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