Lectures on Choquet's Theorem
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2001, 2001
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| Edition: | 2nd ed. 2001 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- The Krein-Milman theorem as an integral representation theorem
- Application of the Krein-Milman theorem to completely monotonic functions
- Choquet’s theorem: The metrizable case.
- The Choquet-Bishop-de Leeuw existence theorem
- Applications to Rainwater’s and Haydon’s theorems
- A new setting: The Choquet boundary
- Applications of the Choquet boundary to resolvents
- The Choquet boundary for uniform algebras
- The Choquet boundary and approximation theory
- Uniqueness of representing measures.
- Properties of the resultant map
- Application to invariant and ergodic measures
- A method for extending the representation theorems: Caps
- A different method for extending the representation theorems
- Orderings and dilations of measures
- Additional Topics