Titlebook: Non-Additive Measure and Integral; Dieter Denneberg Book 1994 Springer Science+Business Media Dordrecht 1994 artificial intelligence.bound

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insipid

Construction of Measures using Topology,ciently many compact sets allows to construct broad classes of measures starting with finitely additive set functions which are regular, i.e. compatible with the given topology. On the real line, essentially these are the Lebesgue-Stieltjes measures. The main idea of this construction generalizes to

cloture

Distribution Functions, Measurability and Comonotonicity of Functions, the next chapter, the integral. No measurability requirements have to be imposed on the function if the set function is defined on the whole power set. For many questions this can be supposed but for some topics (Radon-Nikodym-Theorem, conditional expectation) set functions with restricted domains

bourgeois

修正案

The Symmetric Integral,tions. The alternative integral to be defined here, coincides with the usual integral in all cases of additive set functions. For nonadditive set functions our old integral and the new one differ in two relevant points: asymmetry is replaced by symmetry and comonotonic additivity is lost for functio

Semblance

絕緣

Nullfunctions and the Lebesgue Spaces Lp, in the σ-additive theory) there are functions, not identically zero, having norm nought. Those are the nullfunctions, we start with. Then the Lebesgue space ..(.) of a submodular . is shown to be a normed linear space and to be a Banach space if . is continuous from below. These results translate t

慢跑鞋

Esalate

Densities and the Radon-Nikodym Theorem,is absolutely continuous with respect to ., . ? .. In case of measures the condition . ? . is also sufficient for . having a density. This is the important Radon-Nikodym theorem. Closely related to these questions is the problem of representing a given functional on a function space through an integ