Sur les nombres normaux liés à des bases nonéquivalentes

Abstract

For every Pisot number $\theta$, and everyreal 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.