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Integration of Non-Measurable Functions

Published online by Cambridge University Press:  20 November 2018

Elias Zakon
Elias Zakon*
Affiliation:
University of Windsor, Canada
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This is primarily an expository paper based on (and generalizing) some ideas of J. Pierpont [6], W.H. Young [8], R. L. Jeffery [4] and S. C. Fan [2]. Our aim is to give a simple and easily applicable theory of integration for arbitrary extended - real functions over arbitrary sets in a measure space. This will be achieved by using a generalized version of Pierpont1 s upper and lower integrals (with the upper integral playing the main role), and by appropriately defining the operations in the extended real number system, henceforth denoted by E*, so as to make it a commutative semigroup under addition and multiplication.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 3 , August 1966 , pp. 307 - 330
Copyright
Copyright © Canadian Mathematical Society 1966

References

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8. Young, W.H., On the general theory of integration, Philos. Trans. 204(1905), 221-252.Google Scholar