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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41420

    Title: Appendix to the paper by T. Luczak--a simple proof of the lower bound : On the fractional dimension of sets of continued fractions
    Authors: Feng, Jun-de;Wu, Jun.;Liang, Jhy-ching;Tseng, Shio-jenn
    Contributors: 淡江大學數學學系
    Keywords: 11J70: NUMBER THEORY;Diophantine approximation;Continued fractions
    Date: 1997-06
    Issue Date: 2010-01-28 07:31:49 (UTC+8)
    Publisher: London Mathematical Society
    Abstract: 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
    Relation: Mathematika 44(1), pp.54-55
    DOI: 10.1112/S0025579300011967
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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