Quasiopen and p-path open sets, and characterizations of quasicontinuity
Björn, Anders · Björn, Jana · Malý, Jan
Functional Analysis
Analysis of PDEs
Primary: 31E05, Secondary: 28A05, 30L99, 31C15, 31C40, 31C45, 46E35
Original · EN
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.
English translation
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