Advanced Integration Theory / Edition 1
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Advanced Integration Theory / Edition 1

by Corneliu Constantinescu, Wolfgang Filter, K. Weber
     
 

ISBN-10: 0792352343

ISBN-13: 9780792352341

Pub. Date: 10/31/1998

Publisher: Springer Netherlands

This book gives a general definition of the (abstract) integral, using the Daniell method. A most welcome consequence of this approach is the fact that integration theory on Hausdorff topological spaces appears simply to be a special case of abstract integration theory. The most important tool for the development of the abstract theory is the theory of vector

Overview

This book gives a general definition of the (abstract) integral, using the Daniell method. A most welcome consequence of this approach is the fact that integration theory on Hausdorff topological spaces appears simply to be a special case of abstract integration theory. The most important tool for the development of the abstract theory is the theory of vector lattices which is presented here in great detail. Its consequent application not only yields new insight into integration theory, but also simplifies many proofs. For example, the space of real-valued measures on a delta-ring turns out to be an order complete vector lattice, which permits a coherent development of the theory and the elegant derivation of many classical and new results.
The exercises occupy an important part of the volume. In addition to their usual role, some of them treat separate topics related to vector lattices and integration theory.
Audience: This work will be of interest to graduate-level students and researchers with a background in real analysis, whose work involves (abstract) measure and integration, vector lattices, real functions of a real variable, probability theory and integral transforms.

Product Details

ISBN-13:
9780792352341
Publisher:
Springer Netherlands
Publication date:
10/31/1998
Series:
Mathematics and Its Applications (closed) Series, #454
Edition description:
1998
Pages:
876
Product dimensions:
6.10(w) x 9.25(h) x 0.07(d)

Table of Contents

Preface. Introduction. Suggestions to the Reader. 0. Preliminaries. 1. Vector Lattices. 2. Elementary Integration Theory. 3. Lp-Spaces. 4. Real Measures. 5. The Radon-Nikodym Theorem Duality. 6. The Classical Theory of Real Functions. Historical Remarks. Name Index. Subject Index. Symbol Index.

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