Superadditive set function

In mathematics, a superadditive set function is a set function whose value, informally, has the property that the value of function on the union of two disjoint sets is at least the sum of values of the function on each of the sets. This is thematically related to the superadditivity property of real-valued functions. It is contrasted to subadditive set function.

Definition

Let $\Omega$ be a set and $f \colon 2^{\Omega} \rightarrow \mathbb{R}$ be a set function, where $2^\Omega$ denotes the power set of $\Omega$. The function f is superadditive if for any pair of disjoint subsets $S,T$ of $\Omega$, we have $f(S) + f(T) \leq f(S \cup T)$.^[1]

See also

• Utility functions on indivisible goods

Citations

1. Nimrod Megiddo (1988). "ON FINDING ADDITIVE, SUPERADDITIVE AND SUBADDITIVE SET-FUNCTIONS SUBJECT TO LINEAR INEQUALITIES" (PDF). Retrieved 21 December 2015.