Quantization dimension of probability measures supported on Cantor-like sets |
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Authors: | Sanguo Zhu |
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Institution: | Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, PR China |
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Abstract: | Let μ be an arbitrary probability measure supported on a Cantor-like set E with bounded distortion. We establish a relationship between the quantization dimension of μ and its mass distribution on cylinder sets under a hereditary condition. As an application, we determine the quantization dimensions of probability measures supported on E which have explicit mass distributions on cylinder sets provided that the hereditary condition is satisfied. |
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Keywords: | Quantization dimension Cantor-like sets Bounded distortion Hereditary condition |
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