Theorems · Theorem · approximation theory
Asymptotics.IsBigO.isBigOWith
∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {f : α → E} {g : α → F} {l : Filter α},
f =O[l] g → ∃ c, Asymptotics.IsBigOWith c l f g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigOWithstatement · cited by 187
- Asymptotics.isBigO_iff_isBigOWithproof · cited by 8
Cited by21
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.transproof · cited by 56
- Asymptotics.IsBigO.comp_tendstoproof · cited by 33
- Asymptotics.IsBigO.mulproof · cited by 29
- Asymptotics.IsBigO.addproof · cited by 21
- Asymptotics.IsBigO.exists_posproof · cited by 19
- Asymptotics.IsBigO.const_mul_leftproof · cited by 16
- Asymptotics.IsBigO.monoproof · cited by 16
- Asymptotics.IsBigO.exists_nonnegproof · cited by 10
- Asymptotics.IsBigO.powproof · cited by 8
- summable_of_isBigOproof · cited by 8
- Asymptotics.IsBigO.smulproof · cited by 4
- Asymptotics.IsBigO.eq_zero_impproof · cited by 4