A Daniell-Stone approach to the general Denjoy integral
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- by Cornel Leinenkugel PDF
- Proc. Amer. Math. Soc. 114 (1992), 39-52 Request permission
Abstract:
In this note we shall introduce a, as far as we know, new kind of derivative (diagonal derivative), characterizing a certain class of functions ${\mathcal {E}_d}$ and a generalized Daniell integral ${I_d}$ on this class. We follow Leinert and König to obtain a class of integrable functions $\mathcal {L}_d^1$ belonging to ${\mathcal {E}_d}$, using the method of Daniell-Stone integration without the lattice condition as described in [1] or similarly in [3]. Our main purpose is to show that we obtain exactly the Denjoy integrable functions.References
- Michael Leinert, Daniell-Stone integration without the lattice condition, Arch. Math. (Basel) 38 (1982), no. 3, 258–265. MR 656192, DOI 10.1007/BF01304785
- Heinz König, Integraltheorie ohne Verbandspostulat, Math. Ann. 258 (1981/82), no. 4, 447–458 (German). MR 650949, DOI 10.1007/BF01453978 S. Saks, Theory of the integral, Hafner Publishing Co., New York and Warszawa, 1937.
- Andrew M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, vol. 659, Springer, Berlin, 1978. MR 507448
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 39-52
- MSC: Primary 26A39; Secondary 26A24, 28C05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1031669-4
- MathSciNet review: 1031669