Measure and Integration
This collection of Heinz König’s 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 Carathéodory 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.
Heinz König’s recent and most influential works in one single volume For the first time ever: Entirely uniform treatment of abstract and topological measure theoryNew “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which leads to much simpler and more explicit treatmentThe incorporation of non-sequential and of inner regular versions leads to much more comprehensive results