id	sid	tid	token	lemma	pos
ap-1865	1	1	acta	acta	PROPN
ap-1865	1	2	polytechnica	polytechnica	PROPN
ap-1865	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1865	1	4	/	/	SYM
ap-1865	1	5	ap.2013.53.0457	ap.2013.53.0457	PROPN
ap-1865	1	6	acta	acta	PROPN
ap-1865	1	7	polytechnica	polytechnica	PROPN
ap-1865	1	8	53(5):457–461	53(5):457–461	PROPN
ap-1865	1	9	,	,	PUNCT
ap-1865	1	10	2013	2013	NUM
ap-1865	1	11	©	©	PROPN
ap-1865	1	12	czech	czech	PROPN
ap-1865	1	13	technical	technical	PROPN
ap-1865	1	14	university	university	PROPN
ap-1865	1	15	in	in	ADP
ap-1865	1	16	prague	prague	PROPN
ap-1865	1	17	,	,	PUNCT
ap-1865	1	18	2013	2013	NUM
ap-1865	1	19	available	available	ADJ
ap-1865	1	20	online	online	ADV
ap-1865	1	21	at	at	ADP
ap-1865	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1865	1	23	maximal	maximal	ADJ
ap-1865	1	24	subsets	subset	NOUN
ap-1865	1	25	of	of	ADP
ap-1865	1	26	pairwise	pairwise	NOUN
ap-1865	1	27	summable	summable	ADJ
ap-1865	1	28	elements	element	NOUN
ap-1865	1	29	in	in	ADP
ap-1865	1	30	generalized	generalized	ADJ
ap-1865	1	31	effect	effect	NOUN
ap-1865	1	32	algebras	algebras	PROPN
ap-1865	1	33	zdenka	zdenka	PROPN
ap-1865	1	34	riečanováa,∗	riečanováa,∗	PROPN
ap-1865	1	35	,	,	PUNCT
ap-1865	1	36	jiří	jiří	NOUN
ap-1865	1	37	jandab	jandab	PROPN
ap-1865	1	38	a	a	DET
ap-1865	1	39	department	department	NOUN
ap-1865	1	40	of	of	ADP
ap-1865	1	41	mathematics	mathematic	NOUN
ap-1865	1	42	,	,	PUNCT
ap-1865	1	43	faculty	faculty	NOUN
ap-1865	1	44	of	of	ADP
ap-1865	1	45	electrical	electrical	ADJ
ap-1865	1	46	engineering	engineering	NOUN
ap-1865	1	47	and	and	CCONJ
ap-1865	1	48	information	information	NOUN
ap-1865	1	49	technology	technology	NOUN
ap-1865	1	50	,	,	PUNCT
ap-1865	1	51	slovak	slovak	ADJ
ap-1865	1	52	university	university	NOUN
ap-1865	1	53	of	of	ADP
ap-1865	1	54	technology	technology	NOUN
ap-1865	1	55	,	,	PUNCT
ap-1865	1	56	ilkovičova	ilkovičova	VERB
ap-1865	1	57	3	3	NUM
ap-1865	1	58	,	,	PUNCT
ap-1865	1	59	sk-812	sk-812	PROPN
ap-1865	1	60	19	19	NUM
ap-1865	1	61	bratislava	bratislava	NOUN
ap-1865	1	62	,	,	PUNCT
ap-1865	1	63	slovak	slovak	ADJ
ap-1865	1	64	republic	republic	NOUN
ap-1865	1	65	.	.	PUNCT
ap-1865	2	1	e	e	X
ap-1865	2	2	-	-	NOUN
ap-1865	2	3	mail	mail	NOUN
ap-1865	2	4	:	:	PUNCT
ap-1865	2	5	zdenka.riecanova@stuba.sk	zdenka.riecanova@stuba.sk	PROPN
ap-1865	2	6	b	b	PROPN
ap-1865	2	7	department	department	NOUN
ap-1865	2	8	of	of	ADP
ap-1865	2	9	mathematics	mathematic	NOUN
ap-1865	2	10	and	and	CCONJ
ap-1865	2	11	statistics	statistic	NOUN
ap-1865	2	12	,	,	PUNCT
ap-1865	2	13	faculty	faculty	NOUN
ap-1865	2	14	of	of	ADP
ap-1865	2	15	science	science	NOUN
ap-1865	2	16	,	,	PUNCT
ap-1865	2	17	masaryk	masaryk	PROPN
ap-1865	2	18	university	university	NOUN
ap-1865	2	19	,	,	PUNCT
ap-1865	2	20	kotlářská	kotlářská	NOUN
ap-1865	2	21	2	2	NUM
ap-1865	2	22	,	,	PUNCT
ap-1865	2	23	cz-611	cz-611	VERB
ap-1865	2	24	37	37	NUM
ap-1865	2	25	brno	brno	NOUN
ap-1865	2	26	,	,	PUNCT
ap-1865	2	27	czech	czech	PROPN
ap-1865	2	28	republic	republic	NOUN
ap-1865	2	29	.	.	PUNCT
ap-1865	3	1	e	e	X
ap-1865	3	2	-	-	NOUN
ap-1865	3	3	mail	mail	NOUN
ap-1865	3	4	:	:	PUNCT
ap-1865	3	5	98599@mail.muni.cz	98599@mail.muni.cz	NOUN
ap-1865	3	6	∗	∗	NOUN
ap-1865	3	7	corresponding	correspond	VERB
ap-1865	3	8	author	author	NOUN
ap-1865	3	9	:	:	PUNCT
ap-1865	3	10	zdenka.riecanova@stuba.sk	zdenka.riecanova@stuba.sk	PROPN
ap-1865	3	11	abstract	abstract	NOUN
ap-1865	3	12	.	.	PUNCT
ap-1865	4	1	we	we	PRON
ap-1865	4	2	show	show	VERB
ap-1865	4	3	that	that	SCONJ
ap-1865	4	4	in	in	ADP
ap-1865	4	5	any	any	DET
ap-1865	4	6	generalized	generalized	ADJ
ap-1865	4	7	effect	effect	NOUN
ap-1865	4	8	algebra	algebra	NOUN
ap-1865	4	9	(	(	PUNCT
ap-1865	4	10	g;⊕	g;⊕	NOUN
ap-1865	4	11	,	,	PUNCT
ap-1865	4	12	0	0	NUM
ap-1865	4	13	)	)	PUNCT
ap-1865	4	14	a	a	DET
ap-1865	4	15	maximal	maximal	ADJ
ap-1865	4	16	pairwise	pairwise	NOUN
ap-1865	4	17	summable	summable	ADJ
ap-1865	4	18	subset	subset	NOUN
ap-1865	4	19	is	be	AUX
ap-1865	4	20	a	a	DET
ap-1865	4	21	sub	sub	ADJ
ap-1865	4	22	-	-	ADJ
ap-1865	4	23	generalized	generalized	ADJ
ap-1865	4	24	effect	effect	NOUN
ap-1865	4	25	algebra	algebra	NOUN
ap-1865	4	26	of	of	ADP
ap-1865	4	27	(	(	PUNCT
ap-1865	4	28	g;⊕	g;⊕	NOUN
ap-1865	4	29	,	,	PUNCT
ap-1865	4	30	0	0	NUM
ap-1865	4	31	)	)	PUNCT
ap-1865	4	32	,	,	PUNCT
ap-1865	4	33	called	call	VERB
ap-1865	4	34	a	a	DET
ap-1865	4	35	summability	summability	NOUN
ap-1865	4	36	block	block	NOUN
ap-1865	4	37	.	.	PUNCT
ap-1865	5	1	if	if	SCONJ
ap-1865	5	2	g	g	PROPN
ap-1865	5	3	is	be	AUX
ap-1865	5	4	lattice	lattice	NOUN
ap-1865	5	5	ordered	order	VERB
ap-1865	5	6	,	,	PUNCT
ap-1865	5	7	then	then	ADV
ap-1865	5	8	every	every	DET
ap-1865	5	9	summability	summability	NOUN
ap-1865	5	10	block	block	NOUN
ap-1865	5	11	in	in	ADP
ap-1865	5	12	g	g	PROPN
ap-1865	5	13	is	be	AUX
ap-1865	5	14	a	a	DET
ap-1865	5	15	generalized	generalized	ADJ
ap-1865	5	16	mv	mv	ADJ
ap-1865	5	17	-	-	PUNCT
ap-1865	5	18	effect	effect	NOUN
ap-1865	5	19	algebra	algebra	NOUN
ap-1865	5	20	.	.	PUNCT
ap-1865	6	1	moreover	moreover	ADV
ap-1865	6	2	,	,	PUNCT
ap-1865	6	3	if	if	SCONJ
ap-1865	6	4	every	every	DET
ap-1865	6	5	element	element	NOUN
ap-1865	6	6	of	of	ADP
ap-1865	6	7	g	g	PROPN
ap-1865	6	8	has	have	VERB
ap-1865	6	9	an	an	DET
ap-1865	6	10	infinite	infinite	ADJ
ap-1865	6	11	isotropic	isotropic	NOUN
ap-1865	6	12	index	index	NOUN
ap-1865	6	13	,	,	PUNCT
ap-1865	6	14	then	then	ADV
ap-1865	6	15	g	g	PROPN
ap-1865	6	16	is	be	AUX
ap-1865	6	17	covered	cover	VERB
ap-1865	6	18	by	by	ADP
ap-1865	6	19	its	its	PRON
ap-1865	6	20	summability	summability	NOUN
ap-1865	6	21	blocks	block	NOUN
ap-1865	6	22	,	,	PUNCT
ap-1865	6	23	which	which	PRON
ap-1865	6	24	are	be	AUX
ap-1865	6	25	generalized	generalized	ADJ
ap-1865	6	26	mv	mv	ADJ
ap-1865	6	27	-	-	PUNCT
ap-1865	6	28	effect	effect	NOUN
ap-1865	6	29	algebras	algebra	NOUN
ap-1865	6	30	in	in	ADP
ap-1865	6	31	the	the	DET
ap-1865	6	32	case	case	NOUN
ap-1865	6	33	that	that	SCONJ
ap-1865	6	34	g	g	PROPN
ap-1865	6	35	is	be	AUX
ap-1865	6	36	lattice	lattice	NOUN
ap-1865	6	37	ordered	order	VERB
ap-1865	6	38	.	.	PUNCT
ap-1865	7	1	we	we	PRON
ap-1865	7	2	also	also	ADV
ap-1865	7	3	present	present	VERB
ap-1865	7	4	the	the	DET
ap-1865	7	5	relations	relation	NOUN
ap-1865	7	6	between	between	ADP
ap-1865	7	7	summability	summability	NOUN
ap-1865	7	8	blocks	block	NOUN
ap-1865	7	9	and	and	CCONJ
ap-1865	7	10	compatibility	compatibility	NOUN
ap-1865	7	11	blocks	block	NOUN
ap-1865	7	12	of	of	ADP
ap-1865	7	13	g.	g.	PROPN
ap-1865	7	14	counterexamples	counterexample	NOUN
ap-1865	7	15	,	,	PUNCT
ap-1865	7	16	to	to	PART
ap-1865	7	17	obtain	obtain	VERB
ap-1865	7	18	the	the	DET
ap-1865	7	19	required	require	VERB
ap-1865	7	20	contradictions	contradiction	NOUN
ap-1865	7	21	in	in	ADP
ap-1865	7	22	some	some	DET
ap-1865	7	23	cases	case	NOUN
ap-1865	7	24	,	,	PUNCT
ap-1865	7	25	are	be	AUX
ap-1865	7	26	given	give	VERB
ap-1865	7	27	.	.	PUNCT
ap-1865	8	1	keywords	keyword	NOUN
ap-1865	8	2	:	:	PUNCT
ap-1865	8	3	(	(	PUNCT
ap-1865	8	4	generalized	generalized	ADJ
ap-1865	8	5	)	)	PUNCT
ap-1865	8	6	effect	effect	NOUN
ap-1865	8	7	algebra	algebra	NOUN
ap-1865	8	8	,	,	PUNCT
ap-1865	8	9	mv	mv	ADJ
ap-1865	8	10	-	-	PUNCT
ap-1865	8	11	effect	effect	NOUN
ap-1865	8	12	algebra	algebra	NOUN
ap-1865	8	13	,	,	PUNCT
ap-1865	8	14	summability	summability	NOUN
ap-1865	8	15	block	block	NOUN
ap-1865	8	16	,	,	PUNCT
ap-1865	8	17	compatibility	compatibility	NOUN
ap-1865	8	18	block	block	NOUN
ap-1865	8	19	,	,	PUNCT
ap-1865	8	20	linear	linear	PROPN
ap-1865	8	21	operators	operator	NOUN
ap-1865	8	22	in	in	ADP
ap-1865	8	23	hilbert	hilbert	PROPN
ap-1865	8	24	spaces	space	NOUN
ap-1865	8	25	.	.	PUNCT
ap-1865	9	1	submitted	submit	VERB
ap-1865	9	2	:	:	PUNCT
ap-1865	9	3	7	7	NUM
ap-1865	9	4	march	march	NOUN
ap-1865	9	5	2013	2013	NUM
ap-1865	9	6	.	.	PUNCT
ap-1865	10	1	accepted	accept	VERB
ap-1865	10	2	:	:	PUNCT
ap-1865	10	3	10	10	NUM
ap-1865	10	4	april	april	PROPN
ap-1865	10	5	2013	2013	NUM
ap-1865	10	6	.	.	PUNCT
ap-1865	11	1	1	1	X
ap-1865	11	2	.	.	X
ap-1865	11	3	introduction	introduction	NOUN
ap-1865	11	4	and	and	CCONJ
ap-1865	11	5	some	some	DET
ap-1865	11	6	basic	basic	ADJ
ap-1865	11	7	definitions	definition	NOUN
ap-1865	11	8	in	in	ADP
ap-1865	11	9	a	a	DET
ap-1865	11	10	hilbert	hilbert	NOUN
ap-1865	11	11	space	space	NOUN
ap-1865	11	12	formalization	formalization	NOUN
ap-1865	11	13	of	of	ADP
ap-1865	11	14	quantum	quantum	ADJ
ap-1865	11	15	mechanics	mechanic	NOUN
ap-1865	11	16	,	,	PUNCT
ap-1865	11	17	g.	g.	PROPN
ap-1865	11	18	birkhoff	birkhoff	PROPN
ap-1865	11	19	and	and	CCONJ
ap-1865	11	20	j.	j.	PROPN
ap-1865	11	21	von	von	PROPN
ap-1865	11	22	neumann	neumann	PROPN
ap-1865	11	23	proposed	propose	VERB
ap-1865	11	24	the	the	DET
ap-1865	11	25	concept	concept	NOUN
ap-1865	11	26	of	of	ADP
ap-1865	11	27	quantum	quantum	NOUN
ap-1865	11	28	logics	logic	NOUN
ap-1865	11	29	(	(	PUNCT
ap-1865	11	30	in	in	ADP
ap-1865	11	31	1936	1936	NUM
ap-1865	11	32	the	the	DET
ap-1865	11	33	concept	concept	NOUN
ap-1865	11	34	of	of	ADP
ap-1865	11	35	modular	modular	ADJ
ap-1865	11	36	ortholattices	ortholattice	NOUN
ap-1865	11	37	and	and	CCONJ
ap-1865	11	38	later	later	ADJ
ap-1865	11	39	orthomodular	orthomodular	ADJ
ap-1865	11	40	lattices	lattice	NOUN
ap-1865	11	41	,	,	PUNCT
ap-1865	11	42	discovered	discover	VERB
ap-1865	11	43	by	by	ADP
ap-1865	11	44	husimi	husimi	PROPN
ap-1865	11	45	in	in	ADP
ap-1865	11	46	1937	1937	NUM
ap-1865	11	47	)	)	PUNCT
ap-1865	11	48	.	.	PUNCT
ap-1865	12	1	nevertheless	nevertheless	ADV
ap-1865	12	2	,	,	PUNCT
ap-1865	12	3	in	in	ADP
ap-1865	12	4	the	the	DET
ap-1865	12	5	set	set	NOUN
ap-1865	12	6	p(h	p(h	NOUN
ap-1865	12	7	)	)	PUNCT
ap-1865	12	8	of	of	ADP
ap-1865	12	9	all	all	DET
ap-1865	12	10	projection	projection	NOUN
ap-1865	12	11	operators	operator	NOUN
ap-1865	12	12	in	in	ADP
ap-1865	12	13	a	a	DET
ap-1865	12	14	separable	separable	ADJ
ap-1865	12	15	hilbert	hilbert	NOUN
ap-1865	12	16	space	space	NOUN
ap-1865	12	17	(	(	PUNCT
ap-1865	12	18	used	use	VERB
ap-1865	12	19	as	as	ADP
ap-1865	12	20	a	a	DET
ap-1865	12	21	model	model	NOUN
ap-1865	12	22	for	for	ADP
ap-1865	12	23	orthomodular	orthomodular	ADJ
ap-1865	12	24	lattices	lattice	NOUN
ap-1865	12	25	)	)	PUNCT
ap-1865	12	26	every	every	DET
ap-1865	12	27	event	event	NOUN
ap-1865	12	28	satisfies	satisfy	VERB
ap-1865	12	29	the	the	DET
ap-1865	12	30	non	non	ADJ
ap-1865	12	31	-	-	ADJ
ap-1865	12	32	contradiction	contradiction	ADJ
ap-1865	12	33	principle	principle	NOUN
ap-1865	12	34	.	.	PUNCT
ap-1865	13	1	thus	thus	ADV
ap-1865	13	2	the	the	DET
ap-1865	13	3	set	set	NOUN
ap-1865	13	4	p(h	p(h	NOUN
ap-1865	13	5	)	)	PUNCT
ap-1865	13	6	is	be	AUX
ap-1865	13	7	not	not	PART
ap-1865	13	8	the	the	DET
ap-1865	13	9	set	set	NOUN
ap-1865	13	10	of	of	ADP
ap-1865	13	11	all	all	DET
ap-1865	13	12	possible	possible	ADJ
ap-1865	13	13	events	event	NOUN
ap-1865	13	14	in	in	ADP
ap-1865	13	15	quantum	quantum	ADJ
ap-1865	13	16	theory	theory	NOUN
ap-1865	13	17	.	.	PUNCT
ap-1865	14	1	in	in	ADP
ap-1865	14	2	1994	1994	NUM
ap-1865	14	3	,	,	PUNCT
ap-1865	14	4	d.	d.	PROPN
ap-1865	14	5	foulis	foulis	PROPN
ap-1865	14	6	introduced	introduce	VERB
ap-1865	14	7	algebraic	algebraic	ADJ
ap-1865	14	8	structures	structure	NOUN
ap-1865	14	9	called	call	VERB
ap-1865	14	10	effect	effect	NOUN
ap-1865	14	11	algebras	algebra	NOUN
ap-1865	14	12	.	.	PUNCT
ap-1865	15	1	equivalent	equivalent	ADJ
ap-1865	15	2	structures	structure	NOUN
ap-1865	15	3	,	,	PUNCT
ap-1865	15	4	in	in	ADP
ap-1865	15	5	some	some	DET
ap-1865	15	6	sense	sense	NOUN
ap-1865	15	7	,	,	PUNCT
ap-1865	15	8	are	be	AUX
ap-1865	15	9	d	d	NOUN
ap-1865	15	10	-	-	PUNCT
ap-1865	15	11	posets	poset	NOUN
ap-1865	15	12	introduced	introduce	VERB
ap-1865	15	13	by	by	ADP
ap-1865	15	14	kôpka	kôpka	NOUN
ap-1865	15	15	and	and	CCONJ
ap-1865	15	16	chovanec	chovanec	NOUN
ap-1865	15	17	in	in	ADP
ap-1865	15	18	1994	1994	NUM
ap-1865	15	19	.	.	PUNCT
ap-1865	16	1	the	the	DET
ap-1865	16	2	prototype	prototype	NOUN
ap-1865	16	3	for	for	ADP
ap-1865	16	4	the	the	DET
ap-1865	16	5	axiomatic	axiomatic	ADJ
ap-1865	16	6	system	system	NOUN
ap-1865	16	7	of	of	ADP
ap-1865	16	8	effect	effect	NOUN
ap-1865	16	9	algebras	algebra	NOUN
ap-1865	16	10	was	be	AUX
ap-1865	16	11	the	the	DET
ap-1865	16	12	set	set	NOUN
ap-1865	16	13	e(h	e(h	PROPN
ap-1865	16	14	)	)	PUNCT
ap-1865	16	15	of	of	ADP
ap-1865	16	16	all	all	DET
ap-1865	16	17	positive	positive	ADJ
ap-1865	16	18	linear	linear	NOUN
ap-1865	16	19	operators	operator	NOUN
ap-1865	16	20	dominated	dominate	VERB
ap-1865	16	21	by	by	ADP
ap-1865	16	22	the	the	DET
ap-1865	16	23	identity	identity	NOUN
ap-1865	16	24	operator	operator	NOUN
ap-1865	16	25	in	in	ADP
ap-1865	16	26	a	a	DET
ap-1865	16	27	hilbert	hilbert	NOUN
ap-1865	16	28	space	space	NOUN
ap-1865	16	29	.	.	PUNCT
ap-1865	17	1	events	event	NOUN
ap-1865	17	2	in	in	ADP
ap-1865	17	3	e(h	e(h	PROPN
ap-1865	17	4	)	)	PUNCT
ap-1865	17	5	,	,	PUNCT
ap-1865	17	6	called	call	VERB
ap-1865	17	7	effects	effect	NOUN
ap-1865	17	8	,	,	PUNCT
ap-1865	17	9	do	do	AUX
ap-1865	17	10	not	not	PART
ap-1865	17	11	satisfy	satisfy	VERB
ap-1865	17	12	the	the	DET
ap-1865	17	13	non	non	ADJ
ap-1865	17	14	-	-	ADJ
ap-1865	17	15	contradiction	contradiction	ADJ
ap-1865	17	16	law	law	NOUN
ap-1865	17	17	(	(	PUNCT
ap-1865	17	18	meaning	mean	VERB
ap-1865	17	19	that	that	SCONJ
ap-1865	17	20	there	there	PRON
ap-1865	17	21	exist	exist	VERB
ap-1865	17	22	unsharp	unsharp	ADJ
ap-1865	17	23	events	event	NOUN
ap-1865	17	24	x	x	PUNCT
ap-1865	17	25	and	and	CCONJ
ap-1865	17	26	non	non	ADJ
ap-1865	17	27	x	x	NOUN
ap-1865	17	28	which	which	PRON
ap-1865	17	29	are	be	AUX
ap-1865	17	30	not	not	PART
ap-1865	17	31	disjoint	disjoint	ADJ
ap-1865	17	32	)	)	PUNCT
ap-1865	17	33	.	.	PUNCT
ap-1865	18	1	they	they	PRON
ap-1865	18	2	represent	represent	VERB
ap-1865	18	3	unsharp	unsharp	ADJ
ap-1865	18	4	measurements	measurement	NOUN
ap-1865	18	5	or	or	CCONJ
ap-1865	18	6	observations	observation	NOUN
ap-1865	18	7	on	on	ADP
ap-1865	18	8	a	a	DET
ap-1865	18	9	quantum	quantum	ADJ
ap-1865	18	10	mechanical	mechanical	ADJ
ap-1865	18	11	system	system	NOUN
ap-1865	18	12	in	in	ADP
ap-1865	18	13	a	a	DET
ap-1865	18	14	hilbert	hilbert	NOUN
ap-1865	18	15	space	space	NOUN
ap-1865	18	16	h.	h.	PROPN
ap-1865	18	17	moreover	moreover	ADV
ap-1865	18	18	,	,	PUNCT
ap-1865	18	19	a	a	DET
ap-1865	18	20	special	special	ADJ
ap-1865	18	21	kind	kind	NOUN
ap-1865	18	22	of	of	ADP
ap-1865	18	23	effect	effect	NOUN
ap-1865	18	24	algebras	algebra	NOUN
ap-1865	18	25	are	be	AUX
ap-1865	18	26	mv	mv	NOUN
ap-1865	18	27	-	-	NOUN
ap-1865	18	28	algebras	algebra	NOUN
ap-1865	18	29	,	,	PUNCT
ap-1865	18	30	which	which	PRON
ap-1865	18	31	are	be	AUX
ap-1865	18	32	algebraic	algebraic	ADJ
ap-1865	18	33	bases	basis	NOUN
ap-1865	18	34	for	for	ADP
ap-1865	18	35	multivalued	multivalued	ADJ
ap-1865	18	36	logic	logic	NOUN
ap-1865	18	37	,	,	PUNCT
ap-1865	18	38	as	as	ADP
ap-1865	18	39	a	a	DET
ap-1865	18	40	generalization	generalization	NOUN
ap-1865	18	41	of	of	ADP
ap-1865	18	42	boolean	boolean	ADJ
ap-1865	18	43	algebras	algebra	NOUN
ap-1865	18	44	.	.	PUNCT
ap-1865	19	1	effect	effect	PROPN
ap-1865	19	2	algebras	algebra	NOUN
ap-1865	19	3	are	be	AUX
ap-1865	19	4	very	very	ADV
ap-1865	19	5	suitable	suitable	ADJ
ap-1865	19	6	algebraic	algebraic	ADJ
ap-1865	19	7	structures	structure	NOUN
ap-1865	19	8	for	for	ADP
ap-1865	19	9	being	be	AUX
ap-1865	19	10	carriers	carrier	NOUN
ap-1865	19	11	of	of	ADP
ap-1865	19	12	probability	probability	NOUN
ap-1865	19	13	measures	measure	NOUN
ap-1865	19	14	when	when	SCONJ
ap-1865	19	15	events	event	NOUN
ap-1865	19	16	may	may	AUX
ap-1865	19	17	be	be	AUX
ap-1865	19	18	unsharp	unsharp	ADJ
ap-1865	19	19	or	or	CCONJ
ap-1865	19	20	pairwise	pairwise	NOUN
ap-1865	19	21	non	non	ADJ
ap-1865	19	22	-	-	ADJ
ap-1865	19	23	compatible	compatible	ADJ
ap-1865	19	24	.	.	PUNCT
ap-1865	20	1	the	the	DET
ap-1865	20	2	mutually	mutually	ADV
ap-1865	20	3	equivalent	equivalent	ADJ
ap-1865	20	4	generalizations	generalization	NOUN
ap-1865	20	5	(	(	PUNCT
ap-1865	20	6	unbounded	unbounded	ADJ
ap-1865	20	7	version	version	NOUN
ap-1865	20	8	)	)	PUNCT
ap-1865	20	9	of	of	ADP
ap-1865	20	10	effect	effect	NOUN
ap-1865	20	11	algebras	algebra	NOUN
ap-1865	20	12	were	be	AUX
ap-1865	20	13	introduced	introduce	VERB
ap-1865	20	14	in	in	ADP
ap-1865	20	15	1994	1994	NUM
ap-1865	20	16	by	by	ADP
ap-1865	20	17	several	several	ADJ
ap-1865	20	18	authors	author	NOUN
ap-1865	20	19	—	—	PUNCT
ap-1865	20	20	d.	d.	PROPN
ap-1865	20	21	foulis	foulis	PROPN
ap-1865	20	22	and	and	CCONJ
ap-1865	20	23	m.k	m.k	PROPN
ap-1865	20	24	.	.	PROPN
ap-1865	20	25	bennett	bennett	PROPN
ap-1865	20	26	,	,	PUNCT
ap-1865	20	27	g.	g.	PROPN
ap-1865	20	28	kalmbach	kalmbach	PROPN
ap-1865	20	29	and	and	CCONJ
ap-1865	20	30	z.	z.	PROPN
ap-1865	20	31	riečanová	riečanová	PROPN
ap-1865	20	32	,	,	PUNCT
ap-1865	20	33	j.	j.	PROPN
ap-1865	20	34	hedlíková	hedlíková	PROPN
ap-1865	20	35	and	and	CCONJ
ap-1865	20	36	s.	s.	PROPN
ap-1865	20	37	pulmannová	pulmannová	PROPN
ap-1865	20	38	,	,	PUNCT
ap-1865	20	39	and	and	CCONJ
ap-1865	20	40	f.	f.	PROPN
ap-1865	20	41	kôpka	kôpka	PROPN
ap-1865	20	42	and	and	CCONJ
ap-1865	20	43	f.	f.	PROPN
ap-1865	20	44	chovanec	chovanec	PROPN
ap-1865	20	45	.	.	PUNCT
ap-1865	21	1	on	on	ADP
ap-1865	21	2	the	the	DET
ap-1865	21	3	other	other	ADJ
ap-1865	21	4	hand	hand	NOUN
ap-1865	21	5	,	,	PUNCT
ap-1865	21	6	all	all	DET
ap-1865	21	7	intervals	interval	NOUN
ap-1865	21	8	in	in	ADP
ap-1865	21	9	these	these	DET
ap-1865	21	10	generalized	generalized	ADJ
ap-1865	21	11	effect	effect	NOUN
ap-1865	21	12	algebras	algebra	NOUN
ap-1865	21	13	are	be	AUX
ap-1865	21	14	effect	effect	NOUN
ap-1865	21	15	algebras	algebra	NOUN
ap-1865	21	16	.	.	PUNCT
ap-1865	22	1	recently	recently	ADV
ap-1865	22	2	,	,	PUNCT
ap-1865	22	3	operator	operator	NOUN
ap-1865	22	4	representations	representation	NOUN
ap-1865	22	5	of	of	ADP
ap-1865	22	6	abstract	abstract	ADJ
ap-1865	22	7	effect	effect	NOUN
ap-1865	22	8	algebras	algebra	NOUN
ap-1865	22	9	(	(	PUNCT
ap-1865	22	10	i.e.	i.e.	X
ap-1865	22	11	their	their	PRON
ap-1865	22	12	isomorphism	isomorphism	NOUN
ap-1865	22	13	with	with	ADP
ap-1865	22	14	sub	sub	ADJ
ap-1865	22	15	-	-	ADJ
ap-1865	22	16	effect	effect	ADJ
ap-1865	22	17	algebras	algebra	NOUN
ap-1865	22	18	of	of	ADP
ap-1865	22	19	the	the	DET
ap-1865	22	20	standard	standard	ADJ
ap-1865	22	21	effect	effect	NOUN
ap-1865	22	22	algebra	algebra	VERB
ap-1865	22	23	e(h	e(h	PROPN
ap-1865	22	24	)	)	PUNCT
ap-1865	22	25	mentioned	mention	VERB
ap-1865	22	26	above	above	ADV
ap-1865	22	27	)	)	PUNCT
ap-1865	22	28	have	have	AUX
ap-1865	22	29	been	be	AUX
ap-1865	22	30	studied	study	VERB
ap-1865	22	31	.	.	PUNCT
ap-1865	23	1	it	it	PRON
ap-1865	23	2	was	be	AUX
ap-1865	23	3	proved	prove	VERB
ap-1865	23	4	in	in	ADP
ap-1865	23	5	[	[	X
ap-1865	23	6	14	14	NUM
ap-1865	23	7	]	]	PUNCT
ap-1865	23	8	that	that	SCONJ
ap-1865	23	9	the	the	DET
ap-1865	23	10	set	set	NOUN
ap-1865	23	11	vd(h	vd(h	NUM
ap-1865	23	12	)	)	PUNCT
ap-1865	23	13	of	of	ADP
ap-1865	23	14	all	all	DET
ap-1865	23	15	positive	positive	ADJ
ap-1865	23	16	linear	linear	ADJ
ap-1865	23	17	operators	operator	NOUN
ap-1865	23	18	in	in	ADP
ap-1865	23	19	an	an	DET
ap-1865	23	20	infinite	infinite	ADJ
ap-1865	23	21	-	-	PUNCT
ap-1865	23	22	dimensional	dimensional	ADJ
ap-1865	23	23	complex	complex	ADJ
ap-1865	23	24	hilbert	hilbert	NOUN
ap-1865	23	25	space	space	NOUN
ap-1865	23	26	h	h	NOUN
ap-1865	23	27	with	with	ADP
ap-1865	23	28	partially	partially	ADV
ap-1865	23	29	defined	define	VERB
ap-1865	23	30	sum	sum	NOUN
ap-1865	23	31	of	of	ADP
ap-1865	23	32	operators	operator	NOUN
ap-1865	23	33	(	(	PUNCT
ap-1865	23	34	which	which	PRON
ap-1865	23	35	coincides	coincide	VERB
ap-1865	23	36	with	with	ADP
ap-1865	23	37	the	the	DET
ap-1865	23	38	usual	usual	ADJ
ap-1865	23	39	sum	sum	NOUN
ap-1865	23	40	)	)	PUNCT
ap-1865	23	41	restricted	restrict	VERB
ap-1865	23	42	to	to	ADP
ap-1865	23	43	the	the	DET
ap-1865	23	44	common	common	ADJ
ap-1865	23	45	domains	domain	NOUN
ap-1865	23	46	of	of	ADP
ap-1865	23	47	operators	operator	NOUN
ap-1865	23	48	forms	form	VERB
