Theorems · Theorem · real analysis
Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le
∀ {a b : ℝ}, a ≤ b → b ≠ 0 → (fun x => x ^ b) =O[nhdsWithin 0 (Set.Ici 0)] fun x => x ^ aIf a ≤ b, b ≠ 0, then x^b = O(x^a) as x → 0, x ≥ 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- nhdsWithinstatement · cited by 1,912
- Set.Icistatement · cited by 1,070
- Asymptotics.IsBigOstatement · cited by 506
- Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_impproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.id_rpow_of_le_oneproof · cited by 1