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Weak Sequential Convergence in Bounded Finitely Additive Measures

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Weak Sequential Convergence in Bounded Finitely Additive Measures

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dc.contributor.author López Alfonso, Salvador es_ES
dc.contributor.author López Pellicer, Manuel es_ES
dc.date.accessioned 2021-11-05T14:09:03Z
dc.date.available 2021-11-05T14:09:03Z
dc.date.issued 2020-03 es_ES
dc.identifier.issn 2305-221X es_ES
dc.identifier.uri http://hdl.handle.net/10251/176355
dc.description.abstract [EN] It is well known that a ¿-algebra ¿ of subsets of a set ¿ verifies both Nikodým property and property (G) for the Banach space ba(¿) of bounded finitely additive measures defined in ¿. A classic result of Valdivia stating that if a ¿-algebra ¿ is covered by an increasing sequence (¿n:n¿N) of subsets, there is p¿N such that ¿p is a Nikodým set for ba(¿) was complemented in Ferrando et al. (2020) proving that there exists p¿N such that ¿p is both a Nikodým and a Grothendieck set for ba(¿). Valdivia result was the first step to get that if (¿¿:¿¿N<¿) is a web in ¿ there exists a chain (¿n:n¿N) in N<¿ such that each ¿¿n, n¿N, is a Nikodým set for ba(¿). In this paper, we develop several properties in Banach spaces that enables us to complement the preceding web result extending the main result in Ferrando et al. (2020) proving that for each web (¿¿:¿¿N<¿) in a ¿-algebra ¿ there exists a chain (¿n:n¿N) in N<¿ such that each ¿¿n, n¿N, is both a Nikodým and a Grothendieck set for ba(¿). As an application we extend some results of classic Banach space theory es_ES
dc.description.sponsorship The second author is supported by Grant PGC2018-094431-B-I00 of the Ministry of Science, Innovation and Universities of Spain. es_ES
dc.language Inglés es_ES
dc.publisher Springer es_ES
dc.relation.ispartof Vietnam Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Algebras and sigma-algebras of sets es_ES
dc.subject Bounded finitely additive measures es_ES
dc.subject Grothendieck es_ES
dc.subject Nikodym and Rainwater sets es_ES
dc.subject Pointwise and weak sequential convergence es_ES
dc.subject Web properties es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.subject.classification CONSTRUCCIONES ARQUITECTONICAS es_ES
dc.title Weak Sequential Convergence in Bounded Finitely Additive Measures es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10013-020-00387-2 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-094431-B-I00/ES/ESPACIOS DE FUNCIONES: FUNCIONES ANALITICAS Y OPERADORES DE COMPOSICION. RENORMAMIENTOS Y TOPOLOGIA DESCRIPTIVA/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Construcciones Arquitectónicas - Departament de Construccions Arquitectòniques es_ES
dc.description.bibliographicCitation López Alfonso, S.; López Pellicer, M. (2020). Weak Sequential Convergence in Bounded Finitely Additive Measures. Vietnam Journal of Mathematics. 48(2):379-389. https://doi.org/10.1007/s10013-020-00387-2 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s10013-020-00387-2 es_ES
dc.description.upvformatpinicio 379 es_ES
dc.description.upvformatpfin 389 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 48 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\404372 es_ES
dc.contributor.funder MINISTERIO DE CIENCIA, INNOVACIÓN y UNIVERSIDADES es_ES
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