Swiatek, Bozena Extending Darboux functions with finite variation. (English) Zbl 0941.26010 Real Anal. Exch. 22(1996-97), No. 2, 590-610 (1997). 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 Keywords:Darboux function; bounded variation; indicatrix; continuity; quasi-continuity × Cite Format Result Cite Review PDF