Definition:Right-Limit Filtration of Sigma-Algebra

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

Let $\sequence {\FF_t}_{t \ge 0}$ be a continuous-time filtration of $\Sigma$.

For each $s \in \hointr 0 \infty$, let $\FF_{s+}$ be the right-limit of $\sequence {\FF_t}_{t \ge 0}$ at $t$.

We say that $\sequence {\FF_{t+} }_{t \ge 0}$ is the right-limit filtration associated with $\sequence {\FF_t}_{t \ge 0}$.

Also see

 * Right-Limits of Filtration of Sigma-Algebra form Filtration proves that $\sequence {\FF_{t+} }_{t \ge 0}$ is indeed a continuous-time filtration.