Local Dimensions of Measures of Finite Type II: Measures Without Full Support and With Non-regular Probabilities

摘要

Consider a finite sequence of linear contractions S-j(x) = rho x + d(j) and probabilities p(j) 0 with Sigma p(j) = 1. We are interested in the self-similar measure mu = Sigma p(j)mu o S-j(-1), of finite type. In this paper we study the multi-fractal analysis of such measures, extending the theory to measures arising from non-regular probabilities and whose support is not necessarily an interval.