Computable Riesz Representation for Locally Compact Hausdorff Spaces

Простая страница элемента
dc.creatorLu,Hong
dc.creatorWeihrauch,Klaus
dc.date2008
dc.date.accessioned2024-02-06T12:56:21Z
dc.date.available2024-02-06T12:56:21Z
dc.descriptionBy the Riesz Representation Theorem for locally compact Hausdorff spaces, for every positive linear functional I on K(X) there is a measure μ such that I(f) =∫ f dμ where K(X) is the set of continuous real functions with compact support on the locally compact Hausdorff space X. In this article we prove a uniformly computable version of this theorem for computably locally compact computable Hausdorff spaces X. We introduce a representation of the positive linear functionals I on K(X) and a representation of the Borel measures on X and prove that for every such functional I a measure μ can be computed and vice versa such that I(f) = ∫ f dμ.
dc.formattext/html
dc.identifierhttps://doi.org/10.3217/jucs-014-06-0845
dc.identifierhttps://lib.jucs.org/article/29006/
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/9665
dc.languageen
dc.publisherJournal of Universal Computer Science
dc.relationinfo:eu-repo/semantics/altIdentifier/eissn/0948-6968
dc.relationinfo:eu-repo/semantics/altIdentifier/pissn/0948-695X
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsJ.UCS License
dc.sourceJUCS - Journal of Universal Computer Science 14(6): 845-860
dc.subjectcomputable analysis
dc.subjectcomputable topology
dc.subjectHausdorff spaces
dc.subjectRiesz representation theorem
dc.titleComputable Riesz Representation for Locally Compact Hausdorff Spaces
dc.typeResearch Article
Файлы
Коллекции