Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T05:51:30.234Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Proof of Integration by Parts for the Perron Integral

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen
P. S. Bullen*
Affiliation:
University of British ColumbiaVancouver, B.C.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

26A39
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 2 , 01 June 1985 , pp. 195 - 199
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.Google Scholar
2. Bullen, P.S., Integration by parts for Perron integrals, to appear.Google Scholar
3. Bullen, P.S. The Burkill approximately continuous integral II, Math. Chron., 12 (1983), pp. 93–98.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. 493–507.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. 394–398; 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. 558–560; M.R., 9, 179.Google Scholar
7. Mařík, J., Základytheorie integrálu euklidoryćh prostorech, II, Časopis Pěst, 77 (1952), pp. 25–145; M.R., 15(2), 691.Google Scholar
8. McShane, E.J., On Perron integration, Bull. Amer. Math. Soc, 48 (1942), pp. 718–726; 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. 227–235; M.R.,8, 506.Google Scholar