Definition 6

The premeasure $\nu$ defined by (3) is called the product premeasure of $\lambda$ and $\mu$, and is denoted $\lambda \otimes \mu$.

This definition obviously extends to the case that $\lambda$ and $\mu$ are complex premeasures, and one then has $|\lambda \otimes \mu| = |\lambda| \otimes |\mu|$ (Ch. III, §4, No. 2, Prop. 3 and Ch. IV, §5, No. 7, Lemma 3).

We conserve the notations of Ch. III, §4 and Ch. V, §8 relative to products of measures and to iterated integrals. In particular, if $f$ and $g$ are two functions defined respectively on $S$ and $T$, with values in $\overline{\mathbf{R}}_+$ or in $\mathbf{C}$, the function $(s, t) \mapsto f(s)g(t)$ on $S \times T$ will be denoted $f \otimes g$.