Theorems · Definition · measure theory
Homeomorph.toMeasurableEquiv
{γ : Type u_3} →
{γ₂ : Type u_4} →
[inst : TopologicalSpace γ] →
[inst_1 : MeasurableSpace γ] →
[BorelSpace γ] →
[inst_3 : TopologicalSpace γ₂] → [inst_4 : MeasurableSpace γ₂] → [BorelSpace γ₂] → γ ≃ₜ γ₂ → γ ≃ᵐ γ₂A homeomorphism between two Borel spaces is a measurable equivalence.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Equivproof · cited by 8,337
- BorelSpacestatement and proof · cited by 1,602
- Homeomorphstatement and proof · cited by 725
- MeasurableEquivstatement · cited by 269
- Homeomorph.toEquivproof · cited by 77
Cited by40
Results whose statement or proof uses this declaration.
- Homeomorph.measurableEmbeddingproof · cited by 21
- Complex.measurableEquivRealProdproof · cited by 11
- MeasureTheory.Measure.Regular.mapproof · cited by 9
- LinearIsometryEquiv.toMeasurableEquivproof · cited by 6
- Submodule.measurableEquivProdproof · cited by 5
- Complex.measurableEquivPiproof · cited by 5
- ProbabilityTheory.gaussianReal_map_const_mulproof · cited by 4
- Topology.IsEmbedding.measurableEmbeddingproof · cited by 3
- MeasureTheory.measure_lt_one_eq_integral_div_gammaproof · cited by 3
- ProbabilityTheory.gaussianReal_map_add_constproof · cited by 3
- MeasureTheory.Measure.integral_comp_smulproof · cited by 3
- ZLattice.covolume.tendsto_card_div_pow''proof · cited by 2