∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} [inst_2 : NormedAddCommGroup E] {f : α → E},
  MeasureTheory.Integrable f μ →
    ∀ (ν : MeasureTheory.Measure β) [MeasureTheory.IsFiniteMeasure ν],
      MeasureTheory.Integrable (fun x => f x.1) (μ.prod ν)