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

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


Also see


Sources