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I'm studying a course on probability and statistics and at some point this symbol comes up without introduction. It looks like the number one, but slightly bigger and with a double vertical line.

First time it comes up is when discussing stochastic/random variables that are neither continuous nor discreet in an example: First example

And somewhat later in a proof:

Second example

Anyone got an idea what this symbol represents?

EDIT: Thanks for the fast answers, I was still editing the question for better (larger) images :)

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@Martin Sleziak, thanks for the corrections! –  Yohsoog May 1 at 19:54
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For those wondering, the symbol (𝟙 in Unicode; fonts may lack it) is the blackboard bold / open face / double-struck digit one — the same style as ℕ, ℝ, ℤ, etc. –  deltab May 2 at 1:13

3 Answers 3

up vote 18 down vote accepted

It's the characteristic function (or indicator function) of the set in the subscript.

$$\mathbb 1_A(x) = \begin{cases} 1\,, & x\in A \\ 0\,, & x\notin A\end{cases}.$$

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I think you mis-wrote that? Your $1_A$ does not appear to be the outline version in the OP. –  KRyan May 2 at 2:49
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@KRyan So? It's still the same object. –  Pierre Arlaud May 2 at 10:57
    
Interestingly, it shows us in "blackboard" font just fine on my desktop, but not on my iPad. Perhaps you should try a different computer, @KRyan. –  Ted Shifrin May 2 at 11:25

It is the indicator function.

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It's the indicator function, you can write $\chi_A(x)=\begin{cases}1, & x\in A\\0, & x\notin A\end{cases}$ instead. It's easier in $\text{LaTeX}$ and everybody knows that you mean the indicator function.

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"everybody knows that you mean the indicator function" -> except for the OP, apparently. –  mikeTheLiar May 1 at 20:47
    
@mikeTheLiar, except for who? –  Milena May 1 at 22:39
    
@Milena the OP (original poster) - the person who asked this question exactly because they didn't know what it meant. –  mikeTheLiar May 1 at 22:41
    
I just wanted to give an alternative possibility to write it in case the OP finds this different notification in context of his literature. Surely the OP does not know it if he did not know the other way to write it. –  math12 May 1 at 22:45
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I knew the double-struck 1 notation but I haven't seen the chi-notation often and would not immediately think of this. So "everybody knows that you mean ... " is a bit of an over-generalization. –  CompuChip May 2 at 10:43

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