Mathematical notation of convergence in latex

As Sigur mentioned in the comments you could use amsmath's \xrightarrow{•}.

f_n \xrightarrow{\mu} f

Unfortunately this leads to a quite short arrow:

There are multiple options to get a longer arrow. You could just add some space at the left and right. But this still leads to differently long arrows depending on the overset content.

f_n \xrightarrow{\enskip\mu\enskip} f
f_n \xrightarrow{\enskip L^p\enskip} f

To prevent this you could use \overset{•}{•} combined with a \longrightarrow.

f_n \overset{\mu}{\longrightarrow} f
f_n \overset{L^p}{\longrightarrow} f

But in this case imho the arrow is still a little bit short. So the best way is probably to define a custom \xrightarrow with a fixed width like this. Change the predefined value 2em to get a shorter or longer arrow.

\newcommand{\myrightarrow}[1]{\xrightarrow{\makebox[2em][c]{$\scriptstyle#1$}}}‌

Which can then easily be used like this:

f_n \myrightarrow{\mu} f
f_n \myrightarrow{L^p} f