajs-2140	20	12	and	and	CCONJ
iajs-2140	20	13	jun	jun	PROPN
iajs-2140	20	14	in	in	ADP
iajs-2140	20	15	2018	2018	NUM
iajs-2140	20	16	,	,	PUNCT
iajs-2140	20	17	where	where	SCONJ
iajs-2140	20	18	be	be	AUX
iajs-2140	20	19	a	a	DET
iajs-2140	20	20	–	–	PUNCT
iajs-2140	20	21	field	field	NOUN
iajs-2140	20	22	,	,	PUNCT
iajs-2140	20	23	then	then	ADV
iajs-2140	20	24	a	a	DET
iajs-2140	20	25	set	set	NOUN
iajs-2140	20	26	function	function	NOUN
iajs-2140	20	27	,	,	PUNCT
iajs-2140	20	28	is	be	AUX
iajs-2140	20	29	called	call	VERB
iajs-2140	20	30	monotone	monotone	ADJ
iajs-2140	20	31	measure	measure	NOUN
iajs-2140	20	32	,	,	PUNCT
iajs-2140	20	33	if	if	SCONJ
iajs-2140	20	34	(	(	PUNCT
iajs-2140	20	35	)	)	PUNCT
iajs-2140	20	36	and	and	CCONJ
iajs-2140	20	37	if	if	SCONJ
iajs-2140	20	38	such	such	ADJ
iajs-2140	20	39	that	that	PRON
iajs-2140	20	40	,	,	PUNCT
iajs-2140	20	41	then	then	ADV
iajs-2140	20	42	(	(	PUNCT
iajs-2140	20	43	)	)	PUNCT
iajs-2140	20	44	(	(	PUNCT
iajs-2140	20	45	)	)	PUNCT
iajs-2140	21	1	[	[	X
iajs-2140	21	2	6	6	NUM
iajs-2140	21	3	]	]	PUNCT
iajs-2140	21	4	.	.	PUNCT
iajs-2140	22	1	on	on	ADP
iajs-2140	22	2	a	a	DET
iajs-2140	22	3	new	new	ADJ
iajs-2140	22	4	kind	kind	NOUN
iajs-2140	22	5	of	of	ADP
iajs-2140	22	6	collection	collection	NOUN
iajs-2140	22	7	of	of	ADP
iajs-2140	22	8	subsets	subset	NOUN
iajs-2140	22	9	noted	note	VERB
iajs-2140	22	10	by	by	ADP
iajs-2140	22	11	𝛅–field	𝛅–field	PROPN
iajs-2140	22	12	and	and	CCONJ
iajs-2140	22	13	some	some	DET
iajs-2140	22	14	concepts	concept	NOUN
iajs-2140	22	15	defined	define	VERB
iajs-2140	22	16	on	on	ADP
iajs-2140	22	17	𝛅–field	𝛅–field	PROPN
iajs-2140	22	18	ibn	ibn	PROPN
iajs-2140	22	19	al	al	PROPN
iajs-2140	22	20	haitham	haitham	PROPN
iajs-2140	22	21	journal	journal	PROPN
iajs-2140	22	22	for	for	ADP
iajs-2140	22	23	pure	pure	ADJ
iajs-2140	22	24	and	and	CCONJ
iajs-2140	22	25	applied	apply	VERB
iajs-2140	22	26	science	science	NOUN
iajs-2140	22	27	journal	journal	PROPN
iajs-2140	22	28	homepage	homepage	NOUN
iajs-2140	22	29	:	:	PUNCT
iajs-2140	22	30	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2140	22	31	hassan	hassan	PROPN
iajs-2140	22	32	h.	h.	PROPN
iajs-2140	22	33	ebrahim	ebrahim	PROPN
iajs-2140	22	34	hassan1962pl@tu.edu.iq	hassan1962pl@tu.edu.iq	PROPN
iajs-2140	22	35	ibrahim	ibrahim	PROPN
iajs-2140	22	36	s.	s.	PROPN
iajs-2140	22	37	ahmed	ahmed	PROPN
iajs-2140	22	38	article	article	PROPN
iajs-2140	22	39	history	history	NOUN
iajs-2140	22	40	:	:	PUNCT
iajs-2140	22	41	received	receive	VERB
iajs-2140	22	42	27	27	NUM
iajs-2140	22	43	january	january	PROPN
iajs-2140	22	44	2019	2019	NUM
iajs-2140	22	45	,	,	PUNCT
iajs-2140	22	46	accepted	accept	VERB
iajs-2140	22	47	13	13	NUM
iajs-2140	22	48	march	march	NOUN
iajs-2140	22	49	2019	2019	NUM
iajs-2140	22	50	,	,	PUNCT
iajs-2140	22	51	publish	publish	VERB
iajs-2140	22	52	may	may	PROPN
iajs-2140	22	53	2019	2019	NUM
iajs-2140	22	54	10.30526/32.2.2140	10.30526/32.2.2140	PROPN
iajs-2140	22	55	doi	doi	NOUN
iajs-2140	22	56	:	:	PUNCT
iajs-2140	22	57	department	department	NOUN
iajs-2140	22	58	of	of	ADP
iajs-2140	22	59	mathematics	mathematics	PROPN
iajs-2140	22	60	,	,	PUNCT
iajs-2140	22	61	college	college	NOUN
iajs-2140	22	62	of	of	ADP
iajs-2140	22	63	computer	computer	NOUN
iajs-2140	22	64	science	science	NOUN
iajs-2140	22	65	and	and	CCONJ
iajs-2140	22	66	mathematics	mathematic	NOUN
iajs-2140	22	67	,	,	PUNCT
iajs-2140	22	68	university	university	NOUN
iajs-2140	22	69	of	of	ADP
iajs-2140	22	70	tikrit	tikrit	NOUN
iajs-2140	22	71	,	,	PUNCT
iajs-2140	22	72	tikrit	tikrit	NOUN
iajs-2140	22	73	,	,	PUNCT
iajs-2140	22	74	iraq	iraq	PROPN
iajs-2140	22	75	.	.	PUNCT
iajs-2140	23	1	ibrahimsalhahmed69@gmail.com	ibrahimsalhahmed69@gmail.com	NOUN
iajs-2140	23	2	mailto:hassan1962pl@tu.edu.iq	mailto:hassan1962pl@tu.edu.iq	PROPN
iajs-2140	23	3	mailto:hassan1962pl@tu.edu.iq	mailto:hassan1962pl@tu.edu.iq	PROPN
iajs-2140	23	4	mailto:ibrahimsalhahmed69@gmail.com	mailto:ibrahimsalhahmed69@gmail.com	PROPN
iajs-2140	23	5	mailto:ibrahimsalhahmed69@gmail.com	mailto:ibrahimsalhahmed69@gmail.com	PROPN
iajs-2140	23	6	26	26	NUM
iajs-2140	23	7	ibn	ibn	PROPN
iajs-2140	23	8	al	al	PROPN
iajs-2140	23	9	-	-	PUNCT
iajs-2140	23	10	haitham	haitham	PROPN
iajs-2140	23	11	jour	jour	X
iajs-2140	23	12	.	.	PROPN
iajs-2140	24	1	for	for	ADP
iajs-2140	24	2	pure	pure	ADJ
iajs-2140	24	3	&	&	CCONJ
iajs-2140	24	4	appl	appl	PROPN
iajs-2140	24	5	.	.	PUNCT
iajs-2140	25	1	sci	sci	PROPN
iajs-2140	25	2	.	.	PROPN
iajs-2140	25	3	32	32	NUM
iajs-2140	25	4	(	(	PUNCT
iajs-2140	25	5	2	2	NUM
iajs-2140	25	6	)	)	PUNCT
iajs-2140	25	7	2019	2019	NUM
iajs-2140	25	8	the	the	DET
iajs-2140	25	9	main	main	ADJ
iajs-2140	25	10	aim	aim	NOUN
iajs-2140	25	11	of	of	ADP
iajs-2140	25	12	this	this	DET
iajs-2140	25	13	paper	paper	NOUN
iajs-2140	25	14	is	be	AUX
iajs-2140	25	15	to	to	PART
iajs-2140	25	16	introduce	introduce	VERB
iajs-2140	25	17	and	and	CCONJ
iajs-2140	25	18	study	study	VERB
iajs-2140	25	19	new	new	ADJ
iajs-2140	25	20	concepts	concept	NOUN
iajs-2140	25	21	such	such	ADJ
iajs-2140	25	22	as	as	ADP
iajs-2140	25	23	–	–	PUNCT
iajs-2140	25	24	field	field	NOUN
iajs-2140	25	25	,	,	PUNCT
iajs-2140	25	26	measure	measure	NOUN
iajs-2140	25	27	on	on	ADP
iajs-2140	25	28	–	–	PUNCT
iajs-2140	25	29	field	field	NOUN
iajs-2140	25	30	,	,	PUNCT
iajs-2140	25	31	outer	outer	ADJ
iajs-2140	25	32	measure	measure	NOUN
iajs-2140	25	33	on	on	ADP
iajs-2140	25	34	–	–	PUNCT
iajs-2140	25	35	field	field	NOUN
iajs-2140	25	36	and	and	CCONJ
iajs-2140	25	37	null	null	NOUN
iajs-2140	25	38	-	-	PUNCT
iajs-2140	25	39	additive	additive	NOUN
iajs-2140	25	40	on	on	ADP
iajs-2140	25	41	–	–	PUNCT
iajs-2140	25	42	field	field	NOUN
iajs-2140	25	43	and	and	CCONJ
iajs-2140	25	44	we	we	PRON
iajs-2140	25	45	give	give	VERB
iajs-2140	25	46	basic	basic	ADJ
iajs-2140	25	47	properties	property	NOUN
iajs-2140	25	48	,	,	PUNCT
iajs-2140	25	49	characterizations	characterization	NOUN
iajs-2140	25	50	and	and	CCONJ
iajs-2140	25	51	examples	example	NOUN
iajs-2140	25	52	of	of	ADP
iajs-2140	25	53	these	these	DET
iajs-2140	25	54	concepts	concept	NOUN
iajs-2140	25	55	.	.	PUNCT
iajs-2140	26	1	2	2	X
iajs-2140	26	2	.	.	X
iajs-2140	26	3	the	the	DET
iajs-2140	26	4	main	main	ADJ
iajs-2140	26	5	results	result	NOUN
iajs-2140	26	6	let	let	AUX
iajs-2140	26	7	be	be	AUX
iajs-2140	26	8	a	a	DET
iajs-2140	26	9	nonempty	nonempty	ADJ
iajs-2140	26	10	set	set	VERB
iajs-2140	26	11	.	.	PUNCT
iajs-2140	27	1	then	then	ADV
iajs-2140	27	2	a	a	DET
iajs-2140	27	3	collection	collection	NOUN
iajs-2140	27	4	of	of	ADP
iajs-2140	27	5	all	all	DET
iajs-2140	27	6	subsets	subset	NOUN
iajs-2140	27	7	of	of	ADP
iajs-2140	27	8	a	a	DET
iajs-2140	27	9	set	set	NOUN
iajs-2140	27	10	,	,	PUNCT
iajs-2140	27	11	denoted	denote	VERB
iajs-2140	27	12	by	by	ADP
iajs-2140	27	13	(	(	PUNCT
iajs-2140	27	14	)	)	PUNCT
iajs-2140	27	15	,	,	PUNCT
iajs-2140	27	16	and	and	CCONJ
iajs-2140	27	17	it	it	PRON
iajs-2140	27	18	's	be	AUX
iajs-2140	27	19	called	call	VERB
iajs-2140	27	20	a	a	DET
iajs-2140	27	21	power	power	NOUN
iajs-2140	27	22	set	set	NOUN
iajs-2140	27	23	of	of	ADP
iajs-2140	27	24	definition	definition	NOUN
iajs-2140	27	25	1	1	NUM
iajs-2140	27	26	let	let	VERB
iajs-2140	27	27	be	be	AUX
iajs-2140	27	28	a	a	DET
iajs-2140	27	29	nonempty	nonempty	ADV
iajs-2140	27	30	set	set	VERB
iajs-2140	27	31	.	.	PUNCT
iajs-2140	28	1	a	a	DET
iajs-2140	28	2	collection	collection	NOUN
iajs-2140	28	3	(	(	PUNCT
iajs-2140	28	4	)	)	PUNCT
iajs-2140	28	5	is	be	AUX
iajs-2140	28	6	said	say	VERB
iajs-2140	28	7	to	to	PART
iajs-2140	28	8	be	be	AUX
iajs-2140	28	9	–	–	PUNCT
iajs-2140	28	10	of	of	ADP
iajs-2140	28	11	a	a	DET
iajs-2140	28	12	set	set	NOUN
iajs-2140	28	13	if	if	SCONJ
iajs-2140	28	14	the	the	DET
iajs-2140	28	15	following	follow	VERB
iajs-2140	28	16	conditions	condition	NOUN
iajs-2140	28	17	are	be	AUX
iajs-2140	28	18	satisfied	satisfied	ADJ
iajs-2140	28	19	:	:	PUNCT
iajs-2140	28	20	1	1	NUM
iajs-2140	28	21	.	.	PUNCT
iajs-2140	28	22	2if	2if	NOUN
iajs-2140	28	23	is	be	AUX
iajs-2140	28	24	a	a	DET
iajs-2140	28	25	nonempty	nonempty	ADJ
iajs-2140	28	26	set	set	VERB
iajs-2140	28	27	in	in	ADP
iajs-2140	28	28	and	and	CCONJ
iajs-2140	28	29	,	,	PUNCT
iajs-2140	28	30	then	then	ADV
iajs-2140	28	31	.	.	PUNCT
iajs-2140	29	1	3if	3if	NOUN
iajs-2140	29	2	,	,	PUNCT
iajs-2140	29	3	then	then	ADV
iajs-2140	29	4	⋂	⋂	PROPN
iajs-2140	29	5	.	.	PUNCT
iajs-2140	30	1	proposition	proposition	NOUN
iajs-2140	30	2	2	2	NUM
iajs-2140	30	3	for	for	ADP
iajs-2140	30	4	any	any	PRON
iajs-2140	30	5	–	–	PUNCT
iajs-2140	30	6	of	of	ADP
iajs-2140	30	7	a	a	DET
iajs-2140	30	8	set	set	NOUN
iajs-2140	30	9	,	,	PUNCT
iajs-2140	30	10	the	the	DET
iajs-2140	30	11	following	follow	VERB
iajs-2140	30	12	hold	hold	NOUN
iajs-2140	30	13	:	:	PUNCT
iajs-2140	30	14	1	1	NUM
iajs-2140	30	15	2if	2if	NOUN
iajs-2140	30	16	,	,	PUNCT
iajs-2140	30	17	then	then	ADV
iajs-2140	30	18	⋂	⋂	PROPN
iajs-2140	30	19	3if	3if	NOUN
iajs-2140	30	20	,	,	PUNCT
iajs-2140	30	21	then	then	ADV
iajs-2140	30	22	⋂	⋂	PROPN
iajs-2140	30	23	.	.	PUNCT
iajs-2140	31	1	4if	4if	NOUN
iajs-2140	31	2	,	,	PUNCT
iajs-2140	31	3	then	then	ADV
iajs-2140	31	4	.	.	PUNCT
iajs-2140	32	1	5	5	NUM
iajs-2140	32	2	,	,	PUNCT
iajs-2140	32	3	then	then	ADV
iajs-2140	32	4	.	.	PUNCT
iajs-2140	33	1	proof	proof	NOUN
iajs-2140	33	2	it	it	PRON
iajs-2140	33	3	is	be	AUX
iajs-2140	33	4	easy	easy	ADJ
iajs-2140	33	5	,	,	PUNCT
iajs-2140	33	6	so	so	ADV
iajs-2140	33	7	we	we	PRON
iajs-2140	33	8	omitted	omit	VERB
iajs-2140	33	9	.	.	PUNCT
iajs-2140	34	1	example	example	NOUN
iajs-2140	34	2	3	3	NUM
iajs-2140	34	3	let	let	VERB
iajs-2140	34	4	=	=	PRON
iajs-2140	34	5	{	{	PUNCT
iajs-2140	34	6	1	1	NUM
iajs-2140	34	7	,	,	PUNCT
iajs-2140	34	8	2	2	NUM
iajs-2140	34	9	,	,	PUNCT
iajs-2140	34	10	3	3	NUM
iajs-2140	34	11	,	,	PUNCT
iajs-2140	34	12	4	4	NUM
iajs-2140	34	13	}	}	PUNCT
iajs-2140	34	14	and	and	CCONJ
iajs-2140	34	15	{	{	PUNCT
iajs-2140	34	16	,	,	PUNCT
iajs-2140	34	17	{	{	PUNCT
iajs-2140	34	18	1,2},{1,2,3	1,2},{1,2,3	NOUN
iajs-2140	34	19	}	}	PUNCT
iajs-2140	34	20	,	,	PUNCT
iajs-2140	34	21	{	{	PUNCT
iajs-2140	34	22	1,2,4	1,2,4	NUM
iajs-2140	34	23	}	}	PUNCT
iajs-2140	34	24	,	,	PUNCT
iajs-2140	34	25	}	}	PUNCT
iajs-2140	34	26	.	.	PUNCT
iajs-2140	35	1	then	then	ADV
iajs-2140	35	2	is	be	AUX
iajs-2140	35	3	a	a	PRON
iajs-2140	35	4	–	–	PUNCT
iajs-2140	35	5	of	of	ADP
iajs-2140	35	6	a	a	DET
iajs-2140	35	7	set	set	NOUN
iajs-2140	35	8	.	.	PUNCT
iajs-2140	36	1	definition	definition	NOUN
iajs-2140	36	2	4	4	NUM
iajs-2140	36	3	let	let	VERB
iajs-2140	36	4	be	be	AUX
iajs-2140	36	5	a	a	DET
iajs-2140	36	6	nonempty	nonempty	ADV
iajs-2140	36	7	set	set	VERB
iajs-2140	36	8	and	and	CCONJ
iajs-2140	36	9	is	be	AUX
iajs-2140	36	10	a	a	PRON
iajs-2140	36	11	–	–	PUNCT
iajs-2140	36	12	of	of	ADP
iajs-2140	36	13	a	a	DET
iajs-2140	36	14	set	set	NOUN
iajs-2140	36	15	.then	.then	PUNCT
iajs-2140	36	16	a	a	DET
iajs-2140	36	17	pair	pair	NOUN
iajs-2140	36	18	(	(	PUNCT
iajs-2140	36	19	,	,	PUNCT
iajs-2140	36	20	)	)	PUNCT
iajs-2140	36	21	is	be	AUX
iajs-2140	36	22	called	call	VERB
iajs-2140	36	23	measurable	measurable	ADJ
iajs-2140	36	24	space	space	NOUN
iajs-2140	36	25	and	and	CCONJ
iajs-2140	36	26	any	any	DET
iajs-2140	36	27	member	member	NOUN
iajs-2140	36	28	of	of	ADP
iajs-2140	36	29	is	be	AUX
iajs-2140	36	30	called	call	VERB
iajs-2140	36	31	a	a	DET
iajs-2140	36	32	measurable	measurable	ADJ
iajs-2140	36	33	set	set	NOUN
iajs-2140	36	34	.	.	PUNCT
iajs-2140	37	1	proposition	proposition	NOUN
iajs-2140	37	2	5	5	NUM
iajs-2140	37	3	let	let	VERB
iajs-2140	37	4	*	*	PUNCT
iajs-2140	38	1	+	+	CCONJ
iajs-2140	38	2	be	be	AUX
iajs-2140	38	3	a	a	DET
iajs-2140	38	4	sequence	sequence	NOUN
iajs-2140	38	5	of	of	ADP
iajs-2140	38	6	–	–	PUNCT
iajs-2140	38	7	of	of	ADP
iajs-2140	38	8	a	a	DET
iajs-2140	38	9	set	set	NOUN
iajs-2140	38	10	.	.	PUNCT
iajs-2140	39	1	then	then	ADV
iajs-2140	39	2	⋂	⋂	PROPN
iajs-2140	39	3	is	be	AUX
iajs-2140	39	4	a	a	PRON
iajs-2140	39	5	–	–	PUNCT
iajs-2140	39	6	of	of	ADP
iajs-2140	39	7	a	a	DET
iajs-2140	39	8	set	set	NOUN
iajs-2140	39	9	.	.	PUNCT
iajs-2140	40	1	proof	proof	NOUN
iajs-2140	40	2	since	since	SCONJ
iajs-2140	40	3	is	be	AUX
iajs-2140	40	4	–	–	PUNCT
iajs-2140	40	5	,	,	PUNCT
iajs-2140	40	6	then	then	ADV
iajs-2140	40	7	,	,	PUNCT
iajs-2140	40	8	,	,	PUNCT
iajs-2140	40	9	hence	hence	ADV
iajs-2140	40	10	and	and	CCONJ
iajs-2140	40	11	⋂	⋂	PROPN
iajs-2140	40	12	,	,	PUNCT
iajs-2140	40	13	therefore	therefore	ADV
iajs-2140	40	14	⋂	⋂	PROPN
iajs-2140	40	15	.	.	PUNCT
iajs-2140	41	1	let	let	VERB
iajs-2140	41	2	⋂	⋂	PROPN
iajs-2140	41	3	such	such	ADJ
iajs-2140	41	4	that	that	PRON
iajs-2140	41	5	,	,	PUNCT
iajs-2140	41	6	then	then	ADV
iajs-2140	41	7	,	,	PUNCT
iajs-2140	41	8	but	but	CCONJ
iajs-2140	41	9	so	so	ADV
iajs-2140	41	10	,	,	PUNCT
iajs-2140	41	11	we	we	PRON
iajs-2140	41	12	get	get	VERB
iajs-2140	41	13	,	,	PUNCT
iajs-2140	41	14	hence	hence	ADV
iajs-2140	41	15	⋂	⋂	PROPN
iajs-2140	41	16	.	.	PUNCT
iajs-2140	42	1	let	let	VERB
iajs-2140	42	2	⋂	⋂	PROPN
iajs-2140	42	3	.	.	PUNCT
iajs-2140	43	1	then	then	ADV
iajs-2140	43	2	,	,	PUNCT
iajs-2140	43	3	and	and	CCONJ
iajs-2140	43	4	⋂	⋂	PROPN
iajs-2140	43	5	,	,	PUNCT
iajs-2140	43	6	which	which	PRON
iajs-2140	43	7	is	be	AUX
iajs-2140	43	8	implies	imply	VERB
iajs-2140	43	9	that	that	SCONJ
iajs-2140	43	10	⋂	⋂	PROPN
iajs-2140	43	11	⋂	⋂	PROPN
iajs-2140	43	12	.	.	PUNCT
iajs-2140	44	1	hence	hence	ADV
iajs-2140	44	2	⋂	⋂	PROPN
iajs-2140	44	3	is	be	AUX
iajs-2140	44	4	a	a	PRON
iajs-2140	44	5	–	–	PUNCT
iajs-2140	44	6	.	.	PUNCT
iajs-2140	45	1	definition	definition	NOUN
iajs-2140	45	2	6	6	NUM
iajs-2140	45	3	let	let	VERB
iajs-2140	45	4	be	be	AUX
iajs-2140	45	5	a	a	PRON
