论文标题
$ \ mathbb {r}^d $中的厚度和间隙引理
Thickness and a gap lemma in $\mathbb{R}^d$
论文作者
论文摘要
我们给出了$ \ mathbb {r}^d $中厚度的定义，即使对于完全断开的集合也很有用，并证明了GAP引理类型结果。我们还保证在任何方向上的距离间隔厚度紧凑，将厚的集合（对于厚度的定义）与获胜组相关联，为较低的许多距离的Hausdorff尺寸提供了较低的限制，其结果是其中许多图案的存在，并保证了与厚度与厚度相关的Hausdorff尺寸的下限。
We give a definition of thickness in $\mathbb{R}^d$ that is useful even for totally disconnected sets, and prove a Gap Lemma type result. We also guarantee an interval of distances in any direction in thick compact sets, relate thick sets (for this definition of thickness) with winning sets, give a lower bound for the Hausdorff dimension of the intersection of countably many of them, a result guaranteeing the presence of large patterns, and lower bounds for the Hausdorff dimension of a set in relationship with its thickness.
