A generalization of a result of R. Lyons about measures on \([0,1)\)
type: Item
instance of: scholarly article
title: A generalization of a result of R. Lyons about measures on \([0,1)\)
zbMATH Open document ID: 0783.28009
DOI: 10.1007/BF02764832
published in: Israel Journal of Mathematics
publication date: 1993-09-07T00:00:00Z
review text: The following is proved: Let \(\mu\) be an invariant measure on \([0,1]\) for \(S(x)= px\text{ mod }1\), where \(p\geq 1\) is an integer. Suppose that there is no invariant component of zero entropy. Denote \(T_ v(x)= vx\) for \(v\geq 1\). Then, for \(\varepsilon>0\), there exist \(b\), \(v\), and \(m\) with \(p^ m b\leq v\leq p^ m(b+1)\) such that the measure \(\mu\circ T^{- 1}_ v\) is \(\varepsilon\)-close to Lebesgue measure (in a metric for the weak topology). The theorem contains results by Furstenberg, Lyons, Rudolph and Johnson.
reviewed by: Manfred Denker
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28D20
zbMATH DE Number: 410017
zbMATH Keywords: invariant measure
zbMATH Keywords: entropy
author: Jacob Feldman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 410017