erdos_520

Let $f$ be a Rademacher multiplicative function. Does there exist some constant $c > 0$ such that, almost surely, \[ \limsup_{N \to \infty} \frac{\sum_{m \leq N} f(m)}{\sqrt{N \log \log N}} = c? \]

theorem erdos_520 :
    answer(sorry) ↔ ∃ c > 0, ∀ (f : ℕ → Ω → ℝ), IsRademacherMultiplicative f →
      ∀ᵐ ω, limsup (fun N ↦ ∑ m ≤ N, f m ω / sqrt (N * log (log N))) atTop = c

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