中文摘要：

该文得到了关于一般可分距离空间上独立随机元序列的几乎处处中心极限定理（almost sure central limittheory，简记为ASCLT）．作为应用，该文给出了取值于可分Banach空间上随机元序列以及一类随机场序列满足ASCLT的充分条件，最后给出了关于多维随机变量序列极值的ASCLT．

英文摘要：

In this paper, the authors get the almost sure central limit theroems in separable metric space. As applications, they discuss the almost sure central limit theroems for the independent identically distributed random element sequence in separable Banach space, a certain independent identically distributed stochastic processes sequence and multidimension independent identically distributed random variables sequence.