Let $K$ denote the usual $1/3$ Cantor set and let $B=B_{C(K)}$ (here $B_{C(K)}$ = {$v \in C(K) : \|v\| \leq 1 $} denotes the closed unit ball of $C(K))$. Then how to prove that $B$ coincides with the norm closure of the convex hull of its set of extreme points?
Do I need to explicitly identify the entire set of extreme points of $B$?
Please help me out. Thank you.