Theorems · Theorem · approximation theory
Asymptotics.IsBigO.const_mul_right
∀ {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] g → f =O[l] fun x => c * g x- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- 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
- Asymptotics.IsBigOWithproof · cited by 187
- NormMulClassstatement and proof · cited by 66
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.IsBigO.exists_nonnegproof · cited by 10
- Asymptotics.IsBigOWith.const_mul_rightproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Asymptotics.isBigO_const_mul_right_iffproof · cited by 1
- ruzsaSzemerediNumberNat_asymptotic_lower_boundproof · cited by 0
- Polynomial.isBigO_cobounded_of_degree_leproof · cited by 0