Choquet type L1-spaces of a vector capacity
Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103812 |
| Acceso en línea: | https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-additive measures Measures of information Choquet integral Fuzzy measure |
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oai:idus.us.es:11441/103812 |
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España |
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Choquet type L1-spaces of a vector capacity Delgado Garrido, Olvido Sánchez Pérez, E. A. Non-additive measures Measures of information Choquet integral Fuzzy measure Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal necessary conditions on Λ are required, several -spaces of integrable functions associated to Λ appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the -spaces and the integration map can be improved in the case when X is an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences. Ministerio de Economía y Competitividad MTM2015-65888-C4-1-P Ministerio de Economía y Competitividad MTM2016-77054-C2-1-P Junta de Andalucía FQM-7276 Elsevier https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |
| title |
Choquet type L1-spaces of a vector capacity |
| spellingShingle |
Choquet type L1-spaces of a vector capacity Delgado Garrido, Olvido Non-additive measures Measures of information Choquet integral Fuzzy measure |
| title_short |
Choquet type L1-spaces of a vector capacity |
| title_full |
Choquet type L1-spaces of a vector capacity |
| title_fullStr |
Choquet type L1-spaces of a vector capacity |
| title_full_unstemmed |
Choquet type L1-spaces of a vector capacity |
| title_sort |
Choquet type L1-spaces of a vector capacity |
| author |
Delgado Garrido, Olvido |
| author_facet |
Delgado Garrido, Olvido Sánchez Pérez, E. A. |
| author_role |
author |
| author2 |
Sánchez Pérez, E. A. |
| author2_role |
author |
| topic |
Non-additive measures Measures of information Choquet integral Fuzzy measure |
| topic_facet |
Non-additive measures Measures of information Choquet integral Fuzzy measure |
| description |
Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal necessary conditions on Λ are required, several -spaces of integrable functions associated to Λ appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the -spaces and the integration map can be improved in the case when X is an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences. |
| publishDate |
2017 |
| format |
article |
| status_str |
submittedVersion |
| url |
https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |
| eu_rights_str_mv |
openAccess |
| publisher |
Elsevier |
| institution |
Universidad de Sevilla (US) |
| collection |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| reponame_str |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| instname_str |
Universidad de Sevilla (US) |
| _version_ |
1878436357019271168 |
| publishDateSort |
2017 |
| author_browse |
Delgado Garrido, Olvido Sánchez Pérez, E. A. |
| publisherStr |
Elsevier |
| score |
6,924472 |