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I have the following line in TeX and my problem is that the backslash is too small and the text under the bigcup becomes very cumbersome:

$$ess \ supp(f) = W \ \backslash \bigcup_{\Omega \subset W 
\text{ open and }  f|_{\Omega}=0 \text{ a.e.}} \Omega$$

Is there any way to remedy those difficulties?

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Is it an option to have the descriptive text open and and a.e. outside of the equation? –  Holene May 4 at 10:13

2 Answers 2

up vote 9 down vote accepted

I think a combination of (i) defining "ess sup" to be an "operator" (so that it's set in the upright font shape) and (ii) using both \mathclap (from the mathtools package) and \substack (from the amsmath package, which is loaded automatically by mathtools) may achieve what you want. Oh, and don't use \backslash -- I believe \setminus is more appropriate in this context.

enter image description here

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator{\esssupp}{ess\,supp} % "essential support"
\setlength\textwidth{3in} % just for this example
\begin{document}
\noindent before:
\[
ess \ supp(f) = W \ \backslash \bigcup_{\Omega \subset W 
\text{ open and }  f|_{\Omega}=0 \text{ a.e.}} \Omega
\]

\noindent after:
\[
\esssupp(f) = W \setminus 
\bigcup_{ \mathclap{\substack{\Omega \subset W \text{\,open,} \\
                              f|_{\Omega}=0 \text{ a.e.}}}} \Omega
\]
\end{document}

Addendum As pointed out by @Manuel in a comment, you may also be interested in using the \smashoperator macro (instead of \mathclap):

enter image description here

\[
\esssupp(f) = W \setminus 
\smashoperator[r]{\bigcup_{ \substack{\Omega \subset W \text{\,open,}  \\ 
                                      f|_{\Omega}=0 \text{ a.e.}}}} \Omega
\]
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2  
mathtools also offers \smashoperator[lr]{…} for this kind of occasions. –  Manuel May 4 at 10:35
    
@Manuel - Thanks for this. I've posted an addendum to the answer to provide an application of this very useful macro. –  Mico May 4 at 10:45
    
It is the essential support, so the operator name should end with to p's. –  egreg May 4 at 11:10
    
@Mico: The horizontal spacing cant be improved (in my opinion) if one asks to use \scriptscriptstyle in each line of the substack. –  Bernard May 4 at 11:22
    
@egreg - thanks for pointing out this mis-interpretation. I'll fix the write-up right away. –  Mico May 4 at 11:23

In my opinion there's no way to make this beautiful with such long conditions below the union symbol. I'd prefer something like

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator{\esssupp}{ess\,supp}
\newcommand\tae{\unskip\text{ a.e.}}

\begin{document}
\noindent before:
\[
ess \ supp(f) = W \ \backslash \bigcup_{\Omega \subset W
\text{ open and }  f|_{\Omega}=0 \text{ a.e.}} \Omega
\]
after:
\[
\esssupp(f) = W \setminus
\bigcup\{\,\Omega: \text{$\Omega \subset W$ open, $f|_{\Omega}=0$ \tae}\,\}
\]
Alternative:
\[
\esssupp(f) = W \setminus
\bigcup_{
  \mspace{-6mu}
  \substack{\Omega\subset W\text{ open}\\f|_{\Omega}=0\tae}
  \mspace{-15mu}
}\Omega
\]
\end{document}

In the alternative way, the conditions should not go too much below the \setminus symbol and the final \Omega should be somewhat on the right of the conditions. But the preferred way should be with the set notation.

enter image description here

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