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October, 2002 Lebesgue points for Sobolev functions on metric spaces
Juha Kinnunen, Visa Latvala
Rev. Mat. Iberoamericana 18(3): 685-700 (October, 2002).


Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.


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Juha Kinnunen. Visa Latvala. "Lebesgue points for Sobolev functions on metric spaces." Rev. Mat. Iberoamericana 18 (3) 685 - 700, October, 2002.


Published: October, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1037.46031
MathSciNet: MR1954868

Primary: 46E35

Keywords: capacity , doubling measures , maximal functions , regularity , Sobolev Spaces , spaces of homogeneous type

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 3 • October, 2002
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