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...

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Detalles Bibliográficos
Autores: Rueda Segado, Maria Pilar, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
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
Descripción
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.