In the definition of super martingale, look what happen if you assume that the inequality is strict (on a non-zero measure set) and you take expectation.
Hello, guys!
Can anybody give a hint on how to prove that (on continuous time setting with t in [0,T]) if M is a supermartingale such that E[M(T)] = M(0), then M is in fact a martingale.
Would appreciate any help. Thanks!