Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces

• Autores: A. Björn, Jana Björn, Nageswari Shanmugalingam
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 4, 2008, págs. 1197-1212
• Idioma: inglés
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• Resumen

  • We show that on complete doubling metric measure spaces X supporting a Poincaré inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every a>0 there is an open subset U of X with capacity less than a and such that the restriction of u to X\U is continuous. This implies that the capacity is an outer capacity