Skip to main content

A new setting: The Choquet boundary

  • 1958 Accesses

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

Abstract

In the Introduction, the Riesz representation theorem was reformulated as a representation theorem of the Choquet type. Although the conclusion of the Riesz theorem is quite sharp (for each element of the convex set X under consideration there exists a unique representing measure supported by ex X), the hypotheses restrict its application to a very special class of compact convex sets. In what follows we will (among other things) describe a related family of sets which appears to be only slightly larger than that involved in the Riesz theorem, but which actually “contains” all the sets which interest us, in the sense that every compact convex subset of a locally convex space is affinely homeomorphic to a member of the family.

Keywords

  • Extreme Point
  • Convex Space
  • Complex Banach Space
  • Compact Convex Subset
  • Closed Boundary

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   44.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2001). A new setting: The Choquet boundary. In: Phelps, R.R. (eds) Lectures on Choquet’s Theorem. Lecture Notes in Mathematics, vol 1757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48719-0_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-48719-0_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41834-4

  • Online ISBN: 978-3-540-48719-7

  • eBook Packages: Springer Book Archive