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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!

Alexander
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  • If your book uses two different notations consistently throughout, it is possible they are different objects. – Pedro Jan 06 '14 at 13:27
  • 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. – Alexander Jan 06 '14 at 13:32
  • Cannot you trace the definitions back in the book? – Pedro Jan 06 '14 at 14:14

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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

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

Alexander
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    ...While the rest of the world would probably use $\delta_{X_n}$ to denote this Dirac measure. – Did Jan 06 '14 at 14:38