In "A domain theoretic account of Picard's theorem" (http://www.doc.ic.ac.uk/~dirk/Publications/icalp2004.pdf), the authors assert the following.

Let $\mathbb{IR}$ be the interval domain $\lbrace [a^-,a⁺] | a^- \leq a^+, a^-, a^+ \in \mathbb{R} \rbrace \cup \lbrace \mathbb{R} \rbrace$.

Suppose $f = [f^-,f^+] : [-a,a] \rightarrow \mathbb{IR}$ is Scott continuous. Then $f^-$ and $f^+$ are measurable.

Their proof consists in asserting that $f⁻$ and $f⁺$ are lower (resp. upper) semi-continuous, which I have tried without success to establish. Can anyone help with either an explanation or a reference that proves it?


Question: Ubuntu 12.04.2 LTS vs. Ubuntu 12.10?
Answer: I think it all depends on when you will upgrade your reinstall your distribution again. If you want it to last for a while and don't really care about having the lastest versions of every piece of sotfware, you should go with 12.04. While 12.10 has some awesome features like the new Nautilus or Gnome 3.6, it may be a little buggier (though it all depends on you computer). You can use Gnome with either of them, and it works very well, but in 12.04 you only get Gnome 3.4, though. Kernel-wise, they use 3.5, so there is not much difference between the distributions.

In my case, I was perfectly happy with 12.04, and only installed 12.10 to try Gnome Shell 3.6 and really like the new Nautilus.

So, in the end, I would suggest 12.10, but you will be happy with wichever you choose.