Advanced Integration Theory / Edition 1

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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. 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. 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.
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Editorial Reviews

Booknews
This book gives a general definition of the abstract integral using the Daniell method. A consequence of this approach is that integration theory on Hausdorff topological spaces appears to be a special case of abstract integration theory. The theory of vector lattices is presented, since it is a tool for the development of the abstract theory. 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 d-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. Exercises accompany each section. For graduate students and researchers. Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

  • ISBN-13: 9780792352341
  • Publisher: Springer Netherlands
  • Publication date: 10/31/1998
  • Series: Mathematics and Its Applications (closed) Series , #454
  • Edition description: 1998
  • Edition number: 1
  • Pages: 24
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.81 (d)

Table of Contents

Preface
Acknowledgements
Introduction 1
Suggestions to the Reader 5
0 Preliminaries 7
1 Vector Lattices 21
2 Elementary Integration Theory 279
3 L[superscript p]-Spaces 447
4 Real Measures 549
5 The Radon-Nikodym Theorem. Duality 637
6 The Classical Theory of Real Functions 681
Historical Remarks 805
Name Index 808
Subject Index 810
Symbol Index 849
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