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Prove combination of two sets contains an open ball

  1. Dec 17, 2011 #1
    So this was an exam question that our professor handed out ( In class. I didn't get the question right)

    Let E be a subset of R^n, n>= 2. Suppose that E measurable and m(E)>0. Prove that:

    E+E = {x+y: x in E, y in E } contains an open ball.

    (The text Zygmund that we used showed an example that E-E defined in similar sense contains an open interval centered at the origin, where E is a subset of R. Stein had another problem that asked to show that E+E contains an open interval.

    I'm assuming that's where he got the problem, but I'm not sure that the same method works, since he gave a hint to prove that the convolution: chi(e)*chi(e) is continuous at the origin. )
     
  2. jcsd
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