Glivenko's theorem (probability theory)

In probability theory, Glivenko's theorem states that if ${\phi }_n,n\in \mathbb{\mathbb{N}}$, $\phi$ are the characteristic functions of some probability distributions ${\mu }_n,\mu$ respectively and ${\phi }_n\to \phi$ almost everywhere, then ${\mu }_n\to \mu$ in the sense of probability distributions.