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

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Mathematica Slovaca

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.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01, Banská Bystrica, Slovakia

    Beloslav Riečan

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-841 01, Bratislava, Slovakia

    Beloslav Riečan

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  1. Beloslav Riečan
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Correspondence to Beloslav Riečan.

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Communicated by Ján Borsík)

Dedicated to Professor Ján Jakubík on the occasion of his 90th birthday

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Riečan, B. On the Kluvánek construction of the Lebesgue integral with respect to a vector measure. Math. Slovaca 64, 727–740 (2014). https://doi.org/10.2478/s12175-014-0236-4

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  • DOI: https://doi.org/10.2478/s12175-014-0236-4

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