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The Exceptional Sets in the Definition of the Pn-Integral

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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Abstract

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It has been recently observed by S. N. Mukhopadhyay that the various definitions of the Pn-integral are not complete unless it is shown that the exceptional scattered set allowed in the definition is not important. Utilizing the fact that on the real line a scattered set is countable, and adapting known methods for coping with exceptional countable sets, it is proved that the definitions of the Pn-integral are complete. It is then clear that the concept of scattered set is not essential to the definition of the Pn-integral.

Keywords

26A3926A51
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 385 - 391
Copyright
Copyright © Canadian Mathematical Society 1982

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