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Lebesgue points, Hölder continuity and Sobolev functions

by Karlsson, John

Abstract (Summary)

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.

Bibliographical Information:

Advisor:

School:Linköpings universitet

School Location:Sweden

Source Type:Master's Thesis

Keywords:lebesgue point hausdorff dimension measure hölder continuity maximal function poincaré inequality sobolev space uniform

ISBN:

Date of Publication:01/01/2009

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