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[Merged by Bors] - feat: MeasurableSpace.generateFrom lemmas #10797

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[Merged by Bors] - feat: MeasurableSpace.generateFrom lemmas #10797

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8 changes: 8 additions & 0 deletions Mathlib/MeasureTheory/MeasurableSpace/Defs.lean
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Expand Up @@ -453,6 +453,14 @@ theorem generateFrom_sup_generateFrom {s t : Set (Set α)} :
(@giGenerateFrom α).gc.l_sup.symm
#align measurable_space.generate_from_sup_generate_from MeasurableSpace.generateFrom_sup_generateFrom

lemma iSup_generateFrom (s : ι → Set (Set α)) :
⨆ i, generateFrom (s i) = generateFrom (⋃ i, s i) :=
(@MeasurableSpace.giGenerateFrom α).gc.l_iSup.symm

@[simp]
lemma generateFrom_empty : generateFrom (∅ : Set (Set α)) = ⊥ :=
le_bot_iff.mp (generateFrom_le (by simp))

theorem generateFrom_singleton_empty : generateFrom {∅} = (⊥ : MeasurableSpace α) :=
bot_unique <| generateFrom_le <| by simp [@MeasurableSet.empty α ⊥]
#align measurable_space.generate_from_singleton_empty MeasurableSpace.generateFrom_singleton_empty
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