Discrete Support of a Random Element

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{B}, \mathbb{P})$ be a Probability Space, let $(S, \mathcal{M})$ be a Measure Space and let $X : \Omega \to S$ be a Random Element. Then the support of $X$ is $$\text{supp} X := {s \in S : \mathbb{P}[X=s] > 0}$$