Theorem 13.6.6 (Minkowski/Krein-Milman).label Let $K\suf\R^{d}$ be a compact convex set. Then $K=Conv(Ext(K))$
Proof. We proceed by induction with base case $d=0$ is trivial since $K$ is a point. If $int(K)=\emp$ then by Theorem 13.6.5 $K$ lies in an affine subspace of dimension $<d$ hence the result follows by induction hypothesis. Suppose $int(K)\neq\emp$.$\square$
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