Almost Sure Convergence

Last updated Nov 1, 2022

Suppose $(\Omega, \mathcal{M}, \mathbb{P})$ is a Probability Space and $(Y, \tau)$ is a Topological Space. Suppose $(X_{n} : \Omega \to Y)$ is a Sequence of Random Elements and $X: \Omega \to Y$ is a Random Element. We say $X_{n} \to X$ almost surely if $X_{n}$ converges almost everywhere to $X$.