iajs-2140	45	6	–	–	PUNCT
iajs-2140	45	7	of	of	ADP
iajs-2140	45	8	a	a	DET
iajs-2140	45	9	set	set	NOUN
iajs-2140	45	10	and	and	CCONJ
iajs-2140	45	11	let	let	VERB
iajs-2140	45	12	be	be	AUX
iajs-2140	45	13	a	a	DET
iajs-2140	45	14	non	non	ADJ
iajs-2140	45	15	-	-	ADJ
iajs-2140	45	16	empty	empty	ADJ
iajs-2140	45	17	subset	subset	NOUN
iajs-2140	45	18	of	of	ADP
iajs-2140	45	19	.	.	PUNCT
iajs-2140	46	1	then	then	ADV
iajs-2140	46	2	the	the	DET
iajs-2140	46	3	restriction	restriction	NOUN
iajs-2140	46	4	of	of	ADP
iajs-2140	46	5	on	on	ADV
iajs-2140	46	6	is	be	AUX
iajs-2140	46	7	denoted	denote	VERB
iajs-2140	46	8	by	by	ADP
iajs-2140	46	9	and	and	CCONJ
iajs-2140	46	10	define	define	VERB
iajs-2140	46	11	as	as	ADP
iajs-2140	46	12	:	:	PUNCT
iajs-2140	46	13	=	=	NOUN
iajs-2140	46	14	{	{	PUNCT
iajs-2140	46	15	:	:	PUNCT
iajs-2140	46	16	=	=	SYM
iajs-2140	46	17	⋂	⋂	PROPN
iajs-2140	46	18	,	,	PUNCT
iajs-2140	46	19	for	for	ADP
iajs-2140	46	20	some	some	PRON
iajs-2140	46	21	}	}	PUNCT
iajs-2140	46	22	.	.	PUNCT
iajs-2140	47	1	proposition	proposition	NOUN
iajs-2140	47	2	7	7	NUM
iajs-2140	47	3	let	let	VERB
iajs-2140	47	4	be	be	AUX
iajs-2140	47	5	a	a	PRON
iajs-2140	47	6	–	–	PUNCT
iajs-2140	47	7	of	of	ADP
iajs-2140	47	8	a	a	DET
iajs-2140	47	9	set	set	NOUN
iajs-2140	47	10	and	and	CCONJ
iajs-2140	47	11	be	be	AUX
iajs-2140	47	12	a	a	DET
iajs-2140	47	13	non	non	ADJ
iajs-2140	47	14	-	-	ADJ
iajs-2140	47	15	empty	empty	ADJ
iajs-2140	47	16	subset	subset	NOUN
iajs-2140	47	17	of	of	ADP
iajs-2140	47	18	such	such	ADJ
iajs-2140	47	19	that	that	PRON
iajs-2140	47	20	.	.	PUNCT
iajs-2140	48	1	then	then	ADV
iajs-2140	48	2	=	=	PRON
iajs-2140	48	3	{	{	PUNCT
iajs-2140	48	4	:	:	PUNCT
iajs-2140	48	5	}	}	PUNCT
iajs-2140	48	6	.	.	PUNCT
iajs-2140	49	1	26	26	NUM
iajs-2140	49	2	ibn	ibn	PROPN
iajs-2140	49	3	al	al	PROPN
iajs-2140	49	4	-	-	PUNCT
iajs-2140	49	5	haitham	haitham	PROPN
iajs-2140	49	6	jour	jour	X
iajs-2140	49	7	.	.	PROPN
iajs-2140	49	8	for	for	ADP
iajs-2140	49	9	pure	pure	ADJ
iajs-2140	49	10	&	&	CCONJ
iajs-2140	49	11	appl	appl	PROPN
iajs-2140	49	12	.	.	PUNCT
iajs-2140	50	1	sci	sci	PROPN
iajs-2140	50	2	.	.	PROPN
iajs-2140	50	3	32	32	NUM
iajs-2140	50	4	(	(	PUNCT
iajs-2140	50	5	2	2	NUM
iajs-2140	50	6	)	)	PUNCT
iajs-2140	50	7	2019	2019	NUM
iajs-2140	50	8	proof	proof	NOUN
iajs-2140	50	9	let	let	VERB
iajs-2140	50	10	.	.	PUNCT
iajs-2140	51	1	then	then	ADV
iajs-2140	51	2	=	=	SYM
iajs-2140	51	3	⋂	⋂	PROPN
iajs-2140	51	4	,	,	PUNCT
iajs-2140	51	5	for	for	ADP
iajs-2140	51	6	some	some	PRON
iajs-2140	51	7	,	,	PUNCT
iajs-2140	51	8	hence	hence	ADV
iajs-2140	51	9	.	.	PUNCT
iajs-2140	52	1	therefore	therefore	ADV
iajs-2140	52	2	{	{	PUNCT
iajs-2140	52	3	:	:	PUNCT
iajs-2140	52	4	}	}	PUNCT
iajs-2140	52	5	and	and	CCONJ
iajs-2140	52	6	{	{	PUNCT
iajs-2140	52	7	:	:	PUNCT
iajs-2140	52	8	}	}	PUNCT
iajs-2140	52	9	.	.	PUNCT
iajs-2140	53	1	let	let	VERB
iajs-2140	53	2	{	{	PUNCT
iajs-2140	53	3	:	:	PUNCT
iajs-2140	53	4	}	}	PUNCT
iajs-2140	53	5	.	.	PUNCT
iajs-2140	54	1	then	then	ADV
iajs-2140	54	2	and	and	CCONJ
iajs-2140	54	3	,	,	PUNCT
iajs-2140	54	4	hence	hence	ADV
iajs-2140	54	5	=	=	SYM
iajs-2140	54	6	⋂	⋂	PROPN
iajs-2140	54	7	,	,	PUNCT
iajs-2140	54	8	but	but	CCONJ
iajs-2140	54	9	,	,	PUNCT
iajs-2140	54	10	then	then	ADV
iajs-2140	54	11	which	which	PRON
iajs-2140	54	12	is	be	AUX
iajs-2140	54	13	implies	imply	VERB
iajs-2140	54	14	that	that	SCONJ
iajs-2140	54	15	{	{	PUNCT
iajs-2140	54	16	:	:	PUNCT
iajs-2140	54	17	}	}	PUNCT
iajs-2140	54	18	,	,	PUNCT
iajs-2140	54	19	therefore	therefore	ADV
iajs-2140	54	20	=	=	X
iajs-2140	54	21	{	{	PUNCT
iajs-2140	54	22	:	:	PUNCT
iajs-2140	54	23	}	}	PUNCT
iajs-2140	54	24	.	.	PUNCT
iajs-2140	55	1	corollary	corollary	ADJ
iajs-2140	55	2	8	8	NUM
iajs-2140	55	3	let	let	VERB
iajs-2140	55	4	be	be	AUX
iajs-2140	55	5	a	a	PRON
iajs-2140	55	6	–	–	PUNCT
iajs-2140	55	7	of	of	ADP
iajs-2140	55	8	a	a	DET
iajs-2140	55	9	set	set	NOUN
iajs-2140	55	10	and	and	CCONJ
iajs-2140	55	11	a	a	DET
iajs-2140	55	12	non	non	ADJ
iajs-2140	55	13	-	-	ADJ
iajs-2140	55	14	empty	empty	ADJ
iajs-2140	55	15	subset	subset	NOUN
iajs-2140	55	16	of	of	ADP
iajs-2140	55	17	such	such	ADJ
iajs-2140	55	18	that	that	PRON
iajs-2140	55	19	.	.	PUNCT
iajs-2140	56	1	then	then	ADV
iajs-2140	56	2	.	.	PUNCT
iajs-2140	57	1	proof	proof	NOUN
iajs-2140	57	2	from	from	ADP
iajs-2140	57	3	proposition	proposition	NOUN
iajs-2140	57	4	7	7	NUM
iajs-2140	57	5	,	,	PUNCT
iajs-2140	57	6	we	we	PRON
iajs-2140	57	7	have	have	VERB
iajs-2140	57	8	=	=	NOUN
iajs-2140	57	9	{	{	PUNCT
iajs-2140	57	10	:	:	PUNCT
iajs-2140	57	11	}	}	PUNCT
iajs-2140	57	12	.	.	PUNCT
iajs-2140	58	1	now	now	ADV
iajs-2140	58	2	,	,	PUNCT
iajs-2140	58	3	for	for	ADP
iajs-2140	58	4	any	any	PRON
iajs-2140	58	5	,	,	PUNCT
iajs-2140	58	6	then	then	ADV
iajs-2140	58	7	{	{	PUNCT
iajs-2140	58	8	:	:	PUNCT
iajs-2140	58	9	}	}	PUNCT
iajs-2140	58	10	.	.	PUNCT
iajs-2140	59	1	hence	hence	ADV
iajs-2140	59	2	and	and	CCONJ
iajs-2140	59	3	,	,	PUNCT
iajs-2140	59	4	therefore	therefore	ADV
iajs-2140	59	5	.	.	PUNCT
iajs-2140	60	1	proposition	proposition	NOUN
iajs-2140	60	2	9	9	NUM
iajs-2140	60	3	let	let	VERB
iajs-2140	60	4	be	be	AUX
iajs-2140	60	5	a	a	PRON
iajs-2140	60	6	–	–	PUNCT
iajs-2140	60	7	of	of	ADP
iajs-2140	60	8	a	a	DET
iajs-2140	60	9	set	set	NOUN
iajs-2140	60	10	and	and	CCONJ
iajs-2140	60	11	let	let	VERB
iajs-2140	60	12	be	be	AUX
iajs-2140	60	13	a	a	DET
iajs-2140	60	14	non	non	ADJ
iajs-2140	60	15	-	-	ADJ
iajs-2140	60	16	empty	empty	ADJ
iajs-2140	60	17	subset	subset	NOUN
iajs-2140	60	18	of	of	ADP
iajs-2140	60	19	such	such	ADJ
iajs-2140	60	20	that	that	PRON
iajs-2140	60	21	.	.	PUNCT
iajs-2140	61	1	then	then	ADV
iajs-2140	61	2	is	be	AUX
iajs-2140	61	3	a	a	DET
iajs-2140	61	4	field	field	NOUN
iajs-2140	61	5	of	of	ADP
iajs-2140	61	6	a	a	DET
iajs-2140	61	7	set	set	NOUN
iajs-2140	61	8	.	.	PUNCT
iajs-2140	62	1	proof	proof	NOUN
iajs-2140	62	2	since	since	SCONJ
iajs-2140	62	3	is	be	AUX
iajs-2140	62	4	a	a	PRON
iajs-2140	62	5	–	–	PUNCT
iajs-2140	62	6	of	of	ADP
iajs-2140	62	7	,	,	PUNCT
iajs-2140	62	8	then	then	ADV
iajs-2140	62	9	.	.	PUNCT
iajs-2140	63	1	since	since	SCONJ
iajs-2140	63	2	,	,	PUNCT
iajs-2140	63	3	then	then	ADV
iajs-2140	63	4	⋂	⋂	PROPN
iajs-2140	63	5	and	and	CCONJ
iajs-2140	63	6	since	since	SCONJ
iajs-2140	63	7	⋂	⋂	PROPN
iajs-2140	63	8	,	,	PUNCT
iajs-2140	63	9	then	then	ADV
iajs-2140	63	10	φ	φ	PROPN
iajs-2140	63	11	let	let	VERB
iajs-2140	63	12	such	such	ADJ
iajs-2140	63	13	that	that	PRON
iajs-2140	63	14	then	then	ADV
iajs-2140	63	15	.	.	PUNCT
iajs-2140	64	1	but	but	CCONJ
iajs-2140	64	2	and	and	CCONJ
iajs-2140	64	3	is	be	AUX
iajs-2140	64	4	a	a	PRON
iajs-2140	64	5	–	–	PUNCT
iajs-2140	64	6	of	of	ADP
iajs-2140	64	7	a	a	DET
iajs-2140	64	8	set	set	NOUN
iajs-2140	64	9	,	,	PUNCT
iajs-2140	64	10	then	then	ADV
iajs-2140	64	11	.	.	PUNCT
iajs-2140	65	1	now	now	ADV
iajs-2140	65	2	,	,	PUNCT
iajs-2140	65	3	and	and	CCONJ
iajs-2140	65	4	,	,	PUNCT
iajs-2140	65	5	then	then	ADV
iajs-2140	65	6	let	let	VERB
iajs-2140	65	7	then	then	ADV
iajs-2140	65	8	there	there	PRON
iajs-2140	65	9	exist	exist	VERB
iajs-2140	65	10	such	such	ADJ
iajs-2140	65	11	that	that	SCONJ
iajs-2140	65	12	=	=	SYM
iajs-2140	65	13	⋂	⋂	PROPN
iajs-2140	65	14	where	where	SCONJ
iajs-2140	65	15	i=1,2	i=1,2	ADJ
iajs-2140	65	16	,	,	PUNCT
iajs-2140	65	17	…	…	PUNCT
iajs-2140	65	18	,	,	PUNCT
iajs-2140	66	1	now	now	ADV
iajs-2140	66	2	⋂	⋂	PROPN
iajs-2140	66	3	=(	=(	NOUN
iajs-2140	66	4	⋂	⋂	PROPN
iajs-2140	66	5	)	)	PUNCT
iajs-2140	66	6	⋂	⋂	PROPN
iajs-2140	66	7	but	but	CCONJ
iajs-2140	66	8	,	,	PUNCT
iajs-2140	66	9	is	be	AUX
iajs-2140	66	10	a	a	DET
iajs-2140	66	11	–	–	PUNCT
iajs-2140	66	12	,	,	PUNCT
iajs-2140	66	13	then	then	ADV
iajs-2140	66	14	⋂	⋂	PROPN
iajs-2140	66	15	.	.	PUNCT
iajs-2140	67	1	hence	hence	ADV
iajs-2140	67	2	⋂	⋂	PROPN
iajs-2140	67	3	.therefore	.therefore	ADP
iajs-2140	67	4	is	be	AUX
iajs-2140	67	5	a	a	PRON
iajs-2140	67	6	–	–	PUNCT
iajs-2140	67	7	of	of	ADP
iajs-2140	67	8	a	a	DET
iajs-2140	67	9	set	set	NOUN
iajs-2140	67	10	.	.	PUNCT
iajs-2140	68	1	if	if	SCONJ
iajs-2140	68	2	we	we	PRON
iajs-2140	68	3	take	take	VERB
iajs-2140	68	4	example	example	NOUN
iajs-2140	68	5	3	3	NUM
iajs-2140	68	6	and	and	CCONJ
iajs-2140	68	7	if	if	SCONJ
iajs-2140	68	8	we	we	PRON
iajs-2140	68	9	assume	assume	VERB
iajs-2140	68	10	that	that	SCONJ
iajs-2140	68	11	=	=	NOUN
iajs-2140	68	12	{	{	PUNCT
iajs-2140	68	13	1,2,4	1,2,4	NUM
iajs-2140	68	14	}	}	PUNCT
iajs-2140	68	15	,	,	PUNCT
iajs-2140	68	16	then	then	ADV
iajs-2140	68	17	=	=	PRON
iajs-2140	68	18	{	{	PUNCT
iajs-2140	68	19	,	,	PUNCT
iajs-2140	68	20	{	{	PUNCT
iajs-2140	68	21	1	1	NUM
iajs-2140	68	22	,	,	PUNCT
iajs-2140	68	23	2	2	NUM
iajs-2140	68	24	}	}	PUNCT
iajs-2140	68	25	,	,	PUNCT
iajs-2140	68	26	}	}	PUNCT
iajs-2140	68	27	is	be	AUX
iajs-2140	68	28	a	a	PRON
iajs-2140	68	29	–	–	PUNCT
iajs-2140	68	30	of	of	ADP
iajs-2140	68	31	a	a	DET
iajs-2140	68	32	set	set	NOUN
iajs-2140	68	33	and	and	CCONJ
iajs-2140	68	34	.	.	PUNCT
iajs-2140	69	1	definition	definition	NOUN
iajs-2140	69	2	10	10	NUM
iajs-2140	69	3	let	let	VERB
iajs-2140	69	4	be	be	AUX
iajs-2140	69	5	a	a	PRON
iajs-2140	69	6	–	–	PUNCT
iajs-2140	69	7	of	of	ADP
iajs-2140	69	8	a	a	DET
iajs-2140	69	9	set	set	NOUN
iajs-2140	69	10	.	.	PUNCT
iajs-2140	70	1	a	a	DET
iajs-2140	70	2	measure	measure	NOUN
iajs-2140	70	3	on	on	ADP
iajs-2140	70	4	is	be	AUX
iajs-2140	70	5	a	a	DET
iajs-2140	70	6	set	set	NOUN
iajs-2140	70	7	function	function	NOUN
iajs-2140	70	8	,	,	PUNCT
iajs-2140	70	9	such	such	ADJ
iajs-2140	70	10	that	that	SCONJ
iajs-2140	70	11	(	(	PUNCT
iajs-2140	70	12	)	)	PUNCT
iajs-2140	70	13	and	and	CCONJ
iajs-2140	70	14	if	if	SCONJ
iajs-2140	70	15	form	form	VERB
iajs-2140	70	16	a	a	DET
iajs-2140	70	17	finite	finite	NOUN
iajs-2140	70	18	or	or	CCONJ
iajs-2140	70	19	countably	countably	ADV
iajs-2140	70	20	infinite	infinite	ADJ
iajs-2140	70	21	collection	collection	NOUN
iajs-2140	70	22	of	of	ADP
iajs-2140	70	23	disjoint	disjoint	NOUN
iajs-2140	70	24	sets	set	NOUN
iajs-2140	70	25	in	in	ADP
iajs-2140	70	26	,	,	PUNCT
iajs-2140	70	27	then	then	ADV
iajs-2140	70	28	(	(	PUNCT
iajs-2140	70	29	)	)	PUNCT
iajs-2140	70	30	∑	∑	PROPN
iajs-2140	70	31	(	(	PUNCT
iajs-2140	70	32	)	)	PUNCT
iajs-2140	70	33	.	.	PUNCT
iajs-2140	71	1	example	example	NOUN
iajs-2140	71	2	11	11	NUM
iajs-2140	71	3	let	let	VERB
iajs-2140	71	4	be	be	AUX
iajs-2140	71	5	a	a	PRON
iajs-2140	71	6	–	–	PUNCT
iajs-2140	71	7	of	of	ADP
iajs-2140	71	8	a	a	DET
iajs-2140	71	9	set	set	NOUN
iajs-2140	71	10	and	and	CCONJ
iajs-2140	71	11	define	define	VERB
iajs-2140	71	12	,	,	PUNCT
iajs-2140	71	13	by	by	ADP
iajs-2140	71	14	(	(	PUNCT
iajs-2140	71	15	)	)	PUNCT
iajs-2140	71	16	=	=	SYM
iajs-2140	71	17	0	0	NUM
iajs-2140	71	18	,	,	PUNCT
iajs-2140	71	19	for	for	ADP
iajs-2140	71	20	all	all	PRON
iajs-2140	71	21	.	.	PUNCT
iajs-2140	72	1	then	then	ADV
iajs-2140	72	2	is	be	AUX
iajs-2140	72	3	a	a	DET
iajs-2140	72	4	measure	measure	NOUN
iajs-2140	72	5	on	on	ADP
iajs-2140	72	6	.	.	PUNCT
iajs-2140	73	1	a	a	DET
iajs-2140	73	2	measure	measure	NOUN
iajs-2140	73	3	space	space	NOUN
iajs-2140	73	4	is	be	AUX
iajs-2140	73	5	a	a	DET
iajs-2140	73	6	triple	triple	ADJ
iajs-2140	73	7	(	(	PUNCT
iajs-2140	73	8	)	)	PUNCT
iajs-2140	73	9	where	where	SCONJ
iajs-2140	73	10	is	be	AUX
iajs-2140	73	11	a	a	DET
iajs-2140	73	12	nonempty	nonempty	ADV
iajs-2140	73	13	set	set	VERB
iajs-2140	73	14	and	and	CCONJ
iajs-2140	73	15	is	be	AUX
iajs-2140	73	16	a	a	PRON
iajs-2140	73	17	–	–	PUNCT
iajs-2140	73	18	of	of	ADP
iajs-2140	73	19	a	a	DET
iajs-2140	73	20	set	set	NOUN
iajs-2140	73	21	and	and	CCONJ
iajs-2140	73	22	is	be	AUX
iajs-2140	73	23	a	a	DET
iajs-2140	73	24	measure	measure	NOUN
iajs-2140	73	25	on	on	ADP
iajs-2140	73	26	definition	definition	NOUN
iajs-2140	73	27	12	12	NUM
iajs-2140	73	28	let	let	AUX
iajs-2140	73	29	be	be	AUX
iajs-2140	73	30	a	a	PRON
iajs-2140	73	31	–	–	PUNCT
iajs-2140	73	32	of	of	ADP
iajs-2140	73	33	a	a	DET
iajs-2140	73	34	set	set	NOUN
iajs-2140	73	35	.	.	PUNCT
iajs-2140	74	1	a	a	DET
iajs-2140	74	2	countably	countably	ADV
iajs-2140	74	3	subadditive	subadditive	ADJ
iajs-2140	74	4	on	on	ADP
iajs-2140	74	5	is	be	AUX
iajs-2140	74	6	a	a	DET
iajs-2140	74	7	set	set	NOUN
iajs-2140	74	8	function	function	NOUN
iajs-2140	74	9	,	,	PUNCT
iajs-2140	74	10	such	such	ADJ
iajs-2140	74	11	that	that	SCONJ
iajs-2140	74	12	(	(	PUNCT
iajs-2140	74	13	)	)	PUNCT
iajs-2140	74	14	∑	∑	PUNCT
iajs-2140	74	15	(	(	PUNCT
iajs-2140	74	16	)	)	PUNCT
iajs-2140	74	17	where	where	SCONJ
iajs-2140	74	18	and	and	CCONJ
iajs-2140	74	19	.	.	PUNCT
iajs-2140	75	1	if	if	SCONJ
iajs-2140	75	2	this	this	DET
iajs-2140	75	3	requirement	requirement	NOUN
iajs-2140	75	4	holds	hold	VERB
iajs-2140	75	5	only	only	ADV
iajs-2140	75	6	for	for	ADP
iajs-2140	75	7	finite	finite	ADJ
iajs-2140	75	8	collection	collection	NOUN
iajs-2140	75	9	of	of	ADP
iajs-2140	75	10	disjoint	disjoint	NOUN
iajs-2140	75	11	sets	set	NOUN
iajs-2140	75	12	in	in	ADP
iajs-2140	75	13	,	,	PUNCT
iajs-2140	75	14	then	then	ADV
iajs-2140	75	15	is	be	AUX
iajs-2140	75	16	said	say	VERB
iajs-2140	75	17	to	to	PART
iajs-2140	75	18	be	be	AUX
iajs-2140	75	19	finitely	finitely	ADV
iajs-2140	75	20	subadditive	subadditive	ADJ
iajs-2140	75	21	on	on	ADP
iajs-2140	75	22	a	a	PRON
iajs-2140	75	23	–	–	PUNCT
iajs-2140	75	24	.	.	PUNCT
iajs-2140	76	1	definition	definition	NOUN
iajs-2140	76	2	13	13	NUM
iajs-2140	76	3	let	let	VERB
iajs-2140	76	4	be	be	AUX
iajs-2140	76	5	a	a	PRON
iajs-2140	76	6	–	–	PUNCT
iajs-2140	76	7	of	of	ADP
iajs-2140	76	8	a	a	DET
iajs-2140	76	9	set	set	NOUN
iajs-2140	76	10	.	.	PUNCT
iajs-2140	77	1	then	then	ADV
iajs-2140	77	2	a	a	DET
iajs-2140	77	3	set	set	NOUN
iajs-2140	77	4	function	function	NOUN
