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  3. Formalized Mathematics
  4. Formalized Mathematics, 2012, Volume 20, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3631
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    Pole DCWartośćJęzyk
    dc.contributor.authorMiyajima, Keiichi-
    dc.contributor.authorKorniłowicz, Artur-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2015-12-06T19:05:20Z-
    dc.date.available2015-12-06T19:05:20Z-
    dc.date.issued2012-
    dc.identifier.citationFormalized Mathematics, Volume 20, Issue 1, 2012, Pages 79-86-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3631-
    dc.description.abstractIn this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21]-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleRiemann Integral of Functions from R into n-dimensional Real Normed Space-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-012-0011-3-
    dc.description.AffiliationMiyajima Keiichi - Faculty of Engineering, Ibaraki University, Hitachi, Japan-
    dc.description.AffiliationKorniłowicz Artur - Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok Poland-
    dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
    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.-
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    dc.description.referencesCzesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.-
    dc.description.referencesCzesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.-
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
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    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.-
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.-
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.-
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    dc.description.referencesKeiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.-
    dc.description.referencesKeiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.-
    dc.description.referencesBeata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.-
    dc.description.referencesJan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.-
    dc.description.referencesKonrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.-
    dc.description.referencesMurray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.-
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
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    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
    dc.description.referencesHiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2012, Volume 20, Issue 1

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