Theorems · Theorem · approximation theory
Asymptotics.isBigO_refl
∀ {α : Type u_1} {E : Type u_3} [inst : Norm E] (f : α → E) (l : Filter α), f =O[l] f- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 105 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.
Cites5
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
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.isBigOWith_reflproof · cited by 1
Cited by51
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.isBigOproof · cited by 13
- Asymptotics.isTheta_reflproof · cited by 12
- IsBoundedBilinearMap.hasStrictFDerivAtproof · cited by 7
- Asymptotics.IsLittleO.tendsto_div_nhds_zeroproof · cited by 7
- Asymptotics.isLittleO_iff_tendsto'proof · cited by 7
- summable_pow_mul_jacobiTheta₂_term_boundproof · cited by 6
- hasFDerivAt_norm_rpowproof · cited by 5
- Filter.EventuallyEq.isBigOproof · cited by 5
- Asymptotics.isLittleO_pow_powproof · cited by 5
- hasStrictDerivAt_invproof · cited by 4
- Asymptotics.isLittleO_pow_pow_cobounded_of_ltproof · cited by 3
- summable_norm_pow_mul_geometric_of_norm_lt_oneproof · cited by 3