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König, Heinz.
Measure and Integration Publications 1997-2011 / [electronic resource] : by Heinz König. - XI, 508 p. 1 illus. in color. online resource.
Image measures and the so-called image measure catastrophe -- The product theory for inner premeasures -- Measure and Integration: Mutual generation of outer and inner premeasures -- Measure and Integration: Integral representations of isotone functionals -- Measure and Integration: Comparison of old and new procedures -- What are signed contents and measures?- Upper envelopes of inner premeasures -- On the inner Daniell-Stone and Riesz representation theorems -- Sublinear functionals and conical measures -- Measure and Integration: An attempt at unified systematization -- New facts around the Choquet integral -- The (sub/super)additivity assertion of Choquet -- Projective limits via inner premeasures and the trueWiener measure -- Stochastic processes in terms of inner premeasures -- New versions of the Radon-Nikodým theorem -- The Lebesgue decomposition theorem for arbitrary contents -- The new maximal measures for stochastic processes -- Stochastic processes on the basis of new measure theory -- New versions of the Daniell-Stone-Riesz representation theorem -- Measure and Integral: New foundations after one hundred years -- Fubini-Tonelli theorems on the basis of inner and outer premeasures -- Measure and Integration: Characterization of the new maximal contents and measures -- Notes on the projective limit theorem of Kolmogorov -- Measure and Integration: The basic extension theorems -- Measure Theory: Transplantation theorems for inner premeasures. .
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.
9783034803823
Mathematics.
Mathematics.
Measure and Integration.
QA312-312.5
515.42
Measure and Integration Publications 1997-2011 / [electronic resource] : by Heinz König. - XI, 508 p. 1 illus. in color. online resource.
Image measures and the so-called image measure catastrophe -- The product theory for inner premeasures -- Measure and Integration: Mutual generation of outer and inner premeasures -- Measure and Integration: Integral representations of isotone functionals -- Measure and Integration: Comparison of old and new procedures -- What are signed contents and measures?- Upper envelopes of inner premeasures -- On the inner Daniell-Stone and Riesz representation theorems -- Sublinear functionals and conical measures -- Measure and Integration: An attempt at unified systematization -- New facts around the Choquet integral -- The (sub/super)additivity assertion of Choquet -- Projective limits via inner premeasures and the trueWiener measure -- Stochastic processes in terms of inner premeasures -- New versions of the Radon-Nikodým theorem -- The Lebesgue decomposition theorem for arbitrary contents -- The new maximal measures for stochastic processes -- Stochastic processes on the basis of new measure theory -- New versions of the Daniell-Stone-Riesz representation theorem -- Measure and Integral: New foundations after one hundred years -- Fubini-Tonelli theorems on the basis of inner and outer premeasures -- Measure and Integration: Characterization of the new maximal contents and measures -- Notes on the projective limit theorem of Kolmogorov -- Measure and Integration: The basic extension theorems -- Measure Theory: Transplantation theorems for inner premeasures. .
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.
9783034803823
Mathematics.
Mathematics.
Measure and Integration.
QA312-312.5
515.42