Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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HAUSDORFF DIMENSION OF DERANGED CANTOR SET WITHOUT SOME BOUNDEDNESS CONDITION

  • Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
  • Published : 2004.01.01
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Abstract

A deranged Cantor set (without the uniform bounded-ness condition away from zero of contraction ratios) whose weak local dimensions for all points coincide has its Hausdorff dimension of the same value of weak local dimension. We will show it using an energy theory instead of Frostman's density lemma which was used for the case of the deranged Cantor set with the uniform boundedness condition of contraction ratios. In the end, we will give an example of such a deranged Cantor set.

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References

  1. Real Analysis Exchange v.19 no.1 Dimensions of the perturbed Cantor set I.S.Baek
  2. Real Analysis Exchange v.26 no.2 Weak local dimension on deranged Cantor sets I.S.Baek
  3. Acta Math. Hungar v.99 no.4 Hausdorff dimension of perturbed Cantor sets without some boundedness condition I.S.Baek https://doi.org/10.1023/A:1024631512342
  4. Fractal geometry K.J.Falconer