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  2. Czasopisma naukowe / Journals
  3. Formalized Mathematics
  4. Formalized Mathematics, 2009, Volume 17, Issue 2

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3528
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    Pole DCWartośćJęzyk
    dc.contributor.authorOkazaki, Hiroyuki-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2015-12-01T19:26:34Z-
    dc.date.available2015-12-01T19:26:34Z-
    dc.date.issued2009-
    dc.identifier.citationFormalized Mathematics, Volume 17, Issue 2, 2009, Pages 129-136-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3528-
    dc.description.abstractIn the various branches of science, probability and randomness provide us with useful theoretical frameworks. The Formalized Mathematics has already published some articles concerning the probability: [23], [24], [25], and [30]. In order to apply those articles, we shall give some theorems concerning the probability and the real-valued random variables to prepare for further studies.-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleProbability on Finite Set and Real-Valued Random Variables-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-009-0014-x-
    dc.description.AffiliationOkazaki Hiroyuki - Shinshu University, Nagano, Japan-
    dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
    dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.-
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
    dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
    dc.description.referencesJózef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.-
    dc.description.referencesJózef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.-
    dc.description.referencesJózef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.-
    dc.description.referencesJózef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.-
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
    dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
    dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
    dc.description.referencesCzesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.-
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
    dc.description.referencesNoboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x.-
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.-
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.-
    dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.-
    dc.description.referencesGrigory E. Ivanov. Definition of convex function and Jensen's inequality. Formalized Mathematics, 11(4):349-354, 2003.-
    dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.-
    dc.description.referencesJarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.-
    dc.description.referencesKeiko Narita, Noboru Endou, and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics, 16(4):319-324, 2008, doi:10.2478/v10037-008-0039-6.-
    dc.description.referencesAndrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.-
    dc.description.referencesAndrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.-
    dc.description.referencesJan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755-760, 1990.-
    dc.description.referencesYasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics, 14(4):143-152, 2006, doi:10.2478/v10037-006-0018-8.-
    dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.-
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
    dc.description.referencesBo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. The relevance of measure and probability, and definition of completeness of probability. Formalized Mathematics, 14(4):225-229, 2006, doi:10.2478/v10037-006-0026-8.-
    Występuje w kolekcji(ach):Formalized Mathematics, 2009, Volume 17, Issue 2

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