∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_2} {mβ : MeasurableSpace β}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] {g : β → ENNReal},
  AEMeasurable g ν → μ.prod (ν.withDensity g) = (μ.prod ν).withDensity fun z => g z.2