## Real Analysis Exchange

### An Alternate Approach to the McShane Integral

#### 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

https://projecteuclid.org/euclid.rae/1230995418

Mathematical Reviews number (MathSciNet)
MR1778536

Zentralblatt MATH identifier
1021.28008

#### 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

#### 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).