Independence, Additivity, Uncertainty

  • Karl Vind

Part of the Studies in Economic Theory book series (ECON.THEORY, volume 14)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction

    1. Karl Vind
      Pages 1-6
  3. Basic Mathematics

    1. Front Matter
      Pages 7-7
    2. Karl Vind
      Pages 9-26
    3. Karl Vind
      Pages 27-30
    4. Karl Vind
      Pages 31-38
    5. Karl Vind
      Pages 39-47
    6. Karl Vind
      Pages 49-67
  4. Relations on Function Spaces

    1. Front Matter
      Pages 81-81
    2. Karl Vind
      Pages 83-111
    3. Karl Vind
      Pages 113-129
  5. Relations on Measures

    1. Front Matter
      Pages 131-131
  6. Integral Representations

    1. Front Matter
      Pages 147-147
  7. Decompositions and Uncertainty

    1. Front Matter
      Pages 187-187
    2. Karl Vind
      Pages 189-199
    3. Karl Vind
      Pages 201-220
    4. Karl Vind
      Pages 221-223
  8. Applications

    1. Front Matter
      Pages 225-225
    2. Karl Vind
      Pages 227-229
    3. Karl Vind
      Pages 231-241
    4. Karl Vind
      Pages 243-252
  9. Back Matter
    Pages 253-277

About this book


The work on this book started many years ago as an attempt to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the re­ sults were representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. It later turned out that t.he approach taken in the earlier versions were also the proper approach in generalizing from preferences which were total preorders to preferences which were not total or tran­ sitive. The same mathematics would even in that situation give representations which were additive. It would also give decomposi­ tions where concepts of uncertainty appeared. Early versions of some of the results appeared as Working Pa­ pers No. 135, 140, 150, and 176 from The Center for Research in Management Science, Berkeley. A first version of chapters 2, 4, 6, 7, and 8 appeared 1969 with the title" Mean Groupoids" [177]. They are essentially unchanged -except for some notes especially in chapter 6. Another version appeared 1990 as [178]. Chapter 10 contains results from the same versions and from [181]. Chapter 11 by Birgit Grodal is based on [91] by Grodal and Jp,an-Francois Mertens. Chapters 11 and 12 - also by Birgit Gro­ dal -contains the results from the earlier versions, but have been extended (by Karl Vind) to take into account the new corollaries of the results in the other chapters.


Keynes Knight Preferences Uncertainty Utility mathematical economics sets statistics

Authors and affiliations

  • Karl Vind
    • 1
  1. 1.Institute of EconomicsUniversity of CopenhagenCopenhagen KDenmark

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41683-8
  • Online ISBN 978-3-540-24757-9
  • Series Print ISSN 1431-8849
  • Buy this book on publisher's site
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