Question:

Suppose that A is a subset of $\displaystyle \mathbb{R}$ with the property that for every

$\displaystyle \epsilon > 0$ there are measurable sets B and C such that $\displaystyle B \subset A

\subset C \,\,and \,\,m(C \cap B^c) < \epsilon$. Prove that A is measurable.

My attempt:

Im finding this stuff really tricky!

I know the definition of a set

being measurable but having real difficulty showing it. I know that i have

to use the fact that B and C are both measurable, but dont know what set to

use in the definition! help please! thanks