Abstract
In [5] James defined an nth order Perron integral, the Pn- ntegral, and developed its properties. His proofs are often indirect, using properties of the CkP-integrals of Burkill, [3]. In this paper a simpler definition of the Pn-integral is given — the original and not completely equivalent definition, was probably chosen as James considered this integral as a special case of one defined in terms of certain symmetric derivatives, [5], when end points of the interval of definition had naturally to be avoided. We then give direct proofs of the basic results, give a characterization of Pn-primitives, and connect the integral with certain work of Denjoy, [4].
Publisher
Cambridge University Press (CUP)
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1. The Perron integral of order k in Riesz spaces;Positivity;2010-04-09
2. Integration by parts for some general integrals;Bulletin of the Australian Mathematical Society;1988-02
3. Riemann derivatives and general integrals;Bulletin of the Australian Mathematical Society;1987-04
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