Theorems · Theorem · abstract harmonic analysis

MeasureTheory.ConvolutionExistsAt.distrib_add

∀ {𝕜 : Type u𝕜} {G : Type uG} {E : Type uE} {E' : Type uE'} {F : Type uF} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup E'] [inst_2 : NormedAddCommGroup F] {f : G → E} {g g' : G → E'}
  [inst_3 : NontriviallyNormedField 𝕜] [inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜 E'] [inst_6 : NormedSpace 𝕜 F]
  {L : E →L[𝕜] E' →L[𝕜] F} [inst_7 : MeasurableSpace G] {μ : MeasureTheory.Measure G} [inst_8 : NormedSpace ℝ F]
  [inst_9 : AddGroup G] {x : G},
  MeasureTheory.ConvolutionExistsAt f g x L μ →
    MeasureTheory.ConvolutionExistsAt f g' x L μ →
      MeasureTheory.convolution f (g + g') L μ x =
        MeasureTheory.convolution f g L μ x + MeasureTheory.convolution f g' L μ x

Defined in

Mathlib.Analysis.Convolution

Cited by

1 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpaceMeasurableSpaceNormedSpaceAddGroup