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On the Henstock Strong Variational Integral

Published online by Cambridge University Press:  20 November 2018

B. S. Thomson
B. S. Thomson*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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The theory of integration in division spaces introduced by Henstock ([3], [4]) serves to unite and simplify much of the classical material on nonabsolute integration as well as to provide a new approach to Lebesgue integration. In this paper we sketch a simplified approach to the division space theory and show how it can lead rapidly to the standard Lebesgue-type theory without a substantial departure from the usual methods; some applications to integration in locally compact spaces are briefly developed.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 87 - 99
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Dinculeanu, N., Vector measures, Pergamon Press, New York, 1967.Google Scholar
2. Henstock, R., Theory of integration, Butterworth, London, 1963.Google Scholar
3 Linear analysis, Butterworth, London, 1967.Google Scholar
4. Henstock, R., Generalized integrals of vector-valued functions, Proc. London Math. Soc. (3) 19 (1969), 509-536.Google Scholar
5. McShane, E. J., A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner, and stochastic integrals, Mem. Amer. Math. Soc, no. 88, 1969.Google Scholar