Measurability of the banach indicatrix

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Abstract

We establish the measurability of the Banach indicatrix for a measurable mapping in a geometrically doubling metric space. This is a generalization of a known result for continuous transformations in Euclidean space. A system of dyadic cubes in metric space is employed to construct a sequence of measurable functions converging to the indicatrix, and we partly follow Banach’s original proof.

Original languageEnglish
Pages (from-to)97-101
Number of pages5
JournalColloquium Mathematicum
Volume153
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Banach indicatrix
  • Doubling metric space

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