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2003-2004 Quantization dimension via quantization numbers.
Marc Kesseböhmer, Sanguo Zhu
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Real Anal. Exchange 29(2): 857-867 (2003-2004).


We give a characterization of the quantization dimension of Borel probability measures on $\mathbb{R}^{d}$ in terms of $\epsilon$-quantization numbers. Using this concept, we show that the upper rate distortion dimension is not greater than the upper quantization dimension of order one. We also prove that the upper quantization dimension of a product measure is not greater than the sum of that of its marginals. Finally, we introduce the notion of the $\epsilon$-essential radius for a given measure to construct an upper bound for its quantization dimension.


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Marc Kesseböhmer. Sanguo Zhu. "Quantization dimension via quantization numbers.." Real Anal. Exchange 29 (2) 857 - 867, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1062.28006
MathSciNet: MR2083820

Primary: 28A75 , 28A80 , 60E05 , 62H30

Keywords: product measures , Quantization dimension , quantization number , rate distortion dimension , Renyi dimension

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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