Real Analysis Exchange

An Alternate Approach to the McShane Integral

B. Bongiorno, L. Di Piazza, and K. Musiał

Full-text: Open access

Abstract

The classical McShane integral has been generalized by D.H. Fremlin [2] to the case of an arbitrary $\sigma$-finite outer regular quasi-Radon measure space. We present an alternate approach to the Fremlin integral for a non-atomic, finite quasi-Radon space.

Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 829-848.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995418

Mathematical Reviews number (MathSciNet)
MR1778536

Zentralblatt MATH identifier
1021.28008

Subjects
Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10]
Secondary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]

Keywords
vector valued function McShane integral

Citation

Bongiorno, B.; Di Piazza, L.; Musiał, K. An Alternate Approach to the McShane Integral. Real Anal. Exchange 25 (1999), no. 2, 829--848. https://projecteuclid.org/euclid.rae/1230995418


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References

  • D. H. Fremlin, Topological Riesz spaces and measure theory, Cambridge Univ. Press, (1974).
  • D. H. Fremlin, The generalized McShane integral, Illinois J. Math., 39(1995), 39–67.
  • R. A. Gordon, The integrals of Lebesgue, Denjoy, Perron and Henstock, Graduate Studies in Matm., vol. 4(1994), AMS.
  • E. Marczewski and R. Sikorski, Remarks on measure and category, Coll. Math., 2(1949), 13–19.
  • E. J. McShane, Unified integration, Academic Press, San Diego, (1983).