Title: Doubling properties of self-similar measures

Authors: Po-Lam Yung

Issue: Volume 56 (2007), Issue 2, 965-990

Abstract: Let $\{F_i\}_{i=1}^N$ be a system of similitudes in $\mathbb{R}^n$. We study necessary and sufficient conditions for their associated self-similar measures to be doubling on its support. An equivalent condition is obtained when $\{F_i\}$ satisfies the open set condition. The condition allows us to construct many examples of interest. In the case where the open set condition is not satisfied, we study an infinitely convoluted Bernoulli measure (associated with the golden ratio $ ho=(sqrt{5}-1)/2$) and give a necessary and sufficient condition for it to be doubling on its support $[0,1]$.