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Non-Additive Measure and Integral / Edition 1
     

Non-Additive Measure and Integral / Edition 1

by D. Denneberg
 

ISBN-10: 079232840X

ISBN-13: 9780792328407

Pub. Date: 05/31/1994

Publisher: Springer Netherlands

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

Overview

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.

Product Details

ISBN-13:
9780792328407
Publisher:
Springer Netherlands
Publication date:
05/31/1994
Series:
Theory and Decision Library B Series , #27
Edition description:
1994
Pages:
178
Product dimensions:
8.27(w) x 11.69(h) x 0.02(d)

Table of Contents

Preface. 1. Integration of Monotone Functions on Intervals. 2. Set Functions and Caratheodory Measurability. 3. Construction of Measures using Topology. 4. Distribution Functions, Measurability and Comonotonicity of Functions. 5. The Asymmetric Integral. 6. The Subadditivity Theorem. 7. The Symmetric Integral. 8. Sequences of Functions and Convergence Theorems. 9. Nullfunctions and the Lebesgue Spaces Lp. 10. Families of Measures and their Envelopes. 11. Densities and the Radon-Nikodym Theorem. 12. Products. 13. Representing Functionals as Integrals. References. Index.

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