OAI/NumberTheory/TotientAsymptotic/NormalizedShell.lean
3 declarations, 0 contain sorry, 0 declared as axioms
Additive boundary slices vanish after the smooth-cofactor cost.
- def
OAI.TotientAsymptotic.normalizedShellLossline 14 - lemma
OAI.TotientAsymptotic.normalizedShellLoss_tendstoline 18 - theorem
OAI.TotientAsymptotic.normalized_additive_shell_lossline 31Source documentation
All retained boundary slices have negligible normalized volume, even after paying for every admissible smooth cofactor.
theorem normalized_additive_shell_loss (hren : FordRenewalInput) (K : ℝ) : ∃ δ : ℕ → ℝ, Tendsto δ atTop (nhds 0) ∧ ∀ᶠ H : ℕ in atTop, ∀ᶠ x : ℝ in atTop, ∀ hRN : R x H ≤ L x H, Real.exp (K*cofactorScale H)* volume.real (additiveBoxShell x (R x H) (L x H) hRN)/G x (m x) ≤ δ H := by …Mentions: OAI.TotientAsymptotic.FordRenewalInput, OAI.TotientAsymptotic.R, OAI.TotientAsymptotic.L, OAI.TotientAsymptotic.cofactorScale, OAI.TotientAsymptotic.additiveBoxShell, OAI.TotientAsymptotic.G, OAI.TotientAsymptotic.m