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Dimensions of distribution sets in the unit interval

백인수
대한수학회 (The Korean Mathematical Society)|2007.10|대한수학회논문집 (Communications of the KMS)|제22권 제4호|pp. 547-552

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참고문헌

키워드

Hausdorff dimensionpacking dimensiondistribution setbounded Vitali covering.
주제분류수학

초록

Abstract

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

참고문헌 (8)

  1. "Relation between spectral classes of a self-similar Cantor set", 292(1), pp.294~302 (2004)
  2. "Another complete decomposition of a self-similar Cantor set"
  3. "Divergence points of self-similar measures andpacking dimension", 214(1), pp.267~287 (2007)
  4. "A note on equivalent interval covering systems for Hausdor dimensionon R" (1988)
  5. "Integral, Probability and Fractal measures" (1998), Springer Verlag
  6. "Techniques in fractal geometry" (1997), John Wiley and Sons
  7. "A note on equivalent interval covering systems for packingdimension of R" (1991)
  8. "Extremely non-normal numbers, Math", 137, pp.43~53 (2004)

관련 논문AI추천

Dimension for a Cantor-like set with overlapsHung Hwan Lee, Jungju Park, Mi Ryeong Lee대한수학회 · 대한수학회논문집2004 · 제19권 제4호Multifractal spectrum in a self-similar attractor in the unit interval백인수대한수학회 · 대한수학회논문집2008 · 제23권 제4호Correlation dimensions of Cantor-like setsHung Hwan Lee, Mi Ryeong Lee대한수학회 · 대한수학회논문집2003 · 제18권 제2호Dimension of deformed self-similar setsHyun Deok Lee, Jungju Park, Taehee Kim대한수학회 · 대한수학회논문집2004 · 제19권 제3호On a Construction of Plane Sets with Pre-assigned Metric DimensionsBO-HYUN CHUNG, BYUNGBAE KIM, SOON-MO JUNG경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호Multifractal Analysis of Perturbed Cantor SetsHung Hwan Lee, Hun Ki Baek경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제4호

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