Random Variable

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{B}, \mathbb{P})$ be a Probability Space. A Random Variable is a Borel Measureable Function $X: \Omega \to \mathbb{R}$.

1. Rather than say $X$ is $(\mathcal{B}, \mathcal{B}(\mathbb{R}))$-measurable, we say $X \in \mathcal{B}$.