The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of the Nikol'skii-type inequality. {In particular, we obtain} some upper bounds on the number of sample points sufficient for good discretization of the integral $L_p$ norms, $1\le p<2$, of functions from finite-dimensional subspaces of continuous functions. Our new results improve upon the known results in this direction. We use a new technique based on deep results of Talagrand from functional analysis.

翻译：本文讨论了对符合某些条件的有限维次空间各组成部分综合规范的抽样分解问题。根据以Nikol'skii类型不平等为标准假设而拟订的标准假设,我们证明抽样分解的结果。{特别是,我们获得了}关于足以使连续功能的有限维次空间的功能合在一起的美元/p$规范、1美元/le p<2美元功能的良好分解的抽样点数目的一些上限。我们的新结果改进了这方面的已知结果。我们使用了基于功能分析Talagrand的深刻结果的新技术。