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

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

Authors

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.
OriginalspracheEnglisch
ZeitschriftActa Mathematica Hungarica
Jahrgang92
Ausgabenummer1-2
Seiten (von - bis)143-161
Anzahl der Seiten19
ISSN0236-5294
DOIs
PublikationsstatusErschienen - 07.2001

DOI

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