Theorems · Theorem · abstract harmonic analysis

BddAbove.continuous_convolution_left_of_integrable

∀ {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 : MeasureTheory.Measure G} [inst_8 : NormedSpace ℝ F]
  [inst_9 : AddCommGroup G] [μ.IsAddLeftInvariant] [μ.IsNegInvariant] [inst_12 : TopologicalSpace G]
  [IsTopologicalAddGroup G] [BorelSpace G] [FirstCountableTopology G] [SecondCountableTopologyEither G E],
  BddAbove (Set.range fun x => ‖f x‖) →
    Continuous f → MeasureTheory.Integrable g μ → Continuous (MeasureTheory.convolution f g L μ)

Defined in

Mathlib.Analysis.Convolution

Cited by

0 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpaceMeasurableSpaceNormedSpaceAddCommGroupMeasureTheory.Measure.IsAddLeftInvariantMeasureTheory.Measure.IsNegInvariantTopologicalSpaceIsTopologicalAddGroupBorelSpaceFirstCountableTopologySecondCountableTopologyEither