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Perron Integrability Versus Lebesgue Integrability

Published online by Cambridge University Press:  20 November 2018

Arlo W. Schurle
Arlo W. Schurle*
Affiliation:
Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Abstract

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The paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.

Keywords

26A3926A42
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 463 - 468
Copyright
Copyright © Canadian Mathematical Society 1985

References

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