How to place a \mathcal{D} below the text "err"

Question

If err is a operator, I know how to do it, but erris a text, I don't know how to do it.

Answer 1

First a glimpse from amsmath manual (page 17):

What you need is

\DeclareMathOperator*{\err}{err}

To have \mathscr, load mathrsfs too.

\documentclass{article}
\usepackage{amsmath,mathrsfs}
\DeclareMathOperator*{\err}{err}
\begin{document}
  \[\err_{\mathscr{D}}(f)\]
\end{document}

As noted by barbara beeton in her comments, the font of err is fraktur. To reproduce the same, load amsfonts package additionally and then define

\DeclareMathOperator*{\err}{\mathfrak{err}}

Answer 2

In addition to Harish Kumar's comment you can also use \underset from the amsmath package to really place it below the err operator. So in addition to declaring the err operator you can set it then like this:

\[
  \underset{\mathcal{D}}{\err}
\]