论文标题
对自我相似措施的顺序看法，或者，马勒和坎托的鬼魂可以教给我们有关维度的知识
A sequential view of self--similar measures, or, What the ghosts of Mahler and Cantor can teach us about dimension
论文作者
论文摘要
我们表明，缺少$ q $ -Ary Digit Sets $ f \ subseteq [0,1] $具有相应的自然相关的可计数二进制$ q $ - 自动序列$ f $。使用此信件，我们表明$ f $的Hausdorff尺寸等于$ f $的Mahler EigenValue的基础-Q $ Q $对数。此外，我们证明了$ f $支撑的标准质量分配$ν_f$等于ghost量$μ_f$ $ f $。
We show that missing $q$-ary digit sets $F\subseteq[0,1]$ have corresponding naturally associated countable binary $q$-automatic sequence $f$. Using this correspondence, we show that the Hausdorff dimension of $F$ is equal to the base-$q$ logarithm of the Mahler eigenvalue of $f$. In addition, we demonstrate that the standard mass distribution $ν_F$ supported on $F$ is equal to the ghost measure $μ_f$ of $f$.
