Solution
= Solution
{c}
Two <sigma-algebras> are independent if every event in one is independent of every event in the other:
$$
\boxed{\mathbb P(G\cap H)=\mathbb P(G)\mathbb P(H)\quad
\text{for all }G\in\mathcal G,\ H\in\mathcal H.}
$$
The same formula defines independence of the generating collections when restricted to their members.