Theorems · Theorem · complex analysis

TendstoLocallyUniformlyOn.deriv

∀ {E : Type u_1} {ι : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {U : Set ℂ} {φ : Filter ι}
  {F : ι → ℂ → E} {f : ℂ → E} [CompleteSpace E],
  TendstoLocallyUniformlyOn F f φ U →
    (∀ᶠ (n : ι) in φ, DifferentiableOn ℂ (F n) U) → IsOpen U → TendstoLocallyUniformlyOn (deriv ∘ F) (deriv f) φ U

Defined in

Mathlib.Analysis.Complex.LocallyUniformLimit

Cited by

3 results in Mathlib

Foundations

Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace