Lebesgue's Convergence Theorem of Complex-Valued Function

• Autorzy: Keiko Narita , Noboru Endou , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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 complex-valued 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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2009
• Tom: 17
• Numer: 2
• Strony: 137-145

Daty

wydano

2009-01-01

online

2009-07-14

Twórcy

autor

Keiko Narita

• Hirosaki-city, Aomori, Japan

autor

Noboru Endou

• Gifu National College of Technology, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

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Identyfikatory

DOI

10.2478/v10037-009-0015-9