Weaker quantization dimension results for self-similar measures

Abstract

In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some level satisfies the separation condition. Further, we study the approximation of the space of Borel probability measures $\mathcal{P}({\mathbb{R}}^m)$ with respect to the geometric mean error, i.e., the quantization dimension of order zero.