A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic rate of growth of the grid sizes and of the comparability constants must grow in a controlled manner. In this paper, we generalize the notion of a WAM to a hierarchical subspaces of not necessarily polynomial functions, and we analyze particular strategies for random sampling as a technique for generating WAM's. Our main results show that WAM's and their stronger variant, admissible meshes (AM's), can be generated by random sampling, and our analysis provides concrete estimates for growth of both the meshes and the discrete-continuum comparability constants.

翻译：在连续的实际价值域上,一个可受理的薄弱网格(WAM)在连续实际价值域上是一个离散的网格序列,这样网格上多元动物的离散最大标准可以与域内多元动物的顶部标准相提并论。网格大小和可比性常数的无症状增长率必须以控制的方式增长。在本文中,我们将WAM的概念推广到一个不一定是多元功能的等级分层子空间,我们分析随机抽样的特定战略,以此作为产生WAM的技术。我们的主要结果显示,WAM及其较强的变异物(可接受的Meshes(AM))可以通过随机取样产生,我们的分析为间壳和离心-内聚素可比性常数的增长提供了具体估计。