ap-1865	23	49	a	a	DET
ap-1865	23	50	generalized	generalized	ADJ
ap-1865	23	51	effect	effect	NOUN
ap-1865	23	52	algebra	algebra	NOUN
ap-1865	23	53	.	.	PUNCT
ap-1865	24	1	this	this	DET
ap-1865	24	2	generalized	generalized	ADJ
ap-1865	24	3	effect	effect	NOUN
ap-1865	24	4	algebra	algebra	NOUN
ap-1865	24	5	vd(h	vd(h	PUNCT
ap-1865	24	6	)	)	PUNCT
ap-1865	24	7	is	be	AUX
ap-1865	24	8	a	a	DET
ap-1865	24	9	union	union	NOUN
ap-1865	24	10	of	of	ADP
ap-1865	24	11	sub	sub	ADJ
ap-1865	24	12	-	-	ADJ
ap-1865	24	13	generalized	generalized	ADJ
ap-1865	24	14	effect	effect	NOUN
ap-1865	24	15	algebras	algebra	NOUN
ap-1865	24	16	of	of	ADP
ap-1865	24	17	maximal	maximal	ADJ
ap-1865	24	18	subsets	subset	NOUN
ap-1865	24	19	of	of	ADP
ap-1865	24	20	pairwise	pairwise	NOUN
ap-1865	24	21	summable	summable	ADJ
ap-1865	24	22	operators	operator	NOUN
ap-1865	24	23	.	.	PUNCT
ap-1865	25	1	moreover	moreover	ADV
ap-1865	25	2	,	,	PUNCT
ap-1865	25	3	all	all	DET
ap-1865	25	4	intervals	interval	NOUN
ap-1865	25	5	are	be	AUX
ap-1865	25	6	effect	effect	NOUN
ap-1865	25	7	algebras	algebra	NOUN
ap-1865	25	8	isomorphic	isomorphic	ADJ
ap-1865	25	9	to	to	ADP
ap-1865	25	10	sub	sub	ADJ
ap-1865	25	11	-	-	ADJ
ap-1865	25	12	effect	effect	ADJ
ap-1865	25	13	algebras	algebra	NOUN
ap-1865	25	14	of	of	ADP
ap-1865	25	15	the	the	DET
ap-1865	25	16	standard	standard	ADJ
ap-1865	25	17	effect	effect	NOUN
ap-1865	25	18	algebra	algebra	VERB
ap-1865	25	19	e(h	e(h	PROPN
ap-1865	25	20	)	)	PUNCT
ap-1865	25	21	for	for	ADP
ap-1865	25	22	some	some	DET
ap-1865	25	23	hilbert	hilbert	NOUN
ap-1865	25	24	space	space	NOUN
ap-1865	25	25	h	h	NOUN
ap-1865	25	26	(	(	PUNCT
ap-1865	25	27	see	see	VERB
ap-1865	25	28	[	[	X
ap-1865	25	29	13	13	NUM
ap-1865	25	30	]	]	NUM
ap-1865	25	31	)	)	PUNCT
ap-1865	25	32	.	.	PUNCT
ap-1865	26	1	we	we	PRON
ap-1865	26	2	are	be	AUX
ap-1865	26	3	going	go	VERB
ap-1865	26	4	to	to	PART
ap-1865	26	5	show	show	VERB
ap-1865	26	6	that	that	SCONJ
ap-1865	26	7	in	in	ADP
ap-1865	26	8	a	a	DET
ap-1865	26	9	generalized	generalized	ADJ
ap-1865	26	10	effect	effect	NOUN
ap-1865	26	11	algebra	algebra	VERB
ap-1865	26	12	g	g	NOUN
ap-1865	26	13	without	without	ADP
ap-1865	26	14	elements	element	NOUN
ap-1865	26	15	with	with	ADP
ap-1865	26	16	finite	finite	ADJ
ap-1865	26	17	isotropic	isotropic	NOUN
ap-1865	26	18	indexes	index	NOUN
ap-1865	26	19	(	(	PUNCT
ap-1865	26	20	which	which	PRON
ap-1865	26	21	corresponds	correspond	VERB
ap-1865	26	22	to	to	ADP
ap-1865	26	23	the	the	DET
ap-1865	26	24	operator	operator	NOUN
ap-1865	26	25	case	case	NOUN
ap-1865	26	26	)	)	PUNCT
ap-1865	26	27	its	its	PRON
ap-1865	26	28	maximal	maximal	ADJ
ap-1865	26	29	subsets	subset	NOUN
ap-1865	26	30	of	of	ADP
ap-1865	26	31	pairwise	pairwise	NOUN
ap-1865	26	32	summable	summable	ADJ
ap-1865	26	33	elements	element	NOUN
ap-1865	26	34	are	be	AUX
ap-1865	26	35	sub	sub	ADJ
ap-1865	26	36	-	-	ADJ
ap-1865	26	37	generalized	generalized	ADJ
ap-1865	26	38	effect	effect	NOUN
ap-1865	26	39	algebras	algebra	NOUN
ap-1865	26	40	.	.	PUNCT
ap-1865	27	1	moreover	moreover	ADV
ap-1865	27	2	,	,	PUNCT
ap-1865	27	3	such	such	ADJ
ap-1865	27	4	g	g	PROPN
ap-1865	27	5	is	be	AUX
ap-1865	27	6	covered	cover	VERB
ap-1865	27	7	by	by	ADP
ap-1865	27	8	those	those	DET
ap-1865	27	9	sub	sub	ADJ
ap-1865	27	10	-	-	ADJ
ap-1865	27	11	generalized	generalized	ADJ
ap-1865	27	12	effect	effect	NOUN
ap-1865	27	13	algebras	algebra	NOUN
ap-1865	27	14	.	.	PUNCT
ap-1865	28	1	definition	definition	NOUN
ap-1865	28	2	1	1	NUM
ap-1865	28	3	(	(	PUNCT
ap-1865	28	4	[	[	X
ap-1865	28	5	3	3	NUM
ap-1865	28	6	]	]	NUM
ap-1865	28	7	)	)	PUNCT
ap-1865	28	8	.	.	PUNCT
ap-1865	29	1	a	a	DET
ap-1865	29	2	partial	partial	ADJ
ap-1865	29	3	algebra	algebra	NOUN
ap-1865	29	4	(	(	PUNCT
ap-1865	29	5	e;⊕	e;⊕	ADJ
ap-1865	29	6	,	,	PUNCT
ap-1865	29	7	0	0	NUM
ap-1865	29	8	,	,	PUNCT
ap-1865	29	9	1	1	NUM
ap-1865	29	10	)	)	PUNCT
ap-1865	29	11	is	be	AUX
ap-1865	29	12	called	call	VERB
ap-1865	29	13	an	an	DET
ap-1865	29	14	effect	effect	NOUN
ap-1865	29	15	algebra	algebra	NOUN
ap-1865	29	16	if	if	SCONJ
ap-1865	29	17	0	0	NUM
ap-1865	29	18	,	,	PUNCT
ap-1865	29	19	1	1	NUM
ap-1865	29	20	∈	∈	NOUN
ap-1865	29	21	e	e	NOUN
ap-1865	29	22	are	be	AUX
ap-1865	29	23	two	two	NUM
ap-1865	29	24	distinguished	distinguished	ADJ
ap-1865	29	25	elements	element	NOUN
ap-1865	29	26	and	and	CCONJ
ap-1865	29	27	⊕	⊕	PROPN
ap-1865	29	28	is	be	AUX
ap-1865	29	29	a	a	DET
ap-1865	29	30	partially	partially	ADV
ap-1865	29	31	defined	define	VERB
ap-1865	29	32	binary	binary	ADJ
ap-1865	29	33	operation	operation	NOUN
ap-1865	29	34	on	on	ADP
ap-1865	29	35	e	e	PROPN
ap-1865	29	36	which	which	PRON
ap-1865	29	37	satisfies	satisfy	VERB
ap-1865	29	38	the	the	DET
ap-1865	29	39	following	follow	VERB
ap-1865	29	40	conditions	condition	NOUN
ap-1865	29	41	for	for	ADP
ap-1865	29	42	any	any	DET
ap-1865	29	43	x	x	NOUN
ap-1865	29	44	,	,	PUNCT
ap-1865	29	45	y	y	PROPN
ap-1865	29	46	,	,	PUNCT
ap-1865	29	47	z	z	NOUN
ap-1865	29	48	∈	∈	PROPN
ap-1865	30	1	e	e	NOUN
ap-1865	30	2	:	:	PUNCT
ap-1865	30	3	(	(	PUNCT
ap-1865	30	4	ei	ei	NOUN
ap-1865	30	5	)	)	PUNCT
ap-1865	30	6	x⊕	x⊕	PROPN
ap-1865	30	7	y	y	PROPN
ap-1865	30	8	=	=	SYM
ap-1865	30	9	y	y	PROPN
ap-1865	30	10	⊕	⊕	PROPN
ap-1865	30	11	x	x	PUNCT
ap-1865	31	1	if	if	SCONJ
ap-1865	31	2	x⊕	x⊕	PROPN
ap-1865	31	3	y	y	PROPN
ap-1865	31	4	is	be	AUX
ap-1865	31	5	defined	define	VERB
ap-1865	31	6	,	,	PUNCT
ap-1865	31	7	(	(	PUNCT
ap-1865	31	8	eii	eii	PROPN
ap-1865	31	9	)	)	PUNCT
ap-1865	31	10	(	(	PUNCT
ap-1865	31	11	x⊕y)⊕	x⊕y)⊕	X
ap-1865	31	12	z	z	NOUN
ap-1865	31	13	=	=	SYM
ap-1865	31	14	x⊕	x⊕	PROPN
ap-1865	31	15	(	(	PUNCT
ap-1865	31	16	y⊕	y⊕	PROPN
ap-1865	31	17	z	z	PROPN
ap-1865	31	18	)	)	PUNCT
ap-1865	31	19	if	if	SCONJ
ap-1865	31	20	one	one	NUM
ap-1865	31	21	side	side	NOUN
ap-1865	31	22	is	be	AUX
ap-1865	31	23	defined	define	VERB
ap-1865	31	24	,	,	PUNCT
ap-1865	31	25	457	457	NUM
ap-1865	31	26	http://dx.doi.org/10.14311/ap.2013.53.0457	http://dx.doi.org/10.14311/ap.2013.53.0457	ADP
ap-1865	31	27	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1865	31	28	z.	z.	PROPN
ap-1865	31	29	riečanová	riečanová	PROPN
ap-1865	31	30	,	,	PUNCT
ap-1865	31	31	j.	j.	PROPN
ap-1865	31	32	janda	janda	PROPN
ap-1865	31	33	acta	acta	PROPN
ap-1865	31	34	polytechnica	polytechnica	PROPN
ap-1865	31	35	(	(	PUNCT
ap-1865	31	36	eiii	eiii	PROPN
ap-1865	31	37	)	)	PUNCT
ap-1865	31	38	for	for	ADP
ap-1865	31	39	every	every	DET
ap-1865	31	40	x	x	SYM
ap-1865	31	41	∈	∈	PROPN
ap-1865	31	42	e	e	NOUN
ap-1865	31	43	there	there	PRON
ap-1865	31	44	exists	exist	VERB
ap-1865	31	45	a	a	DET
ap-1865	31	46	unique	unique	ADJ
ap-1865	31	47	y	y	PROPN
ap-1865	31	48	∈	∈	PROPN
ap-1865	31	49	e	e	NOUN
ap-1865	31	50	such	such	ADJ
ap-1865	31	51	that	that	SCONJ
ap-1865	31	52	x⊕	x⊕	PROPN
ap-1865	31	53	y	y	PROPN
ap-1865	31	54	=	=	SYM
ap-1865	31	55	1	1	NUM
ap-1865	31	56	(	(	PUNCT
ap-1865	31	57	we	we	PRON
ap-1865	31	58	put	put	VERB
ap-1865	31	59	x′	x′	PROPN
ap-1865	32	1	=	=	SYM
ap-1865	32	2	y	y	PROPN
ap-1865	32	3	)	)	PUNCT
ap-1865	32	4	,	,	PUNCT
ap-1865	32	5	(	(	PUNCT
ap-1865	32	6	eiv	eiv	PROPN
ap-1865	32	7	)	)	PUNCT
ap-1865	32	8	if	if	SCONJ
ap-1865	32	9	1⊕	1⊕	NUM
ap-1865	32	10	x	x	SYM
ap-1865	32	11	is	be	AUX
ap-1865	32	12	defined	define	VERB
ap-1865	32	13	then	then	ADV
ap-1865	32	14	x	x	X
ap-1865	32	15	=	=	SYM
ap-1865	32	16	0	0	NUM
ap-1865	32	17	.	.	PUNCT
ap-1865	33	1	the	the	DET
ap-1865	33	2	basic	basic	ADJ
ap-1865	33	3	references	reference	NOUN
ap-1865	33	4	for	for	ADP
ap-1865	33	5	the	the	DET
ap-1865	33	6	present	present	ADJ
ap-1865	33	7	text	text	NOUN
ap-1865	33	8	are	be	AUX
ap-1865	33	9	the	the	DET
ap-1865	33	10	books	book	NOUN
ap-1865	33	11	by	by	ADP
ap-1865	33	12	dvurečenskij	dvurečenskij	NOUN
ap-1865	33	13	and	and	CCONJ
ap-1865	33	14	pulmannová	pulmannová	PROPN
ap-1865	34	1	[	[	X
ap-1865	34	2	2	2	NUM
ap-1865	34	3	]	]	PUNCT
ap-1865	34	4	,	,	PUNCT
ap-1865	34	5	and	and	CCONJ
ap-1865	34	6	blank	blank	ADJ
ap-1865	34	7	,	,	PUNCT
ap-1865	34	8	exner	exner	NOUN
ap-1865	34	9	and	and	CCONJ
ap-1865	34	10	havlíček	havlíček	NOUN
ap-1865	35	1	[	[	X
ap-1865	35	2	1	1	NUM
ap-1865	35	3	]	]	PUNCT
ap-1865	35	4	,	,	PUNCT
ap-1865	35	5	where	where	SCONJ
ap-1865	35	6	unexplained	unexplained	ADJ
ap-1865	35	7	terms	term	NOUN
ap-1865	35	8	and	and	CCONJ
ap-1865	35	9	notations	notation	NOUN
ap-1865	35	10	concerning	concern	VERB
ap-1865	35	11	the	the	DET
ap-1865	35	12	subject	subject	NOUN
ap-1865	35	13	can	can	AUX
ap-1865	35	14	be	be	AUX
ap-1865	35	15	found	find	VERB
ap-1865	35	16	.	.	PUNCT
ap-1865	36	1	in	in	ADP
ap-1865	36	2	1994	1994	NUM
ap-1865	36	3	also	also	ADV
ap-1865	36	4	a	a	DET
ap-1865	36	5	generalization	generalization	NOUN
ap-1865	36	6	of	of	ADP
ap-1865	36	7	effect	effect	NOUN
ap-1865	36	8	algebras	algebra	NOUN
ap-1865	36	9	without	without	SCONJ
ap-1865	36	10	a	a	DET
ap-1865	36	11	top	top	ADJ
ap-1865	36	12	element	element	NOUN
ap-1865	36	13	was	be	AUX
ap-1865	36	14	introduced	introduce	VERB
ap-1865	36	15	by	by	ADP
ap-1865	36	16	several	several	ADJ
ap-1865	36	17	authors	author	NOUN
ap-1865	36	18	(	(	PUNCT
ap-1865	36	19	[	[	X
ap-1865	36	20	3	3	NUM
ap-1865	36	21	,	,	PUNCT
ap-1865	36	22	5	5	NUM
ap-1865	36	23	,	,	PUNCT
ap-1865	36	24	6	6	NUM
ap-1865	36	25	,	,	PUNCT
ap-1865	36	26	8	8	NUM
ap-1865	36	27	]	]	NUM
ap-1865	36	28	)	)	PUNCT
ap-1865	36	29	.	.	PUNCT
ap-1865	37	1	definition	definition	NOUN
ap-1865	37	2	2	2	NUM
ap-1865	37	3	.	.	PUNCT
ap-1865	38	1	a	a	DET
ap-1865	38	2	partial	partial	ADJ
ap-1865	38	3	algebra	algebra	NOUN
ap-1865	38	4	(	(	PUNCT
ap-1865	38	5	e;⊕	e;⊕	ADJ
ap-1865	38	6	,	,	PUNCT
ap-1865	38	7	0	0	NUM
ap-1865	38	8	)	)	PUNCT
ap-1865	38	9	is	be	AUX
ap-1865	38	10	called	call	VERB
ap-1865	38	11	a	a	DET
ap-1865	38	12	generalized	generalized	ADJ
ap-1865	38	13	effect	effect	NOUN
ap-1865	38	14	algebra	algebra	NOUN
ap-1865	38	15	if	if	SCONJ
ap-1865	38	16	0	0	NUM
ap-1865	38	17	∈	∈	NOUN
ap-1865	38	18	e	e	NOUN
ap-1865	38	19	is	be	AUX
ap-1865	38	20	a	a	DET
ap-1865	38	21	distinguished	distinguished	ADJ
ap-1865	38	22	element	element	NOUN
ap-1865	38	23	and	and	CCONJ
ap-1865	38	24	⊕	⊕	PROPN
ap-1865	38	25	is	be	AUX
ap-1865	38	26	a	a	DET
ap-1865	38	27	partially	partially	ADV
ap-1865	38	28	defined	define	VERB
ap-1865	38	29	binary	binary	ADJ
ap-1865	38	30	operation	operation	NOUN
ap-1865	38	31	on	on	ADP
ap-1865	38	32	e	e	PROPN
ap-1865	38	33	which	which	PRON
ap-1865	38	34	satisfies	satisfy	VERB
ap-1865	38	35	the	the	DET
ap-1865	38	36	following	follow	VERB
ap-1865	38	37	conditions	condition	NOUN
ap-1865	38	38	for	for	ADP
ap-1865	38	39	any	any	DET
ap-1865	38	40	x	x	NOUN
ap-1865	38	41	,	,	PUNCT
ap-1865	38	42	y	y	PROPN
ap-1865	38	43	,	,	PUNCT
ap-1865	38	44	z	z	NOUN
ap-1865	38	45	∈	∈	PROPN
ap-1865	39	1	e	e	NOUN
ap-1865	39	2	:	:	PUNCT
ap-1865	39	3	(	(	PUNCT
ap-1865	39	4	gei	gei	PROPN
ap-1865	39	5	)	)	PUNCT
ap-1865	39	6	x⊕	x⊕	PROPN
ap-1865	39	7	y	y	PROPN
ap-1865	39	8	=	=	SYM
ap-1865	39	9	y	y	PROPN
ap-1865	39	10	⊕	⊕	PROPN
ap-1865	39	11	x	x	PROPN
ap-1865	39	12	,	,	PUNCT
ap-1865	39	13	if	if	SCONJ
ap-1865	39	14	one	one	NUM
ap-1865	39	15	side	side	NOUN
ap-1865	39	16	is	be	AUX
ap-1865	39	17	defined	define	VERB
ap-1865	39	18	,	,	PUNCT
ap-1865	39	19	(	(	PUNCT
ap-1865	39	20	geii	geii	NOUN
ap-1865	39	21	)	)	PUNCT
ap-1865	39	22	(	(	PUNCT
ap-1865	39	23	x	x	PROPN
ap-1865	39	24	⊕	⊕	PROPN
ap-1865	39	25	y	y	PROPN
ap-1865	39	26	)	)	PUNCT
ap-1865	39	27	⊕	⊕	PROPN
ap-1865	39	28	z	z	PUNCT
ap-1865	40	1	=	=	PUNCT
ap-1865	40	2	x	x	SYM
ap-1865	40	3	⊕	⊕	PROPN
ap-1865	40	4	(	(	PUNCT
ap-1865	40	5	y	y	PROPN
ap-1865	40	6	⊕	⊕	PROPN
ap-1865	40	7	z	z	PROPN
ap-1865	40	8	)	)	PUNCT
ap-1865	40	9	,	,	PUNCT
ap-1865	40	10	if	if	SCONJ
ap-1865	40	11	one	one	NUM
ap-1865	40	12	side	side	NOUN
ap-1865	40	13	is	be	AUX
ap-1865	40	14	defined	define	VERB
ap-1865	40	15	,	,	PUNCT
ap-1865	40	16	(	(	PUNCT
ap-1865	40	17	geiii	geiii	PROPN
ap-1865	40	18	)	)	PUNCT
ap-1865	40	19	x⊕	x⊕	PROPN
ap-1865	40	20	0	0	PUNCT
ap-1865	41	1	=	=	SYM
ap-1865	41	2	x	x	X
ap-1865	41	3	,	,	PUNCT
ap-1865	41	4	(	(	PUNCT
ap-1865	41	5	geiv	geiv	NOUN
ap-1865	41	6	)	)	PUNCT
ap-1865	41	7	x	x	PUNCT
ap-1865	41	8	⊕	⊕	NOUN
ap-1865	41	9	y	y	NOUN
ap-1865	41	10	=	=	SYM
ap-1865	41	11	x	x	SYM
ap-1865	41	12	⊕	⊕	PROPN
ap-1865	41	13	z	z	PROPN
ap-1865	41	14	implies	imply	VERB
ap-1865	41	15	y	y	PROPN
ap-1865	41	16	=	=	SYM
ap-1865	41	17	z	z	PROPN
ap-1865	41	18	(	(	PUNCT
ap-1865	41	19	cancellation	cancellation	NOUN
ap-1865	41	20	law	law	NOUN
ap-1865	41	21	)	)	PUNCT
ap-1865	41	22	,	,	PUNCT
ap-1865	41	23	(	(	PUNCT
ap-1865	41	24	gev	gev	NOUN
ap-1865	41	25	)	)	PUNCT
ap-1865	41	26	x⊕	x⊕	PROPN
ap-1865	41	27	y	y	PROPN
ap-1865	41	28	=	=	SYM
ap-1865	41	29	0	0	NUM
ap-1865	41	30	implies	imply	VERB
ap-1865	41	31	x	x	PUNCT
ap-1865	41	32	=	=	SYM
ap-1865	41	33	y	y	PROPN
ap-1865	41	34	=	=	SYM
ap-1865	41	35	0	0	PROPN
ap-1865	41	36	.	.	PUNCT
ap-1865	42	1	in	in	ADP
ap-1865	42	2	every	every	DET
ap-1865	42	3	(	(	PUNCT
ap-1865	42	4	generalized	generalized	ADJ
ap-1865	42	5	)	)	PUNCT
ap-1865	42	6	effect	effect	NOUN
ap-1865	42	7	algebra	algebra	NOUN
ap-1865	42	8	e	e	NOUN
ap-1865	42	9	relation	relation	NOUN
ap-1865	42	10	≤	≤	NOUN
ap-1865	42	11	and	and	CCONJ
ap-1865	42	12	the	the	DET
ap-1865	42	13	partial	partial	ADJ
ap-1865	42	14	binary	binary	NOUN
ap-1865	42	15	operation	operation	NOUN
ap-1865	42	16	can	can	AUX
ap-1865	42	17	be	be	AUX
ap-1865	42	18	defined	define	VERB
ap-1865	42	19	by	by	ADP
ap-1865	42	20	(	(	PUNCT
ap-1865	42	21	po	po	NOUN
ap-1865	42	22	)	)	PUNCT
ap-1865	42	23	x	x	SYM
ap-1865	42	24	≤	≤	PROPN
ap-1865	42	25	y	y	PROPN
ap-1865	42	26	iff	iff	PROPN
ap-1865	42	27	there	there	PRON
ap-1865	42	28	exists	exist	VERB
ap-1865	42	29	z	z	NOUN
ap-1865	42	30	∈	∈	PROPN
ap-1865	42	31	e	e	NOUN
ap-1865	43	1	such	such	ADJ
ap-1865	43	2	that	that	PRON
ap-1865	43	3	x⊕z	x⊕z	PROPN
ap-1865	44	1	=	=	PUNCT
ap-1865	44	2	y.	y.	NOUN
ap-1865	44	3	in	in	ADP
ap-1865	44	4	that	that	DET
ap-1865	44	5	case	case	NOUN
ap-1865	44	6	,	,	PUNCT
ap-1865	44	7	such	such	ADJ
ap-1865	44	8	element	element	NOUN
ap-1865	44	9	z	z	PROPN
ap-1865	44	10	is	be	AUX
ap-1865	44	11	unique	unique	ADJ
ap-1865	44	12	and	and	CCONJ
ap-1865	44	13	we	we	PRON
ap-1865	44	14	set	set	VERB
ap-1865	44	15	z	z	NOUN
ap-1865	44	16	=	=	SYM
ap-1865	44	17	y	y	PROPN
ap-1865	44	18	x.	x.	NOUN
ap-1865	44	19	then	then	ADV
ap-1865	44	20	≤	≤	PROPN
ap-1865	44	21	is	be	AUX
ap-1865	44	22	a	a	DET
ap-1865	44	23	partial	partial	ADJ
ap-1865	44	24	order	order	NOUN
ap-1865	44	25	on	on	ADP
ap-1865	44	26	e	e	NOUN
ap-1865	44	27	under	under	ADP
ap-1865	44	28	which	which	PRON
ap-1865	44	29	0	0	NUM
ap-1865	44	30	is	be	AUX
ap-1865	44	31	the	the	DET
ap-1865	44	32	least	least	ADJ
ap-1865	44	33	element	element	NOUN
ap-1865	44	34	of	of	ADP
ap-1865	44	35	e.	e.	PROPN
ap-1865	44	36	a	a	DET
ap-1865	44	37	generalized	generalized	ADJ
ap-1865	44	38	effect	effect	NOUN
ap-1865	44	39	algebra	algebra	NOUN
ap-1865	44	40	(	(	PUNCT
ap-1865	44	41	e;⊕	e;⊕	ADJ
ap-1865	44	42	,	,	PUNCT
ap-1865	44	43	0	0	NUM
ap-1865	44	44	)	)	PUNCT
ap-1865	44	45	is	be	AUX
ap-1865	44	46	called	call	VERB
ap-1865	44	47	a	a	DET
ap-1865	44	48	lattice	lattice	ADJ
ap-1865	44	49	generalized	generalized	ADJ
ap-1865	44	50	effect	effect	NOUN
ap-1865	44	51	algebra	algebra	NOUN
ap-1865	44	52	if	if	SCONJ
ap-1865	44	53	e	e	NOUN
ap-1865	44	54	with	with	ADP
ap-1865	44	55	respect	respect	NOUN
ap-1865	44	56	to	to	ADP
ap-1865	44	57	induced	induce	VERB
ap-1865	44	58	partial	partial	ADJ
ap-1865	44	59	order	order	NOUN
ap-1865	44	60	≤	≤	NOUN
ap-1865	44	61	is	be	AUX
ap-1865	44	62	a	a	DET
ap-1865	44	63	lattice	lattice	NOUN
ap-1865	44	64	.	.	PUNCT
ap-1865	45	1	definition	definition	NOUN
ap-1865	45	2	3	3	X
ap-1865	45	3	.	.	PUNCT
ap-1865	46	1	let	let	VERB
ap-1865	46	2	(	(	PUNCT
ap-1865	46	3	e;⊕	e;⊕	ADJ
ap-1865	46	4	,	,	PUNCT
ap-1865	46	5	0	0	NUM
ap-1865	46	6	,	,	PUNCT
ap-1865	46	7	1	1	NUM
ap-1865	46	8	)	)	PUNCT
ap-1865	46	9	be	be	AUX
ap-1865	46	10	an	an	DET
ap-1865	46	11	effect	effect	NOUN
ap-1865	46	12	algebra	algebra	NOUN
ap-1865	46	13	(	(	PUNCT
ap-1865	46	14	(	(	PUNCT
ap-1865	46	15	e;⊕	e;⊕	ADJ
ap-1865	46	16	,	,	PUNCT
ap-1865	46	17	0	0	NUM
ap-1865	46	18	)	)	PUNCT
ap-1865	46	19	be	be	AUX
ap-1865	46	20	a	a	DET
ap-1865	46	21	generalized	generalized	ADJ
ap-1865	46	22	effect	effect	NOUN
ap-1865	46	23	algebra	algebra	NOUN
ap-1865	46	24	)	)	PUNCT
ap-1865	46	25	.	.	PUNCT
ap-1865	47	1	a	a	DET
ap-1865	47	2	subset	subset	NOUN
ap-1865	47	3	q	q	PUNCT
ap-1865	48	1	⊆	⊆	NUM
ap-1865	48	2	e	e	NOUN
ap-1865	48	3	is	be	AUX
ap-1865	48	4	called	call	VERB
ap-1865	48	5	a	a	DET
ap-1865	48	6	sub	sub	ADJ
ap-1865	48	7	-	-	ADJ
ap-1865	48	8	effect	effect	ADJ
ap-1865	48	9	algebra	algebra	NOUN
ap-1865	48	10	(	(	PUNCT
ap-1865	48	11	sub	sub	ADJ
ap-1865	48	12	-	-	ADJ
ap-1865	48	13	generalized	generalized	ADJ
ap-1865	48	14	effect	effect	NOUN
ap-1865	48	15	algebra	algebra	NOUN
ap-1865	48	16	)	)	PUNCT
ap-1865	48	17	of	of	ADP
ap-1865	48	18	e	e	PROPN
ap-1865	48	19	iff	iff	PROPN
ap-1865	48	20	(	(	PUNCT
ap-1865	48	21	si	si	NOUN
ap-1865	48	22	)	)	PUNCT
ap-1865	48	23	1	1	NUM
ap-1865	48	24	∈	∈	NOUN
ap-1865	48	25	q	q	NOUN
ap-1865	49	1	(	(	PUNCT
ap-1865	49	2	0	0	NUM
ap-1865	49	3	∈	∈	PROPN
ap-1865	49	4	q	q	NOUN
ap-1865	49	5	)	)	PUNCT
ap-1865	49	6	,	,	PUNCT
ap-1865	49	7	(	(	PUNCT
ap-1865	49	8	sii	sii	X
ap-1865	49	9	)	)	PUNCT
ap-1865	49	10	if	if	SCONJ
ap-1865	49	11	a	a	DET
ap-1865	49	12	,	,	PUNCT
ap-1865	49	13	b	b	NOUN
ap-1865	49	14	,	,	PUNCT
ap-1865	49	15	c	c	PROPN
ap-1865	49	16	∈	∈	PROPN
ap-1865	49	17	q	q	NOUN
ap-1865	49	18	with	with	ADP
ap-1865	49	19	a	a	DET
ap-1865	49	20	⊕	⊕	PROPN
ap-1865	49	21	b	b	PROPN
ap-1865	49	22	=	=	SYM
ap-1865	49	23	c	c	PROPN
ap-1865	49	24	and	and	CCONJ
ap-1865	49	25	out	out	ADP
ap-1865	49	26	of	of	ADP
ap-1865	49	27	a	a	DET
ap-1865	49	28	,	,	PUNCT
ap-1865	49	29	b	b	NOUN
ap-1865	49	30	,	,	PUNCT
ap-1865	49	31	c	c	X
ap-1865	49	32	at	at	ADV
ap-1865	49	33	least	least	ADV
ap-1865	49	34	two	two	NUM
ap-1865	49	35	elements	element	NOUN
ap-1865	49	36	are	be	AUX
ap-1865	49	37	in	in	ADP
ap-1865	49	38	q	q	PROPN
ap-1865	49	39	then	then	ADV
ap-1865	49	40	a	a	DET
ap-1865	49	41	,	,	PUNCT
ap-1865	49	42	b	b	NOUN
ap-1865	49	43	,	,	PUNCT
ap-1865	49	44	c	c	PROPN
ap-1865	49	45	∈	∈	PROPN
ap-1865	49	46	q.	q.	PROPN
ap-1865	49	47	let	let	VERB
ap-1865	49	48	(	(	PUNCT
ap-1865	49	49	e;⊕	e;⊕	ADJ
ap-1865	49	50	,	,	PUNCT
ap-1865	49	51	0	0	NUM
ap-1865	49	52	,	,	PUNCT
ap-1865	49	53	1	1	NUM
ap-1865	49	54	)	)	PUNCT
ap-1865	49	55	be	be	AUX
ap-1865	49	56	an	an	DET
ap-1865	49	57	effect	effect	NOUN
ap-1865	49	58	algebra	algebra	NOUN
ap-1865	49	59	and	and	CCONJ
ap-1865	49	60	f	f	PROPN
ap-1865	49	61	⊆	⊆	NUM
ap-1865	49	62	e	e	NOUN
ap-1865	49	63	,	,	PUNCT
ap-1865	49	64	by	by	ADP
ap-1865	49	65	the	the	DET
ap-1865	49	66	symbol	symbol	NOUN
ap-1865	49	67	⊕/f	⊕/f	PROPN
ap-1865	49	68	we	we	PRON
ap-1865	49	69	will	will	AUX
ap-1865	49	70	denote	denote	VERB
ap-1865	49	71	a	a	DET
ap-1865	49	72	restriction	restriction	NOUN
ap-1865	49	73	of	of	ADP
ap-1865	49	74	⊕	⊕	PROPN
ap-1865	49	75	to	to	ADP
ap-1865	49	76	f	f	PROPN
ap-1865	49	77	,	,	PUNCT
ap-1865	49	78	i.e.	i.e.	X
ap-1865	49	79	for	for	SCONJ
ap-1865	49	80	a	a	DET
ap-1865	49	81	,	,	PUNCT
ap-1865	49	82	b	b	PROPN
ap-1865	49	83	∈	∈	PROPN
ap-1865	49	84	f	f	PROPN
ap-1865	49	85	,	,	PUNCT
ap-1865	49	86	a	a	DET
ap-1865	49	87	⊕/f	⊕/f	PROPN
ap-1865	49	88	b	b	PROPN
ap-1865	49	89	is	be	AUX
ap-1865	49	90	defined	define	VERB
ap-1865	49	91	if	if	SCONJ
ap-1865	49	92	and	and	CCONJ
ap-1865	49	93	only	only	ADV
ap-1865	49	94	if	if	SCONJ
ap-1865	49	95	a⊕	a⊕	PROPN
ap-1865	49	96	b	b	PROPN
ap-1865	49	97	is	be	AUX
ap-1865	49	98	defined	define	VERB
ap-1865	49	99	and	and	CCONJ
ap-1865	49	100	a⊕/f	a⊕/f	PROPN
ap-1865	49	101	b	b	PROPN
ap-1865	50	1	=	=	PROPN
ap-1865	50	2	a⊕	a⊕	PROPN
ap-1865	50	3	b.	b.	PROPN
ap-1865	51	1	it	it	PRON
ap-1865	51	2	is	be	AUX
ap-1865	51	3	easy	easy	ADJ
ap-1865	51	4	to	to	PART
ap-1865	51	5	see	see	VERB
ap-1865	51	6	that	that	SCONJ
ap-1865	51	7	sub	sub	ADJ
ap-1865	51	8	-	-	ADJ
ap-1865	51	9	effect	effect	ADJ
ap-1865	51	10	algebra	algebra	NOUN
ap-1865	51	11	(	(	PUNCT
ap-1865	51	12	subgeneralized	subgeneralize	VERB
ap-1865	51	13	effect	effect	NOUN
ap-1865	51	14	algebra	algebra	NOUN
ap-1865	51	15	)	)	PUNCT
ap-1865	51	16	q	q	NOUN
ap-1865	51	17	of	of	ADP
ap-1865	51	18	(	(	PUNCT
ap-1865	51	19	e;⊕	e;⊕	ADJ
ap-1865	51	20	,	,	PUNCT
ap-1865	51	21	0	0	NUM
ap-1865	51	22	,	,	PUNCT
ap-1865	51	23	1	1	NUM
ap-1865	51	24	)	)	PUNCT
ap-1865	51	25	(	(	PUNCT
ap-1865	51	26	(	(	PUNCT
ap-1865	51	27	e;⊕	e;⊕	ADJ
ap-1865	51	28	,	,	PUNCT
ap-1865	51	29	0	0	NUM
ap-1865	51	30	)	)	PUNCT
ap-1865	51	31	)	)	PUNCT
ap-1865	51	32	is	be	AUX
ap-1865	51	33	an	an	DET
ap-1865	51	34	effect	effect	NOUN
ap-1865	51	35	algebra	algebra	NOUN
ap-1865	51	36	(	(	PUNCT
ap-1865	51	37	q;⊕/q	q;⊕/q	NOUN
ap-1865	51	38	,	,	PUNCT
ap-1865	51	39	0	0	NUM
ap-1865	51	40	,	,	PUNCT
ap-1865	51	41	1	1	NUM
ap-1865	51	42	)	)	PUNCT
ap-1865	51	43	(	(	PUNCT
ap-1865	51	44	generalized	generalized	ADJ
ap-1865	51	45	effect	effect	NOUN
ap-1865	51	46	algebra	algebra	NOUN
ap-1865	51	47	(	(	PUNCT
ap-1865	51	48	q;⊕/q	q;⊕/q	NOUN
ap-1865	51	49	,	,	PUNCT
ap-1865	51	50	0	0	NUM
ap-1865	51	51	)	)	PUNCT
ap-1865	51	52	)	)	PUNCT
ap-1865	51	53	in	in	ADP
ap-1865	51	54	its	its	PRON
ap-1865	51	55	own	own	ADJ
ap-1865	51	56	right	right	NOUN
ap-1865	51	57	.	.	PUNCT
ap-1865	52	1	definition	definition	NOUN
ap-1865	52	2	4	4	NUM
ap-1865	52	3	.	.	PUNCT
ap-1865	53	1	let	let	AUX
ap-1865	53	2	(	(	PUNCT
ap-1865	53	3	e;⊕	e;⊕	VERB
ap-1865	53	4	,	,	PUNCT
ap-1865	53	5	0	0	NUM
ap-1865	53	6	)	)	PUNCT
ap-1865	53	7	be	be	AUX
ap-1865	53	8	a	a	DET
ap-1865	53	9	generalized	generalized	ADJ
ap-1865	53	10	effect	effect	NOUN
ap-1865	53	11	algebra	algebra	NOUN
ap-1865	53	12	.	.	PUNCT
ap-1865	54	1	for	for	ADP
ap-1865	54	2	any	any	DET
ap-1865	54	3	x	x	SYM
ap-1865	54	4	∈	∈	PROPN
ap-1865	54	5	e	e	NOUN
ap-1865	54	6	,	,	PUNCT
ap-1865	54	7	if	if	SCONJ
ap-1865	54	8	there	there	PRON
ap-1865	54	9	exists	exist	VERB
ap-1865	54	10	a	a	DET
ap-1865	54	11	natural	natural	ADJ
ap-1865	54	12	number	number	NOUN
ap-1865	54	13	ord(x	ord(x	NOUN
ap-1865	54	14	)	)	PUNCT
ap-1865	54	15	∈	∈	NOUN
ap-1865	55	1	n	n	PRON
ap-1865	55	2	such	such	ADJ
ap-1865	55	3	that	that	SCONJ
ap-1865	55	4	ord(x)·x	ord(x)·x	PROPN
ap-1865	55	5	=	=	SYM
ap-1865	55	6	x⊕x⊕.	x⊕x⊕.	PROPN
ap-1865	55	7	.	.	PUNCT
ap-1865	56	1	.⊕x	.⊕x	PUNCT
ap-1865	56	2	(	(	PUNCT
ap-1865	56	3	ord(x)-times	ord(x)-times	PROPN
ap-1865	56	4	)	)	PUNCT
ap-1865	56	5	is	be	AUX
ap-1865	56	6	defined	define	VERB
ap-1865	56	7	,	,	PUNCT
ap-1865	56	8	but	but	CCONJ
ap-1865	56	9	(	(	PUNCT
ap-1865	56	10	ord(x	ord(x	NOUN
ap-1865	56	11	)	)	PUNCT
ap-1865	57	1	+	+	CCONJ
ap-1865	57	2	1	1	NUM
ap-1865	57	3	)	)	PUNCT
ap-1865	57	4	·	·	PUNCT
ap-1865	58	1	x	x	X
ap-1865	58	2	is	be	AUX
ap-1865	58	3	not	not	PART
ap-1865	58	4	defined	define	VERB
ap-1865	58	5	,	,	PUNCT
ap-1865	58	6	is	be	AUX
ap-1865	58	7	called	call	VERB
ap-1865	58	8	an	an	DET
ap-1865	58	9	isotropic	isotropic	ADJ
ap-1865	58	10	index	index	NOUN
ap-1865	58	11	of	of	ADP
ap-1865	58	12	x.	x.	NOUN
ap-1865	58	13	if	if	SCONJ
ap-1865	58	14	such	such	ADJ
ap-1865	58	15	natural	natural	ADJ
ap-1865	58	16	number	number	NOUN
ap-1865	58	17	does	do	AUX
ap-1865	58	18	not	not	PART
ap-1865	58	19	exist	exist	VERB
ap-1865	58	20	,	,	PUNCT
ap-1865	58	21	we	we	PRON
ap-1865	58	22	set	set	VERB
ap-1865	58	23	ord(x	ord(x	NOUN
ap-1865	58	24	)	)	PUNCT
ap-1865	59	1	=	=	SYM
ap-1865	59	2	∞.	∞.	PROPN
ap-1865	59	3	definition	definition	NOUN
ap-1865	59	4	5	5	NUM
ap-1865	59	5	.	.	PUNCT
ap-1865	59	6	elements	element	NOUN
ap-1865	59	7	a	a	PRON
ap-1865	59	8	,	,	PUNCT
ap-1865	59	9	b	b	X
ap-1865	59	10	∈	∈	PROPN
ap-1865	59	11	e	e	NOUN
ap-1865	59	12	of	of	ADP
ap-1865	59	13	an	an	DET
ap-1865	59	14	effect	effect	NOUN
ap-1865	59	15	algebra	algebra	NOUN
ap-1865	59	16	(	(	PUNCT
ap-1865	59	17	e;⊕	e;⊕	ADJ
ap-1865	59	18	,	,	PUNCT
ap-1865	59	19	0	0	NUM
ap-1865	59	20	,	,	PUNCT
ap-1865	59	21	1	1	NUM
ap-1865	59	22	)	)	PUNCT
ap-1865	59	23	(	(	PUNCT
ap-1865	59	24	generalized	generalized	ADJ
ap-1865	59	25	effect	effect	NOUN
ap-1865	59	26	algebra	algebra	NOUN
ap-1865	59	27	(	(	PUNCT
ap-1865	59	28	e;⊕	e;⊕	ADJ
ap-1865	59	29	,	,	PUNCT
ap-1865	59	30	0	0	NUM
ap-1865	59	31	)	)	PUNCT
ap-1865	59	32	)	)	PUNCT
ap-1865	59	33	are	be	AUX
ap-1865	59	34	called	call	VERB
ap-1865	59	35	compatible	compatible	ADJ
ap-1865	59	36	(	(	PUNCT
ap-1865	59	37	we	we	PRON
ap-1865	59	38	write	write	VERB
ap-1865	59	39	a	a	DET
ap-1865	59	40	↔	↔	PROPN
ap-1865	59	41	b	b	NOUN
ap-1865	59	42	)	)	PUNCT
ap-1865	59	43	if	if	SCONJ
ap-1865	59	44	there	there	PRON
ap-1865	59	45	exist	exist	VERB
ap-1865	59	46	a1	a1	NOUN
ap-1865	59	47	,	,	PUNCT
ap-1865	59	48	c	c	X
ap-1865	59	49	,	,	PUNCT
ap-1865	59	50	b1	b1	NOUN
ap-1865	59	51	∈	∈	PROPN
ap-1865	59	52	e	e	NOUN
ap-1865	59	53	such	such	ADJ
ap-1865	59	54	that	that	DET
ap-1865	59	55	a1	a1	NOUN
ap-1865	59	56	⊕	⊕	PROPN
ap-1865	59	57	c	c	PROPN
ap-1865	59	58	⊕	⊕	PROPN
ap-1865	59	59	b1	b1	PROPN
ap-1865	59	60	is	be	AUX
ap-1865	59	61	defined	define	VERB
ap-1865	59	62	and	and	CCONJ
ap-1865	59	63	a	a	DET
ap-1865	59	64	=	=	NOUN
ap-1865	59	65	a1	a1	NOUN
ap-1865	59	66	⊕	⊕	PROPN
ap-1865	59	67	c	c	PROPN
ap-1865	59	68	,	,	PUNCT
ap-1865	59	69	b	b	X
ap-1865	59	70	=	=	SYM
ap-1865	59	71	b1	b1	PROPN
ap-1865	59	72	⊕	⊕	PROPN
ap-1865	59	73	c.	c.	PROPN
ap-1865	59	74	in	in	ADP
ap-1865	59	75	[	[	X
ap-1865	59	76	11	11	NUM
ap-1865	59	77	]	]	PUNCT
ap-1865	59	78	it	it	PRON
ap-1865	59	79	was	be	AUX
ap-1865	59	80	proved	prove	VERB
ap-1865	59	81	that	that	SCONJ
ap-1865	59	82	in	in	ADP
ap-1865	59	83	any	any	DET
ap-1865	59	84	lattice	lattice	ADJ
ap-1865	59	85	effect	effect	NOUN
ap-1865	59	86	algebra	algebra	NOUN
ap-1865	59	87	e	e	NOUN
ap-1865	59	88	for	for	ADP
ap-1865	59	89	a	a	DET
ap-1865	59	90	,	,	PUNCT
ap-1865	59	91	b	b	X
ap-1865	59	92	∈	∈	NOUN
ap-1865	59	93	e	e	X
ap-1865	59	94	we	we	PRON
ap-1865	59	95	have	have	VERB
ap-1865	59	96	a↔	a↔	NOUN
ap-1865	59	97	b	b	DET
ap-1865	59	98	iff	iff	NOUN
ap-1865	59	99	(	(	PUNCT
ap-1865	59	100	a	a	PRON
ap-1865	59	101	(	(	PUNCT
ap-1865	59	102	a	a	DET
ap-1865	59	103	∧	∧	PROPN
ap-1865	59	104	b))⊕	b))⊕	NOUN
ap-1865	59	105	(	(	PUNCT
ap-1865	59	106	b	b	NOUN
ap-1865	59	107	(	(	PUNCT
ap-1865	59	108	a	a	DET
ap-1865	59	109	∧	∧	PROPN
ap-1865	59	110	b	b	NOUN
ap-1865	59	111	)	)	PUNCT
ap-1865	59	112	)	)	PUNCT
ap-1865	59	113	is	be	AUX
ap-1865	59	114	defined	define	VERB
ap-1865	59	115	in	in	ADP
ap-1865	59	116	e.	e.	PROPN
ap-1865	59	117	moreover	moreover	ADV
ap-1865	59	118	,	,	PUNCT
ap-1865	59	119	we	we	PRON
ap-1865	59	120	call	call	VERB
ap-1865	59	121	every	every	DET
ap-1865	59	122	maximal	maximal	ADJ
ap-1865	59	123	subset	subset	NOUN
ap-1865	59	124	of	of	ADP
ap-1865	59	125	pairwise	pairwise	NOUN
ap-1865	59	126	compatible	compatible	ADJ
ap-1865	59	127	elements	element	NOUN
ap-1865	59	128	of	of	ADP
ap-1865	59	129	e	e	NOUN
ap-1865	59	130	a	a	DET
ap-1865	59	131	compatibility	compatibility	NOUN
ap-1865	59	132	block	block	NOUN
ap-1865	59	133	of	of	ADP
ap-1865	59	134	e.	e.	PROPN
ap-1865	60	1	every	every	DET
ap-1865	60	2	lattice	lattice	ADJ
ap-1865	60	3	effect	effect	NOUN
ap-1865	60	4	algebra	algebra	NOUN
ap-1865	60	5	e	e	NOUN
ap-1865	60	6	is	be	AUX
ap-1865	60	7	a	a	DET
ap-1865	60	8	set	set	NOUN
ap-1865	60	9	-	-	PUNCT
ap-1865	60	10	theoretical	theoretical	ADJ
ap-1865	60	11	union	union	NOUN
ap-1865	60	12	of	of	ADP
ap-1865	60	13	its	its	PRON
ap-1865	60	14	compatibility	compatibility	NOUN
ap-1865	60	15	blocks	block	NOUN
ap-1865	60	16	[	[	X
ap-1865	60	17	10	10	NUM
ap-1865	60	18	,	,	PUNCT
ap-1865	60	19	theorem	theorem	VERB
ap-1865	60	20	3.2	3.2	NUM
ap-1865	60	21	]	]	PUNCT
ap-1865	60	22	.	.	PUNCT
ap-1865	61	1	a	a	DET
ap-1865	61	2	lattice	lattice	ADJ
ap-1865	61	3	effect	effect	NOUN
ap-1865	61	4	algebra	algebra	NOUN
ap-1865	61	5	possessing	possess	VERB
ap-1865	61	6	a	a	DET
ap-1865	61	7	unique	unique	ADJ
ap-1865	61	8	block	block	NOUN
ap-1865	61	9	is	be	AUX
ap-1865	61	10	called	call	VERB
ap-1865	61	11	an	an	DET
ap-1865	61	12	mv	mv	ADJ
ap-1865	61	13	-	-	PUNCT
ap-1865	61	14	effect	effect	NOUN
ap-1865	61	15	algebra	algebra	NOUN
ap-1865	61	16	(	(	PUNCT
ap-1865	61	17	hence	hence	ADV
ap-1865	61	18	a↔	a↔	ADP
ap-1865	61	19	b	b	NOUN
ap-1865	61	20	for	for	ADP
ap-1865	61	21	all	all	DET
ap-1865	61	22	a	a	PRON
ap-1865	61	23	,	,	PUNCT
ap-1865	61	24	b	b	X
ap-1865	61	25	∈	∈	PROPN
ap-1865	61	26	e	e	NOUN
ap-1865	61	27	)	)	PUNCT
ap-1865	61	28	.	.	PUNCT
ap-1865	62	1	2	2	X
ap-1865	62	2	.	.	X
ap-1865	62	3	pairwise	pairwise	NOUN
ap-1865	62	4	summable	summable	ADJ
ap-1865	62	5	generalized	generalized	ADJ
ap-1865	62	6	effect	effect	NOUN
ap-1865	62	7	algebras	algebra	NOUN
ap-1865	62	8	recall	recall	VERB
ap-1865	62	9	that	that	SCONJ
ap-1865	62	10	elements	element	VERB
ap-1865	62	11	a	a	DET
ap-1865	62	12	,	,	PUNCT
ap-1865	62	13	b	b	PROPN
ap-1865	62	14	of	of	ADP
ap-1865	62	15	a	a	DET
ap-1865	62	16	generalized	generalized	ADJ
ap-1865	62	17	effect	effect	NOUN
ap-1865	62	18	algebra	algebra	NOUN
ap-1865	62	19	(	(	PUNCT
ap-1865	62	20	g;⊕	g;⊕	NOUN
ap-1865	62	21	,	,	PUNCT
ap-1865	62	22	0	0	NUM
ap-1865	62	23	)	)	PUNCT
ap-1865	62	24	are	be	AUX
ap-1865	62	25	called	call	VERB
ap-1865	62	26	summable	summable	ADJ
ap-1865	62	27	if	if	SCONJ
ap-1865	62	28	a⊕	a⊕	PROPN
ap-1865	62	29	b	b	PROPN
ap-1865	62	30	exists	exist	VERB
ap-1865	62	31	in	in	ADP
ap-1865	62	32	g.	g.	PROPN
ap-1865	62	33	a	a	DET
ap-1865	62	34	nonempty	nonempty	NOUN
ap-1865	62	35	subset	subset	VERB
ap-1865	62	36	f	f	PROPN
ap-1865	62	37	of	of	ADP
ap-1865	62	38	a	a	DET
ap-1865	62	39	generalized	generalized	ADJ
ap-1865	62	40	effect	effect	NOUN
ap-1865	62	41	algebra	algebra	NOUN
ap-1865	62	42	(	(	PUNCT
ap-1865	62	43	g;⊕	g;⊕	NOUN
ap-1865	62	44	,	,	PUNCT
ap-1865	62	45	0	0	NUM
ap-1865	62	46	)	)	PUNCT
ap-1865	62	47	is	be	AUX
ap-1865	62	48	called	call	VERB
ap-1865	62	49	a	a	DET
ap-1865	62	50	pairwise	pairwise	NOUN
ap-1865	62	51	summable	summable	ADJ
ap-1865	62	52	subset	subset	NOUN
ap-1865	62	53	of	of	ADP
ap-1865	62	54	g	g	PROPN
ap-1865	62	55	if	if	SCONJ
ap-1865	62	56	a⊕	a⊕	PROPN
ap-1865	62	57	b	b	PROPN
ap-1865	62	58	exists	exist	VERB
ap-1865	62	59	for	for	ADP
ap-1865	62	60	every	every	DET
ap-1865	62	61	not	not	PART
ap-1865	62	62	necessarily	necessarily	ADV
ap-1865	62	63	different	different	ADJ
ap-1865	62	64	elements	element	NOUN
ap-1865	62	65	a	a	PRON
ap-1865	62	66	,	,	PUNCT
ap-1865	62	67	b	b	X
ap-1865	62	68	∈	∈	PROPN
ap-1865	62	69	f	f	PROPN
ap-1865	62	70	and	and	CCONJ
ap-1865	63	1	a⊕	a⊕	PROPN
ap-1865	63	2	b	b	PROPN
ap-1865	63	3	∈	∈	PROPN
ap-1865	63	4	f	f	X
ap-1865	63	5	(	(	PUNCT
ap-1865	63	6	hence	hence	ADV
ap-1865	63	7	f	f	PROPN
ap-1865	63	8	is	be	AUX
ap-1865	63	9	closed	close	VERB
ap-1865	63	10	under	under	ADP
ap-1865	63	11	the	the	DET
ap-1865	63	12	partial	partial	ADJ
ap-1865	63	13	operation	operation	NOUN
ap-1865	63	14	⊕	⊕	PROPN
ap-1865	63	15	)	)	PUNCT
ap-1865	63	16	.	.	PUNCT
ap-1865	64	1	evidently	evidently	ADV
ap-1865	64	2	,	,	PUNCT
ap-1865	64	3	in	in	ADP
ap-1865	64	4	this	this	DET
ap-1865	64	5	case	case	NOUN
ap-1865	64	6	,	,	PUNCT
ap-1865	64	7	every	every	DET
ap-1865	64	8	a	a	DET
ap-1865	64	9	∈	∈	PROPN
ap-1865	64	10	f	f	X
ap-1865	64	11	has	have	VERB
ap-1865	64	12	the	the	DET
ap-1865	64	13	infinite	infinite	ADJ
ap-1865	64	14	isotropic	isotropic	NOUN
ap-1865	64	15	index	index	NOUN
ap-1865	64	16	ord(a	ord(a	PROPN
ap-1865	64	17	)	)	PUNCT
ap-1865	65	1	=	=	PRON
ap-1865	65	2	∞.	∞.	PROPN
ap-1865	65	3	a	a	DET
ap-1865	65	4	(	(	PUNCT
ap-1865	65	5	sub-	sub-	ADJ
ap-1865	65	6	)	)	PUNCT
ap-1865	65	7	generalized	generalized	ADJ
ap-1865	65	8	effect	effect	NOUN
ap-1865	65	9	algebra	algebra	NOUN
ap-1865	65	10	e	e	PROPN
ap-1865	65	11	of	of	ADP
ap-1865	65	12	(	(	PUNCT
ap-1865	65	13	g;⊕	g;⊕	NOUN
ap-1865	65	14	,	,	PUNCT
ap-1865	65	15	0	0	NUM
ap-1865	65	16	)	)	PUNCT
ap-1865	65	17	is	be	AUX
ap-1865	65	18	called	call	VERB
ap-1865	65	19	pairwise	pairwise	NOUN
ap-1865	65	20	summable	summable	ADJ
ap-1865	65	21	if	if	SCONJ
ap-1865	65	22	it	it	PRON
ap-1865	65	23	is	be	AUX
ap-1865	65	24	a	a	DET
ap-1865	65	25	pairwise	pairwise	NOUN
ap-1865	65	26	summable	summable	ADJ
ap-1865	65	27	subset	subset	NOUN
ap-1865	65	28	of	of	ADP
ap-1865	65	29	g.	g.	PROPN
ap-1865	65	30	we	we	PRON
ap-1865	65	31	are	be	AUX
ap-1865	65	32	going	go	VERB
ap-1865	65	33	to	to	PART
ap-1865	65	34	show	show	VERB
ap-1865	65	35	that	that	SCONJ
ap-1865	65	36	every	every	DET
ap-1865	65	37	maximal	maximal	ADJ
ap-1865	65	38	subset	subset	NOUN
ap-1865	65	39	of	of	ADP
ap-1865	65	40	pairwise	pairwise	NOUN
ap-1865	65	41	summable	summable	ADJ
ap-1865	65	42	elements	element	NOUN
ap-1865	65	43	of	of	ADP
ap-1865	65	44	a	a	DET
ap-1865	65	45	generalized	generalized	ADJ
ap-1865	65	46	effect	effect	NOUN
ap-1865	65	47	algebra	algebra	NOUN
ap-1865	65	48	g	g	PROPN
ap-1865	65	49	is	be	AUX
ap-1865	65	50	a	a	DET
ap-1865	65	51	sub	sub	ADJ
ap-1865	65	52	-	-	ADJ
ap-1865	65	53	generalized	generalized	ADJ
ap-1865	65	54	effect	effect	NOUN
ap-1865	65	55	algebra	algebra	NOUN
ap-1865	65	56	of	of	ADP
ap-1865	65	57	g.	g.	PROPN
ap-1865	65	58	moreover	moreover	ADV
ap-1865	65	59	,	,	PUNCT
ap-1865	65	60	we	we	PRON
ap-1865	65	61	study	study	VERB
ap-1865	65	62	further	further	ADJ
ap-1865	65	63	properties	property	NOUN
ap-1865	65	64	of	of	ADP
ap-1865	65	65	these	these	DET
ap-1865	65	66	pairwise	pairwise	NOUN
ap-1865	65	67	summable	summable	ADJ
ap-1865	65	68	sub	sub	ADJ
ap-1865	65	69	-	-	ADJ
ap-1865	65	70	generalized	generalized	ADJ
ap-1865	65	71	effect	effect	NOUN
ap-1865	65	72	algebras	algebra	NOUN
ap-1865	65	73	.	.	PUNCT
ap-1865	66	1	theorem	theorem	NOUN
ap-1865	66	2	1	1	NUM
ap-1865	66	3	.	.	PUNCT
ap-1865	67	1	let	let	VERB
ap-1865	67	2	(	(	PUNCT
ap-1865	67	3	g;⊕	g;⊕	NOUN
ap-1865	67	4	,	,	PUNCT
ap-1865	67	5	0	0	NUM
ap-1865	67	6	)	)	PUNCT
ap-1865	67	7	be	be	AUX
ap-1865	67	8	a	a	DET
ap-1865	67	9	generalized	generalized	ADJ
ap-1865	67	10	effect	effect	NOUN
ap-1865	67	11	algebra	algebra	NOUN
ap-1865	67	12	.	.	PUNCT
ap-1865	68	1	let	let	VERB
ap-1865	68	2	a	a	DET
ap-1865	68	3	non	non	ADJ
ap-1865	68	4	-	-	ADJ
ap-1865	68	5	empty	empty	ADJ
ap-1865	68	6	subset	subset	NOUN
ap-1865	68	7	f	f	PROPN
ap-1865	68	8	of	of	ADP
ap-1865	68	9	g	g	PROPN
ap-1865	68	10	satisfy	satisfy	VERB
ap-1865	68	11	the	the	DET
ap-1865	68	12	following	follow	VERB
ap-1865	68	13	conditions	condition	NOUN
ap-1865	68	14	:	:	PUNCT
ap-1865	68	15	(	(	PUNCT
ap-1865	68	16	1	1	NUM
ap-1865	68	17	.	.	PUNCT
ap-1865	68	18	)	)	PUNCT
ap-1865	69	1	for	for	ADP
ap-1865	69	2	every	every	DET
ap-1865	69	3	a	a	PROPN
ap-1865	69	4	,	,	PUNCT
ap-1865	69	5	b	b	X
ap-1865	69	6	∈	∈	ADP
ap-1865	69	7	f	f	NOUN
ap-1865	69	8	there	there	PRON
ap-1865	69	9	exists	exist	VERB
ap-1865	69	10	a⊕	a⊕	PROPN
ap-1865	69	11	b	b	PROPN
ap-1865	69	12	∈	∈	PROPN
ap-1865	69	13	f	f	X
ap-1865	69	14	,	,	PUNCT
ap-1865	69	15	(	(	PUNCT
ap-1865	69	16	2	2	NUM
ap-1865	69	17	.	.	PUNCT
ap-1865	69	18	)	)	PUNCT
ap-1865	70	1	if	if	SCONJ
ap-1865	70	2	a	a	DET
ap-1865	70	3	∈	∈	PROPN
ap-1865	70	4	g	g	NOUN
ap-1865	70	5	and	and	CCONJ
ap-1865	70	6	a	a	DET
ap-1865	70	7	⊕	⊕	PROPN
ap-1865	70	8	e	e	PROPN
ap-1865	70	9	exists	exist	VERB
ap-1865	70	10	for	for	ADP
ap-1865	70	11	every	every	DET
ap-1865	70	12	e	e	PROPN
ap-1865	70	13	∈	∈	PROPN
ap-1865	70	14	f	f	X
ap-1865	70	15	then	then	ADV
ap-1865	70	16	a	a	DET
ap-1865	70	17	∈	∈	PROPN
ap-1865	70	18	f	f	X
ap-1865	70	19	.	.	PUNCT
ap-1865	71	1	then	then	ADV
ap-1865	71	2	f	f	PROPN
ap-1865	71	3	is	be	AUX
ap-1865	71	4	a	a	DET
ap-1865	71	5	sub	sub	ADJ
ap-1865	71	6	-	-	ADJ
ap-1865	71	7	generalized	generalized	ADJ
ap-1865	71	8	effect	effect	NOUN
ap-1865	71	9	algebra	algebra	NOUN
ap-1865	71	10	of	of	ADP
ap-1865	71	11	g.	g.	PROPN
ap-1865	71	12	proof	proof	NOUN
ap-1865	71	13	.	.	PUNCT
ap-1865	72	1	by	by	ADP
ap-1865	72	2	(	(	PUNCT
ap-1865	72	3	2	2	NUM
ap-1865	72	4	.	.	PUNCT
ap-1865	72	5	)	)	PUNCT
ap-1865	72	6	we	we	PRON
ap-1865	72	7	obtain	obtain	VERB
ap-1865	72	8	0	0	NUM
ap-1865	72	9	∈	∈	PROPN
ap-1865	72	10	f	f	NOUN
ap-1865	72	11	,	,	PUNCT
ap-1865	72	12	since	since	SCONJ
ap-1865	72	13	0⊕	0⊕	NUM
ap-1865	72	14	e	e	NOUN
ap-1865	72	15	exists	exist	VERB
ap-1865	72	16	for	for	ADP
ap-1865	72	17	all	all	DET
ap-1865	72	18	e	e	PROPN
ap-1865	72	19	∈	∈	PROPN
ap-1865	72	20	f	f	X
ap-1865	72	21	.	.	PUNCT
ap-1865	72	22	suppose	suppose	VERB
ap-1865	72	23	now	now	ADV
ap-1865	72	24	that	that	SCONJ
ap-1865	72	25	a	a	DET
ap-1865	72	26	⊕	⊕	PROPN
ap-1865	72	27	b	b	PROPN
ap-1865	72	28	=	=	SYM
ap-1865	72	29	c	c	PROPN
ap-1865	72	30	,	,	PUNCT
ap-1865	72	31	for	for	ADP
ap-1865	72	32	a	a	DET
ap-1865	72	33	,	,	PUNCT
ap-1865	72	34	b	b	NOUN
ap-1865	72	35	,	,	PUNCT
ap-1865	72	36	c	c	PROPN
ap-1865	72	37	∈	∈	PROPN
ap-1865	72	38	g.	g.	NOUN
ap-1865	72	39	if	if	SCONJ
ap-1865	72	40	a	a	PRON
ap-1865	72	41	,	,	PUNCT
ap-1865	73	1	b	b	X
ap-1865	73	2	∈	∈	PROPN
ap-1865	73	3	f	f	NOUN
ap-1865	73	4	then	then	ADV
ap-1865	73	5	c	c	X
ap-1865	73	6	=	=	PUNCT
ap-1865	74	1	a	a	DET
ap-1865	74	2	⊕	⊕	PROPN
ap-1865	74	3	b	b	PROPN
ap-1865	74	4	∈	∈	PROPN
ap-1865	74	5	f	f	X
ap-1865	74	6	by	by	ADP
ap-1865	74	7	(	(	PUNCT
ap-1865	74	8	1	1	NUM
ap-1865	74	9	.	.	NUM
ap-1865	74	10	)	)	PUNCT
ap-1865	74	11	.	.	PUNCT
ap-1865	75	1	further	far	ADV
ap-1865	75	2	,	,	PUNCT
ap-1865	75	3	in	in	ADP
ap-1865	75	4	the	the	DET
ap-1865	75	5	case	case	NOUN
ap-1865	75	6	a	a	PRON
ap-1865	75	7	,	,	PUNCT
ap-1865	75	8	c	c	PROPN
ap-1865	75	9	∈	∈	PROPN
ap-1865	75	10	f	f	X
ap-1865	75	11	,	,	PUNCT
ap-1865	75	12	we	we	PRON
ap-1865	75	13	have	have	VERB
ap-1865	75	14	b	b	NOUN
ap-1865	75	15	=	=	SYM
ap-1865	75	16	c	c	PROPN
ap-1865	75	17	a	a	DET
ap-1865	75	18	≤	≤	ADJ
ap-1865	75	19	c.	c.	NOUN
ap-1865	75	20	since	since	SCONJ
ap-1865	75	21	c	c	PROPN
ap-1865	75	22	⊕	⊕	PROPN
ap-1865	75	23	e	e	PROPN
ap-1865	75	24	exists	exist	VERB
ap-1865	75	25	for	for	ADP
ap-1865	75	26	all	all	DET
ap-1865	75	27	e	e	PROPN
ap-1865	75	28	∈	∈	PROPN
ap-1865	75	29	f	f	X
ap-1865	75	30	,	,	PUNCT
ap-1865	75	31	also	also	ADV
ap-1865	75	32	b	b	X
ap-1865	75	33	=	=	SYM
ap-1865	75	34	(	(	PUNCT
ap-1865	75	35	c	c	NOUN
ap-1865	75	36	a)⊕	a)⊕	ADP
ap-1865	75	37	e	e	NOUN
ap-1865	75	38	exists	exist	VERB
ap-1865	75	39	for	for	ADP
ap-1865	75	40	all	all	DET
ap-1865	75	41	e	e	PROPN
ap-1865	75	42	∈	∈	PROPN
ap-1865	75	43	f	f	X
ap-1865	75	44	.	.	PUNCT
ap-1865	76	1	thus	thus	ADV
ap-1865	76	2	by	by	ADP
ap-1865	76	3	(	(	PUNCT
ap-1865	76	4	2	2	NUM
ap-1865	76	5	.	.	PUNCT
ap-1865	76	6	)	)	PUNCT
ap-1865	76	7	b	b	X
ap-1865	77	1	=	=	SYM
ap-1865	77	2	c	c	PROPN
ap-1865	77	3	a	a	DET
ap-1865	77	4	∈	∈	PROPN
ap-1865	77	5	f	f	X
ap-1865	77	6	.	.	PUNCT
ap-1865	78	1	that	that	PRON
ap-1865	78	2	is	be	AUX
ap-1865	78	3	,	,	PUNCT
ap-1865	78	4	f	f	PROPN
ap-1865	78	5	is	be	AUX
ap-1865	78	6	a	a	DET
ap-1865	78	7	sub	sub	ADJ
ap-1865	78	8	-	-	ADJ
ap-1865	78	9	generalized	generalized	ADJ
ap-1865	78	10	effect	effect	NOUN
ap-1865	78	11	algebra	algebra	NOUN
ap-1865	78	12	of	of	ADP
ap-1865	78	13	(	(	PUNCT
ap-1865	78	14	g;⊕	g;⊕	NOUN
ap-1865	78	15	,	,	PUNCT
ap-1865	78	16	0	0	NUM
ap-1865	78	17	)	)	PUNCT
ap-1865	78	18	.	.	PUNCT
ap-1865	79	1	remark	remark	PROPN
ap-1865	79	2	1	1	NUM
ap-1865	79	3	.	.	PUNCT
ap-1865	80	1	condition	condition	NOUN
ap-1865	80	2	(	(	PUNCT
ap-1865	80	3	1	1	NUM
ap-1865	80	4	.	.	PUNCT
ap-1865	80	5	)	)	PUNCT
ap-1865	80	6	on	on	ADP
ap-1865	80	7	a	a	DET
ap-1865	80	8	subset	subset	NOUN
ap-1865	80	9	f	f	NOUN
ap-1865	80	10	⊆	⊆	NUM
ap-1865	80	11	g	g	NOUN
ap-1865	80	12	of	of	ADP
ap-1865	80	13	a	a	DET
ap-1865	80	14	generalized	generalized	ADJ
ap-1865	80	15	effect	effect	NOUN
ap-1865	80	16	algebra	algebra	NOUN
ap-1865	80	17	(	(	PUNCT
ap-1865	80	18	g;⊕	g;⊕	NOUN
ap-1865	80	19	,	,	PUNCT
ap-1865	80	20	0	0	NUM
ap-1865	80	21	)	)	PUNCT
ap-1865	80	22	in	in	ADP
ap-1865	80	23	the	the	DET
ap-1865	80	24	above	above	ADJ
ap-1865	80	25	theorem	theorem	ADJ
ap-1865	80	26	guarantees	guarantee	NOUN
ap-1865	80	27	that	that	SCONJ
ap-1865	80	28	f	f	PROPN
ap-1865	80	29	is	be	AUX
ap-1865	80	30	a	a	DET
ap-1865	80	31	pairwise	pairwise	NOUN
ap-1865	80	32	summable	summable	ADJ
ap-1865	80	33	subset	subset	NOUN
ap-1865	80	34	of	of	ADP
ap-1865	80	35	g.	g.	PROPN
ap-1865	80	36	condition	condition	NOUN
ap-1865	80	37	(	(	PUNCT
ap-1865	80	38	2	2	NUM
ap-1865	80	39	.	.	PUNCT
ap-1865	80	40	)	)	PUNCT
ap-1865	81	1	then	then	ADV
ap-1865	81	2	provides	provide	VERB
ap-1865	81	3	that	that	SCONJ
