Measure and Integration: Publications 1997-2011 - Tapa dura

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Heinz König is a distinguished analyst, who has given lasting contributions to functional analysis, distribution theory, convex analysis, mathematical economics and many other fields of mathematics. Typical of his work is the analysis or creation of basic new concepts from most original viewpoints. Heinz König gave a large number of original, short and elegant proofs of fundamental results in mathematics. Most remarkable is the new theory of measure and integration he developed in the last two decades.

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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.