标题： 概率测度的弱收敛：从拓扑向量空间的角度 显示英文标题

标题： Weak convergence of probability measures: a topological vector space point of view

摘要： 弱收敛性概率测度是概率论和统计学领域最重要的课题之一。 本文是一篇综述性论文，我们从拓扑向量空间的角度考察概率测度的弱收敛性。 我们首先从拓扑向量空间的一般框架下的弱拓扑和弱收敛的关键概念和结果开始。 然后我们将注意力限制在概率测度空间上，看看这些一般性结果如何具体化为概率论中的那些结果。 最后，我们将回顾关于弱拓扑可度量化的一些重要事实。 我们希望本文中回顾的一般方法能提供一种替代的观点和一些见解。 显示英文摘要

摘要： Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view. We start from the key concepts and results about weak topology and weak convergence under the general framework of topological vector spaces. Then we restrict our attention to the space of probability measures and see how the general results specialize to those in probability theory. Finally, we will review some important facts about the metrizability of weak topology. We hope the general approach reviewed in this paper can provide an alternative view and some insights.