∀ {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 : AddGroup G]
  [MeasurableAdd G] [MeasurableNeg G] {x₀ : G} {s : Set G},
  BddAbove ((fun i => ‖g i‖) '' ((fun t => -t + x₀) ⁻¹' s)) →
    MeasurableSet s →
      (Function.support fun t => (L (f t)) (g (x₀ - t))) ⊆ s →
        MeasureTheory.IntegrableOn f s μ →
          MeasureTheory.AEStronglyMeasurable g (MeasureTheory.Measure.map (fun t => x₀ - t) (μ.restrict s)) →
            MeasureTheory.ConvolutionExistsAt f g x₀ L μ