Nikodym boundedness property for webs in sigma-algebras

[EN] A subset B of an algebra A of subsets of Omega is said to have property N if a B-pointwise bounded subset M of ba(A ) is uniformly bounded on A , where ba(A ) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A with the norm variation. Moreo...

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Authors: López Alfonso, Salvador|||0000-0003-1655-2320, Mas Marí, José|||0000-0002-2835-974X, Moll López, Santiago Emmanuel|||0000-0003-3388-5135
Format: article
Publication Date:2016
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/99725
Online Access:https://riunet.upv.es/handle/10251/99725
Access Level:Open access
Keyword:Bounded set
Finitely additive scalar (vector) measure
Inductive limit
NV-tree
Sigma-algebra
Web Nikodym property
MATEMATICA APLICADA
CONSTRUCCIONES ARQUITECTONICAS
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repository_id_str
spelling Nikodym boundedness property for webs in sigma-algebrasLópez Alfonso, Salvador|||0000-0003-1655-2320Mas Marí, José|||0000-0002-2835-974XMoll López, Santiago Emmanuel|||0000-0003-3388-5135Bounded setFinitely additive scalar (vector) measureInductive limitNV-treeSigma-algebraWeb Nikodym propertyMATEMATICA APLICADACONSTRUCCIONES ARQUITECTONICAS[EN] A subset B of an algebra A of subsets of Omega is said to have property N if a B-pointwise bounded subset M of ba(A ) is uniformly bounded on A , where ba(A ) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A with the norm variation. Moreover B is said to have property sN if for each increasing countable covering (B_m)_m of B there exists B_n which has property N and B is said to have property wN if given the increasing countable coverings (B_m_1 )_m_1 of B and (B_m_1m_2...m_pm_(p+1) )_m_(p+1) of B_m_1m_2...m_p , for each p,m_i ∈ N, 1<= i <= p + 1, there exists a sequence (n_i )_i such that each B_n_1n_2...n_r , r ∈ N, has property N. For a σ-algebra S of subsets of Omega it has been proved that S has property N (Nikodym Grothendieck), property sN (Valdivia) and property w(sN) (Kakol López-Pellicer). We give a proof of property wN for a σ-algebra S which is independent of properties N and sN. This result and the equivalence of properties wN and w2N enable us to give some applications to localization of bounded additive vector measures.This work was supported for the second named author by the Spanish Ministerio de Economía y Competitividad under Grant MTM2014-58159-PSpringer-VerlagDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialDepartamento de Construcciones ArquitectónicasEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería Agronómica y del Medio NaturalMinisterio de Economía, Industria y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20162016-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/99725reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICASopen 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:10251/997252026-06-13T07:49:27Z
dc.title.none.fl_str_mv Nikodym boundedness property for webs in sigma-algebras
title Nikodym boundedness property for webs in sigma-algebras
spellingShingle Nikodym boundedness property for webs in sigma-algebras
López Alfonso, Salvador|||0000-0003-1655-2320
Bounded set
Finitely additive scalar (vector) measure
Inductive limit
NV-tree
Sigma-algebra
Web Nikodym property
MATEMATICA APLICADA
CONSTRUCCIONES ARQUITECTONICAS
title_short Nikodym boundedness property for webs in sigma-algebras
title_full Nikodym boundedness property for webs in sigma-algebras
title_fullStr Nikodym boundedness property for webs in sigma-algebras
title_full_unstemmed Nikodym boundedness property for webs in sigma-algebras
title_sort Nikodym boundedness property for webs in sigma-algebras
dc.creator.none.fl_str_mv López Alfonso, Salvador|||0000-0003-1655-2320
Mas Marí, José|||0000-0002-2835-974X
Moll López, Santiago Emmanuel|||0000-0003-3388-5135
author López Alfonso, Salvador|||0000-0003-1655-2320
author_facet López Alfonso, Salvador|||0000-0003-1655-2320
Mas Marí, José|||0000-0002-2835-974X
Moll López, Santiago Emmanuel|||0000-0003-3388-5135
author_role author
author2 Mas Marí, José|||0000-0002-2835-974X
Moll López, Santiago Emmanuel|||0000-0003-3388-5135
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Departamento de Construcciones Arquitectónicas
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural
Ministerio de Economía, Industria y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Bounded set
Finitely additive scalar (vector) measure
Inductive limit
NV-tree
Sigma-algebra
Web Nikodym property
MATEMATICA APLICADA
CONSTRUCCIONES ARQUITECTONICAS
topic Bounded set
Finitely additive scalar (vector) measure
Inductive limit
NV-tree
Sigma-algebra
Web Nikodym property
MATEMATICA APLICADA
CONSTRUCCIONES ARQUITECTONICAS
description [EN] A subset B of an algebra A of subsets of Omega is said to have property N if a B-pointwise bounded subset M of ba(A ) is uniformly bounded on A , where ba(A ) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A with the norm variation. Moreover B is said to have property sN if for each increasing countable covering (B_m)_m of B there exists B_n which has property N and B is said to have property wN if given the increasing countable coverings (B_m_1 )_m_1 of B and (B_m_1m_2...m_pm_(p+1) )_m_(p+1) of B_m_1m_2...m_p , for each p,m_i ∈ N, 1<= i <= p + 1, there exists a sequence (n_i )_i such that each B_n_1n_2...n_r , r ∈ N, has property N. For a σ-algebra S of subsets of Omega it has been proved that S has property N (Nikodym Grothendieck), property sN (Valdivia) and property w(sN) (Kakol López-Pellicer). We give a proof of property wN for a σ-algebra S which is independent of properties N and sN. This result and the equivalence of properties wN and w2N enable us to give some applications to localization of bounded additive vector measures.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
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/10251/99725
url https://riunet.upv.es/handle/10251/99725
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICAS
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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