Thread: measur

If E,F ⊆ ℝ with positive measure then show ∃ y ∈ ℝ : m((E+y)∩ F) > 0
help will be appreciated so much

first, we can prove that for the case of E and F are bounded.
This can be proved by the inner regular property of Lebesgue measure.
the limit that E and f are bonded can be easily removed.
I hope this idea could help.