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The Integration of Exact Peano Derivatives

Published online by Cambridge University Press:  20 November 2018

G. E. Cross
G. E. Cross*
Affiliation:
Department of Purk Mathematics, University of WaterlooWaterloo, Ontario N2L 3G1
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Abstract

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It is well known that the Riemann-complete integral (or equivalently the Perron integral) integrates an everywhere finite ordinary first derivative (which may be thought of as a Peano derivative of order one). It is also known that the Cesàro-Perron integral of order (n - 1) integrates an everywhere finite Peano derivative of order n. The present work concerns itself with necessary and sufficient conditions for the Riemann-complete integrability of an exact Peano derivative of order n. It is shown that when the integral exists, it can be expressed as the ‘Henstock' limit of the sum of a particular kind of interval function. All functions considered will be real valued.

Keywords

26A24, 26A39
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 334 - 340
Copyright
Copyright © Canadian Mathematical Society 1986

References

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