Quantization dimension for condensation systems II: The geometric mean error

Let be a family of similitudes on R1 satisfying the strong separation condition and ν the self-similar measure associated with and a probability vector (t1,…,tN). Let μ be the attracting measure of a condensation system associated with ν, and a probability vector (p0,p1,…,pN). We establish a relationship between the quantization dimension of μ and its mass distribution on cylinder sets.