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On ω-approximately continuous Perron-Stieltjes and Denjoy-Stieltjes integral

Published online by Cambridge University Press:  09 April 2009

D. N. Sarkhel
D. N. Sarkhel
Affiliation:
Department of Mathematics, R. K. Mission Vidyamandira, Belur Math. Howrah, West-Bengal, India.
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The aim of the present paper is to introduce a definition of the Perron-Stieltjes integral employing the notion of approximate derivative with respect to a nondecreasing function ω and to study some of the properties of the integral. Various authors have studied the Perron integral and Perron-Stieltjes integral in different ways, most of which can be found in the references appended in the list of the bibliography. Among them Ridder [10] uses the concept of approximate co-derivative but he assumes that the monotone function a associated with co is continuous. Finally we consider a more general type of integral, the co-approximately continuous Denjoy-Stieltjes integral, defined descriptively by the method of Saks [11].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 129 - 152
Copyright
Copyright © Australian Mathematical Society 1974

References

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