Glivenko's theorem (probability theory)

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