MathGloss

Let $(X_1,\Sigma_1,\mu_1)$ and $(X_2,\Sigma_2,\mu_2)$ be two measure spaces, and let $\Sigma_1\otimes \Sigma_2$ be the σ-algebra generated by sets of the form $B_1\times B_2$ for $B_1\in \Sigma_1$, $B_2\in \Sigma_2$. A product measure $\mu_1\times \mu_2$ is a measure on the measurable space $(X_1\times X_2, \Sigma_1\otimes\Sigma_2)$ such that $$(\mu_1\times\mu_2)(B_1\times B_2) = \mu_1(B_1)\mu_2(B_2)$$ for all $B_1\in \Sigma_1$, $B_2\in \Sigma_2$.

Wikidata ID: Q1572094

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