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A Constructive Definition of the Approximately Continuous Denjoy Integral

Published online by Cambridge University Press:  20 November 2018

Y. Kubota
Y. Kubota*
Affiliation:
Ibaraki University, Mito, Japan
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The author has defined [2] the approximately continuous Denjoy integral (AD-integral) which includes exactly the general Denjoy integral and the AP-integral defined by Burkill [2].

The aim of this paper is to give a constructive definition of the AD-integral.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 103 - 108
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Burkill, J. C., The approximately continuous Perron integral, Math. Z. 34 (1931), 270-278.Google Scholar
2. Kubota, Y., An integral of the Denjoy type. I, II, III, Proc. Japan Acad. 40 (1964), 713-717; 42 (1966), 737-742; 43 (1967), 441-444.Google Scholar
3. Kubota, Y., A characterization of the approximately continuous Denjoy integral, Canad. J. Math. 22 (1970), 219-226.Google Scholar
4. Saks, S., Theory of the integral, G. E. Stechert, New York, 1937.Google Scholar