Indicator function

Definition

The indicator function, given by $I_A:X\rightarrow\{\alpha,\beta\}$ where $A\subseteq X$ and typically $\alpha=0\in\mathbb{R}$ and $\beta=1\in\mathbb{R}$ where:

• $$I_A:x\mapsto \left\{\begin{array}{lr} 1 & x\in A\\ 0 & \text{otherwise} \end{array}\right.$$

It "indicates" whether or not $x$ is in $A$

Other notations

I have also seen: $1_A$ used to denote the indicator function