Theorems · Theorem · potential theory

InnerProductSpace.HarmonicContOnCl.comp_CLM

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  {F : Type u_2} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] {G : Type u_3}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace ℝ G] {f : E → F} {s : Set E},
  InnerProductSpace.HarmonicContOnCl f s → ∀ (l : F →L[ℝ] G), InnerProductSpace.HarmonicContOnCl (⇑l ∘ f) s

Compositions of continuous ℝ-linear maps with functions that are harmonic on a set and continuous on its closure are again harmonic on the set and continuous on its closure.

Defined in

Mathlib.Analysis.Complex.Harmonic.MeanValue

Cited by

1 results in Mathlib

Foundations

Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace