Theorems · Theorem · approximation theory
Asymptotics.isEquivalent_const_iff_tendsto
∀ {α : Type u_1} {β : Type u_2} [inst : NormedAddCommGroup β] {u : α → β} {l : Filter α} {c : β},
c ≠ 0 → (Asymptotics.IsEquivalent l u (Function.const α c) ↔ Filter.Tendsto u l (nhds c))- Cited by
- 4 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- zero_addproof · cited by 2,366
- sub_selfproof · cited by 996
- sub_add_cancelproof · cited by 344
- tendsto_const_nhdsproof · cited by 330
- sub_neg_eq_addproof · cited by 264
- Asymptotics.IsEquivalentstatement · cited by 98
- Filter.Tendsto.subproof · cited by 68
- Asymptotics.isLittleO_const_iffproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.tendsto_nhdsproof · cited by 6
- Asymptotics.IsEquivalent.tendsto_constproof · cited by 2
- AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const_realproof · cited by 2
- AkraBazziRecurrence.isBigO_symm_asympBoundproof · cited by 1