Real Analysis Exchange

A concept of generalized absolute continuity for the ℱ-integral

Thierry De Pauw

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Abstract

We define a concept of generalized absolute continuity for additive functions of figures. This makes it possible to give a descriptive definition of the ℱ-integral introduced by Pfeffer in 1993. Finally, we discuss a possible extension to additive functions of sets of bounded variation.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 350-361.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515227

Mathematical Reviews number (MathSciNet)
MR1433620

Zentralblatt MATH identifier
0891.26005

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
F integral

Citation

De Pauw, Thierry. A concept of generalized absolute continuity for the ℱ-integral. Real Anal. Exchange 22 (1996), no. 1, 350--361. https://projecteuclid.org/euclid.rae/1338515227


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References

  • B. Bongiorno and W. Pfeffer, A concept of absolute continuity and a Riemann type integral, Commentationes Mathematicae Universitatis Carolinae, 33(2) (1992), 189–196.
  • J. Kurzweil and J. Jarní k, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Analysis Exchange, 17 (1991-92), 110–139.
  • W. Pfeffer, A Descriptive Definition of a Variational Integral and Apllications, Indiana University Mathematics Journal, 40(1) (1991), 259–270.
  • W. Pfeffer, The Gauss-Green Theorem, Advances in Mathematics, 87 (1993), 93–147.
  • W. Pfeffer, An Integral in Geometric Measure Theory, Atti Sem. Mat. Fis. Univ. Modena, XLI (1993), 59–76.
  • W. Pfeffer, The Riemann approach to integration. Local geometric theory, Cambridge University Press, Cambridge Tracts in Mathematics, 109, Cambridge-New York-Melbourne, 1993.
  • S. Saks, Theory of the integral, Dover Publications, Inc. Second revised ed., New York, 1964.