Theorems · Theorem · approximation theory
Asymptotics.isEquivalent_of_tendsto_one
∀ {α : Type u_1} {β : Type u_2} [inst : NormedField β] {u v : α → β} {l : Filter α},
Filter.Tendsto (u / v) l (nhds 1) → Asymptotics.IsEquivalent l u v- Cited by
- 5 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- NormedFieldstatement and proof · cited by 1,084
- Filter.Eventually.monoproof · cited by 646
- Filter.Frequentlyproof · cited by 414
- tendsto_const_nhdsproof · cited by 330
- div_zeroproof · cited by 251
- Asymptotics.IsEquivalentstatement · cited by 98
- Filter.Frequently.monoproof · cited by 64
- div_mul_cancel_of_impproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Asymptotics.isEquivalent_iff_tendsto_oneproof · cited by 3
- Asymptotics.isEquivalent_nat_ceilproof · cited by 0
- Asymptotics.isEquivalent_nat_floorproof · cited by 0
- Asymptotics.isEquivalent_of_tendsto_one'proof · cited by 0
- Stirling.factorial_isEquivalent_stirlingproof · cited by 0