α : Type u_2
α' : Type ?u.4451554
β : Type u_1
β' : Type ?u.4451560
γ : Type ?u.4451563
E : Type ?u.4451566
inst✝⁶ : MeasurableSpace α
inst✝⁵ : MeasurableSpace α'
inst✝⁴ : MeasurableSpace β
inst✝³ : MeasurableSpace β'
inst✝² : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝¹ : NormedAddCommGroup E
inst✝ : SigmaFinite ν
s : Set α
hs : MeasurableSet s
h2s : ↑↑μ s = 0
⊢ ↑↑(map Prod.fst (Measure.prod μ ν)) s = 0
α : Type u_2
α' : Type ?u.4451554
β : Type u_1
β' : Type ?u.4451560
γ : Type ?u.4451563
E : Type ?u.4451566
inst✝⁶ : MeasurableSpace α
inst✝⁵ : MeasurableSpace α'
inst✝⁴ : MeasurableSpace β
inst✝³ : MeasurableSpace β'
inst✝² : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝¹ : NormedAddCommGroup E
inst✝ : SigmaFinite ν
⊢ QuasiMeasurePreserving Prod.fst
refine' ⟨measurable_fst, AbsolutelyContinuous.mk fun s hs h2s => _⟩
no goals
α : Type u_2
α' : Type ?u.4451554
β : Type u_1
β' : Type ?u.4451560
γ : Type ?u.4451563
E : Type ?u.4451566
inst✝⁶ : MeasurableSpace α
inst✝⁵ : MeasurableSpace α'
inst✝⁴ : MeasurableSpace β
inst✝³ : MeasurableSpace β'
inst✝² : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝¹ : NormedAddCommGroup E
inst✝ : SigmaFinite ν
s : Set α
hs : MeasurableSet s
h2s : ↑↑μ s = 0
⊢ ↑↑(map Prod.fst (Measure.prod μ ν)) s = 0
rw [map_apply measurable_fst hs, ← prod_univ, prod_prod, h2s, MulZeroClass.zero_mul]