Various Expressions for Modulus of Random Convexity  

作　　者：Xiao Lin ZENG 

机构地区：[1]College of Mathematics and Statistics,Chongqing Technology and Business University

出　　处：《Acta Mathematica Sinica,English Series》2013年第2期263-280,共18页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11171015);Science Foundation of Chongqing Education Board(Grant No.KJ120732)

摘　　要：We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0（F, X） derived from a normed space X by the classical modulus of convexity of X.We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0（F, X） derived from a normed space X by the classical modulus of convexity of X.

关 键 词：Random normed module modulus of random convexity Hahn-Banach theorem for almostsurely bounded random linear functionals 

分 类 号：O211.6[理学—概率论与数理统计]