Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
Let $M = (\Pi, \mathcal{G})$ be a D1108: Measurable space.
A D18: Map $X : \Omega \to \Pi$ is a random variable with respect to $P$ and $M$ if and only if \begin{equation} \sigma^{\leftarrow} \langle X \rangle \subseteq \mathcal{F} \end{equation}