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{enskipmuenskip} f
f_n xrightarrow{enskip L^penskip} 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