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Tytuł: σ-ring and σ-algebra of Sets
Autorzy: Endou, Noboru
Nakasho, Kazuhisa
Shidama, Yasunari
Słowa kluczowe: semiring of sets
σ-ring of sets
σ-algebra of sets
Data wydania: 2015
Data dodania: 6-gru-2016
12-gru-2016
Wydawca: De Gruyter Open
Źródło: Formalized Mathematics, Volume 23, Issue 1, Pages 51–57
Abstrakt: 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].
Afiliacja: Noboru Endou - Gifu National College of Technology, Gifu, Japan
Kazuhisa Nakasho - Shinshu University, Nagano, Japan
Yasunari Shidama - Shinshu University, Nagano, Japan
URI: http://hdl.handle.net/11320/4837
DOI: 10.2478/forma-2015-0004
ISSN: 1426-2630
1898-9934
Typ Dokumentu: Article
Występuje w kolekcji(ach):Formalized Mathematics, 2015, Volume 23, Issue 1

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