Let µn be a probability measure on the Borel sigma-field on D[0, 1] with respect to Skorohod distance, n = 0. Necessary and sufficient conditions for the following statement are provided. On some probability space, there are D[0, 1]-valued random variables Xn such that Xn tilde µn for all n = 0 andn - X0--> 0 in probability, whereis the sup-norm. Such conditions do not require µ0 separable underApplications to exchangeable empirical processes and to pure jump processes are given as well.
Cadlag function Exchangeable empirical process Separable probability measure Skorohod representation theorem Uniform distance Weak convergence of probability measures