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Demonstratio Mathematica

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Volume 47, Issue 4


On Bi-Dimensional Second µ-Variation

Jurancy Ereú
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/ José Giménez / Nelson Merentes
Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0073


In this paper, we present a generalization of the notion of bounded slope variation for functions defined on a rectangle Iba in ℝ2. Given a strictly increasing function µ-defined in a closed real interval, we introduce the class BVµ,2 (Iba ), of functions of bounded second µ-variation on Iba ; and show that this class can be equipped with a norm with respect to which it is a Banach space. We also deal with the important case of factorizable functions in BVµ,2 (Iba ) and finally we exhibit a relation between this class and the one of double Riemann-Stieltjes integrals of functions of bi-dimensional bounded variation.

Keywords: and phrases functions of bounded second variation; functions of bounded variation


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About the article

Received: 2013-08-06

Revised: 2014-02-12

Published Online: 2014-12-11

Published in Print: 2014-12-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 910–932, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0073.

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© by Jurancy Ereú. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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