What does the symbol $\subset\subset$ mean?

Question

In some texts (mainly complex analysis or harmonic analysis) I sometimes see the following double subset symbol $\subset\subset$ for inclusion relation of two regions, e.g., $\Omega$ and $\Omega'$ are two regions in $\mathbb{C}$ such that $\Omega \subset\subset \Omega'$. I never figured out what it means exactly; I always interpreted it as the closure $\overline{\Omega}$ is contained in $\Omega'$ (so that some nasty boundary effects can be avoided). Is that right? Or does $\subset\subset$ mean some other kind of inclusion? Thanks.

Answer 1

It usually (the only meaning I've come across yet) means that $\Omega$ is relatively compact in $\Omega'$, so the closure of $\Omega$ is compact and contained in $\Omega'$.