The Quantization Dimension of Distributions.
Forschungsberichte / Institut für Statistik, 68.
Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.
We show that the asymptotic behavior of the quantization error allows the definition of dimensions for probability distributions, the upper and the lower quantization dimension. These concepts fit into standard geometric measure theory, as the upper quantization dimension is always between the packing and the upper box-counting dimension, whereas the lower quantization dimension is between the Hausdorff and the lower box-counting dimension. (author's abstract)