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A Survey on Nikodým and Vitali-Hahn-Saks Properties

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A Survey on Nikodým and Vitali-Hahn-Saks Properties

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dc.contributor.author López Alfonso, Salvador es_ES
dc.contributor.author López-Pellicer, Manuel es_ES
dc.contributor.author Mas Marí, José es_ES
dc.date.accessioned 2022-03-01T19:02:11Z
dc.date.available 2022-03-01T19:02:11Z
dc.date.issued 2021 es_ES
dc.identifier.uri http://hdl.handle.net/10251/181186
dc.description.abstract [EN] Let ba(A) be the Banach space of the real (or complex) finitely additive measures of bounded variation defined on an algebra A of subsets of Omega and endowed with the variation norm. . A subset B of A is a Nikod ́ym set for ba(A) if each B-pointwise bounded subset M of ba(A) is uniformly bounded on A and B is a strong Nikod´ym set for ba(A) if each increasing covering (Bm)1 m=1 of B contains a Bn which is a Nikod´ym set for ba(A). If, additionally, the Nikod´ym subset B verifies that the sequential B-pointwise convergence in ba(A) implies weak convergence then B has the Vitali-Hahn-Saks property, (VHS ) in brief, and B has the strong (VHS ) property if for each increasing covering (Bm)1m=1 of B there exists Bq that has (VHS ) property Motivated by Valdivia result that every -algebra has strong Nikod´ym property and by his 2013 open question concerning that if Nikod´ym property in an algebra of subsets implies strong Nikod´ym property we survey this Valdivia theorem and we get that in a strong Nikod´ym set the (VHS ) property implies the strong (VHS ) property. es_ES
dc.description.sponsorship Research supported for the second named author by Grant PGC2018-094431-B-I00 of Ministry of Science, Innovation & Universities of Spain. es_ES
dc.language Inglés es_ES
dc.publisher Y&#305 es_ES
dc.publisher lmaz Simsek es_ES
dc.relation.ispartof Montes Taurus Journal of Pure and Applied Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Bounded set es_ES
dc.subject Algebra and sigma-algebra of subsets es_ES
dc.subject Bounded finitely additive scalar measure es_ES
dc.subject Nikodým and strong Nikodým property es_ES
dc.subject Vitali-Hahn-Saks and strong Vitali-Hahn-Saks property es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.subject.classification CONSTRUCCIONES ARQUITECTONICAS es_ES
dc.title A Survey on Nikodým and Vitali-Hahn-Saks Properties es_ES
dc.type Artículo 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 Matemática Aplicada - Departament de Matemàtica Aplicada 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.; Mas Marí, J. (2021). A Survey on Nikodým and Vitali-Hahn-Saks Properties. Montes Taurus Journal of Pure and Applied Mathematics. 3(3):112-121. http://hdl.handle.net/10251/181186 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://mtjpamjournal.com/ es_ES
dc.description.upvformatpinicio 112 es_ES
dc.description.upvformatpfin 121 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 3 es_ES
dc.description.issue 3 es_ES
dc.identifier.eissn 2687-4814 es_ES
dc.relation.pasarela S\436450 es_ES
dc.contributor.funder MINISTERIO DE CIENCIA, INNOVACIÓN y UNIVERSIDADES es_ES


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