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Let S be a nonempty set in Rn, and its support function be σS = sup{...

Let S be a nonempty set in Rn, and its support function be

σS = sup{ <x,z> : z ∈ S}.

let conv(S) denote the convex hull of S. Show that σS (x)= σconv(S) (x), for all x ∈ Rn

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