A supermodular function is also a superadditive function

Dependencies:

1. Supermodular function
2. Subadditive and superadditive set functions

Let $f: 2^{\Omega} \to \mathbb{R}$ be a supermodular function. Then $f$ is also superadditive.

Proof

(Trivially follows from the definition.)

Dependency for: None

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. Supermodular function