Theorems · Theorem · real analysis

ContDiffOn.differentiableOn

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {f : E → F} {n : WithTop ℕ∞}, ContDiffOn 𝕜 n f s → n ≠ 0 → DifferentiableOn 𝕜 f s

If a function is C^n on a set with n ≥ 1, then it is differentiable there.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

11 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace