Algorithms with mediant convergents and their metrical theory
The paper is devoted to the study of two transformations on the unit interval which generate sets of mediant convergents. The first transformation has been considered as an example of an ergodic transformation with \(\sigma\)-finite measure at various instances. The second transformation is a remarkable application of the jump transformation construction [\textit{F. Schweiger}, Isr. J. Math. 21, 308- 318 (1975; Zbl 0314.10037)]. This leads to a new proof of a theorem of \textit{P. Erdős} [Acta Arith. 5, 359-369 (1959; Zbl 0097.035)] on diophantine approximation.
scientific article; zbMATH DE number 4150297