Billingsley dimension on shift spaces
Billingsley dimension on shift spaces
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DOI：
10.1088/0951-7715/16/2/317
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发表时间：
2003-02
期刊：
影响因子：
1.7
通讯作者：
C. Pfister;W. Sullivan
中科院分区：
文献类型：
--
作者：
C. Pfister;W. Sullivan
本文考虑有限字母表上的一类子移位，包括sofic移位。对于一个大类的度量，我们确定的Hausdorff维数的点集定义的极限点集下的经验措施。我们的方法来计算饱和集的Billingsley维数是根本不同的，适用于更一般的移位空间和措施比技术的Billingsley，这是显着开发的Cajar和最近扩展他人。我们的方法的一个主要特点是一个大的（在维理论的意义上）饱和集的子集的算法建设。这推广了法线或一般点子集的类似构造。
We consider a class of subshifts Σ over a finite alphabet, including sofic shifts. For a large class of metrics we determine the Hausdorff dimension of sets of points of Σ defined by their limit-point set under the empirical measure. Our approach to computing the Billingsley dimension of saturated sets is fundamentally different and applies to more general shift spaces and measures than the technique of Billingsley, which was significantly developed by Cajar and recently extended by others. One main feature of our approach is an algorithmic construction of a large (in the sense of dimension theory) subset of a saturated set. This generalizes similar constructions of subsets of normal or generic points.