On the measure of arithmetic sums of Cantor sets
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 \[ {\log 2\over\log(1/\gamma)}+ \frac{\log 2}{\log(1/\lambda)}>1. \]
scientific article; zbMATH DE number 1029292