Measure and Integration: An Advanced Course in Basic Procedures and Applications / Edition 1

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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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Editorial Reviews

From the Publisher
"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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Product Details

  • ISBN-13: 9783540618584
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/14/2011
  • Edition description: 1st Corrected ed. 1997. Corr. 2nd printing 2008
  • Edition number: 1
  • Pages: 260
  • Product dimensions: 0.75 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Ch. I Set Systems and Set Functions 1
Ch. II The Extension Theories Based on Regularity 33
Ch. III Applications of the Extension Theories 79
Ch. IV The Integral 109
Ch. V The Daniell-Stone and Riesz Representation Theorems 143
Ch. VI Transplantation of Contents and Measures 179
Ch. VII Products of Contents and Measures 201
Ch. VIII Applications of the New Contents and Measures 231
Bibliography 249
List of Symbols 255
Index 257
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