Independent sigma-algebras
= Independent sigma-algebras
Two sub-sigma-algebras $\mathcal F_1,\mathcal F_2$ are independent when
$$
\mathbb P(A\cap B)=\mathbb P(A)\mathbb P(B)
$$
for every $A\in\mathcal F_1$ and $B\in\mathcal F_2$.
= Independent sigma-algebras
Two sub-sigma-algebras $\mathcal F_1,\mathcal F_2$ are independent when
$$
\mathbb P(A\cap B)=\mathbb P(A)\mathbb P(B)
$$
for every $A\in\mathcal F_1$ and $B\in\mathcal F_2$.