Corollary 3

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

For, $A \times B'$ is locally $\nu$-negligible (Prop. 4) and $\nu$-moderated (Cor. 2), hence is $\nu$-negligible (§1, No. 2, Cor. 1 of Prop. 7).

Cors. 2 and 3 may be extended to the product of two complex measures, on applying the statement to their absolute values (Ch. III, §4, No. 2, Prop. 3).