论文标题
一套迪里奇莱特的不可分解数字的豪斯多夫度量
The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers
论文作者
论文摘要
令$ψ：\ mathbb r _+\ to \ mathbb r _+$是一个非进口功能。如果系统$$ | qx-p | <\，ψ（t）\ \ {\ text {and}} \ | q | <t $ | q | <t $ 4具有非整数整数解决方案，则据说$ x $可以改善$ψ$ -Dirichlet可以改善。表示此类点的收集$ d（ψ）$。在本文中，我们证明了在自然非限制性条件下对所有维度函数有效的零侵入法。某些后果是零界定律，对于所有基本的亚线性维度函数，Hussain-Kleinbock-Wadleigh-wang（2018）证明了某些非必要的亚线性尺寸函数，并且对于所有维度函数，但在近似函数上具有生长条件。
Let $ψ:\mathbb R_+\to\mathbb R_+$ be a non-increasing function. A real number $x$ is said to be $ψ$-Dirichlet improvable if the system $$|qx-p|< \, ψ(t) \ \ {\text{and}} \ \ |q|<t$$ has a non-trivial integer solution for all large enough $t$. Denote the collection of such points by $D(ψ)$. In this paper, we prove a zero-infinity law valid for all dimension functions under natural non-restrictive conditions. Some of the consequences are zero-infinity laws, for all essentially sub-linear dimension functions proved by Hussain-Kleinbock-Wadleigh-Wang (2018), for some non-essentially sub-linear dimension functions, and for all dimension functions but with a growth condition on the approximating function.
