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An Approximately Continuous Perron Integral

Published online by Cambridge University Press:  20 November 2018

Y. Kubota
Y. Kubota*
Affiliation:
Ibaraki University, Mito, Japan
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J. C. Burkill [1] has defined the AP-integral whose indefinite integral is approximately continuous. An (approximately continuous) function which is approximately derivable at all points of an interval is necessarily an indefinite AP-integral of its approximate derivative.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 261 - 263
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Burkill, J. C., The approximately continuous Perron integral. Math. Z. 34 (1931), 270-278 Google Scholar
2. Burkill, J. C., Integrals and trigonometric series, Proc. London Math. Soc. (3) 1 (1951), 46-57.Google Scholar
3. Goffman, C. and Neugerbauer, C. J., On approximate derivatives, Canad. J. Math. 11 (1960), 962-966.Google Scholar