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A Komlós Theorem for abstract Banach latticesof measurable functions

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A Komlós Theorem for abstract Banach latticesof measurable functions

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dc.contributor.author Jiménez Fernández, Eduardo es_ES
dc.contributor.author Juan Blanco, María Aránzazu es_ES
dc.contributor.author Sánchez Pérez, Enrique Alfonso es_ES
dc.date.accessioned 2013-07-25T06:38:28Z
dc.date.available 2013-07-25T06:38:28Z
dc.date.issued 2011
dc.identifier.issn 0022-247X
dc.identifier.uri http://hdl.handle.net/10251/31401
dc.description.abstract Consider a Banach function space X(mu) of (classes of) locally integrable functions over a sigma-finite measure space (Omega, Sigma, mu) with the weak sigma-Fatou property. Day and Lennard (2010) [9] proved that the theorem of Komlos on convergence of Cesaro sums in L(1) [0, 1] holds also in these spaces; i.e. for every bounded sequence (f(n))(n) in X(mu), there exists a subsequence (f(nk))(k) and a function f is an element of X(mu) such that for any further subsequence (h(j))(j) of (f(nk))(k), the series 1/n Sigma(n)(j=1) h(j) converges mu-a.e. to f. In this paper we generalize this result to a more general class of Banach spaces of classes of measurable functions - spaces L(1) (nu) of integrable functions with respect to a vector measure nu on a delta-ring - and explore to which point the Fatou property and the Komlos property are equivalent. In particular we prove that this always holds for ideals of spaces L(1)(nu) with the weak sigma-Fatou property, and provide an example of a Banach lattice of measurable functions that is Fatou but do not satisfy the Komlos Theorem. (C) 2011 Elsevier Inc. es_ES
dc.description.sponsorship MA. Juan acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the research project MTM2008-04594: Generalitat Valenciana (2009/102) and UPV (PAID-06-08 Ref. 3093). en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Journal of Mathematical Analysis and Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Komlos Theorem es_ES
dc.subject Cesaro convergence es_ES
dc.subject Fatou property es_ES
dc.subject Banach function space es_ES
dc.subject Vector measure es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A Komlós Theorem for abstract Banach latticesof measurable functions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.jmaa.2011.05.010
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2008-04594/ES/ANALISIS DE FOURIER CLASICO, MULTILINEAL Y VECTORIAL/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//GV%2F2009%2F102/ES/Espacios de funciones e integracion en espacios de banach/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UPV//PAID-06-08-3093/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2009-14483-C02-02/ES/Integracion Bilineal, Medidas Vectoriales Y Espacios De Funciones De Banach/ es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Jiménez Fernández, E.; Juan Blanco, MA.; Sánchez Pérez, EA. (2011). A Komlós Theorem for abstract Banach latticesof measurable functions. Journal of Mathematical Analysis and Applications. (383):130-136. https://doi.org/10.1016/j.jmaa.2011.05.010 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jmaa.2011.05.010 es_ES
dc.description.upvformatpinicio 130 es_ES
dc.description.upvformatpfin 136 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.issue 383 es_ES
dc.relation.senia 206071
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Universitat Politècnica de València es_ES


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