Theorems · Theorem · global analysis

uniformCauchySeqOn_ball_of_deriv

∀ {ι : Type u_1} {l : Filter ι} {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {G : Type u_3}
  [inst_1 : NormedAddCommGroup G] [inst_2 : NormedSpace 𝕜 G] {f f' : ι → 𝕜 → G} {x : 𝕜} [IsRCLikeNormedField 𝕜] {r : ℝ},
  UniformCauchySeqOn f' l (Metric.ball x r) →
    (∀ (n : ι), ∀ y ∈ Metric.ball x r, HasDerivAt (f n) (f' n y) y) →
      Cauchy (Filter.map (fun n => f n x) l) → UniformCauchySeqOn f l (Metric.ball x r)

Defined in

Mathlib.Analysis.Calculus.UniformLimitsDeriv

Cited by

0 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceIsRCLikeNormedField