characteristic function

Definition Suppose A is a subset of a set X. Then the functionMathworldPlanetmath

χA(x)={1,when xA,0,when xXA

is the characteristic functionMathworldPlanetmathPlanetmathPlanetmath for A.

0.0.1 Properties

Suppose A,B are subsets of a set X.

  1. 1.

    For set intersectionsDlmfMathworldPlanetmath and set unions, we have

    χAB = χAχB,
    χAB = χA+χB-χAB,
    χAB = min(χA,χB),
    χAB = max(χA,χB).
  2. 2.

    For the symmetric differenceMathworldPlanetmathPlanetmath,

  3. 3.

    For the set complementPlanetmathPlanetmath,


0.0.2 Remarks

A synonym for characteristic function is indicator function [1].


  • 1 G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed, John Wiley & Sons, Inc., 1999.
Title characteristic function
Canonical name CharacteristicFunction
Date of creation 2013-03-22 11:48:31
Last modified on 2013-03-22 11:48:31
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 12
Author bbukh (348)
Entry type Definition
Classification msc 03-00
Classification msc 26-00
Classification msc 26A09
Classification msc 28-00
Synonym indicator function
Related topic SimpleFunction