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Non-Additive Measure and Integral

  • Dieter Denneberg

Part of the Theory and Decision Library book series (TDLB, volume 27)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Dieter Denneberg
    Pages 15-33
  3. Dieter Denneberg
    Pages 35-43
  4. Dieter Denneberg
    Pages 61-70
  5. Dieter Denneberg
    Pages 71-86
  6. Dieter Denneberg
    Pages 87-92
  7. Dieter Denneberg
    Pages 93-102
  8. Dieter Denneberg
    Pages 103-121
  9. Dieter Denneberg
    Pages 123-127
  10. Dieter Denneberg
    Pages 129-144
  11. Dieter Denneberg
    Pages 145-153
  12. Dieter Denneberg
    Pages 155-170
  13. Back Matter
    Pages 171-180

About this book

Introduction

Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc.
Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory.
In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.

Keywords

artificial intelligence bounded mean oscillation decision theory game theory linear optimization mathematics measure probability theory statistics

Authors and affiliations

  • Dieter Denneberg
    • 1
  1. 1.Universität BremenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2434-0
  • Copyright Information Springer Science+Business Media B.V. 1994
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4404-4
  • Online ISBN 978-94-017-2434-0
  • Buy this book on publisher's site