Let $(\Omega, \mathcal F, \mathbb P)$ be a probability space. The variance functional is
\begin{align}
\operatorname{Var}: L^2(\Omega, \mathcal F, \mathbb P) &\to [0,\infty) \\
X &\mapsto \mathbb E[(X - \mathbb E[X])^2].
\end{align}
For a square-integrable real-valued random variable $X: (\Omega, \mathcal F) \to (\mathbb R, \mathcal B(\mathbb R))$, the variance of $X$ is $\operatorname{Var}(X)$.