Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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: $$ H(t) = \mathbf{I}_{[0,\infty)}(t).\, $$

share|cite|improve this answer
...or one could use Iverson brackets as well: $[t \geq 0]$. – J. M. Aug 9 '12 at 10:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.