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Strong approximation of sets of finite perimeter in metric spaces

Abstract

In the setting of a metric space equipped with a doubling measure that supports a Poincaré inequality, we show that any set of finite perimeter can be approximated in the \(\mathrm {BV}\) norm by a set whose topological and measure theoretic boundaries almost coincide. The proof relies on a quasicontinuity-type result for \(\mathrm {BV}\) functions proved by Lahti and Shanmugalingam (J Math Pures Appl 107(2): 150–182, 2017).

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Correspondence to Panu Lahti.

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Lahti, P. Strong approximation of sets of finite perimeter in metric spaces. manuscripta math. 155, 503–522 (2018). https://doi.org/10.1007/s00229-017-0948-1

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Mathematics Subject Classification

  • 30L99
  • 26B30
  • 28A12