Measure and Integration

Publications 1997-2011

Authors: König, Heinz

  • 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
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Hardcover $139.00
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  • ISBN 978-3-0348-0381-6
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Softcover $139.00
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  • ISBN 978-3-0348-0755-5
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About this book

This collection of Heinz König’s publications connects to his book of 1997 “Measure and Integration” and presents significant developments in the subject from then up to the present day. The result is a consistent new version of measure theory, including selected applications. The basic step is the introduction of the inner • (bullet) and outer • (bullet) premeasures and their extension to unique maximal measures. New “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures) have been created, which lead to much simpler and more explicit treatment. In view of these new concepts, the main results are unmatched in scope and plainness, as well as in explicitness. Important examples are the formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits.

About the authors

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.

Reviews

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)


Table of contents (25 chapters)

  • Image measures and the so-called image measure catastrophe

    König, Heinz

    Pages 1-16

  • The product theory for inner premeasures

    König, Heinz

    Pages 17-31

  • Measure and Integration: Mutual generation of outer and inner premeasures

    König, Heinz

    Pages 33-56

  • Measure and Integration: Integral representations of isotone functionals

    König, Heinz

    Pages 57-87

  • Measure and Integration: Comparison of old and new procedures

    König, Heinz

    Pages 89-102

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0382-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-0348-0381-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-0755-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Measure and Integration
Book Subtitle
Publications 1997-2011
Authors
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0382-3
DOI
10.1007/978-3-0348-0382-3
Hardcover ISBN
978-3-0348-0381-6
Softcover ISBN
978-3-0348-0755-5
Edition Number
1
Number of Pages
XII, 512
Topics