关于Ahlfors正则集的计数函数的渐近性
On the asymptotics of counting functions for Ahlfors regular sets
摘要：
本文研究了度量空间中的Ahlfors正则集（也称为$s$ -正则集）.首先，我们表明，这些集对应于某一类树状结构。基于这一观察，我们然后研究以下问题：在什么条件下存在极限$\lim_{\varepsilon\to 0+} \varepsilon^s N(\varepsilon,K)$，其中$K$是$s$ -正则集和$N(\varepsilon,K)$是例如$K$的$\varepsilon$ -堆积数？
英文摘要：
In this paper we deal with the so-called Ahlfors regular sets (also known as $s$-regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: under which conditions does the limit $\lim_{\varepsilon\to 0+} \varepsilon^s N(\varepsilon,K)$ exist, where $K$ is an $s$-regular set and $N(\varepsilon,K)$ is for instance the $\varepsilon$-packing number of $K$?
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
