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Lebesgue points, Hölder continuity and Sobolev functions

<p>This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L<sup>1</sup> 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.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:liu-16759
Date January 2009
CreatorsKarlsson, John
PublisherLinköping University, Linköping University, Linköping University, Department of Mathematics
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, text

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