This paper is concerned with the growth rate of the maximal digits relative to the rate of approximation of the number by its convergents, as well as relative to the rate of the sum of digits for the Lüroth expansion of an irrational number. The Hausdorff dimension of the sets of points with a given relative growth rate is proved to be full.

中文翻译：

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关于 LÜROTH 扩展中最大位数的相对增长率的说明

本文关注的是最大位数的增长率相对于其收敛数的逼近率，以及相对于无理数的 Lüroth 展开的位数之和的速度。具有给定相对增长率的点集的 Hausdorff 维数被证明是满的。