The differentiability of Banach space-valued functions of bounded variation

Abstract

In this paper we consider Banach space-valued functions with the compact range. It is shown that if a Banach space-valued function \(F:[0,1] \rightarrow X\) is of bounded variation with respect to the Minkowski functional \(||.||_{F}\) associated to the closed absolutely convex hull \(C_{F}\) of \(F([0,1])\), then \(F\) is differentiable almost everywhere on \([0,1]\).