  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.
