ABSTRACT
This chapter investigates several aspects of the relationship between spaces of contents or measures on 2 and certain spaces of functions on R, by using the theory of vector lattices. It discusses the functions of locally finite variation and absolutely continuous functions. The chapter presents a theorem to show that the fundamental properties of the important class of functions are a by-product of the general theory of spaces of measures. It proves that integrable functions may be approximated using continuous functions for which the differentiability of the indefinite integral is well known (fundamental theorem of calculus). The chapter also shows that any function of locally finite variation is differentiable by the application of Vitali’s covering theorem.
