Metrical results on normality to distinct bases
The normality of a real number is equivalent to a uniform distribution property which allows the notion of normality to be extended from integer bases to non-integer bases. The authors consider normality to distinct non-integer bases using Riesz products and show that, in contrast to the case of integer bases, for almost all real numbers \(\theta >3\), normality to the base \(\theta^k\) does not imply normality to base \(\theta^l\) unless \(l=k\).
scientific article; zbMATH DE number 809116