Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/5565
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Endou, Noboru | - |
dc.date.accessioned | 2017-06-05T08:32:49Z | - |
dc.date.available | 2017-06-05T08:32:49Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Formalized Mathematics, Volume 25, Issue 1, pp. 1-30 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/5565 | - |
dc.description.abstract | The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.subject | Fubini’s theorem | - |
dc.subject | product measure | - |
dc.title | Fubini’s Theorem on Measure | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2017-0001 | - |
dc.description.Affiliation | National Institute of Technology, Gifu College 2236-2 Kamimakuwa, Motosu, Gifu, Japan | - |
dc.description.references | Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3): 537-541, 1990. | - |
dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | - |
dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. | - |
dc.description.references | Heinz Bauer. Measure and Integration Theory. Walter de Gruyter Inc., 2002. | - |
dc.description.references | Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991. | - |
dc.description.references | Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991. | - |
dc.description.references | Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007. | - |
dc.description.references | Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. | - |
dc.description.references | Czesław Byliński. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241-245, 1996. | - |
dc.description.references | Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. | - |
dc.description.references | Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. | - |
dc.description.references | Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. | - |
dc.description.references | Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. | - |
dc.description.references | Noboru Endou. Product pre-measure. Formalized Mathematics, 24(1):69-79, 2016. | - |
dc.description.references | Gerald B. Folland. Real Analysis: Modern Techniques and Their Applications. Wiley, 2nd edition, 1999. | - |
dc.description.references | P. R. Halmos. Measure Theory. Springer-Verlag, 1974. | - |
dc.description.references | Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990. | - |
dc.description.references | M.M. Rao. Measure Theory and Integration. Marcel Dekker, 2nd edition, 2004. | - |
dc.description.references | Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990. | - |
dc.description.references | Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, and Hiroyuki Okazaki. Inferior limit, superior limit and convergence of sequences of extended real numbers. Formalized Mathematics, 15(4):231-236, 2007. doi: 10.2478/v10037-007-0026-3. | - |
dc.description.references | Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Limit of sequence of subsets. Formalized Mathematics, 13(2):347-352, 2005. | - |
dc.description.references | Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Some equations related to the limit of sequence of subsets. Formalized Mathematics, 13(3):407-412, 2005. | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2017, Volume 25, Issue 1 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
---|---|---|---|---|
forma-2017-0001.pdf | 369,12 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL