A weak equivalence theorem for weak random elements with values in weakly compactly generated Banach spaces and its applications

作     者：郭铁信 

作者机构：Department of Mathematics Xiamen University Xiamen 361005 China 

出 版 物：《Chinese Science Bulletin》 (科学通报(英文版))

年 卷 期：1996年第41卷第1期

页      面：6-10页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：weak random elements strongly measurable random elements weak equivalence theorems reproducing kernel Hilbert spaces. 

摘      要：1 Introduction and preliminaries The aim of this note is to prove the following basic theorem: Let (Ω, σ, u) be a probability space, (B, ‖·‖) a weakly compactly generated Banach space, and a mapping V from Ω to B be a weak random element, then there exists a unique strongly measurable random element V from Ω to B under the sense of almost sure equality such that (?) is weakly equivalent to the weak random dement V. This theorem itself not only removes the limitation that the weak random element considered in a theorem due to Lewis is bounded, but also has many applications to probability theory in Banach spacest. As an example of applications, we give a theorem of properties of the reproducing kernel Hilbert spaces for weak twofold weak random elements.