Theorems · Theorem · approximation theory
Asymptotics.isBigO_iff
∀ {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, ∀ᶠ (x : α) in l, ‖f x‖ ≤ c * ‖g x‖Definition of IsBigO in terms of filters.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Eventuallystatement and proof · cited by 3,134
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigOWith_defproof · cited by 46
- Asymptotics.IsBigO_defproof · cited by 26
Cited by19
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.of_boundproof · cited by 15
- Asymptotics.IsBigO.boundproof · cited by 5
- HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNEproof · cited by 4
- hasSum_choose_mul_geometric_of_norm_lt_one'proof · cited by 4
- Asymptotics.isBigO_iff'proof · cited by 3
- Asymptotics.isBigOTVS_iff_isBigOproof · cited by 3
- tendsto_rpow_atTop_of_base_lt_oneproof · cited by 2
- AkraBazziRecurrence.isBigO_apply_r_sub_bproof · cited by 2
- qExpansion_coeff_isBigO_of_norm_isBigOproof · cited by 2
- HasFPowerSeriesWithinAt.isBigO_sub_partialSum_powproof · cited by 1
- Asymptotics.isBigO_nat_atTop_inductionproof · cited by 1