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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Björn, A., Björn, J. & Malý, J. Quasiopen and p-Path Open Sets, and Characterizations of Quasicontinuity. Potential Anal 46, 181–199 (2017). https://doi.org/10.1007/s11118-016-9580-z
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DOI: https://doi.org/10.1007/s11118-016-9580-z
Keywords
- Analytic set
- Characterization
- Doubling measure
- Fine potential theory
- Metric space
- Newtonian space
- Nonlinear potential theory
- Poincaré inequality
- p-path open
- Quasicontinuous
- Quasiopen
- Sobolev space
- Suslin set