Local dimensions of measures on infinitely generated self-affine sets
| Autor: | Eino Rossi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
matematiikka 28A80 Applied Mathematics ta111 Minkowski–Bouligand dimension Dimension function Metric Geometry (math.MG) Dynamical Systems (math.DS) Complex dimension Effective dimension Packing dimension Mathematics - Metric Geometry Hausdorff dimension FOS: Mathematics dimensions Mathematics - Dynamical Systems Dimension theory (algebra) Inductive dimension ulottuvuudet Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 413(2):1030 |
| ISSN: | 0022-247X |
| Popis: | We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive. Comment: Accepted author manuscript, 10 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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