ap-1865	81	4	f	f	PROPN
ap-1865	81	5	is	be	AUX
ap-1865	81	6	a	a	DET
ap-1865	81	7	maximal	maximal	ADJ
ap-1865	81	8	pairwise	pairwise	NOUN
ap-1865	81	9	summable	summable	ADJ
ap-1865	81	10	subset	subset	NOUN
ap-1865	81	11	of	of	ADP
ap-1865	81	12	g.	g.	PROPN
ap-1865	81	13	458	458	NUM
ap-1865	81	14	vol	vol	NOUN
ap-1865	81	15	.	.	PUNCT
ap-1865	82	1	53	53	NUM
ap-1865	82	2	no	no	NOUN
ap-1865	82	3	.	.	PUNCT
ap-1865	83	1	5/2013	5/2013	NUM
ap-1865	83	2	maximal	maximal	ADJ
ap-1865	83	3	subsets	subset	NOUN
ap-1865	83	4	of	of	ADP
ap-1865	83	5	pairwise	pairwise	NOUN
ap-1865	83	6	summable	summable	ADJ
ap-1865	83	7	elements	element	NOUN
ap-1865	83	8	definition	definition	NOUN
ap-1865	83	9	6	6	NUM
ap-1865	83	10	.	.	PUNCT
ap-1865	84	1	let	let	VERB
ap-1865	84	2	(	(	PUNCT
ap-1865	84	3	g;⊕	g;⊕	NOUN
ap-1865	84	4	,	,	PUNCT
ap-1865	84	5	0	0	NUM
ap-1865	84	6	)	)	PUNCT
ap-1865	84	7	be	be	AUX
ap-1865	84	8	a	a	DET
ap-1865	84	9	generalized	generalized	ADJ
ap-1865	84	10	effect	effect	NOUN
ap-1865	84	11	algebra	algebra	NOUN
ap-1865	84	12	and	and	CCONJ
ap-1865	84	13	f	f	PROPN
ap-1865	84	14	⊆	⊆	NUM
ap-1865	84	15	g	g	NOUN
ap-1865	84	16	be	be	AUX
ap-1865	84	17	a	a	DET
ap-1865	84	18	subset	subset	NOUN
ap-1865	84	19	of	of	ADP
ap-1865	84	20	g	g	NOUN
ap-1865	84	21	that	that	PRON
ap-1865	84	22	satisfies	satisfy	VERB
ap-1865	84	23	conditions	condition	NOUN
ap-1865	84	24	(	(	PUNCT
ap-1865	84	25	1	1	NUM
ap-1865	84	26	.	.	PUNCT
ap-1865	84	27	)	)	PUNCT
ap-1865	85	1	and	and	CCONJ
ap-1865	85	2	(	(	PUNCT
ap-1865	85	3	2	2	NUM
ap-1865	85	4	.	.	PUNCT
ap-1865	85	5	)	)	PUNCT
ap-1865	85	6	from	from	ADP
ap-1865	85	7	theorem	theorem	ADJ
ap-1865	85	8	1	1	NUM
ap-1865	85	9	.	.	PUNCT
ap-1865	86	1	then	then	ADV
ap-1865	86	2	f	f	PROPN
ap-1865	86	3	is	be	AUX
ap-1865	86	4	called	call	VERB
ap-1865	86	5	a	a	DET
ap-1865	86	6	summability	summability	NOUN
ap-1865	86	7	block	block	NOUN
ap-1865	86	8	of	of	ADP
ap-1865	86	9	g.	g.	PROPN
ap-1865	86	10	corollary	corollary	NOUN
ap-1865	86	11	1	1	NUM
ap-1865	86	12	.	.	PUNCT
ap-1865	87	1	every	every	DET
ap-1865	87	2	maximal	maximal	ADJ
ap-1865	87	3	pairwise	pairwise	NOUN
ap-1865	87	4	summable	summable	NOUN
ap-1865	87	5	subset	subset	VERB
ap-1865	87	6	f	f	PROPN
ap-1865	87	7	⊆	⊆	NUM
ap-1865	87	8	g	g	NOUN
ap-1865	87	9	(	(	PUNCT
ap-1865	87	10	a	a	DET
ap-1865	87	11	summability	summability	NOUN
ap-1865	87	12	block	block	NOUN
ap-1865	87	13	)	)	PUNCT
ap-1865	87	14	of	of	ADP
ap-1865	87	15	elements	element	NOUN
ap-1865	87	16	of	of	ADP
ap-1865	87	17	any	any	DET
ap-1865	87	18	generalized	generalized	ADJ
ap-1865	87	19	effect	effect	NOUN
ap-1865	87	20	algebra	algebra	NOUN
ap-1865	87	21	(	(	PUNCT
ap-1865	87	22	g;⊕	g;⊕	NOUN
ap-1865	87	23	,	,	PUNCT
ap-1865	87	24	0	0	NUM
ap-1865	87	25	)	)	PUNCT
ap-1865	87	26	is	be	AUX
ap-1865	87	27	a	a	DET
ap-1865	87	28	sub	sub	ADJ
ap-1865	87	29	-	-	ADJ
ap-1865	87	30	generalized	generalized	ADJ
ap-1865	87	31	effect	effect	NOUN
ap-1865	87	32	algebra	algebra	NOUN
ap-1865	87	33	of	of	ADP
ap-1865	87	34	g.	g.	PROPN
ap-1865	87	35	example	example	NOUN
ap-1865	88	1	1	1	X
ap-1865	88	2	.	.	PUNCT
ap-1865	88	3	let	let	VERB
ap-1865	88	4	h	h	PRON
ap-1865	88	5	be	be	AUX
ap-1865	88	6	an	an	DET
ap-1865	88	7	infinite	infinite	ADJ
ap-1865	88	8	-	-	PUNCT
ap-1865	88	9	dimensional	dimensional	ADJ
ap-1865	88	10	complex	complex	ADJ
ap-1865	88	11	hilbert	hilbert	NOUN
ap-1865	88	12	space	space	NOUN
ap-1865	88	13	and	and	CCONJ
ap-1865	88	14	d	d	NOUN
ap-1865	88	15	=	=	PUNCT
ap-1865	88	16	{	{	PUNCT
ap-1865	88	17	d	d	NOUN
ap-1865	88	18	⊆	⊆	NUM
ap-1865	88	19	h	h	NOUN
ap-1865	89	1	|	|	ADV
ap-1865	89	2	d	d	NOUN
ap-1865	89	3	is	be	AUX
ap-1865	89	4	a	a	DET
ap-1865	89	5	dense	dense	ADJ
ap-1865	89	6	sub	sub	NOUN
ap-1865	89	7	-	-	NOUN
ap-1865	89	8	space	space	NOUN
ap-1865	89	9	of	of	ADP
ap-1865	89	10	h	h	NOUN
ap-1865	89	11	}	}	PUNCT
ap-1865	89	12	.	.	PUNCT
ap-1865	90	1	let	let	VERB
ap-1865	90	2	vd(h	vd(h	PUNCT
ap-1865	90	3	)	)	PUNCT
ap-1865	91	1	=	=	NOUN
ap-1865	91	2	{	{	PUNCT
ap-1865	91	3	a	a	X
ap-1865	91	4	:	:	PUNCT
ap-1865	91	5	d(a)→	d(a)→	PUNCT
ap-1865	91	6	h	h	NOUN
ap-1865	91	7	∣∣	∣∣	X
ap-1865	91	8	(	(	PUNCT
ap-1865	91	9	ax	ax	NOUN
ap-1865	91	10	,	,	PUNCT
ap-1865	91	11	x	x	NOUN
ap-1865	91	12	)	)	PUNCT
ap-1865	91	13	≥	≥	X
ap-1865	91	14	0	0	NUM
ap-1865	91	15	for	for	ADP
ap-1865	91	16	all	all	DET
ap-1865	91	17	x	x	SYM
ap-1865	91	18	∈	∈	PROPN
ap-1865	91	19	d(a	d(a	PROPN
ap-1865	91	20	)	)	PUNCT
ap-1865	91	21	,	,	PUNCT
ap-1865	91	22	d(a	d(a	PROPN
ap-1865	91	23	)	)	PUNCT
ap-1865	91	24	∈	∈	PROPN
ap-1865	91	25	d	d	NOUN
ap-1865	91	26	,	,	PUNCT
ap-1865	91	27	d(a	d(a	PROPN
ap-1865	91	28	)	)	PUNCT
ap-1865	92	1	=	=	SYM
ap-1865	92	2	h	h	NOUN
ap-1865	92	3	if	if	SCONJ
ap-1865	92	4	a	a	PRON
ap-1865	92	5	is	be	AUX
ap-1865	92	6	bounded	bound	VERB
ap-1865	92	7	}	}	PUNCT
ap-1865	92	8	be	be	AUX
ap-1865	92	9	a	a	DET
ap-1865	92	10	set	set	NOUN
ap-1865	92	11	of	of	ADP
ap-1865	92	12	densely	densely	ADV
ap-1865	92	13	defined	define	VERB
ap-1865	92	14	positive	positive	ADJ
ap-1865	92	15	linear	linear	PROPN
ap-1865	92	16	operators	operator	NOUN
ap-1865	92	17	on	on	ADP
ap-1865	92	18	h.	h.	PROPN
ap-1865	92	19	in	in	ADP
ap-1865	92	20	[	[	X
ap-1865	92	21	14	14	NUM
ap-1865	92	22	]	]	X
ap-1865	92	23	it	it	PRON
ap-1865	92	24	was	be	AUX
ap-1865	92	25	shown	show	VERB
ap-1865	92	26	that	that	PRON
ap-1865	92	27	vd(h	vd(h	PUNCT
ap-1865	92	28	)	)	PUNCT
ap-1865	92	29	with	with	ADP
ap-1865	92	30	the	the	DET
ap-1865	92	31	partial	partial	ADJ
ap-1865	92	32	binary	binary	ADJ
ap-1865	92	33	operation	operation	NOUN
ap-1865	92	34	⊕d	⊕d	NOUN
ap-1865	92	35	defined	define	VERB
ap-1865	92	36	for	for	ADP
ap-1865	92	37	every	every	DET
ap-1865	92	38	a	a	PROPN
ap-1865	92	39	,	,	PUNCT
ap-1865	92	40	b	b	PROPN
ap-1865	92	41	∈	∈	PROPN
ap-1865	92	42	vd(h	vd(h	PUNCT
ap-1865	92	43	)	)	PUNCT
ap-1865	92	44	by	by	ADP
ap-1865	92	45	a⊕db	a⊕db	NOUN
ap-1865	92	46	=	=	SYM
ap-1865	92	47	a+b	a+b	X
ap-1865	92	48	(	(	PUNCT
ap-1865	92	49	the	the	DET
ap-1865	92	50	usual	usual	ADJ
ap-1865	92	51	sum	sum	NOUN
ap-1865	92	52	)	)	PUNCT
ap-1865	92	53	if	if	SCONJ
ap-1865	92	54	a	a	PRON
ap-1865	92	55	or	or	CCONJ
ap-1865	92	56	b	b	NOUN
ap-1865	92	57	is	be	AUX
ap-1865	92	58	bounded	bound	VERB
ap-1865	92	59	or	or	CCONJ
ap-1865	92	60	d(a	d(a	PROPN
ap-1865	92	61	)	)	PUNCT
ap-1865	92	62	=	=	SYM
ap-1865	92	63	d(b	d(b	X
ap-1865	92	64	)	)	PUNCT
ap-1865	92	65	if	if	SCONJ
ap-1865	92	66	a	a	PRON
ap-1865	92	67	,	,	PUNCT
ap-1865	92	68	b	b	NOUN
ap-1865	92	69	are	be	AUX
ap-1865	92	70	both	both	ADV
ap-1865	92	71	unbounded	unbounded	ADJ
ap-1865	92	72	,	,	PUNCT
ap-1865	92	73	forms	form	VERB
ap-1865	92	74	a	a	DET
ap-1865	92	75	generalized	generalized	ADJ
ap-1865	92	76	effect	effect	NOUN
ap-1865	92	77	algebra	algebra	NOUN
ap-1865	92	78	(	(	PUNCT
ap-1865	92	79	vd(h);⊕d	vd(h);⊕d	PROPN
ap-1865	92	80	,	,	PUNCT
ap-1865	92	81	0	0	NUM
ap-1865	92	82	)	)	PUNCT
ap-1865	92	83	.	.	PUNCT
ap-1865	93	1	moreover	moreover	ADV
ap-1865	93	2	,	,	PUNCT
ap-1865	93	3	for	for	ADP
ap-1865	93	4	every	every	DET
ap-1865	93	5	d	d	PROPN
ap-1865	93	6	∈	∈	PROPN
ap-1865	93	7	d	d	X
ap-1865	93	8	the	the	DET
ap-1865	93	9	set	set	NOUN
ap-1865	93	10	gd(h	gd(h	NOUN
ap-1865	93	11	)	)	PUNCT
ap-1865	93	12	=	=	PRON
ap-1865	93	13	{	{	PUNCT
ap-1865	93	14	a	a	DET
ap-1865	93	15	∈	∈	PROPN
ap-1865	93	16	vd(h	vd(h	PUNCT
ap-1865	93	17	)	)	PUNCT
ap-1865	93	18	∣∣	∣∣	X
ap-1865	93	19	a	a	PRON
ap-1865	93	20	is	be	AUX
ap-1865	93	21	bounded	bound	VERB
ap-1865	93	22	,	,	PUNCT
ap-1865	93	23	or	or	CCONJ
ap-1865	93	24	d(a	d(a	PROPN
ap-1865	93	25	)	)	PUNCT
ap-1865	94	1	=	=	SYM
ap-1865	95	1	d	d	X
ap-1865	95	2	}	}	PUNCT
ap-1865	95	3	is	be	AUX
ap-1865	95	4	a	a	DET
ap-1865	95	5	sub	sub	ADJ
ap-1865	95	6	-	-	ADJ
ap-1865	95	7	generalized	generalized	ADJ
ap-1865	95	8	effect	effect	NOUN
ap-1865	95	9	algebra	algebra	NOUN
ap-1865	95	10	of	of	ADP
ap-1865	95	11	vd(h	vd(h	PROPN
ap-1865	95	12	)	)	PUNCT
ap-1865	95	13	(	(	PUNCT
ap-1865	95	14	see	see	VERB
ap-1865	95	15	[	[	X
ap-1865	95	16	14	14	NUM
ap-1865	95	17	]	]	SYM
ap-1865	95	18	)	)	PUNCT
ap-1865	95	19	.	.	PUNCT
ap-1865	96	1	for	for	ADP
ap-1865	96	2	every	every	DET
ap-1865	96	3	a	a	PROPN
ap-1865	96	4	,	,	PUNCT
ap-1865	96	5	b	b	PROPN
ap-1865	96	6	∈	∈	PROPN
ap-1865	96	7	gd(h	gd(h	NOUN
ap-1865	96	8	)	)	PUNCT
ap-1865	96	9	,	,	PUNCT
ap-1865	96	10	d	d	PROPN
ap-1865	96	11	∈	∈	PROPN
ap-1865	96	12	d	d	X
ap-1865	96	13	by	by	ADP
ap-1865	96	14	definition	definition	NOUN
ap-1865	96	15	of	of	ADP
ap-1865	96	16	⊕	⊕	PROPN
ap-1865	96	17	the	the	DET
ap-1865	96	18	condition	condition	NOUN
ap-1865	96	19	(	(	PUNCT
ap-1865	96	20	1	1	NUM
ap-1865	96	21	.	.	PUNCT
ap-1865	96	22	)	)	PUNCT
ap-1865	96	23	is	be	AUX
ap-1865	96	24	satisfied	satisfied	ADJ
ap-1865	96	25	.	.	PUNCT
ap-1865	97	1	let	let	VERB
ap-1865	97	2	us	we	PRON
ap-1865	97	3	assume	assume	VERB
ap-1865	97	4	that	that	SCONJ
ap-1865	97	5	there	there	PRON
ap-1865	97	6	exists	exist	VERB
ap-1865	97	7	c	c	PROPN
ap-1865	97	8	∈	∈	PROPN
ap-1865	97	9	vd(h	vd(h	PUNCT
ap-1865	97	10	)	)	PUNCT
ap-1865	97	11	such	such	ADJ
ap-1865	97	12	that	that	SCONJ
ap-1865	97	13	c⊕a	c⊕a	NOUN
ap-1865	97	14	is	be	AUX
ap-1865	97	15	defined	define	VERB
ap-1865	97	16	for	for	ADP
ap-1865	97	17	all	all	DET
ap-1865	97	18	a	a	DET
ap-1865	97	19	∈	∈	PROPN
ap-1865	97	20	gd(h	gd(h	NOUN
ap-1865	97	21	)	)	PUNCT
ap-1865	97	22	.	.	PUNCT
ap-1865	98	1	further	far	ADV
ap-1865	98	2	,	,	PUNCT
ap-1865	98	3	there	there	PRON
ap-1865	98	4	exists	exist	VERB
ap-1865	98	5	some	some	DET
ap-1865	98	6	b	b	PROPN
ap-1865	98	7	∈	∈	PROPN
ap-1865	98	8	gd(h	gd(h	NOUN
ap-1865	98	9	)	)	PUNCT
ap-1865	98	10	with	with	ADP
ap-1865	98	11	d(b	d(b	NOUN
ap-1865	98	12	)	)	PUNCT
ap-1865	98	13	=	=	SYM
ap-1865	99	1	d	d	PROPN
ap-1865	99	2	6=	6=	NUM
ap-1865	99	3	h	h	NOUN
ap-1865	99	4	(	(	PUNCT
ap-1865	99	5	if	if	SCONJ
ap-1865	99	6	not	not	PART
ap-1865	99	7	,	,	PUNCT
ap-1865	99	8	then	then	ADV
ap-1865	99	9	d	d	PROPN
ap-1865	99	10	=	=	SYM
ap-1865	99	11	h	h	NOUN
ap-1865	99	12	)	)	PUNCT
ap-1865	99	13	,	,	PUNCT
ap-1865	99	14	hence	hence	ADV
ap-1865	99	15	by	by	ADP
ap-1865	99	16	the	the	DET
ap-1865	99	17	hellinger	hellinger	NOUN
ap-1865	99	18	-	-	PUNCT
ap-1865	99	19	toeplitz	toeplitz	NOUN
ap-1865	99	20	theorem	theorem	ADJ
ap-1865	99	21	b	b	NOUN
ap-1865	99	22	is	be	AUX
ap-1865	99	23	unbounded	unbounded	ADJ
ap-1865	99	24	.	.	PUNCT
ap-1865	100	1	since	since	SCONJ
ap-1865	100	2	c	c	PROPN
ap-1865	100	3	⊕	⊕	PROPN
ap-1865	100	4	b	b	PROPN
ap-1865	100	5	is	be	AUX
ap-1865	100	6	defined	define	VERB
ap-1865	100	7	we	we	PRON
ap-1865	100	8	have	have	VERB
ap-1865	100	9	d(c	d(c	PROPN
ap-1865	100	10	)	)	PUNCT
ap-1865	101	1	=	=	SYM
ap-1865	101	2	d(b	d(b	PROPN
ap-1865	101	3	)	)	PUNCT
ap-1865	101	4	,	,	PUNCT
ap-1865	101	5	that	that	PRON
ap-1865	101	6	is	be	AUX
ap-1865	101	7	c	c	NOUN
ap-1865	101	8	∈	∈	PROPN
ap-1865	101	9	gd(h	gd(h	NOUN
ap-1865	101	10	)	)	PUNCT
ap-1865	101	11	.	.	PUNCT
ap-1865	102	1	therefore	therefore	ADV
ap-1865	102	2	sets	set	VERB
ap-1865	102	3	gd(h	gd(h	NOUN
ap-1865	102	4	)	)	PUNCT
ap-1865	102	5	are	be	AUX
ap-1865	102	6	for	for	ADP
ap-1865	102	7	d	d	PROPN
ap-1865	102	8	6=	6=	PROPN
ap-1865	102	9	h	h	PROPN
ap-1865	102	10	maximal	maximal	ADJ
ap-1865	102	11	pairwise	pairwise	NOUN
ap-1865	102	12	summable	summable	ADJ
ap-1865	102	13	sub	sub	ADJ
ap-1865	102	14	-	-	ADJ
ap-1865	102	15	generalized	generalized	ADJ
ap-1865	102	16	effect	effect	NOUN
ap-1865	102	17	algebras	algebra	NOUN
ap-1865	102	18	.	.	PUNCT
ap-1865	102	19	example	example	NOUN
ap-1865	103	1	2	2	NUM
ap-1865	103	2	.	.	PUNCT
ap-1865	103	3	according	accord	VERB
ap-1865	103	4	to	to	ADP
ap-1865	103	5	[	[	X
ap-1865	103	6	1	1	NUM
ap-1865	103	7	]	]	PUNCT
ap-1865	103	8	,	,	PUNCT
ap-1865	103	9	every	every	DET
ap-1865	103	10	positive	positive	ADJ
ap-1865	103	11	linear	linear	NOUN
ap-1865	103	12	operator	operator	NOUN
ap-1865	103	13	a	a	DET
ap-1865	103	14	∈	∈	NOUN
ap-1865	103	15	vd(h	vd(h	PUNCT
ap-1865	103	16	)	)	PUNCT
ap-1865	103	17	uniquely	uniquely	ADV
ap-1865	103	18	determines	determine	VERB
ap-1865	103	19	a	a	DET
ap-1865	103	20	positive	positive	ADJ
ap-1865	103	21	sesquilinear	sesquilinear	NOUN
ap-1865	103	22	form	form	NOUN
ap-1865	103	23	ta	ta	X
ap-1865	103	24	on	on	ADP
ap-1865	103	25	d(ta	d(ta	NUM
ap-1865	103	26	)	)	PUNCT
ap-1865	103	27	=	=	SYM
ap-1865	104	1	d(a	d(a	PROPN
ap-1865	104	2	)	)	PUNCT
ap-1865	104	3	by	by	ADP
ap-1865	104	4	ta(x	ta(x	NOUN
ap-1865	104	5	,	,	PUNCT
ap-1865	104	6	y	y	NOUN
ap-1865	104	7	)	)	PUNCT
ap-1865	104	8	=	=	SYM
ap-1865	104	9	(	(	PUNCT
ap-1865	104	10	ax	ax	NOUN
ap-1865	104	11	,	,	PUNCT
ap-1865	104	12	y	y	PROPN
ap-1865	104	13	)	)	PUNCT
ap-1865	104	14	.	.	PUNCT
ap-1865	105	1	let	let	VERB
ap-1865	105	2	us	we	PRON
ap-1865	105	3	denote	denote	VERB
ap-1865	105	4	a	a	DET
ap-1865	105	5	set	set	NOUN
ap-1865	105	6	of	of	ADP
ap-1865	105	7	all	all	DET
ap-1865	105	8	such	such	ADJ
ap-1865	105	9	sesquilinear	sesquilinear	ADJ
ap-1865	105	10	forms	form	NOUN
ap-1865	105	11	by	by	ADP
ap-1865	105	12	fd(h	fd(h	NOUN
ap-1865	105	13	)	)	PUNCT
ap-1865	105	14	,	,	PUNCT
ap-1865	105	15	namely	namely	ADV
ap-1865	105	16	fd(h	fd(h	PUNCT
ap-1865	105	17	)	)	PUNCT
ap-1865	106	1	=	=	PRON
ap-1865	106	2	{	{	PUNCT
ap-1865	106	3	t	t	X
ap-1865	106	4	:	:	PUNCT
ap-1865	106	5	d(t)×d(t)→	d(t)×d(t)→	NOUN
ap-1865	106	6	h	h	NOUN
ap-1865	106	7	∣∣	∣∣	VERB
ap-1865	106	8	there	there	PRON
ap-1865	106	9	exists	exist	VERB
ap-1865	106	10	a	a	DET
ap-1865	106	11	∈	∈	NOUN
ap-1865	106	12	vd(h	vd(h	PUNCT
ap-1865	106	13	)	)	PUNCT
ap-1865	106	14	with	with	ADP
ap-1865	106	15	d(a	d(a	PROPN
ap-1865	106	16	)	)	PUNCT
ap-1865	106	17	=	=	SYM
ap-1865	106	18	d(t	d(t	PROPN
ap-1865	106	19	)	)	PUNCT
ap-1865	106	20	and	and	CCONJ
ap-1865	106	21	t(x	t(x	PROPN
ap-1865	106	22	,	,	PUNCT
ap-1865	106	23	y	y	NOUN
ap-1865	106	24	)	)	PUNCT
ap-1865	106	25	=	=	SYM
ap-1865	106	26	(	(	PUNCT
ap-1865	106	27	ax	ax	NOUN
ap-1865	106	28	,	,	PUNCT
ap-1865	106	29	y	y	PROPN
ap-1865	106	30	)	)	PUNCT
ap-1865	106	31	for	for	ADP
ap-1865	106	32	all	all	DET
ap-1865	106	33	x	x	NOUN
ap-1865	106	34	,	,	PUNCT
ap-1865	106	35	y	y	PROPN
ap-1865	106	36	∈	∈	PROPN
ap-1865	106	37	d(t	d(t	PROPN
ap-1865	106	38	)	)	PUNCT
ap-1865	106	39	}	}	PUNCT
ap-1865	106	40	.	.	PUNCT
ap-1865	107	1	on	on	ADP
ap-1865	107	2	the	the	DET
ap-1865	107	3	set	set	NOUN
ap-1865	107	4	fd(h	fd(h	NUM
ap-1865	107	5	)	)	PUNCT
ap-1865	107	6	,	,	PUNCT
ap-1865	107	7	we	we	PRON
ap-1865	107	8	can	can	AUX
ap-1865	107	9	define	define	VERB
ap-1865	107	10	a	a	DET
ap-1865	107	11	partial	partial	ADJ
ap-1865	107	12	sum	sum	NOUN
ap-1865	107	13	t⊕	t⊕	NOUN
ap-1865	107	14	s	s	NOUN
ap-1865	107	15	for	for	ADP
ap-1865	107	16	any	any	DET
ap-1865	107	17	t	t	NOUN
ap-1865	107	18	,	,	PUNCT
ap-1865	107	19	s	s	PART
ap-1865	107	20	∈	∈	PROPN
ap-1865	107	21	fd(h	fd(h	PUNCT
ap-1865	107	22	)	)	PUNCT
ap-1865	107	23	in	in	ADP
ap-1865	107	24	the	the	DET
ap-1865	107	25	following	following	ADJ
ap-1865	107	26	way	way	NOUN
ap-1865	107	27	:	:	PUNCT
ap-1865	107	28	t	t	PROPN
ap-1865	107	29	⊕	⊕	PROPN
ap-1865	107	30	s	s	PART
ap-1865	107	31	exists	exist	VERB
ap-1865	107	32	whenever	whenever	SCONJ
ap-1865	107	33	d(t	d(t	NOUN
ap-1865	107	34	)	)	PUNCT
ap-1865	107	35	=	=	SYM
ap-1865	108	1	d(s	d(s	PROPN
ap-1865	108	2	)	)	PUNCT
ap-1865	108	3	or	or	CCONJ
ap-1865	108	4	t	t	PROPN
ap-1865	108	5	or	or	CCONJ
ap-1865	108	6	s	s	NOUN
ap-1865	108	7	is	be	AUX
ap-1865	108	8	bounded	bound	VERB
ap-1865	108	9	(	(	PUNCT
ap-1865	108	10	then	then	ADV
ap-1865	108	11	d(t	d(t	PROPN
ap-1865	108	12	⊕	⊕	PROPN
ap-1865	108	13	s	s	PART
ap-1865	108	14	)	)	PUNCT
ap-1865	108	15	=	=	SYM
ap-1865	108	16	d(t	d(t	PROPN
ap-1865	108	17	)	)	PUNCT
ap-1865	108	18	∩	∩	NOUN
ap-1865	108	19	d(s	d(s	PROPN
ap-1865	108	20	)	)	PUNCT
ap-1865	108	21	)	)	PUNCT
ap-1865	108	22	by	by	ADP
ap-1865	108	23	(	(	PUNCT
ap-1865	108	24	t	t	PROPN
ap-1865	108	25	⊕	⊕	PROPN
ap-1865	108	26	s)(x	s)(x	PROPN
ap-1865	108	27	,	,	PUNCT
ap-1865	108	28	y	y	NOUN
ap-1865	108	29	)	)	PUNCT
ap-1865	108	30	=	=	SYM
ap-1865	109	1	t(x	t(x	PROPN
ap-1865	109	2	,	,	PUNCT
ap-1865	109	3	y	y	NOUN
ap-1865	109	4	)	)	PUNCT
ap-1865	109	5	+	+	CCONJ
ap-1865	109	6	s(x	s(x	PROPN
ap-1865	109	7	,	,	PUNCT
ap-1865	109	8	y	y	NOUN
ap-1865	109	9	)	)	PUNCT
ap-1865	109	10	for	for	ADP
ap-1865	109	11	all	all	DET
ap-1865	109	12	x	x	NOUN
ap-1865	109	13	,	,	PUNCT
ap-1865	109	14	y	y	PROPN
ap-1865	109	15	∈	∈	PROPN
ap-1865	109	16	d(t)∩d(s	d(t)∩d(s	PROPN
ap-1865	109	17	)	)	PUNCT
ap-1865	109	18	.	.	PUNCT
ap-1865	110	1	it	it	PRON
ap-1865	110	2	is	be	AUX
ap-1865	110	3	easy	easy	ADJ
ap-1865	110	4	to	to	PART
ap-1865	110	5	show	show	VERB
ap-1865	110	6	that	that	SCONJ
ap-1865	110	7	(	(	PUNCT
ap-1865	110	8	fd(h);⊕	fd(h);⊕	NOUN
ap-1865	110	9	,	,	PUNCT
ap-1865	110	10	0	0	NUM
ap-1865	110	11	)	)	PUNCT
ap-1865	110	12	is	be	AUX
ap-1865	110	13	a	a	DET
ap-1865	110	14	generalized	generalized	ADJ
ap-1865	110	15	effect	effect	NOUN
ap-1865	110	16	algebra	algebra	NOUN
ap-1865	110	17	isomorphic	isomorphic	ADJ
ap-1865	110	18	to	to	ADP
ap-1865	110	19	(	(	PUNCT
ap-1865	110	20	vd(h);⊕d	vd(h);⊕d	PROPN
ap-1865	110	21	,	,	PUNCT
ap-1865	110	22	0	0	NUM
ap-1865	110	23	)	)	PUNCT
ap-1865	110	24	.	.	PUNCT
ap-1865	111	1	as	as	SCONJ
ap-1865	111	2	in	in	ADP
ap-1865	111	3	the	the	DET
ap-1865	111	4	previous	previous	ADJ
ap-1865	111	5	example	example	NOUN
ap-1865	111	6	,	,	PUNCT
ap-1865	111	7	maximal	maximal	ADJ
ap-1865	111	8	pairwise	pairwise	NOUN
ap-1865	111	9	summable	summable	ADJ
ap-1865	111	10	subsets	subset	NOUN
ap-1865	111	11	are	be	AUX
ap-1865	111	12	md(h	md(h	NUM
ap-1865	111	13	)	)	PUNCT
ap-1865	112	1	=	=	PRON
ap-1865	112	2	{	{	PUNCT
ap-1865	112	3	t	t	PROPN
ap-1865	112	4	∈	∈	PROPN
ap-1865	112	5	f(h	f(h	PROPN
ap-1865	112	6	)	)	PUNCT
ap-1865	112	7	∣∣	∣∣	PROPN
ap-1865	112	8	t	t	PROPN
ap-1865	112	9	is	be	AUX
ap-1865	112	10	bounded	bound	VERB
ap-1865	112	11	,	,	PUNCT
ap-1865	112	12	or	or	CCONJ
ap-1865	112	13	d(t	d(t	PROPN
ap-1865	112	14	)	)	PUNCT
ap-1865	112	15	=	=	SYM
ap-1865	113	1	d	d	NOUN
ap-1865	113	2	}	}	PUNCT
ap-1865	113	3	,	,	PUNCT
ap-1865	113	4	hence	hence	ADV
ap-1865	113	5	they	they	PRON
ap-1865	113	6	are	be	AUX
ap-1865	113	7	sub	sub	ADJ
ap-1865	113	8	-	-	ADJ
ap-1865	113	9	generalized	generalized	ADJ
ap-1865	113	10	effect	effect	NOUN
ap-1865	113	11	algebras	algebra	NOUN
ap-1865	113	12	of	of	ADP
ap-1865	113	13	fd(h	fd(h	NOUN
ap-1865	113	14	)	)	PUNCT
ap-1865	113	15	.	.	PUNCT
ap-1865	114	1	example	example	NOUN
ap-1865	115	1	3	3	X
ap-1865	115	2	.	.	PUNCT
ap-1865	115	3	let	let	VERB
ap-1865	115	4	us	we	PRON
ap-1865	115	5	consider	consider	VERB
ap-1865	115	6	chang	chang	PROPN
ap-1865	115	7	’s	’s	PART
ap-1865	115	8	effect	effect	NOUN
ap-1865	115	9	algebra	algebra	NOUN
ap-1865	115	10	(	(	PUNCT
ap-1865	115	11	e;⊕	e;⊕	ADJ
ap-1865	115	12	,	,	PUNCT
ap-1865	115	13	0	0	NUM
ap-1865	115	14	,	,	PUNCT
ap-1865	115	15	1	1	NUM
ap-1865	115	16	)	)	PUNCT
ap-1865	115	17	which	which	PRON
ap-1865	115	18	is	be	AUX
ap-1865	115	19	defined	define	VERB
ap-1865	115	20	by	by	ADP
ap-1865	115	21	e	e	X
ap-1865	115	22	=	=	PUNCT
ap-1865	115	23	{	{	PUNCT
ap-1865	115	24	0	0	NUM
ap-1865	115	25	,	,	PUNCT
ap-1865	115	26	a	a	PRON
ap-1865	115	27	,	,	PUNCT
ap-1865	115	28	2a	2a	NUM
ap-1865	115	29	,	,	PUNCT
ap-1865	115	30	.	.	PUNCT
ap-1865	115	31	.	.	PUNCT
ap-1865	116	1	.	.	PUNCT
ap-1865	117	1	,	,	PUNCT
ap-1865	117	2	(	(	PUNCT
ap-1865	117	3	2a)′	2a)′	NUM
ap-1865	117	4	,	,	PUNCT
ap-1865	117	5	a	a	DET
ap-1865	117	6	′	′	NOUN
ap-1865	117	7	,	,	PUNCT
ap-1865	117	8	1	1	NUM
ap-1865	117	9	}	}	PUNCT
ap-1865	117	10	.	.	PUNCT
ap-1865	118	1	consider	consider	VERB
ap-1865	118	2	its	its	PRON
ap-1865	118	3	subset	subset	NOUN
ap-1865	118	4	f	f	PROPN
ap-1865	118	5	=	=	PUNCT
ap-1865	118	6	{	{	PUNCT
ap-1865	118	7	0	0	NUM
ap-1865	118	8	,	,	PUNCT
ap-1865	118	9	a	a	PRON
ap-1865	118	10	,	,	PUNCT
ap-1865	118	11	2a	2a	NUM
ap-1865	118	12	,	,	PUNCT
ap-1865	118	13	.	.	PUNCT
ap-1865	118	14	.	.	PUNCT
ap-1865	119	1	.	.	PUNCT
ap-1865	120	1	}	}	PUNCT
ap-1865	121	1	⊆	⊆	NUM
ap-1865	121	2	g.	g.	NOUN
ap-1865	121	3	clearly	clearly	ADV
ap-1865	121	4	f	f	X
ap-1865	121	5	satisfies	satisfy	VERB
ap-1865	121	6	condition	condition	NOUN
ap-1865	121	7	(	(	PUNCT
ap-1865	121	8	1	1	NUM
ap-1865	121	9	.	.	NUM
