Pseudo-Fubini entire functions on the plane in the sense of Riemann
We prove the existence of a maximal dimensional vector space of real functions on the real plane all of whose nonzero members are bounded, entire, non-Lebesgue-integrable, and satisfy the equality of the two iterated integrals given in the conclusion of the Fubini theorem, with the additional proper...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::7a7d33a8a9a28c8bab9752cb140fded5 |
| Acceso en línea: | https://hdl.handle.net/11441/184906 https://doi.org/10.36045/j.bbms.220321 |
| Access Level: | acceso abierto |
| Palabra clave: | Dense vector subspace Entire function Fubini theorem Non-integrable function on the plane Riemann integrability |
| Sumario: | We prove the existence of a maximal dimensional vector space of real functions on the real plane all of whose nonzero members are bounded, entire, non-Lebesgue-integrable, and satisfy the equality of the two iterated integrals given in the conclusion of the Fubini theorem, with the additional property that these iterated integrals exist in the Riemann sense, but not in the Lebesgue one. Moreover, this vector space is dense in the space of smooth functions on the plane under its natural topology. |
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