By D. Denneberg
Non-Additive degree and Integral is the 1st systematic method of the topic. a lot of the additive concept (convergence theorems, Lebesgue areas, illustration theorems) is generalized, a minimum of for submodular measures that are characterised via having a subadditive quintessential. the speculation is of curiosity for functions to monetary choice conception (decisions less than possibility and uncertainty), to stats (including trust features, fuzzy measures) to cooperative online game conception, synthetic intelligence, assurance, and so forth.
Non-Additive degree and Integral collects the result of scattered and sometimes remoted techniques to non-additive measures and their integrals which originate in natural arithmetic, capability idea, information, online game concept, financial choice thought and different fields of program. It unifies, simplifies and generalizes identified effects and vitamins the speculation with new effects, hence offering a valid foundation for purposes and additional examine during this transforming into box of accelerating curiosity. It additionally comprises basic result of sigma-additive and finitely additive degree and integration idea and sheds new gentle on additive thought. Non-Additive degree andIntegral employs distribution capabilities and quantile capabilities as foundation instruments, hence last just about the commonplace language of likelihood concept.
as well as serving as an enormous reference, the publication can be utilized as a arithmetic textbook for graduate classes or seminars, containing many workouts to aid or complement the textual content.