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 . https://doi.org/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