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 -