How to write the limit inferior in math environment?

Question

I got it to work with

\mathop{\underline{\lim}}_{n \to \infty} f_n(x)

Above looks exactly how I want it to look, but initiating operators twice is odd and it's far from simple

\lim_{n \to \infty} f_n(x)

Or is it alright?

Answer 1

If you are using the amsmath package, you don't have to define a new operator; the package offers \varliminf with the correct spacing:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[ \varliminf_{n \to \infty} f_n(x) \]
\end{document}

Answer 2

If this is used often, then declare it as a math operator. It promotes consistency (see Consistent typography) and ease-of-use:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\DeclareMathOperator*{\inflim}{\underline{\lim}}
\begin{document}
\[ \mathop{\underline{\lim}}_{n \to \infty} f_n(x) \]
\[ \inflim_{n \to \infty} f_n(x) \]
\end{document}

See the amsmath documentation (section 5.1 Dening new operator names, p 17) for the use of/difference in DeclareMathOperator and its starred variant.