Glivenko's theorem (probability theory) explained

In probability theory, Glivenko's theorem states that if

\varphi _{n,} n\in 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.

References

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Notes and References

1. Book: Itô, Kiyosi . 1984 . Introduction to Probability Theory . Cambridge University Press . 87 . 0 521 26960 1.