Definition

independent classes

Let $\mathcal{C}_i \subset \mathcal{B}$, $i = 1, \dots , n$. The classes $\mathcal{C}_i$ are independent if for any choice $A_1, \dots , A_n$ with $A_i \in \mathcal{C}_i$, $i = 1, \dots , n$, we have the events $A_1, \dots , A_n$ are independent.

If $T$ is an arbitrary index set, we say the classes $\mathcal{C}_t$, $t \in T$ are independent families if for each finite $I \subset T$ the family $\mathcal{C}_t$, $t \in I$ is indepdendent.