iajs-2140	77	5	,	,	PUNCT
iajs-2140	77	6	is	be	AUX
iajs-2140	77	7	said	say	VERB
iajs-2140	77	8	to	to	PART
iajs-2140	77	9	be	be	AUX
iajs-2140	77	10	monotone	monotone	ADJ
iajs-2140	77	11	measure	measure	NOUN
iajs-2140	77	12	,	,	PUNCT
iajs-2140	77	13	if	if	SCONJ
iajs-2140	77	14	it	it	PRON
iajs-2140	77	15	satisfies	satisfy	VERB
iajs-2140	77	16	the	the	DET
iajs-2140	77	17	following	follow	VERB
iajs-2140	77	18	requirements	requirement	NOUN
iajs-2140	77	19	:	:	PUNCT
iajs-2140	77	20	1	1	NUM
iajs-2140	77	21	(	(	PUNCT
iajs-2140	77	22	)	)	PUNCT
iajs-2140	77	23	2if	2if	NOUN
iajs-2140	77	24	and	and	CCONJ
iajs-2140	77	25	,	,	PUNCT
iajs-2140	77	26	then	then	ADV
iajs-2140	77	27	(	(	PUNCT
iajs-2140	77	28	)	)	PUNCT
iajs-2140	77	29	(	(	PUNCT
iajs-2140	77	30	)	)	PUNCT
iajs-2140	77	31	.	.	PUNCT
iajs-2140	78	1	26	26	NUM
iajs-2140	78	2	ibn	ibn	PROPN
iajs-2140	78	3	al	al	PROPN
iajs-2140	78	4	-	-	PUNCT
iajs-2140	78	5	haitham	haitham	PROPN
iajs-2140	78	6	jour	jour	X
iajs-2140	78	7	.	.	PROPN
iajs-2140	78	8	for	for	ADP
iajs-2140	78	9	pure	pure	ADJ
iajs-2140	78	10	&	&	CCONJ
iajs-2140	78	11	appl	appl	PROPN
iajs-2140	78	12	.	.	PUNCT
iajs-2140	79	1	sci	sci	PROPN
iajs-2140	79	2	.	.	PROPN
iajs-2140	79	3	32	32	NUM
iajs-2140	79	4	(	(	PUNCT
iajs-2140	79	5	2	2	NUM
iajs-2140	79	6	)	)	PUNCT
iajs-2140	79	7	2019	2019	NUM
iajs-2140	79	8	definition	definition	NOUN
iajs-2140	79	9	14	14	NUM
iajs-2140	79	10	let	let	VERB
iajs-2140	79	11	be	be	AUX
iajs-2140	79	12	a	a	PRON
iajs-2140	79	13	–	–	PUNCT
iajs-2140	79	14	of	of	ADP
iajs-2140	79	15	a	a	DET
iajs-2140	79	16	set	set	NOUN
iajs-2140	79	17	.	.	PUNCT
iajs-2140	80	1	then	then	ADV
iajs-2140	80	2	a	a	DET
iajs-2140	80	3	set	set	NOUN
iajs-2140	80	4	function	function	NOUN
iajs-2140	80	5	,	,	PUNCT
iajs-2140	80	6	is	be	AUX
iajs-2140	80	7	called	call	VERB
iajs-2140	80	8	outer	outer	ADJ
iajs-2140	80	9	measure	measure	NOUN
iajs-2140	80	10	,	,	PUNCT
iajs-2140	80	11	if	if	SCONJ
iajs-2140	80	12	it	it	PRON
iajs-2140	80	13	satisfies	satisfy	VERB
iajs-2140	80	14	the	the	DET
iajs-2140	80	15	following	follow	VERB
iajs-2140	80	16	requirements	requirement	NOUN
iajs-2140	80	17	:	:	PUNCT
iajs-2140	80	18	1	1	NUM
iajs-2140	80	19	(	(	PUNCT
iajs-2140	80	20	)	)	PUNCT
iajs-2140	80	21	.	.	PUNCT
iajs-2140	81	1	2if	2if	NOUN
iajs-2140	81	2	and	and	CCONJ
iajs-2140	81	3	,	,	PUNCT
iajs-2140	81	4	then	then	ADV
iajs-2140	81	5	(	(	PUNCT
iajs-2140	81	6	)	)	PUNCT
iajs-2140	81	7	(	(	PUNCT
iajs-2140	81	8	)	)	PUNCT
iajs-2140	81	9	.	.	PUNCT
iajs-2140	82	1	3if	3if	NOUN
iajs-2140	82	2	,	,	PUNCT
iajs-2140	82	3	then	then	ADV
iajs-2140	82	4	(	(	PUNCT
iajs-2140	82	5	)	)	PUNCT
iajs-2140	82	6	∑	∑	PROPN
iajs-2140	82	7	(	(	PUNCT
iajs-2140	82	8	)	)	PUNCT
iajs-2140	82	9	.	.	PUNCT
iajs-2140	83	1	lemma	lemma	PROPN
iajs-2140	83	2	15	15	NUM
iajs-2140	83	3	let	let	VERB
iajs-2140	83	4	be	be	AUX
iajs-2140	83	5	an	an	DET
iajs-2140	83	6	outer	outer	ADJ
iajs-2140	83	7	measure	measure	NOUN
iajs-2140	83	8	on	on	ADP
iajs-2140	83	9	–	–	PUNCT
iajs-2140	83	10	of	of	ADP
iajs-2140	83	11	a	a	DET
iajs-2140	83	12	set	set	NOUN
iajs-2140	83	13	and	and	CCONJ
iajs-2140	83	14	,	,	PUNCT
iajs-2140	83	15	)	)	PUNCT
iajs-2140	83	16	.	.	PUNCT
iajs-2140	84	1	if	if	SCONJ
iajs-2140	84	2	:	:	PUNCT
iajs-2140	84	3	,	,	PUNCT
iajs-2140	84	4	is	be	AUX
iajs-2140	84	5	defined	define	VERB
iajs-2140	84	6	by	by	ADP
iajs-2140	84	7	(	(	PUNCT
iajs-2140	84	8	)	)	PUNCT
iajs-2140	84	9	(	(	PUNCT
iajs-2140	84	10	)	)	PUNCT
iajs-2140	84	11	(	(	PUNCT
iajs-2140	84	12	)	)	PUNCT
iajs-2140	84	13	,	,	PUNCT
iajs-2140	84	14	then	then	ADV
iajs-2140	84	15	(	(	PUNCT
iajs-2140	84	16	)	)	PUNCT
iajs-2140	84	17	is	be	AUX
iajs-2140	84	18	an	an	DET
iajs-2140	84	19	outer	outer	ADJ
iajs-2140	84	20	measure	measure	NOUN
iajs-2140	84	21	on	on	ADP
iajs-2140	84	22	.	.	PUNCT
iajs-2140	85	1	proof	proof	NOUN
iajs-2140	85	2	since	since	SCONJ
iajs-2140	85	3	is	be	AUX
iajs-2140	85	4	an	an	DET
iajs-2140	85	5	outer	outer	ADJ
iajs-2140	85	6	measure	measure	NOUN
iajs-2140	85	7	on	on	ADP
iajs-2140	85	8	and	and	CCONJ
iajs-2140	85	9	,	,	PUNCT
iajs-2140	85	10	then	then	ADV
iajs-2140	85	11	(	(	PUNCT
iajs-2140	85	12	)	)	PUNCT
iajs-2140	86	1	=	=	SYM
iajs-2140	86	2	0	0	NUM
iajs-2140	86	3	and	and	CCONJ
iajs-2140	86	4	(	(	PUNCT
iajs-2140	86	5	)	)	PUNCT
iajs-2140	86	6	(	(	PUNCT
iajs-2140	86	7	)	)	PUNCT
iajs-2140	86	8	=	=	SYM
iajs-2140	86	9	0	0	X
iajs-2140	86	10	.	.	PUNCT
iajs-2140	87	1	let	let	VERB
iajs-2140	87	2	and	and	CCONJ
iajs-2140	87	3	,	,	PUNCT
iajs-2140	87	4	then	then	ADV
iajs-2140	87	5	and	and	CCONJ
iajs-2140	87	6	(	(	PUNCT
iajs-2140	87	7	)	)	PUNCT
iajs-2140	87	8	(	(	PUNCT
iajs-2140	87	9	)	)	PUNCT
iajs-2140	87	10	.	.	PUNCT
iajs-2140	88	1	since	since	SCONJ
iajs-2140	88	2	(	(	PUNCT
iajs-2140	88	3	)	)	PUNCT
iajs-2140	88	4	(	(	PUNCT
iajs-2140	88	5	)	)	PUNCT
iajs-2140	88	6	(	(	PUNCT
iajs-2140	88	7	)	)	PUNCT
iajs-2140	88	8	(	(	PUNCT
iajs-2140	88	9	)	)	PUNCT
iajs-2140	88	10	(	(	PUNCT
iajs-2140	88	11	)	)	PUNCT
iajs-2140	88	12	(	(	PUNCT
iajs-2140	88	13	)	)	PUNCT
iajs-2140	88	14	let	let	VERB
iajs-2140	88	15	,	,	PUNCT
iajs-2140	88	16	then	then	ADV
iajs-2140	88	17	so	so	ADV
iajs-2140	88	18	,	,	PUNCT
iajs-2140	88	19	we	we	PRON
iajs-2140	88	20	have	have	VERB
iajs-2140	88	21	(	(	PUNCT
iajs-2140	88	22	)	)	PUNCT
iajs-2140	88	23	(	(	PUNCT
iajs-2140	88	24	)	)	PUNCT
iajs-2140	88	25	(	(	PUNCT
iajs-2140	88	26	)	)	PUNCT
iajs-2140	88	27	∑	∑	PUNCT
iajs-2140	88	28	(	(	PUNCT
iajs-2140	88	29	)	)	PUNCT
iajs-2140	88	30	but	but	CCONJ
iajs-2140	88	31	,	,	PUNCT
iajs-2140	88	32	∑	∑	ADP
iajs-2140	88	33	(	(	PUNCT
iajs-2140	88	34	)	)	PUNCT
iajs-2140	88	35	∑	∑	PUNCT
iajs-2140	88	36	(	(	PUNCT
iajs-2140	88	37	)	)	PUNCT
iajs-2140	88	38	∑	∑	PUNCT
iajs-2140	88	39	(	(	PUNCT
iajs-2140	88	40	)	)	PUNCT
iajs-2140	88	41	(	(	PUNCT
iajs-2140	88	42	)	)	PUNCT
iajs-2140	88	43	.	.	PUNCT
iajs-2140	89	1	therefore	therefore	ADV
iajs-2140	89	2	is	be	AUX
iajs-2140	89	3	an	an	DET
iajs-2140	89	4	outer	outer	ADJ
iajs-2140	89	5	measure	measure	NOUN
iajs-2140	89	6	on	on	ADP
iajs-2140	89	7	.	.	PUNCT
iajs-2140	90	1	lemma	lemma	PROPN
iajs-2140	90	2	16	16	NUM
iajs-2140	90	3	let	let	VERB
iajs-2140	90	4	and	and	CCONJ
iajs-2140	90	5	be	be	AUX
iajs-2140	90	6	two	two	NUM
iajs-2140	90	7	outer	outer	ADJ
iajs-2140	90	8	measures	measure	NOUN
iajs-2140	90	9	on	on	ADP
iajs-2140	90	10	a	a	PRON
iajs-2140	90	11	–	–	PUNCT
iajs-2140	90	12	of	of	ADP
iajs-2140	90	13	a	a	DET
iajs-2140	90	14	set	set	NOUN
iajs-2140	90	15	.	.	PUNCT
iajs-2140	91	1	if	if	SCONJ
iajs-2140	91	2	:	:	PUNCT
iajs-2140	91	3	,	,	PUNCT
iajs-2140	91	4	is	be	AUX
iajs-2140	91	5	defined	define	VERB
iajs-2140	91	6	by	by	ADP
iajs-2140	91	7	(	(	PUNCT
iajs-2140	91	8	)	)	PUNCT
iajs-2140	91	9	(	(	PUNCT
iajs-2140	91	10	)	)	PUNCT
iajs-2140	91	11	(	(	PUNCT
iajs-2140	91	12	)	)	PUNCT
iajs-2140	91	13	(	(	PUNCT
iajs-2140	91	14	)	)	PUNCT
iajs-2140	91	15	,	,	PUNCT
iajs-2140	91	16	,	,	PUNCT
iajs-2140	91	17	then	then	ADV
iajs-2140	91	18	is	be	AUX
iajs-2140	91	19	an	an	DET
iajs-2140	91	20	outer	outer	ADJ
iajs-2140	91	21	measure	measure	NOUN
iajs-2140	91	22	on	on	ADP
iajs-2140	91	23	.	.	PUNCT
iajs-2140	92	1	proof	proof	NOUN
iajs-2140	92	2	since	since	SCONJ
iajs-2140	92	3	and	and	CCONJ
iajs-2140	92	4	are	be	AUX
iajs-2140	92	5	outer	outer	ADJ
iajs-2140	92	6	measure	measure	NOUN
iajs-2140	92	7	on	on	ADP
iajs-2140	92	8	–	–	PUNCT
iajs-2140	92	9	and	and	CCONJ
iajs-2140	92	10	,	,	PUNCT
iajs-2140	92	11	then	then	ADV
iajs-2140	92	12	(	(	PUNCT
iajs-2140	92	13	)	)	PUNCT
iajs-2140	92	14	=	=	SYM
iajs-2140	92	15	(	(	PUNCT
iajs-2140	92	16	)	)	PUNCT
iajs-2140	92	17	=	=	SYM
iajs-2140	92	18	0	0	PUNCT
iajs-2140	92	19	and	and	CCONJ
iajs-2140	92	20	(	(	PUNCT
iajs-2140	92	21	)	)	PUNCT
iajs-2140	92	22	(	(	PUNCT
iajs-2140	92	23	)	)	PUNCT
iajs-2140	92	24	=	=	SYM
iajs-2140	92	25	0	0	X
iajs-2140	92	26	.	.	PUNCT
iajs-2140	93	1	let	let	VERB
iajs-2140	93	2	and	and	CCONJ
iajs-2140	93	3	,	,	PUNCT
iajs-2140	93	4	then	then	ADV
iajs-2140	93	5	and	and	CCONJ
iajs-2140	93	6	(	(	PUNCT
iajs-2140	93	7	)	)	PUNCT
iajs-2140	93	8	(	(	PUNCT
iajs-2140	93	9	)	)	PUNCT
iajs-2140	93	10	and	and	CCONJ
iajs-2140	93	11	(	(	PUNCT
iajs-2140	93	12	)	)	PUNCT
iajs-2140	93	13	(	(	PUNCT
iajs-2140	93	14	)	)	PUNCT
iajs-2140	93	15	.	.	PUNCT
iajs-2140	94	1	so	so	ADV
iajs-2140	94	2	we	we	PRON
iajs-2140	94	3	have	have	VERB
iajs-2140	94	4	,	,	PUNCT
iajs-2140	94	5	(	(	PUNCT
iajs-2140	94	6	)	)	PUNCT
iajs-2140	94	7	(	(	PUNCT
iajs-2140	94	8	)	)	PUNCT
iajs-2140	94	9	(	(	PUNCT
iajs-2140	94	10	)	)	PUNCT
iajs-2140	94	11	(	(	PUNCT
iajs-2140	94	12	)	)	PUNCT
iajs-2140	94	13	(	(	PUNCT
iajs-2140	94	14	)	)	PUNCT
iajs-2140	95	1	+	+	CCONJ
iajs-2140	95	2	(	(	PUNCT
iajs-2140	95	3	)	)	PUNCT
iajs-2140	95	4	(	(	PUNCT
iajs-2140	95	5	)	)	PUNCT
iajs-2140	95	6	(	(	PUNCT
iajs-2140	95	7	)	)	PUNCT
iajs-2140	95	8	let	let	VERB
iajs-2140	95	9	,	,	PUNCT
iajs-2140	95	10	then	then	ADV
iajs-2140	95	11	.	.	PUNCT
iajs-2140	96	1	so	so	ADV
iajs-2140	96	2	,	,	PUNCT
iajs-2140	96	3	we	we	PRON
iajs-2140	96	4	have	have	VERB
iajs-2140	96	5	(	(	PUNCT
iajs-2140	96	6	)	)	PUNCT
iajs-2140	96	7	(	(	PUNCT
iajs-2140	96	8	)	)	PUNCT
iajs-2140	96	9	(	(	PUNCT
iajs-2140	96	10	)	)	PUNCT
iajs-2140	96	11	(	(	PUNCT
iajs-2140	96	12	)	)	PUNCT
iajs-2140	96	13	∑	∑	PUNCT
iajs-2140	96	14	(	(	PUNCT
iajs-2140	96	15	)	)	PUNCT
iajs-2140	96	16	∑	∑	PUNCT
iajs-2140	96	17	(	(	PUNCT
iajs-2140	96	18	)	)	PUNCT
iajs-2140	96	19	∑	∑	INTJ
iajs-2140	96	20	,	,	PUNCT
iajs-2140	96	21	(	(	PUNCT
iajs-2140	96	22	)	)	PUNCT
iajs-2140	96	23	(	(	PUNCT
iajs-2140	96	24	)	)	PUNCT
iajs-2140	96	25	∑	∑	PROPN
iajs-2140	96	26	(	(	PUNCT
iajs-2140	96	27	)	)	PUNCT
iajs-2140	96	28	(	(	PUNCT
iajs-2140	96	29	)	)	PUNCT
iajs-2140	96	30	.	.	PUNCT
iajs-2140	97	1	therefore	therefore	ADV
iajs-2140	97	2	is	be	AUX
iajs-2140	97	3	an	an	DET
iajs-2140	97	4	outer	outer	ADJ
iajs-2140	97	5	measure	measure	NOUN
iajs-2140	97	6	on	on	ADP
iajs-2140	97	7	.	.	PUNCT
iajs-2140	98	1	the	the	DET
iajs-2140	98	2	proof	proof	NOUN
iajs-2140	98	3	of	of	ADP
iajs-2140	98	4	the	the	DET
iajs-2140	98	5	following	follow	VERB
iajs-2140	98	6	proposition	proposition	NOUN
iajs-2140	98	7	consequence	consequence	NOUN
iajs-2140	98	8	from	from	ADP
iajs-2140	98	9	lemma	lemma	PROPN
iajs-2140	98	10	(	(	PUNCT
iajs-2140	98	11	15	15	NUM
iajs-2140	98	12	and	and	CCONJ
iajs-2140	98	13	16	16	NUM
iajs-2140	98	14	)	)	PUNCT
iajs-2140	98	15	with	with	ADP
iajs-2140	98	16	mathematical	mathematical	ADJ
iajs-2140	98	17	induction	induction	NOUN
iajs-2140	98	18	.	.	PUNCT
iajs-2140	99	1	proposition	proposition	NOUN
iajs-2140	99	2	17	17	NUM
iajs-2140	99	3	let	let	VERB
iajs-2140	99	4	,	,	PUNCT
iajs-2140	99	5	,	,	PUNCT
iajs-2140	99	6	…	…	PUNCT
iajs-2140	99	7	,	,	PUNCT
iajs-2140	99	8	be	be	AUX
iajs-2140	99	9	outer	outer	ADJ
iajs-2140	99	10	measure	measure	NOUN
iajs-2140	99	11	on	on	ADP
iajs-2140	99	12	a	a	PRON
iajs-2140	99	13	–	–	PUNCT
iajs-2140	99	14	of	of	ADP
iajs-2140	99	15	a	a	DET
iajs-2140	99	16	set	set	NOUN
iajs-2140	99	17	and	and	CCONJ
iajs-2140	99	18	,	,	PUNCT
iajs-2140	99	19	)	)	PUNCT
iajs-2140	99	20	for	for	ADP
iajs-2140	99	21	all	all	PRON
iajs-2140	99	22	.	.	PUNCT
iajs-2140	100	1	if	if	SCONJ
iajs-2140	100	2	a	a	DET
iajs-2140	100	3	set	set	NOUN
iajs-2140	100	4	function	function	NOUN
iajs-2140	100	5	∑	∑	PUNCT
iajs-2140	100	6	:	:	PUNCT
iajs-2140	100	7	,	,	PUNCT
iajs-2140	100	8	is	be	AUX
iajs-2140	100	9	defined	define	VERB
iajs-2140	100	10	by	by	ADP
iajs-2140	100	11	:	:	PUNCT
iajs-2140	100	12	(	(	PUNCT
iajs-2140	100	13	∑	∑	PROPN
iajs-2140	100	14	)	)	PUNCT
iajs-2140	100	15	(	(	PUNCT
iajs-2140	100	16	)	)	PUNCT
iajs-2140	100	17	∑	∑	PUNCT
iajs-2140	100	18	(	(	PUNCT
iajs-2140	100	19	)	)	PUNCT
iajs-2140	100	20	,	,	PUNCT
iajs-2140	100	21	then	then	ADV
iajs-2140	100	22	∑	∑	PUNCT
iajs-2140	100	23	is	be	AUX
iajs-2140	100	24	an	an	DET
iajs-2140	100	25	outer	outer	ADJ
iajs-2140	100	26	measure	measure	NOUN
iajs-2140	100	27	on	on	ADP
iajs-2140	100	28	–	–	PUNCT
iajs-2140	100	29	.	.	PUNCT
iajs-2140	101	1	proof	proof	NOUN
iajs-2140	101	2	since	since	SCONJ
iajs-2140	101	3	,	,	PUNCT
iajs-2140	101	4	)	)	PUNCT
iajs-2140	101	5	and	and	CCONJ
iajs-2140	101	6	is	be	AUX
iajs-2140	101	7	an	an	DET
iajs-2140	101	8	outer	outer	ADJ
iajs-2140	101	9	measure	measure	NOUN
iajs-2140	101	10	on	on	ADP
iajs-2140	101	11	a	a	PRON
iajs-2140	101	12	–	–	PUNCT
iajs-2140	101	13	for	for	ADP
iajs-2140	101	14	all	all	PRON
iajs-2140	101	15	.	.	PUNCT
iajs-2140	102	1	then	then	ADV
iajs-2140	102	2	by	by	ADP
iajs-2140	102	3	lemma15	lemma15	NOUN
iajs-2140	102	4	we	we	PRON
iajs-2140	102	5	get	get	VERB
iajs-2140	102	6	is	be	AUX
iajs-2140	102	7	an	an	DET
iajs-2140	102	8	outer	outer	ADJ
iajs-2140	102	9	measure	measure	NOUN
iajs-2140	102	10	on	on	ADP
iajs-2140	102	11	a	a	DET
iajs-2140	102	12	–	–	PUNCT
iajs-2140	102	13	=	=	SYM
iajs-2140	102	14	22	22	NUM
iajs-2140	102	15	ibn	ibn	PROPN
iajs-2140	102	16	al	al	PROPN
iajs-2140	102	17	-	-	PUNCT
iajs-2140	102	18	haitham	haitham	PROPN
iajs-2140	102	19	jour	jour	X
iajs-2140	102	20	.	.	PROPN
iajs-2140	103	1	for	for	ADP
iajs-2140	103	2	pure	pure	ADJ
iajs-2140	103	3	&	&	CCONJ
iajs-2140	103	4	appl	appl	PROPN
iajs-2140	103	5	.	.	PUNCT
iajs-2140	104	1	sci	sci	PROPN
iajs-2140	104	2	.	.	PROPN
iajs-2140	104	3	32	32	NUM
iajs-2140	104	4	(	(	PUNCT
iajs-2140	104	5	2	2	NUM
iajs-2140	104	6	)	)	PUNCT
iajs-2140	104	7	2019	2019	NUM
iajs-2140	104	8	let	let	VERB
iajs-2140	104	9	.	.	PUNCT
iajs-2140	105	1	then	then	ADV
iajs-2140	105	2	we	we	PRON
iajs-2140	105	3	prove	prove	VERB
iajs-2140	105	4	that	that	SCONJ
iajs-2140	105	5	(	(	PUNCT
iajs-2140	105	6	∑	∑	PUNCT
iajs-2140	105	7	)	)	PUNCT
iajs-2140	105	8	is	be	AUX
iajs-2140	105	9	an	an	DET
iajs-2140	105	10	outer	outer	ADJ
