# Correct way to typset esssup (essential supremum)

What is the correct way to typeset essential supremum, with the limits underneath the operator? My first try was \operatorname{ess}\sup\limits_{x\in[0, 1]}, but this puts the x\in[0, 1] under the sup only.

The best I got was using \operatorname*{ess\,sup}_{x\in[0, 1]}, but I'm not sure if \, is the correct amount of space. Is there some way to trick \limits to working here?

-

The following defines an new math operator with:

• \DeclareMathOperator{\OperatorCommand}{OperatorName} and
• \DeclareMathOperator*{\OperatorCommand}{OperatorName} if limits are to be used.

\documentclass[letterpaper]{article}
\usepackage{amsmath}
% We use the starred versions since we are interested in using limits.
% You can use \thinspace if you want to use a command. If you want to use more math oriented
% commands you can use \mspace{<length in mu>} like \mspace{2mu}
\DeclareMathOperator*{\esssup}{ess\,sup}

\begin{document}
$\esssup_{x\in[0, 1]}$
\end{document}


The \, and \! commands are the most useful for fine tuning math formulas.

Note that \thinspace is the same thing as \,.

Spaces which are very useful can be:

• \thinspace = \,
• \medspace = \:
• \thickspace = \;

Negative spaces now:

• \negthinspace = \!
• \negmedspace
• \negthickspace

If we get a little bit more technical, in the amsmath.sty, we can find the definitions of the above as:

\DeclareRobustCommand{\tmspace}[3]{%
\ifmmode\mskip#1#2\else\kern#1#3\fi\relax}

\renewcommand{\,}{\tmspace+\thinmuskip{.1667em}}
\let\thinspace\,

\renewcommand{\!}{\tmspace-\thinmuskip{.1667em}}
\let\negthinspace\!

\renewcommand{\:}{\tmspace+\medmuskip{.2222em}}
\let\medspace\:

\newcommand{\negmedspace}{\tmspace-\medmuskip{.2222em}}

\renewcommand{\;}{\tmspace+\thickmuskip{.2777em}}
\let\thickspace\;

\newcommand{\negthickspace}{\tmspace-\thickmuskip{.2777em}}

\newcommand{\mspace}[1]{\mskip#1\relax}


Of course, \mspace{<length>} can be used for both positive and negative spaces. For example, \mspace{1mu} and \mspace{-1mu} where mu means math unit.

Note that \, is used extensively even to define \limsup command in the amsmath package in the following manner:

\def\limsup{\qopname\relax m{lim\,sup}}


The above can be found in amsopn.sty.

-
Note that \, and friends are math spacing whereas \thinspace and co. are text spacing, which is a critical distinction (it produces errors otherwise). –  Alex Nelson Dec 10 '12 at 3:29
@AlexNelson Hmmm is it? I didn't know that. What errors are you talking about? –  azetina Dec 10 '12 at 3:36
sum was a typo. It should be sup everywhere. –  asmeurer Dec 10 '12 at 3:40
@AlexNelson amsmath defines \, as \renewcommand{\,}{\tmspace+\thinmuskip{.1667em}}. This means that +\thinmuskip (\thinmuskip=3mu=3/18em=.1667em) is used in math mode, .1667em in text mode. Furthermore, amsmath lets \thinspace to \,, so they are equal. –  Qrrbrbirlbel Dec 10 '12 at 4:16
@AlexNelson The command \, can be used in both text and math mode, where it has the same behavior. Well, this is not strictly true, of which I can give a wonderful proof, but comments are too short to contain it. –  egreg Dec 10 '12 at 8:41