Theorem 13.1.11 (Convex Properties).label Let $c\suf\R^{n}$ be nonempty then

1. (1)

   $Conv(c)$ is the smallest convex set containing $c$

2. (2)

   $c$ is convex if and only if $Conv(c)=c$

3. (3)

   $Conv(c)=\curl{\sums{m}{i=1}\lam_ix_i:\curl{\lam_i}_1^m\suf[0,1],\curl{x_i}_1^m\suf c,\sums{m }{i=1}\lam_i=1}$