Theorems · Theorem · approximation theory
Asymptotics.IsBigO.trans_isEquivalent
∀ {α : Type u_1} {β : Type u_2} {β₂ : Type u_3} [inst : NormedAddCommGroup β] [inst_1 : Norm β₂] {l : Filter α}
{f : α → β₂} {g₁ g₂ : α → β}, f =O[l] g₁ → Asymptotics.IsEquivalent l g₁ g₂ → f =O[l] g₂- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroupNorm
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Filterstatement and proof · cited by 8,121
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsEquivalentstatement and proof · cited by 98
- Asymptotics.IsBigO.transproof · cited by 56
- Asymptotics.IsEquivalent.isBigOproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isBigO_cobounded_of_degree_leproof · cited by 0