(adsbygoogle = window.adsbygoogle || []).push({}); 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...

Please Reply Over!...

Mike

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# Homework Help: Prove something is Lebesgue measurable

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