Full Individual and Class Differentiation Theorems In Their Relations To Halo and Vitali Properties

Abstract

Introduction. In his article (22), de Possel laid the foundations for an abstract theory of differentiation of set functions, the term “abstract” being meant in the sense of Fréchet-Nikodym, that is, without reference to a euclidean, metric, or topological background. In 1.1, we adopt, substantially, his notion of derivation basis. De Possel considered two Vitali properties for a derivation basis.