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http://hdl.handle.net/11320/4905
Tytuł: | Construction of Measure from Semialgebra of Sets |
Autorzy: | Endou, Noboru |
Słowa kluczowe: | measure theory pre-measure |
Data wydania: | 2015 |
Data dodania: | 16-gru-2016 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 23, Issue 4, 309–323 |
Abstrakt: | In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we give a σ-measure as an extension of the measure on a σ-field. We follow [24], [10], and [31]. |
Afiliacja: | Gifu National College of Technology, Gifu, Japan |
Sponsorzy: | This work was supported by JSPS KAKENHI 23500029 |
URI: | http://hdl.handle.net/11320/4905 |
DOI: | 10.1515/forma-2015-0025 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2015, Volume 23, Issue 4 |
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