The Integration of Exact Peano Derivatives
G. E. Cross · Canadian Mathematical Bulletin · 1986
Abstract 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 ordern.The present work concerns itself with necessary and sufficient conditions for the Riemann-complete integrability of an exact Peano derivative of ordern.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.