How to interpret the identity function in this formula?

Question

I am confused by the identity function notation in a formula:

$f(y|\theta)= \theta\cdot e^{-\theta\cdot y}I_{(0, \infty)}(y)$

Could someone help me understand what $I_{(0, \infty)}(y)$ means in the formula?

Thank you so much in advance!

Answer 1

$I_{(0,\infty)}$ is the "indicator function" or "characteristic function" of the set $(0,\infty)$. It takes the value $1$ if its argument is in the set $(0,\infty)$ and $0$ otherwise. You might write $$I_{(0,\infty)}(y) = \begin{cases} 1&\text{if $0<y<\infty$}\\0 & \text{otherwise.}\end{cases}$$