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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 64, Issue 3

Issues

On the Kluvánek construction of the Lebesgue integral with respect to a vector measure

Beloslav Riečan
  • Department of Mathematics Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01, Banská Bystrica, Slovakia
  • Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-841 01, Bratislava, Slovakia
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Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0236-4

Abstract

The Kluvánek construction of the Lebesgue integral is extended in two directions. First, instead of a compact interval [a, b] in the real line an abstract non-empty set X is considered, instead of the ring generated by subintervals of [a, b] an arbitrary ring A of subsets of X. Secondly, instead of the length of intervals (λ([c, d]) = d−c) any vector measure λ: A→V is considered, where V is a Riesz space.

MSC: Primary 28B05; 28B10; 28B15

Keywords: Lebesgue integral; Riesz space

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 727–740, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0236-4.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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