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A problem in two-dimensional integration

Part of: Real functions

Published online by Cambridge University Press:  09 April 2009

Ralph Henstock
Ralph Henstock
Affiliation:
School of Physical Sciences (Mathematics)The New University of UlsterColeraine Northern, Ireland
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Abstract

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If two functions of a real variable are integrable over two intervals, say of t, τ, respectively, then the product of the two functions should be integrable over the rectangular product of the two intervals of t and τ. For the Lebesgue integral, definable using non-negative functions alone, the proof is easy. For non-absolute integrals such as the Perron, Çesàro-Perron, and Marcinkiewicz-Zygmund integrals we have difficulties since the functions cannot be assumed non-negative. But the present paper gives a proof.

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 386 - 404
Copyright
Copyright © Australian Mathematical Society 1983

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