Let $$\mathcal F_s = \{ A : A\cap \{S \leq t\} \in \mathcal F_t, \forall t \geq 0\}$$
where $\left(\mathcal F_t\right)_{t\geqslant 0}$ is a right continuous filtration.
Let $S$ be a stopping time, let $A \in\mathcal F_s$ and let $R=S$ on $A$ and $R = \infty $ on $A^c$. Show that $R$ is a stopping time.
I'm really lost on this question, it's question 7.3.4 in Rick Durrett's Probability Theory book.