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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 γ₂

A homeomorphism between two Borel spaces is a measurable equivalence.

Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
Cited by
32 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceMeasurableSpaceBorelSpaceTopologicalSpaceMeasurableSpaceBorelSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Homeomorph.measurableEmbedding · cited by 21Homeomorph.measurableEmbe…Complex.measurableEquivRealProd · cited by 11Complex.measurableEquivRe…MeasureTheory.Measure.Regular.map · cited by 9Regular.mapLinearIsometryEquiv.toMeasurableEquiv · cited by 6LinearIsometryEquiv.toMea…Submodule.measurableEquivProd · cited by 5Submodule.measurableEquiv…Complex.measurableEquivPi · cited by 5Complex.measurableEquivPiProbabilityTheory.gaussianReal_map_const_mul · cited by 4ProbabilityTheory.gaussia…Topology.IsEmbedding.measurableEmbedding · cited by 3IsEmbedding.measurableEmb…MeasureTheory.measure_lt_one_eq_integral_div_gamma · cited by 3MeasureTheory.measure_lt_…ProbabilityTheory.gaussianReal_map_add_const · cited by 3ProbabilityTheory.gaussia…MeasureTheory.Measure.integral_comp_smul · cited by 3Measure.integral_comp_smulZLattice.covolume.tendsto_card_div_pow'' · cited by 2covolume.tendsto_card_div…MeasureTheory.integrable_comp_smul_iff · cited by 2MeasureTheory.integrable_…ZLattice.covolume.tendsto_card_le_div'' · cited by 2covolume.tendsto_card_le_…MeasureTheory.Measure.addHaar_preimage_linearMap · cited by 2Measure.addHaar_preimage_…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceEquiv · cited by 8337EquivBorelSpace · cited by 1602BorelSpaceHomeomorph · cited by 725HomeomorphMeasurableEquiv · cited by 269MeasurableEquivHomeomorph.toEquiv · cited by 77Homeomorph.toEquivHomeomorph.toMeasurableEquivCITED BYCITES

Cites7

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Cited by40

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