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Fractal dimension and measure of the subset of Moran set

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  • Dai, Meifeng
  • Jiang, Ying

Abstract

We discuss the fractal dimension and measure for the subset BP(ω) of Moran set E(ω) in Rd satisfying the strong separation condition. Firstly, we give the Hausdorff dimension of subset BP(ω) in compatible case and incompatible case. Then we attain that there exists a subset B of the set BP(ω) such that B has full μP-measure but zero Hausdorff measure in incompatible case. Finally, if the gap condition holds, we see that BP(ω) and E(ω) have the same Hausdorff measure and packing measure, and both of them are α-sets in compatible case.

Suggested Citation

  • Dai, Meifeng & Jiang, Ying, 2009. "Fractal dimension and measure of the subset of Moran set," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 190-196.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:190-196
    DOI: 10.1016/j.chaos.2007.07.042
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    References listed on IDEAS

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    1. Fang-Xiong Zhen, 2006. "Dimensions of subsets of cantor-type sets," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-8, October.
    2. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    3. Dai, Meifeng & Liu, Dehua, 2008. "The local dimension of Moran measures satisfying the strong separation condition," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1025-1030.
    4. Dai, Meifeng, 2006. "The equivalence of measures on Moran set in general metric space," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 55-64.
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