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 ? ? ?.

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