Theorems · Definition · general topology
BaireMeasurableSet
{α : Type u_1} → [TopologicalSpace α] → Set α → PropWe say a set is a BaireMeasurableSet if it differs from some Borel set by
a meager set. This forms a σ-algebra.
It is equivalent, and a more standard definition, to say that the set differs from
some open set by a meager set. See BaireMeasurableSet.iff_residualEq_isOpen
- Defined in
- Mathlib.Topology.Baire.BaireMeasurable
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- MeasurableSetproof · cited by 3,075
Cited by19
Results whose statement or proof uses this declaration.
- BaireMeasurableSet.congrstatement and proof · cited by 1
- BaireMeasurableSet.of_complstatement and proof · cited by 1
- BaireMeasurableSet.of_mem_residualstatement · cited by 1
- BaireMeasurableSet.residualEq_isOpenstatement and proof · cited by 1
- IsOpen.baireMeasurableSetstatement · cited by 1
- MeasurableSet.baireMeasurableSetstatement · cited by 1
- BaireMeasurableSet.biInterstatement and proof · cited by 0
- BaireMeasurableSet.biUnionstatement and proof · cited by 0
- BaireMeasurableSet.complstatement and proof · cited by 0
- BaireMeasurableSet.diffstatement and proof · cited by 0
- BaireMeasurableSet.iInterstatement and proof · cited by 0
- BaireMeasurableSet.iUnionstatement and proof · cited by 0