Module: Mathlib.MeasureTheory.VectorMeasure.AddContent

Goal state before:
pp: case a
α : Type u_1
hα : MeasurableSpace α
E : Type u_2
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
μ : Measure α
m : Set α → E
hm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s
inst✝ : IsFiniteMeasure μ
h'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t
h''m : ∀ (s : Set α), ¬MeasurableSet s → m s = 0
f : ℕ → Set α
f_meas : ∀ (i : ℕ), MeasurableSet (f i)
f_disj : Pairwise (Function.onFun Disjoint f)
A : ∀ (n : ℕ), m (⋃ i ∈ Finset.range n, f i) = ∑ i ∈ Finset.range n, m (f i)
n : ℕ
this : ⋃ i, f i = (⋃ i ∈ Finset.range n, f i) ∪ ⋃ i ∈ Set.Ici n, f i
⊢ MeasurableSet (⋃ i ∈ Finset.range n, f i)

pp: case a
α : Type u_1
hα : MeasurableSpace α
E : Type u_2
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
μ : Measure α
m : Set α → E
hm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s
inst✝ : IsFiniteMeasure μ
h'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t
h''m : ∀ (s : Set α), ¬MeasurableSet s → m s = 0
f : ℕ → Set α
f_meas : ∀ (i : ℕ), MeasurableSet (f i)
f_disj : Pairwise (Function.onFun Disjoint f)
A : ∀ (n : ℕ), m (⋃ i ∈ Finset.range n, f i) = ∑ i ∈ Finset.range n, m (f i)
n : ℕ
this : ⋃ i, f i = (⋃ i ∈ Finset.range n, f i) ∪ ⋃ i ∈ Set.Ici n, f i
⊢ MeasurableSet (⋃ i ∈ Set.Ici n, f i)

pp: case a
α : Type u_1
hα : MeasurableSpace α
E : Type u_2
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
μ : Measure α
m : Set α → E
hm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s
inst✝ : IsFiniteMeasure μ
h'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t
h''m : ∀ (s : Set α), ¬MeasurableSet s → m s = 0
f : ℕ → Set α
f_meas : ∀ (i : ℕ), MeasurableSet (f i)
f_disj : Pairwise (Function.onFun Disjoint f)
A : ∀ (n : ℕ), m (⋃ i ∈ Finset.range n, f i) = ∑ i ∈ Finset.range n, m (f i)
n : ℕ
this : ⋃ i, f i = (⋃ i ∈ Finset.range n, f i) ∪ ⋃ i ∈ Set.Ici n, f i
⊢ Disjoint (⋃ i ∈ Finset.range n, f i) (⋃ i ∈ Set.Ici n, f i)

Tactic:
· exact Finset.measurableSet_biUnion _ (fun i hi ↦ f_meas i)

Goal state after:
case a
α : Type u_1
hα : MeasurableSpace α
E : Type u_2
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
μ : Measure α
m : Set α → E
hm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s
inst✝ : IsFiniteMeasure μ
h'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t
h''m : ∀ (s : Set α), ¬MeasurableSet s → m s = 0
f : ℕ → Set α
f_meas : ∀ (i : ℕ), MeasurableSet (f i)
f_disj : Pairwise (Function.onFun Disjoint f)
A : ∀ (n : ℕ), m (⋃ i ∈ Finset.range n, f i) = ∑ i ∈ Finset.range n, m (f i)
n : ℕ
this : ⋃ i, f i = (⋃ i ∈ Finset.range n, f i) ∪ ⋃ i ∈ Set.Ici n, f i
⊢ MeasurableSet (⋃ i ∈ Set.Ici n, f i)

case a
α : Type u_1
hα : MeasurableSpace α
E : Type u_2
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
μ : Measure α
m : Set α → E
hm : ∀ (s : Set α), ‖m s‖ₑ ≤ μ s
inst✝ : IsFiniteMeasure μ
h'm : ∀ (s t : Set α), MeasurableSet s → MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t
h''m : ∀ (s : Set α), ¬MeasurableSet s → m s = 0
f : ℕ → Set α
f_meas : ∀ (i : ℕ), MeasurableSet (f i)
f_disj : Pairwise (Function.onFun Disjoint f)
A : ∀ (n : ℕ), m (⋃ i ∈ Finset.range n, f i) = ∑ i ∈ Finset.range n, m (f i)
n : ℕ
this : ⋃ i, f i = (⋃ i ∈ Finset.range n, f i) ∪ ⋃ i ∈ Set.Ici n, f i
⊢ Disjoint (⋃ i ∈ Finset.range n, f i) (⋃ i ∈ Set.Ici n, f i)