$A \subset \mathbb R^m$ and $B \subset \mathbb R^n$ are boxes, and $f$ is integrable in the riemann sense on $(A\times B)$.
We define $$A_1 =\left\{a \in A \left|\exists \int_{B}f(a,b)db\right.\right\} \subset A.$$
Show that $A \setminus A_1$ has zero volume.