• Corpus ID: 249209895

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

  title={Quantization dimensions of compactly supported probability measures via R\'enyi dimensions},
  author={Marc Kessebohmer and Aljoscha Niemann and Sanguo Zhu},
A bstract . We provide a complete picture of the upper quantization dimension in terms of the R´enyi dimension by proving that the upper quantization dimension D r ( ν ) of order r > 0 for an arbitrary compactly supported Borel probability measure ν is given by its R´enyi dimension at the point q r where the L q -spectrum of ν and the line through the origin with slope r intersect. In particular, this proves the continuity of r (cid:55)→ D r ( ν ) as conjectured by Lindsay (2001). This… 
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