Integral of Complex-Valued Measurable Function

被引：6

作者：

Narita, Keiko

Endou, Noboru ^{[1
]}

Shidama, Yasunari ^{[2
]}

机构：

[1] Gifu Natl Coll Technol, Motosu, Japan

[2] Shinshu Univ, Nagano, Japan

来源：

FORMALIZED MATHEMATICS | 2008年 / 16卷 / 04期

关键词：

D O I：

10.2478/v10037-008-0039-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered.

引用

页码：319 / 324

页数：6

共 50 条

[11] Lebesgue's Convergence Theorem of Complex-Valued Function
Narita, Keiko
Endou, Noboru
Shidama, Yasunari
FORMALIZED MATHEMATICS, 2009, 17 (02): : 137 - 145
[12] ON THE LIPSCHITZ EXTENSION CONSTANT FOR A COMPLEX-VALUED LIPSCHITZ FUNCTION
Rosoiu, Alexandru
Fratila, Dragos
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2008, 53 (01): : 101 - 107
[13] Complex-Valued Function Modeling of Bilateration and its Applications
Ahn, Heungju
Van Dang, Chien
Lee, Sang C.
IEEE ACCESS, 2023, 11 : 92913 - 92925
[14] BOUNDS FOR DERIVATIVES OF A COMPLEX-VALUED FUNCTION ON A COMPACT INTERVAL
KALLIONIEMI, H
MATHEMATICA SCANDINAVICA, 1976, 39 (02) : 295 - 314
[15] The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
Hofmann, Steve
Kenig, Carlos
Mayboroda, Svitlana
Pipher, Jill
MATHEMATISCHE ANNALEN, 2015, 361 (3-4) : 863 - 907
[16] The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
Steve Hofmann
Carlos Kenig
Svitlana Mayboroda
Jill Pipher
Mathematische Annalen, 2015, 361 : 863 - 907
[17] FOURIER INTEGRAL-OPERATORS WITH COMPLEX-VALUED PHASE FUNCTION AND THE CAUCHY-PROBLEM FOR HYPERBOLIC OPERATORS
KAJITANI, K
LECTURE NOTES IN MATHEMATICS, 1991, 1505 : 1 - 70
[18] Complex-valued tapers
Politis, DN
IEEE SIGNAL PROCESSING LETTERS, 2005, 12 (07) : 512 - 515
[19] Complex-valued autoencoders
Baldi, Pierre
Lu, Zhiqin
NEURAL NETWORKS, 2012, 33 : 136 - 147
[20] Global h Fourier integral operators with complex-valued phase functions
Butler, J
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2002, 34 : 479 - 489

← 1 2 3 4 5 →