Measure and Integration

An Advanced Course in Basic Procedures and Applications

  • Authors
  • Heinz König

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Heinz König
    Pages 1-31
  3. Heinz König
    Pages 79-107
  4. Heinz König
    Pages 109-141
  5. Heinz König
    Pages 179-199
  6. Heinz König
    Pages 201-229
  7. Back Matter
    Pages 249-262

About this book

Introduction

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.

 

Keywords

capacity construction of measures integral integral representation integration measure measure theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89502-2
  • Copyright Information Springer Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61858-4
  • Online ISBN 978-3-540-89502-2
  • About this book