On extending the Lebesgue integral
Proc. Amer. Math. Soc. 81 (1981), 85-88
Primary 26A42; Secondary 26A39
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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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