Theorems · Theorem · general topology
MeasureTheory.AnalyticSet.iUnion
∀ {α : Type u_1} {ι : Type u_2} [inst : TopologicalSpace α] [Countable ι] {s : ι → Set α},
(∀ (n : ι), MeasureTheory.AnalyticSet (s n)) → MeasureTheory.AnalyticSet (⋃ n, s n)A countable union of analytic sets is analytic.
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- 0 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCountable
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangeproof · cited by 4,705
- Continuousproof · cited by 2,592
- Set.iUnionstatement and proof · cited by 2,483
- Countablestatement and proof · cited by 633
- PolishSpaceproof · cited by 57
- MeasureTheory.AnalyticSetstatement and proof · cited by 16
- MeasureTheory.analyticSet_range_of_polishSpaceproof · cited by 6
- MeasureTheory.analyticSet_iff_exists_polishSpace_rangeproof · cited by 4
- Set.range_sigma_eq_iUnion_rangeproof · cited by 3
- continuous_sigmaproof · cited by 1
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