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A Full Descriptive Definition of the Gage Integral

Published online by Cambridge University Press:  20 November 2018

B. Bongiorno ,
W. F. Pfeffer  and
B. S. Thomson
B. Bongiorno
Affiliation:
Department of Mathematics, Simon Fraser University Burnaby, British Columbia V5A 1S6
W. F. Pfeffer
Affiliation:
Department of Mathematics, Simon Fraser University Burnaby, British Columbia V5A 1S6
B. S. Thomson
Affiliation:
Department of Mathematics, Simon Fraser University Burnaby, British Columbia V5A 1S6
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Abstract

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We consider a specific Riemann type integral, called the gage integral. Using variational measures, we characterize all additive functions of intervals that are indefinite gage integrals. The characterization generalizes the descriptive definition of the classical Denjoy-Perron integral to all dimensions.

Keywords

26A3926B30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 395 - 401
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Bongiomo, B., Di Piazza, L. and Skvortsov, V., The essential variation of a function and some convergence theorems, to appear.Google Scholar
2. Bongiomo, B. and Vetro, P., Su un teorema di F. Riesz, Atti Accad. Sci. Lett. Arti Palermo Parte I (4) 37(1979), 3–13.Google Scholar
3. Evans, L. C. and Gariepy, R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992.Google Scholar
4. Falconer, K. J., The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985.Google Scholar
5. Mawhin, J., Generalized multiple Perron integral and the Green-Goursat theorem for differentiable vector fields, Czechoslovak Math. J. 31(1981), 614–632.Google Scholar
6. Pfeffer, W. F., The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993.Google Scholar
7. Saks, S., Theory of the Integral, Dover, New York, 1964.Google Scholar
8. Thomson, B. S., Dérivâtes of Interval Functions, Mem. Amer. Math. Soc. 452, Providence, 1991.Google Scholar