By Gerhard Winkler

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**Extra info for Choquet Order and Simplices: with Applications in Probabilistic Models**

**Example text**

6. ~a. a. b. : Consider V the linear := {f 6 C ( H × H) space : If(x,y) J ~ g(x) + h ( y ) for some continuous g, h 6 [7 (p+q) } . Whenever g and h are a linear subspace W functional k(g® aim To the d e s i r e d := f g d p k to a l l on p a g e Let (V,~) ments. f 6 V measure it r e a d s and subspace with With the natural Next p has f :M ~ that the extension ~. 4 ~ 0 whenever any := i n f { ~ ( x ) U {~} a n d f 6V its p o s i t i v e f 6 V there functional linear above further for t h a t W is are elements k on W which functional ele- - ~ < p(f) ~ ~ f ~ 0.

E x a m p l e tight is a t l e a s t 0-algebra the b a r y c e n t r i c a l Let C be a closed Z(C) which (Phelps(1966)) : subset L e t us o n l y m e n t i o n set measure x. If in g e n e r a l One boundary is a assumptions in uniqueness s e e m to b e Leeuw such approaches of r e p r e s e n t i n g inevitable (cf. type is o b - do n o t w o r k , measures. 6) . 2. Already pactness Edgar's closed - G. Choquet assumption: representation bounded see a l s o convex started "conical two approaches measures" and to g e t "caps".

Ii) p,(M) 2. > ~(r[A ]) = ~(A Let n o w p be arbitrary. ~. such that p(~i) > 0 and : ~T by 1 3 . G ; qi (B) ) = I. C h o o s e p a i r w i s e d i s j o i n t in o c o m p a c t sets p( U ~i) i6~4 = 1. T h e r e is a p - d i l a t i o n T w i t h set :: I IC Tx(B) dp(x) for every B 6 B(F,o). 3 subset a. M b. whenever Proof. ceding q6 P' (E) that a. to g e t a. 2. have bability pleasant measures to n o r m a l i z e ! 4). 3 p