Question:

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

\epsilon > 0 there are measurable sets B and C such that 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