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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.Measure.mapstatement · cited by 858
- Subtype.range_coeproof · cited by 98
- MeasureTheory.Measure.comapstatement · cited by 96
- MeasurableEmbedding.subtype_coeproof · cited by 27
- MeasurableEmbedding.map_comapproof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mulproof · cited by 6
- MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smulproof · cited by 6
- MeasureTheory.integral_subtype_comapproof · cited by 5
- MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaarproof · cited by 3
- MeasureTheory.measurePreserving_subtype_coeproof · cited by 3
- MeasureTheory.setIntegral_countableproof · cited by 2
- MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smulproof · cited by 2
- AddCircle.integral_preimageproof · cited by 2
- MeasureTheory.lintegral_subtype_comapproof · cited by 2
- UnitAddTorus.measurePreserving_equivPiIocproof · cited by 2
- ae_restrict_iff_subtypeproof · cited by 1
- AddCircle.lintegral_preimageproof · cited by 1