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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Document type
- Preprint