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:

Transitive dependencies:

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