Theorems · Theorem · abstract harmonic analysis

MeasureTheory.AEStronglyMeasurable.convolution_integrand

∀ {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 → 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 ν : MeasureTheory.Measure G} [inst_8 : AddGroup G]
  [MeasurableAdd₂ G] [MeasurableNeg G] [MeasureTheory.SFinite μ] [μ.IsAddRightInvariant] [MeasureTheory.SFinite ν],
  MeasureTheory.AEStronglyMeasurable f ν →
    MeasureTheory.AEStronglyMeasurable g μ →
      MeasureTheory.AEStronglyMeasurable (fun p => (L (f p.2)) (g (p.1 - p.2))) (μ.prod ν)

Defined in

Mathlib.Analysis.Convolution

Cited by

2 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpaceMeasurableSpaceAddGroupMeasurableAdd₂MeasurableNegMeasureTheory.SFiniteMeasureTheory.Measure.IsAddRightInvariantMeasureTheory.SFinite