Given a probability space (, F,P), consider a stochastic process {X}, adapted to filtration {Fe}. Assume...

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Given a probability space (, F,P), consider a stochastic process {X}, adapted to filtration {Fe}. Assume that {X+}, is a supermartingale with respect to {F}, and E[X] = const. (constant expected value). Show that {X} must also be a martingale with respect to filtration {F} Given a probability space (, F,P), consider a stochastic process {X}, adapted to filtration {Fe}. Assume that {X+}, is a supermartingale with respect to {F}, and E[X] = const. (constant expected value). Show that {X} must also be a martingale with respect to filtration {F}