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arXiv · 1407.0778

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

Dylan Airey·Bill Mance·Joseph Vandehey
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Abstract

We investigate how non-zero rational multiplication and rational addition affect normality with respect to $Q$-Cantor series expansions. In particular, we show that there exists a $Q$ such that the set of real numbers which are $Q$-normal but not $Q$-distribution normal, and which still have this property when multiplied and added by rational numbers has full Hausdorff dimension. Moreover, we give such a number that is explicit in the sense that it is computable.

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Dylan Airey, Bill Mance, Joseph Vandehey. 2014-07-15. Normality preserving operations for Cantor series expansions and associated fractals part II. https://arxiv.org/abs/1407.0778

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