Semiring of Sets

Pole DC	Wartość	Język
dc.contributor.author	Coghetto, Roland	-
dc.date.accessioned	2015-12-09T20:40:38Z	-
dc.date.available	2015-12-09T20:40:38Z	-
dc.date.issued	2014	-
dc.identifier.citation	Formalized Mathematics, Volume 22, Issue 1, 2014, Pages 79-84	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3704	-
dc.description.abstract	Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	sets	-
dc.subject	set partitions	-
dc.subject	distributive lattice	-
dc.title	Semiring of Sets	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2014-0008	-
dc.description.Affiliation	Rue de la Brasserie 5 7100 La Louvière, Belgium	-
dc.description.references	Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.	-
dc.description.references	Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.	-
dc.description.references	Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.	-
dc.description.references	Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.	-
dc.description.references	Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.	-
dc.description.references	Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.	-
dc.description.references	Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.	-
dc.description.references	Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.	-
dc.description.references	Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.	-
dc.description.references	Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.	-
dc.description.references	Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Formalized Mathematics, 2(4):453-459, 1991.	-
dc.description.references	Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.	-
dc.description.references	Marek Dudzicz. Representation theorem for finite distributive lattices. Formalized Mathematics, 9(2):261-264, 2001.	-
dc.description.references	Mariusz Giero. Hierarchies and classifications of sets. Formalized Mathematics, 9(4): 865-869, 2001.	-
dc.description.references	D.F. Goguadze. About the notion of semiring of sets. Mathematical Notes, 74:346-351, 2003. ISSN 0001-4346. doi:10.1023/A:1026102701631.	-
dc.description.references	Zbigniew Karno. On discrete and almost discrete topological spaces. Formalized Mathematics, 3(2):305-310, 1992.	-
dc.description.references	Shunichi Kobayashi and Kui Jia. A theory of partitions. Part I. Formalized Mathematics, 7(2):243-247, 1998.	-
dc.description.references	Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.	-
dc.description.references	Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.	-
dc.description.references	A. G Patriota. A note on Carathéodory’s extension theorem. ArXiv e-prints, 2011.	-
dc.description.references	Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.	-
dc.description.references	Jean Schmets. Théorie de la mesure. Notes de cours, Université de Liège, 146 pages, 2004.	-
dc.description.references	Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.	-
dc.description.references	Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.	-
dc.description.references	Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.	-
dc.description.references	Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.	-
dc.description.references	Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.	-
dc.description.references	Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.	-
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