Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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DIMENSIONS OF DISTRIBUTION SETS IN THE UNIT INTERVAL

  • Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
  • Published : 2007.10.31
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Abstract

The unit interval is not homeomorphic to a self-similar Cantor set in which we studied the dimensions of distribution subsets. However we show that similar results regarding dimensions of the distribution subsets also hold for the unit interval since the distribution subsets have similar structures with those in a self-similar Cantor set.

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References

  1. I. S. Baek, Relation between spectral classes of a self-similar Cantor set, J. Math. Anal. Appl, 292 (2004), no. 1, 294-302 https://doi.org/10.1016/j.jmaa.2003.12.001
  2. I. S. Baek, Another complete decomposition of a self-similar Cantor set, preprint
  3. I. S. Baek, L. Olsen, and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007), no. 1, 267-287 https://doi.org/10.1016/j.aim.2007.02.003
  4. C. D. Cutler, A note on equivalent interval covering systems for Hausdorff dimension on R, Internat. J. Math. & Math. Sci. 11 (1988), 643-650 https://doi.org/10.1155/S016117128800078X
  5. G. Edgar, Integral, Probability and Fractal measures, Springer Verlag, 1998
  6. K. J. Falconer, Techniques in fractal geometry, John Wiley and Sons, 1997
  7. H. H. Lee and I. S. Baek, A note on equivalent interval covering systems for packing dimension of R, J. Korean Math. Soc. 28 (1991), 195-205
  8. L. Olsen, Extremely non-normal numbers, Math. Proc. Camb. Phil. Soc. 137 (2004), 43-53 https://doi.org/10.1017/S0305004104007601

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