Non-Additive Measure and Integral

1994
ISBN: 978-0-7923-2840-7
Verlag: Springer Netherlands

Buch, Englisch, 178 Seiten, Format (B × H): 215 mm x 303 mm, Gewicht: 1000 g

Reihe: Theory and Decision Library B

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.
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. 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.

Zielgruppe

Research

Autoren/Hrsg.

Denneberg, D.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie

Inhaltsverzeichnis

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.