# 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

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topKeiko 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 -

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