The Quantization Dimension and other Dimensions of Probability Measures
Meifeng Dai, Liu Zheng-ci · 2008
In this paper, we study the lower and the upper quantization dimensions of prob- ability measures and their equivalent definitions. Then we prove that 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. Finally, we give a concrete probability measure which all of its quantization dimension and other dimensions agree.