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
收藏
页码：319 / 324
页数：6
相关论文
共 50 条
  • [21] Novel complex-valued neural network for dynamic complex-valued matrix inversion
    Liao B.
    Xiao L.
    Jin J.
    Ding L.
    Liu M.
    2016, Fuji Technology Press (20) : 132 - 138
  • [22] Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion
    Liao, Bolin
    Xiao, Lin
    Jin, Jie
    Ding, Lei
    Liu, Mei
    JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS, 2016, 20 (01) : 132 - 138
  • [23] The Characters of the Complex Number-Valued Fuzzy Measurable Function
    Ma Shengquan
    Wang Qiang
    FUZZY INFORMATION AND ENGINEERING 2010, VOL 1, 2010, 78 : 49 - 54
  • [24] Function Approximation by Complex-Valued Multilayer Perceptron with Stochastic Resonance
    Ogawa, Kenji
    Isokawa, Teijiro
    Nishimura, Haruhiko
    Kamiura, Naotake
    Matsui, Nobuyuki
    2013 PROCEEDINGS OF SICE ANNUAL CONFERENCE (SICE), 2013, : 1544 - 1547
  • [25] Adaptive complex-valued stepsize based fast learning of complex-valued neural networks
    Zhang, Yongliang
    Huang, He
    NEURAL NETWORKS, 2020, 124 : 233 - 242
  • [26] Integral of Measurable Function
    Endou, Noboru
    Shidama, Yasunari
    FORMALIZED MATHEMATICS, 2006, 14 (02): : 53 - 70
  • [27] COMPLEX-VALUED NEURAL NETWORKS WITH SUPER-ACTIVATION FUNCTION
    Abdullah, Sura Mahmood
    Althabhawee, Ali Fadhil Yaseen
    Al-Saidi, Nadia Mohammed Ghanim
    Samawi, Venus Wazeer
    Farhan, Alaa Kadhim
    International Journal of Innovative Computing, Information and Control, 2024, 20 (06): : 1587 - 1601
  • [28] On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields
    Saveliev, Andrey
    MATHEMATICS, 2021, 9 (19)
  • [29] On energy function for complex-valued neural networks and its applications
    Kuroe, Y
    Hashimoto, N
    Mori, T
    ICONIP'02: PROCEEDINGS OF THE 9TH INTERNATIONAL CONFERENCE ON NEURAL INFORMATION PROCESSING: COMPUTATIONAL INTELLIGENCE FOR THE E-AGE, 2002, : 1079 - 1083
  • [30] CONSTRUCTION OF A COMPLEX-VALUED NONLINEAR DISCRIMINANT FUNCTION FOR PATTERN RECOGNITION
    UESAKA, Y
    IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS, 1971, SMC1 (03): : 194 - +
12345