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On singularity of energy measures on self-similar sets
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  • Published: 27 December 2004

On singularity of energy measures on self-similar sets

  • Masanori Hino1 

Probability Theory and Related Fields volume 132, pages 265–290 (2005)Cite this article

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Abstract.

We provide general criteria for energy measures of regular Dirichlet forms on self-similar sets to be singular to Bernoulli type measures. In particular, every energy measure is proved to be singular to the Hausdorff measure for canonical Dirichlet forms on 2-dimensional Sierpinski carpets.

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Authors and Affiliations

  1. Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masanori Hino

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  1. Masanori Hino
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Correspondence to Masanori Hino.

Additional information

Partially supported by Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Encouragement of Young Scientists, 15740089.

Mathematics Subject Classification (2000): 28A80 (60G30, 31C25, 60J60)

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Hino, M. On singularity of energy measures on self-similar sets. Probab. Theory Relat. Fields 132, 265–290 (2005). https://doi.org/10.1007/s00440-004-0396-1

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  • Received: 24 October 2003

  • Revised: 23 September 2004

  • Published: 27 December 2004

  • Issue Date: June 2005

  • DOI: https://doi.org/10.1007/s00440-004-0396-1

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Keywords

  • Self-similar sets
  • Fractals
  • Energy measures
  • Walk dimension
  • Sierpinski carpets
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