The rate of growth of the denominators in the Oppenheim series
Author:
János Galambos
Journal:
Proc. Amer. Math. Soc. 59 (1976), 913
MSC:
Primary 10K10
MathSciNet review:
0568142
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Abstract: A BorelCantelli 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:
http://dx.doi.org/10.1090/S00029939197605681424
PII:
S 00029939(1976)05681424
Keywords:
Oppenheim series,
denominators,
BorelCantelli lemma,
asymptotic laws,
,
,
Engel series,
Sylvester series,
Cantor product
Article copyright:
© Copyright 1976
American Mathematical Society
