Normality preserving operations for Cantor series expansions and associated fractals part I

Dylan Airey; Bill Mance

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arXiv · 1407.0777

Normality preserving operations for Cantor series expansions and associated fractals part I

Dylan Airey·Bill Mance

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Abstract

It is well known that rational multiplication preserves normality in base $b$. We study related normality preserving operations for the $Q$-Cantor series expansions. In particular, we show that while integer multiplication preserves $Q$-distribution normality, it fails to preserve $Q$-normality in a particularly strong manner. We also show that $Q$-distribution normality is not preserved by non-integer rational multiplication on a set of zero measure and full Hausdorff dimension.

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Dylan Airey, Bill Mance. 2014-07-08. Normality preserving operations for Cantor series expansions and associated fractals part I. https://arxiv.org/abs/1407.0777

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