∀ {α : Type u_1} {P : Set α → Prop} {m : (s : Set α) → P s → ENNReal}
  (PU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ i, f i)) {f : ℕ → Set α} (hm : ∀ (i : ℕ), P (f i)),
  m (⋃ i, f i) ⋯ = ∑' (i : ℕ), m (f i) ⋯ → MeasureTheory.extend m (⋃ i, f i) = ∑' (i : ℕ), MeasureTheory.extend m (f i)