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

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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.

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