关于概率内积空间*
On the Probabilistic Inner Product Spaces
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摘要: 本文给出概率内积空间以一新的定义。借助于这一定义,在本文中建立了概率内积空间的Schwarz不等式、收敛性定理及正交性的概念。并讨论了概率内积空间与概率赋范空间的关系等。Abstract: In this paper a new definition for probabilistic inner product spaces is given. By virtue of this definition, some convergence theorems, Schwarz inequality and the orthogonal concept for probabilistic inner product spaces are established and introduced. Moreover, the relationship between this kind of spaces and probabilistic normed spaces is considered also.
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[1] 张石生,概率内积空间中映象的不动点定理,应用数学和力学,6,1(1985),67-74. [2] Schweizer,B.and A.Sklar,Statistical metric space,Pacific J.Math.,10(1960),313-324. [3] You Zhao-yong,Probabilistic inner product space,Kexue Tongbao,8(1983),456-459. [4] 游兆永、朱林户,概率内积空间,科学通报,8 (1983), 450-459. -
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