Proceedings of the American Mathematical Society

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



A Daniell-Stone approach to the general Denjoy integral

Author: Cornel Leinenkugel
Journal: Proc. Amer. Math. Soc. 114 (1992), 39-52
MSC: Primary 26A39; Secondary 26A24, 28C05
MathSciNet review: 1031669
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A39, 26A24, 28C05

Retrieve articles in all journals with MSC: 26A39, 26A24, 28C05

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society