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A wide Perron integral

Published online by Cambridge University Press:  17 April 2009

D. N. Sarkhel
D. N. Sarkhel
Affiliation:
Department of Mathematics, University of Kalyani, Kalyani, West Bengal, India741235.
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Abstract

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In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 233 - 251
Copyright
Copyright © Australian Mathematical Society 1986

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