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Measure and Integration Publications 1997-2011 /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2012.
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| Edición: | 1st ed. 2012. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a König, Heinz. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Measure and Integration |h [electronic resource] : |b Publications 1997-2011 / |c by Heinz König. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a Basel : |b Springer Basel : |b Imprint: Birkhäuser, |c 2012. | |
| 300 | |a XII, 512 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 505 | 0 | |a 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. . | |
| 520 | |a 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. | ||
| 650 | 0 | |a Measure theory. | |
| 650 | 1 | 4 | |a Measure and Integration. |
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| 776 | 0 | 8 | |i Printed edition: |z 9783034803830 |
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| 776 | 0 | 8 | |i Printed edition: |z 9783034803816 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034809818 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-0348-0382-3 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
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