∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {G' : Type u_7} {G'' : Type u_8}
  [inst : NormedAddCommGroup G''] [inst_1 : PartialOrder G''] [IsOrderedAddMonoid G''] [inst_3 : NormedSpace ℝ G'']
  [inst_4 : CompleteSpace G''] [inst_5 : NormedAddCommGroup G'] [inst_6 : PartialOrder G'] [inst_7 : NormedSpace ℝ G']
  [ClosedIciTopology G''] [IsOrderedAddMonoid G'] {T : Set α → G' →L[ℝ] G''} {C : ℝ}
  (hT : MeasureTheory.DominatedFinMeasAdditive μ T C),
  (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∀ (x : G'), 0 ≤ x → 0 ≤ (T s) x) →
    ∀ {f g : α → G'},
      MeasureTheory.Integrable f μ →
        MeasureTheory.Integrable g μ → f ≤ᵐ[μ] g → MeasureTheory.setToFun μ T hT f ≤ MeasureTheory.setToFun μ T hT g