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.
@article{bwmeta1.element.doi-10_2478_v10037-009-0015-9,
author = {Keiko Narita and Noboru Endou and Yasunari Shidama},
title = {Lebesgue's Convergence Theorem of Complex-Valued Function},
journal = {Formalized Mathematics},
volume = {17},
year = {2009},
pages = {137-145},
zbl = {1298.26030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0015-9}
}
Keiko Narita; Noboru Endou; Yasunari Shidama. Lebesgue's Convergence Theorem of Complex-Valued Function. Formalized Mathematics, Tome 17 (2009) pp. 137-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0015-9/
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