The sets of divergence points of self-similar measures are residual

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:404

Article

Li, Jinjun¹  Wu, Min² 

[1] Zhangzhou Normal Univ, Dept Math, Zhangzhou 363000, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

关键词: Self-similar measure;    Open set condition;    Divergence point;    Residual;   

DOI  :  10.1016/j.jmaa.2013.03.043

来源: Elsevier

【 摘 要 】

Let mu be a self-similar measure supported on a self-similar set K with the open set condition. For x is an element of K, let A(D(x)) be the set of accumulation points of D-r(x) = log mu(B(x.r))/logr as r SE arrow 0. In this paper, we show that for any closed non-singleton subinterval I subset of R, the set of points x for which the set A(D(x)) equals I is either empty or residual. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free