If $S,T$ are two stopping time w.r.t. $\mathcal F_t$
define $R=S\wedge T$.Then $R$ is a stopping time .How to prove $R$ is measurable w.r.t $\mathcal F_T$?
Is there something wrong with this statement? for arbitrary $t'$,we need to show that $\{R\le t'\}\in\mathcal F_T$.so for arbitrary $t$ ,we need to show that $\{R\le t'\}\cap\{T\le t\}\in\mathcal F_t$.The intersection belongs to $\mathcal F_{t'\wedge t}$,not necessary $\mathcal F_t$.