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arXiv · 2504.18192

Recent progress on pointwise normality of self-similar measures

Amir Algom
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Abstract

This article is an exposition of recent results and methods on the prevalence of normal numbers in the support of self-similar measures on the line. We also provide an essentially self-contained proof of a recent Theorem that the Rajchman property (decay of the Fourier transform) implies that typical elements in the support of the measure are normal to all bases; as no decay rate is required, this improves the classical criterion of Davenport, Erdos, and LeVeque (1964). Open problems regarding effective equidistribution, non-integer bases, and higher order correlations, are discussed.

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Amir Algom. 2025-04-25. Recent progress on pointwise normality of self-similar measures. https://arxiv.org/abs/2504.18192

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