Let \((\Omega_1, \mathcal{A}_1)\) and \((\Omega_2, \mathcal{A}_2)\) be measurable spaces. A function \(f\colon \Omega_1 \to \Omega_2\) is called measurable if for every \(A_2\in\mathcal{A}_2\), we have
\begin{equation*} f^{-1}(A_2)\in \mathcal{A}_1. \end{equation*}