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(PVB) functions and integration

Part of: Real functions

Published online by Cambridge University Press:  09 April 2009

D. N. Sarkhel  and
A. B. Kar
D. N. Sarkhel
Affiliation:
Department of Mathematics, University of KalyaniKalyani, West Bengal India
A. B. Kar
Affiliation:
Department of Mathematics, University of KalyaniKalyani, West Bengal India
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Abstract

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We introduce the notion of functions of bounded proximal variation and the notion of orderly connected topology on the real line. Using these notions, we define in a novel way an integral of Perron type, including virtually all the known integrals of Perron and Denjoy types and admitting mean value theorems and integration by parts and the analog of Marcinkiewicz theorem for the ordinary Perron integral.

MSC classification

Secondary: 26A45: Functions of bounded variation, generalizations 26A46: Absolutely continuous functions 26A39: Denjoy and Perron integrals, other special integrals 26A03: Foundations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 335 - 353
Copyright
Copyright © Australian Mathematical Society 1984

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