∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [CompleteSpace E] {μ : MeasureTheory.Measure α} {s : Set E} {t : Set α} {f : α → E} {g : E → ℝ},
  ConvexOn ℝ s g →
    ContinuousOn g s →
      IsClosed s →
        μ t ≠ 0 →
          μ t ≠ ⊤ →
            (∀ᵐ (x : α) ∂μ.restrict t, f x ∈ s) →
              MeasureTheory.IntegrableOn f t μ →
                MeasureTheory.IntegrableOn (g ∘ f) t μ →
                  (⨍ (x : α) in t, f x ∂μ, ⨍ (x : α) in t, g (f x) ∂μ) ∈ {p | p.1 ∈ s ∧ g p.1 ≤ p.2}