# Align consecutive operator subscripts in equation [duplicate]

I have to write the definition of uniform convergence. That is, the superior limit in the succession's pointwise convergence's set of the limit for n to infinite of the absolute value of the difference between the n-th function and the limit function evaluated in x. More difficult said than done. The fact is, written in LaTeX this way:

$\sup_{x\in I}\lim_{n\to\infty}\left|f_n(x)-f(x)\right|=0$


Results in this:

The range of \sup and \lim are not aligned, resulting in a rather displeasant appearance. I tried adding \vphantoms in the subscripts (just in case the problem is in the capital I), but even putting the same subscript in the \lim and the \sup changes nothing, the problem is in the p letter of the latter which shifts the subscript lower than the other one.

Can anybody tell me how to ignore it?

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You can make use of mathtools' \adjustlimits command, which is made for exactly this kind of situation.
\documentclass[border=10pt]{standalone}
$$\displaystyle % <--- Just to get correct size of output in standalone class \adjustlimits\sup_{x\in I}\lim_{n\to\infty}\left|f_n(x)-f(x)\right|=0$$