Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?