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
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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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Online ISBN: 978-3-540-48719-7
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