Theorems · Theorem · functional analysis

ContDiffMapSupportedIn.monoCLM_apply

∀ (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] {n₁ n₂ : ℕ∞} {K₁ K₂ : TopologicalSpace.Compacts E}
  (f : ContDiffMapSupportedIn E F n₁ K₁),
  ⇑((ContDiffMapSupportedIn.monoCLM 𝕜) f) = ⇑(if n₂ ≤ n₁ ∧ K₁ ≤ K₂ then f else 0)

Defined in

Mathlib.Analysis.Distribution.ContDiffMapSupportedIn

Cited by

1 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClass