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Appendix to the paper by T. Łuczak—A simple proof of the lower

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  26 February 2010

Fend De-Jun ,
Wu Jun ,
Jyh-Ching Liang  and
Shiojenn Tseng
Fend De-Jun
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China.
Wu Jun
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China.
Jyh-Ching Liang
Affiliation:
Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
Shiojenn Tseng
Affiliation:
Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
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Extract

In this note we point out that a simple proof of the lower bound of the sets (b, c), and so also of Ξ(b, c), defined in the previous paper [1] can be obtained as a simple application of a general method. By Example 4.6 from [2], if [0, 1] = E0⊃E1⊃ … are sets each of which is a finite union of disjoint closed intervals such that each interval of Ek−1, contains at least mk intervals of Ek which are separated by gaps of lengths at least εk, and if mk≥2 and εk≥εk+1>0, then the dimension of the intersection of Ek is at least

MSC classification

Secondary: 11J70: Continued fractions and generalizations
Type
Research Article
Information
Mathematika , Volume 44 , Issue 1 , June 1997 , pp. 54 - 55
Copyright
Copyright © University College London 1997

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References

1.Luczak, T.. On the fractional dimension of sets of continued fractions. Mathematika, 44 (1997), 50–53.CrossRefGoogle Scholar
2.Falconer, K.. Fractal Geometry (Wiley, 1990)Google Scholar