Open AccessA strong Lebesgue point property for Sobolev functions
Author(s) -
Visa Latvala
Publication year - 2004
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-04-07358-7
Subject(s) - lebesgue integration , sobolev space , property (philosophy) , mathematics , lebesgue–stieltjes integration , pure mathematics , lebesgue's number lemma , point (geometry) , set (abstract data type) , standard probability space , mathematical analysis , riemann integral , computer science , geometry , philosophy , epistemology , operator theory , programming language , fourier integral operator
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.