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Measure of a set E is zero, so is E^2

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data

    If m*(E)=0, then m*(E^2)=0.

    3. The attempt at a solution

    I have observations which may or may not make sense.

    Obviously we have that {Ik} is a cover of E. So we want {I2k} to be a cover E2.

    I have a chain of inequalities which may/may not make sense.

    0 = m*(E) = [itex] \sum [/itex] m*(E [itex]\cap[/itex] Ik) [itex]\geq[/itex] [itex]\sum m^{*}(I_k) > \sum m^{*}(I_k^2) [/itex]

    That's pretty much the extent of my knowledge.
     
  2. jcsd
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