Indicator Function

Products of Indicator Functions

• Because $0\cdot 1=0$, the product of indicator functions can be combined into a single indicator function with a modified condition.
• Examples
  • $I_{\{x<5\}}\cdot I_{\{x\ge 0\}}=I_{\{0\le x<5\}}$
  • $\prod _{i=1}^n{I}_{\left\{x_i<2\right\}}=I_{\left\{x_i<2\text{forall}i\right\}}=I_{\left\{{\max }_i{x}_i<2\right\}}$

Related

References