Measure and Integration

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This volume presents a collection of twenty-five of Heinz König’s recent and most influential works. Connecting to his book of 1997 “Measure and Integration”, the author has developed a consistent new version of measure theory over the past years. For the first time, his publications are collected here in one single volume.Key features include:- A first-time, original and entirely uniform treatment of abstract and topological measure theory- The introduction of the inner • and outer • premeasures and their extension to unique maximal measures- A simplification of the procedure formerly described in Chapter II of the author’s previous book - The creation of new “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which lead to much simpler and more explicit treatment- The formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far beyond the countably determined ones- The incorporation of non-sequential and of inner regular versions, which leads to much more comprehensive results- Significant applications to stochastic processes.“Measure and Integration: Publications 1997–2011” will appeal to both researchers and advanced graduate students in the fields of measure and integration and probabilistic measure theory.