Comparison Between Several Ways of Defining Lebesgue’s Integral After Lebesgue
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,...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Recursos: | Universidade Federal de Minas Gerais (UFMG) |
| Repositorio: | Transversal (Belo Horizonte) |
| Idioma: | inglés |
| OAI Identifier: | oai:periodicos.ufmg.br:article/46708 |
| Acesso em linha: | https://periodicos.ufmg.br/index.php/transversal/article/view/46708 |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 |
| Resumo: | 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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