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Fubini Theorem For a Certain Type of Integral

Published online by Cambridge University Press:  20 November 2018

Charles A. Hayes Jr.
Charles A. Hayes Jr.*
Affiliation:
University of California, Davis, California
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In (1), the writer defined a process of integration that leads to a kind of Riemann integral under certain rather general conditions. The purpose of this paper is to show how it is possible to use the process of integration of (1) to obtain integrals in a product space that satisfy a Fubini theorem. In this connection, we define a class of integrands that are the analogues of continuous functions in the product space, establish some of their properties, and finally arrive at a Fubini theorem for this class.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 142 - 154
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Hayes, C. A. Jr., A Theory of integration, Can. J. Math., 14 (1962), 577–596.Google Scholar
2. Munroe, M. E., Introduction to measure and integration (Reading, 1955).Google Scholar
3. Hahn, Hans and Rosenthal, Arthur, Set functions (Albuquerque, 1948).Google Scholar