Theorems · Theorem · approximation theory
Asymptotics.isEquivalent_iff_exists_eq_mul
∀ {α : Type u_1} {β : Type u_2} [inst : NormedField β] {u v : α → β} {l : Filter α},
Asymptotics.IsEquivalent l u v ↔ ∃ φ, ∃ (_ : Filter.Tendsto φ l (nhds 1)), u =ᶠ[l] φ * v- Cited by
- 4 results in Mathlib
- Foundations
- Depth 166 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.
Cites19
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
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- Filter.EventuallyEqstatement and proof · cited by 1,912
- NormedFieldstatement and proof · cited by 1,084
- sub_selfproof · cited by 996
- add_mulproof · cited by 363
- sub_add_cancelproof · cited by 344
- tendsto_const_nhdsproof · cited by 330
- sub_mulproof · cited by 170
Cited by4
Results whose statement or proof uses this declaration.
- Asymptotics.isEquivalent_of_tendsto_oneproof · cited by 5
- Asymptotics.IsEquivalent.exists_eq_mulproof · cited by 4
- Asymptotics.IsEquivalent.invproof · cited by 3
- Asymptotics.IsEquivalent.rpowproof · cited by 1