Quasiopen and p-Path Open Sets, and Characterizations of Quasicontinuity

详细信息    查看全文

• 作者：Anders Björn ; Jana Björn ; Jan Malý
• 关键词：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
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：46
• 期：1
• 页码：181-199
• 全文大小：315KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

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.