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Fill restriction of a finitely additive measure to a measurable subset #704

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11 changes: 8 additions & 3 deletions Analysis/MeasureTheory/Section_1_4_3.lean
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Expand Up @@ -112,9 +112,14 @@ noncomputable instance FinitelyAdditiveMeasure.instDistribMulAction {X:Type*} {B
def FinitelyAdditiveMeasure.restrict {X:Type*} {B: ConcreteBooleanAlgebra X} (μ: FinitelyAdditiveMeasure B) (A:Set X) (hA:B.measurable A) : FinitelyAdditiveMeasure (B.restrict A) :=
{
measure := fun E => μ.measure E
measure_pos := by sorry
measure_empty := by sorry
measure_finite_additive := by sorry
measure_pos := fun E hE =>
μ.measure_pos (Subtype.val '' E) ((B.restrict_iff hA E).mp hE)
measure_empty := by
simpa using μ.measure_empty
measure_finite_additive := fun E F hE hF hdisj =>
μ.measure_finite_additive (Subtype.val '' E) (Subtype.val '' F)
((B.restrict_iff hA E).mp hE) ((B.restrict_iff hA F).mp hF)
(hdisj.image Subtype.val)
}

/-- Example 1.4.26 (Counting a measure) -/
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