Measure theoretic laws for limsup sets defined by rectangles
Measure theoretic laws for limsup sets defined by rectangles
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DOI：
10.1016/j.aim.2023.109154
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发表时间：
2023-03
影响因子：
1.7
通讯作者：
D. Kleinbock;Baowei Wang
中科院分区：
文献类型：
--
作者：
D. Kleinbock;Baowei Wang
本文在矩形的不确定性假设下，给出了由矩形定义的极限集的Lebesgue测度理论的一般原理。同时给出了丢番图逼近，Khintchine-Groshev定理的矩形和高维收缩目标问题的应用。
In this paper, we present a general principle for the Lebesgue measure theory of limsup sets defined by rectangles under the hypothesis ofubiquity for rectangles. Applications are given for simultaneous Diophantine approximation, Khintchine-Groshev theorem for rectangles and higher dimensional shrinking target problems.