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  4. Formalized Mathematics, 2023, Volume 31, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/15855
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    Pole DCWartośćJęzyk
    dc.contributor.authorEndou, Noboru-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2024-01-25T10:36:12Z-
    dc.date.available2024-01-25T10:36:12Z-
    dc.date.issued2023-
    dc.identifier.citationFormalized Mathematics, Volume 31, Issue 1, Pages 181-192pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/15855-
    dc.description.abstractThis paper introduces multidimensional measure spaces and the integration of functions on these spaces in Mizar. Integrals on the multidimensional Cartesian product measure space are defined and appropriate formal apparatus to deal with this notion is provided as well.pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/pl
    dc.subjectmeasure in product spacespl
    dc.subjectiterated integralpl
    dc.titleMultidimensional Measure Space and Integrationpl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2023-0017-
    dc.description.AffiliationNoboru Endou - National Institute of Technology, Gifu College, 2236-2 Kamimakuwa, Motosu, Gifu, Japanpl
    dc.description.AffiliationYasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japanpl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.pl
    dc.description.referencesVladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.pl
    dc.description.referencesSylvie Boldo, Catherine Lelay, and Guillaume Melquiond. Improving real analysis in Coq: A user-friendly approach to integrals and derivatives. In Chris Hawblitzel and Dale Miller, editors, Certified Programs and Proofs – Second International Conference, CPP 2012, Kyoto, Japan, December 13–15, 2012. Proceedings, volume 7679 of Lecture Notes in Computer Science, pages 289–304. Springer, 2012. doi:10.1007/978-3-642-35308-6_22.pl
    dc.description.referencesSylvie Boldo, Catherine Lelay, and Guillaume Melquiond. Formalization of real analysis: A survey of proof assistants and libraries. Mathematical Structures in Computer Science, 26:1196–1233, 2015.pl
    dc.description.referencesNoboru Endou. Improper integral. Part II. Formalized Mathematics, 29(4):279–294, 2021. doi:10.2478/forma-2021-0024.pl
    dc.description.referencesNoboru Endou. Fubini’s theorem on measure. Formalized Mathematics, 25(1):1–29, 2017. doi:10.1515/forma-2017-0001.pl
    dc.description.referencesNoboru Endou. Fubini’s theorem. Formalized Mathematics, 27(1):67–74, 2019. doi:10.2478/forma-2019-0007.pl
    dc.description.referencesNoboru Endou. Absolutely integrable functions. Formalized Mathematics, 30(1):31–51, 2022. doi:10.2478/forma-2022-0004.pl
    dc.description.referencesJacques D. Fleuriot. On the mechanization of real analysis in Isabelle/HOL. In Mark Aagaard and John Harrison, editors, Theorem Proving in Higher Order Logics, pages 145–161. Springer Berlin Heidelberg, 2000. ISBN 978-3-540-44659-0.pl
    dc.description.referencesRuben Gamboa. Continuity and Differentiability, pages 301–315. Springer US, 2000. ISBN 978-1-4757-3188-0. doi:10.1007/978-1-4757-3188-0_18.pl
    dc.description.referencesAdam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:https://doi.org/10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.pl
    dc.description.referencesJohannes Hölzl and Armin Heller. Three chapters of measure theory in Isabelle/HOL. In Marko C. J. D. van Eekelen, Herman Geuvers, Julien Schmaltz, and Freek Wiedijk, editors, Interactive Theorem Proving (ITP 2011), volume 6898 of LNCS, pages 135–151, 2011.pl
    dc.description.referencesHiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51–59, 2011. doi:10.2478/v10037-011-0009-2.pl
    dc.description.referencesM.M. Rao. Measure Theory and Integration. Marcel Dekker, 2nd edition, 2004.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume31pl
    dc.description.issue1pl
    dc.description.firstpage181pl
    dc.description.lastpage192pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0002-5922-2332-
    Występuje w kolekcji(ach):Formalized Mathematics, 2023, Volume 31, Issue 1

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