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A Riemann integral in a locally compact Hausdorff space

Published online by Cambridge University Press:  09 April 2009

S. I. Ahmed
Affiliation:
Department of Mathematics, King Saud UniversityRiyadh 11451, Saudi Arabia
W. F. Pfeffer
Affiliation:
Department of Mathematics, University of California, Davis, California 95616, U.S.A.
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Abstract

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We present a systematic and self-contained exposition of the generalized Riemann integral in a locally compact Hausdorff space, and we show that it is equivalent to the Perron and variational integrals. We also give a necessary and sufficient condition for its equivalence to the Lebesgue integral with respect to a suitably chosen measure.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1986

References

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