The multiplicative golden mean shift has infinite Hausdorff measure

Yuval Peres, Boris Solomyak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xκ) satisfies xκx = 0 for all κ ≥ 1. Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained.

Original languageEnglish
Title of host publicationFurther Developments in Fractals and Related Fields
EditorsJulien Barral, Stéphane Seuret
Pages193-212
Number of pages20
DOIs
StatePublished - 2013
Externally publishedYes
EventInternational Conference on Fractals and Related Fields, 2011 - Porquerolles Island, France
Duration: 1 Jun 2011 → …

Publication series

NameTrends in Mathematics
Volume55

Conference

ConferenceInternational Conference on Fractals and Related Fields, 2011
Country/TerritoryFrance
CityPorquerolles Island
Period1/06/11 → …

All Science Journal Classification (ASJC) codes

  • General Mathematics

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