<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>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:liu-16759 |
| Date | January 2009 |
| Creators | Karlsson, John |
| Publisher | Linköping University, Linköping University, Linköping University, Department of Mathematics |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, text |
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