The doubling property of conformal measures of infinite iterated function systems
type: Item
instance of: scholarly article
title: The doubling property of conformal measures of infinite iterated function systems
zbMATH Open document ID: 1024.37005
DOI: 10.1016/S0022-314X(03)00065-9
author: R. Daniel Mauldin
author: Mariusz Urbański
published in: Journal of Number Theory
publication date: 2003-08-20T00:00:00Z
review text: A Borel probability measure \(m\) on a compact metric space \((Y,\rho)\) satisfies the doubling property provided there exists a constant \(C>0\) and \(\tau>1\) such that \(m(B(x,\tau r))\leq Cm(B(x,r))\) for \(m\)-almost all \(x\in Y\) and all \(r\leq 1\). (This property holds for some \(\tau>1\) if and only if it holds for \(\tau=2\), and this is known as doubling property). Measures with the doubling property naturally arise in the studies of conformal mappings or finite conformal iterated function systems. The authors investigate conformal measures induced by an infinite conformal iterated function system. They find some easily verifiable conditions under which the conformal measure satisfies (or does not satisfy) the doubling property. A particular attention is given to systems generated by continued fractions with restricted entries.
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37F35
zbMATH DE Number: 1967960
zbMATH Keywords: conformal measure
zbMATH Keywords: doubling property
zbMATH Keywords: continued fractions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1967960