  The main aim of this article is to give an exposition of weak convergence,
Prohorov theorem and Prohorov spaces. In this context we study the relationship
between Levy distance $\ell(F, G)$ between two distribution functions $F$ and
$G$ and the Prohorov distance $\pi( \mu, \nu)$ between the probability measures
$\mu$ and $\nu$ determined by $F$ and $G$ respectively. We study the
relationship among the weak convergence of probability measures ($\mu_n$)
determined by distribution functions ($F_n$) to the probability measure $\mu$
determined by a distribution function $G$, the convergence of $\ell(F_n, G)$
and $\pi( \mu_n, \nu)$ to zero under suitable assumptions on the metric space
on which these measures are defined. Tightness of probability measures and
relative sequential compactness are studied and Prohorov theorem is proved in
different settings. Prohorov spaces and non-Prohorov spaces are discussed.
