# Convergence in probability

From Encyclopedia of Mathematics

Convergence of a sequence of random variables defined on a probability space , to a random variable , defined in the following way: if for any ,

In mathematical analysis, this form of convergence is called convergence in measure. Convergence in distribution follows from convergence in probability.

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See also Weak convergence of probability measures; Convergence, types of; Distributions, convergence of.

**How to Cite This Entry:**

Convergence in probability.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_probability&oldid=15590

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article