Let $(X,\mathcal{M})$ be a measurable space, and let $A \subset X$. Define the indicator function $\mathbb{1}_A: X \to \mathbb{R}$ by setting $\mathbb{1}_A(x)=1$ for $x \in A$ and $\mathbb{1}_A(x)=0$ for $x \in X \setminus A$. Then $\mathbb{1}_A$ is $\mathcal{M}/\mathcal{B}(\mathbb{R})$-measurable if and only if $A \in \mathcal{M}$.