2020年4月7日
Functions of Bounded Variation on Complete and Connected One-Dimensional Metric Spaces
International Mathematics Research Notices
- ,
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/imrn/rnaa064
- 出版者・発行元
- Oxford University Press (OUP)
<title>Abstract</title>
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to this general setting. We show this definition of BV functions is equivalent to the BV functions introduced by Miranda [18]. Furthermore, we study the necessity of conditions on the underlying space in Federer’s characterization of sets of finite perimeter on metric measure spaces. In particular, our examples show that the doubling and Poincaré inequality conditions are essential in showing that a set has finite perimeter if the codimension one Hausdorff measure of the measure-theoretic boundary is finite.
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to this general setting. We show this definition of BV functions is equivalent to the BV functions introduced by Miranda [18]. Furthermore, we study the necessity of conditions on the underlying space in Federer’s characterization of sets of finite perimeter on metric measure spaces. In particular, our examples show that the doubling and Poincaré inequality conditions are essential in showing that a set has finite perimeter if the codimension one Hausdorff measure of the measure-theoretic boundary is finite.
- リンク情報
- ID情報
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- DOI : 10.1093/imrn/rnaa064
- ISSN : 1073-7928
- eISSN : 1687-0247