A note on the weak convergence of probability measures in the D[0,1] space

Abstract

Let τ be a regular metric as defined below for the D = D [ 0 , 1 ] space. Even when ( D , τ ) is not a separable and complete metric space we show (i) that the usual conditions on a sequence of probability measures in ( D , τ ) ensures its weak convergence and (ii) that Prohorov's theorem in ( D , τ ) can be derived as a consequence of our results.