Theorems · Theorem · harmonic analysis

MeasureTheory.AEStronglyMeasurable.fourierSMulRight

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {V : Type u_2} {W : Type u_3}
  [inst_2 : NormedAddCommGroup V] [inst_3 : NormedSpace ℝ V] [inst_4 : NormedAddCommGroup W] [inst_5 : NormedSpace ℝ W]
  [SecondCountableTopologyEither V (W →L[ℝ] ℝ)] [inst_7 : MeasurableSpace V] [BorelSpace V] {L : V →L[ℝ] W →L[ℝ] ℝ}
  {f : V → E} {μ : MeasureTheory.Measure V},
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable (fun v => VectorFourier.fourierSMulRight L f v) μ

Defined in

Mathlib.Analysis.Fourier.FourierTransformDeriv

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceSecondCountableTopologyEitherMeasurableSpaceBorelSpace