Let {T„, n \u3e 1} be an arbitrary sequence of non-lattice random variables and {Sn, n \u3e 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø1n and Ø2n be the moment genereating functions of {Tn, n \u3e 1} and { Sn,n \u3e 1} respectively. Let {an} be a sequence of real numbers such that an —»• oo
