Integrability of Multivariable Continuous Functions

Pole DC	Wartość	Język
dc.contributor.author	Endou, Noboru	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2026-02-02T09:57:57Z	-
dc.date.available	2026-02-02T09:57:57Z	-
dc.date.issued	2025	-
dc.identifier.citation	Formalized Mathematics, Volume 33, Issue 1, Pages 185-206	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/19735	-
dc.description.abstract	In this article, we prove the integrability of continuous functions on n-dimensional real normed spaces, using the Mizar formalism. Generalizing selected theorems from the Mizar Mathematical Library, we prove the integrability of continuous real n-variable functions and then, using the correspondence between product-type and tuple-type spaces, we demonstrate the integrability of continuous functions on the desired multidimensional spaces.	pl
dc.language.iso	en	pl
dc.publisher	University of Białystok	pl
dc.rights	Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)	pl
dc.rights.uri	https://creativecommons.org/licenses/by-sa/4.0/	pl
dc.subject	n-dimensional normed space	pl
dc.subject	product measure	pl
dc.subject	Lebesgue integration	pl
dc.title	Integrability of Multivariable Continuous Functions	pl
dc.type	Article	pl
dc.rights.holder	2025 The Author(s)	pl
dc.rights.holder	CC BY-SA 4.0 license	pl
dc.identifier.doi	10.2478/forma-2025-0015	-
dc.description.Affiliation	Noboru Endou - National Institute of Technology, Gifu College, 2236-2 Kamimakuwa, Motosu, Gifu, Japan	pl
dc.description.Affiliation	Yasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japan	pl
dc.description.references	Charalambos D. Aliprantis and Kim C. Border. Infinite dimensional analysis. Springer-Verlag, Berlin, Heidelberg, 2006.	pl
dc.description.references	Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.	pl
dc.description.references	Sylvie 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.references	Noboru Endou. Reconstruction of the one-dimensional Lebesgue measure. Formalized Mathematics, 28(1):93–104, 2020. doi:10.2478/forma-2020-0008.	pl
dc.description.references	Noboru Endou. Relationship between the Riemann and Lebesgue integrals. Formalized Mathematics, 29(4):185–199, 2021. doi:10.2478/forma-2021-0018.	pl
dc.description.references	Noboru Endou and Yasunari Shidama. Multidimensional measure space and integration. Formalized Mathematics, 31(1):181–192, 2023. doi:10.2478/forma-2023-0017.	pl
dc.description.references	Noboru Endou and Yasunari Shidama. Universality of measure space. Formalized Mathematics, 32(1):149–163, 2024. doi:10.2478/forma-2024-0012.	pl
dc.description.references	Noboru Endou and Yasunari Shidama. Measure for product space of real normed spaces. Formalized Mathematics, 33(1):117–135, 2025. doi:10.2478/forma-2025-0010.	pl
dc.description.references	Noboru Endou and Yasunari Shidama. Integral of continuous functions of two variables. Formalized Mathematics, 31(1):309–324, 2023. doi:10.2478/forma-2023-0025.	pl
dc.description.references	Noboru Endou and Yasunari Shidama. Integral of continuous three variable functions. Formalized Mathematics, 32(1):9–31, 2024. doi:10.2478/forma-2024-0002.	pl
dc.description.references	Noboru 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.	pl
dc.description.references	Adam Grabowski and Christoph Schwarzweller. Revisions as an essential tool to maintain mathematical repositories. In M. Kauers, M. Kerber, R. Miner, and W. Windsteiger, editors, Towards Mechanized Mathematical Assistants. Lecture Notes in Computer Science, volume 4573, pages 235–249. Springer: Berlin, Heidelberg, 2007.	pl
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.	pl
dc.description.references	Johannes Holzl 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.references	M.M. Rao. Measure Theory and Integration. Marcel Dekker, 2nd edition, 2004.	pl
dc.description.references	Colin Rothgang, Artur Korniłowicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205–210, Cham, 2021. Springer International Publishing. doi:10.1007/978-3-030-81097-9_17.	pl
dc.description.references	Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	33	pl
dc.description.issue	1	pl
dc.description.firstpage	185	pl
dc.description.lastpage	206	pl
dc.identifier.citation2	Formalized Mathematics	pl
dc.identifier.orcid	0000-0002-5922-2332	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2025, Volume 33, Issue 1

Pliki w tej pozycji:

Plik	Opis	Rozmiar	Format
Integrability_of_Multivariable_Continuous_Functions.pdf		310,86 kB	Adobe PDF	Otwórz

Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL