On normal numbers and self-similar measures

Simon Baker

Published 2021-07-06Version 1

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