# How is $I_{[0,\infty)}(t)$ defined?

How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.

-
It's likely an indicator function: it has value 1 on $[0,\infty)$ and 0 on $(-\infty,0)$. – David Mitra Jul 4 '12 at 12:55
Although indicator functions come up in probability, it doesn't seem that an indicator over an infinite interval would come up. – Michael Chernick Jul 4 '12 at 15:26

You can use the Heaviside Step Function $H(t)$:
$H(0) = 1$ is used when $H$ needs to be right-continuous. For instance cumulative distribution functions are usually taken to be right continuous, as are functions integrated against in Lebesgue–Stieltjes integration. In this case $H$ is the indicator function of a closed semi-infinite interval: $$H(t) = \mathbf{I}_{[0,\infty)}(t).\,$$
...or one could use Iverson brackets as well: $[t \geq 0]$. – J. M. Aug 9 '12 at 10:49