iajs-2140	105	11	measure	measure	NOUN
iajs-2140	105	12	on	on	ADP
iajs-2140	105	13	by	by	ADP
iajs-2140	105	14	mathematical	mathematical	ADJ
iajs-2140	105	15	induction	induction	NOUN
iajs-2140	105	16	.	.	PUNCT
iajs-2140	106	1	if	if	SCONJ
iajs-2140	106	2	,	,	PUNCT
iajs-2140	106	3	then	then	ADV
iajs-2140	106	4	is	be	AUX
iajs-2140	106	5	an	an	DET
iajs-2140	106	6	outer	outer	ADJ
iajs-2140	106	7	measure	measure	NOUN
iajs-2140	106	8	on	on	ADP
iajs-2140	106	9	by	by	ADP
iajs-2140	106	10	lemma16	lemma16	PROPN
iajs-2140	106	11	.	.	PUNCT
iajs-2140	107	1	suppose	suppose	VERB
iajs-2140	107	2	that	that	SCONJ
iajs-2140	107	3	(	(	PUNCT
iajs-2140	107	4	∑	∑	INTJ
iajs-2140	107	5	)	)	PUNCT
iajs-2140	107	6	is	be	AUX
iajs-2140	107	7	an	an	DET
iajs-2140	107	8	outer	outer	ADJ
iajs-2140	107	9	measure	measure	NOUN
iajs-2140	107	10	on	on	ADP
iajs-2140	107	11	,	,	PUNCT
iajs-2140	107	12	then	then	ADV
iajs-2140	107	13	we	we	PRON
iajs-2140	107	14	must	must	AUX
iajs-2140	107	15	prove	prove	VERB
iajs-2140	107	16	that	that	SCONJ
iajs-2140	107	17	(	(	PUNCT
iajs-2140	107	18	∑	∑	PUNCT
iajs-2140	107	19	)	)	PUNCT
iajs-2140	107	20	is	be	AUX
iajs-2140	107	21	an	an	DET
iajs-2140	107	22	outer	outer	ADJ
iajs-2140	107	23	measure	measure	NOUN
iajs-2140	107	24	on	on	ADP
iajs-2140	107	25	,	,	PUNCT
iajs-2140	107	26	whenever	whenever	SCONJ
iajs-2140	107	27	is	be	AUX
iajs-2140	107	28	an	an	DET
iajs-2140	107	29	outer	outer	ADJ
iajs-2140	107	30	measure	measure	NOUN
iajs-2140	107	31	on	on	ADP
iajs-2140	107	32	.	.	PUNCT
iajs-2140	108	1	(	(	PUNCT
iajs-2140	108	2	∑	∑	PROPN
iajs-2140	108	3	)	)	PUNCT
iajs-2140	108	4	(	(	PUNCT
iajs-2140	108	5	)	)	PUNCT
iajs-2140	108	6	(	(	PUNCT
iajs-2140	108	7	∑	∑	PUNCT
iajs-2140	108	8	)	)	PUNCT
iajs-2140	108	9	(	(	PUNCT
iajs-2140	108	10	)	)	PUNCT
iajs-2140	108	11	(	(	PUNCT
iajs-2140	108	12	∑	∑	PUNCT
iajs-2140	108	13	)	)	PUNCT
iajs-2140	108	14	(	(	PUNCT
iajs-2140	108	15	)	)	PUNCT
iajs-2140	108	16	(	(	PUNCT
iajs-2140	108	17	)	)	PUNCT
iajs-2140	108	18	since	since	SCONJ
iajs-2140	108	19	(	(	PUNCT
iajs-2140	108	20	∑	∑	PUNCT
iajs-2140	108	21	)	)	PUNCT
iajs-2140	108	22	and	and	CCONJ
iajs-2140	108	23	are	be	AUX
iajs-2140	108	24	outer	outer	ADJ
iajs-2140	108	25	measure	measure	NOUN
iajs-2140	108	26	on	on	ADP
iajs-2140	108	27	let	let	NOUN
iajs-2140	108	28	and	and	CCONJ
iajs-2140	108	29	.	.	PUNCT
iajs-2140	109	1	then	then	ADV
iajs-2140	109	2	(	(	PUNCT
iajs-2140	109	3	∑	∑	PUNCT
iajs-2140	109	4	)	)	PUNCT
iajs-2140	109	5	(	(	PUNCT
iajs-2140	109	6	)	)	PUNCT
iajs-2140	109	7	(	(	PUNCT
iajs-2140	109	8	∑	∑	PROPN
iajs-2140	109	9	)	)	PUNCT
iajs-2140	109	10	(	(	PUNCT
iajs-2140	109	11	)	)	PUNCT
iajs-2140	109	12	and	and	CCONJ
iajs-2140	109	13	(	(	PUNCT
iajs-2140	109	14	)	)	PUNCT
iajs-2140	109	15	(	(	PUNCT
iajs-2140	109	16	)	)	PUNCT
iajs-2140	109	17	(	(	PUNCT
iajs-2140	109	18	∑	∑	PROPN
iajs-2140	109	19	)	)	PUNCT
iajs-2140	109	20	(	(	PUNCT
iajs-2140	109	21	)	)	PUNCT
iajs-2140	109	22	(	(	PUNCT
iajs-2140	109	23	∑	∑	PROPN
iajs-2140	109	24	)	)	PUNCT
iajs-2140	109	25	(	(	PUNCT
iajs-2140	109	26	)	)	PUNCT
iajs-2140	109	27	(	(	PUNCT
iajs-2140	109	28	)	)	PUNCT
iajs-2140	109	29	(	(	PUNCT
iajs-2140	109	30	∑	∑	PROPN
iajs-2140	109	31	)	)	PUNCT
iajs-2140	109	32	(	(	PUNCT
iajs-2140	109	33	)	)	PUNCT
iajs-2140	109	34	(	(	PUNCT
iajs-2140	109	35	)	)	PUNCT
iajs-2140	109	36	since	since	SCONJ
iajs-2140	109	37	(	(	PUNCT
iajs-2140	109	38	∑	∑	PUNCT
iajs-2140	109	39	)	)	PUNCT
iajs-2140	109	40	and	and	CCONJ
iajs-2140	109	41	are	be	AUX
iajs-2140	109	42	outer	outer	ADJ
iajs-2140	109	43	measure	measure	NOUN
iajs-2140	109	44	(	(	PUNCT
iajs-2140	109	45	∑	∑	PROPN
iajs-2140	109	46	)	)	PUNCT
iajs-2140	109	47	(	(	PUNCT
iajs-2140	109	48	)	)	PUNCT
iajs-2140	109	49	(	(	PUNCT
iajs-2140	109	50	∑	∑	PUNCT
iajs-2140	109	51	)	)	PUNCT
iajs-2140	109	52	(	(	PUNCT
iajs-2140	109	53	)	)	PUNCT
iajs-2140	109	54	let	let	VERB
iajs-2140	109	55	.	.	PUNCT
iajs-2140	110	1	then	then	ADV
iajs-2140	110	2	(	(	PUNCT
iajs-2140	110	3	∑	∑	PROPN
iajs-2140	110	4	)	)	PUNCT
iajs-2140	110	5	(	(	PUNCT
iajs-2140	110	6	)	)	PUNCT
iajs-2140	110	7	(	(	PUNCT
iajs-2140	110	8	∑	∑	PROPN
iajs-2140	110	9	)	)	PUNCT
iajs-2140	110	10	(	(	PUNCT
iajs-2140	110	11	)	)	PUNCT
iajs-2140	110	12	(	(	PUNCT
iajs-2140	110	13	∑	∑	PROPN
iajs-2140	110	14	)	)	PUNCT
iajs-2140	110	15	(	(	PUNCT
iajs-2140	110	16	)	)	PUNCT
iajs-2140	110	17	(	(	PUNCT
iajs-2140	110	18	)	)	PUNCT
iajs-2140	110	19	∑	∑	PROPN
iajs-2140	110	20	(	(	PUNCT
iajs-2140	110	21	∑	∑	PROPN
iajs-2140	110	22	)	)	PUNCT
iajs-2140	110	23	(	(	PUNCT
iajs-2140	110	24	)	)	PUNCT
iajs-2140	110	25	∑	∑	PUNCT
iajs-2140	110	26	(	(	PUNCT
iajs-2140	110	27	)	)	PUNCT
iajs-2140	110	28	∑	∑	ADV
iajs-2140	110	29	,	,	PUNCT
iajs-2140	110	30	(	(	PUNCT
iajs-2140	110	31	∑	∑	PROPN
iajs-2140	110	32	)	)	PUNCT
iajs-2140	110	33	(	(	PUNCT
iajs-2140	110	34	)	)	PUNCT
iajs-2140	110	35	(	(	PUNCT
iajs-2140	110	36	)	)	PUNCT
iajs-2140	110	37	∑	∑	PROPN
iajs-2140	110	38	(	(	PUNCT
iajs-2140	110	39	∑	∑	PROPN
iajs-2140	110	40	)	)	PUNCT
iajs-2140	110	41	(	(	PUNCT
iajs-2140	110	42	)	)	PUNCT
iajs-2140	110	43	∑	∑	PROPN
iajs-2140	110	44	(	(	PUNCT
iajs-2140	110	45	∑	∑	PROPN
iajs-2140	110	46	)	)	PUNCT
iajs-2140	110	47	(	(	PUNCT
iajs-2140	110	48	)	)	PUNCT
iajs-2140	110	49	.	.	PUNCT
iajs-2140	111	1	therefore	therefore	ADV
iajs-2140	111	2	,	,	PUNCT
iajs-2140	111	3	∑	∑	ADV
iajs-2140	111	4	is	be	AUX
iajs-2140	111	5	an	an	DET
iajs-2140	111	6	outer	outer	ADJ
iajs-2140	111	7	measure	measure	NOUN
iajs-2140	111	8	on	on	ADP
iajs-2140	111	9	definition	definition	NOUN
iajs-2140	111	10	18	18	NUM
iajs-2140	111	11	let	let	VERB
iajs-2140	111	12	be	be	AUX
iajs-2140	111	13	a	a	PRON
iajs-2140	111	14	–	–	PUNCT
iajs-2140	111	15	of	of	ADP
iajs-2140	111	16	a	a	DET
iajs-2140	111	17	set	set	NOUN
iajs-2140	111	18	.	.	PUNCT
iajs-2140	112	1	then	then	ADV
iajs-2140	112	2	a	a	DET
iajs-2140	112	3	set	set	NOUN
iajs-2140	112	4	function	function	NOUN
iajs-2140	112	5	,	,	PUNCT
iajs-2140	112	6	is	be	AUX
iajs-2140	112	7	called	call	VERB
iajs-2140	112	8	null	null	NOUN
iajs-2140	112	9	-	-	PUNCT
iajs-2140	112	10	additive	additive	NOUN
iajs-2140	112	11	on	on	ADP
iajs-2140	112	12	iff	iff	PROPN
iajs-2140	112	13	are	be	AUX
iajs-2140	112	14	disjoint	disjoint	NOUN
iajs-2140	112	15	sets	set	NOUN
iajs-2140	112	16	in	in	ADP
iajs-2140	112	17	and	and	CCONJ
iajs-2140	112	18	(	(	PUNCT
iajs-2140	112	19	)	)	PUNCT
iajs-2140	112	20	,	,	PUNCT
iajs-2140	112	21	then	then	ADV
iajs-2140	112	22	(	(	PUNCT
iajs-2140	112	23	)	)	PUNCT
iajs-2140	112	24	(	(	PUNCT
iajs-2140	112	25	)	)	PUNCT
iajs-2140	112	26	.	.	PUNCT
iajs-2140	113	1	example	example	NOUN
iajs-2140	113	2	19	19	NUM
iajs-2140	113	3	let	let	VERB
iajs-2140	113	4	=	=	PRON
iajs-2140	113	5	{	{	PUNCT
iajs-2140	113	6	1,2	1,2	NUM
iajs-2140	113	7	}	}	PUNCT
iajs-2140	113	8	and	and	CCONJ
iajs-2140	113	9	=	=	PRON
iajs-2140	113	10	{	{	PUNCT
iajs-2140	113	11	,	,	PUNCT
iajs-2140	113	12	{	{	PUNCT
iajs-2140	113	13	1	1	NUM
iajs-2140	113	14	}	}	PUNCT
iajs-2140	113	15	,	,	PUNCT
iajs-2140	113	16	{	{	PUNCT
iajs-2140	113	17	2	2	NUM
iajs-2140	113	18	}	}	PUNCT
iajs-2140	113	19	,	,	PUNCT
iajs-2140	113	20	}	}	PUNCT
iajs-2140	113	21	and	and	CCONJ
iajs-2140	113	22	define	define	VERB
iajs-2140	113	23	,	,	PUNCT
iajs-2140	113	24	by	by	ADP
iajs-2140	113	25	:	:	PUNCT
iajs-2140	113	26	(	(	PUNCT
iajs-2140	113	27	)	)	PUNCT
iajs-2140	113	28	=	=	SYM
iajs-2140	113	29	{	{	PUNCT
iajs-2140	113	30	.	.	PUNCT
iajs-2140	114	1	then	then	ADV
iajs-2140	114	2	is	be	AUX
iajs-2140	114	3	a	a	DET
iajs-2140	114	4	null	null	ADJ
iajs-2140	114	5	-	-	PUNCT
iajs-2140	114	6	additive	additive	NOUN
iajs-2140	114	7	.	.	PUNCT
iajs-2140	115	1	proposition	proposition	NOUN
iajs-2140	115	2	20	20	NUM
iajs-2140	115	3	let	let	VERB
iajs-2140	115	4	be	be	AUX
iajs-2140	115	5	a	a	PRON
iajs-2140	115	6	–	–	PUNCT
iajs-2140	115	7	of	of	ADP
iajs-2140	115	8	a	a	DET
iajs-2140	115	9	set	set	NOUN
iajs-2140	115	10	.	.	PUNCT
iajs-2140	116	1	then	then	ADV
iajs-2140	116	2	every	every	DET
iajs-2140	116	3	measure	measure	NOUN
iajs-2140	116	4	is	be	AUX
iajs-2140	116	5	null	null	ADJ
iajs-2140	116	6	-	-	PUNCT
iajs-2140	116	7	additive	additive	NOUN
iajs-2140	116	8	.	.	PUNCT
iajs-2140	117	1	proof	proof	NOUN
iajs-2140	117	2	let	let	AUX
iajs-2140	117	3	be	be	AUX
iajs-2140	117	4	a	a	DET
iajs-2140	117	5	measure	measure	NOUN
iajs-2140	117	6	on	on	ADP
iajs-2140	117	7	–	–	PUNCT
iajs-2140	117	8	and	and	CCONJ
iajs-2140	117	9	let	let	VERB
iajs-2140	117	10	are	be	AUX
iajs-2140	117	11	disjoint	disjoint	VERB
iajs-2140	117	12	sets	set	NOUN
iajs-2140	117	13	in	in	ADP
iajs-2140	117	14	and	and	CCONJ
iajs-2140	117	15	(	(	PUNCT
iajs-2140	117	16	)	)	PUNCT
iajs-2140	117	17	.	.	PUNCT
iajs-2140	118	1	then	then	ADV
iajs-2140	118	2	(	(	PUNCT
iajs-2140	118	3	)	)	PUNCT
iajs-2140	118	4	(	(	PUNCT
iajs-2140	118	5	)	)	PUNCT
iajs-2140	118	6	+	+	CCONJ
iajs-2140	118	7	(	(	PUNCT
iajs-2140	118	8	)	)	PUNCT
iajs-2140	118	9	(	(	PUNCT
iajs-2140	118	10	)	)	PUNCT
iajs-2140	118	11	.	.	PUNCT
iajs-2140	119	1	hence	hence	ADV
iajs-2140	119	2	is	be	AUX
iajs-2140	119	3	a	a	DET
iajs-2140	119	4	null	null	NOUN
iajs-2140	119	5	-	-	PUNCT
iajs-2140	119	6	additive	additive	NOUN
iajs-2140	119	7	.	.	PUNCT
iajs-2140	120	1	while	while	SCONJ
iajs-2140	120	2	the	the	DET
iajs-2140	120	3	converse	converse	NOUN
iajs-2140	120	4	is	be	AUX
iajs-2140	120	5	not	not	PART
iajs-2140	120	6	true	true	ADJ
iajs-2140	120	7	and	and	CCONJ
iajs-2140	120	8	example	example	NOUN
iajs-2140	120	9	19	19	NUM
iajs-2140	120	10	indicate	indicate	VERB
iajs-2140	120	11	that	that	PRON
iajs-2140	120	12	is	be	AUX
iajs-2140	120	13	null	null	ADJ
iajs-2140	120	14	-	-	PUNCT
iajs-2140	120	15	additive	additive	ADJ
iajs-2140	120	16	but	but	CCONJ
iajs-2140	120	17	not	not	PART
iajs-2140	120	18	measure	measure	NOUN
iajs-2140	120	19	,	,	PUNCT
iajs-2140	120	20	because	because	SCONJ
iajs-2140	120	21	{	{	PUNCT
iajs-2140	120	22	1},{2	1},{2	X
iajs-2140	120	23	}	}	PUNCT
iajs-2140	120	24	are	be	AUX
iajs-2140	120	25	disjoint	disjoint	NOUN
iajs-2140	120	26	sets	set	NOUN
iajs-2140	120	27	in	in	ADP
iajs-2140	120	28	but	but	CCONJ
iajs-2140	120	29	(	(	PUNCT
iajs-2140	120	30	*	*	PUNCT
iajs-2140	120	31	+	+	PUNCT
iajs-2140	120	32	*	*	PUNCT
iajs-2140	120	33	+	+	X
iajs-2140	120	34	)	)	PUNCT
iajs-2140	120	35	(	(	PUNCT
iajs-2140	120	36	*	*	PUNCT
iajs-2140	121	1	+	+	X
iajs-2140	121	2	)	)	PUNCT
iajs-2140	121	3	+	+	CCONJ
iajs-2140	121	4	(	(	PUNCT
iajs-2140	121	5	*	*	PUNCT
iajs-2140	121	6	+	+	NOUN
iajs-2140	121	7	)	)	PUNCT
iajs-2140	121	8	.	.	PUNCT
iajs-2140	122	1	lemma	lemma	PROPN
iajs-2140	122	2	21	21	NUM
iajs-2140	122	3	let	let	VERB
iajs-2140	122	4	be	be	AUX
iajs-2140	122	5	a	a	DET
iajs-2140	122	6	null	null	NOUN
iajs-2140	122	7	-	-	PUNCT
iajs-2140	122	8	additive	additive	NOUN
iajs-2140	122	9	on	on	ADP
iajs-2140	122	10	a	a	PRON
iajs-2140	122	11	–	–	PUNCT
iajs-2140	122	12	of	of	ADP
iajs-2140	122	13	a	a	DET
iajs-2140	122	14	set	set	NOUN
iajs-2140	122	15	and	and	CCONJ
iajs-2140	122	16	(	(	PUNCT
iajs-2140	122	17	)	)	PUNCT
iajs-2140	122	18	.	.	PUNCT
iajs-2140	123	1	if	if	SCONJ
iajs-2140	123	2	:	:	PUNCT
iajs-2140	123	3	,	,	PUNCT
iajs-2140	123	4	is	be	AUX
iajs-2140	123	5	defined	define	VERB
iajs-2140	123	6	by	by	ADP
iajs-2140	123	7	:	:	PUNCT
iajs-2140	123	8	(	(	PUNCT
iajs-2140	123	9	)	)	PUNCT
iajs-2140	123	10	(	(	PUNCT
iajs-2140	123	11	)	)	PUNCT
iajs-2140	123	12	(	(	PUNCT
iajs-2140	123	13	)	)	PUNCT
iajs-2140	123	14	,	,	PUNCT
iajs-2140	123	15	then	then	ADV
iajs-2140	123	16	(	(	PUNCT
iajs-2140	123	17	)	)	PUNCT
iajs-2140	123	18	is	be	AUX
iajs-2140	123	19	a	a	DET
iajs-2140	123	20	null	null	NOUN
iajs-2140	123	21	-	-	PUNCT
iajs-2140	123	22	additive	additive	NOUN
iajs-2140	123	23	on	on	ADP
iajs-2140	123	24	.	.	PUNCT
iajs-2140	124	1	proof	proof	NOUN
iajs-2140	124	2	let	let	AUX
iajs-2140	124	3	be	be	AUX
iajs-2140	124	4	disjoint	disjoint	NOUN
iajs-2140	124	5	sets	set	NOUN
iajs-2140	124	6	in	in	ADP
iajs-2140	124	7	such	such	ADJ
iajs-2140	124	8	that	that	PRON
iajs-2140	124	9	(	(	PUNCT
iajs-2140	124	10	)	)	PUNCT
iajs-2140	124	11	(	(	PUNCT
iajs-2140	124	12	)	)	PUNCT
iajs-2140	124	13	.	.	PUNCT
iajs-2140	125	1	then	then	ADV
iajs-2140	125	2	(	(	PUNCT
iajs-2140	125	3	)	)	PUNCT
iajs-2140	125	4	and	and	CCONJ
iajs-2140	125	5	hence	hence	ADV
iajs-2140	125	6	(	(	PUNCT
iajs-2140	125	7	)	)	PUNCT
iajs-2140	125	8	since	since	SCONJ
iajs-2140	125	9	.	.	PUNCT
iajs-2140	126	1	now	now	ADV
iajs-2140	126	2	,	,	PUNCT
iajs-2140	126	3	(	(	PUNCT
iajs-2140	126	4	)	)	PUNCT
iajs-2140	126	5	(	(	PUNCT
iajs-2140	126	6	)	)	PUNCT
iajs-2140	126	7	(	(	PUNCT
iajs-2140	126	8	)	)	PUNCT
iajs-2140	126	9	(	(	PUNCT
iajs-2140	126	10	)	)	PUNCT
iajs-2140	126	11	(	(	PUNCT
iajs-2140	126	12	)	)	PUNCT
iajs-2140	126	13	(	(	PUNCT
iajs-2140	126	14	)	)	PUNCT
iajs-2140	126	15	therefore	therefore	ADV
iajs-2140	126	16	,	,	PUNCT
iajs-2140	126	17	is	be	AUX
iajs-2140	126	18	a	a	DET
iajs-2140	126	19	null	null	NOUN
iajs-2140	126	20	-	-	PUNCT
iajs-2140	126	21	additive	additive	NOUN
iajs-2140	126	22	on	on	ADP
iajs-2140	126	23	.	.	PUNCT
iajs-2140	127	1	26	26	NUM
iajs-2140	127	2	ibn	ibn	PROPN
iajs-2140	127	3	al	al	PROPN
iajs-2140	127	4	-	-	PUNCT
iajs-2140	127	5	haitham	haitham	PROPN
iajs-2140	127	6	jour	jour	X
iajs-2140	127	7	.	.	PROPN
iajs-2140	127	8	for	for	ADP
iajs-2140	127	9	pure	pure	ADJ
iajs-2140	127	10	&	&	CCONJ
iajs-2140	127	11	appl	appl	PROPN
iajs-2140	127	12	.	.	PUNCT
iajs-2140	128	1	sci	sci	PROPN
iajs-2140	128	2	.	.	PROPN
iajs-2140	128	3	32	32	NUM
iajs-2140	128	4	(	(	PUNCT
iajs-2140	128	5	2	2	NUM
iajs-2140	128	6	)	)	PUNCT
iajs-2140	128	7	2019	2019	NUM
iajs-2140	128	8	lemma	lemma	PROPN
iajs-2140	128	9	22	22	NUM
iajs-2140	128	10	let	let	VERB
