标题： 具有紧致Borel窗的模型集 显示英文标题

标题： Model sets with precompact Borel windows

摘要： 给定一个截断和投影方案以及一个预紧的Borel窗，我们证明几乎所有的窗位置都会产生具有Besicovitch几乎周期性Dirac梳的点集。 特别地，所有这些位置都会导致纯点衍射的点集，其自相关由窗的协变图给出，衍射由窗的傅里叶变换的平方给出。 此外，Fourier-Bohr系数存在，布拉格峰的强度由它们的绝对值平方给出。 我们证明了存在一个具有纯点动力谱的遍历测度，使得所有这些窗位置产生的点集都是该测度的典型集。 最后，我们重新分析了最大密度的弱模型集类。 显示英文摘要

摘要： Given a cut and project scheme and a pre-compact Borel window we show that almost surely all positions of the window give rise to point sets with Besicovitch almost periodic Dirac combs. In particular, all those positions lead to pure point diffractive point sets with autocorrelation given by the covariogram of the window and diffraction given by the square of the Fourier transform of the window. Moreover the Fourier--Bohr coefficients exist and the intensity of the Bragg peaks is given by their absolute value square. We show the existence of an ergodic measure with pure point dynamical spectrum such that all those window positions give rise to point sets which are generic for this measure. We complete the paper by reanalysing the class of weak model sets of maximal density.