Pseudo-Fubini Real-Entire Functions on the Plane
In this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space can be cho...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/144838 |
| Acceso en línea: | https://hdl.handle.net/11441/144838 https://doi.org/10.1007/s00009-022-02149-5 |
| Access Level: | acceso abierto |
| Palabra clave: | Fubini’s theorem real entire functions iterated integrals dense lineability |
| Sumario: | In this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space can be chosen to be dense in the space of all real C∞ -functions on the plane endowed with the topology of uniform convergence on compacta for all derivatives of all orders. If the condition of being entire is dropped, then a closed infinite dimensional subspace satisfying the same properties can be obtained. |
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