Theorems · Theorem · approximation theory
LinearGrowth.linearGrowthSup_comp_le
∀ {u : ℕ → EReal} {v : ℕ → ℕ},
(∃ᶠ (n : ℕ) in Filter.atTop, 0 ≤ u n) →
(LinearGrowth.linearGrowthSup fun n => ↑(v n)) ≠ 0 →
(LinearGrowth.linearGrowthSup fun n => ↑(v n)) ≠ ⊤ →
Filter.Tendsto v Filter.atTop Filter.atTop →
LinearGrowth.linearGrowthSup (u ∘ v) ≤
(LinearGrowth.linearGrowthSup fun n => ↑(v n)) * LinearGrowth.linearGrowthSup u- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Filter.Tendstostatement and proof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- Filter.univ_mem'proof · cited by 1,672
- mul_assocproof · cited by 1,667
- Filter.mp_memproof · cited by 1,537
- ERealstatement and proof · cited by 793
- Filter.Frequentlystatement and proof · cited by 414
Cited by2
Results whose statement or proof uses this declaration.
- Monotone.linearGrowthSup_compproof · cited by 2
- ExpGrowth.expGrowthSup_comp_leproof · cited by 0