Theorems · Theorem · global analysis

UniformCauchySeqOnFilter.one_smulRight

∀ {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' : ι → 𝕜 → G} {l' : Filter 𝕜},
  UniformCauchySeqOnFilter f' l l' → UniformCauchySeqOnFilter (fun n z => ContinuousLinearMap.smulRight 1 (f' n z)) l l'

If our derivatives converge uniformly, then the Fréchet derivatives converge uniformly

Defined in

Mathlib.Analysis.Calculus.UniformLimitsDeriv

Cited by

1 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace