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Measure theory problem

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data
    Let (R,M,m) be Lebesgue measure space in R. Given E contained in R with m(E)>0 show that the set
    E-E defined by

    E-E:={x in R s.t. exists a, b in E with x= a-b }

    contains an interval centered at the origin

    2. Relevant equations

    try to prove by contradiction and use the fact that for every a in (0,1) there exists an interval I s.t. m(E∩ I)>am(I)
  2. jcsd
  3. Apr 21, 2014 #2


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    What have you tried?
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