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Additivity of the Pn -Integral (2)

Published online by Cambridge University Press:  20 November 2018

G. E. Cross
G. E. Cross*
Affiliation:
University of Waterloo, Waterloo, Ontario
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The problem of additivity of the Pn -integral on abutting intervals was considered in [2] and in [5]. It was noted in [2] that the necessary and sufficient conditions for additivity for the P 2-integral obtained by Skvorcov in [5] could be completely generalized to the Pn -integral, n> 2, if a key lemma (corresponding to Skvorcov's Lemma 3 [6]) could be proved. We provide a proof of that lemma in this paper and hence obtain the general additivity result.

The definitions and notation of [2] are used in the following, except that we shall take the following as the definition of Pn -major and minor functions:

Definition 1.1. Let f(x) be a function defined in [a, b] and let a 1, i = 1, 2, …, n, be fixed points such that a = a 1 < a 2 < … < an = b.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 506 - 512
Copyright
Copyright © Canadian Mathematical Society 1982

References

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