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[Merged by Bors] - feat: AEMeasurable.dist #30585

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[Merged by Bors] - feat: AEMeasurable.dist #30585

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14 changes: 10 additions & 4 deletions Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -75,7 +75,13 @@ theorem measurable_dist : Measurable fun p : α × α => dist p.1 p.2 :=
@[measurability, fun_prop]
theorem Measurable.dist {f g : β → α} (hf : Measurable f) (hg : Measurable g) :
Measurable fun b => dist (f b) (g b) :=
(@continuous_dist α _).measurable2 hf hg
continuous_dist.measurable2 hf hg

@[fun_prop, measurability]
lemma AEMeasurable.dist {f g : β → α} {μ : Measure β}
(hf : AEMeasurable f μ) (hg : AEMeasurable g μ) :
AEMeasurable (fun b ↦ dist (f b) (g b)) μ :=
continuous_dist.aemeasurable2 hf hg

@[measurability]
theorem measurable_nndist : Measurable fun p : α × α => nndist p.1 p.2 :=
Expand All @@ -84,7 +90,7 @@ theorem measurable_nndist : Measurable fun p : α × α => nndist p.1 p.2 :=
@[measurability, fun_prop]
theorem Measurable.nndist {f g : β → α} (hf : Measurable f) (hg : Measurable g) :
Measurable fun b => nndist (f b) (g b) :=
(@continuous_nndist α _).measurable2 hf hg
continuous_nndist.measurable2 hf hg

end

Expand Down Expand Up @@ -171,12 +177,12 @@ theorem measurable_edist : Measurable fun p : α × α => edist p.1 p.2 :=
@[measurability, fun_prop]
theorem Measurable.edist {f g : β → α} (hf : Measurable f) (hg : Measurable g) :
Measurable fun b => edist (f b) (g b) :=
(@continuous_edist α _).measurable2 hf hg
continuous_edist.measurable2 hf hg

@[measurability, fun_prop]
theorem AEMeasurable.edist {f g : β → α} {μ : Measure β} (hf : AEMeasurable f μ)
(hg : AEMeasurable g μ) : AEMeasurable (fun a => edist (f a) (g a)) μ :=
(@continuous_edist α _).aemeasurable2 hf hg
continuous_edist.aemeasurable2 hf hg

end PseudoEMetricSpace

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