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dc.contributor.author | Ferrando, J. C. | es_ES |
dc.contributor.author | López Alfonso, Salvador | es_ES |
dc.contributor.author | López Pellicer, Manuel | es_ES |
dc.date.accessioned | 2020-12-05T04:32:26Z | |
dc.date.available | 2020-12-05T04:32:26Z | |
dc.date.issued | 2019 | es_ES |
dc.identifier.issn | 0354-5180 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/156504 | |
dc.description.abstract | [EN] If R is a ring of subsets of a set Omega and ba (R) is the Banach space of bounded finitely additive measures defined on R equipped with the supremum norm, a subfamily Delta of R is called a Nikodym set for ba (R) if each set {mu(a) : alpha is an element of A} in ba (R) which is pointwise bounded on Delta is norm-bounded in ba (R). If the whole ring R is a Nikodym set, R is said to have property (N), which means that R satisfies the Nikodym-Grothendieck boundedness theorem. In this paper we find a class of rings with property (N) that fail Grothendieck's property (G) and prove that a ring R has property (G) if and only if the set of the evaluations on the sets of R is a so-called Rainwater set for ba(R). Recalling that R is called a (wN)-ring if each increasing web in R contains a strand consisting of Nikodym sets, we also give a partial solution to a question raised by Valdivia by providing a class of rings without property (G) for which the relation (N) double left right arrow (wN) holds. | es_ES |
dc.description.sponsorship | The first and the third authors are 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 | National Library of Serbia | es_ES |
dc.relation.ispartof | Filomat | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Ring of subsets | es_ES |
dc.subject | Nikodym boundedness theorem | es_ES |
dc.subject | Bounded finitely additive scalarly-valued measure | es_ES |
dc.subject | Property (N) | es_ES |
dc.subject | Property (G) | es_ES |
dc.subject | Rainwater set | es_ES |
dc.subject.classification | CONSTRUCCIONES ARQUITECTONICAS | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | On Nikodym and Rainwater sets for ba (R) and a Problem of M. Valdivia | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.2298/FIL1908409F | 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 | Ferrando, JC.; López Alfonso, S.; López Pellicer, M. (2019). On Nikodym and Rainwater sets for ba (R) and a Problem of M. Valdivia. Filomat. 33(8):2409-2416. https://doi.org/10.2298/FIL1908409F | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.2298/FIL1908409F | es_ES |
dc.description.upvformatpinicio | 2409 | es_ES |
dc.description.upvformatpfin | 2416 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 33 | es_ES |
dc.description.issue | 8 | es_ES |
dc.relation.pasarela | S\404248 | es_ES |
dc.contributor.funder | Agencia Estatal de Investigación | es_ES |