Measure and Integration: Publications 1997-2011
Autor Heinz Königen Limba Engleză Paperback – 19 iul 2014
Further to the contributions in this volume, after 2011 Heinz König published two more articles that round up his work: On the marginals of probability contents on lattices (Mathematika 58, No. 2, 319-323, 2012), and Measure and integration: the basic extension and representation theorems in terms of new inner and outer envelopes (Indag. Math., New Ser. 25, No. 2, 305-314, 2014).
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (2) | 376.55 lei 6-8 săpt. | |
| Springer Berlin, Heidelberg – 14 oct 2010 | 376.55 lei 6-8 săpt. | |
| Springer – 19 iul 2014 | 389.98 lei 6-8 săpt. | |
| Hardback (2) | 383.65 lei 6-8 săpt. | |
| Springer Berlin, Heidelberg – 18 noi 1996 | 383.65 lei 6-8 săpt. | |
| Springer – 6 iun 2012 | 394.49 lei 6-8 săpt. |
Preț: 389.98 lei
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Specificații
ISBN-13: 9783034807555
ISBN-10: 3034807554
Pagini: 524
Ilustrații: XI, 508 p. 1 illus. in color.
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.73 kg
Ediția:2012
Editura: Springer
Colecția Birkhäuser
Locul publicării:Basel, Switzerland
ISBN-10: 3034807554
Pagini: 524
Ilustrații: XI, 508 p. 1 illus. in color.
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.73 kg
Ediția:2012
Editura: Springer
Colecția Birkhäuser
Locul publicării:Basel, Switzerland
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Public țintă
ResearchCuprins
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.
Recenzii
From the reviews:
“The author took up several of the crucial topics of measure theory and developed them according to his ‘new foundations of measure theory’. The author is offering twenty of his papers in this tome … . This collection of papers along with MI are a must on the bookshelves of any measure theorist. … On the whole the present volume will serve as a useful resource … in MI.” (K. P. S. Bhaskara Rao, Mathematical Reviews, April, 2013)
“The main body of this impressive volume is a collection of twenty-five papers whose sole author is Heinz König, an esteemed analyst. … the volume can be recommended to all those interested in the foundations of measure theory and stochastic processes.” (Zbigniew Lipecki, zbMATH, Vol. 1267, 2013)
“The author took up several of the crucial topics of measure theory and developed them according to his ‘new foundations of measure theory’. The author is offering twenty of his papers in this tome … . This collection of papers along with MI are a must on the bookshelves of any measure theorist. … On the whole the present volume will serve as a useful resource … in MI.” (K. P. S. Bhaskara Rao, Mathematical Reviews, April, 2013)
“The main body of this impressive volume is a collection of twenty-five papers whose sole author is Heinz König, an esteemed analyst. … the volume can be recommended to all those interested in the foundations of measure theory and stochastic processes.” (Zbigniew Lipecki, zbMATH, Vol. 1267, 2013)
Notă biografică
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.
Born in Stettin (Szczecin/Poland), Heinz König has been a professor at the University of Saarland (Germany) since 1965 and a visiting professor at many prestigious universities around the world.
Born in Stettin (Szczecin/Poland), Heinz König has been a professor at the University of Saarland (Germany) since 1965 and a visiting professor at many prestigious universities around the world.
Textul de pe ultima copertă
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.
Caracteristici
Heinz König’s recent and most influential works in one single volume
For the first time ever: Entirely uniform treatment of abstract and topological measure theory
New “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which leads to much simpler and more explicit treatment
The incorporation of non-sequential and of inner regular versions leads to much more comprehensive results
For the first time ever: Entirely uniform treatment of abstract and topological measure theory
New “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which leads to much simpler and more explicit treatment
The incorporation of non-sequential and of inner regular versions leads to much more comprehensive results