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dc.contributor.authorKarak, Nijjwal
dc.date.accessioned2017-05-09T07:53:42Z
dc.date.available2017-05-09T07:53:42Z
dc.date.issued2017
dc.identifier.citationKarak, N. (2017). Generalized Lebesgue points for Sobolev functions. <i>Czechoslovak Mathematical Journal</i>, <i>67</i>(1), 143-150. <a href="https://doi.org/10.21136/CMJ.2017.0405-15" target="_blank">https://doi.org/10.21136/CMJ.2017.0405-15</a>
dc.identifier.otherCONVID_26892570
dc.identifier.otherTUTKAID_73173
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/53839
dc.description.abstractIn many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space (X, d, μ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B(x, r) converge to f(x) when r converges to 0. We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function. We show that a function f ∈ Ms,p(X), 0 < s ≤ 1, 0 < p < 1, where X is a doubling metric measure space, has generalized Lebesgue points outside a set of Hh-Hausdorff measure zero for a suitable gauge function h.
dc.language.isoeng
dc.publisherAcademy of Sciences of the Czech Republic; Springer
dc.relation.ispartofseriesCzechoslovak Mathematical Journal
dc.subject.otherSobolev space
dc.subject.othermetric measure space
dc.subject.othermedian
dc.subject.othergeneralized Lebesgue point
dc.titleGeneralized Lebesgue points for Sobolev functions
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201705052212
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2017-05-05T12:15:13Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange143-150
dc.relation.issn0011-4642
dc.relation.numberinseries1
dc.relation.volume67
dc.type.versionpublishedVersion
dc.rights.copyright© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.21136/CMJ.2017.0405-15


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