Hi,
I have this question that i've been thinking about for weeks and i cannot find an answer or even a hint for it!
let E be a Lebesgue measurable subset of R with 0<λ(E)<∞. For r>=0, set Er=E+r = {x+r : x in E}
a)Show that there is an open interval I such that λ(I)<3/2λ(EI)
b)Prove that λ(EEr)=0 => r>λ(EI)/2
well for the first part i thought that if there exists an interval I then EI is in I and by countable subadditivty
λ(EI)<λ(I) but if we multiply the lefthand side by any number say a>1 then the equation sign will become greater than. But i'm not sure if i'm going in the right direction.
Thanks!!