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My book uses both of the functions $\epsilon _{X_i}(I_n)$ and $1_{X_i\in I_n}$ once with an equality sign, otherwise just the first one. Is this different notation for the same function?

Thanks in advance!

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  • $\begingroup$ If your book uses two different notations consistently throughout, it is possible they are different objects. $\endgroup$
    – Pedro
    Jan 6, 2014 at 13:27
  • $\begingroup$ Yes that is my suspicion, but I have only seen the common notation for the indicator function once, so no real consistency. Don't know if the author was trying to be extra clear there. $\endgroup$
    – Alexander
    Jan 6, 2014 at 13:32
  • $\begingroup$ Cannot you trace the definitions back in the book? $\endgroup$
    – Pedro
    Jan 6, 2014 at 14:14

1 Answer 1

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Now I found the answer myselft, he use it to denote the discrete measure. http://en.wikipedia.org/wiki/Discrete_measure

$$\epsilon _{X_n}(A)=\{_{0, if X_n \setminus A}^{1, if X_n \in A}$$ .

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    $\begingroup$ ...While the rest of the world would probably use $\delta_{X_n}$ to denote this Dirac measure. $\endgroup$
    – Did
    Jan 6, 2014 at 14:38

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