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A survey of the metric theory of continued fractions, fifty years after Doeblin’s 1940 paper. (English) Zbl 0734.11041

Probability theory and mathematical statistics, Proc. 5th Vilnius Conf., Vilnius/Lith. 1989, Vol. I, 550-572 (1990).
[For the entire collection see Zbl 0725.00013.]
The author analyzes the development of the metric theory of continued fractions in the light of Doeblin’s fundamental paper on the subject written 50 years ago [cf. W. Doeblin, Compos. Math. 7, 353–371 (1940; Zbl 0022.37001)]. Both asymptotic distributions and almost sure (Lebesgue) results are discussed. The paper is a clear presentation and has a good list of references.

MSC:

11K50 Metric theory of continued fractions
11-02 Research exposition (monographs, survey articles) pertaining to number theory