Heinz König

Measure and Integration (eBook, PDF)

Publications 1997-2011

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 508
• Erscheinungstermin: 6. Juni 2012
• Englisch
• ISBN-13: 9783034803823
• Artikelnr.: 37342695

Autorenporträt

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.

Inhaltsangabe

Set Systems and Set Functions.- The Extension Theories Based on Regularity.- Applications of the Extension Theories.- The Integral.- The Daniell-Stone and Riesz Representation Theorems.- Transplantation of Contents and Measures.- Products of Contents and Measures.- Applications of the New Contents and Measures.

Rezensionen

Man könnte meinen, dass zum Thema Maß und Integral in zahlreichen Lehrbüchern bereits alles wesentliche festgehalten ist. Der Verfasser beweist jedoch mit diesem Werk, dass das Gebiet lebt und durchaus noch grundlegend neue Einsichten möglich sind. Ich möchte daher das Buch allen an Maß- und Integrationstheorie interessierten Mathematikern nachdrücklich zur Lektüre empfehlen. S. Graf in DMV Jahresbericht Bd. 103, Heft 1, 2001.

"Man könnte meinen, dass zum Thema Maß und Integral in zahlreichen Lehrbüchern bereits alles wesentliche festgehalten ist. Der Verfasser beweist jedoch mit diesem Werk, dass das Gebiet lebt und durchaus noch grundlegend neue Einsichten möglich sind. Ich möchte daher das Buch allen an Maß- und Integrationstheorie interessierten Mathematikern nachdrücklich zur Lektüre empfehlen."S. Graf in DMV Jahresbericht Bd. 103, Heft 1, 2001