, Volume 14, Issue 4, pp 595–612 | Cite as

The Perron integral of order k in Riesz spaces

  • Antonio Boccuto
  • Valentin A. Skvortsov


A Perron-type integral of order k for Riesz-space-valued functions is defined in terms of the Peano derivatives. Some fundamental properties of this integral, including an integration by parts formula, are presented.


Riesz space Perron integral k-convexity Peano derivative Major and minor function Maeda–Ogasawara–Vulikh theorem Integration by parts 

Mathematics Subject Classification (2000)

28B15 46G10 


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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversity of PerugiaPerugiaItaly
  2. 2.Department of MathematicsMoscow State UniversityMoscowRussia
  3. 3.Instytut MatematykiUniwersytet Kazimierza WielkiegoBydgoszczPoland

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