Subadditive and superadditive set functions

Dependencies:

1. Set function

A set function $f: 2^Ω → ℝ$ is subadditive iff $f(A ∪ B) ≤ f(A) + f(B)$ for all disjoint sets $A$ and $B$. $f$ is superadditive iff $f(A ∪ B) ≥ f(A) + f(B)$ for all disjoint sets $A$ and $B$.

Dependency for:

1. A supermodular function is also a superadditive function
2. A set function is additive iff it is submodular and supermodular iff it is subadditive and superadditive.
3. A submodular function is also a subadditive function
4. EEF implies PROP for subadditive valuations
5. PROP implies EF for superadditive identical valuations

Info:

• Depth: 3
• Number of transitive dependencies: 3

Transitive dependencies:

1. /sets-and-relations/countable-set
2. σ-algebra
3. Set function