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Relationships between Different Dimensions of a Measure

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Abstract.

 We establish various relationships of the Hausdorff dimension, entropy dimension and -dimension of a measure without assuming that the local dimension of μ exists μ-a.e. These extend a well known result of Young.

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Authors and Affiliations

  1.  WIPM, The Chinese Academy of Sciences, Wuhan, China, , , , , , CN

    Ai-Hua Fan

  2.  The Chinese University of Hong Kong, Shatin, Hong Kong, , , , , , CN

    Ka-Sing Lau

  3.  Wuhan University, Wuhan, China, , , , , , CN

    Hui Rao

Authors
  1. Ai-Hua Fan
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  2. Ka-Sing Lau
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  3. Hui Rao
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Additional information

Received 2 October 2000; in revised form 20 September 2001

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Fan, AH., Lau, KS. & Rao, H. Relationships between Different Dimensions of a Measure. Mh Math 135, 191–201 (2002). https://doi.org/10.1007/s006050200016

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  • DOI: https://doi.org/10.1007/s006050200016

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