Definition:Pairwise Disjoint Events

Definition

Let $\family {A_i}_{i \mathop \in I}$ be an indexed family of events in a probability space.

Then $\family {A_i}$ is pairwise disjoint if and only if:

$\forall i, j \in I, i \ne j: A_i \cap A_j = \O$

That is, a set of events is pairwise disjoint if and only if every pair of them is disjoint.

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.3$: Probabilities