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

Konig, Heinz

Softcover

ISBN 10: 3642082777 ISBN 13: 9783642082771

Verlag: Springer Berlin Heidelberg, 2010

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Geboren am 16. Mai 1929 in Stettin, gestorben 31. März 2024 in Saarbrücken. Studium und 1952 Promotion zum Dr. rer. nat. an der Universität Kiel. 1956 Habilitation an der Universität Würzburg. 1957-1960 Dozent und 1960-1962 außerordentlicher Professor an der Technischen Hochschule Aachen. 1962-1965 ordentlicher Professor an der Universität Köln, seit 1965 an der Universität des Saarlandes in Saarbrücken. Gastaufenthalte unter anderem am California Institute of Technology in Pasadena und an der University of Washington in Seattle. 1979 Dr. rer. pol. h.c. der Universität Karlsruhe (TH). 1984 korrespondierendes Mitglied der Sociéte Royale des Sciences de Liège.

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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.

 

Details zur Ausgabe

• Verlag: Springer Berlin Heidelberg
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 3642082777
• ISBN 13: 9783642082771
• Einband: Taschenbuch
• Anzahl der Seiten: 284
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland