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 

出　　处：《Acta Mathematica Sinica,English Series》1999年第2期187-196,共10页数学学报（英文版）

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

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.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.

关 键 词：Two-parameter Banach space valued martingale A. S. convergence Radon-Nikodym property F₄ condition Local F₄ condition 

分 类 号：O1[理学—数学]