研究不确定性的数学工具理论

Robert R. Phelps
I Introduction. The Krein-Milman theorem as an inte-
gral representation theorem . . . . . . . . . . . . . . 1
2 Application of the Krein-Milman theorem to com-
pletely monotonic functions . . . . . . . . . . . . . . 9
3 Choquet's theorem: The metrizable case . . . . . . . . 13
4 The Choquet-Bishop-de Leeuw existence theorem . . 17
5 Applications to Rainwater's and Haydon's theorems . 25
6 A new setting: The Choquet boundary . . . . . . . . 27
7 Applications of the Choquet boundary to resolvents . 35
8 The Choquet boundary for uniform algebras . . . . . 39
9 The Choquet boundary and approximation theory . . 47
10 Uniqueness of representing measures . . . . . . . . . . 51
11 Properties of the resultant map . . . . . . . . . . . . 65
12 Application to invariant and ergodic measures . . . . 73
13 A method for extending the representation theorems:
Caps . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
14 A different method for extending the representation
theorems . . . . . . . . . . . . . . . . . . . . . . . . . 88
15 Orderings and dilations of measures . . . . . . . . . . 93
16 Additional Topics . . . . . . . . . . . . . . . . . . . . 101
References . . . . . . . . . . . . . . . . . . . . . . . . 115
Index of symbols . . . . . . . . . . . . . . . . . . . . 122,
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 123