Representation of Banach lattices as L1w spaces of a vector measure defined on a δ-ring
In this paper we prove that every Banach lattice having the Fatou property and having its s-order continuous part as an order dense subset, can be represented as the space L1 w(n) of weakly integrable functions with respect to some vector measure n defined on a d-ring.
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103718 |
| Acesso em linha: | https://hdl.handle.net/11441/103718 https://doi.org/10.36045/bbms/1337864270 |
| Access Level: | acceso abierto |
| Palavra-chave: | Banach lattice d-ring Fatou property Order density Order continuity Integration with respect to vector measures |
| Resumo: | In this paper we prove that every Banach lattice having the Fatou property and having its s-order continuous part as an order dense subset, can be represented as the space L1 w(n) of weakly integrable functions with respect to some vector measure n defined on a d-ring. |
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