2022/04/04 by Édouard Daviaud, Daviaud, Édouard
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2204.01304
openalex publication_date 2022/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.