Let $R$ be an D5119: Ordered division ring.
Let $V$ be a D29: Vector space over $R$.
Let $W$ be an D1963: Ordered vector space over $R$ such that

(i)	$\preceq$ is the D378: Ordering relation on $W$

A D18: Map $f : V \to W$ is sublinear from $V$ to $W$ over $R$ if and only if $$\begin{equation} \forall \, N \in 1, 2, 3, \ldots : \forall \, x \in V^N : \forall \, r \in R^N : f \left( \sum_{n = 1}^N r_n x_n \right) \preceq \sum_{n = 1}^N r_n f(x_n) \end{equation}$$