Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions

For a probability measure P on Rd and n∈N consider where the infimum is taken over all subsets α of Rd with card(α)⩽n and V is a nondecreasing function. Under certain conditions on V, we derive the precise n-asymptotics of en for self-similar distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.