Before revision:  We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes  with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.
After revision:  We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes (which in turn is equivalent to the weak market viability condition of absence of arbitrage of the first kind) with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.