关于具有序列受限部分商的连分数的重对数律
On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients
AI总结：
本文研究了具有序列受限部分商的连分数，为满足特定条件的实数集合建立了重对数律，证明了其Hausdorff维数及测度性质，并基于序列迭代函数系统的强不变原理得出结果。
摘要：
我们对第n个部分商大于$α_n$的实数集合建立了重对数律（LIL），其中$(α_n)$是使得$\sum 1/α_n$有限的序列。在许多情况下，该集合被证明具有Hausdorff维数$1/2$，且LIL中的测度关于Hausdorff测度是绝对连续的。该结果是作为序列迭代函数系统极限集上无界可观测量的强不变原理的应用而获得的。
英文摘要：
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $α_n$, where $(α_n)$ is a sequence such that $\sum 1/α_n$ is finite. This set is shown to have Hausdorff dimension $1/2$ in many cases and the measure in LIL is absolutely continuous to the Hausdorff measure. The result is obtained as an application of a strong invariance principle for unbounded observables on the limit set of a sequential iterated function system.
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。
