  This expository note aims at illustrating weak convergence of probability
measures from a broader view than a previously published paper. Though the
results are standard for functional analysts, this approach is rarely known by
statisticians and our presentation gives an alternative view than most standard
probability textbooks. In particular, this functional approach clarifies the
underlying topological structure of weak convergence. We hope this short note
is helpful for those who are interested in weak convergence as well as
instructors of measure theoretic probability.
