Theorems · Theorem · approximation theory
Asymptotics.IsEquivalent.isBigO
∀ {α : Type u_1} {β : Type u_2} [inst : NormedAddCommGroup β] {u v : α → β} {l : Filter α},
Asymptotics.IsEquivalent l u v → u =O[l] v- Cited by
- 13 results in Mathlib
- Foundations
- Depth 112 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.
Cites8
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
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsEquivalentstatement and proof · cited by 98
- Asymptotics.isBigO_reflproof · cited by 51
- Asymptotics.IsLittleO.isBigOproof · cited by 35
- Asymptotics.IsBigO.symmproof · cited by 2
- Asymptotics.IsBigO.congr_of_subproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.isThetaproof · cited by 9
- Asymptotics.IsEquivalent.transproof · cited by 5
- Asymptotics.IsEquivalent.trans_isBigOproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_leproof · cited by 1
- Asymptotics.IsEquivalent.trans_isLittleOproof · cited by 1
- Asymptotics.IsLittleO.trans_isEquivalentproof · cited by 1
- Asymptotics.IsBigO.trans_isEquivalentproof · cited by 1
- Asymptotics.IsEquivalent.smulproof · cited by 1
- summable_of_isEquivalentproof · cited by 0
- summable_of_isEquivalent_natproof · cited by 0
- Asymptotics.IsEquivalent.isTheta_symmproof · cited by 0