ap-1865	121	10	)	)	PUNCT
ap-1865	121	11	.	.	PUNCT
ap-1865	122	1	since	since	SCONJ
ap-1865	122	2	any	any	DET
ap-1865	122	3	element	element	NOUN
ap-1865	122	4	of	of	ADP
ap-1865	122	5	the	the	DET
ap-1865	122	6	form	form	NOUN
ap-1865	122	7	(	(	PUNCT
ap-1865	122	8	n0a)′	n0a)′	X
ap-1865	122	9	is	be	AUX
ap-1865	122	10	summable	summable	ADJ
ap-1865	122	11	only	only	ADV
ap-1865	122	12	with	with	ADP
ap-1865	122	13	elements	element	NOUN
ap-1865	122	14	na	na	NOUN
ap-1865	122	15	for	for	ADP
ap-1865	122	16	n	n	DET
ap-1865	122	17	≤	≤	PROPN
ap-1865	122	18	n0	n0	NUM
ap-1865	122	19	,	,	PUNCT
ap-1865	122	20	hence	hence	ADV
ap-1865	122	21	(	(	PUNCT
ap-1865	122	22	n0a)′	n0a)′	NUM
ap-1865	122	23	/∈	/∈	PUNCT
ap-1865	122	24	f	f	NOUN
ap-1865	122	25	which	which	PRON
ap-1865	122	26	gives	give	VERB
ap-1865	122	27	that	that	PRON
ap-1865	122	28	(	(	PUNCT
ap-1865	122	29	2	2	NUM
ap-1865	122	30	.	.	PUNCT
ap-1865	122	31	)	)	PUNCT
ap-1865	122	32	is	be	AUX
ap-1865	122	33	satisfied	satisfied	ADJ
ap-1865	122	34	as	as	ADV
ap-1865	122	35	well	well	ADV
ap-1865	122	36	.	.	PUNCT
ap-1865	123	1	3	3	X
ap-1865	123	2	.	.	X
ap-1865	123	3	intervals	interval	NOUN
ap-1865	123	4	in	in	ADP
ap-1865	123	5	pairwise	pairwise	NOUN
ap-1865	123	6	summable	summable	ADJ
ap-1865	123	7	generalized	generalized	ADJ
ap-1865	123	8	effect	effect	NOUN
ap-1865	123	9	algebras	algebra	VERB
ap-1865	123	10	the	the	DET
ap-1865	123	11	significant	significant	ADJ
ap-1865	123	12	property	property	NOUN
ap-1865	123	13	of	of	ADP
ap-1865	123	14	any	any	DET
ap-1865	123	15	generalized	generalized	ADJ
ap-1865	123	16	effect	effect	NOUN
ap-1865	123	17	algebra	algebra	NOUN
ap-1865	123	18	(	(	PUNCT
ap-1865	123	19	g;⊕	g;⊕	NOUN
ap-1865	123	20	,	,	PUNCT
ap-1865	123	21	0	0	NUM
ap-1865	123	22	,	,	PUNCT
ap-1865	123	23	q	q	X
ap-1865	123	24	)	)	PUNCT
ap-1865	123	25	is	be	AUX
ap-1865	123	26	the	the	DET
ap-1865	123	27	fact	fact	NOUN
ap-1865	123	28	that	that	SCONJ
ap-1865	123	29	for	for	ADP
ap-1865	123	30	every	every	DET
ap-1865	123	31	non	non	ADJ
ap-1865	123	32	-	-	ADJ
ap-1865	123	33	zero	zero	NUM
ap-1865	123	34	element	element	NOUN
ap-1865	123	35	q	q	PROPN
ap-1865	123	36	∈	∈	PROPN
ap-1865	123	37	g	g	NOUN
ap-1865	123	38	,	,	PUNCT
ap-1865	123	39	the	the	DET
ap-1865	123	40	interval	interval	NOUN
ap-1865	123	41	[	[	X
ap-1865	123	42	0	0	NUM
ap-1865	123	43	,	,	PUNCT
ap-1865	123	44	q]g	q]g	ADV
ap-1865	123	45	=	=	PUNCT
ap-1865	123	46	{	{	PUNCT
ap-1865	123	47	a	a	DET
ap-1865	123	48	∈	∈	PROPN
ap-1865	123	49	g	g	NOUN
ap-1865	123	50	|	|	ADV
ap-1865	123	51	there	there	PRON
ap-1865	123	52	exists	exist	VERB
ap-1865	123	53	c	c	PROPN
ap-1865	123	54	∈	∈	PROPN
ap-1865	123	55	g	g	PROPN
ap-1865	123	56	with	with	ADP
ap-1865	123	57	a⊕	a⊕	PROPN
ap-1865	124	1	c	c	PROPN
ap-1865	124	2	=	=	PUNCT
ap-1865	124	3	q	q	X
ap-1865	124	4	}	}	PUNCT
ap-1865	124	5	is	be	AUX
ap-1865	124	6	an	an	DET
ap-1865	124	7	effect	effect	NOUN
ap-1865	124	8	algebra	algebra	NOUN
ap-1865	124	9	(	(	PUNCT
ap-1865	124	10	[	[	X
ap-1865	124	11	0	0	NUM
ap-1865	124	12	,	,	PUNCT
ap-1865	124	13	q]g;⊕q	q]g;⊕q	PROPN
ap-1865	124	14	,	,	PUNCT
ap-1865	124	15	0	0	NUM
ap-1865	124	16	)	)	PUNCT
ap-1865	124	17	.	.	PUNCT
ap-1865	125	1	the	the	DET
ap-1865	125	2	partial	partial	ADJ
ap-1865	125	3	operation	operation	NOUN
ap-1865	125	4	⊕q	⊕q	NOUN
ap-1865	125	5	is	be	AUX
ap-1865	125	6	defined	define	VERB
ap-1865	125	7	by	by	ADP
ap-1865	125	8	a⊕q	a⊕q	PROPN
ap-1865	125	9	b	b	PROPN
ap-1865	125	10	exists	exist	VERB
ap-1865	125	11	iff	iff	PROPN
ap-1865	125	12	a⊕	a⊕	PROPN
ap-1865	125	13	b	b	PROPN
ap-1865	125	14	≤	≤	PROPN
ap-1865	126	1	q	q	NOUN
ap-1865	127	1	and	and	CCONJ
ap-1865	127	2	then	then	ADV
ap-1865	127	3	a⊕q	a⊕q	PROPN
ap-1865	127	4	b	b	PROPN
ap-1865	128	1	=	=	SYM
ap-1865	128	2	a⊕	a⊕	PROPN
ap-1865	128	3	b.	b.	PROPN
ap-1865	128	4	further	far	ADV
ap-1865	128	5	,	,	PUNCT
ap-1865	128	6	let	let	VERB
ap-1865	128	7	us	we	PRON
ap-1865	128	8	investigate	investigate	VERB
ap-1865	128	9	intervals	interval	NOUN
ap-1865	128	10	in	in	ADP
ap-1865	128	11	pairwise	pairwise	NOUN
ap-1865	128	12	summable	summable	ADJ
ap-1865	128	13	generalized	generalized	ADJ
ap-1865	128	14	effect	effect	NOUN
ap-1865	128	15	algebras	algebra	NOUN
ap-1865	128	16	.	.	PUNCT
ap-1865	129	1	namely	namely	ADV
ap-1865	129	2	,	,	PUNCT
ap-1865	129	3	we	we	PRON
ap-1865	129	4	are	be	AUX
ap-1865	129	5	going	go	VERB
ap-1865	129	6	to	to	PART
ap-1865	129	7	show	show	VERB
ap-1865	129	8	that	that	SCONJ
ap-1865	129	9	if	if	SCONJ
ap-1865	129	10	g	g	NOUN
ap-1865	129	11	with	with	ADP
ap-1865	129	12	derived	derived	ADJ
ap-1865	129	13	≤	≤	NUM
ap-1865	129	14	is	be	AUX
ap-1865	129	15	a	a	DET
ap-1865	129	16	lattice	lattice	NOUN
ap-1865	129	17	,	,	PUNCT
ap-1865	129	18	then	then	ADV
ap-1865	129	19	these	these	DET
ap-1865	129	20	intervals	interval	NOUN
ap-1865	129	21	are	be	AUX
ap-1865	129	22	mv	mv	ADJ
ap-1865	129	23	-	-	PUNCT
ap-1865	129	24	effect	effect	NOUN
ap-1865	129	25	algebras	algebra	NOUN
ap-1865	129	26	(	(	PUNCT
ap-1865	129	27	hence	hence	ADV
ap-1865	129	28	can	can	AUX
ap-1865	129	29	be	be	AUX
ap-1865	129	30	organized	organize	VERB
ap-1865	129	31	into	into	ADP
ap-1865	129	32	mv	mv	NOUN
ap-1865	129	33	-	-	PUNCT
ap-1865	129	34	algebras	algebra	NOUN
ap-1865	129	35	)	)	PUNCT
ap-1865	129	36	.	.	PUNCT
ap-1865	130	1	we	we	PRON
ap-1865	130	2	start	start	VERB
ap-1865	130	3	with	with	ADP
ap-1865	130	4	the	the	DET
ap-1865	130	5	observation	observation	NOUN
ap-1865	130	6	that	that	SCONJ
ap-1865	130	7	every	every	DET
ap-1865	130	8	pairwise	pairwise	NOUN
ap-1865	130	9	summable	summable	ADJ
ap-1865	130	10	generalized	generalized	ADJ
ap-1865	130	11	effect	effect	NOUN
ap-1865	130	12	algebra	algebra	NOUN
ap-1865	130	13	(	(	PUNCT
ap-1865	130	14	g;⊕	g;⊕	NOUN
ap-1865	130	15	,	,	PUNCT
ap-1865	130	16	0	0	NUM
ap-1865	130	17	)	)	PUNCT
ap-1865	130	18	is	be	AUX
ap-1865	130	19	a	a	DET
ap-1865	130	20	generalized	generalized	ADJ
ap-1865	130	21	mv	mv	NOUN
ap-1865	130	22	-	-	PUNCT
ap-1865	130	23	effect	effect	NOUN
ap-1865	130	24	algebra	algebra	NOUN
ap-1865	130	25	if	if	SCONJ
ap-1865	130	26	and	and	CCONJ
ap-1865	130	27	only	only	ADV
ap-1865	130	28	if	if	SCONJ
ap-1865	130	29	(	(	PUNCT
ap-1865	130	30	g,≤	g,≤	NOUN
ap-1865	130	31	)	)	PUNCT
ap-1865	130	32	is	be	AUX
ap-1865	130	33	a	a	DET
ap-1865	130	34	lattice	lattice	NOUN
ap-1865	130	35	.	.	PUNCT
ap-1865	131	1	recall	recall	VERB
ap-1865	131	2	that	that	SCONJ
ap-1865	131	3	a	a	DET
ap-1865	131	4	non	non	ADJ
ap-1865	131	5	-	-	ADJ
ap-1865	131	6	void	void	ADJ
ap-1865	131	7	subset	subset	VERB
ap-1865	132	1	i	i	PRON
ap-1865	132	2	⊆	⊆	NUM
ap-1865	132	3	l	l	NOUN
ap-1865	132	4	of	of	ADP
ap-1865	132	5	a	a	DET
ap-1865	132	6	partially	partially	ADV
ap-1865	132	7	ordered	order	VERB
ap-1865	132	8	set	set	NOUN
ap-1865	132	9	(	(	PUNCT
ap-1865	132	10	l,≤	l,≤	PROPN
ap-1865	132	11	)	)	PUNCT
ap-1865	132	12	is	be	AUX
ap-1865	132	13	an	an	DET
ap-1865	132	14	order	order	NOUN
ap-1865	132	15	ideal	ideal	NOUN
ap-1865	132	16	if	if	SCONJ
ap-1865	132	17	a	a	DET
ap-1865	132	18	∈	∈	PROPN
ap-1865	132	19	l	l	NOUN
ap-1865	132	20	,	,	PUNCT
ap-1865	132	21	b	b	X
ap-1865	132	22	∈	∈	PROPN
ap-1865	132	23	i	i	PRON
ap-1865	132	24	and	and	CCONJ
ap-1865	132	25	a	a	DET
ap-1865	132	26	≤	≤	NUM
ap-1865	132	27	b	b	NOUN
ap-1865	132	28	implies	imply	VERB
ap-1865	132	29	a	a	DET
ap-1865	132	30	∈	∈	PROPN
ap-1865	132	31	i.	i.	NOUN
ap-1865	132	32	let	let	VERB
ap-1865	132	33	(	(	PUNCT
ap-1865	132	34	p	p	NOUN
ap-1865	132	35	;	;	PUNCT
ap-1865	132	36	≤	≤	NUM
ap-1865	132	37	,	,	PUNCT
ap-1865	132	38	0	0	NUM
ap-1865	132	39	)	)	PUNCT
ap-1865	132	40	be	be	AUX
ap-1865	132	41	a	a	DET
ap-1865	132	42	generalized	generalized	ADJ
ap-1865	132	43	effect	effect	NOUN
ap-1865	132	44	algebra	algebra	NOUN
ap-1865	132	45	.	.	PUNCT
ap-1865	133	1	let	let	VERB
ap-1865	133	2	p	p	PRON
ap-1865	133	3	∗	∗	NOUN
ap-1865	133	4	be	be	AUX
ap-1865	133	5	a	a	DET
ap-1865	133	6	set	set	VERB
ap-1865	133	7	disjoint	disjoint	NOUN
ap-1865	133	8	from	from	ADP
ap-1865	133	9	p	p	NOUN
ap-1865	133	10	with	with	ADP
ap-1865	133	11	the	the	DET
ap-1865	133	12	same	same	ADJ
ap-1865	133	13	cardinality	cardinality	NOUN
ap-1865	133	14	.	.	PUNCT
ap-1865	134	1	consider	consider	VERB
ap-1865	134	2	a	a	DET
ap-1865	134	3	bijection	bijection	NOUN
ap-1865	134	4	a	a	DET
ap-1865	134	5	→	→	SYM
ap-1865	134	6	a∗	a∗	NOUN
ap-1865	134	7	from	from	ADP
ap-1865	134	8	p	p	NOUN
ap-1865	134	9	onto	onto	ADP
ap-1865	134	10	p	p	NOUN
ap-1865	134	11	∗	∗	NOUN
ap-1865	134	12	and	and	CCONJ
ap-1865	134	13	let	let	VERB
ap-1865	134	14	us	we	PRON
ap-1865	134	15	denote	denote	VERB
ap-1865	134	16	p	p	X
ap-1865	134	17	∪̇p	∪̇p	PROPN
ap-1865	134	18	∗	∗	NOUN
ap-1865	134	19	by	by	ADP
ap-1865	134	20	e.	e.	PROPN
ap-1865	134	21	further	far	ADV
ap-1865	134	22	define	define	VERB
ap-1865	134	23	a	a	DET
ap-1865	134	24	partial	partial	ADJ
ap-1865	134	25	binary	binary	ADJ
ap-1865	134	26	operation	operation	NOUN
ap-1865	134	27	⊕∗	⊕∗	VERB
ap-1865	134	28	on	on	ADP
ap-1865	134	29	e	e	NOUN
ap-1865	134	30	by	by	ADP
ap-1865	134	31	the	the	DET
ap-1865	134	32	following	follow	VERB
ap-1865	134	33	rules	rule	NOUN
ap-1865	134	34	.	.	PUNCT
ap-1865	135	1	for	for	ADP
ap-1865	135	2	a	a	DET
ap-1865	135	3	,	,	PUNCT
ap-1865	135	4	b	b	PROPN
ap-1865	135	5	∈	∈	PROPN
ap-1865	135	6	p	p	X
ap-1865	135	7	(	(	PUNCT
ap-1865	135	8	1	1	NUM
ap-1865	135	9	.	.	PUNCT
ap-1865	135	10	)	)	PUNCT
ap-1865	136	1	a	a	DET
ap-1865	136	2	⊕∗	⊕∗	NOUN
ap-1865	136	3	b	b	NOUN
ap-1865	136	4	is	be	AUX
ap-1865	136	5	defined	define	VERB
ap-1865	136	6	if	if	SCONJ
ap-1865	136	7	and	and	CCONJ
ap-1865	136	8	only	only	ADV
ap-1865	136	9	if	if	SCONJ
ap-1865	136	10	a	a	DET
ap-1865	136	11	⊕	⊕	PROPN
ap-1865	136	12	b	b	PROPN
ap-1865	136	13	is	be	AUX
ap-1865	136	14	defined	define	VERB
ap-1865	136	15	,	,	PUNCT
ap-1865	136	16	and	and	CCONJ
ap-1865	136	17	a⊕∗	a⊕∗	ADJ
ap-1865	136	18	b	b	X
ap-1865	136	19	=	=	SYM
ap-1865	136	20	a⊕	a⊕	PROPN
ap-1865	136	21	b	b	NOUN
ap-1865	136	22	,	,	PUNCT
ap-1865	136	23	(	(	PUNCT
ap-1865	136	24	2	2	NUM
ap-1865	136	25	.	.	PUNCT
ap-1865	136	26	)	)	PUNCT
ap-1865	137	1	b∗⊕∗	b∗⊕∗	VERB
ap-1865	137	2	a	a	DET
ap-1865	137	3	and	and	CCONJ
ap-1865	137	4	a⊕∗	a⊕∗	ADJ
ap-1865	137	5	b∗	b∗	ADJ
ap-1865	137	6	are	be	AUX
ap-1865	137	7	defined	define	VERB
ap-1865	137	8	if	if	SCONJ
ap-1865	137	9	and	and	CCONJ
ap-1865	137	10	only	only	ADV
ap-1865	138	1	if	if	SCONJ
ap-1865	138	2	b	b	PROPN
ap-1865	138	3	a	a	PRON
ap-1865	138	4	is	be	AUX
ap-1865	138	5	defined	define	VERB
ap-1865	138	6	and	and	CCONJ
ap-1865	138	7	then	then	ADV
ap-1865	138	8	b∗	b∗	ADV
ap-1865	138	9	⊕∗	⊕∗	VERB
ap-1865	138	10	a	a	PRON
ap-1865	138	11	=	=	X
ap-1865	138	12	(	(	PUNCT
ap-1865	138	13	b	b	X
ap-1865	138	14	a)∗	a)∗	PROPN
ap-1865	138	15	=	=	SYM
ap-1865	138	16	a⊕∗	a⊕∗	ADJ
ap-1865	138	17	b∗.	b∗.	NOUN
ap-1865	138	18	theorem	theorem	VERB
ap-1865	138	19	2	2	NUM
ap-1865	138	20	(	(	PUNCT
ap-1865	138	21	[	[	X
ap-1865	138	22	2	2	NUM
ap-1865	138	23	,	,	PUNCT
ap-1865	138	24	p.	p.	NOUN
ap-1865	138	25	18	18	NUM
ap-1865	138	26	]	]	PUNCT
ap-1865	138	27	)	)	PUNCT
ap-1865	138	28	.	.	PUNCT
ap-1865	139	1	for	for	ADP
ap-1865	139	2	every	every	DET
ap-1865	139	3	generalized	generalized	ADJ
ap-1865	139	4	effect	effect	NOUN
ap-1865	139	5	algebra	algebra	NOUN
ap-1865	139	6	p	p	NOUN
ap-1865	139	7	and	and	CCONJ
ap-1865	139	8	e	e	NOUN
ap-1865	139	9	=	=	SYM
ap-1865	139	10	p	p	X
ap-1865	139	11	∪̇p	∪̇p	PUNCT
ap-1865	139	12	∗	∗	VERB
ap-1865	139	13	the	the	DET
ap-1865	139	14	structure	structure	NOUN
ap-1865	139	15	(	(	PUNCT
ap-1865	139	16	e;⊕∗	e;⊕∗	PROPN
ap-1865	139	17	,	,	PUNCT
ap-1865	139	18	0	0	NUM
ap-1865	139	19	,	,	PUNCT
ap-1865	139	20	0∗	0∗	NUM
ap-1865	139	21	)	)	PUNCT
ap-1865	139	22	is	be	AUX
ap-1865	139	23	an	an	DET
ap-1865	139	24	effect	effect	NOUN
ap-1865	139	25	algebra	algebra	NOUN
ap-1865	139	26	.	.	PUNCT
ap-1865	140	1	moreover	moreover	ADV
ap-1865	140	2	,	,	PUNCT
ap-1865	140	3	p	p	PRON
ap-1865	140	4	is	be	AUX
ap-1865	140	5	a	a	DET
ap-1865	140	6	proper	proper	ADJ
ap-1865	140	7	order	order	NOUN
ap-1865	140	8	ideal	ideal	NOUN
ap-1865	140	9	in	in	ADP
ap-1865	140	10	e	e	NOUN
ap-1865	140	11	closed	close	VERB
ap-1865	140	12	under	under	ADP
ap-1865	140	13	⊕∗	⊕∗	NOUN
ap-1865	140	14	and	and	CCONJ
ap-1865	140	15	the	the	DET
ap-1865	140	16	partial	partial	ADJ
ap-1865	140	17	order	order	NOUN
ap-1865	140	18	induced	induce	VERB
ap-1865	140	19	by	by	ADP
ap-1865	140	20	⊕∗	⊕∗	NOUN
ap-1865	140	21	,	,	PUNCT
ap-1865	140	22	when	when	SCONJ
ap-1865	140	23	restricted	restrict	VERB
ap-1865	140	24	to	to	ADP
ap-1865	140	25	p	p	NOUN
ap-1865	140	26	,	,	PUNCT
ap-1865	140	27	coincides	coincide	VERB
ap-1865	140	28	with	with	ADP
ap-1865	140	29	the	the	DET
ap-1865	140	30	partial	partial	ADJ
ap-1865	140	31	order	order	NOUN
ap-1865	140	32	induced	induce	VERB
ap-1865	140	33	by	by	ADP
ap-1865	140	34	⊕.	⊕.	DET
ap-1865	140	35	the	the	DET
ap-1865	140	36	generalized	generalized	ADJ
ap-1865	140	37	effect	effect	NOUN
ap-1865	140	38	algebra	algebra	NOUN
ap-1865	140	39	p	p	NOUN
ap-1865	140	40	is	be	AUX
ap-1865	140	41	a	a	DET
ap-1865	140	42	sub	sub	ADJ
ap-1865	140	43	-	-	ADJ
ap-1865	140	44	generalized	generalized	ADJ
ap-1865	140	45	effect	effect	NOUN
ap-1865	140	46	algebra	algebra	NOUN
ap-1865	140	47	of	of	ADP
ap-1865	140	48	e	e	PROPN
ap-1865	140	49	and	and	CCONJ
ap-1865	140	50	for	for	ADP
ap-1865	140	51	every	every	DET
ap-1865	140	52	a	a	DET
ap-1865	140	53	∈	∈	PROPN
ap-1865	140	54	p	p	NOUN
ap-1865	140	55	,	,	PUNCT
ap-1865	140	56	a⊕	a⊕	PROPN
ap-1865	140	57	a∗	a∗	PROPN
ap-1865	140	58	=	=	SYM
ap-1865	140	59	0∗.	0∗.	NOUN
ap-1865	140	60	since	since	SCONJ
ap-1865	140	61	the	the	DET
ap-1865	140	62	definition	definition	NOUN
ap-1865	140	63	of	of	ADP
ap-1865	140	64	⊕∗	⊕∗	NOUN
ap-1865	140	65	on	on	ADP
ap-1865	140	66	e	e	X
ap-1865	140	67	=	=	PROPN
ap-1865	140	68	p	p	PROPN
ap-1865	140	69	∪̇p	∪̇p	NOUN
ap-1865	140	70	∗	∗	NOUN
ap-1865	140	71	coincides	coincide	NOUN
ap-1865	140	72	with	with	ADP
ap-1865	140	73	the	the	DET
ap-1865	140	74	⊕-operation	⊕-operation	NOUN
ap-1865	140	75	on	on	ADP
ap-1865	140	76	p	p	PROPN
ap-1865	140	77	,	,	PUNCT
ap-1865	140	78	it	it	PRON
ap-1865	140	79	will	will	AUX
ap-1865	140	80	cause	cause	VERB
ap-1865	140	81	no	no	DET
ap-1865	140	82	confusion	confusion	NOUN
ap-1865	140	83	459	459	NUM
ap-1865	140	84	z.	z.	PROPN
ap-1865	140	85	riečanová	riečanová	PROPN
ap-1865	140	86	,	,	PUNCT
ap-1865	140	87	j.	j.	PROPN
ap-1865	140	88	janda	janda	PROPN
ap-1865	140	89	acta	acta	PROPN
ap-1865	140	90	polytechnica	polytechnica	PROPN
ap-1865	140	91	0	0	PROPN
ap-1865	140	92	a	a	DET
ap-1865	140	93	a⊕	a⊕	PROPN
ap-1865	140	94	c	c	PROPN
ap-1865	140	95	c	c	PROPN
ap-1865	140	96	b	b	PROPN
ap-1865	140	97	b⊕	b⊕	PROPN
ap-1865	140	98	c	c	NOUN
ap-1865	140	99	figure	figure	NOUN
ap-1865	140	100	1	1	NUM
ap-1865	140	101	.	.	PUNCT
ap-1865	140	102	to	to	PART
ap-1865	140	103	example	example	VERB
ap-1865	140	104	4	4	NUM
ap-1865	140	105	:	:	PUNCT
ap-1865	140	106	(	(	PUNCT
ap-1865	140	107	g;⊕	g;⊕	NOUN
ap-1865	140	108	,	,	PUNCT
ap-1865	140	109	0	0	NUM
ap-1865	140	110	)	)	PUNCT
ap-1865	140	111	if	if	SCONJ
ap-1865	140	112	from	from	ADP
ap-1865	140	113	now	now	ADV
ap-1865	140	114	on	on	ADV
ap-1865	140	115	we	we	PRON
ap-1865	140	116	use	use	VERB
ap-1865	140	117	the	the	DET
ap-1865	140	118	notation	notation	NOUN
ap-1865	140	119	⊕	⊕	PROPN
ap-1865	140	120	also	also	ADV
ap-1865	140	121	for	for	ADP
ap-1865	140	122	its	its	PRON
ap-1865	140	123	extension	extension	NOUN
ap-1865	140	124	to	to	ADP
ap-1865	140	125	e.	e.	PROPN
ap-1865	140	126	to	to	PART
ap-1865	140	127	avoid	avoid	VERB
ap-1865	140	128	undue	undue	ADJ
ap-1865	140	129	repetitions	repetition	NOUN
ap-1865	140	130	on	on	ADP
ap-1865	140	131	generalized	generalized	ADJ
ap-1865	140	132	mv	mv	NOUN
ap-1865	140	133	-	-	PUNCT
ap-1865	140	134	effect	effect	NOUN
ap-1865	140	135	algebras	algebra	NOUN
ap-1865	140	136	,	,	PUNCT
ap-1865	140	137	we	we	PRON
ap-1865	140	138	recall	recall	VERB
ap-1865	140	139	the	the	DET
ap-1865	140	140	following	follow	VERB
ap-1865	140	141	statements	statement	NOUN
ap-1865	140	142	from	from	ADP
ap-1865	140	143	[	[	X
ap-1865	140	144	11	11	NUM
ap-1865	140	145	]	]	PUNCT
ap-1865	140	146	,	,	PUNCT
ap-1865	140	147	giving	give	VERB
ap-1865	140	148	their	their	PRON
ap-1865	140	149	equivalent	equivalent	ADJ
ap-1865	140	150	definitions	definition	NOUN
ap-1865	140	151	.	.	PUNCT
ap-1865	141	1	theorem	theorem	ADJ
ap-1865	141	2	3	3	NUM
ap-1865	141	3	(	(	PUNCT
ap-1865	141	4	[	[	X
ap-1865	141	5	11	11	NUM
ap-1865	141	6	,	,	PUNCT
ap-1865	141	7	theorem	theorem	VERB
ap-1865	141	8	3.2	3.2	NUM
ap-1865	141	9	]	]	PUNCT
ap-1865	141	10	)	)	PUNCT
ap-1865	141	11	.	.	PUNCT
ap-1865	142	1	for	for	ADP
ap-1865	142	2	a	a	DET
ap-1865	142	3	generalized	generalized	ADJ
ap-1865	142	4	effect	effect	NOUN
ap-1865	142	5	algebra	algebra	NOUN
ap-1865	142	6	p	p	NOUN
ap-1865	142	7	the	the	DET
ap-1865	142	8	following	follow	VERB
ap-1865	142	9	conditions	condition	NOUN
ap-1865	142	10	are	be	AUX
ap-1865	142	11	equivalent	equivalent	ADJ
ap-1865	142	12	:	:	PUNCT
ap-1865	142	13	(	(	PUNCT
ap-1865	142	14	1	1	NUM
ap-1865	142	15	.	.	PUNCT
ap-1865	142	16	)	)	PUNCT
ap-1865	143	1	p	p	NOUN
ap-1865	143	2	is	be	AUX
ap-1865	143	3	a	a	DET
ap-1865	143	4	generalized	generalized	ADJ
ap-1865	143	5	mv	mv	ADJ
ap-1865	143	6	-	-	PUNCT
ap-1865	143	7	effect	effect	NOUN
ap-1865	143	8	algebra	algebra	NOUN
ap-1865	143	9	,	,	PUNCT
ap-1865	143	10	(	(	PUNCT
ap-1865	143	11	2	2	NUM
ap-1865	143	12	.	.	PUNCT
ap-1865	143	13	)	)	PUNCT
ap-1865	144	1	e	e	X
ap-1865	144	2	=	=	PUNCT
ap-1865	144	3	p	p	X
ap-1865	144	4	∪̇p	∪̇p	PUNCT
ap-1865	144	5	∗	∗	NOUN
ap-1865	144	6	is	be	AUX
ap-1865	144	7	an	an	DET
ap-1865	144	8	mv	mv	ADJ
ap-1865	144	9	-	-	PUNCT
ap-1865	144	10	effect	effect	NOUN
ap-1865	144	11	algebra	algebra	NOUN
ap-1865	144	12	.	.	PUNCT
ap-1865	145	1	theorem	theorem	ADJ
ap-1865	145	2	4	4	NUM
ap-1865	145	3	(	(	PUNCT
ap-1865	145	4	[	[	X
ap-1865	145	5	11	11	NUM
ap-1865	145	6	,	,	PUNCT
ap-1865	145	7	theorem	theorem	VERB
ap-1865	145	8	3.3	3.3	NUM
ap-1865	145	9	]	]	PUNCT
ap-1865	145	10	)	)	PUNCT
ap-1865	145	11	.	.	PUNCT
ap-1865	146	1	a	a	DET
ap-1865	146	2	generalized	generalized	ADJ
ap-1865	146	3	effect	effect	NOUN
ap-1865	146	4	algebra	algebra	NOUN
ap-1865	146	5	p	p	NOUN
ap-1865	146	6	is	be	AUX
ap-1865	146	7	a	a	DET
ap-1865	146	8	generalized	generalized	ADJ
ap-1865	146	9	mv	mv	NOUN
ap-1865	146	10	-	-	PUNCT
ap-1865	146	11	effect	effect	NOUN
ap-1865	146	12	algebra	algebra	NOUN
ap-1865	146	13	iff	iff	VERB
ap-1865	146	14	the	the	DET
ap-1865	146	15	following	follow	VERB
ap-1865	146	16	conditions	condition	NOUN
ap-1865	146	17	are	be	AUX
ap-1865	146	18	satisfied	satisfied	ADJ
ap-1865	146	19	(	(	PUNCT
ap-1865	146	20	1	1	NUM
ap-1865	146	21	.	.	PUNCT
ap-1865	146	22	)	)	PUNCT
ap-1865	147	1	p	p	NOUN
ap-1865	147	2	is	be	AUX
ap-1865	147	3	a	a	DET
ap-1865	147	4	lattice	lattice	NOUN
ap-1865	147	5	,	,	PUNCT
ap-1865	147	6	(	(	PUNCT
ap-1865	147	7	2	2	NUM
ap-1865	147	8	.	.	PUNCT
ap-1865	147	9	)	)	PUNCT
ap-1865	147	10	for	for	ADP
ap-1865	147	11	all	all	DET
ap-1865	147	12	a	a	DET
ap-1865	147	13	,	,	PUNCT
ap-1865	147	14	b	b	NOUN
ap-1865	147	15	,	,	PUNCT
ap-1865	147	16	c	c	PROPN
ap-1865	147	17	∈	∈	PROPN
ap-1865	147	18	p	p	NOUN
ap-1865	147	19	the	the	DET
ap-1865	147	20	existence	existence	NOUN
ap-1865	147	21	of	of	ADP
ap-1865	147	22	a⊕	a⊕	PROPN
ap-1865	147	23	c	c	PROPN
ap-1865	147	24	and	and	CCONJ
ap-1865	147	25	b⊕	b⊕	PROPN
ap-1865	147	26	c	c	PROPN
ap-1865	147	27	implies	imply	VERB
ap-1865	147	28	the	the	DET
ap-1865	147	29	existence	existence	NOUN
ap-1865	147	30	of	of	ADP
ap-1865	147	31	(	(	PUNCT
ap-1865	147	32	a	a	DET
ap-1865	147	33	∨p	∨p	NOUN
ap-1865	147	34	b)⊕	b)⊕	NOUN
ap-1865	147	35	c	c	NOUN
ap-1865	147	36	,	,	PUNCT
ap-1865	147	37	(	(	PUNCT
ap-1865	147	38	3	3	NUM
ap-1865	147	39	.	.	PUNCT
ap-1865	147	40	)	)	PUNCT
ap-1865	148	1	∨	∨	NUM
ap-1865	148	2	{	{	PUNCT
ap-1865	148	3	c	c	NOUN
ap-1865	148	4	∈	∈	PROPN
ap-1865	149	1	p	p	NOUN
ap-1865	149	2	|	|	ADV
ap-1865	149	3	a⊕	a⊕	PROPN
ap-1865	149	4	c	c	PROPN
ap-1865	149	5	exists	exist	VERB
ap-1865	149	6	and	and	CCONJ
ap-1865	149	7	c	c	NOUN
ap-1865	149	8	≤	≤	NUM
ap-1865	149	9	b	b	X
ap-1865	149	10	}	}	PUNCT
