Geodesic
The Integration of Exact Peano Derivatives
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 334-340

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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.
DOI : 10.4153/CMB-1986-051-8
Mots-clés : 26A24, 26A39 
Cross, G. E. The Integration of Exact Peano Derivatives. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 334-340. doi: 10.4153/CMB-1986-051-8
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