Theorems · Theorem · approximation theory
Asymptotics.isLittleO_pow_pow
∀ {𝕜 : Type u_15} [inst : NormedDivisionRing 𝕜] {m n : ℕ}, m < n → (fun x => x ^ n) =o[nhds 0] fun x => x ^ m- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- nhdsstatement and proof · cited by 5,554
- mul_oneproof · cited by 3,885
- one_powproof · cited by 521
- Asymptotics.IsLittleOstatement and proof · cited by 375
- NormedDivisionRingstatement and proof · cited by 360
- pow_addproof · cited by 315
- Filter.tendsto_idproof · cited by 180
- Asymptotics.isBigO_reflproof · cited by 51
- Asymptotics.isLittleO_one_iffproof · cited by 20
- Asymptotics.IsBigO.mul_isLittleOproof · cited by 15
- Asymptotics.IsLittleO.powproof · cited by 3
- lt_iff_exists_addproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_pow_sub_pow_subproof · cited by 1
- Asymptotics.isLittleO_norm_pow_norm_powproof · cited by 1
- Asymptotics.isLittleO_pow_idproof · cited by 1
- Complex.exp_sub_sum_range_succ_isLittleO_powproof · cited by 0
- Real.exp_sub_sum_range_succ_isLittleO_powproof · cited by 0