ap-1865	149	11	exists	exist	VERB
ap-1865	149	12	in	in	ADP
ap-1865	149	13	p	p	NOUN
ap-1865	149	14	,	,	PUNCT
ap-1865	149	15	for	for	ADP
ap-1865	149	16	all	all	DET
ap-1865	149	17	a	a	DET
ap-1865	149	18	,	,	PUNCT
ap-1865	149	19	b	b	PROPN
ap-1865	149	20	∈	∈	PROPN
ap-1865	149	21	p	p	X
ap-1865	149	22	,	,	PUNCT
ap-1865	149	23	(	(	PUNCT
ap-1865	149	24	4	4	NUM
ap-1865	149	25	.	.	NUM
ap-1865	149	26	)	)	PUNCT
ap-1865	150	1	(	(	PUNCT
ap-1865	150	2	a	a	PRON
ap-1865	150	3	(	(	PUNCT
ap-1865	150	4	a∧p	a∧p	NOUN
ap-1865	150	5	b))⊕(b	b))⊕(b	PROPN
ap-1865	150	6	(	(	PUNCT
ap-1865	150	7	a∧p	a∧p	PROPN
ap-1865	150	8	b	b	NOUN
ap-1865	150	9	)	)	PUNCT
ap-1865	150	10	)	)	PUNCT
ap-1865	150	11	exists	exist	VERB
ap-1865	150	12	for	for	ADP
ap-1865	150	13	all	all	DET
ap-1865	150	14	a	a	DET
ap-1865	150	15	,	,	PUNCT
ap-1865	150	16	b	b	PROPN
ap-1865	150	17	∈	∈	PROPN
ap-1865	150	18	p	p	NOUN
ap-1865	150	19	.	.	PUNCT
ap-1865	151	1	lemma	lemma	PROPN
ap-1865	151	2	1	1	X
ap-1865	151	3	.	.	PUNCT
ap-1865	152	1	let	let	VERB
ap-1865	152	2	(	(	PUNCT
ap-1865	152	3	g;⊕	g;⊕	NOUN
ap-1865	152	4	,	,	PUNCT
ap-1865	152	5	0	0	NUM
ap-1865	152	6	)	)	PUNCT
ap-1865	152	7	be	be	AUX
ap-1865	152	8	a	a	DET
ap-1865	152	9	generalized	generalized	ADJ
ap-1865	152	10	mv	mv	ADJ
ap-1865	152	11	-	-	PUNCT
ap-1865	152	12	effect	effect	NOUN
ap-1865	152	13	algebra	algebra	NOUN
ap-1865	152	14	.	.	PUNCT
ap-1865	153	1	then	then	ADV
ap-1865	153	2	for	for	ADP
ap-1865	153	3	every	every	DET
ap-1865	153	4	q	q	PROPN
ap-1865	153	5	∈	∈	PROPN
ap-1865	153	6	g	g	ADP
ap-1865	153	7	the	the	DET
ap-1865	153	8	interval	interval	NOUN
ap-1865	153	9	[	[	X
ap-1865	153	10	0	0	NUM
ap-1865	153	11	,	,	PUNCT
ap-1865	153	12	q]g	q]g	ADV
ap-1865	153	13	⊆	⊆	NUM
ap-1865	153	14	g	g	NOUN
ap-1865	153	15	is	be	AUX
ap-1865	153	16	an	an	DET
ap-1865	153	17	mv	mv	ADJ
ap-1865	153	18	-	-	PUNCT
ap-1865	153	19	effect	effect	NOUN
ap-1865	153	20	algebra	algebra	NOUN
ap-1865	153	21	.	.	PUNCT
ap-1865	154	1	proof	proof	NOUN
ap-1865	154	2	.	.	PUNCT
ap-1865	155	1	clearly	clearly	ADV
ap-1865	155	2	,	,	PUNCT
ap-1865	155	3	for	for	ADP
ap-1865	155	4	every	every	DET
ap-1865	155	5	q	q	PROPN
ap-1865	155	6	∈	∈	PROPN
ap-1865	155	7	g	g	NOUN
ap-1865	155	8	,	,	PUNCT
ap-1865	155	9	the	the	DET
ap-1865	155	10	interval	interval	NOUN
ap-1865	155	11	[	[	X
ap-1865	155	12	0	0	NUM
ap-1865	155	13	,	,	PUNCT
ap-1865	155	14	q]g	q]g	ADV
ap-1865	155	15	⊆	⊆	NUM
ap-1865	155	16	g	g	NOUN
ap-1865	155	17	is	be	AUX
ap-1865	155	18	lattice	lattice	NOUN
ap-1865	155	19	ordered	order	VERB
ap-1865	155	20	,	,	PUNCT
ap-1865	155	21	as	as	ADP
ap-1865	155	22	for	for	ADP
ap-1865	155	23	every	every	DET
ap-1865	155	24	a	a	PROPN
ap-1865	155	25	,	,	PUNCT
ap-1865	155	26	b	b	X
ap-1865	155	27	∈	∈	PROPN
ap-1865	156	1	[	[	X
ap-1865	156	2	0	0	NUM
ap-1865	156	3	,	,	PUNCT
ap-1865	156	4	q]g	q]g	NOUN
ap-1865	156	5	we	we	PRON
ap-1865	156	6	have	have	VERB
ap-1865	156	7	a	a	DET
ap-1865	156	8	∨g	∨g	PROPN
ap-1865	156	9	b	b	NOUN
ap-1865	156	10	,	,	PUNCT
ap-1865	156	11	a	a	DET
ap-1865	156	12	∧g	∧g	PROPN
ap-1865	156	13	b	b	PROPN
ap-1865	156	14	≤	≤	NUM
ap-1865	156	15	q	q	PUNCT
ap-1865	156	16	in	in	ADP
ap-1865	156	17	g.	g.	PROPN
ap-1865	156	18	moreover	moreover	ADV
ap-1865	156	19	,	,	PUNCT
ap-1865	156	20	for	for	ADP
ap-1865	156	21	every	every	DET
ap-1865	156	22	a	a	PROPN
ap-1865	156	23	,	,	PUNCT
ap-1865	156	24	b	b	X
ap-1865	156	25	∈	∈	PROPN
ap-1865	157	1	[	[	X
ap-1865	157	2	0	0	NUM
ap-1865	157	3	,	,	PUNCT
ap-1865	157	4	q]g	q]g	ADV
ap-1865	157	5	⊆	⊆	NUM
ap-1865	157	6	g	g	NOUN
ap-1865	157	7	we	we	PRON
ap-1865	157	8	have	have	VERB
ap-1865	157	9	(	(	PUNCT
ap-1865	157	10	a	a	PRON
ap-1865	157	11	(	(	PUNCT
ap-1865	157	12	a∧g	a∧g	PROPN
ap-1865	157	13	b))⊕(b	b))⊕(b	PROPN
ap-1865	157	14	(	(	PUNCT
ap-1865	157	15	a∧g	a∧g	PROPN
ap-1865	157	16	b	b	X
ap-1865	157	17	)	)	PUNCT
ap-1865	157	18	)	)	PUNCT
ap-1865	157	19	exists	exist	VERB
ap-1865	157	20	in	in	ADP
ap-1865	157	21	g	g	NOUN
ap-1865	157	22	by	by	ADP
ap-1865	157	23	theorem	theorem	NOUN
ap-1865	157	24	4	4	NUM
ap-1865	157	25	.	.	PUNCT
ap-1865	158	1	since	since	SCONJ
ap-1865	158	2	(	(	PUNCT
ap-1865	158	3	a	a	PRON
ap-1865	158	4	(	(	PUNCT
ap-1865	158	5	a∧g	a∧g	PROPN
ap-1865	158	6	b))⊕(b	b))⊕(b	PROPN
ap-1865	158	7	(	(	PUNCT
ap-1865	158	8	a∧g	a∧g	PROPN
ap-1865	158	9	b	b	PROPN
ap-1865	158	10	)	)	PUNCT
ap-1865	158	11	)	)	PUNCT
ap-1865	159	1	=	=	PUNCT
ap-1865	160	1	[	[	X
ap-1865	160	2	(	(	PUNCT
ap-1865	160	3	a	a	DET
ap-1865	160	4	(	(	PUNCT
ap-1865	160	5	a∧g	a∧g	PROPN
ap-1865	160	6	b))∨g	b))∨g	NOUN
ap-1865	160	7	(	(	PUNCT
ap-1865	160	8	b	b	X
ap-1865	160	9	(	(	PUNCT
ap-1865	160	10	a	a	DET
ap-1865	160	11	∧g	∧g	PROPN
ap-1865	160	12	b))]⊕	b))]⊕	PROPN
ap-1865	160	13	[	[	X
ap-1865	160	14	(	(	PUNCT
ap-1865	160	15	a	a	DET
ap-1865	160	16	(	(	PUNCT
ap-1865	160	17	a	a	DET
ap-1865	160	18	∧g	∧g	PROPN
ap-1865	160	19	b	b	NOUN
ap-1865	160	20	)	)	PUNCT
ap-1865	160	21	)	)	PUNCT
ap-1865	160	22	∧g	∧g	PROPN
ap-1865	160	23	(	(	PUNCT
ap-1865	160	24	b	b	NOUN
ap-1865	160	25	(	(	PUNCT
ap-1865	160	26	a	a	DET
ap-1865	160	27	∧g	∧g	PROPN
ap-1865	160	28	b	b	NOUN
ap-1865	160	29	)	)	PUNCT
ap-1865	160	30	)	)	PUNCT
ap-1865	160	31	]	]	PUNCT
ap-1865	161	1	=	=	PUNCT
ap-1865	161	2	(	(	PUNCT
ap-1865	161	3	a	a	PRON
ap-1865	161	4	(	(	PUNCT
ap-1865	161	5	a	a	DET
ap-1865	161	6	∧g	∧g	PROPN
ap-1865	161	7	b	b	NOUN
ap-1865	161	8	)	)	PUNCT
ap-1865	161	9	)	)	PUNCT
ap-1865	161	10	∨g	∨g	NOUN
ap-1865	161	11	(	(	PUNCT
ap-1865	161	12	b	b	NOUN
ap-1865	161	13	(	(	PUNCT
ap-1865	161	14	a	a	DET
ap-1865	161	15	∧g	∧g	PROPN
ap-1865	161	16	b	b	NOUN
ap-1865	161	17	)	)	PUNCT
ap-1865	161	18	)	)	PUNCT
ap-1865	161	19	≤	≤	NOUN
ap-1865	161	20	a	a	DET
ap-1865	161	21	∨g	∨g	NOUN
ap-1865	161	22	b	b	X
ap-1865	161	23	≤	≤	ADJ
ap-1865	162	1	q	q	NOUN
ap-1865	163	1	we	we	PRON
ap-1865	163	2	have	have	VERB
ap-1865	163	3	that	that	DET
ap-1865	163	4	(	(	PUNCT
ap-1865	163	5	a	a	DET
ap-1865	163	6	q	q	X
ap-1865	163	7	(	(	PUNCT
ap-1865	163	8	a	a	DET
ap-1865	163	9	∧q	∧q	PROPN
ap-1865	163	10	b	b	NOUN
ap-1865	163	11	)	)	PUNCT
ap-1865	163	12	)	)	PUNCT
ap-1865	163	13	⊕q	⊕q	NOUN
ap-1865	163	14	(	(	PUNCT
ap-1865	163	15	b	b	X
ap-1865	163	16	q	q	X
ap-1865	163	17	(	(	PUNCT
ap-1865	163	18	a	a	DET
ap-1865	163	19	∧q	∧q	PROPN
ap-1865	163	20	b	b	NOUN
ap-1865	163	21	)	)	PUNCT
ap-1865	163	22	)	)	PUNCT
ap-1865	163	23	also	also	ADV
ap-1865	163	24	exists	exist	VERB
ap-1865	163	25	in	in	ADP
ap-1865	163	26	[	[	X
ap-1865	163	27	0	0	NUM
ap-1865	163	28	,	,	PUNCT
ap-1865	163	29	q]g	q]g	ADV
ap-1865	163	30	(	(	PUNCT
ap-1865	163	31	for	for	ADP
ap-1865	163	32	inequalities	inequality	NOUN
ap-1865	163	33	see	see	VERB
ap-1865	163	34	[	[	X
ap-1865	163	35	2	2	NUM
ap-1865	163	36	,	,	PUNCT
ap-1865	163	37	p.	p.	NOUN
ap-1865	163	38	70	70	NUM
ap-1865	163	39	]	]	PUNCT
ap-1865	163	40	)	)	PUNCT
ap-1865	163	41	.	.	PUNCT
ap-1865	164	1	this	this	PRON
ap-1865	164	2	proves	prove	VERB
ap-1865	164	3	that	that	SCONJ
ap-1865	164	4	a	a	DET
ap-1865	164	5	,	,	PUNCT
ap-1865	164	6	b	b	NOUN
ap-1865	164	7	are	be	AUX
ap-1865	164	8	compatible	compatible	ADJ
ap-1865	164	9	elements	element	NOUN
ap-1865	164	10	of	of	ADP
ap-1865	164	11	a	a	DET
ap-1865	164	12	lattice	lattice	ADJ
ap-1865	164	13	effect	effect	NOUN
ap-1865	164	14	algebra	algebra	NOUN
ap-1865	164	15	(	(	PUNCT
ap-1865	164	16	[	[	X
ap-1865	164	17	0	0	NUM
ap-1865	164	18	,	,	PUNCT
ap-1865	164	19	q]g;⊕q	q]g;⊕q	PROPN
ap-1865	164	20	,	,	PUNCT
ap-1865	164	21	0	0	NUM
ap-1865	164	22	,	,	PUNCT
ap-1865	164	23	q	q	NOUN
ap-1865	164	24	)	)	PUNCT
ap-1865	164	25	.	.	PUNCT
ap-1865	165	1	hence	hence	ADV
ap-1865	165	2	(	(	PUNCT
ap-1865	165	3	[	[	X
ap-1865	165	4	0	0	NUM
ap-1865	165	5	,	,	PUNCT
ap-1865	165	6	q]g;⊕q	q]g;⊕q	PROPN
ap-1865	165	7	,	,	PUNCT
ap-1865	165	8	0	0	NUM
ap-1865	165	9	,	,	PUNCT
ap-1865	165	10	q	q	X
ap-1865	165	11	)	)	PUNCT
ap-1865	165	12	is	be	AUX
ap-1865	165	13	an	an	DET
ap-1865	165	14	mv	mv	ADJ
ap-1865	165	15	-	-	PUNCT
ap-1865	165	16	effect	effect	NOUN
ap-1865	165	17	algebra	algebra	NOUN
ap-1865	165	18	.	.	PUNCT
ap-1865	166	1	the	the	DET
ap-1865	166	2	converse	converse	NOUN
ap-1865	166	3	of	of	ADP
ap-1865	166	4	this	this	DET
ap-1865	166	5	lemma	lemma	PROPN
ap-1865	166	6	,	,	PUNCT
ap-1865	166	7	in	in	ADP
ap-1865	166	8	general	general	ADJ
ap-1865	166	9	,	,	PUNCT
ap-1865	166	10	does	do	AUX
ap-1865	166	11	not	not	PART
ap-1865	166	12	hold	hold	VERB
ap-1865	166	13	as	as	SCONJ
ap-1865	166	14	can	can	AUX
ap-1865	166	15	be	be	AUX
ap-1865	166	16	seen	see	VERB
ap-1865	166	17	in	in	ADP
ap-1865	166	18	the	the	DET
ap-1865	166	19	following	follow	VERB
ap-1865	166	20	example	example	NOUN
ap-1865	166	21	.	.	PUNCT
ap-1865	167	1	example	example	NOUN
ap-1865	168	1	4	4	NUM
ap-1865	168	2	.	.	PUNCT
ap-1865	168	3	let	let	VERB
ap-1865	168	4	us	we	PRON
ap-1865	168	5	have	have	VERB
ap-1865	168	6	a	a	DET
ap-1865	168	7	generalized	generalized	ADJ
ap-1865	168	8	effect	effect	NOUN
ap-1865	168	9	algebra	algebra	NOUN
ap-1865	168	10	(	(	PUNCT
ap-1865	168	11	g;⊕	g;⊕	NOUN
ap-1865	168	12	,	,	PUNCT
ap-1865	168	13	0	0	NUM
ap-1865	168	14	)	)	PUNCT
ap-1865	168	15	given	give	VERB
ap-1865	168	16	by	by	ADP
ap-1865	168	17	g	g	PROPN
ap-1865	168	18	=	=	PUNCT
ap-1865	168	19	{	{	PUNCT
ap-1865	168	20	0	0	NUM
ap-1865	168	21	,	,	PUNCT
ap-1865	168	22	a	a	DET
ap-1865	168	23	,	,	PUNCT
ap-1865	168	24	b	b	NOUN
ap-1865	168	25	,	,	PUNCT
ap-1865	168	26	a	a	DET
ap-1865	168	27	⊕	⊕	PROPN
ap-1865	168	28	c	c	NOUN
ap-1865	168	29	,	,	PUNCT
ap-1865	168	30	b	b	PROPN
ap-1865	168	31	⊕	⊕	PROPN
ap-1865	168	32	c	c	PROPN
ap-1865	168	33	}	}	PUNCT
ap-1865	168	34	(	(	PUNCT
ap-1865	168	35	fig	fig	NOUN
ap-1865	168	36	.	.	PUNCT
ap-1865	168	37	1	1	NUM
ap-1865	168	38	)	)	PUNCT
ap-1865	168	39	.	.	PUNCT
ap-1865	169	1	consider	consider	VERB
ap-1865	169	2	e	e	NOUN
ap-1865	169	3	=	=	SYM
ap-1865	169	4	g	g	PROPN
ap-1865	169	5	∪̇g∗	∪̇g∗	NOUN
ap-1865	169	6	(	(	PUNCT
ap-1865	169	7	fig	fig	NOUN
ap-1865	169	8	.	.	PUNCT
ap-1865	169	9	2	2	NUM
ap-1865	169	10	)	)	PUNCT
ap-1865	169	11	.	.	PUNCT
ap-1865	170	1	(	(	PUNCT
ap-1865	170	2	1	1	NUM
ap-1865	170	3	.	.	PUNCT
ap-1865	170	4	)	)	PUNCT
ap-1865	170	5	clearly	clearly	ADV
ap-1865	170	6	,	,	PUNCT
ap-1865	170	7	a	a	PRON
ap-1865	170	8	is	be	AUX
ap-1865	170	9	not	not	PART
ap-1865	170	10	compatible	compatible	ADJ
ap-1865	170	11	with	with	ADP
ap-1865	170	12	b.	b.	PROPN
ap-1865	170	13	this	this	PRON
ap-1865	170	14	is	be	AUX
ap-1865	170	15	because	because	SCONJ
ap-1865	170	16	a	a	DET
ap-1865	170	17	↔	↔	PROPN
ap-1865	170	18	b	b	NOUN
ap-1865	170	19	if	if	SCONJ
ap-1865	170	20	and	and	CCONJ
ap-1865	170	21	only	only	ADV
ap-1865	170	22	if	if	SCONJ
ap-1865	170	23	there	there	PRON
ap-1865	170	24	exists	exist	VERB
ap-1865	170	25	(	(	PUNCT
ap-1865	170	26	a	a	DET
ap-1865	170	27	(	(	PUNCT
ap-1865	170	28	a	a	DET
ap-1865	170	29	∧g	∧g	ADJ
ap-1865	170	30	b))⊕	b))⊕	NOUN
ap-1865	170	31	(	(	PUNCT
ap-1865	170	32	b	b	NOUN
ap-1865	170	33	(	(	PUNCT
ap-1865	170	34	a	a	DET
ap-1865	170	35	∧g	∧g	PROPN
ap-1865	170	36	b	b	NOUN
ap-1865	170	37	)	)	PUNCT
ap-1865	170	38	)	)	PUNCT
ap-1865	171	1	=	=	PUNCT
ap-1865	171	2	a⊕	a⊕	X
ap-1865	171	3	b	b	NOUN
ap-1865	171	4	which	which	PRON
ap-1865	171	5	is	be	AUX
ap-1865	171	6	not	not	PART
ap-1865	171	7	defined	define	VERB
ap-1865	171	8	.	.	PUNCT
ap-1865	171	9	0	0	PUNCT
ap-1865	172	1	a	a	DET
ap-1865	172	2	a⊕	a⊕	PROPN
ap-1865	172	3	c	c	PROPN
ap-1865	172	4	c	c	PROPN
ap-1865	172	5	b	b	PROPN
ap-1865	172	6	b⊕	b⊕	PROPN
ap-1865	172	7	c	c	NOUN
ap-1865	172	8	0∗	0∗	NOUN
ap-1865	172	9	a∗	a∗	PROPN
ap-1865	172	10	(	(	PUNCT
ap-1865	172	11	a⊕	a⊕	PRON
ap-1865	172	12	c)∗	c)∗	PROPN
ap-1865	172	13	c∗	c∗	PROPN
ap-1865	172	14	b∗	b∗	ADJ
ap-1865	172	15	(	(	PUNCT
ap-1865	172	16	b⊕	b⊕	NOUN
ap-1865	172	17	c)∗	c)∗	ADJ
ap-1865	172	18	figure	figure	NOUN
ap-1865	172	19	2	2	NUM
ap-1865	172	20	.	.	PUNCT
ap-1865	172	21	to	to	PART
ap-1865	172	22	example	example	VERB
ap-1865	172	23	4	4	NUM
ap-1865	172	24	:	:	PUNCT
ap-1865	172	25	e	e	X
ap-1865	172	26	=	=	SYM
ap-1865	172	27	g	g	PROPN
ap-1865	172	28	∪̇g∗	∪̇g∗	NOUN
ap-1865	172	29	(	(	PUNCT
ap-1865	172	30	2	2	NUM
ap-1865	172	31	.	.	PUNCT
ap-1865	172	32	)	)	PUNCT
ap-1865	173	1	e	e	X
ap-1865	173	2	=	=	SYM
ap-1865	173	3	g	g	PROPN
ap-1865	173	4	∪̇g∗	∪̇g∗	NOUN
ap-1865	173	5	is	be	AUX
ap-1865	173	6	a	a	DET
ap-1865	173	7	lattice	lattice	NOUN
ap-1865	173	8	.	.	PUNCT
ap-1865	174	1	(	(	PUNCT
ap-1865	174	2	3	3	NUM
ap-1865	174	3	.	.	PUNCT
ap-1865	174	4	)	)	PUNCT
ap-1865	175	1	g	g	NOUN
ap-1865	175	2	is	be	AUX
ap-1865	175	3	a	a	DET
ap-1865	175	4	prelattice	prelattice	NOUN
ap-1865	175	5	generalized	generalize	VERB
ap-1865	175	6	effect	effect	NOUN
ap-1865	175	7	algebra	algebra	NOUN
ap-1865	175	8	but	but	CCONJ
ap-1865	175	9	it	it	PRON
ap-1865	175	10	is	be	AUX
ap-1865	175	11	not	not	PART
ap-1865	175	12	a	a	DET
ap-1865	175	13	generalized	generalized	ADJ
ap-1865	175	14	mv	mv	ADJ
ap-1865	175	15	-	-	PUNCT
ap-1865	175	16	effect	effect	NOUN
ap-1865	175	17	algebra	algebra	NOUN
ap-1865	175	18	,	,	PUNCT
ap-1865	175	19	since	since	SCONJ
ap-1865	175	20	e	e	NOUN
ap-1865	175	21	=	=	NOUN
ap-1865	175	22	g	g	PROPN
ap-1865	175	23	∪̇g∗	∪̇g∗	NOUN
ap-1865	175	24	is	be	AUX
ap-1865	175	25	not	not	PART
ap-1865	175	26	an	an	DET
ap-1865	175	27	mv	mv	ADJ
ap-1865	175	28	-	-	PUNCT
ap-1865	175	29	effect	effect	NOUN
ap-1865	175	30	algebra	algebra	NOUN
ap-1865	175	31	.	.	PUNCT
ap-1865	176	1	(	(	PUNCT
ap-1865	176	2	4	4	NUM
ap-1865	176	3	.	.	PUNCT
ap-1865	176	4	)	)	PUNCT
ap-1865	177	1	every	every	DET
ap-1865	177	2	interval	interval	NOUN
ap-1865	177	3	of	of	ADP
ap-1865	177	4	g	g	PROPN
ap-1865	177	5	is	be	AUX
ap-1865	177	6	an	an	DET
ap-1865	177	7	mv	mv	ADJ
ap-1865	177	8	-	-	PUNCT
ap-1865	177	9	effect	effect	NOUN
ap-1865	177	10	algebra	algebra	NOUN
ap-1865	177	11	,	,	PUNCT
ap-1865	177	12	namely	namely	ADV
ap-1865	177	13	[	[	X
ap-1865	177	14	0	0	NUM
ap-1865	177	15	,	,	PUNCT
ap-1865	177	16	a⊕c	a⊕c	PROPN
ap-1865	177	17	]	]	PUNCT
ap-1865	177	18	,	,	PUNCT
ap-1865	177	19	[	[	X
ap-1865	177	20	0	0	NUM
ap-1865	177	21	,	,	PUNCT
ap-1865	177	22	b⊕c	b⊕c	PROPN
ap-1865	177	23	]	]	PUNCT
ap-1865	177	24	are	be	AUX
ap-1865	177	25	boolean	boolean	ADJ
ap-1865	177	26	algebras	algebra	NOUN
ap-1865	177	27	which	which	PRON
ap-1865	177	28	are	be	AUX
ap-1865	177	29	mv	mv	ADJ
ap-1865	177	30	-	-	PUNCT
ap-1865	177	31	effect	effect	NOUN
ap-1865	177	32	algebras	algebra	NOUN
ap-1865	177	33	,	,	PUNCT
ap-1865	177	34	and	and	CCONJ
ap-1865	177	35	[	[	X
ap-1865	177	36	0	0	NUM
ap-1865	177	37	,	,	PUNCT
ap-1865	177	38	a	a	PRON
ap-1865	177	39	]	]	X
ap-1865	177	40	,	,	PUNCT
ap-1865	177	41	[	[	X
ap-1865	177	42	0	0	NUM
ap-1865	177	43	,	,	PUNCT
ap-1865	177	44	b	b	NOUN
ap-1865	177	45	]	]	PUNCT
ap-1865	177	46	and	and	CCONJ
ap-1865	177	47	[	[	X
ap-1865	177	48	0	0	NUM
ap-1865	177	49	,	,	PUNCT
ap-1865	177	50	c	c	NOUN
ap-1865	177	51	]	]	PUNCT
ap-1865	177	52	are	be	AUX
ap-1865	177	53	finite	finite	ADJ
ap-1865	177	54	chains	chain	NOUN
ap-1865	177	55	,	,	PUNCT
ap-1865	177	56	which	which	PRON
ap-1865	177	57	are	be	AUX
ap-1865	177	58	mv	mv	ADJ
ap-1865	177	59	-	-	PUNCT
ap-1865	177	60	effect	effect	NOUN
ap-1865	177	61	algebras	algebra	NOUN
ap-1865	177	62	as	as	ADV
ap-1865	177	63	well	well	ADV
ap-1865	177	64	.	.	PUNCT
ap-1865	178	1	nevertheless	nevertheless	ADV
ap-1865	178	2	,	,	PUNCT
ap-1865	178	3	g	g	PROPN
ap-1865	178	4	is	be	AUX
ap-1865	178	5	not	not	PART
ap-1865	178	6	a	a	DET
ap-1865	178	7	generalized	generalized	ADJ
ap-1865	178	8	mv	mv	ADJ
ap-1865	178	9	-	-	PUNCT
ap-1865	178	10	effect	effect	NOUN
ap-1865	178	11	algebra	algebra	NOUN
ap-1865	178	12	since	since	SCONJ
ap-1865	178	13	e	e	PROPN
ap-1865	178	14	=	=	NOUN
ap-1865	178	15	g	g	PROPN
ap-1865	178	16	∪̇g∗	∪̇g∗	NOUN
ap-1865	178	17	is	be	AUX
ap-1865	178	18	not	not	PART
ap-1865	178	19	an	an	DET
ap-1865	178	20	mv	mv	ADJ
ap-1865	178	21	-	-	PUNCT
ap-1865	178	22	effect	effect	NOUN
ap-1865	178	23	algebra	algebra	NOUN
ap-1865	178	24	.	.	PUNCT
ap-1865	179	1	using	use	VERB
ap-1865	179	2	previous	previous	ADJ
ap-1865	179	3	theorems	theorem	NOUN
ap-1865	179	4	we	we	PRON
ap-1865	179	5	obtain	obtain	VERB
ap-1865	179	6	statements	statement	NOUN
ap-1865	179	7	for	for	ADP
ap-1865	179	8	pairwise	pairwise	NOUN
ap-1865	179	9	summable	summable	ADJ
ap-1865	179	10	lattice	lattice	NOUN
ap-1865	179	11	ordered	order	VERB
ap-1865	179	12	generalized	generalized	ADJ
ap-1865	179	13	effect	effect	NOUN
ap-1865	179	14	algebras	algebra	NOUN
ap-1865	179	15	.	.	PUNCT
ap-1865	180	1	theorem	theorem	NOUN
ap-1865	180	2	5	5	NUM
ap-1865	180	3	.	.	PUNCT
ap-1865	181	1	let	let	VERB
ap-1865	181	2	(	(	PUNCT
ap-1865	181	3	g;⊕	g;⊕	NOUN
ap-1865	181	4	,	,	PUNCT
ap-1865	181	5	0	0	NUM
ap-1865	181	6	)	)	PUNCT
ap-1865	181	7	be	be	AUX
ap-1865	181	8	a	a	DET
ap-1865	181	9	pairwise	pairwise	NOUN
ap-1865	181	10	summable	summable	ADJ
ap-1865	181	11	lattice	lattice	NOUN
ap-1865	181	12	ordered	order	VERB
ap-1865	181	13	generalized	generalized	ADJ
ap-1865	181	14	effect	effect	NOUN
ap-1865	181	15	algebra	algebra	NOUN
ap-1865	181	16	.	.	PUNCT
ap-1865	182	1	then	then	ADV
ap-1865	182	2	(	(	PUNCT
ap-1865	182	3	1	1	NUM
ap-1865	182	4	.	.	NUM
ap-1865	182	5	)	)	PUNCT
ap-1865	183	1	(	(	PUNCT
ap-1865	183	2	g;⊕	g;⊕	NOUN
ap-1865	183	3	,	,	PUNCT
ap-1865	183	4	0	0	NUM
ap-1865	183	5	)	)	PUNCT
ap-1865	183	6	is	be	AUX
ap-1865	183	7	a	a	DET
ap-1865	183	8	generalized	generalized	ADJ
ap-1865	183	9	mv	mv	ADJ
ap-1865	183	10	-	-	PUNCT
ap-1865	183	11	effect	effect	NOUN
ap-1865	183	12	algebra	algebra	NOUN
ap-1865	183	13	,	,	PUNCT
ap-1865	183	14	(	(	PUNCT
ap-1865	183	15	2	2	NUM
ap-1865	183	16	.	.	PUNCT
ap-1865	183	17	)	)	PUNCT
ap-1865	184	1	e	e	X
ap-1865	184	2	=	=	SYM
ap-1865	184	3	g	g	PROPN
ap-1865	184	4	∪̇g∗	∪̇g∗	NOUN
ap-1865	184	5	is	be	AUX
ap-1865	184	6	an	an	DET
ap-1865	184	7	mv	mv	ADJ
ap-1865	184	8	-	-	PUNCT
ap-1865	184	9	effect	effect	NOUN
ap-1865	184	10	algebra	algebra	NOUN
ap-1865	184	11	,	,	PUNCT
ap-1865	184	12	(	(	PUNCT
ap-1865	184	13	3	3	NUM
ap-1865	184	14	.	.	PUNCT
ap-1865	184	15	)	)	PUNCT
ap-1865	184	16	for	for	SCONJ
ap-1865	184	17	every	every	DET
ap-1865	184	18	q	q	PROPN
ap-1865	184	19	∈	∈	PROPN
ap-1865	184	20	g	g	ADP
ap-1865	184	21	the	the	DET
ap-1865	184	22	interval	interval	NOUN
ap-1865	184	23	[	[	X
ap-1865	184	24	0	0	NUM
ap-1865	184	25	,	,	PUNCT
ap-1865	184	26	q]g	q]g	ADV
ap-1865	184	27	⊆	⊆	NUM
ap-1865	184	28	g	g	NOUN
ap-1865	184	29	is	be	AUX
ap-1865	184	30	an	an	DET
ap-1865	184	31	mv	mv	ADJ
ap-1865	184	32	-	-	PUNCT
ap-1865	184	33	effect	effect	NOUN
ap-1865	184	34	algebra	algebra	NOUN
ap-1865	184	35	.	.	PUNCT
ap-1865	185	1	proof	proof	NOUN
ap-1865	185	2	.	.	PUNCT
ap-1865	186	1	since	since	SCONJ
ap-1865	186	2	g	g	NOUN
ap-1865	186	3	with	with	ADP
ap-1865	186	4	derived	derive	VERB
ap-1865	186	5	partial	partial	ADJ
ap-1865	186	6	order	order	NOUN
ap-1865	186	7	≤	≤	NOUN
ap-1865	186	8	is	be	AUX
ap-1865	186	9	a	a	DET
ap-1865	186	10	lattice	lattice	NOUN
ap-1865	186	11	and	and	CCONJ
ap-1865	186	12	every	every	DET
ap-1865	186	13	pair	pair	NOUN
ap-1865	186	14	of	of	ADP
ap-1865	186	15	elements	element	NOUN
ap-1865	186	16	of	of	ADP
ap-1865	186	17	g	g	PROPN
ap-1865	186	18	is	be	AUX
ap-1865	186	19	summable	summable	ADJ
ap-1865	186	20	,	,	PUNCT
ap-1865	186	21	g	g	NOUN
ap-1865	186	22	satisfies	satisfy	VERB
ap-1865	186	23	all	all	DET
ap-1865	186	24	conditions	condition	NOUN
ap-1865	186	25	(	(	PUNCT
ap-1865	186	26	1.)–(4	1.)–(4	NUM
ap-1865	186	27	.	.	PUNCT
ap-1865	186	28	)	)	PUNCT
ap-1865	186	29	of	of	ADP
ap-1865	186	30	theorem	theorem	ADJ
ap-1865	186	31	4	4	NUM
ap-1865	186	32	.	.	PUNCT
ap-1865	186	33	further	far	ADV
ap-1865	186	34	(	(	PUNCT
ap-1865	186	35	2	2	NUM
ap-1865	186	36	.	.	PUNCT
ap-1865	186	37	)	)	PUNCT
ap-1865	186	38	follows	follow	VERB
ap-1865	186	39	by	by	ADP
ap-1865	186	40	theorem	theorem	NOUN
ap-1865	186	41	3	3	NUM
ap-1865	186	42	and	and	CCONJ
ap-1865	186	43	(	(	PUNCT
ap-1865	186	44	3	3	NUM
ap-1865	186	45	.	.	PUNCT
ap-1865	186	46	)	)	PUNCT
ap-1865	186	47	by	by	ADP
ap-1865	186	48	(	(	PUNCT
ap-1865	186	49	1	1	NUM
ap-1865	186	50	.	.	PUNCT
ap-1865	186	51	)	)	PUNCT
ap-1865	186	52	and	and	CCONJ
ap-1865	186	53	lemma	lemma	PROPN
ap-1865	186	54	1	1	NUM
ap-1865	186	55	.	.	NOUN
ap-1865	186	56	4	4	NUM
ap-1865	186	57	.	.	X
ap-1865	186	58	blocks	block	NOUN
