Theorems · Definition · approximation theory
Asymptotics.IsTheta
{α : Type u_1} → {E : Type u_3} → {F : Type u_4} → [Norm E] → [Norm F] → Filter α → (α → E) → (α → F) → PropWe say that f is Θ(g) along a filter l (notation: f =Θ[l] g) if f =O[l] g and
g =O[l] f.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 115 results in Mathlib
- Foundations
- Depth 103 from the axioms, rests on 1,963 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOproof · cited by 506
Cited by115
Results whose statement or proof uses this declaration.
- Asymptotics.IsTheta.symmstatement and proof · cited by 12
- Asymptotics.isTheta_reflstatement · cited by 12
- Asymptotics.IsEquivalent.isThetastatement · cited by 9
- Asymptotics.IsTheta.const_mul_leftstatement · cited by 8
- Asymptotics.IsTheta.isBigOstatement and proof · cited by 8
- Complex.isTheta_ofRealstatement and proof · cited by 6
- Asymptotics.IsTheta.invstatement and proof · cited by 5
- Asymptotics.IsThetaTVS.isThetastatement · cited by 4
- Asymptotics.isTheta_rflstatement · cited by 4
- Asymptotics.IsTheta.add_isLittleOstatement and proof · cited by 4
- Asymptotics.IsTheta.isBigO_congr_leftstatement and proof · cited by 4
- Asymptotics.IsTheta.transstatement and proof · cited by 3