有限维Banach空间鞅型序列关系的一个证明方法

A proof of relationship of martingale-like sequences valued in finite dimensional Banach-space

对文献《鞅与Banach空间几何学》中有限维Banach空间鞅型序列关系的定理给出了详细地证明,并且利用此证明思路得到了任意无穷维Banach空间上渐近鞅不是依概极限鞅的反例,对比该文献,本文的方法更为简洁易懂。

A detailed proof of the theorem in the Martingale and Banach-space geometry about the relation-ship of martingale-like sequences valued in finite dimensional Banach-space was given. The counter example of a Banach-space valued amart that is not a game fairer with time in arbitrary infinite dimensional Banach-space, was presented by using the method mentioned. Compared with the literature, our method is more concise and understandable.