There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling discretization results turn out to be very useful in various applications, particularly in sampling recovery. Recent sampling discretization results typically provide existence of good sampling points for discretization. In this paper, we show that independent and identically distributed random points provide good universal discretization with high probability. Furthermore, we demonstrate that a simple greedy algorithm based on those points that are good for universal discretization provides excellent sparse recovery results in the square norm.

翻译：积分范数采样离散化的研究在指定有限维函数空间以及此类函数空间的有限集合（通用离散化）方面取得了显著进展。采样离散化结果在各种应用中非常有用，特别是在采样恢复中。最近的采样离散化结果通常证明了存在用于离散化的良好采样点。在本文中，我们证明独立同分布随机点能够以高概率实现良好的通用离散化。此外，我们证明基于这些适用于通用离散化的点的简单贪心算法在平方范数下能够实现优异的稀疏恢复结果。