Note: I can't finish this till I get Dr Ov's book so I can use Thm 2.4i, 2.4iii, 2.48

### Prove that a function $f $on $[a,b]$ is measurable iff $f$ inverse($U$) is measurable for any open set $U$ of $R$.

$\Rightarrow$
\newline
By Theorem 2.4i, and Theorem 2.4iii, we have 2 open sets:
\newline
$ J = { x: f(x)