@article{1792,
  abstract     = {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.},
  author       = {Pausinger, Florian and Svane, Anne},
  journal      = {Journal of Complexity},
  number       = {6},
  pages        = {773 -- 797},
  publisher    = {Academic Press},
  title        = {{A Koksma-Hlawka inequality for general discrepancy systems}},
  doi          = {10.1016/j.jco.2015.06.002},
  volume       = {31},
  year         = {2015},
}