How do you show $B_T\in\mathcal{F}_T$ for T is a stopping time?
Note the filtration is generated by the Brownian motion (and not necessarily completed, in particular, $\mathcal{F}_T\neq\mathcal{F}_{T+}$)
and a much harder question:
Are all Brownian Motion stopping times previsible? (Please point me to a proof or reference)