The Fatou Completion of a Fréchet Function Space and Applications
Given a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space L 1 (ν) of integrable functions with re...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135783 |
| Acceso en línea: | https://hdl.handle.net/11441/135783 https://doi.org/10.1017/S1446788709000238 |
| Access Level: | acceso abierto |
| Palabra clave: | Fréchet space (lattice) Vector measures Fatou property Lebesgue topology Scalarly integrable function |
| Sumario: | Given a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space L 1 (ν) of integrable functions with respect to a Fréchet-space-valued measure ν is the space L 1 w(ν) of scalarly ν-integrable functions. Further consequences are also given. |
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