具有正勒贝格测度和空内部的无限生成自相似集
An infinitely generated self-similar set with positive Lebesgue measure and empty interior
摘要：
Peres和Solomyak提出了这样一个问题：是否存在内部为空且勒贝格测度为正的自相似集？这个问题得到了肯定的回答Csörnyei等人。他们给出了一个参数化家庭的迭代函数系统，几乎所有相应的自相似集满足所需的属性。然而，它们没有提供明确的例子。出于构造一个明确例子的愿望，本文给出了一个具有正勒贝格测度和空内部的无限生成自相似集的明确构造。
英文摘要：
Peres and Solomyak asked the question: Do there exist self-similar sets with positive Lebesgue measure and empty interior? This question was answered in the affirmative by Csörnyei et al. They gave a parameterised family of iterated function systems for which almost all of the corresponding self-similar sets satisfied the required properties. They do not however provide an explicit example. Motivated by a desire to construct an explicit example, we in this paper provide an explicit construction of an infinitely generated self-similar set with positive Lebesgue measure and empty interior.
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。
