{"scopus_import":1,"quality_controlled":"1","related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"title":"A Koksma-Hlawka inequality for general discrepancy systems","_id":"1792","author":[{"first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anne","full_name":"Svane, Anne","last_name":"Svane"}],"doi":"10.1016/j.jco.2015.06.002","abstract":[{"lang":"eng","text":"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."}],"oa_version":"None","publication_status":"published","issue":"6","publication":"Journal of Complexity","type":"journal_article","date_updated":"2023-09-07T11:41:25Z","publist_id":"5320","volume":31,"language":[{"iso":"eng"}],"intvolume":"        31","day":"01","publisher":"Academic Press","year":"2015","status":"public","page":"773 - 797","date_published":"2015-12-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","department":[{"_id":"HeEd"}],"month":"12","date_created":"2018-12-11T11:54:02Z","citation":{"chicago":"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>.","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","apa":"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>","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ama":"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>","mla":"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>.","ieee":"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."}}