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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On extending the Lebesgue integral

Author: James Foran
Journal: Proc. Amer. Math. Soc. 81 (1981), 85-88
MSC: Primary 26A42; Secondary 26A39
MathSciNet review: 589142
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Abstract: In this paper continuous extensions of the Lebesgue Integral which integrate their almost everywhere approximate derivatives are considered. First, those extensions which are generated by a single function are characterized. Then the largest extension which is contained in all maximal extensions is considered and shown to contain the wide sense Denjoy Integral. Finally, properties are given which characterize this largest extension.

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Keywords: Lebesgue Integral
Article copyright: © Copyright 1981 American Mathematical Society