Before revision:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
After revision:  We obtain the equivalence of (a) the boundedness in probability of the set of terminal wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.