iajs-2140	128	11	and	and	CCONJ
iajs-2140	128	12	be	be	AUX
iajs-2140	128	13	two	two	NUM
iajs-2140	128	14	null	null	ADJ
iajs-2140	128	15	-	-	PUNCT
iajs-2140	128	16	additives	additive	NOUN
iajs-2140	128	17	on	on	ADP
iajs-2140	128	18	a	a	PRON
iajs-2140	128	19	–	–	PUNCT
iajs-2140	128	20	of	of	ADP
iajs-2140	128	21	a	a	DET
iajs-2140	128	22	set	set	NOUN
iajs-2140	128	23	.	.	PUNCT
iajs-2140	129	1	if	if	SCONJ
iajs-2140	129	2	:	:	PUNCT
iajs-2140	129	3	,	,	PUNCT
iajs-2140	129	4	is	be	AUX
iajs-2140	129	5	defined	define	VERB
iajs-2140	129	6	by	by	ADP
iajs-2140	129	7	:	:	PUNCT
iajs-2140	129	8	(	(	PUNCT
iajs-2140	129	9	)	)	PUNCT
iajs-2140	129	10	(	(	PUNCT
iajs-2140	129	11	)	)	PUNCT
iajs-2140	129	12	(	(	PUNCT
iajs-2140	129	13	)	)	PUNCT
iajs-2140	129	14	(	(	PUNCT
iajs-2140	129	15	)	)	PUNCT
iajs-2140	129	16	,	,	PUNCT
iajs-2140	129	17	then	then	ADV
iajs-2140	129	18	is	be	AUX
iajs-2140	129	19	a	a	DET
iajs-2140	129	20	null	null	NOUN
iajs-2140	129	21	-	-	PUNCT
iajs-2140	129	22	additive	additive	NOUN
iajs-2140	129	23	on	on	ADP
iajs-2140	129	24	.	.	PUNCT
iajs-2140	130	1	proof	proof	NOUN
iajs-2140	130	2	let	let	AUX
iajs-2140	130	3	be	be	AUX
iajs-2140	130	4	disjoint	disjoint	NOUN
iajs-2140	130	5	sets	set	NOUN
iajs-2140	130	6	in	in	ADP
iajs-2140	130	7	such	such	ADJ
iajs-2140	130	8	that	that	PRON
iajs-2140	130	9	(	(	PUNCT
iajs-2140	130	10	)	)	PUNCT
iajs-2140	130	11	(	(	PUNCT
iajs-2140	130	12	)	)	PUNCT
iajs-2140	130	13	.	.	PUNCT
iajs-2140	131	1	then	then	ADV
iajs-2140	131	2	(	(	PUNCT
iajs-2140	131	3	)	)	PUNCT
iajs-2140	131	4	(	(	PUNCT
iajs-2140	131	5	)	)	PUNCT
iajs-2140	131	6	,	,	PUNCT
iajs-2140	131	7	hence	hence	ADV
iajs-2140	131	8	(	(	PUNCT
iajs-2140	131	9	)	)	PUNCT
iajs-2140	131	10	(	(	PUNCT
iajs-2140	131	11	)	)	PUNCT
iajs-2140	131	12	since	since	SCONJ
iajs-2140	131	13	and	and	CCONJ
iajs-2140	131	14	are	be	AUX
iajs-2140	131	15	null	null	ADJ
iajs-2140	131	16	-	-	PUNCT
iajs-2140	131	17	additive	additive	NOUN
iajs-2140	131	18	on	on	ADP
iajs-2140	131	19	.	.	PUNCT
iajs-2140	132	1	now	now	ADV
iajs-2140	132	2	,	,	PUNCT
iajs-2140	132	3	(	(	PUNCT
iajs-2140	132	4	)	)	PUNCT
iajs-2140	132	5	(	(	PUNCT
iajs-2140	132	6	)	)	PUNCT
iajs-2140	132	7	(	(	PUNCT
iajs-2140	132	8	)	)	PUNCT
iajs-2140	132	9	+	+	CCONJ
iajs-2140	132	10	(	(	PUNCT
iajs-2140	132	11	)	)	PUNCT
iajs-2140	132	12	(	(	PUNCT
iajs-2140	132	13	)	)	PUNCT
iajs-2140	132	14	+	+	CCONJ
iajs-2140	132	15	(	(	PUNCT
iajs-2140	132	16	)	)	PUNCT
iajs-2140	132	17	(	(	PUNCT
iajs-2140	132	18	+	+	X
iajs-2140	132	19	)	)	PUNCT
iajs-2140	132	20	(	(	PUNCT
iajs-2140	132	21	)	)	PUNCT
iajs-2140	132	22	therefore	therefore	ADV
iajs-2140	132	23	,	,	PUNCT
iajs-2140	132	24	is	be	AUX
iajs-2140	132	25	a	a	DET
iajs-2140	132	26	null	null	NOUN
iajs-2140	132	27	-	-	PUNCT
iajs-2140	132	28	additive	additive	NOUN
iajs-2140	132	29	on	on	ADP
iajs-2140	132	30	.	.	PUNCT
iajs-2140	133	1	proposition	proposition	NOUN
iajs-2140	133	2	23	23	NUM
iajs-2140	133	3	let	let	VERB
iajs-2140	133	4	,	,	PUNCT
iajs-2140	133	5	,	,	PUNCT
iajs-2140	133	6	…	…	PUNCT
iajs-2140	133	7	,	,	PUNCT
iajs-2140	133	8	be	be	AUX
iajs-2140	133	9	a	a	DET
iajs-2140	133	10	null	null	NOUN
iajs-2140	133	11	-	-	PUNCT
iajs-2140	133	12	additive	additive	NOUN
iajs-2140	133	13	on	on	ADP
iajs-2140	133	14	a	a	PRON
iajs-2140	133	15	–	–	PUNCT
iajs-2140	133	16	of	of	ADP
iajs-2140	133	17	a	a	DET
iajs-2140	133	18	set	set	NOUN
iajs-2140	133	19	and	and	CCONJ
iajs-2140	133	20	(	(	PUNCT
iajs-2140	133	21	)	)	PUNCT
iajs-2140	133	22	for	for	ADP
iajs-2140	133	23	all	all	PRON
iajs-2140	133	24	.	.	PUNCT
iajs-2140	134	1	if	if	SCONJ
iajs-2140	134	2	a	a	DET
iajs-2140	134	3	set	set	NOUN
iajs-2140	134	4	function	function	NOUN
iajs-2140	134	5	∑	∑	PUNCT
iajs-2140	134	6	:	:	PUNCT
iajs-2140	134	7	,	,	PUNCT
iajs-2140	134	8	is	be	AUX
iajs-2140	134	9	defined	define	VERB
iajs-2140	134	10	by	by	ADP
iajs-2140	134	11	:	:	PUNCT
iajs-2140	134	12	(	(	PUNCT
iajs-2140	134	13	∑	∑	PROPN
iajs-2140	134	14	)	)	PUNCT
iajs-2140	134	15	(	(	PUNCT
iajs-2140	134	16	)	)	PUNCT
iajs-2140	134	17	∑	∑	PUNCT
iajs-2140	134	18	(	(	PUNCT
iajs-2140	134	19	)	)	PUNCT
iajs-2140	134	20	,	,	PUNCT
iajs-2140	134	21	then	then	ADV
iajs-2140	134	22	∑	∑	PUNCT
iajs-2140	134	23	is	be	AUX
iajs-2140	134	24	a	a	DET
iajs-2140	134	25	null	null	NOUN
iajs-2140	134	26	-	-	PUNCT
iajs-2140	134	27	additive	additive	NOUN
iajs-2140	134	28	on	on	ADP
iajs-2140	134	29	.	.	PUNCT
iajs-2140	135	1	proof	proof	NOUN
iajs-2140	135	2	since	since	SCONJ
iajs-2140	135	3	(	(	PUNCT
iajs-2140	135	4	)	)	PUNCT
iajs-2140	135	5	and	and	CCONJ
iajs-2140	135	6	is	be	AUX
iajs-2140	135	7	null	null	NOUN
iajs-2140	135	8	-	-	PUNCT
iajs-2140	135	9	additive	additive	NOUN
iajs-2140	135	10	on	on	ADP
iajs-2140	135	11	for	for	ADP
iajs-2140	135	12	all	all	PRON
iajs-2140	135	13	,	,	PUNCT
iajs-2140	135	14	then	then	ADV
iajs-2140	135	15	by	by	ADP
iajs-2140	135	16	lemma	lemma	PROPN
iajs-2140	135	17	21	21	NUM
iajs-2140	135	18	,	,	PUNCT
iajs-2140	135	19	we	we	PRON
iajs-2140	135	20	get	get	VERB
iajs-2140	135	21	is	be	AUX
iajs-2140	135	22	a	a	DET
iajs-2140	135	23	null	null	NOUN
iajs-2140	135	24	-	-	PUNCT
iajs-2140	135	25	additive	additive	NOUN
iajs-2140	135	26	on	on	ADP
iajs-2140	135	27	.	.	PUNCT
iajs-2140	136	1	let	let	VERB
iajs-2140	136	2	if	if	SCONJ
iajs-2140	136	3	,	,	PUNCT
iajs-2140	136	4	then	then	ADV
iajs-2140	136	5	is	be	AUX
iajs-2140	136	6	a	a	DET
iajs-2140	136	7	null	null	NOUN
iajs-2140	136	8	-	-	PUNCT
iajs-2140	136	9	additive	additive	NOUN
iajs-2140	136	10	on	on	ADP
iajs-2140	136	11	by	by	ADP
iajs-2140	136	12	lemma	lemma	PROPN
iajs-2140	136	13	22	22	NUM
iajs-2140	136	14	.	.	PUNCT
iajs-2140	137	1	let	let	VERB
iajs-2140	137	2	are	be	AUX
iajs-2140	137	3	disjoint	disjoint	VERB
iajs-2140	137	4	sets	set	NOUN
iajs-2140	137	5	in	in	ADP
iajs-2140	137	6	such	such	ADJ
iajs-2140	137	7	that(∑	that(∑	NOUN
iajs-2140	137	8	)	)	PUNCT
iajs-2140	137	9	(	(	PUNCT
iajs-2140	137	10	)	)	PUNCT
iajs-2140	137	11	.	.	PUNCT
iajs-2140	138	1	then	then	ADV
iajs-2140	138	2	(	(	PUNCT
iajs-2140	138	3	)	)	PUNCT
iajs-2140	138	4	for	for	ADP
iajs-2140	138	5	all	all	PRON
iajs-2140	138	6	.	.	PUNCT
iajs-2140	139	1	(	(	PUNCT
iajs-2140	139	2	∑	∑	PROPN
iajs-2140	139	3	)	)	PUNCT
iajs-2140	139	4	(	(	PUNCT
iajs-2140	139	5	)	)	PUNCT
iajs-2140	139	6	=	=	SYM
iajs-2140	139	7	(	(	PUNCT
iajs-2140	139	8	)	)	PUNCT
iajs-2140	139	9	(	(	PUNCT
iajs-2140	139	10	)	)	PUNCT
iajs-2140	139	11	=	=	SYM
iajs-2140	139	12	(	(	PUNCT
iajs-2140	139	13	)	)	PUNCT
iajs-2140	139	14	(	(	PUNCT
iajs-2140	139	15	)	)	PUNCT
iajs-2140	139	16	since	since	SCONJ
iajs-2140	139	17	is	be	AUX
iajs-2140	139	18	a	a	DET
iajs-2140	139	19	null	null	ADJ
iajs-2140	139	20	-	-	PUNCT
iajs-2140	139	21	additive	additive	NOUN
iajs-2140	139	22	and	and	CCONJ
iajs-2140	139	23	(	(	PUNCT
iajs-2140	139	24	)	)	PUNCT
iajs-2140	139	25	,	,	PUNCT
iajs-2140	139	26	=	=	SYM
iajs-2140	139	27	(	(	PUNCT
iajs-2140	139	28	∑	∑	PROPN
iajs-2140	139	29	)	)	PUNCT
iajs-2140	139	30	(	(	PUNCT
iajs-2140	139	31	)	)	PUNCT
iajs-2140	139	32	.	.	PUNCT
iajs-2140	140	1	hence	hence	ADV
iajs-2140	140	2	∑	∑	PUNCT
iajs-2140	140	3	is	be	AUX
iajs-2140	140	4	a	a	DET
iajs-2140	140	5	null	null	NOUN
iajs-2140	140	6	-	-	PUNCT
iajs-2140	140	7	additive	additive	NOUN
iajs-2140	140	8	on	on	ADP
iajs-2140	140	9	definition	definition	NOUN
iajs-2140	140	10	24	24	NUM
iajs-2140	140	11	let	let	VERB
iajs-2140	140	12	be	be	AUX
iajs-2140	140	13	a	a	PRON
iajs-2140	140	14	–	–	PUNCT
iajs-2140	140	15	of	of	ADP
iajs-2140	140	16	a	a	DET
iajs-2140	140	17	set	set	NOUN
iajs-2140	140	18	and	and	CCONJ
iajs-2140	140	19	let	let	VERB
iajs-2140	140	20	[	[	X
iajs-2140	140	21	0	0	NUM
iajs-2140	140	22	,	,	PUNCT
iajs-2140	140	23	]	]	PUNCT
iajs-2140	140	24	be	be	AUX
iajs-2140	140	25	a	a	DET
iajs-2140	140	26	set	set	NOUN
iajs-2140	140	27	function	function	NOUN
iajs-2140	140	28	and	and	CCONJ
iajs-2140	140	29	.	.	PUNCT
iajs-2140	141	1	if	if	SCONJ
iajs-2140	141	2	:	:	PUNCT
iajs-2140	141	3	[	[	X
iajs-2140	141	4	0	0	NUM
iajs-2140	141	5	,	,	PUNCT
iajs-2140	141	6	]	]	PUNCT
iajs-2140	141	7	is	be	AUX
iajs-2140	141	8	define	define	VERB
iajs-2140	141	9	by	by	ADP
iajs-2140	141	10	(	(	PUNCT
iajs-2140	141	11	)	)	PUNCT
iajs-2140	141	12	=	=	SYM
iajs-2140	141	13	(	(	PUNCT
iajs-2140	141	14	)	)	PUNCT
iajs-2140	141	15	for	for	ADP
iajs-2140	141	16	all	all	PRON
iajs-2140	141	17	,	,	PUNCT
iajs-2140	141	18	then	then	ADV
iajs-2140	141	19	is	be	AUX
iajs-2140	141	20	called	call	VERB
iajs-2140	141	21	–	–	PUNCT
iajs-2140	141	22	restriction	restriction	NOUN
iajs-2140	141	23	of	of	ADP
iajs-2140	141	24	proposition	proposition	NOUN
iajs-2140	141	25	25	25	NUM
iajs-2140	141	26	let	let	AUX
iajs-2140	141	27	be	be	AUX
iajs-2140	141	28	a	a	PRON
iajs-2140	141	29	–	–	PUNCT
iajs-2140	141	30	of	of	ADP
iajs-2140	141	31	a	a	DET
iajs-2140	141	32	set	set	NOUN
iajs-2140	141	33	and	and	CCONJ
iajs-2140	141	34	.	.	PUNCT
iajs-2140	142	1	if	if	SCONJ
iajs-2140	142	2	is	be	AUX
iajs-2140	142	3	a	a	DET
iajs-2140	142	4	measure	measure	NOUN
iajs-2140	142	5	on	on	ADP
iajs-2140	142	6	,	,	PUNCT
iajs-2140	142	7	then	then	ADV
iajs-2140	142	8	:	:	PUNCT
iajs-2140	142	9	(	(	PUNCT
iajs-2140	142	10	1	1	X
iajs-2140	142	11	)	)	PUNCT
iajs-2140	142	12	is	be	AUX
iajs-2140	142	13	a	a	DET
iajs-2140	142	14	measure	measure	NOUN
iajs-2140	142	15	on	on	ADP
iajs-2140	142	16	.	.	PUNCT
iajs-2140	143	1	(	(	PUNCT
iajs-2140	143	2	2	2	X
iajs-2140	143	3	)	)	PUNCT
iajs-2140	143	4	(	(	PUNCT
iajs-2140	143	5	)	)	PUNCT
iajs-2140	143	6	=	=	SYM
iajs-2140	143	7	(	(	PUNCT
iajs-2140	143	8	)	)	PUNCT
iajs-2140	143	9	,	,	PUNCT
iajs-2140	143	10	whenever	whenever	SCONJ
iajs-2140	143	11	.	.	PUNCT
iajs-2140	144	1	(	(	PUNCT
iajs-2140	144	2	3	3	X
iajs-2140	144	3	)	)	PUNCT
iajs-2140	144	4	(	(	PUNCT
iajs-2140	144	5	)	)	PUNCT
iajs-2140	144	6	=	=	SYM
iajs-2140	144	7	0	0	NUM
iajs-2140	144	8	,	,	PUNCT
iajs-2140	144	9	whenever	whenever	SCONJ
iajs-2140	144	10	are	be	AUX
iajs-2140	144	11	disjoint	disjoint	NOUN
iajs-2140	144	12	sets	set	NOUN
iajs-2140	144	13	in	in	ADP
iajs-2140	144	14	.	.	PUNCT
iajs-2140	145	1	proof	proof	NOUN
iajs-2140	145	2	(	(	PUNCT
iajs-2140	145	3	1	1	NUM
iajs-2140	145	4	)	)	PUNCT
iajs-2140	145	5	.	.	PUNCT
iajs-2140	146	1	since	since	SCONJ
iajs-2140	146	2	is	be	AUX
iajs-2140	146	3	a	a	PRON
iajs-2140	146	4	–	–	PUNCT
iajs-2140	146	5	,	,	PUNCT
iajs-2140	146	6	then	then	ADV
iajs-2140	146	7	and	and	CCONJ
iajs-2140	146	8	(	(	PUNCT
iajs-2140	146	9	)	)	PUNCT
iajs-2140	146	10	=	=	SYM
iajs-2140	146	11	0	0	X
iajs-2140	146	12	.	.	PUNCT
iajs-2140	147	1	from	from	ADP
iajs-2140	147	2	definition	definition	NOUN
iajs-2140	147	3	of	of	ADP
iajs-2140	147	4	we	we	PRON
iajs-2140	147	5	get	get	VERB
iajs-2140	147	6	,	,	PUNCT
iajs-2140	147	7	(	(	PUNCT
iajs-2140	147	8	)	)	PUNCT
iajs-2140	147	9	=	=	SYM
iajs-2140	147	10	(	(	PUNCT
iajs-2140	147	11	)	)	PUNCT
iajs-2140	147	12	=	=	SYM
iajs-2140	147	13	(	(	PUNCT
iajs-2140	147	14	)	)	PUNCT
iajs-2140	148	1	=	=	SYM
iajs-2140	148	2	0	0	X
iajs-2140	148	3	.	.	PUNCT
iajs-2140	149	1	let	let	VERB
iajs-2140	149	2	are	be	AUX
iajs-2140	149	3	disjoint	disjoint	VERB
iajs-2140	149	4	sets	set	NOUN
iajs-2140	149	5	in	in	ADP
iajs-2140	149	6	,	,	PUNCT
iajs-2140	149	7	then	then	ADV
iajs-2140	149	8	.	.	PUNCT
iajs-2140	150	1	since	since	SCONJ
iajs-2140	150	2	n=1,2	n=1,2	ADJ
iajs-2140	150	3	,	,	PUNCT
iajs-2140	150	4	…	…	PUNCT
iajs-2140	150	5	,	,	PUNCT
iajs-2140	150	6	then	then	ADV
iajs-2140	150	7	and	and	CCONJ
iajs-2140	150	8	hence	hence	ADV
iajs-2140	150	9	(	(	PUNCT
iajs-2140	150	10	)	)	PUNCT
iajs-2140	150	11	.	.	PUNCT
iajs-2140	151	1	so	so	ADV
iajs-2140	151	2	,	,	PUNCT
iajs-2140	151	3	we	we	PRON
iajs-2140	151	4	have	have	VERB
iajs-2140	151	5	(	(	PUNCT
iajs-2140	151	6	)	)	PUNCT
iajs-2140	151	7	=	=	SYM
iajs-2140	151	8	(	(	PUNCT
iajs-2140	151	9	(	(	PUNCT
iajs-2140	151	10	)	)	PUNCT
iajs-2140	151	11	)	)	PUNCT
iajs-2140	152	1	=	=	PUNCT
iajs-2140	152	2	(	(	PUNCT
iajs-2140	152	3	(	(	PUNCT
iajs-2140	152	4	)	)	PUNCT
iajs-2140	152	5	)	)	PUNCT
iajs-2140	153	1	=	=	PUNCT
iajs-2140	153	2	∑	∑	PUNCT
iajs-2140	153	3	(	(	PUNCT
iajs-2140	153	4	)	)	PUNCT
iajs-2140	153	5	=	=	SYM
iajs-2140	153	6	∑	∑	PUNCT
iajs-2140	153	7	(	(	PUNCT
iajs-2140	153	8	)	)	PUNCT
iajs-2140	153	9	.	.	PUNCT
iajs-2140	154	1	therefore	therefore	ADV
iajs-2140	154	2	,	,	PUNCT
iajs-2140	154	3	is	be	AUX
iajs-2140	154	4	a	a	DET
iajs-2140	154	5	measure	measure	NOUN
iajs-2140	154	6	on	on	ADP
iajs-2140	154	7	(	(	PUNCT
iajs-2140	154	8	2	2	NUM
iajs-2140	154	9	)	)	PUNCT
iajs-2140	154	10	.	.	PUNCT
iajs-2140	155	1	since	since	SCONJ
iajs-2140	155	2	,	,	PUNCT
iajs-2140	155	3	then	then	ADV
iajs-2140	155	4	=	=	PUNCT
iajs-2140	155	5	.	.	PUNCT
iajs-2140	156	1	so	so	ADV
iajs-2140	156	2	,	,	PUNCT
iajs-2140	156	3	we	we	PRON
iajs-2140	156	4	have	have	VERB
iajs-2140	156	5	(	(	PUNCT
iajs-2140	156	6	)	)	PUNCT
iajs-2140	156	7	=	=	SYM
iajs-2140	156	8	(	(	PUNCT
iajs-2140	156	9	)	)	PUNCT
iajs-2140	156	10	=	=	SYM
iajs-2140	156	11	(	(	PUNCT
iajs-2140	156	12	)	)	PUNCT
iajs-2140	156	13	(	(	PUNCT
iajs-2140	156	14	3	3	NUM
iajs-2140	156	15	)	)	PUNCT
iajs-2140	156	16	.	.	PUNCT
iajs-2140	157	1	since	since	SCONJ
iajs-2140	157	2	are	be	AUX
iajs-2140	157	3	disjoint	disjoint	NOUN
iajs-2140	157	4	sets	set	NOUN
iajs-2140	157	5	in	in	ADP
iajs-2140	157	6	,	,	PUNCT
iajs-2140	157	7	then	then	ADV
iajs-2140	157	8	=	=	PUNCT
iajs-2140	157	9	and	and	CCONJ
iajs-2140	157	10	(	(	PUNCT
iajs-2140	157	11	)	)	PUNCT
iajs-2140	157	12	=	=	SYM
iajs-2140	158	1	(	(	PUNCT
iajs-2140	158	2	)	)	PUNCT
iajs-2140	158	3	=	=	SYM
iajs-2140	158	4	(	(	PUNCT
iajs-2140	158	5	)	)	PUNCT
iajs-2140	158	6	=	=	SYM
iajs-2140	158	7	0	0	X
iajs-2140	158	8	.	.	NUM
iajs-2140	158	9	26	26	NUM
iajs-2140	158	10	ibn	ibn	PROPN
iajs-2140	158	11	al	al	PROPN
