# Set function

In mathematics, a set function is a function whose input is a set. The output is usually a number. Often the input is a set of real numbers, a set of points in Euclidean space, or a set of points in some measure space.

## Examples

Examples of set functions include:

• The function that assigns to each set its cardinality, i.e. the number of members of the set, is a set function.
• The function
$d(A) = \lim_{n\to\infty} \frac{|A \cap \{1,\dots,n\}|}{n},$
assigning densities to sufficiently well-behaved subsets A ⊆ {1, 2, 3, ...}, is a set function.

## References

• A.N. Kolmogorov and S.V. Fomin (1975), Introductory Real Analysis, Dover. ISBN 0-486-61226-0