Theorem (Prokhorov)

Let $X$ be a Metric Space and let $\mathcal{B}$ be the Borel σ-algebra of $X$. Let $\Pi$ be a family of Probability Measures on $(X,\mathcal{B})$. Then,

1. If $\Pi$ is Tight then it is Relatively Sequentially Compact.
2. Suppose that $X$ is Separable and Complete (i.e. Polish). If $\Pi$ is Relatively Sequentially Compact, then $\Pi$ is Tight.