Extreme points of the dual unit ball of C(K)
= Extreme points of the dual unit ball of C(K)
{title2=$\{\alpha\delta_x:|\alpha|=1,\ x\in K\}$}
For complex $C(K)$ on a <compact Hausdorff space>, the <extreme points> of its dual unit ball are precisely unimodular multiples of <Dirac measures>. A measure whose <variation measure> has mass on two disjoint sets splits as a nontrivial <convex combination> of normalized restrictions and is not extreme. This description is the key to the <Banach–Stone theorem>.