Non-Additive Measure and Integral

"Non-Additive Measure and Integral" takes a 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) and to co-operative game theory, artificial intelligence, insurance, and so on. "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. It also contains fundamental results of s-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 a reference text, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.