关于概率内积空间定义的平凡性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 512-520.

关于概率内积空间定义的平凡性

朱杏华|肖建中

南京信息工程大学数学与统计学院南京 210044

收稿日期:2012-10-08 修回日期:2013-12-01 出版日期:2014-06-25 发布日期:2014-06-25

The Triviality of Definitions of Probabilistic Inner Product Spaces

ZHU Xing-Hua, XIAO Jian-Zhong

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044

Received:2012-10-08 Revised:2013-12-01 Online:2014-06-25 Published:2014-06-25

摘要/Abstract

摘要：

研究了分布函数拟逆的性质, 进而利用这些性质, 讨论了概率内积空间中半内积族之间的关系, 并证明了几种定义下的概率内积空间等同于通常的内积空间.

关键词: 分布函数, 三角范数, 概率内积空间, 半内积

Abstract:

In the paper some properties concerning the quasi-inverses of distribution functions are studied. By means of these properties some relations among the families of semi-inner products are discussed. It is showed that the probabilistic inner product spaces under several definitions are usual inner product spaces in fact.

Key words: Distribution functions, Triangular norm, Probabilistic inner product space, Semi-inner product.

中图分类号:

46S50

朱杏华, 肖建中. 关于概率内积空间定义的平凡性[J]. 数学物理学报, 2014, 34(3): 512-520.

ZHU Xing-Hua, XIAO Jian-Zhong. The Triviality of Definitions of Probabilistic Inner Product Spaces[J]. Acta mathematica scientia,Series A, 2014, 34(3): 512-520.

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