Theorem (Skohorod)

Let $(\mu_{n})_{n\ge 1}$ be a sequence of Borel Probability Measures that weakly converge to $\mu$. Then there are representative rvs, $X,X_{1},X_{2},\dots$, defined jointly on some Probability Space with $X_{n}\sim\mu_{n},X\sim\mu$, $\forall n\in \mathbb{N}$ such that $X_{n}\to X$ a.s..