Theorems · Theorem · approximation theory
Asymptotics.IsBigO.mono
∀ {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 l' : Filter α}, f =O[l'] g → l ≤ l' → f =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 106 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.
- Realproof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsBigOWithproof · cited by 187
- Asymptotics.IsBigO.isBigOWithproof · cited by 21
- Asymptotics.isBigO_iff_isBigOWithproof · cited by 8
- Asymptotics.IsBigOWith.monoproof · cited by 2
Cited by16
Results whose statement or proof uses this declaration.
- HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_subproof · cited by 2
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- Asymptotics.isBigO_supproof · cited by 2
- Function.Periodic.exp_decay_sub_of_bounded_at_infproof · cited by 2
- log_deriv_riemannZeta_add_inv_sub_sub_isBigOproof · cited by 1
- log_riemannZeta_add_log_sub_isBigO_ofRealproof · cited by 1
- not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_puncturedproof · cited by 1
- inv_riemannZeta_sub_sub_isBigOproof · cited by 1
- Asymptotics.IsTheta.monoproof · cited by 1
- Asymptotics.isBigO_cofinite_iffproof · cited by 1
- DirichletCharacter.LFunction_isBigO_horizontalproof · cited by 0