Corollary 2

— Let $A$ be a $\mu$-moderated subset of $T$, and $A'$ a $\mu'$-moderated subset of $T'$; then $A \times A'$ is $\nu$-moderated in $T \times T'$.

In view of the definition of moderated set (§1, No. 2, Prop. 5), it suffices to show that if $B$ is an integrable open set in $T$, and $B'$ an integrable open set in $T'$, then the open set $B \times B'$ is integrable. This follows at once from Cor. 1.