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Simple measure theory questions (inverse image)

  1. May 4, 2012 #1
    1. The problem statement, all variables and given/known data
    I was wondering if we Let E be some set such that f-1(E) is measurable then so is f-1(E)c.

    2. Relevant equations

    If the set A is measurable then so is its compliment.

    3. The attempt at a solution

    I think the statement is true because f-1(E) is just a set and thus its compliment should also be measurable.

    Thank you for your time.
    Last edited: May 4, 2012
  2. jcsd
  3. May 4, 2012 #2
    Yeah that is correct.
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