A duality theorem by means of Riemann Stieltjes integral

Abstract

Duality between the space of continuous functions and the space of bounded variations functions can be easily characterized by means of Riemann-Stieltjes integrals when we consider real valued functions defined, e.g., on [0,1]; here we give a self-contained exposition of Riemann-Stieltjes integration theory for functions which assumes values in infinite dimensional vector spaces and we show as the duality between the space of continuous functions and the space of bounded variation functions can be represented by means of such theory.