Theorems · Theorem · real analysis

ContDiffOn.sum

∀ {𝕜 : Type u_1} [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] {n : WithTop ℕ∞}
  {ι : Type u_3} {f : ι → E → F} {s : Finset ι} {t : Set E},
  (∀ i ∈ s, ContDiffOn 𝕜 n (fun x => f i x) t) → ContDiffOn 𝕜 n (fun x => ∑ i ∈ s, f i x) t

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

1 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace