The space of scalarly integrable functions for a Fréchet-space-valued measure
The space L1 w (ν) of all scalarly integrable functions with respect to a Fréchet-space-valued vector measure ν is shown to be a complete Fréchet lattice with the σ-Fatou property which contains the (traditional) space L1(ν), of all ν-integrable functions. Indeed, L1(ν) is the σ-order continuous par...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135780 |
| Acceso en línea: | https://hdl.handle.net/11441/135780 https://doi.org/10.1016/j.jmaa.2009.01.036 |
| Access Level: | acceso abierto |
| Palabra clave: | Fréchet space (lattice) Vector measures Fatou property Lebesgue topology Scalarly integrable function |
| Sumario: | The space L1 w (ν) of all scalarly integrable functions with respect to a Fréchet-space-valued vector measure ν is shown to be a complete Fréchet lattice with the σ-Fatou property which contains the (traditional) space L1(ν), of all ν-integrable functions. Indeed, L1(ν) is the σ-order continuous part of L1 w (ν). Every Fréchet lattice with the σ-Fatou property and containing a weak unit in its σ-order continuous part is Fréchet lattice isomorphic to a space of the kind L1 w (ν). |
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