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arXiv · 1201.5842

The Multiplicative golden mean shift has infinite Hausdorff measure

Yuval Peres·Boris Solomyak
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Abstract

In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (x_k) satisfies x_k x_{2k}=0 for all k=1,2... Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained.

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Yuval Peres, Boris Solomyak. 2012-04-18. The Multiplicative golden mean shift has infinite Hausdorff measure. https://arxiv.org/abs/1201.5842

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