Hausdorff dimension and doubling measures on metric spaces

Jang Mei Wu

Research output: Contribution to journalArticlepeer-review


Vol′berg and Konyagin have proved that a compact metric space carries a nontrivial doubling measure if and only if it has finite uniform metric dimension. Their construction of doubling measures requires infinitely many adjustments. We give a simpler and more direct construction, and also prove that for any α > 0, the doubling measure may be chosen to have full measure on a set of Hausdorff dimension at most α.

Original languageEnglish (US)
Pages (from-to)1453-1459
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - 1998


  • Doubling measure
  • Hausdorff dimension
  • Metric space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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