References
P. Billingsley,Ergodic theory and information, John Wiley and Sons (New York, 1965).
Sh. Ito, Some skew product transformations associated with continued fractions and their invariant measures, preprint.
Sh. Ito and H. Nakada, On natural extensions of transformations related to diophantine approximations,Tokyo J. Math.,9 (1986), 115–133.
S. Monteferrante and P. Szüsz, On a generalization of a theorem of Borel,Acta Arith.,16 (1969/70), 393–397.
W. Philipp, Some metrical theorems in number theory,Pacific J. Math.,20 (1967), 109–127.
F. Schweiger and W. Waterman, Some remarks on Kuzmin's theorem forF-expansions,J. Number Th.,5 (1973), 123–131.
V. T. Sós,On the discrepancy of the sequence {nα}, Coll. Math. Soc. J. Bolyai,13 (1976), 359–367.
M. Stewart, Irregularities of uniform distribution,Acta Math. Acad. Sci. Hung.,37 (1981), 185–221.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ito, S., Nakada, H. Approximations of real numbers by the sequence {nα} and their metrical theory. Acta Math Hung 52, 91–100 (1988). https://doi.org/10.1007/BF01952484
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01952484