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Measure and Integration

Publications 1997-2011

  • Book
  • © 2012

Overview

Authors:
  1. Heinz König

    1. , Department of Mathematics, Universität des Saarlandes, Saarbrücken, Germany

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  • 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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Table of contents (26 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Image measures and the so-called image measure catastrophe

    • Heinz König
    Pages 1-16

  3. The product theory for inner premeasures

    • Heinz König
    Pages 17-31

  4. Measure and Integration: Mutual generation of outer and inner premeasures

    • Heinz König
    Pages 33-56

  5. Measure and Integration: Integral representations of isotone functionals

    • Heinz König
    Pages 57-87

  6. Measure and Integration: Comparison of old and new procedures

    • Heinz König
    Pages 89-102

  7. What are signed contents and measures?

    • Heinz König
    Pages 103-126

  8. Upper envelopes of inner premeasures

    • Heinz König
    Pages 127-148

  9. On the inner Daniell-Stone and Riesz representation theorems

    • Heinz König
    Pages 149-163

  10. Sublinear functionals and conical measures

    • Heinz König
    Pages 165-173

  11. Measure and Integration: An attempt at unified systematization

    • Heinz König
    Pages 175-234

  12. New facts around the Choquet integral

    • Heinz König
    Pages 235-244

  13. The (sub/super)additivity assertion of Choquet

    • Heinz König
    Pages 245-271

  14. Projective limits via inner premeasures and the true Wiener measure

    • Heinz König
    Pages 273-312

  15. Stochastic processes in terms of inner premeasures

    • Heinz König
    Pages 313-342

  16. New versions of the Radon-Nikodým theorem

    • Heinz König
    Pages 343-352

  17. The Lebesgue decomposition theorem for arbitrary contents

    • Heinz König
    Pages 353-367

  18. The new maximal measures for stochastic processes

    • Heinz König
    Pages 369-390

  19. Stochastic processes on the basis of new measure theory

    • Heinz König
    Pages 391-404

  20. New versions of the Daniell-Stone-Riesz representation theorem

    • Heinz König
    Pages 405-418
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Keywords

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.

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).



Authors and Affiliations

  • , Department of Mathematics, Universität des Saarlandes, Saarbrücken, Germany

    Heinz König

About the author

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.

Bibliographic Information

  • Book Title: Measure and Integration

  • Book Subtitle: Publications 1997-2011

  • Authors: Heinz König

  • DOI: https://doi.org/10.1007/978-3-0348-0382-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel 2012

  • Hardcover ISBN: 978-3-0348-0381-6Published: 07 June 2012

  • Softcover ISBN: 978-3-0348-0755-5Published: 20 July 2014

  • eBook ISBN: 978-3-0348-0382-3Published: 06 June 2012

  • Edition Number: 1

  • Number of Pages: XI, 508

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Measure and Integration

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