Theorems · Theorem · global analysis

AnalyticOnNhd.deriv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} [CompleteSpace F],
  AnalyticOnNhd 𝕜 f s → AnalyticOnNhd 𝕜 (deriv f) s

If a function is analytic on a set s in a complete space, so is its derivative.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Analytic

Cited by

3 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace