Let $(X,\mathscr{M},\mu),(Y,\mathscr{N},\nu )$ be σ-finite measure spaces. There exists a unique measure on $(X\times Y,\mathscr{P})$ (where $\mathscr{P}$ is the product σ-algebra) denoted by $\mu\times \nu$ satisfying $$\mu\times \nu(A\times B)=\mu(A)\nu(B)$$$\forall A\in\mathscr{M},\forall B\in\mathscr{N}$. Furthermore, $(X\times Y,\mathscr{P}, \mu \times \nu)$ is σ-finite.