Theorems · Theorem · approximation theory
Asymptotics.isBigO_of_le
∀ {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),
(∀ (x : α), ‖f x‖ ≤ ‖g x‖) → f =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 12 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.
Cites7
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
- Norm.normstatement and proof · cited by 5,413
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.isBigOWith_of_leproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.tendsto_div_nhds_zeroproof · cited by 7
- PhragmenLindelof.quadrant_Iproof · cited by 4
- Function.HasTemperateGrowth.isBigO_uniformproof · cited by 2
- FormalMultilinearSeries.min_radius_le_radius_addproof · cited by 2
- isBigO_norm_Icc_restrict_atBotproof · cited by 1
- isBigO_norm_restrict_cocompactproof · cited by 1
- LSeries_eq_mul_integral'proof · cited by 1
- FormalMultilinearSeries.radius_prod_eq_minproof · cited by 1
- Asymptotics.IsBigO.trans_leproof · cited by 1
- Complex.isBigO_cpow_rpowproof · cited by 0
- Complex.isBigO_im_sub_improof · cited by 0
- Complex.isBigO_re_sub_reproof · cited by 0