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Lebesgue points, Hölder continuity and Sobolev functions
Linköping University, Department of Mathematics.
2009 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points.

Place, publisher, year, edition, pages
2009. , 45 p.
Keyword [en]
Lebesgue point, Hausdorff dimension, Hausdorff measure, Hölder continuity, Maximal function, Poincaré inequality, Sobolev space, Uniform continuity
National Category
URN: urn:nbn:se:liu:diva-16759ISRN: LiTH-MAT-EX--08/15--SEOAI: diva2:218045
Subject / course
Applied Mathematics
Physics, Chemistry, Mathematics
Available from: 2009-05-19 Created: 2009-02-13 Last updated: 2011-10-18Bibliographically approved

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Karlsson, John
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Department of Mathematics

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