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