Lebesgue points, Hölder continuity and Sobolev functions
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.
Source Type:Master's Thesis
Keywords:lebesgue point hausdorff dimension measure hölder continuity maximal function poincaré inequality sobolev space uniform
Date of Publication:01/01/2009