Theorems · Theorem · general topology
MeasureTheory.analyticSet_iff_exists_polishSpace_range
∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α},
MeasureTheory.AnalyticSet s ↔ ∃ β h, ∃ (_ : PolishSpace β), ∃ f, Continuous f ∧ Set.range f = sA set is analytic if and only if it is the continuous image of some Polish space.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 167 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.
Cites10
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.rangestatement and proof · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- PolishSpacestatement and proof · cited by 57
- MeasureTheory.AnalyticSetstatement and proof · cited by 16
- Set.range_eq_emptyproof · cited by 14
- MeasureTheory.analyticSet_range_of_polishSpaceproof · cited by 6
- MeasureTheory.AnalyticSet_defproof · cited by 4
- continuous_botproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.AnalyticSet.image_of_continuousOnproof · cited by 1
- MeasureTheory.AnalyticSet.preimageproof · cited by 0
- MeasureTheory.AnalyticSet.iInterproof · cited by 0
- MeasureTheory.AnalyticSet.iUnionproof · cited by 0