Undominated Sequences of Integrable Functions

[EN] In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Specifically, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on...

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Detalles Bibliográficos
Autores: Bernal-González, Luis, Calderón-Moreno, María del Carmen, Murillo Arcila, Marina, Prado-Bassas, José A.
Tipo de recurso: artículo
Fecha de publicación:2020
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:10251/176361
Acceso en línea:https://riunet.upv.es/handle/10251/176361
Access Level:acceso abierto
Palabra clave:Integrable function
Continuous function
Undominated sequence
Lineability
Residual set
MATEMATICA APLICADA
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spelling Undominated Sequences of Integrable FunctionsBernal-González, LuisCalderón-Moreno, María del CarmenMurillo Arcila, MarinaPrado-Bassas, José A.Integrable functionContinuous functionUndominated sequenceLineabilityResidual setMATEMATICA APLICADA[EN] In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Specifically, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on a locally compact space and integrable with respect to a given Borel measure in it, are not controlled by an integrable function.Luis Bernal-Gonzalez, Maria del Carmen Calderon-Moreno, and Jose A. Prado-Bassas have been supported by the Plan Andaluz de Investigacion de la Junta de Andalucia FQM-127 Grant P08-FQM-03543 and by MCINN Grant PGC2018-098474-B-C21. Marina Murillo-Arcila is supported by MEC, Grant MTM2016-75963-P, and PID2019-105011GB-I00.Springer-VerlagJunta de AndalucíaAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-10-20journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/176361reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengJunta de Andalucía http://dx.doi.org/10.13039/501100011011 FQM-127 Análisis Funcional No LinealJunta de Andalucía http://dx.doi.org/10.13039/501100011011 P08-FQM-03543 Análisis matemáticoAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PGC2018-098474-B-C21 MÉTODOS DEL ANÁLISIS FUNCIONAL APLICADOS A: PROBLEMAS NO LINEALES, TEORÍA DE JUEGOS Y LINEABILIDADAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2016-75963-P DINAMICA DE OPERADORESAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105011GB-I00 DINÁMICA DE OPERADORESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1763612026-06-13T07:49:27Z
dc.title.none.fl_str_mv Undominated Sequences of Integrable Functions
title Undominated Sequences of Integrable Functions
spellingShingle Undominated Sequences of Integrable Functions
Bernal-González, Luis
Integrable function
Continuous function
Undominated sequence
Lineability
Residual set
MATEMATICA APLICADA
title_short Undominated Sequences of Integrable Functions
title_full Undominated Sequences of Integrable Functions
title_fullStr Undominated Sequences of Integrable Functions
title_full_unstemmed Undominated Sequences of Integrable Functions
title_sort Undominated Sequences of Integrable Functions
dc.creator.none.fl_str_mv Bernal-González, Luis
Calderón-Moreno, María del Carmen
Murillo Arcila, Marina
Prado-Bassas, José A.
author Bernal-González, Luis
author_facet Bernal-González, Luis
Calderón-Moreno, María del Carmen
Murillo Arcila, Marina
Prado-Bassas, José A.
author_role author
author2 Calderón-Moreno, María del Carmen
Murillo Arcila, Marina
Prado-Bassas, José A.
author2_role author
author
author
dc.contributor.none.fl_str_mv Junta de Andalucía
Agencia Estatal de Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Integrable function
Continuous function
Undominated sequence
Lineability
Residual set
MATEMATICA APLICADA
topic Integrable function
Continuous function
Undominated sequence
Lineability
Residual set
MATEMATICA APLICADA
description [EN] In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Specifically, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on a locally compact space and integrable with respect to a given Borel measure in it, are not controlled by an integrable function.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-10-20
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/176361
url https://riunet.upv.es/handle/10251/176361
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Junta de Andalucía http://dx.doi.org/10.13039/501100011011 FQM-127 Análisis Funcional No Lineal
Junta de Andalucía http://dx.doi.org/10.13039/501100011011 P08-FQM-03543 Análisis matemático
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PGC2018-098474-B-C21 MÉTODOS DEL ANÁLISIS FUNCIONAL APLICADOS A: PROBLEMAS NO LINEALES, TEORÍA DE JUEGOS Y LINEABILIDAD
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2016-75963-P DINAMICA DE OPERADORES
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105011GB-I00 DINÁMICA DE OPERADORES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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