Properties of some overlapping self-similar and some self-affine measures

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We generalize theorems of Peres and Solomyak about the abso- lute continuity resp. singularity of Bernoulli convolutions ([19], [16], [17]) to a broader class of self-similar measures on the real line. Using the dimension the- ory of ergodic measures (see [11] and [2]) we find a formula for the dimension of certain self-affine measures in terms of the dimension of the above mentioned self- similar measures. Combining these results we show the identity of Hausdorff and box-counting dimension of a special class of self-affine sets.
Original languageEnglish
JournalActa Mathematica Hungarica
Issue number1-2
Pages (from-to)143-161
Number of pages19
Publication statusPublished - 07.2001

    Research areas

  • Mathematics
  • self-similar, self-affine, Hausdorff dimension, box-counting dimension