On the measure of arithmetic sums of Cantor sets
type: Item
instance of: scholarly article
title: On the measure of arithmetic sums of Cantor sets
zbMATH Open document ID: 0876.28015
DOI: 10.1016/S0019-3577(97)83357-5
published in: Indagationes Mathematicae. New Series
publication date: 1997-11-23T00:00:00Z
review text: If the middle \(\alpha\)-Cantor set is written as \[ K_\lambda= \Biggl\{x=(1-\lambda) \sum^\infty_{i=0} a_i\lambda^i: a_i\in \{0,1\}\Biggr\} \] for \(0<\lambda<{1\over 2}\) such that \(\alpha= 1-2\lambda\) then for any \(\gamma\in]0,{1\over 2}[\) there exists a subset \(E_\gamma\subset]0,{1\over 2}[\) of zero Lebesgue measure such that for the Cantor sets \(K_\gamma\) and \(K_\lambda\) with \(\lambda\not\in E_\gamma\) the sum \(K_\gamma+ K_\lambda\) has positive Lebesgue measure provided that for their sums of Hausdorff dimensions \[ {\log 2\over\log(1/\gamma)}+ \frac{\log 2}{\log(1/\lambda)}>1. \]
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 1029292
zbMATH Keywords: arithmetic sums of Cantor sets
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: Hausdorff dimensions
author: B. Solomyak
reviewed by: Hermann Haase
MaRDI profile type: Publication
cites work: Bernoulli schemes of the same entropy are finitarily isomorphic
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description: scientific article; zbMATH DE number 1029292