Structure on probabilistic metric spaces

This paper proved: Let (S,F) is a pre-PM space with continuous distribution function fpq for all distinct p,q in S, then (S,F) is a PM space under τM if and only if it is determined by a RM space (or W-space) with the property that there is a nondecreasing, left continuous function fpqr satisfying Xpq(w) = fpqr(Xqr(w)) a.s. for any distinct p,q,r in S. So we answered the open problems 9.6.1 and 9.6.2 that were put forward by Schweizer B. and Sklar A. in [1].