Definition 4.1.3 (Sublinear Functional).label Let $E$ be a vector space over $K\in \curl{\R,\com}$, then a sublinear functional is a mapping $\rho:E\to\R$ such that:

1. (1)

   $\rho(0)=0$

2. (2)

   $\fall x\in E$ and $\lam\geq 0,\rho(\lam x)=\lam\rho(x)$

3. (3)

   $\fall x,y\in E,\rho(x+y)\leq \rho(x)+\rho(y)$