Theorems · Theorem · measure theory
MeasurableSpace.measurableEquiv_nat_bool_of_countablyGenerated
∀ (α : Type u_1) [inst : MeasurableSpace α] [MeasurableSpace.CountablyGenerated α] [MeasurableSpace.SeparatesPoints α], ∃ s, Nonempty (α ≃ᵐ ↑s)
If a measurable space is countably generated and separates points, it is measure equivalent
to some subset of the Cantor space ℕ → Bool (equipped with the product sigma algebra).
Note: s need not be measurable, so this map need not be a MeasurableEmbedding to
the Cantor Space.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Set.rangeproof · cited by 4,705
- Equiv.symmproof · cited by 3,681
- MeasurableSetproof · cited by 3,075
- Measurableproof · cited by 1,499
- MeasurableEquivstatement · cited by 269
- MeasurableSpace.CountablyGeneratedstatement and proof · cited by 124
Cited by1
Results whose statement or proof uses this declaration.
- exists_borelSpace_of_countablyGenerated_of_separatesPointsproof · cited by 1