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Theorems · Theorem · measure theory

map_comap_subtype_coe

∀ {α : Type u_2} {m0 : MeasurableSpace α} {s : Set α},
  MeasurableSet s →
    ∀ (μ : MeasureTheory.Measure α),
      MeasureTheory.Measure.map Subtype.val (MeasureTheory.Measure.comap Subtype.val μ) = μ.restrict s
Defined in
Mathlib.MeasureTheory.Measure.Restrict
Cited by
14 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul · cited by 6MeasureTheory.lintegral_i…MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul · cited by 6MeasureTheory.integral_im…MeasureTheory.integral_subtype_comap · cited by 5MeasureTheory.integral_su…MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar · cited by 3MeasureTheory.restrict_ma…MeasureTheory.measurePreserving_subtype_coe · cited by 3MeasureTheory.measurePres…MeasureTheory.setIntegral_countable · cited by 2MeasureTheory.setIntegral…MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul · cited by 2MeasureTheory.integrableO…AddCircle.integral_preimage · cited by 2AddCircle.integral_preima…MeasureTheory.lintegral_subtype_comap · cited by 2MeasureTheory.lintegral_s…UnitAddTorus.measurePreserving_equivPiIoc · cited by 2UnitAddTorus.measurePrese…ae_restrict_iff_subtype · cited by 1ae_restrict_iff_subtypeAddCircle.lintegral_preimage · cited by 1AddCircle.lintegral_preim…aemeasurable_restrict_iff_comap_subtype · cited by 1aemeasurable_restrict_iff…MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact · cited by 1Measure.exists_innerRegul…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurableSet · cited by 3075MeasurableSetMeasureTheory.Measure.restrict · cited by 1646Measure.restrictMeasureTheory.Measure.map · cited by 858Measure.mapSubtype.range_coe · cited by 98Subtype.range_coeMeasureTheory.Measure.comap · cited by 96Measure.comapMeasurableEmbedding.subtype_coe · cited by 27MeasurableEmbedding.subty…MeasurableEmbedding.map_comap · cited by 8MeasurableEmbedding.map_c…map_comap_subtype_coeCITED BYCITES

Cites10

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Cited by14

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