Measure and Integration Publications 1997-2011 [Paperback]

This collection of Heinz K?nigs publications connects to his book of 1997 Measure and Integration and presents significant developments in the subject from then up to the present day. The result is a consistent new version of measure theory, including selected applications. The basic step is the introduction of the inner (bullet) and outer (bullet) premeasures and their extension to unique maximal measures. New envelopes for the initial set function (to replace the traditional Carath?odory outer measures) have been created, which lead to much simpler and more explicit treatment. In view of these new concepts, the main results are unmatched in scope and plainness, as well as in explicitness. Important examples are the formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits.This collection of Heinz K?nigs publications connects to his 1997 book of the same title, reviewing significant developments in the subject from then to now. The result is a consistent new examination of measure theory, exploring new concepts and applications.Image measures and the so-called image measure catastrophe.- The product theory for inner premeasures.- Measure and Integration: Mutual generation of outer and inner premeasures.- Measure and Integration: Integral representations of isotone functionals.- Measure and Integration: Comparison of old and new procedures.- What are signed contents and measures?- Upper envelopes of inner premeasures.- On the inner Daniell-Stone and Riesz representation theorems.- Sublinear functionals and conical measures.- Measure and Integration: An attempt at unified systematization.- New facts around the Choquet integral.- The (sub/super)additivity assertion of Choquet.- Projective limits via inner premeasures and the trueWiener measure.- Stochastic processes in terms of inner premeasures.- New versions of the Radon-Nikod?m theorem.- The Lebesgue decomposition theorem for arbitrary contents.- The new maximal mel“b