Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.sub
∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {g : α → F}
{l : Filter α} {f₁ f₂ : α → E'}, f₁ =o[l] g → f₂ =o[l] g → (fun x => f₁ x - f₂ x) =o[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormSeminormedAddCommGroup
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.
- Filterstatement and proof · cited by 8,121
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- sub_eq_add_negproof · cited by 1,023
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsLittleO.addproof · cited by 17
- Asymptotics.IsLittleO.neg_leftproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae'proof · cited by 2
- ProbabilityTheory.strong_law_aux6proof · cited by 1
- Convex.isLittleO_alternate_sum_squareproof · cited by 1
- Convex.second_derivative_within_at_symmetric_of_mem_interiorproof · cited by 1
- Asymptotics.IsLittleO.add_iff_leftproof · cited by 0
- Asymptotics.IsLittleO.add_iff_rightproof · cited by 0
- Asymptotics.IsLittleO.sub_iff_rightproof · cited by 0
- Asymptotics.IsLittleO.sub_iff_leftproof · cited by 0
- Asymptotics.IsLittleO.congr_of_subproof · cited by 0