Let $(X,\mathcal{F})$ and $(Y,\mathcal{G})$ be \reftext{def:sigma-algebra-measurable-space-2026a}{measurable spaces}. A \textbf{measurable rectangle} is a subset of the \reftext{def:cartesian-product-sets-2026a}{Cartesian product} $X\times Y$ of the form $A\times B$ with $A\in\mathcal{F}$ and $B\in\mathcal{G}$.

The \textbf{product $\sigma$-algebra} $\mathcal{F}\otimes\mathcal{G}$ on $X\times Y$ is the \reftext{def:generated-sigma-algebra-2026a}{$\sigma$-algebra generated} by the family of all measurable rectangles.