Measure and Integration (eBook, PDF)
Publications 1997-2011
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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 descri...
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.
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.
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