A Notion of Fine Continuity for BV Functions on Metric Spaces

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• 作者：Panu Lahti
• 关键词：Bounded variation ; Metric measure space ; Quasicontinuity ; Fine topology ; Fine continuity ; Upper hemicontinuity
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：46
• 期：2
• 页码：279-294
• 全文大小：
• 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 the setting of a metric space equipped with a doubling measure supporting a Poincaré inequality, we show that BV functions are, in the sense of multiple limits, continuous with respect to a 1-fine topology, at almost every point with respect to the codimension 1 Hausdorff measure.