Theorems · Theorem · real analysis
ContinuousOn.rpow_const
∀ {α : Type u_1} [inst : TopologicalSpace α] {f : α → ℝ} {s : Set α} {p : ℝ},
ContinuousOn f s → (∀ x ∈ s, f x ≠ 0 ∨ 0 ≤ p) → ContinuousOn (fun x => f x ^ p) s- Cited by
- 7 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousWithinAt.rpow_constproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- intervalIntegral.intervalIntegrable_rpow'proof · cited by 6
- Real.GammaIntegral_convergentproof · cited by 5
- Real.continuousOn_rpowIntegrand₀₁_uncurryproof · cited by 2
- Real.continuousOn_rpowIntegrand₀₁proof · cited by 2
- CFC.cfc_rpowproof · cited by 1
- intervalIntegral.intervalIntegrable_rpowproof · cited by 1
- CStarAlgebra.convexOn_ringInverseproof · cited by 1