@article {23,
title = {Optimal quantizers for Radon random vectors in a Banach space},
journal = {J. Approx. Theory},
volume = {144},
number = {1},
year = {2007},
pages = {27{\textendash}53},
publisher = {Academic Press, Inc.},
address = {Orlando, FL, USA},
abstract = {For every integer $n$ and evrery positive real number $r \superior 0$ and a Radon random vector $X$ with values in a Banach space $E$, let $e_{n,r}(X,E) = \inf{\left(E\left[\min\limits_{a \in \alpha} \| X-a \|^r \right]^{1/r}\right)}$, where the infimum is taken over all subsets $\alpha$ of $E$ with $\textrm{card}(\alpha) \leq n$ ($n$-quantizers). We investigate the existence of optimal $n$-quantizers for this $L^r$-quantization problem, derive their stationarity properties and establish for $L^p$-spaces $E$ the pathwise regularity of stationary quantizers.},
issn = {0021-9045},
author = {Siegfried Graf and Harald Luschgy and Gilles Pag{\`e}s}
}