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

  • Fend De-Jun (a1), Wu Jun (a2), Jyh-Ching Liang (a3) and Shiojenn Tseng (a3)

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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] = E0E1⊃ … 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

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1.Luczak, T.. On the fractional dimension of sets of continued fractions. Mathematika, 44 (1997), 5053.
2.Falconer, K.. Fractal Geometry (Wiley, 1990)
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Appendix to the paper by T. Łuczak—A simple proof of the lower

  • Fend De-Jun (a1), Wu Jun (a2), Jyh-Ching Liang (a3) and Shiojenn Tseng (a3)

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