ap-1865	186	59	of	of	ADP
ap-1865	186	60	pairwise	pairwise	NOUN
ap-1865	186	61	summable	summable	ADJ
ap-1865	186	62	elements	element	NOUN
ap-1865	186	63	in	in	ADP
ap-1865	186	64	generalized	generalized	ADJ
ap-1865	186	65	effect	effect	NOUN
ap-1865	186	66	algebras	algebra	NOUN
ap-1865	186	67	in	in	ADP
ap-1865	186	68	[	[	X
ap-1865	186	69	10	10	NUM
ap-1865	186	70	]	]	X
ap-1865	186	71	it	it	PRON
ap-1865	186	72	was	be	AUX
ap-1865	186	73	shown	show	VERB
ap-1865	186	74	that	that	SCONJ
ap-1865	186	75	every	every	DET
ap-1865	186	76	lattice	lattice	ADJ
ap-1865	186	77	effect	effect	NOUN
ap-1865	186	78	algebra	algebra	NOUN
ap-1865	186	79	is	be	AUX
ap-1865	186	80	a	a	DET
ap-1865	186	81	set	set	ADJ
ap-1865	186	82	theoretical	theoretical	ADJ
ap-1865	186	83	union	union	NOUN
ap-1865	186	84	of	of	ADP
ap-1865	186	85	blocks	block	NOUN
ap-1865	186	86	of	of	ADP
ap-1865	186	87	compatible	compatible	ADJ
ap-1865	186	88	elements	element	NOUN
ap-1865	186	89	.	.	PUNCT
ap-1865	187	1	in	in	ADP
ap-1865	187	2	this	this	DET
ap-1865	187	3	section	section	NOUN
ap-1865	187	4	we	we	PRON
ap-1865	187	5	present	present	VERB
ap-1865	187	6	an	an	DET
ap-1865	187	7	analogous	analogous	ADJ
ap-1865	187	8	statement	statement	NOUN
ap-1865	187	9	for	for	ADP
ap-1865	187	10	blocks	block	NOUN
ap-1865	187	11	of	of	ADP
ap-1865	187	12	pairwise	pairwise	NOUN
ap-1865	187	13	summable	summable	ADJ
ap-1865	187	14	elements	element	NOUN
ap-1865	187	15	in	in	ADP
ap-1865	187	16	generalized	generalized	ADJ
ap-1865	187	17	effect	effect	NOUN
ap-1865	187	18	algebras	algebra	NOUN
ap-1865	187	19	.	.	PUNCT
ap-1865	188	1	let	let	VERB
ap-1865	188	2	(	(	PUNCT
ap-1865	188	3	p,≤	p,≤	VERB
ap-1865	188	4	)	)	PUNCT
ap-1865	188	5	be	be	AUX
ap-1865	188	6	a	a	DET
ap-1865	188	7	poset	poset	NOUN
ap-1865	188	8	(	(	PUNCT
ap-1865	188	9	e.g.	e.g.	ADV
ap-1865	188	10	generalized	generalized	ADJ
ap-1865	188	11	effect	effect	NOUN
ap-1865	188	12	algebra	algebra	NOUN
ap-1865	188	13	)	)	PUNCT
ap-1865	188	14	.	.	PUNCT
ap-1865	189	1	we	we	PRON
ap-1865	189	2	call	call	VERB
ap-1865	189	3	(	(	PUNCT
ap-1865	189	4	p,≤	p,≤	X
ap-1865	189	5	)	)	PUNCT
ap-1865	189	6	inductive	inductive	VERB
ap-1865	189	7	if	if	SCONJ
ap-1865	189	8	every	every	DET
ap-1865	189	9	chain	chain	NOUN
ap-1865	189	10	in	in	ADP
ap-1865	189	11	p	p	PROPN
ap-1865	189	12	has	have	VERB
ap-1865	189	13	an	an	DET
ap-1865	189	14	upper	upper	ADJ
ap-1865	189	15	bound	bind	VERB
ap-1865	189	16	.	.	PUNCT
ap-1865	190	1	460	460	NUM
ap-1865	190	2	vol	vol	NOUN
ap-1865	190	3	.	.	PUNCT
ap-1865	191	1	53	53	NUM
ap-1865	191	2	no	no	NOUN
ap-1865	191	3	.	.	PUNCT
ap-1865	192	1	5/2013	5/2013	NUM
ap-1865	192	2	maximal	maximal	ADJ
ap-1865	192	3	subsets	subset	NOUN
ap-1865	192	4	of	of	ADP
ap-1865	192	5	pairwise	pairwise	NOUN
ap-1865	192	6	summable	summable	ADJ
ap-1865	192	7	elements	element	NOUN
ap-1865	192	8	theorem	theorem	VERB
ap-1865	192	9	6	6	NUM
ap-1865	192	10	.	.	PUNCT
ap-1865	193	1	let	let	VERB
ap-1865	193	2	(	(	PUNCT
ap-1865	193	3	g;⊕	g;⊕	NOUN
ap-1865	193	4	,	,	PUNCT
ap-1865	193	5	0	0	NUM
ap-1865	193	6	)	)	PUNCT
ap-1865	193	7	be	be	AUX
ap-1865	193	8	a	a	DET
ap-1865	193	9	generalized	generalized	ADJ
ap-1865	193	10	effect	effect	NOUN
ap-1865	193	11	algebra	algebra	NOUN
ap-1865	193	12	such	such	ADJ
ap-1865	193	13	that	that	PRON
ap-1865	193	14	for	for	ADP
ap-1865	193	15	every	every	DET
ap-1865	193	16	element	element	NOUN
ap-1865	193	17	a	a	DET
ap-1865	193	18	∈	∈	PROPN
ap-1865	193	19	g	g	NOUN
ap-1865	193	20	,	,	PUNCT
ap-1865	193	21	its	its	PRON
ap-1865	193	22	isotropic	isotropic	ADJ
ap-1865	193	23	index	index	NOUN
ap-1865	193	24	ord(a	ord(a	PROPN
ap-1865	193	25	)	)	PUNCT
ap-1865	194	1	=	=	NOUN
ap-1865	194	2	∞.	∞.	PROPN
ap-1865	194	3	then	then	ADV
ap-1865	194	4	g	g	PROPN
ap-1865	194	5	is	be	AUX
ap-1865	194	6	a	a	DET
ap-1865	194	7	set	set	NOUN
ap-1865	194	8	-	-	PUNCT
ap-1865	194	9	theoretical	theoretical	ADJ
ap-1865	194	10	union	union	NOUN
ap-1865	194	11	of	of	ADP
ap-1865	194	12	its	its	PRON
ap-1865	194	13	summability	summability	NOUN
ap-1865	194	14	blocks	block	NOUN
ap-1865	194	15	,	,	PUNCT
ap-1865	194	16	which	which	PRON
ap-1865	194	17	are	be	AUX
ap-1865	194	18	sub	sub	ADJ
ap-1865	194	19	-	-	ADJ
ap-1865	194	20	generalized	generalized	ADJ
ap-1865	194	21	effect	effect	NOUN
ap-1865	194	22	algebras	algebra	NOUN
ap-1865	194	23	of	of	ADP
ap-1865	194	24	g.	g.	PROPN
ap-1865	194	25	proof	proof	PROPN
ap-1865	194	26	.	.	PUNCT
ap-1865	195	1	let	let	VERB
ap-1865	195	2	a	a	DET
ap-1865	195	3	⊆	⊆	NUM
ap-1865	195	4	g	g	NOUN
ap-1865	195	5	be	be	AUX
ap-1865	195	6	a	a	DET
ap-1865	195	7	non	non	ADJ
ap-1865	195	8	-	-	ADJ
ap-1865	195	9	empty	empty	ADJ
ap-1865	195	10	set	set	NOUN
ap-1865	195	11	of	of	ADP
ap-1865	195	12	pairwise	pairwise	NOUN
ap-1865	195	13	summable	summable	ADJ
ap-1865	195	14	elements	element	NOUN
ap-1865	195	15	(	(	PUNCT
ap-1865	195	16	i.e.	i.e.	X
ap-1865	195	17	,	,	PUNCT
ap-1865	195	18	a⊕b	a⊕b	NOUN
ap-1865	195	19	exists	exist	VERB
ap-1865	195	20	for	for	ADP
ap-1865	195	21	every	every	DET
ap-1865	195	22	a	a	PROPN
ap-1865	195	23	,	,	PUNCT
ap-1865	195	24	b	b	PROPN
ap-1865	195	25	∈	∈	PROPN
ap-1865	195	26	a	a	PRON
ap-1865	195	27	)	)	PUNCT
ap-1865	195	28	and	and	CCONJ
ap-1865	195	29	let	let	VERB
ap-1865	195	30	a	a	DET
ap-1865	195	31	=	=	SYM
ap-1865	195	32	{	{	PUNCT
ap-1865	195	33	b	b	NOUN
ap-1865	195	34	⊆	⊆	NUM
ap-1865	195	35	g	g	NOUN
ap-1865	195	36	|	|	ADV
ap-1865	195	37	a	a	DET
ap-1865	195	38	⊆	⊆	NUM
ap-1865	195	39	b	b	NOUN
ap-1865	195	40	,	,	PUNCT
ap-1865	195	41	b	b	PROPN
ap-1865	195	42	is	be	AUX
ap-1865	195	43	a	a	DET
ap-1865	195	44	set	set	NOUN
ap-1865	195	45	of	of	ADP
ap-1865	195	46	pairwise	pairwise	NOUN
ap-1865	195	47	summable	summable	ADJ
ap-1865	195	48	elements	element	NOUN
ap-1865	195	49	}	}	PUNCT
ap-1865	195	50	.	.	PUNCT
ap-1865	196	1	then	then	ADV
ap-1865	196	2	for	for	ADP
ap-1865	196	3	every	every	DET
ap-1865	196	4	chain	chain	NOUN
ap-1865	196	5	b	b	NOUN
ap-1865	196	6	⊆	⊆	NUM
ap-1865	196	7	a	a	DET
ap-1865	196	8	(	(	PUNCT
ap-1865	196	9	i.e.	i.e.	X
ap-1865	196	10	,	,	PUNCT
ap-1865	196	11	for	for	ADP
ap-1865	196	12	x	x	X
ap-1865	196	13	,	,	PUNCT
ap-1865	196	14	y	y	PROPN
ap-1865	196	15	∈	∈	PROPN
ap-1865	196	16	b	b	NOUN
ap-1865	196	17	we	we	PRON
ap-1865	196	18	have	have	VERB
ap-1865	196	19	either	either	CCONJ
ap-1865	196	20	x	x	SYM
ap-1865	196	21	⊆	⊆	NUM
ap-1865	196	22	y	y	NOUN
ap-1865	196	23	or	or	CCONJ
ap-1865	196	24	y	y	PROPN
ap-1865	196	25	⊆	⊆	NUM
ap-1865	196	26	x	x	X
ap-1865	196	27	)	)	PUNCT
ap-1865	196	28	we	we	PRON
ap-1865	196	29	show	show	VERB
ap-1865	196	30	that	that	SCONJ
ap-1865	196	31	⋃	⋃	PROPN
ap-1865	196	32	b	b	PROPN
ap-1865	196	33	∈	∈	PROPN
ap-1865	196	34	a.	a.	NOUN
ap-1865	196	35	let	let	VERB
ap-1865	196	36	us	we	PRON
ap-1865	196	37	have	have	VERB
ap-1865	196	38	x	x	X
ap-1865	196	39	,	,	PUNCT
ap-1865	196	40	y	y	PROPN
ap-1865	196	41	∈	∈	PROPN
ap-1865	196	42	⋃	⋃	PROPN
ap-1865	196	43	b.	b.	NOUN
ap-1865	196	44	then	then	ADV
ap-1865	196	45	there	there	PRON
ap-1865	196	46	exist	exist	VERB
ap-1865	196	47	bx	bx	NOUN
ap-1865	196	48	,	,	PUNCT
ap-1865	196	49	by	by	ADP
ap-1865	196	50	such	such	ADJ
ap-1865	196	51	that	that	SCONJ
ap-1865	196	52	x	x	SYM
ap-1865	196	53	∈	∈	PROPN
ap-1865	196	54	bx	bx	PROPN
ap-1865	196	55	,	,	PUNCT
ap-1865	196	56	y	y	PROPN
ap-1865	196	57	∈	∈	PROPN
ap-1865	196	58	by	by	ADP
ap-1865	196	59	.	.	PUNCT
ap-1865	197	1	by	by	ADP
ap-1865	197	2	assumptions	assumption	NOUN
ap-1865	197	3	bx	bx	X
ap-1865	197	4	⊆	⊆	NUM
ap-1865	197	5	by	by	ADP
ap-1865	197	6	or	or	CCONJ
ap-1865	197	7	by	by	ADP
ap-1865	197	8	⊆	⊆	NUM
ap-1865	197	9	bx	bx	PROPN
ap-1865	197	10	,	,	PUNCT
ap-1865	197	11	hence	hence	ADV
ap-1865	197	12	x	x	X
ap-1865	197	13	,	,	PUNCT
ap-1865	197	14	y	y	PROPN
ap-1865	197	15	∈	∈	PROPN
ap-1865	197	16	bx	bx	PROPN
ap-1865	197	17	or	or	CCONJ
ap-1865	197	18	x	x	NOUN
ap-1865	197	19	,	,	PUNCT
ap-1865	197	20	y	y	PROPN
ap-1865	197	21	∈	∈	PROPN
ap-1865	197	22	by	by	ADP
ap-1865	197	23	i.e.	i.e.	X
ap-1865	197	24	x⊕	x⊕	PROPN
ap-1865	197	25	y	y	PROPN
ap-1865	197	26	exists	exist	VERB
ap-1865	197	27	.	.	PUNCT
ap-1865	198	1	therefore	therefore	ADV
ap-1865	198	2	⋃	⋃	PROPN
ap-1865	198	3	b	b	PROPN
ap-1865	198	4	∈	∈	PROPN
ap-1865	198	5	a	a	DET
ap-1865	198	6	hence	hence	ADV
ap-1865	198	7	a	a	PRON
ap-1865	198	8	is	be	AUX
ap-1865	198	9	inductive	inductive	ADJ
ap-1865	198	10	.	.	PUNCT
ap-1865	199	1	thus	thus	ADV
ap-1865	199	2	a	a	DET
ap-1865	199	3	maximal	maximal	ADJ
ap-1865	199	4	element	element	NOUN
ap-1865	199	5	m	m	VERB
ap-1865	199	6	by	by	ADP
ap-1865	199	7	zorn	zorn	PROPN
ap-1865	199	8	’s	’s	PART
ap-1865	199	9	lemma	lemma	PROPN
ap-1865	199	10	exists	exist	VERB
ap-1865	199	11	in	in	ADP
ap-1865	199	12	a	a	PRON
ap-1865	199	13	and	and	CCONJ
ap-1865	199	14	m	m	NOUN
ap-1865	199	15	is	be	AUX
ap-1865	199	16	clearly	clearly	ADV
ap-1865	199	17	a	a	DET
ap-1865	199	18	summability	summability	NOUN
ap-1865	199	19	block	block	NOUN
ap-1865	199	20	of	of	ADP
ap-1865	199	21	g.	g.	NOUN
ap-1865	199	22	for	for	ADP
ap-1865	199	23	every	every	DET
ap-1865	199	24	a	a	DET
ap-1865	199	25	∈	∈	PROPN
ap-1865	199	26	g	g	NOUN
ap-1865	199	27	,	,	PUNCT
ap-1865	199	28	a	a	DET
ap-1865	199	29	6=	6=	NUM
ap-1865	199	30	0	0	NUM
ap-1865	199	31	there	there	PRON
ap-1865	199	32	exists	exist	VERB
ap-1865	199	33	a	a	DET
ap-1865	199	34	pairwise	pairwise	NOUN
ap-1865	199	35	summable	summable	NOUN
ap-1865	199	36	subset	subset	VERB
ap-1865	199	37	a	a	PRON
ap-1865	199	38	=	=	PUNCT
ap-1865	199	39	{	{	PUNCT
ap-1865	199	40	0	0	NUM
ap-1865	199	41	,	,	PUNCT
ap-1865	199	42	a	a	PRON
ap-1865	199	43	,	,	PUNCT
ap-1865	199	44	2a	2a	NUM
ap-1865	199	45	,	,	PUNCT
ap-1865	199	46	.	.	PUNCT
ap-1865	199	47	.	.	PUNCT
ap-1865	199	48	.	.	PUNCT
ap-1865	200	1	}	}	PUNCT
ap-1865	200	2	∈	∈	PROPN
ap-1865	200	3	g.	g.	NOUN
ap-1865	200	4	by	by	ADP
ap-1865	200	5	previous	previous	ADJ
ap-1865	200	6	a	a	DET
ap-1865	200	7	subset	subset	NOUN
ap-1865	200	8	a	a	DET
ap-1865	200	9	⊆	⊆	NUM
ap-1865	200	10	g	g	NOUN
ap-1865	200	11	is	be	AUX
ap-1865	200	12	contained	contain	VERB
ap-1865	200	13	in	in	ADP
ap-1865	200	14	some	some	DET
ap-1865	200	15	summability	summability	NOUN
ap-1865	200	16	block	block	NOUN
ap-1865	200	17	m	m	NOUN
ap-1865	200	18	.	.	PUNCT
ap-1865	201	1	thus	thus	ADV
ap-1865	201	2	g	g	PROPN
ap-1865	201	3	is	be	AUX
ap-1865	201	4	a	a	DET
ap-1865	201	5	set	set	NOUN
ap-1865	201	6	-	-	PUNCT
ap-1865	201	7	theoretical	theoretical	ADJ
ap-1865	201	8	union	union	NOUN
ap-1865	201	9	of	of	ADP
ap-1865	201	10	summability	summability	NOUN
ap-1865	201	11	blocks	block	NOUN
ap-1865	201	12	m	m	VERB
ap-1865	201	13	.	.	PUNCT
ap-1865	202	1	blocks	block	NOUN
ap-1865	202	2	are	be	AUX
ap-1865	202	3	sub	sub	ADJ
ap-1865	202	4	-	-	ADJ
ap-1865	202	5	generalized	generalized	ADJ
ap-1865	202	6	effect	effect	NOUN
ap-1865	202	7	algebras	algebra	NOUN
ap-1865	202	8	by	by	ADP
ap-1865	202	9	theorem	theorem	ADJ
ap-1865	202	10	1	1	NUM
ap-1865	202	11	(	(	PUNCT
ap-1865	202	12	resp	resp	NOUN
ap-1865	202	13	.	.	PUNCT
ap-1865	203	1	corollary	corollary	ADJ
ap-1865	203	2	1	1	NUM
ap-1865	203	3	)	)	PUNCT
ap-1865	203	4	.	.	PUNCT
ap-1865	204	1	hence	hence	ADV
ap-1865	204	2	any	any	DET
ap-1865	204	3	generalized	generalized	ADJ
ap-1865	204	4	effect	effect	NOUN
ap-1865	204	5	algebra	algebra	NOUN
ap-1865	204	6	without	without	ADP
ap-1865	204	7	elements	element	NOUN
ap-1865	204	8	with	with	ADP
ap-1865	204	9	finite	finite	ADJ
ap-1865	204	10	isotropic	isotropic	NOUN
ap-1865	204	11	index	index	NOUN
ap-1865	204	12	(	(	PUNCT
ap-1865	204	13	g;⊕	g;⊕	NOUN
ap-1865	204	14	,	,	PUNCT
ap-1865	204	15	0	0	NUM
ap-1865	204	16	)	)	PUNCT
ap-1865	204	17	is	be	AUX
ap-1865	204	18	covered	cover	VERB
ap-1865	204	19	by	by	ADP
ap-1865	204	20	its	its	PRON
ap-1865	204	21	summability	summability	NOUN
ap-1865	204	22	blocks	block	NOUN
ap-1865	204	23	.	.	PUNCT
ap-1865	205	1	example	example	NOUN
ap-1865	206	1	5	5	NUM
ap-1865	206	2	.	.	PUNCT
ap-1865	207	1	we	we	PRON
ap-1865	207	2	now	now	ADV
ap-1865	207	3	turn	turn	VERB
ap-1865	207	4	to	to	PART
ap-1865	207	5	example	example	NOUN
ap-1865	207	6	1	1	NUM
ap-1865	207	7	.	.	PUNCT
ap-1865	208	1	let	let	VERB
ap-1865	208	2	h	h	PRON
ap-1865	208	3	be	be	AUX
ap-1865	208	4	an	an	DET
ap-1865	208	5	infinite	infinite	ADJ
ap-1865	208	6	-	-	PUNCT
ap-1865	208	7	dimensional	dimensional	ADJ
ap-1865	208	8	complex	complex	ADJ
ap-1865	208	9	hilbert	hilbert	NOUN
ap-1865	208	10	space	space	NOUN
ap-1865	208	11	.	.	PUNCT
ap-1865	209	1	consider	consider	VERB
ap-1865	209	2	a	a	DET
ap-1865	209	3	generalized	generalized	ADJ
ap-1865	209	4	effect	effect	NOUN
ap-1865	209	5	algebra	algebra	NOUN
ap-1865	209	6	vd(h	vd(h	PUNCT
ap-1865	209	7	)	)	PUNCT
ap-1865	209	8	and	and	CCONJ
ap-1865	209	9	its	its	PRON
ap-1865	209	10	subgeneralized	subgeneralize	VERB
ap-1865	209	11	effect	effect	NOUN
ap-1865	209	12	algebras	algebra	NOUN
ap-1865	209	13	gd(h	gd(h	PROPN
ap-1865	209	14	)	)	PUNCT
ap-1865	209	15	from	from	ADP
ap-1865	209	16	example	example	NOUN
ap-1865	209	17	1	1	NUM
ap-1865	209	18	.	.	PUNCT
ap-1865	210	1	then	then	ADV
ap-1865	210	2	for	for	ADP
ap-1865	210	3	any	any	DET
ap-1865	210	4	d	d	PROPN
ap-1865	210	5	∈	∈	PROPN
ap-1865	210	6	d	d	PROPN
ap-1865	210	7	,	,	PUNCT
ap-1865	210	8	d	d	PROPN
ap-1865	210	9	6=	6=	PROPN
ap-1865	210	10	h	h	PROPN
ap-1865	210	11	,	,	PUNCT
ap-1865	210	12	gd(h	gd(h	ADJ
ap-1865	210	13	)	)	PUNCT
ap-1865	210	14	forms	form	VERB
ap-1865	210	15	a	a	DET
ap-1865	210	16	summability	summability	NOUN
ap-1865	210	17	block	block	NOUN
ap-1865	210	18	of	of	ADP
ap-1865	210	19	vd(h	vd(h	PROPN
ap-1865	210	20	)	)	PUNCT
ap-1865	210	21	.	.	PUNCT
ap-1865	211	1	note	note	VERB
ap-1865	211	2	that	that	SCONJ
ap-1865	211	3	sub	sub	ADJ
ap-1865	211	4	-	-	ADJ
ap-1865	211	5	generalized	generalized	ADJ
ap-1865	211	6	effect	effect	NOUN
ap-1865	211	7	algebras	algebra	NOUN
ap-1865	211	8	gd(h	gd(h	PROPN
ap-1865	211	9	)	)	PUNCT
ap-1865	211	10	are	be	AUX
ap-1865	211	11	also	also	ADV
ap-1865	211	12	compatibility	compatibility	NOUN
ap-1865	211	13	blocks	block	NOUN
ap-1865	211	14	(	(	PUNCT
ap-1865	211	15	see	see	VERB
ap-1865	211	16	[	[	X
ap-1865	211	17	14	14	NUM
ap-1865	211	18	]	]	PUNCT
ap-1865	211	19	,	,	PUNCT
ap-1865	211	20	hence	hence	ADV
ap-1865	211	21	in	in	ADP
ap-1865	211	22	this	this	DET
ap-1865	211	23	case	case	NOUN
ap-1865	211	24	,	,	PUNCT
ap-1865	211	25	compatibility	compatibility	NOUN
ap-1865	211	26	and	and	CCONJ
ap-1865	211	27	summability	summability	NOUN
ap-1865	211	28	blocks	block	NOUN
ap-1865	211	29	coincide	coincide	NOUN
ap-1865	211	30	.	.	PUNCT
ap-1865	212	1	theorem	theorem	VERB
ap-1865	212	2	7	7	NUM
ap-1865	212	3	.	.	PUNCT
ap-1865	213	1	let	let	VERB
ap-1865	213	2	(	(	PUNCT
ap-1865	213	3	g;⊕	g;⊕	NOUN
ap-1865	213	4	,	,	PUNCT
ap-1865	213	5	0	0	NUM
ap-1865	213	6	)	)	PUNCT
ap-1865	213	7	be	be	AUX
ap-1865	213	8	a	a	DET
ap-1865	213	9	lattice	lattice	ADJ
ap-1865	213	10	generalized	generalized	ADJ
ap-1865	213	11	effect	effect	NOUN
ap-1865	213	12	algebra	algebra	NOUN
ap-1865	213	13	such	such	ADJ
ap-1865	213	14	that	that	PRON
ap-1865	213	15	for	for	ADP
ap-1865	213	16	every	every	DET
ap-1865	213	17	element	element	NOUN
ap-1865	213	18	a	a	DET
ap-1865	213	19	∈	∈	PROPN
ap-1865	213	20	g	g	NOUN
ap-1865	213	21	,	,	PUNCT
ap-1865	213	22	its	its	PRON
ap-1865	213	23	isotropic	isotropic	ADJ
ap-1865	213	24	index	index	NOUN
ap-1865	213	25	ord(a	ord(a	PROPN
ap-1865	213	26	)	)	PUNCT
ap-1865	214	1	=	=	SYM
ap-1865	214	2	∞.	∞.	PROPN
ap-1865	214	3	then	then	ADV
ap-1865	214	4	g	g	PROPN
ap-1865	214	5	is	be	AUX
ap-1865	214	6	a	a	DET
ap-1865	214	7	set	set	NOUN
ap-1865	214	8	-	-	PUNCT
ap-1865	214	9	theoretical	theoretical	ADJ
ap-1865	214	10	union	union	NOUN
ap-1865	214	11	of	of	ADP
ap-1865	214	12	its	its	PRON
ap-1865	214	13	blocks	block	NOUN
ap-1865	214	14	,	,	PUNCT
ap-1865	214	15	which	which	PRON
ap-1865	214	16	are	be	AUX
ap-1865	214	17	subgeneralized	subgeneralize	VERB
ap-1865	214	18	effect	effect	NOUN
ap-1865	214	19	algebras	algebra	NOUN
ap-1865	214	20	of	of	ADP
ap-1865	214	21	g	g	PROPN
ap-1865	214	22	and	and	CCONJ
ap-1865	214	23	generalized	generalize	VERB
ap-1865	214	24	mveffect	mveffect	ADJ
ap-1865	214	25	algebras	algebra	NOUN
ap-1865	214	26	in	in	ADP
ap-1865	214	27	its	its	PRON
ap-1865	214	28	own	own	ADJ
ap-1865	214	29	right	right	NOUN
ap-1865	214	30	.	.	PUNCT
ap-1865	215	1	proof	proof	NOUN
ap-1865	215	2	.	.	PUNCT
ap-1865	216	1	this	this	PRON
ap-1865	216	2	follows	follow	VERB
ap-1865	216	3	from	from	ADP
ap-1865	216	4	theorems	theorem	NOUN
ap-1865	216	5	5	5	NUM
ap-1865	216	6	and	and	CCONJ
ap-1865	216	7	6	6	NUM
ap-1865	216	8	.	.	PUNCT
ap-1865	216	9	corollary	corollary	ADJ
ap-1865	216	10	2	2	NUM
ap-1865	216	11	.	.	PUNCT
ap-1865	217	1	for	for	ADP
ap-1865	217	2	every	every	DET
ap-1865	217	3	maximal	maximal	ADJ
ap-1865	217	4	pairwise	pairwise	NOUN
ap-1865	217	5	summable	summable	ADJ
ap-1865	217	6	subset	subset	NOUN
ap-1865	217	7	f	f	PROPN
ap-1865	217	8	of	of	ADP
ap-1865	217	9	a	a	DET
ap-1865	217	10	lattice	lattice	NOUN
ap-1865	217	11	ordered	order	VERB
ap-1865	217	12	generalized	generalized	ADJ
ap-1865	217	13	effect	effect	NOUN
ap-1865	217	14	algebra	algebra	NOUN
ap-1865	217	15	(	(	PUNCT
ap-1865	217	16	g;⊕	g;⊕	NOUN
ap-1865	217	17	,	,	PUNCT
ap-1865	217	18	0	0	NUM
ap-1865	217	19	)	)	PUNCT
ap-1865	217	20	and	and	CCONJ
ap-1865	217	21	any	any	DET
ap-1865	217	22	q	q	NOUN
ap-1865	217	23	∈	∈	PROPN
ap-1865	217	24	g	g	NOUN
ap-1865	217	25	,	,	PUNCT
ap-1865	217	26	q	q	X
ap-1865	218	1	6=	6=	NUM
ap-1865	218	2	0	0	NUM
ap-1865	219	1	the	the	DET
ap-1865	219	2	intervals	interval	NOUN
ap-1865	219	3	[	[	X
ap-1865	219	4	0	0	NUM
ap-1865	219	5	,	,	PUNCT
ap-1865	219	6	q]f	q]f	ADV
ap-1865	219	7	=	=	PUNCT
ap-1865	220	1	[	[	X
ap-1865	220	2	0	0	NUM
ap-1865	220	3	,	,	PUNCT
ap-1865	220	4	q]g	q]g	ADP
ap-1865	220	5	∩	∩	SCONJ
ap-1865	220	6	f	f	PRON
ap-1865	220	7	are	be	AUX
ap-1865	220	8	mv	mv	ADJ
ap-1865	220	9	-	-	PUNCT
ap-1865	220	10	effect	effect	NOUN
ap-1865	220	11	algebras	algebra	NOUN
ap-1865	220	12	in	in	ADP
ap-1865	220	13	its	its	PRON
ap-1865	220	14	own	own	ADJ
ap-1865	220	15	right	right	NOUN
ap-1865	220	16	.	.	PUNCT
ap-1865	221	1	proof	proof	NOUN
ap-1865	221	2	.	.	PUNCT
ap-1865	222	1	the	the	DET
ap-1865	222	2	identical	identical	ADJ
ap-1865	222	3	mapping	mapping	NOUN
ap-1865	222	4	ϕ	ϕ	NOUN
ap-1865	222	5	:	:	PUNCT
ap-1865	223	1	[	[	X
ap-1865	223	2	0	0	NUM
ap-1865	223	3	,	,	PUNCT
ap-1865	223	4	q]g	q]g	ADV
ap-1865	223	5	→	→	PUNCT
ap-1865	223	6	[	[	X
ap-1865	223	7	0	0	NUM
ap-1865	223	8	,	,	PUNCT
ap-1865	223	9	q]g	q]g	NOUN
ap-1865	223	10	restricted	restrict	VERB
ap-1865	223	11	to	to	ADP
ap-1865	223	12	[	[	X
ap-1865	223	13	0	0	NUM
ap-1865	223	14	,	,	PUNCT
ap-1865	223	15	q]f	q]f	ADV
ap-1865	223	16	=	=	PUNCT
ap-1865	224	1	[	[	X
ap-1865	224	2	0	0	NUM
ap-1865	224	3	,	,	PUNCT
ap-1865	224	4	q]g	q]g	ADP
ap-1865	224	5	∩	∩	SCONJ
ap-1865	224	6	f	f	PROPN
ap-1865	224	7	is	be	AUX
ap-1865	224	8	an	an	DET
ap-1865	224	9	embedding	embedding	NOUN
ap-1865	224	10	of	of	ADP
ap-1865	224	11	[	[	X
ap-1865	224	12	0	0	NUM
ap-1865	224	13	,	,	PUNCT
ap-1865	224	14	q]f	q]f	ADV
ap-1865	224	15	into	into	ADP
ap-1865	224	16	[	[	X
ap-1865	224	17	0	0	NUM
ap-1865	224	18	,	,	PUNCT
ap-1865	224	19	q]g	q]g	NOUN
ap-1865	224	20	.	.	PUNCT
ap-1865	225	1	thus	thus	ADV
ap-1865	225	2	if	if	SCONJ
ap-1865	225	3	g	g	PROPN
ap-1865	225	4	is	be	AUX
ap-1865	225	5	a	a	DET
ap-1865	225	6	lattice	lattice	NOUN
ap-1865	225	7	ordered	order	VERB
ap-1865	225	8	generalized	generalized	ADJ
ap-1865	225	9	effect	effect	NOUN
ap-1865	225	10	algebra	algebra	NOUN
ap-1865	225	11	,	,	PUNCT
ap-1865	225	12	then	then	ADV
ap-1865	225	13	[	[	X
ap-1865	225	14	0	0	NUM
ap-1865	225	15	,	,	PUNCT
ap-1865	225	16	q]g	q]g	ADP
ap-1865	225	17	∩	∩	SCONJ
ap-1865	225	18	f	f	PROPN
ap-1865	225	19	is	be	AUX
ap-1865	225	20	a	a	DET
ap-1865	225	21	sub	sub	ADJ
ap-1865	225	22	-	-	ADJ
ap-1865	225	23	effect	effect	ADJ
ap-1865	225	24	algebra	algebra	NOUN
ap-1865	225	25	of	of	ADP
ap-1865	225	26	[	[	X
ap-1865	225	27	0	0	NUM
ap-1865	225	28	,	,	PUNCT
ap-1865	225	29	q]g	q]g	ADV
ap-1865	225	30	(	(	PUNCT
ap-1865	225	31	see	see	VERB
ap-1865	225	32	[	[	X
ap-1865	225	33	7	7	NUM
ap-1865	225	34	,	,	PUNCT
