应用数学2017，Vol.30Issue(2)：469-474,6.
一个关于Cantor展式中收缩靶问题的注记
A Note on the Shrinking Target Problems in Cantor Series Expansion
摘要
Abstract
Let Q ={qk}k≥1 be a sequence of positive integers with qk ≥ 2 for every k ≥ 1.Then each point x ∈ [0,1] is attached with an infinite series expansion which is called the Q-Cantor series expansion of x.Put TnQ(x) =q1…qnx-[q1…qnx」.For any positivefunction φ:N → (0,1) with φ(n) → 0 as n → ∞ and any sequence y ={yn}n≥1 (∈) [0,1],we consider the size of the set Ey(φ):={x ∈ [0,1]:｜TnQ(x)-yn[＜ φ(n) i.o.n}.In this paper,we show that both the Lebesgue measure and the Hausdorff measure of Ey(φ) fulfill a dichotomy law according to the divergence or convergence of certain series.关键词
Cantor展式/收缩靶问题/丢番图逼近/Hausdorff测度Key words
Cantor series expansion/Shrinking target problem/Diophantine approximation/Hausdorff measure分类
数理科学引用本文复制引用
曹春云..一个关于Cantor展式中收缩靶问题的注记[J].应用数学,2017,30(2):469-474,6.基金项目
Supported by the Fundamental Research Funds for the Central University (2662015QC001) and NSFC (11501229) （2662015QC001）
