case pos
Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
s t : Set Ω
inst✝ : IsFiniteMeasure μ
hms : MeasurableSet s
hmt : MeasurableSet t
ht : ↑↑μ t = 0
⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t

case neg
Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
s t : Set Ω
inst✝ : IsFiniteMeasure μ
hms : MeasurableSet s
hmt : MeasurableSet t
ht : ¬↑↑μ t = 0
⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t
Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
s t : Set Ω
inst✝ : IsFiniteMeasure μ
hms : MeasurableSet s
hmt : MeasurableSet t
⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t
by_cases ht : μ t = 0
no goals
case pos
Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
s t : Set Ω
inst✝ : IsFiniteMeasure μ
hms : MeasurableSet s
hmt : MeasurableSet t
ht : ↑↑μ t = 0
⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t
simp [cond, ht, Measure.restrict_apply hmt, Or.inr (measure_inter_null_of_null_left s ht)]
no goals
case neg
Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
s t : Set Ω
inst✝ : IsFiniteMeasure μ
hms : MeasurableSet s
hmt : MeasurableSet t
ht : ¬↑↑μ t = 0
⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t
rw [mul_assoc, cond_mul_eq_inter μ hmt ht s, Set.inter_comm, cond_apply _ hms]