iajs-2140	158	12	-	-	PUNCT
iajs-2140	158	13	haitham	haitham	PROPN
iajs-2140	158	14	jour	jour	X
iajs-2140	158	15	.	.	PROPN
iajs-2140	159	1	for	for	ADP
iajs-2140	159	2	pure	pure	ADJ
iajs-2140	159	3	&	&	CCONJ
iajs-2140	159	4	appl	appl	PROPN
iajs-2140	159	5	.	.	PUNCT
iajs-2140	160	1	sci	sci	PROPN
iajs-2140	160	2	.	.	PROPN
iajs-2140	160	3	32	32	NUM
iajs-2140	160	4	(	(	PUNCT
iajs-2140	160	5	2	2	NUM
iajs-2140	160	6	)	)	PUNCT
iajs-2140	160	7	2019	2019	NUM
iajs-2140	160	8	proposition	proposition	NOUN
iajs-2140	160	9	26	26	NUM
iajs-2140	160	10	let	let	VERB
iajs-2140	160	11	be	be	AUX
iajs-2140	160	12	a	a	PRON
iajs-2140	160	13	–	–	PUNCT
iajs-2140	160	14	of	of	ADP
iajs-2140	160	15	a	a	DET
iajs-2140	160	16	set	set	NOUN
iajs-2140	160	17	and	and	CCONJ
iajs-2140	160	18	.	.	PUNCT
iajs-2140	161	1	if	if	SCONJ
iajs-2140	161	2	is	be	AUX
iajs-2140	161	3	an	an	DET
iajs-2140	161	4	outer	outer	ADJ
iajs-2140	161	5	measure	measure	NOUN
iajs-2140	161	6	on	on	ADP
iajs-2140	161	7	,	,	PUNCT
iajs-2140	161	8	then	then	ADV
iajs-2140	161	9	is	be	AUX
iajs-2140	161	10	an	an	DET
iajs-2140	161	11	outer	outer	ADJ
iajs-2140	161	12	measure	measure	NOUN
iajs-2140	161	13	on	on	ADP
iajs-2140	161	14	proof	proof	NOUN
iajs-2140	161	15	since	since	SCONJ
iajs-2140	161	16	is	be	AUX
iajs-2140	161	17	a	a	PRON
iajs-2140	161	18	–	–	PUNCT
iajs-2140	161	19	,	,	PUNCT
iajs-2140	161	20	then	then	ADV
iajs-2140	161	21	and	and	CCONJ
iajs-2140	161	22	(	(	PUNCT
iajs-2140	161	23	)	)	PUNCT
iajs-2140	161	24	=	=	SYM
iajs-2140	162	1	0	0	X
iajs-2140	162	2	.	.	PUNCT
iajs-2140	163	1	from	from	ADP
iajs-2140	163	2	definition	definition	NOUN
iajs-2140	163	3	of	of	ADP
iajs-2140	163	4	we	we	PRON
iajs-2140	163	5	get	get	VERB
iajs-2140	163	6	,	,	PUNCT
iajs-2140	163	7	(	(	PUNCT
iajs-2140	163	8	)	)	PUNCT
iajs-2140	163	9	=	=	SYM
iajs-2140	163	10	(	(	PUNCT
iajs-2140	163	11	⋂	⋂	PROPN
iajs-2140	163	12	)	)	PUNCT
iajs-2140	163	13	=	=	PRON
iajs-2140	164	1	(	(	PUNCT
iajs-2140	164	2	)	)	PUNCT
iajs-2140	164	3	=	=	SYM
iajs-2140	164	4	0	0	X
iajs-2140	164	5	.	.	PUNCT
iajs-2140	165	1	let	let	VERB
iajs-2140	165	2	and	and	CCONJ
iajs-2140	165	3	,	,	PUNCT
iajs-2140	165	4	then	then	ADV
iajs-2140	165	5	⋂	⋂	PROPN
iajs-2140	165	6	⋂	⋂	PROPN
iajs-2140	165	7	and	and	CCONJ
iajs-2140	165	8	each	each	PRON
iajs-2140	165	9	of	of	ADP
iajs-2140	165	10	⋂	⋂	PROPN
iajs-2140	165	11	⋂	⋂	PROPN
iajs-2140	165	12	.	.	PUNCT
iajs-2140	166	1	since	since	SCONJ
iajs-2140	166	2	is	be	AUX
iajs-2140	166	3	an	an	DET
iajs-2140	166	4	outer	outer	ADJ
iajs-2140	166	5	measure	measure	NOUN
iajs-2140	166	6	on	on	ADP
iajs-2140	166	7	,	,	PUNCT
iajs-2140	166	8	then	then	ADV
iajs-2140	166	9	(	(	PUNCT
iajs-2140	166	10	⋂	⋂	PROPN
iajs-2140	166	11	)	)	PUNCT
iajs-2140	166	12	(	(	PUNCT
iajs-2140	166	13	⋂	⋂	PROPN
iajs-2140	166	14	)	)	PUNCT
iajs-2140	166	15	.so	.so	PUNCT
iajs-2140	166	16	,	,	PUNCT
iajs-2140	166	17	we	we	PRON
iajs-2140	166	18	have	have	VERB
iajs-2140	166	19	(	(	PUNCT
iajs-2140	166	20	)	)	PUNCT
iajs-2140	166	21	(	(	PUNCT
iajs-2140	166	22	)	)	PUNCT
iajs-2140	166	23	.	.	PUNCT
iajs-2140	167	1	let	let	VERB
iajs-2140	167	2	.	.	PUNCT
iajs-2140	168	1	then	then	ADV
iajs-2140	168	2	and	and	CCONJ
iajs-2140	168	3	n=1,2	n=1,2	ADJ
iajs-2140	168	4	,	,	PUNCT
iajs-2140	168	5	…	…	PUNCT
iajs-2140	168	6	,	,	PUNCT
iajs-2140	168	7	hence	hence	ADV
iajs-2140	168	8	(	(	PUNCT
iajs-2140	168	9	)	)	PUNCT
iajs-2140	168	10	.	.	PUNCT
iajs-2140	169	1	so	so	ADV
iajs-2140	169	2	,	,	PUNCT
iajs-2140	169	3	we	we	PRON
iajs-2140	169	4	have	have	VERB
iajs-2140	169	5	,	,	PUNCT
iajs-2140	169	6	(	(	PUNCT
iajs-2140	169	7	)	)	PUNCT
iajs-2140	169	8	=	=	SYM
iajs-2140	169	9	(	(	PUNCT
iajs-2140	169	10	(	(	PUNCT
iajs-2140	169	11	)	)	PUNCT
iajs-2140	169	12	)	)	PUNCT
iajs-2140	170	1	=	=	PUNCT
iajs-2140	170	2	(	(	PUNCT
iajs-2140	170	3	(	(	PUNCT
iajs-2140	170	4	)	)	PUNCT
iajs-2140	170	5	)	)	PUNCT
iajs-2140	170	6	∑	∑	PUNCT
iajs-2140	170	7	(	(	PUNCT
iajs-2140	170	8	)	)	PUNCT
iajs-2140	170	9	=	=	SYM
iajs-2140	170	10	∑	∑	PUNCT
iajs-2140	170	11	(	(	PUNCT
iajs-2140	170	12	)	)	PUNCT
iajs-2140	170	13	therefore	therefore	ADV
iajs-2140	170	14	,	,	PUNCT
iajs-2140	170	15	is	be	AUX
iajs-2140	170	16	an	an	DET
iajs-2140	170	17	outer	outer	ADJ
iajs-2140	170	18	measure	measure	NOUN
iajs-2140	170	19	on	on	ADP
iajs-2140	170	20	from	from	ADP
iajs-2140	170	21	proposition	proposition	NOUN
iajs-2140	170	22	26	26	NUM
iajs-2140	170	23	,	,	PUNCT
iajs-2140	170	24	we	we	PRON
iajs-2140	170	25	conclude	conclude	VERB
iajs-2140	170	26	that	that	SCONJ
iajs-2140	170	27	if	if	SCONJ
iajs-2140	170	28	is	be	AUX
iajs-2140	170	29	a	a	DET
iajs-2140	170	30	monotone	monotone	ADJ
iajs-2140	170	31	measure	measure	NOUN
iajs-2140	170	32	on	on	ADP
iajs-2140	170	33	,	,	PUNCT
iajs-2140	170	34	then	then	ADV
iajs-2140	170	35	is	be	AUX
iajs-2140	170	36	a	a	DET
iajs-2140	170	37	monotone	monotone	ADJ
iajs-2140	170	38	measure	measure	NOUN
iajs-2140	170	39	on	on	ADP
iajs-2140	170	40	,	,	PUNCT
iajs-2140	170	41	where	where	SCONJ
iajs-2140	170	42	is	be	AUX
iajs-2140	170	43	a	a	PRON
iajs-2140	170	44	–	–	PUNCT
iajs-2140	170	45	of	of	ADP
iajs-2140	170	46	a	a	DET
iajs-2140	170	47	set	set	NOUN
iajs-2140	170	48	and	and	CCONJ
iajs-2140	170	49	.	.	PUNCT
iajs-2140	171	1	proposition	proposition	NOUN
iajs-2140	171	2	27	27	NUM
iajs-2140	171	3	let	let	VERB
iajs-2140	171	4	be	be	AUX
iajs-2140	171	5	a	a	PRON
iajs-2140	171	6	–	–	PUNCT
iajs-2140	171	7	of	of	ADP
iajs-2140	171	8	and	and	CCONJ
iajs-2140	171	9	.	.	PUNCT
iajs-2140	172	1	if	if	SCONJ
iajs-2140	172	2	is	be	AUX
iajs-2140	172	3	a	a	DET
iajs-2140	172	4	null	null	NOUN
iajs-2140	172	5	-	-	PUNCT
iajs-2140	172	6	additive	additive	NOUN
iajs-2140	172	7	on	on	ADP
iajs-2140	172	8	,	,	PUNCT
iajs-2140	172	9	then	then	ADV
iajs-2140	172	10	is	be	AUX
iajs-2140	172	11	a	a	DET
iajs-2140	172	12	null	null	NOUN
iajs-2140	172	13	-	-	PUNCT
iajs-2140	172	14	additive	additive	NOUN
iajs-2140	172	15	on	on	ADP
iajs-2140	172	16	proof	proof	NOUN
iajs-2140	172	17	let	let	AUX
iajs-2140	172	18	be	be	AUX
iajs-2140	172	19	disjoint	disjoint	NOUN
iajs-2140	172	20	sets	set	NOUN
iajs-2140	172	21	in	in	ADP
iajs-2140	172	22	and	and	CCONJ
iajs-2140	172	23	(	(	PUNCT
iajs-2140	172	24	)	)	PUNCT
iajs-2140	172	25	.	.	PUNCT
iajs-2140	173	1	then	then	ADV
iajs-2140	173	2	(	(	PUNCT
iajs-2140	173	3	⋂	⋂	PROPN
iajs-2140	173	4	)	)	PUNCT
iajs-2140	173	5	now	now	ADV
iajs-2140	173	6	,	,	PUNCT
iajs-2140	173	7	(	(	PUNCT
iajs-2140	173	8	)	)	PUNCT
iajs-2140	173	9	=	=	SYM
iajs-2140	173	10	(	(	PUNCT
iajs-2140	173	11	,	,	PUNCT
iajs-2140	173	12	-⋂	-⋂	NUM
iajs-2140	173	13	)	)	PUNCT
iajs-2140	173	14	=	=	SYM
iajs-2140	174	1	(	(	PUNCT
iajs-2140	174	2	,	,	PUNCT
iajs-2140	174	3	⋂	⋂	PROPN
iajs-2140	174	4	,	,	PUNCT
iajs-2140	174	5	⋂	⋂	PROPN
iajs-2140	174	6	-	-	PUNCT
iajs-2140	174	7	)	)	PUNCT
iajs-2140	174	8	=	=	PRON
iajs-2140	174	9	(	(	PUNCT
iajs-2140	174	10	⋂	⋂	PROPN
iajs-2140	174	11	)	)	PUNCT
iajs-2140	174	12	since	since	SCONJ
iajs-2140	174	13	is	be	AUX
iajs-2140	174	14	a	a	DET
iajs-2140	174	15	null	null	NOUN
iajs-2140	174	16	-	-	PUNCT
iajs-2140	174	17	additive	additive	NOUN
iajs-2140	174	18	on	on	ADP
iajs-2140	174	19	=	=	PUNCT
iajs-2140	174	20	(	(	PUNCT
iajs-2140	174	21	)	)	PUNCT
iajs-2140	174	22	by	by	ADP
iajs-2140	174	23	definition	definition	NOUN
iajs-2140	174	24	of	of	ADP
iajs-2140	174	25	hence	hence	ADV
iajs-2140	174	26	,	,	PUNCT
iajs-2140	174	27	is	be	AUX
iajs-2140	174	28	a	a	DET
iajs-2140	174	29	null	null	NOUN
iajs-2140	174	30	-	-	PUNCT
iajs-2140	174	31	additive	additive	NOUN
iajs-2140	174	32	on	on	ADP
iajs-2140	174	33	proposition	proposition	NOUN
iajs-2140	174	34	28	28	NUM
iajs-2140	174	35	let	let	VERB
iajs-2140	174	36	be	be	AUX
iajs-2140	174	37	a	a	PRON
iajs-2140	174	38	–	–	PUNCT
iajs-2140	174	39	of	of	ADP
iajs-2140	174	40	and	and	CCONJ
iajs-2140	174	41	.	.	PUNCT
iajs-2140	175	1	if	if	SCONJ
iajs-2140	175	2	is	be	AUX
iajs-2140	175	3	a	a	DET
iajs-2140	175	4	measure	measure	NOUN
iajs-2140	175	5	on	on	ADP
iajs-2140	175	6	,	,	PUNCT
iajs-2140	175	7	then	then	ADV
iajs-2140	175	8	is	be	AUX
iajs-2140	175	9	a	a	DET
iajs-2140	175	10	null	null	NOUN
iajs-2140	175	11	-	-	PUNCT
iajs-2140	175	12	additive	additive	NOUN
iajs-2140	175	13	on	on	ADP
iajs-2140	175	14	proof	proof	NOUN
iajs-2140	175	15	it	it	PRON
iajs-2140	175	16	is	be	AUX
iajs-2140	175	17	easy	easy	ADJ
iajs-2140	175	18	,	,	PUNCT
iajs-2140	175	19	so	so	ADV
iajs-2140	175	20	we	we	PRON
iajs-2140	175	21	omitted	omit	VERB
iajs-2140	175	22	.	.	PUNCT
iajs-2140	176	1	definition	definition	NOUN
iajs-2140	176	2	29	29	NUM
iajs-2140	176	3	let	let	VERB
iajs-2140	176	4	be	be	AUX
iajs-2140	176	5	a	a	PRON
iajs-2140	176	6	–	–	PUNCT
iajs-2140	176	7	of	of	ADP
iajs-2140	176	8	a	a	DET
iajs-2140	176	9	set	set	NOUN
iajs-2140	176	10	and	and	CCONJ
iajs-2140	176	11	[	[	X
iajs-2140	176	12	0	0	NUM
iajs-2140	176	13	,	,	PUNCT
iajs-2140	176	14	]	]	PUNCT
iajs-2140	176	15	be	be	AUX
iajs-2140	176	16	a	a	DET
iajs-2140	176	17	set	set	NOUN
iajs-2140	176	18	function	function	NOUN
iajs-2140	176	19	and	and	CCONJ
iajs-2140	176	20	be	be	AUX
iajs-2140	176	21	a	a	DET
iajs-2140	176	22	non	non	ADJ
iajs-2140	176	23	-	-	ADJ
iajs-2140	176	24	empty	empty	ADJ
iajs-2140	176	25	subsets	subset	NOUN
iajs-2140	176	26	of	of	ADP
iajs-2140	176	27	such	such	ADJ
iajs-2140	176	28	that	that	PRON
iajs-2140	176	29	.	.	PUNCT
iajs-2140	177	1	if	if	SCONJ
iajs-2140	177	2	:	:	PUNCT
iajs-2140	177	3	[	[	X
iajs-2140	177	4	0	0	NUM
iajs-2140	177	5	,	,	PUNCT
iajs-2140	177	6	]	]	PUNCT
iajs-2140	177	7	is	be	AUX
iajs-2140	177	8	define	define	VERB
iajs-2140	177	9	by	by	ADP
iajs-2140	177	10	:	:	PUNCT
iajs-2140	177	11	(	(	PUNCT
iajs-2140	177	12	)	)	PUNCT
iajs-2140	177	13	=	=	SYM
iajs-2140	177	14	(	(	PUNCT
iajs-2140	177	15	)	)	PUNCT
iajs-2140	177	16	for	for	ADP
iajs-2140	177	17	all	all	PRON
iajs-2140	177	18	,	,	PUNCT
iajs-2140	177	19	then	then	ADV
iajs-2140	177	20	is	be	AUX
iajs-2140	177	21	called	call	VERB
iajs-2140	177	22	the	the	DET
iajs-2140	177	23	restriction	restriction	NOUN
iajs-2140	177	24	of	of	ADP
iajs-2140	177	25	on	on	ADP
iajs-2140	177	26	proposition	proposition	NOUN
iajs-2140	177	27	30	30	NUM
iajs-2140	177	28	let	let	VERB
iajs-2140	177	29	be	be	AUX
iajs-2140	177	30	a	a	DET
iajs-2140	177	31	measure	measure	NOUN
iajs-2140	177	32	on	on	ADP
iajs-2140	177	33	–	–	PUNCT
iajs-2140	177	34	of	of	ADP
iajs-2140	177	35	a	a	DET
iajs-2140	177	36	set	set	NOUN
iajs-2140	177	37	and	and	CCONJ
iajs-2140	177	38	such	such	ADJ
iajs-2140	177	39	that	that	PRON
iajs-2140	177	40	.	.	PUNCT
iajs-2140	178	1	then	then	ADV
iajs-2140	178	2	is	be	AUX
iajs-2140	178	3	a	a	DET
iajs-2140	178	4	measure	measure	NOUN
iajs-2140	178	5	on	on	ADP
iajs-2140	178	6	a	a	PRON
iajs-2140	178	7	–	–	PUNCT
iajs-2140	178	8	of	of	ADP
iajs-2140	178	9	a	a	DET
iajs-2140	178	10	set	set	NOUN
iajs-2140	178	11	.	.	PUNCT
iajs-2140	179	1	proof	proof	NOUN
iajs-2140	179	2	since	since	SCONJ
iajs-2140	179	3	is	be	AUX
iajs-2140	179	4	a	a	PRON
iajs-2140	179	5	–	–	PUNCT
iajs-2140	179	6	of	of	ADP
iajs-2140	179	7	a	a	DET
iajs-2140	179	8	set	set	NOUN
iajs-2140	179	9	,	,	PUNCT
iajs-2140	179	10	then	then	ADV
iajs-2140	179	11	and	and	CCONJ
iajs-2140	179	12	(	(	PUNCT
iajs-2140	179	13	)	)	PUNCT
iajs-2140	180	1	=	=	SYM
iajs-2140	180	2	0	0	X
iajs-2140	180	3	.	.	PUNCT
iajs-2140	181	1	since	since	ADV
iajs-2140	181	2	,	,	PUNCT
iajs-2140	181	3	then	then	ADV
iajs-2140	181	4	by	by	ADP
iajs-2140	181	5	definition	definition	NOUN
iajs-2140	181	6	of	of	ADP
iajs-2140	181	7	,	,	PUNCT
iajs-2140	181	8	we	we	PRON
iajs-2140	181	9	get	get	VERB
iajs-2140	181	10	(	(	PUNCT
iajs-2140	181	11	)	)	PUNCT
iajs-2140	181	12	=	=	SYM
iajs-2140	181	13	(	(	PUNCT
iajs-2140	181	14	)	)	PUNCT
iajs-2140	181	15	=	=	SYM
iajs-2140	182	1	0	0	X
iajs-2140	182	2	.	.	PUNCT
iajs-2140	183	1	let	let	AUX
iajs-2140	183	2	be	be	AUX
iajs-2140	183	3	disjoint	disjoint	VERB
iajs-2140	183	4	sets	set	NOUN
iajs-2140	183	5	in	in	ADP
iajs-2140	183	6	.	.	PUNCT
iajs-2140	184	1	then	then	ADV
iajs-2140	184	2	and	and	CCONJ
iajs-2140	184	3	for	for	ADP
iajs-2140	184	4	all	all	DET
iajs-2140	184	5	n=1,2	n=1,2	ADJ
iajs-2140	184	6	,	,	PUNCT
iajs-2140	184	7	…	…	PUNCT
iajs-2140	184	8	,	,	PUNCT
iajs-2140	184	9	hence	hence	ADV
iajs-2140	184	10	.	.	PUNCT
iajs-2140	185	1	so	so	ADV
iajs-2140	185	2	,	,	PUNCT
iajs-2140	185	3	we	we	PRON
iajs-2140	185	4	have	have	VERB
iajs-2140	185	5	(	(	PUNCT
iajs-2140	185	6	)	)	PUNCT
iajs-2140	185	7	=	=	SYM
iajs-2140	185	8	(	(	PUNCT
iajs-2140	185	9	)	)	PUNCT
iajs-2140	185	10	=	=	SYM
iajs-2140	185	11	∑	∑	PUNCT
iajs-2140	185	12	(	(	PUNCT
iajs-2140	185	13	)	)	PUNCT
iajs-2140	185	14	since	since	SCONJ
iajs-2140	185	15	is	be	AUX
iajs-2140	185	16	a	a	DET
iajs-2140	185	17	measure	measure	NOUN
iajs-2140	185	18	on	on	ADP
iajs-2140	185	19	=	=	PUNCT
iajs-2140	185	20	∑	∑	PUNCT
iajs-2140	185	21	(	(	PUNCT
iajs-2140	185	22	)	)	PUNCT
iajs-2140	185	23	therefore	therefore	ADV
iajs-2140	185	24	,	,	PUNCT
iajs-2140	185	25	is	be	AUX
iajs-2140	185	26	a	a	DET
iajs-2140	185	27	measure	measure	NOUN
iajs-2140	185	28	on	on	ADP
iajs-2140	185	29	a	a	PRON
iajs-2140	185	30	–	–	PUNCT
iajs-2140	185	31	of	of	ADP
iajs-2140	185	32	a	a	DET
iajs-2140	185	33	set	set	NOUN
iajs-2140	185	34	.	.	PUNCT
iajs-2140	186	1	26	26	NUM
iajs-2140	187	1	ibn	ibn	PROPN
iajs-2140	187	2	al	al	PROPN
iajs-2140	187	3	-	-	PUNCT
iajs-2140	187	4	haitham	haitham	PROPN
iajs-2140	187	5	jour	jour	X
iajs-2140	187	6	.	.	PROPN
iajs-2140	187	7	for	for	ADP
iajs-2140	187	8	pure	pure	ADJ
iajs-2140	187	9	&	&	CCONJ
iajs-2140	187	10	appl	appl	PROPN
iajs-2140	187	11	.	.	PUNCT
iajs-2140	188	1	sci	sci	PROPN
iajs-2140	188	2	.	.	PROPN
iajs-2140	188	3	32	32	NUM
iajs-2140	188	4	(	(	PUNCT
iajs-2140	188	5	2	2	NUM
