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http://hdl.handle.net/11320/3683
Tytuł: | Riemann Integral of Functions from R into Real Banach Space |
Autorzy: | Narita, Keiko Endou, Noboru Shidama, Yasunari |
Słowa kluczowe: | formalization of Riemann integral |
Data wydania: | 2013 |
Data dodania: | 9-gru-2015 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 21, Issue 2, 2013, Pages 145-152 |
Abstrakt: | In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the convergence of sequences. We applied definitions introduced in the previous article [21] to the proof of integrability. |
Afiliacja: | Narita Keiko - Hirosaki-city Aomori, Japan Endou Noboru - Gifu National College of Technology Japan Shidama Yasunari - Shinshu University Nagano, Japan |
Sponsorzy: | This work was supported by JSPS KAKENHI 22300285 and 23500029 |
URI: | http://hdl.handle.net/11320/3683 |
DOI: | 10.2478/forma-2013-0016 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2013, Volume 21, Issue 2 |
Pliki w tej pozycji:
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forma-2013-0016.pdf | 227,87 kB | Adobe PDF | Otwórz |
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