∀ {Ω : Type u_1} {β : Type u_3} {β' : Type u_4} {m' mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω]
  {hm' : m' ≤ mΩ} {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {f : Ω → β} {g : Ω → β'}
  {mβ : MeasurableSpace β} {mβ' : MeasurableSpace β'},
  Measurable f →
    Measurable g →
      (ProbabilityTheory.CondIndepFun m' hm' f g μ ↔
        ∀ (s : Set β) (t : Set β'),
          MeasurableSet s →
            MeasurableSet t →
              μ[(f ⁻¹' s ∩ g ⁻¹' t).indicator fun ω => 1 | m'] =ᵐ[μ] fun ω =>
                μ[(f ⁻¹' s).indicator fun ω => 1 | m'] ω * μ[(g ⁻¹' t).indicator fun ω => 1 | m'] ω)