B值拟终鞅型序列与Banach空间的几何特征

B-valued quasi-eventual-martingale-like sequences and geometric characters of Banach spaces

设（Ω，，Ｐ）是概率空间，Ｂ是Ｂａｎａｃｈ空间．本文引入了一类新的鞅型序列──（Ｂ值）拟终鞅型序列，并研究了它们的收敛性与Ｂａｎａｃｈ空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性，一致光滑性和ＵＭＤ性的依赖关系．

Let(Ω,F,P) be a probability space and B a Banach space. In the paper, a new kind of martingale-like sequences─ B-valued quasi-eventual-martingale-like sequences is introdued and the relations between it and Radon-Nikodym Property, uniform smoothness as well as UMD property of Banach spases are studied.