# Homework Help: Prove something is Lebesgue measurable

1. Nov 13, 2007

### SNOOTCHIEBOOCHEE

Let A be a subset of [0, 1].
And B is [0, 1] - A.
Assume m_e(A) + m_e(B) = 1.
Prove that A is Lebesgue measurable.

m_e denotes the standard outer measure.

2. Relevant equations

A subset E of R^n is said to be lebesgue measurable, or simply measurable, if given epsilon, there exists an open set G such that E is in G and |G - E|_e < epsilon.

3. The attempt at a solution

I'm trying to use Caratheodory's Theorem, but with no avail. I am now completley lost on this problem...