• Corpus ID: 249209895

Quantization dimensions of compactly supported probability measures via R\'enyi dimensions

@inproceedings{Kessebohmer2022QuantizationDO,
  title={Quantization dimensions of compactly supported probability measures via R\'enyi dimensions},
  author={Marc Kessebohmer and Aljoscha Niemann and Sanguo Zhu},
  year={2022}
}
We provide a full picture of the upper quantization dimension in terms of the Rényi dimension, in that we prove that the upper quantization dimension of order r > 0 for an arbitrary compactly supported Borel probability measure ν is given by its Rényi dimension at the point qr where the Lq-spectrum of ν and the line through the origin with slope r intersect. In particular, this proves the continuity of r 7→ Dr(ν) as conjectured by Lindsay (2001). This viewpoint also sheds new light on the… 

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