Integration between the Lebesgue integral and the Henstock-Kurzweil integral : its relation to local convex vector spaces
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Bibliographic Information
Integration between the Lebesgue integral and the Henstock-Kurzweil integral : its relation to local convex vector spaces
（Series in real analysis, v. 8）
World Sientific, c2002
- : hard
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Note
Includes bibliograhical references and index
Description and Table of Contents
Description
The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.
Table of Contents
- Contents: Basic Concepts and Properties of y-Integration
- Convergence
- Convergence and Locally Convex Spaces
- An Auxiliary Locally Convex Space
- L-Integration
- M-Integration
- Noncompleteness
- S-Integration
- R-Integration
- An Extension of the Concept of y-Integration
- Differentiation and Integration.
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