HAUSDORFF MEASURES of A CLASS of MORAN SETS

Xiaofang Jiang; Qinghui Liu; Guizhen Wang; Zhiying Wen

doi:10.1142/S0218348X2050053X

HAUSDORFF MEASURES of A CLASS of MORAN SETS

Xiaofang Jiang, Qinghui Liu^*, Guizhen Wang, Zhiying Wen

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

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摘要

Let (n,c) be the class of Moran sets with integer n ≥ 2 and real c satisfying nc < 1. It is well known that the Hausdorff dimension of any set in this class is s = -logcn. We show that for any E (n,c), 2s 2 (n - 1)c 1 - cs ≤s(E) ≤ 1, where s(E) denotes s-dimensional Hausdorff measure of E. For any a with 2s 2 (n - 1)c 1 - cs ≤ a ≤ 1, there exists a self-similar set E (n,c) such that s(E) = a.

源语言	英语
文章编号	2050053
期刊	Fractals
卷	28
期	3
DOI	https://doi.org/10.1142/S0218348X2050053X
出版状态	已出版 - 1 5月 2020

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Jiang, X., Liu, Q., Wang, G., & Wen, Z. (2020). HAUSDORFF MEASURES of A CLASS of MORAN SETS. Fractals, 28(3), 文章 2050053. https://doi.org/10.1142/S0218348X2050053X

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abstract = "Let (n,c) be the class of Moran sets with integer n ≥ 2 and real c satisfying nc < 1. It is well known that the Hausdorff dimension of any set in this class is s = -logcn. We show that for any E (n,c), 2s 2 (n - 1)c 1 - cs ≤s(E) ≤ 1, where s(E) denotes s-dimensional Hausdorff measure of E. For any a with 2s 2 (n - 1)c 1 - cs ≤ a ≤ 1, there exists a self-similar set E (n,c) such that s(E) = a.",

keywords = "Hausdorff Dimension, Hausdorff Measure, Moran Sets",

author = "Xiaofang Jiang and Qinghui Liu and Guizhen Wang and Zhiying Wen",

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AU - Jiang, Xiaofang

AU - Liu, Qinghui

AU - Wang, Guizhen

AU - Wen, Zhiying

PY - 2020/5/1

Y1 - 2020/5/1

N2 - Let (n,c) be the class of Moran sets with integer n ≥ 2 and real c satisfying nc < 1. It is well known that the Hausdorff dimension of any set in this class is s = -logcn. We show that for any E (n,c), 2s 2 (n - 1)c 1 - cs ≤s(E) ≤ 1, where s(E) denotes s-dimensional Hausdorff measure of E. For any a with 2s 2 (n - 1)c 1 - cs ≤ a ≤ 1, there exists a self-similar set E (n,c) such that s(E) = a.

AB - Let (n,c) be the class of Moran sets with integer n ≥ 2 and real c satisfying nc < 1. It is well known that the Hausdorff dimension of any set in this class is s = -logcn. We show that for any E (n,c), 2s 2 (n - 1)c 1 - cs ≤s(E) ≤ 1, where s(E) denotes s-dimensional Hausdorff measure of E. For any a with 2s 2 (n - 1)c 1 - cs ≤ a ≤ 1, there exists a self-similar set E (n,c) such that s(E) = a.

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KW - Hausdorff Measure

KW - Moran Sets

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VL - 28

JO - Fractals

JF - Fractals

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HAUSDORFF MEASURES of A CLASS of MORAN SETS

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