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Integration by parts for the generalized Riemann-Stieltjes integral

Part of: Real functions

Published online by Cambridge University Press:  09 April 2009

W. F. Pfeffer
W. F. Pfeffer
Affiliation:
Department of Mathematics University of CaliforniaDavis, California 95616, U.S.A.
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Abstract

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Under the standard assumptions, the formula for integration by parts is obtained by a straightforward calculation.

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 229 - 233
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Gordon, L. and Lasher, S.. ‘An elementary proof of integration by parts for the Perron integral’, Proc. Anier. Math. Soc. 18 (1967), 394–398.CrossRefGoogle Scholar
[2]Marik, J., ‘Foundation of the theory of an integral in Euclidean spaces’, Časopis Pěst. Mat. 77 (1952), 1–51. 125–144, 267–301 (translated to English by Trudzik, L. I., Dept. of Math., Univ. of Melbourne, Parkville, Victoria 3052, Australia).Google Scholar
[3]McLeod, R. M., The generalized Riemann integral (MAA, Providence, 1980).CrossRefGoogle Scholar
[4]Pfeffer, W. F., ‘The Riemann-Stieltjes approach to integration’, TWISK 187, CSIR, Pretoria, 1980.Google Scholar
[5]Saks, S., Theory of the integral (Hafner, New York, 1939).Google Scholar