Doubling properties of self-similar measures

Po Lam Yung*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

Let {Fi}in be a system of similitudes in ℝn. We study necessary and sufficient conditions for their associated selfsimilar measures to be doubling on its support. An equivalent condition is obtained when {Fi} satisfies the open set condition. The condition allows us to construct many examples of interest. In the case where the open set condition is not satisfied, we study an infinitely convoluted Bernoulli measure (associated with the golden ratio ρ = ( √5 -1 ) / 2) and give a necessary and sufficient condition for it to be doubling on its support [0,1], Indiana University Mathematics Journal

Original languageEnglish
Pages (from-to)965-990
Number of pages26
JournalIndiana University Mathematics Journal
Volume56
Issue number2
DOIs
Publication statusPublished - 2007
Externally publishedYes

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