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  3. Formalized Mathematics
  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/11320/15864
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    Pole DCWartośćJęzyk
    dc.contributor.authorEndou, Noboru-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2024-01-26T10:44:44Z-
    dc.date.available2024-01-26T10:44:44Z-
    dc.date.issued2023-
    dc.identifier.citationFormalized Mathematics, Volume 31, Issue 1, Pages 309-324pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/15864-
    dc.description.abstractWe extend the formalization of the integral theory of onevariable functions for Riemann and Lebesgue integrals, showing that the Lebesgue integral of a continuous function of two variables coincides with the Riemann iterated integral of a projective function.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.subjectdouble integralpl
    dc.subjectrepeated integralpl
    dc.titleIntegral of Continuous Functions of Two Variablespl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2023-0025-
    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.referencesTom M. Apostol. Calculus, volume II. Wiley, second edition, 1969.pl
    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.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. Antiderivatives and integration. Formalized Mathematics, 31(1):131–141, 2023. doi:10.2478/forma-2023-0012.pl
    dc.description.referencesNoboru Endou. Product pre-measure. Formalized Mathematics, 24(1):69–79, 2016. doi:10.1515/forma-2016-0006.pl
    dc.description.referencesNoboru Endou. Reconstruction of the one-dimensional Lebesgue measure. Formalized Mathematics, 28(1):93–104, 2020. doi:10.2478/forma-2020-0008.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. Relationship between the Riemann and Lebesgue integrals. Formalized Mathematics, 29(4):185–199, 2021. doi:10.2478/forma-2021-0018.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. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.pl
    dc.description.referencesAdam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Mizar in a nutshell. Journal of Formalized Reasoning, 3(2):153–245, 2010.pl
    dc.description.referencesSerge Lang. Calculus of Several Variables. Springer, third edition, 2012.pl
    dc.description.referencesKazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Implicit function theorem. Part I. Formalized Mathematics, 25(4):269–281, 2017. doi:10.1515/forma-2017-0026.pl
    dc.description.referencesKeiko Narita, Noboru Endou, and Yasunari Shidama. Weak convergence and weak* convergence. Formalized Mathematics, 23(3):231–241, 2015. doi:10.1515/forma-2015-0019.pl
    dc.description.referencesEdward S. Smith, Meyer Salkover, and Howard K. Justice. Calculus. John Wiley and Sons, second edition, 1958.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume31pl
    dc.description.issue1pl
    dc.description.firstpage309pl
    dc.description.lastpage324pl
    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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