Theorems · Theorem · approximation theory
Asymptotics.bound_of_isBigO_nat_atTop
∀ {E : Type u_3} {E'' : Type u_9} [inst : Norm E] [inst_1 : NormedAddCommGroup E''] {f : ℕ → E} {g'' : ℕ → E''},
f =O[Filter.atTop] g'' → ∃ C > 0, ∀ ⦃x : ℕ⦄, g'' x ≠ 0 → ‖f x‖ ≤ C * ‖g'' x‖- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormNormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Filterproof · cited by 8,121
- Norm.normstatement · cited by 5,413
- Filter.atTopstatement and proof · cited by 2,405
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Nat.cofinite_eq_atTopproof · cited by 37
- Asymptotics.bound_of_isBigO_cofiniteproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- Asymptotics.IsBigO.nat_of_atTopproof · cited by 0