Theorems · Theorem · real analysis

ContDiffOn.differentiableOn_iteratedDerivWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} {n : WithTop ℕ∞} {m : ℕ},
  ContDiffOn 𝕜 n f s → ↑m < n → UniqueDiffOn 𝕜 s → DifferentiableOn 𝕜 (iteratedDerivWithin m f s) s

On a set with unique derivatives, a C^n function has derivatives less than n which are differentiable.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Defs

Cited by

6 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace