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| 关于概率内积空间定义的平凡性 | |
| 引用本文： | 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(A辑), 2014, 34(3): 512-520 |
| 作者姓名： | 朱杏华 肖建中 |
| 作者单位： | 南京信息工程大学 数学与统计学院 南京 210044 |
| 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. |
| 收稿时间： | 2012-10-08 |
| 修稿时间： | 2013-12-01 |
The Triviality of Definitions of Probabilistic Inner Product Spaces |
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| ZHU Xing-Hua,XIAO Jian-Zhong. The Triviality of Definitions of Probabilistic Inner Product Spaces[J]. Acta Mathematica Scientia, 2014, 34(3): 512-520 | |
| Authors: | ZHU Xing-Hua XIAO Jian-Zhong |
| Affiliation: | School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044 |
| 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. |
| Keywords: | Distribution functionszz Triangular normzz Probabilistic inner product spacezz Semi-inner product.zz |
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