Submodularity implies subadditivity, supermodularity implies superadditivity

Dependencies:

1. Submodular function
2. Subadditive and superadditive set functions

Let $f: 2^{\Omega} \to \mathbb{R}$ be a set function. If $f$ is submodular, then $f$ is also subadditive. If $f$ is supermodular, then $f$ is also superadditive.

Proof

(Trivially follows from the definition.)

Dependency for:

1. PROPm implies PROP1

Info:

• Depth: 4
• Number of transitive dependencies: 5

Transitive dependencies:

1. /sets-and-relations/countable-set
2. σ-algebra
3. Set function
4. Subadditive and superadditive set functions
5. Submodular function