Functions of Bounded Variation on Complete and Connected One-Dimensional Metric Spaces
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Publication:5021173
DOI10.1093/IMRN/RNAA064zbMATH Open1491.46027arXiv1909.11530OpenAlexW3016000384MaRDI QIDQ5021173
Author name not available (Why is that?)
Publication date: 12 January 2022
Published in: (Search for Journal in Brave)
Abstract: 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. 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 Poincar'e 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.
Full work available at URL: https://arxiv.org/abs/1909.11530
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