Theorems · Theorem · real analysis
Asymptotics.IsLittleO.rpow
∀ {α : Type u_1} {r : ℝ} {l : Filter α} {f g : α → ℝ},
0 < r → 0 ≤ᶠ[l] g → f =o[l] g → (fun x => f x ^ r) =o[l] fun x => g x ^ r- Cited by
- 2 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Filter.EventuallyLEstatement and proof · cited by 383
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsBigOWithproof · cited by 187
- Real.rpow_pos_of_posproof · cited by 155
- Asymptotics.IsLittleO.of_isBigOWithproof · cited by 12
- Real.rpow_inv_rpowproof · cited by 12
- Asymptotics.IsLittleO.forall_isBigOWithproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- isLittleO_log_rpow_rpow_atTopproof · cited by 1
- Asymptotics.IsLittleO.sqrtproof · cited by 0