Compact Convex Sets and Continuous Function Spaces

1962 ◽  
pp. 77-96
Author(s):  
Mahlon M. Day
Keyword(s):  
Continuous Function ◽  
Convex Sets ◽  
Compact Convex ◽  
Function Spaces

Some properties of maximal measures on compact convex sets

1983 ◽  
Vol 94 (2) ◽  
pp. 297-305 ◽  
Author(s):  
C. J. K. Batty
Keyword(s):  
Continuous Function ◽  
State Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Continuous Functions ◽  
Regularity Conditions ◽  
Maximal Measure ◽  
Compact Convex Set ◽  
Almost All

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.

On injections and surjections of continuous function spaces

1973 ◽  
Vol 15 (3) ◽  
pp. 301-310 ◽  
Author(s):  
D. Amir ◽  
B. Arbel
Keyword(s):  
Continuous Function ◽  
Function Spaces

scholarly journals An elementary renewal theorem for random compact convex sets

1995 ◽  
Vol 27 (4) ◽  
pp. 931-942 ◽  
Author(s):  
Ilya S. Molchanov ◽  
Edward Omey ◽  
Eugene Kozarovitzky
Keyword(s):  
Support Function ◽  
Convex Sets ◽  
Compact Convex ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Minkowski Sums ◽  
Image Position ◽  
Unit Vectors

A set-valued analog of the elementary renewal theorem for Minkowski sums of random closed sets is considered. The corresponding renewal function is defined as where are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of H(tK)/t as t tends to infinity. For K containing the origin as an interior point, where hK(u) is the support function of K and is the set of all unit vectors u with EhA(u) > 0. Other set-valued generalizations of the renewal function are also suggested.

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