Quantization dimension for condensation systems II: The geometric mean error

Let {fi }N1 be a family of similitudes on R1 satisfying the strong separation condition and ν the self-similar measure associated with {fi }N1 and a probability vector (t1, . . . , tN). Let μ be the attracting measure of a condensation system associated with ν, {fi }N1 and a probability vector (p0,p1, . . . , pN).We establish a relationship between the quantization dimension of μ and its mass distribution on cylinder sets. © 2008 Elsevier Inc. All rights reserved