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Sets of β -expansions and the Hausdorff measure of slices through fractals

Tom Kempton — 2016

Journal of the European Mathematical Society

We study natural measures on sets of β -expansions and on slices through self similar sets. In the setting of β -expansions, these allow us to better understand the measure of maximal entropy for the random β -transformation and to reinterpret a result of Lindenstrauss, Peres and Schlag in terms of equidistribution. Each of these applications is relevant to the study of Bernoulli convolutions. In the fractal setting this allows us to understand how to disintegrate Hausdorff measure by slicing, leading...

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