On extending the Lebesgue integral
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- by James Foran PDF
- Proc. Amer. Math. Soc. 81 (1981), 85-88 Request permission
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.References
- James Foran, A note on Lusin’s condition $(N).$, Fund. Math. 90 (1975/76), no. 2, 181–186. MR 407220, DOI 10.4064/fm-90-2-181-186
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 85-88
- MSC: Primary 26A42; Secondary 26A39
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589142-6
- MathSciNet review: 589142