A. S. Convergence of Two-Parameter Banach Space Valued Martingales and the Radon-Nikodym Property of Banach Spaces

作     者：Shixin Gan, Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China 

作者机构：Department of Mathematics Wuhan University Wuhan P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1999年第15卷第2期

页      面：187-196页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Project supported by the National Natural Science Foundation of China the State Education Commission Ph. D. Station Foundation 

主　　题：Two-parameter Banach space valued martingale A. S. convergence Radon-Nikodym property F₄ condition Local F₄ condition 

摘      要：In this paper, we prove that under the F4 condition, any L log+ L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F4 condition is replaced by the weaker local F4 condition.