 Let formula_1, formula_2 be a sequence of probability measures on a metric space formula_3 such that formula_1 converges weakly to some probability measure formula_5 on formula_3 as formula_7.Suppose also that the support of formula_5 is separable.Then there exist random variables formula_9 defined on a common probability space formula_10 such that the law of formula_9 is formula_1 for all formula_13 (including formula_14) and such that formula_9 converges to formula_16, formula_17-almost surely.