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A Simple Proof of Integration by Parts for the Perron Integral

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen*
Affiliation:
University of British ColumbiaVancouver, B.C.
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Abstract

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This note presents a very simple proof for the integration by parts formula for the Perron integral.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Bruckner, A., Differentiation of Real Functions, Lecture Notes in Math. No. 659, Berlin-Heidelberg-New York, 1978; M. R., 80h, 26002.CrossRefGoogle Scholar
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3. Bullen, P.S. The Burkill approximately continuous integral II, Math. Chron., 12 (1983), pp. 9398.Google Scholar
4. Chakrabarti, P.S. and Mukhopadhyay, S.N., Integration by parts for certain approximate CP-integrals, Bull. Inst. Math. Acad. Sinica, 9 (1981), pp. 493507.Google Scholar
5. Gordon, L. and Lasher, S., An elementary proof of integration by parts for the Perron integral, Proc. Amer. Math. Soc, 18 (1967), pp. 394398; M.R., 35, No. 1726.Google Scholar
6. Ionescu-Tulcea, C. T., Sur l'intégration des nombres derivés, C. R. Acad. Sci. Paris, 225 (1949), pp. 558560; M.R., 9, 179.Google Scholar
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8. McShane, E.J., On Perron integration, Bull. Amer. Math. Soc, 48 (1942), pp. 718726; M.R., 4, 75.Google Scholar
9. McShane, E.J. Integration, Princeton, 1944; M.R., 6, 43.Google Scholar
10. Ridder, J., Ueber Definitionen von Perron-Integralen I, Indag. Math., 9 (1947), pp. 227235; M.R.,8, 506.Google Scholar
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