Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 512-520.

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The Triviality of Definitions of Probabilistic Inner Product Spaces

 ZHU Xing-Hua, XIAO Jian-Zhong   

  1. 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

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.

CLC Number: 

  • 46S50
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