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

Also see

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