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<p>is the closed convex hull of its extreme points (the <a href="page.php?w=Krein-Milman_theorem">Krein-Milman theorem</a>).</p>

<p>An <b><a href="page.php?w=exposed_face">exposed face</a></b> of  is the subset of points of  where a linear functional achieves its minimum on . Thus, if  is a linear functional on  and , then  is an exposed face of .</p>

<p>An <b><a href="page.php?w=exposed_point">exposed point</a></b> of  is a point   such that  is an exposed face of . That is,  for all . See the figure for examples of extreme points that are not</p><p>
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