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arXiv · 2601.20531

Weaker quantization dimension results for self-similar measures

Saurabh Verma·Shivam Dubey
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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.

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Saurabh Verma, Shivam Dubey. 2026-01-28. Weaker quantization dimension results for self-similar measures. https://arxiv.org/abs/2601.20531

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