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http://hdl.handle.net/11320/9226
Tytuł: | Reconstruction of the One-Dimensional Lebesgue Measure |
Autorzy: | Endou, Noboru |
Słowa kluczowe: | Lebesgue measure algebra of intervals |
Data wydania: | 2020 |
Data dodania: | 16-cze-2020 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 28, Issue 1, Pages 93-104 |
Abstrakt: | In the Mizar system ([1], [2]), Józef Białas has already given the one-dimensional Lebesgue measure [4]. However, the measure introduced by Białas limited the outer measure to a field with finite additivity. So, although it satisfies the nature of the measure, it cannot specify the length of measurable sets and also it cannot determine what kind of set is a measurable set. From the above, the authors first determined the length of the interval by the outer measure. Specifically, we used the compactness of the real space. Next, we constructed the pre-measure by limiting the outer measure to a semialgebra of intervals. Furthermore, by repeating the extension of the previous measure, we reconstructed the one-dimensional Lebesgue measure [7], [3]. |
Afiliacja: | National Institute of Technology, Gifu College, 2236-2 Kamimakuwa, Motosu, Gifu, Japan |
URI: | http://hdl.handle.net/11320/9226 |
DOI: | 10.2478/forma-2020-0008 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
Typ Dokumentu: | Article |
metadata.dc.rights.uri: | http://creativecommons.org/licenses/by-sa/3.0/pl/ |
Występuje w kolekcji(ach): | Formalized Mathematics, 2020, Volume 28, Issue 1 |
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