Definition:Finite Sub-Sigma-Algebra

Definition

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

Let $\AA \subseteq \Sigma$ be a sub-$\sigma$-algebra.

Then, $\AA$ is said to be a finite sub-$\sigma$-algebra if and only if:

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

Also see

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

Sources

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