The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We demonstrate how known results from two areas of research – supervised learning theory and numerical integration – can be used in sampling discretization of the square norm on different function classes.

中文翻译：

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函数类积分范数的抽样离散误差

本文的新内容是，我们考虑了函数的无穷维类，并且考虑了绝对误差设置，而不是先前关于规范离散化的论文中使用的相对误差设置。我们演示了如何将两个研究领域（监督学习理论和数值积分）的已知结果用于不同函数类的平方范数的样本离散化。