erdos_749

Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$?

theorem erdos_749 : answer(sorry) ↔ ∀ ε > (0 : ℝ),
    ∃ A : Set ℕ, 1 - ε ≤ lowerDensity (A + A) ∧
    ((Nat.cast (R

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