# Category:Stopped Sigma-Algebras

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This category contains results about **stopped $\sigma$-algebras**.

Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \ge 0}, \Pr}$ be a filtered probability space.

Let $T$ be a stopping time with respect to $\sequence {\FF_n}_{n \ge 0}$.

Let:

- $\FF_T = \set {A \in \Sigma : A \cap \set {\omega \in \Omega : \map T \omega \le t} \in \FF_t \text { for all } t \in \Z_{\ge 0} }$

We call $\FF_T$ the **stopped $\sigma$-algebra** associated with $T$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Stopped Sigma-Algebras"

The following 6 pages are in this category, out of 6 total.