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The equivalence of multifractal measures on cookie-cutter-like sets

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  • Dai, Meifeng
  • Jiang, Ying

Abstract

In this paper, we concentrate on the properties of the multifractal centered Hausdorff measure and the multifractal packing measure on a class of cookie-cutter-like (CCL) sets. We conclude that these two multifractal measures are equivalent on the CCL sets satisfying the strong separation condition. Then we obtain some relevant conclusions about the image measure of a σ-invariant ergodic Borel probability measure.

Suggested Citation

  • Dai, Meifeng & Jiang, Ying, 2009. "The equivalence of multifractal measures on cookie-cutter-like sets," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1408-1415.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1408-1415
    DOI: 10.1016/j.chaos.2008.05.023
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. Attia, Najmeddine & Selmi, Bilel, 2023. "On the multifractal measures and dimensions of image measures on a class of Moran sets," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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