Theorems · Theorem · functional analysis

ContDiffMapSupportedIn.seminorm_fderivLM_top

∀ (𝕜 : Type u_1) {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace ℝ E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace 𝕜 F]
  [inst_6 : SMulCommClass ℝ 𝕜 F] {K : TopologicalSpace.Compacts E} {i : ℕ} (f : ContDiffMapSupportedIn E F ⊤ K),
  (ContDiffMapSupportedIn.seminorm 𝕜 E (E →L[ℝ] F) ⊤ K i) ((ContDiffMapSupportedIn.fderivLM 𝕜 ⊤ ⊤) f) =
    (ContDiffMapSupportedIn.seminorm 𝕜 E F ⊤ K (i + 1)) f

Defined in

Mathlib.Analysis.Distribution.ContDiffMapSupportedIn

Cited by

0 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClass