向量值鞅型序列与AL空间  

VECTOR VALUED MARTINGALE LIKE SEQUENCES AND AL SPACE

作　　者：万成高[1] 刘旭阳[1] 

机构地区：[1]湖北大学数学系

出　　处：《湖北大学学报（自然科学版）》1996年第3期235-240,共6页Journal of Hubei University：Natural Science

摘　　要：设（Ω，Ｆ，Ｐ）是概率空间，Ｅ是Ｂａｎａｃｈ格，（１）若Ｅ是序连续的，则（ａ）Ｅ同构于一个ＡＬ空间等价于（ｂ）每一满足（Ｃ＋）条件Ｅ值拟上鞅必满足（Ｃ）条件；（２）若Ｅ是ＡＬ空间且具有ＲＮＰ，则（ａ）每一满足（Ｃ＋）条件的Ｅ值拟终下鞅强ａ．ｓ．收敛；（ｂ）每一满足（Ｃ＋）条件的Ｅ值依概渐近下鞅强ａ．ｓ．收敛；Let( Ω ,F,P) be a probability space, and E a Banach lattice. It was proved that (1) if E is order continuous, then the following assertions are equivalent: (a) E is isomorphic to an AL space, (b) every E valued quasi submartingale of calss (C +) is of class (C) ; (2) if E has Radon Nikodym property and is an AL space, then (a) every E valued quasi eventual submartingale of class (C +) is strongly convergent a.s., (b) every E valued subpramart of class (C +) is strongly convergent a.s., (c) every E valued GBT of class (C +) strongly convergent in P .

关 键 词：AL空间 向量值鞅型序列 概率空间 R-N性质 

分 类 号：O211.4[理学—概率论与数理统计]