论文标题
$ \ Mathbb r^d $中的模型集是模型集
Inter model sets in $\mathbb R^d$ are model sets
论文作者
论文摘要
我们表明，模型集的任何翻译都是在某些修改的切割和项目中的模型集。限制在欧几里得直接空间中，我们表明，Inter Model集合的任何翻译都是具有第二个可计数内部空间的一些修改的切割和项目中的模型集。在这两种情况下，修改后的剪切方案中的窗口都继承了原始窗口的拓扑和测量理论特性。实际上，我们的结果适用于超越间模型集的类别，我们称之为几乎模型集。
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original window. Our results hold in fact for a class beyond inter model sets, which we call almost model sets.
