Definition:Filtration of Sigma-Algebra

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

Let $\sequence {\FF_n}_{n \mathop \in \N}$ be an increasing sequence of sub-$\sigma$-algebras of $\Sigma$.

That is:


 * $\FF_i \subseteq \FF_j$ whenever $i \le j$.

We say that $\sequence {\FF_n}_{n \mathop \in \N}$ is a filtration of $\Sigma$.