An almost everywhere existence theorem for solutions of Volterra functional equations

Abstract

1. Introduction. Let C. be the Wiener space, i.e., the collection of real valued functions x(t) defined and continuous on 1: 0 <t ?1 and satisfying x(O) = 0. Let a finite sequence of real valued continuous functions F'(t, u), F2(t, u, VI), , * Fn(t, u, vI, * * *, vn-1) be defined and continuous for tC1 and other variables unrestricted. The Volterra functionals 4k(xlt), Alk(xIt) depending on the function x(.) and the real variable t are defined inductively by (1) AO(x| t) = x(t), on C. X9 I,