The rate of growth of the denominators in the Oppenheim series

Author:
János Galambos

Journal:
Proc. Amer. Math. Soc. **59** (1976), 9-13

MSC:
Primary 10K10

MathSciNet review:
0568142

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Abstract: A Borel-Cantelli lemma is proved for a sequence of functions of the denominators in the Oppenheim expansion of real numbers. This is then applied to the study of the rate of growth of the denominators in the above series. The laws obtained are almost sure type, that is, valid for (Lebesgue) almost all in the unit interval. The results are new even for the classical expansions of Engel, Sylvester and Cantor (product).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0568142-4

Keywords:
Oppenheim series,
denominators,
Borel-Cantelli lemma,
asymptotic laws,
,
,
Engel series,
Sylvester series,
Cantor product

Article copyright:
© Copyright 1976
American Mathematical Society