proof of properties of extreme subsets of a closed convex set
For the first claim, it is obvious that is closed convex subset (http://planetmath.org/ConvexSet) of . Let and , such as
. Then , for all so we have that for all . Therefore
For the second claim suppose , and such as . From the hypothesis we have that and since is an extreme subset of , . Analogously from the hypothesis that is an extreme subset of , we have that .
|Title||proof of properties of extreme subsets of a closed convex set|
|Date of creation||2013-03-22 15:25:12|
|Last modified on||2013-03-22 15:25:12|
|Last modified by||georgiosl (7242)|