A Gauss–Kuz’min–Lévy theorem for Rényi-type continued fractions
Volume 193 / 2020
Acta Arithmetica 193 (2020), 283-292 MSC: Primary 11J70; Secondary 60A10. DOI: 10.4064/aa181009-18-2 Published online: 27 January 2020
We consider an interval map which is a generalization of the Rényi transformation. For the continued fraction expansion arising from this transformation, we prove a result concerning the asymptotic behavior of the distribution functions of this map. More exactly, we use Szüsz’s method to prove a Gauss–Kuz’min–Lévy-type theorem.