User:Caliburn/s/prob/Definition:Square-Integrable Random Variable

Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.

We say that $X$ is square-integrable if and only if ${\size X}^2$ is integrable.