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Ricerche di Matematica

, Volume 68, Issue 2, pp 333–339 | Cite as

A Riemann-type theorem for a Riemann-type integral

  • Aljoša VolčičEmail author
Article
  • 55 Downloads

Abstract

For functions which are Henstock–Kurzweil integrable but not Lebesgue-integrable we prove a theorem which resembles the Riemann theorem on the rearrangement of conditionally convergent series.

Keywords

Rearrangement Henstock–Kurzweil integral Fubini-Tonelli theorem 

Mathematics Subject Classification

26A39 40A10 

Notes

Acknowledgements

The author wants to thank Washek Pfeffer, Piero Papini and Zoltán Buczolich for helpful discussions on several aspects of the paper.

References

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    Rao, G., Tulone, F.: Henstock integral and Dini-Riemann theorem. Le Matematiche, vol. LXIV fasc. II, (2009) 71–77Google Scholar

Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of CalabriaRendeItaly

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