> [!definition] > > Let $\cx$ be a [[Vector Space|vector space]] over $\real$, then a **sublinear functional** is a map $p: \cx \to \real$ such that > $ > p(x + y) \le p(x) + p(y) > $ > and $p(\lambda x) = \lambda p(x)$ for all $x, y \in \cx$ and $\lambda \ge 0$.