Extending Darboux functions with finite variation

Abstract

In this paper we show that a Darboux function with finite variation, which is defined on closed, convex and boundary subset of \(\mathbb{R}^2\), can be extended to a Darboux function with finite variation, which is defined on \(\mathbb{R}^2\). Moreover, the set of all points of continuity and the set of all points of quasi-continuity for the first function are equal to the corresponding sets for the extension of this function.