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Extending Darboux functions with finite variation. (English) Zbl 0941.26010

Summary: In this paper we show that a Darboux function with finite variation, which is defined on a closed convex 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.

MSC:

26B30 Absolutely continuous real functions of several variables, functions of bounded variation
26B05 Continuity and differentiation questions