Let $(X,\mathcal A,\mu)$ be a [measure space](/page/Measure%20Space), let $(Y,\mathcal B)$ be a measurable space, and let $T:(X,\mathcal A)\to (Y,\mathcal B)$ be a measurable map. Suppose $A\in\mathcal A$ is an atom of $\mu$ and $0<\mu(A)<\infty$, meaning that for every $E\in\mathcal A$ with $E\subset A$, either $\mu(E)=0$ or $\mu(E)=\mu(A)$. If $m\in\mathbb N$ and $(B_i)_{i=1}^m$ is a finite measurable partition of $Y$, meaning that $B_i\in\mathcal B$, the sets $B_i$ are pairwise disjoint, and $\bigcup_{i=1}^m B_i=Y$, then at most one index $i\in\{1,\dots,m\}$ satisfies

\begin{align*} \mu(A\cap T^{-1}(B_i))>0. \end{align*}