Measure and Integration
An Advanced Course in Basic Procedures and Applications
(Sprache: Englisch)
This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops...
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Produktinformationen zu „Measure and Integration “
This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond.
Klappentext zu „Measure and Integration “
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.Inhaltsverzeichnis zu „Measure and Integration “
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.
Bibliographische Angaben
- Autor: Heinz König
- 1996, 1997, XXII, 260 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540618589
- ISBN-13: 9783540618584
- Erscheinungsdatum: 12.01.2009
Sprache:
Englisch
Rezension zu „Measure and Integration “
"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
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