---
_id: '1792'
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.
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.
article_processing_charge: No
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
- first_name: Anne
  full_name: Svane, Anne
  last_name: Svane
citation:
  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>
  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>
  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>.
  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.
  ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy
    systems. Journal of Complexity. 31(6), 773–797.
  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>.
  short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2026-04-09T14:26:05Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
external_id:
  isi:
  - '000362926900001'
intvolume: '        31'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 773 - 797
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5320'
quality_controlled: '1'
related_material:
  record:
  - id: '1399'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 31
year: '2015'
...