Definition:Right-Continuous 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 $\Sigma$.

We say that $\sequence {\FF_t}_{t \ge 0}$ is right-continuous for each $t \in \hointr 0 \infty$, we have:


 * $\FF_{t^+} = \FF_t$

where $\FF_{t^+}$ is the right-limit of $\sequence {\FF_t}_{t \ge 0}$ at $t$.