A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is symmetric about $a \in \mathbb{R}$ if and only if \begin{equation} X \overset{d}{=} 2 a - X \end{equation}

Let $M = (\mathbb{R}, \mathcal{B}(\mathbb{R}))$ be the D5072: Standard real borel measurable space.
A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is symmetric about $a \in \mathbb{R}$ if and only if \begin{equation} \forall \, B \in \mathcal{B}(\mathbb{R}) : \mathbb{P}(X \in B) = \mathbb{P}(2 a - X \in B) \end{equation}