A Koksma-Hlawka inequality for general discrepancy systems Pausinger, Florian ; https://orcid.org/0000-0002-8379-3768 Svane, Anne Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology. Academic Press 2015 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1792 Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. 2015;31(6):773-797. doi:<a href="https://doi.org/10.1016/j.jco.2015.06.002">10.1016/j.jco.2015.06.002</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2015.06.002 info:eu-repo/semantics/altIdentifier/wos/000362926900001 info:eu-repo/semantics/closedAccess