Digit frequencies and Bernoulli convolutions
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It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).
Kempton , T M W 2014 , ' Digit frequencies and Bernoulli convolutions ' Indagationes Mathematicae , vol 25 , no. 4 , pp. 832-842 . DOI: 10.1016/j.indag.2014.04.011
© 2014, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.indag.2014.04.011
This work was supported partly by the Dutch Organisation for Scientific Research (NWO) grant number 613.001.022 and partly by the Engineering and Physical Sciences Research Council grant number EP/K029061/1.