6. (20 points) (i) Let S g T be stopping times and E[T]

6. (20 points) (i) Let S T be stopping times and E[T] < oc. Then shows that E[B}] E[BZ] + - Bs)2]. ii) Using the optional sampling theorem, (i) and Fatou's lemma conclude that if E[T] < 00 then EU].