scholarly journals Minimal pairs of compact convex sets

2004 ◽  
Author(s):  
Diethard Pallaschke ◽  
Ryszard Urbański
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Minimal Pairs

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.

SYMMETRIES OF COMPACT CONVEX SETS

1974 ◽  
Vol 25 (1) ◽  
pp. 323-328 ◽  
Author(s):  
E. B. DAVIES
Keyword(s):  
Convex Sets ◽  
Compact Convex
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