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摘要
Let E be a Bedford-McMullen carpet determined by a set of affine mappings (f(ij))((i, j)) (is an element of G) and mu a self-affine measure on E associated with a probability vector (p(ij))((i, j)) (is an element of G). We prove that, for every r is an element of(0, infinity), the upper and lower quantization coefficient are always positive and finite in its exact quantization dimension s(r). As a consequence, the nth quantization error for mu of order r is of the same order as n(-1/sr). In sharp contrast to the Hausdorff measure for Bedford-McMullen carpets, our result is independent of the horizontal fibres of the carpets.
- 出版日期2018-2
- 单位江苏大学
