Theorems · Theorem · general topology
MeasureTheory.exists_subset_real_measurableEquiv
∀ (α : Type u_1) [inst : MeasurableSpace α] [StandardBorelSpace α], ∃ s, MeasurableSet s ∧ Nonempty (α ≃ᵐ ↑s)
Any standard Borel space is measurably equivalent to a subset of the reals.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- MeasurableSetstatement · cited by 3,075
- Finiteproof · cited by 3,029
- Countableproof · cited by 633
- Infiniteproof · cited by 352
- StandardBorelSpacestatement and proof · cited by 304
- MeasurableEquivstatement and proof · cited by 269
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_measurableEmbedding_realproof · cited by 1