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A Riemann integral in a locally compact Hausdorff space

Part of: Set functions and measures on spaces with additional structure Real functions Maps and general types of spaces defined by maps Classical measure theory

Published online by Cambridge University Press:  09 April 2009

S. I. Ahmed  and
W. F. Pfeffer
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.

MSC classification

Secondary: 28A25: Integration with respect to measures and other set functions 26A42: Integrals of Riemann, Stieltjes and Lebesgue type 54C30: Real-valued functions 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 115 - 137
Copyright
Copyright © Australian Mathematical Society 1986

References

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