论文标题
康托尔（Cantor）集合中的二元近似的注释
A note on dyadic approximation in Cantor's set
论文作者
论文摘要
我们考虑中间三分之二插座集中的二元近似的收敛理论，$ k $，用于表格$ψ_τ（n）= n^{ - τ} $的近似函数（$τ\ ge 0 $）。特别是，我们表明，对于$τ$的值以外的一个特定阈值，我们在$ k $中几乎没有任何意义在二元上是$ψ_τ$ - 就$ k $上的自然概率度量而言是近似值。这是通过第一，第三和第四名作者获得的这个方向的先前结果（Arxiv，2020）。
We consider the convergence theory for dyadic approximation in the middle-third Cantor set, $K$, for approximation functions of the form $ψ_τ(n) = n^{-τ}$ ($τ\ge 0$). In particular, we show that for values of $τ$ beyond a certain threshold we have that almost no point in $K$ is dyadically $ψ_τ$-well approximable with respect to the natural probability measure on $K$. This refines a previous result in this direction obtained by the first, third, and fourth named authors (arXiv, 2020).
