发表机构
Nanjing University of Science and Technology（南京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过覆盖构造引入标记填充测度，证明其与经典填充测度等价（相差常数因子），并在自相似集等情形下与标记填充容度相等。
AI 中文摘要
我们通过一个覆盖构造引入标记填充测度，其中每个集合具有一个独立的正标记，该标记限制其直径以及其局部填充代价中的半径。令标记趋于零，定义了一个度量外测度 $M^s$。对于每个 $s>0$ 和每个度量空间 $(X,d)$，我们证明 \\[ 2^{-s}{P}^s(F)\le{M}^s(F) \le C(s) P^s(F)\qquad(F\subset X), \\] 其中 $ P^s(F)$ 是经典填充测度，$C(s)$ 仅依赖于 $s$。因此，标记填充测度与经典填充测度具有相同的零集和临界指数。允许任意有限正标记定义了标记填充容度。在共同的正豪斯多夫维数和填充维数处，该容度与标记填充测度在有限型不可约子移位相关的柱集上一致。特别地，对于非单点自相似吸引子和有限强连通图定向系统的分量，等式成立，无需分离假设。
英文摘要
We introduce labelled packing measure by a covering construction in which each set has an independent positive label bounding its diameter and the radii in its local packing cost. Letting the labels tend to zero defines a metric outer measure $M^s$. For every $s>0$ and every metric space $(X,d)$, we prove \[ 2^{-s}{P}^s(F)\le{M}^s(F) \le C(s) P^s(F)\qquad(F\subset X), \] where $ P^s(F)$ is the classical packing measure and $C(s)$ depends only on $s$. Thus labelled packing measure and classical packing measure have the same null sets and critical exponent. Allowing arbitrary finite positive labels defines labelled packing content. At the common positive Hausdorff and packing dimension, this content and the labelled packing measure agree on cylinders associated with irreducible subshifts of finite type. In particular, equality holds for non-singleton self-similar attractors and components of finite strongly connected graph-directed systems, without separation assumptions.
