Indicator Function
The indicator function of maps when and when .
Definition 2.19 (Indicator Function)
Given a set and , we have the indicator function (or characteristic function) of , defined by
Properties
For subsets of : , , , and .
Proof of property four
, using the De Morgan identity and multiplicativity on intersections.
Related
Stated in
- Definition 2.19 (Indicator Function)§2.2.1 Examples of Functions