ap-1865	225	35	section	section	NOUN
ap-1865	225	36	3	3	NUM
ap-1865	225	37	]	]	PUNCT
ap-1865	225	38	)	)	PUNCT
ap-1865	225	39	and	and	CCONJ
ap-1865	225	40	consequently	consequently	ADV
ap-1865	225	41	it	it	PRON
ap-1865	225	42	is	be	AUX
ap-1865	225	43	an	an	DET
ap-1865	225	44	mv	mv	ADJ
ap-1865	225	45	-	-	PUNCT
ap-1865	225	46	effect	effect	NOUN
ap-1865	225	47	algebra	algebra	NOUN
ap-1865	225	48	in	in	ADP
ap-1865	225	49	its	its	PRON
ap-1865	225	50	own	own	ADJ
ap-1865	225	51	right	right	NOUN
ap-1865	225	52	.	.	PUNCT
ap-1865	226	1	example	example	NOUN
ap-1865	227	1	6	6	NUM
ap-1865	227	2	.	.	PUNCT
ap-1865	228	1	consider	consider	VERB
ap-1865	228	2	chang	chang	PROPN
ap-1865	228	3	’s	’s	PART
ap-1865	228	4	effect	effect	NOUN
ap-1865	228	5	algebra	algebra	NOUN
ap-1865	228	6	(	(	PUNCT
ap-1865	228	7	g;⊕	g;⊕	NOUN
ap-1865	228	8	,	,	PUNCT
ap-1865	228	9	0	0	NUM
ap-1865	228	10	)	)	PUNCT
ap-1865	228	11	mentioned	mention	VERB
ap-1865	228	12	in	in	ADP
ap-1865	228	13	example	example	NOUN
ap-1865	228	14	3	3	X
ap-1865	228	15	.	.	PUNCT
ap-1865	229	1	it	it	PRON
ap-1865	229	2	is	be	AUX
ap-1865	229	3	not	not	PART
ap-1865	229	4	covered	cover	VERB
ap-1865	229	5	by	by	ADP
ap-1865	229	6	summability	summability	NOUN
ap-1865	229	7	blocks	block	NOUN
ap-1865	229	8	since	since	SCONJ
ap-1865	229	9	it	it	PRON
ap-1865	229	10	has	have	VERB
ap-1865	229	11	elements	element	NOUN
ap-1865	229	12	with	with	ADP
ap-1865	229	13	finite	finite	ADJ
ap-1865	229	14	isotropic	isotropic	NOUN
ap-1865	229	15	index	index	NOUN
ap-1865	229	16	.	.	PUNCT
ap-1865	230	1	there	there	PRON
ap-1865	230	2	exists	exist	VERB
ap-1865	230	3	only	only	ADV
ap-1865	230	4	one	one	NUM
ap-1865	230	5	summability	summability	NOUN
ap-1865	230	6	block	block	NOUN
ap-1865	230	7	f	f	NOUN
ap-1865	230	8	=	=	PUNCT
ap-1865	230	9	{	{	PUNCT
ap-1865	230	10	0	0	NUM
ap-1865	230	11	,	,	PUNCT
ap-1865	230	12	a	a	PRON
ap-1865	230	13	,	,	PUNCT
ap-1865	230	14	2a	2a	NUM
ap-1865	230	15	,	,	PUNCT
ap-1865	230	16	.	.	PUNCT
ap-1865	230	17	.	.	PUNCT
ap-1865	231	1	.	.	PUNCT
ap-1865	232	1	}	}	PUNCT
ap-1865	233	1	⊆	⊆	NUM
ap-1865	233	2	g.	g.	NOUN
ap-1865	233	3	on	on	ADP
ap-1865	233	4	the	the	DET
ap-1865	233	5	other	other	ADJ
ap-1865	233	6	hand	hand	NOUN
ap-1865	233	7	,	,	PUNCT
ap-1865	233	8	since	since	SCONJ
ap-1865	233	9	g	g	PROPN
ap-1865	233	10	is	be	AUX
ap-1865	233	11	linearly	linearly	ADV
ap-1865	233	12	ordered	order	VERB
ap-1865	233	13	by	by	ADP
ap-1865	233	14	induced	induce	VERB
ap-1865	233	15	partial	partial	ADJ
ap-1865	233	16	order	order	NOUN
ap-1865	233	17	≤	≤	NOUN
ap-1865	233	18	,	,	PUNCT
ap-1865	233	19	all	all	PRON
ap-1865	233	20	of	of	ADP
ap-1865	233	21	its	its	PRON
ap-1865	233	22	elements	element	NOUN
ap-1865	233	23	are	be	AUX
ap-1865	233	24	pairwise	pairwise	NOUN
ap-1865	233	25	compatible	compatible	ADJ
ap-1865	233	26	,	,	PUNCT
ap-1865	233	27	hence	hence	ADV
ap-1865	233	28	the	the	DET
ap-1865	233	29	only	only	ADJ
ap-1865	233	30	compatibility	compatibility	NOUN
ap-1865	233	31	block	block	NOUN
ap-1865	233	32	is	be	AUX
ap-1865	233	33	g	g	PROPN
ap-1865	233	34	itself	itself	PRON
ap-1865	233	35	(	(	PUNCT
ap-1865	233	36	g	g	NOUN
ap-1865	233	37	is	be	AUX
ap-1865	233	38	an	an	DET
ap-1865	233	39	mv	mv	ADJ
ap-1865	233	40	-	-	PUNCT
ap-1865	233	41	effect	effect	NOUN
ap-1865	233	42	algebra	algebra	NOUN
ap-1865	233	43	)	)	PUNCT
ap-1865	233	44	.	.	PUNCT
ap-1865	234	1	that	that	PRON
ap-1865	234	2	is	be	AUX
ap-1865	234	3	compatibility	compatibility	NOUN
ap-1865	234	4	and	and	CCONJ
ap-1865	234	5	summability	summability	NOUN
ap-1865	234	6	blocks	block	NOUN
ap-1865	234	7	need	need	AUX
ap-1865	234	8	not	not	PART
ap-1865	234	9	coincide	coincide	VERB
ap-1865	234	10	.	.	PUNCT
ap-1865	235	1	acknowledgements	acknowledgement	NOUN
ap-1865	235	2	zdenka	zdenka	PROPN
ap-1865	235	3	riečanová	riečanová	PROPN
ap-1865	235	4	gratefully	gratefully	ADV
ap-1865	235	5	acknowledges	acknowledge	VERB
ap-1865	235	6	support	support	NOUN
ap-1865	235	7	by	by	ADP
ap-1865	235	8	the	the	DET
ap-1865	235	9	science	science	NOUN
ap-1865	235	10	and	and	CCONJ
ap-1865	235	11	technology	technology	NOUN
ap-1865	235	12	assistance	assistance	NOUN
ap-1865	235	13	agency	agency	NOUN
ap-1865	235	14	under	under	ADP
ap-1865	235	15	contract	contract	NOUN
ap-1865	235	16	apvv-0178	apvv-0178	ADV
ap-1865	235	17	-	-	PUNCT
ap-1865	235	18	11	11	NUM
ap-1865	235	19	bratislva	bratislva	PROPN
ap-1865	235	20	sr	sr	PROPN
ap-1865	235	21	,	,	PUNCT
ap-1865	235	22	and	and	CCONJ
ap-1865	235	23	under	under	ADP
ap-1865	235	24	vega	vega	NOUN
ap-1865	235	25	-	-	PUNCT
ap-1865	235	26	grant	grant	NOUN
ap-1865	235	27	of	of	ADP
ap-1865	235	28	mš	mš	PROPN
ap-1865	235	29	sr	sr	PROPN
ap-1865	235	30	no	no	INTJ
ap-1865	235	31	.	.	PUNCT
ap-1865	236	1	1/0297/11	1/0297/11	NUM
ap-1865	236	2	.	.	PUNCT
ap-1865	237	1	jiří	jiří	PROPN
ap-1865	237	2	janda	janda	PROPN
ap-1865	237	3	gratefully	gratefully	ADV
ap-1865	237	4	acknowledges	acknowledge	VERB
ap-1865	237	5	support	support	NOUN
ap-1865	237	6	from	from	ADP
ap-1865	237	7	masaryk	masaryk	PROPN
ap-1865	237	8	university	university	PROPN
ap-1865	237	9	,	,	PUNCT
ap-1865	237	10	grant	grant	VERB
ap-1865	237	11	muni	muni	PROPN
ap-1865	237	12	/	/	SYM
ap-1865	237	13	a/0838/2012	a/0838/2012	PROPN
ap-1865	237	14	and	and	CCONJ
ap-1865	237	15	esf	esf	PROPN
ap-1865	237	16	project	project	PROPN
ap-1865	237	17	cz.1.07/2.3.00/20.0051	cz.1.07/2.3.00/20.0051	PROPN
ap-1865	237	18	algebraic	algebraic	ADJ
ap-1865	237	19	methods	method	NOUN
ap-1865	237	20	in	in	ADP
ap-1865	237	21	quantum	quantum	ADJ
ap-1865	237	22	logic	logic	NOUN
ap-1865	237	23	of	of	ADP
ap-1865	237	24	the	the	DET
ap-1865	237	25	masaryk	masaryk	PROPN
ap-1865	237	26	university	university	PROPN
ap-1865	237	27	.	.	PUNCT
ap-1865	238	1	references	reference	NOUN
ap-1865	238	2	[	[	X
ap-1865	238	3	1	1	NUM
ap-1865	238	4	]	]	PUNCT
ap-1865	238	5	blank	blank	PROPN
ap-1865	238	6	j.	j.	PROPN
ap-1865	238	7	,	,	PUNCT
ap-1865	238	8	exner	exner	PROPN
ap-1865	238	9	p.	p.	PROPN
ap-1865	238	10	,	,	PUNCT
ap-1865	238	11	havlíček	havlíček	NOUN
ap-1865	238	12	m.	m.	NOUN
ap-1865	238	13	,	,	PUNCT
ap-1865	238	14	hilbert	hilbert	NOUN
ap-1865	238	15	space	space	NOUN
ap-1865	238	16	operators	operator	NOUN
ap-1865	238	17	in	in	ADP
ap-1865	238	18	quantum	quantum	ADJ
ap-1865	238	19	physics	physics	NOUN
ap-1865	238	20	,	,	PUNCT
ap-1865	238	21	2nd	2nd	ADJ
ap-1865	238	22	ed	ed	NOUN
ap-1865	238	23	.	.	PUNCT
ap-1865	238	24	springer	springer	PROPN
ap-1865	238	25	,	,	PUNCT
ap-1865	238	26	berlin	berlin	PROPN
ap-1865	238	27	(	(	PUNCT
ap-1865	238	28	2008	2008	NUM
ap-1865	238	29	)	)	PUNCT
ap-1865	238	30	.	.	PUNCT
ap-1865	239	1	[	[	X
ap-1865	239	2	2	2	X
ap-1865	239	3	]	]	PUNCT
ap-1865	239	4	dvurečenskij	dvurečenskij	PROPN
ap-1865	239	5	a.	a.	PROPN
ap-1865	239	6	,	,	PUNCT
ap-1865	239	7	pulmannová	pulmannová	PROPN
ap-1865	239	8	s.	s.	PROPN
ap-1865	239	9	,	,	PUNCT
ap-1865	239	10	new	new	ADJ
ap-1865	239	11	trends	trend	NOUN
ap-1865	239	12	in	in	ADP
ap-1865	239	13	quantum	quantum	ADJ
ap-1865	239	14	structures	structure	NOUN
ap-1865	239	15	,	,	PUNCT
ap-1865	239	16	kluwer	kluwer	NOUN
ap-1865	239	17	acad	acad	PROPN
ap-1865	239	18	.	.	PUNCT
ap-1865	240	1	publ	publ	PROPN
ap-1865	240	2	.	.	PUNCT
ap-1865	240	3	,	,	PUNCT
ap-1865	240	4	dordrecht	dordrecht	PROPN
ap-1865	240	5	/	/	SYM
ap-1865	240	6	ister	ister	PROPN
ap-1865	240	7	science	science	NOUN
ap-1865	240	8	,	,	PUNCT
ap-1865	240	9	bratislava	bratislava	PROPN
ap-1865	240	10	,	,	PUNCT
ap-1865	240	11	2000	2000	NUM
ap-1865	240	12	.	.	PUNCT
ap-1865	241	1	[	[	X
ap-1865	241	2	3	3	X
ap-1865	241	3	]	]	X
ap-1865	241	4	foulis	foulis	PROPN
ap-1865	241	5	d.	d.	PROPN
ap-1865	241	6	j.	j.	PROPN
ap-1865	241	7	,	,	PUNCT
ap-1865	241	8	bennett	bennett	PROPN
ap-1865	241	9	m.	m.	PROPN
ap-1865	241	10	k.	k.	PROPN
ap-1865	241	11	,	,	PUNCT
ap-1865	241	12	effect	effect	NOUN
ap-1865	241	13	algebras	algebra	NOUN
ap-1865	241	14	and	and	CCONJ
ap-1865	241	15	unsharp	unsharp	ADJ
ap-1865	241	16	quantum	quantum	ADJ
ap-1865	241	17	logics	logic	NOUN
ap-1865	241	18	,	,	PUNCT
ap-1865	241	19	found	find	VERB
ap-1865	241	20	.	.	PUNCT
ap-1865	242	1	phys	phy	NOUN
ap-1865	242	2	.	.	PUNCT
ap-1865	243	1	24	24	NUM
ap-1865	243	2	(	(	PUNCT
ap-1865	243	3	1994	1994	NUM
ap-1865	243	4	)	)	PUNCT
ap-1865	243	5	,	,	PUNCT
ap-1865	243	6	1331–1352	1331–1352	NUM
ap-1865	243	7	.	.	PUNCT
ap-1865	244	1	[	[	X
ap-1865	244	2	4	4	NUM
ap-1865	244	3	]	]	X
ap-1865	244	4	gudder	gudder	ADJ
ap-1865	244	5	s.	s.	PROPN
ap-1865	244	6	,	,	PUNCT
ap-1865	244	7	d	d	X
ap-1865	244	8	-	-	PUNCT
ap-1865	244	9	algebras	algebras	X
ap-1865	244	10	,	,	PUNCT
ap-1865	244	11	found	find	VERB
ap-1865	244	12	.	.	PUNCT
ap-1865	245	1	phys	phy	NOUN
ap-1865	245	2	.	.	PUNCT
ap-1865	246	1	26	26	NUM
ap-1865	246	2	,	,	PUNCT
ap-1865	246	3	no	no	INTJ
ap-1865	246	4	.	.	NOUN
ap-1865	246	5	6	6	NUM
ap-1865	246	6	,	,	PUNCT
ap-1865	246	7	(	(	PUNCT
ap-1865	246	8	1996	1996	NUM
ap-1865	246	9	)	)	PUNCT
ap-1865	246	10	,	,	PUNCT
ap-1865	246	11	813–822	813–822	NUM
ap-1865	246	12	.	.	PUNCT
ap-1865	247	1	[	[	X
ap-1865	247	2	5	5	X
ap-1865	247	3	]	]	X
ap-1865	247	4	hedlíková	hedlíková	PROPN
ap-1865	247	5	j.	j.	PROPN
ap-1865	247	6	,	,	PUNCT
ap-1865	247	7	pulmannová	pulmannová	PROPN
ap-1865	247	8	s.	s.	PROPN
ap-1865	247	9	,	,	PUNCT
ap-1865	247	10	generalized	generalized	ADJ
ap-1865	247	11	difference	difference	NOUN
ap-1865	247	12	posets	poset	NOUN
ap-1865	247	13	and	and	CCONJ
ap-1865	247	14	orthoalgebras	orthoalgebra	NOUN
ap-1865	247	15	,	,	PUNCT
ap-1865	247	16	acta	acta	PROPN
ap-1865	247	17	math	math	PROPN
ap-1865	247	18	.	.	PUNCT
ap-1865	248	1	univ	univ	PROPN
ap-1865	248	2	.	.	PROPN
ap-1865	248	3	comenianae	comenianae	PROPN
ap-1865	248	4	lxv	lxv	PROPN
ap-1865	248	5	,	,	PUNCT
ap-1865	248	6	(	(	PUNCT
ap-1865	248	7	1996	1996	NUM
ap-1865	248	8	)	)	PUNCT
ap-1865	248	9	,	,	PUNCT
ap-1865	248	10	247–279	247–279	NUM
ap-1865	248	11	.	.	PUNCT
ap-1865	249	1	[	[	X
ap-1865	249	2	6	6	NUM
ap-1865	249	3	]	]	PUNCT
ap-1865	249	4	kalmbach	kalmbach	PROPN
ap-1865	249	5	g.	g.	PROPN
ap-1865	249	6	,	,	PUNCT
ap-1865	249	7	riečanová	riečanová	PROPN
ap-1865	249	8	z.	z.	PROPN
ap-1865	249	9	an	an	DET
ap-1865	249	10	axiomatization	axiomatization	NOUN
ap-1865	249	11	for	for	ADP
ap-1865	249	12	abelian	abelian	PROPN
ap-1865	249	13	relative	relative	PROPN
ap-1865	249	14	inverses	inverses	PROPN
ap-1865	249	15	,	,	PUNCT
ap-1865	249	16	demonstratio	demonstratio	PROPN
ap-1865	249	17	math	math	PROPN
ap-1865	249	18	.	.	PUNCT
ap-1865	250	1	27	27	NUM
ap-1865	250	2	,	,	PUNCT
ap-1865	250	3	(	(	PUNCT
ap-1865	250	4	1994	1994	NUM
ap-1865	250	5	)	)	PUNCT
ap-1865	250	6	,	,	PUNCT
ap-1865	251	1	769–780	769–780	NUM
ap-1865	251	2	.	.	PUNCT
ap-1865	252	1	[	[	X
ap-1865	252	2	7	7	X
ap-1865	252	3	]	]	X
ap-1865	252	4	janda	janda	PROPN
ap-1865	252	5	j.	j.	PROPN
ap-1865	252	6	,	,	PUNCT
ap-1865	252	7	riečanová	riečanová	PROPN
ap-1865	252	8	z.	z.	PROPN
ap-1865	252	9	intervals	interval	NOUN
ap-1865	252	10	in	in	ADP
ap-1865	252	11	generalized	generalized	ADJ
ap-1865	252	12	effect	effect	NOUN
ap-1865	252	13	algebras	algebra	NOUN
ap-1865	252	14	,	,	PUNCT
ap-1865	252	15	to	to	PART
ap-1865	252	16	appear	appear	VERB
ap-1865	252	17	in	in	ADP
ap-1865	252	18	soft	soft	ADJ
ap-1865	252	19	computing	computing	NOUN
ap-1865	252	20	,	,	PUNCT
ap-1865	252	21	(	(	PUNCT
ap-1865	252	22	2013	2013	NUM
ap-1865	252	23	)	)	PUNCT
ap-1865	252	24	,	,	PUNCT
ap-1865	252	25	doi:10.1007	doi:10.1007	VERB
ap-1865	252	26	/	/	SYM
ap-1865	252	27	s00500	s00500	PROPN
ap-1865	252	28	-	-	PUNCT
ap-1865	252	29	013	013	NUM
ap-1865	252	30	-	-	PUNCT
ap-1865	252	31	1083	1083	NUM
ap-1865	252	32	-	-	SYM
ap-1865	252	33	x.	x.	NOUN
ap-1865	253	1	[	[	X
ap-1865	253	2	8	8	NUM
ap-1865	253	3	]	]	X
ap-1865	253	4	kôpka	kôpka	PROPN
ap-1865	253	5	f.	f.	PROPN
ap-1865	253	6	,	,	PUNCT
ap-1865	253	7	chovanec	chovanec	PROPN
ap-1865	253	8	f.	f.	PROPN
ap-1865	253	9	d	d	PROPN
ap-1865	253	10	-	-	PUNCT
ap-1865	253	11	posets	poset	NOUN
ap-1865	253	12	,	,	PUNCT
ap-1865	253	13	math	math	NOUN
ap-1865	253	14	.	.	PUNCT
ap-1865	254	1	slovaca	slovaca	PROPN
ap-1865	254	2	44	44	NUM
ap-1865	254	3	,	,	PUNCT
ap-1865	254	4	(	(	PUNCT
ap-1865	254	5	1994	1994	NUM
ap-1865	254	6	)	)	PUNCT
ap-1865	254	7	,	,	PUNCT
ap-1865	254	8	21–34	21–34	NUM
ap-1865	254	9	.	.	PUNCT
ap-1865	255	1	[	[	X
ap-1865	255	2	9	9	NUM
ap-1865	255	3	]	]	PUNCT
ap-1865	255	4	riečanová	riečanová	PROPN
ap-1865	255	5	z.	z.	PROPN
ap-1865	255	6	,	,	PUNCT
ap-1865	255	7	subalgebras	subalgebras	PROPN
ap-1865	255	8	,	,	PUNCT
ap-1865	255	9	intervals	interval	NOUN
ap-1865	255	10	and	and	CCONJ
ap-1865	255	11	central	central	ADJ
ap-1865	255	12	elements	element	NOUN
ap-1865	255	13	of	of	ADP
ap-1865	255	14	generalized	generalized	ADJ
ap-1865	255	15	effect	effect	NOUN
ap-1865	255	16	algebras	algebra	NOUN
ap-1865	255	17	,	,	PUNCT
ap-1865	255	18	inter	inter	PROPN
ap-1865	255	19	.	.	PUNCT
ap-1865	256	1	j.	j.	PROPN
ap-1865	256	2	theor	theor	PROPN
ap-1865	256	3	.	.	PUNCT
ap-1865	257	1	phys	phy	NOUN
ap-1865	257	2	.	.	PUNCT
ap-1865	258	1	38	38	NUM
ap-1865	258	2	,	,	PUNCT
ap-1865	258	3	(	(	PUNCT
ap-1865	258	4	1999	1999	NUM
ap-1865	258	5	)	)	PUNCT
ap-1865	258	6	,	,	PUNCT
ap-1865	258	7	3209–3220	3209–3220	NUM
ap-1865	258	8	.	.	PUNCT
ap-1865	259	1	[	[	X
ap-1865	259	2	10	10	NUM
ap-1865	259	3	]	]	X
ap-1865	259	4	riečanová	riečanová	PROPN
ap-1865	259	5	z.	z.	PROPN
ap-1865	259	6	,	,	PUNCT
ap-1865	259	7	generalization	generalization	NOUN
ap-1865	259	8	of	of	ADP
ap-1865	259	9	blocks	block	NOUN
ap-1865	259	10	for	for	ADP
ap-1865	259	11	d	d	NOUN
ap-1865	259	12	-	-	PUNCT
ap-1865	259	13	lattices	lattice	NOUN
ap-1865	259	14	and	and	CCONJ
ap-1865	259	15	lattice	lattice	NOUN
ap-1865	259	16	-	-	PUNCT
ap-1865	259	17	ordered	order	VERB
ap-1865	259	18	effect	effect	NOUN
ap-1865	259	19	algebras	algebra	NOUN
ap-1865	259	20	,	,	PUNCT
ap-1865	259	21	inter	inter	PROPN
ap-1865	259	22	.	.	PUNCT
ap-1865	260	1	j.	j.	PROPN
ap-1865	260	2	theor	theor	PROPN
ap-1865	260	3	.	.	PUNCT
ap-1865	261	1	phys	phy	NOUN
ap-1865	261	2	.	.	PUNCT
ap-1865	262	1	39	39	NUM
ap-1865	262	2	,	,	PUNCT
ap-1865	262	3	(	(	PUNCT
ap-1865	262	4	2000	2000	NUM
ap-1865	262	5	)	)	PUNCT
ap-1865	262	6	,	,	PUNCT
ap-1865	262	7	no	no	INTJ
ap-1865	262	8	.	.	NOUN
ap-1865	263	1	2	2	NUM
ap-1865	263	2	.	.	NUM
ap-1865	263	3	,	,	PUNCT
ap-1865	263	4	pp	pp	ADJ
ap-1865	263	5	.	.	PUNCT
ap-1865	264	1	231–237	231–237	NUM
ap-1865	264	2	.	.	PUNCT
ap-1865	265	1	[	[	X
ap-1865	265	2	11	11	NUM
ap-1865	265	3	]	]	PUNCT
ap-1865	265	4	riečanová	riečanová	PROPN
ap-1865	265	5	z.	z.	PROPN
ap-1865	265	6	,	,	PUNCT
ap-1865	265	7	marinová	marinová	PROPN
ap-1865	265	8	i.	i.	PROPN
ap-1865	265	9	generalized	generalize	VERB
ap-1865	265	10	homogeneous	homogeneous	ADJ
ap-1865	265	11	,	,	PUNCT
ap-1865	265	12	prelattice	prelattice	NOUN
ap-1865	265	13	and	and	CCONJ
ap-1865	265	14	mv	mv	ADJ
ap-1865	265	15	-	-	PUNCT
ap-1865	265	16	effect	effect	NOUN
ap-1865	265	17	algebras	algebra	NOUN
ap-1865	265	18	,	,	PUNCT
ap-1865	265	19	kybernetika	kybernetika	NOUN
ap-1865	265	20	41	41	NUM
ap-1865	265	21	,	,	PUNCT
ap-1865	265	22	(	(	PUNCT
ap-1865	265	23	2005	2005	NUM
ap-1865	265	24	)	)	PUNCT
ap-1865	265	25	,	,	PUNCT
ap-1865	265	26	no	no	INTJ
ap-1865	265	27	.	.	NOUN
ap-1865	265	28	2	2	NUM
ap-1865	265	29	,	,	PUNCT
ap-1865	265	30	pp	pp	ADJ
ap-1865	265	31	.	.	PUNCT
ap-1865	266	1	129–142	129–142	NUM
ap-1865	266	2	.	.	PUNCT
ap-1865	267	1	[	[	X
ap-1865	267	2	12	12	NUM
ap-1865	267	3	]	]	PUNCT
ap-1865	267	4	riečanová	riečanová	PROPN
ap-1865	267	5	z.	z.	PROPN
ap-1865	267	6	,	,	PUNCT
ap-1865	267	7	zajac	zajac	PROPN
ap-1865	267	8	m.	m.	PROPN
ap-1865	267	9	,	,	PUNCT
ap-1865	267	10	intervals	interval	NOUN
ap-1865	267	11	in	in	ADP
ap-1865	267	12	generalized	generalized	ADJ
ap-1865	267	13	effect	effect	NOUN
ap-1865	267	14	algebras	algebra	NOUN
ap-1865	267	15	and	and	CCONJ
ap-1865	267	16	their	their	PRON
ap-1865	267	17	sub	sub	ADJ
ap-1865	267	18	-	-	ADJ
ap-1865	267	19	generalized	generalized	ADJ
ap-1865	267	20	effect	effect	NOUN
ap-1865	267	21	algebras	algebra	NOUN
ap-1865	267	22	,	,	PUNCT
ap-1865	267	23	acta	acta	PROPN
ap-1865	267	24	polytechnica	polytechnica	PROPN
ap-1865	267	25	53	53	NUM
ap-1865	267	26	,	,	PUNCT
ap-1865	267	27	(	(	PUNCT
ap-1865	267	28	2013	2013	NUM
ap-1865	267	29	)	)	PUNCT
ap-1865	267	30	,	,	PUNCT
ap-1865	267	31	no	no	INTJ
ap-1865	267	32	.	.	NOUN
ap-1865	267	33	3	3	NUM
ap-1865	267	34	,	,	PUNCT
ap-1865	267	35	pp	pp	ADJ
ap-1865	267	36	.	.	PUNCT
ap-1865	268	1	314–316	314–316	NUM
ap-1865	268	2	.	.	PUNCT
ap-1865	269	1	[	[	X
ap-1865	269	2	13	13	NUM
ap-1865	269	3	]	]	X
ap-1865	269	4	riečanová	riečanová	PROPN
ap-1865	269	5	z	z	PROPN
ap-1865	269	6	,	,	PUNCT
ap-1865	269	7	zajac	zajac	PROPN
ap-1865	269	8	m.	m.	PROPN
ap-1865	269	9	,	,	PUNCT
ap-1865	269	10	hilbert	hilbert	NOUN
ap-1865	269	11	space	space	NOUN
ap-1865	269	12	effect	effect	NOUN
ap-1865	269	13	-	-	PUNCT
ap-1865	269	14	representations	representation	NOUN
ap-1865	269	15	of	of	ADP
ap-1865	269	16	effect	effect	NOUN
ap-1865	269	17	algebras	algebra	NOUN
ap-1865	269	18	,	,	PUNCT
ap-1865	269	19	rep	rep	PROPN
ap-1865	269	20	.	.	PROPN
ap-1865	269	21	math	math	NOUN
ap-1865	269	22	.	.	PUNCT
ap-1865	270	1	phys	phy	NOUN
ap-1865	270	2	.	.	PUNCT
ap-1865	271	1	70	70	NUM
ap-1865	271	2	,	,	PUNCT
ap-1865	271	3	(	(	PUNCT
ap-1865	271	4	2012	2012	NUM
ap-1865	271	5	)	)	PUNCT
ap-1865	271	6	,	,	PUNCT
ap-1865	271	7	no	no	INTJ
ap-1865	271	8	.	.	NOUN
ap-1865	271	9	2	2	NUM
ap-1865	271	10	,	,	PUNCT
ap-1865	271	11	pp	pp	ADJ
ap-1865	271	12	.	.	PUNCT
ap-1865	272	1	283–290	283–290	NUM
ap-1865	272	2	.	.	PUNCT
ap-1865	273	1	[	[	X
ap-1865	273	2	14	14	NUM
ap-1865	273	3	]	]	X
ap-1865	273	4	riečanová	riečanová	PROPN
ap-1865	273	5	z.	z.	PROPN
ap-1865	273	6	,	,	PUNCT
ap-1865	273	7	zajac	zajac	PROPN
ap-1865	273	8	m.	m.	PROPN
ap-1865	273	9	,	,	PUNCT
ap-1865	273	10	pulmannová	pulmannová	PROPN
ap-1865	273	11	s.	s.	PROPN
ap-1865	273	12	,	,	PUNCT
ap-1865	273	13	effect	effect	NOUN
ap-1865	273	14	algebras	algebra	NOUN
ap-1865	273	15	of	of	ADP
ap-1865	273	16	positive	positive	ADJ
ap-1865	273	17	linear	linear	PROPN
ap-1865	273	18	operators	operator	NOUN
ap-1865	273	19	densely	densely	ADV
ap-1865	273	20	defined	define	VERB
ap-1865	273	21	on	on	ADP
ap-1865	273	22	hilbert	hilbert	PROPN
ap-1865	273	23	spaces	space	NOUN
ap-1865	273	24	,	,	PUNCT
ap-1865	273	25	rep	rep	PROPN
ap-1865	273	26	.	.	PROPN
ap-1865	273	27	math	math	NOUN
ap-1865	273	28	.	.	PUNCT
ap-1865	274	1	phys	phy	NOUN
ap-1865	274	2	.	.	PUNCT
ap-1865	275	1	68	68	NUM
ap-1865	275	2	,	,	PUNCT
ap-1865	275	3	(	(	PUNCT
ap-1865	275	4	2011	2011	NUM
ap-1865	275	5	)	)	PUNCT
ap-1865	275	6	,	,	PUNCT
ap-1865	275	7	261–270	261–270	NUM
ap-1865	275	8	.	.	PUNCT
ap-1865	276	1	461	461	NUM
ap-1865	276	2	http://dx.doi.org/10.1007/s00500-013-1083-x	http://dx.doi.org/10.1007/s00500-013-1083-x	NOUN
ap-1865	276	3	acta	acta	PROPN
ap-1865	276	4	polytechnica	polytechnica	PROPN
ap-1865	276	5	53(5):457–461	53(5):457–461	PROPN
ap-1865	276	6	,	,	PUNCT
ap-1865	276	7	2013	2013	NUM
ap-1865	276	8	1	1	NUM
ap-1865	276	9	introduction	introduction	NOUN
ap-1865	276	10	and	and	CCONJ
ap-1865	276	11	some	some	DET
ap-1865	276	12	basic	basic	ADJ
ap-1865	276	13	definitions	definition	NOUN
ap-1865	276	14	2	2	NUM
ap-1865	276	15	pairwise	pairwise	NOUN
ap-1865	276	16	summable	summable	ADJ
ap-1865	276	17	generalized	generalized	ADJ
ap-1865	276	18	effect	effect	NOUN
ap-1865	276	19	algebras	algebra	VERB
ap-1865	276	20	3	3	NUM
ap-1865	276	21	intervals	interval	NOUN
ap-1865	276	22	in	in	ADP
ap-1865	276	23	pairwise	pairwise	NOUN
ap-1865	276	24	summable	summable	ADJ
ap-1865	276	25	generalized	generalized	ADJ
ap-1865	276	26	effect	effect	NOUN
ap-1865	276	27	algebras	algebra	VERB
ap-1865	276	28	4	4	NUM
ap-1865	276	29	blocks	block	NOUN
ap-1865	276	30	of	of	ADP
ap-1865	276	31	pairwise	pairwise	NOUN
ap-1865	276	32	summable	summable	ADJ
ap-1865	276	33	elements	element	NOUN
ap-1865	276	34	in	in	ADP
ap-1865	276	35	generalized	generalized	ADJ
ap-1865	276	36	effect	effect	NOUN
ap-1865	276	37	algebras	algebra	NOUN
ap-1865	276	38	acknowledgements	acknowledgement	NOUN
ap-1865	276	39	references	reference	NOUN