Continuous maps that preserve Hausdorff measure

Da Wen Deng, Yulan Huang, Sze Man Ngai

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R2.

Original languageEnglish
Article number126485
JournalJournal of Mathematical Analysis and Applications
Volume516
Issue number1
DOIs
StatePublished - Dec 1 2022

Keywords

  • Cantor dust
  • Cantor set
  • Hausdorff measure
  • Homeomorphism
  • Self-similar set

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