关于概率内积空间定义的平凡性  

The Triviality of Definitions of Probabilistic Inner Product Spaces

作　　者：朱杏华[1] 肖建中[1] 

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《数学物理学报（A辑）》2014年第3期512-520,共9页Acta Mathematica Scientia

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.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.

关 键 词：分布函数 三角范数 概率内积空间 半内积 

分 类 号：O177.99[理学—数学]