Definition:Right-Limit of 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 $t \in \hointr 0 \infty$ we define the right-limit at $t$, $\FF_{t^+}$ by:


 * $\ds \FF_{t^+} = \bigcap_{s > t} \FF_s$

Also see

 * Right-Limits of Filtration of Sigma-Algebra form Filtration