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Changing the order of integration

Published online by Cambridge University Press:  09 April 2009

E. R. Love
E. R. Love
Affiliation:
University of Melbourne
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Repeated improper Riemann integrals arise in a variety of contexts, and the validity of changing the order of integration is often in question. Fubini's theorem ensures the equality of two repeated Lebesgue integrals when one of them is absolutely convergent. For many years I have assumed that an analogous test is applicable to repeated improper R-integrals, since they will be absolutely convergent and therefore in agreement with the corresponding L-integrals.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 421 - 432
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Mařík, J., ‘Základy Theorie Integrálu v Euklidových Prostoreh’ (Foundations of the theory of the integral in Euclidean spaces), Časpis Pěst. Mat. 77 (1952) 1–51, 125–145, 267–301; Czech, English review by E. Hewitt, Math. Rev. 15 (1954) 691–692.Google Scholar
[2]Henstock, R., Theory of Integration (Butterworths, 1963).Google Scholar