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  3. Formalized Mathematics
  4. Formalized Mathematics, 2008, Volume 16, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21080
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    Pole DCWartośćJęzyk
    dc.contributor.authorNarita, Keiko-
    dc.contributor.authorEndou, Noboru-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2026-09-22T07:55:17Z-
    dc.date.available2026-09-22T07:55:17Z-
    dc.date.issued2008-
    dc.identifier.citationFormalized Mathematics, Volume 16, Issue 4, 2008, Pages 319-324pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/21080-
    dc.description.abstractIn this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered.pl
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsAttribution-ShareAlike 4.0 Internationalpl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
    dc.titleIntegral of Complex-Valued Measurable Functionpl
    dc.typeArticlepl
    dc.rights.holder© 2009 Keiko Narita, Noboru Endou, Yasunari Shidama, published by University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.identifier.doi10.2478/v10037-008-0039-6-
    dc.description.AffiliationKeiko Narita - Hirosaki-city Aomori, Japanpl
    dc.description.AffiliationNoboru Endou - Gifu National College of Technology, Japanpl
    dc.description.AffiliationYasunari Shidama - Shinshu University Nagano, Japanpl
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.pl
    dc.description.referencesJózef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173–183, 1991.pl
    dc.description.referencesJózef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263–270, 1991.pl
    dc.description.referencesJózef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21–26, 1996.pl
    dc.description.referencesCzesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507–513, 1990.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.pl
    dc.description.referencesNoboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53–70, 2006.pl
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491–494, 2001.pl
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495–500, 2001.pl
    dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35–40, 1990.pl
    dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269–272, 1990.pl
    dc.description.referencesAndrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401–407, 1990.pl
    dc.description.referencesKonrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213–216, 1991.pl
    dc.description.referencesYasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics, 14(4):143–152, 2006.pl
    dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73–83, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume16pl
    dc.description.issue4pl
    dc.description.firstpage319pl
    dc.description.lastpage324pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Formalized Mathematics, 2008, Volume 16, Issue 4

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