iajs-2140	188	6	)	)	PUNCT
iajs-2140	188	7	2019	2019	NUM
iajs-2140	188	8	if	if	SCONJ
iajs-2140	188	9	is	be	AUX
iajs-2140	188	10	an	an	DET
iajs-2140	188	11	outer	outer	ADJ
iajs-2140	188	12	measure	measure	NOUN
iajs-2140	188	13	on	on	ADP
iajs-2140	188	14	–	–	PUNCT
iajs-2140	188	15	of	of	ADP
iajs-2140	188	16	a	a	DET
iajs-2140	188	17	set	set	NOUN
iajs-2140	188	18	,	,	PUNCT
iajs-2140	188	19	then	then	ADV
iajs-2140	188	20	we	we	PRON
iajs-2140	188	21	need	need	VERB
iajs-2140	188	22	the	the	DET
iajs-2140	188	23	following	follow	VERB
iajs-2140	188	24	two	two	NUM
iajs-2140	188	25	facts	fact	NOUN
iajs-2140	188	26	to	to	PART
iajs-2140	188	27	prove	prove	VERB
iajs-2140	188	28	that	that	PRON
iajs-2140	188	29	is	be	AUX
iajs-2140	188	30	an	an	DET
iajs-2140	188	31	outer	outer	ADJ
iajs-2140	188	32	measure	measure	NOUN
iajs-2140	188	33	on	on	ADP
iajs-2140	188	34	a	a	PRON
iajs-2140	188	35	–	–	PUNCT
iajs-2140	188	36	of	of	ADP
iajs-2140	188	37	a	a	DET
iajs-2140	188	38	set	set	NOUN
iajs-2140	188	39	.	.	PUNCT
iajs-2140	189	1	lemma	lemma	PROPN
iajs-2140	189	2	31	31	NUM
iajs-2140	189	3	let	let	AUX
iajs-2140	189	4	be	be	AUX
iajs-2140	189	5	a	a	DET
iajs-2140	189	6	monotone	monotone	ADJ
iajs-2140	189	7	measure	measure	NOUN
iajs-2140	189	8	on	on	ADP
iajs-2140	189	9	–	–	PUNCT
iajs-2140	189	10	of	of	ADP
iajs-2140	189	11	a	a	DET
iajs-2140	189	12	set	set	NOUN
iajs-2140	189	13	and	and	CCONJ
iajs-2140	189	14	such	such	ADJ
iajs-2140	189	15	that	that	PRON
iajs-2140	189	16	.	.	PUNCT
iajs-2140	190	1	then	then	ADV
iajs-2140	190	2	is	be	AUX
iajs-2140	190	3	a	a	DET
iajs-2140	190	4	monotone	monotone	ADJ
iajs-2140	190	5	measure	measure	NOUN
iajs-2140	190	6	on	on	ADP
iajs-2140	190	7	a	a	PRON
iajs-2140	190	8	–	–	PUNCT
iajs-2140	190	9	of	of	ADP
iajs-2140	190	10	a	a	DET
iajs-2140	190	11	set	set	NOUN
iajs-2140	190	12	.	.	PUNCT
iajs-2140	191	1	proof	proof	NOUN
iajs-2140	191	2	let	let	AUX
iajs-2140	191	3	be	be	AUX
iajs-2140	191	4	a	a	DET
iajs-2140	191	5	monotone	monotone	ADJ
iajs-2140	191	6	measure	measure	NOUN
iajs-2140	191	7	on	on	ADP
iajs-2140	191	8	,	,	PUNCT
iajs-2140	191	9	then	then	ADV
iajs-2140	191	10	(	(	PUNCT
iajs-2140	191	11	)	)	PUNCT
iajs-2140	191	12	=	=	SYM
iajs-2140	192	1	0	0	X
iajs-2140	192	2	.	.	PUNCT
iajs-2140	193	1	since	since	SCONJ
iajs-2140	193	2	is	be	AUX
iajs-2140	193	3	a	a	PRON
iajs-2140	193	4	–	–	PUNCT
iajs-2140	193	5	,	,	PUNCT
iajs-2140	193	6	then	then	ADV
iajs-2140	193	7	.	.	PUNCT
iajs-2140	194	1	from	from	ADP
iajs-2140	194	2	definition	definition	NOUN
iajs-2140	194	3	of	of	ADP
iajs-2140	194	4	,	,	PUNCT
iajs-2140	194	5	we	we	PRON
iajs-2140	194	6	get	get	VERB
iajs-2140	194	7	(	(	PUNCT
iajs-2140	194	8	)	)	PUNCT
iajs-2140	194	9	=	=	SYM
iajs-2140	194	10	(	(	PUNCT
iajs-2140	194	11	)	)	PUNCT
iajs-2140	194	12	=	=	SYM
iajs-2140	195	1	0	0	X
iajs-2140	195	2	.	.	PUNCT
iajs-2140	195	3	let	let	VERB
iajs-2140	195	4	such	such	ADJ
iajs-2140	195	5	that	that	PRON
iajs-2140	195	6	,	,	PUNCT
iajs-2140	195	7	then	then	ADV
iajs-2140	195	8	and	and	CCONJ
iajs-2140	195	9	.	.	PUNCT
iajs-2140	196	1	since	since	SCONJ
iajs-2140	196	2	is	be	AUX
iajs-2140	196	3	a	a	DET
iajs-2140	196	4	monotone	monotone	ADJ
iajs-2140	196	5	measure	measure	NOUN
iajs-2140	196	6	on	on	ADP
iajs-2140	196	7	,	,	PUNCT
iajs-2140	196	8	then	then	ADV
iajs-2140	196	9	(	(	PUNCT
iajs-2140	196	10	)	)	PUNCT
iajs-2140	196	11	(	(	PUNCT
iajs-2140	196	12	)	)	PUNCT
iajs-2140	196	13	.	.	PUNCT
iajs-2140	197	1	but	but	CCONJ
iajs-2140	197	2	,	,	PUNCT
iajs-2140	197	3	then	then	ADV
iajs-2140	197	4	(	(	PUNCT
iajs-2140	197	5	)	)	PUNCT
iajs-2140	197	6	=	=	SYM
iajs-2140	197	7	(	(	PUNCT
iajs-2140	197	8	)	)	PUNCT
iajs-2140	197	9	and	and	CCONJ
iajs-2140	197	10	(	(	PUNCT
iajs-2140	197	11	)	)	PUNCT
iajs-2140	197	12	=	=	SYM
iajs-2140	197	13	(	(	PUNCT
iajs-2140	197	14	)	)	PUNCT
iajs-2140	197	15	,	,	PUNCT
iajs-2140	197	16	hence	hence	ADV
iajs-2140	197	17	(	(	PUNCT
iajs-2140	197	18	)	)	PUNCT
iajs-2140	197	19	(	(	PUNCT
iajs-2140	197	20	)	)	PUNCT
iajs-2140	197	21	and	and	CCONJ
iajs-2140	197	22	is	be	AUX
iajs-2140	197	23	monotone	monotone	ADJ
iajs-2140	197	24	measure	measure	NOUN
iajs-2140	197	25	on	on	ADP
iajs-2140	197	26	of	of	ADP
iajs-2140	197	27	.	.	PUNCT
iajs-2140	198	1	lemma	lemma	PROPN
iajs-2140	198	2	32	32	NUM
iajs-2140	198	3	let	let	VERB
iajs-2140	198	4	be	be	AUX
iajs-2140	198	5	a	a	DET
iajs-2140	198	6	countably	countably	ADV
iajs-2140	198	7	subadditive	subadditive	ADJ
iajs-2140	198	8	on	on	ADP
iajs-2140	198	9	–	–	PUNCT
iajs-2140	198	10	of	of	ADP
iajs-2140	198	11	a	a	DET
iajs-2140	198	12	set	set	NOUN
iajs-2140	198	13	and	and	CCONJ
iajs-2140	198	14	such	such	ADJ
iajs-2140	198	15	that	that	PRON
iajs-2140	198	16	,	,	PUNCT
iajs-2140	198	17	then	then	ADV
iajs-2140	198	18	is	be	AUX
iajs-2140	198	19	a	a	DET
iajs-2140	198	20	countably	countably	ADV
iajs-2140	198	21	subadditive	subadditive	ADJ
iajs-2140	198	22	on	on	ADP
iajs-2140	198	23	a	a	PRON
iajs-2140	198	24	–	–	PUNCT
iajs-2140	198	25	of	of	ADP
iajs-2140	198	26	a	a	DET
iajs-2140	198	27	set	set	ADJ
iajs-2140	198	28	proof	proof	NOUN
iajs-2140	198	29	let	let	VERB
iajs-2140	198	30	and	and	CCONJ
iajs-2140	198	31	,	,	PUNCT
iajs-2140	198	32	then	then	ADV
iajs-2140	198	33	and	and	CCONJ
iajs-2140	198	34	.	.	PUNCT
iajs-2140	199	1	since	since	SCONJ
iajs-2140	199	2	be	be	AUX
iajs-2140	199	3	a	a	DET
iajs-2140	199	4	countably	countably	ADV
iajs-2140	199	5	subadditive	subadditive	ADJ
iajs-2140	199	6	on	on	ADP
iajs-2140	199	7	,	,	PUNCT
iajs-2140	199	8	then	then	ADV
iajs-2140	199	9	(	(	PUNCT
iajs-2140	199	10	)	)	PUNCT
iajs-2140	199	11	∑	∑	PROPN
iajs-2140	199	12	(	(	PUNCT
iajs-2140	199	13	)	)	PUNCT
iajs-2140	199	14	,	,	PUNCT
iajs-2140	199	15	but	but	CCONJ
iajs-2140	199	16	.	.	PUNCT
iajs-2140	200	1	so	so	ADV
iajs-2140	200	2	,	,	PUNCT
iajs-2140	200	3	we	we	PRON
iajs-2140	200	4	have	have	VERB
iajs-2140	200	5	(	(	PUNCT
iajs-2140	200	6	)	)	PUNCT
iajs-2140	200	7	(	(	PUNCT
iajs-2140	200	8	)	)	PUNCT
iajs-2140	200	9	and	and	CCONJ
iajs-2140	200	10	(	(	PUNCT
iajs-2140	200	11	)	)	PUNCT
iajs-2140	200	12	(	(	PUNCT
iajs-2140	200	13	)	)	PUNCT
iajs-2140	200	14	for	for	ADP
iajs-2140	200	15	all	all	DET
iajs-2140	200	16	n=1,2	n=1,2	ADJ
iajs-2140	200	17	,	,	PUNCT
iajs-2140	200	18	…	…	PUNCT
iajs-2140	200	19	,	,	PUNCT
iajs-2140	200	20	hence	hence	ADV
iajs-2140	200	21	(	(	PUNCT
iajs-2140	200	22	)	)	PUNCT
iajs-2140	200	23	∑	∑	PUNCT
iajs-2140	200	24	(	(	PUNCT
iajs-2140	200	25	)	)	PUNCT
iajs-2140	200	26	and	and	CCONJ
iajs-2140	200	27	is	be	AUX
iajs-2140	200	28	a	a	DET
iajs-2140	200	29	countably	countably	ADV
iajs-2140	200	30	subadditive	subadditive	ADJ
iajs-2140	200	31	on	on	ADP
iajs-2140	200	32	of	of	ADP
iajs-2140	200	33	a	a	DET
iajs-2140	200	34	set	set	NOUN
iajs-2140	200	35	.	.	PUNCT
iajs-2140	201	1	proposition	proposition	NOUN
iajs-2140	201	2	33	33	NUM
iajs-2140	201	3	let	let	VERB
iajs-2140	201	4	be	be	AUX
iajs-2140	201	5	an	an	DET
iajs-2140	201	6	outer	outer	ADJ
iajs-2140	201	7	measure	measure	NOUN
iajs-2140	201	8	on	on	ADP
iajs-2140	201	9	–	–	PUNCT
iajs-2140	201	10	of	of	ADP
iajs-2140	201	11	a	a	DET
iajs-2140	201	12	set	set	NOUN
iajs-2140	201	13	and	and	CCONJ
iajs-2140	201	14	such	such	ADJ
iajs-2140	201	15	that	that	PRON
iajs-2140	201	16	.	.	PUNCT
iajs-2140	202	1	then	then	ADV
iajs-2140	202	2	is	be	AUX
iajs-2140	202	3	an	an	DET
iajs-2140	202	4	outer	outer	ADJ
iajs-2140	202	5	measure	measure	NOUN
iajs-2140	202	6	on	on	ADP
iajs-2140	202	7	–	–	PUNCT
iajs-2140	202	8	of	of	ADP
iajs-2140	202	9	a	a	DET
iajs-2140	202	10	set	set	NOUN
iajs-2140	202	11	.	.	PUNCT
iajs-2140	203	1	proof	proof	NOUN
iajs-2140	203	2	since	since	SCONJ
iajs-2140	203	3	is	be	AUX
iajs-2140	203	4	an	an	DET
iajs-2140	203	5	outer	outer	ADJ
iajs-2140	203	6	measure	measure	NOUN
iajs-2140	203	7	on	on	ADP
iajs-2140	203	8	,	,	PUNCT
iajs-2140	203	9	then	then	ADV
iajs-2140	203	10	is	be	AUX
iajs-2140	203	11	a	a	DET
iajs-2140	203	12	monotone	monotone	ADJ
iajs-2140	203	13	measure	measure	NOUN
iajs-2140	203	14	and	and	CCONJ
iajs-2140	203	15	countably	countably	ADV
iajs-2140	203	16	subadditive	subadditive	ADJ
iajs-2140	203	17	.	.	PUNCT
iajs-2140	204	1	by	by	ADP
iajs-2140	204	2	lemma	lemma	PROPN
iajs-2140	204	3	31	31	NUM
iajs-2140	204	4	and	and	CCONJ
iajs-2140	204	5	lemma	lemma	PROPN
iajs-2140	204	6	32	32	NUM
iajs-2140	204	7	we	we	PRON
iajs-2140	204	8	have	have	VERB
iajs-2140	204	9	is	be	AUX
iajs-2140	204	10	a	a	DET
iajs-2140	204	11	monotone	monotone	ADJ
iajs-2140	204	12	measure	measure	NOUN
iajs-2140	204	13	and	and	CCONJ
iajs-2140	204	14	countably	countably	ADV
iajs-2140	204	15	subadditive	subadditive	ADJ
iajs-2140	204	16	on	on	ADP
iajs-2140	204	17	of	of	ADP
iajs-2140	204	18	.	.	PUNCT
iajs-2140	205	1	therefore	therefore	ADV
iajs-2140	205	2	is	be	AUX
iajs-2140	205	3	an	an	DET
iajs-2140	205	4	outer	outer	ADJ
iajs-2140	205	5	measure	measure	NOUN
iajs-2140	205	6	on	on	ADP
iajs-2140	205	7	of	of	ADP
iajs-2140	205	8	.	.	PUNCT
iajs-2140	206	1	proposition	proposition	NOUN
iajs-2140	206	2	34	34	NUM
iajs-2140	206	3	let	let	VERB
iajs-2140	206	4	be	be	AUX
iajs-2140	206	5	a	a	DET
iajs-2140	206	6	null	null	NOUN
iajs-2140	206	7	-	-	PUNCT
iajs-2140	206	8	additive	additive	NOUN
iajs-2140	206	9	on	on	ADP
iajs-2140	206	10	–	–	PUNCT
iajs-2140	206	11	of	of	ADP
iajs-2140	206	12	a	a	DET
iajs-2140	206	13	set	set	NOUN
iajs-2140	206	14	and	and	CCONJ
iajs-2140	206	15	such	such	ADJ
iajs-2140	206	16	that	that	PRON
iajs-2140	206	17	.	.	PUNCT
iajs-2140	207	1	then	then	ADV
iajs-2140	207	2	is	be	AUX
iajs-2140	207	3	a	a	DET
iajs-2140	207	4	null	null	NOUN
iajs-2140	207	5	-	-	PUNCT
iajs-2140	207	6	additive	additive	NOUN
iajs-2140	207	7	on	on	ADP
iajs-2140	207	8	–	–	PUNCT
iajs-2140	207	9	.	.	PUNCT
iajs-2140	208	1	proof	proof	NOUN
iajs-2140	208	2	:	:	PUNCT
iajs-2140	208	3	let	let	AUX
iajs-2140	208	4	be	be	AUX
iajs-2140	208	5	disjoint	disjoint	VERB
iajs-2140	208	6	sets	set	NOUN
iajs-2140	208	7	in	in	ADP
iajs-2140	208	8	and	and	CCONJ
iajs-2140	208	9	(	(	PUNCT
iajs-2140	208	10	)	)	PUNCT
iajs-2140	208	11	.	.	PUNCT
iajs-2140	209	1	then	then	ADV
iajs-2140	209	2	(	(	PUNCT
iajs-2140	209	3	)	)	PUNCT
iajs-2140	209	4	now	now	ADV
iajs-2140	209	5	,	,	PUNCT
iajs-2140	209	6	(	(	PUNCT
iajs-2140	209	7	)	)	PUNCT
iajs-2140	209	8	=	=	SYM
iajs-2140	209	9	(	(	PUNCT
iajs-2140	209	10	,	,	PUNCT
iajs-2140	209	11	)	)	PUNCT
iajs-2140	209	12	=	=	SYM
iajs-2140	209	13	(	(	PUNCT
iajs-2140	209	14	)	)	PUNCT
iajs-2140	209	15	since	since	SCONJ
iajs-2140	209	16	is	be	AUX
iajs-2140	209	17	a	a	DET
iajs-2140	209	18	null	null	NOUN
iajs-2140	209	19	-	-	PUNCT
iajs-2140	209	20	additive	additive	NOUN
iajs-2140	209	21	on	on	ADP
iajs-2140	209	22	=	=	PUNCT
iajs-2140	209	23	(	(	PUNCT
iajs-2140	209	24	)	)	PUNCT
iajs-2140	209	25	by	by	ADP
iajs-2140	209	26	definition	definition	NOUN
iajs-2140	209	27	of	of	ADP
iajs-2140	209	28	.	.	PUNCT
iajs-2140	210	1	hence	hence	ADV
iajs-2140	210	2	,	,	PUNCT
iajs-2140	210	3	is	be	AUX
iajs-2140	210	4	a	a	DET
iajs-2140	210	5	null	null	NOUN
iajs-2140	210	6	-	-	PUNCT
iajs-2140	210	7	additive	additive	NOUN
iajs-2140	210	8	on	on	ADP
iajs-2140	210	9	3	3	NUM
iajs-2140	210	10	.	.	PUNCT
iajs-2140	210	11	conclusions	conclusion	NOUN
iajs-2140	210	12	the	the	DET
iajs-2140	210	13	main	main	ADJ
iajs-2140	210	14	results	result	NOUN
iajs-2140	210	15	of	of	ADP
iajs-2140	210	16	this	this	DET
iajs-2140	210	17	paper	paper	NOUN
iajs-2140	210	18	are	be	AUX
iajs-2140	210	19	the	the	DET
iajs-2140	210	20	following	follow	VERB
iajs-2140	210	21	:	:	PUNCT
iajs-2140	210	22	(	(	PUNCT
iajs-2140	210	23	1	1	X
iajs-2140	210	24	)	)	PUNCT
iajs-2140	210	25	let	let	AUX
iajs-2140	210	26	be	be	AUX
iajs-2140	210	27	a	a	DET
iajs-2140	210	28	nonempty	nonempty	ADV
iajs-2140	210	29	set	set	VERB
iajs-2140	210	30	.	.	PUNCT
iajs-2140	211	1	a	a	DET
iajs-2140	211	2	collection	collection	NOUN
iajs-2140	211	3	(	(	PUNCT
iajs-2140	211	4	)	)	PUNCT
iajs-2140	211	5	is	be	AUX
iajs-2140	211	6	said	say	VERB
iajs-2140	211	7	to	to	PART
iajs-2140	211	8	be	be	AUX
iajs-2140	211	9	–	–	PUNCT
iajs-2140	211	10	of	of	ADP
iajs-2140	211	11	a	a	DET
iajs-2140	211	12	set	set	NOUN
iajs-2140	211	13	if	if	SCONJ
iajs-2140	211	14	the	the	DET
iajs-2140	211	15	following	follow	VERB
iajs-2140	211	16	conditions	condition	NOUN
iajs-2140	211	17	are	be	AUX
iajs-2140	211	18	satisfied	satisfied	ADJ
iajs-2140	211	19	:	:	PUNCT
iajs-2140	211	20	1	1	X
iajs-2140	211	21	.	.	PUNCT
iajs-2140	211	22	.	.	PUNCT
iajs-2140	212	1	2	2	X
iajs-2140	212	2	.	.	X
iajs-2140	212	3	if	if	SCONJ
iajs-2140	212	4	is	be	AUX
iajs-2140	212	5	a	a	DET
iajs-2140	212	6	nonempty	nonempty	ADJ
iajs-2140	212	7	set	set	VERB
iajs-2140	212	8	in	in	ADP
iajs-2140	212	9	and	and	CCONJ
iajs-2140	212	10	,	,	PUNCT
iajs-2140	212	11	then	then	ADV
iajs-2140	212	12	.	.	PUNCT
iajs-2140	213	1	3	3	X
iajs-2140	213	2	.	.	X
iajs-2140	214	1	if	if	SCONJ
iajs-2140	214	2	,	,	PUNCT
iajs-2140	214	3	then	then	ADV
iajs-2140	214	4	⋂	⋂	PROPN
iajs-2140	214	5	.	.	PUNCT
iajs-2140	215	1	(	(	PUNCT
iajs-2140	215	2	2	2	X
iajs-2140	215	3	)	)	PUNCT
iajs-2140	215	4	let	let	VERB
iajs-2140	215	5	*	*	PUNCT
iajs-2140	216	1	+	+	CCONJ
iajs-2140	216	2	be	be	AUX
iajs-2140	216	3	a	a	DET
iajs-2140	216	4	sequence	sequence	NOUN
iajs-2140	216	5	of	of	ADP
iajs-2140	216	6	–	–	PUNCT
iajs-2140	216	7	of	of	ADP
iajs-2140	216	8	a	a	DET
iajs-2140	216	9	set	set	NOUN
iajs-2140	216	10	.	.	PUNCT
iajs-2140	217	1	then	then	ADV
iajs-2140	217	2	⋂	⋂	PROPN
iajs-2140	217	3	is	be	AUX
iajs-2140	217	4	a	a	PRON
iajs-2140	217	5	–	–	PUNCT
iajs-2140	217	6	of	of	ADP
iajs-2140	217	7	a	a	DET
iajs-2140	217	8	set	set	NOUN
iajs-2140	217	9	.	.	PUNCT
iajs-2140	218	1	67	67	NUM
iajs-2140	218	2	ibn	ibn	PROPN
iajs-2140	218	3	al	al	PROPN
iajs-2140	218	4	-	-	PUNCT
iajs-2140	218	5	haitham	haitham	PROPN
iajs-2140	218	6	jour	jour	X
iajs-2140	218	7	.	.	PROPN
iajs-2140	218	8	for	for	ADP
iajs-2140	218	9	pure	pure	ADJ
iajs-2140	218	10	&	&	CCONJ
iajs-2140	218	11	appl	appl	PROPN
iajs-2140	218	12	.	.	PUNCT
iajs-2140	219	1	sci	sci	PROPN
iajs-2140	219	2	.	.	PROPN
iajs-2140	219	3	32	32	NUM
iajs-2140	219	4	(	(	PUNCT
iajs-2140	219	5	2	2	NUM
iajs-2140	219	6	)	)	PUNCT
iajs-2140	219	7	2019	2019	NUM
iajs-2140	219	8	(	(	PUNCT
iajs-2140	219	9	3	3	X
iajs-2140	219	10	)	)	PUNCT
iajs-2140	219	11	let	let	AUX
iajs-2140	219	12	be	be	AUX
iajs-2140	219	13	a	a	PRON
iajs-2140	219	14	–	–	PUNCT
iajs-2140	219	15	of	of	ADP
iajs-2140	219	16	a	a	DET
iajs-2140	219	17	set	set	NOUN
iajs-2140	219	18	and	and	CCONJ
iajs-2140	219	19	let	let	VERB
iajs-2140	219	20	be	be	AUX
iajs-2140	219	21	a	a	DET
iajs-2140	219	22	non	non	ADJ
iajs-2140	219	23	-	-	ADJ
iajs-2140	219	24	empty	empty	ADJ
iajs-2140	219	25	subset	subset	NOUN
iajs-2140	219	26	of	of	ADP
iajs-2140	219	27	.	.	PUNCT
iajs-2140	220	1	then	then	ADV
iajs-2140	220	2	the	the	DET
iajs-2140	220	3	restriction	restriction	NOUN
iajs-2140	220	4	of	of	ADP
iajs-2140	220	5	on	on	ADV
iajs-2140	220	6	is	be	AUX
iajs-2140	220	7	denoted	denote	VERB
iajs-2140	220	8	by	by	ADP
iajs-2140	220	9	and	and	CCONJ
iajs-2140	220	10	=	=	NOUN
iajs-2140	220	11	{	{	PUNCT
iajs-2140	220	12	:	:	PUNCT
iajs-2140	220	13	=	=	SYM
iajs-2140	220	14	⋂	⋂	PROPN
iajs-2140	220	15	,	,	PUNCT
iajs-2140	220	16	for	for	ADP
iajs-2140	220	17	some	some	PRON
iajs-2140	220	18	}	}	PUNCT
iajs-2140	220	19	.	.	PUNCT
iajs-2140	221	1	(	(	PUNCT
iajs-2140	221	2	4	4	X
iajs-2140	221	3	)	)	PUNCT
iajs-2140	221	4	let	let	AUX
iajs-2140	221	5	be	be	AUX
iajs-2140	221	6	a	a	PRON
iajs-2140	221	7	–	–	PUNCT
iajs-2140	221	8	of	of	ADP
iajs-2140	221	9	a	a	DET
iajs-2140	221	10	set	set	NOUN
iajs-2140	221	11	.	.	PUNCT
iajs-2140	222	1	then	then	ADV
iajs-2140	222	2	every	every	DET
iajs-2140	222	3	measure	measure	NOUN
iajs-2140	222	4	is	be	AUX
iajs-2140	222	5	null	null	ADJ
iajs-2140	222	6	-	-	PUNCT
iajs-2140	222	7	additive	additive	NOUN
iajs-2140	222	8	.	.	PUNCT
iajs-2140	223	1	(	(	PUNCT
iajs-2140	223	2	5	5	X
iajs-2140	223	3	)	)	PUNCT
iajs-2140	223	4	let	let	VERB
iajs-2140	223	5	,	,	PUNCT
iajs-2140	223	6	,	,	PUNCT
iajs-2140	223	7	…	…	PUNCT
iajs-2140	223	8	,	,	PUNCT
iajs-2140	223	9	be	be	AUX
iajs-2140	223	10	null	null	NOUN
iajs-2140	223	11	-	-	PUNCT
iajs-2140	223	12	additive	additive	NOUN
iajs-2140	223	13	on	on	ADP
iajs-2140	223	14	a	a	PRON
iajs-2140	223	15	–	–	PUNCT
iajs-2140	223	16	of	of	ADP
iajs-2140	223	17	a	a	DET
iajs-2140	223	18	set	set	NOUN
iajs-2140	223	19	and	and	CCONJ
iajs-2140	223	20	(	(	PUNCT
iajs-2140	223	21	)	)	PUNCT
iajs-2140	223	22	for	for	ADP
iajs-2140	223	23	all	all	PRON
iajs-2140	223	24	.	.	PUNCT
iajs-2140	224	1	if	if	SCONJ
iajs-2140	224	2	a	a	DET
iajs-2140	224	3	set	set	NOUN
iajs-2140	224	4	function	function	NOUN
iajs-2140	224	5	∑	∑	PUNCT
iajs-2140	224	6	:	:	PUNCT
iajs-2140	224	7	,	,	PUNCT
iajs-2140	224	8	is	be	AUX
iajs-2140	224	9	defined	define	VERB
iajs-2140	224	10	by	by	ADP
iajs-2140	224	11	:	:	PUNCT
iajs-2140	224	12	(	(	PUNCT
iajs-2140	224	13	∑	∑	PROPN
iajs-2140	224	14	)	)	PUNCT
iajs-2140	224	15	(	(	PUNCT
iajs-2140	224	16	)	)	PUNCT
iajs-2140	224	17	∑	∑	PUNCT
iajs-2140	224	18	(	(	PUNCT
iajs-2140	224	19	)	)	PUNCT
iajs-2140	224	20	,	,	PUNCT
iajs-2140	224	21	then	then	ADV
iajs-2140	224	22	∑	∑	PUNCT
iajs-2140	224	23	is	be	AUX
iajs-2140	224	24	a	a	DET
iajs-2140	224	25	null	null	NOUN
iajs-2140	224	26	-	-	PUNCT
iajs-2140	224	27	additive	additive	NOUN
iajs-2140	224	28	on	on	ADP
iajs-2140	224	29	.	.	PUNCT
iajs-2140	225	1	(	(	PUNCT
iajs-2140	225	2	6	6	X
iajs-2140	225	3	)	)	PUNCT
iajs-2140	225	4	let	let	AUX
iajs-2140	225	5	be	be	AUX
iajs-2140	225	6	a	a	PRON
iajs-2140	225	7	–	–	PUNCT
iajs-2140	225	8	of	of	ADP
iajs-2140	225	9	a	a	DET
iajs-2140	225	10	set	set	NOUN
iajs-2140	225	11	and	and	CCONJ
iajs-2140	225	12	.	.	PUNCT
iajs-2140	226	1	if	if	SCONJ
iajs-2140	226	2	is	be	AUX
iajs-2140	226	3	a	a	DET
iajs-2140	226	4	measure	measure	NOUN
iajs-2140	226	5	on	on	ADP
iajs-2140	226	6	,	,	PUNCT
iajs-2140	226	7	then	then	ADV
iajs-2140	226	8	:	:	PUNCT
iajs-2140	226	9	1	1	X
iajs-2140	226	10	.	.	X
iajs-2140	226	11	is	be	AUX
iajs-2140	226	12	a	a	DET
iajs-2140	226	13	measure	measure	NOUN
iajs-2140	226	14	on	on	ADP
iajs-2140	226	15	.	.	PUNCT
iajs-2140	227	1	2	2	X
iajs-2140	227	2	.	.	PUNCT
iajs-2140	227	3	(	(	PUNCT
iajs-2140	227	4	)	)	PUNCT
iajs-2140	227	5	=	=	SYM
iajs-2140	227	6	(	(	PUNCT
iajs-2140	227	7	)	)	PUNCT
iajs-2140	227	8	,	,	PUNCT
iajs-2140	227	9	whenever	whenever	SCONJ
iajs-2140	227	10	.	.	PUNCT
iajs-2140	228	1	3	3	X
iajs-2140	228	2	.	.	PUNCT
iajs-2140	228	3	(	(	PUNCT
iajs-2140	228	4	)	)	PUNCT
iajs-2140	228	5	=	=	SYM
iajs-2140	228	6	0	0	NUM
iajs-2140	228	7	,	,	PUNCT
iajs-2140	228	8	whenever	whenever	SCONJ
iajs-2140	228	9	are	be	AUX
iajs-2140	228	10	disjoint	disjoint	NOUN
iajs-2140	228	11	sets	set	NOUN
iajs-2140	228	12	in	in	ADP
iajs-2140	228	13	.	.	PUNCT
iajs-2140	229	1	(	(	PUNCT
iajs-2140	229	2	7	7	X
iajs-2140	229	3	)	)	PUNCT
iajs-2140	229	4	let	let	AUX
iajs-2140	229	5	be	be	AUX
iajs-2140	229	6	a	a	PRON
iajs-2140	229	7	–	–	PUNCT
iajs-2140	229	8	of	of	ADP
iajs-2140	229	9	a	a	DET
iajs-2140	229	10	set	set	NOUN
iajs-2140	229	11	and	and	CCONJ
iajs-2140	229	12	.	.	PUNCT
iajs-2140	230	1	if	if	SCONJ
iajs-2140	230	2	is	be	AUX
iajs-2140	230	3	an	an	DET
iajs-2140	230	4	outer	outer	ADJ
iajs-2140	230	5	measure	measure	NOUN
iajs-2140	230	6	on	on	ADP
iajs-2140	230	7	,	,	PUNCT
iajs-2140	230	8	then	then	ADV
iajs-2140	230	9	is	be	AUX
iajs-2140	230	10	an	an	DET
iajs-2140	230	11	outer	outer	ADJ
iajs-2140	230	12	measure	measure	NOUN
iajs-2140	230	13	on	on	ADP
iajs-2140	230	14	(	(	PUNCT
iajs-2140	230	15	8)	8)	NUM
iajs-2140	230	16	let	let	AUX
iajs-2140	230	17	be	be	AUX
iajs-2140	230	18	a	a	PRON
iajs-2140	230	19	–	–	PUNCT
iajs-2140	230	20	of	of	ADP
iajs-2140	230	21	and	and	CCONJ
iajs-2140	230	22	.	.	PUNCT
iajs-2140	231	1	if	if	SCONJ
iajs-2140	231	2	is	be	AUX
iajs-2140	231	3	a	a	DET
iajs-2140	231	4	null	null	NOUN
iajs-2140	231	5	-	-	PUNCT
iajs-2140	231	6	additive	additive	NOUN
iajs-2140	231	7	on	on	ADP
iajs-2140	231	8	,	,	PUNCT
iajs-2140	231	9	then	then	ADV
iajs-2140	231	10	is	be	AUX
iajs-2140	231	11	a	a	DET
iajs-2140	231	12	null	null	NOUN
iajs-2140	231	13	-	-	PUNCT
iajs-2140	231	14	additive	additive	NOUN
iajs-2140	231	15	on	on	ADP
iajs-2140	231	16	(	(	PUNCT
iajs-2140	231	17	9	9	X
iajs-2140	231	18	)	)	PUNCT
iajs-2140	231	19	let	let	AUX
iajs-2140	231	20	be	be	AUX
iajs-2140	231	21	a	a	DET
iajs-2140	231	22	measure	measure	NOUN
iajs-2140	231	23	on	on	ADP
iajs-2140	231	24	–	–	PUNCT
iajs-2140	231	25	of	of	ADP
iajs-2140	231	26	a	a	DET
iajs-2140	231	27	set	set	NOUN
iajs-2140	231	28	and	and	CCONJ
iajs-2140	231	29	such	such	ADJ
iajs-2140	231	30	that	that	PRON
iajs-2140	231	31	.	.	PUNCT
iajs-2140	232	1	then	then	ADV
iajs-2140	232	2	is	be	AUX
iajs-2140	232	3	a	a	DET
iajs-2140	232	4	measure	measure	NOUN
iajs-2140	232	5	on	on	ADP
iajs-2140	232	6	a	a	PRON
iajs-2140	232	7	–	–	PUNCT
iajs-2140	232	8	of	of	ADP
iajs-2140	232	9	a	a	DET
iajs-2140	232	10	set	set	NOUN
iajs-2140	232	11	.	.	PUNCT
iajs-2140	233	1	(	(	PUNCT
iajs-2140	233	2	10	10	NUM
iajs-2140	233	3	)	)	PUNCT
iajs-2140	233	4	let	let	AUX
iajs-2140	233	5	be	be	AUX
iajs-2140	233	6	a	a	DET
iajs-2140	233	7	monotone	monotone	ADJ
iajs-2140	233	8	measure	measure	NOUN
iajs-2140	233	9	on	on	ADP
iajs-2140	233	10	–	–	PUNCT
iajs-2140	233	11	of	of	ADP
iajs-2140	233	12	a	a	DET
iajs-2140	233	13	set	set	NOUN
iajs-2140	233	14	and	and	CCONJ
iajs-2140	233	15	such	such	ADJ
iajs-2140	233	16	that	that	PRON
iajs-2140	233	17	.	.	PUNCT
iajs-2140	234	1	then	then	ADV
iajs-2140	234	2	is	be	AUX
iajs-2140	234	3	a	a	DET
iajs-2140	234	4	monotone	monotone	ADJ
iajs-2140	234	5	measure	measure	NOUN
iajs-2140	234	6	on	on	ADP
iajs-2140	234	7	a	a	PRON
iajs-2140	234	8	–	–	PUNCT
iajs-2140	234	9	of	of	ADP
iajs-2140	234	10	a	a	DET
iajs-2140	234	11	set	set	NOUN
iajs-2140	234	12	.	.	PUNCT
iajs-2140	235	1	references	reference	NOUN
iajs-2140	235	2	1	1	NUM
iajs-2140	235	3	.	.	PUNCT
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iajs-2140	235	5	,	,	PUNCT
iajs-2140	235	6	b.a	b.a	PROPN
iajs-2140	235	7	.	.	PROPN
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iajs-2140	235	9	analysis	analysis	NOUN
iajs-2140	235	10	and	and	CCONJ
iajs-2140	235	11	probability	probability	NOUN
iajs-2140	235	12	,	,	PUNCT
iajs-2140	235	13	academic	academic	ADJ
iajs-2140	235	14	press	press	NOUN
iajs-2140	235	15	,	,	PUNCT
iajs-2140	235	16	inc	inc	PROPN
iajs-2140	235	17	,	,	PUNCT
iajs-2140	235	18	new	new	ADJ
iajs-2140	235	19	york.1972	york.1972	PROPN
iajs-2140	235	20	,	,	PUNCT
iajs-2140	235	21	4	4	NUM
iajs-2140	235	22	-	-	SYM
iajs-2140	235	23	16	16	NUM
iajs-2140	235	24	.	.	PUNCT
iajs-2140	236	1	2	2	X
iajs-2140	236	2	.	.	X
iajs-2140	236	3	dietmar	dietmar	PROPN
iajs-2140	236	4	,	,	PUNCT
iajs-2140	236	5	a.s	a.s	PROPN
iajs-2140	236	6	.	.	PROPN
iajs-2140	236	7	measure	measure	NOUN
iajs-2140	236	8	and	and	CCONJ
iajs-2140	236	9	integration	integration	NOUN
iajs-2140	236	10	,	,	PUNCT
iajs-2140	236	11	eth	eth	PROPN
iajs-2140	236	12	zürich	zürich	PROPN
iajs-2140	237	1	[	[	X
iajs-2140	237	2	internet].2016.available	internet].2016.available	PROPN
iajs-2140	237	3	from	from	ADP
iajs-2140	237	4	:	:	PUNCT
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iajs-2140	237	6	.	.	PUNCT
iajs-2140	238	1	3	3	X
iajs-2140	238	2	.	.	X
iajs-2140	239	1	zhenyuan	zhenyuan	PROPN
iajs-2140	239	2	,	,	PUNCT
iajs-2140	239	3	w.	w.	PROPN
iajs-2140	239	4	;	;	PUNCT
iajs-2140	239	5	george	george	PROPN
iajs-2140	239	6	,	,	PUNCT
iajs-2140	239	7	j.k	j.k	PROPN
iajs-2140	239	8	.	.	PROPN
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iajs-2140	239	11	theory	theory	NOUN
iajs-2140	239	12	,	,	PUNCT
iajs-2140	239	13	springer	springer	NOUN
iajs-2140	239	14	science	science	NOUN
iajs-2140	239	15	and	and	CCONJ
iajs-2140	239	16	business	business	NOUN
iajs-2140	239	17	media	medium	NOUN
iajs-2140	239	18	,	,	PUNCT
iajs-2140	239	19	llc	llc	PROPN
iajs-2140	239	20	.	.	PROPN
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iajs-2140	239	24	-	-	SYM
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iajs-2140	240	1	4	4	NUM
iajs-2140	240	2	.	.	X
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iajs-2140	241	2	,	,	PUNCT
iajs-2140	241	3	li	li	PROPN
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iajs-2140	241	5	;	;	PUNCT
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iajs-2140	241	8	m.	m.	NOUN
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iajs-2140	241	11	,	,	PUNCT
iajs-2140	241	12	p.	p.	NOUN
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iajs-2140	241	17	-	-	PUNCT
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iajs-2140	241	19	monotone	monotone	NOUN
iajs-2140	241	20	measures	measure	NOUN
iajs-2140	241	21	and	and	CCONJ
iajs-2140	241	22	integrals	integral	NOUN
iajs-2140	241	23	.	.	PUNCT
iajs-2140	242	1	information	information	NOUN
iajs-2140	242	2	sciences	sciences	PROPN
iajs-2140	242	3	.	.	PUNCT
iajs-2140	243	1	elsevier	elsevier	PROPN
iajs-2140	243	2	inc	inc	PROPN
iajs-2140	243	3	.	.	PROPN
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iajs-2140	243	5	,	,	PUNCT
iajs-2140	243	6	257	257	NUM
iajs-2140	243	7	,	,	PUNCT
iajs-2140	243	8	183–192	183–192	NUM
iajs-2140	243	9	,	,	PUNCT
iajs-2140	243	10	doi	doi	NOUN
iajs-2140	243	11	:	:	PUNCT
iajs-2140	243	12	10.1016	10.1016	NUM
iajs-2140	243	13	/	/	SYM
iajs-2140	243	14	j.ins.2013.09.013	j.ins.2013.09.013	NOUN
iajs-2140	243	15	.	.	PUNCT
iajs-2140	244	1	5	5	X
iajs-2140	244	2	.	.	X
iajs-2140	244	3	juha	juha	PROPN
iajs-2140	244	4	,	,	PUNCT
iajs-2140	244	5	k.	k.	PROPN
iajs-2140	244	6	measure	measure	NOUN
iajs-2140	244	7	and	and	CCONJ
iajs-2140	244	8	integrals	integral	NOUN
iajs-2140	244	9	.	.	PUNCT
iajs-2140	245	1	aalto	aalto	PROPN
iajs-2140	245	2	math	math	PROPN
iajs-2140	246	1	[	[	X
iajs-2140	246	2	internet].2016.available	internet].2016.available	ADJ
iajs-2140	246	3	form	form	NOUN
iajs-2140	246	4	:	:	PUNCT
iajs-2140	246	5	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	PRON
iajs-2140	246	6	.	.	PUNCT
iajs-2140	247	1	6	6	X
iajs-2140	247	2	.	.	X
iajs-2140	247	3	peipei	peipei	PROPN
iajs-2140	247	4	,	,	PUNCT
iajs-2140	247	5	w.	w.	PROPN
iajs-2140	247	6	;	;	PUNCT
iajs-2140	247	7	minhao	minhao	PROPN
iajs-2140	247	8	,	,	PUNCT
iajs-2140	247	9	yu	yu	PROPN
iajs-2140	247	10	.	.	PROPN
iajs-2140	247	11	;	;	PUNCT
iajs-2140	248	1	jun	jun	PROPN
iajs-2140	248	2	,	,	PUNCT
iajs-2140	248	3	li	li	PROPN
iajs-2140	248	4	.	.	PUNCT
iajs-2140	249	1	monotone	monotone	ADJ
iajs-2140	249	2	measures	measure	NOUN
iajs-2140	249	3	defined	define	VERB
iajs-2140	249	4	by	by	ADP
iajs-2140	249	5	pan	pan	ADJ
iajs-2140	249	6	-	-	ADJ
iajs-2140	249	7	integral	integral	ADJ
iajs-2140	249	8	.	.	PUNCT
iajs-2140	250	1	advances	advance	NOUN
iajs-2140	250	2	in	in	ADP
iajs-2140	250	3	pure	pure	ADJ
iajs-2140	250	4	mathematics	mathematic	NOUN
iajs-2140	250	5	.	.	PUNCT
iajs-2140	251	1	2018	2018	NUM
iajs-2140	251	2	,	,	PUNCT
iajs-2140	251	3	8	8	NUM
iajs-2140	251	4	,	,	PUNCT
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iajs-2140	251	6	,	,	PUNCT
iajs-2140	251	7	doi:10.4236	doi:10.4236	PROPN
iajs-2140	251	8	/	/	SYM
iajs-2140	251	9	apm.2018.86031	apm.2018.86031	PROPN
iajs-2140	251	10	.	.	PUNCT
iajs-2140	252	1	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	PRON
iajs-2140	252	2	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	https://math.aalto.fi/~jkkinnun/files/measure_and_integral.pdf	PRON