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NonAdditive Measure and Integral (Theory and Decision Library B, 27),New
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NonAdditive 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.NonAdditive Measure and Integral collects the results of scattered and often isolated approaches to nonadditive 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 sigmaadditive and finitely additive measure and integration theory and sheds new light on additive theory. NonAdditive 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.
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