Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/4905
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Endou, Noboru | pl |
dc.date.accessioned | 2016-12-16T10:30:41Z | - |
dc.date.available | 2016-12-16T10:30:41Z | - |
dc.date.issued | 2015 | pl |
dc.identifier.citation | Formalized Mathematics, Volume 23, Issue 4, 309–323 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/4905 | - |
dc.description.abstract | 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]. | pl |
dc.description.sponsorship | This work was supported by JSPS KAKENHI 23500029 | pl |
dc.language.iso | en | pl |
dc.publisher | De Gruyter Open | pl |
dc.subject | measure theory | pl |
dc.subject | pre-measure | pl |
dc.title | Construction of Measure from Semialgebra of Sets | pl |
dc.type | Article | pl |
dc.identifier.doi | 10.1515/forma-2015-0025 | pl |
dc.description.Affiliation | Gifu National College of Technology, Gifu, Japan | pl |
dc.description.references | is work was supported by JSPS KAKENHI 23500029.↩ | pl |
dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990. | pl |
dc.description.references | Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589–593, 1990. | pl |
dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990. | pl |
dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990. | pl |
dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990. | pl |
dc.description.references | Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263–270, 1991. | pl |
dc.description.references | Józef Białas. Properties of Caratheodor’s measure. Formalized Mathematics, 3(1):67–70, 1992. | pl |
dc.description.references | Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163–171, 1991. | pl |
dc.description.references | Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173–183, 1991. | pl |
dc.description.references | V.I. Bogachev. Measure Theory, volume 1. Springer, 2006. | pl |
dc.description.references | Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643–649, 1990. | pl |
dc.description.references | Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990. | pl |
dc.description.references | Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990. | pl |
dc.description.references | Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990. | pl |
dc.description.references | Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990. | pl |
dc.description.references | Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990. | pl |
dc.description.references | Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990. | pl |
dc.description.references | Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53–70, 2006. doi:10.2478/v10037-006-0008-x. [Crossref] | pl |
dc.description.references | Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491–494, 2001. | pl |
dc.description.references | Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495–500, 2001. | pl |
dc.description.references | Noboru Endou, Keiko Narita, and Yasunari Shidama. The Lebesgue monotone convergence theorem. Formalized Mathematics, 16(2):167–175, 2008. doi:10.2478/v10037-008-0023-1. [Crossref] | pl |
dc.description.references | Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. Hopf extension theorem of measure. Formalized Mathematics, 17(2):157–162, 2009. doi:10.2478/v10037-009-0018-6. [Crossref] | pl |
dc.description.references | Noboru Endou, Kazuhisa Nakasho, and Yasunari Shidama. σ-ring and σ-algebra of sets. Formalized Mathematics, 23(1):51–57, 2015. doi:10.2478/forma-2015-0004. [Crossref] | pl |
dc.description.references | P. R. Halmos. Measure Theory. Springer-Verlag, 1974. | pl |
dc.description.references | Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4): 573–577, 1997. | pl |
dc.description.references | Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339–345, 1996. | pl |
dc.description.references | Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401–407, 1990. | pl |
dc.description.references | Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745–749, 1990. | pl |
dc.description.references | Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147–152, 1990. | pl |
dc.description.references | Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449–452, 1991. | pl |
dc.description.references | M.M. Rao. Measure Theory and Integration. CRC Press, 2nd edition, 2004. | pl |
dc.description.references | Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187–190, 1990. | pl |
dc.description.references | Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990. | pl |
dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. | pl |
dc.description.references | Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990. | pl |
dc.description.references | Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990. | pl |
Występuje w kolekcji(ach): | Formalized Mathematics, 2015, Volume 23, Issue 4 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
---|---|---|---|---|
forma-2015-0025.pdf | 315,25 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL