Definition:Partition (Probability Theory)

Definition

Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.

A partition of $\Omega$ is a set $\left\{{B_i: i \in I}\right\}$ of disjoint events such that $\bigcup_i B_i = \Omega$.

Thus it can be seen that the usage of partition here is the same as that used in its standard set-theoretical sense.

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

Sources

• Geoffrey Grimmett: Probability: An Introduction (1986): $\S 1.8$