Theorems · Theorem · approximation theory
Asymptotics.IsBigO.of_norm_eventuallyLE
∀ {α : Type u_1} {E : Type u_3} [inst : Norm E] {f : α → E} {l : Filter α} {g : α → ℝ},
(fun x => ‖f x‖) ≤ᶠ[l] g → f =O[l] gSee also Filter.Eventually.isBigO, which is the same lemma
stated using Filter.Eventually instead of Filter.EventuallyLE.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Norm
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.
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Filter.Eventually.monoproof · cited by 646
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement · cited by 506
- Filter.EventuallyLEstatement and proof · cited by 383
- le_abs_selfproof · cited by 113
- Asymptotics.IsBigO.of_bound'proof · cited by 9
Cited by11
Results whose statement or proof uses this declaration.
- Filter.Eventually.isBigOproof · cited by 8
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- PhragmenLindelof.quadrant_Iproof · cited by 4
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- isLittleO_pow_const_mul_const_pow_const_pow_of_norm_ltproof · cited by 2
- Asymptotics.IsBigO.of_norm_leproof · cited by 2
- FormalMultilinearSeries.radius_eq_liminfproof · cited by 2
- isLittleO_log_rpow_rpow_atTopproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1
- ruzsaSzemerediNumberNat_asymptotic_lower_boundproof · cited by 0