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For really long sub(super)scripts, does it look bad to decrease the kerning? i.e.

\lim_{n\to\infty}{\dfrac{1}{s_n^2}\sum_{i=1}^n \int_{|x-\mu_i|>\varepsilon s_n} (x-\mu_i)^2f_i(x)dx}=0

enter image description here

\lim_{n\to\infty}{\dfrac{1}{s_n^2}\sum_{i=1}^n \int_{|x-\mu_i|>\varepsilon s_n} \kern-1cm(x-\mu_i)^2f_i(x)dx}=0

enter image description here

\lim_{n\to\infty}{\dfrac{1}{s_n^2}\sum_{i=1}^n \int_{|x-\mu_i|>\varepsilon s_n|} \kern-1.5cm(x-\mu_i)^2f_i(x)dx}=0

enter image description here

Is it innappropriate to decrease the kerning? If not, which one looks best? Also, is there a better way to do this?

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you need to INcrease not DEcrease the kerning. It's getting less and less readable. I'd put the integral sign on top of the path. You are using that space anyway –  percusse Aug 6 at 19:51
    
I actually did want to decrease the kerning, I did not think the white space between the integral sine and the integrand looked good. Your suggestion of moving the region of integration down is handled by @cmhughes answer. –  Benjamin Aug 6 at 20:12
    
I meant spacing out each operator, not gluing them together –  percusse Aug 6 at 20:13

2 Answers 2

up vote 7 down vote accepted

I prefer the following. The important point is that there's no value to give: it uses the \mathrlap command from mathtools and you decide at which place in the index you set it.

\documentclass{report}
\usepackage{mathtools}

\begin{document}

\[ \lim_{n\to\infty}{\dfrac{1}{s_n^2}\sum_{i=1}^n \int_{|x\mathrlap{-\mu_i|>\varepsilon s_n}} (x-\mu_i)^2f_i(x)dx}=0 \]%

\end{document} 

enter image description here

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For the sake of decent math, please remove the third vertical bar in the limit of integration. For the sake of good TeX code, please remove the curly braces that start before \dfrac and end before =0. –  Mico Aug 6 at 18:37
    
ah completely missed the third vertical bar! Thanks for pointing it out! –  Benjamin Aug 6 at 18:38
    
@Mico: I noticed it but didn't know if there was a seconf absolute value or not. –  Bernard Aug 6 at 18:43
    
@Benjamin: Should it be |sₙ| or sₙ in the subscript? –  Bernard Aug 6 at 18:47
    
@Mico was right its just $s_n$. –  Benjamin Aug 6 at 19:42

Here's some more alternatives for reference:

screenshot

% arara: pdflatex
\documentclass{report}
\usepackage{mathtools}

\begin{document}

\[ 
    \lim_{n\to\infty} \dfrac{1}{s_n^2}\sum_{i=1}^n \int_{|x\mathrlap{-\mu_i|>\varepsilon s_n}} (x-\mu_i)^2f_i(x)dx=0 
\]%
Using \verb!\limits!
\[ 
    \lim_{n\to\infty} \dfrac{1}{s_n^2}\sum_{i=1}^n \int\limits_{|x\mathrlap{-\mu_i|>\varepsilon s_n}} (x-\mu_i)^2f_i(x)dx=0 
\]%
Using a local definition, 
\[ 
\lim_{n\to\infty} \dfrac{1}{s_n^2}\sum_{i=1}^n \int_{a_i} (x-\mu_i)^2f_i(x)dx=0 
\]%
where $a_i=|x-\mu_i|>\varepsilon s_n$

\end{document}
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1  
To make the notation unambiguous, you may want to write a_{i,n} in the limit of integration, i.e., make a a function of both i and n (since it depends on s_n). –  Mico Aug 6 at 19:39
    
Good contribution, however, I like that mathrlap gives me some say in how much overlap there is. –  Benjamin Aug 6 at 19:43
    
@Benjamin - the first proposed solution does include an \rlap directive. –  Mico Aug 6 at 19:45
    
I was just explaining why I chose the other solution as "the" answer –  Benjamin Aug 6 at 19:49
1  
I don't know if it's good math or not, but, if it is, I think placing the subscript below the integral provides better visual separation, making it look less crowded and easier to read. In the accepted answer, it looks less like a subscript and more like a second line. If you can't place the subscript below the integral sign, at least lower it and/or make it smaller. –  trlkly Aug 7 at 4:20

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