On the upper regularity dimensions of measures

Jonathan MacDonald Fraser, Douglas Charles Howroyd

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We study the upper regularity dimension which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of doubling. We conduct a thorough study of the upper regularity dimension, including its relationship with other concepts such as the Assouad dimension, the upper local dimension, the Lq-spectrum and weak tangent measures. We also compute the upper regularity dimension explicitly in a number of important contexts including self-similar measures, self-affine measures, and measures on sequences.
Original languageEnglish
Pages (from-to)685–712
Number of pages22
JournalIndiana University Mathematics Journal
Volume69
Issue number2
DOIs
Publication statusPublished - 1 Feb 2020

Keywords

  • Upper regularity dimension
  • Assouad dimension
  • Local dimension
  • Self-similar measure
  • Self-affine measure
  • Doubling measure
  • Weak tangent
  • Lq-spectrum

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