Measure and Integration: Publications 1997-2011
Measure and Integration: Publications 1997-2011 By Heinz König (auth.)
2012 | 512 Pages | ISBN: 3034803818 | PDF | 17 MB
2012 | 512 Pages | ISBN: 3034803818 | PDF | 17 MB
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.
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