Theorems · Theorem · real analysis

contDiffOn_succ_of_fderivWithin

∀ {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∞},
  DifferentiableOn 𝕜 f s →
    (n = ⊤ → AnalyticOn 𝕜 f s) → ContDiffOn 𝕜 n (fun y => fderivWithin 𝕜 f s y) s → ContDiffOn 𝕜 (n + 1) f s

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

3 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace