Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.const_mul_left
∀ {α : Type u_1} {F : Type u_4} {R : Type u_13} [inst : Norm F] [inst_1 : SeminormedRing R] {g : α → F} {l : Filter α}
{f : α → R}, f =o[l] g → ∀ (c : R), (fun x => c * f x) =o[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormSeminormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Normstatement and proof · cited by 512
- SeminormedRingstatement and proof · cited by 446
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsBigO.trans_isLittleOproof · cited by 32
- Asymptotics.isBigO_const_mul_selfproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- IsBoundedBilinearMap.continuousproof · cited by 11
- Polynomial.isEquivalent_atTop_leadproof · cited by 5
- hasFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- Polynomial.isEquivalent_cobounded_leading_monomialproof · cited by 2
- hasFDerivAt_exp_of_mem_ballproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_cpow_expproof · cited by 1
- Polynomial.isLittleO_cobounded_of_degree_ltproof · cited by 1
- Asymptotics.isLittleO_const_mul_left_iff'proof · cited by 0