article published yes Florian Pausinger author 2A77D7A2-F248-11E8-B48F-1D18A9856A870000-0002-8379-3768 Anne Svane author HeEd department 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 Press2015 eng 00036292690000110.1016/j.jco.2015.06.002 316773 - 797 https://research-explorer.ista.ac.at/record/1399 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> Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797. F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797. Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>. Academic Press, 2015. <a href="https://doi.org/10.1016/j.jco.2015.06.002">https://doi.org/10.1016/j.jco.2015.06.002</a>. F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” <i>Journal of Complexity</i>, vol. 31, no. 6. Academic Press, pp. 773–797, 2015. Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:<a href="https://doi.org/10.1016/j.jco.2015.06.002">10.1016/j.jco.2015.06.002</a>. Pausinger, F., &#38; Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. Academic Press. <a href="https://doi.org/10.1016/j.jco.2015.06.002">https://doi.org/10.1016/j.jco.2015.06.002</a> 17922018-12-11T11:54:02Z2026-04-09T14:26:05Z