Glivenko's theorem (probability theory)

In probability theory, Glivenko's theorem states that if [math]\displaystyle{ \varphi_n, n\in \mathbb N }[/math], [math]\displaystyle{ \varphi }[/math] are the characteristic functions of some probability distributions [math]\displaystyle{ \mu_n, \mu }[/math] respectively and [math]\displaystyle{ \varphi_n \to \varphi }[/math] almost everywhere, then [math]\displaystyle{ \mu_n \to \mu }[/math] in the sense of probability distributions.