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?

1 Answer 1


The following defines an new math operator with:

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

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% 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}

\[\esssup_{x\in[0, 1]}\]

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:









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). Dec 10, 2012 at 3:29
  • @AlexNelson Hmmm is it? I didn't know that. What errors are you talking about?
    – azetina
    Dec 10, 2012 at 3:36
  • 2
    @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. Dec 10, 2012 at 4:16
  • 4
    @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, 2012 at 8:41
  • 3
    @egreg Beautiful! So we must wait 350 years for this proof. ;-) Dec 27, 2017 at 12:25

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