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feat: add lemmas nullMeasurableSet_lt' and nullMeasurableSet_le (#10074)
Prior to this commit the state of Mathlib was: ```lean import Mathlib #check measurableSet_lt -- Exists #check measurableSet_lt' -- Exists #check measurableSet_le -- Exists #check nullMeasurableSet_lt -- Exists #check nullMeasurableSet_lt' -- Missing #check nullMeasurableSet_le -- Missing ``` Co-authored-by: teorth <tao@math.ucla.edu>
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean

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@@ -643,6 +643,15 @@ theorem nullMeasurableSet_lt [SecondCountableTopology α] {μ : Measure δ} {f g
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(hf.prod_mk hg).nullMeasurable measurableSet_lt'
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#align null_measurable_set_lt nullMeasurableSet_lt
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theorem nullMeasurableSet_lt' [SecondCountableTopology α] {μ : Measure (α × α)} :
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NullMeasurableSet { p : α × α | p.1 < p.2 } μ :=
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measurableSet_lt'.nullMeasurableSet
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theorem nullMeasurableSet_le [SecondCountableTopology α] {μ : Measure δ}
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{f g : δ → α} (hf : AEMeasurable f μ) (hg : AEMeasurable g μ) :
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NullMeasurableSet { a | f a ≤ g a } μ :=
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(hf.prod_mk hg).nullMeasurable measurableSet_le'
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theorem Set.OrdConnected.measurableSet (h : OrdConnected s) : MeasurableSet s := by
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let u := ⋃ (x ∈ s) (y ∈ s), Ioo x y
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have huopen : IsOpen u := isOpen_biUnion fun _ _ => isOpen_biUnion fun _ _ => isOpen_Ioo

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