Characteristic function of a set
From Encyclopedia of Mathematics
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in a space
The function that is equal to 1 when and equal to 0 when (where is the complement to in ). Every function on with values in is the characteristic function of some set, namely, the set . Properties of characteristic functions are:
1) , ;
2) if , then ;
3) if , then ;
4) if , then ;
5) if are pairwise disjoint, then ;
6) if , then .
References
[1] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) |
Comments
The characteristic function of a set is also called the indicator function of that set. The symbols or are often used instead of .
How to Cite This Entry:
Characteristic function of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_function_of_a_set&oldid=12927
Characteristic function of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_function_of_a_set&oldid=12927
This article was adapted from an original article by A.A. Konyushkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article