Real Analysis Exchange

Extending Darboux functions with finite variation

Bozena Swiatek

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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.

Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 590-611.

Dates
First available in Project Euclid: 22 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337713143

Mathematical Reviews number (MathSciNet)
MR1460974

Zentralblatt MATH identifier
0941.26010

Subjects
Primary: 26B30: Absolutely continuous functions, functions of bounded variation

Keywords
Darboux finite variation extension

Citation

Swiatek, Bozena. Extending Darboux functions with finite variation. Real Anal. Exchange 22 (1996), no. 2, 590--611. https://projecteuclid.org/euclid.rae/1337713143


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