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arXiv · 1602.05662

On the Hausdorff dimension faithfulness connected with $Q_{infty}$-expansion

Jia Liu·Zhenliang Zhang
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Abstract

In this paper, we show that, the family of all possible union of finite consecutive cylinders of the same rank of $Q_{\infty}$-expansion is faithful for the Hausdorff dimension calculation. Applying this result, we give the necessary and sufficient condition for the family of all cylinders of $Q_{\infty}$-expansion to be faithful for Hausdorff dimension calculation on the unit interval, this answers the open problem mentioned in a paper of S. Albeverio et al..

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Jia Liu, Zhenliang Zhang. 2016-02-21. On the Hausdorff dimension faithfulness connected with $Q_{infty}$-expansion. https://doi.org/10.1088/1361-6544%2Faa67a2

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