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A strong Lebesgue point property for Sobolev functions

Author: Visa Latvala
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2331-2338
MSC (2000): Primary 46E35; Secondary 31C15
Published electronically: February 19, 2004
MathSciNet review: 2052410
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that first-order Sobolev functions fulfill a Wiener integral type Lebesgue point property outside a set of Sobolev capacity zero. Our condition is stronger than the standard Lebesgue point property, but the exceptional set is slightly larger.

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Additional Information

Visa Latvala
Affiliation: Department of Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland

Keywords: Sobolev functions, Lebesgue points, capacity
Received by editor(s): January 23, 2003
Received by editor(s) in revised form: April 29, 2003
Published electronically: February 19, 2004
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society

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