Darboux Properties and Applications to Non-Absolutely Convergent Integrals

Abstract

This paper consists of two parts. The first contains an outline of the theorems and principal results and the second (§§2-6) gives proofs of the theorems and additional details. The theorems concern properties of Darboux continuous functions and functions having generalized Darboux properties. The corresponding results are shown to have interesting applications to the theory of non-absolutely convergent integrals.