Measure and Integration: Publications 1997-2011 - Hardcover

König, Heinz

Hardcover

ISBN 10: 3034803818 ISBN 13: 9783034803816

Publisher: Birkhäuser, 2012

Synopsis

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).

About this title

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.

From the Back Cover

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2012
• Language: English
• ISBN 10: 3034803818
• ISBN 13: 9783034803816
• Binding: Hardcover
• Number of pages: 519