On normal numbers and self-similar measures

Abstract

In this paper we prove that if $\{\ddot{I}{†}_i(x)=\hat{I}»x+t_i\}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $\frac{\log b}{\log |\hat{I}»|}\notin \mathbb{Q},$ then almost every $x$ is normal in base $b$ for any non-atomic self-similar measure of $\{\ddot{I}{†}_i\}$.

This article has been superseded by arXiv:2111.10082