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http://hdl.handle.net/11320/4837
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Pole DC | Wartość | Język |
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dc.contributor.author | Endou, Noboru | pl |
dc.contributor.author | Nakasho, Kazuhisa | pl |
dc.contributor.author | Shidama, Yasunari | pl |
dc.date.accessioned | 2016-12-06T02:00:00Z | pl |
dc.date.accessioned | 2016-12-12T10:36:08Z | - |
dc.date.available | 2016-12-06T02:00:00Z | pl |
dc.date.available | 2016-12-12T10:36:08Z | - |
dc.date.issued | 2015 | pl |
dc.identifier.citation | Formalized Mathematics, Volume 23, Issue 1, Pages 51–57 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/4837 | - |
dc.description.abstract | In 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.iso | en | pl |
dc.publisher | De Gruyter Open | pl |
dc.subject | semiring of sets | pl |
dc.subject | σ-ring of sets | pl |
dc.subject | σ-algebra of sets | pl |
dc.title | σ-ring and σ-algebra of Sets | pl |
dc.type | Article | pl |
dc.identifier.doi | 10.2478/forma-2015-0004 | pl |
dc.description.Affiliation | Noboru Endou - Gifu National College of Technology, Gifu, Japan | pl |
dc.description.Affiliation | Kazuhisa Nakasho - Shinshu University, Nagano, Japan | pl |
dc.description.Affiliation | Yasunari Shidama - Shinshu University, Nagano, Japan | pl |
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Występuje w kolekcji(ach): | Formalized Mathematics, 2015, Volume 23, Issue 1 |
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