= Product probability space
{title2=$(\prod_iX_i,\bigotimes_i\mathcal F_i,\bigotimes_i\mu_i)$}
For finitely many <probability spaces> $(X_i,\mathcal F_i,\mu_i)$, their product <probability> space has underlying <set> $\prod_iX_i$, the <product sigma-algebra> and <product measure> $\bigotimes_i\mu_i$. The coordinate projections are jointly independent: for measurable $B_i\subseteq X_i$, the <probability> of all coordinate conditions is $\prod_i\mu_i(B_i)$. Conversely a family of independent coordinates has this product joint distribution. Product structure permits coordinate exposure and independent resampling in concentration arguments.
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