Summary: A. V. Skorokhod [Teor. Veroyatn. Primen. 1, 289-319 (1956; Zbl 0074.338)] discovered that if a sequence \(Q_ n\) of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are \(Q_ n\)-distributed \(f_ n\) which converge almost surely. This note strengthens Skorokhod’s result by associating, with each probability Q on a Polish space, a random variable \(f_ Q\) on a fixed standard probability space so that for each Q, (a) \(f_ Q\) has distribution Q and (b) with probability 1, \(f_ P\) is continuous at \(P=Q\).