Sur les nombres normaux liés à des bases nonéquivalentes

Abstract

For every Pisot number $\theta$, and every real number $\beta$ greater than one not equivalent to $\theta$, if $\mu$ is a Bernoulli measure relative to the $\theta$-transformation, then for $\mu$-almost all $x$ the sequence $(x\beta^n)_{n\geq 0}$ is uniformly distributed modulo one.