a special case of a simple function

a function whose value is 1 for elements of a given set and 0 for elements not in the set. It is used, for example, to separate documents satisfying a query (1) from those not satisfying it (0).

( of a set ) The function c that is equal to 1 for point belonging to and 0 outside of .

In probability theory, the characteristic function of any random variable completely defines its probability distribution.

In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non-membership) of a given element in that set. It is similar to the usual indicator function, and one can freely convert between the two, but the characteristic function as defined below is better-suited to the methods of convex analysis.