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Measure and Integration: An Advanced Course in Basic Procedures and Applications de Heinz König

Measure and Integration: An Advanced Course in Basic Procedures and Applications

Autor Heinz König
en Limba Engleză Paperback – 14 oct 2010
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).

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Specificații

ISBN-13: 9783642082771
ISBN-10: 3642082777
Pagini: 284
Ilustrații: XXII, 260 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.4 kg
Ediția:1997
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

This book sets out to restructure certain fundamentals in measure and integration theory, and thus to fee the theory from some notorious drawbacks. It centers around the ubiquitous task of producing appropriate contents and measures from more primitive data, in order to extend elementary contents and to represent elementary integrals. This task has not been met with adequate unified means so far. The traditional main tools, the Carathéodory and Daniell-Stone theorems, are too restrictive and had to be supplemented by other ad-hoc procedures. Around 1970 a new approach emerged, based on the notion of regularity, which in traditional measure theory is linked to topology. The present book develops the new approach into a systematic theory. The theory unifies the entire context and is much more powerful than the former means. It has striking implications all over measure theory and beyond. Thus it extends the Riesz representation theorem in terms of Randon measures from locally compact to arbitrary Hausdorff topological spaces. It furthers the methodical unification with non-additive set functions, as shown in natural extensions of the Choquet capacitability theorem. The presentation of this research monograph is self-contained, and starts from the beginning. It is addressed to research workers in mathematical analysis and in applications like mathematical economics, and in particular for university teachers in measure and integration theory. The corrected, second printing includes required corrections and appropriate small alterations of the text and a list of the subsequent articles by the author.
 

Caracteristici

Includes supplementary material: sn.pub/extras

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)

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.