Theorems · Theorem · approximation theory
Asymptotics.isBigOWith_self_const_mul
∀ {α : Type u_1} {S : Type u_17} [inst : NormedRing S] [NormMulClass S] {c : S},
c ≠ 0 → ∀ (f : α → S) (l : Filter α), Asymptotics.IsBigOWith ‖c‖⁻¹ l f fun x => c * f x- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingNormMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallyproof · cited by 3,134
- NormedRingstatement and proof · cited by 924
- Asymptotics.IsBigOWithstatement · cited by 187
- norm_mulproof · cited by 171
- NormMulClassstatement and proof · cited by 66
- norm_ne_zero_iffproof · cited by 65
- inv_mul_cancel_left₀proof · cited by 47
- Asymptotics.IsBigOWith_defproof · cited by 46
Cited by2
Results whose statement or proof uses this declaration.
- Asymptotics.isBigO_self_const_mulproof · cited by 5
- Asymptotics.IsBigOWith.const_mul_rightproof · cited by 1