Measure and Integration

Publications 1997-2011

  • Heinz König

Table of contents

  1. Front Matter
    Pages i-xi
  2. Heinz König
    Pages 17-31
  3. Heinz König
    Pages 103-126
  4. Heinz König
    Pages 127-148
  5. Heinz König
    Pages 165-173
  6. Heinz König
    Pages 235-244
  7. Heinz König
    Pages 343-352

About this book

Introduction

This volume presents a collection of twenty-five of Heinz König’s recent and most influential works. Connecting to his book of 1997 “Measure and Integration”, the author has developed a consistent new version of measure theory over the past years. For the first time, his publications are collected here in one single volume.

Key features include:

- A first-time, original and entirely uniform treatment of abstract and topological measure theory

- The introduction of the inner • and outer • premeasures and their extension to unique maximal measures

- A simplification of the procedure formerly described in Chapter II of the author’s previous book

- The creation of new “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which lead to much simpler and more explicit treatment

- The formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far beyond the countably determined ones

- The incorporation of non-sequential and of inner regular versions, which leads to much more comprehensive results

- Significant applications to stochastic processes.

“Measure and Integration: Publications 1997–2011” will appeal to both researchers and advanced graduate students in the fields of measure and integration and probabilistic measure theory.

Keywords

Mathematics Integration Statistics Theorems Measure

Authors and affiliations

  • Heinz König
    • 1
  1. 1., Department of MathematicsUniversität des SaarlandesSaarbrückenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0382-3
  • Copyright Information Springer Basel 2012
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0381-6
  • Online ISBN 978-3-0348-0382-3
  • About this book