Glivenko's theorem (probability theory)

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In probability theory, Glivenko's theorem states that if ${\displaystyle \varphi _{n},n\in \mathbb {N} }$, ${\displaystyle \varphi }$ are the characteristic functions of some probability distributions ${\displaystyle \mu _{n},\mu }$ respectively and ${\displaystyle \varphi _{n}\to \varphi }$ almost everywhere, then ${\displaystyle \mu _{n}\to \mu }$ in the sense of probability distributions.^[1]

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