On the Hausdorff dimension faithfulness of Oppenheim expansion
Volume 180 / 2017
Acta Arithmetica 180 (2017), 89-99 MSC: Primary 11K55; Secondary 28A80. DOI: 10.4064/aa8648-2-2017 Published online: 25 July 2017
We show that the family of cylinders generated by Oppenheim expansion is not faithful for Hausdorff dimension calculation on the unit interval. On the other hand, we prove that the family of all finite unions of consecutive cylinders of the same rank is faithful. Some special cases such as Lüroth expansion, Engel expansion and Sylvester expansion are included.