ANALOGUE OF WIENER INTEGRAL IN THE SPACE OF SEQUENCES OF REAL NUMBERS

Let T > 0 be given. Let (C[0; T];m ) be the ana- logue of Wiener measure space, associated with the Borel proba- bility measure on R, let (L2[0; T]; e!) be the centered Gaussian measure space with the correlation operator (¡ d2 dx2 )¡1 and (`2; em) be the abstract Wiener measure space. Let U be the space of all sequence hcni in `2 such that the limit limm!1 1 m+1 Pm n=0 Pn k=0 ck cos k¼t T converges uniformly on [0; T] and give a set function m such that for any Borel subset G of `2, m(U \ P¡1 0 ± P0(G)) = em(P¡1 0 ± P0(G)). The goal of this note is to study the relationship among the measures m ; e!; em and m.