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!
$\begingroup$
$\endgroup$
3
-
$\begingroup$ 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. $\endgroup$– AlexanderJan 6, 2014 at 13:32
-
$\begingroup$ Cannot you trace the definitions back in the book? $\endgroup$– Pedro ♦Jan 6, 2014 at 14:14
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
Now I found the answer myselft, he use it to denote the discrete measure. http://en.wikipedia.org/wiki/Discrete_measure
$$\epsilon _{X_n}(A)=\{_{0, if X_n \setminus A}^{1, if X_n \in A}$$ .
-
1$\begingroup$ ...While the rest of the world would probably use $\delta_{X_n}$ to denote this Dirac measure. $\endgroup$– DidJan 6, 2014 at 14:38