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On the upper and lower quantization coefficient for probability measures on multiscale Moran sets

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  • Zhu, Sanguo

Abstract

Given a finite set of patterns, we consider the Moran sets determined by using each of these patterns with a prescribed frequency. For certain infinite product measures μ on such Moran sets, we determine the exact values of the quantization dimensions Dr(μ). We give various sufficient conditions for the Dr(μ)-dimensional upper quantization coefficient and the lower one to be positive and finite. We also construct an example to illustrate our main result.

Suggested Citation

  • Zhu, Sanguo, 2012. "On the upper and lower quantization coefficient for probability measures on multiscale Moran sets," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1437-1443.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1437-1443
    DOI: 10.1016/j.chaos.2012.08.003
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