Here is an excerpt from "All of Statistics" by Larry Wasserman (page 23):

Given an event A, define the indicator function of A by

$$ I_{A}(\omega)= \color{Red}{I(\omega \in A)} =\begin{cases} 1 & \text{ if } \omega \in A \\ 0 & \text{ if } \omega \notin A \end{cases} $$

I am not convinced, referring to term colored red, with the notation here. Since this is a widely referred text, I would like to know that whether this is a typo or I am missing something here.

  • $\begingroup$ @Tim: I can't follow the significance of '>' and '<'. Please explain. $\endgroup$ – zen Apr 12 '15 at 16:06
  • $\begingroup$ Sorry, something strange happen while saving edit. Those signs shouldn't be there - my edit was only to highlight the quote. $\endgroup$ – Tim Apr 12 '15 at 18:52

I see no suggestion there's a typo; it looks reasonably straightforward to me.

I'd informally read it left to right as something like:

"Define the function $I_A(\omega)$ -- an indicator of $(\omega\in A)$ -- which takes the value $1$ when $\omega\in A$ and $0$ otherwise."

  • 4
    $\begingroup$ (+1) This is a most standard notation that indicates whether or not the measurable event "$\omega\in A$" has occurred. $\endgroup$ – Xi'an Apr 12 '15 at 8:31

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