保形图递归集的Hausdorff维数和测度

胥晖

数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 633-640.

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PDF(472 KB)
数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 633-640. DOI: 10.12386/A2001sxxb0083
论文

保形图递归集的Hausdorff维数和测度

    胥晖
作者信息 +

The Hausdorff Dimension and Measure of Conformal Graph-Directed Sets

    Hui XU
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摘要

本文确定了保形图递归集的 Hausdorff维数,证明了相应的 Hausdorff度是正σ-有限的,并且我们给出了 Hausdorff测度为正有限的充分必要条件.

Abstract

in this article, we determine the Hausdorff dimension of the comformal graphdirected set, prove that the associated Hausdorff measure is positive o-finite, and give the sufficient and necessary condition that makes Hausdorff measure be positive finite.

关键词

图递归构造 / 图递归集 / Hausdorff维数 / Hausdorff测度

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胥晖. 保形图递归集的Hausdorff维数和测度. 数学学报, 2001, 44(4): 633-640 https://doi.org/10.12386/A2001sxxb0083
Hui XU. The Hausdorff Dimension and Measure of Conformal Graph-Directed Sets. Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 633-640 https://doi.org/10.12386/A2001sxxb0083
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