Skip to main content

Properties of the resultant map

  • 1952 Accesses

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

Abstract

As was seen in Proposition 1.1, the resultant map from the probability measures P(X) onto the compact convex set X is affine and weak* continuous. By the Choquet-Bishop-deLeeuw theorem, its restriction r to the set Q(X) of maximal probability measures is still surjective, and from the uniqueness theorem we know that r is bijective if and only if X is a simplex. In this section we prove some additional properties of this map, including a simple but potentially useful selection theorem for the metrizable case.

Keywords

  • Compact Hausdorff Space
  • Dense Subspace
  • Metrizable Case
  • Selection Theorem
  • Baire Class

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). Properties of the resultant map. 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_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-48719-0_11

  • 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