We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^p$ with $p>1$ consistency in terms of almost sure convergence

翻译：我们证明了一类随机积分方法，包括基于$(t,d)$-序列的平均值、拉丁超立方体抽样、Frolov点以及Cranley-Patterson旋转，能够一致地估计可积函数的期望。此处的一致性指的是估计量在均值意义上和/或概率意义上收敛于目标积分。此外，我们提出了中位数修正方法，并证明了对于$L^p$（其中$p>1$）中的被积函数，该方法在几乎必然收敛意义上具有一致性。