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.
- James Foran, A note on Lusin’s condition $(N).$, Fund. Math. 90 (1975/76), no. 2, 181–186. MR 407220, DOI https://doi.org/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
J. Foran, A note on Lusin’s condition (N), Fund. Math. 90 (1976), 181-186.
S. Saks, Theory of the integral, 2nd rev. ed., Dover, New York, 1937.