Definition:Right-Limit Filtration of Sigma-Algebra
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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.