Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.def
∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {c : ℝ} {f : α → E} {g : α → F}
{l : Filter α}, f =o[l] g → 0 < c → ∀ᶠ (x : α) in l, ‖f x‖ ≤ c * ‖g x‖- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 9 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 and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement · cited by 5,413
- Filter.Eventuallystatement · cited by 3,134
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.isLittleO_iffproof · cited by 23
Cited by9
Results whose statement or proof uses this declaration.
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- Asymptotics.IsLittleO.eventuallyLEproof · cited by 3
- ApproximatesLinearOn.norm_fderiv_sub_leproof · cited by 3
- Asymptotics.isLittleO_iff_nat_mul_le_auxproof · cited by 3
- HasStrictFDerivAt.approximates_deriv_on_nhdsproof · cited by 2
- Asymptotics.IsLittleO.eventuallyLT_norm_of_eventually_posproof · cited by 1
- LipschitzWith.hasFDerivAt_of_hasLineDerivAt_of_closureproof · cited by 1
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAtproof · cited by 1