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Additional Topics

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

Abstract

Much of the material in these notes (other than the applications) is contained in the outline presented by Choquet [19] at the 1962 International Congress of Mathematicians, and the paper [22] by Choquet and Meyer gives an elegant and very concise treatment of the main parts of the theory. Bauer’s lecture notes [6] contain a detailed development which starts from the very beginning, using (as do Choquet and Meyer) his “potential theoretic” approach to the existence of extreme points via semi-continuous functions on a compact space [3]. Chapter XI of Meyer’s book [57] covers a great deal of ground. He shows, among other things, that the entire subject of maximal measures may be viewed as a special case of an abstract “theory of balayage.”

Keywords

  • Extreme Point
  • Compact Hausdorff Space
  • Choquet Boundary
  • Bauer Simplex
  • Minimal Harmonic Function

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.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Additional Topics. 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_16

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  • DOI: https://doi.org/10.1007/3-540-48719-0_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41834-4

  • Online ISBN: 978-3-540-48719-7

  • eBook Packages: Springer Book Archive