On the upper and lower quantization coefficient for probability measures on multiscale Moran sets |
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| Authors: | Sanguo Zhu |
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| Affiliation: | 1. Twitter, Inc. 1355 Market St, Suite 900, San Francisco, CA 94103, USA;2. Department of Computer Science, Iowa State University, Ames, IA 50011, USA;3. Departamento de Informática e Ingeniería de Sistemas, Instituto de Investigación en Ingeniería de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain;4. Department of Computer Science, National University of Ireland, Maynooth, Maynooth, Co. Kildare, Ireland;1. AXA Equitable Life Insurance Company, Jersey City, NJ 07310, USA;2. School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes SA 5095, Australia;1. Department of Mathematics, Huazhong University Of Science And Technology, Wuhan 430074, China;2. Department of Mathematics, Hubei University of Technology, Wuhan 430068, China;3. Department of Mathematics, Hubei University, Wuhan 430062, China |
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| 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. |
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