Theorems · Theorem · approximation theory
Asymptotics.isLittleO_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 : ℝ⦄, 0 < c → ∀ᶠ (x : α) in l, ‖f x‖ ≤ c * ‖g x‖Definition of IsLittleO in terms of filters.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 23 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.IsLittleOstatement · cited by 375
- Asymptotics.IsBigOWith_defproof · cited by 46
- Asymptotics.IsLittleO_defproof · cited by 19
Cited by23
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.defproof · cited by 9
- Asymptotics.IsLittleO.def'proof · cited by 6
- AkraBazziRecurrence.eventually_bi_mul_le_rproof · cited by 4
- Asymptotics.IsLittleO.boundproof · cited by 4
- HasFDerivAt.le_of_lip'proof · cited by 4
- HasFPowerSeriesWithinAt.hasFDerivWithinAtproof · cited by 3
- AkraBazziRecurrence.eventually_one_add_smoothingFn_posproof · cited by 3
- Filter.Tendsto.integral_sub_linear_isLittleO_aeproof · cited by 3
- Asymptotics.isLittleO_iff_nat_mul_le_auxproof · cited by 3
- Asymptotics.IsLittleO.of_boundproof · cited by 2
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2
- hasStrictFDerivAt_of_hasFDerivAt_of_continuousAtproof · cited by 2