Lebesgue points for Sobolev functions on metric spaces

• Autores: Juha Kinnunen, Visa Latvala
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 18, Nº 3, 2002, págs. 685-700
• Idioma: inglés
• Títulos paralelos:
  • Puntos de Lebesgue para funciones Sobolev en espacios métricos
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• Resumen

  • 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.