Theorems · Theorem · approximation theory
Asymptotics.isBigO_const_mul_right_iff
∀ {α : Type u_1} {E : Type u_3} [inst : Norm E] {S : Type u_17} [inst_1 : NormedRing S] [NormMulClass S] {f : α → E}
{l : Filter α} {g : α → S} {c : S}, c ≠ 0 → ((f =O[l] fun x => c * g x) ↔ f =O[l] g)- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormNormedRingNormMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedRingstatement and proof · cited by 924
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- NormMulClassstatement and proof · cited by 66
- Asymptotics.IsBigO.const_mul_rightproof · cited by 3
- Asymptotics.IsBigO.of_const_mul_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Asymptotics.isBigO_const_smul_rightproof · cited by 2