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Fill the ENNReal action on countably additive measures #710

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27 changes: 23 additions & 4 deletions Analysis/MeasureTheory/Section_1_4_3.lean
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Expand Up @@ -231,10 +231,29 @@ noncomputable instance CountablyAdditiveMeasure.instSmul {X:Type*} {B: ConcreteS

noncomputable instance CountablyAdditiveMeasure.instDistribMulAction {X:Type*} {B: ConcreteSigmaAlgebra X} : DistribMulAction ENNReal (CountablyAdditiveMeasure B) :=
{
smul_zero := by sorry,
smul_add := by sorry,
one_smul := by sorry,
mul_smul := by sorry
smul_zero := by
intro c
congr 1
ext A
simp
smul_add := by
intro c μ ν
cases μ; cases ν
congr 1
ext A
exact left_distrib (c : EReal) _ _
one_smul := by
intro μ
cases μ
congr 1
ext A
exact one_smul EReal _
mul_smul := by
intro a b μ
cases μ
congr 1
ext A
exact mul_assoc (a : EReal) _ _
}

/-- Exercise 1.4.22(ii) -/
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