Definition:Finite Partition (Probability Theory)

Definition

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

Let $\xi$ be a partition of $\Omega$.

Then, $\xi$ said to be a finite partition if and only if:

$\exists A_1, \ldots, A_n \in \Sigma : \xi = \set {A_1, \ldots, A_n}$

Also see

• Definition:Finite Partition Generated by Finite Sub-Sigma-Algebra
• Sigma-Algebra Generated by Finite Partition is Finite Sub-Sigma-Algebra

Sources

• 2013: Peter Walters: An Introduction to Ergodic Theory (4th ed.) $4.1$: Partitions and Subalgebras