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.

Let
Ω
be a set and
f
:
2
Ω
→
R
be a set function, where
2
Ω
denotes the power set of
Ω
. The function *f* is *superadditive* if for any pair of disjoint subsets
S
,
T
of
Ω
, we have
f
(
S
)
+
f
(
T
)
≤
f
(
S
∪
T
)
.