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arXiv · 1509.02326

Quasiopen and p-path open sets, and characterizations of quasicontinuity

Anders Björn·Jana Björn·Jan Malý
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Abstract

In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.

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Anders Björn, Jana Björn, Jan Malý. 2015-09-08. Quasiopen and p-path open sets, and characterizations of quasicontinuity. https://doi.org/10.1007/s11118-016-9580-z

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