Lebesgue's Convergence Theorem of Complex-Valued Function

Keiko Narita; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 137-145
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Keiko Narita, Noboru Endou, and Yasunari Shidama. "Lebesgue's Convergence Theorem of Complex-Valued Function." Formalized Mathematics 17.2 (2009): 137-145. <http://eudml.org/doc/267173>.

@article{KeikoNarita2009,
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 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.},
author = {Keiko Narita, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {formalization of Riemann integral},
language = {eng},
number = {2},
pages = {137-145},
title = {Lebesgue's Convergence Theorem of Complex-Valued Function},
url = {http://eudml.org/doc/267173},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Keiko Narita
AU - Noboru Endou
AU - Yasunari Shidama
TI - Lebesgue's Convergence Theorem of Complex-Valued Function
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 137
EP - 145
AB - 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.
LA - eng
KW - formalization of Riemann integral
UR - http://eudml.org/doc/267173
ER -

References

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