Definition:Subadditive Function (Conventional)

Definition
Let $\struct {S, +_S}$ and $\struct {T, +_T, \preceq}$ be semigroups such that $\struct {T, +_T, \preceq}$ is ordered.

Let $f: S \to T$ be a mapping from $S$ to $T$ which satisfies the relation:
 * $\forall a, b \in S: \map f {a +_S b} \preceq \map f a +_T \map f b$

Then $f$ is defined as being subadditive.

The usual context in which this is encountered is where $S$ and $T$ are both the set of real numbers $\R$ (or a subset of them).

Also see
Compare with the field of measure theory, in which the definition of subadditive function is completely different.