Given a sequence of Marcinkiewicz-Zygmund inequalities in $L^2$, we derive approximation theorems and quadrature rules. The derivation is completely elementary and requires only the definition of Marcinkiewicz-Zygmund inequality, Sobolev spaces, and the solution of least square problems.

中文翻译：

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采样，Marcinkiewicz-Zygmund不等式，逼近和正交规则

给定Marcinkiewicz-Zygmund不等式的序列 ${\mathrm{大号}}^2$，我们得出逼近定理和正交规则。推导完全是基本的，只需要定义Marcinkiewicz-Zygmund不等式，Sobolev空间以及最小二乘问题的解即可。