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A simplified construction of the Lebesgue integral

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Abstract

We present a modification of Riesz’s construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time simplifying the proofs.

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    V. Komornik

  2. Département de mathématique, Université de Strasbourg, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    V. Komornik

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  1. V. Komornik
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Correspondence to V. Komornik.

Additional information

To the memory of Ákos Császár

The author was supported by the grant NSFC No. 11871348.

This work has been done during the author's visit of the Department of Mathematics of the University of Pécs, Hungary. He thanks the members of the department for their hospitality.

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Komornik, V. A simplified construction of the Lebesgue integral. Acta Math. Hungar. 158, 318–337 (2019). https://doi.org/10.1007/s10474-019-00912-x

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  • DOI: https://doi.org/10.1007/s10474-019-00912-x

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