α : Type u_1
β : Type ?u.646530
γ : Type ?u.646533
δ : Type ?u.646536
ι : Type ?u.646539
R : Type ?u.646542
R' : Type ?u.646545
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
inst✝ : IsFiniteMeasure μ
hs : NullMeasurableSet s
h : ↑↑μ s = ↑↑μ univ
⊢ s =ᶠ[ae μ] univ
α : Type u_1
β : Type ?u.646530
γ : Type ?u.646533
δ : Type ?u.646536
ι : Type ?u.646539
R : Type ?u.646542
R' : Type ?u.646545
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
inst✝ : IsFiniteMeasure μ
hs : NullMeasurableSet s
⊢ s =ᶠ[ae μ] univ ↔ ↑↑μ s = ↑↑μ univ
refine' ⟨measure_congr, fun h => _⟩
case intro.intro.intro
α : Type u_1
β : Type ?u.646530
γ : Type ?u.646533
δ : Type ?u.646536
ι : Type ?u.646539
R : Type ?u.646542
R' : Type ?u.646545
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
inst✝ : IsFiniteMeasure μ
hs : NullMeasurableSet s
h : ↑↑μ s = ↑↑μ univ
t : Set α
ht₁ : MeasurableSet t
ht₂ : t =ᶠ[ae μ] s
⊢ s =ᶠ[ae μ] univ
α : Type u_1
β : Type ?u.646530
γ : Type ?u.646533
δ : Type ?u.646536
ι : Type ?u.646539
R : Type ?u.646542
R' : Type ?u.646545
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t : Set α
inst✝ : IsFiniteMeasure μ
hs : NullMeasurableSet s
h : ↑↑μ s = ↑↑μ univ
⊢ s =ᶠ[ae μ] univ
obtain ⟨t, -, ht₁, ht₂⟩ := hs.exists_measurable_subset_ae_eq
no goals
case intro.intro.intro
α : Type u_1
β : Type ?u.646530
γ : Type ?u.646533
δ : Type ?u.646536
ι : Type ?u.646539
R : Type ?u.646542
R' : Type ?u.646545
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
inst✝ : IsFiniteMeasure μ
hs : NullMeasurableSet s
h : ↑↑μ s = ↑↑μ univ
t : Set α
ht₁ : MeasurableSet t
ht₂ : t =ᶠ[ae μ] s
⊢ s =ᶠ[ae μ] univ
exact
  ht₂.symm.trans
    (ae_eq_of_subset_of_measure_ge (subset_univ t) (Eq.le ((measure_congr ht₂).trans h).symm) ht₁
      (measure_ne_top μ univ))