Theorems · Definition · measure theory
AddCircle.measurableEquivIoc
(T : ℝ) → [hT : Fact (0 < T)] → (a : ℝ) → AddCircle T ≃ᵐ ↑(Set.Ioc a (a + T))
The isomorphism AddCircle T ≃ Ioc a (a + T) whose inverse is the natural quotient map,
as an equivalence of measurable spaces.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Equivproof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Factstatement and proof · cited by 2,726
- Set.Iocstatement and proof · cited by 971
- AddSubgroup.zmultiplesstatement · cited by 493
- MeasurableEquivstatement · cited by 269
- AddCirclestatement and proof · cited by 189
- AddCircle.equivIocproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- UnitAddTorus.measurableEquivPiIocproof · cited by 7
- AddCircle.integral_preimageproof · cited by 2
- AddCircle.lintegral_preimageproof · cited by 1
- AddCircle.measurePreserving_equivIocproof · cited by 1
- AddCircle.measurableEquivIoc.congr_simpstatement and proof · cited by 0