Compactness in spaces of p-integrable functions with respect to a vector measure
[EN] We prove that, under some reasonable requirements, the unit balls of the spaces Lp(m) and Loo(m) of a vector measure of compact range m are compact with respect to the topology t_m of pointwise convergence of the integrals. This result can be considered as a generalization of the classical Alao...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/83649 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/83649 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach function space Vector measure Integration Compactness MATEMATICA APLICADA |
| Sumario: | [EN] We prove that, under some reasonable requirements, the unit balls of the spaces Lp(m) and Loo(m) of a vector measure of compact range m are compact with respect to the topology t_m of pointwise convergence of the integrals. This result can be considered as a generalization of the classical Alaoglu Theorem to spaces of p-integrable functions with respect to vector measures with relatively compact range. Some applications to the analysis of the Saks spaces defined by the norm topology and t_m are given. |
|---|