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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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