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Homework Help: Prove something is Lebesgue measurable

  1. Nov 13, 2007 #1
    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!...

    Last edited: Nov 13, 2007
  2. jcsd
  3. Nov 14, 2007 #2


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    I'd try to use the fact that G - A has to be a subset of B.
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