# Convergence, almost-certain

From Encyclopedia of Mathematics

*almost-sure convergence, convergence with probability one*

Convergence of a sequence of random variables defined on a certain probability space , to a random variable , defined in the following way: (or -almost certain) if

In mathematical analysis this form of convergence is called almost-everywhere convergence. Convergence in probability follows from almost-certain convergence.

#### Comments

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

**How to Cite This Entry:**

Convergence, almost-certain. V.I. Bityutskov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Convergence,_almost-certain&oldid=15210

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098