Comparison Between Several Ways of Defining  Lebesgue’s Integral After Lebesgue

Loredana Biacino

doi:10.24117/2526-2270.2023.i14.10

Comparison Between Several Ways of Defining Lebesgue’s Integral After Lebesgue

Authors

Loredana Biacino University “Federico II” of Naples

DOI:

https://doi.org/10.24117/2526-2270.2023.i14.10

Keywords:

Lebesgue’s integral, Integration without recourse to Lebesgue measure theory, Integral as limit of integrals of elementary functions, Lebesgue’ integral as functional prolongation of Cauchy integral, Abstract integration spaces

Abstract

After the publication in 1904 of Lebesgue’s Leçons, many mathematicians had the idea of obtaining a simpler and more natural theory of integration, sometimes for a technical or philosophical purpose, sometime for a didactical purpose. Among them Borel, Riesz, Young, Hahn, Pierpoint, Radon, Fréchet, Daniell and in Italy Tonelli, Vitali, Caccioppoli dealt with this fundamental tool. In this paper, their theories are exposed and compared.

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Published

2023-06-30

Issue

No. 14 (2023): Bruno Latour

Section

Articles

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

“Comparison Between Several Ways of Defining Lebesgue’s Integral After Lebesgue”. 2023. Transversal: International Journal for the Historiography of Science, no. 14 (June). https://doi.org/10.24117/2526-2270.2023.i14.10.