Theorems · Theorem · approximation theory
ExpGrowth.expGrowthInf_le_iff
∀ {u : ℕ → ENNReal} {a : EReal}, ExpGrowth.expGrowthInf u ≤ a ↔ ∀ b > a, ∃ᶠ (n : ℕ) in Filter.atTop, u n ≤ (b * ↑n).exp- Defined in
- Mathlib.Analysis.Asymptotics.ExpGrowth
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- ERealstatement and proof · cited by 793
- Filter.Frequentlystatement and proof · cited by 414
- Filter.eventually_atTopproof · cited by 112
- ENNReal.logproof · cited by 72
- Filter.isBounded_ge_of_botproof · cited by 55
- EReal.expstatement and proof · cited by 46
- ExpGrowth.expGrowthInfstatement · cited by 38
- Filter.isCobounded_ge_of_topproof · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- Frequently.expGrowthInf_leproof · cited by 1
- ExpGrowth.frequently_le_expproof · cited by 0