Theorems · Theorem · approximation theory
Asymptotics.isLittleO_norm_pow_norm_pow
∀ {E' : Type u_6} [inst : SeminormedAddCommGroup E'] {m n : ℕ}, m < n → (fun x => ‖x‖ ^ n) =o[nhds 0] fun x => ‖x‖ ^ m- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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.
- Realstatement · cited by 25,697
- nhdsstatement · cited by 5,554
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Asymptotics.IsLittleOstatement · cited by 375
- Asymptotics.IsLittleO.comp_tendstoproof · cited by 18
- Asymptotics.isLittleO_pow_powproof · cited by 5
- tendsto_norm_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_norm_pow_idproof · cited by 1