REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU

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Pole DCWartośćJęzyk
dc.contributor.authorEndou, Noborupl
dc.contributor.authorNakasho, Kazuhisapl
dc.contributor.authorShidama, Yasunaripl
dc.date.accessioned2016-12-06T02:00:00Zpl
dc.date.accessioned2016-12-12T10:36:08Z-
dc.date.available2016-12-06T02:00:00Zpl
dc.date.available2016-12-12T10:36:08Z-
dc.date.issued2015pl
dc.identifier.citationFormalized Mathematics, Volume 23, Issue 1, Pages 51–57pl
dc.identifier.issn1426-2630pl
dc.identifier.issn1898-9934pl
dc.identifier.urihttp://hdl.handle.net/11320/4837-
dc.description.abstractIn this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets [18], respectively. In the second section, definitions of a ring and a σ-ring of sets, which are based on a semiring and a ring of sets respectively, are formalized and their related theorems are proved. In the third section, definitions of an algebra and a σ-algebra of sets, which are based on a semialgebra and an algebra of sets respectively, are formalized and their related theorems are proved. In the last section, mutual relationships between σ-ring and σ-algebra of sets are formalized and some related examples are given. The formalization is based on [15], and also referred to [9] and [16].pl
dc.language.isoenpl
dc.publisherDe Gruyter Openpl
dc.subjectsemiring of setspl
dc.subjectσ-ring of setspl
dc.subjectσ-algebra of setspl
dc.titleσ-ring and σ-algebra of Setspl
dc.typeArticlepl
dc.identifier.doi10.2478/forma-2015-0004pl
dc.description.AffiliationNoboru Endou - Gifu National College of Technology, Gifu, Japanpl
dc.description.AffiliationKazuhisa Nakasho - Shinshu University, Nagano, Japanpl
dc.description.AffiliationYasunari Shidama - Shinshu University, Nagano, Japanpl
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