Skip to main content
SpringerLink
Log in

Lectures on Choquet's Theorem

  • Book
  • © 2001

Overview

Editors:
  1. Robert R. Phelps

    1. Department of Mathematics, University of Washington, Seattle, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1757)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages I-VII
    Download chapter PDF

  2. Introduction. The Krein-Milman theorem as an integral representation theorem

    Pages 1-8

  3. Application of the Krein-Milman theorem to completely monotonic functions

    Pages 9-12

  4. Choquet’s theorem: The metrizable case.

    Pages 13-16

  5. The Choquet-Bishop-de Leeuw existence theorem

    Pages 17-23

  6. Applications to Rainwater’s and Haydon’s theorems

    Pages 25-26

  7. A new setting: The Choquet boundary

    Pages 27-33

  8. Applications of the Choquet boundary to resolvents

    Pages 35-38

  9. The Choquet boundary for uniform algebras

    Pages 39-45

  10. The Choquet boundary and approximation theory

    Pages 47-49

  11. Uniqueness of representing measures.

    Pages 51-63

  12. Properties of the resultant map

    Pages 65-71

  13. Application to invariant and ergodic measures

    Pages 73-78

  14. A method for extending the representation theorems: Caps

    Pages 79-87

  15. A different method for extending the representation theorems

    Pages 88-91

  16. Orderings and dilations of measures

    Pages 93-99

  17. Additional Topics

    Pages 101-113

  18. Back Matter

    Pages 115-124
    Download chapter PDF
Back to top

Keywords

About this book

A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.

Editors and Affiliations

  • Department of Mathematics, University of Washington, Seattle, USA

    Robert R. Phelps

Bibliographic Information

  • Book Title: Lectures on Choquet's Theorem

  • Editors: Robert R. Phelps

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b76887

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Softcover ISBN: 978-3-540-41834-4Published: 08 May 2001

  • eBook ISBN: 978-3-540-48719-7Published: 01 July 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 2

  • Number of Pages: X, 130

  • Additional Information: Originally published by Van Nostrand, Princeton, USA, 1966

  • Topics: Potential Theory, Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation