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• # Artykuł - szczegóły

## Formalized Mathematics

2009 | 17 | 2 | 137-145

## Lebesgue's Convergence Theorem of Complex-Valued Function

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.

137-145

wydano
2009-01-01
online
2009-07-14

### Twórcy

autor
• Hirosaki-city, Aomori, Japan
autor
• Gifu National College of Technology, Japan
autor
• Shinshu University, Nagano, Japan

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