Convergence, almost-certain

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.