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
Multilevel randomized quasi-Monte Carlo estimator for nested integration
RWTH Aachen University（亚琛工业大学）；King Abdullah University of Science & Technology (KAUST)（阿卜杜拉国王科技大学）；University of Nottingham（诺丁汉大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Double-loop randomized quasi-Monte Carlo estimator for nested integration
RWTH Aachen University（亚琛工业大学）；King Abdullah University of Science & Technology (KAUST)（阿卜杜拉国王科技大学）；University of Nottingham（诺丁汉大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
Department of Computer Science and Software Engineering, Korea University（韩国大学计算机科学与软件工程系）；Department of Aerospace Engineering and Engineering Mechanics, The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与工程力学系，奥登计算工程与科学研究所）
Quasi-Monte Carlo confidence intervals using quantiles of randomized nets
Johann Radon Institute for Computational and Applied Mathematics, ÖAW（约翰·拉多纳计算与应用数学研究所，奥地利科学院）；Institute of Fundamental and Transdisciplinary Research, Zhejiang University（浙江大学基础与交叉研究学院）
Dimension-independent convergence rates of randomized nets using median-of-means
Johann Radon Institute for Computational and Applied Mathematics, ÖAW（约翰·拉登计算与应用数学研究所，奥地利科学院）；Institute of Fundamental and Transdisciplinary Research, Zhejiang University（浙江大学基础与跨学科研究院）
The effect of quadrature rules on finite element solutions of Maxwell variational problems. Consistency estimates on meshes with straight and curved elements
