Indicator function

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

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

It "indicates" whether or not [ilmath]x[/ilmath] is in [ilmath]A[/ilmath]

Other notations

I have also seen: [ilmath]1_A[/ilmath] used to denote the indicator function


  1. Probability and Measure - Anniversary Edition - Patrick Billingsley