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High Quality Content by WIKIPEDIA articles! Let n, n N be a sequence of probability measures on a topological space S; suppose that n converges weakly to some probability measure on S as n . Suppose also that the support of is separable. Then there exist random variables Xn, X defined on a common probability space ( , F, P) such that (Xn) (P) = n (i.e. n is the distribution/law of Xn); X (P) = (i.e. is the distribution/law of X); and Xn( ) X( ) as n for every .