Real Analysis Exchange

A note on a Pettis-Kurzweil-Henstock type integral in Riesz spaces.

A. Boccuto and B. Riečan

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Abstract

Recently a connection has been found between the improper Kurzweil-Henstock integral on the real line and the integral over a compact space. In this paper these results are extended to a Pettis-type integral for the case of functions with values in Riesz spaces with ``enough" order continuous functionals.

Article information

Source
Real Anal. Exchange, Volume 28, Number 1 (2002), 153-162.

Dates
First available in Project Euclid: 12 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1150118728

Mathematical Reviews number (MathSciNet)
MR1973976

Zentralblatt MATH identifier
1067.28008

Subjects
Primary: 28B15: Set functions, measures and integrals with values in ordered spaces 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 28B10: Group- or semigroup-valued set functions, measures and integrals 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]

Keywords
Riesz spaces compact topological spaces order continuous linear functionals Henstock-Kurzweil integral Pettis integral

Citation

Boccuto, A.; Riečan, B. A note on a Pettis-Kurzweil-Henstock type integral in Riesz spaces. Real Anal. Exchange 28 (2002), no. 1, 153--162. https://projecteuclid.org/euclid.rae/1150118728


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