Abstract
We study two classes of sets of real numbers related to Luroth expansions and obtain their Hausdorff dimensions. One is determined by prescribed group frequencies of digits in their Luroth expansions. It is proved that the Hausdorff dimension of such a set is equal to the supremum of the Hausdorff dimensions for sets of real numbers with prescribed digit frequencies in their Luroth expansion. The other is determined by randomly selecting the digits in their Luroth expansion from a finite number of given digit sets.
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