几类特殊的概率度量空间

journal6 ›› 2010, Vol. 31 ›› Issue (4): 24-27.

几类特殊的概率度量空间

（1.西南交通大学力学学院，四川成都 610031；2.河北建筑工程学院数理系，河北张家口075024；3.成都信息工程学院数学学院，四川成都 610225）

出版日期:2010-07-25 发布日期:2012-04-16

Some Special Probabilistic Metric Spaces

(1.School of Mechanics and Engineering,Southwest Jiaotong Univ.,Chengdu 610031,China;2.Department of Mathematics,Hebei Institute of Architecture and Civil Engineering,Zhangjiakou 075024,Hebei China;3.College of Mathematics,Chengdu University of Information Technology,Chengdu 610225,China）

Online:2010-07-25 Published:2012-04-16
About author:LI Liang (1984-),fale,was born in Qufu City,Shandong Provence,doctor;research area are probabilistic metric theory and general mechanics.

摘要/Abstract

摘要：给出了概率度量群和线性概率度量空间的定义,并引进一种特殊的线性概率度量空间——概率赋准范空间.随后定义了概率仿射度量空间,它是一种特殊的概率度量空间,在上面可以构造出一种线性结构使得该度量空间成为一个线性概率度量空间.最后给出了一个概率仿射度量空间的例子,该空间是通过一个非拓扑线性的概率赋范

关键词： 空间构造出来的.概率度量空间, 概率赋范空间, 概率度量群, 概率仿射度量空间, 概率赋准范空间, 拓扑线性空间, 拓扑群

Abstract: The authors give the definitions of PMG and LPM space and introduce a special LPM space,which is called PQN space.Then a special PM space named APM space is also introduced.In each APM space,an linear structure can be constructed such that this PM space is an LPM space.An example of APM space which is constructed by a non-topological vector PN space is given.

Key words: PM space, PN space, PMG, APM space；PQN space, topological vector space, topological group

李亮, 闫常丽, 张敏先. 几类特殊的概率度量空间[J]. journal6, 2010, 31(4): 24-27.

LI Liang, YAN Chang-Li, ZHANG Min-Xian. Some Special Probabilistic Metric Spaces[J]. journal6, 2010, 31(4): 24-27.