# Best spacing around binary relations followed by operators with wide subscripts

I have the following equation:

\documentclass{amsbook}

\usepackage[frenchstyle]{kpfonts}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}
$\abs[\Big]{\varint f(x)\D{x}} = \lim_{k\to +\infty} \abs[\Big]{\varint f_k(x) \D{x}} \leqslant \lim_{k\to +\infty} \int\abs{f_k(x)} \D{x} = \int\abs{f(x)}\D{x}$
\end{document}


which I spaced as follows, by sheer trial and error until I got something aesthetically pleasing:

$\abs[\Big]{\varint f(x)\D{x}\;}\;\: % <-- Pure empirical spacing = \lim_{k\to +\infty} \abs[\Big]{\varint f_k(x) \D{x}\;}\;\: % <-- \leqslant \lim_{k\to +\infty} \int\abs{f_k(x)} \D{x}\; % <-- = \int\abs{f(x)}\D{x}.$


As you can appreciate, for each binary relation I tried to leftwards get the same amount of blank space produced rightwards by either the long subscripts of the limit operators or by the integral symbol, as well as to center the body of the integrals within the absolute value.

My questions are:

1. Am I adding too much, superfluous, blank space? If so,
2. What would be a better, more austere solution?
3. Is there an intrinsic way to measure and reproduce the distance between = or \leqslant to the l of \lim or the midpoint of \int to the right?

I already discarded to use \smashoperator from mathtools.

• Does this help tex.stackexchange.com/q/3782/91556 ? In fact I would prefer using align for equation environment and break the equation manually at the point of my preference. – hesham Jun 9 at 17:30
• @hesham Not at all, because I'm just talking about horizontal spacing. – Fitzcarraldo Jun 9 at 18:11
• it's all very subjective but I prefer the first version (although the spacing is a bit tight) I think you are over-compensating so the relations (especially the <= in the middle) look asymmetric with a bigger gap to the left (because they are asymmetric with a bigger gap to the left:-) – David Carlisle Jun 9 at 20:01
• I tried your example and got ! Undefined control sequence. <recently read> \DeclarePairedDelimiter  – David Carlisle Jun 9 at 20:05

Not sure I like this but just putting it as a possibility.

Keeping the default tighter spacing around relations but shrinking the limit subscripts so they are less disturbing, and adding an extra {} to get mathop spacing before the |

\documentclass{amsbook}
\usepackage{mathtools}%<<<<
\usepackage[frenchstyle]{kpfonts}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}
$\abs[\Big]{\varint f(x)\D{x}} = \lim_{\scriptscriptstyle k\to +\infty}{} \abs[\Big]{\varint f_k(x) \D{x}} \leqslant \lim_{\scriptscriptstyle k\to +\infty} \int\abs{f_k(x)} \D{x} = \int\abs{f(x)}\D{x}$
\end{document}