Theorems · Theorem · measure theory
MeasurableEmbedding.comap_apply
∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} {m1 : MeasurableSpace β} {f : α → β},
MeasurableEmbedding f → ∀ (μ : MeasureTheory.Measure β) (s : Set α), (MeasureTheory.Measure.comap f μ) s = μ (f '' s)- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 20 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.imagestatement and proof · cited by 5,609
- MeasurableEmbeddingstatement and proof · cited by 170
- MeasureTheory.Measure.comapstatement and proof · cited by 96
- Set.image_subset_rangeproof · cited by 76
- Set.inter_eq_self_of_subset_leftproof · cited by 52
- MeasurableEmbedding.injectiveproof · cited by 35
- MeasureTheory.Measure.restrict_apply'proof · cited by 32
Cited by20
Results whose statement or proof uses this declaration.
- unitInterval.volume_applyproof · cited by 11
- MeasureTheory.Measure.toSphere_apply'proof · cited by 3
- MeasurableEmbedding.variation_mapproof · cited by 3
- comap_subtype_coe_applyproof · cited by 2
- MeasureTheory.IsFiniteMeasureOnCompacts.comap'proof · cited by 2
- ProbabilityTheory.setBernoulli_applyproof · cited by 2
- MeasureTheory.Measure.IsCondKernel.apply_of_ne_zeroproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.comapproof · cited by 2
- MeasureTheory.Measure.OuterRegular.comap'proof · cited by 2
- MeasurableEquiv.comap_applyproof · cited by 1
- MeasureTheory.Measure.map_eq_comapproof · cited by 1
- MeasurableEmbedding.comap_mapproof · cited by 1