What does the notation $\subset \subset$ mean?
In my class notes, our prof writes $\Omega \subset \subset \mathbb{R}^{n}$ to mean that "$\Omega$ is a convex subset of $\mathbb{R}^{n}$". Is that all that this means, or is there any more to it than that? I'm just curious because I've never seen this notation before, and don't want any of it's subtleties or nuances lost on me.
Best Answer
The usual meaning is "strongly included": $A\subset\subset B$ when $\overline A$ compact and $\overline A\subset B$.
http://books.google.es/books?id=1bFCAAAAQBAJ&pg=PA583&lpg=PA583&dq=%22strongly+included%22+functional+analysis&source=bl&ots=pLvX3_U1Y6&sig=b2lHPap1QvXi0ITvfTw-DwDVTJQ&hl=en&sa=X&ei=xWHlUtOkEoja0QXyg4HgAg&redir_esc=y#v=onepage&q=%22strongly%20included%22%20functional%20analysis&f=false