Definition:Filtration of Sigma-Algebra

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

Let $\sequence {\mathcal F_n}_{n \mathop \in \N}$ be a sequence of sub-$\sigma$-algebras of $\Sigma$ such that:


 * $\mathcal F_i \subseteq \mathcal F_j$ whenever $i \le j$.

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