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The Perron integral of order k in Riesz spaces

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli, 1, 06123, Perugia, Italy

    Antonio Boccuto

  2. Department of Mathematics, Moscow State University, 119991, Moscow, Russia

    Valentin A. Skvortsov

  3. Instytut Matematyki, Uniwersytet Kazimierza Wielkiego, 85065, Bydgoszcz, Poland

    Valentin A. Skvortsov

Authors
  1. Antonio Boccuto
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  2. Valentin A. Skvortsov
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Corresponding author

Correspondence to Antonio Boccuto.

Additional information

Dedicated to Prof. W. A. J. Luxemburg in honor of his 80th birthday.

This paper was presented at the VI “Positivity Meeting”, El Escorial, July 20–24th 2009. Supported by University of Perugia, RFFI-08-01-00669 and NSh-322.2010.1.

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Boccuto, A., Skvortsov, V.A. The Perron integral of order k in Riesz spaces. Positivity 14, 595–612 (2010). https://doi.org/10.1007/s11117-010-0054-z

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