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January 14th, 2015, 02:56 PM  #1 
Newbie Joined: Oct 2013 Posts: 25 Thanks: 0  Intersection of a closed convex set
Let X be a real Banach Space, C be a closed convex subset of X. Define Lc = {f: f  a ∈ X* for some real number a and f(x) ≥ 0 for all x ∈ C} (X* is the dual space of X) Using a version of the Hahn  Banach Theorem to show that C = ∩ {x ∈ X: f(x) ≥ 0} with the index f ∈ Lc under the intersection Could someone help me to solve this problem, i cant see how Hahn  Banach can imply the above statement ( I used the separation version to obtain g(x)<a<g(y) for some linear functional g) 

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closed, convex, intersection, set 
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