Question: Let (t mapsto X_{t}) be a right continuous stochastic process. Show that for closed sets (F) [mathbb{P}left(X_{t} in F quad forall t in mathbb{R}^{+}ight)=mathbb{P}left(X_{q} in

Let \(t \mapsto X_{t}\) be a right continuous stochastic process. Show that for closed sets \(F\)

\[\mathbb{P}\left(X_{t} \in F \quad \forall t \in \mathbb{R}^{+}ight)=\mathbb{P}\left(X_{q} \in F \quad \forall q \in \mathbb{Q}^{+}ight)\]

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