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feat: the complement of a null set has full measure (#17644)
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YaelDillies committed Oct 11, 2024
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3 changes: 3 additions & 0 deletions Mathlib/MeasureTheory/Measure/NullMeasurable.lean
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Expand Up @@ -280,6 +280,9 @@ theorem measure_union₀' (hs : NullMeasurableSet s μ) (hd : AEDisjoint μ s t)
theorem measure_add_measure_compl₀ {s : Set α} (hs : NullMeasurableSet s μ) :
μ s + μ sᶜ = μ univ := by rw [← measure_union₀' hs aedisjoint_compl_right, union_compl_self]

lemma measure_of_measure_compl_eq_zero (hs : μ sᶜ = 0) : μ s = μ Set.univ := by
simpa [hs] using measure_add_measure_compl₀ <| .of_compl <| .of_null hs

section MeasurableSingletonClass

variable [MeasurableSingletonClass (NullMeasurableSpace α μ)]
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