Let $(X,\mathcal{M})$ be a measurable space, and let $f:(X,\mathcal{M})\to([-\infty,\infty],\mathcal{B}([-\infty,\infty]))$ be a measurable extended real-valued function. Then the sets $\{x\in X:f(x)=\infty\}$, $\{x\in X:f(x)=-\infty\}$, and $\{x\in X:|f(x)|<\infty\}$ belong to $\mathcal{M}$.