[Tex/LaTex] Vertical align \underset

Question

I have this equation:

\lim_{d \rightarrow \infty} \left [ \underset{a\leq x\leq b}{\mathrm{max}_p} \left | f(x) - m(x) \right | \right ] = 0

which produces this:

As you can see the max part is not vertically aligned inside the brackets. The lim is also not aligned with the brackets. I want it to look something like this:

As you can see, the lim and max part is now properly aligned. The absolute | | height should also be adjusted to fit the height of the \underset part of max.

Anyone know how to do this?

Answer 1

The names ‘lim’ and ‘max’ should be at the same level as ‘f’; also the absolute value bars should be as high as necessary to cover the material inside them; what's before the opening bar is irrelevant as far as the absolute value is concerned.

This is a case where \left and \right are plainly wrong, because they produce too large delimiters. I don't think the square brackets are necessary, because ‘max_p’ has obvious precedence over ‘lim’.

Here are two realizations, with and without the brackets; note the definition of the \maxp operator. In the first realization, a thin space \, has been added in order for the bracket not to clash with the subscript.

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator*{\maxp}{max_{\mathnormal{p}}}

\begin{document}
\[
\lim_{p\to\infty}
  \Bigl[
    \,\maxp_{a\le x\le b} \lvert f(x)-m(x)\rvert
  \Bigr]
\]
\[
\lim_{p\to\infty} \maxp_{a\le x\le b} \lvert f(x)-m(x)\rvert
\]
\end{document}

You may want to look at \adjustlimits from the mathtools package:

\documentclass{article}
\usepackage{amsmath,mathtools}

\DeclareMathOperator*{\maxp}{max_{\mathnormal{p}}}

\begin{document}
\[
\adjustlimits\lim_{p\to\infty} \maxp_{a\le x\le b} \lvert f(x)-m(x)\rvert
\]
\end{document}

but I'd prefer the former realization.