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The pn-integral

Published online by Cambridge University Press:  09 April 2009

P. S. Bullen
P. S. Bullen
Affiliation:
Department of Mathematics, The University of British ColumbiaVancouver, 8 Canada
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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].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 2 , September 1972 , pp. 219 - 236
Copyright
Copyright © Australian Mathematical Society 1972

References

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