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...

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Detalles Bibliográficos
Autores: Delgado Garrido, Olvido, Sánchez Pérez, E. A.
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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spelling Choquet type L1-spaces of a vector capacityDelgado Garrido, OlvidoSánchez Pérez, E. A.Non-additive measuresMeasures of informationChoquet integralFuzzy measureGiven 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-PMinisterio de Economía y Competitividad MTM2016-77054-C2-1-PJunta de Andalucía FQM-7276ElsevierMatemática Aplicada IMinisterio de Economía y Competitividad (MINECO). EspañaJunta de Andalucía2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/103812https://doi.org/10.1016/j.fss.2017.05.014reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésFuzzy Sets and Systems, 327 (november 2017), 98-122.MTM2015-65888-C4-1-PMTM2016-77054-C2-1-PFQM-7276https://www.sciencedirect.com/science/article/pii/S0165011417302142info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1038122026-06-17T12:51:07Z
dc.title.none.fl_str_mv Choquet type L1-spaces of a vector capacity
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
dc.creator.none.fl_str_mv Delgado Garrido, Olvido
Sánchez Pérez, E. A.
author Delgado Garrido, Olvido
author_facet Delgado Garrido, Olvido
Sánchez Pérez, E. A.
author_role author
author2 Sánchez Pérez, E. A.
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Economía y Competitividad (MINECO). España
Junta de Andalucía
dc.subject.none.fl_str_mv Non-additive measures
Measures of information
Choquet integral
Fuzzy measure
topic 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
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/103812
https://doi.org/10.1016/j.fss.2017.05.014
url https://hdl.handle.net/11441/103812
https://doi.org/10.1016/j.fss.2017.05.014
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Fuzzy Sets and Systems, 327 (november 2017), 98-122.
MTM2015-65888-C4-1-P
MTM2016-77054-C2-1-P
FQM-7276
https://www.sciencedirect.com/science/article/pii/S0165011417302142
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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