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Measure of a union of translates

  1. May 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Problem 5 of http://www.math.northwestern.edu/graduate/prelims/anal-f06.pdf

    2. Relevant equations



    3. The attempt at a solution

    So I've managed to prove it's true if F is an open set. However, I don't know how else to proceed. I tried setting [tex] \mu (F) = m( \cup_n F + a_n [\tex] (where m is lebesgue measure) but I discovered it it wasn't necessarily a measure.

    I just want some hints, that's all.
     
  2. jcsd
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