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.