Lebesgue's Convergence Theorem of Complex-Valued Function

Pole DC	Wartość	Język
dc.contributor.author	Narita, Keiko	-
dc.contributor.author	Endou, Noboru	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-01T19:26:34Z	-
dc.date.available	2015-12-01T19:26:34Z	-
dc.date.issued	2009	-
dc.identifier.citation	Formalized Mathematics, Volume 17, Issue 2, 2009, Pages 137-145	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3529	-
dc.description.abstract	In this article, we formalized Lebesgue’s Convergence theorem of complex-valued function. We proved Lebesgue’s Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue’s Convergence Theorem of complexvalued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences and showed their properties. In addition, we proved properties of complex-valued simple functions.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.title	Lebesgue's Convergence Theorem of Complex-Valued Function	-
dc.type	Article	-
dc.identifier.doi	10.2478/v10037-009-0015-9	-
dc.description.Affiliation	Narita Keiko - Hirosaki-city, Aomori, Japan	-
dc.description.Affiliation	Endou Noboru - Gifu National College of Technology, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University, Nagano, Japan	-
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