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Volume 17, Issue 2 (Jan 2009)


Lebesgue's Convergence Theorem of Complex-Valued Function

Keiko Narita
  • Hirosaki-city, Aomori, Japan
/ Noboru Endou
  • Gifu National College of Technology, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2009-07-14 | DOI: https://doi.org/10.2478/v10037-009-0015-9

Lebesgue's Convergence Theorem of Complex-Valued Function

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.

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About the article

Published Online: 2009-07-14

Published in Print: 2009-01-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0015-9. Export Citation

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