Simply Regulated Functions and Semivariation in Uniformly Convex Spaces

Abstract

In the last two decades the Riemann generalized integral, having values in Banach spaces, has been increasingly studied. The development in this area concerns mainly with the Henstock-Kurzweil (see e.g.[1], [2]), and the Dushnik and the Young integrals (see e.g.[3]). Recently it has appeared in the literature many proper applications in this field (proper here considered in the sense that the results are not disguises of an essentially finite dimensional frame) (see e.g.[4],[5]). In this paper we give a result having its roots in this frame.