dc.contributor.author Karak, Nijjwal dc.date.accessioned 2017-05-09T07:53:42Z dc.date.available 2017-05-09T07:53:42Z dc.date.issued 2017 dc.identifier.citation Karak, N. (2017). Generalized Lebesgue points for Sobolev functions. Czechoslovak Mathematical Journal, 67(1), 143-150. https://doi.org/10.21136/CMJ.2017.0405-15 dc.identifier.other CONVID_26892570 dc.identifier.other TUTKAID_73173 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/53839 dc.description.abstract In 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.iso eng dc.publisher Academy of Sciences of the Czech Republic; Springer dc.relation.ispartofseries Czechoslovak Mathematical Journal dc.subject.other Sobolev space dc.subject.other metric measure space dc.subject.other median dc.subject.other generalized Lebesgue point dc.title Generalized Lebesgue points for Sobolev functions dc.type article dc.identifier.urn URN:NBN:fi:jyu-201705052212 dc.contributor.laitos Matematiikan ja tilastotieteen laitos fi dc.contributor.laitos Department of Mathematics and Statistics en dc.contributor.oppiaine Matematiikka fi dc.contributor.oppiaine Mathematics en dc.type.uri http://purl.org/eprint/type/JournalArticle dc.date.updated 2017-05-05T12:15:13Z dc.type.coar journal article dc.description.reviewstatus peerReviewed dc.format.pagerange 143-150 dc.relation.issn 0011-4642 dc.relation.numberinseries 1 dc.relation.volume 67 dc.type.version publishedVersion 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.accesslevel openAccess fi dc.relation.doi 10.21136/CMJ.2017.0405-15
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