Vector spaces of non-measurable functions
| dc.contributor.author | García-Pacheco, F.J. | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T10:33:22Z | |
| dc.date.available | 2023-06-20T10:33:22Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimension beta for any cardinality beta. Some techniques involving measure theory and density characters of Banach spaces are used. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20209 | |
| dc.identifier.doi | 10.1007/s10114-005-0726-y | |
| dc.identifier.issn | 1439-8516 | |
| dc.identifier.officialurl | http://link.springer.com/content/pdf/10.1007%2Fs10114-005-0726-y | |
| dc.identifier.relatedurl | http://www.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50492 | |
| dc.issue.number | 6 | |
| dc.journal.title | Acta Mathematica Sinica, English Series | |
| dc.language.iso | eng | |
| dc.page.final | 1808 | |
| dc.page.initial | 1805 | |
| dc.publisher | Springer Heidelberg | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Lineability | |
| dc.subject.keyword | Spaceability Non-measurable functions | |
| dc.subject.keyword | Density character | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Vector spaces of non-measurable functions | |
| dc.type | journal article | |
| dc.volume.number | 22 | |
| dcterms.references | Enflo, P., Gurariy, V.: On lineability and spaceability of sets in function spaces, preprint, 2002 Aron, R., Gurariy, V., Seoane-Sep´ulveda, J. B.:Lineability and spaceability of sets of functions on R. Proc.Amer.Math. Soc., 133, 795–803 (2005) Gurariy, V. I.: Subspaces and bases in spaces of continuous functions (Russian). Dokl. Akad. Nauk SSSR,167, 971–973 (1966) Gurariy, V. I.: Linear spaces composed of nondifferentiable functions. C. R. Acad. Bulgare Sci. 44(5),13–16 (1991) Fonf, V., Gurariy, V., Kadec, V.: An infinite dimensional subspace of C[0, 1] consisting of nowhere differentiable functions. C. R. Acad. Bulgare Sci., 52, 11–12, 13–16 (1999) Rodrıguez-Piazza, L.: Every separable Banach space is isometric to a space of continuous nowhere differentiable functions. Proc. Amer. Math. Soc., 123 12, 3649–3654 (1995) Hencl, S.: Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Holder functions. Proc. Amer.Math. Soc., 128 12, 3505–3511 (2000) Aron, R., Seoane-Sepulveda, J. B.: Algebrability of the set of everywhere surjective functions on C, preprint,2005 Rana, I. K.: An introduction to measure and integration,GSM 45, 2nd edition, American Mathematical Society, 2002 Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I and II, Classics in Mathematics, Springer-Verlag,Berlin,Heidelberg, New York, 1996 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
Download
Original bundle
1 - 1 of 1