Probability measures associated with the continued fractions with odd partial quotients

Abstract

Assume that I denotes the unit interval [0, 1] and B_I is the σ-algebra of all Borel subsets of I. Then any number x ∈ I can be written in a unique way as a continued fraction with odd partial quotients. In this paper we determine a class of probability measures on the measurable space (I,B_I ) under which the rests of the continued fractions with odd partial quotients are identically distributed random variables.

Quaestiones Mathematicae 23(2000), 335–342