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Non-Additive Measure and Integral : Theory and Decision Library B - Dieter Denneberg

Non-Additive Measure and Integral

Theory and Decision Library B

Hardcover Published: 31st May 1994
ISBN: 9780792328407
Number Of Pages: 178

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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.

Preface
Integration of Monotone Functions on Intervalsp. 1
Set Functions and Caratheodory Measurabilityp. 15
Construction of Measures using Topologyp. 35
Distribution Functions, Measurability and Comonotonicity of Functionsp. 45
The Asymmetric Integralp. 61
The Subadditivity Theoremp. 71
The Symmetric Integralp. 87
Sequences of Functions and Convergence Theoremsp. 93
Nullfunctions and the Lebesgue Spaces L[subscript p]p. 103
Families of Measures and their Envelopesp. 123
Densities and the Radon-Nikodym Theoremp. 129
Productsp. 145
Representing Functionals as Integralsp. 155
Referencesp. 171
Indexp. 175
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792328407
ISBN-10: 079232840X
Series: Theory and Decision Library B
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 178
Published: 31st May 1994
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 24.18 x 16.26  x 1.68
Weight (kg): 0.46

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