Abstract
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 language | English |
|---|---|
| Journal | Acta Mathematica Hungarica |
| Volume | 92 |
| Issue number | 1-2 |
| Pages (from-to) | 143-161 |
| Number of pages | 19 |
| ISSN | 0236-5294 |
| DOIs | |
| Publication status | Published - 07.2001 |
Research areas and keywords
- Mathematics
- self-similar
- self-affine
- Hausdorff dimension
- box-counting dimension
ASJC Scopus Subject Areas
- Mathematics(all)
Fingerprint
Dive into the research topics of 'Properties of some overlapping self-similar and some self-affine measures'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver