Definition:Filtered Probability Space

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

Let $\sequence {\mathcal F_n}_{n \mathop \in \N}$ be a filtration of $\Sigma$.

We say that $\struct {\Omega, \Sigma, \sequence {\mathcal F_n}_{n \mathop \in \N}, \Pr}$ is a filtered probability space.

Also known as
A filtered probability space may be known as simply a filtered space.