Abstract
We study pointwise properties of functions of bounded variation on a metric space equipped with a doubling measure and a Poincaré inequality. In particular, we obtain a Lebesgue type result for \(BV\) functions. We also study approximations by Lipschitz continuous functions and a version of the Leibniz rule. We give examples which show that our main result is optimal for \(BV\) functions in this generality.
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Part of this research was conducted during the visit of the third author to Aalto University; she wishes to thank that institution for its kind hospitality. The research is supported by the Academy of Finland.
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Kinnunen, J., Korte, R., Shanmugalingam, N. et al. Pointwise properties of functions of bounded variation in metric spaces. Rev Mat Complut 27, 41–67 (2014). https://doi.org/10.1007/s13163-013-0130-6
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DOI: https://doi.org/10.1007/s13163-013-0130-6
Keywords
- Lebesgue points
- Bounded variation
- Leibniz rule
- Metric measure spaces
- Codimension Hausdorff measure
- Finite perimeter
- Poincare inequality
- Approximate continuity
- Jump sets