@article {18,
title = {Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions},
journal = {Journal of Mathematical Analysis and Applications},
volume = {318},
number = {2},
year = {2006},
pages = {507 - 516},
abstract = {For a probability measure $P$ on $\mathbb{R}^d$ and $n \in \mathbb{N}$ consider $e_n = \inf \displaystyle \int \min_{a \in \alpha} V(\| x-a \| )dP(x)$ where the infimum is taken over all subsets $\alpha$ of $\mathbb{R}^d$ with $\mbox{card} (\alpha) \leq n$ and $V$ is a nondecreasing function. Under certain conditions on $V$, we derive the precise $n$-asymptotics of $e_n$ for nonsingular and for (singular) self-similar distributions $P$ and we find the asymptotic performance of optimal quantizers using weighted empirical measures.},
keywords = {Point density measure},
issn = {0022-247X},
author = {Sylvain Delattre and Siegfried Graf and Harald Luschgy and Gilles Pag{\`e}s}
}