Some properties of maximal measures on compact convex sets
1983 ◽
Vol 94
(2)
◽
pp. 297-305
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Keyword(s):
AbstractLet be a maximal measure on a compact convex set K, K* be the state space of the space of all continuous functions f: KK ℝ which are affine in the first variable, 1 be the -algebra on K generated by the Baire sets and the compact extremal subsets of K, and = {BeK1}. Then(i) For any fixed continuous function g:K ℝ and -almost all x in K, there is a closed face of K containing x on which g is constant.(ii) The image of under the map :KK* defined by f, (x) = f(x, x) is the unique maximal measure on K* representing its barycentre(iii) induces a measure on (eK) satisfying certain regularity conditions.
2001 ◽
Vol 70
(3)
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pp. 323-336
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Keyword(s):
1996 ◽
Vol 28
(02)
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pp. 384-393
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Keyword(s):
1985 ◽
Vol 17
(02)
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pp. 308-329
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Keyword(s):
1987 ◽
Vol 35
(2)
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pp. 267-274
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2003 ◽
Vol 2003
(39)
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pp. 2501-2505
Keyword(s):
1991 ◽
Vol 109
(2)
◽
pp. 351-361
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1977 ◽
Vol 81
(2)
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pp. 225-232
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Keyword(s):
1999 ◽
Vol 59
(1)
◽
pp. 147-152
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Keyword(s):
1985 ◽
Vol 28
(1)
◽
pp. 60-66
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Keyword(s):