This paper generalizes earlier results on the behaviour of uniformly distributed sequences in the unit interval [0,1] to more general domains. We devote special attention to the most interesting special case [0,1] d . This will naturally lead to a problem in geometric probability theory, where we generalize results by Anderssen, Brent, Daley and Moran about random chord lengths in high-dimensional unit cubes, thereby answering a question by Bailey, Borwein and Crandall.
展开▼
机译：本文将单位间隔[0,1]中均匀分布的序列的行为概括到更一般的域的早期结果。我们特别注意最有趣的特殊情况[0,1] d 。这自然会引出几何概率论中的一个问题，我们将安德森（Anderssen），布伦特（Brent），戴利（Daley）和莫兰（Moran）关于高维单位立方体中随机弦长的结果进行概括，从而回答贝利（Bailey），博文（Borwein）和克兰德尔（Crandall）的问题。
展开▼
