论文标题
提取球序列的最佳子序列，并应用于质量转移原理的最佳估计
Extraction of optimal subsequences of sequence of balls, and application to optimality estimates of mass transference principles
论文作者
论文摘要
在本文中，我们证明，从相关的LIMSUP集具有完整$μ$量的任何一系列球中，可以提取球的分布良好的球。由此，我们推断出通过质量转移原理获得的limsup球的Hausdorff尺寸的各种下限的最佳性。我们还建立了一个版本的Borel-cantelli Divergence引理特定，适用于由球产生的LIMSUP集。这种引理与贝尔塞维奇和维拉尼证明的引理非常相似，但是该措施并不是一倍。
In this article, we prove that from any sequence of balls whose associated limsup set has full $μ$-measure, one can extract a well-distributed subsequence of balls. From this, we deduce the optimality of various lower bounds for the Hausdorff dimension of limsup sets of balls obtained by mass transference principles. We also establish a version of Borel-Cantelli divergence lemma particulary suited for limsup set generated by balls. This lemma is very similar to the one proved by Bersnevich and Velani but the measure is not assumed ot be doubling.
