Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.isBigO
∀ {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 : Filter α},
f =o[l] g → f =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.IsLittleO.isBigOWithproof · cited by 2
Cited by35
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.isBigOproof · cited by 13
- Real.GammaIntegral_convergentproof · cited by 5
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- summable_norm_mul_geometric_of_norm_lt_oneproof · cited by 2
- Real.isBigO_log_const_mul_log_atTopproof · cited by 2
- Filter.ZeroAtFilter.boundedAtFilterproof · cited by 2
- FormalMultilinearSeries.min_radius_le_radius_addproof · cited by 2
- UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_leftproof · cited by 2
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_leproof · cited by 1
- Asymptotics.isLittleO_zero_right_iffproof · cited by 1