On the Random Conjugate Spaces of a Random Locally Convex Module  

作　　者：Tie Xin GUO Shi En ZHAO 

机构地区：[1]LMIB and School of Mathematics and Systems Science,Beihang University

出　　处：《Acta Mathematica Sinica,English Series》2012年第4期687-696,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.10871016)

摘　　要：Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.

关 键 词：Random locally convex module （ε λ）-topology locally L0-convex topology random con-jugate space 

分 类 号：O189.11[理学—数学] O211.6[理学—基础数学]