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Packing Measure and Dimension of Random Fractals

Author

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  • Artemi Berlinkov

    (University of North Texas)

  • R. Daniel Mauldin

    (University of North Texas)

Abstract

We consider random fractals generated by random recursive constructions. We prove that the box-counting and packing dimensions of these random fractals, K, equals α, their almost sure Hausdorff dimension. We show that some “almost deterministic” conditions known to ensure that the Hausdorff measure satisfies $$0

Suggested Citation

  • Artemi Berlinkov & R. Daniel Mauldin, 2002. "Packing Measure and Dimension of Random Fractals," Journal of Theoretical Probability, Springer, vol. 15(3), pages 695-713, July.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:3:d:10.1023_a:1016271916074
    DOI: 10.1023/A:1016271916074
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    References listed on IDEAS

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    1. Liu, Quansheng, 2000. "Exact packing measure on a Galton-Watson tree," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 19-28, January.
    2. Yueyun Hu, 1999. "Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion," Journal of Theoretical Probability, Springer, vol. 12(2), pages 313-346, April.
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