I'm a new user of LyX. I'm using it to write math lectures.
How can I make a new symbol from two existing ones? To be more precise, how can I create this:

It's a subset with a circle in it (\subset, \circ).
I'm a new user of LyX. I'm using it to write math lectures.
How can I make a new symbol from two existing ones? To be more precise, how can I create this:

It's a subset with a circle in it (\subset, \circ).
I'm not sure how friendly my answer is to a new LyX user... but
\! can be used to give negative horizontal spacing in math mode.
Wrapping with \mathrel{} adjust the spacing around the new symbol.
\documentclass[varwidth]{standalone}
\usepackage{amsmath}
\newcommand{\subsetcirc}{\mathrel{\subset\!\!\!\!\!\circ}}
\begin{document}
$A \subset B$
$A \subsetcirc B$
\end{document}

See also: question on how to create symbol on top of each other
Here's a solution that uses the TeX "primitive" commands \ooalign, \kern, and \raise (as well as \hss, \cr, and \hbox). It also uses, unsurprisingly, the "standard" symbols \subset and \circ.

If you want to make the circle larger or smaller, change the first argument of the \scalebox command. To shift the circle a bit more to the right, increase the argument of the \kern command. And, if you use a package that uses its own forms of the subset and circle symbols, you may need to tweak the code a bit more to get a satisfactory positioning of the symbols.
\documentclass{article}
\usepackage{graphicx} % for \scalebox macro
\newcommand\subsetcirc{%
\mathrel{\ooalign{\hss$\subset$\hss\cr%
\kern0.6ex\raise0.2ex\hbox{\scalebox{0.7}{$\circ$}}}}}
\begin{document}
$A\subsetcirc B$
\end{document}
Another possibility is
\documentclass{article}
\newcommand*\subsetcircle{\mathrel{\ooalign{$\subset$\cr\hidewidth\hbox{$\circ\mkern 1mu$}\cr}}}
\begin{document}
$A\subsetcircle B$
\end{document}
