Characteristic function

From Citizendium
Jump to: navigation, search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In set theory, the characteristic function or indicator function of a subset X of a set S is the function, often denoted χA or IA, from S to the set {0,1} which takes the value 1 on elements of X and 0 otherwise.

We can express elementary set-theoretic operations in terms of characteristic functions:


In mathematics, characteristic function can refer also to any several distinct concepts:


where "E" means expected value. See characteristic function (probability theory).