Definition:Partition (Probability Theory)

Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

A partition of $\Omega$ is a family $\family {B_i: i \in I}$ of pairwise disjoint events such that $\ds \bigcup_{i \mathop \in I} B_i = \Omega$.

Also see

• Definition:Set Partition: the usage of partition here is the same as this.

However, even though it means the same thing, it is helpful to define it separately, as here, in the more specialised context of probability theory.

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 1.8$: The partition theorem