Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 201 / 3 / a

Prokhorov's theorem says that a sequence of Borel probability measures on $\mathbb{R}$ is relatively compact for weak convergence of probability measures exactly when it is tight: for every $ϵ>0$, some compact $K$ satisfies ${\sup }_n{\mu }_n(\mathbb{R}\setminus K)<ϵ$.