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arXiv · 2107.02699

On normal numbers and self-similar measures

Simon Baker
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Abstract

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 $\{\varphi_i\}$.

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Simon Baker. 2021-07-06. On normal numbers and self-similar measures. https://arxiv.org/abs/2107.02699

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