Recently, there was a big progress in studying sampling discretization of integral norms of finite dimensional subspaces and collections of such subspaces (universal discretization). It was established that sampling discretization results are useful in a number of applications. In particular, they turn out to be useful in sampling recovery. Typically, recent sampling discretization results provide existence of good points for discretization. The main goal of this paper is to show that in the problem of universal discretization the independent random points on a given domain that are identically distributed according to the given probabilistic measure provide good points with high probability. Also, we demonstrate that a simple greedy type algorithm based on good points for universal discretization provide good recovery in the square norm.

翻译：最近,在研究有限维次空间整体规范的抽样分解和这种子空间的收集(通用分解)方面取得了很大进展,确定抽样分解结果在许多应用中有用,特别是,这些结果在取样回收中特别有用,典型的是,最近的抽样分解结果为分解提供了良好的分解点,本文件的主要目的是表明,在普遍分解问题中,特定领域的独立随机点按照给定的概率衡量方法分布相同,提供了很高的分数。此外,我们证明,基于普遍分解良好点的简单贪婪型算法为正方形规范提供了良好的恢复。