Properties of some overlapping self-similar and some self-affine measures
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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in: Acta Mathematica Hungarica, Jahrgang 92, Nr. 1-2, 07.2001, S. 143-161.
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - Properties of some overlapping self-similar and some self-affine measures
AU - Neunhäuserer, Jörg
PY - 2001/7
Y1 - 2001/7
N2 - 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.
AB - 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.
KW - Mathematics
KW - self-similar
KW - self-affine
KW - Hausdorff dimension
KW - box-counting dimension
U2 - 10.1023/A:1013716430425
DO - 10.1023/A:1013716430425
M3 - Journal articles
VL - 92
SP - 143
EP - 161
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
SN - 0236-5294
IS - 1-2
ER -