Local dimensions of measures on infinitely generated self-affine sets

被引：7
|
作者：
Rossi, Eino [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 413卷 / 02期
关键词：
Self-affine; Infinite iterated function system; Local dimension; ITERATED FUNCTION SYSTEMS; HAUSDORFF DIMENSION; FRACTALS;
D O I：
10.1016/j.jmaa.2013.12.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：1030 / 1039
页数：10
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