Abstract
Let {X n, n⩾1} be an arbitrary sequence of random elements defined on a probability space (Ω, A,P) with a nonatomic measure P and taking values in a separable complete metric space ( S, ρ). In this paper we characterize the set of all possible weak limits of the sequences {X N n , n⩾1} , where {N n, n⩾1} is a sequence of positive integer-valued random variables. The proof shows how, for a given probability law F( ) , we can define a random sequence {N n, n⩾1} satisfying X N n → D F( ) .
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