Theorems · Theorem · real analysis

IsBoundedBilinearMap.contDiff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {b : E × F → G} {n : WithTop ℕ∞},
  IsBoundedBilinearMap 𝕜 b → ContDiff 𝕜 n b

Bilinear functions are C^n.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Basic

Cited by

19 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace